LMFDB - Embedded newform 666.2.bs.a.89.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [666,2,Mod(17,666)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(666, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([18, 7]))

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

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

chi := DirichletCharacter("666.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 666 = 2 \cdot 3^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	666.bs (of order $36$, degree $12$, 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:	$5.31803677462$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$6$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			89.3
Character	$\chi$	$=$	666.89
Dual form			666.2.bs.a.449.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.906308 + 0.422618i) q^{2} +(0.642788 - 0.766044i) q^{4} +(2.09980 - 1.47030i) q^{5} +(0.541765 - 3.07250i) q^{7} +(-0.258819 + 0.965926i) q^{8} +O(q^{10})$	\(q+(-0.906308 + 0.422618i) q^{2} +(0.642788 - 0.766044i) q^{4} +(2.09980 - 1.47030i) q^{5} +(0.541765 - 3.07250i) q^{7} +(-0.258819 + 0.965926i) q^{8} +(-1.28169 + 2.21995i) q^{10} +(2.44072 + 4.22744i) q^{11} +(0.0448556 - 0.00392436i) q^{13} +(0.807489 + 3.01359i) q^{14} +(-0.173648 - 0.984808i) q^{16} +(0.526723 + 0.0460823i) q^{17} +(2.76682 - 5.93347i) q^{19} +(0.223413 - 2.55363i) q^{20} +(-3.99864 - 2.79987i) q^{22} +(-1.27808 + 0.342461i) q^{23} +(0.537288 - 1.47619i) q^{25} +(-0.0389945 + 0.0225135i) q^{26} +(-2.00543 - 2.38998i) q^{28} +(-2.36516 - 0.633743i) q^{29} +(-6.30581 - 6.30581i) q^{31} +(0.573576 + 0.819152i) q^{32} +(-0.496848 + 0.180838i) q^{34} +(-3.37989 - 7.24819i) q^{35} +(5.71557 + 2.08142i) q^{37} +6.54685i q^{38} +(0.876728 + 2.40879i) q^{40} +(-3.44954 - 2.89450i) q^{41} +(2.39927 - 2.39927i) q^{43} +(4.80727 + 0.847652i) q^{44} +(1.01361 - 0.850516i) q^{46} +(9.54907 + 5.51316i) q^{47} +(-2.56890 - 0.935004i) q^{49} +(0.136915 + 1.56495i) q^{50} +(0.0258264 - 0.0368839i) q^{52} +(3.28937 - 0.580005i) q^{53} +(11.3406 + 5.28821i) q^{55} +(2.82759 + 1.31853i) q^{56} +(2.41140 - 0.425194i) q^{58} +(0.687101 - 0.981282i) q^{59} +(0.179932 + 2.05663i) q^{61} +(8.37996 + 3.05006i) q^{62} +(-0.866025 - 0.500000i) q^{64} +(0.0884178 - 0.0741913i) q^{65} +(2.59567 + 0.457687i) q^{67} +(0.373872 - 0.373872i) q^{68} +(6.12643 + 5.14069i) q^{70} +(-5.41444 - 14.8761i) q^{71} +10.7530i q^{73} +(-6.05971 + 0.529097i) q^{74} +(-2.76682 - 5.93347i) q^{76} +(14.3111 - 5.20882i) q^{77} +(-5.74249 - 8.20113i) q^{79} +(-1.81258 - 1.81258i) q^{80} +(4.34961 + 1.16547i) q^{82} +(-6.99551 - 8.33692i) q^{83} +(1.17377 - 0.677674i) q^{85} +(-1.16050 + 3.18845i) q^{86} +(-4.71510 + 1.26341i) q^{88} +(7.23130 + 5.06341i) q^{89} +(0.0122436 - 0.139945i) q^{91} +(-0.559195 + 1.19920i) q^{92} +(-10.9844 - 0.961007i) q^{94} +(-2.91418 - 16.5271i) q^{95} +(3.39033 + 12.6529i) q^{97} +(2.72337 - 0.238264i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q+O(q^{10}) $ 72 * q	$ 72 q + 12 q^{13} - 24 q^{19} - 12 q^{22} + 72 q^{34} + 72 q^{37} + 24 q^{40} + 24 q^{43} + 36 q^{46} - 48 q^{49} - 12 q^{52} + 60 q^{55} + 120 q^{61} + 60 q^{67} - 60 q^{70} + 24 q^{76} - 12 q^{79} - 48 q^{82} + 108 q^{85} - 24 q^{88} - 168 q^{91} - 84 q^{94} - 264 q^{97}+O(q^{100}) $ 72 * q + 12 * q^13 - 24 * q^19 - 12 * q^22 + 72 * q^34 + 72 * q^37 + 24 * q^40 + 24 * q^43 + 36 * q^46 - 48 * q^49 - 12 * q^52 + 60 * q^55 + 120 * q^61 + 60 * q^67 - 60 * q^70 + 24 * q^76 - 12 * q^79 - 48 * q^82 + 108 * q^85 - 24 * q^88 - 168 * q^91 - 84 * q^94 - 264 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/666\mathbb{Z}\right)^\times$.

$n$	$371$	$631$
$\chi(n)$	$-1$	$e\left(\frac{13}{36}\right)$

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 $

$2$	−0.906308	+	0.422618i	−0.640856	+	0.298836i
$2$	−0.906308	+	0.422618i	−0.640856	+	0.298836i
$3$		0			0
$3$		0			0
$4$	0.642788	−	0.766044i	0.321394	−	0.383022i
$5$	2.09980	−	1.47030i	0.939059	−	0.657536i	−0.000472216	−	1.00000i	$-0.500150\pi$
$5$	2.09980	−	1.47030i	0.939059	−	0.657536i	0.939531	+	0.342464i	$0.111261\pi$
$6$		0			0
$7$	0.541765	−	3.07250i	0.204768	−	1.16130i	−0.693037	−	0.720902i	$-0.743728\pi$
$7$	0.541765	−	3.07250i	0.204768	−	1.16130i	0.897805	−	0.440394i	$-0.145161\pi$
$8$	−0.258819	+	0.965926i	−0.0915064	+	0.341506i
$9$		0			0
$10$	−1.28169	+	2.21995i	−0.405306	+	0.702011i
$11$	2.44072	+	4.22744i	0.735904	+	1.27462i	0.954326	+	0.298768i	$0.0965757\pi$
$11$	2.44072	+	4.22744i	0.735904	+	1.27462i	−0.218422	+	0.975854i	$0.570091\pi$
$12$		0			0
$13$	0.0448556	−	0.00392436i	0.0124407	−	0.00108842i	−0.0809337	−	0.996719i	$-0.525790\pi$
$13$	0.0448556	−	0.00392436i	0.0124407	−	0.00108842i	0.0933744	+	0.995631i	$0.470235\pi$
$14$	0.807489	+	3.01359i	0.215811	+	0.805416i
$15$		0			0
$16$	−0.173648	−	0.984808i	−0.0434120	−	0.246202i
$17$	0.526723	+	0.0460823i	0.127749	+	0.0111766i	0.150851	−	0.988557i	$-0.451799\pi$
$17$	0.526723	+	0.0460823i	0.127749	+	0.0111766i	−0.0231019	+	0.999733i	$0.507354\pi$
$18$		0			0
$19$	2.76682	−	5.93347i	0.634752	−	1.36123i	−0.281086	−	0.959683i	$-0.590695\pi$
$19$	2.76682	−	5.93347i	0.634752	−	1.36123i	0.915838	−	0.401548i	$-0.131528\pi$
$20$	0.223413	−	2.55363i	0.0499568	−	0.571008i
$21$		0			0
$22$	−3.99864	−	2.79987i	−0.852512	−	0.596935i
$23$	−1.27808	+	0.342461i	−0.266499	+	0.0714081i	−0.389594	−	0.920987i	$-0.627385\pi$
$23$	−1.27808	+	0.342461i	−0.266499	+	0.0714081i	0.123095	+	0.992395i	$0.460718\pi$
$24$		0			0
$25$	0.537288	−	1.47619i	0.107458	−	0.295237i
$26$	−0.0389945	+	0.0225135i	−0.00764744	+	0.00441525i
$27$		0			0
$28$	−2.00543	−	2.38998i	−0.378991	−	0.451664i
$29$	−2.36516	−	0.633743i	−0.439200	−	0.117683i	0.0324418	−	0.999474i	$-0.489672\pi$
$29$	−2.36516	−	0.633743i	−0.439200	−	0.117683i	−0.471641	+	0.881790i	$0.656338\pi$
$30$		0			0
$31$	−6.30581	−	6.30581i	−1.13256	−	1.13256i	−0.989751	−	0.142807i	$-0.954387\pi$
$31$	−6.30581	−	6.30581i	−1.13256	−	1.13256i	−0.142807	−	0.989751i	$-0.545613\pi$
$32$	0.573576	+	0.819152i	0.101395	+	0.144807i
$33$		0			0
$34$	−0.496848	+	0.180838i	−0.0852087	+	0.0310134i
$35$	−3.37989	−	7.24819i	−0.571305	−	1.22517i
$36$		0			0
$37$	5.71557	+	2.08142i	0.939633	+	0.342183i
$37$	5.71557	+	2.08142i	0.939633	+	0.342183i
$38$			6.54685i			1.06204i
$39$		0			0
$40$	0.876728	+	2.40879i	0.138623	+	0.380863i
$41$	−3.44954	−	2.89450i	−0.538727	−	0.452046i	0.332375	−	0.943147i	$-0.392150\pi$
$41$	−3.44954	−	2.89450i	−0.538727	−	0.452046i	−0.871102	+	0.491102i	$0.836594\pi$
$42$		0			0
$43$	2.39927	−	2.39927i	0.365885	−	0.365885i	−0.500089	−	0.865974i	$-0.666699\pi$
$43$	2.39927	−	2.39927i	0.365885	−	0.365885i	0.865974	+	0.500089i	$0.166699\pi$
$44$	4.80727	+	0.847652i	0.724724	+	0.127788i
$45$		0			0
$46$	1.01361	−	0.850516i	0.149448	−	0.125402i
$47$	9.54907	+	5.51316i	1.39288	+	0.804177i	0.993633	−	0.112668i	$-0.0359397\pi$
$47$	9.54907	+	5.51316i	1.39288	+	0.804177i	0.399243	+	0.916845i	$0.369273\pi$
$48$		0			0
$49$	−2.56890	−	0.935004i	−0.366986	−	0.133572i
$50$	0.136915	+	1.56495i	0.0193627	+	0.221317i
$51$		0			0
$52$	0.0258264	−	0.0368839i	0.00358148	−	0.00511488i
$53$	3.28937	−	0.580005i	0.451830	−	0.0796699i	0.0568978	−	0.998380i	$-0.481879\pi$
$53$	3.28937	−	0.580005i	0.451830	−	0.0796699i	0.394933	+	0.918710i	$0.370768\pi$
$54$		0			0
$55$	11.3406	+	5.28821i	1.52917	+	0.713062i
$56$	2.82759	+	1.31853i	0.377852	+	0.176195i
$57$		0			0
$58$	2.41140	−	0.425194i	0.316632	−	0.0558307i
$59$	0.687101	−	0.981282i	0.0894530	−	0.127752i	−0.771931	−	0.635706i	$-0.780709\pi$
$59$	0.687101	−	0.981282i	0.0894530	−	0.127752i	0.861384	+	0.507954i	$0.169598\pi$
$60$		0			0
$61$	0.179932	+	2.05663i	0.0230379	+	0.263325i	0.998975	+	0.0452713i	$0.0144152\pi$
$61$	0.179932	+	2.05663i	0.0230379	+	0.263325i	−0.975937	+	0.218054i	$0.930029\pi$
$62$	8.37996	+	3.05006i	1.06426	+	0.387358i
