LMFDB - Embedded newform 197.4.a.a.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [197,4,Mod(1,197)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(197, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("197.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 197 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	197.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:	$11.6233762711$
Analytic rank:	$1$
Dimension:	$22$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	197.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.44630 q^{2} -3.77168 q^{3} -2.01559 q^{4} +19.5805 q^{5} -9.22669 q^{6} -29.7228 q^{7} -24.5012 q^{8} -12.7744 q^{9} +47.8998 q^{10} +34.7479 q^{11} +7.60218 q^{12} -48.7590 q^{13} -72.7110 q^{14} -73.8513 q^{15} -43.8126 q^{16} +61.7835 q^{17} -31.2501 q^{18} -131.746 q^{19} -39.4662 q^{20} +112.105 q^{21} +85.0039 q^{22} -179.606 q^{23} +92.4108 q^{24} +258.394 q^{25} -119.279 q^{26} +150.016 q^{27} +59.9091 q^{28} -239.803 q^{29} -180.663 q^{30} -143.073 q^{31} +88.8305 q^{32} -131.058 q^{33} +151.141 q^{34} -581.986 q^{35} +25.7480 q^{36} -8.14353 q^{37} -322.291 q^{38} +183.903 q^{39} -479.744 q^{40} -25.2993 q^{41} +274.243 q^{42} +24.2929 q^{43} -70.0376 q^{44} -250.129 q^{45} -439.372 q^{46} +349.378 q^{47} +165.247 q^{48} +540.444 q^{49} +632.111 q^{50} -233.028 q^{51} +98.2783 q^{52} +236.183 q^{53} +366.986 q^{54} +680.379 q^{55} +728.244 q^{56} +496.904 q^{57} -586.632 q^{58} +83.9524 q^{59} +148.854 q^{60} +822.606 q^{61} -350.000 q^{62} +379.691 q^{63} +567.808 q^{64} -954.723 q^{65} -320.608 q^{66} -483.475 q^{67} -124.530 q^{68} +677.418 q^{69} -1423.71 q^{70} -418.244 q^{71} +312.988 q^{72} -164.505 q^{73} -19.9215 q^{74} -974.581 q^{75} +265.546 q^{76} -1032.80 q^{77} +449.884 q^{78} +625.174 q^{79} -857.871 q^{80} -220.906 q^{81} -61.8897 q^{82} +652.986 q^{83} -225.958 q^{84} +1209.75 q^{85} +59.4277 q^{86} +904.463 q^{87} -851.364 q^{88} -1167.04 q^{89} -611.891 q^{90} +1449.25 q^{91} +362.013 q^{92} +539.626 q^{93} +854.685 q^{94} -2579.64 q^{95} -335.041 q^{96} +539.439 q^{97} +1322.09 q^{98} -443.883 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 6 q^{2} - 34 q^{3} + 68 q^{4} - 31 q^{5} - 24 q^{6} - 102 q^{7} - 93 q^{8} + 152 q^{9} - 133 q^{10} - 100 q^{11} - 272 q^{12} - 223 q^{13} - 55 q^{14} - 166 q^{15} + 112 q^{16} - 114 q^{17} - 389 q^{18}+ \cdots - 502 q^{99}+O(q^{100}) $ 22 * q - 6 * q^2 - 34 * q^3 + 68 * q^4 - 31 * q^5 - 24 * q^6 - 102 * q^7 - 93 * q^8 + 152 * q^9 - 133 * q^10 - 100 * q^11 - 272 * q^12 - 223 * q^13 - 55 * q^14 - 166 * q^15 + 112 * q^16 - 114 * q^17 - 389 * q^18 - 529 * q^19 - 441 * q^20 - 148 * q^21 - 671 * q^22 - 208 * q^23 - 555 * q^24 + 35 * q^25 - 408 * q^26 - 994 * q^27 - 1202 * q^28 - 2 * q^29 - 365 * q^30 - 1261 * q^31 - 1020 * q^32 - 790 * q^33 - 814 * q^34 - 968 * q^35 + 94 * q^36 - 792 * q^37 - 184 * q^38 - 368 * q^39 - 1914 * q^40 - 271 * q^41 - 1157 * q^42 - 1349 * q^43 - 998 * q^44 - 1533 * q^45 - 1371 * q^46 - 986 * q^47 - 1966 * q^48 - 40 * q^49 + 1631 * q^50 - 36 * q^51 - 1382 * q^52 + 248 * q^53 + 2903 * q^54 - 566 * q^55 + 4800 * q^56 + 914 * q^57 + 351 * q^58 - 1281 * q^59 + 5149 * q^60 + 510 * q^61 + 2237 * q^62 + 120 * q^63 + 3185 * q^64 + 2558 * q^65 + 8308 * q^66 - 3070 * q^67 + 4625 * q^68 + 302 * q^69 + 2087 * q^70 + 101 * q^71 + 4511 * q^72 - 3352 * q^73 + 4501 * q^74 - 752 * q^75 - 334 * q^76 - 492 * q^77 + 7825 * q^78 - 1313 * q^79 + 3098 * q^80 + 2078 * q^81 - 1243 * q^82 - 2631 * q^83 + 7518 * q^84 + 84 * q^85 + 7448 * q^86 - 1046 * q^87 - 3285 * q^88 + 798 * q^89 + 6009 * q^90 - 3992 * q^91 + 5966 * q^92 + 1978 * q^93 + 3517 * q^94 + 284 * q^95 + 10181 * q^96 - 3693 * q^97 + 2932 * q^98 - 502 * q^99

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	2.44630	0.864899	0.432450	−	0.901658i	$-0.357649\pi$
$2$	2.44630	0.864899	0.432450	+	0.901658i	$0.357649\pi$
$3$	−3.77168	−0.725861	−0.362930	−	0.931816i	$-0.618224\pi$
$3$	−3.77168	−0.725861	−0.362930	+	0.931816i	$0.618224\pi$
$4$	−2.01559	−0.251949
$5$	19.5805	1.75133	0.875665	−	0.482920i	$-0.160424\pi$
$5$	19.5805	1.75133	0.875665	+	0.482920i	$0.160424\pi$
$6$	−9.22669	−0.627797
$7$	−29.7228	−1.60488	−0.802440	−	0.596733i	$-0.796465\pi$
$7$	−29.7228	−1.60488	−0.802440	+	0.596733i	$0.796465\pi$
$8$	−24.5012	−1.08281
$9$	−12.7744	−0.473126
$10$	47.8998	1.51472
$11$	34.7479	0.952443	0.476222	−	0.879325i	$-0.342006\pi$
$11$	34.7479	0.952443	0.476222	+	0.879325i	$0.342006\pi$
$12$	7.60218	0.182880
$13$	−48.7590	−1.04025	−0.520127	−	0.854089i	$-0.674115\pi$
$13$	−48.7590	−1.04025	−0.520127	+	0.854089i	$0.674115\pi$
$14$	−72.7110	−1.38806
$15$	−73.8513	−1.27122
$16$	−43.8126	−0.684572
$17$	61.7835	0.881453	0.440727	−	0.897641i	$-0.354721\pi$
$17$	61.7835	0.881453	0.440727	+	0.897641i	$0.354721\pi$
$18$	−31.2501	−0.409206
$19$	−131.746	−1.59077	−0.795384	−	0.606106i	$-0.792731\pi$
$19$	−131.746	−1.59077	−0.795384	+	0.606106i	$0.792731\pi$
$20$	−39.4662	−0.441246
$21$	112.105	1.16492
$22$	85.0039	0.823768
$23$	−179.606	−1.62828	−0.814141	−	0.580667i	$-0.802792\pi$
$23$	−179.606	−1.62828	−0.814141	+	0.580667i	$0.802792\pi$
$24$	92.4108	0.785970
$25$	258.394	2.06715
$26$	−119.279	−0.899715
$27$	150.016	1.06928
$28$	59.9091	0.404348
$29$	−239.803	−1.53553	−0.767765	−	0.640732i	$-0.778631\pi$
$29$	−239.803	−1.53553	−0.767765	+	0.640732i	$0.778631\pi$
$30$	−180.663	−1.09948
$31$	−143.073	−0.828924	−0.414462	−	0.910067i	$-0.636030\pi$
$31$	−143.073	−0.828924	−0.414462	+	0.910067i	$0.636030\pi$
$32$	88.8305	0.490724
$33$	−131.058	−0.691341
$34$	151.141	0.762368
$35$	−581.986	−2.81067
$36$	25.7480	0.119204
$37$	−8.14353	−0.0361834	−0.0180917	−	0.999836i	$-0.505759\pi$
$37$	−8.14353	−0.0361834	−0.0180917	+	0.999836i	$0.505759\pi$
$38$	−322.291	−1.37585
$39$	183.903	0.755080
$40$	−479.744	−1.89636
$41$	−25.2993	−0.0963678	−0.0481839	−	0.998838i	$-0.515343\pi$
$41$	−25.2993	−0.0963678	−0.0481839	+	0.998838i	$0.515343\pi$
