LMFDB - Embedded newform 570.2.n.a.449.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(179,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("570.179");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.n (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			449.8
Character	$\chi$	$=$	570.449
Dual form			570.2.n.a.179.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(-0.540671 - 1.64550i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.636160 + 2.14367i) q^{5} +(1.29099 + 1.15471i) q^{6} -4.14066i q^{7} +1.00000i q^{8} +(-2.41535 + 1.77935i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.540671 - 1.64550i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.636160 + 2.14367i) q^{5} +(1.29099 + 1.15471i) q^{6} -4.14066i q^{7} +1.00000i q^{8} +(-2.41535 + 1.77935i) q^{9} +(-0.520902 - 2.17455i) q^{10} +0.276925i q^{11} +(-1.69538 - 0.354516i) q^{12} +(-0.418840 + 0.725452i) q^{13} +(2.07033 + 3.58592i) q^{14} +(3.87136 - 0.112214i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.82932 - 4.90052i) q^{17} +(1.20208 - 2.74864i) q^{18} +(-2.04202 + 3.85099i) q^{19} +(1.53839 + 1.62276i) q^{20} +(-6.81346 + 2.23873i) q^{21} +(-0.138462 - 0.239824i) q^{22} +(0.101759 - 0.176252i) q^{23} +(1.64550 - 0.540671i) q^{24} +(-4.19060 - 2.72743i) q^{25} -0.837680i q^{26} +(4.23383 + 3.01242i) q^{27} +(-3.58592 - 2.07033i) q^{28} +(-4.06700 + 7.04425i) q^{29} +(-3.29659 + 2.03286i) q^{30} -5.54805i q^{31} +(0.866025 + 0.500000i) q^{32} +(0.455680 - 0.149725i) q^{33} +(4.90052 + 2.82932i) q^{34} +(8.87619 + 2.63412i) q^{35} +(0.333286 + 2.98143i) q^{36} -1.84341 q^{37} +(-0.157053 - 4.35607i) q^{38} +(1.42019 + 0.296971i) q^{39} +(-2.14367 - 0.636160i) q^{40} +(-2.91976 - 5.05717i) q^{41} +(4.78126 - 5.34553i) q^{42} +(-9.67160 + 5.58390i) q^{43} +(0.239824 + 0.138462i) q^{44} +(-2.27778 - 6.30965i) q^{45} +0.203518i q^{46} +(-5.89995 + 10.2190i) q^{47} +(-1.15471 + 1.29099i) q^{48} -10.1451 q^{49} +(4.99288 + 0.266723i) q^{50} +(-6.53409 + 7.30522i) q^{51} +(0.418840 + 0.725452i) q^{52} +(-8.06300 - 4.65518i) q^{53} +(-5.17282 - 0.491917i) q^{54} +(-0.593634 - 0.176169i) q^{55} +4.14066 q^{56} +(7.44088 + 1.27803i) q^{57} -8.13400i q^{58} +(1.94977 + 3.37710i) q^{59} +(1.83850 - 3.40880i) q^{60} +(-2.56141 + 4.43650i) q^{61} +(2.77402 + 4.80475i) q^{62} +(7.36768 + 10.0011i) q^{63} -1.00000 q^{64} +(-1.28868 - 1.35936i) q^{65} +(-0.319768 + 0.357506i) q^{66} +(5.36719 - 9.29624i) q^{67} -5.65864 q^{68} +(-0.345041 - 0.0721505i) q^{69} +(-9.00406 + 2.15688i) q^{70} +(-5.59684 - 9.69401i) q^{71} +(-1.77935 - 2.41535i) q^{72} +(-5.57300 + 3.21757i) q^{73} +(1.59644 - 0.921703i) q^{74} +(-2.22225 + 8.37028i) q^{75} +(2.31405 + 3.69394i) q^{76} +1.14665 q^{77} +(-1.37840 + 0.452909i) q^{78} +(14.0332 - 8.10205i) q^{79} +(2.17455 - 0.520902i) q^{80} +(2.66783 - 8.59550i) q^{81} +(5.05717 + 2.91976i) q^{82} +1.50224 q^{83} +(-1.46793 + 7.02000i) q^{84} +(12.3050 - 2.94759i) q^{85} +(5.58390 - 9.67160i) q^{86} +(13.7902 + 2.88364i) q^{87} -0.276925 q^{88} +(-3.27700 + 5.67592i) q^{89} +(5.12744 + 4.32543i) q^{90} +(3.00385 + 1.73427i) q^{91} +(-0.101759 - 0.176252i) q^{92} +(-9.12932 + 2.99967i) q^{93} -11.7999i q^{94} +(-6.95619 - 6.82726i) q^{95} +(0.354516 - 1.69538i) q^{96} +(-3.24889 - 5.62724i) q^{97} +(8.78588 - 5.07253i) q^{98} +(-0.492746 - 0.668871i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 40 q^{4}+O(q^{10}) $ 80 * q + 40 * q^4	$ 80 q + 40 q^{4} + 30 q^{15} - 40 q^{16} + 8 q^{19} + 8 q^{25} - 4 q^{30} + 48 q^{39} + 12 q^{45} - 128 q^{49} - 36 q^{54} + 12 q^{55} + 30 q^{60} - 24 q^{61} - 80 q^{64} + 4 q^{66} + 36 q^{70} + 16 q^{76} + 24 q^{79} + 32 q^{81} - 8 q^{85} - 54 q^{90} + 24 q^{91} - 60 q^{99}+O(q^{100}) $ 80 * q + 40 * q^4 + 30 * q^15 - 40 * q^16 + 8 * q^19 + 8 * q^25 - 4 * q^30 + 48 * q^39 + 12 * q^45 - 128 * q^49 - 36 * q^54 + 12 * q^55 + 30 * q^60 - 24 * q^61 - 80 * q^64 + 4 * q^66 + 36 * q^70 + 16 * q^76 + 24 * q^79 + 32 * q^81 - 8 * q^85 - 54 * q^90 + 24 * q^91 - 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	−0.540671	−	1.64550i	−0.312156	−	0.950031i
$3$	−0.540671	−	1.64550i	−0.312156	−	0.950031i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−0.636160	+	2.14367i	−0.284500	+	0.958676i
$5$	−0.636160	+	2.14367i	−0.284500	+	0.958676i
$6$	1.29099	+	1.15471i	0.527043	+	0.471409i
$7$		−	4.14066i		−	1.56502i	−0.622637	−	0.782511i	$-0.713939\pi$
$7$		−	4.14066i		−	1.56502i	0.622637	−	0.782511i	$-0.286061\pi$
$8$			1.00000i			0.353553i
$9$	−2.41535	+	1.77935i	−0.805117	+	0.593116i
$10$	−0.520902	−	2.17455i	−0.164724	−	0.687653i
$11$			0.276925i			0.0834960i	0.999128	+	0.0417480i	$0.0132927\pi$
$11$			0.276925i			0.0834960i	−0.999128	+	0.0417480i	$0.986707\pi$
$12$	−1.69538	−	0.354516i	−0.489414	−	0.102340i
$13$	−0.418840	+	0.725452i	−0.116165	+	0.201204i	−0.918245	−	0.396013i	$-0.870394\pi$
$13$	−0.418840	+	0.725452i	−0.116165	+	0.201204i	0.802080	+	0.597217i	$0.203727\pi$
$14$	2.07033	+	3.58592i	0.553319	+	0.958376i
$15$	3.87136	−	0.112214i	0.999580	−	0.0289736i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−2.82932	−	4.90052i	−0.686210	−	1.18855i	−0.973055	−	0.230574i	$-0.925940\pi$
$17$	−2.82932	−	4.90052i	−0.686210	−	1.18855i	0.286844	−	0.957977i	$-0.407394\pi$
$18$	1.20208	−	2.74864i	0.283333	−	0.647860i
$19$	−2.04202	+	3.85099i	−0.468472	+	0.883478i
$19$	−2.04202	+	3.85099i	−0.468472	+	0.883478i
$20$	1.53839	+	1.62276i	0.343994	+	0.362861i
$21$	−6.81346	+	2.23873i	−1.48682	+	0.488532i
$22$	−0.138462	−	0.239824i	−0.0295203	−	0.0511307i
$23$	0.101759	−	0.176252i	0.0212182	−	0.0367511i	−0.855221	−	0.518263i	$-0.826579\pi$
$23$	0.101759	−	0.176252i	0.0212182	−	0.0367511i	0.876440	+	0.481512i	$0.159912\pi$
$24$	1.64550	−	0.540671i	0.335887	−	0.110364i
$25$	−4.19060	−	2.72743i	−0.838120	−	0.545486i
$26$		−	0.837680i		−	0.164283i
$27$	4.23383	+	3.01242i	0.814801	+	0.579741i
$28$	−3.58592	−	2.07033i	−0.677674	−	0.391256i
$29$	−4.06700	+	7.04425i	−0.755223	+	1.30808i	0.190040	+	0.981776i	$0.439138\pi$
$29$	−4.06700	+	7.04425i	−0.755223	+	1.30808i	−0.945263	+	0.326309i	$0.894195\pi$
$30$	−3.29659	+	2.03286i	−0.601872	+	0.371148i
$31$		−	5.54805i		−	0.996459i	−0.867045	−	0.498229i	$-0.833984\pi$
$31$		−	5.54805i		−	0.996459i	0.867045	−	0.498229i	$-0.166016\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	0.455680	−	0.149725i	0.0793238	−	0.0260638i
$34$	4.90052	+	2.82932i	0.840433	+	0.485224i
$35$	8.87619	+	2.63412i	1.50035	+	0.445248i
$36$	0.333286	+	2.98143i	0.0555477	+	0.496905i
$37$	−1.84341			−0.303054			−0.151527	−	0.988453i	$-0.548419\pi$
$37$	−1.84341			−0.303054			−0.151527	+	0.988453i	$0.548419\pi$
$38$	−0.157053	−	4.35607i	−0.0254774	−	0.706648i
$39$	1.42019	+	0.296971i	0.227412	+	0.0475534i
$40$	−2.14367	−	0.636160i	−0.338943	−	0.100586i
$41$	−2.91976	−	5.05717i	−0.455990	−	0.789798i	0.542755	−	0.839891i	$-0.317381\pi$
$41$	−2.91976	−	5.05717i	−0.455990	−	0.789798i	−0.998745	+	0.0500936i	$0.984048\pi$
$42$	4.78126	−	5.34553i	0.737765	−	0.824833i
$43$	−9.67160	+	5.58390i	−1.47491	+	0.851537i	−0.999600	−	0.0282839i	$-0.990996\pi$
$43$	−9.67160	+	5.58390i	−1.47491	+	0.851537i	−0.475305	+	0.879821i	$0.657662\pi$
$44$	0.239824	+	0.138462i	0.0361548	+	0.0208740i
$45$	−2.27778	−	6.30965i	−0.339551	−	0.940588i
$46$			0.203518i			0.0300071i
$47$	−5.89995	+	10.2190i	−0.860596	+	1.49060i	0.0107588	+	0.999942i	$0.496575\pi$
$47$	−5.89995	+	10.2190i	−0.860596	+	1.49060i	−0.871355	+	0.490654i	$0.836758\pi$
$48$	−1.15471	+	1.29099i	−0.166668	+	0.186338i
$49$	−10.1451			−1.44929
$50$	4.99288	+	0.266723i	0.706100	+	0.0377203i
$51$	−6.53409	+	7.30522i	−0.914955	+	1.02293i
$52$	0.418840	+	0.725452i	0.0580827	+	0.100602i
$53$	−8.06300	−	4.65518i	−1.10754	−	0.639438i	−0.169348	−	0.985556i	$-0.554166\pi$
$53$	−8.06300	−	4.65518i	−1.10754	−	0.639438i	−0.938191	+	0.346119i	$0.887499\pi$
$54$	−5.17282	−	0.491917i	−0.703931	−	0.0669415i
$55$	−0.593634	−	0.176169i	−0.0800456	−	0.0237546i
$56$	4.14066			0.553319
$57$	7.44088	+	1.27803i	0.985568	+	0.169279i
$58$		−	8.13400i		−	1.06805i
$59$	1.94977	+	3.37710i	0.253838	+	0.439661i	0.964579	−	0.263793i	$-0.0849735\pi$
$59$	1.94977	+	3.37710i	0.253838	+	0.439661i	−0.710741	+	0.703454i	$0.751640\pi$
$60$	1.83850	−	3.40880i	0.237349	−	0.440074i
$61$	−2.56141	+	4.43650i	−0.327956	+	0.568036i	−0.982106	−	0.188329i	$-0.939693\pi$
$61$	−2.56141	+	4.43650i	−0.327956	+	0.568036i	0.654151	+	0.756364i	$0.273026\pi$
$62$	2.77402	+	4.80475i	0.352301	+	0.610204i
$63$	7.36768	+	10.0011i	0.928240	+	1.26003i
$64$	−1.00000			−0.125000
$65$	−1.28868	−	1.35936i	−0.159841	−	0.168607i
$66$	−0.319768	+	0.357506i	−0.0393607	+	0.0440060i
$67$	5.36719	−	9.29624i	0.655706	−	1.13572i	−0.326010	−	0.945366i	$-0.605704\pi$
$67$	5.36719	−	9.29624i	0.655706	−	1.13572i	0.981716	−	0.190350i	$-0.0609624\pi$
$68$	−5.65864			−0.686210
$69$	−0.345041	−	0.0721505i	−0.0415380	−	0.00868589i
$70$	−9.00406	+	2.15688i	−1.07619	+	0.257796i
$71$	−5.59684	−	9.69401i	−0.664223	−	1.15047i	−0.979495	−	0.201466i	$-0.935429\pi$
