LMFDB - Embedded newform 810.2.s.a.773.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [810,2,Mod(17,810)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(810, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([22, 9]))

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

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

chi := DirichletCharacter("810.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 810 = 2 \cdot 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	810.s (of order $36$, degree $12$, 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:	$6.46788256372$
Analytic rank:	$0$
Dimension:	$216$
Relative dimension:	$18$ over $\Q(\zeta_{36})$
Twist minimal:	no (minimal twist has level 270)
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			773.9
Character	$\chi$	$=$	810.773
Dual form			810.2.s.a.197.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.996195 - 0.0871557i) q^{2} +(0.984808 + 0.173648i) q^{4} +(2.15090 + 0.611237i) q^{5} +(-3.60150 - 2.52180i) q^{7} +(-0.965926 - 0.258819i) q^{8} +O(q^{10})$	\(q+(-0.996195 - 0.0871557i) q^{2} +(0.984808 + 0.173648i) q^{4} +(2.15090 + 0.611237i) q^{5} +(-3.60150 - 2.52180i) q^{7} +(-0.965926 - 0.258819i) q^{8} +(-2.08945 - 0.796375i) q^{10} +(-0.474884 + 1.30473i) q^{11} +(-0.410808 - 4.69556i) q^{13} +(3.36801 + 2.82610i) q^{14} +(0.939693 + 0.342020i) q^{16} +(-5.62913 + 1.50832i) q^{17} +(-7.17681 + 4.14354i) q^{19} +(2.01209 + 0.975451i) q^{20} +(0.586792 - 1.25838i) q^{22} +(-0.511833 - 0.730973i) q^{23} +(4.25278 + 2.62942i) q^{25} +4.71350i q^{26} +(-3.10888 - 3.10888i) q^{28} +(-4.04977 + 3.39816i) q^{29} +(1.07794 - 6.11333i) q^{31} +(-0.906308 - 0.422618i) q^{32} +(5.73917 - 1.01197i) q^{34} +(-6.20507 - 7.62552i) q^{35} +(0.319303 + 1.19165i) q^{37} +(7.51064 - 3.50227i) q^{38} +(-1.91941 - 1.14710i) q^{40} +(-1.37192 + 1.63499i) q^{41} +(-1.59452 - 3.41946i) q^{43} +(-0.694234 + 1.20245i) q^{44} +(0.446177 + 0.772801i) q^{46} +(-2.26380 + 3.23304i) q^{47} +(4.21722 + 11.5867i) q^{49} +(-4.00743 - 2.99007i) q^{50} +(0.410808 - 4.69556i) q^{52} +(6.56367 - 6.56367i) q^{53} +(-1.81893 + 2.51609i) q^{55} +(2.82610 + 3.36801i) q^{56} +(4.33053 - 3.03227i) q^{58} +(-2.97757 + 1.08375i) q^{59} +(-0.104169 - 0.590769i) q^{61} +(-1.60665 + 5.99611i) q^{62} +(0.866025 + 0.500000i) q^{64} +(1.98649 - 10.3508i) q^{65} +(-1.40032 + 0.122512i) q^{67} +(-5.80553 + 0.507918i) q^{68} +(5.51685 + 8.13731i) q^{70} +(-10.7411 - 6.20139i) q^{71} +(0.128962 - 0.481292i) q^{73} +(-0.214228 - 1.21495i) q^{74} +(-7.78730 + 2.83435i) q^{76} +(5.00057 - 3.50144i) q^{77} +(-7.34219 - 8.75008i) q^{79} +(1.81213 + 1.31003i) q^{80} +(1.50919 - 1.50919i) q^{82} +(-0.841193 + 9.61488i) q^{83} +(-13.0297 - 0.196478i) q^{85} +(1.29043 + 3.54542i) q^{86} +(0.796392 - 1.13737i) q^{88} +(-3.02996 - 5.24805i) q^{89} +(-10.3617 + 17.9471i) q^{91} +(-0.377125 - 0.808747i) q^{92} +(2.53696 - 3.02343i) q^{94} +(-17.9693 + 4.52562i) q^{95} +(-3.52069 + 1.64173i) q^{97} +(-3.19132 - 11.9102i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q+O(q^{10}) $ 216 * q	$ 216 q - 24 q^{11} + 24 q^{20} - 24 q^{23} + 36 q^{25} + 108 q^{35} + 36 q^{38} + 72 q^{41} + 48 q^{47} + 48 q^{50} + 12 q^{56} + 36 q^{61} - 24 q^{65} - 72 q^{67} - 36 q^{68} + 240 q^{77} + 60 q^{83} - 72 q^{86} + 48 q^{92} + 60 q^{95} - 72 q^{97}+O(q^{100}) $ 216 * q - 24 * q^11 + 24 * q^20 - 24 * q^23 + 36 * q^25 + 108 * q^35 + 36 * q^38 + 72 * q^41 + 48 * q^47 + 48 * q^50 + 12 * q^56 + 36 * q^61 - 24 * q^65 - 72 * q^67 - 36 * q^68 + 240 * q^77 + 60 * q^83 - 72 * q^86 + 48 * q^92 + 60 * q^95 - 72 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/810\mathbb{Z}\right)^\times$.

$n$	$487$	$731$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{18}\right)$

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 $

$2$	−0.996195	−	0.0871557i	−0.704416	−	0.0616284i
$2$	−0.996195	−	0.0871557i	−0.704416	−	0.0616284i
$3$		0			0
$3$		0			0
$4$	0.984808	+	0.173648i	0.492404	+	0.0868241i
$5$	2.15090	+	0.611237i	0.961914	+	0.273353i
$5$	2.15090	+	0.611237i	0.961914	+	0.273353i
$6$		0			0
$7$	−3.60150	−	2.52180i	−1.36124	−	0.953151i	−0.999784	−	0.0207619i	$-0.993391\pi$
$7$	−3.60150	−	2.52180i	−1.36124	−	0.953151i	−0.361456	−	0.932389i	$-0.617720\pi$
$8$	−0.965926	−	0.258819i	−0.341506	−	0.0915064i
$9$		0			0
$10$	−2.08945	−	0.796375i	−0.660741	−	0.251836i
$11$	−0.474884	+	1.30473i	−0.143183	+	0.393392i	−0.990467	−	0.137748i	$-0.956014\pi$
$11$	−0.474884	+	1.30473i	−0.143183	+	0.393392i	0.847284	+	0.531139i	$0.178236\pi$
$12$		0			0
$13$	−0.410808	−	4.69556i	−0.113938	−	1.30231i	−0.810891	−	0.585197i	$-0.801017\pi$
$13$	−0.410808	−	4.69556i	−0.113938	−	1.30231i	0.696953	−	0.717117i	$-0.254539\pi$
$14$	3.36801	+	2.82610i	0.900139	+	0.755306i
$15$		0			0
$16$	0.939693	+	0.342020i	0.234923	+	0.0855050i
$17$	−5.62913	+	1.50832i	−1.36527	+	0.365822i	−0.865747	−	0.500482i	$-0.833156\pi$
$17$	−5.62913	+	1.50832i	−1.36527	+	0.365822i	−0.499518	+	0.866303i	$0.666490\pi$
$18$		0			0
$19$	−7.17681	+	4.14354i	−1.64647	+	0.950592i	−0.668016	+	0.744147i	$0.732856\pi$
$19$	−7.17681	+	4.14354i	−1.64647	+	0.950592i	−0.978458	+	0.206446i	$0.933810\pi$
$20$	2.01209	+	0.975451i	0.449916	+	0.218118i
$21$		0			0
$22$	0.586792	−	1.25838i	0.125104	−	0.268287i
$23$	−0.511833	−	0.730973i	−0.106725	−	0.152418i	0.762237	−	0.647298i	$-0.224101\pi$
$23$	−0.511833	−	0.730973i	−0.106725	−	0.152418i	−0.868962	+	0.494880i	$0.835212\pi$
$24$		0			0
$25$	4.25278	+	2.62942i	0.850556	+	0.525885i
$26$			4.71350i			0.924393i
$27$		0			0
$28$	−3.10888	−	3.10888i	−0.587524	−	0.587524i
$29$	−4.04977	+	3.39816i	−0.752023	+	0.631022i	−0.936037	−	0.351901i	$-0.885535\pi$
$29$	−4.04977	+	3.39816i	−0.752023	+	0.631022i	0.184014	+	0.982924i	$0.441091\pi$
$30$		0			0
$31$	1.07794	−	6.11333i	0.193605	−	1.09799i	−0.720788	−	0.693156i	$-0.756220\pi$
$31$	1.07794	−	6.11333i	0.193605	−	1.09799i	0.914392	−	0.404830i	$-0.132669\pi$
$32$	−0.906308	−	0.422618i	−0.160214	−	0.0747091i
$33$		0			0
$34$	5.73917	−	1.01197i	0.984260	−	0.173552i
$35$	−6.20507	−	7.62552i	−1.04885	−	1.28895i
$36$		0			0
$37$	0.319303	+	1.19165i	0.0524930	+	0.195907i	0.987193	−	0.159531i	$-0.0509983\pi$
$37$	0.319303	+	1.19165i	0.0524930	+	0.195907i	−0.934700	+	0.355438i	$0.884332\pi$
$38$	7.51064	−	3.50227i	1.21839	−	0.568143i
$39$		0			0
$40$	−1.91941	−	1.14710i	−0.303486	−	0.181373i
$41$	−1.37192	+	1.63499i	−0.214257	+	0.255342i	−0.862459	−	0.506127i	$-0.831077\pi$
$41$	−1.37192	+	1.63499i	−0.214257	+	0.255342i	0.648202	+	0.761469i	$0.275521\pi$
$42$		0			0
$43$	−1.59452	−	3.41946i	−0.243162	−	0.521463i	0.746413	−	0.665483i	$-0.231775\pi$
$43$	−1.59452	−	3.41946i	−0.243162	−	0.521463i	−0.989575	+	0.144021i	$0.953997\pi$
$44$	−0.694234	+	1.20245i	−0.104660	+	0.181276i
$45$		0			0
$46$	0.446177	+	0.772801i	0.0657852	+	0.113943i
$47$	−2.26380	+	3.23304i	−0.330209	+	0.471587i	−0.949586	−	0.313506i	$-0.898496\pi$
$47$	−2.26380	+	3.23304i	−0.330209	+	0.471587i	0.619377	+	0.785094i	$0.287385\pi$
$48$		0			0
$49$	4.21722	+	11.5867i	0.602459	+	1.65524i
$50$	−4.00743	−	2.99007i	−0.566736	−	0.422860i
$51$		0			0
$52$	0.410808	−	4.69556i	0.0569689	−	0.651157i
$53$	6.56367	−	6.56367i	0.901589	−	0.901589i	−0.0939845	−	0.995574i	$-0.529960\pi$
$53$	6.56367	−	6.56367i	0.901589	−	0.901589i	0.995574	+	0.0939845i	$0.0299604\pi$
$54$		0			0
$55$	−1.81893	+	2.51609i	−0.245265	+	0.339269i
$56$	2.82610	+	3.36801i	0.377653	+	0.450069i
$57$		0			0
$58$	4.33053	−	3.03227i	0.568626	−	0.398156i
$59$	−2.97757	+	1.08375i	−0.387646	+	0.141092i	−0.528489	−	0.848940i	$-0.677241\pi$
$59$	−2.97757	+	1.08375i	−0.387646	+	0.141092i	0.140842	+	0.990032i	$0.455019\pi$
$60$		0			0
$61$	−0.104169	−	0.590769i	−0.0133374	−	0.0756403i	0.977413	−	0.211340i	$-0.0677828\pi$
$61$	−0.104169	−	0.590769i	−0.0133374	−	0.0756403i	−0.990750	+	0.135700i	$0.956672\pi$
