LMFDB - Embedded newform 7381.2.a.r.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7381,2,Mod(1,7381)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7381, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("7381.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7381 = 11^{2} \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7381.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$58.9375817319$
Analytic rank:	$0$
Dimension:	$50$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	7381.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.652724 q^{2} -1.46480 q^{3} -1.57395 q^{4} -3.40759 q^{5} +0.956111 q^{6} +0.171225 q^{7} +2.33280 q^{8} -0.854356 q^{9} +O(q^{10})$	\(q-0.652724 q^{2} -1.46480 q^{3} -1.57395 q^{4} -3.40759 q^{5} +0.956111 q^{6} +0.171225 q^{7} +2.33280 q^{8} -0.854356 q^{9} +2.22421 q^{10} +2.30553 q^{12} +2.26408 q^{13} -0.111762 q^{14} +4.99144 q^{15} +1.62523 q^{16} +3.77557 q^{17} +0.557659 q^{18} +4.37879 q^{19} +5.36338 q^{20} -0.250810 q^{21} +4.59751 q^{23} -3.41709 q^{24} +6.61166 q^{25} -1.47782 q^{26} +5.64587 q^{27} -0.269499 q^{28} +2.50827 q^{29} -3.25803 q^{30} +9.80041 q^{31} -5.72643 q^{32} -2.46440 q^{34} -0.583463 q^{35} +1.34472 q^{36} -3.50409 q^{37} -2.85814 q^{38} -3.31643 q^{39} -7.94923 q^{40} -2.72461 q^{41} +0.163710 q^{42} +5.88833 q^{43} +2.91129 q^{45} -3.00090 q^{46} +2.76074 q^{47} -2.38063 q^{48} -6.97068 q^{49} -4.31559 q^{50} -5.53046 q^{51} -3.56355 q^{52} +13.6702 q^{53} -3.68519 q^{54} +0.399434 q^{56} -6.41406 q^{57} -1.63721 q^{58} -7.41536 q^{59} -7.85629 q^{60} +1.00000 q^{61} -6.39696 q^{62} -0.146287 q^{63} +0.487325 q^{64} -7.71506 q^{65} +1.45198 q^{67} -5.94256 q^{68} -6.73444 q^{69} +0.380840 q^{70} +1.90252 q^{71} -1.99304 q^{72} -8.05818 q^{73} +2.28720 q^{74} -9.68477 q^{75} -6.89200 q^{76} +2.16471 q^{78} -8.90468 q^{79} -5.53810 q^{80} -5.70701 q^{81} +1.77842 q^{82} +0.636557 q^{83} +0.394763 q^{84} -12.8656 q^{85} -3.84345 q^{86} -3.67412 q^{87} +17.4328 q^{89} -1.90027 q^{90} +0.387667 q^{91} -7.23626 q^{92} -14.3557 q^{93} -1.80200 q^{94} -14.9211 q^{95} +8.38809 q^{96} +3.96049 q^{97} +4.54993 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q + 10 q^{2} - 2 q^{3} + 50 q^{4} - 2 q^{5} + 12 q^{6} + 8 q^{7} + 30 q^{8} + 48 q^{9}+O(q^{10}) $ 50 * q + 10 * q^2 - 2 * q^3 + 50 * q^4 - 2 * q^5 + 12 * q^6 + 8 * q^7 + 30 * q^8 + 48 * q^9	\( 50 q + 10 q^{2} - 2 q^{3} + 50 q^{4} - 2 q^{5} + 12 q^{6} + 8 q^{7} + 30 q^{8} + 48 q^{9} + 12 q^{10} - 14 q^{12} + 8 q^{13} - 2 q^{14} - 16 q^{15} + 42 q^{16} + 22 q^{17} + 32 q^{19} - 8 q^{20} + 24 q^{21} + 12 q^{23} - 8 q^{24} + 40 q^{25} + 10 q^{26} - 8 q^{27} + 72 q^{28} + 56 q^{29} + 24 q^{30} + 10 q^{31} + 70 q^{32} - 32 q^{34} + 70 q^{35} + 34 q^{36} - 8 q^{37} - 14 q^{38} + 96 q^{39} - 54 q^{40} + 56 q^{41} - 8 q^{42} + 44 q^{43} - 24 q^{45} - 4 q^{46} - 4 q^{47} - 28 q^{48} + 38 q^{49} + 120 q^{50} + 76 q^{51} + 24 q^{52} + 4 q^{53} + 48 q^{54} - 18 q^{56} + 8 q^{57} + 28 q^{58} + 12 q^{59} - 60 q^{60} + 50 q^{61} + 8 q^{62} + 30 q^{63} + 10 q^{64} + 64 q^{65} + 18 q^{67} - 22 q^{68} - 8 q^{69} + 34 q^{70} + 12 q^{71} + 104 q^{72} - 16 q^{73} + 84 q^{74} - 26 q^{75} + 64 q^{76} + 40 q^{78} + 78 q^{79} - 36 q^{80} + 34 q^{81} + 54 q^{82} + 68 q^{83} - 78 q^{84} - 4 q^{85} + 36 q^{86} + 48 q^{87} + 26 q^{89} - 20 q^{90} + 32 q^{92} + 22 q^{93} + 156 q^{94} + 100 q^{95} - 4 q^{96} - 14 q^{97} + 70 q^{98}+O(q^{100}) \) 50 * q + 10 * q^2 - 2 * q^3 + 50 * q^4 - 2 * q^5 + 12 * q^6 + 8 * q^7 + 30 * q^8 + 48 * q^9 + 12 * q^10 - 14 * q^12 + 8 * q^13 - 2 * q^14 - 16 * q^15 + 42 * q^16 + 22 * q^17 + 32 * q^19 - 8 * q^20 + 24 * q^21 + 12 * q^23 - 8 * q^24 + 40 * q^25 + 10 * q^26 - 8 * q^27 + 72 * q^28 + 56 * q^29 + 24 * q^30 + 10 * q^31 + 70 * q^32 - 32 * q^34 + 70 * q^35 + 34 * q^36 - 8 * q^37 - 14 * q^38 + 96 * q^39 - 54 * q^40 + 56 * q^41 - 8 * q^42 + 44 * q^43 - 24 * q^45 - 4 * q^46 - 4 * q^47 - 28 * q^48 + 38 * q^49 + 120 * q^50 + 76 * q^51 + 24 * q^52 + 4 * q^53 + 48 * q^54 - 18 * q^56 + 8 * q^57 + 28 * q^58 + 12 * q^59 - 60 * q^60 + 50 * q^61 + 8 * q^62 + 30 * q^63 + 10 * q^64 + 64 * q^65 + 18 * q^67 - 22 * q^68 - 8 * q^69 + 34 * q^70 + 12 * q^71 + 104 * q^72 - 16 * q^73 + 84 * q^74 - 26 * q^75 + 64 * q^76 + 40 * q^78 + 78 * q^79 - 36 * q^80 + 34 * q^81 + 54 * q^82 + 68 * q^83 - 78 * q^84 - 4 * q^85 + 36 * q^86 + 48 * q^87 + 26 * q^89 - 20 * q^90 + 32 * q^92 + 22 * q^93 + 156 * q^94 + 100 * q^95 - 4 * q^96 - 14 * q^97 + 70 * q^98

Display 100 coefficients 10 coefficients

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 $

$2$	−0.652724	−0.461545	−0.230773	−	0.973008i	$-0.574125\pi$
$2$	−0.652724	−0.461545	−0.230773	+	0.973008i	$0.574125\pi$
$3$	−1.46480	−0.845704	−0.422852	−	0.906199i	$-0.638971\pi$
$3$	−1.46480	−0.845704	−0.422852	+	0.906199i	$0.638971\pi$
$4$	−1.57395	−0.786976
$5$	−3.40759	−1.52392	−0.761960	−	0.647624i	$-0.775763\pi$
$5$	−3.40759	−1.52392	−0.761960	+	0.647624i	$0.775763\pi$
$6$	0.956111	0.390331
$7$	0.171225	0.0647168	0.0323584	−	0.999476i	$-0.489698\pi$
$7$	0.171225	0.0647168	0.0323584	+	0.999476i	$0.489698\pi$
$8$	2.33280	0.824771
$9$	−0.854356	−0.284785
$10$	2.22421	0.703358
$11$	0	0
$11$	0	0
$12$	2.30553	0.665548
$13$	2.26408	0.627943	0.313972	−	0.949432i	$-0.398340\pi$
$13$	2.26408	0.627943	0.313972	+	0.949432i	$0.398340\pi$
$14$	−0.111762	−0.0298698
$15$	4.99144	1.28878
$16$	1.62523	0.406307
$17$	3.77557	0.915710	0.457855	−	0.889027i	$-0.348618\pi$
$17$	3.77557	0.915710	0.457855	+	0.889027i	$0.348618\pi$
$18$	0.557659	0.131441
$19$	4.37879	1.00456	0.502282	−	0.864704i	$-0.332494\pi$
$19$	4.37879	1.00456	0.502282	+	0.864704i	$0.332494\pi$
$20$	5.36338	1.19929
$21$	−0.250810	−0.0547313
$22$	0	0
$23$	4.59751	0.958647	0.479323	−	0.877638i	$-0.340882\pi$
$23$	4.59751	0.958647	0.479323	+	0.877638i	$0.340882\pi$
$24$	−3.41709	−0.697511
$25$	6.61166	1.32233
$26$	−1.47782	−0.289824
$27$	5.64587	1.08655
$28$	−0.269499	−0.0509306
$29$	2.50827	0.465774	0.232887	−	0.972504i	$-0.425183\pi$
