CoCalc -- twistedlseries-alex.sagews

Project: Harvard Workshop: Distribution of modular symbols and L-values

Path: code / alex / psage / twistedlseries-alex.sagews

Views: ¹⁸⁴⁶⁰⁷

1+1

2

attach("twistedlseries.sage")

E = EllipticCurve(F, [1, a + 1, a, a, 0])
E
L = LSeriesEllipticCurveSqrt5(E)
#L = LSeriesEllipticCurve(E)

Elliptic Curve defined by y^2 + x*y + a*y = x^3 + (a+1)*x^2 + a*x over Number Field in a with defining polynomial x^2 - x - 1

E.torsion_order()

8

vals,nvals,chis = value_search(E,3,1000)

1000 {1: [Fractional ideal (1)], 2: [], 3: [], 4: [Fractional ideal (2)], 5: [Fractional ideal (-2*a + 1)], 6: [], 7: [], 8: [], 9: [Fractional ideal (3)], 10: [], 11: [Fractional ideal (-3*a + 1), Fractional ideal (-3*a + 2)], 12: [], 13: [], 14: [], 15: [], 16: [Fractional ideal (4)], 17: [], 18: [], 19: [Fractional ideal (-4*a + 1), Fractional ideal (4*a - 3)], 20: [Fractional ideal (-4*a + 2)], 21: [], 22: [], 23: [], 24: [], 25: [Fractional ideal (5)], 26: [], 27: [], 28: [], 29: [Fractional ideal (a - 6), Fractional ideal (a + 5)], 30: [], 31: [Fractional ideal (5*a - 3), Fractional ideal (5*a - 2)], 32: [], 33: [], 34: [], 35: [], 36: [Fractional ideal (6)], 37: [], 38: [], 39: [], 40: [], 41: [Fractional ideal (a - 7), Fractional ideal (a + 6)], 42: [], 43: [], 44: [Fractional ideal (-6*a + 2), Fractional ideal (-6*a + 4)], 45: [Fractional ideal (-6*a + 3)], 46: [], 47: [], 48: [], 49: [Fractional ideal (7)], 50: [], 51: [], 52: [], 53: [], 54: [], 55: [Fractional ideal (a + 7), Fractional ideal (-a + 8)], 56: [], 57: [], 58: [], 59: [Fractional ideal (7*a - 5), Fractional ideal (7*a - 2)], 60: [], 61: [Fractional ideal (7*a - 4), Fractional ideal (7*a - 3)], 62: [], 63: [], 64: [Fractional ideal (8)], 65: [], 66: [], 67: [], 68: [], 69: [], 70: [], 71: [Fractional ideal (a - 9), Fractional ideal (a + 8)], 72: [], 73: [], 74: [], 75: [], 76: [Fractional ideal (-8*a + 2), Fractional ideal (8*a - 6)], 77: [], 78: [], 79: [Fractional ideal (-8*a + 3), Fractional ideal (-8*a + 5)], 80: [Fractional ideal (-8*a + 4)], 81: [Fractional ideal (9)], 82: [], 83: [], 84: [], 85: [], 86: [], 87: [], 88: [], 89: [Fractional ideal (a - 10), Fractional ideal (a + 9)], 90: [], 91: [], 92: [], 93: [], 94: [], 95: [Fractional ideal (2*a + 9), Fractional ideal (-2*a + 11)], 96: [], 97: [], 98: [], 99: [Fractional ideal (-9*a + 3), Fractional ideal (-9*a + 6)], 100: [Fractional ideal (10)], 101: [Fractional ideal (9*a - 5), Fractional ideal (9*a - 4)], 102: [], 103: [], 104: [], 105: [], 106: [], 107: [], 108: [], 109: [Fractional ideal (a - 11), Fractional ideal (a + 10)], 110: [], 111: [], 112: [], 113: [], 114: [], 115: [], 116: [Fractional ideal (2*a - 12), Fractional ideal (2*a + 10)], 117: [], 118: [], 119: [], 120: [], 121: [Fractional ideal (10*a - 7), Fractional ideal (11), Fractional ideal (10*a - 3)], 122: [], 123: [], 124: [Fractional ideal (10*a - 6), Fractional ideal (10*a - 4)], 125: [Fractional ideal (-10*a + 5)], 126: [], 127: [], 128: [], 129: [], 130: [], 131: [Fractional ideal (a - 12), Fractional ideal (a + 11)], 132: [], 133: [], 134: [], 135: [], 136: [], 137: [], 138: [], 139: [Fractional ideal (2*a + 11), Fractional ideal (-2*a + 13)], 140: [], 141: [], 142: [], 143: [], 144: [Fractional ideal (12)], 145: [Fractional ideal (-11*a + 8), Fractional ideal (-11*a + 3)], 146: [], 147: [], 148: [], 149: [Fractional ideal (-11*a + 4), Fractional ideal (-11*a + 7)], 150: [], 151: [Fractional ideal (11*a - 6), Fractional ideal (11*a - 5)], 152: [], 153: [], 154: [], 155: [Fractional ideal (a - 13), Fractional ideal (a + 12)], 156: [], 157: [], 158: [], 159: [], 160: [], 161: [], 162: [], 163: [], 164: [Fractional ideal (2*a - 14), Fractional ideal (2*a + 12)], 165: [], 166: [], 167: [], 168: [], 169: [Fractional ideal (13)], 170: [], 171: [Fractional ideal (-12*a + 3), Fractional ideal (12*a - 9)], 172: [], 173: [], 174: [], 175: [], 176: [Fractional ideal (-12*a + 4), Fractional ideal (-12*a + 8)], 177: [], 178: [], 179: [Fractional ideal (-12*a + 5), Fractional ideal (12*a - 7)], 180: [Fractional ideal (-12*a + 6)], 181: [Fractional ideal (a - 14), Fractional ideal (a + 13)], 182: [], 183: [], 184: [], 185: [], 186: [], 187: [], 188: [], 189: [], 190: [], 191: [Fractional ideal (2*a + 13), Fractional ideal (-2*a + 15)], 192: [], 193: [], 194: [], 195: [], 196: [Fractional ideal (14)], 197: [], 198: [], 199: [Fractional ideal (3*a + 13), Fractional ideal (-3*a + 16)], 200: [], 201: [], 202: [], 203: [], 204: [], 205: [Fractional ideal (13*a - 9), Fractional ideal (13*a - 4)], 206: [], 207: [], 208: [], 209: [Fractional ideal (-13*a + 8), Fractional ideal (a + 14), Fractional ideal (a - 15), Fractional ideal (13*a - 5)], 210: [], 211: [Fractional ideal (13*a - 7), Fractional ideal (13*a - 6)], 212: [], 213: [], 214: [], 215: [], 216: [], 217: [], 218: [], 219: [], 220: [Fractional ideal (2*a + 14), Fractional ideal (-2*a + 16)], 221: [], 222: [], 223: [], 224: [], 225: [Fractional ideal (15)], 226: [], 227: [], 228: [], 229: [Fractional ideal (3*a - 17), Fractional ideal (-3*a - 14)], 230: [], 231: [], 232: [], 233: [], 234: [], 235: [], 236: [Fractional ideal (14*a - 10), Fractional ideal (14*a - 4)], 237: [], 238: [], 239: [Fractional ideal (a - 16), Fractional ideal (a + 15)], 240: [], 241: [Fractional ideal (-14*a + 5), Fractional ideal (-14*a + 9)], 242: [], 243: [], 244: [Fractional ideal (14*a - 8), Fractional ideal (14*a - 6)], 245: [Fractional ideal (-14*a + 7)], 246: [], 247: [], 248: [], 249: [], 250: [], 251: [Fractional ideal (2*a + 15), Fractional ideal (-2*a + 17)], 252: [], 253: [], 254: [], 255: [], 256: [Fractional ideal (16)], 257: [], 258: [], 259: [], 260: [], 261: [Fractional ideal (3*a - 18), Fractional ideal (3*a + 15)], 262: [], 263: [], 264: [], 265: [], 266: [], 267: [], 268: [], 269: [Fractional ideal (-15*a + 4), Fractional ideal (-15*a + 11)], 270: [], 271: [Fractional ideal (a - 17), Fractional ideal (a + 16)], 272: [], 273: [], 274: [], 275: [Fractional ideal (-15*a + 5), Fractional ideal (-15*a + 10)], 276: [], 277: [], 278: [], 279: [Fractional ideal (15*a - 9), Fractional ideal (15*a - 6)], 280: [], 281: [Fractional ideal (15*a - 8), Fractional ideal (15*a - 7)], 282: [], 283: [], 284: [Fractional ideal (2*a - 18), Fractional ideal (2*a + 16)], 285: [], 286: [], 287: [], 288: [], 289: [Fractional ideal (17)], 290: [], 291: [], 292: [], 293: [], 294: [], 295: [Fractional ideal (-3*a + 19), Fractional ideal (3*a + 16)], 296: [], 297: [], 298: [], 299: [], 300: [], 301: [], 302: [], 303: [], 304: [Fractional ideal (-16*a + 4), Fractional ideal (16*a - 12)], 305: [Fractional ideal (a - 18), Fractional ideal (a + 17)], 306: [], 307: [], 308: [], 309: [], 310: [], 311: [Fractional ideal (16*a - 11), Fractional ideal (16*a - 5)], 312: [], 313: [], 314: [], 315: [], 316: [Fractional ideal (-16*a + 6), Fractional ideal (-16*a + 10)], 317: [], 318: [], 319: [Fractional ideal (16*a - 9), Fractional ideal (2*a + 17), Fractional ideal (-2*a + 19), Fractional ideal (-16*a + 7)], 320: [Fractional ideal (-16*a + 8)], 321: [], 322: [], 323: [], 324: [Fractional ideal (18)], 325: [], 326: [], 327: [], 328: [], 329: [], 330: [], 331: [Fractional ideal (3*a - 20), Fractional ideal (-3*a - 17)], 332: [], 333: [], 334: [], 335: [], 336: [], 337: [], 338: [], 339: [], 340: [], 341: [Fractional ideal (a + 18), Fractional ideal (-4*a + 21), Fractional ideal (4*a + 17), Fractional ideal (a - 19)], 342: [], 343: [], 344: [], 345: [], 346: [], 347: [], 348: [], 349: [Fractional ideal (-17*a + 5), Fractional ideal (17*a - 12)], 350: [], 351: [], 352: [], 353: [], 354: [], 355: [Fractional ideal (-17*a + 11), Fractional ideal (-17*a + 6)], 356: [Fractional ideal (2*a - 20), Fractional ideal (2*a + 18)], 357: [], 358: [], 359: [Fractional ideal (-17*a + 7), Fractional ideal (17*a - 10)], 360: [], 361: [Fractional ideal (17*a - 9), Fractional ideal (19), Fractional ideal (17*a - 8)], 362: [], 363: [], 364: [], 365: [], 366: [], 367: [], 368: [], 369: [Fractional ideal (3*a - 21), Fractional ideal (3*a + 18)], 370: [], 371: [], 372: [], 373: [], 374: [], 375: [], 376: [], 377: [], 378: [], 379: [Fractional ideal (a - 20), Fractional ideal (a + 19)], 380: [Fractional ideal (4*a + 18), Fractional ideal (-4*a + 22)], 381: [], 382: [], 383: [], 384: [], 385: [], 386: [], 387: [], 388: [], 389: [Fractional ideal (-18*a + 13), Fractional ideal (18*a - 5)], 390: [], 391: [], 392: [], 393: [], 394: [], 395: [Fractional ideal (2*a + 19), Fractional ideal (-2*a + 21)], 396: [Fractional ideal (-18*a + 6), Fractional ideal (-18*a + 12)], 397: [], 398: [], 399: [], 400: [Fractional ideal (20)], 401: [Fractional ideal (-18*a + 11), Fractional ideal (18*a - 7)], 402: [], 403: [], 404: [Fractional ideal (18*a - 10), Fractional ideal (18*a - 8)], 405: [Fractional ideal (-18*a + 9)], 406: [], 407: [], 408: [], 409: [Fractional ideal (3*a + 19), Fractional ideal (-3*a + 22)], 410: [], 411: [], 412: [], 413: [], 414: [], 415: [], 416: [], 417: [], 418: [], 419: [Fractional ideal (a - 21), Fractional ideal (a + 20)], 420: [], 421: [Fractional ideal (4*a - 23), Fractional ideal (-4*a - 19)], 422: [], 423: [], 424: [], 425: [], 426: [], 427: [], 428: [], 429: [], 430: [], 431: [Fractional ideal (-19*a + 5), Fractional ideal (-19*a + 14)], 432: [], 433: [], 434: [], 435: [], 436: [Fractional ideal (2*a - 22), Fractional ideal (2*a + 20)], 437: [], 438: [], 439: [Fractional ideal (19*a - 13), Fractional ideal (19*a - 6)], 440: [], 441: [Fractional ideal (21)], 442: [], 443: [], 444: [], 445: [Fractional ideal (19*a - 12), Fractional ideal (-19*a + 7)], 446: [], 447: [], 448: [], 449: [Fractional ideal (-19*a + 11), Fractional ideal (19*a - 8)], 450: [], 451: [Fractional ideal (19*a - 10), Fractional ideal (-3*a - 20), Fractional ideal (3*a - 23), Fractional ideal (19*a - 9)], 452: [], 453: [], 454: [], 455: [], 456: [], 457: [], 458: [], 459: [], 460: [], 461: [Fractional ideal (a - 22), Fractional ideal (a + 21)], 462: [], 463: [], 464: [Fractional ideal (4*a - 24), Fractional ideal (4*a + 20)], 465: [], 466: [], 467: [], 468: [], 469: [], 470: [], 471: [], 472: [], 473: [], 474: [], 475: [Fractional ideal (-20*a + 5), Fractional ideal (20*a - 15)], 476: [], 477: [], 478: [], 479: [Fractional ideal (2*a + 21), Fractional ideal (-2*a + 23)], 480: [], 481: [], 482: [], 483: [], 484: [Fractional ideal (20*a - 14), Fractional ideal (22), Fractional ideal (20*a - 6)], 485: [], 486: [], 487: [], 488: [], 489: [], 490: [], 491: [Fractional ideal (-20*a + 7), Fractional ideal (-20*a + 13)], 492: [], 493: [], 494: [], 495: [Fractional ideal (3*a + 21), Fractional ideal (-3*a + 24)], 496: [Fractional ideal (20*a - 12), Fractional ideal (20*a - 8)], 497: [], 498: [], 499: [Fractional ideal (-20*a + 9), Fractional ideal (20*a - 11)], 500: [Fractional ideal (-20*a + 10)], 501: [], 502: [], 503: [], 504: [], 505: [Fractional ideal (a - 23), Fractional ideal (a + 22)], 506: [], 507: [], 508: [], 509: [Fractional ideal (4*a + 21), Fractional ideal (-4*a + 25)], 510: [], 511: [], 512: [], 513: [], 514: [], 515: [], 516: [], 517: [], 518: [], 519: [], 520: [], 521: [Fractional ideal (5*a + 21), Fractional ideal (-5*a + 26)], 522: [], 523: [], 524: [Fractional ideal (2*a - 24), Fractional ideal (2*a + 22)], 525: [], 526: [], 527: [], 528: [], 529: [Fractional ideal (23)], 530: [], 531: [Fractional ideal (21*a - 15), Fractional ideal (21*a - 6)], 532: [], 533: [], 534: [], 535: [], 536: [], 537: [], 538: [], 539: [Fractional ideal (-21*a + 7), Fractional ideal (-21*a + 14)], 540: [], 541: [Fractional ideal (3*a + 22), Fractional ideal (-3*a + 25)], 542: [], 543: [], 544: [], 545: [Fractional ideal (-21*a + 13), Fractional ideal (21*a - 8)], 546: [], 547: [], 548: [], 549: [Fractional ideal (21*a - 12), Fractional ideal (21*a - 9)], 550: [], 551: [Fractional ideal (21*a - 10), Fractional ideal (a + 23), Fractional ideal (a - 24), Fractional ideal (21*a - 11)], 552: [], 553: [], 554: [], 555: [], 556: [Fractional ideal (4*a + 22), Fractional ideal (-4*a + 26)], 557: [], 558: [], 559: [], 560: [], 561: [], 562: [], 563: [], 564: [], 565: [], 566: [], 567: [], 568: [], 569: [Fractional ideal (5*a - 27), Fractional ideal (5*a + 22)], 570: [], 571: [Fractional ideal (2*a + 23), Fractional ideal (-2*a + 25)], 572: [], 573: [], 574: [], 575: [], 576: [Fractional ideal (24)], 577: [], 578: [], 579: [], 580: [Fractional ideal (-22*a + 16), Fractional ideal (-22*a + 6)], 581: [], 582: [], 583: [], 584: [], 585: [], 586: [], 