$62$	−1.60665	+	5.99611i	−0.204045	+	0.761507i
$63$		0			0
$64$	0.866025	+	0.500000i	0.108253	+	0.0625000i
$65$	1.98649	−	10.3508i	0.246394	−	1.28386i
$66$		0			0
$67$	−1.40032	+	0.122512i	−0.171076	+	0.0149672i	−0.172372	−	0.985032i	$-0.555143\pi$
$67$	−1.40032	+	0.122512i	−0.171076	+	0.0149672i	0.00129575	+	0.999999i	$0.499588\pi$
$68$	−5.80553	+	0.507918i	−0.704024	+	0.0615941i
$69$		0			0
$70$	5.51685	+	8.13731i	0.659390	+	0.972595i
$71$	−10.7411	−	6.20139i	−1.27474	−	0.735969i	−0.298861	−	0.954297i	$-0.596607\pi$
$71$	−10.7411	−	6.20139i	−1.27474	−	0.735969i	−0.975876	+	0.218328i	$0.929940\pi$
$72$		0			0
$73$	0.128962	−	0.481292i	0.0150938	−	0.0563309i	−0.957968	−	0.286874i	$-0.907384\pi$
$73$	0.128962	−	0.481292i	0.0150938	−	0.0563309i	0.973062	+	0.230544i	$0.0740504\pi$
$74$	−0.214228	−	1.21495i	−0.0249035	−	0.141235i
$75$		0			0
$76$	−7.78730	+	2.83435i	−0.893265	+	0.325122i
$77$	5.00057	−	3.50144i	0.569868	−	0.399026i
$78$		0			0
$79$	−7.34219	−	8.75008i	−0.826060	−	0.984460i	0.173940	−	0.984756i	$-0.444350\pi$
$79$	−7.34219	−	8.75008i	−0.826060	−	0.984460i	−1.00000		0.000295882i	$0.999906\pi$
$80$	1.81213	+	1.31003i	0.202603	+	0.146466i
$81$		0			0
$82$	1.50919	−	1.50919i	0.166663	−	0.166663i
$83$	−0.841193	+	9.61488i	−0.0923329	+	1.05537i	0.798791	+	0.601609i	$0.205473\pi$
$83$	−0.841193	+	9.61488i	−0.0923329	+	1.05537i	−0.891124	+	0.453761i	$0.850082\pi$
$84$		0			0
$85$	−13.0297	−	0.196478i	−1.41327	−	0.0213111i
$86$	1.29043	+	3.54542i	0.139150	+	0.382312i
$87$		0			0
$88$	0.796392	−	1.13737i	0.0848957	−	0.121244i
$89$	−3.02996	−	5.24805i	−0.321175	−	0.556292i	0.659555	−	0.751656i	$-0.270745\pi$
$89$	−3.02996	−	5.24805i	−0.321175	−	0.556292i	−0.980731	+	0.195364i	$0.937411\pi$
$90$		0			0
$91$	−10.3617	+	17.9471i	−1.08621	+	1.88136i
$92$	−0.377125	−	0.808747i	−0.0393180	−	0.0843177i
$93$		0			0
$94$	2.53696	−	3.02343i	0.261668	−	0.311843i
$95$	−17.9693	+	4.52562i	−1.84361	+	0.464318i
$96$		0			0
$97$	−3.52069	+	1.64173i	−0.357472	+	0.166692i	−0.593054	−	0.805162i	$-0.702078\pi$
$97$	−3.52069	+	1.64173i	−0.357472	+	0.166692i	0.235582	+	0.971854i	$0.424300\pi$
$98$	−3.19132	−	11.9102i	−0.322372	−	1.20311i
$99$		0			0
$100$	3.73157	+	3.32796i	0.373157	+	0.332796i
$101$	4.22030	−	0.744152i	0.419935	−	0.0740459i	0.0403122	−	0.999187i	$-0.487165\pi$
$101$	4.22030	−	0.744152i	0.419935	−	0.0740459i	0.379623	+	0.925141i	$0.376054\pi$
$102$		0			0
$103$	−7.95001	−	3.70715i	−0.783338	−	0.365277i	−0.0105529	−	0.999944i	$-0.503359\pi$
$103$	−7.95001	−	3.70715i	−0.783338	−	0.365277i	−0.772785	+	0.634668i	$0.781137\pi$
$104$	−0.818490	+	4.64189i	−0.0802596	+	0.455175i
$105$		0			0
$106$	−7.11075	+	5.96663i	−0.690657	+	0.579530i
$107$	−5.61968	−	5.61968i	−0.543275	−	0.543275i	0.381212	−	0.924488i	$-0.375507\pi$
$107$	−5.61968	−	5.61968i	−0.543275	−	0.543275i	−0.924488	+	0.381212i	$0.875507\pi$
$108$		0			0
$109$		−	15.3242i		−	1.46779i	−0.679261	−	0.733897i	$-0.737700\pi$
$109$		−	15.3242i		−	1.46779i	0.679261	−	0.733897i	$-0.262300\pi$
$110$	2.03130	−	2.34798i	0.193677	−	0.223872i
$111$		0			0
$112$	−2.52180	−	3.60150i	−0.238288	−	0.340310i
$113$	−2.56809	+	5.50729i	−0.241586	+	0.518082i	−0.989292	−	0.145947i	$-0.953377\pi$
$113$	−2.56809	+	5.50729i	−0.241586	+	0.518082i	0.747707	+	0.664029i	$0.231155\pi$
$114$		0			0
$115$	−0.654106	−	1.88510i	−0.0609957	−	0.175787i
$116$	−4.57833	+	2.64330i	−0.425087	+	0.245424i
$117$		0			0
$118$	3.06069	−	0.820110i	0.281760	−	0.0754973i
$119$	24.0770	+	8.76332i	2.20714	+	0.803333i
$120$		0			0
$121$	6.94968	+	5.83147i	0.631789	+	0.530134i
$122$	0.0522832	+	0.597600i	0.00473350	+	0.0541042i
$123$		0			0
$124$	2.12314	−	5.83327i	0.190663	−	0.523843i
$125$	7.54012	+	8.25510i	0.674409	+	0.738358i
$126$		0			0
$127$	−7.32998	−	1.96406i	−0.650431	−	0.174282i	−0.0815072	−	0.996673i	$-0.525973\pi$
$127$	−7.32998	−	1.96406i	−0.650431	−	0.174282i	−0.568924	+	0.822390i	$0.692640\pi$
$128$	−0.819152	−	0.573576i	−0.0724035	−	0.0506975i
$129$		0			0
$130$	−2.88106	+	10.1383i	−0.252686	+	0.889186i
$131$	13.9453	+	2.45893i	1.21841	+	0.214838i	0.745640	−	0.666349i	$-0.232144\pi$
$131$	13.9453	+	2.45893i	1.21841	+	0.214838i	0.472767	+	0.881187i	$0.343255\pi$
$132$		0			0
$133$	36.2965	+	3.17553i	3.14731	+	0.275354i
$134$	1.40567			0.121431
$135$		0			0
$136$	5.82771			0.499722
$137$	−2.20276	−	0.192717i	−0.188195	−	0.0164649i	−0.00733122	−	0.999973i	$-0.502334\pi$
$137$	−2.20276	−	0.192717i	−0.188195	−	0.0164649i	−0.180863	+	0.983508i	$0.557889\pi$
$138$		0			0
$139$	5.67821	+	1.00122i	0.481619	+	0.0849225i	0.409186	−	0.912451i	$-0.365813\pi$
$139$	5.67821	+	1.00122i	0.481619	+	0.0849225i	0.0724330	+	0.997373i	$0.476924\pi$
$140$	−4.78665	−	8.58718i	−0.404545	−	0.725749i
$141$		0			0
$142$	10.1598	+	7.11394i	0.852588	+	0.596989i
$143$	6.32154	+	1.69385i	0.528634	+	0.141647i
$144$		0			0
$145$	−10.7877	+	4.83375i	−0.895873	+	0.401421i
$146$	−0.170418	+	0.468220i	−0.0141039	+	0.0387502i
$147$		0			0
$148$	0.107523	+	1.22900i	0.00883835	+	0.101023i
$149$	1.88858	+	1.58471i	0.154718	+	0.129824i	0.716861	−	0.697216i	$-0.245578\pi$
$149$	1.88858	+	1.58471i	0.154718	+	0.129824i	−0.562142	+	0.827040i	$0.690023\pi$
$150$		0			0
$151$	13.9291	+	5.06979i	1.13354	+	0.412573i	0.839575	−	0.543244i	$-0.182804\pi$
$151$	13.9291	+	5.06979i	1.13354	+	0.412573i	0.293961	+	0.955817i	$0.405026\pi$
$152$	8.00470	−	2.14485i	0.649267	−	0.173970i
$153$		0			0
$154$	−5.28672	+	3.05229i	−0.426016	+	0.245960i
$155$	6.05525	−	12.4903i	0.486369	−	1.00325i
$156$		0			0
$157$	7.40351	−	15.8769i	0.590865	−	1.26711i	−0.352642	−	0.935758i	$-0.614717\pi$
$157$	7.40351	−	15.8769i	0.590865	−	1.26711i	0.943506	−	0.331355i	$-0.107506\pi$
$158$	6.55163	+	9.35669i	0.521219	+	0.744379i
$159$		0			0
$160$	−1.69106	−	1.46298i	−0.133690	−	0.115659i
$161$			3.92334i			0.309203i
$162$		0			0
$163$	−4.71559	−	4.71559i	−0.369354	−	0.369354i	0.497888	−	0.867242i	$-0.334109\pi$
$163$	−4.71559	−	4.71559i	−0.369354	−	0.369354i	−0.867242	+	0.497888i	$0.834109\pi$
$164$	−1.63499	+	1.37192i	−0.127671	+	0.107129i
$165$		0			0
$166$	1.67598	−	9.50497i	0.130082	−	0.737729i
$167$	0.0392724	+	0.0183130i	0.00303899	+	0.00141711i	0.424137	−	0.905598i	$-0.360577\pi$
$167$	0.0392724	+	0.0183130i	0.00303899	+	0.00141711i	−0.421098	+	0.907015i	$0.638355\pi$
$168$		0			0
$169$	−9.07702	+	1.60052i	−0.698232	+	0.123117i
$170$	12.9630	+	1.33134i	0.994214	+	0.102109i
$171$		0			0
$172$	−0.976513	−	3.64440i	−0.0744584	−	0.277883i
$173$	4.28190	−	1.99668i	0.325547	−	0.151805i	−0.252973	−	0.967473i	$-0.581408\pi$
$173$	4.28190	−	1.99668i	0.325547	−	0.151805i	0.578520	+	0.815668i	$0.303631\pi$
$174$		0			0
$175$	−8.68552	−	20.1945i	−0.656563	−	1.52656i
$176$	−0.892490	+	1.06363i	−0.0672740	+	0.0801740i
$177$		0			0
$178$	2.56104	+	5.49216i	0.191958	+	0.411655i
$179$	3.26967	−	5.66323i	0.244387	−	0.423290i	−0.717572	−	0.696484i	$-0.754747\pi$
$179$	3.26967	−	5.66323i	0.244387	−	0.423290i	0.961959	+	0.273194i	$0.0880801\pi$
$180$		0			0
$181$	11.6065	+	20.1031i	0.862707	+	1.49425i	0.869306	+	0.494273i	$0.164566\pi$
$181$	11.6065	+	20.1031i	0.862707	+	1.49425i	−0.00659982	+	0.999978i	$0.502101\pi$
$182$	11.8865	−	16.9757i	0.881086	−	1.25832i
$183$		0			0
$184$	0.305203	+	0.838538i	0.0224999	+	0.0618178i
$185$	−0.0415933	+	2.75830i	−0.00305800	+	0.202794i
$186$		0			0
$187$	0.705228	−	8.06079i	0.0515714	−	0.589464i
$188$	−2.79082	+	2.79082i	−0.203541	+	0.203541i
$189$		0			0
$190$	18.2954	−	2.94226i	1.32729	−	0.213454i
$191$	−10.0109	−	11.9305i	−0.724365	−	0.863264i	0.270683	−	0.962669i	$-0.412751\pi$
$191$	−10.0109	−	11.9305i	−0.724365	−	0.863264i	−0.995047	+	0.0994046i	$0.968306\pi$
$192$		0			0
$193$	3.07209	−	2.15110i	0.221134	−	0.154840i	−0.457760	−	0.889076i	$-0.651348\pi$
$193$	3.07209	−	2.15110i	0.221134	−	0.154840i	0.678894	+	0.734236i	$0.262459\pi$
$194$	3.65038	−	1.32863i	0.262082	−	0.0953901i
