Properties

Label 912.6.a.c.1.1
Level 912912
Weight 66
Character 912.1
Self dual yes
Analytic conductor 146.270146.270
Analytic rank 00
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] = [912,6,Mod(1,912)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(912, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 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("912.1");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: N N == 912=24319 912 = 2^{4} \cdot 3 \cdot 19
Weight: k k == 6 6
Character orbit: [χ][\chi] == 912.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: 146.270043669146.270043669
Analytic rank: 00
Dimension: 11
Coefficient field: Q\mathbb{Q}
Coefficient ring: Z\mathbb{Z}
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 114)
Fricke sign: 1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.1
Character χ\chi == 912.1

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) == q9.00000q354.0000q5104.000q7+81.0000q9+330.000q1146.0000q13+486.000q15618.000q17361.000q19+936.000q21+402.000q23209.000q25729.000q272628.00q29+2368.00q312970.00q33+5616.00q3512130.0q37+414.000q3918864.0q41+10408.0q434374.00q45+4770.00q475991.00q49+5562.00q5119452.0q5317820.0q55+3249.00q5730528.0q59+11138.0q618424.00q63+2484.00q6549508.0q673618.00q697572.00q71+2342.00q73+1881.00q7534320.0q7722424.0q79+6561.00q81+46734.0q83+33372.0q85+23652.0q8770104.0q89+4784.00q9121312.0q93+19494.0q95+105710.q97+26730.0q99+O(q100)q-9.00000 q^{3} -54.0000 q^{5} -104.000 q^{7} +81.0000 q^{9} +330.000 q^{11} -46.0000 q^{13} +486.000 q^{15} -618.000 q^{17} -361.000 q^{19} +936.000 q^{21} +402.000 q^{23} -209.000 q^{25} -729.000 q^{27} -2628.00 q^{29} +2368.00 q^{31} -2970.00 q^{33} +5616.00 q^{35} -12130.0 q^{37} +414.000 q^{39} -18864.0 q^{41} +10408.0 q^{43} -4374.00 q^{45} +4770.00 q^{47} -5991.00 q^{49} +5562.00 q^{51} -19452.0 q^{53} -17820.0 q^{55} +3249.00 q^{57} -30528.0 q^{59} +11138.0 q^{61} -8424.00 q^{63} +2484.00 q^{65} -49508.0 q^{67} -3618.00 q^{69} -7572.00 q^{71} +2342.00 q^{73} +1881.00 q^{75} -34320.0 q^{77} -22424.0 q^{79} +6561.00 q^{81} +46734.0 q^{83} +33372.0 q^{85} +23652.0 q^{87} -70104.0 q^{89} +4784.00 q^{91} -21312.0 q^{93} +19494.0 q^{95} +105710. q^{97} +26730.0 q^{99} +O(q^{100})

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 0 0
33 −9.00000 −0.577350
44 0 0
55 −54.0000 −0.965981 −0.482991 0.875625i 0.660450π-0.660450\pi
−0.482991 + 0.875625i 0.660450π0.660450\pi
66 0 0
77 −104.000 −0.802210 −0.401105 0.916032i 0.631374π-0.631374\pi
−0.401105 + 0.916032i 0.631374π0.631374\pi
88 0 0
99 81.0000 0.333333
1010 0 0
1111 330.000 0.822304 0.411152 0.911567i 0.365127π-0.365127\pi
0.411152 + 0.911567i 0.365127π0.365127\pi
1212 0 0
1313 −46.0000 −0.0754917 −0.0377459 0.999287i 0.512018π-0.512018\pi
−0.0377459 + 0.999287i 0.512018π0.512018\pi
1414 0 0
1515 486.000 0.557710
1616 0 0
1717 −618.000 −0.518640 −0.259320 0.965791i 0.583498π-0.583498\pi
−0.259320 + 0.965791i 0.583498π0.583498\pi
1818 0 0
1919 −361.000 −0.229416
2020 0 0
2121 936.000 0.463156
2222 0 0
2323 402.000 0.158455 0.0792276 0.996857i 0.474755π-0.474755\pi
0.0792276 + 0.996857i 0.474755π0.474755\pi
2424 0 0
2525 −209.000 −0.0668800
2626 0 0
2727 −729.000 −0.192450
2828 0 0
2929 −2628.00 −0.580270 −0.290135 0.956986i 0.593700π-0.593700\pi
−0.290135 + 0.956986i 0.593700π0.593700\pi
3030 0 0
3131 2368.00 0.442565 0.221283 0.975210i 0.428976π-0.428976\pi
0.221283 + 0.975210i 0.428976π0.428976\pi
3232 0 0
3333 −2970.00 −0.474757
3434 0 0
3535 5616.00 0.774920
3636 0 0
3737 −12130.0 −1.45665 −0.728327 0.685230i 0.759702π-0.759702\pi
−0.728327 + 0.685230i 0.759702π0.759702\pi
3838 0 0
3939 414.000 0.0435852
4040 0 0
4141 −18864.0 −1.75257 −0.876283 0.481798i 0.839984π-0.839984\pi
−0.876283 + 0.481798i 0.839984π0.839984\pi
4242 0 0
4343 10408.0 0.858413 0.429206 0.903206i 0.358793π-0.358793\pi
0.429206 + 0.903206i 0.358793π0.358793\pi
4444 0 0
4545 −4374.00 −0.321994
4646 0 0
4747 4770.00 0.314973 0.157487 0.987521i 0.449661π-0.449661\pi
0.157487 + 0.987521i 0.449661π0.449661\pi
4848 0 0
4949 −5991.00 −0.356459
5050 0 0
5151 5562.00 0.299437
5252 0 0
5353 −19452.0 −0.951206 −0.475603 0.879660i 0.657770π-0.657770\pi
−0.475603 + 0.879660i 0.657770π0.657770\pi
5454 0 0
5555 −17820.0 −0.794330
5656 0 0
5757 3249.00 0.132453
5858 0 0
5959 −30528.0 −1.14174 −0.570871 0.821039i 0.693395π-0.693395\pi