$29$	2.50827	0.465774	0.232887	+	0.972504i	$0.425183\pi$
$30$	−3.25803	−0.594833
$31$	9.80041	1.76021	0.880103	−	0.474783i	$-0.157473\pi$
$31$	9.80041	1.76021	0.880103	+	0.474783i	$0.157473\pi$
$32$	−5.72643	−1.01230
$33$	0	0
$34$	−2.46440	−0.422642
$35$	−0.583463	−0.0986233
$36$	1.34472	0.224119
$37$	−3.50409	−0.576068	−0.288034	−	0.957620i	$-0.593002\pi$
$37$	−3.50409	−0.576068	−0.288034	+	0.957620i	$0.593002\pi$
$38$	−2.85814	−0.463652
$39$	−3.31643	−0.531054
$40$	−7.94923	−1.25688
$41$	−2.72461	−0.425513	−0.212756	−	0.977105i	$-0.568244\pi$
$41$	−2.72461	−0.425513	−0.212756	+	0.977105i	$0.568244\pi$
$42$	0.163710	0.0252610
$43$	5.88833	0.897962	0.448981	−	0.893541i	$-0.351787\pi$
$43$	5.88833	0.897962	0.448981	+	0.893541i	$0.351787\pi$
$44$	0	0
$45$	2.91129	0.433990
$46$	−3.00090	−0.442459
$47$	2.76074	0.402695	0.201347	−	0.979520i	$-0.435468\pi$
$47$	2.76074	0.402695	0.201347	+	0.979520i	$0.435468\pi$
$48$	−2.38063	−0.343615
$49$	−6.97068	−0.995812
$50$	−4.31559	−0.610316
$51$	−5.53046	−0.774419
$52$	−3.56355	−0.494176
$53$	13.6702	1.87775	0.938874	−	0.344260i	$-0.111870\pi$
$53$	13.6702	1.87775	0.938874	+	0.344260i	$0.111870\pi$
$54$	−3.68519	−0.501491
$55$	0	0
$56$	0.399434	0.0533766
$57$	−6.41406	−0.849563
$58$	−1.63721	−0.214976
$59$	−7.41536	−0.965397	−0.482699	−	0.875786i	$-0.660343\pi$
$59$	−7.41536	−0.965397	−0.482699	+	0.875786i	$0.660343\pi$
$60$	−7.85629	−1.01424
$61$	1.00000	0.128037
$61$	1.00000	0.128037
$62$	−6.39696	−0.812415
$63$	−0.146287	−0.0184304
$64$	0.487325	0.0609156
$65$	−7.71506	−0.956935
$66$	0	0
$67$	1.45198	0.177388	0.0886939	−	0.996059i	$-0.471731\pi$
$67$	1.45198	0.177388	0.0886939	+	0.996059i	$0.471731\pi$
$68$	−5.94256	−0.720642
$69$	−6.73444	−0.810731
$70$	0.380840	0.0455191
$71$	1.90252	0.225787	0.112894	−	0.993607i	$-0.463988\pi$
$71$	1.90252	0.225787	0.112894	+	0.993607i	$0.463988\pi$
$72$	−1.99304	−0.234883
$73$	−8.05818	−0.943139	−0.471569	−	0.881829i	$-0.656312\pi$
$73$	−8.05818	−0.943139	−0.471569	+	0.881829i	$0.656312\pi$
$74$	2.28720	0.265882
$75$	−9.68477	−1.11830
$76$	−6.89200	−0.790567
$77$	0	0
$78$	2.16471	0.245105
$79$	−8.90468	−1.00185	−0.500927	−	0.865489i	$-0.667008\pi$
$79$	−8.90468	−1.00185	−0.500927	+	0.865489i	$0.667008\pi$
$80$	−5.53810	−0.619179
$81$	−5.70701	−0.634112
$82$	1.77842	0.196393
$83$	0.636557	0.0698712	0.0349356	−	0.999390i	$-0.488877\pi$
$83$	0.636557	0.0698712	0.0349356	+	0.999390i	$0.488877\pi$
$84$	0.394763	0.0430722
$85$	−12.8656	−1.39547
$86$	−3.84345	−0.414450
$87$	−3.67412	−0.393907
$88$	0	0
$89$	17.4328	1.84788	0.923939	−	0.382540i	$-0.124951\pi$
$89$	17.4328	1.84788	0.923939	+	0.382540i	$0.124951\pi$
$90$	−1.90027	−0.200306
$91$	0.387667	0.0406385
$92$	−7.23626	−0.754432
$93$	−14.3557	−1.48861
$94$	−1.80200	−0.185862
$95$	−14.9211	−1.53087
$96$	8.38809	0.856105
$97$	3.96049	0.402127	0.201063	−	0.979578i	$-0.435560\pi$
$97$	3.96049	0.402127	0.201063	+	0.979578i	$0.435560\pi$
$98$	4.54993	0.459612
$99$	0	0
$100$	−10.4064	−1.04064
$101$	13.7996	1.37311	0.686555	−	0.727078i	$-0.259122\pi$
$101$	13.7996	1.37311	0.686555	+	0.727078i	$0.259122\pi$
$102$	3.60986	0.357430
$103$	0.339762	0.0334777	0.0167389	−	0.999860i	$-0.494672\pi$
$103$	0.339762	0.0334777	0.0167389	+	0.999860i	$0.494672\pi$
$104$	5.28166	0.517909
$105$	0.854658	0.0834061
$106$	−8.92287	−0.866666
$107$	−5.47860	−0.529637	−0.264818	−	0.964298i	$-0.585312\pi$
$107$	−5.47860	−0.529637	−0.264818	+	0.964298i	$0.585312\pi$
$108$	−8.88632	−0.855087
$109$	13.5900	1.30168	0.650842	−	0.759213i	$-0.274416\pi$
$109$	13.5900	1.30168	0.650842	+	0.759213i	$0.274416\pi$
$110$	0	0
$111$	5.13279	0.487183
$112$	0.278279	0.0262949
$113$	13.5662	1.27620	0.638098	−	0.769955i	$-0.279721\pi$
$113$	13.5662	1.27620	0.638098	+	0.769955i	$0.279721\pi$
$114$	4.18661	0.392112
$115$	−15.6664	−1.46090
$116$	−3.94790	−0.366553
$117$	−1.93433	−0.178829
$118$	4.84018	0.445575
$119$	0.646471	0.0592619
$120$	11.6441	1.06295
$121$	0	0
$122$	−0.652724	−0.0590948
$123$	3.99101	0.359858
$124$	−15.4254	−1.38524
$125$	−5.49187	−0.491208
$126$	0.0954849	0.00850647
$127$	5.54134	0.491715	0.245857	−	0.969306i	$-0.420931\pi$
$127$	5.54134	0.491715	0.245857	+	0.969306i	$0.420931\pi$
$128$	11.1348	0.984184
$129$	−8.62524	−0.759410
$130$	5.03580	0.441669
$131$	−22.6080	−1.97527	−0.987633	−	0.156781i	$-0.949888\pi$
$131$	−22.6080	−1.97527	−0.987633	+	0.156781i	$0.949888\pi$
$132$	0	0
$133$	0.749757	0.0650122
$134$	−0.947743	−0.0818725
$135$	−19.2388	−1.65581
$136$	8.80766	0.755251
$137$	−16.6277	−1.42060	−0.710299	−	0.703900i	$-0.751440\pi$
$137$	−16.6277	−1.42060	−0.710299	+	0.703900i	$0.751440\pi$
$138$	4.39573	0.374189
$139$	−10.7523	−0.911999	−0.456000	−	0.889980i	$-0.650718\pi$
$139$	−10.7523	−0.911999	−0.456000	+	0.889980i	$0.650718\pi$
$140$	0.918343	0.0776141
$141$	−4.04393	−0.340560
$142$	−1.24182	−0.104211
$143$	0	0
$144$	−1.38852	−0.115710
$145$	−8.54716	−0.709803
$146$	5.25977	0.435301
$147$	10.2107	0.842162
$148$	5.51526	0.453352
$149$	22.7254	1.86174	0.930869	−	0.365353i	$-0.119052\pi$
$149$	22.7254	1.86174	0.930869	+	0.365353i	$0.119052\pi$
$150$	6.32148	0.516147
$151$	−7.87944	−0.641220	−0.320610	−	0.947211i	$-0.603888\pi$
$151$	−7.87944	−0.641220	−0.320610	+	0.947211i	$0.603888\pi$
$152$	10.2149	0.828534
$153$	−3.22568	−0.260781
$154$	0	0
$155$	−33.3958	−2.68241
$156$	5.21990	0.417926
$157$	−12.6142	−1.00672	−0.503361	−	0.864076i	$-0.667903\pi$
$157$	−12.6142	−1.00672	−0.503361	+	0.864076i	$0.667903\pi$
$158$	5.81230	0.462401
$159$	−20.0242	−1.58802
$160$	19.5133	1.54266
$161$	0.787207	0.0620406
$162$	3.72510	0.292671
$163$	2.94746	0.230863	0.115431	−	0.993315i	$-0.463175\pi$
$163$	2.94746	0.230863	0.115431	+	0.993315i	$0.463175\pi$
$164$	4.28840	0.334868
$165$	0	0
$166$	−0.415496	−0.0322487
$167$	16.6409	1.28771	0.643854	−	0.765148i	$-0.277334\pi$
$167$	16.6409	1.28771	0.643854	+	0.765148i	$0.277334\pi$
$168$	−0.585091	−0.0451407
$169$	−7.87394	−0.605687
$170$	8.39768	0.644072
$171$	−3.74105	−0.286085
$172$	−9.26795	−0.706674
