LMFDB - Embedded newform 3850.2.c.s.1849.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3850,2,Mod(1849,3850)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3850, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 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("3850.1849");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3850 = 2 \cdot 5^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3850.c (of order $2$, degree $1$, not minimal)

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:	no
Analytic conductor:	$30.7424047782$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 770)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1849.3
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	3850.1849
Dual form			3850.2.c.s.1849.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} -0.732051i q^{3} -1.00000 q^{4} +0.732051 q^{6} -1.00000i q^{7} -1.00000i q^{8} +2.46410 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} -0.732051i q^{3} -1.00000 q^{4} +0.732051 q^{6} -1.00000i q^{7} -1.00000i q^{8} +2.46410 q^{9} +1.00000 q^{11} +0.732051i q^{12} +5.46410i q^{13} +1.00000 q^{14} +1.00000 q^{16} +3.46410i q^{17} +2.46410i q^{18} -0.732051 q^{19} -0.732051 q^{21} +1.00000i q^{22} +4.73205i q^{23} -0.732051 q^{24} -5.46410 q^{26} -4.00000i q^{27} +1.00000i q^{28} +1.26795 q^{29} -4.92820 q^{31} +1.00000i q^{32} -0.732051i q^{33} -3.46410 q^{34} -2.46410 q^{36} -6.73205i q^{37} -0.732051i q^{38} +4.00000 q^{39} -1.26795 q^{41} -0.732051i q^{42} +8.92820i q^{43} -1.00000 q^{44} -4.73205 q^{46} -0.732051i q^{48} -1.00000 q^{49} +2.53590 q^{51} -5.46410i q^{52} -1.26795i q^{53} +4.00000 q^{54} -1.00000 q^{56} +0.535898i q^{57} +1.26795i q^{58} -13.8564 q^{59} +2.00000 q^{61} -4.92820i q^{62} -2.46410i q^{63} -1.00000 q^{64} +0.732051 q^{66} -2.92820i q^{67} -3.46410i q^{68} +3.46410 q^{69} +2.53590 q^{71} -2.46410i q^{72} +4.53590i q^{73} +6.73205 q^{74} +0.732051 q^{76} -1.00000i q^{77} +4.00000i q^{78} -3.26795 q^{79} +4.46410 q^{81} -1.26795i q^{82} +16.3923i q^{83} +0.732051 q^{84} -8.92820 q^{86} -0.928203i q^{87} -1.00000i q^{88} +8.53590 q^{89} +5.46410 q^{91} -4.73205i q^{92} +3.60770i q^{93} +0.732051 q^{96} -16.1962i q^{97} -1.00000i q^{98} +2.46410 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{4} - 4 q^{6} - 4 q^{9}+O(q^{10}) $ 4 * q - 4 * q^4 - 4 * q^6 - 4 * q^9	$ 4 q - 4 q^{4} - 4 q^{6} - 4 q^{9} + 4 q^{11} + 4 q^{14} + 4 q^{16} + 4 q^{19} + 4 q^{21} + 4 q^{24} - 8 q^{26} + 12 q^{29} + 8 q^{31} + 4 q^{36} + 16 q^{39} - 12 q^{41} - 4 q^{44} - 12 q^{46} - 4 q^{49} + 24 q^{51} + 16 q^{54} - 4 q^{56} + 8 q^{61} - 4 q^{64} - 4 q^{66} + 24 q^{71} + 20 q^{74} - 4 q^{76} - 20 q^{79} + 4 q^{81} - 4 q^{84} - 8 q^{86} + 48 q^{89} + 8 q^{91} - 4 q^{96} - 4 q^{99}+O(q^{100}) $ 4 * q - 4 * q^4 - 4 * q^6 - 4 * q^9 + 4 * q^11 + 4 * q^14 + 4 * q^16 + 4 * q^19 + 4 * q^21 + 4 * q^24 - 8 * q^26 + 12 * q^29 + 8 * q^31 + 4 * q^36 + 16 * q^39 - 12 * q^41 - 4 * q^44 - 12 * q^46 - 4 * q^49 + 24 * q^51 + 16 * q^54 - 4 * q^56 + 8 * q^61 - 4 * q^64 - 4 * q^66 + 24 * q^71 + 20 * q^74 - 4 * q^76 - 20 * q^79 + 4 * q^81 - 4 * q^84 - 8 * q^86 + 48 * q^89 + 8 * q^91 - 4 * q^96 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3850\mathbb{Z}\right)^\times$.

$n$	$1751$	$2201$	$2927$
$\chi(n)$	$1$	$1$	$-1$

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 $

$2$	1.00000i	0.707107i
$2$	1.00000i	0.707107i
$3$	− 0.732051i	− 0.422650i	−0.977416	−	0.211325i	$-0.932222\pi$
$3$	− 0.732051i	− 0.422650i	0.977416	−	0.211325i	$-0.0677778\pi$
$4$	−1.00000	−0.500000
$5$	0	0
$5$	0	0
$6$	0.732051	0.298858
$7$	− 1.00000i	− 0.377964i
$7$	− 1.00000i	− 0.377964i
$8$	− 1.00000i	− 0.353553i
$9$	2.46410	0.821367
$10$	0	0
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	0.732051i	0.211325i
$13$	5.46410i	1.51547i	0.652563	+	0.757735i	$0.273694\pi$
$13$	5.46410i	1.51547i	−0.652563	+	0.757735i	$0.726306\pi$
$14$	1.00000	0.267261
$15$	0	0
$16$	1.00000	0.250000
$17$	3.46410i	0.840168i	0.907485	+	0.420084i	$0.137999\pi$
$17$	3.46410i	0.840168i	−0.907485	+	0.420084i	$0.862001\pi$
$18$	2.46410i	0.580794i
$19$	−0.732051	−0.167944	−0.0839720	−	0.996468i	$-0.526761\pi$
$19$	−0.732051	−0.167944	−0.0839720	+	0.996468i	$0.526761\pi$
$20$	0	0
$21$	−0.732051	−0.159747
$22$	1.00000i	0.213201i
$23$	4.73205i	0.986701i	0.869831	+	0.493350i	$0.164228\pi$
$23$	4.73205i	0.986701i	−0.869831	+	0.493350i	$0.835772\pi$
$24$	−0.732051	−0.149429
$25$	0	0
$26$	−5.46410	−1.07160
$27$	− 4.00000i	− 0.769800i
$28$	1.00000i	0.188982i
$29$	1.26795	0.235452	0.117726	−	0.993046i	$-0.462440\pi$
$29$	1.26795	0.235452	0.117726	+	0.993046i	$0.462440\pi$
$30$	0	0
$31$	−4.92820	−0.885131	−0.442566	−	0.896736i	$-0.645932\pi$
$31$	−4.92820	−0.885131	−0.442566	+	0.896736i	$0.645932\pi$
$32$	1.00000i	0.176777i
$33$	− 0.732051i	− 0.127434i
$34$	−3.46410	−0.594089
$35$	0	0
$36$	−2.46410	−0.410684
$37$	− 6.73205i	− 1.10674i	−0.832935	−	0.553371i	$-0.813341\pi$
$37$	− 6.73205i	− 1.10674i	0.832935	−	0.553371i	$-0.186659\pi$
$38$	− 0.732051i	− 0.118754i
$39$	4.00000	0.640513
$40$	0	0
$41$	−1.26795	−0.198020	−0.0990102	−	0.995086i	$-0.531568\pi$
$41$	−1.26795	−0.198020	−0.0990102	+	0.995086i	$0.531568\pi$
$42$	− 0.732051i	− 0.112958i
$43$	8.92820i	1.36154i	0.732498	+	0.680769i	$0.238354\pi$
$43$	8.92820i	1.36154i	−0.732498	+	0.680769i	$0.761646\pi$
$44$	−1.00000	−0.150756
$45$	0	0
$46$	−4.73205	−0.697703
$47$	0	0	1.00000			$0$
$47$	0	0	−1.00000			$\pi$
$48$	− 0.732051i	− 0.105662i
$49$	−1.00000	−0.142857
$50$	0	0
$51$	2.53590	0.355097
$52$	− 5.46410i	− 0.757735i
$53$	− 1.26795i	− 0.174166i	−0.996201	−	0.0870831i	$-0.972245\pi$
