Properties

Label 525.4.a.g.1.1
Level 525525
Weight 44
Character 525.1
Self dual yes
Analytic conductor 30.97630.976
Analytic rank 11
Dimension 11
CM no
Inner twists 11

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [525,4,Mod(1,525)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(525, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("525.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: N N == 525=3527 525 = 3 \cdot 5^{2} \cdot 7
Weight: k k == 4 4
Character orbit: [χ][\chi] == 525.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: 30.976002753030.9760027530
Analytic rank: 11
Dimension: 11
Coefficient field: Q\mathbb{Q}
Coefficient ring: Z\mathbb{Z}
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 21)
Fricke sign: 1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.1
Character χ\chi == 525.1

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+3.00000q2+3.00000q3+1.00000q4+9.00000q67.00000q721.0000q8+9.00000q936.0000q11+3.00000q12+34.0000q1321.0000q1471.0000q1642.0000q17+27.0000q18124.000q1921.0000q21108.000q2263.0000q24+102.000q26+27.0000q277.00000q28+102.000q29160.000q3145.0000q32108.000q33126.000q34+9.00000q36398.000q37372.000q38+102.000q39318.000q4163.0000q42+268.000q4336.0000q44240.000q47213.000q48+49.0000q49126.000q51+34.0000q52+498.000q53+81.0000q54+147.000q56372.000q57+306.000q58132.000q59+398.000q61480.000q6263.0000q63+433.000q64324.000q6692.0000q6742.0000q68720.000q71189.000q72+502.000q731194.00q74124.000q76+252.000q77+306.000q781024.00q79+81.0000q81954.000q82+204.000q8321.0000q84+804.000q86+306.000q87+756.000q88+354.000q89238.000q91480.000q93720.000q94135.000q96+286.000q97+147.000q98324.000q99+O(q100)q+3.00000 q^{2} +3.00000 q^{3} +1.00000 q^{4} +9.00000 q^{6} -7.00000 q^{7} -21.0000 q^{8} +9.00000 q^{9} -36.0000 q^{11} +3.00000 q^{12} +34.0000 q^{13} -21.0000 q^{14} -71.0000 q^{16} -42.0000 q^{17} +27.0000 q^{18} -124.000 q^{19} -21.0000 q^{21} -108.000 q^{22} -63.0000 q^{24} +102.000 q^{26} +27.0000 q^{27} -7.00000 q^{28} +102.000 q^{29} -160.000 q^{31} -45.0000 q^{32} -108.000 q^{33} -126.000 q^{34} +9.00000 q^{36} -398.000 q^{37} -372.000 q^{38} +102.000 q^{39} -318.000 q^{41} -63.0000 q^{42} +268.000 q^{43} -36.0000 q^{44} -240.000 q^{47} -213.000 q^{48} +49.0000 q^{49} -126.000 q^{51} +34.0000 q^{52} +498.000 q^{53} +81.0000 q^{54} +147.000 q^{56} -372.000 q^{57} +306.000 q^{58} -132.000 q^{59} +398.000 q^{61} -480.000 q^{62} -63.0000 q^{63} +433.000 q^{64} -324.000 q^{66} -92.0000 q^{67} -42.0000 q^{68} -720.000 q^{71} -189.000 q^{72} +502.000 q^{73} -1194.00 q^{74} -124.000 q^{76} +252.000 q^{77} +306.000 q^{78} -1024.00 q^{79} +81.0000 q^{81} -954.000 q^{82} +204.000 q^{83} -21.0000 q^{84} +804.000 q^{86} +306.000 q^{87} +756.000 q^{88} +354.000 q^{89} -238.000 q^{91} -480.000 q^{93} -720.000 q^{94} -135.000 q^{96} +286.000 q^{97} +147.000 q^{98} -324.000 q^{99} +O(q^{100})

Coefficient data

For each nn we display the coefficients of the qq-expansion ana_n, the Satake parameters αp\alpha_p, and the Satake angles θp=Arg(αp)\theta_p = \textrm{Arg}(\alpha_p).



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 3.00000 1.06066 0.530330 0.847791i 0.322068π-0.322068\pi
0.530330 + 0.847791i 0.322068π0.322068\pi
33 3.00000 0.577350
44 1.00000 0.125000
55 0 0
66 9.00000 0.612372
77 −7.00000 −0.377964
88 −21.0000 −0.928078
99 9.00000 0.333333
1010 0 0
1111 −36.0000 −0.986764 −0.493382 0.869813i 0.664240π-0.664240\pi
−0.493382 + 0.869813i 0.664240π0.664240\pi
1212 3.00000 0.0721688
1313 34.0000 0.725377 0.362689 0.931910i 0.381859π-0.381859\pi
0.362689 + 0.931910i 0.381859π0.381859\pi
1414 −21.0000 −0.400892
1515 0 0
1616 −71.0000 −1.10938
1717 −42.0000 −0.599206 −0.299603 0.954064i 0.596854π-0.596854\pi
−0.299603 + 0.954064i 0.596854π0.596854\pi
1818 27.0000 0.353553
1919 −124.000 −1.49724 −0.748620 0.663000i 0.769283π-0.769283\pi
−0.748620 + 0.663000i 0.769283π0.769283\pi
2020 0 0
2121 −21.0000 −0.218218
2222 −108.000 −1.04662
2323 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
2424 −63.0000 −0.535826
2525 0 0
2626 102.000 0.769379
2727 27.0000 0.192450
2828 −7.00000 −0.0472456
2929 102.000 0.653135 0.326568 0.945174i 0.394108π-0.394108\pi
0.326568 + 0.945174i 0.394108π0.394108\pi
3030 0 0
3131 −160.000 −0.926995 −0.463498 0.886098i 0.653406π-0.653406\pi
−0.463498 + 0.886098i 0.653406π0.653406\pi
3232 −45.0000 −0.248592
3333 −108.000 −0.569709
3434 −126.000 −0.635554
3535 0 0
3636 9.00000 0.0416667
3737 −398.000 −1.76840 −0.884200 0.467109i 0.845296π-0.845296\pi
−0.884200 + 0.467109i 0.845296π0.845296\pi
3838 −372.000 −1.58806
3939 102.000 0.418797
4040 0 0
4141 −318.000 −1.21130 −0.605649 0.795732i 0.707087π-0.707087\pi
−0.605649 + 0.795732i 0.707087π0.707087\pi
4242 −63.0000 −0.231455
4343 268.000 0.950456 0.475228 0.879863i 0.342366π-0.342366\pi
0.475228 + 0.879863i 0.342366π0.342366\pi
4444 −36.0000 −0.123346
4545 0 0
4646 0 0
4747 −240.000 −0.744843 −0.372421 0.928064i 0.621472π-0.621472\pi
−0.372421 + 0.928064i 0.621472π0.621472\pi
