LMFDB - Embedded newform 630.2.bi.a.479.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(479,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 3, 1]))

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

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

chi := DirichletCharacter("630.479");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.bi (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:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			479.20
Character	$\chi$	$=$	630.479
Dual form			630.2.bi.a.509.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(1.48333 + 0.894282i) q^{3} +1.00000 q^{4} +(0.990306 - 2.00482i) q^{5} +(-1.48333 - 0.894282i) q^{6} +(-2.20215 - 1.46647i) q^{7} -1.00000 q^{8} +(1.40052 + 2.65303i) q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(1.48333 + 0.894282i) q^{3} +1.00000 q^{4} +(0.990306 - 2.00482i) q^{5} +(-1.48333 - 0.894282i) q^{6} +(-2.20215 - 1.46647i) q^{7} -1.00000 q^{8} +(1.40052 + 2.65303i) q^{9} +(-0.990306 + 2.00482i) q^{10} +(0.646046 - 0.372995i) q^{11} +(1.48333 + 0.894282i) q^{12} +(-1.67087 - 2.89402i) q^{13} +(2.20215 + 1.46647i) q^{14} +(3.26182 - 2.08819i) q^{15} +1.00000 q^{16} +(4.20138 + 2.42567i) q^{17} +(-1.40052 - 2.65303i) q^{18} +(6.50055 - 3.75309i) q^{19} +(0.990306 - 2.00482i) q^{20} +(-1.95507 - 4.14460i) q^{21} +(-0.646046 + 0.372995i) q^{22} +(0.933507 - 1.61688i) q^{23} +(-1.48333 - 0.894282i) q^{24} +(-3.03859 - 3.97077i) q^{25} +(1.67087 + 2.89402i) q^{26} +(-0.295123 + 5.18776i) q^{27} +(-2.20215 - 1.46647i) q^{28} +(-0.644047 - 0.371841i) q^{29} +(-3.26182 + 2.08819i) q^{30} -5.00146i q^{31} -1.00000 q^{32} +(1.29186 + 0.0244738i) q^{33} +(-4.20138 - 2.42567i) q^{34} +(-5.12081 + 2.96266i) q^{35} +(1.40052 + 2.65303i) q^{36} +(5.78366 - 3.33920i) q^{37} +(-6.50055 + 3.75309i) q^{38} +(0.109633 - 5.78701i) q^{39} +(-0.990306 + 2.00482i) q^{40} +(0.849794 + 1.47189i) q^{41} +(1.95507 + 4.14460i) q^{42} +(-7.64047 - 4.41123i) q^{43} +(0.646046 - 0.372995i) q^{44} +(6.70578 - 0.180480i) q^{45} +(-0.933507 + 1.61688i) q^{46} +11.6099i q^{47} +(1.48333 + 0.894282i) q^{48} +(2.69893 + 6.45877i) q^{49} +(3.03859 + 3.97077i) q^{50} +(4.06279 + 7.35528i) q^{51} +(-1.67087 - 2.89402i) q^{52} +(2.94339 - 5.09811i) q^{53} +(0.295123 - 5.18776i) q^{54} +(-0.108003 - 1.66458i) q^{55} +(2.20215 + 1.46647i) q^{56} +(12.9988 + 0.246257i) q^{57} +(0.644047 + 0.371841i) q^{58} -4.66316 q^{59} +(3.26182 - 2.08819i) q^{60} +1.71256i q^{61} +5.00146i q^{62} +(0.806427 - 7.89618i) q^{63} +1.00000 q^{64} +(-7.45666 + 0.483811i) q^{65} +(-1.29186 - 0.0244738i) q^{66} +4.53308i q^{67} +(4.20138 + 2.42567i) q^{68} +(2.83065 - 1.56355i) q^{69} +(5.12081 - 2.96266i) q^{70} +4.17217i q^{71} +(-1.40052 - 2.65303i) q^{72} +(5.10736 - 8.84620i) q^{73} +(-5.78366 + 3.33920i) q^{74} +(-0.956236 - 8.60730i) q^{75} +(6.50055 - 3.75309i) q^{76} +(-1.96968 - 0.126017i) q^{77} +(-0.109633 + 5.78701i) q^{78} -6.21613 q^{79} +(0.990306 - 2.00482i) q^{80} +(-5.07709 + 7.43123i) q^{81} +(-0.849794 - 1.47189i) q^{82} +(2.26849 + 1.30971i) q^{83} +(-1.95507 - 4.14460i) q^{84} +(9.02367 - 6.02085i) q^{85} +(7.64047 + 4.41123i) q^{86} +(-0.622802 - 1.12752i) q^{87} +(-0.646046 + 0.372995i) q^{88} +(7.58595 + 13.1393i) q^{89} +(-6.70578 + 0.180480i) q^{90} +(-0.564503 + 8.82335i) q^{91} +(0.933507 - 1.61688i) q^{92} +(4.47272 - 7.41881i) q^{93} -11.6099i q^{94} +(-1.08673 - 16.7491i) q^{95} +(-1.48333 - 0.894282i) q^{96} +(-2.32004 + 4.01843i) q^{97} +(-2.69893 - 6.45877i) q^{98} +(1.89437 + 1.19159i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 48 q^{2} + 48 q^{4} - 3 q^{7} - 48 q^{8}+O(q^{10}) $ 48 * q - 48 * q^2 + 48 * q^4 - 3 * q^7 - 48 * q^8	$ 48 q - 48 q^{2} + 48 q^{4} - 3 q^{7} - 48 q^{8} + 6 q^{11} + 3 q^{14} + 6 q^{15} + 48 q^{16} + 8 q^{21} - 6 q^{22} - 3 q^{23} + 18 q^{25} - 3 q^{28} - 3 q^{29} - 6 q^{30} - 48 q^{32} - 18 q^{35} - 18 q^{39} - 3 q^{41} - 8 q^{42} + 6 q^{44} + 15 q^{45} + 3 q^{46} + 3 q^{49} - 18 q^{50} + 10 q^{51} + 42 q^{55} + 3 q^{56} + 22 q^{57} + 3 q^{58} + 6 q^{60} + 43 q^{63} + 48 q^{64} - 12 q^{65} - 42 q^{69} + 18 q^{70} + 18 q^{73} + 18 q^{75} + 12 q^{77} + 18 q^{78} + 8 q^{81} + 3 q^{82} - 9 q^{83} + 8 q^{84} + 33 q^{85} + 15 q^{87} - 6 q^{88} - 33 q^{89} - 15 q^{90} - 3 q^{92} + 8 q^{93} + 24 q^{97} - 3 q^{98} - 26 q^{99}+O(q^{100}) $ 48 * q - 48 * q^2 + 48 * q^4 - 3 * q^7 - 48 * q^8 + 6 * q^11 + 3 * q^14 + 6 * q^15 + 48 * q^16 + 8 * q^21 - 6 * q^22 - 3 * q^23 + 18 * q^25 - 3 * q^28 - 3 * q^29 - 6 * q^30 - 48 * q^32 - 18 * q^35 - 18 * q^39 - 3 * q^41 - 8 * q^42 + 6 * q^44 + 15 * q^45 + 3 * q^46 + 3 * q^49 - 18 * q^50 + 10 * q^51 + 42 * q^55 + 3 * q^56 + 22 * q^57 + 3 * q^58 + 6 * q^60 + 43 * q^63 + 48 * q^64 - 12 * q^65 - 42 * q^69 + 18 * q^70 + 18 * q^73 + 18 * q^75 + 12 * q^77 + 18 * q^78 + 8 * q^81 + 3 * q^82 - 9 * q^83 + 8 * q^84 + 33 * q^85 + 15 * q^87 - 6 * q^88 - 33 * q^89 - 15 * q^90 - 3 * q^92 + 8 * q^93 + 24 * q^97 - 3 * q^98 - 26 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	1.48333	+	0.894282i	0.856399	+	0.516314i
$3$	1.48333	+	0.894282i	0.856399	+	0.516314i
$4$	1.00000			0.500000
$5$	0.990306	−	2.00482i	0.442878	−	0.896582i
$5$	0.990306	−	2.00482i	0.442878	−	0.896582i
$6$	−1.48333	−	0.894282i	−0.605566	−	0.365089i
$7$	−2.20215	−	1.46647i	−0.832335	−	0.554274i
$7$	−2.20215	−	1.46647i	−0.832335	−	0.554274i
$8$	−1.00000			−0.353553
$9$	1.40052	+	2.65303i	0.466840	+	0.884342i
$10$	−0.990306	+	2.00482i	−0.313162	+	0.633979i
$11$	0.646046	−	0.372995i	0.194790	−	0.112462i	−0.399433	−	0.916762i	$-0.630793\pi$
$11$	0.646046	−	0.372995i	0.194790	−	0.112462i	0.594223	+	0.804300i	$0.297460\pi$
$12$	1.48333	+	0.894282i	0.428200	+	0.258157i
$13$	−1.67087	−	2.89402i	−0.463415	−	0.802658i	0.535714	−	0.844400i	$-0.320043\pi$
$13$	−1.67087	−	2.89402i	−0.463415	−	0.802658i	−0.999128	+	0.0417418i	$0.986709\pi$
$14$	2.20215	+	1.46647i	0.588549	+	0.391931i
$15$	3.26182	−	2.08819i	0.842198	−	0.539168i
$16$	1.00000			0.250000
$17$	4.20138	+	2.42567i	1.01898	+	0.588311i	0.913810	−	0.406143i	$-0.133127\pi$
$17$	4.20138	+	2.42567i	1.01898	+	0.588311i	0.105175	+	0.994454i	$0.466460\pi$
$18$	−1.40052	−	2.65303i	−0.330106	−	0.625324i
$19$	6.50055	−	3.75309i	1.49133	−	0.861018i	0.491377	−	0.870947i	$-0.336494\pi$
$19$	6.50055	−	3.75309i	1.49133	−	0.861018i	0.999951	+	0.00992860i	$0.00316042\pi$
$20$	0.990306	−	2.00482i	0.221439	−	0.448291i
$21$	−1.95507	−	4.14460i	−0.426632	−	0.904425i
$22$	−0.646046	+	0.372995i	−0.137738	+	0.0795228i
$23$	0.933507	−	1.61688i	0.194650	−	0.337143i	−0.752136	−	0.659008i	$-0.770976\pi$
$23$	0.933507	−	1.61688i	0.194650	−	0.337143i	0.946786	+	0.321865i	$0.104310\pi$
$24$	−1.48333	−	0.894282i	−0.302783	−	0.182545i
$25$	−3.03859	−	3.97077i	−0.607718	−	0.794153i
$26$	1.67087	+	2.89402i	0.327684	+	0.567565i
$27$	−0.295123	+	5.18776i	−0.0567965	+	0.998386i
$28$	−2.20215	−	1.46647i	−0.416167	−	0.277137i
$29$	−0.644047	−	0.371841i	−0.119597	−	0.0690491i	0.439008	−	0.898483i	$-0.355330\pi$
$29$	−0.644047	−	0.371841i	−0.119597	−	0.0690491i	−0.558605	+	0.829434i	$0.688663\pi$
$30$	−3.26182	+	2.08819i	−0.595524	+	0.381249i
$31$		−	5.00146i		−	0.898289i	−0.893459	−	0.449145i	$-0.851729\pi$
$31$		−	5.00146i		−	0.898289i	0.893459	−	0.449145i	$-0.148271\pi$
$32$	−1.00000			−0.176777
$33$	1.29186	+	0.0244738i	0.224884	+	0.00426034i
$34$	−4.20138	−	2.42567i	−0.720531	−	0.415999i
$35$	−5.12081	+	2.96266i	−0.865575	+	0.500780i
$36$	1.40052	+	2.65303i	0.233420	+	0.442171i
$37$	5.78366	−	3.33920i	0.950827	−	0.548960i	0.0574896	−	0.998346i	$-0.481690\pi$
$37$	5.78366	−	3.33920i	0.950827	−	0.548960i	0.893338	+	0.449386i	$0.148357\pi$
$38$	−6.50055	+	3.75309i	−1.05453	+	0.608832i
$39$	0.109633	−	5.78701i	0.0175553	−	0.926663i
$40$	−0.990306	+	2.00482i	−0.156581	+	0.316990i
$41$	0.849794	+	1.47189i	0.132716	+	0.229870i	0.924722	−	0.380642i	$-0.124297\pi$
$41$	0.849794	+	1.47189i	0.132716	+	0.229870i	−0.792007	+	0.610512i	$0.790964\pi$
$42$	1.95507	+	4.14460i	0.301674	+	0.639525i
$43$	−7.64047	−	4.41123i	−1.16516	−	0.672706i	−0.212625	−	0.977134i	$-0.568201\pi$
$43$	−7.64047	−	4.41123i	−1.16516	−	0.672706i	−0.952535	+	0.304428i	$0.901535\pi$
$44$	0.646046	−	0.372995i	0.0973951	−	0.0562311i
$45$	6.70578	−	0.180480i	0.999638	−	0.0269043i
$46$	−0.933507	+	1.61688i	−0.137638	+	0.238396i
$47$			11.6099i			1.69347i	0.532011	+	0.846737i	$0.321436\pi$
$47$			11.6099i			1.69347i	−0.532011	+	0.846737i	$0.678564\pi$
$48$	1.48333	+	0.894282i	0.214100	+	0.129078i
$49$	2.69893	+	6.45877i	0.385562	+	0.922682i
$50$	3.03859	+	3.97077i	0.429721	+	0.561551i
$51$	4.06279	+	7.35528i	0.568904	+	1.02994i
$52$	−1.67087	−	2.89402i	−0.231707	−	0.401329i
$53$	2.94339	−	5.09811i	0.404306	−	0.700279i	−0.589934	−	0.807451i	$-0.700846\pi$
$53$	2.94339	−	5.09811i	0.404306	−	0.700279i	0.994240	+	0.107172i	$0.0341797\pi$
$54$	0.295123	−	5.18776i	0.0401612	−	0.705965i
$55$	−0.108003	−	1.66458i	−0.0145632	−	0.224452i
$56$	2.20215	+	1.46647i	0.294275	+	0.195965i
$57$	12.9988	+	0.246257i	1.72173	+	0.0326175i
$58$	0.644047	+	0.371841i	0.0845675	+	0.0488251i
$59$	−4.66316			−0.607091			−0.303546	−	0.952817i	$-0.598171\pi$
$59$	−4.66316			−0.607091			−0.303546	+	0.952817i	$0.598171\pi$
$60$	3.26182	−	2.08819i	0.421099	−	0.269584i
$61$			1.71256i			0.219270i	0.993972	+	0.109635i	$0.0349683\pi$
