Properties

Label 441.6.a.j.1.1
Level 441441
Weight 66
Character 441.1
Self dual yes
Analytic conductor 70.72970.729
Analytic rank 11
Dimension 11
CM no
Inner twists 11

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [441,6,Mod(1,441)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(441, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("441.1");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: N N == 441=3272 441 = 3^{2} \cdot 7^{2}
Weight: k k == 6 6
Character orbit: [χ][\chi] == 441.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: 70.729264537570.7292645375
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 == 441.1

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+6.00000q2+4.00000q4+78.0000q5168.000q8+468.000q10444.000q11+442.000q131136.00q16126.000q172684.00q19+312.000q202664.00q224200.00q23+2959.00q25+2652.00q26+5442.00q2980.0000q311440.00q32756.000q345434.00q3716104.0q3813104.0q40+7962.00q4111524.0q431776.00q4425200.0q4613920.0q47+17754.0q50+1768.00q52+9594.00q5334632.0q55+32652.0q58+27492.0q5949478.0q61480.000q62+27712.0q64+34476.0q6559356.0q67504.000q6832040.0q71+61846.0q7332604.0q7410736.0q7665776.0q7988608.0q80+47772.0q82+40188.0q839828.00q8569144.0q86+74592.0q887974.00q8916800.0q9283520.0q94209352.q95+143662.q97+O(q100)q+6.00000 q^{2} +4.00000 q^{4} +78.0000 q^{5} -168.000 q^{8} +468.000 q^{10} -444.000 q^{11} +442.000 q^{13} -1136.00 q^{16} -126.000 q^{17} -2684.00 q^{19} +312.000 q^{20} -2664.00 q^{22} -4200.00 q^{23} +2959.00 q^{25} +2652.00 q^{26} +5442.00 q^{29} -80.0000 q^{31} -1440.00 q^{32} -756.000 q^{34} -5434.00 q^{37} -16104.0 q^{38} -13104.0 q^{40} +7962.00 q^{41} -11524.0 q^{43} -1776.00 q^{44} -25200.0 q^{46} -13920.0 q^{47} +17754.0 q^{50} +1768.00 q^{52} +9594.00 q^{53} -34632.0 q^{55} +32652.0 q^{58} +27492.0 q^{59} -49478.0 q^{61} -480.000 q^{62} +27712.0 q^{64} +34476.0 q^{65} -59356.0 q^{67} -504.000 q^{68} -32040.0 q^{71} +61846.0 q^{73} -32604.0 q^{74} -10736.0 q^{76} -65776.0 q^{79} -88608.0 q^{80} +47772.0 q^{82} +40188.0 q^{83} -9828.00 q^{85} -69144.0 q^{86} +74592.0 q^{88} -7974.00 q^{89} -16800.0 q^{92} -83520.0 q^{94} -209352. q^{95} +143662. q^{97} +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 6.00000 1.06066 0.530330 0.847791i 0.322068π-0.322068\pi
0.530330 + 0.847791i 0.322068π0.322068\pi
33 0 0
44 4.00000 0.125000
55 78.0000 1.39531 0.697653 0.716436i 0.254228π-0.254228\pi
0.697653 + 0.716436i 0.254228π0.254228\pi
66 0 0
77 0 0
88 −168.000 −0.928078
99 0 0
1010 468.000 1.47995
1111 −444.000 −1.10637 −0.553186 0.833058i 0.686588π-0.686588\pi
−0.553186 + 0.833058i 0.686588π0.686588\pi
1212 0 0
1313 442.000 0.725377 0.362689 0.931910i 0.381859π-0.381859\pi
0.362689 + 0.931910i 0.381859π0.381859\pi
1414 0 0
1515 0 0
1616 −1136.00 −1.10938
1717 −126.000 −0.105742 −0.0528711 0.998601i 0.516837π-0.516837\pi
−0.0528711 + 0.998601i 0.516837π0.516837\pi
1818 0 0
1919 −2684.00 −1.70568 −0.852842 0.522169i 0.825123π-0.825123\pi
−0.852842 + 0.522169i 0.825123π0.825123\pi
2020 312.000 0.174413
2121 0 0
2222 −2664.00 −1.17348
2323 −4200.00 −1.65550 −0.827751 0.561096i 0.810380π-0.810380\pi
−0.827751 + 0.561096i 0.810380π0.810380\pi
2424 0 0
2525 2959.00 0.946880
2626 2652.00 0.769379
2727 0 0
2828 0 0
2929 5442.00 1.20161 0.600805 0.799396i 0.294847π-0.294847\pi
0.600805 + 0.799396i 0.294847π0.294847\pi
3030 0 0
3131 −80.0000 −0.0149515 −0.00747577 0.999972i 0.502380π-0.502380\pi
−0.00747577 + 0.999972i 0.502380π0.502380\pi
3232 −1440.00 −0.248592
3333 0 0
3434 −756.000 −0.112157
3535 0 0
3636 0 0
3737 −5434.00 −0.652552 −0.326276 0.945274i 0.605794π-0.605794\pi
−0.326276 + 0.945274i 0.605794π0.605794\pi
3838 −16104.0 −1.80915
3939 0 0
4040 −13104.0 −1.29495
4141 7962.00 0.739712 0.369856 0.929089i 0.379407π-0.379407\pi
0.369856 + 0.929089i 0.379407π0.379407\pi
4242 0 0
4343 −11524.0 −0.950456 −0.475228 0.879863i 0.657634π-0.657634\pi
−0.475228 + 0.879863i 0.657634π0.657634\pi
4444 −1776.00 −0.138297
4545 0 0
4646 −25200.0 −1.75592
4747 −13920.0 −0.919167 −0.459584 0.888134i 0.652001π-0.652001\pi
−0.459584 + 0.888134i 0.652001π0.652001\pi
4848 0 0
4949 0 0
5050 17754.0 1.00432
5151 0 0
5252 1768.00 0.0906721
5353 9594.00 0.469148 0.234574 0.972098i 0.424630π-0.424630\pi
0.234574 + 0.972098i 0.424630π0.424630\pi
5454 0 0
5555 −34632.0 −1.54373
5656 0 0
5757 0 0
5858 32652.0 1.27450
5959 27492.0 1.02820 0.514098 0.857731i 0.328127π-0.328127\pi
0.514098 + 0.857731i 0.328127π0.328127\pi
6060 0 0
6161 −49478.0 −1.70250 −0.851251 0.524759i 0.824155π-0.824155\pi
−0.851251 + 0.524759i 0.824155π0.824155\pi
