LMFDB - Embedded newform 627.2.s.a.94.19

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [627,2,Mod(94,627)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("627.94"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(627, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 9, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 627 = 3 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	627.s (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$5.00662020673$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$40$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			94.19
Character	$\chi$	$=$	627.94
Dual form			627.2.s.a.607.19

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.123092 - 0.378837i) q^{2} +(0.587785 - 0.809017i) q^{3} +(1.48967 - 1.08231i) q^{4} +(-0.0677455 + 0.208499i) q^{5} +(-0.378837 - 0.123092i) q^{6} +(-1.61387 - 2.22131i) q^{7} +(-1.23790 - 0.899388i) q^{8} +(-0.309017 - 0.951057i) q^{9} +0.0873262 q^{10} +(-1.51789 - 2.94890i) q^{11} -1.84133i q^{12} +(1.46856 + 4.51977i) q^{13} +(-0.642860 + 0.884821i) q^{14} +(0.128860 + 0.177360i) q^{15} +(0.949659 - 2.92275i) q^{16} +(-3.92180 - 1.27427i) q^{17} +(-0.322258 + 0.234134i) q^{18} +(-1.63338 - 4.04130i) q^{19} +(0.124742 + 0.383916i) q^{20} -2.74569 q^{21} +(-0.930315 + 0.938018i) q^{22} -1.00816 q^{23} +(-1.45524 + 0.472836i) q^{24} +(4.00620 + 2.91068i) q^{25} +(1.53149 - 1.11269i) q^{26} +(-0.951057 - 0.309017i) q^{27} +(-4.80827 - 1.56230i) q^{28} +(2.39873 - 1.74278i) q^{29} +(0.0513291 - 0.0706484i) q^{30} +(2.94290 - 0.956207i) q^{31} -4.28440 q^{32} +(-3.27790 - 0.505324i) q^{33} +1.64258i q^{34} +(0.572474 - 0.186008i) q^{35} +(-1.48967 - 1.08231i) q^{36} +(5.04929 + 6.94975i) q^{37} +(-1.32994 + 1.11623i) q^{38} +(4.51977 + 1.46856i) q^{39} +(0.271384 - 0.197172i) q^{40} +(0.0502511 + 0.0365096i) q^{41} +(0.337971 + 1.04017i) q^{42} -8.34166i q^{43} +(-5.45276 - 2.75006i) q^{44} +0.219229 q^{45} +(0.124097 + 0.381930i) q^{46} +(10.4236 + 7.57316i) q^{47} +(-1.80636 - 2.48624i) q^{48} +(-0.166497 + 0.512425i) q^{49} +(0.609543 - 1.87598i) q^{50} +(-3.33609 + 2.42381i) q^{51} +(7.07944 + 5.14352i) q^{52} +(-5.27720 + 1.71467i) q^{53} +0.398333i q^{54} +(0.717674 - 0.116704i) q^{55} +4.20126i q^{56} +(-4.22955 - 1.05398i) q^{57} +(-0.955495 - 0.694208i) q^{58} +(-5.62832 - 7.74671i) q^{59} +(0.383916 + 0.124742i) q^{60} +(7.78721 + 2.53022i) q^{61} +(-0.724494 - 0.997180i) q^{62} +(-1.61387 + 2.22131i) q^{63} +(-1.37194 - 4.22241i) q^{64} -1.04186 q^{65} +(0.212047 + 1.30399i) q^{66} -4.22505i q^{67} +(-7.22134 + 2.34635i) q^{68} +(-0.592584 + 0.815621i) q^{69} +(-0.140934 - 0.193978i) q^{70} +(-4.76940 - 1.54967i) q^{71} +(-0.472836 + 1.45524i) q^{72} +(-2.71315 - 3.73433i) q^{73} +(2.01130 - 2.76832i) q^{74} +(4.70957 - 1.53023i) q^{75} +(-6.80711 - 4.25237i) q^{76} +(-4.10074 + 8.13085i) q^{77} -1.89302i q^{78} +(-1.12712 - 3.46893i) q^{79} +(0.545056 + 0.396006i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(0.00764570 - 0.0235310i) q^{82} +(1.49428 + 0.485523i) q^{83} +(-4.09016 + 2.97168i) q^{84} +(0.531369 - 0.731367i) q^{85} +(-3.16013 + 1.02679i) q^{86} -2.96500i q^{87} +(-0.773211 + 5.01562i) q^{88} +13.7349i q^{89} +(-0.0269853 - 0.0830522i) q^{90} +(7.66972 - 10.5565i) q^{91} +(-1.50183 + 1.09114i) q^{92} +(0.956207 - 2.94290i) q^{93} +(1.58594 - 4.88103i) q^{94} +(0.953261 - 0.0667783i) q^{95} +(-2.51831 + 3.46615i) q^{96} +(17.4292 - 5.66308i) q^{97} +0.214620 q^{98} +(-2.33552 + 2.35486i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q - 40 q^{4} + 4 q^{5} - 10 q^{7} + 40 q^{9} + 10 q^{11} - 40 q^{16} - 50 q^{17} + 76 q^{20} + 16 q^{23} - 80 q^{25} - 68 q^{26} - 40 q^{35} + 40 q^{36} - 62 q^{38} + 8 q^{42} + 40 q^{44} - 4 q^{45}+ \cdots - 10 q^{99}+O(q^{100}) $ 160 * q - 40 * q^4 + 4 * q^5 - 10 * q^7 + 40 * q^9 + 10 * q^11 - 40 * q^16 - 50 * q^17 + 76 * q^20 + 16 * q^23 - 80 * q^25 - 68 * q^26 - 40 * q^35 + 40 * q^36 - 62 * q^38 + 8 * q^42 + 40 * q^44 - 4 * q^45 + 20 * q^47 + 110 * q^49 - 18 * q^55 - 20 * q^57 - 24 * q^58 + 10 * q^61 + 120 * q^62 - 10 * q^63 - 136 * q^64 - 12 * q^66 + 160 * q^68 + 20 * q^73 - 100 * q^74 + 90 * q^77 - 156 * q^80 - 40 * q^81 + 68 * q^82 - 200 * q^83 + 30 * q^85 - 84 * q^92 - 96 * q^93 - 60 * q^95 + 100 * q^96 - 10 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/627\mathbb{Z}\right)^\times$.

