LMFDB - Embedded newform 504.2.cy.a.347.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(347,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 5, 4]))

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

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

chi := DirichletCharacter("504.347");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.cy (of order $6$, degree $2$, 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:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$184$
Relative dimension:	$92$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			347.17
Character	$\chi$	$=$	504.347
Dual form			504.2.cy.a.443.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.16532 - 0.801263i) q^{2} +(-1.44822 - 0.950089i) q^{3} +(0.715955 + 1.86746i) q^{4} -2.40991 q^{5} +(0.926369 + 2.26756i) q^{6} +(1.71811 - 2.01199i) q^{7} +(0.662008 - 2.74986i) q^{8} +(1.19466 + 2.75187i) q^{9} +O(q^{10})$	\(q+(-1.16532 - 0.801263i) q^{2} +(-1.44822 - 0.950089i) q^{3} +(0.715955 + 1.86746i) q^{4} -2.40991 q^{5} +(0.926369 + 2.26756i) q^{6} +(1.71811 - 2.01199i) q^{7} +(0.662008 - 2.74986i) q^{8} +(1.19466 + 2.75187i) q^{9} +(2.80833 + 1.93097i) q^{10} +4.08461i q^{11} +(0.737395 - 3.38471i) q^{12} +(4.84843 + 2.79924i) q^{13} +(-3.61428 + 0.967965i) q^{14} +(3.49008 + 2.28963i) q^{15} +(-2.97482 + 2.67404i) q^{16} +(-1.62392 - 0.937572i) q^{17} +(0.812802 - 4.16405i) q^{18} +(-2.89421 - 5.01292i) q^{19} +(-1.72539 - 4.50042i) q^{20} +(-4.39976 + 1.28145i) q^{21} +(3.27285 - 4.75989i) q^{22} +4.59423 q^{23} +(-3.57134 + 3.35343i) q^{24} +0.807680 q^{25} +(-3.40706 - 7.14689i) q^{26} +(0.884387 - 5.12034i) q^{27} +(4.98740 + 1.76800i) q^{28} +(-1.75217 - 3.03485i) q^{29} +(-2.23247 - 5.46463i) q^{30} +(8.56793 - 4.94669i) q^{31} +(5.60923 - 0.732503i) q^{32} +(3.88074 - 5.91540i) q^{33} +(1.14115 + 2.39376i) q^{34} +(-4.14049 + 4.84872i) q^{35} +(-4.28368 + 4.20120i) q^{36} +(-0.423619 + 0.244576i) q^{37} +(-0.643977 + 8.16069i) q^{38} +(-4.36205 - 8.66035i) q^{39} +(-1.59538 + 6.62693i) q^{40} +(1.66580 + 0.961751i) q^{41} +(6.15392 + 2.03207i) q^{42} +(-0.875300 - 1.51606i) q^{43} +(-7.62785 + 2.92440i) q^{44} +(-2.87903 - 6.63176i) q^{45} +(-5.35376 - 3.68119i) q^{46} +(5.16049 - 8.93824i) q^{47} +(6.84875 - 1.04624i) q^{48} +(-1.09622 - 6.91363i) q^{49} +(-0.941208 - 0.647164i) q^{50} +(1.46102 + 2.90068i) q^{51} +(-1.75622 + 11.0584i) q^{52} +(2.18330 - 3.78158i) q^{53} +(-5.13333 + 5.25822i) q^{54} -9.84355i q^{55} +(-4.39530 - 6.05651i) q^{56} +(-0.571273 + 10.0095i) q^{57} +(-0.389868 + 4.94053i) q^{58} +(1.50465 - 0.868708i) q^{59} +(-1.77706 + 8.15685i) q^{60} +(-5.69617 - 3.28868i) q^{61} +(-13.9480 - 1.10067i) q^{62} +(7.58929 + 2.32435i) q^{63} +(-7.12349 - 3.64086i) q^{64} +(-11.6843 - 6.74593i) q^{65} +(-9.26211 + 3.78386i) q^{66} +(4.36391 + 7.55852i) q^{67} +(0.588224 - 3.70387i) q^{68} +(-6.65344 - 4.36492i) q^{69} +(8.71011 - 2.33271i) q^{70} -3.91900 q^{71} +(8.35814 - 1.46340i) q^{72} +(-5.41527 + 9.37952i) q^{73} +(0.689623 + 0.0544196i) q^{74} +(-1.16970 - 0.767368i) q^{75} +(7.28930 - 8.99384i) q^{76} +(8.21820 + 7.01779i) q^{77} +(-1.85602 + 13.5873i) q^{78} +(12.1771 + 7.03046i) q^{79} +(7.16905 - 6.44419i) q^{80} +(-6.14556 + 6.57511i) q^{81} +(-1.17058 - 2.45550i) q^{82} +(12.3866 - 7.15139i) q^{83} +(-5.54308 - 7.29892i) q^{84} +(3.91351 + 2.25947i) q^{85} +(-0.194759 + 2.46805i) q^{86} +(-0.345852 + 6.05984i) q^{87} +(11.2321 + 2.70405i) q^{88} +(5.02733 - 2.90253i) q^{89} +(-1.95878 + 10.0350i) q^{90} +(13.9622 - 4.94561i) q^{91} +(3.28926 + 8.57954i) q^{92} +(-17.1080 - 0.976403i) q^{93} +(-13.1755 + 6.28102i) q^{94} +(6.97479 + 12.0807i) q^{95} +(-8.81932 - 4.26844i) q^{96} +(-4.47603 - 7.75271i) q^{97} +(-4.26219 + 8.93497i) q^{98} +(-11.2403 + 4.87973i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 184 q - 3 q^{2} - 2 q^{3} + q^{4} - 2 q^{6} - 2 q^{9}+O(q^{10}) $ 184 * q - 3 * q^2 - 2 * q^3 + q^4 - 2 * q^6 - 2 * q^9	$ 184 q - 3 q^{2} - 2 q^{3} + q^{4} - 2 q^{6} - 2 q^{9} - 6 q^{10} - 5 q^{12} - 3 q^{14} + q^{16} + 5 q^{18} - 4 q^{19} - 6 q^{20} + 2 q^{22} - 8 q^{24} + 148 q^{25} + 6 q^{26} - 8 q^{27} + 24 q^{30} - 33 q^{32} + 22 q^{33} - 4 q^{34} - 30 q^{35} - 38 q^{36} - 12 q^{40} - 12 q^{41} + 7 q^{42} - 4 q^{43} - 9 q^{44} - 6 q^{46} - 5 q^{48} - 2 q^{49} - 21 q^{50} + 26 q^{51} - 18 q^{52} - 40 q^{54} + 18 q^{56} + 4 q^{57} + 6 q^{58} - 6 q^{59} - 2 q^{60} - 8 q^{64} - 6 q^{65} + 43 q^{66} + 2 q^{67} - 18 q^{70} - 11 q^{72} - 4 q^{73} - 36 q^{75} + 2 q^{76} - 29 q^{78} - 87 q^{80} - 10 q^{81} - 4 q^{82} - 72 q^{83} - 65 q^{84} + 14 q^{88} + 24 q^{89} - 49 q^{90} - 36 q^{91} - 36 q^{92} + 9 q^{94} - 88 q^{96} - 4 q^{97} - 57 q^{98} + 10 q^{99}+O(q^{100}) $ 184 * q - 3 * q^2 - 2 * q^3 + q^4 - 2 * q^6 - 2 * q^9 - 6 * q^10 - 5 * q^12 - 3 * q^14 + q^16 + 5 * q^18 - 4 * q^19 - 6 * q^20 + 2 * q^22 - 8 * q^24 + 148 * q^25 + 6 * q^26 - 8 * q^27 + 24 * q^30 - 33 * q^32 + 22 * q^33 - 4 * q^34 - 30 * q^35 - 38 * q^36 - 12 * q^40 - 12 * q^41 + 7 * q^42 - 4 * q^43 - 9 * q^44 - 6 * q^46 - 5 * q^48 - 2 * q^49 - 21 * q^50 + 26 * q^51 - 18 * q^52 - 40 * q^54 + 18 * q^56 + 4 * q^57 + 6 * q^58 - 6 * q^59 - 2 * q^60 - 8 * q^64 - 6 * q^65 + 43 * q^66 + 2 * q^67 - 18 * q^70 - 11 * q^72 - 4 * q^73 - 36 * q^75 + 2 * q^76 - 29 * q^78 - 87 * q^80 - 10 * q^81 - 4 * q^82 - 72 * q^83 - 65 * q^84 + 14 * q^88 + 24 * q^89 - 49 * q^90 - 36 * q^91 - 36 * q^92 + 9 * q^94 - 88 * q^96 - 4 * q^97 - 57 * q^98 + 10 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−1.16532	−	0.801263i	−0.824008	−	0.566579i
$2$	−1.16532	−	0.801263i	−0.824008	−	0.566579i
$3$	−1.44822	−	0.950089i	−0.836128	−	0.548534i
$3$	−1.44822	−	0.950089i	−0.836128	−	0.548534i
$4$	0.715955	+	1.86746i	0.357977	+	0.933730i
$5$	−2.40991			−1.07775			−0.538873	−	0.842387i	$-0.681150\pi$
$5$	−2.40991			−1.07775			−0.538873	+	0.842387i	$0.681150\pi$
$6$	0.926369	+	2.26756i	0.378189	+	0.925729i
$7$	1.71811	−	2.01199i	0.649383	−	0.760461i
$7$	1.71811	−	2.01199i	0.649383	−	0.760461i
$8$	0.662008	−	2.74986i	0.234055	−	0.972223i
$9$	1.19466	+	2.75187i	0.398221	+	0.917289i
$10$	2.80833	+	1.93097i	0.888071	+	0.610628i
$11$			4.08461i			1.23156i	0.787920	+	0.615778i	$0.211158\pi$
$11$			4.08461i			1.23156i	−0.787920	+	0.615778i	$0.788842\pi$
$12$	0.737395	−	3.38471i	0.212868	−	0.977081i
$13$	4.84843	+	2.79924i	1.34471	+	0.776371i	0.987495	−	0.157650i	$-0.0503919\pi$
$13$	4.84843	+	2.79924i	1.34471	+	0.776371i	0.357218	+	0.934021i	$0.383725\pi$
$14$	−3.61428	+	0.967965i	−0.965958	+	0.258699i
$15$	3.49008	+	2.28963i	0.901134	+	0.591180i
$16$	−2.97482	+	2.67404i	−0.743704	+	0.668509i
$17$	−1.62392	−	0.937572i	−0.393859	−	0.227395i	0.289972	−	0.957035i	$-0.406354\pi$
$17$	−1.62392	−	0.937572i	−0.393859	−	0.227395i	−0.683831	+	0.729641i	$0.739687\pi$
$18$	0.812802	−	4.16405i	0.191579	−	0.981477i
$19$	−2.89421	−	5.01292i	−0.663977	−	1.15004i	−0.979562	−	0.201145i	$-0.935534\pi$
$19$	−2.89421	−	5.01292i	−0.663977	−	1.15004i	0.315584	−	0.948898i	$-0.397799\pi$
$20$	−1.72539	−	4.50042i	−0.385809	−	1.00632i
$21$	−4.39976	+	1.28145i	−0.960107	+	0.279635i
$22$	3.27285	−	4.75989i	0.697773	−	1.01481i
$23$	4.59423			0.957963			0.478981	−	0.877825i	$-0.341006\pi$
$23$	4.59423			0.957963			0.478981	+	0.877825i	$0.341006\pi$
$24$	−3.57134	+	3.35343i	−0.728998	+	0.684516i
$25$	0.807680			0.161536
$26$	−3.40706	−	7.14689i	−0.668179	−	1.40162i
$27$	0.884387	−	5.12034i	0.170200	−	0.985409i
$28$	4.98740	+	1.76800i	0.942530	+	0.334121i
$29$	−1.75217	−	3.03485i	−0.325370	−	0.563558i	0.656217	−	0.754572i	$-0.272156\pi$
$29$	−1.75217	−	3.03485i	−0.325370	−	0.563558i	−0.981587	+	0.191015i	$0.938822\pi$
$30$	−2.23247	−	5.46463i	−0.407591	−	0.997700i
$31$	8.56793	−	4.94669i	1.53884	−	0.888453i	0.539938	−	0.841705i	$-0.318448\pi$
$31$	8.56793	−	4.94669i	1.53884	−	0.888453i	0.998907	−	0.0467479i	$-0.0148857\pi$
$32$	5.60923	−	0.732503i	0.991581	−	0.129489i
$33$	3.88074	−	5.91540i	0.675550	−	1.02974i
$34$	1.14115	+	2.39376i	0.195706	+	0.410527i
$35$	−4.14049	+	4.84872i	−0.699870	+	0.819584i
$36$	−4.28368	+	4.20120i	−0.713947	+	0.700200i
$37$	−0.423619	+	0.244576i	−0.0696425	+	0.0402081i	−0.534417	−	0.845221i	$-0.679469\pi$
$37$	−0.423619	+	0.244576i	−0.0696425	+	0.0402081i	0.464774	+	0.885429i	$0.346135\pi$
$38$	−0.643977	+	8.16069i	−0.104467	+	1.32384i
$39$	−4.36205	−	8.66035i	−0.698487	−	1.38677i
$40$	−1.59538	+	6.62693i	−0.252252	+	1.04781i
$41$	1.66580	+	0.961751i	0.260154	+	0.150200i	0.624405	−	0.781101i	$-0.285341\pi$
$41$	1.66580	+	0.961751i	0.260154	+	0.150200i	−0.364251	+	0.931301i	$0.618675\pi$
$42$	6.15392	+	2.03207i	0.949570	+	0.313555i
$43$	−0.875300	−	1.51606i	−0.133482	−	0.231198i	0.791535	−	0.611124i	$-0.209283\pi$
$43$	−0.875300	−	1.51606i	−0.133482	−	0.231198i	−0.925017	+	0.379927i	$0.875949\pi$
$44$	−7.62785	+	2.92440i	−1.14994	+	0.440869i
$45$	−2.87903	−	6.63176i	−0.429181	−	0.988605i
$46$	−5.35376	−	3.68119i	−0.789369	−	0.542761i
$47$	5.16049	−	8.93824i	0.752735	−	1.30378i	−0.193757	−	0.981050i	$-0.562067\pi$
$47$	5.16049	−	8.93824i	0.752735	−	1.30378i	0.946492	−	0.322726i	$-0.104599\pi$
$48$	6.84875	−	1.04624i	0.988532	−	0.151012i
$49$	−1.09622	−	6.91363i	−0.156603	−	0.987662i
$50$	−0.941208	−	0.647164i	−0.133107	−	0.0915229i
$51$	1.46102	+	2.90068i	0.204583	+	0.406176i
$52$	−1.75622	+	11.0584i	−0.243544	+	1.53352i
$53$	2.18330	−	3.78158i	0.299899	−	0.519440i	−0.676214	−	0.736705i	$-0.736380\pi$
$53$	2.18330	−	3.78158i	0.299899	−	0.519440i	0.976113	+	0.217266i	$0.0697138\pi$
