LMFDB - Embedded newform 605.2.m.f.602.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [605,2,Mod(112,605)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(605, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([5, 2]))

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

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

chi := DirichletCharacter("605.112");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.m (of order $20$, degree $8$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			602.8
Character	$\chi$	$=$	605.602
Dual form			605.2.m.f.403.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.290440 - 1.83377i) q^{2} +(-1.37543 - 0.700818i) q^{3} +(-1.37624 - 0.447166i) q^{4} +(-1.96083 - 1.07478i) q^{5} +(-1.68462 + 2.31868i) q^{6} +(-0.937080 - 1.83912i) q^{7} +(0.466067 - 0.914708i) q^{8} +(-0.362685 - 0.499192i) q^{9} +O(q^{10})$	\(q+(0.290440 - 1.83377i) q^{2} +(-1.37543 - 0.700818i) q^{3} +(-1.37624 - 0.447166i) q^{4} +(-1.96083 - 1.07478i) q^{5} +(-1.68462 + 2.31868i) q^{6} +(-0.937080 - 1.83912i) q^{7} +(0.466067 - 0.914708i) q^{8} +(-0.362685 - 0.499192i) q^{9} +(-2.54040 + 3.28355i) q^{10} +(1.57954 + 1.57954i) q^{12} +(2.97603 + 0.471357i) q^{13} +(-3.64469 + 1.18423i) q^{14} +(1.94377 + 2.85247i) q^{15} +(-3.88339 - 2.82145i) q^{16} +(-6.79848 + 1.07677i) q^{17} +(-1.02074 + 0.520094i) q^{18} +(1.26002 + 3.87793i) q^{19} +(2.21796 + 2.35597i) q^{20} +3.18632i q^{21} +(5.40871 - 5.40871i) q^{23} +(-1.28209 + 0.931492i) q^{24} +(2.68970 + 4.21491i) q^{25} +(1.72872 - 5.32045i) q^{26} +(0.873462 + 5.51482i) q^{27} +(0.467250 + 2.95010i) q^{28} +(-1.58644 + 4.88256i) q^{29} +(5.79532 - 2.73594i) q^{30} +(-2.22412 + 1.61592i) q^{31} +(-4.84994 + 4.84994i) q^{32} +12.7796i q^{34} +(-0.139196 + 4.61336i) q^{35} +(0.275918 + 0.849187i) q^{36} +(4.26452 - 2.17288i) q^{37} +(7.47719 - 1.18427i) q^{38} +(-3.76300 - 2.73398i) q^{39} +(-1.89699 + 1.29267i) q^{40} +(-7.18688 + 2.33516i) q^{41} +(5.84296 + 0.925435i) q^{42} +(-2.58034 - 2.58034i) q^{43} +(0.174641 + 1.36864i) q^{45} +(-8.34742 - 11.4892i) q^{46} +(-0.201182 + 0.394842i) q^{47} +(3.36402 + 6.60227i) q^{48} +(1.61024 - 2.21631i) q^{49} +(8.51037 - 3.70811i) q^{50} +(10.1055 + 3.28347i) q^{51} +(-3.88495 - 1.97948i) q^{52} +(1.14667 - 7.23977i) q^{53} +10.3666 q^{54} -2.11900 q^{56} +(0.984657 - 6.21688i) q^{57} +(8.49271 + 4.32725i) q^{58} +(-12.3338 - 4.00750i) q^{59} +(-1.39955 - 4.79486i) q^{60} +(3.14797 - 4.33281i) q^{61} +(2.31725 + 4.54785i) q^{62} +(-0.578212 + 1.13481i) q^{63} +(1.84216 + 2.53551i) q^{64} +(-5.32888 - 4.12282i) q^{65} +(-3.40871 - 3.40871i) q^{67} +(9.83782 + 1.55816i) q^{68} +(-11.2299 + 3.64880i) q^{69} +(8.41941 + 1.59516i) q^{70} +(3.54451 + 2.57524i) q^{71} +(-0.625651 + 0.0990933i) q^{72} +(8.01134 - 4.08198i) q^{73} +(-2.74597 - 8.45123i) q^{74} +(-0.745618 - 7.68233i) q^{75} -5.90039i q^{76} +(-6.10640 + 6.10640i) q^{78} +(-10.2736 + 7.46420i) q^{79} +(4.58224 + 9.70617i) q^{80} +(2.09148 - 6.43690i) q^{81} +(2.19478 + 13.8573i) q^{82} +(0.174702 + 1.10302i) q^{83} +(1.42481 - 4.38513i) q^{84} +(14.4880 + 5.19549i) q^{85} +(-5.48119 + 3.98231i) q^{86} +(5.60383 - 5.60383i) q^{87} -13.5666i q^{89} +(2.56049 + 0.0772559i) q^{90} +(-1.92190 - 5.91499i) q^{91} +(-9.86226 + 5.02507i) q^{92} +(4.19160 - 0.663884i) q^{93} +(0.665617 + 0.483599i) q^{94} +(1.69724 - 8.95820i) q^{95} +(10.0697 - 3.27185i) q^{96} +(-8.32676 - 1.31883i) q^{97} +(-3.59651 - 3.59651i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 4 q^{3} - 4 q^{5}+O(q^{10}) $ 80 * q - 4 * q^3 - 4 * q^5	$ 80 q - 4 q^{3} - 4 q^{5} - 64 q^{12} - 16 q^{15} - 12 q^{16} - 16 q^{20} + 48 q^{23} - 16 q^{25} - 56 q^{26} + 20 q^{27} + 16 q^{31} + 20 q^{36} + 72 q^{37} + 32 q^{38} + 32 q^{42} - 112 q^{45} - 16 q^{47} + 104 q^{48} + 52 q^{53} - 128 q^{56} - 12 q^{58} - 112 q^{60} + 112 q^{67} - 104 q^{70} - 24 q^{71} - 64 q^{75} + 416 q^{78} - 44 q^{80} - 100 q^{81} + 124 q^{82} - 128 q^{86} + 16 q^{92} + 132 q^{93} - 32 q^{97}+O(q^{100}) $ 80 * q - 4 * q^3 - 4 * q^5 - 64 * q^12 - 16 * q^15 - 12 * q^16 - 16 * q^20 + 48 * q^23 - 16 * q^25 - 56 * q^26 + 20 * q^27 + 16 * q^31 + 20 * q^36 + 72 * q^37 + 32 * q^38 + 32 * q^42 - 112 * q^45 - 16 * q^47 + 104 * q^48 + 52 * q^53 - 128 * q^56 - 12 * q^58 - 112 * q^60 + 112 * q^67 - 104 * q^70 - 24 * q^71 - 64 * q^75 + 416 * q^78 - 44 * q^80 - 100 * q^81 + 124 * q^82 - 128 * q^86 + 16 * q^92 + 132 * q^93 - 32 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{10}\right)$

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 $

$2$	0.290440	−	1.83377i	0.205372	−	1.29667i	−0.642425	−	0.766349i	$-0.722071\pi$
$2$	0.290440	−	1.83377i	0.205372	−	1.29667i	0.847797	−	0.530321i	$-0.177929\pi$
$3$	−1.37543	−	0.700818i	−0.794107	−	0.404618i	0.00936808	−	0.999956i	$-0.497018\pi$
$3$	−1.37543	−	0.700818i	−0.794107	−	0.404618i	−0.803475	+	0.595338i	$0.797018\pi$
$4$	−1.37624	−	0.447166i	−0.688118	−	0.223583i
$5$	−1.96083	−	1.07478i	−0.876909	−	0.480656i
$5$	−1.96083	−	1.07478i	−0.876909	−	0.480656i
$6$	−1.68462	+	2.31868i	−0.687743	+	0.946597i
$7$	−0.937080	−	1.83912i	−0.354183	−	0.695123i	0.643331	−	0.765588i	$-0.277552\pi$
$7$	−0.937080	−	1.83912i	−0.354183	−	0.695123i	−0.997514	+	0.0704646i	$0.977552\pi$
$8$	0.466067	−	0.914708i	0.164780	−	0.323398i
$9$	−0.362685	−	0.499192i	−0.120895	−	0.166397i
$10$	−2.54040	+	3.28355i	−0.803345	+	1.03835i
$11$		0			0
$11$		0			0
$12$	1.57954	+	1.57954i	0.455974	+	0.455974i
$13$	2.97603	+	0.471357i	0.825402	+	0.130731i	0.554825	−	0.831967i	$-0.312785\pi$
$13$	2.97603	+	0.471357i	0.825402	+	0.130731i	0.270577	+	0.962698i	$0.412785\pi$
$14$	−3.64469	+	1.18423i	−0.974085	+	0.316499i
$15$	1.94377	+	2.85247i	0.501878	+	0.736505i
$16$	−3.88339	−	2.82145i	−0.970848	−	0.705362i
$17$	−6.79848	+	1.07677i	−1.64887	+	0.261156i	−0.910583	−	0.413326i	$-0.864367\pi$
$17$	−6.79848	+	1.07677i	−1.64887	+	0.261156i	−0.738291	+	0.674482i	$0.764367\pi$
$18$	−1.02074	+	0.520094i	−0.240591	+	0.122587i
$19$	1.26002	+	3.87793i	0.289068	+	0.889659i	0.985150	+	0.171697i	$0.0549249\pi$
$19$	1.26002	+	3.87793i	0.289068	+	0.889659i	−0.696082	+	0.717962i	$0.745075\pi$
$20$	2.21796	+	2.35597i	0.495951	+	0.526810i
$21$			3.18632i			0.695311i
$22$		0			0
$23$	5.40871	−	5.40871i	1.12779	−	1.12779i	0.137259	−	0.990535i	$-0.456171\pi$
$23$	5.40871	−	5.40871i	1.12779	−	1.12779i	0.990535	−	0.137259i	$-0.0438294\pi$
$24$	−1.28209	+	0.931492i	−0.261705	+	0.190140i
$25$	2.68970	+	4.21491i	0.537940	+	0.842983i
$26$	1.72872	−	5.32045i	0.339029	−	1.04343i
$27$	0.873462	+	5.51482i	0.168098	+	1.06133i
$28$	0.467250	+	2.95010i	0.0883020	+	0.557517i
$29$	−1.58644	+	4.88256i	−0.294594	+	0.906668i	0.688763	+	0.724986i	$0.258154\pi$
$29$	−1.58644	+	4.88256i	−0.294594	+	0.906668i	−0.983357	+	0.181682i	$0.941846\pi$
$30$	5.79532	−	2.73594i	1.05808	−	0.499513i
$31$	−2.22412	+	1.61592i	−0.399464	+	0.290228i	−0.769323	−	0.638860i	$-0.779406\pi$
$31$	−2.22412	+	1.61592i	−0.399464	+	0.290228i	0.369859	+	0.929088i	$0.379406\pi$
$32$	−4.84994	+	4.84994i	−0.857357	+	0.857357i
$33$		0			0
$34$			12.7796i			2.19168i
$35$	−0.139196	+	4.61336i	−0.0235284	+	0.779800i
$36$	0.275918	+	0.849187i	0.0459863	+	0.141531i
$37$	4.26452	−	2.17288i	0.701083	−	0.357220i	−0.0668384	−	0.997764i	$-0.521291\pi$
$37$	4.26452	−	2.17288i	0.701083	−	0.357220i	0.767921	+	0.640544i	$0.221291\pi$
$38$	7.47719	−	1.18427i	1.21296	−	0.192114i
$39$	−3.76300	−	2.73398i	−0.602562	−	0.437787i
$40$	−1.89699	+	1.29267i	−0.299940	+	0.204389i
$41$	−7.18688	+	2.33516i	−1.12240	+	0.364690i	−0.810684	−	0.585484i	$-0.800904\pi$
$41$	−7.18688	+	2.33516i	−1.12240	+	0.364690i	−0.311718	+	0.950175i	$0.600904\pi$
$42$	5.84296	+	0.925435i	0.901589	+	0.142798i
$43$	−2.58034	−	2.58034i	−0.393499	−	0.393499i	0.482434	−	0.875932i	$-0.339753\pi$
$43$	−2.58034	−	2.58034i	−0.393499	−	0.393499i	−0.875932	+	0.482434i	$0.839753\pi$
$44$		0			0
$45$	0.174641	+	1.36864i	0.0260340	+	0.204024i
$46$	−8.34742	−	11.4892i	−1.23076	−	1.69400i
$47$	−0.201182	+	0.394842i	−0.0293454	+	0.0575936i	−0.905214	−	0.424957i	$-0.860289\pi$
$47$	−0.201182	+	0.394842i	−0.0293454	+	0.0575936i	0.875868	+	0.482550i	$0.160289\pi$
$48$	3.36402	+	6.60227i	0.485555	+	0.952955i
$49$	1.61024	−	2.21631i	0.230034	−	0.316615i
$50$	8.51037	−	3.70811i	1.20355	−	0.524406i
$51$	10.1055	+	3.28347i	1.41505	+	0.459778i
$52$	−3.88495	−	1.97948i	−0.538745	−	0.274504i
$53$	1.14667	−	7.23977i	0.157507	−	0.994458i	−0.774647	−	0.632394i	$-0.782072\pi$
$53$	1.14667	−	7.23977i	0.157507	−	0.994458i	0.932153	−	0.362064i	$-0.117928\pi$
$54$	10.3666			1.41071
$55$		0			0
$56$	−2.11900			−0.283164
$57$	0.984657	−	6.21688i	0.130421	−	0.823446i
$58$	8.49271	+	4.32725i	1.11515	+	0.568196i
$59$	−12.3338	−	4.00750i	−1.60573	−	0.521732i	−0.637212	−	0.770688i	$-0.719913\pi$
$59$	−12.3338	−	4.00750i	−1.60573	−	0.521732i	−0.968515	+	0.248956i	$0.919913\pi$
$60$	−1.39955	−	4.79486i	−0.180681	−	0.619014i
$61$	3.14797	−	4.33281i	0.403056	−	0.554759i	−0.558452	−	0.829537i	$-0.688604\pi$
$61$	3.14797	−	4.33281i	0.403056	−	0.554759i	0.961508	+	0.274778i	$0.0886044\pi$
$62$	2.31725	+	4.54785i	0.294291	+	0.577578i
