Sharedwww / tables / degphi_table / analysis2.txtOpen in CoCalc
Author: William A. Stein
1
Let E be an elliptic curve of conductor <= 539, and let r and
2
deg(phi) be the congruence modulus and modular degree of E.
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The data below gives
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5
N_E, ord_p(r / deg(phi)), ord_p(N), and ord_p(N) - ord_p(r/deg(phi)).
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In all cases, ord_p(r/deg(phi)) <= ord_p(N) - 1.
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The table is divided into three subtables. The first gives
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the above data for p=2, the second for p=3, and the third
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for all primes p>=5.
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The table was created using the following MAGMA program:
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//////////////////////////////////////////////////
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load "degphi_r_table.m";
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procedure analysis2(N,d,ell)
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for E in d do
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if E[2] ne E[3] then
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dif := E[3] div E[2];
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for p in Factorization(dif) do
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if p[1] eq ell or (ell eq 0 and p[1] gt 3) then
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printf
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"N=%o: ord_{%o}(r/deg(phi))=%o, ord_{%o}(N)=%o, diff=%o\n",
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N, p[1],p[2], p[1], Valuation(N,p[1]),
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Valuation(N,p[1])-p[2];
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end if;
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end for;
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end if;
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end for;
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end procedure;
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procedure iterate(ell)
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for N in [1..#dat] do
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if not (dat[N] cmpeq []) then
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analysis2(N,dat[N],ell);
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end if;