$54$	−5.13333	+	5.25822i	−0.698558	+	0.715553i
$55$		−	9.84355i		−	1.32730i
$56$	−4.39530	−	6.05651i	−0.587347	−	0.809336i
$57$	−0.571273	+	10.0095i	−0.0756670	+	1.32580i
$58$	−0.389868	+	4.94053i	−0.0511921	+	0.648723i
$59$	1.50465	−	0.868708i	0.195888	−	0.113096i	−0.398848	−	0.917017i	$-0.630590\pi$
$59$	1.50465	−	0.868708i	0.195888	−	0.113096i	0.594736	+	0.803921i	$0.297257\pi$
$60$	−1.77706	+	8.15685i	−0.229417	+	1.05305i
$61$	−5.69617	−	3.28868i	−0.729320	−	0.421073i	0.0888537	−	0.996045i	$-0.471680\pi$
$61$	−5.69617	−	3.28868i	−0.729320	−	0.421073i	−0.818173	+	0.574972i	$0.805013\pi$
$62$	−13.9480	−	1.10067i	−1.77140	−	0.139785i
$63$	7.58929	+	2.32435i	0.956161	+	0.292841i
$64$	−7.12349	−	3.64086i	−0.890436	−	0.455108i
$65$	−11.6843	−	6.74593i	−1.44926	−	0.836730i
$66$	−9.26211	+	3.78386i	−1.14009	+	0.465761i
$67$	4.36391	+	7.55852i	0.533137	+	0.923420i	0.999251	+	0.0386958i	$0.0123203\pi$
$67$	4.36391	+	7.55852i	0.533137	+	0.923420i	−0.466114	+	0.884725i	$0.654346\pi$
$68$	0.588224	−	3.70387i	0.0713326	−	0.449160i
$69$	−6.65344	−	4.36492i	−0.800980	−	0.525475i
$70$	8.71011	−	2.33271i	1.04106	−	0.278812i
$71$	−3.91900			−0.465100			−0.232550	−	0.972584i	$-0.574707\pi$
$71$	−3.91900			−0.465100			−0.232550	+	0.972584i	$0.574707\pi$
$72$	8.35814	−	1.46340i	0.985016	−	0.172463i
$73$	−5.41527	+	9.37952i	−0.633809	+	1.09779i	0.352957	+	0.935640i	$0.385176\pi$
$73$	−5.41527	+	9.37952i	−0.633809	+	1.09779i	−0.986766	+	0.162150i	$0.948157\pi$
$74$	0.689623	+	0.0544196i	0.0801670	+	0.00632615i
$75$	−1.16970	−	0.767368i	−0.135065	−	0.0886080i
$76$	7.28930	−	8.99384i	0.836140	−	1.03166i
$77$	8.21820	+	7.01779i	0.936551	+	0.799752i
$78$	−1.85602	+	13.5873i	−0.210153	+	1.53845i
$79$	12.1771	+	7.03046i	1.37003	+	0.790988i	0.990932	−	0.134368i	$-0.0429003\pi$
$79$	12.1771	+	7.03046i	1.37003	+	0.790988i	0.379100	+	0.925356i	$0.376234\pi$
$80$	7.16905	−	6.44419i	0.801524	−	0.720483i
$81$	−6.14556	+	6.57511i	−0.682840	+	0.730568i
$82$	−1.17058	−	2.45550i	−0.129269	−	0.271164i
$83$	12.3866	−	7.15139i	1.35960	−	0.784968i	0.370033	−	0.929018i	$-0.379346\pi$
$83$	12.3866	−	7.15139i	1.35960	−	0.784968i	0.989570	+	0.144051i	$0.0460129\pi$
$84$	−5.54308	−	7.29892i	−0.604800	−	0.796378i
$85$	3.91351	+	2.25947i	0.424480	+	0.245074i
$86$	−0.194759	+	2.46805i	−0.0210014	+	0.266137i
$87$	−0.345852	+	6.05984i	−0.0370793	+	0.649683i
$88$	11.2321	+	2.70405i	1.19735	+	0.288252i
$89$	5.02733	−	2.90253i	0.532896	−	0.307668i	−0.209299	−	0.977852i	$-0.567118\pi$
$89$	5.02733	−	2.90253i	0.532896	−	0.307668i	0.742195	+	0.670184i	$0.233785\pi$
$90$	−1.95878	+	10.0350i	−0.206474	+	1.05778i
$91$	13.9622	−	4.94561i	1.46363	−	0.518440i
$92$	3.28926	+	8.57954i	0.342929	+	0.894479i
$93$	−17.1080	−	0.976403i	−1.77402	−	0.101248i
$94$	−13.1755	+	6.28102i	−1.35895	+	0.647838i
$95$	6.97479	+	12.0807i	0.715599	+	1.23945i
$96$	−8.81932	−	4.26844i	−0.900118	−	0.435646i
$97$	−4.47603	−	7.75271i	−0.454472	−	0.787169i	0.544186	−	0.838965i	$-0.316839\pi$
$97$	−4.47603	−	7.75271i	−0.454472	−	0.787169i	−0.998658	+	0.0517961i	$0.983505\pi$
$98$	−4.26219	+	8.93497i	−0.430546	+	0.902569i
$99$	−11.2403	+	4.87973i	−1.12969	+	0.490432i
$100$	0.578263	+	1.50831i	0.0578263	+	0.150831i
$101$	0.666787			0.0663478			0.0331739	−	0.999450i	$-0.489438\pi$
$101$	0.666787			0.0663478			0.0331739	+	0.999450i	$0.489438\pi$
$102$	0.621652	−	4.55088i	0.0615527	−	0.450605i
$103$			8.37186i			0.824904i	0.910979	+	0.412452i	$0.135327\pi$
$103$			8.37186i			0.824904i	−0.910979	+	0.412452i	$0.864673\pi$
$104$	10.9072	−	11.4794i	1.06954	−	1.12565i
$105$	10.6030	−	3.08817i	1.03475	−	0.301375i
$106$	−5.57428	+	2.65737i	−0.541422	+	0.258106i
$107$	9.30999	−	5.37512i	0.900031	−	0.519633i	0.0228205	−	0.999740i	$-0.492735\pi$
$107$	9.30999	−	5.37512i	0.900031	−	0.519633i	0.877210	+	0.480107i	$0.159402\pi$
$108$	10.1952	−	2.01437i	0.981035	−	0.193833i
$109$	8.99585	+	5.19376i	0.861646	+	0.497472i	0.864563	−	0.502524i	$-0.167595\pi$
$109$	8.99585	+	5.19376i	0.861646	+	0.497472i	−0.00291683	+	0.999996i	$0.500928\pi$
$110$	−7.88728	+	11.4709i	−0.752022	+	1.09371i
$111$	0.845861	+	0.0482757i	0.0802856	+	0.00458213i
$112$	0.269083	+	10.5796i	0.0254260	+	0.999677i
$113$	2.76275	+	1.59508i	0.259898	+	0.150052i	0.624288	−	0.781194i	$-0.285389\pi$
$113$	2.76275	+	1.59508i	0.259898	+	0.150052i	−0.364390	+	0.931246i	$0.618722\pi$
$114$	8.68600	−	11.2066i	0.813518	−	1.04960i
$115$	−11.0717			−1.03244
$116$	4.41299	−	5.44493i	0.409736	−	0.505549i
$117$	−1.91091	+	16.6864i	−0.176663	+	1.54266i
$118$	−2.44946	−	0.193292i	−0.225491	−	0.0177940i
$119$	−4.67646	+	1.65647i	−0.428690	+	0.151848i
$120$	8.60663	−	8.08148i	0.785674	−	0.737734i
$121$	−5.68403			−0.516730
$122$	4.00277	+	8.39651i	0.362394	+	0.760184i
$123$	−1.49869	−	2.97548i	−0.135133	−	0.268290i
$124$	15.3720	+	12.4587i	1.38045	+	1.11882i
$125$	10.1031			0.903651
$126$	−6.98156	−	8.78964i	−0.621967	−	0.783043i
$127$		−	20.3851i		−	1.80888i	−0.426597	−	0.904442i	$-0.640288\pi$
$127$		−	20.3851i		−	1.80888i	0.426597	−	0.904442i	$-0.359712\pi$
$128$	5.38388	+	9.95057i	0.475872	+	0.879515i
$129$	−0.172771	+	3.02720i	−0.0152117	+	0.266530i
$130$	8.21072	+	17.2234i	0.720127	+	1.51059i
$131$		−	6.36296i		−	0.555934i	−0.960591	−	0.277967i	$-0.910339\pi$
$131$		−	6.36296i		−	0.555934i	0.960591	−	0.277967i	$-0.0896606\pi$
$132$	13.8252	+	3.01197i	1.20333	+	0.262158i
$133$	−15.0585	−	2.78960i	−1.30574	−	0.241889i
$134$	0.970995	−	12.3048i	0.0838812	−	1.06297i
$135$	−2.13130	+	12.3396i	−0.183433	+	1.06202i
$136$	−3.65325	+	3.84488i	−0.313263	+	0.329696i
$137$			9.09415i			0.776966i	0.921456	+	0.388483i	$0.127001\pi$
$137$			9.09415i			0.776966i	−0.921456	+	0.388483i	$0.872999\pi$
$138$	4.25595	+	10.4177i	0.362291	+	0.886814i
$139$	−4.22441	+	7.31689i	−0.358310	+	0.620611i	−0.987679	−	0.156496i	$-0.949980\pi$
$139$	−4.22441	+	7.31689i	−0.358310	+	0.620611i	0.629369	+	0.777107i	$0.283314\pi$
$140$	−12.0192	−	4.26073i	−1.01581	−	0.360097i
$141$	−15.9656	+	8.04158i	−1.34455	+	0.677223i
$142$	4.56690	+	3.14015i	0.383246	+	0.263515i
$143$	−11.4338	+	19.8040i	−0.956144	+	1.65609i
$144$	−10.9125	−	4.99173i	−0.909375	−	0.415978i
$145$	4.22258	+	7.31372i	0.350666	+	0.607372i
$146$	13.8260	−	6.59112i	1.14425	−	0.545485i
$147$	−4.98100	+	11.0539i	−0.410826	+	0.911714i
$148$	−0.760029	−	0.615986i	−0.0624740	−	0.0506337i
$149$	−3.92829			−0.321818			−0.160909	−	0.986969i	$-0.551443\pi$
$149$	−3.92829			−0.321818			−0.160909	+	0.986969i	$0.551443\pi$
$150$	0.748210	+	1.83147i	0.0610911	+	0.149539i
$151$		−	13.9138i		−	1.13229i	−0.824307	−	0.566143i	$-0.808435\pi$
$151$		−	13.9138i		−	1.13229i	0.824307	−	0.566143i	$-0.191565\pi$
$152$	−15.7008	+	4.64008i	−1.27351	+	0.376361i
$153$	0.640034	−	5.58890i	0.0517437	−	0.451836i
$154$	−3.95376	−	14.7629i	−0.318603	−	1.18963i
$155$	−20.6480	+	11.9211i	−1.65848	+	0.957526i
$156$	13.0498	−	14.3464i	1.04482	−	1.14863i
$157$	8.11993	−	4.68805i	0.648041	−	0.374147i	−0.139664	−	0.990199i	$-0.544602\pi$
$157$	8.11993	−	4.68805i	0.648041	−	0.374147i	0.787705	+	0.616052i	$0.211269\pi$
$158$	−8.55702	−	17.9498i	−0.680760	−	1.42801i
$159$	−6.75472	+	3.40222i	−0.535684	+	0.269814i
$160$	−13.5178	+	1.76527i	−1.06867	+	0.139557i
$161$	7.89337	−	9.24355i	0.622085	−	0.728494i
$162$	12.4300	−	2.73792i	0.976590	−	0.215111i
$163$	−0.170598	−	0.295484i	−0.0133622	−	0.0231441i	0.859267	−	0.511527i	$-0.170920\pi$
$163$	−0.170598	−	0.295484i	−0.0133622	−	0.0231441i	−0.872629	+	0.488383i	$0.837587\pi$
$164$	−0.603393	+	3.79939i	−0.0471171	+	0.296682i
$165$	−9.35225	+	14.2556i	−0.728071	+	1.10980i
$166$	−20.1645	−	1.59122i	−1.56507	−	0.123503i
$167$	−3.30188	+	5.71902i	−0.255507	+	0.442551i	−0.965033	−	0.262128i	$-0.915576\pi$
$167$	−3.30188	+	5.71902i	−0.255507	+	0.442551i	0.709526	+	0.704679i	$0.248909\pi$
$168$	0.611123	+	12.9471i	0.0471492	+	0.998888i
$169$	9.17154	+	15.8856i	0.705503	+	1.22197i
$170$	−2.75008	−	5.76876i	−0.210921	−	0.442444i
$171$	10.3373	−	13.9532i	0.790512	−	1.06703i
$172$	2.20452	−	2.72002i	0.168093	−	0.207400i
$173$	6.25190	−	10.8286i	0.475323	−	0.823283i	−0.524278	−	0.851547i	$-0.675665\pi$
$173$	6.25190	−	10.8286i	0.475323	−	0.823283i	0.999600	+	0.0282641i	$0.00899794\pi$
$174$	5.25855	−	6.78455i	0.398650	−	0.514335i
$175$	1.38768	−	1.62505i	0.104899	−	0.122842i
$176$	−10.9224	−	12.1510i	−0.823306	−	0.915914i
$177$	−3.00440	−	0.171470i	−0.225825	−	0.0128885i
$178$	−8.18416	−	0.645829i	−0.613429	−	0.0484070i
$179$	−7.21541	−	4.16582i	−0.539305	−	0.311368i	0.205492	−	0.978659i	$-0.434121\pi$
$179$	−7.21541	−	4.16582i	−0.539305	−	0.311368i	−0.744797	+	0.667291i	$0.767454\pi$
$180$	10.3233	−	10.1245i	0.769453	−	0.754638i
$181$			9.12597i			0.678328i	0.940727	+	0.339164i	$0.110144\pi$
$181$			9.12597i			0.678328i	−0.940727	+	0.339164i	$0.889856\pi$
$182$	−20.2332	−	5.42415i	−1.49978	−	0.402065i
$183$	5.12474	+	10.1746i	0.378832	+	0.752127i
$184$	3.04142	−	12.6335i	0.224216	−	0.931354i
$185$	1.02088	−	0.589408i	0.0750569	−	0.0433341i
$186$	19.1540	+	14.8458i	1.40444	+	1.08855i
$187$	3.82962	−	6.63309i	0.280049	−	0.485060i
$188$	20.3865	+	3.23764i	1.48684	+	0.236129i
$189$	−8.78261	−	10.5767i	−0.638841	−	0.769339i
$190$	1.55193	−	19.6666i	0.112589	−	1.42676i
$191$	1.47787	−	2.55975i	0.106935	−	0.185217i	−0.807592	−	0.589741i	$-0.799230\pi$
$191$	1.47787	−	2.55975i	0.106935	−	0.185217i	0.914527	+	0.404525i	$0.132563\pi$
$192$	6.85721	+	12.0407i	0.494877	+	0.868963i
$193$	3.81931	+	6.61525i	0.274920	+	0.476176i	0.970115	−	0.242646i	$-0.0780152\pi$