$42$	274.243	1.00754
$43$	24.2929	0.0861541	0.0430771	−	0.999072i	$-0.486284\pi$
$43$	24.2929	0.0861541	0.0430771	+	0.999072i	$0.486284\pi$
$44$	−70.0376	−0.239967
$45$	−250.129	−0.828599
$46$	−439.372	−1.40830
$47$	349.378	1.08430	0.542149	−	0.840282i	$-0.317611\pi$
$47$	349.378	1.08430	0.542149	+	0.840282i	$0.317611\pi$
$48$	165.247	0.496904
$49$	540.444	1.57564
$50$	632.111	1.78788
$51$	−233.028	−0.639813
$52$	98.2783	0.262091
$53$	236.183	0.612118	0.306059	−	0.952013i	$-0.400989\pi$
$53$	236.183	0.612118	0.306059	+	0.952013i	$0.400989\pi$
$54$	366.986	0.924823
$55$	680.379	1.66804
$56$	728.244	1.73778
$57$	496.904	1.15468
$58$	−586.632	−1.32808
$59$	83.9524	0.185249	0.0926243	−	0.995701i	$-0.470474\pi$
$59$	83.9524	0.185249	0.0926243	+	0.995701i	$0.470474\pi$
$60$	148.854	0.320283
$61$	822.606	1.72662	0.863310	−	0.504673i	$-0.168387\pi$
$61$	822.606	1.72662	0.863310	+	0.504673i	$0.168387\pi$
$62$	−350.000	−0.716936
$63$	379.691	0.759310
$64$	567.808	1.10900
$65$	−954.723	−1.82183
$66$	−320.608	−0.597941
$67$	−483.475	−0.881579	−0.440790	−	0.897610i	$-0.645302\pi$
$67$	−483.475	−0.881579	−0.440790	+	0.897610i	$0.645302\pi$
$68$	−124.530	−0.222081
$69$	677.418	1.18191
$70$	−1423.71	−2.43095
$71$	−418.244	−0.699105	−0.349552	−	0.936917i	$-0.613666\pi$
$71$	−418.244	−0.699105	−0.349552	+	0.936917i	$0.613666\pi$
$72$	312.988	0.512305
$73$	−164.505	−0.263751	−0.131876	−	0.991266i	$-0.542100\pi$
$73$	−164.505	−0.263751	−0.131876	+	0.991266i	$0.542100\pi$
$74$	−19.9215	−0.0312950
$75$	−974.581	−1.50047
$76$	265.546	0.400793
$77$	−1032.80	−1.52856
$78$	449.884	0.653068
$79$	625.174	0.890350	0.445175	−	0.895444i	$-0.353142\pi$
$79$	625.174	0.890350	0.445175	+	0.895444i	$0.353142\pi$
$80$	−857.871	−1.19891
$81$	−220.906	−0.303026
$82$	−61.8897	−0.0833485
$83$	652.986	0.863548	0.431774	−	0.901982i	$-0.357888\pi$
$83$	652.986	0.863548	0.431774	+	0.901982i	$0.357888\pi$
$84$	−225.958	−0.293501
$85$	1209.75	1.54371
$86$	59.4277	0.0745146
$87$	904.463	1.11458
$88$	−851.364	−1.03132
$89$	−1167.04	−1.38996	−0.694979	−	0.719030i	$-0.744586\pi$
$89$	−1167.04	−1.38996	−0.694979	+	0.719030i	$0.744586\pi$
$90$	−611.891	−0.716655
$91$	1449.25	1.66948
$92$	362.013	0.410245
$93$	539.626	0.601684
$94$	854.685	0.937809
$95$	−2579.64	−2.78596
$96$	−335.041	−0.356197
$97$	539.439	0.564657	0.282329	−	0.959318i	$-0.408893\pi$
$97$	539.439	0.564657	0.282329	+	0.959318i	$0.408893\pi$
$98$	1322.09	1.36277
$99$	−443.883	−0.450626
$100$	−520.818	−0.520818
$101$	1191.08	1.17343	0.586717	−	0.809792i	$-0.300420\pi$
$101$	1191.08	1.17343	0.586717	+	0.809792i	$0.300420\pi$
$102$	−570.057	−0.553373
$103$	−1381.69	−1.32176	−0.660881	−	0.750491i	$-0.729817\pi$
$103$	−1381.69	−1.32176	−0.660881	+	0.750491i	$0.729817\pi$
$104$	1194.65	1.12640
$105$	2195.07	2.04016
$106$	577.776	0.529421
$107$	−1870.22	−1.68973	−0.844863	−	0.534982i	$-0.820318\pi$
$107$	−1870.22	−1.68973	−0.844863	+	0.534982i	$0.820318\pi$
$108$	−302.372	−0.269405
$109$	509.839	0.448016	0.224008	−	0.974587i	$-0.428086\pi$
$109$	509.839	0.448016	0.224008	+	0.974587i	$0.428086\pi$
$110$	1664.41	1.44269
$111$	30.7148	0.0262641
$112$	1302.23	1.09866
$113$	−1256.21	−1.04579	−0.522894	−	0.852398i	$-0.675148\pi$
$113$	−1256.21	−1.04579	−0.522894	+	0.852398i	$0.675148\pi$
$114$	1215.58	0.998678
$115$	−3516.77	−2.85166
$116$	483.346	0.386876
$117$	622.866	0.492171
$118$	205.373	0.160221
$119$	−1836.38	−1.41463
$120$	1809.44	1.37649
$121$	−123.586	−0.0928516
$122$	2012.34	1.49335
$123$	95.4208	0.0699496
$124$	288.377	0.208847
$125$	2611.92	1.86894
$126$	928.839	0.656727
$127$	−2058.78	−1.43848	−0.719239	−	0.694763i	$-0.755509\pi$
$127$	−2058.78	−1.43848	−0.719239	+	0.694763i	$0.755509\pi$
$128$	678.386	0.468449
$129$	−91.6250	−0.0625359
$130$	−2335.54	−1.57570
$131$	868.516	0.579257	0.289628	−	0.957139i	$-0.406468\pi$
$131$	868.516	0.579257	0.289628	+	0.957139i	$0.406468\pi$
$132$	264.160	0.174183
$133$	3915.86	2.55299
$134$	−1182.73	−0.762477
$135$	2937.39	1.87267
$136$	−1513.77	−0.954446
$137$	−2928.41	−1.82621	−0.913104	−	0.407726i	$-0.866322\pi$
$137$	−2928.41	−1.82621	−0.913104	+	0.407726i	$0.866322\pi$
$138$	1657.17	1.02223
$139$	324.789	0.198189	0.0990945	−	0.995078i	$-0.468405\pi$
$139$	324.789	0.198189	0.0990945	+	0.995078i	$0.468405\pi$
$140$	1173.05	0.708147
$141$	−1317.74	−0.787050
$142$	−1023.15	−0.604655
$143$	−1694.27	−0.990783
$144$	559.680	0.323889
$145$	−4695.46	−2.68922
$146$	−402.429	−0.228118
$147$	−2038.39	−1.14370
$148$	16.4140	0.00911639
$149$	2152.52	1.18350	0.591751	−	0.806121i	$-0.298437\pi$
$149$	2152.52	1.18350	0.591751	+	0.806121i	$0.298437\pi$
$150$	−2384.12	−1.29775
$151$	−13.7027	−0.00738485	−0.00369242	−	0.999993i	$-0.501175\pi$
$151$	−13.7027	−0.00738485	−0.00369242	+	0.999993i	$0.501175\pi$
$152$	3227.93	1.72250
$153$	−789.247	−0.417038
$154$	−2526.55	−1.32205
$155$	−2801.43	−1.45172
$156$	−370.675	−0.190242
$157$	922.330	0.468853	0.234426	−	0.972134i	$-0.424679\pi$
$157$	922.330	0.468853	0.234426	+	0.972134i	$0.424679\pi$
$158$	1529.37	0.770063
$159$	−890.809	−0.444313
$160$	1739.34	0.859419
$161$	5338.40	2.61320
$162$	−540.403	−0.262087
$163$	−1226.81	−0.589519	−0.294759	−	0.955572i	$-0.595239\pi$
$163$	−1226.81	−0.589519	−0.294759	+	0.955572i	$0.595239\pi$
$164$	50.9930	0.0242798
$165$	−2566.18	−1.21077
$166$	1597.40	0.746882
$167$	−902.067	−0.417988	−0.208994	−	0.977917i	$-0.567019\pi$
$167$	−902.067	−0.417988	−0.208994	+	0.977917i	$0.567019\pi$
$168$	−2746.71	−1.26139
$169$	180.436	0.0821286
$170$	2959.42	1.33516
$171$	1682.97	0.752633
$172$	−48.9645	−0.0217065
$173$	−707.455	−0.310906	−0.155453	−	0.987843i	$-0.549684\pi$
$173$	−707.455	−0.310906	−0.155453	+	0.987843i	$0.549684\pi$
$174$	2212.59	0.964000
$175$	−7680.20	−3.31753
$176$	−1522.40	−0.652016
$177$	−316.642	−0.134465
$178$	−2854.94	−1.20217
$179$	−39.4168	−0.0164590	−0.00822948	−	0.999966i	$-0.502620\pi$
$179$	−39.4168	−0.0164590	−0.00822948	+	0.999966i	$0.502620\pi$
