LMFDB - Embedded newform 804.2.l.a.431.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(431,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("804.431");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.l (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:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$264$
Relative dimension:	$132$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			431.20
Character	$\chi$	$=$	804.431
Dual form			804.2.l.a.707.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.23331 - 0.692067i) q^{2} +(-1.71207 - 0.262337i) q^{3} +(1.04209 + 1.70706i) q^{4} -2.53500i q^{5} +(1.92995 + 1.50841i) q^{6} +(-3.95663 + 2.28436i) q^{7} +(-0.103813 - 2.82652i) q^{8} +(2.86236 + 0.898278i) q^{9} +O(q^{10})$	\(q+(-1.23331 - 0.692067i) q^{2} +(-1.71207 - 0.262337i) q^{3} +(1.04209 + 1.70706i) q^{4} -2.53500i q^{5} +(1.92995 + 1.50841i) q^{6} +(-3.95663 + 2.28436i) q^{7} +(-0.103813 - 2.82652i) q^{8} +(2.86236 + 0.898278i) q^{9} +(-1.75439 + 3.12643i) q^{10} +(1.70732 + 2.95717i) q^{11} +(-1.33630 - 3.19598i) q^{12} +(0.773102 - 1.33905i) q^{13} +(6.46067 - 0.0790646i) q^{14} +(-0.665024 + 4.34009i) q^{15} +(-1.82811 + 3.55781i) q^{16} +(-0.652493 - 0.376717i) q^{17} +(-2.90850 - 3.08880i) q^{18} +(2.56300 + 1.47975i) q^{19} +(4.32739 - 2.64169i) q^{20} +(7.37330 - 2.87301i) q^{21} +(-0.0590926 - 4.82868i) q^{22} +(1.51001 - 2.61541i) q^{23} +(-0.563767 + 4.86643i) q^{24} -1.42621 q^{25} +(-1.88018 + 1.11642i) q^{26} +(-4.66490 - 2.28882i) q^{27} +(-8.02270 - 4.37370i) q^{28} +(-7.40542 + 4.27552i) q^{29} +(3.82381 - 4.89242i) q^{30} +(6.14263 - 3.54645i) q^{31} +(4.71686 - 3.12270i) q^{32} +(-2.14728 - 5.51077i) q^{33} +(0.544010 + 0.916176i) q^{34} +(5.79085 + 10.0300i) q^{35} +(1.44941 + 5.82230i) q^{36} +(-3.65856 + 6.33681i) q^{37} +(-2.13688 - 3.59875i) q^{38} +(-1.67489 + 2.08973i) q^{39} +(-7.16522 + 0.263166i) q^{40} +(8.79694 - 5.07892i) q^{41} +(-11.0819 - 1.55951i) q^{42} -5.96556i q^{43} +(-3.26889 + 5.99613i) q^{44} +(2.27713 - 7.25607i) q^{45} +(-3.67233 + 2.18057i) q^{46} +(-1.15140 - 1.99428i) q^{47} +(4.06319 - 5.61164i) q^{48} +(6.93663 - 12.0146i) q^{49} +(1.75895 + 0.987029i) q^{50} +(1.01829 + 0.816139i) q^{51} +(3.09148 - 0.0756774i) q^{52} +1.78213i q^{53} +(4.16924 + 6.05124i) q^{54} +(7.49642 - 4.32806i) q^{55} +(6.86755 + 10.9464i) q^{56} +(-3.99984 - 3.20580i) q^{57} +(12.0921 - 0.147981i) q^{58} -6.04085 q^{59} +(-8.10180 + 3.38751i) q^{60} +(6.13660 - 10.6289i) q^{61} +(-10.0301 + 0.122747i) q^{62} +(-13.3773 + 2.98451i) q^{63} +(-7.97845 + 0.586859i) q^{64} +(-3.39449 - 1.95981i) q^{65} +(-1.16557 + 8.28253i) q^{66} +(2.58397 - 7.76679i) q^{67} +(-0.0368761 - 1.50642i) q^{68} +(-3.27135 + 4.08162i) q^{69} +(-0.200429 - 16.3778i) q^{70} +(-7.67806 - 13.2988i) q^{71} +(2.24185 - 8.18377i) q^{72} +(2.04919 - 3.54930i) q^{73} +(8.89761 - 5.28326i) q^{74} +(2.44176 + 0.374147i) q^{75} +(0.144850 + 5.91723i) q^{76} +(-13.5105 - 7.80029i) q^{77} +(3.51188 - 1.41815i) q^{78} +(-2.42055 + 1.39750i) q^{79} +(9.01904 + 4.63425i) q^{80} +(7.38619 + 5.14239i) q^{81} +(-14.3643 + 0.175788i) q^{82} +(0.916490 - 1.58741i) q^{83} +(12.5880 + 9.59273i) q^{84} +(-0.954976 + 1.65407i) q^{85} +(-4.12857 + 7.35736i) q^{86} +(13.8002 - 5.37727i) q^{87} +(8.18126 - 5.13278i) q^{88} -1.89388i q^{89} +(-7.83008 + 7.37302i) q^{90} +7.06418i q^{91} +(6.03821 - 0.147811i) q^{92} +(-11.4470 + 4.46033i) q^{93} +(0.0398514 + 3.25641i) q^{94} +(3.75116 - 6.49720i) q^{95} +(-8.89479 + 4.10886i) q^{96} +(8.00236 - 13.8605i) q^{97} +(-16.8699 + 10.0171i) q^{98} +(2.23061 + 9.99814i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 264 q - 2 q^{4} - 3 q^{6} - 12 q^{9}+O(q^{10}) $ 264 * q - 2 * q^4 - 3 * q^6 - 12 * q^9	$ 264 q - 2 q^{4} - 3 q^{6} - 12 q^{9} + 2 q^{10} + 2 q^{12} - 18 q^{16} + q^{18} - 4 q^{22} - 248 q^{25} + 7 q^{30} - 38 q^{34} + 13 q^{36} + 4 q^{37} + 48 q^{40} - 12 q^{42} + 48 q^{45} - 2 q^{46} - 11 q^{48} + 128 q^{49} + 32 q^{52} - 8 q^{54} - 2 q^{57} - 32 q^{58} + 68 q^{60} - 8 q^{61} + 4 q^{64} + 30 q^{66} - 40 q^{69} - 140 q^{70} + 108 q^{72} - 4 q^{73} - 120 q^{76} + 44 q^{78} - 28 q^{81} - 64 q^{82} + 33 q^{84} + 16 q^{85} - 14 q^{88} + 42 q^{90} + 16 q^{93} - 12 q^{94} - 4 q^{96} + 20 q^{97}+O(q^{100}) $ 264 * q - 2 * q^4 - 3 * q^6 - 12 * q^9 + 2 * q^10 + 2 * q^12 - 18 * q^16 + q^18 - 4 * q^22 - 248 * q^25 + 7 * q^30 - 38 * q^34 + 13 * q^36 + 4 * q^37 + 48 * q^40 - 12 * q^42 + 48 * q^45 - 2 * q^46 - 11 * q^48 + 128 * q^49 + 32 * q^52 - 8 * q^54 - 2 * q^57 - 32 * q^58 + 68 * q^60 - 8 * q^61 + 4 * q^64 + 30 * q^66 - 40 * q^69 - 140 * q^70 + 108 * q^72 - 4 * q^73 - 120 * q^76 + 44 * q^78 - 28 * q^81 - 64 * q^82 + 33 * q^84 + 16 * q^85 - 14 * q^88 + 42 * q^90 + 16 * q^93 - 12 * q^94 - 4 * q^96 + 20 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$-1$

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 $

$2$	−1.23331	−	0.692067i	−0.872079	−	0.489365i
$2$	−1.23331	−	0.692067i	−0.872079	−	0.489365i
$3$	−1.71207	−	0.262337i	−0.988463	−	0.151460i
$3$	−1.71207	−	0.262337i	−0.988463	−	0.151460i
$4$	1.04209	+	1.70706i	0.521044	+	0.853530i
$5$		−	2.53500i		−	1.13368i	−0.823826	−	0.566842i	$-0.808165\pi$
$5$		−	2.53500i		−	1.13368i	0.823826	−	0.566842i	$-0.191835\pi$
$6$	1.92995	+	1.50841i	0.787899	+	0.615805i
$7$	−3.95663	+	2.28436i	−1.49547	+	0.863408i	−0.999986	−	0.00521136i	$-0.998341\pi$
$7$	−3.95663	+	2.28436i	−1.49547	+	0.863408i	−0.495480	+	0.868619i	$0.665008\pi$
$8$	−0.103813	−	2.82652i	−0.0367034	−	0.999326i
$9$	2.86236	+	0.898278i	0.954119	+	0.299426i
$10$	−1.75439	+	3.12643i	−0.554786	+	0.988663i
$11$	1.70732	+	2.95717i	0.514777	+	0.891621i	0.999853	+	0.0171484i	$0.00545876\pi$
$11$	1.70732	+	2.95717i	0.514777	+	0.891621i	−0.485076	+	0.874472i	$0.661208\pi$
$12$	−1.33630	−	3.19598i	−0.385757	−	0.922601i
$13$	0.773102	−	1.33905i	0.214420	−	0.371386i	−0.738673	−	0.674064i	$-0.764547\pi$
$13$	0.773102	−	1.33905i	0.214420	−	0.371386i	0.953093	+	0.302678i	$0.0978806\pi$
$14$	6.46067	−	0.0790646i	1.72669	−	0.0211309i
$15$	−0.665024	+	4.34009i	−0.171708	+	1.12061i
$16$	−1.82811	+	3.55781i	−0.457027	+	0.889453i
$17$	−0.652493	−	0.376717i	−0.158253	−	0.0913673i	0.418782	−	0.908087i	$-0.362457\pi$
$17$	−0.652493	−	0.376717i	−0.158253	−	0.0913673i	−0.577035	+	0.816719i	$0.695790\pi$
$18$	−2.90850	−	3.08880i	−0.685539	−	0.728036i
$19$	2.56300	+	1.47975i	0.587993	+	0.339478i	0.764303	−	0.644857i	$-0.223083\pi$
$19$	2.56300	+	1.47975i	0.587993	+	0.339478i	−0.176311	+	0.984335i	$0.556416\pi$
$20$	4.32739	−	2.64169i	0.967634	−	0.590699i
$21$	7.37330	−	2.87301i	1.60899	−	0.626943i
$22$	−0.0590926	−	4.82868i	−0.0125986	−	1.02948i
$23$	1.51001	−	2.61541i	0.314858	−	0.545350i	−0.664549	−	0.747244i	$-0.731376\pi$
$23$	1.51001	−	2.61541i	0.314858	−	0.545350i	0.979407	+	0.201894i	$0.0647098\pi$
$24$	−0.563767	+	4.86643i	−0.115078	+	0.993356i
$25$	−1.42621			−0.285241
$26$	−1.88018	+	1.11642i	−0.368734	+	0.218948i
$27$	−4.66490	−	2.28882i	−0.897761	−	0.440483i
$28$	−8.02270	−	4.37370i	−1.51615	−	0.826552i
$29$	−7.40542	+	4.27552i	−1.37515	+	0.793945i	−0.991571	−	0.129562i	$-0.958643\pi$
$29$	−7.40542	+	4.27552i	−1.37515	+	0.793945i	−0.383582	+	0.923507i	$0.625309\pi$
$30$	3.82381	−	4.89242i	0.698129	−	0.893229i
$31$	6.14263	−	3.54645i	1.10325	−	0.636961i	0.166177	−	0.986096i	$-0.446858\pi$
$31$	6.14263	−	3.54645i	1.10325	−	0.636961i	0.937073	+	0.349135i	$0.113524\pi$
$32$	4.71686	−	3.12270i	0.833831	−	0.552020i
$33$	−2.14728	−	5.51077i	−0.373793	−	0.959303i
$34$	0.544010	+	0.916176i	0.0932970	+	0.157123i
$35$	5.79085	+	10.0300i	0.978832	+	1.69539i
$36$	1.44941	+	5.82230i	0.241569	+	0.970384i
$37$	−3.65856	+	6.33681i	−0.601463	+	1.04176i	0.391137	+	0.920333i	$0.372082\pi$
$37$	−3.65856	+	6.33681i	−0.601463	+	1.04176i	−0.992600	+	0.121432i	$0.961251\pi$
$38$	−2.13688	−	3.59875i	−0.346648	−	0.583795i
$39$	−1.67489	+	2.08973i	−0.268196	+	0.334625i
$40$	−7.16522	+	0.263166i	−1.13292	+	0.0416101i
$41$	8.79694	−	5.07892i	1.37385	−	0.793193i	0.382441	−	0.923980i	$-0.375084\pi$
$41$	8.79694	−	5.07892i	1.37385	−	0.793193i	0.991411	+	0.130787i	$0.0417503\pi$
$42$	−11.0819	−	1.55951i	−1.70997	−	0.240638i
$43$		−	5.96556i		−	0.909740i	−0.890558	−	0.454870i	$-0.849686\pi$
$43$		−	5.96556i		−	0.909740i	0.890558	−	0.454870i	$-0.150314\pi$
$44$	−3.26889	+	5.99613i	−0.492803	+	0.903951i
$45$	2.27713	−	7.25607i	0.339455	−	1.08167i
$46$	−3.67233	+	2.18057i	−0.541456	+	0.321508i
$47$	−1.15140	−	1.99428i	−0.167949	−	0.290896i	0.769750	−	0.638346i	$-0.220381\pi$
$47$	−1.15140	−	1.99428i	−0.167949	−	0.290896i	−0.937699	+	0.347450i	$0.887048\pi$
$48$	4.06319	−	5.61164i	0.586471	−	0.809970i
$49$	6.93663	−	12.0146i	0.990947	−	1.71637i
$50$	1.75895	+	0.987029i	0.248753	+	0.139587i
$51$	1.01829	+	0.816139i	0.142589	+	0.114282i
$52$	3.09148	−	0.0756774i	0.428711	−	0.0104946i
$53$			1.78213i			0.244795i	0.992481	+	0.122397i	$0.0390583\pi$
$53$			1.78213i			0.244795i	−0.992481	+	0.122397i	$0.960942\pi$
$54$	4.16924	+	6.05124i	0.567361	+	0.823469i
$55$	7.49642	−	4.32806i	1.01082	−	0.583595i
$56$	6.86755	+	10.9464i	0.917715	+	1.46277i
$57$	−3.99984	−	3.20580i	−0.529792	−	0.424619i
$58$	12.0921	−	0.147981i	1.58777	−	0.0194309i
$59$	−6.04085			−0.786451			−0.393226	−	0.919442i	$-0.628641\pi$
$59$	−6.04085			−0.786451			−0.393226	+	0.919442i	$0.628641\pi$