$61$			1.71256i			0.219270i	−0.993972	+	0.109635i	$0.965032\pi$
$62$			5.00146i			0.635187i
$63$	0.806427	−	7.89618i	0.101600	−	0.994825i
$64$	1.00000			0.125000
$65$	−7.45666	+	0.483811i	−0.924885	+	0.0600094i
$66$	−1.29186	−	0.0244738i	−0.159017	−	0.00301252i
$67$			4.53308i			0.553804i	0.960898	+	0.276902i	$0.0893077\pi$
$67$			4.53308i			0.553804i	−0.960898	+	0.276902i	$0.910692\pi$
$68$	4.20138	+	2.42567i	0.509492	+	0.294155i
$69$	2.83065	−	1.56355i	0.340770	−	0.188229i
$70$	5.12081	−	2.96266i	0.612054	−	0.354105i
$71$			4.17217i			0.495145i	0.968869	+	0.247573i	$0.0796329\pi$
$71$			4.17217i			0.495145i	−0.968869	+	0.247573i	$0.920367\pi$
$72$	−1.40052	−	2.65303i	−0.165053	−	0.312662i
$73$	5.10736	−	8.84620i	0.597771	−	1.03537i	−0.395378	−	0.918518i	$-0.629387\pi$
$73$	5.10736	−	8.84620i	0.597771	−	1.03537i	0.993149	−	0.116851i	$-0.0372802\pi$
$74$	−5.78366	+	3.33920i	−0.672337	+	0.388174i
$75$	−0.956236	−	8.60730i	−0.110417	−	0.993885i
$76$	6.50055	−	3.75309i	0.745664	−	0.430509i
$77$	−1.96968	−	0.126017i	−0.224466	−	0.0143609i
$78$	−0.109633	+	5.78701i	−0.0124135	+	0.655250i
$79$	−6.21613			−0.699369			−0.349685	−	0.936867i	$-0.613711\pi$
$79$	−6.21613			−0.699369			−0.349685	+	0.936867i	$0.613711\pi$
$80$	0.990306	−	2.00482i	0.110720	−	0.224145i
$81$	−5.07709	+	7.43123i	−0.564121	+	0.825692i
$82$	−0.849794	−	1.47189i	−0.0938441	−	0.162543i
$83$	2.26849	+	1.30971i	0.248999	+	0.143760i	0.619306	−	0.785150i	$-0.287414\pi$
$83$	2.26849	+	1.30971i	0.248999	+	0.143760i	−0.370307	+	0.928910i	$0.620747\pi$
$84$	−1.95507	−	4.14460i	−0.213316	−	0.452213i
$85$	9.02367	−	6.02085i	0.978755	−	0.653052i
$86$	7.64047	+	4.41123i	0.823893	+	0.475675i
$87$	−0.622802	−	1.12752i	−0.0667714	−	0.120883i
$88$	−0.646046	+	0.372995i	−0.0688688	+	0.0397614i
$89$	7.58595	+	13.1393i	0.804109	+	1.39276i	0.916891	+	0.399138i	$0.130691\pi$
$89$	7.58595	+	13.1393i	0.804109	+	1.39276i	−0.112782	+	0.993620i	$0.535976\pi$
$90$	−6.70578	+	0.180480i	−0.706851	+	0.0190242i
$91$	−0.564503	+	8.82335i	−0.0591760	+	0.924938i
$92$	0.933507	−	1.61688i	0.0973249	−	0.168572i
$93$	4.47272	−	7.41881i	0.463799	−	0.769295i
$94$		−	11.6099i		−	1.19747i
$95$	−1.08673	−	16.7491i	−0.111497	−	1.71842i
$96$	−1.48333	−	0.894282i	−0.151391	−	0.0912723i
$97$	−2.32004	+	4.01843i	−0.235565	+	0.408010i	−0.959437	−	0.281924i	$-0.909027\pi$
$97$	−2.32004	+	4.01843i	−0.235565	+	0.408010i	0.723872	+	0.689934i	$0.242361\pi$
$98$	−2.69893	−	6.45877i	−0.272633	−	0.652435i
$99$	1.89437	+	1.19159i	0.190391	+	0.119759i
$100$	−3.03859	−	3.97077i	−0.303859	−	0.397077i
$101$	−5.48710	−	9.50393i	−0.545986	−	0.945676i	−0.998544	−	0.0539412i	$-0.982822\pi$
$101$	−5.48710	−	9.50393i	−0.545986	−	0.945676i	0.452558	−	0.891735i	$-0.350512\pi$
$102$	−4.06279	−	7.35528i	−0.402276	−	0.728281i
$103$	3.33713	−	5.78008i	0.328817	−	0.569528i	−0.653460	−	0.756961i	$-0.726683\pi$
$103$	3.33713	−	5.78008i	0.328817	−	0.569528i	0.982277	+	0.187433i	$0.0600166\pi$
$104$	1.67087	+	2.89402i	0.163842	+	0.283782i
$105$	−10.2453	−	0.184858i	−0.999837	−	0.0180403i
$106$	−2.94339	+	5.09811i	−0.285888	+	0.495172i
$107$	−6.82770	−	11.8259i	−0.660058	−	1.14325i	−0.980600	−	0.196020i	$-0.937198\pi$
$107$	−6.82770	−	11.8259i	−0.660058	−	1.14325i	0.320541	−	0.947234i	$-0.396135\pi$
$108$	−0.295123	+	5.18776i	−0.0283982	+	0.499193i
$109$	−5.13894	+	8.90090i	−0.492221	+	0.852551i	−0.999960	−	0.00895944i	$-0.997148\pi$
$109$	−5.13894	+	8.90090i	−0.492221	+	0.852551i	0.507739	+	0.861511i	$0.330481\pi$
$110$	0.108003	+	1.66458i	0.0102977	+	0.158712i
$111$	11.5652	+	0.219099i	1.09772	+	0.0207960i
$112$	−2.20215	−	1.46647i	−0.208084	−	0.138568i
$113$	10.0641	+	17.4316i	0.946754	+	1.63983i	0.752201	+	0.658934i	$0.228992\pi$
$113$	10.0641	+	17.4316i	0.946754	+	1.63983i	0.194553	+	0.980892i	$0.437674\pi$
$114$	−12.9988	−	0.246257i	−1.21745	−	0.0230640i
$115$	−2.31710	−	3.47272i	−0.216070	−	0.323833i
$116$	−0.644047	−	0.371841i	−0.0597983	−	0.0345245i
$117$	5.33784	−	8.48599i	0.493483	−	0.784530i
$118$	4.66316			0.429278
$119$	−5.69490	−	11.5029i	−0.522051	−	1.05447i
$120$	−3.26182	+	2.08819i	−0.297762	+	0.190625i
$121$	−5.22175	+	9.04434i	−0.474704	+	0.822212i
$122$		−	1.71256i		−	0.155048i
$123$	−0.0557586	+	2.94324i	−0.00502759	+	0.265383i
$124$		−	5.00146i		−	0.449145i
$125$	−10.9698	+	2.15954i	−0.981168	+	0.193155i
$126$	−0.806427	+	7.89618i	−0.0718423	+	0.703448i
$127$			2.11883i			0.188015i	0.995571	+	0.0940077i	$0.0299678\pi$
$127$			2.11883i			0.188015i	−0.995571	+	0.0940077i	$0.970032\pi$
$128$	−1.00000			−0.0883883
$129$	−7.38843	−	13.3760i	−0.650515	−	1.17769i
$130$	7.45666	−	0.483811i	0.653992	−	0.0424330i
$131$	−7.87875	+	13.6464i	−0.688370	+	1.19229i	0.283995	+	0.958826i	$0.408340\pi$
$131$	−7.87875	+	13.6464i	−0.688370	+	1.19229i	−0.972365	+	0.233465i	$0.924993\pi$
$132$	1.29186	+	0.0244738i	0.112442	+	0.00213017i
$133$	−19.8190	−	1.26798i	−1.71852	−	0.109948i
$134$		−	4.53308i		−	0.391599i
$135$	10.1083	+	5.72914i	0.869980	+	0.493086i
$136$	−4.20138	−	2.42567i	−0.360265	−	0.207999i
$137$	5.50358	+	9.53248i	0.470202	+	0.814415i	0.999419	−	0.0340720i	$-0.0108475\pi$
$137$	5.50358	+	9.53248i	0.470202	+	0.814415i	−0.529217	+	0.848487i	$0.677514\pi$
$138$	−2.83065	+	1.56355i	−0.240961	+	0.133098i
$139$	−14.5065	+	8.37531i	−1.23042	+	0.710385i	−0.967118	−	0.254328i	$-0.918146\pi$
$139$	−14.5065	+	8.37531i	−1.23042	+	0.710385i	−0.263304	+	0.964713i	$0.584812\pi$
$140$	−5.12081	+	2.96266i	−0.432787	+	0.250390i
$141$	−10.3825	+	17.2212i	−0.874364	+	1.45029i
$142$		−	4.17217i		−	0.350121i
$143$	−2.15891	−	1.24645i	−0.180537	−	0.104233i
$144$	1.40052	+	2.65303i	0.116710	+	0.221085i
$145$	−1.38328	+	0.922960i	−0.114875	+	0.0766477i
$146$	−5.10736	+	8.84620i	−0.422688	+	0.732117i
$147$	−1.77257	+	11.9941i	−0.146199	+	0.989255i
$148$	5.78366	−	3.33920i	0.475414	−	0.274480i
$149$	18.6650	+	10.7762i	1.52909	+	0.882823i	0.999400	+	0.0346347i	$0.0110268\pi$
$149$	18.6650	+	10.7762i	1.52909	+	0.882823i	0.529695	+	0.848188i	$0.322307\pi$
$150$	0.956236	+	8.60730i	0.0780763	+	0.702783i
$151$	7.68913	+	13.3180i	0.625732	+	1.08380i	0.988399	+	0.151881i	$0.0485332\pi$
$151$	7.68913	+	13.3180i	0.625732	+	1.08380i	−0.362666	+	0.931919i	$0.618133\pi$
$152$	−6.50055	+	3.75309i	−0.527264	+	0.304416i
$153$	−0.551242	+	14.5436i	−0.0445653	+	1.17578i
$154$	1.96968	+	0.126017i	0.158721	+	0.0101547i
$155$	−10.0270	−	4.95298i	−0.805390	−	0.397833i
$156$	0.109633	−	5.78701i	0.00877764	−	0.463332i
$157$	−7.04317			−0.562106			−0.281053	−	0.959692i	$-0.590684\pi$
$157$	−7.04317			−0.562106			−0.281053	+	0.959692i	$0.590684\pi$
$158$	6.21613			0.494529
$159$	8.92516	−	4.92994i	0.707811	−	0.390970i
$160$	−0.990306	+	2.00482i	−0.0782906	+	0.158495i
$161$	−4.42683	+	2.19166i	−0.348883	+	0.172727i
$162$	5.07709	−	7.43123i	0.398894	−	0.583853i
$163$	−6.38815	+	3.68820i	−0.500359	+	0.288882i	−0.728862	−	0.684661i	$-0.759950\pi$
$163$	−6.38815	+	3.68820i	−0.500359	+	0.288882i	0.228503	+	0.973543i	$0.426617\pi$
$164$	0.849794	+	1.47189i	0.0663578	+	0.114935i
$165$	1.32840	−	2.56571i	0.103416	−	0.199740i
$166$	−2.26849	−	1.30971i	−0.176069	−	0.101653i
$167$	−14.6090	+	8.43452i	−1.13048	+	0.652683i	−0.944055	−	0.329787i	$-0.893023\pi$
$167$	−14.6090	+	8.43452i	−1.13048	+	0.652683i	−0.186424	+	0.982469i	$0.559690\pi$
$168$	1.95507	+	4.14460i	0.150837	+	0.319763i
$169$	0.916415	−	1.58728i	0.0704935	−	0.122098i
$170$	−9.02367	+	6.02085i	−0.692084	+	0.461778i
$171$	19.0612	+	11.9898i	1.45765	+	0.916886i
$172$	−7.64047	−	4.41123i	−0.582580	−	0.336353i
$173$		−	10.2449i		−	0.778905i	−0.921046	−	0.389453i	$-0.872664\pi$
$173$		−	10.2449i		−	0.778905i	0.921046	−	0.389453i	$-0.127336\pi$
$174$	0.622802	+	1.12752i	0.0472145	+	0.0854771i
$175$	0.868416	+	13.2002i	0.0656461	+	0.997843i
$176$	0.646046	−	0.372995i	0.0486976	−	0.0281156i
$177$	−6.91699	−	4.17018i	−0.519913	−	0.313450i
$178$	−7.58595	−	13.1393i	−0.568591	−	0.984829i
$179$	−16.4577	−	9.50188i	−1.23011	−	0.710204i	−0.263056	−	0.964780i	$-0.584731\pi$
$179$	−16.4577	−	9.50188i	−1.23011	−	0.710204i	−0.967053	+	0.254577i	$0.918064\pi$
$180$	6.70578	−	0.180480i	0.499819	−	0.0134522i
$181$			5.53416i			0.411351i	0.978620	+	0.205676i	$0.0659391\pi$
$181$			5.53416i			0.411351i	−0.978620	+	0.205676i	$0.934061\pi$
$182$	0.564503	−	8.82335i	0.0418437	−	0.654030i
$183$	−1.53151	+	2.54028i	−0.113212	+	0.187783i
$184$	−0.933507	+	1.61688i	−0.0688191	+	0.119198i
$185$	−0.966888	−	14.9020i	−0.0710870	−	1.09562i
$186$	−4.47272	+	7.41881i	−0.327956	+	0.543973i
$187$	3.61905			0.264651
$188$			11.6099i			0.846737i
$189$	8.25761	−	10.9914i	0.600653	−	0.799510i
$190$	1.08673	+	16.7491i	0.0788400	+	1.21511i
$191$		−	20.0241i		−	1.44889i	−0.689330	−	0.724447i	$-0.742095\pi$
$191$		−	20.0241i		−	1.44889i	0.689330	−	0.724447i	$-0.257905\pi$
$192$	1.48333	+	0.894282i	0.107050	+	0.0645392i
$193$		−	19.0139i		−	1.36865i	−0.729176	−	0.684327i	$-0.760096\pi$
$193$		−	19.0139i		−	1.36865i	0.729176	−	0.684327i	$-0.239904\pi$
$194$	2.32004	−	4.01843i	0.166569	−	0.288506i
$195$	−11.4933	−	5.95071i	−0.823054	−	0.426139i
$196$	2.69893	+	6.45877i	0.192781	+	0.461341i
$197$	6.94184			0.494586			0.247293	−	0.968941i	$-0.420459\pi$
$197$	6.94184			0.494586			0.247293	+	0.968941i	$0.420459\pi$
$198$	−1.89437	−	1.19159i	−0.134627	−	0.0846826i
$199$	−3.90645	−	2.25539i	−0.276921	−	0.159880i	0.355108	−	0.934825i	$-0.384444\pi$
