Properties

Label 624.6.c.a.337.2
Level 624624
Weight 66
Character 624.337
Analytic conductor 100.080100.080
Analytic rank 00
Dimension 44
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [624,6,Mod(337,624)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(624, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("624.337");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: N N == 624=24313 624 = 2^{4} \cdot 3 \cdot 13
Weight: k k == 6 6
Character orbit: [χ][\chi] == 624.c (of order 22, degree 11, not minimal)

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: no
Analytic conductor: 100.079503563100.079503563
Analytic rank: 00
Dimension: 44
Coefficient field: 4.0.31066572.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x4+53x2+300 x^{4} + 53x^{2} + 300 Copy content Toggle raw display
Coefficient ring: Z[a1,,a13]\Z[a_1, \ldots, a_{13}]
Coefficient ring index: 24 2^{4}
Twist minimal: no (minimal twist has level 39)
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 337.2
Root 6.82321i-6.82321i of defining polynomial
Character χ\chi == 624.337
Dual form 624.6.c.a.337.3

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) == q9.00000q333.0580iq5+61.2631iq7+81.0000q9+164.669iq11+(443.460+417.895i)q13+297.522iq15+336.674q17+69.6517iq19551.368iq213734.76q23+2032.17q25729.000q27+4304.83q291850.83iq311482.02iq33+2025.24q352739.27iq37+(3991.143761.05i)q39+12031.5iq41+2161.44q432677.70iq4510338.2iq47+13053.8q493030.07q51696.674q53+5443.64q55626.866iq57+24274.8iq5926772.3q61+4962.31iq63+(13814.8+14659.9i)q6568687.0iq67+33612.9q69+16366.0iq71+83795.1iq7318289.5q7510088.2q77+16999.8q79+6561.00q81+38542.9iq8311129.8iq8538743.5q87140248.iq89+(25601.527167.8i)q91+16657.5iq93+2302.55q9587328.3iq97+13338.2iq99+O(q100)q-9.00000 q^{3} -33.0580i q^{5} +61.2631i q^{7} +81.0000 q^{9} +164.669i q^{11} +(-443.460 + 417.895i) q^{13} +297.522i q^{15} +336.674 q^{17} +69.6517i q^{19} -551.368i q^{21} -3734.76 q^{23} +2032.17 q^{25} -729.000 q^{27} +4304.83 q^{29} -1850.83i q^{31} -1482.02i q^{33} +2025.24 q^{35} -2739.27i q^{37} +(3991.14 - 3761.05i) q^{39} +12031.5i q^{41} +2161.44 q^{43} -2677.70i q^{45} -10338.2i q^{47} +13053.8 q^{49} -3030.07 q^{51} -696.674 q^{53} +5443.64 q^{55} -626.866i q^{57} +24274.8i q^{59} -26772.3 q^{61} +4962.31i q^{63} +(13814.8 + 14659.9i) q^{65} -68687.0i q^{67} +33612.9 q^{69} +16366.0i q^{71} +83795.1i q^{73} -18289.5 q^{75} -10088.2 q^{77} +16999.8 q^{79} +6561.00 q^{81} +38542.9i q^{83} -11129.8i q^{85} -38743.5 q^{87} -140248. i q^{89} +(-25601.5 - 27167.8i) q^{91} +16657.5i q^{93} +2302.55 q^{95} -87328.3i q^{97} +13338.2i q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 4q36q3+324q9+312q13+384q172424q23+748q252916q273960q29+20616q352808q394832q43+31036q493456q511824q53+10864q55+322920q95+O(q100) 4 q - 36 q^{3} + 324 q^{9} + 312 q^{13} + 384 q^{17} - 2424 q^{23} + 748 q^{25} - 2916 q^{27} - 3960 q^{29} + 20616 q^{35} - 2808 q^{39} - 4832 q^{43} + 31036 q^{49} - 3456 q^{51} - 1824 q^{53} + 10864 q^{55}+ \cdots - 322920 q^{95}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/624Z)×\left(\mathbb{Z}/624\mathbb{Z}\right)^\times.

nn 7979 145145 209209 469469
χ(n)\chi(n) 11 1-1 11 11

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 33.0580i 0.591360i −0.955287 0.295680i 0.904454π-0.904454\pi
0.955287 0.295680i 0.0955462π-0.0955462\pi
66 0 0
77 61.2631i 0.472557i 0.971685 + 0.236278i 0.0759277π0.0759277\pi
−0.971685 + 0.236278i 0.924072π0.924072\pi
88 0 0
99 81.0000 0.333333
1010 0 0
1111 164.669i 0.410328i 0.978728 + 0.205164i 0.0657727π0.0657727\pi
−0.978728 + 0.205164i 0.934227π0.934227\pi
1212 0 0
1313 −443.460 + 417.895i −0.727774 + 0.685817i
1414 0 0
1515 297.522i 0.341422i
1616 0 0
1717 336.674 0.282545 0.141272 0.989971i 0.454881π-0.454881\pi
0.141272 + 0.989971i 0.454881π0.454881\pi
1818 0 0
1919 69.6517i 0.0442637i 0.999755 + 0.0221319i 0.00704537π0.00704537\pi
−0.999755 + 0.0221319i 0.992955π0.992955\pi
2020 0 0
2121 551.368i 0.272831i
2222 0 0
2323 −3734.76 −1.47212 −0.736060 0.676916i 0.763316π-0.763316\pi
−0.736060 + 0.676916i 0.763316π0.763316\pi
2424 0 0
2525 2032.17 0.650294
2626 0 0
2727 −729.000 −0.192450
2828 0 0
2929 4304.83 0.950519 0.475260 0.879846i 0.342354π-0.342354\pi
0.475260 + 0.879846i 0.342354π0.342354\pi
3030 0 0
3131 1850.83i 0.345910i −0.984930 0.172955i 0.944668π-0.944668\pi
0.984930 0.172955i 0.0553315π-0.0553315\pi
3232 0 0
3333 1482.02i 0.236903i
3434 0 0
3535 2025.24 0.279451
3636 0 0
3737 2739.27i 0.328950i −0.986381 0.164475i 0.947407π-0.947407\pi
0.986381 0.164475i 0.0525931π-0.0525931\pi
3838 0 0
3939 3991.14 3761.05i 0.420180 0.395957i
4040 0 0