$193$	3.81931	+	6.61525i	0.274920	+	0.476176i	−0.695195	+	0.718821i	$0.744682\pi$
$194$	−0.995941	+	12.6209i	−0.0715044	+	0.906127i
$195$	10.5122	+	20.8707i	0.752792	+	1.49458i
$196$	12.1261	−	6.99700i	0.866149	−	0.499785i
$197$	14.8845			1.06048			0.530239	−	0.847848i	$-0.322102\pi$
$197$	14.8845			1.06048			0.530239	+	0.847848i	$0.322102\pi$
$198$	17.0085	+	3.31998i	1.20874	+	0.235941i
$199$	−12.0022	−	6.92948i	−0.850814	−	0.491218i	0.0101116	−	0.999949i	$-0.496781\pi$
$199$	−12.0022	−	6.92948i	−0.850814	−	0.491218i	−0.860925	+	0.508731i	$0.830115\pi$
$200$	0.534691	−	2.22101i	0.0378084	−	0.157049i
$201$	0.861371	−	15.0925i	0.0607564	−	1.06454i
$202$	−0.777022	−	0.534272i	−0.0546711	−	0.0375912i
$203$	−9.11651	−	1.68884i	−0.639854	−	0.118533i
$204$	−4.37088	+	4.80514i	−0.306023	+	0.336427i
$205$	−4.01444	−	2.31774i	−0.280380	−	0.161878i
$206$	6.70806	−	9.75592i	0.467373	−	0.679727i
$207$	5.48856	+	12.6427i	0.381481	+	0.878729i
$208$	−21.9085	+	4.63764i	−1.51908	+	0.321563i
$209$	20.4758	−	11.8217i	1.41634	−	0.817725i
$210$	−14.8304	−	4.89710i	−1.02340	−	0.337932i
$211$	6.32343	−	10.9525i	0.435323	−	0.754002i	−0.561999	−	0.827138i	$-0.689967\pi$
$211$	6.32343	−	10.9525i	0.435323	−	0.754002i	0.997322	+	0.0731362i	$0.0233008\pi$
$212$	8.62509	+	1.36978i	0.592374	+	0.0940768i
$213$	5.67556	+	3.72340i	0.388883	+	0.255123i
$214$	−15.1560	−	1.19599i	−1.03604	−	0.0817565i
$215$	2.10940	+	3.65358i	0.143860	+	0.249172i
$216$	−13.4948	−	5.82165i	−0.918202	−	0.396113i
$217$	4.76790	−	25.7375i	0.323666	−	1.74718i
$218$	−6.32151	−	13.2605i	−0.428146	−	0.898111i
$219$	16.7539	−	8.43859i	1.13212	−	0.570227i
$220$	18.3824	−	7.04754i	1.23934	−	0.475145i
$221$	−5.24899	−	9.09151i	−0.353085	−	0.611561i
$222$	−0.947020	−	0.734014i	−0.0635598	−	0.0492638i
$223$	−20.0610	+	11.5822i	−1.34338	+	0.775603i	−0.987302	−	0.158852i	$-0.949221\pi$
$223$	−20.0610	+	11.5822i	−1.34338	+	0.775603i	−0.356081	+	0.934455i	$0.615887\pi$
$224$	8.16346	−	12.5442i	0.545444	−	0.838147i
$225$	0.964906	+	2.22263i	0.0643271	+	0.148175i
$226$	−1.94142	−	4.07247i	−0.129142	−	0.270897i
$227$		−	17.7848i		−	1.18042i	−0.807249	−	0.590210i	$-0.799045\pi$
$227$		−	17.7848i		−	1.18042i	0.807249	−	0.590210i	$-0.200955\pi$
$228$	−19.1014	+	6.09955i	−1.26502	+	0.403953i
$229$		−	10.1410i		−	0.670135i	−0.942194	−	0.335068i	$-0.891241\pi$
$229$		−	10.1410i		−	0.670135i	0.942194	−	0.335068i	$-0.108759\pi$
$230$	12.9021	+	8.87134i	0.850739	+	0.584959i
$231$	−5.23421	−	17.9713i	−0.344386	−	1.18243i
$232$	−9.50537	+	2.80913i	−0.624058	+	0.184429i
$233$	−10.1055	+	5.83444i	−0.662036	+	0.382227i	−0.793052	−	0.609153i	$-0.791509\pi$
$233$	−10.1055	+	5.83444i	−0.662036	+	0.382227i	0.131016	+	0.991380i	$0.458176\pi$
$234$	15.5970	−	17.9139i	1.01961	−	1.17107i
$235$	−12.4363	+	21.5404i	−0.811257	+	1.40514i
$236$	2.69954	+	2.18791i	0.175725	+	0.142421i
$237$	−10.9555	−	21.7510i	−0.711638	−	1.41288i
$238$	6.77685	+	1.81675i	0.439278	+	0.117763i
$239$	−14.6865	+	25.4378i	−0.949992	+	1.64544i	−0.204560	+	0.978854i	$0.565576\pi$
$239$	−14.6865	+	25.4378i	−0.949992	+	1.64544i	−0.745432	+	0.666581i	$0.767757\pi$
$240$	−16.5049	+	2.52135i	−1.06539	+	0.162753i
$241$	11.1271			0.716757			0.358378	−	0.933576i	$-0.383330\pi$
$241$	11.1271			0.716757			0.358378	+	0.933576i	$0.383330\pi$
$242$	6.62374	+	4.55441i	0.425790	+	0.292768i
$243$	15.1470	−	3.68336i	0.971683	−	0.236288i
$244$	2.06329	−	12.9919i	0.132088	−	0.831722i
$245$	2.64179	+	16.6613i	0.168778	+	1.06445i
$246$	−0.637683	+	4.66825i	−0.0406572	+	0.297636i
$247$		−	32.4064i		−	2.06197i
$248$	−7.93069	−	26.8354i	−0.503599	−	1.70405i
$249$	−24.7329	−	1.41158i	−1.56738	−	0.0894551i
$250$	−11.7734	−	8.09526i	−0.744615	−	0.511989i
$251$			17.5250i			1.10617i	0.833125	+	0.553085i	$0.186549\pi$
$251$			17.5250i			1.10617i	−0.833125	+	0.553085i	$0.813451\pi$
$252$	1.09296	+	15.8368i	0.0688501	+	0.997627i
$253$			18.7656i			1.17978i
$254$	−16.3338	+	23.7552i	−1.02487	+	1.49053i
$255$	−3.52092	−	6.99038i	−0.220489	−	0.437755i
$256$	1.69907	−	15.9095i	0.106192	−	0.994346i
$257$			31.5599i			1.96865i	0.176362	+	0.984325i	$0.443567\pi$
$257$			31.5599i			1.96865i	−0.176362	+	0.984325i	$0.556433\pi$
$258$	2.62692	−	3.38923i	0.163545	−	0.211005i
$259$	−0.235736	+	1.27253i	−0.0146480	+	0.0790709i
$260$	4.23233	−	26.6498i	0.262478	−	1.65275i
$261$	6.25825	−	8.44737i	0.387376	−	0.522879i
$262$	−5.09840	+	7.41490i	−0.314980	+	0.458094i
$263$	10.1682			0.626996			0.313498	−	0.949589i	$-0.398499\pi$
$263$	10.1682			0.626996			0.313498	+	0.949589i	$0.398499\pi$
$264$	−13.6975	−	14.5875i	−0.843020	−	0.897802i
$265$	−5.26155	+	9.11328i	−0.323215	+	0.559824i
$266$	15.3128	+	15.3166i	0.938889	+	0.939122i
$267$	−10.0383	−	0.572916i	−0.614336	−	0.0350619i
$268$	−10.9909	+	13.5610i	−0.671375	+	0.828370i
$269$	−3.35555	+	5.81198i	−0.204591	+	0.354363i	−0.950002	−	0.312242i	$-0.898920\pi$
$269$	−3.35555	+	5.81198i	−0.204591	+	0.354363i	0.745411	+	0.666605i	$0.232253\pi$
$270$	12.3709	−	12.6719i	0.752868	−	0.771184i
$271$	1.18718	−	0.685421i	0.0721163	−	0.0416364i	−0.463508	−	0.886093i	$-0.653410\pi$
$271$	1.18718	−	0.685421i	0.0721163	−	0.0416364i	0.535625	+	0.844456i	$0.320076\pi$
$272$	7.33797	−	1.55332i	0.444930	−	0.0941839i
$273$	−24.9190	−	6.10300i	−1.50817	−	0.369370i
$274$	7.28681	−	10.5976i	0.440212	−	0.640226i
$275$			3.29906i			0.198941i
$276$	3.38776	−	15.5501i	0.203919	−	0.936007i
$277$			4.42301i			0.265753i	0.991133	+	0.132876i	$0.0424213\pi$
$277$			4.42301i			0.265753i	−0.991133	+	0.132876i	$0.957579\pi$
$278$	10.7856	−	5.14168i	0.646875	−	0.308377i
$279$	23.8484	+	17.6682i	1.42777	+	1.05777i
$280$	10.5923	+	14.5957i	0.633010	+	0.872258i
$281$	−16.2990	+	9.41023i	−0.972317	+	0.561367i	−0.899942	−	0.436010i	$-0.856391\pi$
$281$	−16.2990	+	9.41023i	−0.972317	+	0.561367i	−0.0723750	+	0.997377i	$0.523058\pi$
$282$	25.0485	+	3.42163i	1.49162	+	0.203755i
$283$	−14.6302	−	25.3402i	−0.869673	−	1.50632i	−0.862331	−	0.506344i	$-0.830996\pi$
$283$	−14.6302	−	25.3402i	−0.869673	−	1.50632i	−0.00734135	−	0.999973i	$-0.502337\pi$
$284$	−2.80583	−	7.31858i	−0.166495	−	0.434278i
$285$	1.37672	−	24.1221i	0.0815498	−	1.42887i
$286$	29.1923	−	13.9165i	1.72618	−	0.822900i
$287$	4.79706	−	1.69919i	0.283161	−	0.100300i
$288$	8.71689	+	14.5608i	0.513648	+	0.858001i
$289$	−6.74192	−	11.6773i	−0.396583	−	0.686903i
$290$	0.939547	−	11.9062i	0.0551721	−	0.699159i
$291$	−0.883501	+	15.4802i	−0.0517918	+	0.907467i
$292$	−21.3930	−	3.39749i	−1.25193	−	0.198823i
$293$	−4.68489	+	8.11447i	−0.273694	+	0.474052i	−0.969805	−	0.243882i	$-0.921579\pi$
$293$	−4.68489	+	8.11447i	−0.273694	+	0.474052i	0.696111	+	0.717934i	$0.254912\pi$
$294$	14.6616	−	8.89032i	0.855081	−	0.518494i
$295$	−3.62607	+	2.09351i	−0.211118	+	0.121889i
$296$	0.392112	+	1.32681i	0.0227911	+	0.0771190i
$297$	20.9146	+	3.61238i	1.21359	+	0.209611i
$298$	4.57773	+	3.14759i	0.265181	+	0.182335i
$299$	22.2748	+	12.8604i	1.28819	+	0.743734i
$300$	0.595579	−	2.73376i	0.0343858	−	0.157834i
$301$	−4.55417	−	0.843664i	−0.262498	−	0.0486280i
$302$	−11.1486	+	16.2140i	−0.641529	+	0.933012i
$303$	−0.965652	−	0.633507i	−0.0554753	−	0.0363940i
$304$	22.0145	+	7.17330i	1.26262	+	0.411417i
$305$	13.7273	+	7.92544i	0.786021	+	0.453809i
$306$	−5.22403	+	6.00004i	−0.298638	+	0.343000i
$307$	−17.7081			−1.01065			−0.505327	−	0.862928i	$-0.668628\pi$
$307$	−17.7081			−1.01065			−0.505327	+	0.862928i	$0.668628\pi$
$308$	−7.22159	+	20.3716i	−0.411488	+	1.16078i
$309$	7.95401	−	12.1243i	0.452488	−	0.689725i
$310$	33.6135	+	2.65251i	1.90912	+	0.150652i
$311$	0.742482	+	1.28602i	0.0421023	+	0.0729233i	0.886309	−	0.463095i	$-0.153261\pi$
$311$	0.742482	+	1.28602i	0.0421023	+	0.0729233i	−0.844206	+	0.536018i	$0.819928\pi$
$312$	−26.7025	+	6.26182i	−1.51173	+	0.354506i
$313$	−1.33372	+	2.31006i	−0.0753861	+	0.130573i	−0.901254	−	0.433291i	$-0.857352\pi$
$313$	−1.33372	+	2.31006i	−0.0753861	+	0.130573i	0.825868	+	0.563863i	$0.190686\pi$
$314$	−13.2187	−	1.04312i	−0.745974	−	0.0588664i
$315$	−18.2895	−	5.60148i	−1.03050	−	0.315608i
$316$	−4.41084	+	27.7738i	−0.248129	+	1.56240i
$317$	8.27656	−	14.3354i	0.464858	−	0.805158i	−0.534337	−	0.845272i	$-0.679439\pi$
$317$	8.27656	−	14.3354i	0.464858	−	0.805158i	0.999195	+	0.0401136i	$0.0127720\pi$
$318$	10.5975	+	1.44762i	0.594279	+	0.0811786i
$319$	12.3962	−	7.15694i	0.694053	−	0.400712i
$320$	17.1670	+	8.77417i	0.959664	+	0.490491i
$321$	−18.5897	−	1.06097i	−1.03758	−	0.0592175i
$322$	−16.6048	+	4.44705i	−0.925352	+	0.247824i
$323$			10.8541i			0.603939i
$324$	−16.6787	−	6.76910i	−0.926595	−	0.376061i
$325$	3.91598	+	2.26089i	0.217220	+	0.125412i
$326$	−0.0379589	+	0.481028i	−0.00210235	+	0.0266417i
$327$	−8.09341	−	16.0685i	−0.447567	−	0.888593i
$328$	3.74746	−	3.94404i	0.206919	−	0.217773i
$329$	−9.11738	−	25.7397i	−0.502657	−	1.41908i
$330$	22.3209	−	9.11876i	1.22872	−	0.501971i
$331$	−12.6997	+	21.9966i	−0.698041	+	1.20904i	0.271104	+	0.962550i	$0.412611\pi$
$331$	−12.6997	+	21.9966i	−0.698041	+	1.20904i	−0.969145	+	0.246492i	$0.920722\pi$
$332$	22.2232	+	18.0114i	1.21966	+	0.988502i
$333$	−1.17912	−	0.873557i	−0.0646156	−	0.0478706i
$334$	8.43019	−	4.01883i	0.461279	−	0.219901i
$335$	−10.5167	−	18.2154i	−0.574586	−	0.995213i
$336$	9.66185	−	15.5772i	0.527097	−	0.849805i
$337$	12.1576	−	21.0576i	0.662269	−	1.14708i	−0.317749	−	0.948175i	$-0.602927\pi$
$337$	12.1576	−	21.0576i	0.662269	−	1.14708i	0.980018	−	0.198908i	$-0.0637396\pi$
$338$	2.04072	−	25.8606i	0.111000	−	1.40663i