6262 −480.000 −0.0158585
6363 0 0
6464 27712.0 0.845703
6565 34476.0 1.01212
6666 0 0
6767 −59356.0 −1.61539 −0.807695 0.589600i 0.799285π-0.799285\pi
−0.807695 + 0.589600i 0.799285π0.799285\pi
6868 −504.000 −0.0132178
6969 0 0
7070 0 0
7171 −32040.0 −0.754304 −0.377152 0.926151i 0.623097π-0.623097\pi
−0.377152 + 0.926151i 0.623097π0.623097\pi
7272 0 0
7373 61846.0 1.35833 0.679164 0.733987i 0.262343π-0.262343\pi
0.679164 + 0.733987i 0.262343π0.262343\pi
7474 −32604.0 −0.692136
7575 0 0
7676 −10736.0 −0.213210
7777 0 0
7878 0 0
7979 −65776.0 −1.18577 −0.592884 0.805288i 0.702011π-0.702011\pi
−0.592884 + 0.805288i 0.702011π0.702011\pi
8080 −88608.0 −1.54792
8181 0 0
8282 47772.0 0.784583
8383 40188.0 0.640326 0.320163 0.947362i 0.396262π-0.396262\pi
0.320163 + 0.947362i 0.396262π0.396262\pi
8484 0 0
8585 −9828.00 −0.147543
8686 −69144.0 −1.00811
8787 0 0
8888 74592.0 1.02680
8989 −7974.00 −0.106709 −0.0533545 0.998576i 0.516991π-0.516991\pi
−0.0533545 + 0.998576i 0.516991π0.516991\pi
9090 0 0
9191 0 0
9292 −16800.0 −0.206938
9393 0 0
9494 −83520.0 −0.974924
9595 −209352. −2.37995
9696 0 0
9797 143662. 1.55029 0.775144 0.631784i 0.217677π-0.217677\pi
0.775144 + 0.631784i 0.217677π0.217677\pi
9898 0 0
9999 0 0
100100 11836.0 0.118360
101101 −2706.00 −0.0263952 −0.0131976 0.999913i 0.504201π-0.504201\pi
−0.0131976 + 0.999913i 0.504201π0.504201\pi
102102 0 0
103103 −131768. −1.22382 −0.611909 0.790928i 0.709598π-0.709598\pi
−0.611909 + 0.790928i 0.709598π0.709598\pi
104104 −74256.0 −0.673206
105105 0 0
106106 57564.0 0.497607
107107 128916. 1.08855 0.544274 0.838908i 0.316805π-0.316805\pi
0.544274 + 0.838908i 0.316805π0.316805\pi
108108 0 0
109109 −100978. −0.814068 −0.407034 0.913413i 0.633437π-0.633437\pi
−0.407034 + 0.913413i 0.633437π0.633437\pi
110110 −207792. −1.63737
111111 0 0
112112 0 0
113113 −220146. −1.62186 −0.810932 0.585140i 0.801040π-0.801040\pi
−0.810932 + 0.585140i 0.801040π0.801040\pi
114114 0 0
115115 −327600. −2.30993
116116 21768.0 0.150201
117117 0 0
118118 164952. 1.09057
119119 0 0
120120 0 0
121121 36085.0 0.224059
122122 −296868. −1.80578
123123 0 0
124124 −320.000 −0.00186894
125125 −12948.0 −0.0741187
126126 0 0
127127 −74320.0 −0.408880 −0.204440 0.978879i 0.565537π-0.565537\pi
−0.204440 + 0.978879i 0.565537π0.565537\pi
128128 212352. 1.14560
129129 0 0
130130 206856. 1.07352
131131 −155316. −0.790748 −0.395374 0.918520i 0.629385π-0.629385\pi
−0.395374 + 0.918520i 0.629385π0.629385\pi
132132 0 0
133133 0 0
134134 −356136. −1.71338
135135 0 0
136136 21168.0 0.0981369
137137 264246. 1.20284 0.601419 0.798934i 0.294602π-0.294602\pi
0.601419 + 0.798934i 0.294602π0.294602\pi
138138 0 0
139139 −224612. −0.986043 −0.493022 0.870017i 0.664108π-0.664108\pi
−0.493022 + 0.870017i 0.664108π0.664108\pi
140140 0 0
141141 0 0
142142 −192240. −0.800061
143143 −196248. −0.802537
144144 0 0
145145 424476. 1.67661
146146 371076. 1.44072
147147 0 0
148148 −21736.0 −0.0815690
149149 82074.0 0.302859 0.151429 0.988468i 0.451612π-0.451612\pi
0.151429 + 0.988468i 0.451612π0.451612\pi
150150 0 0
151151 −287032. −1.02444 −0.512222 0.858853i 0.671177π-0.671177\pi
−0.512222 + 0.858853i 0.671177π0.671177\pi
152152 450912. 1.58301
153153 0 0
154154 0 0
155155 −6240.00 −0.0208620
156156 0 0
157157 −129878. −0.420520 −0.210260 0.977646i 0.567431π-0.567431\pi
−0.210260 + 0.977646i 0.567431π0.567431\pi
158158 −394656. −1.25770
159159 0 0
160160 −112320. −0.346862
161161 0 0
162162 0 0
163163 555284. 1.63699 0.818495 0.574513i 0.194809π-0.194809\pi
0.818495 + 0.574513i 0.194809π0.194809\pi
164164 31848.0 0.0924640
165165 0 0
166166 241128. 0.679168
167167 43512.0 0.120731 0.0603654 0.998176i 0.480773π-0.480773\pi
0.0603654 + 0.998176i 0.480773π0.480773\pi
168168 0 0
169169 −175929. −0.473828
170170 −58968.0 −0.156493
171171 0 0
172172 −46096.0 −0.118807
173173 −18330.0 −0.0465637 −0.0232818 0.999729i 0.507412π-0.507412\pi
−0.0232818 + 0.999729i 0.507412π0.507412\pi
174174 0 0
175175 0 0
176176 504384. 1.22738
177177 0 0
178178 −47844.0 −0.113182
179179 153324. 0.357666 0.178833 0.983879i 0.442768π-0.442768\pi
0.178833 + 0.983879i 0.442768π0.442768\pi
180180 0 0
181181 382066. 0.866846 0.433423 0.901191i 0.357306π-0.357306\pi
0.433423 + 0.901191i 0.357306π0.357306\pi
182182 0 0
183183 0 0
184184 705600. 1.53643
185185 −423852. −0.910510
186186 0 0
187187 55944.0 0.116990
188188 −55680.0 −0.114896
189189 0 0
190190 −1.25611e6 −2.52432
191191 273408. 0.542285 0.271143 0.962539i 0.412598π-0.412598\pi
0.271143 + 0.962539i 0.412598π0.412598\pi
192192 0 0
