Properties

Label 9025.2.a.ct.1.20
Level 90259025
Weight 22
Character 9025.1
Self dual yes
Analytic conductor 72.06572.065
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] = [9025,2,Mod(1,9025)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(9025, 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("9025.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 9025=52192 9025 = 5^{2} \cdot 19^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 9025.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: 72.064987824272.0649878242
Analytic rank: 11
Dimension: 2424
Twist minimal: no (minimal twist has level 95)
Fricke sign: +1+1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.20
Character χ\chi == 9025.1

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+1.78468q2+2.38377q3+1.18508q4+4.25426q64.23911q71.45438q8+2.68235q90.490889q11+2.82495q12+4.16199q137.56544q144.96575q16+2.03619q17+4.78713q1810.1050q210.876080q224.39525q233.46689q24+7.42782q260.757211q275.02367q28+3.26270q294.08833q315.95351q321.17017q33+3.63395q34+3.17879q362.14440q37+9.92123q394.36602q4118.0343q4210.6241q430.581742q447.84410q462.62142q4711.8372q48+10.9700q49+4.85381q51+4.93228q52+11.4341q531.35138q54+6.16526q56+5.82287q58+0.542306q5913.6423q617.29635q6211.3708q630.693606q642.08837q667.15699q67+2.41305q6810.4772q696.03858q713.90114q722.05419q733.82707q74+2.08093q77+17.7062q785.34029q799.85206q817.79193q828.11578q8311.9753q8418.9605q86+7.77752q87+0.713937q88+4.34099q8917.6431q915.20871q929.74562q934.67839q9414.1918q96+5.64669q97+19.5780q981.31674q99+O(q100)q+1.78468 q^{2} +2.38377 q^{3} +1.18508 q^{4} +4.25426 q^{6} -4.23911 q^{7} -1.45438 q^{8} +2.68235 q^{9} -0.490889 q^{11} +2.82495 q^{12} +4.16199 q^{13} -7.56544 q^{14} -4.96575 q^{16} +2.03619 q^{17} +4.78713 q^{18} -10.1050 q^{21} -0.876080 q^{22} -4.39525 q^{23} -3.46689 q^{24} +7.42782 q^{26} -0.757211 q^{27} -5.02367 q^{28} +3.26270 q^{29} -4.08833 q^{31} -5.95351 q^{32} -1.17017 q^{33} +3.63395 q^{34} +3.17879 q^{36} -2.14440 q^{37} +9.92123 q^{39} -4.36602 q^{41} -18.0343 q^{42} -10.6241 q^{43} -0.581742 q^{44} -7.84410 q^{46} -2.62142 q^{47} -11.8372 q^{48} +10.9700 q^{49} +4.85381 q^{51} +4.93228 q^{52} +11.4341 q^{53} -1.35138 q^{54} +6.16526 q^{56} +5.82287 q^{58} +0.542306 q^{59} -13.6423 q^{61} -7.29635 q^{62} -11.3708 q^{63} -0.693606 q^{64} -2.08837 q^{66} -7.15699 q^{67} +2.41305 q^{68} -10.4772 q^{69} -6.03858 q^{71} -3.90114 q^{72} -2.05419 q^{73} -3.82707 q^{74} +2.08093 q^{77} +17.7062 q^{78} -5.34029 q^{79} -9.85206 q^{81} -7.79193 q^{82} -8.11578 q^{83} -11.9753 q^{84} -18.9605 q^{86} +7.77752 q^{87} +0.713937 q^{88} +4.34099 q^{89} -17.6431 q^{91} -5.20871 q^{92} -9.74562 q^{93} -4.67839 q^{94} -14.1918 q^{96} +5.64669 q^{97} +19.5780 q^{98} -1.31674 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 24q+18q412q6+12q9+12q1124q14+6q166q2142q2412q2636q2942q316q346q36+24q3960q4130q446q46+12q49+120q96+O(q100) 24 q + 18 q^{4} - 12 q^{6} + 12 q^{9} + 12 q^{11} - 24 q^{14} + 6 q^{16} - 6 q^{21} - 42 q^{24} - 12 q^{26} - 36 q^{29} - 42 q^{31} - 6 q^{34} - 6 q^{36} + 24 q^{39} - 60 q^{41} - 30 q^{44} - 6 q^{46} + 12 q^{49}+ \cdots - 120 q^{96}+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 1.78468 1.26196 0.630979 0.775800i 0.282653π-0.282653\pi
0.630979 + 0.775800i 0.282653π0.282653\pi
33 2.38377 1.37627 0.688134 0.725583i 0.258430π-0.258430\pi
0.688134 + 0.725583i 0.258430π0.258430\pi
44 1.18508 0.592538
55 0 0
66 4.25426 1.73679
77 −4.23911 −1.60223 −0.801116 0.598509i 0.795760π-0.795760\pi
−0.801116 + 0.598509i 0.795760π0.795760\pi
88 −1.45438 −0.514199
99 2.68235 0.894116
1010 0 0
1111 −0.490889 −0.148009 −0.0740043 0.997258i 0.523578π-0.523578\pi
−0.0740043 + 0.997258i 0.523578π0.523578\pi
1212 2.82495 0.815492
1313 4.16199 1.15433 0.577165 0.816628i 0.304159π-0.304159\pi
0.577165 + 0.816628i 0.304159π0.304159\pi
1414 −7.56544 −2.02195
1515 0 0
1616 −4.96575 −1.24144
1717 2.03619 0.493850 0.246925 0.969035i 0.420580π-0.420580\pi
0.246925 + 0.969035i 0.420580π0.420580\pi
1818 4.78713 1.12834
1919 0 0
2020 0 0
2121 −10.1050 −2.20510
2222 −0.876080 −0.186781
2323 −4.39525 −0.916472 −0.458236 0.888830i 0.651519π-0.651519\pi
−0.458236 + 0.888830i 0.651519π0.651519\pi
2424 −3.46689 −0.707677
2525 0 0
2626 7.42782 1.45672
2727 −0.757211 −0.145725
2828 −5.02367 −0.949384
2929 3.26270 0.605869 0.302934 0.953011i 0.402034π-0.402034\pi
0.302934 + 0.953011i 0.402034π0.402034\pi
3030 0 0
3131 −4.08833 −0.734285 −0.367143 0.930165i 0.619664π-0.619664\pi
−0.367143 + 0.930165i 0.619664π0.619664\pi
3232 −5.95351 −1.05244
3333 −1.17017 −0.203700
3434 3.63395 0.623218
3535 0 0
3636 3.17879 0.529798
3737 −2.14440 −0.352538 −0.176269 0.984342i 0.556403π-0.556403\pi
−0.176269 + 0.984342i 0.556403π0.556403\pi
3838 0 0
3939 9.92123 1.58867
4040 0 0
4141 −4.36602 −0.681857 −0.340929 0.940089i 0.610741π-0.610741\pi
−0.340929 + 0.940089i 0.610741π0.610741\pi
4242 −18.0343 −2.78275
4343 −10.6241 −1.62015 −0.810077 0.586324i 0.800575π-0.800575\pi
