LMFDB - Embedded newform 787.4.a.b.1.17

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [787,4,Mod(1,787)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("787.1"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(787, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 787 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	787.a (trivial)

Newform invariants

comment:select newform

sage:traces = [103] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$46.4345031745$
Analytic rank:	$0$
Dimension:	$103$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	787.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-4.20325 q^{2} -6.09175 q^{3} +9.66730 q^{4} -9.51255 q^{5} +25.6051 q^{6} +0.938997 q^{7} -7.00807 q^{8} +10.1094 q^{9} +39.9836 q^{10} -16.6420 q^{11} -58.8908 q^{12} -87.0560 q^{13} -3.94684 q^{14} +57.9480 q^{15} -47.8817 q^{16} +28.6558 q^{17} -42.4924 q^{18} +121.447 q^{19} -91.9606 q^{20} -5.72013 q^{21} +69.9503 q^{22} +41.2891 q^{23} +42.6914 q^{24} -34.5115 q^{25} +365.918 q^{26} +102.893 q^{27} +9.07756 q^{28} -264.938 q^{29} -243.570 q^{30} +9.41489 q^{31} +257.323 q^{32} +101.379 q^{33} -120.447 q^{34} -8.93225 q^{35} +97.7308 q^{36} -335.824 q^{37} -510.473 q^{38} +530.324 q^{39} +66.6646 q^{40} -440.138 q^{41} +24.0431 q^{42} -218.351 q^{43} -160.883 q^{44} -96.1663 q^{45} -173.548 q^{46} -51.5437 q^{47} +291.684 q^{48} -342.118 q^{49} +145.060 q^{50} -174.564 q^{51} -841.597 q^{52} -359.565 q^{53} -432.486 q^{54} +158.307 q^{55} -6.58055 q^{56} -739.827 q^{57} +1113.60 q^{58} -370.972 q^{59} +560.201 q^{60} -112.796 q^{61} -39.5731 q^{62} +9.49271 q^{63} -698.540 q^{64} +828.125 q^{65} -426.120 q^{66} -260.955 q^{67} +277.024 q^{68} -251.523 q^{69} +37.5445 q^{70} -788.550 q^{71} -70.8475 q^{72} +2.67867 q^{73} +1411.55 q^{74} +210.235 q^{75} +1174.07 q^{76} -15.6268 q^{77} -2229.08 q^{78} -466.853 q^{79} +455.477 q^{80} -899.754 q^{81} +1850.01 q^{82} +1495.54 q^{83} -55.2982 q^{84} -272.589 q^{85} +917.783 q^{86} +1613.93 q^{87} +116.628 q^{88} -1406.43 q^{89} +404.211 q^{90} -81.7454 q^{91} +399.154 q^{92} -57.3532 q^{93} +216.651 q^{94} -1155.27 q^{95} -1567.55 q^{96} -1436.21 q^{97} +1438.01 q^{98} -168.241 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 103 q + 27 q^{2} + 25 q^{3} + 439 q^{4} + 169 q^{5} + 45 q^{6} + 80 q^{7} + 327 q^{8} + 1114 q^{9} + 61 q^{10} + 241 q^{11} + 264 q^{12} + 291 q^{13} + 341 q^{14} + 278 q^{15} + 2003 q^{16} + 504 q^{17}+ \cdots + 6933 q^{99}+O(q^{100}) $ 103 * q + 27 * q^2 + 25 * q^3 + 439 * q^4 + 169 * q^5 + 45 * q^6 + 80 * q^7 + 327 * q^8 + 1114 * q^9 + 61 * q^10 + 241 * q^11 + 264 * q^12 + 291 * q^13 + 341 * q^14 + 278 * q^15 + 2003 * q^16 + 504 * q^17 + 857 * q^18 + 157 * q^19 + 1459 * q^20 + 588 * q^21 + 706 * q^22 + 1310 * q^23 + 815 * q^24 + 3342 * q^25 + 847 * q^26 + 784 * q^27 + 1260 * q^28 + 1587 * q^29 + 684 * q^30 + 686 * q^31 + 3398 * q^32 + 1528 * q^33 + 522 * q^34 + 1328 * q^35 + 6172 * q^36 + 2351 * q^37 + 1601 * q^38 + 1194 * q^39 + 582 * q^40 + 1584 * q^41 + 1074 * q^42 + 737 * q^43 + 2391 * q^44 + 3939 * q^45 + 746 * q^46 + 3424 * q^47 + 2278 * q^48 + 6527 * q^49 + 3051 * q^50 + 1150 * q^51 + 1588 * q^52 + 6855 * q^53 + 1809 * q^54 + 1564 * q^55 + 2549 * q^56 + 3448 * q^57 + 2786 * q^58 + 3511 * q^59 + 2701 * q^60 + 2465 * q^61 + 4001 * q^62 + 2984 * q^63 + 10803 * q^64 + 5576 * q^65 + 22 * q^66 + 2379 * q^67 + 5133 * q^68 + 2540 * q^69 + 2002 * q^70 + 4756 * q^71 + 8442 * q^72 + 4522 * q^73 + 2744 * q^74 + 5077 * q^75 + 2280 * q^76 + 10830 * q^77 + 3891 * q^78 + 2022 * q^79 + 10184 * q^80 + 14275 * q^81 + 2590 * q^82 + 7541 * q^83 + 4671 * q^84 + 8112 * q^85 + 3825 * q^86 + 4814 * q^87 + 6617 * q^88 + 5956 * q^89 + 3777 * q^90 + 2862 * q^91 + 15806 * q^92 + 15612 * q^93 - 881 * q^94 + 6664 * q^95 + 9772 * q^96 + 4374 * q^97 + 11934 * q^98 + 6933 * 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 $

$2$	−4.20325	−1.48607	−0.743036	−	0.669251i	$-0.766615\pi$
$2$	−4.20325	−1.48607	−0.743036	+	0.669251i	$0.766615\pi$
$3$	−6.09175	−1.17236	−0.586179	−	0.810182i	$-0.699368\pi$
$3$	−6.09175	−1.17236	−0.586179	+	0.810182i	$0.699368\pi$
$4$	9.66730	1.20841
$5$	−9.51255	−0.850828	−0.425414	−	0.904999i	$-0.639871\pi$
$5$	−9.51255	−0.850828	−0.425414	+	0.904999i	$0.639871\pi$
$6$	25.6051	1.74221
$7$	0.938997	0.0507011	0.0253505	−	0.999679i	$-0.491930\pi$
$7$	0.938997	0.0507011	0.0253505	+	0.999679i	$0.491930\pi$
$8$	−7.00807	−0.309716
$9$	10.1094	0.374423
$10$	39.9836	1.26439
$11$	−16.6420	−0.456158	−0.228079	−	0.973643i	$-0.573245\pi$
$11$	−16.6420	−0.456158	−0.228079	+	0.973643i	$0.573245\pi$
$12$	−58.8908	−1.41669
$13$	−87.0560	−1.85731	−0.928654	−	0.370947i	$-0.879033\pi$
$13$	−87.0560	−1.85731	−0.928654	+	0.370947i	$0.879033\pi$
$14$	−3.94684	−0.0753455
$15$	57.9480	0.997475
$16$	−47.8817	−0.748152
$17$	28.6558	0.408826	0.204413	−	0.978885i	$-0.434471\pi$
$17$	28.6558	0.408826	0.204413	+	0.978885i	$0.434471\pi$
$18$	−42.4924	−0.556420
$19$	121.447	1.46642	0.733208	−	0.680004i	$-0.238022\pi$
$19$	121.447	1.46642	0.733208	+	0.680004i	$0.238022\pi$
$20$	−91.9606	−1.02815
$21$	−5.72013	−0.0594398
$22$	69.9503	0.677885
$23$	41.2891	0.374320	0.187160	−	0.982329i	$-0.440072\pi$
$23$	41.2891	0.374320	0.187160	+	0.982329i	$0.440072\pi$
$24$	42.6914	0.363098
$25$	−34.5115	−0.276092
$26$	365.918	2.76009
$27$	102.893	0.733400
$28$	9.07756	0.0612678
$29$	−264.938	−1.69647	−0.848236	−	0.529619i	$-0.822335\pi$
$29$	−264.938	−1.69647	−0.848236	+	0.529619i	$0.822335\pi$
$30$	−243.570	−1.48232
$31$	9.41489	0.0545472	0.0272736	−	0.999628i	$-0.491317\pi$
$31$	9.41489	0.0545472	0.0272736	+	0.999628i	$0.491317\pi$
$32$	257.323	1.42152
$33$	101.379	0.534781
$34$	−120.447	−0.607546
$35$	−8.93225	−0.0431379
$36$	97.7308	0.452457
$37$	−335.824	−1.49214	−0.746070	−	0.665868i	$-0.768061\pi$
$37$	−335.824	−1.49214	−0.746070	+	0.665868i	$0.768061\pi$
$38$	−510.473	−2.17920
$39$	530.324	2.17743
$40$	66.6646	0.263515