193193 153602. 0.296827 0.148414 0.988925i 0.452583π-0.452583\pi
0.148414 + 0.988925i 0.452583π0.452583\pi
194194 861972. 1.64433
195195 0 0
196196 0 0
197197 −154422. −0.283494 −0.141747 0.989903i 0.545272π-0.545272\pi
−0.141747 + 0.989903i 0.545272π0.545272\pi
198198 0 0
199199 366856. 0.656694 0.328347 0.944557i 0.393508π-0.393508\pi
0.328347 + 0.944557i 0.393508π0.393508\pi
200200 −497112. −0.878778
201201 0 0
202202 −16236.0 −0.0279963
203203 0 0
204204 0 0
205205 621036. 1.03212
206206 −790608. −1.29806
207207 0 0
208208 −502112. −0.804715
209209 1.19170e6 1.88712
210210 0 0
211211 520244. 0.804453 0.402227 0.915540i 0.368236π-0.368236\pi
0.402227 + 0.915540i 0.368236π0.368236\pi
212212 38376.0 0.0586435
213213 0 0
214214 773496. 1.15458
215215 −898872. −1.32618
216216 0 0
217217 0 0
218218 −605868. −0.863449
219219 0 0
220220 −138528. −0.192966
221221 −55692.0 −0.0767030
222222 0 0
223223 −304736. −0.410357 −0.205178 0.978725i 0.565777π-0.565777\pi
−0.205178 + 0.978725i 0.565777π0.565777\pi
224224 0 0
225225 0 0
226226 −1.32088e6 −1.72025
227227 288588. 0.371718 0.185859 0.982576i 0.440493π-0.440493\pi
0.185859 + 0.982576i 0.440493π0.440493\pi
228228 0 0
229229 −772190. −0.973051 −0.486525 0.873666i 0.661736π-0.661736\pi
−0.486525 + 0.873666i 0.661736π0.661736\pi
230230 −1.96560e6 −2.45005
231231 0 0
232232 −914256. −1.11519
233233 −252234. −0.304378 −0.152189 0.988351i 0.548632π-0.548632\pi
−0.152189 + 0.988351i 0.548632π0.548632\pi
234234 0 0
235235 −1.08576e6 −1.28252
236236 109968. 0.128525
237237 0 0
238238 0 0
239239 1.45114e6 1.64329 0.821643 0.570002i 0.193058π-0.193058\pi
0.821643 + 0.570002i 0.193058π0.193058\pi
240240 0 0
241241 146398. 0.162365 0.0811825 0.996699i 0.474130π-0.474130\pi
0.0811825 + 0.996699i 0.474130π0.474130\pi
242242 216510. 0.237651
243243 0 0
244244 −197912. −0.212813
245245 0 0
246246 0 0
247247 −1.18633e6 −1.23726
248248 13440.0 0.0138762
249249 0 0
250250 −77688.0 −0.0786147
251251 607860. 0.609003 0.304501 0.952512i 0.401510π-0.401510\pi
0.304501 + 0.952512i 0.401510π0.401510\pi
252252 0 0
253253 1.86480e6 1.83160
254254 −445920. −0.433683
255255 0 0
256256 387328. 0.369385
257257 95586.0 0.0902737 0.0451369 0.998981i 0.485628π-0.485628\pi
0.0451369 + 0.998981i 0.485628π0.485628\pi
258258 0 0
259259 0 0
260260 137904. 0.126515
261261 0 0
262262 −931896. −0.838715
263263 2.20034e6 1.96156 0.980779 0.195121i 0.0625100π-0.0625100\pi
0.980779 + 0.195121i 0.0625100π0.0625100\pi
264264 0 0
265265 748332. 0.654605
266266 0 0
267267 0 0
268268 −237424. −0.201924
269269 1.77025e6 1.49160 0.745801 0.666169i 0.232067π-0.232067\pi
0.745801 + 0.666169i 0.232067π0.232067\pi
270270 0 0
271271 223504. 0.184868 0.0924341 0.995719i 0.470535π-0.470535\pi
0.0924341 + 0.995719i 0.470535π0.470535\pi
272272 143136. 0.117308
273273 0 0
274274 1.58548e6 1.27580
275275 −1.31380e6 −1.04760
276276 0 0
277277 −342778. −0.268419 −0.134210 0.990953i 0.542850π-0.542850\pi
−0.134210 + 0.990953i 0.542850π0.542850\pi
278278 −1.34767e6 −1.04586
279279 0 0
280280 0 0
281281 −480378. −0.362925 −0.181463 0.983398i 0.558083π-0.558083\pi
−0.181463 + 0.983398i 0.558083π0.558083\pi
282282 0 0
283283 29980.0 0.0222518 0.0111259 0.999938i 0.496458π-0.496458\pi
0.0111259 + 0.999938i 0.496458π0.496458\pi
284284 −128160. −0.0942880
285285 0 0
286286 −1.17749e6 −0.851219
287287 0 0
288288 0 0
289289 −1.40398e6 −0.988819
290290 2.54686e6 1.77832
291291 0 0
292292 247384. 0.169791
293293 −198066. −0.134785 −0.0673924 0.997727i 0.521468π-0.521468\pi
−0.0673924 + 0.997727i 0.521468π0.521468\pi
294294 0 0
295295 2.14438e6 1.43465
296296 912912. 0.605619
297297 0 0
298298 492444. 0.321230
299299 −1.85640e6 −1.20086
300300 0 0
301301 0 0
302302 −1.72219e6 −1.08659
303303 0 0
304304 3.04902e6 1.89224
305305 −3.85928e6 −2.37551
306306 0 0
307307 1.04564e6 0.633191 0.316595 0.948561i 0.397460π-0.397460\pi
0.316595 + 0.948561i 0.397460π0.397460\pi
308308 0 0
309309 0 0
310310 −37440.0 −0.0221275
311311 1.83718e6 1.07708 0.538542 0.842598i 0.318975π-0.318975\pi
0.538542 + 0.842598i 0.318975π0.318975\pi
312312 0 0
313313 365494. 0.210872 0.105436 0.994426i 0.466376π-0.466376\pi
0.105436 + 0.994426i 0.466376π0.466376\pi
314314 −779268. −0.446029
315315 0 0
316316 −263104. −0.148221
317317 28338.0 0.0158388 0.00791938 0.999969i 0.497479π-0.497479\pi
0.00791938 + 0.999969i 0.497479π0.497479\pi
318318 0 0
319319 −2.41625e6 −1.32943
320320 2.16154e6 1.18001
321321 0 0
322322 0 0
323323 338184. 0.180363
324324 0 0
325325 1.30788e6 0.686845
326326 3.33170e6 1.73629
327327 0 0
328328 −1.33762e6 −0.686510