−0.810077 + 0.586324i 0.800575π0.800575\pi
4444 −0.581742 −0.0877008
4545 0 0
4646 −7.84410 −1.15655
4747 −2.62142 −0.382373 −0.191187 0.981554i 0.561234π-0.561234\pi
−0.191187 + 0.981554i 0.561234π0.561234\pi
4848 −11.8372 −1.70855
4949 10.9700 1.56715
5050 0 0
5151 4.85381 0.679670
5252 4.93228 0.683985
5353 11.4341 1.57059 0.785296 0.619121i 0.212511π-0.212511\pi
0.785296 + 0.619121i 0.212511π0.212511\pi
5454 −1.35138 −0.183899
5555 0 0
5656 6.16526 0.823867
5757 0 0
5858 5.82287 0.764581
5959 0.542306 0.0706022 0.0353011 0.999377i 0.488761π-0.488761\pi
0.0353011 + 0.999377i 0.488761π0.488761\pi
6060 0 0
6161 −13.6423 −1.74671 −0.873356 0.487083i 0.838061π-0.838061\pi
−0.873356 + 0.487083i 0.838061π0.838061\pi
6262 −7.29635 −0.926637
6363 −11.3708 −1.43258
6464 −0.693606 −0.0867007
6565 0 0
6666 −2.08837 −0.257061
6767 −7.15699 −0.874365 −0.437182 0.899373i 0.644024π-0.644024\pi
−0.437182 + 0.899373i 0.644024π0.644024\pi
6868 2.41305 0.292625
6969 −10.4772 −1.26131
7070 0 0
7171 −6.03858 −0.716647 −0.358324 0.933597i 0.616652π-0.616652\pi
−0.358324 + 0.933597i 0.616652π0.616652\pi
7272 −3.90114 −0.459754
7373 −2.05419 −0.240425 −0.120212 0.992748i 0.538358π-0.538358\pi
−0.120212 + 0.992748i 0.538358π0.538358\pi
7474 −3.82707 −0.444888
7575 0 0
7676 0 0
7777 2.08093 0.237144
7878 17.7062 2.00483
7979 −5.34029 −0.600830 −0.300415 0.953809i 0.597125π-0.597125\pi
−0.300415 + 0.953809i 0.597125π0.597125\pi
8080 0 0
8181 −9.85206 −1.09467
8282 −7.79193 −0.860475
8383 −8.11578 −0.890823 −0.445411 0.895326i 0.646943π-0.646943\pi
−0.445411 + 0.895326i 0.646943π0.646943\pi
8484 −11.9753 −1.30661
8585 0 0
8686 −18.9605 −2.04457
8787 7.77752 0.833838
8888 0.713937 0.0761060
8989 4.34099 0.460144 0.230072 0.973174i 0.426104π-0.426104\pi
0.230072 + 0.973174i 0.426104π0.426104\pi
9090 0 0
9191 −17.6431 −1.84950
9292 −5.20871 −0.543045
9393 −9.74562 −1.01057
9494 −4.67839 −0.482539
9595 0 0
9696 −14.1918 −1.44844
9797 5.64669 0.573335 0.286667 0.958030i 0.407453π-0.407453\pi
0.286667 + 0.958030i 0.407453π0.407453\pi
9898 19.5780 1.97768
9999 −1.31674 −0.132337
100100 0 0
101101 −3.30082 −0.328444 −0.164222 0.986423i 0.552511π-0.552511\pi
−0.164222 + 0.986423i 0.552511π0.552511\pi
102102 8.66250 0.857715
103103 −3.41567 −0.336556 −0.168278 0.985740i 0.553821π-0.553821\pi
−0.168278 + 0.985740i 0.553821π0.553821\pi
104104 −6.05310 −0.593556
105105 0 0
106106 20.4062 1.98202
107107 −1.75252 −0.169422 −0.0847110 0.996406i 0.526997π-0.526997\pi
−0.0847110 + 0.996406i 0.526997π0.526997\pi
108108 −0.897354 −0.0863479
109109 3.51923 0.337081 0.168541 0.985695i 0.446095π-0.446095\pi
0.168541 + 0.985695i 0.446095π0.446095\pi
110110 0 0
111111 −5.11176 −0.485186
112112 21.0503 1.98907
113113 13.2583 1.24723 0.623616 0.781731i 0.285663π-0.285663\pi
0.623616 + 0.781731i 0.285663π0.285663\pi
114114 0 0
115115 0 0
116116 3.86655 0.359000
117117 11.1639 1.03210
118118 0.967842 0.0890971
119119 −8.63165 −0.791262
120120 0 0
121121 −10.7590 −0.978093
122122 −24.3470 −2.20428
123123 −10.4076 −0.938419
124124 −4.84498 −0.435092
125125 0 0
126126 −20.2931 −1.80786
127127 −19.8082 −1.75769 −0.878846 0.477105i 0.841686π-0.841686\pi
−0.878846 + 0.477105i 0.841686π0.841686\pi
128128 10.6692 0.943029
129129 −25.3253 −2.22977
130130 0 0
131131 −3.43004 −0.299684 −0.149842 0.988710i 0.547876π-0.547876\pi
−0.149842 + 0.988710i 0.547876π0.547876\pi
132132 −1.38674 −0.120700
133133 0 0
134134 −12.7729 −1.10341
135135 0 0
136136 −2.96139 −0.253937
137137 −0.608296 −0.0519702 −0.0259851 0.999662i 0.508272π-0.508272\pi
−0.0259851 + 0.999662i 0.508272π0.508272\pi
138138 −18.6985 −1.59172
139139 −8.45799 −0.717397 −0.358699 0.933453i 0.616779π-0.616779\pi
−0.358699 + 0.933453i 0.616779π0.616779\pi
140140 0 0
141141 −6.24885 −0.526248
142142 −10.7769 −0.904379
143143 −2.04308 −0.170851
144144 −13.3199 −1.10999
145145 0 0
146146 −3.66607 −0.303406
147147 26.1500 2.15682
148148 −2.54128 −0.208892
149149 −4.63735 −0.379907 −0.189953 0.981793i 0.560834π-0.560834\pi
−0.189953 + 0.981793i 0.560834π0.560834\pi
150150 0 0
151151 −14.2109 −1.15646 −0.578232 0.815872i 0.696257π-0.696257\pi
−0.578232 + 0.815872i 0.696257π0.696257\pi
152152 0 0
153153 5.46178 0.441559
154154 3.71380 0.299266
155155 0 0
156156 11.7574 0.941347
157157 −10.7281 −0.856194 −0.428097 0.903733i 0.640816π-0.640816\pi
−0.428097 + 0.903733i 0.640816π0.640816\pi
158158 −9.53071 −0.758222
159159 27.2562 2.16156
160160 0 0
161161 18.6319 1.46840
162162 −17.5828 −1.38143
163163 16.9366 1.32658 0.663289 0.748363i 0.269160π-0.269160\pi
0.663289 + 0.748363i 0.269160π0.269160\pi
164164 −5.17406 −0.404027
165165 0 0
166166 −14.4841 −1.12418
167167 16.2567 1.25798 0.628991 0.777412i 0.283468π-0.283468\pi
0.628991 + 0.777412i 0.283468π0.283468\pi
168168 14.6965 1.13386
169169 4.32219 0.332476
170170 0 0
171171 0 0
172172 −12.5903 −0.960003
173173 8.59112 0.653171 0.326585 0.945168i 0.394102π-0.394102\pi
0.326585 + 0.945168i 0.394102π0.394102\pi
174174 13.8804 1.05227
175175 0 0