$60$	−8.10180	+	3.38751i	−1.04594	+	0.437326i
$61$	6.13660	−	10.6289i	0.785711	−	1.36089i	−0.142862	−	0.989743i	$-0.545631\pi$
$61$	6.13660	−	10.6289i	0.785711	−	1.36089i	0.928573	−	0.371149i	$-0.121036\pi$
$62$	−10.0301	+	0.122747i	−1.27383	+	0.0155889i
$63$	−13.3773	+	2.98451i	−1.68538	+	0.376013i
$64$	−7.97845	+	0.586859i	−0.997306	+	0.0733574i
$65$	−3.39449	−	1.95981i	−0.421035	−	0.243084i
$66$	−1.16557	+	8.28253i	−0.143472	+	1.01951i
$67$	2.58397	−	7.76679i	0.315682	−	0.948865i
$67$	2.58397	−	7.76679i	0.315682	−	0.948865i
$68$	−0.0368761	−	1.50642i	−0.00447188	−	0.182680i
$69$	−3.27135	+	4.08162i	−0.393824	+	0.491370i
$70$	−0.200429	−	16.3778i	−0.0239558	−	1.95752i
$71$	−7.67806	−	13.2988i	−0.911219	−	1.57828i	−0.812345	−	0.583177i	$-0.801809\pi$
$71$	−7.67806	−	13.2988i	−0.911219	−	1.57828i	−0.0988734	−	0.995100i	$-0.531524\pi$
$72$	2.24185	−	8.18377i	0.264205	−	0.964467i
$73$	2.04919	−	3.54930i	0.239839	−	0.415414i	−0.720829	−	0.693113i	$-0.756239\pi$
$73$	2.04919	−	3.54930i	0.239839	−	0.415414i	0.960668	+	0.277700i	$0.0895720\pi$
$74$	8.89761	−	5.28326i	1.03433	−	0.614166i
$75$	2.44176	+	0.374147i	0.281950	+	0.0432027i
$76$	0.144850	+	5.91723i	0.0166154	+	0.678752i
$77$	−13.5105	−	7.80029i	−1.53966	−	0.888926i
$78$	3.51188	−	1.41815i	0.397642	−	0.160574i
$79$	−2.42055	+	1.39750i	−0.272333	+	0.157231i	−0.629947	−	0.776638i	$-0.716924\pi$
$79$	−2.42055	+	1.39750i	−0.272333	+	0.157231i	0.357614	+	0.933869i	$0.383590\pi$
$80$	9.01904	+	4.63425i	1.00836	+	0.518125i
$81$	7.38619	+	5.14239i	0.820688	+	0.571377i
$82$	−14.3643	+	0.175788i	−1.58627	+	0.0194125i
$83$	0.916490	−	1.58741i	0.100598	−	0.174240i	−0.811333	−	0.584584i	$-0.801258\pi$
$83$	0.916490	−	1.58741i	0.100598	−	0.174240i	0.911931	+	0.410343i	$0.134591\pi$
$84$	12.5880	+	9.59273i	1.37347	+	1.04665i
$85$	−0.954976	+	1.65407i	−0.103582	+	0.179409i
$86$	−4.12857	+	7.35736i	−0.445195	+	0.793365i
$87$	13.8002	−	5.37727i	1.47954	−	0.576504i
$88$	8.18126	−	5.13278i	0.872126	−	0.547156i
$89$		−	1.89388i		−	0.200751i	−0.994950	−	0.100376i	$-0.967996\pi$
$89$		−	1.89388i		−	0.200751i	0.994950	−	0.100376i	$-0.0320044\pi$
$90$	−7.83008	+	7.37302i	−0.825363	+	0.777185i
$91$			7.06418i			0.740527i
$92$	6.03821	−	0.147811i	0.629527	−	0.0154104i
$93$	−11.4470	+	4.46033i	−1.18700	+	0.462514i
$94$	0.0398514	+	3.25641i	0.00411035	+	0.335873i
$95$	3.75116	−	6.49720i	0.384861	−	0.666599i
$96$	−8.89479	+	4.10886i	−0.907820	+	0.419359i
$97$	8.00236	−	13.8605i	0.812516	−	1.40732i	−0.0985815	−	0.995129i	$-0.531431\pi$
$97$	8.00236	−	13.8605i	0.812516	−	1.40732i	0.911098	−	0.412190i	$-0.135236\pi$
$98$	−16.8699	+	10.0171i	−1.70412	+	1.01188i
$99$	2.23061	+	9.99814i	0.224185	+	1.00485i
$100$	−1.48623	−	2.43462i	−0.148623	−	0.243462i
$101$	−1.03526	+	0.597706i	−0.103012	+	0.0594739i	−0.550621	−	0.834755i	$-0.685609\pi$
$101$	−1.03526	+	0.597706i	−0.103012	+	0.0594739i	0.447609	+	0.894229i	$0.352276\pi$
$102$	−0.691036	−	1.71127i	−0.0684228	−	0.169441i
$103$	−14.1829	+	8.18852i	−1.39749	+	0.806839i	−0.994129	−	0.108204i	$-0.965490\pi$
$103$	−14.1829	+	8.18852i	−1.39749	+	0.806839i	−0.403357	+	0.915043i	$0.632157\pi$
$104$	−3.86512	−	2.04618i	−0.379006	−	0.200644i
$105$	−7.28308	−	18.6913i	−0.710756	−	1.82408i
$106$	1.23336	−	2.19792i	0.119794	−	0.213481i
$107$	14.8282			1.43349			0.716747	−	0.697333i	$-0.245630\pi$
$107$	14.8282			1.43349			0.716747	+	0.697333i	$0.245630\pi$
$108$	−0.954087	−	10.3484i	−0.0918071	−	0.995777i
$109$	3.38066			0.323809			0.161904	−	0.986806i	$-0.448236\pi$
$109$	3.38066			0.323809			0.161904	+	0.986806i	$0.448236\pi$
$110$	−12.2407	+	0.149799i	−1.16710	+	0.0142828i
$111$	7.92608	−	9.88927i	0.752310	−	0.938648i
$112$	−0.894179	−	18.2530i	−0.0844920	−	1.72475i
$113$	12.2429	−	7.06843i	1.15171	−	0.664942i	0.202409	−	0.979301i	$-0.435123\pi$
$113$	12.2429	−	7.06843i	1.15171	−	0.664942i	0.949304	+	0.314359i	$0.101790\pi$
$114$	2.71440	+	6.72189i	0.254227	+	0.629563i
$115$	−6.63004	−	3.82786i	−0.618255	−	0.356950i
$116$	−15.0157	−	8.18604i	−1.39417	−	0.760054i
$117$	3.41574	−	3.13838i	0.315785	−	0.290144i
$118$	7.45021	+	4.18067i	0.685847	+	0.384862i
$119$	3.44223			0.315549
$120$	12.3364	+	1.42915i	1.12615	+	0.130463i
$121$	−0.329907	+	0.571415i	−0.0299915	+	0.0519468i
$122$	−14.9242	+	8.86175i	−1.35118	+	0.802305i
$123$	−16.3934	+	6.38769i	−1.47814	+	0.575958i
$124$	12.4552	+	6.79013i	1.11851	+	0.609772i
$125$		−	9.05956i		−	0.810311i
$126$	18.5638	+	5.57717i	1.65379	+	0.496854i
$127$	3.74692	−	2.16329i	0.332486	−	0.191961i	−0.324459	−	0.945900i	$-0.605182\pi$
$127$	3.74692	−	2.16329i	0.332486	−	0.191961i	0.656944	+	0.753939i	$0.271849\pi$
$128$	10.2460	+	4.79784i	0.905628	+	0.424073i
$129$	−1.56499	+	10.2135i	−0.137790	+	0.899244i
$130$	2.83013	+	4.76626i	0.248218	+	0.418029i
$131$	9.75821			0.852579			0.426290	−	0.904587i	$-0.359820\pi$
$131$	9.75821			0.852579			0.426290	+	0.904587i	$0.359820\pi$
$132$	7.16957	−	9.40824i	0.624031	−	0.818882i
$133$	−13.5211			−1.17243
$134$	−8.56197	+	7.79055i	−0.739641	+	0.673001i
$135$	−5.80214	+	11.8255i	−0.499369	+	1.01778i
$136$	−0.997062	+	1.88339i	−0.0854973	+	0.161500i
$137$			18.2345i			1.55788i	0.627100	+	0.778939i	$0.284242\pi$
$137$			18.2345i			1.55788i	−0.627100	+	0.778939i	$0.715758\pi$
$138$	6.85933	−	2.76990i	0.583905	−	0.235789i
$139$		−	6.78115i		−	0.575170i	−0.957755	−	0.287585i	$-0.907148\pi$
$139$		−	6.78115i		−	0.575170i	0.957755	−	0.287585i	$-0.0928523\pi$
$140$	−11.0873	+	20.3375i	−0.937050	+	1.71883i
$141$	1.44810	+	3.71640i	0.121952	+	0.312978i
$142$	0.265747	+	21.7152i	0.0223010	+	1.82230i
$143$	5.27974			0.441514
$144$	−8.42861	+	8.54158i	−0.702384	+	0.711798i
$145$	10.8384	+	18.7727i	0.900083	+	1.55899i
$146$	−4.98362	+	2.95919i	−0.412448	+	0.244905i
$147$	−15.0279	+	18.7501i	−1.23948	+	1.54648i
$148$	−14.6298	+	0.358129i	−1.20257	+	0.0294380i
$149$			8.81220i			0.721924i	0.932581	+	0.360962i	$0.117552\pi$
$149$			8.81220i			0.721924i	−0.932581	+	0.360962i	$0.882448\pi$
$150$	−2.75250	−	2.15130i	−0.224741	−	0.175653i
$151$	0.0184044	+	0.0106258i	0.00149773	+	0.000864713i	0.500749	−	0.865593i	$-0.333058\pi$
$151$	0.0184044	+	0.0106258i	0.00149773	+	0.000864713i	−0.499251	+	0.866457i	$0.666391\pi$
$152$	3.91647	−	7.39800i	0.317668	−	0.600057i
$153$	−1.52927	−	1.66442i	−0.123634	−	0.134560i
$154$	11.2643	+	18.9703i	0.907700	+	1.52867i
$155$	−8.99024	−	15.5716i	−0.722113	−	1.25074i
$156$	−5.31268	−	0.681445i	−0.425355	−	0.0545593i
$157$	−4.85134	+	8.40277i	−0.387179	+	0.670614i	−0.992069	−	0.125695i	$-0.959884\pi$
$157$	−4.85134	+	8.40277i	−0.387179	+	0.670614i	0.604890	+	0.796309i	$0.293217\pi$
$158$	3.95244	−	0.0483693i	0.314439	−	0.00384806i
$159$	0.467520	−	3.05114i	0.0370767	−	0.241971i
$160$	−7.91602	−	11.9572i	−0.625817	−	0.945301i
$161$			13.7976i			1.08740i
$162$	−5.55056	−	11.4539i	−0.436093	−	0.899902i
$163$	1.44483	−	0.834174i	0.113168	−	0.0653376i	−0.442348	−	0.896844i	$-0.645854\pi$
$163$	1.44483	−	0.834174i	0.113168	−	0.0653376i	0.555516	+	0.831506i	$0.312521\pi$
$164$	17.8372	+	9.72423i	1.39285	+	0.759335i
$165$	−13.9698	+	5.44334i	−1.08755	+	0.423764i
$166$	−2.22890	+	1.32349i	−0.172996	+	0.102722i
$167$	7.50320	+	12.9959i	0.580615	+	1.00565i	0.995407	+	0.0957380i	$0.0305211\pi$
$167$	7.50320	+	12.9959i	0.580615	+	1.00565i	−0.414792	+	0.909916i	$0.636146\pi$
$168$	−8.88608	−	20.5425i	−0.685576	−	1.58489i
$169$	5.30463	+	9.18788i	0.408048	+	0.706760i
$170$	2.32250	−	1.37906i	0.178128	−	0.105769i
$171$	6.00700	+	6.53786i	0.459367	+	0.499963i
$172$	10.1836	−	6.21664i	0.776490	−	0.474014i
$173$	17.0509	+	9.84432i	1.29635	+	0.748450i	0.979772	−	0.200116i	$-0.0641319\pi$
$173$	17.0509	+	9.84432i	1.29635	+	0.748450i	0.316581	+	0.948566i	$0.397465\pi$
$174$	−20.7413	−	2.91885i	−1.57240	−	0.221278i
$175$	5.64297	−	3.25797i	0.426568	−	0.246279i
$176$	−13.6422	+	0.668306i	−1.02832	+	0.0503755i
$177$	10.3423	+	1.58474i	0.777378	+	0.119116i
$178$	−1.31069	+	2.33574i	−0.0982406	+	0.175071i
$179$	−10.7958			−0.806917			−0.403458	−	0.914998i	$-0.632192\pi$
$179$	−10.7958			−0.806917			−0.403458	+	0.914998i	$0.632192\pi$
$180$	14.7595	−	3.67425i	1.10011	−	0.273863i
$181$	−8.44994	−	14.6357i	−0.628079	−	1.08786i	−0.987937	−	0.154857i	$-0.950508\pi$
$181$	−8.44994	−	14.6357i	−0.628079	−	1.08786i	0.359858	−	0.933007i	$-0.382825\pi$
$182$	4.88888	−	8.71229i	0.362388	−	0.645798i
$183$	−13.2946	+	16.5876i	−0.982768	+	1.22619i
$184$	−7.54926	−	3.99655i	−0.556539	−	0.294630i
$185$	16.0638	+	9.27443i	1.18103	+	0.681870i
$186$	17.2045	+	2.42112i	1.26149	+	0.177525i
$187$		−	2.57271i		−	0.188135i
$188$	2.20450	−	4.04372i	0.160780	−	0.294919i
$189$	23.6858	−	1.60032i	1.72289	−	0.116406i
$190$	−9.12282	+	5.41698i	−0.661839	+	0.392989i
$191$	3.06064	−	5.30118i	0.221460	−	0.383580i	−0.733792	−	0.679375i	$-0.762251\pi$
$191$	3.06064	−	5.30118i	0.221460	−	0.383580i	0.955251	+	0.295795i	$0.0955845\pi$
$192$	13.8136	+	1.08830i	0.996911	+	0.0785412i
$193$	9.78265			0.704170			0.352085	−	0.935968i	$-0.385473\pi$
$193$	9.78265			0.704170			0.352085	+	0.935968i	$0.385473\pi$
$194$	−19.4617	+	11.5561i	−1.39727	+	0.829677i
$195$	5.29747	+	4.24583i	0.379360	+	0.304050i
$196$	27.7382	−	0.679013i	1.98130	−	0.0485009i
$197$	8.75235	−	5.05317i	0.623579	−	0.360024i	−0.154682	−	0.987964i	$-0.549435\pi$
$197$	8.75235	−	5.05317i	0.623579	−	0.360024i	0.778261	+	0.627941i	$0.216102\pi$