$53$	− 1.26795i	− 0.174166i	0.996201	−	0.0870831i	$-0.0277546\pi$
$54$	4.00000	0.544331
$55$	0	0
$56$	−1.00000	−0.133631
$57$	0.535898i	0.0709815i
$58$	1.26795i	0.166490i
$59$	−13.8564	−1.80395	−0.901975	−	0.431788i	$-0.857883\pi$
$59$	−13.8564	−1.80395	−0.901975	+	0.431788i	$0.857883\pi$
$60$	0	0
$61$	2.00000	0.256074	0.128037	−	0.991769i	$-0.459132\pi$
$61$	2.00000	0.256074	0.128037	+	0.991769i	$0.459132\pi$
$62$	− 4.92820i	− 0.625882i
$63$	− 2.46410i	− 0.310448i
$64$	−1.00000	−0.125000
$65$	0	0
$66$	0.732051	0.0901092
$67$	− 2.92820i	− 0.357737i	−0.983873	−	0.178868i	$-0.942756\pi$
$67$	− 2.92820i	− 0.357737i	0.983873	−	0.178868i	$-0.0572437\pi$
$68$	− 3.46410i	− 0.420084i
$69$	3.46410	0.417029
$70$	0	0
$71$	2.53590	0.300956	0.150478	−	0.988613i	$-0.451919\pi$
$71$	2.53590	0.300956	0.150478	+	0.988613i	$0.451919\pi$
$72$	− 2.46410i	− 0.290397i
$73$	4.53590i	0.530887i	0.964126	+	0.265443i	$0.0855183\pi$
$73$	4.53590i	0.530887i	−0.964126	+	0.265443i	$0.914482\pi$
$74$	6.73205	0.782585
$75$	0	0
$76$	0.732051	0.0839720
$77$	− 1.00000i	− 0.113961i
$78$	4.00000i	0.452911i
$79$	−3.26795	−0.367673	−0.183837	−	0.982957i	$-0.558852\pi$
$79$	−3.26795	−0.367673	−0.183837	+	0.982957i	$0.558852\pi$
$80$	0	0
$81$	4.46410	0.496011
$82$	− 1.26795i	− 0.140022i
$83$	16.3923i	1.79929i	0.436623	+	0.899645i	$0.356174\pi$
$83$	16.3923i	1.79929i	−0.436623	+	0.899645i	$0.643826\pi$
$84$	0.732051	0.0798733
$85$	0	0
$86$	−8.92820	−0.962753
$87$	− 0.928203i	− 0.0995138i
$88$	− 1.00000i	− 0.106600i
$89$	8.53590	0.904803	0.452402	−	0.891814i	$-0.350567\pi$
$89$	8.53590	0.904803	0.452402	+	0.891814i	$0.350567\pi$
$90$	0	0
$91$	5.46410	0.572793
$92$	− 4.73205i	− 0.493350i
$93$	3.60770i	0.374101i
$94$	0	0
$95$	0	0
$96$	0.732051	0.0747146
$97$	− 16.1962i	− 1.64447i	−0.569148	−	0.822235i	$-0.692727\pi$
$97$	− 16.1962i	− 1.64447i	0.569148	−	0.822235i	$-0.307273\pi$
$98$	− 1.00000i	− 0.101015i
$99$	2.46410	0.247652
$100$	0	0
$101$	−6.00000	−0.597022	−0.298511	−	0.954406i	$-0.596490\pi$
$101$	−6.00000	−0.597022	−0.298511	+	0.954406i	$0.596490\pi$
$102$	2.53590i	0.251091i
$103$	17.4641i	1.72079i	0.509629	+	0.860395i	$0.329783\pi$
$103$	17.4641i	1.72079i	−0.509629	+	0.860395i	$0.670217\pi$
$104$	5.46410	0.535799
$105$	0	0
$106$	1.26795	0.123154
$107$	12.9282i	1.24982i	0.780698	+	0.624908i	$0.214864\pi$
$107$	12.9282i	1.24982i	−0.780698	+	0.624908i	$0.785136\pi$
$108$	4.00000i	0.384900i
$109$	12.1962	1.16818	0.584090	−	0.811689i	$-0.301452\pi$
$109$	12.1962	1.16818	0.584090	+	0.811689i	$0.301452\pi$
$110$	0	0
$111$	−4.92820	−0.467764
$112$	− 1.00000i	− 0.0944911i
$113$	− 0.928203i	− 0.0873180i	−0.999046	−	0.0436590i	$-0.986098\pi$
$113$	− 0.928203i	− 0.0873180i	0.999046	−	0.0436590i	$-0.0139015\pi$
$114$	−0.535898	−0.0501915
$115$	0	0
$116$	−1.26795	−0.117726
$117$	13.4641i	1.24476i
$118$	− 13.8564i	− 1.27559i
$119$	3.46410	0.317554
$120$	0	0
$121$	1.00000	0.0909091
$122$	2.00000i	0.181071i
$123$	0.928203i	0.0836933i
$124$	4.92820	0.442566
$125$	0	0
$126$	2.46410	0.219520
$127$	17.8564i	1.58450i	0.610197	+	0.792250i	$0.291090\pi$
$127$	17.8564i	1.58450i	−0.610197	+	0.792250i	$0.708910\pi$
$128$	− 1.00000i	− 0.0883883i
$129$	6.53590	0.575454
$130$	0	0
$131$	−0.339746	−0.0296837	−0.0148419	−	0.999890i	$-0.504724\pi$
$131$	−0.339746	−0.0296837	−0.0148419	+	0.999890i	$0.504724\pi$
$132$	0.732051i	0.0637168i
$133$	0.732051i	0.0634769i
$134$	2.92820	0.252958
$135$	0	0
$136$	3.46410	0.297044
$137$	19.8564i	1.69645i	0.529638	+	0.848224i	$0.322328\pi$
$137$	19.8564i	1.69645i	−0.529638	+	0.848224i	$0.677672\pi$
$138$	3.46410i	0.294884i
$139$	6.19615	0.525551	0.262775	−	0.964857i	$-0.415362\pi$
$139$	6.19615	0.525551	0.262775	+	0.964857i	$0.415362\pi$
$140$	0	0
$141$	0	0
$142$	2.53590i	0.212808i
$143$	5.46410i	0.456931i
$144$	2.46410	0.205342
$145$	0	0
$146$	−4.53590	−0.375394
$147$	0.732051i	0.0603785i
$148$	6.73205i	0.553371i
$149$	10.7321	0.879204	0.439602	−	0.898193i	$-0.355120\pi$
$149$	10.7321	0.879204	0.439602	+	0.898193i	$0.355120\pi$
$150$	0	0
$151$	−18.1962	−1.48078	−0.740391	−	0.672177i	$-0.765360\pi$
$151$	−18.1962	−1.48078	−0.740391	+	0.672177i	$0.765360\pi$
$152$	0.732051i	0.0593772i
$153$	8.53590i	0.690086i
$154$	1.00000	0.0805823
$155$	0	0
$156$	−4.00000	−0.320256
$157$	14.3923i	1.14863i	0.818634	+	0.574315i	$0.194732\pi$
$157$	14.3923i	1.14863i	−0.818634	+	0.574315i	$0.805268\pi$
$158$	− 3.26795i	− 0.259984i
$159$	−0.928203	−0.0736113
$160$	0	0
$161$	4.73205	0.372938
$162$	4.46410i	0.350733i
$163$	8.00000i	0.626608i	0.949653	+	0.313304i	$0.101436\pi$
$163$	8.00000i	0.626608i	−0.949653	+	0.313304i	$0.898564\pi$
$164$	1.26795	0.0990102
$165$	0	0
$166$	−16.3923	−1.27229
$167$	− 13.8564i	− 1.07224i	−0.844141	−	0.536120i	$-0.819889\pi$
$167$	− 13.8564i	− 1.07224i	0.844141	−	0.536120i	$-0.180111\pi$
$168$	0.732051i	0.0564789i
$169$	−16.8564	−1.29665
$170$	0	0
$171$	−1.80385	−0.137944
$172$	− 8.92820i	− 0.680769i
$173$	− 12.9282i	− 0.982913i	−0.870902	−	0.491457i	$-0.836465\pi$
$173$	− 12.9282i	− 0.982913i	0.870902	−	0.491457i	$-0.163535\pi$
$174$	0.928203	0.0703669
$175$	0	0
$176$	1.00000	0.0753778
$177$	10.1436i	0.762439i
$178$	8.53590i	0.639793i
$179$	−7.85641	−0.587215	−0.293608	−	0.955926i	$-0.594856\pi$
$179$	−7.85641	−0.587215	−0.293608	+	0.955926i	$0.594856\pi$
$180$	0	0
$181$	15.8564	1.17860	0.589299	−	0.807915i	$-0.299404\pi$
$181$	15.8564	1.17860	0.589299	+	0.807915i	$0.299404\pi$
$182$	5.46410i	0.405026i
$183$	− 1.46410i	− 0.108230i
$184$	4.73205	0.348851
$185$	0	0
$186$	−3.60770	−0.264529
$187$	3.46410i	0.253320i
$188$	0	0
$189$	−4.00000	−0.290957
$190$	0	0
$191$	−6.92820	−0.501307	−0.250654	−	0.968077i	$-0.580646\pi$