329329 0 0
330330 0 0
331331 1.93392e6 0.970214 0.485107 0.874455i 0.338781π-0.338781\pi
0.485107 + 0.874455i 0.338781π0.338781\pi
332332 160752. 0.0800408
333333 0 0
334334 261072. 0.128054
335335 −4.62977e6 −2.25397
336336 0 0
337337 −1.88817e6 −0.905664 −0.452832 0.891596i 0.649586π-0.649586\pi
−0.452832 + 0.891596i 0.649586π0.649586\pi
338338 −1.05557e6 −0.502570
339339 0 0
340340 −39312.0 −0.0184428
341341 35520.0 0.0165420
342342 0 0
343343 0 0
344344 1.93603e6 0.882097
345345 0 0
346346 −109980. −0.0493882
347347 −2.91937e6 −1.30156 −0.650782 0.759264i 0.725559π-0.725559\pi
−0.650782 + 0.759264i 0.725559π0.725559\pi
348348 0 0
349349 780682. 0.343092 0.171546 0.985176i 0.445124π-0.445124\pi
0.171546 + 0.985176i 0.445124π0.445124\pi
350350 0 0
351351 0 0
352352 639360. 0.275036
353353 1.33437e6 0.569954 0.284977 0.958534i 0.408014π-0.408014\pi
0.284977 + 0.958534i 0.408014π0.408014\pi
354354 0 0
355355 −2.49912e6 −1.05249
356356 −31896.0 −0.0133386
357357 0 0
358358 919944. 0.379362
359359 −1.01743e6 −0.416648 −0.208324 0.978060i 0.566801π-0.566801\pi
−0.208324 + 0.978060i 0.566801π0.566801\pi
360360 0 0
361361 4.72776e6 1.90936
362362 2.29240e6 0.919429
363363 0 0
364364 0 0
365365 4.82399e6 1.89528
366366 0 0
367367 −837680. −0.324648 −0.162324 0.986737i 0.551899π-0.551899\pi
−0.162324 + 0.986737i 0.551899π0.551899\pi
368368 4.77120e6 1.83657
369369 0 0
370370 −2.54311e6 −0.965742
371371 0 0
372372 0 0
373373 −1.51993e6 −0.565655 −0.282827 0.959171i 0.591272π-0.591272\pi
−0.282827 + 0.959171i 0.591272π0.591272\pi
374374 335664. 0.124087
375375 0 0
376376 2.33856e6 0.853059
377377 2.40536e6 0.871620
378378 0 0
379379 2.64465e6 0.945737 0.472869 0.881133i 0.343219π-0.343219\pi
0.472869 + 0.881133i 0.343219π0.343219\pi
380380 −837408. −0.297494
381381 0 0
382382 1.64045e6 0.575180
383383 2.01336e6 0.701333 0.350667 0.936500i 0.385955π-0.385955\pi
0.350667 + 0.936500i 0.385955π0.385955\pi
384384 0 0
385385 0 0
386386 921612. 0.314833
387387 0 0
388388 574648. 0.193786
389389 726234. 0.243334 0.121667 0.992571i 0.461176π-0.461176\pi
0.121667 + 0.992571i 0.461176π0.461176\pi
390390 0 0
391391 529200. 0.175056
392392 0 0
393393 0 0
394394 −926532. −0.300691
395395 −5.13053e6 −1.65451
396396 0 0
397397 −4.57578e6 −1.45710 −0.728549 0.684993i 0.759805π-0.759805\pi
−0.728549 + 0.684993i 0.759805π0.759805\pi
398398 2.20114e6 0.696529
399399 0 0
400400 −3.36142e6 −1.05045
401401 33870.0 0.0105185 0.00525926 0.999986i 0.498326π-0.498326\pi
0.00525926 + 0.999986i 0.498326π0.498326\pi
402402 0 0
403403 −35360.0 −0.0108455
404404 −10824.0 −0.00329940
405405 0 0
406406 0 0
407407 2.41270e6 0.721966
408408 0 0
409409 5.86178e6 1.73269 0.866346 0.499444i 0.166462π-0.166462\pi
0.866346 + 0.499444i 0.166462π0.166462\pi
410410 3.72622e6 1.09473
411411 0 0
412412 −527072. −0.152977
413413 0 0
414414 0 0
415415 3.13466e6 0.893451
416416 −636480. −0.180323
417417 0 0
418418 7.15018e6 2.00159
419419 302748. 0.0842454 0.0421227 0.999112i 0.486588π-0.486588\pi
0.0421227 + 0.999112i 0.486588π0.486588\pi
420420 0 0
421421 −5.36708e6 −1.47582 −0.737909 0.674900i 0.764187π-0.764187\pi
−0.737909 + 0.674900i 0.764187π0.764187\pi
422422 3.12146e6 0.853252
423423 0 0
424424 −1.61179e6 −0.435406
425425 −372834. −0.100125
426426 0 0
427427 0 0
428428 515664. 0.136068
429429 0 0
430430 −5.39323e6 −1.40662
431431 −1.17706e6 −0.305214 −0.152607 0.988287i 0.548767π-0.548767\pi
−0.152607 + 0.988287i 0.548767π0.548767\pi
432432 0 0
433433 3.66249e6 0.938766 0.469383 0.882995i 0.344476π-0.344476\pi
0.469383 + 0.882995i 0.344476π0.344476\pi
434434 0 0
435435 0 0
436436 −403912. −0.101758
437437 1.12728e7 2.82376
438438 0 0
439439 2.53674e6 0.628225 0.314113 0.949386i 0.398293π-0.398293\pi
0.314113 + 0.949386i 0.398293π0.398293\pi
440440 5.81818e6 1.43270
441441 0 0
442442 −334152. −0.0813558
443443 −6.01504e6 −1.45623 −0.728113 0.685457i 0.759603π-0.759603\pi
−0.728113 + 0.685457i 0.759603π0.759603\pi
444444 0 0
445445 −621972. −0.148892
446446 −1.82842e6 −0.435249
447447 0 0
448448 0 0
449449 −5.65965e6 −1.32487 −0.662436 0.749119i 0.730477π-0.730477\pi
−0.662436 + 0.749119i 0.730477π0.730477\pi
450450 0 0
451451 −3.53513e6 −0.818397
452452 −880584. −0.202733
453453 0 0
454454 1.73153e6 0.394267
455455 0 0
456456 0 0
457457 −6.46159e6 −1.44727 −0.723634 0.690184i 0.757530π-0.757530\pi
−0.723634 + 0.690184i 0.757530π0.757530\pi
458458 −4.63314e6 −1.03208
459459 0 0
460460 −1.31040e6 −0.288742
461461 −3.37353e6 −0.739320 −0.369660 0.929167i 0.620526π-0.620526\pi
−0.369660 + 0.929167i 0.620526π0.620526\pi