4848 −213.000 −0.640498
4949 49.0000 0.142857
5050 0 0
5151 −126.000 −0.345952
5252 34.0000 0.0906721
5353 498.000 1.29067 0.645335 0.763899i 0.276718π-0.276718\pi
0.645335 + 0.763899i 0.276718π0.276718\pi
5454 81.0000 0.204124
5555 0 0
5656 147.000 0.350780
5757 −372.000 −0.864432
5858 306.000 0.692755
5959 −132.000 −0.291270 −0.145635 0.989338i 0.546523π-0.546523\pi
−0.145635 + 0.989338i 0.546523π0.546523\pi
6060 0 0
6161 398.000 0.835388 0.417694 0.908588i 0.362838π-0.362838\pi
0.417694 + 0.908588i 0.362838π0.362838\pi
6262 −480.000 −0.983227
6363 −63.0000 −0.125988
6464 433.000 0.845703
6565 0 0
6666 −324.000 −0.604267
6767 −92.0000 −0.167755 −0.0838775 0.996476i 0.526730π-0.526730\pi
−0.0838775 + 0.996476i 0.526730π0.526730\pi
6868 −42.0000 −0.0749007
6969 0 0
7070 0 0
7171 −720.000 −1.20350 −0.601748 0.798686i 0.705529π-0.705529\pi
−0.601748 + 0.798686i 0.705529π0.705529\pi
7272 −189.000 −0.309359
7373 502.000 0.804858 0.402429 0.915451i 0.368166π-0.368166\pi
0.402429 + 0.915451i 0.368166π0.368166\pi
7474 −1194.00 −1.87567
7575 0 0
7676 −124.000 −0.187155
7777 252.000 0.372962
7878 306.000 0.444201
7979 −1024.00 −1.45834 −0.729171 0.684332i 0.760094π-0.760094\pi
−0.729171 + 0.684332i 0.760094π0.760094\pi
8080 0 0
8181 81.0000 0.111111
8282 −954.000 −1.28478
8383 204.000 0.269782 0.134891 0.990860i 0.456932π-0.456932\pi
0.134891 + 0.990860i 0.456932π0.456932\pi
8484 −21.0000 −0.0272772
8585 0 0
8686 804.000 1.00811
8787 306.000 0.377088
8888 756.000 0.915794
8989 354.000 0.421617 0.210809 0.977527i 0.432390π-0.432390\pi
0.210809 + 0.977527i 0.432390π0.432390\pi
9090 0 0
9191 −238.000 −0.274167
9292 0 0
9393 −480.000 −0.535201
9494 −720.000 −0.790025
9595 0 0
9696 −135.000 −0.143525
9797 286.000 0.299370 0.149685 0.988734i 0.452174π-0.452174\pi
0.149685 + 0.988734i 0.452174π0.452174\pi
9898 147.000 0.151523
9999 −324.000 −0.328921
100100 0 0
101101 414.000 0.407867 0.203933 0.978985i 0.434627π-0.434627\pi
0.203933 + 0.978985i 0.434627π0.434627\pi
102102 −378.000 −0.366937
103103 −56.0000 −0.0535713 −0.0267857 0.999641i 0.508527π-0.508527\pi
−0.0267857 + 0.999641i 0.508527π0.508527\pi
104104 −714.000 −0.673206
105105 0 0
106106 1494.00 1.36896
107107 −12.0000 −0.0108419 −0.00542095 0.999985i 0.501726π-0.501726\pi
−0.00542095 + 0.999985i 0.501726π0.501726\pi
108108 27.0000 0.0240563
109109 1478.00 1.29878 0.649389 0.760457i 0.275025π-0.275025\pi
0.649389 + 0.760457i 0.275025π0.275025\pi
110110 0 0
111111 −1194.00 −1.02099
112112 497.000 0.419304
113113 −402.000 −0.334664 −0.167332 0.985901i 0.553515π-0.553515\pi
−0.167332 + 0.985901i 0.553515π0.553515\pi
114114 −1116.00 −0.916868
115115 0 0
116116 102.000 0.0816419
117117 306.000 0.241792
118118 −396.000 −0.308939
119119 294.000 0.226478
120120 0 0
121121 −35.0000 −0.0262960
122122 1194.00 0.886063
123123 −954.000 −0.699344
124124 −160.000 −0.115874
125125 0 0
126126 −189.000 −0.133631
127127 −1280.00 −0.894344 −0.447172 0.894448i 0.647569π-0.647569\pi
−0.447172 + 0.894448i 0.647569π0.647569\pi
128128 1659.00 1.14560
129129 804.000 0.548746
130130 0 0
131131 1764.00 1.17650 0.588250 0.808679i 0.299817π-0.299817\pi
0.588250 + 0.808679i 0.299817π0.299817\pi
132132 −108.000 −0.0712136
133133 868.000 0.565903
134134 −276.000 −0.177931
135135 0 0
136136 882.000 0.556109
137137 2358.00 1.47049 0.735246 0.677800i 0.237066π-0.237066\pi
0.735246 + 0.677800i 0.237066π0.237066\pi
138138 0 0
139139 −52.0000 −0.0317308 −0.0158654 0.999874i 0.505050π-0.505050\pi
−0.0158654 + 0.999874i 0.505050π0.505050\pi
140140 0 0
141141 −720.000 −0.430035
142142 −2160.00 −1.27650
143143 −1224.00 −0.715776
144144 −639.000 −0.369792
145145 0 0
146146 1506.00 0.853681
147147 147.000 0.0824786
148148 −398.000 −0.221050
149149 −1746.00 −0.959986 −0.479993 0.877272i 0.659361π-0.659361\pi
−0.479993 + 0.877272i 0.659361π0.659361\pi
150150 0 0
151151 −232.000 −0.125032 −0.0625162 0.998044i 0.519913π-0.519913\pi
−0.0625162 + 0.998044i 0.519913π0.519913\pi
152152 2604.00 1.38955
153153 −378.000 −0.199735
154154 756.000 0.395586
155155 0 0
156156 102.000 0.0523496
157157 −1694.00 −0.861120 −0.430560 0.902562i 0.641684π-0.641684\pi
−0.430560 + 0.902562i 0.641684π0.641684\pi
158158 −3072.00 −1.54681
159159 1494.00 0.745169
160160 0 0
161161 0 0
162162 243.000 0.117851
163163 2932.00 1.40891 0.704454 0.709750i 0.251192π-0.251192\pi
0.704454 + 0.709750i 0.251192π0.251192\pi
164164 −318.000 −0.151412
165165 0 0
166166 612.000 0.286147
167167 −1176.00 −0.544920 −0.272460 0.962167i 0.587837π-0.587837\pi
−0.272460 + 0.962167i 0.587837π0.587837\pi
168168 441.000 0.202523
169169 −1041.00 −0.473828
170170 0 0
171171 −1116.00 −0.499080
172172 268.000 0.118807
173173 −870.000 −0.382340 −0.191170 0.981557i 0.561228π-0.561228\pi
−0.191170 + 0.981557i 0.561228π0.561228\pi
174174 918.000 0.399962
175175 0 0
176176 2556.00 1.09469
177177 −396.000 −0.168165
178178 1062.00 0.447193
179179 −2316.00 −0.967072 −0.483536 0.875324i 0.660648π-0.660648\pi
−0.483536 + 0.875324i 0.660648π0.660648\pi
