LMFDB - Embedded newform 5819.2.a.t.1.18

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [5819,2,Mod(1,5819)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(5819, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("5819.1"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 5819 = 11 \cdot 23^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5819.a (trivial)

Newform invariants

comment:select newform

sage:traces = [60,5,9,73,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	yes
Analytic conductor:	$46.4649489362$
Analytic rank:	$0$
Dimension:	$60$
Twist minimal:	no (minimal twist has level 253)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	5819.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.37192 q^{2} -3.24389 q^{3} -0.117831 q^{4} -1.23015 q^{5} +4.45036 q^{6} -3.99271 q^{7} +2.90550 q^{8} +7.52280 q^{9} +1.68767 q^{10} -1.00000 q^{11} +0.382229 q^{12} -2.35213 q^{13} +5.47768 q^{14} +3.99048 q^{15} -3.75045 q^{16} +4.79234 q^{17} -10.3207 q^{18} -0.189173 q^{19} +0.144950 q^{20} +12.9519 q^{21} +1.37192 q^{22} -9.42511 q^{24} -3.48672 q^{25} +3.22694 q^{26} -14.6714 q^{27} +0.470463 q^{28} +9.80675 q^{29} -5.47462 q^{30} +1.10911 q^{31} -0.665665 q^{32} +3.24389 q^{33} -6.57472 q^{34} +4.91164 q^{35} -0.886416 q^{36} +5.60736 q^{37} +0.259530 q^{38} +7.63006 q^{39} -3.57421 q^{40} +10.4777 q^{41} -17.7690 q^{42} +0.255808 q^{43} +0.117831 q^{44} -9.25420 q^{45} +3.04112 q^{47} +12.1660 q^{48} +8.94171 q^{49} +4.78351 q^{50} -15.5458 q^{51} +0.277153 q^{52} +13.0157 q^{53} +20.1281 q^{54} +1.23015 q^{55} -11.6008 q^{56} +0.613655 q^{57} -13.4541 q^{58} +5.85897 q^{59} -0.470200 q^{60} -2.53555 q^{61} -1.52161 q^{62} -30.0363 q^{63} +8.41415 q^{64} +2.89349 q^{65} -4.45036 q^{66} -6.20764 q^{67} -0.564685 q^{68} -6.73839 q^{70} -8.80904 q^{71} +21.8575 q^{72} -4.73282 q^{73} -7.69285 q^{74} +11.3105 q^{75} +0.0222903 q^{76} +3.99271 q^{77} -10.4678 q^{78} -1.45162 q^{79} +4.61363 q^{80} +25.0241 q^{81} -14.3746 q^{82} -5.75581 q^{83} -1.52613 q^{84} -5.89532 q^{85} -0.350949 q^{86} -31.8120 q^{87} -2.90550 q^{88} +9.91146 q^{89} +12.6960 q^{90} +9.39138 q^{91} -3.59782 q^{93} -4.17218 q^{94} +0.232712 q^{95} +2.15934 q^{96} -5.66413 q^{97} -12.2673 q^{98} -7.52280 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 5 q^{2} + 9 q^{3} + 73 q^{4} - 8 q^{5} + 26 q^{6} + 30 q^{8} + 75 q^{9} + 7 q^{10} - 60 q^{11} + 41 q^{12} + 46 q^{13} - 16 q^{14} - 4 q^{15} + 99 q^{16} + 5 q^{17} + 36 q^{18} + 8 q^{19} - 82 q^{20}+ \cdots - 75 q^{99}+O(q^{100}) $ 60 * q + 5 * q^2 + 9 * q^3 + 73 * q^4 - 8 * q^5 + 26 * q^6 + 30 * q^8 + 75 * q^9 + 7 * q^10 - 60 * q^11 + 41 * q^12 + 46 * q^13 - 16 * q^14 - 4 * q^15 + 99 * q^16 + 5 * q^17 + 36 * q^18 + 8 * q^19 - 82 * q^20 + 13 * q^21 - 5 * q^22 + 54 * q^24 + 96 * q^25 + 31 * q^26 + 54 * q^27 + 29 * q^28 + 42 * q^29 + 14 * q^30 + 71 * q^31 + 40 * q^32 - 9 * q^33 - 10 * q^34 + 9 * q^35 + 93 * q^36 + 5 * q^37 + 11 * q^38 + 56 * q^39 + 40 * q^40 + 62 * q^41 - 43 * q^42 + 2 * q^43 - 73 * q^44 + q^45 - q^47 + 71 * q^48 + 138 * q^49 - 18 * q^50 + 27 * q^51 + 102 * q^52 - 11 * q^53 + 69 * q^54 + 8 * q^55 - 13 * q^56 - 38 * q^57 + 58 * q^58 + 57 * q^59 + 49 * q^60 + 26 * q^61 + 17 * q^62 + 41 * q^63 + 184 * q^64 + 19 * q^65 - 26 * q^66 - 7 * q^67 + 76 * q^68 + 43 * q^70 + 33 * q^71 + 100 * q^72 + 108 * q^73 + 63 * q^74 + q^75 + 42 * q^76 - 3 * q^78 + 25 * q^79 - 148 * q^80 + 68 * q^81 + 59 * q^82 + 41 * q^83 + 97 * q^84 + 160 * q^85 - 78 * q^86 + 41 * q^87 - 30 * q^88 - 51 * q^89 + 53 * q^90 + 65 * q^93 + 121 * q^94 - 14 * q^95 + 82 * q^96 + 13 * q^97 - 75 * q^98 - 75 * 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 $

$2$	−1.37192	−0.970095	−0.485048	−	0.874488i	$-0.661198\pi$
$2$	−1.37192	−0.970095	−0.485048	+	0.874488i	$0.661198\pi$
$3$	−3.24389	−1.87286	−0.936429	−	0.350856i	$-0.885891\pi$
$3$	−3.24389	−1.87286	−0.936429	+	0.350856i	$0.885891\pi$
$4$	−0.117831	−0.0589153
$5$	−1.23015	−0.550141	−0.275071	−	0.961424i	$-0.588701\pi$
$5$	−1.23015	−0.550141	−0.275071	+	0.961424i	$0.588701\pi$
$6$	4.45036	1.81685
$7$	−3.99271	−1.50910	−0.754551	−	0.656242i	$-0.772145\pi$
$7$	−3.99271	−1.50910	−0.754551	+	0.656242i	$0.772145\pi$
$8$	2.90550	1.02725
$9$	7.52280	2.50760
$10$	1.68767	0.533689
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	0.382229	0.110340
$13$	−2.35213	−0.652365	−0.326182	−	0.945307i	$-0.605762\pi$
$13$	−2.35213	−0.652365	−0.326182	+	0.945307i	$0.605762\pi$
$14$	5.47768	1.46397
$15$	3.99048	1.03034
$16$	−3.75045	−0.937614
$17$	4.79234	1.16231	0.581157	−	0.813791i	$-0.302600\pi$
$17$	4.79234	1.16231	0.581157	+	0.813791i	$0.302600\pi$
$18$	−10.3207	−2.43261
$19$	−0.189173	−0.0433992	−0.0216996	−	0.999765i	$-0.506908\pi$
$19$	−0.189173	−0.0433992	−0.0216996	+	0.999765i	$0.506908\pi$
$20$	0.144950	0.0324117
$21$	12.9519	2.82633
$22$	1.37192	0.292495
$23$	0	0
$23$	0	0
$24$	−9.42511	−1.92389
$25$	−3.48672	−0.697345
$26$	3.22694	0.632856
$27$	−14.6714	−2.82352
$28$	0.470463	0.0889091
$29$	9.80675	1.82107	0.910534	−	0.413434i	$-0.135671\pi$
$29$	9.80675	1.82107	0.910534	+	0.413434i	$0.135671\pi$
$30$	−5.47462	−0.999525
$31$	1.10911	0.199201	0.0996007	−	0.995027i	$-0.468243\pi$
$31$	1.10911	0.199201	0.0996007	+	0.995027i	$0.468243\pi$
$32$	−0.665665	−0.117674
$33$	3.24389	0.564688
$34$	−6.57472	−1.12756
$35$	4.91164	0.830219
$36$	−0.886416	−0.147736
$37$	5.60736	0.921844	0.460922	−	0.887441i	$-0.347519\pi$
$37$	5.60736	0.921844	0.460922	+	0.887441i	$0.347519\pi$
$38$	0.259530	0.0421014
$39$	7.63006	1.22179
$40$	−3.57421	−0.565132
$41$	10.4777	1.63634	0.818169	−	0.574978i	$-0.194989\pi$
$41$	10.4777	1.63634	0.818169	+	0.574978i	$0.194989\pi$
$42$	−17.7690	−2.74181
$43$	0.255808	0.0390104	0.0195052	−	0.999810i	$-0.493791\pi$
$43$	0.255808	0.0390104	0.0195052	+	0.999810i	$0.493791\pi$
$44$	0.117831	0.0177636