$41$	−440.138	−1.67654	−0.838268	−	0.545259i	$-0.816431\pi$
$41$	−440.138	−1.67654	−0.838268	+	0.545259i	$0.816431\pi$
$42$	24.0431	0.0883319
$43$	−218.351	−0.774377	−0.387188	−	0.922001i	$-0.626554\pi$
$43$	−218.351	−0.774377	−0.387188	+	0.922001i	$0.626554\pi$
$44$	−160.883	−0.551227
$45$	−96.1663	−0.318569
$46$	−173.548	−0.556267
$47$	−51.5437	−0.159966	−0.0799832	−	0.996796i	$-0.525487\pi$
$47$	−51.5437	−0.159966	−0.0799832	+	0.996796i	$0.525487\pi$
$48$	291.684	0.877102
$49$	−342.118	−0.997429
$50$	145.060	0.410293
$51$	−174.564	−0.479291
$52$	−841.597	−2.24439
$53$	−359.565	−0.931889	−0.465944	−	0.884814i	$-0.654285\pi$
$53$	−359.565	−0.931889	−0.465944	+	0.884814i	$0.654285\pi$
$54$	−432.486	−1.08989
$55$	158.307	0.388112
$56$	−6.58055	−0.0157029
$57$	−739.827	−1.71917
$58$	1113.60	2.52108
$59$	−370.972	−0.818584	−0.409292	−	0.912404i	$-0.634224\pi$
$59$	−370.972	−0.818584	−0.409292	+	0.912404i	$0.634224\pi$
$60$	560.201	1.20536
$61$	−112.796	−0.236755	−0.118378	−	0.992969i	$-0.537769\pi$
$61$	−112.796	−0.236755	−0.118378	+	0.992969i	$0.537769\pi$
$62$	−39.5731	−0.0810612
$63$	9.49271	0.0189836
$64$	−698.540	−1.36434
$65$	828.125	1.58025
$66$	−426.120	−0.794723
$67$	−260.955	−0.475831	−0.237915	−	0.971286i	$-0.576464\pi$
$67$	−260.955	−0.475831	−0.237915	+	0.971286i	$0.576464\pi$
$68$	277.024	0.494031
$69$	−251.523	−0.438838
$70$	37.5445	0.0641060
$71$	−788.550	−1.31808	−0.659040	−	0.752108i	$-0.729037\pi$
$71$	−788.550	−1.31808	−0.659040	+	0.752108i	$0.729037\pi$
$72$	−70.8475	−0.115965
$73$	2.67867	0.00429473	0.00214736	−	0.999998i	$-0.499316\pi$
$73$	2.67867	0.00429473	0.00214736	+	0.999998i	$0.499316\pi$
$74$	1411.55	2.21743
$75$	210.235	0.323678
$76$	1174.07	1.77204
$77$	−15.6268	−0.0231277
$78$	−2229.08	−3.23582
$79$	−466.853	−0.664874	−0.332437	−	0.943125i	$-0.607871\pi$
$79$	−466.853	−0.664874	−0.332437	+	0.943125i	$0.607871\pi$
$80$	455.477	0.636549
$81$	−899.754	−1.23423
$82$	1850.01	2.49145
$83$	1495.54	1.97779	0.988894	−	0.148622i	$-0.0474836\pi$
$83$	1495.54	1.97779	0.988894	+	0.148622i	$0.0474836\pi$
$84$	−55.2982	−0.0718278
$85$	−272.589	−0.347841
$86$	917.783	1.15078
$87$	1613.93	1.98887
$88$	116.628	0.141279
$89$	−1406.43	−1.67507	−0.837533	−	0.546387i	$-0.816003\pi$
$89$	−1406.43	−1.67507	−0.837533	+	0.546387i	$0.816003\pi$
$90$	404.211	0.473417
$91$	−81.7454	−0.0941675
$92$	399.154	0.452333
$93$	−57.3532	−0.0639489
$94$	216.651	0.237722
$95$	−1155.27	−1.24767
$96$	−1567.55	−1.66654
$97$	−1436.21	−1.50335	−0.751674	−	0.659534i	$-0.770754\pi$
$97$	−1436.21	−1.50335	−0.751674	+	0.659534i	$0.770754\pi$
$98$	1438.01	1.48225
$99$	−168.241	−0.170796
$100$	−333.633	−0.333633
$101$	1133.34	1.11655	0.558277	−	0.829654i	$-0.311463\pi$
$101$	1133.34	1.11655	0.558277	+	0.829654i	$0.311463\pi$
$102$	733.735	0.712261
$103$	−417.371	−0.399270	−0.199635	−	0.979870i	$-0.563976\pi$
$103$	−417.371	−0.399270	−0.199635	+	0.979870i	$0.563976\pi$
$104$	610.095	0.575237
$105$	54.4130	0.0505730
$106$	1511.34	1.38485
$107$	811.458	0.733145	0.366573	−	0.930389i	$-0.380531\pi$
$107$	811.458	0.733145	0.366573	+	0.930389i	$0.380531\pi$
$108$	994.699	0.886250
$109$	−653.827	−0.574543	−0.287272	−	0.957849i	$-0.592748\pi$
$109$	−653.827	−0.574543	−0.287272	+	0.957849i	$0.592748\pi$
$110$	−665.406	−0.576763
$111$	2045.76	1.74932
$112$	−44.9608	−0.0379321
$113$	861.730	0.717387	0.358693	−	0.933455i	$-0.383222\pi$
$113$	861.730	0.717387	0.358693	+	0.933455i	$0.383222\pi$
$114$	3109.68	2.55480
$115$	−392.764	−0.318482
$116$	−2561.23	−2.05004
$117$	−880.086	−0.695419
$118$	1559.29	1.21647
$119$	26.9077	0.0207279
$120$	−406.104	−0.308934
$121$	−1054.04	−0.791920
$122$	474.110	0.351835
$123$	2681.21	1.96550
$124$	91.0166	0.0659156
$125$	1517.36	1.08573
$126$	−39.9002	−0.0282111
$127$	−2220.99	−1.55182	−0.775909	−	0.630845i	$-0.782708\pi$
$127$	−2220.99	−1.55182	−0.775909	+	0.630845i	$0.782708\pi$
$128$	877.551	0.605979
$129$	1330.14	0.907847
$130$	−3480.81	−2.34837
$131$	−1172.20	−0.781796	−0.390898	−	0.920434i	$-0.627835\pi$
$131$	−1172.20	−0.781796	−0.390898	+	0.920434i	$0.627835\pi$
$132$	980.058	0.646236
$133$	114.039	0.0743489
$134$	1096.86	0.707119
$135$	−978.776	−0.623997
$136$	−200.822	−0.126620
$137$	−568.759	−0.354689	−0.177344	−	0.984149i	$-0.556751\pi$
$137$	−568.759	−0.354689	−0.177344	+	0.984149i	$0.556751\pi$
$138$	1057.21	0.652145
$139$	−892.092	−0.544362	−0.272181	−	0.962246i	$-0.587745\pi$
$139$	−892.092	−0.544362	−0.272181	+	0.962246i	$0.587745\pi$
$140$	−86.3507	−0.0521283
$141$	313.991	0.187538
$142$	3314.47	1.95876
$143$	1448.78	0.847227
$144$	−484.057	−0.280125
$145$	2520.23	1.44341
$146$	−11.2591	−0.00638227
$147$	2084.10	1.16934
$148$	−3246.51	−1.80312
$149$	2337.40	1.28515	0.642575	−	0.766223i	$-0.277866\pi$
$149$	2337.40	1.28515	0.642575	+	0.766223i	$0.277866\pi$
$150$	−883.671	−0.481010
$151$	−1507.87	−0.812640	−0.406320	−	0.913731i	$-0.633188\pi$
$151$	−1507.87	−0.812640	−0.406320	+	0.913731i	$0.633188\pi$
$152$	−851.111	−0.454172
$153$	289.693	0.153074
$154$	65.6831	0.0343695
$155$	−89.5596	−0.0464103
$156$	5126.80	2.63123
$157$	−1353.06	−0.687806	−0.343903	−	0.939005i	$-0.611749\pi$
$157$	−1353.06	−0.687806	−0.343903	+	0.939005i	$0.611749\pi$
$158$	1962.30	0.988051
$159$	2190.38	1.09251
$160$	−2447.80	−1.20947
$161$	38.7703	0.0189784
$162$	3781.89	1.83416
$163$	3151.01	1.51415	0.757075	−	0.653328i	$-0.226628\pi$
$163$	3151.01	1.51415	0.757075	+	0.653328i	$0.226628\pi$
$164$	−4254.94	−2.02595
$165$	−964.370	−0.455006
$166$	−6286.11	−2.93914
$167$	1047.49	0.485372	0.242686	−	0.970105i	$-0.421972\pi$
$167$	1047.49	0.485372	0.242686	+	0.970105i	$0.421972\pi$
$168$	40.0871	0.0184094
$169$	5381.75	2.44959
$170$	1145.76	0.516917
$171$	1227.76	0.549060
$172$	−2110.86	−0.935766
$173$	2197.02	0.965526	0.482763	−	0.875751i	$-0.339633\pi$
$173$	2197.02	0.965526	0.482763	+	0.875751i	$0.339633\pi$
$174$	−6783.76	−2.95561
$175$	−32.4062	−0.0139982
$176$	796.846	0.341276
$177$	2259.87	0.959673
