LMFDB - Embedded newform 2023.4.a.v.1.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2023,4,Mod(1,2023)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2023, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2023.1"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 2023 = 7 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2023.a (trivial)

Newform invariants

comment:select newform

sage:traces = [56,8,24,240,80,68] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	yes
Analytic conductor:	$119.360863942$
Analytic rank:	$0$
Dimension:	$56$
Twist minimal:	no (minimal twist has level 119)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	2023.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.82994 q^{2} -6.04539 q^{3} +0.00856474 q^{4} -19.0541 q^{5} +17.1081 q^{6} +7.00000 q^{7} +22.6153 q^{8} +9.54677 q^{9} +53.9220 q^{10} +12.4321 q^{11} -0.0517772 q^{12} -11.3957 q^{13} -19.8096 q^{14} +115.189 q^{15} -64.0684 q^{16} -27.0168 q^{18} +36.0415 q^{19} -0.163193 q^{20} -42.3177 q^{21} -35.1821 q^{22} +89.1121 q^{23} -136.718 q^{24} +238.059 q^{25} +32.2492 q^{26} +105.512 q^{27} +0.0599532 q^{28} +257.951 q^{29} -325.979 q^{30} +76.4937 q^{31} +0.387596 q^{32} -75.1569 q^{33} -133.379 q^{35} +0.0817656 q^{36} +217.753 q^{37} -101.995 q^{38} +68.8915 q^{39} -430.914 q^{40} +134.166 q^{41} +119.757 q^{42} +443.100 q^{43} +0.106478 q^{44} -181.905 q^{45} -252.182 q^{46} +529.146 q^{47} +387.319 q^{48} +49.0000 q^{49} -673.692 q^{50} -0.0976012 q^{52} +79.9294 q^{53} -298.592 q^{54} -236.882 q^{55} +158.307 q^{56} -217.885 q^{57} -729.985 q^{58} -529.638 q^{59} +0.986568 q^{60} +817.455 q^{61} -216.473 q^{62} +66.8274 q^{63} +511.451 q^{64} +217.135 q^{65} +212.690 q^{66} -940.437 q^{67} -538.718 q^{69} +377.454 q^{70} +604.979 q^{71} +215.903 q^{72} -493.233 q^{73} -616.227 q^{74} -1439.16 q^{75} +0.308686 q^{76} +87.0247 q^{77} -194.959 q^{78} +549.419 q^{79} +1220.77 q^{80} -895.622 q^{81} -379.682 q^{82} -127.880 q^{83} -0.362440 q^{84} -1253.95 q^{86} -1559.41 q^{87} +281.156 q^{88} -151.731 q^{89} +514.781 q^{90} -79.7699 q^{91} +0.763222 q^{92} -462.435 q^{93} -1497.45 q^{94} -686.739 q^{95} -2.34317 q^{96} -1086.93 q^{97} -138.667 q^{98} +118.686 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 8 q^{2} + 24 q^{3} + 240 q^{4} + 80 q^{5} + 68 q^{6} + 392 q^{7} + 96 q^{8} + 576 q^{9} + 80 q^{10} + 176 q^{11} + 288 q^{12} - 96 q^{13} + 56 q^{14} + 192 q^{15} + 1088 q^{16} + 216 q^{18} + 48 q^{19}+ \cdots + 6576 q^{99}+O(q^{100}) $ 56 * q + 8 * q^2 + 24 * q^3 + 240 * q^4 + 80 * q^5 + 68 * q^6 + 392 * q^7 + 96 * q^8 + 576 * q^9 + 80 * q^10 + 176 * q^11 + 288 * q^12 - 96 * q^13 + 56 * q^14 + 192 * q^15 + 1088 * q^16 + 216 * q^18 + 48 * q^19 + 1660 * q^20 + 168 * q^21 + 352 * q^22 + 608 * q^23 + 736 * q^24 + 1792 * q^25 + 864 * q^27 + 1680 * q^28 + 928 * q^29 - 100 * q^30 + 496 * q^31 + 436 * q^32 + 384 * q^33 + 560 * q^35 + 2804 * q^36 + 1392 * q^37 + 624 * q^39 - 1020 * q^40 + 2088 * q^41 + 476 * q^42 + 1312 * q^43 + 2112 * q^44 + 4840 * q^45 + 736 * q^46 + 5228 * q^48 + 2744 * q^49 + 2020 * q^50 - 1536 * q^52 + 1272 * q^53 + 2268 * q^54 - 336 * q^55 + 672 * q^56 + 2448 * q^57 + 1376 * q^58 + 2372 * q^60 + 976 * q^61 + 3776 * q^62 + 4032 * q^63 + 5376 * q^64 + 6080 * q^65 + 976 * q^67 + 1248 * q^69 + 560 * q^70 + 3216 * q^71 + 4532 * q^72 + 4088 * q^73 - 2456 * q^74 - 760 * q^75 - 2640 * q^76 + 1232 * q^77 + 3744 * q^78 + 1792 * q^79 + 13920 * q^80 + 4184 * q^81 + 8204 * q^82 - 2832 * q^83 + 2016 * q^84 + 4908 * q^86 + 832 * q^87 + 2424 * q^88 - 2768 * q^89 + 8660 * q^90 - 672 * q^91 + 6784 * q^92 + 784 * q^93 - 928 * q^94 + 4560 * q^95 + 6656 * q^96 + 9464 * q^97 + 392 * q^98 + 6576 * 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 $

$2$	−2.82994	−1.00054	−0.500268	−	0.865871i	$-0.666765\pi$
$2$	−2.82994	−1.00054	−0.500268	+	0.865871i	$0.666765\pi$
$3$	−6.04539	−1.16344	−0.581718	−	0.813390i	$-0.697619\pi$
$3$	−6.04539	−1.16344	−0.581718	+	0.813390i	$0.697619\pi$
$4$	0.00856474	0.00107059
$5$	−19.0541	−1.70425	−0.852125	−	0.523338i	$-0.824686\pi$
$5$	−19.0541	−1.70425	−0.852125	+	0.523338i	$0.824686\pi$
$6$	17.1081	1.16406
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	22.6153	0.999464
$9$	9.54677	0.353584
$10$	53.9220	1.70516
$11$	12.4321	0.340765	0.170383	−	0.985378i	$-0.445500\pi$
$11$	12.4321	0.340765	0.170383	+	0.985378i	$0.445500\pi$
$12$	−0.0517772	−0.00124557
$13$	−11.3957	−0.243123	−0.121561	−	0.992584i	$-0.538790\pi$
$13$	−11.3957	−0.243123	−0.121561	+	0.992584i	$0.538790\pi$
$14$	−19.8096	−0.378167
$15$	115.189	1.98279
$16$	−64.0684	−1.00107
$17$	0	0
$17$	0	0
$18$	−27.0168	−0.353773
$19$	36.0415	0.435184	0.217592	−	0.976040i	$-0.430180\pi$
$19$	36.0415	0.435184	0.217592	+	0.976040i	$0.430180\pi$
$20$	−0.163193	−0.00182456
$21$	−42.3177	−0.439738
$22$	−35.1821	−0.340948
$23$	89.1121	0.807876	0.403938	−	0.914786i	$-0.367641\pi$
$23$	89.1121	0.807876	0.403938	+	0.914786i	$0.367641\pi$
$24$	−136.718	−1.16281
$25$	238.059	1.90447
$26$	32.2492	0.243253
$27$	105.512	0.752064
$28$	0.0599532	0.000404646 0
$29$	257.951	1.65173	0.825866	−	0.563866i	$-0.190687\pi$
$29$	257.951	1.65173	0.825866	+	0.563866i	$0.190687\pi$
$30$	−325.979	−1.98385
$31$	76.4937	0.443183	0.221592	−	0.975140i	$-0.428875\pi$
$31$	76.4937	0.443183	0.221592	+	0.975140i	$0.428875\pi$
$32$	0.387596	0.00214118
$33$	−75.1569	−0.396459
$34$	0	0
$35$	−133.379	−0.644146
$36$	0.0817656	0.000378544 0
$37$	217.753	0.967523	0.483761	−	0.875200i	$-0.339270\pi$
$37$	217.753	0.967523	0.483761	+	0.875200i	$0.339270\pi$
$38$	−101.995	−0.435417
$39$	68.8915	0.282858
$40$	−430.914	−1.70334
$41$	134.166	0.511053	0.255527	−	0.966802i	$-0.417751\pi$
$41$	134.166	0.511053	0.255527	+	0.966802i	$0.417751\pi$
$42$	119.757	0.439973
$43$	443.100	1.57144	0.785722	−	0.618579i	$-0.212291\pi$
$43$	443.100	1.57144	0.785722	+	0.618579i	$0.212291\pi$