$45$	−9.25420	−1.37953
$46$	0	0
$47$	3.04112	0.443594	0.221797	−	0.975093i	$-0.428808\pi$
$47$	3.04112	0.443594	0.221797	+	0.975093i	$0.428808\pi$
$48$	12.1660	1.75602
$49$	8.94171	1.27739
$50$	4.78351	0.676491
$51$	−15.5458	−2.17685
$52$	0.277153	0.0384342
$53$	13.0157	1.78784	0.893919	−	0.448228i	$-0.147945\pi$
$53$	13.0157	1.78784	0.893919	+	0.448228i	$0.147945\pi$
$54$	20.1281	2.73908
$55$	1.23015	0.165874
$56$	−11.6008	−1.55022
$57$	0.613655	0.0812806
$58$	−13.4541	−1.76661
$59$	5.85897	0.762773	0.381386	−	0.924416i	$-0.375447\pi$
$59$	5.85897	0.762773	0.381386	+	0.924416i	$0.375447\pi$
$60$	−0.470200	−0.0607026
$61$	−2.53555	−0.324644	−0.162322	−	0.986738i	$-0.551898\pi$
$61$	−2.53555	−0.324644	−0.162322	+	0.986738i	$0.551898\pi$
$62$	−1.52161	−0.193244
$63$	−30.0363	−3.78422
$64$	8.41415	1.05177
$65$	2.89349	0.358893
$66$	−4.45036	−0.547801
$67$	−6.20764	−0.758384	−0.379192	−	0.925318i	$-0.623798\pi$
$67$	−6.20764	−0.758384	−0.379192	+	0.925318i	$0.623798\pi$
$68$	−0.564685	−0.0684781
$69$	0	0
$70$	−6.73839	−0.805391
$71$	−8.80904	−1.04544	−0.522721	−	0.852504i	$-0.675083\pi$
$71$	−8.80904	−1.04544	−0.522721	+	0.852504i	$0.675083\pi$
$72$	21.8575	2.57593
$73$	−4.73282	−0.553935	−0.276967	−	0.960879i	$-0.589329\pi$
$73$	−4.73282	−0.553935	−0.276967	+	0.960879i	$0.589329\pi$
$74$	−7.69285	−0.894276
$75$	11.3105	1.30603
$76$	0.0222903	0.00255688
$77$	3.99271	0.455011
$78$	−10.4678	−1.18525
$79$	−1.45162	−0.163320	−0.0816599	−	0.996660i	$-0.526022\pi$
$79$	−1.45162	−0.163320	−0.0816599	+	0.996660i	$0.526022\pi$
$80$	4.61363	0.515820
$81$	25.0241	2.78046
$82$	−14.3746	−1.58740
$83$	−5.75581	−0.631782	−0.315891	−	0.948796i	$-0.602303\pi$
$83$	−5.75581	−0.631782	−0.315891	+	0.948796i	$0.602303\pi$
$84$	−1.52613	−0.166514
$85$	−5.89532	−0.639437
$86$	−0.350949	−0.0378438
$87$	−31.8120	−3.41060
$88$	−2.90550	−0.309727
$89$	9.91146	1.05061	0.525306	−	0.850913i	$-0.323951\pi$
$89$	9.91146	1.05061	0.525306	+	0.850913i	$0.323951\pi$
$90$	12.6960	1.33828
$91$	9.39138	0.984484
$92$	0	0
$93$	−3.59782	−0.373076
$94$	−4.17218	−0.430328
$95$	0.232712	0.0238757
$96$	2.15934	0.220387
$97$	−5.66413	−0.575106	−0.287553	−	0.957765i	$-0.592842\pi$
$97$	−5.66413	−0.575106	−0.287553	+	0.957765i	$0.592842\pi$
$98$	−12.2673	−1.23919
$99$	−7.52280	−0.756070
$100$	0.410843	0.0410843
$101$	8.29477	0.825360	0.412680	−	0.910876i	$-0.364593\pi$
$101$	8.29477	0.825360	0.412680	+	0.910876i	$0.364593\pi$
$102$	21.3276	2.11175
$103$	−1.40436	−0.138375	−0.0691877	−	0.997604i	$-0.522041\pi$
$103$	−1.40436	−0.138375	−0.0691877	+	0.997604i	$0.522041\pi$
$104$	−6.83412	−0.670141
$105$	−15.9328	−1.55488
$106$	−17.8565	−1.73437
$107$	−3.81633	−0.368939	−0.184469	−	0.982838i	$-0.559057\pi$
$107$	−3.81633	−0.368939	−0.184469	+	0.982838i	$0.559057\pi$
$108$	1.72875	0.166349
$109$	−9.56978	−0.916618	−0.458309	−	0.888793i	$-0.651545\pi$
$109$	−9.56978	−0.916618	−0.458309	+	0.888793i	$0.651545\pi$
$110$	−1.68767	−0.160913
$111$	−18.1896	−1.72648
$112$	14.9745	1.41495
$113$	−10.9444	−1.02956	−0.514781	−	0.857322i	$-0.672127\pi$
$113$	−10.9444	−1.02956	−0.514781	+	0.857322i	$0.672127\pi$
$114$	−0.841887	−0.0788500
$115$	0	0
$116$	−1.15554	−0.107289
$117$	−17.6946	−1.63587
$118$	−8.03805	−0.739962
$119$	−19.1344	−1.75405
$120$	11.5943	1.05841
$121$	1.00000	0.0909091
$122$	3.47858	0.314936
$123$	−33.9884	−3.06463
$124$	−0.130687	−0.0117360
$125$	10.4400	0.933779
$126$	41.2075	3.67106
$127$	−17.2547	−1.53111	−0.765554	−	0.643372i	$-0.777535\pi$
$127$	−17.2547	−1.53111	−0.765554	+	0.643372i	$0.777535\pi$
$128$	−10.2122	−0.902642
$129$	−0.829813	−0.0730610
$130$	−3.96964	−0.348160
$131$	7.34827	0.642021	0.321011	−	0.947076i	$-0.395977\pi$
$131$	7.34827	0.642021	0.321011	+	0.947076i	$0.395977\pi$
$132$	−0.382229	−0.0332688
$133$	0.755312	0.0654938
$134$	8.51639	0.735704
$135$	18.0481	1.55334
$136$	13.9241	1.19399
$137$	1.34457	0.114874	0.0574372	−	0.998349i	$-0.481707\pi$
$137$	1.34457	0.114874	0.0574372	+	0.998349i	$0.481707\pi$
$138$	0	0
$139$	−8.53553	−0.723974	−0.361987	−	0.932183i	$-0.617902\pi$
$139$	−8.53553	−0.723974	−0.361987	+	0.932183i	$0.617902\pi$
$140$	−0.578742	−0.0489126
$141$	−9.86506	−0.830788
$142$	12.0853	1.01418
$143$	2.35213	0.196695
$144$	−28.2139	−2.35116
$145$	−12.0638	−1.00184
$146$	6.49306	0.537369
$147$	−29.0059	−2.39237
$148$	−0.660718	−0.0543107
$149$	−4.51694	−0.370042	−0.185021	−	0.982735i	$-0.559235\pi$
$149$	−4.51694	−0.370042	−0.185021	+	0.982735i	$0.559235\pi$
$150$	−15.5172	−1.26697
$151$	2.70230	0.219910	0.109955	−	0.993937i	$-0.464929\pi$
$151$	2.70230	0.219910	0.109955	+	0.993937i	$0.464929\pi$
$152$	−0.549641	−0.0445818
$153$	36.0518	2.91462
$154$	−5.47768	−0.441404
$155$	−1.36437	−0.109589
$156$	−0.899054	−0.0719819
$157$	−17.1186	−1.36621	−0.683107	−	0.730318i	$-0.739372\pi$
$157$	−17.1186	−1.36621	−0.683107	+	0.730318i	$0.739372\pi$
$158$	1.99151	0.158436
$159$	−42.2213	−3.34837
$160$	0.818870	0.0647374
$161$	0	0
$162$	−34.3311	−2.69731
$163$	8.84919	0.693122	0.346561	−	0.938027i	$-0.387349\pi$
$163$	8.84919	0.693122	0.346561	+	0.938027i	$0.387349\pi$
$164$	−1.23459	−0.0964053
$165$	−3.99048	−0.310658
$166$	7.89652	0.612889
$167$	5.90443	0.456899	0.228449	−	0.973556i	$-0.426634\pi$
$167$	5.90443	0.456899	0.228449	+	0.973556i	$0.426634\pi$
$168$	37.6317	2.90335
$169$	−7.46747	−0.574420
$170$	8.08791	0.620315
$171$	−1.42311	−0.108828
$172$	−0.0301420	−0.00229831
$173$	17.8149	1.35444	0.677221	−	0.735780i	$-0.263184\pi$
$173$	17.8149	1.35444	0.677221	+	0.735780i	$0.263184\pi$
$174$	43.6436	3.30861
$175$	13.9215	1.05236
$176$	3.75045	0.282701
$177$	−19.0058	−1.42857
$178$	−13.5977	−1.01919
$179$	4.92358	0.368006	0.184003	−	0.982926i	$-0.441094\pi$
$179$	4.92358	0.368006	0.184003	+	0.982926i	$0.441094\pi$
$180$	1.09043	0.0812756
$181$	−13.4358	−0.998672	−0.499336	−	0.866409i	$-0.666423\pi$
