LMFDB - Embedded newform 435.2.a.f.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [435,2,Mod(1,435)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(435, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("435.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 435 = 3 \cdot 5 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	435.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:	$3.47349248793$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{21}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 5 $ x^2 - x - 5
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-1.79129$ of defining polynomial
Character	$\chi$	$=$	435.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.79129 q^{2} +1.00000 q^{3} +1.20871 q^{4} +1.00000 q^{5} +1.79129 q^{6} +1.00000 q^{7} -1.41742 q^{8} +1.00000 q^{9} +1.79129 q^{10} +5.00000 q^{11} +1.20871 q^{12} -4.58258 q^{13} +1.79129 q^{14} +1.00000 q^{15} -4.95644 q^{16} -3.00000 q^{17} +1.79129 q^{18} +3.58258 q^{19} +1.20871 q^{20} +1.00000 q^{21} +8.95644 q^{22} -4.00000 q^{23} -1.41742 q^{24} +1.00000 q^{25} -8.20871 q^{26} +1.00000 q^{27} +1.20871 q^{28} +1.00000 q^{29} +1.79129 q^{30} +4.00000 q^{31} -6.04356 q^{32} +5.00000 q^{33} -5.37386 q^{34} +1.00000 q^{35} +1.20871 q^{36} -4.00000 q^{37} +6.41742 q^{38} -4.58258 q^{39} -1.41742 q^{40} -9.16515 q^{41} +1.79129 q^{42} -9.58258 q^{43} +6.04356 q^{44} +1.00000 q^{45} -7.16515 q^{46} +10.5826 q^{47} -4.95644 q^{48} -6.00000 q^{49} +1.79129 q^{50} -3.00000 q^{51} -5.53901 q^{52} +0.417424 q^{53} +1.79129 q^{54} +5.00000 q^{55} -1.41742 q^{56} +3.58258 q^{57} +1.79129 q^{58} -7.58258 q^{59} +1.20871 q^{60} +12.7477 q^{61} +7.16515 q^{62} +1.00000 q^{63} -0.912878 q^{64} -4.58258 q^{65} +8.95644 q^{66} -4.16515 q^{67} -3.62614 q^{68} -4.00000 q^{69} +1.79129 q^{70} -9.58258 q^{71} -1.41742 q^{72} +4.00000 q^{73} -7.16515 q^{74} +1.00000 q^{75} +4.33030 q^{76} +5.00000 q^{77} -8.20871 q^{78} +7.58258 q^{79} -4.95644 q^{80} +1.00000 q^{81} -16.4174 q^{82} -11.5826 q^{83} +1.20871 q^{84} -3.00000 q^{85} -17.1652 q^{86} +1.00000 q^{87} -7.08712 q^{88} +1.41742 q^{89} +1.79129 q^{90} -4.58258 q^{91} -4.83485 q^{92} +4.00000 q^{93} +18.9564 q^{94} +3.58258 q^{95} -6.04356 q^{96} +11.5826 q^{97} -10.7477 q^{98} +5.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} + 2 q^{3} + 7 q^{4} + 2 q^{5} - q^{6} + 2 q^{7} - 12 q^{8} + 2 q^{9} - q^{10} + 10 q^{11} + 7 q^{12} - q^{14} + 2 q^{15} + 13 q^{16} - 6 q^{17} - q^{18} - 2 q^{19} + 7 q^{20} + 2 q^{21}+ \cdots + 10 q^{99}+O(q^{100}) $ 2 * q - q^2 + 2 * q^3 + 7 * q^4 + 2 * q^5 - q^6 + 2 * q^7 - 12 * q^8 + 2 * q^9 - q^10 + 10 * q^11 + 7 * q^12 - q^14 + 2 * q^15 + 13 * q^16 - 6 * q^17 - q^18 - 2 * q^19 + 7 * q^20 + 2 * q^21 - 5 * q^22 - 8 * q^23 - 12 * q^24 + 2 * q^25 - 21 * q^26 + 2 * q^27 + 7 * q^28 + 2 * q^29 - q^30 + 8 * q^31 - 35 * q^32 + 10 * q^33 + 3 * q^34 + 2 * q^35 + 7 * q^36 - 8 * q^37 + 22 * q^38 - 12 * q^40 - q^42 - 10 * q^43 + 35 * q^44 + 2 * q^45 + 4 * q^46 + 12 * q^47 + 13 * q^48 - 12 * q^49 - q^50 - 6 * q^51 + 21 * q^52 + 10 * q^53 - q^54 + 10 * q^55 - 12 * q^56 - 2 * q^57 - q^58 - 6 * q^59 + 7 * q^60 - 2 * q^61 - 4 * q^62 + 2 * q^63 + 44 * q^64 - 5 * q^66 + 10 * q^67 - 21 * q^68 - 8 * q^69 - q^70 - 10 * q^71 - 12 * q^72 + 8 * q^73 + 4 * q^74 + 2 * q^75 - 28 * q^76 + 10 * q^77 - 21 * q^78 + 6 * q^79 + 13 * q^80 + 2 * q^81 - 42 * q^82 - 14 * q^83 + 7 * q^84 - 6 * q^85 - 16 * q^86 + 2 * q^87 - 60 * q^88 + 12 * q^89 - q^90 - 28 * q^92 + 8 * q^93 + 15 * q^94 - 2 * q^95 - 35 * q^96 + 14 * q^97 + 6 * q^98 + 10 * q^99

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.79129	1.26663	0.633316	−	0.773893i	$-0.281693\pi$
$2$	1.79129	1.26663	0.633316	+	0.773893i	$0.281693\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.20871	0.604356
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	1.79129	0.731290
$7$	1.00000	0.377964	0.188982	−	0.981981i	$-0.439481\pi$
$7$	1.00000	0.377964	0.188982	+	0.981981i	$0.439481\pi$
$8$	−1.41742	−0.501135
$9$	1.00000	0.333333
$10$	1.79129	0.566455
$11$	5.00000	1.50756	0.753778	−	0.657129i	$-0.228229\pi$
$11$	5.00000	1.50756	0.753778	+	0.657129i	$0.228229\pi$
$12$	1.20871	0.348925
$13$	−4.58258	−1.27098	−0.635489	−	0.772110i	$-0.719201\pi$
$13$	−4.58258	−1.27098	−0.635489	+	0.772110i	$0.719201\pi$
$14$	1.79129	0.478742
$15$	1.00000	0.258199
$16$	−4.95644	−1.23911
$17$	−3.00000	−0.727607	−0.363803	−	0.931476i	$-0.618522\pi$
$17$	−3.00000	−0.727607	−0.363803	+	0.931476i	$0.618522\pi$
$18$	1.79129	0.422211
$19$	3.58258	0.821899	0.410950	−	0.911658i	$-0.365197\pi$
$19$	3.58258	0.821899	0.410950	+	0.911658i	$0.365197\pi$
$20$	1.20871	0.270276
$21$	1.00000	0.218218
$22$	8.95644	1.90952
$23$	−4.00000	−0.834058	−0.417029	−	0.908893i	$-0.636929\pi$
$23$	−4.00000	−0.834058	−0.417029	+	0.908893i	$0.636929\pi$
$24$	−1.41742	−0.289331
$25$	1.00000	0.200000
$26$	−8.20871	−1.60986
$27$	1.00000	0.192450
$28$	1.20871	0.228425
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	1.79129	0.327043
$31$	4.00000	0.718421	0.359211	−	0.933257i	$-0.383046\pi$
$31$	4.00000	0.718421	0.359211	+	0.933257i	$0.383046\pi$
$32$	−6.04356	−1.06836
$33$	5.00000	0.870388
$34$	−5.37386	−0.921610
$35$	1.00000	0.169031
$36$	1.20871	0.201452
$37$	−4.00000	−0.657596	−0.328798	−	0.944400i	$-0.606644\pi$
$37$	−4.00000	−0.657596	−0.328798	+	0.944400i	$0.606644\pi$
$38$	6.41742	1.04104
$39$	−4.58258	−0.733799
$40$	−1.41742	−0.224114
$41$	−9.16515	−1.43136	−0.715678	−	0.698430i	$-0.753882\pi$
$41$	−9.16515	−1.43136	−0.715678	+	0.698430i	$0.753882\pi$
$42$	1.79129	0.276402
$43$	−9.58258	−1.46133	−0.730665	−	0.682737i	$-0.760790\pi$
$43$	−9.58258	−1.46133	−0.730665	+	0.682737i	$0.760790\pi$
$44$	6.04356	0.911101
$45$	1.00000	0.149071
$46$	−7.16515	−1.05644
$47$	10.5826	1.54363	0.771814	−	0.635849i	$-0.219350\pi$
$47$	10.5826	1.54363	0.771814	+	0.635849i	$0.219350\pi$