587: [], 588: [], 589: [Fractional ideal (-3*a - 23), Fractional ideal (22*a - 7), Fractional ideal (22*a - 15), Fractional ideal (3*a - 26)], 590: [], 591: [], 592: [], 593: [], 594: [], 595: [], 596: [Fractional ideal (-22*a + 8), Fractional ideal (-22*a + 14)], 597: [], 598: [], 599: [Fractional ideal (a - 25), Fractional ideal (a + 24)], 600: [], 601: [Fractional ideal (-22*a + 9), Fractional ideal (22*a - 13)], 602: [], 603: [], 604: [Fractional ideal (22*a - 12), Fractional ideal (22*a - 10)], 605: [Fractional ideal (4*a - 27), Fractional ideal (-22*a + 11), Fractional ideal (-4*a - 23)], 606: [], 607: [], 608: [], 609: [], 610: [], 611: [], 612: [], 613: [], 614: [], 615: [], 616: [], 617: [], 618: [], 619: [Fractional ideal (-5*a - 23), Fractional ideal (-5*a + 28)], 620: [Fractional ideal (2*a - 26), Fractional ideal (2*a + 24)], 621: [], 622: [], 623: [], 624: [], 625: [Fractional ideal (25)], 626: [], 627: [], 628: [], 629: [], 630: [], 631: [Fractional ideal (-23*a + 6), Fractional ideal (-23*a + 17)], 632: [], 633: [], 634: [], 635: [], 636: [], 637: [], 638: [], 639: [Fractional ideal (3*a - 27), Fractional ideal (3*a + 24)], 640: [], 641: [Fractional ideal (-23*a + 7), Fractional ideal (23*a - 16)], 642: [], 643: [], 644: [], 645: [], 646: [], 647: [], 648: [], 649: [Fractional ideal (a - 26), Fractional ideal (-23*a + 8), Fractional ideal (-23*a + 15), Fractional ideal (a + 25)], 650: [], 651: [], 652: [], 653: [], 654: [], 655: [Fractional ideal (-23*a + 14), Fractional ideal (23*a - 9)], 656: [Fractional ideal (4*a - 28), Fractional ideal (4*a + 24)], 657: [], 658: [], 659: [Fractional ideal (-23*a + 10), Fractional ideal (23*a - 13)], 660: [], 661: [Fractional ideal (23*a - 12), Fractional ideal (23*a - 11)], 662: [], 663: [], 664: [], 665: [], 666: [], 667: [], 668: [], 669: [], 670: [], 671: [Fractional ideal (2*a + 25), Fractional ideal (5*a - 29), Fractional ideal (-5*a - 24), Fractional ideal (-2*a + 27)], 672: [], 673: [], 674: [], 675: [], 676: [Fractional ideal (26)], 677: [], 678: [], 679: [], 680: [], 681: [], 682: [], 683: [], 684: [Fractional ideal (-24*a + 6), Fractional ideal (24*a - 18)], 685: [], 686: [], 687: [], 688: [], 689: [], 690: [], 691: [Fractional ideal (3*a + 25), Fractional ideal (-3*a + 28)], 692: [], 693: [], 694: [], 695: [Fractional ideal (-24*a + 7), Fractional ideal (24*a - 17)], 696: [], 697: [], 698: [], 699: [], 700: [], 701: [Fractional ideal (a - 27), Fractional ideal (a + 26)], 702: [], 703: [], 704: [Fractional ideal (-24*a + 8), Fractional ideal (-24*a + 16)], 705: [], 706: [], 707: [], 708: [], 709: [Fractional ideal (4*a + 25), Fractional ideal (-4*a + 29)], 710: [], 711: [Fractional ideal (-24*a + 9), Fractional ideal (-24*a + 15)], 712: [], 713: [], 714: [], 715: [], 716: [Fractional ideal (-24*a + 10), Fractional ideal (24*a - 14)], 717: [], 718: [], 719: [Fractional ideal (-24*a + 11), Fractional ideal (24*a - 13)], 720: [Fractional ideal (-24*a + 12)], 721: [], 722: [], 723: [], 724: [Fractional ideal (2*a - 28), Fractional ideal (2*a + 26)], 725: [Fractional ideal (5*a - 30), Fractional ideal (5*a + 25)], 726: [], 727: [], 728: [], 729: [Fractional ideal (27)], 730: [], 731: [], 732: [], 733: [], 734: [], 735: [], 736: [], 737: [], 738: [], 739: [Fractional ideal (6*a + 25), Fractional ideal (-6*a + 31)], 740: [], 741: [], 742: [], 743: [], 744: [], 745: [Fractional ideal (-3*a - 26), Fractional ideal (3*a - 29)], 746: [], 747: [], 748: [], 749: [], 750: [], 751: [Fractional ideal (-25*a + 18), Fractional ideal (25*a - 7)], 752: [], 753: [], 754: [], 755: [Fractional ideal (a - 28), Fractional ideal (a + 27)], 756: [], 757: [], 758: [], 759: [], 760: [], 761: [Fractional ideal (25*a - 17), Fractional ideal (25*a - 8)], 762: [], 763: [], 764: [Fractional ideal (4*a + 26), Fractional ideal (-4*a + 30)], 765: [], 766: [], 767: [], 768: [], 769: [Fractional ideal (25*a - 16), Fractional ideal (-25*a + 9)], 770: [], 771: [], 772: [], 773: [], 774: [], 775: [Fractional ideal (25*a - 15), Fractional ideal (25*a - 10)], 776: [], 777: [], 778: [], 779: [Fractional ideal (25*a - 11), Fractional ideal (2*a + 27), Fractional ideal (-2*a + 29), Fractional ideal (-25*a + 14)], 780: [], 781: [Fractional ideal (25*a - 12), Fractional ideal (5*a + 26), Fractional ideal (-5*a + 31), Fractional ideal (25*a - 13)], 782: [], 783: [], 784: [Fractional ideal (28)], 785: [], 786: [], 787: [], 788: [], 789: [], 790: [], 791: [], 792: [], 793: [], 794: [], 795: [], 796: [Fractional ideal (6*a + 26), Fractional ideal (-6*a + 32)], 797: [], 798: [], 799: [], 800: [], 801: [Fractional ideal (3*a - 30), Fractional ideal (3*a + 27)], 802: [], 803: [], 804: [], 805: [], 806: [], 807: [], 808: [], 809: [Fractional ideal (26*a - 19), Fractional ideal (-26*a + 7)], 810: [], 811: [Fractional ideal (a - 29), Fractional ideal (a + 28)], 812: [], 813: [], 814: [], 815: [], 816: [], 817: [], 818: [], 819: [], 820: [Fractional ideal (26*a - 18), Fractional ideal (26*a - 8)], 821: [Fractional ideal (4*a - 31), Fractional ideal (-4*a - 27)], 822: [], 823: [], 824: [], 825: [], 826: [], 827: [], 828: [], 829: [Fractional ideal (-26*a + 9), Fractional ideal (-26*a + 17)], 830: [], 831: [], 832: [], 833: [], 834: [], 835: [], 836: [Fractional ideal (-26*a + 16), Fractional ideal (2*a + 28), Fractional ideal (2*a - 30), Fractional ideal (26*a - 10)], 837: [], 838: [], 839: [Fractional ideal (5*a - 32), Fractional ideal (5*a + 27)], 840: [], 841: [Fractional ideal (26*a - 11), Fractional ideal (29), Fractional ideal (-26*a + 15)], 842: [], 843: [], 844: [Fractional ideal (26*a - 14), Fractional ideal (26*a - 12)], 845: [Fractional ideal (-26*a + 13)], 846: [], 847: [], 848: [], 849: [], 850: [], 851: [], 852: [], 853: [], 854: [], 855: [Fractional ideal (6*a + 27), Fractional ideal (-6*a + 33)], 856: [], 857: [], 858: [], 859: [Fractional ideal (3*a + 28), Fractional ideal (-3*a + 31)], 860: [], 861: [], 862: [], 863: [], 864: [], 865: [], 866: [], 867: [], 868: [], 869: [Fractional ideal (-27*a + 20), Fractional ideal (a - 30), Fractional ideal (a + 29), Fractional ideal (-27*a + 7)], 870: [], 871: [], 872: [], 873: [], 874: [], 875: [], 876: [], 877: [], 878: [], 879: [], 880: [Fractional ideal (4*a + 28), Fractional ideal (-4*a + 32)], 881: [Fractional ideal (-27*a + 19), Fractional ideal (27*a - 8)], 882: [], 883: [], 884: [], 885: [], 886: [], 887: [], 888: [], 889: [], 890: [], 891: [Fractional ideal (-27*a + 9), Fractional ideal (-27*a + 18)], 892: [], 893: [], 894: [], 895: [Fractional ideal (2*a + 29), Fractional ideal (-2*a + 31)], 896: [], 897: [], 898: [], 899: [Fractional ideal (-5*a - 28), Fractional ideal (-27*a + 10), Fractional ideal (27*a - 17), Fractional ideal (-5*a + 33)], 900: [Fractional ideal (30)], 901: [], 902: [], 903: [], 904: [], 905: [Fractional ideal (27*a - 16), Fractional ideal (-27*a + 11)], 906: [], 907: [], 908: [], 909: [Fractional ideal (27*a - 15), Fractional ideal (27*a - 12)], 910: [], 911: [Fractional ideal (27*a - 14), Fractional ideal (27*a - 13)], 912: [], 913: [], 914: [], 915: [], 916: [Fractional ideal (6*a - 34), Fractional ideal (-6*a - 28)], 917: [], 918: [], 919: [Fractional ideal (3*a - 32), Fractional ideal (-3*a - 29)], 920: [], 921: [], 922: [], 923: [], 924: [], 925: [], 926: [], 927: [], 928: [], 929: [Fractional ideal (a - 31), Fractional ideal (a + 30)], 930: [], 931: [Fractional ideal (-28*a + 7), Fractional ideal (28*a - 21)], 932: [], 933: [], 934: [], 935: [], 936: [], 937: [], 938: [], 939: [], 940: [], 941: [Fractional ideal (4*a + 29), Fractional ideal (-4*a + 33)], 942: [], 943: [], 944: [Fractional ideal (28*a - 20), Fractional ideal (28*a - 8)], 945: [], 946: [], 947: [], 948: [], 949: [], 950: [], 951: [], 952: [], 953: [], 954: [], 955: [Fractional ideal (28*a - 9), Fractional ideal (28*a - 19)], 956: [Fractional ideal (2*a - 32), Fractional ideal (2*a + 30)], 957: [], 958: [], 959: [], 960: [], 961: [Fractional ideal (5*a - 34), Fractional ideal (31), Fractional ideal (-5*a - 29)], 962: [], 963: [], 964: [Fractional ideal (-28*a + 10), Fractional ideal (-28*a + 18)], 965: [], 966: [], 967: [], 968: [], 969: [], 970: [], 971: [Fractional ideal (-28*a + 17), Fractional ideal (28*a - 11)], 972: [], 973: [], 974: [], 975: [], 976: [Fractional ideal (28*a - 16), Fractional ideal (28*a - 12)], 977: [], 978: [], 979: [Fractional ideal (-28*a + 13), Fractional ideal (-6*a - 29), Fractional ideal (6*a - 35), Fractional ideal (28*a - 15)], 980: [Fractional ideal (-28*a + 14)], 981: [Fractional ideal (3*a - 33), Fractional ideal (3*a + 30)], 982: [], 983: [], 984: [], 985: [], 986: [], 987: [], 988: [], 989: [], 990: [], 991: [Fractional ideal (a - 32), Fractional ideal (a + 31)], 992: [], 993: [], 994: [], 995: [Fractional ideal (29*a - 7), Fractional ideal (29*a - 22)], 996: [], 997: [], 998: [], 999: [], 1000: []}
Fractional ideal (7) 49 Fractional ideal (7) [1]
raw value 4.23997384119518e-16 + 4.63884971589829e-16*I
normalised 6.83594740282864e-17 - 3.75785568287707e-16*I
algdeprts [(0.000000000000000, 1)]
Fractional ideal (-8*a + 2) 76 (Fractional ideal (2)) * (Fractional ideal (-4*a + 1)) [1, 1]
raw value 1.77476876452316 + 1.95759988981642*I
normalised 0.999999999999998 - 1.73205080756888*I
algdeprts [(1.00000000000000 - 1.73205080756888*I, 1), (1.00000000000000 + 1.73205080756888*I, 1)]
Fractional ideal (8*a - 6) 76 (Fractional ideal (2)) * (Fractional ideal (4*a - 3)) [1, 1]
raw value 5.19285520077821e-17 - 5.43601270621147e-17*I
normalised -5.11928948197067e-17 - 2.48414402630533e-17*I
algdeprts [(0.000000000000000, 1)]
Fractional ideal (2*a + 11) 139 Fractional ideal (2*a + 11) [1]
raw value 1.94848534487254 - 0.144575522568633*I
normalised 0.999999999999995 + 1.73205080756887*I
algdeprts [(1.00000000000000 - 1.73205080756888*I, 1), (1.00000000000000 + 1.73205080756888*I, 1)]
Fractional ideal (-2*a + 13) 139 Fractional ideal (-2*a + 13) [1]
raw value -1.09944874774612 - 1.61515004627698*I
normalised 0.999999999999997 - 1.73205080756887*I
algdeprts [(1.00000000000000 - 1.73205080756888*I, 1), (1.00000000000000 + 1.73205080756888*I, 1)]
Fractional ideal (11*a - 6) 151 Fractional ideal (11*a - 6) [1]
raw value 1.28139749191622 - 1.36826182656356*I
normalised -1.99999999999999 - 1.54228076864596e-16*I
algdeprts [(-2.00000000000000, 1)]
Fractional ideal (11*a - 5) 151 Fractional ideal (11*a - 5) [1]
raw value 3.84419247574867 - 4.10478547969069*I
normalised -5.99999999999998 - 4.31838615220870e-15*I
algdeprts [(-6.00000000000000, 1)]
Fractional ideal (13) 169 Fractional ideal (13) [1]
raw value 1.54579562381928 + 0.866227961755149*I
normalised 2.00000000000000 - 1.85073692237516e-15*I
algdeprts [(2.00000000000000, 1)]
Fractional ideal (3*a + 13) 199 Fractional ideal (3*a + 13) [1]
raw value 1.29290702755217 + 0.997438946405499*I
normalised 2.00000000000001 - 6.94026345890684e-15*I
algdeprts [(2.00000000000000, 1)]
Fractional ideal (-3*a + 16) 199 Fractional ideal (-3*a + 16) [1]
raw value 1.51026098008723 - 0.620970857388854*I
normalised 0.999999999999999 - 1.73205080756889*I
algdeprts [(1.00000000000000 - 1.73205080756888*I, 1), (1.00000000000000 + 1.73205080756888*I, 1)]
Fractional ideal (14*a - 8) 244 (Fractional ideal (2)) * (Fractional ideal (7*a - 4)) [1, 2]
raw value 0.0314883405142133 + 1.47435757599598*I
normalised -2.00000000000000 + 1.00248249961988e-15*I
algdeprts [(-2.00000000000000, 1)]
Fractional ideal (14*a - 6) 244 (Fractional ideal (2)) * (Fractional ideal (7*a - 3)) [1, 2]
raw value 1.29257528533167 + 0.709909085189665*I
normalised -0.999999999999998 + 1.73205080756888*I
algdeprts [(-1.00000000000000 - 1.73205080756888*I, 1), (-1.00000000000000 + 1.73205080756888*I, 1)]
Fractional ideal (-16*a + 6) 316 (Fractional ideal (2)) * (Fractional ideal (-8*a + 3)) [1, 2]
raw value 1.28951584857673 - 0.127923516106711*I
normalised 1.00000000000000 - 1.73205080756887*I
algdeprts [(1.00000000000000 - 1.73205080756888*I, 1), (1.00000000000000 + 1.73205080756888*I, 1)]
Fractional ideal (-16*a + 10) 316 (Fractional ideal (2)) * (Fractional ideal (-8*a + 5)) [1, 1]
raw value 0.533972909598525 + 1.18071524150345*I
normalised -1.00000000000000 + 1.73205080756888*I
algdeprts [(-1.00000000000000 - 1.73205080756888*I, 1), (-1.00000000000000 + 1.73205080756888*I, 1)]
Fractional ideal (3*a - 20) 331 Fractional ideal (3*a - 20) [1]
raw value 5.51133057385612 - 3.11499430386439*I
normalised 9.99999999999998 - 1.85073692237516e-15*I
algdeprts [(10.0000000000000, 1)]
Fractional ideal (-3*a - 17) 331 Fractional ideal (-3*a - 17) [1]