4141 12031.5i 1.11779i 0.829239 + 0.558894i 0.188774π0.188774\pi
−0.829239 + 0.558894i 0.811226π0.811226\pi
4242 0 0
4343 2161.44 0.178267 0.0891336 0.996020i 0.471590π-0.471590\pi
0.0891336 + 0.996020i 0.471590π0.471590\pi
4444 0 0
4545 2677.70i 0.197120i
4646 0 0
4747 10338.2i 0.682651i −0.939945 0.341325i 0.889124π-0.889124\pi
0.939945 0.341325i 0.110876π-0.110876\pi
4848 0 0
4949 13053.8 0.776690
5050 0 0
5151 −3030.07 −0.163127
5252 0 0
5353 −696.674 −0.0340675 −0.0170337 0.999855i 0.505422π-0.505422\pi
−0.0170337 + 0.999855i 0.505422π0.505422\pi
5454 0 0
5555 5443.64 0.242651
5656 0 0
5757 626.866i 0.0255557i
5858 0 0
5959 24274.8i 0.907876i 0.891033 + 0.453938i 0.149981π0.149981\pi
−0.891033 + 0.453938i 0.850019π0.850019\pi
6060 0 0
6161 −26772.3 −0.921214 −0.460607 0.887604i 0.652368π-0.652368\pi
−0.460607 + 0.887604i 0.652368π0.652368\pi
6262 0 0
6363 4962.31i 0.157519i
6464 0 0
6565 13814.8 + 14659.9i 0.405565 + 0.430376i
6666 0 0
6767 68687.0i 1.86934i −0.355522 0.934668i 0.615697π-0.615697\pi
0.355522 0.934668i 0.384303π-0.384303\pi
6868 0 0
6969 33612.9 0.849929
7070 0 0
7171 16366.0i 0.385298i 0.981268 + 0.192649i 0.0617079π0.0617079\pi
−0.981268 + 0.192649i 0.938292π0.938292\pi
7272 0 0
7373 83795.1i 1.84040i 0.391451 + 0.920199i 0.371973π0.371973\pi
−0.391451 + 0.920199i 0.628027π0.628027\pi
7474 0 0
7575 −18289.5 −0.375447
7676 0 0
7777 −10088.2 −0.193903
7878 0 0
7979 16999.8 0.306462 0.153231 0.988190i 0.451032π-0.451032\pi
0.153231 + 0.988190i 0.451032π0.451032\pi
8080 0 0
8181 6561.00 0.111111
8282 0 0
8383 38542.9i 0.614114i 0.951691 + 0.307057i 0.0993442π0.0993442\pi
−0.951691 + 0.307057i 0.900656π0.900656\pi
8484 0 0
8585 11129.8i 0.167086i
8686 0 0
8787 −38743.5 −0.548783
8888 0 0
8989 140248.i 1.87681i −0.345531 0.938407i 0.612301π-0.612301\pi
0.345531 0.938407i 0.387699π-0.387699\pi
9090 0 0
9191 −25601.5 27167.8i −0.324088 0.343915i
9292 0 0
9393 16657.5i 0.199711i
9494 0 0
9595 2302.55 0.0261758
9696 0 0
9797 87328.3i 0.942379i −0.882032 0.471189i 0.843825π-0.843825\pi
0.882032 0.471189i 0.156175π-0.156175\pi
9898 0 0
9999 13338.2i 0.136776i
100100 0 0
101101 −128464. −1.25308 −0.626539 0.779390i 0.715529π-0.715529\pi
−0.626539 + 0.779390i 0.715529π0.715529\pi
102102 0 0
103103 63628.0 0.590956 0.295478 0.955350i 0.404521π-0.404521\pi
0.295478 + 0.955350i 0.404521π0.404521\pi
104104 0 0
105105 −18227.1 −0.161341
106106 0 0
107107 −125275. −1.05780 −0.528900 0.848684i 0.677395π-0.677395\pi
−0.528900 + 0.848684i 0.677395π0.677395\pi
108108 0 0
109109 56877.0i 0.458533i −0.973364 0.229267i 0.926367π-0.926367\pi
0.973364 0.229267i 0.0736327π-0.0736327\pi
110110 0 0
111111 24653.4i 0.189920i
112112 0 0
113113 −235161. −1.73249 −0.866243 0.499623i 0.833472π-0.833472\pi
−0.866243 + 0.499623i 0.833472π0.833472\pi
114114 0 0
115115 123464.i 0.870553i
116116 0 0
117117 −35920.3 + 33849.5i −0.242591 + 0.228606i
118118 0 0
119119 20625.7i 0.133518i
120120 0 0
121121 133935. 0.831631
122122 0 0
123123 108283.i 0.645356i
124124 0 0
125125 170486.i 0.975917i
126126 0 0
127127 −109597. −0.602961 −0.301481 0.953472i 0.597481π-0.597481\pi
−0.301481 + 0.953472i 0.597481π0.597481\pi
128128 0 0
129129 −19452.9 −0.102923
130130 0 0
131131 219695. 1.11851 0.559257 0.828994i 0.311087π-0.311087\pi
0.559257 + 0.828994i 0.311087π0.311087\pi
132132 0 0
133133 −4267.08 −0.0209171
134134 0 0
135135 24099.3i 0.113807i
136136 0 0
137137 9145.44i 0.0416297i −0.999783 0.0208148i 0.993374π-0.993374\pi
0.999783 0.0208148i 0.00662605π-0.00662605\pi
138138 0 0
139139 −146786. −0.644390 −0.322195 0.946673i 0.604421π-0.604421\pi
−0.322195 + 0.946673i 0.604421π0.604421\pi
140140 0 0
141141 93043.4i 0.394129i
142142 0 0
143143 −68814.4 73024.3i −0.281410 0.298626i
144144 0 0
145145 142309.i 0.562099i
146146 0 0
147147 −117484. −0.448422
148148 0 0
149149 205420.i 0.758012i 0.925394 + 0.379006i 0.123734π0.123734\pi
−0.925394 + 0.379006i 0.876266π0.876266\pi
150150 0 0
151151 325694.i 1.16243i −0.813749 0.581216i 0.802577π-0.802577\pi
0.813749 0.581216i 0.197423π-0.197423\pi
152152 0 0
153153 27270.6 0.0941816
154154 0 0
155155 −61184.9 −0.204557
156156 0 0
157157 −557622. −1.80547 −0.902735 0.430196i 0.858444π-0.858444\pi
−0.902735 + 0.430196i 0.858444π0.858444\pi
158158 0 0
159159 6270.07 0.0196689
160160 0 0
161161 228803.i 0.695661i
162162 0 0
163163 635012.i 1.87203i −0.351958 0.936016i 0.614484π-0.614484\pi
0.351958 0.936016i 0.385516π-0.385516\pi
164164 0 0
165165 −48992.8 −0.140095
166166 0 0
167167 480228.i 1.33247i −0.745743 0.666234i 0.767905π-0.767905\pi
0.745743 0.666234i 0.232095π-0.232095\pi
168168 0 0
169169 22021.3 370639.i 0.0593099 0.998240i
170170 0 0
171171 5641.79i 0.0147546i