$63$		0			0
$64$	−0.866025	−	0.500000i	−0.108253	−	0.0625000i
$65$	0.0884178	−	0.0741913i	0.0109669	−	0.00920230i
$66$		0			0
$67$	2.59567	+	0.457687i	0.317112	+	0.0559154i	0.329939	−	0.944002i	$-0.392972\pi$
$67$	2.59567	+	0.457687i	0.317112	+	0.0559154i	−0.0128268	+	0.999918i	$0.504083\pi$
$68$	0.373872	−	0.373872i	0.0453386	−	0.0453386i
$69$		0			0
$70$	6.12643	+	5.14069i	0.732249	+	0.614430i
$71$	−5.41444	−	14.8761i	−0.642576	−	1.76546i	−0.643478	−	0.765465i	$-0.722509\pi$
$71$	−5.41444	−	14.8761i	−0.642576	−	1.76546i	0.000901686	−	1.00000i	$-0.499713\pi$
$72$		0			0
$73$			10.7530i			1.25854i	0.777186	+	0.629271i	$0.216646\pi$
$73$			10.7530i			1.25854i	−0.777186	+	0.629271i	$0.783354\pi$
$74$	−6.05971	+	0.529097i	−0.704427	+	0.0615062i
$75$		0			0
$76$	−2.76682	−	5.93347i	−0.317376	−	0.680615i
$77$	14.3111	−	5.20882i	1.63090	−	0.593600i
$78$		0			0
$79$	−5.74249	−	8.20113i	−0.646081	−	0.922699i	0.353840	−	0.935306i	$-0.384876\pi$
$79$	−5.74249	−	8.20113i	−0.646081	−	0.922699i	−0.999921	+	0.0126069i	$0.995987\pi$
$80$	−1.81258	−	1.81258i	−0.202653	−	0.202653i
$81$		0			0
$82$	4.34961	+	1.16547i	0.480334	+	0.128705i
$83$	−6.99551	−	8.33692i	−0.767857	−	0.915096i	0.230461	−	0.973082i	$-0.425977\pi$
$83$	−6.99551	−	8.33692i	−0.767857	−	0.915096i	−0.998317	+	0.0579855i	$0.981532\pi$
$84$		0			0
$85$	1.17377	−	0.677674i	0.127313	−	0.0735041i
$86$	−1.16050	+	3.18845i	−0.125140	+	0.343819i
$87$		0			0
$88$	−4.71510	+	1.26341i	−0.502631	+	0.134680i
$89$	7.23130	+	5.06341i	0.766517	+	0.536721i	0.890183	−	0.455603i	$-0.150576\pi$
$89$	7.23130	+	5.06341i	0.766517	+	0.536721i	−0.123666	+	0.992324i	$0.539465\pi$
$90$		0			0
$91$	0.0122436	−	0.139945i	0.00128348	−	0.0146702i
$92$	−0.559195	+	1.19920i	−0.0583001	+	0.125025i
$93$		0			0
$94$	−10.9844	−	0.961007i	−1.13295	−	0.0991203i
$95$	−2.91418	−	16.5271i	−0.298988	−	1.69565i
$96$		0			0
$97$	3.39033	+	12.6529i	0.344236	+	1.28470i	0.893503	+	0.449058i	$0.148240\pi$
$97$	3.39033	+	12.6529i	0.344236	+	1.28470i	−0.549267	+	0.835647i	$0.685093\pi$
$98$	2.72337	−	0.238264i	0.275102	−	0.0240683i
$99$		0			0
$100$	−0.785463	−	1.36046i	−0.0785463	−	0.136046i
$101$	−2.16318	+	3.74674i	−0.215244	+	0.372814i	−0.953348	−	0.301873i	$-0.902388\pi$
$101$	−2.16318	+	3.74674i	−0.215244	+	0.372814i	0.738104	+	0.674687i	$0.235721\pi$
$102$		0			0
$103$	−3.35159	+	12.5083i	−0.330242	+	1.23248i	0.578695	+	0.815544i	$0.303562\pi$
$103$	−3.35159	+	12.5083i	−0.330242	+	1.23248i	−0.908937	+	0.416935i	$0.863104\pi$
$104$	−0.00781884	+	0.0443429i	−0.000766701	+	0.00434818i
$105$		0			0
$106$	−2.73606	+	1.91581i	−0.265750	+	0.186080i
$107$	−8.32636	+	9.92297i	−0.804940	+	0.959290i	−0.999768	−	0.0215473i	$-0.993141\pi$
$107$	−8.32636	+	9.92297i	−0.804940	+	0.959290i	0.194828	+	0.980837i	$0.437585\pi$
$108$		0			0
$109$	18.6345	−	8.68939i	1.78486	−	0.832293i	0.818752	−	0.574147i	$-0.194666\pi$
$109$	18.6345	−	8.68939i	1.78486	−	0.832293i	0.966106	−	0.258146i	$-0.0831116\pi$
$110$	−12.5130			−1.19307
$111$		0			0
$112$	−3.11990			−0.294803
$113$	−1.72063	+	0.802345i	−0.161864	+	0.0754783i	−0.501862	−	0.864948i	$-0.667351\pi$
$113$	−1.72063	+	0.802345i	−0.161864	+	0.0754783i	0.339998	+	0.940426i	$0.389574\pi$
$114$		0			0
$115$	−2.18020	+	2.59826i	−0.203305	+	0.242289i
$116$	−2.00577	+	1.40446i	−0.186231	+	0.130401i
$117$		0			0
$118$	−0.208017	+	1.17973i	−0.0191496	+	0.108603i
$119$	0.426948	−	1.59339i	0.0391382	−	0.146066i
$120$		0			0
$121$	−6.41419	+	11.1097i	−0.583108	+	1.00997i
$122$	−1.03224	−	1.78790i	−0.0934550	−	0.161869i
$123$		0			0
$124$	−8.88383	+	0.777235i	−0.797792	+	0.0697977i
$125$	2.27503	+	8.49051i	0.203485	+	0.759415i
$126$		0			0
$127$	−2.35296	−	13.3443i	−0.208792	−	1.18412i	−0.891361	−	0.453295i	$-0.850249\pi$
$127$	−2.35296	−	13.3443i	−0.208792	−	1.18412i	0.682569	−	0.730821i	$-0.260863\pi$
$128$	0.996195	+	0.0871557i	0.0880520	+	0.00770355i
$129$		0			0
$130$	−0.0487791	+	0.104607i	−0.00427821	+	0.00917465i
$131$	−0.731402	+	8.35997i	−0.0639029	+	0.730414i	0.894886	+	0.446295i	$0.147257\pi$
$131$	−0.731402	+	8.35997i	−0.0639029	+	0.730414i	−0.958789	+	0.284119i	$0.908299\pi$
$132$		0			0
$133$	−16.7316	−	11.7156i	−1.45081	−	1.01587i
$134$	−2.54591	+	0.682173i	−0.219933	+	0.0589308i
$135$		0			0
$136$	−0.180838	+	0.496848i	−0.0155067	+	0.0426044i
$137$	−18.8856	+	10.9036i	−1.61351	+	0.931559i	−0.624960	+	0.780657i	$0.714885\pi$
$137$	−18.8856	+	10.9036i	−1.61351	+	0.931559i	−0.988549	+	0.150902i	$0.951782\pi$
$138$		0			0
$139$	5.18250	+	6.17626i	0.439574	+	0.523863i	0.939659	−	0.342113i	$-0.111142\pi$
$139$	5.18250	+	6.17626i	0.439574	+	0.523863i	−0.500085	+	0.865976i	$0.666698\pi$
$140$	−7.72498	−	2.06990i	−0.652880	−	0.174939i
$141$		0			0
$142$	11.1941	+	11.1941i	0.939384	+	0.939384i
$143$	0.126070	+	0.180046i	0.0105425	+	0.0150562i
$144$		0			0
$145$	−5.89816	+	2.14675i	−0.489815	+	0.178278i
$146$	−4.54441	−	9.74552i	−0.376098	−	0.806545i
$147$		0			0
$148$	5.26835	−	3.04047i	0.433056	−	0.249925i
$149$		−	0.756557i		−	0.0619796i	−0.999520	−	0.0309898i	$-0.990134\pi$
$149$		−	0.756557i		−	0.0619796i	0.999520	−	0.0309898i	$-0.00986594\pi$
$150$		0			0
$151$	6.13871	+	16.8660i	0.499561	+	1.37253i	0.891700	+	0.452627i	$0.149513\pi$
$151$	6.13871	+	16.8660i	0.499561	+	1.37253i	−0.392138	+	0.919906i	$0.628265\pi$
$152$	5.01518	+	4.20824i	0.406785	+	0.341333i
$153$		0			0
$154$	−10.7689	+	10.7689i	−0.867786	+	0.867786i
$155$	−22.5124	−	3.96954i	−1.80824	−	0.318841i
$156$		0			0
$157$	−0.734453	+	0.616279i	−0.0586157	+	0.0491845i	−0.671625	−	0.740891i	$-0.734403\pi$
$157$	−0.734453	+	0.616279i	−0.0586157	+	0.0491845i	0.613009	+	0.790076i	$0.289959\pi$
$158$	8.67041	+	5.00587i	0.689781	+	0.398245i
$159$		0			0
$160$	2.40879	+	0.876728i	0.190432	+	0.0693114i
$161$	0.359792	+	4.11244i	0.0283556	+	0.324106i
$162$		0			0
$163$	5.49783	−	7.85171i	0.430623	−	0.614994i	−0.543935	−	0.839127i	$-0.683066\pi$
$163$	5.49783	−	7.85171i	0.430623	−	0.614994i	0.974558	+	0.224134i	$0.0719552\pi$
$164$	−4.43464	+	0.781946i	−0.346287	+	0.0610597i
$165$		0			0
$166$	9.86342	+	4.59939i	0.765550	+	0.356982i
$167$	9.02827	+	4.20995i	0.698629	+	0.325776i	0.739281	−	0.673398i	$-0.235166\pi$
$167$	9.02827	+	4.20995i	0.698629	+	0.325776i	−0.0406520	+	0.999173i	$0.512944\pi$
$168$		0			0
$169$	−12.8005	+	2.25707i	−0.984654	+	0.173621i
$170$	−0.777396	+	1.11024i	−0.0596236	+	0.0851513i
$171$		0			0
$172$	−0.295726	−	3.38016i	−0.0225489	−	0.257735i
$173$	−15.3649	−	5.59237i	−1.16817	−	0.425180i	−0.316162	−	0.948705i	$-0.602394\pi$
$173$	−15.3649	−	5.59237i	−1.16817	−	0.425180i	−0.852010	+	0.523525i	$0.824617\pi$
$174$		0			0
$175$	−4.24450	−	2.45056i	−0.320854	−	0.185245i
$176$	3.73939	−	3.13772i	0.281867	−	0.236515i
$177$		0			0
$178$	−8.69368	−	1.53293i	−0.651619	−	0.114898i
$179$	1.79219	−	1.79219i	0.133955	−	0.133955i	−0.636950	−	0.770905i	$-0.719804\pi$
$179$	1.79219	−	1.79219i	0.133955	−	0.133955i	0.770905	+	0.636950i	$0.219804\pi$
$180$		0			0
$181$	−5.90128	−	4.95176i	−0.438638	−	0.368061i	0.396561	−	0.918008i	$-0.370203\pi$
$181$	−5.90128	−	4.95176i	−0.438638	−	0.368061i	−0.835200	+	0.549947i	$0.814648\pi$
$182$	0.0480468	+	0.132008i	0.00356147	+	0.00978505i
$183$		0			0
$184$		−	1.32317i		−	0.0975453i
$185$	15.0618	−	4.03301i	1.10737	−	0.296513i
$186$		0			0
$187$	1.09077	+	2.33916i	0.0797650	+	0.171057i
$188$	10.3614	−	3.77122i	0.755679	−	0.275045i
$189$		0			0
$190$	9.62581	+	13.7471i	0.698330	+	0.997318i
$191$	−15.3851	−	15.3851i	−1.11323	−	1.11323i	−0.992711	−	0.120518i	$-0.961544\pi$
$191$	−15.3851	−	15.3851i	−1.11323	−	1.11323i	−0.120518	−	0.992711i	$-0.538456\pi$
$192$		0			0
$193$	4.24593	+	1.13769i	0.305628	+	0.0818929i	0.408374	−	0.912815i	$-0.366096\pi$
$193$	4.24593	+	1.13769i	0.305628	+	0.0818929i	−0.102745	+	0.994708i	$0.532763\pi$
$194$	−8.42001	−	10.0346i	−0.604522	−	0.720441i
$195$		0			0