$181$	−13.4358	−0.998672	−0.499336	+	0.866409i	$0.666423\pi$
$182$	−12.8842	−0.955044
$183$	8.22505	0.608013
$184$	0	0
$185$	−6.89791	−0.507144
$186$	4.93592	0.361919
$187$	−4.79234	−0.350451
$188$	−0.358337	−0.0261344
$189$	58.5788	4.26098
$190$	−0.319262	−0.0231617
$191$	13.0470	0.944048	0.472024	−	0.881586i	$-0.343523\pi$
$191$	13.0470	0.944048	0.472024	+	0.881586i	$0.343523\pi$
$192$	−27.2945	−1.96981
$193$	−0.857818	−0.0617471	−0.0308735	−	0.999523i	$-0.509829\pi$
$193$	−0.857818	−0.0617471	−0.0308735	+	0.999523i	$0.509829\pi$
$194$	7.77075	0.557907
$195$	−9.38614	−0.672155
$196$	−1.05361	−0.0752576
$197$	−5.65622	−0.402989	−0.201494	−	0.979490i	$-0.564580\pi$
$197$	−5.65622	−0.402989	−0.201494	+	0.979490i	$0.564580\pi$
$198$	10.3207	0.733460
$199$	23.7722	1.68517	0.842583	−	0.538567i	$-0.181034\pi$
$199$	23.7722	1.68517	0.842583	+	0.538567i	$0.181034\pi$
$200$	−10.1307	−0.716346
$201$	20.1369	1.42035
$202$	−11.3798	−0.800678
$203$	−39.1555	−2.74818
$204$	1.83177	0.128250
$205$	−12.8891	−0.900217
$206$	1.92667	0.134237
$207$	0	0
$208$	8.82157	0.611666
$209$	0.189173	0.0130854
$210$	21.8586	1.50838
$211$	7.80198	0.537111	0.268555	−	0.963264i	$-0.413454\pi$
$211$	7.80198	0.537111	0.268555	+	0.963264i	$0.413454\pi$
$212$	−1.53364	−0.105331
$213$	28.5755	1.95796
$214$	5.23571	0.357906
$215$	−0.314683	−0.0214612
$216$	−42.6279	−2.90046
$217$	−4.42834	−0.300615
$218$	13.1290	0.889207
$219$	15.3527	1.03744
$220$	−0.144950	−0.00977250
$221$	−11.2722	−0.758253
$222$	24.9547	1.67485
$223$	18.2906	1.22483	0.612413	−	0.790538i	$-0.290199\pi$
$223$	18.2906	1.22483	0.612413	+	0.790538i	$0.290199\pi$
$224$	2.65781	0.177582
$225$	−26.2299	−1.74866
$226$	15.0148	0.998772
$227$	24.1573	1.60337	0.801687	−	0.597744i	$-0.203936\pi$
$227$	24.1573	1.60337	0.801687	+	0.597744i	$0.203936\pi$
$228$	−0.0723074	−0.00478867
$229$	−12.6252	−0.834299	−0.417150	−	0.908838i	$-0.636971\pi$
$229$	−12.6252	−0.834299	−0.417150	+	0.908838i	$0.636971\pi$
$230$	0	0
$231$	−12.9519	−0.852172
$232$	28.4935	1.87069
$233$	11.3055	0.740647	0.370323	−	0.928903i	$-0.379247\pi$
$233$	11.3055	0.740647	0.370323	+	0.928903i	$0.379247\pi$
$234$	24.2757	1.58695
$235$	−3.74105	−0.244039
$236$	−0.690366	−0.0449390
$237$	4.70889	0.305875
$238$	26.2509	1.70160
$239$	−19.3570	−1.25210	−0.626050	−	0.779783i	$-0.715330\pi$
$239$	−19.3570	−1.25210	−0.626050	+	0.779783i	$0.715330\pi$
$240$	−14.9661	−0.966058
$241$	−27.7855	−1.78982	−0.894912	−	0.446243i	$-0.852762\pi$
$241$	−27.7855	−1.78982	−0.894912	+	0.446243i	$0.852762\pi$
$242$	−1.37192	−0.0881905
$243$	−37.1610	−2.38388
$244$	0.298766	0.0191265
$245$	−10.9997	−0.702743
$246$	46.6294	2.97298
$247$	0.444960	0.0283121
$248$	3.22251	0.204629
$249$	18.6712	1.18324
$250$	−14.3228	−0.905855
$251$	16.7436	1.05685	0.528425	−	0.848980i	$-0.322783\pi$
$251$	16.7436	1.05685	0.528425	+	0.848980i	$0.322783\pi$
$252$	3.53920	0.222949
$253$	0	0
$254$	23.6721	1.48532
$255$	19.1237	1.19757
$256$	−2.81793	−0.176120
$257$	−28.1826	−1.75798	−0.878992	−	0.476837i	$-0.841783\pi$
$257$	−28.1826	−1.75798	−0.878992	+	0.476837i	$0.841783\pi$
$258$	1.13844	0.0708761
$259$	−22.3885	−1.39116
$260$	−0.340941	−0.0211443
$261$	73.7742	4.56651
$262$	−10.0813	−0.622822
$263$	−12.7117	−0.783836	−0.391918	−	0.920000i	$-0.628188\pi$
$263$	−12.7117	−0.783836	−0.391918	+	0.920000i	$0.628188\pi$
$264$	9.42511	0.580075
$265$	−16.0113	−0.983564
$266$	−1.03623	−0.0635353
$267$	−32.1516	−1.96765
$268$	0.731450	0.0446804
$269$	−5.78672	−0.352822	−0.176411	−	0.984317i	$-0.556449\pi$
$269$	−5.78672	−0.352822	−0.176411	+	0.984317i	$0.556449\pi$
$270$	−24.7606	−1.50688
$271$	9.99129	0.606928	0.303464	−	0.952843i	$-0.401857\pi$
$271$	9.99129	0.606928	0.303464	+	0.952843i	$0.401857\pi$
$272$	−17.9735	−1.08980
$273$	−30.4646	−1.84380
$274$	−1.84465	−0.111439
$275$	3.48672	0.210257
$276$	0	0
$277$	7.79230	0.468194	0.234097	−	0.972213i	$-0.424787\pi$
$277$	7.79230	0.468194	0.234097	+	0.972213i	$0.424787\pi$
$278$	11.7101	0.702324
$279$	8.34359	0.499518
$280$	14.2708	0.852841
$281$	−4.85861	−0.289840	−0.144920	−	0.989443i	$-0.546292\pi$
$281$	−4.85861	−0.289840	−0.144920	+	0.989443i	$0.546292\pi$
$282$	13.5341	0.805943
$283$	−15.3267	−0.911080	−0.455540	−	0.890215i	$-0.650554\pi$
$283$	−15.3267	−0.911080	−0.455540	+	0.890215i	$0.650554\pi$
$284$	1.03797	0.0615925
$285$	−0.754890	−0.0447158
$286$	−3.22694	−0.190813
$287$	−41.8343	−2.46940
$288$	−5.00767	−0.295080
$289$	5.96656	0.350974
$290$	16.5506	0.971885
$291$	18.3738	1.07709
$292$	0.557671	0.0326352
$293$	−1.38274	−0.0807804	−0.0403902	−	0.999184i	$-0.512860\pi$
$293$	−1.38274	−0.0807804	−0.0403902	+	0.999184i	$0.512860\pi$
$294$	39.7938	2.32082
$295$	−7.20743	−0.419633
$296$	16.2922	0.946962
$297$	14.6714	0.851324
$298$	6.19689	0.358976
$299$	0	0
$300$	−1.33273	−0.0769450
$301$	−1.02137	−0.0588707
$302$	−3.70735	−0.213334
$303$	−26.9073	−1.54578
$304$	0.709484	0.0406917
$305$	3.11912	0.178600
$306$	−49.4603	−2.82746
$307$	0.728973	0.0416047	0.0208024	−	0.999784i	$-0.493378\pi$
$307$	0.728973	0.0416047	0.0208024	+	0.999784i	$0.493378\pi$
$308$	−0.470463	−0.0268071
$309$	4.55558	0.259158
$310$	1.87181	0.106312
$311$	−11.2930	−0.640369	−0.320185	−	0.947355i	$-0.603745\pi$
$311$	−11.2930	−0.640369	−0.320185	+	0.947355i	$0.603745\pi$
$312$	22.1691	1.25508
$313$	14.8533	0.839559	0.419779	−	0.907626i	$-0.362107\pi$
$313$	14.8533	0.839559	0.419779	+	0.907626i	$0.362107\pi$
$314$	23.4854	1.32536
$315$	36.9493	2.08186
$316$	0.171045	0.00962204
$317$	8.19350	0.460193	0.230096	−	0.973168i	$-0.426096\pi$
$317$	8.19350	0.460193	0.230096	+	0.973168i	$0.426096\pi$
$318$	57.9244	3.24824
$319$	−9.80675	−0.549073
$320$	−10.3507	−0.578621
$321$	12.3798	0.690970
$322$	0	0
$323$	−0.906581	−0.0504435
$324$	−2.94861	−0.163811
$325$	8.20124	0.454923
$326$	−12.1404	−0.672394
$327$	31.0433	1.71670
$328$	30.4429	1.68093