172172 0 0
173173 −337273. −0.856774 −0.428387 0.903595i 0.640918π-0.640918\pi
−0.428387 + 0.903595i 0.640918π0.640918\pi
174174 0 0
175175 124497.i 0.307301i
176176 0 0
177177 218474.i 0.524162i
178178 0 0
179179 −570180. −1.33009 −0.665043 0.746805i 0.731587π-0.731587\pi
−0.665043 + 0.746805i 0.731587π0.731587\pi
180180 0 0
181181 192663. 0.437121 0.218560 0.975823i 0.429864π-0.429864\pi
0.218560 + 0.975823i 0.429864π0.429864\pi
182182 0 0
183183 240950. 0.531863
184184 0 0
185185 −90554.8 −0.194528
186186 0 0
187187 55439.9i 0.115936i
188188 0 0
189189 44660.8i 0.0909436i
190190 0 0
191191 320668. 0.636023 0.318011 0.948087i 0.396985π-0.396985\pi
0.318011 + 0.948087i 0.396985π0.396985\pi
192192 0 0
193193 386084.i 0.746086i −0.927814 0.373043i 0.878314π-0.878314\pi
0.927814 0.373043i 0.121686π-0.121686\pi
194194 0 0
195195 −124333. 131939.i −0.234153 0.248478i
196196 0 0
197197 891618.i 1.63687i −0.574602 0.818433i 0.694843π-0.694843\pi
0.574602 0.818433i 0.305157π-0.305157\pi
198198 0 0
199199 −700392. −1.25374 −0.626872 0.779123i 0.715665π-0.715665\pi
−0.626872 + 0.779123i 0.715665π0.715665\pi
200200 0 0
201201 618183.i 1.07926i
202202 0 0
203203 263727.i 0.449174i
204204 0 0
205205 397737. 0.661015
206206 0 0
207207 −302516. −0.490707
208208 0 0
209209 −11469.5 −0.0181626
210210 0 0
211211 −598648. −0.925689 −0.462845 0.886439i 0.653171π-0.653171\pi
−0.462845 + 0.886439i 0.653171π0.653171\pi
212212 0 0
213213 147294.i 0.222452i
214214 0 0
215215 71452.8i 0.105420i
216216 0 0
217217 113388. 0.163462
218218 0 0
219219 754156.i 1.06255i
220220 0 0
221221 −149302. + 140694.i −0.205629 + 0.193774i
222222 0 0
223223 694921.i 0.935778i 0.883787 + 0.467889i 0.154985π0.154985\pi
−0.883787 + 0.467889i 0.845015π0.845015\pi
224224 0 0
225225 164606. 0.216765
226226 0 0
227227 1.06606e6i 1.37315i −0.727059 0.686575i 0.759113π-0.759113\pi
0.727059 0.686575i 0.240887π-0.240887\pi
228228 0 0
229229 985635.i 1.24202i 0.783804 + 0.621008i 0.213277π0.213277\pi
−0.783804 + 0.621008i 0.786723π0.786723\pi
230230 0 0
231231 90793.4 0.111950
232232 0 0
233233 −1.01282e6 −1.22220 −0.611098 0.791555i 0.709272π-0.709272\pi
−0.611098 + 0.791555i 0.709272π0.709272\pi
234234 0 0
235235 −341759. −0.403692
236236 0 0
237237 −152999. −0.176936
238238 0 0
239239 112715.i 0.127640i 0.997961 + 0.0638201i 0.0203284π0.0203284\pi
−0.997961 + 0.0638201i 0.979672π0.979672\pi
240240 0 0
241241 940022.i 1.04255i 0.853390 + 0.521273i 0.174543π0.174543\pi
−0.853390 + 0.521273i 0.825457π0.825457\pi
242242 0 0
243243 −59049.0 −0.0641500
244244 0 0
245245 431534.i 0.459303i
246246 0 0
247247 −29107.1 30887.8i −0.0303568 0.0322140i
248248 0 0
249249 346886.i 0.354559i
250250 0 0
251251 −1.22654e6 −1.22885 −0.614423 0.788977i 0.710611π-0.710611\pi
−0.614423 + 0.788977i 0.710611π0.710611\pi
252252 0 0
253253 615001.i 0.604052i
254254 0 0
255255 100168.i 0.0964669i
256256 0 0
257257 810365. 0.765328 0.382664 0.923888i 0.375007π-0.375007\pi
0.382664 + 0.923888i 0.375007π0.375007\pi
258258 0 0
259259 167816. 0.155448
260260 0 0
261261 348691. 0.316840
262262 0 0
263263 25213.2 0.0224770 0.0112385 0.999937i 0.496423π-0.496423\pi
0.0112385 + 0.999937i 0.496423π0.496423\pi
264264 0 0
265265 23030.7i 0.0201461i
266266 0 0
267267 1.26223e6i 1.08358i
268268 0 0
269269 −498829. −0.420311 −0.210156 0.977668i 0.567397π-0.567397\pi
−0.210156 + 0.977668i 0.567397π0.567397\pi
270270 0 0
271271 541761.i 0.448110i 0.974577 + 0.224055i 0.0719295π0.0719295\pi
−0.974577 + 0.224055i 0.928070π0.928070\pi
272272 0 0
273273 230414. + 244510.i 0.187112 + 0.198559i
274274 0 0
275275 334636.i 0.266834i
276276 0 0
277277 −1.42654e6 −1.11708 −0.558540 0.829478i 0.688638π-0.688638\pi
−0.558540 + 0.829478i 0.688638π0.688638\pi
278278 0 0
279279 149917.i 0.115303i
280280 0 0
281281 186175.i 0.140655i 0.997524 + 0.0703274i 0.0224044π0.0224044\pi
−0.997524 + 0.0703274i 0.977596π0.977596\pi
282282 0 0
283283 1.64391e6 1.22015 0.610073 0.792345i 0.291140π-0.291140\pi
0.610073 + 0.792345i 0.291140π0.291140\pi
284284 0 0
285285 −20722.9 −0.0151126
286286 0 0
287287 −737086. −0.528219
288288 0 0
289289 −1.30651e6 −0.920168
290290 0 0
291291 785954.i 0.544083i
292292 0 0
293293 2.04281e6i 1.39014i −0.718940 0.695072i 0.755373π-0.755373\pi
0.718940 0.695072i 0.244627π-0.244627\pi
294294 0 0
295295 802478. 0.536881
296296 0 0
297297 120044.i 0.0789676i
298298 0 0
299299 1.65622e6 1.56074e6i 1.07137 1.00961i
300300 0 0
301301 132416.i 0.0842414i
302302 0 0
303303 1.15618e6 0.723465
304304 0 0
305305 885038.i 0.544769i
306306 0 0
307307 3.15457e6i 1.91026i −0.296179 0.955132i 0.595713π-0.595713\pi
0.296179 0.955132i 0.404287π-0.404287\pi
308308 0 0