180180 0 0
181181 −106.000 −0.0435299 −0.0217650 0.999763i 0.506929π-0.506929\pi
−0.0217650 + 0.999763i 0.506929π0.506929\pi
182182 −714.000 −0.290798
183183 1194.00 0.482312
184184 0 0
185185 0 0
186186 −1440.00 −0.567666
187187 1512.00 0.591275
188188 −240.000 −0.0931053
189189 −189.000 −0.0727393
190190 0 0
191191 −1128.00 −0.427326 −0.213663 0.976907i 0.568539π-0.568539\pi
−0.213663 + 0.976907i 0.568539π0.568539\pi
192192 1299.00 0.488267
193193 −4034.00 −1.50453 −0.752263 0.658862i 0.771038π-0.771038\pi
−0.752263 + 0.658862i 0.771038π0.771038\pi
194194 858.000 0.317530
195195 0 0
196196 49.0000 0.0178571
197197 1314.00 0.475221 0.237611 0.971360i 0.423636π-0.423636\pi
0.237611 + 0.971360i 0.423636π0.423636\pi
198198 −972.000 −0.348874
199199 5096.00 1.81531 0.907653 0.419722i 0.137872π-0.137872\pi
0.907653 + 0.419722i 0.137872π0.137872\pi
200200 0 0
201201 −276.000 −0.0968534
202202 1242.00 0.432608
203203 −714.000 −0.246862
204204 −126.000 −0.0432439
205205 0 0
206206 −168.000 −0.0568209
207207 0 0
208208 −2414.00 −0.804715
209209 4464.00 1.47742
210210 0 0
211211 −3076.00 −1.00360 −0.501802 0.864982i 0.667330π-0.667330\pi
−0.501802 + 0.864982i 0.667330π0.667330\pi
212212 498.000 0.161334
213213 −2160.00 −0.694839
214214 −36.0000 −0.0114996
215215 0 0
216216 −567.000 −0.178609
217217 1120.00 0.350371
218218 4434.00 1.37756
219219 1506.00 0.464685
220220 0 0
221221 −1428.00 −0.434650
222222 −3582.00 −1.08292
223223 1888.00 0.566950 0.283475 0.958980i 0.408513π-0.408513\pi
0.283475 + 0.958980i 0.408513π0.408513\pi
224224 315.000 0.0939590
225225 0 0
226226 −1206.00 −0.354964
227227 4716.00 1.37891 0.689454 0.724330i 0.257851π-0.257851\pi
0.689454 + 0.724330i 0.257851π0.257851\pi
228228 −372.000 −0.108054
229229 −1690.00 −0.487678 −0.243839 0.969816i 0.578407π-0.578407\pi
−0.243839 + 0.969816i 0.578407π0.578407\pi
230230 0 0
231231 756.000 0.215330
232232 −2142.00 −0.606160
233233 −138.000 −0.0388012 −0.0194006 0.999812i 0.506176π-0.506176\pi
−0.0194006 + 0.999812i 0.506176π0.506176\pi
234234 918.000 0.256460
235235 0 0
236236 −132.000 −0.0364088
237237 −3072.00 −0.841974
238238 882.000 0.240217
239239 1896.00 0.513147 0.256573 0.966525i 0.417406π-0.417406\pi
0.256573 + 0.966525i 0.417406π0.417406\pi
240240 0 0
241241 −3598.00 −0.961691 −0.480846 0.876805i 0.659670π-0.659670\pi
−0.480846 + 0.876805i 0.659670π0.659670\pi
242242 −105.000 −0.0278911
243243 243.000 0.0641500
244244 398.000 0.104424
245245 0 0
246246 −2862.00 −0.741766
247247 −4216.00 −1.08606
248248 3360.00 0.860323
249249 612.000 0.155759
250250 0 0
251251 −3060.00 −0.769504 −0.384752 0.923020i 0.625713π-0.625713\pi
−0.384752 + 0.923020i 0.625713π0.625713\pi
252252 −63.0000 −0.0157485
253253 0 0
254254 −3840.00 −0.948595
255255 0 0
256256 1513.00 0.369385
257257 6822.00 1.65582 0.827908 0.560864i 0.189531π-0.189531\pi
0.827908 + 0.560864i 0.189531π0.189531\pi
258258 2412.00 0.582033
259259 2786.00 0.668392
260260 0 0
261261 918.000 0.217712
262262 5292.00 1.24787
263263 −2592.00 −0.607717 −0.303858 0.952717i 0.598275π-0.598275\pi
−0.303858 + 0.952717i 0.598275π0.598275\pi
264264 2268.00 0.528734
265265 0 0
266266 2604.00 0.600231
267267 1062.00 0.243421
268268 −92.0000 −0.0209694
269269 8214.00 1.86177 0.930886 0.365311i 0.119037π-0.119037\pi
0.930886 + 0.365311i 0.119037π0.119037\pi
270270 0 0
271271 −5344.00 −1.19788 −0.598939 0.800795i 0.704411π-0.704411\pi
−0.598939 + 0.800795i 0.704411π0.704411\pi
272272 2982.00 0.664744
273273 −714.000 −0.158290
274274 7074.00 1.55969
275275 0 0
276276 0 0
277277 6514.00 1.41295 0.706477 0.707736i 0.250283π-0.250283\pi
0.706477 + 0.707736i 0.250283π0.250283\pi
278278 −156.000 −0.0336556
279279 −1440.00 −0.308998
280280 0 0
281281 6618.00 1.40497 0.702485 0.711698i 0.252074π-0.252074\pi
0.702485 + 0.711698i 0.252074π0.252074\pi
282282 −2160.00 −0.456121
283283 −3260.00 −0.684759 −0.342380 0.939562i 0.611233π-0.611233\pi
−0.342380 + 0.939562i 0.611233π0.611233\pi
284284 −720.000 −0.150437
285285 0 0
286286 −3672.00 −0.759195
287287 2226.00 0.457828
288288 −405.000 −0.0828641
289289 −3149.00 −0.640953
290290 0 0
291291 858.000 0.172841
292292 502.000 0.100607
293293 −5118.00 −1.02047 −0.510233 0.860036i 0.670441π-0.670441\pi
−0.510233 + 0.860036i 0.670441π0.670441\pi
294294 441.000 0.0874818
295295 0 0
296296 8358.00 1.64121
297297 −972.000 −0.189903
298298 −5238.00 −1.01822
299299 0 0
300300 0 0
301301 −1876.00 −0.359239
302302 −696.000 −0.132617
303303 1242.00 0.235482
304304 8804.00 1.66100
305305 0 0
306306 −1134.00 −0.211851
307307 −452.000 −0.0840293 −0.0420147 0.999117i 0.513378π-0.513378\pi
−0.0420147 + 0.999117i 0.513378π0.513378\pi
308308 252.000 0.0466202
309309 −168.000 −0.0309294
310310 0 0
311311 5016.00 0.914570 0.457285 0.889320i 0.348822π-0.348822\pi
0.457285 + 0.889320i 0.348822π0.348822\pi
312312 −2142.00 −0.388676
313313 −5402.00 −0.975524 −0.487762 0.872977i 0.662187π-0.662187\pi
−0.487762 + 0.872977i 0.662187π0.662187\pi
314314 −5082.00 −0.913356
315315 0 0
316316 −1024.00 −0.182293
