LMFDB - Embedded newform 7381.2.a.v.1.7

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:	$64$
Twist minimal:	no (minimal twist has level 671)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
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)

$f(q)$	$=$	$q-2.36361 q^{2} -0.120226 q^{3} +3.58664 q^{4} -1.13694 q^{5} +0.284166 q^{6} +2.88472 q^{7} -3.75020 q^{8} -2.98555 q^{9} +O(q^{10})$	\(q-2.36361 q^{2} -0.120226 q^{3} +3.58664 q^{4} -1.13694 q^{5} +0.284166 q^{6} +2.88472 q^{7} -3.75020 q^{8} -2.98555 q^{9} +2.68729 q^{10} -0.431206 q^{12} -1.50422 q^{13} -6.81834 q^{14} +0.136690 q^{15} +1.69073 q^{16} +1.37717 q^{17} +7.05666 q^{18} -6.31432 q^{19} -4.07781 q^{20} -0.346817 q^{21} +2.25207 q^{23} +0.450871 q^{24} -3.70736 q^{25} +3.55539 q^{26} +0.719616 q^{27} +10.3465 q^{28} -10.4749 q^{29} -0.323081 q^{30} -2.04513 q^{31} +3.50420 q^{32} -3.25508 q^{34} -3.27976 q^{35} -10.7081 q^{36} -2.90975 q^{37} +14.9246 q^{38} +0.180846 q^{39} +4.26377 q^{40} -8.11198 q^{41} +0.819739 q^{42} -5.38765 q^{43} +3.39439 q^{45} -5.32300 q^{46} -0.377075 q^{47} -0.203268 q^{48} +1.32160 q^{49} +8.76275 q^{50} -0.165571 q^{51} -5.39510 q^{52} +10.5682 q^{53} -1.70089 q^{54} -10.8183 q^{56} +0.759143 q^{57} +24.7586 q^{58} +9.03832 q^{59} +0.490257 q^{60} +1.00000 q^{61} +4.83389 q^{62} -8.61246 q^{63} -11.6640 q^{64} +1.71021 q^{65} +7.31363 q^{67} +4.93941 q^{68} -0.270756 q^{69} +7.75206 q^{70} -12.1691 q^{71} +11.1964 q^{72} -9.65360 q^{73} +6.87751 q^{74} +0.445720 q^{75} -22.6472 q^{76} -0.427448 q^{78} -3.66125 q^{79} -1.92226 q^{80} +8.87012 q^{81} +19.1735 q^{82} -4.14249 q^{83} -1.24391 q^{84} -1.56576 q^{85} +12.7343 q^{86} +1.25935 q^{87} -0.402184 q^{89} -8.02302 q^{90} -4.33925 q^{91} +8.07736 q^{92} +0.245877 q^{93} +0.891258 q^{94} +7.17902 q^{95} -0.421294 q^{96} -7.99844 q^{97} -3.12374 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 5 q^{2} + 19 q^{3} + 73 q^{4} + 21 q^{5} - q^{6} + 6 q^{7} + 3 q^{8} + 81 q^{9}+O(q^{10}) $ 64 * q + 5 * q^2 + 19 * q^3 + 73 * q^4 + 21 * q^5 - q^6 + 6 * q^7 + 3 * q^8 + 81 * q^9	\( 64 q + 5 q^{2} + 19 q^{3} + 73 q^{4} + 21 q^{5} - q^{6} + 6 q^{7} + 3 q^{8} + 81 q^{9} - 4 q^{10} + 41 q^{12} - q^{13} + 41 q^{14} + 28 q^{15} + 107 q^{16} + 13 q^{17} + 38 q^{18} - q^{19} + 65 q^{20} + q^{21} + 52 q^{23} + 3 q^{24} + 87 q^{25} + 37 q^{26} + 88 q^{27} - q^{28} + 19 q^{29} - 19 q^{30} + 45 q^{31} - 24 q^{32} - 23 q^{34} + 10 q^{35} + 146 q^{36} + 26 q^{37} - 4 q^{38} - 6 q^{39} + 84 q^{40} - 12 q^{41} + 28 q^{42} + 5 q^{43} + 71 q^{45} - 5 q^{46} + 63 q^{47} + 85 q^{48} + 78 q^{49} + 14 q^{50} + 22 q^{51} - 24 q^{52} + 86 q^{53} - 114 q^{54} + 119 q^{56} - 29 q^{57} + q^{58} + 119 q^{59} - 22 q^{60} + 64 q^{61} + 13 q^{62} - 28 q^{63} + 135 q^{64} - 30 q^{65} + 2 q^{67} + 59 q^{68} + 63 q^{69} - 2 q^{70} + 126 q^{71} + 48 q^{72} + 8 q^{73} - 27 q^{74} + 107 q^{75} - 82 q^{76} - 13 q^{78} - 5 q^{79} + 119 q^{80} + 96 q^{81} - 27 q^{82} + 14 q^{83} + 182 q^{84} - 52 q^{85} + 60 q^{86} - 8 q^{87} + 59 q^{89} - 45 q^{90} + 83 q^{91} + 111 q^{92} - 7 q^{93} + 21 q^{94} - 26 q^{95} - 86 q^{96} - 39 q^{97} - 57 q^{98}+O(q^{100}) \) 64 * q + 5 * q^2 + 19 * q^3 + 73 * q^4 + 21 * q^5 - q^6 + 6 * q^7 + 3 * q^8 + 81 * q^9 - 4 * q^10 + 41 * q^12 - q^13 + 41 * q^14 + 28 * q^15 + 107 * q^16 + 13 * q^17 + 38 * q^18 - q^19 + 65 * q^20 + q^21 + 52 * q^23 + 3 * q^24 + 87 * q^25 + 37 * q^26 + 88 * q^27 - q^28 + 19 * q^29 - 19 * q^30 + 45 * q^31 - 24 * q^32 - 23 * q^34 + 10 * q^35 + 146 * q^36 + 26 * q^37 - 4 * q^38 - 6 * q^39 + 84 * q^40 - 12 * q^41 + 28 * q^42 + 5 * q^43 + 71 * q^45 - 5 * q^46 + 63 * q^47 + 85 * q^48 + 78 * q^49 + 14 * q^50 + 22 * q^51 - 24 * q^52 + 86 * q^53 - 114 * q^54 + 119 * q^56 - 29 * q^57 + q^58 + 119 * q^59 - 22 * q^60 + 64 * q^61 + 13 * q^62 - 28 * q^63 + 135 * q^64 - 30 * q^65 + 2 * q^67 + 59 * q^68 + 63 * q^69 - 2 * q^70 + 126 * q^71 + 48 * q^72 + 8 * q^73 - 27 * q^74 + 107 * q^75 - 82 * q^76 - 13 * q^78 - 5 * q^79 + 119 * q^80 + 96 * q^81 - 27 * q^82 + 14 * q^83 + 182 * q^84 - 52 * q^85 + 60 * q^86 - 8 * q^87 + 59 * q^89 - 45 * q^90 + 83 * q^91 + 111 * q^92 - 7 * q^93 + 21 * q^94 - 26 * q^95 - 86 * q^96 - 39 * q^97 - 57 * 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 $

$2$	−2.36361	−1.67132	−0.835662	−	0.549245i	$-0.814916\pi$
$2$	−2.36361	−1.67132	−0.835662	+	0.549245i	$0.814916\pi$
$3$	−0.120226	−0.0694123	−0.0347061	−	0.999398i	$-0.511050\pi$
$3$	−0.120226	−0.0694123	−0.0347061	+	0.999398i	$0.511050\pi$
$4$	3.58664	1.79332
$5$	−1.13694	−0.508456	−0.254228	−	0.967144i	$-0.581821\pi$
$5$	−1.13694	−0.508456	−0.254228	+	0.967144i	$0.581821\pi$
$6$	0.284166	0.116010
$7$	2.88472	1.09032	0.545160	−	0.838332i	$-0.316469\pi$
$7$	2.88472	1.09032	0.545160	+	0.838332i	$0.316469\pi$
$8$	−3.75020	−1.32590
$9$	−2.98555	−0.995182
$10$	2.68729	0.849794
$11$	0	0
$11$	0	0
$12$	−0.431206	−0.124479
$13$	−1.50422	−0.417195	−0.208598	−	0.978002i	$-0.566890\pi$
$13$	−1.50422	−0.417195	−0.208598	+	0.978002i	$0.566890\pi$
$14$	−6.81834	−1.82228
$15$	0.136690	0.0352931
$16$	1.69073	0.422681
$17$	1.37717	0.334012	0.167006	−	0.985956i	$-0.446590\pi$
$17$	1.37717	0.334012	0.167006	+	0.985956i	$0.446590\pi$
$18$	7.05666	1.66327
$19$	−6.31432	−1.44860	−0.724302	−	0.689482i	$-0.757838\pi$
$19$	−6.31432	−1.44860	−0.724302	+	0.689482i	$0.757838\pi$
$20$	−4.07781	−0.911825
$21$	−0.346817	−0.0756817
$22$	0	0
$23$	2.25207	0.469588	0.234794	−	0.972045i	$-0.424558\pi$
$23$	2.25207	0.469588	0.234794	+	0.972045i	$0.424558\pi$
$24$	0.450871	0.0920336
$25$	−3.70736	−0.741472
$26$	3.55539	0.697268
$27$	0.719616	0.138490
$28$	10.3465	1.95530
$29$	−10.4749	−1.94515	−0.972573	−	0.232599i	$-0.925277\pi$
$29$	−10.4749	−1.94515	−0.972573	+	0.232599i	$0.925277\pi$
$30$	−0.323081	−0.0589862
$31$	−2.04513	−0.367316	−0.183658	−	0.982990i	$-0.558794\pi$
$31$	−2.04513	−0.367316	−0.183658	+	0.982990i	$0.558794\pi$
$32$	3.50420	0.619460
$33$	0	0
$34$	−3.25508	−0.558242