309309 −572652. −0.341189
310310 0 0
311311 270180. 0.158399 0.0791994 0.996859i 0.474764π-0.474764\pi
0.0791994 + 0.996859i 0.474764π0.474764\pi
312312 0 0
313313 −1.05582e6 −0.609157 −0.304578 0.952487i 0.598516π-0.598516\pi
−0.304578 + 0.952487i 0.598516π0.598516\pi
314314 0 0
315315 164044. 0.0931504
316316 0 0
317317 165844.i 0.0926938i 0.998925 + 0.0463469i 0.0147580π0.0147580\pi
−0.998925 + 0.0463469i 0.985242π0.985242\pi
318318 0 0
319319 708873.i 0.390024i
320320 0 0
321321 1.12747e6 0.610722
322322 0 0
323323 23449.9i 0.0125065i
324324 0 0
325325 −901186. + 849232.i −0.473267 + 0.445983i
326326 0 0
327327 511893.i 0.264734i
328328 0 0
329329 633348. 0.322591
330330 0 0
331331 2.29011e6i 1.14891i 0.818535 + 0.574456i 0.194787π0.194787\pi
−0.818535 + 0.574456i 0.805213π0.805213\pi
332332 0 0
333333 221881.i 0.109650i
334334 0 0
335335 −2.27065e6 −1.10545
336336 0 0
337337 1.89805e6 0.910402 0.455201 0.890389i 0.349567π-0.349567\pi
0.455201 + 0.890389i 0.349567π0.349567\pi
338338 0 0
339339 2.11645e6 1.00025
340340 0 0
341341 304775. 0.141936
342342 0 0
343343 1.82937e6i 0.839587i
344344 0 0
345345 1.11117e6i 0.502614i
346346 0 0
347347 −3.22565e6 −1.43812 −0.719058 0.694950i 0.755426π-0.755426\pi
−0.719058 + 0.694950i 0.755426π0.755426\pi
348348 0 0
349349 2.95721e6i 1.29963i −0.760094 0.649813i 0.774847π-0.774847\pi
0.760094 0.649813i 0.225153π-0.225153\pi
350350 0 0
351351 323283. 304645.i 0.140060 0.131986i
352352 0 0
353353 101605.i 0.0433987i −0.999765 0.0216993i 0.993092π-0.993092\pi
0.999765 0.0216993i 0.00690766π-0.00690766\pi
354354 0 0
355355 541028. 0.227850
356356 0 0
357357 185631.i 0.0770869i
358358 0 0
359359 3.01953e6i 1.23653i −0.785971 0.618263i 0.787837π-0.787837\pi
0.785971 0.618263i 0.212163π-0.212163\pi
360360 0 0
361361 2.47125e6 0.998041
362362 0 0
363363 −1.20542e6 −0.480142
364364 0 0
365365 2.77010e6 1.08834
366366 0 0
367367 3.66414e6 1.42006 0.710031 0.704170i 0.248681π-0.248681\pi
0.710031 + 0.704170i 0.248681π0.248681\pi
368368 0 0
369369 974550.i 0.372596i
370370 0 0
371371 42680.4i 0.0160988i
372372 0 0
373373 2.15700e6 0.802746 0.401373 0.915915i 0.368533π-0.368533\pi
0.401373 + 0.915915i 0.368533π0.368533\pi
374374 0 0
375375 1.53437e6i 0.563446i
376376 0 0
377377 −1.90902e6 + 1.79896e6i −0.691763 + 0.651882i
378378 0 0
379379 474934.i 0.169838i 0.996388 + 0.0849191i 0.0270632π0.0270632\pi
−0.996388 + 0.0849191i 0.972937π0.972937\pi
380380 0 0
381381 986373. 0.348120
382382 0 0
383383 1.52732e6i 0.532025i 0.963970 + 0.266012i 0.0857062π0.0857062\pi
−0.963970 + 0.266012i 0.914294π0.914294\pi
384384 0 0
385385 333494.i 0.114667i
386386 0 0
387387 175076. 0.0594224
388388 0 0
389389 −2.38936e6 −0.800585 −0.400293 0.916387i 0.631092π-0.631092\pi
−0.400293 + 0.916387i 0.631092π0.631092\pi
390390 0 0
391391 −1.25740e6 −0.415940
392392 0 0
393393 −1.97725e6 −0.645774
394394 0 0
395395 561981.i 0.181229i
396396 0 0
397397 2.68613e6i 0.855363i 0.903930 + 0.427681i 0.140669π0.140669\pi
−0.903930 + 0.427681i 0.859331π0.859331\pi
398398 0 0
399399 38403.8 0.0120765
400400 0 0
401401 2.14312e6i 0.665557i −0.943005 0.332779i 0.892014π-0.892014\pi
0.943005 0.332779i 0.107986π-0.107986\pi
402402 0 0
403403 773453. + 820771.i 0.237231 + 0.251744i
404404 0 0
405405 216894.i 0.0657066i
406406 0 0
407407 451074. 0.134977
408408 0 0
409409 3.97614e6i 1.17531i 0.809110 + 0.587657i 0.199949π0.199949\pi
−0.809110 + 0.587657i 0.800051π0.800051\pi
410410 0 0
411411 82309.0i 0.0240349i
412412 0 0
413413 −1.48715e6 −0.429023
414414 0 0
415415 1.27415e6 0.363162
416416 0 0
417417 1.32108e6 0.372039
418418 0 0
419419 −2.59228e6 −0.721352 −0.360676 0.932691i 0.617454π-0.617454\pi
−0.360676 + 0.932691i 0.617454π0.617454\pi
420420 0 0
421421 2.81076e6i 0.772890i −0.922312 0.386445i 0.873703π-0.873703\pi
0.922312 0.386445i 0.126297π-0.126297\pi
422422 0 0
423423 837391.i 0.227550i
424424 0 0
425425 684178. 0.183737
426426 0 0
427427 1.64015e6i 0.435326i
428428 0 0
429429 619330. + 657219.i 0.162472 + 0.172412i
430430 0 0
431431 1.22819e6i 0.318472i 0.987241 + 0.159236i 0.0509030π0.0509030\pi
−0.987241 + 0.159236i 0.949097π0.949097\pi
432432 0 0
433433 5.44083e6 1.39459 0.697294 0.716785i 0.254387π-0.254387\pi
0.697294 + 0.716785i 0.254387π0.254387\pi
434434 0 0
435435 1.28078e6i 0.324528i
436436 0 0
437437 260133.i 0.0651616i
438438 0 0
439439 −211253. −0.0523169 −0.0261585 0.999658i 0.508327π-0.508327\pi
−0.0261585 + 0.999658i 0.508327π0.508327\pi
440440 0 0
441441 1.05736e6 0.258897
442442 0 0
443443 −2.23978e6 −0.542246 −0.271123 0.962545i 0.587395π-0.587395\pi
−0.271123 + 0.962545i 0.587395π0.587395\pi
444444 0 0
445445 −4.63632e6 −1.10987