$339$	−2.48560	−	4.93488i	−0.134999	−	0.268026i
$340$	−1.41757	+	8.92601i	−0.0768784	+	0.484081i
$341$	20.2053	+	34.9966i	1.09418	+	1.89517i
$342$	−23.2265	+	7.97714i	−1.25594	+	0.431354i
$343$	−15.7936	−	9.67277i	−0.852774	−	0.522280i
$344$	−4.74843	+	1.40331i	−0.256018	+	0.0756613i
$345$	16.0342	+	10.5191i	0.863253	+	0.566329i
$346$	−15.9620	+	7.60940i	−0.858124	+	0.409084i
$347$	26.0735	−	15.0535i	1.39970	−	0.808117i	0.405339	−	0.914167i	$-0.367154\pi$
$347$	26.0735	−	15.0535i	1.39970	−	0.808117i	0.994361	+	0.106050i	$0.0338203\pi$
$348$	−11.5641	+	3.69271i	−0.619902	+	0.197950i
$349$	−13.0185	+	7.51622i	−0.696863	+	0.402334i	−0.806178	−	0.591673i	$-0.798468\pi$
$349$	−13.0185	+	7.51622i	−0.696863	+	0.402334i	0.109315	+	0.994007i	$0.465134\pi$
$350$	−2.91919	+	0.781806i	−0.156037	+	0.0417893i
$351$	18.6210	−	22.3500i	0.993914	−	1.19295i
$352$	2.99199	+	22.9115i	0.159474	+	1.22119i
$353$			7.71744i			0.410758i	0.978683	+	0.205379i	$0.0658427\pi$
$353$			7.71744i			0.410758i	−0.978683	+	0.205379i	$0.934157\pi$
$354$	3.36371	+	2.60714i	0.178779	+	0.138568i
$355$	9.44445			0.501259
$356$	9.01971	+	7.31026i	0.478044	+	0.387443i
$357$	8.34632	+	2.04412i	0.441734	+	0.108186i
$358$	5.07037	+	10.6360i	0.267977	+	0.562129i
$359$	−1.47236	−	2.55021i	−0.0777083	−	0.134595i	0.824553	−	0.565785i	$-0.191427\pi$
$359$	−1.47236	−	2.55021i	−0.0777083	−	0.134595i	−0.902261	+	0.431191i	$0.858094\pi$
$360$	−20.1424	+	3.52667i	−1.06160	+	0.185872i
$361$	−7.25290	+	12.5624i	−0.381731	+	0.661178i
$362$	7.31231	−	10.6347i	0.384326	−	0.558948i
$363$	8.23171	+	5.40034i	0.432053	+	0.283444i
$364$	19.2320	+	22.5330i	1.00803	+	1.18105i
$365$	13.0503	−	22.6038i	0.683085	−	1.18314i
$366$	2.18054	−	15.9630i	0.113979	−	0.834397i
$367$		−	7.50190i		−	0.391596i	−0.980644	−	0.195798i	$-0.937270\pi$
$367$		−	7.50190i		−	0.391596i	0.980644	−	0.195798i	$-0.0627297\pi$
$368$	−13.6670	+	12.2851i	−0.712441	+	0.640407i
$369$	−0.656540	+	5.73303i	−0.0341781	+	0.298450i
$370$	−1.66193	−	0.131146i	−0.0863997	−	0.00681798i
$371$	−3.85737	−	10.8899i	−0.200265	−	0.565377i
$372$	−10.4252	−	32.6476i	−0.540520	−	1.69270i
$373$			33.9212i			1.75637i	0.478320	+	0.878186i	$0.341246\pi$
$373$			33.9212i			1.75637i	−0.478320	+	0.878186i	$0.658754\pi$
$374$	−9.77759	+	4.66116i	−0.505587	+	0.241023i
$375$	−14.6315	−	9.59886i	−0.755568	−	0.495683i
$376$	−21.1626	−	20.1078i	−1.09138	−	1.03698i
$377$		−	19.6190i		−	1.01043i
$378$	1.75988	+	19.3624i	0.0905184	+	0.995895i
$379$	0.589516			0.0302814			0.0151407	−	0.999885i	$-0.495180\pi$
$379$	0.589516			0.0302814			0.0151407	+	0.999885i	$0.495180\pi$
$380$	−17.5666	+	21.6744i	−0.901147	+	1.11187i
$381$	−19.3676	+	29.5220i	−0.992234	+	1.51246i
$382$	−3.77323	+	1.79877i	−0.193055	+	0.0920330i
$383$	−25.5606			−1.30609			−0.653043	−	0.757321i	$-0.726508\pi$
$383$	−25.5606			−1.30609			−0.653043	+	0.757321i	$0.726508\pi$
$384$	1.65691	−	19.5257i	0.0845537	−	0.996419i
$385$	−19.8051	−	16.9123i	−1.00936	−	0.861929i
$386$	0.849818	−	10.7692i	0.0432546	−	0.548137i
$387$	3.12632	−	4.21990i	0.158920	−	0.214510i
$388$	11.2732	−	13.9094i	0.572313	−	0.706143i
$389$	−2.74983			−0.139422			−0.0697108	−	0.997567i	$-0.522208\pi$
$389$	−2.74983			−0.139422			−0.0697108	+	0.997567i	$0.522208\pi$
$390$	4.47285	−	32.7441i	0.226492	−	1.65806i
$391$	−7.46067	−	4.30742i	−0.377302	−	0.217836i
$392$	−19.7372	−	1.56243i	−0.996881	−	0.0789145i
$393$	−6.04537	+	9.21494i	−0.304949	+	0.464832i
$394$	−17.3453	−	11.9264i	−0.873842	−	0.600844i
$395$	−29.3458	−	16.9428i	−1.47655	−	0.852484i
$396$	−17.1603	−	17.4972i	−0.862336	−	0.879265i
$397$	9.86336	−	5.69461i	0.495028	−	0.285804i	−0.231630	−	0.972804i	$-0.574406\pi$
$397$	9.86336	−	5.69461i	0.495028	−	0.285804i	0.726658	+	0.686999i	$0.241073\pi$
$398$	8.43411	+	17.6920i	0.422764	+	0.886820i
$399$	19.1576	+	18.3469i	0.959080	+	0.918492i
$400$	−2.40270	+	2.15977i	−0.120135	+	0.107988i
$401$		−	0.711978i		−	0.0355545i	−0.999842	−	0.0177772i	$-0.994341\pi$
$401$		−	0.711978i		−	0.0355545i	0.999842	−	0.0177772i	$-0.00565897\pi$
$402$	−13.0968	+	16.8974i	−0.653210	+	0.842767i
$403$	55.3880			2.75907
$404$	0.477389	+	1.24520i	0.0237510	+	0.0619509i
$405$	14.8103	−	15.8454i	0.735928	−	0.787367i
$406$	9.27047	+	9.27277i	0.460086	+	0.460200i
$407$	−0.998999	−	1.73032i	−0.0495185	−	0.0857686i
$408$	8.94367	−	2.09732i	0.442778	−	0.103833i
$409$	5.86792	+	10.1635i	0.290150	+	0.502554i	0.973845	−	0.227214i	$-0.0729615\pi$
$409$	5.86792	+	10.1635i	0.290150	+	0.502554i	−0.683695	+	0.729768i	$0.739628\pi$
$410$	2.82100	+	5.91753i	0.139319	+	0.292246i
$411$	8.64025	−	13.1703i	0.426192	−	0.649643i
$412$	−15.6341	+	5.99387i	−0.770237	+	0.295297i
$413$	0.837309	−	4.51987i	0.0412013	−	0.222408i
$414$	3.73420	−	19.1306i	0.183526	−	0.940219i
$415$	−29.8506	+	17.2342i	−1.46531	+	0.845995i
$416$	29.2464	+	12.1501i	1.43392	+	0.595708i
$417$	13.0696	−	6.58288i	0.640019	−	0.322365i
$418$	−33.3332	−	2.63040i	−1.63038	−	0.128657i
$419$	−0.304787	−	0.175969i	−0.0148898	−	0.00859663i	0.492537	−	0.870292i	$-0.336070\pi$
$419$	−0.304787	−	0.175969i	−0.0148898	−	0.00859663i	−0.507426	+	0.861695i	$0.669403\pi$
$420$	13.3583	+	17.5898i	0.651820	+	0.858293i
$421$	7.58160	−	4.37724i	0.369504	−	0.213333i	−0.303738	−	0.952756i	$-0.598235\pi$
$421$	7.58160	−	4.37724i	0.369504	−	0.213333i	0.673242	+	0.739422i	$0.264901\pi$
$422$	−16.1447	+	7.69648i	−0.785911	+	0.374659i
$423$	30.7619	+	3.52281i	1.49570	+	0.171285i
$424$	−8.95346	−	8.50720i	−0.434819	−	0.413146i
$425$	−1.31161	−	0.757259i	−0.0636225	−	0.0367324i
$426$	−3.63044	−	8.88657i	−0.175895	−	0.430556i
$427$	−16.4034	+	5.81033i	−0.793817	+	0.281182i
$428$	16.7034	+	13.5377i	0.807388	+	0.654369i
$429$	35.3742	−	17.8173i	1.70788	−	0.860226i
$430$	0.469353	−	5.94779i	0.0226342	−	0.286828i
$431$	−15.4431	+	26.7483i	−0.743869	+	1.28842i	0.206853	+	0.978372i	$0.433678\pi$
$431$	−15.4431	+	26.7483i	−0.743869	+	1.28842i	−0.950721	+	0.310046i	$0.899655\pi$
$432$	11.0611	+	17.5970i	0.532176	+	0.846634i
$433$	12.3593			0.593948			0.296974	−	0.954886i	$-0.404023\pi$
$433$	12.3593			0.593948			0.296974	+	0.954886i	$0.404023\pi$
$434$	−26.1787	+	26.1722i	−1.25662	+	1.25631i
$435$	0.833474	−	14.6037i	0.0399620	−	0.700193i
$436$	−3.25851	+	20.5179i	−0.156054	+	0.982629i
$437$	−13.2967	−	23.0305i	−0.636065	−	1.10170i
$438$	−26.2852	−	3.59056i	−1.25595	−	0.171564i
$439$	8.53561	+	4.92804i	0.407382	+	0.235202i	0.689664	−	0.724129i	$-0.257758\pi$
$439$	8.53561	+	4.92804i	0.407382	+	0.235202i	−0.282282	+	0.959331i	$0.591091\pi$
$440$	−27.0684	−	6.51652i	−1.29044	−	0.310663i
$441$	17.7158	−	11.2761i	0.843609	−	0.536958i
$442$	−1.16793	+	14.8004i	−0.0555527	+	0.703982i
$443$	20.1312	+	11.6228i	0.956464	+	0.552214i	0.895083	−	0.445900i	$-0.147116\pi$
$443$	20.1312	+	11.6228i	0.956464	+	0.552214i	0.0613807	+	0.998114i	$0.480450\pi$
$444$	0.515445	+	1.61418i	0.0244620	+	0.0766054i
$445$	−12.1154	+	6.99485i	−0.574327	+	0.331588i
$446$	32.6579	+	2.57711i	1.54640	+	0.122030i
$447$	5.68902	+	3.73222i	0.269081	+	0.176528i
$448$	−19.5643	+	8.07701i	−0.924326	+	0.381603i
$449$			29.2674i			1.38122i	0.723229	+	0.690608i	$0.242657\pi$
$449$			29.2674i			1.38122i	−0.723229	+	0.690608i	$0.757343\pi$
$450$	0.656484	−	3.36323i	0.0309470	−	0.158544i
$451$	−3.92838	+	6.80415i	−0.184980	+	0.320395i
$452$	−1.00074	+	6.30134i	−0.0470706	+	0.296390i
$453$	−13.2193	+	20.1501i	−0.621097	+	0.946736i
$454$	−14.2503	+	20.7251i	−0.668801	+	0.972676i
$455$	−33.6476	+	11.9185i	−1.57743	+	0.558747i
$456$	27.1467	+	8.19733i	1.27126	+	0.383875i
$457$	−7.35445	+	12.7383i	−0.344027	+	0.595872i	−0.985176	−	0.171544i	$-0.945124\pi$
$457$	−7.35445	+	12.7383i	−0.344027	+	0.595872i	0.641150	+	0.767416i	$0.278458\pi$
$458$	−8.12560	+	11.8175i	−0.379684	+	0.552197i
$459$	−6.23686	+	7.48586i	−0.291112	+	0.349410i
$460$	−7.92683	−	20.6759i	−0.369590	−	0.964021i
$461$	−6.68999	−	11.5874i	−0.311584	−	0.539679i	0.667122	−	0.744949i	$-0.267526\pi$
$461$	−6.68999	−	11.5874i	−0.311584	−	0.539679i	−0.978705	+	0.205270i	$0.934193\pi$
$462$	−8.30020	+	25.1364i	−0.386160	+	1.16945i
$463$	26.3899	+	15.2362i	1.22644	+	0.708088i	0.966284	−	0.257477i	$-0.0828912\pi$
$463$	26.3899	+	15.2362i	1.22644	+	0.708088i	0.260160	+	0.965565i	$0.416225\pi$
$464$	13.3277	+	4.34276i	0.618722	+	0.201607i
$465$	41.2288	+	2.35305i	1.91194	+	0.109120i
$466$	16.4511	+	1.29819i	0.762085	+	0.0601377i
$467$	−1.78889	+	1.03281i	−0.0827798	+	0.0477930i	−0.540819	−	0.841139i	$-0.681885\pi$
$467$	−1.78889	+	1.03281i	−0.0827798	+	0.0477930i	0.458039	+	0.888932i	$0.348552\pi$
$468$	−32.5293	+	8.37817i	−1.50367	+	0.387281i
$469$	22.7054	+	4.20619i	1.04844	+	0.194224i
$470$	31.7519	−	15.1367i	1.46460	−	0.698204i
$471$	−16.2135	−	0.925350i	−0.747078	−	0.0426379i
$472$	−1.39274	−	4.71266i	−0.0641060	−	0.216918i
$473$	6.19253	−	3.57526i	0.284733	−	0.164391i
$474$	−4.66150	+	34.1251i	−0.214110	+	1.56742i
$475$	−2.33760	−	4.04884i	−0.107256	−	0.185773i
$476$	−6.44153	−	7.54715i	−0.295247	−	0.345923i
$477$	13.0147	+	1.49043i	0.595903	+	0.0682420i
$478$	37.4969	−	17.8755i	1.71507	−	0.817606i
$479$	0.714020			0.0326244			0.0163122	−	0.999867i	$-0.494807\pi$
$479$	0.714020			0.0326244			0.0163122	+	0.999867i	$0.494807\pi$
$480$	21.2538	+	10.2866i	0.970099	+	0.469515i
$481$	−2.73852			−0.124866
$482$	−12.9666	−	8.91570i	−0.590613	−	0.406099i
$483$	−20.2135	+	5.88726i	−0.919746	+	0.267880i
$484$	−4.06951	−	10.6147i	−0.184978	−	0.482487i
$485$	10.7868	+	18.6834i	0.489805	+	0.848368i