−0.570871 + 0.821039i 0.693395π0.693395\pi
6060 0 0
6161 11138.0 0.383250 0.191625 0.981468i 0.438624π-0.438624\pi
0.191625 + 0.981468i 0.438624π0.438624\pi
6262 0 0
6363 −8424.00 −0.267403
6464 0 0
6565 2484.00 0.0729236
6666 0 0
6767 −49508.0 −1.34737 −0.673687 0.739016i 0.735291π-0.735291\pi
−0.673687 + 0.739016i 0.735291π0.735291\pi
6868 0 0
6969 −3618.00 −0.0914841
7070 0 0
7171 −7572.00 −0.178264 −0.0891322 0.996020i 0.528409π-0.528409\pi
−0.0891322 + 0.996020i 0.528409π0.528409\pi
7272 0 0
7373 2342.00 0.0514375 0.0257187 0.999669i 0.491813π-0.491813\pi
0.0257187 + 0.999669i 0.491813π0.491813\pi
7474 0 0
7575 1881.00 0.0386132
7676 0 0
7777 −34320.0 −0.659660
7878 0 0
7979 −22424.0 −0.404246 −0.202123 0.979360i 0.564784π-0.564784\pi
−0.202123 + 0.979360i 0.564784π0.564784\pi
8080 0 0
8181 6561.00 0.111111
8282 0 0
8383 46734.0 0.744625 0.372313 0.928107i 0.378565π-0.378565\pi
0.372313 + 0.928107i 0.378565π0.378565\pi
8484 0 0
8585 33372.0 0.500997
8686 0 0
8787 23652.0 0.335019
8888 0 0
8989 −70104.0 −0.938140 −0.469070 0.883161i 0.655411π-0.655411\pi
−0.469070 + 0.883161i 0.655411π0.655411\pi
9090 0 0
9191 4784.00 0.0605603
9292 0 0
9393 −21312.0 −0.255515
9494 0 0
9595 19494.0 0.221611
9696 0 0
9797 105710. 1.14074 0.570370 0.821388i 0.306800π-0.306800\pi
0.570370 + 0.821388i 0.306800π0.306800\pi
9898 0 0
9999 26730.0 0.274101
100100 0 0
101101 124542. 1.21482 0.607411 0.794388i 0.292208π-0.292208\pi
0.607411 + 0.794388i 0.292208π0.292208\pi
102102 0 0
103103 −6488.00 −0.0602584 −0.0301292 0.999546i 0.509592π-0.509592\pi
−0.0301292 + 0.999546i 0.509592π0.509592\pi
104104 0 0
105105 −50544.0 −0.447400
106106 0 0
107107 −50040.0 −0.422530 −0.211265 0.977429i 0.567758π-0.567758\pi
−0.211265 + 0.977429i 0.567758π0.567758\pi
108108 0 0
109109 88706.0 0.715133 0.357566 0.933888i 0.383607π-0.383607\pi
0.357566 + 0.933888i 0.383607π0.383607\pi
110110 0 0
111111 109170. 0.841000
112112 0 0
113113 −156792. −1.15512 −0.577561 0.816348i 0.695995π-0.695995\pi
−0.577561 + 0.816348i 0.695995π0.695995\pi
114114 0 0
115115 −21708.0 −0.153065
116116 0 0
117117 −3726.00 −0.0251639
118118 0 0
119119 64272.0 0.416059
120120 0 0
121121 −52151.0 −0.323817
122122 0 0
123123 169776. 1.01184
124124 0 0
125125 180036. 1.03059
126126 0 0
127127 211768. 1.16507 0.582534 0.812807i 0.302061π-0.302061\pi
0.582534 + 0.812807i 0.302061π0.302061\pi
128128 0 0
129129 −93672.0 −0.495605
130130 0 0
131131 4410.00 0.0224523 0.0112261 0.999937i 0.496427π-0.496427\pi
0.0112261 + 0.999937i 0.496427π0.496427\pi
132132 0 0
133133 37544.0 0.184040
134134 0 0
135135 39366.0 0.185903
136136 0 0
137137 205974. 0.937586 0.468793 0.883308i 0.344689π-0.344689\pi
0.468793 + 0.883308i 0.344689π0.344689\pi
138138 0 0
139139 −315908. −1.38683 −0.693416 0.720538i 0.743895π-0.743895\pi
−0.693416 + 0.720538i 0.743895π0.743895\pi
140140 0 0
141141 −42930.0 −0.181850
142142 0 0
143143 −15180.0 −0.0620771
144144 0 0
145145 141912. 0.560530
146146 0 0
147147 53919.0 0.205801
148148 0 0
149149 211158. 0.779187 0.389594 0.920987i 0.372615π-0.372615\pi
0.389594 + 0.920987i 0.372615π0.372615\pi
150150 0 0
151151 118120. 0.421581 0.210791 0.977531i 0.432396π-0.432396\pi
0.210791 + 0.977531i 0.432396π0.432396\pi
152152 0 0
153153 −50058.0 −0.172880
154154 0 0
155155 −127872. −0.427510
156156 0 0
157157 −163990. −0.530968 −0.265484 0.964115i 0.585532π-0.585532\pi
−0.265484 + 0.964115i 0.585532π0.585532\pi
158158 0 0
159159 175068. 0.549179
160160 0 0
161161 −41808.0 −0.127114
162162 0 0
163163 −26948.0 −0.0794433 −0.0397217 0.999211i 0.512647π-0.512647\pi
−0.0397217 + 0.999211i 0.512647π0.512647\pi
164164 0 0
165165 160380. 0.458607
166166 0 0
167167 −5808.00 −0.0161152 −0.00805759 0.999968i 0.502565π-0.502565\pi
−0.00805759 + 0.999968i 0.502565π0.502565\pi
168168 0 0
169169 −369177. −0.994301
170170 0 0
171171 −29241.0 −0.0764719
172172 0 0
173173 37104.0 0.0942552 0.0471276 0.998889i 0.484993π-0.484993\pi
0.0471276 + 0.998889i 0.484993π0.484993\pi
174174 0 0
175175 21736.0 0.0536518
176176 0 0
177177 274752. 0.659186
178178 0 0
179179 −198360. −0.462723 −0.231362 0.972868i 0.574318π-0.574318\pi
−0.231362 + 0.972868i 0.574318π0.574318\pi
180180 0 0
181181 −276838. −0.628101 −0.314050 0.949406i 0.601686π-0.601686\pi
−0.314050 + 0.949406i 0.601686π0.601686\pi
182182 0 0
183183 −100242. −0.221270
184184 0 0
185185 655020. 1.40710
