Properties

Label 7225.2.a.bx.1.15
Level 72257225
Weight 22
Character 7225.1
Self dual yes
Analytic conductor 57.69257.692
Analytic rank 11
Dimension 2424
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [7225,2,Mod(1,7225)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(7225, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("7225.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 7225=52172 7225 = 5^{2} \cdot 17^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 7225.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: 57.691915460457.6919154604
Analytic rank: 11
Dimension: 2424
Twist minimal: no (minimal twist has level 425)
Fricke sign: +1+1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.15
Character χ\chi == 7225.1

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+0.555780q22.50339q31.69111q41.39134q6+4.03587q72.05144q8+3.26698q9+0.420560q11+4.23351q12+4.96035q13+2.24306q14+2.24207q16+1.81572q185.04055q1910.1034q21+0.233739q228.05347q23+5.13557q24+2.75686q260.668350q276.82510q280.185558q293.41416q31+5.34898q321.05283q335.52481q36+3.81527q372.80144q3812.4177q39+3.90854q415.61525q425.15014q430.711213q444.47596q466.56400q475.61277q48+9.28828q498.38849q520.871603q530.371456q548.27937q56+12.6185q570.103129q5814.3445q59+3.41024q611.89752q62+13.1851q631.51128q640.585140q66+7.21621q67+20.1610q697.48836q716.70202q72+3.58559q73+2.12045q74+8.52413q76+1.69733q776.90151q78+14.0842q798.12779q81+2.17229q8213.6689q83+17.0859q842.86234q86+0.464523q870.862755q88+15.1176q89+20.0193q91+13.6193q92+8.54699q933.64814q9413.3906q9610.1591q97+5.16224q98+1.37396q99+O(q100)q+0.555780 q^{2} -2.50339 q^{3} -1.69111 q^{4} -1.39134 q^{6} +4.03587 q^{7} -2.05144 q^{8} +3.26698 q^{9} +0.420560 q^{11} +4.23351 q^{12} +4.96035 q^{13} +2.24306 q^{14} +2.24207 q^{16} +1.81572 q^{18} -5.04055 q^{19} -10.1034 q^{21} +0.233739 q^{22} -8.05347 q^{23} +5.13557 q^{24} +2.75686 q^{26} -0.668350 q^{27} -6.82510 q^{28} -0.185558 q^{29} -3.41416 q^{31} +5.34898 q^{32} -1.05283 q^{33} -5.52481 q^{36} +3.81527 q^{37} -2.80144 q^{38} -12.4177 q^{39} +3.90854 q^{41} -5.61525 q^{42} -5.15014 q^{43} -0.711213 q^{44} -4.47596 q^{46} -6.56400 q^{47} -5.61277 q^{48} +9.28828 q^{49} -8.38849 q^{52} -0.871603 q^{53} -0.371456 q^{54} -8.27937 q^{56} +12.6185 q^{57} -0.103129 q^{58} -14.3445 q^{59} +3.41024 q^{61} -1.89752 q^{62} +13.1851 q^{63} -1.51128 q^{64} -0.585140 q^{66} +7.21621 q^{67} +20.1610 q^{69} -7.48836 q^{71} -6.70202 q^{72} +3.58559 q^{73} +2.12045 q^{74} +8.52413 q^{76} +1.69733 q^{77} -6.90151 q^{78} +14.0842 q^{79} -8.12779 q^{81} +2.17229 q^{82} -13.6689 q^{83} +17.0859 q^{84} -2.86234 q^{86} +0.464523 q^{87} -0.862755 q^{88} +15.1176 q^{89} +20.0193 q^{91} +13.6193 q^{92} +8.54699 q^{93} -3.64814 q^{94} -13.3906 q^{96} -10.1591 q^{97} +5.16224 q^{98} +1.37396 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 24q8q2+24q424q8+24q916q13+24q1640q1816q2116q2656q3248q33+24q3648q3832q4388q47+16q4948q52+48q98+O(q100) 24 q - 8 q^{2} + 24 q^{4} - 24 q^{8} + 24 q^{9} - 16 q^{13} + 24 q^{16} - 40 q^{18} - 16 q^{21} - 16 q^{26} - 56 q^{32} - 48 q^{33} + 24 q^{36} - 48 q^{38} - 32 q^{43} - 88 q^{47} + 16 q^{49} - 48 q^{52}+ \cdots - 48 q^{98}+O(q^{100}) Copy content Toggle raw display

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 0.555780 0.392996 0.196498 0.980504i 0.437043π-0.437043\pi
0.196498 + 0.980504i 0.437043π0.437043\pi
33 −2.50339 −1.44533 −0.722667 0.691196i 0.757084π-0.757084\pi
−0.722667 + 0.691196i 0.757084π0.757084\pi
44 −1.69111 −0.845554
55 0 0
66 −1.39134 −0.568010
77 4.03587 1.52542 0.762709 0.646742i 0.223869π-0.223869\pi
0.762709 + 0.646742i 0.223869π0.223869\pi
88 −2.05144 −0.725295
99 3.26698 1.08899
1010 0 0
1111 0.420560 0.126804 0.0634018 0.997988i 0.479805π-0.479805\pi
0.0634018 + 0.997988i 0.479805π0.479805\pi
1212 4.23351 1.22211
1313 4.96035 1.37575 0.687877 0.725828i 0.258543π-0.258543\pi
0.687877 + 0.725828i 0.258543π0.258543\pi
1414 2.24306 0.599482
1515 0 0
1616 2.24207 0.560517
1717 0 0
1818 1.81572 0.427969
1919 −5.04055 −1.15638 −0.578191 0.815901i 0.696241π-0.696241\pi
−0.578191 + 0.815901i 0.696241π0.696241\pi
2020 0 0
2121 −10.1034 −2.20474
2222 0.233739 0.0498333
2323 −8.05347 −1.67927 −0.839633 0.543155i 0.817230π-0.817230\pi
−0.839633 + 0.543155i 0.817230π0.817230\pi
2424 5.13557 1.04829
2525 0 0
2626 2.75686 0.540665
2727 −0.668350 −0.128624
2828 −6.82510 −1.28982
2929 −0.185558 −0.0344572 −0.0172286 0.999852i 0.505484π-0.505484\pi
−0.0172286 + 0.999852i 0.505484π0.505484\pi
3030 0 0
3131 −3.41416 −0.613201 −0.306601 0.951838i 0.599192π-0.599192\pi
−0.306601 + 0.951838i 0.599192π0.599192\pi
3232 5.34898 0.945575
3333 −1.05283 −0.183274
3434 0 0
3535 0 0
3636 −5.52481 −0.920802
3737 3.81527 0.627227 0.313614 0.949551i 0.398460π-0.398460\pi
0.313614 + 0.949551i 0.398460π0.398460\pi
3838 −2.80144 −0.454453
3939 −12.4177 −1.98842
4040 0 0
4141 3.90854 0.610411 0.305206 0.952287i 0.401275π-0.401275\pi