317317 −10086.0 −1.78702 −0.893511 0.449041i 0.851766π-0.851766\pi
−0.893511 + 0.449041i 0.851766π0.851766\pi
318318 4482.00 0.790371
319319 −3672.00 −0.644491
320320 0 0
321321 −36.0000 −0.00625958
322322 0 0
323323 5208.00 0.897154
324324 81.0000 0.0138889
325325 0 0
326326 8796.00 1.49437
327327 4434.00 0.749849
328328 6678.00 1.12418
329329 1680.00 0.281524
330330 0 0
331331 −8044.00 −1.33577 −0.667883 0.744267i 0.732799π-0.732799\pi
−0.667883 + 0.744267i 0.732799π0.732799\pi
332332 204.000 0.0337228
333333 −3582.00 −0.589467
334334 −3528.00 −0.577975
335335 0 0
336336 1491.00 0.242085
337337 −4178.00 −0.675342 −0.337671 0.941264i 0.609639π-0.609639\pi
−0.337671 + 0.941264i 0.609639π0.609639\pi
338338 −3123.00 −0.502570
339339 −1206.00 −0.193218
340340 0 0
341341 5760.00 0.914726
342342 −3348.00 −0.529354
343343 −343.000 −0.0539949
344344 −5628.00 −0.882097
345345 0 0
346346 −2610.00 −0.405533
347347 −156.000 −0.0241341 −0.0120670 0.999927i 0.503841π-0.503841\pi
−0.0120670 + 0.999927i 0.503841π0.503841\pi
348348 306.000 0.0471360
349349 −12418.0 −1.90464 −0.952321 0.305097i 0.901311π-0.901311\pi
−0.952321 + 0.305097i 0.901311π0.901311\pi
350350 0 0
351351 918.000 0.139599
352352 1620.00 0.245302
353353 7830.00 1.18059 0.590296 0.807187i 0.299011π-0.299011\pi
0.590296 + 0.807187i 0.299011π0.299011\pi
354354 −1188.00 −0.178366
355355 0 0
356356 354.000 0.0527021
357357 882.000 0.130757
358358 −6948.00 −1.02574
359359 −9312.00 −1.36899 −0.684497 0.729016i 0.739978π-0.739978\pi
−0.684497 + 0.729016i 0.739978π0.739978\pi
360360 0 0
361361 8517.00 1.24173
362362 −318.000 −0.0461705
363363 −105.000 −0.0151820
364364 −238.000 −0.0342709
365365 0 0
366366 3582.00 0.511569
367367 3760.00 0.534797 0.267398 0.963586i 0.413836π-0.413836\pi
0.267398 + 0.963586i 0.413836π0.413836\pi
368368 0 0
369369 −2862.00 −0.403766
370370 0 0
371371 −3486.00 −0.487828
372372 −480.000 −0.0669001
373373 −5870.00 −0.814845 −0.407422 0.913240i 0.633572π-0.633572\pi
−0.407422 + 0.913240i 0.633572π0.633572\pi
374374 4536.00 0.627142
375375 0 0
376376 5040.00 0.691272
377377 3468.00 0.473769
378378 −567.000 −0.0771517
379379 −1852.00 −0.251005 −0.125502 0.992093i 0.540054π-0.540054\pi
−0.125502 + 0.992093i 0.540054π0.540054\pi
380380 0 0
381381 −3840.00 −0.516350
382382 −3384.00 −0.453247
383383 −2160.00 −0.288175 −0.144087 0.989565i 0.546025π-0.546025\pi
−0.144087 + 0.989565i 0.546025π0.546025\pi
384384 4977.00 0.661410
385385 0 0
386386 −12102.0 −1.59579
387387 2412.00 0.316819
388388 286.000 0.0374213
389389 −6786.00 −0.884483 −0.442241 0.896896i 0.645817π-0.645817\pi
−0.442241 + 0.896896i 0.645817π0.645817\pi
390390 0 0
391391 0 0
392392 −1029.00 −0.132583
393393 5292.00 0.679252
394394 3942.00 0.504048
395395 0 0
396396 −324.000 −0.0411152
397397 6514.00 0.823497 0.411748 0.911298i 0.364918π-0.364918\pi
0.411748 + 0.911298i 0.364918π0.364918\pi
398398 15288.0 1.92542
399399 2604.00 0.326724
400400 0 0
401401 3330.00 0.414694 0.207347 0.978267i 0.433517π-0.433517\pi
0.207347 + 0.978267i 0.433517π0.433517\pi
402402 −828.000 −0.102729
403403 −5440.00 −0.672421
404404 414.000 0.0509833
405405 0 0
406406 −2142.00 −0.261837
407407 14328.0 1.74499
408408 2646.00 0.321070
409409 −5398.00 −0.652601 −0.326301 0.945266i 0.605802π-0.605802\pi
−0.326301 + 0.945266i 0.605802π0.605802\pi
410410 0 0
411411 7074.00 0.848990
412412 −56.0000 −0.00669641
413413 924.000 0.110090
414414 0 0
415415 0 0
416416 −1530.00 −0.180323
417417 −156.000 −0.0183198
418418 13392.0 1.56704
419419 13092.0 1.52646 0.763229 0.646128i 0.223613π-0.223613\pi
0.763229 + 0.646128i 0.223613π0.223613\pi
420420 0 0
421421 −322.000 −0.0372763 −0.0186381 0.999826i 0.505933π-0.505933\pi
−0.0186381 + 0.999826i 0.505933π0.505933\pi
422422 −9228.00 −1.06448
423423 −2160.00 −0.248281
424424 −10458.0 −1.19784
425425 0 0
426426 −6480.00 −0.736988
427427 −2786.00 −0.315747
428428 −12.0000 −0.00135524
429429 −3672.00 −0.413254
430430 0 0
431431 2616.00 0.292363 0.146181 0.989258i 0.453302π-0.453302\pi
0.146181 + 0.989258i 0.453302π0.453302\pi
432432 −1917.00 −0.213499
433433 −4322.00 −0.479681 −0.239841 0.970812i 0.577095π-0.577095\pi
−0.239841 + 0.970812i 0.577095π0.577095\pi
434434 3360.00 0.371625
435435 0 0
436436 1478.00 0.162347
437437 0 0
438438 4518.00 0.492873
439439 −9016.00 −0.980205 −0.490103 0.871665i 0.663041π-0.663041\pi
−0.490103 + 0.871665i 0.663041π0.663041\pi
440440 0 0
441441 441.000 0.0476190
442442 −4284.00 −0.461016
443443 5268.00 0.564989 0.282495 0.959269i 0.408838π-0.408838\pi
0.282495 + 0.959269i 0.408838π0.408838\pi
444444 −1194.00 −0.127623
445445 0 0
446446 5664.00 0.601341
447447 −5238.00 −0.554248
448448 −3031.00 −0.319646
449449 −5310.00 −0.558117 −0.279058 0.960274i 0.590022π-0.590022\pi
−0.279058 + 0.960274i 0.590022π0.590022\pi
450450 0 0
451451 11448.0 1.19527
452452 −402.000 −0.0418329
453453 −696.000 −0.0721875
454454 14148.0 1.46255
455455 0 0
456456 7812.00 0.802260
457457 −15770.0 −1.61420 −0.807100 0.590415i 0.798964π-0.798964\pi