$63$	−0.578212	+	1.13481i	−0.0728479	+	0.142972i
$64$	1.84216	+	2.53551i	0.230269	+	0.316939i
$65$	−5.32888	−	4.12282i	−0.660966	−	0.511373i
$66$		0			0
$67$	−3.40871	−	3.40871i	−0.416441	−	0.416441i	0.467534	−	0.883975i	$-0.345142\pi$
$67$	−3.40871	−	3.40871i	−0.416441	−	0.416441i	−0.883975	+	0.467534i	$0.845142\pi$
$68$	9.83782	+	1.55816i	1.19301	+	0.188954i
$69$	−11.2299	+	3.64880i	−1.35192	+	0.439264i
$70$	8.41941	+	1.59516i	1.00631	+	0.190658i
$71$	3.54451	+	2.57524i	0.420656	+	0.305625i	0.777902	−	0.628386i	$-0.216284\pi$
$71$	3.54451	+	2.57524i	0.420656	+	0.305625i	−0.357246	+	0.934011i	$0.616284\pi$
$72$	−0.625651	+	0.0990933i	−0.0737336	+	0.0116783i
$73$	8.01134	−	4.08198i	0.937656	−	0.477760i	0.0827663	−	0.996569i	$-0.473625\pi$
$73$	8.01134	−	4.08198i	0.937656	−	0.477760i	0.854890	+	0.518809i	$0.173625\pi$
$74$	−2.74597	−	8.45123i	−0.319213	−	0.982436i
$75$	−0.745618	−	7.68233i	−0.0860965	−	0.887079i
$76$		−	5.90039i		−	0.676821i
$77$		0			0
$78$	−6.10640	+	6.10640i	−0.691414	+	0.691414i
$79$	−10.2736	+	7.46420i	−1.15587	+	0.839788i	−0.989250	−	0.146234i	$-0.953285\pi$
$79$	−10.2736	+	7.46420i	−1.15587	+	0.839788i	−0.166619	+	0.986021i	$0.553285\pi$
$80$	4.58224	+	9.70617i	0.512309	+	1.08518i
$81$	2.09148	−	6.43690i	0.232386	−	0.715211i
$82$	2.19478	+	13.8573i	0.242373	+	1.53028i
$83$	0.174702	+	1.10302i	0.0191760	+	0.121073i	0.995419	−	0.0956041i	$-0.0304783\pi$
$83$	0.174702	+	1.10302i	0.0191760	+	0.121073i	−0.976243	+	0.216677i	$0.930478\pi$
$84$	1.42481	−	4.38513i	0.155460	−	0.478456i
$85$	14.4880	+	5.19549i	1.57144	+	0.563530i
$86$	−5.48119	+	3.98231i	−0.591051	+	0.429424i
$87$	5.60383	−	5.60383i	0.600793	−	0.600793i
$88$		0			0
$89$		−	13.5666i		−	1.43806i	−0.694981	−	0.719028i	$-0.744587\pi$
$89$		−	13.5666i		−	1.43806i	0.694981	−	0.719028i	$-0.255413\pi$
$90$	2.56049	+	0.0772559i	0.269899	+	0.00814349i
$91$	−1.92190	−	5.91499i	−0.201469	−	0.620059i
$92$	−9.86226	+	5.02507i	−1.02821	+	0.523900i
$93$	4.19160	−	0.663884i	0.434648	−	0.0688415i
$94$	0.665617	+	0.483599i	0.0686532	+	0.0498795i
$95$	1.69724	−	8.95820i	0.174133	−	0.919092i
$96$	10.0697	−	3.27185i	1.02774	−	0.333931i
$97$	−8.32676	−	1.31883i	−0.845454	−	0.133907i	−0.281345	−	0.959607i	$-0.590780\pi$
$97$	−8.32676	−	1.31883i	−0.845454	−	0.133907i	−0.564110	+	0.825700i	$0.690780\pi$
$98$	−3.59651	−	3.59651i	−0.363303	−	0.363303i
$99$		0			0
$100$	−1.81690	−	7.00346i	−0.181690	−	0.700346i
$101$	0.876896	+	1.20694i	0.0872544	+	0.120095i	0.850413	−	0.526116i	$-0.176352\pi$
$101$	0.876896	+	1.20694i	0.0872544	+	0.120095i	−0.763158	+	0.646212i	$0.776352\pi$
$102$	8.95617	−	17.5775i	0.886793	−	1.74043i
$103$	3.21885	+	6.31735i	0.317163	+	0.622467i	0.993462	−	0.114160i	$-0.0364176\pi$
$103$	3.21885	+	6.31735i	0.317163	+	0.622467i	−0.676300	+	0.736627i	$0.736418\pi$
$104$	1.81818	−	2.50251i	0.178288	−	0.245392i
$105$	3.42458	−	6.24782i	0.334205	−	0.609725i
$106$	−12.9430	−	4.20544i	−1.25714	−	0.408468i
$107$	−13.5205	−	6.88905i	−1.30708	−	0.665990i	−0.344959	−	0.938618i	$-0.612107\pi$
$107$	−13.5205	−	6.88905i	−1.30708	−	0.665990i	−0.962119	+	0.272628i	$0.912107\pi$
$108$	1.26395	−	7.98028i	0.121624	−	0.767903i
$109$	1.85686			0.177855			0.0889275	−	0.996038i	$-0.471656\pi$
$109$	1.85686			0.177855			0.0889275	+	0.996038i	$0.471656\pi$
$110$		0			0
$111$	−7.38836			−0.701272
$112$	−1.54994	+	9.78596i	−0.146456	+	0.924687i
$113$	−7.47860	−	3.81054i	−0.703528	−	0.358465i	0.0653490	−	0.997862i	$-0.479184\pi$
$113$	−7.47860	−	3.81054i	−0.703528	−	0.358465i	−0.768877	+	0.639397i	$0.779184\pi$
$114$	−11.1143	−	3.61127i	−1.04095	−	0.338226i
$115$	−16.4187	+	4.79239i	−1.53105	+	0.446893i
$116$	4.36663	−	6.01015i	0.405432	−	0.558029i
$117$	−0.844062	−	1.65657i	−0.0780336	−	0.153149i
$118$	−10.9311	+	21.4534i	−1.00629	+	1.97495i
$119$	8.35105	+	11.4942i	0.765539	+	1.05367i
$120$	3.51510	−	0.448535i	0.320884	−	0.0409455i
$121$		0			0
$122$	−7.03106	−	7.03106i	−0.636563	−	0.636563i
$123$	11.5216	+	1.82484i	1.03887	+	0.164540i
$124$	3.78350	−	1.22933i	0.339769	−	0.110398i
$125$	−0.743948	−	11.1556i	−0.0665407	−	0.997784i
$126$	1.91303	+	1.38990i	0.170427	+	0.123822i
$127$	−1.31049	+	0.207561i	−0.116287	+	0.0184181i	−0.214307	−	0.976766i	$-0.568749\pi$
$127$	−1.31049	+	0.207561i	−0.116287	+	0.0184181i	0.0980197	+	0.995184i	$0.468749\pi$
$128$	−7.03800	+	3.58604i	−0.622077	+	0.316964i
$129$	1.74074	+	5.35744i	0.153263	+	0.471696i
$130$	−9.10802	+	8.57450i	−0.798826	+	0.752033i
$131$			9.41359i			0.822469i	0.911530	+	0.411235i	$0.134902\pi$
$131$			9.41359i			0.822469i	−0.911530	+	0.411235i	$0.865098\pi$
$132$		0			0
$133$	5.95126	−	5.95126i	0.516040	−	0.516040i
$134$	−7.24082	+	5.26076i	−0.625511	+	0.454461i
$135$	4.21450	−	11.7524i	0.362727	−	1.01149i
$136$	−2.18362	+	6.72048i	−0.187243	+	0.576276i
$137$	−1.90908	−	12.0534i	−0.163103	−	1.02979i	−0.924409	−	0.381402i	$-0.875441\pi$
$137$	−1.90908	−	12.0534i	−0.163103	−	1.02979i	0.761306	−	0.648393i	$-0.224559\pi$
$138$	3.42945	+	21.6527i	0.291934	+	1.84320i
$139$	2.16939	−	6.67668i	0.184005	−	0.566309i	−0.815925	−	0.578158i	$-0.803772\pi$
$139$	2.16939	−	6.67668i	0.184005	−	0.566309i	0.999930	+	0.0118491i	$0.00377177\pi$
$140$	2.25451	−	6.28683i	0.190541	−	0.531334i
$141$	0.553425	−	0.402087i	0.0466068	−	0.0338618i
$142$	5.75186	−	5.75186i	0.482686	−	0.482686i
$143$		0			0
$144$			2.96186i			0.246821i
$145$	8.35840	−	7.86879i	0.694128	−	0.653467i
$146$	−5.15859	−	15.8765i	−0.426928	−	1.31395i
$147$	−3.76801	+	1.91990i	−0.310780	+	0.158350i
$148$	−6.84063	+	1.08345i	−0.562296	+	0.0890590i
$149$	1.08836	+	0.790739i	0.0891618	+	0.0647798i	0.631473	−	0.775398i	$-0.282451\pi$
$149$	1.08836	+	0.790739i	0.0891618	+	0.0647798i	−0.542311	+	0.840178i	$0.682451\pi$
$150$	−14.3042	−	0.863968i	−1.16793	−	0.0705427i
$151$	−2.80475	+	0.911319i	−0.228247	+	0.0741621i	−0.420908	−	0.907103i	$-0.638288\pi$
$151$	−2.80475	+	0.911319i	−0.228247	+	0.0741621i	0.192660	+	0.981265i	$0.438288\pi$
$152$	4.13443	+	0.654829i	0.335346	+	0.0531137i
$153$	3.00322	+	3.00322i	0.242796	+	0.242796i
$154$		0			0
$155$	6.09788	−	0.778103i	0.489793	−	0.0624987i
$156$	3.95623	+	5.44528i	0.316752	+	0.435972i
$157$	1.12482	−	2.20759i	0.0897705	−	0.176185i	−0.841756	−	0.539858i	$-0.818478\pi$
$157$	1.12482	−	2.20759i	0.0897705	−	0.176185i	0.931526	+	0.363674i	$0.118478\pi$
$158$	10.7037	+	21.0073i	0.851544	+	1.67125i
$159$	−6.65093	+	9.15421i	−0.527453	+	0.725976i
$160$	14.7225	−	4.29730i	1.16392	−	0.339731i
$161$	−15.0157	−	4.87889i	−1.18340	−	0.384511i
$162$	−11.1963	−	5.70482i	−0.879667	−	0.448213i
$163$	−1.49397	+	9.43258i	−0.117017	+	0.738816i	0.857497	+	0.514489i	$0.172018\pi$
$163$	−1.49397	+	9.43258i	−0.117017	+	0.738816i	−0.974514	+	0.224327i	$0.927982\pi$
$164$	10.9350			0.853884
$165$		0			0
$166$	2.07343			0.160929
$167$	−1.20043	+	7.57923i	−0.0928922	+	0.586498i	0.896705	+	0.442629i	$0.145954\pi$
$167$	−1.20043	+	7.57923i	−0.0928922	+	0.586498i	−0.989597	+	0.143869i	$0.954046\pi$
$168$	2.91455	+	1.48504i	0.224862	+	0.114573i
$169$	−3.72916	−	1.21168i	−0.286859	−	0.0932060i
$170$	13.7352	−	25.0586i	1.05344	−	1.92190i
$171$	1.47885	−	2.03546i	0.113090	−	0.155655i
$172$	2.39732	+	4.70501i	0.182794	+	0.358753i
$173$	6.21685	−	12.2013i	0.472658	−	0.927644i	−0.524435	−	0.851451i	$-0.675723\pi$
$173$	6.21685	−	12.2013i	0.472658	−	0.927644i	0.997093	−	0.0761935i	$-0.0242767\pi$
$174$	−8.64854	−	11.9037i	−0.655644	−	0.902417i
$175$	5.23128	−	8.89641i	0.395448	−	0.672505i
$176$		0			0
$177$	14.1558	+	14.1558i	1.06402	+	1.06402i
$178$	−24.8780	−	3.94029i	−1.86468	−	0.295337i
$179$	13.2716	−	4.31220i	0.991966	−	0.322309i	0.232315	−	0.972641i	$-0.425370\pi$
$179$	13.2716	−	4.31220i	0.991966	−	0.322309i	0.759651	+	0.650331i	$0.225370\pi$
$180$	0.371661	−	1.96166i	0.0277020	−	0.146214i
$181$	−16.0147	−	11.6354i	−1.19037	−	0.864852i	−0.197063	−	0.980391i	$-0.563140\pi$
$181$	−16.0147	−	11.6354i	−1.19037	−	0.864852i	−0.993303	+	0.115539i	$0.963140\pi$
$182$	−11.4049	+	1.80636i	−0.845388	+	0.133896i
$183$	−7.36633	+	3.75333i	−0.544535	+	0.277454i
$184$	−2.42657	−	7.46822i	−0.178889	−	0.550564i
$185$	−10.6974	−	0.322765i	−0.786486	−	0.0237301i
$186$		−	7.87924i		−	0.577734i
$187$		0			0
$188$	0.453434	−	0.453434i	0.0330701	−	0.0330701i
$189$	9.32394	−	6.77424i	0.678217	−	0.492753i
$190$	−15.9343	−	5.71417i	−1.15600	−	0.414549i
$191$	−0.169695	+	0.522269i	−0.0122787	+	0.0377900i	−0.957008	−	0.290061i	$-0.906324\pi$
$191$	−0.169695	+	0.522269i	−0.0122787	+	0.0377900i	0.944729	+	0.327851i	$0.106324\pi$
$192$	−0.756831	−	4.77844i	−0.0546196	−	0.344854i
$193$	0.791355	+	4.99642i	0.0569630	+	0.359650i	0.999662	+	0.0260052i	$0.00827865\pi$
$193$	0.791355	+	4.99642i	0.0569630	+	0.359650i	−0.942699	+	0.333645i	$0.891721\pi$
$194$	−4.83685	+	14.8863i	−0.347266	+	1.06877i
$195$	4.44017	+	9.40525i	0.317967	+	0.673524i
$196$	−3.20713	+	2.33012i	−0.229081	+	0.166437i
$197$	5.33112	−	5.33112i	0.379827	−	0.379827i	−0.491213	−	0.871040i	$-0.663446\pi$
$197$	5.33112	−	5.33112i	0.379827	−	0.379827i	0.871040	+	0.491213i	$0.163446\pi$
$198$		0			0
$199$			5.88702i			0.417320i	0.977988	+	0.208660i	$0.0669102\pi$
