LMFDB - Embedded newform 639.2.z.a.269.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [639,2,Mod(35,639)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(639, base_ring=CyclotomicField(70))

chi = DirichletCharacter(H, H._module([35, 29]))

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

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

chi := DirichletCharacter("639.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 639 = 3^{2} \cdot 71 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	639.z (of order $70$, degree $24$, 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:	$5.10244068916$
Analytic rank:	$0$
Dimension:	$576$
Relative dimension:	$24$ over $\Q(\zeta_{70})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{70}]$

Embedding invariants

Embedding label			269.15
Character	$\chi$	$=$	639.269
Dual form			639.2.z.a.620.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.742017 + 0.317153i) q^{2} +(-0.932123 - 0.974924i) q^{4} +(-0.618013 - 0.200804i) q^{5} +(-0.732035 - 0.837882i) q^{7} +(-0.949537 - 2.53003i) q^{8} +O(q^{10})$	\(q+(0.742017 + 0.317153i) q^{2} +(-0.932123 - 0.974924i) q^{4} +(-0.618013 - 0.200804i) q^{5} +(-0.732035 - 0.837882i) q^{7} +(-0.949537 - 2.53003i) q^{8} +(-0.394890 - 0.345005i) q^{10} +(-2.86141 + 0.789699i) q^{11} +(-0.525599 + 1.90447i) q^{13} +(-0.277446 - 0.853890i) q^{14} +(-0.0231941 + 0.516458i) q^{16} +(-5.70281 + 4.14333i) q^{17} +(-1.80869 - 3.36110i) q^{19} +(0.380294 + 0.789690i) q^{20} +(-2.37367 - 0.321536i) q^{22} +(-0.286865 + 1.25684i) q^{23} +(-3.70347 - 2.69073i) q^{25} +(-0.994011 + 1.24645i) q^{26} +(-0.134524 + 1.49469i) q^{28} +(1.89072 - 0.256116i) q^{29} +(0.233334 - 0.0104790i) q^{31} +(-2.52602 + 5.24533i) q^{32} +(-5.54565 + 1.26576i) q^{34} +(0.284157 + 0.664818i) q^{35} +(-2.57038 - 11.2616i) q^{37} +(-0.276091 - 3.06762i) q^{38} +(0.0787841 + 1.75426i) q^{40} +(-3.04186 - 3.81437i) q^{41} +(2.14795 + 0.193319i) q^{43} +(3.43708 + 2.05356i) q^{44} +(-0.611469 + 0.841615i) q^{46} +(6.34876 - 1.15213i) q^{47} +(0.773463 - 5.70993i) q^{49} +(-1.89466 - 3.17113i) q^{50} +(2.34663 - 1.26278i) q^{52} +(-4.52197 + 4.72961i) q^{53} +(1.92696 + 0.0865400i) q^{55} +(-1.42477 + 2.64767i) q^{56} +(1.48418 + 0.409607i) q^{58} +(2.91451 + 4.41529i) q^{59} +(5.28690 - 6.05135i) q^{61} +(0.176461 + 0.0662270i) q^{62} +(-2.75928 + 2.41071i) q^{64} +(0.707252 - 1.07144i) q^{65} +(-8.38154 + 8.01357i) q^{67} +(9.35514 + 1.69771i) q^{68} +0.583427i q^{70} +(-7.37577 + 4.07407i) q^{71} +(0.351975 - 0.823487i) q^{73} +(1.66438 - 9.17147i) q^{74} +(-1.59090 + 4.89629i) q^{76} +(2.75633 + 1.81944i) q^{77} +(10.8927 - 4.08808i) q^{79} +(0.118041 - 0.314520i) q^{80} +(-1.04737 - 3.79506i) q^{82} +(4.13843 - 2.73176i) q^{83} +(4.35641 - 1.41548i) q^{85} +(1.53250 + 0.824674i) q^{86} +(4.71498 + 6.48962i) q^{88} +(-2.51991 - 2.40928i) q^{89} +(1.98047 - 0.953746i) q^{91} +(1.49271 - 0.891855i) q^{92} +(5.07629 + 1.15863i) q^{94} +(0.442866 + 2.44040i) q^{95} +(9.12090 + 7.27367i) q^{97} +(2.38484 - 3.99156i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 576 q - 24 q^{4}+O(q^{10}) $ 576 * q - 24 * q^4	$ 576 q - 24 q^{4} - 16 q^{10} + 76 q^{16} - 8 q^{19} + 20 q^{22} + 168 q^{25} - 20 q^{28} - 28 q^{31} + 40 q^{37} + 32 q^{40} + 52 q^{43} - 20 q^{46} - 208 q^{52} - 92 q^{55} + 56 q^{58} + 56 q^{61} - 144 q^{64} - 16 q^{67} - 44 q^{73} - 336 q^{76} + 88 q^{79} - 124 q^{82} + 60 q^{85} - 260 q^{88} + 80 q^{91} + 56 q^{94} - 56 q^{97}+O(q^{100}) $ 576 * q - 24 * q^4 - 16 * q^10 + 76 * q^16 - 8 * q^19 + 20 * q^22 + 168 * q^25 - 20 * q^28 - 28 * q^31 + 40 * q^37 + 32 * q^40 + 52 * q^43 - 20 * q^46 - 208 * q^52 - 92 * q^55 + 56 * q^58 + 56 * q^61 - 144 * q^64 - 16 * q^67 - 44 * q^73 - 336 * q^76 + 88 * q^79 - 124 * q^82 + 60 * q^85 - 260 * q^88 + 80 * q^91 + 56 * q^94 - 56 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/639\mathbb{Z}\right)^\times$.

$n$	$433$	$569$
$\chi(n)$	$e\left(\frac{19}{70}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.742017	+	0.317153i	0.524685	+	0.224261i	0.639033	−	0.769180i	$-0.279335\pi$
$2$	0.742017	+	0.317153i	0.524685	+	0.224261i	−0.114348	+	0.993441i	$0.536478\pi$
$3$		0			0
$3$		0			0
$4$	−0.932123	−	0.974924i	−0.466061	−	0.487462i
$5$	−0.618013	−	0.200804i	−0.276384	−	0.0898025i	0.167546	−	0.985864i	$-0.446416\pi$
$5$	−0.618013	−	0.200804i	−0.276384	−	0.0898025i	−0.443929	+	0.896062i	$0.646416\pi$
$6$		0			0
$7$	−0.732035	−	0.837882i	−0.276683	−	0.316690i	0.597894	−	0.801575i	$-0.296004\pi$
$7$	−0.732035	−	0.837882i	−0.276683	−	0.316690i	−0.874578	+	0.484885i	$0.838861\pi$
$8$	−0.949537	−	2.53003i	−0.335712	−	0.894502i
$9$		0			0
$10$	−0.394890	−	0.345005i	−0.124875	−	0.109100i
$11$	−2.86141	+	0.789699i	−0.862748	+	0.238103i	−0.669286	−	0.743005i	$-0.733400\pi$
$11$	−2.86141	+	0.789699i	−0.862748	+	0.238103i	−0.193462	+	0.981108i	$0.561972\pi$
$12$		0			0
$13$	−0.525599	+	1.90447i	−0.145775	+	0.528204i	0.854191	+	0.519959i	$0.174053\pi$
$13$	−0.525599	+	1.90447i	−0.145775	+	0.528204i	−0.999966	+	0.00824441i	$0.997376\pi$
$14$	−0.277446	−	0.853890i	−0.0741505	−	0.228212i
$15$		0			0
$16$	−0.0231941	+	0.516458i	−0.00579854	+	0.129114i
$17$	−5.70281	+	4.14333i	−1.38313	+	1.00491i	−0.386554	+	0.922267i	$0.626335\pi$
$17$	−5.70281	+	4.14333i	−1.38313	+	1.00491i	−0.996580	+	0.0826385i	$0.973665\pi$
$18$		0			0
$19$	−1.80869	−	3.36110i	−0.414941	−	0.771090i	0.584239	−	0.811582i	$-0.301393\pi$
$19$	−1.80869	−	3.36110i	−0.414941	−	0.771090i	−0.999180	+	0.0404922i	$0.987107\pi$
$20$	0.380294	+	0.789690i	0.0850364	+	0.176580i
$21$		0			0
$22$	−2.37367	−	0.321536i	−0.506068	−	0.0685516i
$23$	−0.286865	+	1.25684i	−0.0598155	+	0.262069i	−0.995990	−	0.0894675i	$-0.971483\pi$
$23$	−0.286865	+	1.25684i	−0.0598155	+	0.262069i	0.936174	+	0.351536i	$0.114341\pi$
$24$		0			0
$25$	−3.70347	−	2.69073i	−0.740694	−	0.538145i
$26$	−0.994011	+	1.24645i	−0.194942	+	0.244449i
$27$		0			0
$28$	−0.134524	+	1.49469i	−0.0254227	+	0.282469i
$29$	1.89072	−	0.256116i	0.351098	−	0.0475595i	0.0434391	−	0.999056i	$-0.486169\pi$
$29$	1.89072	−	0.256116i	0.351098	−	0.0475595i	0.307659	+	0.951497i	$0.400454\pi$
$30$		0			0
$31$	0.233334	−	0.0104790i	0.0419080	−	0.00188209i	−0.0239009	−	0.999714i	$-0.507609\pi$
$31$	0.233334	−	0.0104790i	0.0419080	−	0.00188209i	0.0658090	+	0.997832i	$0.479037\pi$
$32$	−2.52602	+	5.24533i	−0.446541	+	0.927252i
$33$		0			0
$34$	−5.54565	+	1.26576i	−0.951071	+	0.217076i
$35$	0.284157	+	0.664818i	0.0480312	+	0.112375i
$36$		0			0
$37$	−2.57038	−	11.2616i	−0.422567	−	1.85139i	−0.517184	−	0.855874i	$-0.673020\pi$
$37$	−2.57038	−	11.2616i	−0.422567	−	1.85139i	0.0946168	−	0.995514i	$-0.469837\pi$
$38$	−0.276091	−	3.06762i	−0.0447879	−	0.497634i
$39$		0			0
$40$	0.0787841	+	1.75426i	0.0124569	+	0.277373i
$41$	−3.04186	−	3.81437i	−0.475058	−	0.595704i	0.485343	−	0.874324i	$-0.338695\pi$
$41$	−3.04186	−	3.81437i	−0.475058	−	0.595704i	−0.960402	+	0.278620i	$0.910123\pi$
$42$		0			0
$43$	2.14795	+	0.193319i	0.327559	+	0.0294808i	0.252198	−	0.967676i	$-0.418846\pi$
$43$	2.14795	+	0.193319i	0.327559	+	0.0294808i	0.0753603	+	0.997156i	$0.475989\pi$
$44$	3.43708	+	2.05356i	0.518160	+	0.309586i
$45$		0			0
$46$	−0.611469	+	0.841615i	−0.0901561	+	0.124089i
$47$	6.34876	−	1.15213i	0.926062	−	0.168056i	0.305481	−	0.952198i	$-0.401183\pi$
$47$	6.34876	−	1.15213i	0.926062	−	0.168056i	0.620581	+	0.784142i	$0.286897\pi$
$48$		0			0
$49$	0.773463	−	5.70993i	0.110495	−	0.815704i
$50$	−1.89466	−	3.17113i	−0.267946	−	0.448466i
$51$		0			0
$52$	2.34663	−	1.26278i	0.325419	−	0.175116i
$53$	−4.52197	+	4.72961i	−0.621140	+	0.649662i	−0.956261	−	0.292513i	$-0.905508\pi$
$53$	−4.52197	+	4.72961i	−0.621140	+	0.649662i	0.335121	+	0.942175i	$0.391223\pi$
$54$		0			0
$55$	1.92696	+	0.0865400i	0.259832	+	0.0116691i
$56$	−1.42477	+	2.64767i	−0.190393	+	0.353810i
$57$		0			0
$58$	1.48418	+	0.409607i	0.194882	+	0.0537840i
$59$	2.91451	+	4.41529i	0.379437	+	0.574822i	0.973241	−	0.229787i	$-0.0738031\pi$