$198$	4.16835	−	13.8745i	0.296232	−	0.986017i
$199$	15.4518	+	8.92109i	1.09535	+	0.632399i	0.934995	−	0.354660i	$-0.115404\pi$
$199$	15.4518	+	8.92109i	1.09535	+	0.632399i	0.160353	+	0.987060i	$0.448737\pi$
$200$	0.148059	+	4.03120i	0.0104693	+	0.285049i
$201$	−6.46145	+	12.6194i	−0.455756	+	0.890105i
$202$	1.69044	−	0.0206873i	0.118939	−	0.00145556i
$203$	19.5337	−	33.8334i	1.37100	−	2.37464i
$204$	−0.332055	+	2.58876i	−0.0232485	+	0.181250i
$205$	−12.8750	−	22.3002i	−0.899231	−	1.55751i
$206$	23.1589	−	0.283415i	1.61356	−	0.0197464i
$207$	6.67154	−	6.12982i	0.463704	−	0.426052i
$208$	3.35078	+	5.19848i	0.232335	+	0.360450i
$209$			10.1056i			0.699022i
$210$	−3.95335	+	28.0925i	−0.272807	+	1.93856i
$211$	−14.6384	−	8.45147i	−1.00775	−	0.581823i	−0.0972159	−	0.995263i	$-0.530994\pi$
$211$	−14.6384	−	8.45147i	−1.00775	−	0.581823i	−0.910531	+	0.413440i	$0.864327\pi$
$212$	−3.04221	+	1.85714i	−0.208940	+	0.127549i
$213$	9.65661	+	24.7827i	0.661660	+	1.69808i
$214$	−18.2877	−	10.2621i	−1.25012	−	0.701502i
$215$	−15.1227			−1.03136
$216$	−5.98511	+	13.4231i	−0.407235	+	0.913323i
$217$	−16.2028	+	28.0640i	−1.09992	+	1.90511i
$218$	−4.16939	−	2.33964i	−0.282387	−	0.158461i
$219$	−4.43946	+	5.53906i	−0.299991	+	0.374295i
$220$	15.2002	+	8.28662i	1.02480	+	0.558684i
$221$	−1.00889	+	0.582481i	−0.0678651	+	0.0391819i
$222$	−16.6193	+	6.71112i	−1.11542	+	0.450421i
$223$		−	16.2422i		−	1.08766i	−0.839197	−	0.543828i	$-0.816974\pi$
$223$		−	16.2422i		−	1.08766i	0.839197	−	0.543828i	$-0.183026\pi$
$224$	−11.5295	+	23.1304i	−0.770348	+	1.54546i
$225$	−4.08231	−	1.28113i	−0.272154	−	0.0854086i
$226$	−19.9910	+	0.244647i	−1.32978	+	0.0162737i
$227$	−2.22353	−	3.85126i	−0.147581	−	0.255617i	0.782752	−	0.622334i	$-0.213815\pi$
$227$	−2.22353	−	3.85126i	−0.147581	−	0.255617i	−0.930333	+	0.366716i	$0.880482\pi$
$228$	1.30432	−	10.1687i	0.0863804	−	0.673438i
$229$	−8.33660	+	14.4394i	−0.550898	+	0.954183i	0.447312	+	0.894378i	$0.352381\pi$
$229$	−8.33660	+	14.4394i	−0.550898	+	0.954183i	−0.998210	+	0.0598052i	$0.980952\pi$
$230$	5.52774	+	9.30935i	0.364488	+	0.613841i
$231$	21.0846	+	16.8989i	1.38726	+	1.11187i
$232$	12.8536	+	20.4877i	0.843883	+	1.34509i
$233$	9.18178	−	5.30110i	0.601519	−	0.347287i	−0.168120	−	0.985767i	$-0.553770\pi$
$233$	9.18178	−	5.30110i	0.601519	−	0.347287i	0.769639	+	0.638480i	$0.220436\pi$
$234$	−6.38462	+	1.50667i	−0.417376	+	0.0984942i
$235$	−5.05550	+	2.91879i	−0.329784	+	0.190401i
$236$	−6.29509	−	10.3121i	−0.409775	−	0.671260i
$237$	4.51076	−	1.75762i	0.293005	−	0.114170i
$238$	−4.24533	−	2.38226i	−0.275184	−	0.154419i
$239$	−5.41531	−	9.37960i	−0.350288	−	0.606716i	0.636012	−	0.771679i	$-0.280583\pi$
$239$	−5.41531	−	9.37960i	−0.350288	−	0.606716i	−0.986300	+	0.164963i	$0.947249\pi$
$240$	−14.2255	−	10.3002i	−0.918251	−	0.664874i
$241$	19.2399			1.23935			0.619675	−	0.784858i	$-0.287264\pi$
$241$	19.2399			1.23935			0.619675	+	0.784858i	$0.287264\pi$
$242$	0.802334	−	0.476412i	0.0515760	−	0.0306250i
$243$	−11.2966	−	10.7418i	−0.724679	−	0.689087i
$244$	24.5390	−	0.600700i	1.57095	−	0.0384559i
$245$	−30.4569	−	17.5843i	−1.94582	−	1.12342i
$246$	24.6387	+	3.46732i	1.57091	+	0.221068i
$247$	3.96292	−	2.28799i	0.252155	−	0.145582i
$248$	−10.6618	−	16.9941i	−0.677025	−	1.07913i
$249$	−1.98553	+	2.47732i	−0.125828	+	0.156994i
$250$	−6.26982	+	11.1732i	−0.396538	+	0.706655i
$251$	−2.16554	+	3.75083i	−0.136688	+	0.236750i	−0.926241	−	0.376932i	$-0.876979\pi$
$251$	−2.16554	+	3.75083i	−0.136688	+	0.236750i	0.789553	+	0.613682i	$0.210312\pi$
$252$	−19.0350	−	19.7257i	−1.19909	−	1.24260i
$253$	10.3123			0.648327
$254$	−6.11824	+	0.0748740i	−0.383892	+	0.00469801i
$255$	2.06891	−	2.58135i	0.129560	−	0.161650i
$256$	−9.31604	−	13.0081i	−0.582253	−	0.813008i
$257$	5.26011	−	3.03692i	0.328116	−	0.189438i	−0.326888	−	0.945063i	$-0.606000\pi$
$257$	5.26011	−	3.03692i	0.328116	−	0.189438i	0.655005	+	0.755625i	$0.272667\pi$
$258$	8.99850	−	11.5132i	0.560222	−	0.716783i
$259$		−	33.4299i		−	2.07723i
$260$	−0.191842	−	7.83689i	−0.0118975	−	0.486023i
$261$	−25.0376	+	5.58595i	−1.54979	+	0.345762i
$262$	−12.0349	−	6.75334i	−0.743516	−	0.417222i
$263$	22.2151			1.36984			0.684921	−	0.728617i	$-0.259837\pi$
$263$	22.2151			1.36984			0.684921	+	0.728617i	$0.259837\pi$
$264$	−15.3534	+	6.64142i	−0.944937	+	0.408751i
$265$	4.51770			0.277520
$266$	16.6757	+	9.35753i	1.02245	+	0.573747i
$267$	−0.496836	+	3.24246i	−0.0304059	+	0.198435i
$268$	15.9511	−	3.68268i	0.974369	−	0.224956i
$269$			10.3883i			0.633384i	0.948528	+	0.316692i	$0.102572\pi$
$269$			10.3883i			0.633384i	−0.948528	+	0.316692i	$0.897428\pi$
$270$	15.3399	−	10.5690i	0.933554	−	0.643209i
$271$			6.03636i			0.366683i	0.983049	+	0.183341i	$0.0586913\pi$
$271$			6.03636i			0.366683i	−0.983049	+	0.183341i	$0.941309\pi$
$272$	2.53312	−	1.63277i	0.153593	−	0.0990011i
$273$	1.85320	−	12.0944i	0.112161	−	0.731984i
$274$	12.6195	−	22.4887i	0.762371	−	1.35859i
$275$	−2.43499	−	4.21753i	−0.146836	−	0.254327i
$276$	−10.3766	−	1.33098i	−0.624599	−	0.0801158i
$277$	−1.15959			−0.0696733			−0.0348366	−	0.999393i	$-0.511091\pi$
$277$	−1.15959			−0.0696733			−0.0348366	+	0.999393i	$0.511091\pi$
$278$	−4.69301	+	8.36323i	−0.281468	+	0.501593i
$279$	20.7681	−	4.63342i	1.24335	−	0.277396i
$280$	27.7490	−	17.4092i	1.65832	−	1.04040i
$281$	−17.5818	−	10.1509i	−1.04884	−	0.605549i	−0.126517	−	0.991964i	$-0.540380\pi$
$281$	−17.5818	−	10.1509i	−1.04884	−	0.605549i	−0.922325	+	0.386415i	$0.873713\pi$
$282$	0.786048	−	5.58564i	0.0468085	−	0.332620i
$283$			14.4812i			0.860819i	0.902634	+	0.430409i	$0.141631\pi$
$283$			14.4812i			0.860819i	−0.902634	+	0.430409i	$0.858369\pi$
$284$	14.7006	−	26.9654i	0.872322	−	1.60010i
$285$	−8.12670	+	10.1396i	−0.481384	+	0.600617i
$286$	−6.51153	−	3.65393i	−0.385035	−	0.216062i
$287$	−23.2042	+	40.1908i	−1.36970	+	2.37239i
$288$	16.3064	−	4.70122i	0.960863	−	0.277022i
$289$	−8.21617	−	14.2308i	−0.483304	−	0.837107i
$290$	−0.375132	−	30.6534i	−0.0220285	−	1.80003i
$291$	−17.3367	+	21.6308i	−1.01630	+	1.26802i
$292$	8.19429	−	0.200591i	0.479535	−	0.0117387i
$293$			0.556572i			0.0325153i	0.999868	+	0.0162576i	$0.00517519\pi$
$293$			0.556572i			0.0325153i	−0.999868	+	0.0162576i	$0.994825\pi$
$294$	31.5102	−	12.7243i	1.83771	−	0.742096i
$295$			15.3135i			0.891588i
$296$	18.2909	+	9.68315i	1.06314	+	0.562822i
$297$	−1.19607	−	17.7027i	−0.0694032	−	1.02721i
$298$	6.09863	−	10.8681i	0.353284	−	0.629574i
$299$	−2.33478	−	4.04395i	−0.135024	−	0.233868i
$300$	1.90584	+	4.55813i	0.110034	+	0.263164i
$301$	13.6275	+	23.6035i	0.785476	+	1.36048i
$302$	−0.0153445	−	0.0258419i	−0.000882976	−	0.00148703i
$303$	1.92923	−	0.751727i	0.110831	−	0.0431856i
$304$	−9.95011	+	6.41353i	−0.570678	+	0.367841i
$305$	−26.9442	−	15.5563i	−1.54282	−	0.890749i
$306$	0.734171	+	3.11110i	0.0419698	+	0.177850i
$307$	0.298725	+	0.172469i	0.0170491	+	0.00984332i	0.508500	−	0.861062i	$-0.330200\pi$
$307$	0.298725	+	0.172469i	0.0170491	+	0.00984332i	−0.491451	+	0.870905i	$0.663533\pi$
$308$	−0.763555	−	31.1918i	−0.0435076	−	1.77732i
$309$	26.4303	−	10.2986i	1.50357	−	0.585867i
$310$	0.311163	+	25.4263i	0.0176729	+	1.44412i
$311$	24.5611			1.39273			0.696366	−	0.717687i	$-0.254799\pi$
$311$	24.5611			1.39273			0.696366	+	0.717687i	$0.254799\pi$
$312$	6.08055	+	4.51716i	0.344244	+	0.255734i
$313$	−32.8730			−1.85809			−0.929046	−	0.369965i	$-0.879370\pi$
$313$	−32.8730			−1.85809			−0.929046	+	0.369965i	$0.879370\pi$
$314$	11.7985	−	7.00573i	0.665826	−	0.395356i
$315$	7.56572	+	33.9114i	0.426280	+	1.91069i
$316$	−4.90805	−	2.67570i	−0.276099	−	0.150520i
$317$	−23.4802	−	13.5563i	−1.31878	−	0.761397i	−0.335246	−	0.942131i	$-0.608819\pi$
$317$	−23.4802	−	13.5563i	−1.31878	−	0.761397i	−0.983532	+	0.180734i	$0.942153\pi$
$318$	−2.68818	+	3.43943i	−0.150746	+	0.192874i
$319$	−25.2869	−	14.5994i	−1.41580	−	0.817410i
$320$	1.48769	+	20.2253i	0.0831642	+	1.13063i
$321$	−25.3869	−	3.88998i	−1.41696	−	0.217118i
$322$	9.54886	−	17.0167i	0.532137	−	0.948302i
$323$	−1.11489	−	1.93105i	−0.0620344	−	0.107447i
$324$	−1.08131	+	17.9675i	−0.0600729	+	0.998194i
$325$	−1.10260	+	1.90976i	−0.0611613	+	0.105935i
$326$	−2.35922	+	0.0288718i	−0.130665	+	0.00159906i
$327$	−5.78792	−	0.886873i	−0.320073	−	0.0490442i
$328$	−15.2689	−	24.3375i	−0.843084	−	1.34381i
$329$	9.11133	+	5.26043i	0.502324	+	0.290017i
$330$	20.9962	+	2.95472i	1.15580	+	0.162652i
$331$	0.314165	−	0.181383i	0.0172681	−	0.00996974i	−0.491341	−	0.870967i	$-0.663493\pi$
$331$	0.314165	−	0.181383i	0.0172681	−	0.00996974i	0.508609	+	0.860997i	$0.330160\pi$
$332$	3.66486	−	0.0897134i	0.201135	−	0.00492366i
$333$	−16.1643	+	14.8518i	−0.885799	+	0.813874i
$334$	−0.259695	−	21.2207i	−0.0142099	−	1.16114i
$335$	−19.6888	−	6.55036i	−1.07571	−	0.357884i
$336$	−3.25755	+	31.4850i	−0.177714	+	1.71765i
$337$	−6.13745	+	10.6304i	−0.334328	+	0.579074i	−0.983356	−	0.181692i	$-0.941843\pi$
$337$	−6.13745	+	10.6304i	−0.334328	+	0.579074i	0.649027	+	0.760765i	$0.275176\pi$
$338$	−0.183600	−	15.0026i	−0.00998651	−	0.816035i
$339$	−22.8150	+	8.88987i	−1.23914	+	0.482832i
$340$	−3.81876	+	0.0934807i	−0.207101	+	0.00506971i
$341$	20.9749	+	12.1099i	1.13586	+	0.655787i
$342$	−2.88383	−	12.2204i	−0.155940	−	0.660805i
$343$			31.4020i			1.69555i
$344$	−16.8618	+	0.619303i	−0.909127	+	0.0333906i