$n$	$343$	$419$	$496$
$\chi(n)$	$e\left(\frac{9}{10}\right)$	$1$	$-1$

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 $

$2$	−0.123092	−	0.378837i	−0.0870390	−	0.267879i	0.898058	−	0.439876i	$-0.144978\pi$
$2$	−0.123092	−	0.378837i	−0.0870390	−	0.267879i	−0.985097	+	0.171998i	$0.944978\pi$
$3$	0.587785	−	0.809017i	0.339358	−	0.467086i
$3$	0.587785	−	0.809017i	0.339358	−	0.467086i
$4$	1.48967	−	1.08231i	0.744834	−	0.541153i
$5$	−0.0677455	+	0.208499i	−0.0302967	+	0.0932437i	−0.965061	−	0.262024i	$-0.915610\pi$
$5$	−0.0677455	+	0.208499i	−0.0302967	+	0.0932437i	0.934765	+	0.355267i	$0.115610\pi$
$6$	−0.378837	−	0.123092i	−0.154660	−	0.0502520i
$7$	−1.61387	−	2.22131i	−0.609987	−	0.839575i	0.386589	−	0.922252i	$-0.373653\pi$
$7$	−1.61387	−	2.22131i	−0.609987	−	0.839575i	−0.996576	+	0.0826767i	$0.973653\pi$
$8$	−1.23790	−	0.899388i	−0.437664	−	0.317982i
$9$	−0.309017	−	0.951057i	−0.103006	−	0.317019i
$10$	0.0873262			0.0276150
$11$	−1.51789	−	2.94890i	−0.457660	−	0.889127i
$11$	−1.51789	−	2.94890i	−0.457660	−	0.889127i
$12$		−	1.84133i		−	0.531546i
$13$	1.46856	+	4.51977i	0.407305	+	1.25356i	0.918955	+	0.394363i	$0.129035\pi$
$13$	1.46856	+	4.51977i	0.407305	+	1.25356i	−0.511649	+	0.859194i	$0.670965\pi$
$14$	−0.642860	+	0.884821i	−0.171811	+	0.236478i
$15$	0.128860	+	0.177360i	0.0332714	+	0.0457942i
$16$	0.949659	−	2.92275i	0.237415	−	0.730687i
$17$	−3.92180	−	1.27427i	−0.951177	−	0.309056i	−0.207983	−	0.978132i	$-0.566690\pi$
$17$	−3.92180	−	1.27427i	−0.951177	−	0.309056i	−0.743194	+	0.669076i	$0.766690\pi$
$18$	−0.322258	+	0.234134i	−0.0759570	+	0.0551860i
$19$	−1.63338	−	4.04130i	−0.374723	−	0.927137i
$19$	−1.63338	−	4.04130i	−0.374723	−	0.927137i
$20$	0.124742	+	0.383916i	0.0278931	+	0.0858462i
$21$	−2.74569			−0.599158
$22$	−0.930315	+	0.938018i	−0.198344	+	0.199986i
$23$	−1.00816			−0.210217			−0.105108	−	0.994461i	$-0.533519\pi$
$23$	−1.00816			−0.210217			−0.105108	+	0.994461i	$0.533519\pi$
$24$	−1.45524	+	0.472836i	−0.297050	+	0.0965173i
$25$	4.00620	+	2.91068i	0.801240	+	0.582135i
$26$	1.53149	−	1.11269i	0.300350	−	0.218217i
$27$	−0.951057	−	0.309017i	−0.183031	−	0.0594703i
$28$	−4.80827	−	1.56230i	−0.908678	−	0.295247i
$29$	2.39873	−	1.74278i	0.445434	−	0.323626i	−0.342357	−	0.939570i	$-0.611225\pi$
$29$	2.39873	−	1.74278i	0.445434	−	0.323626i	0.787790	+	0.615944i	$0.211225\pi$
$30$	0.0513291	−	0.0706484i	0.00937136	−	0.0128986i
$31$	2.94290	−	0.956207i	0.528561	−	0.171740i	−0.0325662	−	0.999470i	$-0.510368\pi$
$31$	2.94290	−	0.956207i	0.528561	−	0.171740i	0.561127	+	0.827730i	$0.310368\pi$
$32$	−4.28440			−0.757382
$33$	−3.27790	−	0.505324i	−0.570610	−	0.0879655i
$34$			1.64258i			0.281700i
$35$	0.572474	−	0.186008i	0.0967657	−	0.0314411i
$36$	−1.48967	−	1.08231i	−0.248278	−	0.180384i
$37$	5.04929	+	6.94975i	0.830098	+	1.14253i	0.987905	+	0.155062i	$0.0495577\pi$
$37$	5.04929	+	6.94975i	0.830098	+	1.14253i	−0.157807	+	0.987470i	$0.550442\pi$
$38$	−1.32994	+	1.11623i	−0.215745	+	0.181077i
$39$	4.51977	+	1.46856i	0.723742	+	0.235158i
$40$	0.271384	−	0.197172i	0.0429096	−	0.0311756i
$41$	0.0502511	+	0.0365096i	0.00784791	+	0.00570184i	0.591702	−	0.806157i	$-0.298456\pi$