$48$	−4.95644	−0.715400
$49$	−6.00000	−0.857143
$50$	1.79129	0.253326
$51$	−3.00000	−0.420084
$52$	−5.53901	−0.768123
$53$	0.417424	0.0573376	0.0286688	−	0.999589i	$-0.490873\pi$
$53$	0.417424	0.0573376	0.0286688	+	0.999589i	$0.490873\pi$
$54$	1.79129	0.243763
$55$	5.00000	0.674200
$56$	−1.41742	−0.189411
$57$	3.58258	0.474524
$58$	1.79129	0.235208
$59$	−7.58258	−0.987167	−0.493584	−	0.869698i	$-0.664313\pi$
$59$	−7.58258	−0.987167	−0.493584	+	0.869698i	$0.664313\pi$
$60$	1.20871	0.156044
$61$	12.7477	1.63218	0.816090	−	0.577925i	$-0.196138\pi$
$61$	12.7477	1.63218	0.816090	+	0.577925i	$0.196138\pi$
$62$	7.16515	0.909975
$63$	1.00000	0.125988
$64$	−0.912878	−0.114110
$65$	−4.58258	−0.568399
$66$	8.95644	1.10246
$67$	−4.16515	−0.508854	−0.254427	−	0.967092i	$-0.581887\pi$
$67$	−4.16515	−0.508854	−0.254427	+	0.967092i	$0.581887\pi$
$68$	−3.62614	−0.439734
$69$	−4.00000	−0.481543
$70$	1.79129	0.214100
$71$	−9.58258	−1.13724	−0.568621	−	0.822599i	$-0.692523\pi$
$71$	−9.58258	−1.13724	−0.568621	+	0.822599i	$0.692523\pi$
$72$	−1.41742	−0.167045
$73$	4.00000	0.468165	0.234082	−	0.972217i	$-0.424791\pi$
$73$	4.00000	0.468165	0.234082	+	0.972217i	$0.424791\pi$
$74$	−7.16515	−0.832932
$75$	1.00000	0.115470
$76$	4.33030	0.496720
$77$	5.00000	0.569803
$78$	−8.20871	−0.929454
$79$	7.58258	0.853106	0.426553	−	0.904462i	$-0.359728\pi$
$79$	7.58258	0.853106	0.426553	+	0.904462i	$0.359728\pi$
$80$	−4.95644	−0.554147
$81$	1.00000	0.111111
$82$	−16.4174	−1.81300
$83$	−11.5826	−1.27135	−0.635676	−	0.771956i	$-0.719279\pi$
$83$	−11.5826	−1.27135	−0.635676	+	0.771956i	$0.719279\pi$
$84$	1.20871	0.131881
$85$	−3.00000	−0.325396
$86$	−17.1652	−1.85097
$87$	1.00000	0.107211
$88$	−7.08712	−0.755490
$89$	1.41742	0.150247	0.0751233	−	0.997174i	$-0.476065\pi$
$89$	1.41742	0.150247	0.0751233	+	0.997174i	$0.476065\pi$
$90$	1.79129	0.188818
$91$	−4.58258	−0.480384
$92$	−4.83485	−0.504068
$93$	4.00000	0.414781
$94$	18.9564	1.95521
$95$	3.58258	0.367565
$96$	−6.04356	−0.616818
$97$	11.5826	1.17603	0.588016	−	0.808849i	$-0.299909\pi$
$97$	11.5826	1.17603	0.588016	+	0.808849i	$0.299909\pi$
$98$	−10.7477	−1.08568
$99$	5.00000	0.502519
$100$	1.20871	0.120871
$101$	−0.582576	−0.0579684	−0.0289842	−	0.999580i	$-0.509227\pi$
$101$	−0.582576	−0.0579684	−0.0289842	+	0.999580i	$0.509227\pi$
$102$	−5.37386	−0.532092
$103$	15.1652	1.49427	0.747133	−	0.664674i	$-0.231430\pi$
$103$	15.1652	1.49427	0.747133	+	0.664674i	$0.231430\pi$
$104$	6.49545	0.636932
$105$	1.00000	0.0975900
$106$	0.747727	0.0726257
$107$	5.16515	0.499334	0.249667	−	0.968332i	$-0.419679\pi$
$107$	5.16515	0.499334	0.249667	+	0.968332i	$0.419679\pi$
$108$	1.20871	0.116308
$109$	14.1652	1.35678	0.678388	−	0.734704i	$-0.262679\pi$
$109$	14.1652	1.35678	0.678388	+	0.734704i	$0.262679\pi$
$110$	8.95644	0.853963
$111$	−4.00000	−0.379663
$112$	−4.95644	−0.468339
$113$	−14.1652	−1.33255	−0.666273	−	0.745708i	$-0.732111\pi$
$113$	−14.1652	−1.33255	−0.666273	+	0.745708i	$0.732111\pi$
$114$	6.41742	0.601047
$115$	−4.00000	−0.373002
$116$	1.20871	0.112226
$117$	−4.58258	−0.423659
$118$	−13.5826	−1.25038
$119$	−3.00000	−0.275010
$120$	−1.41742	−0.129393
$121$	14.0000	1.27273
$122$	22.8348	2.06737
$123$	−9.16515	−0.826394
$124$	4.83485	0.434182
$125$	1.00000	0.0894427
$126$	1.79129	0.159581
$127$	2.00000	0.177471	0.0887357	−	0.996055i	$-0.471717\pi$
$127$	2.00000	0.177471	0.0887357	+	0.996055i	$0.471717\pi$
$128$	10.4519	0.923826
$129$	−9.58258	−0.843699
$130$	−8.20871	−0.719952
$131$	−15.0000	−1.31056	−0.655278	−	0.755388i	$-0.727449\pi$
$131$	−15.0000	−1.31056	−0.655278	+	0.755388i	$0.727449\pi$
$132$	6.04356	0.526024
$133$	3.58258	0.310649
$134$	−7.46099	−0.644531
$135$	1.00000	0.0860663
$136$	4.25227	0.364629
$137$	16.3303	1.39519	0.697596	−	0.716491i	$-0.254253\pi$
$137$	16.3303	1.39519	0.697596	+	0.716491i	$0.254253\pi$
$138$	−7.16515	−0.609938
$139$	−9.41742	−0.798776	−0.399388	−	0.916782i	$-0.630777\pi$
$139$	−9.41742	−0.798776	−0.399388	+	0.916782i	$0.630777\pi$
$140$	1.20871	0.102155
$141$	10.5826	0.891214
$142$	−17.1652	−1.44047
$143$	−22.9129	−1.91607
$144$	−4.95644	−0.413037
$145$	1.00000	0.0830455
$146$	7.16515	0.592992
$147$	−6.00000	−0.494872
$148$	−4.83485	−0.397422
$149$	16.7477	1.37203	0.686014	−	0.727589i	$-0.259359\pi$
$149$	16.7477	1.37203	0.686014	+	0.727589i	$0.259359\pi$
$150$	1.79129	0.146258
$151$	7.16515	0.583092	0.291546	−	0.956557i	$-0.405830\pi$
$151$	7.16515	0.583092	0.291546	+	0.956557i	$0.405830\pi$
$152$	−5.07803	−0.411883
$153$	−3.00000	−0.242536
$154$	8.95644	0.721730
$155$	4.00000	0.321288
$156$	−5.53901	−0.443476
$157$	10.7477	0.857762	0.428881	−	0.903361i	$-0.358908\pi$
$157$	10.7477	0.857762	0.428881	+	0.903361i	$0.358908\pi$
$158$	13.5826	1.08057
$159$	0.417424	0.0331039
$160$	−6.04356	−0.477785
$161$	−4.00000	−0.315244
$162$	1.79129	0.140737
$163$	7.58258	0.593913	0.296957	−	0.954891i	$-0.404028\pi$
$163$	7.58258	0.593913	0.296957	+	0.954891i	$0.404028\pi$
$164$	−11.0780	−0.865049
$165$	5.00000	0.389249
$166$	−20.7477	−1.61034
$167$	0	0		−	1.00000i	$-0.5\pi$
$167$	0	0			1.00000i	$0.5\pi$
$168$	−1.41742	−0.109357
$169$	8.00000	0.615385
$170$	−5.37386	−0.412157
$171$	3.58258	0.273966
$172$	−11.5826	−0.883163
$173$	−3.16515	−0.240642	−0.120321	−	0.992735i	$-0.538392\pi$
$173$	−3.16515	−0.240642	−0.120321	+	0.992735i	$0.538392\pi$
$174$	1.79129	0.135797
$175$	1.00000	0.0755929
$176$	−24.7822	−1.86803
$177$	−7.58258	−0.569941
$178$	2.53901	0.190307
$179$	4.74773	0.354862	0.177431	−	0.984133i	$-0.443221\pi$
$179$	4.74773	0.354862	0.177431	+	0.984133i	$0.443221\pi$
$180$	1.20871	0.0900921
$181$	16.1652	1.20155	0.600773	−	0.799420i	$-0.294860\pi$
$181$	16.1652	1.20155	0.600773	+	0.799420i	$0.294860\pi$
$182$	−8.20871	−0.608470
$183$	12.7477	0.942339
$184$	5.66970	0.417976
$185$	−4.00000	−0.294086
$186$	7.16515	0.525374
$187$	−15.0000	−1.09691
$188$	12.7913	0.932901
$189$	1.00000	0.0727393
