LMFDB - Embedded newform 3240.2.q.be.1081.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3240,2,Mod(1081,3240)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3240, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2, 0]))

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

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

chi := DirichletCharacter("3240.1081");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3240 = 2^{3} \cdot 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3240.q (of order $3$, degree $2$, 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:	$25.8715302549$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-19})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 4x^{2} - 5x + 25 $ x^4 - x^3 - 4x^2 - 5x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1081.2
Root			$2.13746 + 0.656712i$ of defining polynomial
Character	$\chi$	$=$	3240.1081
Dual form			3240.2.q.be.2161.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{5} +(1.63746 + 2.83616i) q^{7} +O(q^{10})$	$q+(0.500000 - 0.866025i) q^{5} +(1.63746 + 2.83616i) q^{7} +(3.13746 + 5.43424i) q^{11} +(0.637459 - 1.10411i) q^{13} -2.00000 q^{17} +1.00000 q^{19} +(-3.63746 + 6.30026i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(3.13746 + 5.43424i) q^{29} +(-3.13746 + 5.43424i) q^{31} +3.27492 q^{35} -10.5498 q^{37} +(3.77492 - 6.53835i) q^{41} +(-2.00000 - 3.46410i) q^{43} +(-0.637459 - 1.10411i) q^{47} +(-1.86254 + 3.22602i) q^{49} -0.725083 q^{53} +6.27492 q^{55} +(-6.50000 + 11.2583i) q^{59} +(-4.27492 - 7.40437i) q^{61} +(-0.637459 - 1.10411i) q^{65} +(-0.274917 + 0.476171i) q^{67} +8.27492 q^{71} +15.0997 q^{73} +(-10.2749 + 17.7967i) q^{77} +(-5.27492 - 9.13642i) q^{79} +(-1.27492 - 2.20822i) q^{83} +(-1.00000 + 1.73205i) q^{85} -12.8248 q^{89} +4.17525 q^{91} +(0.500000 - 0.866025i) q^{95} +(-8.00000 - 13.8564i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{5} - q^{7}+O(q^{10}) $ 4 * q + 2 * q^5 - q^7	$ 4 q + 2 q^{5} - q^{7} + 5 q^{11} - 5 q^{13} - 8 q^{17} + 4 q^{19} - 7 q^{23} - 2 q^{25} + 5 q^{29} - 5 q^{31} - 2 q^{35} - 12 q^{37} - 8 q^{43} + 5 q^{47} - 15 q^{49} - 18 q^{53} + 10 q^{55} - 26 q^{59} - 2 q^{61} + 5 q^{65} + 14 q^{67} + 18 q^{71} - 26 q^{77} - 6 q^{79} + 10 q^{83} - 4 q^{85} - 6 q^{89} + 62 q^{91} + 2 q^{95} - 32 q^{97}+O(q^{100}) $ 4 * q + 2 * q^5 - q^7 + 5 * q^11 - 5 * q^13 - 8 * q^17 + 4 * q^19 - 7 * q^23 - 2 * q^25 + 5 * q^29 - 5 * q^31 - 2 * q^35 - 12 * q^37 - 8 * q^43 + 5 * q^47 - 15 * q^49 - 18 * q^53 + 10 * q^55 - 26 * q^59 - 2 * q^61 + 5 * q^65 + 14 * q^67 + 18 * q^71 - 26 * q^77 - 6 * q^79 + 10 * q^83 - 4 * q^85 - 6 * q^89 + 62 * q^91 + 2 * q^95 - 32 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3240\mathbb{Z}\right)^\times$.

$n$	$1297$	$1621$	$2431$	$3161$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$		0			0
$7$	1.63746	+	2.83616i	0.618901	+	1.07197i	0.989687	+	0.143250i	$0.0457552\pi$
$7$	1.63746	+	2.83616i	0.618901	+	1.07197i	−0.370785	+	0.928719i	$0.620911\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	3.13746	+	5.43424i	0.945979	+	1.63848i	0.753778	+	0.657129i	$0.228229\pi$
$11$	3.13746	+	5.43424i	0.945979	+	1.63848i	0.192201	+	0.981356i	$0.438437\pi$
$12$		0			0
$13$	0.637459	−	1.10411i	0.176799	−	0.306225i	−0.763983	−	0.645236i	$-0.776759\pi$
$13$	0.637459	−	1.10411i	0.176799	−	0.306225i	0.940782	+	0.339011i	$0.110092\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−2.00000			−0.485071			−0.242536	−	0.970143i	$-0.577979\pi$
$17$	−2.00000			−0.485071			−0.242536	+	0.970143i	$0.577979\pi$
$18$		0			0
$19$	1.00000			0.229416			0.114708	−	0.993399i	$-0.463407\pi$
$19$	1.00000			0.229416			0.114708	+	0.993399i	$0.463407\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−3.63746	+	6.30026i	−0.758463	+	1.31370i	0.185172	+	0.982706i	$0.440716\pi$
$23$	−3.63746	+	6.30026i	−0.758463	+	1.31370i	−0.943634	+	0.330990i	$0.892618\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	3.13746	+	5.43424i	0.582611	+	1.00911i	0.995169	+	0.0981809i	$0.0313024\pi$
$29$	3.13746	+	5.43424i	0.582611	+	1.00911i	−0.412557	+	0.910932i	$0.635364\pi$
$30$		0			0
$31$	−3.13746	+	5.43424i	−0.563504	+	0.976018i	0.433683	+	0.901066i	$0.357214\pi$
$31$	−3.13746	+	5.43424i	−0.563504	+	0.976018i	−0.997187	+	0.0749524i	$0.976120\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	3.27492			0.553562
$36$		0			0
$37$	−10.5498			−1.73438			−0.867191	−	0.497976i	$-0.834077\pi$
$37$	−10.5498			−1.73438			−0.867191	+	0.497976i	$0.834077\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	3.77492	−	6.53835i	0.589543	−	1.02112i	−0.404749	−	0.914428i	$-0.632641\pi$
$41$	3.77492	−	6.53835i	0.589543	−	1.02112i	0.994292	−	0.106691i	$-0.0340255\pi$
$42$		0			0
$43$	−2.00000	−	3.46410i	−0.304997	−	0.528271i	0.672264	−	0.740312i	$-0.265322\pi$
$43$	−2.00000	−	3.46410i	−0.304997	−	0.528271i	−0.977261	+	0.212041i	$0.931989\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−0.637459	−	1.10411i	−0.0929829	−	0.161051i	0.815782	−	0.578359i	$-0.196307\pi$
$47$	−0.637459	−	1.10411i	−0.0929829	−	0.161051i	−0.908765	+	0.417308i	$0.862974\pi$
$48$		0			0
$49$	−1.86254	+	3.22602i	−0.266077	+	0.460859i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−0.725083			−0.0995978			−0.0497989	−	0.998759i	$-0.515858\pi$
$53$	−0.725083			−0.0995978			−0.0497989	+	0.998759i	$0.515858\pi$
$54$		0			0
$55$	6.27492			0.846110
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−6.50000	+	11.2583i	−0.846228	+	1.46571i	0.0383226	+	0.999265i	$0.487799\pi$
$59$	−6.50000	+	11.2583i	−0.846228	+	1.46571i	−0.884551	+	0.466444i	$0.845535\pi$
$60$		0			0
$61$	−4.27492	−	7.40437i	−0.547347	−	0.948033i	−0.998455	−	0.0555636i	$-0.982304\pi$
$61$	−4.27492	−	7.40437i	−0.547347	−	0.948033i	0.451108	−	0.892469i	$-0.351029\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−0.637459	−	1.10411i	−0.0790670	−	0.136948i