$59$	2.91451	+	4.41529i	0.379437	+	0.574822i	−0.593804	+	0.804610i	$0.702375\pi$
$60$		0			0
$61$	5.28690	−	6.05135i	0.676918	−	0.774795i	−0.307327	−	0.951604i	$-0.599434\pi$
$61$	5.28690	−	6.05135i	0.676918	−	0.774795i	0.984245	+	0.176809i	$0.0565773\pi$
$62$	0.176461	+	0.0662270i	0.0224106	+	0.00841084i
$63$		0			0
$64$	−2.75928	+	2.41071i	−0.344909	+	0.301338i
$65$	0.707252	−	1.07144i	0.0877238	−	0.132896i
$66$		0			0
$67$	−8.38154	+	8.01357i	−1.02397	+	0.979014i	−0.999786	−	0.0206939i	$-0.993412\pi$
$67$	−8.38154	+	8.01357i	−1.02397	+	0.979014i	−0.0241821	+	0.999708i	$0.507698\pi$
$68$	9.35514	+	1.69771i	1.13448	+	0.205877i
$69$		0			0
$70$			0.583427i			0.0697329i
$71$	−7.37577	+	4.07407i	−0.875343	+	0.483503i
$71$	−7.37577	+	4.07407i	−0.875343	+	0.483503i
$72$		0			0
$73$	0.351975	−	0.823487i	0.0411956	−	0.0963819i	−0.897666	−	0.440676i	$-0.854739\pi$
$73$	0.351975	−	0.823487i	0.0411956	−	0.0963819i	0.938862	+	0.344294i	$0.111882\pi$
$74$	1.66438	−	9.17147i	0.193480	−	1.06616i
$75$		0			0
$76$	−1.59090	+	4.89629i	−0.182489	+	0.561643i
$77$	2.75633	+	1.81944i	0.314113	+	0.207344i
$78$		0			0
$79$	10.8927	−	4.08808i	1.22552	−	0.459945i	0.347096	−	0.937830i	$-0.387168\pi$
$79$	10.8927	−	4.08808i	1.22552	−	0.459945i	0.878423	+	0.477885i	$0.158596\pi$
$80$	0.118041	−	0.314520i	0.0131974	−	0.0351644i
$81$		0			0
$82$	−1.04737	−	3.79506i	−0.115663	−	0.419094i
$83$	4.13843	−	2.73176i	0.454252	−	0.299849i	−0.302978	−	0.952998i	$-0.597981\pi$
$83$	4.13843	−	2.73176i	0.454252	−	0.299849i	0.757230	+	0.653148i	$0.226552\pi$
$84$		0			0
$85$	4.35641	−	1.41548i	0.472518	−	0.153531i
$86$	1.53250	+	0.824674i	0.165254	+	0.0889268i
$87$		0			0
$88$	4.71498	+	6.48962i	0.502619	+	0.691795i
$89$	−2.51991	−	2.40928i	−0.267110	−	0.255383i	0.545608	−	0.838040i	$-0.316299\pi$
$89$	−2.51991	−	2.40928i	−0.267110	−	0.255383i	−0.812718	+	0.582657i	$0.802013\pi$
$90$		0			0
$91$	1.98047	−	0.953746i	0.207610	−	0.0999798i
$92$	1.49271	−	0.891855i	0.155626	−	0.0929823i
$93$		0			0
$94$	5.07629	+	1.15863i	0.523579	+	0.119504i
$95$	0.442866	+	2.44040i	0.0454371	+	0.250379i
$96$		0			0
$97$	9.12090	+	7.27367i	0.926087	+	0.738530i	0.965421	−	0.260697i	$-0.0839522\pi$
$97$	9.12090	+	7.27367i	0.926087	+	0.738530i	−0.0393340	+	0.999226i	$0.512524\pi$
$98$	2.38484	−	3.99156i	0.240906	−	0.403208i
$99$		0			0
$100$	0.828832	+	6.11869i	0.0828832	+	0.611869i
$101$	0.570642	−	0.455071i	0.0567810	−	0.0452813i	−0.594688	−	0.803956i	$-0.702724\pi$
$101$	0.570642	−	0.455071i	0.0567810	−	0.0452813i	0.651469	+	0.758675i	$0.274153\pi$
$102$		0			0
$103$	−12.2539	−	5.90115i	−1.20741	−	0.581458i	−0.281630	−	0.959523i	$-0.590875\pi$
$103$	−12.2539	−	5.90115i	−1.20741	−	0.581458i	−0.925779	+	0.378065i	$0.876589\pi$
$104$	5.31744	−	0.478578i	0.521417	−	0.0469284i
$105$		0			0
$106$	−4.85539	+	2.07529i	−0.471597	+	0.201570i
$107$	−7.54466	+	3.22474i	−0.729369	+	0.311747i	−0.725478	−	0.688245i	$-0.758381\pi$
$107$	−7.54466	+	3.22474i	−0.729369	+	0.311747i	−0.00389110	+	0.999992i	$0.501239\pi$
$108$		0			0
$109$	11.0228	−	0.992067i	1.05579	−	0.0950228i	0.451882	−	0.892078i	$-0.350753\pi$
$109$	11.0228	−	0.992067i	1.05579	−	0.0950228i	0.603907	+	0.797055i	$0.293610\pi$
$110$	1.40239	+	0.675357i	0.133713	+	0.0643927i
$111$		0			0
$112$	0.449710	−	0.358631i	0.0424936	−	0.0338875i
$113$	−0.942948	−	6.96112i	−0.0887051	−	0.654847i	−0.979647	−	0.200729i	$-0.935669\pi$
$113$	−0.942948	−	6.96112i	−0.0887051	−	0.654847i	0.890942	−	0.454118i	$-0.150046\pi$
$114$		0			0
$115$	0.429665	−	0.719138i	0.0400665	−	0.0670599i
$116$	−2.01208	−	1.60458i	−0.186817	−	0.148981i
$117$		0			0
$118$	0.762291	+	4.20057i	0.0701746	+	0.386694i
$119$	7.64628	+	1.74521i	0.700933	+	0.159983i
$120$		0			0
$121$	−1.87889	+	1.12258i	−0.170808	+	0.102053i
$122$	5.84217	−	2.81344i	0.528926	−	0.254717i
$123$		0			0
$124$	−0.227712	−	0.217715i	−0.0204492	−	0.0195514i
$125$	3.65824	+	5.03514i	0.327203	+	0.450357i
$126$		0			0
$127$	−2.32377	−	1.25047i	−0.206201	−	0.110961i	0.367509	−	0.930020i	$-0.380211\pi$
$127$	−2.32377	−	1.25047i	−0.206201	−	0.110961i	−0.573710	+	0.819058i	$0.694496\pi$
$128$	8.26187	−	2.68444i	0.730253	−	0.237274i
$129$		0			0
$130$	0.864604	−	0.570720i	0.0758308	−	0.0500555i
$131$	−3.76630	−	13.6469i	−0.329063	−	1.19233i	−0.922033	−	0.387110i	$-0.873473\pi$
$131$	−3.76630	−	13.6469i	−0.329063	−	1.19233i	0.592970	−	0.805225i	$-0.297955\pi$
$132$		0			0
$133$	−1.49218	+	3.97591i	−0.129389	+	0.344755i
$134$	−8.76077	+	3.28797i	−0.756816	+	0.284038i
$135$		0			0
$136$	15.8978	+	10.4940i	1.36322	+	0.899856i
$137$	5.53531	−	17.0359i	0.472913	−	1.45548i	−0.375838	−	0.926685i	$-0.622645\pi$
$137$	5.53531	−	17.0359i	0.472913	−	1.45548i	0.848752	−	0.528792i	$-0.177355\pi$
$138$		0			0
$139$	−2.26945	+	12.5057i	−0.192492	+	1.06072i	0.732510	+	0.680756i	$0.238349\pi$
$139$	−2.26945	+	12.5057i	−0.192492	+	1.06072i	−0.925002	+	0.379962i	$0.875937\pi$
$140$	0.383278	−	0.896723i	0.0323929	−	0.0757869i
$141$		0			0
$142$	−6.76505	+	0.683779i	−0.567710	+	0.0573815i
$143$		−	5.86452i		−	0.490416i
$144$		0			0
$145$	−1.21992	−	0.221383i	−0.101309	−	0.0183848i
$146$	0.522343	−	0.499411i	0.0432294	−	0.0413316i
$147$		0			0
$148$	−8.58325	+	13.0031i	−0.705539	+	1.06885i
$149$	−8.87042	+	7.74986i	−0.726693	+	0.634893i	−0.939638	−	0.342171i	$-0.888838\pi$
$149$	−8.87042	+	7.74986i	−0.726693	+	0.634893i	0.212944	+	0.977064i	$0.431695\pi$
$150$		0			0
$151$	−14.3265	−	5.37684i	−1.16588	−	0.437561i	−0.307985	−	0.951391i	$-0.599655\pi$
$151$	−14.3265	−	5.37684i	−1.16588	−	0.437561i	−0.857892	+	0.513831i	$0.828226\pi$
$152$	−6.78628	+	7.76753i	−0.550440	+	0.630029i
$153$		0			0
$154$	1.46820	+	2.22423i	0.118311	+	0.179234i
$155$	−0.146308	−	0.0403783i	−0.0117517	−	0.00324327i
$156$		0			0
$157$	2.13482	−	3.96717i	0.170377	−	0.316614i	−0.781060	−	0.624456i	$-0.785321\pi$
$157$	2.13482	−	3.96717i	0.170377	−	0.316614i	0.951438	+	0.307841i	$0.0996066\pi$
$158$	9.37908	+	0.421215i	0.746159	+	0.0335101i
$159$		0			0
$160$	2.61440	−	2.73444i	0.206686	−	0.216177i
$161$	1.26308	−	0.679691i	0.0995444	−	0.0535671i
$162$		0			0
$163$	8.19552	+	13.7170i	0.641923	+	1.07440i	0.990552	+	0.137137i	$0.0437902\pi$
$163$	8.19552	+	13.7170i	0.641923	+	1.07440i	−0.348629	+	0.937261i	$0.613353\pi$
$164$	−0.883334	+	6.52103i	−0.0689768	+	0.509207i
$165$		0			0
$166$	3.93717	−	0.714492i	0.305584	−	0.0554553i
$167$	−4.23631	+	5.83078i	−0.327816	+	0.451200i	−0.940833	−	0.338870i	$-0.889955\pi$
$167$	−4.23631	+	5.83078i	−0.327816	+	0.451200i	0.613018	+	0.790069i	$0.289955\pi$
$168$		0			0
$169$	7.80910	+	4.66572i	0.600700	+	0.358902i
$170$	3.68145	+	0.331337i	0.282354	+	0.0254124i
$171$		0			0
$172$	−1.81368	−	2.27428i	−0.138292	−	0.173412i
$173$	−0.564184	−	12.5625i	−0.0428941	−	0.955111i	−0.898902	−	0.438149i	$-0.855634\pi$
$173$	−0.564184	−	12.5625i	−0.0428941	−	0.955111i	0.856008	−	0.516962i	$-0.172937\pi$
$174$		0			0
$175$	0.456558	+	5.07278i	0.0345125	+	0.383466i
$176$	−0.341478	−	1.49611i	−0.0257399	−	0.112774i
$177$		0			0
$178$	−1.10570	−	2.58692i	−0.0828760	−	0.193898i
$179$	−7.54830	+	1.72285i	−0.564186	+	0.128772i	−0.495095	−	0.868839i	$-0.664867\pi$
$179$	−7.54830	+	1.72285i	−0.564186	+	0.128772i	−0.0690907	+	0.997610i	$0.522010\pi$
$180$		0			0
$181$	2.71691	−	5.64173i	0.201947	−	0.419347i	−0.775258	−	0.631644i	$-0.782380\pi$
$181$	2.71691	−	5.64173i	0.201947	−	0.419347i	0.977205	+	0.212298i	$0.0680946\pi$
$182$	1.77203	−	0.0795819i	0.131352	−	0.00589900i
$183$		0			0
$184$	3.45223	−	0.467636i	0.254502	−	0.0344746i
$185$	−0.672845	+	7.47593i	−0.0494686	+	0.549641i
$186$		0			0
$187$	13.0461	−	16.3593i	0.954024	−	1.19631i
$188$	−7.04106	−	5.11563i	−0.513522	−	0.373096i
$189$		0			0
$190$	−0.445365	+	1.95127i	−0.0323102	+	0.141560i
$191$	2.03344	+	0.275448i	0.147134	+	0.0199307i	0.207430	−	0.978250i	$-0.433490\pi$
$191$	2.03344	+	0.275448i	0.147134	+	0.0199307i	−0.0602956	+	0.998181i	$0.519204\pi$
$192$		0			0
$193$	5.68960	+	11.8146i	0.409546	+	0.850432i	0.999088	+	0.0426938i	$0.0135940\pi$