$71$	−5.59684	−	9.69401i	−0.664223	−	1.15047i	0.315273	−	0.949001i	$-0.397904\pi$
$72$	−1.77935	−	2.41535i	−0.209698	−	0.284652i
$73$	−5.57300	+	3.21757i	−0.652270	+	0.376588i	−0.789325	−	0.613975i	$-0.789569\pi$
$73$	−5.57300	+	3.21757i	−0.652270	+	0.376588i	0.137055	+	0.990563i	$0.456236\pi$
$74$	1.59644	−	0.921703i	0.185582	−	0.107146i
$75$	−2.22225	+	8.37028i	−0.256604	+	0.966517i
$76$	2.31405	+	3.69394i	0.265439	+	0.423724i
$77$	1.14665			0.130673
$78$	−1.37840	+	0.452909i	−0.156074	+	0.0512819i
$79$	14.0332	−	8.10205i	1.57885	−	0.911552i	0.583834	−	0.811873i	$-0.301552\pi$
$79$	14.0332	−	8.10205i	1.57885	−	0.911552i	0.995020	−	0.0996789i	$-0.0317816\pi$
$80$	2.17455	−	0.520902i	0.243122	−	0.0582386i
$81$	2.66783	−	8.59550i	0.296426	−	0.955056i
$82$	5.05717	+	2.91976i	0.558471	+	0.322434i
$83$	1.50224			0.164892			0.0824461	−	0.996596i	$-0.473727\pi$
$83$	1.50224			0.164892			0.0824461	+	0.996596i	$0.473727\pi$
$84$	−1.46793	+	7.02000i	−0.160164	+	0.765944i
$85$	12.3050	−	2.94759i	1.33466	−	0.319711i
$86$	5.58390	−	9.67160i	0.602128	−	1.04292i
$87$	13.7902	+	2.88364i	1.47847	+	0.309158i
$88$	−0.276925			−0.0295203
$89$	−3.27700	+	5.67592i	−0.347361	+	0.601647i	−0.985780	−	0.168042i	$-0.946255\pi$
$89$	−3.27700	+	5.67592i	−0.347361	+	0.601647i	0.638419	+	0.769689i	$0.279589\pi$
$90$	5.12744	+	4.32543i	0.540480	+	0.455940i
$91$	3.00385	+	1.73427i	0.314889	+	0.181801i
$92$	−0.101759	−	0.176252i	−0.0106091	−	0.0183755i
$93$	−9.12932	+	2.99967i	−0.946666	+	0.311051i
$94$		−	11.7999i		−	1.21707i
$95$	−6.95619	−	6.82726i	−0.713690	−	0.700462i
$96$	0.354516	−	1.69538i	0.0361827	−	0.173034i
$97$	−3.24889	−	5.62724i	−0.329874	−	0.571359i	0.652612	−	0.757692i	$-0.273673\pi$
$97$	−3.24889	−	5.62724i	−0.329874	−	0.571359i	−0.982487	+	0.186333i	$0.940340\pi$
$98$	8.78588	−	5.07253i	0.887508	−	0.512403i
$99$	−0.492746	−	0.668871i	−0.0495229	−	0.0672240i
$100$	−4.45732	+	2.26545i	−0.445732	+	0.226545i
$101$	3.02926	+	1.74894i	0.301422	+	0.174026i	0.643082	−	0.765798i	$-0.277656\pi$
$101$	3.02926	+	1.74894i	0.301422	+	0.174026i	−0.341659	+	0.939824i	$0.610989\pi$
$102$	2.00608	−	9.59355i	0.198631	−	0.949903i
$103$	6.70352			0.660517			0.330259	−	0.943890i	$-0.392864\pi$
$103$	6.70352			0.660517			0.330259	+	0.943890i	$0.392864\pi$
$104$	−0.725452	−	0.418840i	−0.0711364	−	0.0410706i
$105$	−0.464642	−	16.0300i	−0.0453444	−	1.56437i
$106$	9.31035			0.904302
$107$		−	5.90110i		−	0.570481i	−0.958456	−	0.285240i	$-0.907927\pi$
$107$		−	5.90110i		−	0.570481i	0.958456	−	0.285240i	$-0.0920734\pi$
$108$	4.72575	−	2.16039i	0.454735	−	0.207884i
$109$	9.70976	−	5.60593i	0.930026	−	0.536951i	0.0432062	−	0.999066i	$-0.486243\pi$
$109$	9.70976	−	5.60593i	0.930026	−	0.536951i	0.886820	+	0.462115i	$0.152909\pi$
$110$	0.602187	−	0.144251i	0.0574163	−	0.0137538i
$111$	0.996675	+	3.03333i	0.0946002	+	0.287911i
$112$	−3.58592	+	2.07033i	−0.338837	+	0.195628i
$113$		−	2.63010i		−	0.247419i	−0.992318	−	0.123710i	$-0.960521\pi$
$113$		−	2.63010i		−	0.247419i	0.992318	−	0.123710i	$-0.0394791\pi$
$114$	−7.08300	+	2.61363i	−0.663384	+	0.244789i
$115$	0.313090	+	0.330262i	0.0291958	+	0.0307971i
$116$	4.06700	+	7.04425i	0.377612	+	0.654042i
$117$	−0.279187	−	2.49748i	−0.0258109	−	0.230892i
$118$	−3.37710	−	1.94977i	−0.310887	−	0.179491i
$119$	−20.2914	+	11.7152i	−1.86011	+	1.07393i
$120$	0.112214	+	3.87136i	0.0102437	+	0.353405i
$121$	10.9233			0.993028
$122$		−	5.12283i		−	0.463799i
$123$	−6.74296	+	7.53874i	−0.607992	+	0.679745i
$124$	−4.80475	−	2.77402i	−0.431479	−	0.249115i
$125$	8.51259	−	7.24816i	0.761389	−	0.648295i
$126$	−11.3812	−	4.97740i	−1.01391	−	0.443422i
$127$	−3.14595	+	5.44894i	−0.279158	+	0.483515i	−0.971176	−	0.238365i	$-0.923389\pi$
$127$	−3.14595	+	5.44894i	−0.279158	+	0.483515i	0.692018	+	0.721880i	$0.256722\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	14.4175	+	12.8956i	1.26939	+	1.13539i
$130$	1.79571	+	0.532899i	0.157494	+	0.0467383i
$131$	0.437520	−	0.252602i	0.0382263	−	0.0220700i	−0.480765	−	0.876849i	$-0.659641\pi$
$131$	0.437520	−	0.252602i	0.0382263	−	0.0220700i	0.518991	+	0.854779i	$0.326308\pi$
$132$	0.0981744	−	0.469493i	0.00854498	−	0.0408642i
$133$	15.9456	+	8.45532i	1.38266	+	0.733169i
$134$			10.7344i			0.927309i
$135$	−9.15102	+	7.15953i	−0.787594	+	0.616195i
$136$	4.90052	−	2.82932i	0.420216	−	0.242612i
$137$	0.0331892	−	0.0574854i	0.00283555	−	0.00491131i	−0.864604	−	0.502454i	$-0.832431\pi$
$137$	0.0331892	−	0.0574854i	0.00283555	−	0.00491131i	0.867440	+	0.497542i	$0.165764\pi$
$138$	0.334889	−	0.110036i	0.0285077	−	0.00936691i
$139$	0.588959	−	1.02011i	0.0499548	−	0.0865243i	−0.839967	−	0.542638i	$-0.817426\pi$
$139$	0.588959	−	1.02011i	0.0499548	−	0.0865243i	0.889922	+	0.456114i	$0.150759\pi$
$140$	6.71931	−	6.36994i	0.567885	−	0.538358i
$141$	20.0053	+	4.18325i	1.68475	+	0.352293i
$142$	9.69401	+	5.59684i	0.813503	+	0.469676i
$143$	−0.200896	−	0.115987i	−0.0167998	−	0.00969934i
$144$	2.74864	+	1.20208i	0.229053	+	0.100173i
$145$	−12.5133	−	13.1996i	−1.03917	−	1.09616i
$146$	3.21757	−	5.57300i	0.266288	−	0.461224i
$147$	5.48514	+	16.6937i	0.452406	+	1.37687i
$148$	−0.921703	+	1.59644i	−0.0757635	+	0.131226i
$149$	5.80877	−	3.35370i	0.475873	−	0.274745i	−0.242822	−	0.970071i	$-0.578073\pi$
$149$	5.80877	−	3.35370i	0.475873	−	0.274745i	0.718695	+	0.695325i	$0.244740\pi$
$150$	−2.26061	−	8.36000i	−0.184578	−	0.682591i
$151$		−	11.6812i		−	0.950601i	−0.879823	−	0.475301i	$-0.842339\pi$
$151$		−	11.6812i		−	0.950601i	0.879823	−	0.475301i	$-0.157661\pi$
$152$	−3.85099	−	2.04202i	−0.312357	−	0.165630i
$153$	15.5535	+	6.80213i	1.25743	+	0.549920i
$154$	−0.993030	+	0.573326i	−0.0800206	+	0.0461999i
$155$	11.8932	+	3.52945i	0.955281	+	0.283492i
$156$	0.967278	−	1.08143i	0.0774442	−	0.0865839i
$157$	0.115351	−	0.0665981i	0.00920603	−	0.00531511i	−0.495390	−	0.868671i	$-0.664975\pi$
$157$	0.115351	−	0.0665981i	0.00920603	−	0.00531511i	0.504596	+	0.863356i	$0.331641\pi$
$158$	−8.10205	+	14.0332i	−0.644564	+	1.11642i
$159$	−3.30067	+	15.7846i	−0.261760	+	1.25180i
$160$	−1.62276	+	1.53839i	−0.128291	+	0.121620i
$161$	−0.729799	−	0.421350i	−0.0575162	−	0.0332070i
$162$	1.98734	+	8.77784i	0.156140	+	0.689652i
$163$		−	4.40488i		−	0.345017i	−0.985008	−	0.172508i	$-0.944813\pi$
$163$		−	4.40488i		−	0.345017i	0.985008	−	0.172508i	$-0.0551872\pi$
$164$	−5.83952			−0.455990
$165$	0.0310750	+	1.07208i	0.00241918	+	0.0834610i
$166$	−1.30098	+	0.751119i	−0.100975	+	0.0582982i
$167$	6.03723	+	3.48560i	0.467175	+	0.269724i	0.715056	−	0.699067i	$-0.246401\pi$
$167$	6.03723	+	3.48560i	0.467175	+	0.269724i	−0.247881	+	0.968790i	$0.579734\pi$
$168$	−2.23873	−	6.81346i	−0.172722	−	0.525670i
$169$	6.14915	+	10.6506i	0.473011	+	0.819279i
$170$	−9.18263	+	8.70518i	−0.704275	+	0.667657i
$171$	−1.92006	−	12.9350i	−0.146831	−	0.989162i
$172$			11.1678i			0.851537i
$173$	20.7581	−	11.9847i	1.57821	−	0.911181i	0.583102	−	0.812399i	$-0.301839\pi$
$173$	20.7581	−	11.9847i	1.57821	−	0.911181i	0.995109	−	0.0987817i	$-0.0314946\pi$
$174$	−13.3845	+	4.39782i	−1.01468	+	0.333398i
$175$	−11.2934	+	17.3518i	−0.853697	+	1.31168i
$176$	0.239824	−	0.138462i	0.0180774	−	0.0104370i
$177$	4.50284	−	5.03425i	0.338454	−	0.378397i
$178$		−	6.55399i		−	0.491242i
$179$	−13.0272			−0.973695			−0.486848	−	0.873487i	$-0.661853\pi$
$179$	−13.0272			−0.973695			−0.486848	+	0.873487i	$0.661853\pi$
$180$	−6.60321	−	1.18221i	−0.492174	−	0.0881169i
$181$	−13.0547	−	7.53713i	−0.970347	−	0.560230i	−0.0710052	−	0.997476i	$-0.522621\pi$
$181$	−13.0547	−	7.53713i	−0.970347	−	0.560230i	−0.899342	+	0.437246i	$0.855954\pi$
$182$	−3.46855			−0.257106
$183$	8.68515	+	1.81613i	0.642025	+	0.134252i
$184$	0.176252	+	0.101759i	0.0129935	+	0.00750178i
$185$	1.17270	−	3.95164i	0.0862187	−	0.290531i
$186$	6.40639	−	7.16245i	0.469739	−	0.525176i
$187$	1.35708	−	0.783509i	0.0992393	−	0.0572958i
$188$	5.89995	+	10.2190i	0.430298	+	0.745298i
$189$	12.4734	−	17.5309i	0.907307	−	1.27518i
$190$	9.43786	+	2.43449i	0.684695	+	0.176616i
$191$			8.16641i			0.590901i	0.955358	+	0.295450i	$0.0954697\pi$
$191$			8.16641i			0.590901i	−0.955358	+	0.295450i	$0.904530\pi$
$192$	0.540671	+	1.64550i	0.0390196	+	0.118754i
$193$	11.0461	+	19.1325i	0.795118	+	1.37718i	0.922764	+	0.385365i	$0.125924\pi$
$193$	11.0461	+	19.1325i	0.795118	+	1.37718i	−0.127646	+	0.991820i	$0.540742\pi$
$194$	5.62724	+	3.24889i	0.404012	+	0.233256i
$195$	−1.54007	+	2.85548i	−0.110287	+	0.204486i
$196$	−5.07253	+	8.78588i	−0.362324	+	0.627563i
$197$	−26.9122			−1.91742			−0.958708	−	0.284391i	$-0.908209\pi$
$197$	−26.9122			−1.91742			−0.958708	+	0.284391i	$0.908209\pi$
$198$	0.761166	+	0.332886i	0.0540937	+	0.0236572i
$199$	−1.85693	+	3.21630i	−0.131635	+	0.227998i	−0.924307	−	0.381650i	$-0.875356\pi$
$199$	−1.85693	+	3.21630i	−0.131635	+	0.227998i	0.792672	+	0.609648i	$0.208689\pi$
$200$	2.72743	−	4.19060i	0.192858	−	0.296320i
$201$	−18.1989	−	3.80551i	−1.28365	−	0.268420i
$202$	−3.49788			−0.246110
$203$	29.1679	+	16.8401i	2.04718	+	1.18194i
$204$	3.05946	+	9.31129i	0.214205	+	0.651921i
$205$	12.6983	−	3.04182i	0.886889	−	0.212450i
