LMFDB - Embedded newform 315.2.bh.c.169.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(169,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 3, 0]))

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

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

chi := DirichletCharacter("315.169");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.bh (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:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			169.16
Character	$\chi$	$=$	315.169
Dual form			315.2.bh.c.274.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0813489 - 0.0469668i) q^{2} +(-1.71108 + 0.268687i) q^{3} +(-0.995588 - 1.72441i) q^{4} +(-1.28952 + 1.82678i) q^{5} +(0.151814 + 0.0585067i) q^{6} +(0.866025 + 0.500000i) q^{7} +0.374905i q^{8} +(2.85561 - 0.919491i) q^{9} +O(q^{10})$	\(q+(-0.0813489 - 0.0469668i) q^{2} +(-1.71108 + 0.268687i) q^{3} +(-0.995588 - 1.72441i) q^{4} +(-1.28952 + 1.82678i) q^{5} +(0.151814 + 0.0585067i) q^{6} +(0.866025 + 0.500000i) q^{7} +0.374905i q^{8} +(2.85561 - 0.919491i) q^{9} +(0.190699 - 0.0880417i) q^{10} +(0.322559 - 0.558689i) q^{11} +(2.16686 + 2.68311i) q^{12} +(4.19970 - 2.42470i) q^{13} +(-0.0469668 - 0.0813489i) q^{14} +(1.71565 - 3.47225i) q^{15} +(-1.97357 + 3.41832i) q^{16} +4.21737i q^{17} +(-0.275487 - 0.0593195i) q^{18} +7.19335 q^{19} +(4.43395 + 0.404947i) q^{20} +(-1.61619 - 0.622852i) q^{21} +(-0.0524796 + 0.0302991i) q^{22} +(6.44746 - 3.72244i) q^{23} +(-0.100732 - 0.641495i) q^{24} +(-1.67425 - 4.71136i) q^{25} -0.455521 q^{26} +(-4.63914 + 2.34059i) q^{27} -1.99118i q^{28} +(-1.11013 + 1.92280i) q^{29} +(-0.302647 + 0.201885i) q^{30} +(0.253837 + 0.439659i) q^{31} +(0.970450 - 0.560290i) q^{32} +(-0.401813 + 1.04263i) q^{33} +(0.198077 - 0.343079i) q^{34} +(-2.03015 + 0.937276i) q^{35} +(-4.42860 - 4.00881i) q^{36} -1.60777i q^{37} +(-0.585171 - 0.337849i) q^{38} +(-6.53456 + 5.27727i) q^{39} +(-0.684870 - 0.483450i) q^{40} +(5.46633 + 9.46797i) q^{41} +(0.102221 + 0.126575i) q^{42} +(-5.40817 - 3.12241i) q^{43} -1.28454 q^{44} +(-2.00268 + 6.40229i) q^{45} -0.699325 q^{46} +(5.34492 + 3.08589i) q^{47} +(2.45848 - 6.37930i) q^{48} +(0.500000 + 0.866025i) q^{49} +(-0.0850787 + 0.461898i) q^{50} +(-1.13315 - 7.21628i) q^{51} +(-8.36235 - 4.82800i) q^{52} +1.46595i q^{53} +(0.487319 + 0.0274811i) q^{54} +(0.604654 + 1.30969i) q^{55} +(-0.187453 + 0.324678i) q^{56} +(-12.3084 + 1.93276i) q^{57} +(0.180615 - 0.104278i) q^{58} +(-6.91952 - 11.9850i) q^{59} +(-7.69567 + 0.498446i) q^{60} +(-6.28389 + 10.8840i) q^{61} -0.0476877i q^{62} +(2.93278 + 0.631505i) q^{63} +7.78901 q^{64} +(-0.986226 + 10.7986i) q^{65} +(0.0816561 - 0.0659449i) q^{66} +(7.50426 - 4.33259i) q^{67} +(7.27248 - 4.19877i) q^{68} +(-10.0320 + 8.10176i) q^{69} +(0.209171 + 0.0191033i) q^{70} +2.74476 q^{71} +(0.344722 + 1.07059i) q^{72} -9.89216i q^{73} +(-0.0755116 + 0.130790i) q^{74} +(4.13067 + 7.61168i) q^{75} +(-7.16162 - 12.4043i) q^{76} +(0.558689 - 0.322559i) q^{77} +(0.779435 - 0.122393i) q^{78} +(-0.580387 + 1.00526i) q^{79} +(-3.69956 - 8.01328i) q^{80} +(7.30907 - 5.25142i) q^{81} -1.02694i q^{82} +(5.43115 + 3.13568i) q^{83} +(0.535003 + 3.40707i) q^{84} +(-7.70422 - 5.43841i) q^{85} +(0.293299 + 0.508009i) q^{86} +(1.38289 - 3.58835i) q^{87} +(0.209455 + 0.120929i) q^{88} -6.61117 q^{89} +(0.463610 - 0.426759i) q^{90} +4.84940 q^{91} +(-12.8380 - 7.41204i) q^{92} +(-0.552468 - 0.684091i) q^{93} +(-0.289869 - 0.502068i) q^{94} +(-9.27601 + 13.1407i) q^{95} +(-1.50998 + 1.21945i) q^{96} +(6.03755 + 3.48578i) q^{97} -0.0939336i q^{98} +(0.407395 - 1.89199i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 34 q^{4} - 10 q^{5} - 18 q^{6} - 14 q^{9}+O(q^{10}) $ 64 * q + 34 * q^4 - 10 * q^5 - 18 * q^6 - 14 * q^9	$ 64 q + 34 q^{4} - 10 q^{5} - 18 q^{6} - 14 q^{9} - 4 q^{10} + 18 q^{11} - 6 q^{14} - 14 q^{15} - 46 q^{16} + 48 q^{19} - 2 q^{20} - 2 q^{21} - 12 q^{24} + 18 q^{25} - 12 q^{26} - 30 q^{29} - 4 q^{30} - 4 q^{31} + 34 q^{34} + 8 q^{35} - 42 q^{36} - 8 q^{39} - 6 q^{40} + 28 q^{41} + 68 q^{44} - 6 q^{45} - 24 q^{46} + 32 q^{49} - 58 q^{50} + 62 q^{51} + 54 q^{54} - 12 q^{55} + 18 q^{56} + 16 q^{59} - 66 q^{60} + 40 q^{61} - 100 q^{64} - 18 q^{65} - 146 q^{66} - 20 q^{69} - 4 q^{70} - 176 q^{71} - 20 q^{74} + 60 q^{75} - 22 q^{79} + 64 q^{80} - 58 q^{81} - 4 q^{84} - 14 q^{85} + 60 q^{86} - 200 q^{89} + 8 q^{90} - 16 q^{91} - 42 q^{94} + 68 q^{95} + 210 q^{96} + 90 q^{99}+O(q^{100}) $ 64 * q + 34 * q^4 - 10 * q^5 - 18 * q^6 - 14 * q^9 - 4 * q^10 + 18 * q^11 - 6 * q^14 - 14 * q^15 - 46 * q^16 + 48 * q^19 - 2 * q^20 - 2 * q^21 - 12 * q^24 + 18 * q^25 - 12 * q^26 - 30 * q^29 - 4 * q^30 - 4 * q^31 + 34 * q^34 + 8 * q^35 - 42 * q^36 - 8 * q^39 - 6 * q^40 + 28 * q^41 + 68 * q^44 - 6 * q^45 - 24 * q^46 + 32 * q^49 - 58 * q^50 + 62 * q^51 + 54 * q^54 - 12 * q^55 + 18 * q^56 + 16 * q^59 - 66 * q^60 + 40 * q^61 - 100 * q^64 - 18 * q^65 - 146 * q^66 - 20 * q^69 - 4 * q^70 - 176 * q^71 - 20 * q^74 + 60 * q^75 - 22 * q^79 + 64 * q^80 - 58 * q^81 - 4 * q^84 - 14 * q^85 + 60 * q^86 - 200 * q^89 + 8 * q^90 - 16 * q^91 - 42 * q^94 + 68 * q^95 + 210 * q^96 + 90 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$-1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−0.0813489	−	0.0469668i	−0.0575223	−	0.0332105i	0.470963	−	0.882153i	$-0.343907\pi$
$2$	−0.0813489	−	0.0469668i	−0.0575223	−	0.0332105i	−0.528485	+	0.848942i	$0.677240\pi$
$3$	−1.71108	+	0.268687i	−0.987895	+	0.155126i
$3$	−1.71108	+	0.268687i	−0.987895	+	0.155126i
$4$	−0.995588	−	1.72441i	−0.497794	−	0.862205i
$5$	−1.28952	+	1.82678i	−0.576693	+	0.816961i
$5$	−1.28952	+	1.82678i	−0.576693	+	0.816961i
$6$	0.151814	+	0.0585067i	0.0619778	+	0.0238853i
$7$	0.866025	+	0.500000i	0.327327	+	0.188982i
$7$	0.866025	+	0.500000i	0.327327	+	0.188982i
$8$			0.374905i			0.132549i
$9$	2.85561	−	0.919491i	0.951872	−	0.306497i
$10$	0.190699	−	0.0880417i	0.0603044	−	0.0278412i
$11$	0.322559	−	0.558689i	0.0972552	−	0.168451i	−0.813292	−	0.581855i	$-0.802327\pi$
$11$	0.322559	−	0.558689i	0.0972552	−	0.168451i	0.910548	+	0.413404i	$0.135660\pi$
$12$	2.16686	+	2.68311i	0.625519	+	0.774546i
$13$	4.19970	−	2.42470i	1.16479	−	0.672491i	0.212341	−	0.977196i	$-0.431891\pi$
$13$	4.19970	−	2.42470i	1.16479	−	0.672491i	0.952447	+	0.304705i	$0.0985578\pi$
$14$	−0.0469668	−	0.0813489i	−0.0125524	−	0.0217414i
$15$	1.71565	−	3.47225i	0.442980	−	0.896532i
$16$	−1.97357	+	3.41832i	−0.493392	+	0.854580i
$17$			4.21737i			1.02286i	0.859324	+	0.511432i	$0.170885\pi$
$17$			4.21737i			1.02286i	−0.859324	+	0.511432i	$0.829115\pi$
$18$	−0.275487	−	0.0593195i	−0.0649328	−	0.0139817i
$19$	7.19335			1.65027			0.825134	−	0.564937i	$-0.191099\pi$
$19$	7.19335			1.65027			0.825134	+	0.564937i	$0.191099\pi$
$20$	4.43395	+	0.404947i	0.991462	+	0.0905489i
$21$	−1.61619	−	0.622852i	−0.352681	−	0.135918i
$22$	−0.0524796	+	0.0302991i	−0.0111887	+	0.00645980i
$23$	6.44746	−	3.72244i	1.34439	−	0.776183i	0.356940	−	0.934127i	$-0.383820\pi$
$23$	6.44746	−	3.72244i	1.34439	−	0.776183i	0.987448	+	0.157944i	$0.0504867\pi$
$24$	−0.100732	−	0.641495i	−0.0205619	−	0.130945i
$25$	−1.67425	−	4.71136i	−0.334851	−	0.942271i
$26$	−0.455521			−0.0893351
$27$	−4.63914	+	2.34059i	−0.892803	+	0.450447i
$28$		−	1.99118i		−	0.376297i
$29$	−1.11013	+	1.92280i	−0.206146	+	0.357055i	−0.950497	−	0.310733i	$-0.899425\pi$
$29$	−1.11013	+	1.92280i	−0.206146	+	0.357055i	0.744351	+	0.667788i	$0.232759\pi$
$30$	−0.302647	+	0.201885i	−0.0552555	+	0.0368590i
$31$	0.253837	+	0.439659i	0.0455905	+	0.0789651i	0.887920	−	0.459998i	$-0.152150\pi$
$31$	0.253837	+	0.439659i	0.0455905	+	0.0789651i	−0.842330	+	0.538963i	$0.818816\pi$
$32$	0.970450	−	0.560290i	0.171553	−	0.0990462i
$33$	−0.401813	+	1.04263i	−0.0699467	+	0.181499i
$34$	0.198077	−	0.343079i	0.0339698	−	0.0588375i
$35$	−2.03015	+	0.937276i	−0.343158	+	0.158429i
$36$	−4.42860	−	4.00881i	−0.738099	−	0.668136i
$37$		−	1.60777i		−	0.264315i	−0.991229	−	0.132158i	$-0.957810\pi$
$37$		−	1.60777i		−	0.264315i	0.991229	−	0.132158i	$-0.0421905\pi$
$38$	−0.585171	−	0.337849i	−0.0949273	−	0.0548063i
$39$	−6.53456	+	5.27727i	−1.04637	+	0.845039i
$40$	−0.684870	−	0.483450i	−0.108287	−	0.0764401i
$41$	5.46633	+	9.46797i	0.853698	+	1.47865i	0.877848	+	0.478940i	$0.158979\pi$
$41$	5.46633	+	9.46797i	0.853698	+	1.47865i	−0.0241501	+	0.999708i	$0.507688\pi$
$42$	0.102221	+	0.126575i	0.0157731	+	0.0195310i
$43$	−5.40817	−	3.12241i	−0.824738	−	0.476163i	0.0273094	−	0.999627i	$-0.491306\pi$
$43$	−5.40817	−	3.12241i	−0.824738	−	0.476163i	−0.852048	+	0.523464i	$0.824639\pi$
$44$	−1.28454			−0.193652
$45$	−2.00268	+	6.40229i	−0.298542	+	0.954397i
$46$	−0.699325			−0.103110
$47$	5.34492	+	3.08589i	0.779637	+	0.450124i	0.836302	−	0.548270i	$-0.184713\pi$
$47$	5.34492	+	3.08589i	0.779637	+	0.450124i	−0.0566646	+	0.998393i	$0.518047\pi$
$48$	2.45848	−	6.37930i	0.354851	−	0.920773i
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$	−0.0850787	+	0.461898i	−0.0120319	+	0.0653222i
$51$	−1.13315	−	7.21628i	−0.158673	−	1.01048i
$52$	−8.36235	−	4.82800i	−1.15965	−	0.669524i
$53$			1.46595i			0.201364i	0.994919	+	0.100682i	$0.0321024\pi$
$53$			1.46595i			0.201364i	−0.994919	+	0.100682i	$0.967898\pi$
$54$	0.487319	+	0.0274811i	0.0663157	+	0.00373970i
$55$	0.604654	+	1.30969i	0.0815315	+	0.176598i
$56$	−0.187453	+	0.324678i	−0.0250494	+	0.0433869i