$44$	0.106478	0.000364821 0
$45$	−181.905	−0.602596
$46$	−252.182	−0.808309
$47$	529.146	1.64221	0.821105	−	0.570777i	$-0.193358\pi$
$47$	529.146	1.64221	0.821105	+	0.570777i	$0.193358\pi$
$48$	387.319	1.16468
$49$	49.0000	0.142857
$50$	−673.692	−1.90549
$51$	0	0
$52$	−0.0976012	−0.000260286 0
$53$	79.9294	0.207154	0.103577	−	0.994621i	$-0.466971\pi$
$53$	79.9294	0.207154	0.103577	+	0.994621i	$0.466971\pi$
$54$	−298.592	−0.752466
$55$	−236.882	−0.580749
$56$	158.307	0.377762
$57$	−217.885	−0.506309
$58$	−729.985	−1.65262
$59$	−529.638	−1.16869	−0.584347	−	0.811504i	$-0.698649\pi$
$59$	−529.638	−1.16869	−0.584347	+	0.811504i	$0.698649\pi$
$60$	0.986568	0.00212276
$61$	817.455	1.71581	0.857905	−	0.513809i	$-0.171766\pi$
$61$	817.455	1.71581	0.857905	+	0.513809i	$0.171766\pi$
$62$	−216.473	−0.443420
$63$	66.8274	0.133642
$64$	511.451	0.998927
$65$	217.135	0.414342
$66$	212.690	0.396671
$67$	−940.437	−1.71482	−0.857408	−	0.514637i	$-0.827927\pi$
$67$	−940.437	−1.71482	−0.857408	+	0.514637i	$0.827927\pi$
$68$	0	0
$69$	−538.718	−0.939913
$70$	377.454	0.644491
$71$	604.979	1.01124	0.505618	−	0.862757i	$-0.331264\pi$
$71$	604.979	1.01124	0.505618	+	0.862757i	$0.331264\pi$
$72$	215.903	0.353395
$73$	−493.233	−0.790802	−0.395401	−	0.918509i	$-0.629394\pi$
$73$	−493.233	−0.790802	−0.395401	+	0.918509i	$0.629394\pi$
$74$	−616.227	−0.968040
$75$	−1439.16	−2.21573
$76$	0.308686	0.000465905 0
$77$	87.0247	0.128797
$78$	−194.959	−0.283009
$79$	549.419	0.782462	0.391231	−	0.920292i	$-0.372049\pi$
$79$	549.419	0.782462	0.391231	+	0.920292i	$0.372049\pi$
$80$	1220.77	1.70607
$81$	−895.622	−1.22856
$82$	−379.682	−0.511327
$83$	−127.880	−0.169116	−0.0845580	−	0.996419i	$-0.526948\pi$
$83$	−127.880	−0.169116	−0.0845580	+	0.996419i	$0.526948\pi$
$84$	−0.362440	−0.000470780 0
$85$	0	0
$86$	−1253.95	−1.57229
$87$	−1559.41	−1.92169
$88$	281.156	0.340583
$89$	−151.731	−0.180713	−0.0903566	−	0.995909i	$-0.528801\pi$
$89$	−151.731	−0.180713	−0.0903566	+	0.995909i	$0.528801\pi$
$90$	514.781	0.602918
$91$	−79.7699	−0.0918918
$92$	0.763222	0.000864906 0
$93$	−462.435	−0.515615
$94$	−1497.45	−1.64309
$95$	−686.739	−0.741662
$96$	−2.34317	−0.00249113
$97$	−1086.93	−1.13774	−0.568870	−	0.822427i	$-0.692619\pi$
$97$	−1086.93	−1.13774	−0.568870	+	0.822427i	$0.692619\pi$
$98$	−138.667	−0.142934
$99$	118.686	0.120489
$100$	2.03891	0.00203891
$101$	−1170.18	−1.15285	−0.576424	−	0.817151i	$-0.695552\pi$
$101$	−1170.18	−1.15285	−0.576424	+	0.817151i	$0.695552\pi$
$102$	0	0
$103$	124.416	0.119020	0.0595100	−	0.998228i	$-0.481046\pi$
$103$	124.416	0.119020	0.0595100	+	0.998228i	$0.481046\pi$
$104$	−257.717	−0.242993
$105$	806.326	0.749423
$106$	−226.196	−0.207265
$107$	485.260	0.438428	0.219214	−	0.975677i	$-0.429651\pi$
$107$	485.260	0.438428	0.219214	+	0.975677i	$0.429651\pi$
$108$	0.903680	0.000805154 0
$109$	760.519	0.668298	0.334149	−	0.942520i	$-0.391551\pi$
$109$	760.519	0.668298	0.334149	+	0.942520i	$0.391551\pi$
$110$	670.363	0.581060
$111$	−1316.40	−1.12565
$112$	−448.479	−0.378369
$113$	150.053	0.124919	0.0624593	−	0.998048i	$-0.480106\pi$
$113$	150.053	0.124919	0.0624593	+	0.998048i	$0.480106\pi$
$114$	616.602	0.506580
$115$	−1697.95	−1.37682
$116$	2.20928	0.00176833
$117$	−108.792	−0.0859644
$118$	1498.84	1.16932
$119$	0	0
$120$	2605.04	1.98172
$121$	−1176.44	−0.883879
$122$	−2313.35	−1.71673
$123$	−811.085	−0.594578
$124$	0.655149	0.000474469 0
$125$	−2154.23	−1.54144
$126$	−189.118	−0.133714
$127$	−138.570	−0.0968194	−0.0484097	−	0.998828i	$-0.515415\pi$
$127$	−138.570	−0.0968194	−0.0484097	+	0.998828i	$0.515415\pi$
$128$	−1450.48	−1.00160
$129$	−2678.71	−1.82828
$130$	−614.478	−0.414564
$131$	−526.333	−0.351038	−0.175519	−	0.984476i	$-0.556160\pi$
$131$	−526.333	−0.351038	−0.175519	+	0.984476i	$0.556160\pi$
$132$	−0.643700	−0.000424446 0
$133$	252.291	0.164484
$134$	2661.38	1.71573
$135$	−2010.43	−1.28170
$136$	0	0
$137$	1482.24	0.924353	0.462177	−	0.886788i	$-0.347069\pi$
$137$	1482.24	0.924353	0.462177	+	0.886788i	$0.347069\pi$
$138$	1524.54	0.940416
$139$	1941.51	1.18473	0.592364	−	0.805671i	$-0.298195\pi$
$139$	1941.51	1.18473	0.592364	+	0.805671i	$0.298195\pi$
$140$	−1.14235	−0.000689618 0
$141$	−3198.90	−1.91061
$142$	−1712.05	−1.01178
$143$	−141.672	−0.0828479
$144$	−611.647	−0.353962
$145$	−4915.02	−2.81497
$146$	1395.82	0.791225
$147$	−296.224	−0.166205
$148$	1.86500	0.00103582
$149$	2555.91	1.40529	0.702645	−	0.711541i	$-0.252002\pi$
$149$	2555.91	1.40529	0.702645	+	0.711541i	$0.252002\pi$
$150$	4072.73	2.21691
$151$	2684.62	1.44683	0.723415	−	0.690413i	$-0.242571\pi$
$151$	2684.62	1.44683	0.723415	+	0.690413i	$0.242571\pi$
$152$	815.090	0.434951
$153$	0	0
$154$	−246.275	−0.128866
$155$	−1457.52	−0.755295
$156$	0.590038	0.000302826 0
$157$	2096.12	1.06553	0.532767	−	0.846262i	$-0.321152\pi$
$157$	2096.12	1.06553	0.532767	+	0.846262i	$0.321152\pi$
$158$	−1554.82	−0.782881
$159$	−483.205	−0.241010
$160$	−7.38529	−0.00364911
$161$	623.785	0.305349
$162$	2534.56	1.22922
$163$	2154.64	1.03537	0.517683	−	0.855573i	$-0.326795\pi$
$163$	2154.64	1.03537	0.517683	+	0.855573i	$0.326795\pi$
$164$	1.14910	0.000547130 0
$165$	1432.05	0.675665
$166$	361.892	0.169207
$167$	2039.70	0.945132	0.472566	−	0.881295i	$-0.343328\pi$
$167$	2039.70	0.945132	0.472566	+	0.881295i	$0.343328\pi$
$168$	−957.028	−0.439502
$169$	−2067.14	−0.940891
$170$	0	0
$171$	344.080	0.153874
$172$	3.79504	0.00168238
$173$	2586.41	1.13665	0.568326	−	0.822803i	$-0.307591\pi$
$173$	2586.41	1.13665	0.568326	+	0.822803i	$0.307591\pi$
$174$	4413.05	1.92271
$175$	1666.41	0.719821
$176$	−796.505	−0.341130
$177$	3201.87	1.35970
$178$	429.390	0.180810
$179$	791.869	0.330654	0.165327	−	0.986239i	$-0.447132\pi$
$179$	791.869	0.330654	0.165327	+	0.986239i	$0.447132\pi$
$180$	−1.55797	−0.000645134 0
$181$	113.864	0.0467592	0.0233796	−	0.999727i	$-0.492557\pi$