$190$	6.41742	0.465569
$191$	−4.00000	−0.289430	−0.144715	−	0.989473i	$-0.546227\pi$
$191$	−4.00000	−0.289430	−0.144715	+	0.989473i	$0.546227\pi$
$192$	−0.912878	−0.0658813
$193$	−20.3303	−1.46341	−0.731704	−	0.681623i	$-0.761274\pi$
$193$	−20.3303	−1.46341	−0.731704	+	0.681623i	$0.761274\pi$
$194$	20.7477	1.48960
$195$	−4.58258	−0.328165
$196$	−7.25227	−0.518019
$197$	−16.3303	−1.16349	−0.581743	−	0.813373i	$-0.697629\pi$
$197$	−16.3303	−1.16349	−0.581743	+	0.813373i	$0.697629\pi$
$198$	8.95644	0.636506
$199$	13.4174	0.951136	0.475568	−	0.879679i	$-0.342243\pi$
$199$	13.4174	0.951136	0.475568	+	0.879679i	$0.342243\pi$
$200$	−1.41742	−0.100227
$201$	−4.16515	−0.293787
$202$	−1.04356	−0.0734247
$203$	1.00000	0.0701862
$204$	−3.62614	−0.253880
$205$	−9.16515	−0.640122
$206$	27.1652	1.89269
$207$	−4.00000	−0.278019
$208$	22.7133	1.57488
$209$	17.9129	1.23906
$210$	1.79129	0.123611
$211$	20.3303	1.39960	0.699798	−	0.714341i	$-0.253273\pi$
$211$	20.3303	1.39960	0.699798	+	0.714341i	$0.253273\pi$
$212$	0.504546	0.0346523
$213$	−9.58258	−0.656587
$214$	9.25227	0.632472
$215$	−9.58258	−0.653526
$216$	−1.41742	−0.0964435
$217$	4.00000	0.271538
$218$	25.3739	1.71853
$219$	4.00000	0.270295
$220$	6.04356	0.407457
$221$	13.7477	0.924772
$222$	−7.16515	−0.480893
$223$	7.00000	0.468755	0.234377	−	0.972146i	$-0.424695\pi$
$223$	7.00000	0.468755	0.234377	+	0.972146i	$0.424695\pi$
$224$	−6.04356	−0.403802
$225$	1.00000	0.0666667
$226$	−25.3739	−1.68784
$227$	−7.58258	−0.503273	−0.251637	−	0.967822i	$-0.580969\pi$
$227$	−7.58258	−0.503273	−0.251637	+	0.967822i	$0.580969\pi$
$228$	4.33030	0.286781
$229$	−17.1652	−1.13431	−0.567153	−	0.823613i	$-0.691955\pi$
$229$	−17.1652	−1.13431	−0.567153	+	0.823613i	$0.691955\pi$
$230$	−7.16515	−0.472456
$231$	5.00000	0.328976
$232$	−1.41742	−0.0930585
$233$	−13.1652	−0.862478	−0.431239	−	0.902238i	$-0.641923\pi$
$233$	−13.1652	−0.862478	−0.431239	+	0.902238i	$0.641923\pi$
$234$	−8.20871	−0.536620
$235$	10.5826	0.690331
$236$	−9.16515	−0.596601
$237$	7.58258	0.492541
$238$	−5.37386	−0.348336
$239$	−26.0000	−1.68180	−0.840900	−	0.541190i	$-0.817974\pi$
$239$	−26.0000	−1.68180	−0.840900	+	0.541190i	$0.817974\pi$
$240$	−4.95644	−0.319937
$241$	29.3303	1.88933	0.944665	−	0.328035i	$-0.106387\pi$
$241$	29.3303	1.88933	0.944665	+	0.328035i	$0.106387\pi$
$242$	25.0780	1.61208
$243$	1.00000	0.0641500
$244$	15.4083	0.986417
$245$	−6.00000	−0.383326
$246$	−16.4174	−1.04674
$247$	−16.4174	−1.04462
$248$	−5.66970	−0.360026
$249$	−11.5826	−0.734016
$250$	1.79129	0.113291
$251$	16.1652	1.02034	0.510168	−	0.860075i	$-0.329583\pi$
$251$	16.1652	1.02034	0.510168	+	0.860075i	$0.329583\pi$
$252$	1.20871	0.0761417
$253$	−20.0000	−1.25739
$254$	3.58258	0.224791
$255$	−3.00000	−0.187867
$256$	20.5481	1.28426
$257$	12.7477	0.795181	0.397591	−	0.917563i	$-0.369846\pi$
$257$	12.7477	0.795181	0.397591	+	0.917563i	$0.369846\pi$
$258$	−17.1652	−1.06866
$259$	−4.00000	−0.248548
$260$	−5.53901	−0.343515
$261$	1.00000	0.0618984
$262$	−26.8693	−1.65999
$263$	30.3303	1.87025	0.935123	−	0.354322i	$-0.115288\pi$
$263$	30.3303	1.87025	0.935123	+	0.354322i	$0.115288\pi$
$264$	−7.08712	−0.436182
$265$	0.417424	0.0256422
$266$	6.41742	0.393478
$267$	1.41742	0.0867450
$268$	−5.03447	−0.307529
$269$	22.5826	1.37688	0.688442	−	0.725291i	$-0.258295\pi$
$269$	22.5826	1.37688	0.688442	+	0.725291i	$0.258295\pi$
$270$	1.79129	0.109014
$271$	1.16515	0.0707779	0.0353890	−	0.999374i	$-0.488733\pi$
$271$	1.16515	0.0707779	0.0353890	+	0.999374i	$0.488733\pi$
$272$	14.8693	0.901585
$273$	−4.58258	−0.277350
$274$	29.2523	1.76719
$275$	5.00000	0.301511
$276$	−4.83485	−0.291024
$277$	−24.9129	−1.49687	−0.748435	−	0.663208i	$-0.769194\pi$
$277$	−24.9129	−1.49687	−0.748435	+	0.663208i	$0.769194\pi$
$278$	−16.8693	−1.01175
$279$	4.00000	0.239474
$280$	−1.41742	−0.0847073
$281$	−0.417424	−0.0249014	−0.0124507	−	0.999922i	$-0.503963\pi$
$281$	−0.417424	−0.0249014	−0.0124507	+	0.999922i	$0.503963\pi$
$282$	18.9564	1.12884
$283$	−0.834849	−0.0496266	−0.0248133	−	0.999692i	$-0.507899\pi$
$283$	−0.834849	−0.0496266	−0.0248133	+	0.999692i	$0.507899\pi$
$284$	−11.5826	−0.687299
$285$	3.58258	0.212213
$286$	−41.0436	−2.42696
$287$	−9.16515	−0.541002
$288$	−6.04356	−0.356120
$289$	−8.00000	−0.470588
$290$	1.79129	0.105188
$291$	11.5826	0.678983
$292$	4.83485	0.282938
$293$	30.1652	1.76227	0.881133	−	0.472868i	$-0.156781\pi$
$293$	30.1652	1.76227	0.881133	+	0.472868i	$0.156781\pi$
$294$	−10.7477	−0.626820
$295$	−7.58258	−0.441475
$296$	5.66970	0.329544
$297$	5.00000	0.290129
$298$	30.0000	1.73785
$299$	18.3303	1.06007
$300$	1.20871	0.0697850
$301$	−9.58258	−0.552330
$302$	12.8348	0.738563
$303$	−0.582576	−0.0334681
$304$	−17.7568	−1.01842
$305$	12.7477	0.729933
$306$	−5.37386	−0.307203
$307$	0	0		−	1.00000i	$-0.5\pi$
$307$	0	0			1.00000i	$0.5\pi$
$308$	6.04356	0.344364
$309$	15.1652	0.862715
$310$	7.16515	0.406953
$311$	−3.00000	−0.170114	−0.0850572	−	0.996376i	$-0.527107\pi$
$311$	−3.00000	−0.170114	−0.0850572	+	0.996376i	$0.527107\pi$
$312$	6.49545	0.367733
$313$	10.5826	0.598163	0.299081	−	0.954228i	$-0.403320\pi$
$313$	10.5826	0.598163	0.299081	+	0.954228i	$0.403320\pi$
$314$	19.2523	1.08647
$315$	1.00000	0.0563436
$316$	9.16515	0.515580
$317$	−25.0000	−1.40414	−0.702070	−	0.712108i	$-0.747741\pi$
$317$	−25.0000	−1.40414	−0.702070	+	0.712108i	$0.747741\pi$
$318$	0.747727	0.0419305
$319$	5.00000	0.279946
$320$	−0.912878	−0.0510315
$321$	5.16515	0.288291
$322$	−7.16515	−0.399298
$323$	−10.7477	−0.598020
$324$	1.20871	0.0671507
$325$	−4.58258	−0.254196
$326$	13.5826	0.752269
$327$	14.1652	0.783335
$328$	12.9909	0.717303
$329$	10.5826	0.583436
$330$	8.95644	0.493036
$331$	−8.33030	−0.457875	−0.228937	−	0.973441i	$-0.573525\pi$
$331$	−8.33030	−0.457875	−0.228937	+	0.973441i	$0.573525\pi$
$332$	−14.0000	−0.768350
$333$	−4.00000	−0.219199
$334$	0	0
$335$	−4.16515	−0.227567