$66$		0			0
$67$	−0.274917	+	0.476171i	−0.0335865	+	0.0581735i	−0.882330	−	0.470631i	$-0.844026\pi$
$67$	−0.274917	+	0.476171i	−0.0335865	+	0.0581735i	0.848744	+	0.528805i	$0.177360\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	8.27492			0.982052			0.491026	−	0.871145i	$-0.336622\pi$
$71$	8.27492			0.982052			0.491026	+	0.871145i	$0.336622\pi$
$72$		0			0
$73$	15.0997			1.76728			0.883641	−	0.468165i	$-0.155085\pi$
$73$	15.0997			1.76728			0.883641	+	0.468165i	$0.155085\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−10.2749	+	17.7967i	−1.17094	+	2.02812i
$78$		0			0
$79$	−5.27492	−	9.13642i	−0.593475	−	1.02793i	−0.993760	−	0.111538i	$-0.964422\pi$
$79$	−5.27492	−	9.13642i	−0.593475	−	1.02793i	0.400286	−	0.916390i	$-0.368911\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−1.27492	−	2.20822i	−0.139940	−	0.242384i	0.787533	−	0.616272i	$-0.211358\pi$
$83$	−1.27492	−	2.20822i	−0.139940	−	0.242384i	−0.927474	+	0.373888i	$0.878024\pi$
$84$		0			0
$85$	−1.00000	+	1.73205i	−0.108465	+	0.187867i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−12.8248			−1.35942			−0.679710	−	0.733481i	$-0.737895\pi$
$89$	−12.8248			−1.35942			−0.679710	+	0.733481i	$0.737895\pi$
$90$		0			0
$91$	4.17525			0.437685
$92$		0			0
$93$		0			0
$94$		0			0
$95$	0.500000	−	0.866025i	0.0512989	−	0.0888523i
$96$		0			0
$97$	−8.00000	−	13.8564i	−0.812277	−	1.40690i	−0.911267	−	0.411816i	$-0.864894\pi$
$97$	−8.00000	−	13.8564i	−0.812277	−	1.40690i	0.0989899	−	0.995088i	$-0.468439\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	4.86254	+	8.42217i	0.483841	+	0.838037i	0.999828	−	0.0185594i	$-0.00590799\pi$
$101$	4.86254	+	8.42217i	0.483841	+	0.838037i	−0.515987	+	0.856597i	$0.672575\pi$
$102$		0			0
$103$	2.91238	−	5.04438i	0.286965	−	0.497038i	−0.686119	−	0.727489i	$-0.740687\pi$
$103$	2.91238	−	5.04438i	0.286965	−	0.497038i	0.973084	+	0.230452i	$0.0740204\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−15.0997			−1.45974			−0.729870	−	0.683586i	$-0.760419\pi$
$107$	−15.0997			−1.45974			−0.729870	+	0.683586i	$0.760419\pi$
$108$		0			0
$109$	−6.27492			−0.601028			−0.300514	−	0.953777i	$-0.597158\pi$
$109$	−6.27492			−0.601028			−0.300514	+	0.953777i	$0.597158\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−3.00000	+	5.19615i	−0.282216	+	0.488813i	−0.971930	−	0.235269i	$-0.924403\pi$
$113$	−3.00000	+	5.19615i	−0.282216	+	0.488813i	0.689714	+	0.724082i	$0.257736\pi$
$114$		0			0
$115$	3.63746	+	6.30026i	0.339195	+	0.587503i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−3.27492	−	5.67232i	−0.300211	−	0.519981i
$120$		0			0
$121$	−14.1873	+	24.5731i	−1.28975	+	2.23392i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	11.2749			1.00049			0.500244	−	0.865885i	$-0.333244\pi$
$127$	11.2749			1.00049			0.500244	+	0.865885i	$0.333244\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	0.774917	−	1.34220i	0.0677048	−	0.117268i	−0.830186	−	0.557487i	$-0.811766\pi$
$131$	0.774917	−	1.34220i	0.0677048	−	0.117268i	0.897891	+	0.440219i	$0.145099\pi$
$132$		0			0
$133$	1.63746	+	2.83616i	0.141986	+	0.245926i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	7.27492	+	12.6005i	0.621538	+	1.07654i	0.989199	+	0.146576i	$0.0468252\pi$
$137$	7.27492	+	12.6005i	0.621538	+	1.07654i	−0.367661	+	0.929960i	$0.619841\pi$
$138$		0			0
$139$	4.50000	−	7.79423i	0.381685	−	0.661098i	−0.609618	−	0.792695i	$-0.708677\pi$
$139$	4.50000	−	7.79423i	0.381685	−	0.661098i	0.991303	+	0.131597i	$0.0420106\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	8.00000			0.668994
$144$		0			0
$145$	6.27492			0.521104
$146$		0			0
$147$		0			0
$148$		0			0
$149$	1.00000	−	1.73205i	0.0819232	−	0.141895i	−0.822153	−	0.569267i	$-0.807227\pi$
$149$	1.00000	−	1.73205i	0.0819232	−	0.141895i	0.904076	+	0.427372i	$0.140560\pi$
$150$		0			0
$151$	6.13746	+	10.6304i	0.499459	+	0.865089i	1.00000		0.000624236i	$-0.000198701\pi$
$151$	6.13746	+	10.6304i	0.499459	+	0.865089i	−0.500541	+	0.865713i	$0.666865\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	3.13746	+	5.43424i	0.252007	+	0.436488i
$156$		0			0
$157$	−5.36254	+	9.28819i	−0.427977	+	0.741279i	−0.996693	−	0.0812554i	$-0.974107\pi$
$157$	−5.36254	+	9.28819i	−0.427977	+	0.741279i	0.568716	+	0.822534i	$0.307440\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−23.8248			−1.87765
$162$		0			0
$163$	20.5498			1.60959			0.804794	−	0.593555i	$-0.202276\pi$
$163$	20.5498			1.60959			0.804794	+	0.593555i	$0.202276\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−3.72508	+	6.45203i	−0.288256	+	0.499273i	−0.973393	−	0.229140i	$-0.926409\pi$
$167$	−3.72508	+	6.45203i	−0.288256	+	0.499273i	0.685138	+	0.728413i	$0.259742\pi$
$168$		0			0
$169$	5.68729	+	9.85068i	0.437484	+	0.757745i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	4.36254	+	7.55614i	0.331678	+	0.574483i	0.982841	−	0.184455i	$-0.0590520\pi$
$173$	4.36254	+	7.55614i	0.331678	+	0.574483i	−0.651163	+	0.758938i	$0.725719\pi$
$174$		0			0
$175$	1.63746	−	2.83616i	0.123780	−	0.214394i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	11.5498			0.863275			0.431638	−	0.902047i	$-0.357936\pi$
$179$	11.5498			0.863275			0.431638	+	0.902047i	$0.357936\pi$
$180$		0			0
$181$	16.2749			1.20971			0.604853	−	0.796337i	$-0.293232\pi$
$181$	16.2749			1.20971			0.604853	+	0.796337i	$0.293232\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−5.27492	+	9.13642i	−0.387820	+	0.671723i
$186$		0			0
$187$	−6.27492	−	10.8685i	−0.458867	−	0.794782i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	9.68729	+	16.7789i	0.700948	+	1.21408i	0.968134	+	0.250432i	$0.0805728\pi$
$191$	9.68729	+	16.7789i	0.700948	+	1.21408i	−0.267186	+	0.963645i	$0.586094\pi$
$192$		0			0
$193$	−2.00000	+	3.46410i	−0.143963	+	0.249351i	−0.928986	−	0.370116i	$-0.879318\pi$