0.305206 + 0.952287i 0.401275π0.401275\pi
4242 −5.61525 −0.866453
4343 −5.15014 −0.785389 −0.392694 0.919669i 0.628457π-0.628457\pi
−0.392694 + 0.919669i 0.628457π0.628457\pi
4444 −0.711213 −0.107219
4545 0 0
4646 −4.47596 −0.659944
4747 −6.56400 −0.957458 −0.478729 0.877963i 0.658902π-0.658902\pi
−0.478729 + 0.877963i 0.658902π0.658902\pi
4848 −5.61277 −0.810134
4949 9.28828 1.32690
5050 0 0
5151 0 0
5252 −8.38849 −1.16327
5353 −0.871603 −0.119724 −0.0598619 0.998207i 0.519066π-0.519066\pi
−0.0598619 + 0.998207i 0.519066π0.519066\pi
5454 −0.371456 −0.0505487
5555 0 0
5656 −8.27937 −1.10638
5757 12.6185 1.67136
5858 −0.103129 −0.0135415
5959 −14.3445 −1.86749 −0.933746 0.357937i 0.883480π-0.883480\pi
−0.933746 + 0.357937i 0.883480π0.883480\pi
6060 0 0
6161 3.41024 0.436637 0.218318 0.975878i 0.429943π-0.429943\pi
0.218318 + 0.975878i 0.429943π0.429943\pi
6262 −1.89752 −0.240985
6363 13.1851 1.66117
6464 −1.51128 −0.188910
6565 0 0
6666 −0.585140 −0.0720257
6767 7.21621 0.881601 0.440800 0.897605i 0.354695π-0.354695\pi
0.440800 + 0.897605i 0.354695π0.354695\pi
6868 0 0
6969 20.1610 2.42710
7070 0 0
7171 −7.48836 −0.888705 −0.444352 0.895852i 0.646566π-0.646566\pi
−0.444352 + 0.895852i 0.646566π0.646566\pi
7272 −6.70202 −0.789841
7373 3.58559 0.419662 0.209831 0.977738i 0.432709π-0.432709\pi
0.209831 + 0.977738i 0.432709π0.432709\pi
7474 2.12045 0.246498
7575 0 0
7676 8.52413 0.977784
7777 1.69733 0.193428
7878 −6.90151 −0.781442
7979 14.0842 1.58459 0.792296 0.610137i 0.208886π-0.208886\pi
0.792296 + 0.610137i 0.208886π0.208886\pi
8080 0 0
8181 −8.12779 −0.903088
8282 2.17229 0.239889
8383 −13.6689 −1.50035 −0.750177 0.661237i 0.770032π-0.770032\pi
−0.750177 + 0.661237i 0.770032π0.770032\pi
8484 17.0859 1.86423
8585 0 0
8686 −2.86234 −0.308654
8787 0.464523 0.0498021
8888 −0.862755 −0.0919700
8989 15.1176 1.60246 0.801231 0.598355i 0.204179π-0.204179\pi
0.801231 + 0.598355i 0.204179π0.204179\pi
9090 0 0
9191 20.0193 2.09860
9292 13.6193 1.41991
9393 8.54699 0.886281
9494 −3.64814 −0.376277
9595 0 0
9696 −13.3906 −1.36667
9797 −10.1591 −1.03150 −0.515751 0.856738i 0.672487π-0.672487\pi
−0.515751 + 0.856738i 0.672487π0.672487\pi
9898 5.16224 0.521465
9999 1.37396 0.138088
100100 0 0
101101 −0.340331 −0.0338642 −0.0169321 0.999857i 0.505390π-0.505390\pi
−0.0169321 + 0.999857i 0.505390π0.505390\pi
102102 0 0
103103 0.688204 0.0678107 0.0339054 0.999425i 0.489206π-0.489206\pi
0.0339054 + 0.999425i 0.489206π0.489206\pi
104104 −10.1759 −0.997827
105105 0 0
106106 −0.484419 −0.0470510
107107 9.68440 0.936226 0.468113 0.883669i 0.344934π-0.344934\pi
0.468113 + 0.883669i 0.344934π0.344934\pi
108108 1.13025 0.108759
109109 10.4494 1.00087 0.500436 0.865774i 0.333173π-0.333173\pi
0.500436 + 0.865774i 0.333173π0.333173\pi
110110 0 0
111111 −9.55113 −0.906553
112112 9.04870 0.855022
113113 9.01565 0.848121 0.424061 0.905634i 0.360604π-0.360604\pi
0.424061 + 0.905634i 0.360604π0.360604\pi
114114 7.01310 0.656837
115115 0 0
116116 0.313798 0.0291354
117117 16.2054 1.49819
118118 −7.97237 −0.733916
119119 0 0
120120 0 0
121121 −10.8231 −0.983921
122122 1.89534 0.171596
123123 −9.78461 −0.882248
124124 5.77372 0.518495
125125 0 0
126126 7.32802 0.652832
127127 −13.6042 −1.20718 −0.603590 0.797295i 0.706264π-0.706264\pi
−0.603590 + 0.797295i 0.706264π0.706264\pi
128128 −11.5379 −1.01982
129129 12.8928 1.13515
130130 0 0
131131 13.5224 1.18145 0.590727 0.806871i 0.298841π-0.298841\pi
0.590727 + 0.806871i 0.298841π0.298841\pi
132132 1.78044 0.154968
133133 −20.3430 −1.76397
134134 4.01063 0.346465
135135 0 0
136136 0 0
137137 8.57682 0.732768 0.366384 0.930464i 0.380596π-0.380596\pi
0.366384 + 0.930464i 0.380596π0.380596\pi
138138 11.2051 0.953840
139139 13.1182 1.11267 0.556336 0.830958i 0.312207π-0.312207\pi
0.556336 + 0.830958i 0.312207π0.312207\pi
140140 0 0
141141 16.4323 1.38385
142142 −4.16188 −0.349257
143143 2.08612 0.174450
144144 7.32478 0.610398
145145 0 0
146146 1.99280 0.164925
147147 −23.2522 −1.91781
148148 −6.45204 −0.530355
149149 −8.25712 −0.676450 −0.338225 0.941065i 0.609826π-0.609826\pi
−0.338225 + 0.941065i 0.609826π0.609826\pi
150150 0 0
151151 6.34217 0.516118 0.258059 0.966129i 0.416917π-0.416917\pi
0.258059 + 0.966129i 0.416917π0.416917\pi
152152 10.3404 0.838718
153153 0 0
154154 0.943340 0.0760165
155155 0 0
156156 20.9997 1.68132
157157 −21.7433 −1.73531 −0.867653 0.497169i 0.834373π-0.834373\pi
−0.867653 + 0.497169i 0.834373π0.834373\pi
158158 7.82769 0.622738
159159 2.18196 0.173041
160160 0 0
161161 −32.5028 −2.56158
162162 −4.51726 −0.354910
163163 −13.5699 −1.06288 −0.531440 0.847096i 0.678349π-0.678349\pi
−0.531440 + 0.847096i 0.678349π0.678349\pi
164164 −6.60976 −0.516136
165165 0 0
166166 −7.59688 −0.589633
167167 −15.9981 −1.23797 −0.618986 0.785402i 0.712456π-0.712456\pi
−0.618986 + 0.785402i 0.712456π0.712456\pi
168168 20.7265 1.59909
169169 11.6051 0.892697
170170 0 0
171171 −16.4674 −1.25929
172172 8.70944 0.664089