$191$	−6.92820	−0.501307	−0.250654	+	0.968077i	$0.580646\pi$
$192$	0.732051i	0.0528312i
$193$	− 18.5359i	− 1.33424i	−0.744949	−	0.667122i	$-0.767526\pi$
$193$	− 18.5359i	− 1.33424i	0.744949	−	0.667122i	$-0.232474\pi$
$194$	16.1962	1.16282
$195$	0	0
$196$	1.00000	0.0714286
$197$	1.60770i	0.114544i	0.998359	+	0.0572718i	$0.0182402\pi$
$197$	1.60770i	0.114544i	−0.998359	+	0.0572718i	$0.981760\pi$
$198$	2.46410i	0.175116i
$199$	−16.7846	−1.18983	−0.594915	−	0.803789i	$-0.702814\pi$
$199$	−16.7846	−1.18983	−0.594915	+	0.803789i	$0.702814\pi$
$200$	0	0
$201$	−2.14359	−0.151197
$202$	− 6.00000i	− 0.422159i
$203$	− 1.26795i	− 0.0889926i
$204$	−2.53590	−0.177548
$205$	0	0
$206$	−17.4641	−1.21678
$207$	11.6603i	0.810444i
$208$	5.46410i	0.378867i
$209$	−0.732051	−0.0506370
$210$	0	0
$211$	8.00000	0.550743	0.275371	−	0.961338i	$-0.411199\pi$
$211$	8.00000	0.550743	0.275371	+	0.961338i	$0.411199\pi$
$212$	1.26795i	0.0870831i
$213$	− 1.85641i	− 0.127199i
$214$	−12.9282	−0.883754
$215$	0	0
$216$	−4.00000	−0.272166
$217$	4.92820i	0.334548i
$218$	12.1962i	0.826028i
$219$	3.32051	0.224379
$220$	0	0
$221$	−18.9282	−1.27325
$222$	− 4.92820i	− 0.330759i
$223$	12.3923i	0.829850i	0.909856	+	0.414925i	$0.136192\pi$
$223$	12.3923i	0.829850i	−0.909856	+	0.414925i	$0.863808\pi$
$224$	1.00000	0.0668153
$225$	0	0
$226$	0.928203	0.0617432
$227$	13.8564i	0.919682i	0.888001	+	0.459841i	$0.152094\pi$
$227$	13.8564i	0.919682i	−0.888001	+	0.459841i	$0.847906\pi$
$228$	− 0.535898i	− 0.0354907i
$229$	6.53590	0.431904	0.215952	−	0.976404i	$-0.430714\pi$
$229$	6.53590	0.431904	0.215952	+	0.976404i	$0.430714\pi$
$230$	0	0
$231$	−0.732051	−0.0481654
$232$	− 1.26795i	− 0.0832449i
$233$	− 19.8564i	− 1.30084i	−0.759576	−	0.650418i	$-0.774594\pi$
$233$	− 19.8564i	− 1.30084i	0.759576	−	0.650418i	$-0.225406\pi$
$234$	−13.4641	−0.880176
$235$	0	0
$236$	13.8564	0.901975
$237$	2.39230i	0.155397i
$238$	3.46410i	0.224544i
$239$	14.1962	0.918273	0.459136	−	0.888366i	$-0.348159\pi$
$239$	14.1962	0.918273	0.459136	+	0.888366i	$0.348159\pi$
$240$	0	0
$241$	−7.80385	−0.502690	−0.251345	−	0.967898i	$-0.580873\pi$
$241$	−7.80385	−0.502690	−0.251345	+	0.967898i	$0.580873\pi$
$242$	1.00000i	0.0642824i
$243$	− 15.2679i	− 0.979439i
$244$	−2.00000	−0.128037
$245$	0	0
$246$	−0.928203	−0.0591801
$247$	− 4.00000i	− 0.254514i
$248$	4.92820i	0.312941i
$249$	12.0000	0.760469
$250$	0	0
$251$	0	0		−	1.00000i	$-0.5\pi$
$251$	0	0			1.00000i	$0.5\pi$
$252$	2.46410i	0.155224i
$253$	4.73205i	0.297501i
$254$	−17.8564	−1.12041
$255$	0	0
$256$	1.00000	0.0625000
$257$	28.9808i	1.80777i	0.427775	+	0.903885i	$0.359297\pi$
$257$	28.9808i	1.80777i	−0.427775	+	0.903885i	$0.640703\pi$
$258$	6.53590i	0.406907i
$259$	−6.73205	−0.418309
$260$	0	0
$261$	3.12436	0.193393
$262$	− 0.339746i	− 0.0209896i
$263$	5.07180i	0.312740i	0.987699	+	0.156370i	$0.0499793\pi$
$263$	5.07180i	0.312740i	−0.987699	+	0.156370i	$0.950021\pi$
$264$	−0.732051	−0.0450546
$265$	0	0
$266$	−0.732051	−0.0448849
$267$	− 6.24871i	− 0.382415i
$268$	2.92820i	0.178868i
$269$	16.3923	0.999456	0.499728	−	0.866182i	$-0.333433\pi$
$269$	16.3923	0.999456	0.499728	+	0.866182i	$0.333433\pi$
$270$	0	0
$271$	3.60770	0.219152	0.109576	−	0.993978i	$-0.465051\pi$
$271$	3.60770	0.219152	0.109576	+	0.993978i	$0.465051\pi$
$272$	3.46410i	0.210042i
$273$	− 4.00000i	− 0.242091i
$274$	−19.8564	−1.19957
$275$	0	0
$276$	−3.46410	−0.208514
$277$	− 0.143594i	− 0.00862770i	−0.999991	−	0.00431385i	$-0.998627\pi$
$277$	− 0.143594i	− 0.00862770i	0.999991	−	0.00431385i	$-0.00137315\pi$
$278$	6.19615i	0.371621i
$279$	−12.1436	−0.727018
$280$	0	0
$281$	10.3923	0.619953	0.309976	−	0.950744i	$-0.399679\pi$
$281$	10.3923	0.619953	0.309976	+	0.950744i	$0.399679\pi$
$282$	0	0
$283$	2.92820i	0.174064i	0.996206	+	0.0870318i	$0.0277382\pi$
$283$	2.92820i	0.174064i	−0.996206	+	0.0870318i	$0.972262\pi$
$284$	−2.53590	−0.150478
$285$	0	0
$286$	−5.46410	−0.323099
$287$	1.26795i	0.0748447i
$288$	2.46410i	0.145199i
$289$	5.00000	0.294118
$290$	0	0
$291$	−11.8564	−0.695035
$292$	− 4.53590i	− 0.265443i
$293$	− 9.46410i	− 0.552899i	−0.961028	−	0.276449i	$-0.910842\pi$
$293$	− 9.46410i	− 0.552899i	0.961028	−	0.276449i	$-0.0891578\pi$
$294$	−0.732051	−0.0426941
$295$	0	0
$296$	−6.73205	−0.391293
$297$	− 4.00000i	− 0.232104i
$298$	10.7321i	0.621691i
$299$	−25.8564	−1.49531
$300$	0	0
$301$	8.92820	0.514613
$302$	− 18.1962i	− 1.04707i
$303$	4.39230i	0.252331i
$304$	−0.732051	−0.0419860
$305$	0	0
$306$	−8.53590	−0.487965
$307$	3.32051i	0.189511i	0.995501	+	0.0947557i	$0.0302070\pi$
$307$	3.32051i	0.189511i	−0.995501	+	0.0947557i	$0.969793\pi$
$308$	1.00000i	0.0569803i
$309$	12.7846	0.727291
$310$	0	0
$311$	−19.8564	−1.12595	−0.562977	−	0.826473i	$-0.690344\pi$
$311$	−19.8564	−1.12595	−0.562977	+	0.826473i	$0.690344\pi$
$312$	− 4.00000i	− 0.226455i
$313$	30.7321i	1.73708i	0.495621	+	0.868539i	$0.334941\pi$
$313$	30.7321i	1.73708i	−0.495621	+	0.868539i	$0.665059\pi$
$314$	−14.3923	−0.812205
$315$	0	0
$316$	3.26795	0.183837
$317$	− 26.4449i	− 1.48529i	−0.669684	−	0.742646i	$-0.733571\pi$
$317$	− 26.4449i	− 1.48529i	0.669684	−	0.742646i	$-0.266429\pi$
$318$	− 0.928203i	− 0.0520511i
$319$	1.26795	0.0709915
$320$	0	0
$321$	9.46410	0.528235
$322$	4.73205i	0.263707i
$323$	− 2.53590i	− 0.141101i
$324$	−4.46410	−0.248006
$325$	0	0
$326$	−8.00000	−0.443079
$327$	− 8.92820i	− 0.493731i
$328$	1.26795i	0.0700108i
$329$	0	0
$330$	0	0
$331$	8.92820	0.490738	0.245369	−	0.969430i	$-0.421091\pi$
$331$	8.92820	0.490738	0.245369	+	0.969430i	$0.421091\pi$
$332$	− 16.3923i	− 0.899645i
$333$	− 16.5885i	− 0.909042i
$334$	13.8564	0.758189
$335$	0	0
$336$	−0.732051	−0.0399366