$199$	−3.90645	−	2.25539i	−0.276921	−	0.159880i	−0.632029	+	0.774945i	$0.717777\pi$
$200$	3.03859	+	3.97077i	0.214861	+	0.280776i
$201$	−4.05385	+	6.72404i	−0.285937	+	0.474277i
$202$	5.48710	+	9.50393i	0.386071	+	0.668694i
$203$	0.872995	+	1.76332i	0.0612722	+	0.123761i
$204$	4.06279	+	7.35528i	0.284452	+	0.514972i
$205$	3.79242	−	0.246064i	0.264874	−	0.0171859i
$206$	−3.33713	+	5.78008i	−0.232509	+	0.402717i
$207$	5.59702	+	0.212143i	0.389020	+	0.0147450i
$208$	−1.67087	−	2.89402i	−0.115854	−	0.200664i
$209$	2.79977	−	4.84934i	0.193664	−	0.335436i
$210$	10.2453	+	0.184858i	0.706992	+	0.0127564i
$211$	3.92397	+	6.79652i	0.270137	+	0.467892i	0.968897	−	0.247465i	$-0.0795976\pi$
$211$	3.92397	+	6.79652i	0.270137	+	0.467892i	−0.698759	+	0.715357i	$0.746264\pi$
$212$	2.94339	−	5.09811i	0.202153	−	0.350140i
$213$	−3.73110	+	6.18869i	−0.255650	+	0.424042i
$214$	6.82770	+	11.8259i	0.466732	+	0.808403i
$215$	−16.4101	+	10.9493i	−1.11916	+	0.746735i
$216$	0.295123	−	5.18776i	0.0200806	−	0.352983i
$217$	−7.33450	+	11.0140i	−0.497898	+	0.747677i
$218$	5.13894	−	8.90090i	0.348053	−	0.602845i
$219$	15.4869	−	8.55440i	1.04651	−	0.578053i
$220$	−0.108003	−	1.66458i	−0.00728159	−	0.112226i
$221$		−	16.2119i		−	1.09053i
$222$	−11.5652	−	0.219099i	−0.776208	−	0.0147050i
$223$	−10.7610	+	18.6387i	−0.720612	+	1.24814i	0.240143	+	0.970738i	$0.422806\pi$
$223$	−10.7610	+	18.6387i	−0.720612	+	1.24814i	−0.960755	+	0.277399i	$0.910528\pi$
$224$	2.20215	+	1.46647i	0.147137	+	0.0979827i
$225$	6.27894	−	13.6226i	0.418596	−	0.908173i
$226$	−10.0641	−	17.4316i	−0.669456	−	1.15953i
$227$	6.95237	−	4.01395i	0.461445	−	0.266415i	−0.251207	−	0.967933i	$-0.580827\pi$
$227$	6.95237	−	4.01395i	0.461445	−	0.266415i	0.712652	+	0.701518i	$0.247494\pi$
$228$	12.9988	+	0.246257i	0.860864	+	0.0163087i
$229$	−16.6860	−	9.63368i	−1.10264	−	0.636612i	−0.165730	−	0.986171i	$-0.552998\pi$
$229$	−16.6860	−	9.63368i	−1.10264	−	0.636612i	−0.936914	+	0.349560i	$0.886331\pi$
$230$	2.31710	+	3.47272i	0.152785	+	0.228984i
$231$	−2.80898	−	1.94837i	−0.184817	−	0.128193i
$232$	0.644047	+	0.371841i	0.0422837	+	0.0244125i
$233$	−0.572350	−	0.991339i	−0.0374959	−	0.0649448i	0.846668	−	0.532121i	$-0.178605\pi$
$233$	−0.572350	−	0.991339i	−0.0374959	−	0.0649448i	−0.884164	+	0.467176i	$0.845271\pi$
$234$	−5.33784	+	8.48599i	−0.348945	+	0.554746i
$235$	23.2757	+	11.4973i	1.51834	+	0.750003i
$236$	−4.66316			−0.303546
$237$	−9.22055	−	5.55897i	−0.598939	−	0.361094i
$238$	5.69490	+	11.5029i	0.369145	+	0.745621i
$239$	10.1997	−	5.88880i	0.659764	−	0.380915i	−0.132423	−	0.991193i	$-0.542276\pi$
$239$	10.1997	−	5.88880i	0.659764	−	0.380915i	0.792187	+	0.610279i	$0.208942\pi$
$240$	3.26182	−	2.08819i	0.210550	−	0.134792i
$241$	19.9120	−	11.4962i	1.28265	−	0.740536i	0.305314	−	0.952252i	$-0.401238\pi$
$241$	19.9120	−	11.4962i	1.28265	−	0.740536i	0.977331	+	0.211716i	$0.0679051\pi$
$242$	5.22175	−	9.04434i	0.335667	−	0.581392i
$243$	−14.1766	+	6.48260i	−0.909429	+	0.415859i
$244$			1.71256i			0.109635i
$245$	15.6214	+	0.985300i	0.998017	+	0.0629485i
$246$	0.0557586	−	2.94324i	0.00355504	−	0.187654i
$247$	−21.7231	−	12.5418i	−1.38221	−	0.798017i
$248$			5.00146i			0.317593i
$249$	2.19366	+	3.97140i	0.139018	+	0.251677i
$250$	10.9698	−	2.15954i	0.693791	−	0.136581i
$251$	1.44964			0.0915002			0.0457501	−	0.998953i	$-0.485432\pi$
$251$	1.44964			0.0915002			0.0457501	+	0.998953i	$0.485432\pi$
$252$	0.806427	−	7.89618i	0.0508002	−	0.497413i
$253$		−	1.39277i		−	0.0875630i
$254$		−	2.11883i		−	0.132947i
$255$	18.7694	−	0.861179i	1.17538	−	0.0539291i
$256$	1.00000			0.0625000
$257$	6.07764	+	3.50893i	0.379113	+	0.218881i	0.677432	−	0.735585i	$-0.263093\pi$
$257$	6.07764	+	3.50893i	0.379113	+	0.218881i	−0.298319	+	0.954466i	$0.596426\pi$
$258$	7.38843	+	13.3760i	0.459984	+	0.832755i
$259$	−17.6333	−	1.12815i	−1.09568	−	0.0700998i
$260$	−7.45666	+	0.483811i	−0.462442	+	0.0300047i
$261$	0.0845022	−	2.22944i	0.00523056	−	0.137999i
$262$	7.87875	−	13.6464i	0.486751	−	0.843077i
$263$	−1.32494	−	2.29487i	−0.0816996	−	0.141508i	0.822281	−	0.569082i	$-0.192701\pi$
$263$	−1.32494	−	2.29487i	−0.0816996	−	0.141508i	−0.903980	+	0.427575i	$0.859368\pi$
$264$	−1.29186	−	0.0244738i	−0.0795085	−	0.00150626i
$265$	−7.30592	−	10.9497i	−0.448799	−	0.672632i
$266$	19.8190	+	1.26798i	1.21518	+	0.0777451i
$267$	−0.497747	+	26.2738i	−0.0304616	+	1.60793i
$268$			4.53308i			0.276902i
$269$	−11.9338	+	20.6700i	−0.727618	+	1.26027i	0.230269	+	0.973127i	$0.426039\pi$
$269$	−11.9338	+	20.6700i	−0.727618	+	1.26027i	−0.957887	+	0.287145i	$0.907294\pi$
$270$	−10.1083	−	5.72914i	−0.615169	−	0.348665i
$271$	−16.9678	+	9.79635i	−1.03072	+	0.595086i	−0.917190	−	0.398449i	$-0.869549\pi$
$271$	−16.9678	+	9.79635i	−1.03072	+	0.595086i	−0.113528	+	0.993535i	$0.536215\pi$
$272$	4.20138	+	2.42567i	0.254746	+	0.147078i
$273$	−8.72791	+	12.5831i	−0.528237	+	0.761563i
$274$	−5.50358	−	9.53248i	−0.332483	−	0.575878i
$275$	−3.44414	−	1.43192i	−0.207690	−	0.0863481i
$276$	2.83065	−	1.56355i	0.170385	−	0.0941145i
$277$	17.2708	−	9.97128i	1.03770	−	0.599116i	0.118519	−	0.992952i	$-0.462185\pi$
$277$	17.2708	−	9.97128i	1.03770	−	0.599116i	0.919181	+	0.393835i	$0.128852\pi$
$278$	14.5065	−	8.37531i	0.870040	−	0.502318i
$279$	13.2690	−	7.00465i	0.794395	−	0.419357i
$280$	5.12081	−	2.96266i	0.306027	−	0.177053i
$281$	−2.03902	−	1.17723i	−0.121638	−	0.0702277i	0.437947	−	0.899001i	$-0.355706\pi$
$281$	−2.03902	−	1.17723i	−0.121638	−	0.0702277i	−0.559584	+	0.828773i	$0.689039\pi$
$282$	10.3825	−	17.2212i	0.618269	−	1.02551i
$283$	−8.82966			−0.524869			−0.262434	−	0.964950i	$-0.584525\pi$
$283$	−8.82966			−0.524869			−0.262434	+	0.964950i	$0.584525\pi$
$284$			4.17217i			0.247573i
$285$	13.3665	−	25.8163i	0.791760	−	1.52922i
$286$	2.15891	+	1.24645i	0.127659	+	0.0737041i
$287$	0.287103	−	4.48751i	0.0169472	−	0.264889i
$288$	−1.40052	−	2.65303i	−0.0825264	−	0.156331i
$289$	3.26772	+	5.65986i	0.192219	+	0.332933i
$290$	1.38328	−	0.922960i	0.0812288	−	0.0541981i
$291$	−7.03499	+	3.88588i	−0.412398	+	0.227794i
$292$	5.10736	−	8.84620i	0.298886	−	0.517685i
$293$	8.74058	−	5.04638i	0.510630	−	0.294812i	−0.222463	−	0.974941i	$-0.571410\pi$
$293$	8.74058	−	5.04638i	0.510630	−	0.294812i	0.733093	+	0.680129i	$0.238076\pi$
$294$	1.77257	−	11.9941i	0.103378	−	0.699509i
$295$	−4.61795	+	9.34878i	−0.268868	+	0.544307i
$296$	−5.78366	+	3.33920i	−0.336168	+	0.194087i
$297$	1.74435	+	3.46162i	0.101217	+	0.200863i
$298$	−18.6650	−	10.7762i	−1.08123	−	0.624250i
$299$	−6.23906			−0.360814
$300$	−0.956236	−	8.60730i	−0.0552083	−	0.496943i
$301$	10.3565	+	20.9187i	0.596940	+	1.20573i
$302$	−7.68913	−	13.3180i	−0.442460	−	0.766363i
$303$	0.360032	−	19.0044i	0.0206833	−	1.09178i
$304$	6.50055	−	3.75309i	0.372832	−	0.215255i
$305$	3.43336	+	1.69596i	0.196594	+	0.0971101i
$306$	0.551242	−	14.5436i	0.0315124	−	0.831400i
$307$	10.7285			0.612306			0.306153	−	0.951982i	$-0.400958\pi$
$307$	10.7285			0.612306			0.306153	+	0.951982i	$0.400958\pi$
$308$	−1.96968	−	0.126017i	−0.112233	−	0.00718046i
$309$	10.1191	−	5.58942i	0.575654	−	0.317971i
$310$	10.0270	+	4.95298i	0.569497	+	0.281310i
$311$	−4.99022			−0.282969			−0.141485	−	0.989940i	$-0.545188\pi$
$311$	−4.99022			−0.282969			−0.141485	+	0.989940i	$0.545188\pi$
$312$	−0.109633	+	5.78701i	−0.00620673	+	0.327625i
$313$	20.1068			1.13651			0.568253	−	0.822854i	$-0.307620\pi$
$313$	20.1068			1.13651			0.568253	+	0.822854i	$0.307620\pi$
$314$	7.04317			0.397469
$315$	−15.0318	−	9.43638i	−0.846946	−	0.531680i
$316$	−6.21613			−0.349685
$317$	−26.0102			−1.46088			−0.730440	−	0.682977i	$-0.760685\pi$
$317$	−26.0102			−1.46088			−0.730440	+	0.682977i	$0.760685\pi$
$318$	−8.92516	+	4.92994i	−0.500498	+	0.276457i
$319$	−0.554779			−0.0310616
$320$	0.990306	−	2.00482i	0.0553598	−	0.112073i
$321$	0.447995	−	23.6476i	0.0250046	−	1.31988i
$322$	4.42683	−	2.19166i	0.246698	−	0.122136i
$323$	36.4150			2.02619
$324$	−5.07709	+	7.43123i	−0.282060	+	0.412846i
$325$	−6.41442	+	15.4284i	−0.355808	+	0.855812i
$326$	6.38815	−	3.68820i	0.353807	−	0.204271i
$327$	−15.5826	+	8.60729i	−0.861722	+	0.475984i
$328$	−0.849794	−	1.47189i	−0.0469220	−	0.0812713i
$329$	17.0255	−	25.5667i	0.938648	−	1.40954i
$330$	−1.32840	+	2.56571i	−0.0731262	+	0.141238i
$331$	13.3980			0.736418			0.368209	−	0.929743i	$-0.379971\pi$
$331$	13.3980			0.736418			0.368209	+	0.929743i	$0.379971\pi$
$332$	2.26849	+	1.30971i	0.124500	+	0.0718798i
$333$	16.9591	+	10.6676i	0.929353	+	0.584580i
$334$	14.6090	−	8.43452i	0.799370	−	0.461516i
$335$	9.08800	+	4.48914i	0.496531	+	0.245268i
$336$	−1.95507	−	4.14460i	−0.106658	−	0.226106i
$337$	7.18391	−	4.14763i	0.391333	−	0.225936i	−0.291405	−	0.956600i	$-0.594123\pi$
$337$	7.18391	−	4.14763i	0.391333	−	0.225936i	0.682737	+	0.730664i	$0.260789\pi$
$338$	−0.916415	+	1.58728i	−0.0498464	+	0.0863366i
$339$	−0.660351	+	34.8569i	−0.0358653	+	1.89317i
$340$	9.02367	−	6.02085i	0.489377	−	0.326526i
$341$	−1.86552	−	3.23118i	−0.101024	−	0.174978i
$342$	−19.0612	−	11.9898i	−1.03071	−	0.648336i
$343$	3.52815	−	18.1811i	0.190502	−	0.981687i
$344$	7.64047	+	4.41123i	0.411946	+	0.237837i
$345$	−0.331421	−	7.22332i	−0.0178431	−	0.388890i
$346$			10.2449i			0.550769i
$347$	−16.4408			−0.882591			−0.441295	−	0.897362i	$-0.645481\pi$