$178$	5911.56	2.48927
$179$	2804.72	1.17114	0.585572	−	0.810620i	$-0.300870\pi$
$179$	2804.72	1.17114	0.585572	+	0.810620i	$0.300870\pi$
$180$	−929.668	−0.384963
$181$	468.135	0.192244	0.0961222	−	0.995370i	$-0.469356\pi$
$181$	468.135	0.192244	0.0961222	+	0.995370i	$0.469356\pi$
$182$	343.596	0.139940
$183$	687.126	0.277562
$184$	−289.357	−0.115933
$185$	3194.54	1.26955
$186$	241.070	0.0950327
$187$	−476.889	−0.186490
$188$	−498.288	−0.193305
$189$	96.6164	0.0371842
$190$	4855.90	1.85413
$191$	1023.81	0.387853	0.193927	−	0.981016i	$-0.437878\pi$
$191$	1023.81	0.387853	0.193927	+	0.981016i	$0.437878\pi$
$192$	4255.33	1.59949
$193$	−3042.34	−1.13468	−0.567338	−	0.823485i	$-0.692027\pi$
$193$	−3042.34	−1.13468	−0.567338	+	0.823485i	$0.692027\pi$
$194$	6036.74	2.23409
$195$	−5044.73	−1.85262
$196$	−3307.36	−1.20531
$197$	1103.85	0.399220	0.199610	−	0.979875i	$-0.436033\pi$
$197$	1103.85	0.399220	0.199610	+	0.979875i	$0.436033\pi$
$198$	707.157	0.253816
$199$	−1931.47	−0.688031	−0.344016	−	0.938964i	$-0.611787\pi$
$199$	−1931.47	−0.688031	−0.344016	+	0.938964i	$0.611787\pi$
$200$	241.859	0.0855100
$201$	1589.67	0.557844
$202$	−4763.73	−1.65928
$203$	−248.776	−0.0860129
$204$	−1687.56	−0.579181
$205$	4186.83	1.42644
$206$	1754.31	0.593344
$207$	417.409	0.140154
$208$	4168.39	1.38955
$209$	−2021.12	−0.668918
$210$	−228.712	−0.0751552
$211$	1588.86	0.518396	0.259198	−	0.965824i	$-0.416542\pi$
$211$	1588.86	0.518396	0.259198	+	0.965824i	$0.416542\pi$
$212$	−3476.03	−1.12611
$213$	4803.65	1.54526
$214$	−3410.76	−1.08951
$215$	2077.07	0.658861
$216$	−721.082	−0.227146
$217$	8.84055	0.00276560
$218$	2748.20	0.853813
$219$	−16.3178	−0.00503495
$220$	1530.41	0.469000
$221$	−2494.66	−0.759316
$222$	−8598.83	−2.59962
$223$	−3504.77	−1.05245	−0.526227	−	0.850344i	$-0.676394\pi$
$223$	−3504.77	−1.05245	−0.526227	+	0.850344i	$0.676394\pi$
$224$	241.626	0.0720728
$225$	−348.891	−0.103375
$226$	−3622.06	−1.06609
$227$	−1438.24	−0.420525	−0.210262	−	0.977645i	$-0.567432\pi$
$227$	−1438.24	−0.420525	−0.210262	+	0.977645i	$0.567432\pi$
$228$	−7152.12	−2.07746
$229$	−501.597	−0.144744	−0.0723722	−	0.997378i	$-0.523057\pi$
$229$	−501.597	−0.144744	−0.0723722	+	0.997378i	$0.523057\pi$
$230$	1650.89	0.473288
$231$	95.1943	0.0271140
$232$	1856.70	0.525424
$233$	−3385.65	−0.951937	−0.475969	−	0.879462i	$-0.657902\pi$
$233$	−3385.65	−0.951937	−0.475969	+	0.879462i	$0.657902\pi$
$234$	3699.22	1.03344
$235$	490.312	0.136104
$236$	−3586.30	−0.989186
$237$	2843.95	0.779470
$238$	−113.100	−0.0308032
$239$	−7125.62	−1.92853	−0.964263	−	0.264946i	$-0.914646\pi$
$239$	−7125.62	−1.92853	−0.964263	+	0.264946i	$0.914646\pi$
$240$	−2774.65	−0.746263
$241$	−2039.04	−0.545005	−0.272502	−	0.962155i	$-0.587851\pi$
$241$	−2039.04	−0.545005	−0.272502	+	0.962155i	$0.587851\pi$
$242$	4430.41	1.17685
$243$	2702.96	0.713560
$244$	−1090.43	−0.286098
$245$	3254.42	0.848641
$246$	−11269.8	−2.92087
$247$	−10572.7	−2.72359
$248$	−65.9802	−0.0168941
$249$	−9110.43	−2.31868
$250$	−6377.84	−1.61348
$251$	2361.01	0.593729	0.296864	−	0.954920i	$-0.404059\pi$
$251$	2361.01	0.593729	0.296864	+	0.954920i	$0.404059\pi$
$252$	91.7689	0.0229401
$253$	−687.132	−0.170749
$254$	9335.37	2.30611
$255$	1660.55	0.407794
$256$	1899.76	0.463808
$257$	−7881.69	−1.91302	−0.956510	−	0.291699i	$-0.905780\pi$
$257$	−7881.69	−1.91302	−0.956510	+	0.291699i	$0.905780\pi$
$258$	−5590.90	−1.34913
$259$	−315.338	−0.0756531
$260$	8005.73	1.90959
$261$	−2678.36	−0.635198
$262$	4927.03	1.16181
$263$	6933.28	1.62557	0.812784	−	0.582566i	$-0.197951\pi$
$263$	6933.28	1.62557	0.812784	+	0.582566i	$0.197951\pi$
$264$	−710.469	−0.165630
$265$	3420.38	0.792877
$266$	−479.333	−0.110488
$267$	8567.60	1.96378
$268$	−2522.73	−0.575000
$269$	4326.07	0.980539	0.490269	−	0.871571i	$-0.336898\pi$
$269$	4326.07	0.980539	0.490269	+	0.871571i	$0.336898\pi$
$270$	4114.04	0.927305
$271$	3839.78	0.860701	0.430351	−	0.902662i	$-0.358390\pi$
$271$	3839.78	0.860701	0.430351	+	0.902662i	$0.358390\pi$
$272$	−1372.09	−0.305864
$273$	497.972	0.110398
$274$	2390.63	0.527093
$275$	574.339	0.125942
$276$	−2431.55	−0.530297
$277$	3688.07	0.799981	0.399991	−	0.916519i	$-0.369013\pi$
$277$	3688.07	0.799981	0.399991	+	0.916519i	$0.369013\pi$
$278$	3749.69	0.808961
$279$	95.1791	0.0204237
$280$	62.5978	0.0133605
$281$	−7909.61	−1.67917	−0.839586	−	0.543226i	$-0.817203\pi$
$281$	−7909.61	−1.67917	−0.839586	+	0.543226i	$0.817203\pi$
$282$	−1319.78	−0.278695
$283$	−7038.40	−1.47841	−0.739204	−	0.673482i	$-0.764798\pi$
$283$	−7038.40	−1.47841	−0.739204	+	0.673482i	$0.764798\pi$
$284$	−7623.15	−1.59278
$285$	7037.63	1.46271
$286$	−6089.60	−1.25904
$287$	−413.288	−0.0850021
$288$	2601.39	0.532251
$289$	−4091.85	−0.832861
$290$	−10593.2	−2.14500
$291$	8749.02	1.76246
$292$	25.8955	0.00518980
$293$	7861.96	1.56758	0.783790	−	0.621026i	$-0.213284\pi$
$293$	7861.96	1.56758	0.783790	+	0.621026i	$0.213284\pi$
$294$	−8759.99	−1.73773
$295$	3528.89	0.696474
$296$	2353.48	0.462139
$297$	−1712.35	−0.334547
$298$	−9824.67	−1.90983
$299$	−3594.47	−0.695228
$300$	2032.41	0.391137
$301$	−205.031	−0.0392617
$302$	6337.95	1.20764
$303$	−6904.05	−1.30900
$304$	−5815.11	−1.09710
$305$	1072.98	0.201438
$306$	−1217.65	−0.227479
$307$	5864.39	1.09022	0.545111	−	0.838364i	$-0.316487\pi$
$307$	5864.39	1.09022	0.545111	+	0.838364i	$0.316487\pi$
$308$	−151.069	−0.0279478
$309$	2542.52	0.468087
$310$	376.441	0.0689691
$311$	5679.35	1.03552	0.517759	−	0.855526i	$-0.326766\pi$
$311$	5679.35	1.03552	0.517759	+	0.855526i	$0.326766\pi$
$312$	−3716.54	−0.674384
$313$	−9075.35	−1.63888	−0.819439	−	0.573166i	$-0.805715\pi$
$313$	−9075.35	−1.63888	−0.819439	+	0.573166i	$0.805715\pi$
$314$	5687.23	1.02213
$315$	−90.2999	−0.0161518
$316$	−4513.20	−0.803442
$317$	8276.10	1.46635	0.733174	−	0.680042i	$-0.238038\pi$
$317$	8276.10	1.46635	0.733174	+	0.680042i	$0.238038\pi$
$318$	−9206.72	−1.62355
$319$	4409.08	0.773860
$320$	6644.89	1.16082
$321$	−4943.20	−0.859509