$173$	7.85916	0.597521	0.298761	−	0.954328i	$-0.403427\pi$
$173$	7.85916	0.597521	0.298761	+	0.954328i	$0.403427\pi$
$174$	2.39819	0.181806
$175$	1.13208	0.0855771
$176$	0	0
$177$	10.8620	0.816440
$178$	−11.3788	−0.852880
$179$	0.762348	0.0569806	0.0284903	−	0.999594i	$-0.490930\pi$
$179$	0.762348	0.0569806	0.0284903	+	0.999594i	$0.490930\pi$
$180$	−4.58224	−0.341540
$181$	−7.28537	−0.541517	−0.270759	−	0.962647i	$-0.587274\pi$
$181$	−7.28537	−0.541517	−0.270759	+	0.962647i	$0.587274\pi$
$182$	−0.253039	−0.0187565
$183$	−1.46480	−0.108281
$184$	10.7251	0.790664
$185$	11.9405	0.877882
$186$	9.37028	0.687062
$187$	0	0
$188$	−4.34527	−0.316911
$189$	0.966712	0.0703179
$190$	9.73936	0.706568
$191$	6.52458	0.472102	0.236051	−	0.971741i	$-0.424147\pi$
$191$	6.52458	0.472102	0.236051	+	0.971741i	$0.424147\pi$
$192$	−0.713834	−0.0515165
$193$	10.1690	0.731978	0.365989	−	0.930619i	$-0.380731\pi$
$193$	10.1690	0.731978	0.365989	+	0.930619i	$0.380731\pi$
$194$	−2.58511	−0.185600
$195$	11.3010	0.809283
$196$	10.9715	0.783680
$197$	12.1544	0.865963	0.432982	−	0.901403i	$-0.357461\pi$
$197$	12.1544	0.865963	0.432982	+	0.901403i	$0.357461\pi$
$198$	0	0
$199$	19.8163	1.40474	0.702372	−	0.711810i	$-0.252124\pi$
$199$	19.8163	1.40474	0.702372	+	0.711810i	$0.252124\pi$
$200$	15.4237	1.09062
$201$	−2.12686	−0.150017
$202$	−9.00731	−0.633752
$203$	0.429478	0.0301434
$204$	8.70468	0.609449
$205$	9.28435	0.648447
$206$	−0.221771	−0.0154515
$207$	−3.92791	−0.273009
$208$	3.67965	0.255138
$209$	0	0
$210$	−0.557856	−0.0384957
$211$	−1.72884	−0.119018	−0.0595090	−	0.998228i	$-0.518953\pi$
$211$	−1.72884	−0.119018	−0.0595090	+	0.998228i	$0.518953\pi$
$212$	−21.5163	−1.47774
$213$	−2.78681	−0.190949
$214$	3.57601	0.244451
$215$	−20.0650	−1.36842
$216$	13.1707	0.896153
$217$	1.67807	0.113915
$218$	−8.87050	−0.600786
$219$	11.8036	0.797616
$220$	0	0
$221$	8.54820	0.575014
$222$	−3.35029	−0.224857
$223$	9.91287	0.663815	0.331908	−	0.943312i	$-0.392308\pi$
$223$	9.91287	0.663815	0.331908	+	0.943312i	$0.392308\pi$
$224$	−0.980506	−0.0655128
$225$	−5.64871	−0.376581
$226$	−8.85495	−0.589023
$227$	3.26316	0.216583	0.108292	−	0.994119i	$-0.465462\pi$
$227$	3.26316	0.216583	0.108292	+	0.994119i	$0.465462\pi$
$228$	10.0954	0.668585
$229$	4.46298	0.294922	0.147461	−	0.989068i	$-0.452890\pi$
$229$	4.46298	0.294922	0.147461	+	0.989068i	$0.452890\pi$
$230$	10.2258	0.674272
$231$	0	0
$232$	5.85130	0.384157
$233$	15.5253	1.01710	0.508549	−	0.861033i	$-0.330182\pi$
$233$	15.5253	1.01710	0.508549	+	0.861033i	$0.330182\pi$
$234$	1.26258	0.0825377
$235$	−9.40745	−0.613675
$236$	11.6714	0.759744
$237$	13.0436	0.847272
$238$	−0.421967	−0.0273520
$239$	−21.6385	−1.39968	−0.699840	−	0.714299i	$-0.746746\pi$
$239$	−21.6385	−1.39968	−0.699840	+	0.714299i	$0.746746\pi$
$240$	8.11222	0.523642
$241$	−10.3245	−0.665059	−0.332530	−	0.943093i	$-0.607902\pi$
$241$	−10.3245	−0.665059	−0.332530	+	0.943093i	$0.607902\pi$
$242$	0	0
$243$	−8.57797	−0.550277
$244$	−1.57395	−0.100762
$245$	23.7532	1.51754
$246$	−2.60503	−0.166091
$247$	9.91393	0.630808
$248$	22.8624	1.45177
$249$	−0.932430	−0.0590903
$250$	3.58467	0.226715
$251$	22.1873	1.40045	0.700225	−	0.713922i	$-0.253083\pi$
$251$	22.1873	1.40045	0.700225	+	0.713922i	$0.253083\pi$
$252$	0.230248	0.0145043
$253$	0	0
$254$	−3.61697	−0.226949
$255$	18.8455	1.18015
$256$	−8.24258	−0.515161
$257$	−24.6971	−1.54056	−0.770281	−	0.637704i	$-0.779884\pi$
$257$	−24.6971	−1.54056	−0.770281	+	0.637704i	$0.779884\pi$
$258$	5.62990	0.350502
$259$	−0.599986	−0.0372813
$260$	12.1431	0.753085
$261$	−2.14296	−0.132646
$262$	14.7568	0.911675
$263$	5.78579	0.356767	0.178383	−	0.983961i	$-0.442913\pi$
$263$	5.78579	0.356767	0.178383	+	0.983961i	$0.442913\pi$
$264$	0	0
$265$	−46.5825	−2.86154
$266$	−0.489384	−0.0300061
$267$	−25.5357	−1.56276
$268$	−2.28535	−0.139600
$269$	−12.0380	−0.733969	−0.366985	−	0.930227i	$-0.619610\pi$
$269$	−12.0380	−0.733969	−0.366985	+	0.930227i	$0.619610\pi$
$270$	12.5576	0.764232
$271$	−28.1694	−1.71117	−0.855584	−	0.517664i	$-0.826802\pi$
$271$	−28.1694	−1.71117	−0.855584	+	0.517664i	$0.826802\pi$
$272$	6.13616	0.372059
$273$	−0.567855	−0.0343681
$274$	10.8533	0.655671
$275$	0	0
$276$	10.5997	0.638026
$277$	−16.0368	−0.963557	−0.481779	−	0.876293i	$-0.660009\pi$
$277$	−16.0368	−0.963557	−0.481779	+	0.876293i	$0.660009\pi$
$278$	7.01829	0.420929
$279$	−8.37304	−0.501281
$280$	−1.36111	−0.0813416
$281$	−14.0728	−0.839511	−0.419756	−	0.907637i	$-0.637884\pi$
$281$	−14.0728	−0.839511	−0.419756	+	0.907637i	$0.637884\pi$
$282$	2.63957	0.157184
$283$	−6.03954	−0.359014	−0.179507	−	0.983757i	$-0.557450\pi$
$283$	−6.03954	−0.359014	−0.179507	+	0.983757i	$0.557450\pi$
$284$	−2.99447	−0.177689
$285$	21.8565	1.29467
$286$	0	0
$287$	−0.466520	−0.0275378
$288$	4.89241	0.288288
$289$	−2.74507	−0.161475
$290$	5.57893	0.327606
$291$	−5.80133	−0.340080
$292$	12.6832	0.742227
$293$	9.86502	0.576321	0.288160	−	0.957582i	$-0.406956\pi$
$293$	9.86502	0.576321	0.288160	+	0.957582i	$0.406956\pi$
$294$	−6.66475	−0.388696
$295$	25.2685	1.47119
$296$	−8.17434	−0.475124
$297$	0	0
$298$	−14.8334	−0.859277
$299$	10.4091	0.601976
$300$	15.2434	0.880076
$301$	1.00823	0.0581133
$302$	5.14310	0.295952
$303$	−20.2136	−1.16124
$304$	7.11652	0.408161
$305$	−3.40759	−0.195118
$306$	2.10548	0.120362
$307$	2.00391	0.114369	0.0571845	−	0.998364i	$-0.481788\pi$
$307$	2.00391	0.114369	0.0571845	+	0.998364i	$0.481788\pi$
$308$	0	0
$309$	−0.497684	−0.0283122
$310$	21.7982	1.23806
$311$	2.84391	0.161263	0.0806316	−	0.996744i	$-0.474306\pi$
$311$	2.84391	0.161263	0.0806316	+	0.996744i	$0.474306\pi$
$312$	−7.73658	−0.437998
$313$	21.6021	1.22102	0.610510	−	0.792008i	$-0.290964\pi$
$313$	21.6021	1.22102	0.610510	+	0.792008i	$0.290964\pi$
$314$	8.23358	0.464648
$315$	0.498485	0.0280865
$316$	14.0155	0.788435
$317$	0.175916	0.00988041	0.00494021	−	0.999988i	$-0.498427\pi$
$317$	0.175916	0.00988041	0.00494021	+	0.999988i	$0.498427\pi$
$318$	13.0702	0.732943
$319$	0	0
$320$	−1.66060	−0.0928305