$336$	−4.95644	−0.270396
$337$	−21.1652	−1.15294	−0.576470	−	0.817119i	$-0.695570\pi$
$337$	−21.1652	−1.15294	−0.576470	+	0.817119i	$0.695570\pi$
$338$	14.3303	0.779466
$339$	−14.1652	−0.769345
$340$	−3.62614	−0.196655
$341$	20.0000	1.08306
$342$	6.41742	0.347015
$343$	−13.0000	−0.701934
$344$	13.5826	0.732323
$345$	−4.00000	−0.215353
$346$	−5.66970	−0.304805
$347$	7.16515	0.384645	0.192323	−	0.981332i	$-0.438398\pi$
$347$	7.16515	0.384645	0.192323	+	0.981332i	$0.438398\pi$
$348$	1.20871	0.0647938
$349$	−4.33030	−0.231796	−0.115898	−	0.993261i	$-0.536975\pi$
$349$	−4.33030	−0.231796	−0.115898	+	0.993261i	$0.536975\pi$
$350$	1.79129	0.0957484
$351$	−4.58258	−0.244600
$352$	−30.2178	−1.61061
$353$	−14.8348	−0.789579	−0.394790	−	0.918772i	$-0.629183\pi$
$353$	−14.8348	−0.789579	−0.394790	+	0.918772i	$0.629183\pi$
$354$	−13.5826	−0.721906
$355$	−9.58258	−0.508590
$356$	1.71326	0.0908025
$357$	−3.00000	−0.158777
$358$	8.50455	0.449479
$359$	−27.1652	−1.43372	−0.716861	−	0.697216i	$-0.754422\pi$
$359$	−27.1652	−1.43372	−0.716861	+	0.697216i	$0.754422\pi$
$360$	−1.41742	−0.0747048
$361$	−6.16515	−0.324482
$362$	28.9564	1.52192
$363$	14.0000	0.734809
$364$	−5.53901	−0.290323
$365$	4.00000	0.209370
$366$	22.8348	1.19360
$367$	−37.4955	−1.95725	−0.978623	−	0.205661i	$-0.934066\pi$
$367$	−37.4955	−1.95725	−0.978623	+	0.205661i	$0.934066\pi$
$368$	19.8258	1.03349
$369$	−9.16515	−0.477119
$370$	−7.16515	−0.372498
$371$	0.417424	0.0216716
$372$	4.83485	0.250675
$373$	28.3303	1.46689	0.733444	−	0.679750i	$-0.237912\pi$
$373$	28.3303	1.46689	0.733444	+	0.679750i	$0.237912\pi$
$374$	−26.8693	−1.38938
$375$	1.00000	0.0516398
$376$	−15.0000	−0.773566
$377$	−4.58258	−0.236015
$378$	1.79129	0.0921339
$379$	−26.0000	−1.33553	−0.667765	−	0.744372i	$-0.732749\pi$
$379$	−26.0000	−1.33553	−0.667765	+	0.744372i	$0.732749\pi$
$380$	4.33030	0.222140
$381$	2.00000	0.102463
$382$	−7.16515	−0.366601
$383$	3.58258	0.183061	0.0915305	−	0.995802i	$-0.470824\pi$
$383$	3.58258	0.183061	0.0915305	+	0.995802i	$0.470824\pi$
$384$	10.4519	0.533371
$385$	5.00000	0.254824
$386$	−36.4174	−1.85360
$387$	−9.58258	−0.487110
$388$	14.0000	0.710742
$389$	−6.58258	−0.333750	−0.166875	−	0.985978i	$-0.553368\pi$
$389$	−6.58258	−0.333750	−0.166875	+	0.985978i	$0.553368\pi$
$390$	−8.20871	−0.415664
$391$	12.0000	0.606866
$392$	8.50455	0.429544
$393$	−15.0000	−0.756650
$394$	−29.2523	−1.47371
$395$	7.58258	0.381521
$396$	6.04356	0.303700
$397$	10.8348	0.543785	0.271893	−	0.962328i	$-0.412350\pi$
$397$	10.8348	0.543785	0.271893	+	0.962328i	$0.412350\pi$
$398$	24.0345	1.20474
$399$	3.58258	0.179353
$400$	−4.95644	−0.247822
$401$	12.4174	0.620097	0.310048	−	0.950721i	$-0.399655\pi$
$401$	12.4174	0.620097	0.310048	+	0.950721i	$0.399655\pi$
$402$	−7.46099	−0.372120
$403$	−18.3303	−0.913097
$404$	−0.704166	−0.0350336
$405$	1.00000	0.0496904
$406$	1.79129	0.0889001
$407$	−20.0000	−0.991363
$408$	4.25227	0.210519
$409$	−2.74773	−0.135866	−0.0679332	−	0.997690i	$-0.521640\pi$
$409$	−2.74773	−0.135866	−0.0679332	+	0.997690i	$0.521640\pi$
$410$	−16.4174	−0.810799
$411$	16.3303	0.805514
$412$	18.3303	0.903069
$413$	−7.58258	−0.373114
$414$	−7.16515	−0.352148
$415$	−11.5826	−0.568566
$416$	27.6951	1.35786
$417$	−9.41742	−0.461173
$418$	32.0871	1.56943
$419$	−37.1652	−1.81564	−0.907818	−	0.419364i	$-0.862253\pi$
$419$	−37.1652	−1.81564	−0.907818	+	0.419364i	$0.862253\pi$
$420$	1.20871	0.0589791
$421$	4.41742	0.215292	0.107646	−	0.994189i	$-0.465669\pi$
$421$	4.41742	0.215292	0.107646	+	0.994189i	$0.465669\pi$
$422$	36.4174	1.77277
$423$	10.5826	0.514542
$424$	−0.591667	−0.0287339
$425$	−3.00000	−0.145521
$426$	−17.1652	−0.831654
$427$	12.7477	0.616906
$428$	6.24318	0.301776
$429$	−22.9129	−1.10624
$430$	−17.1652	−0.827777
$431$	−39.1652	−1.88652	−0.943259	−	0.332057i	$-0.892258\pi$
$431$	−39.1652	−1.88652	−0.943259	+	0.332057i	$0.892258\pi$
$432$	−4.95644	−0.238467
$433$	25.0780	1.20517	0.602587	−	0.798053i	$-0.294137\pi$
$433$	25.0780	1.20517	0.602587	+	0.798053i	$0.294137\pi$
$434$	7.16515	0.343938
$435$	1.00000	0.0479463
$436$	17.1216	0.819975
$437$	−14.3303	−0.685511
$438$	7.16515	0.342364
$439$	−16.9129	−0.807208	−0.403604	−	0.914934i	$-0.632243\pi$
$439$	−16.9129	−0.807208	−0.403604	+	0.914934i	$0.632243\pi$
$440$	−7.08712	−0.337865
$441$	−6.00000	−0.285714
$442$	24.6261	1.17135
$443$	0.582576	0.0276790	0.0138395	−	0.999904i	$-0.495595\pi$
$443$	0.582576	0.0276790	0.0138395	+	0.999904i	$0.495595\pi$
$444$	−4.83485	−0.229452
$445$	1.41742	0.0671924
$446$	12.5390	0.593740
$447$	16.7477	0.792140
$448$	−0.912878	−0.0431295
$449$	−30.0780	−1.41947	−0.709735	−	0.704469i	$-0.751185\pi$
$449$	−30.0780	−1.41947	−0.709735	+	0.704469i	$0.751185\pi$
$450$	1.79129	0.0844421
$451$	−45.8258	−2.15785
$452$	−17.1216	−0.805332
$453$	7.16515	0.336648
$454$	−13.5826	−0.637462
$455$	−4.58258	−0.214834
$456$	−5.07803	−0.237801
$457$	−3.74773	−0.175311	−0.0876556	−	0.996151i	$-0.527938\pi$
$457$	−3.74773	−0.175311	−0.0876556	+	0.996151i	$0.527938\pi$
$458$	−30.7477	−1.43675
$459$	−3.00000	−0.140028
$460$	−4.83485	−0.225426
$461$	−9.16515	−0.426864	−0.213432	−	0.976958i	$-0.568464\pi$
$461$	−9.16515	−0.426864	−0.213432	+	0.976958i	$0.568464\pi$
$462$	8.95644	0.416691
$463$	−0.165151	−0.00767524	−0.00383762	−	0.999993i	$-0.501222\pi$
$463$	−0.165151	−0.00767524	−0.00383762	+	0.999993i	$0.501222\pi$
$464$	−4.95644	−0.230097
$465$	4.00000	0.185496
$466$	−23.5826	−1.09244
$467$	−8.00000	−0.370196	−0.185098	−	0.982720i	$-0.559260\pi$
$467$	−8.00000	−0.370196	−0.185098	+	0.982720i	$0.559260\pi$
$468$	−5.53901	−0.256041
$469$	−4.16515	−0.192329
$470$	18.9564	0.874395
$471$	10.7477	0.495229
$472$	10.7477	0.494704
$473$	−47.9129	−2.20304
$474$	13.5826	0.623868
$475$	3.58258	0.164380
$476$	−3.62614	−0.166204
$477$	0.417424	0.0191125
$478$	−46.5735	−2.13022
$479$	−19.1652	−0.875678	−0.437839	−	0.899053i	$-0.644256\pi$