446446 0 0
447447 1.84878e6i 0.437639i
448448 0 0
449449 5.59942e6i 1.31077i 0.755294 + 0.655386i 0.227494π0.227494\pi
−0.755294 + 0.655386i 0.772506π0.772506\pi
450450 0 0
451451 −1.98122e6 −0.458660
452452 0 0
453453 2.93125e6i 0.671131i
454454 0 0
455455 −898113. + 846336.i −0.203377 + 0.191652i
456456 0 0
457457 2.28019e6i 0.510718i 0.966846 + 0.255359i 0.0821937π0.0821937\pi
−0.966846 + 0.255359i 0.917806π0.917806\pi
458458 0 0
459459 −245435. −0.0543758
460460 0 0
461461 1.16004e6i 0.254227i 0.991888 + 0.127114i 0.0405713π0.0405713\pi
−0.991888 + 0.127114i 0.959429π0.959429\pi
462462 0 0
463463 5.43708e6i 1.17873i 0.807868 + 0.589364i 0.200621π0.200621\pi
−0.807868 + 0.589364i 0.799379π0.799379\pi
464464 0 0
465465 550664. 0.118101
466466 0 0
467467 6.30219e6 1.33721 0.668605 0.743618i 0.266892π-0.266892\pi
0.668605 + 0.743618i 0.266892π0.266892\pi
468468 0 0
469469 4.20798e6 0.883368
470470 0 0
471471 5.01859e6 1.04239
472472 0 0
473473 355922.i 0.0731480i
474474 0 0
475475 141544.i 0.0287844i
476476 0 0
477477 −56430.6 −0.0113558
478478 0 0
479479 6.02572e6i 1.19997i −0.800011 0.599985i 0.795173π-0.795173\pi
0.800011 0.599985i 0.204827π-0.204827\pi
480480 0 0
481481 1.14473e6 + 1.21476e6i 0.225600 + 0.239402i
482482 0 0
483483 2.05923e6i 0.401640i
484484 0 0
485485 −2.88690e6 −0.557285
486486 0 0
487487 6.09211e6i 1.16398i −0.813196 0.581990i 0.802274π-0.802274\pi
0.813196 0.581990i 0.197726π-0.197726\pi
488488 0 0
489489 5.71511e6i 1.08082i
490490 0 0
491491 −1.65104e6 −0.309068 −0.154534 0.987987i 0.549388π-0.549388\pi
−0.154534 + 0.987987i 0.549388π0.549388\pi
492492 0 0
493493 1.44932e6 0.268564
494494 0 0
495495 440935. 0.0808838
496496 0 0
497497 −1.00263e6 −0.182075
498498 0 0
499499 1.06216e7i 1.90958i 0.297279 + 0.954791i 0.403921π0.403921\pi
−0.297279 + 0.954791i 0.596079π0.596079\pi
500500 0 0
501501 4.32205e6i 0.769300i
502502 0 0
503503 4.17356e6 0.735506 0.367753 0.929923i 0.380127π-0.380127\pi
0.367753 + 0.929923i 0.380127π0.380127\pi
504504 0 0
505505 4.24677e6i 0.741020i
506506 0 0
507507 −198192. + 3.33575e6i −0.0342426 + 0.576334i
508508 0 0
509509 6.50979e6i 1.11371i −0.830610 0.556855i 0.812008π-0.812008\pi
0.830610 0.556855i 0.187992π-0.187992\pi
510510 0 0
511511 −5.13355e6 −0.869692
512512 0 0
513513 50776.1i 0.00851856i
514514 0 0
515515 2.10341e6i 0.349468i
516516 0 0
517517 1.70238e6 0.280111
518518 0 0
519519 3.03546e6 0.494659
520520 0 0
521521 5.00448e6 0.807727 0.403864 0.914819i 0.367667π-0.367667\pi
0.403864 + 0.914819i 0.367667π0.367667\pi
522522 0 0
523523 5.64842e6 0.902969 0.451484 0.892279i 0.350895π-0.350895\pi
0.451484 + 0.892279i 0.350895π0.350895\pi
524524 0 0
525525 1.12047e6i 0.177420i
526526 0 0
527527 623127.i 0.0977350i
528528 0 0
529529 7.51211e6 1.16714
530530 0 0
531531 1.96626e6i 0.302625i
532532 0 0
533533 −5.02789e6 5.33549e6i −0.766598 0.813497i
534534 0 0
535535 4.14133e6i 0.625541i
536536 0 0
537537 5.13162e6 0.767925
538538 0 0
539539 2.14956e6i 0.318697i
540540 0 0
541541 1.27506e7i 1.87300i −0.350670 0.936499i 0.614046π-0.614046\pi
0.350670 0.936499i 0.385954π-0.385954\pi
542542 0 0
543543 −1.73396e6 −0.252372
544544 0 0
545545 −1.88024e6 −0.271158
546546 0 0
547547 1.22119e7 1.74507 0.872537 0.488547i 0.162473π-0.162473\pi
0.872537 + 0.488547i 0.162473π0.162473\pi
548548 0 0
549549 −2.16855e6 −0.307071
550550 0 0
551551 299839.i 0.0420735i
552552 0 0
553553 1.04146e6i 0.144821i
554554 0 0
555555 814993. 0.112311
556556 0 0
557557 3.33060e6i 0.454867i −0.973794 0.227433i 0.926967π-0.926967\pi
0.973794 0.227433i 0.0730334π-0.0730334\pi
558558 0 0
559559 −958512. + 903253.i −0.129738 + 0.122259i
560560 0 0
561561 498959.i 0.0669357i
562562 0 0
563563 −5.83292e6 −0.775559 −0.387779 0.921752i 0.626758π-0.626758\pi
−0.387779 + 0.921752i 0.626758π0.626758\pi
564564 0 0
565565 7.77396e6i 1.02452i
566566 0 0
567567 401947.i 0.0525063i
568568 0 0
569569 −237693. −0.0307777 −0.0153888 0.999882i 0.504899π-0.504899\pi
−0.0153888 + 0.999882i 0.504899π0.504899\pi
570570 0 0
571571 7.42085e6 0.952496 0.476248 0.879311i 0.341996π-0.341996\pi
0.476248 + 0.879311i 0.341996π0.341996\pi
572572 0 0
573573 −2.88602e6 −0.367208
574574 0 0
575575 −7.58966e6 −0.957311
576576 0 0
577577 6.17238e6i 0.771814i 0.922538 + 0.385907i 0.126112π0.126112\pi
−0.922538 + 0.385907i 0.873888π0.873888\pi
578578 0 0
579579 3.47476e6i 0.430753i
580580 0 0
581581 −2.36126e6 −0.290204
582582 0 0
583583 114721.i 0.0139788i
584584 0 0
585585 1.11900e6 + 1.18745e6i 0.135188 + 0.143459i
586586 0 0
587587 4.27561e6i 0.512157i −0.966656 0.256078i 0.917569π-0.917569\pi
0.966656 0.256078i 0.0824305π-0.0824305\pi
588588 0 0
589589 128914. 0.0153113