raw value 0.0116002174275343 - 1.26608988750909*I
normalised 0.999999999999996 - 1.73205080756887*I
algdeprts [(1.00000000000000 - 1.73205080756888*I, 1), (1.00000000000000 + 1.73205080756888*I, 1)]
Fractional ideal (19) 361 (Fractional ideal (4*a - 3)) * (Fractional ideal (-4*a + 1)) [1, 1]
raw value 3.31254869309870 - 1.50202417497642*I
normalised -2.99999999999999 + 5.19615242270663*I
algdeprts [(-3.00000000000000 - 5.19615242270663*I, 1), (-3.00000000000000 + 5.19615242270663*I, 1)]
Fractional ideal (2*a - 22) 436 (Fractional ideal (2)) * (Fractional ideal (a - 11)) [1, 1]
raw value 0.105811424643225 + 3.30790252782655*I
normalised 6.00000000000002 - 9.71636884246957e-15*I
algdeprts [(6.00000000000000, 1)]
Fractional ideal (2*a + 20) 436 (Fractional ideal (2)) * (Fractional ideal (a + 10)) [1, 1]
raw value 0.937273970006310 - 0.581862215221642*I
normalised -1.00000000000000 - 1.73205080756887*I
algdeprts [(-1.00000000000000 - 1.73205080756888*I, 1), (-1.00000000000000 + 1.73205080756888*I, 1)]
Fractional ideal (3*a + 22) 541 Fractional ideal (3*a + 22) [1]
raw value 0.220342943690387 - 0.965548904601734*I
normalised -0.999999999999960 - 1.73205080756884*I
algdeprts [(-1.00000000000000 - 1.73205080756888*I, 1), (-1.00000000000000 + 1.73205080756888*I, 1)]
Fractional ideal (-3*a + 25) 541 Fractional ideal (-3*a + 25) [1]
raw value 5.67816811095919 - 1.75171119312209*I
normalised 5.99999999999994 - 10.3923048454130*I
algdeprts [(6.00000000000000 - 10.3923048454133*I, 1), (6.00000000000000 + 10.3923048454133*I, 1)]
Fractional ideal (-5*a - 23) 619 Fractional ideal (-5*a - 23) [1]
raw value 2.97938352704803e-17 + 3.43681605226057e-16*I
normalised 7.44849374231626e-16 + 2.21641516343011e-17*I
algdeprts [(0.000000000000000, 1)]
Fractional ideal (-5*a + 28) 619 Fractional ideal (-5*a + 28) [1]
raw value 0.850102587652341 + 0.366833047835574*I
normalised 0.999999999999995 - 1.73205080756885*I
algdeprts [(1.00000000000000 - 1.73205080756888*I, 1), (1.00000000000000 + 1.73205080756888*I, 1)]
Fractional ideal (23*a - 12) 661 Fractional ideal (23*a - 12) [1]
raw value -1.05030706605215 - 1.45187533489213*I
normalised -1.99999999999996 - 3.46410161513771*I
algdeprts [(-2.00000000000000 - 3.46410161513775*I, 1), (-2.00000000000000 + 3.46410161513775*I, 1)]
Fractional ideal (23*a - 11) 661 Fractional ideal (23*a - 11) [1]
raw value 2.67377168425605 - 0.275482400294101*I
normalised 5.99999999999991 + 2.15919307610435e-14*I
algdeprts [(6.00000000000000, 1)]
Fractional ideal (4*a + 25) 709 Fractional ideal (4*a + 25) [1]
raw value 0.407925749775957 + 0.762902270422673*I
normalised -0.999999999999962 - 1.73205080756885*I
algdeprts [(-1.00000000000000 - 1.73205080756888*I, 1), (-1.00000000000000 + 1.73205080756888*I, 1)]
Fractional ideal (-4*a + 29) 709 Fractional ideal (-4*a + 29) [1]
raw value 3.65383897522305 - 5.87780157900103*I
normalised -7.99999999999996 + 13.8564064605506*I
algdeprts [(-8.00000000000000 - 13.8564064605510*I, 1), (-8.00000000000000 + 13.8564064605510*I, 1)]
Fractional ideal (2*a - 28) 724 (Fractional ideal (2)) * (Fractional ideal (a - 14)) [1, 1]
raw value 0.0750071924253409 - 0.852813699004227*I
normalised 1.00000000000000 - 1.73205080756888*I
algdeprts [(1.00000000000000 - 1.73205080756888*I, 1), (1.00000000000000 + 1.73205080756888*I, 1)]
Fractional ideal (2*a + 26) 724 (Fractional ideal (2)) * (Fractional ideal (a + 13)) [1, 2]
raw value 2.10316419546110 - 1.47409495082702*I
normalised 3.00000000000001 - 5.19615242270665*I
algdeprts [(3.00000000000000 - 5.19615242270663*I, 1), (3.00000000000000 + 5.19615242270663*I, 1)]
Fractional ideal (a - 29) 811 Fractional ideal (a - 29) [1]
raw value 2.42211496159430 - 0.148329222983797*I
normalised 3.00000000000004 + 5.19615242270670*I
algdeprts [(3.00000000000000 - 5.19615242270663*I, 1), (3.00000000000000 + 5.19615242270663*I, 1)]
Fractional ideal (a + 28) 811 Fractional ideal (a + 28) [1]
raw value 0.807371653864767 - 0.0494430743279323*I
normalised 1.00000000000001 + 1.73205080756890*I
algdeprts [(1.00000000000000 - 1.73205080756888*I, 1), (1.00000000000000 + 1.73205080756888*I, 1)]
Fractional ideal (-26*a + 9) 829 Fractional ideal (-26*a + 9) [1]
raw value -0.708540684817226 - 0.371560340655551*I
normalised -2.00000000000000 + 2.00496499923975e-15*I
algdeprts [(-2.00000000000000, 1)]
Fractional ideal (-26*a + 17) 829 Fractional ideal (-26*a + 17) [1]
raw value -0.0649792967242118 - 1.59878880598863*I
normalised -2.00000000000001 - 3.46410161513776*I
algdeprts [(-2.00000000000000 - 3.46410161513775*I, 1), (-2.00000000000000 + 3.46410161513775*I, 1)]
Fractional ideal (26*a - 14) 844 (Fractional ideal (2)) * (Fractional ideal (13*a - 7)) [1, 2]
raw value -4.23663230448205e-17 + 1.61753552578096e-16*I
normalised -2.46810589924953e-16 + 3.42003916777016e-16*I
algdeprts [(0.000000000000000, 1)]
Fractional ideal (26*a - 12) 844 (Fractional ideal (2)) * (Fractional ideal (13*a - 6)) [1, 1]
 1.29257528533167 + 0.709909085189665*I
normalised -0.999999999999998 + 1.73205080756888*I
algdeprts [(-1.00000000000000 - 1.73205080756888*I, 1), (-1.00000000000000 + 1.73205080756888*I, 1)]
Fractional ideal (-16*a + 6) 316 (Fractional ideal (2)) * (Fractional ideal (-8*a + 3)) [1, 2]
raw value 1.28951584857673 - 0.127923516106711*I
normalised 1.00000000000000 - 1.73205080756887*I
algdeprts [(1.00000000000000 - 1.73205080756888*I, 1), (1.00000000000000 + 1.73205080756888*I, 1)]
Fractional ideal (-16*a + 10) 316 (Fractional ideal (2)) * (Fractional ideal (-8*a + 5)) [1, 1]
raw value 0.533972909598525 + 1.18071524150345*I
normalised -1.00000000000000 + 1.73205080756888*I
algdeprts [(-1.00000000000000 - 1.73205080756888*I, 1), (-1.00000000000000 + 1.73205080756888*I, 1)]
Fractional ideal (3*a - 20) 331 Fractional ideal (3*a - 20) [1]
raw value 5.51133057385612 - 3.11499430386439*I
normalised 9.99999999999998 - 1.85073692237516e-15*I
algdeprts [(10.0000000000000, 1)]
Fractional ideal (-3*a - 17) 331 Fractional ideal (-3*a - 17) [1]
raw value 0.0116002174275343 - 1.26608988750909*I
normalised 0.999999999999996 - 1.73205080756887*I
algdeprts [(1.00000000000000 - 1.73205080756888*I, 1), (1.00000000000000 + 1.73205080756888*I, 1)]
Fractional ideal (19) 361 (Fractional ideal (4*a - 3)) * (Fractional ideal (-4*a + 1)) [1, 1]
raw value 3.31254869309870 - 1.50202417497642*I
normalised -2.99999999999999 + 5.19615242270663*I
algdeprts [(-3.00000000000000 - 5.19615242270663*I, 1), (-3.00000000000000 + 5.19615242270663*I, 1)]
Fractional ideal (2*a - 22) 436 (Fractional ideal (2)) * (Fractional ideal (a - 11)) [1, 1]
raw value 0.105811424643225 + 3.30790252782655*I
normalised 6.00000000000002 - 9.71636884246957e-15*I
algdeprts [(6.00000000000000, 1)]
Fractional ideal (2*a + 20) 436 (Fractional ideal (2)) * (Fractional ideal (a + 10)) [1, 1]
raw value 0.937273970006310 - 0.581862215221642*I
normalised -1.00000000000000 - 1.73205080756887*I
algdeprts [(-1.00000000000000 - 1.73205080756888*I, 1), (-1.00000000000000 + 1.73205080756888*I, 1)]
Fractional ideal (3*a + 22) 541 Fractional ideal (3*a + 22) [1]
raw value 0.220342943690387 - 0.965548904601734*I
normalised -0.999999999999960 - 1.73205080756884*I
algdeprts [(-1.00000000000000 - 1.73205080756888*I, 1), (-1.00000000000000 + 1.73205080756888*I, 1)]
Fractional ideal (-3*a + 25) 541 Fractional ideal (-3*a + 25) [1]
raw value 5.67816811095919 - 1.75171119312209*I
normalised 5.99999999999994 - 10.3923048454130*I
algdeprts [(6.00000000000000 - 10.3923048454133*I, 1), (6.00000000000000 + 10.3923048454133*I, 1)]
Fractional ideal (-5*a - 23) 619 Fractional ideal (-5*a - 23) [1]
raw value 2.97938352704803e-17 + 3.43681605226057e-16*I
normalised 7.44849374231626e-16 + 2.21641516343011e-17*I
algdeprts [(0.000000000000000, 1)]
Fractional ideal (-5*a + 28) 619 Fractional ideal (-5*a + 28) [1]
raw value 0.850102587652341 + 0.366833047835574*I
normalised 0.999999999999995 - 1.73205080756885*I
algdeprts [(1.00000000000000 - 1.73205080756888*I, 1), (1.00000000000000 + 1.73205080756888*I, 1)]
Fractional ideal (23*a - 12) 661 Fractional ideal (23*a - 12) [1]
raw value -1.05030706605215 - 1.45187533489213*I
normalised -1.99999999999996 - 3.46410161513771*I
algdeprts [(-2.00000000000000 - 3.46410161513775*I, 1), (-2.00000000000000 + 3.46410161513775*I, 1)]
Fractional ideal (23*a - 11) 661 Fractional ideal (23*a - 11) [1]
raw value 2.67377168425605 - 0.275482400294101*I
normalised 5.99999999999991 + 2.15919307610435e-14*I
algdeprts [(6.00000000000000, 1)]
Fractional ideal (4*a + 25) 709 Fractional ideal (4*a + 25) [1]
raw value 0.407925749775957 + 0.762902270422673*I
normalised -0.999999999999962 - 1.73205080756885*I
algdeprts [(-1.00000000000000 - 1.73205080756888*I, 1), (-1.00000000000000 + 1.73205080756888*I, 1)]
Fractional ideal (-4*a + 29) 709 Fractional ideal (-4*a + 29) [1]
raw value 3.65383897522305 - 5.87780157900103*I
normalised -7.99999999999996 + 13.8564064605506*I
algdeprts [(-8.00000000000000 - 13.8564064605510*I, 1), (-8.00000000000000 + 13.8564064605510*I, 1)]
Fractional ideal (2*a - 28) 724 (Fractional ideal (2)) * (Fractional ideal (a - 14)) [1, 1]
raw value 0.0750071924253409 - 0.852813699004227*I
normalised 1.00000000000000 - 1.73205080756888*I
algdeprts [(1.00000000000000 - 1.73205080756888*I, 1), (1.00000000000000 + 1.73205080756888*I, 1)]
Fractional ideal (2*a + 26) 724 (Fractional ideal (2)) * (Fractional ideal (a + 13)) [1, 2]
raw value 2.10316419546110 - 1.47409495082702*I
normalised 3.00000000000001 - 5.19615242270665*I
algdeprts [(3.00000000000000 - 5.19615242270663*I, 1), (3.00000000000000 + 5.19615242270663*I, 1)]
Fractional ideal (a - 29) 811 Fractional ideal (a - 29) [1]
raw value 2.42211496159430 - 0.148329222983797*I
normalised 3.00000000000004 + 5.19615242270670*I
algdeprts [(3.00000000000000 - 5.19615242270663*I, 1), (3.00000000000000 + 5.19615242270663*I, 1)]
Fractional ideal (a + 28) 811 Fractional ideal (a + 28) [1]
raw value 0.807371653864767 - 0.0494430743279323*I
normalised 1.00000000000001 + 1.73205080756890*I
algdeprts [(1.00000000000000 - 1.73205080756888*I, 1), (1.00000000000000 + 1.73205080756888*I, 1)]
Fractional ideal (-26*a + 9) 829 Fractional ideal (-26*a + 9) [1]
raw value -0.708540684817226 - 0.371560340655551*I
normalised -2.00000000000000 + 2.00496499923975e-15*I
algdeprts [(-2.00000000000000, 1)]
Fractional ideal (-26*a + 17) 829 Fractional ideal (-26*a + 17) [1]
raw value -0.0649792967242118 - 1.59878880598863*I
normalised -2.00000000000001 - 3.46410161513776*I
algdeprts [(-2.00000000000000 - 3.46410161513775*I, 1), (-2.00000000000000 + 3.46410161513775*I, 1)]
Fractional ideal (26*a - 14) 844 (Fractional ideal (2)) * (Fractional ideal (13*a - 7)) [1, 2]
raw value -4.23663230448205e-17 + 1.61753552578096e-16*I
normalised -2.46810589924953e-16 + 3.42003916777016e-16*I
algdeprts [(0.000000000000000, 1)]
Fractional ideal (26*a - 12) 844 (Fractional ideal (2)) * (Fractional ideal (13*a - 6)) [1, 1]
raw value 0.739554891290375 + 0.285953838871922*I
normalised 2.00000000000000 - 5.39798269026087e-16*I
algdeprts [(2.00000000000000, 1)]
Fractional ideal (6*a - 34) 916 (Fractional ideal (2)) * (Fractional ideal (3*a - 17)) [1, 2]
raw value 2.13227688423814 - 2.17303439866661*I
normalised 4.00000000000000 - 6.92820323027548*I
algdeprts [(4.00000000000000 - 6.92820323027551*I, 1), (4.00000000000000 + 6.92820323027551*I, 1)]
Fractional ideal (-6*a - 28) 916 (Fractional ideal (2)) * (Fractional ideal (-3*a - 14)) [1, 2]
raw value 0.407882275211829 + 1.46656157449293*I
normalised 1.99999999999999 + 3.46410161513775*I
algdeprts [(2.00000000000000 - 3.46410161513775*I, 1), (2.00000000000000 + 3.46410161513775*I, 1)]
Fractional ideal (3*a - 32) 919 Fractional ideal (3*a - 32) [1]
raw value 1.47488307737899 - 1.73819870330501*I
normalised 2.99999999999996 + 5.19615242270652*I
algdeprts [(3.00000000000000 - 5.19615242270663*I, 1), (3.00000000000000 + 5.19615242270663*I, 1)]
Fractional ideal (-3*a - 29) 919 Fractional ideal (-3*a - 29) [1]
raw value 0.747588590858935 + 0.136062286989824*I
normalised -0.999999999999973 + 1.73205080756885*I
algdeprts [(-1.00000000000000 - 1.73205080756888*I, 1), (-1.00000000000000 + 1.73205080756888*I, 1)]
Fractional ideal (-28*a + 10) 964 (Fractional ideal (2)) * (Fractional ideal (-14*a + 5)) [1, 2]
raw value -8.13331843618429e-17 + 3.80334660780596e-16*I
normalised 5.08223035342031e-16 + 9.17036300304053e-16*I
algdeprts [(0.000000000000000, 1)]
Fractional ideal (-28*a + 18) 964 (Fractional ideal (2)) * (Fractional ideal (-14*a + 9)) [1, 2]