$329$	−12.1423	−0.669428
$330$	5.47462	0.301368
$331$	22.6120	1.24287	0.621435	−	0.783466i	$-0.286550\pi$
$331$	22.6120	1.24287	0.621435	+	0.783466i	$0.286550\pi$
$332$	0.678210	0.0372216
$333$	42.1830	2.31161
$334$	−8.10042	−0.443235
$335$	7.63635	0.417218
$336$	−48.5755	−2.65001
$337$	−28.2597	−1.53940	−0.769701	−	0.638405i	$-0.779595\pi$
$337$	−28.2597	−1.53940	−0.769701	+	0.638405i	$0.779595\pi$
$338$	10.2448	0.557242
$339$	35.5023	1.92822
$340$	0.694649	0.0376726
$341$	−1.10911	−0.0600615
$342$	1.95240	0.105573
$343$	−7.75268	−0.418605
$344$	0.743251	0.0400734
$345$	0	0
$346$	−24.4406	−1.31394
$347$	10.2728	0.551474	0.275737	−	0.961233i	$-0.411078\pi$
$347$	10.2728	0.551474	0.275737	+	0.961233i	$0.411078\pi$
$348$	3.74842	0.200937
$349$	31.3368	1.67742	0.838710	−	0.544578i	$-0.183310\pi$
$349$	31.3368	1.67742	0.838710	+	0.544578i	$0.183310\pi$
$350$	−19.0992	−1.02089
$351$	34.5092	1.84197
$352$	0.665665	0.0354801
$353$	−7.12311	−0.379125	−0.189563	−	0.981869i	$-0.560707\pi$
$353$	−7.12311	−0.379125	−0.189563	+	0.981869i	$0.560707\pi$
$354$	26.0745	1.38584
$355$	10.8365	0.575140
$356$	−1.16787	−0.0618971
$357$	62.0699	3.28509
$358$	−6.75477	−0.357001
$359$	33.1543	1.74982	0.874908	−	0.484289i	$-0.160922\pi$
$359$	33.1543	1.74982	0.874908	+	0.484289i	$0.160922\pi$
$360$	−26.8880	−1.41712
$361$	−18.9642	−0.998117
$362$	18.4328	0.968807
$363$	−3.24389	−0.170260
$364$	−1.10659	−0.0580012
$365$	5.82209	0.304742
$366$	−11.2841	−0.589831
$367$	25.5793	1.33523	0.667613	−	0.744508i	$-0.267316\pi$
$367$	25.5793	1.33523	0.667613	+	0.744508i	$0.267316\pi$
$368$	0	0
$369$	78.8215	4.10328
$370$	9.46339	0.491978
$371$	−51.9677	−2.69803
$372$	0.423933	0.0219799
$373$	−10.0264	−0.519148	−0.259574	−	0.965723i	$-0.583582\pi$
$373$	−10.0264	−0.519148	−0.259574	+	0.965723i	$0.583582\pi$
$374$	6.57472	0.339971
$375$	−33.8661	−1.74884
$376$	8.83598	0.455681
$377$	−23.0668	−1.18800
$378$	−80.3655	−4.13356
$379$	18.3701	0.943611	0.471805	−	0.881703i	$-0.343603\pi$
$379$	18.3701	0.943611	0.471805	+	0.881703i	$0.343603\pi$
$380$	−0.0274205	−0.00140664
$381$	55.9723	2.86755
$382$	−17.8995	−0.915817
$383$	−27.5710	−1.40881	−0.704406	−	0.709797i	$-0.748787\pi$
$383$	−27.5710	−1.40881	−0.704406	+	0.709797i	$0.748787\pi$
$384$	33.1273	1.69052
$385$	−4.91164	−0.250320
$386$	1.17686	0.0599005
$387$	1.92439	0.0978225
$388$	0.667408	0.0338825
$389$	−4.04267	−0.204971	−0.102486	−	0.994734i	$-0.532680\pi$
$389$	−4.04267	−0.204971	−0.102486	+	0.994734i	$0.532680\pi$
$390$	12.8770	0.652055
$391$	0	0
$392$	25.9801	1.31219
$393$	−23.8370	−1.20242
$394$	7.75989	0.390937
$395$	1.78571	0.0898490
$396$	0.886416	0.0445441
$397$	2.32015	0.116445	0.0582225	−	0.998304i	$-0.481457\pi$
$397$	2.32015	0.116445	0.0582225	+	0.998304i	$0.481457\pi$
$398$	−32.6136	−1.63477
$399$	−2.45015	−0.122661
$400$	13.0768	0.653840
$401$	−12.6180	−0.630111	−0.315055	−	0.949073i	$-0.602023\pi$
$401$	−12.6180	−0.630111	−0.315055	+	0.949073i	$0.602023\pi$
$402$	−27.6262	−1.37787
$403$	−2.60877	−0.129952
$404$	−0.977377	−0.0486263
$405$	−30.7835	−1.52964
$406$	53.7183	2.66599
$407$	−5.60736	−0.277946
$408$	−45.1683	−2.23617
$409$	−7.64906	−0.378222	−0.189111	−	0.981956i	$-0.560561\pi$
$409$	−7.64906	−0.378222	−0.189111	+	0.981956i	$0.560561\pi$
$410$	17.6829	0.873296
$411$	−4.36164	−0.215144
$412$	0.165476	0.00815243
$413$	−23.3932	−1.15110
$414$	0	0
$415$	7.08052	0.347569
$416$	1.56573	0.0767664
$417$	27.6883	1.35590
$418$	−0.259530	−0.0126940
$419$	20.4884	1.00093	0.500463	−	0.865758i	$-0.333163\pi$
$419$	20.4884	1.00093	0.500463	+	0.865758i	$0.333163\pi$
$420$	1.87737	0.0916064
$421$	−29.1001	−1.41825	−0.709126	−	0.705082i	$-0.750910\pi$
$421$	−29.1001	−1.41825	−0.709126	+	0.705082i	$0.750910\pi$
$422$	−10.7037	−0.521048
$423$	22.8778	1.11236
$424$	37.8170	1.83655
$425$	−16.7096	−0.810533
$426$	−39.2034	−1.89941
$427$	10.1237	0.489921
$428$	0.449681	0.0217361
$429$	−7.63006	−0.368383
$430$	0.431721	0.0208194
$431$	32.1876	1.55042	0.775211	−	0.631703i	$-0.217644\pi$
$431$	32.1876	1.55042	0.775211	+	0.631703i	$0.217644\pi$
$432$	55.0246	2.64737
$433$	16.1475	0.776002	0.388001	−	0.921659i	$-0.373166\pi$
$433$	16.1475	0.776002	0.388001	+	0.921659i	$0.373166\pi$
$434$	6.07533	0.291625
$435$	39.1336	1.87631
$436$	1.12761	0.0540028
$437$	0	0
$438$	−21.0627	−1.00642
$439$	14.5985	0.696748	0.348374	−	0.937356i	$-0.386734\pi$
$439$	14.5985	0.696748	0.348374	+	0.937356i	$0.386734\pi$
$440$	3.57421	0.170394
$441$	67.2667	3.20318
$442$	15.4646	0.735577
$443$	23.4070	1.11210	0.556050	−	0.831149i	$-0.312316\pi$
$443$	23.4070	1.11210	0.556050	+	0.831149i	$0.312316\pi$
$444$	2.14329	0.101716
$445$	−12.1926	−0.577985
$446$	−25.0932	−1.18820
$447$	14.6524	0.693037
$448$	−33.5952	−1.58723
$449$	28.6568	1.35240	0.676198	−	0.736720i	$-0.263626\pi$
$449$	28.6568	1.35240	0.676198	+	0.736720i	$0.263626\pi$
$450$	35.9854	1.69637
$451$	−10.4777	−0.493375
$452$	1.28958	0.0606569
$453$	−8.76596	−0.411861
$454$	−33.1419	−1.55543
$455$	−11.5528	−0.541605
$456$	1.78297	0.0834954
$457$	13.9166	0.650989	0.325494	−	0.945544i	$-0.394469\pi$
$457$	13.9166	0.650989	0.325494	+	0.945544i	$0.394469\pi$
$458$	17.3208	0.809350
$459$	−70.3106	−3.28182
$460$	0	0
$461$	8.00154	0.372669	0.186334	−	0.982486i	$-0.440339\pi$
$461$	8.00154	0.372669	0.186334	+	0.982486i	$0.440339\pi$
$462$	17.7690	0.826688
$463$	−38.8745	−1.80665	−0.903325	−	0.428958i	$-0.858881\pi$
$463$	−38.8745	−1.80665	−0.903325	+	0.428958i	$0.858881\pi$
$464$	−36.7798	−1.70746
$465$	4.42587	0.205245
$466$	−15.5102	−0.718498
$467$	−21.7071	−1.00448	−0.502242	−	0.864727i	$-0.667491\pi$
$467$	−21.7071	−1.00448	−0.502242	+	0.864727i	$0.667491\pi$
$468$	2.08497	0.0963777
$469$	24.7853	1.14448
$470$	5.13243	0.236741
$471$	55.5309	2.55873
$472$	17.0232	0.783557
$473$	−0.255808	−0.0117621
$474$	−6.46022	−0.296728
$475$	0.659593	0.0302642