590590 0 0
591591 8.02456e6i 0.945045i
592592 0 0
593593 1.00584e6i 0.117460i −0.998274 0.0587302i 0.981295π-0.981295\pi
0.998274 0.0587302i 0.0187052π-0.0187052\pi
594594 0 0
595595 681845. 0.0789575
596596 0 0
597597 6.30353e6 0.723849
598598 0 0
599599 2.06786e6 0.235480 0.117740 0.993044i 0.462435π-0.462435\pi
0.117740 + 0.993044i 0.462435π0.462435\pi
600600 0 0
601601 4.96901e6 0.561157 0.280578 0.959831i 0.409474π-0.409474\pi
0.280578 + 0.959831i 0.409474π0.409474\pi
602602 0 0
603603 5.56365e6i 0.623112i
604604 0 0
605605 4.42763e6i 0.491793i
606606 0 0
607607 7.68015e6 0.846054 0.423027 0.906117i 0.360968π-0.360968\pi
0.423027 + 0.906117i 0.360968π0.360968\pi
608608 0 0
609609 2.37355e6i 0.259331i
610610 0 0
611611 4.32026e6 + 4.58456e6i 0.468174 + 0.496815i
612612 0 0
613613 1.42866e7i 1.53560i 0.640689 + 0.767801i 0.278649π0.278649\pi
−0.640689 + 0.767801i 0.721351π0.721351\pi
614614 0 0
615615 −3.57963e6 −0.381637
616616 0 0
617617 1.20205e7i 1.27119i −0.772022 0.635596i 0.780754π-0.780754\pi
0.772022 0.635596i 0.219246π-0.219246\pi
618618 0 0
619619 6.90208e6i 0.724025i 0.932173 + 0.362013i 0.117910π0.117910\pi
−0.932173 + 0.362013i 0.882090π0.882090\pi
620620 0 0
621621 2.72264e6 0.283310
622622 0 0
623623 8.59202e6 0.886901
624624 0 0
625625 714605. 0.0731755
626626 0 0
627627 103226. 0.0104862
628628 0 0
629629 922241.i 0.0929432i
630630 0 0
631631 8.31995e6i 0.831855i 0.909398 + 0.415927i 0.136543π0.136543\pi
−0.909398 + 0.415927i 0.863457π0.863457\pi
632632 0 0
633633 5.38783e6 0.534447
634634 0 0
635635 3.62306e6i 0.356567i
636636 0 0
637637 −5.78886e6 + 5.45512e6i −0.565255 + 0.532667i
638638 0 0
639639 1.32565e6i 0.128433i
640640 0 0
641641 5.62851e6 0.541064 0.270532 0.962711i 0.412800π-0.412800\pi
0.270532 + 0.962711i 0.412800π0.412800\pi
642642 0 0
643643 1.34363e7i 1.28160i −0.767708 0.640799i 0.778603π-0.778603\pi
0.767708 0.640799i 0.221397π-0.221397\pi
644644 0 0
645645 643075.i 0.0608643i
646646 0 0
647647 −1.14169e7 −1.07223 −0.536115 0.844145i 0.680109π-0.680109\pi
−0.536115 + 0.844145i 0.680109π0.680109\pi
648648 0 0
649649 −3.99732e6 −0.372527
650650 0 0
651651 −1.02049e6 −0.0943749
652652 0 0
653653 −1.01592e7 −0.932345 −0.466173 0.884694i 0.654367π-0.654367\pi
−0.466173 + 0.884694i 0.654367π0.654367\pi
654654 0 0
655655 7.26267e6i 0.661444i
656656 0 0
657657 6.78741e6i 0.613466i
658658 0 0
659659 7.04782e6 0.632181 0.316090 0.948729i 0.397630π-0.397630\pi
0.316090 + 0.948729i 0.397630π0.397630\pi
660660 0 0
661661 1.08823e7i 0.968762i −0.874857 0.484381i 0.839045π-0.839045\pi
0.874857 0.484381i 0.160955π-0.160955\pi
662662 0 0
663663 1.34371e6 1.26625e6i 0.118720 0.111876i
664664 0 0
665665 141061.i 0.0123695i
666666 0 0
667667 −1.60775e7 −1.39928
668668 0 0
669669 6.25429e6i 0.540272i
670670 0 0
671671 4.40857e6i 0.378000i
672672 0 0
673673 2.82794e6 0.240676 0.120338 0.992733i 0.461602π-0.461602\pi
0.120338 + 0.992733i 0.461602π0.461602\pi
674674 0 0
675675 −1.48145e6 −0.125149
676676 0 0
677677 −2.19071e7 −1.83702 −0.918508 0.395401i 0.870605π-0.870605\pi
−0.918508 + 0.395401i 0.870605π0.870605\pi
678678 0 0
679679 5.35000e6 0.445328
680680 0 0
681681 9.59456e6i 0.792788i
682682 0 0
683683 7.16197e6i 0.587463i 0.955888 + 0.293732i 0.0948972π0.0948972\pi
−0.955888 + 0.293732i 0.905103π0.905103\pi
684684 0 0
685685 −302330. −0.0246181
686686 0 0
687687 8.87071e6i 0.717078i
688688 0 0
689689 308947. 291136.i 0.0247934 0.0233641i
690690 0 0
691691 1.89454e7i 1.50941i −0.656062 0.754707i 0.727779π-0.727779\pi
0.656062 0.754707i 0.272221π-0.272221\pi
692692 0 0
693693 −817141. −0.0646344
694694 0 0
695695 4.85247e6i 0.381066i
696696 0 0
697697 4.05069e6i 0.315825i
698698 0 0
699699 9.11534e6 0.705635
700700 0 0
701701 −2.38204e7 −1.83085 −0.915426 0.402487i 0.868146π-0.868146\pi
−0.915426 + 0.402487i 0.868146π0.868146\pi
702702 0 0
703703 190795. 0.0145606
704704 0 0
705705 3.07583e6 0.233072
706706 0 0
707707 7.87011e6i 0.592151i
708708 0 0
709709 1.15066e7i 0.859666i −0.902908 0.429833i 0.858572π-0.858572\pi
0.902908 0.429833i 0.141428π-0.141428\pi
710710 0 0
711711 1.37699e6 0.102154
712712 0 0
713713 6.91242e6i 0.509221i
714714 0 0
715715 −2.41404e6 + 2.27487e6i −0.176595 + 0.166414i
716716 0 0
717717 1.01444e6i 0.0736931i
718718 0 0
719719 −2.25090e7 −1.62381 −0.811903 0.583792i 0.801568π-0.801568\pi
−0.811903 + 0.583792i 0.801568π0.801568\pi
720720 0 0
721721 3.89805e6i 0.279260i
722722 0 0
723723 8.46020e6i 0.601915i
724724 0 0
725725 8.74813e6 0.618117
726726 0 0
727727 −1.44393e7 −1.01323 −0.506617 0.862171i 0.669104π-0.669104\pi
−0.506617 + 0.862171i 0.669104π0.669104\pi
728728 0 0
729729 531441. 0.0370370
730730 0 0