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end for;
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end procedure;
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"ell = 2";
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iterate(2);
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"\n\nell = 3";
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iterate(3);
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"\n\nell > 3";
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iterate(0);
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//////////////////////////////////////////////////
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This is the output it produces:
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ell = 2
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N=64: ord_{2}(r/deg(phi))=1, ord_{2}(N)=6, diff=5
53
N=72: ord_{2}(r/deg(phi))=1, ord_{2}(N)=3, diff=2
54
N=80: ord_{2}(r/deg(phi))=1, ord_{2}(N)=4, diff=3
55
N=88: ord_{2}(r/deg(phi))=1, ord_{2}(N)=3, diff=2
56
N=92: ord_{2}(r/deg(phi))=1, ord_{2}(N)=2, diff=1
57
N=96: ord_{2}(r/deg(phi))=1, ord_{2}(N)=5, diff=4
58
N=96: ord_{2}(r/deg(phi))=1, ord_{2}(N)=5, diff=4
59
N=112: ord_{2}(r/deg(phi))=1, ord_{2}(N)=4, diff=3
60
N=112: ord_{2}(r/deg(phi))=1, ord_{2}(N)=4, diff=3
61
N=112: ord_{2}(r/deg(phi))=1, ord_{2}(N)=4, diff=3
62
N=120: ord_{2}(r/deg(phi))=1, ord_{2}(N)=3, diff=2
63
N=124: ord_{2}(r/deg(phi))=1, ord_{2}(N)=2, diff=1
64
N=128: ord_{2}(r/deg(phi))=3, ord_{2}(N)=7, diff=4
65
N=128: ord_{2}(r/deg(phi))=2, ord_{2}(N)=7, diff=5
66
N=128: ord_{2}(r/deg(phi))=3, ord_{2}(N)=7, diff=4
67
N=128: ord_{2}(r/deg(phi))=2, ord_{2}(N)=7, diff=5
68
N=144: ord_{2}(r/deg(phi))=1, ord_{2}(N)=4, diff=3
69
N=144: ord_{2}(r/deg(phi))=1, ord_{2}(N)=4, diff=3
70
N=152: ord_{2}(r/deg(phi))=1, ord_{2}(N)=3, diff=2
71
N=160: ord_{2}(r/deg(phi))=1, ord_{2}(N)=5, diff=4
72
N=160: ord_{2}(r/deg(phi))=1, ord_{2}(N)=5, diff=4
73
N=168: ord_{2}(r/deg(phi))=1, ord_{2}(N)=3, diff=2
74
N=168: ord_{2}(r/deg(phi))=1, ord_{2}(N)=3, diff=2
75
N=176: ord_{2}(r/deg(phi))=2, ord_{2}(N)=4, diff=2
76
N=176: ord_{2}(r/deg(phi))=1, ord_{2}(N)=4, diff=3
77
N=176: ord_{2}(r/deg(phi))=2, ord_{2}(N)=4, diff=2
78
N=184: ord_{2}(r/deg(phi))=1, ord_{2}(N)=3, diff=2
79
N=184: ord_{2}(r/deg(phi))=1, ord_{2}(N)=3, diff=2
80
N=184: ord_{2}(r/deg(phi))=1, ord_{2}(N)=3, diff=2
81
N=192: ord_{2}(r/deg(phi))=2, ord_{2}(N)=6, diff=4
82
N=192: ord_{2}(r/deg(phi))=2, ord_{2}(N)=6, diff=4
83
N=192: ord_{2}(r/deg(phi))=2, ord_{2}(N)=6, diff=4
84
N=192: ord_{2}(r/deg(phi))=2, ord_{2}(N)=6, diff=4
85
N=200: ord_{2}(r/deg(phi))=1, ord_{2}(N)=3, diff=2