$180$	504.157	0.208765
$181$	−762.476	−0.313118	−0.156559	−	0.987669i	$-0.550040\pi$
$181$	−762.476	−0.313118	−0.156559	+	0.987669i	$0.550040\pi$
$182$	3545.31	1.44393
$183$	−3102.61	−1.25329
$184$	4400.57	1.76312
$185$	−159.454	−0.0633691
$186$	1320.09	0.520396
$187$	2146.85	0.839534
$188$	−704.204	−0.273188
$189$	−4458.91	−1.71607
$190$	−6310.60	−2.40957
$191$	−1344.50	−0.509343	−0.254671	−	0.967028i	$-0.581967\pi$
$191$	−1344.50	−0.509343	−0.254671	+	0.967028i	$0.581967\pi$
$192$	−2141.59	−0.804979
$193$	658.622	0.245641	0.122820	−	0.992429i	$-0.460806\pi$
$193$	658.622	0.245641	0.122820	+	0.992429i	$0.460806\pi$
$194$	1319.63	0.488371
$195$	3600.91	1.32239
$196$	−1089.32	−0.396981
$197$	197.000	0.0712470
$197$	197.000	0.0712470
$198$	−1085.87	−0.389746
$199$	1629.94	0.580621	0.290311	−	0.956932i	$-0.406241\pi$
$199$	1629.94	0.580621	0.290311	+	0.956932i	$0.406241\pi$
$200$	−6330.97	−2.23833
$201$	1823.51	0.639904
$202$	2913.74	1.01490
$203$	7127.63	2.46434
$204$	469.690	0.161200
$205$	−495.371	−0.168772
$206$	−3380.02	−1.14319
$207$	2294.36	0.770383
$208$	2136.26	0.712129
$209$	−4577.89	−1.51512
$210$	5369.80	1.76453
$211$	1838.29	0.599779	0.299889	−	0.953974i	$-0.403050\pi$
$211$	1838.29	0.599779	0.299889	+	0.953974i	$0.403050\pi$
$212$	−476.050	−0.154223
$213$	1577.48	0.507453
$214$	−4575.12	−1.46144
$215$	475.665	0.150884
$216$	−3675.58	−1.15783
$217$	4252.53	1.33032
$218$	1247.22	0.387489
$219$	620.461	0.191447
$220$	−1371.37	−0.420262
$221$	−3012.50	−0.916935
$222$	75.1378	0.0227158
$223$	−2470.42	−0.741845	−0.370922	−	0.928664i	$-0.620958\pi$
$223$	−2470.42	−0.741845	−0.370922	+	0.928664i	$0.620958\pi$
$224$	−2640.29	−0.787553
$225$	−3300.83	−0.978024
$226$	−3073.07	−0.904501
$227$	−5573.30	−1.62957	−0.814787	−	0.579761i	$-0.803146\pi$
$227$	−5573.30	−1.62957	−0.814787	+	0.579761i	$0.803146\pi$
$228$	−1001.56	−0.290920
$229$	−5255.66	−1.51661	−0.758306	−	0.651899i	$-0.773973\pi$
$229$	−5255.66	−1.51661	−0.758306	+	0.651899i	$0.773973\pi$
$230$	−8603.10	−2.46640
$231$	3895.41	1.10952
$232$	5875.47	1.66269
$233$	−768.357	−0.216038	−0.108019	−	0.994149i	$-0.534451\pi$
$233$	−768.357	−0.216038	−0.108019	+	0.994149i	$0.534451\pi$
$234$	1523.72	0.425678
$235$	6840.98	1.89896
$236$	−169.214	−0.0466733
$237$	−2357.96	−0.646270
$238$	−4492.34	−1.22351
$239$	6527.50	1.76665	0.883324	−	0.468763i	$-0.155300\pi$
$239$	6527.50	1.76665	0.883324	+	0.468763i	$0.155300\pi$
$240$	3235.62	0.870243
$241$	−1386.77	−0.370663	−0.185331	−	0.982676i	$-0.559336\pi$
$241$	−1386.77	−0.370663	−0.185331	+	0.982676i	$0.559336\pi$
$242$	−302.328	−0.0803073
$243$	−3217.26	−0.849330
$244$	−1658.04	−0.435021
$245$	10582.1	2.75946
$246$	233.428	0.0604994
$247$	6423.79	1.65480
$248$	3505.46	0.897568
$249$	−2462.86	−0.626816
$250$	6389.55	1.61644
$251$	590.235	0.148427	0.0742137	−	0.997242i	$-0.476355\pi$
$251$	590.235	0.148427	0.0742137	+	0.997242i	$0.476355\pi$
$252$	−765.302	−0.191308
$253$	−6240.94	−1.55085
$254$	−5036.39	−1.24414
$255$	−4562.79	−1.12052
$256$	−2882.92	−0.703838
$257$	−501.796	−0.121794	−0.0608972	−	0.998144i	$-0.519396\pi$
$257$	−501.796	−0.121794	−0.0608972	+	0.998144i	$0.519396\pi$
$258$	−224.143	−0.0540873
$259$	242.048	0.0580701
$260$	1924.33	0.459008
$261$	3063.34	0.726499
$262$	2124.65	0.500999
$263$	3390.32	0.794890	0.397445	−	0.917626i	$-0.369897\pi$
$263$	3390.32	0.794890	0.397445	+	0.917626i	$0.369897\pi$
$264$	3211.08	0.748591
$265$	4624.58	1.07202
$266$	9579.37	2.20808
$267$	4401.72	1.00892
$268$	974.488	0.222113
$269$	4452.69	1.00924	0.504619	−	0.863342i	$-0.331633\pi$
$269$	4452.69	1.00924	0.504619	+	0.863342i	$0.331633\pi$
$270$	7185.75	1.61967
$271$	1010.04	0.226403	0.113202	−	0.993572i	$-0.463889\pi$
$271$	1010.04	0.226403	0.113202	+	0.993572i	$0.463889\pi$
$272$	−2706.90	−0.603419
$273$	−5466.12	−1.21181
$274$	−7163.77	−1.57949
$275$	8978.65	1.96885
$276$	−1365.40	−0.297780
$277$	1972.74	0.427908	0.213954	−	0.976844i	$-0.431366\pi$
$277$	1972.74	0.427908	0.213954	+	0.976844i	$0.431366\pi$
$278$	794.533	0.171413
$279$	1827.67	0.392186
$280$	14259.3	3.04342
$281$	−6379.02	−1.35424	−0.677118	−	0.735875i	$-0.736771\pi$
$281$	−6379.02	−1.35424	−0.677118	+	0.735875i	$0.736771\pi$
$282$	−3223.60	−0.680719
$283$	−8779.30	−1.84408	−0.922041	−	0.387091i	$-0.873480\pi$
$283$	−8779.30	−1.84408	−0.922041	+	0.387091i	$0.873480\pi$
$284$	843.010	0.176139
$285$	9729.60	2.02222
$286$	−4144.70	−0.856928
$287$	751.965	0.154659
$288$	−1134.76	−0.232174
$289$	−1095.80	−0.223040
$290$	−11486.5	−2.32590
$291$	−2034.59	−0.409863
$292$	331.575	0.0664520
$293$	−148.856	−0.0296801	−0.0148401	−	0.999890i	$-0.504724\pi$
$293$	−148.856	−0.0296801	−0.0148401	+	0.999890i	$0.504724\pi$
$294$	−4986.51	−0.989181
$295$	1643.83	0.324431
$296$	199.526	0.0391798
$297$	5212.75	1.01843
$298$	5265.73	1.02361
$299$	8757.42	1.69383
$300$	1964.36	0.378041
$301$	−722.052	−0.138267
$302$	−33.5210	−0.00638715
$303$	−4492.38	−0.851750
$304$	5772.13	1.08900
$305$	16107.0	3.02388
$306$	−1930.74	−0.360696
$307$	1414.28	0.262922	0.131461	−	0.991321i	$-0.458033\pi$
$307$	1414.28	0.262922	0.131461	+	0.991321i	$0.458033\pi$
$308$	2081.71	0.385119
$309$	5211.28	0.959416
$310$	−6853.16	−1.25559
$311$	1707.82	0.311388	0.155694	−	0.987805i	$-0.450239\pi$
$311$	1707.82	0.311388	0.155694	+	0.987805i	$0.450239\pi$
$312$	−4505.85	−0.817608
$313$	−205.966	−0.0371945	−0.0185973	−	0.999827i	$-0.505920\pi$
$313$	−205.966	−0.0371945	−0.0185973	+	0.999827i	$0.505920\pi$
$314$	2256.30	0.405511
$315$	7434.52	1.32980
$316$	−1260.10	−0.224323
$317$	−4531.53	−0.802890	−0.401445	−	0.915883i	$-0.631492\pi$
$317$	−4531.53	−0.802890	−0.401445	+	0.915883i	$0.631492\pi$
$318$	−2179.19	−0.384286
$319$	−8332.66	−1.46251
$320$	11117.9	1.94222
$321$	7053.87	1.22651
$322$	13059.4	2.26015
$323$	−8139.72	−1.40219
$324$	445.257	0.0763472
$325$	−12599.0	−2.15036
$326$	−3001.16	−0.509874
$327$	−1922.95	−0.325197