$322$	−162.961	−0.0282034
$323$	3480.17	0.599510
$324$	−8698.19	−1.49146
$325$	3004.43	0.512788
$326$	−13244.5	−2.25014
$327$	3982.95	0.673570
$328$	3084.51	0.519249
$329$	−48.3994	−0.00811047
$330$	4053.48	0.676173
$331$	−7209.68	−1.19722	−0.598610	−	0.801040i	$-0.704280\pi$
$331$	−7209.68	−1.19722	−0.598610	+	0.801040i	$0.704280\pi$
$332$	14457.8	2.38998
$333$	−3394.99	−0.558691
$334$	−4402.85	−0.721298
$335$	2482.34	0.404850
$336$	273.890	0.0444700
$337$	10949.0	1.76983	0.884914	−	0.465754i	$-0.154217\pi$
$337$	10949.0	1.76983	0.884914	+	0.465754i	$0.154217\pi$
$338$	−22620.9	−3.64027
$339$	−5249.44	−0.841034
$340$	−2635.20	−0.420335
$341$	−156.682	−0.0248822
$342$	−5160.59	−0.815943
$343$	−643.324	−0.101272
$344$	1530.22	0.239837
$345$	2392.62	0.373375
$346$	−9234.60	−1.43484
$347$	−11588.2	−1.79276	−0.896380	−	0.443287i	$-0.853812\pi$
$347$	−11588.2	−1.79276	−0.896380	+	0.443287i	$0.853812\pi$
$348$	15602.4	2.40338
$349$	−3930.79	−0.602895	−0.301448	−	0.953483i	$-0.597470\pi$
$349$	−3930.79	−0.602895	−0.301448	+	0.953483i	$0.597470\pi$
$350$	136.211	0.0208023
$351$	−8957.47	−1.36215
$352$	−4282.37	−0.648440
$353$	7323.65	1.10424	0.552122	−	0.833763i	$-0.313818\pi$
$353$	7323.65	1.10424	0.552122	+	0.833763i	$0.313818\pi$
$354$	−9498.79	−1.42614
$355$	7501.12	1.12146
$356$	−13596.3	−2.02417
$357$	−163.915	−0.0243006
$358$	−11789.0	−1.74041
$359$	9276.20	1.36373	0.681865	−	0.731478i	$-0.261169\pi$
$359$	9276.20	1.36373	0.681865	+	0.731478i	$0.261169\pi$
$360$	673.940	0.0986660
$361$	7890.45	1.15038
$362$	−1967.69	−0.285689
$363$	6420.98	0.928413
$364$	−790.257	−0.113793
$365$	−25.4810	−0.00365407
$366$	−2888.16	−0.412477
$367$	1993.53	0.283545	0.141773	−	0.989899i	$-0.454720\pi$
$367$	1993.53	0.283545	0.141773	+	0.989899i	$0.454720\pi$
$368$	−1976.99	−0.280049
$369$	−4449.54	−0.627733
$370$	−13427.5	−1.88665
$371$	−337.631	−0.0472478
$372$	−554.450	−0.0772766
$373$	360.662	0.0500654	0.0250327	−	0.999687i	$-0.492031\pi$
$373$	360.662	0.0500654	0.0250327	+	0.999687i	$0.492031\pi$
$374$	2004.48	0.277137
$375$	−9243.38	−1.27287
$376$	361.222	0.0495441
$377$	23064.4	3.15087
$378$	−406.103	−0.0552584
$379$	−13068.6	−1.77121	−0.885607	−	0.464436i	$-0.846257\pi$
$379$	−13068.6	−1.77121	−0.885607	+	0.464436i	$0.846257\pi$
$380$	−11168.4	−1.50770
$381$	13529.7	1.81929
$382$	−4303.31	−0.576378
$383$	−9535.38	−1.27215	−0.636077	−	0.771625i	$-0.719444\pi$
$383$	−9535.38	−1.27215	−0.636077	+	0.771625i	$0.719444\pi$
$384$	−5345.82	−0.710424
$385$	148.650	0.0196777
$386$	12787.7	1.68621
$387$	−2207.40	−0.289944
$388$	−13884.3	−1.81667
$389$	−10588.9	−1.38015	−0.690074	−	0.723739i	$-0.742422\pi$
$389$	−10588.9	−1.38015	−0.690074	+	0.723739i	$0.742422\pi$
$390$	21204.2	2.75312
$391$	1183.17	0.153032
$392$	2397.59	0.308920
$393$	7140.73	0.916545
$394$	−4639.77	−0.593270
$395$	4440.96	0.565693
$396$	−1626.43	−0.206392
$397$	−2540.16	−0.321126	−0.160563	−	0.987026i	$-0.551331\pi$
$397$	−2540.16	−0.321126	−0.160563	+	0.987026i	$0.551331\pi$
$398$	8118.45	1.02246
$399$	−694.695	−0.0871635
$400$	1652.47	0.206559
$401$	−8703.51	−1.08387	−0.541936	−	0.840420i	$-0.682308\pi$
$401$	−8703.51	−1.08387	−0.541936	+	0.840420i	$0.682308\pi$
$402$	−6681.78	−0.828997
$403$	−819.623	−0.101311
$404$	10956.4	1.34926
$405$	8558.95	1.05012
$406$	1045.67	0.127821
$407$	5588.78	0.680652
$408$	1223.36	0.148444
$409$	−10946.4	−1.32339	−0.661694	−	0.749774i	$-0.730162\pi$
$409$	−10946.4	−1.32339	−0.661694	+	0.749774i	$0.730162\pi$
$410$	−17598.3	−2.11980
$411$	3464.74	0.415822
$412$	−4034.85	−0.482483
$413$	−348.342	−0.0415031
$414$	−1754.47	−0.208279
$415$	−14226.4	−1.68276
$416$	−22401.6	−2.64021
$417$	5434.40	0.638187
$418$	8495.28	0.994061
$419$	−4553.41	−0.530904	−0.265452	−	0.964124i	$-0.585521\pi$
$419$	−4553.41	−0.530904	−0.265452	+	0.964124i	$0.585521\pi$
$420$	526.027	0.0611131
$421$	5225.23	0.604898	0.302449	−	0.953166i	$-0.402196\pi$
$421$	5225.23	0.604898	0.302449	+	0.953166i	$0.402196\pi$
$422$	−6678.37	−0.770374
$423$	−521.077	−0.0598951
$424$	2519.86	0.288621
$425$	−988.954	−0.112874
$426$	−20190.9	−2.29637
$427$	−105.915	−0.0120037
$428$	7844.60	0.885942
$429$	−8825.63	−0.993253
$430$	−8730.45	−0.979116
$431$	7113.34	0.794983	0.397491	−	0.917606i	$-0.369881\pi$
$431$	7113.34	0.794983	0.397491	+	0.917606i	$0.369881\pi$
$432$	−4926.70	−0.548695
$433$	14674.0	1.62860	0.814302	−	0.580442i	$-0.197120\pi$
$433$	14674.0	1.62860	0.814302	+	0.580442i	$0.197120\pi$
$434$	−37.1590	−0.00410989
$435$	−15352.6	−1.69219
$436$	−6320.74	−0.694285
$437$	5014.45	0.548910
$438$	68.5878	0.00748231
$439$	9523.73	1.03540	0.517702	−	0.855561i	$-0.326787\pi$
$439$	9523.73	1.03540	0.517702	+	0.855561i	$0.326787\pi$
$440$	−1109.43	−0.120204
$441$	−3458.62	−0.373460
$442$	10485.7	1.12840
$443$	5309.60	0.569451	0.284725	−	0.958609i	$-0.408098\pi$
$443$	5309.60	0.569451	0.284725	+	0.958609i	$0.408098\pi$
$444$	19776.9	2.11390
$445$	13378.7	1.42519
$446$	14731.4	1.56402
$447$	−14238.9	−1.50665
$448$	−655.927	−0.0691733
$449$	−264.529	−0.0278038	−0.0139019	−	0.999903i	$-0.504425\pi$
$449$	−264.529	−0.0278038	−0.0139019	+	0.999903i	$0.504425\pi$
$450$	1466.48	0.153623
$451$	7324.75	0.764765
$452$	8330.60	0.866899
$453$	9185.57	0.952705
$454$	6045.27	0.624931
$455$	777.606	0.0801203
$456$	5184.75	0.532453
$457$	−4776.41	−0.488908	−0.244454	−	0.969661i	$-0.578609\pi$
$457$	−4776.41	−0.488908	−0.244454	+	0.969661i	$0.578609\pi$
$458$	2108.34	0.215101
$459$	2948.49	0.299833
$460$	−3796.97	−0.384858
$461$	−5640.16	−0.569823	−0.284912	−	0.958554i	$-0.591964\pi$
$461$	−5640.16	−0.569823	−0.284912	+	0.958554i	$0.591964\pi$
$462$	−400.125	−0.0402933
$463$	16112.5	1.61730	0.808652	−	0.588288i	$-0.200198\pi$
$463$	16112.5	1.61730	0.808652	+	0.588288i	$0.200198\pi$
$464$	12685.7	1.26922
$465$	545.575	0.0544095
$466$	14230.7	1.41465
$467$	−3908.61	−0.387300	−0.193650	−	0.981071i	$-0.562033\pi$
$467$	−3908.61	−0.387300	−0.193650	+	0.981071i	$0.562033\pi$
