LMFDB - Embedded newform 660.2.be.b.151.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [660,2,Mod(151,660)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(660, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 0, 0, 3]))

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

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

chi := DirichletCharacter("660.151");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 660 = 2^{2} \cdot 3 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	660.be (of order $10$, degree $4$, 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:	$5.27012653340$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$24$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			151.16
Character	$\chi$	$=$	660.151
Dual form			660.2.be.b.271.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.737307 + 1.20681i) q^{2} +(0.951057 - 0.309017i) q^{3} +(-0.912758 + 1.77957i) q^{4} +(0.809017 + 0.587785i) q^{5} +(1.07414 + 0.919900i) q^{6} +(-0.917712 + 2.82443i) q^{7} +(-2.82058 + 0.210569i) q^{8} +(0.809017 - 0.587785i) q^{9} +O(q^{10})$	\(q+(0.737307 + 1.20681i) q^{2} +(0.951057 - 0.309017i) q^{3} +(-0.912758 + 1.77957i) q^{4} +(0.809017 + 0.587785i) q^{5} +(1.07414 + 0.919900i) q^{6} +(-0.917712 + 2.82443i) q^{7} +(-2.82058 + 0.210569i) q^{8} +(0.809017 - 0.587785i) q^{9} +(-0.112849 + 1.40970i) q^{10} +(2.02135 - 2.62948i) q^{11} +(-0.318167 + 1.97453i) q^{12} +(3.66706 + 5.04728i) q^{13} +(-4.08517 + 0.974969i) q^{14} +(0.951057 + 0.309017i) q^{15} +(-2.33375 - 3.24863i) q^{16} +(-2.72813 + 3.75495i) q^{17} +(1.30584 + 0.542948i) q^{18} +(-2.26269 - 6.96384i) q^{19} +(-1.78444 + 0.903198i) q^{20} +2.96978i q^{21} +(4.66362 + 0.500639i) q^{22} +3.27820i q^{23} +(-2.61746 + 1.07187i) q^{24} +(0.309017 + 0.951057i) q^{25} +(-3.38733 + 8.14682i) q^{26} +(0.587785 - 0.809017i) q^{27} +(-4.18862 - 4.21115i) q^{28} +(-5.89824 - 1.91645i) q^{29} +(0.328297 + 1.37558i) q^{30} +(3.80138 + 5.23216i) q^{31} +(2.19978 - 5.21162i) q^{32} +(1.10986 - 3.12541i) q^{33} +(-6.54296 - 0.523773i) q^{34} +(-2.40260 + 1.74559i) q^{35} +(0.307569 + 1.97621i) q^{36} +(-0.980600 + 3.01798i) q^{37} +(6.73570 - 7.86511i) q^{38} +(5.04728 + 3.66706i) q^{39} +(-2.40566 - 1.48754i) q^{40} +(8.30424 - 2.69821i) q^{41} +(-3.58394 + 2.18964i) q^{42} -7.55765 q^{43} +(2.83435 + 5.99721i) q^{44} +1.00000 q^{45} +(-3.95615 + 2.41704i) q^{46} +(5.94611 - 1.93201i) q^{47} +(-3.22341 - 2.36847i) q^{48} +(-1.47208 - 1.06953i) q^{49} +(-0.919900 + 1.07414i) q^{50} +(-1.43426 + 4.41421i) q^{51} +(-12.3291 + 1.91886i) q^{52} +(9.57075 - 6.95356i) q^{53} +(1.40970 + 0.112849i) q^{54} +(3.18087 - 0.939176i) q^{55} +(1.99374 - 8.15976i) q^{56} +(-4.30389 - 5.92379i) q^{57} +(-2.03602 - 8.53104i) q^{58} +(0.763489 + 0.248073i) q^{59} +(-1.41800 + 1.41042i) q^{60} +(-0.659995 + 0.908405i) q^{61} +(-3.51141 + 8.44523i) q^{62} +(0.917712 + 2.82443i) q^{63} +(7.91132 - 1.18785i) q^{64} +6.23878i q^{65} +(4.59007 - 0.965002i) q^{66} -6.76265i q^{67} +(-4.19208 - 8.28226i) q^{68} +(1.01302 + 3.11776i) q^{69} +(-3.87804 - 1.61244i) q^{70} +(6.36208 - 8.75666i) q^{71} +(-2.15813 + 1.82825i) q^{72} +(4.92604 + 1.60057i) q^{73} +(-4.36511 + 1.04178i) q^{74} +(0.587785 + 0.809017i) q^{75} +(14.4579 + 2.32968i) q^{76} +(5.57176 + 8.12225i) q^{77} +(-0.704038 + 8.79483i) q^{78} +(-4.04389 + 2.93806i) q^{79} +(0.0214590 - 3.99994i) q^{80} +(0.309017 - 0.951057i) q^{81} +(9.37899 + 8.03219i) q^{82} +(-2.60607 - 1.89342i) q^{83} +(-5.28493 - 2.71069i) q^{84} +(-4.41421 + 1.43426i) q^{85} +(-5.57231 - 9.12061i) q^{86} -6.20177 q^{87} +(-5.14768 + 7.84228i) q^{88} +5.45533 q^{89} +(0.737307 + 1.20681i) q^{90} +(-17.6210 + 5.72540i) q^{91} +(-5.83379 - 2.99220i) q^{92} +(5.23216 + 3.80138i) q^{93} +(6.71567 + 5.75132i) q^{94} +(2.26269 - 6.96384i) q^{95} +(0.481639 - 5.63631i) q^{96} +(9.36103 - 6.80119i) q^{97} +(0.205338 - 2.56508i) q^{98} +(0.0897345 - 3.31541i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 8 q^{4} + 24 q^{5} + 24 q^{9}+O(q^{10}) $ 96 * q + 8 * q^4 + 24 * q^5 + 24 * q^9	$ 96 q + 8 q^{4} + 24 q^{5} + 24 q^{9} - 20 q^{13} - 4 q^{14} + 8 q^{16} + 10 q^{18} + 2 q^{20} + 30 q^{22} + 30 q^{24} - 24 q^{25} - 60 q^{28} + 20 q^{29} + 8 q^{34} - 8 q^{36} + 8 q^{37} - 58 q^{38} + 20 q^{41} - 42 q^{42} - 54 q^{44} + 96 q^{45} - 10 q^{46} + 16 q^{48} + 20 q^{49} + 56 q^{53} - 8 q^{56} - 68 q^{58} - 10 q^{64} + 54 q^{66} + 8 q^{69} + 4 q^{70} - 10 q^{72} - 40 q^{73} - 50 q^{74} - 32 q^{77} + 8 q^{78} + 2 q^{80} - 24 q^{81} - 24 q^{82} - 60 q^{84} - 84 q^{86} - 72 q^{88} + 72 q^{89} + 2 q^{92} + 80 q^{94} - 50 q^{96} - 8 q^{97}+O(q^{100}) $ 96 * q + 8 * q^4 + 24 * q^5 + 24 * q^9 - 20 * q^13 - 4 * q^14 + 8 * q^16 + 10 * q^18 + 2 * q^20 + 30 * q^22 + 30 * q^24 - 24 * q^25 - 60 * q^28 + 20 * q^29 + 8 * q^34 - 8 * q^36 + 8 * q^37 - 58 * q^38 + 20 * q^41 - 42 * q^42 - 54 * q^44 + 96 * q^45 - 10 * q^46 + 16 * q^48 + 20 * q^49 + 56 * q^53 - 8 * q^56 - 68 * q^58 - 10 * q^64 + 54 * q^66 + 8 * q^69 + 4 * q^70 - 10 * q^72 - 40 * q^73 - 50 * q^74 - 32 * q^77 + 8 * q^78 + 2 * q^80 - 24 * q^81 - 24 * q^82 - 60 * q^84 - 84 * q^86 - 72 * q^88 + 72 * q^89 + 2 * q^92 + 80 * q^94 - 50 * q^96 - 8 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/660\mathbb{Z}\right)^\times$.

$n$	$221$	$331$	$397$	$541$
$\chi(n)$	$1$	$-1$	$1$	$e\left(\frac{3}{10}\right)$

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 $

$2$	0.737307	+	1.20681i	0.521355	+	0.853340i
$2$	0.737307	+	1.20681i	0.521355	+	0.853340i
$3$	0.951057	−	0.309017i	0.549093	−	0.178411i
$3$	0.951057	−	0.309017i	0.549093	−	0.178411i
$4$	−0.912758	+	1.77957i	−0.456379	+	0.889786i
$5$	0.809017	+	0.587785i	0.361803	+	0.262866i
$5$	0.809017	+	0.587785i	0.361803	+	0.262866i
$6$	1.07414	+	0.919900i	0.438517	+	0.375547i
$7$	−0.917712	+	2.82443i	−0.346863	+	1.06753i	0.613717	+	0.789526i	$0.289674\pi$
$7$	−0.917712	+	2.82443i	−0.346863	+	1.06753i	−0.960579	+	0.278007i	$0.910326\pi$
$8$	−2.82058	+	0.210569i	−0.997225	+	0.0744473i
$9$	0.809017	−	0.587785i	0.269672	−	0.195928i
$10$	−0.112849	+	1.40970i	−0.0356859	+	0.445788i
$11$	2.02135	−	2.62948i	0.609459	−	0.792818i
$11$	2.02135	−	2.62948i	0.609459	−	0.792818i
$12$	−0.318167	+	1.97453i	−0.0918468	+	0.569998i
$13$	3.66706	+	5.04728i	1.01706	+	1.39986i	0.914245	+	0.405162i	$0.132785\pi$
$13$	3.66706	+	5.04728i	1.01706	+	1.39986i	0.102815	+	0.994700i	$0.467215\pi$
$14$	−4.08517	+	0.974969i	−1.09181	+	0.260572i
$15$	0.951057	+	0.309017i	0.245562	+	0.0797878i
$16$	−2.33375	−	3.24863i	−0.583437	−	0.812159i
$17$	−2.72813	+	3.75495i	−0.661669	+	0.910709i	−0.999535	−	0.0304851i	$-0.990295\pi$
$17$	−2.72813	+	3.75495i	−0.661669	+	0.910709i	0.337866	+	0.941194i	$0.390295\pi$
$18$	1.30584	+	0.542948i	0.307788	+	0.127974i
$19$	−2.26269	−	6.96384i	−0.519096	−	1.59761i	−0.775703	−	0.631098i	$-0.782604\pi$
$19$	−2.26269	−	6.96384i	−0.519096	−	1.59761i	0.256607	−	0.966516i	$-0.417396\pi$
$20$	−1.78444	+	0.903198i	−0.399013	+	0.201961i
$21$			2.96978i			0.648059i
$22$	4.66362	+	0.500639i	0.994287	+	0.106737i
$23$			3.27820i			0.683552i	0.939781	+	0.341776i	$0.111028\pi$
$23$			3.27820i			0.683552i	−0.939781	+	0.341776i	$0.888972\pi$
$24$	−2.61746	+	1.07187i	−0.534287	+	0.218794i
$25$	0.309017	+	0.951057i	0.0618034	+	0.190211i
$26$	−3.38733	+	8.14682i	−0.664310	+	1.59772i
$27$	0.587785	−	0.809017i	0.113119	−	0.155695i
$28$	−4.18862	−	4.21115i	−0.791575	−	0.795833i
$29$	−5.89824	−	1.91645i	−1.09528	−	0.355877i	−0.294993	−	0.955500i	$-0.595317\pi$
$29$	−5.89824	−	1.91645i	−1.09528	−	0.355877i	−0.800283	+	0.599623i	$0.795317\pi$
$30$	0.328297	+	1.37558i	0.0599386	+	0.251145i
$31$	3.80138	+	5.23216i	0.682749	+	0.939723i	0.999963	−	0.00863097i	$-0.00274736\pi$
$31$	3.80138	+	5.23216i	0.682749	+	0.939723i	−0.317214	+	0.948354i	$0.602747\pi$
$32$	2.19978	−	5.21162i	0.388870	−	0.921293i
$33$	1.10986	−	3.12541i	0.193202	−	0.544065i
$34$	−6.54296	−	0.523773i	−1.12211	−	0.0898263i
$35$	−2.40260	+	1.74559i	−0.406114	+	0.295059i
$36$	0.307569	+	1.97621i	0.0512615	+	0.329368i
$37$	−0.980600	+	3.01798i	−0.161210	+	0.496152i	−0.998737	−	0.0502430i	$-0.984000\pi$
$37$	−0.980600	+	3.01798i	−0.161210	+	0.496152i	0.837527	+	0.546395i	$0.184000\pi$
$38$	6.73570	−	7.86511i	1.09268	−	1.27589i
$39$	5.04728	+	3.66706i	0.808211	+	0.587200i
$40$	−2.40566	−	1.48754i	−0.380369	−	0.235201i
$41$	8.30424	−	2.69821i	1.29690	−	0.421390i	0.422401	−	0.906409i	$-0.361187\pi$
$41$	8.30424	−	2.69821i	1.29690	−	0.421390i	0.874504	+	0.485019i	$0.161187\pi$
$42$	−3.58394	+	2.18964i	−0.553015	+	0.337868i
$43$	−7.55765			−1.15253			−0.576265	−	0.817263i	$-0.695491\pi$
$43$	−7.55765			−1.15253			−0.576265	+	0.817263i	$0.695491\pi$
$44$	2.83435	+	5.99721i	0.427294	+	0.904113i
$45$	1.00000			0.149071
$46$	−3.95615	+	2.41704i	−0.583303	+	0.356373i
$47$	5.94611	−	1.93201i	0.867330	−	0.281812i	0.158643	−	0.987336i	$-0.449288\pi$
$47$	5.94611	−	1.93201i	0.867330	−	0.281812i	0.708687	+	0.705523i	$0.249288\pi$
$48$	−3.22341	−	2.36847i	−0.465259	−	0.341859i
$49$	−1.47208	−	1.06953i	−0.210297	−	0.152789i
$50$	−0.919900	+	1.07414i	−0.130093	+	0.151907i
$51$	−1.43426	+	4.41421i	−0.200837	+	0.618113i
$52$	−12.3291	+	1.91886i	−1.70974	+	0.266097i
$53$	9.57075	−	6.95356i	1.31464	−	0.955145i	0.314661	−	0.949204i	$-0.398109\pi$
$53$	9.57075	−	6.95356i	1.31464	−	0.955145i	0.999982	−	0.00594055i	$-0.00189095\pi$
$54$	1.40970	+	0.112849i	0.191836	+	0.0153568i
$55$	3.18087	−	0.939176i	0.428909	−	0.126638i