$199$			5.88702i			0.417320i	−0.977988	+	0.208660i	$0.933090\pi$
$200$	5.10900	−	0.495860i	0.361261	−	0.0350626i
$201$	2.29957	+	7.07735i	0.162199	+	0.499198i
$202$	2.46794	−	1.25748i	0.173644	−	0.0884759i
$203$	10.4662	−	1.65769i	0.734586	−	0.116347i
$204$	−12.4393	−	9.03767i	−0.870924	−	0.632763i
$205$	16.6020	+	3.14545i	1.15953	+	0.219688i
$206$	12.5194	−	4.06781i	0.872270	−	0.283418i
$207$	−4.66164	−	0.738332i	−0.324007	−	0.0513176i
$208$	−10.2272	−	10.2272i	−0.709127	−	0.709127i
$209$		0			0
$210$	−10.4624	−	8.09451i	−0.721975	−	0.558574i
$211$	8.91493	+	12.2703i	0.613729	+	0.844725i	0.996878	−	0.0789613i	$-0.0251604\pi$
$211$	8.91493	+	12.2703i	0.613729	+	0.844725i	−0.383149	+	0.923687i	$0.625160\pi$
$212$	−4.81547	+	9.45088i	−0.330728	+	0.649089i
$213$	−3.07047	−	6.02613i	−0.210385	−	0.412904i
$214$	−16.5598	+	22.7926i	−1.13201	+	1.55807i
$215$	2.28631	+	7.83291i	0.155925	+	0.534200i
$216$	5.45154	+	1.77131i	0.370931	+	0.120523i
$217$	5.05606	+	2.57619i	0.343227	+	0.174883i
$218$	0.539307	−	3.40505i	0.0365265	−	0.230619i
$219$	−13.8798			−0.937910
$220$		0			0
$221$	−20.7400			−1.39513
$222$	−2.14588	+	13.5485i	−0.144022	+	0.909319i
$223$	2.67317	+	1.36205i	0.179009	+	0.0912095i	0.541198	−	0.840895i	$-0.317971\pi$
$223$	2.67317	+	1.36205i	0.179009	+	0.0912095i	−0.362190	+	0.932104i	$0.617971\pi$
$224$	13.4644	+	4.37486i	0.899630	+	0.292308i
$225$	1.12854	−	2.87136i	0.0752360	−	0.191424i
$226$	−9.15973	+	12.6073i	−0.609296	+	0.838624i
$227$	0.340752	+	0.668764i	0.0226165	+	0.0443874i	0.902038	−	0.431656i	$-0.142071\pi$
$227$	0.340752	+	0.668764i	0.0226165	+	0.0443874i	−0.879422	+	0.476043i	$0.842071\pi$
$228$	−4.13510	+	8.11560i	−0.273854	+	0.537468i
$229$	4.74155	+	6.52618i	0.313330	+	0.431262i	0.936416	−	0.350891i	$-0.114121\pi$
$229$	4.74155	+	6.52618i	0.313330	+	0.431262i	−0.623086	+	0.782153i	$0.714121\pi$
$230$	4.01948	+	31.5000i	0.265037	+	2.07705i
$231$		0			0
$232$	3.72673	+	3.72673i	0.244672	+	0.244672i
$233$	−1.65310	−	0.261825i	−0.108298	−	0.0171527i	0.102050	−	0.994779i	$-0.467460\pi$
$233$	−1.65310	−	0.261825i	−0.108298	−	0.0171527i	−0.210348	+	0.977627i	$0.567460\pi$
$234$	−3.28291	+	1.06668i	−0.214610	+	0.0697311i
$235$	0.818852	−	0.557992i	0.0534160	−	0.0363994i
$236$	15.1822	+	11.0305i	0.988280	+	0.718027i
$237$	19.3617	−	3.06659i	1.25768	−	0.199196i
$238$	23.5032	−	11.9755i	1.52349	−	0.776256i
$239$	−5.09940	−	15.6943i	−0.329853	−	1.01518i	−0.969202	−	0.246266i	$-0.920796\pi$
$239$	−5.09940	−	15.6943i	−0.329853	−	1.01518i	0.639350	−	0.768916i	$-0.279204\pi$
$240$	0.499700	−	16.5615i	0.0322555	−	1.06904i
$241$			21.2562i			1.36923i	0.728903	+	0.684617i	$0.240030\pi$
$241$			21.2562i			1.36923i	−0.728903	+	0.684617i	$0.759970\pi$
$242$		0			0
$243$	4.45674	−	4.45674i	0.285900	−	0.285900i
$244$	−6.26983	+	4.55530i	−0.401385	+	0.291623i
$245$	−5.53944	+	2.61515i	−0.353902	+	0.167075i
$246$	6.69267	−	20.5979i	0.426709	−	1.31328i
$247$	1.92196	+	12.1348i	0.122291	+	0.772116i
$248$	0.441504	+	2.78755i	0.0280356	+	0.177010i
$249$	0.532729	−	1.63957i	0.0337603	−	0.103904i
$250$	−20.6728	−	1.87580i	−1.30746	−	0.118636i
$251$	21.0751	−	15.3119i	1.33025	−	0.966481i	0.330505	−	0.943804i	$-0.392781\pi$
$251$	21.0751	−	15.3119i	1.33025	−	0.966481i	0.999743	−	0.0226769i	$-0.00721890\pi$
$252$	1.30320	−	1.30320i	0.0820941	−	0.0820941i
$253$		0			0
$254$			2.46342i			0.154568i
$255$	−16.2861	−	17.2995i	−1.01988	−	1.08334i
$256$	6.46880	+	19.9089i	0.404300	+	1.24431i
$257$	−2.18909	+	1.11540i	−0.136552	+	0.0695766i	−0.520932	−	0.853598i	$-0.674415\pi$
$257$	−2.18909	+	1.11540i	−0.136552	+	0.0695766i	0.384380	+	0.923175i	$0.374415\pi$
$258$	10.3299	−	1.63609i	0.643111	−	0.101859i
$259$	−7.99240	−	5.80682i	−0.496623	−	0.360818i
$260$	5.49021	+	8.05688i	0.340489	+	0.499666i
$261$	3.01271	−	0.978890i	0.186482	−	0.0605917i
$262$	17.2623	+	2.73409i	1.06647	+	0.168912i
$263$	−14.2199	−	14.2199i	−0.876839	−	0.876839i	0.116367	−	0.993206i	$-0.462875\pi$
$263$	−14.2199	−	14.2199i	−0.876839	−	0.876839i	−0.993206	+	0.116367i	$0.962875\pi$
$264$		0			0
$265$	−10.0296	+	12.9635i	−0.616111	+	0.796344i
$266$	−9.18475	−	12.6417i	−0.563153	−	0.775113i
$267$	−9.50772	+	18.6599i	−0.581863	+	1.14197i
$268$	3.16693	+	6.21546i	0.193451	+	0.379670i
$269$	1.31547	−	1.81059i	0.0802055	−	0.110393i	−0.767029	−	0.641612i	$-0.778266\pi$
$269$	1.31547	−	1.81059i	0.0802055	−	0.110393i	0.847235	+	0.531219i	$0.178266\pi$
$270$	−20.3271	−	11.1418i	−1.23707	−	0.678068i
$271$	2.81475	+	0.914566i	0.170984	+	0.0555559i	0.393258	−	0.919428i	$-0.371348\pi$
$271$	2.81475	+	0.914566i	0.170984	+	0.0555559i	−0.222274	+	0.974984i	$0.571348\pi$
$272$	29.4392	+	15.0000i	1.78502	+	0.909511i
$273$	−1.50189	+	9.48257i	−0.0908986	+	0.573911i
$274$	−22.6577			−1.36880
$275$		0			0
$276$	17.0866			1.02849
$277$	4.32414	−	27.3016i	0.259813	−	1.64039i	−0.420373	−	0.907352i	$-0.638101\pi$
$277$	4.32414	−	27.3016i	0.259813	−	1.64039i	0.680185	−	0.733040i	$-0.261899\pi$
$278$	−11.6134	−	5.91733i	−0.696526	−	0.354898i
$279$	1.61331	+	0.524196i	0.0965863	+	0.0313828i
$280$	4.15500	+	2.27746i	0.248309	+	0.136104i
$281$	17.4272	−	23.9864i	1.03962	−	1.43091i	0.142142	−	0.989846i	$-0.454601\pi$
$281$	17.4272	−	23.9864i	1.03962	−	1.43091i	0.897475	−	0.441064i	$-0.145399\pi$
$282$	−0.576597	−	1.13164i	−0.0343359	−	0.0673879i
$283$	−4.15007	+	8.14498i	−0.246696	+	0.484169i	−0.980837	−	0.194828i	$-0.937585\pi$
$283$	−4.15007	+	8.14498i	−0.246696	+	0.484169i	0.734141	+	0.678997i	$0.237585\pi$
$284$	−3.72653	−	5.12913i	−0.221129	−	0.304358i
$285$	−8.61251	+	11.1320i	−0.510161	+	0.659400i
$286$		0			0
$287$	11.0293	+	11.0293i	0.651040	+	0.651040i
$288$	4.18006	+	0.662056i	0.246312	+	0.0390120i
$289$	28.8920	−	9.38757i	1.69953	−	0.552210i
$290$	−12.0019	−	17.6128i	−0.704777	−	1.03426i
$291$	10.5286	+	7.64951i	0.617200	+	0.448422i
$292$	−12.8508	+	2.03537i	−0.752038	+	0.119111i
$293$	1.57072	−	0.800320i	0.0917622	−	0.0467552i	−0.407507	−	0.913202i	$-0.633602\pi$
$293$	1.57072	−	0.800320i	0.0917622	−	0.0467552i	0.499269	+	0.866447i	$0.333602\pi$
$294$	2.42626	+	7.46727i	0.141502	+	0.435500i
$295$	19.8773	+	21.1142i	1.15730	+	1.22931i
$296$		−	4.91350i		−	0.285591i
$297$		0			0
$298$	1.76613	−	1.76613i	0.102309	−	0.102309i
$299$	18.6459	−	13.5471i	1.07832	−	0.783446i
$300$	−2.40913	+	10.9061i	−0.139091	+	0.629665i
$301$	−2.32758	+	7.16356i	−0.134160	+	0.412901i
$302$	0.856535	+	5.40795i	0.0492880	+	0.311192i
$303$	−0.360264	−	2.27461i	−0.0206966	−	0.130673i
$304$	6.04825	−	18.6146i	0.346891	−	1.06762i
$305$	−10.8294	+	5.11252i	−0.620091	+	0.292742i
$306$	6.37947	−	4.63496i	0.364690	−	0.264963i
$307$	10.6721	−	10.6721i	0.609087	−	0.609087i	−0.333621	−	0.942707i	$-0.608270\pi$
$307$	10.6721	−	10.6721i	0.609087	−	0.609087i	0.942707	+	0.333621i	$0.108270\pi$
$308$		0			0
$309$		−	10.9449i		−	0.622635i
$310$	0.344209	−	11.4081i	0.0195498	−	0.647936i
$311$	8.43735	+	25.9675i	0.478438	+	1.47248i	0.841264	+	0.540624i	$0.181812\pi$
$311$	8.43735	+	25.9675i	0.478438	+	1.47248i	−0.362826	+	0.931857i	$0.618188\pi$
$312$	−4.25460	+	2.16783i	−0.240869	+	0.122729i
$313$	26.4908	−	4.19572i	1.49735	−	0.237156i	0.646639	−	0.762796i	$-0.276174\pi$
$313$	26.4908	−	4.19572i	1.49735	−	0.237156i	0.850707	+	0.525640i	$0.176174\pi$
$314$	−3.72151	−	2.70383i	−0.210017	−	0.152586i
$315$	2.35344	−	1.60371i	0.132601	−	0.0903588i
$316$	17.4766	−	5.67850i	0.983137	−	0.319441i
$317$	−1.94185	−	0.307559i	−0.109065	−	0.0172742i	0.101663	−	0.994819i	$-0.467584\pi$
$317$	−1.94185	−	0.307559i	−0.109065	−	0.0172742i	−0.210728	+	0.977545i	$0.567584\pi$
$318$	14.8550	+	14.8550i	0.833027	+	0.833027i
$319$		0			0
$320$	−0.887041	−	6.95161i	−0.0495871	−	0.388607i
$321$	13.7686	+	18.9509i	0.768489	+	1.05773i
$322$	−13.3079	+	26.1183i	−0.741621	+	1.45551i
$323$	−12.7419	−	25.0073i	−0.708976	−	1.39144i
$324$	−5.75673	+	7.92346i	−0.319819	+	0.440192i
$325$	6.01791	+	13.8115i	0.333813	+	0.766125i
$326$	16.8632	+	5.47920i	0.933969	+	0.303465i
$327$	−2.55399	−	1.30132i	−0.141236	−	0.0719633i
$328$	−1.21358	+	7.66223i	−0.0670087	+	0.423076i
$329$	0.914687			0.0504283
$330$		0			0
$331$	24.3840			1.34027			0.670133	−	0.742241i	$-0.266237\pi$
$331$	24.3840			1.34027			0.670133	+	0.742241i	$0.266237\pi$
$332$	0.252804	−	1.59614i	0.0138744	−	0.0875997i
$333$	−2.63136	−	1.34075i	−0.144198	−	0.0734724i
$334$	13.5499	+	4.40263i	0.741417	+	0.240901i
$335$	3.02029	+	10.3475i	0.165016	+	0.565345i
$336$	8.99003	−	12.3737i	0.490446	−	0.675041i
$337$	3.66337	+	7.18976i	0.199556	+	0.391651i	0.968999	−	0.247065i	$-0.0794660\pi$
$337$	3.66337	+	7.18976i	0.199556	+	0.391651i	−0.769443	+	0.638716i	$0.779466\pi$
$338$	−3.30504	+	6.48650i	−0.179770	+	0.352819i
$339$	7.61582	+	10.4823i	0.413635	+	0.569319i
$340$	−17.6156	−	13.6288i	−0.955341	−	0.739123i
$341$		0			0
$342$	−3.30304	−	3.30304i	−0.178608	−	0.178608i
$343$	−19.8558	−	3.14485i	−1.07211	−	0.169806i
$344$	−3.56287	+	1.15765i	−0.192097	+	0.0624162i
$345$	25.9415	+	4.91493i	1.39664	+	0.264611i
$346$	−20.5686	−	14.9440i	−1.10578	−	0.803394i
$347$	−28.6419	+	4.53644i	−1.53758	+	0.243529i	−0.867000	−	0.498308i	$-0.833955\pi$