$181$	113.864	0.0467592	0.0233796	+	0.999727i	$0.492557\pi$
$182$	225.744	0.0919410
$183$	−4941.84	−1.99624
$184$	2015.30	0.807443
$185$	−4149.08	−1.64890
$186$	1308.66	0.515891
$187$	0	0
$188$	4.53200	0.00175814
$189$	738.581	0.284253
$190$	1943.43	0.742059
$191$	3370.96	1.27704	0.638518	−	0.769607i	$-0.279548\pi$
$191$	3370.96	1.27704	0.638518	+	0.769607i	$0.279548\pi$
$192$	−3091.92	−1.16219
$193$	−4458.03	−1.66267	−0.831337	−	0.555768i	$-0.812424\pi$
$193$	−4458.03	−1.66267	−0.831337	+	0.555768i	$0.812424\pi$
$194$	3075.94	1.13835
$195$	−1312.66	−0.482061
$196$	0.419672	0.000152942 0
$197$	−1801.60	−0.651568	−0.325784	−	0.945444i	$-0.605628\pi$
$197$	−1801.60	−0.651568	−0.325784	+	0.945444i	$0.605628\pi$
$198$	−335.875	−0.120554
$199$	691.389	0.246288	0.123144	−	0.992389i	$-0.460702\pi$
$199$	691.389	0.246288	0.123144	+	0.992389i	$0.460702\pi$
$200$	5383.76	1.90345
$201$	5685.31	1.99508
$202$	3311.55	1.15346
$203$	1805.65	0.624296
$204$	0	0
$205$	−2556.41	−0.870963
$206$	−352.089	−0.119084
$207$	850.733	0.285652
$208$	730.105	0.243383
$209$	448.072	0.148296
$210$	−2281.86	−0.749824
$211$	766.819	0.250190	0.125095	−	0.992145i	$-0.460076\pi$
$211$	766.819	0.250190	0.125095	+	0.992145i	$0.460076\pi$
$212$	0.684575	0.000221777 0
$213$	−3657.33	−1.17651
$214$	−1373.26	−0.438663
$215$	−8442.87	−2.67814
$216$	2386.18	0.751661
$217$	535.456	0.167507
$218$	−2152.22	−0.668656
$219$	2981.79	0.920048
$220$	−2.02884	−0.000621746 0
$221$	0	0
$222$	3725.34	1.12625
$223$	3683.10	1.10600	0.553001	−	0.833181i	$-0.313483\pi$
$223$	3683.10	1.10600	0.553001	+	0.833181i	$0.313483\pi$
$224$	2.71317	0.000809291 0
$225$	2272.69	0.673390
$226$	−424.641	−0.124985
$227$	4616.68	1.34987	0.674934	−	0.737878i	$-0.264172\pi$
$227$	4616.68	1.34987	0.674934	+	0.737878i	$0.264172\pi$
$228$	−1.86613	−0.000542050 0
$229$	−4567.90	−1.31815	−0.659073	−	0.752079i	$-0.729051\pi$
$229$	−4567.90	−1.31815	−0.659073	+	0.752079i	$0.729051\pi$
$230$	4805.10	1.37756
$231$	−526.098	−0.149847
$232$	5833.63	1.65085
$233$	−3635.14	−1.02209	−0.511043	−	0.859555i	$-0.670741\pi$
$233$	−3635.14	−1.02209	−0.511043	+	0.859555i	$0.670741\pi$
$234$	307.875	0.0860104
$235$	−10082.4	−2.79874
$236$	−4.53621	−0.00125120
$237$	−3321.46	−0.910345
$238$	0	0
$239$	4513.28	1.22151	0.610753	−	0.791821i	$-0.290867\pi$
$239$	4513.28	1.22151	0.610753	+	0.791821i	$0.290867\pi$
$240$	−7380.01	−1.98491
$241$	81.8676	0.0218820	0.0109410	−	0.999940i	$-0.496517\pi$
$241$	81.8676	0.0218820	0.0109410	+	0.999940i	$0.496517\pi$
$242$	3329.26	0.884352
$243$	2565.57	0.677290
$244$	7.00129	0.00183693
$245$	−933.651	−0.243464
$246$	2295.32	0.594896
$247$	−410.719	−0.105803
$248$	1729.93	0.442946
$249$	773.084	0.196756
$250$	6096.34	1.54227
$251$	−2491.54	−0.626551	−0.313275	−	0.949662i	$-0.601426\pi$
$251$	−2491.54	−0.626551	−0.313275	+	0.949662i	$0.601426\pi$
$252$	0.572359	0.000143076 0
$253$	1107.85	0.275296
$254$	392.144	0.0968712
$255$	0	0
$256$	13.1554	0.00321177
$257$	102.802	0.0249518	0.0124759	−	0.999922i	$-0.496029\pi$
$257$	102.802	0.0249518	0.0124759	+	0.999922i	$0.496029\pi$
$258$	7580.60	1.82925
$259$	1524.27	0.365689
$260$	1.85970	0.000443592 0
$261$	2462.60	0.584026
$262$	1489.49	0.351226
$263$	3365.35	0.789037	0.394518	−	0.918888i	$-0.370911\pi$
$263$	3365.35	0.789037	0.394518	+	0.918888i	$0.370911\pi$
$264$	−1699.70	−0.396246
$265$	−1522.98	−0.353042
$266$	−713.968	−0.164572
$267$	917.274	0.210248
$268$	−8.05460	−0.00183587
$269$	−7194.88	−1.63078	−0.815390	−	0.578912i	$-0.803477\pi$
$269$	−7194.88	−1.63078	−0.815390	+	0.578912i	$0.803477\pi$
$270$	5689.39	1.28239
$271$	−2609.90	−0.585019	−0.292510	−	0.956263i	$-0.594490\pi$
$271$	−2609.90	−0.585019	−0.292510	+	0.956263i	$0.594490\pi$
$272$	0	0
$273$	482.240	0.106910
$274$	−4194.66	−0.924848
$275$	2959.57	0.648977
$276$	−4.61398	−0.00100626
$277$	4920.27	1.06726	0.533628	−	0.845719i	$-0.320828\pi$
$277$	4920.27	1.06726	0.533628	+	0.845719i	$0.320828\pi$
$278$	−5494.37	−1.18536
$279$	730.268	0.156703
$280$	−3016.40	−0.643801
$281$	5288.45	1.12271	0.561356	−	0.827574i	$-0.310280\pi$
$281$	5288.45	1.12271	0.561356	+	0.827574i	$0.310280\pi$
$282$	9052.69	1.91163
$283$	−1232.53	−0.258891	−0.129445	−	0.991587i	$-0.541320\pi$
$283$	−1232.53	−0.258891	−0.129445	+	0.991587i	$0.541320\pi$
$284$	5.18149	0.00108262
$285$	4151.61	0.862877
$286$	400.925	0.0828922
$287$	939.161	0.193160
$288$	3.70029	0.000757089 0
$289$	0	0
$290$	13909.2	2.81647
$291$	6570.91	1.32369
$292$	−4.22441	−0.000846627 0
$293$	7435.36	1.48252	0.741260	−	0.671218i	$-0.234229\pi$
$293$	7435.36	1.48252	0.741260	+	0.671218i	$0.234229\pi$
$294$	838.297	0.166294
$295$	10091.8	1.99175
$296$	4924.54	0.967004
$297$	1311.73	0.256277
$298$	−7233.07	−1.40604
$299$	−1015.49	−0.196413
$300$	−12.3260	−0.00237214
$301$	3101.70	0.593950
$302$	−7597.32	−1.44760
$303$	7074.22	1.34126
$304$	−2309.13	−0.435649
$305$	−15575.9	−2.92417
$306$	0	0
$307$	−10355.6	−1.92516	−0.962578	−	0.271004i	$-0.912644\pi$
$307$	−10355.6	−1.92516	−0.962578	+	0.271004i	$0.912644\pi$
$308$	0.745344	0.000137889 0
$309$	−752.143	−0.138472
$310$	4124.69	0.755699
$311$	9478.42	1.72821	0.864103	−	0.503316i	$-0.167887\pi$
$311$	9478.42	1.72821	0.864103	+	0.503316i	$0.167887\pi$
$312$	1558.00	0.282706
$313$	1855.50	0.335077	0.167538	−	0.985866i	$-0.446418\pi$
$313$	1855.50	0.335077	0.167538	+	0.985866i	$0.446418\pi$
$314$	−5931.90	−1.06610
$315$	−1273.34	−0.227760
$316$	4.70563	0.000837698 0
$317$	−2184.14	−0.386983	−0.193491	−	0.981102i	$-0.561981\pi$
$317$	−2184.14	−0.386983	−0.193491	+	0.981102i	$0.561981\pi$
$318$	1367.44	0.241139
$319$	3206.87	0.562853
$320$	−9745.23	−1.70242
$321$	−2933.59	−0.510084
$322$	−1765.27	−0.305512
$323$	0	0
$324$	−7.67077	−0.00131529
$325$	−2712.84	−0.463020
$326$	−6097.51	−1.03592
$327$	−4597.64	−0.777523
$328$	3034.20	0.510780
$329$	3704.02	0.620697
$330$	−4052.61	−0.676027