176176 2.43763 0.183743
177177 1.29273 0.0971677
178178 7.74728 0.580683
179179 23.5276 1.75853 0.879267 0.476330i 0.158033π-0.158033\pi
0.879267 + 0.476330i 0.158033π0.158033\pi
180180 0 0
181181 16.6135 1.23487 0.617434 0.786623i 0.288172π-0.288172\pi
0.617434 + 0.786623i 0.288172π0.288172\pi
182182 −31.4873 −2.33400
183183 −32.5200 −2.40394
184184 6.39234 0.471250
185185 0 0
186186 −17.3928 −1.27530
187187 −0.999546 −0.0730941
188188 −3.10658 −0.226571
189189 3.20990 0.233486
190190 0 0
191191 −12.8109 −0.926965 −0.463482 0.886106i 0.653400π-0.653400\pi
−0.463482 + 0.886106i 0.653400π0.653400\pi
192192 −1.65339 −0.119323
193193 9.63983 0.693890 0.346945 0.937885i 0.387219π-0.387219\pi
0.346945 + 0.937885i 0.387219π0.387219\pi
194194 10.0775 0.723525
195195 0 0
196196 13.0003 0.928596
197197 −3.10241 −0.221038 −0.110519 0.993874i 0.535251π-0.535251\pi
−0.110519 + 0.993874i 0.535251π0.535251\pi
198198 −2.34995 −0.167004
199199 0.524290 0.0371659 0.0185830 0.999827i 0.494085π-0.494085\pi
0.0185830 + 0.999827i 0.494085π0.494085\pi
200200 0 0
201201 −17.0606 −1.20336
202202 −5.89091 −0.414483
203203 −13.8309 −0.970742
204204 5.75214 0.402731
205205 0 0
206206 −6.09586 −0.424719
207207 −11.7896 −0.819432
208208 −20.6674 −1.43303
209209 0 0
210210 0 0
211211 19.0637 1.31240 0.656201 0.754586i 0.272162π-0.272162\pi
0.656201 + 0.754586i 0.272162π0.272162\pi
212212 13.5503 0.930636
213213 −14.3946 −0.986299
214214 −3.12768 −0.213804
215215 0 0
216216 1.10127 0.0749319
217217 17.3309 1.17650
218218 6.28069 0.425382
219219 −4.89671 −0.330889
220220 0 0
221221 8.47463 0.570065
222222 −9.12284 −0.612285
223223 −3.16283 −0.211799 −0.105899 0.994377i 0.533772π-0.533772\pi
−0.105899 + 0.994377i 0.533772π0.533772\pi
224224 25.2376 1.68626
225225 0 0
226226 23.6617 1.57395
227227 −9.04654 −0.600440 −0.300220 0.953870i 0.597060π-0.597060\pi
−0.300220 + 0.953870i 0.597060π0.597060\pi
228228 0 0
229229 −17.8920 −1.18234 −0.591168 0.806549i 0.701333π-0.701333\pi
−0.591168 + 0.806549i 0.701333π0.701333\pi
230230 0 0
231231 4.96046 0.326374
232232 −4.74519 −0.311537
233233 −6.44330 −0.422114 −0.211057 0.977474i 0.567691π-0.567691\pi
−0.211057 + 0.977474i 0.567691π0.567691\pi
234234 19.9240 1.30247
235235 0 0
236236 0.642674 0.0418345
237237 −12.7300 −0.826903
238238 −15.4047 −0.998539
239239 −13.4742 −0.871571 −0.435785 0.900051i 0.643529π-0.643529\pi
−0.435785 + 0.900051i 0.643529π0.643529\pi
240240 0 0
241241 17.6351 1.13598 0.567990 0.823036i 0.307721π-0.307721\pi
0.567990 + 0.823036i 0.307721π0.307721\pi
242242 −19.2014 −1.23431
243243 −21.2134 −1.36084
244244 −16.1671 −1.03499
245245 0 0
246246 −18.5742 −1.18424
247247 0 0
248248 5.94596 0.377569
249249 −19.3461 −1.22601
250250 0 0
251251 17.7326 1.11927 0.559636 0.828738i 0.310941π-0.310941\pi
0.559636 + 0.828738i 0.310941π0.310941\pi
252252 −13.4752 −0.848859
253253 2.15758 0.135646
254254 −35.3513 −2.21813
255255 0 0
256256 20.4282 1.27676
257257 27.7475 1.73084 0.865421 0.501046i 0.167051π-0.167051\pi
0.865421 + 0.501046i 0.167051π0.167051\pi
258258 −45.1975 −2.81387
259259 9.09035 0.564847
260260 0 0
261261 8.75170 0.541716
262262 −6.12152 −0.378189
263263 5.56032 0.342864 0.171432 0.985196i 0.445161π-0.445161\pi
0.171432 + 0.985196i 0.445161π0.445161\pi
264264 1.70186 0.104742
265265 0 0
266266 0 0
267267 10.3479 0.633282
268268 −8.48158 −0.518095
269269 4.62765 0.282153 0.141076 0.989999i 0.454944π-0.454944\pi
0.141076 + 0.989999i 0.454944π0.454944\pi
270270 0 0
271271 −7.60838 −0.462176 −0.231088 0.972933i 0.574229π-0.574229\pi
−0.231088 + 0.972933i 0.574229π0.574229\pi
272272 −10.1112 −0.613083
273273 −42.0571 −2.54541
274274 −1.08561 −0.0655843
275275 0 0
276276 −12.4163 −0.747376
277277 7.53544 0.452761 0.226380 0.974039i 0.427311π-0.427311\pi
0.226380 + 0.974039i 0.427311π0.427311\pi
278278 −15.0948 −0.905325
279279 −10.9663 −0.656536
280280 0 0
281281 18.2549 1.08900 0.544499 0.838762i 0.316720π-0.316720\pi
0.544499 + 0.838762i 0.316720π0.316720\pi
282282 −11.1522 −0.664103
283283 −30.9333 −1.83880 −0.919398 0.393328i 0.871324π-0.871324\pi
−0.919398 + 0.393328i 0.871324π0.871324\pi
284284 −7.15618 −0.424641
285285 0 0
286286 −3.64624 −0.215607
287287 18.5080 1.09249
288288 −15.9694 −0.941004
289289 −12.8539 −0.756112
290290 0 0
291291 13.4604 0.789063
292292 −2.43437 −0.142461
293293 −21.8992 −1.27937 −0.639683 0.768639i 0.720934π-0.720934\pi
−0.639683 + 0.768639i 0.720934π0.720934\pi
294294 46.6694 2.72181
295295 0 0
296296 3.11877 0.181275
297297 0.371707 0.0215686
298298 −8.27618 −0.479426
299299 −18.2930 −1.05791
300300 0 0
301301 45.0365 2.59586
302302 −25.3618 −1.45941
303303 −7.86840 −0.452028
304304 0 0
305305 0 0
306306 9.74752 0.557229
307307 5.45543 0.311358 0.155679 0.987808i 0.450243π-0.450243\pi
0.155679 + 0.987808i 0.450243π0.450243\pi
308308 2.46607 0.140517
309309 −8.14215 −0.463191
310310 0 0
311311 6.69721 0.379764 0.189882 0.981807i 0.439189π-0.439189\pi
0.189882 + 0.981807i 0.439189π0.439189\pi
312312 −14.4292 −0.816892