186186 0 0
187187 −203940. −0.426480
188188 0 0
189189 75816.0 0.154385
190190 0 0
191191 531222. 1.05364 0.526820 0.849977i 0.323384π-0.323384\pi
0.526820 + 0.849977i 0.323384π0.323384\pi
192192 0 0
193193 −245062. −0.473568 −0.236784 0.971562i 0.576093π-0.576093\pi
−0.236784 + 0.971562i 0.576093π0.576093\pi
194194 0 0
195195 −22356.0 −0.0421025
196196 0 0
197197 219906. 0.403712 0.201856 0.979415i 0.435303π-0.435303\pi
0.201856 + 0.979415i 0.435303π0.435303\pi
198198 0 0
199199 1.01820e6 1.82265 0.911323 0.411693i 0.135062π-0.135062\pi
0.911323 + 0.411693i 0.135062π0.135062\pi
200200 0 0
201201 445572. 0.777907
202202 0 0
203203 273312. 0.465499
204204 0 0
205205 1.01866e6 1.69295
206206 0 0
207207 32562.0 0.0528184
208208 0 0
209209 −119130. −0.188649
210210 0 0
211211 −105020. −0.162392 −0.0811962 0.996698i 0.525874π-0.525874\pi
−0.0811962 + 0.996698i 0.525874π0.525874\pi
212212 0 0
213213 68148.0 0.102921
214214 0 0
215215 −562032. −0.829211
216216 0 0
217217 −246272. −0.355031
218218 0 0
219219 −21078.0 −0.0296974
220220 0 0
221221 28428.0 0.0391531
222222 0 0
223223 −988304. −1.33085 −0.665424 0.746466i 0.731749π-0.731749\pi
−0.665424 + 0.746466i 0.731749π0.731749\pi
224224 0 0
225225 −16929.0 −0.0222933
226226 0 0
227227 515940. 0.664561 0.332280 0.943181i 0.392182π-0.392182\pi
0.332280 + 0.943181i 0.392182π0.392182\pi
228228 0 0
229229 −277354. −0.349499 −0.174749 0.984613i 0.555912π-0.555912\pi
−0.174749 + 0.984613i 0.555912π0.555912\pi
230230 0 0
231231 308880. 0.380855
232232 0 0
233233 1.54151e6 1.86019 0.930096 0.367317i 0.119724π-0.119724\pi
0.930096 + 0.367317i 0.119724π0.119724\pi
234234 0 0
235235 −257580. −0.304258
236236 0 0
237237 201816. 0.233391
238238 0 0
239239 314310. 0.355929 0.177965 0.984037i 0.443049π-0.443049\pi
0.177965 + 0.984037i 0.443049π0.443049\pi
240240 0 0
241241 24566.0 0.0272453 0.0136227 0.999907i 0.495664π-0.495664\pi
0.0136227 + 0.999907i 0.495664π0.495664\pi
242242 0 0
243243 −59049.0 −0.0641500
244244 0 0
245245 323514. 0.344332
246246 0 0
247247 16606.0 0.0173190
248248 0 0
249249 −420606. −0.429910
250250 0 0
251251 −661290. −0.662533 −0.331267 0.943537i 0.607476π-0.607476\pi
−0.331267 + 0.943537i 0.607476π0.607476\pi
252252 0 0
253253 132660. 0.130298
254254 0 0
255255 −300348. −0.289251
256256 0 0
257257 1.05035e6 0.991974 0.495987 0.868330i 0.334806π-0.334806\pi
0.495987 + 0.868330i 0.334806π0.334806\pi
258258 0 0
259259 1.26152e6 1.16854
260260 0 0
261261 −212868. −0.193423
262262 0 0
263263 465510. 0.414992 0.207496 0.978236i 0.433469π-0.433469\pi
0.207496 + 0.978236i 0.433469π0.433469\pi
264264 0 0
265265 1.05041e6 0.918847
266266 0 0
267267 630936. 0.541636
268268 0 0
269269 −317112. −0.267197 −0.133599 0.991036i 0.542653π-0.542653\pi
−0.133599 + 0.991036i 0.542653π0.542653\pi
270270 0 0
271271 1.48901e6 1.23162 0.615808 0.787897i 0.288830π-0.288830\pi
0.615808 + 0.787897i 0.288830π0.288830\pi
272272 0 0
273273 −43056.0 −0.0349645
274274 0 0
275275 −68970.0 −0.0549957
276276 0 0
277277 −1.54028e6 −1.20615 −0.603074 0.797685i 0.706058π-0.706058\pi
−0.603074 + 0.797685i 0.706058π0.706058\pi
278278 0 0
279279 191808. 0.147522
280280 0 0
281281 1.99595e6 1.50794 0.753969 0.656910i 0.228137π-0.228137\pi
0.753969 + 0.656910i 0.228137π0.228137\pi
282282 0 0
283283 946936. 0.702837 0.351418 0.936219i 0.385699π-0.385699\pi
0.351418 + 0.936219i 0.385699π0.385699\pi
284284 0 0
285285 −175446. −0.127947
286286 0 0
287287 1.96186e6 1.40593
288288 0 0
289289 −1.03793e6 −0.731012
290290 0 0
291291 −951390. −0.658607
292292 0 0
293293 2.18170e6 1.48465 0.742327 0.670038i 0.233722π-0.233722\pi
0.742327 + 0.670038i 0.233722π0.233722\pi
294294 0 0
295295 1.64851e6 1.10290
296296 0 0
297297 −240570. −0.158252
298298 0 0
299299 −18492.0 −0.0119621
300300 0 0
301301 −1.08243e6 −0.688628
302302 0 0
303303 −1.12088e6 −0.701377
304304 0 0
305305 −601452. −0.370213
306306 0 0
307307 2.50414e6 1.51640 0.758198 0.652024i 0.226080π-0.226080\pi
0.758198 + 0.652024i 0.226080π0.226080\pi
308308 0 0
309309 58392.0 0.0347902
310310 0 0
311311 785658. 0.460609 0.230305 0.973119i 0.426028π-0.426028\pi
0.230305 + 0.973119i 0.426028π0.426028\pi
312312 0 0
313313 364334. 0.210203 0.105101 0.994462i 0.466483π-0.466483\pi
0.105101 + 0.994462i 0.466483π0.466483\pi
314314 0 0
315315 454896. 0.258307
316316 0 0
317317 −1.46938e6 −0.821268 −0.410634 0.911800i 0.634693π-0.634693\pi