$331$	−11621.0	−1.92975	−0.964875	−	0.262710i	$-0.915384\pi$
$331$	−11621.0	−1.92975	−0.964875	+	0.262710i	$0.915384\pi$
$332$	−1.09526	−0.000181054 0
$333$	2078.84	0.342101
$334$	−5772.24	−0.945638
$335$	17919.2	2.92248
$336$	2711.23	0.440208
$337$	1359.52	0.219757	0.109878	−	0.993945i	$-0.464954\pi$
$337$	1359.52	0.219757	0.109878	+	0.993945i	$0.464954\pi$
$338$	5849.88	0.941395
$339$	−907.130	−0.145335
$340$	0	0
$341$	950.978	0.151021
$342$	−973.727	−0.153956
$343$	343.000	0.0539949
$344$	10020.8	1.57060
$345$	10264.8	1.60185
$346$	−7319.38	−1.13726
$347$	−5430.63	−0.840148	−0.420074	−	0.907490i	$-0.637996\pi$
$347$	−5430.63	−0.840148	−0.420074	+	0.907490i	$0.637996\pi$
$348$	−13.3560	−0.00205734
$349$	11091.4	1.70118	0.850588	−	0.525833i	$-0.176246\pi$
$349$	11091.4	1.70118	0.850588	+	0.525833i	$0.176246\pi$
$350$	−4715.84	−0.720207
$351$	−1202.38	−0.182844
$352$	4.81863	0.000729641 0
$353$	−12189.8	−1.83796	−0.918978	−	0.394309i	$-0.870984\pi$
$353$	−12189.8	−1.83796	−0.918978	+	0.394309i	$0.870984\pi$
$354$	−9061.10	−1.36043
$355$	−11527.3	−1.72340
$356$	−1.29954	−0.000193470 0
$357$	0	0
$358$	−2240.94	−0.330831
$359$	445.787	0.0655369	0.0327685	−	0.999463i	$-0.489568\pi$
$359$	445.787	0.0655369	0.0327685	+	0.999463i	$0.489568\pi$
$360$	−4113.84	−0.602273
$361$	−5560.01	−0.810615
$362$	−322.227	−0.0467842
$363$	7112.06	1.02834
$364$	−0.683208	−9.83787e−5 0
$365$	9398.11	1.34772
$366$	13985.1	1.99730
$367$	−7190.02	−1.02266	−0.511330	−	0.859384i	$-0.670847\pi$
$367$	−7190.02	−1.02266	−0.511330	+	0.859384i	$0.670847\pi$
$368$	−5709.27	−0.808740
$369$	1280.85	0.180700
$370$	11741.7	1.64978
$371$	559.506	0.0782968
$372$	−3.96063	−0.000552014 0
$373$	−9755.17	−1.35416	−0.677082	−	0.735907i	$-0.736756\pi$
$373$	−9755.17	−1.35416	−0.677082	+	0.735907i	$0.736756\pi$
$374$	0	0
$375$	13023.2	1.79337
$376$	11966.8	1.64133
$377$	−2939.53	−0.401574
$378$	−2090.14	−0.284406
$379$	1130.46	0.153213	0.0766064	−	0.997061i	$-0.475592\pi$
$379$	1130.46	0.153213	0.0766064	+	0.997061i	$0.475592\pi$
$380$	−5.88174	−0.000794018 0
$381$	837.708	0.112643
$382$	−9539.61	−1.27772
$383$	8218.30	1.09644	0.548219	−	0.836335i	$-0.315306\pi$
$383$	8218.30	1.09644	0.548219	+	0.836335i	$0.315306\pi$
$384$	8768.70	1.16530
$385$	−1658.18	−0.219503
$386$	12616.0	1.66356
$387$	4230.17	0.555638
$388$	−9.30926	−0.00121806
$389$	−3602.96	−0.469608	−0.234804	−	0.972043i	$-0.575445\pi$
$389$	−3602.96	−0.469608	−0.234804	+	0.972043i	$0.575445\pi$
$390$	3714.76	0.482319
$391$	0	0
$392$	1108.15	0.142781
$393$	3181.89	0.408410
$394$	5098.43	0.651917
$395$	−10468.7	−1.33351
$396$	1.01652	0.000128995 0
$397$	−8036.29	−1.01594	−0.507972	−	0.861374i	$-0.669605\pi$
$397$	−8036.29	−1.01594	−0.507972	+	0.861374i	$0.669605\pi$
$398$	−1956.59	−0.246420
$399$	−1525.20	−0.191367
$400$	−15252.0	−1.90651
$401$	11241.3	1.39990	0.699952	−	0.714190i	$-0.253205\pi$
$401$	11241.3	1.39990	0.699952	+	0.714190i	$0.253205\pi$
$402$	−16089.1	−1.99615
$403$	−871.700	−0.107748
$404$	−10.0223	−0.00123423
$405$	17065.3	2.09378
$406$	−5109.90	−0.624630
$407$	2707.12	0.329698
$408$	0	0
$409$	−3601.32	−0.435388	−0.217694	−	0.976017i	$-0.569853\pi$
$409$	−3601.32	−0.435388	−0.217694	+	0.976017i	$0.569853\pi$
$410$	7234.49	0.871429
$411$	−8960.73	−1.07543
$412$	1.06559	0.000127422 0
$413$	−3707.46	−0.441725
$414$	−2407.52	−0.285805
$415$	2436.63	0.288216
$416$	−4.41692	−0.000520571 0
$417$	−11737.2	−1.37836
$418$	−1268.02	−0.148375
$419$	−9935.38	−1.15841	−0.579207	−	0.815181i	$-0.696638\pi$
$419$	−9935.38	−1.15841	−0.579207	+	0.815181i	$0.696638\pi$
$420$	6.90598	0.000802326 0
$421$	−2147.79	−0.248639	−0.124319	−	0.992242i	$-0.539675\pi$
$421$	−2147.79	−0.248639	−0.124319	+	0.992242i	$0.539675\pi$
$422$	−2170.05	−0.250323
$423$	5051.64	0.580659
$424$	1807.63	0.207043
$425$	0	0
$426$	10350.0	1.17714
$427$	5722.19	0.648515
$428$	4.15612	0.000469378 0
$429$	856.466	0.0963882
$430$	23892.8	2.67957
$431$	16969.2	1.89646	0.948232	−	0.317580i	$-0.102870\pi$
$431$	16969.2	1.89646	0.948232	+	0.317580i	$0.102870\pi$
$432$	−6759.97	−0.752868
$433$	−411.427	−0.0456626	−0.0228313	−	0.999739i	$-0.507268\pi$
$433$	−411.427	−0.0456626	−0.0228313	+	0.999739i	$0.507268\pi$
$434$	−1515.31	−0.167597
$435$	29713.2	3.27503
$436$	6.51365	0.000715475 0
$437$	3211.74	0.351575
$438$	−8438.28	−0.920540
$439$	1562.83	0.169909	0.0849545	−	0.996385i	$-0.472926\pi$
$439$	1562.83	0.169909	0.0849545	+	0.996385i	$0.472926\pi$
$440$	−5357.16	−0.580438
$441$	467.792	0.0505120
$442$	0	0
$443$	−7046.86	−0.755771	−0.377885	−	0.925852i	$-0.623349\pi$
$443$	−7046.86	−0.755771	−0.377885	+	0.925852i	$0.623349\pi$
$444$	−11.2746	−0.00120511
$445$	2891.10	0.307980
$446$	−10422.9	−1.10659
$447$	−15451.5	−1.63496
$448$	3580.15	0.377559
$449$	13387.4	1.40710	0.703551	−	0.710645i	$-0.251597\pi$
$449$	13387.4	1.40710	0.703551	+	0.710645i	$0.251597\pi$
$450$	−6431.58	−0.673750
$451$	1667.96	0.174149
$452$	1.28517	0.000133737 0
$453$	−16229.6	−1.68330
$454$	−13064.9	−1.35059
$455$	1519.94	0.156607
$456$	−4927.54	−0.506038
$457$	11716.8	1.19932	0.599658	−	0.800257i	$-0.295303\pi$
$457$	11716.8	1.19932	0.599658	+	0.800257i	$0.295303\pi$
$458$	12926.9	1.31885
$459$	0	0
$460$	−14.5425	−0.00147402
$461$	−18214.8	−1.84024	−0.920119	−	0.391638i	$-0.871908\pi$
$461$	−18214.8	−1.84024	−0.920119	+	0.391638i	$0.871908\pi$
$462$	1488.83	0.149928
$463$	6716.97	0.674221	0.337110	−	0.941465i	$-0.390550\pi$
$463$	6716.97	0.674221	0.337110	+	0.941465i	$0.390550\pi$
$464$	−16526.5	−1.65350
$465$	8811.27	0.878738
$466$	10287.2	1.02263
$467$	15598.0	1.54559	0.772793	−	0.634659i	$-0.218859\pi$
$467$	15598.0	1.54559	0.772793	+	0.634659i	$0.218859\pi$
$468$	−0.931776	−9.20328e−5 0
$469$	−6583.06	−0.648140
$470$	28532.6	2.80024
$471$	−12671.9	−1.23968
$472$	−11977.9	−1.16807
$473$	5508.67	0.535494
$474$	9399.52	0.910832
$475$	8580.00	0.828794