$35$	−3.27976	−0.554380
$36$	−10.7081	−1.78468
$37$	−2.90975	−0.478360	−0.239180	−	0.970975i	$-0.576879\pi$
$37$	−2.90975	−0.478360	−0.239180	+	0.970975i	$0.576879\pi$
$38$	14.9246	2.42109
$39$	0.180846	0.0289585
$40$	4.26377	0.674161
$41$	−8.11198	−1.26688	−0.633439	−	0.773792i	$-0.718357\pi$
$41$	−8.11198	−1.26688	−0.633439	+	0.773792i	$0.718357\pi$
$42$	0.819739	0.126489
$43$	−5.38765	−0.821610	−0.410805	−	0.911723i	$-0.634752\pi$
$43$	−5.38765	−0.821610	−0.410805	+	0.911723i	$0.634752\pi$
$44$	0	0
$45$	3.39439	0.506006
$46$	−5.32300	−0.784834
$47$	−0.377075	−0.0550021	−0.0275010	−	0.999622i	$-0.508755\pi$
$47$	−0.377075	−0.0550021	−0.0275010	+	0.999622i	$0.508755\pi$
$48$	−0.203268	−0.0293393
$49$	1.32160	0.188799
$50$	8.76275	1.23924
$51$	−0.165571	−0.0231845
$52$	−5.39510	−0.748166
$53$	10.5682	1.45165	0.725826	−	0.687878i	$-0.241458\pi$
$53$	10.5682	1.45165	0.725826	+	0.687878i	$0.241458\pi$
$54$	−1.70089	−0.231462
$55$	0	0
$56$	−10.8183	−1.44565
$57$	0.759143	0.100551
$58$	24.7586	3.25097
$59$	9.03832	1.17669	0.588344	−	0.808610i	$-0.299780\pi$
$59$	9.03832	1.17669	0.588344	+	0.808610i	$0.299780\pi$
$60$	0.490257	0.0632919
$61$	1.00000	0.128037
$61$	1.00000	0.128037
$62$	4.83389	0.613904
$63$	−8.61246	−1.08507
$64$	−11.6640	−1.45800
$65$	1.71021	0.212126
$66$	0	0
$67$	7.31363	0.893502	0.446751	−	0.894658i	$-0.352581\pi$
$67$	7.31363	0.893502	0.446751	+	0.894658i	$0.352581\pi$
$68$	4.93941	0.598991
$69$	−0.270756	−0.0325952
$70$	7.75206	0.926549
$71$	−12.1691	−1.44420	−0.722101	−	0.691788i	$-0.756823\pi$
$71$	−12.1691	−1.44420	−0.722101	+	0.691788i	$0.756823\pi$
$72$	11.1964	1.31951
$73$	−9.65360	−1.12987	−0.564934	−	0.825136i	$-0.691099\pi$
$73$	−9.65360	−1.12987	−0.564934	+	0.825136i	$0.691099\pi$
$74$	6.87751	0.799494
$75$	0.445720	0.0514673
$76$	−22.6472	−2.59781
$77$	0	0
$78$	−0.427448	−0.0483990
$79$	−3.66125	−0.411923	−0.205962	−	0.978560i	$-0.566032\pi$
$79$	−3.66125	−0.411923	−0.205962	+	0.978560i	$0.566032\pi$
$80$	−1.92226	−0.214915
$81$	8.87012	0.985569
$82$	19.1735	2.11736
$83$	−4.14249	−0.454698	−0.227349	−	0.973813i	$-0.573006\pi$
$83$	−4.14249	−0.454698	−0.227349	+	0.973813i	$0.573006\pi$
$84$	−1.24391	−0.135722
$85$	−1.56576	−0.169830
$86$	12.7343	1.37318
$87$	1.25935	0.135017
$88$	0	0
$89$	−0.402184	−0.0426314	−0.0213157	−	0.999773i	$-0.506786\pi$
$89$	−0.402184	−0.0426314	−0.0213157	+	0.999773i	$0.506786\pi$
$90$	−8.02302	−0.845700
$91$	−4.33925	−0.454877
$92$	8.07736	0.842123
$93$	0.245877	0.0254963
$94$	0.891258	0.0919262
$95$	7.17902	0.736552
$96$	−0.421294	−0.0429981
$97$	−7.99844	−0.812118	−0.406059	−	0.913847i	$-0.633097\pi$
$97$	−7.99844	−0.812118	−0.406059	+	0.913847i	$0.633097\pi$
$98$	−3.12374	−0.315545
$99$	0	0
$100$	−13.2970	−1.32970
$101$	6.12383	0.609344	0.304672	−	0.952457i	$-0.401453\pi$
$101$	6.12383	0.609344	0.304672	+	0.952457i	$0.401453\pi$
$102$	0.391344	0.0387489
$103$	10.6807	1.05240	0.526200	−	0.850361i	$-0.323616\pi$
$103$	10.6807	1.05240	0.526200	+	0.850361i	$0.323616\pi$
$104$	5.64113	0.553158
$105$	0.394311	0.0384808
$106$	−24.9790	−2.42618
$107$	−4.08289	−0.394708	−0.197354	−	0.980332i	$-0.563235\pi$
$107$	−4.08289	−0.394708	−0.197354	+	0.980332i	$0.563235\pi$
$108$	2.58101	0.248357
$109$	3.92318	0.375773	0.187886	−	0.982191i	$-0.439836\pi$
$109$	3.92318	0.375773	0.187886	+	0.982191i	$0.439836\pi$
$110$	0	0
$111$	0.349826	0.0332041
$112$	4.87727	0.460858
$113$	20.8111	1.95774	0.978870	−	0.204485i	$-0.0655518\pi$
$113$	20.8111	1.95774	0.978870	+	0.204485i	$0.0655518\pi$
$114$	−1.79432	−0.168053
$115$	−2.56047	−0.238765
$116$	−37.5698	−3.48827
$117$	4.49092	0.415185
$118$	−21.3630	−1.96663
$119$	3.97274	0.364180
$120$	−0.512614	−0.0467950
$121$	0	0
$122$	−2.36361	−0.213991
$123$	0.975268	0.0879369
$124$	−7.33516	−0.658717
$125$	9.89977	0.885462
$126$	20.3565	1.81350
$127$	11.3689	1.00883	0.504415	−	0.863461i	$-0.331708\pi$
$127$	11.3689	1.00883	0.504415	+	0.863461i	$0.331708\pi$
$128$	20.5607	1.81733
$129$	0.647734	0.0570298
$130$	−4.04227	−0.354530
$131$	18.8915	1.65056	0.825278	−	0.564726i	$-0.191018\pi$
$131$	18.8915	1.65056	0.825278	+	0.564726i	$0.191018\pi$
$132$	0	0
$133$	−18.2150	−1.57944
$134$	−17.2865	−1.49333
$135$	−0.818162	−0.0704161
$136$	−5.16466	−0.442866
$137$	1.85697	0.158652	0.0793258	−	0.996849i	$-0.474723\pi$
$137$	1.85697	0.158652	0.0793258	+	0.996849i	$0.474723\pi$
$138$	0.639961	0.0544771
$139$	−18.0519	−1.53115	−0.765573	−	0.643349i	$-0.777544\pi$
$139$	−18.0519	−1.53115	−0.765573	+	0.643349i	$0.777544\pi$
$140$	−11.7633	−0.994182
$141$	0.0453341	0.00381782
$142$	28.7629	2.41373
$143$	0	0
$144$	−5.04774	−0.420645
$145$	11.9094	0.989021
$146$	22.8173	1.88838
$147$	−0.158890	−0.0131050
$148$	−10.4362	−0.857853
$149$	6.73860	0.552048	0.276024	−	0.961151i	$-0.410983\pi$
$149$	6.73860	0.552048	0.276024	+	0.961151i	$0.410983\pi$
$150$	−1.05351	−0.0860185
$151$	−14.8805	−1.21096	−0.605478	−	0.795862i	$-0.707018\pi$
$151$	−14.8805	−1.21096	−0.605478	+	0.795862i	$0.707018\pi$
$152$	23.6800	1.92070
$153$	−4.11160	−0.332403
$154$	0	0
$155$	2.32520	0.186764
$156$	0.648629	0.0519319
$157$	7.95277	0.634700	0.317350	−	0.948308i	$-0.397207\pi$
$157$	7.95277	0.634700	0.317350	+	0.948308i	$0.397207\pi$
$158$	8.65377	0.688457
$159$	−1.27057	−0.100762
$160$	−3.98407	−0.314968
$161$	6.49657	0.512002
$162$	−20.9655	−1.64720
$163$	18.8520	1.47660	0.738300	−	0.674473i	$-0.235629\pi$
$163$	18.8520	1.47660	0.738300	+	0.674473i	$0.235629\pi$
$164$	−29.0948	−2.27192
$165$	0	0
$166$	9.79123	0.759947
$167$	17.0216	1.31717	0.658586	−	0.752506i	$-0.271155\pi$
$167$	17.0216	1.31717	0.658586	+	0.752506i	$0.271155\pi$
$168$	1.30063	0.100346
$169$	−10.7373	−0.825948
$170$	3.70084	0.283842
$171$	18.8517	1.44163
$172$	−19.3236	−1.47341
$173$	8.35272	0.635045	0.317523	−	0.948251i	$-0.397149\pi$
$173$	8.35272	0.635045	0.317523	+	0.948251i	$0.397149\pi$
$174$	−2.97662	−0.225657
$175$	−10.6947	−0.808443
$176$	0	0
$177$	−1.08664	−0.0816766
$178$	0.950605	0.0712508