$328$	619.862	0.104348
$329$	−10384.5	−1.74017
$330$	−6277.65	−1.04719
$331$	−5420.54	−0.900120	−0.450060	−	0.892998i	$-0.648597\pi$
$331$	−5420.54	−0.900120	−0.450060	+	0.892998i	$0.648597\pi$
$332$	−1316.15	−0.217570
$333$	104.029	0.0171193
$334$	−2206.73	−0.361518
$335$	−9466.65	−1.54394
$336$	−4911.61	−0.797472
$337$	−3944.11	−0.637535	−0.318768	−	0.947833i	$-0.603269\pi$
$337$	−3944.11	−0.637535	−0.318768	+	0.947833i	$0.603269\pi$
$338$	441.403	0.0710330
$339$	4738.02	0.759097
$340$	−2438.36	−0.388938
$341$	−4971.48	−0.789503
$342$	4117.07	0.650952
$343$	−5868.60	−0.923833
$344$	−595.204	−0.0932885
$345$	13264.2	2.06991
$346$	−1730.65	−0.268903
$347$	10530.9	1.62920	0.814598	−	0.580026i	$-0.196958\pi$
$347$	10530.9	1.62920	0.814598	+	0.580026i	$0.196958\pi$
$348$	−1823.03	−0.280818
$349$	9352.24	1.43442	0.717212	−	0.696855i	$-0.245418\pi$
$349$	9352.24	1.43442	0.717212	+	0.696855i	$0.245418\pi$
$350$	−18788.1	−2.86933
$351$	−7314.65	−1.11233
$352$	3086.67	0.467387
$353$	−9442.24	−1.42368	−0.711841	−	0.702341i	$-0.752138\pi$
$353$	−9442.24	−1.42368	−0.711841	+	0.702341i	$0.752138\pi$
$354$	−774.603	−0.116298
$355$	−8189.41	−1.22436
$356$	2352.28	0.350199
$357$	6926.24	1.02682
$358$	−96.4256	−0.0142353
$359$	−3014.81	−0.443220	−0.221610	−	0.975135i	$-0.571131\pi$
$359$	−3014.81	−0.443220	−0.221610	+	0.975135i	$0.571131\pi$
$360$	6128.45	0.897215
$361$	10498.0	1.53054
$362$	−1865.25	−0.270816
$363$	466.126	0.0673974
$364$	−2921.10	−0.420625
$365$	−3221.08	−0.461916
$366$	−7589.93	−1.08397
$367$	8964.30	1.27502	0.637511	−	0.770441i	$-0.279964\pi$
$367$	8964.30	1.27502	0.637511	+	0.770441i	$0.279964\pi$
$368$	7869.02	1.11468
$369$	323.183	0.0455941
$370$	−390.073	−0.0548079
$371$	−7020.03	−0.982376
$372$	−1087.67	−0.151594
$373$	13074.6	1.81495	0.907476	−	0.420105i	$-0.138007\pi$
$373$	13074.6	1.81495	0.907476	+	0.420105i	$0.138007\pi$
$374$	5251.84	0.726113
$375$	−9851.33	−1.35659
$376$	−8560.18	−1.17409
$377$	11692.6	1.59734
$378$	−10907.8	−1.48423
$379$	−2987.82	−0.404945	−0.202473	−	0.979288i	$-0.564898\pi$
$379$	−2987.82	−0.404945	−0.202473	+	0.979288i	$0.564898\pi$
$380$	5199.51	0.701920
$381$	7765.05	1.04414
$382$	−3289.05	−0.440530
$383$	−10973.6	−1.46403	−0.732017	−	0.681286i	$-0.761421\pi$
$383$	−10973.6	−1.46403	−0.732017	+	0.681286i	$0.761421\pi$
$384$	−2558.66	−0.340029
$385$	−20222.8	−2.67701
$386$	1611.19	0.212454
$387$	−310.327	−0.0407617
$388$	−1087.29	−0.142265
$389$	−89.5078	−0.0116664	−0.00583320	−	0.999983i	$-0.501857\pi$
$389$	−89.5078	−0.0116664	−0.00583320	+	0.999983i	$0.501857\pi$
$390$	8808.93	1.14374
$391$	−11096.7	−1.43525
$392$	−13241.5	−1.70612
$393$	−3275.77	−0.420460
$394$	481.922	0.0616215
$395$	12241.2	1.55930
$396$	894.688	0.113535
$397$	−6119.89	−0.773674	−0.386837	−	0.922148i	$-0.626432\pi$
$397$	−6119.89	−0.773674	−0.386837	+	0.922148i	$0.626432\pi$
$398$	3987.34	0.502179
$399$	−14769.4	−1.85312
$400$	−11320.9	−1.41512
$401$	11137.1	1.38694	0.693468	−	0.720487i	$-0.256082\pi$
$401$	11137.1	1.38694	0.693468	+	0.720487i	$0.256082\pi$
$402$	4460.87	0.553453
$403$	6976.09	0.862292
$404$	−2400.73	−0.295646
$405$	−4325.44	−0.530698
$406$	17436.3	2.13141
$407$	−282.970	−0.0344627
$408$	5709.46	0.692795
$409$	−357.815	−0.0432587	−0.0216294	−	0.999766i	$-0.506885\pi$
$409$	−357.815	−0.0432587	−0.0216294	+	0.999766i	$0.506885\pi$
$410$	−1211.83	−0.145971
$411$	11045.0	1.32557
$412$	2784.92	0.333017
$413$	−2495.30	−0.297302
$414$	5612.71	0.666303
$415$	12785.8	1.51236
$416$	−4331.28	−0.510477
$417$	−1225.00	−0.143858
$418$	−11198.9	−1.31042
$419$	−8863.01	−1.03338	−0.516690	−	0.856172i	$-0.672836\pi$
$419$	−8863.01	−1.03338	−0.516690	+	0.856172i	$0.672836\pi$
$420$	−4424.36	−0.514016
$421$	1359.01	0.157326	0.0786630	−	0.996901i	$-0.474935\pi$
$421$	1359.01	0.157326	0.0786630	+	0.996901i	$0.474935\pi$
$422$	4497.02	0.518748
$423$	−4463.09	−0.513010
$424$	−5786.77	−0.662808
$425$	15964.5	1.82210
$426$	3859.01	0.438896
$427$	−24450.1	−2.77102
$428$	3769.60	0.425725
$429$	6390.25	0.719171
$430$	1163.62	0.130500
$431$	11087.8	1.23916	0.619582	−	0.784932i	$-0.287302\pi$
$431$	11087.8	1.23916	0.619582	+	0.784932i	$0.287302\pi$
$432$	−6572.62	−0.732003
$433$	−3356.33	−0.372505	−0.186253	−	0.982502i	$-0.559634\pi$
$433$	−3356.33	−0.372505	−0.186253	+	0.982502i	$0.559634\pi$
$434$	10403.0	1.15060
$435$	17709.8	1.95200
$436$	−1027.63	−0.112877
$437$	23662.4	2.59022
$438$	1517.84	0.165582
$439$	17776.1	1.93259	0.966297	−	0.257431i	$-0.0828759\pi$
$439$	17776.1	1.93259	0.966297	+	0.257431i	$0.0828759\pi$
$440$	−16670.1	−1.80617
$441$	−6903.85	−0.745476
$442$	−7369.49	−0.793057
$443$	8865.94	0.950865	0.475433	−	0.879752i	$-0.342292\pi$
$443$	8865.94	0.950865	0.475433	+	0.879752i	$0.342292\pi$
$444$	−61.9086	−0.00661723
$445$	−22851.2	−2.43427
$446$	−6043.39	−0.641621
$447$	−8118.64	−0.859057
$448$	−16876.8	−1.77981
$449$	−3877.46	−0.407547	−0.203774	−	0.979018i	$-0.565321\pi$
$449$	−3877.46	−0.407547	−0.203774	+	0.979018i	$0.565321\pi$
$450$	−8074.84	−0.845892
$451$	−879.095	−0.0917849
$452$	2532.00	0.263485
$453$	51.6824	0.00536037
$454$	−13634.0	−1.40942
$455$	28377.0	2.92381
$456$	−12174.7	−1.25029
$457$	−9115.81	−0.933084	−0.466542	−	0.884499i	$-0.654500\pi$
$457$	−9115.81	−0.933084	−0.466542	+	0.884499i	$0.654500\pi$
$458$	−12857.0	−1.31172
$459$	9268.55	0.942524
$460$	7088.38	0.718473
$461$	−13424.1	−1.35623	−0.678116	−	0.734955i	$-0.737203\pi$
$461$	−13424.1	−1.35623	−0.678116	+	0.734955i	$0.737203\pi$
$462$	9529.36	0.959623
$463$	−14927.9	−1.49840	−0.749199	−	0.662345i	$-0.769561\pi$
$463$	−14927.9	−1.49840	−0.749199	+	0.662345i	$0.769561\pi$
$464$	10506.4	1.05118
$465$	10566.1	1.05375
$466$	−1879.64	−0.186851
$467$	3644.85	0.361164	0.180582	−	0.983560i	$-0.442202\pi$
$467$	3644.85	0.361164	0.180582	+	0.983560i	$0.442202\pi$
$468$	−1255.45	−0.124002
$469$	14370.2	1.41483
$470$	16735.1	1.64241
$471$	−3478.74	−0.340322
$472$	−2056.93	−0.200589
$473$	844.125	0.0820569