$347$	−16.4408			−0.882591			−0.441295	+	0.897362i	$0.645481\pi$
$348$	−0.622802	−	1.12752i	−0.0333857	−	0.0604415i
$349$	−26.2420	−	15.1508i	−1.40470	−	0.811004i	−0.409830	−	0.912162i	$-0.634412\pi$
$349$	−26.2420	−	15.1508i	−1.40470	−	0.811004i	−0.994870	+	0.101158i	$0.967745\pi$
$350$	−0.868416	−	13.2002i	−0.0464188	−	0.705582i
$351$	15.5066	−	7.81396i	0.827683	−	0.417079i
$352$	−0.646046	+	0.372995i	−0.0344344	+	0.0198807i
$353$	10.7919	−	6.23074i	0.574398	−	0.331629i	−0.184506	−	0.982831i	$-0.559069\pi$
$353$	10.7919	−	6.23074i	0.574398	−	0.331629i	0.758904	+	0.651203i	$0.225735\pi$
$354$	6.91699	+	4.17018i	0.367634	+	0.221642i
$355$	8.36444	+	4.13173i	0.443938	+	0.219289i
$356$	7.58595	+	13.1393i	0.402055	+	0.696379i
$357$	1.83942	−	22.1554i	0.0973523	−	1.17259i
$358$	16.4577	+	9.50188i	0.869818	+	0.502190i
$359$	1.01914	−	0.588399i	0.0537880	−	0.0310545i	−0.472865	−	0.881135i	$-0.656780\pi$
$359$	1.01914	−	0.588399i	0.0537880	−	0.0310545i	0.526653	+	0.850080i	$0.323447\pi$
$360$	−6.70578	+	0.180480i	−0.353425	+	0.00951212i
$361$	18.6714	−	32.3398i	0.982705	−	1.70210i
$362$		−	5.53416i		−	0.290869i
$363$	−15.8337	+	8.74599i	−0.831056	+	0.459046i
$364$	−0.564503	+	8.82335i	−0.0295880	+	0.462469i
$365$	−12.6772	−	18.9998i	−0.663554	−	0.994493i
$366$	1.53151	−	2.54028i	0.0800532	−	0.132783i
$367$	17.7200	+	30.6920i	0.924978	+	1.60211i	0.791596	+	0.611045i	$0.209251\pi$
$367$	17.7200	+	30.6920i	0.924978	+	1.60211i	0.133383	+	0.991065i	$0.457416\pi$
$368$	0.933507	−	1.61688i	0.0486624	−	0.0842858i
$369$	−2.71480	+	4.31593i	−0.141327	+	0.224678i
$370$	0.966888	+	14.9020i	0.0502661	+	0.774718i
$371$	−13.9580	+	6.91040i	−0.724664	+	0.358770i
$372$	4.47272	−	7.41881i	0.231900	−	0.384647i
$373$	21.9698	+	12.6843i	1.13755	+	0.656767i	0.945824	−	0.324680i	$-0.105257\pi$
$373$	21.9698	+	12.6843i	1.13755	+	0.656767i	0.191730	+	0.981448i	$0.438590\pi$
$374$	−3.61905			−0.187136
$375$	−18.2030	−	6.60678i	−0.940001	−	0.341173i
$376$		−	11.6099i		−	0.598734i
$377$			2.48518i			0.127993i
$378$	−8.25761	+	10.9914i	−0.424725	+	0.565339i
$379$	24.3494			1.25075			0.625373	−	0.780326i	$-0.284947\pi$
$379$	24.3494			1.25075			0.625373	+	0.780326i	$0.284947\pi$
$380$	−1.08673	−	16.7491i	−0.0557483	−	0.859212i
$381$	−1.89483	+	3.14291i	−0.0970750	+	0.161016i
$382$			20.0241i			1.02452i
$383$	11.3669	+	6.56268i	0.580821	+	0.335337i	0.761460	−	0.648212i	$-0.224483\pi$
$383$	11.3669	+	6.56268i	0.580821	+	0.335337i	−0.180639	+	0.983550i	$0.557816\pi$
$384$	−1.48333	−	0.894282i	−0.0756957	−	0.0456361i
$385$	−2.20322	+	3.82405i	−0.112287	+	0.194892i
$386$			19.0139i			0.967784i
$387$	1.00247	−	26.4484i	0.0509583	−	1.34445i
$388$	−2.32004	+	4.01843i	−0.117782	+	0.204005i
$389$	16.7387	−	9.66411i	0.848688	−	0.489990i	−0.0115202	−	0.999934i	$-0.503667\pi$
$389$	16.7387	−	9.66411i	0.848688	−	0.489990i	0.860208	+	0.509944i	$0.170334\pi$
$390$	11.4933	+	5.95071i	0.581987	+	0.301326i
$391$	7.84404	−	4.52876i	0.396690	−	0.229029i
$392$	−2.69893	−	6.45877i	−0.136317	−	0.326217i
$393$	−23.8905	+	13.1962i	−1.20512	+	0.665663i
$394$	−6.94184			−0.349725
$395$	−6.15587	+	12.4622i	−0.309735	+	0.627042i
$396$	1.89437	+	1.19159i	0.0951955	+	0.0598797i
$397$	18.0143	+	31.2016i	0.904111	+	1.56597i	0.822107	+	0.569334i	$0.192799\pi$
$397$	18.0143	+	31.2016i	0.904111	+	1.56597i	0.0820040	+	0.996632i	$0.473868\pi$
$398$	3.90645	+	2.25539i	0.195812	+	0.113052i
$399$	−28.2641	−	19.6046i	−1.41497	−	0.981457i
$400$	−3.03859	−	3.97077i	−0.151929	−	0.198538i
$401$	−2.72857	−	1.57534i	−0.136258	−	0.0786688i	0.430321	−	0.902676i	$-0.358400\pi$
$401$	−2.72857	−	1.57534i	−0.136258	−	0.0786688i	−0.566580	+	0.824007i	$0.691734\pi$
$402$	4.05385	−	6.72404i	0.202188	−	0.335365i
$403$	−14.4744	+	8.35677i	−0.721019	+	0.416281i
$404$	−5.48710	−	9.50393i	−0.272993	−	0.472838i
$405$	9.87039	+	17.5378i	0.490464	+	0.871462i
$406$	−0.872995	−	1.76332i	−0.0433260	−	0.0875123i
$407$	2.49101	−	4.31455i	0.123475	−	0.213864i
$408$	−4.06279	−	7.35528i	−0.201138	−	0.364140i
$409$		−	15.9469i		−	0.788525i	−0.918998	−	0.394262i	$-0.871000\pi$
$409$		−	15.9469i		−	0.788525i	0.918998	−	0.394262i	$-0.129000\pi$
$410$	−3.79242	+	0.246064i	−0.187294	+	0.0121522i
$411$	−0.361114	+	19.0615i	−0.0178124	+	0.940236i
$412$	3.33713	−	5.78008i	0.164409	−	0.284764i
$413$	10.2690	+	6.83838i	0.505303	+	0.336495i
$414$	−5.59702	−	0.212143i	−0.275079	−	0.0104263i
$415$	4.87224	−	3.25089i	0.239169	−	0.159580i
$416$	1.67087	+	2.89402i	0.0819209	+	0.141891i
$417$	−29.0077	−	0.549540i	−1.42051	−	0.0269111i
$418$	−2.79977	+	4.84934i	−0.136941	+	0.237189i
$419$	17.4629	+	30.2467i	0.853120	+	1.47765i	0.878378	+	0.477966i	$0.158626\pi$
$419$	17.4629	+	30.2467i	0.853120	+	1.47765i	−0.0252584	+	0.999681i	$0.508041\pi$
$420$	−10.2453	−	0.184858i	−0.499919	−	0.00902016i
$421$	18.6679	−	32.3338i	0.909818	−	1.57585i	0.0955030	−	0.995429i	$-0.469554\pi$
$421$	18.6679	−	32.3338i	0.909818	−	1.57585i	0.814315	−	0.580423i	$-0.197113\pi$
$422$	−3.92397	−	6.79652i	−0.191016	−	0.330849i
$423$	−30.8013	+	16.2599i	−1.49761	+	0.790582i
$424$	−2.94339	+	5.09811i	−0.142944	+	0.247586i
$425$	−3.13450	−	24.0533i	−0.152046	−	1.16676i
$426$	3.73110	−	6.18869i	0.180772	−	0.299843i
$427$	2.51141	−	3.77131i	0.121536	−	0.182506i
$428$	−6.82770	−	11.8259i	−0.330029	−	0.571627i
$429$	−2.08770	−	3.77957i	−0.100795	−	0.182479i
$430$	16.4101	−	10.9493i	0.791366	−	0.528021i
$431$	−7.75117	−	4.47514i	−0.373361	−	0.215560i	0.301565	−	0.953446i	$-0.402491\pi$
$431$	−7.75117	−	4.47514i	−0.373361	−	0.215560i	−0.674926	+	0.737886i	$0.735824\pi$
$432$	−0.295123	+	5.18776i	−0.0141991	+	0.249596i
$433$	−12.0060			−0.576972			−0.288486	−	0.957484i	$-0.593152\pi$
$433$	−12.0060			−0.576972			−0.288486	+	0.957484i	$0.593152\pi$
$434$	7.33450	−	11.0140i	0.352067	−	0.528688i
$435$	−2.87724	+	0.132014i	−0.137953	+	0.00632957i
$436$	−5.13894	+	8.90090i	−0.246110	+	0.426276i
$437$		−	14.0142i		−	0.670388i
$438$	−15.4869	+	8.55440i	−0.739992	+	0.408745i
$439$			32.7739i			1.56422i	0.623144	+	0.782108i	$0.285855\pi$
$439$			32.7739i			1.56422i	−0.623144	+	0.782108i	$0.714145\pi$
$440$	0.108003	+	1.66458i	0.00514886	+	0.0793559i
$441$	−13.3554	+	16.2060i	−0.635971	+	0.771713i
$442$			16.2119i			0.771119i
$443$	6.10539			0.290076			0.145038	−	0.989426i	$-0.453670\pi$
$443$	6.10539			0.290076			0.145038	+	0.989426i	$0.453670\pi$
$444$	11.5652	+	0.219099i	0.548862	+	0.0103980i
$445$	33.8542	−	2.19657i	1.60484	−	0.104127i
$446$	10.7610	−	18.6387i	0.509550	−	0.882566i
$447$	18.0493	+	32.6764i	0.853702	+	1.54554i
$448$	−2.20215	−	1.46647i	−0.104042	−	0.0692842i
$449$			4.39667i			0.207492i	0.994604	+	0.103746i	$0.0330828\pi$
$449$			4.39667i			0.207492i	−0.994604	+	0.103746i	$0.966917\pi$
$450$	−6.27894	+	13.6226i	−0.295992	+	0.642175i
$451$	1.09801	+	0.633938i	0.0517034	+	0.0298510i
$452$	10.0641	+	17.4316i	0.473377	+	0.819913i
$453$	−0.504517	+	26.6311i	−0.0237043	+	1.25124i
$454$	−6.95237	+	4.01395i	−0.326291	+	0.188384i
$455$	17.1302	+	9.86954i	0.803075	+	0.462691i
$456$	−12.9988	−	0.246257i	−0.608723	−	0.0115320i
$457$			33.2534i			1.55553i	0.628555	+	0.777765i	$0.283647\pi$
$457$			33.2534i			1.55553i	−0.628555	+	0.777765i	$0.716353\pi$
$458$	16.6860	+	9.63368i	0.779687	+	0.450152i
$459$	−13.8237	+	21.0799i	−0.645236	+	0.983925i
$460$	−2.31710	−	3.47272i	−0.108035	−	0.161916i
$461$	6.22235	−	10.7774i	0.289804	−	0.501955i	−0.683959	−	0.729520i	$-0.739743\pi$
$461$	6.22235	−	10.7774i	0.289804	−	0.501955i	0.973763	+	0.227566i	$0.0730766\pi$
$462$	2.80898	+	1.94837i	0.130686	+	0.0906464i
$463$	2.79388	−	1.61305i	0.129843	−	0.0749647i	−0.433672	−	0.901071i	$-0.642782\pi$
$463$	2.79388	−	1.61305i	0.129843	−	0.0749647i	0.563514	+	0.826106i	$0.309449\pi$
$464$	−0.644047	−	0.371841i	−0.0298991	−	0.0172623i
$465$	−10.4440	−	16.3139i	−0.484329	−	0.756538i
$466$	0.572350	+	0.991339i	0.0265136	+	0.0459229i
$467$	−36.0480	+	20.8123i	−1.66810	+	0.963080i	−0.699443	+	0.714688i	$0.746569\pi$
$467$	−36.0480	+	20.8123i	−1.66810	+	0.963080i	−0.968660	+	0.248392i	$0.920098\pi$
$468$	5.33784	−	8.48599i	0.246742	−	0.392265i
$469$	6.64763	−	9.98253i	0.306959	−	0.460950i
$470$	−23.2757	−	11.4973i	−1.07363	−	0.530332i
$471$	−10.4473	−	6.29858i	−0.481387	−	0.290223i
$472$	4.66316			0.214639
$473$	−6.58146			−0.302616
$474$	9.22055	+	5.55897i	0.423514	+	0.255332i
$475$	−34.6551	−	14.4081i	−1.59009	−	0.661087i
$476$	−5.69490	−	11.5029i	−0.261025	−	0.527234i
$477$	17.6477	+	0.668898i	0.808032	+	0.0306267i
$478$	−10.1997	+	5.88880i	−0.466523	+	0.269347i
$479$	−11.5051	−	19.9275i	−0.525683	−	0.910509i	−0.999552	−	0.0299141i	$-0.990477\pi$
$479$	−11.5051	−	19.9275i	−0.525683	−	0.910509i	0.473870	−	0.880595i	$-0.342857\pi$
$480$	−3.26182	+	2.08819i	−0.148881	+	0.0953123i
$481$	−19.3274	−	11.1587i	−0.881255	−	0.508793i
$482$	−19.9120	+	11.4962i	−0.906967	+	0.523638i
$483$	−8.52640	−	0.707892i	−0.387965	−	0.0322102i
$484$	−5.22175	+	9.04434i	−0.237352	+	0.411106i
$485$	5.75867	+	8.63074i	0.261488	+	0.391902i
$486$	14.1766	−	6.48260i	0.643064	−	0.294057i
$487$	9.17108	+	5.29492i	0.415581	+	0.239936i	0.693185	−	0.720760i	$-0.256207\pi$
$487$	9.17108	+	5.29492i	0.415581	+	0.239936i	−0.277604	+	0.960696i	$0.589540\pi$
$488$		−	1.71256i		−	0.0775238i
$489$	−12.7740	−	0.241999i	−0.577661	−	0.0109436i
$490$	−15.6214	−	0.985300i	−0.705704	−	0.0445113i