$321$	8.02507	0.447916
$322$	−0.513829	−0.0286346
$323$	16.5324	0.919889
$324$	8.98255	0.499031
$325$	14.9693	0.830349
$326$	−1.92388	−0.106554
$327$	−19.9066	−1.10084
$328$	−6.35598	−0.350950
$329$	0.472706	0.0260611
$330$	0	0
$331$	−27.8054	−1.52833	−0.764163	−	0.645024i	$-0.776848\pi$
$331$	−27.8054	−1.52833	−0.764163	+	0.645024i	$0.776848\pi$
$332$	−1.00191	−0.0549869
$333$	2.99374	0.164056
$334$	−10.8619	−0.594336
$335$	−4.94775	−0.270325
$336$	−0.407623	−0.0222377
$337$	23.4149	1.27549	0.637745	−	0.770248i	$-0.279867\pi$
$337$	23.4149	1.27549	0.637745	+	0.770248i	$0.279867\pi$
$338$	5.13951	0.279552
$339$	−19.8717	−1.07928
$340$	20.2498	1.09820
$341$	0	0
$342$	2.44187	0.132041
$343$	−2.39213	−0.129163
$344$	13.7363	0.740613
$345$	22.9482	1.23549
$346$	−5.12986	−0.275783
$347$	−18.0983	−0.971568	−0.485784	−	0.874079i	$-0.661466\pi$
$347$	−18.0983	−0.971568	−0.485784	+	0.874079i	$0.661466\pi$
$348$	5.78289	0.309995
$349$	3.72819	0.199565	0.0997827	−	0.995009i	$-0.468185\pi$
$349$	3.72819	0.199565	0.0997827	+	0.995009i	$0.468185\pi$
$350$	−0.738935	−0.0394977
$351$	12.7827	0.682290
$352$	0	0
$353$	14.0409	0.747321	0.373661	−	0.927566i	$-0.378103\pi$
$353$	14.0409	0.747321	0.373661	+	0.927566i	$0.378103\pi$
$354$	−7.08991	−0.376824
$355$	−6.48300	−0.344082
$356$	−27.4385	−1.45424
$357$	−0.946951	−0.0501180
$358$	−0.497603	−0.0262991
$359$	6.78874	0.358296	0.179148	−	0.983822i	$-0.442666\pi$
$359$	6.78874	0.358296	0.179148	+	0.983822i	$0.442666\pi$
$360$	6.79148	0.357942
$361$	0.173791	0.00914691
$362$	4.75533	0.249935
$363$	0	0
$364$	−0.610168	−0.0319815
$365$	27.4590	1.43727
$366$	0.956111	0.0499767
$367$	16.9143	0.882918	0.441459	−	0.897281i	$-0.354461\pi$
$367$	16.9143	0.882918	0.441459	+	0.897281i	$0.354461\pi$
$368$	7.47199	0.389505
$369$	2.32779	0.121180
$370$	−7.79384	−0.405182
$371$	2.34068	0.121522
$372$	22.5951	1.17150
$373$	−13.8215	−0.715652	−0.357826	−	0.933788i	$-0.616482\pi$
$373$	−13.8215	−0.715652	−0.357826	+	0.933788i	$0.616482\pi$
$374$	0	0
$375$	8.04450	0.415416
$376$	6.44026	0.332131
$377$	5.67893	0.292480
$378$	−0.630996	−0.0324549
$379$	3.03575	0.155936	0.0779680	−	0.996956i	$-0.475157\pi$
$379$	3.03575	0.155936	0.0779680	+	0.996956i	$0.475157\pi$
$380$	23.4851	1.20476
$381$	−8.11697	−0.415845
$382$	−4.25875	−0.217897
$383$	−17.6775	−0.903278	−0.451639	−	0.892201i	$-0.649161\pi$
$383$	−17.6775	−0.903278	−0.451639	+	0.892201i	$0.649161\pi$
$384$	−16.3102	−0.832328
$385$	0	0
$386$	−6.63752	−0.337841
$387$	−5.03073	−0.255726
$388$	−6.23362	−0.316464
$389$	−18.6047	−0.943296	−0.471648	−	0.881787i	$-0.656341\pi$
$389$	−18.6047	−0.943296	−0.471648	+	0.881787i	$0.656341\pi$
$390$	−7.37645	−0.373521
$391$	17.3582	0.877843
$392$	−16.2612	−0.821316
$393$	33.1162	1.67049
$394$	−7.93345	−0.399681
$395$	30.3435	1.52675
$396$	0	0
$397$	11.3643	0.570356	0.285178	−	0.958475i	$-0.407947\pi$
$397$	11.3643	0.570356	0.285178	+	0.958475i	$0.407947\pi$
$398$	−12.9346	−0.648353
$399$	−1.09824	−0.0549810
$400$	10.7454	0.537272
$401$	−37.7161	−1.88345	−0.941727	−	0.336377i	$-0.890798\pi$
$401$	−37.7161	−1.88345	−0.941727	+	0.336377i	$0.890798\pi$
$402$	1.38825	0.0692399
$403$	22.1889	1.10531
$404$	−21.7199	−1.08060
$405$	19.4471	0.966336
$406$	−0.280330	−0.0139126
$407$	0	0
$408$	−12.9015	−0.638718
$409$	32.6159	1.61275	0.806377	−	0.591401i	$-0.201425\pi$
$409$	32.6159	1.61275	0.806377	+	0.591401i	$0.201425\pi$
$410$	−6.06012	−0.299288
$411$	24.3563	1.20141
$412$	−0.534769	−0.0263462
$413$	−1.26969	−0.0624775
$414$	2.56384	0.126006
$415$	−2.16912	−0.106478
$416$	−12.9651	−0.635667
$417$	15.7500	0.771281
$418$	0	0
$419$	2.42637	0.118536	0.0592680	−	0.998242i	$-0.481123\pi$
$419$	2.42637	0.118536	0.0592680	+	0.998242i	$0.481123\pi$
$420$	−1.34519	−0.0656386
$421$	13.5776	0.661730	0.330865	−	0.943678i	$-0.392659\pi$
$421$	13.5776	0.661730	0.330865	+	0.943678i	$0.392659\pi$
$422$	1.12845	0.0549322
$423$	−2.35865	−0.114682
$424$	31.8899	1.54871
$425$	24.9628	1.21087
$426$	1.81902	0.0881317
$427$	0.171225	0.00828614
$428$	8.62306	0.416811
$429$	0	0
$430$	13.0969	0.631589
$431$	33.5056	1.61391	0.806953	−	0.590615i	$-0.201115\pi$
$431$	33.5056	1.61391	0.806953	+	0.590615i	$0.201115\pi$
$432$	9.17581	0.441472
$433$	−6.44033	−0.309503	−0.154751	−	0.987953i	$-0.549458\pi$
$433$	−6.44033	−0.309503	−0.154751	+	0.987953i	$0.549458\pi$
$434$	−1.09532	−0.0525769
$435$	12.5199	0.600283
$436$	−21.3900	−1.02439
$437$	20.1315	0.963021
$438$	−7.70452	−0.368136
$439$	13.7361	0.655589	0.327794	−	0.944749i	$-0.393695\pi$
$439$	13.7361	0.655589	0.327794	+	0.944749i	$0.393695\pi$
$440$	0	0
$441$	5.95544	0.283593
$442$	−5.57961	−0.265395
$443$	−0.580611	−0.0275857	−0.0137928	−	0.999905i	$-0.504391\pi$
$443$	−0.580611	−0.0275857	−0.0137928	+	0.999905i	$0.504391\pi$
$444$	−8.07876	−0.383401
$445$	−59.4040	−2.81602
$446$	−6.47037	−0.306381
$447$	−33.2882	−1.57448
$448$	0.0834420	0.00394226
$449$	−2.50186	−0.118070	−0.0590350	−	0.998256i	$-0.518802\pi$
$449$	−2.50186	−0.118070	−0.0590350	+	0.998256i	$0.518802\pi$
$450$	3.68705	0.173809
$451$	0	0
$452$	−21.3525	−1.00434
$453$	11.5418	0.542282
$454$	−2.12994	−0.0999630
$455$	−1.32101	−0.0619298
$456$	−14.9627	−0.700694
$457$	−27.2130	−1.27297	−0.636485	−	0.771289i	$-0.719612\pi$
$457$	−27.2130	−1.27297	−0.636485	+	0.771289i	$0.719612\pi$
$458$	−2.91309	−0.136120
$459$	21.3164	0.994963
$460$	24.6582	1.14969
$461$	24.1115	1.12298	0.561492	−	0.827482i	$-0.310227\pi$
$461$	24.1115	1.12298	0.561492	+	0.827482i	$0.310227\pi$
$462$	0	0
$463$	12.3013	0.571690	0.285845	−	0.958276i	$-0.407726\pi$
$463$	12.3013	0.571690	0.285845	+	0.958276i	$0.407726\pi$
$464$	4.07651	0.189247
$465$	48.9182	2.26853
$466$	−10.1338	−0.469437
$467$	35.1475	1.62643	0.813216	−	0.581963i	$-0.197715\pi$
$467$	35.1475	1.62643	0.813216	+	0.581963i	$0.197715\pi$
$468$	3.04454	0.140734
$469$	0.248615	0.0114800
$470$	6.14047	0.283239
$471$	18.4773	0.851388
$472$	−17.2986	−0.796231
$473$	0	0
$474$	−8.51386	−0.391055
$475$	28.9511	1.32837
$476$	−1.01751	−0.0466377