$56$	1.99374	−	8.15976i	0.266425	−	1.09039i
$57$	−4.30389	−	5.92379i	−0.570064	−	0.784626i
$58$	−2.03602	−	8.53104i	−0.267343	−	1.12018i
$59$	0.763489	+	0.248073i	0.0993978	+	0.0322963i	0.358294	−	0.933609i	$-0.383359\pi$
$59$	0.763489	+	0.248073i	0.0993978	+	0.0322963i	−0.258896	+	0.965905i	$0.583359\pi$
$60$	−1.41800	+	1.41042i	−0.183063	+	0.182084i
$61$	−0.659995	+	0.908405i	−0.0845037	+	0.116309i	−0.849176	−	0.528110i	$-0.822901\pi$
$61$	−0.659995	+	0.908405i	−0.0845037	+	0.116309i	0.764672	+	0.644419i	$0.222901\pi$
$62$	−3.51141	+	8.44523i	−0.445949	+	1.07255i
$63$	0.917712	+	2.82443i	0.115621	+	0.355844i
$64$	7.91132	−	1.18785i	0.988915	−	0.148481i
$65$			6.23878i			0.773825i
$66$	4.59007	−	0.965002i	0.564999	−	0.118784i
$67$		−	6.76265i		−	0.826189i	−0.910688	−	0.413095i	$-0.864448\pi$
$67$		−	6.76265i		−	0.826189i	0.910688	−	0.413095i	$-0.135552\pi$
$68$	−4.19208	−	8.28226i	−0.508364	−	1.00437i
$69$	1.01302	+	3.11776i	0.121953	+	0.375334i
$70$	−3.87804	−	1.61244i	−0.463515	−	0.192723i
$71$	6.36208	−	8.75666i	0.755041	−	1.03922i	−0.242570	−	0.970134i	$-0.577990\pi$
$71$	6.36208	−	8.75666i	0.755041	−	1.03922i	0.997610	−	0.0690902i	$-0.0220096\pi$
$72$	−2.15813	+	1.82825i	−0.254338	+	0.215461i
$73$	4.92604	+	1.60057i	0.576549	+	0.187332i	0.582754	−	0.812649i	$-0.301975\pi$
$73$	4.92604	+	1.60057i	0.576549	+	0.187332i	−0.00620508	+	0.999981i	$0.501975\pi$
$74$	−4.36511	+	1.04178i	−0.507434	+	0.121105i
$75$	0.587785	+	0.809017i	0.0678716	+	0.0934172i
$76$	14.4579	+	2.32968i	1.65844	+	0.267233i
$77$	5.57176	+	8.12225i	0.634961	+	0.925616i
$78$	−0.704038	+	8.79483i	−0.0797166	+	0.995818i
$79$	−4.04389	+	2.93806i	−0.454973	+	0.330557i	−0.791556	−	0.611097i	$-0.790729\pi$
$79$	−4.04389	+	2.93806i	−0.454973	+	0.330557i	0.336583	+	0.941654i	$0.390729\pi$
$80$	0.0214590	−	3.99994i	0.00239919	−	0.447207i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	9.37899	+	8.03219i	1.03574	+	0.887008i
$83$	−2.60607	−	1.89342i	−0.286054	−	0.207830i	0.435500	−	0.900189i	$-0.356572\pi$
$83$	−2.60607	−	1.89342i	−0.286054	−	0.207830i	−0.721553	+	0.692359i	$0.756572\pi$
$84$	−5.28493	−	2.71069i	−0.576633	−	0.295760i
$85$	−4.41421	+	1.43426i	−0.478788	+	0.155568i
$86$	−5.57231	−	9.12061i	−0.600877	−	0.983501i
$87$	−6.20177			−0.664900
$88$	−5.14768	+	7.84228i	−0.548744	+	0.835990i
$89$	5.45533			0.578264			0.289132	−	0.957289i	$-0.406633\pi$
$89$	5.45533			0.578264			0.289132	+	0.957289i	$0.406633\pi$
$90$	0.737307	+	1.20681i	0.0777189	+	0.127208i
$91$	−17.6210	+	5.72540i	−1.84718	+	0.600185i
$92$	−5.83379	−	2.99220i	−0.608215	−	0.311959i
$93$	5.23216	+	3.80138i	0.542549	+	0.394185i
$94$	6.71567	+	5.75132i	0.692668	+	0.593203i
$95$	2.26269	−	6.96384i	0.232147	−	0.714475i
$96$	0.481639	−	5.63631i	0.0491571	−	0.575254i
$97$	9.36103	−	6.80119i	0.950469	−	0.690556i	−0.000449019	−	1.00000i	$-0.500143\pi$
$97$	9.36103	−	6.80119i	0.950469	−	0.690556i	0.950918	+	0.309444i	$0.100143\pi$
$98$	0.205338	−	2.56508i	0.0207423	−	0.259112i
$99$	0.0897345	−	3.31541i	0.00901865	−	0.333211i
$100$	−1.97453	−	0.318167i	−0.197453	−	0.0318167i
$101$	−6.62284	−	9.11556i	−0.658998	−	0.907032i	0.340450	−	0.940263i	$-0.389421\pi$
$101$	−6.62284	−	9.11556i	−0.658998	−	0.907032i	−0.999448	+	0.0332302i	$0.989421\pi$
$102$	−6.38458	+	1.52375i	−0.632168	+	0.150874i
$103$	−12.5443	−	4.07588i	−1.23602	−	0.401609i	−0.383131	−	0.923694i	$-0.625154\pi$
$103$	−12.5443	−	4.07588i	−1.23602	−	0.401609i	−0.852893	+	0.522085i	$0.825154\pi$
$104$	−11.4060	−	13.4641i	−1.11845	−	1.32026i
$105$	−1.74559	+	2.40260i	−0.170352	+	0.234470i
$106$	15.4482	+	6.42313i	1.50046	+	0.623869i
$107$	−1.46888	−	4.52074i	−0.142002	−	0.437036i	0.854612	−	0.519268i	$-0.173795\pi$
$107$	−1.46888	−	4.52074i	−0.142002	−	0.437036i	−0.996613	+	0.0822315i	$0.973795\pi$
$108$	0.903198	+	1.78444i	0.0869102	+	0.171708i
$109$		−	14.5721i		−	1.39576i	−0.716216	−	0.697879i	$-0.754128\pi$
$109$		−	14.5721i		−	1.39576i	0.716216	−	0.697879i	$-0.245872\pi$
$110$	3.47868	+	3.14623i	0.331679	+	0.299982i
$111$			3.17329i			0.301195i
$112$	11.3172	−	3.61019i	1.06938	−	0.341131i
$113$	1.17323	+	3.61083i	0.110368	+	0.339678i	0.990953	−	0.134210i	$-0.0428498\pi$
$113$	1.17323	+	3.61083i	0.110368	+	0.339678i	−0.880585	+	0.473889i	$0.842850\pi$
$114$	3.97558	−	9.56161i	0.372347	−	0.895527i
$115$	−1.92688	+	2.65212i	−0.179682	+	0.247312i
$116$	8.79413	−	8.74708i	0.816514	−	0.812146i
$117$	5.93343	+	1.92789i	0.548546	+	0.178233i
$118$	0.263550	+	1.10429i	0.0242618	+	0.101658i
$119$	−8.10194	−	11.1514i	−0.742704	−	1.02224i
$120$	−2.74760	−	0.671344i	−0.250820	−	0.0612850i
$121$	−2.82832	−	10.6302i	−0.257120	−	0.966380i
$122$	−1.58289	−	0.126712i	−0.143308	−	0.0114720i
$123$	7.06401	−	5.13230i	0.636940	−	0.462764i
$124$	−12.7807	+	1.98914i	−1.14774	+	0.178630i
$125$	−0.309017	+	0.951057i	−0.0276393	+	0.0850651i
$126$	−2.73190	+	3.18997i	−0.243377	+	0.284185i
$127$	−4.52002	−	3.28398i	−0.401087	−	0.291407i	0.368897	−	0.929470i	$-0.379736\pi$
$127$	−4.52002	−	3.28398i	−0.401087	−	0.291407i	−0.769983	+	0.638064i	$0.779736\pi$
$128$	7.26657	+	8.67161i	0.642281	+	0.766470i
$129$	−7.18775	+	2.33544i	−0.632846	+	0.205624i
$130$	−7.52899	+	4.59989i	−0.660336	+	0.403437i
$131$	17.0791			1.49221			0.746104	−	0.665829i	$-0.231922\pi$
$131$	17.0791			1.49221			0.746104	+	0.665829i	$0.231922\pi$
$132$	4.54886	+	4.82782i	0.395928	+	0.420208i
$133$	21.7454			1.88556
$134$	8.16120	−	4.98615i	0.705020	−	0.430737i
$135$	0.951057	−	0.309017i	0.0818539	−	0.0265959i
$136$	6.90423	−	11.1656i	0.592033	−	0.957441i
$137$	−6.62340	−	4.81218i	−0.565875	−	0.411132i	0.267729	−	0.963494i	$-0.413727\pi$
$137$	−6.62340	−	4.81218i	−0.565875	−	0.411132i	−0.833604	+	0.552362i	$0.813727\pi$
$138$	−3.01562	+	3.52126i	−0.256706	+	0.299750i
$139$	−6.48190	+	19.9492i	−0.549788	+	1.69207i	0.159538	+	0.987192i	$0.449000\pi$
$139$	−6.48190	+	19.9492i	−0.549788	+	1.69207i	−0.709326	+	0.704881i	$0.751000\pi$
$140$	−0.913412	−	5.86890i	−0.0771974	−	0.496013i
$141$	5.05807	−	3.67490i	0.425966	−	0.309482i
$142$	15.2584	+	1.22145i	1.28046	+	0.102502i
$143$	20.6841	+	0.559833i	1.72969	+	0.0468156i
$144$	−3.79754	−	1.25646i	−0.316462	−	0.104705i
$145$	−3.64531	−	5.01734i	−0.302727	−	0.416667i
$146$	1.70043	+	7.12487i	0.140728	+	0.589659i
$147$	−1.73053	−	0.562283i	−0.142732	−	0.0463763i
$148$	−4.47565	−	4.49973i	−0.367897	−	0.369876i
$149$	4.38421	−	6.03435i	0.359168	−	0.494353i	−0.590748	−	0.806856i	$-0.701167\pi$
$149$	4.38421	−	6.03435i	0.359168	−	0.494353i	0.949917	+	0.312503i	$0.101167\pi$
$150$	−0.542948	+	1.30584i	−0.0443315	+	0.106621i
$151$	4.98015	+	15.3273i	0.405279	+	1.24732i	0.920662	+	0.390361i	$0.127650\pi$
$151$	4.98015	+	15.3273i	0.405279	+	1.24732i	−0.515383	+	0.856960i	$0.672350\pi$
$152$	7.84846	+	19.1656i	0.636594	+	1.55454i
$153$			4.64137i			0.375233i
$154$	−5.69388	+	12.7126i	−0.458826	+	1.02441i
$155$			6.46730i			0.519466i
$156$	−11.1327	+	5.63485i	−0.891332	+	0.451149i
$157$	−0.954459	−	2.93752i	−0.0761741	−	0.234440i	0.905718	−	0.423881i	$-0.139332\pi$
$157$	−0.954459	−	2.93752i	−0.0761741	−	0.234440i	−0.981892	+	0.189441i	$0.939332\pi$
$158$	−6.52725	−	2.71394i	−0.519280	−	0.215909i
$159$	6.95356	−	9.57075i	0.551453	−	0.759010i
$160$	4.84297	−	2.92329i	0.382871	−	0.231106i
$161$	−9.25905	−	3.00845i	−0.729715	−	0.237099i
$162$	1.37558	−	0.328297i	0.108076	−	0.0257934i
$163$	−6.22522	−	8.56829i	−0.487597	−	0.671120i	0.492345	−	0.870400i	$-0.336140\pi$
$163$	−6.22522	−	8.56829i	−0.487597	−	0.671120i	−0.979943	+	0.199280i	$0.936140\pi$
$164$	−2.77810	+	17.2408i	−0.216933	+	1.34628i
$165$	2.73497	−	1.87615i	0.212917	−	0.146058i
$166$	0.363517	−	4.54105i	0.0282144	−	0.352454i
$167$	−8.89040	+	6.45925i	−0.687960	+	0.499832i	−0.875989	−	0.482332i	$-0.839790\pi$
$167$	−8.89040	+	6.45925i	−0.687960	+	0.499832i	0.188029	+	0.982163i	$0.439790\pi$
$168$	−0.625343	−	8.37649i	−0.0482462	−	0.646261i
$169$	−8.01045	+	24.6536i	−0.616188	+	1.89643i
$170$	−4.98550	−	4.26960i	−0.382370	−	0.327463i
$171$	−5.92379	−	4.30389i	−0.453004	−	0.329127i
$172$	6.89830	−	13.4494i	0.525991	−	1.02551i
$173$	20.0687	−	6.52071i	1.52579	−	0.495760i	0.578379	−	0.815768i	$-0.303686\pi$
$173$	20.0687	−	6.52071i	1.52579	−	0.495760i	0.947415	+	0.320008i	$0.103686\pi$
$174$	−4.57261	−	7.48433i	−0.346649	−	0.567386i
$175$	−2.96978			−0.224494
$176$	−13.2595	−	0.430078i	−0.999474	−	0.0324184i
$177$	0.802780			0.0603406
$178$	4.02225	+	6.58352i	0.301480	+	0.493456i
$179$	11.5690	−	3.75901i	0.864710	−	0.280961i	0.157116	−	0.987580i	$-0.449780\pi$
$179$	11.5690	−	3.75901i	0.864710	−	0.280961i	0.707594	+	0.706619i	$0.249780\pi$
$180$	−0.912758	+	1.77957i	−0.0680329	+	0.132641i
$181$	0.809007	+	0.587778i	0.0601330	+	0.0436892i	0.617446	−	0.786614i	$-0.288168\pi$
$181$	0.809007	+	0.587778i	0.0601330	+	0.0436892i	−0.557313	+	0.830303i	$0.688168\pi$
$182$	−19.9015	−	17.0437i	−1.47520	−	1.26336i
$183$	−0.346980	+	1.06789i	−0.0256495	+	0.0789410i
$184$	−0.690287	−	9.24643i	−0.0508886	−	0.681656i
$185$	−2.56724	+	1.86521i	−0.188748	+	0.137133i
$186$	−0.729827	+	9.11698i	−0.0535135	+	0.668489i
$187$	4.35906	+	14.7636i	0.318766	+	1.07962i
$188$	−1.98921	+	12.3450i	−0.145078	+	0.900351i
$189$	1.74559	+	2.40260i	0.126973	+	0.174764i
$190$	10.0723	−	2.40386i	0.730721	−	0.174394i
$191$	−3.12118	−	1.01413i	−0.225841	−	0.0733801i	0.193911	−	0.981019i	$-0.437883\pi$
$191$	−3.12118	−	1.01413i	−0.225841	−	0.0733801i	−0.419751	+	0.907639i	$0.637883\pi$
$192$	7.15705	−	3.57445i	0.516515	−	0.257963i