$179$	−22.5230	−1.68345	−0.841723	−	0.539910i	$-0.818458\pi$
$179$	−22.5230	−1.68345	−0.841723	+	0.539910i	$0.818458\pi$
$180$	12.1745	0.907432
$181$	20.4485	1.51993	0.759963	−	0.649966i	$-0.225217\pi$
$181$	20.4485	1.51993	0.759963	+	0.649966i	$0.225217\pi$
$182$	10.2563	0.760246
$183$	−0.120226	−0.00888733
$184$	−8.44571	−0.622626
$185$	3.30822	0.243225
$186$	−0.581157	−0.0426125
$187$	0	0
$188$	−1.35243	−0.0986364
$189$	2.07589	0.150999
$190$	−16.9684	−1.23102
$191$	2.84730	0.206023	0.103012	−	0.994680i	$-0.467152\pi$
$191$	2.84730	0.206023	0.103012	+	0.994680i	$0.467152\pi$
$192$	1.40231	0.101203
$193$	−7.15735	−0.515197	−0.257599	−	0.966252i	$-0.582931\pi$
$193$	−7.15735	−0.515197	−0.257599	+	0.966252i	$0.582931\pi$
$194$	18.9052	1.35731
$195$	−0.205611	−0.0147241
$196$	4.74010	0.338578
$197$	6.94624	0.494899	0.247450	−	0.968901i	$-0.420408\pi$
$197$	6.94624	0.494899	0.247450	+	0.968901i	$0.420408\pi$
$198$	0	0
$199$	4.81077	0.341027	0.170513	−	0.985355i	$-0.445457\pi$
$199$	4.81077	0.341027	0.170513	+	0.985355i	$0.445457\pi$
$200$	13.9034	0.983116
$201$	−0.879285	−0.0620200
$202$	−14.4743	−1.01841
$203$	−30.2172	−2.12083
$204$	−0.593843	−0.0415773
$205$	9.22285	0.644152
$206$	−25.2450	−1.75890
$207$	−6.72365	−0.467326
$208$	−2.54322	−0.176341
$209$	0	0
$210$	−0.931996	−0.0643138
$211$	−6.36156	−0.437948	−0.218974	−	0.975731i	$-0.570271\pi$
$211$	−6.36156	−0.437948	−0.218974	+	0.975731i	$0.570271\pi$
$212$	37.9043	2.60328
$213$	1.46303	0.100245
$214$	9.65036	0.659685
$215$	6.12545	0.417752
$216$	−2.69871	−0.183624
$217$	−5.89963	−0.400493
$218$	−9.27287	−0.628038
$219$	1.16061	0.0784268
$220$	0	0
$221$	−2.07156	−0.139348
$222$	−0.826853	−0.0554947
$223$	26.4794	1.77319	0.886597	−	0.462543i	$-0.153063\pi$
$223$	26.4794	1.77319	0.886597	+	0.462543i	$0.153063\pi$
$224$	10.1086	0.675410
$225$	11.0685	0.737900
$226$	−49.1892	−3.27202
$227$	−18.8670	−1.25225	−0.626123	−	0.779724i	$-0.715359\pi$
$227$	−18.8670	−1.25225	−0.626123	+	0.779724i	$0.715359\pi$
$228$	2.72278	0.180320
$229$	−7.18828	−0.475015	−0.237507	−	0.971386i	$-0.576330\pi$
$229$	−7.18828	−0.475015	−0.237507	+	0.971386i	$0.576330\pi$
$230$	6.05194	0.399053
$231$	0	0
$232$	39.2831	2.57906
$233$	11.0298	0.722584	0.361292	−	0.932453i	$-0.382336\pi$
$233$	11.0298	0.722584	0.361292	+	0.932453i	$0.382336\pi$
$234$	−10.6148	−0.693909
$235$	0.428713	0.0279661
$236$	32.4172	2.11018
$237$	0.440176	0.0285925
$238$	−9.39000	−0.608663
$239$	2.56895	0.166171	0.0830857	−	0.996542i	$-0.473522\pi$
$239$	2.56895	0.166171	0.0830857	+	0.996542i	$0.473522\pi$
$240$	0.231105	0.0149177
$241$	−22.1023	−1.42373	−0.711867	−	0.702314i	$-0.752150\pi$
$241$	−22.1023	−1.42373	−0.711867	+	0.702314i	$0.752150\pi$
$242$	0	0
$243$	−3.22526	−0.206901
$244$	3.58664	0.229611
$245$	−1.50258	−0.0959962
$246$	−2.30515	−0.146971
$247$	9.49812	0.604351
$248$	7.66966	0.487024
$249$	0.498034	0.0315616
$250$	−23.3992	−1.47989
$251$	−18.2441	−1.15156	−0.575780	−	0.817605i	$-0.695301\pi$
$251$	−18.2441	−1.15156	−0.575780	+	0.817605i	$0.695301\pi$
$252$	−30.8898	−1.94588
$253$	0	0
$254$	−26.8717	−1.68608
$255$	0.188244	0.0117883
$256$	−25.2695	−1.57934
$257$	19.8237	1.23657	0.618284	−	0.785954i	$-0.287828\pi$
$257$	19.8237	1.23657	0.618284	+	0.785954i	$0.287828\pi$
$258$	−1.53099	−0.0953152
$259$	−8.39381	−0.521566
$260$	6.13392	0.380409
$261$	31.2734	1.93577
$262$	−44.6521	−2.75861
$263$	−4.35960	−0.268825	−0.134412	−	0.990925i	$-0.542915\pi$
$263$	−4.35960	−0.268825	−0.134412	+	0.990925i	$0.542915\pi$
$264$	0	0
$265$	−12.0154	−0.738101
$266$	43.0532	2.63976
$267$	0.0483528	0.00295914
$268$	26.2314	1.60234
$269$	−3.41915	−0.208469	−0.104235	−	0.994553i	$-0.533239\pi$
$269$	−3.41915	−0.208469	−0.104235	+	0.994553i	$0.533239\pi$
$270$	1.93381	0.117688
$271$	31.4226	1.90879	0.954394	−	0.298550i	$-0.0965028\pi$
$271$	31.4226	1.90879	0.954394	+	0.298550i	$0.0965028\pi$
$272$	2.32841	0.141181
$273$	0.521689	0.0315740
$274$	−4.38915	−0.265158
$275$	0	0
$276$	−0.971105	−0.0584537
$277$	−20.5651	−1.23564	−0.617819	−	0.786320i	$-0.711984\pi$
$277$	−20.5651	−1.23564	−0.617819	+	0.786320i	$0.711984\pi$
$278$	42.6677	2.55904
$279$	6.10583	0.365547
$280$	12.2998	0.735051
$281$	−1.76379	−0.105219	−0.0526094	−	0.998615i	$-0.516754\pi$
$281$	−1.76379	−0.105219	−0.0526094	+	0.998615i	$0.516754\pi$
$282$	−0.107152	−0.00638081
$283$	4.35659	0.258972	0.129486	−	0.991581i	$-0.458667\pi$
$283$	4.35659	0.258972	0.129486	+	0.991581i	$0.458667\pi$
$284$	−43.6461	−2.58992
$285$	−0.863102	−0.0511257
$286$	0	0
$287$	−23.4008	−1.38130
$288$	−10.4619	−0.616475
$289$	−15.1034	−0.888436
$290$	−28.1491	−1.65297
$291$	0.961617	0.0563710
$292$	−34.6240	−2.02622
$293$	15.5631	0.909209	0.454604	−	0.890693i	$-0.349781\pi$
$293$	15.5631	0.909209	0.454604	+	0.890693i	$0.349781\pi$
$294$	0.375553	0.0219027
$295$	−10.2760	−0.598294
$296$	10.9122	0.634256
$297$	0	0
$298$	−15.9274	−0.922650
$299$	−3.38760	−0.195910
$300$	1.59864	0.0922974
$301$	−15.5419	−0.895818
$302$	35.1716	2.02390
$303$	−0.736242	−0.0422960
$304$	−10.6758	−0.612298
$305$	−1.13694	−0.0651011
$306$	9.71820	0.555553
$307$	1.47904	0.0844130	0.0422065	−	0.999109i	$-0.486561\pi$
$307$	1.47904	0.0844130	0.0422065	+	0.999109i	$0.486561\pi$
$308$	0	0
$309$	−1.28409	−0.0730495
$310$	−5.49585	−0.312143
$311$	−5.43768	−0.308342	−0.154171	−	0.988044i	$-0.549271\pi$
$311$	−5.43768	−0.308342	−0.154171	+	0.988044i	$0.549271\pi$
$312$	−0.678208	−0.0383960
$313$	3.17243	0.179316	0.0896582	−	0.995973i	$-0.471423\pi$
$313$	3.17243	0.179316	0.0896582	+	0.995973i	$0.471423\pi$
$314$	−18.7972	−1.06079
$315$	9.79187	0.551709
$316$	−13.1316	−0.738711
$317$	−16.7550	−0.941055	−0.470527	−	0.882385i	$-0.655936\pi$
$317$	−16.7550	−0.941055	−0.470527	+	0.882385i	$0.655936\pi$
$318$	3.00312	0.168407
$319$	0	0
$320$	13.2613	0.741329
$321$	0.490868	0.0273976
$322$	−15.3554	−0.855720
$323$	−8.69588	−0.483851
$324$	31.8140	1.76744
$325$	5.57669	0.309339
$326$	−44.5586	−2.46788