$479$	−19.1652	−0.875678	−0.437839	+	0.899053i	$0.644256\pi$
$480$	−6.04356	−0.275850
$481$	18.3303	0.835790
$482$	52.5390	2.39309
$483$	−4.00000	−0.182006
$484$	16.9220	0.769180
$485$	11.5826	0.525938
$486$	1.79129	0.0812545
$487$	2.33030	0.105596	0.0527980	−	0.998605i	$-0.483186\pi$
$487$	2.33030	0.105596	0.0527980	+	0.998605i	$0.483186\pi$
$488$	−18.0689	−0.817942
$489$	7.58258	0.342896
$490$	−10.7477	−0.485533
$491$	16.0000	0.722070	0.361035	−	0.932552i	$-0.382424\pi$
$491$	16.0000	0.722070	0.361035	+	0.932552i	$0.382424\pi$
$492$	−11.0780	−0.499436
$493$	−3.00000	−0.135113
$494$	−29.4083	−1.32314
$495$	5.00000	0.224733
$496$	−19.8258	−0.890203
$497$	−9.58258	−0.429837
$498$	−20.7477	−0.929728
$499$	−13.4174	−0.600646	−0.300323	−	0.953837i	$-0.597095\pi$
$499$	−13.4174	−0.600646	−0.300323	+	0.953837i	$0.597095\pi$
$500$	1.20871	0.0540553
$501$	0	0
$502$	28.9564	1.29239
$503$	−22.9129	−1.02163	−0.510817	−	0.859689i	$-0.670657\pi$
$503$	−22.9129	−1.02163	−0.510817	+	0.859689i	$0.670657\pi$
$504$	−1.41742	−0.0631371
$505$	−0.582576	−0.0259243
$506$	−35.8258	−1.59265
$507$	8.00000	0.355292
$508$	2.41742	0.107256
$509$	26.7477	1.18557	0.592786	−	0.805360i	$-0.298028\pi$
$509$	26.7477	1.18557	0.592786	+	0.805360i	$0.298028\pi$
$510$	−5.37386	−0.237959
$511$	4.00000	0.176950
$512$	15.9038	0.702855
$513$	3.58258	0.158175
$514$	22.8348	1.00720
$515$	15.1652	0.668256
$516$	−11.5826	−0.509894
$517$	52.9129	2.32711
$518$	−7.16515	−0.314819
$519$	−3.16515	−0.138935
$520$	6.49545	0.284845
$521$	43.0780	1.88728	0.943641	−	0.330970i	$-0.107376\pi$
$521$	43.0780	1.88728	0.943641	+	0.330970i	$0.107376\pi$
$522$	1.79129	0.0784025
$523$	−33.3303	−1.45743	−0.728716	−	0.684816i	$-0.759883\pi$
$523$	−33.3303	−1.45743	−0.728716	+	0.684816i	$0.759883\pi$
$524$	−18.1307	−0.792043
$525$	1.00000	0.0436436
$526$	54.3303	2.36891
$527$	−12.0000	−0.522728
$528$	−24.7822	−1.07851
$529$	−7.00000	−0.304348
$530$	0.747727	0.0324792
$531$	−7.58258	−0.329056
$532$	4.33030	0.187742
$533$	42.0000	1.81922
$534$	2.53901	0.109874
$535$	5.16515	0.223309
$536$	5.90379	0.255005
$537$	4.74773	0.204880
$538$	40.4519	1.74400
$539$	−30.0000	−1.29219
$540$	1.20871	0.0520147
$541$	−31.4955	−1.35410	−0.677048	−	0.735939i	$-0.736741\pi$
$541$	−31.4955	−1.35410	−0.677048	+	0.735939i	$0.736741\pi$
$542$	2.08712	0.0896495
$543$	16.1652	0.693713
$544$	18.1307	0.777347
$545$	14.1652	0.606768
$546$	−8.20871	−0.351300
$547$	4.16515	0.178089	0.0890445	−	0.996028i	$-0.471619\pi$
$547$	4.16515	0.178089	0.0890445	+	0.996028i	$0.471619\pi$
$548$	19.7386	0.843193
$549$	12.7477	0.544060
$550$	8.95644	0.381904
$551$	3.58258	0.152623
$552$	5.66970	0.241318
$553$	7.58258	0.322444
$554$	−44.6261	−1.89598
$555$	−4.00000	−0.169791
$556$	−11.3830	−0.482745
$557$	−22.7477	−0.963852	−0.481926	−	0.876212i	$-0.660063\pi$
$557$	−22.7477	−0.963852	−0.481926	+	0.876212i	$0.660063\pi$
$558$	7.16515	0.303325
$559$	43.9129	1.85732
$560$	−4.95644	−0.209448
$561$	−15.0000	−0.633300
$562$	−0.747727	−0.0315410
$563$	−14.5826	−0.614582	−0.307291	−	0.951616i	$-0.599423\pi$
$563$	−14.5826	−0.614582	−0.307291	+	0.951616i	$0.599423\pi$
$564$	12.7913	0.538610
$565$	−14.1652	−0.595932
$566$	−1.49545	−0.0628586
$567$	1.00000	0.0419961
$568$	13.5826	0.569912
$569$	28.5826	1.19824	0.599122	−	0.800658i	$-0.295516\pi$
$569$	28.5826	1.19824	0.599122	+	0.800658i	$0.295516\pi$
$570$	6.41742	0.268796
$571$	12.0000	0.502184	0.251092	−	0.967963i	$-0.419210\pi$
$571$	12.0000	0.502184	0.251092	+	0.967963i	$0.419210\pi$
$572$	−27.6951	−1.15799
$573$	−4.00000	−0.167102
$574$	−16.4174	−0.685250
$575$	−4.00000	−0.166812
$576$	−0.912878	−0.0380366
$577$	−19.1652	−0.797856	−0.398928	−	0.916982i	$-0.630618\pi$
$577$	−19.1652	−0.797856	−0.398928	+	0.916982i	$0.630618\pi$
$578$	−14.3303	−0.596062
$579$	−20.3303	−0.844899
$580$	1.20871	0.0501890
$581$	−11.5826	−0.480526
$582$	20.7477	0.860021
$583$	2.08712	0.0864397
$584$	−5.66970	−0.234614
$585$	−4.58258	−0.189466
$586$	54.0345	2.23214
$587$	−11.5826	−0.478064	−0.239032	−	0.971012i	$-0.576830\pi$
$587$	−11.5826	−0.478064	−0.239032	+	0.971012i	$0.576830\pi$
$588$	−7.25227	−0.299079
$589$	14.3303	0.590470
$590$	−13.5826	−0.559186
$591$	−16.3303	−0.671739
$592$	19.8258	0.814834
$593$	8.41742	0.345662	0.172831	−	0.984951i	$-0.444709\pi$
$593$	8.41742	0.345662	0.172831	+	0.984951i	$0.444709\pi$
$594$	8.95644	0.367487
$595$	−3.00000	−0.122988
$596$	20.2432	0.829193
$597$	13.4174	0.549139
$598$	32.8348	1.34272
$599$	0.165151	0.00674790	0.00337395	−	0.999994i	$-0.498926\pi$
$599$	0.165151	0.00674790	0.00337395	+	0.999994i	$0.498926\pi$
$600$	−1.41742	−0.0578661
$601$	−32.3303	−1.31878	−0.659390	−	0.751801i	$-0.729185\pi$
$601$	−32.3303	−1.31878	−0.659390	+	0.751801i	$0.729185\pi$
$602$	−17.1652	−0.699599
$603$	−4.16515	−0.169618
$604$	8.66061	0.352395
$605$	14.0000	0.569181
$606$	−1.04356	−0.0423918
$607$	3.58258	0.145412	0.0727061	−	0.997353i	$-0.476836\pi$
$607$	3.58258	0.145412	0.0727061	+	0.997353i	$0.476836\pi$
$608$	−21.6515	−0.878085
$609$	1.00000	0.0405220
$610$	22.8348	0.924556
$611$	−48.4955	−1.96192
$612$	−3.62614	−0.146578
$613$	−43.7477	−1.76695	−0.883477	−	0.468474i	$-0.844804\pi$
$613$	−43.7477	−1.76695	−0.883477	+	0.468474i	$0.844804\pi$
$614$	0	0
$615$	−9.16515	−0.369575
$616$	−7.08712	−0.285548
$617$	15.4955	0.623823	0.311912	−	0.950111i	$-0.399031\pi$
$617$	15.4955	0.623823	0.311912	+	0.950111i	$0.399031\pi$
$618$	27.1652	1.09274
$619$	13.1652	0.529152	0.264576	−	0.964365i	$-0.414768\pi$
$619$	13.1652	0.529152	0.264576	+	0.964365i	$0.414768\pi$
$620$	4.83485	0.194172
$621$	−4.00000	−0.160514
$622$	−5.37386	−0.215472
$623$	1.41742	0.0567879
$624$	22.7133	0.909258
$625$	1.00000	0.0400000
$626$	18.9564	0.757652
$627$	17.9129	0.715371
$628$	12.9909	0.518394
$629$	12.0000	0.478471
$630$	1.79129	0.0713666
$631$	10.9129	0.434435	0.217217	−	0.976123i	$-0.430302\pi$