$206$	−5.80542	+	3.35176i	−0.404483	+	0.233528i
$207$	0.0678298	+	0.606775i	0.00471450	+	0.0421738i
$208$	0.837680			0.0580827
$209$	−1.06644	−	0.565487i	−0.0737669	−	0.0391156i
$210$	8.41738	+	13.6500i	0.580854	+	0.941942i
$211$	1.72302	−	0.994784i	0.118617	−	0.0684837i	−0.439517	−	0.898234i	$-0.644851\pi$
$211$	1.72302	−	0.994784i	0.118617	−	0.0684837i	0.558135	+	0.829750i	$0.311517\pi$
$212$	−8.06300	+	4.65518i	−0.553769	+	0.319719i
$213$	−12.9255	+	14.4509i	−0.885638	+	0.990158i
$214$	2.95055	+	5.11050i	0.201695	+	0.349347i
$215$	−5.81733	−	24.2849i	−0.396738	−	1.65622i
$216$	−3.01242	+	4.23383i	−0.204969	+	0.288076i
$217$	−22.9726			−1.55948
$218$	−5.60593	+	9.70976i	−0.379682	+	0.657628i
$219$	8.30767	+	7.43073i	0.561381	+	0.502122i
$220$	−0.449384	+	0.426018i	−0.0302974	+	0.0287221i
$221$	4.74013			0.318855
$222$	−2.37981	−	2.12860i	−0.159722	−	0.142862i
$223$	−11.2416	−	19.4711i	−0.752794	−	1.30388i	−0.946463	−	0.322811i	$-0.895372\pi$
$223$	−11.2416	−	19.4711i	−0.752794	−	1.30388i	0.193669	−	0.981067i	$-0.437961\pi$
$224$	2.07033	−	3.58592i	0.138330	−	0.239594i
$225$	14.9748	−	0.868844i	0.998321	−	0.0579229i
$226$	1.31505	+	2.27774i	0.0874759	+	0.151513i
$227$		−	28.1102i		−	1.86574i	−0.360216	−	0.932869i	$-0.617297\pi$
$227$		−	28.1102i		−	1.86574i	0.360216	−	0.932869i	$-0.382703\pi$
$228$	4.82725	−	5.80497i	0.319692	−	0.384444i
$229$	−22.6293			−1.49538			−0.747692	−	0.664046i	$-0.768838\pi$
$229$	−22.6293			−1.49538			−0.747692	+	0.664046i	$0.768838\pi$
$230$	−0.436275	−	0.129470i	−0.0287671	−	0.00853701i
$231$	−0.619961	−	1.88682i	−0.0407905	−	0.124143i
$232$	−7.04425	−	4.06700i	−0.462478	−	0.267012i
$233$	−9.37752	−	16.2423i	−0.614342	−	1.06407i	−0.990500	−	0.137515i	$-0.956088\pi$
$233$	−9.37752	−	16.2423i	−0.614342	−	1.06407i	0.376158	−	0.926556i	$-0.377245\pi$
$234$	1.49053	+	2.02329i	0.0974387	+	0.132267i
$235$	−18.1528	−	19.1484i	−1.18416	−	1.24911i
$236$	3.89954			0.253838
$237$	−20.9193	−	18.7110i	−1.35885	−	1.21541i
$238$	11.7152	−	20.2914i	0.759386	−	1.31530i
$239$		−	9.41201i		−	0.608812i	−0.952542	−	0.304406i	$-0.901542\pi$
$239$		−	9.41201i		−	0.608812i	0.952542	−	0.304406i	$-0.0984580\pi$
$240$	−2.03286	−	3.29659i	−0.131220	−	0.212794i
$241$	6.84761	+	3.95347i	0.441093	+	0.254665i	0.704061	−	0.710139i	$-0.251368\pi$
$241$	6.84761	+	3.95347i	0.441093	+	0.254665i	−0.262968	+	0.964805i	$0.584701\pi$
$242$	−9.45987	+	5.46166i	−0.608103	+	0.351089i
$243$	−15.5863	+	0.257413i	−0.999864	+	0.0165130i
$244$	2.56141	+	4.43650i	0.163978	+	0.284018i
$245$	6.45388	−	21.7476i	0.412323	−	1.38940i
$246$	2.07020	−	9.90022i	0.131991	−	0.631215i
$247$	−1.93843	−	3.09434i	−0.123339	−	0.196888i
$248$	5.54805			0.352301
$249$	−0.812217	−	2.47194i	−0.0514721	−	0.156653i
$250$	−3.74804	+	10.5334i	−0.237047	+	0.666190i
$251$	11.6568	+	6.73004i	0.735769	+	0.424796i	0.820529	−	0.571605i	$-0.193679\pi$
$251$	11.6568	+	6.73004i	0.735769	+	0.424796i	−0.0847602	+	0.996401i	$0.527012\pi$
$252$	12.3451	−	1.38003i	0.777667	−	0.0869334i
$253$	0.0488085	+	0.0281796i	0.00306857	+	0.00177164i
$254$		−	6.29189i		−	0.394788i
$255$	−11.5032	−	18.6542i	−0.720359	−	1.16817i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−12.2806	−	7.09019i	−0.766040	−	0.442274i	0.0654199	−	0.997858i	$-0.479161\pi$
$257$	−12.2806	−	7.09019i	−0.766040	−	0.442274i	−0.831460	+	0.555584i	$0.812495\pi$
$258$	−18.9337	−	3.95917i	−1.17876	−	0.246487i
$259$			7.63291i			0.474286i
$260$	−1.82158	+	0.436349i	−0.112969	+	0.0270612i
$261$	−2.71095	−	24.2510i	−0.167804	−	1.50110i
$262$	−0.252602	+	0.437520i	−0.0156058	+	0.0270301i
$263$	0.000326808	0	0.000566048i	2.01518e−5	0	3.49040e-5i	0.866035	−	0.499983i	$-0.166660\pi$
$263$	0.000326808	0	0.000566048i	2.01518e−5	0	3.49040e-5i	−0.866015	+	0.500017i	$0.833327\pi$
$264$	0.149725	+	0.455680i	0.00921495	+	0.0280452i
$265$	15.1085	−	14.3229i	0.928108	−	0.879851i
$266$	−18.0370	+	0.650304i	−1.10592	+	0.0398727i
$267$	11.1115	+	2.32350i	0.680014	+	0.142196i
$268$	−5.36719	−	9.29624i	−0.327853	−	0.567858i
$269$	2.56468	+	4.44215i	0.156371	+	0.270843i	0.933557	−	0.358428i	$-0.116687\pi$
$269$	2.56468	+	4.44215i	0.156371	+	0.270843i	−0.777186	+	0.629270i	$0.783354\pi$
$270$	4.34525	−	10.7758i	0.264443	−	0.655797i
$271$	1.83855	+	3.18447i	0.111684	+	0.193443i	0.916449	−	0.400151i	$-0.131042\pi$
$271$	1.83855	+	3.18447i	0.111684	+	0.193443i	−0.804765	+	0.593593i	$0.797709\pi$
$272$	−2.82932	+	4.90052i	−0.171553	+	0.297138i
$273$	1.22966	−	5.88051i	0.0744222	−	0.355905i
$274$			0.0663784i			0.00401007i
$275$	0.755293	−	1.16048i	0.0455459	−	0.0699797i
$276$	−0.235005	+	0.262739i	−0.0141456	+	0.0158150i
$277$		−	25.8215i		−	1.55146i	−0.631064	−	0.775731i	$-0.717381\pi$
$277$		−	25.8215i		−	1.55146i	0.631064	−	0.775731i	$-0.282619\pi$
$278$			1.17792i			0.0706468i
$279$	9.87191	+	13.4005i	0.591016	+	0.802266i
$280$	−2.63412	+	8.87619i	−0.157419	+	0.530454i
$281$	−4.30234	+	7.45188i	−0.256656	+	0.444542i	−0.965344	−	0.260980i	$-0.915954\pi$
$281$	−4.30234	+	7.45188i	−0.256656	+	0.444542i	0.708688	+	0.705522i	$0.249288\pi$
$282$	−19.4167	+	6.37986i	−1.15625	+	0.379915i
$283$	−12.9655	+	7.48566i	−0.770722	+	0.444976i	−0.833132	−	0.553074i	$-0.813455\pi$
$283$	−12.9655	+	7.48566i	−0.770722	+	0.444976i	0.0624104	+	0.998051i	$0.480121\pi$
$284$	−11.1937			−0.664223
$285$	−7.47326	+	15.1377i	−0.442678	+	0.896681i
$286$	0.231975			0.0137169
$287$	−20.9400	+	12.0897i	−1.23605	+	0.713634i
$288$	−2.98143	+	0.333286i	−0.175682	+	0.0196391i
$289$	−7.51008	+	13.0078i	−0.441769	+	0.765167i
$290$	17.4366	+	5.17453i	1.02391	+	0.303859i
$291$	−7.50305	+	8.38853i	−0.439836	+	0.491744i
$292$			6.43514i			0.376588i
$293$			9.99594i			0.583969i	0.956423	+	0.291984i	$0.0943155\pi$
$293$			9.99594i			0.583969i	−0.956423	+	0.291984i	$0.905684\pi$
$294$	−13.0971	−	11.7146i	−0.763840	−	0.683210i
$295$	−8.47974	+	2.03128i	−0.493709	+	0.118265i
$296$		−	1.84341i		−	0.107146i
$297$	−0.834214	+	1.17245i	−0.0484060	+	0.0680327i
$298$	−3.35370	+	5.80877i	−0.194274	+	0.336493i
$299$	0.0852415	+	0.147643i	0.00492965	+	0.00853840i
$300$	6.13775	+	6.10967i	0.354363	+	0.352742i
$301$	23.1210	+	40.0468i	1.33267	+	2.30826i
$302$	5.84059	+	10.1162i	0.336088	+	0.582122i
$303$	1.24006	−	5.93025i	0.0712394	−	0.340684i
$304$	4.35607	−	0.157053i	0.249838	−	0.00900762i
$305$	−7.88090	−	8.31314i	−0.451259	−	0.476009i
$306$	−16.8708	+	1.88595i	−0.964441	+	0.107812i
$307$	14.4133	+	24.9645i	0.822608	+	1.42480i	0.903733	+	0.428096i	$0.140815\pi$
$307$	14.4133	+	24.9645i	0.822608	+	1.42480i	−0.0811250	+	0.996704i	$0.525851\pi$
$308$	0.573326	−	0.993030i	0.0326683	−	0.0565831i
$309$	−3.62440	−	11.0307i	−0.206185	−	0.627512i
$310$	−12.0645	+	2.88999i	−0.685217	+	0.164140i
$311$		−	19.0823i		−	1.08206i	−0.841003	−	0.541030i	$-0.818034\pi$
$311$		−	19.0823i		−	1.08206i	0.841003	−	0.541030i	$-0.181966\pi$
$312$	−0.296971	+	1.42019i	−0.0168127	+	0.0804023i
$313$	12.6849	+	7.32365i	0.716995	+	0.413957i	0.813646	−	0.581361i	$-0.197480\pi$
$313$	12.6849	+	7.32365i	0.716995	+	0.413957i	−0.0966505	+	0.995318i	$0.530813\pi$
$314$	−0.0665981	+	0.115351i	−0.00375835	+	0.00650965i
$315$	−26.1261	+	9.43151i	−1.47204	+	0.531405i
$316$		−	16.2041i		−	0.911552i
$317$	−2.79008	−	1.61085i	−0.156706	−	0.0904744i	0.419596	−	0.907711i	$-0.362172\pi$
$317$	−2.79008	−	1.61085i	−0.156706	−	0.0904744i	−0.576303	+	0.817236i	$0.695505\pi$
$318$	−5.03384	−	15.3202i	−0.282284	−	0.859114i
$319$	−1.95073	−	1.12625i	−0.109220	−	0.0630581i
$320$	0.636160	−	2.14367i	0.0355624	−	0.119835i
$321$	−9.71027	+	3.19055i	−0.541974	+	0.178079i
$322$	0.842699			0.0469618
$323$	24.6494	−	0.888707i	1.37153	−	0.0494490i
$324$	−6.11001	−	6.60816i	−0.339445	−	0.367120i
$325$	3.73381	−	1.89772i	0.207115	−	0.105267i
$326$	2.20244	+	3.81474i	0.121982	+	0.211279i
$327$	−14.4743	−	12.9465i	−0.800433	−	0.715941i
$328$	5.05717	−	2.91976i	0.279236	−	0.161217i
$329$	42.3134	+	24.4297i	2.33282	+	1.34685i
$330$	−0.562950	−	0.912907i	−0.0309894	−	0.0502539i
$331$			12.4330i			0.683377i	0.939813	+	0.341689i	$0.110999\pi$
$331$			12.4330i			0.683377i	−0.939813	+	0.341689i	$0.889001\pi$
$332$	0.751119	−	1.30098i	0.0412230	−	0.0714004i
$333$	4.45247	−	3.28006i	0.243994	−	0.179746i
$334$	−6.97119			−0.381447
$335$	16.5136	+	17.4194i	0.902236	+	0.951721i
$336$	5.34553	+	4.78126i	0.291623	+	0.260839i
$337$	0.671895	+	1.16376i	0.0366005	+	0.0633939i	0.883745	−	0.467968i	$-0.155014\pi$
$337$	0.671895	+	1.16376i	0.0366005	+	0.0633939i	−0.847145	+	0.531362i	$0.821680\pi$
$338$	−10.6506	−	6.14915i	−0.579318	−	0.334469i
$339$	−4.32784	+	1.42202i	−0.235056	+	0.0772335i
$340$	3.59980	−	12.1302i	0.195227	−	0.657854i
$341$	1.53639			0.0832003
$342$	8.13031	+	10.2420i	0.439637	+	0.553823i
$343$			13.0226i			0.703155i
$344$	−5.58390	−	9.67160i	−0.301064	−	0.521458i
$345$	0.374168	−	0.693753i	0.0201445	−	0.0373504i
$346$	−11.9847	+	20.7581i	−0.644302	+	1.11596i
$347$	11.9747	+	20.7407i	0.642834	+	1.11342i	0.984797	+	0.173708i	$0.0555748\pi$
$347$	11.9747	+	20.7407i	0.642834	+	1.11342i	−0.341963	+	0.939713i	$0.611092\pi$