$486$	−20.6025	−	7.84446i	−0.934550	−	0.355832i
$487$	−15.8202	−	9.13377i	−0.716880	−	0.413891i	0.0967233	−	0.995311i	$-0.469164\pi$
$487$	−15.8202	−	9.13377i	−0.716880	−	0.413891i	−0.813603	+	0.581420i	$0.802497\pi$
$488$	−12.8143	+	13.4865i	−0.580078	+	0.610507i
$489$	−0.0336734	+	0.590008i	−0.00152276	+	0.0266811i
$490$	10.2715	−	21.5325i	0.464019	−	0.972740i
$491$	7.90831	+	4.56587i	0.356897	+	0.206055i	0.667719	−	0.744414i	$-0.267271\pi$
$491$	7.90831	+	4.56587i	0.356897	+	0.206055i	−0.310822	+	0.950468i	$0.600604\pi$
$492$	4.48360	−	4.92906i	0.202136	−	0.222219i
$493$			6.57115i			0.295950i
$494$	−25.9660	+	37.7639i	−1.16827	+	1.69908i
$495$	27.0882	−	11.7597i	1.21752	−	0.528561i
$496$	−12.2604	+	37.6264i	−0.550507	+	1.68948i
$497$	−6.73326	+	7.88499i	−0.302028	+	0.353690i
$498$	27.6908	+	21.4625i	1.24085	+	0.961758i
$499$	−10.4868			−0.469454			−0.234727	−	0.972061i	$-0.575420\pi$
$499$	−10.4868			−0.469454			−0.234727	+	0.972061i	$0.575420\pi$
$500$	7.23338	+	18.8672i	0.323487	+	0.843766i
$501$	10.2154	−	5.14530i	0.456391	−	0.229875i
$502$	14.0422	−	20.4223i	0.626732	−	0.911492i
$503$	15.6922			0.699680			0.349840	−	0.936809i	$-0.386236\pi$
$503$	15.6922			0.699680			0.349840	+	0.936809i	$0.386236\pi$
$504$	11.4158	−	19.3308i	0.508501	−	0.861061i
$505$	−1.60690			−0.0715060
$506$	15.0362	−	21.8680i	0.668441	−	0.972152i
$507$	1.81032	−	31.7195i	0.0803993	−	1.40871i
$508$	38.0683	−	14.5948i	1.68901	−	0.647540i
$509$	2.30533			0.102182			0.0510910	−	0.998694i	$-0.483730\pi$
$509$	2.30533			0.102182			0.0510910	+	0.998694i	$0.483730\pi$
$510$	−1.49813	+	10.9672i	−0.0663381	+	0.485637i
$511$	9.56751	+	27.0105i	0.423242	+	1.19487i
$512$	−14.7277	+	17.1783i	−0.650878	+	0.759182i
$513$	−28.2274	+	10.3860i	−1.24627	+	0.458552i
$514$	25.2878	−	36.7774i	1.11540	−	1.62218i
$515$		−	20.1754i		−	0.889036i
$516$	−5.77688	+	1.84470i	−0.254313	+	0.0812083i
$517$	36.5092	+	21.0786i	1.60567	+	0.927036i
$518$	1.29434	−	1.29402i	0.0568699	−	0.0568558i
$519$	−19.3422	+	9.74231i	−0.849030	+	0.427640i
$520$	−26.2855	+	27.6644i	−1.15270	+	1.21316i
$521$	−37.2657	−	21.5153i	−1.63264	−	0.942605i	−0.983275	−	0.182127i	$-0.941702\pi$
$521$	−37.2657	−	21.5153i	−1.63264	−	0.942605i	−0.649364	−	0.760478i	$-0.724965\pi$
$522$	−14.0615	+	4.82941i	−0.615453	+	0.211377i
$523$	6.14915	+	10.6506i	0.268884	+	0.465720i	0.968574	−	0.248726i	$-0.0800119\pi$
$523$	6.14915	+	10.6506i	0.268884	+	0.465720i	−0.699690	+	0.714446i	$0.746679\pi$
$524$	11.8826	−	4.55559i	0.519093	−	0.199012i
$525$	−3.55360	+	1.03500i	−0.155092	+	0.0451711i
$526$	−11.8492	−	8.14738i	−0.516650	−	0.355243i
$527$	−18.5515			−0.808117
$528$	4.27349	+	27.9745i	0.185980	+	1.21743i
$529$	−1.89306			−0.0823072
$530$	13.4335	−	6.40402i	0.583516	−	0.278173i
$531$	4.18812	+	3.10277i	0.181749	+	0.134649i
$532$	−5.57174	−	30.1184i	−0.241566	−	1.30580i
$533$	5.38435	+	9.32597i	0.233222	+	0.403953i
$534$	11.2388	+	8.71098i	0.486352	+	0.376961i
$535$	−22.4363	+	12.9536i	−0.970004	+	0.560032i
$536$	23.6738	−	6.99636i	1.02255	−	0.302197i
$537$	6.49158	+	12.8883i	0.280133	+	0.556171i
$538$	8.56722	−	4.08416i	0.369359	−	0.176080i
$539$	28.2395	−	4.47763i	1.21636	−	0.192865i
$540$	−24.5696	+	4.85446i	−1.05731	+	0.208903i
$541$	16.9066	−	9.76105i	0.726873	−	0.419660i	−0.0904042	−	0.995905i	$-0.528816\pi$
$541$	16.9066	−	9.76105i	0.726873	−	0.419660i	0.817277	+	0.576245i	$0.195483\pi$
$542$	−1.93266	−	0.152510i	−0.0830147	−	0.00655086i
$543$	8.67048	−	13.2164i	0.372086	−	0.567169i
$544$	−9.79573	−	4.06953i	−0.419988	−	0.174480i
$545$	−21.6792	−	12.5165i	−0.928636	−	0.536148i
$546$	24.1486	+	27.0787i	1.03346	+	1.15886i
$547$	−2.25682	−	3.90894i	−0.0964949	−	0.167134i	0.813737	−	0.581234i	$-0.197430\pi$
$547$	−2.25682	−	3.90894i	−0.0964949	−	0.167134i	−0.910232	+	0.414100i	$0.864096\pi$
$548$	−16.9830	+	6.51100i	−0.725477	+	0.278136i
$549$	2.24502	−	19.6040i	0.0958152	−	0.836677i
$550$	2.64341	−	3.84447i	0.112716	−	0.163929i
$551$	−10.1423	+	17.5670i	−0.432077	+	0.748379i
$552$	−16.4076	+	15.4064i	−0.698353	+	0.655741i
$553$	35.0668	−	12.4212i	1.49119	−	0.528202i
$554$	3.54399	−	5.15423i	0.150570	−	0.218982i
$555$	−2.03845	−	0.116340i	−0.0865274	−	0.00493837i
$556$	−16.6885	−	2.65035i	−0.707750	−	0.112400i
$557$	19.2729	−	33.3817i	0.816620	−	1.41443i	−0.0915393	−	0.995801i	$-0.529179\pi$
$557$	19.2729	−	33.3817i	0.816620	−	1.41443i	0.908159	−	0.418625i	$-0.137488\pi$
$558$	−13.6343	−	39.6980i	−0.577185	−	1.68055i
$559$		−	9.80072i		−	0.414526i
$560$	−0.648468	−	25.4959i	−0.0274028	−	1.07740i
$561$	−11.8481	+	5.96768i	−0.500229	+	0.251956i
$562$	26.5337	+	2.09383i	1.11926	+	0.0883228i
$563$	−38.1123	+	22.0042i	−1.60624	+	0.927365i	−0.616043	+	0.787712i	$0.711265\pi$
$563$	−38.1123	+	22.0042i	−1.60624	+	0.927365i	−0.990201	+	0.139653i	$0.955401\pi$
$564$	−26.4480	−	24.0578i	−1.11366	−	1.01302i
$565$	−6.65800	−	3.84400i	−0.280104	−	0.161718i
$566$	−3.25529	+	41.2521i	−0.136830	+	1.73396i
$567$	2.67035	+	23.6616i	0.112144	+	0.993692i
$568$	−2.59441	+	10.7767i	−0.108859	+	0.452181i
$569$	−1.96774	−	1.13608i	−0.0824921	−	0.0476268i	0.458187	−	0.888856i	$-0.348499\pi$
$569$	−1.96774	−	1.13608i	−0.0824921	−	0.0476268i	−0.540679	+	0.841229i	$0.681832\pi$
$570$	−20.9325	+	27.0070i	−0.876766	+	1.13120i
$571$	15.9657	+	27.6534i	0.668143	+	1.15726i	0.978423	+	0.206612i	$0.0662439\pi$
$571$	15.9657	+	27.6534i	0.668143	+	1.15726i	−0.310280	+	0.950645i	$0.600423\pi$
$572$	−45.1692	−	7.17347i	−1.88862	−	0.299938i
$573$	−4.57226	+	2.30296i	−0.191009	+	0.0962075i
$574$	−6.95162	−	1.86360i	−0.290155	−	0.0777853i
$575$	3.71067			0.154746
$576$	1.50901	−	23.9525i	0.0628753	−	0.998021i
$577$	−1.17928	+	2.04257i	−0.0490940	+	0.0850333i	−0.889528	−	0.456880i	$-0.848967\pi$
$577$	−1.17928	+	2.04257i	−0.0490940	+	0.0850333i	0.840434	+	0.541914i	$0.182300\pi$
$578$	−1.50011	+	19.0099i	−0.0623965	+	0.790709i
$579$	0.753875	−	13.2090i	0.0313300	−	0.548947i
$580$	−10.6349	+	13.1218i	−0.441591	+	0.544853i
$581$	6.89292	−	37.2085i	0.285966	−	1.54367i
$582$	13.4333	−	17.3316i	0.556828	−	0.718416i
$583$	15.4463	+	8.91791i	0.639719	+	0.369342i
$584$	22.2074	+	21.1006i	0.918950	+	0.873148i
$585$	4.60512	−	40.2128i	0.190398	−	1.66259i
$586$	11.9612	−	5.70214i	0.494114	−	0.235553i
$587$	−30.8328	+	17.8013i	−1.27261	+	0.734740i	−0.975478	−	0.220097i	$-0.929363\pi$
$587$	−30.8328	+	17.8013i	−1.27261	+	0.734740i	−0.297130	+	0.954837i	$0.596029\pi$
$588$	−24.2090	−	1.38769i	−0.998361	−	0.0572275i
$589$	−49.5947	−	28.6335i	−2.04352	−	1.17982i
$590$	5.90299	+	0.465817i	0.243022	+	0.0191774i
$591$	−21.5560	−	14.1416i	−0.886695	−	0.581708i
$592$	0.606182	−	1.86034i	0.0249139	−	0.0764596i
$593$	21.8715	−	12.6275i	0.898154	−	0.518549i	0.0215531	−	0.999768i	$-0.493139\pi$
$593$	21.8715	−	12.6275i	0.898154	−	0.518549i	0.876601	+	0.481218i	$0.159806\pi$
$594$	−21.4778	−	20.9677i	−0.881244	−	0.860314i
$595$	11.2699	−	3.99195i	0.462019	−	0.163654i
$596$	−2.81248	−	7.33593i	−0.115204	−	0.300491i
$597$	10.7982	+	21.4385i	0.441940	+	0.877421i
$598$	−15.6528	−	32.8345i	−0.640091	−	1.34270i
$599$	−18.5239	−	32.0842i	−0.756864	−	1.31093i	−0.944442	−	0.328677i	$-0.893397\pi$
$599$	−18.5239	−	32.0842i	−0.756864	−	1.31093i	0.187578	−	0.982250i	$-0.439936\pi$
$600$	−2.88451	+	2.70850i	−0.117759	+	0.110574i
$601$	3.21361	+	5.56614i	0.131086	+	0.227048i	0.924095	−	0.382162i	$-0.124820\pi$
$601$	3.21361	+	5.56614i	0.131086	+	0.227048i	−0.793009	+	0.609209i	$0.791487\pi$
$602$	4.63108	+	4.63223i	0.188749	+	0.188796i
$603$	−15.5866	+	21.0388i	−0.634737	+	0.856767i
$604$	25.9834	−	9.96162i	1.05725	−	0.405333i
$605$	13.6980			0.556904
$606$	0.617691	+	1.51198i	0.0250920	+	0.0614200i
$607$		−	10.3172i		−	0.418761i	−0.977834	−	0.209381i	$-0.932855\pi$
$607$		−	10.3172i		−	0.418761i	0.977834	−	0.209381i	$-0.0671448\pi$
$608$	−19.9063	−	25.9986i	−0.807305	−	1.05438i
$609$	11.5981	+	11.1073i	0.469980	+	0.450091i
$610$	−9.64634	−	20.2349i	−0.390569	−	0.819285i
$611$	50.0406	−	28.8910i	2.02443	−	1.16880i
$612$	10.8953	−	2.80617i	0.440416	−	0.113432i
$613$	13.0257	+	7.52042i	0.526105	+	0.303747i	0.739429	−	0.673235i	$-0.235096\pi$
$613$	13.0257	+	7.52042i	0.526105	+	0.303747i	−0.213324	+	0.976982i	$0.568429\pi$
$614$	20.6356	+	14.1888i	0.832786	+	0.572615i
$615$	3.61172	+	7.17065i	0.145639	+	0.289149i
$616$	24.7385	−	17.9531i	0.996742	−	0.723350i
$617$	3.99679	+	2.30755i	0.160905	+	0.0928983i	0.578290	−	0.815831i	$-0.303720\pi$
$617$	3.99679	+	2.30755i	0.160905	+	0.0928983i	−0.417385	+	0.908730i	$0.637054\pi$
$618$	−18.9837	+	7.75543i	−0.763637	+	0.311969i
$619$	−28.6798			−1.15274			−0.576370	−	0.817189i	$-0.695531\pi$
$619$	−28.6798			−1.15274			−0.576370	+	0.817189i	$0.695531\pi$
$620$	−37.0452	−	30.0243i	−1.48777	−	1.20580i
$621$	4.06308	−	23.5240i	0.163046	−	0.943986i
$622$	0.165206	−	2.09355i	0.00662417	−	0.0839437i
$623$	2.79762	−	15.1018i	0.112084	−	0.605041i
$624$	36.1344	+	14.0987i	1.44653	+	0.564399i
$625$	−28.3861			−1.13544
$626$	3.40518	−	1.62331i	0.136098	−	0.0648806i
$627$	−40.8851	−	2.33343i	−1.63279	−	0.0931882i
$628$	14.5682	+	11.8072i	0.581336	+	0.471160i
$629$	0.917232			0.0365724
$630$	16.8250	+	21.1823i	0.670322	+	0.843922i
$631$		−	5.71889i		−	0.227665i	−0.993500	−	0.113833i	$-0.963687\pi$
$631$		−	5.71889i		−	0.227665i	0.993500	−	0.113833i	$-0.0363128\pi$
$632$	27.3941	−	28.8311i	1.08968	−	1.14684i
$633$	−19.5636	+	9.85379i	−0.777582	+	0.391653i
$634$	−21.1313	+	10.0737i	−0.839232	+	0.400078i
$635$			49.1263i			1.94952i
$636$	−11.1896	−	10.1783i	−0.443696	−	0.403597i