$196$	−2.36751	+	1.36688i	−0.169108	+	0.0976346i
$197$	−1.05369	+	2.89499i	−0.0750723	+	0.206259i	−0.971552	−	0.236824i	$-0.923893\pi$
$197$	−1.05369	+	2.89499i	−0.0750723	+	0.206259i	0.896480	+	0.443084i	$0.146116\pi$
$198$		0			0
$199$	−12.2171	+	3.27356i	−0.866048	+	0.232057i	−0.664378	−	0.747397i	$-0.731303\pi$
$199$	−12.2171	+	3.27356i	−0.866048	+	0.232057i	−0.201670	+	0.979454i	$0.564637\pi$
$200$	1.28683	+	0.901046i	0.0909924	+	0.0637136i
$201$		0			0
$202$	0.377067	−	4.30989i	0.0265303	−	0.303243i
$203$	−3.22854	+	6.92362i	−0.226599	+	0.485943i
$204$		0			0
$205$	−11.4991	−	1.00604i	−0.803133	−	0.0702650i
$206$	−2.24866	−	12.7528i	−0.156672	−	0.888530i
$207$		0			0
$208$	−0.0116538	−	0.0434927i	−0.000808048	−	0.00301567i
$209$	31.8364	−	2.78533i	2.20217	−	0.192665i
$210$		0			0
$211$	0.141386	+	0.244888i	0.00973344	+	0.0168588i	0.870851	−	0.491547i	$-0.163568\pi$
$211$	0.141386	+	0.244888i	0.00973344	+	0.0168588i	−0.861118	+	0.508406i	$0.830235\pi$
$212$	1.67006	−	2.89263i	0.114700	−	0.198666i
$213$		0			0
$214$	3.35262	−	12.5121i	0.229180	−	0.855312i
$215$	1.51035	−	8.56561i	0.103005	−	0.584170i
$216$		0			0
$217$	−22.7909	+	15.9584i	−1.54715	+	1.08332i
$218$	−13.2163	+	15.7505i	−0.895118	+	1.06676i
$219$		0			0
$220$	11.3406	−	5.28821i	0.764583	−	0.356531i
$221$	0.0238073			0.00160145
$222$		0			0
$223$	−9.00954			−0.603324			−0.301662	−	0.953415i	$-0.597541\pi$
$223$	−9.00954			−0.603324			−0.301662	+	0.953415i	$0.597541\pi$
$224$	2.82759	−	1.31853i	0.188926	−	0.0880977i
$225$		0			0
$226$	1.22034	−	1.45434i	0.0811757	−	0.0967414i
$227$	−17.1474	+	12.0067i	−1.13811	+	0.796914i	−0.981635	−	0.190768i	$-0.938902\pi$
$227$	−17.1474	+	12.0067i	−1.13811	+	0.796914i	−0.156476	+	0.987682i	$0.550013\pi$
$228$		0			0
$229$	−5.12628	+	29.0726i	−0.338754	+	1.92117i	0.0477035	+	0.998862i	$0.484810\pi$
$229$	−5.12628	+	29.0726i	−0.338754	+	1.92117i	−0.386457	+	0.922307i	$0.626301\pi$
$230$	0.877859	−	3.27621i	0.0578843	−	0.216027i
$231$		0			0
$232$	1.22430	−	2.12055i	0.0803791	−	0.139221i
$233$	10.4982	+	18.1834i	0.687760	+	1.19123i	0.972561	+	0.232648i	$0.0747390\pi$
$233$	10.4982	+	18.1834i	0.687760	+	1.19123i	−0.284801	+	0.958587i	$0.591928\pi$
$234$		0			0
$235$	28.1571	−	2.46343i	1.83677	−	0.160696i
$236$	−0.310046	−	1.15711i	−0.0201823	−	0.0753212i
$237$		0			0
$238$	0.286450	+	1.62454i	0.0185678	+	0.105303i
$239$	−6.56164	−	0.574069i	−0.424437	−	0.0371334i	−0.127063	−	0.991895i	$-0.540555\pi$
$239$	−6.56164	−	0.574069i	−0.424437	−	0.0371334i	−0.297374	+	0.954761i	$0.596111\pi$
$240$		0			0
$241$	11.6091	−	24.8958i	0.747807	−	1.60368i	−0.0485291	−	0.998822i	$-0.515453\pi$
$241$	11.6091	−	24.8958i	0.747807	−	1.60368i	0.796336	−	0.604855i	$-0.206769\pi$
$242$	1.11807	−	12.7796i	0.0718721	−	0.821501i
$243$		0			0
$244$	1.69113	+	1.18414i	0.108264	+	0.0758070i
$245$	−6.76891	+	1.81373i	−0.432450	+	0.115875i
$246$		0			0
$247$	0.100822	−	0.277007i	0.00641517	−	0.0176255i
$248$	7.72301	−	4.45888i	0.490412	−	0.283139i
$249$		0			0
$250$	−5.65012	−	6.73355i	−0.357345	−	0.425867i
$251$	−3.12691	−	0.837853i	−0.197369	−	0.0528848i	0.158780	−	0.987314i	$-0.449244\pi$
$251$	−3.12691	−	0.837853i	−0.197369	−	0.0528848i	−0.356149	+	0.934429i	$0.615911\pi$
$252$		0			0
$253$	−4.56717	−	4.56717i	−0.287136	−	0.287136i
$254$	7.77205	+	11.0996i	0.487662	+	0.696454i
$255$		0			0
$256$	−0.939693	+	0.342020i	−0.0587308	+	0.0213763i
$257$	8.84202	+	18.9618i	0.551550	+	1.18280i	0.962534	+	0.271160i	$0.0874073\pi$
$257$	8.84202	+	18.9618i	0.551550	+	1.18280i	−0.410984	+	0.911642i	$0.634815\pi$
$258$		0			0
$259$	9.49165	−	16.4334i	0.589783	−	1.02112i
$260$		−	0.115421i		−	0.00715812i
$261$		0			0
$262$	−2.87020	−	7.88581i	−0.177321	−	0.487187i
$263$	6.91210	+	5.79994i	0.426219	+	0.357640i	0.830523	−	0.556985i	$-0.188042\pi$
$263$	6.91210	+	5.79994i	0.426219	+	0.357640i	−0.404304	+	0.914625i	$0.632486\pi$
$264$		0			0
$265$	6.05425	−	6.05425i	0.371909	−	0.371909i
$266$	20.1152	+	3.54686i	1.23334	+	0.217472i
$267$		0			0
$268$	2.01908	−	1.69421i	0.123335	−	0.103490i
$269$	17.4154	+	10.0548i	1.06184	+	0.613052i	0.925940	−	0.377671i	$-0.123275\pi$
$269$	17.4154	+	10.0548i	1.06184	+	0.613052i	0.135897	+	0.990723i	$0.456608\pi$
$270$		0			0
$271$	26.8836	+	9.78482i	1.63306	+	0.594385i	0.985806	−	0.167889i	$-0.0536949\pi$
$271$	26.8836	+	9.78482i	1.63306	+	0.594385i	0.647254	+	0.762274i	$0.275917\pi$
$272$	−0.0460823	−	0.526723i	−0.00279415	−	0.0319372i
$273$		0			0
$274$	12.5081	−	17.8635i	0.755643	−	1.07917i
$275$	7.55187	−	1.33160i	0.455395	−	0.0802984i
$276$		0			0
$277$	6.26182	+	2.91994i	0.376236	+	0.175442i	0.601532	−	0.798848i	$-0.294557\pi$
$277$	6.26182	+	2.91994i	0.376236	+	0.175442i	−0.225296	+	0.974290i	$0.572335\pi$
$278$	−7.30713	−	3.40737i	−0.438253	−	0.204361i
$279$		0			0
$280$	7.87599	−	1.38875i	0.470681	−	0.0829937i
$281$	−7.92885	+	11.3236i	−0.472995	+	0.675508i	−0.982777	−	0.184796i	$-0.940837\pi$
$281$	−7.92885	+	11.3236i	−0.472995	+	0.675508i	0.509781	+	0.860304i	$0.329726\pi$
$282$		0			0
$283$	0.180814	+	2.06671i	0.0107483	+	0.122853i	0.999673	−	0.0255633i	$-0.00813793\pi$
$283$	0.180814	+	2.06671i	0.0107483	+	0.122853i	−0.988925	+	0.148417i	$0.952582\pi$
$284$	−14.8761	−	5.41444i	−0.882732	−	0.321288i
$285$		0			0
$286$	−0.190349	−	0.109898i	−0.0112556	−	0.00649840i
$287$	−10.7622	+	9.03056i	−0.635273	+	0.533057i
$288$		0			0
$289$	−16.4664	−	2.90347i	−0.968613	−	0.170793i
$290$	4.43829	−	4.43829i	0.260625	−	0.260625i
$291$		0			0
$292$	8.23727	+	6.91189i	0.482050	+	0.404488i
$293$	−6.80345	−	18.6923i	−0.397462	−	1.09202i	−0.963516	−	0.267649i	$-0.913753\pi$
$293$	−6.80345	−	18.6923i	−0.397462	−	1.09202i	0.566055	−	0.824368i	$-0.308469\pi$
$294$		0			0
$295$		−	3.07074i		−	0.178785i
$296$	−3.48979	+	4.98210i	−0.202840	+	0.289579i
$297$		0			0
$298$	0.319735	+	0.685674i	0.0185217	+	0.0397200i
$299$	−0.0559852	+	0.0203770i	−0.00323771	+	0.00117843i
$300$		0			0
$301$	−6.07191	−	8.67159i	−0.349979	−	0.499822i
$302$	−12.6914	−	12.6914i	−0.730310	−	0.730310i
$303$		0			0
$304$	−6.32378	−	1.69445i	−0.362693	−	0.0971834i
$305$	3.40168	+	4.05396i	0.194780	+	0.232129i
$306$		0			0
$307$	−5.39485	+	3.11472i	−0.307900	+	0.177766i	−0.645987	−	0.763349i	$-0.723554\pi$
$307$	−5.39485	+	3.11472i	−0.307900	+	0.177766i	0.338086	+	0.941115i	$0.390220\pi$
$308$	5.20882	−	14.3111i	0.296800	−	0.815452i
$309$		0			0
$310$	22.0807	−	5.91651i	1.25410	−	0.336035i
$311$	13.9994	+	9.80249i	0.793834	+	0.555848i	0.898662	−	0.438642i	$-0.144540\pi$
$311$	13.9994	+	9.80249i	0.793834	+	0.555848i	−0.104828	+	0.994490i	$0.533429\pi$
$312$		0			0
$313$	0.00713811	−	0.0815889i	0.000403470	−	0.00461168i	−0.995990	−	0.0894613i	$-0.971485\pi$
$313$	0.00713811	−	0.0815889i	0.000403470	−	0.00461168i	0.996394	+	0.0848497i	$0.0270410\pi$
$314$	0.405190	−	0.868932i	0.0228662	−	0.0490367i
$315$		0			0
$316$	−9.97363	−	0.872580i	−0.561061	−	0.0490865i
$317$	1.61066	+	9.13453i	0.0904639	+	0.513046i	0.996043	+	0.0888693i	$0.0283254\pi$
$317$	1.61066	+	9.13453i	0.0904639	+	0.513046i	−0.905579	+	0.424177i	$0.860564\pi$
$318$		0			0
$319$	−3.09358	−	11.5454i	−0.173207	−	0.646417i
$320$	−2.55363	+	0.223413i	−0.142752	+	0.0124892i
$321$		0			0
$322$	−2.06408	−	3.57508i	−0.115026	−	0.199232i
$323$	1.73077	−	2.99779i	0.0963029	−	0.166801i
$324$		0			0
$325$	0.0183073	−	0.0683237i	0.00101551	−	0.00378992i
$326$	−1.66445	+	9.43955i	−0.0921852	+	0.522808i
$327$		0			0
$328$	3.68868	−	2.58284i	0.203673	−	0.142614i
$329$	22.1125	−	26.3527i	1.21910	−	1.45287i
$330$		0			0
$331$	−0.00184953		0.000862448i	−0.000101659		4.74044e-5i	−0.422669	−	0.906284i	$-0.638907\pi$
$331$	−0.00184953		0.000862448i	−0.000101659		4.74044e-5i	0.422567	+	0.906331i	$0.361129\pi$
$332$	−10.8831			−0.597287
$333$		0			0
$334$	−9.96159			−0.545074
$335$	6.12333	−	2.85535i	0.334553	−	0.156005i
$336$		0			0