173173 −2.51999 −0.191591 −0.0957955 0.995401i 0.530539π-0.530539\pi
−0.0957955 + 0.995401i 0.530539π0.530539\pi
174174 0.258173 0.0195720
175175 0 0
176176 0.942923 0.0710755
177177 35.9099 2.69915
178178 8.40206 0.629761
179179 7.45781 0.557423 0.278711 0.960375i 0.410093π-0.410093\pi
0.278711 + 0.960375i 0.410093π0.410093\pi
180180 0 0
181181 16.3032 1.21181 0.605904 0.795538i 0.292812π-0.292812\pi
0.605904 + 0.795538i 0.292812π0.292812\pi
182182 11.1263 0.824740
183183 −8.53718 −0.631086
184184 16.5212 1.21796
185185 0 0
186186 4.75024 0.348305
187187 0 0
188188 11.1004 0.809583
189189 −2.69738 −0.196205
190190 0 0
191191 4.90447 0.354875 0.177437 0.984132i 0.443219π-0.443219\pi
0.177437 + 0.984132i 0.443219π0.443219\pi
192192 3.78332 0.273038
193193 6.29053 0.452802 0.226401 0.974034i 0.427304π-0.427304\pi
0.226401 + 0.974034i 0.427304π0.427304\pi
194194 −5.64624 −0.405376
195195 0 0
196196 −15.7075 −1.12196
197197 −22.8122 −1.62530 −0.812650 0.582752i 0.801976π-0.801976\pi
−0.812650 + 0.582752i 0.801976π0.801976\pi
198198 0.763619 0.0542680
199199 −23.4002 −1.65880 −0.829398 0.558658i 0.811317π-0.811317\pi
−0.829398 + 0.558658i 0.811317π0.811317\pi
200200 0 0
201201 −18.0650 −1.27421
202202 −0.189149 −0.0133085
203203 −0.748887 −0.0525615
204204 0 0
205205 0 0
206206 0.382490 0.0266493
207207 −26.3105 −1.82871
208208 11.1214 0.771133
209209 −2.11986 −0.146633
210210 0 0
211211 −1.80689 −0.124392 −0.0621959 0.998064i 0.519810π-0.519810\pi
−0.0621959 + 0.998064i 0.519810π0.519810\pi
212212 1.47398 0.101233
213213 18.7463 1.28448
214214 5.38239 0.367933
215215 0 0
216216 1.37108 0.0932904
217217 −13.7791 −0.935388
218218 5.80757 0.393338
219219 −8.97614 −0.606552
220220 0 0
221221 0 0
222222 −5.30832 −0.356271
223223 8.89829 0.595874 0.297937 0.954586i 0.403702π-0.403702\pi
0.297937 + 0.954586i 0.403702π0.403702\pi
224224 21.5878 1.44240
225225 0 0
226226 5.01072 0.333308
227227 16.6329 1.10397 0.551983 0.833855i 0.313871π-0.313871\pi
0.551983 + 0.833855i 0.313871π0.313871\pi
228228 −21.3392 −1.41323
229229 1.37325 0.0907468 0.0453734 0.998970i 0.485552π-0.485552\pi
0.0453734 + 0.998970i 0.485552π0.485552\pi
230230 0 0
231231 −4.24908 −0.279569
232232 0.380661 0.0249916
233233 1.66320 0.108960 0.0544800 0.998515i 0.482650π-0.482650\pi
0.0544800 + 0.998515i 0.482650π0.482650\pi
234234 9.00661 0.588780
235235 0 0
236236 24.2581 1.57907
237237 −35.2582 −2.29027
238238 0 0
239239 −18.0943 −1.17042 −0.585212 0.810880i 0.698989π-0.698989\pi
−0.585212 + 0.810880i 0.698989π0.698989\pi
240240 0 0
241241 7.01381 0.451799 0.225900 0.974151i 0.427468π-0.427468\pi
0.225900 + 0.974151i 0.427468π0.427468\pi
242242 −6.01528 −0.386677
243243 22.3521 1.43389
244244 −5.76709 −0.369200
245245 0 0
246246 −5.43809 −0.346720
247247 −25.0029 −1.59090
248248 7.00396 0.444752
249249 34.2186 2.16851
250250 0 0
251251 −5.17763 −0.326809 −0.163405 0.986559i 0.552248π-0.552248\pi
−0.163405 + 0.986559i 0.552248π0.552248\pi
252252 −22.2975 −1.40461
253253 −3.38697 −0.212937
254254 −7.56096 −0.474417
255255 0 0
256256 −3.38998 −0.211874
257257 −2.70058 −0.168457 −0.0842287 0.996446i 0.526843π-0.526843\pi
−0.0842287 + 0.996446i 0.526843π0.526843\pi
258258 7.16557 0.446109
259259 15.3980 0.956783
260260 0 0
261261 −0.606212 −0.0375236
262262 7.51545 0.464306
263263 −24.3885 −1.50386 −0.751931 0.659242i 0.770877π-0.770877\pi
−0.751931 + 0.659242i 0.770877π0.770877\pi
264264 2.15981 0.132927
265265 0 0
266266 −11.3063 −0.693231
267267 −37.8453 −2.31610
268268 −12.2034 −0.745442
269269 −7.65414 −0.466681 −0.233340 0.972395i 0.574966π-0.574966\pi
−0.233340 + 0.972395i 0.574966π0.574966\pi
270270 0 0
271271 0.0146097 0.000887478 0 0.000443739 1.00000i 0.499859π-0.499859\pi
0.000443739 1.00000i 0.499859π0.499859\pi
272272 0 0
273273 −50.1163 −3.03318
274274 4.76683 0.287974
275275 0 0
276276 −34.0945 −2.05225
277277 −2.43015 −0.146014 −0.0730068 0.997331i 0.523259π-0.523259\pi
−0.0730068 + 0.997331i 0.523259π0.523259\pi
278278 7.29083 0.437275
279279 −11.1540 −0.667772
280280 0 0
281281 7.50385 0.447642 0.223821 0.974630i 0.428147π-0.428147\pi
0.223821 + 0.974630i 0.428147π0.428147\pi
282282 9.13273 0.543846
283283 −8.59847 −0.511126 −0.255563 0.966792i 0.582261π-0.582261\pi
−0.255563 + 0.966792i 0.582261π0.582261\pi
284284 12.6636 0.751448
285285 0 0
286286 1.15943 0.0685583
287287 15.7744 0.931131
288288 17.4750 1.02972
289289 0 0
290290 0 0
291291 25.4323 1.49087
292292 −6.06362 −0.354847
293293 −20.6490 −1.20633 −0.603164 0.797617i 0.706094π-0.706094\pi
−0.603164 + 0.797617i 0.706094π0.706094\pi
294294 −12.9231 −0.753691
295295 0 0
296296 −7.82682 −0.454925
297297 −0.281081 −0.0163100
298298 −4.58914 −0.265842
299299 −39.9480 −2.31025
300300 0 0
301301 −20.7853 −1.19805
302302 3.52485 0.202832
303303 0.851981 0.0489450
304304 −11.3013 −0.648172
305305 0 0
306306 0 0
307307 −29.4692 −1.68190 −0.840949 0.541115i 0.818002π-0.818002\pi
−0.840949 + 0.541115i 0.818002π0.818002\pi
308308 −2.87036 −0.163554