len(set([c._conductor for c in chis]))

41

len(vals);len(nvals);len(chis)

45
45
45

hvals,nvals,[c._conductor.norm() for c in chis]

([4.23997384119518e-16 + 4.63884971589829e-16*I, 1.77476876452316 + 1.95759988981642*I, 5.19285520077821e-17 - 5.43601270621147e-17*I, 1.94848534487254 - 0.144575522568633*I, -1.09944874774612 - 1.61515004627698*I, 1.28139749191622 - 1.36826182656356*I, 3.84419247574867 - 4.10478547969069*I, 1.54579562381928 + 0.866227961755149*I, 1.29290702755217 + 0.997438946405499*I, 1.51026098008723 - 0.620970857388854*I, 0.0314883405142133 + 1.47435757599598*I, 1.29257528533167 - 0.709909085189666*I, 1.77476876452315 - 1.95759988981642*I, 3.96635225811821e-16 + 8.65558293069396e-16*I, 1.28951584857673 + 0.127923516106712*I, 0.533972909598524 - 1.18071524150345*I, 5.51133057385612 - 3.11499430386439*I, 0.0116002174275343 - 1.26608988750909*I, 3.31254869309870 - 1.50202417497642*I, 0.105811424643225 + 3.30790252782655*I, 0.937273970006310 - 0.581862215221642*I, 0.220342943690387 - 0.965548904601734*I, 5.67816811095919 - 1.75171119312209*I, 2.97938352704803e-17 + 3.43681605226057e-16*I, 0.850102587652341 + 0.366833047835574*I, -1.05030706605215 - 1.45187533489213*I, 2.67377168425605 - 0.275482400294101*I, 0.407925749775957 + 0.762902270422673*I, 3.65383897522305 - 5.87780157900103*I, 0.0750071924253409 - 0.852813699004227*I, 2.10316419546110 - 1.47409495082702*I, 2.42211496159430 - 0.148329222983797*I, 0.807371653864767 - 0.0494430743279323*I, -0.708540684817226 - 0.371560340655551*I, -0.0649792967242118 - 1.59878880598863*I, -2.44044271498545e-17 + 3.90218477182619e-16*I, 0.739554891290374 - 0.285953838871922*I, 2.13227688423814 + 2.17303439866661*I, 0.407882275211828 - 1.46656157449293*I, 1.47488307737899 - 1.73819870330501*I, 0.747588590858935 + 0.136062286989824*I, 1.14136788920694e-16 + 4.08823369652626e-16*I, -0.142403971843641 + 0.728127296244202*I, 0.0314883405142133 + 1.47435757599598*I, 1.29257528533167 - 0.709909085189666*I], [6.83594740282864e-17 - 3.75785568287707e-16*I, 0.999999999999998 - 1.73205080756888*I, -5.11928948197067e-17 - 2.48414402630533e-17*I, 0.999999999999995 + 1.73205080756887*I, 0.999999999999997 - 1.73205080756887*I, -1.99999999999999 - 1.54228076864596e-16*I, -5.99999999999998 - 4.31838615220870e-15*I, 2.00000000000000 - 1.85073692237516e-15*I, 2.00000000000001 - 6.94026345890684e-15*I, 0.999999999999999 - 1.73205080756889*I, -2.00000000000000 + 1.00248249961988e-15*I, -0.999999999999999 - 1.73205080756887*I, 1.00000000000000 + 1.73205080756888*I, -7.15561925897464e-16 + 8.55135113864284e-17*I, 0.999999999999997 + 1.73205080756888*I, -0.999999999999997 - 1.73205080756887*I, 9.99999999999998 - 1.85073692237516e-15*I, 0.999999999999996 - 1.73205080756887*I, -2.99999999999999 + 5.19615242270663*I, 6.00000000000002 - 9.71636884246957e-15*I, -1.00000000000000 - 1.73205080756887*I, -0.999999999999960 - 1.73205080756884*I, 5.99999999999994 - 10.3923048454130*I, 7.44849374231626e-16 + 2.21641516343011e-17*I, 0.999999999999995 - 1.73205080756885*I, -1.99999999999996 - 3.46410161513771*I, 5.99999999999991 + 2.15919307610435e-14*I, -0.999999999999962 - 1.73205080756885*I, -7.99999999999996 + 13.8564064605506*I, 1.00000000000000 - 1.73205080756888*I, 3.00000000000001 - 5.19615242270665*I, 3.00000000000004 + 5.19615242270670*I, 1.00000000000001 + 1.73205080756890*I, -2.00000000000000 + 2.00496499923975e-15*I, -2.00000000000001 - 3.46410161513776*I, 2.97548644273395e-16 + 9.40230110669508e-16*I, 2.00000000000000 - 3.85570192161491e-15*I, 3.99999999999997 + 6.92820323027550*I, 2.00000000000000 - 3.46410161513774*I, 2.99999999999996 + 5.19615242270652*I, -0.999999999999973 + 1.73205080756885*I, -4.92001994552848e-16 + 1.03302898020866e-15*I, 1.00000000000001 + 1.73205080756889*I, -2.00000000000000 + 1.00248249961988e-15*I, -0.999999999999999 - 1.73205080756887*I], [49, 76, 76, 139, 139, 151, 151, 169, 199, 199, 244, 244, 76, 76, 316, 316, 331, 331, 361, 436, 436, 541, 541, 619, 619, 661, 661, 709, 709, 724, 724, 811, 811, 829, 829, 844, 844, 916, 916, 919, 919, 964, 964, 244, 244])