$631$	10.9129	0.434435	0.217217	+	0.976123i	$0.430302\pi$
$632$	−10.7477	−0.427522
$633$	20.3303	0.808057
$634$	−44.7822	−1.77853
$635$	2.00000	0.0793676
$636$	0.504546	0.0200065
$637$	27.4955	1.08941
$638$	8.95644	0.354589
$639$	−9.58258	−0.379081
$640$	10.4519	0.413147
$641$	−6.58258	−0.259996	−0.129998	−	0.991514i	$-0.541497\pi$
$641$	−6.58258	−0.259996	−0.129998	+	0.991514i	$0.541497\pi$
$642$	9.25227	0.365158
$643$	43.6606	1.72181	0.860903	−	0.508769i	$-0.169899\pi$
$643$	43.6606	1.72181	0.860903	+	0.508769i	$0.169899\pi$
$644$	−4.83485	−0.190520
$645$	−9.58258	−0.377314
$646$	−19.2523	−0.757471
$647$	24.7477	0.972934	0.486467	−	0.873699i	$-0.338285\pi$
$647$	24.7477	0.972934	0.486467	+	0.873699i	$0.338285\pi$
$648$	−1.41742	−0.0556817
$649$	−37.9129	−1.48821
$650$	−8.20871	−0.321972
$651$	4.00000	0.156772
$652$	9.16515	0.358935
$653$	26.1652	1.02392	0.511961	−	0.859009i	$-0.328919\pi$
$653$	26.1652	1.02392	0.511961	+	0.859009i	$0.328919\pi$
$654$	25.3739	0.992197
$655$	−15.0000	−0.586098
$656$	45.4265	1.77361
$657$	4.00000	0.156055
$658$	18.9564	0.738999
$659$	18.1652	0.707614	0.353807	−	0.935318i	$-0.384887\pi$
$659$	18.1652	0.707614	0.353807	+	0.935318i	$0.384887\pi$
$660$	6.04356	0.235245
$661$	25.0000	0.972387	0.486194	−	0.873851i	$-0.338385\pi$
$661$	25.0000	0.972387	0.486194	+	0.873851i	$0.338385\pi$
$662$	−14.9220	−0.579959
$663$	13.7477	0.533917
$664$	16.4174	0.637120
$665$	3.58258	0.138926
$666$	−7.16515	−0.277644
$667$	−4.00000	−0.154881
$668$	0	0
$669$	7.00000	0.270636
$670$	−7.46099	−0.288243
$671$	63.7386	2.46060
$672$	−6.04356	−0.233135
$673$	1.74773	0.0673699	0.0336850	−	0.999433i	$-0.489276\pi$
$673$	1.74773	0.0673699	0.0336850	+	0.999433i	$0.489276\pi$
$674$	−37.9129	−1.46035
$675$	1.00000	0.0384900
$676$	9.66970	0.371911
$677$	44.8258	1.72279	0.861397	−	0.507932i	$-0.169590\pi$
$677$	44.8258	1.72279	0.861397	+	0.507932i	$0.169590\pi$
$678$	−25.3739	−0.974477
$679$	11.5826	0.444498
$680$	4.25227	0.163067
$681$	−7.58258	−0.290565
$682$	35.8258	1.37184
$683$	7.16515	0.274167	0.137083	−	0.990560i	$-0.456227\pi$
$683$	7.16515	0.274167	0.137083	+	0.990560i	$0.456227\pi$
$684$	4.33030	0.165573
$685$	16.3303	0.623949
$686$	−23.2867	−0.889092
$687$	−17.1652	−0.654891
$688$	47.4955	1.81075
$689$	−1.91288	−0.0728749
$690$	−7.16515	−0.272773
$691$	42.9129	1.63248	0.816241	−	0.577711i	$-0.196054\pi$
$691$	42.9129	1.63248	0.816241	+	0.577711i	$0.196054\pi$
$692$	−3.82576	−0.145433
$693$	5.00000	0.189934
$694$	12.8348	0.487204
$695$	−9.41742	−0.357223
$696$	−1.41742	−0.0537273
$697$	27.4955	1.04146
$698$	−7.75682	−0.293600
$699$	−13.1652	−0.497952
$700$	1.20871	0.0456850
$701$	−23.0780	−0.871645	−0.435823	−	0.900033i	$-0.643542\pi$
$701$	−23.0780	−0.871645	−0.435823	+	0.900033i	$0.643542\pi$
$702$	−8.20871	−0.309818
$703$	−14.3303	−0.540478
$704$	−4.56439	−0.172027
$705$	10.5826	0.398563
$706$	−26.5735	−1.00011
$707$	−0.582576	−0.0219100
$708$	−9.16515	−0.344447
$709$	10.0000	0.375558	0.187779	−	0.982211i	$-0.439871\pi$
$709$	10.0000	0.375558	0.187779	+	0.982211i	$0.439871\pi$
$710$	−17.1652	−0.644197
$711$	7.58258	0.284369
$712$	−2.00909	−0.0752939
$713$	−16.0000	−0.599205
$714$	−5.37386	−0.201112
$715$	−22.9129	−0.856893
$716$	5.73864	0.214463
$717$	−26.0000	−0.970988
$718$	−48.6606	−1.81600
$719$	7.91288	0.295101	0.147550	−	0.989055i	$-0.452861\pi$
$719$	7.91288	0.295101	0.147550	+	0.989055i	$0.452861\pi$
$720$	−4.95644	−0.184716
$721$	15.1652	0.564780
$722$	−11.0436	−0.410999
$723$	29.3303	1.09081
$724$	19.5390	0.726162
$725$	1.00000	0.0371391
$726$	25.0780	0.930733
$727$	9.66970	0.358629	0.179315	−	0.983792i	$-0.442612\pi$
$727$	9.66970	0.358629	0.179315	+	0.983792i	$0.442612\pi$
$728$	6.49545	0.240738
$729$	1.00000	0.0370370
$730$	7.16515	0.265194
$731$	28.7477	1.06327
$732$	15.4083	0.569508
$733$	−38.4174	−1.41898	−0.709490	−	0.704716i	$-0.751075\pi$
$733$	−38.4174	−1.41898	−0.709490	+	0.704716i	$0.751075\pi$
$734$	−67.1652	−2.47911
$735$	−6.00000	−0.221313
$736$	24.1742	0.891074
$737$	−20.8258	−0.767127
$738$	−16.4174	−0.604334
$739$	19.2523	0.708206	0.354103	−	0.935206i	$-0.384786\pi$
$739$	19.2523	0.708206	0.354103	+	0.935206i	$0.384786\pi$
$740$	−4.83485	−0.177733
$741$	−16.4174	−0.603109
$742$	0.747727	0.0274499
$743$	29.7477	1.09134	0.545669	−	0.838001i	$-0.316276\pi$
$743$	29.7477	1.09134	0.545669	+	0.838001i	$0.316276\pi$
$744$	−5.66970	−0.207861
$745$	16.7477	0.613589
$746$	50.7477	1.85801
$747$	−11.5826	−0.423784
$748$	−18.1307	−0.662923
$749$	5.16515	0.188731
$750$	1.79129	0.0654086
$751$	−17.4955	−0.638418	−0.319209	−	0.947684i	$-0.603417\pi$
$751$	−17.4955	−0.638418	−0.319209	+	0.947684i	$0.603417\pi$
$752$	−52.4519	−1.91272
$753$	16.1652	0.589091
$754$	−8.20871	−0.298944
$755$	7.16515	0.260767
$756$	1.20871	0.0439604
$757$	−2.33030	−0.0846963	−0.0423481	−	0.999103i	$-0.513484\pi$
$757$	−2.33030	−0.0846963	−0.0423481	+	0.999103i	$0.513484\pi$
$758$	−46.5735	−1.69163
$759$	−20.0000	−0.725954
$760$	−5.07803	−0.184200
$761$	36.4174	1.32013	0.660065	−	0.751208i	$-0.270529\pi$
$761$	36.4174	1.32013	0.660065	+	0.751208i	$0.270529\pi$
$762$	3.58258	0.129783
$763$	14.1652	0.512813
$764$	−4.83485	−0.174919
$765$	−3.00000	−0.108465
$766$	6.41742	0.231871
$767$	34.7477	1.25467
$768$	20.5481	0.741466
$769$	25.5826	0.922531	0.461266	−	0.887262i	$-0.347396\pi$
$769$	25.5826	0.922531	0.461266	+	0.887262i	$0.347396\pi$
$770$	8.95644	0.322768
$771$	12.7477	0.459098
$772$	−24.5735	−0.884419
$773$	−5.16515	−0.185778	−0.0928888	−	0.995676i	$-0.529610\pi$
$773$	−5.16515	−0.185778	−0.0928888	+	0.995676i	$0.529610\pi$
$774$	−17.1652	−0.616989
$775$	4.00000	0.143684
$776$	−16.4174	−0.589351
$777$	−4.00000	−0.143499
$778$	−11.7913	−0.422738
$779$	−32.8348	−1.17643
$780$	−5.53901	−0.198329
$781$	−47.9129	−1.71446
$782$	21.4955	0.768676
$783$	1.00000	0.0357371
$784$	29.7386	1.06209
$785$	10.7477	0.383603