86
N=200: ord_{2}(r/deg(phi))=1, ord_{2}(N)=3, diff=2
87
N=200: ord_{2}(r/deg(phi))=1, ord_{2}(N)=3, diff=2
88
N=208: ord_{2}(r/deg(phi))=1, ord_{2}(N)=4, diff=3
89
N=208: ord_{2}(r/deg(phi))=1, ord_{2}(N)=4, diff=3
90
N=208: ord_{2}(r/deg(phi))=1, ord_{2}(N)=4, diff=3
91
N=216: ord_{2}(r/deg(phi))=1, ord_{2}(N)=3, diff=2
92
N=216: ord_{2}(r/deg(phi))=1, ord_{2}(N)=3, diff=2
93
N=224: ord_{2}(r/deg(phi))=2, ord_{2}(N)=5, diff=3
94
N=224: ord_{2}(r/deg(phi))=2, ord_{2}(N)=5, diff=3
95
N=236: ord_{2}(r/deg(phi))=1, ord_{2}(N)=2, diff=1
96
N=240: ord_{2}(r/deg(phi))=1, ord_{2}(N)=4, diff=3
97
N=240: ord_{2}(r/deg(phi))=1, ord_{2}(N)=4, diff=3
98
N=240: ord_{2}(r/deg(phi))=1, ord_{2}(N)=4, diff=3
99
N=240: ord_{2}(r/deg(phi))=1, ord_{2}(N)=4, diff=3
100
N=248: ord_{2}(r/deg(phi))=1, ord_{2}(N)=3, diff=2
101
N=248: ord_{2}(r/deg(phi))=1, ord_{2}(N)=3, diff=2
102
N=256: ord_{2}(r/deg(phi))=3, ord_{2}(N)=8, diff=5
103
N=256: ord_{2}(r/deg(phi))=2, ord_{2}(N)=8, diff=6
104
N=256: ord_{2}(r/deg(phi))=3, ord_{2}(N)=8, diff=5
105
N=256: ord_{2}(r/deg(phi))=2, ord_{2}(N)=8, diff=6
106
N=260: ord_{2}(r/deg(phi))=1, ord_{2}(N)=2, diff=1
107
N=264: ord_{2}(r/deg(phi))=1, ord_{2}(N)=3, diff=2
108
N=272: ord_{2}(r/deg(phi))=1, ord_{2}(N)=4, diff=3
109
N=272: ord_{2}(r/deg(phi))=1, ord_{2}(N)=4, diff=3
110
N=272: ord_{2}(r/deg(phi))=1, ord_{2}(N)=4, diff=3
111
N=272: ord_{2}(r/deg(phi))=1, ord_{2}(N)=4, diff=3
112
N=280: ord_{2}(r/deg(phi))=1, ord_{2}(N)=3, diff=2
113
N=280: ord_{2}(r/deg(phi))=1, ord_{2}(N)=3, diff=2
114
N=288: ord_{2}(r/deg(phi))=1, ord_{2}(N)=5, diff=4
115
N=288: ord_{2}(r/deg(phi))=1, ord_{2}(N)=5, diff=4
116
N=288: ord_{2}(r/deg(phi))=1, ord_{2}(N)=5, diff=4
117
N=288: ord_{2}(r/deg(phi))=1, ord_{2}(N)=5, diff=4
118
N=288: ord_{2}(r/deg(phi))=1, ord_{2}(N)=5, diff=4
119
N=296: ord_{2}(r/deg(phi))=1, ord_{2}(N)=3, diff=2
120
N=296: ord_{2}(r/deg(phi))=1, ord_{2}(N)=3, diff=2
121
N=304: ord_{2}(r/deg(phi))=1, ord_{2}(N)=4, diff=3
122
N=304: ord_{2}(r/deg(phi))=2, ord_{2}(N)=4, diff=2
123
N=304: ord_{2}(r/deg(phi))=1, ord_{2}(N)=4, diff=3
124
N=304: ord_{2}(r/deg(phi))=1, ord_{2}(N)=4, diff=3
125
N=304: ord_{2}(r/deg(phi))=1, ord_{2}(N)=4, diff=3
126
N=304: ord_{2}(r/deg(phi))=2, ord_{2}(N)=4, diff=2
127
N=312: ord_{2}(r/deg(phi))=1, ord_{2}(N)=3, diff=2
128
N=312: ord_{2}(r/deg(phi))=1, ord_{2}(N)=3, diff=2
129
N=312: ord_{2}(r/deg(phi))=1, ord_{2}(N)=3, diff=2
130
N=312: ord_{2}(r/deg(phi))=1, ord_{2}(N)=3, diff=2
131
N=312: ord_{2}(r/deg(phi))=1, ord_{2}(N)=3, diff=2
132
N=312: ord_{2}(r/deg(phi))=1, ord_{2}(N)=3, diff=2
133
N=320: ord_{2}(r/deg(phi))=2, ord_{2}(N)=6, diff=4
134