$193$	5.68960	+	11.8146i	0.409546	+	0.850432i	−0.589542	+	0.807738i	$0.700692\pi$
$194$	4.46099	+	8.28991i	0.320280	+	0.595181i
$195$		0			0
$196$	−6.28771	+	4.56829i	−0.449122	+	0.326306i
$197$	0.231743	−	5.16016i	0.0165110	−	0.367646i	−0.973679	−	0.227922i	$-0.926807\pi$
$197$	0.231743	−	5.16016i	0.0165110	−	0.367646i	0.990190	−	0.139724i	$-0.0446216\pi$
$198$		0			0
$199$	5.39055	+	16.5904i	0.382126	+	1.17606i	0.938544	+	0.345159i	$0.112175\pi$
$199$	5.39055	+	16.5904i	0.382126	+	1.17606i	−0.556418	+	0.830902i	$0.687825\pi$
$200$	−3.29105	+	11.9248i	−0.232712	+	0.843214i
$201$		0			0
$202$	0.567753	−	0.156690i	0.0399470	−	0.0110247i
$203$	−1.59867	−	1.39672i	−0.112205	−	0.0980303i
$204$		0			0
$205$	1.11396	+	2.96815i	0.0778026	+	0.207304i
$206$	−7.22100	−	8.26511i	−0.503111	−	0.575857i
$207$		0			0
$208$	−0.971385	−	0.315622i	−0.0673535	−	0.0218845i
$209$	7.82965	+	8.18918i	0.541589	+	0.566457i
$210$		0			0
$211$	−19.5995	−	8.37724i	−1.34929	−	0.576713i	−0.407587	−	0.913166i	$-0.633630\pi$
$211$	−19.5995	−	8.37724i	−1.34929	−	0.576713i	−0.941700	+	0.336453i	$0.890773\pi$
$212$	8.82603			0.606174
$213$		0			0
$214$	−6.62100			−0.452602
$215$	−1.28864	−	0.550790i	−0.0878844	−	0.0375636i
$216$		0			0
$217$	−0.179589	−	0.187835i	−0.0121913	−	0.0127511i
$218$	8.49371	+	2.75978i	0.575267	+	0.186916i
$219$		0			0
$220$	−1.71180	−	1.95931i	−0.115409	−	0.132097i
$221$	−4.89344	−	13.0385i	−0.329168	−	0.877066i
$222$		0			0
$223$	−4.68797	−	4.09576i	−0.313930	−	0.274272i	0.486523	−	0.873668i	$-0.338265\pi$
$223$	−4.68797	−	4.09576i	−0.313930	−	0.274272i	−0.800453	+	0.599395i	$0.795408\pi$
$224$	6.24410	−	1.72326i	0.417201	−	0.115140i
$225$		0			0
$226$	1.50806	−	5.46433i	0.100315	−	0.363482i
$227$	0.706871	+	2.17552i	0.0469167	+	0.144395i	0.971771	−	0.235928i	$-0.0758129\pi$
$227$	0.706871	+	2.17552i	0.0469167	+	0.144395i	−0.924854	+	0.380323i	$0.875813\pi$
$228$		0			0
$229$	0.685981	−	15.2745i	0.0453309	−	1.00937i	−0.839471	−	0.543404i	$-0.817135\pi$
$229$	0.685981	−	15.2745i	0.0453309	−	1.00937i	0.884802	−	0.465967i	$-0.154293\pi$
$230$	0.546895	−	0.397343i	0.0360612	−	0.0262000i
$231$		0			0
$232$	−2.44329	−	4.54040i	−0.160410	−	0.298092i
$233$	−12.6723	−	26.3143i	−0.830191	−	1.72391i	−0.677354	−	0.735657i	$-0.736873\pi$
$233$	−12.6723	−	26.3143i	−0.830191	−	1.72391i	−0.152837	−	0.988251i	$-0.548841\pi$
$234$		0			0
$235$	−4.15497	−	0.562829i	−0.271040	−	0.0367149i
$236$	1.58789	−	6.95702i	0.103363	−	0.452864i
$237$		0			0
$238$	5.12017	+	3.72002i	0.331891	+	0.241133i
$239$	10.6390	−	13.3408i	0.688177	−	0.862947i	−0.307902	−	0.951418i	$-0.599627\pi$
$239$	10.6390	−	13.3408i	0.688177	−	0.862947i	0.996079	+	0.0884716i	$0.0281982\pi$
$240$		0			0
$241$	0.480991	−	5.34425i	0.0309833	−	0.344253i	−0.965496	−	0.260417i	$-0.916140\pi$
$241$	0.480991	−	5.34425i	0.0309833	−	0.344253i	0.996480	−	0.0838361i	$-0.0267172\pi$
$242$	−1.75020	+	0.237080i	−0.112507	+	0.0152401i
$243$		0			0
$244$	−10.8276	+	0.486270i	−0.693169	+	0.0311302i
$245$	−1.62459	+	3.37349i	−0.103791	+	0.215525i
$246$		0			0
$247$	7.35175	−	1.67799i	0.467780	−	0.106768i
$248$	−0.248072	−	0.580393i	−0.0157526	−	0.0368550i
$249$		0			0
$250$	1.11757	+	4.89638i	0.0706812	+	0.309674i
$251$	0.655940	+	7.28809i	0.0414025	+	0.460020i	0.989752	+	0.142794i	$0.0456086\pi$
$251$	0.655940	+	7.28809i	0.0414025	+	0.460020i	−0.948350	+	0.317226i	$0.897249\pi$
$252$		0			0
$253$	−0.171685	−	3.82287i	−0.0107938	−	0.240342i
$254$	−1.32768	−	1.66486i	−0.0833062	−	0.104463i
$255$		0			0
$256$	14.2804	+	1.28526i	0.892524	+	0.0803286i
$257$	−6.07139	−	3.62748i	−0.378723	−	0.226276i	0.310904	−	0.950441i	$-0.399368\pi$
$257$	−6.07139	−	3.62748i	−0.378723	−	0.226276i	−0.689627	+	0.724165i	$0.742225\pi$
$258$		0			0
$259$	−7.55425	+	10.3975i	−0.469398	+	0.646071i
$260$	−1.70382	+	0.309198i	−0.105666	+	0.0191756i
$261$		0			0
$262$	1.53350	−	11.3207i	0.0947397	−	0.699396i
$263$	11.9909	+	20.0694i	0.739391	+	1.23753i	0.964727	+	0.263251i	$0.0847946\pi$
$263$	11.9909	+	20.0694i	0.739391	+	1.23753i	−0.225337	+	0.974281i	$0.572348\pi$
$264$		0			0
$265$	3.74436	−	2.01493i	0.230014	−	0.123776i
$266$	−2.36820	+	2.47694i	−0.145204	+	0.151871i
$267$		0			0
$268$	15.6252	+	0.701730i	0.954464	+	0.0428650i
$269$	−13.0751	+	24.2977i	−0.797206	+	1.48146i	0.0776009	+	0.996984i	$0.475274\pi$
$269$	−13.0751	+	24.2977i	−0.797206	+	1.48146i	−0.874807	+	0.484472i	$0.839012\pi$
$270$		0			0
$271$	−8.31653	−	2.29522i	−0.505193	−	0.139424i	0.00414415	−	0.999991i	$-0.498681\pi$
$271$	−8.31653	−	2.29522i	−0.505193	−	0.139424i	−0.509337	+	0.860567i	$0.670109\pi$
$272$	−2.00758	−	3.04136i	−0.121728	−	0.184410i
$273$		0			0
$274$	9.51029	−	10.8854i	0.574538	−	0.657611i
$275$	12.7220	+	4.77465i	0.767166	+	0.287922i
$276$		0			0
$277$	−10.2559	+	8.96029i	−0.616216	+	0.538372i	−0.908460	−	0.417972i	$-0.862741\pi$
$277$	−10.2559	+	8.96029i	−0.616216	+	0.538372i	0.292244	+	0.956344i	$0.405598\pi$
$278$	−5.65019	+	8.55967i	−0.338876	+	0.513375i
$279$		0			0
$280$	1.41219	−	1.35019i	0.0843947	−	0.0806896i
$281$	6.85200	+	1.24346i	0.408756	+	0.0741783i	0.379041	−	0.925380i	$-0.376254\pi$
$281$	6.85200	+	1.24346i	0.408756	+	0.0741783i	0.0297157	+	0.999558i	$0.490540\pi$
$282$		0			0
$283$		−	4.29568i		−	0.255352i	−0.991816	−	0.127676i	$-0.959248\pi$
$283$		−	4.29568i		−	0.255352i	0.991816	−	0.127676i	$-0.0407517\pi$
$284$	10.8470	+	3.39328i	0.643653	+	0.201354i
$285$		0			0
$286$	1.85995	−	4.35158i	0.109981	−	0.257314i
$287$	−0.969243	+	5.34097i	−0.0572126	+	0.315267i
$288$		0			0
$289$	10.1015	−	31.0893i	0.594207	−	1.82878i
$290$	−0.834989	−	0.551171i	−0.0490322	−	0.0323659i
$291$		0			0
$292$	−1.13092	+	0.424442i	−0.0661822	+	0.0248386i
$293$	−1.66247	+	4.42963i	−0.0971224	+	0.258782i	−0.975812	−	0.218612i	$-0.929847\pi$
$293$	−1.66247	+	4.42963i	−0.0971224	+	0.258782i	0.878689	+	0.477394i	$0.158419\pi$
$294$		0			0
$295$	−0.914593	−	3.31395i	−0.0532497	−	0.192946i
$296$	−26.0514	+	17.1964i	−1.51421	+	0.999520i
$297$		0			0
$298$	−9.03989	+	2.93724i	−0.523667	+	0.170150i
$299$	−2.24283	−	1.20692i	−0.129706	−	0.0697978i
$300$		0			0
$301$	−1.41039	−	1.94124i	−0.0812938	−	0.111891i
$302$	−8.92524	−	8.53341i	−0.513590	−	0.491042i
$303$		0			0
$304$	1.77782	−	0.856152i	0.101965	−	0.0491037i
$305$	−4.48251	+	2.67817i	−0.256668	+	0.153352i
$306$		0			0
$307$	−24.5364	−	5.60028i	−1.40037	−	0.319625i	−0.545344	−	0.838212i	$-0.683601\pi$
$307$	−24.5364	−	5.60028i	−1.40037	−	0.319625i	−0.855025	+	0.518587i	$0.826458\pi$
$308$	−0.795424	−	4.38315i	−0.0453235	−	0.249753i
$309$		0			0
$310$	−0.0957566	−	0.0763634i	−0.00543861	−	0.00433715i
$311$	5.62702	−	9.41805i	0.319079	−	0.534049i	−0.656323	−	0.754480i	$-0.727889\pi$
$311$	5.62702	−	9.41805i	0.319079	−	0.534049i	0.975403	+	0.220431i	$0.0707464\pi$
$312$		0			0
$313$	2.39577	+	17.6863i	0.135417	+	0.999686i	0.923359	+	0.383937i	$0.125432\pi$
$313$	2.39577	+	17.6863i	0.135417	+	0.999686i	−0.787942	+	0.615749i	$0.788854\pi$
$314$	2.84228	−	2.26664i	0.160399	−	0.127914i
$315$		0			0
$316$	−14.1389	−	6.80891i	−0.795372	−	0.383031i
$317$	−30.2812	+	2.72536i	−1.70076	+	0.153071i	−0.897045	−	0.441940i	$-0.854290\pi$
$317$	−30.2812	+	2.72536i	−1.70076	+	0.153071i	−0.803717	+	0.595011i	$0.797147\pi$
$318$		0			0
$319$	−5.20788	+	2.22596i	−0.291585	+	0.124630i
$320$	2.18935	−	0.935772i	0.122388	−	0.0523113i
$321$		0			0
$322$	1.15279	−	0.103753i	0.0642425	−	0.00578193i
$323$	24.2407	+	11.6737i	1.34879	+	0.649543i
$324$		0			0
$325$	7.07094	−	5.63888i	0.392225	−	0.312789i
$326$	1.73083	+	12.7775i	0.0958617	+	0.707679i
$327$		0			0
$328$	−6.76212	+	11.3179i	−0.373375	+	0.624925i
$329$	−5.61287	−	4.47611i	−0.309447	−	0.246776i
$330$		0			0
$331$	−3.30523	−	18.2133i	−0.181672	−	1.00109i	−0.937931	−	0.346822i	$-0.887261\pi$
$331$	−3.30523	−	18.2133i	−0.181672	−	1.00109i	0.756259	−	0.654272i	$-0.227025\pi$
$332$	−6.52078	−	1.48833i	−0.357874	−	0.0816825i
$333$		0			0
$334$	−4.99267	+	2.98298i	−0.273187	+	0.163221i