$337$	− 10.7846i	− 0.587475i	−0.955886	−	0.293738i	$-0.905101\pi$
$337$	− 10.7846i	− 0.587475i	0.955886	−	0.293738i	$-0.0948992\pi$
$338$	− 16.8564i	− 0.916868i
$339$	−0.679492	−0.0369049
$340$	0	0
$341$	−4.92820	−0.266877
$342$	− 1.80385i	− 0.0975409i
$343$	1.00000i	0.0539949i
$344$	8.92820	0.481376
$345$	0	0
$346$	12.9282	0.695025
$347$	19.8564i	1.06595i	0.846132	+	0.532974i	$0.178926\pi$
$347$	19.8564i	1.06595i	−0.846132	+	0.532974i	$0.821074\pi$
$348$	0.928203i	0.0497569i
$349$	−9.60770	−0.514288	−0.257144	−	0.966373i	$-0.582781\pi$
$349$	−9.60770	−0.514288	−0.257144	+	0.966373i	$0.582781\pi$
$350$	0	0
$351$	21.8564	1.16661
$352$	1.00000i	0.0533002i
$353$	26.4449i	1.40752i	0.710439	+	0.703759i	$0.248497\pi$
$353$	26.4449i	1.40752i	−0.710439	+	0.703759i	$0.751503\pi$
$354$	−10.1436	−0.539126
$355$	0	0
$356$	−8.53590	−0.452402
$357$	− 2.53590i	− 0.134214i
$358$	− 7.85641i	− 0.415224i
$359$	4.73205	0.249748	0.124874	−	0.992173i	$-0.460147\pi$
$359$	4.73205	0.249748	0.124874	+	0.992173i	$0.460147\pi$
$360$	0	0
$361$	−18.4641	−0.971795
$362$	15.8564i	0.833394i
$363$	− 0.732051i	− 0.0384227i
$364$	−5.46410	−0.286397
$365$	0	0
$366$	1.46410	0.0765298
$367$	− 22.5359i	− 1.17636i	−0.808728	−	0.588182i	$-0.799844\pi$
$367$	− 22.5359i	− 1.17636i	0.808728	−	0.588182i	$-0.200156\pi$
$368$	4.73205i	0.246675i
$369$	−3.12436	−0.162647
$370$	0	0
$371$	−1.26795	−0.0658286
$372$	− 3.60770i	− 0.187050i
$373$	9.60770i	0.497468i	0.968572	+	0.248734i	$0.0800144\pi$
$373$	9.60770i	0.497468i	−0.968572	+	0.248734i	$0.919986\pi$
$374$	−3.46410	−0.179124
$375$	0	0
$376$	0	0
$377$	6.92820i	0.356821i
$378$	− 4.00000i	− 0.205738i
$379$	31.7128	1.62898	0.814489	−	0.580179i	$-0.197017\pi$
$379$	31.7128	1.62898	0.814489	+	0.580179i	$0.197017\pi$
$380$	0	0
$381$	13.0718	0.669688
$382$	− 6.92820i	− 0.354478i
$383$	− 4.39230i	− 0.224436i	−0.993684	−	0.112218i	$-0.964204\pi$
$383$	− 4.39230i	− 0.224436i	0.993684	−	0.112218i	$-0.0357955\pi$
$384$	−0.732051	−0.0373573
$385$	0	0
$386$	18.5359	0.943452
$387$	22.0000i	1.11832i
$388$	16.1962i	0.822235i
$389$	−24.2487	−1.22946	−0.614729	−	0.788738i	$-0.710735\pi$
$389$	−24.2487	−1.22946	−0.614729	+	0.788738i	$0.710735\pi$
$390$	0	0
$391$	−16.3923	−0.828994
$392$	1.00000i	0.0505076i
$393$	0.248711i	0.0125458i
$394$	−1.60770	−0.0809945
$395$	0	0
$396$	−2.46410	−0.123826
$397$	17.6077i	0.883705i	0.897088	+	0.441852i	$0.145679\pi$
$397$	17.6077i	0.883705i	−0.897088	+	0.441852i	$0.854321\pi$
$398$	− 16.7846i	− 0.841336i
$399$	0.535898	0.0268285
$400$	0	0
$401$	37.1769	1.85653	0.928263	−	0.371924i	$-0.121302\pi$
$401$	37.1769	1.85653	0.928263	+	0.371924i	$0.121302\pi$
$402$	− 2.14359i	− 0.106913i
$403$	− 26.9282i	− 1.34139i
$404$	6.00000	0.298511
$405$	0	0
$406$	1.26795	0.0629273
$407$	− 6.73205i	− 0.333695i
$408$	− 2.53590i	− 0.125546i
$409$	−11.8038	−0.583663	−0.291831	−	0.956470i	$-0.594265\pi$
$409$	−11.8038	−0.583663	−0.291831	+	0.956470i	$0.594265\pi$
$410$	0	0
$411$	14.5359	0.717003
$412$	− 17.4641i	− 0.860395i
$413$	13.8564i	0.681829i
$414$	−11.6603	−0.573070
$415$	0	0
$416$	−5.46410	−0.267900
$417$	− 4.53590i	− 0.222124i
$418$	− 0.732051i	− 0.0358058i
$419$	8.78461	0.429156	0.214578	−	0.976707i	$-0.431162\pi$
$419$	8.78461	0.429156	0.214578	+	0.976707i	$0.431162\pi$
$420$	0	0
$421$	−30.7846	−1.50035	−0.750175	−	0.661239i	$-0.770031\pi$
$421$	−30.7846	−1.50035	−0.750175	+	0.661239i	$0.770031\pi$
$422$	8.00000i	0.389434i
$423$	0	0
$424$	−1.26795	−0.0615771
$425$	0	0
$426$	1.85641	0.0899432
$427$	− 2.00000i	− 0.0967868i
$428$	− 12.9282i	− 0.624908i
$429$	4.00000	0.193122
$430$	0	0
$431$	35.6603	1.71769	0.858847	−	0.512232i	$-0.171181\pi$
$431$	35.6603	1.71769	0.858847	+	0.512232i	$0.171181\pi$
$432$	− 4.00000i	− 0.192450i
$433$	− 2.73205i	− 0.131294i	−0.997843	−	0.0656470i	$-0.979089\pi$
$433$	− 2.73205i	− 0.131294i	0.997843	−	0.0656470i	$-0.0209111\pi$
$434$	−4.92820	−0.236561
$435$	0	0
$436$	−12.1962	−0.584090
$437$	− 3.46410i	− 0.165710i
$438$	3.32051i	0.158660i
$439$	−15.6077	−0.744915	−0.372457	−	0.928049i	$-0.621485\pi$
$439$	−15.6077	−0.744915	−0.372457	+	0.928049i	$0.621485\pi$
$440$	0	0
$441$	−2.46410	−0.117338
$442$	− 18.9282i	− 0.900323i
$443$	− 20.7846i	− 0.987507i	−0.869602	−	0.493753i	$-0.835625\pi$
$443$	− 20.7846i	− 0.987507i	0.869602	−	0.493753i	$-0.164375\pi$
$444$	4.92820	0.233882
$445$	0	0
$446$	−12.3923	−0.586793
$447$	− 7.85641i	− 0.371595i
$448$	1.00000i	0.0472456i
$449$	0.679492	0.0320672	0.0160336	−	0.999871i	$-0.494896\pi$
$449$	0.679492	0.0320672	0.0160336	+	0.999871i	$0.494896\pi$
$450$	0	0
$451$	−1.26795	−0.0597054
$452$	0.928203i	0.0436590i
$453$	13.3205i	0.625852i
$454$	−13.8564	−0.650313
$455$	0	0
$456$	0.535898	0.0250957
$457$	34.0000i	1.59045i	0.606313	+	0.795226i	$0.292648\pi$
$457$	34.0000i	1.59045i	−0.606313	+	0.795226i	$0.707352\pi$
$458$	6.53590i	0.305402i
$459$	13.8564	0.646762
$460$	0	0
$461$	−5.32051	−0.247801	−0.123900	−	0.992295i	$-0.539540\pi$
$461$	−5.32051	−0.247801	−0.123900	+	0.992295i	$0.539540\pi$
$462$	− 0.732051i	− 0.0340581i
$463$	− 38.9808i	− 1.81159i	−0.423717	−	0.905795i	$-0.639275\pi$
$463$	− 38.9808i	− 1.81159i	0.423717	−	0.905795i	$-0.360725\pi$
$464$	1.26795	0.0588631
$465$	0	0
$466$	19.8564	0.919830
$467$	− 0.339746i	− 0.0157216i	−0.999969	−	0.00786078i	$-0.997498\pi$
$467$	− 0.339746i	− 0.0157216i	0.999969	−	0.00786078i	$-0.00250219\pi$
$468$	− 13.4641i	− 0.622378i
$469$	−2.92820	−0.135212
$470$	0	0
$471$	10.5359	0.485469
$472$	13.8564i	0.637793i
$473$	8.92820i	0.410519i
$474$	−2.39230	−0.109882
$475$	0	0
$476$	−3.46410	−0.158777
$477$	− 3.12436i	− 0.143054i
$478$	14.1962i	0.649317i
$479$	13.8564	0.633115	0.316558	−	0.948573i	$-0.397473\pi$