−0.807100 + 0.590415i 0.798964π0.798964\pi
458458 −5070.00 −0.517261
459459 −1134.00 −0.115317
460460 0 0
461461 −5370.00 −0.542529 −0.271264 0.962505i 0.587442π-0.587442\pi
−0.271264 + 0.962505i 0.587442π0.587442\pi
462462 2268.00 0.228392
463463 3328.00 0.334050 0.167025 0.985953i 0.446584π-0.446584\pi
0.167025 + 0.985953i 0.446584π0.446584\pi
464464 −7242.00 −0.724572
465465 0 0
466466 −414.000 −0.0411549
467467 −4548.00 −0.450656 −0.225328 0.974283i 0.572345π-0.572345\pi
−0.225328 + 0.974283i 0.572345π0.572345\pi
468468 306.000 0.0302240
469469 644.000 0.0634055
470470 0 0
471471 −5082.00 −0.497168
472472 2772.00 0.270321
473473 −9648.00 −0.937876
474474 −9216.00 −0.893048
475475 0 0
476476 294.000 0.0283098
477477 4482.00 0.430224
478478 5688.00 0.544274
479479 −8064.00 −0.769214 −0.384607 0.923080i 0.625663π-0.625663\pi
−0.384607 + 0.923080i 0.625663π0.625663\pi
480480 0 0
481481 −13532.0 −1.28276
482482 −10794.0 −1.02003
483483 0 0
484484 −35.0000 −0.00328700
485485 0 0
486486 729.000 0.0680414
487487 −16616.0 −1.54608 −0.773042 0.634355i 0.781266π-0.781266\pi
−0.773042 + 0.634355i 0.781266π0.781266\pi
488488 −8358.00 −0.775305
489489 8796.00 0.813433
490490 0 0
491491 −7140.00 −0.656260 −0.328130 0.944633i 0.606418π-0.606418\pi
−0.328130 + 0.944633i 0.606418π0.606418\pi
492492 −954.000 −0.0874180
493493 −4284.00 −0.391362
494494 −12648.0 −1.15194
495495 0 0
496496 11360.0 1.02839
497497 5040.00 0.454879
498498 1836.00 0.165207
499499 −9124.00 −0.818530 −0.409265 0.912416i 0.634215π-0.634215\pi
−0.409265 + 0.912416i 0.634215π0.634215\pi
500500 0 0
501501 −3528.00 −0.314610
502502 −9180.00 −0.816182
503503 6552.00 0.580794 0.290397 0.956906i 0.406213π-0.406213\pi
0.290397 + 0.956906i 0.406213π0.406213\pi
504504 1323.00 0.116927
505505 0 0
506506 0 0
507507 −3123.00 −0.273565
508508 −1280.00 −0.111793
509509 2790.00 0.242956 0.121478 0.992594i 0.461237π-0.461237\pi
0.121478 + 0.992594i 0.461237π0.461237\pi
510510 0 0
511511 −3514.00 −0.304208
512512 −8733.00 −0.753804
513513 −3348.00 −0.288144
514514 20466.0 1.75626
515515 0 0
516516 804.000 0.0685933
517517 8640.00 0.734984
518518 8358.00 0.708937
519519 −2610.00 −0.220744
520520 0 0
521521 −14862.0 −1.24974 −0.624871 0.780728i 0.714849π-0.714849\pi
−0.624871 + 0.780728i 0.714849π0.714849\pi
522522 2754.00 0.230918
523523 −17660.0 −1.47652 −0.738258 0.674518i 0.764351π-0.764351\pi
−0.738258 + 0.674518i 0.764351π0.764351\pi
524524 1764.00 0.147062
525525 0 0
526526 −7776.00 −0.644581
527527 6720.00 0.555461
528528 7668.00 0.632021
529529 −12167.0 −1.00000
530530 0 0
531531 −1188.00 −0.0970900
532532 868.000 0.0707379
533533 −10812.0 −0.878649
534534 3186.00 0.258187
535535 0 0
536536 1932.00 0.155690
537537 −6948.00 −0.558340
538538 24642.0 1.97471
539539 −1764.00 −0.140966
540540 0 0
541541 −19834.0 −1.57621 −0.788106 0.615540i 0.788938π-0.788938\pi
−0.788106 + 0.615540i 0.788938π0.788938\pi
542542 −16032.0 −1.27054
543543 −318.000 −0.0251320
544544 1890.00 0.148958
545545 0 0
546546 −2142.00 −0.167892
547547 −20972.0 −1.63930 −0.819651 0.572863i 0.805833π-0.805833\pi
−0.819651 + 0.572863i 0.805833π0.805833\pi
548548 2358.00 0.183812
549549 3582.00 0.278463
550550 0 0
551551 −12648.0 −0.977900
552552 0 0
553553 7168.00 0.551201
554554 19542.0 1.49866
555555 0 0
556556 −52.0000 −0.00396635
557557 −21174.0 −1.61072 −0.805360 0.592786i 0.798028π-0.798028\pi
−0.805360 + 0.592786i 0.798028π0.798028\pi
558558 −4320.00 −0.327742
559559 9112.00 0.689439
560560 0 0
561561 4536.00 0.341373
562562 19854.0 1.49020
563563 17772.0 1.33037 0.665187 0.746677i 0.268352π-0.268352\pi
0.665187 + 0.746677i 0.268352π0.268352\pi
564564 −720.000 −0.0537544
565565 0 0
566566 −9780.00 −0.726297
567567 −567.000 −0.0419961
568568 15120.0 1.11694
569569 8250.00 0.607835 0.303917 0.952698i 0.401705π-0.401705\pi
0.303917 + 0.952698i 0.401705π0.401705\pi
570570 0 0
571571 20756.0 1.52121 0.760606 0.649214i 0.224902π-0.224902\pi
0.760606 + 0.649214i 0.224902π0.224902\pi
572572 −1224.00 −0.0894720
573573 −3384.00 −0.246717
574574 6678.00 0.485600
575575 0 0
576576 3897.00 0.281901
577577 −2.00000 −0.000144300 0 −7.21500e−5 1.00000i 0.500023π-0.500023\pi
−7.21500e−5 1.00000i 0.500023π0.500023\pi
578578 −9447.00 −0.679833
579579 −12102.0 −0.868639
580580 0 0
581581 −1428.00 −0.101968
582582 2574.00 0.183326
583583 −17928.0 −1.27359
584584 −10542.0 −0.746971
585585 0 0
586586 −15354.0 −1.08237
587587 −26364.0 −1.85376 −0.926881 0.375354i 0.877521π-0.877521\pi
−0.926881 + 0.375354i 0.877521π0.877521\pi
588588 147.000 0.0103098
589589 19840.0 1.38793
590590 0 0
591591 3942.00 0.274369
592592 28258.0 1.96182
593593 −2298.00 −0.159136 −0.0795679 0.996829i 0.525354π-0.525354\pi
−0.0795679 + 0.996829i 0.525354π0.525354\pi
594594 −2916.00 −0.201422
595595 0 0
596596 −1746.00 −0.119998
597597 15288.0 1.04807
598598 0 0
599599 3072.00 0.209547 0.104773 0.994496i 0.466588π-0.466588\pi
0.104773 + 0.994496i 0.466588π0.466588\pi
600600 0 0
601601 24554.0 1.66652 0.833260 0.552881i 0.186472π-0.186472\pi