$348$	9.39242	−	10.5009i	0.503487	−	0.562906i
$349$	−29.4972			−1.57895			−0.789474	−	0.613784i	$-0.789646\pi$
$349$	−29.4972			−1.57895			−0.789474	+	0.613784i	$0.789646\pi$
$350$	1.10441	−	20.6738i	0.0590331	−	1.10506i
$351$	−3.95867	+	1.80972i	−0.211298	+	0.0965957i
$352$	−0.138462	+	0.239824i	−0.00738008	+	0.0127827i
$353$	−29.0595			−1.54668			−0.773339	−	0.633992i	$-0.781415\pi$
$353$	−29.0595			−1.54668			−0.773339	+	0.633992i	$0.781415\pi$
$354$	−1.38245	+	6.61121i	−0.0734764	+	0.351382i
$355$	24.3412	−	5.83081i	1.29190	−	0.309467i
$356$	3.27700	+	5.67592i	0.173680	+	0.300823i
$357$	30.2484	+	27.0554i	1.60092	+	1.43193i
$358$	11.2818	−	6.51358i	0.596264	−	0.344253i
$359$	29.7773	−	17.1919i	1.57159	−	0.907356i	0.575611	−	0.817724i	$-0.304764\pi$
$359$	29.7773	−	17.1919i	1.57159	−	0.907356i	0.995975	−	0.0896318i	$-0.0285690\pi$
$360$	6.30965	−	2.27778i	0.332548	−	0.120049i
$361$	−10.6603	−	15.7276i	−0.561068	−	0.827770i
$362$	15.0743			0.792285
$363$	−5.90592	−	17.9743i	−0.309980	−	0.943408i
$364$	3.00385	−	1.73427i	0.157445	−	0.0909007i
$365$	−3.35208	−	13.9935i	−0.175456	−	0.732455i
$366$	−8.42962	+	2.76976i	−0.440623	+	0.144778i
$367$	9.51432	+	5.49310i	0.496644	+	0.286737i	0.727326	−	0.686292i	$-0.240763\pi$
$367$	9.51432	+	5.49310i	0.496644	+	0.286737i	−0.230683	+	0.973029i	$0.574096\pi$
$368$	−0.203518			−0.0106091
$369$	16.0507	+	7.01957i	0.835567	+	0.365424i
$370$	0.960233	+	4.00857i	0.0499201	+	0.208396i
$371$	−19.2755	+	33.3861i	−1.00073	+	1.73332i
$372$	−1.96687	+	9.40606i	−0.101978	+	0.487681i
$373$	−2.18309			−0.113036			−0.0565180	−	0.998402i	$-0.518000\pi$
$373$	−2.18309			−0.113036			−0.0565180	+	0.998402i	$0.518000\pi$
$374$	−0.783509	+	1.35708i	−0.0405143	+	0.0701728i
$375$	−16.5294	−	10.0886i	−0.853573	−	0.520973i
$376$	−10.2190	−	5.89995i	−0.527005	−	0.304267i
$377$	−3.40685	−	5.90083i	−0.175462	−	0.303908i
$378$	−2.03686	+	21.4189i	−0.104765	+	1.10167i
$379$		−	9.44771i		−	0.485296i	−0.970114	−	0.242648i	$-0.921984\pi$
$379$		−	9.44771i		−	0.485296i	0.970114	−	0.242648i	$-0.0780160\pi$
$380$	−9.39067	+	2.61060i	−0.481731	+	0.133921i
$381$	10.6672	+	2.23058i	0.546495	+	0.114276i
$382$	−4.08321	−	7.07232i	−0.208915	−	0.361851i
$383$	−22.9528	+	13.2518i	−1.17283	+	0.677136i	−0.954346	−	0.298703i	$-0.903446\pi$
$383$	−22.9528	+	13.2518i	−1.17283	+	0.677136i	−0.218488	+	0.975840i	$0.570113\pi$
$384$	−1.29099	−	1.15471i	−0.0658803	−	0.0589261i
$385$	−0.729454	+	2.45804i	−0.0371764	+	0.125273i
$386$	−19.1325	−	11.0461i	−0.973817	−	0.562233i
$387$	13.4246	−	30.6962i	0.682410	−	1.56038i
$388$	−6.49777			−0.329874
$389$	−30.4555	−	17.5835i	−1.54415	−	0.891518i	−0.998570	−	0.0534626i	$-0.982974\pi$
$389$	−30.4555	−	17.5835i	−1.54415	−	0.891518i	−0.545585	−	0.838056i	$-0.683692\pi$
$390$	−0.0939998	−	3.24296i	−0.00475986	−	0.164214i
$391$	−1.15163			−0.0582407
$392$		−	10.1451i		−	0.512403i
$393$	−0.652211	−	0.583365i	−0.0328997	−	0.0294269i
$394$	23.3067	−	13.4561i	1.17417	−	0.677909i
$395$	8.44074	+	35.2366i	0.424700	+	1.77295i
$396$	−0.825632	+	0.0922953i	−0.0414896	+	0.00463801i
$397$	−12.7678	+	7.37147i	−0.640796	+	0.369963i	−0.784921	−	0.619596i	$-0.787296\pi$
$397$	−12.7678	+	7.37147i	−0.640796	+	0.369963i	0.144125	+	0.989559i	$0.453963\pi$
$398$		−	3.71387i		−	0.186159i
$399$	5.29189	−	30.8101i	0.264926	−	1.54244i
$400$	−0.266723	+	4.99288i	−0.0133361	+	0.249644i
$401$	10.0032	+	17.3261i	0.499537	+	0.865224i	1.00000		0.000534108i	$-0.000170012\pi$
$401$	10.0032	+	17.3261i	0.499537	+	0.865224i	−0.500462	+	0.865758i	$0.666837\pi$
$402$	17.6634	−	5.80376i	0.880972	−	0.289465i
$403$	4.02484	+	2.32374i	0.200492	+	0.115754i
$404$	3.02926	−	1.74894i	0.150711	−	0.0870131i
$405$	16.7287	+	11.1871i	0.831256	+	0.555889i
$406$	−33.6801			−1.67152
$407$		−	0.510485i		−	0.0253038i
$408$	−7.30522	−	6.53409i	−0.361662	−	0.323486i
$409$	6.13313	+	3.54097i	0.303264	+	0.175089i	0.643908	−	0.765103i	$-0.277312\pi$
$409$	6.13313	+	3.54097i	0.303264	+	0.175089i	−0.340644	+	0.940192i	$0.610645\pi$
$410$	−9.47616	+	8.98345i	−0.467994	+	0.443661i
$411$	−0.112537	−	0.0235322i	−0.00555103	−	0.00116076i
$412$	3.35176	−	5.80542i	0.165129	−	0.286012i
$413$	13.9834	−	8.07333i	0.688079	−	0.397263i
$414$	−0.362130	−	0.491568i	−0.0177977	−	0.0241592i
$415$	−0.955665	+	3.22030i	−0.0469117	+	0.158078i
$416$	−0.725452	+	0.418840i	−0.0355682	+	0.0205353i
$417$	−1.99702	−	0.417591i	−0.0977945	−	0.0204495i
$418$	1.20630	−	0.0434920i	0.0590023	−	0.00212726i
$419$			15.8313i			0.773409i	0.922204	+	0.386705i	$0.126387\pi$
$419$			15.8313i			0.773409i	−0.922204	+	0.386705i	$0.873613\pi$
$420$	−14.1147	−	7.61259i	−0.688726	−	0.371457i
$421$	9.83472	−	5.67808i	0.479315	−	0.276733i	−0.240816	−	0.970571i	$-0.577415\pi$
$421$	9.83472	−	5.67808i	0.479315	−	0.276733i	0.720131	+	0.693838i	$0.244082\pi$
$422$	−0.994784	+	1.72302i	−0.0484253	+	0.0838751i
$423$	−3.93274	−	35.1806i	−0.191217	−	1.71054i
$424$	4.65518	−	8.06300i	0.226075	−	0.391574i
$425$	−1.50929	+	28.2529i	−0.0732112	+	1.37047i
$426$	3.96834	−	18.9776i	0.192267	−	0.919466i
$427$	18.3700	+	10.6059i	0.888988	+	0.513258i
$428$	−5.11050	−	2.95055i	−0.247025	−	0.142620i
$429$	−0.0822387	+	0.393285i	−0.00397052	+	0.0189880i
$430$	17.1804	+	18.1227i	0.828513	+	0.873954i
$431$	6.74460	−	11.6820i	0.324876	−	0.562702i	−0.656611	−	0.754229i	$-0.728011\pi$
$431$	6.74460	−	11.6820i	0.324876	−	0.562702i	0.981487	+	0.191527i	$0.0613441\pi$
$432$	0.491917	−	5.17282i	0.0236674	−	0.248877i
$433$	−7.19759	+	12.4666i	−0.345894	+	0.599106i	−0.985516	−	0.169584i	$-0.945758\pi$
$433$	−7.19759	+	12.4666i	−0.345894	+	0.599106i	0.639622	+	0.768690i	$0.279091\pi$
$434$	19.8948	−	11.4863i	0.954982	−	0.551359i
$435$	−14.9543	+	27.7272i	−0.717006	+	1.32942i
$436$		−	11.2119i		−	0.536951i
$437$	0.470950	+	0.751784i	0.0225286	+	0.0359627i
$438$	−10.9100	−	2.28136i	−0.521301	−	0.109008i
$439$	−19.8233	+	11.4450i	−0.946117	+	0.546241i	−0.891873	−	0.452287i	$-0.850608\pi$
$439$	−19.8233	+	11.4450i	−0.946117	+	0.546241i	−0.0542443	+	0.998528i	$0.517275\pi$
$440$	0.176169	−	0.593634i	0.00839851	−	0.0283004i
$441$	24.5039	−	18.0516i	1.16685	−	0.859600i
$442$	−4.10507	+	2.37006i	−0.195258	+	0.112732i
$443$	2.22771	−	3.85851i	0.105842	−	0.183324i	−0.808240	−	0.588853i	$-0.799580\pi$
$443$	2.22771	−	3.85851i	0.105842	−	0.183324i	0.914082	+	0.405530i	$0.132913\pi$
$444$	3.12527	+	0.653517i	0.148319	+	0.0310145i
$445$	−10.0826	−	10.6356i	−0.477960	−	0.504175i
$446$	19.4711	+	11.2416i	0.921981	+	0.532306i
$447$	−8.65914	−	7.74510i	−0.409563	−	0.366330i
$448$			4.14066i			0.195628i
$449$	−22.9854			−1.08475			−0.542375	−	0.840137i	$-0.682475\pi$
$449$	−22.9854			−1.08475			−0.542375	+	0.840137i	$0.682475\pi$
$450$	−12.5341	+	8.23985i	−0.590865	+	0.388430i
$451$	1.40046	−	0.808555i	0.0659450	−	0.0380733i
$452$	−2.27774	−	1.31505i	−0.107136	−	0.0618548i
$453$	−19.2214	+	6.31567i	−0.903100	+	0.296736i
$454$	14.0551	+	24.3441i	0.659638	+	1.14253i
$455$	−5.62863	+	5.33597i	−0.263874	+	0.250154i
$456$	−1.27803	+	7.44088i	−0.0598493	+	0.348451i
$457$			13.1695i			0.616045i	0.951379	+	0.308022i	$0.0996672\pi$
$457$			13.1695i			0.616045i	−0.951379	+	0.308022i	$0.900333\pi$
$458$	19.5975	−	11.3146i	0.915732	−	0.528698i
$459$	2.78358	−	29.2711i	0.129926	−	1.36626i
$460$	0.442560	−	0.106013i	0.0206345	−	0.00494288i
$461$	12.4399	−	7.18219i	0.579385	−	0.334508i	−0.181504	−	0.983390i	$-0.558097\pi$
$461$	12.4399	−	7.18219i	0.579385	−	0.334508i	0.760889	+	0.648882i	$0.224763\pi$
$462$	1.48031	+	1.32405i	0.0688703	+	0.0616004i
$463$			29.1669i			1.35550i	0.735292	+	0.677750i	$0.237045\pi$
$463$			29.1669i			1.35550i	−0.735292	+	0.677750i	$0.762955\pi$
$464$	8.13400			0.377612
$465$	−0.622571	−	21.4785i	−0.0288710	−	0.996040i
$466$	16.2423	+	9.37752i	0.752412	+	0.434405i
$467$	29.0053			1.34221			0.671103	−	0.741364i	$-0.265821\pi$
$467$	29.0053			1.34221			0.671103	+	0.741364i	$0.265821\pi$
$468$	−2.30248	−	1.00696i	−0.106432	−	0.0465467i
$469$	−38.4926	−	22.2237i	−1.77742	−	1.02619i
$470$	25.2950	+	7.50663i	1.16677	+	0.346255i
$471$	−0.171954	−	0.153803i	−0.00792324	−	0.00708687i
$472$	−3.37710	+	1.94977i	−0.155444	+	0.0897454i
$473$	−1.54632	−	2.67831i	−0.0711000	−	0.123149i
$474$	27.4721	+	5.74461i	1.26184	+	0.263859i
$475$	19.0606	−	10.5685i	0.874561	−	0.484916i
$476$			23.4305i			1.07393i
$477$	27.7582	−	3.10301i	1.27096	−	0.142077i
$478$	4.70600	+	8.15104i	0.215248	+	0.372820i
$479$	−22.9576	−	13.2546i	−1.04896	−	0.605617i	−0.126602	−	0.991954i	$-0.540407\pi$
$479$	−22.9576	−	13.2546i	−1.04896	−	0.605617i	−0.922358	+	0.386336i	$0.873740\pi$
$480$	3.40880	+	1.83850i	0.155590	+	0.0839156i
$481$	0.772092	−	1.33730i	0.0352044	−	0.0609757i
$482$	−7.90693			−0.360151
$483$	−0.298750	+	1.42870i	−0.0135936	+	0.0650079i
$484$	5.46166	−	9.45987i	0.248257	−	0.429994i
$485$	14.1297	−	3.38470i	0.641598	−	0.153691i
$486$	13.3695	−	8.01609i	0.606451	−	0.363617i
$487$	11.6600			0.528366			0.264183	−	0.964473i	$-0.414898\pi$
$487$	11.6600			0.528366			0.264183	+	0.964473i	$0.414898\pi$
$488$	−4.43650	−	2.56141i	−0.200831	−	0.115950i