$477$	−11.6792	−0.534755
$478$	14.1240	0.646016
$479$	−22.6880	−1.03664	−0.518321	−	0.855186i	$-0.673443\pi$
$479$	−22.6880	−1.03664	−0.518321	+	0.855186i	$0.673443\pi$
$480$	−28.5831	−1.30464
$481$	−7.93353	−0.361738
$482$	6.73904	0.306955
$483$	−1.15310	−0.0524680
$484$	0	0
$485$	−13.4957	−0.612809
$486$	5.59904	0.253978
$487$	13.0727	0.592382	0.296191	−	0.955129i	$-0.404284\pi$
$487$	13.0727	0.592382	0.296191	+	0.955129i	$0.404284\pi$
$488$	2.33280	0.105601
$489$	−4.31744	−0.195242
$490$	−15.5043	−0.700412
$491$	43.5763	1.96657	0.983285	−	0.182072i	$-0.0582804\pi$
$491$	43.5763	1.96657	0.983285	+	0.182072i	$0.0582804\pi$
$492$	−6.28166	−0.283199
$493$	9.47015	0.426514
$494$	−6.47106	−0.291147
$495$	0	0
$496$	15.9279	0.715183
$497$	0.325758	0.0146122
$498$	0.608619	0.0272729
$499$	21.5681	0.965520	0.482760	−	0.875753i	$-0.339634\pi$
$499$	21.5681	0.965520	0.482760	+	0.875753i	$0.339634\pi$
$500$	8.64394	0.386569
$501$	−24.3756	−1.08902
$502$	−14.4822	−0.646372
$503$	0.836302	0.0372889	0.0186444	−	0.999826i	$-0.494065\pi$
$503$	0.836302	0.0372889	0.0186444	+	0.999826i	$0.494065\pi$
$504$	−0.341258	−0.0152009
$505$	−47.0233	−2.09251
$506$	0	0
$507$	11.5338	0.512232
$508$	−8.72180	−0.386967
$509$	4.11837	0.182544	0.0912719	−	0.995826i	$-0.470907\pi$
$509$	4.11837	0.182544	0.0912719	+	0.995826i	$0.470907\pi$
$510$	−12.3009	−0.544694
$511$	−1.37976	−0.0610370
$512$	−16.8894	−0.746414
$513$	24.7221	1.09151
$514$	16.1204	0.711040
$515$	−1.15777	−0.0510174
$516$	13.5757	0.597637
$517$	0	0
$518$	0.391625	0.0172070
$519$	−11.5121	−0.505326
$520$	−17.9977	−0.789252
$521$	10.8045	0.473354	0.236677	−	0.971588i	$-0.423942\pi$
$521$	10.8045	0.473354	0.236677	+	0.971588i	$0.423942\pi$
$522$	1.39876	0.0612220
$523$	10.9911	0.480609	0.240304	−	0.970698i	$-0.422753\pi$
$523$	10.9911	0.480609	0.240304	+	0.970698i	$0.422753\pi$
$524$	35.5838	1.55449
$525$	−1.65827	−0.0723729
$526$	−3.77652	−0.164664
$527$	37.0021	1.61184
$528$	0	0
$529$	−1.86292	−0.0809964
$530$	30.4055	1.32073
$531$	6.33536	0.274931
$532$	−1.18008	−0.0511630
$533$	−6.16874	−0.267198
$534$	16.6677	0.721283
$535$	18.6688	0.807124
$536$	3.38719	0.146304
$537$	−1.11669	−0.0481887
$538$	7.85749	0.338760
$539$	0	0
$540$	30.2809	1.30308
$541$	−31.8202	−1.36806	−0.684029	−	0.729455i	$-0.739774\pi$
$541$	−31.8202	−1.36806	−0.684029	+	0.729455i	$0.739774\pi$
$542$	18.3868	0.789782
$543$	10.6716	0.457963
$544$	−21.6205	−0.926973
$545$	−46.3090	−1.98366
$546$	0.370652	0.0158625
$547$	11.0490	0.472421	0.236210	−	0.971702i	$-0.424095\pi$
$547$	11.0490	0.472421	0.236210	+	0.971702i	$0.424095\pi$
$548$	26.1712	1.11798
$549$	−0.854356	−0.0364630
$550$	0	0
$551$	10.9832	0.467900
$552$	−15.7101	−0.668667
$553$	−1.52470	−0.0648369
$554$	10.4676	0.444726
$555$	−17.4904	−0.742428
$556$	16.9236	0.717721
$557$	15.7223	0.666174	0.333087	−	0.942896i	$-0.391910\pi$
$557$	15.7223	0.666174	0.333087	+	0.942896i	$0.391910\pi$
$558$	5.46528	0.231364
$559$	13.3317	0.563869
$560$	−0.948260	−0.0400713
$561$	0	0
$562$	9.18564	0.387473
$563$	−23.5160	−0.991079	−0.495540	−	0.868585i	$-0.665030\pi$
$563$	−23.5160	−0.991079	−0.495540	+	0.868585i	$0.665030\pi$
$564$	6.36495	0.268013
$565$	−46.2279	−1.94482
$566$	3.94215	0.165701
$567$	−0.977181	−0.0410377
$568$	4.43820	0.186223
$569$	−4.39082	−0.184073	−0.0920364	−	0.995756i	$-0.529338\pi$
$569$	−4.39082	−0.184073	−0.0920364	+	0.995756i	$0.529338\pi$
$570$	−14.2662	−0.597547
$571$	−19.6493	−0.822299	−0.411149	−	0.911568i	$-0.634873\pi$
$571$	−19.6493	−0.822299	−0.411149	+	0.911568i	$0.634873\pi$
$572$	0	0
$573$	−9.55722	−0.399259
$574$	0.304509	0.0127100
$575$	30.3972	1.26765
$576$	−0.416349	−0.0173479
$577$	3.58801	0.149371	0.0746854	−	0.997207i	$-0.476205\pi$
$577$	3.58801	0.149371	0.0746854	+	0.997207i	$0.476205\pi$
$578$	1.79178	0.0745280
$579$	−14.8955	−0.619036
$580$	13.4528	0.558597
$581$	0.108994	0.00452184
$582$	3.78667	0.156962
$583$	0	0
$584$	−18.7982	−0.777873
$585$	6.59141	0.272521
$586$	−6.43913	−0.265998
$587$	−1.83308	−0.0756592	−0.0378296	−	0.999284i	$-0.512044\pi$
$587$	−1.83308	−0.0756592	−0.0378296	+	0.999284i	$0.512044\pi$
$588$	−16.0711	−0.662761
$589$	42.9139	1.76824
$590$	−16.4933	−0.679020
$591$	−17.8037	−0.732348
$592$	−5.69493	−0.234060
$593$	−12.1007	−0.496918	−0.248459	−	0.968642i	$-0.579924\pi$
$593$	−12.1007	−0.496918	−0.248459	+	0.968642i	$0.579924\pi$
$594$	0	0
$595$	−2.20291	−0.0903103
$596$	−35.7687	−1.46514
$597$	−29.0270	−1.18800
$598$	−6.79429	−0.277839
$599$	−20.3859	−0.832947	−0.416474	−	0.909148i	$-0.636734\pi$
$599$	−20.3859	−0.832947	−0.416474	+	0.909148i	$0.636734\pi$
$600$	−22.5927	−0.922342
$601$	−40.0034	−1.63177	−0.815887	−	0.578212i	$-0.803751\pi$
$601$	−40.0034	−1.63177	−0.815887	+	0.578212i	$0.803751\pi$
$602$	−0.658094	−0.0268219
$603$	−1.24051	−0.0505174
$604$	12.4019	0.504624
$605$	0	0
$606$	13.1939	0.535967
$607$	−34.3159	−1.39284	−0.696419	−	0.717635i	$-0.745225\pi$
$607$	−34.3159	−1.39284	−0.696419	+	0.717635i	$0.745225\pi$
$608$	−25.0748	−1.01692
$609$	−0.629100	−0.0254924
$610$	2.22421	0.0900558
$611$	6.25053	0.252869
$612$	5.07707	0.205228
$613$	15.0108	0.606279	0.303140	−	0.952946i	$-0.401965\pi$
$613$	15.0108	0.606279	0.303140	+	0.952946i	$0.401965\pi$
$614$	−1.30800	−0.0527865
$615$	−13.5997	−0.548394
$616$	0	0
$617$	40.1074	1.61466	0.807332	−	0.590098i	$-0.200911\pi$
$617$	40.1074	1.61466	0.807332	+	0.590098i	$0.200911\pi$
$618$	0.324850	0.0130674
$619$	42.1375	1.69365	0.846824	−	0.531873i	$-0.178512\pi$
$619$	42.1375	1.69365	0.846824	+	0.531873i	$0.178512\pi$
$620$	52.5633	2.11099
$621$	25.9569	1.04162
$622$	−1.85629	−0.0744303
$623$	2.98493	0.119589
$624$	−5.38995	−0.215771
$625$	−14.3443	−0.573770
$626$	−14.1002	−0.563556
$627$	0	0
$628$	19.8541	0.792265
$629$	−13.2299	−0.527511
$630$	−0.325373	−0.0129632
$631$	−23.8582	−0.949781	−0.474891	−	0.880045i	$-0.657512\pi$
$631$	−23.8582	−0.949781	−0.474891	+	0.880045i	$0.657512\pi$
$632$	−20.7729	−0.826300
$633$	2.53240	0.100654
$634$	−0.114824	−0.00456026