$327$	−0.471667	−0.0260832
$328$	30.4216	1.67975
$329$	−1.08776	−0.0599699
$330$	0	0
$331$	16.3046	0.896180	0.448090	−	0.893988i	$-0.352104\pi$
$331$	16.3046	0.896180	0.448090	+	0.893988i	$0.352104\pi$
$332$	−14.8576	−0.815419
$333$	8.68719	0.476055
$334$	−40.2324	−2.20142
$335$	−8.31517	−0.454306
$336$	−0.586372	−0.0319892
$337$	−0.382357	−0.0208283	−0.0104141	−	0.999946i	$-0.503315\pi$
$337$	−0.382357	−0.0208283	−0.0104141	+	0.999946i	$0.503315\pi$
$338$	25.3788	1.38043
$339$	−2.50202	−0.135891
$340$	−5.61582	−0.304561
$341$	0	0
$342$	−44.5580	−2.40942
$343$	−16.3806	−0.884469
$344$	20.2048	1.08937
$345$	0.307834	0.0165732
$346$	−19.7425	−1.06137
$347$	18.6590	1.00167	0.500834	−	0.865543i	$-0.333027\pi$
$347$	18.6590	1.00167	0.500834	+	0.865543i	$0.333027\pi$
$348$	4.51686	0.242129
$349$	14.4574	0.773886	0.386943	−	0.922104i	$-0.373531\pi$
$349$	14.4574	0.773886	0.386943	+	0.922104i	$0.373531\pi$
$350$	25.2781	1.35117
$351$	−1.08246	−0.0577774
$352$	0	0
$353$	22.8056	1.21382	0.606910	−	0.794771i	$-0.292409\pi$
$353$	22.8056	1.21382	0.606910	+	0.794771i	$0.292409\pi$
$354$	2.56838	0.136508
$355$	13.8355	0.734313
$356$	−1.44249	−0.0764518
$357$	−0.477625	−0.0252786
$358$	53.2355	2.81358
$359$	−31.3522	−1.65470	−0.827352	−	0.561684i	$-0.810154\pi$
$359$	−31.3522	−1.65470	−0.827352	+	0.561684i	$0.810154\pi$
$360$	−12.7297	−0.670912
$361$	20.8707	1.09846
$362$	−48.3323	−2.54029
$363$	0	0
$364$	−15.5633	−0.815740
$365$	10.9756	0.574489
$366$	0.284166	0.0148536
$367$	−24.4837	−1.27804	−0.639019	−	0.769191i	$-0.720659\pi$
$367$	−24.4837	−1.27804	−0.639019	+	0.769191i	$0.720659\pi$
$368$	3.80763	0.198486
$369$	24.2187	1.26077
$370$	−7.81933	−0.406508
$371$	30.4862	1.58277
$372$	0.881874	0.0457230
$373$	3.15478	0.163349	0.0816743	−	0.996659i	$-0.473973\pi$
$373$	3.15478	0.163349	0.0816743	+	0.996659i	$0.473973\pi$
$374$	0	0
$375$	−1.19021	−0.0614619
$376$	1.41411	0.0729271
$377$	15.7566	0.811506
$378$	−4.90659	−0.252368
$379$	−36.7754	−1.88903	−0.944514	−	0.328472i	$-0.893466\pi$
$379$	−36.7754	−1.88903	−0.944514	+	0.328472i	$0.893466\pi$
$380$	25.7486	1.32087
$381$	−1.36684	−0.0700252
$382$	−6.72990	−0.344332
$383$	−0.161893	−0.00827234	−0.00413617	−	0.999991i	$-0.501317\pi$
$383$	−0.161893	−0.00827234	−0.00413617	+	0.999991i	$0.501317\pi$
$384$	−2.47193	−0.126145
$385$	0	0
$386$	16.9172	0.861061
$387$	16.0851	0.817651
$388$	−28.6876	−1.45639
$389$	31.4610	1.59514	0.797569	−	0.603227i	$-0.206119\pi$
$389$	31.4610	1.59514	0.797569	+	0.603227i	$0.206119\pi$
$390$	0.485984	0.0246088
$391$	3.10147	0.156848
$392$	−4.95626	−0.250329
$393$	−2.27124	−0.114569
$394$	−16.4182	−0.827137
$395$	4.16263	0.209445
$396$	0	0
$397$	−22.3332	−1.12087	−0.560435	−	0.828198i	$-0.689366\pi$
$397$	−22.3332	−1.12087	−0.560435	+	0.828198i	$0.689366\pi$
$398$	−11.3708	−0.569966
$399$	2.18991	0.109633
$400$	−6.26813	−0.313407
$401$	−23.9904	−1.19802	−0.599012	−	0.800740i	$-0.704440\pi$
$401$	−23.9904	−1.19802	−0.599012	+	0.800740i	$0.704440\pi$
$402$	2.07829	0.103655
$403$	3.07633	0.153243
$404$	21.9640	1.09275
$405$	−10.0848	−0.501119
$406$	71.4217	3.54460
$407$	0	0
$408$	0.620924	0.0307403
$409$	4.23256	0.209286	0.104643	−	0.994510i	$-0.466630\pi$
$409$	4.23256	0.209286	0.104643	+	0.994510i	$0.466630\pi$
$410$	−21.7992	−1.07659
$411$	−0.223255	−0.0110124
$412$	38.3079	1.88729
$413$	26.0730	1.28297
$414$	15.8921	0.781052
$415$	4.70978	0.231194
$416$	−5.27108	−0.258436
$417$	2.17031	0.106280
$418$	0	0
$419$	16.3571	0.799095	0.399548	−	0.916712i	$-0.369167\pi$
$419$	16.3571	0.799095	0.399548	+	0.916712i	$0.369167\pi$
$420$	1.41425	0.0690084
$421$	3.89249	0.189709	0.0948543	−	0.995491i	$-0.469761\pi$
$421$	3.89249	0.189709	0.0948543	+	0.995491i	$0.469761\pi$
$422$	15.0362	0.731952
$423$	1.12577	0.0547371
$424$	−39.6329	−1.92474
$425$	−5.10566	−0.247661
$426$	−3.45804	−0.167542
$427$	2.88472	0.139601
$428$	−14.6439	−0.707839
$429$	0	0
$430$	−14.4782	−0.698199
$431$	12.6078	0.607295	0.303648	−	0.952784i	$-0.401795\pi$
$431$	12.6078	0.607295	0.303648	+	0.952784i	$0.401795\pi$
$432$	1.21667	0.0585372
$433$	−16.7534	−0.805116	−0.402558	−	0.915394i	$-0.631879\pi$
$433$	−16.7534	−0.805116	−0.402558	+	0.915394i	$0.631879\pi$
$434$	13.9444	0.669353
$435$	−1.43181	−0.0686502
$436$	14.0711	0.673882
$437$	−14.2203	−0.680248
$438$	−2.74323	−0.131077
$439$	−33.3956	−1.59389	−0.796943	−	0.604055i	$-0.793551\pi$
$439$	−33.3956	−1.59389	−0.796943	+	0.604055i	$0.793551\pi$
$440$	0	0
$441$	−3.94569	−0.187890
$442$	4.89636	0.232896
$443$	34.1600	1.62299	0.811494	−	0.584360i	$-0.198655\pi$
$443$	34.1600	1.62299	0.811494	+	0.584360i	$0.198655\pi$
$444$	1.25470	0.0595456
$445$	0.457260	0.0216762
$446$	−62.5870	−2.96358
$447$	−0.810152	−0.0383189
$448$	−33.6473	−1.58969
$449$	34.0220	1.60560	0.802799	−	0.596250i	$-0.203343\pi$
$449$	34.0220	1.60560	0.802799	+	0.596250i	$0.203343\pi$
$450$	−26.1616	−1.23327
$451$	0	0
$452$	74.6418	3.51086
$453$	1.78901	0.0840552
$454$	44.5942	2.09291
$455$	4.93347	0.231285
$456$	−2.84694	−0.133320
$457$	11.4089	0.533687	0.266844	−	0.963740i	$-0.414019\pi$
$457$	11.4089	0.533687	0.266844	+	0.963740i	$0.414019\pi$
$458$	16.9903	0.793903
$459$	0.991031	0.0462574
$460$	−9.18349	−0.428182
$461$	−6.18781	−0.288195	−0.144098	−	0.989563i	$-0.546028\pi$
$461$	−6.18781	−0.288195	−0.144098	+	0.989563i	$0.546028\pi$
$462$	0	0
$463$	−12.3938	−0.575988	−0.287994	−	0.957632i	$-0.592988\pi$
$463$	−12.3938	−0.575988	−0.287994	+	0.957632i	$0.592988\pi$
$464$	−17.7102	−0.822177
$465$	−0.279548	−0.0129637
$466$	−26.0700	−1.20767
$467$	−34.6417	−1.60303	−0.801514	−	0.597976i	$-0.795972\pi$
$467$	−34.6417	−1.60303	−0.801514	+	0.597976i	$0.795972\pi$
$468$	16.1073	0.744561
$469$	21.0978	0.974204
$470$	−1.01331	−0.0467404
$471$	−0.956127	−0.0440560
$472$	−33.8955	−1.56017
$473$	0	0
$474$	−1.04040	−0.0477874
$475$	23.4095	1.07410
$476$	14.2488	0.653093
$477$	−31.5518	−1.44466
$478$	−6.07199	−0.277726
$479$	5.53913	0.253089	0.126545	−	0.991961i	$-0.459611\pi$