309309 −1.72284 −0.0980092
310310 0 0
311311 4.29068 0.243302 0.121651 0.992573i 0.461181π-0.461181\pi
0.121651 + 0.992573i 0.461181π0.461181\pi
312312 25.4742 1.44219
313313 10.5224 0.594761 0.297381 0.954759i 0.403887π-0.403887\pi
0.297381 + 0.954759i 0.403887π0.403887\pi
314314 −12.0845 −0.681968
315315 0 0
316316 −23.8178 −1.33986
317317 −15.2781 −0.858105 −0.429052 0.903280i 0.641152π-0.641152\pi
−0.429052 + 0.903280i 0.641152π0.641152\pi
318318 1.21269 0.0680044
319319 −0.0780381 −0.00436929
320320 0 0
321321 −24.2439 −1.35316
322322 −18.0644 −1.00669
323323 0 0
324324 13.7450 0.763610
325325 0 0
326326 −7.54190 −0.417707
327327 −26.1590 −1.44660
328328 −8.01815 −0.442728
329329 −26.4915 −1.46052
330330 0 0
331331 −12.7193 −0.699114 −0.349557 0.936915i 0.613668π-0.613668\pi
−0.349557 + 0.936915i 0.613668π0.613668\pi
332332 23.1156 1.26863
333333 12.4644 0.683046
334334 −8.89144 −0.486518
335335 0 0
336336 −22.6525 −1.23579
337337 1.89743 0.103360 0.0516798 0.998664i 0.483542π-0.483542\pi
0.0516798 + 0.998664i 0.483542π0.483542\pi
338338 6.44986 0.350826
339339 −22.5697 −1.22582
340340 0 0
341341 −1.43586 −0.0777561
342342 −9.15224 −0.494896
343343 9.23521 0.498654
344344 10.5652 0.569638
345345 0 0
346346 −1.40056 −0.0752944
347347 −25.5714 −1.37275 −0.686373 0.727250i 0.740798π-0.740798\pi
−0.686373 + 0.727250i 0.740798π0.740798\pi
348348 −0.785560 −0.0421104
349349 15.3328 0.820746 0.410373 0.911918i 0.365399π-0.365399\pi
0.410373 + 0.911918i 0.365399π0.365399\pi
350350 0 0
351351 −3.31525 −0.176955
352352 2.24957 0.119902
353353 −20.0627 −1.06783 −0.533915 0.845538i 0.679280π-0.679280\pi
−0.533915 + 0.845538i 0.679280π0.679280\pi
354354 19.9580 1.06075
355355 0 0
356356 −25.5655 −1.35497
357357 0 0
358358 4.14490 0.219065
359359 −16.7709 −0.885137 −0.442568 0.896735i 0.645933π-0.645933\pi
−0.442568 + 0.896735i 0.645933π0.645933\pi
360360 0 0
361361 6.40719 0.337221
362362 9.06099 0.476235
363363 27.0945 1.42210
364364 −33.8549 −1.77448
365365 0 0
366366 −4.74479 −0.248014
367367 9.66088 0.504294 0.252147 0.967689i 0.418863π-0.418863\pi
0.252147 + 0.967689i 0.418863π0.418863\pi
368368 −18.0564 −0.941256
369369 12.7691 0.664733
370370 0 0
371371 −3.51768 −0.182629
372372 −14.4539 −0.749399
373373 −8.84764 −0.458113 −0.229057 0.973413i 0.573564π-0.573564\pi
−0.229057 + 0.973413i 0.573564π0.573564\pi
374374 0 0
375375 0 0
376376 13.4657 0.694440
377377 −0.920430 −0.0474046
378378 −1.49915 −0.0771078
379379 −9.05019 −0.464877 −0.232438 0.972611i 0.574670π-0.574670\pi
−0.232438 + 0.972611i 0.574670π0.574670\pi
380380 0 0
381381 34.0568 1.74478
382382 2.72580 0.139464
383383 −16.4906 −0.842631 −0.421315 0.906914i 0.638431π-0.638431\pi
−0.421315 + 0.906914i 0.638431π0.638431\pi
384384 28.8839 1.47398
385385 0 0
386386 3.49615 0.177949
387387 −16.8254 −0.855282
388388 17.1802 0.872192
389389 −26.3924 −1.33815 −0.669074 0.743196i 0.733309π-0.733309\pi
−0.669074 + 0.743196i 0.733309π0.733309\pi
390390 0 0
391391 0 0
392392 −19.0544 −0.962392
393393 −33.8518 −1.70760
394394 −12.6785 −0.638736
395395 0 0
396396 −2.32352 −0.116761
397397 −0.897712 −0.0450549 −0.0225274 0.999746i 0.507171π-0.507171\pi
−0.0225274 + 0.999746i 0.507171π0.507171\pi
398398 −13.0054 −0.651900
399399 50.9266 2.54952
400400 0 0
401401 −15.2264 −0.760371 −0.380186 0.924910i 0.624140π-0.624140\pi
−0.380186 + 0.924910i 0.624140π0.624140\pi
402402 −10.0402 −0.500758
403403 −16.9354 −0.843614
404404 0.575536 0.0286340
405405 0 0
406406 −0.416216 −0.0206565
407407 1.60455 0.0795346
408408 0 0
409409 5.69707 0.281702 0.140851 0.990031i 0.455016π-0.455016\pi
0.140851 + 0.990031i 0.455016π0.455016\pi
410410 0 0
411411 −21.4712 −1.05909
412412 −1.16383 −0.0573377
413413 −57.8925 −2.84870
414414 −14.6229 −0.718674
415415 0 0
416416 26.5328 1.30088
417417 −32.8400 −1.60818
418418 −1.17817 −0.0576263
419419 −2.42262 −0.118353 −0.0591764 0.998248i 0.518847π-0.518847\pi
−0.0591764 + 0.998248i 0.518847π0.518847\pi
420420 0 0
421421 35.5336 1.73180 0.865901 0.500215i 0.166746π-0.166746\pi
0.865901 + 0.500215i 0.166746π0.166746\pi
422422 −1.00424 −0.0488854
423423 −21.4445 −1.04266
424424 1.78804 0.0868351
425425 0 0
426426 10.4188 0.504793
427427 13.7633 0.666053
428428 −16.3774 −0.791630
429429 −5.22239 −0.252139
430430 0 0
431431 11.1438 0.536778 0.268389 0.963311i 0.413509π-0.413509\pi
0.268389 + 0.963311i 0.413509π0.413509\pi
432432 −1.49849 −0.0720959
433433 −24.2605 −1.16589 −0.582944 0.812513i 0.698099π-0.698099\pi
−0.582944 + 0.812513i 0.698099π0.698099\pi
434434 −7.65816 −0.367603
435435 0 0
436436 −17.6711 −0.846292
437437 40.5940 1.94187
438438 −4.98876 −0.238372
439439 18.9055 0.902312 0.451156 0.892445i 0.351012π-0.351012\pi
0.451156 + 0.892445i 0.351012π0.351012\pi
440440 0 0
441441 30.3446 1.44498
442442 0 0
443443 8.80318 0.418252 0.209126 0.977889i 0.432938π-0.432938\pi
0.209126 + 0.977889i 0.432938π0.432938\pi
444444 16.1520 0.766540
445445 0 0
446446 4.94549 0.234176