$337$	−3.43354	+	4.09194i	−0.187037	+	0.222902i	−0.851412	−	0.524497i	$-0.824253\pi$
$337$	−3.43354	+	4.09194i	−0.187037	+	0.222902i	0.664375	+	0.747399i	$0.268698\pi$
$338$	10.6473	−	7.45533i	0.579138	−	0.405517i
$339$		0			0
$340$	0.235354	−	1.33476i	0.0127639	−	0.0723874i
$341$	11.2668	−	42.0482i	0.610130	−	2.27704i
$342$		0			0
$343$	6.65510	−	11.5270i	0.359342	−	0.622398i
$344$	1.69654	+	2.93849i	0.0914712	+	0.158433i
$345$		0			0
$346$	16.2888	−	1.42508i	0.875690	−	0.0766130i
$347$	5.80818	+	21.6764i	0.311799	+	1.16365i	0.926933	+	0.375228i	$0.122435\pi$
$347$	5.80818	+	21.6764i	0.311799	+	1.16365i	−0.615133	+	0.788423i	$0.710898\pi$
$348$		0			0
$349$	5.44436	+	30.8765i	0.291430	+	1.65278i	0.681369	+	0.731940i	$0.261385\pi$
$349$	5.44436	+	30.8765i	0.291430	+	1.65278i	−0.389940	+	0.920840i	$0.627504\pi$
$350$	4.88248	+	0.427161i	0.260979	+	0.0228327i
$351$		0			0
$352$	−2.06298	+	4.42408i	−0.109957	+	0.235804i
$353$	−2.14500	+	24.5174i	−0.114167	+	1.30493i	0.695706	+	0.718327i	$0.255092\pi$
$353$	−2.14500	+	24.5174i	−0.114167	+	1.30493i	−0.809873	+	0.586606i	$0.800464\pi$
$354$		0			0
$355$	−33.2415	−	23.2759i	−1.76427	−	1.23536i
$356$	8.52699	−	2.28480i	0.451930	−	0.121094i
$357$		0			0
$358$	−0.866866	+	2.38169i	−0.0458153	+	0.125876i
$359$	22.6978	−	13.1046i	1.19794	−	0.691632i	0.237846	−	0.971303i	$-0.423559\pi$
$359$	22.6978	−	13.1046i	1.19794	−	0.691632i	0.960096	+	0.279671i	$0.0902253\pi$
$360$		0			0
$361$	−15.3377	−	18.2788i	−0.807250	−	0.962043i
$362$	7.44108	+	1.99383i	0.391094	+	0.104793i
$363$		0			0
$364$	−0.0993340	−	0.0993340i	−0.00520652	−	0.00520652i
$365$	15.8101	+	22.5791i	0.827537	+	1.18185i
$366$		0			0
$367$	2.97782	−	1.08384i	0.155441	−	0.0565760i	−0.263128	−	0.964761i	$-0.584754\pi$
$367$	2.97782	−	1.08384i	0.155441	−	0.0565760i	0.418569	+	0.908185i	$0.362532\pi$
$368$	0.559195	+	1.19920i	0.0291501	+	0.0625125i
$369$		0			0
$370$	−11.9462	+	10.0206i	−0.621056	+	0.520944i
$371$		−	10.4208i		−	0.541023i
$372$		0			0
$373$	2.13256	+	5.85915i	0.110420	+	0.303375i	0.982579	−	0.185847i	$-0.0595029\pi$
$373$	2.13256	+	5.85915i	0.110420	+	0.303375i	−0.872159	+	0.489222i	$0.837281\pi$
$374$	−1.97715	−	1.65902i	−0.102236	−	0.0857860i
$375$		0			0
$376$	−7.79679	+	7.79679i	−0.402089	+	0.402089i
$377$	−0.108578	−	0.0191452i	−0.00559204	−	0.000986028i
$378$		0			0
$379$	8.48365	−	7.11863i	0.435776	−	0.365659i	−0.398350	−	0.917233i	$-0.630417\pi$
$379$	8.48365	−	7.11863i	0.435776	−	0.365659i	0.834126	+	0.551574i	$0.185973\pi$
$380$	−14.5337	−	8.39104i	−0.745564	−	0.430451i
$381$		0			0
$382$	20.4457	+	7.44163i	1.04609	+	0.380747i
$383$	−1.35256	−	15.4598i	−0.0691126	−	0.789961i	−0.949102	−	0.314968i	$-0.898006\pi$
$383$	−1.35256	−	15.4598i	−0.0691126	−	0.789961i	0.879990	−	0.474993i	$-0.157549\pi$
$384$		0			0
$385$	22.3920	−	31.9791i	1.14120	−	1.62980i
$386$	−4.32893	+	0.763306i	−0.220337	+	0.0388513i
$387$		0			0
$388$	11.8719	+	5.53597i	0.602706	+	0.281046i
$389$	7.59239	+	3.54039i	0.384950	+	0.179505i	0.605453	−	0.795881i	$-0.292992\pi$
$389$	7.59239	+	3.54039i	0.384950	+	0.179505i	−0.220503	+	0.975386i	$0.570770\pi$
$390$		0			0
$391$	−0.688976	+	0.121485i	−0.0348430	+	0.00614377i
$392$	1.56803	−	2.23937i	0.0791973	−	0.113105i
$393$		0			0
$394$	−0.268508	−	3.06906i	−0.0135272	−	0.154617i
$395$	−24.1162	−	8.77757i	−1.21342	−	0.441647i
$396$		0			0
$397$	0.784657	+	0.453022i	0.0393808	+	0.0227365i	0.519561	−	0.854433i	$-0.326095\pi$
$397$	0.784657	+	0.453022i	0.0393808	+	0.0227365i	−0.480180	+	0.877170i	$0.659429\pi$
$398$	9.68899	−	8.13003i	0.485665	−	0.407522i
$399$		0			0
$400$	−1.54706	−	0.272788i	−0.0773530	−	0.0136394i
$401$	18.5466	−	18.5466i	0.926171	−	0.926171i	−0.0712853	−	0.997456i	$-0.522710\pi$
$401$	18.5466	−	18.5466i	0.926171	−	0.926171i	0.997456	+	0.0712853i	$0.0227101\pi$
$402$		0			0
$403$	−0.307597	−	0.258105i	−0.0153225	−	0.0128571i
$404$	1.47970	+	4.06545i	0.0736179	+	0.202264i
$405$		0			0
$406$		−	7.63937i		−	0.379136i
$407$	5.15099	+	29.2424i	0.255325	+	1.44949i
$408$		0			0
$409$	−7.63399	−	16.3711i	−0.377476	−	0.809501i	−0.999646	−	0.0266179i	$-0.991526\pi$
$409$	−7.63399	−	16.3711i	−0.377476	−	0.809501i	0.622169	−	0.782883i	$-0.286252\pi$
$410$	10.8469	−	3.94795i	0.535690	−	0.194975i
$411$		0			0
$412$	7.42755	+	10.6076i	0.365929	+	0.522601i
$413$	−2.64274	−	2.64274i	−0.130041	−	0.130041i
$414$		0			0
$415$	−26.9469	−	7.22040i	−1.32277	−	0.354436i
$416$	0.0289428	+	0.0344926i	0.00141904	+	0.00169114i
$417$		0			0
$418$	−27.6765	+	15.9790i	−1.35370	+	0.781559i
$419$	−10.4702	+	28.7666i	−0.511501	+	1.40534i	0.368171	+	0.929758i	$0.379984\pi$
$419$	−10.4702	+	28.7666i	−0.511501	+	1.40534i	−0.879672	+	0.475581i	$0.842238\pi$
$420$		0			0
$421$	17.1875	−	4.60539i	0.837669	−	0.224453i	0.185613	−	0.982623i	$-0.440573\pi$
$421$	17.1875	−	4.60539i	0.837669	−	0.224453i	0.652057	+	0.758170i	$0.273906\pi$
$422$	−0.231634	−	0.162192i	−0.0112758	−	0.00789537i
$423$		0			0
$424$	−0.291111	+	3.32741i	−0.0141376	+	0.161593i
$425$	0.351028	−	0.752782i	0.0170274	−	0.0365153i
$426$		0			0
$427$	6.41649	+	0.561370i	0.310516	+	0.0271666i
$428$	2.24936	+	12.7567i	0.108727	+	0.616620i
$429$		0			0
$430$	2.25114	+	8.40138i	0.108560	+	0.405151i
$431$	17.7579	−	1.55361i	0.855368	−	0.0748350i	0.348969	−	0.937134i	$-0.386532\pi$
$431$	17.7579	−	1.55361i	0.855368	−	0.0748350i	0.506399	+	0.862299i	$0.330976\pi$
$432$		0			0
$433$	15.1714	+	26.2777i	0.729093	+	1.26283i	0.957267	+	0.289205i	$0.0933910\pi$
$433$	15.1714	+	26.2777i	0.729093	+	1.26283i	−0.228174	+	0.973620i	$0.573276\pi$
$434$	13.9113	−	24.0950i	0.667762	−	1.15660i
$435$		0			0
$436$	5.32154	−	19.8603i	0.254856	−	0.951134i
$437$	−1.50424	+	8.53099i	−0.0719577	+	0.408093i
$438$		0			0
$439$	−27.4932	+	19.2509i	−1.31218	+	0.918796i	−0.999517	−	0.0310688i	$-0.990109\pi$
$439$	−27.4932	+	19.2509i	−1.31218	+	0.918796i	−0.312660	+	0.949865i	$0.601220\pi$
$440$	−8.04318	+	9.58549i	−0.383444	+	0.456970i
$441$		0			0
$442$	−0.0215767	+	0.0100614i	−0.00102630	+	0.000478572i
$443$	−33.0683			−1.57112			−0.785561	−	0.618784i	$-0.787626\pi$
$443$	−33.0683			−1.57112			−0.785561	+	0.618784i	$0.787626\pi$
$444$		0			0
$445$	22.6290			1.07272
$446$	8.16542	−	3.80760i	0.386644	−	0.180295i
$447$		0			0
$448$	−2.00543	+	2.38998i	−0.0947478	+	0.112916i
$449$	−21.6061	+	15.1287i	−1.01965	+	0.713969i	−0.958772	−	0.284176i	$-0.908280\pi$
$449$	−21.6061	+	15.1287i	−1.01965	+	0.713969i	−0.0608812	+	0.998145i	$0.519391\pi$
$450$		0			0
$451$	3.81702	−	21.6474i	0.179736	−	1.01934i
$452$	−0.491370	+	1.83382i	−0.0231121	+	0.0862556i
$453$		0			0
$454$	10.4665	−	18.1286i	0.491219	−	0.850816i
$455$	−0.180051	−	0.311858i	−0.00844093	−	0.0146201i
$456$		0			0
$457$	33.3886	−	2.92112i	1.56185	−	0.136644i	0.726813	−	0.686835i	$-0.241001\pi$
$457$	33.3886	−	2.92112i	1.56185	−	0.136644i	0.835039	+	0.550191i	$0.185445\pi$
$458$	−7.64061	−	28.5151i	−0.357022	−	1.33243i
$459$		0			0
$460$	0.588977	+	3.34026i	0.0274612	+	0.155740i
$461$	−5.66329	−	0.495474i	−0.263766	−	0.0230765i	−0.0454943	−	0.998965i	$-0.514486\pi$
$461$	−5.66329	−	0.495474i	−0.263766	−	0.0230765i	−0.218271	+	0.975888i	$0.570042\pi$
$462$		0			0
$463$	2.65470	−	5.69302i	0.123374	−	0.264577i	−0.834914	−	0.550380i	$-0.814483\pi$
$463$	2.65470	−	5.69302i	0.123374	−	0.264577i	0.958288	+	0.285803i	$0.0922605\pi$
$464$	−0.213409	+	2.43928i	−0.00990727	+	0.113241i
$465$		0			0
$466$	−17.1992	−	12.0430i	−0.796739	−	0.557883i
$467$	−5.87899	+	1.57527i	−0.272047	+	0.0728948i	−0.392263	−	0.919853i	$-0.628308\pi$
$467$	−5.87899	+	1.57527i	−0.272047	+	0.0728948i	0.120216	+	0.992748i	$0.461641\pi$
$468$		0			0
$469$	2.81249	−	7.72725i	0.129869	−	0.356811i
$470$	−24.4779	+	14.1323i	−1.12908	+	0.651876i
$471$		0			0
$472$	0.770011	+	0.917663i	0.0354426	+	0.0422389i
$473$	15.9987	+	4.28684i	0.735621	+	0.197109i
$474$		0			0
$475$	−7.27232	−	7.27232i	−0.333677	−	0.333677i