$195$		0			0
$196$	2.14114	+	12.1430i	0.152938	+	0.867356i
$197$	−0.478146	+	1.78447i	−0.0340665	+	0.127138i	−0.980865	−	0.194689i	$-0.937630\pi$
$197$	−0.478146	+	1.78447i	−0.0340665	+	0.127138i	0.946799	+	0.321827i	$0.104297\pi$
$198$		0			0
$199$	22.1698	+	12.7997i	1.57157	+	0.907349i	0.995976	+	0.0896167i	$0.0285642\pi$
$199$	22.1698	+	12.7997i	1.57157	+	0.907349i	0.575599	+	0.817732i	$0.304769\pi$
$200$	−3.42732	−	3.64053i	−0.242348	−	0.257424i
$201$		0			0
$202$	−4.26910	+	0.373497i	−0.300373	+	0.0262792i
$203$	23.1547	−	2.02578i	1.62514	−	0.142182i
$204$		0			0
$205$	−3.95022	+	2.67813i	−0.275896	+	0.187049i
$206$	7.59666	+	4.38593i	0.529284	+	0.305583i
$207$		0			0
$208$	1.21994	−	4.55289i	0.0845878	−	0.315686i
$209$	−1.99805	−	11.3315i	−0.138208	−	0.783818i
$210$		0			0
$211$	8.46275	−	3.08019i	0.582600	−	0.212049i	−0.0338717	−	0.999426i	$-0.510784\pi$
$211$	8.46275	−	3.08019i	0.582600	−	0.212049i	0.616472	+	0.787377i	$0.288562\pi$
$212$	7.60372	−	5.32418i	0.522226	−	0.365666i
$213$		0			0
$214$	5.10851	+	6.08809i	0.349211	+	0.416173i
$215$	−1.33956	−	8.32956i	−0.0913573	−	0.568071i
$216$		0			0
$217$	−19.2988	+	19.2988i	−1.31009	+	1.31009i
$218$	−1.33559	+	15.2659i	−0.0904578	+	1.03394i
$219$		0			0
$220$	−2.22821	+	2.16201i	−0.150226	+	0.145763i
$221$	9.39491	+	25.8123i	0.631970	+	1.73632i
$222$		0			0
$223$	−1.52020	+	2.17107i	−0.101800	+	0.145386i	−0.866820	−	0.498621i	$-0.833840\pi$
$223$	−1.52020	+	2.17107i	−0.101800	+	0.145386i	0.765020	+	0.644006i	$0.222729\pi$
$224$	2.19831	+	3.80759i	0.146881	+	0.254405i
$225$		0			0
$226$	3.03831	−	5.26251i	0.202105	−	0.350057i
$227$	3.88805	+	8.33794i	0.258059	+	0.553409i	0.992064	−	0.125735i	$-0.0401290\pi$
$227$	3.88805	+	8.33794i	0.258059	+	0.553409i	−0.734005	+	0.679144i	$0.762351\pi$
$228$		0			0
$229$	7.72285	−	9.20373i	0.510340	−	0.608200i	−0.447928	−	0.894069i	$-0.647838\pi$
$229$	7.72285	−	9.20373i	0.510340	−	0.608200i	0.958269	+	0.285870i	$0.0922825\pi$
$230$	0.487319	+	1.93494i	0.0321329	+	0.127586i
$231$		0			0
$232$	4.79128	−	2.23421i	0.314563	−	0.146683i
$233$	−2.10559	−	7.85817i	−0.137942	−	0.514806i	−0.999968	−	0.00794300i	$-0.997472\pi$
$233$	−2.10559	−	7.85817i	−0.137942	−	0.514806i	0.862027	−	0.506863i	$-0.169195\pi$
$234$		0			0
$235$	−6.84536	+	5.57024i	−0.446542	+	0.363362i
$236$	−3.12052	+	0.550232i	−0.203129	+	0.0358171i
$237$		0			0
$238$	−23.2216	−	10.8284i	−1.50524	−	0.701903i
$239$	0.678158	−	3.84603i	0.0438664	−	0.248779i	−0.954987	−	0.296647i	$-0.904132\pi$
$239$	0.678158	−	3.84603i	0.0438664	−	0.248779i	0.998854	+	0.0478681i	$0.0152427\pi$
$240$		0			0
$241$	−11.6772	+	9.79830i	−0.752192	+	0.631164i	−0.936082	−	0.351783i	$-0.885575\pi$
$241$	−11.6772	+	9.79830i	−0.752192	+	0.631164i	0.183890	+	0.982947i	$0.441131\pi$
$242$	−6.41498	−	6.41498i	−0.412371	−	0.412371i
$243$		0			0
$244$		−	0.599883i		−	0.0384036i
$245$	1.98861	+	27.4996i	0.127047	+	1.75689i
$246$		0			0
$247$	22.4045	+	31.9970i	1.42557	+	2.03592i
$248$	−2.62346	+	5.62603i	−0.166590	+	0.357253i
$249$		0			0
$250$	−6.79195	−	8.88085i	−0.429561	−	0.561674i
$251$	−7.92222	+	4.57390i	−0.500046	+	0.288702i	−0.728733	−	0.684798i	$-0.759890\pi$
$251$	−7.92222	+	4.57390i	−0.500046	+	0.288702i	0.228686	+	0.973500i	$0.426557\pi$
$252$		0			0
$253$	1.19679	−	0.320678i	0.0752413	−	0.0201608i
$254$	7.13091	+	2.59544i	0.447433	+	0.162852i
$255$		0			0
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	−1.04969	−	11.9980i	−0.0654777	−	0.748413i	−0.955980	−	0.293433i	$-0.905202\pi$
$257$	−1.04969	−	11.9980i	−0.0654777	−	0.748413i	0.890502	−	0.454980i	$-0.150353\pi$
$258$		0			0
$259$	1.85514	−	5.09696i	0.115273	−	0.316710i
$260$	3.75371	−	9.84860i	0.232795	−	0.610784i
$261$		0			0
$262$	−13.6779	−	3.66499i	−0.845025	−	0.226424i
$263$	−22.7191	−	15.9081i	−1.40092	−	0.980935i	−0.997835	−	0.0657721i	$-0.979049\pi$
$263$	−22.7191	−	15.9081i	−1.40092	−	0.980935i	−0.403085	−	0.915163i	$-0.632062\pi$
$264$		0			0
$265$	18.1298	−	10.1059i	1.11370	−	0.620798i
$266$	−35.8816	−	6.32690i	−2.20004	−	0.387927i
$267$		0			0
$268$	−1.40032	−	0.122512i	−0.0855381	−	0.00748361i
$269$	−29.9331			−1.82506			−0.912528	−	0.409014i	$-0.865873\pi$
$269$	−29.9331			−1.82506			−0.912528	+	0.409014i	$0.865873\pi$
$270$		0			0
$271$	11.0344			0.670294			0.335147	−	0.942166i	$-0.391214\pi$
$271$	11.0344			0.670294			0.335147	+	0.942166i	$0.391214\pi$
$272$	−5.80553	−	0.507918i	−0.352012	−	0.0307971i
$273$		0			0
$274$	2.17758	+	0.383967i	0.131553	+	0.0231963i
$275$	−5.45027	+	4.30007i	−0.328664	+	0.259304i
$276$		0			0
$277$	−4.31295	−	3.01996i	−0.259140	−	0.181452i	0.436786	−	0.899566i	$-0.356117\pi$
$277$	−4.31295	−	3.01996i	−0.259140	−	0.181452i	−0.695926	+	0.718114i	$0.745006\pi$
$278$	−5.56934	−	1.49230i	−0.334027	−	0.0895022i
$279$		0			0
$280$	4.02001	+	8.97168i	0.240242	+	0.536161i
$281$	4.80911	−	13.2129i	0.286887	−	0.788216i	−0.709610	−	0.704594i	$-0.751129\pi$
$281$	4.80911	−	13.2129i	0.286887	−	0.788216i	0.996498	−	0.0836218i	$-0.0266488\pi$
$282$		0			0
$283$	0.632047	+	7.22433i	0.0375713	+	0.429442i	0.991565	+	0.129614i	$0.0413738\pi$
$283$	0.632047	+	7.22433i	0.0375713	+	0.429442i	−0.953993	+	0.299828i	$0.903071\pi$
$284$	−9.50108	−	7.97235i	−0.563785	−	0.473072i
$285$		0			0
$286$	−6.14985	−	2.23836i	−0.363649	−	0.132357i
$287$	9.06407	−	2.42871i	0.535035	−	0.143362i
$288$		0			0
$289$	14.6897	−	8.48109i	0.864098	−	0.498887i
$290$	11.1680	−	3.87514i	0.655807	−	0.227556i
$291$		0			0
$292$	0.210578	−	0.451586i	0.0123231	−	0.0264271i
$293$	2.99206	+	4.27310i	0.174798	+	0.249637i	0.896985	−	0.442060i	$-0.145752\pi$
$293$	2.99206	+	4.27310i	0.174798	+	0.249637i	−0.722188	+	0.691697i	$0.756863\pi$
$294$		0			0
$295$	−7.06689	+	0.511035i	−0.411450	+	0.0297536i
$296$		−	1.23369i		−	0.0717068i
$297$		0			0
$298$	−1.74328	−	1.74328i	−0.100985	−	0.100985i
$299$	−3.22206	+	2.70363i	−0.186337	+	0.156355i
$300$		0			0
$301$	−2.88052	+	16.3363i	−0.166031	+	0.941607i
$302$	−13.4343	−	6.26450i	−0.773055	−	0.360481i
$303$		0			0
$304$	−8.16117	+	1.43903i	−0.468075	+	0.0825343i
$305$	0.137043	−	1.33436i	0.00784708	−	0.0764052i
$306$		0			0
$307$	1.91714	+	7.15488i	0.109417	+	0.408351i	0.998809	−	0.0487956i	$-0.0155383\pi$
$307$	1.91714	+	7.15488i	0.109417	+	0.408351i	−0.889392	+	0.457146i	$0.848872\pi$
$308$	5.53262	−	2.57990i	0.315250	−	0.147004i
$309$		0			0
$310$	−7.12081	+	11.9150i	−0.404435	+	0.676728i
$311$	−3.90191	+	4.65012i	−0.221257	+	0.263684i	−0.865242	−	0.501354i	$-0.832835\pi$
$311$	−3.90191	+	4.65012i	−0.221257	+	0.263684i	0.643985	+	0.765038i	$0.277280\pi$
$312$		0			0
$313$	4.24022	+	9.09318i	0.239671	+	0.513977i	0.988945	−	0.148284i	$-0.0473749\pi$
$313$	4.24022	+	9.09318i	0.239671	+	0.513977i	−0.749273	+	0.662261i	$0.769597\pi$
$314$	−8.75910	+	15.1712i	−0.494305	+	0.856161i
$315$		0			0
$316$	−5.71121	−	9.89210i	−0.321280	−	0.556474i
$317$	−10.2335	+	14.6150i	−0.574772	+	0.820859i	−0.996299	−	0.0859568i	$-0.972605\pi$
$317$	−10.2335	+	14.6150i	−0.574772	+	0.820859i	0.421527	+	0.906816i	$0.361494\pi$
$318$		0			0
$319$	−2.51052	−	6.89760i	−0.140562	−	0.386191i
$320$	1.55712	+	1.60480i	0.0870456	+	0.0897110i
$321$		0			0
$322$	0.341942	−	3.90841i	0.0190557	−	0.217807i
$323$	34.1495	−	34.1495i	1.90013	−	1.90013i
$324$		0			0
$325$	10.5995	−	21.0494i	0.587957	−	1.16761i
$326$	4.28666	+	5.10864i	0.237416	+	0.282941i
$327$		0			0
$328$	1.74833	−	1.22420i	0.0965356	−	0.0675950i
$329$	16.3062	−	5.93496i	0.898987	−	0.327205i
$330$		0			0
$331$	−0.266990	−	1.51418i	−0.0146751	−	0.0832267i	0.976591	−	0.215106i	$-0.0690098\pi$
$331$	−0.266990	−	1.51418i	−0.0146751	−	0.0832267i	−0.991266	+	0.131880i	$0.957899\pi$
$332$	−2.49802	+	9.32273i	−0.137097	+	0.511651i
$333$		0			0
$334$	−0.0375269	−	0.0216662i	−0.00205338	−	0.00118552i
$335$	−3.08684	−	0.592415i	−0.168652	−	0.0323671i
$336$		0			0
$337$	−14.7881	+	1.29379i	−0.805558	+	0.0704772i	−0.482493	−	0.875900i	$-0.660269\pi$