N=320: ord_{2}(r/deg(phi))=2, ord_{2}(N)=6, diff=4
135
N=320: ord_{2}(r/deg(phi))=2, ord_{2}(N)=6, diff=4
136
N=320: ord_{2}(r/deg(phi))=2, ord_{2}(N)=6, diff=4
137
N=320: ord_{2}(r/deg(phi))=2, ord_{2}(N)=6, diff=4
138
N=320: ord_{2}(r/deg(phi))=2, ord_{2}(N)=6, diff=4
139
N=336: ord_{2}(r/deg(phi))=1, ord_{2}(N)=4, diff=3
140
N=336: ord_{2}(r/deg(phi))=1, ord_{2}(N)=4, diff=3
141
N=336: ord_{2}(r/deg(phi))=1, ord_{2}(N)=4, diff=3
142
N=336: ord_{2}(r/deg(phi))=1, ord_{2}(N)=4, diff=3
143
N=336: ord_{2}(r/deg(phi))=1, ord_{2}(N)=4, diff=3
144
N=336: ord_{2}(r/deg(phi))=1, ord_{2}(N)=4, diff=3
145
N=340: ord_{2}(r/deg(phi))=1, ord_{2}(N)=2, diff=1
146
N=344: ord_{2}(r/deg(phi))=1, ord_{2}(N)=3, diff=2
147
N=348: ord_{2}(r/deg(phi))=1, ord_{2}(N)=2, diff=1
148
N=348: ord_{2}(r/deg(phi))=1, ord_{2}(N)=2, diff=1
149
N=352: ord_{2}(r/deg(phi))=1, ord_{2}(N)=5, diff=4
150
N=352: ord_{2}(r/deg(phi))=1, ord_{2}(N)=5, diff=4
151
N=352: ord_{2}(r/deg(phi))=1, ord_{2}(N)=5, diff=4
152
N=352: ord_{2}(r/deg(phi))=1, ord_{2}(N)=5, diff=4
153
N=352: ord_{2}(r/deg(phi))=1, ord_{2}(N)=5, diff=4
154
N=352: ord_{2}(r/deg(phi))=1, ord_{2}(N)=5, diff=4
155
N=360: ord_{2}(r/deg(phi))=1, ord_{2}(N)=3, diff=2
156
N=360: ord_{2}(r/deg(phi))=1, ord_{2}(N)=3, diff=2
157
N=368: ord_{2}(r/deg(phi))=1, ord_{2}(N)=4, diff=3
158
N=368: ord_{2}(r/deg(phi))=2, ord_{2}(N)=4, diff=2
159
N=368: ord_{2}(r/deg(phi))=2, ord_{2}(N)=4, diff=2
160
N=368: ord_{2}(r/deg(phi))=2, ord_{2}(N)=4, diff=2
161
N=368: ord_{2}(r/deg(phi))=1, ord_{2}(N)=4, diff=3
162
N=368: ord_{2}(r/deg(phi))=2, ord_{2}(N)=4, diff=2
163
N=368: ord_{2}(r/deg(phi))=2, ord_{2}(N)=4, diff=2
164
N=384: ord_{2}(r/deg(phi))=3, ord_{2}(N)=7, diff=4
165
N=384: ord_{2}(r/deg(phi))=3, ord_{2}(N)=7, diff=4
166
N=384: ord_{2}(r/deg(phi))=3, ord_{2}(N)=7, diff=4
167
N=384: ord_{2}(r/deg(phi))=3, ord_{2}(N)=7, diff=4
168
N=384: ord_{2}(r/deg(phi))=3, ord_{2}(N)=7, diff=4
169
N=384: ord_{2}(r/deg(phi))=3, ord_{2}(N)=7, diff=4
170
N=384: ord_{2}(r/deg(phi))=3, ord_{2}(N)=7, diff=4
171
N=384: ord_{2}(r/deg(phi))=3, ord_{2}(N)=7, diff=4
172
N=392: ord_{2}(r/deg(phi))=1, ord_{2}(N)=3, diff=2
173
N=392: ord_{2}(r/deg(phi))=1, ord_{2}(N)=3, diff=2
174
N=392: ord_{2}(r/deg(phi))=1, ord_{2}(N)=3, diff=2
175
N=392: ord_{2}(r/deg(phi))=1, ord_{2}(N)=3, diff=2
176
N=400: ord_{2}(r/deg(phi))=1, ord_{2}(N)=4, diff=3
177
N=400: ord_{2}(r/deg(phi))=1, ord_{2}(N)=4, diff=3
178
N=400: ord_{2}(r/deg(phi))=1, ord_{2}(N)=4, diff=3
179
N=400: ord_{2}(r/deg(phi))=1, ord_{2}(N)=4, diff=3
180
N=400: ord_{2}(r/deg(phi))=1, ord_{2}(N)=4, diff=3
181
N=400: ord_{2}(r/deg(phi))=1, ord_{2}(N)=4, diff=3
182