$468$	−8508.05	−0.840352
$469$	−245.036	−0.0241251
$470$	−2060.90	−0.202260
$471$	8242.48	0.806355
$472$	2599.80	0.253528
$473$	3633.79	0.353238
$474$	−11953.8	−1.15835
$475$	−4191.33	−0.404866
$476$	260.125	0.0250479
$477$	−3635.00	−0.348921
$478$	29950.7	2.86593
$479$	−858.414	−0.0818830	−0.0409415	−	0.999162i	$-0.513036\pi$
$479$	−858.414	−0.0818830	−0.0409415	+	0.999162i	$0.513036\pi$
$480$	14911.4	1.41793
$481$	29235.5	2.77136
$482$	8570.59	0.809916
$483$	−236.179	−0.0222495
$484$	−10189.8	−0.956965
$485$	13662.0	1.27909
$486$	−11361.2	−1.06040
$487$	13348.6	1.24206	0.621028	−	0.783789i	$-0.286715\pi$
$487$	13348.6	1.24206	0.621028	+	0.783789i	$0.286715\pi$
$488$	790.482	0.0733268
$489$	−19195.2	−1.77513
$490$	−13679.1	−1.26114
$491$	−11664.9	−1.07216	−0.536081	−	0.844166i	$-0.680096\pi$
$491$	−11664.9	−1.07216	−0.536081	+	0.844166i	$0.680096\pi$
$492$	25920.0	2.37513
$493$	−7591.99	−0.693562
$494$	44439.8	4.04745
$495$	1600.40	0.145318
$496$	−450.801	−0.0408096
$497$	−740.446	−0.0668281
$498$	38293.4	3.44572
$499$	5742.96	0.515211	0.257606	−	0.966250i	$-0.417066\pi$
$499$	5742.96	0.515211	0.257606	+	0.966250i	$0.417066\pi$
$500$	14668.8	1.31201
$501$	−6381.04	−0.569029
$502$	−9923.93	−0.882324
$503$	20819.6	1.84552	0.922762	−	0.385371i	$-0.125927\pi$
$503$	20819.6	1.84552	0.922762	+	0.385371i	$0.125927\pi$
$504$	−66.5256	−0.00587953
$505$	−10781.0	−0.949996
$506$	2888.19	0.253746
$507$	−32784.3	−2.87180
$508$	−21471.0	−1.87524
$509$	−7623.78	−0.663886	−0.331943	−	0.943299i	$-0.607704\pi$
$509$	−7623.78	−0.663886	−0.331943	+	0.943299i	$0.607704\pi$
$510$	−6979.69	−0.606012
$511$	2.51527	0.000217747 0
$512$	−15005.6	−1.29523
$513$	12496.1	1.07547
$514$	33128.7	2.84289
$515$	3970.26	0.339710
$516$	12858.8	1.09705
$517$	857.789	0.0729700
$518$	1325.44	0.112426
$519$	−13383.7	−1.13194
$520$	−5803.55	−0.489428
$521$	−16462.3	−1.38431	−0.692156	−	0.721748i	$-0.743339\pi$
$521$	−16462.3	−1.38431	−0.692156	+	0.721748i	$0.743339\pi$
$522$	11257.8	0.943950
$523$	6342.62	0.530294	0.265147	−	0.964208i	$-0.414580\pi$
$523$	6342.62	0.530294	0.265147	+	0.964208i	$0.414580\pi$
$524$	−11332.0	−0.944732
$525$	197.410	0.0164108
$526$	−29142.3	−2.41571
$527$	269.791	0.0223004
$528$	−4854.19	−0.400097
$529$	−10462.2	−0.859884
$530$	−14376.7	−1.17827
$531$	−3750.31	−0.306496
$532$	1102.45	0.0898441
$533$	38316.6	3.11384
$534$	−36011.7	−2.91831
$535$	−7719.03	−0.623781
$536$	1828.79	0.147372
$537$	−17085.7	−1.37300
$538$	−18183.5	−1.45715
$539$	5693.52	0.454986
$540$	−9462.12	−0.754046
$541$	11333.9	0.900704	0.450352	−	0.892851i	$-0.351299\pi$
$541$	11333.9	0.900704	0.450352	+	0.892851i	$0.351299\pi$
$542$	−16139.6	−1.27906
$543$	−2851.76	−0.225379
$544$	7373.80	0.581157
$545$	6219.55	0.488838
$546$	−2093.10	−0.164059
$547$	9917.03	0.775176	0.387588	−	0.921833i	$-0.373308\pi$
$547$	9917.03	0.775176	0.387588	+	0.921833i	$0.373308\pi$
$548$	−5498.36	−0.428610
$549$	−1140.30	−0.0886465
$550$	−2414.09	−0.187158
$551$	−32175.9	−2.48773
$552$	1762.69	0.135915
$553$	−438.373	−0.0337098
$554$	−15501.9	−1.18883
$555$	−19460.4	−1.48837
$556$	−8624.12	−0.657813
$557$	−10130.9	−0.770667	−0.385334	−	0.922777i	$-0.625914\pi$
$557$	−10130.9	−0.770667	−0.385334	+	0.922777i	$0.625914\pi$
$558$	−400.061	−0.0303512
$559$	19008.8	1.43826
$560$	427.692	0.0322737
$561$	2905.09	0.218633
$562$	33246.0	2.49537
$563$	−10063.3	−0.753316	−0.376658	−	0.926352i	$-0.622927\pi$
$563$	−10063.3	−0.753316	−0.376658	+	0.926352i	$0.622927\pi$
$564$	3035.45	0.226623
$565$	−8197.24	−0.610373
$566$	29584.1	2.19702
$567$	−844.866	−0.0625768
$568$	5526.21	0.408230
$569$	−18809.4	−1.38582	−0.692911	−	0.721023i	$-0.743672\pi$
$569$	−18809.4	−1.38582	−0.692911	+	0.721023i	$0.743672\pi$
$570$	−29580.9	−2.17370
$571$	11953.2	0.876050	0.438025	−	0.898963i	$-0.355678\pi$
$571$	11953.2	0.876050	0.438025	+	0.898963i	$0.355678\pi$
$572$	14005.8	1.02380
$573$	−6236.76	−0.454703
$574$	1737.15	0.126319
$575$	−1424.95	−0.103347
$576$	−7061.84	−0.510839
$577$	−8032.69	−0.579559	−0.289779	−	0.957093i	$-0.593582\pi$
$577$	−8032.69	−0.579559	−0.289779	+	0.957093i	$0.593582\pi$
$578$	17199.0	1.23769
$579$	18533.2	1.33025
$580$	24363.8	1.74423
$581$	1404.30	0.100276
$582$	−36774.3	−2.61915
$583$	5983.88	0.425089
$584$	−18.7723	−0.00133014
$585$	8371.86	0.591682
$586$	−33045.8	−2.32954
$587$	18441.3	1.29668	0.648341	−	0.761350i	$-0.275463\pi$
$587$	18441.3	1.29668	0.648341	+	0.761350i	$0.275463\pi$
$588$	20147.6	1.41305
$589$	1143.41	0.0799890
$590$	−14832.8	−1.03501
$591$	−6724.40	−0.468028
$592$	16079.8	1.11635
$593$	−16045.6	−1.11115	−0.555575	−	0.831466i	$-0.687502\pi$
$593$	−16045.6	−1.11115	−0.555575	+	0.831466i	$0.687502\pi$
$594$	7197.41	0.497161
$595$	−255.961	−0.0176359
$596$	22596.3	1.55299
$597$	11766.0	0.806619
$598$	15108.4	1.03316
$599$	3229.06	0.220260	0.110130	−	0.993917i	$-0.464873\pi$
$599$	3229.06	0.220260	0.110130	+	0.993917i	$0.464873\pi$
$600$	−1473.34	−0.100248
$601$	8862.75	0.601529	0.300765	−	0.953698i	$-0.402758\pi$
$601$	8862.75	0.601529	0.300765	+	0.953698i	$0.402758\pi$
$602$	861.795	0.0583458
$603$	−2638.10	−0.178162
$604$	−14577.0	−0.982005
$605$	10026.6	0.673787
$606$	29019.4	1.94527
$607$	−7207.53	−0.481952	−0.240976	−	0.970531i	$-0.577467\pi$
$607$	−7207.53	−0.481952	−0.240976	+	0.970531i	$0.577467\pi$
$608$	31251.2	2.08455
$609$	1515.48	0.100838
$610$	−4509.99	−0.299351
$611$	4487.19	0.297107
$612$	2800.55	0.184976
$613$	1955.74	0.128861	0.0644303	−	0.997922i	$-0.479477\pi$
$613$	1955.74	0.128861	0.0644303	+	0.997922i	$0.479477\pi$
$614$	−24649.5	−1.62015
$615$	−25505.1	−1.67230
$616$	109.513	0.00716302
$617$	−12462.2	−0.813140	−0.406570	−	0.913620i	$-0.633275\pi$
$617$	−12462.2	−0.813140	−0.406570	+	0.913620i	$0.633275\pi$
$618$	−10686.8	−0.695612
$619$	−14381.1	−0.933807	−0.466904	−	0.884308i	$-0.654630\pi$
$619$	−14381.1	−0.933807	−0.466904	+	0.884308i	$0.654630\pi$
$620$	−865.799	−0.0560828
$621$	4248.37	0.274527
$622$	−23871.7	−1.53886