$474$	−5768.29	−0.558959
$475$	−34042.4	−3.28836
$476$	3701.39	0.356414
$477$	−3017.10	−0.289609
$478$	15968.2	1.52797
$479$	−1391.90	−0.132772	−0.0663858	−	0.997794i	$-0.521147\pi$
$479$	−1391.90	−0.132772	−0.0663858	+	0.997794i	$0.521147\pi$
$480$	−6560.25	−0.623819
$481$	397.070	0.0376400
$482$	−3392.46	−0.320586
$483$	−20134.8	−1.89682
$484$	249.098	0.0233939
$485$	10562.5	0.988900
$486$	−7870.39	−0.734585
$487$	5488.25	0.510670	0.255335	−	0.966853i	$-0.417814\pi$
$487$	5488.25	0.510670	0.255335	+	0.966853i	$0.417814\pi$
$488$	−20154.8	−1.86960
$489$	4627.16	0.427909
$490$	25887.2	2.38666
$491$	−1395.02	−0.128221	−0.0641105	−	0.997943i	$-0.520421\pi$
$491$	−1395.02	−0.128221	−0.0641105	+	0.997943i	$0.520421\pi$
$492$	−192.330	−0.0176238
$493$	−14815.9	−1.35350
$494$	15714.6	1.43124
$495$	−8691.43	−0.789194
$496$	6268.40	0.567459
$497$	12431.4	1.12198
$498$	−6024.90	−0.542133
$499$	15006.6	1.34627	0.673133	−	0.739521i	$-0.264948\pi$
$499$	15006.6	1.34627	0.673133	+	0.739521i	$0.264948\pi$
$500$	−5264.57	−0.470877
$501$	3402.31	0.303401
$502$	1443.89	0.128375
$503$	−10586.6	−0.938434	−0.469217	−	0.883083i	$-0.655464\pi$
$503$	−10586.6	−0.938434	−0.469217	+	0.883083i	$0.655464\pi$
$504$	−9302.88	−0.822189
$505$	23321.9	2.05507
$506$	−15267.2	−1.34133
$507$	−680.550	−0.0596139
$508$	4149.65	0.362423
$509$	−6397.76	−0.557123	−0.278561	−	0.960418i	$-0.589858\pi$
$509$	−6397.76	−0.557123	−0.278561	+	0.960418i	$0.589858\pi$
$510$	−11162.0	−0.969139
$511$	4889.55	0.423289
$512$	−12479.6	−1.07720
$513$	−19764.1	−1.70098
$514$	−1227.55	−0.105340
$515$	−27054.0	−2.31484
$516$	184.679	0.0157559
$517$	12140.1	1.03273
$518$	592.124	0.0502248
$519$	2668.30	0.225675
$520$	23391.8	1.97269
$521$	16587.4	1.39483	0.697415	−	0.716667i	$-0.254333\pi$
$521$	16587.4	1.39483	0.697415	+	0.716667i	$0.254333\pi$
$522$	7493.87	0.628348
$523$	−4338.63	−0.362744	−0.181372	−	0.983415i	$-0.558054\pi$
$523$	−4338.63	−0.362744	−0.181372	+	0.983415i	$0.558054\pi$
$524$	−1750.58	−0.145943
$525$	28967.3	2.40807
$526$	8293.75	0.687500
$527$	−8839.55	−0.730658
$528$	5742.00	0.473273
$529$	20091.4	1.65130
$530$	11313.1	0.927190
$531$	−1072.44	−0.0876459
$532$	−7892.77	−0.643224
$533$	1233.57	0.100247
$534$	10767.9	0.872611
$535$	−36619.7	−2.95927
$536$	11845.7	0.954583
$537$	148.668	0.0119469
$538$	10892.6	0.872890
$539$	18779.3	1.50071
$540$	−5920.59	−0.471818
$541$	22797.1	1.81169	0.905845	−	0.423609i	$-0.139237\pi$
$541$	22797.1	1.81169	0.905845	+	0.423609i	$0.139237\pi$
$542$	2470.85	0.195816
$543$	2875.82	0.227280
$544$	5488.26	0.432550
$545$	9982.88	0.784623
$546$	−13371.8	−1.04810
$547$	22637.9	1.76952	0.884761	−	0.466045i	$-0.154322\pi$
$547$	22637.9	1.76952	0.884761	+	0.466045i	$0.154322\pi$
$548$	5902.48	0.460112
$549$	−10508.3	−0.816909
$550$	21964.5	1.70285
$551$	31593.1	2.44267
$552$	−16597.6	−1.27978
$553$	−18581.9	−1.42890
$554$	4825.93	0.370097
$555$	601.410	0.0459972
$556$	−654.643	−0.0499336
$557$	−13376.1	−1.01753	−0.508763	−	0.860906i	$-0.669897\pi$
$557$	−13376.1	−1.01753	−0.508763	+	0.860906i	$0.669897\pi$
$558$	4471.04	0.339201
$559$	−1184.49	−0.0896222
$560$	25498.3	1.92411
$561$	−8097.22	−0.609385
$562$	−15605.0	−1.17128
$563$	20233.4	1.51463	0.757314	−	0.653051i	$-0.226511\pi$
$563$	20233.4	1.51463	0.757314	+	0.653051i	$0.226511\pi$
$564$	2656.04	0.198297
$565$	−24597.1	−1.83152
$566$	−21476.9	−1.59495
$567$	6565.94	0.486320
$568$	10247.5	0.756998
$569$	4519.64	0.332993	0.166497	−	0.986042i	$-0.446755\pi$
$569$	4519.64	0.332993	0.166497	+	0.986042i	$0.446755\pi$
$570$	23801.6	1.74901
$571$	5228.63	0.383207	0.191604	−	0.981472i	$-0.438631\pi$
$571$	5228.63	0.383207	0.191604	+	0.981472i	$0.438631\pi$
$572$	3414.96	0.249627
$573$	5071.02	0.369712
$574$	1839.53	0.133764
$575$	−46409.2	−3.36591
$576$	−7253.40	−0.524696
$577$	−15182.0	−1.09538	−0.547690	−	0.836681i	$-0.684493\pi$
$577$	−15182.0	−1.09538	−0.547690	+	0.836681i	$0.684493\pi$
$578$	−2680.65	−0.192907
$579$	−2484.11	−0.178301
$580$	9464.14	0.677546
$581$	−19408.6	−1.38589
$582$	−4977.24	−0.354490
$583$	8206.87	0.583008
$584$	4030.57	0.285593
$585$	12196.0	0.861954
$586$	−364.148	−0.0256703
$587$	−14179.3	−0.997003	−0.498502	−	0.866889i	$-0.666116\pi$
$587$	−14179.3	−0.997003	−0.498502	+	0.866889i	$0.666116\pi$
$588$	4108.56	0.288153
$589$	18849.3	1.31863
$590$	4021.30	0.280600
$591$	−743.022	−0.0517155
$592$	356.789	0.0247702
$593$	15752.2	1.09083	0.545417	−	0.838165i	$-0.316371\pi$
$593$	15752.2	1.09083	0.545417	+	0.838165i	$0.316371\pi$
$594$	12752.0	0.880842
$595$	−35957.1	−2.47748
$596$	−4338.62	−0.298182
$597$	−6147.63	−0.421450
$598$	21423.3	1.46499
$599$	−28701.1	−1.95775	−0.978877	−	0.204449i	$-0.934460\pi$
$599$	−28701.1	−1.95775	−0.978877	+	0.204449i	$0.934460\pi$
$600$	23878.4	1.62472
$601$	−3716.66	−0.252255	−0.126128	−	0.992014i	$-0.540255\pi$
$601$	−3716.66	−0.252255	−0.126128	+	0.992014i	$0.540255\pi$
$602$	−1766.36	−0.119587
$603$	6176.10	0.417098
$604$	27.6191	0.00186061
$605$	−2419.86	−0.162614
$606$	−10989.7	−0.736678
$607$	8011.17	0.535689	0.267844	−	0.963462i	$-0.413689\pi$
$607$	8011.17	0.535689	0.267844	+	0.963462i	$0.413689\pi$
$608$	−11703.1	−0.780627
$609$	−26883.2	−1.78877
$610$	39402.6	2.61535
$611$	−17035.3	−1.12795
$612$	1590.80	0.105072
$613$	−20884.4	−1.37604	−0.688019	−	0.725693i	$-0.741519\pi$
$613$	−20884.4	−1.37604	−0.688019	+	0.725693i	$0.741519\pi$
$614$	3459.76	0.227401
$615$	1868.38	0.122505
$616$	25304.9	1.65514
$617$	−1868.87	−0.121941	−0.0609706	−	0.998140i	$-0.519420\pi$
$617$	−1868.87	−0.121941	−0.0609706	+	0.998140i	$0.519420\pi$
$618$	12748.4	0.829798
$619$	−21980.2	−1.42724	−0.713618	−	0.700535i	$-0.752945\pi$
$619$	−21980.2	−1.42724	−0.713618	+	0.700535i	$0.752945\pi$
$620$	5646.55	0.365760
$621$	−26943.9	−1.74110
$622$	4177.85	0.269319
$623$	34687.8	2.23072
$624$	−8057.29	−0.516907
$625$	18843.3	1.20597
$626$	−503.855	−0.0321695
$627$	17266.3	1.09976
$628$	−1859.04	−0.118127