$41$	0.0502511	+	0.0365096i	0.00784791	+	0.00570184i	−0.583854	+	0.811858i	$0.698456\pi$
$42$	0.337971	+	1.04017i	0.0521501	+	0.160502i
$43$		−	8.34166i		−	1.27209i	−0.771652	−	0.636045i	$-0.780569\pi$
$43$		−	8.34166i		−	1.27209i	0.771652	−	0.636045i	$-0.219431\pi$
$44$	−5.45276	−	2.75006i	−0.822035	−	0.414588i
$45$	0.219229			0.0326807
$46$	0.124097	+	0.381930i	0.0182970	+	0.0563125i
$47$	10.4236	+	7.57316i	1.52043	+	1.10466i	0.961273	+	0.275599i	$0.0888762\pi$
$47$	10.4236	+	7.57316i	1.52043	+	1.10466i	0.559160	+	0.829060i	$0.311124\pi$
$48$	−1.80636	−	2.48624i	−0.260725	−	0.358858i
$49$	−0.166497	+	0.512425i	−0.0237853	+	0.0732036i
$50$	0.609543	−	1.87598i	0.0862024	−	0.265304i
$51$	−3.33609	+	2.42381i	−0.467145	+	0.339401i
$52$	7.07944	+	5.14352i	0.981742	+	0.713277i
$53$	−5.27720	+	1.71467i	−0.724879	+	0.235527i	−0.648137	−	0.761524i	$-0.724452\pi$
$53$	−5.27720	+	1.71467i	−0.724879	+	0.235527i	−0.0767418	+	0.997051i	$0.524452\pi$
$54$			0.398333i			0.0542063i
$55$	0.717674	−	0.116704i	0.0967711	−	0.0157363i
$56$			4.20126i			0.561417i
$57$	−4.22955	−	1.05398i	−0.560218	−	0.139604i
$58$	−0.955495	−	0.694208i	−0.125463	−	0.0911540i
$59$	−5.62832	−	7.74671i	−0.732744	−	1.00854i	−0.999003	−	0.0446344i	$-0.985788\pi$
$59$	−5.62832	−	7.74671i	−0.732744	−	1.00854i	0.266259	−	0.963901i	$-0.414212\pi$
$60$	0.383916	+	0.124742i	0.0495634	+	0.0161041i
$61$	7.78721	+	2.53022i	0.997050	+	0.323961i	0.761686	−	0.647946i	$-0.224372\pi$
$61$	7.78721	+	2.53022i	0.997050	+	0.323961i	0.235364	+	0.971907i	$0.424372\pi$
$62$	−0.724494	−	0.997180i	−0.0920108	−	0.126642i
$63$	−1.61387	+	2.22131i	−0.203329	+	0.279858i
$64$	−1.37194	−	4.22241i	−0.171493	−	0.527801i
$65$	−1.04186			−0.129226
$66$	0.212047	+	1.30399i	0.0261012	+	0.160510i
$67$		−	4.22505i		−	0.516172i	−0.966122	−	0.258086i	$-0.916908\pi$
$67$		−	4.22505i		−	0.516172i	0.966122	−	0.258086i	$-0.0830917\pi$
$68$	−7.22134	+	2.34635i	−0.875716	+	0.284537i
$69$	−0.592584	+	0.815621i	−0.0713387	+	0.0981893i
$70$	−0.140934	−	0.193978i	−0.0168448	−	0.0231849i
$71$	−4.76940	−	1.54967i	−0.566023	−	0.183912i	0.0120063	−	0.999928i	$-0.496178\pi$
$71$	−4.76940	−	1.54967i	−0.566023	−	0.183912i	−0.578030	+	0.816016i	$0.696178\pi$
$72$	−0.472836	+	1.45524i	−0.0557243	+	0.171502i
$73$	−2.71315	−	3.73433i	−0.317550	−	0.437071i	0.620167	−	0.784470i	$-0.287065\pi$
$73$	−2.71315	−	3.73433i	−0.317550	−	0.437071i	−0.937717	+	0.347399i	$0.887065\pi$
$74$	2.01130	−	2.76832i	0.233809	−	0.321810i
$75$	4.70957	−	1.53023i	0.543815	−	0.176696i
$76$	−6.80711	−	4.25237i	−0.780829	−	0.487781i
$77$	−4.10074	+	8.13085i	−0.467322	+	0.926596i
$78$		−	1.89302i		−	0.214343i
$79$	−1.12712	−	3.46893i	−0.126811	−	0.390285i	0.867415	−	0.497585i	$-0.165780\pi$
$79$	−1.12712	−	3.46893i	−0.126811	−	0.390285i	−0.994227	+	0.107299i	$0.965780\pi$
$80$	0.545056	+	0.396006i	0.0609391	+	0.0442748i
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$	0.00764570	−	0.0235310i	0.000844326	−	0.00259857i
$83$	1.49428	+	0.485523i	0.164019	+	0.0532930i	0.389876	−	0.920868i	$-0.372518\pi$
$83$	1.49428	+	0.485523i	0.164019	+	0.0532930i	−0.225856	+	0.974161i	$0.572518\pi$
$84$	−4.09016	+	2.97168i	−0.446273	+	0.324236i
$85$	0.531369	−	0.731367i	0.0576351	−	0.0793279i