313313 4.58279 0.259035 0.129517 0.991577i 0.458657π-0.458657\pi
0.129517 + 0.991577i 0.458657π0.458657\pi
314314 −19.1462 −1.08048
315315 0 0
316316 −6.32866 −0.356015
317317 27.6794 1.55463 0.777314 0.629113i 0.216582π-0.216582\pi
0.777314 + 0.629113i 0.216582π0.216582\pi
318318 48.6435 2.72779
319319 −1.60163 −0.0896738
320320 0 0
321321 −4.17759 −0.233170
322322 33.2520 1.85306
323323 0 0
324324 −11.6754 −0.648636
325325 0 0
326326 30.2264 1.67409
327327 8.38903 0.463914
328328 6.34983 0.350611
329329 11.1125 0.612651
330330 0 0
331331 14.1302 0.776665 0.388332 0.921519i 0.373051π-0.373051\pi
0.388332 + 0.921519i 0.373051π0.373051\pi
332332 −9.61782 −0.527847
333333 −5.75203 −0.315209
334334 29.0130 1.58752
335335 0 0
336336 50.1791 2.73749
337337 −14.9974 −0.816962 −0.408481 0.912767i 0.633941π-0.633941\pi
−0.408481 + 0.912767i 0.633941π0.633941\pi
338338 7.71372 0.419571
339339 31.6046 1.71653
340340 0 0
341341 2.00692 0.108681
342342 0 0
343343 −16.8294 −0.908703
344344 15.4514 0.833082
345345 0 0
346346 15.3324 0.824274
347347 −20.9133 −1.12268 −0.561342 0.827584i 0.689715π-0.689715\pi
−0.561342 + 0.827584i 0.689715π0.689715\pi
348348 9.21696 0.494081
349349 −3.13055 −0.167574 −0.0837872 0.996484i 0.526702π-0.526702\pi
−0.0837872 + 0.996484i 0.526702π0.526702\pi
350350 0 0
351351 −3.15151 −0.168215
352352 2.92251 0.155771
353353 8.04538 0.428212 0.214106 0.976810i 0.431316π-0.431316\pi
0.214106 + 0.976810i 0.431316π0.431316\pi
354354 2.30711 0.122622
355355 0 0
356356 5.14441 0.272653
357357 −20.5758 −1.08899
358358 41.9891 2.21920
359359 30.5842 1.61417 0.807087 0.590432i 0.201043π-0.201043\pi
0.807087 + 0.590432i 0.201043π0.201043\pi
360360 0 0
361361 0 0
362362 29.6497 1.55835
363363 −25.6470 −1.34612
364364 −20.9085 −1.09590
365365 0 0
366366 −58.0377 −3.03368
367367 −9.95175 −0.519477 −0.259739 0.965679i 0.583636π-0.583636\pi
−0.259739 + 0.965679i 0.583636π0.583636\pi
368368 21.8257 1.13774
369369 −11.7112 −0.609659
370370 0 0
371371 −48.4703 −2.51645
372372 −11.5493 −0.598804
373373 9.27611 0.480299 0.240149 0.970736i 0.422804π-0.422804\pi
0.240149 + 0.970736i 0.422804π0.422804\pi
374374 −1.78387 −0.0922416
375375 0 0
376376 3.81253 0.196616
377377 13.5793 0.699372
378378 5.72864 0.294649
379379 21.1472 1.08626 0.543129 0.839649i 0.317239π-0.317239\pi
0.543129 + 0.839649i 0.317239π0.317239\pi
380380 0 0
381381 −47.2181 −2.41906
382382 −22.8634 −1.16979
383383 15.1501 0.774136 0.387068 0.922051i 0.373488π-0.373488\pi
0.387068 + 0.922051i 0.373488π0.373488\pi
384384 25.4328 1.29786
385385 0 0
386386 17.2040 0.875660
387387 −28.4974 −1.44860
388388 6.69177 0.339723
389389 −31.4483 −1.59449 −0.797247 0.603653i 0.793711π-0.793711\pi
−0.797247 + 0.603653i 0.793711π0.793711\pi
390390 0 0
391391 −8.94958 −0.452600
392392 −15.9546 −0.805827
393393 −8.17642 −0.412446
394394 −5.53681 −0.278940
395395 0 0
396396 −1.56043 −0.0784147
397397 −9.38559 −0.471049 −0.235525 0.971868i 0.575681π-0.575681\pi
−0.235525 + 0.971868i 0.575681π0.575681\pi
398398 0.935689 0.0469019
399399 0 0
400400 0 0
401401 −6.16049 −0.307640 −0.153820 0.988099i 0.549158π-0.549158\pi
−0.153820 + 0.988099i 0.549158π0.549158\pi
402402 −30.4477 −1.51859
403403 −17.0156 −0.847607
404404 −3.91173 −0.194616
405405 0 0
406406 −24.6838 −1.22504
407407 1.05266 0.0521786
408408 −7.05927 −0.349486
409409 −2.28482 −0.112977 −0.0564885 0.998403i 0.517990π-0.517990\pi
−0.0564885 + 0.998403i 0.517990π0.517990\pi
410410 0 0
411411 −1.45004 −0.0715250
412412 −4.04783 −0.199422
413413 −2.29889 −0.113121
414414 −21.0406 −1.03409
415415 0 0
416416 −24.7785 −1.21486
417417 −20.1619 −0.987332
418418 0 0
419419 −22.6494 −1.10649 −0.553247 0.833017i 0.686611π-0.686611\pi
−0.553247 + 0.833017i 0.686611π0.686611\pi
420420 0 0
421421 22.9969 1.12080 0.560400 0.828222i 0.310647π-0.310647\pi
0.560400 + 0.828222i 0.310647π0.310647\pi
422422 34.0226 1.65620
423423 −7.03155 −0.341886
424424 −16.6294 −0.807597
425425 0 0
426426 −25.6897 −1.24467
427427 57.8310 2.79864
428428 −2.07687 −0.100389
429429 −4.87022 −0.235137
430430 0 0
431431 −25.6319 −1.23465 −0.617323 0.786710i 0.711783π-0.711783\pi
−0.617323 + 0.786710i 0.711783π0.711783\pi
432432 3.76012 0.180909
433433 2.36330 0.113573 0.0567864 0.998386i 0.481915π-0.481915\pi
0.0567864 + 0.998386i 0.481915π0.481915\pi
434434 30.9300 1.48469
435435 0 0
436436 4.17056 0.199734
437437 0 0
438438 −8.73906 −0.417568
439439 6.31659 0.301474 0.150737 0.988574i 0.451835π-0.451835\pi
0.150737 + 0.988574i 0.451835π0.451835\pi
440440 0 0
441441 29.4254 1.40121
442442 15.1245 0.719399
443443 −31.5246 −1.49778 −0.748890 0.662694i 0.769413π-0.769413\pi
−0.748890 + 0.662694i 0.769413π0.769413\pi
444444 −6.05782 −0.287492
445445 0 0
446446 −5.64463 −0.267281
447447 −11.0544 −0.522854
448448 2.94027 0.138915
449449 15.0828 0.711803 0.355902 0.934523i 0.384174π-0.384174\pi
0.355902 + 0.934523i 0.384174π0.384174\pi
450450 0 0
451451 2.14323 0.100921
452452 15.7121 0.739033
453453 −33.8754 −1.59161
454454 −16.1452 −0.757730