$479$	5.53913	0.253089	0.126545	+	0.991961i	$0.459611\pi$
$480$	0.478987	0.0218627
$481$	4.37690	0.199570
$482$	52.2412	2.37952
$483$	−0.781054	−0.0355392
$484$	0	0
$485$	9.09376	0.412927
$486$	7.62326	0.345798
$487$	−8.62634	−0.390897	−0.195448	−	0.980714i	$-0.562616\pi$
$487$	−8.62634	−0.390897	−0.195448	+	0.980714i	$0.562616\pi$
$488$	−3.75020	−0.169764
$489$	−2.26649	−0.102494
$490$	3.55151	0.160441
$491$	7.02639	0.317097	0.158548	−	0.987351i	$-0.449319\pi$
$491$	7.02639	0.317097	0.158548	+	0.987351i	$0.449319\pi$
$492$	3.49794	0.157699
$493$	−14.4257	−0.649702
$494$	−22.4498	−1.01007
$495$	0	0
$496$	−3.45776	−0.155258
$497$	−35.1043	−1.57464
$498$	−1.17716	−0.0527497
$499$	−2.60554	−0.116640	−0.0583200	−	0.998298i	$-0.518574\pi$
$499$	−2.60554	−0.116640	−0.0583200	+	0.998298i	$0.518574\pi$
$500$	35.5069	1.58792
$501$	−2.04643	−0.0914279
$502$	43.1220	1.92463
$503$	−7.01744	−0.312892	−0.156446	−	0.987686i	$-0.550004\pi$
$503$	−7.01744	−0.312892	−0.156446	+	0.987686i	$0.550004\pi$
$504$	32.2985	1.43869
$505$	−6.96245	−0.309825
$506$	0	0
$507$	1.29090	0.0573309
$508$	40.7763	1.80916
$509$	15.7667	0.698846	0.349423	−	0.936965i	$-0.386378\pi$
$509$	15.7667	0.698846	0.349423	+	0.936965i	$0.386378\pi$
$510$	−0.444936	−0.0197021
$511$	−27.8479	−1.23192
$512$	18.6058	0.822266
$513$	−4.54389	−0.200617
$514$	−46.8555	−2.06671
$515$	−12.1433	−0.535099
$516$	2.32319	0.102273
$517$	0	0
$518$	19.8397	0.871705
$519$	−1.00421	−0.0440799
$520$	−6.41364	−0.281257
$521$	−5.01505	−0.219713	−0.109857	−	0.993947i	$-0.535039\pi$
$521$	−5.01505	−0.219713	−0.109857	+	0.993947i	$0.535039\pi$
$522$	−73.9180	−3.23530
$523$	−9.48795	−0.414879	−0.207440	−	0.978248i	$-0.566513\pi$
$523$	−9.48795	−0.414879	−0.207440	+	0.978248i	$0.566513\pi$
$524$	67.7570	2.95998
$525$	1.28578	0.0561159
$526$	10.3044	0.449293
$527$	−2.81649	−0.122688
$528$	0	0
$529$	−17.9282	−0.779487
$530$	28.3997	1.23361
$531$	−26.9843	−1.17102
$532$	−65.3308	−2.83245
$533$	12.2022	0.528536
$534$	−0.114287	−0.00494568
$535$	4.64201	0.200692
$536$	−27.4276	−1.18469
$537$	2.70784	0.116852
$538$	8.08154	0.348420
$539$	0	0
$540$	−2.93445	−0.126279
$541$	−19.1526	−0.823435	−0.411718	−	0.911312i	$-0.635071\pi$
$541$	−19.1526	−0.823435	−0.411718	+	0.911312i	$0.635071\pi$
$542$	−74.2708	−3.19020
$543$	−2.45844	−0.105502
$544$	4.82586	0.206907
$545$	−4.46043	−0.191064
$546$	−1.23307	−0.0527704
$547$	20.8114	0.889830	0.444915	−	0.895573i	$-0.353234\pi$
$547$	20.8114	0.889830	0.444915	+	0.895573i	$0.353234\pi$
$548$	6.66029	0.284514
$549$	−2.98555	−0.127420
$550$	0	0
$551$	66.1421	2.81775
$552$	1.01539	0.0432179
$553$	−10.5617	−0.449129
$554$	48.6079	2.06515
$555$	−0.397732	−0.0168828
$556$	−64.7459	−2.74584
$557$	20.6177	0.873601	0.436801	−	0.899558i	$-0.356111\pi$
$557$	20.6177	0.873601	0.436801	+	0.899558i	$0.356111\pi$
$558$	−14.4318	−0.610947
$559$	8.10421	0.342772
$560$	−5.54517	−0.234326
$561$	0	0
$562$	4.16890	0.175855
$563$	−12.2853	−0.517765	−0.258882	−	0.965909i	$-0.583354\pi$
$563$	−12.2853	−0.517765	−0.258882	+	0.965909i	$0.583354\pi$
$564$	0.162597	0.00684658
$565$	−23.6610	−0.995425
$566$	−10.2973	−0.432826
$567$	25.5878	1.07459
$568$	45.6365	1.91486
$569$	1.10758	0.0464320	0.0232160	−	0.999730i	$-0.492609\pi$
$569$	1.10758	0.0464320	0.0232160	+	0.999730i	$0.492609\pi$
$570$	2.04003	0.0854476
$571$	−1.57105	−0.0657465	−0.0328733	−	0.999460i	$-0.510466\pi$
$571$	−1.57105	−0.0657465	−0.0328733	+	0.999460i	$0.510466\pi$
$572$	0	0
$573$	−0.342318	−0.0143006
$574$	55.3103	2.30861
$575$	−8.34922	−0.348187
$576$	34.8234	1.45097
$577$	30.0050	1.24913	0.624563	−	0.780975i	$-0.285277\pi$
$577$	30.0050	1.24913	0.624563	+	0.780975i	$0.285277\pi$
$578$	35.6985	1.48486
$579$	0.860496	0.0357610
$580$	42.7147	1.77363
$581$	−11.9499	−0.495766
$582$	−2.27289	−0.0942142
$583$	0	0
$584$	36.2030	1.49809
$585$	−5.10591	−0.211103
$586$	−36.7852	−1.51958
$587$	−28.5636	−1.17895	−0.589473	−	0.807788i	$-0.700665\pi$
$587$	−28.5636	−1.17895	−0.589473	+	0.807788i	$0.700665\pi$
$588$	−0.569881	−0.0235015
$589$	12.9136	0.532096
$590$	24.2885	0.999944
$591$	−0.835116	−0.0343521
$592$	−4.91959	−0.202194
$593$	38.0744	1.56353	0.781765	−	0.623574i	$-0.214320\pi$
$593$	38.0744	1.56353	0.781765	+	0.623574i	$0.214320\pi$
$594$	0	0
$595$	−4.51677	−0.185170
$596$	24.1690	0.989999
$597$	−0.578378	−0.0236714
$598$	8.00696	0.327429
$599$	22.0188	0.899666	0.449833	−	0.893113i	$-0.351484\pi$
$599$	22.0188	0.899666	0.449833	+	0.893113i	$0.351484\pi$
$600$	−1.67154	−0.0682403
$601$	9.35476	0.381589	0.190794	−	0.981630i	$-0.438894\pi$
$601$	9.35476	0.381589	0.190794	+	0.981630i	$0.438894\pi$
$602$	36.7349	1.49720
$603$	−21.8352	−0.889197
$604$	−53.3709	−2.17163
$605$	0	0
$606$	1.74019	0.0706903
$607$	−30.3051	−1.23005	−0.615024	−	0.788509i	$-0.710853\pi$
$607$	−30.3051	−1.23005	−0.615024	+	0.788509i	$0.710853\pi$
$608$	−22.1266	−0.897353
$609$	3.63288	0.147212
$610$	2.68729	0.108805
$611$	0.567204	0.0229466
$612$	−14.7468	−0.596105
$613$	−21.4765	−0.867428	−0.433714	−	0.901050i	$-0.642797\pi$
$613$	−21.4765	−0.867428	−0.433714	+	0.901050i	$0.642797\pi$
$614$	−3.49586	−0.141081
$615$	−1.10882	−0.0447121
$616$	0	0
$617$	27.7600	1.11757	0.558787	−	0.829311i	$-0.311267\pi$
$617$	27.7600	1.11757	0.558787	+	0.829311i	$0.311267\pi$
$618$	3.03509	0.122089
$619$	20.6758	0.831032	0.415516	−	0.909586i	$-0.363601\pi$
$619$	20.6758	0.831032	0.415516	+	0.909586i	$0.363601\pi$
$620$	8.33965	0.334928
$621$	1.62062	0.0650333
$622$	12.8525	0.515340
$623$	−1.16019	−0.0464819
$624$	0.305760	0.0122402
$625$	7.28135	0.291254
$626$	−7.49838	−0.299696
$627$	0	0
$628$	28.5238	1.13822
$629$	−4.00721	−0.159778
$630$	−23.1441	−0.922084
$631$	−16.2063	−0.645161	−0.322581	−	0.946542i	$-0.604550\pi$
$631$	−16.2063	−0.645161	−0.322581	+	0.946542i	$0.604550\pi$
$632$	13.7305	0.546168
$633$	0.764822	0.0303989
$634$	39.6023	1.57281
$635$	−12.9258	−0.512946
$636$	−4.55707	−0.180700
$637$	−1.98797	−0.0787663
$638$	0	0