$629$	−503.136	−0.0318940
$630$	18187.1	1.15014
$631$	−6770.55	−0.427149	−0.213575	−	0.976927i	$-0.568511\pi$
$631$	−6770.55	−0.427149	−0.213575	+	0.976927i	$0.568511\pi$
$632$	−15317.5	−0.964079
$633$	−6933.46	−0.435356
$634$	−11085.5	−0.694419
$635$	−40311.8	−2.51925
$636$	1795.51	0.111944
$637$	−26351.5	−1.63907
$638$	−20384.2	−1.26492
$639$	5342.82	0.330765
$640$	13283.1	0.820408
$641$	−20276.9	−1.24944	−0.624719	−	0.780849i	$-0.714787\pi$
$641$	−20276.9	−1.24944	−0.624719	+	0.780849i	$0.714787\pi$
$642$	17255.9	1.06080
$643$	20182.3	1.23781	0.618906	−	0.785465i	$-0.287576\pi$
$643$	20182.3	1.23781	0.618906	+	0.785465i	$0.287576\pi$
$644$	−10760.0	−0.658393
$645$	−1794.06	−0.109521
$646$	−19912.2	−1.21275
$647$	1344.63	0.0817045	0.0408523	−	0.999165i	$-0.486993\pi$
$647$	1344.63	0.0817045	0.0408523	+	0.999165i	$0.486993\pi$
$648$	5412.46	0.328120
$649$	2917.17	0.176439
$650$	−30821.1	−1.85985
$651$	−16039.2	−0.965630
$652$	2472.76	0.148529
$653$	−14950.3	−0.895944	−0.447972	−	0.894048i	$-0.647854\pi$
$653$	−14950.3	−0.895944	−0.447972	+	0.894048i	$0.647854\pi$
$654$	−4704.13	−0.281263
$655$	17005.9	1.01447
$656$	1108.43	0.0659707
$657$	2101.45	0.124788
$658$	−25403.6	−1.50507
$659$	−5197.57	−0.307236	−0.153618	−	0.988130i	$-0.549092\pi$
$659$	−5197.57	−0.307236	−0.153618	+	0.988130i	$0.549092\pi$
$660$	5172.37	0.305052
$661$	−2966.36	−0.174551	−0.0872755	−	0.996184i	$-0.527816\pi$
$661$	−2966.36	−0.174551	−0.0872755	+	0.996184i	$0.527816\pi$
$662$	−13260.3	−0.778513
$663$	11362.2	0.665568
$664$	−15998.9	−0.935059
$665$	76674.2	4.47113
$666$	254.486	0.0148065
$667$	43070.2	2.50028
$668$	1818.20	0.105312
$669$	9317.64	0.538476
$670$	−23158.3	−1.33535
$671$	28583.8	1.64451
$672$	9958.34	0.571654
$673$	4688.36	0.268534	0.134267	−	0.990945i	$-0.457132\pi$
$673$	4688.36	0.268534	0.134267	+	0.990945i	$0.457132\pi$
$674$	−9648.50	−0.551404
$675$	38763.4	2.21038
$676$	−363.687	−0.0206922
$677$	−13529.6	−0.768071	−0.384035	−	0.923318i	$-0.625466\pi$
$677$	−13529.6	−0.768071	−0.384035	+	0.923318i	$0.625466\pi$
$678$	11590.6	0.656542
$679$	−16033.6	−0.906207
$680$	−29640.3	−1.67155
$681$	21020.7	1.18284
$682$	−12161.8	−0.682841
$683$	4196.21	0.235086	0.117543	−	0.993068i	$-0.462498\pi$
$683$	4196.21	0.235086	0.117543	+	0.993068i	$0.462498\pi$
$684$	−3392.19	−0.189625
$685$	−57339.5	−3.19829
$686$	−14356.4	−0.799022
$687$	19822.7	1.10085
$688$	−1064.33	−0.0589787
$689$	−11516.1	−0.636759
$690$	32448.2	1.79026
$691$	6599.02	0.363298	0.181649	−	0.983363i	$-0.441857\pi$
$691$	6599.02	0.363298	0.181649	+	0.983363i	$0.441857\pi$
$692$	1425.94	0.0783326
$693$	13193.4	0.723200
$694$	25761.9	1.40909
$695$	6359.52	0.347094
$696$	−22160.4	−1.20688
$697$	−1563.08	−0.0849437
$698$	22878.4	1.24063
$699$	2898.00	0.156813
$700$	15480.2	0.835850
$701$	29627.2	1.59630	0.798149	−	0.602460i	$-0.205813\pi$
$701$	29627.2	1.59630	0.798149	+	0.602460i	$0.205813\pi$
$702$	−17893.9	−0.962051
$703$	1072.88	0.0575594
$704$	19730.1	1.05626
$705$	−25802.0	−1.37838
$706$	−23098.6	−1.23134
$707$	−35402.2	−1.88322
$708$	638.221	0.0338783
$709$	−3093.41	−0.163858	−0.0819291	−	0.996638i	$-0.526108\pi$
$709$	−3093.41	−0.163858	−0.0819291	+	0.996638i	$0.526108\pi$
$710$	−20033.8	−1.05895
$711$	−7986.23	−0.421247
$712$	28593.9	1.50506
$713$	25696.8	1.34972
$714$	16943.7	0.888098
$715$	−33174.6	−1.73519
$716$	79.4483	0.00414682
$717$	−24619.7	−1.28234
$718$	−7375.15	−0.383340
$719$	−23540.4	−1.22101	−0.610506	−	0.792011i	$-0.709034\pi$
$719$	−23540.4	−1.22101	−0.610506	+	0.792011i	$0.709034\pi$
$720$	10958.8	0.567236
$721$	41067.6	2.12127
$722$	25681.2	1.32376
$723$	5230.46	0.269050
$724$	1536.84	0.0788899
$725$	−61963.8	−3.17418
$726$	1140.29	0.0582919
$727$	−819.013	−0.0417820	−0.0208910	−	0.999782i	$-0.506650\pi$
$727$	−819.013	−0.0417820	−0.0208910	+	0.999782i	$0.506650\pi$
$728$	−35508.4	−1.80773
$729$	18098.9	0.919521
$730$	−7879.75	−0.399510
$731$	1500.90	0.0759408
$732$	6253.60	0.315765
$733$	22457.7	1.13164	0.565821	−	0.824528i	$-0.308559\pi$
$733$	22457.7	1.13164	0.565821	+	0.824528i	$0.308559\pi$
$734$	21929.4	1.10277
$735$	−39912.5	−2.00299
$736$	−15954.5	−0.799037
$737$	−16799.7	−0.839655
$738$	790.604	0.0394343
$739$	26510.7	1.31964	0.659819	−	0.751425i	$-0.270633\pi$
$739$	26510.7	1.31964	0.659819	+	0.751425i	$0.270633\pi$
$740$	321.394	0.0159658
$741$	−24228.5	−1.20116
$742$	−17173.1	−0.849657
$743$	−16698.8	−0.824523	−0.412262	−	0.911065i	$-0.635261\pi$
$743$	−16698.8	−0.824523	−0.412262	+	0.911065i	$0.635261\pi$
$744$	−13221.5	−0.651509
$745$	42147.4	2.07270
$746$	31984.4	1.56975
$747$	−8341.50	−0.408567
$748$	−4327.17	−0.211520
$749$	55588.1	2.71181
$750$	−24099.4	−1.17331
$751$	16445.2	0.799061	0.399530	−	0.916720i	$-0.369173\pi$
$751$	16445.2	0.799061	0.399530	+	0.916720i	$0.369173\pi$
$752$	−15307.2	−0.742281
$753$	−2226.18	−0.107738
$754$	28603.6	1.38154
$755$	−268.306	−0.0129333
$756$	8987.35	0.432363
$757$	−9282.20	−0.445663	−0.222832	−	0.974857i	$-0.571530\pi$
$757$	−9282.20	−0.445663	−0.222832	+	0.974857i	$0.571530\pi$
$758$	−7309.13	−0.350237
$759$	23538.8	1.12570
$760$	63204.4	3.01666
$761$	−20972.8	−0.999031	−0.499515	−	0.866305i	$-0.666489\pi$
$761$	−20972.8	−0.999031	−0.499515	+	0.866305i	$0.666489\pi$
$762$	18995.7	0.903072
$763$	−15153.8	−0.719012
$764$	2709.96	0.128329
$765$	−15453.8	−0.730371
$766$	−26844.8	−1.26624
$767$	−4093.43	−0.192706
$768$	10873.5	0.510889
$769$	−7189.31	−0.337130	−0.168565	−	0.985691i	$-0.553913\pi$
$769$	−7189.31	−0.337130	−0.168565	+	0.985691i	$0.553913\pi$
$770$	−49471.0	−2.31534
$771$	1892.62	0.0884058
$772$	−1327.51	−0.0618890
$773$	30817.5	1.43393	0.716965	−	0.697109i	$-0.245531\pi$
$773$	30817.5	1.43393	0.716965	+	0.697109i	$0.245531\pi$
$774$	−759.154	−0.0352548
$775$	−36969.2	−1.71351
$776$	−13216.9	−0.611416
$777$	−912.930	−0.0421508
$778$	−218.963	−0.0100903
$779$	3333.07	0.153299
$780$	−7257.98	−0.333176
$781$	−14533.1	−0.665858