$476$	2.25462	0.103340
$477$	97.9142	4.48318
$478$	26.5563	1.21466
$479$	−13.5790	−0.620442	−0.310221	−	0.950664i	$-0.600403\pi$
$479$	−13.5790	−0.620442	−0.310221	+	0.950664i	$0.600403\pi$
$480$	−2.65632	−0.121244
$481$	−13.1893	−0.601378
$482$	38.1196	1.73630
$483$	0	0
$484$	−0.117831	−0.00535593
$485$	6.96775	0.316389
$486$	50.9820	2.31259
$487$	−38.1095	−1.72691	−0.863453	−	0.504429i	$-0.831703\pi$
$487$	−38.1095	−1.72691	−0.863453	+	0.504429i	$0.831703\pi$
$488$	−7.36705	−0.333491
$489$	−28.7058	−1.29812
$490$	15.0907	0.681728
$491$	−29.4176	−1.32760	−0.663800	−	0.747910i	$-0.731057\pi$
$491$	−29.4176	−1.32760	−0.663800	+	0.747910i	$0.731057\pi$
$492$	4.00487	0.180554
$493$	46.9973	2.11665
$494$	−0.610450	−0.0274655
$495$	9.25420	0.415945
$496$	−4.15966	−0.186774
$497$	35.1719	1.57768
$498$	−25.6154	−1.14785
$499$	−0.159870	−0.00715676	−0.00357838	−	0.999994i	$-0.501139\pi$
$499$	−0.159870	−0.00715676	−0.00357838	+	0.999994i	$0.501139\pi$
$500$	−1.23015	−0.0550139
$501$	−19.1533	−0.855707
$502$	−22.9710	−1.02524
$503$	−20.1798	−0.899773	−0.449887	−	0.893086i	$-0.648536\pi$
$503$	−20.1798	−0.899773	−0.449887	+	0.893086i	$0.648536\pi$
$504$	−87.2705	−3.88734
$505$	−10.2038	−0.454065
$506$	0	0
$507$	24.2236	1.07581
$508$	2.03313	0.0902056
$509$	18.5104	0.820461	0.410230	−	0.911982i	$-0.365448\pi$
$509$	18.5104	0.820461	0.410230	+	0.911982i	$0.365448\pi$
$510$	−26.2363	−1.16176
$511$	18.8968	0.835944
$512$	24.2904	1.07350
$513$	2.77544	0.122539
$514$	38.6643	1.70541
$515$	1.72757	0.0761260
$516$	0.0977774	0.00430441
$517$	−3.04112	−0.133748
$518$	30.7153	1.34955
$519$	−57.7895	−2.53668
$520$	8.40702	0.368672
$521$	21.1474	0.926485	0.463243	−	0.886232i	$-0.346686\pi$
$521$	21.1474	0.926485	0.463243	+	0.886232i	$0.346686\pi$
$522$	−101.212	−4.42995
$523$	−5.94231	−0.259839	−0.129920	−	0.991525i	$-0.541472\pi$
$523$	−5.94231	−0.259839	−0.129920	+	0.991525i	$0.541472\pi$
$524$	−0.865851	−0.0378249
$525$	−45.1596	−1.97093
$526$	17.4394	0.760396
$527$	5.31522	0.231535
$528$	−12.1660	−0.529459
$529$	0	0
$530$	21.9662	0.954151
$531$	44.0759	1.91273
$532$	−0.0889988	−0.00385859
$533$	−24.6449	−1.06749
$534$	44.1095	1.90881
$535$	4.69468	0.202969
$536$	−18.0363	−0.779049
$537$	−15.9715	−0.689223
$538$	7.93892	0.342271
$539$	−8.94171	−0.385147
$540$	−2.12662	−0.0915152
$541$	25.3875	1.09149	0.545747	−	0.837950i	$-0.316246\pi$
$541$	25.3875	1.09149	0.545747	+	0.837950i	$0.316246\pi$
$542$	−13.7073	−0.588778
$543$	43.5841	1.87037
$544$	−3.19010	−0.136774
$545$	11.7723	0.504270
$546$	41.7950	1.78866
$547$	19.6197	0.838877	0.419438	−	0.907784i	$-0.362227\pi$
$547$	19.6197	0.838877	0.419438	+	0.907784i	$0.362227\pi$
$548$	−0.158432	−0.00676786
$549$	−19.0745	−0.814078
$550$	−4.78351	−0.203970
$551$	−1.85517	−0.0790330
$552$	0	0
$553$	5.79589	0.246466
$554$	−10.6904	−0.454193
$555$	22.3760	0.949809
$556$	1.00575	0.0426531
$557$	6.35076	0.269091	0.134545	−	0.990907i	$-0.457043\pi$
$557$	6.35076	0.269091	0.134545	+	0.990907i	$0.457043\pi$
$558$	−11.4468	−0.484580
$559$	−0.601696	−0.0254490
$560$	−18.4209	−0.778425
$561$	15.5458	0.656345
$562$	6.66563	0.281172
$563$	14.4861	0.610515	0.305258	−	0.952270i	$-0.401257\pi$
$563$	14.4861	0.610515	0.305258	+	0.952270i	$0.401257\pi$
$564$	1.16241	0.0489461
$565$	13.4633	0.566404
$566$	21.0271	0.883834
$567$	−99.9140	−4.19599
$568$	−25.5947	−1.07393
$569$	−27.5334	−1.15426	−0.577131	−	0.816652i	$-0.695828\pi$
$569$	−27.5334	−1.15426	−0.577131	+	0.816652i	$0.695828\pi$
$570$	1.03565	0.0433786
$571$	−23.8046	−0.996192	−0.498096	−	0.867122i	$-0.665967\pi$
$571$	−23.8046	−0.996192	−0.498096	+	0.867122i	$0.665967\pi$
$572$	−0.277153	−0.0115884
$573$	−42.3230	−1.76807
$574$	57.3934	2.39555
$575$	0	0
$576$	63.2980	2.63742
$577$	42.0713	1.75145	0.875726	−	0.482808i	$-0.160383\pi$
$577$	42.0713	1.75145	0.875726	+	0.482808i	$0.160383\pi$
$578$	−8.18565	−0.340478
$579$	2.78266	0.115644
$580$	1.42149	0.0590240
$581$	22.9812	0.953423
$582$	−25.2074	−1.04488
$583$	−13.0157	−0.539054
$584$	−13.7512	−0.569029
$585$	21.7671	0.899959
$586$	1.89701	0.0783647
$587$	−26.1505	−1.07934	−0.539672	−	0.841875i	$-0.681452\pi$
$587$	−26.1505	−1.07934	−0.539672	+	0.841875i	$0.681452\pi$
$588$	3.41778	0.140947
$589$	−0.209813	−0.00864519
$590$	9.88803	0.407084
$591$	18.3481	0.754741
$592$	−21.0301	−0.864333
$593$	30.6551	1.25885	0.629427	−	0.777059i	$-0.283289\pi$
$593$	30.6551	1.25885	0.629427	+	0.777059i	$0.283289\pi$
$594$	−20.1281	−0.825865
$595$	23.5383	0.964975
$596$	0.532234	0.0218011
$597$	−77.1143	−3.15608
$598$	0	0
$599$	22.2683	0.909860	0.454930	−	0.890527i	$-0.349664\pi$
$599$	22.2683	0.909860	0.454930	+	0.890527i	$0.349664\pi$
$600$	32.8627	1.34162
$601$	8.35696	0.340887	0.170444	−	0.985367i	$-0.445480\pi$
$601$	8.35696	0.340887	0.170444	+	0.985367i	$0.445480\pi$
$602$	1.40124	0.0571101
$603$	−46.6988	−1.90172
$604$	−0.318414	−0.0129561
$605$	−1.23015	−0.0500128
$606$	36.9147	1.49956
$607$	−2.04950	−0.0831867	−0.0415933	−	0.999135i	$-0.513243\pi$
$607$	−2.04950	−0.0831867	−0.0415933	+	0.999135i	$0.513243\pi$
$608$	0.125926	0.00510697
$609$	127.016	5.14695
$610$	−4.27919	−0.173259
$611$	−7.15313	−0.289385
$612$	−4.24801	−0.171716
$613$	−22.9368	−0.926409	−0.463205	−	0.886251i	$-0.653300\pi$
$613$	−22.9368	−0.926409	−0.463205	+	0.886251i	$0.653300\pi$
$614$	−1.00009	−0.0403605
$615$	41.8109	1.68598
$616$	11.6008	0.467410
$617$	48.3801	1.94771	0.973854	−	0.227174i	$-0.0729486\pi$
$617$	48.3801	1.94771	0.973854	+	0.227174i	$0.0729486\pi$
$618$	−6.24989	−0.251408
$619$	30.0411	1.20745	0.603726	−	0.797192i	$-0.293682\pi$
$619$	30.0411	1.20745	0.603726	+	0.797192i	$0.293682\pi$
$620$	0.160765	0.00645646
$621$	0	0
$622$	15.4932	0.621219
$623$	−39.5736	−1.58548
$624$	−28.6162	−1.14556
$625$	4.59085	0.183634
$626$	−20.3776	−0.814452
$627$	−0.613655	−0.0245070
$628$	2.01710	0.0804909