$491$	2.99490	−	1.72911i	0.135158	−	0.0780336i	−0.430896	−	0.902401i	$-0.641803\pi$
$491$	2.99490	−	1.72911i	0.135158	−	0.0780336i	0.566054	+	0.824368i	$0.308469\pi$
$492$	−0.0557586	+	2.94324i	−0.00251379	+	0.132692i
$493$	−1.80392	−	3.12449i	−0.0812446	−	0.140720i
$494$	21.7231	+	12.5418i	0.977368	+	0.564283i
$495$	4.26492	−	2.61782i	0.191694	−	0.117662i
$496$		−	5.00146i		−	0.224572i
$497$	6.11836	−	9.18775i	0.274446	−	0.412127i
$498$	−2.19366	−	3.97140i	−0.0983003	−	0.177963i
$499$	7.23460	−	12.5307i	0.323865	−	0.560951i	−0.657417	−	0.753527i	$-0.728351\pi$
$499$	7.23460	−	12.5307i	0.323865	−	0.560951i	0.981282	+	0.192576i	$0.0616843\pi$
$500$	−10.9698	+	2.15954i	−0.490584	+	0.0965776i
$501$	−29.2128	−	0.553425i	−1.30513	−	0.0247252i
$502$	−1.44964			−0.0647004
$503$		−	33.2244i		−	1.48140i	−0.671833	−	0.740702i	$-0.734493\pi$
$503$		−	33.2244i		−	1.48140i	0.671833	−	0.740702i	$-0.265507\pi$
$504$	−0.806427	+	7.89618i	−0.0359211	+	0.351724i
$505$	−24.4876	+	1.58883i	−1.08968	+	0.0707019i
$506$			1.39277i			0.0619164i
$507$	2.77882	−	1.53492i	0.123412	−	0.0681682i
$508$			2.11883i			0.0940077i
$509$	−20.9146	+	36.2251i	−0.927023	+	1.60565i	−0.138748	+	0.990328i	$0.544308\pi$
$509$	−20.9146	+	36.2251i	−0.927023	+	1.60565i	−0.788275	+	0.615323i	$0.789026\pi$
$510$	−18.7694	+	0.861179i	−0.831123	+	0.0381336i
$511$	−24.2199	+	11.9909i	−1.07142	+	0.530445i
$512$	−1.00000			−0.0441942
$513$	17.5517	+	34.8309i	0.774926	+	1.53782i
$514$	−6.07764	−	3.50893i	−0.268073	−	0.154772i
$515$	−8.28323	−	12.4144i	−0.365003	−	0.547043i
$516$	−7.38843	−	13.3760i	−0.325258	−	0.588847i
$517$	4.33043	+	7.50052i	0.190452	+	0.329872i
$518$	17.6333	+	1.12815i	0.774763	+	0.0495680i
$519$	9.16183	−	15.1965i	0.402160	−	0.667054i
$520$	7.45666	−	0.483811i	0.326996	−	0.0212165i
$521$	−11.1096	+	19.2425i	−0.486722	+	0.843027i	−0.999883	−	0.0152648i	$-0.995141\pi$
$521$	−11.1096	+	19.2425i	−0.486722	+	0.843027i	0.513161	+	0.858292i	$0.328474\pi$
$522$	−0.0845022	+	2.22944i	−0.00369856	+	0.0975801i
$523$	−15.3867	−	26.6505i	−0.672813	−	1.16535i	−0.977103	−	0.212766i	$-0.931753\pi$
$523$	−15.3867	−	26.6505i	−0.672813	−	1.16535i	0.304291	−	0.952579i	$-0.401581\pi$
$524$	−7.87875	+	13.6464i	−0.344185	+	0.596146i
$525$	−10.5166	+	20.3569i	−0.458981	+	0.888446i
$526$	1.32494	+	2.29487i	0.0577703	+	0.100061i
$527$	12.1319	−	21.0130i	0.528473	−	0.915343i
$528$	1.29186	+	0.0244738i	0.0562210	+	0.00106509i
$529$	9.75713	+	16.8998i	0.424223	+	0.734776i
$530$	7.30592	+	10.9497i	0.317349	+	0.475623i
$531$	−6.53085	−	12.3715i	−0.283415	−	0.536876i
$532$	−19.8190	−	1.26798i	−0.859262	−	0.0549741i
$533$	2.83978	−	4.91865i	0.123005	−	0.213050i
$534$	0.497747	−	26.2738i	0.0215396	−	1.13698i
$535$	−30.4703	+	1.97701i	−1.31735	+	0.0854735i
$536$		−	4.53308i		−	0.195799i
$537$	−15.9149	−	28.8122i	−0.686777	−	1.24334i
$538$	11.9338	−	20.6700i	0.514504	−	0.891147i
$539$	4.15272	+	3.16598i	0.178871	+	0.136368i
$540$	10.1083	+	5.72914i	0.434990	+	0.246543i
$541$	2.61686	+	4.53253i	0.112508	+	0.194869i	0.916781	−	0.399391i	$-0.130778\pi$
$541$	2.61686	+	4.53253i	0.112508	+	0.194869i	−0.804273	+	0.594260i	$0.797445\pi$
$542$	16.9678	−	9.79635i	0.728828	−	0.420789i
$543$	−4.94910	+	8.20897i	−0.212386	+	0.352281i
$544$	−4.20138	−	2.42567i	−0.180133	−	0.104000i
$545$	12.7556	+	19.1172i	0.546388	+	0.818893i
$546$	8.72791	−	12.5831i	0.373520	−	0.538507i
$547$	3.57961	+	2.06669i	0.153053	+	0.0883652i	0.574571	−	0.818455i	$-0.305169\pi$
$547$	3.57961	+	2.06669i	0.153053	+	0.0883652i	−0.421518	+	0.906820i	$0.638502\pi$
$548$	5.50358	+	9.53248i	0.235101	+	0.407207i
$549$	−4.54346	+	2.39847i	−0.193910	+	0.102364i
$550$	3.44414	+	1.43192i	0.146859	+	0.0610573i
$551$	−5.58221			−0.237810
$552$	−2.83065	+	1.56355i	−0.120480	+	0.0665490i
$553$	13.6889	+	9.11577i	0.582109	+	0.387642i
$554$	−17.2708	+	9.97128i	−0.733765	+	0.423639i
$555$	11.8924	−	22.9692i	0.504803	−	0.974989i
$556$	−14.5065	+	8.37531i	−0.615211	+	0.355192i
$557$	6.66281	−	11.5403i	0.282312	−	0.488979i	−0.689642	−	0.724151i	$-0.742232\pi$
$557$	6.66281	−	11.5403i	0.282312	−	0.488979i	0.971954	+	0.235172i	$0.0755652\pi$
$558$	−13.2690	+	7.00465i	−0.561722	+	0.296530i
$559$			29.4823i			1.24697i
$560$	−5.12081	+	2.96266i	−0.216394	+	0.125195i
$561$	5.36823	+	3.23645i	0.226647	+	0.136643i
$562$	2.03902	+	1.17723i	0.0860110	+	0.0496585i
$563$		−	9.39051i		−	0.395763i	−0.980226	−	0.197881i	$-0.936594\pi$
$563$		−	9.39051i		−	0.395763i	0.980226	−	0.197881i	$-0.0634061\pi$
$564$	−10.3825	+	17.2212i	−0.437182	+	0.725145i
$565$	44.9137	−	2.91414i	1.88953	−	0.122599i
$566$	8.82966			0.371138
$567$	22.0782	−	8.91929i	0.927197	−	0.374575i
$568$		−	4.17217i		−	0.175060i
$569$			34.6834i			1.45400i	0.686635	+	0.727002i	$0.259087\pi$
$569$			34.6834i			1.45400i	−0.686635	+	0.727002i	$0.740913\pi$
$570$	−13.3665	+	25.8163i	−0.559859	+	1.08132i
$571$	11.4946			0.481034			0.240517	−	0.970645i	$-0.422683\pi$
$571$	11.4946			0.481034			0.240517	+	0.970645i	$0.422683\pi$
$572$	−2.15891	−	1.24645i	−0.0902687	−	0.0521167i
$573$	17.9072	−	29.7023i	0.748085	−	1.24083i
$574$	−0.287103	+	4.48751i	−0.0119835	+	0.187305i
$575$	−9.25680	+	1.20630i	−0.386035	+	0.0503061i
$576$	1.40052	+	2.65303i	0.0583550	+	0.110543i
$577$	−8.61149	+	14.9155i	−0.358501	+	0.620942i	−0.987711	−	0.156293i	$-0.950045\pi$
$577$	−8.61149	+	14.9155i	−0.358501	+	0.620942i	0.629209	+	0.777236i	$0.283379\pi$
$578$	−3.26772	−	5.65986i	−0.135919	−	0.235419i
$579$	17.0038	−	28.2039i	0.706655	−	1.17211i
$580$	−1.38328	+	0.922960i	−0.0574374	+	0.0383238i
$581$	−3.07490	−	6.21086i	−0.127568	−	0.257670i
$582$	7.03499	−	3.88588i	0.291610	−	0.161075i
$583$		−	4.39148i		−	0.181877i
$584$	−5.10736	+	8.84620i	−0.211344	+	0.366059i
$585$	−11.7268	−	19.1051i	−0.484842	−	0.789900i
$586$	−8.74058	+	5.04638i	−0.361070	+	0.208464i
$587$	18.3983	+	10.6223i	0.759380	+	0.438428i	0.829073	−	0.559140i	$-0.188869\pi$
$587$	18.3983	+	10.6223i	0.759380	+	0.438428i	−0.0696932	+	0.997568i	$0.522202\pi$
$588$	−1.77257	+	11.9941i	−0.0730994	+	0.494628i
$589$	−18.7710	−	32.5122i	−0.773444	−	1.33964i
$590$	4.61795	−	9.34878i	0.190118	−	0.384883i
$591$	10.2970	+	6.20796i	0.423563	+	0.255361i
$592$	5.78366	−	3.33920i	0.237707	−	0.137240i
$593$	−5.35047	+	3.08910i	−0.219718	+	0.126854i	−0.605819	−	0.795602i	$-0.707155\pi$
$593$	−5.35047	+	3.08910i	−0.219718	+	0.126854i	0.386102	+	0.922456i	$0.373821\pi$
$594$	−1.74435	−	3.46162i	−0.0715714	−	0.142032i
$595$	−28.7009	+	0.0258613i	−1.17662	+	0.00106021i
$596$	18.6650	+	10.7762i	0.764547	+	0.441412i
$597$	−3.77759	−	6.83894i	−0.154606	−	0.279899i
$598$	6.23906			0.255134
$599$		−	20.2605i		−	0.827821i	−0.910318	−	0.413911i	$-0.864163\pi$
$599$		−	20.2605i		−	0.827821i	0.910318	−	0.413911i	$-0.135837\pi$
$600$	0.956236	+	8.60730i	0.0390382	+	0.351392i
$601$	−1.81095	−	1.04555i	−0.0738700	−	0.0426489i	0.462610	−	0.886562i	$-0.346913\pi$
$601$	−1.81095	−	1.04555i	−0.0738700	−	0.0426489i	−0.536480	+	0.843913i	$0.680246\pi$
$602$	−10.3565	−	20.9187i	−0.422100	−	0.852583i
$603$	−12.0264	+	6.34867i	−0.489752	+	0.258538i
$604$	7.68913	+	13.3180i	0.312866	+	0.541900i
$605$	12.9611	+	19.4253i	0.526944	+	0.789751i
$606$	−0.360032	+	19.0044i	−0.0146253	+	0.772003i
$607$	−6.73968	+	11.6735i	−0.273555	+	0.473812i	−0.969770	−	0.244022i	$-0.921533\pi$
$607$	−6.73968	+	11.6735i	−0.273555	+	0.473812i	0.696214	+	0.717834i	$0.254866\pi$
$608$	−6.50055	+	3.75309i	−0.263632	+	0.152208i
$609$	−0.281972	+	3.39629i	−0.0114261	+	0.137625i
$610$	−3.43336	−	1.69596i	−0.139013	−	0.0686672i
$611$	33.5993	−	19.3985i	1.35928	−	0.784781i
$612$	−0.551242	+	14.5436i	−0.0222826	+	0.587889i
$613$	−9.41875	−	5.43792i	−0.380420	−	0.219636i	0.297581	−	0.954697i	$-0.403820\pi$
$613$	−9.41875	−	5.43792i	−0.380420	−	0.219636i	−0.678001	+	0.735061i	$0.737153\pi$
$614$	−10.7285			−0.432965
$615$	5.84545	+	3.02650i	0.235711	+	0.122040i
$616$	1.96968	+	0.126017i	0.0793605	+	0.00507735i
$617$	0.714583	+	1.23769i	0.0287680	+	0.0498277i	0.880051	−	0.474879i	$-0.157508\pi$
$617$	0.714583	+	1.23769i	0.0287680	+	0.0498277i	−0.851283	+	0.524707i	$0.824175\pi$
$618$	−10.1191	+	5.58942i	−0.407049	+	0.224839i
$619$	−19.3002	+	11.1430i	−0.775739	+	0.447873i	−0.834918	−	0.550374i	$-0.814485\pi$
$619$	−19.3002	+	11.1430i	−0.775739	+	0.447873i	0.0591788	+	0.998247i	$0.481152\pi$
$620$	−10.0270	−	4.95298i	−0.402695	−	0.198916i
$621$	8.11250	+	5.32000i	0.325544	+	0.213484i
$622$	4.99022			0.200089
$623$	2.56292	−	40.0592i	0.102681	−	1.60494i
$624$	0.109633	−	5.78701i	0.00438882	−	0.231666i
$625$	−6.53397	+	24.1310i	−0.261359	+	0.965242i
$626$	−20.1068			−0.803631
$627$	8.48965	−	4.68938i	0.339044	−	0.187276i
$628$	−7.04317			−0.281053
$629$	32.3991			1.29184
$630$	15.0318	+	9.43638i	0.598881	+	0.375954i
$631$	13.9478			0.555255			0.277627	−	0.960689i	$-0.410452\pi$
$631$	13.9478			0.555255			0.277627	+	0.960689i	$0.410452\pi$
$632$	6.21613			0.247264
$633$	−0.257469	+	13.5906i	−0.0102335	+	0.540178i
$634$	26.0102			1.03300
$635$	4.24786	+	2.09829i	0.168571	+	0.0832680i
$636$	8.92516	−	4.92994i	0.353906	−	0.195485i
$637$	14.1823	−	18.6025i	0.561923	−	0.737059i
$638$	0.554779			0.0219639
$639$	−11.0689	+	5.84321i	−0.437878	+	0.231154i
$640$	−0.990306	+	2.00482i	−0.0391453	+	0.0792474i
$641$	7.54412	−	4.35560i	0.297975	−	0.172036i	−0.343558	−	0.939132i	$-0.611632\pi$