$476$	−0.946171	−	1.35127i	−0.0433677	−	0.0619355i
$477$		0			0
$478$	6.18948	−	2.25279i	0.283100	−	0.103040i
$479$	−6.51030	−	13.9614i	−0.297463	−	0.637912i	0.699597	−	0.714538i	$-0.253363\pi$
$479$	−6.51030	−	13.9614i	−0.297463	−	0.637912i	−0.997060	+	0.0766260i	$0.975585\pi$
$480$		0			0
$481$	0.264543	+	0.0709333i	0.0120621	+	0.00323428i
$482$			27.4694i			1.25120i
$483$		0			0
$484$	4.38756	+	12.0547i	0.199435	+	0.547942i
$485$	25.7225	+	21.5837i	1.16800	+	0.980066i
$486$		0			0
$487$	9.95908	−	9.95908i	0.451289	−	0.451289i	−0.444493	−	0.895782i	$-0.646616\pi$
$487$	9.95908	−	9.95908i	0.451289	−	0.451289i	0.895782	+	0.444493i	$0.146616\pi$
$488$	−2.03313	−	0.358495i	−0.0920353	−	0.0162283i
$489$		0			0
$490$	5.36821	−	4.50446i	0.242511	−	0.203491i
$491$	−17.7559	−	10.2514i	−0.801312	−	0.462638i	0.0426175	−	0.999091i	$-0.486430\pi$
$491$	−17.7559	−	10.2514i	−0.801312	−	0.462638i	−0.843930	+	0.536454i	$0.819764\pi$
$492$		0			0
$493$	−1.21658	−	0.442799i	−0.0547920	−	0.0199427i
$494$	0.0256922	+	0.293663i	0.00115595	+	0.0132125i
$495$		0			0
$496$	−5.11502	+	7.30501i	−0.229671	+	0.328005i
$497$	−48.6401	+	8.57656i	−2.18181	+	0.384711i
$498$		0			0
$499$	−28.3194	−	13.2056i	−1.26775	−	0.591163i	−0.331820	−	0.943343i	$-0.607663\pi$
$499$	−28.3194	−	13.2056i	−1.26775	−	0.591163i	−0.935932	+	0.352180i	$0.885441\pi$
$500$	7.96647	+	3.71483i	0.356271	+	0.166132i
$501$		0			0
$502$	3.18804	−	0.562137i	0.142289	−	0.0250894i
$503$	10.8126	−	15.4419i	0.482108	−	0.688522i	−0.502246	−	0.864725i	$-0.667493\pi$
$503$	10.8126	−	15.4419i	0.482108	−	0.688522i	0.984354	+	0.176203i	$0.0563816\pi$
$504$		0			0
$505$	0.966566	+	11.0479i	0.0430116	+	0.491625i
$506$	6.06943	+	2.20909i	0.269819	+	0.0982062i
$507$		0			0
$508$	−11.7348	−	6.77508i	−0.520647	−	0.300596i
$509$	−22.5146	+	18.8920i	−0.997941	+	0.837372i	−0.986698	−	0.162565i	$-0.948023\pi$
$509$	−22.5146	+	18.8920i	−0.997941	+	0.837372i	−0.0112430	+	0.999937i	$0.503579\pi$
$510$		0			0
$511$	33.0386	+	5.82559i	1.46154	+	0.257709i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$		0			0
$514$	−16.0272	−	13.4484i	−0.706929	−	0.593184i
$515$	11.3532	+	31.1927i	0.500283	+	1.37452i
$516$		0			0
$517$			53.8242i			2.36719i
$518$	−1.65729	+	18.9051i	−0.0728170	+	0.830643i
$519$		0			0
$520$	0.0487791	+	0.104607i	0.00213911	+	0.00458733i
$521$	−9.88377	+	3.59740i	−0.433016	+	0.157605i	−0.549326	−	0.835608i	$-0.685116\pi$
$521$	−9.88377	+	3.59740i	−0.433016	+	0.157605i	0.116310	+	0.993213i	$0.462893\pi$
$522$		0			0
$523$	−13.9093	−	19.8646i	−0.608212	−	0.868617i	0.390434	−	0.920631i	$-0.372325\pi$
$523$	−13.9093	−	19.8646i	−0.608212	−	0.868617i	−0.998646	+	0.0520137i	$0.983436\pi$
$524$	5.93397	+	5.93397i	0.259227	+	0.259227i
$525$		0			0
$526$	−8.71566	−	2.33535i	−0.380021	−	0.101826i
$527$	−3.03083	−	3.61200i	−0.132025	−	0.157341i
$528$		0			0
$529$	−18.4024	+	10.6246i	−0.800103	+	0.461940i
$530$	−2.92838	+	8.04565i	−0.127201	+	0.349481i
$531$		0			0
$532$	−19.7295	+	5.28651i	−0.855384	+	0.229199i
$533$	−0.166090	−	0.116297i	−0.00719416	−	0.00503740i
$534$		0			0
$535$	−2.89399	+	33.0785i	−0.125118	+	1.43011i
$536$	−1.11390	+	2.38877i	−0.0481132	+	0.103179i
$537$		0			0
$538$	−20.0331	−	1.75267i	−0.863687	−	0.0755628i
$539$	−2.31728	−	13.1420i	−0.0998125	−	0.566065i
$540$		0			0
$541$	−11.4449	−	42.7128i	−0.492053	−	1.83637i	−0.545946	−	0.837820i	$-0.683830\pi$
$541$	−11.4449	−	42.7128i	−0.492053	−	1.83637i	0.0538932	−	0.998547i	$-0.482837\pi$
$542$	−28.5000	+	2.49343i	−1.22418	+	0.107102i
$543$		0			0
$544$	0.264367	+	0.457898i	0.0113347	+	0.0196322i
$545$	26.3527	−	45.6442i	1.12882	−	1.95518i
$546$		0			0
$547$	−8.15834	+	30.4473i	−0.348825	+	1.30183i	0.539254	+	0.842143i	$0.318706\pi$
$547$	−8.15834	+	30.4473i	−0.348825	+	1.30183i	−0.888079	+	0.459691i	$0.847960\pi$
$548$	−3.78679	+	21.4759i	−0.161764	+	0.917407i
$549$		0			0
$550$	−6.28156	+	4.39839i	−0.267846	+	0.187548i
$551$	−10.3043	+	12.2802i	−0.438977	+	0.523152i
$552$		0			0
$553$	−28.3091	+	13.2007i	−1.20382	+	0.561352i
$554$	−6.90916			−0.293542
$555$		0			0
$556$	8.06253			0.341927
$557$	2.19643	−	1.02421i	0.0930658	−	0.0433973i	−0.375528	−	0.926811i	$-0.622539\pi$
$557$	2.19643	−	1.02421i	0.0930658	−	0.0433973i	0.468594	+	0.883414i	$0.344761\pi$
$558$		0			0
$559$	0.0982050	−	0.117036i	0.00415363	−	0.00495010i
$560$	−6.55116	+	4.58717i	−0.276837	+	0.193843i
$561$		0			0
$562$	2.40043	−	13.6135i	0.101256	−	0.574251i
$563$	6.56049	−	24.4841i	0.276492	−	1.03188i	−0.678344	−	0.734745i	$-0.737302\pi$
$563$	6.56049	−	24.4841i	0.276492	−	1.03188i	0.954835	−	0.297136i	$-0.0960315\pi$
$564$		0			0
$565$	−2.43330	+	4.21460i	−0.102370	+	0.177310i
$566$	−1.03730	−	1.79666i	−0.0436011	−	0.0755193i
$567$		0			0
$568$	15.7705	−	1.37974i	0.661717	−	0.0578927i
$569$	−7.88907	−	29.4424i	−0.330727	−	1.23429i	−0.908428	−	0.418041i	$-0.862717\pi$
$569$	−7.88907	−	29.4424i	−0.330727	−	1.23429i	0.577701	−	0.816248i	$-0.303950\pi$
$570$		0			0
$571$	0.222253	+	1.26046i	0.00930100	+	0.0527486i	0.989105	−	0.147212i	$-0.0470298\pi$
$571$	0.222253	+	1.26046i	0.00930100	+	0.0527486i	−0.979804	+	0.199960i	$0.935919\pi$
$572$	0.218960	+	0.0191565i	0.00915516	+	0.000800973i
$573$		0			0
$574$	5.93739	−	12.7328i	0.247822	−	0.531456i
$575$	−0.181162	+	2.07069i	−0.00755497	+	0.0863537i
$576$		0			0
$577$	27.1317	+	18.9978i	1.12951	+	0.790889i	0.980221	−	0.197905i	$-0.0634138\pi$
$577$	27.1317	+	18.9978i	1.12951	+	0.790889i	0.149285	+	0.988794i	$0.452303\pi$
$578$	16.1507	−	4.32757i	0.671781	−	0.180003i
$579$		0			0
$580$	−2.14675	+	5.89816i	−0.0891391	+	0.244908i
$581$	−29.4051	+	16.9771i	−1.21993	+	0.704327i
$582$		0			0
$583$	10.4804	+	12.4900i	0.434053	+	0.517284i
$584$	−10.3866	−	2.78308i	−0.429800	−	0.115165i
$585$		0			0
$586$	14.0657	+	14.0657i	0.581050	+	0.581050i
$587$	−6.25878	−	8.93846i	−0.258327	−	0.368930i	0.668948	−	0.743309i	$-0.266745\pi$
$587$	−6.25878	−	8.93846i	−0.258327	−	0.368930i	−0.927276	+	0.374379i	$0.877856\pi$
$588$		0			0
$589$	−54.8624	+	19.9683i	−2.26057	+	0.822779i
$590$	1.29775	+	2.78303i	0.0534275	+	0.114576i
$591$		0			0
$592$	1.05730	−	5.99017i	0.0434547	−	0.246194i
$593$		−	27.4535i		−	1.12738i	−0.825987	−	0.563690i	$-0.809381\pi$
$593$		−	27.4535i		−	1.12738i	0.825987	−	0.563690i	$-0.190619\pi$
$594$		0			0
$595$	−1.44625	−	3.97354i	−0.0592904	−	0.162899i
$596$	−0.579556	−	0.486306i	−0.0237396	−	0.0199199i
$597$		0			0
$598$	0.0421282	−	0.0421282i	0.00172275	−	0.00172275i
$599$	14.9977	+	2.64450i	0.612789	+	0.108051i	0.471425	−	0.881906i	$-0.343740\pi$
$599$	14.9977	+	2.64450i	0.612789	+	0.108051i	0.141364	+	0.989958i	$0.454851\pi$
$600$		0			0
$601$	22.7870	−	19.1206i	0.929502	−	0.779945i	−0.0462259	−	0.998931i	$-0.514719\pi$
$601$	22.7870	−	19.1206i	0.929502	−	0.779945i	0.975728	+	0.218986i	$0.0702750\pi$
$602$	9.16779	+	5.29303i	0.373651	+	0.215728i
$603$		0			0
$604$	16.8660	+	6.13871i	0.686267	+	0.249781i
$605$	2.86603	+	32.7589i	0.116521	+	1.33184i
$606$		0			0
$607$	−3.96793	+	5.66679i	−0.161053	+	0.230008i	−0.891566	−	0.452892i	$-0.850392\pi$
$607$	−3.96793	+	5.66679i	−0.161053	+	0.230008i	0.730512	+	0.682900i	$0.239281\pi$
$608$	6.44739	−	1.13685i	0.261476	−	0.0461053i
$609$		0			0
$610$	−4.79625	−	2.23653i	−0.194194	−	0.0905543i
$611$	0.449965	+	0.209822i	0.0182036	+	0.00848849i
$612$		0			0
$613$	−34.7807	+	6.13278i	−1.40478	+	0.247701i	−0.824106	−	0.566435i	$-0.808322\pi$
$613$	−34.7807	+	6.13278i	−1.40478	+	0.247701i	−0.580674	+	0.814136i	$0.697211\pi$
$614$	3.57306	−	5.10286i	0.144197	−	0.205935i
$615$		0			0
$616$	1.32734	+	15.1716i	0.0534803	+	0.611282i
$617$	−29.1913	−	10.6248i	−1.17520	−	0.427737i	−0.320695	−	0.947183i	$-0.603916\pi$
$617$	−29.1913	−	10.6248i	−1.17520	−	0.427737i	−0.854504	+	0.519445i	$0.826139\pi$
$618$		0			0
$619$	−5.04620	−	2.91342i	−0.202824	−	0.117100i	0.395148	−	0.918617i	$-0.370693\pi$