$86$	−3.16013	+	1.02679i	−0.340766	+	0.110722i
$87$		−	2.96500i		−	0.317881i
$88$	−0.773211	+	5.01562i	−0.0824245	+	0.534667i
$89$			13.7349i			1.45589i	0.685635	+	0.727946i	$0.259525\pi$
$89$			13.7349i			1.45589i	−0.685635	+	0.727946i	$0.740475\pi$
$90$	−0.0269853	−	0.0830522i	−0.00284450	−	0.00875447i
$91$	7.66972	−	10.5565i	0.804005	−	1.10662i
$92$	−1.50183	+	1.09114i	−0.156576	+	0.113759i
$93$	0.956207	−	2.94290i	0.0991540	−	0.305165i
$94$	1.58594	−	4.88103i	0.163577	−	0.503440i
$95$	0.953261	−	0.0667783i	0.0978025	−	0.00685131i
$96$	−2.51831	+	3.46615i	−0.257024	+	0.353763i
$97$	17.4292	−	5.66308i	1.76966	−	0.574998i	0.771537	−	0.636185i	$-0.219488\pi$
$97$	17.4292	−	5.66308i	1.76966	−	0.574998i	0.998126	+	0.0611864i	$0.0194884\pi$
$98$	0.214620			0.0216799
$99$	−2.33552	+	2.35486i	−0.234728	+	0.236672i
$100$	9.11816			0.911816
$101$	4.93071	−	1.60208i	0.490624	−	0.159413i	−0.0532487	−	0.998581i	$-0.516958\pi$
$101$	4.93071	−	1.60208i	0.490624	−	0.159413i	0.543872	+	0.839168i	$0.316958\pi$
$102$	1.32887	+	0.965483i	0.131578	+	0.0955971i
$103$	−0.594537	−	0.818310i	−0.0585815	−	0.0806305i	0.778721	−	0.627370i	$-0.215869\pi$
$103$	−0.594537	−	0.818310i	−0.0585815	−	0.0806305i	−0.837303	+	0.546740i	$0.815869\pi$
$104$	2.24709	−	6.91583i	0.220345	−	0.678153i
$105$	0.186008	−	0.572474i	0.0181525	−	0.0558677i
$106$	1.29916	+	1.78814i	0.126185	+	0.173679i
$107$	13.4190	+	9.74945i	1.29726	+	0.942515i	0.999925	−	0.0122583i	$-0.00390204\pi$
$107$	13.4190	+	9.74945i	1.29726	+	0.942515i	0.297335	+	0.954773i	$0.403902\pi$
$108$	−1.75121	+	0.569002i	−0.168510	+	0.0547523i
$109$	−3.25200			−0.311485			−0.155743	−	0.987798i	$-0.549777\pi$
$109$	−3.25200			−0.311485			−0.155743	+	0.987798i	$0.549777\pi$
$110$	−0.132551	−	0.257516i	−0.0126383	−	0.0245532i
$111$	8.59036			0.815361
$112$	−8.02495	+	2.60747i	−0.758287	+	0.246382i
$113$	10.7751	−	14.8306i	1.01363	−	1.39515i	0.0970619	−	0.995278i	$-0.469056\pi$
$113$	10.7751	−	14.8306i	1.01363	−	1.39515i	0.916572	−	0.399869i	$-0.130944\pi$
$114$	0.121334	+	1.73205i	0.0113640	+	0.162221i
$115$	0.0682985	−	0.210201i	0.00636887	−	0.0196014i
$116$	1.68709	−	5.19233i	0.156642	−	0.482096i
$117$	3.84474	−	2.79337i	0.355447	−	0.258247i
$118$	−2.24195	+	3.08577i	−0.206388	+	0.284068i
$119$	3.49875	+	10.7680i	0.320730	+	0.987105i
$120$		−	0.335449i		−	0.0306222i
$121$	−6.39203	+	8.95220i	−0.581094	+	0.813836i
$122$		−	3.26154i		−	0.295286i
$123$	0.0590737	−	0.0191942i	0.00532650	−	0.00173068i
$124$	3.34904	−	4.60955i	0.300752	−	0.413950i
$125$	−1.76508	+	1.28240i	−0.157873	+	0.114702i
$126$	1.04017	+	0.337971i	0.0926656	+	0.0301089i
$127$	−3.67865	+	11.3217i	−0.326428	+	1.00464i	0.644364	+	0.764719i	$0.277122\pi$
$127$	−3.67865	+	11.3217i	−0.326428	+	1.00464i	−0.970792	+	0.239923i	$0.922878\pi$
$128$	−8.36304	+	6.07610i	−0.739195	+	0.537057i
$129$	−6.74854	−	4.90310i	−0.594176	−	0.431694i
$130$	0.128244	+	0.394694i	0.0112477	+	0.0346170i
$131$			13.0775i			1.14259i	0.820746	+	0.571294i	$0.193558\pi$
$131$			13.0775i			1.14259i	−0.820746	+	0.571294i	$0.806442\pi$
$132$	−5.42990	+	2.79493i	−0.472612	+	0.243268i
$133$	−6.34090	+	10.1504i	−0.549825	+	0.880149i
$134$	−1.60061	+	0.520068i	−0.138271	+	0.0449271i