$57$	−12.3084	+	1.93276i	−1.63029	+	0.256000i
$58$	0.180615	−	0.104278i	0.0237160	−	0.0136924i
$59$	−6.91952	−	11.9850i	−0.900845	−	1.56031i	−0.826400	−	0.563084i	$-0.809615\pi$
$59$	−6.91952	−	11.9850i	−0.900845	−	1.56031i	−0.0744450	−	0.997225i	$-0.523719\pi$
$60$	−7.69567	+	0.498446i	−0.993506	+	0.0643491i
$61$	−6.28389	+	10.8840i	−0.804569	+	1.39355i	0.112012	+	0.993707i	$0.464270\pi$
$61$	−6.28389	+	10.8840i	−0.804569	+	1.39355i	−0.916582	+	0.399848i	$0.869063\pi$
$62$		−	0.0476877i		−	0.00605634i
$63$	2.93278	+	0.631505i	0.369496	+	0.0795621i
$64$	7.78901			0.973627
$65$	−0.986226	+	10.7986i	−0.122326	+	1.33941i
$66$	0.0816561	−	0.0659449i	0.0100512	−	0.00811726i
$67$	7.50426	−	4.33259i	0.916792	−	0.529310i	0.0341815	−	0.999416i	$-0.489118\pi$
$67$	7.50426	−	4.33259i	0.916792	−	0.529310i	0.882610	+	0.470106i	$0.155784\pi$
$68$	7.27248	−	4.19877i	0.881918	−	0.509175i
$69$	−10.0320	+	8.10176i	−1.20771	+	0.975337i
$70$	0.209171	+	0.0191033i	0.0250008	+	0.00228329i
$71$	2.74476			0.325743			0.162871	−	0.986647i	$-0.447924\pi$
$71$	2.74476			0.325743			0.162871	+	0.986647i	$0.447924\pi$
$72$	0.344722	+	1.07059i	0.0406259	+	0.126170i
$73$		−	9.89216i		−	1.15779i	−0.815402	−	0.578895i	$-0.803484\pi$
$73$		−	9.89216i		−	1.15779i	0.815402	−	0.578895i	$-0.196516\pi$
$74$	−0.0755116	+	0.130790i	−0.00877805	+	0.0152040i
$75$	4.13067	+	7.61168i	0.476968	+	0.878921i
$76$	−7.16162	−	12.4043i	−0.821494	−	1.42287i
$77$	0.558689	−	0.322559i	0.0636685	−	0.0367590i
$78$	0.779435	−	0.122393i	0.0882537	−	0.0138582i
$79$	−0.580387	+	1.00526i	−0.0652986	+	0.113100i	−0.896826	−	0.442383i	$-0.854133\pi$
$79$	−0.580387	+	1.00526i	−0.0652986	+	0.113100i	0.831528	+	0.555483i	$0.187467\pi$
$80$	−3.69956	−	8.01328i	−0.413623	−	0.895912i
$81$	7.30907	−	5.25142i	0.812119	−	0.583492i
$82$		−	1.02694i		−	0.113407i
$83$	5.43115	+	3.13568i	0.596146	+	0.344185i	0.767524	−	0.641020i	$-0.221488\pi$
$83$	5.43115	+	3.13568i	0.596146	+	0.344185i	−0.171378	+	0.985205i	$0.554822\pi$
$84$	0.535003	+	3.40707i	0.0583736	+	0.371742i
$85$	−7.70422	−	5.43841i	−0.835640	−	0.589878i
$86$	0.293299	+	0.508009i	0.0316272	+	0.0547800i
$87$	1.38289	−	3.58835i	0.148262	−	0.384711i
$88$	0.209455	+	0.120929i	0.0223280	+	0.0128911i
$89$	−6.61117			−0.700783			−0.350392	−	0.936603i	$-0.613951\pi$
$89$	−6.61117			−0.700783			−0.350392	+	0.936603i	$0.613951\pi$
$90$	0.463610	−	0.426759i	0.0488688	−	0.0449844i
$91$	4.84940			0.508355
$92$	−12.8380	−	7.41204i	−1.33846	−	0.772759i
$93$	−0.552468	−	0.684091i	−0.0572882	−	0.0709369i
$94$	−0.289869	−	0.502068i	−0.0298977	−	0.0517843i
$95$	−9.27601	+	13.1407i	−0.951698	+	1.34821i
$96$	−1.50998	+	1.21945i	−0.154112	+	0.124460i
$97$	6.03755	+	3.48578i	0.613021	+	0.353928i	0.774147	−	0.633006i	$-0.218179\pi$
$97$	6.03755	+	3.48578i	0.613021	+	0.353928i	−0.161126	+	0.986934i	$0.551513\pi$
$98$		−	0.0939336i		−	0.00948872i
$99$	0.407395	−	1.89199i	0.0409448	−	0.190152i
$100$	−6.45744	+	7.57767i	−0.645744	+	0.757767i
$101$	0.771152	−	1.33567i	0.0767325	−	0.132905i	−0.825106	−	0.564978i	$-0.808885\pi$
$101$	0.771152	−	1.33567i	0.0767325	−	0.132905i	0.901838	+	0.432074i	$0.142218\pi$
$102$	−0.246745	+	0.640257i	−0.0244314	+	0.0633949i
$103$	9.36998	−	5.40976i	0.923251	−	0.533039i	0.0385803	−	0.999256i	$-0.487716\pi$
$103$	9.36998	−	5.40976i	0.923251	−	0.533039i	0.884671	+	0.466216i	$0.154383\pi$
$104$	0.909033	+	1.57449i	0.0891380	+	0.154392i
$105$	3.22193	−	2.14923i	0.314428	−	0.209744i
$106$	0.0688509	−	0.119253i	0.00668739	−	0.0115829i
$107$		−	0.577954i		−	0.0558730i	−0.999610	−	0.0279365i	$-0.991106\pi$
$107$		−	0.577954i		−	0.0558730i	0.999610	−	0.0279365i	$-0.00889361\pi$
$108$	8.65481	+	5.66951i	0.832810	+	0.545549i
$109$	7.66606			0.734275			0.367138	−	0.930167i	$-0.380338\pi$
$109$	7.66606			0.734275			0.367138	+	0.930167i	$0.380338\pi$
$110$	0.0123239	−	0.134940i	0.00117504	−	0.0128660i
$111$	0.431985	+	2.75102i	0.0410022	+	0.261115i
$112$	−3.41832	+	1.97357i	−0.323001	+	0.186485i
$113$	−7.55880	+	4.36408i	−0.711072	+	0.410538i	−0.811458	−	0.584411i	$-0.801326\pi$
$113$	−7.55880	+	4.36408i	−0.711072	+	0.410538i	0.100386	+	0.994949i	$0.467992\pi$
$114$	1.09205	+	0.420860i	0.102280	+	0.0394171i
$115$	−1.51407	+	16.5783i	−0.141188	+	1.54593i
$116$	4.42092			0.410473
$117$	9.76325	−	10.7856i	0.902612	−	0.997129i
$118$			1.29995i			0.119670i
$119$	−2.10869	+	3.65235i	−0.193303	+	0.334811i
$120$	1.30177	+	0.643208i	0.118834	+	0.0587166i
$121$	5.29191	+	9.16586i	0.481083	+	0.833260i
$122$	1.02237	−	0.590268i	0.0925614	−	0.0534403i
$123$	−11.8973	−	14.7318i	−1.07274	−	1.32832i
$124$	0.505435	−	0.875439i	0.0453894	−	0.0786167i
$125$	10.7656	+	3.01692i	0.962905	+	0.269841i
$126$	−0.208919	−	0.189115i	−0.0186119	−	0.0168477i
$127$			7.56999i			0.671728i	0.941911	+	0.335864i	$0.109028\pi$
$127$			7.56999i			0.671728i	−0.941911	+	0.335864i	$0.890972\pi$
$128$	−2.57453	−	1.48640i	−0.227558	−	0.131381i
$129$	10.0928	+	3.88960i	0.888620	+	0.342460i
$130$	0.587406	−	0.832138i	0.0515189	−	0.0729833i
$131$	−5.86760	−	10.1630i	−0.512654	−	0.887943i	−0.999892	−	0.0146741i	$-0.995329\pi$
$131$	−5.86760	−	10.1630i	−0.512654	−	0.887943i	0.487238	−	0.873269i	$-0.338004\pi$
$132$	2.19796	−	0.345140i	0.191308	−	0.0300406i
$133$	6.22963	+	3.59668i	0.540177	+	0.311871i
$134$	−0.813951			−0.0703147
$135$	1.70654	−	11.4929i	0.146875	−	0.989155i
$136$	−1.58112			−0.135580
$137$	4.06518	+	2.34703i	0.347312	+	0.200520i	0.663501	−	0.748176i	$-0.269070\pi$
$137$	4.06518	+	2.34703i	0.347312	+	0.200520i	−0.316189	+	0.948696i	$0.602403\pi$
$138$	1.19660	−	0.187899i	0.101862	−	0.0159950i
$139$	1.75358	+	3.03730i	0.148737	+	0.257620i	0.930761	−	0.365628i	$-0.119146\pi$
$139$	1.75358	+	3.03730i	0.148737	+	0.257620i	−0.782024	+	0.623248i	$0.785813\pi$
$140$	3.63744	+	2.56767i	0.307420	+	0.217008i
$141$	−9.97475	−	3.84411i	−0.840025	−	0.323732i
$142$	−0.223283	−	0.128912i	−0.0187375	−	0.0108181i
$143$		−	3.12844i		−	0.261613i
$144$	−2.49264	+	11.5761i	−0.207720	+	0.964674i
$145$	−2.08099	−	4.50746i	−0.172817	−	0.374324i
$146$	−0.464603	+	0.804716i	−0.0384508	+	0.0665987i
$147$	−1.08823	−	1.34750i	−0.0897558	−	0.111140i
$148$	−2.77245	+	1.60067i	−0.227894	+	0.131574i
$149$	−9.20478	−	15.9431i	−0.754085	−	1.30611i	−0.945828	−	0.324668i	$-0.894747\pi$
$149$	−9.20478	−	15.9431i	−0.754085	−	1.30611i	0.191743	−	0.981445i	$-0.438586\pi$
$150$	0.0214710	−	0.813205i	0.00175310	−	0.0663979i
$151$	7.52857	−	13.0399i	0.612666	−	1.06117i	−0.378123	−	0.925755i	$-0.623430\pi$
$151$	7.52857	−	13.0399i	0.612666	−	1.06117i	0.990789	−	0.135414i	$-0.0432363\pi$
$152$			2.69683i			0.218742i
$153$	3.87784	+	12.0432i	0.313505	+	0.973635i
$154$	−0.0605983			−0.00488315
$155$	−1.13049	−	0.103246i	−0.0908032	−	0.00829294i
$156$	15.6059	+	6.01427i	1.24947	+	0.481527i
$157$	−17.3892	+	10.0397i	−1.38781	+	0.801252i	−0.993068	−	0.117540i	$-0.962499\pi$
$157$	−17.3892	+	10.0397i	−1.38781	+	0.801252i	−0.394741	+	0.918792i	$0.629166\pi$
$158$	0.0944276	−	0.0545178i	0.00751226	−	0.00433720i
$159$	−0.393881	−	2.50836i	−0.0312368	−	0.198926i
$160$	−0.227893	+	2.49531i	−0.0180165	+	0.197271i
$161$	7.44488			0.586739
$162$	−0.841227	+	0.0839137i	−0.0660931	+	0.00659288i
$163$			12.6859i			0.993639i	0.867854	+	0.496820i	$0.165499\pi$
$163$			12.6859i			0.993639i	−0.867854	+	0.496820i	$0.834501\pi$
$164$	10.8844	−	18.8524i	0.849931	−	1.47212i
$165$	−1.38651	−	2.07852i	−0.107940	−	0.161813i
$166$	−0.294545	−	0.510168i	−0.0228612	−	0.0395967i
$167$	−8.21434	+	4.74255i	−0.635644	+	0.366990i	−0.782935	−	0.622104i	$-0.786278\pi$
$167$	−8.21434	+	4.74255i	−0.635644	+	0.366990i	0.147290	+	0.989093i	$0.452945\pi$
$168$	0.233511	−	0.605917i	0.0180157	−	0.0467475i
$169$	5.25834	−	9.10771i	0.404487	−	0.700593i
$170$	0.371305	+	0.804251i	0.0284778	+	0.0616832i
$171$	20.5415	−	6.61422i	1.57084	−	0.505802i
$172$			12.4345i			0.948124i
$173$	−10.1626	−	5.86740i	−0.772650	−	0.446090i	0.0611689	−	0.998127i	$-0.480517\pi$
$173$	−10.1626	−	5.86740i	−0.772650	−	0.446090i	−0.833819	+	0.552038i	$0.813851\pi$
$174$	−0.281030	+	0.226958i	−0.0213048	+	0.0172056i
$175$	0.905732	−	4.91728i	0.0684669	−	0.371711i
$176$	1.27318	+	2.20522i	0.0959699	+	0.166225i
$177$	15.0601	+	18.6481i	1.13198	+	1.40168i
$178$	0.537812	+	0.310506i	0.0403107	+	0.0232734i
$179$	4.11378			0.307478			0.153739	−	0.988111i	$-0.450868\pi$
$179$	4.11378			0.307478			0.153739	+	0.988111i	$0.450868\pi$
$180$	13.0340	−	2.92061i	0.971497	−	0.217689i
$181$	−4.23094			−0.314483			−0.157242	−	0.987560i	$-0.550260\pi$
$181$	−4.23094			−0.314483			−0.157242	+	0.987560i	$0.550260\pi$
$182$	−0.394493	−	0.227761i	−0.0292418	−	0.0168827i
$183$	7.82787	−	20.3118i	0.578652	−	1.50149i
$184$	1.39556	+	2.41719i	0.102882	+	0.178197i
$185$	2.93704	+	2.07325i	0.215935	+	0.152429i
$186$	0.0128131	+	0.0815976i	0.000939499	+	0.00598303i
$187$	2.35620	+	1.36035i	0.172302	+	0.0994788i
$188$		−	12.2891i		−	0.896276i
$189$	−5.18791	−	0.292559i	−0.377365	−	0.0212805i
$190$	1.37177	−	0.633315i	0.0995185	−	0.0459455i
$191$	8.03834	−	13.9228i	0.581634	−	1.00742i	−0.413652	−	0.910435i	$-0.635747\pi$
$191$	8.03834	−	13.9228i	0.581634	−	1.00742i	0.995286	−	0.0969842i	$-0.0309196\pi$
$192$	−13.3277	+	2.09280i	−0.961841	+	0.151035i
$193$	−4.59001	+	2.65005i	−0.330396	+	0.190754i	−0.656017	−	0.754746i	$-0.727760\pi$
$193$	−4.59001	+	2.65005i	−0.330396	+	0.190754i	0.325621	+	0.945500i	$0.394427\pi$