$629$	26.8724	1.07147
$630$	−50.6915	−2.01960
$631$	−35.4559	−1.41148	−0.705738	−	0.708473i	$-0.749384\pi$
$631$	−35.4559	−1.41148	−0.705738	+	0.708473i	$0.749384\pi$
$632$	−4.21768	−0.167770
$633$	−25.3087	−1.00593
$634$	−11.2408	−0.446431
$635$	21.2259	0.842325
$636$	4.97496	0.197270
$637$	−21.0321	−0.833322
$638$	13.4541	0.532653
$639$	−66.2687	−2.62155
$640$	12.5626	0.496580
$641$	0.232870	0.00919782	0.00459891	−	0.999989i	$-0.498536\pi$
$641$	0.232870	0.00919782	0.00459891	+	0.999989i	$0.498536\pi$
$642$	−16.9841	−0.670307
$643$	33.0573	1.30365	0.651827	−	0.758368i	$-0.274003\pi$
$643$	33.0573	1.30365	0.651827	+	0.758368i	$0.274003\pi$
$644$	0	0
$645$	1.02080	0.0401939
$646$	1.24376	0.0489350
$647$	−26.7833	−1.05296	−0.526480	−	0.850188i	$-0.676488\pi$
$647$	−26.7833	−1.05296	−0.526480	+	0.850188i	$0.676488\pi$
$648$	72.7075	2.85622
$649$	−5.85897	−0.229985
$650$	−11.2515	−0.441319
$651$	14.3650	0.563010
$652$	−1.04271	−0.0408355
$653$	−17.8478	−0.698440	−0.349220	−	0.937041i	$-0.613553\pi$
$653$	−17.8478	−0.698440	−0.349220	+	0.937041i	$0.613553\pi$
$654$	−42.5889	−1.66536
$655$	−9.03950	−0.353202
$656$	−39.2961	−1.53425
$657$	−35.6041	−1.38905
$658$	16.6583	0.649409
$659$	−48.9394	−1.90641	−0.953204	−	0.302326i	$-0.902237\pi$
$659$	−48.9394	−1.90641	−0.953204	+	0.302326i	$0.902237\pi$
$660$	0.470200	0.0183025
$661$	−5.60649	−0.218067	−0.109033	−	0.994038i	$-0.534776\pi$
$661$	−5.60649	−0.218067	−0.109033	+	0.994038i	$0.534776\pi$
$662$	−31.0219	−1.20570
$663$	36.5658	1.42010
$664$	−16.7235	−0.648997
$665$	−0.929149	−0.0360309
$666$	−57.8718	−2.24249
$667$	0	0
$668$	−0.695723	−0.0269183
$669$	−59.3325	−2.29393
$670$	−10.4765	−0.404741
$671$	2.53555	0.0978840
$672$	−8.62162	−0.332586
$673$	−46.2043	−1.78105	−0.890523	−	0.454939i	$-0.849661\pi$
$673$	−46.2043	−1.78105	−0.890523	+	0.454939i	$0.849661\pi$
$674$	38.7700	1.49337
$675$	51.1553	1.96897
$676$	0.879896	0.0338421
$677$	−1.30310	−0.0500821	−0.0250411	−	0.999686i	$-0.507972\pi$
$677$	−1.30310	−0.0500821	−0.0250411	+	0.999686i	$0.507972\pi$
$678$	−48.7064	−1.87056
$679$	22.6152	0.867893
$680$	−17.1288	−0.656861
$681$	−78.3634	−3.00289
$682$	1.52161	0.0582654
$683$	−47.8924	−1.83255	−0.916276	−	0.400547i	$-0.868820\pi$
$683$	−47.8924	−1.83255	−0.916276	+	0.400547i	$0.868820\pi$
$684$	0.167686	0.00641163
$685$	−1.65403	−0.0631972
$686$	10.6361	0.406087
$687$	40.9548	1.56252
$688$	−0.959398	−0.0365767
$689$	−30.6146	−1.16632
$690$	0	0
$691$	34.9666	1.33019	0.665096	−	0.746757i	$-0.268390\pi$
$691$	34.9666	1.33019	0.665096	+	0.746757i	$0.268390\pi$
$692$	−2.09914	−0.0797973
$693$	30.0363	1.14099
$694$	−14.0935	−0.534982
$695$	10.5000	0.398288
$696$	−92.4297	−3.50354
$697$	50.2126	1.90194
$698$	−42.9916	−1.62726
$699$	−36.6737	−1.38713
$700$	−1.64037	−0.0620003
$701$	−4.50343	−0.170092	−0.0850461	−	0.996377i	$-0.527104\pi$
$701$	−4.50343	−0.170092	−0.0850461	+	0.996377i	$0.527104\pi$
$702$	−47.3439	−1.78688
$703$	−1.06076	−0.0400073
$704$	−8.41415	−0.317120
$705$	12.1355	0.457051
$706$	9.77235	0.367787
$707$	−33.1186	−1.24555
$708$	2.23947	0.0841644
$709$	9.29682	0.349149	0.174575	−	0.984644i	$-0.444145\pi$
$709$	9.29682	0.349149	0.174575	+	0.984644i	$0.444145\pi$
$710$	−14.8668	−0.557941
$711$	−10.9202	−0.409541
$712$	28.7977	1.07924
$713$	0	0
$714$	−85.1550	−3.18685
$715$	−2.89349	−0.108210
$716$	−0.580149	−0.0216812
$717$	62.7919	2.34501
$718$	−45.4851	−1.69749
$719$	33.6739	1.25582	0.627912	−	0.778284i	$-0.283910\pi$
$719$	33.6739	1.25582	0.627912	+	0.778284i	$0.283910\pi$
$720$	34.7074	1.29347
$721$	5.60719	0.208823
$722$	26.0174	0.968268
$723$	90.1331	3.35209
$724$	1.58314	0.0588370
$725$	−34.1934	−1.26991
$726$	4.45036	0.165168
$727$	−30.0787	−1.11556	−0.557779	−	0.829990i	$-0.688346\pi$
$727$	−30.0787	−1.11556	−0.557779	+	0.829990i	$0.688346\pi$
$728$	27.2866	1.01131
$729$	45.4738	1.68422
$730$	−7.98746	−0.295629
$731$	1.22592	0.0453423
$732$	−0.969162	−0.0358213
$733$	18.7515	0.692603	0.346301	−	0.938123i	$-0.387437\pi$
$733$	18.7515	0.692603	0.346301	+	0.938123i	$0.387437\pi$
$734$	−35.0927	−1.29530
$735$	35.6817	1.31614
$736$	0	0
$737$	6.20764	0.228661
$738$	−108.137	−3.98057
$739$	25.3477	0.932432	0.466216	−	0.884671i	$-0.345617\pi$
$739$	25.3477	0.932432	0.466216	+	0.884671i	$0.345617\pi$
$740$	0.812784	0.0298785
$741$	−1.44340	−0.0530246
$742$	71.2957	2.61735
$743$	4.94098	0.181267	0.0906336	−	0.995884i	$-0.471111\pi$
$743$	4.94098	0.181267	0.0906336	+	0.995884i	$0.471111\pi$
$744$	−10.4534	−0.383242
$745$	5.55653	0.203576
$746$	13.7554	0.503623
$747$	−43.2998	−1.58426
$748$	0.564685	0.0206469
$749$	15.2375	0.556766
$750$	46.4616	1.69654
$751$	−20.8682	−0.761491	−0.380745	−	0.924680i	$-0.624333\pi$
$751$	−20.8682	−0.761491	−0.380745	+	0.924680i	$0.624333\pi$
$752$	−11.4056	−0.415919
$753$	−54.3145	−1.97933
$754$	31.6458	1.15247
$755$	−3.32425	−0.120982
$756$	−6.90237	−0.251037
$757$	19.7079	0.716296	0.358148	−	0.933665i	$-0.383408\pi$
$757$	19.7079	0.716296	0.358148	+	0.933665i	$0.383408\pi$
$758$	−25.2024	−0.915392
$759$	0	0
$760$	0.676143	0.0245263
$761$	30.8222	1.11730	0.558651	−	0.829403i	$-0.311319\pi$
$761$	30.8222	1.11730	0.558651	+	0.829403i	$0.311319\pi$
$762$	−76.7896	−2.78179
$763$	38.2093	1.38327
$764$	−1.53734	−0.0556189
$765$	−44.3493	−1.60345
$766$	37.8253	1.36668
$767$	−13.7811	−0.497606
$768$	9.14103	0.329848
$769$	−30.5881	−1.10303	−0.551517	−	0.834163i	$-0.685951\pi$
$769$	−30.5881	−1.10303	−0.551517	+	0.834163i	$0.685951\pi$
$770$	6.73839	0.242835
$771$	91.4212	3.29245
$772$	0.101077	0.00363785
$773$	−1.70903	−0.0614696	−0.0307348	−	0.999528i	$-0.509785\pi$
$773$	−1.70903	−0.0614696	−0.0307348	+	0.999528i	$0.509785\pi$
$774$	−2.64012	−0.0948971
$775$	−3.86715	−0.138912
$776$	−16.4571	−0.590777
$777$	72.6258	2.60544
$778$	5.54622	0.198842
$779$	−1.98209	−0.0710158
$780$	1.10597	0.0396002