$786$	−26.8693	−0.958397
$787$	−24.0000	−0.855508	−0.427754	−	0.903895i	$-0.640695\pi$
$787$	−24.0000	−0.855508	−0.427754	+	0.903895i	$0.640695\pi$
$788$	−19.7386	−0.703160
$789$	30.3303	1.07979
$790$	13.5826	0.483246
$791$	−14.1652	−0.503655
$792$	−7.08712	−0.251830
$793$	−58.4174	−2.07446
$794$	19.4083	0.688776
$795$	0.417424	0.0148045
$796$	16.2178	0.574825
$797$	32.3303	1.14520	0.572599	−	0.819836i	$-0.305935\pi$
$797$	32.3303	1.14520	0.572599	+	0.819836i	$0.305935\pi$
$798$	6.41742	0.227174
$799$	−31.7477	−1.12315
$800$	−6.04356	−0.213672
$801$	1.41742	0.0500822
$802$	22.2432	0.785434
$803$	20.0000	0.705785
$804$	−5.03447	−0.177552
$805$	−4.00000	−0.140981
$806$	−32.8348	−1.15656
$807$	22.5826	0.794944
$808$	0.825757	0.0290500
$809$	44.0780	1.54970	0.774851	−	0.632145i	$-0.217825\pi$
$809$	44.0780	1.54970	0.774851	+	0.632145i	$0.217825\pi$
$810$	1.79129	0.0629394
$811$	32.5826	1.14413	0.572064	−	0.820209i	$-0.306143\pi$
$811$	32.5826	1.14413	0.572064	+	0.820209i	$0.306143\pi$
$812$	1.20871	0.0424175
$813$	1.16515	0.0408636
$814$	−35.8258	−1.25569
$815$	7.58258	0.265606
$816$	14.8693	0.520530
$817$	−34.3303	−1.20107
$818$	−4.92197	−0.172093
$819$	−4.58258	−0.160128
$820$	−11.0780	−0.386862
$821$	−31.4955	−1.09920	−0.549599	−	0.835428i	$-0.685220\pi$
$821$	−31.4955	−1.09920	−0.549599	+	0.835428i	$0.685220\pi$
$822$	29.2523	1.02029
$823$	51.0780	1.78047	0.890234	−	0.455503i	$-0.150541\pi$
$823$	51.0780	1.78047	0.890234	+	0.455503i	$0.150541\pi$
$824$	−21.4955	−0.748830
$825$	5.00000	0.174078
$826$	−13.5826	−0.472598
$827$	−43.8258	−1.52397	−0.761985	−	0.647594i	$-0.775775\pi$
$827$	−43.8258	−1.52397	−0.761985	+	0.647594i	$0.775775\pi$
$828$	−4.83485	−0.168023
$829$	4.00000	0.138926	0.0694629	−	0.997585i	$-0.477871\pi$
$829$	4.00000	0.138926	0.0694629	+	0.997585i	$0.477871\pi$
$830$	−20.7477	−0.720164
$831$	−24.9129	−0.864218
$832$	4.18333	0.145031
$833$	18.0000	0.623663
$834$	−16.8693	−0.584137
$835$	0	0
$836$	21.6515	0.748833
$837$	4.00000	0.138260
$838$	−66.5735	−2.29974
$839$	−48.4955	−1.67425	−0.837125	−	0.547012i	$-0.815765\pi$
$839$	−48.4955	−1.67425	−0.837125	+	0.547012i	$0.815765\pi$
$840$	−1.41742	−0.0489058
$841$	1.00000	0.0344828
$842$	7.91288	0.272696
$843$	−0.417424	−0.0143769
$844$	24.5735	0.845854
$845$	8.00000	0.275208
$846$	18.9564	0.651736
$847$	14.0000	0.481046
$848$	−2.06894	−0.0710476
$849$	−0.834849	−0.0286519
$850$	−5.37386	−0.184322
$851$	16.0000	0.548473
$852$	−11.5826	−0.396813
$853$	20.7477	0.710389	0.355194	−	0.934792i	$-0.384415\pi$
$853$	20.7477	0.710389	0.355194	+	0.934792i	$0.384415\pi$
$854$	22.8348	0.781392
$855$	3.58258	0.122522
$856$	−7.32121	−0.250234
$857$	−46.6606	−1.59390	−0.796948	−	0.604048i	$-0.793554\pi$
$857$	−46.6606	−1.59390	−0.796948	+	0.604048i	$0.793554\pi$
$858$	−41.0436	−1.40120
$859$	−47.5826	−1.62350	−0.811748	−	0.584007i	$-0.801484\pi$
$859$	−47.5826	−1.62350	−0.811748	+	0.584007i	$0.801484\pi$
$860$	−11.5826	−0.394963
$861$	−9.16515	−0.312348
$862$	−70.1561	−2.38952
$863$	−6.41742	−0.218452	−0.109226	−	0.994017i	$-0.534837\pi$
$863$	−6.41742	−0.218452	−0.109226	+	0.994017i	$0.534837\pi$
$864$	−6.04356	−0.205606
$865$	−3.16515	−0.107618
$866$	44.9220	1.52651
$867$	−8.00000	−0.271694
$868$	4.83485	0.164105
$869$	37.9129	1.28611
$870$	1.79129	0.0607303
$871$	19.0871	0.646742
$872$	−20.0780	−0.679928
$873$	11.5826	0.392011
$874$	−25.6697	−0.868290
$875$	1.00000	0.0338062
$876$	4.83485	0.163354
$877$	19.6697	0.664198	0.332099	−	0.943244i	$-0.392243\pi$
$877$	19.6697	0.664198	0.332099	+	0.943244i	$0.392243\pi$
$878$	−30.2958	−1.02243
$879$	30.1652	1.01745
$880$	−24.7822	−0.835408
$881$	−32.0780	−1.08074	−0.540368	−	0.841429i	$-0.681715\pi$
$881$	−32.0780	−1.08074	−0.540368	+	0.841429i	$0.681715\pi$
$882$	−10.7477	−0.361895
$883$	16.0000	0.538443	0.269221	−	0.963078i	$-0.413234\pi$
$883$	16.0000	0.538443	0.269221	+	0.963078i	$0.413234\pi$
$884$	16.6170	0.558892
$885$	−7.58258	−0.254885
$886$	1.04356	0.0350591
$887$	−44.9129	−1.50803	−0.754013	−	0.656859i	$-0.771885\pi$
$887$	−44.9129	−1.50803	−0.754013	+	0.656859i	$0.771885\pi$
$888$	5.66970	0.190263
$889$	2.00000	0.0670778
$890$	2.53901	0.0851080
$891$	5.00000	0.167506
$892$	8.46099	0.283295
$893$	37.9129	1.26871
$894$	30.0000	1.00335
$895$	4.74773	0.158699
$896$	10.4519	0.349173
$897$	18.3303	0.612031
$898$	−53.8784	−1.79795
$899$	4.00000	0.133407
$900$	1.20871	0.0402904
$901$	−1.25227	−0.0417193
$902$	−82.0871	−2.73320
$903$	−9.58258	−0.318888
$904$	20.0780	0.667785
$905$	16.1652	0.537348
$906$	12.8348	0.426409
$907$	23.5826	0.783047	0.391523	−	0.920168i	$-0.371948\pi$
$907$	23.5826	0.783047	0.391523	+	0.920168i	$0.371948\pi$
$908$	−9.16515	−0.304156
$909$	−0.582576	−0.0193228
$910$	−8.20871	−0.272116
$911$	−50.8258	−1.68393	−0.841966	−	0.539530i	$-0.818602\pi$
$911$	−50.8258	−1.68393	−0.841966	+	0.539530i	$0.818602\pi$
$912$	−17.7568	−0.587987
$913$	−57.9129	−1.91664
$914$	−6.71326	−0.222055
$915$	12.7477	0.421427
$916$	−20.7477	−0.685524
$917$	−15.0000	−0.495344
$918$	−5.37386	−0.177364
$919$	18.9129	0.623878	0.311939	−	0.950102i	$-0.399021\pi$
$919$	18.9129	0.623878	0.311939	+	0.950102i	$0.399021\pi$
$920$	5.66970	0.186924
$921$	0	0
$922$	−16.4174	−0.540679
$923$	43.9129	1.44541
$924$	6.04356	0.198819
$925$	−4.00000	−0.131519
$926$	−0.295834	−0.00972170
$927$	15.1652	0.498089
$928$	−6.04356	−0.198390
$929$	15.6697	0.514106	0.257053	−	0.966397i	$-0.417248\pi$
$929$	15.6697	0.514106	0.257053	+	0.966397i	$0.417248\pi$
$930$	7.16515	0.234955
$931$	−21.4955	−0.704485
$932$	−15.9129	−0.521244
$933$	−3.00000	−0.0982156
$934$	−14.3303	−0.468902
$935$	−15.0000	−0.490552
$936$	6.49545	0.212311
$937$	−18.5826	−0.607066	−0.303533	−	0.952821i	$-0.598166\pi$
$937$	−18.5826	−0.607066	−0.303533	+	0.952821i	$0.598166\pi$
$938$	−7.46099	−0.243610
$939$	10.5826	0.345349
$940$	12.7913	0.417206
$941$	19.9129	0.649141	0.324571	−	0.945861i	$-0.394780\pi$