$193$	−2.00000	+	3.46410i	−0.143963	+	0.249351i	0.785022	+	0.619467i	$0.212651\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	22.3746			1.59412			0.797062	−	0.603898i	$-0.206387\pi$
$197$	22.3746			1.59412			0.797062	+	0.603898i	$0.206387\pi$
$198$		0			0
$199$	8.00000			0.567105			0.283552	−	0.958957i	$-0.408487\pi$
$199$	8.00000			0.567105			0.283552	+	0.958957i	$0.408487\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−10.2749	+	17.7967i	−0.721158	+	1.24908i
$204$		0			0
$205$	−3.77492	−	6.53835i	−0.263652	−	0.456658i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	3.13746	+	5.43424i	0.217023	+	0.375894i
$210$		0			0
$211$	8.04983	−	13.9427i	0.554173	−	0.959857i	−0.443794	−	0.896129i	$-0.646368\pi$
$211$	8.04983	−	13.9427i	0.554173	−	0.959857i	0.997967	−	0.0637277i	$-0.0202989\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−4.00000			−0.272798
$216$		0			0
$217$	−20.5498			−1.39501
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−1.27492	+	2.20822i	−0.0857602	+	0.148541i
$222$		0			0
$223$	−4.00000	−	6.92820i	−0.267860	−	0.463947i	0.700449	−	0.713702i	$-0.252983\pi$
$223$	−4.00000	−	6.92820i	−0.267860	−	0.463947i	−0.968309	+	0.249756i	$0.919650\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−3.72508	−	6.45203i	−0.247242	−	0.428236i	0.715517	−	0.698595i	$-0.246191\pi$
$227$	−3.72508	−	6.45203i	−0.247242	−	0.428236i	−0.962760	+	0.270359i	$0.912858\pi$
$228$		0			0
$229$	−4.27492	+	7.40437i	−0.282494	+	0.489295i	−0.971998	−	0.234987i	$-0.924495\pi$
$229$	−4.27492	+	7.40437i	−0.282494	+	0.489295i	0.689504	+	0.724282i	$0.257829\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	9.09967			0.596139			0.298070	−	0.954544i	$-0.403657\pi$
$233$	9.09967			0.596139			0.298070	+	0.954544i	$0.403657\pi$
$234$		0			0
$235$	−1.27492			−0.0831664
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−6.72508	+	11.6482i	−0.435009	+	0.753458i	−0.997296	−	0.0734837i	$-0.976588\pi$
$239$	−6.72508	+	11.6482i	−0.435009	+	0.753458i	0.562287	+	0.826942i	$0.309922\pi$
$240$		0			0
$241$	12.1375	+	21.0227i	0.781842	+	1.35419i	0.930867	+	0.365357i	$0.119053\pi$
$241$	12.1375	+	21.0227i	0.781842	+	1.35419i	−0.149025	+	0.988833i	$0.547613\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	1.86254	+	3.22602i	0.118993	+	0.206103i
$246$		0			0
$247$	0.637459	−	1.10411i	0.0405605	−	0.0702529i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−18.7251			−1.18192			−0.590958	−	0.806702i	$-0.701250\pi$
$251$	−18.7251			−1.18192			−0.590958	+	0.806702i	$0.701250\pi$
$252$		0			0
$253$	−45.6495			−2.86996
$254$		0			0
$255$		0			0
$256$		0			0
$257$	1.54983	−	2.68439i	0.0966760	−	0.167448i	−0.813631	−	0.581382i	$-0.802512\pi$
$257$	1.54983	−	2.68439i	0.0966760	−	0.167448i	0.910307	+	0.413934i	$0.135846\pi$
$258$		0			0
$259$	−17.2749	−	29.9210i	−1.07341	−	1.85920i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−0.362541	−	0.627940i	−0.0223553	−	0.0387204i	0.854631	−	0.519235i	$-0.173783\pi$
$263$	−0.362541	−	0.627940i	−0.0223553	−	0.0387204i	−0.876987	+	0.480515i	$0.840450\pi$
$264$		0			0
$265$	−0.362541	+	0.627940i	−0.0222707	+	0.0385741i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	25.9244			1.58064			0.790320	−	0.612694i	$-0.209914\pi$
$269$	25.9244			1.58064			0.790320	+	0.612694i	$0.209914\pi$
$270$		0			0
$271$	13.4502			0.817039			0.408520	−	0.912750i	$-0.366045\pi$
$271$	13.4502			0.817039			0.408520	+	0.912750i	$0.366045\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	3.13746	−	5.43424i	0.189196	−	0.327697i
$276$		0			0
$277$	−12.6375	−	21.8887i	−0.759311	−	1.31517i	−0.943202	−	0.332219i	$-0.892203\pi$
$277$	−12.6375	−	21.8887i	−0.759311	−	1.31517i	0.183891	−	0.982947i	$-0.441131\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	3.08762	+	5.34792i	0.184192	+	0.319030i	0.943304	−	0.331930i	$-0.107700\pi$
$281$	3.08762	+	5.34792i	0.184192	+	0.319030i	−0.759112	+	0.650960i	$0.774366\pi$
$282$		0			0
$283$	5.72508	−	9.91613i	0.340321	−	0.589453i	−0.644171	−	0.764881i	$-0.722798\pi$
$283$	5.72508	−	9.91613i	0.340321	−	0.589453i	0.984492	+	0.175428i	$0.0561310\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	24.7251			1.45948
$288$		0			0
$289$	−13.0000			−0.764706
$290$		0			0
$291$		0			0
$292$		0			0
$293$	5.36254	−	9.28819i	0.313283	−	0.542622i	−0.665788	−	0.746141i	$-0.731904\pi$
$293$	5.36254	−	9.28819i	0.313283	−	0.542622i	0.979071	+	0.203519i	$0.0652378\pi$
$294$		0			0
$295$	6.50000	+	11.2583i	0.378445	+	0.655485i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	4.63746	+	8.03231i	0.268191	+	0.464521i
$300$		0			0
$301$	6.54983	−	11.3446i	0.377526	−	0.653895i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−8.54983			−0.489562
$306$		0			0
$307$	1.09967			0.0627614			0.0313807	−	0.999508i	$-0.490010\pi$
$307$	1.09967			0.0627614			0.0313807	+	0.999508i	$0.490010\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−12.9622	+	22.4512i	−0.735020	+	1.27309i	0.219695	+	0.975569i	$0.429494\pi$
$311$	−12.9622	+	22.4512i	−0.735020	+	1.27309i	−0.954715	+	0.297523i	$0.903840\pi$
$312$		0			0
$313$	−4.00000	−	6.92820i	−0.226093	−	0.391605i	0.730554	−	0.682855i	$-0.239262\pi$
$313$	−4.00000	−	6.92820i	−0.226093	−	0.391605i	−0.956647	+	0.291250i	$0.905929\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	2.63746	+	4.56821i	0.148134	+	0.256576i	0.930538	−	0.366195i	$-0.119340\pi$
$317$	2.63746	+	4.56821i	0.148134	+	0.256576i	−0.782404	+	0.622772i	$0.786007\pi$
$318$		0			0
$319$	−19.6873	+	34.0994i	−1.10228	+	1.90920i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−2.00000			−0.111283
$324$		0			0
$325$	−1.27492			−0.0707197
$326$		0			0
$327$		0			0
$328$		0			0
$329$	2.08762	−	3.61587i	0.115094	−	0.199349i
$330$		0			0
$331$	9.41238	+	16.3027i	0.517351	+	0.896078i	0.999797	+	0.0201524i	$0.00641515\pi$
$331$	9.41238	+	16.3027i	0.517351	+	0.896078i	−0.482446	+	0.875926i	$0.660252\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	0.274917	+	0.476171i	0.0150203	+	0.0260160i