$476$	0	0
$477$	763.068	0.0732463
$478$	−12772.3	−1.22216
$479$	6987.73	0.666550	0.333275	−	0.942830i	$-0.391846\pi$
$479$	6987.73	0.666550	0.333275	+	0.942830i	$0.391846\pi$
$480$	44.6469	0.00424551
$481$	−2481.45	−0.235227
$482$	−231.680	−0.0218937
$483$	−3771.02	−0.355254
$484$	−10.0759	−0.000946274 0
$485$	20710.4	1.93899
$486$	−7260.42	−0.677653
$487$	15387.8	1.43180	0.715902	−	0.698201i	$-0.246016\pi$
$487$	15387.8	1.43180	0.715902	+	0.698201i	$0.246016\pi$
$488$	18487.0	1.71489
$489$	−13025.7	−1.20458
$490$	2642.18	0.243595
$491$	2418.05	0.222251	0.111125	−	0.993806i	$-0.464554\pi$
$491$	2418.05	0.222251	0.111125	+	0.993806i	$0.464554\pi$
$492$	−6.94674	−0.000636551 0
$493$	0	0
$494$	1162.31	0.105860
$495$	−2261.46	−0.205344
$496$	−4900.83	−0.443657
$497$	4234.85	0.382211
$498$	−2187.78	−0.196861
$499$	6632.84	0.595043	0.297522	−	0.954715i	$-0.403840\pi$
$499$	6632.84	0.595043	0.297522	+	0.954715i	$0.403840\pi$
$500$	−18.4504	−0.00165025
$501$	−12330.8	−1.09960
$502$	7050.90	0.626886
$503$	12133.2	1.07553	0.537766	−	0.843094i	$-0.319268\pi$
$503$	12133.2	1.07553	0.537766	+	0.843094i	$0.319268\pi$
$504$	1511.32	0.133571
$505$	22296.8	1.96474
$506$	−3135.15	−0.275444
$507$	12496.7	1.09467
$508$	−1.18681	−0.000103654 0
$509$	−4404.74	−0.383569	−0.191785	−	0.981437i	$-0.561427\pi$
$509$	−4404.74	−0.383569	−0.191785	+	0.981437i	$0.561427\pi$
$510$	0	0
$511$	−3452.63	−0.298895
$512$	11566.6	0.998389
$513$	3802.80	0.327286
$514$	−290.924	−0.0249652
$515$	−2370.63	−0.202840
$516$	−22.9425	−0.00195734
$517$	6578.40	0.559609
$518$	−4313.59	−0.365885
$519$	−15635.8	−1.32242
$520$	4910.57	0.414120
$521$	13542.5	1.13878	0.569391	−	0.822067i	$-0.307179\pi$
$521$	13542.5	1.13878	0.569391	+	0.822067i	$0.307179\pi$
$522$	−6969.00	−0.584339
$523$	−5483.81	−0.458490	−0.229245	−	0.973369i	$-0.573626\pi$
$523$	−5483.81	−0.458490	−0.229245	+	0.973369i	$0.573626\pi$
$524$	−4.50791	−0.000375818 0
$525$	−10074.1	−0.837466
$526$	−9523.75	−0.789459
$527$	0	0
$528$	4815.19	0.396883
$529$	−4226.04	−0.347336
$530$	4309.95	0.353231
$531$	−5056.33	−0.413232
$532$	2.16080	0.000176095 0
$533$	−1528.91	−0.124249
$534$	−2595.83	−0.210361
$535$	−9246.19	−0.747192
$536$	−21268.3	−1.71390
$537$	−4787.16	−0.384695
$538$	20361.1	1.63165
$539$	609.173	0.0486808
$540$	−17.2188	−0.00137218
$541$	−12134.7	−0.964347	−0.482174	−	0.876076i	$-0.660153\pi$
$541$	−12134.7	−0.964347	−0.482174	+	0.876076i	$0.660153\pi$
$542$	7385.87	0.585332
$543$	−688.350	−0.0544014
$544$	0	0
$545$	−14491.0	−1.13895
$546$	−1364.71	−0.106968
$547$	11.9363	0.000933018 0	0.000466509	−	1.00000i	$-0.499852\pi$
$547$	11.9363	0.000933018 0	0.000466509		1.00000i	$0.499852\pi$
$548$	12.6950	0.000989606 0
$549$	7804.05	0.606683
$550$	−8375.40	−0.649324
$551$	9296.94	0.718808
$552$	−12183.3	−0.939409
$553$	3845.94	0.295743
$554$	−13924.1	−1.06783
$555$	25082.8	1.91839
$556$	16.6286	0.00126836
$557$	15599.2	1.18664	0.593321	−	0.804966i	$-0.297816\pi$
$557$	15599.2	1.18664	0.593321	+	0.804966i	$0.297816\pi$
$558$	−2066.62	−0.156786
$559$	−5049.44	−0.382054
$560$	8545.36	0.644835
$561$	0	0
$562$	−14966.0	−1.12331
$563$	17866.7	1.33746	0.668732	−	0.743504i	$-0.266837\pi$
$563$	17866.7	1.33746	0.668732	+	0.743504i	$0.266837\pi$
$564$	−27.3977	−0.00204548
$565$	−2859.13	−0.212893
$566$	3487.97	0.259029
$567$	−6269.35	−0.464353
$568$	13681.8	1.01069
$569$	−5035.23	−0.370980	−0.185490	−	0.982646i	$-0.559387\pi$
$569$	−5035.23	−0.370980	−0.185490	+	0.982646i	$0.559387\pi$
$570$	−11748.8	−0.863339
$571$	−8838.82	−0.647799	−0.323899	−	0.946092i	$-0.604994\pi$
$571$	−8838.82	−0.647799	−0.323899	+	0.946092i	$0.604994\pi$
$572$	−1.21339	−8.86963e−5 0
$573$	−20378.8	−1.48575
$574$	−2657.77	−0.193263
$575$	21213.9	1.53857
$576$	4882.70	0.353205
$577$	7247.92	0.522938	0.261469	−	0.965212i	$-0.415793\pi$
$577$	7247.92	0.522938	0.261469	+	0.965212i	$0.415793\pi$
$578$	0	0
$579$	26950.6	1.93442
$580$	−42.0958	−0.00301368
$581$	−895.159	−0.0639199
$582$	−18595.3	−1.32440
$583$	993.691	0.0705908
$584$	−11154.6	−0.790378
$585$	2072.94	0.146505
$586$	−21041.6	−1.48331
$587$	881.106	0.0619542	0.0309771	−	0.999520i	$-0.490138\pi$
$587$	881.106	0.0619542	0.0309771	+	0.999520i	$0.490138\pi$
$588$	−2.53708	−0.000177938 0
$589$	2756.95	0.192866
$590$	−28559.1	−1.99281
$591$	10891.4	0.758058
$592$	−13951.1	−0.968557
$593$	−1540.15	−0.106655	−0.0533275	−	0.998577i	$-0.516983\pi$
$593$	−1540.15	−0.106655	−0.0533275	+	0.998577i	$0.516983\pi$
$594$	−3712.12	−0.256414
$595$	0	0
$596$	21.8907	0.00150449
$597$	−4179.72	−0.286540
$598$	2873.79	0.196518
$599$	−12524.3	−0.854305	−0.427153	−	0.904180i	$-0.640483\pi$
$599$	−12524.3	−0.854305	−0.427153	+	0.904180i	$0.640483\pi$
$600$	−32547.0	−2.21454
$601$	−7292.80	−0.494974	−0.247487	−	0.968891i	$-0.579605\pi$
$601$	−7292.80	−0.494974	−0.247487	+	0.968891i	$0.579605\pi$
$602$	−8777.63	−0.594268
$603$	−8978.14	−0.606332
$604$	22.9931	0.00154897
$605$	22416.1	1.50635
$606$	−20019.6	−1.34198
$607$	−22734.7	−1.52022	−0.760111	−	0.649794i	$-0.774855\pi$
$607$	−22734.7	−1.52022	−0.760111	+	0.649794i	$0.774855\pi$
$608$	13.9695	0.000931809 0
$609$	−10915.9	−0.726329
$610$	44078.8	2.92573
$611$	−6029.99	−0.399259
$612$	0	0
$613$	−13218.7	−0.870960	−0.435480	−	0.900198i	$-0.643421\pi$
$613$	−13218.7	−0.870960	−0.435480	+	0.900198i	$0.643421\pi$
$614$	29305.6	1.92619
$615$	15454.5	1.01331
$616$	1968.09	0.128728
$617$	23085.4	1.50629	0.753145	−	0.657854i	$-0.228536\pi$
$617$	23085.4	1.50629	0.753145	+	0.657854i	$0.228536\pi$
$618$	2128.52	0.138546
$619$	−8169.60	−0.530475	−0.265238	−	0.964183i	$-0.585450\pi$
$619$	−8169.60	−0.530475	−0.265238	+	0.964183i	$0.585450\pi$
$620$	−12.4833	−0.000808613 0
$621$	9402.36	0.607575
$622$	−26823.4	−1.72913
$623$	−1062.12	−0.0683032
$624$	−4413.77	−0.283161
$625$	11289.6	0.722531
$626$	−5250.96	−0.335256
$627$	−2708.77	−0.172533
$628$	17.9527	0.00114075