$335$	6.78906	−	3.26944i	0.370926	−	0.178628i
$336$		0			0
$337$	−13.9456	−	13.3333i	−0.759664	−	0.726313i	0.208118	−	0.978104i	$-0.433266\pi$
$337$	−13.9456	−	13.3333i	−0.759664	−	0.726313i	−0.967782	+	0.251790i	$0.918981\pi$
$338$	4.31474	+	5.93872i	0.234691	+	0.323024i
$339$		0			0
$340$	−5.44069	−	2.92776i	−0.295063	−	0.158780i
$341$	−0.659390	+	0.214249i	−0.0357079	+	0.0116022i
$342$		0			0
$343$	−11.8504	+	7.82237i	−0.639861	+	0.422368i
$344$	−1.55045	−	5.61794i	−0.0835948	−	0.302899i
$345$		0			0
$346$	3.56561	−	9.50054i	0.191688	−	0.510752i
$347$	−5.16004	+	1.93659i	−0.277005	+	0.103962i	−0.486011	−	0.873953i	$-0.661549\pi$
$347$	−5.16004	+	1.93659i	−0.277005	+	0.103962i	0.209006	+	0.977914i	$0.432977\pi$
$348$		0			0
$349$	−5.08270	−	3.35506i	−0.272071	−	0.179592i	0.407494	−	0.913208i	$-0.366403\pi$
$349$	−5.08270	−	3.35506i	−0.272071	−	0.179592i	−0.679565	+	0.733616i	$0.737831\pi$
$350$	−1.27007	+	3.90888i	−0.0678883	+	0.208939i
$351$		0			0
$352$	3.08574	−	17.0038i	0.164471	−	0.906307i
$353$	0.437072	−	1.02258i	0.0232630	−	0.0544265i	−0.907493	−	0.420066i	$-0.862007\pi$
$353$	0.437072	−	1.02258i	0.0232630	−	0.0544265i	0.930757	+	0.365640i	$0.119150\pi$
$354$		0			0
$355$	5.37641	−	1.03674i	0.285350	−	0.0550244i
$356$			4.70246i			0.249230i
$357$		0			0
$358$	−6.14737	−	1.11558i	−0.324899	−	0.0589604i
$359$	−17.2569	+	16.4993i	−0.910786	+	0.870800i	−0.992044	−	0.125893i	$-0.959821\pi$
$359$	−17.2569	+	16.4993i	−0.910786	+	0.870800i	0.0812580	+	0.996693i	$0.474106\pi$
$360$		0			0
$361$	2.44138	−	3.69854i	0.128494	−	0.194660i
$362$	3.80529	−	3.32458i	0.200002	−	0.174736i
$363$		0			0
$364$	−2.77587	−	1.04180i	−0.145495	−	0.0546053i
$365$	−0.382885	+	0.438247i	−0.0200411	+	0.0229389i
$366$		0			0
$367$	4.32139	+	6.54663i	0.225575	+	0.341731i	0.929682	−	0.368362i	$-0.120081\pi$
$367$	4.32139	+	6.54663i	0.225575	+	0.341731i	−0.704108	+	0.710093i	$0.748653\pi$
$368$	−0.642450	−	0.177305i	−0.0334900	−	0.00924266i
$369$		0			0
$370$	−2.87028	+	5.33387i	−0.149219	+	0.277295i
$371$	7.27309	+	0.326635i	0.377600	+	0.0169580i
$372$		0			0
$373$	−17.1411	+	17.9282i	−0.887533	+	0.928286i	−0.997845	−	0.0656106i	$-0.979100\pi$
$373$	−17.1411	+	17.9282i	−0.887533	+	0.928286i	0.110313	+	0.993897i	$0.464815\pi$
$374$	14.8688	−	8.00125i	0.768848	−	0.413735i
$375$		0			0
$376$	−8.94331	−	14.9686i	−0.461216	−	0.771946i
$377$	−0.505998	+	3.73543i	−0.0260602	+	0.192384i
$378$		0			0
$379$	7.13825	−	1.29540i	0.366667	−	0.0665403i	0.00790378	−	0.999969i	$-0.497484\pi$
$379$	7.13825	−	1.29540i	0.366667	−	0.0665403i	0.358764	+	0.933428i	$0.383198\pi$
$380$	1.96639	−	2.70651i	0.100874	−	0.138841i
$381$		0			0
$382$	1.42149	+	0.849298i	0.0727295	+	0.0434539i
$383$	1.08209	+	0.0973900i	0.0552923	+	0.00497640i	0.117251	−	0.993102i	$-0.462592\pi$
$383$	1.08209	+	0.0973900i	0.0552923	+	0.00497640i	−0.0619586	+	0.998079i	$0.519735\pi$
$384$		0			0
$385$	−1.33810	−	1.67792i	−0.0681956	−	0.0855146i
$386$	0.474748	+	10.5711i	0.0241640	+	0.538054i
$387$		0			0
$388$	−1.41052	−	15.6721i	−0.0716082	−	0.795632i
$389$	−1.80315	−	7.90013i	−0.0914235	−	0.400552i	0.908423	−	0.418051i	$-0.137287\pi$
$389$	−1.80315	−	7.90013i	−0.0914235	−	0.400552i	−0.999847	+	0.0174989i	$0.994430\pi$
$390$		0			0
$391$	−3.57156	−	8.35608i	−0.180621	−	0.422585i
$392$	−15.1807	+	3.46491i	−0.766743	+	0.175004i
$393$		0			0
$394$	1.80852	−	3.75543i	0.0911119	−	0.189196i
$395$	−7.55270	+	0.339192i	−0.380018	+	0.0170666i
$396$		0			0
$397$	−15.5357	+	2.10445i	−0.779714	+	0.105619i	−0.513266	−	0.858230i	$-0.671564\pi$
$397$	−15.5357	+	2.10445i	−0.779714	+	0.105619i	−0.266448	+	0.963849i	$0.585850\pi$
$398$	−1.26182	+	14.0200i	−0.0632494	+	0.702758i
$399$		0			0
$400$	1.47555	−	1.85028i	0.0737773	−	0.0925138i
$401$	12.1601	+	8.83483i	0.607247	+	0.441190i	0.848444	−	0.529286i	$-0.177540\pi$
$401$	12.1601	+	8.83483i	0.607247	+	0.441190i	−0.241197	+	0.970476i	$0.577540\pi$
$402$		0			0
$403$	−0.102683	+	0.449884i	−0.00511501	+	0.0224103i
$404$	−0.975568	−	0.132150i	−0.0485363	−	0.00657469i
$405$		0			0
$406$	−0.743268	−	1.54341i	−0.0368877	−	0.0765982i
$407$	16.2481	+	30.1941i	0.805391	+	1.49667i
$408$		0			0
$409$	26.8231	−	19.4881i	1.32632	−	0.963624i	0.326485	−	0.945202i	$-0.394136\pi$
$409$	26.8231	−	19.4881i	1.32632	−	0.963624i	0.999830	−	0.0184220i	$-0.00586423\pi$
$410$	−0.114777	+	2.55571i	−0.00566844	+	0.126218i
$411$		0			0
$412$	5.66893	+	17.4472i	0.279288	+	0.859561i
$413$	1.56597	−	5.67417i	0.0770564	−	0.279208i
$414$		0			0
$415$	−3.10615	+	0.857244i	−0.152475	+	0.0420804i
$416$	−8.66187	−	7.56765i	−0.424683	−	0.371035i
$417$		0			0
$418$	3.21251	+	8.55971i	0.157129	+	0.418669i
$419$	−18.9044	−	21.6378i	−0.923540	−	1.05708i	−0.998206	−	0.0598679i	$-0.980932\pi$
$419$	−18.9044	−	21.6378i	−0.923540	−	1.05708i	0.0746664	−	0.997209i	$-0.476211\pi$
$420$		0			0
$421$	−15.9054	−	5.16797i	−0.775181	−	0.251872i	−0.105400	−	0.994430i	$-0.533612\pi$
$421$	−15.9054	−	5.16797i	−0.775181	−	0.251872i	−0.669781	+	0.742558i	$0.733612\pi$
$422$	−11.8863	−	12.4321i	−0.578617	−	0.605186i
$423$		0			0
$424$	16.2598	+	6.94979i	0.789648	+	0.337512i
$425$	32.2687			1.56526
$426$		0			0
$427$	−8.94051			−0.432662
$428$	10.1764	+	4.34961i	0.491896	+	0.210246i
$429$		0			0
$430$	−0.781506	−	0.817392i	−0.0376876	−	0.0394181i
$431$	−5.56823	−	1.80923i	−0.268212	−	0.0871475i	0.171823	−	0.985128i	$-0.445034\pi$
$431$	−5.56823	−	1.80923i	−0.268212	−	0.0871475i	−0.440036	+	0.897980i	$0.645034\pi$
$432$		0			0
$433$	8.45252	+	9.67468i	0.406202	+	0.464936i	0.919394	−	0.393338i	$-0.128680\pi$
$433$	8.45252	+	9.67468i	0.406202	+	0.464936i	−0.513192	+	0.858274i	$0.671537\pi$
$434$	−0.0736855	−	0.196334i	−0.00353702	−	0.00942435i
$435$		0			0
$436$	−11.2418	−	9.82163i	−0.538383	−	0.470371i
$437$	4.74321	−	1.30904i	0.226898	−	0.0626200i
$438$		0			0
$439$	−7.37640	+	26.7278i	−0.352056	+	1.27565i	0.546748	+	0.837297i	$0.315865\pi$
$439$	−7.37640	+	26.7278i	−0.352056	+	1.27565i	−0.898804	+	0.438350i	$0.855563\pi$
$440$	−1.61077	−	4.95745i	−0.0767907	−	0.236337i
$441$		0			0
$442$	0.504195	−	11.2268i	0.0239821	−	0.534003i
$443$	−13.9237	+	10.1161i	−0.661533	+	0.480632i	−0.867180	−	0.497994i	$-0.834070\pi$
$443$	−13.9237	+	10.1161i	−0.661533	+	0.480632i	0.205647	+	0.978626i	$0.434070\pi$
$444$		0			0
$445$	1.07354	+	1.99497i	0.0508907	+	0.0945708i
$446$	−2.17957	−	4.52592i	−0.103206	−	0.214309i
$447$		0			0
$448$	4.03978	+	0.547225i	0.190861	+	0.0258539i
$449$	3.19496	−	13.9980i	0.150779	−	0.660608i	−0.841880	−	0.539665i	$-0.818551\pi$
$449$	3.19496	−	13.9980i	0.150779	−	0.660608i	0.992659	−	0.120943i	$-0.0385918\pi$
$450$		0			0
$451$	11.7162	+	8.51232i	0.551695	+	0.400830i
$452$	−5.90762	+	7.40792i	−0.277871	+	0.348439i
$453$		0			0
$454$	−0.165465	+	1.83846i	−0.00776564	+	0.0862833i
$455$	−1.41547	+	0.191739i	−0.0663585	+	0.00898887i
$456$		0			0
$457$	33.9184	−	1.52328i	1.58664	−	0.0712559i	0.766051	−	0.642780i	$-0.222219\pi$
$457$	33.9184	−	1.52328i	1.58664	−	0.0712559i	0.820585	+	0.571524i	$0.193648\pi$
$458$	5.35338	−	11.1164i	0.250147	−	0.519436i
$459$		0			0
$460$	−1.10160	+	0.251434i	−0.0513626	+	0.0117232i
$461$	−15.3094	−	35.8181i	−0.713030	−	1.66822i	−0.743548	−	0.668682i	$-0.766859\pi$
$461$	−15.3094	−	35.8181i	−0.713030	−	1.66822i	0.0305186	−	0.999534i	$-0.490284\pi$
$462$		0			0
$463$	2.67029	+	11.6993i	0.124099	+	0.543713i	0.998307	+	0.0581617i	$0.0185239\pi$
$463$	2.67029	+	11.6993i	0.124099	+	0.543713i	−0.874208	+	0.485551i	$0.838619\pi$
$464$	0.0884193	+	0.982419i	0.00410476	+	0.0456077i
$465$		0			0
$466$	−1.05740	−	23.5447i	−0.0489829	−	1.09069i
$467$	−17.2326	−	21.6091i	−0.797432	−	0.999948i	−0.999787	−	0.0206356i	$-0.993431\pi$
$467$	−17.2326	−	21.6091i	−0.797432	−	0.999948i	0.202355	−	0.979312i	$-0.435140\pi$
$468$		0			0
$469$	12.8500	+	1.15652i	0.593358	+	0.0534032i
$470$	−2.90455	−	1.73539i	−0.133977	−	0.0800476i
$471$		0			0
$472$	8.40340	−	11.5663i	0.386798	−	0.532382i
$473$	−6.29882	+	1.14307i	−0.289620	+	0.0525583i
$474$		0			0