$135$	0.128860	−	0.177360i	0.0110905	−	0.0152647i
$136$	3.70874	+	5.10464i	0.318022	+	0.437720i
$137$	0.797237	−	2.45364i	0.0681125	−	0.209629i	−0.911207	−	0.411949i	$-0.864848\pi$
$137$	0.797237	−	2.45364i	0.0681125	−	0.209629i	0.979319	+	0.202320i	$0.0648482\pi$
$138$	0.381930	+	0.124097i	0.0325120	+	0.0105638i
$139$	6.00317	+	8.26265i	0.509182	+	0.700829i	0.983781	−	0.179373i	$-0.0574070\pi$
$139$	6.00317	+	8.26265i	0.509182	+	0.700829i	−0.474599	+	0.880202i	$0.657407\pi$
$140$	0.651478	−	0.896682i	0.0550599	−	0.0757835i
$141$	12.2536	−	3.98145i	1.03194	−	0.335298i
$142$			1.99758i			0.167633i
$143$	11.0992	−	11.1911i	0.928164	−	0.935850i
$144$	−3.07316			−0.256097
$145$	0.200865	+	0.618200i	0.0166810	+	0.0513387i
$146$	−1.08074	+	1.48751i	−0.0894426	+	0.123107i
$147$	0.316696	+	0.435895i	0.0261207	+	0.0359520i
$148$	15.0435	+	4.88794i	1.23657	+	0.401786i
$149$	−7.83801	−	2.54672i	−0.642114	−	0.208636i	−0.0301805	−	0.999544i	$-0.509608\pi$
$149$	−7.83801	−	2.54672i	−0.642114	−	0.208636i	−0.611934	+	0.790909i	$0.709608\pi$
$150$	−1.15942	−	1.59580i	−0.0946662	−	0.130297i
$151$	−0.687847	−	0.499750i	−0.0559762	−	0.0406691i	0.559445	−	0.828867i	$-0.311014\pi$
$151$	−0.687847	−	0.499750i	−0.0559762	−	0.0406691i	−0.615421	+	0.788198i	$0.711014\pi$
$152$	−1.61273	+	6.47176i	−0.130810	+	0.524929i
$153$			4.12363i			0.333376i
$154$	3.58504	+	0.552672i	0.288891	+	0.0445355i
$155$			0.678371i			0.0544881i
$156$	8.32238	−	2.70411i	0.666324	−	0.216502i
$157$	16.6316	+	12.0836i	1.32735	+	0.964375i	0.999809	+	0.0195368i	$0.00621916\pi$
$157$	16.6316	+	12.0836i	1.32735	+	0.964375i	0.327539	+	0.944838i	$0.393781\pi$
$158$	−1.17542	+	0.853994i	−0.0935115	+	0.0679401i
$159$	−1.71467	+	5.27720i	−0.135982	+	0.418509i
$160$	0.290249	−	0.893294i	0.0229462	−	0.0706211i
$161$	1.62705	+	2.23944i	0.128229	+	0.176493i
$162$	0.322258	+	0.234134i	0.0253190	+	0.0183953i
$163$	4.14929	+	12.7702i	0.324998	+	1.00024i	0.971442	+	0.237279i	$0.0762554\pi$
$163$	4.14929	+	12.7702i	0.324998	+	1.00024i	−0.646444	+	0.762962i	$0.723745\pi$
$164$	0.114372			0.00893096
$165$	0.327423	−	0.649207i	0.0254898	−	0.0505407i
$166$		−	0.625855i		−	0.0485758i
$167$	−5.27589	−	16.2375i	−0.408260	−	1.25650i	−0.918142	−	0.396252i	$-0.870311\pi$
$167$	−5.27589	−	16.2375i	−0.408260	−	1.25650i	0.509881	−	0.860245i	$-0.329689\pi$
$168$	3.39889	+	2.46944i	0.262230	+	0.190521i
$169$	−7.75439	+	5.63389i	−0.596491	+	0.433376i
$170$	−0.342476	−	0.111277i	−0.0262667	−	0.00853458i
$171$	−3.33876	+	2.80226i	−0.255321	+	0.214294i
$172$	−9.02823	−	12.4263i	−0.688396	−	0.947496i
$173$	17.9524	+	13.0432i	1.36490	+	0.991655i	0.998117	+	0.0613468i	$0.0195396\pi$
$173$	17.9524	+	13.0432i	1.36490	+	0.991655i	0.366779	+	0.930308i	$0.380460\pi$
$174$	−1.12325	+	0.364967i	−0.0851535	+	0.0276681i
$175$		−	13.5965i		−	1.02780i
$176$	−10.0604	+	1.63595i	−0.758329	+	0.123315i
$177$	−9.57546			−0.719736
$178$	5.20328	−	1.69065i	0.390002	−	0.126719i
$179$	2.72034	−	3.74422i	0.203328	−	0.279856i	−0.695160	−	0.718855i	$-0.744667\pi$
$179$	2.72034	−	3.74422i	0.203328	−	0.279856i	0.898488	+	0.438998i	$0.144667\pi$
$180$	0.326579	−	0.237273i	0.0243417	−	0.0176853i