$629$	0	0
$630$	3603.46	0.227882
$631$	15440.3	0.974119	0.487059	−	0.873369i	$-0.338069\pi$
$631$	15440.3	0.974119	0.487059	+	0.873369i	$0.338069\pi$
$632$	12425.3	0.782043
$633$	−4635.72	−0.291080
$634$	6180.99	0.387190
$635$	2640.32	0.165004
$636$	−4.13852	−0.000258024 0
$637$	−558.389	−0.0347319
$638$	−9075.25	−0.563155
$639$	5775.59	0.357557
$640$	27637.5	1.70698
$641$	15819.3	0.974765	0.487382	−	0.873189i	$-0.337952\pi$
$641$	15819.3	0.974765	0.487382	+	0.873189i	$0.337952\pi$
$642$	8301.88	0.510357
$643$	254.478	0.0156075	0.00780374	−	0.999970i	$-0.497516\pi$
$643$	254.478	0.0156075	0.00780374	+	0.999970i	$0.497516\pi$
$644$	5.34255	0.000326904 0
$645$	51040.5	3.11584
$646$	0	0
$647$	4865.23	0.295629	0.147814	−	0.989015i	$-0.452776\pi$
$647$	4865.23	0.295629	0.147814	+	0.989015i	$0.452776\pi$
$648$	−20254.7	−1.22790
$649$	−6584.51	−0.398251
$650$	7677.19	0.463268
$651$	−3237.04	−0.194884
$652$	18.4539	0.00110845
$653$	−20286.4	−1.21572	−0.607862	−	0.794042i	$-0.707973\pi$
$653$	−20286.4	−1.21572	−0.607862	+	0.794042i	$0.707973\pi$
$654$	13011.0	0.777939
$655$	10028.8	0.598256
$656$	−8595.80	−0.511600
$657$	−4708.78	−0.279615
$658$	−10482.2	−0.621029
$659$	−19377.3	−1.14542	−0.572709	−	0.819758i	$-0.694108\pi$
$659$	−19377.3	−1.14542	−0.572709	+	0.819758i	$0.694108\pi$
$660$	12.2651	0.000723362 0
$661$	−31223.6	−1.83730	−0.918651	−	0.395070i	$-0.870721\pi$
$661$	−31223.6	−1.83730	−0.918651	+	0.395070i	$0.870721\pi$
$662$	32886.7	1.93078
$663$	0	0
$664$	−2892.04	−0.169025
$665$	−4807.17	−0.280322
$666$	−5882.98	−0.342284
$667$	22986.5	1.33440
$668$	17.4695	0.00101185
$669$	−22265.8	−1.28676
$670$	−50710.2	−2.92404
$671$	10162.7	0.584689
$672$	−16.4022	−0.000941559 0
$673$	−3179.56	−0.182114	−0.0910572	−	0.995846i	$-0.529025\pi$
$673$	−3179.56	−0.182114	−0.0910572	+	0.995846i	$0.529025\pi$
$674$	−3847.38	−0.219874
$675$	25117.9	1.43228
$676$	−17.7045	−0.00100731
$677$	19143.9	1.08679	0.543397	−	0.839476i	$-0.317138\pi$
$677$	19143.9	1.08679	0.543397	+	0.839476i	$0.317138\pi$
$678$	2567.12	0.145413
$679$	−7608.50	−0.430026
$680$	0	0
$681$	−27909.7	−1.57049
$682$	−2691.21	−0.151102
$683$	9159.45	0.513143	0.256571	−	0.966525i	$-0.417407\pi$
$683$	9159.45	0.513143	0.256571	+	0.966525i	$0.417407\pi$
$684$	2.94696	0.000164736 0
$685$	−28242.8	−1.57533
$686$	−970.670	−0.0540238
$687$	27614.7	1.53358
$688$	−28388.7	−1.57313
$689$	−910.852	−0.0503638
$690$	−29048.7	−1.60270
$691$	−30368.3	−1.67187	−0.835937	−	0.548825i	$-0.815075\pi$
$691$	−30368.3	−1.67187	−0.835937	+	0.548825i	$0.815075\pi$
$692$	22.1519	0.00121689
$693$	830.805	0.0455406
$694$	15368.4	0.840598
$695$	−36993.8	−2.01907
$696$	−35266.6	−1.92066
$697$	0	0
$698$	−31388.1	−1.70209
$699$	21975.8	1.18913
$700$	14.2724	0.000770635 0
$701$	−29510.8	−1.59002	−0.795012	−	0.606593i	$-0.792536\pi$
$701$	−29510.8	−1.59002	−0.795012	+	0.606593i	$0.792536\pi$
$702$	3402.66	0.182942
$703$	7848.15	0.421050
$704$	6358.41	0.340400
$705$	60952.1	3.25615
$706$	34496.5	1.83894
$707$	−8191.28	−0.435735
$708$	27.4232	0.00145569
$709$	30766.2	1.62969	0.814845	−	0.579678i	$-0.196822\pi$
$709$	30766.2	1.62969	0.814845	+	0.579678i	$0.196822\pi$
$710$	32621.6	1.72432
$711$	5245.18	0.276666
$712$	−3431.44	−0.180616
$713$	6816.52	0.358037
$714$	0	0
$715$	2699.44	0.141194
$716$	6.78215	0.000353996 0
$717$	−27284.5	−1.42114
$718$	−1261.55	−0.0655720
$719$	−33888.2	−1.75774	−0.878872	−	0.477058i	$-0.841703\pi$
$719$	−33888.2	−1.75774	−0.878872	+	0.477058i	$0.841703\pi$
$720$	11654.4	0.603240
$721$	870.911	0.0449853
$722$	15734.5	0.811049
$723$	−494.922	−0.0254583
$724$	0.975212	5.00601e−5 0
$725$	61407.4	3.14567
$726$	−20126.7	−1.02889
$727$	4424.80	0.225732	0.112866	−	0.993610i	$-0.463997\pi$
$727$	4424.80	0.225732	0.112866	+	0.993610i	$0.463997\pi$
$728$	−1804.02	−0.0918426
$729$	8671.90	0.440578
$730$	−26596.1	−1.34845
$731$	0	0
$732$	−42.3255	−0.00213715
$733$	16009.3	0.806706	0.403353	−	0.915045i	$-0.367845\pi$
$733$	16009.3	0.806706	0.403353	+	0.915045i	$0.367845\pi$
$734$	20347.3	1.02321
$735$	5644.28	0.283255
$736$	34.5395	0.00172981
$737$	−11691.6	−0.584350
$738$	−3624.73	−0.180797
$739$	7490.73	0.372870	0.186435	−	0.982467i	$-0.440307\pi$
$739$	7490.73	0.372870	0.186435	+	0.982467i	$0.440307\pi$
$740$	−35.5358	−0.00176530
$741$	2482.96	0.123095
$742$	−1583.37	−0.0783387
$743$	−1961.39	−0.0968457	−0.0484228	−	0.998827i	$-0.515420\pi$
$743$	−1961.39	−0.0968457	−0.0484228	+	0.998827i	$0.515420\pi$
$744$	−10458.1	−0.515339
$745$	−48700.5	−2.39496
$746$	27606.5	1.35489
$747$	−1220.84	−0.0597967
$748$	0	0
$749$	3396.82	0.165710
$750$	−36854.8	−1.79433
$751$	13401.7	0.651177	0.325588	−	0.945512i	$-0.394438\pi$
$751$	13401.7	0.651177	0.325588	+	0.945512i	$0.394438\pi$
$752$	−33901.6	−1.64397
$753$	15062.3	0.728952
$754$	8318.69	0.401789
$755$	−51153.0	−2.46576
$756$	6.32576	0.000304320 0
$757$	−7212.75	−0.346303	−0.173152	−	0.984895i	$-0.555395\pi$
$757$	−7212.75	−0.346303	−0.173152	+	0.984895i	$0.555395\pi$
$758$	−3199.13	−0.153295
$759$	−6697.39	−0.320290
$760$	−15530.8	−0.741265
$761$	−36579.0	−1.74243	−0.871213	−	0.490905i	$-0.836666\pi$
$761$	−36579.0	−1.74243	−0.871213	+	0.490905i	$0.836666\pi$
$762$	−2370.66	−0.112703
$763$	5323.63	0.252593
$764$	28.8714	0.00136719
$765$	0	0
$766$	−23257.3	−1.09702
$767$	6035.59	0.284136
$768$	−79.5297	−0.00373669
$769$	26039.3	1.22107	0.610534	−	0.791990i	$-0.290955\pi$
$769$	26039.3	1.22107	0.610534	+	0.791990i	$0.290955\pi$
$770$	4692.54	0.219620
$771$	−621.479	−0.0290299
$772$	−38.1819	−0.00178005
$773$	17507.0	0.814597	0.407299	−	0.913295i	$-0.366471\pi$
$773$	17507.0	0.814597	0.407299	+	0.913295i	$0.366471\pi$
$774$	−11971.1	−0.555935
$775$	18210.0	0.844028
$776$	−24581.2	−1.13713
$777$	−9214.81	−0.425456
$778$	10196.2	0.469859
$779$	4835.55	0.222402
$780$	−11.2426	−0.000516091 0
$781$	7521.16	0.344594
$782$	0	0