$194$	−0.327432	−	0.567129i	−0.0235083	−	0.0407175i
$195$	−1.21394	−	18.7424i	−0.0869318	−	1.34217i
$196$	0.995588	−	1.72441i	0.0711134	−	0.123172i
$197$			3.34357i			0.238219i	0.992881	+	0.119110i	$0.0380040\pi$
$197$			3.34357i			0.238219i	−0.992881	+	0.119110i	$0.961996\pi$
$198$	−0.122002	+	0.134777i	−0.00867029	+	0.00957820i
$199$	4.12588			0.292476			0.146238	−	0.989249i	$-0.453283\pi$
$199$	4.12588			0.292476			0.146238	+	0.989249i	$0.453283\pi$
$200$	1.76631	−	0.627687i	0.124897	−	0.0443841i
$201$	−11.6763	+	9.42972i	−0.823584	+	0.665121i
$202$	−0.125465	+	0.0724371i	−0.00882766	+	0.00509665i
$203$	−1.92280	+	1.11013i	−0.134954	+	0.0779158i
$204$	−11.3157	+	9.13846i	−0.792255	+	0.639820i
$205$	−24.3449	−	2.22339i	−1.70032	−	0.155288i
$206$	−1.01632			−0.0708101
$207$	14.9887	−	16.5582i	1.04179	−	1.15088i
$208$			19.1412i			1.32721i
$209$	2.32028	−	4.01885i	0.160497	−	0.277989i
$210$	−0.363042	+	0.0235141i	−0.0250523	+	0.00162263i
$211$	−5.79786	−	10.0422i	−0.399141	−	0.691333i	0.594479	−	0.804111i	$-0.297358\pi$
$211$	−5.79786	−	10.0422i	−0.399141	−	0.691333i	−0.993620	+	0.112778i	$0.964025\pi$
$212$	2.52790	−	1.45948i	0.173617	−	0.100238i
$213$	−4.69651	+	0.737480i	−0.321799	+	0.0505313i
$214$	−0.0271447	+	0.0470159i	−0.00185557	+	0.00321394i
$215$	12.6779	−	5.85312i	0.864627	−	0.399179i
$216$	−0.877501	−	1.73924i	−0.0597064	−	0.118340i
$217$			0.507675i			0.0344632i
$218$	−0.623625	−	0.360050i	−0.0422372	−	0.0243857i
$219$	2.65789	+	16.9263i	0.179604	+	1.14377i
$220$	1.65645	−	2.34658i	0.111678	−	0.158206i
$221$	10.2259	+	17.7117i	0.687866	+	1.19142i
$222$	0.0940652	−	0.244081i	0.00631324	−	0.0163817i
$223$	7.18595	+	4.14881i	0.481207	+	0.277825i	0.720919	−	0.693019i	$-0.243720\pi$
$223$	7.18595	+	4.14881i	0.481207	+	0.277825i	−0.239712	+	0.970844i	$0.577053\pi$
$224$	1.12058			0.0748719
$225$	−9.11307	−	11.9144i	−0.607538	−	0.794291i
$226$	0.819867			0.0545367
$227$	2.61987	+	1.51258i	0.173887	+	0.100394i	0.584417	−	0.811453i	$-0.301323\pi$
$227$	2.61987	+	1.51258i	0.173887	+	0.100394i	−0.410530	+	0.911847i	$0.634656\pi$
$228$	15.5870	+	19.3005i	1.03227	+	1.27821i
$229$	1.69410	+	2.93426i	0.111949	+	0.193902i	0.916556	−	0.399906i	$-0.130957\pi$
$229$	1.69410	+	2.93426i	0.111949	+	0.193902i	−0.804607	+	0.593808i	$0.797624\pi$
$230$	0.901796	−	1.27751i	0.0594627	−	0.0842367i
$231$	−0.869296	+	0.702038i	−0.0571955	+	0.0461907i
$232$	−0.720868	−	0.416193i	−0.0473273	−	0.0273244i
$233$			3.71850i			0.243607i	0.992554	+	0.121803i	$0.0388677\pi$
$233$			3.71850i			0.243607i	−0.992554	+	0.121803i	$0.961132\pi$
$234$	−1.30079	+	0.418848i	−0.0850356	+	0.0273809i
$235$	−12.5297	+	5.78467i	−0.817345	+	0.377350i
$236$	−13.7780	+	23.8642i	−0.896870	+	1.55343i
$237$	0.722990	−	1.87602i	0.0469633	−	0.121861i
$238$	0.343079	−	0.198077i	0.0222385	−	0.0128394i
$239$	1.47239	+	2.55025i	0.0952409	+	0.164962i	0.909709	−	0.415246i	$-0.136305\pi$
$239$	1.47239	+	2.55025i	0.0952409	+	0.164962i	−0.814468	+	0.580208i	$0.802971\pi$
$240$	8.48331	+	12.7174i	0.547596	+	0.820903i
$241$	−12.7528	+	22.0885i	−0.821480	+	1.42285i	0.0830997	+	0.996541i	$0.473518\pi$
$241$	−12.7528	+	22.0885i	−0.821480	+	1.42285i	−0.904580	+	0.426304i	$0.859815\pi$
$242$		−	0.994176i		−	0.0639081i
$243$	−11.0954	+	10.9495i	−0.711773	+	0.702409i
$244$	25.0247			1.60204
$245$	−2.22680	−	0.203371i	−0.142265	−	0.0129929i
$246$	0.275926	+	1.75719i	0.0175924	+	0.112034i
$247$	30.2100	−	17.4417i	1.92221	−	1.10979i
$248$	−0.164831	+	0.0951650i	−0.0104668	+	0.00604298i
$249$	−10.1357	−	3.90613i	−0.642322	−	0.247541i
$250$	−0.734075	−	0.751049i	−0.0464270	−	0.0475005i
$251$	−24.8314			−1.56734			−0.783671	−	0.621176i	$-0.786655\pi$
$251$	−24.8314			−1.56734			−0.783671	+	0.621176i	$0.786655\pi$
$252$	−1.83087	−	5.68603i	−0.115334	−	0.358186i
$253$		−	4.80283i		−	0.301951i
$254$	0.355538	−	0.615810i	0.0223084	−	0.0386393i
$255$	14.6438	+	7.23555i	0.917030	+	0.453108i
$256$	−7.64939	−	13.2491i	−0.478087	−	0.828071i
$257$	16.4979	−	9.52508i	1.02911	−	0.594158i	0.112382	−	0.993665i	$-0.464152\pi$
$257$	16.4979	−	9.52508i	1.02911	−	0.594158i	0.916730	+	0.399507i	$0.130819\pi$
$258$	−0.638354	−	0.790440i	−0.0397422	−	0.0492107i
$259$	0.803883	−	1.39237i	0.0499509	−	0.0865174i
$260$	19.6032	−	9.05035i	1.21574	−	0.561279i
$261$	−1.40210	+	6.51153i	−0.0867880	+	0.403053i
$262$			1.10233i			0.0681021i
$263$	−15.5984	−	9.00572i	−0.961836	−	0.555316i	−0.0650985	−	0.997879i	$-0.520736\pi$
$263$	−15.5984	−	9.00572i	−0.961836	−	0.555316i	−0.896738	+	0.442562i	$0.854069\pi$
$264$	−0.390888	−	0.150642i	−0.0240575	−	0.00927138i
$265$	−2.67797	−	1.89038i	−0.164506	−	0.116125i
$266$	−0.337849	−	0.585171i	−0.0207148	−	0.0358792i
$267$	11.3123	−	1.77633i	0.692300	−	0.108710i
$268$	−14.9423	−	8.62695i	−0.912747	−	0.526975i
$269$	−28.7486			−1.75283			−0.876417	−	0.481552i	$-0.840073\pi$
$269$	−28.7486			−1.75283			−0.876417	+	0.481552i	$0.840073\pi$
$270$	−0.678612	+	0.854787i	−0.0412990	+	0.0520207i
$271$	−28.2992			−1.71905			−0.859526	−	0.511092i	$-0.829241\pi$
$271$	−28.2992			−1.71905			−0.859526	+	0.511092i	$0.829241\pi$
$272$	−14.4163	−	8.32328i	−0.874119	−	0.504673i
$273$	−8.29773	+	1.30297i	−0.502201	+	0.0788593i
$274$	−0.220465	−	0.381857i	−0.0133188	−	0.0230688i
$275$	−3.17223	−	0.584304i	−0.191292	−	0.0352349i
$276$	23.9585	+	9.23321i	1.44213	+	0.555774i
$277$	−1.27604	−	0.736724i	−0.0766700	−	0.0442654i	0.461175	−	0.887309i	$-0.347428\pi$
$277$	−1.27604	−	0.736724i	−0.0766700	−	0.0442654i	−0.537845	+	0.843044i	$0.680761\pi$
$278$		−	0.329441i		−	0.0197586i
$279$	1.12912	+	1.02210i	0.0675989	+	0.0611913i
$280$	−0.351390	−	0.761115i	−0.0209996	−	0.0454853i
$281$	−8.18276	+	14.1730i	−0.488143	+	0.845488i	−0.999907	−	0.0136379i	$-0.995659\pi$
$281$	−8.18276	+	14.1730i	−0.488143	+	0.845488i	0.511764	+	0.859126i	$0.328992\pi$
$282$	0.630889	+	0.781196i	0.0375689	+	0.0465195i
$283$	−17.9035	+	10.3366i	−1.06425	+	0.614446i	−0.926605	−	0.376036i	$-0.877287\pi$
$283$	−17.9035	+	10.3366i	−1.06425	+	0.614446i	−0.137646	+	0.990482i	$0.543954\pi$
$284$	−2.73265	−	4.73308i	−0.162153	−	0.280857i
$285$	12.3413	−	24.9771i	0.731035	−	1.47952i
$286$	−0.146933	+	0.254495i	−0.00868831	+	0.0150486i
$287$			10.9327i			0.645335i
$288$	2.25605	−	2.49229i	0.132939	−	0.146860i
$289$	−0.786245			−0.0462497
$290$	−0.0424144	+	0.464414i	−0.00249066	+	0.0272713i
$291$	−11.2673	−	4.34226i	−0.660503	−	0.254548i
$292$	−17.0581	+	9.84851i	−0.998251	+	0.576341i
$293$	−9.06503	+	5.23370i	−0.529585	+	0.305756i	−0.740847	−	0.671673i	$-0.765576\pi$
$293$	−9.06503	+	5.23370i	−0.529585	+	0.305756i	0.211263	+	0.977429i	$0.432243\pi$
$294$	0.0252387	+	0.160728i	0.00147195	+	0.00937386i
$295$	30.8168	+	2.81446i	1.79422	+	0.163864i
$296$	0.602760			0.0350347
$297$	−0.188735	+	3.34681i	−0.0109515	+	0.194202i
$298$			1.72928i			0.100174i
$299$	18.0516	−	31.2663i	1.04395	−	1.80818i
$300$	9.01320	−	14.7011i	0.520377	−	0.848766i
$301$	−3.12241	−	5.40817i	−0.179973	−	0.311722i
$302$	−1.22488	+	0.707185i	−0.0704840	+	0.0406939i
$303$	−0.960628	+	2.49265i	−0.0551866	+	0.143199i
$304$	−14.1966	+	24.5892i	−0.814230	+	1.41029i
$305$	−11.7795	−	25.5145i	−0.674490	−	1.46095i
$306$	0.250173	−	1.16183i	0.0143014	−	0.0664174i
$307$		−	9.31987i		−	0.531913i	−0.963985	−	0.265956i	$-0.914312\pi$
$307$		−	9.31987i		−	0.531913i	0.963985	−	0.265956i	$-0.0856877\pi$
$308$	−1.11245	−	0.642272i	−0.0633876	−	0.0365968i
$309$	−14.5793	+	11.7741i	−0.829386	+	0.669807i
$310$	0.0871150	+	0.0614945i	0.00494780	+	0.00349265i
$311$	−14.1247	−	24.4647i	−0.800940	−	1.38727i	−0.918998	−	0.394261i	$-0.871000\pi$
$311$	−14.1247	−	24.4647i	−0.800940	−	1.38727i	0.118059	−	0.993007i	$-0.462333\pi$
$312$	−1.97848	−	2.44984i	−0.112009	−	0.138695i
$313$	−2.81172	−	1.62334i	−0.158928	−	0.0917569i	0.418427	−	0.908250i	$-0.362582\pi$
$313$	−2.81172	−	1.62334i	−0.158928	−	0.0917569i	−0.577355	+	0.816494i	$0.695915\pi$
$314$	1.88612			0.106440
$315$	−4.93551	+	4.54320i	−0.278085	+	0.255981i
$316$	2.31130			0.130021
$317$	−28.8560	−	16.6600i	−1.62072	−	0.935721i	−0.986728	−	0.162379i	$-0.948083\pi$
$317$	−28.8560	−	16.6600i	−1.62072	−	0.935721i	−0.633989	−	0.773342i	$-0.718583\pi$
$318$	−0.0857679	+	0.222552i	−0.00480963	+	0.0124801i
$319$	0.716164	+	1.24043i	0.0400975	+	0.0694509i
$320$	−10.0441	+	14.2288i	−0.561484	+	0.795415i
$321$	0.155289	+	0.988928i	0.00866737	+	0.0551966i
$322$	−0.605633	−	0.349662i	−0.0337506	−	0.0194859i
$323$			30.3371i			1.68800i
$324$	−16.3324	−	7.37558i	−0.907357	−	0.409754i
$325$	−18.4550	−	15.7267i	−1.02370	−	0.872362i
$326$	0.595818	−	1.03199i	0.0329993	−	0.0571565i
$327$	−13.1173	+	2.05977i	−0.725387	+	0.113905i
$328$	−3.54959	+	2.04936i	−0.195993	+	0.113157i
$329$	3.08589	+	5.34492i	0.170131	+	0.294675i
$330$	0.0151694	+	0.234205i	0.000835048	+	0.0128926i
$331$	8.18792	−	14.1819i	0.450049	−	0.779508i	−0.548340	−	0.836256i	$-0.684740\pi$
$331$	8.18792	−	14.1819i	0.450049	−	0.779508i	0.998389	+	0.0567482i	$0.0180732\pi$
$332$		−	12.4874i		−	0.685334i
$333$	−1.47833	−	4.59116i	−0.0810118	−	0.251594i
$334$	0.890969			0.0487517
$335$	−1.76224	+	19.2956i	−0.0962817	+	1.05423i
$336$	5.31876	−	4.29540i	0.290162	−	0.234333i
$337$	19.0714	−	11.0109i	1.03889	−	0.599801i	0.119369	−	0.992850i	$-0.461913\pi$
$337$	19.0714	−	11.0109i	1.03889	−	0.599801i	0.919518	+	0.393049i	$0.128580\pi$