$489$	−7.24823	+	2.38159i	−0.327776	+	0.107699i
$490$	5.28458	+	22.0609i	0.238733	+	0.996611i
$491$	0.670228	−	0.386956i	0.0302470	−	0.0174631i	−0.484800	−	0.874625i	$-0.661108\pi$
$491$	0.670228	−	0.386956i	0.0302470	−	0.0174631i	0.515047	+	0.857162i	$0.327774\pi$
$492$	3.15726	+	9.60894i	0.142340	+	0.433204i
$493$	46.0274			2.07297
$494$	3.22590	+	1.71056i	0.145140	+	0.0769618i
$495$	1.74730	−	0.630774i	0.0785353	−	0.0283512i
$496$	−4.80475	+	2.77402i	−0.215740	+	0.124557i
$497$	−40.1396	+	23.1746i	−1.80051	+	1.03952i
$498$	1.93937	+	1.73465i	0.0869052	+	0.0777316i
$499$	5.69523	+	9.86443i	0.254953	+	0.441592i	0.964883	−	0.262680i	$-0.0846065\pi$
$499$	5.69523	+	9.86443i	0.254953	+	0.441592i	−0.709929	+	0.704273i	$0.751273\pi$
$500$	−2.02080	−	10.9962i	−0.0903728	−	0.491765i
$501$	2.47140	−	11.8188i	0.110414	−	0.528027i
$502$	−13.4601			−0.600753
$503$	15.2932	−	26.4887i	0.681892	−	1.18107i	−0.292511	−	0.956262i	$-0.594491\pi$
$503$	15.2932	−	26.4887i	0.681892	−	1.18107i	0.974403	−	0.224809i	$-0.0721759\pi$
$504$	−10.0011	+	7.36768i	−0.445486	+	0.328182i
$505$	−5.67624	+	5.38110i	−0.252589	+	0.239456i
$506$	−0.0563593			−0.00250547
$507$	14.2010	−	15.8769i	0.630687	−	0.705119i
$508$	3.14595	+	5.44894i	0.139579	+	0.241758i
$509$	11.0074	−	19.0654i	0.487894	−	0.845058i	−0.512009	−	0.858980i	$-0.671098\pi$
$509$	11.0074	−	19.0654i	0.487894	−	0.845058i	0.999903	+	0.0139223i	$0.00443174\pi$
$510$	19.2892	+	10.4034i	0.854138	+	0.460670i
$511$	13.3229	+	23.0759i	0.589369	+	1.02082i
$512$		−	1.00000i		−	0.0441942i
$513$	−20.2464	+	10.1530i	−0.893900	+	0.448267i
$514$	14.1804			0.625469
$515$	−4.26451	+	14.3701i	−0.187917	+	0.633222i
$516$	18.3766	−	6.03810i	0.808986	−	0.265813i
$517$	−2.82990	−	1.63384i	−0.124459	−	0.0718563i
$518$	−3.81646	−	6.61030i	−0.167685	−	0.290440i
$519$	−30.9442	−	27.6777i	−1.35830	−	1.21492i
$520$	1.35936	−	1.28868i	0.0596117	−	0.0565122i
$521$	−24.9351			−1.09243			−0.546214	−	0.837646i	$-0.683931\pi$
$521$	−24.9351			−1.09243			−0.546214	+	0.837646i	$0.683931\pi$
$522$	14.4732	+	19.6465i	0.633476	+	0.859902i
$523$	−8.63200	+	14.9511i	−0.377451	+	0.653764i	−0.990691	−	0.136133i	$-0.956533\pi$
$523$	−8.63200	+	14.9511i	−0.377451	+	0.653764i	0.613240	+	0.789897i	$0.289866\pi$
$524$		−	0.505204i		−	0.0220700i
$525$	34.6585	+	9.20159i	1.51262	+	0.401591i
$526$	−0.000566048	0	0.000326808i	−2.46809e−5	0	1.42495e-5i
$527$	−27.1883	+	15.6972i	−1.18434	+	0.683780i
$528$	−0.357506	−	0.319768i	−0.0155585	−	0.0139161i
$529$	11.4793	+	19.8827i	0.499100	+	0.864466i
$530$	−5.92288	+	19.9583i	−0.257273	+	0.866932i
$531$	−10.7184	−	4.68756i	−0.465140	−	0.203423i
$532$	15.2953	−	9.58168i	0.663137	−	0.415418i
$533$	4.89165			0.211881
$534$	−10.7846	+	3.54355i	−0.466695	+	0.153344i
$535$	12.6500	+	3.75405i	0.546906	+	0.162302i
$536$	9.29624	+	5.36719i	0.401537	+	0.231827i
$537$	7.04340	+	21.4362i	0.303945	+	0.925040i
$538$	−4.44215	−	2.56468i	−0.191515	−	0.110571i
$539$		−	2.80942i		−	0.121010i
$540$	1.62483	+	11.5048i	0.0699216	+	0.495087i
$541$	1.98420	−	3.43673i	0.0853073	−	0.147757i	−0.820215	−	0.572056i	$-0.806146\pi$
$541$	1.98420	−	3.43673i	0.0853073	−	0.147757i	0.905522	+	0.424299i	$0.139479\pi$
$542$	−3.18447	−	1.83855i	−0.136785	−	0.0789726i
$543$	−5.34407	+	25.5566i	−0.229336	+	1.09674i
$544$		−	5.65864i		−	0.242612i
$545$	5.84028	+	24.3807i	0.250170	+	1.04436i
$546$	1.87534	+	5.70750i	0.0802572	+	0.244258i
$547$	−1.00884	+	1.74735i	−0.0431347	+	0.0747115i	−0.886787	−	0.462179i	$-0.847068\pi$
$547$	−1.00884	+	1.74735i	−0.0431347	+	0.0747115i	0.843652	+	0.536890i	$0.180401\pi$
$548$	−0.0331892	−	0.0574854i	−0.00141777	−	0.00245566i
$549$	−1.70737	−	15.2734i	−0.0728687	−	0.651851i
$550$	−0.0738622	+	1.38265i	−0.00314949	+	0.0589565i
$551$	−18.8225	−	30.0465i	−0.801864	−	1.28002i
$552$	0.0721505	−	0.345041i	0.00307093	−	0.0146859i
$553$	−33.5478	−	58.1065i	−1.42660	−	2.47094i
$554$	12.9107	+	22.3621i	0.548525	+	0.950073i
$555$	−7.13648	+	0.206857i	−0.302927	+	0.00878057i
$556$	−0.588959	−	1.02011i	−0.0249774	−	0.0432622i
$557$	−12.2671	+	21.2472i	−0.519773	+	0.900274i	0.479963	+	0.877289i	$0.340650\pi$
$557$	−12.2671	+	21.2472i	−0.519773	+	0.900274i	−0.999736	+	0.0229846i	$0.992683\pi$
$558$	−15.2496	−	6.66920i	−0.645566	−	0.282330i
$559$		−	9.35505i		−	0.395676i
$560$	−2.15688	−	9.00406i	−0.0911446	−	0.380491i
$561$	−2.02300	−	1.80945i	−0.0854110	−	0.0763951i
$562$		−	8.60469i		−	0.362967i
$563$			27.1996i			1.14633i	0.819441	+	0.573164i	$0.194284\pi$
$563$			27.1996i			1.14633i	−0.819441	+	0.573164i	$0.805716\pi$
$564$	13.6255	−	15.2335i	0.573736	−	0.641446i
$565$	5.63806	+	1.67317i	0.237195	+	0.0703907i
$566$	7.48566	−	12.9655i	0.314646	−	0.544982i
$567$	−35.5910	−	11.0466i	−1.49468	−	0.463913i
$568$	9.69401	−	5.59684i	0.406752	−	0.234838i
$569$	14.1549			0.593405			0.296702	−	0.954970i	$-0.404113\pi$
$569$	14.1549			0.593405			0.296702	+	0.954970i	$0.404113\pi$
$570$	−1.09682	−	16.8463i	−0.0459408	−	0.705613i
$571$	29.8156			1.24774			0.623871	−	0.781527i	$-0.285559\pi$
$571$	29.8156			1.24774			0.623871	+	0.781527i	$0.285559\pi$
$572$	−0.200896	+	0.115987i	−0.00839988	+	0.00484967i
$573$	13.4378	−	4.41534i	0.561374	−	0.184454i
$574$	12.0897	−	20.9400i	0.504616	−	0.874020i
$575$	−0.907146	+	0.461060i	−0.0378306	+	0.0192276i
$576$	2.41535	−	1.77935i	0.100640	−	0.0741395i
$577$		−	10.8282i		−	0.450785i	−0.974268	−	0.225393i	$-0.927634\pi$
$577$		−	10.8282i		−	0.450785i	0.974268	−	0.225393i	$-0.0723665\pi$
$578$		−	15.0202i		−	0.624756i
$579$	25.5102	−	28.5208i	1.06017	−	1.18528i
$580$	−17.6878	+	4.23702i	−0.734445	+	0.175932i
$581$		−	6.22026i		−	0.258060i
$582$	2.30356	−	11.0162i	0.0954858	−	0.456636i
$583$	1.28913	−	2.23285i	0.0533905	−	0.0924751i
$584$	−3.21757	−	5.57300i	−0.133144	−	0.230612i
$585$	5.53138	+	0.990316i	0.228694	+	0.0409445i
$586$	−4.99797	−	8.65674i	−0.206464	−	0.357606i
$587$	−7.46457	−	12.9290i	−0.308096	−	0.533638i	0.669850	−	0.742496i	$-0.266358\pi$
$587$	−7.46457	−	12.9290i	−0.308096	−	0.533638i	−0.977946	+	0.208859i	$0.933025\pi$
$588$	17.1997	+	3.59659i	0.709306	+	0.148321i
$589$	21.3655	+	11.3292i	0.880350	+	0.466813i
$590$	6.32803	−	5.99901i	0.260521	−	0.246975i
$591$	14.5507	+	44.2841i	0.598534	+	1.82160i
$592$	0.921703	+	1.59644i	0.0378817	+	0.0656131i
$593$	−16.9851	+	29.4191i	−0.697494	+	1.20810i	0.271838	+	0.962343i	$0.412368\pi$
$593$	−16.9851	+	29.4191i	−0.697494	+	1.20810i	−0.969333	+	0.245753i	$0.920965\pi$
$594$	0.136224	−	1.43248i	0.00558934	−	0.0587754i
$595$	−12.2050	−	50.9507i	−0.500355	−	2.08878i
$596$		−	6.70739i		−	0.274745i
$597$	6.29642	+	1.31663i	0.257695	+	0.0538859i
$598$	−0.147643	−	0.0852415i	−0.00603756	−	0.00348579i
$599$	18.2404	−	31.5932i	0.745281	−	1.29086i	−0.204782	−	0.978808i	$-0.565649\pi$
$599$	18.2404	−	31.5932i	0.745281	−	1.29086i	0.950063	−	0.312057i	$-0.101018\pi$
$600$	−8.37028	−	2.22225i	−0.341715	−	0.0907231i
$601$		−	6.32670i		−	0.258072i	−0.991640	−	0.129036i	$-0.958812\pi$
$601$		−	6.32670i		−	0.258072i	0.991640	−	0.129036i	$-0.0411882\pi$
$602$	−40.0468	−	23.1210i	−1.63219	−	0.942343i
$603$	3.57762	+	32.0038i	0.145692	+	1.30329i
$604$	−10.1162	−	5.84059i	−0.411622	−	0.237650i
$605$	−6.94898	+	23.4159i	−0.282516	+	0.951993i
$606$	1.89120	+	5.75577i	0.0768249	+	0.233812i
$607$	30.0680			1.22042			0.610212	−	0.792238i	$-0.291084\pi$
$607$	30.0680			1.22042			0.610212	+	0.792238i	$0.291084\pi$
$608$	−3.69394	+	2.31405i	−0.149809	+	0.0938470i
$609$	11.9402	−	57.1007i	0.483839	−	2.31384i
$610$	10.9816	+	3.25894i	0.444633	+	0.131951i
$611$	−4.94227	−	8.56026i	−0.199943	−	0.346311i
$612$	13.6676	−	10.0687i	0.552479	−	0.407003i
$613$	10.8242	−	6.24937i	0.437187	−	0.252410i	−0.265217	−	0.964189i	$-0.585444\pi$
$613$	10.8242	−	6.24937i	0.437187	−	0.252410i	0.702403	+	0.711779i	$0.252110\pi$
$614$	−24.9645	−	14.4133i	−1.00749	−	0.581672i
$615$	−11.8709	−	19.2505i	−0.478682	−	0.776255i
$616$			1.14665i			0.0461999i
$617$	14.8991	−	25.8061i	0.599817	−	1.03891i	−0.393031	−	0.919525i	$-0.628574\pi$
$617$	14.8991	−	25.8061i	0.599817	−	1.03891i	0.992848	−	0.119388i	$-0.0380931\pi$
$618$	8.65415	+	7.74063i	0.348121	+	0.311374i
$619$	4.81279			0.193443			0.0967213	−	0.995312i	$-0.469164\pi$
$619$	4.81279			0.193443			0.0967213	+	0.995312i	$0.469164\pi$
$620$	9.00317	−	8.53505i	0.361576	−	0.342776i
$621$	0.961775	−	0.439679i	0.0385947	−	0.0176437i
$622$	9.54117	+	16.5258i	0.382566	+	0.662624i
$623$	23.5021	+	13.5689i	0.941590	+	0.543627i
$624$	−0.452909	−	1.37840i	−0.0181309	−	0.0551803i
$625$	10.1223	+	22.8591i	0.404890	+	0.914365i
$626$	−14.6473			−0.585424
$627$	−0.353919	+	2.06056i	−0.0141342	+	0.0822910i
$628$		−	0.133196i		−	0.00531511i
$629$	5.21558	+	9.03365i	0.207959	+	0.360195i
$630$	17.9101	−	21.2310i	0.713557	−	0.845863i
$631$	9.66769	−	16.7449i	0.384865	−	0.666605i	−0.606886	−	0.794789i	$-0.707581\pi$
$631$	9.66769	−	16.7449i	0.384865	−	0.666605i	0.991750	+	0.128184i	$0.0409147\pi$
$632$	8.10205	+	14.0332i	0.322282	+	0.558209i
$633$	−2.56850	−	2.29738i	−0.102089	−	0.0913125i