$639$	36.3313	1.43724
$640$	−23.3764	−0.924032
$641$	43.2100	1.70669	0.853346	−	0.521345i	$-0.174570\pi$
$641$	43.2100	1.70669	0.853346	+	0.521345i	$0.174570\pi$
$642$	−1.16022	−0.0457902
$643$	−29.4824	−1.16267	−0.581337	−	0.813663i	$-0.697470\pi$
$643$	−29.4824	−1.16267	−0.581337	+	0.813663i	$0.697470\pi$
$644$	23.3009	0.918184
$645$	−0.736436	−0.0289971
$646$	20.5536	0.808672
$647$	−34.1710	−1.34340	−0.671700	−	0.740823i	$-0.734436\pi$
$647$	−34.1710	−1.34340	−0.671700	+	0.740823i	$0.734436\pi$
$648$	−33.2648	−1.30676
$649$	0	0
$650$	−13.1811	−0.517005
$651$	0.709286	0.0277991
$652$	67.6153	2.64802
$653$	−24.6293	−0.963819	−0.481910	−	0.876221i	$-0.660057\pi$
$653$	−24.6293	−0.963819	−0.481910	+	0.876221i	$0.660057\pi$
$654$	1.11484	0.0435935
$655$	−21.4785	−0.839235
$656$	−13.7151	−0.535486
$657$	28.8213	1.12443
$658$	2.57103	0.100229
$659$	16.5452	0.644510	0.322255	−	0.946653i	$-0.395559\pi$
$659$	16.5452	0.644510	0.322255	+	0.946653i	$0.395559\pi$
$660$	0	0
$661$	10.8911	0.423613	0.211807	−	0.977312i	$-0.432065\pi$
$661$	10.8911	0.423613	0.211807	+	0.977312i	$0.432065\pi$
$662$	−38.5376	−1.49781
$663$	0.249055	0.00967248
$664$	15.5352	0.602883
$665$	20.7094	0.803078
$666$	−20.5331	−0.795642
$667$	−23.5902	−0.913417
$668$	61.0504	2.36211
$669$	−3.18350	−0.123081
$670$	19.6538	0.759293
$671$	0	0
$672$	−1.21531	−0.0468818
$673$	9.83124	0.378966	0.189483	−	0.981884i	$-0.439319\pi$
$673$	9.83124	0.378966	0.189483	+	0.981884i	$0.439319\pi$
$674$	0.903741	0.0348108
$675$	−2.66788	−0.102687
$676$	−38.5110	−1.48119
$677$	−21.7331	−0.835270	−0.417635	−	0.908615i	$-0.637141\pi$
$677$	−21.7331	−0.835270	−0.417635	+	0.908615i	$0.637141\pi$
$678$	5.91380	0.227118
$679$	−23.0732	−0.885470
$680$	5.87192	0.225178
$681$	2.26830	0.0869213
$682$	0	0
$683$	28.2964	1.08273	0.541366	−	0.840787i	$-0.317907\pi$
$683$	28.2964	1.08273	0.541366	+	0.840787i	$0.317907\pi$
$684$	67.6143	2.58530
$685$	−2.11127	−0.0806674
$686$	38.7173	1.47823
$687$	0.864215	0.0329718
$688$	−9.10905	−0.347279
$689$	−15.8969	−0.605622
$690$	−0.727599	−0.0276992
$691$	33.9679	1.29220	0.646100	−	0.763253i	$-0.276399\pi$
$691$	33.9679	1.29220	0.646100	+	0.763253i	$0.276399\pi$
$692$	29.9582	1.13884
$693$	0	0
$694$	−44.1026	−1.67411
$695$	20.5240	0.778521
$696$	−4.72284	−0.179019
$697$	−11.1716	−0.423153
$698$	−34.1716	−1.29341
$699$	−1.32606	−0.0501562
$700$	−38.3581	−1.44980
$701$	−0.411663	−0.0155483	−0.00777415	−	0.999970i	$-0.502475\pi$
$701$	−0.411663	−0.0155483	−0.00777415	+	0.999970i	$0.502475\pi$
$702$	2.55851	0.0965648
$703$	18.3731	0.692955
$704$	0	0
$705$	−0.0515422	−0.00194119
$706$	−53.9035	−2.02869
$707$	17.6655	0.664381
$708$	−3.89738	−0.146473
$709$	32.0138	1.20230	0.601152	−	0.799134i	$-0.294708\pi$
$709$	32.0138	1.20230	0.601152	+	0.799134i	$0.294708\pi$
$710$	−32.7018	−1.22727
$711$	10.9308	0.409939
$712$	1.50827	0.0565248
$713$	−4.60577	−0.172487
$714$	1.12892	0.0422487
$715$	0	0
$716$	−80.7818	−3.01896
$717$	−0.308853	−0.0115343
$718$	74.1042	2.76555
$719$	35.7385	1.33282	0.666410	−	0.745586i	$-0.267830\pi$
$719$	35.7385	1.33282	0.666410	+	0.745586i	$0.267830\pi$
$720$	5.73899	0.213879
$721$	30.8108	1.14745
$722$	−49.3301	−1.83587
$723$	2.65726	0.0988247
$724$	73.3416	2.72572
$725$	38.8344	1.44227
$726$	0	0
$727$	−22.1826	−0.822709	−0.411354	−	0.911476i	$-0.634944\pi$
$727$	−22.1826	−0.822709	−0.411354	+	0.911476i	$0.634944\pi$
$728$	16.2731	0.603120
$729$	−26.2226	−0.971208
$730$	−25.9420	−0.960156
$731$	−7.41970	−0.274428
$732$	−0.431206	−0.0159378
$733$	47.0583	1.73814	0.869069	−	0.494691i	$-0.164719\pi$
$733$	47.0583	1.73814	0.869069	+	0.494691i	$0.164719\pi$
$734$	57.8698	2.13601
$735$	0.180648	0.00666332
$736$	7.89168	0.290891
$737$	0	0
$738$	−57.2435	−2.10716
$739$	−1.49506	−0.0549968	−0.0274984	−	0.999622i	$-0.508754\pi$
$739$	−1.49506	−0.0549968	−0.0274984	+	0.999622i	$0.508754\pi$
$740$	11.8654	0.436181
$741$	−1.14192	−0.0419494
$742$	−72.0575	−2.64531
$743$	9.91209	0.363639	0.181820	−	0.983332i	$-0.441801\pi$
$743$	9.91209	0.363639	0.181820	+	0.983332i	$0.441801\pi$
$744$	−0.922089	−0.0338054
$745$	−7.66140	−0.280692
$746$	−7.45667	−0.273008
$747$	12.3676	0.452507
$748$	0	0
$749$	−11.7780	−0.430358
$750$	2.81318	0.102723
$751$	20.4963	0.747920	0.373960	−	0.927445i	$-0.378000\pi$
$751$	20.4963	0.747920	0.373960	+	0.927445i	$0.378000\pi$
$752$	−0.637531	−0.0232483
$753$	2.19341	0.0799324
$754$	−37.2424	−1.35629
$755$	16.9182	0.615718
$756$	7.44547	0.270789
$757$	16.0638	0.583850	0.291925	−	0.956441i	$-0.405704\pi$
$757$	16.0638	0.583850	0.291925	+	0.956441i	$0.405704\pi$
$758$	86.9227	3.15718
$759$	0	0
$760$	−26.9228	−0.976592
$761$	−42.3539	−1.53533	−0.767664	−	0.640852i	$-0.778581\pi$
$761$	−42.3539	−1.53533	−0.767664	+	0.640852i	$0.778581\pi$
$762$	3.23067	0.117035
$763$	11.3173	0.409713
$764$	10.2122	0.369466
$765$	4.67465	0.169012
$766$	0.382652	0.0138258
$767$	−13.5956	−0.490909
$768$	3.03804	0.109626
$769$	42.3396	1.52681	0.763403	−	0.645923i	$-0.223527\pi$
$769$	42.3396	1.52681	0.763403	+	0.645923i	$0.223527\pi$
$770$	0	0
$771$	−2.38332	−0.0858331
$772$	−25.6709	−0.923914
$773$	25.2408	0.907848	0.453924	−	0.891040i	$-0.350024\pi$
$773$	25.2408	0.907848	0.453924	+	0.891040i	$0.350024\pi$
$774$	−38.0188	−1.36656
$775$	7.58204	0.272355
$776$	29.9958	1.07679
$777$	1.00915	0.0362031
$778$	−74.3616	−2.66599
$779$	51.2217	1.83521
$780$	−0.737454	−0.0264051
$781$	0	0
$782$	−7.33066	−0.262144
$783$	−7.53792	−0.269383
$784$	2.23446	0.0798020
$785$	−9.04184	−0.322717
$786$	5.36832	0.191482
$787$	−23.3437	−0.832113	−0.416057	−	0.909339i	$-0.636588\pi$
$787$	−23.3437	−0.832113	−0.416057	+	0.909339i	$0.636588\pi$
$788$	24.9137	0.887514
$789$	0.524136	0.0186597
$790$	−9.83884	−0.350050
$791$	60.0340	2.13456
$792$	0	0
$793$	−1.50422	−0.0534164
$794$	52.7869	1.87334
$795$	1.44456	0.0512333
$796$	17.2545	0.611570
$797$	−51.1893	−1.81322	−0.906608	−	0.421973i	$-0.861338\pi$
$797$	−51.1893	−1.81322	−0.906608	+	0.421973i	$0.861338\pi$