455455 0 0
456456 0 0
457457 −20.1347 −0.941861 −0.470930 0.882170i 0.656082π-0.656082\pi
−0.470930 + 0.882170i 0.656082π0.656082\pi
458458 −31.9314 −1.49206
459459 −1.54183 −0.0719664
460460 0 0
461461 −7.48489 −0.348606 −0.174303 0.984692i 0.555767π-0.555767\pi
−0.174303 + 0.984692i 0.555767π0.555767\pi
462462 8.85283 0.411871
463463 21.5973 1.00371 0.501855 0.864952i 0.332651π-0.332651\pi
0.501855 + 0.864952i 0.332651π0.332651\pi
464464 −16.2017 −0.752147
465465 0 0
466466 −11.4992 −0.532691
467467 27.0503 1.25174 0.625870 0.779927i 0.284744π-0.284744\pi
0.625870 + 0.779927i 0.284744π0.284744\pi
468468 13.2301 0.611561
469469 30.3392 1.40094
470470 0 0
471471 −25.5732 −1.17835
472472 −0.788717 −0.0363036
473473 5.21524 0.239797
474474 −22.7190 −1.04352
475475 0 0
476476 −10.2292 −0.468853
477477 30.6702 1.40429
478478 −24.0470 −1.09989
479479 −38.0534 −1.73870 −0.869352 0.494193i 0.835464π-0.835464\pi
−0.869352 + 0.494193i 0.835464π0.835464\pi
480480 0 0
481481 −8.92499 −0.406944
482482 31.4731 1.43356
483483 44.4142 2.02092
484484 −12.7503 −0.579558
485485 0 0
486486 −37.8591 −1.71732
487487 −18.3353 −0.830851 −0.415426 0.909627i 0.636367π-0.636367\pi
−0.415426 + 0.909627i 0.636367π0.636367\pi
488488 19.8410 0.898158
489489 40.3730 1.82573
490490 0 0
491491 −15.0675 −0.679986 −0.339993 0.940428i 0.610425π-0.610425\pi
−0.339993 + 0.940428i 0.610425π0.610425\pi
492492 −12.3338 −0.556049
493493 6.64350 0.299208
494494 0 0
495495 0 0
496496 20.3016 0.911568
497497 25.5982 1.14824
498498 −34.5266 −1.54717
499499 34.5299 1.54577 0.772886 0.634545i 0.218812π-0.218812\pi
0.772886 + 0.634545i 0.218812π0.218812\pi
500500 0 0
501501 38.7522 1.73132
502502 31.6470 1.41247
503503 30.8704 1.37644 0.688221 0.725501i 0.258392π-0.258392\pi
0.688221 + 0.725501i 0.258392π0.258392\pi
504504 16.5374 0.736632
505505 0 0
506506 3.85059 0.171179
507507 10.3031 0.457577
508508 −23.4742 −1.04150
509509 −10.1777 −0.451118 −0.225559 0.974230i 0.572421π-0.572421\pi
−0.225559 + 0.974230i 0.572421π0.572421\pi
510510 0 0
511511 8.70794 0.385217
512512 15.1195 0.668194
513513 0 0
514514 49.5204 2.18425
515515 0 0
516516 −30.0124 −1.32122
517517 1.28683 0.0565946
518518 16.2234 0.712813
519519 20.4792 0.898938
520520 0 0
521521 −16.5423 −0.724732 −0.362366 0.932036i 0.618031π-0.618031\pi
−0.362366 + 0.932036i 0.618031π0.618031\pi
522522 15.6190 0.683624
523523 −7.99801 −0.349729 −0.174864 0.984593i 0.555949π-0.555949\pi
−0.174864 + 0.984593i 0.555949π0.555949\pi
524524 −4.06486 −0.177574
525525 0 0
526526 9.92338 0.432680
527527 −8.32463 −0.362626
528528 5.81075 0.252880
529529 −3.68180 −0.160078
530530 0 0
531531 1.45465 0.0631266
532532 0 0
533533 −18.1713 −0.787088
534534 18.4677 0.799176
535535 0 0
536536 10.4089 0.449598
537537 56.0843 2.42021
538538 8.25886 0.356065
539539 −5.38507 −0.231952
540540 0 0
541541 5.20048 0.223586 0.111793 0.993732i 0.464341π-0.464341\pi
0.111793 + 0.993732i 0.464341π0.464341\pi
542542 −13.5785 −0.583247
543543 39.6026 1.69951
544544 −12.1225 −0.519748
545545 0 0
546546 −75.0585 −3.21221
547547 11.0339 0.471777 0.235889 0.971780i 0.424200π-0.424200\pi
0.235889 + 0.971780i 0.424200π0.424200\pi
548548 −0.720878 −0.0307944
549549 −36.5933 −1.56176
550550 0 0
551551 0 0
552552 15.2379 0.648566
553553 22.6381 0.962669
554554 13.4483 0.571365
555555 0 0
556556 −10.0234 −0.425086
557557 21.2817 0.901735 0.450867 0.892591i 0.351115π-0.351115\pi
0.450867 + 0.892591i 0.351115π0.351115\pi
558558 −19.5713 −0.828521
559559 −44.2173 −1.87019
560560 0 0
561561 −2.38269 −0.100597
562562 32.5792 1.37427
563563 14.7072 0.619833 0.309917 0.950764i 0.399699π-0.399699\pi
0.309917 + 0.950764i 0.399699π0.399699\pi
564564 −7.40537 −0.311822
565565 0 0
566566 −55.2061 −2.32048
567567 41.7639 1.75392
568568 8.78236 0.368500
569569 −40.6551 −1.70435 −0.852174 0.523258i 0.824716π-0.824716\pi
−0.852174 + 0.523258i 0.824716π0.824716\pi
570570 0 0
571571 −24.3240 −1.01793 −0.508964 0.860788i 0.669972π-0.669972\pi
−0.508964 + 0.860788i 0.669972π0.669972\pi
572572 −2.42120 −0.101236
573573 −30.5382 −1.27575
574574 33.0308 1.37868
575575 0 0
576576 −1.86049 −0.0775204
577577 −33.6876 −1.40243 −0.701216 0.712949i 0.747359π-0.747359\pi
−0.701216 + 0.712949i 0.747359π0.747359\pi
578578 −22.9401 −0.954182
579579 22.9791 0.954979
580580 0 0
581581 34.4037 1.42730
582582 24.0225 0.995764
583583 −5.61287 −0.232461
584584 2.98757 0.123626
585585 0 0
586586 −39.0830 −1.61451
587587 2.24977 0.0928580 0.0464290 0.998922i 0.485216π-0.485216\pi
0.0464290 + 0.998922i 0.485216π0.485216\pi
588588 30.9898 1.27800
589589 0 0
590590 0 0
591591 −7.39543 −0.304207
592592 10.6486 0.437653
593593 31.3871 1.28891 0.644457 0.764640i 0.277083π-0.277083\pi
0.644457 + 0.764640i 0.277083π0.277083\pi
594594 0.663377 0.0272187
595595 0 0
596596 −5.49562 −0.225109
597597 1.24979 0.0511503
598598 −32.6471 −1.33504
599599 −10.4068 −0.425212 −0.212606 0.977138i 0.568195π-0.568195\pi
−0.212606 + 0.977138i 0.568195π0.568195\pi
600600 0 0
