LMFDB - Embedded newform 570.2.n.a.179.16

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			179.16
Character	$\chi$	$=$	570.179
Dual form			570.2.n.a.449.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(1.15471 - 1.29099i) q^{3} +(0.500000 + 0.866025i) q^{4} +(2.17455 - 0.520902i) q^{5} +(-1.64550 + 0.540671i) q^{6} -4.14066i q^{7} -1.00000i q^{8} +(-0.333286 - 2.98143i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(1.15471 - 1.29099i) q^{3} +(0.500000 + 0.866025i) q^{4} +(2.17455 - 0.520902i) q^{5} +(-1.64550 + 0.540671i) q^{6} -4.14066i q^{7} -1.00000i q^{8} +(-0.333286 - 2.98143i) q^{9} +(-2.14367 - 0.636160i) q^{10} +0.276925i q^{11} +(1.69538 + 0.354516i) q^{12} +(0.418840 + 0.725452i) q^{13} +(-2.07033 + 3.58592i) q^{14} +(1.83850 - 3.40880i) 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} +(-5.34553 - 4.78126i) q^{21} +(0.138462 - 0.239824i) q^{22} +(0.101759 + 0.176252i) q^{23} +(-1.29099 - 1.15471i) q^{24} +(4.45732 - 2.26545i) 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} +(0.357506 + 0.319768i) q^{33} +(4.90052 - 2.82932i) q^{34} +(-2.15688 - 9.00406i) q^{35} +(2.41535 - 1.77935i) q^{36} +1.84341 q^{37} +(-0.157053 + 4.35607i) q^{38} +(1.42019 + 0.296971i) q^{39} +(-0.520902 - 2.17455i) q^{40} +(2.91976 - 5.05717i) q^{41} +(2.23873 + 6.81346i) 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} +(0.540671 + 1.64550i) q^{48} -10.1451 q^{49} +(-4.99288 - 0.266723i) q^{50} +(3.05946 + 9.31129i) q^{51} +(-0.418840 + 0.725452i) q^{52} +(-8.06300 + 4.65518i) q^{53} +(2.16039 + 4.72575i) q^{54} +(0.144251 + 0.602187i) q^{55} -4.14066 q^{56} +(-7.32952 - 1.81056i) q^{57} -8.13400i q^{58} +(-1.94977 + 3.37710i) q^{59} +(3.87136 - 0.112214i) q^{60} +(-2.56141 - 4.43650i) q^{61} +(2.77402 - 4.80475i) q^{62} +(-12.3451 + 1.38003i) q^{63} -1.00000 q^{64} +(1.28868 + 1.35936i) q^{65} +(-0.149725 - 0.455680i) q^{66} +(-5.36719 - 9.29624i) q^{67} -5.65864 q^{68} +(0.345041 + 0.0721505i) q^{69} +(-2.63412 + 8.87619i) q^{70} +(5.59684 - 9.69401i) q^{71} +(-2.98143 + 0.333286i) 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} +(-1.08143 - 0.967278i) q^{78} +(14.0332 + 8.10205i) q^{79} +(-0.636160 + 2.14367i) q^{80} +(-8.77784 + 1.98734i) q^{81} +(-5.05717 + 2.91976i) q^{82} +1.50224 q^{83} +(1.46793 - 7.02000i) q^{84} +(-3.59980 + 12.1302i) q^{85} +(-5.58390 - 9.67160i) q^{86} +(13.7902 + 2.88364i) q^{87} +0.276925 q^{88} +(3.27700 + 5.67592i) q^{89} +(-1.18221 + 6.60321i) q^{90} +(3.00385 - 1.73427i) q^{91} +(-0.101759 + 0.176252i) q^{92} +(7.16245 + 6.40639i) q^{93} +11.7999i q^{94} +(-6.44646 - 7.31048i) q^{95} +(0.354516 - 1.69538i) q^{96} +(3.24889 - 5.62724i) q^{97} +(8.78588 + 5.07253i) q^{98} +(0.825632 - 0.0922953i) 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 $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

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

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
$3$	1.15471	−	1.29099i	0.666673	−	0.745351i
$3$	1.15471	−	1.29099i	0.666673	−	0.745351i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	2.17455	−	0.520902i	0.972488	−	0.232954i
$5$	2.17455	−	0.520902i	0.972488	−	0.232954i
$6$	−1.64550	+	0.540671i	−0.671773	+	0.220728i
$7$		−	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
$9$	−0.333286	−	2.98143i	−0.111095	−	0.993810i
$10$	−2.14367	−	0.636160i	−0.677886	−	0.201172i
$11$			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	$-0.129606\pi$
$13$	0.418840	+	0.725452i	0.116165	+	0.201204i	−0.802080	+	0.597217i	$0.796273\pi$
$14$	−2.07033	+	3.58592i	−0.553319	+	0.958376i
$15$	1.83850	−	3.40880i	0.474698	−	0.880149i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.82932	+	4.90052i	−0.686210	+	1.18855i	0.286844	+	0.957977i	$0.407394\pi$
$17$	−2.82932	+	4.90052i	−0.686210	+	1.18855i	−0.973055	+	0.230574i	$0.925940\pi$
$18$	−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
$21$	−5.34553	−	4.78126i	−1.16649	−	1.04336i
$22$	0.138462	−	0.239824i	0.0295203	−	0.0511307i
$23$	0.101759	+	0.176252i	0.0212182	+	0.0367511i	0.876440	−	0.481512i	$-0.159912\pi$
$23$	0.101759	+	0.176252i	0.0212182	+	0.0367511i	−0.855221	+	0.518263i	$0.826579\pi$
$24$	−1.29099	−	1.15471i	−0.263521	−	0.235704i
$25$	4.45732	−	2.26545i	0.891465	−	0.453090i
$26$		−	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	0.945263	+	0.326309i	$0.105805\pi$
$29$	4.06700	+	7.04425i	0.755223	+	1.30808i	−0.190040	+	0.981776i	$0.560862\pi$
$30$	−3.29659	+	2.03286i	−0.601872	+	0.371148i
$31$			5.54805i			0.996459i	0.867045	+	0.498229i	$0.166016\pi$
$31$			5.54805i			0.996459i	−0.867045	+	0.498229i	$0.833984\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	0.357506	+	0.319768i	0.0622338	+	0.0556645i
$34$	4.90052	−	2.82932i	0.840433	−	0.485224i
$35$	−2.15688	−	9.00406i	−0.364579	−	1.52196i
$36$	2.41535	−	1.77935i	0.402558	−	0.296558i
$37$	1.84341			0.303054			0.151527	−	0.988453i	$-0.451581\pi$
$37$	1.84341			0.303054			0.151527	+	0.988453i	$0.451581\pi$
$38$	−0.157053	+	4.35607i	−0.0254774	+	0.706648i
$39$	1.42019	+	0.296971i	0.227412	+	0.0475534i
$40$	−0.520902	−	2.17455i	−0.0823618	−	0.343826i
$41$	2.91976	−	5.05717i	0.455990	−	0.789798i	−0.542755	−	0.839891i	$-0.682619\pi$
$41$	2.91976	−	5.05717i	0.455990	−	0.789798i	0.998745	+	0.0500936i	$0.0159520\pi$
$42$	2.23873	+	6.81346i	0.345444	+	1.05134i
$43$	9.67160	+	5.58390i	1.47491	+	0.851537i	0.999600	−	0.0282839i	$-0.00900424\pi$
$43$	9.67160	+	5.58390i	1.47491	+	0.851537i	0.475305	+	0.879821i	$0.342338\pi$
$44$	−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	−0.871355	−	0.490654i	$-0.836758\pi$
$47$	−5.89995	−	10.2190i	−0.860596	−	1.49060i	0.0107588	−	0.999942i	$-0.496575\pi$
$48$	0.540671	+	1.64550i	0.0780391	+	0.237508i
$49$	−10.1451			−1.44929
$50$	−4.99288	−	0.266723i	−0.706100	−	0.0377203i
$51$	3.05946	+	9.31129i	0.428410	+	1.30384i
$52$	−0.418840	+	0.725452i	−0.0580827	+	0.100602i
$53$	−8.06300	+	4.65518i	−1.10754	+	0.639438i	−0.938191	−	0.346119i	$-0.887499\pi$
$53$	−8.06300	+	4.65518i	−1.10754	+	0.639438i	−0.169348	+	0.985556i	$0.554166\pi$
$54$	2.16039	+	4.72575i	0.293992	+	0.643093i
$55$	0.144251	+	0.602187i	0.0194508	+	0.0811989i
$56$	−4.14066			−0.553319
$57$	−7.32952	−	1.81056i	−0.970819	−	0.239815i
$58$		−	8.13400i		−	1.06805i
$59$	−1.94977	+	3.37710i	−0.253838	+	0.439661i	−0.964579	−	0.263793i	$-0.915026\pi$
$59$	−1.94977	+	3.37710i	−0.253838	+	0.439661i	0.710741	+	0.703454i	$0.248360\pi$
$60$	3.87136	−	0.112214i	0.499790	−	0.0144868i
$61$	−2.56141	−	4.43650i	−0.327956	−	0.568036i	0.654151	−	0.756364i	$-0.273026\pi$
$61$	−2.56141	−	4.43650i	−0.327956	−	0.568036i	−0.982106	+	0.188329i	$0.939693\pi$
$62$	2.77402	−	4.80475i	0.352301	−	0.610204i
$63$	−12.3451	+	1.38003i	−1.55533	+	0.173867i
$64$	−1.00000			−0.125000
$65$	1.28868	+	1.35936i	0.159841	+	0.168607i
$66$	−0.149725	−	0.455680i	−0.0184299	−	0.0560904i
$67$	−5.36719	−	9.29624i	−0.655706	−	1.13572i	−0.981716	−	0.190350i	$-0.939038\pi$
$67$	−5.36719	−	9.29624i	−0.655706	−	1.13572i	0.326010	−	0.945366i	$-0.394296\pi$
$68$	−5.65864			−0.686210
$69$	0.345041	+	0.0721505i	0.0415380	+	0.00868589i
$70$	−2.63412	+	8.87619i	−0.314838	+	1.06091i
$71$	5.59684	−	9.69401i	0.664223	−	1.15047i	−0.315273	−	0.949001i	$-0.602096\pi$
$71$	5.59684	−	9.69401i	0.664223	−	1.15047i	0.979495	−	0.201466i	$-0.0645706\pi$
$72$	−2.98143	+	0.333286i	−0.351365	+	0.0392782i