$337$	−14.7881	+	1.29379i	−0.805558	+	0.0704772i	−0.323065	+	0.946377i	$0.604713\pi$
$338$	9.18197	−	0.803319i	0.499434	−	0.0436948i
$339$		0			0
$340$	−12.7976	−	2.45607i	−0.694047	−	0.133199i
$341$	7.46436	+	4.30955i	0.404218	+	0.233375i
$342$		0			0
$343$	6.06552	−	22.6368i	0.327507	−	1.22227i
$344$	0.655167	+	3.71564i	0.0353242	+	0.200334i
$345$		0			0
$346$	−4.43963	+	1.61589i	−0.238676	+	0.0868710i
$347$	9.33725	−	6.53801i	0.501250	−	0.350979i	−0.295446	−	0.955359i	$-0.595468\pi$
$347$	9.33725	−	6.53801i	0.501250	−	0.350979i	0.796696	+	0.604381i	$0.206579\pi$
$348$		0			0
$349$	−8.42006	−	10.0346i	−0.450715	−	0.537142i	0.492064	−	0.870559i	$-0.336243\pi$
$349$	−8.42006	−	10.0346i	−0.450715	−	0.537142i	−0.942779	+	0.333417i	$0.891798\pi$
$350$	6.89240	+	20.8747i	0.368414	+	1.11580i
$351$		0			0
$352$	0.981795	−	0.981795i	0.0523299	−	0.0523299i
$353$	−1.17943	+	13.4809i	−0.0627747	+	0.717518i	0.897965	+	0.440067i	$0.145045\pi$
$353$	−1.17943	+	13.4809i	−0.0627747	+	0.717518i	−0.960740	+	0.277451i	$0.910510\pi$
$354$		0			0
$355$	−19.3126	−	19.9040i	−1.02501	−	1.05639i
$356$	−2.07262	−	5.69447i	−0.109848	−	0.301806i
$357$		0			0
$358$	−3.75081	+	5.35671i	−0.198236	+	0.283111i
$359$	15.7985	+	27.3638i	0.833813	+	1.44421i	0.894993	+	0.446080i	$0.147180\pi$
$359$	15.7985	+	27.3638i	0.833813	+	1.44421i	−0.0611799	+	0.998127i	$0.519486\pi$
$360$		0			0
$361$	24.8378	−	43.0203i	1.30725	−	2.26423i
$362$	−9.81026	−	21.0382i	−0.515616	−	1.10574i
$363$		0			0
$364$	−13.3208	+	15.8751i	−0.698199	+	0.832082i
$365$	0.571568	−	0.956386i	0.0299172	−	0.0500595i
$366$		0			0
$367$	−14.2686	+	6.65357i	−0.744816	+	0.347314i	−0.757700	−	0.652603i	$-0.773677\pi$
$367$	−14.2686	+	6.65357i	−0.744816	+	0.347314i	0.0128833	+	0.999917i	$0.495899\pi$
$368$	−0.230958	−	0.861947i	−0.0120395	−	0.0449321i
$369$		0			0
$370$	0.281837	−	2.74418i	0.0146520	−	0.142663i
$371$	−40.1913	+	7.08682i	−2.08663	+	0.367929i
$372$		0			0
$373$	11.1955	+	5.22054i	0.579680	+	0.270309i	0.690264	−	0.723558i	$-0.257494\pi$
$373$	11.1955	+	5.22054i	0.579680	+	0.270309i	−0.110584	+	0.993867i	$0.535272\pi$
$374$	−1.40509	+	7.96866i	−0.0726554	+	0.412049i
$375$		0			0
$376$	3.02343	−	2.53696i	0.155922	−	0.130834i
$377$	17.6199	+	17.6199i	0.907473	+	0.907473i
$378$		0			0
$379$			0.946103i			0.0485981i	0.999705	+	0.0242990i	$0.00773538\pi$
$379$			0.946103i			0.0485981i	−0.999705	+	0.0242990i	$0.992265\pi$
$380$	−18.4822	+	1.33652i	−0.948117	+	0.0685621i
$381$		0			0
$382$	8.93301	+	12.7577i	0.457052	+	0.652738i
$383$	1.60403	−	3.43984i	0.0819619	−	0.175768i	−0.861056	−	0.508511i	$-0.830196\pi$
$383$	1.60403	−	3.43984i	0.0819619	−	0.175768i	0.943018	+	0.332743i	$0.107974\pi$
$384$		0			0
$385$	12.8960	−	4.47473i	0.657239	−	0.228053i
$386$	−3.24788	+	1.87517i	−0.165313	+	0.0954434i
$387$		0			0
$388$	−3.75229	+	1.00542i	−0.190494	+	0.0510426i
$389$	31.8322	+	11.5860i	1.61396	+	0.587432i	0.982217	−	0.187748i	$-0.0601188\pi$
$389$	31.8322	+	11.5860i	1.61396	+	0.587432i	0.631740	+	0.775180i	$0.282341\pi$
$390$		0			0
$391$	3.98372	+	3.34274i	0.201465	+	0.169049i
$392$	−1.07466	−	12.2834i	−0.0542784	−	0.620405i
$393$		0			0
$394$	0.631853	−	1.73600i	0.0318323	−	0.0874586i
$395$	−10.4440	−	23.3084i	−0.525493	−	1.17277i
$396$		0			0
$397$	−20.9983	−	5.62649i	−1.05388	−	0.282385i	−0.310024	−	0.950729i	$-0.600337\pi$
$397$	−20.9983	−	5.62649i	−1.05388	−	0.282385i	−0.743853	+	0.668343i	$0.767004\pi$
$398$	−20.9699	−	14.6833i	−1.05112	−	0.736005i
$399$		0			0
$400$	3.09699	+	3.92539i	0.154849	+	0.196269i
$401$	−22.4914	−	3.96583i	−1.12316	−	0.198044i	−0.418935	−	0.908016i	$-0.637596\pi$
$401$	−22.4914	−	3.96583i	−1.12316	−	0.198044i	−0.704230	+	0.709972i	$0.748708\pi$
$402$		0			0
$403$	−29.1483	−	2.55015i	−1.45198	−	0.127032i
$404$	4.28540			0.213207
$405$		0			0
$406$	−23.2432			−1.15354
$407$	−1.70642	−	0.149293i	−0.0845842	−	0.00740016i
$408$		0			0
$409$	−2.35080	−	0.414510i	−0.116240	−	0.0204962i	0.115226	−	0.993339i	$-0.463241\pi$
$409$	−2.35080	−	0.414510i	−0.116240	−	0.0204962i	−0.231465	+	0.972843i	$0.574352\pi$
$410$	4.16861	−	2.32366i	0.205873	−	0.114757i
$411$		0			0
$412$	−7.18549	−	5.03134i	−0.354004	−	0.247876i
$413$	13.4567	+	3.60572i	0.662162	+	0.177426i
$414$		0			0
$415$	−7.68629	+	20.1665i	−0.377305	+	0.989935i
$416$	−1.61211	+	4.42924i	−0.0790402	+	0.217161i
$417$		0			0
$418$	1.00284	+	11.4625i	0.0490507	+	0.560652i
$419$	−3.27500	−	2.74805i	−0.159994	−	0.134251i	0.559276	−	0.828982i	$-0.311079\pi$
$419$	−3.27500	−	2.74805i	−0.159994	−	0.134251i	−0.719270	+	0.694730i	$0.755524\pi$
$420$		0			0
$421$	−8.02958	−	2.92253i	−0.391338	−	0.142435i	0.138854	−	0.990313i	$-0.455658\pi$
$421$	−8.02958	−	2.92253i	−0.391338	−	0.142435i	−0.530192	+	0.847878i	$0.677880\pi$
$422$	−8.69900	+	2.33089i	−0.423461	+	0.113466i
$423$		0			0
$424$	−8.03882	+	4.64121i	−0.390400	+	0.225397i
$425$	−27.9055	−	8.38682i	−1.35361	−	0.406821i
$426$		0			0
$427$	−1.11464	+	2.39035i	−0.0539412	+	0.115677i
$428$	−4.55846	−	6.51015i	−0.220341	−	0.314680i
$429$		0			0
$430$	0.608494	+	8.41461i	0.0293442	+	0.405789i
$431$			25.4203i			1.22445i	0.790683	+	0.612226i	$0.209726\pi$
$431$			25.4203i			1.22445i	−0.790683	+	0.612226i	$0.790274\pi$
$432$		0			0
$433$	6.38067	+	6.38067i	0.306636	+	0.306636i	0.843603	−	0.536967i	$-0.180430\pi$
$433$	6.38067	+	6.38067i	0.306636	+	0.306636i	−0.536967	+	0.843603i	$0.680430\pi$
$434$	20.9074	−	17.5434i	1.00359	−	0.842109i
$435$		0			0
$436$	2.66102	−	15.0914i	0.127440	−	0.722747i
$437$	6.70214	+	3.12526i	0.320607	+	0.149501i
$438$		0			0
$439$	2.09741	−	0.369829i	0.100104	−	0.0176510i	−0.123372	−	0.992361i	$-0.539371\pi$
$439$	2.09741	−	0.369829i	0.100104	−	0.0176510i	0.223476	+	0.974710i	$0.428260\pi$
$440$	2.40816	−	1.95958i	0.114805	−	0.0934194i
$441$		0			0
$442$	−7.10947	−	26.5329i	−0.338163	−	1.26204i
$443$	−31.9681	+	14.9070i	−1.51885	+	0.708252i	−0.990079	−	0.140511i	$-0.955125\pi$
$443$	−31.9681	+	14.9070i	−1.51885	+	0.708252i	−0.528773	+	0.848764i	$0.677348\pi$
$444$		0			0
$445$	−3.30936	−	13.1401i	−0.156879	−	0.622899i
$446$	1.70364	−	2.03032i	0.0806696	−	0.0961383i
$447$		0			0
$448$	−1.85809	−	3.98470i	−0.0877867	−	0.188259i
$449$	−19.4107	+	33.6203i	−0.916048	+	1.58664i	−0.110689	+	0.993855i	$0.535306\pi$
$449$	−19.4107	+	33.6203i	−0.916048	+	1.58664i	−0.805359	+	0.592787i	$0.798028\pi$
$450$		0			0
$451$	−1.48172	−	2.56641i	−0.0697714	−	0.120848i
$452$	−3.48541	+	4.97768i	−0.163940	+	0.234130i
$453$		0			0
$454$	−3.14655	−	8.64508i	−0.147675	−	0.405734i
$455$	−33.2570	+	32.2689i	−1.55911	+	1.51279i
$456$		0			0
$457$	−0.426665	+	4.87680i	−0.0199585	+	0.228127i	0.979664	+	0.200646i	$0.0643041\pi$
$457$	−0.426665	+	4.87680i	−0.0199585	+	0.228127i	−0.999622	+	0.0274810i	$0.991251\pi$
$458$	−8.49562	+	8.49562i	−0.396974	+	0.396974i
$459$		0			0
$460$	−0.316824	−	1.97005i	−0.0147720	−	0.0918540i
$461$	3.85944	+	4.59950i	0.179752	+	0.214220i	0.848395	−	0.529363i	$-0.177569\pi$
$461$	3.85944	+	4.59950i	0.179752	+	0.214220i	−0.668643	+	0.743583i	$0.733125\pi$
$462$		0			0
$463$	−32.0879	+	22.4682i	−1.49125	+	1.04419i	−0.508122	+	0.861285i	$0.669660\pi$
$463$	−32.0879	+	22.4682i	−1.49125	+	1.04419i	−0.983131	+	0.182901i	$0.941451\pi$
$464$	−4.96778	+	1.80812i	−0.230623	+	0.0839400i
$465$		0			0
$466$	1.41269	+	8.01179i	0.0654418	+	0.371139i
$467$	7.59632	−	28.3498i	0.351516	−	1.31187i	−0.533298	−	0.845928i	$-0.679047\pi$
$467$	7.59632	−	28.3498i	0.351516	−	1.31187i	0.884813	−	0.465946i	$-0.154286\pi$
$468$		0			0
$469$	5.35221	+	3.09010i	0.247142	+	0.142687i
$470$	7.30479	−	4.95243i	0.336945	−	0.228439i
$471$		0			0
$472$	3.15660	−	0.276167i	0.145295	−	0.0127116i
$473$	5.21869	−	0.456577i	0.239956	−	0.0209934i
$474$		0			0
$475$	−41.4165	−	1.24935i	−1.90032	−	0.0573240i
$476$	22.1895	+	12.8111i	1.01705	+	0.587197i
$477$		0			0