$338$	−0.855520	+	0.493934i	−0.0465341	+	0.0268665i
$339$	11.7612	−	9.49825i	0.638779	−	0.515874i
$340$	−1.70781	+	18.6996i	−0.0926192	+	1.01413i
$341$	0.327510			0.0177357
$342$	−1.98167	−	0.426706i	−0.107157	−	0.0230736i
$343$			1.00000i			0.0539949i
$344$	1.17061	−	2.02755i	0.0631150	−	0.109318i
$345$	−1.86366	−	28.7736i	−0.100336	−	1.54912i
$346$	0.551146	+	0.954612i	0.0296298	+	0.0513203i
$347$	7.35607	−	4.24703i	0.394895	−	0.227993i	−0.289384	−	0.957213i	$-0.593450\pi$
$347$	7.35607	−	4.24703i	0.394895	−	0.227993i	0.684279	+	0.729221i	$0.260117\pi$
$348$	−7.56457	+	1.18784i	−0.405504	+	0.0636751i
$349$	7.27656	−	12.6034i	0.389505	−	0.674643i	−0.602878	−	0.797834i	$-0.705979\pi$
$349$	7.27656	−	12.6034i	0.389505	−	0.674643i	0.992383	+	0.123191i	$0.0393127\pi$
$350$	−0.304629	+	0.357476i	−0.0162831	+	0.0191079i
$351$	−13.8078	+	21.0783i	−0.737005	+	1.12508i
$352$		−	0.722906i		−	0.0385310i
$353$	19.0561	+	11.0020i	1.01425	+	0.585579i	0.912434	−	0.409224i	$-0.134201\pi$
$353$	19.0561	+	11.0020i	1.01425	+	0.585579i	0.101819	+	0.994803i	$0.467534\pi$
$354$	−0.349279	−	2.22432i	−0.0185640	−	0.118222i
$355$	−3.53943	+	5.01407i	−0.187853	+	0.266119i
$356$	6.58201	+	11.4004i	0.348846	+	0.604219i
$357$	2.62680	−	6.81606i	0.139025	−	0.360744i
$358$	−0.334652	−	0.193211i	−0.0176869	−	0.0102115i
$359$	−7.93944			−0.419027			−0.209514	−	0.977806i	$-0.567188\pi$
$359$	−7.93944			−0.419027			−0.209514	+	0.977806i	$0.567188\pi$
$360$	−2.40025	−	0.750815i	−0.126504	−	0.0395714i
$361$	32.7443			1.72339
$362$	0.344182	+	0.198714i	0.0180898	+	0.0104442i
$363$	−11.5176	−	14.2617i	−0.604520	−	0.748544i
$364$	−4.82800	−	8.36235i	−0.253056	−	0.438306i
$365$	18.0708	+	12.7562i	0.945869	+	0.667689i
$366$	−1.59077	+	1.28470i	−0.0831509	+	0.0671521i
$367$	16.4829	+	9.51638i	0.860398	+	0.496751i	0.864146	−	0.503242i	$-0.167860\pi$
$367$	16.4829	+	9.51638i	0.860398	+	0.496751i	−0.00374742	+	0.999993i	$0.501193\pi$
$368$			29.3860i			1.53185i
$369$	24.3155	+	22.0106i	1.26581	+	1.14583i
$370$	−0.141550	−	0.306600i	−0.00735886	−	0.0159394i
$371$	−0.732975	+	1.26955i	−0.0380542	+	0.0659117i
$372$	−0.629623	+	1.63375i	−0.0326444	+	0.0847062i
$373$	2.23894	−	1.29265i	0.115928	−	0.0669309i	−0.440915	−	0.897549i	$-0.645346\pi$
$373$	2.23894	−	1.29265i	0.115928	−	0.0669309i	0.556843	+	0.830618i	$0.312013\pi$
$374$	−0.127783	−	0.221326i	−0.00660749	−	0.0114445i
$375$	−19.2315	−	2.26962i	−0.993108	−	0.117203i
$376$	−1.15692	+	2.00384i	−0.0596635	+	0.103340i
$377$			10.7669i			0.554524i
$378$	0.408290	+	0.267459i	0.0210002	+	0.0137566i
$379$	2.62943			0.135065			0.0675323	−	0.997717i	$-0.478487\pi$
$379$	2.62943			0.135065			0.0675323	+	0.997717i	$0.478487\pi$
$380$	31.8950	+	2.91293i	1.63618	+	0.149430i
$381$	−2.03395	−	12.9529i	−0.104203	−	0.663596i
$382$	−1.30782	+	0.755070i	−0.0669139	+	0.0386327i
$383$	−6.23964	+	3.60246i	−0.318831	+	0.184077i	−0.650871	−	0.759188i	$-0.725596\pi$
$383$	−6.23964	+	3.60246i	−0.318831	+	0.184077i	0.332041	+	0.943265i	$0.392263\pi$
$384$	4.80461	+	1.85162i	0.245184	+	0.0944901i
$385$	−0.131198	+	1.43655i	−0.00668648	+	0.0732133i
$386$	0.497856			0.0253402
$387$	−18.3147	−	3.94363i	−0.930987	−	0.200466i
$388$		−	13.8816i		−	0.704732i
$389$	−12.6558	+	21.9205i	−0.641673	+	1.11141i	0.343386	+	0.939194i	$0.388426\pi$
$389$	−12.6558	+	21.9205i	−0.641673	+	1.11141i	−0.985059	+	0.172216i	$0.944907\pi$
$390$	−0.781517	+	1.58169i	−0.0395736	+	0.0800918i
$391$	15.6989	+	27.1913i	0.793929	+	1.37513i
$392$	−0.324678	+	0.187453i	−0.0163987	+	0.00946779i
$393$	12.7706	+	15.8132i	0.644192	+	0.797668i
$394$	0.157037	−	0.271996i	0.00791140	−	0.0137029i
$395$	−1.08796	−	2.35655i	−0.0547414	−	0.118571i
$396$	−3.66816	+	1.18113i	−0.184332	+	0.0593539i
$397$		−	14.2214i		−	0.713750i	−0.934152	−	0.356875i	$-0.883842\pi$
$397$		−	14.2214i		−	0.713750i	0.934152	−	0.356875i	$-0.116158\pi$
$398$	−0.335636	−	0.193780i	−0.0168239	−	0.00971329i
$399$	−11.6258	−	4.48040i	−0.582018	−	0.224300i
$400$	19.4092	+	3.57505i	0.970459	+	0.178753i
$401$	−1.69451	−	2.93498i	−0.0846199	−	0.146566i	0.820609	−	0.571490i	$-0.193634\pi$
$401$	−1.69451	−	2.93498i	−0.0846199	−	0.146566i	−0.905229	+	0.424924i	$0.860301\pi$
$402$	1.39274	−	0.218698i	0.0694635	−	0.0109077i
$403$	2.13208	+	1.23096i	0.106207	+	0.0613184i
$404$	−3.07100			−0.152788
$405$	0.167970	+	20.1239i	0.00834649	+	0.999965i
$406$	0.208557			0.0103505
$407$	−0.898241	−	0.518599i	−0.0445241	−	0.0257060i
$408$	2.70542	−	0.424825i	0.133938	−	0.0210320i
$409$	6.48786	+	11.2373i	0.320804	+	0.555649i	0.980654	−	0.195748i	$-0.0627136\pi$
$409$	6.48786	+	11.2373i	0.320804	+	0.555649i	−0.659850	+	0.751397i	$0.729380\pi$
$410$	1.87600	+	1.32427i	0.0926491	+	0.0654010i
$411$	−7.58648	−	2.92371i	−0.374213	−	0.144216i
$412$	−18.6573	−	10.7718i	−0.919178	−	0.530688i
$413$		−	13.8390i		−	0.680975i
$414$	−1.99700	+	0.643023i	−0.0981473	+	0.0316028i
$415$	−12.7318	+	5.87799i	−0.624979	+	0.288539i
$416$	2.71707	−	4.70610i	0.133215	−	0.230736i
$417$	−3.81661	−	4.72591i	−0.186900	−	0.231429i
$418$	−0.377505	+	0.217952i	−0.0184644	+	0.0106604i
$419$	−6.95377	−	12.0443i	−0.339714	−	0.588402i	0.644665	−	0.764465i	$-0.276997\pi$
$419$	−6.95377	−	12.0443i	−0.339714	−	0.588402i	−0.984379	+	0.176063i	$0.943664\pi$
$420$	−6.91387	−	3.41617i	−0.337362	−	0.166692i
$421$	−0.847630	+	1.46814i	−0.0413110	+	0.0715527i	−0.885942	−	0.463797i	$-0.846487\pi$
$421$	−0.847630	+	1.46814i	−0.0413110	+	0.0715527i	0.844631	+	0.535350i	$0.179820\pi$
$422$			1.08923i			0.0530228i
$423$	18.1005	+	3.89751i	0.880076	+	0.189504i
$424$	−0.549592			−0.0266906
$425$	19.8696	−	7.06095i	0.963815	−	0.342506i
$426$	0.416693	+	0.160587i	0.0201888	+	0.00778046i
$427$	−10.8840	+	6.28389i	−0.526714	+	0.304099i
$428$	−0.996630	+	0.575405i	−0.0481739	+	0.0278132i
$429$	0.840569	+	5.35302i	0.0405831	+	0.258446i
$430$	−1.30624	−	0.119297i	−0.0629923	−	0.00575301i
$431$	13.7872			0.664108			0.332054	−	0.943260i	$-0.392258\pi$
$431$	13.7872			0.664108			0.332054	+	0.943260i	$0.392258\pi$
$432$	1.15477	−	20.4774i	0.0555588	−	0.985219i
$433$			26.4182i			1.26958i	0.772685	+	0.634789i	$0.218913\pi$
$433$			26.4182i			1.26958i	−0.772685	+	0.634789i	$0.781087\pi$
$434$	0.0238439	−	0.0412988i	0.00114454	−	0.00198240i
$435$	4.77185	+	7.15350i	0.228793	+	0.342984i
$436$	−7.63224	−	13.2194i	−0.365518	−	0.633096i
$437$	46.3789	−	26.7768i	2.21860	−	1.28091i
$438$	0.578758	−	1.50177i	0.0276541	−	0.0717573i
$439$	4.00590	−	6.93842i	0.191191	−	0.331153i	−0.754454	−	0.656353i	$-0.772098\pi$
$439$	4.00590	−	6.93842i	0.191191	−	0.331153i	0.945645	+	0.325200i	$0.105432\pi$
$440$	−0.491009	+	0.226688i	−0.0234079	+	0.0108069i
$441$	2.22411	+	2.01329i	0.105910	+	0.0958709i
$442$		−	1.92110i		−	0.0913776i
$443$	9.96142	+	5.75123i	0.473282	+	0.273249i	0.717612	−	0.696443i	$-0.245235\pi$
$443$	9.96142	+	5.75123i	0.473282	+	0.273249i	−0.244331	+	0.969692i	$0.578568\pi$
$444$	4.31381	−	3.48380i	0.204724	−	0.165334i
$445$	8.52527	−	12.0772i	0.404137	−	0.572512i
$446$	−0.389713	−	0.675002i	−0.0184534	−	0.0319623i
$447$	20.0339	+	24.8069i	0.947569	+	1.17332i
$448$	6.74548	+	3.89451i	0.318694	+	0.183998i
$449$	27.3274			1.28966			0.644831	−	0.764325i	$-0.276928\pi$
$449$	27.3274			1.28966			0.644831	+	0.764325i	$0.276928\pi$
$450$	0.181759	+	1.39723i	0.00856819	+	0.0658661i
$451$	7.05286			0.332106
$452$	15.0509	+	8.68965i	0.707935	+	0.408727i
$453$	−9.37837	+	24.3351i	−0.440634	+	1.14336i
$454$	−0.142082	−	0.246094i	−0.00666826	−	0.0115498i
$455$	−6.25342	+	8.85879i	−0.293165	+	0.415306i
$456$	−0.724602	−	4.61450i	−0.0339326	−	0.216094i
$457$	−20.3796	−	11.7662i	−0.953316	−	0.550397i	−0.0592067	−	0.998246i	$-0.518857\pi$
$457$	−20.3796	−	11.7662i	−0.953316	−	0.550397i	−0.894110	+	0.447848i	$0.852190\pi$
$458$		−	0.318265i		−	0.0148716i
$459$	−9.87115	−	19.5650i	−0.460746	−	0.913216i
$460$	30.0951	−	13.8943i	1.40319	−	0.647823i
$461$	14.9810	−	25.9478i	0.697733	−	1.20851i	−0.271518	−	0.962434i	$-0.587525\pi$
$461$	14.9810	−	25.9478i	0.697733	−	1.20851i	0.969251	−	0.246076i	$-0.0791412\pi$
$462$	0.103689	−	0.0162819i	0.00482403	−	0.000757505i
$463$	−11.7209	+	6.76707i	−0.544717	+	0.314493i	−0.746989	−	0.664837i	$-0.768501\pi$
$463$	−11.7209	+	6.76707i	−0.544717	+	0.314493i	0.202271	+	0.979330i	$0.435168\pi$
$464$	−4.38183	−	7.58955i	−0.203421	−	0.352336i
$465$	1.96210	−	0.127085i	0.0909904	−	0.00589342i
$466$	0.174646	−	0.302495i	0.00809031	−	0.0140128i
$467$			26.0901i			1.20731i	0.797247	+	0.603653i	$0.206289\pi$
$467$			26.0901i			1.20731i	−0.797247	+	0.603653i	$0.793711\pi$
$468$	−28.3190	−	6.09782i	−1.30904	−	0.281872i
$469$	8.66518			0.400121
$470$	1.29096	+	0.117902i	0.0595476	+	0.00543840i
$471$	27.0569	−	21.8509i	1.24671	−	1.00684i
$472$	4.49323	−	2.59417i	0.206818	−	0.119406i
$473$	−3.48891	+	2.01432i	−0.160420	+	0.0926187i
$474$	−0.146925	+	0.118656i	−0.00674850	+	0.00545005i
$475$	−12.0435	−	33.8905i	−0.552593	−	1.55500i
$476$	8.39754			0.384900
$477$	1.34793	+	4.18619i	0.0617173	+	0.191672i
$478$		−	0.276614i		−	0.0126520i
$479$	−11.2363	+	19.4618i	−0.513399	+	0.889233i	0.486480	+	0.873692i	$0.338281\pi$
$479$	−11.2363	+	19.4618i	−0.513399	+	0.889233i	−0.999879	+	0.0155418i	$0.995053\pi$
$480$	−0.280512	−	4.33091i	−0.0128035	−	0.197678i
$481$	−3.89835	−	6.75214i	−0.177749	−	0.307871i
$482$	2.07485	−	1.19792i	0.0945069	−	0.0545636i
$483$	−12.7388	+	2.00034i	−0.579636	+	0.0910187i