$623$	−1320.63	−0.0849276
$624$	−25392.8	−1.62905
$625$	−10120.0	−0.647681
$626$	38145.9	2.43549
$627$	12312.2	0.784212
$628$	−13080.4	−0.831154
$629$	−9623.31	−0.610026
$630$	379.553	0.0240028
$631$	−5639.32	−0.355781	−0.177891	−	0.984050i	$-0.556927\pi$
$631$	−5639.32	−0.355781	−0.177891	+	0.984050i	$0.556927\pi$
$632$	3271.74	0.205922
$633$	−9678.93	−0.607745
$634$	−34786.5	−2.17910
$635$	21127.3	1.32033
$636$	21175.1	1.32020
$637$	29783.5	1.85253
$638$	−18532.5	−1.15001
$639$	−7971.78	−0.493519
$640$	−8347.74	−0.515584
$641$	1238.65	0.0763240	0.0381620	−	0.999272i	$-0.487850\pi$
$641$	1238.65	0.0763240	0.0381620	+	0.999272i	$0.487850\pi$
$642$	20777.5	1.27729
$643$	−9532.14	−0.584621	−0.292310	−	0.956324i	$-0.594424\pi$
$643$	−9532.14	−0.584621	−0.292310	+	0.956324i	$0.594424\pi$
$644$	374.804	0.0229338
$645$	−12653.0	−0.772421
$646$	−14628.0	−0.890915
$647$	−2040.31	−0.123976	−0.0619882	−	0.998077i	$-0.519744\pi$
$647$	−2040.31	−0.123976	−0.0619882	+	0.998077i	$0.519744\pi$
$648$	6305.54	0.382261
$649$	6173.70	0.373404
$650$	−12628.4	−0.762040
$651$	−53.8544	−0.00324228
$652$	30461.8	1.82972
$653$	−19533.3	−1.17059	−0.585295	−	0.810820i	$-0.699021\pi$
$653$	−19533.3	−1.17059	−0.585295	+	0.810820i	$0.699021\pi$
$654$	−16741.3	−1.00097
$655$	11150.6	0.665174
$656$	21074.5	1.25430
$657$	27.0798	0.00160804
$658$	203.435	0.0120527
$659$	14112.2	0.834192	0.417096	−	0.908863i	$-0.363048\pi$
$659$	14112.2	0.834192	0.417096	+	0.908863i	$0.363048\pi$
$660$	−9322.85	−0.549835
$661$	−28892.4	−1.70013	−0.850064	−	0.526679i	$-0.823437\pi$
$661$	−28892.4	−1.70013	−0.850064	+	0.526679i	$0.823437\pi$
$662$	30304.1	1.77916
$663$	15196.8	0.890191
$664$	−10480.8	−0.612552
$665$	−1084.80	−0.0632581
$666$	14270.0	0.830256
$667$	−10939.0	−0.635024
$668$	10126.4	0.586529
$669$	21350.2	1.23385
$670$	−10433.9	−0.601637
$671$	1877.15	0.107998
$672$	−1471.92	−0.0844951
$673$	10386.7	0.594917	0.297458	−	0.954735i	$-0.403861\pi$
$673$	10386.7	0.594917	0.297458	+	0.954735i	$0.403861\pi$
$674$	−46021.5	−2.63009
$675$	−3551.00	−0.202486
$676$	52027.0	2.96012
$677$	−6282.45	−0.356653	−0.178327	−	0.983971i	$-0.557068\pi$
$677$	−6282.45	−0.356653	−0.178327	+	0.983971i	$0.557068\pi$
$678$	22064.7	1.24984
$679$	−1348.60	−0.0762214
$680$	1910.33	0.107732
$681$	8761.38	0.493006
$682$	658.575	0.0369767
$683$	−9052.95	−0.507176	−0.253588	−	0.967312i	$-0.581611\pi$
$683$	−9052.95	−0.507176	−0.253588	+	0.967312i	$0.581611\pi$
$684$	11869.1	0.663491
$685$	5410.34	0.301779
$686$	2704.05	0.150497
$687$	3055.61	0.169692
$688$	10455.0	0.579352
$689$	31302.3	1.73080
$690$	−10056.8	−0.554863
$691$	−22872.6	−1.25921	−0.629604	−	0.776916i	$-0.716783\pi$
$691$	−22872.6	−1.25921	−0.629604	+	0.776916i	$0.716783\pi$
$692$	21239.2	1.16675
$693$	−157.977	−0.00865955
$694$	48708.1	2.66417
$695$	8486.07	0.463158
$696$	−11310.6	−0.615985
$697$	−12612.5	−0.685412
$698$	16522.1	0.895946
$699$	20624.5	1.11601
$700$	−313.280	−0.0169155
$701$	30455.4	1.64092	0.820460	−	0.571705i	$-0.193718\pi$
$701$	30455.4	1.64092	0.820460	+	0.571705i	$0.193718\pi$
$702$	37650.5	2.02425
$703$	−40784.9	−2.18810
$704$	11625.1	0.622353
$705$	−2986.86	−0.159562
$706$	−30783.1	−1.64099
$707$	1064.21	0.0566105
$708$	21846.8	1.15968
$709$	−5436.94	−0.287995	−0.143998	−	0.989578i	$-0.545996\pi$
$709$	−5436.94	−0.287995	−0.143998	+	0.989578i	$0.545996\pi$
$710$	−31529.1	−1.66657
$711$	−4719.61	−0.248944
$712$	9856.33	0.518794
$713$	388.732	0.0204181
$714$	688.975	0.0361124
$715$	−13781.6	−0.720844
$716$	27114.1	1.41523
$717$	43407.5	2.26092
$718$	−38990.2	−2.02660
$719$	23256.8	1.20630	0.603151	−	0.797627i	$-0.293912\pi$
$719$	23256.8	1.20630	0.603151	+	0.797627i	$0.293912\pi$
$720$	4604.61	0.238338
$721$	−391.910	−0.0202434
$722$	−33165.5	−1.70955
$723$	12421.3	0.638940
$724$	4525.60	0.232310
$725$	9143.39	0.468382
$726$	−26989.0	−1.37969
$727$	32105.1	1.63784	0.818921	−	0.573907i	$-0.194573\pi$
$727$	32105.1	1.63784	0.818921	+	0.573907i	$0.194573\pi$
$728$	572.877	0.0291652
$729$	7827.60	0.397683
$730$	107.103	0.00543022
$731$	−6257.02	−0.316586
$732$	6642.65	0.335409
$733$	−28243.0	−1.42316	−0.711582	−	0.702603i	$-0.752021\pi$
$733$	−28243.0	−1.42316	−0.711582	+	0.702603i	$0.752021\pi$
$734$	−8379.28	−0.421369
$735$	−19825.1	−0.994911
$736$	10624.6	0.532106
$737$	4342.80	0.217054
$738$	18702.5	0.932857
$739$	−26274.5	−1.30788	−0.653941	−	0.756546i	$-0.726885\pi$
$739$	−26274.5	−1.30788	−0.653941	+	0.756546i	$0.726885\pi$
$740$	30882.6	1.53414
$741$	64406.4	3.19302
$742$	1419.15	0.0702136
$743$	21933.1	1.08297	0.541484	−	0.840711i	$-0.317862\pi$
$743$	21933.1	1.08297	0.541484	+	0.840711i	$0.317862\pi$
$744$	401.935	0.0198060
$745$	−22234.6	−1.09344
$746$	−1515.95	−0.0744008
$747$	15119.0	0.740529
$748$	−4610.22	−0.225356
$749$	761.956	0.0371713
$750$	38852.2	1.89158
$751$	9345.76	0.454103	0.227052	−	0.973883i	$-0.427091\pi$
$751$	9345.76	0.454103	0.227052	+	0.973883i	$0.427091\pi$
$752$	2468.00	0.119679
$753$	−14382.7	−0.696062
$754$	−96945.5	−4.68242
$755$	14343.7	0.691417
$756$	934.020	0.0449338
$757$	−6107.50	−0.293238	−0.146619	−	0.989193i	$-0.546839\pi$
$757$	−6107.50	−0.293238	−0.146619	+	0.989193i	$0.546839\pi$
$758$	54930.6	2.63215
$759$	4185.83	0.200179
$760$	8096.23	0.386423
$761$	22807.0	1.08640	0.543201	−	0.839603i	$-0.317212\pi$
$761$	22807.0	1.08640	0.543201	+	0.839603i	$0.317212\pi$
$762$	−56868.7	−2.70359
$763$	−613.941	−0.0291300
$764$	9897.43	0.468686
$765$	−2755.72	−0.130240
$766$	40079.6	1.89051
$767$	32295.3	1.52036
$768$	−11572.8	−0.543749
$769$	19477.8	0.913378	0.456689	−	0.889626i	$-0.349035\pi$
$769$	19477.8	0.913378	0.456689	+	0.889626i	$0.349035\pi$
$770$	−624.814	−0.0292425
$771$	48013.3	2.24274
$772$	−29411.2	−1.37116
$773$	28994.8	1.34912	0.674560	−	0.738220i	$-0.264333\pi$
$773$	28994.8	1.34912	0.674560	+	0.738220i	$0.264333\pi$
$774$	9278.25	0.430878
$775$	−324.922	−0.0150600
$776$	10065.0	0.465611
$777$	1920.96	0.0886925
$778$	44507.7	2.05100