$478$	−1.01078	+	3.77228i	−0.0462320	+	0.172540i
$479$	−4.01942	−	22.7952i	−0.183652	−	1.04154i	−0.927675	−	0.373388i	$-0.878196\pi$
$479$	−4.01942	−	22.7952i	−0.183652	−	1.04154i	0.744024	−	0.668153i	$-0.232915\pi$
$480$		0			0
$481$	5.46431	−	1.98885i	0.249151	−	0.0906836i
$482$	12.4867	−	8.74328i	0.568754	−	0.398246i
$483$		0			0
$484$	5.83147	+	6.94968i	0.265067	+	0.315894i
$485$	−8.57616	+	1.37922i	−0.389423	+	0.0626271i
$486$		0			0
$487$	−0.826467	+	0.826467i	−0.0374508	+	0.0374508i	−0.725584	−	0.688133i	$-0.758430\pi$
$487$	−0.826467	+	0.826467i	−0.0374508	+	0.0374508i	0.688133	+	0.725584i	$0.258430\pi$
$488$	−0.0522832	+	0.597600i	−0.00236675	+	0.0270521i
$489$		0			0
$490$	0.415710	−	27.5683i	0.0187799	−	1.24541i
$491$	−13.4472	−	36.9458i	−0.606863	−	1.66734i	−0.737038	−	0.675851i	$-0.763776\pi$
$491$	−13.4472	−	36.9458i	−0.606863	−	1.66734i	0.130175	−	0.991491i	$-0.458446\pi$
$492$		0			0
$493$	17.6712	−	25.2370i	0.795869	−	1.13662i
$494$	−19.5305	−	33.8279i	−0.878721	−	1.52199i
$495$		0			0
$496$	3.10382	−	5.37597i	0.139366	−	0.241388i
$497$	23.0455	+	49.4213i	1.03373	+	2.21685i
$498$		0			0
$499$	14.9769	−	17.8488i	0.670460	−	0.799023i	−0.318387	−	0.947961i	$-0.603141\pi$
$499$	14.9769	−	17.8488i	0.670460	−	0.799023i	0.988847	+	0.148938i	$0.0475855\pi$
$500$	5.99209	+	9.43901i	0.267974	+	0.422125i
$501$		0			0
$502$	8.29072	−	3.86602i	0.370033	−	0.172549i
$503$	6.15484	+	22.9702i	0.274431	+	1.02419i	0.956222	+	0.292643i	$0.0945347\pi$
$503$	6.15484	+	22.9702i	0.274431	+	1.02419i	−0.681791	+	0.731547i	$0.738799\pi$
$504$		0			0
$505$	9.53231	+	0.979001i	0.424182	+	0.0435650i
$506$	−1.22018	+	0.215151i	−0.0542437	+	0.00956462i
$507$		0			0
$508$	−6.87757	−	3.20706i	−0.305143	−	0.142290i
$509$	3.92206	−	22.2431i	0.173842	−	0.985909i	−0.765629	−	0.643282i	$-0.777572\pi$
$509$	3.92206	−	22.2431i	0.173842	−	0.985909i	0.939472	−	0.342627i	$-0.111317\pi$
$510$		0			0
$511$	−1.67818	+	1.40816i	−0.0742382	+	0.0622933i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$		0			0
$514$			12.0438i			0.531229i
$515$	−14.8338	−	12.8331i	−0.653654	−	0.565493i
$516$		0			0
$517$	−3.14321	−	4.48897i	−0.138238	−	0.197425i
$518$	−2.29231	+	4.91588i	−0.100718	+	0.215991i
$519$		0			0
$520$	−4.59779	+	9.48397i	−0.201626	+	0.415899i
$521$	8.99235	−	5.19174i	0.393962	−	0.227454i	−0.289913	−	0.957053i	$-0.593626\pi$
$521$	8.99235	−	5.19174i	0.393962	−	0.227454i	0.683875	+	0.729599i	$0.260293\pi$
$522$		0			0
$523$	−14.7753	+	3.95904i	−0.646080	+	0.173117i	−0.566956	−	0.823748i	$-0.691879\pi$
$523$	−14.7753	+	3.95904i	−0.646080	+	0.173117i	−0.0791243	+	0.996865i	$0.525212\pi$
$524$	13.3065	+	4.84315i	0.581295	+	0.211574i
$525$		0			0
$526$	21.2462	+	17.8277i	0.926377	+	0.777323i
$527$	3.15297	+	36.0386i	0.137346	+	1.56987i
$528$		0			0
$529$	7.59411	−	20.8647i	0.330179	−	0.907159i
$530$	−18.9416	+	8.48730i	−0.822769	+	0.368665i
$531$		0			0
$532$	35.1937	+	9.43011i	1.52584	+	0.408847i
$533$	8.24077	+	5.77025i	0.356947	+	0.249937i
$534$		0			0
$535$	−8.65244	−	15.5224i	−0.374078	−	0.671090i
$536$	1.38431	+	0.244092i	0.0597932	+	0.0105432i
$537$		0			0
$538$	29.8192	+	2.60885i	1.28560	+	0.112475i
$539$	−17.1202			−0.737421
$540$		0			0
$541$	−32.9979			−1.41869			−0.709346	−	0.704860i	$-0.751010\pi$
$541$	−32.9979			−1.41869			−0.709346	+	0.704860i	$0.751010\pi$
$542$	−10.9924	−	0.961715i	−0.472166	−	0.0413092i
$543$		0			0
$544$	5.73917	+	1.01197i	0.246065	+	0.0433879i
$545$	9.36673	−	32.9609i	0.401226	−	1.41189i
$546$		0			0
$547$	14.1235	+	9.88938i	0.603877	+	0.422839i	0.835129	−	0.550055i	$-0.185393\pi$
$547$	14.1235	+	9.88938i	0.603877	+	0.422839i	−0.231252	+	0.972894i	$0.574282\pi$
$548$	−2.13583	−	0.572294i	−0.0912382	−	0.0244472i
$549$		0			0
$550$	5.80431	−	3.80868i	0.247497	−	0.162403i
$551$	14.9840	−	41.1683i	0.638342	−	1.75383i
$552$		0			0
$553$	4.37697	+	50.0290i	0.186128	+	2.12745i
$554$	4.03333	+	3.38436i	0.171360	+	0.143788i
$555$		0			0
$556$	5.41808	+	1.97202i	0.229778	+	0.0836323i
$557$	−33.7033	+	9.03077i	−1.42805	+	0.382646i	−0.888334	−	0.459198i	$-0.848137\pi$
$557$	−33.7033	+	9.03077i	−1.42805	+	0.382646i	−0.539721	+	0.841844i	$0.681470\pi$
$558$		0			0
$559$	−15.4012	+	8.89191i	−0.651403	+	0.376088i
$560$	−3.22278	−	9.28791i	−0.136187	−	0.392486i
$561$		0			0
$562$	−5.94239	+	12.7435i	−0.250664	+	0.537552i
$563$	12.2898	+	17.5516i	0.517952	+	0.739713i	0.989877	−	0.141926i	$-0.0453295\pi$
$563$	12.2898	+	17.5516i	0.517952	+	0.739713i	−0.471925	+	0.881639i	$0.656441\pi$
$564$		0			0
$565$	−8.88998	+	10.2759i	−0.374004	+	0.432312i
$566$		−	7.25193i		−	0.304821i
$567$		0			0
$568$	8.77009	+	8.77009i	0.367985	+	0.367985i
$569$	−4.91484	+	4.12404i	−0.206041	+	0.172889i	−0.739969	−	0.672641i	$-0.765160\pi$
$569$	−4.91484	+	4.12404i	−0.206041	+	0.172889i	0.533928	+	0.845530i	$0.320715\pi$
$570$		0			0
$571$	0.109047	−	0.618438i	0.00456349	−	0.0258808i	−0.982441	−	0.186574i	$-0.940262\pi$
$571$	0.109047	−	0.618438i	0.00456349	−	0.0258808i	0.987004	+	0.160693i	$0.0513728\pi$
$572$	5.93137	+	2.76584i	0.248003	+	0.115646i
$573$		0			0
$574$	−9.24126	+	1.62948i	−0.385723	+	0.0680133i
$575$	−0.254674	−	4.45449i	−0.0106206	−	0.185765i
$576$		0			0
$577$	−7.44143	−	27.7718i	−0.309791	−	1.15616i	−0.928742	−	0.370726i	$-0.879109\pi$
$577$	−7.44143	−	27.7718i	−0.309791	−	1.15616i	0.618951	−	0.785429i	$-0.287558\pi$
$578$	−15.3730	+	7.16852i	−0.639430	+	0.298171i
$579$		0			0
$580$	−11.4632	+	2.88704i	−0.475985	+	0.119878i
$581$	27.2764	−	32.5067i	1.13161	−	1.34861i
$582$		0			0
$583$	5.44685	+	11.6808i	0.225586	+	0.483770i
$584$	−0.249135	+	0.431514i	−0.0103093	+	0.0178562i
$585$		0			0
$586$	−2.60825	−	4.51762i	−0.107746	−	0.186621i
$587$	12.7802	−	18.2520i	0.527494	−	0.753340i	−0.463666	−	0.886010i	$-0.653466\pi$
$587$	12.7802	−	18.2520i	0.527494	−	0.753340i	0.991160	+	0.132670i	$0.0423552\pi$
$588$		0			0
$589$	17.5946	+	48.3407i	0.724972	+	1.99184i
$590$	7.08454	+	0.106830i	0.291666	+	0.00439812i
$591$		0			0
$592$	−0.107523	+	1.22900i	−0.00441918	+	0.0505114i
$593$	−16.4390	+	16.4390i	−0.675067	+	0.675067i	−0.958880	−	0.283813i	$-0.908401\pi$
$593$	−16.4390	+	16.4390i	−0.675067	+	0.675067i	0.283813	+	0.958880i	$0.408401\pi$
$594$		0			0
$595$	46.4309	+	33.5658i	1.90348	+	1.37607i
$596$	1.58471	+	1.88858i	0.0649121	+	0.0773592i
$597$		0			0
$598$	3.44544	−	2.41252i	0.140894	−	0.0986554i
$599$	4.23613	−	1.54182i	0.173084	−	0.0629972i	−0.254025	−	0.967198i	$-0.581755\pi$
$599$	4.23613	−	1.54182i	0.173084	−	0.0629972i	0.427108	+	0.904200i	$0.359532\pi$
$600$		0			0
$601$	−7.14929	−	40.5456i	−0.291626	−	1.65389i	−0.680610	−	0.732646i	$-0.738285\pi$
$601$	−7.14929	−	40.5456i	−0.291626	−	1.65389i	0.388984	−	0.921245i	$-0.372826\pi$
$602$	4.29336	−	16.0230i	0.174984	−	0.653051i
$603$		0			0
$604$	12.8372	+	7.41153i	0.522336	+	0.301571i
$605$	11.3837	+	16.7908i	0.462812	+	0.682644i
$606$		0			0
$607$	13.4556	−	1.17722i	0.546147	−	0.0477817i	0.189256	−	0.981928i	$-0.439392\pi$
$607$	13.4556	−	1.17722i	0.546147	−	0.0477817i	0.356891	+	0.934146i	$0.383837\pi$
$608$	8.25554	−	0.722266i	0.334806	−	0.0292918i
$609$		0			0
$610$	−0.252819	+	1.31734i	−0.0102363	+	0.0533375i
$611$	16.1109	+	9.30164i	0.651778	+	0.376304i
$612$		0			0
$613$	11.7552	−	43.8710i	0.474788	−	1.77193i	−0.147410	−	0.989075i	$-0.547094\pi$
$613$	11.7552	−	43.8710i	0.474788	−	1.77193i	0.622199	−	0.782859i	$-0.286240\pi$
$614$	−1.28626	−	7.29474i	−0.0519092	−	0.294392i
$615$		0			0
$616$	−5.73642	+	2.08789i	−0.231127	+	0.0841234i
$617$	23.4805	−	16.4412i	0.945291	−	0.661900i	0.00417736	−	0.999991i	$-0.498670\pi$
$617$	23.4805	−	16.4412i	0.945291	−	0.661900i	0.941113	+	0.338092i	$0.109781\pi$
$618$		0			0
$619$	−16.8234	−	20.0493i	−0.676188	−	0.805849i	0.313424	−	0.949613i	$-0.398524\pi$
$619$	−16.8234	−	20.0493i	−0.676188	−	0.805849i	−0.989612	+	0.143764i	$0.954079\pi$
$620$	8.13217	−	11.2491i	0.326596	−	0.451773i