$637$	14.0380	−	36.5889i	0.556206	−	1.44970i
$638$	−20.1801	−	1.59246i	−0.798939	−	0.0630460i
$639$	−4.68188	−	10.7846i	−0.185212	−	0.426631i
$640$	−12.9747	−	23.9800i	−0.512869	−	0.947893i
$641$		−	32.8939i		−	1.29923i	−0.760263	−	0.649615i	$-0.774930\pi$
$641$		−	32.8939i		−	1.29923i	0.760263	−	0.649615i	$-0.225070\pi$
$642$	20.8129	+	16.1316i	0.821420	+	0.636665i
$643$	2.66478	−	4.61553i	0.105088	−	0.182019i	−0.808686	−	0.588241i	$-0.799821\pi$
$643$	2.66478	−	4.61553i	0.105088	−	0.182019i	0.913774	+	0.406222i	$0.133154\pi$
$644$	22.9133	+	8.12260i	0.902909	+	0.320075i
$645$	0.416363	−	7.29530i	0.0163943	−	0.287252i
$646$	8.69701	−	12.6486i	0.342179	−	0.497651i
$647$	14.3734	−	24.8955i	0.565077	−	0.978741i	−0.431966	−	0.901890i	$-0.642180\pi$
$647$	14.3734	−	24.8955i	0.565077	−	0.978741i	0.997043	−	0.0768515i	$-0.0244867\pi$
$648$	14.0122	+	21.2522i	0.550453	+	0.834866i
$649$	3.54833	+	6.14589i	0.139284	+	0.241247i
$650$	−2.75181	−	5.77241i	−0.107935	−	0.226412i
$651$	−31.3579	+	32.7436i	−1.22901	+	1.28332i
$652$	0.429664	−	0.530138i	0.0168270	−	0.0207618i
$653$	−34.8304			−1.36302			−0.681509	−	0.731810i	$-0.738676\pi$
$653$	−34.8304			−1.36302			−0.681509	+	0.731810i	$0.738676\pi$
$654$	−3.44369	+	25.2100i	−0.134659	+	0.985789i
$655$			15.3342i			0.599156i
$656$	−7.52721	+	1.59338i	−0.293888	+	0.0622110i
$657$	−32.2806	−	3.69674i	−1.25939	−	0.144223i
$658$	−9.99959	+	37.3005i	−0.389825	+	1.45412i
$659$	−31.6102	+	18.2502i	−1.23136	+	0.710926i	−0.967313	−	0.253584i	$-0.918391\pi$
$659$	−31.6102	+	18.2502i	−1.23136	+	0.710926i	−0.264047	+	0.964510i	$0.585057\pi$
$660$	−33.3176	−	7.25859i	−1.29688	−	0.282540i
$661$	−28.7619	+	16.6057i	−1.11871	+	0.645887i	−0.941071	−	0.338209i	$-0.890179\pi$
$661$	−28.7619	+	16.6057i	−1.11871	+	0.645887i	−0.177638	+	0.984096i	$0.556846\pi$
$662$	32.4244	−	15.4573i	1.26021	−	0.600765i
$663$	−1.03607	+	18.1535i	−0.0402377	+	0.705023i
$664$	−11.4653	−	38.7957i	−0.444941	−	1.50556i
$665$	36.2897	+	6.72270i	1.40725	+	0.260695i
$666$	0.674111	+	1.96276i	0.0261213	+	0.0760556i
$667$	−8.04988	−	13.9428i	−0.311692	−	0.539867i
$668$	−13.0440	−	2.07156i	−0.504689	−	0.0801512i
$669$	40.0568	+	2.28616i	1.54869	+	0.0883879i
$670$	−2.34001	+	29.6534i	−0.0904026	+	1.14561i
$671$	13.4330	−	23.2666i	0.518575	−	0.898198i
$672$	−23.7406	+	10.4108i	−0.915813	+	0.401604i
$673$	3.83518	+	6.64272i	0.147835	+	0.256058i	0.930427	−	0.366477i	$-0.119436\pi$
$673$	3.83518	+	6.64272i	0.147835	+	0.256058i	−0.782592	+	0.622535i	$0.786103\pi$
$674$	−31.0403	+	14.7975i	−1.19563	+	0.569978i
$675$	0.714302	−	4.13560i	0.0274935	−	0.159179i
$676$	−23.0993	+	28.5008i	−0.888433	+	1.09619i
$677$	17.7508	−	30.7453i	0.682218	−	1.18164i	−0.292084	−	0.956393i	$-0.594349\pi$
$677$	17.7508	−	30.7453i	0.682218	−	1.18164i	0.974302	−	0.225244i	$-0.0723179\pi$
$678$	−1.05761	+	7.74235i	−0.0406171	+	0.297343i
$679$	−23.2887	−	4.31425i	−0.893738	−	0.165566i
$680$	8.80400	−	9.26583i	0.337618	−	0.355329i
$681$	−16.8972	+	25.7563i	−0.647501	+	0.986983i
$682$	4.49579	−	56.9721i	0.172153	−	2.18158i
$683$	2.21414	+	1.27834i	0.0847219	+	0.0489142i	0.541762	−	0.840532i	$-0.317757\pi$
$683$	2.21414	+	1.27834i	0.0847219	+	0.0489142i	−0.457041	+	0.889446i	$0.651091\pi$
$684$	33.4581	+	9.31458i	1.27930	+	0.356152i
$685$		−	21.9161i		−	0.837372i
$686$	10.6542	+	23.9267i	0.406779	+	0.913526i
$687$	−9.63484	+	14.6863i	−0.367592	+	0.560319i
$688$	6.65787	+	2.16943i	0.253829	+	0.0827088i
$689$	21.1711	−	12.2232i	0.806556	−	0.465665i
$690$	−10.2565	−	25.1058i	−0.390457	−	0.955760i
$691$	4.30114	−	7.44979i	0.163623	−	0.283403i	−0.772542	−	0.634963i	$-0.781015\pi$
$691$	4.30114	−	7.44979i	0.163623	−	0.283403i	0.936165	+	0.351560i	$0.114349\pi$
$692$	24.6981	+	3.92238i	0.938879	+	0.149106i
$693$	−9.49406	+	30.9993i	−0.360650	+	1.17757i
$694$	−42.4459	−	3.34950i	−1.61122	−	0.127145i
$695$	10.1805	−	17.6331i	0.386167	−	0.668861i
$696$	16.4348	+	4.96271i	0.622958	+	0.188111i
$697$	−1.80342	−	3.12362i	−0.0683095	−	0.118315i
$698$	21.1932	+	1.67240i	0.802174	+	0.0633013i
$699$	20.1783	+	1.15163i	0.763212	+	0.0435587i
$700$	4.02823	+	1.42798i	0.152253	+	0.0539726i
$701$	−3.78931			−0.143120			−0.0715602	−	0.997436i	$-0.522798\pi$
$701$	−3.78931			−0.143120			−0.0715602	+	0.997436i	$0.522798\pi$
$702$	−39.6077	+	11.1247i	−1.49490	+	0.419874i
$703$	2.45208	+	1.41571i	0.0924820	+	0.0533945i
$704$	14.8715	−	29.0967i	0.560491	−	1.09662i
$705$	38.4758	−	19.3795i	1.44908	−	0.729874i
$706$	6.18370	−	8.99332i	0.232727	−	0.338468i
$707$	1.14561	−	1.34157i	0.0430851	−	0.0504549i
$708$	−1.83080	−	5.73337i	−0.0688058	−	0.215473i
$709$	20.5477	+	11.8632i	0.771685	+	0.445533i	0.833476	−	0.552556i	$-0.186348\pi$
$709$	20.5477	+	11.8632i	0.771685	+	0.445533i	−0.0617901	+	0.998089i	$0.519681\pi$
$710$	−11.0058	−	7.56749i	−0.413041	−	0.284003i
$711$	−4.79935	+	41.9088i	−0.179990	+	1.57170i
$712$	−4.65343	−	15.7460i	−0.174395	−	0.590105i
$713$	39.3630	−	22.7262i	1.47416	−	0.851105i
$714$	−8.08828	−	9.06966i	−0.302696	−	0.339424i
$715$	27.5545	−	47.7258i	1.03048	−	1.78484i
$716$	2.61360	−	16.4570i	0.0976746	−	0.615029i
$717$	45.4374	−	22.8860i	1.69689	−	0.854692i
$718$	−0.327609	+	4.15156i	−0.0122262	+	0.154935i
$719$	−12.7870	−	22.1477i	−0.476873	−	0.825969i	0.522776	−	0.852470i	$-0.324897\pi$
$719$	−12.7870	−	22.1477i	−0.476873	−	0.825969i	−0.999649	+	0.0265017i	$0.991563\pi$
$720$	26.2982	+	12.0296i	0.980075	+	0.448318i
$721$	16.8441	+	14.3837i	0.627307	+	0.535679i
$722$	18.5177	−	8.82776i	0.689159	−	0.328535i
$723$	−16.1144	−	10.5717i	−0.599301	−	0.393165i
$724$	−17.0424	+	6.53379i	−0.633376	+	0.242826i
$725$	−1.41519	−	2.45119i	−0.0525590	−	0.0910349i
$726$	−5.26551	−	12.8889i	−0.195422	−	0.478352i
$727$	23.6223	−	13.6383i	0.876103	−	0.505818i	0.00673158	−	0.999977i	$-0.497857\pi$
$727$	23.6223	−	13.6383i	0.876103	−	0.505818i	0.869372	+	0.494159i	$0.164524\pi$
$728$	−4.35666	−	41.6681i	−0.161469	−	1.54432i
$729$	−25.4357	−	9.05672i	−0.942064	−	0.335434i
$730$	−33.3195	+	15.8840i	−1.23321	+	0.587894i
$731$			3.28263i			0.121412i
$732$	−15.3316	+	16.8548i	−0.566671	+	0.622972i
$733$			49.3306i			1.82207i	0.412333	+	0.911033i	$0.364714\pi$
$733$			49.3306i			1.82207i	−0.412333	+	0.911033i	$0.635286\pi$
$734$	−6.01099	+	8.74213i	−0.221870	+	0.322678i
$735$	12.0038	−	26.6390i	0.442766	−	0.982596i
$736$	25.7701	−	3.36529i	0.949898	−	0.124046i
$737$	−30.8736	+	17.8249i	−1.13724	+	0.656588i
$738$	5.35875	−	6.15478i	0.197258	−	0.226560i
$739$	21.6705	−	37.5343i	0.797161	−	1.38072i	−0.124297	−	0.992245i	$-0.539668\pi$
$739$	21.6705	−	37.5343i	0.797161	−	1.38072i	0.921458	−	0.388478i	$-0.126999\pi$
$740$	1.83160	+	1.48447i	0.0673311	+	0.0545703i
$741$	−30.7889	+	46.9315i	−1.13106	+	1.72407i
$742$	−4.23062	+	15.7811i	−0.155311	+	0.579341i
$743$	12.7227	−	22.0363i	0.466749	−	0.808433i	−0.532529	−	0.846411i	$-0.678758\pi$
$743$	12.7227	−	22.0363i	0.466749	−	0.808433i	0.999279	+	0.0379783i	$0.0120918\pi$
$744$	−14.0106	+	46.3983i	−0.513654	+	1.70104i
$745$	9.46684			0.346838
$746$	27.1798	−	39.5291i	0.995123	−	1.44726i
$747$	34.4775	+	25.5427i	1.26147	+	0.934559i
$748$	15.1289	+	2.40266i	0.553166	+	0.0878501i
$749$	5.18085	−	27.9667i	0.189304	−	1.02188i
$750$	9.35922	+	22.9095i	0.341751	+	0.836536i
$751$			19.6414i			0.716724i	0.933583	+	0.358362i	$0.116665\pi$
$751$			19.6414i			0.716724i	−0.933583	+	0.358362i	$0.883335\pi$
$752$	8.54964	+	40.3890i	0.311773	+	1.47283i
$753$	16.6503	−	25.3800i	0.606772	−	0.924900i
$754$	−15.7200	+	22.8625i	−0.572489	+	0.832603i
$755$			33.5309i			1.22032i
$756$	13.4636	−	23.9736i	0.489665	−	0.871911i
$757$			7.29815i			0.265256i	0.991166	+	0.132628i	$0.0423415\pi$
$757$			7.29815i			0.265256i	−0.991166	+	0.132628i	$0.957658\pi$
$758$	−0.686977	−	0.472358i	−0.0249521	−	0.0171568i
$759$	17.8290	−	27.1767i	0.647152	−	0.986452i
$760$	37.8376	−	11.1822i	1.37251	−	0.405621i
$761$			30.0158i			1.08807i	0.839062	+	0.544036i	$0.183104\pi$
$761$			30.0158i			1.08807i	−0.839062	+	0.544036i	$0.816896\pi$
$762$	46.2245	−	18.8841i	1.67454	−	0.684099i
$763$	25.9056	−	9.17615i	0.937847	−	0.332199i
$764$	5.83831	+	0.927201i	0.211223	+	0.0335450i
$765$	−1.54243	+	13.4688i	−0.0557666	+	0.486965i
$766$	29.7864	+	20.4808i	1.07623	+	0.740001i
$767$	9.72690			0.351218
$768$	−17.5761	+	21.4262i	−0.634222	+	0.773151i
$769$	−27.1355	+	47.0000i	−0.978530	+	1.69486i	−0.310775	+	0.950484i	$0.600589\pi$
$769$	−27.1355	+	47.0000i	−0.978530	+	1.69486i	−0.667755	+	0.744381i	$0.732745\pi$
$770$	9.52821	+	35.5774i	0.343373	+	1.28212i
$771$	29.9847	−	45.7055i	1.07987	−	1.64604i
$772$	−9.61926	+	11.8686i	−0.346205	+	0.427162i
$773$	−0.0679877	+	0.117758i	−0.00244535	+	0.00423547i	−0.867245	−	0.497881i	$-0.834112\pi$
$773$	−0.0679877	+	0.117758i	−0.00244535	+	0.00423547i	0.864800	+	0.502116i	$0.167445\pi$
$774$	−7.02442	+	2.41254i	−0.252488	+	0.0867169i
$775$	6.92015	−	3.99535i	0.248579	−	0.143517i
$776$	−24.2821	+	7.17611i	−0.871675	+	0.257607i
$777$	1.55041	−	1.61892i	0.0556206	−	0.0580785i
$778$	3.20443	+	2.20333i	0.114885	+	0.0789933i
$779$		−	11.1340i		−	0.398918i
$780$	−31.4490	+	34.5735i	−1.12605	+	1.23793i
$781$		−	16.0076i		−	0.572796i
$782$	5.24271	+	10.9975i	0.187479	+	0.393270i
$783$	−17.0891	+	6.28773i	−0.610713	+	0.224705i
$784$	21.7483	+	17.6355i	0.776727	+	0.629838i
$785$	−19.5683	+	11.2978i	−0.698424	+	0.403235i
$786$	14.4284	−	5.89445i	0.514644	−	0.210248i
$787$	16.5191	+	28.6119i	0.588842	+	1.01990i	0.994384	+	0.105828i	$0.0337492\pi$