$73$	5.57300	+	3.21757i	0.652270	+	0.376588i	0.789325	−	0.613975i	$-0.210431\pi$
$73$	5.57300	+	3.21757i	0.652270	+	0.376588i	−0.137055	+	0.990563i	$0.543764\pi$
$74$	−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
$78$	−1.08143	−	0.967278i	−0.122448	−	0.109523i
$79$	14.0332	+	8.10205i	1.57885	+	0.911552i	0.995020	+	0.0996789i	$0.0317816\pi$
$79$	14.0332	+	8.10205i	1.57885	+	0.911552i	0.583834	+	0.811873i	$0.301552\pi$
$80$	−0.636160	+	2.14367i	−0.0711249	+	0.239669i
$81$	−8.77784	+	1.98734i	−0.975316	+	0.220815i
$82$	−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
$85$	−3.59980	+	12.1302i	−0.390453	+	1.31571i
$86$	−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	$-0.0537446\pi$
$89$	3.27700	+	5.67592i	0.347361	+	0.601647i	−0.638419	+	0.769689i	$0.720411\pi$
$90$	−1.18221	+	6.60321i	−0.124616	+	0.696039i
$91$	3.00385	−	1.73427i	0.314889	−	0.181801i
$92$	−0.101759	+	0.176252i	−0.0106091	+	0.0183755i
$93$	7.16245	+	6.40639i	0.742711	+	0.664312i
$94$			11.7999i			1.21707i
$95$	−6.44646	−	7.31048i	−0.661393	−	0.750039i
$96$	0.354516	−	1.69538i	0.0361827	−	0.173034i
$97$	3.24889	−	5.62724i	0.329874	−	0.571359i	−0.652612	−	0.757692i	$-0.726327\pi$
$97$	3.24889	−	5.62724i	0.329874	−	0.571359i	0.982487	+	0.186333i	$0.0596603\pi$
$98$	8.78588	+	5.07253i	0.887508	+	0.512403i
$99$	0.825632	−	0.0922953i	0.0829792	−	0.00927603i
$100$	4.19060	+	2.72743i	0.419060	+	0.272743i
$101$	−3.02926	+	1.74894i	−0.301422	+	0.174026i	−0.643082	−	0.765798i	$-0.722344\pi$
$101$	−3.02926	+	1.74894i	−0.301422	+	0.174026i	0.341659	+	0.939824i	$0.389011\pi$
$102$	2.00608	−	9.59355i	0.198631	−	0.949903i
$103$	−6.70352			−0.660517			−0.330259	−	0.943890i	$-0.607136\pi$
$103$	−6.70352			−0.660517			−0.330259	+	0.943890i	$0.607136\pi$
$104$	0.725452	−	0.418840i	0.0711364	−	0.0410706i
$105$	−14.1147	−	7.61259i	−1.37745	−	0.742913i
$106$	9.31035			0.904302
$107$			5.90110i			0.570481i	0.958456	+	0.285240i	$0.0920734\pi$
$107$			5.90110i			0.570481i	−0.958456	+	0.285240i	$0.907927\pi$
$108$	0.491917	−	5.17282i	0.0473348	−	0.497754i
$109$	9.70976	+	5.60593i	0.930026	+	0.536951i	0.886820	−	0.462115i	$-0.152909\pi$
$109$	9.70976	+	5.60593i	0.930026	+	0.536951i	0.0432062	+	0.999066i	$0.486243\pi$
$110$	0.176169	−	0.593634i	0.0167970	−	0.0566008i
$111$	2.12860	−	2.37981i	0.202038	−	0.225881i
$112$	3.58592	+	2.07033i	0.338837	+	0.195628i
$113$			2.63010i			0.247419i	0.992318	+	0.123710i	$0.0394791\pi$
$113$			2.63010i			0.247419i	−0.992318	+	0.123710i	$0.960521\pi$
$114$	5.44227	+	5.23275i	0.509715	+	0.490092i
$115$	0.313090	+	0.330262i	0.0291958	+	0.0307971i
$116$	−4.06700	+	7.04425i	−0.377612	+	0.654042i
$117$	2.02329	−	1.49053i	0.187053	−	0.137799i
$118$	3.37710	−	1.94977i	0.310887	−	0.179491i
$119$	20.2914	+	11.7152i	1.86011	+	1.07393i
$120$	−3.40880	−	1.83850i	−0.311180	−	0.167831i
$121$	10.9233			0.993028
$122$			5.12283i			0.463799i
$123$	−3.15726	−	9.60894i	−0.284680	−	0.866409i
$124$	−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	$-0.0766115\pi$
$127$	3.14595	+	5.44894i	0.279158	+	0.483515i	−0.692018	+	0.721880i	$0.743278\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	18.3766	−	6.03810i	1.61797	−	0.531625i
$130$	−0.436349	−	1.82158i	−0.0382703	−	0.159763i
$131$	−0.437520	−	0.252602i	−0.0382263	−	0.0220700i	0.480765	−	0.876849i	$-0.340359\pi$
$131$	−0.437520	−	0.252602i	−0.0382263	−	0.0220700i	−0.518991	+	0.854779i	$0.673692\pi$
$132$	−0.0981744	+	0.469493i	−0.00854498	+	0.0408642i
$133$	−15.9456	+	8.45532i	−1.38266	+	0.733169i
$134$			10.7344i			0.927309i
$135$	−10.7758	−	4.34525i	−0.927437	−	0.373979i
$136$	4.90052	+	2.82932i	0.420216	+	0.242612i
$137$	0.0331892	+	0.0574854i	0.00283555	+	0.00491131i	0.867440	−	0.497542i	$-0.165764\pi$
$137$	0.0331892	+	0.0574854i	0.00283555	+	0.00491131i	−0.864604	+	0.502454i	$0.832431\pi$
$138$	−0.262739	−	0.235005i	−0.0223658	−	0.0200049i
$139$	0.588959	+	1.02011i	0.0499548	+	0.0865243i	0.889922	−	0.456114i	$-0.150759\pi$
$139$	0.588959	+	1.02011i	0.0499548	+	0.0865243i	−0.839967	+	0.542638i	$0.817426\pi$
$140$	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
$147$	−11.7146	+	13.0971i	−0.966205	+	1.08023i
$148$	0.921703	+	1.59644i	0.0757635	+	0.131226i
$149$	−5.80877	−	3.35370i	−0.475873	−	0.274745i	0.242822	−	0.970071i	$-0.421927\pi$
$149$	−5.80877	−	3.35370i	−0.475873	−	0.274745i	−0.718695	+	0.695325i	$0.755260\pi$
$150$	−6.10967	+	6.13775i	−0.498852	+	0.501145i
$151$			11.6812i			0.950601i	0.879823	+	0.475301i	$0.157661\pi$
$151$			11.6812i			0.950601i	−0.879823	+	0.475301i	$0.842339\pi$
$152$	−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
$155$	2.88999	+	12.0645i	0.232129	+	0.969044i
$156$	0.452909	+	1.37840i	0.0362618	+	0.110361i
$157$	−0.115351	−	0.0665981i	−0.00920603	−	0.00531511i	0.495390	−	0.868671i	$-0.335025\pi$
$157$	−0.115351	−	0.0665981i	−0.00920603	−	0.00531511i	−0.504596	+	0.863356i	$0.668359\pi$
$158$	−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
$162$	8.59550	+	2.66783i	0.675326	+	0.209605i
$163$		−	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
$165$	0.943982	+	0.509126i	0.0734889	+	0.0396354i
$166$	−1.30098	−	0.751119i	−0.100975	−	0.0582982i
$167$	6.03723	−	3.48560i	0.467175	−	0.269724i	−0.247881	−	0.968790i	$-0.579734\pi$
$167$	6.03723	−	3.48560i	0.467175	−	0.269724i	0.715056	+	0.699067i	$0.246401\pi$
$168$	−4.78126	+	5.34553i	−0.368882	+	0.412417i
$169$	6.14915	−	10.6506i	0.473011	−	0.819279i
$170$	9.18263	−	8.70518i	0.704275	−	0.667657i
$171$	−10.8009	+	7.37163i	−0.825964	+	0.563723i
$172$			11.1678i			0.851537i
$173$	20.7581	+	11.9847i	1.57821	+	0.911181i	0.995109	+	0.0987817i	$0.0314946\pi$
$173$	20.7581	+	11.9847i	1.57821	+	0.911181i	0.583102	+	0.812399i	$0.301839\pi$
$174$	−10.5009	−	9.39242i	−0.796070	−	0.712038i
$175$	−9.38046	−	18.4563i	−0.709096	−	1.39516i
$176$	−0.239824	−	0.138462i	−0.0180774	−	0.0104370i
$177$	2.10837	+	6.41670i	0.158475	+	0.482309i
$178$		−	6.55399i		−	0.491242i
$179$	13.0272			0.973695			0.486848	−	0.873487i	$-0.338147\pi$
$179$	13.0272			0.973695			0.486848	+	0.873487i	$0.338147\pi$
$180$	4.32543	−	5.12744i	0.322399	−	0.382177i
$181$	−13.0547	+	7.53713i	−0.970347	+	0.560230i	−0.899342	−	0.437246i	$-0.855954\pi$
$181$	−13.0547	+	7.53713i	−0.970347	+	0.560230i	−0.0710052	+	0.997476i	$0.522621\pi$
$182$	−3.46855			−0.257106
$183$	−8.68515	−	1.81613i	−0.642025	−	0.134252i
$184$	0.176252	−	0.101759i	0.0129935	−	0.00750178i
$185$	4.00857	−	0.960233i	0.294716	−	0.0705977i
$186$	−2.99967	−	9.12932i	−0.219946	−	0.669394i
$187$	−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
$190$	1.92756	+	9.55429i	0.139840	+	0.693141i
$191$			8.16641i			0.590901i	0.955358	+	0.295450i	$0.0954697\pi$
$191$			8.16641i			0.590901i	−0.955358	+	0.295450i	$0.904530\pi$
$192$	−1.15471	+	1.29099i	−0.0833341	+	0.0931688i
$193$	−11.0461	+	19.1325i	−0.795118	+	1.37718i	0.127646	+	0.991820i	$0.459258\pi$
$193$	−11.0461	+	19.1325i	−0.795118	+	1.37718i	−0.922764	+	0.385365i	$0.874076\pi$
$194$	−5.62724	+	3.24889i	−0.404012	+	0.233256i
$195$	3.24296	−	0.0939998i	0.232233	−	0.00673146i
$196$	−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	0.792672	−	0.609648i	$-0.208689\pi$
$199$	−1.85693	−	3.21630i	−0.131635	−	0.227998i	−0.924307	+	0.381650i	$0.875356\pi$
$200$	−2.26545	−	4.45732i	−0.160192	−	0.315180i
$201$	−18.1989	−	3.80551i	−1.28365	−	0.268420i
$202$	3.49788			0.246110