$336$		0			0
$337$	−2.72508	+	4.71998i	−0.148445	+	0.257114i	−0.930653	−	0.365903i	$-0.880760\pi$
$337$	−2.72508	+	4.71998i	−0.148445	+	0.257114i	0.782208	+	0.623017i	$0.214093\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−39.3746			−2.13225
$342$		0			0
$343$	10.7251			0.579100
$344$		0			0
$345$		0			0
$346$		0			0
$347$	7.00000	−	12.1244i	0.375780	−	0.650870i	−0.614664	−	0.788789i	$-0.710708\pi$
$347$	7.00000	−	12.1244i	0.375780	−	0.650870i	0.990443	+	0.137920i	$0.0440416\pi$
$348$		0			0
$349$	−6.41238	−	11.1066i	−0.343247	−	0.594521i	0.641787	−	0.766883i	$-0.278193\pi$
$349$	−6.41238	−	11.1066i	−0.343247	−	0.594521i	−0.985034	+	0.172362i	$0.944860\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	3.27492	+	5.67232i	0.174306	+	0.301907i	0.939921	−	0.341392i	$-0.110898\pi$
$353$	3.27492	+	5.67232i	0.174306	+	0.301907i	−0.765615	+	0.643299i	$0.777565\pi$
$354$		0			0
$355$	4.13746	−	7.16629i	0.219594	−	0.380347i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−0.824752			−0.0435287			−0.0217644	−	0.999763i	$-0.506928\pi$
$359$	−0.824752			−0.0435287			−0.0217644	+	0.999763i	$0.506928\pi$
$360$		0			0
$361$	−18.0000			−0.947368
$362$		0			0
$363$		0			0
$364$		0			0
$365$	7.54983	−	13.0767i	0.395176	−	0.684466i
$366$		0			0
$367$	−6.27492	−	10.8685i	−0.327548	−	0.567330i	0.654477	−	0.756082i	$-0.272889\pi$
$367$	−6.27492	−	10.8685i	−0.327548	−	0.567330i	−0.982025	+	0.188752i	$0.939556\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−1.18729	−	2.05645i	−0.0616412	−	0.106766i
$372$		0			0
$373$	−15.5498	+	26.9331i	−0.805140	+	1.39454i	0.111057	+	0.993814i	$0.464576\pi$
$373$	−15.5498	+	26.9331i	−0.805140	+	1.39454i	−0.916197	+	0.400729i	$0.868757\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	8.00000			0.412021
$378$		0			0
$379$	9.27492			0.476420			0.238210	−	0.971214i	$-0.423439\pi$
$379$	9.27492			0.476420			0.238210	+	0.971214i	$0.423439\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	1.18729	−	2.05645i	0.0606678	−	0.105080i	−0.834096	−	0.551619i	$-0.814010\pi$
$383$	1.18729	−	2.05645i	0.0606678	−	0.105080i	0.894764	+	0.446539i	$0.147344\pi$
$384$		0			0
$385$	10.2749	+	17.7967i	0.523658	+	0.907003i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−8.27492	−	14.3326i	−0.419555	−	0.726691i	0.576340	−	0.817210i	$-0.304481\pi$
$389$	−8.27492	−	14.3326i	−0.419555	−	0.726691i	−0.995895	+	0.0905197i	$0.971147\pi$
$390$		0			0
$391$	7.27492	−	12.6005i	0.367908	−	0.637236i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−10.5498			−0.530820
$396$		0			0
$397$	7.09967			0.356322			0.178161	−	0.984001i	$-0.442985\pi$
$397$	7.09967			0.356322			0.178161	+	0.984001i	$0.442985\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	11.6375	−	20.1567i	0.581147	−	1.00658i	−0.414197	−	0.910187i	$-0.635937\pi$
$401$	11.6375	−	20.1567i	0.581147	−	1.00658i	0.995344	−	0.0963887i	$-0.0307292\pi$
$402$		0			0
$403$	4.00000	+	6.92820i	0.199254	+	0.345118i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−33.0997	−	57.3303i	−1.64069	−	2.84176i
$408$		0			0
$409$	14.9124	−	25.8290i	0.737370	−	1.27716i	−0.216306	−	0.976326i	$-0.569401\pi$
$409$	14.9124	−	25.8290i	0.737370	−	1.27716i	0.953676	−	0.300836i	$-0.0972657\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−42.5739			−2.09493
$414$		0			0
$415$	−2.54983			−0.125166
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−4.54983	+	7.88054i	−0.222274	+	0.384990i	−0.955498	−	0.294997i	$-0.904681\pi$
$419$	−4.54983	+	7.88054i	−0.222274	+	0.384990i	0.733224	+	0.679987i	$0.238015\pi$
$420$		0			0
$421$	16.1375	+	27.9509i	0.786492	+	1.36224i	0.928104	+	0.372321i	$0.121438\pi$
$421$	16.1375	+	27.9509i	0.786492	+	1.36224i	−0.141612	+	0.989922i	$0.545229\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	1.00000	+	1.73205i	0.0485071	+	0.0840168i
$426$		0			0
$427$	14.0000	−	24.2487i	0.677507	−	1.17348i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	6.27492			0.302252			0.151126	−	0.988514i	$-0.451710\pi$
$431$	6.27492			0.302252			0.151126	+	0.988514i	$0.451710\pi$
$432$		0			0
$433$	12.5498			0.603107			0.301553	−	0.953449i	$-0.402495\pi$
$433$	12.5498			0.603107			0.301553	+	0.953449i	$0.402495\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−3.63746	+	6.30026i	−0.174003	+	0.301382i
$438$		0			0
$439$	12.6873	+	21.9750i	0.605531	+	1.04881i	0.991967	+	0.126495i	$0.0403727\pi$
$439$	12.6873	+	21.9750i	0.605531	+	1.04881i	−0.386436	+	0.922316i	$0.626294\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	5.27492	+	9.13642i	0.250619	+	0.434085i	0.963696	−	0.267001i	$-0.0860326\pi$
$443$	5.27492	+	9.13642i	0.250619	+	0.434085i	−0.713077	+	0.701085i	$0.752699\pi$
$444$		0			0
$445$	−6.41238	+	11.1066i	−0.303976	+	0.526501i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−1.54983			−0.0731412			−0.0365706	−	0.999331i	$-0.511643\pi$
$449$	−1.54983			−0.0731412			−0.0365706	+	0.999331i	$0.511643\pi$
$450$		0			0
$451$	47.3746			2.23078
$452$		0			0
$453$		0			0
$454$		0			0
$455$	2.08762	−	3.61587i	0.0978693	−	0.169515i
$456$		0			0
$457$	−8.00000	−	13.8564i	−0.374224	−	0.648175i	0.615986	−	0.787757i	$-0.288758\pi$
$457$	−8.00000	−	13.8564i	−0.374224	−	0.648175i	−0.990211	+	0.139581i	$0.955424\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−11.6873	−	20.2430i	−0.544332	−	0.942810i	−0.998649	−	0.0519698i	$-0.983450\pi$
$461$	−11.6873	−	20.2430i	−0.544332	−	0.942810i	0.454317	−	0.890840i	$-0.349883\pi$
$462$		0			0
$463$	−20.7371	+	35.9178i	−0.963736	+	1.66924i	−0.250763	+	0.968049i	$0.580681\pi$
$463$	−20.7371	+	35.9178i	−0.963736	+	1.66924i	−0.712973	+	0.701191i	$0.752652\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	40.1993			1.86020			0.930102	−	0.367302i	$-0.119718\pi$
$467$	40.1993			1.86020			0.930102	+	0.367302i	$0.119718\pi$