$193$	−6.28387	+	8.64900i	−0.452323	+	0.622569i	−0.972895	−	0.231249i	$-0.925719\pi$
$193$	−6.28387	+	8.64900i	−0.452323	+	0.622569i	0.520572	+	0.853818i	$0.325719\pi$
$194$	15.1097	+	6.28238i	1.08481	+	0.451049i
$195$	1.92789	+	5.93343i	0.138059	+	0.424902i
$196$	3.24695	−	1.64345i	0.231925	−	0.117389i
$197$			4.02560i			0.286812i	0.989664	+	0.143406i	$0.0458055\pi$
$197$			4.02560i			0.286812i	−0.989664	+	0.143406i	$0.954195\pi$
$198$	4.06722	−	2.33618i	0.289045	−	0.166025i
$199$			19.0279i			1.34885i	0.738344	+	0.674424i	$0.235608\pi$
$199$			19.0279i			1.34885i	−0.738344	+	0.674424i	$0.764392\pi$
$200$	−1.07187	−	2.61746i	−0.0757926	−	0.185082i
$201$	−2.08977	−	6.43166i	−0.147401	−	0.453654i
$202$	6.11764	−	14.7134i	0.430436	−	1.03523i
$203$	10.8258	−	14.9004i	0.759820	−	1.04580i
$204$	−6.54626	−	6.58148i	−0.458330	−	0.460795i
$205$	8.30424	+	2.69821i	0.579994	+	0.188451i
$206$	−4.33018	−	18.1437i	−0.301698	−	1.26413i
$207$	1.92688	+	2.65212i	0.133927	+	0.184335i
$208$	7.83877	−	23.6920i	0.543521	−	1.64275i
$209$	−22.8849	−	8.12664i	−1.58298	−	0.562131i
$210$	−4.18651	−	0.335136i	−0.288897	−	0.0231266i
$211$	−7.68530	+	5.58370i	−0.529078	+	0.384398i	−0.820013	−	0.572345i	$-0.806034\pi$
$211$	−7.68530	+	5.58370i	−0.529078	+	0.384398i	0.290935	+	0.956743i	$0.406034\pi$
$212$	3.63857	+	23.3787i	0.249898	+	1.60566i
$213$	3.34475	−	10.2941i	0.229178	−	0.705338i
$214$	4.37264	−	5.10582i	0.298907	−	0.349027i
$215$	−6.11427	−	4.44227i	−0.416990	−	0.302961i
$216$	−1.48754	+	2.40566i	−0.101214	+	0.163685i
$217$	−18.2664	+	5.93512i	−1.24001	+	0.402902i
$218$	17.5857	−	10.7441i	1.19106	−	0.727684i
$219$	5.17954			0.350001
$220$	−1.23204	+	6.51783i	−0.0830639	+	0.439432i
$221$	−28.9565			−1.94782
$222$	−3.82954	+	2.33969i	−0.257022	+	0.157030i
$223$	4.27545	−	1.38918i	0.286305	−	0.0930262i	−0.162344	−	0.986734i	$-0.551905\pi$
$223$	4.27545	−	1.38918i	0.286305	−	0.0930262i	0.448649	+	0.893708i	$0.351905\pi$
$224$	12.7011	+	10.9959i	0.848626	+	0.734694i
$225$	0.809017	+	0.587785i	0.0539345	+	0.0391857i
$226$	−3.49254	+	4.07815i	−0.232320	+	0.271275i
$227$	−3.05767	+	9.41055i	−0.202945	+	0.624600i	0.796847	+	0.604182i	$0.206500\pi$
$227$	−3.05767	+	9.41055i	−0.202945	+	0.624600i	−0.999792	+	0.0204186i	$0.993500\pi$
$228$	14.4702	−	2.25209i	0.958314	−	0.149148i
$229$	−11.2263	+	8.15636i	−0.741853	+	0.538987i	−0.893291	−	0.449479i	$-0.851610\pi$
$229$	−11.2263	+	8.15636i	−0.741853	+	0.538987i	0.151438	+	0.988467i	$0.451610\pi$
$230$	−4.62129	−	0.369941i	−0.304719	−	0.0243932i
$231$	7.80897	+	6.00295i	0.513793	+	0.394965i
$232$	17.0400	+	4.16352i	1.11873	+	0.273349i
$233$	17.7457	+	24.4249i	1.16256	+	1.60013i	0.701314	+	0.712853i	$0.252597\pi$
$233$	17.7457	+	24.4249i	1.16256	+	1.60013i	0.461245	+	0.887273i	$0.347403\pi$
$234$	2.04817	+	8.58194i	0.133893	+	0.561019i
$235$	5.94611	+	1.93201i	0.387882	+	0.126030i
$236$	−1.13834	+	1.13225i	−0.0740999	+	0.0737034i
$237$	−2.93806	+	4.04389i	−0.190847	+	0.262679i
$238$	7.48391	−	17.9994i	0.485110	−	1.16673i
$239$	−0.414344	−	1.27522i	−0.0268017	−	0.0824871i	0.936761	−	0.349970i	$-0.113808\pi$
$239$	−0.414344	−	1.27522i	−0.0268017	−	0.0824871i	−0.963563	+	0.267483i	$0.913808\pi$
$240$	−1.21564	−	3.81080i	−0.0784693	−	0.245986i
$241$		−	6.57597i		−	0.423595i	−0.977314	−	0.211798i	$-0.932068\pi$
$241$		−	6.57597i		−	0.423595i	0.977314	−	0.211798i	$-0.0679318\pi$
$242$	10.7432	−	11.2509i	0.690600	−	0.723237i
$243$		−	1.00000i		−	0.0641500i
$244$	−1.01416	−	2.00366i	−0.0649247	−	0.128271i
$245$	−0.562283	−	1.73053i	−0.0359230	−	0.110560i
$246$	11.4020	+	4.74080i	0.726967	+	0.302263i
$247$	26.8510	−	36.9572i	1.70849	−	2.35153i
$248$	−11.8238	−	13.9573i	−0.750814	−	0.886286i
$249$	−3.06362	−	0.995431i	−0.194149	−	0.0630829i
$250$	−1.37558	+	0.328297i	−0.0869993	+	0.0207633i
$251$	−18.2295	−	25.0907i	−1.15064	−	1.58371i	−0.741061	−	0.671437i	$-0.765677\pi$
$251$	−18.2295	−	25.0907i	−1.15064	−	1.58371i	−0.409574	−	0.912277i	$-0.634323\pi$
$252$	−5.86392	−	0.944884i	−0.369392	−	0.0595221i
$253$	8.61996	+	6.62638i	0.541933	+	0.416597i
$254$	0.630491	−	7.87608i	0.0395605	−	0.494189i
$255$	−3.75495	+	2.72813i	−0.235144	+	0.170842i
$256$	−5.10726	+	15.1630i	−0.319203	+	0.947686i
$257$	2.26153	−	6.96027i	0.141070	−	0.434169i	−0.855415	−	0.517944i	$-0.826698\pi$
$257$	2.26153	−	6.96027i	0.141070	−	0.434169i	0.996485	+	0.0837746i	$0.0266976\pi$
$258$	−8.11800	−	6.95228i	−0.505405	−	0.432830i
$259$	−7.62415	−	5.53927i	−0.473742	−	0.344193i
$260$	−11.1023	−	5.69449i	−0.688538	−	0.353157i
$261$	−5.89824	+	1.91645i	−0.365092	+	0.118626i
$262$	12.5925	+	20.6112i	0.777970	+	1.27336i
$263$	−6.44328			−0.397310			−0.198655	−	0.980069i	$-0.563657\pi$
$263$	−6.44328			−0.397310			−0.198655	+	0.980069i	$0.563657\pi$
$264$	−2.47233	+	9.04917i	−0.152162	+	0.556938i
$265$	11.8301			0.726717
$266$	16.0330	+	26.2424i	0.983046	+	1.60903i
$267$	5.18833	−	1.68579i	0.317520	−	0.103169i
$268$	12.0346	+	6.17266i	0.735131	+	0.377055i
$269$	−6.16729	−	4.48080i	−0.376026	−	0.273199i	0.383679	−	0.923466i	$-0.374657\pi$
$269$	−6.16729	−	4.48080i	−0.376026	−	0.273199i	−0.759705	+	0.650267i	$0.774657\pi$
$270$	1.07414	+	0.919900i	0.0653703	+	0.0559833i
$271$	6.80303	−	20.9376i	0.413255	−	1.27187i	−0.500548	−	0.865709i	$-0.666868\pi$
$271$	6.80303	−	20.9376i	0.413255	−	1.27187i	0.913803	−	0.406158i	$-0.133132\pi$
$272$	18.5652	+	0.0995994i	1.12568	+	0.00603910i
$273$	−14.9893	+	10.8904i	−0.907194	+	0.659115i
$274$	0.923889	−	11.5412i	0.0558142	−	0.697230i
$275$	3.12541	+	1.10986i	0.188470	+	0.0669271i
$276$	−6.47291	−	1.04301i	−0.389623	−	0.0627821i
$277$	−14.1531	−	19.4801i	−0.850378	−	1.17044i	−0.983779	−	0.179383i	$-0.942590\pi$
$277$	−14.1531	−	19.4801i	−0.850378	−	1.17044i	0.133402	−	0.991062i	$-0.457410\pi$
$278$	−28.8540	+	6.88632i	−1.73055	+	0.413014i
$279$	6.15077	+	1.99851i	0.368237	+	0.119647i
$280$	6.40916	−	5.42949i	0.383020	−	0.324474i
$281$	−3.73087	+	5.13511i	−0.222565	+	0.306335i	−0.905668	−	0.423987i	$-0.860630\pi$
$281$	−3.73087	+	5.13511i	−0.222565	+	0.306335i	0.683103	+	0.730322i	$0.260630\pi$
$282$	8.16423	+	3.39457i	0.486173	+	0.202144i
$283$	3.32958	+	10.2474i	0.197923	+	0.609145i	0.999930	+	0.0118299i	$0.00376565\pi$
$283$	3.32958	+	10.2474i	0.197923	+	0.609145i	−0.802007	+	0.597315i	$0.796234\pi$
$284$	9.77605	+	19.3145i	0.580102	+	1.14610i
$285$		−	7.32221i		−	0.433730i
$286$	14.5749	+	25.3745i	0.861833	+	1.50042i
$287$			25.9309i			1.53065i
$288$	−1.28365	−	5.50929i	−0.0756398	−	0.324638i
$289$	−1.40366	−	4.32002i	−0.0825683	−	0.254119i
$290$	3.36724	−	8.09850i	0.197731	−	0.475560i
$291$	6.80119	−	9.36103i	0.398693	−	0.548753i
$292$	−7.34460	+	7.30530i	−0.429810	+	0.427510i
$293$	−8.94182	−	2.90537i	−0.522387	−	0.169734i	0.0359415	−	0.999354i	$-0.488557\pi$
$293$	−8.94182	−	2.90537i	−0.522387	−	0.169734i	−0.558328	+	0.829620i	$0.688557\pi$
$294$	−0.597365	−	2.50299i	−0.0348390	−	0.145977i
$295$	0.471862	+	0.649463i	0.0274729	+	0.0378132i
$296$	2.13037	−	8.71892i	0.123825	−	0.506777i
$297$	−0.939176	−	3.18087i	−0.0544965	−	0.184573i
$298$	10.5148	+	0.841723i	0.609105	+	0.0487597i
$299$	−16.5460	+	12.0214i	−0.956880	+	0.695214i
$300$	−1.97621	+	0.307569i	−0.114096	+	0.0177575i
$301$	6.93575	−	21.3460i	0.399770	−	1.23036i
$302$	−14.8252	+	17.3110i	−0.853095	+	0.996138i
$303$	−9.11556	−	6.62284i	−0.523675	−	0.380472i
$304$	−17.3424	+	23.6025i	−0.994656	+	1.35370i
$305$	−1.06789	+	0.346980i	−0.0611475	+	0.0198680i
$306$	−5.60123	+	3.42212i	−0.320201	+	0.195629i
$307$	−12.0954			−0.690319			−0.345160	−	0.938544i	$-0.612175\pi$
$307$	−12.0954			−0.690319			−0.345160	+	0.938544i	$0.612175\pi$
$308$	−19.5398	+	2.50169i	−1.11338	+	0.142547i
$309$	−13.1898			−0.750343
$310$	−7.80477	+	4.76838i	−0.443281	+	0.270826i
$311$	−21.5463	+	7.00081i	−1.22178	+	0.396980i	−0.847729	−	0.530429i	$-0.822031\pi$
$311$	−21.5463	+	7.00081i	−1.22178	+	0.396980i	−0.374049	+	0.927409i	$0.622031\pi$
$312$	−15.0084	−	9.28043i	−0.849684	−	0.525401i
$313$	−9.22329	−	6.70111i	−0.521331	−	0.378769i	0.295774	−	0.955258i	$-0.404423\pi$
$313$	−9.22329	−	6.70111i	−0.521331	−	0.378769i	−0.817105	+	0.576489i	$0.804423\pi$
$314$	2.84129	−	3.31770i	0.160343	−	0.187229i
$315$	−0.917712	+	2.82443i	−0.0517072	+	0.159138i
$316$	−1.53739	−	9.87812i	−0.0864850	−	0.555688i
$317$	−6.31326	+	4.58685i	−0.354588	+	0.257623i	−0.750791	−	0.660539i	$-0.770328\pi$
$317$	−6.31326	+	4.58685i	−0.354588	+	0.257623i	0.396203	+	0.918163i	$0.370328\pi$
$318$	16.6769	+	1.33501i	0.935196	+	0.0748637i
$319$	−16.9617	+	11.6355i	−0.949670	+	0.651462i
$320$	7.09859	+	3.68917i	0.396824	+	0.206231i
$321$	−2.79397	−	3.84557i	−0.155944	−	0.214639i
$322$	−3.19615	−	13.3920i	−0.178114	−	0.746308i
$323$	32.3218	+	10.5020i	1.79843	+	0.584346i
$324$	1.41042	+	1.41800i	0.0783564	+	0.0787779i
$325$	−3.66706	+	5.04728i	−0.203412	+	0.279973i
$326$	5.75035	−	13.8301i	0.318483	−	0.765978i
$327$	−4.50304	−	13.8589i	−0.249018	−	0.766400i
$328$	−22.8546	+	9.35913i	−1.26193	+	0.516772i
$329$			18.5674i			1.02365i
$330$	4.28066	+	1.91727i	0.235643	+	0.105542i
$331$			9.62943i			0.529281i	0.964347	+	0.264641i	$0.0852533\pi$
$331$			9.62943i			0.529281i	−0.964347	+	0.264641i	$0.914747\pi$
$332$	5.74819	−	2.90945i	0.315473	−	0.159677i
$333$	0.980600	+	3.01798i	0.0537366	+	0.165384i
$334$	−14.3500	−	5.96653i	−0.785197	−	0.326474i
$335$	3.97499	−	5.47110i	0.217177	−	0.298918i
$336$	9.64773	−	6.93071i	0.526327	−	0.378101i
$337$	−16.2829	−	5.29064i	−0.886987	−	0.288199i	−0.170131	−	0.985421i	$-0.554419\pi$