$345$	10.3469	+	8.29286i	0.557058	+	0.446473i
$346$	−14.2160	−	23.9414i	−0.764257	−	1.28710i
$347$	−5.33509	−	9.24065i	−0.286403	−	0.496064i	0.686546	−	0.727087i	$-0.259126\pi$
$347$	−5.33509	−	9.24065i	−0.286403	−	0.496064i	−0.972948	+	0.231022i	$0.925793\pi$
$348$	23.5604	+	17.9542i	1.26297	+	0.962447i
$349$	25.0460			1.34068			0.670340	−	0.742054i	$-0.266148\pi$
$349$	25.0460			1.34068			0.670340	+	0.742054i	$0.266148\pi$
$350$	−9.21424	+	0.112762i	−0.492522	+	0.00602740i
$351$	−6.67129	+	4.47706i	−0.356087	+	0.238968i
$352$	17.2876	+	8.61711i	0.921430	+	0.459293i
$353$	−3.54869	−	2.04884i	−0.188878	−	0.109049i	0.402579	−	0.915385i	$-0.368114\pi$
$353$	−3.54869	−	2.04884i	−0.188878	−	0.109049i	−0.591457	+	0.806337i	$0.701447\pi$
$354$	−11.6585	−	9.11206i	−0.619644	−	0.484300i
$355$	−33.7124	+	19.4639i	−1.78927	+	1.03303i
$356$	3.23297	−	1.97359i	0.171347	−	0.104600i
$357$	−5.89334	−	0.903026i	−0.311909	−	0.0477932i
$358$	13.3145	+	7.47142i	0.703695	+	0.394877i
$359$	17.8603			0.942629			0.471315	−	0.881965i	$-0.343780\pi$
$359$	17.8603			0.942629			0.471315	+	0.881965i	$0.343780\pi$
$360$	−20.7458	−	5.68309i	−1.09340	−	0.299525i
$361$	−5.12068	−	8.86928i	−0.269510	−	0.466804i
$362$	0.292463	+	23.8982i	0.0153715	+	1.25606i
$363$	0.714727	−	0.891756i	0.0375134	−	0.0468050i
$364$	−12.0590	+	7.36149i	−0.632062	+	0.385847i
$365$	−8.99745	−	5.19468i	−0.470948	−	0.271902i
$366$	27.8761	−	11.2568i	1.45710	−	0.588400i
$367$	26.2595	−	15.1609i	1.37073	−	0.791394i	0.379713	−	0.925104i	$-0.376023\pi$
$367$	26.2595	−	15.1609i	1.37073	−	0.791394i	0.991020	+	0.133711i	$0.0426893\pi$
$368$	6.54467	+	10.1536i	0.341164	+	0.529291i
$369$	29.7423	−	6.63558i	1.54832	−	0.345434i
$370$	−13.3930	−	22.5554i	−0.696271	−	1.17260i
$371$	−4.07104	−	7.05125i	−0.211358	−	0.366083i
$372$	−19.5428	−	14.8926i	−1.01325	−	0.772147i
$373$	−15.5659	−	26.9609i	−0.805970	−	1.39598i	−0.915635	−	0.402012i	$-0.868311\pi$
$373$	−15.5659	−	26.9609i	−0.805970	−	1.39598i	0.109665	−	0.993969i	$-0.465022\pi$
$374$	−1.78049	+	3.17294i	−0.0920668	+	0.164069i
$375$	−2.37666	+	15.5106i	−0.122730	+	0.800963i
$376$	−5.51735	+	3.46149i	−0.284536	+	0.178513i
$377$			13.2217i			0.680950i
$378$	−30.3194	−	14.4185i	−1.55946	−	0.741606i
$379$	12.8337	+	7.40955i	0.659224	+	0.380603i	0.791981	−	0.610546i	$-0.209050\pi$
$379$	12.8337	+	7.40955i	0.659224	+	0.380603i	−0.132757	+	0.991149i	$0.542383\pi$
$380$	15.0001	−	0.367194i	0.769491	−	0.0188366i
$381$	−6.98250	+	2.72074i	−0.357724	+	0.139388i
$382$	−7.44347	+	4.41981i	−0.380841	+	0.226137i
$383$	1.81823	−	3.14927i	0.0929072	−	0.160920i	−0.815826	−	0.578297i	$-0.803717\pi$
$383$	1.81823	−	3.14927i	0.0929072	−	0.160920i	0.908733	+	0.417377i	$0.137051\pi$
$384$	−16.2832	−	10.9021i	−0.830950	−	0.556348i
$385$	−19.7737	+	34.2491i	−1.00776	+	1.74549i
$386$	−12.0650	−	6.77025i	−0.614092	−	0.344596i
$387$	5.35873	−	17.0756i	0.272400	−	0.868000i
$388$	31.9998	−	0.783335i	1.62455	−	0.0397678i
$389$	−19.0110	−	10.9760i	−0.963895	−	0.556505i	−0.0665257	−	0.997785i	$-0.521191\pi$
$389$	−19.0110	−	10.9760i	−0.963895	−	0.556505i	−0.897370	+	0.441279i	$0.854525\pi$
$390$	−3.59500	−	8.90261i	−0.182040	−	0.450801i
$391$	−1.97054	+	1.13769i	−0.0996543	+	0.0575354i
$392$	−34.6796	−	18.3593i	−1.75158	−	0.927282i
$393$	−16.7067	−	2.55994i	−0.842743	−	0.129132i
$394$	−14.2915	+	0.174897i	−0.719993	+	0.00881116i
$395$	3.54267	+	6.13608i	0.178251	+	0.308740i
$396$	−14.7429	+	14.2267i	−0.740860	+	0.714919i
$397$	−24.8826			−1.24882			−0.624411	−	0.781096i	$-0.714661\pi$
$397$	−24.8826			−1.24882			−0.624411	+	0.781096i	$0.714661\pi$
$398$	−12.8828	−	21.6961i	−0.645756	−	1.08753i
$399$	23.1491	+	3.54710i	1.15891	+	0.177577i
$400$	2.60726	−	5.07417i	0.130363	−	0.253708i
$401$			22.2000i			1.10862i	0.832311	+	0.554308i	$0.187017\pi$
$401$			22.2000i			1.10862i	−0.832311	+	0.554308i	$0.812983\pi$
$402$	16.7024	−	11.0918i	0.833041	−	0.553211i
$403$		−	10.9671i		−	0.546309i
$404$	−2.09915	−	1.14438i	−0.104436	−	0.0569352i
$405$	13.0359	−	18.7240i	0.647761	−	0.930401i
$406$	−47.5060	+	28.2083i	−2.35768	+	1.39995i
$407$	−24.9854			−1.23848
$408$	2.20112	−	2.96293i	0.108972	−	0.146687i
$409$	−1.79841	−	3.11493i	−0.0889254	−	0.154023i	0.818132	−	0.575031i	$-0.195010\pi$
$409$	−1.79841	−	3.11493i	−0.0889254	−	0.154023i	−0.907057	+	0.421007i	$0.861677\pi$
$410$	0.445621	+	36.4134i	0.0220076	+	1.79833i
$411$	4.78358	−	31.2187i	0.235957	−	1.53990i
$412$	−28.7581	−	15.6780i	−1.41681	−	0.772398i
$413$	23.9014	−	13.7995i	1.17611	−	0.679028i
$414$	−12.4703	+	2.94280i	−0.612882	+	0.144631i
$415$	−4.02407	−	2.32330i	−0.197534	−	0.114046i
$416$	−0.534840	−	8.73028i	−0.0262227	−	0.428037i
$417$	−1.77895	+	11.6098i	−0.0871154	+	0.568534i
$418$	6.99378	−	12.4634i	0.342077	−	0.609603i
$419$	10.6708	−	18.4824i	0.521303	−	0.902923i	−0.478390	−	0.878148i	$-0.658779\pi$
$419$	10.6708	−	18.4824i	0.521303	−	0.902923i	0.999693	−	0.0247759i	$-0.00788722\pi$
$420$	24.3175	−	31.9106i	1.18657	−	1.55708i
$421$	0.679704	−	1.17728i	0.0331268	−	0.0573772i	−0.848987	−	0.528414i	$-0.822787\pi$
$421$	0.679704	−	1.17728i	0.0331268	−	0.0573772i	0.882113	+	0.471037i	$0.156120\pi$
$422$	12.2046	+	20.5540i	0.594111	+	1.00055i
$423$	−1.50430	−	6.74263i	−0.0731414	−	0.327838i
$424$	5.03724	−	0.185009i	0.244630	−	0.00898481i
$425$	0.930589	+	0.537276i	0.0451402	+	0.0260617i
$426$	5.24173	−	37.2477i	0.253963	−	1.80466i
$427$			56.0729i			2.71356i
$428$	15.4523	+	25.3126i	0.746913	+	1.22353i
$429$	−9.03928	−	1.38507i	−0.436420	−	0.0668719i
$430$	18.6509	+	10.4659i	0.899426	+	0.504710i
$431$	−1.15281	−	1.99673i	−0.0555290	−	0.0961790i	0.836925	−	0.547318i	$-0.184351\pi$
$431$	−1.15281	−	1.99673i	−0.0555290	−	0.0961790i	−0.892454	+	0.451139i	$0.851018\pi$
$432$	16.6711	−	12.4126i	0.802090	−	0.597203i
$433$	−15.2166	−	26.3560i	−0.731264	−	1.26659i	−0.956343	−	0.292246i	$-0.905597\pi$
$433$	−15.2166	−	26.3560i	−0.731264	−	1.26659i	0.225079	−	0.974340i	$-0.427736\pi$
$434$	39.4051	−	23.3981i	1.89151	−	1.12315i
$435$	−13.6314	−	34.9835i	−0.653574	−	1.67733i
$436$	3.52294	+	5.77099i	0.168718	+	0.276380i
$437$	7.74029	−	4.46886i	0.370268	−	0.213775i
$438$	9.30861	−	3.75895i	0.444783	−	0.179610i
$439$	−4.68909	−	2.70725i	−0.223798	−	0.129210i	0.383910	−	0.923371i	$-0.374577\pi$
$439$	−4.68909	−	2.70725i	−0.223798	−	0.129210i	−0.607708	+	0.794161i	$0.707911\pi$
$440$	−13.0116	−	20.7395i	−0.620302	−	0.988716i
$441$	30.6476	−	28.1590i	1.45941	−	1.34091i
$442$	1.64738	−	0.0201604i	0.0783580	−	0.000958932i
$443$	−11.8978	−	20.6075i	−0.565280	−	0.979093i	−0.997024	−	0.0770968i	$-0.975435\pi$
$443$	−11.8978	−	20.6075i	−0.565280	−	0.979093i	0.431744	−	0.901996i	$-0.357898\pi$
$444$	25.1413	+	3.22481i	1.19315	+	0.153043i
$445$	−4.80099			−0.227589
$446$	−11.2407	+	20.0316i	−0.532261	+	0.948522i
$447$	2.31177	−	15.0871i	0.109343	−	0.713595i
$448$	30.2272	−	20.5477i	1.42810	−	0.970785i
$449$	20.9665	−	12.1050i	0.989471	−	0.571271i	0.0843548	−	0.996436i	$-0.473117\pi$
$449$	20.9665	−	12.1050i	0.989471	−	0.571271i	0.905116	+	0.425164i	$0.139784\pi$
$450$	4.14811	+	4.40526i	0.195544	+	0.207666i
$451$	30.0384	+	17.3427i	1.41445	+	0.816636i
$452$	24.8244	+	13.5334i	1.16764	+	0.636558i
$453$	−0.0287220	−	0.0230202i	−0.00134948	−	0.00108158i
$454$	0.0769590	+	6.28861i	0.00361186	+	0.295139i
$455$	17.9077			0.839524
$456$	−8.64604	+	11.6384i	−0.404888	+	0.545020i
$457$	16.1694	+	28.0063i	0.756375	+	1.31008i	0.944688	+	0.327971i	$0.106365\pi$
$457$	16.1694	+	28.0063i	0.756375	+	1.31008i	−0.188313	+	0.982109i	$0.560302\pi$
$458$	20.2746	−	12.0387i	0.947370	−	0.562533i
$459$	2.18158	+	3.25079i	0.101827	+	0.151734i
$460$	−0.374701	−	15.3068i	−0.0174705	−	0.713685i
$461$			10.9975i			0.512206i	0.966650	+	0.256103i	$0.0824386\pi$
$461$			10.9975i			0.512206i	−0.966650	+	0.256103i	$0.917561\pi$
$462$	−14.3086	−	35.4335i	−0.665695	−	1.64852i
$463$	−26.0271	−	15.0268i	−1.20958	−	0.698353i	−0.246915	−	0.969037i	$-0.579417\pi$
$463$	−26.0271	−	15.0268i	−1.20958	−	0.698353i	−0.962668	+	0.270684i	$0.912750\pi$
$464$	−1.67359	−	34.1632i	−0.0776944	−	1.58599i
$465$	11.3069	+	29.0180i	0.524345	+	1.34568i
$466$	−14.9927	+	0.183478i	−0.694522	+	0.00849944i
$467$	6.27895	−	10.8755i	0.290555	−	0.503256i	−0.683386	−	0.730057i	$-0.739493\pi$
$467$	6.27895	−	10.8755i	0.290555	−	0.503256i	0.973941	+	0.226801i	$0.0728267\pi$
$468$	8.91691	+	2.56039i	0.412184	+	0.118354i
$469$	7.51835	+	36.6331i	0.347165	+	1.69156i
$470$	8.25498	−	0.101023i	0.380774	−	0.00465985i
$471$	10.5102	−	13.1134i	0.484284	−	0.604235i
$472$	0.627118	+	17.0746i	0.0288655	+	0.785921i
$473$	17.6412	−	10.1851i	0.811143	−	0.468313i
$474$	−6.77954	−	0.954061i	−0.311395	−	0.0438215i
$475$	−3.65537	−	2.11043i	−0.167720	−	0.0968330i
$476$	3.58711	+	5.87610i	0.164415	+	0.269331i
$477$	−1.60085	+	5.10111i	−0.0732980	+	0.233564i
$478$	0.187431	+	15.3157i	0.00857288	+	0.700523i
$479$	15.1249	−	26.1970i	0.691072	−	1.19697i	−0.280415	−	0.959879i	$-0.590472\pi$
$479$	15.1249	−	26.1970i	0.691072	−	1.19697i	0.971487	−	0.237093i	$-0.0761947\pi$
$480$	10.4160	+	22.5483i	0.475421	+	1.02918i
$481$	5.65687	+	9.79799i	0.257931	+	0.446750i
$482$	−23.7287	−	13.3153i	−1.08081	−	0.606495i
$483$	3.61962	−	23.6224i	0.164699	−	1.07486i
$484$	−1.31923	+	0.0322939i	−0.0599651	+	0.00146791i
$485$	−35.1363	−	20.2859i	−1.59546	−	0.921137i