$181$	−9.58060	−	3.11293i	−0.712121	−	0.231382i	−0.0695170	−	0.997581i	$-0.522146\pi$
$181$	−9.58060	−	3.11293i	−0.712121	−	0.231382i	−0.642604	+	0.766199i	$0.722146\pi$
$182$	−4.94326	−	1.60616i	−0.366419	−	0.119057i
$183$	6.62420	−	4.81276i	0.489675	−	0.355770i
$184$	1.24801	+	0.906730i	0.0920042	+	0.0668450i
$185$	−1.79108	+	0.581959i	−0.131683	+	0.0427864i
$186$	−1.23258			−0.0903773
$187$	2.19516	+	13.4992i	0.160526	+	0.987160i
$188$	23.7241			1.73026
$189$	0.848464	+	2.61130i	0.0617167	+	0.189944i
$190$	−0.142637	−	0.352911i	−0.0103480	−	0.0256029i
$191$	1.42597	−	1.03602i	0.103179	−	0.0749641i	−0.534999	−	0.844852i	$-0.679688\pi$
$191$	1.42597	−	1.03602i	0.103179	−	0.0749641i	0.638179	+	0.769888i	$0.279688\pi$
$192$	−4.22241	−	1.37194i	−0.304726	−	0.0990114i
$193$	−6.36523	+	19.5902i	−0.458179	+	1.41013i	0.409182	+	0.912453i	$0.365814\pi$
$193$	−6.36523	+	19.5902i	−0.458179	+	1.41013i	−0.867362	+	0.497678i	$0.834186\pi$
$194$	−4.29077	−	5.90574i	−0.308059	−	0.424007i
$195$	−0.612388	+	0.842879i	−0.0438540	+	0.0603598i
$196$	0.306576	+	0.943545i	0.0218983	+	0.0673960i
$197$		−	4.77201i		−	0.339991i	−0.985445	−	0.169996i	$-0.945625\pi$
$197$		−	4.77201i		−	0.339991i	0.985445	−	0.169996i	$-0.0543754\pi$
$198$	1.17959	+	0.594918i	0.0838299	+	0.0422790i
$199$	9.02844			0.640009			0.320004	−	0.947416i	$-0.396316\pi$
$199$	9.02844			0.640009			0.320004	+	0.947416i	$0.396316\pi$
$200$	−2.34146	−	7.20626i	−0.165566	−	0.509559i
$201$	−3.41813	−	2.48342i	−0.241097	−	0.175167i
$202$	−1.21386	−	1.67073i	−0.0854068	−	0.117552i
$203$	−7.74251	−	2.51569i	−0.543418	−	0.176567i
$204$	−2.34635	+	7.22134i	−0.164278	+	0.505595i
$205$	−0.0110165	+	0.00800396i	−0.000769426	+	0.000559021i
$206$	−0.236824	+	0.325960i	−0.0165003	+	0.0227107i
$207$	0.311540	+	0.958820i	0.0216535	+	0.0666426i
$208$	14.6048			1.01266
$209$	−9.43810	+	10.9509i	−0.652847	+	0.757490i
$210$	−0.239770			−0.0165457
$211$	−2.34900	−	7.22949i	−0.161712	−	0.497699i	0.837067	−	0.547101i	$-0.184269\pi$
$211$	−2.34900	−	7.22949i	−0.161712	−	0.497699i	−0.998779	+	0.0494018i	$0.984269\pi$
$212$	−6.00548	+	8.26583i	−0.412458	+	0.567700i
$213$	−4.05709	+	2.94765i	−0.277987	+	0.201970i
$214$	2.04169	−	6.28368i	0.139567	−	0.429544i
$215$	1.73923	+	0.565110i	0.118614	+	0.0385402i
$216$	0.899388	+	1.23790i	0.0611956	+	0.0842285i
$217$	−6.87350	−	4.99389i	−0.466604	−	0.339007i
$218$	0.400295	+	1.23198i	0.0271114	+	0.0834402i
$219$	−4.61589			−0.311913
$220$	0.942786	−	0.950593i	0.0635626	−	0.0640890i
$221$		−	19.5970i		−	1.31824i
$222$	−1.05740	−	3.25435i	−0.0709682	−	0.218418i
$223$	−6.18600	+	8.51430i	−0.414245	+	0.570160i	−0.964247	−	0.265003i	$-0.914627\pi$
$223$	−6.18600	+	8.51430i	−0.414245	+	0.570160i	0.550002	+	0.835163i	$0.314627\pi$
$224$	6.91448	+	9.51697i	0.461993	+	0.635879i
$225$	1.53023	−	4.70957i	0.102016	−	0.313972i
$226$	−6.94472	−	2.25648i	−0.461956	−	0.150099i
$227$	−15.2597	+	11.0868i	−1.01282	+	0.735857i	−0.964799	−	0.262989i	$-0.915292\pi$
$227$	−15.2597	+	11.0868i	−1.01282	+	0.735857i	−0.0480216	+	0.998846i	$0.515292\pi$
$228$	−7.44136	+	3.00759i	−0.492816	+	0.199182i
$229$	−8.40827	−	25.8780i	−0.555634	−	1.71007i	−0.694262	−	0.719722i	$-0.744269\pi$