$779$	−53453.5	−2.45850
$780$	−48768.9	−2.23873
$781$	13123.0	0.601253
$782$	−4973.16	−0.227417
$783$	−27260.3	−1.24419
$784$	16381.2	0.746229
$785$	12871.0	0.585205
$786$	−30014.3	−1.36205
$787$	−787.000	−0.0356462
$787$	−787.000	−0.0356462
$788$	10671.3	0.482422
$789$	−42235.8	−1.90575
$790$	−18666.4	−0.840661
$791$	809.162	0.0363723
$792$	1179.04	0.0528983
$793$	9819.58	0.439727
$794$	10676.9	0.477216
$795$	−20836.1	−0.929536
$796$	−18672.1	−0.831426
$797$	−6581.99	−0.292530	−0.146265	−	0.989245i	$-0.546725\pi$
$797$	−6581.99	−0.292530	−0.146265	+	0.989245i	$0.546725\pi$
$798$	2919.98	0.129531
$799$	−1477.03	−0.0653985
$800$	−8880.61	−0.392471
$801$	−14218.1	−0.627183
$802$	36583.0	1.61071
$803$	−44.5784	−0.00195907
$804$	15367.8	0.674106
$805$	−368.805	−0.0161474
$806$	3445.08	0.150556
$807$	−26353.3	−1.14954
$808$	−7942.56	−0.345815
$809$	−27282.8	−1.18567	−0.592837	−	0.805322i	$-0.701992\pi$
$809$	−27282.8	−1.18567	−0.592837	+	0.805322i	$0.701992\pi$
$810$	−35975.4	−1.56055
$811$	−40731.9	−1.76361	−0.881807	−	0.471611i	$-0.843673\pi$
$811$	−40731.9	−1.76361	−0.881807	+	0.471611i	$0.843673\pi$
$812$	−2404.99	−0.103939
$813$	−23391.0	−1.00905
$814$	−23491.0	−1.01150
$815$	−29974.2	−1.28828
$816$	8358.42	0.358582
$817$	−26518.1	−1.13556
$818$	46010.6	1.96665
$819$	−826.398	−0.0352585
$820$	40475.3	1.72373
$821$	20558.4	0.873927	0.436964	−	0.899479i	$-0.356054\pi$
$821$	20558.4	0.873927	0.436964	+	0.899479i	$0.356054\pi$
$822$	−14563.1	−0.617942
$823$	−23107.8	−0.978722	−0.489361	−	0.872081i	$-0.662770\pi$
$823$	−23107.8	−0.978722	−0.489361	+	0.872081i	$0.662770\pi$
$824$	2924.97	0.123660
$825$	−3498.73	−0.147649
$826$	1464.17	0.0616766
$827$	23277.4	0.978760	0.489380	−	0.872071i	$-0.337223\pi$
$827$	23277.4	0.978760	0.489380	+	0.872071i	$0.337223\pi$
$828$	4035.21	0.169364
$829$	12147.6	0.508931	0.254465	−	0.967082i	$-0.418101\pi$
$829$	12147.6	0.508931	0.254465	+	0.967082i	$0.418101\pi$
$830$	59796.9	2.50070
$831$	−22466.8	−0.937865
$832$	60812.1	2.53399
$833$	−9803.67	−0.407775
$834$	−22842.2	−0.948392
$835$	−9964.28	−0.412968
$836$	−19538.8	−0.808329
$837$	968.728	0.0400050
$838$	19139.1	0.788962
$839$	20481.3	0.842780	0.421390	−	0.906880i	$-0.361542\pi$
$839$	20481.3	0.842780	0.421390	+	0.906880i	$0.361542\pi$
$840$	−381.330	−0.0156633
$841$	45802.9	1.87801
$842$	−21962.9	−0.898923
$843$	48183.4	1.96859
$844$	15360.0	0.626436
$845$	−51194.2	−2.08418
$846$	2190.22	0.0890085
$847$	−989.745	−0.0401512
$848$	17216.6	0.697195
$849$	42876.2	1.73322
$850$	4156.82	0.167738
$851$	−13865.9	−0.558538
$852$	46438.3	1.86731
$853$	31547.1	1.26630	0.633149	−	0.774030i	$-0.281762\pi$
$853$	31547.1	1.26630	0.633149	+	0.774030i	$0.281762\pi$
$854$	445.188	0.0178384
$855$	−11679.1	−0.467156
$856$	−5686.75	−0.227067
$857$	7044.06	0.280771	0.140385	−	0.990097i	$-0.455166\pi$
$857$	7044.06	0.280771	0.140385	+	0.990097i	$0.455166\pi$
$858$	37096.3	1.47605
$859$	6718.61	0.266864	0.133432	−	0.991058i	$-0.457400\pi$
$859$	6718.61	0.266864	0.133432	+	0.991058i	$0.457400\pi$
$860$	20079.7	0.796176
$861$	2517.65	0.0996529
$862$	−29899.1	−1.18140
$863$	−21216.3	−0.836863	−0.418431	−	0.908248i	$-0.637420\pi$
$863$	−21216.3	−0.836863	−0.418431	+	0.908248i	$0.637420\pi$
$864$	26476.8	1.04255
$865$	−20899.2	−0.821497
$866$	−61678.3	−2.42022
$867$	24926.5	0.976411
$868$	85.4643	0.00334199
$869$	7769.35	0.303288
$870$	64530.8	2.51471
$871$	22717.7	0.883765
$872$	4582.06	0.177945
$873$	−14519.2	−0.562888
$874$	−21077.0	−0.815720
$875$	1424.80	0.0550479
$876$	−157.749	−0.00608430
$877$	34202.5	1.31692	0.658458	−	0.752617i	$-0.271209\pi$
$877$	34202.5	1.31692	0.658458	+	0.752617i	$0.271209\pi$
$878$	−40030.6	−1.53869
$879$	−47893.1	−1.83776
$880$	−7580.04	−0.290367
$881$	−36599.5	−1.39962	−0.699811	−	0.714328i	$-0.746733\pi$
$881$	−36599.5	−1.39962	−0.699811	+	0.714328i	$0.746733\pi$
$882$	14537.4	0.554989
$883$	−21908.3	−0.834964	−0.417482	−	0.908685i	$-0.637087\pi$
$883$	−21908.3	−0.834964	−0.417482	+	0.908685i	$0.637087\pi$
$884$	−24116.6	−0.917567
$885$	−21497.1	−0.816516
$886$	−22317.6	−0.846245
$887$	−51532.2	−1.95071	−0.975356	−	0.220638i	$-0.929186\pi$
$887$	−51532.2	−1.95071	−0.975356	+	0.220638i	$0.929186\pi$
$888$	−14336.8	−0.541792
$889$	−2085.50	−0.0786788
$890$	−56234.0	−2.11794
$891$	14973.7	0.563005
$892$	−33881.7	−1.27180
$893$	−6259.84	−0.234577
$894$	59849.4	2.23900
$895$	−26680.1	−0.996443
$896$	824.018	0.0307238
$897$	21896.6	0.815056
$898$	1111.88	0.0413184
$899$	−2494.36	−0.0925378
$900$	−3372.83	−0.124920
$901$	−10303.6	−0.380981
$902$	−30787.8	−1.13650
$903$	1249.00	0.0460288
$904$	−6039.06	−0.222186
$905$	−4453.16	−0.163567
$906$	−38609.2	−1.41579
$907$	33617.9	1.23072	0.615361	−	0.788246i	$-0.289010\pi$
$907$	33617.9	1.23072	0.615361	+	0.788246i	$0.289010\pi$
$908$	−13903.9	−0.508168
$909$	11457.5	0.418064
$910$	−3268.47	−0.119065
$911$	19741.3	0.717956	0.358978	−	0.933346i	$-0.383125\pi$
$911$	19741.3	0.717956	0.358978	+	0.933346i	$0.383125\pi$
$912$	35424.2	1.28620
$913$	−24888.7	−0.902185
$914$	20076.4	0.726553
$915$	−6536.31	−0.236157
$916$	−4849.09	−0.174911
$917$	−1100.69	−0.0396379
$918$	−12393.2	−0.445574
$919$	40191.8	1.44266	0.721331	−	0.692591i	$-0.243531\pi$
$919$	40191.8	1.44266	0.721331	+	0.692591i	$0.243531\pi$
$920$	2752.52	0.0986390
$921$	−35724.4	−1.27813
$922$	23707.0	0.846798
$923$	68648.0	2.44808
$924$	920.272	0.0327648
$925$	11589.8	0.411968
$926$	−67724.8	−2.40343
$927$	−4219.38	−0.149496
$928$	−68174.6	−2.41157
$929$	−53517.9	−1.89006	−0.945030	−	0.326984i	$-0.893968\pi$
$929$	−53517.9	−1.89006	−0.945030	+	0.326984i	$0.893968\pi$
$930$	−2293.19	−0.0808565
$931$	−41549.3	−1.46265
$932$	−32730.1	−1.15033
$933$	−34597.2	−1.21400
$934$	16428.9	0.575555
$935$	4536.42	0.158671
$936$	6167.70	0.215382
$937$	5281.42	0.184137	0.0920686	−	0.995753i	$-0.470652\pi$
$937$	5281.42	0.184137	0.0920686	+	0.995753i	$0.470652\pi$
$938$	1029.95	0.0358517
$939$	55284.8	1.92135
$940$	4739.99	0.164470