0.833260 + 0.552881i 0.186472π0.186472\pi
602602 −5628.00 −0.381030
603603 −828.000 −0.0559184
604604 −232.000 −0.0156290
605605 0 0
606606 3726.00 0.249766
607607 −16832.0 −1.12552 −0.562759 0.826621i 0.690260π-0.690260\pi
−0.562759 + 0.826621i 0.690260π0.690260\pi
608608 5580.00 0.372202
609609 −2142.00 −0.142526
610610 0 0
611611 −8160.00 −0.540292
612612 −378.000 −0.0249669
613613 2482.00 0.163535 0.0817676 0.996651i 0.473943π-0.473943\pi
0.0817676 + 0.996651i 0.473943π0.473943\pi
614614 −1356.00 −0.0891266
615615 0 0
616616 −5292.00 −0.346138
617617 15798.0 1.03080 0.515400 0.856950i 0.327643π-0.327643\pi
0.515400 + 0.856950i 0.327643π0.327643\pi
618618 −504.000 −0.0328056
619619 −15460.0 −1.00386 −0.501930 0.864908i 0.667377π-0.667377\pi
−0.501930 + 0.864908i 0.667377π0.667377\pi
620620 0 0
621621 0 0
622622 15048.0 0.970048
623623 −2478.00 −0.159356
624624 −7242.00 −0.464603
625625 0 0
626626 −16206.0 −1.03470
627627 13392.0 0.852990
628628 −1694.00 −0.107640
629629 16716.0 1.05964
630630 0 0
631631 −7720.00 −0.487050 −0.243525 0.969895i 0.578304π-0.578304\pi
−0.243525 + 0.969895i 0.578304π0.578304\pi
632632 21504.0 1.35345
633633 −9228.00 −0.579431
634634 −30258.0 −1.89542
635635 0 0
636636 1494.00 0.0931462
637637 1666.00 0.103625
638638 −11016.0 −0.683586
639639 −6480.00 −0.401166
640640 0 0
641641 −17262.0 −1.06366 −0.531832 0.846850i 0.678496π-0.678496\pi
−0.531832 + 0.846850i 0.678496π0.678496\pi
642642 −108.000 −0.00663928
643643 12220.0 0.749471 0.374735 0.927132i 0.377734π-0.377734\pi
0.374735 + 0.927132i 0.377734π0.377734\pi
644644 0 0
645645 0 0
646646 15624.0 0.951576
647647 −13560.0 −0.823955 −0.411977 0.911194i 0.635162π-0.635162\pi
−0.411977 + 0.911194i 0.635162π0.635162\pi
648648 −1701.00 −0.103120
649649 4752.00 0.287415
650650 0 0
651651 3360.00 0.202287
652652 2932.00 0.176113
653653 −23094.0 −1.38398 −0.691989 0.721908i 0.743265π-0.743265\pi
−0.691989 + 0.721908i 0.743265π0.743265\pi
654654 13302.0 0.795335
655655 0 0
656656 22578.0 1.34378
657657 4518.00 0.268286
658658 5040.00 0.298601
659659 22548.0 1.33285 0.666423 0.745574i 0.267825π-0.267825\pi
0.666423 + 0.745574i 0.267825π0.267825\pi
660660 0 0
661661 17462.0 1.02752 0.513762 0.857933i 0.328252π-0.328252\pi
0.513762 + 0.857933i 0.328252π0.328252\pi
662662 −24132.0 −1.41679
663663 −4284.00 −0.250945
664664 −4284.00 −0.250379
665665 0 0
666666 −10746.0 −0.625224
667667 0 0
668668 −1176.00 −0.0681150
669669 5664.00 0.327329
670670 0 0
671671 −14328.0 −0.824331
672672 945.000 0.0542473
673673 22462.0 1.28655 0.643274 0.765636i 0.277576π-0.277576\pi
0.643274 + 0.765636i 0.277576π0.277576\pi
674674 −12534.0 −0.716308
675675 0 0
676676 −1041.00 −0.0592285
677677 25554.0 1.45069 0.725347 0.688383i 0.241679π-0.241679\pi
0.725347 + 0.688383i 0.241679π0.241679\pi
678678 −3618.00 −0.204939
679679 −2002.00 −0.113151
680680 0 0
681681 14148.0 0.796112
682682 17280.0 0.970213
683683 −9276.00 −0.519672 −0.259836 0.965653i 0.583669π-0.583669\pi
−0.259836 + 0.965653i 0.583669π0.583669\pi
684684 −1116.00 −0.0623850
685685 0 0
686686 −1029.00 −0.0572703
687687 −5070.00 −0.281561
688688 −19028.0 −1.05441
689689 16932.0 0.936223
690690 0 0
691691 27380.0 1.50736 0.753679 0.657243i 0.228277π-0.228277\pi
0.753679 + 0.657243i 0.228277π0.228277\pi
692692 −870.000 −0.0477925
693693 2268.00 0.124321
694694 −468.000 −0.0255980
695695 0 0
696696 −6426.00 −0.349967
697697 13356.0 0.725817
698698 −37254.0 −2.02018
699699 −414.000 −0.0224019
700700 0 0
701701 25830.0 1.39171 0.695853 0.718184i 0.255027π-0.255027\pi
0.695853 + 0.718184i 0.255027π0.255027\pi
702702 2754.00 0.148067
703703 49352.0 2.64772
704704 −15588.0 −0.834510
705705 0 0
706706 23490.0 1.25221
707707 −2898.00 −0.154159
708708 −396.000 −0.0210206
709709 −6226.00 −0.329792 −0.164896 0.986311i 0.552729π-0.552729\pi
−0.164896 + 0.986311i 0.552729π0.552729\pi
710710 0 0
711711 −9216.00 −0.486114
712712 −7434.00 −0.391293
713713 0 0
714714 2646.00 0.138689
715715 0 0
716716 −2316.00 −0.120884
717717 5688.00 0.296265
718718 −27936.0 −1.45204
719719 −15072.0 −0.781767 −0.390884 0.920440i 0.627831π-0.627831\pi
−0.390884 + 0.920440i 0.627831π0.627831\pi
720720 0 0
721721 392.000 0.0202480
722722 25551.0 1.31705
723723 −10794.0 −0.555233
724724 −106.000 −0.00544124
725725 0 0
726726 −315.000 −0.0161030
727727 32920.0 1.67942 0.839708 0.543038i 0.182726π-0.182726\pi
0.839708 + 0.543038i 0.182726π0.182726\pi
728728 4998.00 0.254448
729729 729.000 0.0370370
730730 0 0
731731 −11256.0 −0.569519
732732 1194.00 0.0602889
733733 6946.00 0.350009 0.175004 0.984568i 0.444006π-0.444006\pi
0.175004 + 0.984568i 0.444006π0.444006\pi
734734 11280.0 0.567238
735735 0 0
736736 0 0
737737 3312.00 0.165535
738738 −8586.00 −0.428259
739739 −2356.00 −0.117276 −0.0586379 0.998279i 0.518676π-0.518676\pi
−0.0586379 + 0.998279i 0.518676π0.518676\pi
740740 0 0
741741 −12648.0 −0.627039
742742 −10458.0 −0.517419
743743 23520.0 1.16133 0.580663 0.814144i 0.302793π-0.302793\pi