$475$	−2.34540	+	17.3144i	−0.107614	+	0.794440i
$476$	−5.42582	−	9.08129i	−0.248692	−	0.416240i
$477$		0			0
$478$	12.1254	−	6.52494i	0.554602	−	0.298444i
$479$	2.04910	−	2.14319i	0.0936260	−	0.0979251i	−0.674322	−	0.738438i	$-0.735564\pi$
$479$	2.04910	−	2.14319i	0.0936260	−	0.0979251i	0.767948	+	0.640513i	$0.221278\pi$
$480$		0			0
$481$	22.7982	+	1.02387i	1.03951	+	0.0466844i
$482$	2.05185	−	3.81297i	0.0934591	−	0.173676i
$483$		0			0
$484$	2.84578	+	0.785386i	0.129354	+	0.0356994i
$485$	−4.17624	−	6.32674i	−0.189633	−	0.287282i
$486$		0			0
$487$	−27.8288	+	31.8526i	−1.26104	+	1.44338i	−0.415394	+	0.909642i	$0.636356\pi$
$487$	−27.8288	+	31.8526i	−1.26104	+	1.44338i	−0.845650	+	0.533738i	$0.820787\pi$
$488$	−20.3302	−	7.63006i	−0.920306	−	0.345396i
$489$		0			0
$490$	−2.27539	+	1.98795i	−0.102792	+	0.0898062i
$491$	−13.9385	+	21.1159i	−0.629034	+	0.952946i	0.370673	+	0.928763i	$0.379127\pi$
$491$	−13.9385	+	21.1159i	−0.629034	+	0.952946i	−0.999708	+	0.0241827i	$0.992302\pi$
$492$		0			0
$493$	−9.72125	+	9.29447i	−0.437823	+	0.418602i
$494$	5.98730	+	1.08653i	0.269381	+	0.0488855i
$495$		0			0
$496$			0.120750i			0.00542185i
$497$	8.81291	+	3.19766i	0.395313	+	0.143435i
$498$		0			0
$499$	−11.2497	+	26.3201i	−0.503607	+	1.17825i	0.454217	+	0.890891i	$0.349919\pi$
$499$	−11.2497	+	26.3201i	−0.503607	+	1.17825i	−0.957824	+	0.287356i	$0.907224\pi$
$500$	1.49895	−	8.25988i	0.0670349	−	0.369393i
$501$		0			0
$502$	−1.82472	+	5.61592i	−0.0814413	+	0.250651i
$503$	15.3000	+	10.0995i	0.682194	+	0.450312i	0.843882	−	0.536530i	$-0.180265\pi$
$503$	15.3000	+	10.0995i	0.682194	+	0.450312i	−0.161687	+	0.986842i	$0.551694\pi$
$504$		0			0
$505$	−0.444044	+	0.166653i	−0.0197597	+	0.00741594i
$506$	1.08504	−	2.89108i	0.0482360	−	0.128524i
$507$		0			0
$508$	0.946921	+	3.43109i	0.0420128	+	0.152230i
$509$	31.5009	−	20.7936i	1.39625	−	0.921659i	0.396260	−	0.918138i	$-0.370308\pi$
$509$	31.5009	−	20.7936i	1.39625	−	0.921659i	0.999994	−	0.00352122i	$-0.00112084\pi$
$510$		0			0
$511$	−0.947644	+	0.307908i	−0.0419213	+	0.0136211i
$512$	−5.11088	−	2.75028i	−0.225871	−	0.121547i
$513$		0			0
$514$	−3.35460	−	4.61721i	−0.147965	−	0.203657i
$515$	6.38807	+	6.10762i	0.281492	+	0.269134i
$516$		0			0
$517$	−17.2566	+	8.31033i	−0.758944	+	0.365488i
$518$	−8.90299	+	5.31929i	−0.391175	+	0.233716i
$519$		0			0
$520$	−3.38234	−	0.771998i	−0.148326	−	0.0338543i
$521$	−1.68777	−	9.30037i	−0.0739425	−	0.407457i	−0.999578	−	0.0290409i	$-0.990755\pi$
$521$	−1.68777	−	9.30037i	−0.0739425	−	0.407457i	0.925636	−	0.378416i	$-0.123531\pi$
$522$		0			0
$523$	31.5122	+	25.1301i	1.37793	+	1.09886i	0.983693	+	0.179855i	$0.0575628\pi$
$523$	31.5122	+	25.1301i	1.37793	+	1.09886i	0.394238	+	0.919008i	$0.371009\pi$
$524$	−9.79402	+	16.3924i	−0.427854	+	0.716107i
$525$		0			0
$526$	2.53238	+	18.6948i	0.110417	+	0.815131i
$527$	−1.28724	+	1.02654i	−0.0560731	+	0.0447168i
$528$		0			0
$529$	19.2249	+	9.25824i	0.835867	+	0.402532i
$530$	3.41742	−	0.307573i	0.148443	−	0.0133601i
$531$		0			0
$532$	5.26711	−	2.25127i	0.228358	−	0.0976049i
$533$	8.86313	−	3.78828i	0.383905	−	0.164089i
$534$		0			0
$535$	5.31024	−	0.477930i	0.229582	−	0.0206627i
$536$	28.2332	+	13.5964i	1.21949	+	0.587274i
$537$		0			0
$538$	−17.4081	+	13.8825i	−0.750515	+	0.598516i
$539$	2.29593	+	16.9493i	0.0988929	+	0.730056i
$540$		0			0
$541$	0.295829	−	0.495134i	0.0127187	−	0.0212875i	−0.852023	−	0.523504i	$-0.824625\pi$
$541$	0.295829	−	0.495134i	0.0127187	−	0.0212875i	0.864742	+	0.502216i	$0.167482\pi$
$542$	−5.44307	−	4.34070i	−0.233800	−	0.186449i
$543$		0			0
$544$	−7.32775	−	40.3792i	−0.314174	−	1.73124i
$545$	−7.01142	−	1.60031i	−0.300336	−	0.0685498i
$546$		0			0
$547$	−8.79890	+	5.25710i	−0.376214	+	0.224777i	−0.688541	−	0.725197i	$-0.741749\pi$
$547$	−8.79890	+	5.25710i	−0.376214	+	0.224777i	0.312327	+	0.949975i	$0.398891\pi$
$548$	−21.7683	+	10.4831i	−0.929896	+	0.447814i
$549$		0			0
$550$	7.92565	+	7.57770i	0.337951	+	0.323114i
$551$	−4.28056	−	5.89168i	−0.182358	−	0.250994i
$552$		0			0
$553$	−11.3991	−	6.13414i	−0.484740	−	0.260850i
$554$	−10.4518	+	3.39600i	−0.444055	+	0.144282i
$555$		0			0
$556$	14.3075	−	9.44430i	0.606773	−	0.400527i
$557$	5.96208	+	21.6031i	0.252621	+	0.915353i	0.974695	+	0.223537i	$0.0717603\pi$
$557$	5.96208	+	21.6031i	0.252621	+	0.915353i	−0.722074	+	0.691816i	$0.756811\pi$
$558$		0			0
$559$	−1.49713	+	3.98908i	−0.0633217	+	0.168720i
$560$	−0.349941	+	0.131335i	−0.0147877	+	0.00554992i
$561$		0			0
$562$	4.68993	+	3.09580i	0.197833	+	0.130588i
$563$	11.6674	−	35.9084i	0.491720	−	1.51336i	−0.330286	−	0.943881i	$-0.607145\pi$
$563$	11.6674	−	35.9084i	0.491720	−	1.51336i	0.822006	−	0.569479i	$-0.192855\pi$
$564$		0			0
$565$	−0.815071	+	4.49141i	−0.0342903	+	0.188955i
$566$	1.36239	−	3.18747i	0.0572655	−	0.133979i
$567$		0			0
$568$	17.3111	+	14.7925i	0.726357	+	0.620678i
$569$		−	10.6324i		−	0.445734i	−0.974849	−	0.222867i	$-0.928458\pi$
$569$		−	10.6324i		−	0.445734i	0.974849	−	0.222867i	$-0.0715415\pi$
$570$		0			0
$571$	−3.11372	−	0.565056i	−0.130305	−	0.0236469i	0.113013	−	0.993594i	$-0.463950\pi$
$571$	−3.11372	−	0.565056i	−0.130305	−	0.0236469i	−0.243318	+	0.969947i	$0.578236\pi$
$572$	−5.71746	+	5.46646i	−0.239059	+	0.228564i
$573$		0			0
$574$	−2.41310	+	3.65569i	−0.100721	+	0.152586i
$575$	4.44420	−	3.88278i	0.185336	−	0.161923i
$576$		0			0
$577$	−0.859229	−	0.322474i	−0.0357702	−	0.0134248i	0.333426	−	0.942776i	$-0.391795\pi$
$577$	−0.859229	−	0.322474i	−0.0357702	−	0.0134248i	−0.369196	+	0.929352i	$0.620367\pi$
$578$	17.3555	−	19.8650i	0.721896	−	0.826276i
$579$		0			0
$580$	0.921283	+	1.39568i	0.0382542	+	0.0579527i
$581$	−5.31837	−	1.46778i	−0.220643	−	0.0608936i
$582$		0			0
$583$	9.20424	−	17.1043i	0.381201	−	0.708390i
$584$	−2.41766	−	0.108577i	−0.100044	−	0.00449297i
$585$		0			0
$586$	−2.63845	+	2.75960i	−0.108993	+	0.113998i
$587$	41.0859	−	22.1093i	1.69580	−	0.912547i	0.719969	−	0.694007i	$-0.244156\pi$
$587$	41.0859	−	22.1093i	1.69580	−	0.912547i	0.975828	−	0.218540i	$-0.0701295\pi$
$588$		0			0
$589$	−0.457249	−	0.765306i	−0.0188406	−	0.0315339i
$590$	0.372388	−	2.74908i	0.0153310	−	0.113178i
$591$		0			0
$592$	5.87574	−	1.06629i	0.241491	−	0.0438242i
$593$	13.0364	−	17.9431i	0.535343	−	0.736836i	−0.452590	−	0.891719i	$-0.649500\pi$
$593$	13.0364	−	17.9431i	0.535343	−	0.736836i	0.987933	+	0.154883i	$0.0495000\pi$
$594$		0			0
$595$	−4.37505	−	2.61397i	−0.179360	−	0.107162i
$596$	15.8238	+	1.42417i	0.648170	+	0.0583363i
$597$		0			0
$598$	−1.28144	−	1.60687i	−0.0524019	−	0.0657099i
$599$	0.992603	+	22.1020i	0.0405566	+	0.903064i	0.911405	+	0.411511i	$0.134999\pi$
$599$	0.992603	+	22.1020i	0.0405566	+	0.903064i	−0.870848	+	0.491552i	$0.836430\pi$
$600$		0			0
$601$	−3.36503	−	37.3886i	−0.137262	−	1.52511i	−0.709314	−	0.704893i	$-0.750995\pi$
$601$	−3.36503	−	37.3886i	−0.137262	−	1.52511i	0.572051	−	0.820218i	$-0.306148\pi$
$602$	−0.430865	−	1.88774i	−0.0175608	−	0.0769387i
$603$		0			0
$604$	8.11208	+	18.9791i	0.330076	+	0.772250i
$605$	1.38659	−	0.316481i	0.0563731	−	0.0128668i
$606$		0			0
$607$	5.42435	−	11.2638i	0.220168	−	0.457183i	−0.761404	−	0.648278i	$-0.775490\pi$
$607$	5.42435	−	11.2638i	0.220168	−	0.457183i	0.981572	+	0.191095i	$0.0612038\pi$
$608$	22.1988	−	0.996951i	0.900282	−	0.0404317i
$609$		0			0
$610$	−4.17549	+	0.565608i	−0.169061	+	0.0229008i
$611$	−1.14271	+	12.6966i	−0.0462291	+	0.513648i
$612$		0			0
$613$	−19.0954	+	23.9448i	−0.771254	+	0.967122i	−0.999980	−	0.00636857i	$-0.997973\pi$
$613$	−19.0954	+	23.9448i	−0.771254	+	0.967122i	0.228725	+	0.973491i	$0.426544\pi$
$614$	−16.4303	−	11.9373i	−0.663073	−	0.481751i
$615$		0			0
$616$	1.98600	−	8.70123i	0.0800181	−	0.350582i
$617$	2.59069	+	0.350933i	0.104297	+	0.0141280i	0.186196	−	0.982513i	$-0.440384\pi$
$617$	2.59069	+	0.350933i	0.104297	+	0.0141280i	−0.0818986	+	0.996641i	$0.526098\pi$
$618$		0			0
$619$	−2.02629	−	4.20763i	−0.0814434	−	0.169119i	0.856270	−	0.516528i	$-0.172776\pi$
$619$	−2.02629	−	4.20763i	−0.0814434	−	0.169119i	−0.937714	+	0.347409i	$0.887062\pi$