$787$	16.5191	+	28.6119i	0.588842	+	1.01990i	−0.405543	+	0.914076i	$0.632917\pi$
$788$	10.6566	+	27.7962i	0.379627	+	0.990200i
$789$	−14.7257	−	9.66066i	−0.524249	−	0.343929i
$790$	20.6217	+	43.2575i	0.733686	+	1.53903i
$791$	7.95599	−	2.81813i	0.282882	−	0.100201i
$792$	5.97742	+	34.1397i	0.212398	+	1.21310i
$793$	−18.4117	−	31.8899i	−0.653817	−	1.13244i
$794$	−16.0569	−	1.26708i	−0.569837	−	0.0449671i
$795$	16.2783	−	8.19906i	0.577331	−	0.290791i
$796$	4.34749	−	27.3748i	0.154093	−	0.970275i
$797$	−18.6164	+	32.2445i	−0.659425	+	1.14216i	0.321339	+	0.946964i	$0.395867\pi$
$797$	−18.6164	+	32.2445i	−0.659425	+	1.14216i	−0.980765	+	0.195194i	$0.937466\pi$
$798$	−7.62414	−	36.7303i	−0.269892	−	1.30024i
$799$	−16.7605	+	9.67667i	−0.592943	+	0.342336i
$800$	4.53046	−	0.591628i	0.160176	−	0.0209172i
$801$	13.9934	+	10.3670i	0.494431	+	0.366300i
$802$	−0.570482	+	0.829684i	−0.0201444	+	0.0292972i
$803$	−38.3117	−	22.1193i	−1.35199	−	0.780572i
$804$	28.8013	−	9.19696i	1.01574	−	0.324352i
$805$	−19.0223	+	22.2761i	−0.670450	+	0.785131i
$806$	−64.5449	−	44.3804i	−2.27350	−	1.56323i
$807$	10.3815	−	5.22894i	0.365444	−	0.184067i
$808$	0.441419	−	1.83357i	0.0155291	−	0.0645049i
$809$	−27.2533	−	15.7347i	−0.958174	−	0.553202i	−0.0625635	−	0.998041i	$-0.519928\pi$
$809$	−27.2533	−	15.7347i	−0.958174	−	0.553202i	−0.895611	+	0.444839i	$0.853261\pi$
$810$	−29.9551	+	6.59815i	−1.05252	+	0.231835i
$811$	−36.4540			−1.28007			−0.640037	−	0.768344i	$-0.721081\pi$
$811$	−36.4540			−1.28007			−0.640037	+	0.768344i	$0.721081\pi$
$812$	−3.37317	−	18.2339i	−0.118375	−	0.639883i
$813$	−2.37051	−	0.135292i	−0.0831374	−	0.00474489i
$814$	−0.222283	+	2.81684i	−0.00779101	+	0.0987302i
$815$	0.411126	+	0.712091i	0.0144011	+	0.0249434i
$816$	−12.1028	−	4.72218i	−0.423682	−	0.165309i
$817$	−5.06661	+	8.77562i	−0.177258	+	0.307020i
$818$	1.30564	−	16.5455i	0.0456507	−	0.578501i
$819$	30.2898	+	32.5137i	1.05841	+	1.13612i
$820$	1.45412	−	9.15620i	0.0507802	−	0.319748i
$821$	−13.5920	+	23.5420i	−0.474364	+	0.821622i	−0.999569	−	0.0293536i	$-0.990655\pi$
$821$	−13.5920	+	23.5420i	−0.474364	+	0.821622i	0.525205	+	0.850975i	$0.323988\pi$
$822$	−20.6216	+	8.42454i	−0.719260	+	0.293840i
$823$	10.8461	−	6.26199i	0.378071	−	0.218279i	−0.298908	−	0.954282i	$-0.596622\pi$
$823$	10.8461	−	6.26199i	0.378071	−	0.218279i	0.676979	+	0.736003i	$0.263289\pi$
$824$	23.0215	+	5.54224i	0.801990	+	0.193073i
$825$	3.13440	−	4.77775i	0.109126	−	0.166340i
$826$	−4.59734	+	4.59620i	−0.159962	+	0.159922i
$827$		−	24.7293i		−	0.859923i	−0.902847	−	0.429961i	$-0.858527\pi$
$827$		−	24.7293i		−	0.859923i	0.902847	−	0.429961i	$-0.141473\pi$
$828$	−19.6802	+	19.3013i	−0.683934	+	0.670766i
$829$	16.1050	+	9.29820i	0.559348	+	0.322940i	0.752884	−	0.658153i	$-0.228662\pi$
$829$	16.1050	+	9.29820i	0.559348	+	0.322940i	−0.193535	+	0.981093i	$0.561995\pi$
$830$	48.5947	+	3.83471i	1.68675	+	0.133105i
$831$	4.20225	−	6.40547i	0.145774	−	0.222203i
$832$	−24.3461	−	37.5929i	−0.844049	−	1.30330i
$833$	−4.70185	+	12.2550i	−0.162910	+	0.424610i
$834$	−20.5049	−	2.80097i	−0.710026	−	0.0969897i
$835$	7.95723	−	13.7823i	0.275371	−	0.476957i
$836$	36.7363	+	29.7740i	1.27055	+	1.02975i
$837$	−17.7514	−	48.2455i	−0.613578	−	1.66761i
$838$	0.214178	+	0.449274i	0.00739864	+	0.0155199i
$839$	16.9174	+	29.3019i	0.584055	+	1.01161i	0.994993	+	0.0999496i	$0.0318681\pi$
$839$	16.9174	+	29.3019i	0.584055	+	1.01161i	−0.410937	+	0.911664i	$0.634799\pi$
$840$	−1.47275	−	31.2013i	−0.0508148	−	1.07655i
$841$	8.35979	−	14.4796i	0.288269	−	0.499296i
$842$	−12.3423	−	0.973959i	−0.425345	−	0.0335648i
$843$	32.5450	+	1.85744i	1.12091	+	0.0639736i
$844$	24.9807	+	3.96726i	0.859870	+	0.136559i
$845$	−22.1026	−	38.2828i	−0.760353	−	1.31697i
$846$	−33.0249	−	28.7536i	−1.13542	−	0.988569i
$847$	−9.76578	+	11.4362i	−0.335556	+	0.392953i
$848$	3.61717	+	17.0877i	0.124214	+	0.586795i
$849$	−2.88777	+	50.5980i	−0.0991081	+	1.73652i
$850$	0.921686	+	1.93340i	0.0316136	+	0.0663149i
$851$	−1.94620	+	1.12364i	−0.0667149	+	0.0385179i
$852$	−2.88985	+	13.2647i	−0.0990046	+	0.454440i
$853$	23.4329	−	13.5290i	0.802328	−	0.463224i	−0.0419565	−	0.999119i	$-0.513359\pi$
$853$	23.4329	−	13.5290i	0.802328	−	0.463224i	0.844285	+	0.535895i	$0.180026\pi$
$854$	23.7709	+	6.37255i	0.813423	+	0.218064i
$855$	−24.9120	+	33.6261i	−0.851971	+	1.14999i
$856$	−8.61756	−	29.1596i	−0.294542	−	0.996653i
$857$		−	1.62808i		−	0.0556141i	−0.999613	−	0.0278070i	$-0.991148\pi$
$857$		−	1.62808i		−	0.0556141i	0.999613	−	0.0278070i	$-0.00885240\pi$
$858$	−55.4986	−	7.58113i	−1.89469	−	0.258815i
$859$	−13.5853			−0.463525			−0.231763	−	0.972772i	$-0.574449\pi$
$859$	−13.5853			−0.463525			−0.231763	+	0.972772i	$0.574449\pi$
$860$	−5.31269	+	6.55502i	−0.181161	+	0.223524i
$861$	−8.56156	−	2.09684i	−0.291777	−	0.0714601i
$862$	39.4286	−	18.7964i	1.34294	−	0.640207i
$863$	−2.31876	−	4.01620i	−0.0789314	−	0.136713i	0.823858	−	0.566797i	$-0.191817\pi$
$863$	−2.31876	−	4.01620i	−0.0789314	−	0.136713i	−0.902789	+	0.430083i	$0.858484\pi$
$864$	1.21007	−	29.3690i	0.0411673	−	0.999152i
$865$	−15.0665	+	26.0960i	−0.512277	+	0.887290i
$866$	−14.4025	−	9.90301i	−0.489418	−	0.336518i
$867$	−1.33075	+	23.3167i	−0.0451947	+	0.791878i
$868$	51.4774	−	9.52305i	1.74726	−	0.323233i
$869$	−28.7167	+	49.7387i	−0.974146	+	1.68727i
$870$	−12.6727	+	16.3502i	−0.429643	+	0.554323i
$871$			48.8627i			1.65565i
$872$	20.2375	−	21.2990i	0.685327	−	0.721277i
$873$	15.9871	−	21.5793i	0.541081	−	0.730350i
$874$	−2.95858	+	37.4921i	−0.100075	+	1.26819i
$875$	17.3582	−	20.3274i	0.586816	−	0.687192i
$876$	27.7537	+	25.2455i	0.937712	+	0.852967i
$877$		−	41.2788i		−	1.39388i	−0.717127	−	0.696942i	$-0.754543\pi$
$877$		−	41.2788i		−	1.39388i	0.717127	−	0.696942i	$-0.245457\pi$
$878$	−5.99809	−	12.5820i	−0.202426	−	0.424623i
$879$	14.4942	−	7.30045i	0.488877	−	0.246238i
$880$	26.3220	+	29.2828i	0.887315	+	0.987122i
$881$		−	5.75924i		−	0.194034i	−0.995283	−	0.0970168i	$-0.969070\pi$
$881$		−	5.75924i		−	0.194034i	0.995283	−	0.0970168i	$-0.0309301\pi$
$882$	−29.6798	−	1.05469i	−0.999369	−	0.0355133i
$883$	24.6267			0.828753			0.414376	−	0.910106i	$-0.364000\pi$
$883$	24.6267			0.828753			0.414376	+	0.910106i	$0.364000\pi$
$884$	13.2200	−	16.3114i	0.444637	−	0.548611i
$885$	7.24035	+	0.413227i	0.243382	+	0.0138905i
$886$	−14.1465	−	29.6747i	−0.475260	−	0.996941i
$887$	44.6290			1.49850			0.749248	−	0.662289i	$-0.230415\pi$
$887$	44.6290			1.49850			0.749248	+	0.662289i	$0.230415\pi$
$888$	0.692719	−	2.29404i	0.0232461	−	0.0769830i
$889$	−41.0146	−	35.0237i	−1.37559	−	1.17466i
$890$	19.7231	+	1.55639i	0.661120	+	0.0521704i
$891$	−26.8568	−	25.1022i	−0.899736	−	0.840956i
$892$	−35.9921	−	29.1708i	−1.20510	−	0.976710i
$893$	−59.7422			−1.99920
$894$	−3.63905	−	8.90764i	−0.121708	−	0.297916i
$895$	17.3885	+	10.0393i	0.581234	+	0.335576i
$896$	29.2705	+	6.26383i	0.977860	+	0.209260i
$897$	−20.0403	−	39.7876i	−0.669125	−	1.32847i
$898$	23.4509	−	34.1060i	0.782567	−	1.13813i
$899$	−30.0250	−	17.3349i	−1.00139	−	0.578152i
$900$	−3.45984	+	3.39323i	−0.115328	+	0.113108i
$901$	−7.09101	+	4.09399i	−0.236236	+	0.136391i
$902$	10.0297	−	4.78137i	0.333954	−	0.159202i
$903$	5.79387	+	5.54867i	0.192808	+	0.184648i
$904$	6.21521	−	6.54124i	0.206715	−	0.217558i
$905$		−	21.9928i		−	0.731065i
$906$	31.5503	−	12.8893i	1.04819	−	0.428217i
$907$	−41.5296			−1.37897			−0.689484	−	0.724301i	$-0.742163\pi$
$907$	−41.5296			−1.37897			−0.689484	+	0.724301i	$0.742163\pi$
$908$	33.2125	−	12.7331i	1.10219	−	0.422564i
$909$	0.796586	+	1.83491i	0.0264211	+	0.0608601i
$910$	48.7602	+	13.0717i	1.61638	+	0.433324i
$911$	−21.0584	−	36.4743i	−0.697697	−	1.20845i	−0.969263	−	0.246027i	$-0.920875\pi$
$911$	−21.0584	−	36.4743i	−0.697697	−	1.20845i	0.271566	−	0.962420i	$-0.412459\pi$
$912$	−25.0664	−	31.3042i	−0.830033	−	1.03658i
$913$	29.2107	+	50.5943i	0.966732	+	1.67443i
$914$	18.7770	−	8.95136i	0.621089	−	0.296085i
$915$	−12.3502	−	24.5199i	−0.408285	−	0.810602i
$916$	18.9379	−	7.26049i	0.625726	−	0.239893i
$917$	−12.8022	−	10.9322i	−0.422766	−	0.361014i
$918$	13.2661	−	3.72607i	0.437846	−	0.122979i
$919$	−1.99093	+	1.14947i	−0.0656748	+	0.0379174i	−0.532478	−	0.846444i	$-0.678739\pi$
$919$	−1.99093	+	1.14947i	−0.0656748	+	0.0379174i	0.466803	+	0.884361i	$0.345406\pi$
$920$	−7.32955	+	30.4456i	−0.241648	+	1.00376i
$921$	25.6451	+	16.8242i	0.845036	+	0.554378i
$922$	−1.48856	+	18.8635i	−0.0490231	+	0.621236i
$923$	−19.0010	−	10.9702i	−0.625426	−	0.361090i
$924$	29.8132	−	22.6413i	0.980784	−	0.744845i
$925$	−0.342149	+	0.197540i	−0.0112498	+	0.00649506i
$926$	−18.5446	−	38.9004i	−0.609412	−	1.27835i
$927$	−23.0382	+	10.0016i	−0.756675	+	0.328494i
$928$	−12.0514	−	15.7397i	−0.395606	−	0.516681i
$929$	−5.51286	−	3.18285i	−0.180871	−	0.104426i	0.406831	−	0.913504i	$-0.366634\pi$
$929$	−5.51286	−	3.18285i	−0.180871	−	0.104426i	−0.587702	+	0.809078i	$0.699967\pi$
$930$	−46.1595	−	35.7772i	−1.51363	−	1.17318i
$931$	−31.4848	+	25.5048i	−1.03187	+	0.835885i
$932$	−18.1307	−	14.6945i	−0.593891	−	0.481335i
$933$	0.146555	−	2.56786i	0.00479799	−	0.0840678i
$934$	2.91219	+	0.229807i	0.0952897	+	0.00751951i
$935$	−9.22904	+	15.9852i	−0.301822	+	0.522771i
$936$	44.6203	+	16.3013i	1.45846	+	0.532824i
$937$	−16.0958			−0.525826			−0.262913	−	0.964820i	$-0.584683\pi$
$937$	−16.0958			−0.525826			−0.262913	+	0.964820i	$0.584683\pi$
$938$	−23.0888	−	23.0945i	−0.753876	−	0.754063i
$939$	4.12627	−	2.07832i	0.134656	−	0.0678236i
$940$	−49.1297	−	7.80244i	−1.60243	−	0.254487i