$484$	10.5371	−	18.2508i	0.478960	−	0.829584i
$485$	−14.1533	+	6.53428i	−0.642670	+	0.296706i
$486$	1.41686	−	0.369610i	0.0642703	−	0.0167659i
$487$		−	9.25941i		−	0.419584i	−0.977746	−	0.209792i	$-0.932721\pi$
$487$		−	9.25941i		−	0.419584i	0.977746	−	0.209792i	$-0.0672786\pi$
$488$	−4.08047	−	2.35586i	−0.184714	−	0.106645i
$489$	−3.40854	−	21.7067i	−0.154140	−	0.981611i
$490$	0.171596	+	0.121130i	0.00775192	+	0.00547208i
$491$	6.78668	+	11.7549i	0.306279	+	0.530490i	0.977545	−	0.210726i	$-0.0675828\pi$
$491$	6.78668	+	11.7549i	0.306279	+	0.530490i	−0.671267	+	0.741216i	$0.734249\pi$
$492$	−13.5588	+	35.1825i	−0.611277	+	1.58615i
$493$	−8.10917	−	4.68183i	−0.365218	−	0.210859i
$494$	−3.27673			−0.147427
$495$	2.93090	+	3.18399i	0.131734	+	0.143110i
$496$	−2.00386			−0.0899760
$497$	2.37703	+	1.37238i	0.106624	+	0.0615596i
$498$	0.641067	+	0.793799i	0.0287269	+	0.0355710i
$499$	13.7316	+	23.7838i	0.614709	+	1.06471i	0.990436	+	0.137976i	$0.0440598\pi$
$499$	13.7316	+	23.7838i	0.614709	+	1.06471i	−0.375727	+	0.926731i	$0.622607\pi$
$500$	−5.51571	−	21.5679i	−0.246670	−	0.964546i
$501$	12.7812	−	10.3220i	0.571020	−	0.461152i
$502$	2.02000	+	1.16625i	0.0901572	+	0.0520523i
$503$		−	25.7171i		−	1.14667i	−0.819321	−	0.573334i	$-0.805650\pi$
$503$		−	25.7171i		−	1.14667i	0.819321	−	0.573334i	$-0.194350\pi$
$504$	−0.236755	+	1.09952i	−0.0105459	+	0.0489763i
$505$	1.44556	+	3.13111i	0.0643268	+	0.139333i
$506$	−0.225574	+	0.390705i	−0.0100280	+	0.0173689i
$507$	−6.55033	+	16.9969i	−0.290911	+	0.754859i
$508$	13.0538	−	7.53659i	0.579167	−	0.334382i
$509$	4.38212	+	7.59005i	0.194234	+	0.336423i	0.946649	−	0.322266i	$-0.104445\pi$
$509$	4.38212	+	7.59005i	0.194234	+	0.336423i	−0.752415	+	0.658689i	$0.771111\pi$
$510$	−0.851425	−	1.27638i	−0.0377017	−	0.0565189i
$511$	4.94608	−	8.56686i	0.218802	−	0.378975i
$512$			7.38269i			0.326272i
$513$	−33.3710	+	16.8367i	−1.47337	+	0.743359i
$514$	−1.78945			−0.0789292
$515$	−2.20037	+	24.0929i	−0.0969601	+	1.06166i
$516$	−3.34099	−	21.2765i	−0.147079	−	0.936647i
$517$	3.44811	−	1.99077i	0.151648	−	0.0875538i
$518$	−0.130790	+	0.0755116i	−0.00574658	+	0.00331779i
$519$	18.9656	+	7.30904i	0.832498	+	0.320831i
$520$	−4.04847	−	0.369742i	−0.177537	−	0.0162142i
$521$	17.4597			0.764924			0.382462	−	0.923971i	$-0.375076\pi$
$521$	17.4597			0.764924			0.382462	+	0.923971i	$0.375076\pi$
$522$	0.419885	−	0.463853i	0.0183779	−	0.0203023i
$523$		−	36.7301i		−	1.60610i	−0.595914	−	0.803049i	$-0.703210\pi$
$523$		−	36.7301i		−	1.60610i	0.595914	−	0.803049i	$-0.296790\pi$
$524$	−11.6834	+	20.2363i	−0.510393	+	0.884026i
$525$	−0.228576	+	8.65724i	−0.00997588	+	0.377833i
$526$	0.845939	+	1.46521i	0.0368847	+	0.0638862i
$527$	−1.85421	+	1.07053i	−0.0807705	+	0.0466329i
$528$	−2.77104	−	3.43123i	−0.120594	−	0.149325i
$529$	16.2132	−	28.0820i	0.704920	−	1.22096i
$530$	0.129065	+	0.279556i	0.00560621	+	0.0121431i
$531$	−30.7795	−	27.8620i	−1.33572	−	1.20911i
$532$		−	14.3232i		−	0.620991i
$533$	45.9139	+	26.5084i	1.98875	+	1.14821i
$534$	−1.00367	−	0.386798i	−0.0434330	−	0.0167384i
$535$	1.05580	+	0.745286i	0.0456460	+	0.0322215i
$536$	1.62431	+	2.81339i	0.0701596	+	0.121520i
$537$	−7.03903	+	1.10532i	−0.303756	+	0.0476980i
$538$	2.33867	+	1.35023i	0.100827	+	0.0582126i
$539$	0.645118			0.0277872
$540$	−21.5175	+	8.49947i	−0.925968	+	0.365759i
$541$	−8.95134			−0.384848			−0.192424	−	0.981312i	$-0.561635\pi$
$541$	−8.95134			−0.384848			−0.192424	+	0.981312i	$0.561635\pi$
$542$	2.30211	+	1.32912i	0.0988839	+	0.0570906i
$543$	7.23949	−	1.13680i	0.310676	−	0.0487846i
$544$	2.36295	+	4.09275i	0.101311	+	0.175475i
$545$	−9.88557	+	14.0042i	−0.423451	+	0.599874i
$546$	0.736207	+	0.283723i	0.0315068	+	0.0121422i
$547$	21.9752	+	12.6874i	0.939591	+	0.542473i	0.889832	−	0.456288i	$-0.150821\pi$
$547$	21.9752	+	12.6874i	0.939591	+	0.542473i	0.0497592	+	0.998761i	$0.484155\pi$
$548$		−	9.34671i		−	0.399272i
$549$	−7.93661	+	36.8585i	−0.338726	+	1.57308i
$550$	0.230614	+	0.196522i	0.00983342	+	0.00837972i
$551$	−7.98555	+	13.8314i	−0.340196	+	0.589237i
$552$	−3.03739	−	3.76104i	−0.129280	−	0.160081i
$553$	−1.00526	+	0.580387i	−0.0427480	+	0.0246805i
$554$	0.0692031	+	0.119863i	0.00294016	+	0.00509250i
$555$	−5.58257	−	2.75837i	−0.236967	−	0.117086i
$556$	3.49170	−	6.04780i	0.148081	−	0.256484i
$557$			17.6518i			0.747932i	0.927442	+	0.373966i	$0.122002\pi$
$557$			17.6518i			0.747932i	−0.927442	+	0.373966i	$0.877998\pi$
$558$	−0.0438484	−	0.136178i	−0.00185625	−	0.00576486i
$559$	−30.2836			−1.28086
$560$	0.802732	−	8.78949i	0.0339216	−	0.371424i
$561$	−4.39716	−	1.69460i	−0.185648	−	0.0715460i
$562$	1.33132	−	0.768636i	0.0561582	−	0.0324230i
$563$	−19.2105	+	11.0912i	−0.809625	+	0.467437i	−0.846826	−	0.531870i	$-0.821489\pi$
$563$	−19.2105	+	11.0912i	−0.809625	+	0.467437i	0.0372004	+	0.999308i	$0.488156\pi$
$564$	3.30192	+	21.0277i	0.139036	+	0.885426i
$565$	1.77505	−	19.4359i	0.0746770	−	0.817673i
$566$	1.94190			0.0816243
$567$	8.95555	−	0.893330i	0.376098	−	0.0375163i
$568$			1.02902i			0.0431769i
$569$	−3.34702	+	5.79720i	−0.140314	+	0.243031i	−0.927615	−	0.373538i	$-0.878145\pi$
$569$	−3.34702	+	5.79720i	−0.140314	+	0.243031i	0.787301	+	0.616569i	$0.211478\pi$
$570$	−2.17705	+	1.45223i	−0.0911865	+	0.0608273i
$571$	16.4124	+	28.4271i	0.686838	+	1.18964i	0.972855	+	0.231414i	$0.0743351\pi$
$571$	16.4124	+	28.4271i	0.686838	+	1.18964i	−0.286018	+	0.958224i	$0.592332\pi$
$572$	−5.39470	+	3.11463i	−0.225564	+	0.130229i
$573$	−10.0134	+	25.9829i	−0.418316	+	1.08545i
$574$	0.513472	−	0.889360i	0.0214319	−	0.0371212i
$575$	−28.3324	−	24.1440i	−1.18154	−	1.00687i
$576$	22.2424	−	7.16193i	0.926768	−	0.298414i
$577$		−	11.9331i		−	0.496781i	−0.968660	−	0.248391i	$-0.920098\pi$
$577$		−	11.9331i		−	0.496781i	0.968660	−	0.248391i	$-0.0799016\pi$
$578$	0.0639602	+	0.0369274i	0.00266039	+	0.00153598i
$579$	7.14186	−	5.76772i	0.296806	−	0.239698i
$580$	−5.70089	+	8.07606i	−0.236717	+	0.335340i
$581$	3.13568	+	5.43115i	0.130090	+	0.225322i
$582$	0.712644	+	0.882429i	0.0295400	+	0.0365778i
$583$	0.819009	+	0.472855i	0.0339199	+	0.0195837i
$584$	3.70862			0.153464
$585$	7.11297	+	31.7436i	0.294085	+	1.31244i
$586$	0.983240			0.0406173
$587$	−13.5293	−	7.81116i	−0.558415	−	0.322401i	0.194094	−	0.980983i	$-0.437823\pi$
$587$	−13.5293	−	7.81116i	−0.558415	−	0.322401i	−0.752509	+	0.658582i	$0.771157\pi$
$588$	−1.24021	+	3.21811i	−0.0511454	+	0.132713i
$589$	1.82594	+	3.16262i	0.0752366	+	0.130314i
$590$	−2.37472	−	1.67632i	−0.0977659	−	0.0690129i
$591$	−0.898373	−	5.72113i	−0.0369541	−	0.235336i
$592$	5.49586	+	3.17304i	0.225878	+	0.130411i
$593$		−	41.9858i		−	1.72415i	−0.506782	−	0.862074i	$-0.669165\pi$
$593$		−	41.9858i		−	1.72415i	0.506782	−	0.862074i	$-0.330835\pi$
$594$	0.172543	−	0.263395i	0.00707951	−	0.0108072i
$595$	−3.95284	−	8.56191i	−0.162051	−	0.351004i
$596$	−18.3283	+	31.7456i	−0.750758	+	1.30035i
$597$	−7.05973	+	1.10857i	−0.288936	+	0.0453708i
$598$	−2.93696	+	1.69565i	−0.120101	+	0.0693404i
$599$	−1.21833	−	2.11022i	−0.0497798	−	0.0862211i	0.840062	−	0.542491i	$-0.182519\pi$
$599$	−1.21833	−	2.11022i	−0.0497798	−	0.0862211i	−0.889842	+	0.456270i	$0.849185\pi$
$600$	−2.85366	+	1.54861i	−0.116500	+	0.0632217i
$601$	3.85723	−	6.68092i	0.157340	−	0.272520i	−0.776569	−	0.630032i	$-0.783042\pi$
$601$	3.85723	−	6.68092i	0.157340	−	0.272520i	0.933909	+	0.357512i	$0.116375\pi$
$602$			0.586598i			0.0239080i
$603$	17.4455	−	19.2723i	0.710436	−	0.784829i
$604$	−29.9814			−1.21993
$605$	−23.5681	−	2.15244i	−0.958178	−	0.0875092i
$606$	0.195218	−	0.157657i	0.00793018	−	0.00640436i
$607$	−26.3221	+	15.1971i	−1.06838	+	0.616831i	−0.927739	−	0.373229i	$-0.878250\pi$
$607$	−26.3221	+	15.1971i	−1.06838	+	0.616831i	−0.140643	+	0.990060i	$0.544917\pi$
$608$	6.98079	−	4.03036i	0.283109	−	0.163453i
$609$	2.99179	−	2.41615i	0.121234	−	0.0979075i
$610$	−0.240087	+	2.62882i	−0.00972082	+	0.106438i
$611$	29.9294			1.21082
$612$	16.9067	−	18.6770i	0.683412	−	0.754975i
$613$		−	32.0360i		−	1.29392i	−0.762523	−	0.646961i	$-0.776040\pi$
$613$		−	32.0360i		−	1.29392i	0.762523	−	0.646961i	$-0.223960\pi$
$614$	−0.437724	+	0.758161i	−0.0176651	+	0.0305969i
$615$	42.2535	−	2.73674i	1.70383	−	0.110356i
$616$	0.120929	+	0.209455i	0.00487238	+	0.00843920i
$617$	26.6301	−	15.3749i	1.07209	−	0.618969i	0.143335	−	0.989674i	$-0.454217\pi$
$617$	26.6301	−	15.3749i	1.07209	−	0.618969i	0.928751	+	0.370705i	$0.120884\pi$
$618$	1.73900	−	0.273071i	0.0699529	−	0.0109845i
$619$	−4.08095	+	7.06841i	−0.164027	+	0.284104i	−0.936309	−	0.351176i	$-0.885782\pi$
$619$	−4.08095	+	7.06841i	−0.164027	+	0.284104i	0.772282	+	0.635280i	$0.219115\pi$
$620$	0.947464	+	2.05222i	0.0380511	+	0.0824191i
$621$	−21.1980	+	32.3598i	−0.850645	+	1.29855i
$622$			2.65357i			0.106399i
$623$	−5.72545	−	3.30559i	−0.229385	−	0.132436i
$624$	−5.14300	−	32.7523i	−0.205885	−	1.31114i
$625$	−19.3938	+	15.7760i	−0.775750	+	0.631040i
$626$	0.152487	+	0.264115i	0.00609459	+	0.0105561i
$627$	−2.89039	+	7.50001i	−0.115431	+	0.299522i
$628$	34.6250	+	19.9907i	1.38169	+	0.797717i
$629$	6.78055			0.270358
$630$	0.614878	−	0.137779i	0.0244973	−	0.00548926i
$631$	−38.4292			−1.52984			−0.764920	−	0.644125i	$-0.777222\pi$
$631$	−38.4292			−1.52984			−0.764920	+	0.644125i	$0.777222\pi$
$632$	−0.376877	−	0.217590i	−0.0149914	−	0.00865527i