$468$		0			0
$469$	−1.80066			−0.0831469
$470$		0			0
$471$		0			0
$472$		0			0
$473$	12.5498	−	21.7370i	0.577042	−	0.999466i
$474$		0			0
$475$	−0.500000	−	0.866025i	−0.0229416	−	0.0397360i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−2.13746	−	3.70219i	−0.0976630	−	0.169157i	0.813054	−	0.582188i	$-0.197803\pi$
$479$	−2.13746	−	3.70219i	−0.0976630	−	0.169157i	−0.910717	+	0.413031i	$0.864470\pi$
$480$		0			0
$481$	−6.72508	+	11.6482i	−0.306637	+	0.531112i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−16.0000			−0.726523
$486$		0			0
$487$	−37.2749			−1.68909			−0.844544	−	0.535486i	$-0.820128\pi$
$487$	−37.2749			−1.68909			−0.844544	+	0.535486i	$0.820128\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	7.50000	−	12.9904i	0.338470	−	0.586248i	−0.645675	−	0.763612i	$-0.723424\pi$
$491$	7.50000	−	12.9904i	0.338470	−	0.586248i	0.984145	+	0.177365i	$0.0567572\pi$
$492$		0			0
$493$	−6.27492	−	10.8685i	−0.282608	−	0.489492i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	13.5498	+	23.4690i	0.607793	+	1.05273i
$498$		0			0
$499$	14.7749	−	25.5909i	0.661416	−	1.14561i	−0.318828	−	0.947813i	$-0.603289\pi$
$499$	14.7749	−	25.5909i	0.661416	−	1.14561i	0.980244	−	0.197794i	$-0.0633776\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		0			0			−	1.00000i	$-0.5\pi$
$503$		0			0				1.00000i	$0.5\pi$
$504$		0			0
$505$	9.72508			0.432761
$506$		0			0
$507$		0			0
$508$		0			0
$509$	14.0997	−	24.4213i	0.624957	−	1.08246i	−0.363592	−	0.931558i	$-0.618450\pi$
$509$	14.0997	−	24.4213i	0.624957	−	1.08246i	0.988549	−	0.150899i	$-0.0482168\pi$
$510$		0			0
$511$	24.7251	+	42.8251i	1.09377	+	1.89447i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−2.91238	−	5.04438i	−0.128335	−	0.222282i
$516$		0			0
$517$	4.00000	−	6.92820i	0.175920	−	0.304702i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	26.9244			1.17958			0.589790	−	0.807557i	$-0.299210\pi$
$521$	26.9244			1.17958			0.589790	+	0.807557i	$0.299210\pi$
$522$		0			0
$523$	−39.6495			−1.73375			−0.866876	−	0.498524i	$-0.833876\pi$
$523$	−39.6495			−1.73375			−0.866876	+	0.498524i	$0.833876\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	6.27492	−	10.8685i	0.273340	−	0.473438i
$528$		0			0
$529$	−14.9622	−	25.9153i	−0.650531	−	1.12675i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−4.81271	−	8.33585i	−0.208461	−	0.361066i
$534$		0			0
$535$	−7.54983	+	13.0767i	−0.326408	+	0.565355i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−23.3746			−1.00681
$540$		0			0
$541$	43.9244			1.88846			0.944229	−	0.329289i	$-0.106809\pi$
$541$	43.9244			1.88846			0.944229	+	0.329289i	$0.106809\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−3.13746	+	5.43424i	−0.134394	+	0.232777i
$546$		0			0
$547$	−10.0000	−	17.3205i	−0.427569	−	0.740571i	0.569087	−	0.822277i	$-0.307297\pi$
$547$	−10.0000	−	17.3205i	−0.427569	−	0.740571i	−0.996657	+	0.0817056i	$0.973963\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	3.13746	+	5.43424i	0.133660	+	0.231506i
$552$		0			0
$553$	17.2749	−	29.9210i	0.734604	−	1.27237i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−32.9244			−1.39505			−0.697526	−	0.716559i	$-0.745716\pi$
$557$	−32.9244			−1.39505			−0.697526	+	0.716559i	$0.745716\pi$
$558$		0			0
$559$	−5.09967			−0.215693
$560$		0			0
$561$		0			0
$562$		0			0
$563$	18.5498	−	32.1293i	0.781782	−	1.35409i	−0.149120	−	0.988819i	$-0.547644\pi$
$563$	18.5498	−	32.1293i	0.781782	−	1.35409i	0.930903	−	0.365268i	$-0.119023\pi$
$564$		0			0
$565$	3.00000	+	5.19615i	0.126211	+	0.218604i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−13.2251	−	22.9065i	−0.554424	−	0.960291i	−0.997948	−	0.0640285i	$-0.979605\pi$
$569$	−13.2251	−	22.9065i	−0.554424	−	0.960291i	0.443524	−	0.896263i	$-0.353728\pi$
$570$		0			0
$571$	0.587624	−	1.01779i	0.0245913	−	0.0425934i	−0.853468	−	0.521145i	$-0.825505\pi$
$571$	0.587624	−	1.01779i	0.0245913	−	0.0425934i	0.878059	+	0.478552i	$0.158838\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	7.27492			0.303385
$576$		0			0
$577$	−11.4502			−0.476677			−0.238338	−	0.971182i	$-0.576603\pi$
$577$	−11.4502			−0.476677			−0.238338	+	0.971182i	$0.576603\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	4.17525	−	7.23174i	0.173218	−	0.300023i
$582$		0			0
$583$	−2.27492	−	3.94027i	−0.0942174	−	0.163189i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−17.2749	−	29.9210i	−0.713012	−	1.23497i	−0.963721	−	0.266911i	$-0.913997\pi$
$587$	−17.2749	−	29.9210i	−0.713012	−	1.23497i	0.250709	−	0.968062i	$-0.419336\pi$
$588$		0			0
$589$	−3.13746	+	5.43424i	−0.129277	+	0.223914i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	48.1993			1.97931			0.989655	−	0.143469i	$-0.0458258\pi$
$593$	48.1993			1.97931			0.989655	+	0.143469i	$0.0458258\pi$
$594$		0			0
$595$	−6.54983			−0.268517
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−7.86254	+	13.6183i	−0.321255	+	0.556430i	−0.980747	−	0.195282i	$-0.937438\pi$
$599$	−7.86254	+	13.6183i	−0.321255	+	0.556430i	0.659492	+	0.751711i	$0.270771\pi$
$600$		0			0
$601$	0.950166	+	1.64574i	0.0387581	+	0.0671309i	0.884754	−	0.466059i	$-0.154327\pi$
$601$	0.950166	+	1.64574i	0.0387581	+	0.0671309i	−0.845996	+	0.533190i	$0.820993\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	14.1873	+	24.5731i	0.576795	+	0.999039i
$606$		0			0
$607$	12.0000	−	20.7846i	0.487065	−	0.843621i	−0.512824	−	0.858494i	$-0.671401\pi$
$607$	12.0000	−	20.7846i	0.487065	−	0.843621i	0.999889	+	0.0148722i	$0.00473415\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−1.62541			−0.0657572
$612$		0			0
$613$	−46.0241			−1.85890			−0.929448	−	0.368954i	$-0.879716\pi$
$613$	−46.0241			−1.85890			−0.929448	+	0.368954i	$0.879716\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−21.8248	+	37.8016i	−0.878631	+	1.52183i	−0.0257881	+	0.999667i	$0.508210\pi$
$617$	−21.8248	+	37.8016i	−0.878631	+	1.52183i	−0.852843	+	0.522167i	$0.825124\pi$