$619$	−5.04620	−	2.91342i	−0.202824	−	0.117100i	−0.597972	+	0.801517i	$0.704027\pi$
$620$	−17.5115	+	14.6939i	−0.703279	+	0.590121i
$621$		0			0
$622$	−16.8305	−	2.96767i	−0.674841	−	0.118993i
$623$	19.4750	−	19.4750i	0.780250	−	0.780250i
$624$		0			0
$625$	23.2777	+	19.5323i	0.931106	+	0.781291i
$626$	0.0280117	+	0.0769614i	0.00111957	+	0.00307600i
$627$		0			0
$628$			0.958761i			0.0382587i
$629$	2.91460	+	1.35972i	0.116213	+	0.0542154i
$630$		0			0
$631$	5.51573	+	11.8285i	0.219578	+	0.470886i	0.984981	−	0.172665i	$-0.0552379\pi$
$631$	5.51573	+	11.8285i	0.219578	+	0.470886i	−0.765403	+	0.643552i	$0.777460\pi$
$632$	9.40795	−	3.42421i	0.374228	−	0.136208i
$633$		0			0
$634$	−5.32017	−	7.59800i	−0.211291	−	0.301755i
$635$	−24.5608	−	24.5608i	−0.974666	−	0.974666i
$636$		0			0
$637$	−0.118899	−	0.0318589i	−0.00471095	−	0.00126229i
$638$	7.68302	+	9.15627i	0.304174	+	0.362500i
$639$		0			0
$640$	2.21995	−	1.28169i	0.0877514	−	0.0506633i
$641$	10.9981	−	30.2171i	0.434400	−	1.19350i	−0.508685	−	0.860953i	$-0.669868\pi$
$641$	10.9981	−	30.2171i	0.434400	−	1.19350i	0.943085	−	0.332551i	$-0.107909\pi$
$642$		0			0
$643$	29.3914	−	7.87540i	1.15908	−	0.310575i	0.372483	−	0.928039i	$-0.378506\pi$
$643$	29.3914	−	7.87540i	1.15908	−	0.310575i	0.786600	+	0.617463i	$0.211840\pi$
$644$	3.38158	+	2.36781i	0.133253	+	0.0933048i
$645$		0			0
$646$	−0.301694	+	3.44838i	−0.0118700	+	0.135675i
$647$	13.3865	−	28.7075i	0.526279	−	1.12861i	−0.446053	−	0.895007i	$-0.647171\pi$
$647$	13.3865	−	28.7075i	0.526279	−	1.12861i	0.972332	−	0.233603i	$-0.0750517\pi$
$648$		0			0
$649$	5.82533	+	0.509651i	0.228664	+	0.0200055i
$650$	0.0122828	+	0.0696593i	0.000481772	+	0.00273226i
$651$		0			0
$652$	−2.48083	−	9.25857i	−0.0971566	−	0.362593i
$653$	−21.9804	+	1.92303i	−0.860159	+	0.0752541i	−0.508694	−	0.860947i	$-0.669872\pi$
$653$	−21.9804	+	1.92303i	−0.860159	+	0.0752541i	−0.351464	+	0.936201i	$0.614316\pi$
$654$		0			0
$655$	10.7558	+	18.6296i	0.420265	+	0.727920i
$656$	−2.25152	+	3.89975i	−0.0879073	+	0.152260i
$657$		0			0
$658$	−8.90364	+	33.2288i	−0.347100	+	1.29539i
$659$	8.60127	−	48.7802i	0.335058	−	1.90021i	−0.0916030	−	0.995796i	$-0.529199\pi$
$659$	8.60127	−	48.7802i	0.335058	−	1.90021i	0.426661	−	0.904412i	$-0.359690\pi$
$660$		0			0
$661$	−11.9021	+	8.33397i	−0.462940	+	0.324154i	−0.781671	−	0.623691i	$-0.785632\pi$
$661$	−11.9021	+	8.33397i	−0.462940	+	0.324154i	0.318731	+	0.947845i	$0.396743\pi$
$662$	0.00131175	−	0.00156329i	5.09827e−5	−	6.07589e-5i
$663$		0			0
$664$	9.86342	−	4.59939i	0.382775	−	0.178491i
$665$	−52.3584			−2.03037
$666$		0			0
$667$	3.23991			0.125450
$668$	9.02827	−	4.20995i	0.349314	−	0.162888i
$669$		0			0
$670$	−4.34289	+	5.17566i	−0.167781	+	0.199953i
$671$	−8.25514	+	5.78031i	−0.318686	+	0.223146i
$672$		0			0
$673$	5.32087	−	30.1762i	0.205105	−	1.16321i	−0.692170	−	0.721734i	$-0.743345\pi$
$673$	5.32087	−	30.1762i	0.205105	−	1.16321i	0.897275	−	0.441472i	$-0.145544\pi$
$674$	1.38252	−	5.15963i	0.0532527	−	0.198742i
$675$		0			0
$676$	−6.49899	+	11.2566i	−0.249961	+	0.432945i
$677$	−13.5092	−	23.3987i	−0.519202	−	0.899285i	−0.999751	−	0.0223167i	$-0.992896\pi$
$677$	−13.5092	−	23.3987i	−0.519202	−	0.899285i	0.480549	−	0.876968i	$-0.340438\pi$
$678$		0			0
$679$	40.7127	−	3.56190i	1.56241	−	0.136693i
$680$	0.350790	+	1.30917i	0.0134522	+	0.0502042i
$681$		0			0
$682$	7.55916	+	42.8701i	0.289455	+	1.64158i
$683$	−0.428052	−	0.0374497i	−0.0163790	−	0.00143297i	0.0789633	−	0.996878i	$-0.474839\pi$
$683$	−0.428052	−	0.0374497i	−0.0163790	−	0.00143297i	−0.0953423	+	0.995445i	$0.530395\pi$
$684$		0			0
$685$	−23.6245	+	50.6629i	−0.902645	+	1.93573i
$686$	−1.16006	+	13.2596i	−0.0442913	+	0.506252i
$687$		0			0
$688$	−2.77945	−	1.94619i	−0.105965	−	0.0741977i
$689$	0.145271	−	0.0389252i	0.00553437	−	0.00148293i
$690$		0			0
$691$	−8.46352	+	23.2533i	−0.321968	+	0.884599i	0.668108	+	0.744064i	$0.267104\pi$
$691$	−8.46352	+	23.2533i	−0.321968	+	0.884599i	−0.990076	+	0.140535i	$0.955118\pi$
$692$	−14.1604	+	8.17550i	−0.538297	+	0.310786i
$693$		0			0
$694$	−14.4248	−	17.1909i	−0.547560	−	0.652556i
$695$	19.9631	+	5.34910i	0.757244	+	0.202903i
$696$		0			0
$697$	−1.68356	−	1.68356i	−0.0637695	−	0.0637695i
$698$	−17.9832	−	25.6827i	−0.680675	−	0.972105i
$699$		0			0
$700$	−4.60555	+	1.67628i	−0.174074	+	0.0633576i
$701$	0.817764	+	1.75370i	0.0308865	+	0.0662364i	0.921146	−	0.389218i	$-0.127255\pi$
$701$	0.817764	+	1.75370i	0.0308865	+	0.0662364i	−0.890259	+	0.455454i	$0.849477\pi$
$702$		0			0
$703$	28.1640	−	28.1542i	1.06222	−	1.06186i
$704$		−	4.88143i		−	0.183976i
$705$		0			0
$706$	−8.41749	−	23.1269i	−0.316797	−	0.870391i
$707$	10.3399	+	8.67622i	0.388873	+	0.326303i
$708$		0			0
$709$	−7.33847	+	7.33847i	−0.275602	+	0.275602i	−0.831350	−	0.555749i	$-0.812432\pi$
$709$	−7.33847	+	7.33847i	−0.275602	+	0.275602i	0.555749	+	0.831350i	$0.312432\pi$
$710$	39.9638	+	7.04670i	1.49982	+	0.264458i
$711$		0			0
$712$	−6.76248	+	5.67439i	−0.253435	+	0.212657i
$713$	10.2189	+	5.89986i	0.382699	+	0.220951i
$714$		0			0
$715$	0.529442	+	0.192701i	0.0198000	+	0.00720662i
$716$	−0.220900	−	2.52490i	−0.00825543	−	0.0943600i
$717$		0			0
$718$	−15.0329	+	21.4693i	−0.561024	+	0.801225i
$719$	27.3834	−	4.82843i	1.02123	−	0.180070i	0.362130	−	0.932127i	$-0.382050\pi$
$719$	27.3834	−	4.82843i	1.02123	−	0.180070i	0.659098	+	0.752057i	$0.270938\pi$
$720$		0			0
$721$	36.6160	+	17.0743i	1.36365	+	0.635880i
$722$	21.6257	+	10.0842i	0.804825	+	0.375296i
$723$		0			0
$724$	−7.58653	+	1.33771i	−0.281951	+	0.0497156i
$725$	−2.20630	+	3.15092i	−0.0819398	+	0.117022i
$726$		0			0
$727$	4.20775	+	48.0948i	0.156057	+	1.78374i	0.521845	+	0.853040i	$0.325244\pi$
$727$	4.20775	+	48.0948i	0.156057	+	1.78374i	−0.365788	+	0.930698i	$0.619201\pi$
$728$	0.132008	+	0.0480468i	0.00489252	+	0.00178073i
$729$		0			0
$730$	−23.8711	−	13.7820i	−0.883510	−	0.510095i
$731$	1.37431	−	1.15318i	0.0508308	−	0.0426521i
$732$		0			0
$733$	27.8107	+	4.90377i	1.02721	+	0.181125i	0.661767	−	0.749709i	$-0.269807\pi$
$733$	27.8107	+	4.90377i	1.02721	+	0.181125i	0.365442	+	0.930834i	$0.380918\pi$
$734$	−2.24077	+	2.24077i	−0.0827085	+	0.0827085i
$735$		0			0
$736$	−1.01361	−	0.850516i	−0.0373620	−	0.0313505i
$737$	4.40045	+	12.0901i	0.162093	+	0.445346i
$738$		0			0
$739$			17.7297i			0.652199i	0.945336	+	0.326099i	$0.105734\pi$
$739$			17.7297i			0.652199i	−0.945336	+	0.326099i	$0.894266\pi$
$740$	6.59210	−	14.1304i	0.242330	−	0.519444i
$741$		0			0
$742$	4.40403	+	9.44448i	0.161677	+	0.346718i
$743$	0.548452	−	0.199620i	0.0201208	−	0.00732336i	−0.331940	−	0.943300i	$-0.607703\pi$
$743$	0.548452	−	0.199620i	0.0201208	−	0.00732336i	0.352061	+	0.935977i	$0.385481\pi$
$744$		0			0
$745$	−1.11236	−	1.58862i	−0.0407538	−	0.0582025i
$746$	−4.40894	−	4.40894i	−0.161423	−	0.161423i
$747$		0			0
$748$	2.49304	+	0.668007i	0.0911545	+	0.0244248i
$749$	25.9774	+	30.9587i	0.949194	+	1.13121i
$750$		0			0
$751$	−43.1642	+	24.9209i	−1.57508	+	0.909375i	−0.579554	+	0.814934i	$0.696773\pi$
$751$	−43.1642	+	24.9209i	−1.57508	+	0.909375i	−0.995530	+	0.0944410i	$0.969894\pi$
$752$	3.77122	−	10.3614i	0.137522	−	0.377840i
$753$		0			0
$754$	0.106496	−	0.0285355i	0.00387836	−	0.00103920i
$755$	37.6880	+	26.3894i	1.37161	+	0.960410i
$756$		0			0
$757$	0.341618	−	3.90471i	0.0124163	−	0.141919i	−0.987456	−	0.157894i	$-0.949530\pi$
$757$	0.341618	−	3.90471i	0.0124163	−	0.141919i	0.999872	+	0.0159748i	$0.00508514\pi$
$758$	−4.68034	+	10.0370i	−0.169997	+	0.364561i
$759$		0			0
$760$	16.7182	+	1.46266i	0.606434	+	0.0530561i
$761$	0.290556	+	1.64782i	0.0105326	+	0.0597335i	0.989621	−	0.143702i	$-0.0459005\pi$
$761$	0.290556	+	1.64782i	0.0105326	+	0.0597335i	−0.979088	+	0.203435i	$0.934789\pi$
$762$		0			0
$763$	−16.6027	−	61.9620i	−0.601057	−	2.24318i
$764$	−21.6751	+	1.89632i	−0.784176	+	0.0686065i
$765$		0			0
$766$	7.75945	+	13.4398i	0.280360	+	0.485598i