$203$	29.1679	−	16.8401i	2.04718	−	1.18194i
$204$	−6.53409	+	7.30522i	−0.457478	+	0.511467i
$205$	3.71487	−	12.5180i	0.259458	−	0.874293i
$206$	5.80542	+	3.35176i	0.404483	+	0.233528i
$207$	0.491568	−	0.362130i	0.0341663	−	0.0251698i
$208$	−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	0.558135	−	0.829750i	$-0.311517\pi$
$211$	1.72302	+	0.994784i	0.118617	+	0.0684837i	−0.439517	+	0.898234i	$0.644851\pi$
$212$	−8.06300	−	4.65518i	−0.553769	−	0.319719i
$213$	−6.05209	−	18.4192i	−0.414683	−	1.26206i
$214$	2.95055	−	5.11050i	0.201695	−	0.349347i
$215$	23.9400	+	7.10451i	1.63270	+	0.484524i
$216$	−3.01242	+	4.23383i	−0.204969	+	0.288076i
$217$	22.9726			1.55948
$218$	−5.60593	−	9.70976i	−0.379682	−	0.657628i
$219$	10.5890	−	3.47929i	0.715541	−	0.235109i
$220$	−0.449384	+	0.426018i	−0.0302974	+	0.0287221i
$221$	−4.74013			−0.318855
$222$	−3.03333	+	0.996675i	−0.203584	+	0.0668925i
$223$	11.2416	−	19.4711i	0.752794	−	1.30388i	−0.193669	−	0.981067i	$-0.562039\pi$
$223$	11.2416	−	19.4711i	0.752794	−	1.30388i	0.946463	−	0.322811i	$-0.104628\pi$
$224$	−2.07033	−	3.58592i	−0.138330	−	0.239594i
$225$	−8.23985	−	12.5341i	−0.549323	−	0.835610i
$226$	1.31505	−	2.27774i	0.0874759	−	0.151513i
$227$			28.1102i			1.86574i	0.360216	+	0.932869i	$0.382703\pi$
$227$			28.1102i			1.86574i	−0.360216	+	0.932869i	$0.617297\pi$
$228$	−2.09677	−	7.25283i	−0.138862	−	0.480331i
$229$	−22.6293			−1.49538			−0.747692	−	0.664046i	$-0.768838\pi$
$229$	−22.6293			−1.49538			−0.747692	+	0.664046i	$0.768838\pi$
$230$	−0.106013	−	0.442560i	−0.00699028	−	0.0291815i
$231$	1.32405	−	1.48031i	0.0871162	−	0.0973973i
$232$	7.04425	−	4.06700i	0.462478	−	0.267012i
$233$	−9.37752	+	16.2423i	−0.614342	+	1.06407i	0.376158	+	0.926556i	$0.377245\pi$
$233$	−9.37752	+	16.2423i	−0.614342	+	1.06407i	−0.990500	+	0.137515i	$0.956088\pi$
$234$	−2.49748	+	0.279187i	−0.163266	+	0.0182510i
$235$	−18.1528	−	19.1484i	−1.18416	−	1.24911i
$236$	−3.89954			−0.253838
$237$	26.6639	−	8.76108i	1.73200	−	0.569093i
$238$	−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	−0.262968	−	0.964805i	$-0.584701\pi$
$241$	6.84761	−	3.95347i	0.441093	−	0.254665i	0.704061	+	0.710139i	$0.251368\pi$
$242$	−9.45987	−	5.46166i	−0.608103	−	0.351089i
$243$	−7.57024	+	13.6269i	−0.485631	+	0.874164i
$244$	2.56141	−	4.43650i	0.163978	−	0.284018i
$245$	−22.0609	+	5.28458i	−1.40942	+	0.337619i
$246$	−2.07020	+	9.90022i	−0.131991	+	0.631215i
$247$	1.93843	−	3.09434i	0.123339	−	0.196888i
$248$	5.54805			0.352301
$249$	1.73465	−	1.93937i	0.109929	−	0.122902i
$250$	−10.9962	+	2.02080i	−0.695461	+	0.127806i
$251$	−11.6568	+	6.73004i	−0.735769	+	0.424796i	−0.820529	−	0.571605i	$-0.806321\pi$
$251$	−11.6568	+	6.73004i	−0.735769	+	0.424796i	0.0847602	+	0.996401i	$0.472988\pi$
$252$	−7.36768	−	10.0011i	−0.464120	−	0.630013i
$253$	−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	−0.831460	−	0.555584i	$-0.812495\pi$
$257$	−12.2806	+	7.09019i	−0.766040	+	0.442274i	0.0654199	+	0.997858i	$0.479161\pi$
$258$	−18.9337	−	3.95917i	−1.17876	−	0.246487i
$259$		−	7.63291i		−	0.474286i
$260$	−0.532899	+	1.79571i	−0.0330490	+	0.111365i
$261$	19.6465	−	14.4732i	1.21609	−	0.895871i
$262$	0.252602	+	0.437520i	0.0156058	+	0.0270301i
$263$	0.000326808	0	0.000566048i	2.01518e−5	0	3.49040e-5i	−0.866015	−	0.500017i	$-0.833327\pi$
$263$	0.000326808	0	0.000566048i	2.01518e−5	0	3.49040e-5i	0.866035	+	0.499983i	$0.166660\pi$
$264$	0.319768	−	0.357506i	0.0196804	−	0.0220030i
$265$	−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	$-0.883313\pi$
$269$	−2.56468	+	4.44215i	−0.156371	+	0.270843i	0.777186	+	0.629270i	$0.216646\pi$
$270$	7.15953	+	9.15102i	0.435715	+	0.556913i
$271$	1.83855	−	3.18447i	0.111684	−	0.193443i	−0.804765	−	0.593593i	$-0.797709\pi$
$271$	1.83855	−	3.18447i	0.111684	−	0.193443i	0.916449	+	0.400151i	$0.131042\pi$
$272$	−2.82932	−	4.90052i	−0.171553	−	0.297138i
$273$	1.22966	−	5.88051i	0.0744222	−	0.355905i
$274$		−	0.0663784i		−	0.00401007i
$275$	0.627360	+	1.23434i	0.0378312	+	0.0744337i
$276$	0.110036	+	0.334889i	0.00662341	+	0.0201580i
$277$		−	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
$279$	16.5411	−	1.84909i	0.990290	−	0.110702i
$280$	−9.00406	+	2.15688i	−0.538096	+	0.128898i
$281$	4.30234	+	7.45188i	0.256656	+	0.444542i	0.965344	−	0.260980i	$-0.0840458\pi$
$281$	4.30234	+	7.45188i	0.256656	+	0.444542i	−0.708688	+	0.705522i	$0.750712\pi$
$282$	15.2335	+	13.6255i	0.907141	+	0.811385i
$283$	12.9655	+	7.48566i	0.770722	+	0.444976i	0.833132	−	0.553074i	$-0.186545\pi$
$283$	12.9655	+	7.48566i	0.770722	+	0.444976i	−0.0624104	+	0.998051i	$0.519879\pi$
$284$	11.1937			0.664223
$285$	−16.8815	−	0.119195i	−0.999975	−	0.00706053i
$286$	0.231975			0.0137169
$287$	−20.9400	−	12.0897i	−1.23605	−	0.713634i
$288$	−1.77935	−	2.41535i	−0.104849	−	0.142326i
$289$	−7.51008	−	13.0078i	−0.441769	−	0.765167i
$290$	−4.23702	−	17.6878i	−0.248806	−	1.03866i
$291$	−3.51316	−	10.6921i	−0.205945	−	0.626782i
$292$			6.43514i			0.376588i
$293$		−	9.99594i		−	0.583969i	−0.956423	−	0.291984i	$-0.905684\pi$
$293$		−	9.99594i		−	0.583969i	0.956423	−	0.291984i	$-0.0943155\pi$
$294$	16.6937	−	5.48514i	0.973597	−	0.319900i
$295$	−2.48073	+	8.35931i	−0.144434	+	0.486698i
$296$		−	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
$300$	8.36000	−	2.26061i	0.482665	−	0.130516i
$301$	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
$306$	−10.0687	−	13.6676i	−0.575589	−	0.781324i
$307$	−14.4133	+	24.9645i	−0.822608	+	1.42480i	0.0811250	+	0.996704i	$0.474149\pi$
$307$	−14.4133	+	24.9645i	−0.822608	+	1.42480i	−0.903733	+	0.428096i	$0.859185\pi$
$308$	0.573326	+	0.993030i	0.0326683	+	0.0565831i
$309$	−7.74063	+	8.65415i	−0.440349	+	0.492317i
$310$	3.52945	−	11.8932i	0.200459	−	0.675486i
$311$		−	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	$-0.802520\pi$
$313$	−12.6849	+	7.32365i	−0.716995	+	0.413957i	0.0966505	+	0.995318i	$0.469187\pi$
$314$	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	−0.576303	−	0.817236i	$-0.695505\pi$
$317$	−2.79008	+	1.61085i	−0.156706	+	0.0904744i	0.419596	+	0.907711i	$0.362172\pi$
$318$	10.7508	−	12.0195i	0.602873	−	0.674022i
$319$	−1.95073	+	1.12625i	−0.109220	+	0.0630581i
$320$	−2.17455	+	0.520902i	−0.121561	+	0.0291193i
$321$	7.61823	+	6.81406i	0.425208	+	0.380324i
$322$	−0.842699			−0.0469618
$323$	24.6494	+	0.888707i	1.37153	+	0.0494490i
$324$	−6.11001	−	6.60816i	−0.339445	−	0.367120i
$325$	3.51038	+	2.28471i	0.194721	+	0.126733i
$326$	−2.20244	+	3.81474i	−0.121982	+	0.211279i
$327$	18.4491	−	6.06193i	1.02024	−	0.335225i
$328$	−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	$-0.889001\pi$
$331$		−	12.4330i		−	0.683377i	0.939813	−	0.341689i	$-0.110999\pi$
$332$	0.751119	+	1.30098i	0.0412230	+	0.0714004i
$333$	−0.614382	−	5.49598i	−0.0336679	−	0.301178i
$334$	−6.97119			−0.381447
$335$	−16.5136	−	17.4194i	−0.902236	−	0.951721i
$336$	6.81346	−	2.23873i	0.371705	−	0.122133i
$337$	−0.671895	+	1.16376i	−0.0366005	+	0.0633939i	−0.883745	−	0.467968i	$-0.844986\pi$
$337$	−0.671895	+	1.16376i	−0.0366005	+	0.0633939i	0.847145	+	0.531362i	$0.178320\pi$
$338$	−10.6506	+	6.14915i	−0.579318	+	0.334469i
$339$	3.39543	+	3.03701i	0.184414	+	0.164948i
$340$	−12.3050	+	2.94759i	−0.667331	+	0.159856i
$341$	−1.53639			−0.0832003
$342$	13.0397	−	0.983575i	0.705104	−	0.0531857i
$343$			13.0226i			0.703155i
$344$	5.58390	−	9.67160i	0.301064	−	0.521458i