$798$	−5.17610	−0.183232
$799$	−0.519295	−0.0183714
$800$	−12.9913	−0.459313
$801$	1.20074	0.0424260
$802$	56.7040	2.00229
$803$	0	0
$804$	−3.15368	−0.111222
$805$	−7.38623	−0.260330
$806$	−7.27123	−0.256118
$807$	0.411070	0.0144703
$808$	−22.9656	−0.807928
$809$	−36.4413	−1.28121	−0.640604	−	0.767872i	$-0.721316\pi$
$809$	−36.4413	−1.28121	−0.640604	+	0.767872i	$0.721316\pi$
$810$	23.8366	0.837531
$811$	47.4628	1.66664	0.833322	−	0.552787i	$-0.186436\pi$
$811$	47.4628	1.66664	0.833322	+	0.552787i	$0.186436\pi$
$812$	−108.378	−3.80334
$813$	−3.77780	−0.132493
$814$	0	0
$815$	−21.4336	−0.750786
$816$	−0.279935	−0.00979967
$817$	34.0194	1.19019
$818$	−10.0041	−0.349785
$819$	12.9550	0.452685
$820$	33.0791	1.15517
$821$	13.5568	0.473134	0.236567	−	0.971615i	$-0.423978\pi$
$821$	13.5568	0.473134	0.236567	+	0.971615i	$0.423978\pi$
$822$	0.527688	0.0184052
$823$	24.1145	0.840577	0.420288	−	0.907391i	$-0.361929\pi$
$823$	24.1145	0.840577	0.420288	+	0.907391i	$0.361929\pi$
$824$	−40.0548	−1.39538
$825$	0	0
$826$	−61.6263	−2.14425
$827$	7.94249	0.276188	0.138094	−	0.990419i	$-0.455902\pi$
$827$	7.94249	0.276188	0.138094	+	0.990419i	$0.455902\pi$
$828$	−24.1153	−0.838065
$829$	37.2409	1.29343	0.646714	−	0.762732i	$-0.276143\pi$
$829$	37.2409	1.29343	0.646714	+	0.762732i	$0.276143\pi$
$830$	−11.1321	−0.386400
$831$	2.47246	0.0857685
$832$	17.5452	0.608271
$833$	1.82006	0.0630613
$834$	−5.12975	−0.177629
$835$	−19.3526	−0.669724
$836$	0	0
$837$	−1.47171	−0.0508697
$838$	−38.6617	−1.33555
$839$	13.3386	0.460498	0.230249	−	0.973132i	$-0.426046\pi$
$839$	13.3386	0.460498	0.230249	+	0.973132i	$0.426046\pi$
$840$	−1.47875	−0.0510216
$841$	80.7242	2.78359
$842$	−9.20033	−0.317064
$843$	0.212052	0.00730347
$844$	−22.8166	−0.785381
$845$	12.2077	0.419958
$846$	−2.66089	−0.0914833
$847$	0	0
$848$	17.8679	0.613586
$849$	−0.523773	−0.0179758
$850$	12.0678	0.413921
$851$	−6.55295	−0.224632
$852$	5.24738	0.179772
$853$	47.6259	1.63068	0.815339	−	0.578983i	$-0.196550\pi$
$853$	47.6259	1.63068	0.815339	+	0.578983i	$0.196550\pi$
$854$	−6.81834	−0.233319
$855$	−21.4333	−0.733003
$856$	15.3117	0.523342
$857$	8.14780	0.278323	0.139162	−	0.990270i	$-0.455559\pi$
$857$	8.14780	0.278323	0.139162	+	0.990270i	$0.455559\pi$
$858$	0	0
$859$	−6.32615	−0.215845	−0.107923	−	0.994159i	$-0.534420\pi$
$859$	−6.32615	−0.215845	−0.107923	+	0.994159i	$0.534420\pi$
$860$	21.9698	0.749164
$861$	2.81337	0.0958795
$862$	−29.7999	−1.01499
$863$	35.2046	1.19838	0.599188	−	0.800608i	$-0.295490\pi$
$863$	35.2046	1.19838	0.599188	+	0.800608i	$0.295490\pi$
$864$	2.52167	0.0857891
$865$	−9.49656	−0.322893
$866$	39.5984	1.34561
$867$	1.81582	0.0616684
$868$	−21.1599	−0.718212
$869$	0	0
$870$	3.38425	0.114737
$871$	−11.0013	−0.372765
$872$	−14.7127	−0.498236
$873$	23.8797	0.808206
$874$	33.6111	1.13691
$875$	28.5580	0.965438
$876$	4.16270	0.140644
$877$	34.7134	1.17219	0.586094	−	0.810243i	$-0.300665\pi$
$877$	34.7134	1.17219	0.586094	+	0.810243i	$0.300665\pi$
$878$	78.9342	2.66390
$879$	−1.87109	−0.0631102
$880$	0	0
$881$	0.166248	0.00560104	0.00280052	−	0.999996i	$-0.499109\pi$
$881$	0.166248	0.00560104	0.00280052	+	0.999996i	$0.499109\pi$
$882$	9.32606	0.314025
$883$	17.9993	0.605723	0.302862	−	0.953035i	$-0.402058\pi$
$883$	17.9993	0.605723	0.302862	+	0.953035i	$0.402058\pi$
$884$	−7.42995	−0.249896
$885$	1.23544	0.0415290
$886$	−80.7408	−2.71254
$887$	13.2907	0.446259	0.223129	−	0.974789i	$-0.428373\pi$
$887$	13.2907	0.446259	0.223129	+	0.974789i	$0.428373\pi$
$888$	−1.31192	−0.0440252
$889$	32.7962	1.09995
$890$	−1.08078	−0.0362279
$891$	0	0
$892$	94.9723	3.17991
$893$	2.38097	0.0796762
$894$	1.91488	0.0640432
$895$	25.6073	0.855958
$896$	59.3119	1.98147
$897$	0.407276	0.0135986
$898$	−80.4147	−2.68347
$899$	21.4226	0.714484
$900$	39.6988	1.32329
$901$	14.5542	0.484869
$902$	0	0
$903$	1.86853	0.0621808
$904$	−78.0457	−2.59576
$905$	−23.2488	−0.772816
$906$	−4.22853	−0.140483
$907$	−0.0878874	−0.00291825	−0.00145913	−	0.999999i	$-0.500464\pi$
$907$	−0.0878874	−0.00291825	−0.00145913	+	0.999999i	$0.500464\pi$
$908$	−67.6692	−2.24568
$909$	−18.2830	−0.606408
$910$	−11.6608	−0.386552
$911$	17.2959	0.573039	0.286520	−	0.958074i	$-0.407502\pi$
$911$	17.2959	0.573039	0.286520	+	0.958074i	$0.407502\pi$
$912$	1.28350	0.0425010
$913$	0	0
$914$	−26.9662	−0.891964
$915$	0.136690	0.00451882
$916$	−25.7818	−0.851854
$917$	54.4966	1.79964
$918$	−2.34241	−0.0773110
$919$	38.5199	1.27066	0.635328	−	0.772243i	$-0.280865\pi$
$919$	38.5199	1.27066	0.635328	+	0.772243i	$0.280865\pi$
$920$	9.60228	0.316578
$921$	−0.177818	−0.00585930
$922$	14.6256	0.481667
$923$	18.3049	0.602514
$924$	0	0
$925$	10.7875	0.354691
$926$	29.2941	0.962663
$927$	−31.8877	−1.04733
$928$	−36.7062	−1.20494
$929$	−14.1971	−0.465793	−0.232896	−	0.972502i	$-0.574820\pi$
$929$	−14.1971	−0.465793	−0.232896	+	0.972502i	$0.574820\pi$
$930$	0.660742	0.0216666
$931$	−8.34498	−0.273496
$932$	39.5598	1.29583
$933$	0.653748	0.0214027
$934$	81.8794	2.67918
$935$	0	0
$936$	−16.8418	−0.550493
$937$	−21.3979	−0.699038	−0.349519	−	0.936929i	$-0.613655\pi$
$937$	−21.3979	−0.699038	−0.349519	+	0.936929i	$0.613655\pi$
$938$	−49.8668	−1.62821
$939$	−0.381407	−0.0124468
$940$	1.53764	0.0501523
$941$	17.8643	0.582360	0.291180	−	0.956668i	$-0.405952\pi$
$941$	17.8643	0.582360	0.291180	+	0.956668i	$0.405952\pi$
$942$	2.25991	0.0736318
$943$	−18.2687	−0.594911
$944$	15.2813	0.497364
$945$	−2.36017	−0.0767762
$946$	0	0
$947$	31.9161	1.03714	0.518568	−	0.855037i	$-0.326465\pi$
$947$	31.9161	1.03714	0.518568	+	0.855037i	$0.326465\pi$
$948$	1.57876	0.0512756
$949$	14.5211	0.471376
$950$	−55.3308	−1.79517
$951$	2.01438	0.0653208
$952$	−14.8986	−0.482866
$953$	−51.2402	−1.65983	−0.829916	−	0.557888i	$-0.811612\pi$
$953$	−51.2402	−1.65983	−0.829916	+	0.557888i	$0.811612\pi$
$954$	74.5761	2.41449
$955$	−3.23722	−0.104754
$956$	9.21390	0.297999
$957$	0	0
$958$	−13.0923	−0.422994
$959$	5.35684	0.172981