$782$	−27145.9	−1.24135
$783$	−35974.5	−1.64192
$784$	−23678.3	−1.07864
$785$	18059.6	0.821116
$786$	−8013.53	−0.363655
$787$	−37730.1	−1.70894	−0.854468	−	0.519503i	$-0.826117\pi$
$787$	−37730.1	−1.70894	−0.854468	+	0.519503i	$0.826117\pi$
$788$	−397.072	−0.0179506
$789$	−12787.2	−0.576980
$790$	29945.7	1.34863
$791$	37338.0	1.67836
$792$	10875.7	0.487942
$793$	−40109.4	−1.79612
$794$	−14971.1	−0.669150
$795$	−17442.4	−0.778138
$796$	−3285.30	−0.146287
$797$	10140.2	0.450670	0.225335	−	0.974281i	$-0.427652\pi$
$797$	10140.2	0.450670	0.225335	+	0.974281i	$0.427652\pi$
$798$	−36130.4	−1.60276
$799$	21585.8	0.955758
$800$	22953.3	1.01440
$801$	14908.3	0.657625
$802$	27244.8	1.19956
$803$	−5716.20	−0.251208
$804$	−3675.46	−0.161223
$805$	104528.	4.57657
$806$	17065.6	0.745796
$807$	−16794.1	−0.732567
$808$	−29182.9	−1.27061
$809$	−30039.1	−1.30546	−0.652732	−	0.757589i	$-0.726377\pi$
$809$	−30039.1	−1.30546	−0.652732	+	0.757589i	$0.726377\pi$
$810$	−10581.3	−0.459001
$811$	−9005.67	−0.389928	−0.194964	−	0.980810i	$-0.562459\pi$
$811$	−9005.67	−0.389928	−0.194964	+	0.980810i	$0.562459\pi$
$812$	−14366.4	−0.620889
$813$	−3809.54	−0.164337
$814$	−692.231	−0.0298067
$815$	−24021.6	−1.03244
$816$	10209.6	0.437998
$817$	−3200.48	−0.137051
$818$	−875.325	−0.0374145
$819$	−18513.3	−0.789876
$820$	998.467	0.0425219
$821$	−15576.5	−0.662149	−0.331075	−	0.943605i	$-0.607411\pi$
$821$	−15576.5	−0.662149	−0.331075	+	0.943605i	$0.607411\pi$
$822$	27019.5	1.14649
$823$	16136.1	0.683438	0.341719	−	0.939802i	$-0.388991\pi$
$823$	16136.1	0.683438	0.341719	+	0.939802i	$0.388991\pi$
$824$	33852.9	1.43122
$825$	−33864.6	−1.42911
$826$	−6104.26	−0.257136
$827$	34193.0	1.43774	0.718868	−	0.695147i	$-0.244661\pi$
$827$	34193.0	1.43774	0.718868	+	0.695147i	$0.244661\pi$
$828$	−4624.50	−0.194097
$829$	−21259.1	−0.890663	−0.445331	−	0.895366i	$-0.646914\pi$
$829$	−21259.1	−0.890663	−0.445331	+	0.895366i	$0.646914\pi$
$830$	31277.9	1.30804
$831$	−7440.56	−0.310602
$832$	−27685.7	−1.15364
$833$	33390.6	1.38885
$834$	−2996.73	−0.124422
$835$	−17662.9	−0.732035
$836$	9227.16	0.381732
$837$	−21463.3	−0.886356
$838$	−21681.6	−0.893770
$839$	−3387.03	−0.139372	−0.0696860	−	0.997569i	$-0.522200\pi$
$839$	−3387.03	−0.139372	−0.0696860	+	0.997569i	$0.522200\pi$
$840$	−53781.8	−2.20910
$841$	33116.6	1.35785
$842$	3324.56	0.136071
$843$	24059.6	0.982987
$844$	−3705.25	−0.151114
$845$	3533.03	0.143834
$846$	−10918.1	−0.443702
$847$	3673.31	0.149016
$848$	−10347.8	−0.419039
$849$	33112.8	1.33855
$850$	39054.0	1.57593
$851$	1462.63	0.0589169
$852$	−3179.57	−0.127852
$853$	−3736.34	−0.149976	−0.0749882	−	0.997184i	$-0.523892\pi$
$853$	−3736.34	−0.149976	−0.0749882	+	0.997184i	$0.523892\pi$
$854$	−59812.5	−2.39665
$855$	32953.4	1.31811
$856$	45822.6	1.82965
$857$	−43938.7	−1.75136	−0.875682	−	0.482889i	$-0.839588\pi$
$857$	−43938.7	−1.75136	−0.875682	+	0.482889i	$0.839588\pi$
$858$	15632.5	0.622010
$859$	3789.65	0.150525	0.0752627	−	0.997164i	$-0.476020\pi$
$859$	3789.65	0.150525	0.0752627	+	0.997164i	$0.476020\pi$
$860$	−958.748	−0.0380152
$861$	−2836.17	−0.112261
$862$	27124.1	1.07175
$863$	−25491.3	−1.00549	−0.502744	−	0.864436i	$-0.667676\pi$
$863$	−25491.3	−1.00549	−0.502744	+	0.864436i	$0.667676\pi$
$864$	13326.0	0.524723
$865$	−13852.3	−0.544499
$866$	−8210.60	−0.322180
$867$	4133.00	0.161896
$868$	−8571.37	−0.335174
$869$	21723.5	0.848008
$870$	43323.5	1.68828
$871$	23573.7	0.917067
$872$	−12491.7	−0.485116
$873$	−6891.01	−0.267154
$874$	57885.4	2.24028
$875$	−77633.5	−2.99942
$876$	−1250.60	−0.0482349
$877$	38703.2	1.49021	0.745106	−	0.666946i	$-0.232399\pi$
$877$	38703.2	1.49021	0.745106	+	0.666946i	$0.232399\pi$
$878$	43485.8	1.67150
$879$	561.439	0.0215436
$880$	−29809.2	−1.14190
$881$	−25222.2	−0.964536	−0.482268	−	0.876024i	$-0.660187\pi$
$881$	−25222.2	−0.964536	−0.482268	+	0.876024i	$0.660187\pi$
$882$	−16888.9	−0.644762
$883$	1049.21	0.0399873	0.0199936	−	0.999800i	$-0.493635\pi$
$883$	1049.21	0.0399873	0.0199936	+	0.999800i	$0.493635\pi$
$884$	6071.98	0.231021
$885$	−6199.99	−0.235492
$886$	21688.8	0.822403
$887$	22550.1	0.853618	0.426809	−	0.904342i	$-0.359638\pi$
$887$	22550.1	0.853618	0.426809	+	0.904342i	$0.359638\pi$
$888$	−752.549	−0.0284391
$889$	61192.5	2.30858
$890$	−55901.1	−2.10540
$891$	−7676.01	−0.288615
$892$	4979.36	0.186907
$893$	−46029.1	−1.72487
$894$	−19860.7	−0.742998
$895$	−771.800	−0.0288250
$896$	−20163.5	−0.751804
$897$	−33030.2	−1.22948
$898$	−9485.45	−0.352487
$899$	34309.4	1.27284
$900$	6653.13	0.246412
$901$	14592.2	0.539554
$902$	−2150.53	−0.0793847
$903$	2723.35	0.100363
$904$	30778.6	1.13239
$905$	−14929.6	−0.548373
$906$	126.431	0.00463618
$907$	−32020.5	−1.17224	−0.586120	−	0.810224i	$-0.699345\pi$
$907$	−32020.5	−1.17224	−0.586120	+	0.810224i	$0.699345\pi$
$908$	11233.5	0.410570
$909$	−15215.3	−0.555182
$910$	69418.8	2.52880
$911$	11058.4	0.402176	0.201088	−	0.979573i	$-0.435552\pi$
$911$	11058.4	0.402176	0.201088	+	0.979573i	$0.435552\pi$
$912$	−21770.7	−0.790459
$913$	22689.9	0.822481
$914$	−22300.0	−0.807024
$915$	−60750.5	−2.19492
$916$	10593.3	0.382109
$917$	−25814.7	−0.929637
$918$	22673.7	0.815189
$919$	33722.5	1.21045	0.605224	−	0.796055i	$-0.293084\pi$
$919$	33722.5	1.21045	0.605224	+	0.796055i	$0.293084\pi$
$920$	86165.1	3.08780
$921$	−5334.21	−0.190845
$922$	−32839.4	−1.17300
$923$	20393.1	0.727247
$924$	−7851.56	−0.279543
$925$	−2104.24	−0.0747967
$926$	−36518.2	−1.29596
$927$	17650.2	0.625360
$928$	−21301.9	−0.753521
$929$	−34701.4	−1.22553	−0.612764	−	0.790266i	$-0.709942\pi$
$929$	−34701.4	−1.22553	−0.612764	+	0.790266i	$0.709942\pi$
$930$	25847.9	0.911384
$931$	−71201.3	−2.50648
$932$	1548.70	0.0544305
$933$	−6441.37	−0.226025
$934$	8916.41	0.312370
$935$	42036.2	1.47030
$936$	−15261.0	−0.532928
$937$	12222.0	0.426121	0.213061	−	0.977039i	$-0.431657\pi$
$937$	12222.0	0.426121	0.213061	+	0.977039i	$0.431657\pi$
$938$	35153.9	1.22368
$939$	776.838	0.0269980