$347$	−28.6419	+	4.53644i	−1.53758	+	0.243529i	−0.670580	+	0.741837i	$0.733955\pi$
$348$	−10.2180	+	5.20635i	−0.547744	+	0.279090i
$349$	−1.06444	−	3.27600i	−0.0569780	−	0.175360i	0.918517	−	0.395381i	$-0.129387\pi$
$349$	−1.06444	−	3.27600i	−0.0569780	−	0.175360i	−0.975495	+	0.220021i	$0.929387\pi$
$350$	−14.7946	−	12.1768i	−0.790803	−	0.650879i
$351$			16.8240i			0.897998i
$352$		0			0
$353$	−7.44497	+	7.44497i	−0.396256	+	0.396256i	−0.876910	−	0.480654i	$-0.840399\pi$
$353$	−7.44497	+	7.44497i	−0.396256	+	0.396256i	0.480654	+	0.876910i	$0.340399\pi$
$354$	30.0699	−	21.8471i	1.59820	−	1.16116i
$355$	−4.18237	−	8.85917i	−0.221977	−	0.470196i
$356$	−6.06652	+	18.6708i	−0.321525	+	0.989553i
$357$	−3.43094	−	21.6621i	−0.181585	−	1.14648i
$358$	−4.05297	−	25.5895i	−0.214206	−	1.35245i
$359$	−4.66630	+	14.3614i	−0.246278	+	0.757965i	0.749146	+	0.662405i	$0.230464\pi$
$359$	−4.66630	+	14.3614i	−0.246278	+	0.757965i	−0.995424	+	0.0955602i	$0.969536\pi$
$360$	1.33330	+	0.478131i	0.0702710	+	0.0251997i
$361$	1.92061	−	1.39540i	0.101085	−	0.0734423i
$362$	−25.9879	+	25.9879i	−1.36590	+	1.36590i
$363$		0			0
$364$			8.99983i			0.471719i
$365$	−20.0961	−	0.606347i	−1.05188	−	0.0317377i
$366$	4.74326	+	14.5983i	0.247934	+	0.763063i
$367$	−29.8064	+	15.1871i	−1.55588	+	0.792762i	−0.999277	−	0.0380157i	$-0.987896\pi$
$367$	−29.8064	+	15.1871i	−1.55588	+	0.792762i	−0.556605	+	0.830777i	$0.687896\pi$
$368$	−36.2646	+	5.74374i	−1.89042	+	0.299413i
$369$	3.77226	+	2.74071i	0.196376	+	0.142676i
$370$	−3.69882	+	19.5227i	−0.192293	+	1.01494i
$371$	−14.3893	+	4.67538i	−0.747058	+	0.242734i
$372$	−6.06550	−	0.960680i	−0.314481	−	0.0498090i
$373$	0.821903	+	0.821903i	0.0425565	+	0.0425565i	0.728065	−	0.685508i	$-0.240420\pi$
$373$	0.821903	+	0.821903i	0.0425565	+	0.0425565i	−0.685508	+	0.728065i	$0.740420\pi$
$374$		0			0
$375$	−6.79477	+	15.8651i	−0.350881	+	0.819271i
$376$	0.267401	+	0.368046i	0.0137902	+	0.0189805i
$377$	−7.02271	+	13.7829i	−0.361688	+	0.709853i
$378$	−9.71433	−	19.0654i	−0.499651	−	0.980621i
$379$	7.02572	−	9.67008i	0.360887	−	0.496719i	−0.589508	−	0.807762i	$-0.700679\pi$
$379$	7.02572	−	9.67008i	0.360887	−	0.496719i	0.950396	+	0.311044i	$0.100679\pi$
$380$	−6.34161	+	11.5697i	−0.325318	+	0.593511i
$381$	1.94795	+	0.632928i	0.0997966	+	0.0324259i
$382$	0.908433	+	0.462870i	0.0464795	+	0.0236825i
$383$	3.07077	−	19.3881i	0.156909	−	0.990684i	−0.776042	−	0.630681i	$-0.782776\pi$
$383$	3.07077	−	19.3881i	0.156909	−	0.990684i	0.932951	−	0.360003i	$-0.117224\pi$
$384$	12.1935			0.622245
$385$		0			0
$386$	9.39212			0.478046
$387$	−0.352237	+	2.22394i	−0.0179052	+	0.113049i
$388$	10.8699	+	5.53847i	0.551833	+	0.281173i
$389$	33.6777	+	10.9425i	1.70753	+	0.554809i	0.989918	−	0.141639i	$-0.0452374\pi$
$389$	33.6777	+	10.9425i	1.70753	+	0.554809i	0.717607	+	0.696448i	$0.245237\pi$
$390$	18.5366	−	5.41058i	0.938640	−	0.273976i
$391$	−30.9471	+	42.5950i	−1.56506	+	2.15412i
$392$	−1.27679	−	2.50585i	−0.0644878	−	0.126564i
$393$	6.59722	−	12.9478i	0.332786	−	0.653129i
$394$	−8.22766	−	11.3244i	−0.414504	−	0.570515i
$395$	28.1671	−	3.59419i	1.41724	−	0.180843i
$396$		0			0
$397$	−13.8345	−	13.8345i	−0.694333	−	0.694333i	0.268849	−	0.963182i	$-0.413357\pi$
$397$	−13.8345	−	13.8345i	−0.694333	−	0.694333i	−0.963182	+	0.268849i	$0.913357\pi$
$398$	10.7954	+	1.70983i	0.541126	+	0.0857059i
$399$	−12.3563	+	4.01481i	−0.618590	+	0.200992i
$400$	1.44700	−	23.9570i	0.0723499	−	1.19785i
$401$	−5.37959	−	3.90850i	−0.268644	−	0.195181i	0.445305	−	0.895379i	$-0.353095\pi$
$401$	−5.37959	−	3.90850i	−0.268644	−	0.195181i	−0.713949	+	0.700198i	$0.753095\pi$
$402$	13.6461	−	2.16133i	0.680606	−	0.107797i
$403$	−7.38073	+	3.76067i	−0.367660	+	0.187332i
$404$	−0.667111	−	2.05316i	−0.0331900	−	0.102148i
$405$	−11.0193	+	10.3738i	−0.547552	+	0.515478i
$406$		−	19.6741i		−	0.976411i
$407$		0			0
$408$	7.71325	−	7.71325i	0.381863	−	0.381863i
$409$	−23.6337	+	17.1709i	−1.16861	+	0.849047i	−0.990842	−	0.135025i	$-0.956889\pi$
$409$	−23.6337	+	17.1709i	−1.16861	+	0.849047i	−0.177771	+	0.984072i	$0.556889\pi$
$410$	10.5899	−	29.5307i	0.522999	−	1.45842i
$411$	−5.82146	+	17.9166i	−0.287152	+	0.883762i
$412$	−1.60499	−	10.1335i	−0.0790723	−	0.499243i
$413$	4.18749	+	26.4388i	0.206053	+	1.30097i
$414$	−2.70786	+	8.33393i	−0.133084	+	0.409591i
$415$	0.842946	−	2.35061i	0.0413786	−	0.115387i
$416$	−16.7196	+	12.1475i	−0.819747	+	0.595581i
$417$	−7.66299	+	7.66299i	−0.375258	+	0.375258i
$418$		0			0
$419$			19.2755i			0.941672i	0.882221	+	0.470836i	$0.156048\pi$
$419$			19.2755i			0.941672i	−0.882221	+	0.470836i	$0.843952\pi$
$420$	−7.50685	+	7.06712i	−0.366297	+	0.344840i
$421$	−11.2868	−	34.7372i	−0.550085	−	1.69299i	−0.708582	−	0.705629i	$-0.750665\pi$
$421$	−11.2868	−	34.7372i	−0.550085	−	1.69299i	0.158497	−	0.987359i	$-0.449335\pi$
$422$	25.0902	−	12.7841i	1.22137	−	0.622320i
$423$	0.270068	−	0.0427745i	0.0131311	−	0.00207977i
$424$	−6.08785	−	4.42308i	−0.295652	−	0.214804i
$425$	−22.8244	−	25.7588i	−1.10715	−	1.24949i
$426$	−11.9423	+	3.88029i	−0.578607	+	0.188001i
$427$	−10.9185	−	1.72931i	−0.528381	−	0.0836874i
$428$	15.5269	+	15.5269i	0.750520	+	0.750520i
$429$		0			0
$430$	15.0278	−	1.91758i	0.724704	−	0.0924738i
$431$	7.12379	+	9.80505i	0.343141	+	0.472293i	0.945355	−	0.326041i	$-0.105715\pi$
$431$	7.12379	+	9.80505i	0.343141	+	0.472293i	−0.602215	+	0.798334i	$0.705715\pi$
$432$	12.1678	−	23.8806i	0.585423	−	1.14896i
$433$	−2.14939	−	4.21842i	−0.103293	−	0.202725i	0.833576	−	0.552406i	$-0.186290\pi$
$433$	−2.14939	−	4.21842i	−0.103293	−	0.202725i	−0.936869	+	0.349681i	$0.886290\pi$
$434$	6.19262	−	8.52340i	0.297255	−	0.409136i
$435$	−17.0110	+	4.96528i	−0.815616	+	0.238067i
$436$	−2.55548	−	0.830326i	−0.122385	−	0.0397654i
$437$	27.7897	+	14.1596i	1.32936	+	0.677343i
$438$	−4.03125	+	25.4523i	−0.192621	+	1.21616i
$439$	−26.1692			−1.24899			−0.624494	−	0.781029i	$-0.714695\pi$
$439$	−26.1692			−1.24899			−0.624494	+	0.781029i	$0.714695\pi$
$440$		0			0
$441$	−1.69037			−0.0804939
$442$	−6.02374	+	38.0324i	−0.286520	+	1.80902i
$443$	−25.4718	−	12.9785i	−1.21020	−	0.616629i	−0.271860	−	0.962337i	$-0.587639\pi$
$443$	−25.4718	−	12.9785i	−1.21020	−	0.616629i	−0.938342	+	0.345708i	$0.887639\pi$
$444$	10.1681	+	3.30383i	0.482558	+	0.156793i
$445$	−14.5811	+	26.6018i	−0.691209	+	1.26104i
$446$	3.27408	−	4.50638i	0.155032	−	0.213383i
$447$	−0.942801	−	1.85035i	−0.0445929	−	0.0875186i
$448$	2.93687	−	5.76393i	0.138754	−	0.272320i
$449$	−2.78863	−	3.83822i	−0.131603	−	0.181137i	0.738130	−	0.674659i	$-0.235709\pi$
$449$	−2.78863	−	3.83822i	−0.131603	−	0.181137i	−0.869733	+	0.493522i	$0.835709\pi$
$450$	−4.93764	−	2.90344i	−0.232763	−	0.136869i
$451$		0			0
$452$	8.58838	+	8.58838i	0.403963	+	0.403963i
$453$	4.49642	+	0.712163i	0.211260	+	0.0334603i
$454$	1.32533	−	0.430625i	0.0622007	−	0.0202102i
$455$	−2.58879	+	13.6639i	−0.121364	+	0.640573i
$456$	−5.22772	−	3.79816i	−0.244810	−	0.177865i
$457$	33.4359	−	5.29572i	1.56406	−	0.247724i	0.686481	−	0.727147i	$-0.259154\pi$
$457$	33.4359	−	5.29572i	1.56406	−	0.247724i	0.877584	+	0.479424i	$0.159154\pi$
$458$	13.3446	−	6.79943i	0.623554	−	0.317716i
$459$	−11.8764	−	36.5519i	−0.554344	−	1.70610i
$460$	24.7391	+	0.746436i	1.15346	+	0.0348028i
$461$		−	28.3761i		−	1.32161i	−0.750559	−	0.660803i	$-0.770216\pi$
$461$		−	28.3761i		−	1.32161i	0.750559	−	0.660803i	$-0.229784\pi$
$462$		0			0
$463$	−16.0155	+	16.0155i	−0.744304	+	0.744304i	−0.973403	−	0.229099i	$-0.926422\pi$
$463$	−16.0155	+	16.0155i	−0.744304	+	0.744304i	0.229099	+	0.973403i	$0.426422\pi$
$464$	19.9367	−	14.4848i	0.925536	−	0.672441i
$465$	−8.93253	−	3.20328i	−0.414236	−	0.148548i
$466$	−0.960252	+	2.95535i	−0.0444828	+	0.136904i
$467$	0.689823	+	4.35537i	0.0319212	+	0.201543i	0.998495	−	0.0548469i	$-0.0174671\pi$
$467$	0.689823	+	4.35537i	0.0319212	+	0.201543i	−0.966574	+	0.256389i	$0.917467\pi$
$468$	0.420869	+	2.65726i	0.0194547	+	0.122832i
$469$	−3.07481	+	9.46328i	−0.141981	+	0.436974i
$470$	−0.785400	−	1.66365i	−0.0362278	−	0.0767383i
$471$	−3.09423	+	2.24809i	−0.142575	+	0.103587i
$472$	−9.41408	+	9.41408i	−0.433318	+	0.433318i
$473$		0			0
$474$		−	36.3955i		−	1.67170i
$475$	−12.9561	+	15.7413i	−0.594466	+	0.722262i
$476$	−6.35318	−	19.5531i	−0.291198	−	0.896214i
$477$	−4.02991	+	2.05334i	−0.184517	+	0.0940162i
$478$	−30.2608	+	4.79285i	−1.38410	+	0.219220i
$479$	14.1416	+	10.2744i	0.646144	+	0.469451i	0.861956	−	0.506984i	$-0.169240\pi$
$479$	14.1416	+	10.2744i	0.646144	+	0.469451i	−0.215811	+	0.976435i	$0.569240\pi$
$480$	−23.2615	−	4.40717i	−1.06174	−	0.201159i
$481$	13.7155	−	4.45645i	0.625375	−	0.203197i
$482$	38.9790	+	6.17366i	1.77544	+	0.281203i
$483$	17.2339	+	17.2339i	0.784168	+	0.784168i
$484$		0			0
$485$	14.9099	+	11.5354i	0.677024	+	0.523797i
$486$	−6.87822	−	9.46705i	−0.312002	−	0.429434i
$487$	8.38431	−	16.4551i	0.379929	−	0.745653i	−0.619290	−	0.785162i	$-0.712579\pi$
$487$	8.38431	−	16.4551i	0.379929	−	0.745653i	0.999219	+	0.0395092i	$0.0125795\pi$
$488$	−2.49609	−	4.89885i	−0.112993	−	0.221760i
$489$	8.66539	−	11.9269i	0.391862	−	0.539352i
$490$	3.18669	+	10.9176i	0.143960	+	0.493207i