462462 0 0
463463 −4.54974e6 −0.986358 −0.493179 0.869928i 0.664165π-0.664165\pi
−0.493179 + 0.869928i 0.664165π0.664165\pi
464464 −6.18211e6 −1.33304
465465 0 0
466466 −1.51340e6 −0.322842
467467 2.01136e6 0.426773 0.213386 0.976968i 0.431551π-0.431551\pi
0.213386 + 0.976968i 0.431551π0.431551\pi
468468 0 0
469469 0 0
470470 −6.51456e6 −1.36032
471471 0 0
472472 −4.61866e6 −0.954247
473473 5.11666e6 1.05156
474474 0 0
475475 −7.94196e6 −1.61508
476476 0 0
477477 0 0
478478 8.70682e6 1.74297
479479 −7.60402e6 −1.51427 −0.757137 0.653257i 0.773402π-0.773402\pi
−0.757137 + 0.653257i 0.773402π0.773402\pi
480480 0 0
481481 −2.40183e6 −0.473347
482482 878388. 0.172214
483483 0 0
484484 144340. 0.0280074
485485 1.12056e7 2.16313
486486 0 0
487487 673112. 0.128607 0.0643035 0.997930i 0.479517π-0.479517\pi
0.0643035 + 0.997930i 0.479517π0.479517\pi
488488 8.31230e6 1.58005
489489 0 0
490490 0 0
491491 2.47170e6 0.462692 0.231346 0.972872i 0.425687π-0.425687\pi
0.231346 + 0.972872i 0.425687π0.425687\pi
492492 0 0
493493 −685692. −0.127061
494494 −7.11797e6 −1.31232
495495 0 0
496496 90880.0 0.0165869
497497 0 0
498498 0 0
499499 6.08152e6 1.09335 0.546677 0.837343i 0.315892π-0.315892\pi
0.546677 + 0.837343i 0.315892π0.315892\pi
500500 −51792.0 −0.00926483
501501 0 0
502502 3.64716e6 0.645945
503503 −846216. −0.149129 −0.0745644 0.997216i 0.523757π-0.523757\pi
−0.0745644 + 0.997216i 0.523757π0.523757\pi
504504 0 0
505505 −211068. −0.0368293
506506 1.11888e7 1.94271
507507 0 0
508508 −297280. −0.0511101
509509 −7.66785e6 −1.31183 −0.655917 0.754833i 0.727718π-0.727718\pi
−0.655917 + 0.754833i 0.727718π0.727718\pi
510510 0 0
511511 0 0
512512 −4.47130e6 −0.753804
513513 0 0
514514 573516. 0.0957498
515515 −1.02779e7 −1.70760
516516 0 0
517517 6.18048e6 1.01694
518518 0 0
519519 0 0
520520 −5.79197e6 −0.939329
521521 −9.68938e6 −1.56387 −0.781937 0.623357i 0.785768π-0.785768\pi
−0.781937 + 0.623357i 0.785768π0.785768\pi
522522 0 0
523523 7.51678e6 1.20165 0.600824 0.799381i 0.294839π-0.294839\pi
0.600824 + 0.799381i 0.294839π0.294839\pi
524524 −621264. −0.0988435
525525 0 0
526526 1.32021e7 2.08055
527527 10080.0 0.00158101
528528 0 0
529529 1.12037e7 1.74069
530530 4.48999e6 0.694314
531531 0 0
532532 0 0
533533 3.51920e6 0.536570
534534 0 0
535535 1.00554e7 1.51886
536536 9.97181e6 1.49921
537537 0 0
538538 1.06215e7 1.58208
539539 0 0
540540 0 0
541541 7.34325e6 1.07869 0.539343 0.842086i 0.318673π-0.318673\pi
0.539343 + 0.842086i 0.318673π0.318673\pi
542542 1.34102e6 0.196082
543543 0 0
544544 181440. 0.0262867
545545 −7.87628e6 −1.13587
546546 0 0
547547 2.18296e6 0.311945 0.155973 0.987761i 0.450149π-0.450149\pi
0.155973 + 0.987761i 0.450149π0.450149\pi
548548 1.05698e6 0.150355
549549 0 0
550550 −7.88278e6 −1.11115
551551 −1.46063e7 −2.04957
552552 0 0
553553 0 0
554554 −2.05667e6 −0.284702
555555 0 0
556556 −898448. −0.123255
557557 −1.25466e7 −1.71351 −0.856755 0.515724i 0.827523π-0.827523\pi
−0.856755 + 0.515724i 0.827523π0.827523\pi
558558 0 0
559559 −5.09361e6 −0.689439
560560 0 0
561561 0 0
562562 −2.88227e6 −0.384940
563563 5.15972e6 0.686050 0.343025 0.939326i 0.388549π-0.388549\pi
0.343025 + 0.939326i 0.388549π0.388549\pi
564564 0 0
565565 −1.71714e7 −2.26300
566566 179880. 0.0236016
567567 0 0
568568 5.38272e6 0.700053
569569 −1.17452e7 −1.52083 −0.760414 0.649439i 0.775004π-0.775004\pi
−0.760414 + 0.649439i 0.775004π0.775004\pi
570570 0 0
571571 −7.54728e6 −0.968725 −0.484362 0.874867i 0.660948π-0.660948\pi
−0.484362 + 0.874867i 0.660948π0.660948\pi
572572 −784992. −0.100317
573573 0 0
574574 0 0
575575 −1.24278e7 −1.56756
576576 0 0
577577 −9.28483e6 −1.16101 −0.580503 0.814258i 0.697144π-0.697144\pi
−0.580503 + 0.814258i 0.697144π0.697144\pi
578578 −8.42389e6 −1.04880
579579 0 0
580580 1.69790e6 0.209577
581581 0 0
582582 0 0
583583 −4.25974e6 −0.519053
584584 −1.03901e7 −1.26063
585585 0 0
586586 −1.18840e6 −0.142961
587587 1.47623e6 0.176831 0.0884155 0.996084i 0.471820π-0.471820\pi
0.0884155 + 0.996084i 0.471820π0.471820\pi
588588 0 0
589589 214720. 0.0255026
590590 1.28663e7 1.52168
591591 0 0
592592 6.17302e6 0.723925
593593 −1.24007e7 −1.44813 −0.724067 0.689729i 0.757730π-0.757730\pi
−0.724067 + 0.689729i 0.757730π0.757730\pi
594594 0 0
595595 0 0
596596 328296. 0.0378573
597597 0 0
598598 −1.11384e7 −1.27371
599599 3.69127e6 0.420348 0.210174 0.977664i 0.432597π-0.432597\pi
0.210174 + 0.977664i 0.432597π0.432597\pi
600600 0 0
601601 −9.12223e6 −1.03018 −0.515092 0.857135i 0.672242π-0.672242\pi
−0.515092 + 0.857135i 0.672242π0.672242\pi