$641$	7.54412	−	4.35560i	0.297975	−	0.172036i	0.641533	+	0.767096i	$0.278299\pi$
$642$	−0.447995	+	23.6476i	−0.0176809	+	0.933296i
$643$	−21.6235	−	37.4529i	−0.852746	−	1.47700i	−0.878720	−	0.477337i	$-0.841602\pi$
$643$	−21.6235	−	37.4529i	−0.852746	−	1.47700i	0.0259739	−	0.999663i	$-0.491731\pi$
$644$	−4.42683	+	2.19166i	−0.174442	+	0.0863634i
$645$	−34.1333	+	1.56611i	−1.34400	+	0.0616654i
$646$	−36.4150			−1.43273
$647$	31.0729	+	17.9400i	1.22160	+	0.705293i	0.965260	−	0.261293i	$-0.0841487\pi$
$647$	31.0729	+	17.9400i	1.22160	+	0.705293i	0.256344	+	0.966586i	$0.417482\pi$
$648$	5.07709	−	7.43123i	0.199447	−	0.291926i
$649$	−3.01262	+	1.73933i	−0.118256	+	0.0682748i
$650$	6.41442	−	15.4284i	0.251594	−	0.605150i
$651$	−20.7291	+	9.77822i	−0.812436	+	0.383239i
$652$	−6.38815	+	3.68820i	−0.250179	+	0.144441i
$653$	1.94271	−	3.36488i	0.0760243	−	0.131678i	−0.825507	−	0.564392i	$-0.809111\pi$
$653$	1.94271	−	3.36488i	0.0760243	−	0.131678i	0.901531	+	0.432714i	$0.142444\pi$
$654$	15.5826	−	8.60729i	0.609329	−	0.336572i
$655$	19.5562	+	29.3096i	0.764122	+	1.14522i
$656$	0.849794	+	1.47189i	0.0331789	+	0.0574675i
$657$	30.6222	+	1.16067i	1.19468	+	0.0452819i
$658$	−17.0255	+	25.5667i	−0.663725	+	0.996693i
$659$	−12.1007	−	6.98632i	−0.471375	−	0.272149i	0.245440	−	0.969412i	$-0.421068\pi$
$659$	−12.1007	−	6.98632i	−0.471375	−	0.272149i	−0.716815	+	0.697263i	$0.754401\pi$
$660$	1.32840	−	2.56571i	0.0517080	−	0.0998701i
$661$		−	44.7175i		−	1.73931i	−0.493662	−	0.869654i	$-0.664342\pi$
$661$		−	44.7175i		−	1.73931i	0.493662	−	0.869654i	$-0.335658\pi$
$662$	−13.3980			−0.520726
$663$	14.4980	−	24.0475i	0.563055	−	0.933927i
$664$	−2.26849	−	1.30971i	−0.0880345	−	0.0508267i
$665$	−22.1689	+	38.4777i	−0.859674	+	1.49210i
$666$	−16.9591	−	10.6676i	−0.657152	−	0.413360i
$667$	−1.20244	+	0.694232i	−0.0465589	+	0.0268808i
$668$	−14.6090	+	8.43452i	−0.565240	+	0.326341i
$669$	−32.6304	+	18.0238i	−1.26156	+	0.696842i
$670$	−9.08800	−	4.48914i	−0.351100	−	0.173431i
$671$	0.638775	+	1.10639i	0.0246596	+	0.0427118i
$672$	1.95507	+	4.14460i	0.0754185	+	0.159881i
$673$	−32.2357	−	18.6113i	−1.24259	−	0.717412i	−0.272973	−	0.962022i	$-0.588007\pi$
$673$	−32.2357	−	18.6113i	−1.24259	−	0.717412i	−0.969622	+	0.244610i	$0.921340\pi$
$674$	−7.18391	+	4.14763i	−0.276714	+	0.159761i
$675$	21.4962	−	14.5916i	0.827388	−	0.561631i
$676$	0.916415	−	1.58728i	0.0352467	−	0.0610492i
$677$			12.5830i			0.483605i	0.970325	+	0.241803i	$0.0777386\pi$
$677$			12.5830i			0.483605i	−0.970325	+	0.241803i	$0.922261\pi$
$678$	0.660351	−	34.8569i	0.0253606	−	1.33867i
$679$	11.0020	−	5.44692i	0.422218	−	0.209033i
$680$	−9.02367	+	6.02085i	−0.346042	+	0.230889i
$681$	13.9022	+	0.263373i	0.532735	+	0.0100925i
$682$	1.86552	+	3.23118i	0.0714345	+	0.123728i
$683$	8.98544	−	15.5632i	0.343818	−	0.595511i	−0.641320	−	0.767274i	$-0.721613\pi$
$683$	8.98544	−	15.5632i	0.343818	−	0.595511i	0.985138	+	0.171763i	$0.0549462\pi$
$684$	19.0612	+	11.9898i	0.728823	+	0.458443i
$685$	24.5611	−	1.59360i	0.938432	−	0.0608884i
$686$	−3.52815	+	18.1811i	−0.134705	+	0.694157i
$687$	−16.1356	−	29.2119i	−0.615612	−	1.11450i
$688$	−7.64047	−	4.41123i	−0.291290	−	0.168176i
$689$	−19.6721			−0.749446
$690$	0.331421	+	7.22332i	0.0126170	+	0.274987i
$691$		−	44.2400i		−	1.68297i	−0.540280	−	0.841485i	$-0.681682\pi$
$691$		−	44.2400i		−	1.68297i	0.540280	−	0.841485i	$-0.318318\pi$
$692$		−	10.2449i		−	0.389453i
$693$	−2.42425	−	5.40209i	−0.0920895	−	0.205208i
$694$	16.4408			0.624086
$695$	2.42513	+	37.3769i	0.0919905	+	1.41779i
$696$	0.622802	+	1.12752i	0.0236072	+	0.0427386i
$697$			8.24527i			0.312312i
$698$	26.2420	+	15.1508i	0.993273	+	0.573466i
$699$	0.0375544	−	1.98232i	0.00142044	−	0.0749783i
$700$	0.868416	+	13.2002i	0.0328231	+	0.498921i
$701$			29.6654i			1.12045i	0.828342	+	0.560223i	$0.189284\pi$
$701$			29.6654i			1.12045i	−0.828342	+	0.560223i	$0.810716\pi$
$702$	−15.5066	+	7.81396i	−0.585260	+	0.294919i
$703$	25.0646	−	43.4132i	0.945330	−	1.63736i
$704$	0.646046	−	0.372995i	0.0243488	−	0.0140578i
$705$	24.2436	+	37.8693i	0.913067	+	1.42624i
$706$	−10.7919	+	6.23074i	−0.406160	+	0.234497i
$707$	−1.85382	+	28.9757i	−0.0697200	+	1.08974i
$708$	−6.91699	−	4.17018i	−0.259956	−	0.156725i
$709$	36.7363			1.37966			0.689831	−	0.723971i	$-0.257685\pi$
$709$	36.7363			1.37966			0.689831	+	0.723971i	$0.257685\pi$
$710$	−8.36444	−	4.13173i	−0.313912	−	0.155061i
$711$	−8.70581	−	16.4916i	−0.326494	−	0.618481i
$712$	−7.58595	−	13.1393i	−0.284296	−	0.492414i
$713$	−8.08678	−	4.66890i	−0.302852	−	0.174852i
$714$	−1.83942	+	22.1554i	−0.0688385	+	0.829144i
$715$	−4.63689	+	3.09386i	−0.173410	+	0.115704i
$716$	−16.4577	−	9.50188i	−0.615054	−	0.355102i
$717$	20.3957	+	0.386389i	0.761693	+	0.0144300i
$718$	−1.01914	+	0.588399i	−0.0380339	+	0.0219589i
$719$	−15.0842	−	26.1266i	−0.562546	−	0.974358i	−0.997273	−	0.0737961i	$-0.976489\pi$
$719$	−15.0842	−	26.1266i	−0.562546	−	0.974358i	0.434727	−	0.900562i	$-0.356845\pi$
$720$	6.70578	−	0.180480i	0.249910	−	0.00672608i
$721$	−15.8252	+	7.83480i	−0.589360	+	0.291783i
$722$	−18.6714	+	32.3398i	−0.694878	+	1.20356i
$723$	39.8169	+	0.754316i	1.48081	+	0.0280533i
$724$			5.53416i			0.205676i
$725$	0.480501	+	3.68723i	0.0178453	+	0.136940i
$726$	15.8337	−	8.74599i	0.587646	−	0.324594i
$727$	2.77440	−	4.80540i	0.102897	−	0.178222i	−0.809980	−	0.586457i	$-0.800522\pi$
$727$	2.77440	−	4.80540i	0.102897	−	0.178222i	0.912877	+	0.408235i	$0.133856\pi$
$728$	0.564503	−	8.82335i	0.0209219	−	0.327015i
$729$	−26.8258	−	3.06206i	−0.993548	−	0.113410i
$730$	12.6772	+	18.9998i	0.469203	+	0.703213i
$731$	−21.4003	−	37.0665i	−0.791520	−	1.37095i
$732$	−1.53151	+	2.54028i	−0.0566062	+	0.0938915i
$733$	−10.1357	+	17.5555i	−0.374370	+	0.648428i	−0.990233	−	0.139426i	$-0.955474\pi$
$733$	−10.1357	+	17.5555i	−0.374370	+	0.648428i	0.615863	+	0.787854i	$0.288808\pi$
$734$	−17.7200	−	30.6920i	−0.654059	−	1.13286i
$735$	22.2906	+	15.4315i	0.822200	+	0.569199i
$736$	−0.933507	+	1.61688i	−0.0344095	+	0.0595991i
$737$	1.69082	+	2.92858i	0.0622820	+	0.107876i
$738$	2.71480	−	4.31593i	0.0999331	−	0.158872i
$739$	24.5774	−	42.5693i	0.904095	−	1.56594i	0.0819667	−	0.996635i	$-0.473880\pi$
$739$	24.5774	−	42.5693i	0.904095	−	1.56594i	0.822128	−	0.569303i	$-0.192787\pi$
$740$	−0.966888	−	14.9020i	−0.0355435	−	0.547809i
$741$	−21.0065	−	38.0302i	−0.771693	−	1.39707i
$742$	13.9580	−	6.91040i	0.512415	−	0.253689i
$743$	13.5537	+	23.4757i	0.497237	+	0.861240i	0.999995	−	0.00318755i	$-0.00101463\pi$
$743$	13.5537	+	23.4757i	0.497237	+	0.861240i	−0.502758	+	0.864427i	$0.667681\pi$
$744$	−4.47272	+	7.41881i	−0.163978	+	0.271987i
$745$	40.0884	−	26.7481i	1.46873	−	0.979975i
$746$	−21.9698	−	12.6843i	−0.804372	−	0.464405i
$747$	−0.297637	+	7.85264i	−0.0108900	+	0.287313i
$748$	3.61905			0.132325
$749$	−2.30674	+	36.0551i	−0.0842865	+	1.31742i
$750$	18.2030	+	6.60678i	0.664681	+	0.241246i
$751$	−20.6403	+	35.7500i	−0.753174	+	1.30454i	0.193102	+	0.981179i	$0.438145\pi$
$751$	−20.6403	+	35.7500i	−0.753174	+	1.30454i	−0.946277	+	0.323358i	$0.895188\pi$
$752$			11.6099i			0.423369i
$753$	2.15028	+	1.29638i	0.0783607	+	0.0472428i
$754$		−	2.48518i		−	0.0905050i
$755$	34.3147	−	2.22644i	1.24884	−	0.0810285i
$756$	8.25761	−	10.9914i	0.300326	−	0.399755i
$757$		−	37.6630i		−	1.36888i	−0.729067	−	0.684442i	$-0.760046\pi$
$757$		−	37.6630i		−	1.36888i	0.729067	−	0.684442i	$-0.239954\pi$
$758$	−24.3494			−0.884411
$759$	1.24553	−	2.06594i	0.0452100	−	0.0749889i
$760$	1.08673	+	16.7491i	0.0394200	+	0.607554i
$761$	10.0532	−	17.4126i	0.364427	−	0.631207i	−0.624257	−	0.781219i	$-0.714598\pi$
$761$	10.0532	−	17.4126i	0.364427	−	0.631207i	0.988684	+	0.150013i	$0.0479314\pi$
$762$	1.89483	−	3.14291i	0.0686424	−	0.113856i
$763$	24.3696	−	12.0650i	0.882239	−	0.436783i
$764$		−	20.0241i		−	0.724447i
$765$	28.6113	+	15.5077i	1.03444	+	0.560683i
$766$	−11.3669	−	6.56268i	−0.410702	−	0.237119i
$767$	7.79151	+	13.4953i	0.281335	+	0.487287i
$768$	1.48333	+	0.894282i	0.0535250	+	0.0322696i
$769$	24.3791	−	14.0753i	0.879134	−	0.507568i	0.00876117	−	0.999962i	$-0.497211\pi$
$769$	24.3791	−	14.0753i	0.879134	−	0.507568i	0.870373	+	0.492393i	$0.163878\pi$
$770$	2.20322	−	3.82405i	0.0793987	−	0.137809i
$771$	5.87716	+	10.6400i	0.211661	+	0.383191i
$772$		−	19.0139i		−	0.684327i
$773$	−37.3009	−	21.5357i	−1.34162	−	0.774585i	−0.354576	−	0.935027i	$-0.615375\pi$
$773$	−37.3009	−	21.5357i	−1.34162	−	0.774585i	−0.987045	+	0.160442i	$0.948708\pi$
$774$	−1.00247	+	26.4484i	−0.0360330	+	0.950667i
$775$	−19.8596	+	15.1974i	−0.713380	+	0.545906i
$776$	2.32004	−	4.01843i	0.0832846	−	0.144253i
$777$	−25.1471	−	17.4426i	−0.902147	−	0.625749i
$778$	−16.7387	+	9.66411i	−0.600113	+	0.346475i
$779$	11.0483	+	6.37871i	0.395845	+	0.228541i
$780$	−11.4933	−	5.95071i	−0.411527	−	0.213069i
$781$	1.55620	+	2.69541i	0.0556852	+	0.0964495i
$782$	−7.84404	+	4.52876i	−0.280502	+	0.161948i
$783$	2.11909	−	3.23142i	0.0757303	−	0.115482i
$784$	2.69893	+	6.45877i	0.0963904	+	0.230671i
$785$	−6.97489	+	14.1203i	−0.248945	+	0.503974i
$786$	23.8905	−	13.1962i	0.852146	−	0.470695i
$787$	35.3175			1.25893			0.629466	−	0.777028i	$-0.283274\pi$
$787$	35.3175			1.25893			0.629466	+	0.777028i	$0.283274\pi$
$788$	6.94184			0.247293
$789$	0.0869353	−	4.58892i	0.00309498	−	0.163370i
$790$	6.15587	−	12.4622i	0.219016	−	0.443385i