$621$		0			0
$622$	4.29235	−	4.29235i	0.172108	−	0.172108i
$623$	−2.32211	+	26.5418i	−0.0930334	+	1.06338i
$624$		0			0
$625$	11.1723	+	22.3647i	0.446890	+	0.894589i
$626$	−3.43156	−	9.42814i	−0.137153	−	0.376824i
$627$		0			0
$628$	10.0480	−	14.3501i	0.400960	−	0.572630i
$629$	−3.59479	−	6.22637i	−0.143334	−	0.248261i
$630$		0			0
$631$	11.9202	−	20.6463i	0.474534	−	0.821917i	−0.525041	−	0.851077i	$-0.675950\pi$
$631$	11.9202	−	20.6463i	0.474534	−	0.821917i	0.999575	+	0.0291601i	$0.00928326\pi$
$632$	4.82732	+	10.3522i	0.192020	+	0.411789i
$633$		0			0
$634$	11.4684	−	13.6675i	0.455467	−	0.542804i
$635$	−14.5656	−	8.70487i	−0.578018	−	0.345442i
$636$		0			0
$637$	52.6736	−	24.5621i	2.08700	−	0.973186i
$638$	1.89980	+	7.09016i	0.0752139	+	0.280702i
$639$		0			0
$640$	−1.41133	−	1.73440i	−0.0557876	−	0.0685583i
$641$	39.5884	−	6.98050i	1.56365	−	0.275713i	0.676233	−	0.736688i	$-0.263611\pi$
$641$	39.5884	−	6.98050i	1.56365	−	0.275713i	0.887413	+	0.460975i	$0.152500\pi$
$642$		0			0
$643$	36.0714	+	16.8204i	1.42252	+	0.663330i	0.973183	−	0.230033i	$-0.0738836\pi$
$643$	36.0714	+	16.8204i	1.42252	+	0.663330i	0.449334	+	0.893364i	$0.351661\pi$
$644$	−0.681281	+	3.86374i	−0.0268462	+	0.152253i
$645$		0			0
$646$	−36.9958	+	31.0432i	−1.45558	+	1.22138i
$647$	4.04354	+	4.04354i	0.158968	+	0.158968i	0.782109	−	0.623141i	$-0.214144\pi$
$647$	4.04354	+	4.04354i	0.158968	+	0.158968i	−0.623141	+	0.782109i	$0.714144\pi$
$648$		0			0
$649$		−	4.39959i		−	0.172699i
$650$	−12.3938	+	20.0455i	−0.486124	+	0.786248i
$651$		0			0
$652$	−3.82510	−	5.46281i	−0.149802	−	0.213940i
$653$	2.53008	−	5.42577i	0.0990097	−	0.212327i	−0.850564	−	0.525872i	$-0.823739\pi$
$653$	2.53008	−	5.42577i	0.0990097	−	0.212327i	0.949573	+	0.313545i	$0.101517\pi$
$654$		0			0
$655$	28.4920	+	13.8128i	1.11328	+	0.539711i
$656$	−1.84838	+	1.06716i	−0.0721670	+	0.0416657i
$657$		0			0
$658$	−16.7614	+	4.49120i	−0.653426	+	0.175085i
$659$	−42.7421	−	15.5568i	−1.66500	−	0.606009i	−0.673859	−	0.738860i	$-0.735365\pi$
$659$	−42.7421	−	15.5568i	−1.66500	−	0.606009i	−0.991136	+	0.132851i	$0.957587\pi$
$660$		0			0
$661$	−19.1548	−	16.0728i	−0.745034	−	0.625158i	0.189150	−	0.981948i	$-0.439427\pi$
$661$	−19.1548	−	16.0728i	−0.745034	−	0.625158i	−0.934184	+	0.356790i	$0.883871\pi$
$662$	0.134005	+	1.53169i	0.00520826	+	0.0595306i
$663$		0			0
$664$	3.30104	−	9.06954i	0.128105	−	0.351966i
$665$	76.1293	+	29.0160i	2.95217	+	1.12519i
$666$		0			0
$667$	4.55677	+	1.22098i	0.176439	+	0.0472766i
$668$	0.0354958	+	0.0248544i	0.00137337	+	0.000961646i
$669$		0			0
$670$	3.02346	+	0.859196i	0.116806	+	0.0331936i
$671$	0.820264	+	0.144635i	0.0316660	+	0.00558356i
$672$		0			0
$673$	0.161110	+	0.0140953i	0.00621033	+	0.000543334i	0.0902605	−	0.995918i	$-0.471230\pi$
$673$	0.161110	+	0.0140953i	0.00621033	+	0.000543334i	−0.0840502	+	0.996462i	$0.526786\pi$
$674$	14.8446			0.571791
$675$		0			0
$676$	−9.21705			−0.354502
$677$	−19.3434	−	1.69232i	−0.743425	−	0.0650413i	−0.290852	−	0.956768i	$-0.593939\pi$
$677$	−19.3434	−	1.69232i	−0.743425	−	0.0650413i	−0.452574	+	0.891727i	$0.649494\pi$
$678$		0			0
$679$	16.8199	+	2.96580i	0.645488	+	0.113817i
$680$	12.5348	+	3.56211i	0.480689	+	0.136601i
$681$		0			0
$682$	−7.06035	−	4.94371i	−0.270355	−	0.189305i
$683$	−26.6223	−	7.13342i	−1.01867	−	0.272953i	−0.289424	−	0.957201i	$-0.593464\pi$
$683$	−26.6223	−	7.13342i	−1.01867	−	0.272953i	−0.729249	+	0.684248i	$0.760131\pi$
$684$		0			0
$685$	−4.62013	−	1.76092i	−0.176526	−	0.0672814i
$686$	−8.01537	+	22.0221i	−0.306028	+	0.840806i
$687$		0			0
$688$	−0.328835	−	3.75860i	−0.0125367	−	0.143295i
$689$	−33.5165	−	28.1237i	−1.27688	−	1.07143i
$690$		0			0
$691$	−27.8057	−	10.1204i	−1.05778	−	0.385000i	−0.246185	−	0.969223i	$-0.579177\pi$
$691$	−27.8057	−	10.1204i	−1.05778	−	0.385000i	−0.811593	+	0.584223i	$0.801399\pi$
$692$	4.56357	−	1.22281i	0.173481	−	0.0464841i
$693$		0			0
$694$	−9.87155	+	5.69934i	−0.374719	+	0.216344i
$695$	11.6013	+	5.62426i	0.440062	+	0.213340i
$696$		0			0
$697$	5.25661	−	11.2728i	0.199108	−	0.426989i
$698$	7.51344	+	10.7303i	0.284388	+	0.406148i
$699$		0			0
$700$	−5.04682	−	21.3960i	−0.190752	−	0.808692i
$701$			13.5377i			0.511313i	0.966768	+	0.255656i	$0.0822916\pi$
$701$			13.5377i			0.511313i	−0.966768	+	0.255656i	$0.917708\pi$
$702$		0			0
$703$	−7.22924	−	7.22924i	−0.272656	−	0.272656i
$704$	−1.06363	+	0.892490i	−0.0400870	+	0.0336370i
$705$		0			0
$706$	2.34988	−	13.3269i	0.0884390	−	0.501563i
$707$	−17.0760	−	7.96268i	−0.642210	−	0.299467i
$708$		0			0
$709$	−31.3016	+	5.51931i	−1.17555	+	0.207282i	−0.727105	−	0.686526i	$-0.759135\pi$
$709$	−31.3016	+	5.51931i	−1.17555	+	0.207282i	−0.448450	+	0.893808i	$0.648024\pi$
$710$	17.5044	+	21.5114i	0.656927	+	0.807309i
$711$		0			0
$712$	1.56842	+	5.85344i	0.0587792	+	0.219367i
$713$	−5.02040	+	2.34105i	−0.188016	+	0.0876731i
$714$		0			0
$715$	12.5617	+	7.50727i	0.469780	+	0.280756i
$716$	4.20341	−	5.00942i	0.157089	−	0.187211i
$717$		0			0
$718$	−13.3535	−	28.6366i	−0.498347	−	1.06871i
$719$	21.9051	−	37.9408i	0.816923	−	1.41495i	−0.0910162	−	0.995849i	$-0.529012\pi$
$719$	21.9051	−	37.9408i	0.816923	−	1.41495i	0.907939	−	0.419102i	$-0.137655\pi$
$720$		0			0
$721$	19.2833	+	33.3997i	0.718148	+	1.24387i
$722$	−28.4927	+	40.6918i	−1.06039	+	1.51439i
$723$		0			0
$724$	7.93933	+	21.8131i	0.295063	+	0.810679i
$725$	−26.1580	+	3.80306i	−0.971483	+	0.141242i
$726$		0			0
$727$	−1.52045	+	17.3788i	−0.0563904	+	0.644545i	0.914431	+	0.404742i	$0.132639\pi$
$727$	−1.52045	+	17.3788i	−0.0563904	+	0.644545i	−0.970821	+	0.239803i	$0.922917\pi$
$728$	14.6537	−	14.6537i	0.543103	−	0.543103i
$729$		0			0
$730$	−0.652747	+	0.902931i	−0.0241593	+	0.0334190i
$731$	14.1334	+	16.8435i	0.522743	+	0.622981i
$732$		0			0
$733$	−41.8568	+	29.3084i	−1.54602	+	1.08253i	−0.583215	+	0.812317i	$0.698206\pi$
$733$	−41.8568	+	29.3084i	−1.54602	+	1.08253i	−0.962800	+	0.270214i	$0.912905\pi$
$734$	14.7942	−	5.38466i	0.546065	−	0.198751i
$735$		0			0
$736$	0.154956	+	0.878797i	0.00571174	+	0.0323929i
$737$	0.505144	−	1.88522i	0.0186072	−	0.0694430i
$738$		0			0
$739$	3.49091	+	2.01548i	0.128415	+	0.0741406i	0.562832	−	0.826572i	$-0.309712\pi$
$739$	3.49091	+	2.01548i	0.128415	+	0.0741406i	−0.434416	+	0.900712i	$0.643045\pi$
$740$	−0.519936	+	2.70917i	−0.0191132	+	0.0995913i
$741$		0			0
$742$	40.6561	−	3.55694i	1.49253	−	0.130580i
$743$	45.9636	−	4.02129i	1.68624	−	0.147527i	0.796698	−	0.604378i	$-0.206578\pi$
$743$	45.9636	−	4.02129i	1.68624	−	0.147527i	0.889543	+	0.456851i	$0.151023\pi$
$744$		0			0
$745$	3.09352	+	4.56292i	0.113338	+	0.167173i
$746$	−10.6979	−	6.17642i	−0.391677	−	0.226135i
$747$		0			0
$748$	2.09426	−	7.81587i	0.0765736	−	0.285777i
$749$	6.06759	+	34.4110i	0.221705	+	1.25735i
$750$		0			0
$751$	15.2615	−	5.55472i	0.556899	−	0.202695i	−0.0482103	−	0.998837i	$-0.515352\pi$
$751$	15.2615	−	5.55472i	0.556899	−	0.202695i	0.605109	+	0.796143i	$0.293130\pi$
$752$	−3.23304	+	2.26380i	−0.117897	+	0.0825522i
$753$		0			0
$754$	−16.0172	−	19.0886i	−0.583312	−	0.695165i
$755$	26.8614	+	19.4186i	0.977586	+	0.706716i
$756$		0			0
$757$	−27.1579	+	27.1579i	−0.987071	+	0.987071i	−0.999917	−	0.0128466i	$-0.995911\pi$
$757$	−27.1579	+	27.1579i	−0.987071	+	0.987071i	0.0128466	+	0.999917i	$0.495911\pi$
$758$	0.0824583	−	0.942503i	0.00299502	−	0.0342333i
$759$		0			0
$760$	18.5284	+	0.279394i	0.672094	+	0.0101347i
$761$	8.99890	+	24.7243i	0.326210	+	0.896254i	0.989062	+	0.147503i	$0.0471237\pi$
$761$	8.99890	+	24.7243i	0.326210	+	0.896254i	−0.662852	+	0.748751i	$0.730654\pi$
$762$		0			0
$763$	−38.6446	+	55.1902i	−1.39903	+	1.99802i
$764$	−7.78711	−	13.4877i	−0.281728	−	0.487967i
$765$		0			0
$766$	−1.89772	+	3.28695i	−0.0685675	+	0.118762i
$767$	6.31201	+	13.5361i	0.227913	+	0.488762i
$768$		0			0
$769$	−31.0385	+	36.9902i	−1.11928	+	1.33390i	−0.182808	+	0.983149i	$0.558519\pi$