$229$	−8.40827	−	25.8780i	−0.555634	−	1.71007i	0.138628	−	0.990345i	$-0.455731\pi$
$230$	−0.0880391			−0.00580513
$231$	4.16764	+	8.09676i	0.274211	+	0.532728i
$232$	−4.53683			−0.297858
$233$	15.4895	−	5.03283i	1.01475	−	0.329712i	0.246004	−	0.969269i	$-0.420882\pi$
$233$	15.4895	−	5.03283i	1.01475	−	0.329712i	0.768744	+	0.639557i	$0.220882\pi$
$234$	−1.53149	−	1.11269i	−0.100117	−	0.0727389i
$235$	−2.28515	+	1.66026i	−0.149067	+	0.108303i
$236$	−16.7686	−	5.44846i	−1.09155	−	0.354665i
$237$	−3.46893	−	1.12712i	−0.225331	−	0.0732146i
$238$	3.64867	−	2.65091i	0.236508	−	0.171833i
$239$	0.284594	−	0.391710i	0.0184089	−	0.0253376i	−0.799713	−	0.600382i	$-0.795015\pi$
$239$	0.284594	−	0.391710i	0.0184089	−	0.0253376i	0.818122	+	0.575044i	$0.195015\pi$
$240$	0.640752	−	0.208193i	0.0413603	−	0.0134388i
$241$	−18.0232			−1.16097			−0.580487	−	0.814270i	$-0.697138\pi$
$241$	−18.0232			−1.16097			−0.580487	+	0.814270i	$0.697138\pi$
$242$	4.17824	+	1.31960i	0.268587	+	0.0848271i
$243$			1.00000i			0.0641500i
$244$	14.3388	−	4.65897i	0.917950	−	0.298260i
$245$	−0.0955609	−	0.0694291i	−0.00610516	−	0.00443566i
$246$	−0.0145430	−	0.0200167i	−0.000927227	−	0.00127622i
$247$	15.8670	−	13.3174i	1.00959	−	0.847364i
$248$	−4.50302	−	1.46312i	−0.285942	−	0.0929082i
$249$	1.27111	−	0.923519i	0.0805536	−	0.0585256i
$250$	0.703089	+	0.510824i	0.0444672	+	0.0323073i
$251$	4.59276	+	14.1351i	0.289892	+	0.892197i	0.984889	+	0.173185i	$0.0554057\pi$
$251$	4.59276	+	14.1351i	0.289892	+	0.892197i	−0.694997	+	0.719013i	$0.744594\pi$
$252$			5.05572i			0.318480i
$253$	1.53028	+	2.97297i	0.0962078	+	0.186909i
$254$	4.74191			0.297534
$255$	−0.279357	−	0.859773i	−0.0174940	−	0.0538411i
$256$	−3.85231	−	2.79887i	−0.240769	−	0.174929i
$257$	3.11587	+	4.28862i	0.194362	+	0.267517i	0.895064	−	0.445937i	$-0.147130\pi$
$257$	3.11587	+	4.28862i	0.194362	+	0.267517i	−0.700702	+	0.713454i	$0.747130\pi$
$258$	−1.02679	+	3.16013i	−0.0639251	+	0.196741i
$259$	7.28861	−	22.4320i	0.452892	−	1.39386i
$260$	−1.55202	+	1.12761i	−0.0962522	+	0.0699313i
$261$	−2.39873	−	1.74278i	−0.148478	−	0.107875i
$262$	4.95425	−	1.60973i	0.306075	−	0.0994497i
$263$		−	24.1228i		−	1.48748i	−0.668471	−	0.743739i	$-0.733051\pi$
$263$		−	24.1228i		−	1.48748i	0.668471	−	0.743739i	$-0.266949\pi$
$264$	3.60324	+	3.57365i	0.221764	+	0.219943i
$265$		−	1.21645i		−	0.0747261i
$266$	4.62585	+	1.15274i	0.283629	+	0.0706791i
$267$	11.1117	+	8.07315i	0.680027	+	0.494068i
$268$	−4.57280	−	6.29391i	−0.279328	−	0.384462i
$269$	−9.61130	−	3.12290i	−0.586011	−	0.190407i	0.000980615	−	1.00000i	$-0.499688\pi$
$269$	−9.61130	−	3.12290i	−0.586011	−	0.190407i	−0.586992	+	0.809593i	$0.699688\pi$
$270$	−0.0830522	−	0.0269853i	−0.00505439	−	0.00164227i
$271$	3.40539	+	4.68712i	0.206863	+	0.284722i	0.899824	−	0.436252i	$-0.143694\pi$
$271$	3.40539	+	4.68712i	0.206863	+	0.284722i	−0.692962	+	0.720974i	$0.743694\pi$
$272$	−7.44875	+	10.2523i	−0.451647	+	0.621638i
$273$	−4.03221	−	12.4099i	−0.244040	−	0.751079i
$274$	−1.02766			−0.0620835
$275$	2.50233	−	16.2320i	0.150896	−	0.978825i
$276$			1.85636i			0.111740i
$277$	20.1885	−	6.55963i	1.21301	−	0.394130i	0.368477	−	0.929637i	$-0.379879\pi$