$783$	27216.8	1.24221
$784$	−3139.35	−0.143010
$785$	−39939.7	−1.81594
$786$	−9004.56	−0.408629
$787$	−36203.6	−1.63980	−0.819899	−	0.572509i	$-0.805970\pi$
$787$	−36203.6	−1.63980	−0.819899	+	0.572509i	$0.805970\pi$
$788$	−15.4303	−0.000697564 0
$789$	−20344.9	−0.917994
$790$	29625.8	1.33422
$791$	1050.37	0.0472148
$792$	2684.13	0.120425
$793$	−9315.47	−0.417153
$794$	22742.2	1.01649
$795$	9207.03	0.410742
$796$	5.92157	0.000263674 0
$797$	8657.44	0.384771	0.192385	−	0.981319i	$-0.438378\pi$
$797$	8657.44	0.384771	0.192385	+	0.981319i	$0.438378\pi$
$798$	4316.22	0.191469
$799$	0	0
$800$	92.2705	0.00407782
$801$	−1448.54	−0.0638973
$802$	−31812.1	−1.40065
$803$	−6131.92	−0.269478
$804$	48.6932	0.00213592
$805$	−11885.7	−0.520390
$806$	2466.86	0.107806
$807$	43495.9	1.89731
$808$	−26464.0	−1.15223
$809$	7213.71	0.313499	0.156749	−	0.987638i	$-0.449899\pi$
$809$	7213.71	0.313499	0.156749	+	0.987638i	$0.449899\pi$
$810$	−48293.7	−2.09490
$811$	−11663.3	−0.504997	−0.252498	−	0.967597i	$-0.581252\pi$
$811$	−11663.3	−0.504997	−0.252498	+	0.967597i	$0.581252\pi$
$812$	15.4650	0.000668367 0
$813$	15777.9	0.680633
$814$	−7661.00	−0.329875
$815$	−41054.7	−1.76452
$816$	0	0
$817$	15970.0	0.683868
$818$	10191.5	0.435621
$819$	−761.545	−0.0324915
$820$	−21.8950	−0.000932446 0
$821$	5985.64	0.254446	0.127223	−	0.991874i	$-0.459394\pi$
$821$	5985.64	0.254446	0.127223	+	0.991874i	$0.459394\pi$
$822$	25358.3	1.07600
$823$	6169.70	0.261315	0.130657	−	0.991428i	$-0.458291\pi$
$823$	6169.70	0.261315	0.130657	+	0.991428i	$0.458291\pi$
$824$	2813.70	0.118956
$825$	−17891.7	−0.755043
$826$	10491.9	0.441961
$827$	5294.00	0.222600	0.111300	−	0.993787i	$-0.464499\pi$
$827$	5294.00	0.222600	0.111300	+	0.993787i	$0.464499\pi$
$828$	7.28630	0.000305817 0
$829$	−8856.63	−0.371054	−0.185527	−	0.982639i	$-0.559399\pi$
$829$	−8856.63	−0.371054	−0.185527	+	0.982639i	$0.559399\pi$
$830$	−6895.53	−0.288370
$831$	−29744.9	−1.24169
$832$	−5828.34	−0.242862
$833$	0	0
$834$	33215.6	1.37909
$835$	−38864.7	−1.61074
$836$	3.83762	0.000158764 0
$837$	8070.98	0.333302
$838$	28116.5	1.15903
$839$	−27056.7	−1.11335	−0.556675	−	0.830730i	$-0.687923\pi$
$839$	−27056.7	−1.11335	−0.556675	+	0.830730i	$0.687923\pi$
$840$	18235.3	0.749021
$841$	42149.6	1.72822
$842$	6078.12	0.248772
$843$	−31970.7	−1.30620
$844$	6.56761	0.000267851 0
$845$	39387.4	1.60351
$846$	−14295.8	−0.580970
$847$	−8235.10	−0.334075
$848$	−5120.95	−0.207375
$849$	7451.10	0.301203
$850$	0	0
$851$	19404.4	0.781639
$852$	−31.3241	−0.00125956
$853$	−16062.8	−0.644760	−0.322380	−	0.946610i	$-0.604483\pi$
$853$	−16062.8	−0.644760	−0.322380	+	0.946610i	$0.604483\pi$
$854$	−16193.4	−0.648862
$855$	−6556.14	−0.262240
$856$	10974.3	0.438193
$857$	3326.12	0.132576	0.0662882	−	0.997801i	$-0.478884\pi$
$857$	3326.12	0.132576	0.0662882	+	0.997801i	$0.478884\pi$
$858$	−2423.75	−0.0964398
$859$	21523.5	0.854914	0.427457	−	0.904036i	$-0.359410\pi$
$859$	21523.5	0.854914	0.427457	+	0.904036i	$0.359410\pi$
$860$	−72.3110	−0.00286719
$861$	−5677.60	−0.224729
$862$	−48021.7	−1.89748
$863$	23115.1	0.911760	0.455880	−	0.890041i	$-0.349325\pi$
$863$	23115.1	0.911760	0.455880	+	0.890041i	$0.349325\pi$
$864$	40.8959	0.00161031
$865$	−49281.6	−1.93714
$866$	1164.31	0.0456871
$867$	0	0
$868$	4.58604	0.000179332 0
$869$	6830.44	0.266636
$870$	−84086.6	−3.27679
$871$	10716.9	0.416911
$872$	17199.4	0.667940
$873$	−10376.7	−0.402287
$874$	−9089.03	−0.351763
$875$	−15079.6	−0.582610
$876$	25.5382	0.000984996 0
$877$	−39192.2	−1.50904	−0.754520	−	0.656277i	$-0.772130\pi$
$877$	−39192.2	−1.50904	−0.754520	+	0.656277i	$0.772130\pi$
$878$	−4422.73	−0.170000
$879$	−44949.7	−1.72482
$880$	15176.7	0.581371
$881$	−3511.36	−0.134280	−0.0671400	−	0.997744i	$-0.521387\pi$
$881$	−3511.36	−0.134280	−0.0671400	+	0.997744i	$0.521387\pi$
$882$	−1323.82	−0.0505390
$883$	22388.9	0.853279	0.426640	−	0.904422i	$-0.359697\pi$
$883$	22388.9	0.853279	0.426640	+	0.904422i	$0.359697\pi$
$884$	0	0
$885$	−61008.7	−2.31727
$886$	19942.2	0.756175
$887$	13858.0	0.524583	0.262292	−	0.964989i	$-0.415522\pi$
$887$	13858.0	0.524583	0.262292	+	0.964989i	$0.415522\pi$
$888$	−29770.8	−1.12505
$889$	−969.987	−0.0365943
$890$	−8181.64	−0.308145
$891$	−11134.5	−0.418652
$892$	31.5448	0.00118408
$893$	19071.2	0.714664
$894$	43726.7	1.63584
$895$	−15088.4	−0.563517
$896$	−10153.3	−0.378570
$897$	6139.06	0.228514
$898$	−37885.5	−1.40786
$899$	19731.6	0.732020
$900$	19.4650	0.000720926 0
$901$	0	0
$902$	−4720.24	−0.174243
$903$	−18751.0	−0.691023
$904$	3393.49	0.124852
$905$	−2169.57	−0.0796894
$906$	45928.8	1.68420
$907$	18692.1	0.684299	0.342150	−	0.939645i	$-0.388845\pi$
$907$	18692.1	0.684299	0.342150	+	0.939645i	$0.388845\pi$
$908$	39.5407	0.00144516
$909$	−11171.5	−0.407628
$910$	−4301.35	−0.156690
$911$	−2438.93	−0.0886997	−0.0443499	−	0.999016i	$-0.514122\pi$
$911$	−2438.93	−0.0886997	−0.0443499	+	0.999016i	$0.514122\pi$
$912$	13959.6	0.506850
$913$	−1589.81	−0.0576289
$914$	−33157.8	−1.19996
$915$	94162.2	3.40208
$916$	−39.1229	−0.00141120
$917$	−3684.33	−0.132680
$918$	0	0
$919$	−16453.0	−0.590570	−0.295285	−	0.955409i	$-0.595415\pi$
$919$	−16453.0	−0.590570	−0.295285	+	0.955409i	$0.595415\pi$
$920$	−38399.6	−1.37609
$921$	62603.4	2.23980
$922$	51546.9	1.84122
$923$	−6894.16	−0.245855
$924$	−4.50590	−0.000160425 0
$925$	51837.9	1.84262
$926$	−19008.6	−0.674581
$927$	1187.77	0.0420836
$928$	99.9806	0.00353666
$929$	14795.7	0.522531	0.261266	−	0.965267i	$-0.415860\pi$
$929$	14795.7	0.522531	0.261266	+	0.965267i	$0.415860\pi$
$930$	−24935.4	−0.879208
$931$	1766.04	0.0621691
$932$	−31.1340	−0.00109424
$933$	−57300.8	−2.01066
$934$	−44141.3	−1.54641
$935$	0	0
$936$	−2460.37	−0.0859183
$937$	−23609.8	−0.823157	−0.411578	−	0.911374i	$-0.635022\pi$
$937$	−23609.8	−0.823157	−0.411578	+	0.911374i	$0.635022\pi$
$938$	18629.7	0.648487
$939$	−11217.2	−0.389841