602602 0 0
603603 0 0
604604 −1.14813e6 −0.128055
605605 2.81463e6 0.312632
606606 0 0
607607 5.67914e6 0.625620 0.312810 0.949816i 0.398730π-0.398730\pi
0.312810 + 0.949816i 0.398730π0.398730\pi
608608 3.86496e6 0.424020
609609 0 0
610610 −2.31557e7 −2.51961
611611 −6.15264e6 −0.666743
612612 0 0
613613 −1.40106e7 −1.50593 −0.752966 0.658060i 0.771377π-0.771377\pi
−0.752966 + 0.658060i 0.771377π0.771377\pi
614614 6.27382e6 0.671600
615615 0 0
616616 0 0
617617 253686. 0.0268277 0.0134139 0.999910i 0.495730π-0.495730\pi
0.0134139 + 0.999910i 0.495730π0.495730\pi
618618 0 0
619619 −4.30034e6 −0.451103 −0.225552 0.974231i 0.572418π-0.572418\pi
−0.225552 + 0.974231i 0.572418π0.572418\pi
620620 −24960.0 −0.00260775
621621 0 0
622622 1.10231e7 1.14242
623623 0 0
624624 0 0
625625 −1.02568e7 −1.05030
626626 2.19296e6 0.223664
627627 0 0
628628 −519512. −0.0525650
629629 684684. 0.0690023
630630 0 0
631631 1.04150e7 1.04132 0.520662 0.853763i 0.325685π-0.325685\pi
0.520662 + 0.853763i 0.325685π0.325685\pi
632632 1.10504e7 1.10048
633633 0 0
634634 170028. 0.0167995
635635 −5.79696e6 −0.570514
636636 0 0
637637 0 0
638638 −1.44975e7 −1.41007
639639 0 0
640640 1.65635e7 1.59846
641641 −4.52714e6 −0.435190 −0.217595 0.976039i 0.569821π-0.569821\pi
−0.217595 + 0.976039i 0.569821π0.569821\pi
642642 0 0
643643 −1.49687e7 −1.42776 −0.713882 0.700266i 0.753065π-0.753065\pi
−0.713882 + 0.700266i 0.753065π0.753065\pi
644644 0 0
645645 0 0
646646 2.02910e6 0.191304
647647 −1.73020e7 −1.62493 −0.812465 0.583010i 0.801875π-0.801875\pi
−0.812465 + 0.583010i 0.801875π0.801875\pi
648648 0 0
649649 −1.22064e7 −1.13757
650650 7.84727e6 0.728509
651651 0 0
652652 2.22114e6 0.204624
653653 −4.07470e6 −0.373949 −0.186975 0.982365i 0.559868π-0.559868\pi
−0.186975 + 0.982365i 0.559868π0.559868\pi
654654 0 0
655655 −1.21146e7 −1.10334
656656 −9.04483e6 −0.820618
657657 0 0
658658 0 0
659659 3.79475e6 0.340384 0.170192 0.985411i 0.445561π-0.445561\pi
0.170192 + 0.985411i 0.445561π0.445561\pi
660660 0 0
661661 −1.64261e7 −1.46228 −0.731142 0.682225i 0.761012π-0.761012\pi
−0.731142 + 0.682225i 0.761012π0.761012\pi
662662 1.16035e7 1.02907
663663 0 0
664664 −6.75158e6 −0.594272
665665 0 0
666666 0 0
667667 −2.28564e7 −1.98927
668668 174048. 0.0150913
669669 0 0
670670 −2.77786e7 −2.39069
671671 2.19682e7 1.88360
672672 0 0
673673 5.50675e6 0.468660 0.234330 0.972157i 0.424710π-0.424710\pi
0.234330 + 0.972157i 0.424710π0.424710\pi
674674 −1.13290e7 −0.960602
675675 0 0
676676 −703716. −0.0592285
677677 1.83957e7 1.54257 0.771286 0.636488i 0.219614π-0.219614\pi
0.771286 + 0.636488i 0.219614π0.219614\pi
678678 0 0
679679 0 0
680680 1.65110e6 0.136931
681681 0 0
682682 213120. 0.0175454
683683 −1.75835e6 −0.144229 −0.0721146 0.997396i 0.522975π-0.522975\pi
−0.0721146 + 0.997396i 0.522975π0.522975\pi
684684 0 0
685685 2.06112e7 1.67833
686686 0 0
687687 0 0
688688 1.30913e7 1.05441
689689 4.24055e6 0.340309
690690 0 0
691691 5.36314e6 0.427291 0.213646 0.976911i 0.431466π-0.431466\pi
0.213646 + 0.976911i 0.431466π0.431466\pi
692692 −73320.0 −0.00582046
693693 0 0
694694 −1.75162e7 −1.38052
695695 −1.75197e7 −1.37583
696696 0 0
697697 −1.00321e6 −0.0782187
698698 4.68409e6 0.363904
699699 0 0
700700 0 0
701701 2.12606e7 1.63411 0.817054 0.576561i 0.195606π-0.195606\pi
0.817054 + 0.576561i 0.195606π0.195606\pi
702702 0 0
703703 1.45849e7 1.11305
704704 −1.23041e7 −0.935662
705705 0 0
706706 8.00622e6 0.604527
707707 0 0
708708 0 0
709709 2.07729e6 0.155196 0.0775980 0.996985i 0.475275π-0.475275\pi
0.0775980 + 0.996985i 0.475275π0.475275\pi
710710 −1.49947e7 −1.11633
711711 0 0
712712 1.33963e6 0.0990343
713713 336000. 0.0247523
714714 0 0
715715 −1.53073e7 −1.11979
716716 613296. 0.0447082
717717 0 0
718718 −6.10459e6 −0.441922
719719 4.23619e6 0.305600 0.152800 0.988257i 0.451171π-0.451171\pi
0.152800 + 0.988257i 0.451171π0.451171\pi
720720 0 0
721721 0 0
722722 2.83665e7 2.02518
723723 0 0
724724 1.52826e6 0.108356
725725 1.61029e7 1.13778
726726 0 0
727727 −2.14524e7 −1.50536 −0.752678 0.658389i 0.771238π-0.771238\pi
−0.752678 + 0.658389i 0.771238π0.771238\pi
728728 0 0
729729 0 0
730730 2.89439e7 2.01025
731731 1.45202e6 0.100503
732732 0 0
733733 1.48892e7 1.02355 0.511777 0.859118i 0.328987π-0.328987\pi
0.511777 + 0.859118i 0.328987π0.328987\pi
734734 −5.02608e6 −0.344341
735735 0 0
736736 6.04800e6 0.411545
737737 2.63541e7 1.78722
738738 0 0
739739 6.99324e6 0.471050 0.235525 0.971868i 0.424319π-0.424319\pi
0.235525 + 0.971868i 0.424319π0.424319\pi
740740 −1.69541e6 −0.113814
741741 0 0