$767$	0.0269694	−	0.0467124i	0.000973810	−	0.00168669i
$768$		0			0
$769$	5.08763	−	18.9873i	0.183465	−	0.684699i	−0.811489	−	0.584367i	$-0.801343\pi$
$769$	5.08763	−	18.9873i	0.183465	−	0.684699i	0.994954	−	0.100332i	$-0.0319905\pi$
$770$	−6.77909	+	38.4461i	−0.244301	+	1.38550i
$771$		0			0
$772$	3.60075	−	2.52127i	0.129594	−	0.0907426i
$773$	15.9160	−	18.9679i	0.572457	−	0.682228i	−0.399676	−	0.916656i	$-0.630877\pi$
$773$	15.9160	−	18.9679i	0.572457	−	0.682228i	0.972133	+	0.234429i	$0.0753219\pi$
$774$		0			0
$775$	−12.6966	+	5.92052i	−0.456075	+	0.212671i
$776$	−13.0992			−0.470234
$777$		0			0
$778$	−8.37728			−0.300340
$779$	−26.7187	+	12.4591i	−0.957296	+	0.446395i
$780$		0			0
$781$	49.6726	−	59.1975i	1.77743	−	2.11825i
$782$	0.573083	−	0.401277i	0.0204934	−	0.0143496i
$783$		0			0
$784$	−0.474714	+	2.69224i	−0.0169541	+	0.0961514i
$785$	−0.636092	+	2.37393i	−0.0227031	+	0.0847291i
$786$		0			0
$787$	6.73146	−	11.6592i	0.239951	−	0.415607i	−0.720749	−	0.693196i	$-0.756202\pi$
$787$	6.73146	−	11.6592i	0.239951	−	0.415607i	0.960700	+	0.277589i	$0.0895354\pi$
$788$	1.54039	+	2.66804i	0.0548742	+	0.0950449i
$789$		0			0
$790$	25.5662	−	2.23676i	0.909606	−	0.0795802i
$791$	1.53303	+	5.72133i	0.0545081	+	0.203427i
$792$		0			0
$793$	0.0161419	+	0.0915454i	0.000573216	+	0.00325087i
$794$	−0.902597	−	0.0789670i	−0.0320320	−	0.00280243i
$795$		0			0
$796$	−5.34531	+	11.4631i	−0.189460	+	0.406297i
$797$	2.93712	−	33.5714i	0.104038	−	1.18916i	−0.747279	−	0.664510i	$-0.768640\pi$
$797$	2.93712	−	33.5714i	0.104038	−	1.18916i	0.851318	−	0.524651i	$-0.175804\pi$
$798$		0			0
$799$	4.77565	+	3.34395i	0.168951	+	0.118300i
$800$	1.51740	−	0.406585i	0.0536481	−	0.0143750i
$801$		0			0
$802$	−8.97077	+	24.6470i	−0.316769	+	0.870316i
$803$	−45.4577	+	26.2450i	−1.60417	+	0.926166i
$804$		0			0
$805$	6.80200	+	8.10631i	0.239739	+	0.285710i
$806$	0.387858	+	0.103926i	0.0136617	+	0.00366064i
$807$		0			0
$808$	−3.05920	−	3.05920i	−0.107622	−	0.107622i
$809$	−19.0357	−	27.1858i	−0.669259	−	0.955800i	−0.999927	−	0.0120536i	$-0.996163\pi$
$809$	−19.0357	−	27.1858i	−0.669259	−	0.955800i	0.330669	−	0.943747i	$-0.392726\pi$
$810$		0			0
$811$	5.41403	−	1.97055i	0.190112	−	0.0691953i	−0.245210	−	0.969470i	$-0.578857\pi$
$811$	5.41403	−	1.97055i	0.190112	−	0.0691953i	0.435322	+	0.900275i	$0.356635\pi$
$812$	3.22854	+	6.92362i	0.113299	+	0.242972i
$813$		0			0
$814$	−17.0268	−	24.3257i	−0.596787	−	0.852615i
$815$		−	24.5705i		−	0.860665i
$816$		0			0
$817$	−7.59763	−	20.8743i	−0.265807	−	0.730300i
$818$	13.8375	+	11.6110i	0.483816	+	0.405970i
$819$		0			0
$820$	−8.16216	+	8.16216i	−0.285035	+	0.285035i
$821$	−33.6018	−	5.92491i	−1.17271	−	0.206781i	−0.446842	−	0.894613i	$-0.647452\pi$
$821$	−33.6018	−	5.92491i	−1.17271	−	0.206781i	−0.725870	+	0.687832i	$0.758563\pi$
$822$		0			0
$823$	30.5820	−	25.6613i	1.06602	−	0.894498i	0.0713349	−	0.997452i	$-0.477274\pi$
$823$	30.5820	−	25.6613i	1.06602	−	0.894498i	0.994686	+	0.102955i	$0.0328297\pi$
$824$	−11.2146	−	6.47477i	−0.390680	−	0.225559i
$825$		0			0
$826$	3.51201	+	1.27827i	0.122198	+	0.0444766i
$827$	0.577691	+	6.60304i	0.0200883	+	0.229610i	0.999601	+	0.0282301i	$0.00898711\pi$
$827$	0.577691	+	6.60304i	0.0200883	+	0.229610i	−0.979513	+	0.201380i	$0.935457\pi$
$828$		0			0
$829$	16.5697	−	23.6640i	0.575490	−	0.821885i	−0.420871	−	0.907121i	$-0.638275\pi$
$829$	16.5697	−	23.6640i	0.575490	−	0.821885i	0.996361	+	0.0852354i	$0.0271642\pi$
$830$	27.4737	−	4.84435i	0.953625	−	0.168150i
$831$		0			0
$832$	−0.0408083	−	0.0190292i	−0.00141477	−	0.000659719i
$833$	−1.31001	−	0.610869i	−0.0453892	−	0.0211653i
$834$		0			0
$835$	25.1474	−	4.43417i	0.870263	−	0.153451i
$836$	18.3304	−	26.1785i	0.633969	−	0.905402i
$837$		0			0
$838$	−2.66808	−	30.4963i	−0.0921672	−	1.05348i
$839$	7.05058	+	2.56620i	0.243413	+	0.0885952i	0.460846	−	0.887480i	$-0.347546\pi$
$839$	7.05058	+	2.56620i	0.243413	+	0.0885952i	−0.217433	+	0.976075i	$0.569768\pi$
$840$		0			0
$841$	−19.9224	−	11.5022i	−0.686978	−	0.396627i
$842$	−13.6309	+	11.4377i	−0.469751	+	0.394168i
$843$		0			0
$844$	0.278477	+	0.0491030i	0.00958557	+	0.00169019i
$845$	−23.5599	+	23.5599i	−0.810486	+	0.810486i
$846$		0			0
$847$	30.6596	+	25.7264i	1.05348	+	0.883971i
$848$	−1.14239	−	3.13868i	−0.0392298	−	0.107783i
$849$		0			0
$850$			0.830603i			0.0284894i
$851$	−8.01777	−	0.702865i	−0.274846	−	0.0240939i
$852$		0			0
$853$	−22.7636	−	48.8167i	−0.779411	−	1.67145i	−0.740355	−	0.672216i	$-0.765343\pi$
$853$	−22.7636	−	48.8167i	−0.779411	−	1.67145i	−0.0390563	−	0.999237i	$-0.512435\pi$
$854$	−6.05256	+	2.20295i	−0.207114	+	0.0753834i
$855$		0			0
$856$	−7.42984	−	10.6109i	−0.253947	−	0.362673i
$857$	−3.55564	−	3.55564i	−0.121458	−	0.121458i	0.643765	−	0.765223i	$-0.277371\pi$
$857$	−3.55564	−	3.55564i	−0.121458	−	0.121458i	−0.765223	+	0.643765i	$0.777371\pi$
$858$		0			0
$859$	−33.2060	−	8.89753i	−1.13298	−	0.303580i	−0.356852	−	0.934161i	$-0.616150\pi$
$859$	−33.2060	−	8.89753i	−1.13298	−	0.303580i	−0.776123	+	0.630581i	$0.782817\pi$
$860$	−5.59081	−	6.66286i	−0.190645	−	0.227202i
$861$		0			0
$862$	−15.4375	+	8.91286i	−0.525804	+	0.303573i
$863$	−14.6225	+	40.1751i	−0.497757	+	1.36757i	0.395681	+	0.918388i	$0.370509\pi$
$863$	−14.6225	+	40.1751i	−0.497757	+	1.36757i	−0.893438	+	0.449187i	$0.851714\pi$
$864$		0			0
$865$	−40.4857	+	10.8481i	−1.37655	+	0.368847i
$866$	−24.8554	−	17.4040i	−0.844622	−	0.591410i
$867$		0			0
$868$	−2.42489	+	27.7167i	−0.0823063	+	0.940765i
$869$	20.6540	−	44.2927i	0.700640	−	1.50253i
$870$		0			0
$871$	0.118227	+	0.0103435i	0.00400595	+	0.000350476i
$872$	3.57036	+	20.2485i	0.120908	+	0.685701i
$873$		0			0
$874$	−2.24204	−	8.36742i	−0.0758383	−	0.283032i
$875$	27.3196	−	2.39016i	0.923572	−	0.0808021i
$876$		0			0
$877$	6.10121	+	10.5676i	0.206023	+	0.356843i	0.950458	−	0.310852i	$-0.100614\pi$
$877$	6.10121	+	10.5676i	0.206023	+	0.356843i	−0.744435	+	0.667695i	$0.767281\pi$
$878$	16.7815	−	29.0664i	0.566347	−	0.980943i
$879$		0			0
$880$	3.23860	−	12.0866i	0.109173	−	0.407439i
$881$	−2.57819	+	14.6217i	−0.0868615	+	0.492616i	0.910078	+	0.414437i	$0.136022\pi$
$881$	−2.57819	+	14.6217i	−0.0868615	+	0.492616i	−0.996939	+	0.0781788i	$0.975090\pi$
$882$		0			0
$883$	−20.4642	+	14.3292i	−0.688675	+	0.482215i	−0.864777	−	0.502157i	$-0.832540\pi$
$883$	−20.4642	+	14.3292i	−0.688675	+	0.482215i	0.176102	+	0.984372i	$0.443651\pi$
$884$	0.0153030	−	0.0182374i	0.000514697	−	0.000613392i
$885$		0			0
$886$	29.9701	−	13.9753i	1.00686	−	0.469508i
$887$	−4.71281			−0.158241			−0.0791203	−	0.996865i	$-0.525211\pi$
$887$	−4.71281			−0.158241			−0.0791203	+	0.996865i	$0.525211\pi$
$888$		0			0
$889$	−42.2751			−1.41786
$890$	−20.5088	+	9.56343i	−0.687458	+	0.320567i
$891$		0			0
$892$	−5.79122	+	6.90171i	−0.193904	+	0.231086i
$893$	59.1327	−	41.4052i	1.97880	−	1.38557i
$894$		0			0
$895$	1.12819	−	6.39830i	0.0377114	−	0.213872i
$896$	0.807489	−	3.01359i	0.0269763	−	0.100677i
$897$		0			0
$898$	13.1881	−	22.8424i	0.440092	−	0.762261i
$899$	10.9180	+	18.9105i	0.364136	+	0.630702i
$900$		0			0
$901$	1.75932	−	0.153920i	0.0586113	−	0.00512783i
$902$	5.68919	+	21.2323i	0.189429	+	0.706959i
$903$		0			0
$904$	−0.329673	−	1.86967i	−0.0109648	−	0.0621842i
$905$	−19.6720	−	1.72108i	−0.653921	−	0.0572107i
$906$		0			0
$907$	15.9869	−	34.2841i	0.530837	−	1.13838i	−0.439858	−	0.898067i	$-0.644971\pi$
$907$	15.9869	−	34.2841i	0.530837	−	1.13838i	0.970695	−	0.240316i	$-0.0772510\pi$
$908$	−1.82444	+	20.8534i	−0.0605461	+	0.692045i
$909$		0			0
$910$	0.294979	+	0.206546i	0.00977845	+	0.00684694i
$911$	30.0099	−	8.04112i	0.994272	−	0.266414i	0.275228	−	0.961379i	$-0.411247\pi$
$911$	30.0099	−	8.04112i	0.994272	−	0.266414i	0.719044	+	0.694965i	$0.244580\pi$
$912$		0			0
$913$	18.1698	−	49.9212i	0.601333	−	1.65215i
$914$	−29.0258	+	16.7581i	−0.960089	+	0.554307i
$915$		0			0