$618$		0			0
$619$	9.18729	+	15.9129i	0.369268	+	0.639592i	0.989451	−	0.144865i	$-0.0462749\pi$
$619$	9.18729	+	15.9129i	0.369268	+	0.639592i	−0.620183	+	0.784457i	$0.712942\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−21.0000	−	36.3731i	−0.841347	−	1.45726i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	21.0997			0.841299
$630$		0			0
$631$	24.4743			0.974305			0.487152	−	0.873317i	$-0.338036\pi$
$631$	24.4743			0.974305			0.487152	+	0.873317i	$0.338036\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	5.63746	−	9.76436i	0.223716	−	0.387487i
$636$		0			0
$637$	2.37459	+	4.11290i	0.0940845	+	0.162959i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	16.9622	+	29.3794i	0.669967	+	1.16042i	0.977913	+	0.209013i	$0.0670251\pi$
$641$	16.9622	+	29.3794i	0.669967	+	1.16042i	−0.307946	+	0.951404i	$0.599642\pi$
$642$		0			0
$643$	16.5498	−	28.6652i	0.652662	−	1.13044i	−0.329813	−	0.944046i	$-0.606986\pi$
$643$	16.5498	−	28.6652i	0.652662	−	1.13044i	0.982475	−	0.186397i	$-0.0596811\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	28.5498			1.12241			0.561205	−	0.827677i	$-0.310338\pi$
$647$	28.5498			1.12241			0.561205	+	0.827677i	$0.310338\pi$
$648$		0			0
$649$	−81.5739			−3.20206
$650$		0			0
$651$		0			0
$652$		0			0
$653$	4.72508	−	8.18408i	0.184907	−	0.320268i	−0.758638	−	0.651512i	$-0.774135\pi$
$653$	4.72508	−	8.18408i	0.184907	−	0.320268i	0.943545	+	0.331244i	$0.107468\pi$
$654$		0			0
$655$	−0.774917	−	1.34220i	−0.0302785	−	0.0524439i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−8.63746	−	14.9605i	−0.336468	−	0.582779i	0.647298	−	0.762237i	$-0.275899\pi$
$659$	−8.63746	−	14.9605i	−0.336468	−	0.582779i	−0.983766	+	0.179458i	$0.942566\pi$
$660$		0			0
$661$	19.9622	−	34.5756i	0.776440	−	1.34483i	−0.157542	−	0.987512i	$-0.550357\pi$
$661$	19.9622	−	34.5756i	0.776440	−	1.34483i	0.933982	−	0.357321i	$-0.116310\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	3.27492			0.126996
$666$		0			0
$667$	−45.6495			−1.76756
$668$		0			0
$669$		0			0
$670$		0			0
$671$	26.8248	−	46.4618i	1.03556	−	1.79364i
$672$		0			0
$673$	4.45017	+	7.70791i	0.171541	+	0.297118i	0.938959	−	0.344029i	$-0.111792\pi$
$673$	4.45017	+	7.70791i	0.171541	+	0.297118i	−0.767418	+	0.641148i	$0.778459\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−13.4622	−	23.3172i	−0.517395	−	0.896154i	−0.999796	−	0.0202036i	$-0.993569\pi$
$677$	−13.4622	−	23.3172i	−0.517395	−	0.896154i	0.482401	−	0.875950i	$-0.339765\pi$
$678$		0			0
$679$	26.1993	−	45.3786i	1.00544	−	1.74147i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	1.45017			0.0554890			0.0277445	−	0.999615i	$-0.491168\pi$
$683$	1.45017			0.0554890			0.0277445	+	0.999615i	$0.491168\pi$
$684$		0			0
$685$	14.5498			0.555921
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−0.462210	+	0.800572i	−0.0176088	+	0.0304994i
$690$		0			0
$691$	3.91238	+	6.77643i	0.148834	+	0.257788i	0.930797	−	0.365537i	$-0.119115\pi$
$691$	3.91238	+	6.77643i	0.148834	+	0.257788i	−0.781963	+	0.623325i	$0.785781\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−4.50000	−	7.79423i	−0.170695	−	0.295652i
$696$		0			0
$697$	−7.54983	+	13.0767i	−0.285970	+	0.495315i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	33.3746			1.26054			0.630270	−	0.776376i	$-0.282944\pi$
$701$	33.3746			1.26054			0.630270	+	0.776376i	$0.282944\pi$
$702$		0			0
$703$	−10.5498			−0.397895
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−15.9244	+	27.5819i	−0.598899	+	1.03732i
$708$		0			0
$709$	0.450166	+	0.779710i	0.0169063	+	0.0292826i	0.874355	−	0.485287i	$-0.161285\pi$
$709$	0.450166	+	0.779710i	0.0169063	+	0.0292826i	−0.857448	+	0.514570i	$0.827952\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−22.8248	−	39.5336i	−0.854794	−	1.48055i
$714$		0			0
$715$	4.00000	−	6.92820i	0.149592	−	0.259100i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	44.8248			1.67168			0.835841	−	0.548972i	$-0.184981\pi$
$719$	44.8248			1.67168			0.835841	+	0.548972i	$0.184981\pi$
$720$		0			0
$721$	19.0756			0.710412
$722$		0			0
$723$		0			0
$724$		0			0
$725$	3.13746	−	5.43424i	0.116522	−	0.201823i
$726$		0			0
$727$	15.1873	+	26.3052i	0.563266	+	0.975604i	0.997209	+	0.0746643i	$0.0237885\pi$
$727$	15.1873	+	26.3052i	0.563266	+	0.975604i	−0.433943	+	0.900940i	$0.642878\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	4.00000	+	6.92820i	0.147945	+	0.256249i
$732$		0			0
$733$	3.00000	−	5.19615i	0.110808	−	0.191924i	−0.805289	−	0.592883i	$-0.797990\pi$
$733$	3.00000	−	5.19615i	0.110808	−	0.191924i	0.916096	+	0.400959i	$0.131323\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−3.45017			−0.127088
$738$		0			0
$739$	15.9244			0.585789			0.292895	−	0.956145i	$-0.405381\pi$
$739$	15.9244			0.585789			0.292895	+	0.956145i	$0.405381\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−14.2749	+	24.7249i	−0.523696	+	0.907068i	0.475924	+	0.879487i	$0.342114\pi$
$743$	−14.2749	+	24.7249i	−0.523696	+	0.907068i	−0.999620	+	0.0275813i	$0.991219\pi$
$744$		0			0
$745$	−1.00000	−	1.73205i	−0.0366372	−	0.0634574i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−24.7251	−	42.8251i	−0.903435	−	1.56480i
$750$		0			0
$751$	−17.2749	+	29.9210i	−0.630371	+	1.09183i	0.357105	+	0.934064i	$0.383764\pi$
$751$	−17.2749	+	29.9210i	−0.630371	+	1.09183i	−0.987476	+	0.157770i	$0.949570\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	12.2749			0.446730
$756$		0			0
$757$	34.3746			1.24937			0.624683	−	0.780879i	$-0.285228\pi$
$757$	34.3746			1.24937			0.624683	+	0.780879i	$0.285228\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	24.7749	−	42.9114i	0.898090	−	1.55554i	0.0681570	−	0.997675i	$-0.478288\pi$
$761$	24.7749	−	42.9114i	0.898090	−	1.55554i	0.829933	−	0.557863i	$-0.188379\pi$
$762$		0			0