$479$	13.8564	0.633115	0.316558	+	0.948573i	$0.397473\pi$
$480$	0	0
$481$	36.7846	1.67723
$482$	− 7.80385i	− 0.355456i
$483$	− 3.46410i	− 0.157622i
$484$	−1.00000	−0.0454545
$485$	0	0
$486$	15.2679	0.692568
$487$	− 29.1244i	− 1.31975i	−0.751375	−	0.659875i	$-0.770609\pi$
$487$	− 29.1244i	− 1.31975i	0.751375	−	0.659875i	$-0.229391\pi$
$488$	− 2.00000i	− 0.0905357i
$489$	5.85641	0.264836
$490$	0	0
$491$	29.0718	1.31199	0.655996	−	0.754764i	$-0.272249\pi$
$491$	29.0718	1.31199	0.655996	+	0.754764i	$0.272249\pi$
$492$	− 0.928203i	− 0.0418466i
$493$	4.39230i	0.197819i
$494$	4.00000	0.179969
$495$	0	0
$496$	−4.92820	−0.221283
$497$	− 2.53590i	− 0.113751i
$498$	12.0000i	0.537733i
$499$	−2.00000	−0.0895323	−0.0447661	−	0.998997i	$-0.514254\pi$
$499$	−2.00000	−0.0895323	−0.0447661	+	0.998997i	$0.514254\pi$
$500$	0	0
$501$	−10.1436	−0.453182
$502$	0	0
$503$	− 5.07180i	− 0.226140i	−0.993587	−	0.113070i	$-0.963932\pi$
$503$	− 5.07180i	− 0.226140i	0.993587	−	0.113070i	$-0.0360685\pi$
$504$	−2.46410	−0.109760
$505$	0	0
$506$	−4.73205	−0.210365
$507$	12.3397i	0.548027i
$508$	− 17.8564i	− 0.792250i
$509$	38.7846	1.71910	0.859549	−	0.511054i	$-0.170745\pi$
$509$	38.7846	1.71910	0.859549	+	0.511054i	$0.170745\pi$
$510$	0	0
$511$	4.53590	0.200656
$512$	1.00000i	0.0441942i
$513$	2.92820i	0.129283i
$514$	−28.9808	−1.27829
$515$	0	0
$516$	−6.53590	−0.287727
$517$	0	0
$518$	− 6.73205i	− 0.295789i
$519$	−9.46410	−0.415428
$520$	0	0
$521$	−10.3923	−0.455295	−0.227648	−	0.973744i	$-0.573103\pi$
$521$	−10.3923	−0.455295	−0.227648	+	0.973744i	$0.573103\pi$
$522$	3.12436i	0.136749i
$523$	− 15.3205i	− 0.669919i	−0.942233	−	0.334960i	$-0.891277\pi$
$523$	− 15.3205i	− 0.669919i	0.942233	−	0.334960i	$-0.108723\pi$
$524$	0.339746	0.0148419
$525$	0	0
$526$	−5.07180	−0.221141
$527$	− 17.0718i	− 0.743659i
$528$	− 0.732051i	− 0.0318584i
$529$	0.607695	0.0264215
$530$	0	0
$531$	−34.1436	−1.48171
$532$	− 0.732051i	− 0.0317384i
$533$	− 6.92820i	− 0.300094i
$534$	6.24871	0.270408
$535$	0	0
$536$	−2.92820	−0.126479
$537$	5.75129i	0.248186i
$538$	16.3923i	0.706722i
$539$	−1.00000	−0.0430730
$540$	0	0
$541$	−7.12436	−0.306300	−0.153150	−	0.988203i	$-0.548942\pi$
$541$	−7.12436	−0.306300	−0.153150	+	0.988203i	$0.548942\pi$
$542$	3.60770i	0.154964i
$543$	− 11.6077i	− 0.498134i
$544$	−3.46410	−0.148522
$545$	0	0
$546$	4.00000	0.171184
$547$	36.7846i	1.57280i	0.617720	+	0.786398i	$0.288057\pi$
$547$	36.7846i	1.57280i	−0.617720	+	0.786398i	$0.711943\pi$
$548$	− 19.8564i	− 0.848224i
$549$	4.92820	0.210331
$550$	0	0
$551$	−0.928203	−0.0395428
$552$	− 3.46410i	− 0.147442i
$553$	3.26795i	0.138967i
$554$	0.143594	0.00610070
$555$	0	0
$556$	−6.19615	−0.262775
$557$	− 36.2487i	− 1.53591i	−0.640505	−	0.767954i	$-0.721275\pi$
$557$	− 36.2487i	− 1.53591i	0.640505	−	0.767954i	$-0.278725\pi$
$558$	− 12.1436i	− 0.514079i
$559$	−48.7846	−2.06337
$560$	0	0
$561$	2.53590	0.107066
$562$	10.3923i	0.438373i
$563$	20.7846i	0.875967i	0.898983	+	0.437983i	$0.144307\pi$
$563$	20.7846i	0.875967i	−0.898983	+	0.437983i	$0.855693\pi$
$564$	0	0
$565$	0	0
$566$	−2.92820	−0.123082
$567$	− 4.46410i	− 0.187475i
$568$	− 2.53590i	− 0.106404i
$569$	30.0000	1.25767	0.628833	−	0.777541i	$-0.283533\pi$
$569$	30.0000	1.25767	0.628833	+	0.777541i	$0.283533\pi$
$570$	0	0
$571$	0.392305	0.0164174	0.00820872	−	0.999966i	$-0.497387\pi$
$571$	0.392305	0.0164174	0.00820872	+	0.999966i	$0.497387\pi$
$572$	− 5.46410i	− 0.228466i
$573$	5.07180i	0.211877i
$574$	−1.26795	−0.0529232
$575$	0	0
$576$	−2.46410	−0.102671
$577$	− 25.6603i	− 1.06825i	−0.845405	−	0.534125i	$-0.820641\pi$
$577$	− 25.6603i	− 1.06825i	0.845405	−	0.534125i	$-0.179359\pi$
$578$	5.00000i	0.207973i
$579$	−13.5692	−0.563918
$580$	0	0
$581$	16.3923	0.680067
$582$	− 11.8564i	− 0.491464i
$583$	− 1.26795i	− 0.0525131i
$584$	4.53590	0.187697
$585$	0	0
$586$	9.46410	0.390958
$587$	− 22.9808i	− 0.948518i	−0.880385	−	0.474259i	$-0.842716\pi$
$587$	− 22.9808i	− 0.948518i	0.880385	−	0.474259i	$-0.157284\pi$
$588$	− 0.732051i	− 0.0301893i
$589$	3.60770	0.148652
$590$	0	0
$591$	1.17691	0.0484118
$592$	− 6.73205i	− 0.276686i
$593$	39.4641i	1.62060i	0.586018	+	0.810298i	$0.300695\pi$
$593$	39.4641i	1.62060i	−0.586018	+	0.810298i	$0.699305\pi$
$594$	4.00000	0.164122
$595$	0	0
$596$	−10.7321	−0.439602
$597$	12.2872i	0.502881i
$598$	− 25.8564i	− 1.05735i
$599$	−44.1051	−1.80209	−0.901043	−	0.433730i	$-0.857197\pi$
$599$	−44.1051	−1.80209	−0.901043	+	0.433730i	$0.857197\pi$
$600$	0	0
$601$	−30.4449	−1.24187	−0.620936	−	0.783861i	$-0.713247\pi$
$601$	−30.4449	−1.24187	−0.620936	+	0.783861i	$0.713247\pi$
$602$	8.92820i	0.363886i
$603$	− 7.21539i	− 0.293833i
$604$	18.1962	0.740391
$605$	0	0
$606$	−4.39230	−0.178425
$607$	6.78461i	0.275379i	0.990475	+	0.137689i	$0.0439676\pi$
$607$	6.78461i	0.275379i	−0.990475	+	0.137689i	$0.956032\pi$
$608$	− 0.732051i	− 0.0296886i
$609$	−0.928203	−0.0376127
$610$	0	0
$611$	0	0
$612$	− 8.53590i	− 0.345043i
$613$	− 35.1769i	− 1.42078i	−0.703807	−	0.710391i	$-0.748518\pi$
$613$	− 35.1769i	− 1.42078i	0.703807	−	0.710391i	$-0.251482\pi$
$614$	−3.32051	−0.134005
$615$	0	0
$616$	−1.00000	−0.0402911
$617$	− 15.4641i	− 0.622561i	−0.950318	−	0.311281i	$-0.899242\pi$
$617$	− 15.4641i	− 0.622561i	0.950318	−	0.311281i	$-0.100758\pi$
$618$	12.7846i	0.514272i
$619$	−2.92820	−0.117694	−0.0588472	−	0.998267i	$-0.518742\pi$
$619$	−2.92820	−0.117694	−0.0588472	+	0.998267i	$0.518742\pi$
$620$	0	0
$621$	18.9282	0.759563
$622$	− 19.8564i	− 0.796169i
$623$	− 8.53590i	− 0.341984i
$624$	4.00000	0.160128
$625$	0	0
$626$	−30.7321	−1.22830
$627$	0.535898i	0.0214017i
$628$	− 14.3923i	− 0.574315i
$629$	23.3205	0.929850
$630$	0	0