$620$	0.0970108	+	0.180276i	0.00389605	+	0.00724007i
$621$		0			0
$622$	7.16231	−	5.20372i	0.287183	−	0.208650i
$623$	−0.174029	+	3.87506i	−0.00697233	+	0.155251i
$624$		0			0
$625$	5.82323	+	17.9221i	0.232929	+	0.716883i
$626$	−3.83155	+	13.8833i	−0.153140	+	0.554889i
$627$		0			0
$628$	−5.85760	+	1.61660i	−0.233744	+	0.0645092i
$629$	61.3187	+	53.5725i	2.44494	+	2.13608i
$630$		0			0
$631$	4.03450	+	10.7499i	0.160611	+	0.427947i	0.991761	−	0.128102i	$-0.0408884\pi$
$631$	4.03450	+	10.7499i	0.160611	+	0.427947i	−0.831150	+	0.556048i	$0.812317\pi$
$632$	−20.6860	−	23.6770i	−0.822843	−	0.941820i
$633$		0			0
$634$	−23.3335	−	7.58152i	−0.926692	−	0.301101i
$635$	1.18502	+	1.23943i	0.0470260	+	0.0491853i
$636$		0			0
$637$	10.4678	+	4.47417i	0.414751	+	0.177273i
$638$	−4.57031			−0.180940
$639$		0			0
$640$	−5.64499			−0.223138
$641$	8.41935	+	3.59860i	0.332544	+	0.142136i	0.552818	−	0.833302i	$-0.313552\pi$
$641$	8.41935	+	3.59860i	0.332544	+	0.142136i	−0.220274	+	0.975438i	$0.570695\pi$
$642$		0			0
$643$	33.6143	+	35.1578i	1.32562	+	1.38649i	0.867371	+	0.497662i	$0.165808\pi$
$643$	33.6143	+	35.1578i	1.32562	+	1.38649i	0.458247	+	0.888825i	$0.348478\pi$
$644$	−1.83999	−	0.597849i	−0.0725057	−	0.0235585i
$645$		0			0
$646$	14.2847	+	16.3501i	0.562023	+	0.643287i
$647$	−1.76734	−	4.70907i	−0.0694815	−	0.185133i	0.896907	−	0.442220i	$-0.145809\pi$
$647$	−1.76734	−	4.70907i	−0.0694815	−	0.185133i	−0.966388	+	0.257087i	$0.917237\pi$
$648$		0			0
$649$	−11.8264	−	10.3324i	−0.464226	−	0.405582i
$650$	7.03514	−	1.94158i	0.275941	−	0.0761549i
$651$		0			0
$652$	5.73379	−	20.7759i	0.224553	−	0.813648i
$653$	−4.66741	−	14.3648i	−0.182650	−	0.562139i	0.817250	−	0.576283i	$-0.195498\pi$
$653$	−4.66741	−	14.3648i	−0.182650	−	0.562139i	−0.999900	+	0.0141444i	$0.995498\pi$
$654$		0			0
$655$	−0.412734	+	9.19024i	−0.0161269	+	0.359093i
$656$	2.04051	−	1.48252i	0.0796686	−	0.0578827i
$657$		0			0
$658$	−2.74523	−	5.10149i	−0.107020	−	0.198877i
$659$	9.02957	+	18.7501i	0.351742	+	0.730400i	0.999506	−	0.0314415i	$-0.0100098\pi$
$659$	9.02957	+	18.7501i	0.351742	+	0.730400i	−0.647764	+	0.761841i	$0.724296\pi$
$660$		0			0
$661$	35.1421	+	4.76032i	1.36687	+	0.185155i	0.780636	−	0.624986i	$-0.214896\pi$
$661$	35.1421	+	4.76032i	1.36687	+	0.185155i	0.586234	+	0.810142i	$0.300610\pi$
$662$	3.32387	−	14.5628i	0.129186	−	0.566001i
$663$		0			0
$664$	−10.8410	−	7.87647i	−0.420714	−	0.305666i
$665$	1.72057	−	2.15753i	0.0667208	−	0.0836653i
$666$		0			0
$667$	−0.220486	+	2.44980i	−0.00853726	+	0.0948567i
$668$	9.63333	−	1.30492i	0.372725	−	0.0504890i
$669$		0			0
$670$	6.07451	−	0.272806i	0.234679	−	0.0105394i
$671$	−10.3493	+	21.4905i	−0.399529	+	0.829630i
$672$		0			0
$673$	32.4118	−	7.39779i	1.24938	−	0.285164i	0.453853	−	0.891077i	$-0.350049\pi$
$673$	32.4118	−	7.39779i	1.24938	−	0.285164i	0.795531	+	0.605913i	$0.207192\pi$
$674$	−6.11914	−	14.3164i	−0.235701	−	0.551449i
$675$		0			0
$676$	−2.73032	−	11.9623i	−0.105012	−	0.460088i
$677$	3.16647	+	35.1823i	0.121697	+	1.35217i	0.792201	+	0.610261i	$0.208935\pi$
$677$	3.16647	+	35.1823i	0.121697	+	1.35217i	−0.670503	+	0.741907i	$0.733922\pi$
$678$		0			0
$679$	−0.582341	−	12.9668i	−0.0223482	−	0.497621i
$680$	−7.71778	−	9.67780i	−0.295964	−	0.371127i
$681$		0			0
$682$	−0.557228	−	0.0501514i	−0.0213374	−	0.00192040i
$683$	41.3536	+	24.7076i	1.58235	+	0.945412i	0.990211	+	0.139578i	$0.0445745\pi$
$683$	41.3536	+	24.7076i	1.58235	+	0.945412i	0.592142	+	0.805834i	$0.298283\pi$
$684$		0			0
$685$	−6.84178	+	9.41690i	−0.261411	+	0.359801i
$686$	−11.2741	+	2.04594i	−0.430446	+	0.0781145i
$687$		0			0
$688$	−0.149661	+	1.10484i	−0.00570576	+	0.0421216i
$689$	−6.63063	−	11.0978i	−0.252607	−	0.422793i
$690$		0			0
$691$	1.66835	−	0.897780i	0.0634672	−	0.0341531i	−0.441827	−	0.897100i	$-0.645670\pi$
$691$	1.66835	−	0.897780i	0.0634672	−	0.0341531i	0.505294	+	0.862947i	$0.331384\pi$
$692$	−11.7216	+	12.2598i	−0.445589	+	0.466049i
$693$		0			0
$694$	−4.44303	−	0.199537i	−0.168655	−	0.00757431i
$695$	3.91375	−	7.27296i	0.148457	−	0.275879i
$696$		0			0
$697$	33.1513	+	9.14918i	1.25569	+	0.346550i
$698$	−2.70738	−	4.10151i	−0.102476	−	0.155244i
$699$		0			0
$700$	4.52000	−	5.17356i	0.170840	−	0.195542i
$701$	−38.8030	−	14.5630i	−1.46557	−	0.550037i	−0.514085	−	0.857739i	$-0.671868\pi$
$701$	−38.8030	−	14.5630i	−1.46557	−	0.550037i	−0.951483	+	0.307702i	$0.900440\pi$
$702$		0			0
$703$	−33.2022	+	29.0079i	−1.25225	+	1.09405i
$704$	5.99169	−	9.07702i	0.225820	−	0.342103i
$705$		0			0
$706$	0.648630	−	0.620154i	0.0244115	−	0.0233398i
$707$	−0.799026	−	0.145002i	−0.0300505	−	0.00545335i
$708$		0			0
$709$		−	7.57783i		−	0.284592i	−0.989824	−	0.142296i	$-0.954552\pi$
$709$		−	7.57783i		−	0.284592i	0.989824	−	0.142296i	$-0.0454484\pi$
$710$	4.31819	+	0.935868i	0.162059	+	0.0351225i
$711$		0			0
$712$	−3.70281	+	8.66315i	−0.138769	+	0.324665i
$713$	−0.0537649	+	0.296269i	−0.00201351	+	0.0110954i
$714$		0			0
$715$	−1.17762	+	3.62435i	−0.0440406	+	0.135543i
$716$	8.71558	+	5.75311i	0.325717	+	0.215004i
$717$		0			0
$718$	−18.0377	+	6.76968i	−0.673163	+	0.252642i
$719$	15.7529	−	41.9735i	0.587485	−	1.56535i	−0.220026	−	0.975494i	$-0.570614\pi$
$719$	15.7529	−	41.9735i	0.587485	−	1.56535i	0.807511	−	0.589853i	$-0.200814\pi$
$720$		0			0
$721$	4.02580	+	14.5871i	0.149928	+	0.543254i
$722$	2.98455	−	1.97008i	0.111073	−	0.0733190i
$723$		0			0
$724$	−8.03275	+	2.61000i	−0.298535	+	0.0969999i
$725$	−7.69137	−	4.13890i	−0.285650	−	0.153715i
$726$		0			0
$727$	18.6666	+	25.6923i	0.692305	+	0.952876i	0.999999	+	0.00139100i	$0.000442771\pi$
$727$	18.6666	+	25.6923i	0.692305	+	0.952876i	−0.307694	+	0.951485i	$0.599557\pi$
$728$	−4.29354	−	4.10505i	−0.159129	−	0.152143i
$729$		0			0
$730$	−0.423099	+	0.203754i	−0.0156596	+	0.00754126i
$731$	−13.0503	+	7.79719i	−0.482683	+	0.288390i
$732$		0			0
$733$	−8.13980	−	1.85786i	−0.300651	−	0.0686215i	0.0695346	−	0.997580i	$-0.477849\pi$
$733$	−8.13980	−	1.85786i	−0.300651	−	0.0686215i	−0.370185	+	0.928958i	$0.620706\pi$
$734$	1.13026	+	6.22826i	0.0417187	+	0.229889i
$735$		0			0
$736$	−5.86790	−	4.67949i	−0.216294	−	0.172488i
$737$	17.6547	−	29.5490i	0.650320	−	1.08845i
$738$		0			0
$739$	−1.28900	−	9.51580i	−0.0474168	−	0.350045i	−0.999079	−	0.0428993i	$-0.986341\pi$
$739$	−1.28900	−	9.51580i	−0.0474168	−	0.350045i	0.951663	−	0.307145i	$-0.0993737\pi$
$740$	7.91563	−	6.31251i	0.290984	−	0.232052i
$741$		0			0
$742$	5.29316	+	2.54905i	0.194318	+	0.0935787i
$743$	−1.43196	+	0.128878i	−0.0525334	+	0.00472809i	−0.115875	−	0.993264i	$-0.536967\pi$
$743$	−1.43196	+	0.128878i	−0.0525334	+	0.00472809i	0.0633414	+	0.997992i	$0.479824\pi$
$744$		0			0
$745$	7.03824	−	3.00829i	0.257861	−	0.110215i
$746$	−18.4050	+	7.86666i	−0.673854	+	0.288019i
$747$		0			0
$748$	−28.1096	+	2.52991i	−1.02779	+	0.0925027i
$749$	8.22491	+	3.96091i	0.300532	+	0.144728i
$750$		0			0
$751$	0.865830	−	0.690476i	0.0315946	−	0.0251958i	−0.607565	−	0.794270i	$-0.707854\pi$
$751$	0.865830	−	0.690476i	0.0315946	−	0.0251958i	0.639160	+	0.769074i	$0.279282\pi$
$752$	0.447773	+	3.30559i	0.0163286	+	0.120543i
$753$		0			0
$754$	−1.56016	+	2.61127i	−0.0568178	+	0.0950970i
$755$	7.77428	+	6.19978i	0.282935	+	0.225633i
$756$		0			0
$757$	−2.47669	−	13.6477i	−0.0900170	−	0.496035i	−0.997167	−	0.0752261i	$-0.976032\pi$
$757$	−2.47669	−	13.6477i	−0.0900170	−	0.496035i	0.907150	−	0.420808i	$-0.138254\pi$
$758$	5.70754	+	1.30271i	0.207307	+	0.0473166i
$759$		0			0
$760$	5.75376	−	3.43771i	0.208711	−	0.124699i
$761$	−22.1845	+	10.6835i	−0.804188	+	0.387276i	−0.790371	−	0.612628i	$-0.790112\pi$
$761$	−22.1845	+	10.6835i	−0.804188	+	0.387276i	−0.0138166	+	0.999905i	$0.504398\pi$
$762$		0			0
$763$	−8.90029	−	8.50955i	−0.322212	−	0.308066i
$764$	−1.62687	−	2.23920i	−0.0588582	−	0.0810113i
$765$		0			0
$766$	0.772043	+	0.415454i	0.0278950	+	0.0150110i
$767$	−9.94064	+	3.22991i	−0.358936	+	0.116625i
$768$		0			0
$769$	34.8037	−	22.9737i	1.25505	−	0.828454i	0.264342	−	0.964429i	$-0.414845\pi$