731731 727700. 0.0503685
732732 0 0
733733 1.27813e6i 0.0878648i 0.999035 + 0.0439324i 0.0139886π0.0139886\pi
−0.999035 + 0.0439324i 0.986011π0.986011\pi
734734 0 0
735735 3.88380e6i 0.265179i
736736 0 0
737737 1.13106e7 0.767040
738738 0 0
739739 8.59162e6i 0.578714i 0.957221 + 0.289357i 0.0934414π0.0934414\pi
−0.957221 + 0.289357i 0.906559π0.906559\pi
740740 0 0
741741 261964. + 277990.i 0.0175265 + 0.0185988i
742742 0 0
743743 1.97043e7i 1.30945i −0.755866 0.654727i 0.772784π-0.772784\pi
0.755866 0.654727i 0.227216π-0.227216\pi
744744 0 0
745745 6.79076e6 0.448258
746746 0 0
747747 3.12197e6i 0.204705i
748748 0 0
749749 7.67472e6i 0.499871i
750750 0 0
751751 −1.40159e7 −0.906818 −0.453409 0.891302i 0.649792π-0.649792\pi
−0.453409 + 0.891302i 0.649792π0.649792\pi
752752 0 0
753753 1.10389e7 0.709474
754754 0 0
755755 −1.07668e7 −0.687416
756756 0 0
757757 −1.63210e7 −1.03516 −0.517581 0.855634i 0.673167π-0.673167\pi
−0.517581 + 0.855634i 0.673167π0.673167\pi
758758 0 0
759759 5.53501e6i 0.348750i
760760 0 0
761761 1.94245e7i 1.21587i −0.793987 0.607935i 0.791998π-0.791998\pi
0.793987 0.607935i 0.208002π-0.208002\pi
762762 0 0
763763 3.48446e6 0.216683
764764 0 0
765765 901512.i 0.0556952i
766766 0 0
767767 −1.01443e7 1.07649e7i −0.622637 0.660728i
768768 0 0
769769 1.44865e7i 0.883378i 0.897168 + 0.441689i 0.145620π0.145620\pi
−0.897168 + 0.441689i 0.854380π0.854380\pi
770770 0 0
771771 −7.29328e6 −0.441862
772772 0 0
773773 1.93608e7i 1.16540i −0.812687 0.582700i 0.801996π-0.801996\pi
0.812687 0.582700i 0.198004π-0.198004\pi
774774 0 0
775775 3.76120e6i 0.224943i
776776 0 0
777777 −1.51035e6 −0.0897478
778778 0 0
779779 −838014. −0.0494775
780780 0 0
781781 −2.69498e6 −0.158099
782782 0 0
783783 −3.13822e6 −0.182928
784784 0 0
785785 1.84339e7i 1.06768i
786786 0 0
787787 1.82561e6i 0.105068i −0.998619 0.0525341i 0.983270π-0.983270\pi
0.998619 0.0525341i 0.0167298π-0.0167298\pi
788788 0 0
789789 −226919. −0.0129771
790790 0 0
791791 1.44067e7i 0.818698i
792792 0 0
793793 1.18724e7 1.11880e7i 0.670436 0.631784i
794794 0 0
795795 207276.i 0.0116314i
796796 0 0
797797 −4.34190e6 −0.242122 −0.121061 0.992645i 0.538630π-0.538630\pi
−0.121061 + 0.992645i 0.538630π0.538630\pi
798798 0 0
799799 3.48059e6i 0.192879i
800800 0 0
801801 1.13601e7i 0.625605i
802802 0 0
803803 −1.37985e7 −0.755166
804804 0 0
805805 −7.56378e6 −0.411386
806806 0 0
807807 4.48946e6 0.242667
808808 0 0
809809 −2.31393e7 −1.24302 −0.621510 0.783406i 0.713480π-0.713480\pi
−0.621510 + 0.783406i 0.713480π0.713480\pi
810810 0 0
811811 1.93460e6i 0.103285i 0.998666 + 0.0516427i 0.0164457π0.0164457\pi
−0.998666 + 0.0516427i 0.983554π0.983554\pi
812812 0 0
813813 4.87585e6i 0.258716i
814814 0 0
815815 −2.09922e7 −1.10704
816816 0 0
817817 150548.i 0.00789077i
818818 0 0
819819 −2.07372e6 2.20059e6i −0.108029 0.114638i
820820 0 0
821821 1.93584e7i 1.00233i −0.865352 0.501165i 0.832905π-0.832905\pi
0.865352 0.501165i 0.167095π-0.167095\pi
822822 0 0
823823 1.38012e6 0.0710260 0.0355130 0.999369i 0.488693π-0.488693\pi
0.0355130 + 0.999369i 0.488693π0.488693\pi
824824 0 0
825825 3.01172e6i 0.154056i
826826 0 0
827827 595025.i 0.0302532i 0.999886 + 0.0151266i 0.00481513π0.00481513\pi
−0.999886 + 0.0151266i 0.995185π0.995185\pi
828828 0 0
829829 −1.58534e7 −0.801193 −0.400597 0.916254i 0.631197π-0.631197\pi
−0.400597 + 0.916254i 0.631197π0.631197\pi
830830 0 0
831831 1.28388e7 0.644946
832832 0 0
833833 4.39489e6 0.219450
834834 0 0
835835 −1.58754e7 −0.787967
836836 0 0
837837 1.34926e6i 0.0665704i
838838 0 0
839839 3.11440e7i 1.52746i −0.645538 0.763728i 0.723367π-0.723367\pi
0.645538 0.763728i 0.276633π-0.276633\pi
840840 0 0
841841 −1.97959e6 −0.0965131
842842 0 0
843843 1.67557e6i 0.0812071i
844844 0 0
845845 −1.22526e7 727982.i −0.590319 0.0350735i
846846 0 0
847847 8.20528e6i 0.392993i
848848 0 0
849849 −1.47952e7 −0.704452
850850 0 0
851851 1.02305e7i 0.484255i
852852 0 0
853853 6.07749e6i 0.285991i −0.989723 0.142995i 0.954327π-0.954327\pi
0.989723 0.142995i 0.0456734π-0.0456734\pi
854854 0 0
855855 186506. 0.00872526
856856 0 0
857857 1.18639e7 0.551790 0.275895 0.961188i 0.411026π-0.411026\pi
0.275895 + 0.961188i 0.411026π0.411026\pi
858858 0 0
859859 8.22653e6 0.380394 0.190197 0.981746i 0.439087π-0.439087\pi
0.190197 + 0.981746i 0.439087π0.439087\pi
860860 0 0
861861 6.63378e6 0.304967
862862 0 0
863863 1.04409e7i 0.477212i −0.971116 0.238606i 0.923310π-0.923310\pi
0.971116 0.238606i 0.0766905π-0.0766905\pi
864864 0 0
865865 1.11496e7i 0.506662i
866866 0 0
867867 1.17586e7 0.531259
868868 0 0
869869 2.79935e6i 0.125750i
870870 0 0
871871 2.87039e7 + 3.04600e7i 1.28202 + 1.36045i
872872 0 0