$631$	28.7846	1.14590	0.572949	−	0.819591i	$-0.305799\pi$
$631$	28.7846	1.14590	0.572949	+	0.819591i	$0.305799\pi$
$632$	3.26795i	0.129992i
$633$	− 5.85641i	− 0.232771i
$634$	26.4449	1.05026
$635$	0	0
$636$	0.928203	0.0368057
$637$	− 5.46410i	− 0.216496i
$638$	1.26795i	0.0501986i
$639$	6.24871	0.247195
$640$	0	0
$641$	−7.85641	−0.310309	−0.155155	−	0.987890i	$-0.549588\pi$
$641$	−7.85641	−0.310309	−0.155155	+	0.987890i	$0.549588\pi$
$642$	9.46410i	0.373518i
$643$	− 11.2679i	− 0.444365i	−0.975005	−	0.222182i	$-0.928682\pi$
$643$	− 11.2679i	− 0.444365i	0.975005	−	0.222182i	$-0.0713180\pi$
$644$	−4.73205	−0.186469
$645$	0	0
$646$	2.53590	0.0997736
$647$	25.1769i	0.989807i	0.868948	+	0.494903i	$0.164797\pi$
$647$	25.1769i	0.989807i	−0.868948	+	0.494903i	$0.835203\pi$
$648$	− 4.46410i	− 0.175366i
$649$	−13.8564	−0.543912
$650$	0	0
$651$	3.60770	0.141397
$652$	− 8.00000i	− 0.313304i
$653$	− 20.1962i	− 0.790337i	−0.918609	−	0.395168i	$-0.870686\pi$
$653$	− 20.1962i	− 0.790337i	0.918609	−	0.395168i	$-0.129314\pi$
$654$	8.92820	0.349120
$655$	0	0
$656$	−1.26795	−0.0495051
$657$	11.1769i	0.436053i
$658$	0	0
$659$	42.2487	1.64578	0.822888	−	0.568204i	$-0.192361\pi$
$659$	42.2487	1.64578	0.822888	+	0.568204i	$0.192361\pi$
$660$	0	0
$661$	−23.8564	−0.927907	−0.463953	−	0.885860i	$-0.653569\pi$
$661$	−23.8564	−0.927907	−0.463953	+	0.885860i	$0.653569\pi$
$662$	8.92820i	0.347004i
$663$	13.8564i	0.538138i
$664$	16.3923	0.636145
$665$	0	0
$666$	16.5885	0.642790
$667$	6.00000i	0.232321i
$668$	13.8564i	0.536120i
$669$	9.07180	0.350736
$670$	0	0
$671$	2.00000	0.0772091
$672$	− 0.732051i	− 0.0282395i
$673$	− 47.8564i	− 1.84473i	−0.386321	−	0.922364i	$-0.626254\pi$
$673$	− 47.8564i	− 1.84473i	0.386321	−	0.922364i	$-0.373746\pi$
$674$	10.7846	0.415408
$675$	0	0
$676$	16.8564	0.648323
$677$	7.85641i	0.301946i	0.988538	+	0.150973i	$0.0482407\pi$
$677$	7.85641i	0.301946i	−0.988538	+	0.150973i	$0.951759\pi$
$678$	− 0.679492i	− 0.0260957i
$679$	−16.1962	−0.621551
$680$	0	0
$681$	10.1436	0.388703
$682$	− 4.92820i	− 0.188711i
$683$	− 6.24871i	− 0.239100i	−0.992828	−	0.119550i	$-0.961855\pi$
$683$	− 6.24871i	− 0.239100i	0.992828	−	0.119550i	$-0.0381452\pi$
$684$	1.80385	0.0689718
$685$	0	0
$686$	−1.00000	−0.0381802
$687$	− 4.78461i	− 0.182544i
$688$	8.92820i	0.340385i
$689$	6.92820	0.263944
$690$	0	0
$691$	−3.32051	−0.126318	−0.0631590	−	0.998003i	$-0.520118\pi$
$691$	−3.32051	−0.126318	−0.0631590	+	0.998003i	$0.520118\pi$
$692$	12.9282i	0.491457i
$693$	− 2.46410i	− 0.0936035i
$694$	−19.8564	−0.753739
$695$	0	0
$696$	−0.928203	−0.0351835
$697$	− 4.39230i	− 0.166370i
$698$	− 9.60770i	− 0.363657i
$699$	−14.5359	−0.549798
$700$	0	0
$701$	3.80385	0.143669	0.0718347	−	0.997417i	$-0.477115\pi$
$701$	3.80385	0.143669	0.0718347	+	0.997417i	$0.477115\pi$
$702$	21.8564i	0.824917i
$703$	4.92820i	0.185871i
$704$	−1.00000	−0.0376889
$705$	0	0
$706$	−26.4449	−0.995266
$707$	6.00000i	0.225653i
$708$	− 10.1436i	− 0.381220i
$709$	−18.3923	−0.690738	−0.345369	−	0.938467i	$-0.612246\pi$
$709$	−18.3923	−0.690738	−0.345369	+	0.938467i	$0.612246\pi$
$710$	0	0
$711$	−8.05256	−0.301995
$712$	− 8.53590i	− 0.319896i
$713$	− 23.3205i	− 0.873360i
$714$	2.53590	0.0949036
$715$	0	0
$716$	7.85641	0.293608
$717$	− 10.3923i	− 0.388108i
$718$	4.73205i	0.176599i
$719$	−24.0000	−0.895049	−0.447524	−	0.894272i	$-0.647694\pi$
$719$	−24.0000	−0.895049	−0.447524	+	0.894272i	$0.647694\pi$
$720$	0	0
$721$	17.4641	0.650397
$722$	− 18.4641i	− 0.687163i
$723$	5.71281i	0.212462i
$724$	−15.8564	−0.589299
$725$	0	0
$726$	0.732051	0.0271690
$727$	− 30.6410i	− 1.13641i	−0.822886	−	0.568206i	$-0.807638\pi$
$727$	− 30.6410i	− 1.13641i	0.822886	−	0.568206i	$-0.192362\pi$
$728$	− 5.46410i	− 0.202513i
$729$	2.21539	0.0820515
$730$	0	0
$731$	−30.9282	−1.14392
$732$	1.46410i	0.0541148i
$733$	2.00000i	0.0738717i	0.999318	+	0.0369358i	$0.0117597\pi$
$733$	2.00000i	0.0738717i	−0.999318	+	0.0369358i	$0.988240\pi$
$734$	22.5359	0.831815
$735$	0	0
$736$	−4.73205	−0.174426
$737$	− 2.92820i	− 0.107862i
$738$	− 3.12436i	− 0.115009i
$739$	−45.8564	−1.68686	−0.843428	−	0.537243i	$-0.819466\pi$
$739$	−45.8564	−1.68686	−0.843428	+	0.537243i	$0.819466\pi$
$740$	0	0
$741$	−2.92820	−0.107570
$742$	− 1.26795i	− 0.0465479i
$743$	− 51.7128i	− 1.89716i	−0.316539	−	0.948580i	$-0.602521\pi$
$743$	− 51.7128i	− 1.89716i	0.316539	−	0.948580i	$-0.397479\pi$
$744$	3.60770	0.132265
$745$	0	0
$746$	−9.60770	−0.351763
$747$	40.3923i	1.47788i
$748$	− 3.46410i	− 0.126660i
$749$	12.9282	0.472386
$750$	0	0
$751$	−46.2487	−1.68764	−0.843820	−	0.536627i	$-0.819698\pi$
$751$	−46.2487	−1.68764	−0.843820	+	0.536627i	$0.819698\pi$
$752$	0	0
$753$	0	0
$754$	−6.92820	−0.252310
$755$	0	0
$756$	4.00000	0.145479
$757$	49.3731i	1.79449i	0.441528	+	0.897247i	$0.354436\pi$
$757$	49.3731i	1.79449i	−0.441528	+	0.897247i	$0.645564\pi$
$758$	31.7128i	1.15186i
$759$	3.46410	0.125739
$760$	0	0
$761$	22.7321	0.824036	0.412018	−	0.911176i	$-0.364824\pi$
$761$	22.7321	0.824036	0.412018	+	0.911176i	$0.364824\pi$
$762$	13.0718i	0.473541i
$763$	− 12.1962i	− 0.441530i
$764$	6.92820	0.250654
$765$	0	0
$766$	4.39230	0.158700
$767$	− 75.7128i	− 2.73383i
$768$	− 0.732051i	− 0.0264156i
$769$	−34.4449	−1.24211	−0.621057	−	0.783766i	$-0.713296\pi$
$769$	−34.4449	−1.24211	−0.621057	+	0.783766i	$0.713296\pi$
$770$	0	0
$771$	21.2154	0.764054
$772$	18.5359i	0.667122i
$773$	30.0000i	1.07903i	0.841978	+	0.539513i	$0.181391\pi$
$773$	30.0000i	1.07903i	−0.841978	+	0.539513i	$0.818609\pi$
$774$	−22.0000	−0.790774
$775$	0	0
$776$	−16.1962	−0.581408
$777$	4.92820i	0.176798i
$778$	− 24.2487i	− 0.869358i
$779$	0.928203	0.0332563
$780$	0	0
$781$	2.53590	0.0907416