$633$	12.6188	+	15.6252i	0.501553	+	0.621047i
$634$	1.56494	+	2.71055i	0.0621516	+	0.107650i
$635$	−13.8287	−	9.76168i	−0.548775	−	0.387381i
$636$	−3.93330	+	3.17651i	−0.155965	+	0.125957i
$637$	4.19970	+	2.42470i	0.166398	+	0.0960701i
$638$		−	0.134544i		−	0.00532664i
$639$	7.83797	−	2.52378i	0.310065	−	0.0998392i
$640$	6.03525	−	2.78634i	0.238564	−	0.110140i
$641$	20.6653	−	35.7934i	0.816232	−	1.41376i	−0.0922081	−	0.995740i	$-0.529392\pi$
$641$	20.6653	−	35.7934i	0.816232	−	1.41376i	0.908440	−	0.418015i	$-0.137274\pi$
$642$	0.0338142	−	0.0877416i	0.00133454	−	0.00346288i
$643$	19.9951	−	11.5442i	0.788528	−	0.455257i	−0.0509161	−	0.998703i	$-0.516214\pi$
$643$	19.9951	−	11.5442i	0.788528	−	0.455257i	0.839444	+	0.543446i	$0.182881\pi$
$644$	−7.41204	−	12.8380i	−0.292075	−	0.505889i
$645$	−20.1203	+	13.4216i	−0.792237	+	0.528474i
$646$	1.42483	−	2.46789i	0.0560594	−	0.0970977i
$647$			38.8470i			1.52723i	0.645671	+	0.763616i	$0.276578\pi$
$647$			38.8470i			1.52723i	−0.645671	+	0.763616i	$0.723422\pi$
$648$	1.96879	+	2.74021i	0.0773413	+	0.107646i
$649$	−8.92782			−0.350447
$650$	0.762658	+	2.14612i	0.0299139	+	0.0841779i
$651$	−0.136405	−	0.868674i	−0.00534615	−	0.0340460i
$652$	21.8757	−	12.6300i	0.856720	−	0.494628i
$653$	5.11375	−	2.95242i	0.200116	−	0.115537i	−0.396593	−	0.917994i	$-0.629808\pi$
$653$	5.11375	−	2.95242i	0.200116	−	0.115537i	0.596710	+	0.802457i	$0.296474\pi$
$654$	1.16382	+	0.448516i	0.0455088	+	0.0175384i
$655$	26.1319	+	2.38660i	1.02106	+	0.0932520i
$656$	−43.1527			−1.68483
$657$	−9.09575	−	28.2482i	−0.354859	−	1.10207i
$658$		−	0.579738i		−	0.0226005i
$659$	1.78657	−	3.09443i	0.0695949	−	0.120542i	−0.829128	−	0.559059i	$-0.811163\pi$
$659$	1.78657	−	3.09443i	0.0695949	−	0.120542i	0.898723	+	0.438517i	$0.144496\pi$
$660$	−2.20383	+	4.46026i	−0.0857840	+	0.173615i
$661$	10.8072	+	18.7186i	0.420351	+	0.728070i	0.995974	−	0.0896457i	$-0.0285735\pi$
$661$	10.8072	+	18.7186i	0.420351	+	0.728070i	−0.575622	+	0.817716i	$0.695240\pi$
$662$	−1.33216	+	0.769121i	−0.0517757	+	0.0298927i
$663$	−22.2562	−	27.5587i	−0.864360	−	1.07029i
$664$	−1.17558	+	2.03617i	−0.0456215	+	0.0790187i
$665$	−14.6036	+	6.74216i	−0.566303	+	0.261450i
$666$	−0.0953719	+	0.442918i	−0.00369559	+	0.0171627i
$667$			16.5296i			0.640027i
$668$	16.3562	+	9.44325i	0.632840	+	0.365370i
$669$	−13.4105	−	5.16820i	−0.518480	−	0.199814i
$670$	1.04961	−	1.48691i	0.0405500	−	0.0574443i
$671$	4.05385	+	7.02147i	0.156497	+	0.271061i
$672$	−1.91741	+	0.301085i	−0.0739655	+	0.0116146i
$673$	−29.0132	−	16.7508i	−1.11838	−	0.645695i	−0.177390	−	0.984141i	$-0.556765\pi$
$673$	−29.0132	−	16.7508i	−1.11838	−	0.645695i	−0.940986	+	0.338446i	$0.890099\pi$
$674$	−2.06858			−0.0796789
$675$	18.7945	+	17.9379i	0.723399	+	0.690430i
$676$	−20.9406			−0.805406
$677$	−7.45432	−	4.30375i	−0.286493	−	0.165407i	0.349866	−	0.936800i	$-0.386227\pi$
$677$	−7.45432	−	4.30375i	−0.286493	−	0.165407i	−0.636359	+	0.771393i	$0.719560\pi$
$678$	−1.40286	+	0.220287i	−0.0538765	+	0.00846008i
$679$	3.48578	+	6.03755i	0.133772	+	0.231700i
$680$	2.03889	−	2.88835i	0.0781878	−	0.110763i
$681$	−4.88923	−	1.88423i	−0.187356	−	0.0722040i
$682$	−0.0266426	−	0.0153821i	−0.00102020	−	0.000589011i
$683$		−	17.9730i		−	0.687717i	−0.939021	−	0.343859i	$-0.888266\pi$
$683$		−	17.9730i		−	0.687717i	0.939021	−	0.343859i	$-0.111734\pi$
$684$	−31.8565	−	28.8368i	−1.21806	−	1.10260i
$685$	−9.52966	+	4.39963i	−0.364110	+	0.168101i
$686$	0.0469668	−	0.0813489i	0.00179320	−	0.00310591i
$687$	−3.68714	−	4.56559i	−0.140673	−	0.174188i
$688$	21.3468	−	12.3246i	0.813839	−	0.469870i
$689$	3.55449	+	6.15655i	0.135415	+	0.234546i
$690$	−1.19980	+	2.42823i	−0.0456755	+	0.0924412i
$691$	−18.1089	+	31.3655i	−0.688895	+	1.19320i	0.283301	+	0.959031i	$0.408571\pi$
$691$	−18.1089	+	31.3655i	−0.688895	+	1.19320i	−0.972196	+	0.234170i	$0.924763\pi$
$692$			23.3660i			0.888244i
$693$	1.29881	−	1.43481i	0.0493377	−	0.0545041i
$694$	−0.797878			−0.0302870
$695$	−7.80977	−	0.713256i	−0.296241	−	0.0270553i
$696$	1.34529	+	0.518454i	0.0509931	+	0.0196520i
$697$	−39.9300	+	23.0536i	−1.51245	+	0.873216i
$698$	−1.18388	+	0.683513i	−0.0448105	+	0.0258714i
$699$	−0.999111	−	6.36266i	−0.0377898	−	0.240658i
$700$	−9.38114	+	3.33373i	−0.354574	+	0.126003i
$701$	−10.2558			−0.387357			−0.193678	−	0.981065i	$-0.562042\pi$
$701$	−10.2558			−0.387357			−0.193678	+	0.981065i	$0.562042\pi$
$702$	2.11323	−	1.06619i	0.0797587	−	0.0402407i
$703$		−	11.5652i		−	0.436191i
$704$	2.51242	−	4.35163i	0.0946903	−	0.164008i
$705$	19.8850	−	13.2646i	0.748913	−	0.499574i
$706$	−1.03346	−	1.79001i	−0.0388948	−	0.0673677i
$707$	1.33567	−	0.771152i	0.0502332	−	0.0290022i
$708$	17.1633	−	44.5356i	0.645036	−	1.67375i
$709$	7.87910	−	13.6470i	0.295906	−	0.512524i	−0.679289	−	0.733871i	$-0.737712\pi$
$709$	7.87910	−	13.6470i	0.295906	−	0.512524i	0.975195	+	0.221346i	$0.0710452\pi$
$710$	0.523423	−	0.241653i	0.0196437	−	0.00906908i
$711$	−0.733034	+	3.40429i	−0.0274909	+	0.127671i
$712$		−	2.47857i		−	0.0928882i
$713$	3.27321	+	1.88979i	0.122583	+	0.0707732i
$714$	−0.533816	+	0.431106i	−0.0199776	+	0.0161337i
$715$	5.71496	+	4.03419i	0.213728	+	0.150870i
$716$	−4.09563	−	7.09384i	−0.153061	−	0.265109i
$717$	−3.20460	−	3.96808i	−0.119678	−	0.148191i
$718$	0.645864	+	0.372890i	0.0241034	+	0.0139161i
$719$	14.4957			0.540598			0.270299	−	0.962776i	$-0.412878\pi$
$719$	14.4957			0.540598			0.270299	+	0.962776i	$0.412878\pi$
$720$	−17.9327	−	19.4811i	−0.668310	−	0.726019i
$721$	10.8195			0.402940
$722$	−2.66372	−	1.53790i	−0.0991332	−	0.0572346i
$723$	15.8862	−	41.2218i	0.590815	−	1.53305i
$724$	4.21227	+	7.29587i	0.156548	+	0.271149i
$725$	10.9176	+	2.01096i	0.405471	+	0.0746852i
$726$	0.267122	+	1.70112i	0.00991383	+	0.0631344i
$727$	9.74715	+	5.62752i	0.361502	+	0.208713i	0.669739	−	0.742596i	$-0.266406\pi$
$727$	9.74715	+	5.62752i	0.361502	+	0.208713i	−0.308238	+	0.951309i	$0.599739\pi$
$728$			1.81807i			0.0673820i
$729$	16.0433	−	21.7167i	0.594195	−	0.804321i
$730$	−0.870922	−	1.88643i	−0.0322343	−	0.0698198i
$731$	13.1684	−	22.8083i	0.487050	−	0.843595i
$732$	−42.8193	+	6.72379i	−1.58265	+	0.248518i
$733$	−16.0320	+	9.25609i	−0.592156	+	0.341881i	−0.765950	−	0.642901i	$-0.777731\pi$
$733$	−16.0320	+	9.25609i	−0.592156	+	0.341881i	0.173794	+	0.984782i	$0.444397\pi$
$734$	−0.893908	−	1.54829i	−0.0329947	−	0.0571486i
$735$	3.86489	−	0.250327i	0.142558	−	0.00923346i
$736$	4.17129	−	7.22489i	0.153756	−	0.266313i
$737$		−	5.59006i		−	0.205913i
$738$	−0.944266	−	2.93256i	−0.0347589	−	0.107949i
$739$	−29.7101			−1.09290			−0.546451	−	0.837491i	$-0.684022\pi$
$739$	−29.7101			−1.09290			−0.546451	+	0.837491i	$0.684022\pi$
$740$	0.651060	−	7.12876i	0.0239335	−	0.262058i
$741$	−47.0054	+	37.9613i	−1.72679	+	1.39454i
$742$	0.119253	−	0.0688509i	0.00437793	−	0.00252760i
$743$	−43.1299	+	24.9010i	−1.58228	+	0.913531i	−0.587756	+	0.809038i	$0.699989\pi$
$743$	−43.1299	+	24.9010i	−1.58228	+	0.913531i	−0.994526	+	0.104493i	$0.966678\pi$
$744$	0.256469	−	0.207123i	0.00940263	−	0.00759350i
$745$	40.9944	+	3.74397i	1.50192	+	0.137168i
$746$	−0.242847			−0.00889125
$747$	18.3925	+	3.96039i	0.672947	+	0.144903i
$748$		−	5.41740i		−	0.198080i
$749$	0.288977	−	0.500523i	0.0105590	−	0.0182887i
$750$	1.45786	+	1.08787i	0.0532335	+	0.0397234i
$751$	17.6564	+	30.5818i	0.644291	+	1.11595i	0.984465	+	0.175583i	$0.0561809\pi$
$751$	17.6564	+	30.5818i	0.644291	+	1.11595i	−0.340173	+	0.940363i	$0.610486\pi$
$752$	−21.0971	+	12.1804i	−0.769334	+	0.444175i
$753$	42.4886	−	6.67186i	1.54837	−	0.243136i
$754$	0.505687	−	0.875876i	0.0184161	−	0.0318975i
$755$	14.1127	+	30.5683i	0.513613	+	1.11249i
$756$	4.66053	+	9.23735i	0.169502	+	0.335959i
$757$			21.7094i			0.789040i	0.918887	+	0.394520i	$0.129089\pi$
$757$			21.7094i			0.789040i	−0.918887	+	0.394520i	$0.870911\pi$
$758$	−0.213901	−	0.123496i	−0.00776924	−	0.00448557i
$759$	1.29046	+	8.21804i	0.0468406	+	0.298296i
$760$	−4.92651	−	3.47763i	−0.178703	−	0.126147i
$761$	−18.5172	−	32.0728i	−0.671249	−	1.16264i	−0.977550	−	0.210703i	$-0.932425\pi$
$761$	−18.5172	−	32.0728i	−0.671249	−	1.16264i	0.306301	−	0.951935i	$-0.400909\pi$
$762$	−0.442895	+	1.14923i	−0.0160444	+	0.0416322i
$763$	6.63900	+	3.83303i	0.240348	+	0.138765i
$764$	−32.0115			−1.15814
$765$	−27.0008	−	8.44604i	−0.976217	−	0.305367i
$766$	0.676783			0.0244532
$767$	−58.1199	−	33.5555i	−2.09859	−	1.21162i
$768$	16.6486	+	20.6151i	0.600755	+	0.743883i
$769$	−18.3606	−	31.8015i	−0.662100	−	1.14679i	−0.980063	−	0.198688i	$-0.936332\pi$
$769$	−18.3606	−	31.8015i	−0.662100	−	1.14679i	0.317963	−	0.948103i	$-0.397001\pi$
$770$	0.0781429	−	0.110700i	0.00281608	−	0.00398934i
$771$	−25.6701	+	20.7310i	−0.924484	+	0.746608i
$772$	9.13953	+	5.27671i	0.328939	+	0.189913i
$773$		−	7.46987i		−	0.268672i	−0.990936	−	0.134336i	$-0.957110\pi$
$773$		−	7.46987i		−	0.268672i	0.990936	−	0.134336i	$-0.0428902\pi$
$774$	1.30466	+	1.18099i	0.0468950	+	0.0424499i
$775$	1.64640	−	1.93202i	0.0591405	−	0.0694002i
$776$	−1.30684	+	2.26351i	−0.0469128	+	0.0812553i
$777$	−1.00140	+	2.59845i	−0.0359251	+	0.0932188i
$778$	2.05907	−	1.18880i	0.0738211	−	0.0426206i
$779$	39.3213	+	68.1064i	1.40883	+	2.44017i
$780$	−31.1109	+	20.7530i	−1.11395	+	0.743077i
$781$	0.885346	−	1.53346i	0.0316802	−	0.0548717i
$782$		−	2.94931i		−	0.105467i
$783$	0.649555	−	11.5185i	0.0232132	−	0.411637i