$345$	0.787891	−	0.0228377i	0.0424186	−	0.00122954i
$346$	−11.9847	−	20.7581i	−0.644302	−	1.11596i
$347$	11.9747	−	20.7407i	0.642834	−	1.11342i	−0.341963	−	0.939713i	$-0.611092\pi$
$347$	11.9747	−	20.7407i	0.642834	−	1.11342i	0.984797	−	0.173708i	$-0.0555748\pi$
$348$	4.39782	+	13.3845i	0.235748	+	0.717485i
$349$	−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
$351$	0.412069	−	4.33316i	0.0219946	−	0.231287i
$352$	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
$355$	7.12097	−	23.9955i	0.377942	−	1.27355i
$356$	−3.27700	+	5.67592i	−0.173680	+	0.300823i
$357$	38.5549	−	12.6682i	2.04054	−	0.670471i
$358$	−11.2818	−	6.51358i	−0.596264	−	0.344253i
$359$	−29.7773	−	17.1919i	−1.57159	−	0.907356i	−0.995975	−	0.0896318i	$-0.971431\pi$
$359$	−29.7773	−	17.1919i	−1.57159	−	0.907356i	−0.575611	−	0.817724i	$-0.695236\pi$
$360$	−6.30965	+	2.27778i	−0.332548	+	0.120049i
$361$	−10.6603	+	15.7276i	−0.561068	+	0.827770i
$362$	15.0743			0.792285
$363$	12.6133	−	14.1018i	0.662025	−	0.740154i
$364$	3.00385	+	1.73427i	0.157445	+	0.0909007i
$365$	13.7948	+	4.09378i	0.722052	+	0.214278i
$366$	6.61350	+	5.91539i	0.345693	+	0.309202i
$367$	−9.51432	+	5.49310i	−0.496644	+	0.286737i	−0.727326	−	0.686292i	$-0.759237\pi$
$367$	−9.51432	+	5.49310i	−0.496644	+	0.286737i	0.230683	+	0.973029i	$0.425904\pi$
$368$	−0.203518			−0.0106091
$369$	−16.0507	−	7.01957i	−0.835567	−	0.365424i
$370$	−3.95164	−	1.17270i	−0.205436	−	0.0609658i
$371$	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	$-0.482000\pi$
$373$	2.18309			0.113036			0.0565180	+	0.998402i	$0.482000\pi$
$374$	0.783509	+	1.35708i	0.0405143	+	0.0701728i
$375$	0.472306	−	19.3592i	0.0243898	−	0.999703i
$376$	−10.2190	+	5.89995i	−0.527005	+	0.304267i
$377$	−3.40685	+	5.90083i	−0.175462	+	0.303908i
$378$	19.5677	−	8.94546i	1.00645	−	0.460105i
$379$			9.44771i			0.485296i	0.970114	+	0.242648i	$0.0780160\pi$
$379$			9.44771i			0.485296i	−0.970114	+	0.242648i	$0.921984\pi$
$380$	3.10783	−	9.23804i	0.159428	−	0.473902i
$381$	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	−0.218488	−	0.975840i	$-0.570113\pi$
$383$	−22.9528	−	13.2518i	−1.17283	−	0.677136i	−0.954346	+	0.298703i	$0.903446\pi$
$384$	1.64550	−	0.540671i	0.0839716	−	0.0275910i
$385$	2.49345	−	0.597293i	0.127078	−	0.0304409i
$386$	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	0.545585	−	0.838056i	$-0.316308\pi$
$389$	30.4555	−	17.5835i	1.54415	−	0.891518i	0.998570	−	0.0534626i	$-0.0170258\pi$
$390$	−2.85548	−	1.54007i	−0.144593	−	0.0779846i
$391$	−1.15163			−0.0582407
$392$			10.1451i			0.512403i
$393$	−0.831315	+	0.273149i	−0.0419343	+	0.0137786i
$394$	23.3067	+	13.4561i	1.17417	+	0.677909i
$395$	34.7362	+	10.3084i	1.74777	+	0.518672i
$396$	0.492746	+	0.668871i	0.0247614	+	0.0336120i
$397$	12.7678	+	7.37147i	0.640796	+	0.369963i	0.784921	−	0.619596i	$-0.212704\pi$
$397$	12.7678	+	7.37147i	0.640796	+	0.369963i	−0.144125	+	0.989559i	$0.546037\pi$
$398$			3.71387i			0.186159i
$399$	−7.49692	+	30.3490i	−0.375315	+	1.51935i
$400$	−0.266723	+	4.99288i	−0.0133361	+	0.249644i
$401$	−10.0032	+	17.3261i	−0.499537	+	0.865224i	−1.00000		0.000534108i	$-0.999830\pi$
$401$	−10.0032	+	17.3261i	−0.499537	+	0.865224i	0.500462	+	0.865758i	$0.333163\pi$
$402$	13.8579	+	12.3951i	0.691170	+	0.618211i
$403$	−4.02484	+	2.32374i	−0.200492	+	0.115754i
$404$	−3.02926	−	1.74894i	−0.150711	−	0.0870131i
$405$	−18.0526	+	8.89396i	−0.897042	+	0.441944i
$406$	−33.6801			−1.67152
$407$			0.510485i			0.0253038i
$408$	9.31129	−	3.05946i	0.460978	−	0.151466i
$409$	6.13313	−	3.54097i	0.303264	−	0.175089i	−0.340644	−	0.940192i	$-0.610645\pi$
$409$	6.13313	−	3.54097i	0.303264	−	0.175089i	0.643908	+	0.765103i	$0.277312\pi$
$410$	−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
$414$	−0.606775	+	0.0678298i	−0.0298214	+	0.00333365i
$415$	3.26669	−	0.782519i	0.160356	−	0.0384123i
$416$	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	$0.873613\pi$
$420$	−0.464642	−	16.0300i	−0.0226722	−	0.782183i
$421$	9.83472	+	5.67808i	0.479315	+	0.276733i	0.720131	−	0.693838i	$-0.244082\pi$
$421$	9.83472	+	5.67808i	0.479315	+	0.276733i	−0.240816	+	0.970571i	$0.577415\pi$
$422$	−0.994784	−	1.72302i	−0.0484253	−	0.0838751i
$423$	−28.5009	+	20.9961i	−1.38576	+	1.02087i
$424$	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	$-0.271989\pi$
$431$	−6.74460	−	11.6820i	−0.324876	−	0.562702i	−0.981487	+	0.191527i	$0.938656\pi$
$432$	4.72575	−	2.16039i	0.227368	−	0.103942i
$433$	7.19759	+	12.4666i	0.345894	+	0.599106i	0.985516	−	0.169584i	$-0.0542423\pi$
$433$	7.19759	+	12.4666i	0.345894	+	0.599106i	−0.639622	+	0.768690i	$0.720909\pi$
$434$	−19.8948	−	11.4863i	−0.954982	−	0.551359i
$435$	31.4896	−	0.912752i	1.50981	−	0.0437631i
$436$			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	−0.0542443	−	0.998528i	$-0.517275\pi$
$439$	−19.8233	−	11.4450i	−0.946117	−	0.546241i	−0.891873	+	0.452287i	$0.850608\pi$
$440$	0.602187	−	0.144251i	0.0287081	−	0.00687688i
$441$	3.38121	+	30.2468i	0.161010	+	1.44032i
$442$	4.10507	+	2.37006i	0.195258	+	0.112732i
$443$	2.22771	+	3.85851i	0.105842	+	0.183324i	0.914082	−	0.405530i	$-0.132913\pi$
$443$	2.22771	+	3.85851i	0.105842	+	0.183324i	−0.808240	+	0.588853i	$0.799580\pi$
$444$	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
$447$	−11.0370	+	3.62649i	−0.522033	+	0.171527i
$448$			4.14066i			0.195628i
$449$	22.9854			1.08475			0.542375	−	0.840137i	$-0.317525\pi$
$449$	22.9854			1.08475			0.542375	+	0.840137i	$0.317525\pi$
$450$	0.868844	+	14.9748i	0.0409577	+	0.705920i
$451$	1.40046	+	0.808555i	0.0659450	+	0.0380733i
$452$	−2.27774	+	1.31505i	−0.107136	+	0.0618548i
$453$	15.0802	+	13.4884i	0.708531	+	0.633740i
$454$	14.0551	−	24.3441i	0.659638	−	1.14253i
$455$	5.62863	−	5.33597i	0.263874	−	0.250154i
$456$	−1.81056	+	7.32952i	−0.0847873	+	0.343236i
$457$			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
$459$	26.7413	−	12.2249i	1.24818	−	0.570609i
$460$	−0.129470	+	0.436275i	−0.00603658	+	0.0203414i
$461$	−12.4399	−	7.18219i	−0.579385	−	0.334508i	0.181504	−	0.983390i	$-0.441903\pi$
$461$	−12.4399	−	7.18219i	−0.579385	−	0.334508i	−0.760889	+	0.648882i	$0.775237\pi$
$462$	−1.88682	+	0.619961i	−0.0877827	+	0.0288432i
$463$			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
$465$	18.9122	+	10.2001i	0.877032	+	0.473017i
$466$	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
$470$	6.14659	+	25.6594i	0.283521	+	1.18358i
$471$	−0.219174	+	0.0720153i	−0.0100990	+	0.00331829i
$472$	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
$475$	−17.8262	−	12.5390i	−0.817922	−	0.575329i
$476$			23.4305i			1.07393i
$477$	16.5664	+	22.4878i	0.758522	+	1.02964i
$478$	−4.70600	+	8.15104i	−0.215248	+	0.372820i
$479$	22.9576	−	13.2546i	1.04896	−	0.605617i	0.126602	−	0.991954i	$-0.459593\pi$
$479$	22.9576	−	13.2546i	1.04896	−	0.605617i	0.922358	+	0.386336i	$0.126260\pi$
$480$	−0.112214	−	3.87136i	−0.00512186	−	0.176702i
$481$	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
$485$	4.13362	−	13.9290i	0.187698	−	0.632485i
$486$	13.3695	−	8.01609i	0.606451	−	0.363617i
$487$	−11.6600			−0.528366			−0.264183	−	0.964473i	$-0.585102\pi$
$487$	−11.6600			−0.528366			−0.264183	+	0.964473i	$0.585102\pi$
$488$	−4.43650	+	2.56141i	−0.200831	+	0.115950i
$489$	−5.68663	−	5.08636i	−0.257158	−	0.230013i
$490$	21.7476	+	6.45388i	0.982457	+	0.291557i
$491$	−0.670228	−	0.386956i	−0.0302470	−	0.0174631i	0.484800	−	0.874625i	$-0.338892\pi$