$782$	− 16.3923i	− 0.586188i
$783$	− 5.07180i	− 0.181251i
$784$	−1.00000	−0.0357143
$785$	0	0
$786$	−0.248711	−0.00887124
$787$	28.0000i	0.998092i	0.866575	+	0.499046i	$0.166316\pi$
$787$	28.0000i	0.998092i	−0.866575	+	0.499046i	$0.833684\pi$
$788$	− 1.60770i	− 0.0572718i
$789$	3.71281	0.132180
$790$	0	0
$791$	−0.928203	−0.0330031
$792$	− 2.46410i	− 0.0875580i
$793$	10.9282i	0.388072i
$794$	−17.6077	−0.624874
$795$	0	0
$796$	16.7846	0.594915
$797$	− 41.3205i	− 1.46365i	−0.681494	−	0.731824i	$-0.738669\pi$
$797$	− 41.3205i	− 1.46365i	0.681494	−	0.731824i	$-0.261331\pi$
$798$	0.535898i	0.0189706i
$799$	0	0
$800$	0	0
$801$	21.0333	0.743176
$802$	37.1769i	1.31276i
$803$	4.53590i	0.160068i
$804$	2.14359	0.0755987
$805$	0	0
$806$	26.9282	0.948506
$807$	− 12.0000i	− 0.422420i
$808$	6.00000i	0.211079i
$809$	29.3205	1.03085	0.515427	−	0.856933i	$-0.327633\pi$
$809$	29.3205	1.03085	0.515427	+	0.856933i	$0.327633\pi$
$810$	0	0
$811$	26.5885	0.933647	0.466824	−	0.884351i	$-0.345398\pi$
$811$	26.5885	0.933647	0.466824	+	0.884351i	$0.345398\pi$
$812$	1.26795i	0.0444963i
$813$	− 2.64102i	− 0.0926245i
$814$	6.73205	0.235958
$815$	0	0
$816$	2.53590	0.0887742
$817$	− 6.53590i	− 0.228662i
$818$	− 11.8038i	− 0.412712i
$819$	13.4641	0.470474
$820$	0	0
$821$	13.9474	0.486769	0.243385	−	0.969930i	$-0.421742\pi$
$821$	13.9474	0.486769	0.243385	+	0.969930i	$0.421742\pi$
$822$	14.5359i	0.506998i
$823$	− 13.8038i	− 0.481172i	−0.970628	−	0.240586i	$-0.922660\pi$
$823$	− 13.8038i	− 0.481172i	0.970628	−	0.240586i	$-0.0773396\pi$
$824$	17.4641	0.608391
$825$	0	0
$826$	−13.8564	−0.482126
$827$	29.5692i	1.02822i	0.857724	+	0.514111i	$0.171878\pi$
$827$	29.5692i	1.02822i	−0.857724	+	0.514111i	$0.828122\pi$
$828$	− 11.6603i	− 0.405222i
$829$	36.1051	1.25398	0.626991	−	0.779026i	$-0.284286\pi$
$829$	36.1051	1.25398	0.626991	+	0.779026i	$0.284286\pi$
$830$	0	0
$831$	−0.105118	−0.00364649
$832$	− 5.46410i	− 0.189434i
$833$	− 3.46410i	− 0.120024i
$834$	4.53590	0.157065
$835$	0	0
$836$	0.732051	0.0253185
$837$	19.7128i	0.681374i
$838$	8.78461i	0.303459i
$839$	−2.78461	−0.0961354	−0.0480677	−	0.998844i	$-0.515306\pi$
$839$	−2.78461	−0.0961354	−0.0480677	+	0.998844i	$0.515306\pi$
$840$	0	0
$841$	−27.3923	−0.944562
$842$	− 30.7846i	− 1.06091i
$843$	− 7.60770i	− 0.262023i
$844$	−8.00000	−0.275371
$845$	0	0
$846$	0	0
$847$	− 1.00000i	− 0.0343604i
$848$	− 1.26795i	− 0.0435416i
$849$	2.14359	0.0735679
$850$	0	0
$851$	31.8564	1.09202
$852$	1.85641i	0.0635994i
$853$	7.07180i	0.242134i	0.992644	+	0.121067i	$0.0386315\pi$
$853$	7.07180i	0.242134i	−0.992644	+	0.121067i	$0.961368\pi$
$854$	2.00000	0.0684386
$855$	0	0
$856$	12.9282	0.441877
$857$	− 43.1769i	− 1.47490i	−0.675404	−	0.737448i	$-0.736031\pi$
$857$	− 43.1769i	− 1.47490i	0.675404	−	0.737448i	$-0.263969\pi$
$858$	4.00000i	0.136558i
$859$	0.784610	0.0267705	0.0133853	−	0.999910i	$-0.495739\pi$
$859$	0.784610	0.0267705	0.0133853	+	0.999910i	$0.495739\pi$
$860$	0	0
$861$	0.928203	0.0316331
$862$	35.6603i	1.21459i
$863$	− 6.58846i	− 0.224274i	−0.993693	−	0.112137i	$-0.964230\pi$
$863$	− 6.58846i	− 0.224274i	0.993693	−	0.112137i	$-0.0357695\pi$
$864$	4.00000	0.136083
$865$	0	0
$866$	2.73205	0.0928389
$867$	− 3.66025i	− 0.124309i
$868$	− 4.92820i	− 0.167274i
$869$	−3.26795	−0.110858
$870$	0	0
$871$	16.0000	0.542139
$872$	− 12.1962i	− 0.413014i
$873$	− 39.9090i	− 1.35071i
$874$	3.46410	0.117175
$875$	0	0
$876$	−3.32051	−0.112190
$877$	− 39.1769i	− 1.32291i	−0.749985	−	0.661455i	$-0.769939\pi$
$877$	− 39.1769i	− 1.32291i	0.749985	−	0.661455i	$-0.230061\pi$
$878$	− 15.6077i	− 0.526734i
$879$	−6.92820	−0.233682
$880$	0	0
$881$	11.0718	0.373018	0.186509	−	0.982453i	$-0.440283\pi$
$881$	11.0718	0.373018	0.186509	+	0.982453i	$0.440283\pi$
$882$	− 2.46410i	− 0.0829706i
$883$	21.1769i	0.712660i	0.934360	+	0.356330i	$0.115972\pi$
$883$	21.1769i	0.712660i	−0.934360	+	0.356330i	$0.884028\pi$
$884$	18.9282	0.636624
$885$	0	0
$886$	20.7846	0.698273
$887$	− 24.0000i	− 0.805841i	−0.915235	−	0.402921i	$-0.867995\pi$
$887$	− 24.0000i	− 0.805841i	0.915235	−	0.402921i	$-0.132005\pi$
$888$	4.92820i	0.165380i
$889$	17.8564	0.598885
$890$	0	0
$891$	4.46410	0.149553
$892$	− 12.3923i	− 0.414925i
$893$	0	0
$894$	7.85641	0.262758
$895$	0	0
$896$	−1.00000	−0.0334077
$897$	18.9282i	0.631994i
$898$	0.679492i	0.0226749i
$899$	−6.24871	−0.208406
$900$	0	0
$901$	4.39230	0.146329
$902$	− 1.26795i	− 0.0422181i
$903$	− 6.53590i	− 0.217501i
$904$	−0.928203	−0.0308716
$905$	0	0
$906$	−13.3205	−0.442544
$907$	− 19.3205i	− 0.641527i	−0.947159	−	0.320763i	$-0.896061\pi$
$907$	− 19.3205i	− 0.641527i	0.947159	−	0.320763i	$-0.103939\pi$
$908$	− 13.8564i	− 0.459841i
$909$	−14.7846	−0.490375
$910$	0	0
$911$	21.4641	0.711137	0.355569	−	0.934650i	$-0.384287\pi$
$911$	21.4641	0.711137	0.355569	+	0.934650i	$0.384287\pi$
$912$	0.535898i	0.0177454i
$913$	16.3923i	0.542506i
$914$	−34.0000	−1.12462
$915$	0	0
$916$	−6.53590	−0.215952
$917$	0.339746i	0.0112194i
$918$	13.8564i	0.457330i
$919$	26.9808	0.890013	0.445007	−	0.895527i	$-0.353201\pi$
$919$	26.9808	0.890013	0.445007	+	0.895527i	$0.353201\pi$
$920$	0	0
$921$	2.43078	0.0800969
$922$	− 5.32051i	− 0.175222i
$923$	13.8564i	0.456089i
$924$	0.732051	0.0240827
$925$	0	0
$926$	38.9808	1.28099
$927$	43.0333i	1.41340i
$928$	1.26795i	0.0416225i
$929$	50.1051	1.64390	0.821948	−	0.569563i	$-0.192887\pi$
$929$	50.1051	1.64390	0.821948	+	0.569563i	$0.192887\pi$
$930$	0	0
$931$	0.732051	0.0239920
$932$	19.8564i	0.650418i
$933$	14.5359i	0.475884i
$934$	0.339746	0.0111168
$935$	0	0
$936$	13.4641	0.440088
$937$	− 26.0000i	− 0.849383i	−0.905338	−	0.424691i	$-0.860383\pi$
$937$	− 26.0000i	− 0.849383i	0.905338	−	0.424691i	$-0.139617\pi$