$635$	−18.8826	−0.749334
$636$	31.5170	1.24973
$637$	−15.7822	−0.625313
$638$	0	0
$639$	−1.62543	−0.0643009
$640$	−37.9427	−1.49982
$641$	−2.50947	−0.0991181	−0.0495590	−	0.998771i	$-0.515782\pi$
$641$	−2.50947	−0.0991181	−0.0495590	+	0.998771i	$0.515782\pi$
$642$	−5.23815	−0.206733
$643$	28.8400	1.13734	0.568669	−	0.822567i	$-0.307459\pi$
$643$	28.8400	1.13734	0.568669	+	0.822567i	$0.307459\pi$
$644$	−1.23903	−0.0488244
$645$	29.3913	1.15728
$646$	−10.7911	−0.424570
$647$	−24.4801	−0.962413	−0.481206	−	0.876607i	$-0.659801\pi$
$647$	−24.4801	−0.962413	−0.481206	+	0.876607i	$0.659801\pi$
$648$	−13.3133	−0.522997
$649$	0	0
$650$	−9.77084	−0.383244
$651$	−2.45804	−0.0963383
$652$	−4.63916	−0.181684
$653$	3.68121	0.144057	0.0720284	−	0.997403i	$-0.477053\pi$
$653$	3.68121	0.144057	0.0720284	+	0.997403i	$0.477053\pi$
$654$	12.9935	0.508087
$655$	77.0386	3.01015
$656$	−4.42811	−0.172889
$657$	6.88456	0.268592
$658$	−0.308547	−0.0120284
$659$	−11.8943	−0.463338	−0.231669	−	0.972795i	$-0.574419\pi$
$659$	−11.8943	−0.463338	−0.231669	+	0.972795i	$0.574419\pi$
$660$	0	0
$661$	27.2745	1.06086	0.530429	−	0.847730i	$-0.322031\pi$
$661$	27.2745	1.06086	0.530429	+	0.847730i	$0.322031\pi$
$662$	18.1493	0.705392
$663$	−12.5214	−0.486291
$664$	1.48496	0.0576277
$665$	−2.55486	−0.0990733
$666$	−1.95408	−0.0757192
$667$	11.5318	0.446513
$668$	−26.1919	−1.01339
$669$	−14.5204	−0.561391
$670$	3.22952	0.124767
$671$	0	0
$672$	1.43625	0.0554044
$673$	−7.06630	−0.272386	−0.136193	−	0.990682i	$-0.543487\pi$
$673$	−7.06630	−0.272386	−0.136193	+	0.990682i	$0.543487\pi$
$674$	−15.2835	−0.588697
$675$	37.3285	1.43678
$676$	12.3932	0.476661
$677$	36.3278	1.39619	0.698096	−	0.716004i	$-0.254031\pi$
$677$	36.3278	1.39619	0.698096	+	0.716004i	$0.254031\pi$
$678$	12.9707	0.498139
$679$	0.678133	0.0260244
$680$	−30.0129	−1.15094
$681$	−4.77987	−0.183165
$682$	0	0
$683$	1.03892	0.0397533	0.0198766	−	0.999802i	$-0.493673\pi$
$683$	1.03892	0.0397533	0.0198766	+	0.999802i	$0.493673\pi$
$684$	5.88822	0.225142
$685$	56.6603	2.16488
$686$	1.56140	0.0596144
$687$	−6.53738	−0.249416
$688$	9.56987	0.364848
$689$	30.9505	1.17912
$690$	−14.9788	−0.570234
$691$	−45.7189	−1.73923	−0.869615	−	0.493730i	$-0.835633\pi$
$691$	−45.7189	−1.73923	−0.869615	+	0.493730i	$0.835633\pi$
$692$	−12.3699	−0.470235
$693$	0	0
$694$	11.8132	0.448423
$695$	36.6395	1.38981
$696$	−8.57100	−0.324883
$697$	−10.2870	−0.389646
$698$	−2.43348	−0.0921085
$699$	−22.7415	−0.860164
$700$	−1.78184	−0.0673471
$701$	51.4517	1.94330	0.971651	−	0.236419i	$-0.0759738\pi$
$701$	51.4517	1.94330	0.971651	+	0.236419i	$0.0759738\pi$
$702$	−8.34357	−0.314908
$703$	−15.3436	−0.578697
$704$	0	0
$705$	13.7801	0.518987
$706$	−9.16482	−0.344923
$707$	2.36283	0.0888633
$708$	−17.0963	−0.642519
$709$	8.61993	0.323728	0.161864	−	0.986813i	$-0.448249\pi$
$709$	8.61993	0.323728	0.161864	+	0.986813i	$0.448249\pi$
$710$	4.23161	0.158809
$711$	7.60777	0.285314
$712$	40.6674	1.52408
$713$	45.0575	1.68742
$714$	0.618098	0.0231317
$715$	0	0
$716$	−1.19990	−0.0448423
$717$	31.6962	1.18372
$718$	−4.43117	−0.165370
$719$	−23.7050	−0.884049	−0.442024	−	0.897003i	$-0.645740\pi$
$719$	−23.7050	−0.884049	−0.442024	+	0.897003i	$0.645740\pi$
$720$	4.73151	0.176333
$721$	0.0581756	0.00216657
$722$	−0.113438	−0.00422171
$723$	15.1233	0.562443
$724$	11.4668	0.426161
$725$	16.5838	0.615908
$726$	0	0
$727$	−46.8661	−1.73817	−0.869084	−	0.494665i	$-0.835291\pi$
$727$	−46.8661	−1.73817	−0.869084	+	0.494665i	$0.835291\pi$
$728$	0.904350	0.0335174
$729$	29.6860	1.09948
$730$	−17.9231	−0.663365
$731$	22.2318	0.822273
$732$	2.30553	0.0852147
$733$	3.13726	0.115877	0.0579387	−	0.998320i	$-0.481547\pi$
$733$	3.13726	0.115877	0.0579387	+	0.998320i	$0.481547\pi$
$734$	−11.0403	−0.407507
$735$	−34.7937	−1.28339
$736$	−26.3273	−0.970438
$737$	0	0
$738$	−1.51940	−0.0559300
$739$	−49.5301	−1.82199	−0.910997	−	0.412413i	$-0.864686\pi$
$739$	−49.5301	−1.82199	−0.910997	+	0.412413i	$0.864686\pi$
$740$	−18.7937	−0.690872
$741$	−14.5219	−0.533477
$742$	−1.52782	−0.0560879
$743$	−40.6091	−1.48980	−0.744901	−	0.667175i	$-0.767503\pi$
$743$	−40.6091	−1.48980	−0.744901	+	0.667175i	$0.767503\pi$
$744$	−33.4889	−1.22776
$745$	−77.4388	−2.83714
$746$	9.02165	0.330306
$747$	−0.543846	−0.0198983
$748$	0	0
$749$	−0.938072	−0.0342764
$750$	−5.25084	−0.191733
$751$	−26.3295	−0.960776	−0.480388	−	0.877056i	$-0.659504\pi$
$751$	−26.3295	−0.960776	−0.480388	+	0.877056i	$0.659504\pi$
$752$	4.48682	0.163618
$753$	−32.5000	−1.18437
$754$	−3.70677	−0.134993
$755$	26.8499	0.977167
$756$	−1.52156	−0.0553385
$757$	−1.78561	−0.0648992	−0.0324496	−	0.999473i	$-0.510331\pi$
$757$	−1.78561	−0.0648992	−0.0324496	+	0.999473i	$0.510331\pi$
$758$	−1.98151	−0.0719715
$759$	0	0
$760$	−34.8080	−1.26262
$761$	−24.7374	−0.896729	−0.448365	−	0.893851i	$-0.647993\pi$
$761$	−24.7374	−0.896729	−0.448365	+	0.893851i	$0.647993\pi$
$762$	5.29814	0.191931
$763$	2.32694	0.0842408
$764$	−10.2694	−0.371533
$765$	10.9918	0.397409
$766$	11.5385	0.416904
$767$	−16.7890	−0.606215
$768$	12.0737	0.435674
$769$	47.1413	1.69996	0.849980	−	0.526815i	$-0.176614\pi$
$769$	47.1413	1.69996	0.849980	+	0.526815i	$0.176614\pi$
$770$	0	0
$771$	36.1764	1.30286
$772$	−16.0055	−0.576049
$773$	−5.55108	−0.199659	−0.0998293	−	0.995005i	$-0.531830\pi$
$773$	−5.55108	−0.199659	−0.0998293	+	0.995005i	$0.531830\pi$
$774$	3.28368	0.118029
$775$	64.7970	2.32758
$776$	9.23904	0.331662
$777$	0.878860	0.0315289
$778$	12.1437	0.435374
$779$	−11.9305	−0.427454
$780$	−17.7873	−0.636886
$781$	0	0
$782$	−11.3301	−0.405164
$783$	14.1614	0.506086
$784$	−11.3289	−0.404605
$785$	42.9839	1.53416
$786$	−21.6157	−0.771007
$787$	22.6092	0.805932	0.402966	−	0.915215i	$-0.367979\pi$
$787$	22.6092	0.805932	0.402966	+	0.915215i	$0.367979\pi$
$788$	−19.1304	−0.681492
$789$	−8.47503	−0.301719
$790$	−19.8059	−0.704663
$791$	2.32286	0.0825914
$792$	0	0
$793$	2.26408	0.0803999
$794$	−7.41772	−0.263245
$795$	68.2341	2.42001
$796$	−31.1900	−1.10550