$491$	−0.670228	−	0.386956i	−0.0302470	−	0.0174631i	−0.515047	+	0.857162i	$0.672226\pi$
$492$	6.74296	−	7.53874i	0.303996	−	0.339872i
$493$	−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
$498$	−2.47194	+	0.812217i	−0.110770	+	0.0363963i
$499$	5.69523	−	9.86443i	0.254953	−	0.441592i	−0.709929	−	0.704273i	$-0.751273\pi$
$499$	5.69523	−	9.86443i	0.254953	−	0.441592i	0.964883	+	0.262680i	$0.0846065\pi$
$500$	10.5334	+	3.74804i	0.471067	+	0.167617i
$501$	2.47140	−	11.8188i	0.110414	−	0.528027i
$502$	13.4601			0.600753
$503$	15.2932	+	26.4887i	0.681892	+	1.18107i	0.974403	+	0.224809i	$0.0721759\pi$
$503$	15.2932	+	26.4887i	0.681892	+	1.18107i	−0.292511	+	0.956262i	$0.594491\pi$
$504$	1.38003	+	12.3451i	0.0614712	+	0.549894i
$505$	−5.67624	+	5.38110i	−0.252589	+	0.239456i
$506$	0.0563593			0.00250547
$507$	−6.64933	−	20.2369i	−0.295307	−	0.898750i
$508$	−3.14595	+	5.44894i	−0.139579	+	0.241758i
$509$	−11.0074	−	19.0654i	−0.487894	−	0.845058i	0.512009	−	0.858980i	$-0.328902\pi$
$509$	−11.0074	−	19.0654i	−0.487894	−	0.845058i	−0.999903	+	0.0139223i	$0.995568\pi$
$510$	−0.634980	−	21.9066i	−0.0281174	−	0.970041i
$511$	13.3229	−	23.0759i	0.589369	−	1.02082i
$512$			1.00000i			0.0441942i
$513$	−2.95523	+	22.4559i	−0.130477	+	0.991451i
$514$	14.1804			0.625469
$515$	−14.5771	+	3.49187i	−0.642345	+	0.153870i
$516$	14.4175	+	12.8956i	0.634694	+	0.567696i
$517$	2.82990	−	1.63384i	0.124459	−	0.0718563i
$518$	−3.81646	+	6.61030i	−0.167685	+	0.290440i
$519$	39.4417	−	12.9596i	1.73130	−	0.568862i
$520$	1.35936	−	1.28868i	0.0596117	−	0.0565122i
$521$	24.9351			1.09243			0.546214	−	0.837646i	$-0.316069\pi$
$521$	24.9351			1.09243			0.546214	+	0.837646i	$0.316069\pi$
$522$	−24.2510	+	2.71095i	−1.06144	+	0.118655i
$523$	8.63200	+	14.9511i	0.377451	+	0.653764i	0.990691	−	0.136133i	$-0.0434674\pi$
$523$	8.63200	+	14.9511i	0.377451	+	0.653764i	−0.613240	+	0.789897i	$0.710134\pi$
$524$		−	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
$528$	−0.455680	+	0.149725i	−0.0198309	+	0.00651595i
$529$	11.4793	−	19.8827i	0.499100	−	0.864466i
$530$	20.2458	−	4.84978i	0.879422	−	0.210661i
$531$	10.7184	+	4.68756i	0.465140	+	0.203423i
$532$	−15.2953	−	9.58168i	−0.663137	−	0.415418i
$533$	4.89165			0.211881
$534$	−8.46111	−	7.56796i	−0.366148	−	0.327498i
$535$	3.07389	+	12.8322i	0.132896	+	0.554786i
$536$	−9.29624	+	5.36719i	−0.401537	+	0.231827i
$537$	15.0426	−	16.8179i	0.649136	−	0.725744i
$538$	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	0.905522	−	0.424299i	$-0.139479\pi$
$541$	1.98420	+	3.43673i	0.0853073	+	0.147757i	−0.820215	+	0.572056i	$0.806146\pi$
$542$	−3.18447	+	1.83855i	−0.136785	+	0.0789726i
$543$	−5.34407	+	25.5566i	−0.229336	+	1.09674i
$544$			5.65864i			0.242612i
$545$	24.0345	+	7.13254i	1.02952	+	0.305524i
$546$	−4.00517	+	4.47784i	−0.171405	+	0.191634i
$547$	1.00884	+	1.74735i	0.0431347	+	0.0747115i	0.886787	−	0.462179i	$-0.152932\pi$
$547$	1.00884	+	1.74735i	0.0431347	+	0.0747115i	−0.843652	+	0.536890i	$0.819599\pi$
$548$	−0.0331892	+	0.0574854i	−0.00141777	+	0.00245566i
$549$	−12.3734	+	9.11530i	−0.528085	+	0.389032i
$550$	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
$555$	3.38910	−	6.28380i	0.143859	−	0.266733i
$556$	−0.588959	+	1.02011i	−0.0249774	+	0.0432622i
$557$	−12.2671	−	21.2472i	−0.519773	−	0.900274i	−0.999736	−	0.0229846i	$-0.992683\pi$
$557$	−12.2671	−	21.2472i	−0.519773	−	0.900274i	0.479963	−	0.877289i	$-0.340650\pi$
$558$	−15.2496	−	6.66920i	−0.645566	−	0.282330i
$559$			9.35505i			0.395676i
$560$	8.87619	+	2.63412i	0.375087	+	0.111312i
$561$	−2.57853	+	0.847241i	−0.108866	+	0.0357705i
$562$		−	8.60469i		−	0.362967i
$563$		−	27.1996i		−	1.14633i	−0.819441	−	0.573164i	$-0.805716\pi$
$563$		−	27.1996i		−	1.14633i	0.819441	−	0.573164i	$-0.194284\pi$
$564$	−6.37986	−	19.4167i	−0.268641	−	0.817593i
$565$	1.37003	+	5.71929i	0.0576374	+	0.240612i
$566$	−7.48566	−	12.9655i	−0.314646	−	0.544982i
$567$	8.22890	+	36.3460i	0.345581	+	1.52639i
$568$	−9.69401	−	5.59684i	−0.406752	−	0.234838i
$569$	−14.1549			−0.593405			−0.296702	−	0.954970i	$-0.595887\pi$
$569$	−14.1549			−0.593405			−0.296702	+	0.954970i	$0.595887\pi$
$570$	14.5602	+	8.54399i	0.609861	+	0.357868i
$571$	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
$573$	10.5427	+	9.42985i	0.440428	+	0.393937i
$574$	12.0897	+	20.9400i	0.504616	+	0.874020i
$575$	0.852863	+	0.555081i	0.0355668	+	0.0231485i
$576$	0.333286	+	2.98143i	0.0138869	+	0.124226i
$577$		−	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
$579$	11.9446	+	36.3529i	0.496402	+	1.51077i
$580$	−5.17453	+	17.4366i	−0.214861	+	0.724015i
$581$		−	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
$585$	3.62333	−	4.29516i	0.149806	−	0.177583i
$586$	−4.99797	+	8.65674i	−0.206464	+	0.357606i
$587$	−7.46457	+	12.9290i	−0.308096	+	0.533638i	−0.977946	−	0.208859i	$-0.933025\pi$
$587$	−7.46457	+	12.9290i	−0.308096	+	0.533638i	0.669850	+	0.742496i	$0.266358\pi$
$588$	−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
$591$	−31.0758	+	34.7433i	−1.27829	+	1.42915i
$592$	−0.921703	+	1.59644i	−0.0378817	+	0.0656131i
$593$	−16.9851	−	29.4191i	−0.697494	−	1.20810i	−0.969333	−	0.245753i	$-0.920965\pi$
$593$	−16.9851	−	29.4191i	−0.697494	−	1.20810i	0.271838	−	0.962343i	$-0.412368\pi$
$594$	−1.30868	+	0.598267i	−0.0536957	+	0.0245472i
$595$	50.2271	+	14.9055i	2.05911	+	0.611068i
$596$		−	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	−0.950063	−	0.312057i	$-0.898982\pi$
$599$	−18.2404	−	31.5932i	−0.745281	−	1.29086i	0.204782	−	0.978808i	$-0.434351\pi$
$600$	−8.37028	−	2.22225i	−0.341715	−	0.0907231i
$601$			6.32670i			0.258072i	0.991640	+	0.129036i	$0.0411882\pi$
$601$			6.32670i			0.258072i	−0.991640	+	0.129036i	$0.958812\pi$
$602$	−40.0468	+	23.1210i	−1.63219	+	0.942343i
$603$	−25.9273	+	19.1002i	−1.05584	+	0.777820i
$604$	−10.1162	+	5.84059i	−0.411622	+	0.237650i
$605$	23.7533	−	5.68997i	0.965708	−	0.231330i
$606$	4.03904	−	4.51572i	0.164075	−	0.183438i
$607$	−30.0680			−1.22042			−0.610212	−	0.792238i	$-0.708916\pi$
$607$	−30.0680			−1.22042			−0.610212	+	0.792238i	$0.708916\pi$
$608$	−3.69394	−	2.31405i	−0.149809	−	0.0938470i
$609$	11.9402	−	57.1007i	0.483839	−	2.31384i
$610$	2.66849	+	11.1398i	0.108044	+	0.451039i
$611$	4.94227	−	8.56026i	0.199943	−	0.346311i
$612$	1.88595	+	16.8708i	0.0762349	+	0.681963i
$613$	−10.8242	−	6.24937i	−0.437187	−	0.252410i	0.265217	−	0.964189i	$-0.414556\pi$
$613$	−10.8242	−	6.24937i	−0.437187	−	0.252410i	−0.702403	+	0.711779i	$0.747890\pi$
$614$	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	0.992848	+	0.119388i	$0.0380931\pi$
$617$	14.8991	+	25.8061i	0.599817	+	1.03891i	−0.393031	+	0.919525i	$0.628574\pi$
$618$	11.0307	−	3.62440i	0.443718	−	0.145795i
$619$	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
$621$	0.100114	−	1.05276i	0.00401744	−	0.0422459i
$622$	−9.54117	+	16.5258i	−0.382566	+	0.662624i
$623$	23.5021	−	13.5689i	0.941590	−	0.543627i
$624$	−0.967278	+	1.08143i	−0.0387221	+	0.0432920i
$625$	14.7355	−	20.1957i	0.589418	−	0.807828i
$626$	14.6473			0.585424
$627$	0.501390	−	2.02973i	0.0200236	−	0.0810595i
$628$		−	0.133196i		−	0.00531511i
$629$	−5.21558	+	9.03365i	−0.207959	+	0.360195i
$630$	27.3416	+	4.89514i	1.08932	+	0.195027i
$631$	9.66769	+	16.7449i	0.384865	+	0.666605i	0.991750	−	0.128184i	$-0.0409147\pi$