0.580663 + 0.814144i 0.302793π0.302793\pi
744744 10080.0 0.496708
745745 0 0
746746 −17610.0 −0.864273
747747 1836.00 0.0899273
748748 1512.00 0.0739094
749749 84.0000 0.00409785
750750 0 0
751751 3008.00 0.146156 0.0730782 0.997326i 0.476718π-0.476718\pi
0.0730782 + 0.997326i 0.476718π0.476718\pi
752752 17040.0 0.826310
753753 −9180.00 −0.444273
754754 10404.0 0.502508
755755 0 0
756756 −189.000 −0.00909241
757757 20770.0 0.997224 0.498612 0.866825i 0.333843π-0.333843\pi
0.498612 + 0.866825i 0.333843π0.333843\pi
758758 −5556.00 −0.266231
759759 0 0
760760 0 0
761761 11538.0 0.549609 0.274804 0.961500i 0.411387π-0.411387\pi
0.274804 + 0.961500i 0.411387π0.411387\pi
762762 −11520.0 −0.547671
763763 −10346.0 −0.490892
764764 −1128.00 −0.0534157
765765 0 0
766766 −6480.00 −0.305655
767767 −4488.00 −0.211281
768768 4539.00 0.213264
769769 8498.00 0.398499 0.199249 0.979949i 0.436150π-0.436150\pi
0.199249 + 0.979949i 0.436150π0.436150\pi
770770 0 0
771771 20466.0 0.955986
772772 −4034.00 −0.188066
773773 32322.0 1.50393 0.751967 0.659200i 0.229105π-0.229105\pi
0.751967 + 0.659200i 0.229105π0.229105\pi
774774 7236.00 0.336037
775775 0 0
776776 −6006.00 −0.277839
777777 8358.00 0.385896
778778 −20358.0 −0.938136
779779 39432.0 1.81360
780780 0 0
781781 25920.0 1.18757
782782 0 0
783783 2754.00 0.125696
784784 −3479.00 −0.158482
785785 0 0
786786 15876.0 0.720456
787787 −26228.0 −1.18796 −0.593982 0.804479i 0.702445π-0.702445\pi
−0.593982 + 0.804479i 0.702445π0.702445\pi
788788 1314.00 0.0594027
789789 −7776.00 −0.350866
790790 0 0
791791 2814.00 0.126491
792792 6804.00 0.305265
793793 13532.0 0.605972
794794 19542.0 0.873450
795795 0 0
796796 5096.00 0.226913
797797 43338.0 1.92611 0.963056 0.269302i 0.0867931π-0.0867931\pi
0.963056 + 0.269302i 0.0867931π0.0867931\pi
798798 7812.00 0.346544
799799 10080.0 0.446314
800800 0 0
801801 3186.00 0.140539
802802 9990.00 0.439849
803803 −18072.0 −0.794206
804804 −276.000 −0.0121067
805805 0 0
806806 −16320.0 −0.713210
807807 24642.0 1.07489
808808 −8694.00 −0.378532
809809 −28902.0 −1.25604 −0.628022 0.778195i 0.716135π-0.716135\pi
−0.628022 + 0.778195i 0.716135π0.716135\pi
810810 0 0
811811 27164.0 1.17615 0.588075 0.808807i 0.299886π-0.299886\pi
0.588075 + 0.808807i 0.299886π0.299886\pi
812812 −714.000 −0.0308577
813813 −16032.0 −0.691595
814814 42984.0 1.85085
815815 0 0
816816 8946.00 0.383790
817817 −33232.0 −1.42306
818818 −16194.0 −0.692188
819819 −2142.00 −0.0913889
820820 0 0
821821 −17202.0 −0.731247 −0.365624 0.930763i 0.619144π-0.619144\pi
−0.365624 + 0.930763i 0.619144π0.619144\pi
822822 21222.0 0.900489
823823 5992.00 0.253789 0.126894 0.991916i 0.459499π-0.459499\pi
0.126894 + 0.991916i 0.459499π0.459499\pi
824824 1176.00 0.0497183
825825 0 0
826826 2772.00 0.116768
827827 −25884.0 −1.08836 −0.544181 0.838968i 0.683159π-0.683159\pi
−0.544181 + 0.838968i 0.683159π0.683159\pi
828828 0 0
829829 −1474.00 −0.0617541 −0.0308770 0.999523i 0.509830π-0.509830\pi
−0.0308770 + 0.999523i 0.509830π0.509830\pi
830830 0 0
831831 19542.0 0.815770
832832 14722.0 0.613454
833833 −2058.00 −0.0856008
834834 −468.000 −0.0194311
835835 0 0
836836 4464.00 0.184678
837837 −4320.00 −0.178400
838838 39276.0 1.61905
839839 33528.0 1.37964 0.689818 0.723983i 0.257690π-0.257690\pi
0.689818 + 0.723983i 0.257690π0.257690\pi
840840 0 0
841841 −13985.0 −0.573414
842842 −966.000 −0.0395375
843843 19854.0 0.811160
844844 −3076.00 −0.125451
845845 0 0
846846 −6480.00 −0.263342
847847 245.000 0.00993896
848848 −35358.0 −1.43184
849849 −9780.00 −0.395346
850850 0 0
851851 0 0
852852 −2160.00 −0.0868549
853853 −1190.00 −0.0477665 −0.0238832 0.999715i 0.507603π-0.507603\pi
−0.0238832 + 0.999715i 0.507603π0.507603\pi
854854 −8358.00 −0.334900
855855 0 0
856856 252.000 0.0100621
857857 −34578.0 −1.37825 −0.689126 0.724642i 0.742005π-0.742005\pi
−0.689126 + 0.724642i 0.742005π0.742005\pi
858858 −11016.0 −0.438322
859859 −44404.0 −1.76373 −0.881865 0.471501i 0.843712π-0.843712\pi
−0.881865 + 0.471501i 0.843712π0.843712\pi
860860 0 0
861861 6678.00 0.264327
862862 7848.00 0.310097
863863 38328.0 1.51182 0.755910 0.654676i 0.227195π-0.227195\pi
0.755910 + 0.654676i 0.227195π0.227195\pi
864864 −1215.00 −0.0478416
865865 0 0
866866 −12966.0 −0.508779
867867 −9447.00 −0.370054
868868 1120.00 0.0437964
869869 36864.0 1.43904
870870 0 0
871871 −3128.00 −0.121686
872872 −31038.0 −1.20537
873873 2574.00 0.0997900
874874 0 0
875875 0 0
876876 1506.00 0.0580856
877877 38842.0 1.49555 0.747777 0.663950i 0.231121π-0.231121\pi
0.747777 + 0.663950i 0.231121π0.231121\pi
878878 −27048.0 −1.03966
879879 −15354.0 −0.589167
880880 0 0
881881 −35046.0 −1.34022 −0.670108 0.742264i 0.733752π-0.733752\pi
−0.670108 + 0.742264i 0.733752π0.733752\pi
882882 1323.00 0.0505076
883883 −14204.0 −0.541339 −0.270670 0.962672i 0.587245π-0.587245\pi
−0.270670 + 0.962672i 0.587245π0.587245\pi
884884 −1428.00 −0.0543313
885885 0 0
886886 15804.0 0.599262
887887 26136.0 0.989359 0.494679 0.869076i 0.335286π-0.335286\pi