−0.410634 + 0.911800i 0.634693π0.634693\pi
318318 0 0
319319 −867240. −0.477158
320320 0 0
321321 450360. 0.243948
322322 0 0
323323 223098. 0.118984
324324 0 0
325325 9614.00 0.00504889
326326 0 0
327327 −798354. −0.412882
328328 0 0
329329 −496080. −0.252675
330330 0 0
331331 −1.67414e6 −0.839889 −0.419944 0.907550i 0.637950π-0.637950\pi
−0.419944 + 0.907550i 0.637950π0.637950\pi
332332 0 0
333333 −982530. −0.485551
334334 0 0
335335 2.67343e6 1.30154
336336 0 0
337337 3.02010e6 1.44859 0.724297 0.689488i 0.242164π-0.242164\pi
0.724297 + 0.689488i 0.242164π0.242164\pi
338338 0 0
339339 1.41113e6 0.666910
340340 0 0
341341 781440. 0.363923
342342 0 0
343343 2.37099e6 1.08817
344344 0 0
345345 195372. 0.0883720
346346 0 0
347347 −2.79531e6 −1.24625 −0.623127 0.782121i 0.714138π-0.714138\pi
−0.623127 + 0.782121i 0.714138π0.714138\pi
348348 0 0
349349 −3.92975e6 −1.72703 −0.863517 0.504320i 0.831743π-0.831743\pi
−0.863517 + 0.504320i 0.831743π0.831743\pi
350350 0 0
351351 33534.0 0.0145284
352352 0 0
353353 −1.56554e6 −0.668693 −0.334347 0.942450i 0.608516π-0.608516\pi
−0.334347 + 0.942450i 0.608516π0.608516\pi
354354 0 0
355355 408888. 0.172200
356356 0 0
357357 −578448. −0.240211
358358 0 0
359359 2.19680e6 0.899609 0.449805 0.893127i 0.351494π-0.351494\pi
0.449805 + 0.893127i 0.351494π0.351494\pi
360360 0 0
361361 130321. 0.0526316
362362 0 0
363363 469359. 0.186956
364364 0 0
365365 −126468. −0.0496877
366366 0 0
367367 4.24772e6 1.64623 0.823115 0.567875i 0.192234π-0.192234\pi
0.823115 + 0.567875i 0.192234π0.192234\pi
368368 0 0
369369 −1.52798e6 −0.584188
370370 0 0
371371 2.02301e6 0.763067
372372 0 0
373373 4.24597e6 1.58018 0.790088 0.612994i 0.210035π-0.210035\pi
0.790088 + 0.612994i 0.210035π0.210035\pi
374374 0 0
375375 −1.62032e6 −0.595009
376376 0 0
377377 120888. 0.0438056
378378 0 0
379379 −3.06794e6 −1.09711 −0.548553 0.836116i 0.684821π-0.684821\pi
−0.548553 + 0.836116i 0.684821π0.684821\pi
380380 0 0
381381 −1.90591e6 −0.672652
382382 0 0
383383 −5.23012e6 −1.82186 −0.910929 0.412564i 0.864633π-0.864633\pi
−0.910929 + 0.412564i 0.864633π0.864633\pi
384384 0 0
385385 1.85328e6 0.637220
386386 0 0
387387 843048. 0.286138
388388 0 0
389389 −3.36209e6 −1.12651 −0.563256 0.826282i 0.690452π-0.690452\pi
−0.563256 + 0.826282i 0.690452π0.690452\pi
390390 0 0
391391 −248436. −0.0821812
392392 0 0
393393 −39690.0 −0.0129628
394394 0 0
395395 1.21090e6 0.390494
396396 0 0
397397 2.92432e6 0.931211 0.465606 0.884992i 0.345836π-0.345836\pi
0.465606 + 0.884992i 0.345836π0.345836\pi
398398 0 0
399399 −337896. −0.106255
400400 0 0
401401 5.80702e6 1.80340 0.901700 0.432362i 0.142320π-0.142320\pi
0.901700 + 0.432362i 0.142320π0.142320\pi
402402 0 0
403403 −108928. −0.0334100
404404 0 0
405405 −354294. −0.107331
406406 0 0
407407 −4.00290e6 −1.19781
408408 0 0
409409 1.80028e6 0.532147 0.266073 0.963953i 0.414274π-0.414274\pi
0.266073 + 0.963953i 0.414274π0.414274\pi
410410 0 0
411411 −1.85377e6 −0.541315
412412 0 0
413413 3.17491e6 0.915918
414414 0 0
415415 −2.52364e6 −0.719294
416416 0 0
417417 2.84317e6 0.800687
418418 0 0
419419 1.38477e6 0.385339 0.192669 0.981264i 0.438286π-0.438286\pi
0.192669 + 0.981264i 0.438286π0.438286\pi
420420 0 0
421421 −315598. −0.0867819 −0.0433909 0.999058i 0.513816π-0.513816\pi
−0.0433909 + 0.999058i 0.513816π0.513816\pi
422422 0 0
423423 386370. 0.104991
424424 0 0
425425 129162. 0.0346867
426426 0 0
427427 −1.15835e6 −0.307447
428428 0 0
429429 136620. 0.0358403
430430 0 0
431431 6.52696e6 1.69246 0.846228 0.532821i 0.178868π-0.178868\pi
0.846228 + 0.532821i 0.178868π0.178868\pi
432432 0 0
433433 2.63139e6 0.674473 0.337237 0.941420i 0.390508π-0.390508\pi
0.337237 + 0.941420i 0.390508π0.390508\pi
434434 0 0
435435 −1.27721e6 −0.323622
436436 0 0
437437 −145122. −0.0363521
438438 0 0
439439 −3.09445e6 −0.766341 −0.383170 0.923678i 0.625168π-0.625168\pi
−0.383170 + 0.923678i 0.625168π0.625168\pi
440440 0 0
441441 −485271. −0.118820
442442 0 0
443443 −985086. −0.238487 −0.119244 0.992865i 0.538047π-0.538047\pi
−0.119244 + 0.992865i 0.538047π0.538047\pi
444444 0 0
445445 3.78562e6 0.906226
446446 0 0
447447 −1.90042e6 −0.449864
448448 0 0
449449 −2.91582e6 −0.682566 −0.341283 0.939961i 0.610862π-0.610862\pi
−0.341283 + 0.939961i 0.610862π0.610862\pi
450450 0 0
451451 −6.22512e6 −1.44114
452452 0 0