$763$	−10.2749	−	17.7967i	−0.371977	−	0.644283i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	8.28696	+	14.3534i	0.299225	+	0.518273i
$768$		0			0
$769$	8.13746	−	14.0945i	0.293444	−	0.508260i	−0.681178	−	0.732118i	$-0.738532\pi$
$769$	8.13746	−	14.0945i	0.293444	−	0.508260i	0.974622	+	0.223858i	$0.0718652\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−31.6495			−1.13835			−0.569177	−	0.822215i	$-0.692738\pi$
$773$	−31.6495			−1.13835			−0.569177	+	0.822215i	$0.692738\pi$
$774$		0			0
$775$	6.27492			0.225402
$776$		0			0
$777$		0			0
$778$		0			0
$779$	3.77492	−	6.53835i	0.135250	−	0.234261i
$780$		0			0
$781$	25.9622	+	44.9679i	0.929001	+	1.60908i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	5.36254	+	9.28819i	0.191397	+	0.331510i
$786$		0			0
$787$	17.0000	−	29.4449i	0.605985	−	1.04960i	−0.385911	−	0.922536i	$-0.626113\pi$
$787$	17.0000	−	29.4449i	0.605985	−	1.04960i	0.991895	−	0.127060i	$-0.0405540\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−19.6495			−0.698656
$792$		0			0
$793$	−10.9003			−0.387082
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−12.7251	+	22.0405i	−0.450746	+	0.780714i	−0.998432	−	0.0559691i	$-0.982175\pi$
$797$	−12.7251	+	22.0405i	−0.450746	+	0.780714i	0.547687	+	0.836683i	$0.315508\pi$
$798$		0			0
$799$	1.27492	+	2.20822i	0.0451033	+	0.0781213i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	47.3746	+	82.0552i	1.67181	+	2.89566i
$804$		0			0
$805$	−11.9124	+	20.6328i	−0.419856	+	0.727212i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−16.6495			−0.585365			−0.292683	−	0.956210i	$-0.594548\pi$
$809$	−16.6495			−0.585365			−0.292683	+	0.956210i	$0.594548\pi$
$810$		0			0
$811$	13.1752			0.462646			0.231323	−	0.972877i	$-0.425695\pi$
$811$	13.1752			0.462646			0.231323	+	0.972877i	$0.425695\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	10.2749	−	17.7967i	0.359915	−	0.623390i
$816$		0			0
$817$	−2.00000	−	3.46410i	−0.0699711	−	0.121194i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	2.41238	+	4.17836i	0.0841925	+	0.145826i	0.905047	−	0.425312i	$-0.139836\pi$
$821$	2.41238	+	4.17836i	0.0841925	+	0.145826i	−0.820854	+	0.571138i	$0.806502\pi$
$822$		0			0
$823$	−11.7251	+	20.3084i	−0.408711	+	0.707908i	−0.994746	−	0.102378i	$-0.967355\pi$
$823$	−11.7251	+	20.3084i	−0.408711	+	0.707908i	0.586035	+	0.810286i	$0.300688\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−21.0997			−0.733707			−0.366854	−	0.930279i	$-0.619565\pi$
$827$	−21.0997			−0.733707			−0.366854	+	0.930279i	$0.619565\pi$
$828$		0			0
$829$	−13.1752			−0.457595			−0.228798	−	0.973474i	$-0.573479\pi$
$829$	−13.1752			−0.457595			−0.228798	+	0.973474i	$0.573479\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	3.72508	−	6.45203i	0.129066	−	0.223550i
$834$		0			0
$835$	3.72508	+	6.45203i	0.128912	+	0.223282i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	26.2371	+	45.4440i	0.905806	+	1.56890i	0.819831	+	0.572605i	$0.194067\pi$
$839$	26.2371	+	45.4440i	0.905806	+	1.56890i	0.0859749	+	0.996297i	$0.472600\pi$
$840$		0			0
$841$	−5.18729	+	8.98466i	−0.178872	+	0.309816i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	11.3746			0.391298
$846$		0			0
$847$	−92.9244			−3.19292
$848$		0			0
$849$		0			0
$850$		0			0
$851$	38.3746	−	66.4667i	1.31546	−	2.27845i
$852$		0			0
$853$	24.6495	+	42.6942i	0.843983	+	1.46182i	0.886502	+	0.462726i	$0.153128\pi$
$853$	24.6495	+	42.6942i	0.843983	+	1.46182i	−0.0425186	+	0.999096i	$0.513538\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−26.3746	−	45.6821i	−0.900939	−	1.56047i	−0.826278	−	0.563263i	$-0.809546\pi$
$857$	−26.3746	−	45.6821i	−0.900939	−	1.56047i	−0.0746608	−	0.997209i	$-0.523787\pi$
$858$		0			0
$859$	−26.2371	+	45.4440i	−0.895199	+	1.55053i	−0.0616414	+	0.998098i	$0.519634\pi$
$859$	−26.2371	+	45.4440i	−0.895199	+	1.55053i	−0.833558	+	0.552432i	$0.813700\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−23.2749			−0.792287			−0.396144	−	0.918189i	$-0.629652\pi$
$863$	−23.2749			−0.792287			−0.396144	+	0.918189i	$0.629652\pi$
$864$		0			0
$865$	8.72508			0.296662
$866$		0			0
$867$		0			0
$868$		0			0
$869$	33.0997	−	57.3303i	1.12283	−	1.94480i
$870$		0			0
$871$	0.350497	+	0.607078i	0.0118761	+	0.0205701i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−1.63746	−	2.83616i	−0.0553562	−	0.0958798i
$876$		0			0
$877$	6.63746	−	11.4964i	0.224131	−	0.388206i	−0.731927	−	0.681383i	$-0.761379\pi$
$877$	6.63746	−	11.4964i	0.224131	−	0.388206i	0.956058	+	0.293176i	$0.0947123\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−18.6254			−0.627506			−0.313753	−	0.949505i	$-0.601586\pi$
$881$	−18.6254			−0.627506			−0.313753	+	0.949505i	$0.601586\pi$
$882$		0			0
$883$	32.1993			1.08359			0.541797	−	0.840509i	$-0.317744\pi$
$883$	32.1993			1.08359			0.541797	+	0.840509i	$0.317744\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	0.0876242	−	0.151770i	0.00294213	−	0.00509592i	−0.864551	−	0.502546i	$-0.832397\pi$
$887$	0.0876242	−	0.151770i	0.00294213	−	0.00509592i	0.867493	+	0.497450i	$0.165730\pi$
$888$		0			0
$889$	18.4622	+	31.9775i	0.619203	+	1.07249i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−0.637459	−	1.10411i	−0.0213317	−	0.0369477i
$894$		0			0
$895$	5.77492	−	10.0025i	0.193034	−	0.334345i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−39.3746			−1.31322
$900$		0			0
$901$	1.45017			0.0483120
$902$		0			0
$903$		0			0
$904$		0			0
$905$	8.13746	−	14.0945i	0.270498	−	0.468517i
$906$		0			0
$907$	−25.5498	−	44.2536i	−0.848368	−	1.46942i	−0.882664	−	0.470005i	$-0.844252\pi$
$907$	−25.5498	−	44.2536i	−0.848368	−	1.46942i	0.0342953	−	0.999412i	$-0.489081\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−13.5120	−	23.4035i	−0.447674	−	0.775394i	0.550560	−	0.834795i	$-0.314414\pi$
$911$	−13.5120	−	23.4035i	−0.447674	−	0.775394i	−0.998234	+	0.0594013i	$0.981081\pi$
$912$		0			0