$631$	9.66769	+	16.7449i	0.384865	+	0.666605i	−0.606886	+	0.794789i	$0.707581\pi$
$632$	8.10205	−	14.0332i	0.322282	−	0.558209i
$633$	3.27384	−	1.07570i	0.130123	−	0.0427553i
$634$	3.22170			0.127950
$635$	9.67937	+	10.2103i	0.384114	+	0.405182i
$636$	−15.3202	+	5.03384i	−0.607485	+	0.199605i
$637$	−4.24916	−	7.35976i	−0.168358	−	0.291604i
$638$	2.25251			0.0891777
$639$	−30.7674	−	13.4557i	−1.21714	−	0.532299i
$640$	2.14367	+	0.636160i	0.0847358	+	0.0251464i
$641$	8.82740	−	15.2895i	0.348661	−	0.603899i	−0.637351	−	0.770574i	$-0.719970\pi$
$641$	8.82740	−	15.2895i	0.348661	−	0.603899i	0.986012	+	0.166675i	$0.0533030\pi$
$642$	−3.19055	−	9.71027i	−0.125921	−	0.383234i
$643$	22.5254	+	13.0051i	0.888315	+	0.512869i	0.873391	−	0.487019i	$-0.161916\pi$
$643$	22.5254	+	13.0051i	0.888315	+	0.512869i	0.0149244	+	0.999889i	$0.495249\pi$
$644$	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	$0.719949\pi$
$648$	1.98734	+	8.77784i	0.0780701	+	0.344826i
$649$	−0.935204	−	0.539940i	−0.0367099	−	0.0211945i
$650$	−1.89772	−	3.73381i	−0.0744349	−	0.146452i
$651$	26.5267	−	29.6573i	1.03966	−	1.16236i
$652$	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
$655$	−1.08299	−	0.321391i	−0.0423159	−	0.0125578i
$656$	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	−0.949496	−	0.313779i	$-0.898405\pi$
$659$	−19.1631	−	33.1915i	−0.746489	−	1.29296i	0.203007	−	0.979177i	$-0.434928\pi$
$660$	0.0310750	+	1.07208i	0.00120959	+	0.0417305i
$661$	6.47622	−	3.73905i	0.251896	−	0.145432i	−0.368736	−	0.929534i	$-0.620209\pi$
$661$	6.47622	−	3.73905i	0.251896	−	0.145432i	0.620632	+	0.784102i	$0.286876\pi$
$662$	−6.21648	+	10.7673i	−0.241610	+	0.418481i
$663$	−5.47347	+	6.11943i	−0.212572	+	0.237659i
$664$		−	1.50224i		−	0.0582982i
$665$	−30.2702	+	26.6926i	−1.17383	+	1.03510i
$666$	−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
$669$	−12.1560	−	36.9962i	−0.469979	−	1.43036i
$670$	5.59155	+	23.3424i	0.216021	+	0.901796i
$671$	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	$-0.745727\pi$
$673$	−36.1921			−1.39510			−0.697551	+	0.716535i	$0.745727\pi$
$674$	1.16376	−	0.671895i	0.0448262	−	0.0258804i
$675$	−25.6960	−	3.83579i	−0.989041	−	0.147640i
$676$	12.2983			0.473011
$677$			4.59634i			0.176652i	0.996092	+	0.0883258i	$0.0281516\pi$
$677$			4.59634i			0.176652i	−0.996092	+	0.0883258i	$0.971848\pi$
$678$	−1.42202	−	4.32784i	−0.0546124	−	0.166210i
$679$	−23.3005	−	13.4525i	−0.894190	−	0.516261i
$680$	12.1302	+	3.59980i	0.465173	+	0.138046i
$681$	36.2898	+	32.4591i	1.39063	+	1.24384i
$682$	1.33056	+	0.768196i	0.0509496	+	0.0294158i
$683$			20.8899i			0.799330i	0.916661	+	0.399665i	$0.130874\pi$
$683$			20.8899i			0.799330i	−0.916661	+	0.399665i	$0.869126\pi$
$684$	−11.7845	−	5.66803i	−0.450590	−	0.216722i
$685$	0.102116	+	0.107717i	0.00390164	+	0.00411564i
$686$	6.51131	−	11.2779i	0.248603	−	0.430593i
$687$	−26.1303	+	29.2141i	−0.996932	+	1.11459i
$688$	−9.67160	+	5.58390i	−0.368726	+	0.212884i
$689$	−6.75422	−	3.89955i	−0.257315	−	0.148561i
$690$	−0.693753	−	0.374168i	−0.0264107	−	0.0142443i
$691$	−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
$693$	−0.382163	−	3.41866i	−0.0145172	−	0.129864i
$694$	−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
$699$	10.1403	+	30.8614i	0.383541	+	1.16729i
$700$	11.2934	−	17.3518i	0.426849	−	0.655838i
$701$	−14.7634	−	8.52364i	−0.557605	−	0.321933i	0.194579	−	0.980887i	$-0.437666\pi$
$701$	−14.7634	−	8.52364i	−0.557605	−	0.321933i	−0.752184	+	0.658954i	$0.770999\pi$
$702$	−2.52344	+	3.54660i	−0.0952413	+	0.133858i
$703$	−3.76427	−	7.09894i	−0.141972	−	0.267742i
$704$		−	0.276925i		−	0.0104370i
$705$	−45.6816	+	1.32412i	−1.72047	+	0.0498692i
$706$	25.1662	+	14.5297i	0.947143	+	0.546834i
$707$	7.24177	+	12.5431i	0.272355	+	0.471733i
$708$	−4.50284	+	5.03425i	−0.169227	+	0.189199i
$709$	8.29143	+	14.3612i	0.311391	+	0.539345i	0.978664	−	0.205468i	$-0.0658717\pi$
$709$	8.29143	+	14.3612i	0.311391	+	0.539345i	−0.667273	+	0.744814i	$0.732538\pi$
$710$	−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
$717$	−12.1508	−	10.8681i	−0.453778	−	0.405878i
$718$	17.1919	+	29.7773i	0.641597	+	1.11128i
$719$	−22.8964	−	13.2192i	−0.853892	−	0.492994i	0.00807046	−	0.999967i	$-0.497431\pi$
$719$	−22.8964	−	13.2192i	−0.853892	−	0.492994i	−0.861962	+	0.506973i	$0.830764\pi$
$720$	6.60321	+	1.18221i	0.246087	+	0.0440585i
$721$			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
$725$	34.0864	+	22.1849i	1.26594	+	0.823927i
$726$	−17.9743	+	5.90592i	−0.667090	+	0.219189i
$727$	4.72362	+	2.72718i	0.175189	+	0.101146i	0.585031	−	0.811011i	$-0.301083\pi$
$727$	4.72362	+	2.72718i	0.175189	+	0.101146i	−0.409841	+	0.912157i	$0.634416\pi$
$728$	−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
$732$	−2.76976	−	8.42962i	−0.102373	−	0.311568i
$733$		−	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
$735$	−18.6517	+	34.5825i	−0.687977	+	1.27559i
$736$	0.176252	+	0.101759i	0.00649673	+	0.00375089i
$737$	2.57436	−	1.48631i	0.0948278	−	0.0547489i
$738$	10.3905	+	14.1045i	0.382481	+	0.519193i
$739$	−7.84449	+	13.5871i	−0.288564	+	0.499808i	−0.973467	−	0.228826i	$-0.926511\pi$
$739$	−7.84449	+	13.5871i	−0.288564	+	0.499808i	0.684903	+	0.728634i	$0.259845\pi$
$740$	2.83587	+	2.99141i	0.104249	+	0.109966i
$741$	−1.75642	−	6.07555i	−0.0645237	−	0.223191i
$742$		−	38.5510i		−	1.41525i
$743$	−17.9419	−	10.3588i	−0.658225	−	0.380026i	0.133375	−	0.991066i	$-0.457418\pi$
$743$	−17.9419	−	10.3588i	−0.658225	−	0.380026i	−0.791600	+	0.611039i	$0.790752\pi$
$744$	6.40639	−	7.16245i	0.234870	−	0.262588i
$745$	−14.3784	−	4.26698i	−0.526784	−	0.156330i
$746$	−1.89061	−	1.09154i	−0.0692201	−	0.0399643i
$747$	−0.500676	−	4.47882i	−0.0183188	−	0.163871i
$748$		−	1.56702i		−	0.0572958i
$749$	24.4344			0.892815
$750$	−10.0886	+	16.5294i	−0.368384	+	0.603567i
$751$	−44.2932	+	25.5727i	−1.61628	+	0.933161i	−0.628411	+	0.777881i	$0.716294\pi$
$751$	−44.2932	+	25.5727i	−1.61628	+	0.933161i	−0.987871	+	0.155279i	$0.950372\pi$
$752$	11.7999			0.430298
$753$	−4.77181	+	22.8200i	−0.173895	+	0.831606i
$754$	5.90083	−	3.40685i	0.214896	−	0.124070i
$755$	6.08475	+	25.4013i	0.221447	+	0.924448i
$756$	−21.4189	−	2.03686i	−0.778997	−	0.0740799i
$757$	22.3683	+	12.9143i	0.812988	+	0.469379i	0.847993	−	0.530008i	$-0.177811\pi$
$757$	22.3683	+	12.9143i	0.812988	+	0.469379i	−0.0350041	+	0.999387i	$0.511144\pi$
$758$	4.72385	−	8.18196i	0.171578	−	0.297182i
$759$	−0.0199803	+	0.0955504i	−0.000725238	+	0.00346826i
$760$	−7.31048	+	6.44646i	−0.265179	+	0.233838i
$761$			1.34313i			0.0486886i	0.999704	+	0.0243443i	$0.00774979\pi$
$761$			1.34313i			0.0486886i	−0.999704	+	0.0243443i	$0.992250\pi$
$762$	−8.12274	−	7.26532i	−0.294256	−	0.263195i
$763$	23.2122	−	40.2048i	0.840340	−	1.45551i
$764$	−7.07232	+	4.08321i	−0.255868	+	0.147725i
$765$	37.3652	+	6.68971i	1.35094	+	0.241867i
$766$	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	−0.719461	−	0.694533i	$-0.755611\pi$
$769$	−26.6553	−	46.1683i	−0.961214	−	1.66487i	−0.241753	−	0.970338i	$-0.577722\pi$
$770$	−2.45804	−	0.729454i	−0.0885815	−	0.0262877i
$771$	−5.02717	+	24.0411i	−0.181049	+	0.865820i
$772$	−22.0923			−0.795118
$773$	22.3337	−	12.8944i	0.803289	−	0.463779i	−0.0413311	−	0.999146i	$-0.513160\pi$
$773$	22.3337	−	12.8944i	0.803289	−	0.463779i	0.844620	+	0.535366i	$0.179826\pi$
$774$	−26.9742	+	19.8714i	−0.969566	+	0.714263i