453453 −1.06308e6 −0.243400
454454 0 0
455455 −258336. −0.0585001
456456 0 0
457457 −3.54721e6 −0.794505 −0.397252 0.917709i 0.630036π-0.630036\pi
−0.397252 + 0.917709i 0.630036π0.630036\pi
458458 0 0
459459 450522. 0.0998124
460460 0 0
461461 4.57057e6 1.00165 0.500827 0.865547i 0.333029π-0.333029\pi
0.500827 + 0.865547i 0.333029π0.333029\pi
462462 0 0
463463 −5.91304e6 −1.28191 −0.640957 0.767577i 0.721462π-0.721462\pi
−0.640957 + 0.767577i 0.721462π0.721462\pi
464464 0 0
465465 1.15085e6 0.246823
466466 0 0
467467 3.73808e6 0.793152 0.396576 0.918002i 0.370198π-0.370198\pi
0.396576 + 0.918002i 0.370198π0.370198\pi
468468 0 0
469469 5.14883e6 1.08088
470470 0 0
471471 1.47591e6 0.306554
472472 0 0
473473 3.43464e6 0.705876
474474 0 0
475475 75449.0 0.0153433
476476 0 0
477477 −1.57561e6 −0.317069
478478 0 0
479479 3.79193e6 0.755130 0.377565 0.925983i 0.376761π-0.376761\pi
0.377565 + 0.925983i 0.376761π0.376761\pi
480480 0 0
481481 557980. 0.109965
482482 0 0
483483 376272. 0.0733895
484484 0 0
485485 −5.70834e6 −1.10193
486486 0 0
487487 −2.78559e6 −0.532225 −0.266112 0.963942i 0.585739π-0.585739\pi
−0.266112 + 0.963942i 0.585739π0.585739\pi
488488 0 0
489489 242532. 0.0458666
490490 0 0
491491 −1.70523e6 −0.319212 −0.159606 0.987181i 0.551022π-0.551022\pi
−0.159606 + 0.987181i 0.551022π0.551022\pi
492492 0 0
493493 1.62410e6 0.300952
494494 0 0
495495 −1.44342e6 −0.264777
496496 0 0
497497 787488. 0.143006
498498 0 0
499499 −3.60026e6 −0.647266 −0.323633 0.946183i 0.604904π-0.604904\pi
−0.323633 + 0.946183i 0.604904π0.604904\pi
500500 0 0
501501 52272.0 0.00930411
502502 0 0
503503 8.68129e6 1.52990 0.764952 0.644087i 0.222763π-0.222763\pi
0.764952 + 0.644087i 0.222763π0.222763\pi
504504 0 0
505505 −6.72527e6 −1.17349
506506 0 0
507507 3.32259e6 0.574060
508508 0 0
509509 −1.09767e7 −1.87792 −0.938962 0.344022i 0.888211π-0.888211\pi
−0.938962 + 0.344022i 0.888211π0.888211\pi
510510 0 0
511511 −243568. −0.0412637
512512 0 0
513513 263169. 0.0441511
514514 0 0
515515 350352. 0.0582085
516516 0 0
517517 1.57410e6 0.259004
518518 0 0
519519 −333936. −0.0544183
520520 0 0
521521 −9.09036e6 −1.46719 −0.733596 0.679586i 0.762159π-0.762159\pi
−0.733596 + 0.679586i 0.762159π0.762159\pi
522522 0 0
523523 −8.46276e6 −1.35287 −0.676437 0.736500i 0.736477π-0.736477\pi
−0.676437 + 0.736500i 0.736477π0.736477\pi
524524 0 0
525525 −195624. −0.0309759
526526 0 0
527527 −1.46342e6 −0.229532
528528 0 0
529529 −6.27474e6 −0.974892
530530 0 0
531531 −2.47277e6 −0.380581
532532 0 0
533533 867744. 0.132304
534534 0 0
535535 2.70216e6 0.408156
536536 0 0
537537 1.78524e6 0.267154
538538 0 0
539539 −1.97703e6 −0.293117
540540 0 0
541541 −8.03851e6 −1.18082 −0.590408 0.807105i 0.701033π-0.701033\pi
−0.590408 + 0.807105i 0.701033π0.701033\pi
542542 0 0
543543 2.49154e6 0.362634
544544 0 0
545545 −4.79012e6 −0.690805
546546 0 0
547547 1.32779e7 1.89741 0.948704 0.316167i 0.102396π-0.102396\pi
0.948704 + 0.316167i 0.102396π0.102396\pi
548548 0 0
549549 902178. 0.127750
550550 0 0
551551 948708. 0.133123
552552 0 0
553553 2.33210e6 0.324290
554554 0 0
555555 −5.89518e6 −0.812390
556556 0 0
557557 −9.11080e6 −1.24428 −0.622141 0.782905i 0.713737π-0.713737\pi
−0.622141 + 0.782905i 0.713737π0.713737\pi
558558 0 0
559559 −478768. −0.0648031
560560 0 0
561561 1.83546e6 0.246228
562562 0 0
563563 5.07313e6 0.674536 0.337268 0.941409i 0.390497π-0.390497\pi
0.337268 + 0.941409i 0.390497π0.390497\pi
564564 0 0
565565 8.46677e6 1.11583
566566 0 0
567567 −682344. −0.0891345
568568 0 0
569569 2.30192e6 0.298065 0.149032 0.988832i 0.452384π-0.452384\pi
0.149032 + 0.988832i 0.452384π0.452384\pi
570570 0 0
571571 1.14948e7 1.47540 0.737702 0.675127i 0.235911π-0.235911\pi
0.737702 + 0.675127i 0.235911π0.235911\pi
572572 0 0
573573 −4.78100e6 −0.608320
574574 0 0
575575 −84018.0 −0.0105975
576576 0 0
577577 308198. 0.0385381 0.0192690 0.999814i 0.493866π-0.493866\pi
0.0192690 + 0.999814i 0.493866π0.493866\pi
578578 0 0
579579 2.20556e6 0.273415
580580 0 0
581581 −4.86034e6 −0.597346
582582 0 0
583583 −6.41916e6 −0.782180
584584 0 0
585585 201204. 0.0243079
586586 0 0
587587 −5.02053e6 −0.601387 −0.300694 0.953721i 0.597218π-0.597218\pi
−0.300694 + 0.953721i 0.597218π0.597218\pi
588588 0 0
589589 −854848. −0.101531
590590 0 0
591591 −1.97915e6 −0.233083
592592 0 0
593593 1.70294e7 1.98867 0.994335 0.106288i 0.0338967π-0.0338967\pi