$769$	−31.0385	+	36.9902i	−1.11928	+	1.33390i	−0.936468	+	0.350753i	$0.885926\pi$
$770$	−13.2369	+	3.33374i	−0.477024	+	0.120140i
$771$		0			0
$772$	3.39895	−	1.58496i	0.122331	−	0.0570439i
$773$	−12.4330	−	46.4005i	−0.447183	−	1.66891i	−0.710106	−	0.704094i	$-0.751353\pi$
$773$	−12.4330	−	46.4005i	−0.447183	−	1.66891i	0.262923	−	0.964817i	$-0.415313\pi$
$774$		0			0
$775$	20.6588	−	23.1643i	0.742086	−	0.832085i
$776$	3.82564	−	0.674563i	0.137332	−	0.0242154i
$777$		0			0
$778$	−30.7013	−	14.3162i	−1.10069	−	0.513262i
$779$	3.07137	−	17.4186i	0.110043	−	0.624085i
$780$		0			0
$781$	13.1919	−	11.0694i	0.472045	−	0.396093i
$782$	−3.67722	−	3.67722i	−0.131497	−	0.131497i
$783$		0			0
$784$			12.3303i			0.440368i
$785$	25.6288	−	29.6244i	0.914730	−	1.05734i
$786$		0			0
$787$	−1.35804	−	1.93949i	−0.0484090	−	0.0691353i	0.794218	−	0.607633i	$-0.207881\pi$
$787$	−1.35804	−	1.93949i	−0.0484090	−	0.0691353i	−0.842627	+	0.538498i	$0.818992\pi$
$788$	−0.780752	+	1.67433i	−0.0278131	+	0.0596454i
$789$		0			0
$790$	8.37277	+	24.1299i	0.297890	+	0.858505i
$791$	23.1373	−	13.3583i	0.822667	−	0.474967i
$792$		0			0
$793$	−2.73120	+	0.731823i	−0.0969877	+	0.0259878i
$794$	20.4281	+	7.43520i	0.724965	+	0.263866i
$795$		0			0
$796$	19.6103	+	16.4550i	0.695070	+	0.583233i
$797$	0.382519	+	4.37222i	0.0135495	+	0.154872i	0.999955	−	0.00945613i	$-0.00301002\pi$
$797$	0.382519	+	4.37222i	0.0135495	+	0.154872i	−0.986406	+	0.164328i	$0.947454\pi$
$798$		0			0
$799$	7.86676	−	21.6137i	0.278306	−	0.764639i
$800$	−2.74308	−	4.18037i	−0.0969827	−	0.147798i
$801$		0			0
$802$	22.0601	+	5.91099i	0.778970	+	0.208724i
$803$	0.566715	+	0.396818i	0.0199989	+	0.0140034i
$804$		0			0
$805$	−2.39809	+	8.43874i	−0.0845216	+	0.297426i
$806$	28.8151	+	5.08089i	1.01497	+	0.178967i
$807$		0			0
$808$	−4.26910	−	0.373497i	−0.150186	−	0.0131396i
$809$	−30.4042			−1.06896			−0.534478	−	0.845183i	$-0.679492\pi$
$809$	−30.4042			−1.06896			−0.534478	+	0.845183i	$0.679492\pi$
$810$		0			0
$811$	33.7945			1.18669			0.593343	−	0.804950i	$-0.297808\pi$
$811$	33.7945			1.18669			0.593343	+	0.804950i	$0.297808\pi$
$812$	23.1547	+	2.02578i	0.812572	+	0.0710908i
$813$		0			0
$814$	1.68692	+	0.297449i	0.0591264	+	0.0104256i
$815$	−7.26045	−	13.0251i	−0.254322	−	0.456251i
$816$		0			0
$817$	25.6122	+	17.9339i	0.896059	+	0.627427i
$818$	2.30573	+	0.617819i	0.0806180	+	0.0216015i
$819$		0			0
$820$	−4.35526	+	1.95150i	−0.152092	+	0.0681492i
$821$	11.9252	−	32.7641i	0.416191	−	1.14348i	−0.537651	−	0.843167i	$-0.680688\pi$
$821$	11.9252	−	32.7641i	0.416191	−	1.14348i	0.953842	−	0.300308i	$-0.0970896\pi$
$822$		0			0
$823$	−3.09272	−	35.3499i	−0.107805	−	1.23222i	−0.836725	−	0.547623i	$-0.815533\pi$
$823$	−3.09272	−	35.3499i	−0.107805	−	1.23222i	0.728920	−	0.684599i	$-0.240023\pi$
$824$	6.71964	+	5.63845i	0.234090	+	0.196425i
$825$		0			0
$826$	−13.0913	−	4.76483i	−0.455503	−	0.165790i
$827$	−30.9813	+	8.30141i	−1.07733	+	0.288668i	−0.753500	−	0.657448i	$-0.771636\pi$
$827$	−30.9813	+	8.30141i	−1.07733	+	0.288668i	−0.323826	+	0.946117i	$0.604969\pi$
$828$		0			0
$829$	−46.8669	+	27.0586i	−1.62776	+	0.939785i	−0.642995	+	0.765870i	$0.722308\pi$
$829$	−46.8669	+	27.0586i	−1.62776	+	0.939785i	−0.984761	+	0.173915i	$0.944358\pi$
$830$	9.41467	−	19.4199i	0.326788	−	0.674073i
$831$		0			0
$832$	1.99201	−	4.27188i	0.0690605	−	0.148101i
$833$	−41.2157	−	58.8622i	−1.42804	−	2.03945i
$834$		0			0
$835$	0.0732777	+	0.0633944i	0.00253588	+	0.00219385i
$836$		−	11.5063i		−	0.397955i
$837$		0			0
$838$	3.02303	+	3.02303i	0.104429	+	0.104429i
$839$	−26.5644	+	22.2901i	−0.917103	+	0.769541i	−0.973457	−	0.228870i	$-0.926497\pi$
$839$	−26.5644	+	22.2901i	−0.917103	+	0.769541i	0.0563536	+	0.998411i	$0.482053\pi$
$840$		0			0
$841$	−0.182658	+	1.03591i	−0.00629856	+	0.0357209i
$842$	7.74431	+	3.61123i	0.266886	+	0.124451i
$843$		0			0
$844$	8.86905	−	1.56385i	0.305285	−	0.0538300i
$845$	−20.5021	−	2.10564i	−0.705294	−	0.0724361i
$846$		0			0
$847$	−10.3235	−	38.5278i	−0.354719	−	1.32383i
$848$	8.41274	−	3.92292i	0.288895	−	0.134714i
$849$		0			0
$850$	27.0683	+	10.7870i	0.928436	+	0.369992i
$851$	0.707637	−	0.843329i	0.0242575	−	0.0289089i
$852$		0			0
$853$	11.7530	+	25.2043i	0.402414	+	0.862979i	0.998208	+	0.0598421i	$0.0190597\pi$
$853$	11.7530	+	25.2043i	0.402414	+	0.862979i	−0.595794	+	0.803137i	$0.703162\pi$
$854$	1.31873	−	2.28411i	0.0451260	−	0.0781605i
$855$		0			0
$856$	3.97372	+	6.88268i	0.135819	+	0.235245i
$857$	6.22901	−	8.89595i	0.212779	−	0.303880i	−0.698548	−	0.715563i	$-0.746170\pi$
$857$	6.22901	−	8.89595i	0.212779	−	0.303880i	0.911327	+	0.411683i	$0.135059\pi$
$858$		0			0
$859$	−0.198448	−	0.545231i	−0.00677095	−	0.0186030i	0.936261	−	0.351305i	$-0.114262\pi$
$859$	−0.198448	−	0.545231i	−0.00677095	−	0.0186030i	−0.943032	+	0.332702i	$0.892040\pi$
$860$	0.127203	−	8.43563i	0.00433760	−	0.287653i
$861$		0			0
$862$	2.21553	−	25.3236i	0.0754611	−	0.862524i
$863$	−8.19741	+	8.19741i	−0.279043	+	0.279043i	−0.832727	−	0.553684i	$-0.813222\pi$
$863$	−8.19741	+	8.19741i	−0.279043	+	0.279043i	0.553684	+	0.832727i	$0.313222\pi$
$864$		0			0
$865$	10.4304	−	1.67742i	0.354645	−	0.0570340i
$866$	−5.80028	−	6.91251i	−0.197102	−	0.234897i
$867$		0			0
$868$	−22.3568	+	15.6544i	−0.758840	+	0.531345i
$869$	14.9032	−	5.42432i	0.505556	−	0.184007i
$870$		0			0
$871$	1.15053	+	6.52495i	0.0389841	+	0.221090i
$872$	−3.96620	+	14.8021i	−0.134312	+	0.501261i
$873$		0			0
$874$	−6.40425	−	3.69750i	−0.216627	−	0.125070i
$875$	−6.33807	−	48.7454i	−0.214266	−	1.64790i
$876$		0			0
$877$	29.6544	−	2.59443i	1.00136	−	0.0876075i	0.425331	−	0.905038i	$-0.360158\pi$
$877$	29.6544	−	2.59443i	1.00136	−	0.0876075i	0.576028	+	0.817430i	$0.304602\pi$
$878$	−2.12166	+	0.185621i	−0.0716024	+	0.00626440i
$879$		0			0
$880$	−2.56979	+	1.74224i	−0.0866276	+	0.0587309i
$881$	0.107904	+	0.0622985i	0.00363538	+	0.00209889i	0.501817	−	0.864974i	$-0.332665\pi$
$881$	0.107904	+	0.0622985i	0.00363538	+	0.00209889i	−0.498181	+	0.867073i	$0.665999\pi$
$882$		0			0
$883$	0.665661	−	2.48428i	0.0224013	−	0.0836026i	−0.953820	−	0.300378i	$-0.902887\pi$
$883$	0.665661	−	2.48428i	0.0224013	−	0.0836026i	0.976222	+	0.216775i	$0.0695539\pi$
$884$	4.76992	+	27.0516i	0.160430	+	0.909843i
$885$		0			0
$886$	33.1457	−	12.0641i	1.11355	−	0.405300i
$887$	18.5247	−	12.9711i	0.621997	−	0.435527i	−0.219632	−	0.975583i	$-0.570486\pi$
$887$	18.5247	−	12.9711i	0.621997	−	0.435527i	0.841629	+	0.540056i	$0.181597\pi$
$888$		0			0
$889$	21.4460	+	25.5583i	0.719275	+	0.857199i
$890$	2.15153	+	13.3785i	0.0721195	+	0.448449i
$891$		0			0
$892$	−1.87411	+	1.87411i	−0.0627498	+	0.0627498i
$893$	2.85065	−	32.5830i	0.0953933	−	1.09035i
$894$		0			0
$895$	10.4943	−	10.1825i	0.350787	−	0.340364i
$896$	1.50373	+	4.13148i	0.0502362	+	0.138023i
$897$		0			0
$898$	22.2671	−	31.8006i	0.743061	−	1.06120i
$899$	16.4086	+	28.4206i	0.547259	+	0.947880i
$900$		0			0
$901$	−27.0476	+	46.8479i	−0.901087	+	1.56073i
$902$	1.25240	+	2.68579i	0.0417005	+	0.0894270i
$903$		0			0
$904$	3.90598	−	4.65496i	0.129911	−	0.154822i
$905$	12.6768	+	50.3342i	0.421390	+	1.67316i
$906$		0			0
$907$	−48.3880	+	22.5637i	−1.60670	+	0.749215i	−0.998989	−	0.0449468i	$-0.985688\pi$
$907$	−48.3880	+	22.5637i	−1.60670	+	0.749215i	−0.607707	+	0.794161i	$0.707910\pi$
$908$	2.38111	+	8.88642i	0.0790199	+	0.294906i
$909$		0			0
$910$	35.9429	−	29.2476i	1.19149	−	0.969548i
$911$	−12.2061	+	2.15226i	−0.404405	+	0.0713075i	−0.372151	−	0.928172i	$-0.621380\pi$
$911$	−12.2061	+	2.15226i	−0.404405	+	0.0713075i	−0.0322539	+	0.999480i	$0.510269\pi$
$912$		0			0
$913$	−12.1454	−	5.66348i	−0.401953	−	0.187434i
$914$	0.850083	−	4.82106i	0.0281182	−	0.159466i
$915$		0			0
$916$	9.20373	−	7.72285i	0.304100	−	0.255170i
$917$	−44.0231	−	44.0231i	−1.45377	−	1.45377i
$918$		0			0
$919$		−	18.8513i		−	0.621846i	−0.950435	−	0.310923i	$-0.899362\pi$