742742 0 0
743743 −1.90428e6 −0.126549 −0.0632745 0.997996i 0.520154π-0.520154\pi
−0.0632745 + 0.997996i 0.520154π0.520154\pi
744744 0 0
745745 6.40177e6 0.422581
746746 −9.11958e6 −0.599968
747747 0 0
748748 223776. 0.0146238
749749 0 0
750750 0 0
751751 1.95361e7 1.26398 0.631988 0.774978i 0.282239π-0.282239\pi
0.631988 + 0.774978i 0.282239π0.282239\pi
752752 1.58131e7 1.01970
753753 0 0
754754 1.44322e7 0.924493
755755 −2.23885e7 −1.42941
756756 0 0
757757 1.25183e6 0.0793973 0.0396986 0.999212i 0.487360π-0.487360\pi
0.0396986 + 0.999212i 0.487360π0.487360\pi
758758 1.58679e7 1.00311
759759 0 0
760760 3.51711e7 2.20878
761761 2.04472e7 1.27989 0.639944 0.768422i 0.278958π-0.278958\pi
0.639944 + 0.768422i 0.278958π0.278958\pi
762762 0 0
763763 0 0
764764 1.09363e6 0.0677857
765765 0 0
766766 1.20802e7 0.743876
767767 1.21515e7 0.745831
768768 0 0
769769 −2.21064e6 −0.134804 −0.0674020 0.997726i 0.521471π-0.521471\pi
−0.0674020 + 0.997726i 0.521471π0.521471\pi
770770 0 0
771771 0 0
772772 614408. 0.0371034
773773 1.29151e7 0.777405 0.388703 0.921363i 0.372923π-0.372923\pi
0.388703 + 0.921363i 0.372923π0.372923\pi
774774 0 0
775775 −236720. −0.0141573
776776 −2.41352e7 −1.43879
777777 0 0
778778 4.35740e6 0.258095
779779 −2.13700e7 −1.26171
780780 0 0
781781 1.42258e7 0.834541
782782 3.17520e6 0.185675
783783 0 0
784784 0 0
785785 −1.01305e7 −0.586754
786786 0 0
787787 1.35499e7 0.779830 0.389915 0.920851i 0.372504π-0.372504\pi
0.389915 + 0.920851i 0.372504π0.372504\pi
788788 −617688. −0.0354367
789789 0 0
790790 −3.07832e7 −1.75487
791791 0 0
792792 0 0
793793 −2.18693e7 −1.23496
794794 −2.74547e7 −1.54549
795795 0 0
796796 1.46742e6 0.0820867
797797 −2.45956e7 −1.37155 −0.685776 0.727813i 0.740537π-0.740537\pi
−0.685776 + 0.727813i 0.740537π0.740537\pi
798798 0 0
799799 1.75392e6 0.0971948
800800 −4.26096e6 −0.235387
801801 0 0
802802 203220. 0.0111566
803803 −2.74596e7 −1.50282
804804 0 0
805805 0 0
806806 −212160. −0.0115034
807807 0 0
808808 454608. 0.0244968
809809 −1.55237e7 −0.833920 −0.416960 0.908925i 0.636905π-0.636905\pi
−0.416960 + 0.908925i 0.636905π0.636905\pi
810810 0 0
811811 2.66262e7 1.42153 0.710766 0.703429i 0.248349π-0.248349\pi
0.710766 + 0.703429i 0.248349π0.248349\pi
812812 0 0
813813 0 0
814814 1.44762e7 0.765760
815815 4.33122e7 2.28410
816816 0 0
817817 3.09304e7 1.62118
818818 3.51707e7 1.83780
819819 0 0
820820 2.48414e6 0.129016
821821 1.23891e7 0.641477 0.320739 0.947168i 0.396069π-0.396069\pi
0.320739 + 0.947168i 0.396069π0.396069\pi
822822 0 0
823823 −3.65630e6 −0.188166 −0.0940831 0.995564i 0.529992π-0.529992\pi
−0.0940831 + 0.995564i 0.529992π0.529992\pi
824824 2.21370e7 1.13580
825825 0 0
826826 0 0
827827 −2.80463e7 −1.42597 −0.712987 0.701178i 0.752658π-0.752658\pi
−0.712987 + 0.701178i 0.752658π0.752658\pi
828828 0 0
829829 −2.11153e7 −1.06712 −0.533558 0.845763i 0.679145π-0.679145\pi
−0.533558 + 0.845763i 0.679145π0.679145\pi
830830 1.88080e7 0.947648
831831 0 0
832832 1.22487e7 0.613454
833833 0 0
834834 0 0
835835 3.39394e6 0.168456
836836 4.76678e6 0.235890
837837 0 0
838838 1.81649e6 0.0893557
839839 1.33947e7 0.656944 0.328472 0.944514i 0.393466π-0.393466\pi
0.328472 + 0.944514i 0.393466π0.393466\pi
840840 0 0
841841 9.10422e6 0.443867
842842 −3.22025e7 −1.56534
843843 0 0
844844 2.08098e6 0.100557
845845 −1.37225e7 −0.661135
846846 0 0
847847 0 0
848848 −1.08988e7 −0.520461
849849 0 0
850850 −2.23700e6 −0.106199
851851 2.28228e7 1.08030
852852 0 0
853853 −3.01513e7 −1.41884 −0.709420 0.704786i 0.751043π-0.751043\pi
−0.709420 + 0.704786i 0.751043π0.751043\pi
854854 0 0
855855 0 0
856856 −2.16579e7 −1.01026
857857 2.39894e7 1.11575 0.557875 0.829925i 0.311617π-0.311617\pi
0.557875 + 0.829925i 0.311617π0.311617\pi
858858 0 0
859859 8.87576e6 0.410414 0.205207 0.978719i 0.434213π-0.434213\pi
0.205207 + 0.978719i 0.434213π0.434213\pi
860860 −3.59549e6 −0.165772
861861 0 0
862862 −7.06234e6 −0.323728
863863 8.71286e6 0.398230 0.199115 0.979976i 0.436193π-0.436193\pi
0.199115 + 0.979976i 0.436193π0.436193\pi
864864 0 0
865865 −1.42974e6 −0.0649706
866866 2.19750e7 0.995711
867867 0 0
868868 0 0
869869 2.92045e7 1.31190
870870 0 0
871871 −2.62354e7 −1.17177
872872 1.69643e7 0.755518
873873 0 0
874874 6.76368e7 2.99505
875875 0 0
876876 0 0
877877 −2.95788e7 −1.29862 −0.649310 0.760524i 0.724942π-0.724942\pi
−0.649310 + 0.760524i 0.724942π0.724942\pi
878878 1.52205e7 0.666333
879879 0 0
880880 3.93420e7 1.71257
881881 2.45670e7 1.06638 0.533190 0.845995i 0.320993π-0.320993\pi
0.533190 + 0.845995i 0.320993π0.320993\pi
882882 0 0