$491$	−12.6037	−	4.09521i	−0.568799	−	0.184814i	0.0104775	−	0.999945i	$-0.496665\pi$
$491$	−12.6037	−	4.09521i	−0.568799	−	0.184814i	−0.579277	+	0.815131i	$0.696665\pi$
$492$	−15.0404	−	7.66348i	−0.678075	−	0.345497i
$493$	5.52797	−	34.9022i	0.248967	−	1.57192i
$494$	22.8105			1.02629
$495$		0			0
$496$	13.1964			0.592534
$497$	1.41469	−	8.93200i	0.0634575	−	0.400655i
$498$	−2.85186	−	1.45310i	−0.127795	−	0.0651149i
$499$	11.0332	+	3.58490i	0.493913	+	0.160482i	0.545374	−	0.838193i	$-0.316388\pi$
$499$	11.0332	+	3.58490i	0.493913	+	0.160482i	−0.0514608	+	0.998675i	$0.516388\pi$
$500$	−3.96454	+	15.6854i	−0.177300	+	0.701471i
$501$	6.96278	−	9.58344i	0.311074	−	0.428156i
$502$	−21.9575	−	43.0940i	−0.980011	−	1.92338i
$503$	−1.91581	+	3.75999i	−0.0854218	+	0.167650i	−0.929766	−	0.368152i	$-0.879991\pi$
$503$	−1.91581	+	3.75999i	−0.0854218	+	0.167650i	0.844344	+	0.535802i	$0.179991\pi$
$504$	0.768530	+	1.05779i	0.0342330	+	0.0471177i
$505$	−0.422246	−	3.30908i	−0.0187897	−	0.147252i
$506$		0			0
$507$	4.28005	+	4.28005i	0.190084	+	0.190084i
$508$	1.89636	+	0.300353i	0.0841372	+	0.0133260i
$509$	25.8090	−	8.38584i	1.14396	−	0.371696i	0.325097	−	0.945681i	$-0.394603\pi$
$509$	25.8090	−	8.38584i	1.14396	−	0.371696i	0.818866	+	0.573985i	$0.194603\pi$
$510$	−36.4534	+	24.8405i	−1.61418	+	1.09996i
$511$	−15.0145	−	10.9087i	−0.664204	−	0.482572i
$512$	22.7838	−	3.60860i	1.00691	−	0.159479i
$513$	−20.2855	+	10.3360i	−0.895628	+	0.456345i
$514$	1.40958	+	4.33824i	0.0621739	+	0.191352i
$515$	0.478135	−	15.8468i	0.0210692	−	0.698293i
$516$		−	8.15151i		−	0.358850i
$517$		0			0
$518$	−12.9697	+	12.9697i	−0.569855	+	0.569855i
$519$	−17.1017	+	12.4251i	−0.750683	+	0.545403i
$520$	−6.25480	+	2.95286i	−0.274291	+	0.129491i
$521$	3.57064	−	10.9893i	0.156433	−	0.481450i	−0.841871	−	0.539679i	$-0.818545\pi$
$521$	3.57064	−	10.9893i	0.156433	−	0.481450i	0.998303	+	0.0582294i	$0.0185455\pi$
$522$	−0.920043	−	5.80892i	−0.0402692	−	0.254250i
$523$	−4.46255	−	28.1755i	−0.195134	−	1.23203i	−0.869613	−	0.493733i	$-0.835632\pi$
$523$	−4.46255	−	28.1755i	−0.195134	−	1.23203i	0.674480	−	0.738294i	$-0.264368\pi$
$524$	4.20944	−	12.9553i	0.183890	−	0.565956i
$525$	−13.4300	+	8.57024i	−0.586135	+	0.374036i
$526$	−30.2061	+	21.9460i	−1.31705	+	0.956892i
$527$	13.3807	−	13.3807i	0.582871	−	0.582871i
$528$		0			0
$529$		−	35.5083i		−	1.54384i
$530$	20.8591	+	22.1570i	0.906062	+	0.962440i
$531$	2.47277	+	7.61041i	0.107309	+	0.330264i
$532$	−10.8515	+	5.52914i	−0.470474	+	0.239719i
$533$	−22.4890	+	3.56192i	−0.974109	+	0.154284i
$534$	31.4566	+	22.8545i	1.36126	+	0.989013i
$535$	19.1072	+	28.0398i	0.826078	+	1.21227i
$536$	−4.70667	+	1.52929i	−0.203297	+	0.0660552i
$537$	−21.2763	−	3.36983i	−0.918139	−	0.145419i
$538$	−2.93813	−	2.93813i	−0.126672	−	0.126672i
$539$		0			0
$540$	−11.0554	+	14.2895i	−0.475750	+	0.614922i
$541$	−12.5833	−	17.3194i	−0.540996	−	0.744618i	0.447760	−	0.894154i	$-0.352222\pi$
$541$	−12.5833	−	17.3194i	−0.540996	−	0.744618i	−0.988756	+	0.149536i	$0.952222\pi$
$542$	2.49462	−	4.89596i	0.107153	−	0.210300i
$543$	13.8729	+	27.2271i	0.595344	+	1.16843i
$544$	27.7500	−	38.1946i	1.18977	−	1.63758i
$545$	−3.64099	−	1.99571i	−0.155963	−	0.0854870i
$546$	16.9526	+	5.50824i	0.725505	+	0.235731i
$547$	−4.05305	−	2.06513i	−0.173296	−	0.0882987i	0.365191	−	0.930933i	$-0.381004\pi$
$547$	−4.05305	−	2.06513i	−0.173296	−	0.0882987i	−0.538487	+	0.842634i	$0.681004\pi$
$548$	−2.76255	+	17.4421i	−0.118010	+	0.745088i
$549$	−3.30462			−0.141038
$550$		0			0
$551$	−20.9332			−0.891783
$552$	−1.89628	+	11.9726i	−0.0807109	+	0.509589i
$553$	23.3548	+	11.8998i	0.993145	+	0.506033i
$554$	−48.8088	−	15.8590i	−2.07369	−	0.673782i
$555$	14.4873	+	7.94085i	0.614952	+	0.337070i
$556$	−5.97118	+	8.21862i	−0.253234	+	0.348547i
$557$	4.29124	+	8.42203i	0.181826	+	0.356853i	0.963871	−	0.266368i	$-0.0858237\pi$
$557$	4.29124	+	8.42203i	0.181826	+	0.356853i	−0.782046	+	0.623221i	$0.785824\pi$
$558$	1.42982	−	2.80619i	0.0605293	−	0.118795i
$559$	−6.46291	−	8.89544i	−0.273352	−	0.376237i
$560$	13.5569	−	17.5228i	0.572884	−	0.740472i
$561$		0			0
$562$	−38.9240	−	38.9240i	−1.64191	−	1.64191i
$563$	32.9011	+	5.21103i	1.38662	+	0.219619i	0.804726	−	0.593647i	$-0.202312\pi$
$563$	32.9011	+	5.21103i	1.38662	+	0.219619i	0.581892	+	0.813266i	$0.302312\pi$
$564$	−0.941444	+	0.305894i	−0.0396419	+	0.0128804i
$565$	10.5688	+	15.5097i	0.444632	+	0.652496i
$566$	13.7306	+	9.97590i	0.577142	+	0.419318i
$567$	−13.7981	+	2.18541i	−0.579467	+	0.0917786i
$568$	4.00757	−	2.04196i	0.168154	−	0.0856788i
$569$	11.7947	+	36.3003i	0.494459	+	1.52179i	0.817798	+	0.575506i	$0.195195\pi$
$569$	11.7947	+	36.3003i	0.494459	+	1.52179i	−0.323338	+	0.946283i	$0.604805\pi$
$570$	17.9120	+	19.0265i	0.750251	+	0.796933i
$571$		−	0.631817i		−	0.0264407i	−0.999913	−	0.0132204i	$-0.995792\pi$
$571$		−	0.631817i		−	0.0264407i	0.999913	−	0.0132204i	$-0.00420829\pi$
$572$		0			0
$573$	0.599420	−	0.599420i	0.0250411	−	0.0250411i
$574$	23.4286	−	17.0219i	0.977890	−	0.710479i
$575$	37.3451	+	8.24943i	1.55740	+	0.344025i
$576$	0.597586	−	1.83918i	0.0248994	−	0.0766325i
$577$	−1.53195	−	9.67233i	−0.0637758	−	0.402665i	−0.998839	−	0.0481823i	$-0.984657\pi$
$577$	−1.53195	−	9.67233i	−0.0637758	−	0.402665i	0.935063	−	0.354482i	$-0.115343\pi$
$578$	−8.82323	−	55.7077i	−0.366998	−	2.31714i
$579$	2.41313	−	7.42684i	0.100286	−	0.308649i
$580$	−15.0218	+	7.09172i	−0.623746	+	0.294468i
$581$	1.86489	−	1.35492i	0.0773685	−	0.0562115i
$582$	17.0854	−	17.0854i	0.708211	−	0.708211i
$583$		0			0
$584$		−	9.23051i		−	0.381961i
$585$	−0.125379	+	4.15542i	−0.00518378	+	0.171806i
$586$	−1.01140	−	3.11277i	−0.0417806	−	0.128588i
$587$	12.1249	−	6.17797i	0.500450	−	0.254992i	−0.185495	−	0.982645i	$-0.559389\pi$
$587$	12.1249	−	6.17797i	0.500450	−	0.254992i	0.685945	+	0.727653i	$0.259389\pi$
$588$	6.04418	−	0.957304i	0.249258	−	0.0394786i
$589$	−9.06885	−	6.58891i	−0.373676	−	0.271491i
$590$	44.4916	−	30.3180i	1.83169	−	1.24817i
$591$	−11.0687	+	3.59645i	−0.455307	+	0.147938i
$592$	−22.6915	−	3.59398i	−0.932614	−	0.147712i
$593$	6.27189	+	6.27189i	0.257555	+	0.257555i	0.824059	−	0.566504i	$-0.191704\pi$
$593$	6.27189	+	6.27189i	0.257555	+	0.257555i	−0.566504	+	0.824059i	$0.691704\pi$
$594$		0			0
$595$	−4.02123	−	31.5137i	−0.164854	−	1.29194i
$596$	−1.14425	−	1.57492i	−0.0468702	−	0.0645113i
$597$	4.12573	−	8.09721i	0.168855	−	0.331397i
$598$	−19.4266	−	38.1269i	−0.794414	−	1.55913i
$599$	−14.2632	+	19.6316i	−0.582779	+	0.802126i	−0.993997	−	0.109411i	$-0.965104\pi$
$599$	−14.2632	+	19.6316i	−0.582779	+	0.802126i	0.411218	+	0.911537i	$0.365104\pi$
$600$	−7.37460	−	2.89846i	−0.301067	−	0.118329i
$601$	−22.2254	−	7.22146i	−0.906592	−	0.294570i	−0.181637	−	0.983366i	$-0.558140\pi$
$601$	−22.2254	−	7.22146i	−0.906592	−	0.294570i	−0.724955	+	0.688796i	$0.758140\pi$
$602$	12.4603	+	6.34883i	0.507843	+	0.258759i
$603$	−0.465316	+	2.93789i	−0.0189491	+	0.119640i
$604$	4.26751			0.173643
$605$		0			0
$606$	−4.27575			−0.173691
$607$	2.80466	−	17.7079i	0.113838	−	0.718743i	−0.863070	−	0.505084i	$-0.831462\pi$
$607$	2.80466	−	17.7079i	0.113838	−	0.718743i	0.976908	−	0.213660i	$-0.0685383\pi$
$608$	−24.9188	−	12.6967i	−1.01059	−	0.514921i
$609$	−15.5574	−	5.05490i	−0.630416	−	0.204835i
$610$	6.22988	+	21.3435i	0.252240	+	0.864175i
$611$	−0.784835	+	1.08023i	−0.0317510	+	0.0437016i
$612$	−2.79020	−	5.47609i	−0.112787	−	0.221358i
$613$	17.3350	−	34.0219i	0.700156	−	1.37413i	−0.217225	−	0.976122i	$-0.569701\pi$
$613$	17.3350	−	34.0219i	0.700156	−	1.37413i	0.917381	−	0.398011i	$-0.130299\pi$
$614$	−16.4705	−	22.6697i	−0.664695	−	0.914874i
$615$	−20.6306	−	15.9614i	−0.831905	−	0.643624i
$616$		0			0
$617$	−9.02298	−	9.02298i	−0.363252	−	0.363252i	0.501757	−	0.865009i	$-0.332687\pi$
$617$	−9.02298	−	9.02298i	−0.363252	−	0.363252i	−0.865009	+	0.501757i	$0.832687\pi$
$618$	−20.0704	−	3.17885i	−0.807352	−	0.127872i
$619$	−38.0001	+	12.3470i	−1.52735	+	0.496267i	−0.947853	−	0.318707i	$-0.896751\pi$
$619$	−38.0001	+	12.3470i	−1.52735	+	0.496267i	−0.579498	+	0.814973i	$0.696751\pi$
$620$	−8.74007	−	1.65591i	−0.351009	−	0.0665030i
$621$	34.5524	+	25.1038i	1.38654	+	1.00738i
$622$	50.0689	−	7.93013i	2.00758	−	0.317969i
$623$	−24.9506	+	12.7130i	−0.999626	+	0.509335i
$624$	6.89941	+	21.2342i	0.276197	+	0.850048i
$625$	−10.5310	+	22.6737i	−0.421240	+	0.906949i
$626$		−	49.7965i		−	1.99027i
$627$		0			0
$628$	−2.53518	+	2.53518i	−0.101165	+	0.101165i
$629$	−26.6526	+	19.3642i	−1.06271	+	0.772102i
$630$	−2.25730	−	4.78144i	−0.0899329	−	0.190497i
$631$	−2.70001	+	8.30977i	−0.107486	+	0.330807i	−0.990306	−	0.138904i	$-0.955642\pi$
$631$	−2.70001	+	8.30977i	−0.107486	+	0.330807i	0.882820	+	0.469711i	$0.155642\pi$
$632$	2.03938	+	12.8762i	0.0811223	+	0.512186i
$633$	−3.66261	−	23.1248i	−0.145576	−	0.919128i
$634$	−1.12798	+	3.47157i	−0.0447979	+	0.137874i
$635$	2.79273	+	1.00149i	0.110826	+	0.0397430i
$636$	13.2467	−	9.62430i	0.525266	−	0.381628i
$637$	5.83679	−	5.83679i	0.231262	−	0.231262i
$638$		0			0
$639$		−	2.70339i		−	0.106945i
$640$	17.6545	+	0.532679i	0.697856	+	0.0210560i