$781$	8.80904	0.315212
$782$	0	0
$783$	−143.879	−5.14182
$784$	−33.5355	−1.19770
$785$	21.0585	0.751611
$786$	32.7024	1.16646
$787$	−21.4116	−0.763242	−0.381621	−	0.924319i	$-0.624634\pi$
$787$	−21.4116	−0.763242	−0.381621	+	0.924319i	$0.624634\pi$
$788$	0.666475	0.0237422
$789$	41.2353	1.46801
$790$	−2.44986	−0.0871621
$791$	43.6977	1.55371
$792$	−21.8575	−0.776672
$793$	5.96396	0.211787
$794$	−3.18307	−0.112963
$795$	51.9387	1.84208
$796$	−2.80109	−0.0992820
$797$	26.7963	0.949174	0.474587	−	0.880209i	$-0.342597\pi$
$797$	26.7963	0.949174	0.474587	+	0.880209i	$0.342597\pi$
$798$	3.36141	0.118993
$799$	14.5741	0.515595
$800$	2.32099	0.0820594
$801$	74.5619	2.63452
$802$	17.3109	0.611268
$803$	4.73282	0.167018
$804$	−2.37274	−0.0836801
$805$	0	0
$806$	3.57903	0.126066
$807$	18.7714	0.660786
$808$	24.1004	0.847850
$809$	−22.7104	−0.798454	−0.399227	−	0.916852i	$-0.630722\pi$
$809$	−22.7104	−0.798454	−0.399227	+	0.916852i	$0.630722\pi$
$810$	42.2325	1.48390
$811$	11.0095	0.386595	0.193298	−	0.981140i	$-0.438082\pi$
$811$	11.0095	0.386595	0.193298	+	0.981140i	$0.438082\pi$
$812$	4.61371	0.161910
$813$	−32.4106	−1.13669
$814$	7.69285	0.269634
$815$	−10.8859	−0.381315
$816$	58.3039	2.04104
$817$	−0.0483920	−0.00169302
$818$	10.4939	0.366911
$819$	70.6495	2.46869
$820$	1.51874	0.0530365
$821$	27.0333	0.943470	0.471735	−	0.881740i	$-0.343628\pi$
$821$	27.0333	0.943470	0.471735	+	0.881740i	$0.343628\pi$
$822$	5.98382	0.208710
$823$	−14.0370	−0.489298	−0.244649	−	0.969612i	$-0.578673\pi$
$823$	−14.0370	−0.489298	−0.244649	+	0.969612i	$0.578673\pi$
$824$	−4.08036	−0.142146
$825$	−11.3105	−0.393782
$826$	32.0936	1.11668
$827$	−9.76163	−0.339445	−0.169723	−	0.985492i	$-0.554287\pi$
$827$	−9.76163	−0.339445	−0.169723	+	0.985492i	$0.554287\pi$
$828$	0	0
$829$	−40.4957	−1.40647	−0.703237	−	0.710955i	$-0.748263\pi$
$829$	−40.4957	−1.40647	−0.703237	+	0.710955i	$0.748263\pi$
$830$	−9.71393	−0.337175
$831$	−25.2773	−0.876861
$832$	−19.7912	−0.686137
$833$	42.8517	1.48472
$834$	−37.9862	−1.31535
$835$	−7.26336	−0.251359
$836$	−0.0222903	−0.000770928 0
$837$	−16.2722	−0.562450
$838$	−28.1085	−0.970993
$839$	−36.7795	−1.26977	−0.634885	−	0.772607i	$-0.718952\pi$
$839$	−36.7795	−1.26977	−0.634885	+	0.772607i	$0.718952\pi$
$840$	−46.2927	−1.59725
$841$	67.1724	2.31629
$842$	39.9230	1.37584
$843$	15.7608	0.542830
$844$	−0.919312	−0.0316440
$845$	9.18613	0.316012
$846$	−31.3865	−1.07909
$847$	−3.99271	−0.137191
$848$	−48.8147	−1.67630
$849$	49.7182	1.70632
$850$	22.9242	0.786295
$851$	0	0
$852$	−3.36707	−0.115354
$853$	−5.75961	−0.197205	−0.0986026	−	0.995127i	$-0.531437\pi$
$853$	−5.75961	−0.197205	−0.0986026	+	0.995127i	$0.531437\pi$
$854$	−13.8890	−0.475270
$855$	1.75064	0.0598707
$856$	−11.0883	−0.378992
$857$	−11.2601	−0.384639	−0.192320	−	0.981332i	$-0.561601\pi$
$857$	−11.2601	−0.384639	−0.192320	+	0.981332i	$0.561601\pi$
$858$	10.4678	0.357366
$859$	20.4905	0.699127	0.349563	−	0.936913i	$-0.386330\pi$
$859$	20.4905	0.699127	0.349563	+	0.936913i	$0.386330\pi$
$860$	0.0370793	0.00126439
$861$	135.706	4.62484
$862$	−44.1588	−1.50406
$863$	34.6889	1.18082	0.590412	−	0.807102i	$-0.298965\pi$
$863$	34.6889	1.18082	0.590412	+	0.807102i	$0.298965\pi$
$864$	9.76627	0.332255
$865$	−21.9151	−0.745134
$866$	−22.1532	−0.752795
$867$	−19.3548	−0.657324
$868$	0.521794	0.0177108
$869$	1.45162	0.0492428
$870$	−53.6883	−1.82020
$871$	14.6012	0.494743
$872$	−27.8050	−0.941595
$873$	−42.6102	−1.44214
$874$	0	0
$875$	−41.6837	−1.40917
$876$	−1.80902	−0.0611212
$877$	12.7578	0.430801	0.215401	−	0.976526i	$-0.430894\pi$
$877$	12.7578	0.430801	0.215401	+	0.976526i	$0.430894\pi$
$878$	−20.0280	−0.675912
$879$	4.48544	0.151290
$880$	−4.61363	−0.155526
$881$	−19.6112	−0.660718	−0.330359	−	0.943855i	$-0.607170\pi$
$881$	−19.6112	−0.660718	−0.330359	+	0.943855i	$0.607170\pi$
$882$	−92.2846	−3.10739
$883$	2.72550	0.0917205	0.0458603	−	0.998948i	$-0.485397\pi$
$883$	2.72550	0.0917205	0.0458603	+	0.998948i	$0.485397\pi$
$884$	1.32821	0.0446727
$885$	23.3801	0.785913
$886$	−32.1126	−1.07884
$887$	14.8874	0.499870	0.249935	−	0.968263i	$-0.419591\pi$
$887$	14.8874	0.499870	0.249935	+	0.968263i	$0.419591\pi$
$888$	−52.8499	−1.77353
$889$	68.8930	2.31060
$890$	16.7273	0.560701
$891$	−25.0241	−0.838339
$892$	−2.15519	−0.0721610
$893$	−0.575298	−0.0192516
$894$	−20.1020	−0.672312
$895$	−6.05676	−0.202455
$896$	40.7744	1.36218
$897$	0	0
$898$	−39.3148	−1.31195
$899$	10.8767	0.362759
$900$	3.09069	0.103023
$901$	62.3755	2.07803
$902$	14.3746	0.478620
$903$	3.31320	0.110256
$904$	−31.7989	−1.05762
$905$	16.5280	0.549410
$906$	12.0262	0.399544
$907$	−10.2394	−0.339994	−0.169997	−	0.985445i	$-0.554376\pi$
$907$	−10.2394	−0.339994	−0.169997	+	0.985445i	$0.554376\pi$
$908$	−2.84646	−0.0944632
$909$	62.3999	2.06967
$910$	15.8496	0.525409
$911$	14.6756	0.486224	0.243112	−	0.969998i	$-0.421832\pi$
$911$	14.6756	0.486224	0.243112	+	0.969998i	$0.421832\pi$
$912$	−2.30149	−0.0762098
$913$	5.75581	0.190489
$914$	−19.0924	−0.631521
$915$	−10.1181	−0.334493
$916$	1.48764	0.0491530
$917$	−29.3395	−0.968875
$918$	96.4607	3.18368
$919$	−25.7121	−0.848164	−0.424082	−	0.905624i	$-0.639403\pi$
$919$	−25.7121	−0.848164	−0.424082	+	0.905624i	$0.639403\pi$
$920$	0	0
$921$	−2.36471	−0.0779197
$922$	−10.9775	−0.361524
$923$	20.7201	0.682009
$924$	1.52613	0.0502059
$925$	−19.5513	−0.642843
$926$	53.3327	1.75262
$927$	−10.5647	−0.346990
$928$	−6.52801	−0.214292
$929$	9.09209	0.298302	0.149151	−	0.988814i	$-0.452346\pi$
$929$	9.09209	0.298302	0.149151	+	0.988814i	$0.452346\pi$
$930$	−6.07194	−0.199107
$931$	−1.69153	−0.0554376
$932$	−1.33213	−0.0436354
$933$	36.6333	1.19932
$934$	29.7804	0.974444
$935$	5.89532	0.192797
$936$	−51.4117	−1.68044
$937$	−12.6743	−0.414053	−0.207026	−	0.978335i	$-0.566379\pi$
$937$	−12.6743	−0.414053	−0.207026	+	0.978335i	$0.566379\pi$