$769$	34.8037	−	22.9737i	1.25505	−	0.828454i	0.990712	+	0.135975i	$0.0434166\pi$
$770$	−0.460732	−	1.66942i	−0.0166036	−	0.0601619i
$771$		0			0
$772$	6.21490	−	16.5596i	0.223679	−	0.595991i
$773$	−15.6527	+	5.87457i	−0.562990	+	0.211294i	−0.616611	−	0.787268i	$-0.711495\pi$
$773$	−15.6527	+	5.87457i	−0.562990	+	0.211294i	0.0536214	+	0.998561i	$0.482924\pi$
$774$		0			0
$775$	−0.892342	−	0.589029i	−0.0320539	−	0.0211586i
$776$	9.74200	−	29.9828i	0.349717	−	1.07632i
$777$		0			0
$778$	1.16758	−	6.43390i	0.0418598	−	0.230667i
$779$	−7.31871	+	17.1230i	−0.262220	+	0.613494i
$780$		0			0
$781$	17.8878	−	17.4822i	0.640076	−	0.625563i
$782$		−	7.33308i		−	0.262230i
$783$		0			0
$784$	2.93100	+	0.531898i	0.104679	+	0.0189963i
$785$	−2.11597	+	2.02308i	−0.0755223	+	0.0722067i
$786$		0			0
$787$	17.7511	−	26.8918i	0.632759	−	0.958589i	−0.366840	−	0.930284i	$-0.619560\pi$
$787$	17.7511	−	26.8918i	0.632759	−	0.958589i	0.999599	−	0.0283053i	$-0.00901106\pi$
$788$	−5.24678	+	4.58397i	−0.186909	+	0.163297i
$789$		0			0
$790$	−5.71181	−	2.14368i	−0.203217	−	0.0762686i
$791$	−5.14233	+	5.88587i	−0.182840	+	0.209277i
$792$		0			0
$793$	8.74579	+	13.2493i	0.310572	+	0.470497i
$794$	−12.1952	−	3.36566i	−0.432791	−	0.119443i
$795$		0			0
$796$	11.1497	−	20.7196i	0.395191	−	0.734388i
$797$	15.1844	+	0.681933i	0.537860	+	0.0241553i	0.312139	−	0.950037i	$-0.398955\pi$
$797$	15.1844	+	0.681933i	0.537860	+	0.0241553i	0.225721	+	0.974192i	$0.427526\pi$
$798$		0			0
$799$	−31.4321	+	32.8754i	−1.11199	+	1.16305i
$800$	23.4688	−	12.6291i	0.829746	−	0.446505i
$801$		0			0
$802$	6.22101	+	10.4122i	0.219671	+	0.367668i
$803$	−0.356839	+	2.63429i	−0.0125926	+	0.0929621i
$804$		0			0
$805$	−0.917082	+	0.166426i	−0.0323229	+	0.00586574i
$806$	−0.218875	+	0.301256i	−0.00770954	+	0.0106113i
$807$		0			0
$808$	−1.69319	−	1.01163i	−0.0595662	−	0.0355892i
$809$	−19.3333	−	1.74003i	−0.679724	−	0.0611762i	−0.255603	−	0.966782i	$-0.582274\pi$
$809$	−19.3333	−	1.74003i	−0.679724	−	0.0611762i	−0.424121	+	0.905606i	$0.639417\pi$
$810$		0			0
$811$	−32.3996	−	40.6279i	−1.13771	−	1.42664i	−0.888911	−	0.458081i	$-0.848537\pi$
$811$	−32.3996	−	40.6279i	−1.13771	−	1.42664i	−0.248795	−	0.968556i	$-0.580034\pi$
$812$	0.128465	+	2.86049i	0.00450823	+	0.100384i
$813$		0			0
$814$	2.48024	+	27.5577i	0.0869323	+	0.965897i
$815$	−2.31050	−	10.1230i	−0.0809334	−	0.354592i
$816$		0			0
$817$	−3.23520	−	7.56912i	−0.113185	−	0.264810i
$818$	26.0839	−	5.95347i	0.912001	−	0.208158i
$819$		0			0
$820$	1.85536	−	3.85270i	0.0647921	−	0.134542i
$821$	−2.95611	+	0.132759i	−0.103169	+	0.00463332i	−0.0963895	−	0.995344i	$-0.530729\pi$
$821$	−2.95611	+	0.132759i	−0.103169	+	0.00463332i	−0.00677951	+	0.999977i	$0.502158\pi$
$822$		0			0
$823$	−7.53799	+	1.02109i	−0.262758	+	0.0355930i	−0.264427	−	0.964406i	$-0.585183\pi$
$823$	−7.53799	+	1.02109i	−0.262758	+	0.0355930i	0.00166941	+	0.999999i	$0.499469\pi$
$824$	−3.29460	+	36.6060i	−0.114773	+	1.27523i
$825$		0			0
$826$	2.96156	−	3.71368i	0.103046	−	0.129215i
$827$	29.0157	+	21.0811i	1.00898	+	0.733063i	0.963994	−	0.265925i	$-0.0856772\pi$
$827$	29.0157	+	21.0811i	1.00898	+	0.733063i	0.0449812	+	0.998988i	$0.485677\pi$
$828$		0			0
$829$	1.10867	−	4.85738i	0.0385055	−	0.168704i	−0.952019	−	0.306038i	$-0.900996\pi$
$829$	1.10867	−	4.85738i	0.0385055	−	0.168704i	0.990525	+	0.137335i	$0.0438536\pi$
$830$	−2.57670	−	0.349037i	−0.0894384	−	0.0121153i
$831$		0			0
$832$	−3.14083	−	6.52201i	−0.108889	−	0.226110i
$833$	19.2472	+	35.7673i	0.666877	+	1.23926i
$834$		0			0
$835$	3.78894	−	2.75283i	0.131122	−	0.0952655i
$836$	0.685625	−	15.2666i	0.0237128	−	0.528007i
$837$		0			0
$838$	−7.16487	−	22.0512i	−0.247506	−	0.761746i
$839$	−8.53118	+	30.9120i	−0.294529	+	1.06720i	0.655540	+	0.755161i	$0.272441\pi$
$839$	−8.53118	+	30.9120i	−0.294529	+	1.06720i	−0.950069	+	0.312041i	$0.898987\pi$
$840$		0			0
$841$	−24.4457	+	6.74658i	−0.842955	+	0.232641i
$842$	−10.1630	−	8.87917i	−0.350241	−	0.305996i
$843$		0			0
$844$	10.1020	+	26.9167i	0.347725	+	0.926510i
$845$	−3.88923	−	4.45158i	−0.133793	−	0.153139i
$846$		0			0
$847$	2.31600	+	0.752515i	0.0795788	+	0.0258567i
$848$	−2.33776	−	2.44510i	−0.0802790	−	0.0839652i
$849$		0			0
$850$	23.9439	+	10.2341i	0.821270	+	0.351028i
$851$	14.8913			0.510467
$852$		0			0
$853$	−18.0408			−0.617704			−0.308852	−	0.951110i	$-0.599945\pi$
$853$	−18.0408			−0.617704			−0.308852	+	0.951110i	$0.599945\pi$
$854$	−6.63401	−	2.83551i	−0.227011	−	0.0970292i
$855$		0			0
$856$	15.3226	+	16.0262i	0.523717	+	0.547765i
$857$	−26.6942	−	8.67348i	−0.911858	−	0.296281i	−0.184735	−	0.982788i	$-0.559143\pi$
$857$	−26.6942	−	8.67348i	−0.911858	−	0.296281i	−0.727122	+	0.686508i	$0.759143\pi$
$858$		0			0
$859$	−29.3259	−	33.5662i	−1.00059	−	1.14526i	−0.989384	−	0.145326i	$-0.953577\pi$
$859$	−29.3259	−	33.5662i	−1.00059	−	1.14526i	−0.0112023	−	0.999937i	$-0.503566\pi$
$860$	0.664190	+	1.76973i	0.0226487	+	0.0603472i
$861$		0			0
$862$	−3.55792	−	3.10846i	−0.121183	−	0.105875i
$863$	46.9793	−	12.9655i	1.59919	−	0.441350i	0.651010	−	0.759069i	$-0.274346\pi$
$863$	46.9793	−	12.9655i	1.59919	−	0.441350i	0.948185	+	0.317720i	$0.102917\pi$
$864$		0			0
$865$	−2.17394	+	7.87709i	−0.0739161	+	0.267829i
$866$	3.20355	+	9.85952i	0.108861	+	0.335040i
$867$		0			0
$868$	−0.0157262	+	0.350171i	−0.000533782	+	0.0118856i
$869$	−27.9400	+	20.2996i	−0.947800	+	0.688617i
$870$		0			0
$871$	−10.8562	−	20.1743i	−0.367850	−	0.683579i
$872$	−12.9765	−	26.9460i	−0.439439	−	0.912505i
$873$		0			0
$874$	3.93471	+	0.532992i	0.133093	+	0.0180287i
$875$	1.54089	−	6.75108i	0.0520916	−	0.228228i
$876$		0			0
$877$	−6.67648	−	4.85074i	−0.225449	−	0.163798i	0.469327	−	0.883024i	$-0.344496\pi$
$877$	−6.67648	−	4.85074i	−0.225449	−	0.163798i	−0.694776	+	0.719226i	$0.744496\pi$
$878$	−13.9502	+	17.4930i	−0.470797	+	0.590360i
$879$		0			0
$880$	−0.0893886	+	0.993188i	−0.00301329	+	0.0334804i
$881$	−36.0496	+	4.88325i	−1.21454	+	0.164521i	−0.713345	−	0.700813i	$-0.752821\pi$
$881$	−36.0496	+	4.88325i	−1.21454	+	0.164521i	−0.501196	+	0.865334i	$0.667106\pi$
$882$		0			0
$883$	−30.2861	+	1.36015i	−1.01921	+	0.0457727i	−0.548193	−	0.836352i	$-0.684684\pi$
$883$	−30.2861	+	1.36015i	−1.01921	+	0.0457727i	−0.471016	+	0.882125i	$0.656113\pi$
$884$	−8.15028	+	16.9242i	−0.274124	+	0.569224i
$885$		0			0
$886$	−13.5399	+	3.09040i	−0.454883	+	0.103824i
$887$	−10.7337	−	25.1127i	−0.360402	−	0.843204i	−0.997381	−	0.0723222i	$-0.976959\pi$
$887$	−10.7337	−	25.1127i	−0.360402	−	0.843204i	0.636979	−	0.770881i	$-0.280184\pi$
$888$		0			0
$889$	0.653332	+	2.86243i	0.0219120	+	0.0960029i
$890$	0.163873	+	1.82078i	0.00549304	+	0.0610327i
$891$		0			0
$892$	0.376713	+	8.38816i	0.0126133	+	0.280856i
$893$	−15.3553	−	19.2550i	−0.513847	−	0.644344i
$894$		0			0
$895$	5.01090	+	0.450989i	0.167496	+	0.0150749i
$896$	−8.29723	−	4.95736i	−0.277191	−	0.165614i
$897$		0			0
$898$	6.81023	−	9.37348i	0.227260	−	0.312797i
$899$	0.438486	−	0.0795735i	0.0146243	−	0.00265393i
$900$		0			0
$901$	6.19157	−	45.7080i	0.206271	−	1.52276i
$902$	5.99391	+	10.0321i	0.199575	+	0.334033i
$903$		0			0
$904$	−16.7165	+	8.99553i	−0.555983	+	0.299187i
$905$	−2.81197	+	2.94109i	−0.0934731	+	0.0977652i
$906$		0			0
$907$	3.81486	+	0.171325i	0.126670	+	0.00568877i	0.108110	−	0.994139i	$-0.465520\pi$
$907$	3.81486	+	0.171325i	0.126670	+	0.00568877i	0.0185606	+	0.999828i	$0.494092\pi$
$908$	1.46208	−	2.71700i	0.0485208	−	0.0901668i
$909$		0			0
$910$	−1.11112	−	0.306649i	−0.0368332	−	0.0101653i
$911$	−20.8997	−	31.6617i	−0.692437	−	1.04900i	−0.995382	−	0.0959897i	$-0.969398\pi$
$911$	−20.8997	−	31.6617i	−0.692437	−	1.04900i	0.302945	−	0.953008i	$-0.402030\pi$
$912$		0			0
$913$	−9.68450	+	11.0848i	−0.320510	+	0.366853i
$914$	25.6511	+	9.62703i	0.848464	+	0.318434i
$915$		0			0
$916$	−15.5309	+	13.5690i	−0.513157	+	0.448331i
$917$	−8.67742	+	13.1457i	−0.286554	+	0.434110i
$918$		0			0
$919$	35.0624	−	33.5231i	1.15660	−	1.10582i	0.163746	−	0.986502i	$-0.447642\pi$