$784$	−3.94714			−0.140969
$785$	4.08355	−	44.7126i	0.145748	−	1.59586i
$786$	−0.296181	−	1.88618i	−0.0105644	−	0.0672777i
$787$	−19.8364	+	11.4525i	−0.707091	+	0.408239i	−0.809983	−	0.586454i	$-0.800524\pi$
$787$	−19.8364	+	11.4525i	−0.707091	+	0.408239i	0.102892	+	0.994693i	$0.467190\pi$
$788$	5.76568	−	3.32882i	0.205394	−	0.118584i
$789$	29.1098	+	11.2185i	1.03634	+	0.399388i
$790$	−0.0221747	+	0.242800i	−0.000788939	+	0.00863845i
$791$	−8.72815			−0.310337
$792$	0.709317	+	0.152735i	0.0252045	+	0.00542719i
$793$			60.9461i			2.16426i
$794$	−0.667932	+	1.15689i	−0.0237040	+	0.0410566i
$795$	5.09015	+	2.51506i	0.180529	+	0.0892000i
$796$	−4.10768	−	7.11471i	−0.145593	−	0.252174i
$797$	38.0574	−	21.9725i	1.34806	−	0.778305i	0.360089	−	0.932918i	$-0.382746\pi$
$797$	38.0574	−	21.9725i	1.34806	−	0.778305i	0.987975	+	0.154613i	$0.0494132\pi$
$798$	0.735315	+	0.910501i	0.0260299	+	0.0322314i
$799$	−13.0144	+	22.5415i	−0.460415	+	0.797462i
$800$	−4.26450	−	3.63407i	−0.150773	−	0.128484i
$801$	−18.8790	+	6.07892i	−0.667056	+	0.214788i
$802$			0.318343i			0.0112411i
$803$	−5.52664	−	3.19080i	−0.195031	−	0.112601i
$804$	27.8855	+	10.7466i	0.983445	+	0.379004i
$805$	−9.60036	+	13.6002i	−0.338368	+	0.479343i
$806$	−0.115628	−	0.200274i	−0.00407284	−	0.00705436i
$807$	49.1913	−	7.72437i	1.73162	−	0.271911i
$808$	0.500752	+	0.289109i	0.0176164	+	0.0101708i
$809$	27.9158			0.981469			0.490734	−	0.871309i	$-0.336729\pi$
$809$	27.9158			0.981469			0.490734	+	0.871309i	$0.336729\pi$
$810$	0.931491	−	1.64495i	0.0327293	−	0.0577975i
$811$	−12.7374			−0.447270			−0.223635	−	0.974673i	$-0.571792\pi$
$811$	−12.7374			−0.447270			−0.223635	+	0.974673i	$0.571792\pi$
$812$	3.82863	+	2.21046i	0.134359	+	0.0775720i
$813$	48.4223	−	7.60361i	1.69824	−	0.266670i
$814$	0.0487139	+	0.0843750i	0.00170742	+	0.00295734i
$815$	−23.1744	−	16.3588i	−0.811765	−	0.573025i
$816$	26.9039	+	10.3683i	0.941825	+	0.362965i
$817$	−38.9029	−	22.4606i	−1.36104	−	0.785797i
$818$		−	1.21886i		−	0.0426163i
$819$	13.8480	−	4.45898i	0.483889	−	0.155809i
$820$	20.4034	+	44.1941i	0.712519	+	1.54332i
$821$	−17.3466	+	30.0452i	−0.605400	+	1.04858i	0.386588	+	0.922253i	$0.373654\pi$
$821$	−17.3466	+	30.0452i	−0.605400	+	1.04858i	−0.991988	+	0.126331i	$0.959680\pi$
$822$	0.479834	+	0.594153i	0.0167361	+	0.0207235i
$823$	−29.7038	+	17.1495i	−1.03541	+	0.597795i	−0.918530	−	0.395351i	$-0.870623\pi$
$823$	−29.7038	+	17.1495i	−1.03541	+	0.597795i	−0.116881	+	0.993146i	$0.537290\pi$
$824$	2.02815	+	3.51286i	0.0706539	+	0.122376i
$825$	5.58494	+	0.147459i	0.194443	+	0.00513385i
$826$	−0.649975	+	1.12579i	−0.0226155	+	0.0391713i
$827$		−	35.7724i		−	1.24393i	−0.783046	−	0.621964i	$-0.786335\pi$
$827$		−	35.7724i		−	1.24393i	0.783046	−	0.621964i	$-0.213665\pi$
$828$	−43.4758	−	9.36148i	−1.51089	−	0.325334i
$829$	−21.9716			−0.763105			−0.381552	−	0.924347i	$-0.624610\pi$
$829$	−21.9716			−0.763105			−0.381552	+	0.924347i	$0.624610\pi$
$830$	1.31179	+	0.119804i	0.0455328	+	0.00415845i
$831$	2.38136	+	0.917740i	0.0826086	+	0.0318361i
$832$	32.7115	−	18.8860i	1.13407	−	0.654755i
$833$	−3.65235	+	2.10869i	−0.126547	+	0.0730617i
$834$	0.0885164	+	0.563701i	0.00306507	+	0.0195194i
$835$	1.92899	−	21.1214i	0.0667555	−	0.730937i
$836$	−9.24018			−0.319578
$837$	−2.20665	−	1.44551i	−0.0762730	−	0.0499642i
$838$			1.30639i			0.0451283i
$839$	−3.76511	+	6.52136i	−0.129986	+	0.225142i	−0.923671	−	0.383187i	$-0.874827\pi$
$839$	−3.76511	+	6.52136i	−0.129986	+	0.225142i	0.793685	+	0.608329i	$0.208160\pi$
$840$	0.805759	+	1.20792i	0.0278013	+	0.0416771i
$841$	12.0352	+	20.8456i	0.415008	+	0.718815i
$842$	0.137908	−	0.0796210i	0.00475261	−	0.00274392i
$843$	10.1933	−	26.4497i	0.351076	−	0.910977i
$844$	−11.5446	+	19.9958i	−0.397380	+	0.688283i
$845$	9.85703	+	21.3504i	0.339092	+	0.734477i
$846$	−1.28940	−	1.16718i	−0.0443305	−	0.0401285i
$847$			10.5838i			0.363664i
$848$	−5.01109	−	2.89315i	−0.172081	−	0.0993512i
$849$	27.8570	−	22.4972i	0.956051	−	0.772101i
$850$	−1.94800	−	0.358809i	−0.0668157	−	0.0123070i
$851$	−5.98482	−	10.3660i	−0.205157	−	0.355342i
$852$	5.94751	+	7.36448i	0.203758	+	0.252303i
$853$	−1.00230	−	0.578680i	−0.0343182	−	0.0198136i	0.482743	−	0.875762i	$-0.339641\pi$
$853$	−1.00230	−	0.578680i	−0.0343182	−	0.0198136i	−0.517061	+	0.855949i	$0.672974\pi$
$854$	1.18054			0.0403971
$855$	−14.4060	+	46.0539i	−0.492674	+	1.57501i
$856$	0.216678			0.00740591
$857$	−23.5634	−	13.6043i	−0.804909	−	0.464714i	0.0402760	−	0.999189i	$-0.487176\pi$
$857$	−23.5634	−	13.6043i	−0.804909	−	0.464714i	−0.845185	+	0.534474i	$0.820510\pi$
$858$	0.183035	−	0.474941i	0.00624870	−	0.0162142i
$859$	−8.44888	−	14.6339i	−0.288272	−	0.499302i	0.685125	−	0.728425i	$-0.259747\pi$
$859$	−8.44888	−	14.6339i	−0.288272	−	0.499302i	−0.973397	+	0.229123i	$0.926414\pi$
$860$	−22.7152	−	16.0346i	−0.774581	−	0.546777i
$861$	−2.93746	−	18.7067i	−0.100108	−	0.637523i
$862$	−1.12158	−	0.647542i	−0.0382010	−	0.0220554i
$863$		−	53.1850i		−	1.81044i	−0.424946	−	0.905219i	$-0.639707\pi$
$863$		−	53.1850i		−	1.81044i	0.424946	−	0.905219i	$-0.360293\pi$
$864$	−3.19065	+	4.87069i	−0.108548	+	0.165704i
$865$	23.8234	−	10.9987i	0.810020	−	0.373968i
$866$	1.24078	−	2.14909i	0.0421634	−	0.0730291i
$867$	1.34533	−	0.211254i	0.0456898	−	0.00717455i
$868$	0.875439	−	0.505435i	0.0297143	−	0.0171556i
$869$	0.374418	+	0.648511i	0.0127013	+	0.0219992i
$870$	−0.0522074	−	0.806048i	−0.00177000	−	0.0273276i
$871$	21.0104	−	36.3912i	0.711912	−	1.23307i
$872$			2.87405i			0.0973275i
$873$	20.4461	+	4.40258i	0.691995	+	0.149005i
$874$	−5.03049			−0.170159
$875$	7.81483	+	7.99553i	0.264189	+	0.270298i
$876$	26.5417	−	21.4349i	0.896761	−	0.724219i
$877$	−4.08343	+	2.35757i	−0.137888	+	0.0796095i	−0.567357	−	0.823472i	$-0.692034\pi$
$877$	−4.08343	+	2.35757i	−0.137888	+	0.0796095i	0.429469	+	0.903081i	$0.358701\pi$
$878$	−0.651751	+	0.376288i	−0.0219955	+	0.0126991i
$879$	14.1048	−	11.3910i	0.475743	−	0.384207i
$880$	−5.67026	−	0.517857i	−0.191144	−	0.0174570i
$881$	18.5676			0.625557			0.312779	−	0.949826i	$-0.398740\pi$
$881$	18.5676			0.625557			0.312779	+	0.949826i	$0.398740\pi$
$882$	−0.0863711	−	0.268238i	−0.00290827	−	0.00903205i
$883$		−	42.9623i		−	1.44580i	−0.690954	−	0.722899i	$-0.742809\pi$
$883$		−	42.9623i		−	1.44580i	0.690954	−	0.722899i	$-0.257191\pi$
$884$	20.3615	−	35.2672i	0.684831	−	1.18616i
$885$	−53.4863	+	3.46429i	−1.79792	+	0.116451i
$886$	−0.540234	−	0.935712i	−0.0181495	−	0.0314359i
$887$	−15.3835	+	8.88167i	−0.516527	+	0.298217i	−0.735513	−	0.677511i	$-0.763059\pi$
$887$	−15.3835	+	8.88167i	−0.516527	+	0.298217i	0.218985	+	0.975728i	$0.429725\pi$
$888$	−1.03137	+	0.161954i	−0.0346106	+	0.00543481i
$889$	−3.78499	+	6.55580i	−0.126945	+	0.219874i
$890$	−1.26075	+	0.582059i	−0.0422603	+	0.0195107i
$891$	−0.576304	−	5.77739i	−0.0193069	−	0.193550i
$892$		−	16.5220i		−	0.553199i
$893$	38.4479	+	22.1979i	1.28661	+	0.742825i
$894$	−0.464633	−	2.95894i	−0.0155397	−	0.0989616i
$895$	−5.30482	+	7.51498i	−0.177321	+	0.251198i
$896$	−1.48640	−	2.57453i	−0.0496573	−	0.0860090i
$897$	−22.4870	+	58.3495i	−0.750818	+	1.94823i
$898$	−2.22306	−	1.28348i	−0.0741843	−	0.0428303i
$899$	−1.12717			−0.0375932
$900$	−11.4724	+	27.5765i	−0.382412	+	0.919215i
$901$	−6.18246			−0.205968
$902$	−0.573742	−	0.331250i	−0.0191035	−	0.0110294i
$903$	6.79581	+	8.41488i	0.226150	+	0.280030i
$904$	−1.63612	−	2.83384i	−0.0544164	−	0.0942520i
$905$	5.45590	−	7.72899i	0.181360	−	0.256920i
$906$	1.90586	−	1.53916i	0.0633180	−	0.0511353i
$907$	27.2976	+	15.7603i	0.906403	+	0.523312i	0.879272	−	0.476320i	$-0.158030\pi$
$907$	27.2976	+	15.7603i	0.906403	+	0.523312i	0.0271308	+	0.999632i	$0.491363\pi$
$908$		−	6.02365i		−	0.199902i
$909$	0.973972	−	4.52324i	0.0323046	−	0.150026i
$910$	0.924777	−	0.426949i	0.0306561	−	0.0141532i
$911$	18.5421	−	32.1158i	0.614327	−	1.06404i	−0.376176	−	0.926548i	$-0.622761\pi$
$911$	18.5421	−	32.1158i	0.614327	−	1.06404i	0.990502	−	0.137497i	$-0.0439056\pi$
$912$	17.6847	−	45.8886i	0.585600	−	1.51952i
$913$	3.50374	−	2.02288i	0.115957	−	0.0669476i
$914$	1.10524	+	1.91433i	0.0365580	+	0.0633203i
$915$	27.0111	+	40.4924i	0.892958	+	1.33864i
$916$	3.37325	−	5.84264i	0.111455	−	0.193046i
$917$		−	11.7352i		−	0.387530i
$918$	−0.115898	+	2.05521i	−0.00382520	+	0.0678319i
$919$	−23.5208			−0.775879			−0.387939	−	0.921685i	$-0.626813\pi$
$919$	−23.5208			−0.775879			−0.387939	+	0.921685i	$0.626813\pi$
$920$	−6.21529	−	0.567634i	−0.204912	−	0.0187143i
$921$	2.50412	+	15.9471i	0.0825137	+	0.525474i
$922$	−2.43737	+	1.40722i	−0.0802705	+	0.0463442i
$923$	11.5272	−	6.65521i	0.379421	−	0.219059i
$924$	2.07606	+	0.800081i	0.0682974	+	0.0263207i
$925$	−7.57476	+	2.69181i	−0.249057	+	0.0885061i
$926$	1.27131			0.0417779
$927$	21.7828	−	24.0638i	0.715442	−	0.790359i
$928$			2.48798i			0.0816718i
$929$	−10.1789	+	17.6304i	−0.333960	+	0.578436i	−0.983285	−	0.182076i	$-0.941718\pi$
$929$	−10.1789	+	17.6304i	−0.333960	+	0.578436i	0.649324	+	0.760512i	$0.275052\pi$
$930$	−0.165584	−	0.0818155i	−0.00542970	−	0.00268284i
$931$	3.59668	+	6.22963i	0.117876	+	0.204168i
$932$	6.41221	−	3.70209i	0.210039	−	0.121266i
$933$	30.7419	+	38.0661i	1.00645	+	1.24623i
$934$	1.22537	−	2.12240i	0.0400953	−	0.0694470i
$935$	−5.52344	+	2.55005i	−0.180636	+	0.0833956i
$936$	4.04358	+	3.66029i	0.132169	+	0.119640i
$937$			26.0298i			0.850355i	0.905110	+	0.425178i	$0.139788\pi$