$634$	3.22170			0.127950
$635$	−9.67937	−	10.2103i	−0.384114	−	0.405182i
$636$	12.0195	+	10.7508i	0.476605	+	0.426296i
$637$	4.24916	−	7.35976i	0.168358	−	0.291604i
$638$	2.25251			0.0891777
$639$	30.7674	+	13.4557i	1.21714	+	0.532299i
$640$	0.520902	+	2.17455i	0.0205904	+	0.0859566i
$641$	−8.82740	−	15.2895i	−0.348661	−	0.603899i	0.637351	−	0.770574i	$-0.280030\pi$
$641$	−8.82740	−	15.2895i	−0.348661	−	0.603899i	−0.986012	+	0.166675i	$0.946697\pi$
$642$	6.81406	−	7.61823i	0.268930	−	0.300668i
$643$	−22.5254	+	13.0051i	−0.888315	+	0.512869i	−0.873391	−	0.487019i	$-0.838084\pi$
$643$	−22.5254	+	13.0051i	−0.888315	+	0.512869i	−0.0149244	+	0.999889i	$0.504751\pi$
$644$	−0.729799	+	0.421350i	−0.0287581	+	0.0166035i
$645$	−36.8156	+	22.7026i	−1.44961	+	0.893913i
$646$	−20.9027	+	13.0943i	−0.822404	+	0.515190i
$647$	−32.4210			−1.27460			−0.637300	−	0.770616i	$-0.719949\pi$
$647$	−32.4210			−1.27460			−0.637300	+	0.770616i	$0.719949\pi$
$648$	8.59550	+	2.66783i	0.337663	+	0.104802i
$649$	−0.935204	+	0.539940i	−0.0367099	+	0.0211945i
$650$	−2.28471	+	3.51038i	−0.0896138	+	0.137689i
$651$	12.4206	+	37.8014i	0.486802	+	1.48155i
$652$	−3.81474	−	2.20244i	−0.149397	−	0.0862541i
$653$	−6.39815			−0.250379			−0.125190	−	0.992133i	$-0.539954\pi$
$653$	−6.39815			−0.250379			−0.125190	+	0.992133i	$0.539954\pi$
$654$	19.0084	+	3.97479i	0.743286	+	0.155426i
$655$	0.263162	+	1.09859i	0.0102826	+	0.0429255i
$656$	−2.91976	+	5.05717i	−0.113997	+	0.197449i
$657$	7.73556	−	17.6879i	0.301793	−	0.690069i
$658$	−48.8593			−1.90474
$659$	19.1631	−	33.1915i	0.746489	−	1.29296i	−0.203007	−	0.979177i	$-0.565072\pi$
$659$	19.1631	−	33.1915i	0.746489	−	1.29296i	0.949496	−	0.313779i	$-0.101595\pi$
$660$	0.943982	+	0.509126i	0.0367445	+	0.0198177i
$661$	6.47622	+	3.73905i	0.251896	+	0.145432i	0.620632	−	0.784102i	$-0.286876\pi$
$661$	6.47622	+	3.73905i	0.251896	+	0.145432i	−0.368736	+	0.929534i	$0.620209\pi$
$662$	−6.21648	−	10.7673i	−0.241610	−	0.418481i
$663$	−2.56285	−	7.79989i	−0.0995328	−	0.302922i
$664$			1.50224i			0.0582982i
$665$	−28.2694	+	28.8032i	−1.09624	+	1.11694i
$666$	−2.21592	+	5.06685i	−0.0858652	+	0.196336i
$667$	0.827708	+	1.43363i	0.0320490	+	0.0555105i
$668$	6.03723	−	3.48560i	0.233588	−	0.134862i
$669$	−25.9616	+	29.0255i	−1.00373	+	1.12219i
$670$	−23.0109	−	6.82878i	−0.888989	−	0.263819i
$671$	−1.22858	−	0.709320i	−0.0474287	−	0.0273830i
$672$	−7.02000	−	1.46793i	−0.270802	−	0.0566266i
$673$	36.1921			1.39510			0.697551	−	0.716535i	$-0.254273\pi$
$673$	36.1921			1.39510			0.697551	+	0.716535i	$0.254273\pi$
$674$	−1.16376	−	0.671895i	−0.0448262	−	0.0258804i
$675$	−9.52613	−	24.1713i	−0.366661	−	0.930355i
$676$	12.2983			0.473011
$677$		−	4.59634i		−	0.176652i	−0.996092	−	0.0883258i	$-0.971848\pi$
$677$		−	4.59634i		−	0.176652i	0.996092	−	0.0883258i	$-0.0281516\pi$
$678$	3.03701	−	3.39543i	0.116636	−	0.130401i
$679$	−23.3005	+	13.4525i	−0.894190	+	0.516261i
$680$	2.94759	+	12.3050i	0.113035	+	0.471874i
$681$	−46.2553	+	15.1984i	−1.77251	+	0.582402i
$682$	−1.33056	+	0.768196i	−0.0509496	+	0.0294158i
$683$		−	20.8899i		−	0.799330i	−0.916661	−	0.399665i	$-0.869126\pi$
$683$		−	20.8899i		−	0.799330i	0.916661	−	0.399665i	$-0.130874\pi$
$684$	−12.1620	−	4.80466i	−0.465027	−	0.183711i
$685$	0.102116	+	0.107717i	0.00390164	+	0.00411564i
$686$	−6.51131	−	11.2779i	−0.248603	−	0.430593i
$687$	12.2350	+	37.2365i	0.466794	+	1.42066i
$688$	9.67160	+	5.58390i	0.368726	+	0.212884i
$689$	6.75422	−	3.89955i	0.257315	−	0.148561i
$690$	0.0228377	+	0.787891i	0.000869415	+	0.0299945i
$691$	−37.5189			−1.42729			−0.713644	−	0.700509i	$-0.752957\pi$
$691$	−37.5189			−1.42729			−0.713644	+	0.700509i	$0.752957\pi$
$692$		−	23.9694i		−	0.911181i
$693$	−2.76957	+	2.04029i	−0.105207	+	0.0775044i
$694$	−20.7407	−	11.9747i	−0.787308	−	0.454552i
$695$	1.81210	+	1.91148i	0.0687367	+	0.0725066i
$696$	−2.88364	+	13.7902i	−0.109304	+	0.522718i
$697$	−16.5219	+	28.6167i	−0.625810	+	1.08393i
$698$	25.5453	−	14.7486i	0.966904	−	0.558242i
$699$	−21.6566	+	24.2125i	−0.819129	+	0.915800i
$700$	9.38046	+	18.4563i	0.354548	+	0.697581i
$701$	14.7634	−	8.52364i	0.557605	−	0.321933i	−0.194579	−	0.980887i	$-0.562334\pi$
$701$	14.7634	−	8.52364i	0.557605	−	0.321933i	0.752184	+	0.658954i	$0.229001\pi$
$702$	2.52344	−	3.54660i	0.0952413	−	0.133858i
$703$	3.76427	−	7.09894i	0.141972	−	0.267742i
$704$		−	0.276925i		−	0.0104370i
$705$	−21.6941	+	40.2235i	−0.817047	+	1.51490i
$706$	25.1662	−	14.5297i	0.947143	−	0.546834i
$707$	7.24177	−	12.5431i	0.272355	−	0.471733i
$708$	−2.10837	−	6.41670i	−0.0792373	−	0.241154i
$709$	8.29143	−	14.3612i	0.311391	−	0.539345i	−0.667273	−	0.744814i	$-0.732538\pi$
$709$	8.29143	−	14.3612i	0.311391	−	0.539345i	0.978664	+	0.205468i	$0.0658717\pi$
$710$	−18.1647	+	17.2202i	−0.681709	+	0.646263i
$711$	−19.4786	+	44.5392i	−0.730506	+	1.67035i
$712$	−5.67592	−	3.27700i	−0.212714	−	0.122811i
$713$	−0.977854	−	0.564564i	−0.0366209	−	0.0211431i
$714$	−39.7236	−	8.30648i	−1.48662	−	0.310862i
$715$	0.376440	−	0.356867i	0.0140781	−	0.0133461i
$716$	−6.51358	+	11.2818i	−0.243424	+	0.421622i
$717$	−15.4875	+	5.08880i	−0.578390	+	0.190045i
$718$	−17.1919	+	29.7773i	−0.641597	+	1.11128i
$719$	22.8964	−	13.2192i	0.853892	−	0.492994i	−0.00807046	−	0.999967i	$-0.502569\pi$
$719$	22.8964	−	13.2192i	0.853892	−	0.492994i	0.861962	+	0.506973i	$0.169236\pi$
$720$	−4.32543	+	5.12744i	−0.161199	+	0.191088i
$721$		−	27.7570i		−	1.03372i
$722$	17.0959	+	8.29038i	0.636243	+	0.308536i
$723$	2.80314	−	13.4053i	0.104250	−	0.498547i
$724$	−13.0547	+	7.53713i	−0.485174	+	0.280115i
$725$	36.2559	−	18.4272i	1.34651	−	0.684369i
$726$	14.1018	+	12.6133i	0.523368	+	0.468122i
$727$	−4.72362	+	2.72718i	−0.175189	+	0.101146i	−0.585031	−	0.811011i	$-0.698917\pi$
$727$	−4.72362	+	2.72718i	−0.175189	+	0.101146i	0.409841	+	0.912157i	$0.365584\pi$
$728$	−1.73427	+	3.00385i	−0.0642765	+	0.111330i
$729$	8.85065	+	25.5082i	0.327802	+	0.944747i
$730$	9.89975	+	10.4427i	0.366406	+	0.386502i
$731$	54.7281	+	31.5973i	2.02419	+	1.16867i
$732$	5.91539	−	6.61350i	0.218639	−	0.244442i
$733$		−	6.23280i		−	0.230214i	−0.993353	−	0.115107i	$-0.963279\pi$
$733$		−	6.23280i		−	0.230214i	0.993353	−	0.115107i	$-0.0367210\pi$
$734$	−10.9862			−0.405508
$735$	−39.2751	+	1.13842i	−1.44869	+	0.0419913i
$736$	0.176252	−	0.101759i	0.00649673	−	0.00375089i
$737$	2.57436	+	1.48631i	0.0948278	+	0.0547489i
$738$	−17.4101	+	1.94623i	−0.640875	+	0.0716418i
$739$	−7.84449	−	13.5871i	−0.288564	−	0.499808i	0.684903	−	0.728634i	$-0.259845\pi$
$739$	−7.84449	−	13.5871i	−0.288564	−	0.499808i	−0.973467	+	0.228826i	$0.926511\pi$
$740$	−2.83587	−	2.99141i	−0.104249	−	0.109966i
$741$	−4.04369	+	4.86271i	−0.148549	+	0.178636i
$742$		−	38.5510i		−	1.41525i
$743$	−17.9419	+	10.3588i	−0.658225	+	0.380026i	−0.791600	−	0.611039i	$-0.790752\pi$
$743$	−17.9419	+	10.3588i	−0.658225	+	0.380026i	0.133375	+	0.991066i	$0.457418\pi$
$744$	−2.99967	−	9.12932i	−0.109973	−	0.334697i
$745$	3.49389	+	14.5855i	0.128006	+	0.534373i
$746$	1.89061	−	1.09154i	0.0692201	−	0.0399643i
$747$	−3.62843	+	2.67301i	−0.132757	+	0.0978002i
$748$		−	1.56702i		−	0.0572958i
$749$	−24.4344			−0.892815
$750$	19.3592	+	0.472306i	0.706896	+	0.0172462i
$751$	−44.2932	−	25.5727i	−1.61628	−	0.933161i	−0.987871	−	0.155279i	$-0.950372\pi$
$751$	−44.2932	−	25.5727i	−1.61628	−	0.933161i	−0.628411	−	0.777881i	$-0.716294\pi$
$752$	11.7999			0.430298
$753$	4.77181	−	22.8200i	0.173895	−	0.831606i
$754$	5.90083	+	3.40685i	0.214896	+	0.124070i
$755$	25.0405	+	7.43110i	0.911319	+	0.270446i
$756$	−8.94546	−	19.5677i	−0.325343	−	0.711671i
$757$	−22.3683	+	12.9143i	−0.812988	+	0.469379i	−0.847993	−	0.530008i	$-0.822189\pi$
$757$	−22.3683	+	12.9143i	−0.812988	+	0.469379i	0.0350041	+	0.999387i	$0.488856\pi$
$758$	4.72385	+	8.18196i	0.171578	+	0.297182i
$759$	0.0199803	−	0.0955504i	0.000725238	−	0.00346826i
$760$	6.82726	−	6.95619i	0.247651	−	0.252327i
$761$			1.34313i			0.0486886i	0.999704	+	0.0243443i	$0.00774979\pi$
$761$			1.34313i			0.0486886i	−0.999704	+	0.0243443i	$0.992250\pi$
$762$	−10.3533	+	3.40184i	−0.375061	+	0.123236i
$763$	−23.2122	−	40.2048i	−0.840340	−	1.45551i
$764$	7.07232	+	4.08321i	0.255868	+	0.147725i
$765$	−24.4760	+	29.0143i	−0.884933	+	1.04901i
$766$	13.2518	−	22.9528i	0.478808	−	0.829319i
$767$	−3.26657			−0.117949
$768$	1.69538	+	0.354516i	0.0611768	+	0.0127925i
$769$	−26.6553	+	46.1683i	−0.961214	+	1.66487i	−0.241753	+	0.970338i	$0.577722\pi$
$769$	−26.6553	+	46.1683i	−0.961214	+	1.66487i	−0.719461	+	0.694533i	$0.755611\pi$
$770$	−0.597293	−	2.49345i	−0.0215249	−	0.0898577i
$771$	−5.02717	+	24.0411i	−0.181049	+	0.865820i
$772$	22.0923			0.795118
$773$	22.3337	+	12.8944i	0.803289	+	0.463779i	0.844620	−	0.535366i	$-0.179826\pi$
$773$	22.3337	+	12.8944i	0.803289	+	0.463779i	−0.0413311	+	0.999146i	$0.513160\pi$
$774$	3.72208	+	33.2960i	0.133787	+	1.19680i
$775$	−15.1319	+	23.2496i	−0.543554	+	0.835152i
$776$	5.62724	−	3.24889i	0.202006	−	0.116628i
$777$	12.5600	−	4.12689i	0.450586	−	0.148051i
$778$	35.1670			1.26080
$779$	25.4374	−	0.917115i	0.911388	−	0.0328591i