$641$	6.80796	+	20.9528i	0.268898	+	0.827584i	0.990770	+	0.135557i	$0.0432823\pi$
$641$	6.80796	+	20.9528i	0.268898	+	0.827584i	−0.721871	+	0.692027i	$0.756718\pi$
$642$	38.7504	−	19.7443i	1.52936	−	0.779247i
$643$	43.4989	−	6.88955i	1.71543	−	0.271697i	0.780146	−	0.625597i	$-0.215145\pi$
$643$	43.4989	−	6.88955i	1.71543	−	0.271697i	0.935283	+	0.353900i	$0.115145\pi$
$644$	18.4835	+	13.4290i	0.728351	+	0.529178i
$645$	2.34477	−	12.3759i	0.0923253	−	0.487302i
$646$	−49.5583	+	16.1025i	−1.94985	+	0.633544i
$647$	−37.4969	−	5.93893i	−1.47416	−	0.233484i	−0.632948	−	0.774194i	$-0.718155\pi$
$647$	−37.4969	−	5.93893i	−1.47416	−	0.233484i	−0.841209	+	0.540711i	$0.818155\pi$
$648$	−4.91312	−	4.91312i	−0.193006	−	0.193006i
$649$		0			0
$650$	27.0750	−	7.02402i	1.06197	−	0.275505i
$651$	−5.14883	−	7.08675i	−0.201798	−	0.277752i
$652$	6.27399	−	12.3134i	0.245709	−	0.482230i
$653$	−3.68718	−	7.23650i	−0.144290	−	0.283186i	0.807539	−	0.589814i	$-0.200799\pi$
$653$	−3.68718	−	7.23650i	−0.144290	−	0.283186i	−0.951829	+	0.306628i	$0.900799\pi$
$654$	−3.12811	+	4.30547i	−0.122319	+	0.168357i
$655$	10.1175	−	18.4584i	0.395324	−	0.721231i
$656$	34.4980	+	11.2091i	1.34692	+	0.437641i
$657$	−4.94328	−	2.51873i	−0.192856	−	0.0982650i
$658$	0.265662	−	1.67732i	0.0103566	−	0.0653889i
$659$	35.1688			1.36998			0.684990	−	0.728552i	$-0.259806\pi$
$659$	35.1688			1.36998			0.684990	+	0.728552i	$0.259806\pi$
$660$		0			0
$661$	−40.3405			−1.56906			−0.784531	−	0.620090i	$-0.787096\pi$
$661$	−40.3405			−1.56906			−0.784531	+	0.620090i	$0.787096\pi$
$662$	7.08210	−	44.7146i	0.275254	−	1.73788i
$663$	28.5265	+	14.5350i	1.10788	+	0.564492i
$664$	1.09037	+	0.354282i	0.0423145	+	0.0137488i
$665$	−18.0657	+	5.27312i	−0.700557	+	0.204483i
$666$	−3.22287	+	4.43590i	−0.124884	+	0.171888i
$667$	17.8278	+	34.9889i	0.690293	+	1.35478i
$668$	5.04125	−	9.89402i	0.195052	−	0.382811i
$669$	−2.72222	−	3.74681i	−0.105247	−	0.144860i
$670$	19.8522	−	2.53318i	0.766956	−	0.0978653i
$671$		0			0
$672$	−15.4535	−	15.4535i	−0.596130	−	0.596130i
$673$	−29.5233	−	4.67604i	−1.13804	−	0.180248i	−0.441155	−	0.897431i	$-0.645431\pi$
$673$	−29.5233	−	4.67604i	−1.13804	−	0.180248i	−0.696885	+	0.717183i	$0.745431\pi$
$674$	14.2483	−	4.62957i	0.548826	−	0.178324i
$675$	−20.8951	+	18.5148i	−0.804255	+	0.712635i
$676$	4.59039	+	3.33511i	0.176553	+	0.128274i
$677$	−12.4267	+	1.96819i	−0.477596	+	0.0756438i	−0.390591	−	0.920564i	$-0.627729\pi$
$677$	−12.4267	+	1.96819i	−0.477596	+	0.0756438i	−0.0870046	+	0.996208i	$0.527729\pi$
$678$	21.4340	−	10.9212i	0.823168	−	0.419425i
$679$	5.37735	+	16.5498i	0.206364	+	0.635123i
$680$	11.5047	−	10.8308i	0.441186	−	0.415342i
$681$		−	1.15865i		−	0.0443994i
$682$		0			0
$683$	1.03200	−	1.03200i	0.0394883	−	0.0394883i	−0.687087	−	0.726575i	$-0.741111\pi$
$683$	1.03200	−	1.03200i	0.0394883	−	0.0394883i	0.726575	+	0.687087i	$0.241111\pi$
$684$	−2.94543	+	2.13998i	−0.112621	+	0.0818242i
$685$	−9.21140	+	25.6866i	−0.351950	+	0.981433i
$686$	−11.5338	+	35.4975i	−0.440364	+	1.35530i
$687$	−1.94802	−	12.2993i	−0.0743214	−	0.469247i
$688$	2.74018	+	17.3008i	0.104468	+	0.659586i
$689$	6.82503	−	21.0053i	0.260013	−	0.800237i
$690$	16.5473	−	46.1431i	0.629945	−	1.75664i
$691$	32.0075	−	23.2548i	1.21762	−	0.884654i	0.221722	−	0.975110i	$-0.428832\pi$
$691$	32.0075	−	23.2548i	1.21762	−	0.884654i	0.995900	+	0.0904558i	$0.0288324\pi$
$692$	−14.0118	+	14.0118i	−0.532651	+	0.532651i
$693$		0			0
$694$			53.8402i			2.04375i
$695$	−11.4297	+	10.7602i	−0.433555	+	0.408159i
$696$	−2.51411	−	7.73763i	−0.0952970	−	0.293294i
$697$	46.3454	−	23.6142i	1.75546	−	0.894451i
$698$	−6.31658	+	1.00045i	−0.239086	+	0.0378675i
$699$	2.09023	+	1.51864i	0.0790599	+	0.0574404i
$700$	−11.1777	+	9.90431i	−0.422476	+	0.374348i
$701$	1.11844	−	0.363404i	0.0422430	−	0.0137256i	−0.287819	−	0.957685i	$-0.592930\pi$
$701$	1.11844	−	0.363404i	0.0422430	−	0.0137256i	0.330062	+	0.943959i	$0.392930\pi$
$702$	30.8513	+	4.88636i	1.16441	+	0.184424i
$703$	13.7997	+	13.7997i	0.520464	+	0.520464i
$704$		0			0
$705$	−1.51733	+	0.193614i	−0.0571458	+	0.00729194i
$706$	11.4900	+	15.8147i	0.432433	+	0.595193i
$707$	1.39800	−	2.74372i	0.0525771	−	0.103188i
$708$	−13.1518	−	25.8118i	−0.494273	−	0.970066i
$709$	17.3156	−	23.8329i	0.650301	−	0.895063i	−0.348811	−	0.937193i	$-0.613415\pi$
$709$	17.3156	−	23.8329i	0.650301	−	0.895063i	0.999112	+	0.0421305i	$0.0134145\pi$
$710$	−17.4604	+	5.09644i	−0.655277	+	0.191266i
$711$	7.45214	+	2.42135i	0.279477	+	0.0908076i
$712$	−12.4095	−	6.32294i	−0.465065	−	0.236962i
$713$	−3.28959	+	20.7697i	−0.123196	+	0.777830i
$714$	−40.7198			−1.52390
$715$		0			0
$716$	−20.1931			−0.754653
$717$	−3.98499	+	25.1603i	−0.148822	+	0.939627i
$718$	24.9802	+	12.7280i	0.932252	+	0.475006i
$719$	14.4170	+	4.68435i	0.537662	+	0.174697i	0.565246	−	0.824923i	$-0.308781\pi$
$719$	14.4170	+	4.68435i	0.537662	+	0.174697i	−0.0275840	+	0.999619i	$0.508781\pi$
$720$	3.18334	−	5.80769i	0.118636	−	0.216440i
$721$	8.60206	−	11.8397i	0.320358	−	0.440934i
$722$	−2.00102	−	3.92723i	−0.0744704	−	0.146156i
$723$	14.8967	−	29.2365i	0.554016	−	1.08732i
$724$	16.8371	+	23.1743i	0.625747	+	0.861266i
$725$	−24.8466	+	6.44592i	−0.922780	+	0.239395i
$726$		0			0
$727$	6.89315	+	6.89315i	0.255653	+	0.255653i	0.823283	−	0.567631i	$-0.192140\pi$
$727$	6.89315	+	6.89315i	0.255653	+	0.255653i	−0.567631	+	0.823283i	$0.692140\pi$
$728$	−6.30622	−	0.998807i	−0.233724	−	0.0370182i
$729$	−28.5640	+	9.28102i	−1.05793	+	0.343741i
$730$	−6.94862	+	36.6755i	−0.257180	+	1.35742i
$731$	20.3209	+	14.7640i	0.751594	+	0.546065i
$732$	11.8162	−	1.87150i	0.436739	−	0.0691726i
$733$	8.01134	−	4.08198i	0.295906	−	0.150771i	−0.299735	−	0.954022i	$-0.596898\pi$
$733$	8.01134	−	4.08198i	0.295906	−	0.150771i	0.595641	+	0.803251i	$0.296898\pi$
$734$	19.1927	+	59.0690i	0.708415	+	2.18028i
$735$	9.45188	+	0.285186i	0.348638	+	0.0105192i
$736$			52.4639i			1.93385i
$737$		0			0
$738$	6.12144	−	6.12144i	0.225333	−	0.225333i
$739$	7.29302	−	5.29869i	0.268278	−	0.194915i	−0.445511	−	0.895277i	$-0.646978\pi$
$739$	7.29302	−	5.29869i	0.268278	−	0.194915i	0.713788	+	0.700361i	$0.246978\pi$
$740$	14.5778	+	5.22770i	0.535890	+	0.192174i
$741$	5.86074	−	18.0375i	0.215300	−	0.662624i
$742$	4.39432	+	27.7446i	0.161321	+	1.01854i
$743$	−5.60782	−	35.4064i	−0.205731	−	1.29894i	−0.846989	−	0.531610i	$-0.821587\pi$
$743$	−5.60782	−	35.4064i	−0.205731	−	1.29894i	0.641258	−	0.767325i	$-0.278413\pi$
$744$	1.34631	−	4.14350i	0.0493580	−	0.151908i
$745$	−1.28422	−	2.72025i	−0.0470500	−	0.0996622i
$746$	1.74589	−	1.26847i	0.0639217	−	0.0464419i
$747$	0.487259	−	0.487259i	0.0178279	−	0.0178279i
$748$		0			0
$749$			31.3215i			1.14446i
$750$	27.1195	+	17.0679i	0.990262	+	0.623232i
$751$	−8.62499	−	26.5450i	−0.314730	−	0.968640i	−0.975865	−	0.218373i	$-0.929925\pi$
$751$	−8.62499	−	26.5450i	−0.314730	−	0.968640i	0.661135	−	0.750267i	$-0.270075\pi$
$752$	1.89530	−	0.965702i	0.0691143	−	0.0352155i
$753$	−39.7183	+	6.29076i	−1.44741	+	0.229248i
$754$	23.2349	+	16.8811i	0.846164	+	0.614774i
$755$	6.47911	+	1.22755i	0.235799	+	0.0446750i
$756$	−15.8612	+	5.15360i	−0.576865	+	0.187435i
$757$	42.8987	+	6.79448i	1.55918	+	0.246950i	0.875640	−	0.482965i	$-0.160440\pi$
$757$	42.8987	+	6.79448i	1.55918	+	0.246950i	0.683538	+	0.729915i	$0.260440\pi$
$758$	−15.6921	−	15.6921i	−0.569964	−	0.569964i
$759$		0			0
$760$	−7.40311	−	5.72760i	−0.268539	−	0.207762i
$761$	1.89773	+	2.61200i	0.0687925	+	0.0946848i	0.842027	−	0.539436i	$-0.181362\pi$
$761$	1.89773	+	2.61200i	0.0687925	+	0.0946848i	−0.773234	+	0.634120i	$0.781362\pi$
$762$	1.72641	−	3.38826i	0.0625411	−	0.122744i
$763$	−1.74003	−	3.41500i	−0.0629933	−	0.123631i
$764$	0.467082	−	0.642883i	0.0168984	−	0.0232587i
$765$	−2.66101	−	9.11660i	−0.0962089	−	0.329612i
$766$	−34.6613	−	11.2622i	−1.25236	−	0.406918i
$767$	−34.8169	−	17.7401i	−1.25716	−	0.640557i
$768$	5.05514	−	31.9169i	0.182412	−	1.15170i
$769$	−5.00727			−0.180567			−0.0902834	−	0.995916i	$-0.528777\pi$
$769$	−5.00727			−0.180567			−0.0902834	+	0.995916i	$0.528777\pi$
$770$		0			0
$771$	3.79264			0.136589
$772$	1.14514	−	7.23012i	0.0412145	−	0.260218i
$773$	−7.52455	−	3.83395i	−0.270639	−	0.137898i	0.313405	−	0.949620i	$-0.398530\pi$
$773$	−7.52455	−	3.83395i	−0.270639	−	0.137898i	−0.584044	+	0.811722i	$0.698530\pi$
$774$	3.97588	+	1.29184i	0.142910	+	0.0464343i
$775$	−12.7932	−	5.02814i	−0.459545	−	0.180616i
$776$	−5.08717	+	7.00189i	−0.182619	+	0.251353i
$777$	6.92349	+	13.5881i	0.248379	+	0.487471i
$778$	29.8474	−	58.5789i	1.07008	−	2.10015i
$779$	−18.1112	−	24.9279i	−0.648900	−	0.893134i
$780$	−1.90502	−	14.9293i	−0.0682106	−	0.534556i
$781$		0			0
$782$	69.1211	+	69.1211i	2.47176	+	2.47176i
$783$	−28.3121	−	4.48420i	−1.01179	−	0.160252i
$784$	−12.5064	+	4.06357i	−0.446657	+	0.145128i
$785$	−4.57825	+	3.11977i	−0.163405	+	0.111349i
$786$	−21.8271	−	15.8583i	−0.778547	−	0.565648i
$787$	11.2860	−	1.78753i	0.402302	−	0.0637184i	0.0479951	−	0.998848i	$-0.484717\pi$
$787$	11.2860	−	1.78753i	0.402302	−	0.0637184i	0.354307	+	0.935129i	$0.384717\pi$
$788$	−9.72078	+	4.95299i	−0.346288	+	0.176443i