601601 1.29592 0.0528616 0.0264308 0.999651i 0.491586π-0.491586\pi
0.0264308 + 0.999651i 0.491586π0.491586\pi
602602 80.3757 3.27587
603603 −19.1975 −0.781783
604604 −16.8410 −0.685249
605605 0 0
606606 −14.0426 −0.570440
607607 5.50902 0.223604 0.111802 0.993730i 0.464338π-0.464338\pi
0.111802 + 0.993730i 0.464338π0.464338\pi
608608 0 0
609609 −32.9698 −1.33600
610610 0 0
611611 −10.9103 −0.441385
612612 6.47263 0.261641
613613 40.6727 1.64275 0.821376 0.570386i 0.193207π-0.193207\pi
0.821376 + 0.570386i 0.193207π0.193207\pi
614614 9.73619 0.392921
615615 0 0
616616 −3.02646 −0.121939
617617 −30.5053 −1.22810 −0.614049 0.789268i 0.710460π-0.710460\pi
−0.614049 + 0.789268i 0.710460π0.710460\pi
618618 −14.5311 −0.584527
619619 5.80411 0.233287 0.116643 0.993174i 0.462787π-0.462787\pi
0.116643 + 0.993174i 0.462787π0.462787\pi
620620 0 0
621621 3.32813 0.133553
622622 11.9524 0.479246
623623 −18.4019 −0.737258
624624 −49.2663 −1.97223
625625 0 0
626626 8.17881 0.326891
627627 0 0
628628 −12.7136 −0.507328
629629 −4.36642 −0.174101
630630 0 0
631631 −23.3642 −0.930116 −0.465058 0.885280i 0.653967π-0.653967\pi
−0.465058 + 0.885280i 0.653967π0.653967\pi
632632 7.76679 0.308946
633633 45.4435 1.80622
634634 49.3987 1.96187
635635 0 0
636636 32.3007 1.28080
637637 45.6572 1.80901
638638 −2.85839 −0.113165
639639 −16.1976 −0.640766
640640 0 0
641641 −18.3459 −0.724621 −0.362311 0.932057i 0.618012π-0.618012\pi
−0.362311 + 0.932057i 0.618012π0.618012\pi
642642 −7.45565 −0.294251
643643 −15.7630 −0.621633 −0.310817 0.950470i 0.600603π-0.600603\pi
−0.310817 + 0.950470i 0.600603π0.600603\pi
644644 22.0803 0.870084
645645 0 0
646646 0 0
647647 25.0443 0.984592 0.492296 0.870428i 0.336158π-0.336158\pi
0.492296 + 0.870428i 0.336158π0.336158\pi
648648 14.3286 0.562880
649649 −0.266212 −0.0104497
650650 0 0
651651 41.3127 1.61917
652652 20.0712 0.786049
653653 −2.98852 −0.116950 −0.0584749 0.998289i 0.518624π-0.518624\pi
−0.0584749 + 0.998289i 0.518624π0.518624\pi
654654 14.9717 0.585440
655655 0 0
656656 21.6805 0.846482
657657 −5.51005 −0.214968
658658 19.8322 0.773140
659659 35.7695 1.39338 0.696691 0.717372i 0.254655π-0.254655\pi
0.696691 + 0.717372i 0.254655π0.254655\pi
660660 0 0
661661 −3.22147 −0.125301 −0.0626503 0.998036i 0.519955π-0.519955\pi
−0.0626503 + 0.998036i 0.519955π0.519955\pi
662662 25.2178 0.980118
663663 20.2015 0.784563
664664 11.8034 0.458061
665665 0 0
666666 −10.2655 −0.397781
667667 −14.3404 −0.555262
668668 19.2655 0.745403
669669 −7.53945 −0.291492
670670 0 0
671671 6.69684 0.258529
672672 60.1605 2.32074
673673 −0.639706 −0.0246588 −0.0123294 0.999924i 0.503925π-0.503925\pi
−0.0123294 + 0.999924i 0.503925π0.503925\pi
674674 −26.7656 −1.03097
675675 0 0
676676 5.12213 0.197005
677677 25.8005 0.991592 0.495796 0.868439i 0.334876π-0.334876\pi
0.495796 + 0.868439i 0.334876π0.334876\pi
678678 56.4041 2.16618
679679 −23.9369 −0.918616
680680 0 0
681681 −21.5648 −0.826366
682682 3.58170 0.137150
683683 5.33696 0.204213 0.102107 0.994773i 0.467442π-0.467442\pi
0.102107 + 0.994773i 0.467442π0.467442\pi
684684 0 0
685685 0 0
686686 −30.0351 −1.14675
687687 −42.6503 −1.62721
688688 52.7564 2.01132
689689 47.5886 1.81298
690690 0 0
691691 13.2507 0.504079 0.252040 0.967717i 0.418899π-0.418899\pi
0.252040 + 0.967717i 0.418899π0.418899\pi
692692 10.1811 0.387029
693693 5.58178 0.212034
694694 −37.3235 −1.41678
695695 0 0
696696 −11.3114 −0.428759
697697 −8.89006 −0.336735
698698 −5.58702 −0.211472
699699 −15.3593 −0.580943
700700 0 0
701701 40.8699 1.54363 0.771817 0.635845i 0.219348π-0.219348\pi
0.771817 + 0.635845i 0.219348π0.219348\pi
702702 −5.62443 −0.212280
703703 0 0
704704 0.340484 0.0128325
705705 0 0
706706 14.3584 0.540386
707707 13.9925 0.526244
708708 1.53199 0.0575756
709709 7.35745 0.276315 0.138157 0.990410i 0.455882π-0.455882\pi
0.138157 + 0.990410i 0.455882π0.455882\pi
710710 0 0
711711 −14.3245 −0.537211
712712 −6.31344 −0.236606
713713 17.9692 0.672952
714714 −36.7213 −1.37426
715715 0 0
716716 27.8820 1.04200
717717 −32.1193 −1.19952
718718 54.5830 2.03702
719719 −31.9597 −1.19190 −0.595948 0.803023i 0.703224π-0.703224\pi
−0.595948 + 0.803023i 0.703224π0.703224\pi
720720 0 0
721721 14.4794 0.539240
722722 0 0
723723 42.0381 1.56341
724724 19.6882 0.731707
725725 0 0
726726 −45.7717 −1.69875
727727 29.3883 1.08995 0.544976 0.838452i 0.316539π-0.316539\pi
0.544976 + 0.838452i 0.316539π0.316539\pi
728728 25.6598 0.951014
729729 −21.0116 −0.778207
730730 0 0
731731 −21.6326 −0.800112
732732 −38.5387 −1.42443
733733 50.8285 1.87739 0.938696 0.344745i 0.112035π-0.112035\pi
0.938696 + 0.344745i 0.112035π0.112035\pi
734734 −17.7607 −0.655559
735735 0 0
736736 26.1671 0.964534
737737 3.51329 0.129414
738738 −20.9007 −0.769364
739739 14.7245 0.541650 0.270825 0.962629i 0.412704π-0.412704\pi
0.270825 + 0.962629i 0.412704π0.412704\pi
740740 0 0
741741 0 0
742742 −86.5039 −3.17566
743743 34.6568 1.27144 0.635718 0.771922i 0.280704π-0.280704\pi
0.635718 + 0.771922i 0.280704π0.280704\pi
744744 14.1738 0.519636