$913$	8.00000	−	13.8564i	0.264761	−	0.458580i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	5.07558			0.167610
$918$		0			0
$919$	11.9244			0.393350			0.196675	−	0.980469i	$-0.436986\pi$
$919$	11.9244			0.393350			0.196675	+	0.980469i	$0.436986\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	5.27492	−	9.13642i	0.173626	−	0.300729i
$924$		0			0
$925$	5.27492	+	9.13642i	0.173438	+	0.300404i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−30.0619	−	52.0687i	−0.986298	−	1.70832i	−0.636019	−	0.771673i	$-0.719420\pi$
$929$	−30.0619	−	52.0687i	−0.986298	−	1.70832i	−0.350279	−	0.936645i	$-0.613913\pi$
$930$		0			0
$931$	−1.86254	+	3.22602i	−0.0610423	+	0.105728i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−12.5498			−0.410423
$936$		0			0
$937$	−0.549834			−0.0179623			−0.00898115	−	0.999960i	$-0.502859\pi$
$937$	−0.549834			−0.0179623			−0.00898115	+	0.999960i	$0.502859\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	3.54983	−	6.14849i	0.115721	−	0.200435i	−0.802347	−	0.596858i	$-0.796415\pi$
$941$	3.54983	−	6.14849i	0.115721	−	0.200435i	0.918068	+	0.396423i	$0.129749\pi$
$942$		0			0
$943$	27.4622	+	47.5659i	0.894293	+	1.54896i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−13.7251	−	23.7725i	−0.446005	−	0.772504i	0.552116	−	0.833767i	$-0.313820\pi$
$947$	−13.7251	−	23.7725i	−0.446005	−	0.772504i	−0.998122	+	0.0612633i	$0.980487\pi$
$948$		0			0
$949$	9.62541	−	16.6717i	0.312454	−	0.541186i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	33.0997			1.07220			0.536102	−	0.844153i	$-0.319896\pi$
$953$	33.0997			1.07220			0.536102	+	0.844153i	$0.319896\pi$
$954$		0			0
$955$	19.3746			0.626947
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−23.8248	+	41.2657i	−0.769341	+	1.33254i
$960$		0			0
$961$	−4.18729	−	7.25260i	−0.135074	−	0.233955i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	2.00000	+	3.46410i	0.0643823	+	0.111513i
$966$		0			0
$967$	−5.17525	+	8.96379i	−0.166425	+	0.288256i	−0.937160	−	0.348899i	$-0.886556\pi$
$967$	−5.17525	+	8.96379i	−0.166425	+	0.288256i	0.770736	+	0.637155i	$0.219889\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−36.6495			−1.17614			−0.588069	−	0.808811i	$-0.700112\pi$
$971$	−36.6495			−1.17614			−0.588069	+	0.808811i	$0.700112\pi$
$972$		0			0
$973$	29.4743			0.944901
$974$		0			0
$975$		0			0
$976$		0			0
$977$	1.82475	−	3.16056i	0.0583790	−	0.101115i	−0.835359	−	0.549705i	$-0.814740\pi$
$977$	1.82475	−	3.16056i	0.0583790	−	0.101115i	0.893738	+	0.448590i	$0.148073\pi$
$978$		0			0
$979$	−40.2371	−	69.6927i	−1.28598	−	2.22739i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−23.3746	−	40.4860i	−0.745534	−	1.29130i	−0.949945	−	0.312417i	$-0.898861\pi$
$983$	−23.3746	−	40.4860i	−0.745534	−	1.29130i	0.204412	−	0.978885i	$-0.434472\pi$
$984$		0			0
$985$	11.1873	−	19.3770i	0.356457	−	0.617401i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	29.0997			0.925316
$990$		0			0
$991$	−1.72508			−0.0547991			−0.0273995	−	0.999625i	$-0.508723\pi$
$991$	−1.72508			−0.0547991			−0.0273995	+	0.999625i	$0.508723\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	4.00000	−	6.92820i	0.126809	−	0.219639i
$996$		0			0
$997$	−4.18729	−	7.25260i	−0.132613	−	0.229692i	0.792070	−	0.610430i	$-0.209003\pi$
$997$	−4.18729	−	7.25260i	−0.132613	−	0.229692i	−0.924683	+	0.380738i	$0.875670\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3240.2.q.be.1081.2		4
3.2	odd	2		3240.2.q.y.1081.2		4
9.2	odd	6		3240.2.q.y.2161.2		4
9.4	even	3		3240.2.a.h.1.1	✓	2
9.5	odd	6		3240.2.a.n.1.1	yes	2
9.7	even	3	inner	3240.2.q.be.2161.2		4
36.23	even	6		6480.2.a.bm.1.2		2
36.31	odd	6		6480.2.a.bf.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3240.2.a.h.1.1	✓	2	9.4	even	3
3240.2.a.n.1.1	yes	2	9.5	odd	6
3240.2.q.y.1081.2		4	3.2	odd	2
3240.2.q.y.2161.2		4	9.2	odd	6
3240.2.q.be.1081.2		4	1.1	even	1	trivial
3240.2.q.be.2161.2		4	9.7	even	3	inner
6480.2.a.bf.1.2		2	36.31	odd	6
6480.2.a.bm.1.2		2	36.23	even	6

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:	\( N \)	\(=\)	\( 3240 = 2^{3} \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3240.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{5} +(1.63746 + 2.83616i) q^{7} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{5} +(1.63746 + 2.83616i) q^{7} +(3.13746 + 5.43424i) q^{11} +(0.637459 - 1.10411i) q^{13} -2.00000 q^{17} +1.00000 q^{19} +(-3.63746 + 6.30026i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(3.13746 + 5.43424i) q^{29} +(-3.13746 + 5.43424i) q^{31} +3.27492 q^{35} -10.5498 q^{37} +(3.77492 - 6.53835i) q^{41} +(-2.00000 - 3.46410i) q^{43} +(-0.637459 - 1.10411i) q^{47} +(-1.86254 + 3.22602i) q^{49} -0.725083 q^{53} +6.27492 q^{55} +(-6.50000 + 11.2583i) q^{59} +(-4.27492 - 7.40437i) q^{61} +(-0.637459 - 1.10411i) q^{65} +(-0.274917 + 0.476171i) q^{67} +8.27492 q^{71} +15.0997 q^{73} +(-10.2749 + 17.7967i) q^{77} +(-5.27492 - 9.13642i) q^{79} +(-1.27492 - 2.20822i) q^{83} +(-1.00000 + 1.73205i) q^{85} -12.8248 q^{89} +4.17525 q^{91} +(0.500000 - 0.866025i) q^{95} +(-8.00000 - 13.8564i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{5} - q^{7}+O(q^{10}) \) 4 * q + 2 * q^5 - q^7	\( 4 q + 2 q^{5} - q^{7} + 5 q^{11} - 5 q^{13} - 8 q^{17} + 4 q^{19} - 7 q^{23} - 2 q^{25} + 5 q^{29} - 5 q^{31} - 2 q^{35} - 12 q^{37} - 8 q^{43} + 5 q^{47} - 15 q^{49} - 18 q^{53} + 10 q^{55} - 26 q^{59} - 2 q^{61} + 5 q^{65} + 14 q^{67} + 18 q^{71} - 26 q^{77} - 6 q^{79} + 10 q^{83} - 4 q^{85} - 6 q^{89} + 62 q^{91} + 2 q^{95} - 32 q^{97}+O(q^{100}) \) 4 * q + 2 * q^5 - q^7 + 5 * q^11 - 5 * q^13 - 8 * q^17 + 4 * q^19 - 7 * q^23 - 2 * q^25 + 5 * q^29 - 5 * q^31 - 2 * q^35 - 12 * q^37 - 8 * q^43 + 5 * q^47 - 15 * q^49 - 18 * q^53 + 10 * q^55 - 26 * q^59 - 2 * q^61 + 5 * q^65 + 14 * q^67 + 18 * q^71 - 26 * q^77 - 6 * q^79 + 10 * q^83 - 4 * q^85 - 6 * q^89 + 62 * q^91 + 2 * q^95 - 32 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more