$937$			26.0298i			0.850355i	−0.905110	+	0.425178i	$0.860212\pi$
$938$	−0.704902	−	0.406976i	−0.0230159	−	0.0132882i
$939$	5.24725	+	2.02221i	0.171238	+	0.0659923i
$940$	22.4495	+	15.8471i	0.732222	+	0.516876i
$941$	23.6633	+	40.9860i	0.771402	+	1.33611i	0.936795	+	0.349879i	$0.113777\pi$
$941$	23.6633	+	40.9860i	0.771402	+	1.33611i	−0.165393	+	0.986228i	$0.552889\pi$
$942$	−3.22731	+	0.506776i	−0.105152	+	0.0165117i
$943$	70.4879	+	40.6962i	2.29540	+	1.32525i
$944$	54.6246			1.77788
$945$	7.22438	−	9.09991i	0.235009	−	0.296020i
$946$	0.378425			0.0123037
$947$	10.0457	+	5.79988i	0.326441	+	0.188471i	0.654260	−	0.756270i	$-0.272980\pi$
$947$	10.0457	+	5.79988i	0.326441	+	0.188471i	−0.327819	+	0.944741i	$0.606314\pi$
$948$	−3.95484	+	0.621017i	−0.128447	+	0.0201697i
$949$	−23.9855	−	41.5441i	−0.778602	−	1.34858i
$950$	−0.612001	+	3.32259i	−0.0198559	+	0.107799i
$951$	53.8514	+	20.7535i	1.74625	+	0.672978i
$952$	−1.36929	−	0.790558i	−0.0443789	−	0.0256221i
$953$			18.1777i			0.588833i	0.955677	+	0.294416i	$0.0951252\pi$
$953$			18.1777i			0.588833i	−0.955677	+	0.294416i	$0.904875\pi$
$954$	0.0869594	−	0.403849i	0.00281541	−	0.0130751i
$955$	15.0683	+	32.6381i	0.487598	+	1.05614i
$956$	2.93179	−	5.07800i	0.0948207	−	0.164234i
$957$	−1.55870	−	1.93006i	−0.0503858	−	0.0623900i
$958$	1.82812	−	1.05546i	0.0590638	−	0.0341005i
$959$	2.34703	+	4.06518i	0.0757896	+	0.131271i
$960$	13.3632	−	27.0454i	0.431297	−	0.872887i
$961$	15.3711	−	26.6236i	0.495843	−	0.858825i
$962$			0.732372i			0.0236126i
$963$	−0.531424	−	1.65041i	−0.0171249	−	0.0531839i
$964$	50.7862			1.63571
$965$	1.07788	−	11.8022i	0.0346983	−	0.379928i
$966$	1.13024	+	0.435576i	0.0363648	+	0.0140144i
$967$	−15.7986	+	9.12132i	−0.508048	+	0.293322i	−0.732031	−	0.681271i	$-0.761427\pi$
$967$	−15.7986	+	9.12132i	−0.508048	+	0.293322i	0.223983	+	0.974593i	$0.428094\pi$
$968$	−3.43633	+	1.98397i	−0.110448	+	0.0637671i
$969$	−8.15117	−	51.9093i	−0.261853	−	1.66757i
$970$	1.45825	+	0.133180i	0.0468216	+	0.00427616i
$971$	11.2880			0.362249			0.181125	−	0.983460i	$-0.442026\pi$
$971$	11.2880			0.362249			0.181125	+	0.983460i	$0.442026\pi$
$972$	29.9279	+	8.23192i	0.959937	+	0.264039i
$973$			3.50717i			0.112435i
$974$	−0.434885	+	0.753242i	−0.0139346	+	0.0241354i
$975$	35.8036	+	21.9512i	1.14663	+	0.702999i
$976$	−24.8034	−	42.9607i	−0.793936	−	1.37514i
$977$	−11.9224	+	6.88338i	−0.381430	+	0.220219i	−0.678440	−	0.734655i	$-0.737344\pi$
$977$	−11.9224	+	6.88338i	−0.381430	+	0.220219i	0.297010	+	0.954874i	$0.404010\pi$
$978$	−0.742213	+	1.92590i	−0.0237334	+	0.0615836i
$979$	−2.13249	+	3.69359i	−0.0681548	+	0.118048i
$980$	1.86628	+	4.04239i	0.0596162	+	0.129129i
$981$	21.8913	−	7.04887i	0.698936	−	0.225053i
$982$		−	1.27499i		−	0.0406867i
$983$	−29.7614	−	17.1828i	−0.949242	−	0.548045i	−0.0563966	−	0.998408i	$-0.517961\pi$
$983$	−29.7614	−	17.1828i	−0.949242	−	0.548045i	−0.892845	+	0.450363i	$0.851294\pi$
$984$	5.52301	−	4.46035i	0.176067	−	0.142191i
$985$	−6.10797	−	4.31161i	−0.194616	−	0.137379i
$986$	0.439781	+	0.761723i	0.0140055	+	0.0242582i
$987$	−6.71633	−	8.31647i	−0.213783	−	0.264716i
$988$	−60.1533	−	34.7296i	−1.91373	−	1.10489i
$989$	−46.4919			−1.47836
$990$	−0.0888840	−	0.396669i	−0.00282492	−	0.0126070i
$991$	26.1741			0.831446			0.415723	−	0.909491i	$-0.363529\pi$
$991$	26.1741			0.831446			0.415723	+	0.909491i	$0.363529\pi$
$992$	0.492673	+	0.284445i	0.0156424	+	0.00903114i
$993$	−10.1997	+	26.4664i	−0.323679	+	0.839886i
$994$	−0.128912	−	0.223283i	−0.00408885	−	0.00708210i
$995$	−5.32043	+	7.53708i	−0.168669	+	0.238942i
$996$	3.35519	+	21.3669i	0.106313	+	0.677038i
$997$	28.9678	+	16.7245i	0.917418	+	0.529672i	0.882810	−	0.469729i	$-0.155649\pi$
$997$	28.9678	+	16.7245i	0.917418	+	0.529672i	0.0346075	+	0.999401i	$0.488982\pi$
$998$		−	2.57971i		−	0.0816592i
$999$	3.76312	+	7.45865i	0.119060	+	0.235981i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.bh.c.169.16	✓	64
3.2	odd	2		945.2.bh.c.694.17		64
5.4	even	2	inner	315.2.bh.c.169.17	yes	64
9.4	even	3	inner	315.2.bh.c.274.17	yes	64
9.5	odd	6		945.2.bh.c.64.16		64
15.14	odd	2		945.2.bh.c.694.16		64
45.4	even	6	inner	315.2.bh.c.274.16	yes	64
45.14	odd	6		945.2.bh.c.64.17		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.bh.c.169.16	✓	64	1.1	even	1	trivial
315.2.bh.c.169.17	yes	64	5.4	even	2	inner
315.2.bh.c.274.16	yes	64	45.4	even	6	inner
315.2.bh.c.274.17	yes	64	9.4	even	3	inner
945.2.bh.c.64.16		64	9.5	odd	6
945.2.bh.c.64.17		64	45.14	odd	6
945.2.bh.c.694.16		64	15.14	odd	2
945.2.bh.c.694.17		64	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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.bh (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0813489 - 0.0469668i) q^{2} +(-1.71108 + 0.268687i) q^{3} +(-0.995588 - 1.72441i) q^{4} +(-1.28952 + 1.82678i) q^{5} +(0.151814 + 0.0585067i) q^{6} +(0.866025 + 0.500000i) q^{7} +0.374905i q^{8} +(2.85561 - 0.919491i) q^{9} +O(q^{10})\)	\(q+(-0.0813489 - 0.0469668i) q^{2} +(-1.71108 + 0.268687i) q^{3} +(-0.995588 - 1.72441i) q^{4} +(-1.28952 + 1.82678i) q^{5} +(0.151814 + 0.0585067i) q^{6} +(0.866025 + 0.500000i) q^{7} +0.374905i q^{8} +(2.85561 - 0.919491i) q^{9} +(0.190699 - 0.0880417i) q^{10} +(0.322559 - 0.558689i) q^{11} +(2.16686 + 2.68311i) q^{12} +(4.19970 - 2.42470i) q^{13} +(-0.0469668 - 0.0813489i) q^{14} +(1.71565 - 3.47225i) q^{15} +(-1.97357 + 3.41832i) q^{16} +4.21737i q^{17} +(-0.275487 - 0.0593195i) q^{18} +7.19335 q^{19} +(4.43395 + 0.404947i) q^{20} +(-1.61619 - 0.622852i) q^{21} +(-0.0524796 + 0.0302991i) q^{22} +(6.44746 - 3.72244i) q^{23} +(-0.100732 - 0.641495i) q^{24} +(-1.67425 - 4.71136i) q^{25} -0.455521 q^{26} +(-4.63914 + 2.34059i) q^{27} -1.99118i q^{28} +(-1.11013 + 1.92280i) q^{29} +(-0.302647 + 0.201885i) q^{30} +(0.253837 + 0.439659i) q^{31} +(0.970450 - 0.560290i) q^{32} +(-0.401813 + 1.04263i) q^{33} +(0.198077 - 0.343079i) q^{34} +(-2.03015 + 0.937276i) q^{35} +(-4.42860 - 4.00881i) q^{36} -1.60777i q^{37} +(-0.585171 - 0.337849i) q^{38} +(-6.53456 + 5.27727i) q^{39} +(-0.684870 - 0.483450i) q^{40} +(5.46633 + 9.46797i) q^{41} +(0.102221 + 0.126575i) q^{42} +(-5.40817 - 3.12241i) q^{43} -1.28454 q^{44} +(-2.00268 + 6.40229i) q^{45} -0.699325 q^{46} +(5.34492 + 3.08589i) q^{47} +(2.45848 - 6.37930i) q^{48} +(0.500000 + 0.866025i) q^{49} +(-0.0850787 + 0.461898i) q^{50} +(-1.13315 - 7.21628i) q^{51} +(-8.36235 - 4.82800i) q^{52} +1.46595i q^{53} +(0.487319 + 0.0274811i) q^{54} +(0.604654 + 1.30969i) q^{55} +(-0.187453 + 0.324678i) q^{56} +(-12.3084 + 1.93276i) q^{57} +(0.180615 - 0.104278i) q^{58} +(-6.91952 - 11.9850i) q^{59} +(-7.69567 + 0.498446i) q^{60} +(-6.28389 + 10.8840i) q^{61} -0.0476877i q^{62} +(2.93278 + 0.631505i) q^{63} +7.78901 q^{64} +(-0.986226 + 10.7986i) q^{65} +(0.0816561 - 0.0659449i) q^{66} +(7.50426 - 4.33259i) q^{67} +(7.27248 - 4.19877i) q^{68} +(-10.0320 + 8.10176i) q^{69} +(0.209171 + 0.0191033i) q^{70} +2.74476 q^{71} +(0.344722 + 1.07059i) q^{72} -9.89216i q^{73} +(-0.0755116 + 0.130790i) q^{74} +(4.13067 + 7.61168i) q^{75} +(-7.16162 - 12.4043i) q^{76} +(0.558689 - 0.322559i) q^{77} +(0.779435 - 0.122393i) q^{78} +(-0.580387 + 1.00526i) q^{79} +(-3.69956 - 8.01328i) q^{80} +(7.30907 - 5.25142i) q^{81} -1.02694i q^{82} +(5.43115 + 3.13568i) q^{83} +(0.535003 + 3.40707i) q^{84} +(-7.70422 - 5.43841i) q^{85} +(0.293299 + 0.508009i) q^{86} +(1.38289 - 3.58835i) q^{87} +(0.209455 + 0.120929i) q^{88} -6.61117 q^{89} +(0.463610 - 0.426759i) q^{90} +4.84940 q^{91} +(-12.8380 - 7.41204i) q^{92} +(-0.552468 - 0.684091i) q^{93} +(-0.289869 - 0.502068i) q^{94} +(-9.27601 + 13.1407i) q^{95} +(-1.50998 + 1.21945i) q^{96} +(6.03755 + 3.48578i) q^{97} -0.0939336i q^{98} +(0.407395 - 1.89199i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 34 q^{4} - 10 q^{5} - 18 q^{6} - 14 q^{9}+O(q^{10}) \) 64 * q + 34 * q^4 - 10 * q^5 - 18 * q^6 - 14 * q^9	\( 64 q + 34 q^{4} - 10 q^{5} - 18 q^{6} - 14 q^{9} - 4 q^{10} + 18 q^{11} - 6 q^{14} - 14 q^{15} - 46 q^{16} + 48 q^{19} - 2 q^{20} - 2 q^{21} - 12 q^{24} + 18 q^{25} - 12 q^{26} - 30 q^{29} - 4 q^{30} - 4 q^{31} + 34 q^{34} + 8 q^{35} - 42 q^{36} - 8 q^{39} - 6 q^{40} + 28 q^{41} + 68 q^{44} - 6 q^{45} - 24 q^{46} + 32 q^{49} - 58 q^{50} + 62 q^{51} + 54 q^{54} - 12 q^{55} + 18 q^{56} + 16 q^{59} - 66 q^{60} + 40 q^{61} - 100 q^{64} - 18 q^{65} - 146 q^{66} - 20 q^{69} - 4 q^{70} - 176 q^{71} - 20 q^{74} + 60 q^{75} - 22 q^{79} + 64 q^{80} - 58 q^{81} - 4 q^{84} - 14 q^{85} + 60 q^{86} - 200 q^{89} + 8 q^{90} - 16 q^{91} - 42 q^{94} + 68 q^{95} + 210 q^{96} + 90 q^{99}+O(q^{100}) \) 64 * q + 34 * q^4 - 10 * q^5 - 18 * q^6 - 14 * q^9 - 4 * q^10 + 18 * q^11 - 6 * q^14 - 14 * q^15 - 46 * q^16 + 48 * q^19 - 2 * q^20 - 2 * q^21 - 12 * q^24 + 18 * q^25 - 12 * q^26 - 30 * q^29 - 4 * q^30 - 4 * q^31 + 34 * q^34 + 8 * q^35 - 42 * q^36 - 8 * q^39 - 6 * q^40 + 28 * q^41 + 68 * q^44 - 6 * q^45 - 24 * q^46 + 32 * q^49 - 58 * q^50 + 62 * q^51 + 54 * q^54 - 12 * q^55 + 18 * q^56 + 16 * q^59 - 66 * q^60 + 40 * q^61 - 100 * q^64 - 18 * q^65 - 146 * q^66 - 20 * q^69 - 4 * q^70 - 176 * q^71 - 20 * q^74 + 60 * q^75 - 22 * q^79 + 64 * q^80 - 58 * q^81 - 4 * q^84 - 14 * q^85 + 60 * q^86 - 200 * q^89 + 8 * q^90 - 16 * q^91 - 42 * q^94 + 68 * q^95 + 210 * q^96 + 90 * q^99

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