$486$	6.49816	+	21.0659i	0.294762	+	0.955571i
$487$	4.76531	+	2.75125i	0.215937	+	0.124671i	0.604067	−	0.796933i	$-0.293546\pi$
$487$	4.76531	+	2.75125i	0.215937	+	0.124671i	−0.388131	+	0.921604i	$0.626879\pi$
$488$	−30.6799	−	16.2418i	−1.38881	−	0.735232i
$489$	−2.69249	+	1.04913i	−0.121758	+	0.0474433i
$490$	25.3932	+	42.7651i	1.14715	+	1.93193i
$491$	−8.64296			−0.390051			−0.195026	−	0.980798i	$-0.562479\pi$
$491$	−8.64296			−0.390051			−0.195026	+	0.980798i	$0.562479\pi$
$492$	−27.9875	−	21.3279i	−1.26177	−	0.961536i
$493$	6.44265			0.290162
$494$	−6.47094	+	0.0791903i	−0.291141	+	0.00356294i
$495$	25.3452	−	5.65458i	1.13918	−	0.254155i
$496$	1.38820	+	28.3376i	0.0623322	+	1.27240i
$497$	60.7586	+	35.0790i	2.72539	+	1.57351i
$498$	4.16323	−	1.68117i	0.186559	−	0.0753352i
$499$	19.7567	+	11.4066i	0.884433	+	0.510628i	0.872117	−	0.489297i	$-0.162746\pi$
$499$	19.7567	+	11.4066i	0.884433	+	0.510628i	0.0123155	+	0.999924i	$0.496080\pi$
$500$	15.4652	−	9.44085i	0.691625	−	0.422208i
$501$	−9.43668	−	24.2183i	−0.421600	−	1.08199i
$502$	5.26660	−	3.12722i	0.235060	−	0.139575i
$503$	22.1279	+	38.3267i	0.986634	+	1.70890i	0.634435	+	0.772976i	$0.281233\pi$
$503$	22.1279	+	38.3267i	0.986634	+	1.70890i	0.352199	+	0.935925i	$0.385434\pi$
$504$	9.82451	+	37.5014i	0.437619	+	1.67044i
$505$	1.51518	+	2.62437i	0.0674247	+	0.116783i
$506$	−12.7182	−	7.13678i	−0.565392	−	0.317269i
$507$	−6.67156	−	17.1219i	−0.296295	−	0.760410i
$508$	7.59748	+	4.14189i	0.337084	+	0.183767i
$509$		−	9.23163i		−	0.409185i	−0.978847	−	0.204592i	$-0.934413\pi$
$509$		−	9.23163i		−	0.409185i	0.978847	−	0.204592i	$-0.0655869\pi$
$510$	−4.33806	+	1.75177i	−0.192093	+	0.0775698i
$511$			18.7243i			0.828316i
$512$	2.48704	+	22.4903i	0.109913	+	0.993941i
$513$	−8.56928	−	12.7691i	−0.378343	−	0.563771i
$514$	−8.58907	+	0.105112i	−0.378848	+	0.00463628i
$515$	20.7579	+	35.9537i	0.914701	+	1.58431i
$516$	−19.0658	+	7.97178i	−0.839326	+	0.350938i
$517$	3.93162	−	6.80977i	0.172913	−	0.299493i
$518$	−23.1357	+	41.2293i	−1.01653	+	1.81151i
$519$	−26.6097	−	21.3272i	−1.16804	−	0.936161i
$520$	−5.18705	+	9.79805i	−0.227467	+	0.429673i
$521$		−	8.08904i		−	0.354387i	−0.984176	−	0.177194i	$-0.943298\pi$
$521$		−	8.08904i		−	0.354387i	0.984176	−	0.177194i	$-0.0567019\pi$
$522$	34.7449	+	10.4385i	1.52074	+	0.456881i
$523$	32.7980	+	18.9359i	1.43415	+	0.828009i	0.997434	−	0.0715879i	$-0.0228066\pi$
$523$	32.7980	+	18.9359i	1.43415	+	0.828009i	0.436720	+	0.899597i	$0.356140\pi$
$524$	10.1689	+	16.6579i	0.444231	+	0.727702i
$525$	−10.5158	+	4.09751i	−0.458949	+	0.178830i
$526$	−27.3980	−	15.3743i	−1.19461	−	0.670353i
$527$	−5.34403			−0.232790
$528$	23.5318	+	2.43468i	1.02409	+	0.105956i
$529$	6.93977	+	12.0200i	0.301729	+	0.522610i
$530$	−5.57171	−	3.12655i	−0.242020	−	0.135809i
$531$	−17.2911	−	5.42636i	−0.750368	−	0.235484i
$532$	−14.0902	−	23.0814i	−0.610888	−	1.00071i
$533$		−	15.7061i		−	0.680306i
$534$	2.85675	−	3.65510i	0.123624	−	0.158172i
$535$		−	37.5894i		−	1.62513i
$536$	−22.2213	−	6.49736i	−0.959812	−	0.280643i
$537$	18.4832	+	2.83214i	0.797608	+	0.122216i
$538$	7.18937	−	12.8119i	0.309956	−	0.552361i
$539$	47.3723			2.04047
$540$	−26.2332	+	2.41861i	−1.12890	+	0.104080i
$541$	10.9754			0.471869			0.235934	−	0.971769i	$-0.424185\pi$
$541$	10.9754			0.471869			0.235934	+	0.971769i	$0.424185\pi$
$542$	4.17756	−	7.44467i	0.179442	−	0.319776i
$543$	10.6274	+	27.2741i	0.456064	+	1.17044i
$544$	−4.25409	+	0.260617i	−0.182393	+	0.0111738i
$545$		−	8.56996i		−	0.367097i
$546$	−10.6557	+	13.6335i	−0.456020	+	0.583460i
$547$	23.9225	−	13.8117i	1.02285	−	0.590545i	0.107924	−	0.994159i	$-0.465580\pi$
$547$	23.9225	−	13.8117i	1.02285	−	0.590545i	0.914929	+	0.403615i	$0.132246\pi$
$548$	−31.1274	+	19.0019i	−1.32970	+	0.811722i
$549$	27.1129	−	24.9114i	1.15715	−	1.06319i
$550$	0.0842781	+	6.88669i	0.00359363	+	0.293649i
$551$	−25.3068			−1.07811
$552$	11.8764	+	8.82282i	0.505493	+	0.375524i
$553$	6.38481	−	11.0588i	0.271510	−	0.470269i
$554$	1.43013	+	0.802517i	0.0607606	+	0.0340957i
$555$	−25.0693	−	20.0926i	−1.06413	−	0.852883i
$556$	11.5758	−	7.06655i	0.490925	−	0.299689i
$557$	−16.9130	+	9.76471i	−0.716625	+	0.413744i	−0.813509	−	0.581552i	$-0.802446\pi$
$557$	−16.9130	+	9.76471i	−0.716625	+	0.413744i	0.0968840	+	0.995296i	$0.469112\pi$
$558$	−28.8201	−	8.65850i	−1.22005	−	0.366544i
$559$	−7.98819	−	4.61199i	−0.337865	−	0.195066i
$560$	−46.2713	+	2.26674i	−1.95532	+	0.0957873i
$561$	−0.674918	+	4.40466i	−0.0284951	+	0.185965i
$562$	14.6587	+	24.6869i	0.618338	+	1.04135i
$563$	−33.5226			−1.41281			−0.706404	−	0.707808i	$-0.749684\pi$
$563$	−33.5226			−1.41281			−0.706404	+	0.707808i	$0.749684\pi$
$564$	−4.83508	+	6.34481i	−0.203593	+	0.267165i
$565$	−17.9184	−	31.0356i	−0.753834	−	1.30568i
$566$	10.0220	−	17.8598i	0.421255	−	0.750702i
$567$	−40.9715	−	3.47380i	−1.72064	−	0.145886i
$568$	−36.7923	+	23.0828i	−1.54377	+	0.968533i
$569$	−16.3125	+	9.41802i	−0.683855	+	0.394824i	−0.801306	−	0.598255i	$-0.795861\pi$
$569$	−16.3125	+	9.41802i	−0.683855	+	0.394824i	0.117451	+	0.993079i	$0.462528\pi$
$570$	17.0400	−	6.88099i	0.713726	−	0.288213i
$571$	20.6224	−	11.9064i	0.863022	−	0.498266i	−0.00200103	−	0.999998i	$-0.500637\pi$
$571$	20.6224	−	11.9064i	0.863022	−	0.498266i	0.865023	+	0.501732i	$0.167304\pi$
$572$	5.50195	+	9.01283i	0.230048	+	0.376845i
$573$	−6.63072	+	8.27306i	−0.277002	+	0.345612i
$574$	56.4326	−	33.5087i	2.35545	−	1.39863i
$575$	−2.15358	+	3.73011i	−0.0898104	+	0.155556i
$576$	−23.3643	−	5.48706i	−0.973514	−	0.228628i
$577$	12.0730	+	20.9110i	0.502605	+	0.870537i	0.999995	+	0.00301050i	$0.000958275\pi$
$577$	12.0730	+	20.9110i	0.502605	+	0.870537i	−0.497391	+	0.867527i	$0.665708\pi$
$578$	0.284372	+	23.2371i	0.0118283	+	0.966536i
$579$	−16.7486	−	2.56635i	−0.696047	−	0.106654i
$580$	−20.7516	+	38.0647i	−0.861662	+	1.58055i
$581$			8.37438i			0.347428i
$582$	36.3514	−	14.6792i	1.50681	−	0.608474i
$583$	−5.27008	+	3.04268i	−0.218264	+	0.126015i
$584$	−10.2449	−	5.42361i	−0.423937	−	0.224430i
$585$	−7.95579	−	8.65888i	−0.328932	−	0.358000i
$586$	0.385185	−	0.686423i	0.0159118	−	0.0283559i
$587$	−17.4365	+	30.2009i	−0.719681	+	1.24652i	0.241445	+	0.970414i	$0.422379\pi$
$587$	−17.4365	+	30.2009i	−0.719681	+	1.24652i	−0.961126	+	0.276109i	$0.910955\pi$
$588$	−47.6678	−	6.11424i	−1.96579	−	0.252147i
$589$	20.9914			0.864937
$590$	10.5980	−	18.8863i	0.436312	−	0.777535i
$591$	−16.3103	+	6.35531i	−0.670914	+	0.261423i
$592$	−15.8569	−	24.6008i	−0.651716	−	1.01109i
$593$	−4.78526	−	2.76277i	−0.196507	−	0.113453i	0.398518	−	0.917160i	$-0.369525\pi$
$593$	−4.78526	−	2.76277i	−0.196507	−	0.113453i	−0.595025	+	0.803707i	$0.702858\pi$
$594$	−10.7763	+	22.6606i	−0.442157	+	0.929774i
$595$		−	8.72605i		−	0.357733i
$596$	−15.0430	+	9.18308i	−0.616183	+	0.376154i
$597$	−24.1142	−	19.3271i	−0.986928	−	0.791005i
$598$	0.0808095	+	6.60325i	0.00330454	+	0.270027i
$599$	−11.5990	−	20.0901i	−0.473923	−	0.820859i	0.525631	−	0.850712i	$-0.323829\pi$
$599$	−11.5990	−	20.0901i	−0.473923	−	0.820859i	−0.999554	+	0.0298539i	$0.990496\pi$
$600$	0.804047	−	6.94053i	0.0328251	−	0.283346i
$601$	−17.2180	+	29.8224i	−0.702335	+	1.21648i	0.265310	+	0.964163i	$0.414526\pi$
$601$	−17.2180	+	29.8224i	−0.702335	+	1.21648i	−0.967645	+	0.252317i	$0.918808\pi$
$602$	−0.471665	−	38.5415i	−0.0192236	−	1.57084i
$603$	14.3730	−	19.9102i	0.585314	−	0.810807i
$604$	0.00104014	+	0.0424904i	4.23225e−5	+	0.00172891i
$605$	1.44854	+	0.836312i	0.0588913	+	0.0340009i
$606$	−2.89958	−	0.408047i	−0.117787	−	0.0165758i
$607$	3.19501	−	1.84464i	0.129681	−	0.0748715i	−0.433756	−	0.901030i	$-0.642812\pi$
$607$	3.19501	−	1.84464i	0.129681	−	0.0748715i	0.563437	+	0.826159i	$0.309479\pi$
$608$	16.7101	−	1.02371i	0.677685	−	0.0415168i
$609$	−42.3188	+	52.8006i	−1.71484	+	2.13959i
$610$	22.4645	+	37.8328i	0.909561	+	1.53181i
$611$	−3.56060			−0.144046
$612$	1.24763	−	4.34503i	0.0504324	−	0.175637i
$613$	9.95543	−	17.2433i	0.402096	−	0.696451i	−0.591883	−	0.806024i	$-0.701615\pi$
$613$	9.95543	−	17.2433i	0.402096	−	0.696451i	0.993979	+	0.109573i	$0.0349485\pi$
$614$	−0.249059	−	0.419445i	−0.0100512	−	0.0169274i
$615$	16.1928	+	41.5571i	0.652955	+	1.67574i
$616$	−20.6451	+	38.9975i	−0.831816	+	1.57125i
$617$			1.25179i			0.0503950i	0.999682	+	0.0251975i	$0.00802147\pi$
$617$			1.25179i			0.0503950i	−0.999682	+	0.0251975i	$0.991979\pi$
$618$	−39.7240	−	5.59021i	−1.59793	−	0.224871i
$619$	−12.8399	−	7.41312i	−0.516079	−	0.297959i	0.219250	−	0.975669i	$-0.429639\pi$
$619$	−12.8399	−	7.41312i	−0.516079	−	0.297959i	−0.735329	+	0.677710i	$0.762972\pi$
$620$	17.2130	−	31.5738i	0.691289	−	1.26803i
$621$	−13.0302	+	8.74449i	−0.522884	+	0.350904i
$622$	−30.2913	−	16.9979i	−1.21457	−	0.681554i
$623$	4.32632	+	7.49340i	0.173330	+	0.300217i
$624$	−4.37301	−	9.77919i	−0.175060	−	0.391481i
$625$	−30.0970			−1.20388
$626$	40.5425	+	22.7503i	1.62040	+	0.909285i
$627$	2.65109	−	17.3016i	0.105874	−	0.690958i
$628$	−19.3996	+	0.474888i	−0.774126	+	0.0189501i
$629$	4.77437	−	2.75648i	0.190366	−	0.109908i
$630$	14.1381	−	47.0591i	0.563275	−	1.87488i
$631$	1.25819	+	0.726418i	0.0500879	+	0.0289183i	0.524835	−	0.851204i	$-0.324127\pi$
$631$	1.25819	+	0.726418i	0.0500879	+	0.0289183i	−0.474747	+	0.880122i	$0.657460\pi$
$632$	4.20136	+	6.69665i	0.167121	+	0.266378i