$780$	1.70289	+	2.76149i	0.0609731	+	0.0988770i
$781$	2.68451	−	1.54990i	0.0960594	−	0.0554599i
$782$	0.997345	−	0.575817i	0.0356650	−	0.0205912i
$783$	−38.4392	+	17.5727i	−1.37371	+	0.627996i
$784$	5.07253	+	8.78588i	0.181162	+	0.313781i
$785$	0.0693821	+	0.289642i	0.00247635	+	0.0103377i
$786$	0.856514	+	0.179103i	0.0305508	+	0.00638840i
$787$	40.3027			1.43664			0.718318	−	0.695715i	$-0.244912\pi$
$787$	40.3027			1.43664			0.718318	+	0.695715i	$0.244912\pi$
$788$	−13.4561	+	23.3067i	−0.479354	+	0.830266i
$789$	0.000754737	0	0.000843809i	2.68694e−5	0	3.00404e-5i
$790$	−24.9282	−	26.2954i	−0.886905	−	0.935549i
$791$	−10.8904			−0.387217
$792$	0.668871	−	0.492746i	0.0237673	−	0.0175090i
$793$	−2.14565	−	3.71637i	−0.0761941	−	0.131972i
$794$	7.37147	−	12.7678i	0.261604	−	0.453111i
$795$	−31.7371	−	17.1171i	−1.12560	−	0.607080i
$796$	1.85693	+	3.21630i	0.0658173	+	0.113999i
$797$		−	2.02959i		−	0.0718919i	−0.999354	−	0.0359459i	$-0.988556\pi$
$797$		−	2.02959i		−	0.0718919i	0.999354	−	0.0359459i	$-0.0114444\pi$
$798$	10.8222	+	29.3283i	0.383100	+	1.03821i
$799$	66.7713			2.36220
$800$	−2.26545	−	4.45732i	−0.0800958	−	0.157590i
$801$	−2.18436	−	19.5403i	−0.0771804	−	0.690421i
$802$	−17.3261	−	10.0032i	−0.611806	−	0.353226i
$803$	−0.891026	−	1.54330i	−0.0314436	−	0.0544619i
$804$	−12.3951	+	13.8579i	−0.437141	+	0.488731i
$805$	1.36750	−	1.29640i	0.0481981	−	0.0456920i
$806$	−4.64749			−0.163701
$807$	5.92292	−	6.62192i	0.208497	−	0.233102i
$808$	−1.74894	+	3.02926i	−0.0615276	+	0.106569i
$809$			10.3990i			0.365610i	0.983149	+	0.182805i	$0.0585177\pi$
$809$			10.3990i			0.365610i	−0.983149	+	0.182805i	$0.941482\pi$
$810$	−20.0810	−	1.32392i	−0.705575	−	0.0465179i
$811$	−27.5159	−	15.8863i	−0.966213	−	0.557844i	−0.0681337	−	0.997676i	$-0.521704\pi$
$811$	−27.5159	−	15.8863i	−0.966213	−	0.557844i	−0.898080	+	0.439833i	$0.855038\pi$
$812$	29.1679	−	16.8401i	1.02359	−	0.590971i
$813$	4.24599	−	4.74709i	0.148913	−	0.166488i
$814$	0.255242	+	0.442093i	0.00894624	+	0.0154953i
$815$	9.44258	+	2.80221i	0.330759	+	0.0981570i
$816$	9.59355	+	2.00608i	0.335841	+	0.0702268i
$817$	−1.75394	−	48.6477i	−0.0613626	−	1.70197i
$818$	−7.08193			−0.247614
$819$	−10.3412	+	1.15602i	−0.361352	+	0.0403946i
$820$	3.71487	−	12.5180i	0.129729	−	0.437147i
$821$	−24.2301	−	13.9892i	−0.845635	−	0.488227i	0.0135409	−	0.999908i	$-0.495690\pi$
$821$	−24.2301	−	13.9892i	−0.845635	−	0.488227i	−0.859176	+	0.511681i	$0.829023\pi$
$822$	0.109226	−	0.0358889i	0.00380969	−	0.00125177i
$823$	−15.3764	−	8.87756i	−0.535987	−	0.309452i	0.207464	−	0.978243i	$-0.433479\pi$
$823$	−15.3764	−	8.87756i	−0.535987	−	0.309452i	−0.743451	+	0.668790i	$0.766812\pi$
$824$			6.70352i			0.233528i
$825$	−2.31794	−	0.615398i	−0.0807003	−	0.0214254i
$826$	−8.07333	+	13.9834i	−0.280907	+	0.486546i
$827$	33.6861	+	19.4487i	1.17138	+	0.676297i	0.954005	−	0.299791i	$-0.0969170\pi$
$827$	33.6861	+	19.4487i	1.17138	+	0.676297i	0.217376	+	0.976088i	$0.430250\pi$
$828$	0.559397	+	0.244645i	0.0194404	+	0.00850200i
$829$		−	39.6887i		−	1.37845i	−0.724549	−	0.689223i	$-0.757952\pi$
$829$		−	39.6887i		−	1.37845i	0.724549	−	0.689223i	$-0.242048\pi$
$830$	−0.782519	−	3.26669i	−0.0271616	−	0.113389i
$831$	−42.4893	+	13.9609i	−1.47394	+	0.484299i
$832$	0.418840	−	0.725452i	0.0145207	−	0.0251505i
$833$	28.7036	+	49.7161i	0.994521	+	1.72256i
$834$	1.93827	−	0.636866i	0.0671166	−	0.0220529i
$835$	−11.3126	+	10.7244i	−0.391489	+	0.371133i
$836$	−1.02294	+	0.640817i	−0.0353793	+	0.0221631i
$837$	16.7131	−	23.4895i	0.577688	−	0.811916i
$838$	−7.91565	−	13.7103i	−0.273442	−	0.473615i
$839$	−18.2446	−	31.6006i	−0.629875	−	1.09098i	−0.987576	−	0.157139i	$-0.949773\pi$
$839$	−18.2446	−	31.6006i	−0.629875	−	1.09098i	0.357701	−	0.933836i	$-0.383561\pi$
$840$	16.0300	−	0.464642i	0.553087	−	0.0160317i
$841$	−18.5810	−	32.1832i	−0.640724	−	1.10977i
$842$	−5.67808	+	9.83472i	−0.195680	+	0.338927i
$843$	14.5882	+	3.05050i	0.502445	+	0.105065i
$844$		−	1.98957i		−	0.0684837i
$845$	−26.7432	+	6.40620i	−0.919995	+	0.220380i
$846$	20.9961	+	28.5009i	0.721862	+	0.979881i
$847$		−	45.2297i		−	1.55411i
$848$			9.31035i			0.319719i
$849$	19.3278	+	17.2875i	0.663327	+	0.593307i
$850$	−12.8194	−	25.2224i	−0.439701	−	0.865120i
$851$	−0.187583	+	0.324904i	−0.00643027	+	0.0111376i
$852$	6.05209	+	18.4192i	0.207341	+	0.631032i
$853$	−40.1675	+	23.1907i	−1.37531	+	0.794035i	−0.991591	−	0.129415i	$-0.958690\pi$
$853$	−40.1675	+	23.1907i	−1.37531	+	0.794035i	−0.383719	+	0.923450i	$0.625357\pi$
$854$	−21.2119			−0.725856
$855$	28.9497	+	4.11274i	0.990059	+	0.140653i
$856$	5.90110			0.201695
$857$	1.30783	−	0.755079i	0.0446748	−	0.0257930i	−0.477496	−	0.878634i	$-0.658456\pi$
$857$	1.30783	−	0.755079i	0.0446748	−	0.0257930i	0.522171	+	0.852841i	$0.325122\pi$
$858$	−0.125422	−	0.381714i	−0.00428183	−	0.0130315i
$859$	−4.51223	+	7.81542i	−0.153955	+	0.266659i	−0.932678	−	0.360710i	$-0.882535\pi$
$859$	−4.51223	+	7.81542i	−0.153955	+	0.266659i	0.778723	+	0.627368i	$0.215868\pi$
$860$	−23.9400	−	7.10451i	−0.816348	−	0.242262i
$861$	31.2153	+	27.9203i	1.06382	+	0.951521i
$862$			13.4892i			0.459444i
$863$			3.88212i			0.132149i	0.997815	+	0.0660744i	$0.0210475\pi$
$863$			3.88212i			0.132149i	−0.997815	+	0.0660744i	$0.978953\pi$
$864$	2.16039	+	4.72575i	0.0734981	+	0.160773i
$865$	12.4857	+	52.1227i	0.424527	+	1.77222i
$866$		−	14.3952i		−	0.489168i
$867$	25.4649	+	5.32489i	0.864833	+	0.180843i
$868$	−11.4863	+	19.8948i	−0.389870	+	0.675275i
$869$	2.24366	+	3.88613i	0.0761109	+	0.131828i
$870$	−0.912752	−	31.4896i	−0.0309452	−	1.06760i
$871$	4.49599	+	7.78728i	0.152341	+	0.263862i
$872$	5.60593	+	9.70976i	0.189841	+	0.328814i
$873$	17.8600	+	7.81084i	0.604470	+	0.264357i
$874$	−0.783747	−	0.415589i	−0.0265106	−	0.0140575i
$875$	−30.0122	−	35.2477i	−1.01460	−	1.19159i
$876$	10.5890	−	3.47929i	0.357770	−	0.117554i
$877$	−17.1099	−	29.6353i	−0.577762	−	1.00071i	−0.995736	−	0.0922533i	$-0.970593\pi$
$877$	−17.1099	−	29.6353i	−0.577762	−	1.00071i	0.417974	−	0.908459i	$-0.362740\pi$
$878$	11.4450	−	19.8233i	0.386251	−	0.669006i
$879$	16.4483	−	5.40451i	0.554788	−	0.182290i
$880$	0.144251	+	0.602187i	0.00486269	+	0.0202997i
$881$			38.9936i			1.31373i	0.754009	+	0.656864i	$0.228117\pi$
$881$			38.9936i			1.31373i	−0.754009	+	0.656864i	$0.771883\pi$
$882$	−12.1952	+	27.8851i	−0.410633	+	0.938939i
$883$	−9.23516	−	5.33192i	−0.310788	−	0.179434i	0.336491	−	0.941687i	$-0.390760\pi$
$883$	−9.23516	−	5.33192i	−0.310788	−	0.179434i	−0.647279	+	0.762253i	$0.724093\pi$
$884$	2.37006	−	4.10507i	0.0797139	−	0.138068i
$885$	7.92722	+	12.8552i	0.266470	+	0.432122i
$886$			4.45543i			0.149683i
$887$	−3.57716	−	2.06527i	−0.120109	−	0.0693451i	0.438742	−	0.898613i	$-0.355424\pi$
$887$	−3.57716	−	2.06527i	−0.120109	−	0.0693451i	−0.558851	+	0.829268i	$0.688758\pi$
$888$	−3.03333	+	0.996675i	−0.101792	+	0.0334462i
$889$	22.5622	+	13.0263i	0.756712	+	0.436888i
$890$	14.0496	+	4.16939i	0.470942	+	0.139758i
$891$	2.38031	+	0.738790i	0.0797434	+	0.0247504i
$892$	−22.4832			−0.752794
$893$	−27.3055	−	43.5881i	−0.913744	−	1.45862i
$894$	11.3716	+	2.37788i	0.380323	+	0.0795281i
$895$	8.28736	−	27.9259i	0.277016	−	0.933458i
$896$	−2.07033	−	3.58592i	−0.0691649	−	0.119797i
$897$	0.196859	−	0.220091i	0.00657292	−	0.00734863i
$898$	19.9060	−	11.4927i	0.664271	−	0.383517i
$899$	39.0818	+	22.5639i	1.30345	+	0.752549i
$900$	6.73497	−	13.4030i	0.224499	−	0.446766i
$901$			52.6839i			1.75516i
$902$	−0.808555	+	1.40046i	−0.0269219	+	0.0466301i
$903$	53.3962	−	59.6978i	1.77691	−	1.98662i
$904$	2.63010			0.0874759
$905$	24.4620	−	23.1901i	0.813143	−	0.770864i
$906$	13.4884	−	15.0802i	0.448122	−	0.501007i
$907$	12.3433	+	21.3793i	0.409854	+	0.709888i	0.994873	−	0.101132i	$-0.0322463\pi$
$907$	12.3433	+	21.3793i	0.409854	+	0.709888i	−0.585019	+	0.811020i	$0.698913\pi$
$908$	−24.3441	−	14.0551i	−0.807888	−	0.466434i
$909$	−10.4287	+	1.16580i	−0.345898	+	0.0386671i
$910$	2.20655	−	7.43541i	0.0731465	−	0.246481i
$911$	54.4425			1.80376			0.901881	−	0.431985i	$-0.142187\pi$
$911$	54.4425			1.80376			0.901881	+	0.431985i	$0.142187\pi$
$912$	−2.61363	−	7.08300i	−0.0865459	−	0.234542i
$913$			0.416007i			0.0137678i
$914$	−6.58477	−	11.4051i	−0.217805	−	0.377249i
$915$	−9.41831	+	17.4627i	−0.311360	+	0.577299i
$916$	−11.3146	+	19.5975i	−0.373846	+	0.647520i
$917$	−1.04594	−	1.81162i	−0.0345400	−	0.0598250i
$918$	12.2249	+	26.7413i	0.403481	+	0.882594i
$919$	−56.7388			−1.87164			−0.935820	−	0.352478i	$-0.885339\pi$
$919$	−56.7388			−1.87164			−0.935820	+	0.352478i	$0.885339\pi$
$920$	−0.330262	+	0.313090i	−0.0108884	+	0.0103223i
$921$	33.2863	−	37.2146i	1.09682	−	1.22626i
$922$	−7.18219	+	12.4399i	−0.236533	+	0.409687i
$923$	9.37672			0.308639
$924$	−1.94401	−	0.406507i	−0.0639533	−	0.0133731i
$925$	7.72497	+	5.02776i	0.253996	+	0.165312i
$926$	−14.5835	−	25.2593i	−0.479242	−	0.830071i
$927$	−16.1913	+	11.9279i	−0.531794	+	0.391764i
$928$	−7.04425	+	4.06700i	−0.231239	+	0.133506i
$929$	−29.8371	+	17.2265i	−0.978923	+	0.565182i	−0.901945	−	0.431851i	$-0.857861\pi$