447447 20.6708 0.977697
448448 −6.09932 −0.288166
449449 −37.8204 −1.78486 −0.892428 0.451190i 0.851000π-0.851000\pi
−0.892428 + 0.451190i 0.851000π0.851000\pi
450450 0 0
451451 1.64377 0.0774023
452452 −15.2464 −0.717133
453453 −15.8769 −0.745964
454454 9.24425 0.433854
455455 0 0
456456 −25.8861 −1.21223
457457 −1.10481 −0.0516807 −0.0258404 0.999666i 0.508226π-0.508226\pi
−0.0258404 + 0.999666i 0.508226π0.508226\pi
458458 0.763223 0.0356631
459459 0 0
460460 0 0
461461 5.67143 0.264145 0.132072 0.991240i 0.457837π-0.457837\pi
0.132072 + 0.991240i 0.457837π0.457837\pi
462462 −2.36155 −0.109869
463463 −8.91271 −0.414209 −0.207104 0.978319i 0.566404π-0.566404\pi
−0.207104 + 0.978319i 0.566404π0.566404\pi
464464 −0.416032 −0.0193138
465465 0 0
466466 0.924374 0.0428208
467467 10.4339 0.482822 0.241411 0.970423i 0.422390π-0.422390\pi
0.241411 + 0.970423i 0.422390π0.422390\pi
468468 −27.4050 −1.26680
469469 29.1237 1.34481
470470 0 0
471471 54.4321 2.50810
472472 29.4269 1.35448
473473 −2.16594 −0.0995901
474474 −19.5958 −0.900064
475475 0 0
476476 0 0
477477 −2.84751 −0.130378
478478 −10.0565 −0.459972
479479 −33.0306 −1.50921 −0.754603 0.656181i 0.772171π-0.772171\pi
−0.754603 + 0.656181i 0.772171π0.772171\pi
480480 0 0
481481 18.9251 0.862910
482482 3.89814 0.177555
483483 81.3673 3.70234
484484 18.3031 0.831959
485485 0 0
486486 12.4228 0.563512
487487 −25.3479 −1.14862 −0.574312 0.818636i 0.694730π-0.694730\pi
−0.574312 + 0.818636i 0.694730π0.694730\pi
488488 −6.99592 −0.316690
489489 33.9709 1.53622
490490 0 0
491491 26.0273 1.17460 0.587298 0.809371i 0.300192π-0.300192\pi
0.587298 + 0.809371i 0.300192π0.300192\pi
492492 16.5468 0.745989
493493 0 0
494494 −13.8961 −0.625216
495495 0 0
496496 −7.65478 −0.343710
497497 −30.2221 −1.35565
498498 19.0180 0.852216
499499 18.2209 0.815679 0.407840 0.913054i 0.366282π-0.366282\pi
0.407840 + 0.913054i 0.366282π0.366282\pi
500500 0 0
501501 40.0496 1.78929
502502 −2.87762 −0.128435
503503 20.0595 0.894407 0.447204 0.894432i 0.352420π-0.352420\pi
0.447204 + 0.894432i 0.352420π0.352420\pi
504504 −27.0485 −1.20484
505505 0 0
506506 −1.88241 −0.0836833
507507 −29.0520 −1.29025
508508 23.0062 1.02074
509509 −8.75911 −0.388241 −0.194120 0.980978i 0.562185π-0.562185\pi
−0.194120 + 0.980978i 0.562185π0.562185\pi
510510 0 0
511511 14.4710 0.640159
512512 21.1917 0.936551
513513 3.36886 0.148739
514514 −1.50093 −0.0662030
515515 0 0
516516 −21.8032 −0.959831
517517 −2.76056 −0.121409
518518 8.55788 0.376011
519519 6.30852 0.276913
520520 0 0
521521 −20.5856 −0.901870 −0.450935 0.892557i 0.648909π-0.648909\pi
−0.450935 + 0.892557i 0.648909π0.648909\pi
522522 −0.336921 −0.0147466
523523 36.8267 1.61032 0.805159 0.593059i 0.202080π-0.202080\pi
0.805159 + 0.593059i 0.202080π0.202080\pi
524524 −22.8678 −0.998984
525525 0 0
526526 −13.5547 −0.591011
527527 0 0
528528 −2.36051 −0.102728
529529 41.8584 1.81993
530530 0 0
531531 −46.8631 −2.03368
532532 34.4023 1.49153
533533 19.3877 0.839775
534534 −21.0337 −0.910215
535535 0 0
536536 −14.8037 −0.639421
537537 −18.6698 −0.805663
538538 −4.25401 −0.183404
539539 3.90628 0.168255
540540 0 0
541541 −39.3467 −1.69165 −0.845823 0.533464i 0.820890π-0.820890\pi
−0.845823 + 0.533464i 0.820890π0.820890\pi
542542 0.00811979 0.000348775 0
543543 −40.8133 −1.75147
544544 0 0
545545 0 0
546546 −27.8536 −1.19203
547547 16.4348 0.702702 0.351351 0.936244i 0.385722π-0.385722\pi
0.351351 + 0.936244i 0.385722π0.385722\pi
548548 −14.5043 −0.619595
549549 11.1412 0.475494
550550 0 0
551551 0.935313 0.0398457
552552 −41.3592 −1.76036
553553 56.8419 2.41716
554554 −1.35063 −0.0573827
555555 0 0
556556 −22.1843 −0.940824
557557 −8.41654 −0.356620 −0.178310 0.983974i 0.557063π-0.557063\pi
−0.178310 + 0.983974i 0.557063π0.557063\pi
558558 −6.19916 −0.262431
559559 −25.5465 −1.08050
560560 0 0
561561 0 0
562562 4.17049 0.175921
563563 −12.6973 −0.535126 −0.267563 0.963540i 0.586218π-0.586218\pi
−0.267563 + 0.963540i 0.586218π0.586218\pi
564564 −27.7888 −1.17012
565565 0 0
566566 −4.77886 −0.200870
567567 −32.8027 −1.37759
568568 15.3619 0.644573
569569 16.8526 0.706499 0.353249 0.935529i 0.385077π-0.385077\pi
0.353249 + 0.935529i 0.385077π0.385077\pi
570570 0 0
571571 4.03344 0.168794 0.0843972 0.996432i 0.473104π-0.473104\pi
0.0843972 + 0.996432i 0.473104π0.473104\pi
572572 −3.52786 −0.147507
573573 −12.2778 −0.512913
574574 8.76707 0.365931
575575 0 0
576576 −4.93731 −0.205721
577577 12.3496 0.514119 0.257060 0.966396i 0.417246π-0.417246\pi
0.257060 + 0.966396i 0.417246π0.417246\pi
578578 0 0
579579 −15.7477 −0.654451
580580 0 0
581581 −55.1659 −2.28867
582582 14.1347 0.585904
583583 −0.366561 −0.0151814
584584 −7.35564 −0.304378
585585 0 0
586586 −11.4763 −0.474082
587587 36.6844 1.51413 0.757064 0.653341i 0.226633π-0.226633\pi
0.757064 + 0.653341i 0.226633π0.226633\pi
588588 39.3220 1.62161
589589 17.2093 0.709095
590590 0 0
591591 57.1078 2.34910
592592 8.55410 0.351571