$789$	9.59298	+	29.5242i	0.341519	+	1.05109i
$790$	1.58996	−	52.6958i	0.0565682	−	1.87483i
$791$			17.3249i			0.616001i
$792$		0			0
$793$	11.4107	−	11.4107i	0.405207	−	0.405207i
$794$	−29.3873	+	21.3511i	−1.04292	+	0.757724i
$795$	22.8801	−	10.8016i	0.811473	−	0.383092i
$796$	2.63248	−	8.10193i	0.0933057	−	0.287165i
$797$	−2.93414	−	18.5254i	−0.103933	−	0.656204i	−0.983566	−	0.180551i	$-0.942212\pi$
$797$	−2.93414	−	18.5254i	−0.103933	−	0.656204i	0.879633	−	0.475653i	$-0.157788\pi$
$798$	3.77346	+	23.8247i	0.133579	+	0.843385i
$799$	0.942577	−	2.90096i	0.0333460	−	0.102628i
$800$	−33.4870	−	7.39719i	−1.18394	−	0.261530i
$801$	−6.77234	+	4.92039i	−0.239289	+	0.173854i
$802$	−8.72973	+	8.72973i	−0.308258	+	0.308258i
$803$		0			0
$804$		−	10.7684i		−	0.379772i
$805$	24.1995	+	25.7052i	0.852919	+	0.905990i
$806$	4.75253	+	14.6268i	0.167401	+	0.515207i
$807$	−3.07823	+	1.56844i	−0.108359	+	0.0552116i
$808$	1.51269	−	0.239587i	0.0532164	−	0.00842864i
$809$	41.0380	+	29.8158i	1.44282	+	1.04827i	0.987444	+	0.157970i	$0.0504949\pi$
$809$	41.0380	+	29.8158i	1.44282	+	1.04827i	0.455375	+	0.890300i	$0.349505\pi$
$810$	15.8227	+	23.2198i	0.555953	+	0.815859i
$811$	34.3089	−	11.1476i	1.20475	−	0.391446i	0.363242	−	0.931695i	$-0.381670\pi$
$811$	34.3089	−	11.1476i	1.20475	−	0.391446i	0.841506	+	0.540248i	$0.181670\pi$
$812$	−15.1453	−	2.39878i	−0.531496	−	0.0841807i
$813$	−3.23055	−	3.23055i	−0.113300	−	0.113300i
$814$		0			0
$815$	13.0674	−	16.8900i	0.457730	−	0.591630i
$816$	−29.9794	−	41.2631i	−1.04949	−	1.44450i
$817$	6.75512	−	13.2577i	0.236332	−	0.463827i
$818$	24.6233	+	48.3259i	0.860933	+	1.68968i
$819$	−2.25567	+	3.10467i	−0.0788196	+	0.108486i
$820$	−21.4418	−	11.7528i	−0.748779	−	0.410424i
$821$	−9.80876	−	3.18706i	−0.342328	−	0.111229i	0.132807	−	0.991142i	$-0.457601\pi$
$821$	−9.80876	−	3.18706i	−0.342328	−	0.111229i	−0.475135	+	0.879913i	$0.657601\pi$
$822$	31.1641	+	15.8789i	1.08697	+	0.553841i
$823$	−8.60181	+	54.3097i	−0.299840	+	1.89312i	0.132136	+	0.991232i	$0.457817\pi$
$823$	−8.60181	+	54.3097i	−0.299840	+	1.89312i	−0.431976	+	0.901885i	$0.642183\pi$
$824$	7.27873			0.253567
$825$		0			0
$826$	49.6988			1.72924
$827$	4.21763	−	26.6290i	0.146661	−	0.925983i	−0.799118	−	0.601174i	$-0.794700\pi$
$827$	4.21763	−	26.6290i	0.146661	−	0.925983i	0.945780	−	0.324809i	$-0.105300\pi$
$828$	6.08537	+	3.10065i	0.211481	+	0.107755i
$829$	4.90606	+	1.59408i	0.170395	+	0.0553645i	0.392972	−	0.919551i	$-0.371447\pi$
$829$	4.90606	+	1.59408i	0.170395	+	0.0553645i	−0.222577	+	0.974915i	$0.571447\pi$
$830$	−4.06564	−	2.22848i	−0.141120	−	0.0773516i
$831$	−25.0810	+	34.5211i	−0.870051	+	1.19752i
$832$	4.28718	+	8.41406i	0.148631	+	0.291705i
$833$	−8.56073	+	16.8014i	−0.296612	+	0.582133i
$834$	11.8265	+	16.2778i	0.409518	+	0.563654i
$835$	10.4998	−	13.5714i	0.363362	−	0.469657i
$836$		0			0
$837$	−10.8542	−	10.8542i	−0.375176	−	0.375176i
$838$	35.3469	+	5.59839i	1.22104	+	0.193393i
$839$	−46.1151	+	14.9837i	−1.59207	+	0.517295i	−0.965130	−	0.261771i	$-0.915693\pi$
$839$	−46.1151	+	14.9837i	−1.59207	+	0.517295i	−0.626941	+	0.779066i	$0.715693\pi$
$840$	−4.11885	−	6.04440i	−0.142114	−	0.208552i
$841$	2.13892	+	1.55402i	0.0737559	+	0.0535868i
$842$	−66.9781	+	10.6083i	−2.30822	+	0.365586i
$843$	−40.7800	+	20.7785i	−1.40454	+	0.715649i
$844$	−6.78216	−	20.8734i	−0.233452	−	0.718490i
$845$	6.00996	+	6.38392i	0.206749	+	0.219613i
$846$		−	0.507665i		−	0.0174539i
$847$		0			0
$848$	−24.8796	+	24.8796i	−0.854369	+	0.854369i
$849$	11.4163	−	8.29443i	0.391806	−	0.284664i
$850$	−53.8648	+	34.3733i	−1.84755	+	1.17899i
$851$	11.3131	−	34.8181i	0.387807	−	1.19355i
$852$	1.53101	+	9.66639i	0.0524514	+	0.331165i
$853$	2.20022	+	13.8916i	0.0753341	+	0.475640i	0.996296	+	0.0859883i	$0.0274048\pi$
$853$	2.20022	+	13.8916i	0.0753341	+	0.475640i	−0.920962	+	0.389652i	$0.872595\pi$
$854$	−6.34232	+	19.5197i	−0.217030	+	0.667949i
$855$	−5.08743	+	2.40175i	−0.173986	+	0.0821382i
$856$	−12.6029	+	9.15657i	−0.430760	+	0.312965i
$857$	−25.9087	+	25.9087i	−0.885023	+	0.885023i	−0.994040	−	0.109017i	$-0.965230\pi$
$857$	−25.9087	+	25.9087i	−0.885023	+	0.885023i	0.109017	+	0.994040i	$0.465230\pi$
$858$		0			0
$859$			12.2122i			0.416675i	0.978057	+	0.208337i	$0.0668052\pi$
$859$			12.2122i			0.416675i	−0.978057	+	0.208337i	$0.933195\pi$
$860$	0.356103	−	11.8023i	0.0121430	−	0.402455i
$861$	−7.44055	−	22.8997i	−0.253573	−	0.780418i
$862$	20.0492	−	10.2156i	0.682879	−	0.347944i
$863$	−8.31104	+	1.31634i	−0.282911	+	0.0448087i	−0.296277	−	0.955102i	$-0.595745\pi$
$863$	−8.31104	+	1.31634i	−0.282911	+	0.0448087i	0.0133663	+	0.999911i	$0.495745\pi$
$864$	−30.9828	−	22.5103i	−1.05406	−	0.765817i
$865$	−25.3038	+	17.2428i	−0.860356	+	0.586274i
$866$	−8.35988	+	2.71629i	−0.284080	+	0.0923033i
$867$	−46.3180	−	7.33605i	−1.57304	−	0.249145i
$868$	−5.80634	−	5.80634i	−0.197080	−	0.197080i
$869$		0			0
$870$	4.16448	+	32.6364i	0.141189	+	1.10648i
$871$	−8.53771	−	11.7511i	−0.289289	−	0.398172i
$872$	0.865422	−	1.69849i	0.0293069	−	0.0575180i
$873$	2.36164	+	4.63497i	0.0799293	+	0.156870i
$874$	34.0366	−	46.8473i	1.15130	−	1.58463i
$875$	−19.8193	+	11.8219i	−0.670015	+	0.399652i
$876$	19.1019	+	6.20658i	0.645393	+	0.209701i
$877$	24.4288	+	12.4471i	0.824900	+	0.420308i	0.814871	−	0.579642i	$-0.196808\pi$
$877$	24.4288	+	12.4471i	0.824900	+	0.420308i	0.0100291	+	0.999950i	$0.496808\pi$
$878$	−7.60059	+	47.9883i	−0.256508	+	1.61953i
$879$	−2.72129			−0.0917870
$880$		0			0
$881$	13.9259			0.469176			0.234588	−	0.972095i	$-0.424626\pi$
$881$	13.9259			0.469176			0.234588	+	0.972095i	$0.424626\pi$
$882$	−0.490952	+	3.09975i	−0.0165312	+	0.104374i
$883$	2.64057	+	1.34544i	0.0888623	+	0.0452776i	0.497857	−	0.867259i	$-0.334121\pi$
$883$	2.64057	+	1.34544i	0.0888623	+	0.0452776i	−0.408995	+	0.912537i	$0.634121\pi$
$884$	28.5432	+	9.27425i	0.960011	+	0.311927i
$885$	−12.5428	−	42.9715i	−0.421621	−	1.44447i
$886$	−31.1977	+	42.9399i	−1.04811	+	1.44259i
$887$	−16.4609	−	32.3064i	−0.552703	−	1.08474i	−0.983265	−	0.182180i	$-0.941685\pi$
$887$	−16.4609	−	32.3064i	−0.552703	−	1.08474i	0.430562	−	0.902561i	$-0.358315\pi$
$888$	−3.44347	+	6.75819i	−0.115555	+	0.226790i
$889$	1.60976	+	2.21565i	0.0539897	+	0.0743105i
$890$	44.5465	+	34.4645i	1.49320	+	1.15525i
$891$		0			0
$892$	−3.06985	−	3.06985i	−0.102786	−	0.102786i
$893$	−1.78466	−	0.282663i	−0.0597215	−	0.00945896i
$894$	−3.66694	+	1.19146i	−0.122641	+	0.0398484i
$895$	−30.6580	−	5.80853i	−1.02478	−	0.194158i
$896$	13.1903	+	9.58335i	0.440659	+	0.320157i
$897$	−35.1403	+	5.56567i	−1.17330	+	0.185832i
$898$	−7.84833	+	3.99892i	−0.261902	+	0.133446i
$899$	−4.36138	−	13.4230i	−0.145460	−	0.447681i
$900$	−2.83712	+	3.44703i	−0.0945705	+	0.114901i
$901$			50.4541i			1.68087i
$902$		0			0
$903$	8.22179	−	8.22179i	0.273604	−	0.273604i
$904$	−6.97106	+	5.06477i	−0.231854	+	0.168452i
$905$	18.8967	+	40.0273i	0.628148	+	1.33055i
$906$	2.61188	−	8.03855i	0.0867740	−	0.267063i
$907$	−3.26601	−	20.6208i	−0.108446	−	0.684703i	−0.980681	−	0.195615i	$-0.937330\pi$
$907$	−3.26601	−	20.6208i	−0.108446	−	0.684703i	0.872235	−	0.489088i	$-0.162670\pi$
$908$	−0.169907	−	1.07275i	−0.00563856	−	0.0356005i
$909$	0.284460	−	0.875479i	0.00943496	−	0.0290378i
$910$	24.3045	+	8.71579i	0.805687	+	0.288925i
$911$	−5.53607	+	4.02219i	−0.183418	+	0.133261i	−0.675706	−	0.737172i	$-0.736161\pi$
$911$	−5.53607	+	4.02219i	−0.183418	+	0.133261i	0.492287	+	0.870433i	$0.336161\pi$
$912$	−21.3644	+	21.3644i	−0.707447	+	0.707447i
$913$		0			0
$914$		−	62.8518i		−	2.07895i
$915$	18.4781	+	0.557529i	0.610868	+	0.0184313i
$916$	−3.60720	−	11.1018i	−0.119185	−	0.366815i
$917$	17.3128	−	8.82129i	0.571718	−	0.291305i
$918$	−70.4771	+	11.1625i	−2.32609	+	0.368417i
$919$	−22.4253	−	16.2930i	−0.739744	−	0.537455i	0.152887	−	0.988244i	$-0.451143\pi$
$919$	−22.4253	−	16.2930i	−0.739744	−	0.537455i	−0.892631	+	0.450788i	$0.851143\pi$
$920$	−3.26859	+	17.2519i	−0.107762	+	0.568779i
$921$	−22.1579	+	7.19954i	−0.730128	+	0.237233i
$922$	−52.0352	−	8.24156i	−1.71369	−	0.271421i
$923$	9.33472	+	9.33472i	0.307256	+	0.307256i
$924$		0			0
$925$	20.6288	+	12.1302i	0.678271	+	0.398838i
$926$	24.7172	+	34.0203i	0.812258	+	1.11798i
$927$	1.98615	−	3.89803i	0.0652336	−	0.128028i
$928$	−15.9860	−	31.3743i	−0.524766	−	1.02991i
$929$	−20.4219	+	28.1083i	−0.670020	+	0.922204i	−0.999761	−	0.0218676i	$-0.993039\pi$
$929$	−20.4219	+	28.1083i	−0.670020	+	0.922204i	0.329740	+	0.944072i	$0.393039\pi$
$930$	−8.46843	+	15.4498i	−0.277691	+	0.506620i
$931$	10.6236	+	3.45182i	0.348175	+	0.113129i
$932$	2.15797	+	1.09954i	0.0706868	+	0.0360167i
$933$	6.59348	−	41.6296i	0.215861	−	1.36289i
$934$	8.18709			0.267890
$935$		0			0
$936$	−1.90866			−0.0623866
$937$	7.13046	−	45.0200i	0.232942	−	1.47074i	−0.542893	−	0.839802i	$-0.682671\pi$
$937$	7.13046	−	45.0200i	0.232942	−	1.47074i	0.775835	−	0.630936i	$-0.217329\pi$
$938$	16.4604	+	8.38700i	0.537452	+	0.273845i
$939$	−39.3767	−	12.7943i	−1.28501	−	0.417525i
$940$	−1.37645	+	0.401766i	−0.0448948	+	0.0131042i
$941$	5.13895	−	7.07316i	0.167525	−	0.230578i	−0.716998	−	0.697076i	$-0.754484\pi$