$929$	−29.8371	+	17.2265i	−0.978923	+	0.565182i	−0.0769784	+	0.997033i	$0.524527\pi$
$930$	11.2784	+	18.2896i	0.369833	+	0.599740i
$931$	20.7164	−	39.0685i	0.678954	−	1.28042i
$932$	−18.7550			−0.614342
$933$	−31.4000	+	10.3173i	−1.02799	+	0.337772i
$934$	−25.1194	+	14.5027i	−0.821930	+	0.474542i
$935$	0.816262	+	3.40756i	0.0266946	+	0.111439i
$936$	2.49748	−	0.279187i	0.0816328	−	0.00912552i
$937$	−40.1661	−	23.1899i	−1.31217	−	0.757581i	−0.329714	−	0.944081i	$-0.606952\pi$
$937$	−40.1661	−	23.1899i	−1.31217	−	0.757581i	−0.982455	+	0.186500i	$0.940286\pi$
$938$	44.4474			1.45126
$939$	5.19271	−	24.8328i	0.169458	−	0.810387i
$940$	−25.6594	+	6.14659i	−0.836919	+	0.200479i
$941$	−30.0669	+	52.0774i	−0.980153	+	1.69767i	−0.318391	+	0.947959i	$0.603143\pi$
$941$	−30.0669	+	52.0774i	−0.980153	+	1.69767i	−0.661761	+	0.749714i	$0.730191\pi$
$942$	0.225818	+	0.0472202i	0.00735756	+	0.00153852i
$943$	−1.18845			−0.0387012
$944$	1.94977	−	3.37710i	0.0634596	−	0.109915i
$945$	29.6452	+	37.8912i	0.964358	+	1.23260i
$946$	2.67831	+	1.54632i	0.0870793	+	0.0502753i
$947$	−0.0348151	−	0.0603015i	−0.00113134	−	0.00195953i	0.865459	−	0.500979i	$-0.167027\pi$
$947$	−0.0348151	−	0.0603015i	−0.00113134	−	0.00195953i	−0.866591	+	0.499020i	$0.833693\pi$
$948$	−26.6639	+	8.76108i	−0.866002	+	0.284547i
$949$		−	5.39059i		−	0.174986i
$950$	−11.2227	+	18.6829i	−0.364113	+	0.606153i
$951$	−1.14215	+	5.46201i	−0.0370366	+	0.177118i
$952$	−11.7152	−	20.2914i	−0.379693	−	0.657648i
$953$	24.4450	−	14.1133i	0.791851	−	0.457175i	−0.0487631	−	0.998810i	$-0.515528\pi$
$953$	24.4450	−	14.1133i	0.791851	−	0.457175i	0.840614	+	0.541635i	$0.182195\pi$
$954$	−22.4878	+	16.5664i	−0.728068	+	0.536356i
$955$	−17.5061	−	5.19515i	−0.566483	−	0.168111i
$956$	−8.15104	−	4.70600i	−0.263623	−	0.152203i
$957$	−0.798551	+	3.81886i	−0.0258135	+	0.123446i
$958$	26.5092			0.856472
$959$	−0.238028	−	0.137425i	−0.00768631	−	0.00443769i
$960$	−3.87136	+	0.112214i	−0.124948	+	0.00362170i
$961$	0.219173			0.00707008
$962$			1.54418i			0.0497865i
$963$	10.5001	+	14.2532i	0.338362	+	0.459304i
$964$	6.84761	−	3.95347i	0.220547	−	0.127333i
$965$	−48.0407	+	11.5079i	−1.54648	+	0.370452i
$966$	−0.455623	−	1.38666i	−0.0146594	−	0.0446151i
$967$	−3.39153	+	1.95810i	−0.109064	+	0.0629683i	−0.553540	−	0.832823i	$-0.686723\pi$
$967$	−3.39153	+	1.95810i	−0.109064	+	0.0629683i	0.444476	+	0.895791i	$0.353390\pi$
$968$			10.9233i			0.351089i
$969$	−14.7896	−	40.0801i	−0.475110	−	1.28756i
$970$	−10.5443	+	9.99610i	−0.338559	+	0.320955i
$971$	−10.0201	−	17.3553i	−0.321560	−	0.556959i	0.659250	−	0.751924i	$-0.270874\pi$
$971$	−10.0201	−	17.3553i	−0.321560	−	0.556959i	−0.980810	+	0.194965i	$0.937541\pi$
$972$	−7.57024	+	13.6269i	−0.242816	+	0.437082i
$973$	−4.22391	−	2.43868i	−0.135412	−	0.0781804i
$974$	−10.0979	+	5.83002i	−0.323557	+	0.186806i
$975$	−5.14147	−	5.11795i	−0.164659	−	0.163905i
$976$	5.12283			0.163978
$977$			39.0176i			1.24828i	0.781311	+	0.624142i	$0.214551\pi$
$977$			39.0176i			1.24828i	−0.781311	+	0.624142i	$0.785449\pi$
$978$	5.08636	−	5.68663i	0.162644	−	0.181838i
$979$	−1.57180	−	0.907482i	−0.0502351	−	0.0290032i
$980$	−15.6070	−	16.4630i	−0.498549	−	0.525892i
$981$	−13.4776	+	30.8173i	−0.430305	+	0.983922i
$982$	−0.386956	+	0.670228i	−0.0123483	+	0.0213878i
$983$	−24.4818	+	14.1346i	−0.780850	+	0.450824i	−0.836731	−	0.547614i	$-0.815536\pi$
$983$	−24.4818	+	14.1346i	−0.780850	+	0.450824i	0.0558817	+	0.998437i	$0.482203\pi$
$984$	−7.53874	−	6.74296i	−0.240326	−	0.214958i
$985$	17.1205	−	57.6908i	0.545504	−	1.83818i
$986$	−39.8609	+	23.0137i	−1.26943	+	0.732905i
$987$	17.3214	−	82.8352i	0.551347	−	2.63667i
$988$	−3.64899	+	0.131560i	−0.116090	+	0.00418549i
$989$			2.27285i			0.0722724i
$990$	−1.19782	+	1.41992i	−0.0380692	+	0.0451279i
$991$	−34.6905	+	20.0285i	−1.10198	+	0.636228i	−0.936740	−	0.350026i	$-0.886173\pi$
$991$	−34.6905	+	20.0285i	−1.10198	+	0.636228i	−0.165239	+	0.986254i	$0.552839\pi$
$992$	2.77402	−	4.80475i	0.0880753	−	0.152551i
$993$	20.4585	−	6.72214i	0.649230	−	0.213321i
$994$	23.1746	−	40.1396i	0.735054	−	1.27315i
$995$	−5.71337	−	6.02673i	−0.181126	−	0.191060i
$996$	−2.54687	−	0.532568i	−0.0807006	−	0.0168751i
$997$	28.9663	+	16.7237i	0.917373	+	0.529645i	0.882796	−	0.469757i	$-0.155658\pi$
$997$	28.9663	+	16.7237i	0.917373	+	0.529645i	0.0345769	+	0.999402i	$0.488992\pi$
$998$	−9.86443	−	5.69523i	−0.312253	−	0.180279i
$999$	−7.80467	−	5.55311i	−0.246929	−	0.175693i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.n.a.449.8	yes	80
3.2	odd	2	inner	570.2.n.a.449.25	yes	80
5.4	even	2	inner	570.2.n.a.449.33	yes	80
15.14	odd	2	inner	570.2.n.a.449.16	yes	80
19.8	odd	6	inner	570.2.n.a.179.16	yes	80
57.8	even	6	inner	570.2.n.a.179.33	yes	80
95.84	odd	6	inner	570.2.n.a.179.25	yes	80
285.179	even	6	inner	570.2.n.a.179.8	✓	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.n.a.179.8	✓	80	285.179	even	6	inner
570.2.n.a.179.16	yes	80	19.8	odd	6	inner
570.2.n.a.179.25	yes	80	95.84	odd	6	inner
570.2.n.a.179.33	yes	80	57.8	even	6	inner
570.2.n.a.449.8	yes	80	1.1	even	1	trivial
570.2.n.a.449.16	yes	80	15.14	odd	2	inner
570.2.n.a.449.25	yes	80	3.2	odd	2	inner
570.2.n.a.449.33	yes	80	5.4	even	2	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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.540671 - 1.64550i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.636160 + 2.14367i) q^{5} +(1.29099 + 1.15471i) q^{6} -4.14066i q^{7} +1.00000i q^{8} +(-2.41535 + 1.77935i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.540671 - 1.64550i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.636160 + 2.14367i) q^{5} +(1.29099 + 1.15471i) q^{6} -4.14066i q^{7} +1.00000i q^{8} +(-2.41535 + 1.77935i) q^{9} +(-0.520902 - 2.17455i) q^{10} +0.276925i q^{11} +(-1.69538 - 0.354516i) q^{12} +(-0.418840 + 0.725452i) q^{13} +(2.07033 + 3.58592i) q^{14} +(3.87136 - 0.112214i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.82932 - 4.90052i) q^{17} +(1.20208 - 2.74864i) q^{18} +(-2.04202 + 3.85099i) q^{19} +(1.53839 + 1.62276i) q^{20} +(-6.81346 + 2.23873i) q^{21} +(-0.138462 - 0.239824i) q^{22} +(0.101759 - 0.176252i) q^{23} +(1.64550 - 0.540671i) q^{24} +(-4.19060 - 2.72743i) q^{25} -0.837680i q^{26} +(4.23383 + 3.01242i) q^{27} +(-3.58592 - 2.07033i) q^{28} +(-4.06700 + 7.04425i) q^{29} +(-3.29659 + 2.03286i) q^{30} -5.54805i q^{31} +(0.866025 + 0.500000i) q^{32} +(0.455680 - 0.149725i) q^{33} +(4.90052 + 2.82932i) q^{34} +(8.87619 + 2.63412i) q^{35} +(0.333286 + 2.98143i) q^{36} -1.84341 q^{37} +(-0.157053 - 4.35607i) q^{38} +(1.42019 + 0.296971i) q^{39} +(-2.14367 - 0.636160i) q^{40} +(-2.91976 - 5.05717i) q^{41} +(4.78126 - 5.34553i) q^{42} +(-9.67160 + 5.58390i) q^{43} +(0.239824 + 0.138462i) q^{44} +(-2.27778 - 6.30965i) q^{45} +0.203518i q^{46} +(-5.89995 + 10.2190i) q^{47} +(-1.15471 + 1.29099i) q^{48} -10.1451 q^{49} +(4.99288 + 0.266723i) q^{50} +(-6.53409 + 7.30522i) q^{51} +(0.418840 + 0.725452i) q^{52} +(-8.06300 - 4.65518i) q^{53} +(-5.17282 - 0.491917i) q^{54} +(-0.593634 - 0.176169i) q^{55} +4.14066 q^{56} +(7.44088 + 1.27803i) q^{57} -8.13400i q^{58} +(1.94977 + 3.37710i) q^{59} +(1.83850 - 3.40880i) q^{60} +(-2.56141 + 4.43650i) q^{61} +(2.77402 + 4.80475i) q^{62} +(7.36768 + 10.0011i) q^{63} -1.00000 q^{64} +(-1.28868 - 1.35936i) q^{65} +(-0.319768 + 0.357506i) q^{66} +(5.36719 - 9.29624i) q^{67} -5.65864 q^{68} +(-0.345041 - 0.0721505i) q^{69} +(-9.00406 + 2.15688i) q^{70} +(-5.59684 - 9.69401i) q^{71} +(-1.77935 - 2.41535i) q^{72} +(-5.57300 + 3.21757i) q^{73} +(1.59644 - 0.921703i) q^{74} +(-2.22225 + 8.37028i) q^{75} +(2.31405 + 3.69394i) q^{76} +1.14665 q^{77} +(-1.37840 + 0.452909i) q^{78} +(14.0332 - 8.10205i) q^{79} +(2.17455 - 0.520902i) q^{80} +(2.66783 - 8.59550i) q^{81} +(5.05717 + 2.91976i) q^{82} +1.50224 q^{83} +(-1.46793 + 7.02000i) q^{84} +(12.3050 - 2.94759i) q^{85} +(5.58390 - 9.67160i) q^{86} +(13.7902 + 2.88364i) q^{87} -0.276925 q^{88} +(-3.27700 + 5.67592i) q^{89} +(5.12744 + 4.32543i) q^{90} +(3.00385 + 1.73427i) q^{91} +(-0.101759 - 0.176252i) q^{92} +(-9.12932 + 2.99967i) q^{93} -11.7999i q^{94} +(-6.95619 - 6.82726i) q^{95} +(0.354516 - 1.69538i) q^{96} +(-3.24889 - 5.62724i) q^{97} +(8.78588 - 5.07253i) q^{98} +(-0.492746 - 0.668871i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 40 q^{4}+O(q^{10}) \) 80 * q + 40 * q^4	\( 80 q + 40 q^{4} + 30 q^{15} - 40 q^{16} + 8 q^{19} + 8 q^{25} - 4 q^{30} + 48 q^{39} + 12 q^{45} - 128 q^{49} - 36 q^{54} + 12 q^{55} + 30 q^{60} - 24 q^{61} - 80 q^{64} + 4 q^{66} + 36 q^{70} + 16 q^{76} + 24 q^{79} + 32 q^{81} - 8 q^{85} - 54 q^{90} + 24 q^{91} - 60 q^{99}+O(q^{100}) \) 80 * q + 40 * q^4 + 30 * q^15 - 40 * q^16 + 8 * q^19 + 8 * q^25 - 4 * q^30 + 48 * q^39 + 12 * q^45 - 128 * q^49 - 36 * q^54 + 12 * q^55 + 30 * q^60 - 24 * q^61 - 80 * q^64 + 4 * q^66 + 36 * q^70 + 16 * q^76 + 24 * q^79 + 32 * q^81 - 8 * q^85 - 54 * q^90 + 24 * q^91 - 60 * q^99

Introduction

L-functions

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