593593 17.1445 0.704041 0.352021 0.935992i 0.385495π-0.385495\pi
0.352021 + 0.935992i 0.385495π0.385495\pi
594594 −0.156219 −0.00640976
595595 0 0
596596 13.9637 0.571975
597597 58.5799 2.39752
598598 −22.2023 −0.907920
599599 19.1061 0.780654 0.390327 0.920676i 0.372362π-0.372362\pi
0.390327 + 0.920676i 0.372362π0.372362\pi
600600 0 0
601601 3.60770 0.147161 0.0735807 0.997289i 0.476557π-0.476557\pi
0.0735807 + 0.997289i 0.476557π0.476557\pi
602602 −11.5521 −0.470827
603603 23.5752 0.960057
604604 −10.7253 −0.436406
605605 0 0
606606 0.473514 0.0192352
607607 24.0681 0.976893 0.488447 0.872594i 0.337564π-0.337564\pi
0.488447 + 0.872594i 0.337564π0.337564\pi
608608 −26.9618 −1.09345
609609 1.87476 0.0759690
610610 0 0
611611 −32.5597 −1.31723
612612 0 0
613613 −1.37144 −0.0553919 −0.0276959 0.999616i 0.508817π-0.508817\pi
−0.0276959 + 0.999616i 0.508817π0.508817\pi
614614 −16.3784 −0.660978
615615 0 0
616616 −3.48197 −0.140293
617617 −9.37017 −0.377229 −0.188614 0.982051i 0.560400π-0.560400\pi
−0.188614 + 0.982051i 0.560400π0.560400\pi
618618 −0.957522 −0.0385172
619619 −26.7267 −1.07424 −0.537118 0.843507i 0.680487π-0.680487\pi
−0.537118 + 0.843507i 0.680487π0.680487\pi
620620 0 0
621621 5.38254 0.215994
622622 2.38467 0.0956168
623623 61.0127 2.44442
624624 −27.8413 −1.11454
625625 0 0
626626 5.84814 0.233739
627627 5.30683 0.211934
628628 36.7703 1.46730
629629 0 0
630630 0 0
631631 −0.0544273 −0.00216672 −0.00108336 0.999999i 0.500345π-0.500345\pi
−0.00108336 + 0.999999i 0.500345π0.500345\pi
632632 −28.8929 −1.14930
633633 4.52337 0.179788
634634 −8.49127 −0.337231
635635 0 0
636636 −3.68994 −0.146316
637637 46.0731 1.82548
638638 −0.0433720 −0.00171711
639639 −24.4643 −0.967793
640640 0 0
641641 −35.0538 −1.38454 −0.692272 0.721637i 0.743390π-0.743390\pi
−0.692272 + 0.721637i 0.743390π0.743390\pi
642642 −13.4742 −0.531786
643643 31.7691 1.25285 0.626425 0.779481i 0.284517π-0.284517\pi
0.626425 + 0.779481i 0.284517π0.284517\pi
644644 54.9658 2.16596
645645 0 0
646646 0 0
647647 −47.2437 −1.85734 −0.928671 0.370904i 0.879048π-0.879048\pi
−0.928671 + 0.370904i 0.879048π0.879048\pi
648648 16.6737 0.655005
649649 −6.03271 −0.236805
650650 0 0
651651 34.4946 1.35195
652652 22.9483 0.898723
653653 −18.2590 −0.714530 −0.357265 0.934003i 0.616291π-0.616291\pi
−0.357265 + 0.934003i 0.616291π0.616291\pi
654654 −14.5386 −0.568506
655655 0 0
656656 8.76320 0.342146
657657 11.7140 0.457008
658658 −14.7234 −0.573979
659659 31.0240 1.20852 0.604261 0.796786i 0.293468π-0.293468\pi
0.604261 + 0.796786i 0.293468π0.293468\pi
660660 0 0
661661 −26.5079 −1.03104 −0.515519 0.856878i 0.672401π-0.672401\pi
−0.515519 + 0.856878i 0.672401π0.672401\pi
662662 −7.06911 −0.274749
663663 0 0
664664 28.0409 1.08820
665665 0 0
666666 6.92747 0.268434
667667 1.49438 0.0578627
668668 27.0546 1.04677
669669 −22.2759 −0.861237
670670 0 0
671671 1.43421 0.0553671
672672 −54.0428 −2.08475
673673 −42.1664 −1.62539 −0.812697 0.582687i 0.802001π-0.802001\pi
−0.812697 + 0.582687i 0.802001π0.802001\pi
674674 1.05455 0.0406199
675675 0 0
676676 −19.6254 −0.754824
677677 −9.02111 −0.346710 −0.173355 0.984859i 0.555461π-0.555461\pi
−0.173355 + 0.984859i 0.555461π0.555461\pi
678678 −12.5438 −0.481741
679679 −41.0009 −1.57347
680680 0 0
681681 −41.6388 −1.59560
682682 −0.798022 −0.0305578
683683 32.1144 1.22883 0.614413 0.788985i 0.289393π-0.289393\pi
0.614413 + 0.788985i 0.289393π0.289393\pi
684684 27.8481 1.06480
685685 0 0
686686 5.13274 0.195969
687687 −3.43778 −0.131159
688688 −11.5470 −0.440223
689689 −4.32345 −0.164711
690690 0 0
691691 −8.79278 −0.334493 −0.167247 0.985915i 0.553488π-0.553488\pi
−0.167247 + 0.985915i 0.553488π0.553488\pi
692692 4.26157 0.162001
693693 5.54513 0.210642
694694 −14.2121 −0.539483
695695 0 0
696696 −0.952944 −0.0361212
697697 0 0
698698 8.52166 0.322549
699699 −4.16365 −0.157484
700700 0 0
701701 19.0206 0.718399 0.359199 0.933261i 0.383050π-0.383050\pi
0.359199 + 0.933261i 0.383050π0.383050\pi
702702 −1.84255 −0.0695425
703703 −19.2311 −0.725314
704704 −0.635583 −0.0239544
705705 0 0
706706 −11.1504 −0.419652
707707 −1.37353 −0.0516570
708708 −60.7275 −2.28228
709709 −21.9528 −0.824454 −0.412227 0.911081i 0.635249π-0.635249\pi
−0.412227 + 0.911081i 0.635249π0.635249\pi
710710 0 0
711711 46.0126 1.72561
712712 −31.0129 −1.16226
713713 27.4959 1.02973
714714 0 0
715715 0 0
716716 −12.6120 −0.471331
717717 45.2972 1.69166
718718 −9.32095 −0.347855
719719 36.9733 1.37887 0.689436 0.724346i 0.257858π-0.257858\pi
0.689436 + 0.724346i 0.257858π0.257858\pi
720720 0 0
721721 2.77750 0.103440
722722 3.56099 0.132526
723723 −17.5583 −0.653001
724724 −27.5705 −1.02465
725725 0 0
726726 15.0586 0.558877
727727 −44.1513 −1.63748 −0.818741 0.574163i 0.805328π-0.805328\pi
−0.818741 + 0.574163i 0.805328π0.805328\pi
728728 −41.0686 −1.52210
729729 −31.5727 −1.16936
730730 0 0
731731 0 0
732732 14.4373 0.533618
733733 5.30089 0.195793 0.0978965 0.995197i 0.468789π-0.468789\pi