$941$	19.9129	0.649141	0.324571	+	0.945861i	$0.394780\pi$
$942$	19.2523	0.627273
$943$	36.6606	1.19383
$944$	37.5826	1.22321
$945$	1.00000	0.0325300
$946$	−85.8258	−2.79044
$947$	−54.9129	−1.78443	−0.892214	−	0.451612i	$-0.850849\pi$
$947$	−54.9129	−1.78443	−0.892214	+	0.451612i	$0.850849\pi$
$948$	9.16515	0.297670
$949$	−18.3303	−0.595027
$950$	6.41742	0.208209
$951$	−25.0000	−0.810681
$952$	4.25227	0.137817
$953$	−37.5826	−1.21742	−0.608710	−	0.793393i	$-0.708313\pi$
$953$	−37.5826	−1.21742	−0.608710	+	0.793393i	$0.708313\pi$
$954$	0.747727	0.0242086
$955$	−4.00000	−0.129437
$956$	−31.4265	−1.01641
$957$	5.00000	0.161627
$958$	−34.3303	−1.10916
$959$	16.3303	0.527333
$960$	−0.912878	−0.0294630
$961$	−15.0000	−0.483871
$962$	32.8348	1.05864
$963$	5.16515	0.166445
$964$	35.4519	1.14183
$965$	−20.3303	−0.654456
$966$	−7.16515	−0.230535
$967$	9.25227	0.297533	0.148767	−	0.988872i	$-0.452470\pi$
$967$	9.25227	0.297533	0.148767	+	0.988872i	$0.452470\pi$
$968$	−19.8439	−0.637808
$969$	−10.7477	−0.345267
$970$	20.7477	0.666169
$971$	20.0000	0.641831	0.320915	−	0.947108i	$-0.396010\pi$
$971$	20.0000	0.641831	0.320915	+	0.947108i	$0.396010\pi$
$972$	1.20871	0.0387695
$973$	−9.41742	−0.301909
$974$	4.17424	0.133751
$975$	−4.58258	−0.146760
$976$	−63.1833	−2.02245
$977$	−2.50455	−0.0801275	−0.0400638	−	0.999197i	$-0.512756\pi$
$977$	−2.50455	−0.0801275	−0.0400638	+	0.999197i	$0.512756\pi$
$978$	13.5826	0.434323
$979$	7.08712	0.226505
$980$	−7.25227	−0.231665
$981$	14.1652	0.452258
$982$	28.6606	0.914597
$983$	55.1652	1.75950	0.879748	−	0.475441i	$-0.157712\pi$
$983$	55.1652	1.75950	0.879748	+	0.475441i	$0.157712\pi$
$984$	12.9909	0.414135
$985$	−16.3303	−0.520327
$986$	−5.37386	−0.171139
$987$	10.5826	0.336847
$988$	−19.8439	−0.631320
$989$	38.3303	1.21883
$990$	8.95644	0.284654
$991$	16.0780	0.510735	0.255368	−	0.966844i	$-0.417803\pi$
$991$	16.0780	0.510735	0.255368	+	0.966844i	$0.417803\pi$
$992$	−24.1742	−0.767533
$993$	−8.33030	−0.264354
$994$	−17.1652	−0.544446
$995$	13.4174	0.425361
$996$	−14.0000	−0.443607
$997$	−0.834849	−0.0264399	−0.0132200	−	0.999913i	$-0.504208\pi$
$997$	−0.834849	−0.0264399	−0.0132200	+	0.999913i	$0.504208\pi$
$998$	−24.0345	−0.760798
$999$	−4.00000	−0.126554

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	435.2.a.f.1.2	✓	2
3.2	odd	2		1305.2.a.m.1.1		2
4.3	odd	2		6960.2.a.bw.1.1		2
5.2	odd	4		2175.2.c.f.349.3		4
5.3	odd	4		2175.2.c.f.349.2		4
5.4	even	2		2175.2.a.r.1.1		2
15.14	odd	2		6525.2.a.t.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
435.2.a.f.1.2	✓	2	1.1	even	1	trivial
1305.2.a.m.1.1		2	3.2	odd	2
2175.2.a.r.1.1		2	5.4	even	2
2175.2.c.f.349.2		4	5.3	odd	4
2175.2.c.f.349.3		4	5.2	odd	4
6525.2.a.t.1.2		2	15.14	odd	2
6960.2.a.bw.1.1		2	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 435 = 3 \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	435.a (trivial)

\(f(q)\)	\(=\)	\(q+1.79129 q^{2} +1.00000 q^{3} +1.20871 q^{4} +1.00000 q^{5} +1.79129 q^{6} +1.00000 q^{7} -1.41742 q^{8} +1.00000 q^{9} +1.79129 q^{10} +5.00000 q^{11} +1.20871 q^{12} -4.58258 q^{13} +1.79129 q^{14} +1.00000 q^{15} -4.95644 q^{16} -3.00000 q^{17} +1.79129 q^{18} +3.58258 q^{19} +1.20871 q^{20} +1.00000 q^{21} +8.95644 q^{22} -4.00000 q^{23} -1.41742 q^{24} +1.00000 q^{25} -8.20871 q^{26} +1.00000 q^{27} +1.20871 q^{28} +1.00000 q^{29} +1.79129 q^{30} +4.00000 q^{31} -6.04356 q^{32} +5.00000 q^{33} -5.37386 q^{34} +1.00000 q^{35} +1.20871 q^{36} -4.00000 q^{37} +6.41742 q^{38} -4.58258 q^{39} -1.41742 q^{40} -9.16515 q^{41} +1.79129 q^{42} -9.58258 q^{43} +6.04356 q^{44} +1.00000 q^{45} -7.16515 q^{46} +10.5826 q^{47} -4.95644 q^{48} -6.00000 q^{49} +1.79129 q^{50} -3.00000 q^{51} -5.53901 q^{52} +0.417424 q^{53} +1.79129 q^{54} +5.00000 q^{55} -1.41742 q^{56} +3.58258 q^{57} +1.79129 q^{58} -7.58258 q^{59} +1.20871 q^{60} +12.7477 q^{61} +7.16515 q^{62} +1.00000 q^{63} -0.912878 q^{64} -4.58258 q^{65} +8.95644 q^{66} -4.16515 q^{67} -3.62614 q^{68} -4.00000 q^{69} +1.79129 q^{70} -9.58258 q^{71} -1.41742 q^{72} +4.00000 q^{73} -7.16515 q^{74} +1.00000 q^{75} +4.33030 q^{76} +5.00000 q^{77} -8.20871 q^{78} +7.58258 q^{79} -4.95644 q^{80} +1.00000 q^{81} -16.4174 q^{82} -11.5826 q^{83} +1.20871 q^{84} -3.00000 q^{85} -17.1652 q^{86} +1.00000 q^{87} -7.08712 q^{88} +1.41742 q^{89} +1.79129 q^{90} -4.58258 q^{91} -4.83485 q^{92} +4.00000 q^{93} +18.9564 q^{94} +3.58258 q^{95} -6.04356 q^{96} +11.5826 q^{97} -10.7477 q^{98} +5.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} + 2 q^{3} + 7 q^{4} + 2 q^{5} - q^{6} + 2 q^{7} - 12 q^{8} + 2 q^{9} - q^{10} + 10 q^{11} + 7 q^{12} - q^{14} + 2 q^{15} + 13 q^{16} - 6 q^{17} - q^{18} - 2 q^{19} + 7 q^{20} + 2 q^{21}+ \cdots + 10 q^{99}+O(q^{100}) \) 2 * q - q^2 + 2 * q^3 + 7 * q^4 + 2 * q^5 - q^6 + 2 * q^7 - 12 * q^8 + 2 * q^9 - q^10 + 10 * q^11 + 7 * q^12 - q^14 + 2 * q^15 + 13 * q^16 - 6 * q^17 - q^18 - 2 * q^19 + 7 * q^20 + 2 * q^21 - 5 * q^22 - 8 * q^23 - 12 * q^24 + 2 * q^25 - 21 * q^26 + 2 * q^27 + 7 * q^28 + 2 * q^29 - q^30 + 8 * q^31 - 35 * q^32 + 10 * q^33 + 3 * q^34 + 2 * q^35 + 7 * q^36 - 8 * q^37 + 22 * q^38 - 12 * q^40 - q^42 - 10 * q^43 + 35 * q^44 + 2 * q^45 + 4 * q^46 + 12 * q^47 + 13 * q^48 - 12 * q^49 - q^50 - 6 * q^51 + 21 * q^52 + 10 * q^53 - q^54 + 10 * q^55 - 12 * q^56 - 2 * q^57 - q^58 - 6 * q^59 + 7 * q^60 - 2 * q^61 - 4 * q^62 + 2 * q^63 + 44 * q^64 - 5 * q^66 + 10 * q^67 - 21 * q^68 - 8 * q^69 - q^70 - 10 * q^71 - 12 * q^72 + 8 * q^73 + 4 * q^74 + 2 * q^75 - 28 * q^76 + 10 * q^77 - 21 * q^78 + 6 * q^79 + 13 * q^80 + 2 * q^81 - 42 * q^82 - 14 * q^83 + 7 * q^84 - 6 * q^85 - 16 * q^86 + 2 * q^87 - 60 * q^88 + 12 * q^89 - q^90 - 28 * q^92 + 8 * q^93 + 15 * q^94 - 2 * q^95 - 35 * q^96 + 14 * q^97 + 6 * q^98 + 10 * q^99

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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