745745 0 0
746746 16.5549 0.606117
747747 −21.7693 −0.796498
748748 −1.18454 −0.0433110
749749 7.42910 0.271453
750750 0 0
751751 8.35539 0.304893 0.152446 0.988312i 0.451285π-0.451285\pi
0.152446 + 0.988312i 0.451285π0.451285\pi
752752 13.0173 0.474692
753753 42.2704 1.54042
754754 24.2348 0.882578
755755 0 0
756756 3.80398 0.138349
757757 −13.8709 −0.504146 −0.252073 0.967708i 0.581112π-0.581112\pi
−0.252073 + 0.967708i 0.581112π0.581112\pi
758758 37.7410 1.37081
759759 5.14317 0.186685
760760 0 0
761761 44.3970 1.60939 0.804696 0.593687i 0.202328π-0.202328\pi
0.804696 + 0.593687i 0.202328π0.202328\pi
762762 −84.2692 −3.05275
763763 −14.9184 −0.540082
764764 −15.1819 −0.549262
765765 0 0
766766 27.0381 0.976927
767767 2.25707 0.0814983
768768 48.6961 1.75717
769769 19.0001 0.685160 0.342580 0.939489i 0.388699π-0.388699\pi
0.342580 + 0.939489i 0.388699π0.388699\pi
770770 0 0
771771 66.1436 2.38210
772772 11.4239 0.411157
773773 −1.86738 −0.0671650 −0.0335825 0.999436i 0.510692π-0.510692\pi
−0.0335825 + 0.999436i 0.510692π0.510692\pi
774774 −50.8587 −1.82808
775775 0 0
776776 −8.21241 −0.294808
777777 21.6693 0.777381
778778 −56.1252 −2.01218
779779 0 0
780780 0 0
781781 2.96427 0.106070
782782 −15.9721 −0.571162
783783 −2.47055 −0.0882904
784784 −54.4744 −1.94552
785785 0 0
786786 −14.5923 −0.520489
787787 12.9689 0.462291 0.231146 0.972919i 0.425753π-0.425753\pi
0.231146 + 0.972919i 0.425753π0.425753\pi
788788 −3.67660 −0.130973
789789 13.2545 0.471873
790790 0 0
791791 −56.2032 −1.99836
792792 1.91503 0.0680476
793793 −56.7790 −2.01628
794794 −16.7503 −0.594444
795795 0 0
796796 0.621324 0.0220222
797797 −29.9226 −1.05991 −0.529956 0.848025i 0.677791π-0.677791\pi
−0.529956 + 0.848025i 0.677791π0.677791\pi
798798 0 0
799799 −5.33772 −0.188835
800800 0 0
801801 11.6441 0.411422
802802 −10.9945 −0.388229
803803 1.00838 0.0355850
804804 −20.2181 −0.713038
805805 0 0
806806 −30.3674 −1.06964
807807 11.0312 0.388318
808808 4.80064 0.168886
809809 42.4578 1.49274 0.746369 0.665532i 0.231795π-0.231795\pi
0.746369 + 0.665532i 0.231795π0.231795\pi
810810 0 0
811811 31.1514 1.09387 0.546936 0.837174i 0.315794π-0.315794\pi
0.546936 + 0.837174i 0.315794π0.315794\pi
812812 −16.3907 −0.575202
813813 −18.1366 −0.636079
814814 1.87867 0.0658472
815815 0 0
816816 −24.1028 −0.843767
817817 0 0
818818 −4.07767 −0.142572
819819 −47.3250 −1.65367
820820 0 0
821821 −6.20740 −0.216640 −0.108320 0.994116i 0.534547π-0.534547\pi
−0.108320 + 0.994116i 0.534547π0.534547\pi
822822 −2.58785 −0.0902616
823823 −35.9702 −1.25384 −0.626921 0.779083i 0.715685π-0.715685\pi
−0.626921 + 0.779083i 0.715685π0.715685\pi
824824 4.96766 0.173057
825825 0 0
826826 −4.10279 −0.142754
827827 −15.3837 −0.534945 −0.267473 0.963565i 0.586189π-0.586189\pi
−0.267473 + 0.963565i 0.586189π0.586189\pi
828828 −13.9716 −0.485545
829829 24.1941 0.840295 0.420148 0.907456i 0.361978π-0.361978\pi
0.420148 + 0.907456i 0.361978π0.361978\pi
830830 0 0
831831 17.9627 0.623120
832832 −2.88678 −0.100081
833833 22.3371 0.773936
834834 −35.9825 −1.24597
835835 0 0
836836 0 0
837837 3.09573 0.107004
838838 −40.4218 −1.39635
839839 −12.4265 −0.429012 −0.214506 0.976723i 0.568814π-0.568814\pi
−0.214506 + 0.976723i 0.568814π0.568814\pi
840840 0 0
841841 −18.3548 −0.632923
842842 41.0420 1.41440
843843 43.5155 1.49875
844844 22.5920 0.777649
845845 0 0
846846 −12.5491 −0.431446
847847 45.6087 1.56713
848848 −56.7787 −1.94979
849849 −73.7379 −2.53068
850850 0 0
851851 9.42518 0.323091
852852 −17.0587 −0.584420
853853 23.1527 0.792734 0.396367 0.918092i 0.370271π-0.370271\pi
0.396367 + 0.918092i 0.370271π0.370271\pi
854854 103.210 3.53176
855855 0 0
856856 2.54882 0.0871167
857857 2.84272 0.0971054 0.0485527 0.998821i 0.484539π-0.484539\pi
0.0485527 + 0.998821i 0.484539π0.484539\pi
858858 −8.69178 −0.296733
859859 −25.8715 −0.882725 −0.441363 0.897329i 0.645505π-0.645505\pi
−0.441363 + 0.897329i 0.645505π0.645505\pi
860860 0 0
861861 44.1188 1.50356
862862 −45.7447 −1.55807
863863 38.0032 1.29365 0.646823 0.762641i 0.276097π-0.276097\pi
0.646823 + 0.762641i 0.276097π0.276097\pi
864864 4.50806 0.153367
865865 0 0
866866 4.21773 0.143324
867867 −30.6407 −1.04061
868868 20.5384 0.697119
869869 2.62149 0.0889281
870870 0 0
871871 −29.7873 −1.00931
872872 −5.11828 −0.173327
873873 15.1464 0.512628
874874 0 0
875875 0 0
876876 −5.80298 −0.196065
877877 −49.0943 −1.65780 −0.828898 0.559400i 0.811032π-0.811032\pi
−0.828898 + 0.559400i 0.811032π0.811032\pi
878878 11.2731 0.380448
879879 −52.2026 −1.76075
880880 0 0
881881 −55.7494 −1.87825 −0.939123 0.343581i 0.888360π-0.888360\pi
−0.939123 + 0.343581i 0.888360π0.888360\pi
882882 52.5150 1.76827
883883 −16.6355 −0.559828 −0.279914 0.960025i 0.590306π-0.590306\pi
−0.279914 + 0.960025i 0.590306π0.590306\pi
884884 10.0431 0.337786
885885 0 0
886886 −56.2613 −1.89014
887887 −43.3883 −1.45684 −0.728418 0.685133i 0.759744π-0.759744\pi
−0.728418 + 0.685133i 0.759744π0.759744\pi
888888 7.43441 0.249483
889889 83.9691 2.81623