0.994335 + 0.106288i 0.0338967π0.0338967\pi
594594 0 0
595595 −3.47069e6 −0.401905
596596 0 0
597597 −9.16384e6 −1.05230
598598 0 0
599599 −2.86572e6 −0.326337 −0.163169 0.986598i 0.552171π-0.552171\pi
−0.163169 + 0.986598i 0.552171π0.552171\pi
600600 0 0
601601 −1.03461e7 −1.16840 −0.584200 0.811609i 0.698592π-0.698592\pi
−0.584200 + 0.811609i 0.698592π0.698592\pi
602602 0 0
603603 −4.01015e6 −0.449125
604604 0 0
605605 2.81615e6 0.312801
606606 0 0
607607 −3.56084e6 −0.392266 −0.196133 0.980577i 0.562838π-0.562838\pi
−0.196133 + 0.980577i 0.562838π0.562838\pi
608608 0 0
609609 −2.45981e6 −0.268756
610610 0 0
611611 −219420. −0.0237779
612612 0 0
613613 7.56115e6 0.812712 0.406356 0.913715i 0.366799π-0.366799\pi
0.406356 + 0.913715i 0.366799π0.366799\pi
614614 0 0
615615 −9.16790e6 −0.977422
616616 0 0
617617 5.03233e6 0.532177 0.266088 0.963949i 0.414269π-0.414269\pi
0.266088 + 0.963949i 0.414269π0.414269\pi
618618 0 0
619619 5.87528e6 0.616313 0.308157 0.951336i 0.400288π-0.400288\pi
0.308157 + 0.951336i 0.400288π0.400288\pi
620620 0 0
621621 −293058. −0.0304947
622622 0 0
623623 7.29082e6 0.752586
624624 0 0
625625 −9.06882e6 −0.928647
626626 0 0
627627 1.07217e6 0.108917
628628 0 0
629629 7.49634e6 0.755479
630630 0 0
631631 4.33809e6 0.433735 0.216868 0.976201i 0.430416π-0.430416\pi
0.216868 + 0.976201i 0.430416π0.430416\pi
632632 0 0
633633 945180. 0.0937573
634634 0 0
635635 −1.14355e7 −1.12543
636636 0 0
637637 275586. 0.0269097
638638 0 0
639639 −613332. −0.0594215
640640 0 0
641641 1.35603e7 1.30354 0.651769 0.758417i 0.274027π-0.274027\pi
0.651769 + 0.758417i 0.274027π0.274027\pi
642642 0 0
643643 −6.02612e6 −0.574792 −0.287396 0.957812i 0.592789π-0.592789\pi
−0.287396 + 0.957812i 0.592789π0.592789\pi
644644 0 0
645645 5.05829e6 0.478745
646646 0 0
647647 8.69474e6 0.816574 0.408287 0.912854i 0.366126π-0.366126\pi
0.408287 + 0.912854i 0.366126π0.366126\pi
648648 0 0
649649 −1.00742e7 −0.938859
650650 0 0
651651 2.21645e6 0.204977
652652 0 0
653653 −1.09929e6 −0.100886 −0.0504428 0.998727i 0.516063π-0.516063\pi
−0.0504428 + 0.998727i 0.516063π0.516063\pi
654654 0 0
655655 −238140. −0.0216885
656656 0 0
657657 189702. 0.0171458
658658 0 0
659659 3.94808e6 0.354138 0.177069 0.984198i 0.443338π-0.443338\pi
0.177069 + 0.984198i 0.443338π0.443338\pi
660660 0 0
661661 −1.96958e7 −1.75335 −0.876676 0.481082i 0.840244π-0.840244\pi
−0.876676 + 0.481082i 0.840244π0.840244\pi
662662 0 0
663663 −255852. −0.0226050
664664 0 0
665665 −2.02738e6 −0.177779
666666 0 0
667667 −1.05646e6 −0.0919468
668668 0 0
669669 8.89474e6 0.768365
670670 0 0
671671 3.67554e6 0.315148
672672 0 0
673673 −2.06650e7 −1.75873 −0.879363 0.476151i 0.842031π-0.842031\pi
−0.879363 + 0.476151i 0.842031π0.842031\pi
674674 0 0
675675 152361. 0.0128711
676676 0 0
677677 1.64591e7 1.38018 0.690090 0.723724i 0.257571π-0.257571\pi
0.690090 + 0.723724i 0.257571π0.257571\pi
678678 0 0
679679 −1.09938e7 −0.915114
680680 0 0
681681 −4.64346e6 −0.383684
682682 0 0
683683 876672. 0.0719094 0.0359547 0.999353i 0.488553π-0.488553\pi
0.0359547 + 0.999353i 0.488553π0.488553\pi
684684 0 0
685685 −1.11226e7 −0.905690
686686 0 0
687687 2.49619e6 0.201783
688688 0 0
689689 894792. 0.0718082
690690 0 0
691691 −1.64070e7 −1.30717 −0.653586 0.756852i 0.726736π-0.726736\pi
−0.653586 + 0.756852i 0.726736π0.726736\pi
692692 0 0
693693 −2.77992e6 −0.219887
694694 0 0
695695 1.70590e7 1.33965
696696 0 0
697697 1.16580e7 0.908951
698698 0 0
699699 −1.38736e7 −1.07398
700700 0 0
701701 1.03676e6 0.0796861 0.0398430 0.999206i 0.487314π-0.487314\pi
0.0398430 + 0.999206i 0.487314π0.487314\pi
702702 0 0
703703 4.37893e6 0.334179
704704 0 0
705705 2.31822e6 0.175664
706706 0 0
707707 −1.29524e7 −0.974542
708708 0 0
709709 −2.00637e6 −0.149898 −0.0749491 0.997187i 0.523879π-0.523879\pi
−0.0749491 + 0.997187i 0.523879π0.523879\pi
710710 0 0
711711 −1.81634e6 −0.134749
712712 0 0
713713 951936. 0.0701268
714714 0 0
715715 819720. 0.0599654
716716 0 0
717717 −2.82879e6 −0.205496
718718 0 0
719719 8.95036e6 0.645682 0.322841 0.946453i 0.395362π-0.395362\pi
0.322841 + 0.946453i 0.395362π0.395362\pi
720720 0 0
721721 674752. 0.0483399
722722 0 0
723723 −221094. −0.0157301
724724 0 0
725725 549252. 0.0388085
726726 0 0
727727 614668. 0.0431325 0.0215662 0.999767i 0.493135π-0.493135\pi
0.0215662 + 0.999767i 0.493135π0.493135\pi