$633$	22.8448	+	18.3097i	0.907998	+	0.727745i
$634$	19.5764	+	32.9689i	0.777478	+	1.30936i
$635$	−5.48392	−	9.49843i	−0.217623	−	0.376934i
$636$	5.69567	−	2.38147i	0.225848	−	0.0944312i
$637$	−10.7254	−	18.5770i	−0.424957	−	0.736048i
$638$	21.0827	+	35.5058i	0.834673	+	1.40569i
$639$	−10.0313	−	44.9630i	−0.396834	−	1.77871i
$640$	12.1625	−	25.9736i	0.480765	−	1.02670i
$641$	10.7515	−	6.20739i	0.424660	−	0.245177i	−0.272409	−	0.962181i	$-0.587820\pi$
$641$	10.7515	−	6.20739i	0.424660	−	0.245177i	0.697069	+	0.717004i	$0.254487\pi$
$642$	28.6176	+	22.3669i	1.12945	+	0.882753i
$643$			45.8492i			1.80811i	0.427411	+	0.904057i	$0.359426\pi$
$643$			45.8492i			1.80811i	−0.427411	+	0.904057i	$0.640574\pi$
$644$	−23.5533	+	14.3783i	−0.928131	+	0.566585i
$645$	25.8911	+	3.96724i	1.01946	+	0.156210i
$646$	0.0385879	+	3.15316i	0.00151822	+	0.124059i
$647$	−17.0232	+	29.4850i	−0.669250	+	1.15918i	0.308864	+	0.951106i	$0.400051\pi$
$647$	−17.0232	+	29.4850i	−0.669250	+	1.15918i	−0.978114	+	0.208069i	$0.933282\pi$
$648$	13.7683	−	21.4111i	0.540870	−	0.841106i
$649$	−10.3137	−	17.8638i	−0.404847	−	0.701216i
$650$	2.68153	−	1.59225i	0.105178	−	0.0624531i
$651$	35.1025	−	43.7969i	1.37577	−	1.71654i
$652$	2.92963	+	1.59713i	0.114733	+	0.0625485i
$653$	−34.3617	−	19.8388i	−1.34468	−	0.776351i	−0.357189	−	0.934032i	$-0.616265\pi$
$653$	−34.3617	−	19.8388i	−1.34468	−	0.776351i	−0.987490	+	0.157681i	$0.949598\pi$
$654$	6.52451	+	5.09941i	0.255128	+	0.199403i
$655$		−	24.7370i		−	0.966556i
$656$	1.98806	+	40.5827i	0.0776209	+	1.58449i
$657$	9.05376	−	8.31862i	0.353221	−	0.324540i
$658$	−7.59649	−	12.7934i	−0.296142	−	0.498737i
$659$	2.29545	+	3.97583i	0.0894180	+	0.154876i	0.907265	−	0.420559i	$-0.138166\pi$
$659$	2.29545	+	3.97583i	0.0894180	+	0.154876i	−0.817847	+	0.575435i	$0.804833\pi$
$660$	−23.8499	−	18.1748i	−0.928354	−	0.707454i
$661$	−23.4720			−0.912955			−0.456477	−	0.889735i	$-0.650889\pi$
$661$	−23.4720			−0.912955			−0.456477	+	0.889735i	$0.650889\pi$
$662$	−0.512991	+	0.00627791i	−0.0199380	+	0.000243998i
$663$	1.88009	−	0.732579i	0.0730167	−	0.0284510i
$664$	−4.58198	−	2.42568i	−0.177815	−	0.0941348i
$665$			34.2760i			1.32917i
$666$	30.2140	−	7.13004i	1.17077	−	0.276283i
$667$			25.8243i			0.999919i
$668$	−14.3658	+	26.3513i	−0.555831	+	1.01956i
$669$	−4.26092	+	27.8077i	−0.164737	+	1.07511i
$670$	19.7490	+	21.7046i	0.762971	+	0.838520i
$671$	41.9086			1.61787
$672$	25.8073	−	36.5762i	0.995537	−	1.41096i
$673$	24.0278			0.926205			0.463103	−	0.886305i	$-0.346736\pi$
$673$	24.0278			0.926205			0.463103	+	0.886305i	$0.346736\pi$
$674$	14.9263	−	8.86298i	0.574939	−	0.341389i
$675$	6.65311	+	3.26432i	0.256078	+	0.125644i
$676$	−10.1564	+	18.6299i	−0.390630	+	0.716534i
$677$	9.01206	−	5.20312i	0.346362	−	0.199972i	−0.316720	−	0.948519i	$-0.602582\pi$
$677$	9.01206	−	5.20312i	0.346362	−	0.199972i	0.663082	+	0.748547i	$0.269248\pi$
$678$	34.2902	+	4.82554i	1.31691	+	0.185324i
$679$			73.1211i			2.80613i
$680$	4.77440	+	2.52755i	0.183090	+	0.0969270i
$681$	2.79650	+	7.17693i	0.107162	+	0.275021i
$682$	−17.4877	−	29.4512i	−0.669637	−	1.12775i
$683$	3.31029	−	5.73359i	0.126665	−	0.219390i	−0.795718	−	0.605668i	$-0.792906\pi$
$683$	3.31029	−	5.73359i	0.126665	−	0.219390i	0.922382	+	0.386278i	$0.126239\pi$
$684$	−4.90070	+	17.0673i	−0.187383	+	0.652586i
$685$	46.2244			1.76614
$686$	21.7323	−	38.7283i	0.829742	−	1.47865i
$687$	18.0608	−	22.5343i	0.689063	−	0.859736i
$688$	21.2243	+	10.9057i	0.809170	+	0.415776i
$689$	2.38637	+	1.37777i	0.0909134	+	0.0524889i
$690$	−7.02168	−	17.3884i	−0.267311	−	0.661964i
$691$	−14.6487	+	8.45741i	−0.557261	+	0.321735i	−0.752046	−	0.659111i	$-0.770933\pi$
$691$	−14.6487	+	8.45741i	−0.557261	+	0.321735i	0.194784	+	0.980846i	$0.437599\pi$
$692$	0.963641	+	39.3655i	0.0366321	+	1.49645i
$693$	−31.6651	−	34.4634i	−1.20286	−	1.30916i
$694$	0.184654	+	15.0888i	0.00700938	+	0.572763i
$695$	−17.1902			−0.652061
$696$	−16.6316	−	38.4484i	−0.630420	−	1.45738i
$697$	−7.65326			−0.289888
$698$	−30.8893	−	17.3335i	−1.16918	−	0.656082i
$699$	−17.1105	+	6.66713i	−0.647179	+	0.252174i
$700$	11.4420	+	6.23780i	0.432468	+	0.235767i
$701$	−3.04330	+	1.75705i	−0.114944	+	0.0663628i	−0.556370	−	0.830935i	$-0.687806\pi$
$701$	−3.04330	+	1.75705i	−0.114944	+	0.0663628i	0.441426	+	0.897298i	$0.354473\pi$
$702$	11.3262	−	0.904603i	0.427478	−	0.0341420i
$703$	−18.7538	+	10.8275i	−0.707312	+	0.408367i
$704$	−15.3572	−	22.5917i	−0.578797	−	0.851456i
$705$	9.42107	−	3.67093i	0.354818	−	0.138255i
$706$	2.95869	+	4.98277i	0.111352	+	0.187529i
$707$	2.73075	−	4.72980i	0.102701	−	0.177883i
$708$	8.07238	+	19.3064i	0.303379	+	0.725580i
$709$	−20.6250	+	35.7235i	−0.774588	+	1.34163i	0.160438	+	0.987046i	$0.448709\pi$
$709$	−20.6250	+	35.7235i	−0.774588	+	1.34163i	−0.935026	+	0.354580i	$0.884624\pi$
$710$	55.0480	−	0.673668i	2.06591	−	0.0252823i
$711$	−8.18382	+	1.82583i	−0.306917	+	0.0684740i
$712$	−5.35310	+	0.196610i	−0.200616	+	0.00736826i
$713$		−	21.4206i		−	0.802209i
$714$	6.64334	+	5.19229i	0.248621	+	0.194317i
$715$		−	13.3841i		−	0.500538i
$716$	−11.2502	−	18.4291i	−0.420439	−	0.688728i
$717$	6.81077	+	17.4792i	0.254353	+	0.652771i
$718$	−22.0272	−	12.3605i	−0.822047	−	0.461290i
$719$	12.8027	−	22.1750i	0.477461	−	0.826986i	−0.522205	−	0.852820i	$-0.674891\pi$
$719$	12.8027	−	22.1750i	0.477461	−	0.826986i	0.999666	+	0.0258333i	$0.00822392\pi$
$720$	21.6529	+	21.3665i	0.806955	+	0.796282i
$721$	37.4111	−	64.7979i	1.39326	−	2.41320i
$722$	0.177233	+	14.4824i	0.00659593	+	0.538979i
$723$	−32.9400	−	5.04734i	−1.22505	−	0.187713i
$724$	16.1785	−	29.6762i	0.601268	−	1.10291i
$725$	10.5617	−	6.09777i	0.392250	−	0.226466i
$726$	−1.49863	+	0.605169i	−0.0556194	+	0.0224599i
$727$	−42.3125	−	24.4291i	−1.56928	−	0.906026i	−0.996252	−	0.0864931i	$-0.972434\pi$
$727$	−42.3125	−	24.4291i	−1.56928	−	0.906026i	−0.573031	−	0.819533i	$-0.694233\pi$
$728$	19.9671	−	0.733353i	0.740028	−	0.0271799i
$729$	16.5226	+	21.3542i	0.611949	+	0.790897i
$730$	7.50154	+	12.6335i	0.277645	+	0.467586i
$731$	−2.24733	+	3.89249i	−0.0831204	+	0.143969i
$732$	−42.1701	−	5.40906i	−1.55865	−	0.199925i
$733$	−12.6930	−	21.9848i	−0.468825	−	0.812029i	0.530540	−	0.847660i	$-0.321989\pi$
$733$	−12.6930	−	21.9848i	−0.468825	−	0.812029i	−0.999365	+	0.0356313i	$0.988656\pi$
$734$	−42.8783	+	0.524738i	−1.58267	+	0.0193684i
$735$	47.5313	+	38.0956i	1.75322	+	1.40518i
$736$	−1.04464	−	17.0518i	−0.0385058	−	0.628537i
$737$	27.3794	−	5.61919i	1.00853	−	0.206985i
$738$	−41.2736	−	12.3999i	−1.51930	−	0.456448i
$739$	−9.58856	−	5.53596i	−0.352721	−	0.203643i	0.313162	−	0.949700i	$-0.398612\pi$
$739$	−9.58856	−	5.53596i	−0.352721	−	0.203643i	−0.665883	+	0.746056i	$0.731945\pi$
$740$	0.907856	+	37.0866i	0.0333734	+	1.36333i
$741$	−7.38502	+	2.87758i	−0.271296	+	0.105711i
$742$	0.140904	+	11.5138i	0.00517274	+	0.422684i
$743$	−23.3385	+	40.4235i	−0.856208	+	1.48300i	0.0193117	+	0.999814i	$0.493853\pi$
$743$	−23.3385	+	40.4235i	−0.856208	+	1.48300i	−0.875520	+	0.483182i	$0.839481\pi$
$744$	13.7956	+	31.8921i	0.505770	+	1.16922i
$745$	22.3389			0.818434
$746$	0.538754	+	44.0236i	0.0197252	+	1.61182i
$747$	4.04925	−	3.72046i	0.148154	−	0.136125i
$748$	4.39177	−	2.68099i	0.160579	−	0.0980267i
$749$	−58.6697	+	33.8729i	−2.14374	+	1.23769i
$750$	13.6655	−	17.4845i	0.498994	−	0.638443i
$751$		−	28.2156i		−	1.02960i	−0.857310	−	0.514801i	$-0.827866\pi$
$751$		−	28.2156i		−	1.02960i	0.857310	−	0.514801i	$-0.172134\pi$
$752$	9.20016	−	0.450698i	0.335495	−	0.0164353i
$753$	4.69154	−	5.85358i	0.170969	−	0.213316i
$754$	9.15027	−	16.3064i	0.333233	−	0.593842i
$755$	0.0269363	−	0.0466550i	0.000980312	−	0.00169795i
$756$	27.4145	+	38.7654i	0.997056	+	1.40988i
$757$	6.56534	+	11.3715i	0.238621	+	0.413304i	0.960319	−	0.278904i	$-0.0899712\pi$
$757$	6.56534	+	11.3715i	0.238621	+	0.413304i	−0.721698	+	0.692208i	$0.756638\pi$
$758$	−10.7000	−	18.0200i	−0.388641	−	0.654517i
$759$	−17.6553	−	2.70529i	−0.640847	−	0.0981959i
$760$	−18.7539	−	9.92824i	−0.680275	−	0.360135i
$761$			22.0492i			0.799285i	0.916671	+	0.399642i	$0.130866\pi$
$761$			22.0492i			0.799285i	−0.916671	+	0.399642i	$0.869134\pi$
$762$	10.4945	+	1.47685i	0.380175	+	0.0535007i
$763$	−13.3760	+	7.72266i	−0.484245	+	0.279579i
$764$	12.2389	−	0.299600i	0.442787	−	0.0108391i
$765$	−4.21930	+	3.87670i	−0.152549	+	0.140162i
$766$	−4.42194	+	2.62567i	−0.159771	+	0.0948694i
$767$	−4.67019	+	8.08900i	−0.168631	+	0.292077i
$768$	12.5372	+	24.7148i	0.452397	+	0.891817i
$769$	−4.68461	−	8.11399i	−0.168931	−	0.292598i	0.769113	−	0.639113i	$-0.220698\pi$
$769$	−4.68461	−	8.11399i	−0.168931	−	0.292598i	−0.938044	+	0.346515i	$0.887365\pi$
$770$	48.0897	−	28.5549i	1.73303	−	1.02905i
$771$	−9.80236	+	3.81950i	−0.353023	+	0.137556i
$772$	10.1944	+	16.6996i	0.366904	+	0.601031i
$773$	26.9438	−	15.5560i	0.969103	−	0.559512i	0.0701402	−	0.997537i	$-0.477655\pi$
$773$	26.9438	−	15.5560i	0.969103	−	0.559512i	0.898963	+	0.438025i	$0.144322\pi$
$774$	−18.4264	+	17.3508i	−0.662323	+	0.623662i
$775$	−8.76066	+	5.05797i	−0.314692	+	0.181688i
$776$	−40.0077	−	21.1799i	−1.43619	−	0.760315i
$777$	−8.76990	+	57.2343i	−0.314618	+	2.05327i
$778$	15.8502	+	26.6936i	0.568259	+	0.957013i
$779$	30.0621			1.07709
$780$	−1.72746	+	13.4676i	−0.0618530	+	0.482218i
$781$	26.2179	−	45.4107i	0.938149	−	1.62492i