0.0978965 + 0.995197i 0.468789π0.468789\pi
734734 5.36932 0.198185
735735 0 0
736736 −43.0779 −1.58787
737737 3.03485 0.111790
738738 7.09681 0.261237
739739 2.64136 0.0971642 0.0485821 0.998819i 0.484530π-0.484530\pi
0.0485821 + 0.998819i 0.484530π0.484530\pi
740740 0 0
741741 62.5921 2.29938
742742 −1.95506 −0.0717723
743743 11.7618 0.431497 0.215748 0.976449i 0.430781π-0.430781\pi
0.215748 + 0.976449i 0.430781π0.430781\pi
744744 −17.5337 −0.642815
745745 0 0
746746 −4.91734 −0.180037
747747 −44.6559 −1.63387
748748 0 0
749749 39.0850 1.42814
750750 0 0
751751 15.3736 0.560990 0.280495 0.959855i 0.409501π-0.409501\pi
0.280495 + 0.959855i 0.409501π0.409501\pi
752752 −14.7169 −0.536671
753753 12.9617 0.472349
754754 −0.511556 −0.0186298
755755 0 0
756756 4.56156 0.165902
757757 6.04560 0.219731 0.109866 0.993946i 0.464958π-0.464958\pi
0.109866 + 0.993946i 0.464958π0.464958\pi
758758 −5.02991 −0.182695
759759 8.47891 0.307765
760760 0 0
761761 −13.0506 −0.473084 −0.236542 0.971621i 0.576014π-0.576014\pi
−0.236542 + 0.971621i 0.576014π0.576014\pi
762762 18.9281 0.685691
763763 42.1725 1.52675
764764 −8.29399 −0.300066
765765 0 0
766766 −9.16515 −0.331150
767767 −71.1536 −2.56921
768768 8.48645 0.306228
769769 −33.3051 −1.20101 −0.600507 0.799620i 0.705034π-0.705034\pi
−0.600507 + 0.799620i 0.705034π0.705034\pi
770770 0 0
771771 6.76061 0.243477
772772 −10.6380 −0.382869
773773 10.2351 0.368131 0.184065 0.982914i 0.441074π-0.441074\pi
0.184065 + 0.982914i 0.441074π0.441074\pi
774774 −9.35121 −0.336122
775775 0 0
776776 20.8409 0.748144
777777 −38.5472 −1.38287
778778 −14.6684 −0.525886
779779 −19.7012 −0.705869
780780 0 0
781781 −3.14930 −0.112691
782782 0 0
783783 0.124017 0.00443202
784784 20.8249 0.743748
785785 0 0
786786 −18.8141 −0.671078
787787 2.89479 0.103188 0.0515941 0.998668i 0.483570π-0.483570\pi
0.0515941 + 0.998668i 0.483570π0.483570\pi
788788 38.5779 1.37428
789789 61.0541 2.17358
790790 0 0
791791 36.3860 1.29374
792792 −2.81860 −0.100155
793793 16.9160 0.600705
794794 −0.498930 −0.0177064
795795 0 0
796796 39.5723 1.40260
797797 −17.3882 −0.615923 −0.307961 0.951399i 0.599647π-0.599647\pi
−0.307961 + 0.951399i 0.599647π0.599647\pi
798798 28.3040 1.00195
799799 0 0
800800 0 0
801801 49.3889 1.74507
802802 −8.46254 −0.298823
803803 1.50796 0.0532146
804804 30.5499 1.07741
805805 0 0
806806 −9.41237 −0.331537
807807 19.1613 0.674510
808808 0.698169 0.0245615
809809 −37.8663 −1.33131 −0.665654 0.746261i 0.731847π-0.731847\pi
−0.665654 + 0.746261i 0.731847π0.731847\pi
810810 0 0
811811 −4.46329 −0.156727 −0.0783636 0.996925i 0.524970π-0.524970\pi
−0.0783636 + 0.996925i 0.524970π0.524970\pi
812812 1.26645 0.0444436
813813 −0.0365739 −0.00128270
814814 0.891777 0.0312568
815815 0 0
816816 0 0
817817 25.9596 0.908210
818818 3.16632 0.110708
819819 65.4028 2.28536
820820 0 0
821821 3.36602 0.117475 0.0587375 0.998273i 0.481293π-0.481293\pi
0.0587375 + 0.998273i 0.481293π0.481293\pi
822822 −11.9332 −0.416219
823823 −12.1803 −0.424579 −0.212289 0.977207i 0.568092π-0.568092\pi
−0.212289 + 0.977207i 0.568092π0.568092\pi
824824 −1.41181 −0.0491828
825825 0 0
826826 −32.1755 −1.11953
827827 18.4858 0.642816 0.321408 0.946941i 0.395844π-0.395844\pi
0.321408 + 0.946941i 0.395844π0.395844\pi
828828 44.4939 1.54627
829829 −27.8002 −0.965540 −0.482770 0.875747i 0.660369π-0.660369\pi
−0.482770 + 0.875747i 0.660369π0.660369\pi
830830 0 0
831831 6.08362 0.211038
832832 −7.49646 −0.259893
833833 0 0
834834 −18.2518 −0.632009
835835 0 0
836836 3.58491 0.123987
837837 2.28186 0.0788724
838838 −1.34644 −0.0465121
839839 −39.9107 −1.37787 −0.688935 0.724823i 0.741922π-0.741922\pi
−0.688935 + 0.724823i 0.741922π0.741922\pi
840840 0 0
841841 −28.9656 −0.998813
842842 19.7489 0.680591
843843 −18.7851 −0.646993
844844 3.05565 0.105180
845845 0 0
846846 −11.9184 −0.409763
847847 −43.6808 −1.50089
848848 −1.95419 −0.0671072
849849 21.5254 0.738749
850850 0 0
851851 −30.7262 −1.05328
852852 −31.7020 −1.08609
853853 −41.6170 −1.42494 −0.712469 0.701703i 0.752423π-0.752423\pi
−0.712469 + 0.701703i 0.752423π0.752423\pi
854854 7.64937 0.261756
855855 0 0
856856 −19.8670 −0.679040
857857 −10.6131 −0.362538 −0.181269 0.983434i 0.558020π-0.558020\pi
−0.181269 + 0.983434i 0.558020π0.558020\pi
858858 −2.90250 −0.0990897
859859 45.3309 1.54667 0.773335 0.633998i 0.218587π-0.218587\pi
0.773335 + 0.633998i 0.218587π0.218587\pi
860860 0 0
861861 −39.4894 −1.34580
862862 6.19350 0.210952
863863 −8.98488 −0.305849 −0.152925 0.988238i 0.548869π-0.548869\pi
−0.152925 + 0.988238i 0.548869π0.548869\pi
864864 −3.57499 −0.121624
865865 0 0
866866 −13.4835 −0.458189
867867 0 0
868868 23.3020 0.790921
869869 5.92323 0.200932
870870 0 0
871871 35.7949 1.21287
872872 −21.4364 −0.725927
873873 −33.1896 −1.12330
874874 22.5613 0.763148
875875 0 0
876876 15.1796 0.512872
877877 11.7160 0.395622 0.197811 0.980240i 0.436617π-0.436617\pi
0.197811 + 0.980240i 0.436617π0.436617\pi