vals,nvals,chis

([4.23997384119518e-16 + 4.63884971589829e-16*I, 1.77476876452316 + 1.95759988981642*I, 5.19285520077821e-17 - 5.43601270621147e-17*I, 1.94848534487254 - 0.144575522568633*I, -1.09944874774612 - 1.61515004627698*I, 1.28139749191622 - 1.36826182656356*I, 3.84419247574867 - 4.10478547969069*I, 1.54579562381928 + 0.866227961755149*I, 1.29290702755217 + 0.997438946405499*I, 1.51026098008723 - 0.620970857388854*I, 0.0314883405142133 + 1.47435757599598*I, 1.29257528533167 - 0.709909085189666*I, 1.77476876452315 - 1.95759988981642*I, 3.96635225811821e-16 + 8.65558293069396e-16*I, 1.28951584857673 + 0.127923516106712*I, 0.533972909598524 - 1.18071524150345*I, 5.51133057385612 - 3.11499430386439*I, 0.0116002174275343 - 1.26608988750909*I, 3.31254869309870 - 1.50202417497642*I, 0.105811424643225 + 3.30790252782655*I, 0.937273970006310 - 0.581862215221642*I, 0.220342943690387 - 0.965548904601734*I, 5.67816811095919 - 1.75171119312209*I, 2.97938352704803e-17 + 3.43681605226057e-16*I, 0.850102587652341 + 0.366833047835574*I, -1.05030706605215 - 1.45187533489213*I, 2.67377168425605 - 0.275482400294101*I, 0.407925749775957 + 0.762902270422673*I, 3.65383897522305 - 5.87780157900103*I, 0.0750071924253409 - 0.852813699004227*I, 2.10316419546110 - 1.47409495082702*I, 2.42211496159430 - 0.148329222983797*I, 0.807371653864767 - 0.0494430743279323*I, -0.708540684817226 - 0.371560340655551*I, -0.0649792967242118 - 1.59878880598863*I, -2.44044271498545e-17 + 3.90218477182619e-16*I, 0.739554891290374 - 0.285953838871922*I, 2.13227688423814 + 2.17303439866661*I, 0.407882275211828 - 1.46656157449293*I, 1.47488307737899 - 1.73819870330501*I, 0.747588590858935 + 0.136062286989824*I, 1.14136788920694e-16 + 4.08823369652626e-16*I, -0.142403971843641 + 0.728127296244202*I, 0.0314883405142133 + 1.47435757599598*I, 1.29257528533167 - 0.709909085189666*I], [6.83594740282864e-17 - 3.75785568287707e-16*I, 0.999999999999998 - 1.73205080756888*I, -5.11928948197067e-17 - 2.48414402630533e-17*I, 0.999999999999995 + 1.73205080756887*I, 0.999999999999997 - 1.73205080756887*I, -1.99999999999999 - 1.54228076864596e-16*I, -5.99999999999998 - 4.31838615220870e-15*I, 2.00000000000000 - 1.85073692237516e-15*I, 2.00000000000001 - 6.94026345890684e-15*I, 0.999999999999999 - 1.73205080756889*I, -2.00000000000000 + 1.00248249961988e-15*I, -0.999999999999999 - 1.73205080756887*I, 1.00000000000000 + 1.73205080756888*I, -7.15561925897464e-16 + 8.55135113864284e-17*I, 0.999999999999997 + 1.73205080756888*I, -0.999999999999997 - 1.73205080756887*I, 9.99999999999998 - 1.85073692237516e-15*I, 0.999999999999996 - 1.73205080756887*I, -2.99999999999999 + 5.19615242270663*I, 6.00000000000002 - 9.71636884246957e-15*I, -1.00000000000000 - 1.73205080756887*I, -0.999999999999960 - 1.73205080756884*I, 5.99999999999994 - 10.3923048454130*I, 7.44849374231626e-16 + 2.21641516343011e-17*I, 0.999999999999995 - 1.73205080756885*I, -1.99999999999996 - 3.46410161513771*I, 5.99999999999991 + 2.15919307610435e-14*I, -0.999999999999962 - 1.73205080756885*I, -7.99999999999996 + 13.8564064605506*I, 1.00000000000000 - 1.73205080756888*I, 3.00000000000001 - 5.19615242270665*I, 3.00000000000004 + 5.19615242270670*I, 1.00000000000001 + 1.73205080756890*I, -2.00000000000000 + 2.00496499923975e-15*I, -2.00000000000001 - 3.46410161513776*I, 2.97548644273395e-16 + 9.40230110669508e-16*I, 2.00000000000000 - 3.85570192161491e-15*I, 3.99999999999997 + 6.92820323027550*I, 2.00000000000000 - 3.46410161513774*I, 2.99999999999996 + 5.19615242270652*I, -0.999999999999973 + 1.73205080756885*I, -4.92001994552848e-16 + 1.03302898020866e-15*I, 1.00000000000001 + 1.73205080756889*I, -2.00000000000000 + 1.00248249961988e-15*I, -0.999999999999999 - 1.73205080756887*I], [Hecke character of modulus Fractional ideal (7) and order 3, Hecke character of modulus Fractional ideal (-8*a + 2) and order 3, Hecke character of modulus Fractional ideal (8*a - 6) and order 3, Hecke character of modulus Fractional ideal (2*a + 11) and order 3, Hecke character of modulus Fractional ideal (-2*a + 13) and order 3, Hecke character of modulus Fractional ideal (11*a - 6) and order 3, Hecke character of modulus Fractional ideal (11*a - 5) and order 3, Hecke character of modulus Fractional ideal (13) and order 3, Hecke character of modulus Fractional ideal (3*a + 13) and order 3, Hecke character of modulus Fractional ideal (-3*a + 16) and order 3, Hecke character of modulus Fractional ideal (14*a - 8) and order 3, Hecke character of modulus Fractional ideal (14*a - 6) and order 3, Hecke character of modulus Fractional ideal (-8*a + 2) and order 3, Hecke character of modulus Fractional ideal (8*a - 6) and order 3, Hecke character of modulus Fractional ideal (-16*a + 6) and order 3, Hecke character of modulus Fractional ideal (-16*a + 10) and order 3, Hecke character of modulus Fractional ideal (3*a - 20) and order 3, Hecke character of modulus Fractional ideal (-3*a - 17) and order 3, Hecke character of modulus Fractional ideal (19) and order 3, Hecke character of modulus Fractional ideal (2*a - 22) and order 3, Hecke character of modulus Fractional ideal (2*a + 20) and order 3, Hecke character of modulus Fractional ideal (3*a + 22) and order 3, Hecke character of modulus Fractional ideal (-3*a + 25) and order 3, Hecke character of modulus Fractional ideal (-5*a - 23) and order 3, Hecke character of modulus Fractional ideal (-5*a + 28) and order 3, Hecke character of modulus Fractional ideal (23*a - 12) and order 3, Hecke character of modulus Fractional ideal (23*a - 11) and order 3, Hecke character of modulus Fractional ideal (4*a + 25) and order 3, Hecke character of modulus Fractional ideal (-4*a + 29) and order 3, Hecke character of modulus Fractional ideal (2*a - 28) and order 3, Hecke character of modulus Fractional ideal (2*a + 26) and order 3, Hecke character of modulus Fractional ideal (a - 29) and order 3, Hecke character of modulus Fractional ideal (a + 28) and order 3, Hecke character of modulus Fractional ideal (-26*a + 9) and order 3, Hecke character of modulus Fractional ideal (-26*a + 17) and order 3, Hecke character of modulus Fractional ideal (26*a - 14) and order 3, Hecke character of modulus Fractional ideal (26*a - 12) and order 3, Hecke character of modulus Fractional ideal (6*a - 34) and order 3, Hecke character of modulus Fractional ideal (-6*a - 28) and order 3, Hecke character of modulus Fractional ideal (3*a - 32) and order 3, Hecke character of modulus Fractional ideal (-3*a - 29) and order 3, Hecke character of modulus Fractional ideal (-28*a + 10) and order 3, Hecke character of modulus Fractional ideal (-28*a + 18) and order 3, Hecke character of modulus Fractional ideal (14*a - 8) and order 3, Hecke character of modulus Fractional ideal (14*a - 6) and order 3])

vals,nvals,chis

([4.23997384119518e-16 + 4.63884971589829e-16*I, 1.77476876452315 - 1.95759988981642*I, 3.96635225811821e-16 + 8.65558293069396e-16*I, 1.94848534487254 - 0.144575522568633*I, -1.09944874774612 - 1.61515004627698*I, 1.28139749191622 - 1.36826182656356*I, 3.84419247574867 - 4.10478547969069*I, 1.54579562381928 + 0.866227961755149*I, 1.29290702755217 + 0.997438946405499*I, 1.51026098008723 - 0.620970857388854*I, 0.0314883405142133 + 1.47435757599598*I, 1.29257528533167 - 0.709909085189666*I, 1.77476876452315 - 1.95759988981642*I, 5.19285520077821e-17 - 5.43601270621147e-17*I, 1.28951584857673 - 0.127923516106711*I, 0.533972909598524 - 1.18071524150345*I, 5.51133057385612 - 3.11499430386439*I, 0.0116002174275343 - 1.26608988750909*I, 3.31254869309870 - 1.50202417497642*I, 0.105811424643223 - 3.30790252782655*I, 0.937273970006310 - 0.581862215221642*I, 0.220342943690387 - 0.965548904601734*I, 5.67816811095919 - 1.75171119312209*I, 2.97938352704803e-17 + 3.43681605226057e-16*I, 0.850102587652341 + 0.366833047835574*I, -1.05030706605215 - 1.45187533489213*I, 2.67377168425605 - 0.275482400294101*I, 0.407925749775957 + 0.762902270422673*I, 3.65383897522305 - 5.87780157900103*I, 0.0750071924253417 + 0.852813699004227*I, 2.10316419546110 + 1.47409495082702*I, 2.42211496159430 - 0.148329222983797*I, 0.807371653864767 - 0.0494430743279323*I, -0.708540684817226 - 0.371560340655551*I, -0.0649792967242118 - 1.59878880598863*I, -2.44044271498545e-17 + 3.90218477182619e-16*I, 0.739554891290375 + 0.285953838871922*I, 2.13227688423814 - 2.17303439866661*I, 0.407882275211829 + 1.46656157449293*I, 1.47488307737899 - 1.73819870330501*I, 0.747588590858935 + 0.136062286989824*I, 1.14136788920694e-16 + 4.08823369652626e-16*I, -0.142403971843642 - 0.728127296244201*I, 0.0314883405142133 + 1.47435757599598*I, 1.29257528533167 + 0.709909085189665*I], [6.83594740282864e-17 - 3.75785568287707e-16*I, 1.00000000000000 + 1.73205080756888*I, -7.15561925897464e-16 + 8.55135113864284e-17*I, 0.999999999999995 + 1.73205080756887*I, 0.999999999999997 - 1.73205080756887*I, -1.99999999999999 - 1.54228076864596e-16*I, -5.99999999999998 - 4.31838615220870e-15*I, 2.00000000000000 - 1.85073692237516e-15*I, 2.00000000000001 - 6.94026345890684e-15*I, 0.999999999999999 - 1.73205080756889*I, -2.00000000000000 + 1.00248249961988e-15*I, -0.999999999999999 - 1.73205080756887*I, 1.00000000000000 + 1.73205080756888*I, -5.11928948197067e-17 - 2.48414402630533e-17*I, 1.00000000000000 - 1.73205080756887*I, -0.999999999999997 - 1.73205080756887*I, 9.99999999999998 - 1.85073692237516e-15*I, 0.999999999999996 - 1.73205080756887*I, -2.99999999999999 + 5.19615242270663*I, 6.00000000000001 - 8.09697403539131e-15*I, -1.00000000000000 - 1.73205080756887*I, -0.999999999999960 - 1.73205080756884*I, 5.99999999999994 - 10.3923048454130*I, 7.44849374231626e-16 + 2.21641516343011e-17*I, 0.999999999999995 - 1.73205080756885*I, -1.99999999999996 - 3.46410161513771*I, 5.99999999999991 + 2.15919307610435e-14*I, -0.999999999999962 - 1.73205080756885*I, -7.99999999999996 + 13.8564064605506*I, 1.00000000000000 + 1.73205080756888*I, 3.00000000000001 + 5.19615242270664*I, 3.00000000000004 + 5.19615242270670*I, 1.00000000000001 + 1.73205080756890*I, -2.00000000000000 + 2.00496499923975e-15*I, -2.00000000000001 - 3.46410161513776*I, 2.97548644273395e-16 + 9.40230110669508e-16*I, 2.00000000000000 - 5.39798269026087e-16*I, 4.00000000000000 - 6.92820323027548*I, 1.99999999999999 + 3.46410161513775*I, 2.99999999999996 + 5.19615242270652*I, -0.999999999999973 + 1.73205080756885*I, -4.92001994552848e-16 + 1.03302898020866e-15*I, 1.00000000000001 - 1.73205080756889*I, -2.00000000000000 + 1.00248249961988e-15*I, -0.999999999999998 + 1.73205080756888*I], [Hecke character of modulus Fractional ideal (7) and order 3, Hecke character of modulus Fractional ideal (-8*a + 2) and order 3, Hecke character of modulus Fractional ideal (8*a - 6) and order 3, Hecke character of modulus Fractional ideal (2*a + 11) and order 3, Hecke character of modulus Fractional ideal (-2*a + 13) and order 3, Hecke character of modulus Fractional ideal (11*a - 6) and order 3, Hecke character of modulus Fractional ideal (11*a - 5) and order 3, Hecke character of modulus Fractional ideal (13) and order 3, Hecke character of modulus Fractional ideal (3*a + 13) and order 3, Hecke character of modulus Fractional ideal (-3*a + 16) and order 3, Hecke character of modulus Fractional ideal (14*a - 8) and order 3, Hecke character of modulus Fractional ideal (14*a - 6) and order 3, Hecke character of modulus Fractional ideal (-8*a + 2) and order 3, Hecke character of modulus Fractional ideal (8*a - 6) and order 3, Hecke character of modulus Fractional ideal (-16*a + 6) and order 3, Hecke character of modulus Fractional ideal (-16*a + 10) and order 3, Hecke character of modulus Fractional ideal (3*a - 20) and order 3, Hecke character of modulus Fractional ideal (-3*a - 17) and order 3, Hecke character of modulus Fractional ideal (19) and order 3, Hecke character of modulus Fractional ideal (2*a - 22) and order 3, Hecke character of modulus Fractional ideal (2*a + 20) and order 3, Hecke character of modulus Fractional ideal (3*a + 22) and order 3, Hecke character of modulus Fractional ideal (-3*a + 25) and order 3, Hecke character of modulus Fractional ideal (-5*a - 23) and order 3, Hecke character of modulus Fractional ideal (-5*a + 28) and order 3, Hecke character of modulus Fractional ideal (23*a - 12) and order 3, Hecke character of modulus Fractional ideal (23*a - 11) and order 3, Hecke character of modulus Fractional ideal (4*a + 25) and order 3, Hecke character of modulus Fractional ideal (-4*a + 29) and order 3, Hecke character of modulus Fractional ideal (2*a - 28) and order 3, Hecke character of modulus Fractional ideal (2*a + 26) and order 3, Hecke character of modulus Fractional ideal (a - 29) and order 3, Hecke character of modulus Fractional ideal (a + 28) and order 3, Hecke character of modulus Fractional ideal (-26*a + 9) and order 3, Hecke character of modulus Fractional ideal (-26*a + 17) and order 3, Hecke character of modulus Fractional ideal (26*a - 14) and order 3, Hecke character of modulus Fractional ideal (26*a - 12) and order 3, Hecke character of modulus Fractional ideal (6*a - 34) and order 3, Hecke character of modulus Fractional ideal (-6*a - 28) and order 3, Hecke character of modulus Fractional ideal (3*a - 32) and order 3, Hecke character of modulus Fractional ideal (-3*a - 29) and order 3, Hecke character of modulus Fractional ideal (-28*a + 10) and order 3, Hecke character of modulus Fractional ideal (-28*a + 18) and order 3, Hecke character of modulus Fractional ideal (14*a - 8) and order 3, Hecke character of modulus Fractional ideal (14*a - 6) and order 3])

for v,c in zip(nvals,chis):
    print (v.conjugate()+v),(v.conjugate()*v),c,c.conductor(),c.gauss_sum().norm()