728728 0 0
729729 531441. 0.0370370
730730 0 0
731731 −6.43214e6 −0.445207
732732 0 0
733733 −8.47041e6 −0.582297 −0.291149 0.956678i 0.594037π-0.594037\pi
−0.291149 + 0.956678i 0.594037π0.594037\pi
734734 0 0
735735 −2.91163e6 −0.198800
736736 0 0
737737 −1.63376e7 −1.10795
738738 0 0
739739 9.40491e6 0.633495 0.316748 0.948510i 0.397409π-0.397409\pi
0.316748 + 0.948510i 0.397409π0.397409\pi
740740 0 0
741741 −149454. −0.00999913
742742 0 0
743743 −2.73198e7 −1.81554 −0.907769 0.419471i 0.862216π-0.862216\pi
−0.907769 + 0.419471i 0.862216π0.862216\pi
744744 0 0
745745 −1.14025e7 −0.752680
746746 0 0
747747 3.78545e6 0.248208
748748 0 0
749749 5.20416e6 0.338958
750750 0 0
751751 1.07808e7 0.697509 0.348755 0.937214i 0.386605π-0.386605\pi
0.348755 + 0.937214i 0.386605π0.386605\pi
752752 0 0
753753 5.95161e6 0.382514
754754 0 0
755755 −6.37848e6 −0.407239
756756 0 0
757757 −543058. −0.0344434 −0.0172217 0.999852i 0.505482π-0.505482\pi
−0.0172217 + 0.999852i 0.505482π0.505482\pi
758758 0 0
759759 −1.19394e6 −0.0752277
760760 0 0
761761 9.07913e6 0.568307 0.284153 0.958779i 0.408288π-0.408288\pi
0.284153 + 0.958779i 0.408288π0.408288\pi
762762 0 0
763763 −9.22542e6 −0.573687
764764 0 0
765765 2.70313e6 0.166999
766766 0 0
767767 1.40429e6 0.0861922
768768 0 0
769769 5.14583e6 0.313790 0.156895 0.987615i 0.449852π-0.449852\pi
0.156895 + 0.987615i 0.449852π0.449852\pi
770770 0 0
771771 −9.45313e6 −0.572717
772772 0 0
773773 7.50322e6 0.451647 0.225823 0.974168i 0.427493π-0.427493\pi
0.225823 + 0.974168i 0.427493π0.427493\pi
774774 0 0
775775 −494912. −0.0295988
776776 0 0
777777 −1.13537e7 −0.674659
778778 0 0
779779 6.80990e6 0.402066
780780 0 0
781781 −2.49876e6 −0.146588
782782 0 0
783783 1.91581e6 0.111673
784784 0 0
785785 8.85546e6 0.512905
786786 0 0
787787 −1.48747e7 −0.856076 −0.428038 0.903761i 0.640795π-0.640795\pi
−0.428038 + 0.903761i 0.640795π0.640795\pi
788788 0 0
789789 −4.18959e6 −0.239596
790790 0 0
791791 1.63064e7 0.926651
792792 0 0
793793 −512348. −0.0289322
794794 0 0
795795 −9.45367e6 −0.530497
796796 0 0
797797 2.77279e7 1.54622 0.773109 0.634273i 0.218701π-0.218701\pi
0.773109 + 0.634273i 0.218701π0.218701\pi
798798 0 0
799799 −2.94786e6 −0.163358
800800 0 0
801801 −5.67842e6 −0.312713
802802 0 0
803803 772860. 0.0422972
804804 0 0
805805 2.25763e6 0.122790
806806 0 0
807807 2.85401e6 0.154266
808808 0 0
809809 −3.46147e7 −1.85947 −0.929735 0.368229i 0.879964π-0.879964\pi
−0.929735 + 0.368229i 0.879964π0.879964\pi
810810 0 0
811811 −1.42801e7 −0.762392 −0.381196 0.924494i 0.624488π-0.624488\pi
−0.381196 + 0.924494i 0.624488π0.624488\pi
812812 0 0
813813 −1.34011e7 −0.711073
814814 0 0
815815 1.45519e6 0.0767408
816816 0 0
817817 −3.75729e6 −0.196933
818818 0 0
819819 387504. 0.0201868
820820 0 0
821821 3.69632e6 0.191387 0.0956933 0.995411i 0.469493π-0.469493\pi
0.0956933 + 0.995411i 0.469493π0.469493\pi
822822 0 0
823823 −2.05703e7 −1.05862 −0.529310 0.848428i 0.677549π-0.677549\pi
−0.529310 + 0.848428i 0.677549π0.677549\pi
824824 0 0
825825 620730. 0.0317518
826826 0 0
827827 2.42257e7 1.23172 0.615860 0.787856i 0.288809π-0.288809\pi
0.615860 + 0.787856i 0.288809π0.288809\pi
828828 0 0
829829 −1.93936e7 −0.980102 −0.490051 0.871694i 0.663022π-0.663022\pi
−0.490051 + 0.871694i 0.663022π0.663022\pi
830830 0 0
831831 1.38625e7 0.696370
832832 0 0
833833 3.70244e6 0.184874
834834 0 0
835835 313632. 0.0155670
836836 0 0
837837 −1.72627e6 −0.0851718
838838 0 0
839839 3.44560e7 1.68990 0.844949 0.534847i 0.179631π-0.179631\pi
0.844949 + 0.534847i 0.179631π0.179631\pi
840840 0 0
841841 −1.36048e7 −0.663286
842842 0 0
843843 −1.79635e7 −0.870608
844844 0 0
845845 1.99356e7 0.960476
846846 0 0
847847 5.42370e6 0.259769
848848 0 0
849849 −8.52242e6 −0.405783
850850 0 0
851851 −4.87626e6 −0.230814
852852 0 0
853853 1.43023e7 0.673029 0.336514 0.941678i 0.390752π-0.390752\pi
0.336514 + 0.941678i 0.390752π0.390752\pi
854854 0 0
855855 1.57901e6 0.0738704
856856 0 0
857857 1.96706e7 0.914882 0.457441 0.889240i 0.348766π-0.348766\pi
0.457441 + 0.889240i 0.348766π0.348766\pi
858858 0 0
859859 −9.60088e6 −0.443944 −0.221972 0.975053i 0.571249π-0.571249\pi
−0.221972 + 0.975053i 0.571249π0.571249\pi
860860 0 0
861861 −1.76567e7 −0.811712
862862 0 0
863863 −1.46481e7 −0.669508 −0.334754 0.942306i 0.608653π-0.608653\pi
−0.334754 + 0.942306i 0.608653π0.608653\pi
864864 0 0