N=400: ord_{2}(r/deg(phi))=1, ord_{2}(N)=4, diff=3
183
N=400: ord_{2}(r/deg(phi))=1, ord_{2}(N)=4, diff=3
184
N=408: ord_{2}(r/deg(phi))=1, ord_{2}(N)=3, diff=2
185
N=408: ord_{2}(r/deg(phi))=1, ord_{2}(N)=3, diff=2
186
N=416: ord_{2}(r/deg(phi))=2, ord_{2}(N)=5, diff=3
187
N=416: ord_{2}(r/deg(phi))=2, ord_{2}(N)=5, diff=3
188
N=428: ord_{2}(r/deg(phi))=1, ord_{2}(N)=2, diff=1
189
N=432: ord_{2}(r/deg(phi))=1, ord_{2}(N)=4, diff=3
190
N=432: ord_{2}(r/deg(phi))=1, ord_{2}(N)=4, diff=3
191
N=432: ord_{2}(r/deg(phi))=2, ord_{2}(N)=4, diff=2
192
N=432: ord_{2}(r/deg(phi))=2, ord_{2}(N)=4, diff=2
193
N=432: ord_{2}(r/deg(phi))=1, ord_{2}(N)=4, diff=3
194
N=432: ord_{2}(r/deg(phi))=1, ord_{2}(N)=4, diff=3
195
N=432: ord_{2}(r/deg(phi))=2, ord_{2}(N)=4, diff=2
196
N=432: ord_{2}(r/deg(phi))=1, ord_{2}(N)=4, diff=3
197
N=440: ord_{2}(r/deg(phi))=1, ord_{2}(N)=3, diff=2
198
N=440: ord_{2}(r/deg(phi))=1, ord_{2}(N)=3, diff=2
199
N=440: ord_{2}(r/deg(phi))=1, ord_{2}(N)=3, diff=2
200
N=448: ord_{2}(r/deg(phi))=2, ord_{2}(N)=6, diff=4
201
N=448: ord_{2}(r/deg(phi))=2, ord_{2}(N)=6, diff=4
202
N=448: ord_{2}(r/deg(phi))=2, ord_{2}(N)=6, diff=4
203
N=448: ord_{2}(r/deg(phi))=2, ord_{2}(N)=6, diff=4
204
N=448: ord_{2}(r/deg(phi))=2, ord_{2}(N)=6, diff=4
205
N=448: ord_{2}(r/deg(phi))=2, ord_{2}(N)=6, diff=4
206
N=448: ord_{2}(r/deg(phi))=2, ord_{2}(N)=6, diff=4
207
N=448: ord_{2}(r/deg(phi))=2, ord_{2}(N)=6, diff=4
208
N=456: ord_{2}(r/deg(phi))=1, ord_{2}(N)=3, diff=2
209
N=456: ord_{2}(r/deg(phi))=1, ord_{2}(N)=3, diff=2
210
N=464: ord_{2}(r/deg(phi))=1, ord_{2}(N)=4, diff=3
211
N=464: ord_{2}(r/deg(phi))=1, ord_{2}(N)=4, diff=3
212
N=464: ord_{2}(r/deg(phi))=1, ord_{2}(N)=4, diff=3
213
N=464: ord_{2}(r/deg(phi))=1, ord_{2}(N)=4, diff=3
214
N=464: ord_{2}(r/deg(phi))=1, ord_{2}(N)=4, diff=3
215
N=464: ord_{2}(r/deg(phi))=1, ord_{2}(N)=4, diff=3
216
N=472: ord_{2}(r/deg(phi))=1, ord_{2}(N)=3, diff=2
217
N=480: ord_{2}(r/deg(phi))=1, ord_{2}(N)=5, diff=4
218
N=480: ord_{2}(r/deg(phi))=1, ord_{2}(N)=5, diff=4
219
N=480: ord_{2}(r/deg(phi))=1, ord_{2}(N)=5, diff=4
220
N=480: ord_{2}(r/deg(phi))=1, ord_{2}(N)=5, diff=4
221
N=480: ord_{2}(r/deg(phi))=1, ord_{2}(N)=5, diff=4
222
N=480: ord_{2}(r/deg(phi))=1, ord_{2}(N)=5, diff=4
223
N=480: ord_{2}(r/deg(phi))=1, ord_{2}(N)=5, diff=4
224
N=480: ord_{2}(r/deg(phi))=1, ord_{2}(N)=5, diff=4
225
N=496: ord_{2}(r/deg(phi))=2, ord_{2}(N)=4, diff=2
226
N=496: ord_{2}(r/deg(phi))=2, ord_{2}(N)=4, diff=2
227
N=496: ord_{2}(r/deg(phi))=1, ord_{2}(N)=4, diff=3
228
N=496: ord_{2}(r/deg(phi))=2, ord_{2}(N)=4, diff=2
229
N=496: ord_{2}(r/deg(phi))=2, ord_{2}(N)=4, diff=2
230