-1.68724448590490e-16 1.24265876999646e-31 Hecke character of modulus Fractional ideal (7) and order 3 49 49.0000000000000
1.99999999999999 3.99999999999997 Hecke character of modulus Fractional ideal (2*a + 11) and order 3 139 138.999999999999
1.99999999999999 3.99999999999997 Hecke character of modulus Fractional ideal (-2*a + 13) and order 3 139 138.999999999999
-3.99999999999999 3.99999999999998 Hecke character of modulus Fractional ideal (11*a - 6) and order 3 151 150.999999999999
-12.0000000000000 35.9999999999998 Hecke character of modulus Fractional ideal (11*a - 5) and order 3 151 150.999999999999
4.00000000000000 4.00000000000000 Hecke character of modulus Fractional ideal (13) and order 3 169 169.000000000000
4.00000000000002 4.00000000000004 Hecke character of modulus Fractional ideal (3*a + 13) and order 3 199 199.000000000004
2.00000000000000 4.00000000000004 Hecke character of modulus Fractional ideal (-3*a + 16) and order 3 199 199.000000000004

for v,c in zip(nvals,chis):
    print (v.conjugate()+v)/2,(v.conjugate()*v)/4,c,c.conductor(),c.gauss_sum().norm()

-8.43622242952448e-17 3.10664692499116e-32 Hecke character of modulus Fractional ideal (7) and order 3 49 49.0000000000000
0.999999999999995 0.999999999999993 Hecke character of modulus Fractional ideal (2*a + 11) and order 3 139 138.999999999999
0.999999999999997 0.999999999999992 Hecke character of modulus Fractional ideal (-2*a + 13) and order 3 139 138.999999999999
-1.99999999999999 0.999999999999995 Hecke character of modulus Fractional ideal (11*a - 6) and order 3 151 150.999999999999
-5.99999999999998 8.99999999999996 Hecke character of modulus Fractional ideal (11*a - 5) and order 3 151 150.999999999999
2.00000000000000 1.00000000000000 Hecke character of modulus Fractional ideal (13) and order 3 169 169.000000000000
2.00000000000001 1.00000000000001 Hecke character of modulus Fractional ideal (3*a + 13) and order 3 199 199.000000000004
0.999999999999999 1.00000000000001 Hecke character of modulus Fractional ideal (-3*a + 16) and order 3 199 199.000000000004
9.99999999999998 24.9999999999999 Hecke character of modulus Fractional ideal (3*a - 20) and order 3 331 330.999999999998
0.999999999999996 0.999999999999994 Hecke character of modulus Fractional ideal (-3*a - 17) and order 3 331 330.999999999998
-2.99999999999999 8.99999999999999 Hecke character of modulus Fractional ideal (19) and order 3 361 360.999999999999
-0.999999999999960 0.999999999999951 Hecke character of modulus Fractional ideal (3*a + 22) and order 3 541 540.999999999968
5.99999999999994 35.9999999999982 Hecke character of modulus Fractional ideal (-3*a + 25) and order 3 541 540.999999999968

omega = prod([E.period_lattice(phi).basis(prec=1000)[0] for phi in F.embeddings(RR)])

R.<y> = QQ[]
thetas = []
minpols = []
d=3
zeta_d = CC.zeta(d)
v0 = L(1)*CC(sqrt(5))/omega;
for v1,c in zip(nvals,chis):
    a1 = -v1-v1.conjugate()
    a0 = v1*v1.conjugate()
    b1 = ZZ(round(a1.real_part()))
    b0 = ZZ(round(a0.real_part()))
    assert abs(a1-b1)< 10^(-10)
    assert abs(a0-b0)< 10^(-10)
    minpols.append(y^2+b1/2*y+b0/4)
    print minpols[-1]
    if (minpols[-1]).is_irreducible():
        assert QQ.extension(minpols[-1],'a').discriminant()==-3
    thetas.append([])
    v = [v0,v1,v1.conjugate()]
    #print "minpol",v1+v1.conjugate(),v1*v1.conjugate()
    #print "x",v1*zeta_d+v1.conjugate()*zeta_d^2
    #print "y",v1*zeta_d^2+v1.conjugate()*zeta_d
    print c._conductor.norm().factor()
    for j in range(d):
        x0 = sum([v[i]*zeta_d**((i*j)%d) for i in range(3)])*32
        x = ZZ(round(x0.real_part()))
        assert abs(x-x0)< 10^(-10),abs(x-x0)
        print j,x
        thetas[-1].append(x)

y^2
7^2
0 1
1 1
2 1
y^2 - y + 1
2^2 * 19
0 65
1 65
2 -127
y^2
2^2 * 19
0 1
1 1
2 1
y^2 - y + 1
139
0 65
1 -127
2 65
y^2 - y + 1
139
0 65
1 65
2 -127
y^2 + 2*y + 1
151
0 -127
1 65
2 65
y^2 + 6*y + 9
151
0 -383
1 193
2 193
y^2 - 2*y + 1
13^2
0 129
1 -63
2 -63
y^2 - 2*y + 1
199
0 129
1 -63
2 -63
y^2 - y + 1
199
0 65
1 65
2 -127
y^2 + 2*y + 1
2^2 * 61
0 -127
1 65
2 65
y^2 + y + 1
2^2 * 61
0 -63
1 129
2 -63
y^2 - y + 1
2^2 * 19
0 65
1 -127
2 65
y^2
2^2 * 19
0 1
1 1
2 1
y^2 - y + 1
2^2 * 79
0 65
1 -127
2 65
y^2 + y + 1
2^2 * 79
0 -63
1 129
2 -63
y^2 - 10*y + 25
331
0 641
1 -319
2 -319
y^2 - y + 1
331
0 65
1 65
2 -127
y^2 + 3*y + 9
19^2
0 -191
1 -191
2 385
y^2 - 6*y + 9
2^2 * 109
0 385
1 -191
2 -191
y^2 + y + 1
2^2 * 109
0 -63
1 129
2 -63
y^2 + y + 1
541
0 -63
1 129
2 -63
y^2 - 6*y + 36
541
0 385
1 385
2 -767
y^2
619
0 1
1 1
2 1
y^2 - y + 1
619
0 65
1 65
2 -127
y^2 + 2*y + 4
661
0 -127
1 257
2 -127
y^2 - 6*y + 9
661
0 385
1 -191
2 -191
y^2 + y + 1
709
0 -63
1 129
2 -63
y^2 + 8*y + 64
709
0 -511
1 -511
2 1025
y^2 - y + 1
2^2 * 181
0 65
1 65
2 -127
y^2 - 3*y + 9
2^2 * 181
0 193
1 193
2 -383
y^2 - 3*y + 9
811
0 193
1 -383
2 193
y^2 - y + 1
811
0 65
1 -127
2 65
y^2 + 2*y + 1
829
0 -127
1 65
2 65
y^2 + 2*y + 4
829
0 -127
1 257
2 -127
y^2
2^2 * 211
0 1
1 1
2 1
y^2 - 2*y + 1
2^2 * 211
0 129
1 -63
2 -63
y^2 - 4*y + 16
2^2 * 229
0 257
1 -511
2 257
y^2 - 2*y + 4
2^2 * 229
0 129
1 129
2 -255
y^2 - 3*y + 9
919
0 193
1 -383
2 193
y^2 + y + 1
919
0 -63
1 -63
2 129
y^2
2^2 * 241
0 1
1 1
2 1
y^2 - y + 1
2^2 * 241
0 65
1 -127
2 65
y^2 + 2*y + 1
2^2 * 61
0 -127
1 65
2 65
y^2 + y + 1
2^2 * 61
0 -63
1 129
2 -63

thetas
[f.factor() for f in minpols]
[i._conductor.norm() for i in chis]

[[1, 1, 1], [65, 65, -127], [1, 1, 1], [65, -127, 65], [65, 65, -127], [-127, 65, 65], [-383, 193, 193], [129, -63, -63], [129, -63, -63], [65, 65, -127], [-127, 65, 65], [-63, 129, -63], [65, -127, 65], [1, 1, 1], [65, -127, 65], [-63, 129, -63], [641, -319, -319], [65, 65, -127], [-191, -191, 385], [385, -191, -191], [-63, 129, -63], [-63, 129, -63], [385, 385, -767], [1, 1, 1], [65, 65, -127], [-127, 257, -127], [385, -191, -191], [-63, 129, -63], [-511, -511, 1025], [65, 65, -127], [193, 193, -383], [193, -383, 193], [65, -127, 65], [-127, 65, 65], [-127, 257, -127], [1, 1, 1], [129, -63, -63], [257, -511, 257], [129, 129, -255], [193, -383, 193], [-63, -63, 129], [1, 1, 1], [65, -127, 65], [-127, 65, 65], [-63, 129, -63]]
[y^2, y^2 - y + 1, y^2, y^2 - y + 1, y^2 - y + 1, (y + 1)^2, (y + 3)^2, (y - 1)^2, (y - 1)^2, y^2 - y + 1, (y + 1)^2, y^2 + y + 1, y^2 - y + 1, y^2, y^2 - y + 1, y^2 + y + 1, (y - 5)^2, y^2 - y + 1, y^2 + 3*y + 9, (y - 3)^2, y^2 + y + 1, y^2 + y + 1, y^2 - 6*y + 36, y^2, y^2 - y + 1, y^2 + 2*y + 4, (y - 3)^2, y^2 + y + 1, y^2 + 8*y + 64, y^2 - y + 1, y^2 - 3*y + 9, y^2 - 3*y + 9, y^2 - y + 1, (y + 1)^2, y^2 + 2*y + 4, y^2, (y - 1)^2, y^2 - 4*y + 16, y^2 - 2*y + 4, y^2 - 3*y + 9, y^2 + y + 1, y^2, y^2 - y + 1, (y + 1)^2, y^2 + y + 1]
[49, 76, 76, 139, 139, 151, 151, 169, 199, 199, 244, 244, 76, 76, 316, 316, 331, 331, 361, 436, 436, 541, 541, 619, 619, 661, 661, 709, 709, 724, 724, 811, 811, 829, 829, 844, 844, 916, 916, 919, 919, 964, 964, 244, 244]

set(map(tuple,thetas))

set([(129, -63, -63), (-127, 257, -127), (385, -191, -191), (641, -319, -319), (193, -383, 193), (-63, 129, -63), (193, 193, -383), (-191, -191, 385), (-383, 193, 193), (257, -511, 257), (-511, -511, 1025), (385, 385, -767), (-127, 65, 65), (-63, -63, 129), (65, -127, 65), (65, 65, -127), (1, 1, 1), (129, 129, -255)])

chis

[Hecke character of modulus Fractional ideal (7) and order 3, Hecke character of modulus Fractional ideal (-8*a + 2) and order 3, Hecke character of modulus Fractional ideal (8*a - 6) and order 3, Hecke character of modulus Fractional ideal (2*a + 11) and order 3, Hecke character of modulus Fractional ideal (-2*a + 13) and order 3, Hecke character of modulus Fractional ideal (11*a - 6) and order 3, Hecke character of modulus Fractional ideal (11*a - 5) and order 3, Hecke character of modulus Fractional ideal (13) and order 3, Hecke character of modulus Fractional ideal (3*a + 13) and order 3, Hecke character of modulus Fractional ideal (-3*a + 16) and order 3, Hecke character of modulus Fractional ideal (14*a - 8) and order 3, Hecke character of modulus Fractional ideal (14*a - 6) and order 3, Hecke character of modulus Fractional ideal (-8*a + 2) and order 3, Hecke character of modulus Fractional ideal (8*a - 6) and order 3, Hecke character of modulus Fractional ideal (-16*a + 6) and order 3, Hecke character of modulus Fractional ideal (-16*a + 10) and order 3, Hecke character of modulus Fractional ideal (3*a - 20) and order 3, Hecke character of modulus Fractional ideal (-3*a - 17) and order 3, Hecke character of modulus Fractional ideal (19) and order 3, Hecke character of modulus Fractional ideal (2*a - 22) and order 3, Hecke character of modulus Fractional ideal (2*a + 20) and order 3, Hecke character of modulus Fractional ideal (3*a + 22) and order 3, Hecke character of modulus Fractional ideal (-3*a + 25) and order 3, Hecke character of modulus Fractional ideal (-5*a - 23) and order 3, Hecke character of modulus Fractional ideal (-5*a + 28) and order 3, Hecke character of modulus Fractional ideal (23*a - 12) and order 3, Hecke character of modulus Fractional ideal (23*a - 11) and order 3, Hecke character of modulus Fractional ideal (4*a + 25) and order 3, Hecke character of modulus Fractional ideal (-4*a + 29) and order 3, Hecke character of modulus Fractional ideal (2*a - 28) and order 3, Hecke character of modulus Fractional ideal (2*a + 26) and order 3, Hecke character of modulus Fractional ideal (a - 29) and order 3, Hecke character of modulus Fractional ideal (a + 28) and order 3, Hecke character of modulus Fractional ideal (-26*a + 9) and order 3, Hecke character of modulus Fractional ideal (-26*a + 17) and order 3, Hecke character of modulus Fractional ideal (26*a - 14) and order 3, Hecke character of modulus Fractional ideal (26*a - 12) and order 3, Hecke character of modulus Fractional ideal (6*a - 34) and order 3, Hecke character of modulus Fractional ideal (-6*a - 28) and order 3, Hecke character of modulus Fractional ideal (3*a - 32) and order 3, Hecke character of modulus Fractional ideal (-3*a - 29) and order 3, Hecke character of modulus Fractional ideal (-28*a + 10) and order 3, Hecke character of modulus Fractional ideal (-28*a + 18) and order 3, Hecke character of modulus Fractional ideal (14*a - 8) and order 3, Hecke character of modulus Fractional ideal (14*a - 6) and order 3]

len(thetas);len(minpols);len(chis);