$337$	−16.2829	−	5.29064i	−0.886987	−	0.288199i	−0.716855	+	0.697222i	$0.754419\pi$
$338$	−35.6583	+	8.51023i	−1.93955	+	0.462895i
$339$	2.23162	+	3.07156i	0.121205	+	0.166824i
$340$	1.47673	−	9.16453i	0.0800869	−	0.497016i
$341$	21.4418	+	0.580340i	1.16114	+	0.0314272i
$342$	0.826302	−	10.3222i	0.0446813	−	0.558158i
$343$	−12.4465	+	9.04289i	−0.672046	+	0.488270i
$344$	21.3169	−	1.59140i	1.14933	−	0.0858028i
$345$	−1.01302	+	3.11776i	−0.0545392	+	0.167854i
$346$	22.6660	+	19.4112i	1.21853	+	1.04355i
$347$	2.91324	+	2.11659i	0.156391	+	0.113625i	0.663229	−	0.748417i	$-0.269186\pi$
$347$	2.91324	+	2.11659i	0.156391	+	0.113625i	−0.506838	+	0.862041i	$0.669186\pi$
$348$	5.66072	−	11.0365i	0.303446	−	0.591618i
$349$	−16.2256	+	5.27201i	−0.868536	+	0.282204i	−0.709189	−	0.705018i	$-0.750939\pi$
$349$	−16.2256	+	5.27201i	−0.868536	+	0.282204i	−0.159347	+	0.987223i	$0.550939\pi$
$350$	−2.18964	−	3.58394i	−0.117041	−	0.191570i
$351$	6.23878			0.333001
$352$	−9.25732	−	16.3188i	−0.493417	−	0.869793i
$353$	−18.9250			−1.00727			−0.503637	−	0.863915i	$-0.668005\pi$
$353$	−18.9250			−1.00727			−0.503637	+	0.863915i	$0.668005\pi$
$354$	0.591895	+	0.968799i	0.0314589	+	0.0514911i
$355$	10.2941	−	3.34475i	0.546352	−	0.177521i
$356$	−4.97939	+	9.70815i	−0.263907	+	0.514531i
$357$	−11.1514	−	8.10194i	−0.590193	−	0.428800i
$358$	13.0663	+	11.1900i	0.690576	+	0.591412i
$359$	−7.33432	+	22.5727i	−0.387090	+	1.19134i	0.547862	+	0.836569i	$0.315442\pi$
$359$	−7.33432	+	22.5727i	−0.387090	+	1.19134i	−0.934952	+	0.354773i	$0.884558\pi$
$360$	−2.82058	+	0.210569i	−0.148658	+	0.0110979i
$361$	−28.0040	+	20.3461i	−1.47389	+	1.07085i
$362$	−0.112847	+	1.40969i	−0.00593112	+	0.0740915i
$363$	−5.97480	−	9.23590i	−0.313595	−	0.484759i
$364$	5.89492	−	36.5837i	0.308978	−	1.91751i
$365$	3.04446	+	4.19034i	0.159354	+	0.219332i
$366$	−1.54457	+	0.368628i	−0.0807360	+	0.0192685i
$367$	−19.5990	−	6.36812i	−1.02306	−	0.332413i	−0.251018	−	0.967982i	$-0.580765\pi$
$367$	−19.5990	−	6.36812i	−1.02306	−	0.332413i	−0.772044	+	0.635569i	$0.780765\pi$
$368$	10.6497	−	7.65049i	0.555153	−	0.398810i
$369$	5.13230	−	7.06401i	0.267177	−	0.367738i
$370$	−4.14379	−	1.72293i	−0.215426	−	0.0895709i
$371$	10.8566	+	33.4133i	0.563648	+	1.73473i
$372$	−11.5405	+	5.84125i	−0.598348	+	0.302855i
$373$			27.0934i			1.40284i	0.712748	+	0.701420i	$0.247450\pi$
$373$			27.0934i			1.40284i	−0.712748	+	0.701420i	$0.752550\pi$
$374$	−14.6028	+	16.1459i	−0.755095	+	0.834882i
$375$			1.00000i			0.0516398i
$376$	−16.3647	+	6.70145i	−0.843943	+	0.345601i
$377$	−11.9563	−	36.7978i	−0.615782	−	1.89518i
$378$	−1.61244	+	3.87804i	−0.0829347	+	0.199465i
$379$	14.8027	−	20.3741i	0.760361	−	1.04655i	−0.236823	−	0.971553i	$-0.576106\pi$
$379$	14.8027	−	20.3741i	0.760361	−	1.04655i	0.997184	−	0.0749946i	$-0.0238939\pi$
$380$	10.3274	+	10.3829i	0.529782	+	0.532632i
$381$	−5.31360	−	1.72649i	−0.272224	−	0.0884509i
$382$	−1.07741	−	4.51438i	−0.0551249	−	0.230976i
$383$	1.99665	+	2.74815i	0.102024	+	0.140424i	0.856976	−	0.515356i	$-0.172340\pi$
$383$	1.99665	+	2.74815i	0.102024	+	0.140424i	−0.754953	+	0.655779i	$0.772340\pi$
$384$	9.59060	+	6.00170i	0.489418	+	0.306273i
$385$	−0.266492	+	9.84604i	−0.0135817	+	0.501800i
$386$	−15.0708	−	1.20644i	−0.767084	−	0.0614061i
$387$	−6.11427	+	4.44227i	−0.310806	+	0.225814i
$388$	3.55884	+	22.8665i	0.180673	+	1.16087i
$389$	−8.55127	+	26.3181i	−0.433567	+	1.33438i	0.460981	+	0.887410i	$0.347498\pi$
$389$	−8.55127	+	26.3181i	−0.433567	+	1.33438i	−0.894548	+	0.446972i	$0.852502\pi$
$390$	−5.73905	+	6.70134i	−0.290608	+	0.339336i
$391$	−12.3095	−	8.94336i	−0.622517	−	0.452285i
$392$	4.37732	+	2.70671i	0.221088	+	0.136709i
$393$	16.2432	−	5.27774i	0.819361	−	0.266227i
$394$	−4.85811	+	2.96810i	−0.244748	+	0.149531i
$395$	−4.99852			−0.251503
$396$	5.81810	+	3.18586i	0.292371	+	0.160095i
$397$	11.6029			0.582332			0.291166	−	0.956673i	$-0.405957\pi$
$397$	11.6029			0.582332			0.291166	+	0.956673i	$0.405957\pi$
$398$	−22.9629	+	14.0294i	−1.15103	+	0.703228i
$399$	20.6811	−	6.71968i	1.03535	−	0.336405i
$400$	2.36847	−	3.22341i	0.118423	−	0.161170i
$401$	−13.8039	−	10.0291i	−0.689332	−	0.500829i	0.187108	−	0.982339i	$-0.440088\pi$
$401$	−13.8039	−	10.0291i	−0.689332	−	0.500829i	−0.876441	+	0.481510i	$0.840088\pi$
$402$	6.22096	−	7.26406i	0.310273	−	0.362298i
$403$	−12.4682	+	38.3733i	−0.621087	+	1.91151i
$404$	22.2668	−	3.46552i	1.10782	−	0.172416i
$405$	0.809017	−	0.587785i	0.0402004	−	0.0292073i
$406$	25.9638	+	2.07844i	1.28856	+	0.103151i
$407$	5.95357	+	8.67884i	0.295108	+	0.430194i
$408$	3.11596	−	12.7526i	0.154263	−	0.631349i
$409$	2.37266	+	3.26569i	0.117321	+	0.161478i	0.863638	−	0.504112i	$-0.168180\pi$
$409$	2.37266	+	3.26569i	0.117321	+	0.161478i	−0.746318	+	0.665590i	$0.768180\pi$
$410$	2.86656	+	12.0110i	0.141569	+	0.593182i
$411$	−7.78627	−	2.52991i	−0.384068	−	0.124791i
$412$	18.7032	−	18.6031i	0.921441	−	0.916511i
$413$	−1.40133	+	1.92876i	−0.0689548	+	0.0949081i
$414$	−1.77989	+	4.28079i	−0.0874770	+	0.210390i
$415$	−0.995431	−	3.06362i	−0.0488638	−	0.150387i
$416$	34.3712	−	8.00841i	1.68519	−	0.392645i
$417$			20.9759i			1.02719i
$418$	−7.06595	−	33.6095i	−0.345607	−	1.64389i
$419$		−	31.8025i		−	1.55365i	−0.629715	−	0.776826i	$-0.716828\pi$
$419$		−	31.8025i		−	1.55365i	0.629715	−	0.776826i	$-0.283172\pi$
$420$	−2.68230	−	5.29940i	−0.130883	−	0.258584i
$421$	3.81966	+	11.7557i	0.186159	+	0.572938i	0.999966	−	0.00819671i	$-0.00260912\pi$
$421$	3.81966	+	11.7557i	0.186159	+	0.572938i	−0.813808	+	0.581134i	$0.802609\pi$
$422$	−12.4049	−	5.15777i	−0.603859	−	0.251076i
$423$	3.67490	−	5.05807i	0.178680	−	0.245932i
$424$	−25.5308	+	21.6284i	−1.23989	+	1.05037i
$425$	−4.41421	−	1.43426i	−0.214121	−	0.0695720i
$426$	14.8890	−	3.55343i	0.721376	−	0.172164i
$427$	−1.96004	−	2.69776i	−0.0948530	−	0.130554i
$428$	9.38571	+	1.51237i	0.453675	+	0.0731031i
$429$	19.8448	−	5.85931i	0.958114	−	0.282890i
$430$	0.852871	−	10.6540i	0.0411291	−	0.513784i
$431$	14.0600	−	10.2152i	0.677247	−	0.492049i	−0.195196	−	0.980764i	$-0.562534\pi$
$431$	14.0600	−	10.2152i	0.677247	−	0.492049i	0.872443	+	0.488716i	$0.162534\pi$
$432$	−3.99994	−	0.0214590i	−0.192447	−	0.00103245i
$433$	1.50812	−	4.64150i	0.0724754	−	0.223056i	−0.908257	−	0.418413i	$-0.862586\pi$
$433$	1.50812	−	4.64150i	0.0724754	−	0.223056i	0.980732	+	0.195357i	$0.0625864\pi$
$434$	−20.6305	−	17.6680i	−0.990295	−	0.848092i
$435$	−5.01734	−	3.64531i	−0.240563	−	0.174779i
$436$	25.9321	+	13.3008i	1.24192	+	0.636994i
$437$	22.8289	−	7.41755i	1.09205	−	0.354830i
$438$	3.81891	+	6.25070i	0.182475	+	0.298670i
$439$	1.10389			0.0526856			0.0263428	−	0.999653i	$-0.491614\pi$
$439$	1.10389			0.0526856			0.0263428	+	0.999653i	$0.491614\pi$
$440$	−8.77414	+	3.31881i	−0.418291	+	0.158218i
$441$	−1.81959			−0.0866470
$442$	−21.3498	−	34.9448i	−1.01551	−	1.66216i
$443$	−4.62129	+	1.50155i	−0.219564	+	0.0713408i	−0.416733	−	0.909029i	$-0.636825\pi$
$443$	−4.62129	+	1.50155i	−0.219564	+	0.0713408i	0.197169	+	0.980369i	$0.436825\pi$
$444$	−5.64709	−	2.89644i	−0.267999	−	0.137459i
$445$	4.41345	+	3.20656i	0.209218	+	0.152006i
$446$	4.82878	+	4.13538i	0.228649	+	0.195816i
$447$	2.30491	−	7.09380i	0.109019	−	0.335525i
$448$	−3.90532	+	23.4351i	−0.184509	+	1.10720i
$449$	7.98695	−	5.80286i	0.376928	−	0.273854i	−0.383150	−	0.923686i	$-0.625161\pi$
$449$	7.98695	−	5.80286i	0.376928	−	0.273854i	0.760078	+	0.649832i	$0.225161\pi$
$450$	−0.112849	+	1.40970i	−0.00531974	+	0.0664541i
$451$	9.69086	−	27.2899i	0.456325	−	1.28503i
$452$	−7.49661	−	1.20797i	−0.352611	−	0.0568180i
$453$	9.47282	+	13.0382i	0.445072	+	0.612589i
$454$	−13.6111	+	3.24845i	−0.638803	+	0.152457i
$455$	−17.6210	−	5.72540i	−0.826084	−	0.268411i
$456$	13.3868	+	15.8023i	0.626895	+	0.740009i
$457$	2.04902	−	2.82024i	0.0958493	−	0.131925i	−0.758399	−	0.651791i	$-0.774018\pi$
$457$	2.04902	−	2.82024i	0.0958493	−	0.131925i	0.854248	+	0.519866i	$0.174018\pi$
$458$	−18.1203	−	7.53418i	−0.846708	−	0.352049i
$459$	1.43426	+	4.41421i	0.0669457	+	0.206038i
$460$	−2.96086	−	5.84976i	−0.138051	−	0.272747i
$461$		−	16.1204i		−	0.750800i	−0.926863	−	0.375400i	$-0.877505\pi$
$461$		−	16.1204i		−	0.750800i	0.926863	−	0.375400i	$-0.122495\pi$
$462$	−1.48679	+	13.8499i	−0.0691716	+	0.644357i
$463$		−	9.27879i		−	0.431222i	−0.976479	−	0.215611i	$-0.930826\pi$
$463$		−	9.27879i		−	0.431222i	0.976479	−	0.215611i	$-0.0691743\pi$
$464$	7.53913	+	23.6337i	0.349995	+	1.09717i
$465$	1.99851	+	6.15077i	0.0926785	+	0.285235i
$466$	−16.3920	+	39.4242i	−0.759346	+	1.82629i
$467$	−10.2560	+	14.1162i	−0.474593	+	0.653221i	−0.977455	−	0.211146i	$-0.932280\pi$
$467$	−10.2560	+	14.1162i	−0.474593	+	0.653221i	0.502862	+	0.864367i	$0.332280\pi$
$468$	−8.84660	+	8.79927i	−0.408934	+	0.406746i
$469$	19.1006	+	6.20617i	0.881984	+	0.286574i
$470$	2.05255	+	8.60028i	0.0946771	+	0.396701i
$471$	−1.81549	−	2.49881i	−0.0836533	−	0.115139i
$472$	−2.20572	−	0.538941i	−0.101526	−	0.0248068i
$473$	−15.2766	+	19.8727i	−0.702420	+	0.913747i
$474$	−7.04644	−	0.564077i	−0.323653	−	0.0259089i
$475$	5.92379	−	4.30389i	0.271802	−	0.197476i
$476$	27.2398	−	4.23949i	1.24853	−	0.194317i
$477$	3.65570	−	11.2511i	0.167383	−	0.515152i
$478$	1.23344	−	1.44026i	0.0564164	−	0.0658760i
$479$	−1.35827	−	0.986838i	−0.0620607	−	0.0450898i	0.556322	−	0.830967i	$-0.312212\pi$
$479$	−1.35827	−	0.986838i	−0.0620607	−	0.0450898i	−0.618383	+	0.785877i	$0.712212\pi$
$480$	3.70260	−	4.27677i	0.169000	−	0.195207i