N=496: ord_{2}(r/deg(phi))=1, ord_{2}(N)=4, diff=3
231
N=504: ord_{2}(r/deg(phi))=1, ord_{2}(N)=3, diff=2
232
N=504: ord_{2}(r/deg(phi))=1, ord_{2}(N)=3, diff=2
233
N=504: ord_{2}(r/deg(phi))=1, ord_{2}(N)=3, diff=2
234
N=504: ord_{2}(r/deg(phi))=1, ord_{2}(N)=3, diff=2
235
N=504: ord_{2}(r/deg(phi))=1, ord_{2}(N)=3, diff=2
236
N=504: ord_{2}(r/deg(phi))=1, ord_{2}(N)=3, diff=2
237
N=528: ord_{2}(r/deg(phi))=1, ord_{2}(N)=4, diff=3
238
N=528: ord_{2}(r/deg(phi))=1, ord_{2}(N)=4, diff=3
239
N=528: ord_{2}(r/deg(phi))=1, ord_{2}(N)=4, diff=3
240
N=528: ord_{2}(r/deg(phi))=1, ord_{2}(N)=4, diff=3
241
N=528: ord_{2}(r/deg(phi))=1, ord_{2}(N)=4, diff=3
242
N=528: ord_{2}(r/deg(phi))=1, ord_{2}(N)=4, diff=3
243
N=528: ord_{2}(r/deg(phi))=1, ord_{2}(N)=4, diff=3
244
N=528: ord_{2}(r/deg(phi))=1, ord_{2}(N)=4, diff=3
245
N=528: ord_{2}(r/deg(phi))=1, ord_{2}(N)=4, diff=3
246
N=528: ord_{2}(r/deg(phi))=1, ord_{2}(N)=4, diff=3
247
248
249
ell = 3
250
N=54: ord_{3}(r/deg(phi))=1, ord_{3}(N)=3, diff=2
251
N=99: ord_{3}(r/deg(phi))=1, ord_{3}(N)=2, diff=1
252
N=108: ord_{3}(r/deg(phi))=1, ord_{3}(N)=3, diff=2
253
N=126: ord_{3}(r/deg(phi))=1, ord_{3}(N)=2, diff=1
254
N=135: ord_{3}(r/deg(phi))=1, ord_{3}(N)=3, diff=2
255
N=153: ord_{3}(r/deg(phi))=1, ord_{3}(N)=2, diff=1
256
N=153: ord_{3}(r/deg(phi))=1, ord_{3}(N)=2, diff=1
257
N=162: ord_{3}(r/deg(phi))=1, ord_{3}(N)=4, diff=3
258
N=162: ord_{3}(r/deg(phi))=1, ord_{3}(N)=4, diff=3
259
N=162: ord_{3}(r/deg(phi))=1, ord_{3}(N)=4, diff=3
260
N=162: ord_{3}(r/deg(phi))=1, ord_{3}(N)=4, diff=3
261
N=171: ord_{3}(r/deg(phi))=1, ord_{3}(N)=2, diff=1
262
N=189: ord_{3}(r/deg(phi))=1, ord_{3}(N)=3, diff=2
263
N=189: ord_{3}(r/deg(phi))=1, ord_{3}(N)=3, diff=2
264
N=189: ord_{3}(r/deg(phi))=1, ord_{3}(N)=3, diff=2
265
N=216: ord_{3}(r/deg(phi))=1, ord_{3}(N)=3, diff=2
266
N=216: ord_{3}(r/deg(phi))=1, ord_{3}(N)=3, diff=2
267
N=234: ord_{3}(r/deg(phi))=1, ord_{3}(N)=2, diff=1
268
N=234: ord_{3}(r/deg(phi))=1, ord_{3}(N)=2, diff=1
269
N=234: ord_{3}(r/deg(phi))=1, ord_{3}(N)=2, diff=1
270
N=243: ord_{3}(r/deg(phi))=2, ord_{3}(N)=5, diff=3
271
N=243: ord_{3}(r/deg(phi))=1, ord_{3}(N)=5, diff=4
272
N=270: ord_{3}(r/deg(phi))=1, ord_{3}(N)=3, diff=2
273
N=270: ord_{3}(r/deg(phi))=1, ord_{3}(N)=3, diff=2
274
N=270: ord_{3}(r/deg(phi))=1, ord_{3}(N)=3, diff=2
275
N=288: ord_{3}(r/deg(phi))=1, ord_{3}(N)=2, diff=1
276
N=288: ord_{3}(r/deg(phi))=1, ord_{3}(N)=2, diff=1
277
N=297: ord_{3}(r/deg(phi))=1, ord_{3}(N)=3, diff=2
278
N=297: ord_{3}(r/deg(phi))=1, ord_{3}(N)=3, diff=2
279
N=315: ord_{3}(r/deg(phi))=1, ord_{3}(N)=2, diff=1
280
N=324: ord_{3}(r/deg(phi))=1, ord_{3}(N)=4, diff=3