$797$	−2.44833	−0.0867242	−0.0433621	−	0.999059i	$-0.513807\pi$
$797$	−2.44833	−0.0867242	−0.0433621	+	0.999059i	$0.513807\pi$
$798$	0.716851	0.0253762
$799$	10.4234	0.368752
$800$	−37.8612	−1.33860
$801$	−14.8939	−0.526249
$802$	24.6182	0.869300
$803$	0	0
$804$	3.34758	0.118060
$805$	−2.68248	−0.0945449
$806$	−14.4832	−0.510150
$807$	17.6333	0.620721
$808$	32.1917	1.13250
$809$	37.2019	1.30795	0.653975	−	0.756516i	$-0.273100\pi$
$809$	37.2019	1.30795	0.653975	+	0.756516i	$0.273100\pi$
$810$	−12.6936	−0.446008
$811$	19.9199	0.699482	0.349741	−	0.936847i	$-0.386270\pi$
$811$	19.9199	0.699482	0.349741	+	0.936847i	$0.386270\pi$
$812$	−0.675977	−0.0237222
$813$	41.2625	1.44714
$814$	0	0
$815$	−10.0437	−0.351817
$816$	−8.98825	−0.314652
$817$	25.7838	0.902059
$818$	−21.2892	−0.744360
$819$	−0.331205	−0.0115733
$820$	−14.6131	−0.510312
$821$	−31.1489	−1.08710	−0.543552	−	0.839375i	$-0.682921\pi$
$821$	−31.1489	−1.08710	−0.543552	+	0.839375i	$0.682921\pi$
$822$	−15.8979	−0.554503
$823$	9.60357	0.334759	0.167380	−	0.985893i	$-0.446469\pi$
$823$	9.60357	0.334759	0.167380	+	0.985893i	$0.446469\pi$
$824$	0.792598	0.0276114
$825$	0	0
$826$	0.828758	0.0288362
$827$	35.6132	1.23839	0.619195	−	0.785237i	$-0.287459\pi$
$827$	35.6132	1.23839	0.619195	+	0.785237i	$0.287459\pi$
$828$	6.18234	0.214851
$829$	−35.6189	−1.23710	−0.618548	−	0.785747i	$-0.712279\pi$
$829$	−35.6189	−1.23710	−0.618548	+	0.785747i	$0.712279\pi$
$830$	1.41584	0.0491445
$831$	23.4907	0.814884
$832$	1.10334	0.0382515
$833$	−26.3183	−0.911875
$834$	−10.2804	−0.355981
$835$	−56.7052	−1.96236
$836$	0	0
$837$	55.3318	1.91255
$838$	−1.58375	−0.0547097
$839$	13.7933	0.476198	0.238099	−	0.971241i	$-0.423476\pi$
$839$	13.7933	0.476198	0.238099	+	0.971241i	$0.423476\pi$
$840$	1.99375	0.0687909
$841$	−22.7086	−0.783054
$842$	−8.86241	−0.305419
$843$	20.6138	0.709978
$844$	2.72110	0.0936642
$845$	26.8311	0.923019
$846$	1.53955	0.0529308
$847$	0	0
$848$	22.2172	0.762942
$849$	8.84673	0.303619
$850$	−16.2938	−0.558873
$851$	−16.1101	−0.552246
$852$	4.38631	0.150272
$853$	−51.4758	−1.76250	−0.881249	−	0.472652i	$-0.843297\pi$
$853$	−51.4758	−1.76250	−0.881249	+	0.472652i	$0.843297\pi$
$854$	−0.111762	−0.00382443
$855$	12.7479	0.435970
$856$	−12.7805	−0.436829
$857$	−50.0716	−1.71041	−0.855207	−	0.518287i	$-0.826570\pi$
$857$	−50.0716	−1.71041	−0.855207	+	0.518287i	$0.826570\pi$
$858$	0	0
$859$	35.4226	1.20860	0.604301	−	0.796756i	$-0.293452\pi$
$859$	35.4226	1.20860	0.604301	+	0.796756i	$0.293452\pi$
$860$	31.5813	1.07691
$861$	0.683360	0.0232888
$862$	−21.8699	−0.744891
$863$	−9.89128	−0.336703	−0.168352	−	0.985727i	$-0.553844\pi$
$863$	−9.89128	−0.336703	−0.168352	+	0.985727i	$0.553844\pi$
$864$	−32.3307	−1.09991
$865$	−26.7808	−0.910574
$866$	4.20376	0.142850
$867$	4.02099	0.136560
$868$	−2.64120	−0.0896483
$869$	0	0
$870$	−8.17203	−0.277058
$871$	3.28740	0.111389
$872$	31.7027	1.07359
$873$	−3.38367	−0.114520
$874$	−13.1403	−0.444478
$875$	−0.940344	−0.0317894
$876$	−18.5784	−0.627704
$877$	−58.4583	−1.97400	−0.986998	−	0.160733i	$-0.948614\pi$
$877$	−58.4583	−1.97400	−0.986998	+	0.160733i	$0.948614\pi$
$878$	−8.96588	−0.302584
$879$	−14.4503	−0.487396
$880$	0	0
$881$	−17.4421	−0.587638	−0.293819	−	0.955861i	$-0.594926\pi$
$881$	−17.4421	−0.587638	−0.293819	+	0.955861i	$0.594926\pi$
$882$	−3.88726	−0.130891
$883$	−29.3347	−0.987193	−0.493596	−	0.869691i	$-0.664318\pi$
$883$	−29.3347	−0.987193	−0.493596	+	0.869691i	$0.664318\pi$
$884$	−13.4544	−0.452522
$885$	−37.0133	−1.24419
$886$	0.378979	0.0127320
$887$	25.9206	0.870329	0.435165	−	0.900351i	$-0.356690\pi$
$887$	25.9206	0.870329	0.435165	+	0.900351i	$0.356690\pi$
$888$	11.9738	0.401814
$889$	0.948815	0.0318222
$890$	38.7744	1.29972
$891$	0	0
$892$	−15.6024	−0.522406
$893$	12.0887	0.404532
$894$	21.7280	0.726693
$895$	−2.59777	−0.0868338
$896$	1.90655	0.0636933
$897$	−15.2473	−0.509093
$898$	1.63302	0.0544946
$899$	24.5821	0.819859
$900$	8.89080	0.296360
$901$	51.6128	1.71947
$902$	0	0
$903$	−1.47685	−0.0491466
$904$	31.6472	1.05257
$905$	24.8255	0.825229
$906$	−7.53362	−0.250288
$907$	−15.9709	−0.530304	−0.265152	−	0.964207i	$-0.585422\pi$
$907$	−15.9709	−0.530304	−0.265152	+	0.964207i	$0.585422\pi$
$908$	−5.13605	−0.170446
$909$	−11.7898	−0.391041
$910$	0.862254	0.0285834
$911$	7.11074	0.235589	0.117795	−	0.993038i	$-0.462418\pi$
$911$	7.11074	0.235589	0.117795	+	0.993038i	$0.462418\pi$
$912$	−10.4243	−0.345183
$913$	0	0
$914$	17.7626	0.587533
$915$	4.99144	0.165012
$916$	−7.02451	−0.232096
$917$	−3.87104	−0.127833
$918$	−13.9137	−0.459221
$919$	27.6262	0.911303	0.455652	−	0.890158i	$-0.349406\pi$
$919$	27.6262	0.911303	0.455652	+	0.890158i	$0.349406\pi$
$920$	−36.5467	−1.20491
$921$	−2.93533	−0.0967223
$922$	−15.7382	−0.518308
$923$	4.30745	0.141782
$924$	0	0
$925$	−23.1678	−0.761753
$926$	−8.02935	−0.263861
$927$	−0.290278	−0.00953397
$928$	−14.3634	−0.471503
$929$	1.06854	0.0350575	0.0175288	−	0.999846i	$-0.494420\pi$
$929$	1.06854	0.0350575	0.0175288	+	0.999846i	$0.494420\pi$
$930$	−31.9301	−1.04703
$931$	−30.5231	−1.00036
$932$	−24.4361	−0.800432
$933$	−4.16576	−0.136381
$934$	−22.9416	−0.750672
$935$	0	0
$936$	−4.51242	−0.147493
$937$	27.7004	0.904934	0.452467	−	0.891781i	$-0.350544\pi$
$937$	27.7004	0.904934	0.452467	+	0.891781i	$0.350544\pi$
$938$	−0.162277	−0.00529853
$939$	−31.6427	−1.03262
$940$	14.8069	0.482947
$941$	−28.2707	−0.921598	−0.460799	−	0.887505i	$-0.652437\pi$
$941$	−28.2707	−0.921598	−0.460799	+	0.887505i	$0.652437\pi$
$942$	−12.0606	−0.392954
$943$	−12.5264	−0.407916
$944$	−12.0516	−0.392247
$945$	−3.29416	−0.107159
$946$	0	0
$947$	21.7597	0.707095	0.353548	−	0.935417i	$-0.384975\pi$
$947$	21.7597	0.707095	0.353548	+	0.935417i	$0.384975\pi$
$948$	−20.5300	−0.666783
$949$	−18.2444	−0.592238
$950$	−18.8970	−0.613101
$951$	−0.257682	−0.00835590
$952$	1.50809	0.0488774
$953$	−24.8479	−0.804903	−0.402452	−	0.915441i	$-0.631842\pi$
$953$	−24.8479	−0.804903	−0.402452	+	0.915441i	$0.631842\pi$
$954$	7.62331	0.246814
$955$	−22.2331	−0.719446