$782$	3.21763	−	0.0393768i	0.115062	−	0.00140811i
$783$	44.3315	−	2.99524i	1.58428	−	0.107041i
$784$	30.0647	+	46.6432i	1.07374	+	1.66583i
$785$	21.3010	+	12.2981i	0.760265	+	0.438939i
$786$	18.8329	+	14.7194i	0.671746	+	0.525022i
$787$	6.96219	+	4.01962i	0.248175	+	0.143284i	0.618928	−	0.785447i	$-0.287567\pi$
$787$	6.96219	+	4.01962i	0.248175	+	0.143284i	−0.370753	+	0.928731i	$0.620900\pi$
$788$	17.7468	+	9.67494i	0.632203	+	0.344656i
$789$	−38.0338	−	5.82785i	−1.35404	−	0.207477i
$790$	−0.122616	−	10.0194i	−0.00436248	−	0.356475i
$791$	−32.2937	+	55.9343i	−1.14823	+	1.98880i
$792$	28.0284	−	7.34280i	0.995945	−	0.260915i
$793$	−9.48843	−	16.4344i	−0.336944	−	0.583604i
$794$	30.6879	+	17.2204i	1.08907	+	0.611130i
$795$	−7.73462	−	1.18516i	−0.274319	−	0.0420333i
$796$	0.873268	+	35.6737i	0.0309522	+	1.26442i
$797$	−4.06433	+	2.34654i	−0.143966	+	0.0831187i	−0.570253	−	0.821469i	$-0.693155\pi$
$797$	−4.06433	+	2.34654i	−0.143966	+	0.0831187i	0.426287	+	0.904588i	$0.359821\pi$
$798$	−26.0951	−	20.3954i	−0.923757	−	0.721989i
$799$			1.73501i			0.0613801i
$800$	−6.72721	+	4.45361i	−0.237843	+	0.157459i
$801$	1.70123	−	5.42097i	0.0601102	−	0.191541i
$802$	15.3639	−	27.3794i	0.542518	−	0.966801i
$803$	13.9945			0.493855
$804$	−28.2755	+	2.12044i	−0.997200	+	0.0747821i
$805$	34.9769			1.23277
$806$	−7.58994	+	13.5258i	−0.267344	+	0.476424i
$807$	2.72523	−	17.7854i	0.0959326	−	0.626077i
$808$	1.79690	+	2.86413i	0.0632148	+	0.100760i
$809$			21.2786i			0.748114i	0.927406	+	0.374057i	$0.122034\pi$
$809$			21.2786i			0.748114i	−0.927406	+	0.374057i	$0.877966\pi$
$810$	−29.0355	+	14.0706i	−1.02020	+	0.494392i
$811$	−47.8273	+	27.6131i	−1.67944	+	0.969627i	−0.717429	+	0.696632i	$0.754681\pi$
$811$	−47.8273	+	27.6131i	−1.67944	+	0.969627i	−0.962015	+	0.272996i	$0.911986\pi$
$812$	78.1114	−	1.91211i	2.74117	−	0.0671021i
$813$	1.58356	−	10.3347i	0.0555379	−	0.362452i
$814$	30.8146	+	17.2915i	1.08005	+	0.606068i
$815$	−2.11463	−	3.66264i	−0.0740722	−	0.128297i
$816$	−4.76520	+	2.13088i	−0.166816	+	0.0745957i
$817$	8.82754	−	15.2897i	0.308836	−	0.534920i
$818$	0.0622450	+	5.08628i	0.00217635	+	0.177838i
$819$	−6.34560	+	20.2202i	−0.221733	+	0.706551i
$820$	24.6509	−	45.2172i	0.860846	−	1.57905i
$821$	16.1931	+	9.34911i	0.565144	+	0.326286i	0.755208	−	0.655486i	$-0.227536\pi$
$821$	16.1931	+	9.34911i	0.565144	+	0.326286i	−0.190064	+	0.981772i	$0.560869\pi$
$822$	−27.5050	+	35.1916i	−0.959349	+	1.22745i
$823$	2.92127	+	1.68660i	0.101829	+	0.0587910i	0.550050	−	0.835132i	$-0.314609\pi$
$823$	2.92127	+	1.68660i	0.101829	+	0.0587910i	−0.448221	+	0.893923i	$0.647942\pi$
$824$	24.6174	+	39.2383i	0.857588	+	1.36693i
$825$	3.06246	+	7.85949i	0.106621	+	0.273632i
$826$	−39.0279	+	0.477617i	−1.35795	+	0.0166184i
$827$	−18.4518	+	31.9594i	−0.641632	+	1.11134i	0.343437	+	0.939176i	$0.388409\pi$
$827$	−18.4518	+	31.9594i	−0.641632	+	1.11134i	−0.985069	+	0.172163i	$0.944924\pi$
$828$	17.4163	+	5.00091i	0.605258	+	0.173794i
$829$	8.25183			0.286598			0.143299	−	0.989679i	$-0.454229\pi$
$829$	8.25183			0.286598			0.143299	+	0.989679i	$0.454229\pi$
$830$	3.35503	+	5.65026i	0.116455	+	0.196123i
$831$	1.98531	+	0.304205i	0.0688695	+	0.0105527i
$832$	−5.38232	+	11.1373i	−0.186598	+	0.386115i
$833$	−9.05220	+	5.22629i	−0.313640	+	0.181080i
$834$	10.2287	−	13.0873i	0.354192	−	0.453175i
$835$	32.9446	−	19.0206i	1.14009	−	0.658234i
$836$	−17.2509	+	10.5310i	−0.596636	+	0.364221i
$837$	−36.7720	+	2.48448i	−1.27103	+	0.0858763i
$838$	−25.9514	+	15.4095i	−0.896477	+	0.532313i
$839$	−9.39904	−	16.2796i	−0.324491	−	0.562035i	0.656918	−	0.753962i	$-0.271860\pi$
$839$	−9.39904	−	16.2796i	−0.324491	−	0.562035i	−0.981409	+	0.191927i	$0.938526\pi$
$840$	−52.0752	+	22.5262i	−1.79677	+	0.777227i
$841$	22.0602	−	38.2094i	0.760697	−	1.31757i
$842$	−1.65304	+	0.981548i	−0.0569675	+	0.0338264i
$843$	27.4383	+	21.9913i	0.945025	+	0.757421i
$844$	−0.827298	−	33.7958i	−0.0284768	−	1.16330i
$845$	23.2913	−	13.4472i	0.801243	−	0.462598i
$846$	−2.81109	+	9.35680i	−0.0966473	+	0.321693i
$847$		−	3.01451i		−	0.103580i
$848$	−6.34050	−	3.25793i	−0.217734	−	0.111878i
$849$	3.79896	−	24.7928i	0.130380	−	0.850888i
$850$	−0.775870	−	1.30666i	−0.0266121	−	0.0448179i
$851$	11.0489	+	19.1372i	0.378751	+	0.656016i
$852$	−32.2425	+	42.3101i	−1.10461	+	1.44952i
$853$	−18.8131	+	32.5853i	−0.644149	+	1.11570i	0.340349	+	0.940299i	$0.389455\pi$
$853$	−18.8131	+	32.5853i	−0.644149	+	1.11570i	−0.984497	+	0.175399i	$0.943879\pi$
$854$	38.8062	−	69.1550i	1.32792	−	2.36644i
$855$	16.5735	−	15.2277i	0.566800	−	0.520777i
$856$	−1.53936	−	41.9122i	−0.0526142	−	1.43253i
$857$		−	16.3495i		−	0.558489i	−0.960220	−	0.279245i	$-0.909916\pi$
$857$		−	16.3495i		−	0.558489i	0.960220	−	0.279245i	$-0.0900840\pi$
$858$	10.1896	+	7.96400i	0.347868	+	0.271886i
$859$	36.3331	−	20.9769i	1.23967	−	0.715723i	0.270642	−	0.962680i	$-0.412764\pi$
$859$	36.3331	−	20.9769i	1.23967	−	0.715723i	0.969026	+	0.246957i	$0.0794307\pi$
$860$	−15.7591	−	25.8153i	−0.537382	−	0.880295i
$861$	50.2707	−	62.7221i	1.71322	−	2.13756i
$862$	0.0399002	+	3.26040i	0.00135901	+	0.111050i
$863$	−15.2184			−0.518039			−0.259020	−	0.965872i	$-0.583399\pi$
$863$	−15.2184			−0.518039			−0.259020	+	0.965872i	$0.583399\pi$
$864$	−29.1510	+	3.77105i	−0.991736	+	0.128294i
$865$	24.9553	−	43.2239i	0.848506	−	1.46966i
$866$	0.526666	+	43.0359i	0.0178968	+	1.46242i
$867$	10.3334	+	26.5195i	0.350940	+	0.900651i
$868$	−64.7916	+	1.58606i	−2.19917	+	0.0538343i
$869$	−8.26532	−	4.77198i	−0.280382	−	0.161878i
$870$	−7.39928	+	52.5792i	−0.250859	+	1.78260i
$871$	−8.40246	−	9.46459i	−0.284707	−	0.320695i
$872$	−0.350956	−	9.55551i	−0.0118849	−	0.323590i
$873$	35.3562	−	32.4853i	1.19663	−	1.09946i
$874$	−12.6389	+	0.154673i	−0.427517	+	0.00523188i
$875$	20.6953	+	35.8453i	0.699629	+	1.21179i
$876$	−14.0818	−	1.80624i	−0.475780	−	0.0610273i
$877$	−17.9432	+	31.0785i	−0.605898	+	1.04945i	0.386011	+	0.922494i	$0.373853\pi$
$877$	−17.9432	+	31.0785i	−0.605898	+	1.04945i	−0.991909	+	0.126952i	$0.959481\pi$
$878$	3.90949	+	6.58403i	0.131939	+	0.222200i
$879$	0.146009	−	0.952889i	0.00492478	−	0.0321402i
$880$	1.69415	+	34.5830i	0.0571099	+	1.16579i
$881$	9.04088	+	5.21976i	0.304595	+	0.175858i	0.644505	−	0.764600i	$-0.277063\pi$
$881$	9.04088	+	5.21976i	0.304595	+	0.175858i	−0.339910	+	0.940458i	$0.610397\pi$
$882$	−57.2858	+	13.5186i	−1.92891	+	0.455193i
$883$	27.8377	−	16.0721i	0.936815	−	0.540870i	0.0478543	−	0.998854i	$-0.484762\pi$
$883$	27.8377	−	16.0721i	0.936815	−	0.540870i	0.888960	+	0.457984i	$0.151428\pi$
$884$	−2.04568	−	1.11523i	−0.0688036	−	0.0375094i
$885$	4.01730	−	26.2178i	0.135040	−	0.881302i
$886$	0.411796	+	33.6494i	0.0138346	+	1.13047i
$887$	11.6929	−	20.2527i	0.392609	−	0.680019i	−0.600184	−	0.799862i	$-0.704906\pi$
$887$	11.6929	−	20.2527i	0.392609	−	0.680019i	0.992793	+	0.119843i	$0.0382393\pi$
$888$	−28.7751	−	21.3766i	−0.965628	−	0.717352i
$889$	−9.88346	+	17.1187i	−0.331481	+	0.574141i
$890$	5.92108	+	3.32260i	0.198475	+	0.111374i
$891$	−2.59631	+	30.6220i	−0.0869796	+	1.02587i
$892$	27.7264	−	16.9258i	0.928347	−	0.566716i
$893$		−	6.81513i		−	0.228060i
$894$	−13.2924	+	17.0071i	−0.444564	+	0.568803i
$895$			27.3673i			0.914789i
$896$	−51.4997	+	4.42232i	−1.72048	+	0.147739i
$897$	2.93642	+	7.53602i	0.0980441	+	0.251620i
$898$	−34.2356	+	0.418970i	−1.14246	+	0.0139812i
$899$	−30.3259	+	52.5260i	−1.01142	+	1.75184i
$900$	−2.06716	−	8.30380i	−0.0689053	−	0.276793i
$901$	0.671360	−	1.16283i	0.0223663	−	0.0387395i
$902$	−25.0443	−	42.1775i	−0.833883	−	1.40436i
$903$	−17.1391	−	43.9859i	−0.570355	−	1.46376i
$904$	−21.2500	−	33.8710i	−0.706765	−	1.12653i
$905$	−37.1015	+	21.4206i	−1.23330	+	0.712043i
$906$	0.0194915	+	0.0482685i	0.000647563	+	0.00160361i
$907$	43.5113	−	25.1212i	1.44477	−	0.834137i	0.446606	−	0.894731i	$-0.352633\pi$
$907$	43.5113	−	25.1212i	1.44477	−	0.834137i	0.998163	+	0.0605935i	$0.0192993\pi$
$908$	4.25722	−	7.80904i	0.141281	−	0.259152i
$909$	−3.50018	+	0.780899i	−0.116094	+	0.0259008i
$910$	−22.0856	−	12.3933i	−0.732132	−	0.410834i
$911$	−33.6915			−1.11625			−0.558125	−	0.829757i	$-0.688479\pi$
$911$	−33.6915			−1.11625			−0.558125	+	0.829757i	$0.688479\pi$
$912$	18.7178	−	8.37013i	0.619808	−	0.277163i
$913$	6.25898			0.207142
$914$	−0.559645	−	45.7307i	−0.0185114	−	1.51264i
$915$	42.0494	+	33.7019i	1.39011	+	1.11415i
$916$	−33.3364	+	0.816053i	−1.10147	+	0.0269632i
$917$	−38.6097	+	22.2913i	−1.27500	+	0.736124i
$918$	−0.440795	−	5.51901i	−0.0145484	−	0.182155i
$919$	−8.59619	−	4.96301i	−0.283562	−	0.163715i	0.351473	−	0.936198i	$-0.385681\pi$
$919$	−8.59619	−	4.96301i	−0.283562	−	0.163715i	−0.635035	+	0.772483i	$0.719014\pi$
$920$	−10.1312	+	19.1373i	−0.334017	+	0.630939i
$921$	−0.466193	−	0.373645i	−0.0153616	−	0.0123120i
$922$	7.61102	−	13.5633i	0.250656	−	0.446684i
$923$	−23.7437			−0.781533
$924$	−6.87552	+	53.6029i	−0.226188	+	1.76340i
$925$	5.21785	−	9.03759i	0.171562	−	0.297154i
$926$	21.6999	+	36.5451i	0.713103	+	1.20095i
$927$	−47.9522	+	10.6983i	−1.57496	+	0.351377i
$928$	−21.5792	+	43.2919i	−0.708371	+	1.42113i
$929$			8.52276i			0.279623i	0.990178	+	0.139811i	$0.0446496\pi$
$929$			8.52276i			0.279623i	−0.990178	+	0.139811i	$0.955350\pi$
$930$	6.13754	−	43.6133i	0.201258	−	1.43014i
$931$	35.5572	−	20.5289i	1.16534	−	0.672809i
$932$	18.6175	+	10.1496i	0.609837	+	0.332463i