865865 −2.00362e6 −0.0910488
866866 0 0
867867 9.34140e6 0.422050
868868 0 0
869869 −7.39992e6 −0.332413
870870 0 0
871871 2.27737e6 0.101716
872872 0 0
873873 8.56251e6 0.380247
874874 0 0
875875 −1.87237e7 −0.826747
876876 0 0
877877 −1.17035e7 −0.513825 −0.256913 0.966435i 0.582705π-0.582705\pi
−0.256913 + 0.966435i 0.582705π0.582705\pi
878878 0 0
879879 −1.96353e7 −0.857165
880880 0 0
881881 −4.52787e7 −1.96541 −0.982706 0.185171i 0.940716π-0.940716\pi
−0.982706 + 0.185171i 0.940716π0.940716\pi
882882 0 0
883883 −2.59473e7 −1.11993 −0.559965 0.828517i 0.689185π-0.689185\pi
−0.559965 + 0.828517i 0.689185π0.689185\pi
884884 0 0
885885 −1.48366e7 −0.636761
886886 0 0
887887 2.07015e7 0.883473 0.441737 0.897145i 0.354363π-0.354363\pi
0.441737 + 0.897145i 0.354363π0.354363\pi
888888 0 0
889889 −2.20239e7 −0.934629
890890 0 0
891891 2.16513e6 0.0913671
892892 0 0
893893 −1.72197e6 −0.0722598
894894 0 0
895895 1.07114e7 0.446982
896896 0 0
897897 166428. 0.00690630
898898 0 0
899899 −6.22310e6 −0.256808
900900 0 0
901901 1.20213e7 0.493334
902902 0 0
903903 9.74189e6 0.397579
904904 0 0
905905 1.49493e7 0.606734
906906 0 0
907907 −4.76595e7 −1.92367 −0.961836 0.273628i 0.911776π-0.911776\pi
−0.961836 + 0.273628i 0.911776π0.911776\pi
908908 0 0
909909 1.00879e7 0.404940
910910 0 0
911911 387816. 0.0154821 0.00774105 0.999970i 0.497536π-0.497536\pi
0.00774105 + 0.999970i 0.497536π0.497536\pi
912912 0 0
913913 1.54222e7 0.612308
914914 0 0
915915 5.41307e6 0.213742
916916 0 0
917917 −458640. −0.0180114
918918 0 0
919919 −3.45269e7 −1.34855 −0.674277 0.738479i 0.735545π-0.735545\pi
−0.674277 + 0.738479i 0.735545π0.735545\pi
920920 0 0
921921 −2.25373e7 −0.875492
922922 0 0
923923 348312. 0.0134575
924924 0 0
925925 2.53517e6 0.0974210
926926 0 0
927927 −525528. −0.0200861
928928 0 0
929929 3.96164e7 1.50604 0.753018 0.657999i 0.228597π-0.228597\pi
0.753018 + 0.657999i 0.228597π0.228597\pi
930930 0 0
931931 2.16275e6 0.0817772
932932 0 0
933933 −7.07092e6 −0.265933
934934 0 0
935935 1.10128e7 0.411971
936936 0 0
937937 −1.42780e7 −0.531272 −0.265636 0.964073i 0.585582π-0.585582\pi
−0.265636 + 0.964073i 0.585582π0.585582\pi
938938 0 0
939939 −3.27901e6 −0.121361
940940 0 0
941941 −2.33088e6 −0.0858116 −0.0429058 0.999079i 0.513662π-0.513662\pi
−0.0429058 + 0.999079i 0.513662π0.513662\pi
942942 0 0
943943 −7.58333e6 −0.277703
944944 0 0
945945 −4.09406e6 −0.149133
946946 0 0
947947 2.93987e7 1.06526 0.532628 0.846350i 0.321205π-0.321205\pi
0.532628 + 0.846350i 0.321205π0.321205\pi
948948 0 0
949949 −107732. −0.00388311
950950 0 0
951951 1.32244e7 0.474159
952952 0 0
953953 −2.26835e7 −0.809055 −0.404528 0.914526i 0.632564π-0.632564\pi
−0.404528 + 0.914526i 0.632564π0.632564\pi
954954 0 0
955955 −2.86860e7 −1.01780
956956 0 0
957957 7.80516e6 0.275488
958958 0 0
959959 −2.14213e7 −0.752141
960960 0 0
961961 −2.30217e7 −0.804136
962962 0 0
963963 −4.05324e6 −0.140843
964964 0 0
965965 1.32333e7 0.457458
966966 0 0
967967 2.50637e7 0.861944 0.430972 0.902365i 0.358171π-0.358171\pi
0.430972 + 0.902365i 0.358171π0.358171\pi
968968 0 0
969969 −2.00788e6 −0.0686956
970970 0 0
971971 −2.93328e7 −0.998402 −0.499201 0.866486i 0.666373π-0.666373\pi
−0.499201 + 0.866486i 0.666373π0.666373\pi
972972 0 0
973973 3.28544e7 1.11253
974974 0 0
975975 −86526.0 −0.00291498
976976 0 0
977977 4.53306e7 1.51934 0.759670 0.650309i 0.225361π-0.225361\pi
0.759670 + 0.650309i 0.225361π0.225361\pi
978978 0 0
979979 −2.31343e7 −0.771436
980980 0 0
981981 7.18519e6 0.238378
982982 0 0
983983 2.13167e7 0.703615 0.351808 0.936072i 0.385567π-0.385567\pi
0.351808 + 0.936072i 0.385567π0.385567\pi
984984 0 0
985985 −1.18749e7 −0.389978
986986 0 0
987987 4.46472e6 0.145882
988988 0 0
989989 4.18402e6 0.136020
990990 0 0
991991 3.14104e7 1.01599 0.507996 0.861360i 0.330387π-0.330387\pi
0.507996 + 0.861360i 0.330387π0.330387\pi
992992 0 0
993993 1.50673e7 0.484910
994994 0 0
995995 −5.49830e7 −1.76064
996996 0 0
997997 9.54091e6 0.303985 0.151992 0.988382i 0.451431π-0.451431\pi
0.151992 + 0.988382i 0.451431π0.451431\pi
998998 0 0
999999 8.84277e6 0.280333
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 912.6.a.c.1.1 1
4.3 odd 2 114.6.a.a.1.1 1
12.11 even 2 342.6.a.f.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
114.6.a.a.1.1 1 4.3 odd 2
342.6.a.f.1.1 1 12.11 even 2
912.6.a.c.1.1 1 1.1 even 1 trivial