$919$	35.0624	−	33.5231i	1.15660	−	1.10582i	0.992856	−	0.119322i	$-0.0380722\pi$
$920$	−2.22742	−	0.404218i	−0.0734360	−	0.0133267i
$921$		0			0
$922$		−	31.4331i		−	1.03519i
$923$	−3.88223	−	16.1882i	−0.127785	−	0.532842i
$924$		0			0
$925$	−20.7825	+	48.6230i	−0.683323	+	1.59871i
$926$	−1.72907	+	9.52797i	−0.0568208	+	0.313109i
$927$		0			0
$928$	−3.43259	+	10.5644i	−0.112680	+	0.346794i
$929$	−35.6895	−	23.5584i	−1.17093	−	0.772927i	−0.192869	−	0.981225i	$-0.561779\pi$
$929$	−35.6895	−	23.5584i	−1.17093	−	0.772927i	−0.978065	+	0.208298i	$0.933208\pi$
$930$		0			0
$931$	−20.5906	+	7.72778i	−0.674830	+	0.253268i
$932$	−13.8423	+	36.8827i	−0.453420	+	1.20813i
$933$		0			0
$934$	−5.93353	−	21.4997i	−0.194151	−	0.703491i
$935$	−11.3477	+	7.49053i	−0.371108	+	0.244966i
$936$		0			0
$937$	−23.4835	+	7.63026i	−0.767173	+	0.249270i	−0.666354	−	0.745635i	$-0.732146\pi$
$937$	−23.4835	+	7.63026i	−0.767173	+	0.249270i	−0.100819	+	0.994905i	$0.532146\pi$
$938$	9.16813	+	4.93358i	0.299350	+	0.161087i
$939$		0			0
$940$	3.32422	+	4.57540i	0.108424	+	0.149233i
$941$	−35.7270	−	34.1585i	−1.16467	−	1.11354i	−0.991695	−	0.128610i	$-0.958948\pi$
$941$	−35.7270	−	34.1585i	−1.16467	−	1.11354i	−0.172973	−	0.984927i	$-0.555337\pi$
$942$		0			0
$943$	5.66664	−	2.72891i	0.184531	−	0.0888656i
$944$	−2.34791	+	1.40281i	−0.0764181	+	0.0456577i
$945$		0			0
$946$	−5.03636	−	1.14952i	−0.163746	−	0.0373740i
$947$	4.81958	+	26.5581i	0.156615	+	0.863021i	0.962568	+	0.271041i	$0.0873679\pi$
$947$	4.81958	+	26.5581i	0.156615	+	0.863021i	−0.805953	+	0.591980i	$0.798346\pi$
$948$		0			0
$949$	1.38331	+	1.10315i	0.0449040	+	0.0358097i
$950$	−7.23164	+	12.1037i	−0.234626	+	0.392697i
$951$		0			0
$952$	−2.84498	−	21.0025i	−0.0922063	−	0.680694i
$953$	21.9240	−	17.4838i	0.710188	−	0.566356i	−0.200379	−	0.979719i	$-0.564217\pi$
$953$	21.9240	−	17.4838i	0.710188	−	0.566356i	0.910566	+	0.413363i	$0.135646\pi$
$954$		0			0
$955$	−1.20138	−	0.578554i	−0.0388757	−	0.0187216i
$956$	−22.9231	+	2.06312i	−0.741386	+	0.0667260i
$957$		0			0
$958$	2.20019	−	0.940407i	0.0710849	−	0.0303832i
$959$	−18.3261	+	7.83296i	−0.591782	+	0.252940i
$960$		0			0
$961$	−30.8209	+	2.77393i	−0.994222	+	0.0894816i
$962$	16.5919	+	7.99026i	0.534946	+	0.257616i
$963$		0			0
$964$	−5.65857	+	4.51256i	−0.182250	+	0.145340i
$965$	−1.14382	−	8.44405i	−0.0368210	−	0.271824i
$966$		0			0
$967$	−8.01607	+	13.4166i	−0.257779	+	0.431450i	−0.959791	−	0.280715i	$-0.909428\pi$
$967$	−8.01607	+	13.4166i	−0.257779	+	0.431450i	0.702012	+	0.712166i	$0.252285\pi$
$968$	4.62424	+	3.68771i	0.148629	+	0.118527i
$969$		0			0
$970$	−1.09230	−	6.01906i	−0.0350716	−	0.193260i
$971$	45.6358	+	10.4161i	1.46452	+	0.334268i	0.879169	−	0.476510i	$-0.158098\pi$
$971$	45.6358	+	10.4161i	1.46452	+	0.334268i	0.585354	+	0.810778i	$0.300955\pi$
$972$		0			0
$973$	12.1396	−	7.25308i	0.389178	−	0.232523i
$974$	−30.7516	+	14.8092i	−0.985345	+	0.474517i
$975$		0			0
$976$	3.00264	+	2.87082i	0.0961122	+	0.0918926i
$977$	4.92852	+	6.78353i	0.157677	+	0.217024i	0.880545	−	0.473962i	$-0.157177\pi$
$977$	4.92852	+	6.78353i	0.157677	+	0.217024i	−0.722868	+	0.690986i	$0.757177\pi$
$978$		0			0
$979$	9.11310	+	4.90397i	0.291256	+	0.156731i
$980$	4.80322	−	1.56066i	0.153433	−	0.0498534i
$981$		0			0
$982$	−17.0395	+	11.2477i	−0.543754	+	0.358929i
$983$	−15.5327	−	56.2813i	−0.495415	−	1.79510i	−0.599321	−	0.800509i	$-0.704563\pi$
$983$	−15.5327	−	56.2813i	−0.495415	−	1.79510i	0.103906	−	0.994587i	$-0.466866\pi$
$984$		0			0
$985$	−1.17940	+	3.14251i	−0.0375789	+	0.100129i
$986$	−10.1611	+	3.81353i	−0.323595	+	0.121447i
$987$		0			0
$988$	−8.48864	−	5.60330i	−0.270060	−	0.178265i
$989$	−0.859141	+	2.64416i	−0.0273191	+	0.0840795i
$990$		0			0
$991$	2.48888	−	13.7149i	0.0790619	−	0.435667i	−0.919983	−	0.391959i	$-0.871797\pi$
$991$	2.48888	−	13.7149i	0.0790619	−	0.435667i	0.999044	−	0.0437074i	$-0.0139169\pi$
$992$	−0.534440	+	1.25038i	−0.0169685	+	0.0396997i
$993$		0			0
$994$	5.52518	+	5.16776i	0.175248	+	0.163911i
$995$		−	11.3355i		−	0.359360i
$996$		0			0
$997$	0.964390	+	0.175011i	0.0305425	+	0.00554265i	0.193807	−	0.981040i	$-0.437917\pi$
$997$	0.964390	+	0.175011i	0.0305425	+	0.00554265i	−0.163264	+	0.986582i	$0.552202\pi$
$998$	−16.6950	+	15.9620i	−0.528470	+	0.505269i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	639.2.z.a.269.15	yes	576
3.2	odd	2	inner	639.2.z.a.269.10	✓	576
71.52	odd	70	inner	639.2.z.a.620.10	yes	576
213.194	even	70	inner	639.2.z.a.620.15	yes	576

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
639.2.z.a.269.10	✓	576	3.2	odd	2	inner
639.2.z.a.269.15	yes	576	1.1	even	1	trivial
639.2.z.a.620.10	yes	576	71.52	odd	70	inner
639.2.z.a.620.15	yes	576	213.194	even	70	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:	\( N \)	\(=\)	\( 639 = 3^{2} \cdot 71 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	639.z (of order \(70\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(0.742017 + 0.317153i) q^{2} +(-0.932123 - 0.974924i) q^{4} +(-0.618013 - 0.200804i) q^{5} +(-0.732035 - 0.837882i) q^{7} +(-0.949537 - 2.53003i) q^{8} +O(q^{10})\)	\(q+(0.742017 + 0.317153i) q^{2} +(-0.932123 - 0.974924i) q^{4} +(-0.618013 - 0.200804i) q^{5} +(-0.732035 - 0.837882i) q^{7} +(-0.949537 - 2.53003i) q^{8} +(-0.394890 - 0.345005i) q^{10} +(-2.86141 + 0.789699i) q^{11} +(-0.525599 + 1.90447i) q^{13} +(-0.277446 - 0.853890i) q^{14} +(-0.0231941 + 0.516458i) q^{16} +(-5.70281 + 4.14333i) q^{17} +(-1.80869 - 3.36110i) q^{19} +(0.380294 + 0.789690i) q^{20} +(-2.37367 - 0.321536i) q^{22} +(-0.286865 + 1.25684i) q^{23} +(-3.70347 - 2.69073i) q^{25} +(-0.994011 + 1.24645i) q^{26} +(-0.134524 + 1.49469i) q^{28} +(1.89072 - 0.256116i) q^{29} +(0.233334 - 0.0104790i) q^{31} +(-2.52602 + 5.24533i) q^{32} +(-5.54565 + 1.26576i) q^{34} +(0.284157 + 0.664818i) q^{35} +(-2.57038 - 11.2616i) q^{37} +(-0.276091 - 3.06762i) q^{38} +(0.0787841 + 1.75426i) q^{40} +(-3.04186 - 3.81437i) q^{41} +(2.14795 + 0.193319i) q^{43} +(3.43708 + 2.05356i) q^{44} +(-0.611469 + 0.841615i) q^{46} +(6.34876 - 1.15213i) q^{47} +(0.773463 - 5.70993i) q^{49} +(-1.89466 - 3.17113i) q^{50} +(2.34663 - 1.26278i) q^{52} +(-4.52197 + 4.72961i) q^{53} +(1.92696 + 0.0865400i) q^{55} +(-1.42477 + 2.64767i) q^{56} +(1.48418 + 0.409607i) q^{58} +(2.91451 + 4.41529i) q^{59} +(5.28690 - 6.05135i) q^{61} +(0.176461 + 0.0662270i) q^{62} +(-2.75928 + 2.41071i) q^{64} +(0.707252 - 1.07144i) q^{65} +(-8.38154 + 8.01357i) q^{67} +(9.35514 + 1.69771i) q^{68} +0.583427i q^{70} +(-7.37577 + 4.07407i) q^{71} +(0.351975 - 0.823487i) q^{73} +(1.66438 - 9.17147i) q^{74} +(-1.59090 + 4.89629i) q^{76} +(2.75633 + 1.81944i) q^{77} +(10.8927 - 4.08808i) q^{79} +(0.118041 - 0.314520i) q^{80} +(-1.04737 - 3.79506i) q^{82} +(4.13843 - 2.73176i) q^{83} +(4.35641 - 1.41548i) q^{85} +(1.53250 + 0.824674i) q^{86} +(4.71498 + 6.48962i) q^{88} +(-2.51991 - 2.40928i) q^{89} +(1.98047 - 0.953746i) q^{91} +(1.49271 - 0.891855i) q^{92} +(5.07629 + 1.15863i) q^{94} +(0.442866 + 2.44040i) q^{95} +(9.12090 + 7.27367i) q^{97} +(2.38484 - 3.99156i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 576 q - 24 q^{4}+O(q^{10}) \) 576 * q - 24 * q^4	\( 576 q - 24 q^{4} - 16 q^{10} + 76 q^{16} - 8 q^{19} + 20 q^{22} + 168 q^{25} - 20 q^{28} - 28 q^{31} + 40 q^{37} + 32 q^{40} + 52 q^{43} - 20 q^{46} - 208 q^{52} - 92 q^{55} + 56 q^{58} + 56 q^{61} - 144 q^{64} - 16 q^{67} - 44 q^{73} - 336 q^{76} + 88 q^{79} - 124 q^{82} + 60 q^{85} - 260 q^{88} + 80 q^{91} + 56 q^{94} - 56 q^{97}+O(q^{100}) \) 576 * q - 24 * q^4 - 16 * q^10 + 76 * q^16 - 8 * q^19 + 20 * q^22 + 168 * q^25 - 20 * q^28 - 28 * q^31 + 40 * q^37 + 32 * q^40 + 52 * q^43 - 20 * q^46 - 208 * q^52 - 92 * q^55 + 56 * q^58 + 56 * q^61 - 144 * q^64 - 16 * q^67 - 44 * q^73 - 336 * q^76 + 88 * q^79 - 124 * q^82 + 60 * q^85 - 260 * q^88 + 80 * q^91 + 56 * q^94 - 56 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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