890890 0 0
891891 4.83627 0.162021
892892 −3.74820 −0.125499
893893 0 0
894894 −19.7285 −0.659819
895895 0 0
896896 −45.2277 −1.51095
897897 −43.6062 −1.45597
898898 26.9180 0.898266
899899 −13.3390 −0.444880
900900 0 0
901901 23.2820 0.775636
902902 3.82498 0.127358
903903 107.357 3.57260
904904 −19.2825 −0.641326
905905 0 0
906906 −60.4567 −2.00854
907907 −19.8364 −0.658656 −0.329328 0.944216i 0.606822π-0.606822\pi
−0.329328 + 0.944216i 0.606822π0.606822\pi
908908 −10.7208 −0.355784
909909 −8.85395 −0.293667
910910 0 0
911911 −15.4076 −0.510478 −0.255239 0.966878i 0.582154π-0.582154\pi
−0.255239 + 0.966878i 0.582154π0.582154\pi
912912 0 0
913913 3.98395 0.131849
914914 −35.9339 −1.18859
915915 0 0
916916 −21.2034 −0.700579
917917 14.5403 0.480163
918918 −2.75167 −0.0908186
919919 −13.2561 −0.437278 −0.218639 0.975806i 0.570162π-0.570162\pi
−0.218639 + 0.975806i 0.570162π0.570162\pi
920920 0 0
921921 13.0045 0.428512
922922 −13.3581 −0.439926
923923 −25.1325 −0.827247
924924 5.87853 0.193389
925925 0 0
926926 38.5442 1.26664
927927 −9.16200 −0.300920
928928 −19.4245 −0.637641
929929 31.2016 1.02369 0.511846 0.859077i 0.328962π-0.328962\pi
0.511846 + 0.859077i 0.328962π0.328962\pi
930930 0 0
931931 0 0
932932 −7.63580 −0.250119
933933 15.9646 0.522658
934934 48.2762 1.57964
935935 0 0
936936 −16.2365 −0.530707
937937 −16.2187 −0.529840 −0.264920 0.964270i 0.585346π-0.585346\pi
−0.264920 + 0.964270i 0.585346π0.585346\pi
938938 54.1458 1.76792
939939 10.9243 0.356502
940940 0 0
941941 −35.1748 −1.14666 −0.573332 0.819323i 0.694350π-0.694350\pi
−0.573332 + 0.819323i 0.694350π0.694350\pi
942942 −45.6400 −1.48703
943943 19.1897 0.624903
944944 −2.69295 −0.0876482
945945 0 0
946946 9.30752 0.302614
947947 −22.2784 −0.723950 −0.361975 0.932188i 0.617897π-0.617897\pi
−0.361975 + 0.932188i 0.617897π0.617897\pi
948948 −15.0860 −0.489972
949949 −8.54953 −0.277530
950950 0 0
951951 65.9811 2.13958
952952 12.5537 0.406866
953953 4.25996 0.137994 0.0689968 0.997617i 0.478020π-0.478020\pi
0.0689968 + 0.997617i 0.478020π0.478020\pi
954954 54.7364 1.77216
955955 0 0
956956 −15.9679 −0.516439
957957 −3.81790 −0.123415
958958 −67.9131 −2.19417
959959 2.57863 0.0832684
960960 0 0
961961 −14.2856 −0.460825
962962 −15.9282 −0.513547
963963 −4.70085 −0.151483
964964 20.8990 0.673111
965965 0 0
966966 79.2650 2.55031
967967 −1.21906 −0.0392023 −0.0196012 0.999808i 0.506240π-0.506240\pi
−0.0196012 + 0.999808i 0.506240π0.506240\pi
968968 15.6477 0.502935
969969 0 0
970970 0 0
971971 4.34003 0.139278 0.0696391 0.997572i 0.477815π-0.477815\pi
0.0696391 + 0.997572i 0.477815π0.477815\pi
972972 −25.1395 −0.806349
973973 35.8543 1.14944
974974 −32.7226 −1.04850
975975 0 0
976976 67.7440 2.16843
977977 −21.5270 −0.688710 −0.344355 0.938840i 0.611902π-0.611902\pi
−0.344355 + 0.938840i 0.611902π0.611902\pi
978978 72.0527 2.30399
979979 −2.13095 −0.0681054
980980 0 0
981981 9.43980 0.301389
982982 −26.8906 −0.858114
983983 −14.5998 −0.465661 −0.232830 0.972517i 0.574799π-0.574799\pi
−0.232830 + 0.972517i 0.574799π0.574799\pi
984984 15.1365 0.482534
985985 0 0
986986 11.8565 0.377588
987987 26.4896 0.843172
988988 0 0
989989 46.6954 1.48483
990990 0 0
991991 −31.9286 −1.01425 −0.507123 0.861874i 0.669291π-0.669291\pi
−0.507123 + 0.861874i 0.669291π0.669291\pi
992992 24.3399 0.772792
993993 33.6831 1.06890
994994 45.6845 1.44903
995995 0 0
996996 −22.9267 −0.726459
997997 55.1812 1.74761 0.873803 0.486280i 0.161647π-0.161647\pi
0.873803 + 0.486280i 0.161647π0.161647\pi
998998 61.6248 1.95070
999999 1.62377 0.0513737
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 9025.2.a.ct.1.20 24
5.2 odd 4 1805.2.b.l.1084.20 24
5.3 odd 4 1805.2.b.l.1084.5 24
5.4 even 2 inner 9025.2.a.ct.1.5 24
19.14 odd 18 475.2.l.f.101.2 48
19.15 odd 18 475.2.l.f.301.2 48
19.18 odd 2 9025.2.a.cu.1.5 24
95.14 odd 18 475.2.l.f.101.7 48
95.18 even 4 1805.2.b.k.1084.20 24
95.33 even 36 95.2.p.a.44.7 yes 48
95.34 odd 18 475.2.l.f.301.7 48
95.37 even 4 1805.2.b.k.1084.5 24
95.52 even 36 95.2.p.a.44.2 48
95.53 even 36 95.2.p.a.54.2 yes 48
95.72 even 36 95.2.p.a.54.7 yes 48
95.94 odd 2 9025.2.a.cu.1.20 24
285.53 odd 36 855.2.da.b.244.7 48
285.128 odd 36 855.2.da.b.424.2 48
285.167 odd 36 855.2.da.b.244.2 48
285.242 odd 36 855.2.da.b.424.7 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
95.2.p.a.44.2 48 95.52 even 36
95.2.p.a.44.7 yes 48 95.33 even 36
95.2.p.a.54.2 yes 48 95.53 even 36
95.2.p.a.54.7 yes 48 95.72 even 36
475.2.l.f.101.2 48 19.14 odd 18
475.2.l.f.101.7 48 95.14 odd 18
475.2.l.f.301.2 48 19.15 odd 18
475.2.l.f.301.7 48 95.34 odd 18
855.2.da.b.244.2 48 285.167 odd 36
855.2.da.b.244.7 48 285.53 odd 36
855.2.da.b.424.2 48 285.128 odd 36
855.2.da.b.424.7 48 285.242 odd 36
1805.2.b.k.1084.5 24 95.37 even 4
1805.2.b.k.1084.20 24 95.18 even 4
1805.2.b.l.1084.5 24 5.3 odd 4
1805.2.b.l.1084.20 24 5.2 odd 4
9025.2.a.ct.1.5 24 5.4 even 2 inner
9025.2.a.ct.1.20 24 1.1 even 1 trivial
9025.2.a.cu.1.5 24 19.18 odd 2
9025.2.a.cu.1.20 24 95.94 odd 2