$941$	−33250.2	−1.15189	−0.575944	−	0.817489i	$-0.695365\pi$
$941$	−33250.2	−1.15189	−0.575944	+	0.817489i	$0.695365\pi$
$942$	−34645.2	−1.19830
$943$	−18172.9	−0.627561
$944$	17762.8	0.612425
$945$	−919.068	−0.0316373
$946$	−15273.7	−0.524938
$947$	−6563.53	−0.225223	−0.112612	−	0.993639i	$-0.535922\pi$
$947$	−6563.53	−0.225223	−0.112612	+	0.993639i	$0.535922\pi$
$948$	27493.3	0.941921
$949$	−233.195	−0.00797663
$950$	17617.2	0.601660
$951$	−50415.9	−1.71908
$952$	−188.571	−0.00641977
$953$	3534.69	0.120147	0.0600734	−	0.998194i	$-0.480867\pi$
$953$	3534.69	0.120147	0.0600734	+	0.998194i	$0.480867\pi$
$954$	15278.8	0.518521
$955$	−9738.99	−0.329996
$956$	−68885.5	−2.33046
$957$	−26859.0	−0.907240
$958$	3608.13	0.121684
$959$	−534.063	−0.0179831
$960$	−40479.0	−1.36089
$961$	−29702.4	−0.997025
$962$	−122884.	−4.11845
$963$	8203.36	0.274506
$964$	−19712.0	−0.658590
$965$	28940.4	0.965415
$966$	992.720	0.0330644
$967$	−29760.4	−0.989689	−0.494845	−	0.868981i	$-0.664775\pi$
$967$	−29760.4	−0.989689	−0.494845	+	0.868981i	$0.664775\pi$
$968$	7386.82	0.245270
$969$	−21200.3	−0.702840
$970$	−57424.8	−1.90082
$971$	1374.22	0.0454180	0.0227090	−	0.999742i	$-0.492771\pi$
$971$	1374.22	0.0454180	0.0227090	+	0.999742i	$0.492771\pi$
$972$	26130.3	0.862274
$973$	−837.672	−0.0275997
$974$	−56107.3	−1.84578
$975$	−18302.3	−0.601171
$976$	5400.87	0.177129
$977$	53237.7	1.74332	0.871661	−	0.490109i	$-0.163043\pi$
$977$	53237.7	1.74332	0.871661	+	0.490109i	$0.163043\pi$
$978$	80682.1	2.63797
$979$	23405.7	0.764095
$980$	31461.4	1.02551
$981$	−6609.81	−0.215122
$982$	49030.7	1.59331
$983$	−31580.2	−1.02467	−0.512335	−	0.858786i	$-0.671219\pi$
$983$	−31580.2	−1.02467	−0.512335	+	0.858786i	$0.671219\pi$
$984$	−18790.1	−0.608746
$985$	−10500.5	−0.339667
$986$	31911.0	1.03068
$987$	294.837	0.00950837
$988$	−102210.	−3.29122
$989$	−9015.51	−0.289865
$990$	−6726.86	−0.215953
$991$	−30939.6	−0.991753	−0.495877	−	0.868393i	$-0.665153\pi$
$991$	−30939.6	−0.991753	−0.495877	+	0.868393i	$0.665153\pi$
$992$	2422.67	0.0775402
$993$	43919.6	1.40357
$994$	3112.28	0.0993114
$995$	18373.2	0.585396
$996$	−88073.3	−2.80192
$997$	23213.0	0.737375	0.368687	−	0.929553i	$-0.379807\pi$
$997$	23213.0	0.737375	0.368687	+	0.929553i	$0.379807\pi$
$998$	−24139.1	−0.765641
$999$	−34554.0	−1.09434

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	787.4.a.b.1.17	✓	103

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
787.4.a.b.1.17	✓	103	1.1	even	1	trivial

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 787 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	787.a (trivial)

\(f(q)\)	\(=\)	\(q-4.20325 q^{2} -6.09175 q^{3} +9.66730 q^{4} -9.51255 q^{5} +25.6051 q^{6} +0.938997 q^{7} -7.00807 q^{8} +10.1094 q^{9} +39.9836 q^{10} -16.6420 q^{11} -58.8908 q^{12} -87.0560 q^{13} -3.94684 q^{14} +57.9480 q^{15} -47.8817 q^{16} +28.6558 q^{17} -42.4924 q^{18} +121.447 q^{19} -91.9606 q^{20} -5.72013 q^{21} +69.9503 q^{22} +41.2891 q^{23} +42.6914 q^{24} -34.5115 q^{25} +365.918 q^{26} +102.893 q^{27} +9.07756 q^{28} -264.938 q^{29} -243.570 q^{30} +9.41489 q^{31} +257.323 q^{32} +101.379 q^{33} -120.447 q^{34} -8.93225 q^{35} +97.7308 q^{36} -335.824 q^{37} -510.473 q^{38} +530.324 q^{39} +66.6646 q^{40} -440.138 q^{41} +24.0431 q^{42} -218.351 q^{43} -160.883 q^{44} -96.1663 q^{45} -173.548 q^{46} -51.5437 q^{47} +291.684 q^{48} -342.118 q^{49} +145.060 q^{50} -174.564 q^{51} -841.597 q^{52} -359.565 q^{53} -432.486 q^{54} +158.307 q^{55} -6.58055 q^{56} -739.827 q^{57} +1113.60 q^{58} -370.972 q^{59} +560.201 q^{60} -112.796 q^{61} -39.5731 q^{62} +9.49271 q^{63} -698.540 q^{64} +828.125 q^{65} -426.120 q^{66} -260.955 q^{67} +277.024 q^{68} -251.523 q^{69} +37.5445 q^{70} -788.550 q^{71} -70.8475 q^{72} +2.67867 q^{73} +1411.55 q^{74} +210.235 q^{75} +1174.07 q^{76} -15.6268 q^{77} -2229.08 q^{78} -466.853 q^{79} +455.477 q^{80} -899.754 q^{81} +1850.01 q^{82} +1495.54 q^{83} -55.2982 q^{84} -272.589 q^{85} +917.783 q^{86} +1613.93 q^{87} +116.628 q^{88} -1406.43 q^{89} +404.211 q^{90} -81.7454 q^{91} +399.154 q^{92} -57.3532 q^{93} +216.651 q^{94} -1155.27 q^{95} -1567.55 q^{96} -1436.21 q^{97} +1438.01 q^{98} -168.241 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 103 q + 27 q^{2} + 25 q^{3} + 439 q^{4} + 169 q^{5} + 45 q^{6} + 80 q^{7} + 327 q^{8} + 1114 q^{9} + 61 q^{10} + 241 q^{11} + 264 q^{12} + 291 q^{13} + 341 q^{14} + 278 q^{15} + 2003 q^{16} + 504 q^{17}+ \cdots + 6933 q^{99}+O(q^{100}) \) 103 * q + 27 * q^2 + 25 * q^3 + 439 * q^4 + 169 * q^5 + 45 * q^6 + 80 * q^7 + 327 * q^8 + 1114 * q^9 + 61 * q^10 + 241 * q^11 + 264 * q^12 + 291 * q^13 + 341 * q^14 + 278 * q^15 + 2003 * q^16 + 504 * q^17 + 857 * q^18 + 157 * q^19 + 1459 * q^20 + 588 * q^21 + 706 * q^22 + 1310 * q^23 + 815 * q^24 + 3342 * q^25 + 847 * q^26 + 784 * q^27 + 1260 * q^28 + 1587 * q^29 + 684 * q^30 + 686 * q^31 + 3398 * q^32 + 1528 * q^33 + 522 * q^34 + 1328 * q^35 + 6172 * q^36 + 2351 * q^37 + 1601 * q^38 + 1194 * q^39 + 582 * q^40 + 1584 * q^41 + 1074 * q^42 + 737 * q^43 + 2391 * q^44 + 3939 * q^45 + 746 * q^46 + 3424 * q^47 + 2278 * q^48 + 6527 * q^49 + 3051 * q^50 + 1150 * q^51 + 1588 * q^52 + 6855 * q^53 + 1809 * q^54 + 1564 * q^55 + 2549 * q^56 + 3448 * q^57 + 2786 * q^58 + 3511 * q^59 + 2701 * q^60 + 2465 * q^61 + 4001 * q^62 + 2984 * q^63 + 10803 * q^64 + 5576 * q^65 + 22 * q^66 + 2379 * q^67 + 5133 * q^68 + 2540 * q^69 + 2002 * q^70 + 4756 * q^71 + 8442 * q^72 + 4522 * q^73 + 2744 * q^74 + 5077 * q^75 + 2280 * q^76 + 10830 * q^77 + 3891 * q^78 + 2022 * q^79 + 10184 * q^80 + 14275 * q^81 + 2590 * q^82 + 7541 * q^83 + 4671 * q^84 + 8112 * q^85 + 3825 * q^86 + 4814 * q^87 + 6617 * q^88 + 5956 * q^89 + 3777 * q^90 + 2862 * q^91 + 15806 * q^92 + 15612 * q^93 - 881 * q^94 + 6664 * q^95 + 9772 * q^96 + 4374 * q^97 + 11934 * q^98 + 6933 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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