45
45
45

for v1,theta in zip(nvals,thetas):
    print v1- sum(theta[i]*zeta_d^(2*i) for i in range(d))/3/32
    print sum(theta)

-8.89881535645163e-17 - 3.48052614951716e-16*I
3
-6.55031584528842e-15 - 5.10702591327572e-15*I
3
-1.55431223447522e-15 + 7.99360577730113e-15*I
3
4.88498130835069e-15 - 5.24302418406315e-16*I
3
1.33226762955019e-14 - 5.20656457190882e-15*I
3
8.88178419700125e-16 - 1.48066258083344e-15*I
3
1.11022302462516e-14 - 6.57018911736512e-15*I
3
-1.11022302462516e-16 - 1.19904086659517e-14*I
3
-1.95399252334028e-14 - 7.43800829749059e-17*I
3
-2.33146835171283e-15 + 4.88498130835069e-15*I
3
5.32907051820075e-15 + 1.77635683940025e-15*I
3
4.11892742135933e-14 + 3.33066907387547e-14*I
3
-5.06261699229071e-14 + 3.09086090055644e-13*I
3

len(thetas);len(minpols);len(chis)

45
45
45

E.two_torsion_rank()

1

value_search(E,3,100)

Fractional ideal (7) 49 Fractional ideal (7) [1]
raw value 5.01151740011611e-16 + 5.55709521912110e-16*I
normalisd 8.43838963899053e-17 - 4.46894271673792e-16*I
algdeprts [(0.000000000000000, 1)]
Fractional ideal (2*a + 11) 139 Fractional ideal (2*a + 11) [1]
raw value 1.94848534487254 - 0.144575522568630*I
normalisd 0.999999999999992 + 1.73205080756887*I
algdeprts [(1.00000000000000 - 1.73205080756888*I, 1), (1.00000000000000 + 1.73205080756888*I, 1)]
Fractional ideal (-2*a + 13) 139 Fractional ideal (-2*a + 13) [1]
raw value -1.09944874774612 - 1.61515004627698*I
normalisd 0.999999999999997 - 1.73205080756887*I
algdeprts [(1.00000000000000 - 1.73205080756888*I, 1), (1.00000000000000 + 1.73205080756888*I, 1)]
Fractional ideal (11*a - 6) 151 Fractional ideal (11*a - 6) [1]
raw value 1.28139749191622 - 1.36826182656356*I
normalisd -1.99999999999999 + 7.71140384322982e-16*I
algdeprts [(-2.00000000000000, 1)]
Fractional ideal (11*a - 5) 151 Fractional ideal (11*a - 5) [1]
raw value 3.84419247574867 - 4.10478547969069*I
normalisd -5.99999999999998 - 4.31838615220870e-15*I
algdeprts [(-6.00000000000000, 1)]
Fractional ideal (13) 169 Fractional ideal (13) [1]
raw value 1.54579562381928 + 0.866227961755149*I
normalisd 2.00000000000000 - 1.69650884551056e-15*I
algdeprts [(2.00000000000000, 1)]
Fractional ideal (3*a + 13) 199 Fractional ideal (3*a + 13) [1]
raw value 1.29290702755217 + 0.997438946405499*I
normalisd 2.00000000000001 - 7.09449153577143e-15*I
algdeprts [(2.00000000000000, 1)]
Fractional ideal (-3*a + 16) 199 Fractional ideal (-3*a + 16) [1]
raw value 1.51026098008723 - 0.620970857388854*I
normalisd 0.999999999999999 - 1.73205080756889*I
algdeprts [(1.00000000000000 - 1.73205080756888*I, 1), (1.00000000000000 + 1.73205080756888*I, 1)]
Fractional ideal (3*a - 20) 331 Fractional ideal (3*a - 20) [1]
raw value 5.51133057385612 - 3.11499430386439*I
normalisd 9.99999999999997 - 3.08456153729193e-15*I
algdeprts [(10.0000000000000, 1)]
Fractional ideal (-3*a - 17) 331 Fractional ideal (-3*a - 17) [1]
raw value 0.0116002174275345 - 1.26608988750909*I
normalisd 0.999999999999997 - 1.73205080756887*I
algdeprts [(1.00000000000000 - 1.73205080756888*I, 1), (1.00000000000000 + 1.73205080756888*I, 1)]
Fractional ideal (19) 361 (Fractional ideal (4*a - 3)) * (Fractional ideal (-4*a + 1)) [1, 1]
raw value 3.31254869309870 - 1.50202417497642*I
normalisd -2.99999999999999 + 5.19615242270663*I
algdeprts [(-3.00000000000000 - 5.19615242270663*I, 1), (-3.00000000000000 + 5.19615242270663*I, 1)]
Fractional ideal (3*a + 22) 541 Fractional ideal (3*a + 22) [1]
raw value 0.220342943690387 - 0.965548904601734*I
normalisd -0.999999999999960 - 1.73205080756884*I
algdeprts [(-1.00000000000000 - 1.73205080756888*I, 1), (-1.00000000000000 + 1.73205080756888*I, 1)]
Fractional ideal (-3*a + 25) 541 Fractional ideal (-3*a + 25) [1]
raw value 5.67816811095919 - 1.75171119312209*I
normalisd 5.99999999999994 - 10.3923048454130*I
algdeprts [(6.00000000000000 - 10.3923048454133*I, 1), (6.00000000000000 + 10.3923048454133*I, 1)]
Fractional ideal (-3*a - 23) 589 (Fractional ideal (-4*a + 1)) * (Fractional ideal (5*a - 3)) [1, 1]
raw value 1.86011792285857 - 2.15594343218160*I
normalisd 3.00000000000000 - 5.19615242270663*I
algdeprts [(3.00000000000000 - 5.19615242270663*I, 1), (3.00000000000000 + 5.19615242270663*I, 1)]
Fractional ideal (22*a - 7) 589 (Fractional ideal (4*a - 3)) * (Fractional ideal (5*a - 3)) [1, 2]
raw value 4.65484426813973 - 3.28099800642935*I
normalisd 12.0000000000000 - 9.87059691933417e-15*I
algdeprts [(12.0000000000000, 1)]
Fractional ideal (22*a - 15) 589 (Fractional ideal (-4*a + 1)) * (Fractional ideal (5*a - 2)) [1, 2]
raw value -0.0856675815439997 - 0.945285398347338*I
normalisd 1.00000000000001 - 1.73205080756886*I
algdeprts [(1.00000000000000 - 1.73205080756888*I, 1), (1.00000000000000 + 1.73205080756888*I, 1)]
Fractional ideal (3*a - 26) 589 (Fractional ideal (4*a - 3)) * (Fractional ideal (5*a - 2)) [1, 1]
raw value 2.99370444680520e-16 + 6.82769503939551e-17*I
normalisd 6.46591406839553e-16 + 2.32624427287458e-17*I
algdeprts [(0.000000000000000, 1)]
Fractional ideal (-5*a - 23) 619 Fractional ideal (-5*a - 23) [1]
raw value 1.16293111365538e-15 - 3.77673294732337e-15*I
normalisd -7.81187150752790e-15 - 3.44115654976350e-15*I
algdeprts [(0.000000000000000, 1)]
Fractional ideal (-5*a + 28) 619 Fractional ideal (-5*a + 28) [1]
raw value 0.850102587652340 + 0.366833047835574*I
normalisd 0.999999999999994 - 1.73205080756885*I
algdeprts [(1.00000000000000 - 1.73205080756888*I, 1), (1.00000000000000 + 1.73205080756888*I, 1)]
Fractional ideal (23*a - 12) 661 Fractional ideal (23*a - 12) [1]
raw value -1.05030706605215 - 1.45187533489213*I
normalisd -1.99999999999996 - 3.46410161513771*I
algdeprts [(-2.00000000000000 - 3.46410161513775*I, 1), (-2.00000000000000 + 3.46410161513775*I, 1)]
Fractional ideal (23*a - 11) 661 Fractional ideal (23*a - 11) [1]
raw value 2.67377168425605 - 0.275482400294099*I
normalisd 5.99999999999991 + 2.64501151822783e-14*I
algdeprts [(6.00000000000000, 1)]
Fractional ideal (4*a + 25) 709 Fractional ideal (4*a + 25) [1]
raw value 1.16293111365538e-15 - 3.77673294732337e-15*I
normalisd -7.81187150752790e-15 - 3.44115654976350e-15*I
algdeprts [(0.000000000000000, 1)]
Fractional ideal (-5*a + 28) 619 Fractional ideal (-5*a + 28) [1]
raw value 0.850102587652340 + 0.366833047835574*I
normalisd 0.999999999999994 - 1.73205080756885*I
algdeprts [(1.00000000000000 - 1.73205080756888*I, 1), (1.00000000000000 + 1.73205080756888*I, 1)]
Fractional ideal (23*a - 12) 661 Fractional ideal (23*a - 12) [1]
raw value -1.05030706605215 - 1.45187533489213*I
normalisd -1.99999999999996 - 3.46410161513771*I
algdeprts [(-2.00000000000000 - 3.46410161513775*I, 1), (-2.00000000000000 + 3.46410161513775*I, 1)]
Fractional ideal (23*a - 11) 661 Fractional ideal (23*a - 11) [1]
raw value 2.67377168425605 - 0.275482400294099*I
normalisd 5.99999999999991 + 2.64501151822783e-14*I
algdeprts [(6.00000000000000, 1)]
Fractional ideal (4*a + 25) 709 Fractional ideal (4*a + 25) [1]
raw value 0.407925749775956 + 0.762902270422672*I
normalisd -0.999999999999960 - 1.73205080756885*I
algdeprts [(-1.00000000000000 - 1.73205080756888*I, 1), (-1.00000000000000 + 1.73205080756888*I, 1)]
Fractional ideal (-4*a + 29) 709 Fractional ideal (-4*a + 29) [1]
raw value 3.65383897522305 - 5.87780157900103*I
normalisd -7.99999999999996 + 13.8564064605506*I
algdeprts [(-8.00000000000000 - 13.8564064605510*I, 1), (-8.00000000000000 + 13.8564064605510*I, 1)]
Fractional ideal (a - 29) 811 Fractional ideal (a - 29) [1]
raw value 2.42211496159430 - 0.148329222983796*I
normalisd 3.00000000000004 + 5.19615242270670*I
algdeprts [(3.00000000000000 - 5.19615242270663*I, 1), (3.00000000000000 + 5.19615242270663*I, 1)]
Fractional ideal (a + 28) 811 Fractional ideal (a + 28) [1]
raw value 0.807371653864767 - 0.0494430743279323*I
normalisd 1.00000000000001 + 1.73205080756890*I
algdeprts [(1.00000000000000 - 1.73205080756888*I, 1), (1.00000000000000 + 1.73205080756888*I, 1)]
Fractional ideal (-26*a + 9) 829 Fractional ideal (-26*a + 9) [1]
raw value -0.708540684817226 - 0.371560340655551*I
normalisd -2.00000000000000 + 2.00496499923975e-15*I
algdeprts [(-2.00000000000000, 1)]
Fractional ideal (-26*a + 17) 829 Fractional ideal (-26*a + 17) [1]
raw value -0.0649792967242121 - 1.59878880598863*I
normalisd -2.00000000000001 - 3.46410161513776*I
algdeprts [(-2.00000000000000 - 3.46410161513775*I, 1), (-2.00000000000000 + 3.46410161513775*I, 1)]
Fractional ideal (3*a - 32) 919 Fractional ideal (3*a - 32) [1]
raw value 1.47488307737899 - 1.73819870330501*I
normalisd 2.99999999999996 + 5.19615242270652*I
algdeprts [(3.00000000000000 - 5.19615242270663*I, 1), (3.00000000000000 + 5.19615242270663*I, 1)]
Fractional ideal (-3*a - 29) 919 Fractional ideal (-3*a - 29) [1]
raw value 0.747588590858935 + 0.136062286989825*I
normalisd -0.999999999999974 + 1.73205080756885*I
algdeprts [(-1.00000000000000 - 1.73205080756888*I, 1), (-1.00000000000000 + 1.73205080756888*I, 1)]
Fractional ideal (31) 961 (Fractional ideal (5*a - 2)) * (Fractional ideal (5*a - 3)) [1, 1]
raw value 4.32662646875764e-16 - 3.69338416262855e-16*I
normalisd 9.47802756605315e-17 - 1.52816668209505e-15*I
algdeprts [(0.000000000000000, 1)]
[5.01151740011611e-16 + 5.55709521912110e-16*I, 1.94848534487254 - 0.144575522568630*I, -1.09944874774612 - 1.61515004627698*I, 1.28139749191622 - 1.36826182656356*I, 3.84419247574867 - 4.10478547969069*I, 1.54579562381928 + 0.866227961755149*I, 1.29290702755217 + 0.997438946405499*I, 1.51026098008723 - 0.620970857388854*I, 5.51133057385612 - 3.11499430386439*I, 0.0116002174275345 - 1.26608988750909*I, 3.31254869309870 - 1.50202417497642*I, 0.220342943690387 - 0.965548904601734*I, 5.67816811095919 - 1.75171119312209*I, 1.86011792285857 - 2.15594343218160*I, 4.65484426813973 - 3.28099800642935*I, -0.0856675815439997 - 0.945285398347338*I, 2.99370444680520e-16 + 6.82769503939551e-17*I, 1.16293111365538e-15 - 3.77673294732337e-15*I, 0.850102587652340 + 0.366833047835574*I, -1.05030706605215 - 1.45187533489213*I, 2.67377168425605 - 0.275482400294099*I, 0.407925749775956 + 0.762902270422672*I, 3.65383897522305 - 5.87780157900103*I, 2.42211496159430 - 0.148329222983796*I, 0.807371653864767 - 0.0494430743279323*I, -0.708540684817226 - 0.371560340655551*I, -0.0649792967242121 - 1.59878880598863*I, 1.47488307737899 - 1.73819870330501*I, 0.747588590858935 + 0.136062286989825*I, 4.32662646875764e-16 - 3.69338416262855e-16*I]

value_search(E,5,1000,checkfe=True)