$775$	12.5688	+	24.7294i	0.451486	+	0.888308i
$776$	−5.62724	−	3.24889i	−0.202006	−	0.116628i
$777$	−9.85398	−	8.81381i	−0.353509	−	0.316194i
$778$	−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
$783$	4.00126	−	42.0757i	0.142993	−	1.50366i
$784$	5.07253	−	8.78588i	0.181162	−	0.313781i
$785$	−0.285528	−	0.0847341i	−0.0101909	−	0.00302429i
$786$	0.856514	+	0.179103i	0.0305508	+	0.00638840i
$787$	−40.3027			−1.43664			−0.718318	−	0.695715i	$-0.755088\pi$
$787$	−40.3027			−1.43664			−0.718318	+	0.695715i	$0.755088\pi$
$788$	−13.4561	−	23.3067i	−0.479354	−	0.830266i
$789$	−0.000353391	−	0.00107553i	−1.25811e−5	−	3.82897e-5i
$790$	−24.9282	−	26.2954i	−0.886905	−	0.935549i
$791$	10.8904			0.387217
$792$	−0.0922953	−	0.825632i	−0.00327957	−	0.0293376i
$793$	2.14565	−	3.71637i	0.0761941	−	0.131972i
$794$	−7.37147	−	12.7678i	−0.261604	−	0.453111i
$795$	1.04476	+	36.0437i	0.0370537	+	1.27834i
$796$	1.85693	−	3.21630i	0.0658173	−	0.113999i
$797$			2.02959i			0.0718919i	0.999354	+	0.0359459i	$0.0114444\pi$
$797$			2.02959i			0.0718919i	−0.999354	+	0.0359459i	$0.988556\pi$
$798$	21.6670	−	22.5346i	0.767005	−	0.797716i
$799$	66.7713			2.36220
$800$	2.72743	−	4.19060i	0.0964292	−	0.148160i
$801$	15.8302	−	11.6618i	0.559332	−	0.412051i
$802$	17.3261	−	10.0032i	0.611806	−	0.353226i
$803$	−0.891026	+	1.54330i	−0.0314436	+	0.0544619i
$804$	−5.80376	−	17.6634i	−0.204683	−	0.622941i
$805$	1.36750	−	1.29640i	0.0481981	−	0.0456920i
$806$	4.64749			0.163701
$807$	2.77329	+	8.44035i	0.0976244	+	0.297115i
$808$	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	−0.898080	−	0.439833i	$-0.855038\pi$
$811$	−27.5159	+	15.8863i	−0.966213	+	0.557844i	−0.0681337	+	0.997676i	$0.521704\pi$
$812$	29.1679	+	16.8401i	1.02359	+	0.590971i
$813$	−1.98810	−	6.05068i	−0.0697258	−	0.212207i
$814$	0.255242	−	0.442093i	0.00894624	−	0.0154953i
$815$	−2.29451	−	9.57862i	−0.0803731	−	0.335524i
$816$	−9.59355	−	2.00608i	−0.335841	−	0.0702268i
$817$	1.75394	−	48.6477i	0.0613626	−	1.70197i
$818$	−7.08193			−0.247614
$819$	−6.17176	−	8.37776i	−0.215659	−	0.292743i
$820$	12.6983	−	3.04182i	0.443445	−	0.106225i
$821$	24.2301	−	13.9892i	0.845635	−	0.488227i	−0.0135409	−	0.999908i	$-0.504310\pi$
$821$	24.2301	−	13.9892i	0.845635	−	0.488227i	0.859176	+	0.511681i	$0.170977\pi$
$822$	−0.0856936	−	0.0766479i	−0.00298891	−	0.00267340i
$823$	15.3764	−	8.87756i	0.535987	−	0.309452i	−0.207464	−	0.978243i	$-0.566521\pi$
$823$	15.3764	−	8.87756i	0.535987	−	0.309452i	0.743451	+	0.668790i	$0.233188\pi$
$824$			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	0.217376	−	0.976088i	$-0.430250\pi$
$827$	33.6861	−	19.4487i	1.17138	−	0.676297i	0.954005	+	0.299791i	$0.0969170\pi$
$828$	0.559397	+	0.244645i	0.0194404	+	0.00850200i
$829$			39.6887i			1.37845i	0.724549	+	0.689223i	$0.242048\pi$
$829$			39.6887i			1.37845i	−0.724549	+	0.689223i	$0.757952\pi$
$830$	−3.22030	−	0.955665i	−0.111778	−	0.0331716i
$831$	−33.3351	−	29.8163i	−1.15638	−	1.03432i
$832$	−0.418840	−	0.725452i	−0.0145207	−	0.0251505i
$833$	28.7036	−	49.7161i	0.994521	−	1.72256i
$834$	−1.52067	−	1.36015i	−0.0526567	−	0.0470983i
$835$	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	−0.357701	−	0.933836i	$-0.616439\pi$
$839$	18.2446	−	31.6006i	0.629875	−	1.09098i	0.987576	−	0.157139i	$-0.0502272\pi$
$840$	−7.61259	+	14.1147i	−0.262659	+	0.487003i
$841$	−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
$845$	7.82368	−	26.3634i	0.269143	−	0.906929i
$846$	35.1806	−	3.93274i	1.20953	−	0.135211i
$847$		−	45.2297i		−	1.55411i
$848$		−	9.31035i		−	0.319719i
$849$	24.6353	−	8.09455i	0.845482	−	0.277804i
$850$	15.4335	−	23.7131i	0.529366	−	0.813352i
$851$	0.187583	+	0.324904i	0.00643027	+	0.0111376i
$852$	12.9255	−	14.4509i	0.442819	−	0.495079i
$853$	40.1675	+	23.1907i	1.37531	+	0.794035i	0.991591	−	0.129415i	$-0.0413099\pi$
$853$	40.1675	+	23.1907i	1.37531	+	0.794035i	0.383719	+	0.923450i	$0.374643\pi$
$854$	21.2119			0.725856
$855$	−19.6472	+	21.6562i	−0.671918	+	0.740625i
$856$	5.90110			0.201695
$857$	1.30783	+	0.755079i	0.0446748	+	0.0257930i	0.522171	−	0.852841i	$-0.325122\pi$
$857$	1.30783	+	0.755079i	0.0446748	+	0.0257930i	−0.477496	+	0.878634i	$0.658456\pi$
$858$	0.267864	−	0.299476i	0.00914471	−	0.0102239i
$859$	−4.51223	−	7.81542i	−0.153955	−	0.266659i	0.778723	−	0.627368i	$-0.215868\pi$
$859$	−4.51223	−	7.81542i	−0.153955	−	0.266659i	−0.932678	+	0.360710i	$0.882535\pi$
$860$	5.81733	+	24.2849i	0.198369	+	0.828109i
$861$	−39.7873	+	13.0731i	−1.35595	+	0.445531i
$862$			13.4892i			0.459444i
$863$		−	3.88212i		−	0.132149i	−0.997815	−	0.0660744i	$-0.978953\pi$
$863$		−	3.88212i		−	0.132149i	0.997815	−	0.0660744i	$-0.0210475\pi$
$864$	−5.17282	−	0.491917i	−0.175983	−	0.0167354i
$865$	51.3824	+	15.2484i	1.74705	+	0.518461i
$866$		−	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
$870$	−27.7272	−	14.9543i	−0.940040	−	0.507000i
$871$	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
$876$	8.30767	+	7.43073i	0.280690	+	0.251061i
$877$	17.1099	−	29.6353i	0.577762	−	1.00071i	−0.417974	−	0.908459i	$-0.637260\pi$
$877$	17.1099	−	29.6353i	0.577762	−	1.00071i	0.995736	−	0.0922533i	$-0.0294070\pi$
$878$	11.4450	+	19.8233i	0.386251	+	0.669006i
$879$	−12.9046	−	11.5424i	−0.435262	−	0.389316i
$880$	−0.593634	−	0.176169i	−0.0200114	−	0.00593864i
$881$			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	$-0.609240\pi$
$883$	9.23516	−	5.33192i	0.310788	−	0.179434i	0.647279	+	0.762253i	$0.275907\pi$
$884$	−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	−0.558851	−	0.829268i	$-0.688758\pi$
$887$	−3.57716	+	2.06527i	−0.120109	+	0.0693451i	0.438742	+	0.898613i	$0.355424\pi$
$888$	−2.37981	−	2.12860i	−0.0798612	−	0.0714311i
$889$	22.5622	−	13.0263i	0.756712	−	0.436888i
$890$	−3.41398	−	14.2520i	−0.114437	−	0.477727i
$891$	−0.550344	−	2.43080i	−0.0184372	−	0.0814350i
$892$	22.4832			0.752794
$893$	−27.3055	+	43.5881i	−0.913744	+	1.45862i
$894$	11.3716	+	2.37788i	0.380323	+	0.0795281i
$895$	28.3282	−	6.78586i	0.946906	−	0.226826i
$896$	2.07033	−	3.58592i	0.0691649	−	0.119797i
$897$	0.0921752	+	0.280530i	0.00307764	+	0.00936663i
$898$	−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
$903$	−25.0017	−	76.0914i	−0.832006	−	2.53216i
$904$	2.63010			0.0874759
$905$	−24.4620	+	23.1901i	−0.813143	+	0.770864i
$906$	−6.31567	−	19.2214i	−0.209824	−	0.638588i
$907$	−12.3433	+	21.3793i	−0.409854	+	0.709888i	−0.994873	−	0.101132i	$-0.967754\pi$
$907$	−12.3433	+	21.3793i	−0.409854	+	0.709888i	0.585019	+	0.811020i	$0.301087\pi$
$908$	−24.3441	+	14.0551i	−0.807888	+	0.466434i
$909$	6.22396	+	8.44862i	0.206436	+	0.280223i
$910$	−7.54253	+	1.80677i	−0.250032	+	0.0598939i
$911$	−54.4425			−1.80376			−0.901881	−	0.431985i	$-0.857813\pi$
$911$	−54.4425			−1.80376			−0.901881	+	0.431985i	$0.857813\pi$
$912$	5.23275	−	5.44227i	0.173274	−	0.180212i
$913$			0.416007i			0.0137678i
$914$	6.58477	−	11.4051i	0.217805	−	0.377249i
$915$	−19.8323	+	0.574855i	−0.655636	+	0.0190041i
$916$	−11.3146	−	19.5975i	−0.373846	−	0.647520i
$917$	−1.04594	+	1.81162i	−0.0345400	+	0.0598250i
$918$	−29.2711	−	2.78358i	−0.966089	−	0.0918718i
$919$	−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
$921$	15.5857	+	47.4341i	0.513565	+	1.56301i
$922$	7.18219	+	12.4399i	0.236533	+	0.409687i
$923$	9.37672			0.308639
$924$	1.94401	+	0.406507i	0.0639533	+	0.0133731i
$925$	8.21665	−	4.17615i	0.270162	−	0.137311i