$940$	−86.3531	−0.00299631
$941$	16274.8	0.563806	0.281903	−	0.959443i	$-0.409034\pi$
$941$	16274.8	0.563806	0.281903	+	0.959443i	$0.409034\pi$
$942$	35860.7	1.24034
$943$	11955.8	0.412868
$944$	33933.1	1.16994
$945$	−14073.0	−0.484439
$946$	−15589.2	−0.535781
$947$	−52352.8	−1.79645	−0.898225	−	0.439536i	$-0.855143\pi$
$947$	−52352.8	−1.79645	−0.898225	+	0.439536i	$0.855143\pi$
$948$	−28.4474	−0.000974608 0
$949$	5620.73	0.192262
$950$	−24280.9	−0.829238
$951$	13204.0	0.450230
$952$	0	0
$953$	−6452.24	−0.219316	−0.109658	−	0.993969i	$-0.534976\pi$
$953$	−6452.24	−0.219316	−0.109658	+	0.993969i	$0.534976\pi$
$954$	−2159.44	−0.0732855
$955$	−64230.5	−2.17639
$956$	38.6551	0.00130773
$957$	−19386.8	−0.654844
$958$	−19774.9	−0.666907
$959$	10375.7	0.349373
$960$	58913.7	1.98066
$961$	−23939.7	−0.803589
$962$	7022.34	0.235353
$963$	4632.66	0.155021
$964$	0.701174	2.34267e−5 0
$965$	84943.8	2.83361
$966$	10671.8	0.355444
$967$	18493.5	0.615005	0.307503	−	0.951547i	$-0.400507\pi$
$967$	18493.5	0.615005	0.307503	+	0.951547i	$0.400507\pi$
$968$	−26605.6	−0.883405
$969$	0	0
$970$	−58609.3	−1.94003
$971$	−57561.9	−1.90242	−0.951209	−	0.308546i	$-0.900157\pi$
$971$	−57561.9	−1.90242	−0.951209	+	0.308546i	$0.900157\pi$
$972$	21.9735	0.000725102 0
$973$	13590.6	0.447785
$974$	−43546.6	−1.43257
$975$	16400.2	0.538694
$976$	−52373.1	−1.71764
$977$	−23551.1	−0.771204	−0.385602	−	0.922665i	$-0.626006\pi$
$977$	−23551.1	−0.771204	−0.385602	+	0.922665i	$0.626006\pi$
$978$	36861.8	1.20523
$979$	−1886.34	−0.0615808
$980$	−7.99647	−0.000260651 0
$981$	7260.50	0.236300
$982$	−6842.95	−0.222370
$983$	−8593.21	−0.278821	−0.139410	−	0.990235i	$-0.544521\pi$
$983$	−8593.21	−0.278821	−0.139410	+	0.990235i	$0.544521\pi$
$984$	−18342.9	−0.594259
$985$	34327.9	1.11043
$986$	0	0
$987$	−22392.3	−0.722142
$988$	−3.51770	−0.000113272 0
$989$	39485.6	1.26953
$990$	6399.80	0.205454
$991$	21895.7	0.701855	0.350927	−	0.936403i	$-0.385866\pi$
$991$	21895.7	0.701855	0.350927	+	0.936403i	$0.385866\pi$
$992$	29.6486	0.000948937 0
$993$	70253.4	2.24514
$994$	−11984.4	−0.382416
$995$	−13173.8	−0.419736
$996$	6.62126	0.000210645 0
$997$	10773.4	0.342222	0.171111	−	0.985252i	$-0.445264\pi$
$997$	10773.4	0.342222	0.171111	+	0.985252i	$0.445264\pi$
$998$	−18770.5	−0.595362
$999$	22975.4	0.727639

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2023.4.a.v.1.15		56
17.11	odd	16		119.4.k.a.36.8	✓	112
17.14	odd	16		119.4.k.a.43.8	yes	112
17.16	even	2		2023.4.a.u.1.15		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
119.4.k.a.36.8	✓	112	17.11	odd	16
119.4.k.a.43.8	yes	112	17.14	odd	16
2023.4.a.u.1.15		56	17.16	even	2
2023.4.a.v.1.15		56	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:	\( N \)	\(=\)	\( 2023 = 7 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2023.a (trivial)

\(f(q)\)	\(=\)	\(q-2.82994 q^{2} -6.04539 q^{3} +0.00856474 q^{4} -19.0541 q^{5} +17.1081 q^{6} +7.00000 q^{7} +22.6153 q^{8} +9.54677 q^{9} +53.9220 q^{10} +12.4321 q^{11} -0.0517772 q^{12} -11.3957 q^{13} -19.8096 q^{14} +115.189 q^{15} -64.0684 q^{16} -27.0168 q^{18} +36.0415 q^{19} -0.163193 q^{20} -42.3177 q^{21} -35.1821 q^{22} +89.1121 q^{23} -136.718 q^{24} +238.059 q^{25} +32.2492 q^{26} +105.512 q^{27} +0.0599532 q^{28} +257.951 q^{29} -325.979 q^{30} +76.4937 q^{31} +0.387596 q^{32} -75.1569 q^{33} -133.379 q^{35} +0.0817656 q^{36} +217.753 q^{37} -101.995 q^{38} +68.8915 q^{39} -430.914 q^{40} +134.166 q^{41} +119.757 q^{42} +443.100 q^{43} +0.106478 q^{44} -181.905 q^{45} -252.182 q^{46} +529.146 q^{47} +387.319 q^{48} +49.0000 q^{49} -673.692 q^{50} -0.0976012 q^{52} +79.9294 q^{53} -298.592 q^{54} -236.882 q^{55} +158.307 q^{56} -217.885 q^{57} -729.985 q^{58} -529.638 q^{59} +0.986568 q^{60} +817.455 q^{61} -216.473 q^{62} +66.8274 q^{63} +511.451 q^{64} +217.135 q^{65} +212.690 q^{66} -940.437 q^{67} -538.718 q^{69} +377.454 q^{70} +604.979 q^{71} +215.903 q^{72} -493.233 q^{73} -616.227 q^{74} -1439.16 q^{75} +0.308686 q^{76} +87.0247 q^{77} -194.959 q^{78} +549.419 q^{79} +1220.77 q^{80} -895.622 q^{81} -379.682 q^{82} -127.880 q^{83} -0.362440 q^{84} -1253.95 q^{86} -1559.41 q^{87} +281.156 q^{88} -151.731 q^{89} +514.781 q^{90} -79.7699 q^{91} +0.763222 q^{92} -462.435 q^{93} -1497.45 q^{94} -686.739 q^{95} -2.34317 q^{96} -1086.93 q^{97} -138.667 q^{98} +118.686 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 8 q^{2} + 24 q^{3} + 240 q^{4} + 80 q^{5} + 68 q^{6} + 392 q^{7} + 96 q^{8} + 576 q^{9} + 80 q^{10} + 176 q^{11} + 288 q^{12} - 96 q^{13} + 56 q^{14} + 192 q^{15} + 1088 q^{16} + 216 q^{18} + 48 q^{19}+ \cdots + 6576 q^{99}+O(q^{100}) \) 56 * q + 8 * q^2 + 24 * q^3 + 240 * q^4 + 80 * q^5 + 68 * q^6 + 392 * q^7 + 96 * q^8 + 576 * q^9 + 80 * q^10 + 176 * q^11 + 288 * q^12 - 96 * q^13 + 56 * q^14 + 192 * q^15 + 1088 * q^16 + 216 * q^18 + 48 * q^19 + 1660 * q^20 + 168 * q^21 + 352 * q^22 + 608 * q^23 + 736 * q^24 + 1792 * q^25 + 864 * q^27 + 1680 * q^28 + 928 * q^29 - 100 * q^30 + 496 * q^31 + 436 * q^32 + 384 * q^33 + 560 * q^35 + 2804 * q^36 + 1392 * q^37 + 624 * q^39 - 1020 * q^40 + 2088 * q^41 + 476 * q^42 + 1312 * q^43 + 2112 * q^44 + 4840 * q^45 + 736 * q^46 + 5228 * q^48 + 2744 * q^49 + 2020 * q^50 - 1536 * q^52 + 1272 * q^53 + 2268 * q^54 - 336 * q^55 + 672 * q^56 + 2448 * q^57 + 1376 * q^58 + 2372 * q^60 + 976 * q^61 + 3776 * q^62 + 4032 * q^63 + 5376 * q^64 + 6080 * q^65 + 976 * q^67 + 1248 * q^69 + 560 * q^70 + 3216 * q^71 + 4532 * q^72 + 4088 * q^73 - 2456 * q^74 - 760 * q^75 - 2640 * q^76 + 1232 * q^77 + 3744 * q^78 + 1792 * q^79 + 13920 * q^80 + 4184 * q^81 + 8204 * q^82 - 2832 * q^83 + 2016 * q^84 + 4908 * q^86 + 832 * q^87 + 2424 * q^88 - 2768 * q^89 + 8660 * q^90 - 672 * q^91 + 6784 * q^92 + 784 * q^93 - 928 * q^94 + 4560 * q^95 + 6656 * q^96 + 9464 * q^97 + 392 * q^98 + 6576 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more