$941$	1.79506	+	3.10913i	0.0585172	+	0.101355i	0.893800	−	0.448466i	$-0.148029\pi$
$941$	1.79506	+	3.10913i	0.0585172	+	0.101355i	−0.835283	+	0.549821i	$0.814696\pi$
$942$	18.1525	+	14.0696i	0.591440	+	0.458412i
$943$	7.65307	+	4.41850i	0.249218	+	0.143886i
$944$	−2.15309	+	6.60772i	−0.0700772	+	0.215063i
$945$	21.1653	+	25.4888i	0.688508	+	0.829152i
$946$	−10.0810	−	0.795515i	−0.327762	−	0.0258644i
$947$	19.8722	+	11.4732i	0.645761	+	0.372830i	0.786830	−	0.617170i	$-0.211721\pi$
$947$	19.8722	+	11.4732i	0.645761	+	0.372830i	−0.141069	+	0.990000i	$0.545054\pi$
$948$	32.7754	−	36.0317i	1.06449	−	1.17026i
$949$	−52.5111	+	30.3173i	−1.70458	+	0.984142i
$950$	−0.520128	+	6.59123i	−0.0168752	+	0.213848i
$951$	−25.6062	+	12.8973i	−0.830337	+	0.418225i
$952$	1.45921	+	13.9562i	0.0472932	+	0.452324i
$953$			57.5931i			1.86562i	0.360366	+	0.932811i	$0.382652\pi$
$953$			57.5931i			1.86562i	−0.360366	+	0.932811i	$0.617348\pi$
$954$	−13.9721	−	12.1650i	−0.452364	−	0.393858i
$955$	−3.56154	+	6.16877i	−0.115249	+	0.199617i
$956$	−58.0190	−	9.21418i	−1.87647	−	0.298008i
$957$	−24.7521	−	1.41267i	−0.800121	−	0.0456652i
$958$	−0.832064	−	0.572118i	−0.0268828	−	0.0184843i
$959$	18.2974	+	15.6247i	0.590853	+	0.504549i
$960$	−16.5253	−	29.0171i	−0.533351	−	0.936521i
$961$	33.4396	−	57.9190i	1.07870	−	1.86836i
$962$	3.19126	+	2.19427i	0.102890	+	0.0707462i
$963$	25.9139	+	19.1984i	0.835065	+	0.618660i
$964$	7.96647	+	20.7793i	0.256583	+	0.669258i
$965$	−9.20422	−	15.9422i	−0.296294	−	0.513197i
$966$	28.2725	+	9.33578i	0.909653	+	0.300374i
$967$	−37.2468	−	21.5045i	−1.19778	−	0.691537i	−0.237718	−	0.971334i	$-0.576399\pi$
$967$	−37.2468	−	21.5045i	−1.19778	−	0.691537i	−0.960059	+	0.279798i	$0.909733\pi$
$968$	−3.76288	+	15.6303i	−0.120944	+	0.502377i
$969$	10.3124	−	15.7191i	0.331281	−	0.504971i
$970$	2.40013	−	30.4153i	0.0770636	−	0.976575i
$971$	−31.4145	+	18.1372i	−1.00814	+	0.582050i	−0.910646	−	0.413186i	$-0.864416\pi$
$971$	−31.4145	+	18.1372i	−1.00814	+	0.582050i	−0.0974933	+	0.995236i	$0.531082\pi$
$972$	17.7231	+	25.6494i	0.568470	+	0.822704i
$973$	7.46354	+	21.0707i	0.239270	+	0.675495i
$974$	11.1170	+	23.3199i	0.356213	+	0.747218i
$975$	−3.52314	−	6.99480i	−0.112831	−	0.224013i
$976$	25.7391	−	5.44852i	0.823889	−	0.174403i
$977$	−7.12716	+	4.11487i	−0.228018	+	0.131646i	−0.609657	−	0.792665i	$-0.708693\pi$
$977$	−7.12716	+	4.11487i	−0.228018	+	0.131646i	0.381639	+	0.924311i	$0.375360\pi$
$978$	0.511992	−	0.660568i	0.0163717	−	0.0211226i
$979$	11.8557	+	20.5347i	0.378910	+	0.656292i
$980$	−29.2228	+	16.8622i	−0.933489	+	0.538642i
$981$	−3.54552	+	30.9602i	−0.113200	+	0.988483i
$982$	−5.55728	−	11.6574i	−0.177340	−	0.372001i
$983$	15.6273			0.498434			0.249217	−	0.968448i	$-0.419827\pi$
$983$	15.6273			0.498434			0.249217	+	0.968448i	$0.419827\pi$
$984$	−9.17432	+	2.15141i	−0.292467	+	0.0685843i
$985$	−35.8704			−1.14293
$986$	5.26522	−	7.65751i	0.167679	−	0.243865i
$987$	−11.2511	+	45.9390i	−0.358125	+	1.46225i
$988$	60.5177	−	23.2015i	1.92532	−	0.738139i
$989$	−4.02133	−	6.96515i	−0.127871	−	0.221479i
$990$	−40.9891	−	8.00086i	−1.30272	−	0.254284i
$991$	28.7025	+	16.5714i	0.911764	+	0.526407i	0.880998	−	0.473120i	$-0.156872\pi$
$991$	28.7025	+	16.5714i	0.911764	+	0.526407i	0.0307654	+	0.999527i	$0.490206\pi$
$992$	44.4360	−	34.0232i	1.41084	−	1.08024i
$993$	39.2907	−	19.7900i	1.24685	−	0.628016i
$994$	14.1644	−	3.79345i	0.449267	−	0.120321i
$995$	28.9243	+	16.6994i	0.916961	+	0.529408i
$996$	−15.0716	−	47.1984i	−0.477561	−	1.49554i
$997$			4.47112i			0.141602i	0.997490	+	0.0708009i	$0.0225555\pi$
$997$			4.47112i			0.141602i	−0.997490	+	0.0708009i	$0.977445\pi$
$998$	12.2205	+	8.40269i	0.386833	+	0.265982i
$999$	0.877671	+	2.38537i	0.0277683	+	0.0754698i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.cy.a.347.17	yes	184
7.2	even	3		504.2.bt.a.275.45	yes	184
8.3	odd	2	inner	504.2.cy.a.347.15	yes	184
9.2	odd	6		504.2.bt.a.11.48	yes	184
56.51	odd	6		504.2.bt.a.275.48	yes	184
63.2	odd	6	inner	504.2.cy.a.443.15	yes	184
72.11	even	6		504.2.bt.a.11.45	✓	184
504.443	even	6	inner	504.2.cy.a.443.17	yes	184

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bt.a.11.45	✓	184	72.11	even	6
504.2.bt.a.11.48	yes	184	9.2	odd	6
504.2.bt.a.275.45	yes	184	7.2	even	3
504.2.bt.a.275.48	yes	184	56.51	odd	6
504.2.cy.a.347.15	yes	184	8.3	odd	2	inner
504.2.cy.a.347.17	yes	184	1.1	even	1	trivial
504.2.cy.a.443.15	yes	184	63.2	odd	6	inner
504.2.cy.a.443.17	yes	184	504.443	even	6	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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.cy (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.16532 - 0.801263i) q^{2} +(-1.44822 - 0.950089i) q^{3} +(0.715955 + 1.86746i) q^{4} -2.40991 q^{5} +(0.926369 + 2.26756i) q^{6} +(1.71811 - 2.01199i) q^{7} +(0.662008 - 2.74986i) q^{8} +(1.19466 + 2.75187i) q^{9} +O(q^{10})\)	\(q+(-1.16532 - 0.801263i) q^{2} +(-1.44822 - 0.950089i) q^{3} +(0.715955 + 1.86746i) q^{4} -2.40991 q^{5} +(0.926369 + 2.26756i) q^{6} +(1.71811 - 2.01199i) q^{7} +(0.662008 - 2.74986i) q^{8} +(1.19466 + 2.75187i) q^{9} +(2.80833 + 1.93097i) q^{10} +4.08461i q^{11} +(0.737395 - 3.38471i) q^{12} +(4.84843 + 2.79924i) q^{13} +(-3.61428 + 0.967965i) q^{14} +(3.49008 + 2.28963i) q^{15} +(-2.97482 + 2.67404i) q^{16} +(-1.62392 - 0.937572i) q^{17} +(0.812802 - 4.16405i) q^{18} +(-2.89421 - 5.01292i) q^{19} +(-1.72539 - 4.50042i) q^{20} +(-4.39976 + 1.28145i) q^{21} +(3.27285 - 4.75989i) q^{22} +4.59423 q^{23} +(-3.57134 + 3.35343i) q^{24} +0.807680 q^{25} +(-3.40706 - 7.14689i) q^{26} +(0.884387 - 5.12034i) q^{27} +(4.98740 + 1.76800i) q^{28} +(-1.75217 - 3.03485i) q^{29} +(-2.23247 - 5.46463i) q^{30} +(8.56793 - 4.94669i) q^{31} +(5.60923 - 0.732503i) q^{32} +(3.88074 - 5.91540i) q^{33} +(1.14115 + 2.39376i) q^{34} +(-4.14049 + 4.84872i) q^{35} +(-4.28368 + 4.20120i) q^{36} +(-0.423619 + 0.244576i) q^{37} +(-0.643977 + 8.16069i) q^{38} +(-4.36205 - 8.66035i) q^{39} +(-1.59538 + 6.62693i) q^{40} +(1.66580 + 0.961751i) q^{41} +(6.15392 + 2.03207i) q^{42} +(-0.875300 - 1.51606i) q^{43} +(-7.62785 + 2.92440i) q^{44} +(-2.87903 - 6.63176i) q^{45} +(-5.35376 - 3.68119i) q^{46} +(5.16049 - 8.93824i) q^{47} +(6.84875 - 1.04624i) q^{48} +(-1.09622 - 6.91363i) q^{49} +(-0.941208 - 0.647164i) q^{50} +(1.46102 + 2.90068i) q^{51} +(-1.75622 + 11.0584i) q^{52} +(2.18330 - 3.78158i) q^{53} +(-5.13333 + 5.25822i) q^{54} -9.84355i q^{55} +(-4.39530 - 6.05651i) q^{56} +(-0.571273 + 10.0095i) q^{57} +(-0.389868 + 4.94053i) q^{58} +(1.50465 - 0.868708i) q^{59} +(-1.77706 + 8.15685i) q^{60} +(-5.69617 - 3.28868i) q^{61} +(-13.9480 - 1.10067i) q^{62} +(7.58929 + 2.32435i) q^{63} +(-7.12349 - 3.64086i) q^{64} +(-11.6843 - 6.74593i) q^{65} +(-9.26211 + 3.78386i) q^{66} +(4.36391 + 7.55852i) q^{67} +(0.588224 - 3.70387i) q^{68} +(-6.65344 - 4.36492i) q^{69} +(8.71011 - 2.33271i) q^{70} -3.91900 q^{71} +(8.35814 - 1.46340i) q^{72} +(-5.41527 + 9.37952i) q^{73} +(0.689623 + 0.0544196i) q^{74} +(-1.16970 - 0.767368i) q^{75} +(7.28930 - 8.99384i) q^{76} +(8.21820 + 7.01779i) q^{77} +(-1.85602 + 13.5873i) q^{78} +(12.1771 + 7.03046i) q^{79} +(7.16905 - 6.44419i) q^{80} +(-6.14556 + 6.57511i) q^{81} +(-1.17058 - 2.45550i) q^{82} +(12.3866 - 7.15139i) q^{83} +(-5.54308 - 7.29892i) q^{84} +(3.91351 + 2.25947i) q^{85} +(-0.194759 + 2.46805i) q^{86} +(-0.345852 + 6.05984i) q^{87} +(11.2321 + 2.70405i) q^{88} +(5.02733 - 2.90253i) q^{89} +(-1.95878 + 10.0350i) q^{90} +(13.9622 - 4.94561i) q^{91} +(3.28926 + 8.57954i) q^{92} +(-17.1080 - 0.976403i) q^{93} +(-13.1755 + 6.28102i) q^{94} +(6.97479 + 12.0807i) q^{95} +(-8.81932 - 4.26844i) q^{96} +(-4.47603 - 7.75271i) q^{97} +(-4.26219 + 8.93497i) q^{98} +(-11.2403 + 4.87973i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 184 q - 3 q^{2} - 2 q^{3} + q^{4} - 2 q^{6} - 2 q^{9}+O(q^{10}) \) 184 * q - 3 * q^2 - 2 * q^3 + q^4 - 2 * q^6 - 2 * q^9	\( 184 q - 3 q^{2} - 2 q^{3} + q^{4} - 2 q^{6} - 2 q^{9} - 6 q^{10} - 5 q^{12} - 3 q^{14} + q^{16} + 5 q^{18} - 4 q^{19} - 6 q^{20} + 2 q^{22} - 8 q^{24} + 148 q^{25} + 6 q^{26} - 8 q^{27} + 24 q^{30} - 33 q^{32} + 22 q^{33} - 4 q^{34} - 30 q^{35} - 38 q^{36} - 12 q^{40} - 12 q^{41} + 7 q^{42} - 4 q^{43} - 9 q^{44} - 6 q^{46} - 5 q^{48} - 2 q^{49} - 21 q^{50} + 26 q^{51} - 18 q^{52} - 40 q^{54} + 18 q^{56} + 4 q^{57} + 6 q^{58} - 6 q^{59} - 2 q^{60} - 8 q^{64} - 6 q^{65} + 43 q^{66} + 2 q^{67} - 18 q^{70} - 11 q^{72} - 4 q^{73} - 36 q^{75} + 2 q^{76} - 29 q^{78} - 87 q^{80} - 10 q^{81} - 4 q^{82} - 72 q^{83} - 65 q^{84} + 14 q^{88} + 24 q^{89} - 49 q^{90} - 36 q^{91} - 36 q^{92} + 9 q^{94} - 88 q^{96} - 4 q^{97} - 57 q^{98} + 10 q^{99}+O(q^{100}) \) 184 * q - 3 * q^2 - 2 * q^3 + q^4 - 2 * q^6 - 2 * q^9 - 6 * q^10 - 5 * q^12 - 3 * q^14 + q^16 + 5 * q^18 - 4 * q^19 - 6 * q^20 + 2 * q^22 - 8 * q^24 + 148 * q^25 + 6 * q^26 - 8 * q^27 + 24 * q^30 - 33 * q^32 + 22 * q^33 - 4 * q^34 - 30 * q^35 - 38 * q^36 - 12 * q^40 - 12 * q^41 + 7 * q^42 - 4 * q^43 - 9 * q^44 - 6 * q^46 - 5 * q^48 - 2 * q^49 - 21 * q^50 + 26 * q^51 - 18 * q^52 - 40 * q^54 + 18 * q^56 + 4 * q^57 + 6 * q^58 - 6 * q^59 - 2 * q^60 - 8 * q^64 - 6 * q^65 + 43 * q^66 + 2 * q^67 - 18 * q^70 - 11 * q^72 - 4 * q^73 - 36 * q^75 + 2 * q^76 - 29 * q^78 - 87 * q^80 - 10 * q^81 - 4 * q^82 - 72 * q^83 - 65 * q^84 + 14 * q^88 + 24 * q^89 - 49 * q^90 - 36 * q^91 - 36 * q^92 + 9 * q^94 - 88 * q^96 - 4 * q^97 - 57 * q^98 + 10 * q^99

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