281
N=324: ord_{3}(r/deg(phi))=1, ord_{3}(N)=4, diff=3
282
N=324: ord_{3}(r/deg(phi))=1, ord_{3}(N)=4, diff=3
283
N=324: ord_{3}(r/deg(phi))=1, ord_{3}(N)=4, diff=3
284
N=333: ord_{3}(r/deg(phi))=1, ord_{3}(N)=2, diff=1
285
N=333: ord_{3}(r/deg(phi))=1, ord_{3}(N)=2, diff=1
286
N=333: ord_{3}(r/deg(phi))=1, ord_{3}(N)=2, diff=1
287
N=342: ord_{3}(r/deg(phi))=1, ord_{3}(N)=2, diff=1
288
N=342: ord_{3}(r/deg(phi))=1, ord_{3}(N)=2, diff=1
289
N=360: ord_{3}(r/deg(phi))=1, ord_{3}(N)=2, diff=1
290
N=360: ord_{3}(r/deg(phi))=1, ord_{3}(N)=2, diff=1
291
N=378: ord_{3}(r/deg(phi))=1, ord_{3}(N)=3, diff=2
292
N=378: ord_{3}(r/deg(phi))=1, ord_{3}(N)=3, diff=2
293
N=378: ord_{3}(r/deg(phi))=1, ord_{3}(N)=3, diff=2
294
N=378: ord_{3}(r/deg(phi))=1, ord_{3}(N)=3, diff=2
295
N=378: ord_{3}(r/deg(phi))=1, ord_{3}(N)=3, diff=2
296
N=378: ord_{3}(r/deg(phi))=1, ord_{3}(N)=3, diff=2
297
N=387: ord_{3}(r/deg(phi))=1, ord_{3}(N)=2, diff=1
298
N=405: ord_{3}(r/deg(phi))=1, ord_{3}(N)=4, diff=3
299
N=405: ord_{3}(r/deg(phi))=2, ord_{3}(N)=4, diff=2
300
N=405: ord_{3}(r/deg(phi))=2, ord_{3}(N)=4, diff=2
301
N=405: ord_{3}(r/deg(phi))=1, ord_{3}(N)=4, diff=3
302
N=405: ord_{3}(r/deg(phi))=1, ord_{3}(N)=4, diff=3
303
N=405: ord_{3}(r/deg(phi))=1, ord_{3}(N)=4, diff=3
304
N=414: ord_{3}(r/deg(phi))=1, ord_{3}(N)=2, diff=1
305
N=423: ord_{3}(r/deg(phi))=1, ord_{3}(N)=2, diff=1
306
N=432: ord_{3}(r/deg(phi))=1, ord_{3}(N)=3, diff=2
307
N=432: ord_{3}(r/deg(phi))=1, ord_{3}(N)=3, diff=2
308
N=432: ord_{3}(r/deg(phi))=1, ord_{3}(N)=3, diff=2
309
N=432: ord_{3}(r/deg(phi))=1, ord_{3}(N)=3, diff=2
310
N=432: ord_{3}(r/deg(phi))=1, ord_{3}(N)=3, diff=2
311
N=432: ord_{3}(r/deg(phi))=1, ord_{3}(N)=3, diff=2
312
N=441: ord_{3}(r/deg(phi))=1, ord_{3}(N)=2, diff=1
313
N=459: ord_{3}(r/deg(phi))=1, ord_{3}(N)=3, diff=2
314
N=459: ord_{3}(r/deg(phi))=1, ord_{3}(N)=3, diff=2
315
N=459: ord_{3}(r/deg(phi))=1, ord_{3}(N)=3, diff=2
316
N=459: ord_{3}(r/deg(phi))=1, ord_{3}(N)=3, diff=2
317
N=468: ord_{3}(r/deg(phi))=1, ord_{3}(N)=2, diff=1
318
N=468: ord_{3}(r/deg(phi))=1, ord_{3}(N)=2, diff=1
319
N=477: ord_{3}(r/deg(phi))=1, ord_{3}(N)=2, diff=1
320
N=486: ord_{3}(r/deg(phi))=2, ord_{3}(N)=5, diff=3
321
N=486: ord_{3}(r/deg(phi))=2, ord_{3}(N)=5, diff=3
322
N=486: ord_{3}(r/deg(phi))=1, ord_{3}(N)=5, diff=4
323
N=486: ord_{3}(r/deg(phi))=2, ord_{3}(N)=5, diff=3
324
N=486: ord_{3}(r/deg(phi))=2, ord_{3}(N)=5, diff=3
325
N=486: ord_{3}(r/deg(phi))=1, ord_{3}(N)=5, diff=4
326
N=495: ord_{3}(r/deg(phi))=1, ord_{3}(N)=2, diff=1
327
N=504: ord_{3}(r/deg(phi))=1, ord_{3}(N)=2, diff=1
328
N=504: ord_{3}(r/deg(phi))=1, ord_{3}(N)=2, diff=1