$791$	3.40017	−	53.1457i	0.120896	−	1.88964i
$792$	−1.89437	−	1.19159i	−0.0673134	−	0.0423413i
$793$	4.95618	−	2.86145i	0.175999	−	0.101613i
$794$	−18.0143	−	31.2016i	−0.639303	−	1.10730i
$795$	−1.04499	−	22.7755i	−0.0370618	−	0.807763i
$796$	−3.90645	−	2.25539i	−0.138460	−	0.0799401i
$797$	14.2561	−	8.23077i	0.504978	−	0.291549i	−0.225789	−	0.974176i	$-0.572496\pi$
$797$	14.2561	−	8.23077i	0.504978	−	0.291549i	0.730767	+	0.682627i	$0.239163\pi$
$798$	28.2641	+	19.6046i	1.00054	+	0.693995i
$799$	−28.1617	+	48.7775i	−0.996289	+	1.72562i
$800$	3.03859	+	3.97077i	0.107430	+	0.140388i
$801$	−24.2345	+	38.5275i	−0.856284	+	1.36130i
$802$	2.72857	+	1.57534i	0.0963492	+	0.0556272i
$803$		−	7.62008i		−	0.268907i
$804$	−4.05385	+	6.72404i	−0.142968	+	0.237139i
$805$	0.00995261	+	11.0454i	0.000350784	+	0.389299i
$806$	14.4744	−	8.35677i	0.509838	−	0.294355i
$807$	−36.1866	+	19.9882i	−1.27383	+	0.703617i
$808$	5.48710	+	9.50393i	0.193035	+	0.334347i
$809$	−21.2722	−	12.2815i	−0.747890	−	0.431795i	0.0770407	−	0.997028i	$-0.475453\pi$
$809$	−21.2722	−	12.2815i	−0.747890	−	0.431795i	−0.824931	+	0.565233i	$0.808786\pi$
$810$	−9.87039	−	17.5378i	−0.346810	−	0.616216i
$811$			7.28238i			0.255719i	0.991792	+	0.127860i	$0.0408107\pi$
$811$			7.28238i			0.255719i	−0.991792	+	0.127860i	$0.959189\pi$
$812$	0.872995	+	1.76332i	0.0306361	+	0.0618806i
$813$	−33.9295	−	0.642781i	−1.18996	−	0.0225433i
$814$	−2.49101	+	4.31455i	−0.0873097	+	0.151225i
$815$	1.06795	+	16.4595i	0.0374085	+	0.576552i
$816$	4.06279	+	7.35528i	0.142226	+	0.257486i
$817$	−66.2230			−2.31685
$818$			15.9469i			0.557571i
$819$	−24.1992	+	10.8596i	−0.845587	+	0.379466i
$820$	3.79242	−	0.246064i	0.132437	−	0.00859293i
$821$			6.68610i			0.233346i	0.993170	+	0.116673i	$0.0372230\pi$
$821$			6.68610i			0.233346i	−0.993170	+	0.116673i	$0.962777\pi$
$822$	0.361114	−	19.0615i	0.0125953	−	0.664847i
$823$		−	11.4060i		−	0.397589i	−0.980041	−	0.198794i	$-0.936297\pi$
$823$		−	11.4060i		−	0.397589i	0.980041	−	0.198794i	$-0.0637026\pi$
$824$	−3.33713	+	5.78008i	−0.116254	+	0.201359i
$825$	−3.82825	−	5.20404i	−0.133283	−	0.181182i
$826$	−10.2690	−	6.83838i	−0.357303	−	0.237938i
$827$	−9.16990			−0.318868			−0.159434	−	0.987209i	$-0.550967\pi$
$827$	−9.16990			−0.318868			−0.159434	+	0.987209i	$0.550967\pi$
$828$	5.59702	+	0.212143i	0.194510	+	0.00737248i
$829$	13.6953	+	7.90700i	0.475659	+	0.274622i	0.718605	−	0.695418i	$-0.244781\pi$
$829$	13.6953	+	7.90700i	0.475659	+	0.274622i	−0.242947	+	0.970040i	$0.578114\pi$
$830$	−4.87224	+	3.25089i	−0.169118	+	0.112840i
$831$	34.5353	+	0.654259i	1.19802	+	0.0226960i
$832$	−1.67087	−	2.89402i	−0.0579268	−	0.100332i
$833$	−4.32761	+	33.6825i	−0.149943	+	1.16703i
$834$	29.0077	+	0.549540i	1.00446	+	0.0190290i
$835$	2.44228	+	37.6412i	0.0845184	+	1.30263i
$836$	2.79977	−	4.84934i	0.0968320	−	0.167718i
$837$	25.9464	+	1.47605i	0.896839	+	0.0510197i
$838$	−17.4629	−	30.2467i	−0.603247	−	1.04485i
$839$	−14.0897	+	24.4040i	−0.486429	+	0.842520i	−0.999878	−	0.0156002i	$-0.995034\pi$
$839$	−14.0897	+	24.4040i	−0.486429	+	0.842520i	0.513449	+	0.858120i	$0.328367\pi$
$840$	10.2453	+	0.184858i	0.353496	+	0.00637821i
$841$	−14.2235	−	24.6358i	−0.490464	−	0.849509i
$842$	−18.6679	+	32.3338i	−0.643339	+	1.11430i
$843$	−1.97176	−	3.56968i	−0.0679111	−	0.122946i
$844$	3.92397	+	6.79652i	0.135069	+	0.233946i
$845$	−2.27467	−	3.40914i	−0.0782511	−	0.117278i
$846$	30.8013	−	16.2599i	1.05897	−	0.559026i
$847$	24.7623	−	12.2594i	0.850844	−	0.421240i
$848$	2.94339	−	5.09811i	0.101077	−	0.175070i
$849$	−13.0973	−	7.89620i	−0.449497	−	0.270997i
$850$	3.13450	+	24.0533i	0.107512	+	0.825021i
$851$		−	12.4687i		−	0.427420i
$852$	−3.73110	+	6.18869i	−0.127825	+	0.212021i
$853$	−4.37925	+	7.58508i	−0.149943	+	0.259708i	−0.931206	−	0.364493i	$-0.881242\pi$
$853$	−4.37925	+	7.58508i	−0.149943	+	0.259708i	0.781263	+	0.624201i	$0.214576\pi$
$854$	−2.51141	+	3.77131i	−0.0859388	+	0.129051i
$855$	42.9138	−	26.3406i	1.46762	−	0.900830i
$856$	6.82770	+	11.8259i	0.233366	+	0.404202i
$857$	−27.6321	+	15.9534i	−0.943894	+	0.544958i	−0.891179	−	0.453652i	$-0.850121\pi$
$857$	−27.6321	+	15.9534i	−0.943894	+	0.544958i	−0.0527153	+	0.998610i	$0.516788\pi$
$858$	2.08770	+	3.77957i	0.0712728	+	0.129032i
$859$	39.6265	+	22.8784i	1.35204	+	0.780601i	0.988535	−	0.150992i	$-0.0482466\pi$
$859$	39.6265	+	22.8784i	1.35204	+	0.780601i	0.363505	+	0.931592i	$0.381580\pi$
$860$	−16.4101	+	10.9493i	−0.559580	+	0.373367i
$861$	4.43897	−	6.39970i	0.151280	−	0.218101i
$862$	7.75117	+	4.47514i	0.264006	+	0.152424i
$863$	21.5708	+	37.3618i	0.734280	+	1.27181i	0.955039	+	0.296481i	$0.0958132\pi$
$863$	21.5708	+	37.3618i	0.734280	+	1.27181i	−0.220759	+	0.975328i	$0.570853\pi$
$864$	0.295123	−	5.18776i	0.0100403	−	0.176491i
$865$	−20.5392	−	10.1456i	−0.698352	−	0.344960i
$866$	12.0060			0.407981
$867$	−0.214409	+	11.3177i	−0.00728173	+	0.384369i
$868$	−7.33450	+	11.0140i	−0.248949	+	0.373839i
$869$	−4.01591	+	2.31859i	−0.136230	+	0.0786526i
$870$	2.87724	−	0.132014i	0.0975475	−	0.00447568i
$871$	13.1188	−	7.57417i	0.444515	−	0.256641i
$872$	5.13894	−	8.90090i	0.174026	−	0.301422i
$873$	−13.9103	−	0.527238i	−0.470791	−	0.0178443i
$874$			14.0142i			0.474036i
$875$	27.3240	+	11.3312i	0.923721	+	0.383066i
$876$	15.4869	−	8.55440i	0.523253	−	0.289026i
$877$	−15.9331	−	9.19897i	−0.538022	−	0.310627i	0.206255	−	0.978498i	$-0.433872\pi$
$877$	−15.9331	−	9.19897i	−0.538022	−	0.310627i	−0.744277	+	0.667871i	$0.767206\pi$
$878$		−	32.7739i		−	1.10607i
$879$	17.4780	+	0.331114i	0.589519	+	0.0111682i
$880$	−0.108003	−	1.66458i	−0.00364079	−	0.0561131i
$881$	−8.81308			−0.296920			−0.148460	−	0.988918i	$-0.547432\pi$
$881$	−8.81308			−0.296920			−0.148460	+	0.988918i	$0.547432\pi$
$882$	13.3554	−	16.2060i	0.449699	−	0.545684i
$883$		−	2.02023i		−	0.0679863i	−0.999422	−	0.0339931i	$-0.989178\pi$
$883$		−	2.02023i		−	0.0679863i	0.999422	−	0.0339931i	$-0.0108224\pi$
$884$		−	16.2119i		−	0.545264i
$885$	−15.2104	+	9.73755i	−0.511291	+	0.327324i
$886$	−6.10539			−0.205115
$887$	−28.8147	−	16.6362i	−0.967504	−	0.558589i	−0.0690297	−	0.997615i	$-0.521990\pi$
$887$	−28.8147	−	16.6362i	−0.967504	−	0.558589i	−0.898474	+	0.439026i	$0.855324\pi$
$888$	−11.5652	−	0.219099i	−0.388104	−	0.00735248i
$889$	3.10720	−	4.66597i	0.104212	−	0.156492i
$890$	−33.8542	+	2.19657i	−1.13480	+	0.0736291i
$891$	−0.508222	+	6.69465i	−0.0170261	+	0.224279i
$892$	−10.7610	+	18.6387i	−0.360306	+	0.624068i
$893$	43.5729	+	75.4705i	1.45811	+	2.52553i
$894$	−18.0493	−	32.6764i	−0.603658	−	1.09286i
$895$	−35.3477	+	23.5850i	−1.18154	+	0.788359i
$896$	2.20215	+	1.46647i	0.0735687	+	0.0489913i
$897$	−9.25457	−	5.57948i	−0.309001	−	0.186293i
$898$		−	4.39667i		−	0.146719i
$899$	−1.85975	+	3.22118i	−0.0620261	+	0.107432i
$900$	6.27894	−	13.6226i	0.209298	−	0.454086i
$901$	24.7326	−	14.2794i	0.823963	−	0.475715i
$902$	−1.09801	−	0.633938i	−0.0365598	−	0.0211078i
$903$	−3.34510	+	40.2909i	−0.111318	+	1.34080i
$904$	−10.0641	−	17.4316i	−0.334728	−	0.579766i
$905$	11.0950	+	5.48051i	0.368810	+	0.182178i
$906$	0.504517	−	26.6311i	0.0167615	−	0.884761i
$907$	−9.65915	+	5.57672i	−0.320727	+	0.185172i	−0.651717	−	0.758463i	$-0.725951\pi$
$907$	−9.65915	+	5.57672i	−0.320727	+	0.185172i	0.330990	+	0.943634i	$0.392617\pi$
$908$	6.95237	−	4.01395i	0.230722	−	0.133208i
$909$	17.5294	−	27.8678i	0.581413	−	0.924318i
$910$	−17.1302	−	9.86954i	−0.567860	−	0.327172i
$911$	33.9893	+	19.6237i	1.12612	+	0.650163i	0.942955	−	0.332920i	$-0.108034\pi$
$911$	33.9893	+	19.6237i	1.12612	+	0.650163i	0.183160	+	0.983083i	$0.441367\pi$
$912$	12.9988	+	0.246257i	0.430432	+	0.00815437i
$913$	1.95407			0.0646701
$914$		−	33.2534i		−	1.09993i
$915$	3.57614	+	5.58605i	0.118224	+	0.184669i
$916$	−16.6860	−	9.63368i	−0.551322	−	0.318306i
$917$	37.3622	−	18.4975i	1.23381	−	0.610840i
$918$	13.8237	−	21.0799i	0.456251	−	0.695740i
$919$	−13.5598	−	23.4863i	−0.447298	−	0.774743i	0.550911	−	0.834564i	$-0.314280\pi$
$919$	−13.5598	−	23.4863i	−0.447298	−	0.774743i	−0.998209	+	0.0598209i	$0.980947\pi$
$920$	2.31710	+	3.47272i	0.0763924	+	0.114492i
$921$	15.9138	+	9.59427i	0.524378	+	0.316142i
$922$	−6.22235	+	10.7774i	−0.204922	+	0.354936i
$923$	12.0744	−	6.97114i	0.397432	−	0.229458i
$924$	−2.80898	−	1.94837i	−0.0924087	−	0.0640967i
$925$	−30.8333	−	12.8191i	−1.01379	−	0.421490i
$926$	−2.79388	+	1.61305i	−0.0918126	+	0.0530080i
$927$	20.0084	+	0.758376i	0.657163	+	0.0249083i
$928$	0.644047	+	0.371841i	0.0211419	+	0.0122063i
$929$	44.1075			1.44712			0.723559	−	0.690262i	$-0.242505\pi$
$929$	44.1075			1.44712			0.723559	+	0.690262i	$0.242505\pi$
$930$	10.4440	+	16.3139i	0.342472	+	0.534953i
$931$	41.7849	+	31.8562i	1.36944	+	1.04405i
$932$	−0.572350	−	0.991339i	−0.0187479	−	0.0324724i
$933$	−7.40213	−	4.46266i	−0.242335	−	0.146101i
$934$	36.0480	−	20.8123i	1.17953	−	0.681000i
$935$	3.58396	−	7.25553i	0.117208	−	0.237281i
$936$	−5.33784	+	8.48599i	−0.174473	+	0.277373i
$937$	−31.2098			−1.01958			−0.509789	−	0.860299i	$-0.670277\pi$
$937$	−31.2098			−1.01958			−0.509789	+	0.860299i	$0.670277\pi$
$938$	−6.64763	+	9.98253i	−0.217053	+	0.325941i
$939$	29.8250	+	17.9812i	0.973303	+	0.586793i
$940$	23.2757	+	11.4973i	0.759169	+	0.375002i
$941$	6.51025			0.212228			0.106114	−	0.994354i	$-0.466159\pi$
$941$	6.51025			0.212228			0.106114	+	0.994354i	$0.466159\pi$