$916$	18.9758	+	22.6144i	0.626977	+	0.747202i
$917$	25.2898	+	6.77637i	0.835141	+	0.223775i
$918$		0			0
$919$	−23.2185	−	23.2185i	−0.765907	−	0.765907i	0.211476	−	0.977383i	$-0.432173\pi$
$919$	−23.2185	−	23.2185i	−0.765907	−	0.765907i	−0.977383	+	0.211476i	$0.932173\pi$
$920$	−1.94545	−	2.77839i	−0.0641395	−	0.0916008i
$921$		0			0
$922$	5.34208	−	1.94436i	0.175932	−	0.0640340i
$923$	−0.301247	−	0.646027i	−0.00991567	−	0.0212642i
$924$		0			0
$925$	6.14347	−	7.31892i	0.201996	−	0.240645i
$926$			6.28155i			0.206425i
$927$		0			0
$928$	−0.837469	−	2.30093i	−0.0274913	−	0.0755317i
$929$	−1.43818	−	1.20677i	−0.0471850	−	0.0395929i	0.618890	−	0.785478i	$-0.287583\pi$
$929$	−1.43818	−	1.20677i	−0.0471850	−	0.0395929i	−0.666075	+	0.745885i	$0.732027\pi$
$930$		0			0
$931$	−12.6555	+	12.6555i	−0.414768	+	0.414768i
$932$	20.6774	+	3.64598i	0.677311	+	0.119428i
$933$		0			0
$934$	4.66243	−	3.91225i	0.152559	−	0.128013i
$935$	5.72966	+	3.30802i	0.187380	+	0.108184i
$936$		0			0
$937$	32.2384	+	11.7338i	1.05318	+	0.383327i	0.809863	−	0.586619i	$-0.199541\pi$
$937$	32.2384	+	11.7338i	1.05318	+	0.383327i	0.243320	+	0.969946i	$0.421764\pi$
$938$	0.716696	+	8.19187i	0.0234010	+	0.267474i
$939$		0			0
$940$	16.2119	−	23.1531i	0.528775	−	0.755170i
$941$	−15.6270	+	2.75546i	−0.509425	+	0.0898253i	−0.422452	−	0.906385i	$-0.638830\pi$
$941$	−15.6270	+	2.75546i	−0.509425	+	0.0898253i	−0.0869728	+	0.996211i	$0.527719\pi$
$942$		0			0
$943$	5.40005	+	2.51808i	0.175850	+	0.0820001i
$944$	−1.08569	−	0.506265i	−0.0353361	−	0.0164775i
$945$		0			0
$946$	−16.3114	+	2.87615i	−0.530331	+	0.0935116i
$947$	24.6832	−	35.2513i	0.802096	−	1.14551i	−0.184580	−	0.982817i	$-0.559093\pi$
$947$	24.6832	−	35.2513i	0.802096	−	1.14551i	0.986676	−	0.162695i	$-0.0520186\pi$
$948$		0			0
$949$	0.0421986	+	0.482332i	0.00136982	+	0.0156571i
$950$	9.66438	+	3.51755i	0.313554	+	0.114124i
$951$		0			0
$952$	1.42859	+	0.824799i	0.0463010	+	0.0267319i
$953$	0.0649663	−	0.0545132i	0.00210446	−	0.00176585i	−0.641735	−	0.766927i	$-0.721785\pi$
$953$	0.0649663	−	0.0545132i	0.00210446	−	0.00176585i	0.643839	+	0.765161i	$0.277341\pi$
$954$		0			0
$955$	−54.9264	−	9.68500i	−1.77738	−	0.313399i
$956$	−4.65750	+	4.65750i	−0.150634	+	0.150634i
$957$		0			0
$958$	11.8007	+	9.90194i	0.381262	+	0.319917i
$959$	23.2698	+	63.9333i	0.751422	+	2.06451i
$960$		0			0
$961$			48.5266i			1.56537i
$962$	−0.269735	+	0.0475134i	−0.00869662	+	0.00153189i
$963$		0			0
$964$	−11.6091	−	24.8958i	−0.373903	−	0.801838i
$965$	10.5883	−	3.85384i	0.340851	−	0.124059i
$966$		0			0
$967$	33.0235	+	47.1624i	1.06196	+	1.51664i	0.840757	+	0.541413i	$0.182110\pi$
$967$	33.0235	+	47.1624i	1.06196	+	1.51664i	0.221206	+	0.975227i	$0.429001\pi$
$968$	−9.07103	−	9.07103i	−0.291554	−	0.291554i
$969$		0			0
$970$	−32.4341	−	8.69070i	−1.04140	−	0.279042i
$971$	17.8418	+	21.2631i	0.572572	+	0.682364i	0.972157	−	0.234332i	$-0.0752903\pi$
$971$	17.8418	+	21.2631i	0.572572	+	0.682364i	−0.399585	+	0.916696i	$0.630846\pi$
$972$		0			0
$973$	21.7842	−	12.5771i	0.698371	−	0.403205i
$974$	−4.81710	+	13.2349i	−0.154350	+	0.424073i
$975$		0			0
$976$	1.99414	−	0.534329i	0.0638310	−	0.0171035i
$977$	36.1009	+	25.2781i	1.15497	+	0.808719i	0.984282	−	0.176606i	$-0.0565120\pi$
$977$	36.1009	+	25.2781i	1.15497	+	0.808719i	0.170688	+	0.985325i	$0.445401\pi$
$978$		0			0
$979$	−3.75574	+	42.9283i	−0.120034	+	1.37199i
$980$	−2.96158	+	6.35113i	−0.0946042	+	0.202879i
$981$		0			0
$982$	20.4247	+	1.78693i	0.651779	+	0.0570233i
$983$	6.18476	+	35.0755i	0.197263	+	1.11873i	0.909159	+	0.416450i	$0.136726\pi$
$983$	6.18476	+	35.0755i	0.197263	+	1.11873i	−0.711896	+	0.702285i	$0.752163\pi$
$984$		0			0
$985$	2.04395	+	7.62813i	0.0651257	+	0.243053i
$986$	1.28973	−	0.112837i	0.0410734	−	0.00359346i
$987$		0			0
$988$	−0.147392	−	0.255291i	−0.00468918	−	0.00812189i
$989$	−2.24481	+	3.88812i	−0.0713807	+	0.123635i
$990$		0			0
$991$	−7.88283	+	29.4191i	−0.250406	+	0.934530i	0.720182	+	0.693785i	$0.244058\pi$
$991$	−7.88283	+	29.4191i	−0.250406	+	0.934530i	−0.970589	+	0.240745i	$0.922608\pi$
$992$	1.54855	−	8.78229i	0.0491666	−	0.278838i
$993$		0			0
$994$	40.4583	−	28.3292i	1.28326	−	0.898547i
$995$	−20.8404	+	24.8366i	−0.660684	+	0.787373i
$996$		0			0
$997$	27.8199	−	12.9726i	0.881066	−	0.410848i	0.0711992	−	0.997462i	$-0.477317\pi$
$997$	27.8199	−	12.9726i	0.881066	−	0.410848i	0.809866	+	0.586615i	$0.199540\pi$
$998$	31.2471			0.989108
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	666.2.bs.a.89.3	✓	72
3.2	odd	2	inner	666.2.bs.a.89.4	yes	72
37.5	odd	36	inner	666.2.bs.a.449.4	yes	72
111.5	even	36	inner	666.2.bs.a.449.3	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
666.2.bs.a.89.3	✓	72	1.1	even	1	trivial
666.2.bs.a.89.4	yes	72	3.2	odd	2	inner
666.2.bs.a.449.3	yes	72	111.5	even	36	inner
666.2.bs.a.449.4	yes	72	37.5	odd	36	inner

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:	\( N \)	\(=\)	\( 666 = 2 \cdot 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	666.bs (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.906308 + 0.422618i) q^{2} +(0.642788 - 0.766044i) q^{4} +(2.09980 - 1.47030i) q^{5} +(0.541765 - 3.07250i) q^{7} +(-0.258819 + 0.965926i) q^{8} +O(q^{10})\)	\(q+(-0.906308 + 0.422618i) q^{2} +(0.642788 - 0.766044i) q^{4} +(2.09980 - 1.47030i) q^{5} +(0.541765 - 3.07250i) q^{7} +(-0.258819 + 0.965926i) q^{8} +(-1.28169 + 2.21995i) q^{10} +(2.44072 + 4.22744i) q^{11} +(0.0448556 - 0.00392436i) q^{13} +(0.807489 + 3.01359i) q^{14} +(-0.173648 - 0.984808i) q^{16} +(0.526723 + 0.0460823i) q^{17} +(2.76682 - 5.93347i) q^{19} +(0.223413 - 2.55363i) q^{20} +(-3.99864 - 2.79987i) q^{22} +(-1.27808 + 0.342461i) q^{23} +(0.537288 - 1.47619i) q^{25} +(-0.0389945 + 0.0225135i) q^{26} +(-2.00543 - 2.38998i) q^{28} +(-2.36516 - 0.633743i) q^{29} +(-6.30581 - 6.30581i) q^{31} +(0.573576 + 0.819152i) q^{32} +(-0.496848 + 0.180838i) q^{34} +(-3.37989 - 7.24819i) q^{35} +(5.71557 + 2.08142i) q^{37} +6.54685i q^{38} +(0.876728 + 2.40879i) q^{40} +(-3.44954 - 2.89450i) q^{41} +(2.39927 - 2.39927i) q^{43} +(4.80727 + 0.847652i) q^{44} +(1.01361 - 0.850516i) q^{46} +(9.54907 + 5.51316i) q^{47} +(-2.56890 - 0.935004i) q^{49} +(0.136915 + 1.56495i) q^{50} +(0.0258264 - 0.0368839i) q^{52} +(3.28937 - 0.580005i) q^{53} +(11.3406 + 5.28821i) q^{55} +(2.82759 + 1.31853i) q^{56} +(2.41140 - 0.425194i) q^{58} +(0.687101 - 0.981282i) q^{59} +(0.179932 + 2.05663i) q^{61} +(8.37996 + 3.05006i) q^{62} +(-0.866025 - 0.500000i) q^{64} +(0.0884178 - 0.0741913i) q^{65} +(2.59567 + 0.457687i) q^{67} +(0.373872 - 0.373872i) q^{68} +(6.12643 + 5.14069i) q^{70} +(-5.41444 - 14.8761i) q^{71} +10.7530i q^{73} +(-6.05971 + 0.529097i) q^{74} +(-2.76682 - 5.93347i) q^{76} +(14.3111 - 5.20882i) q^{77} +(-5.74249 - 8.20113i) q^{79} +(-1.81258 - 1.81258i) q^{80} +(4.34961 + 1.16547i) q^{82} +(-6.99551 - 8.33692i) q^{83} +(1.17377 - 0.677674i) q^{85} +(-1.16050 + 3.18845i) q^{86} +(-4.71510 + 1.26341i) q^{88} +(7.23130 + 5.06341i) q^{89} +(0.0122436 - 0.139945i) q^{91} +(-0.559195 + 1.19920i) q^{92} +(-10.9844 - 0.961007i) q^{94} +(-2.91418 - 16.5271i) q^{95} +(3.39033 + 12.6529i) q^{97} +(2.72337 - 0.238264i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q+O(q^{10}) \) 72 * q	\( 72 q + 12 q^{13} - 24 q^{19} - 12 q^{22} + 72 q^{34} + 72 q^{37} + 24 q^{40} + 24 q^{43} + 36 q^{46} - 48 q^{49} - 12 q^{52} + 60 q^{55} + 120 q^{61} + 60 q^{67} - 60 q^{70} + 24 q^{76} - 12 q^{79} - 48 q^{82} + 108 q^{85} - 24 q^{88} - 168 q^{91} - 84 q^{94} - 264 q^{97}+O(q^{100}) \) 72 * q + 12 * q^13 - 24 * q^19 - 12 * q^22 + 72 * q^34 + 72 * q^37 + 24 * q^40 + 24 * q^43 + 36 * q^46 - 48 * q^49 - 12 * q^52 + 60 * q^55 + 120 * q^61 + 60 * q^67 - 60 * q^70 + 24 * q^76 - 12 * q^79 - 48 * q^82 + 108 * q^85 - 24 * q^88 - 168 * q^91 - 84 * q^94 - 264 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more