$938$	−34.0035	−1.11025
$939$	−48.1824	−1.57237
$940$	0.440810	0.0143776
$941$	−42.7437	−1.39341	−0.696703	−	0.717360i	$-0.745350\pi$
$941$	−42.7437	−1.39341	−0.696703	+	0.717360i	$0.745350\pi$
$942$	−76.1840	−2.48221
$943$	0	0
$944$	−21.9738	−0.715186
$945$	−72.0609	−2.34414
$946$	0.350949	0.0114103
$947$	8.35261	0.271423	0.135712	−	0.990748i	$-0.456668\pi$
$947$	8.35261	0.271423	0.135712	+	0.990748i	$0.456668\pi$
$948$	−0.554851	−0.0180207
$949$	11.1322	0.361367
$950$	−0.904911	−0.0293592
$951$	−26.5788	−0.861876
$952$	−55.5950	−1.80185
$953$	10.0321	0.324972	0.162486	−	0.986711i	$-0.448049\pi$
$953$	10.0321	0.324972	0.162486	+	0.986711i	$0.448049\pi$
$954$	−134.331	−4.34912
$955$	−16.0498	−0.519360
$956$	2.28085	0.0737679
$957$	31.8120	1.02834
$958$	18.6294	0.601888
$959$	−5.36848	−0.173357
$960$	33.5765	1.08368
$961$	−29.7699	−0.960319
$962$	18.0946	0.583394
$963$	−28.7095	−0.925151
$964$	3.27399	0.105448
$965$	1.05525	0.0339696
$966$	0	0
$967$	30.1635	0.969992	0.484996	−	0.874516i	$-0.338821\pi$
$967$	30.1635	0.969992	0.484996	+	0.874516i	$0.338821\pi$
$968$	2.90550	0.0933862
$969$	2.94085	0.0944736
$970$	−9.55921	−0.306928
$971$	24.5376	0.787449	0.393725	−	0.919228i	$-0.371186\pi$
$971$	24.5376	0.787449	0.393725	+	0.919228i	$0.371186\pi$
$972$	4.37871	0.140447
$973$	34.0799	1.09255
$974$	52.2833	1.67526
$975$	−26.6039	−0.852006
$976$	9.50948	0.304391
$977$	−53.0918	−1.69856	−0.849279	−	0.527944i	$-0.822963\pi$
$977$	−53.0918	−1.69856	−0.849279	+	0.527944i	$0.822963\pi$
$978$	39.3821	1.25930
$979$	−9.91146	−0.316772
$980$	1.29610	0.0414023
$981$	−71.9915	−2.29851
$982$	40.3587	1.28790
$983$	−47.6674	−1.52035	−0.760177	−	0.649717i	$-0.774888\pi$
$983$	−47.6674	−1.52035	−0.760177	+	0.649717i	$0.774888\pi$
$984$	−98.7532	−3.14814
$985$	6.95801	0.221701
$986$	−64.4766	−2.05335
$987$	39.3883	1.25374
$988$	−0.0524299	−0.00166802
$989$	0	0
$990$	−12.6960	−0.403506
$991$	14.1129	0.448310	0.224155	−	0.974553i	$-0.428038\pi$
$991$	14.1129	0.448310	0.224155	+	0.974553i	$0.428038\pi$
$992$	−0.738294	−0.0234408
$993$	−73.3508	−2.32772
$994$	−48.2531	−1.53050
$995$	−29.2434	−0.927079
$996$	−2.20004	−0.0697108
$997$	1.20969	0.0383112	0.0191556	−	0.999817i	$-0.493902\pi$
$997$	1.20969	0.0383112	0.0191556	+	0.999817i	$0.493902\pi$
$998$	0.219329	0.00694274
$999$	−82.2680	−2.60284

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5819.2.a.t.1.18		60
23.15	odd	22		253.2.i.b.133.9	yes	120
23.20	odd	22		253.2.i.b.78.9	✓	120
23.22	odd	2		5819.2.a.u.1.18		60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
253.2.i.b.78.9	✓	120	23.20	odd	22
253.2.i.b.133.9	yes	120	23.15	odd	22
5819.2.a.t.1.18		60	1.1	even	1	trivial
5819.2.a.u.1.18		60	23.22	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 5819 = 11 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5819.a (trivial)

\(f(q)\)	\(=\)	\(q-1.37192 q^{2} -3.24389 q^{3} -0.117831 q^{4} -1.23015 q^{5} +4.45036 q^{6} -3.99271 q^{7} +2.90550 q^{8} +7.52280 q^{9} +1.68767 q^{10} -1.00000 q^{11} +0.382229 q^{12} -2.35213 q^{13} +5.47768 q^{14} +3.99048 q^{15} -3.75045 q^{16} +4.79234 q^{17} -10.3207 q^{18} -0.189173 q^{19} +0.144950 q^{20} +12.9519 q^{21} +1.37192 q^{22} -9.42511 q^{24} -3.48672 q^{25} +3.22694 q^{26} -14.6714 q^{27} +0.470463 q^{28} +9.80675 q^{29} -5.47462 q^{30} +1.10911 q^{31} -0.665665 q^{32} +3.24389 q^{33} -6.57472 q^{34} +4.91164 q^{35} -0.886416 q^{36} +5.60736 q^{37} +0.259530 q^{38} +7.63006 q^{39} -3.57421 q^{40} +10.4777 q^{41} -17.7690 q^{42} +0.255808 q^{43} +0.117831 q^{44} -9.25420 q^{45} +3.04112 q^{47} +12.1660 q^{48} +8.94171 q^{49} +4.78351 q^{50} -15.5458 q^{51} +0.277153 q^{52} +13.0157 q^{53} +20.1281 q^{54} +1.23015 q^{55} -11.6008 q^{56} +0.613655 q^{57} -13.4541 q^{58} +5.85897 q^{59} -0.470200 q^{60} -2.53555 q^{61} -1.52161 q^{62} -30.0363 q^{63} +8.41415 q^{64} +2.89349 q^{65} -4.45036 q^{66} -6.20764 q^{67} -0.564685 q^{68} -6.73839 q^{70} -8.80904 q^{71} +21.8575 q^{72} -4.73282 q^{73} -7.69285 q^{74} +11.3105 q^{75} +0.0222903 q^{76} +3.99271 q^{77} -10.4678 q^{78} -1.45162 q^{79} +4.61363 q^{80} +25.0241 q^{81} -14.3746 q^{82} -5.75581 q^{83} -1.52613 q^{84} -5.89532 q^{85} -0.350949 q^{86} -31.8120 q^{87} -2.90550 q^{88} +9.91146 q^{89} +12.6960 q^{90} +9.39138 q^{91} -3.59782 q^{93} -4.17218 q^{94} +0.232712 q^{95} +2.15934 q^{96} -5.66413 q^{97} -12.2673 q^{98} -7.52280 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 5 q^{2} + 9 q^{3} + 73 q^{4} - 8 q^{5} + 26 q^{6} + 30 q^{8} + 75 q^{9} + 7 q^{10} - 60 q^{11} + 41 q^{12} + 46 q^{13} - 16 q^{14} - 4 q^{15} + 99 q^{16} + 5 q^{17} + 36 q^{18} + 8 q^{19} - 82 q^{20}+ \cdots - 75 q^{99}+O(q^{100}) \) 60 * q + 5 * q^2 + 9 * q^3 + 73 * q^4 - 8 * q^5 + 26 * q^6 + 30 * q^8 + 75 * q^9 + 7 * q^10 - 60 * q^11 + 41 * q^12 + 46 * q^13 - 16 * q^14 - 4 * q^15 + 99 * q^16 + 5 * q^17 + 36 * q^18 + 8 * q^19 - 82 * q^20 + 13 * q^21 - 5 * q^22 + 54 * q^24 + 96 * q^25 + 31 * q^26 + 54 * q^27 + 29 * q^28 + 42 * q^29 + 14 * q^30 + 71 * q^31 + 40 * q^32 - 9 * q^33 - 10 * q^34 + 9 * q^35 + 93 * q^36 + 5 * q^37 + 11 * q^38 + 56 * q^39 + 40 * q^40 + 62 * q^41 - 43 * q^42 + 2 * q^43 - 73 * q^44 + q^45 - q^47 + 71 * q^48 + 138 * q^49 - 18 * q^50 + 27 * q^51 + 102 * q^52 - 11 * q^53 + 69 * q^54 + 8 * q^55 - 13 * q^56 - 38 * q^57 + 58 * q^58 + 57 * q^59 + 49 * q^60 + 26 * q^61 + 17 * q^62 + 41 * q^63 + 184 * q^64 + 19 * q^65 - 26 * q^66 - 7 * q^67 + 76 * q^68 + 43 * q^70 + 33 * q^71 + 100 * q^72 + 108 * q^73 + 63 * q^74 + q^75 + 42 * q^76 - 3 * q^78 + 25 * q^79 - 148 * q^80 + 68 * q^81 + 59 * q^82 + 41 * q^83 + 97 * q^84 + 160 * q^85 - 78 * q^86 + 41 * q^87 - 30 * q^88 - 51 * q^89 + 53 * q^90 + 65 * q^93 + 121 * q^94 - 14 * q^95 + 82 * q^96 + 13 * q^97 - 75 * q^98 - 75 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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