$942$	10.4473	+	6.29858i	0.340392	+	0.205219i
$943$	3.17316			0.103332
$944$	−4.66316			−0.151773
$945$	−13.8583	−	27.4399i	−0.450810	−	0.892620i
$946$	6.58146			0.213982
$947$	−33.4969			−1.08850			−0.544252	−	0.838922i	$-0.683186\pi$
$947$	−33.4969			−1.08850			−0.544252	+	0.838922i	$0.683186\pi$
$948$	−9.22055	−	5.55897i	−0.299470	−	0.180547i
$949$	−34.1348			−1.10806
$950$	34.6551	+	14.4081i	1.12436	+	0.467459i
$951$	−38.5817	−	23.2605i	−1.25110	−	0.754272i
$952$	5.69490	+	11.5029i	0.184573	+	0.372811i
$953$	−9.08698			−0.294356			−0.147178	−	0.989110i	$-0.547019\pi$
$953$	−9.08698			−0.294356			−0.147178	+	0.989110i	$0.547019\pi$
$954$	−17.6477	−	0.668898i	−0.571365	−	0.0216564i
$955$	−40.1447	−	19.8300i	−1.29905	−	0.641684i
$956$	10.1997	−	5.88880i	0.329882	−	0.190457i
$957$	−0.822918	−	0.496129i	−0.0266012	−	0.0160376i
$958$	11.5051	+	19.9275i	0.371714	+	0.643827i
$959$	1.85939	−	29.0628i	0.0600427	−	0.938486i
$960$	3.26182	−	2.08819i	0.105275	−	0.0673960i
$961$	5.98536			0.193076
$962$	19.3274	+	11.1587i	0.623141	+	0.359771i
$963$	21.8121	−	34.6765i	0.702886	−	1.11743i
$964$	19.9120	−	11.4962i	0.641323	−	0.370268i
$965$	−38.1195	−	18.8296i	−1.22711	−	0.606147i
$966$	8.52640	+	0.707892i	0.274332	+	0.0227761i
$967$	−0.584986	+	0.337742i	−0.0188119	+	0.0108610i	−0.509376	−	0.860544i	$-0.670124\pi$
$967$	−0.584986	+	0.337742i	−0.0188119	+	0.0108610i	0.490565	+	0.871405i	$0.336791\pi$
$968$	5.22175	−	9.04434i	0.167833	−	0.290696i
$969$	54.0154	+	32.5653i	1.73522	+	1.04615i
$970$	−5.75867	−	8.63074i	−0.184900	−	0.277116i
$971$	−3.90049	−	6.75585i	−0.125173	−	0.216805i	0.796628	−	0.604470i	$-0.206615\pi$
$971$	−3.90049	−	6.75585i	−0.125173	−	0.216805i	−0.921800	+	0.387665i	$0.873282\pi$
$972$	−14.1766	+	6.48260i	−0.454715	+	0.207929i
$973$	44.2276	+	2.82960i	1.41787	+	0.0907129i
$974$	−9.17108	−	5.29492i	−0.293860	−	0.169660i
$975$	−23.3120	+	17.1490i	−0.746581	+	0.549208i
$976$			1.71256i			0.0548176i
$977$	−45.4500			−1.45407			−0.727037	−	0.686598i	$-0.759103\pi$
$977$	−45.4500			−1.45407			−0.727037	+	0.686598i	$0.759103\pi$
$978$	12.7740	+	0.241999i	0.408468	+	0.00773827i
$979$	9.80175	+	5.65904i	0.313265	+	0.180864i
$980$	15.6214	+	0.985300i	0.499008	+	0.0314743i
$981$	−30.8115	−	1.16784i	−0.983735	−	0.0372864i
$982$	−2.99490	+	1.72911i	−0.0955713	+	0.0551781i
$983$	−51.2704	+	29.6010i	−1.63527	+	0.944125i	−0.652843	+	0.757493i	$0.726424\pi$
$983$	−51.2704	+	29.6010i	−1.63527	+	0.944125i	−0.982430	+	0.186632i	$0.940243\pi$
$984$	0.0557586	−	2.94324i	0.00177752	−	0.0938272i
$985$	6.87455	−	13.9171i	0.219041	−	0.443436i
$986$	1.80392	+	3.12449i	0.0574486	+	0.0995039i
$987$	48.1183	−	22.6981i	1.53162	−	0.722490i
$988$	−21.7231	−	12.5418i	−0.691103	−	0.399009i
$989$	−14.2649	+	8.23582i	−0.453596	+	0.261884i
$990$	−4.26492	+	2.61782i	−0.135548	+	0.0831997i
$991$	−3.52175	+	6.09985i	−0.111872	+	0.193768i	−0.916525	−	0.399977i	$-0.869018\pi$
$991$	−3.52175	+	6.09985i	−0.111872	+	0.193768i	0.804653	+	0.593745i	$0.202351\pi$
$992$			5.00146i			0.158797i
$993$	19.8736	+	11.9816i	0.630668	+	0.380223i
$994$	−6.11836	+	9.18775i	−0.194063	+	0.291418i
$995$	−8.39022	+	5.59819i	−0.265988	+	0.177474i
$996$	2.19366	+	3.97140i	0.0695088	+	0.125839i
$997$	−21.9085	−	37.9467i	−0.693851	−	1.20178i	−0.970567	−	0.240833i	$-0.922580\pi$
$997$	−21.9085	−	37.9467i	−0.693851	−	1.20178i	0.276716	−	0.960952i	$-0.410754\pi$
$998$	−7.23460	+	12.5307i	−0.229007	+	0.396652i
$999$	15.6161	+	30.9897i	0.494071	+	0.980472i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.bi.a.479.20	yes	48
3.2	odd	2		1890.2.bi.b.899.9		48
5.4	even	2		630.2.bi.b.479.5	yes	48
7.5	odd	6		630.2.r.b.299.21	yes	48
9.4	even	3		1890.2.r.b.1529.1		48
9.5	odd	6		630.2.r.a.59.4	✓	48
15.14	odd	2		1890.2.bi.a.899.7		48
21.5	even	6		1890.2.r.a.89.1		48
35.19	odd	6		630.2.r.a.299.4	yes	48
45.4	even	6		1890.2.r.a.1529.1		48
45.14	odd	6		630.2.r.b.59.21	yes	48
63.5	even	6		630.2.bi.b.509.5	yes	48
63.40	odd	6		1890.2.bi.a.719.7		48
105.89	even	6		1890.2.r.b.89.1		48
315.194	even	6	inner	630.2.bi.a.509.20	yes	48
315.229	odd	6		1890.2.bi.b.719.9		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.r.a.59.4	✓	48	9.5	odd	6
630.2.r.a.299.4	yes	48	35.19	odd	6
630.2.r.b.59.21	yes	48	45.14	odd	6
630.2.r.b.299.21	yes	48	7.5	odd	6
630.2.bi.a.479.20	yes	48	1.1	even	1	trivial
630.2.bi.a.509.20	yes	48	315.194	even	6	inner
630.2.bi.b.479.5	yes	48	5.4	even	2
630.2.bi.b.509.5	yes	48	63.5	even	6
1890.2.r.a.89.1		48	21.5	even	6
1890.2.r.a.1529.1		48	45.4	even	6
1890.2.r.b.89.1		48	105.89	even	6
1890.2.r.b.1529.1		48	9.4	even	3
1890.2.bi.a.719.7		48	63.40	odd	6
1890.2.bi.a.899.7		48	15.14	odd	2
1890.2.bi.b.719.9		48	315.229	odd	6
1890.2.bi.b.899.9		48	3.2	odd	2

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:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.bi (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(1.48333 + 0.894282i) q^{3} +1.00000 q^{4} +(0.990306 - 2.00482i) q^{5} +(-1.48333 - 0.894282i) q^{6} +(-2.20215 - 1.46647i) q^{7} -1.00000 q^{8} +(1.40052 + 2.65303i) q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(1.48333 + 0.894282i) q^{3} +1.00000 q^{4} +(0.990306 - 2.00482i) q^{5} +(-1.48333 - 0.894282i) q^{6} +(-2.20215 - 1.46647i) q^{7} -1.00000 q^{8} +(1.40052 + 2.65303i) q^{9} +(-0.990306 + 2.00482i) q^{10} +(0.646046 - 0.372995i) q^{11} +(1.48333 + 0.894282i) q^{12} +(-1.67087 - 2.89402i) q^{13} +(2.20215 + 1.46647i) q^{14} +(3.26182 - 2.08819i) q^{15} +1.00000 q^{16} +(4.20138 + 2.42567i) q^{17} +(-1.40052 - 2.65303i) q^{18} +(6.50055 - 3.75309i) q^{19} +(0.990306 - 2.00482i) q^{20} +(-1.95507 - 4.14460i) q^{21} +(-0.646046 + 0.372995i) q^{22} +(0.933507 - 1.61688i) q^{23} +(-1.48333 - 0.894282i) q^{24} +(-3.03859 - 3.97077i) q^{25} +(1.67087 + 2.89402i) q^{26} +(-0.295123 + 5.18776i) q^{27} +(-2.20215 - 1.46647i) q^{28} +(-0.644047 - 0.371841i) q^{29} +(-3.26182 + 2.08819i) q^{30} -5.00146i q^{31} -1.00000 q^{32} +(1.29186 + 0.0244738i) q^{33} +(-4.20138 - 2.42567i) q^{34} +(-5.12081 + 2.96266i) q^{35} +(1.40052 + 2.65303i) q^{36} +(5.78366 - 3.33920i) q^{37} +(-6.50055 + 3.75309i) q^{38} +(0.109633 - 5.78701i) q^{39} +(-0.990306 + 2.00482i) q^{40} +(0.849794 + 1.47189i) q^{41} +(1.95507 + 4.14460i) q^{42} +(-7.64047 - 4.41123i) q^{43} +(0.646046 - 0.372995i) q^{44} +(6.70578 - 0.180480i) q^{45} +(-0.933507 + 1.61688i) q^{46} +11.6099i q^{47} +(1.48333 + 0.894282i) q^{48} +(2.69893 + 6.45877i) q^{49} +(3.03859 + 3.97077i) q^{50} +(4.06279 + 7.35528i) q^{51} +(-1.67087 - 2.89402i) q^{52} +(2.94339 - 5.09811i) q^{53} +(0.295123 - 5.18776i) q^{54} +(-0.108003 - 1.66458i) q^{55} +(2.20215 + 1.46647i) q^{56} +(12.9988 + 0.246257i) q^{57} +(0.644047 + 0.371841i) q^{58} -4.66316 q^{59} +(3.26182 - 2.08819i) q^{60} +1.71256i q^{61} +5.00146i q^{62} +(0.806427 - 7.89618i) q^{63} +1.00000 q^{64} +(-7.45666 + 0.483811i) q^{65} +(-1.29186 - 0.0244738i) q^{66} +4.53308i q^{67} +(4.20138 + 2.42567i) q^{68} +(2.83065 - 1.56355i) q^{69} +(5.12081 - 2.96266i) q^{70} +4.17217i q^{71} +(-1.40052 - 2.65303i) q^{72} +(5.10736 - 8.84620i) q^{73} +(-5.78366 + 3.33920i) q^{74} +(-0.956236 - 8.60730i) q^{75} +(6.50055 - 3.75309i) q^{76} +(-1.96968 - 0.126017i) q^{77} +(-0.109633 + 5.78701i) q^{78} -6.21613 q^{79} +(0.990306 - 2.00482i) q^{80} +(-5.07709 + 7.43123i) q^{81} +(-0.849794 - 1.47189i) q^{82} +(2.26849 + 1.30971i) q^{83} +(-1.95507 - 4.14460i) q^{84} +(9.02367 - 6.02085i) q^{85} +(7.64047 + 4.41123i) q^{86} +(-0.622802 - 1.12752i) q^{87} +(-0.646046 + 0.372995i) q^{88} +(7.58595 + 13.1393i) q^{89} +(-6.70578 + 0.180480i) q^{90} +(-0.564503 + 8.82335i) q^{91} +(0.933507 - 1.61688i) q^{92} +(4.47272 - 7.41881i) q^{93} -11.6099i q^{94} +(-1.08673 - 16.7491i) q^{95} +(-1.48333 - 0.894282i) q^{96} +(-2.32004 + 4.01843i) q^{97} +(-2.69893 - 6.45877i) q^{98} +(1.89437 + 1.19159i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 48 q^{2} + 48 q^{4} - 3 q^{7} - 48 q^{8}+O(q^{10}) \) 48 * q - 48 * q^2 + 48 * q^4 - 3 * q^7 - 48 * q^8	\( 48 q - 48 q^{2} + 48 q^{4} - 3 q^{7} - 48 q^{8} + 6 q^{11} + 3 q^{14} + 6 q^{15} + 48 q^{16} + 8 q^{21} - 6 q^{22} - 3 q^{23} + 18 q^{25} - 3 q^{28} - 3 q^{29} - 6 q^{30} - 48 q^{32} - 18 q^{35} - 18 q^{39} - 3 q^{41} - 8 q^{42} + 6 q^{44} + 15 q^{45} + 3 q^{46} + 3 q^{49} - 18 q^{50} + 10 q^{51} + 42 q^{55} + 3 q^{56} + 22 q^{57} + 3 q^{58} + 6 q^{60} + 43 q^{63} + 48 q^{64} - 12 q^{65} - 42 q^{69} + 18 q^{70} + 18 q^{73} + 18 q^{75} + 12 q^{77} + 18 q^{78} + 8 q^{81} + 3 q^{82} - 9 q^{83} + 8 q^{84} + 33 q^{85} + 15 q^{87} - 6 q^{88} - 33 q^{89} - 15 q^{90} - 3 q^{92} + 8 q^{93} + 24 q^{97} - 3 q^{98} - 26 q^{99}+O(q^{100}) \) 48 * q - 48 * q^2 + 48 * q^4 - 3 * q^7 - 48 * q^8 + 6 * q^11 + 3 * q^14 + 6 * q^15 + 48 * q^16 + 8 * q^21 - 6 * q^22 - 3 * q^23 + 18 * q^25 - 3 * q^28 - 3 * q^29 - 6 * q^30 - 48 * q^32 - 18 * q^35 - 18 * q^39 - 3 * q^41 - 8 * q^42 + 6 * q^44 + 15 * q^45 + 3 * q^46 + 3 * q^49 - 18 * q^50 + 10 * q^51 + 42 * q^55 + 3 * q^56 + 22 * q^57 + 3 * q^58 + 6 * q^60 + 43 * q^63 + 48 * q^64 - 12 * q^65 - 42 * q^69 + 18 * q^70 + 18 * q^73 + 18 * q^75 + 12 * q^77 + 18 * q^78 + 8 * q^81 + 3 * q^82 - 9 * q^83 + 8 * q^84 + 33 * q^85 + 15 * q^87 - 6 * q^88 - 33 * q^89 - 15 * q^90 - 3 * q^92 + 8 * q^93 + 24 * q^97 - 3 * q^98 - 26 * q^99

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