$956$	34.0580	1.10151
$957$	0	0
$958$	14.8090	0.478458
$959$	−2.84707	−0.0919367
$960$	2.43245	0.0785071
$961$	65.0481	2.09833
$962$	5.17841	0.166959
$963$	4.68068	0.150833
$964$	16.2503	0.523385
$965$	−34.6516	−1.11548
$966$	0.752657	0.0242163
$967$	−9.08559	−0.292173	−0.146086	−	0.989272i	$-0.546668\pi$
$967$	−9.08559	−0.292173	−0.146086	+	0.989272i	$0.546668\pi$
$968$	0	0
$969$	−24.2167	−0.777953
$970$	8.80897	0.282839
$971$	−2.51768	−0.0807962	−0.0403981	−	0.999184i	$-0.512863\pi$
$971$	−2.51768	−0.0807962	−0.0403981	+	0.999184i	$0.512863\pi$
$972$	13.5013	0.433055
$973$	−1.84106	−0.0590217
$974$	−8.53288	−0.273411
$975$	−21.9271	−0.702229
$976$	1.62523	0.0520222
$977$	4.64153	0.148496	0.0742478	−	0.997240i	$-0.476344\pi$
$977$	4.64153	0.148496	0.0742478	+	0.997240i	$0.476344\pi$
$978$	2.81810	0.0901129
$979$	0	0
$980$	−37.3864	−1.19427
$981$	−11.6107	−0.370700
$982$	−28.4433	−0.907662
$983$	−6.53246	−0.208353	−0.104177	−	0.994559i	$-0.533221\pi$
$983$	−6.53246	−0.208353	−0.104177	+	0.994559i	$0.533221\pi$
$984$	9.31025	0.296800
$985$	−41.4171	−1.31966
$986$	−6.18139	−0.196856
$987$	−0.692421	−0.0220400
$988$	−15.6041	−0.496431
$989$	27.0716	0.860828
$990$	0	0
$991$	40.8864	1.29880	0.649399	−	0.760448i	$-0.275020\pi$
$991$	40.8864	1.29880	0.649399	+	0.760448i	$0.275020\pi$
$992$	−56.1214	−1.78186
$993$	40.7295	1.29251
$994$	−0.212630	−0.00674421
$995$	−67.5260	−2.14072
$996$	1.46760	0.0465027
$997$	−3.36068	−0.106434	−0.0532168	−	0.998583i	$-0.516947\pi$
$997$	−3.36068	−0.106434	−0.0532168	+	0.998583i	$0.516947\pi$
$998$	−14.0780	−0.445631
$999$	−19.7836	−0.625925

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7381.2.a.r.1.18	yes	50
11.10	odd	2		7381.2.a.q.1.33	✓	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7381.2.a.q.1.33	✓	50	11.10	odd	2
7381.2.a.r.1.18	yes	50	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 7381 = 11^{2} \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7381.a (trivial)

\(f(q)\)	\(=\)	\(q-0.652724 q^{2} -1.46480 q^{3} -1.57395 q^{4} -3.40759 q^{5} +0.956111 q^{6} +0.171225 q^{7} +2.33280 q^{8} -0.854356 q^{9} +O(q^{10})\)	\(q-0.652724 q^{2} -1.46480 q^{3} -1.57395 q^{4} -3.40759 q^{5} +0.956111 q^{6} +0.171225 q^{7} +2.33280 q^{8} -0.854356 q^{9} +2.22421 q^{10} +2.30553 q^{12} +2.26408 q^{13} -0.111762 q^{14} +4.99144 q^{15} +1.62523 q^{16} +3.77557 q^{17} +0.557659 q^{18} +4.37879 q^{19} +5.36338 q^{20} -0.250810 q^{21} +4.59751 q^{23} -3.41709 q^{24} +6.61166 q^{25} -1.47782 q^{26} +5.64587 q^{27} -0.269499 q^{28} +2.50827 q^{29} -3.25803 q^{30} +9.80041 q^{31} -5.72643 q^{32} -2.46440 q^{34} -0.583463 q^{35} +1.34472 q^{36} -3.50409 q^{37} -2.85814 q^{38} -3.31643 q^{39} -7.94923 q^{40} -2.72461 q^{41} +0.163710 q^{42} +5.88833 q^{43} +2.91129 q^{45} -3.00090 q^{46} +2.76074 q^{47} -2.38063 q^{48} -6.97068 q^{49} -4.31559 q^{50} -5.53046 q^{51} -3.56355 q^{52} +13.6702 q^{53} -3.68519 q^{54} +0.399434 q^{56} -6.41406 q^{57} -1.63721 q^{58} -7.41536 q^{59} -7.85629 q^{60} +1.00000 q^{61} -6.39696 q^{62} -0.146287 q^{63} +0.487325 q^{64} -7.71506 q^{65} +1.45198 q^{67} -5.94256 q^{68} -6.73444 q^{69} +0.380840 q^{70} +1.90252 q^{71} -1.99304 q^{72} -8.05818 q^{73} +2.28720 q^{74} -9.68477 q^{75} -6.89200 q^{76} +2.16471 q^{78} -8.90468 q^{79} -5.53810 q^{80} -5.70701 q^{81} +1.77842 q^{82} +0.636557 q^{83} +0.394763 q^{84} -12.8656 q^{85} -3.84345 q^{86} -3.67412 q^{87} +17.4328 q^{89} -1.90027 q^{90} +0.387667 q^{91} -7.23626 q^{92} -14.3557 q^{93} -1.80200 q^{94} -14.9211 q^{95} +8.38809 q^{96} +3.96049 q^{97} +4.54993 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q + 10 q^{2} - 2 q^{3} + 50 q^{4} - 2 q^{5} + 12 q^{6} + 8 q^{7} + 30 q^{8} + 48 q^{9}+O(q^{10}) \) 50 * q + 10 * q^2 - 2 * q^3 + 50 * q^4 - 2 * q^5 + 12 * q^6 + 8 * q^7 + 30 * q^8 + 48 * q^9	\( 50 q + 10 q^{2} - 2 q^{3} + 50 q^{4} - 2 q^{5} + 12 q^{6} + 8 q^{7} + 30 q^{8} + 48 q^{9} + 12 q^{10} - 14 q^{12} + 8 q^{13} - 2 q^{14} - 16 q^{15} + 42 q^{16} + 22 q^{17} + 32 q^{19} - 8 q^{20} + 24 q^{21} + 12 q^{23} - 8 q^{24} + 40 q^{25} + 10 q^{26} - 8 q^{27} + 72 q^{28} + 56 q^{29} + 24 q^{30} + 10 q^{31} + 70 q^{32} - 32 q^{34} + 70 q^{35} + 34 q^{36} - 8 q^{37} - 14 q^{38} + 96 q^{39} - 54 q^{40} + 56 q^{41} - 8 q^{42} + 44 q^{43} - 24 q^{45} - 4 q^{46} - 4 q^{47} - 28 q^{48} + 38 q^{49} + 120 q^{50} + 76 q^{51} + 24 q^{52} + 4 q^{53} + 48 q^{54} - 18 q^{56} + 8 q^{57} + 28 q^{58} + 12 q^{59} - 60 q^{60} + 50 q^{61} + 8 q^{62} + 30 q^{63} + 10 q^{64} + 64 q^{65} + 18 q^{67} - 22 q^{68} - 8 q^{69} + 34 q^{70} + 12 q^{71} + 104 q^{72} - 16 q^{73} + 84 q^{74} - 26 q^{75} + 64 q^{76} + 40 q^{78} + 78 q^{79} - 36 q^{80} + 34 q^{81} + 54 q^{82} + 68 q^{83} - 78 q^{84} - 4 q^{85} + 36 q^{86} + 48 q^{87} + 26 q^{89} - 20 q^{90} + 32 q^{92} + 22 q^{93} + 156 q^{94} + 100 q^{95} - 4 q^{96} - 14 q^{97} + 70 q^{98}+O(q^{100}) \) 50 * q + 10 * q^2 - 2 * q^3 + 50 * q^4 - 2 * q^5 + 12 * q^6 + 8 * q^7 + 30 * q^8 + 48 * q^9 + 12 * q^10 - 14 * q^12 + 8 * q^13 - 2 * q^14 - 16 * q^15 + 42 * q^16 + 22 * q^17 + 32 * q^19 - 8 * q^20 + 24 * q^21 + 12 * q^23 - 8 * q^24 + 40 * q^25 + 10 * q^26 - 8 * q^27 + 72 * q^28 + 56 * q^29 + 24 * q^30 + 10 * q^31 + 70 * q^32 - 32 * q^34 + 70 * q^35 + 34 * q^36 - 8 * q^37 - 14 * q^38 + 96 * q^39 - 54 * q^40 + 56 * q^41 - 8 * q^42 + 44 * q^43 - 24 * q^45 - 4 * q^46 - 4 * q^47 - 28 * q^48 + 38 * q^49 + 120 * q^50 + 76 * q^51 + 24 * q^52 + 4 * q^53 + 48 * q^54 - 18 * q^56 + 8 * q^57 + 28 * q^58 + 12 * q^59 - 60 * q^60 + 50 * q^61 + 8 * q^62 + 30 * q^63 + 10 * q^64 + 64 * q^65 + 18 * q^67 - 22 * q^68 - 8 * q^69 + 34 * q^70 + 12 * q^71 + 104 * q^72 - 16 * q^73 + 84 * q^74 - 26 * q^75 + 64 * q^76 + 40 * q^78 + 78 * q^79 - 36 * q^80 + 34 * q^81 + 54 * q^82 + 68 * q^83 - 78 * q^84 - 4 * q^85 + 36 * q^86 + 48 * q^87 + 26 * q^89 - 20 * q^90 + 32 * q^92 + 22 * q^93 + 156 * q^94 + 100 * q^95 - 4 * q^96 - 14 * q^97 + 70 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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