$940$	−13788.6	−0.478442
$941$	10416.6	0.360863	0.180432	−	0.983588i	$-0.442251\pi$
$941$	10416.6	0.360863	0.180432	+	0.983588i	$0.442251\pi$
$942$	−8510.05	−0.294344
$943$	4543.91	0.156914
$944$	−3678.18	−0.126816
$945$	−87307.5	−3.00541
$946$	2064.99	0.0709710
$947$	22067.6	0.757235	0.378617	−	0.925553i	$-0.376400\pi$
$947$	22067.6	0.757235	0.378617	+	0.925553i	$0.376400\pi$
$948$	4752.69	0.162827
$949$	8021.09	0.274369
$950$	−83278.0	−2.84410
$951$	17091.5	0.582786
$952$	44993.5	1.53177
$953$	−12861.7	−0.437178	−0.218589	−	0.975817i	$-0.570145\pi$
$953$	−12861.7	−0.437178	−0.218589	+	0.975817i	$0.570145\pi$
$954$	−7380.74	−0.250483
$955$	−26325.9	−0.892027
$956$	−13156.8	−0.445105
$957$	31428.1	1.06158
$958$	−3405.02	−0.114834
$959$	87040.4	2.93085
$960$	−41933.3	−1.40978
$961$	−9321.14	−0.312884
$962$	971.354	0.0325548
$963$	23890.9	0.799453
$964$	2795.17	0.0933882
$965$	12896.1	0.430198
$966$	−49255.8	−1.64056
$967$	49854.4	1.65792	0.828960	−	0.559308i	$-0.188933\pi$
$967$	49854.4	1.65792	0.828960	+	0.559308i	$0.188933\pi$
$968$	3027.99	0.100541
$969$	30700.5	1.01779
$970$	25839.0	0.855299
$971$	−33796.3	−1.11697	−0.558483	−	0.829516i	$-0.688616\pi$
$971$	−33796.3	−1.11697	−0.558483	+	0.829516i	$0.688616\pi$
$972$	6484.68	0.213988
$973$	−9653.64	−0.318069
$974$	13425.9	0.441678
$975$	47519.6	1.56087
$976$	−36040.5	−1.18200
$977$	47512.4	1.55584	0.777920	−	0.628363i	$-0.216275\pi$
$977$	47512.4	1.55584	0.777920	+	0.628363i	$0.216275\pi$
$978$	11319.4	0.370098
$979$	−40552.2	−1.32386
$980$	−21329.3	−0.695245
$981$	−6512.89	−0.211968
$982$	−3412.65	−0.110898
$983$	−35948.3	−1.16640	−0.583201	−	0.812328i	$-0.698200\pi$
$983$	−35948.3	−1.16640	−0.583201	+	0.812328i	$0.698200\pi$
$984$	−2337.92	−0.0757422
$985$	3857.35	0.124777
$986$	−36244.2	−1.17064
$987$	39167.0	1.26312
$988$	−12947.8	−0.416926
$989$	−4363.15	−0.140283
$990$	−21261.9	−0.682573
$991$	49867.5	1.59848	0.799239	−	0.601013i	$-0.205236\pi$
$991$	49867.5	1.59848	0.799239	+	0.601013i	$0.205236\pi$
$992$	−12709.2	−0.406773
$993$	20444.6	0.653362
$994$	30410.9	0.970399
$995$	31915.0	1.01686
$996$	4964.12	0.157926
$997$	−39869.5	−1.26648	−0.633239	−	0.773956i	$-0.718275\pi$
$997$	−39869.5	−1.26648	−0.633239	+	0.773956i	$0.718275\pi$
$998$	36710.7	1.16439
$999$	−1221.66	−0.0386904

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	197.4.a.a.1.16	✓	22
3.2	odd	2		1773.4.a.c.1.7		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
197.4.a.a.1.16	✓	22	1.1	even	1	trivial
1773.4.a.c.1.7		22	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 197 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	197.a (trivial)

\(f(q)\)	\(=\)	\(q+2.44630 q^{2} -3.77168 q^{3} -2.01559 q^{4} +19.5805 q^{5} -9.22669 q^{6} -29.7228 q^{7} -24.5012 q^{8} -12.7744 q^{9} +47.8998 q^{10} +34.7479 q^{11} +7.60218 q^{12} -48.7590 q^{13} -72.7110 q^{14} -73.8513 q^{15} -43.8126 q^{16} +61.7835 q^{17} -31.2501 q^{18} -131.746 q^{19} -39.4662 q^{20} +112.105 q^{21} +85.0039 q^{22} -179.606 q^{23} +92.4108 q^{24} +258.394 q^{25} -119.279 q^{26} +150.016 q^{27} +59.9091 q^{28} -239.803 q^{29} -180.663 q^{30} -143.073 q^{31} +88.8305 q^{32} -131.058 q^{33} +151.141 q^{34} -581.986 q^{35} +25.7480 q^{36} -8.14353 q^{37} -322.291 q^{38} +183.903 q^{39} -479.744 q^{40} -25.2993 q^{41} +274.243 q^{42} +24.2929 q^{43} -70.0376 q^{44} -250.129 q^{45} -439.372 q^{46} +349.378 q^{47} +165.247 q^{48} +540.444 q^{49} +632.111 q^{50} -233.028 q^{51} +98.2783 q^{52} +236.183 q^{53} +366.986 q^{54} +680.379 q^{55} +728.244 q^{56} +496.904 q^{57} -586.632 q^{58} +83.9524 q^{59} +148.854 q^{60} +822.606 q^{61} -350.000 q^{62} +379.691 q^{63} +567.808 q^{64} -954.723 q^{65} -320.608 q^{66} -483.475 q^{67} -124.530 q^{68} +677.418 q^{69} -1423.71 q^{70} -418.244 q^{71} +312.988 q^{72} -164.505 q^{73} -19.9215 q^{74} -974.581 q^{75} +265.546 q^{76} -1032.80 q^{77} +449.884 q^{78} +625.174 q^{79} -857.871 q^{80} -220.906 q^{81} -61.8897 q^{82} +652.986 q^{83} -225.958 q^{84} +1209.75 q^{85} +59.4277 q^{86} +904.463 q^{87} -851.364 q^{88} -1167.04 q^{89} -611.891 q^{90} +1449.25 q^{91} +362.013 q^{92} +539.626 q^{93} +854.685 q^{94} -2579.64 q^{95} -335.041 q^{96} +539.439 q^{97} +1322.09 q^{98} -443.883 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 6 q^{2} - 34 q^{3} + 68 q^{4} - 31 q^{5} - 24 q^{6} - 102 q^{7} - 93 q^{8} + 152 q^{9} - 133 q^{10} - 100 q^{11} - 272 q^{12} - 223 q^{13} - 55 q^{14} - 166 q^{15} + 112 q^{16} - 114 q^{17} - 389 q^{18}+ \cdots - 502 q^{99}+O(q^{100}) \) 22 * q - 6 * q^2 - 34 * q^3 + 68 * q^4 - 31 * q^5 - 24 * q^6 - 102 * q^7 - 93 * q^8 + 152 * q^9 - 133 * q^10 - 100 * q^11 - 272 * q^12 - 223 * q^13 - 55 * q^14 - 166 * q^15 + 112 * q^16 - 114 * q^17 - 389 * q^18 - 529 * q^19 - 441 * q^20 - 148 * q^21 - 671 * q^22 - 208 * q^23 - 555 * q^24 + 35 * q^25 - 408 * q^26 - 994 * q^27 - 1202 * q^28 - 2 * q^29 - 365 * q^30 - 1261 * q^31 - 1020 * q^32 - 790 * q^33 - 814 * q^34 - 968 * q^35 + 94 * q^36 - 792 * q^37 - 184 * q^38 - 368 * q^39 - 1914 * q^40 - 271 * q^41 - 1157 * q^42 - 1349 * q^43 - 998 * q^44 - 1533 * q^45 - 1371 * q^46 - 986 * q^47 - 1966 * q^48 - 40 * q^49 + 1631 * q^50 - 36 * q^51 - 1382 * q^52 + 248 * q^53 + 2903 * q^54 - 566 * q^55 + 4800 * q^56 + 914 * q^57 + 351 * q^58 - 1281 * q^59 + 5149 * q^60 + 510 * q^61 + 2237 * q^62 + 120 * q^63 + 3185 * q^64 + 2558 * q^65 + 8308 * q^66 - 3070 * q^67 + 4625 * q^68 + 302 * q^69 + 2087 * q^70 + 101 * q^71 + 4511 * q^72 - 3352 * q^73 + 4501 * q^74 - 752 * q^75 - 334 * q^76 - 492 * q^77 + 7825 * q^78 - 1313 * q^79 + 3098 * q^80 + 2078 * q^81 - 1243 * q^82 - 2631 * q^83 + 7518 * q^84 + 84 * q^85 + 7448 * q^86 - 1046 * q^87 - 3285 * q^88 + 798 * q^89 + 6009 * q^90 - 3992 * q^91 + 5966 * q^92 + 1978 * q^93 + 3517 * q^94 + 284 * q^95 + 10181 * q^96 - 3693 * q^97 + 2932 * q^98 - 502 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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