883883 1.45682e7 0.628788 0.314394 0.949293i 0.398199π-0.398199\pi
0.314394 + 0.949293i 0.398199π0.398199\pi
884884 −222768. −0.00958787
885885 0 0
886886 −3.60902e7 −1.54456
887887 1.61714e7 0.690141 0.345070 0.938577i 0.387855π-0.387855\pi
0.345070 + 0.938577i 0.387855π0.387855\pi
888888 0 0
889889 0 0
890890 −3.73183e6 −0.157924
891891 0 0
892892 −1.21894e6 −0.0512946
893893 3.73613e7 1.56781
894894 0 0
895895 1.19593e7 0.499054
896896 0 0
897897 0 0
898898 −3.39579e7 −1.40524
899899 −435360. −0.0179659
900900 0 0
901901 −1.20884e6 −0.0496087
902902 −2.12108e7 −0.868041
903903 0 0
904904 3.69845e7 1.50522
905905 2.98011e7 1.20952
906906 0 0
907907 3.14446e7 1.26919 0.634596 0.772844i 0.281167π-0.281167\pi
0.634596 + 0.772844i 0.281167π0.281167\pi
908908 1.15435e6 0.0464648
909909 0 0
910910 0 0
911911 −1.51427e7 −0.604514 −0.302257 0.953227i 0.597740π-0.597740\pi
−0.302257 + 0.953227i 0.597740π0.597740\pi
912912 0 0
913913 −1.78435e7 −0.708439
914914 −3.87695e7 −1.53506
915915 0 0
916916 −3.08876e6 −0.121631
917917 0 0
918918 0 0
919919 4.14876e7 1.62043 0.810214 0.586134i 0.199351π-0.199351\pi
0.810214 + 0.586134i 0.199351π0.199351\pi
920920 5.50368e7 2.14380
921921 0 0
922922 −2.02412e7 −0.784167
923923 −1.41617e7 −0.547155
924924 0 0
925925 −1.60792e7 −0.617889
926926 −2.72985e7 −1.04619
927927 0 0
928928 −7.83648e6 −0.298711
929929 −1.78495e7 −0.678556 −0.339278 0.940686i 0.610183π-0.610183\pi
−0.339278 + 0.940686i 0.610183π0.610183\pi
930930 0 0
931931 0 0
932932 −1.00894e6 −0.0380473
933933 0 0
934934 1.20681e7 0.452661
935935 4.36363e6 0.163237
936936 0 0
937937 −2.96399e7 −1.10288 −0.551439 0.834215i 0.685921π-0.685921\pi
−0.551439 + 0.834215i 0.685921π0.685921\pi
938938 0 0
939939 0 0
940940 −4.34304e6 −0.160315
941941 −3.22282e7 −1.18648 −0.593242 0.805024i 0.702152π-0.702152\pi
−0.593242 + 0.805024i 0.702152π0.702152\pi
942942 0 0
943943 −3.34404e7 −1.22459
944944 −3.12309e7 −1.14066
945945 0 0
946946 3.06999e7 1.11535
947947 −4.84885e7 −1.75697 −0.878484 0.477772i 0.841444π-0.841444\pi
−0.878484 + 0.477772i 0.841444π0.841444\pi
948948 0 0
949949 2.73359e7 0.985300
950950 −4.76517e7 −1.71305
951951 0 0
952952 0 0
953953 2.03264e7 0.724983 0.362491 0.931987i 0.381926π-0.381926\pi
0.362491 + 0.931987i 0.381926π0.381926\pi
954954 0 0
955955 2.13258e7 0.756654
956956 5.80454e6 0.205411
957957 0 0
958958 −4.56241e7 −1.60613
959959 0 0
960960 0 0
961961 −2.86228e7 −0.999776
962962 −1.44110e7 −0.502060
963963 0 0
964964 585592. 0.0202956
965965 1.19810e7 0.414165
966966 0 0
967967 −3.66292e6 −0.125968 −0.0629841 0.998015i 0.520062π-0.520062\pi
−0.0629841 + 0.998015i 0.520062π0.520062\pi
968968 −6.06228e6 −0.207945
969969 0 0
970970 6.72338e7 2.29434
971971 1.48741e6 0.0506271 0.0253136 0.999680i 0.491942π-0.491942\pi
0.0253136 + 0.999680i 0.491942π0.491942\pi
972972 0 0
973973 0 0
974974 4.03867e6 0.136408
975975 0 0
976976 5.62070e7 1.88871
977977 −4.07930e7 −1.36725 −0.683627 0.729831i 0.739599π-0.739599\pi
−0.683627 + 0.729831i 0.739599π0.739599\pi
978978 0 0
979979 3.54046e6 0.118060
980980 0 0
981981 0 0
982982 1.48302e7 0.490759
983983 −9.26326e6 −0.305759 −0.152880 0.988245i 0.548855π-0.548855\pi
−0.152880 + 0.988245i 0.548855π0.548855\pi
984984 0 0
985985 −1.20449e7 −0.395561
986986 −4.11415e6 −0.134768
987987 0 0
988988 −4.74531e6 −0.154658
989989 4.84008e7 1.57348
990990 0 0
991991 −5.22051e7 −1.68861 −0.844303 0.535866i 0.819985π-0.819985\pi
−0.844303 + 0.535866i 0.819985π0.819985\pi
992992 115200. 0.00371684
993993 0 0
994994 0 0
995995 2.86148e7 0.916289
996996 0 0
997997 1.86609e7 0.594560 0.297280 0.954790i 0.403921π-0.403921\pi
0.297280 + 0.954790i 0.403921π0.403921\pi
998998 3.64891e7 1.15968
999999 0 0
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 441.6.a.j.1.1 1
3.2 odd 2 147.6.a.b.1.1 1
7.6 odd 2 63.6.a.d.1.1 1
21.2 odd 6 147.6.e.i.67.1 2
21.5 even 6 147.6.e.j.67.1 2
21.11 odd 6 147.6.e.i.79.1 2
21.17 even 6 147.6.e.j.79.1 2
21.20 even 2 21.6.a.a.1.1 1
28.27 even 2 1008.6.a.c.1.1 1
84.83 odd 2 336.6.a.r.1.1 1
105.62 odd 4 525.6.d.b.274.1 2
105.83 odd 4 525.6.d.b.274.2 2
105.104 even 2 525.6.a.d.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
21.6.a.a.1.1 1 21.20 even 2
63.6.a.d.1.1 1 7.6 odd 2
147.6.a.b.1.1 1 3.2 odd 2
147.6.e.i.67.1 2 21.2 odd 6
147.6.e.i.79.1 2 21.11 odd 6
147.6.e.j.67.1 2 21.5 even 6
147.6.e.j.79.1 2 21.17 even 6
336.6.a.r.1.1 1 84.83 odd 2
441.6.a.j.1.1 1 1.1 even 1 trivial
525.6.a.d.1.1 1 105.104 even 2
525.6.d.b.274.1 2 105.62 odd 4
525.6.d.b.274.2 2 105.83 odd 4
1008.6.a.c.1.1 1 28.27 even 2