878878 10.5073 0.354605
879879 51.6926 1.74355
880880 0 0
881881 4.31806 0.145479 0.0727396 0.997351i 0.476826π-0.476826\pi
0.0727396 + 0.997351i 0.476826π0.476826\pi
882882 16.8649 0.567871
883883 −29.8534 −1.00465 −0.502323 0.864680i 0.667521π-0.667521\pi
−0.502323 + 0.864680i 0.667521π0.667521\pi
884884 0 0
885885 0 0
886886 4.89263 0.164371
887887 11.4344 0.383928 0.191964 0.981402i 0.438514π-0.438514\pi
0.191964 + 0.981402i 0.438514π0.438514\pi
888888 19.5936 0.657518
889889 −54.9050 −1.84145
890890 0 0
891891 −3.41822 −0.114515
892892 −15.0480 −0.503844
893893 33.0862 1.10719
894894 11.4884 0.384231
895895 0 0
896896 −46.5655 −1.55564
897897 100.006 3.33909
898898 −21.0198 −0.701441
899899 0.633523 0.0211292
900900 0 0
901901 0 0
902902 0.913577 0.0304188
903903 52.0338 1.73158
904904 −18.4951 −0.615138
905905 0 0
906906 −8.82408 −0.293161
907907 −34.2774 −1.13816 −0.569081 0.822282i 0.692701π-0.692701\pi
−0.569081 + 0.822282i 0.692701π0.692701\pi
908908 −28.1281 −0.933463
909909 −1.11185 −0.0368778
910910 0 0
911911 −24.2471 −0.803342 −0.401671 0.915784i 0.631570π-0.631570\pi
−0.401671 + 0.915784i 0.631570π0.631570\pi
912912 28.2915 0.936825
913913 −5.74858 −0.190250
914914 −0.614030 −0.0203103
915915 0 0
916916 −2.32231 −0.0767313
917917 54.5745 1.80221
918918 0 0
919919 −42.9958 −1.41830 −0.709151 0.705057i 0.750921π-0.750921\pi
−0.709151 + 0.705057i 0.750921π0.750921\pi
920920 0 0
921921 73.7731 2.43091
922922 3.15207 0.103808
923923 −37.1449 −1.22264
924924 7.18565 0.236391
925925 0 0
926926 −4.95350 −0.162782
927927 2.24835 0.0738454
928928 −0.992544 −0.0325819
929929 29.4737 0.967001 0.483500 0.875344i 0.339365π-0.339365\pi
0.483500 + 0.875344i 0.339365π0.339365\pi
930930 0 0
931931 −46.8181 −1.53440
932932 −2.81265 −0.0921316
933933 −10.7413 −0.351653
934934 5.79894 0.189747
935935 0 0
936936 −33.2444 −1.08663
937937 −22.9716 −0.750450 −0.375225 0.926934i 0.622435π-0.622435\pi
−0.375225 + 0.926934i 0.622435π0.622435\pi
938938 16.1864 0.528504
939939 −26.3417 −0.859629
940940 0 0
941941 6.91682 0.225482 0.112741 0.993624i 0.464037π-0.464037\pi
0.112741 + 0.993624i 0.464037π0.464037\pi
942942 30.2523 0.985672
943943 −31.4773 −1.02504
944944 −32.1613 −1.04676
945945 0 0
946946 −1.20379 −0.0391385
947947 39.4991 1.28355 0.641774 0.766894i 0.278199π-0.278199\pi
0.641774 + 0.766894i 0.278199π0.278199\pi
948948 59.6254 1.93654
949949 17.7858 0.577351
950950 0 0
951951 38.2471 1.24025
952952 0 0
953953 30.8702 0.999983 0.499992 0.866030i 0.333336π-0.333336\pi
0.499992 + 0.866030i 0.333336π0.333336\pi
954954 −1.58259 −0.0512381
955955 0 0
956956 30.5995 0.989658
957957 0.195360 0.00631509
958958 −18.3577 −0.593112
959959 34.6150 1.11778
960960 0 0
961961 −19.3435 −0.623984
962962 10.5182 0.339120
963963 31.6387 1.01954
964964 −11.8611 −0.382021
965965 0 0
966966 45.2223 1.45500
967967 −12.1454 −0.390569 −0.195285 0.980747i 0.562563π-0.562563\pi
−0.195285 + 0.980747i 0.562563π0.562563\pi
968968 22.2030 0.713633
969969 0 0
970970 0 0
971971 59.3265 1.90388 0.951939 0.306287i 0.0990867π-0.0990867\pi
0.951939 + 0.306287i 0.0990867π0.0990867\pi
972972 −37.7998 −1.21243
973973 52.9434 1.69729
974974 −14.0879 −0.451404
975975 0 0
976976 7.64599 0.244742
977977 2.28110 0.0729788 0.0364894 0.999334i 0.488382π-0.488382\pi
0.0364894 + 0.999334i 0.488382π0.488382\pi
978978 18.8804 0.603727
979979 6.35786 0.203198
980980 0 0
981981 34.1380 1.08994
982982 14.4654 0.461611
983983 0.541983 0.0172866 0.00864328 0.999963i 0.497249π-0.497249\pi
0.00864328 + 0.999963i 0.497249π0.497249\pi
984984 20.0726 0.639890
985985 0 0
986986 0 0
987987 66.3186 2.11094
988988 42.2826 1.34519
989989 41.4765 1.31888
990990 0 0
991991 −12.9204 −0.410430 −0.205215 0.978717i 0.565789π-0.565789\pi
−0.205215 + 0.978717i 0.565789π0.565789\pi
992992 −18.2623 −0.579828
993993 31.8413 1.01045
994994 −16.7968 −0.532763
995995 0 0
996996 −57.8673 −1.83360
997997 12.3411 0.390847 0.195424 0.980719i 0.437392π-0.437392\pi
0.195424 + 0.980719i 0.437392π0.437392\pi
998998 10.1268 0.320558
999999 −2.54994 −0.0806765
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 7225.2.a.bx.1.15 24
5.4 even 2 7225.2.a.cb.1.10 24
17.3 odd 16 425.2.m.c.26.4 24
17.6 odd 16 425.2.m.c.376.4 yes 24
17.16 even 2 inner 7225.2.a.bx.1.16 24
85.3 even 16 425.2.n.e.349.3 24
85.23 even 16 425.2.n.d.274.4 24
85.37 even 16 425.2.n.d.349.4 24
85.54 odd 16 425.2.m.d.26.3 yes 24
85.57 even 16 425.2.n.e.274.3 24
85.74 odd 16 425.2.m.d.376.3 yes 24
85.84 even 2 7225.2.a.cb.1.9 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
425.2.m.c.26.4 24 17.3 odd 16
425.2.m.c.376.4 yes 24 17.6 odd 16
425.2.m.d.26.3 yes 24 85.54 odd 16
425.2.m.d.376.3 yes 24 85.74 odd 16
425.2.n.d.274.4 24 85.23 even 16
425.2.n.d.349.4 24 85.37 even 16
425.2.n.e.274.3 24 85.57 even 16
425.2.n.e.349.3 24 85.3 even 16
7225.2.a.bx.1.15 24 1.1 even 1 trivial
7225.2.a.bx.1.16 24 17.16 even 2 inner
7225.2.a.cb.1.9 24 85.84 even 2
7225.2.a.cb.1.10 24 5.4 even 2