$938$	− 2.92820i	− 0.0956092i
$939$	22.4974	0.734176
$940$	0	0
$941$	47.5692	1.55071	0.775356	−	0.631524i	$-0.217570\pi$
$941$	47.5692	1.55071	0.775356	+	0.631524i	$0.217570\pi$
$942$	10.5359i	0.343278i
$943$	− 6.00000i	− 0.195387i
$944$	−13.8564	−0.450988
$945$	0	0
$946$	−8.92820	−0.290281
$947$	− 37.1769i	− 1.20809i	−0.796951	−	0.604044i	$-0.793555\pi$
$947$	− 37.1769i	− 1.20809i	0.796951	−	0.604044i	$-0.206445\pi$
$948$	− 2.39230i	− 0.0776984i
$949$	−24.7846	−0.804542
$950$	0	0
$951$	−19.3590	−0.627758
$952$	− 3.46410i	− 0.112272i
$953$	23.3205i	0.755425i	0.925923	+	0.377713i	$0.123289\pi$
$953$	23.3205i	0.755425i	−0.925923	+	0.377713i	$0.876711\pi$
$954$	3.12436	0.101155
$955$	0	0
$956$	−14.1962	−0.459136
$957$	− 0.928203i	− 0.0300045i
$958$	13.8564i	0.447680i
$959$	19.8564	0.641197
$960$	0	0
$961$	−6.71281	−0.216542
$962$	36.7846i	1.18598i
$963$	31.8564i	1.02656i
$964$	7.80385	0.251345
$965$	0	0
$966$	3.46410	0.111456
$967$	53.8564i	1.73191i	0.500126	+	0.865953i	$0.333287\pi$
$967$	53.8564i	1.73191i	−0.500126	+	0.865953i	$0.666713\pi$
$968$	− 1.00000i	− 0.0321412i
$969$	−1.85641	−0.0596364
$970$	0	0
$971$	22.1436	0.710622	0.355311	−	0.934748i	$-0.384375\pi$
$971$	22.1436	0.710622	0.355311	+	0.934748i	$0.384375\pi$
$972$	15.2679i	0.489720i
$973$	− 6.19615i	− 0.198640i
$974$	29.1244	0.933205
$975$	0	0
$976$	2.00000	0.0640184
$977$	− 12.9282i	− 0.413610i	−0.978382	−	0.206805i	$-0.933693\pi$
$977$	− 12.9282i	− 0.413610i	0.978382	−	0.206805i	$-0.0663065\pi$
$978$	5.85641i	0.187267i
$979$	8.53590	0.272808
$980$	0	0
$981$	30.0526	0.959504
$982$	29.0718i	0.927718i
$983$	− 28.3923i	− 0.905574i	−0.891619	−	0.452787i	$-0.850430\pi$
$983$	− 28.3923i	− 0.905574i	0.891619	−	0.452787i	$-0.149570\pi$
$984$	0.928203	0.0295900
$985$	0	0
$986$	−4.39230	−0.139879
$987$	0	0
$988$	4.00000i	0.127257i
$989$	−42.2487	−1.34343
$990$	0	0
$991$	−9.07180	−0.288175	−0.144088	−	0.989565i	$-0.546025\pi$
$991$	−9.07180	−0.288175	−0.144088	+	0.989565i	$0.546025\pi$
$992$	− 4.92820i	− 0.156471i
$993$	− 6.53590i	− 0.207410i
$994$	2.53590	0.0804338
$995$	0	0
$996$	−12.0000	−0.380235
$997$	− 3.85641i	− 0.122134i	−0.998134	−	0.0610668i	$-0.980550\pi$
$997$	− 3.85641i	− 0.122134i	0.998134	−	0.0610668i	$-0.0194503\pi$
$998$	− 2.00000i	− 0.0633089i
$999$	−26.9282	−0.851971

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3850.2.c.s.1849.3		4
5.2	odd	4		770.2.a.h.1.1	✓	2
5.3	odd	4		3850.2.a.bm.1.2		2
5.4	even	2	inner	3850.2.c.s.1849.2		4
15.2	even	4		6930.2.a.ca.1.2		2
20.7	even	4		6160.2.a.v.1.2		2
35.27	even	4		5390.2.a.bk.1.2		2
55.32	even	4		8470.2.a.ce.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.a.h.1.1	✓	2	5.2	odd	4
3850.2.a.bm.1.2		2	5.3	odd	4
3850.2.c.s.1849.2		4	5.4	even	2	inner
3850.2.c.s.1849.3		4	1.1	even	1	trivial
5390.2.a.bk.1.2		2	35.27	even	4
6160.2.a.v.1.2		2	20.7	even	4
6930.2.a.ca.1.2		2	15.2	even	4
8470.2.a.ce.1.1		2	55.32	even	4

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:	\( N \)	\(=\)	\( 3850 = 2 \cdot 5^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3850.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -0.732051i q^{3} -1.00000 q^{4} +0.732051 q^{6} -1.00000i q^{7} -1.00000i q^{8} +2.46410 q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} -0.732051i q^{3} -1.00000 q^{4} +0.732051 q^{6} -1.00000i q^{7} -1.00000i q^{8} +2.46410 q^{9} +1.00000 q^{11} +0.732051i q^{12} +5.46410i q^{13} +1.00000 q^{14} +1.00000 q^{16} +3.46410i q^{17} +2.46410i q^{18} -0.732051 q^{19} -0.732051 q^{21} +1.00000i q^{22} +4.73205i q^{23} -0.732051 q^{24} -5.46410 q^{26} -4.00000i q^{27} +1.00000i q^{28} +1.26795 q^{29} -4.92820 q^{31} +1.00000i q^{32} -0.732051i q^{33} -3.46410 q^{34} -2.46410 q^{36} -6.73205i q^{37} -0.732051i q^{38} +4.00000 q^{39} -1.26795 q^{41} -0.732051i q^{42} +8.92820i q^{43} -1.00000 q^{44} -4.73205 q^{46} -0.732051i q^{48} -1.00000 q^{49} +2.53590 q^{51} -5.46410i q^{52} -1.26795i q^{53} +4.00000 q^{54} -1.00000 q^{56} +0.535898i q^{57} +1.26795i q^{58} -13.8564 q^{59} +2.00000 q^{61} -4.92820i q^{62} -2.46410i q^{63} -1.00000 q^{64} +0.732051 q^{66} -2.92820i q^{67} -3.46410i q^{68} +3.46410 q^{69} +2.53590 q^{71} -2.46410i q^{72} +4.53590i q^{73} +6.73205 q^{74} +0.732051 q^{76} -1.00000i q^{77} +4.00000i q^{78} -3.26795 q^{79} +4.46410 q^{81} -1.26795i q^{82} +16.3923i q^{83} +0.732051 q^{84} -8.92820 q^{86} -0.928203i q^{87} -1.00000i q^{88} +8.53590 q^{89} +5.46410 q^{91} -4.73205i q^{92} +3.60770i q^{93} +0.732051 q^{96} -16.1962i q^{97} -1.00000i q^{98} +2.46410 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4} - 4 q^{6} - 4 q^{9}+O(q^{10}) \) 4 * q - 4 * q^4 - 4 * q^6 - 4 * q^9	\( 4 q - 4 q^{4} - 4 q^{6} - 4 q^{9} + 4 q^{11} + 4 q^{14} + 4 q^{16} + 4 q^{19} + 4 q^{21} + 4 q^{24} - 8 q^{26} + 12 q^{29} + 8 q^{31} + 4 q^{36} + 16 q^{39} - 12 q^{41} - 4 q^{44} - 12 q^{46} - 4 q^{49} + 24 q^{51} + 16 q^{54} - 4 q^{56} + 8 q^{61} - 4 q^{64} - 4 q^{66} + 24 q^{71} + 20 q^{74} - 4 q^{76} - 20 q^{79} + 4 q^{81} - 4 q^{84} - 8 q^{86} + 48 q^{89} + 8 q^{91} - 4 q^{96} - 4 q^{99}+O(q^{100}) \) 4 * q - 4 * q^4 - 4 * q^6 - 4 * q^9 + 4 * q^11 + 4 * q^14 + 4 * q^16 + 4 * q^19 + 4 * q^21 + 4 * q^24 - 8 * q^26 + 12 * q^29 + 8 * q^31 + 4 * q^36 + 16 * q^39 - 12 * q^41 - 4 * q^44 - 12 * q^46 - 4 * q^49 + 24 * q^51 + 16 * q^54 - 4 * q^56 + 8 * q^61 - 4 * q^64 - 4 * q^66 + 24 * q^71 + 20 * q^74 - 4 * q^76 - 20 * q^79 + 4 * q^81 - 4 * q^84 - 8 * q^86 + 48 * q^89 + 8 * q^91 - 4 * q^96 - 4 * q^99

Introduction

L-functions

Modular forms

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Database

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