873873 7.07359e6i 0.314126i
874874 0 0
875875 1.04445e7 0.461176
876876 0 0
877877 3.73473e7i 1.63968i −0.572590 0.819842i 0.694061π-0.694061\pi
0.572590 0.819842i 0.305939π-0.305939\pi
878878 0 0
879879 1.83853e7i 0.802600i
880880 0 0
881881 1.87870e7 0.815489 0.407745 0.913096i 0.366315π-0.366315\pi
0.407745 + 0.913096i 0.366315π0.366315\pi
882882 0 0
883883 671977. 0.0290036 0.0145018 0.999895i 0.495384π-0.495384\pi
0.0145018 + 0.999895i 0.495384π0.495384\pi
884884 0 0
885885 −7.22230e6 −0.309968
886886 0 0
887887 1.74761e6 0.0745823 0.0372912 0.999304i 0.488127π-0.488127\pi
0.0372912 + 0.999304i 0.488127π0.488127\pi
888888 0 0
889889 6.71426e6i 0.284934i
890890 0 0
891891 1.08040e6i 0.0455920i
892892 0 0
893893 720071. 0.0302167
894894 0 0
895895 1.88490e7i 0.786559i
896896 0 0
897897 −1.49060e7 + 1.40466e7i −0.618556 + 0.582896i
898898 0 0
899899 7.96752e6i 0.328794i
900900 0 0
901901 −234552. −0.00962559
902902 0 0
903903 1.19175e6i 0.0486368i
904904 0 0
905905 6.36905e6i 0.258496i
906906 0 0
907907 −3.53654e7 −1.42745 −0.713723 0.700428i 0.752993π-0.752993\pi
−0.713723 + 0.700428i 0.752993π0.752993\pi
908908 0 0
909909 −1.04056e7 −0.417693
910910 0 0
911911 8.75487e6 0.349505 0.174753 0.984612i 0.444087π-0.444087\pi
0.174753 + 0.984612i 0.444087π0.444087\pi
912912 0 0
913913 −6.34683e6 −0.251988
914914 0 0
915915 7.96534e6i 0.314522i
916916 0 0
917917 1.34592e7i 0.528561i
918918 0 0
919919 4.34862e6 0.169849 0.0849243 0.996387i 0.472935π-0.472935\pi
0.0849243 + 0.996387i 0.472935π0.472935\pi
920920 0 0
921921 2.83911e7i 1.10289i
922922 0 0
923923 −6.83927e6 7.25768e6i −0.264244 0.280410i
924924 0 0
925925 5.56666e6i 0.213914i
926926 0 0
927927 5.15387e6 0.196985
928928 0 0
929929 3.42017e7i 1.30019i 0.759851 + 0.650097i 0.225272π0.225272\pi
−0.759851 + 0.650097i 0.774728π0.774728\pi
930930 0 0
931931 909222.i 0.0343792i
932932 0 0
933933 −2.43162e6 −0.0914515
934934 0 0
935935 1.83273e6 0.0685599
936936 0 0
937937 2.46362e7 0.916697 0.458348 0.888773i 0.348441π-0.348441\pi
0.458348 + 0.888773i 0.348441π0.348441\pi
938938 0 0
939939 9.50238e6 0.351697
940940 0 0
941941 1.57679e7i 0.580496i −0.956951 0.290248i 0.906262π-0.906262\pi
0.956951 0.290248i 0.0937378π-0.0937378\pi
942942 0 0
943943 4.49347e7i 1.64552i
944944 0 0
945945 −1.47640e6 −0.0537804
946946 0 0
947947 4.99665e7i 1.81052i −0.424857 0.905261i 0.639675π-0.639675\pi
0.424857 0.905261i 0.360325π-0.360325\pi
948948 0 0
949949 −3.50175e7 3.71598e7i −1.26218 1.33939i
950950 0 0
951951 1.49259e6i 0.0535168i
952952 0 0
953953 −2.99714e7 −1.06899 −0.534496 0.845171i 0.679499π-0.679499\pi
−0.534496 + 0.845171i 0.679499π0.679499\pi
954954 0 0
955955 1.06007e7i 0.376118i
956956 0 0
957957 6.37986e6i 0.225181i
958958 0 0
959959 560278. 0.0196724
960960 0 0
961961 2.52036e7 0.880346
962962 0 0
963963 −1.01472e7 −0.352600
964964 0 0
965965 −1.27632e7 −0.441205
966966 0 0
967967 3.53755e6i 0.121657i −0.998148 0.0608284i 0.980626π-0.980626\pi
0.998148 0.0608284i 0.0193743π-0.0193743\pi
968968 0 0
969969 211049.i 0.00722062i
970970 0 0
971971 4.50145e6 0.153216 0.0766081 0.997061i 0.475591π-0.475591\pi
0.0766081 + 0.997061i 0.475591π0.475591\pi
972972 0 0
973973 8.99259e6i 0.304511i
974974 0 0
975975 8.11067e6 7.64309e6i 0.273241 0.257488i
976976 0 0
977977 3.17740e6i 0.106497i −0.998581 0.0532483i 0.983043π-0.983043\pi
0.998581 0.0532483i 0.0169575π-0.0169575\pi
978978 0 0
979979 2.30945e7 0.770109
980980 0 0
981981 4.60704e6i 0.152844i
982982 0 0
983983 4.62115e7i 1.52534i 0.646789 + 0.762669i 0.276112π0.276112\pi
−0.646789 + 0.762669i 0.723888π0.723888\pi
984984 0 0
985985 −2.94751e7 −0.967977
986986 0 0
987987 −5.70013e6 −0.186248
988988 0 0
989989 −8.07245e6 −0.262431
990990 0 0
991991 −2.68291e7 −0.867803 −0.433902 0.900960i 0.642863π-0.642863\pi
−0.433902 + 0.900960i 0.642863π0.642863\pi
992992 0 0
993993 2.06110e7i 0.663325i
994994 0 0
995995 2.31536e7i 0.741413i
996996 0 0
997997 2.27086e7 0.723524 0.361762 0.932271i 0.382175π-0.382175\pi
0.361762 + 0.932271i 0.382175π0.382175\pi
998998 0 0
999999 1.99693e6i 0.0633065i
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 624.6.c.a.337.2 4
4.3 odd 2 39.6.b.a.25.1 4
12.11 even 2 117.6.b.b.64.4 4
13.12 even 2 inner 624.6.c.a.337.3 4
52.31 even 4 507.6.a.f.1.1 4
52.47 even 4 507.6.a.f.1.4 4
52.51 odd 2 39.6.b.a.25.4 yes 4
156.155 even 2 117.6.b.b.64.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
39.6.b.a.25.1 4 4.3 odd 2
39.6.b.a.25.4 yes 4 52.51 odd 2
117.6.b.b.64.1 4 156.155 even 2
117.6.b.b.64.4 4 12.11 even 2
507.6.a.f.1.1 4 52.31 even 4
507.6.a.f.1.4 4 52.47 even 4
624.6.c.a.337.2 4 1.1 even 1 trivial
624.6.c.a.337.3 4 13.12 even 2 inner