$926$	14.5835	−	25.2593i	0.479242	−	0.830071i
$927$	2.23419	+	19.9861i	0.0733805	+	0.656429i
$928$	7.04425	+	4.06700i	0.231239	+	0.133506i
$929$	29.8371	+	17.2265i	0.978923	+	0.565182i	0.901945	−	0.431851i	$-0.142139\pi$
$929$	29.8371	+	17.2265i	0.978923	+	0.565182i	0.0769784	+	0.997033i	$0.475473\pi$
$930$	−11.2784	−	18.2896i	−0.369833	−	0.599740i
$931$	20.7164	+	39.0685i	0.678954	+	1.28042i
$932$	−18.7550			−0.614342
$933$	−24.6350	−	22.0346i	−0.806515	−	0.721380i
$934$	−25.1194	−	14.5027i	−0.821930	−	0.474542i
$935$	−3.35916	−	0.996874i	−0.109856	−	0.0326013i
$936$	−1.49053	−	2.02329i	−0.0487193	−	0.0661333i
$937$	40.1661	−	23.1899i	1.31217	−	0.757581i	0.329714	−	0.944081i	$-0.393048\pi$
$937$	40.1661	−	23.1899i	1.31217	−	0.757581i	0.982455	+	0.186500i	$0.0597144\pi$
$938$	44.4474			1.45126
$939$	−5.19271	+	24.8328i	−0.169458	+	0.810387i
$940$	7.50663	−	25.2950i	0.244839	−	0.825033i
$941$	30.0669	+	52.0774i	0.980153	+	1.69767i	0.661761	+	0.749714i	$0.269809\pi$
$941$	30.0669	+	52.0774i	0.980153	+	1.69767i	0.318391	+	0.947959i	$0.396857\pi$
$942$	0.225818	+	0.0472202i	0.00735756	+	0.00153852i
$943$	1.18845			0.0387012
$944$	−1.94977	−	3.37710i	−0.0634596	−	0.109915i
$945$	−17.9922	+	44.6191i	−0.585286	+	1.45146i
$946$	2.67831	−	1.54632i	0.0870793	−	0.0502753i
$947$	−0.0348151	+	0.0603015i	−0.00113134	+	0.00195953i	−0.866591	−	0.499020i	$-0.833693\pi$
$947$	−0.0348151	+	0.0603015i	−0.00113134	+	0.00195953i	0.865459	+	0.500979i	$0.167027\pi$
$948$	20.9193	+	18.7110i	0.679426	+	0.607707i
$949$			5.39059i			0.174986i
$950$	9.16843	+	19.7722i	0.297463	+	0.641495i
$951$	−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	0.840614	−	0.541635i	$-0.182195\pi$
$953$	24.4450	+	14.1133i	0.791851	+	0.457175i	−0.0487631	+	0.998810i	$0.515528\pi$
$954$	−3.10301	−	27.7582i	−0.100464	−	0.898704i
$955$	4.25390	+	17.7583i	0.137653	+	0.574644i
$956$	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
$960$	−1.83850	+	3.40880i	−0.0593373	+	0.110019i
$961$	0.219173			0.00707008
$962$		−	1.54418i		−	0.0497865i
$963$	17.5937	−	1.96676i	0.566949	−	0.0633778i
$964$	6.84761	+	3.95347i	0.220547	+	0.127333i
$965$	−14.0542	+	47.3584i	−0.452421	+	1.52452i
$966$	−0.973074	+	1.08791i	−0.0313081	+	0.0350030i
$967$	3.39153	+	1.95810i	0.109064	+	0.0629683i	0.553540	−	0.832823i	$-0.313277\pi$
$967$	3.39153	+	1.95810i	0.109064	+	0.0629683i	−0.444476	+	0.895791i	$0.646610\pi$
$968$		−	10.9233i		−	0.351089i
$969$	29.6102	−	30.7958i	0.951218	−	0.989304i
$970$	−10.5443	+	9.99610i	−0.338559	+	0.320955i
$971$	10.0201	−	17.3553i	0.321560	−	0.556959i	−0.659250	−	0.751924i	$-0.729126\pi$
$971$	10.0201	−	17.3553i	0.321560	−	0.556959i	0.980810	+	0.194965i	$0.0624594\pi$
$972$	−15.5863	+	0.257413i	−0.499932	+	0.00825651i
$973$	4.22391	−	2.43868i	0.135412	−	0.0781804i
$974$	10.0979	+	5.83002i	0.323557	+	0.186806i
$975$	7.00301	−	1.89367i	0.224276	−	0.0606460i
$976$	5.12283			0.163978
$977$		−	39.0176i		−	1.24828i	−0.781311	−	0.624142i	$-0.785449\pi$
$977$		−	39.0176i		−	1.24828i	0.781311	−	0.624142i	$-0.214551\pi$
$978$	2.38159	+	7.24823i	0.0761548	+	0.231773i
$979$	−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	0.0558817	−	0.998437i	$-0.482203\pi$
$983$	−24.4818	−	14.1346i	−0.780850	−	0.450824i	−0.836731	+	0.547614i	$0.815536\pi$
$984$	−9.60894	+	3.15726i	−0.306322	+	0.100650i
$985$	−58.5219	+	14.0186i	−1.86466	+	0.446670i
$986$	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
$990$	−1.82859	−	0.327384i	−0.0581165	−	0.0104050i
$991$	−34.6905	−	20.0285i	−1.10198	−	0.636228i	−0.165239	−	0.986254i	$-0.552839\pi$
$991$	−34.6905	−	20.0285i	−1.10198	−	0.636228i	−0.936740	+	0.350026i	$0.886173\pi$
$992$	2.77402	+	4.80475i	0.0880753	+	0.152551i
$993$	−16.0508	−	14.3565i	−0.509356	−	0.455589i
$994$	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	$-0.844342\pi$
$997$	−28.9663	+	16.7237i	−0.917373	+	0.529645i	−0.0345769	+	0.999402i	$0.511008\pi$
$998$	−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.179.16	yes	80
3.2	odd	2	inner	570.2.n.a.179.33	yes	80
5.4	even	2	inner	570.2.n.a.179.25	yes	80
15.14	odd	2	inner	570.2.n.a.179.8	✓	80
19.12	odd	6	inner	570.2.n.a.449.8	yes	80
57.50	even	6	inner	570.2.n.a.449.25	yes	80
95.69	odd	6	inner	570.2.n.a.449.33	yes	80
285.164	even	6	inner	570.2.n.a.449.16	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.n.a.179.8	✓	80	15.14	odd	2	inner
570.2.n.a.179.16	yes	80	1.1	even	1	trivial
570.2.n.a.179.25	yes	80	5.4	even	2	inner
570.2.n.a.179.33	yes	80	3.2	odd	2	inner
570.2.n.a.449.8	yes	80	19.12	odd	6	inner
570.2.n.a.449.16	yes	80	285.164	even	6	inner
570.2.n.a.449.25	yes	80	57.50	even	6	inner
570.2.n.a.449.33	yes	80	95.69	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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(1.15471 - 1.29099i) q^{3} +(0.500000 + 0.866025i) q^{4} +(2.17455 - 0.520902i) q^{5} +(-1.64550 + 0.540671i) q^{6} -4.14066i q^{7} -1.00000i q^{8} +(-0.333286 - 2.98143i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(1.15471 - 1.29099i) q^{3} +(0.500000 + 0.866025i) q^{4} +(2.17455 - 0.520902i) q^{5} +(-1.64550 + 0.540671i) q^{6} -4.14066i q^{7} -1.00000i q^{8} +(-0.333286 - 2.98143i) q^{9} +(-2.14367 - 0.636160i) q^{10} +0.276925i q^{11} +(1.69538 + 0.354516i) q^{12} +(0.418840 + 0.725452i) q^{13} +(-2.07033 + 3.58592i) q^{14} +(1.83850 - 3.40880i) 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} +(-5.34553 - 4.78126i) q^{21} +(0.138462 - 0.239824i) q^{22} +(0.101759 + 0.176252i) q^{23} +(-1.29099 - 1.15471i) q^{24} +(4.45732 - 2.26545i) 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} +(0.357506 + 0.319768i) q^{33} +(4.90052 - 2.82932i) q^{34} +(-2.15688 - 9.00406i) q^{35} +(2.41535 - 1.77935i) q^{36} +1.84341 q^{37} +(-0.157053 + 4.35607i) q^{38} +(1.42019 + 0.296971i) q^{39} +(-0.520902 - 2.17455i) q^{40} +(2.91976 - 5.05717i) q^{41} +(2.23873 + 6.81346i) 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} +(0.540671 + 1.64550i) q^{48} -10.1451 q^{49} +(-4.99288 - 0.266723i) q^{50} +(3.05946 + 9.31129i) q^{51} +(-0.418840 + 0.725452i) q^{52} +(-8.06300 + 4.65518i) q^{53} +(2.16039 + 4.72575i) q^{54} +(0.144251 + 0.602187i) q^{55} -4.14066 q^{56} +(-7.32952 - 1.81056i) q^{57} -8.13400i q^{58} +(-1.94977 + 3.37710i) q^{59} +(3.87136 - 0.112214i) q^{60} +(-2.56141 - 4.43650i) q^{61} +(2.77402 - 4.80475i) q^{62} +(-12.3451 + 1.38003i) q^{63} -1.00000 q^{64} +(1.28868 + 1.35936i) q^{65} +(-0.149725 - 0.455680i) q^{66} +(-5.36719 - 9.29624i) q^{67} -5.65864 q^{68} +(0.345041 + 0.0721505i) q^{69} +(-2.63412 + 8.87619i) q^{70} +(5.59684 - 9.69401i) q^{71} +(-2.98143 + 0.333286i) 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} +(-1.08143 - 0.967278i) q^{78} +(14.0332 + 8.10205i) q^{79} +(-0.636160 + 2.14367i) q^{80} +(-8.77784 + 1.98734i) q^{81} +(-5.05717 + 2.91976i) q^{82} +1.50224 q^{83} +(1.46793 - 7.02000i) q^{84} +(-3.59980 + 12.1302i) q^{85} +(-5.58390 - 9.67160i) q^{86} +(13.7902 + 2.88364i) q^{87} +0.276925 q^{88} +(3.27700 + 5.67592i) q^{89} +(-1.18221 + 6.60321i) q^{90} +(3.00385 - 1.73427i) q^{91} +(-0.101759 + 0.176252i) q^{92} +(7.16245 + 6.40639i) q^{93} +11.7999i q^{94} +(-6.44646 - 7.31048i) q^{95} +(0.354516 - 1.69538i) q^{96} +(3.24889 - 5.62724i) q^{97} +(8.78588 + 5.07253i) q^{98} +(0.825632 - 0.0922953i) 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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