$941$	5.13895	−	7.07316i	0.167525	−	0.230578i	0.884523	+	0.466497i	$0.154484\pi$
$942$	3.22379	+	6.32704i	0.105037	+	0.206146i
$943$	−26.2416	+	51.5019i	−0.854542	+	1.67713i
$944$	36.5901	+	50.3620i	1.19091	+	1.63914i
$945$	−25.5634	+	3.26195i	−0.831579	+	0.106111i
$946$		0			0
$947$	−8.84044	−	8.84044i	−0.287276	−	0.287276i	0.548726	−	0.836002i	$-0.315113\pi$
$947$	−8.84044	−	8.84044i	−0.287276	−	0.287276i	−0.836002	+	0.548726i	$0.815113\pi$
$948$	−28.0175	−	4.43754i	−0.909967	−	0.144125i
$949$	25.7660	−	8.37190i	0.836401	−	0.271763i
$950$	25.1030	+	28.3304i	0.814449	+	0.919159i
$951$	2.45534	+	1.78391i	0.0796199	+	0.0578473i
$952$	14.4060	−	2.28169i	0.466902	−	0.0739499i
$953$	14.1996	−	7.23507i	0.459971	−	0.234367i	−0.208621	−	0.977997i	$-0.566897\pi$
$953$	14.1996	−	7.23507i	0.459971	−	0.234367i	0.668592	+	0.743630i	$0.266897\pi$
$954$	2.59491	+	7.98630i	0.0840132	+	0.258566i
$955$	0.894067	−	0.841695i	0.0289313	−	0.0272366i
$956$			23.8794i			0.772315i
$957$		0			0
$958$	22.9482	−	22.9482i	0.741424	−	0.741424i
$959$	−20.3788	+	14.8061i	−0.658066	+	0.478113i
$960$	−3.65175	+	10.1831i	−0.117860	+	0.328659i
$961$	−7.24400	+	22.2948i	−0.233678	+	0.719186i
$962$	−4.18855	−	26.4455i	−0.135044	−	0.852636i
$963$	1.46472	+	9.24789i	0.0472000	+	0.298009i
$964$	9.50507	−	29.2536i	0.306138	−	0.942195i
$965$	3.81833	−	10.6477i	0.122916	−	0.342760i
$966$	36.6083	−	26.5975i	1.17785	−	0.855761i
$967$	12.0840	−	12.0840i	0.388597	−	0.388597i	−0.485590	−	0.874187i	$-0.661395\pi$
$967$	12.0840	−	12.0840i	0.388597	−	0.388597i	0.874187	+	0.485590i	$0.161395\pi$
$968$		0			0
$969$			43.3256i			1.39182i
$970$	25.4837	−	23.9910i	0.818233	−	0.770303i
$971$	−11.7573	−	36.1853i	−0.377310	−	1.16124i	−0.941907	−	0.335874i	$-0.890968\pi$
$971$	−11.7573	−	36.1853i	−0.377310	−	1.16124i	0.564596	−	0.825367i	$-0.309032\pi$
$972$	−8.12644	+	4.14063i	−0.260656	+	0.132811i
$973$	−14.3121	+	2.26682i	−0.458826	+	0.0726709i
$974$	−27.7398	−	20.1541i	−0.888839	−	0.645779i
$975$	1.40214	−	23.2143i	0.0449043	−	0.743452i
$976$	−24.4496	+	7.94415i	−0.782612	+	0.254286i
$977$	28.3194	+	4.48535i	0.906017	+	0.143499i	0.592018	−	0.805924i	$-0.298331\pi$
$977$	28.3194	+	4.48535i	0.906017	+	0.143499i	0.313999	+	0.949423i	$0.398331\pi$
$978$	−19.3544	−	19.3544i	−0.618884	−	0.618884i
$979$		0			0
$980$	8.79299	−	1.12201i	0.280882	−	0.0358412i
$981$	−0.673455	−	0.926931i	−0.0215018	−	0.0295946i
$982$	−11.1703	+	21.9229i	−0.356458	+	0.699589i
$983$	−0.846804	−	1.66195i	−0.0270089	−	0.0530079i	0.877108	−	0.480294i	$-0.159470\pi$
$983$	−0.846804	−	1.66195i	−0.0270089	−	0.0530079i	−0.904117	+	0.427286i	$0.859470\pi$
$984$	7.03903	−	9.68840i	0.224396	−	0.308855i
$985$	−16.1832	+	4.72364i	−0.515639	+	0.150508i
$986$	−62.3970	−	20.2740i	−1.98713	−	0.645656i
$987$	−1.25809	−	0.641030i	−0.0400455	−	0.0204042i
$988$	2.78119	−	17.5597i	0.0884814	−	0.558650i
$989$	−27.9127			−0.887571
$990$		0			0
$991$	44.4865			1.41316			0.706580	−	0.707634i	$-0.250237\pi$
$991$	44.4865			1.41316			0.706580	+	0.707634i	$0.250237\pi$
$992$	2.94975	−	18.6240i	0.0936546	−	0.591312i
$993$	−33.5386	−	17.0888i	−1.06432	−	0.542296i
$994$	−15.9683	−	5.18843i	−0.506485	−	0.164567i
$995$	6.32724	−	11.5434i	0.200587	−	0.365952i
$996$	−1.46632	+	2.01822i	−0.0464622	+	0.0639497i
$997$	3.78144	+	7.42150i	0.119759	+	0.235041i	0.943102	−	0.332504i	$-0.107893\pi$
$997$	3.78144	+	7.42150i	0.119759	+	0.235041i	−0.823343	+	0.567545i	$0.807893\pi$
$998$	9.77835	−	19.1911i	0.309528	−	0.607483i
$999$	15.7080	+	21.6201i	0.496978	+	0.684031i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.m.f.602.8		80
5.3	odd	4	inner	605.2.m.f.118.3		80
11.2	odd	10		605.2.e.a.362.8	yes	20
11.3	even	5	inner	605.2.m.f.457.3		80
11.4	even	5	inner	605.2.m.f.282.8		80
11.5	even	5	inner	605.2.m.f.112.8		80
11.6	odd	10	inner	605.2.m.f.112.3		80
11.7	odd	10	inner	605.2.m.f.282.3		80
11.8	odd	10	inner	605.2.m.f.457.8		80
11.9	even	5		605.2.e.a.362.3	✓	20
11.10	odd	2	inner	605.2.m.f.602.3		80
55.3	odd	20	inner	605.2.m.f.578.3		80
55.8	even	20	inner	605.2.m.f.578.8		80
55.13	even	20		605.2.e.a.483.3	yes	20
55.18	even	20	inner	605.2.m.f.403.8		80
55.28	even	20	inner	605.2.m.f.233.3		80
55.38	odd	20	inner	605.2.m.f.233.8		80
55.43	even	4	inner	605.2.m.f.118.8		80
55.48	odd	20	inner	605.2.m.f.403.3		80
55.53	odd	20		605.2.e.a.483.8	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
605.2.e.a.362.3	✓	20	11.9	even	5
605.2.e.a.362.8	yes	20	11.2	odd	10
605.2.e.a.483.3	yes	20	55.13	even	20
605.2.e.a.483.8	yes	20	55.53	odd	20
605.2.m.f.112.3		80	11.6	odd	10	inner
605.2.m.f.112.8		80	11.5	even	5	inner
605.2.m.f.118.3		80	5.3	odd	4	inner
605.2.m.f.118.8		80	55.43	even	4	inner
605.2.m.f.233.3		80	55.28	even	20	inner
605.2.m.f.233.8		80	55.38	odd	20	inner
605.2.m.f.282.3		80	11.7	odd	10	inner
605.2.m.f.282.8		80	11.4	even	5	inner
605.2.m.f.403.3		80	55.48	odd	20	inner
605.2.m.f.403.8		80	55.18	even	20	inner
605.2.m.f.457.3		80	11.3	even	5	inner
605.2.m.f.457.8		80	11.8	odd	10	inner
605.2.m.f.578.3		80	55.3	odd	20	inner
605.2.m.f.578.8		80	55.8	even	20	inner
605.2.m.f.602.3		80	11.10	odd	2	inner
605.2.m.f.602.8		80	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.m (of order \(20\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.290440 - 1.83377i) q^{2} +(-1.37543 - 0.700818i) q^{3} +(-1.37624 - 0.447166i) q^{4} +(-1.96083 - 1.07478i) q^{5} +(-1.68462 + 2.31868i) q^{6} +(-0.937080 - 1.83912i) q^{7} +(0.466067 - 0.914708i) q^{8} +(-0.362685 - 0.499192i) q^{9} +O(q^{10})\)	\(q+(0.290440 - 1.83377i) q^{2} +(-1.37543 - 0.700818i) q^{3} +(-1.37624 - 0.447166i) q^{4} +(-1.96083 - 1.07478i) q^{5} +(-1.68462 + 2.31868i) q^{6} +(-0.937080 - 1.83912i) q^{7} +(0.466067 - 0.914708i) q^{8} +(-0.362685 - 0.499192i) q^{9} +(-2.54040 + 3.28355i) q^{10} +(1.57954 + 1.57954i) q^{12} +(2.97603 + 0.471357i) q^{13} +(-3.64469 + 1.18423i) q^{14} +(1.94377 + 2.85247i) q^{15} +(-3.88339 - 2.82145i) q^{16} +(-6.79848 + 1.07677i) q^{17} +(-1.02074 + 0.520094i) q^{18} +(1.26002 + 3.87793i) q^{19} +(2.21796 + 2.35597i) q^{20} +3.18632i q^{21} +(5.40871 - 5.40871i) q^{23} +(-1.28209 + 0.931492i) q^{24} +(2.68970 + 4.21491i) q^{25} +(1.72872 - 5.32045i) q^{26} +(0.873462 + 5.51482i) q^{27} +(0.467250 + 2.95010i) q^{28} +(-1.58644 + 4.88256i) q^{29} +(5.79532 - 2.73594i) q^{30} +(-2.22412 + 1.61592i) q^{31} +(-4.84994 + 4.84994i) q^{32} +12.7796i q^{34} +(-0.139196 + 4.61336i) q^{35} +(0.275918 + 0.849187i) q^{36} +(4.26452 - 2.17288i) q^{37} +(7.47719 - 1.18427i) q^{38} +(-3.76300 - 2.73398i) q^{39} +(-1.89699 + 1.29267i) q^{40} +(-7.18688 + 2.33516i) q^{41} +(5.84296 + 0.925435i) q^{42} +(-2.58034 - 2.58034i) q^{43} +(0.174641 + 1.36864i) q^{45} +(-8.34742 - 11.4892i) q^{46} +(-0.201182 + 0.394842i) q^{47} +(3.36402 + 6.60227i) q^{48} +(1.61024 - 2.21631i) q^{49} +(8.51037 - 3.70811i) q^{50} +(10.1055 + 3.28347i) q^{51} +(-3.88495 - 1.97948i) q^{52} +(1.14667 - 7.23977i) q^{53} +10.3666 q^{54} -2.11900 q^{56} +(0.984657 - 6.21688i) q^{57} +(8.49271 + 4.32725i) q^{58} +(-12.3338 - 4.00750i) q^{59} +(-1.39955 - 4.79486i) q^{60} +(3.14797 - 4.33281i) q^{61} +(2.31725 + 4.54785i) q^{62} +(-0.578212 + 1.13481i) q^{63} +(1.84216 + 2.53551i) q^{64} +(-5.32888 - 4.12282i) q^{65} +(-3.40871 - 3.40871i) q^{67} +(9.83782 + 1.55816i) q^{68} +(-11.2299 + 3.64880i) q^{69} +(8.41941 + 1.59516i) q^{70} +(3.54451 + 2.57524i) q^{71} +(-0.625651 + 0.0990933i) q^{72} +(8.01134 - 4.08198i) q^{73} +(-2.74597 - 8.45123i) q^{74} +(-0.745618 - 7.68233i) q^{75} -5.90039i q^{76} +(-6.10640 + 6.10640i) q^{78} +(-10.2736 + 7.46420i) q^{79} +(4.58224 + 9.70617i) q^{80} +(2.09148 - 6.43690i) q^{81} +(2.19478 + 13.8573i) q^{82} +(0.174702 + 1.10302i) q^{83} +(1.42481 - 4.38513i) q^{84} +(14.4880 + 5.19549i) q^{85} +(-5.48119 + 3.98231i) q^{86} +(5.60383 - 5.60383i) q^{87} -13.5666i q^{89} +(2.56049 + 0.0772559i) q^{90} +(-1.92190 - 5.91499i) q^{91} +(-9.86226 + 5.02507i) q^{92} +(4.19160 - 0.663884i) q^{93} +(0.665617 + 0.483599i) q^{94} +(1.69724 - 8.95820i) q^{95} +(10.0697 - 3.27185i) q^{96} +(-8.32676 - 1.31883i) q^{97} +(-3.59651 - 3.59651i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 4 q^{3} - 4 q^{5}+O(q^{10}) \) 80 * q - 4 * q^3 - 4 * q^5	\( 80 q - 4 q^{3} - 4 q^{5} - 64 q^{12} - 16 q^{15} - 12 q^{16} - 16 q^{20} + 48 q^{23} - 16 q^{25} - 56 q^{26} + 20 q^{27} + 16 q^{31} + 20 q^{36} + 72 q^{37} + 32 q^{38} + 32 q^{42} - 112 q^{45} - 16 q^{47} + 104 q^{48} + 52 q^{53} - 128 q^{56} - 12 q^{58} - 112 q^{60} + 112 q^{67} - 104 q^{70} - 24 q^{71} - 64 q^{75} + 416 q^{78} - 44 q^{80} - 100 q^{81} + 124 q^{82} - 128 q^{86} + 16 q^{92} + 132 q^{93} - 32 q^{97}+O(q^{100}) \) 80 * q - 4 * q^3 - 4 * q^5 - 64 * q^12 - 16 * q^15 - 12 * q^16 - 16 * q^20 + 48 * q^23 - 16 * q^25 - 56 * q^26 + 20 * q^27 + 16 * q^31 + 20 * q^36 + 72 * q^37 + 32 * q^38 + 32 * q^42 - 112 * q^45 - 16 * q^47 + 104 * q^48 + 52 * q^53 - 128 * q^56 - 12 * q^58 - 112 * q^60 + 112 * q^67 - 104 * q^70 - 24 * q^71 - 64 * q^75 + 416 * q^78 - 44 * q^80 - 100 * q^81 + 124 * q^82 - 128 * q^86 + 16 * q^92 + 132 * q^93 - 32 * q^97

Introduction

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