$481$	−18.8285	+	6.11775i	−0.858505	+	0.278945i
$482$	7.93591	−	4.84851i	0.361471	−	0.220843i
$483$	−9.73554			−0.442982
$484$	21.4987	+	4.66958i	0.977215	+	0.212254i
$485$	11.5709			0.525406
$486$	1.20681	−	0.737307i	0.0547418	−	0.0334449i
$487$	31.4247	−	10.2105i	1.42399	−	0.462683i	0.507123	−	0.861874i	$-0.330709\pi$
$487$	31.4247	−	10.2105i	1.42399	−	0.462683i	0.916868	+	0.399191i	$0.130709\pi$
$488$	1.67029	−	2.70120i	0.0756103	−	0.122278i
$489$	−8.56829	−	6.22522i	−0.387471	−	0.281514i
$490$	1.67384	−	1.95450i	0.0756163	−	0.0882952i
$491$	8.60287	−	26.4769i	0.388242	−	1.19489i	−0.545859	−	0.837877i	$-0.683797\pi$
$491$	8.60287	−	26.4769i	0.388242	−	1.19489i	0.934101	−	0.357009i	$-0.116203\pi$
$492$	2.68557	+	17.2555i	0.121075	+	0.777936i
$493$	23.2873	−	16.9192i	1.04881	−	0.762005i
$494$	64.3976	+	5.15512i	2.89739	+	0.231940i
$495$	2.02135	−	2.62948i	0.0908528	−	0.118186i
$496$	8.12590	−	24.5598i	0.364864	−	1.10277i
$497$	18.8940	+	26.0053i	0.847511	+	1.16650i
$498$	−1.05754	−	4.43113i	−0.0473894	−	0.198564i
$499$	30.7530	+	9.99225i	1.37669	+	0.447314i	0.901581	−	0.432611i	$-0.142408\pi$
$499$	30.7530	+	9.99225i	1.37669	+	0.447314i	0.475111	+	0.879926i	$0.342408\pi$
$500$	−1.41042	−	1.41800i	−0.0630757	−	0.0634150i
$501$	−6.45925	+	8.89040i	−0.288578	+	0.397194i
$502$	16.8389	−	40.4990i	0.751558	−	1.80756i
$503$	11.6131	+	35.7415i	0.517804	+	1.59364i	0.778122	+	0.628114i	$0.216173\pi$
$503$	11.6131	+	35.7415i	0.517804	+	1.59364i	−0.260318	+	0.965523i	$0.583827\pi$
$504$	−3.18321	−	7.77328i	−0.141792	−	0.346249i
$505$		−	11.2675i		−	0.501395i
$506$	−1.64120	+	15.2883i	−0.0729600	+	0.679648i
$507$			25.9223i			1.15125i
$508$	9.96977	−	5.04621i	0.442337	−	0.223889i
$509$	−5.10663	−	15.7166i	−0.226347	−	0.696626i	−0.998152	−	0.0607660i	$-0.980646\pi$
$509$	−5.10663	−	15.7166i	−0.226347	−	0.696626i	0.771805	−	0.635860i	$-0.219354\pi$
$510$	−6.06087	−	2.52002i	−0.268380	−	0.111589i
$511$	−9.04137	+	12.4444i	−0.399966	+	0.550507i
$512$	−22.0644	+	5.01630i	−0.975117	+	0.221691i
$513$	−6.96384	−	2.26269i	−0.307461	−	0.0999001i
$514$	10.0671	−	2.40263i	0.444042	−	0.105975i
$515$	−7.75279	−	10.6708i	−0.341629	−	0.470212i
$516$	2.40459	−	14.9228i	0.105856	−	0.656940i
$517$	6.93897	−	19.5404i	0.305176	−	0.859387i
$518$	1.06348	−	13.2850i	0.0467267	−	0.583710i
$519$	17.0714	−	12.4031i	0.749353	−	0.544437i
$520$	−1.31369	−	17.5970i	−0.0576092	−	0.771678i
$521$	−6.92524	+	21.3137i	−0.303400	+	0.933769i	0.676869	+	0.736103i	$0.263336\pi$
$521$	−6.92524	+	21.3137i	−0.303400	+	0.933769i	−0.980269	+	0.197666i	$0.936664\pi$
$522$	−6.66160	−	5.70501i	−0.291570	−	0.249702i
$523$	−22.9136	−	16.6477i	−1.00194	−	0.727954i	−0.0394391	−	0.999222i	$-0.512557\pi$
$523$	−22.9136	−	16.6477i	−1.00194	−	0.727954i	−0.962504	+	0.271268i	$0.912557\pi$
$524$	−15.5891	+	30.3935i	−0.681013	+	1.32775i
$525$	−2.82443	+	0.917712i	−0.123268	+	0.0400522i
$526$	−4.75068	−	7.77579i	−0.207139	−	0.339040i
$527$	−30.0172			−1.30757
$528$	−12.7435	+	3.68839i	−0.554588	+	0.160517i
$529$	12.2534			0.532756
$530$	8.72241	+	14.2766i	0.378877	+	0.620137i
$531$	0.763489	−	0.248073i	0.0331326	−	0.0107654i
$532$	−19.8482	+	38.6974i	−0.860530	+	1.67775i
$533$	44.0708	+	32.0193i	1.90892	+	1.38691i
$534$	5.85981	+	5.01836i	0.253579	+	0.217166i
$535$	1.46888	−	4.52074i	0.0635051	−	0.195449i
$536$	1.42400	+	19.0746i	0.0615075	+	0.823896i
$537$	9.84121	−	7.15006i	0.424680	−	0.308548i
$538$	0.860267	−	10.7464i	0.0370888	−	0.463312i
$539$	−5.78787	+	1.70891i	−0.249301	+	0.0736080i
$540$	−0.318167	+	1.97453i	−0.0136917	+	0.0849703i
$541$	3.20855	+	4.41619i	0.137946	+	0.189867i	0.872401	−	0.488791i	$-0.162562\pi$
$541$	3.20855	+	4.41619i	0.137946	+	0.189867i	−0.734455	+	0.678658i	$0.762562\pi$
$542$	30.2835	−	7.22748i	1.30079	−	0.310447i
$543$	0.951045	+	0.309013i	0.0408132	+	0.0132610i
$544$	13.5681	+	22.4780i	0.581726	+	0.963738i
$545$	8.56528	−	11.7891i	0.366896	−	0.504990i
$546$	−24.1943	−	10.0596i	−1.03542	−	0.430512i
$547$	8.84566	+	27.2242i	0.378213	+	1.16402i	0.941285	+	0.337613i	$0.109619\pi$
$547$	8.84566	+	27.2242i	0.378213	+	1.16402i	−0.563072	+	0.826408i	$0.690381\pi$
$548$	14.6092	−	7.39445i	0.624073	−	0.315875i
$549$			1.12285i			0.0479221i
$550$	0.965002	+	4.59007i	0.0411478	+	0.195721i
$551$			45.4107i			1.93456i
$552$	−3.51380	−	8.58056i	−0.149557	−	0.365213i
$553$	−4.58720	−	14.1180i	−0.195068	−	0.600357i
$554$	13.0735	−	31.4428i	0.555439	−	1.33588i
$555$	−1.86521	+	2.56724i	−0.0791739	+	0.108973i
$556$	−29.5847	−	29.7438i	−1.25467	−	1.26142i
$557$	1.80712	+	0.587170i	0.0765702	+	0.0248792i	0.347052	−	0.937846i	$-0.387183\pi$
$557$	1.80712	+	0.587170i	0.0765702	+	0.0248792i	−0.270481	+	0.962725i	$0.587183\pi$
$558$	2.12320	+	8.89629i	0.0898820	+	0.376610i
$559$	−27.7144	−	38.1456i	−1.17219	−	1.61338i
$560$	11.2779	+	3.73141i	0.476576	+	0.157681i
$561$	8.70792	+	12.6940i	0.367649	+	0.535941i
$562$	−8.94787	−	0.716289i	−0.377443	−	0.0302148i
$563$	20.7002	−	15.0396i	0.872410	−	0.633843i	−0.0588222	−	0.998268i	$-0.518735\pi$
$563$	20.7002	−	15.0396i	0.872410	−	0.633843i	0.931233	+	0.364425i	$0.118735\pi$
$564$	1.92296	+	12.3555i	0.0809711	+	0.520260i
$565$	−1.17323	+	3.61083i	−0.0493582	+	0.151909i
$566$	−9.91169	+	11.5736i	−0.416619	+	0.486476i
$567$	2.40260	+	1.74559i	0.100900	+	0.0733080i
$568$	−16.1009	+	26.0385i	−0.675578	+	1.09255i
$569$	20.8411	−	6.77168i	0.873703	−	0.283883i	0.162363	−	0.986731i	$-0.448088\pi$
$569$	20.8411	−	6.77168i	0.873703	−	0.283883i	0.711340	+	0.702848i	$0.248088\pi$
$570$	8.83649	−	5.39872i	0.370120	−	0.226127i
$571$	−34.2611			−1.43378			−0.716891	−	0.697185i	$-0.754435\pi$
$571$	−34.2611			−1.43378			−0.716891	+	0.697185i	$0.754435\pi$
$572$	−19.8758	+	36.2979i	−0.831051	+	1.51769i
$573$	−3.28180			−0.137099
$574$	−31.2936	+	19.1190i	−1.30617	+	0.798013i
$575$	−3.11776	+	1.01302i	−0.130019	+	0.0422459i
$576$	5.70219	−	5.61115i	0.237591	−	0.233798i
$577$	8.83101	+	6.41611i	0.367640	+	0.267106i	0.756232	−	0.654304i	$-0.227038\pi$
$577$	8.83101	+	6.41611i	0.367640	+	0.267106i	−0.388592	+	0.921410i	$0.627038\pi$
$578$	4.17850	−	4.87913i	0.173803	−	0.202945i
$579$	−3.30363	+	10.1675i	−0.137294	+	0.422547i
$580$	12.2560	−	1.90747i	0.508903	−	0.0792035i
$581$	7.73946	−	5.62304i	0.321087	−	0.233283i
$582$	16.3115	+	1.30576i	0.676133	+	0.0541254i
$583$	1.06157	−	39.2216i	0.0439656	−	1.62439i
$584$	−14.2313	−	3.47725i	−0.588895	−	0.143890i
$585$	3.66706	+	5.04728i	0.151614	+	0.208679i
$586$	−3.08664	−	12.9332i	−0.127508	−	0.534265i
$587$	−9.20285	−	2.99019i	−0.379842	−	0.123418i	0.112872	−	0.993610i	$-0.463995\pi$
$587$	−9.20285	−	2.99019i	−0.379842	−	0.123418i	−0.492714	+	0.870191i	$0.663995\pi$
$588$	2.58018	−	2.56637i	0.106405	−	0.105835i
$589$	27.8345	−	38.3110i	1.14690	−	1.57858i
$590$	−0.435868	+	1.04830i	−0.0179444	+	0.0431578i
$591$	1.24398	+	3.82857i	0.0511704	+	0.157486i
$592$	12.0928	−	3.85758i	0.497010	−	0.158546i
$593$		−	22.4103i		−	0.920283i	−0.887846	−	0.460141i	$-0.847799\pi$
$593$		−	22.4103i		−	0.920283i	0.887846	−	0.460141i	$-0.152201\pi$
$594$	3.14623	−	3.47868i	0.129092	−	0.142732i
$595$		−	13.7839i		−	0.565083i
$596$	6.73683	+	13.3099i	0.275951	+	0.545195i
$597$	5.87993	+	18.0966i	0.240650	+	0.740643i
$598$	−26.7069	−	11.1044i	−1.09213	−	0.454091i
$599$	1.38851	−	1.91113i	0.0567332	−	0.0780865i	−0.779708	−	0.626144i	$-0.784632\pi$
$599$	1.38851	−	1.91113i	0.0567332	−	0.0780865i	0.836441	+	0.548057i	$0.184632\pi$
$600$	−1.82825	−	2.15813i	−0.0746379	−	0.0881051i
$601$	−42.0065	−	13.6487i	−1.71348	−	0.556744i	−0.722575	−	0.691293i	$-0.757041\pi$
$601$	−42.0065	−	13.6487i	−1.71348	−	0.556744i	−0.990907	+	0.134549i	$0.957041\pi$
$602$	30.8743	−	7.36848i	1.25834	−	0.300317i
$603$	−3.97499	−	5.47110i	−0.161874	−	0.222800i
$604$	−31.8218	−	5.12761i	−1.29481	−	0.208639i
$605$	3.96010	−	10.2624i	0.161001	−	0.417227i
$606$	1.27152	−	15.8838i	0.0516519	−	0.645234i
$607$	38.7885	−	28.1815i	1.57438	−	1.14385i	0.651567	−	0.758591i	$-0.274112\pi$
$607$	38.7885	−	28.1815i	1.57438	−	1.14385i	0.922808	−	0.385259i	$-0.125888\pi$
$608$	−41.2703	−	3.52666i	−1.67373	−	0.143025i
$609$	5.69144	−	17.5165i	0.230629	−	0.709803i
$610$	−1.20610	−	1.03291i	−0.0488337	−	0.0418213i
$611$	31.5561	+	22.9269i	1.27663	+	0.927522i
$612$	−8.25965	−	4.23645i	−0.333877	−	0.171248i
$613$	−28.1887	+	9.15906i	−1.13853	+	0.369931i	−0.816811	−	0.576905i	$-0.804260\pi$
$613$	−28.1887	+	9.15906i	−1.13853	+	0.369931i	−0.321718	+	0.946835i	$0.604260\pi$
$614$	−8.91800	−	14.5968i	−0.359901	−	0.589077i
$615$	8.73160			0.352092
$616$	−17.4259	−	21.7362i	−0.702108	−	0.875777i
$617$	−39.7657			−1.60091			−0.800453	−	0.599396i	$-0.795408\pi$
$617$	−39.7657			−1.60091			−0.800453	+	0.599396i	$0.795408\pi$
$618$	−9.72495	−	15.9176i	−0.391195	−	0.640298i
$619$	31.4517	−	10.2193i	1.26415	−	0.410747i	0.401178	−	0.916000i	$-0.368601\pi$
$619$	31.4517	−	10.2193i	1.26415	−	0.410747i	0.862971	+	0.505253i	$0.168601\pi$
$620$	−11.5090	−	5.90308i	−0.462213	−	0.237073i
$621$	2.65212	+	1.92688i	0.106426	+	0.0773230i
$622$	−24.3348	−	20.8404i	−0.975738	−	0.835625i
$623$	−5.00642	+	15.4082i	−0.200578	+	0.617316i
$624$	0.133878	−	24.9548i	0.00535942	−	0.998990i
$625$	−0.809017	+	0.587785i	−0.0323607	+	0.0235114i
$626$	1.28654	−	16.0715i	0.0514207	−	0.642346i
$627$	−24.2761	−	0.657055i	−0.969496	−	0.0262402i
$628$	6.09872	+	0.982719i	0.243365	+	0.0392148i
$629$	−8.65715	−	11.9155i	−0.345183	−	0.475104i
$630$	−4.08517	+	0.974969i	−0.162757	+	0.0388437i