$960$	−1.59435	−0.0514573
$961$	−26.8174	−0.865079
$962$	−10.3453	−0.333545
$963$	12.1897	0.392806
$964$	−79.2731	−2.55321
$965$	8.13749	0.261955
$966$	1.84611	0.0593975
$967$	16.0380	0.515748	0.257874	−	0.966179i	$-0.416978\pi$
$967$	16.0380	0.515748	0.257874	+	0.966179i	$0.416978\pi$
$968$	0	0
$969$	1.04547	0.0335852
$970$	−21.4941	−0.690134
$971$	33.9023	1.08798	0.543989	−	0.839092i	$-0.316913\pi$
$971$	33.9023	1.08798	0.543989	+	0.839092i	$0.316913\pi$
$972$	−11.5679	−0.371040
$973$	−52.0748	−1.66944
$974$	20.3893	0.653315
$975$	−0.670460	−0.0214719
$976$	1.69073	0.0541188
$977$	−33.6941	−1.07797	−0.538984	−	0.842316i	$-0.681192\pi$
$977$	−33.6941	−1.07797	−0.538984	+	0.842316i	$0.681192\pi$
$978$	5.35709	0.171301
$979$	0	0
$980$	−5.38921	−0.172152
$981$	−11.7128	−0.373962
$982$	−16.6076	−0.529971
$983$	6.48211	0.206747	0.103374	−	0.994643i	$-0.467036\pi$
$983$	6.48211	0.206747	0.103374	+	0.994643i	$0.467036\pi$
$984$	−3.65745	−0.116595
$985$	−7.89748	−0.251635
$986$	34.0968	1.08586
$987$	0.130776	0.00416265
$988$	34.0664	1.08380
$989$	−12.1334	−0.385818
$990$	0	0
$991$	54.9073	1.74419	0.872095	−	0.489337i	$-0.162761\pi$
$991$	54.9073	1.74419	0.872095	+	0.489337i	$0.162761\pi$
$992$	−7.16654	−0.227538
$993$	−1.96023	−0.0622059
$994$	82.9728	2.63174
$995$	−5.46957	−0.173397
$996$	1.78627	0.0566001
$997$	51.8137	1.64096	0.820478	−	0.571677i	$-0.193707\pi$
$997$	51.8137	1.64096	0.820478	+	0.571677i	$0.193707\pi$
$998$	6.15847	0.194943
$999$	−2.09390	−0.0662481

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7381.2.a.v.1.7		64
11.3	even	5		671.2.j.c.306.3	✓	128
11.4	even	5		671.2.j.c.489.3	yes	128
11.10	odd	2		7381.2.a.u.1.58		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
671.2.j.c.306.3	✓	128	11.3	even	5
671.2.j.c.489.3	yes	128	11.4	even	5
7381.2.a.u.1.58		64	11.10	odd	2
7381.2.a.v.1.7		64	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)

\(f(q)\)	\(=\)	\(q-2.36361 q^{2} -0.120226 q^{3} +3.58664 q^{4} -1.13694 q^{5} +0.284166 q^{6} +2.88472 q^{7} -3.75020 q^{8} -2.98555 q^{9} +O(q^{10})\)	\(q-2.36361 q^{2} -0.120226 q^{3} +3.58664 q^{4} -1.13694 q^{5} +0.284166 q^{6} +2.88472 q^{7} -3.75020 q^{8} -2.98555 q^{9} +2.68729 q^{10} -0.431206 q^{12} -1.50422 q^{13} -6.81834 q^{14} +0.136690 q^{15} +1.69073 q^{16} +1.37717 q^{17} +7.05666 q^{18} -6.31432 q^{19} -4.07781 q^{20} -0.346817 q^{21} +2.25207 q^{23} +0.450871 q^{24} -3.70736 q^{25} +3.55539 q^{26} +0.719616 q^{27} +10.3465 q^{28} -10.4749 q^{29} -0.323081 q^{30} -2.04513 q^{31} +3.50420 q^{32} -3.25508 q^{34} -3.27976 q^{35} -10.7081 q^{36} -2.90975 q^{37} +14.9246 q^{38} +0.180846 q^{39} +4.26377 q^{40} -8.11198 q^{41} +0.819739 q^{42} -5.38765 q^{43} +3.39439 q^{45} -5.32300 q^{46} -0.377075 q^{47} -0.203268 q^{48} +1.32160 q^{49} +8.76275 q^{50} -0.165571 q^{51} -5.39510 q^{52} +10.5682 q^{53} -1.70089 q^{54} -10.8183 q^{56} +0.759143 q^{57} +24.7586 q^{58} +9.03832 q^{59} +0.490257 q^{60} +1.00000 q^{61} +4.83389 q^{62} -8.61246 q^{63} -11.6640 q^{64} +1.71021 q^{65} +7.31363 q^{67} +4.93941 q^{68} -0.270756 q^{69} +7.75206 q^{70} -12.1691 q^{71} +11.1964 q^{72} -9.65360 q^{73} +6.87751 q^{74} +0.445720 q^{75} -22.6472 q^{76} -0.427448 q^{78} -3.66125 q^{79} -1.92226 q^{80} +8.87012 q^{81} +19.1735 q^{82} -4.14249 q^{83} -1.24391 q^{84} -1.56576 q^{85} +12.7343 q^{86} +1.25935 q^{87} -0.402184 q^{89} -8.02302 q^{90} -4.33925 q^{91} +8.07736 q^{92} +0.245877 q^{93} +0.891258 q^{94} +7.17902 q^{95} -0.421294 q^{96} -7.99844 q^{97} -3.12374 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 5 q^{2} + 19 q^{3} + 73 q^{4} + 21 q^{5} - q^{6} + 6 q^{7} + 3 q^{8} + 81 q^{9}+O(q^{10}) \) 64 * q + 5 * q^2 + 19 * q^3 + 73 * q^4 + 21 * q^5 - q^6 + 6 * q^7 + 3 * q^8 + 81 * q^9	\( 64 q + 5 q^{2} + 19 q^{3} + 73 q^{4} + 21 q^{5} - q^{6} + 6 q^{7} + 3 q^{8} + 81 q^{9} - 4 q^{10} + 41 q^{12} - q^{13} + 41 q^{14} + 28 q^{15} + 107 q^{16} + 13 q^{17} + 38 q^{18} - q^{19} + 65 q^{20} + q^{21} + 52 q^{23} + 3 q^{24} + 87 q^{25} + 37 q^{26} + 88 q^{27} - q^{28} + 19 q^{29} - 19 q^{30} + 45 q^{31} - 24 q^{32} - 23 q^{34} + 10 q^{35} + 146 q^{36} + 26 q^{37} - 4 q^{38} - 6 q^{39} + 84 q^{40} - 12 q^{41} + 28 q^{42} + 5 q^{43} + 71 q^{45} - 5 q^{46} + 63 q^{47} + 85 q^{48} + 78 q^{49} + 14 q^{50} + 22 q^{51} - 24 q^{52} + 86 q^{53} - 114 q^{54} + 119 q^{56} - 29 q^{57} + q^{58} + 119 q^{59} - 22 q^{60} + 64 q^{61} + 13 q^{62} - 28 q^{63} + 135 q^{64} - 30 q^{65} + 2 q^{67} + 59 q^{68} + 63 q^{69} - 2 q^{70} + 126 q^{71} + 48 q^{72} + 8 q^{73} - 27 q^{74} + 107 q^{75} - 82 q^{76} - 13 q^{78} - 5 q^{79} + 119 q^{80} + 96 q^{81} - 27 q^{82} + 14 q^{83} + 182 q^{84} - 52 q^{85} + 60 q^{86} - 8 q^{87} + 59 q^{89} - 45 q^{90} + 83 q^{91} + 111 q^{92} - 7 q^{93} + 21 q^{94} - 26 q^{95} - 86 q^{96} - 39 q^{97} - 57 q^{98}+O(q^{100}) \) 64 * q + 5 * q^2 + 19 * q^3 + 73 * q^4 + 21 * q^5 - q^6 + 6 * q^7 + 3 * q^8 + 81 * q^9 - 4 * q^10 + 41 * q^12 - q^13 + 41 * q^14 + 28 * q^15 + 107 * q^16 + 13 * q^17 + 38 * q^18 - q^19 + 65 * q^20 + q^21 + 52 * q^23 + 3 * q^24 + 87 * q^25 + 37 * q^26 + 88 * q^27 - q^28 + 19 * q^29 - 19 * q^30 + 45 * q^31 - 24 * q^32 - 23 * q^34 + 10 * q^35 + 146 * q^36 + 26 * q^37 - 4 * q^38 - 6 * q^39 + 84 * q^40 - 12 * q^41 + 28 * q^42 + 5 * q^43 + 71 * q^45 - 5 * q^46 + 63 * q^47 + 85 * q^48 + 78 * q^49 + 14 * q^50 + 22 * q^51 - 24 * q^52 + 86 * q^53 - 114 * q^54 + 119 * q^56 - 29 * q^57 + q^58 + 119 * q^59 - 22 * q^60 + 64 * q^61 + 13 * q^62 - 28 * q^63 + 135 * q^64 - 30 * q^65 + 2 * q^67 + 59 * q^68 + 63 * q^69 - 2 * q^70 + 126 * q^71 + 48 * q^72 + 8 * q^73 - 27 * q^74 + 107 * q^75 - 82 * q^76 - 13 * q^78 - 5 * q^79 + 119 * q^80 + 96 * q^81 - 27 * q^82 + 14 * q^83 + 182 * q^84 - 52 * q^85 + 60 * q^86 - 8 * q^87 + 59 * q^89 - 45 * q^90 + 83 * q^91 + 111 * q^92 - 7 * q^93 + 21 * q^94 - 26 * q^95 - 86 * q^96 - 39 * q^97 - 57 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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