$933$	−42.0503	−	6.44328i	−1.37666	−	0.210944i
$934$	−15.2704	+	9.06731i	−0.499663	+	0.296692i
$935$	−6.52181			−0.213286
$936$	−9.22531	−	9.32884i	−0.301539	−	0.304923i
$937$	−39.0153			−1.27458			−0.637288	−	0.770626i	$-0.719944\pi$
$937$	−39.0153			−1.27458			−0.637288	+	0.770626i	$0.719944\pi$
$938$	16.0801	−	50.3830i	0.525034	−	1.64506i
$939$	56.2808	+	8.62381i	1.83666	+	0.281427i
$940$	−10.2508	−	5.58840i	−0.334345	−	0.182274i
$941$		−	17.8668i		−	0.582441i	−0.956656	−	0.291221i	$-0.905939\pi$
$941$		−	17.8668i		−	0.582441i	0.956656	−	0.291221i	$-0.0940614\pi$
$942$	−22.0376	+	8.89912i	−0.718025	+	0.289949i
$943$		−	30.6768i		−	0.998973i
$944$	11.0433	−	21.4922i	0.359429	−	0.699511i
$945$	−4.05681	−	60.0434i	−0.131968	−	1.95321i
$946$	−28.8058	+	0.352520i	−0.936557	+	0.0114614i
$947$	7.95360			0.258457			0.129229	−	0.991615i	$-0.458750\pi$
$947$	7.95360			0.258457			0.129229	+	0.991615i	$0.458750\pi$
$948$	7.70098	+	5.86854i	0.250116	+	0.190601i
$949$	−3.16846	−	5.48793i	−0.102853	−	0.178146i
$950$	3.04763	+	5.13256i	0.0988781	+	0.166522i
$951$	36.6434	+	29.3690i	1.18824	+	0.952356i
$952$	−0.357349	−	9.72955i	−0.0115817	−	0.315336i
$953$			41.0315i			1.32914i	0.747226	+	0.664571i	$0.231385\pi$
$953$			41.0315i			1.32914i	−0.747226	+	0.664571i	$0.768615\pi$
$954$	5.50465	−	5.18333i	0.178220	−	0.167816i
$955$	−13.4385	−	7.75870i	−0.434859	−	0.251066i
$956$	10.3683	−	19.0186i	0.335335	−	0.615106i
$957$	39.4630	+	31.6289i	1.27566	+	1.02242i
$958$	−36.7837	+	21.8415i	−1.18843	+	0.705668i
$959$	−41.6542	−	72.1472i	−1.34508	−	2.32975i
$960$	2.75883	−	35.0174i	0.0890410	−	1.13018i
$961$	9.65463	−	16.7223i	0.311440	−	0.539429i
$962$	−0.195791	−	15.9989i	−0.00631257	−	0.515824i
$963$	42.4436	+	13.3198i	1.36773	+	0.429226i
$964$	20.0497	+	32.8437i	0.645756	+	1.05782i
$965$		−	24.7990i		−	0.798307i
$966$	−20.8124	+	26.6287i	−0.669628	+	0.856764i
$967$	0.155766	−	0.0899315i	0.00500910	−	0.00289200i	−0.497493	−	0.867468i	$-0.665746\pi$
$967$	0.155766	−	0.0899315i	0.00500910	−	0.00289200i	0.502502	+	0.864576i	$0.332413\pi$
$968$	1.64937	+	0.873168i	0.0530126	+	0.0280647i
$969$	1.40219	+	3.59857i	0.0450448	+	0.115603i
$970$	29.2946	+	49.3354i	0.940592	+	1.58407i
$971$	0.608744	+	1.05438i	0.0195355	+	0.0338365i	0.875628	−	0.482986i	$-0.160448\pi$
$971$	0.608744	+	1.05438i	0.0195355	+	0.0338365i	−0.856092	+	0.516823i	$0.827115\pi$
$972$	6.56482	−	30.4779i	0.210567	−	0.977579i
$973$	15.4906	+	26.8305i	0.496606	+	0.860147i
$974$	−3.97303	−	6.69105i	−0.127304	−	0.214395i
$975$	2.38873	−	2.98039i	0.0765006	−	0.0954489i
$976$	26.5973	+	41.2637i	0.851358	+	1.32082i
$977$	−9.67094	−	5.58352i	−0.309401	−	0.178633i	0.337257	−	0.941412i	$-0.390501\pi$
$977$	−9.67094	−	5.58352i	−0.309401	−	0.178633i	−0.646658	+	0.762780i	$0.723834\pi$
$978$	4.04673	+	0.569482i	0.129400	+	0.0182100i
$979$	5.60054	−	3.23347i	0.178994	−	0.103342i
$980$	−1.72129	−	70.3162i	−0.0549847	−	2.24617i
$981$	9.67666	+	3.03677i	0.308952	+	0.0969568i
$982$	10.6594	+	5.98150i	0.340155	+	0.190877i
$983$	58.6888			1.87188			0.935940	−	0.352158i	$-0.114552\pi$
$983$	58.6888			1.87188			0.935940	+	0.352158i	$0.114552\pi$
$984$	19.7568	+	45.6730i	0.629823	+	1.45600i
$985$	−12.8098	−	22.1872i	−0.408153	−	0.706942i
$986$	−7.94576	−	4.45874i	−0.253045	−	0.141995i
$987$	−14.2192	−	11.3965i	−0.452603	−	0.362753i
$988$	8.03545	+	4.38066i	0.255642	+	0.139367i
$989$	−15.6024	−	9.00803i	−0.496126	−	0.286439i
$990$	−35.1718	−	10.5668i	−1.11783	−	0.335834i
$991$		−	23.1327i		−	0.734834i	−0.930056	−	0.367417i	$-0.880242\pi$
$991$		−	23.1327i		−	0.734834i	0.930056	−	0.367417i	$-0.119758\pi$
$992$	17.8994	−	35.9097i	0.568308	−	1.14013i
$993$	−0.585456	+	0.228124i	−0.0185789	+	0.00723929i
$994$	−50.6569	−	85.3121i	−1.60674	−	2.70593i
$995$	22.6149	−	39.1702i	0.716941	−	1.24178i
$996$	−6.29803	−	0.807834i	−0.199561	−	0.0255972i
$997$	−23.0450			−0.729843			−0.364921	−	0.931038i	$-0.618904\pi$
$997$	−23.0450			−0.729843			−0.364921	+	0.931038i	$0.618904\pi$
$998$	−16.4720	−	27.7408i	−0.521412	−	0.878118i
$999$	31.5706	−	21.1868i	0.998850	−	0.670321i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.l.a.431.20	✓	264
3.2	odd	2	inner	804.2.l.a.431.113	yes	264
4.3	odd	2	inner	804.2.l.a.431.23	yes	264
12.11	even	2	inner	804.2.l.a.431.110	yes	264
67.37	even	3	inner	804.2.l.a.707.110	yes	264
201.104	odd	6	inner	804.2.l.a.707.23	yes	264
268.171	odd	6	inner	804.2.l.a.707.113	yes	264
804.707	even	6	inner	804.2.l.a.707.20	yes	264

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.l.a.431.20	✓	264	1.1	even	1	trivial
804.2.l.a.431.23	yes	264	4.3	odd	2	inner
804.2.l.a.431.110	yes	264	12.11	even	2	inner
804.2.l.a.431.113	yes	264	3.2	odd	2	inner
804.2.l.a.707.20	yes	264	804.707	even	6	inner
804.2.l.a.707.23	yes	264	201.104	odd	6	inner
804.2.l.a.707.110	yes	264	67.37	even	3	inner
804.2.l.a.707.113	yes	264	268.171	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.l (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.23331 - 0.692067i) q^{2} +(-1.71207 - 0.262337i) q^{3} +(1.04209 + 1.70706i) q^{4} -2.53500i q^{5} +(1.92995 + 1.50841i) q^{6} +(-3.95663 + 2.28436i) q^{7} +(-0.103813 - 2.82652i) q^{8} +(2.86236 + 0.898278i) q^{9} +O(q^{10})\)	\(q+(-1.23331 - 0.692067i) q^{2} +(-1.71207 - 0.262337i) q^{3} +(1.04209 + 1.70706i) q^{4} -2.53500i q^{5} +(1.92995 + 1.50841i) q^{6} +(-3.95663 + 2.28436i) q^{7} +(-0.103813 - 2.82652i) q^{8} +(2.86236 + 0.898278i) q^{9} +(-1.75439 + 3.12643i) q^{10} +(1.70732 + 2.95717i) q^{11} +(-1.33630 - 3.19598i) q^{12} +(0.773102 - 1.33905i) q^{13} +(6.46067 - 0.0790646i) q^{14} +(-0.665024 + 4.34009i) q^{15} +(-1.82811 + 3.55781i) q^{16} +(-0.652493 - 0.376717i) q^{17} +(-2.90850 - 3.08880i) q^{18} +(2.56300 + 1.47975i) q^{19} +(4.32739 - 2.64169i) q^{20} +(7.37330 - 2.87301i) q^{21} +(-0.0590926 - 4.82868i) q^{22} +(1.51001 - 2.61541i) q^{23} +(-0.563767 + 4.86643i) q^{24} -1.42621 q^{25} +(-1.88018 + 1.11642i) q^{26} +(-4.66490 - 2.28882i) q^{27} +(-8.02270 - 4.37370i) q^{28} +(-7.40542 + 4.27552i) q^{29} +(3.82381 - 4.89242i) q^{30} +(6.14263 - 3.54645i) q^{31} +(4.71686 - 3.12270i) q^{32} +(-2.14728 - 5.51077i) q^{33} +(0.544010 + 0.916176i) q^{34} +(5.79085 + 10.0300i) q^{35} +(1.44941 + 5.82230i) q^{36} +(-3.65856 + 6.33681i) q^{37} +(-2.13688 - 3.59875i) q^{38} +(-1.67489 + 2.08973i) q^{39} +(-7.16522 + 0.263166i) q^{40} +(8.79694 - 5.07892i) q^{41} +(-11.0819 - 1.55951i) q^{42} -5.96556i q^{43} +(-3.26889 + 5.99613i) q^{44} +(2.27713 - 7.25607i) q^{45} +(-3.67233 + 2.18057i) q^{46} +(-1.15140 - 1.99428i) q^{47} +(4.06319 - 5.61164i) q^{48} +(6.93663 - 12.0146i) q^{49} +(1.75895 + 0.987029i) q^{50} +(1.01829 + 0.816139i) q^{51} +(3.09148 - 0.0756774i) q^{52} +1.78213i q^{53} +(4.16924 + 6.05124i) q^{54} +(7.49642 - 4.32806i) q^{55} +(6.86755 + 10.9464i) q^{56} +(-3.99984 - 3.20580i) q^{57} +(12.0921 - 0.147981i) q^{58} -6.04085 q^{59} +(-8.10180 + 3.38751i) q^{60} +(6.13660 - 10.6289i) q^{61} +(-10.0301 + 0.122747i) q^{62} +(-13.3773 + 2.98451i) q^{63} +(-7.97845 + 0.586859i) q^{64} +(-3.39449 - 1.95981i) q^{65} +(-1.16557 + 8.28253i) q^{66} +(2.58397 - 7.76679i) q^{67} +(-0.0368761 - 1.50642i) q^{68} +(-3.27135 + 4.08162i) q^{69} +(-0.200429 - 16.3778i) q^{70} +(-7.67806 - 13.2988i) q^{71} +(2.24185 - 8.18377i) q^{72} +(2.04919 - 3.54930i) q^{73} +(8.89761 - 5.28326i) q^{74} +(2.44176 + 0.374147i) q^{75} +(0.144850 + 5.91723i) q^{76} +(-13.5105 - 7.80029i) q^{77} +(3.51188 - 1.41815i) q^{78} +(-2.42055 + 1.39750i) q^{79} +(9.01904 + 4.63425i) q^{80} +(7.38619 + 5.14239i) q^{81} +(-14.3643 + 0.175788i) q^{82} +(0.916490 - 1.58741i) q^{83} +(12.5880 + 9.59273i) q^{84} +(-0.954976 + 1.65407i) q^{85} +(-4.12857 + 7.35736i) q^{86} +(13.8002 - 5.37727i) q^{87} +(8.18126 - 5.13278i) q^{88} -1.89388i q^{89} +(-7.83008 + 7.37302i) q^{90} +7.06418i q^{91} +(6.03821 - 0.147811i) q^{92} +(-11.4470 + 4.46033i) q^{93} +(0.0398514 + 3.25641i) q^{94} +(3.75116 - 6.49720i) q^{95} +(-8.89479 + 4.10886i) q^{96} +(8.00236 - 13.8605i) q^{97} +(-16.8699 + 10.0171i) q^{98} +(2.23061 + 9.99814i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 264 q - 2 q^{4} - 3 q^{6} - 12 q^{9}+O(q^{10}) \) 264 * q - 2 * q^4 - 3 * q^6 - 12 * q^9	\( 264 q - 2 q^{4} - 3 q^{6} - 12 q^{9} + 2 q^{10} + 2 q^{12} - 18 q^{16} + q^{18} - 4 q^{22} - 248 q^{25} + 7 q^{30} - 38 q^{34} + 13 q^{36} + 4 q^{37} + 48 q^{40} - 12 q^{42} + 48 q^{45} - 2 q^{46} - 11 q^{48} + 128 q^{49} + 32 q^{52} - 8 q^{54} - 2 q^{57} - 32 q^{58} + 68 q^{60} - 8 q^{61} + 4 q^{64} + 30 q^{66} - 40 q^{69} - 140 q^{70} + 108 q^{72} - 4 q^{73} - 120 q^{76} + 44 q^{78} - 28 q^{81} - 64 q^{82} + 33 q^{84} + 16 q^{85} - 14 q^{88} + 42 q^{90} + 16 q^{93} - 12 q^{94} - 4 q^{96} + 20 q^{97}+O(q^{100}) \) 264 * q - 2 * q^4 - 3 * q^6 - 12 * q^9 + 2 * q^10 + 2 * q^12 - 18 * q^16 + q^18 - 4 * q^22 - 248 * q^25 + 7 * q^30 - 38 * q^34 + 13 * q^36 + 4 * q^37 + 48 * q^40 - 12 * q^42 + 48 * q^45 - 2 * q^46 - 11 * q^48 + 128 * q^49 + 32 * q^52 - 8 * q^54 - 2 * q^57 - 32 * q^58 + 68 * q^60 - 8 * q^61 + 4 * q^64 + 30 * q^66 - 40 * q^69 - 140 * q^70 + 108 * q^72 - 4 * q^73 - 120 * q^76 + 44 * q^78 - 28 * q^81 - 64 * q^82 + 33 * q^84 + 16 * q^85 - 14 * q^88 + 42 * q^90 + 16 * q^93 - 12 * q^94 - 4 * q^96 + 20 * q^97

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