0.494679 + 0.869076i 0.335286π0.335286\pi
888888 25074.0 0.947554
889889 8960.00 0.338030
890890 0 0
891891 −2916.00 −0.109640
892892 1888.00 0.0708687
893893 29760.0 1.11521
894894 −15714.0 −0.587869
895895 0 0
896896 −11613.0 −0.432995
897897 0 0
898898 −15930.0 −0.591972
899899 −16320.0 −0.605453
900900 0 0
901901 −20916.0 −0.773377
902902 34344.0 1.26777
903903 −5628.00 −0.207407
904904 8442.00 0.310594
905905 0 0
906906 −2088.00 −0.0765664
907907 9052.00 0.331386 0.165693 0.986177i 0.447014π-0.447014\pi
0.165693 + 0.986177i 0.447014π0.447014\pi
908908 4716.00 0.172363
909909 3726.00 0.135956
910910 0 0
911911 5016.00 0.182423 0.0912116 0.995832i 0.470926π-0.470926\pi
0.0912116 + 0.995832i 0.470926π0.470926\pi
912912 26412.0 0.958979
913913 −7344.00 −0.266211
914914 −47310.0 −1.71212
915915 0 0
916916 −1690.00 −0.0609598
917917 −12348.0 −0.444675
918918 −3402.00 −0.122312
919919 44552.0 1.59917 0.799584 0.600555i 0.205054π-0.205054\pi
0.799584 + 0.600555i 0.205054π0.205054\pi
920920 0 0
921921 −1356.00 −0.0485144
922922 −16110.0 −0.575439
923923 −24480.0 −0.872989
924924 756.000 0.0269162
925925 0 0
926926 9984.00 0.354314
927927 −504.000 −0.0178571
928928 −4590.00 −0.162364
929929 24234.0 0.855858 0.427929 0.903812i 0.359243π-0.359243\pi
0.427929 + 0.903812i 0.359243π0.359243\pi
930930 0 0
931931 −6076.00 −0.213891
932932 −138.000 −0.00485015
933933 15048.0 0.528027
934934 −13644.0 −0.477993
935935 0 0
936936 −6426.00 −0.224402
937937 13894.0 0.484415 0.242208 0.970224i 0.422128π-0.422128\pi
0.242208 + 0.970224i 0.422128π0.422128\pi
938938 1932.00 0.0672516
939939 −16206.0 −0.563219
940940 0 0
941941 46758.0 1.61984 0.809919 0.586542i 0.199511π-0.199511\pi
0.809919 + 0.586542i 0.199511π0.199511\pi
942942 −15246.0 −0.527326
943943 0 0
944944 9372.00 0.323128
945945 0 0
946946 −28944.0 −0.994768
947947 −13812.0 −0.473949 −0.236974 0.971516i 0.576156π-0.576156\pi
−0.236974 + 0.971516i 0.576156π0.576156\pi
948948 −3072.00 −0.105247
949949 17068.0 0.583826
950950 0 0
951951 −30258.0 −1.03174
952952 −6174.00 −0.210190
953953 58518.0 1.98907 0.994535 0.104402i 0.0332930π-0.0332930\pi
0.994535 + 0.104402i 0.0332930π0.0332930\pi
954954 13446.0 0.456321
955955 0 0
956956 1896.00 0.0641433
957957 −11016.0 −0.372097
958958 −24192.0 −0.815875
959959 −16506.0 −0.555794
960960 0 0
961961 −4191.00 −0.140680
962962 −40596.0 −1.36057
963963 −108.000 −0.00361397
964964 −3598.00 −0.120211
965965 0 0
966966 0 0
967967 −19640.0 −0.653133 −0.326567 0.945174i 0.605892π-0.605892\pi
−0.326567 + 0.945174i 0.605892π0.605892\pi
968968 735.000 0.0244047
969969 15624.0 0.517972
970970 0 0
971971 −58308.0 −1.92708 −0.963539 0.267568i 0.913780π-0.913780\pi
−0.963539 + 0.267568i 0.913780π0.913780\pi
972972 243.000 0.00801875
973973 364.000 0.0119931
974974 −49848.0 −1.63987
975975 0 0
976976 −28258.0 −0.926759
977977 23550.0 0.771168 0.385584 0.922673i 0.374000π-0.374000\pi
0.385584 + 0.922673i 0.374000π0.374000\pi
978978 26388.0 0.862776
979979 −12744.0 −0.416037
980980 0 0
981981 13302.0 0.432926
982982 −21420.0 −0.696069
983983 −15768.0 −0.511619 −0.255809 0.966727i 0.582342π-0.582342\pi
−0.255809 + 0.966727i 0.582342π0.582342\pi
984984 20034.0 0.649045
985985 0 0
986986 −12852.0 −0.415102
987987 5040.00 0.162538
988988 −4216.00 −0.135758
989989 0 0
990990 0 0
991991 35264.0 1.13037 0.565186 0.824964i 0.308805π-0.308805\pi
0.565186 + 0.824964i 0.308805π0.308805\pi
992992 7200.00 0.230444
993993 −24132.0 −0.771204
994994 15120.0 0.482472
995995 0 0
996996 612.000 0.0194698
997997 29338.0 0.931940 0.465970 0.884801i 0.345706π-0.345706\pi
0.465970 + 0.884801i 0.345706π0.345706\pi
998998 −27372.0 −0.868182
999999 −10746.0 −0.340329
Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 525.4.a.g.1.1 1
3.2 odd 2 1575.4.a.b.1.1 1
5.2 odd 4 525.4.d.c.274.2 2
5.3 odd 4 525.4.d.c.274.1 2
5.4 even 2 21.4.a.a.1.1 1
15.14 odd 2 63.4.a.c.1.1 1
20.19 odd 2 336.4.a.f.1.1 1
35.4 even 6 147.4.e.i.79.1 2
35.9 even 6 147.4.e.i.67.1 2
35.19 odd 6 147.4.e.g.67.1 2
35.24 odd 6 147.4.e.g.79.1 2
35.34 odd 2 147.4.a.c.1.1 1
40.19 odd 2 1344.4.a.n.1.1 1
40.29 even 2 1344.4.a.ba.1.1 1
60.59 even 2 1008.4.a.v.1.1 1
105.44 odd 6 441.4.e.b.361.1 2
105.59 even 6 441.4.e.d.226.1 2
105.74 odd 6 441.4.e.b.226.1 2
105.89 even 6 441.4.e.d.361.1 2
105.104 even 2 441.4.a.j.1.1 1
140.139 even 2 2352.4.a.r.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
21.4.a.a.1.1 1 5.4 even 2
63.4.a.c.1.1 1 15.14 odd 2
147.4.a.c.1.1 1 35.34 odd 2
147.4.e.g.67.1 2 35.19 odd 6
147.4.e.g.79.1 2 35.24 odd 6
147.4.e.i.67.1 2 35.9 even 6
147.4.e.i.79.1 2 35.4 even 6
336.4.a.f.1.1 1 20.19 odd 2
441.4.a.j.1.1 1 105.104 even 2
441.4.e.b.226.1 2 105.74 odd 6
441.4.e.b.361.1 2 105.44 odd 6
441.4.e.d.226.1 2 105.59 even 6
441.4.e.d.361.1 2 105.89 even 6
525.4.a.g.1.1 1 1.1 even 1 trivial
525.4.d.c.274.1 2 5.3 odd 4
525.4.d.c.274.2 2 5.2 odd 4
1008.4.a.v.1.1 1 60.59 even 2
1344.4.a.n.1.1 1 40.19 odd 2
1344.4.a.ba.1.1 1 40.29 even 2
1575.4.a.b.1.1 1 3.2 odd 2
2352.4.a.r.1.1 1 140.139 even 2