$631$	−0.181530	−	0.0589826i	−0.00722658	−	0.00234806i	0.305401	−	0.952224i	$-0.401209\pi$
$631$	−0.181530	−	0.0589826i	−0.00722658	−	0.00234806i	−0.312628	+	0.949876i	$0.601209\pi$
$632$	10.7874	−	9.13854i	0.429101	−	0.363511i
$633$	−5.58370	+	7.68530i	−0.221932	+	0.305463i
$634$	−10.1903	−	4.23696i	−0.404707	−	0.168271i
$635$	−1.72649	−	5.31360i	−0.0685138	−	0.210864i
$636$	10.6849	+	21.1101i	0.423685	+	0.837071i
$637$		−	11.3520i		−	0.449783i
$638$	−26.5477	−	11.8905i	−1.05103	−	0.470749i
$639$		−	10.8238i		−	0.428184i
$640$	0.781736	+	11.2867i	0.0309008	+	0.446145i
$641$	−2.18073	−	6.71160i	−0.0861337	−	0.265092i	0.898708	−	0.438547i	$-0.144507\pi$
$641$	−2.18073	−	6.71160i	−0.0861337	−	0.265092i	−0.984842	+	0.173455i	$0.944507\pi$
$642$	2.58084	−	6.20714i	0.101858	−	0.244976i
$643$	−3.12032	+	4.29475i	−0.123053	+	0.169368i	−0.866099	−	0.499872i	$-0.833380\pi$
$643$	−3.12032	+	4.29475i	−0.123053	+	0.169368i	0.743046	+	0.669240i	$0.233380\pi$
$644$	13.8050	−	13.7311i	0.543994	−	0.541083i
$645$	−7.18775	−	2.33544i	−0.283017	−	0.0919579i
$646$	11.1572	+	46.7493i	0.438975	+	1.83933i
$647$	4.75129	+	6.53958i	0.186792	+	0.257098i	0.892135	−	0.451769i	$-0.149207\pi$
$647$	4.75129	+	6.53958i	0.186792	+	0.257098i	−0.705343	+	0.708867i	$0.749207\pi$
$648$	−0.671344	+	2.74760i	−0.0263729	+	0.107936i
$649$	2.19558	−	1.50614i	0.0861840	−	0.0591211i
$650$	−8.79483	−	0.704038i	−0.344962	−	0.0276146i
$651$	−15.5383	+	11.2893i	−0.608996	+	0.442461i
$652$	20.9300	−	3.25746i	0.819682	−	0.127572i
$653$	1.75517	−	5.40185i	0.0686850	−	0.211391i	−0.910823	−	0.412798i	$-0.864551\pi$
$653$	1.75517	−	5.40185i	0.0686850	−	0.211391i	0.979508	+	0.201407i	$0.0645515\pi$
$654$	13.4049	−	15.6526i	0.524173	−	0.612064i
$655$	13.8173	+	10.0389i	0.539886	+	0.392250i
$656$	−28.1455	−	20.6805i	−1.09890	−	0.807438i
$657$	4.92604	−	1.60057i	0.192183	−	0.0624440i
$658$	−22.4072	+	13.6899i	−0.873525	+	0.533686i
$659$	−39.6975			−1.54639			−0.773197	−	0.634166i	$-0.781344\pi$
$659$	−39.6975			−1.54639			−0.773197	+	0.634166i	$0.781344\pi$
$660$	0.842384	+	6.57954i	0.0327897	+	0.256108i
$661$	38.6966			1.50512			0.752562	−	0.658521i	$-0.228818\pi$
$661$	38.6966			1.50512			0.752562	+	0.658521i	$0.228818\pi$
$662$	−11.6208	+	7.09984i	−0.451657	+	0.275943i
$663$	−27.5393	+	8.94805i	−1.06954	+	0.347513i
$664$	7.74932	+	4.79179i	0.300732	+	0.185957i
$665$	17.5924	+	12.7816i	0.682203	+	0.495649i
$666$	−2.91911	+	3.40857i	−0.113113	+	0.132079i
$667$	6.28252	−	19.3356i	0.243260	−	0.748678i
$668$	−3.37992	−	21.7168i	−0.130773	−	0.840249i
$669$	3.63691	−	2.64237i	0.140611	−	0.102160i
$670$	9.53333	+	0.763156i	0.368305	+	0.0294833i
$671$	1.05455	+	3.57164i	0.0407106	+	0.137882i
$672$	15.4774	+	6.53287i	0.597052	+	0.252011i
$673$	−1.35876	−	1.87017i	−0.0523762	−	0.0720897i	0.782026	−	0.623246i	$-0.214187\pi$
$673$	−1.35876	−	1.87017i	−0.0523762	−	0.0720897i	−0.834402	+	0.551157i	$0.814187\pi$
$674$	−5.62073	−	23.5511i	−0.216502	−	0.907155i
$675$	0.951057	+	0.309017i	0.0366062	+	0.0118941i
$676$	−36.5613	−	36.7579i	−1.40620	−	1.41377i
$677$	18.0625	−	24.8608i	0.694197	−	0.955480i	−0.305798	−	0.952097i	$-0.598923\pi$
$677$	18.0625	−	24.8608i	0.694197	−	0.955480i	0.999994	−	0.00338313i	$-0.00107689\pi$
$678$	−2.06139	+	4.95781i	−0.0791670	+	0.190403i
$679$	10.6187	+	32.6811i	0.407509	+	1.25418i
$680$	12.1486	−	4.97495i	0.465878	−	0.190780i
$681$			9.89484i			0.379171i
$682$	15.1088	+	26.3039i	0.578546	+	1.00723i
$683$			7.11006i			0.272059i	0.990705	+	0.136029i	$0.0434342\pi$
$683$			7.11006i			0.272059i	−0.990705	+	0.136029i	$0.956566\pi$
$684$	13.0661	−	6.61341i	0.499594	−	0.252870i
$685$	−2.52991	−	7.78627i	−0.0966630	−	0.297498i
$686$	−20.0899	−	8.35308i	−0.767035	−	0.318922i
$687$	−8.15636	+	11.2263i	−0.311185	+	0.428309i
$688$	17.6376	+	24.5520i	0.672429	+	0.936038i
$689$	70.1931	+	22.8071i	2.67414	+	0.868882i
$690$	−4.50943	+	1.07622i	−0.171671	+	0.0409711i
$691$	−9.41260	−	12.9553i	−0.358072	−	0.492844i	0.591538	−	0.806277i	$-0.298521\pi$
$691$	−9.41260	−	12.9553i	−0.358072	−	0.492844i	−0.949610	+	0.313433i	$0.898521\pi$
$692$	−6.71378	+	41.6655i	−0.255220	+	1.58388i
$693$	9.28179	+	3.29604i	0.352586	+	0.125206i
$694$	−0.406364	+	5.07629i	−0.0154254	+	0.192694i
$695$	−16.9698	+	12.3293i	−0.643703	+	0.467677i
$696$	17.4926	−	1.30590i	0.663055	−	0.0495000i
$697$	−12.5234	+	38.5431i	−0.474358	+	1.45992i
$698$	−18.3255	−	15.6940i	−0.693632	−	0.594028i
$699$	24.4249	+	17.7457i	0.923833	+	0.671204i
$700$	2.71069	−	5.28493i	0.102454	−	0.199752i
$701$	23.6440	−	7.68242i	0.893023	−	0.290161i	0.173669	−	0.984804i	$-0.444438\pi$
$701$	23.6440	−	7.68242i	0.893023	−	0.290161i	0.719354	+	0.694643i	$0.244438\pi$
$702$	4.59989	+	7.52899i	0.173612	+	0.284163i
$703$	23.2355			0.876343
$704$	12.8681	−	23.2037i	0.484984	−	0.874523i
$705$	6.25211			0.235468
$706$	−13.9535	−	22.8388i	−0.525147	−	0.859548i
$707$	31.8241	−	10.3403i	1.19687	−	0.388886i
$708$	−0.732744	+	1.42860i	−0.0275382	+	0.0536902i
$709$	24.3716	+	17.7070i	0.915296	+	0.665001i	0.942349	−	0.334633i	$-0.108612\pi$
$709$	24.3716	+	17.7070i	0.915296	+	0.665001i	−0.0270528	+	0.999634i	$0.508612\pi$
$710$	11.6263	+	9.95683i	0.436329	+	0.373673i
$711$	−1.54463	+	4.75388i	−0.0579281	+	0.178284i
$712$	−15.3872	+	1.14872i	−0.576659	+	0.0430502i
$713$	−17.1521	+	12.4617i	−0.642350	+	0.466695i
$714$	1.55549	−	19.4311i	0.0582127	−	0.727192i
$715$	16.4047	+	12.6107i	0.613502	+	0.471615i
$716$	−3.87031	+	24.0190i	−0.144640	+	0.897632i
$717$	−0.788130	−	1.08477i	−0.0294332	−	0.0405114i
$718$	−32.6485	+	7.79191i	−1.21843	+	0.290792i
$719$	−3.92290	−	1.27463i	−0.146299	−	0.0475356i	0.234952	−	0.972007i	$-0.424507\pi$
$719$	−3.92290	−	1.27463i	−0.146299	−	0.0475356i	−0.381251	+	0.924471i	$0.624507\pi$
$720$	−2.33375	−	3.24863i	−0.0869736	−	0.121069i
$721$	23.0241	−	31.6899i	0.857461	−	1.18019i
$722$	−45.2013	−	18.7940i	−1.68222	−	0.699442i
$723$	−2.03209	−	6.25412i	−0.0755741	−	0.232593i
$724$	−1.78442	+	0.903187i	−0.0663175	+	0.0335667i
$725$		−	6.20177i		−	0.230328i
$726$	6.74067	−	14.0201i	0.250170	−	0.520335i
$727$			40.8967i			1.51677i	0.651804	+	0.758387i	$0.274012\pi$
$727$			40.8967i			1.51677i	−0.651804	+	0.758387i	$0.725988\pi$
$728$	48.4957	−	19.8594i	1.79737	−	0.736037i
$729$	−0.309017	−	0.951057i	−0.0114451	−	0.0352243i
$730$	−2.81222	+	6.76363i	−0.104085	+	0.250333i
$731$	20.6183	−	28.3786i	0.762594	−	1.04962i
$732$	−1.58369	−	1.59220i	−0.0585347	−	0.0588496i
$733$	40.5994	+	13.1915i	1.49957	+	0.487240i	0.939893	−	0.341470i	$-0.110925\pi$
$733$	40.5994	+	13.1915i	1.49957	+	0.487240i	0.559678	+	0.828710i	$0.310925\pi$
$734$	−6.76543	−	28.3475i	−0.249717	−	1.04632i
$735$	−1.06953	−	1.47208i	−0.0394501	−	0.0542984i
$736$	17.0847	+	7.21133i	0.629752	+	0.265813i
$737$	−17.7822	−	13.6697i	−0.655017	−	0.503528i
$738$	12.3090	+	0.985350i	0.453099	+	0.0362712i
$739$	−20.8785	+	15.1691i	−0.768028	+	0.558005i	−0.901362	−	0.433066i	$-0.857432\pi$
$739$	−20.8785	+	15.1691i	−0.768028	+	0.558005i	0.133334	+	0.991071i	$0.457432\pi$
$740$	−0.976006	−	6.27108i	−0.0358787	−	0.230530i
$741$	14.1164	−	43.4458i	0.518579	−	1.59602i
$742$	−32.3186	+	37.7376i	−1.18645	+	1.38539i
$743$	−35.4994	−	25.7919i	−1.30235	−	0.946211i	−0.302372	−	0.953190i	$-0.597779\pi$
$743$	−35.4994	−	25.7919i	−1.30235	−	0.946211i	−0.999976	+	0.00697867i	$0.997779\pi$
$744$	−15.5582	−	9.62037i	−0.570390	−	0.352700i
$745$	7.09380	−	2.30491i	0.259897	−	0.0844455i
$746$	−32.6964	+	19.9761i	−1.19710	+	0.731377i
$747$	−3.22128			−0.117861
$748$	−30.2517	−	5.71834i	−1.10611	−	0.209083i
$749$	14.1165			0.515806
$750$	−1.20681	+	0.737307i	−0.0440663	+	0.0269226i
$751$	17.0224	−	5.53092i	0.621157	−	0.201826i	0.0185029	−	0.999829i	$-0.494110\pi$
$751$	17.0224	−	5.53092i	0.621157	−	0.201826i	0.602654	+	0.798003i	$0.294110\pi$
$752$	−20.1531	−	14.8079i	−0.734908	−	0.539990i
$753$	−25.0907	−	18.2295i	−0.914358	−	0.664320i
$754$	35.5923	−	41.5602i	1.29619	−	1.51353i
$755$	−4.98015	+	15.3273i	−0.181246	+	0.557819i
$756$	−5.86890	+	0.913412i	−0.213450	+	0.0332205i
$757$	−4.47760	+	3.25316i	−0.162741	+	0.118238i	−0.666175	−	0.745795i	$-0.732070\pi$
$757$	−4.47760	+	3.25316i	−0.162741	+	0.118238i	0.503434	+	0.864034i	$0.332070\pi$
$758$	35.5017	+	2.84196i	1.28948	+	0.103225i
$759$	10.2457	+	3.63835i	0.371897	+	0.132064i
$760$	−4.91572	+	20.1185i	−0.178312	+	0.729775i
$761$	−15.1534	−	20.8569i	−0.549311	−	0.756062i	0.440607	−	0.897700i	$-0.354763\pi$
$761$	−15.1534	−	20.8569i	−0.549311	−	0.756062i	−0.989919	+	0.141638i	$0.954763\pi$
$762$	−1.83421	−	7.68543i	−0.0664465	−	0.278414i
$763$	41.1579	+	13.3730i	1.49002	+	0.484136i
$764$	4.65360	−	4.62870i	0.168361	−	0.167461i
$765$	−2.72813	+	3.75495i	−0.0986358	+	0.135760i
$766$	−1.84434	+	4.43579i	−0.0666386	+	0.160272i
$767$	1.54767	+	4.76324i	0.0558831	+	0.171991i
$768$	−0.171670	+	15.9991i	−0.00619460	+	0.577317i
$769$		−	28.8233i		−	1.03939i	−0.854351	−	0.519697i	$-0.826045\pi$
$769$		−	28.8233i		−	1.03939i	0.854351	−	0.519697i	$-0.173955\pi$
$770$	−12.0787	+	6.93795i	−0.435287	+	0.250026i
$771$		−	7.31846i		−	0.263568i
$772$	−9.65587	−	19.0770i	−0.347522	−	0.686598i
$773$	−2.41156	−	7.42202i	−0.0867378	−	0.266952i	0.898275	−	0.439434i	$-0.144821\pi$
$773$	−2.41156	−	7.42202i	−0.0867378	−	0.266952i	−0.985013	+	0.172483i	$0.944821\pi$
$774$	−9.86905	−	4.10341i	−0.354736	−	0.147494i
$775$	−3.80138	+	5.23216i	−0.136550	+	0.187945i
$776$	−24.9714	+	21.1544i	−0.896421	+	0.759399i
$777$	−8.96273	−	2.91217i	−0.321536	−	0.104473i