329
N=504: ord_{3}(r/deg(phi))=1, ord_{3}(N)=2, diff=1
330
N=513: ord_{3}(r/deg(phi))=1, ord_{3}(N)=3, diff=2
331
N=522: ord_{3}(r/deg(phi))=1, ord_{3}(N)=2, diff=1
332
N=522: ord_{3}(r/deg(phi))=1, ord_{3}(N)=2, diff=1
333
N=522: ord_{3}(r/deg(phi))=1, ord_{3}(N)=2, diff=1
334
335
336
ell > 3
337
N=147: ord_{7}(r/deg(phi))=1, ord_{7}(N)=2, diff=1
338
N=150: ord_{5}(r/deg(phi))=1, ord_{5}(N)=2, diff=1
339
N=175: ord_{5}(r/deg(phi))=1, ord_{5}(N)=2, diff=1
340
N=196: ord_{7}(r/deg(phi))=1, ord_{7}(N)=2, diff=1
341
N=200: ord_{5}(r/deg(phi))=1, ord_{5}(N)=2, diff=1
342
N=200: ord_{5}(r/deg(phi))=1, ord_{5}(N)=2, diff=1
343
N=225: ord_{5}(r/deg(phi))=1, ord_{5}(N)=2, diff=1
344
N=242: ord_{11}(r/deg(phi))=1, ord_{11}(N)=2, diff=1
345
N=245: ord_{7}(r/deg(phi))=1, ord_{7}(N)=2, diff=1
346
N=275: ord_{5}(r/deg(phi))=1, ord_{5}(N)=2, diff=1
347
N=294: ord_{7}(r/deg(phi))=1, ord_{7}(N)=2, diff=1
348
N=294: ord_{7}(r/deg(phi))=1, ord_{7}(N)=2, diff=1
349
N=294: ord_{7}(r/deg(phi))=1, ord_{7}(N)=2, diff=1
350
N=300: ord_{5}(r/deg(phi))=1, ord_{5}(N)=2, diff=1
351
N=300: ord_{5}(r/deg(phi))=1, ord_{5}(N)=2, diff=1
352
N=325: ord_{5}(r/deg(phi))=1, ord_{5}(N)=2, diff=1
353
N=338: ord_{13}(r/deg(phi))=1, ord_{13}(N)=2, diff=1
354
N=338: ord_{13}(r/deg(phi))=1, ord_{13}(N)=2, diff=1
355
N=350: ord_{5}(r/deg(phi))=1, ord_{5}(N)=2, diff=1
356
N=350: ord_{5}(r/deg(phi))=1, ord_{5}(N)=2, diff=1
357
N=350: ord_{5}(r/deg(phi))=1, ord_{5}(N)=2, diff=1
358
N=363: ord_{11}(r/deg(phi))=1, ord_{11}(N)=2, diff=1
359
N=392: ord_{7}(r/deg(phi))=1, ord_{7}(N)=2, diff=1
360
N=392: ord_{7}(r/deg(phi))=1, ord_{7}(N)=2, diff=1
361
N=400: ord_{5}(r/deg(phi))=1, ord_{5}(N)=2, diff=1
362
N=400: ord_{5}(r/deg(phi))=1, ord_{5}(N)=2, diff=1
363
N=425: ord_{5}(r/deg(phi))=1, ord_{5}(N)=2, diff=1
364
N=425: ord_{5}(r/deg(phi))=1, ord_{5}(N)=2, diff=1
365
N=441: ord_{7}(r/deg(phi))=1, ord_{7}(N)=2, diff=1
366
N=441: ord_{7}(r/deg(phi))=1, ord_{7}(N)=2, diff=1
367
N=450: ord_{5}(r/deg(phi))=1, ord_{5}(N)=2, diff=1
368
N=475: ord_{5}(r/deg(phi))=1, ord_{5}(N)=2, diff=1
369
N=475: ord_{5}(r/deg(phi))=1, ord_{5}(N)=2, diff=1
370
N=490: ord_{7}(r/deg(phi))=1, ord_{7}(N)=2, diff=1
371
N=490: ord_{7}(r/deg(phi))=1, ord_{7}(N)=2, diff=1
372
N=490: ord_{7}(r/deg(phi))=1, ord_{7}(N)=2, diff=1
373
N=490: ord_{7}(r/deg(phi))=1, ord_{7}(N)=2, diff=1
374
N=490: ord_{7}(r/deg(phi))=1, ord_{7}(N)=2, diff=1
375
N=507: ord_{13}(r/deg(phi))=1, ord_{13}(N)=2, diff=1
376
N=525: ord_{5}(r/deg(phi))=1, ord_{5}(N)=2, diff=1
377
N=525: ord_{5}(r/deg(phi))=1, ord_{5}(N)=2, diff=1
378
N=539: ord_{7}(r/deg(phi))=1, ord_{7}(N)=2, diff=1