$919$		−	18.8513i		−	0.621846i	0.950435	−	0.310923i	$-0.100638\pi$
$920$	0.143917	+	1.99017i	0.00474480	+	0.0656138i
$921$		0			0
$922$	−3.44388	−	4.91837i	−0.113418	−	0.161978i
$923$	−24.7064	+	52.9831i	−0.813223	+	1.74396i
$924$		0			0
$925$	−1.77544	+	5.90742i	−0.0583761	+	0.194235i
$926$	33.9241	−	19.5861i	1.11481	−	0.643638i
$927$		0			0
$928$	5.10646	−	1.36827i	0.167628	−	0.0449157i
$929$	−37.3384	−	13.5901i	−1.22503	−	0.445875i	−0.353139	−	0.935571i	$-0.614886\pi$
$929$	−37.3384	−	13.5901i	−1.22503	−	0.445875i	−0.871893	+	0.489696i	$0.837108\pi$
$930$		0			0
$931$	−78.2761	−	65.6814i	−2.56540	−	2.15262i
$932$	−0.709045	−	8.10442i	−0.0232255	−	0.265469i
$933$		0			0
$934$	−10.0383	+	27.5799i	−0.328462	+	0.902442i
$935$	6.44393	−	16.9069i	0.210739	−	0.552916i
$936$		0			0
$937$	38.0315	+	10.1905i	1.24243	+	0.332909i	0.819410	−	0.573208i	$-0.194301\pi$
$937$	38.0315	+	10.1905i	1.24243	+	0.332909i	0.423025	+	0.906118i	$0.360968\pi$
$938$	−5.06252	−	3.54481i	−0.165297	−	0.115742i
$939$		0			0
$940$	−7.70863	+	4.29693i	−0.251428	+	0.140150i
$941$	15.6376	+	2.75733i	0.509772	+	0.0898865i	0.422617	−	0.906308i	$-0.361111\pi$
$941$	15.6376	+	2.75733i	0.509772	+	0.0898865i	0.0871545	+	0.996195i	$0.472223\pi$
$942$		0			0
$943$	1.89732	+	0.165994i	0.0617853	+	0.00540552i
$944$	−3.16866			−0.103131
$945$		0			0
$946$	−5.23863			−0.170323
$947$	44.2558	+	3.87188i	1.43812	+	0.125819i	0.779380	−	0.626552i	$-0.215534\pi$
$947$	44.2558	+	3.87188i	1.43812	+	0.125819i	0.658740	+	0.752371i	$0.271090\pi$
$948$		0			0
$949$	−2.31291	−	0.407829i	−0.0750803	−	0.0132387i
$950$	41.1500	+	4.85428i	1.33508	+	0.157494i
$951$		0			0
$952$	−20.9885	−	14.6963i	−0.680242	−	0.476310i
$953$	9.54106	+	2.55652i	0.309065	+	0.0828138i	0.410018	−	0.912077i	$-0.365522\pi$
$953$	9.54106	+	2.55652i	0.309065	+	0.0828138i	−0.100953	+	0.994891i	$0.532189\pi$
$954$		0			0
$955$	−14.2401	−	31.7805i	−0.460800	−	1.02839i
$956$	1.33571	−	3.66983i	0.0432000	−	0.118691i
$957$		0			0
$958$	2.01738	+	23.0588i	0.0651787	+	0.744996i
$959$	7.44726	+	6.24899i	0.240485	+	0.201791i
$960$		0			0
$961$	−7.08032	−	2.57703i	−0.228398	−	0.0831299i
$962$	−5.61685	+	1.50503i	−0.181095	+	0.0485242i
$963$		0			0
$964$	−13.2012	+	7.62172i	−0.425182	+	0.245479i
$965$	7.92261	−	2.74904i	0.255038	−	0.0884947i
$966$		0			0
$967$	−23.6281	+	50.6706i	−0.759829	+	1.62946i	0.0170879	+	0.999854i	$0.494560\pi$
$967$	−23.6281	+	50.6706i	−0.759829	+	1.62946i	−0.776916	+	0.629604i	$0.783217\pi$
$968$	−5.20358	−	7.43148i	−0.167249	−	0.238857i
$969$		0			0
$970$	8.66373	−	0.626509i	0.278176	−	0.0201160i
$971$		−	10.2108i		−	0.327681i	−0.986487	−	0.163840i	$-0.947612\pi$
$971$		−	10.2108i		−	0.327681i	0.986487	−	0.163840i	$-0.0523882\pi$
$972$		0			0
$973$	−17.9252	−	17.9252i	−0.574656	−	0.574656i
$974$	0.895354	−	0.751291i	0.0286890	−	0.0240729i
$975$		0			0
$976$	0.104169	−	0.590769i	0.00333435	−	0.0189101i
$977$	−54.0536	−	25.2056i	−1.72933	−	0.806399i	−0.991299	−	0.131632i	$-0.957978\pi$
$977$	−54.0536	−	25.2056i	−1.72933	−	0.806399i	−0.738030	−	0.674767i	$-0.764244\pi$
$978$		0			0
$979$	8.28619	−	1.46108i	0.264828	−	0.0466963i
$980$	−2.81686	+	27.4271i	−0.0899814	+	0.876128i
$981$		0			0
$982$	10.1760	+	37.9772i	0.324728	+	1.21190i
$983$	−17.6156	+	8.21427i	−0.561849	+	0.261994i	−0.682728	−	0.730673i	$-0.739207\pi$
$983$	−17.6156	+	8.21427i	−0.561849	+	0.261994i	0.120879	+	0.992667i	$0.461429\pi$
$984$		0			0
$985$	−2.11918	+	3.54596i	−0.0675227	+	0.112984i
$986$	−19.8035	+	23.6009i	−0.630671	+	0.751605i
$987$		0			0
$988$	16.5079	+	35.4014i	0.525187	+	1.12627i
$989$	−1.68341	+	2.91574i	−0.0535292	+	0.0927152i
$990$		0			0
$991$	13.2002	+	22.8635i	0.419319	+	0.726283i	0.995871	−	0.0907781i	$-0.0289354\pi$
$991$	13.2002	+	22.8635i	0.419319	+	0.726283i	−0.576552	+	0.817061i	$0.695602\pi$
$992$	−3.56055	+	5.08500i	−0.113048	+	0.161449i
$993$		0			0
$994$	−18.6505	−	51.2418i	−0.591557	−	1.62529i
$995$	39.8614	+	41.0820i	1.26369	+	1.30239i
$996$		0			0
$997$	−1.76325	+	20.1540i	−0.0558426	+	0.638283i	0.915770	+	0.401704i	$0.131582\pi$
$997$	−1.76325	+	20.1540i	−0.0558426	+	0.638283i	−0.971612	+	0.236579i	$0.923974\pi$
$998$	−16.4756	+	16.4756i	−0.521525	+	0.521525i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	810.2.s.a.773.9		216
3.2	odd	2		270.2.r.a.113.11	✓	216
5.2	odd	4	inner	810.2.s.a.287.13		216
15.2	even	4		270.2.r.a.167.3	yes	216
27.11	odd	18	inner	810.2.s.a.683.13		216
27.16	even	9		270.2.r.a.173.3	yes	216
135.92	even	36	inner	810.2.s.a.197.9		216
135.97	odd	36		270.2.r.a.227.11	yes	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
270.2.r.a.113.11	✓	216	3.2	odd	2
270.2.r.a.167.3	yes	216	15.2	even	4
270.2.r.a.173.3	yes	216	27.16	even	9
270.2.r.a.227.11	yes	216	135.97	odd	36
810.2.s.a.197.9		216	135.92	even	36	inner
810.2.s.a.287.13		216	5.2	odd	4	inner
810.2.s.a.683.13		216	27.11	odd	18	inner
810.2.s.a.773.9		216	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 810 = 2 \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	810.s (of order \(36\), degree \(12\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.996195 - 0.0871557i) q^{2} +(0.984808 + 0.173648i) q^{4} +(2.15090 + 0.611237i) q^{5} +(-3.60150 - 2.52180i) q^{7} +(-0.965926 - 0.258819i) q^{8} +O(q^{10})\)	\(q+(-0.996195 - 0.0871557i) q^{2} +(0.984808 + 0.173648i) q^{4} +(2.15090 + 0.611237i) q^{5} +(-3.60150 - 2.52180i) q^{7} +(-0.965926 - 0.258819i) q^{8} +(-2.08945 - 0.796375i) q^{10} +(-0.474884 + 1.30473i) q^{11} +(-0.410808 - 4.69556i) q^{13} +(3.36801 + 2.82610i) q^{14} +(0.939693 + 0.342020i) q^{16} +(-5.62913 + 1.50832i) q^{17} +(-7.17681 + 4.14354i) q^{19} +(2.01209 + 0.975451i) q^{20} +(0.586792 - 1.25838i) q^{22} +(-0.511833 - 0.730973i) q^{23} +(4.25278 + 2.62942i) q^{25} +4.71350i q^{26} +(-3.10888 - 3.10888i) q^{28} +(-4.04977 + 3.39816i) q^{29} +(1.07794 - 6.11333i) q^{31} +(-0.906308 - 0.422618i) q^{32} +(5.73917 - 1.01197i) q^{34} +(-6.20507 - 7.62552i) q^{35} +(0.319303 + 1.19165i) q^{37} +(7.51064 - 3.50227i) q^{38} +(-1.91941 - 1.14710i) q^{40} +(-1.37192 + 1.63499i) q^{41} +(-1.59452 - 3.41946i) q^{43} +(-0.694234 + 1.20245i) q^{44} +(0.446177 + 0.772801i) q^{46} +(-2.26380 + 3.23304i) q^{47} +(4.21722 + 11.5867i) q^{49} +(-4.00743 - 2.99007i) q^{50} +(0.410808 - 4.69556i) q^{52} +(6.56367 - 6.56367i) q^{53} +(-1.81893 + 2.51609i) q^{55} +(2.82610 + 3.36801i) q^{56} +(4.33053 - 3.03227i) q^{58} +(-2.97757 + 1.08375i) q^{59} +(-0.104169 - 0.590769i) q^{61} +(-1.60665 + 5.99611i) q^{62} +(0.866025 + 0.500000i) q^{64} +(1.98649 - 10.3508i) q^{65} +(-1.40032 + 0.122512i) q^{67} +(-5.80553 + 0.507918i) q^{68} +(5.51685 + 8.13731i) q^{70} +(-10.7411 - 6.20139i) q^{71} +(0.128962 - 0.481292i) q^{73} +(-0.214228 - 1.21495i) q^{74} +(-7.78730 + 2.83435i) q^{76} +(5.00057 - 3.50144i) q^{77} +(-7.34219 - 8.75008i) q^{79} +(1.81213 + 1.31003i) q^{80} +(1.50919 - 1.50919i) q^{82} +(-0.841193 + 9.61488i) q^{83} +(-13.0297 - 0.196478i) q^{85} +(1.29043 + 3.54542i) q^{86} +(0.796392 - 1.13737i) q^{88} +(-3.02996 - 5.24805i) q^{89} +(-10.3617 + 17.9471i) q^{91} +(-0.377125 - 0.808747i) q^{92} +(2.53696 - 3.02343i) q^{94} +(-17.9693 + 4.52562i) q^{95} +(-3.52069 + 1.64173i) q^{97} +(-3.19132 - 11.9102i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q+O(q^{10}) \) 216 * q	\( 216 q - 24 q^{11} + 24 q^{20} - 24 q^{23} + 36 q^{25} + 108 q^{35} + 36 q^{38} + 72 q^{41} + 48 q^{47} + 48 q^{50} + 12 q^{56} + 36 q^{61} - 24 q^{65} - 72 q^{67} - 36 q^{68} + 240 q^{77} + 60 q^{83} - 72 q^{86} + 48 q^{92} + 60 q^{95} - 72 q^{97}+O(q^{100}) \) 216 * q - 24 * q^11 + 24 * q^20 - 24 * q^23 + 36 * q^25 + 108 * q^35 + 36 * q^38 + 72 * q^41 + 48 * q^47 + 48 * q^50 + 12 * q^56 + 36 * q^61 - 24 * q^65 - 72 * q^67 - 36 * q^68 + 240 * q^77 + 60 * q^83 - 72 * q^86 + 48 * q^92 + 60 * q^95 - 72 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more