$778$	−38.0658	+	9.08480i	−1.36472	+	0.325706i
$779$	−37.5798	−	51.7242i	−1.34644	−	1.85321i
$780$	−12.3187	−	1.98497i	−0.441079	−	0.0710733i
$781$	−10.1655	−	34.4292i	−0.363749	−	1.23197i
$782$	1.71703	−	21.4492i	0.0614010	−	0.767020i
$783$	−5.01734	+	3.64531i	−0.179305	+	0.130273i
$784$	−0.0390466	+	7.27824i	−0.00139452	+	0.259937i
$785$	0.954459	−	2.93752i	0.0340661	−	0.104845i
$786$	18.3454	+	15.7111i	0.654359	+	0.560395i
$787$	−2.20354	−	1.60097i	−0.0785478	−	0.0570683i	0.547818	−	0.836597i	$-0.315458\pi$
$787$	−2.20354	−	1.60097i	−0.0785478	−	0.0570683i	−0.626366	+	0.779529i	$0.715458\pi$
$788$	−7.16384	−	3.67440i	−0.255201	−	0.130895i
$789$	−6.12793	+	1.99108i	−0.218160	+	0.0708845i
$790$	−3.68544	−	6.03224i	−0.131122	−	0.214618i
$791$	−11.2752			−0.400901
$792$	0.445019	+	9.37027i	0.0158131	+	0.332958i
$793$	−7.00522			−0.248762
$794$	8.55489	+	14.0024i	0.303602	+	0.496927i
$795$	11.2511	−	3.65570i	0.399035	−	0.129654i
$796$	−33.8614	−	17.3678i	−1.20019	−	0.615586i
$797$	7.44029	+	5.40569i	0.263549	+	0.191479i	0.711710	−	0.702473i	$-0.247921\pi$
$797$	7.44029	+	5.40569i	0.263549	+	0.191479i	−0.448161	+	0.893953i	$0.647921\pi$
$798$	23.3576	+	20.0035i	0.826851	+	0.708118i
$799$	−8.96717	+	27.5981i	−0.317236	+	0.976351i
$800$	5.63631	+	0.481639i	0.199274	+	0.0170285i
$801$	4.41345	−	3.20656i	0.155942	−	0.113298i
$802$	1.92548	−	24.0531i	0.0679912	−	0.849345i
$803$	14.1659	−	9.71761i	0.499903	−	0.342927i
$804$	13.3531	+	2.15165i	0.470926	+	0.0758828i
$805$	−5.72240	−	7.87621i	−0.201688	−	0.277600i
$806$	−55.5020	+	13.2461i	−1.95497	+	0.466575i
$807$	−7.25009	−	2.35570i	−0.255215	−	0.0829244i
$808$	20.5997	+	24.3166i	0.724695	+	0.855455i
$809$	−21.4833	+	29.5692i	−0.755313	+	1.03960i	0.242277	+	0.970207i	$0.422106\pi$
$809$	−21.4833	+	29.5692i	−0.755313	+	1.03960i	−0.997590	+	0.0693915i	$0.977894\pi$
$810$	1.30584	+	0.542948i	0.0458824	+	0.0190772i
$811$	−3.86799	−	11.9044i	−0.135823	−	0.418022i	0.859894	−	0.510473i	$-0.170530\pi$
$811$	−3.86799	−	11.9044i	−0.135823	−	0.418022i	−0.995717	+	0.0924514i	$0.970530\pi$
$812$	16.6350	+	32.8657i	0.583774	+	1.15336i
$813$		−	22.0151i		−	0.772102i
$814$	−6.08406	+	13.5838i	−0.213246	+	0.476111i
$815$		−	10.5910i		−	0.370986i
$816$	17.6874	−	5.64225i	0.619181	−	0.197518i
$817$	17.1006	+	52.6302i	0.598274	+	1.84130i
$818$	−2.19167	+	5.27116i	−0.0766300	+	0.184302i
$819$	−10.8904	+	14.9893i	−0.380540	+	0.523768i
$820$	−12.3814	+	12.3152i	−0.432378	+	0.430065i
$821$	32.6749	+	10.6167i	1.14036	+	0.370526i	0.817505	−	0.575922i	$-0.195357\pi$
$821$	32.6749	+	10.6167i	1.14036	+	0.370526i	0.322857	+	0.946448i	$0.395357\pi$
$822$	−2.68776	−	11.2618i	−0.0937463	−	0.392802i
$823$	−6.39775	−	8.80575i	−0.223012	−	0.306949i	0.682820	−	0.730586i	$-0.260753\pi$
$823$	−6.39775	−	8.80575i	−0.223012	−	0.306949i	−0.905832	+	0.423637i	$0.860753\pi$
$824$	36.2404	+	8.85491i	1.26249	+	0.308475i
$825$	3.31541	+	0.0897345i	0.115428	+	0.00312415i
$826$	−3.36085	−	0.269040i	−0.116939	−	0.00936111i
$827$	28.1730	−	20.4689i	0.979670	−	0.711772i	0.0220353	−	0.999757i	$-0.492985\pi$
$827$	28.1730	−	20.4689i	0.979670	−	0.711772i	0.957635	+	0.287985i	$0.0929854\pi$
$828$	−6.47841	+	1.00827i	−0.225140	+	0.0350399i
$829$	7.68879	−	23.6637i	0.267043	−	0.821873i	−0.724173	−	0.689618i	$-0.757778\pi$
$829$	7.68879	−	23.6637i	0.267043	−	0.821873i	0.991216	−	0.132255i	$-0.0422217\pi$
$830$	2.96326	−	3.46012i	0.102856	−	0.120102i
$831$	−19.4801	−	14.1531i	−0.675757	−	0.490966i
$832$	35.0067	+	35.5747i	1.21364	+	1.23333i
$833$	8.03204	−	2.60977i	0.278294	−	0.0904231i
$834$	−25.3138	+	15.4657i	−0.876545	+	0.535532i
$835$	−10.9891			−0.380295
$836$	35.3503	−	33.3077i	1.22262	−	1.15197i
$837$	6.46730			0.223543
$838$	38.3794	−	23.4482i	1.32579	−	0.810004i
$839$	−27.7360	+	9.01199i	−0.957555	+	0.311128i	−0.745782	−	0.666190i	$-0.767924\pi$
$839$	−27.7360	+	9.01199i	−0.957555	+	0.311128i	−0.211773	+	0.977319i	$0.567924\pi$
$840$	4.41767	−	7.14429i	0.152424	−	0.246502i
$841$	7.65492	+	5.56163i	0.263963	+	0.191780i
$842$	−11.3706	+	13.2771i	−0.391856	+	0.457560i
$843$	−1.96144	+	6.03668i	−0.0675555	+	0.207914i
$844$	−2.92177	−	18.7731i	−0.100571	−	0.646197i
$845$	−20.9716	+	15.2368i	−0.721446	+	0.524161i
$846$	8.81363	+	0.705543i	0.303019	+	0.0242571i
$847$	32.6197	+	1.76706i	1.12083	+	0.0607168i
$848$	−44.9253	−	14.8640i	−1.54274	−	0.510433i
$849$	6.33324	+	8.71696i	0.217356	+	0.299165i
$850$	−1.52375	−	6.38458i	−0.0522641	−	0.218989i
$851$	−9.89354	−	3.21461i	−0.339146	−	0.110195i
$852$	15.2661	+	15.3482i	0.523007	+	0.525821i
$853$	−19.9704	+	27.4869i	−0.683773	+	0.941133i	−0.999971	−	0.00755989i	$-0.997594\pi$
$853$	−19.9704	+	27.4869i	−0.683773	+	0.941133i	0.316198	+	0.948693i	$0.397594\pi$
$854$	1.81052	−	4.35446i	0.0619549	−	0.149007i
$855$	−2.26269	−	6.96384i	−0.0773823	−	0.238158i
$856$	5.09501	+	12.4418i	0.174144	+	0.425252i
$857$		−	11.5500i		−	0.394539i	−0.980349	−	0.197270i	$-0.936793\pi$
$857$		−	11.5500i		−	0.394539i	0.980349	−	0.197270i	$-0.0632075\pi$
$858$	21.7027	+	19.6286i	0.740918	+	0.670111i
$859$			12.5945i			0.429718i	0.976645	+	0.214859i	$0.0689293\pi$
$859$			12.5945i			0.429718i	−0.976645	+	0.214859i	$0.931071\pi$
$860$	13.4862	−	6.82605i	0.459875	−	0.232766i
$861$	8.01309	+	24.6618i	0.273086	+	0.840471i
$862$	22.6943	+	9.43596i	0.772970	+	0.321390i
$863$	−18.2616	+	25.1350i	−0.621633	+	0.855604i	−0.997471	−	0.0710816i	$-0.977355\pi$
$863$	−18.2616	+	25.1350i	−0.621633	+	0.855604i	0.375838	+	0.926685i	$0.377355\pi$
$864$	−2.92329	−	4.84297i	−0.0994523	−	0.164761i
$865$	20.0687	+	6.52071i	0.682356	+	0.221711i
$866$	6.71334	−	1.60221i	0.228128	−	0.0544453i
$867$	−2.66992	−	3.67483i	−0.0906753	−	0.124804i
$868$	6.11085	−	37.9237i	0.207416	−	1.28722i
$869$	−0.448540	+	16.5722i	−0.0152157	+	0.562172i
$870$	0.699862	−	8.74267i	0.0237276	−	0.296404i
$871$	34.1330	−	24.7990i	1.15655	−	0.840284i
$872$	3.06844	+	41.1018i	0.103910	+	1.39188i
$873$	3.57560	−	11.0046i	0.121016	−	0.372448i
$874$	25.7834	+	22.0810i	0.872137	+	0.746901i
$875$	−2.40260	−	1.74559i	−0.0812228	−	0.0590118i
$876$	−4.72767	+	9.21736i	−0.159733	+	0.311426i
$877$	25.8485	−	8.39868i	0.872841	−	0.283603i	0.161860	−	0.986814i	$-0.448251\pi$
$877$	25.8485	−	8.39868i	0.872841	−	0.283603i	0.710982	+	0.703210i	$0.248251\pi$
$878$	0.813903	+	1.33218i	0.0274679	+	0.0449587i
$879$	−9.40199			−0.317121
$880$	−10.4744	−	8.14169i	−0.353092	−	0.274456i
$881$	2.04167			0.0687855			0.0343928	−	0.999408i	$-0.489050\pi$
$881$	2.04167			0.0687855			0.0343928	+	0.999408i	$0.489050\pi$
$882$	−1.34159	−	2.19589i	−0.0451738	−	0.0739394i
$883$	−12.2874	+	3.99243i	−0.413505	+	0.134356i	−0.508379	−	0.861133i	$-0.669755\pi$
$883$	−12.2874	+	3.99243i	−0.413505	+	0.134356i	0.0948743	+	0.995489i	$0.469755\pi$
$884$	26.4303	−	51.5301i	0.888946	−	1.73315i
$885$	0.649463	+	0.471862i	0.0218314	+	0.0158615i
$886$	−5.21939	−	4.46990i	−0.175349	−	0.150169i
$887$	6.97931	−	21.4801i	0.234342	−	0.721231i	−0.762866	−	0.646557i	$-0.776208\pi$
$887$	6.97931	−	21.4801i	0.234342	−	0.721231i	0.997208	−	0.0746742i	$-0.0237917\pi$
$888$	−0.668195	−	8.95051i	−0.0224232	−	0.300359i
$889$	13.4235	−	9.75271i	0.450208	−	0.327095i
$890$	−0.615627	+	7.69040i	−0.0206359	+	0.257783i
$891$	−1.87615	−	2.73497i	−0.0628535	−	0.0916249i
$892$	−1.43031	+	8.87644i	−0.0478903	+	0.297205i
$893$	−26.9084	−	37.0362i	−0.900455	−	1.23937i
$894$	10.2603	−	2.44872i	0.343154	−	0.0818975i
$895$	11.5690	+	3.75901i	0.386710	+	0.125650i
$896$	−31.1610	+	12.5659i	−1.04101	+	0.419796i
$897$	−12.0214	+	16.5460i	−0.401382	+	0.552455i
$898$	12.8918	+	5.36021i	0.430203	+	0.178872i
$899$	−12.3943	−	38.1457i	−0.413372	−	1.27223i
$900$	−1.78444	+	0.903198i	−0.0594814	+	0.0301066i
$901$			54.9079i			1.82925i
$902$	40.0787	−	8.42601i	1.33447	−	0.280556i
$903$		−	22.4445i		−	0.746908i
$904$	−4.06952	−	9.93759i	−0.135350	−	0.330519i
$905$	0.309013	+	0.951045i	0.0102719	+	0.0316138i
$906$	−8.75021	+	21.0450i	−0.290706	+	0.699174i
$907$	7.81276	−	10.7533i	0.259418	−	0.357059i	−0.659364	−	0.751824i	$-0.729174\pi$
$907$	7.81276	−	10.7533i	0.259418	−	0.357059i	0.918782	+	0.394765i	$0.129174\pi$
$908$	−13.9558	−	14.0309i	−0.463141	−	0.465632i
$909$	−10.7160	−	3.48184i	−0.355427	−	0.115485i
$910$	−6.08262	−	25.4865i	−0.201637	−	0.844868i
$911$	−3.74575	−	5.15558i	−0.124102	−	0.170812i	0.742445	−	0.669907i	$-0.233666\pi$
$911$	−3.74575	−	5.15558i	−0.124102	−	0.170812i	−0.866547	+	0.499095i	$0.833666\pi$
$912$	−9.20006	+	27.8064i	−0.304644	+	0.920762i
$913$	−10.2465	+	3.02535i	−0.339109	+	0.100124i
$914$	4.91424	+	0.393391i	0.162549	+	0.0130122i
$915$	−0.908405	+	0.659995i	−0.0300310	+	0.0218188i
$916$	−4.26796	−	27.4227i	−0.141017	−	0.906072i
$917$	−15.6737	+	48.2387i	−0.517591	+	1.59298i
$918$	−4.26960	+	4.98550i	−0.140918	+	0.164546i
$919$	36.6295	+	26.6129i	1.20829	+	0.877877i	0.995075	−	0.0991273i	$-0.0316051\pi$
$919$	36.6295	+	26.6129i	1.20829	+	0.877877i	0.213219	+	0.977004i	$0.431605\pi$
$920$	4.87646	−	7.88626i	0.160772	−	0.260002i
$921$	−11.5034	+	3.73767i	−0.379049	+	0.123161i
$922$	19.4541	−	11.8857i	0.640688	−	0.391433i
$923$	67.5274			2.22269
$924$	−17.8104	+	8.41738i	−0.585918	+	0.276911i
$925$	−3.17329			−0.104337
$926$	11.1977	−	6.84131i	0.367979	−	0.224819i
$927$	−12.5443	+	4.07588i	−0.412008	+	0.133870i
$928$	−22.9627	+	26.5236i	−0.753786	+	0.870679i
$929$	−8.18672	−	5.94800i	−0.268598	−	0.195148i	0.445331	−	0.895366i	$-0.353086\pi$
$929$	−8.18672	−	5.94800i	−0.268598	−	0.195148i	−0.713929	+	0.700218i	$0.753086\pi$