Fractional ideal (11) 121 (Fractional ideal (-3*a + 2)) * (Fractional ideal (-3*a + 1)) [1, 1]
2.64349400471371 + 2.11967871863359*I
Fractional ideal (11) 121 (Fractional ideal (-3*a + 2)) * (Fractional ideal (-3*a + 1)) [2, 2]
1.11220914931987 + 0.661861385341200*I
Fractional ideal (13*a - 7) 211 Fractional ideal (13*a - 7) [1]
0.270190673698379 - 0.542132654592904*I
Fractional ideal (13*a - 7) 211 Fractional ideal (13*a - 7) [2]
3.11862573530779 + 2.74065169134376*I
Fractional ideal (13*a - 6) 211 Fractional ideal (13*a - 6) [1]
0.537246425899483 - 0.279780437464388*I
Fractional ideal (13*a - 6) 211 Fractional ideal (13*a - 6) [2]
1.64280629864264 - 3.81289727573790*I
Fractional ideal (15*a - 8) 281 Fractional ideal (15*a - 8) [1]
0.799630931041636 + 1.11756918601580*I
Fractional ideal (15*a - 8) 281 Fractional ideal (15*a - 8) [2]
0.668896193321883 + 1.20039509911113*I
Fractional ideal (15*a - 7) 281 Fractional ideal (15*a - 7) [1]
-0.0199513470320928 + 2.74828746483946*I
Fractional ideal (15*a - 7) 281 Fractional ideal (15*a - 7) [2]
1.86988657985847 - 2.01420113794708*I
Fractional ideal (a + 18) 341 (Fractional ideal (-3*a + 1)) * (Fractional ideal (5*a - 3)) [2, 1]
1.45101120578398 - 0.521617430312478*I
Fractional ideal (a + 18) 341 (Fractional ideal (-3*a + 1)) * (Fractional ideal (5*a - 3)) [1, 3]
0.0563577153762502 + 4.03640637307097*I
Fractional ideal (-4*a + 21) 341 (Fractional ideal (-3*a + 2)) * (Fractional ideal (5*a - 3)) [1, 2]
-0.187408727583072 + 0.227149243377430*I
Fractional ideal (-4*a + 21) 341 (Fractional ideal (-3*a + 2)) * (Fractional ideal (5*a - 3)) [2, 4]
3.35911784120422 + 4.07915613997706*I
Fractional ideal (4*a + 17) 341 (Fractional ideal (-3*a + 1)) * (Fractional ideal (5*a - 2)) [1, 2]
1.95432257382921 - 0.504540808641061*I
Fractional ideal (4*a + 17) 341 (Fractional ideal (-3*a + 1)) * (Fractional ideal (5*a - 2)) [2, 4]
-0.414566859796096 + 0.650010680287581*I
Fractional ideal (a - 19) 341 (Fractional ideal (-3*a + 2)) * (Fractional ideal (5*a - 2)) [2, 1]
0.457497113063718 + 0.133150979825481*I
Fractional ideal (a - 19) 341 (Fractional ideal (-3*a + 2)) * (Fractional ideal (5*a - 2)) [1, 3]
3.11978478978151 + 0.965738790066169*I
Fractional ideal (4*a - 23) 421 Fractional ideal (4*a - 23) [1]
-0.173473179001174 - 0.392171167853184*I
Fractional ideal (4*a - 23) 421 Fractional ideal (4*a - 23) [2]
-1.05352097604217 - 2.74391401694691*I
Fractional ideal (-4*a - 19) 421 Fractional ideal (-4*a - 19) [1]
2.50837070501377 - 2.24761113109585*I
Fractional ideal (-4*a - 19) 421 Fractional ideal (-4*a - 19) [2]
2.82480889498959 + 1.83415759878612*I
Fractional ideal (19*a - 10) 451 (Fractional ideal (-3*a + 1)) * (Fractional ideal (a - 7)) [1, 2]
1.74195490107801 + 0.214214428817783*I
Fractional ideal (19*a - 10) 451 (Fractional ideal (-3*a + 1)) * (Fractional ideal (a - 7)) [2, 4]
-0.0519138603730805 - 0.668366584325319*I
Fractional ideal (-3*a - 20) 451 (Fractional ideal (-3*a + 2)) * (Fractional ideal (a - 7)) [2, 1]
2.71280780767583 + 0.839636835607123*I
Fractional ideal (-3*a - 20) 451 (Fractional ideal (-3*a + 2)) * (Fractional ideal (a - 7)) [1, 3]
0.157124164344829 + 0.383367887529125*I
Fractional ideal (3*a - 23) 451 (Fractional ideal (-3*a + 1)) * (Fractional ideal (a + 6)) [2, 1]
1.01162633804443 - 1.43419205515797*I
Fractional ideal (3*a - 23) 451 (Fractional ideal (-3*a + 1)) * (Fractional ideal (a + 6)) [1, 3]
0.570282728927224 + 0.352401119505667*I
Fractional ideal (19*a - 9) 451 (Fractional ideal (-3*a + 2)) * (Fractional ideal (a + 6)) [1, 2]
3.66283754896376 + 3.41692663384365*I
Fractional ideal (19*a - 9) 451 (Fractional ideal (-3*a + 2)) * (Fractional ideal (a + 6)) [2, 4]
2.38804832930688 - 0.986301878397431*I
Fractional ideal (a - 22) 461 Fractional ideal (a - 22) [1]
0.592624522722177 + 0.297416455467599*I
Fractional ideal (a - 22) 461 Fractional ideal (a - 22) [2]
0.355187803254333 - 1.69921118490180*I
Fractional ideal (a + 21) 461 Fractional ideal (a + 21) [1]
1.04198734456946 - 1.05478160693580*I
Fractional ideal (a + 21) 461 Fractional ideal (a + 21) [2]
2.87586123719103 - 2.60706871347921*I
Fractional ideal (5*a + 21) 521 Fractional ideal (5*a + 21) [1]
1.44989533175720 - 1.72923169012777*I
Fractional ideal (5*a + 21) 521 Fractional ideal (5*a + 21) [2]
-1.05605483689566 - 1.99428856805196*I
Fractional ideal (-5*a + 26) 521 Fractional ideal (-5*a + 26) [1]
2.26678589086563 + 3.62459690292654*I
Fractional ideal (-5*a + 26) 521 Fractional ideal (-5*a + 26) [2]
0.0335560110819777 - 0.235865153603701*I
Fractional ideal (2*a + 25) 671 (Fractional ideal (-3*a + 1)) * (Fractional ideal (7*a - 4)) [1, 1]
3.16173309874920 - 2.62076356138794*I
Fractional ideal (2*a + 25) 671 (Fractional ideal (-3*a + 1)) * (Fractional ideal (7*a - 4)) [2, 2]
1.72223827055726 - 1.23318746438282*I
Fractional ideal (5*a - 29) 671 (Fractional ideal (-3*a + 2)) * (Fractional ideal (7*a - 4)) [2, 3]
0.576962938871172 + 1.31813344465100*I
Fractional ideal (5*a - 29) 671 (Fractional ideal (-3*a + 2)) * (Fractional ideal (7*a - 4)) [1, 4]
0.110703846598091 + 0.538336702135814*I
Fractional ideal (-5*a - 24) 671 (Fractional ideal (-3*a + 1)) * (Fractional ideal (7*a - 3)) [2, 3]
-0.356582706471412 - 0.814651270502296*I
Fractional ideal (-5*a - 24) 671 (Fractional ideal (-3*a + 1)) * (Fractional ideal (7*a - 3)) [1, 4]
0.179122586481065 + 0.871047081447274*I
Fractional ideal (-2*a + 27) 671 (Fractional ideal (-3*a + 2)) * (Fractional ideal (7*a - 3)) [1, 1]
5.37730432650301 - 4.45725265139172*I
Fractional ideal (-2*a + 27) 671 (Fractional ideal (-3*a + 2)) * (Fractional ideal (7*a - 3)) [2, 2]
0.828521246130364 - 0.593252415864733*I
Fractional ideal (3*a + 25) 691 Fractional ideal (3*a + 25) [1]
1.06157700434569 + 0.582794376197248*I
Fractional ideal (3*a + 25) 691 Fractional ideal (3*a + 25) [2]
2.60691982850923 + 1.80448353426136*I
Fractional ideal (-3*a + 28) 691 Fractional ideal (-3*a + 28) [1]
0.285390297333253 + 0.605560846196166*I
Fractional ideal (-3*a + 28) 691 Fractional ideal (-3*a + 28) [2]
1.31780852265751 - 4.39510688945541*I
Fractional ideal (25*a - 12) 781 (Fractional ideal (-3*a + 1)) * (Fractional ideal (a - 9)) [2, 3]
3.83644169730400e-17 - 7.04724581904932e-17*I
Fractional ideal (25*a - 12) 781 (Fractional ideal (-3*a + 1)) * (Fractional ideal (a - 9)) [1, 4]
3.42977727319086e-17 + 1.84234224012911e-16*I
Fractional ideal (5*a + 26) 781 (Fractional ideal (-3*a + 2)) * (Fractional ideal (a - 9)) [1, 1]
1.60607128200680 - 4.55025585434421*I
Fractional ideal (5*a + 26) 781 (Fractional ideal (-3*a + 2)) * (Fractional ideal (a - 9)) [2, 2]
-0.0260551329148557 + 0.703531163673378*I
Fractional ideal (-5*a + 31) 781 (Fractional ideal (-3*a + 1)) * (Fractional ideal (a + 8)) [1, 1]
-0.404475524735724 - 0.309705325184351*I
Fractional ideal (-5*a + 31) 781 (Fractional ideal (-3*a + 1)) * (Fractional ideal (a + 8)) [2, 2]
0.823326180236132 - 1.04923578306954*I
Fractional ideal (25*a - 13) 781 (Fractional ideal (-3*a + 2)) * (Fractional ideal (a + 8)) [2, 3]
-0.105658214514747 - 0.817473463628480*I
Fractional ideal (25*a - 13) 781 (Fractional ideal (-3*a + 2)) * (Fractional ideal (a + 8)) [1, 4]
0.824066632887496 + 0.0184582391536358*I
Fractional ideal (-27*a + 19) 881 Fractional ideal (-27*a + 19) [1]
-1.24642063263489 - 1.45856298909875*I
Fractional ideal (-27*a + 19) 881 Fractional ideal (-27*a + 19) [2]
1.63756401143936 - 4.74848717731481*I
Fractional ideal (27*a - 8) 881 Fractional ideal (27*a - 8) [1]
0.504187736970598 + 0.590001122773605*I
Fractional ideal (27*a - 8) 881 Fractional ideal (27*a - 8) [2]
0.253017554455786 - 0.733681617680901*I
Fractional ideal (31) 961 (Fractional ideal (5*a - 2)) * (Fractional ideal (5*a - 3)) [1, 1]
-0.405261681029562 + 1.13196904833940*I
Fractional ideal (31) 961 (Fractional ideal (5*a - 2)) * (Fractional ideal (5*a - 3)) [2, 2]
0.350128779134148 + 0.297184649980406*I
Fractional ideal (a - 32) 991 Fractional ideal (a - 32) [1]
5.69044556466475 - 0.805705773491573*I
Fractional ideal (a - 32) 991 Fractional ideal (a - 32) [2]
0.639827141127917 - 0.541952664851865*I
Fractional ideal (a + 31) 991 Fractional ideal (a + 31) [1]
2.75339013068939 - 2.66439309673583*I
Fractional ideal (a + 31) 991 Fractional ideal (a + 31) [2]
0.211806768906683 + 0.517322903638813*I
0.211806768906683 + 0.517322903638813*I

vals,nvals,chis = value_search(E,3,100)

Fractional ideal (29) 841 (Fractional ideal (a + 5)) * (Fractional ideal (a - 6)) [1, 1]

Exception 

chi = NFChar([F.prime_above(139)],[1],3)
LEchi = L.twist(chi, epsilon='solve')
omega = prod([E.period_lattice(phi).basis(prec=1000)[0] for phi in F.embeddings(RR)])
val = LEchi(1)
val

-1.09944874774612 - 1.61515004627698*I

normalised = val*chi.conjugate().gauss_sum()*CC(sqrt(5))/omega
normalised
algdep(normalised, 2, known_bits=53).roots(CC)

-2*a + 1
0.999999999999997 - 1.73205080756887*I
[(1.00000000000000 - 1.73205080756888*I, 1), (1.00000000000000 + 1.73205080756888*I, 1)]