$930$	−5.94927	+	6.94681i	−0.195084	+	0.227795i
$931$	−4.11716	+	12.6713i	−0.134934	+	0.415285i
$932$	−59.6633	+	9.28575i	−1.95434	+	0.304165i
$933$	−18.3284	+	13.3163i	−0.600044	+	0.435957i
$934$	−24.5974	−	1.96905i	−0.804851	−	0.0644294i
$935$	−5.15128	+	14.5062i	−0.168465	+	0.474404i
$936$	−17.1417	−	4.18836i	−0.560293	−	0.136901i
$937$	26.6068	+	36.6211i	0.869205	+	1.19636i	0.979295	+	0.202436i	$0.0648859\pi$
$937$	26.6068	+	36.6211i	0.869205	+	1.19636i	−0.110091	+	0.993922i	$0.535114\pi$
$938$	6.59338	+	27.6266i	0.215281	+	0.902039i
$939$	−10.8426	−	3.52298i	−0.353836	−	0.114968i
$940$	−8.86551	+	8.81807i	−0.289161	+	0.287614i
$941$	−16.5025	+	22.7137i	−0.537965	+	0.740445i	−0.988318	−	0.152406i	$-0.951298\pi$
$941$	−16.5025	+	22.7137i	−0.537965	+	0.740445i	0.450353	+	0.892850i	$0.351298\pi$
$942$	1.67700	−	4.03333i	0.0546396	−	0.131413i
$943$	8.84529	+	27.2230i	0.288042	+	0.886503i
$944$	−0.975893	−	3.05924i	−0.0317626	−	0.0995697i
$945$			2.96978i			0.0966069i
$946$	−35.2460	−	3.78365i	−1.14595	−	0.123017i
$947$			6.62654i			0.215334i	0.994187	+	0.107667i	$0.0343380\pi$
$947$			6.62654i			0.215334i	−0.994187	+	0.107667i	$0.965662\pi$
$948$	−4.51465	−	8.91957i	−0.146629	−	0.289694i
$949$	9.98557	+	30.7324i	0.324145	+	0.997617i
$950$	9.56161	+	3.97558i	0.310220	+	0.128985i
$951$	−4.58685	+	6.31326i	−0.148739	+	0.204722i
$952$	25.2003	+	29.7473i	0.816746	+	0.964115i
$953$	−44.6018	−	14.4920i	−1.44479	−	0.469442i	−0.521405	−	0.853309i	$-0.674592\pi$
$953$	−44.6018	−	14.4920i	−1.44479	−	0.469442i	−0.923388	+	0.383868i	$0.874592\pi$
$954$	16.2732	−	3.88379i	0.526866	−	0.125742i
$955$	−1.92900	−	2.65503i	−0.0624208	−	0.0859149i
$956$	2.64754	+	0.426612i	0.0856276	+	0.0137976i
$957$	−12.5359	+	16.3074i	−0.405229	+	0.527145i
$958$	0.189463	−	2.36676i	0.00612126	−	0.0764667i
$959$	19.6700	−	14.2911i	0.635178	−	0.461484i
$960$	7.89118	+	1.31502i	0.254687	+	0.0424421i
$961$	−3.34541	+	10.2961i	−0.107917	+	0.332133i
$962$	−21.2653	−	18.2117i	−0.685621	−	0.587168i
$963$	−3.84557	−	2.79397i	−0.123922	−	0.0900344i
$964$	11.7024	+	6.00227i	0.376909	+	0.193320i
$965$	−10.1675	+	3.30363i	−0.327304	+	0.106347i
$966$	−7.17808	−	11.7489i	−0.230951	−	0.378015i
$967$	−30.2565			−0.972983			−0.486492	−	0.873685i	$-0.661724\pi$
$967$	−30.2565			−0.972983			−0.486492	+	0.873685i	$0.661724\pi$
$968$	10.2159	+	29.3877i	0.328351	+	0.944556i
$969$	33.9851			1.09176
$970$	8.53128	+	13.9638i	0.273923	+	0.448350i
$971$	28.1996	−	9.16259i	0.904967	−	0.294042i	0.180681	−	0.983542i	$-0.442170\pi$
$971$	28.1996	−	9.16259i	0.904967	−	0.294042i	0.724286	+	0.689500i	$0.242170\pi$
$972$	1.77957	+	0.912758i	0.0570798	+	0.0292767i
$973$	−50.3967	−	36.6153i	−1.61564	−	1.17383i
$974$	35.4918	+	30.3953i	1.13723	+	0.973927i
$975$	−1.92789	+	5.93343i	−0.0617418	+	0.190022i
$976$	4.49134	+	0.0240953i	0.143764	+	0.000771271i
$977$	−11.0207	+	8.00698i	−0.352582	+	0.256166i	−0.749951	−	0.661493i	$-0.769923\pi$
$977$	−11.0207	+	8.00698i	−0.352582	+	0.256166i	0.397369	+	0.917659i	$0.369923\pi$
$978$	1.19518	−	14.9302i	0.0382176	−	0.477414i
$979$	11.0271	−	14.3447i	0.352428	−	0.458458i
$980$	3.59283	+	0.578932i	0.114769	+	0.0184933i
$981$	−8.56528	−	11.7891i	−0.273468	−	0.376397i
$982$	38.2954	−	9.13961i	1.22206	−	0.291657i
$983$	−25.8974	−	8.41456i	−0.825998	−	0.268383i	−0.134639	−	0.990895i	$-0.542987\pi$
$983$	−25.8974	−	8.41456i	−0.825998	−	0.268383i	−0.691359	+	0.722512i	$0.742987\pi$
$984$	−18.8439	+	15.9635i	−0.600721	+	0.508899i
$985$	−2.36619	+	3.25678i	−0.0753930	+	0.103770i
$986$	37.5882	+	15.6286i	1.19705	+	0.497717i
$987$	5.73764	+	17.6586i	0.182631	+	0.562081i
$988$	41.2596	+	81.5163i	1.31264	+	2.59338i
$989$		−	24.7755i		−	0.787815i
$990$	4.66362	+	0.500639i	0.148220	+	0.0159113i
$991$			32.9942i			1.04809i	0.851689	+	0.524047i	$0.175579\pi$
$991$			32.9942i			1.04809i	−0.851689	+	0.524047i	$0.824421\pi$
$992$	35.6302	−	8.30175i	1.13126	−	0.263581i
$993$	2.97566	+	9.15813i	0.0944296	+	0.290624i
$994$	−17.4527	+	41.9753i	−0.553567	+	1.33137i
$995$	−11.1843	+	15.3939i	−0.354566	+	0.488018i
$996$	4.56778	−	4.54334i	0.144736	−	0.143961i
$997$	−0.348104	−	0.113106i	−0.0110246	−	0.00358210i	0.303500	−	0.952832i	$-0.401845\pi$
$997$	−0.348104	−	0.113106i	−0.0110246	−	0.00358210i	−0.314524	+	0.949249i	$0.601845\pi$
$998$	10.6157	+	44.4802i	0.336033	+	1.40800i
$999$	1.86521	+	2.56724i	0.0590127	+	0.0812240i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	660.2.be.b.151.16	✓	96
4.3	odd	2	inner	660.2.be.b.151.18	yes	96
11.7	odd	10	inner	660.2.be.b.271.18	yes	96
44.7	even	10	inner	660.2.be.b.271.16	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
660.2.be.b.151.16	✓	96	1.1	even	1	trivial
660.2.be.b.151.18	yes	96	4.3	odd	2	inner
660.2.be.b.271.16	yes	96	44.7	even	10	inner
660.2.be.b.271.18	yes	96	11.7	odd	10	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:	\( N \)	\(=\)	\( 660 = 2^{2} \cdot 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	660.be (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.737307 + 1.20681i) q^{2} +(0.951057 - 0.309017i) q^{3} +(-0.912758 + 1.77957i) q^{4} +(0.809017 + 0.587785i) q^{5} +(1.07414 + 0.919900i) q^{6} +(-0.917712 + 2.82443i) q^{7} +(-2.82058 + 0.210569i) q^{8} +(0.809017 - 0.587785i) q^{9} +O(q^{10})\)	\(q+(0.737307 + 1.20681i) q^{2} +(0.951057 - 0.309017i) q^{3} +(-0.912758 + 1.77957i) q^{4} +(0.809017 + 0.587785i) q^{5} +(1.07414 + 0.919900i) q^{6} +(-0.917712 + 2.82443i) q^{7} +(-2.82058 + 0.210569i) q^{8} +(0.809017 - 0.587785i) q^{9} +(-0.112849 + 1.40970i) q^{10} +(2.02135 - 2.62948i) q^{11} +(-0.318167 + 1.97453i) q^{12} +(3.66706 + 5.04728i) q^{13} +(-4.08517 + 0.974969i) q^{14} +(0.951057 + 0.309017i) q^{15} +(-2.33375 - 3.24863i) q^{16} +(-2.72813 + 3.75495i) q^{17} +(1.30584 + 0.542948i) q^{18} +(-2.26269 - 6.96384i) q^{19} +(-1.78444 + 0.903198i) q^{20} +2.96978i q^{21} +(4.66362 + 0.500639i) q^{22} +3.27820i q^{23} +(-2.61746 + 1.07187i) q^{24} +(0.309017 + 0.951057i) q^{25} +(-3.38733 + 8.14682i) q^{26} +(0.587785 - 0.809017i) q^{27} +(-4.18862 - 4.21115i) q^{28} +(-5.89824 - 1.91645i) q^{29} +(0.328297 + 1.37558i) q^{30} +(3.80138 + 5.23216i) q^{31} +(2.19978 - 5.21162i) q^{32} +(1.10986 - 3.12541i) q^{33} +(-6.54296 - 0.523773i) q^{34} +(-2.40260 + 1.74559i) q^{35} +(0.307569 + 1.97621i) q^{36} +(-0.980600 + 3.01798i) q^{37} +(6.73570 - 7.86511i) q^{38} +(5.04728 + 3.66706i) q^{39} +(-2.40566 - 1.48754i) q^{40} +(8.30424 - 2.69821i) q^{41} +(-3.58394 + 2.18964i) q^{42} -7.55765 q^{43} +(2.83435 + 5.99721i) q^{44} +1.00000 q^{45} +(-3.95615 + 2.41704i) q^{46} +(5.94611 - 1.93201i) q^{47} +(-3.22341 - 2.36847i) q^{48} +(-1.47208 - 1.06953i) q^{49} +(-0.919900 + 1.07414i) q^{50} +(-1.43426 + 4.41421i) q^{51} +(-12.3291 + 1.91886i) q^{52} +(9.57075 - 6.95356i) q^{53} +(1.40970 + 0.112849i) q^{54} +(3.18087 - 0.939176i) q^{55} +(1.99374 - 8.15976i) q^{56} +(-4.30389 - 5.92379i) q^{57} +(-2.03602 - 8.53104i) q^{58} +(0.763489 + 0.248073i) q^{59} +(-1.41800 + 1.41042i) q^{60} +(-0.659995 + 0.908405i) q^{61} +(-3.51141 + 8.44523i) q^{62} +(0.917712 + 2.82443i) q^{63} +(7.91132 - 1.18785i) q^{64} +6.23878i q^{65} +(4.59007 - 0.965002i) q^{66} -6.76265i q^{67} +(-4.19208 - 8.28226i) q^{68} +(1.01302 + 3.11776i) q^{69} +(-3.87804 - 1.61244i) q^{70} +(6.36208 - 8.75666i) q^{71} +(-2.15813 + 1.82825i) q^{72} +(4.92604 + 1.60057i) q^{73} +(-4.36511 + 1.04178i) q^{74} +(0.587785 + 0.809017i) q^{75} +(14.4579 + 2.32968i) q^{76} +(5.57176 + 8.12225i) q^{77} +(-0.704038 + 8.79483i) q^{78} +(-4.04389 + 2.93806i) q^{79} +(0.0214590 - 3.99994i) q^{80} +(0.309017 - 0.951057i) q^{81} +(9.37899 + 8.03219i) q^{82} +(-2.60607 - 1.89342i) q^{83} +(-5.28493 - 2.71069i) q^{84} +(-4.41421 + 1.43426i) q^{85} +(-5.57231 - 9.12061i) q^{86} -6.20177 q^{87} +(-5.14768 + 7.84228i) q^{88} +5.45533 q^{89} +(0.737307 + 1.20681i) q^{90} +(-17.6210 + 5.72540i) q^{91} +(-5.83379 - 2.99220i) q^{92} +(5.23216 + 3.80138i) q^{93} +(6.71567 + 5.75132i) q^{94} +(2.26269 - 6.96384i) q^{95} +(0.481639 - 5.63631i) q^{96} +(9.36103 - 6.80119i) q^{97} +(0.205338 - 2.56508i) q^{98} +(0.0897345 - 3.31541i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 8 q^{4} + 24 q^{5} + 24 q^{9}+O(q^{10}) \) 96 * q + 8 * q^4 + 24 * q^5 + 24 * q^9	\( 96 q + 8 q^{4} + 24 q^{5} + 24 q^{9} - 20 q^{13} - 4 q^{14} + 8 q^{16} + 10 q^{18} + 2 q^{20} + 30 q^{22} + 30 q^{24} - 24 q^{25} - 60 q^{28} + 20 q^{29} + 8 q^{34} - 8 q^{36} + 8 q^{37} - 58 q^{38} + 20 q^{41} - 42 q^{42} - 54 q^{44} + 96 q^{45} - 10 q^{46} + 16 q^{48} + 20 q^{49} + 56 q^{53} - 8 q^{56} - 68 q^{58} - 10 q^{64} + 54 q^{66} + 8 q^{69} + 4 q^{70} - 10 q^{72} - 40 q^{73} - 50 q^{74} - 32 q^{77} + 8 q^{78} + 2 q^{80} - 24 q^{81} - 24 q^{82} - 60 q^{84} - 84 q^{86} - 72 q^{88} + 72 q^{89} + 2 q^{92} + 80 q^{94} - 50 q^{96} - 8 q^{97}+O(q^{100}) \) 96 * q + 8 * q^4 + 24 * q^5 + 24 * q^9 - 20 * q^13 - 4 * q^14 + 8 * q^16 + 10 * q^18 + 2 * q^20 + 30 * q^22 + 30 * q^24 - 24 * q^25 - 60 * q^28 + 20 * q^29 + 8 * q^34 - 8 * q^36 + 8 * q^37 - 58 * q^38 + 20 * q^41 - 42 * q^42 - 54 * q^44 + 96 * q^45 - 10 * q^46 + 16 * q^48 + 20 * q^49 + 56 * q^53 - 8 * q^56 - 68 * q^58 - 10 * q^64 + 54 * q^66 + 8 * q^69 + 4 * q^70 - 10 * q^72 - 40 * q^73 - 50 * q^74 - 32 * q^77 + 8 * q^78 + 2 * q^80 - 24 * q^81 - 24 * q^82 - 60 * q^84 - 84 * q^86 - 72 * q^88 + 72 * q^89 + 2 * q^92 + 80 * q^94 - 50 * q^96 - 8 * q^97

Introduction

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