$277$	20.1885	−	6.55963i	1.21301	−	0.394130i	0.844531	+	0.535507i	$0.179879\pi$
$278$	2.39126	−	3.29129i	0.143418	−	0.197398i
$279$	−1.81881	−	2.50338i	−0.108889	−	0.149874i
$280$	−0.875959	−	0.284616i	−0.0523486	−	0.0170091i
$281$	1.28385	−	3.95130i	0.0765883	−	0.235715i	−0.905432	−	0.424492i	$-0.860453\pi$
$281$	1.28385	−	3.95130i	0.0765883	−	0.235715i	0.982020	+	0.188778i	$0.0604526\pi$
$282$	−3.01664	−	4.15205i	−0.179638	−	0.247251i
$283$	−15.9555	+	21.9608i	−0.948453	+	1.30543i	0.00375781	+	0.999993i	$0.498804\pi$
$283$	−15.9555	+	21.9608i	−0.948453	+	1.30543i	−0.952211	+	0.305441i	$0.901196\pi$
$284$	−8.78204	+	2.85346i	−0.521118	+	0.169322i
$285$	0.506288	−	0.810456i	0.0299899	−	0.0480073i
$286$	−5.60584	−	2.82727i	−0.331481	−	0.167180i
$287$		−	0.170545i		−	0.0100670i
$288$	1.32395	+	4.07471i	0.0780147	+	0.240104i
$289$	0.00348566	+	0.00253248i	0.000205039	+	0.000148969i
$290$	0.209472	−	0.152191i	0.0123006	−	0.00893694i
$291$	5.66308	−	17.4292i	0.331975	−	1.02172i
$292$	−8.08339	−	2.62645i	−0.473045	−	0.153702i
$293$	22.6583	−	16.4622i	1.32371	−	0.961734i	0.323836	−	0.946113i	$-0.395027\pi$
$293$	22.6583	−	16.4622i	1.32371	−	0.961734i	0.999878	−	0.0156210i	$-0.00497252\pi$
$294$	0.126151	−	0.173632i	0.00735726	−	0.0101264i
$295$	1.99648	−	0.648695i	0.116239	−	0.0377685i
$296$		−	13.1444i		−	0.764001i
$297$	0.532336	+	3.27362i	0.0308893	+	0.189955i
$298$			3.28281i			0.190168i
$299$	−1.48055	−	4.55666i	−0.0856224	−	0.263519i
$300$	5.35952	−	7.37674i	0.309432	−	0.425896i
$301$	−18.5294	+	13.4624i	−1.06802	+	0.775959i
$302$	−0.104656	+	0.322097i	−0.00602226	+	0.0185346i
$303$	1.60208	−	4.93071i	0.0920373	−	0.283262i
$304$	−13.3628	+	0.936100i	−0.766412	+	0.0536890i
$305$	−1.05510	+	1.45222i	−0.0604147	+	0.0831537i
$306$	1.56218	−	0.507585i	0.0893041	−	0.0290167i
$307$	−4.59875			−0.262465			−0.131232	−	0.991352i	$-0.541893\pi$
$307$	−4.59875			−0.262465			−0.131232	+	0.991352i	$0.541893\pi$
$308$	2.69134	+	16.5505i	0.153353	+	0.943053i
$309$	−1.01149			−0.0575415
$310$	0.256992	−	0.0835019i	0.0145962	−	0.00474259i
$311$	3.69907	+	2.68753i	0.209755	+	0.152396i	0.687703	−	0.725992i	$-0.258619\pi$
$311$	3.69907	+	2.68753i	0.209755	+	0.152396i	−0.477948	+	0.878388i	$0.658619\pi$
$312$	−4.27422	−	5.88295i	−0.241980	−	0.333057i
$313$	−1.24092	+	3.81915i	−0.0701409	+	0.215871i	−0.979982	−	0.199085i	$-0.936203\pi$
$313$	−1.24092	+	3.81915i	−0.0701409	+	0.215871i	0.909841	+	0.414956i	$0.136203\pi$
$314$	2.53050	−	7.78807i	0.142804	−	0.439506i
$315$	−0.353808	−	0.486975i	−0.0199348	−	0.0274379i
$316$	−5.43349	−	3.94766i	−0.305658	−	0.222073i
$317$	−24.1098	+	7.83376i	−1.35414	+	0.439988i	−0.894083	−	0.447901i	$-0.852172\pi$
$317$	−24.1098	+	7.83376i	−1.35414	+	0.439988i	−0.460059	+	0.887888i	$0.652172\pi$
$318$	2.21026			0.123945
$319$	−8.78030	−	4.42828i	−0.491602	−	0.247936i
$320$	0.973311			0.0544098
$321$	15.7749	−	5.12559i	0.880471	−	0.286082i
$322$	0.648108	−	0.892044i	0.0361176	−	0.0497116i
$323$	1.25608	+	17.9305i	0.0698900	+	0.997682i
$324$	−0.569002	+	1.75121i	−0.0316112	+	0.0972894i
$325$	−7.27222	+	22.3816i	−0.403390	+	1.24151i
$326$	4.32709	−	3.14381i	0.239655	−	0.174120i
$327$	−1.91148	+	2.63092i	−0.105705	+	0.145490i
$328$	−0.0293697	−	0.0903905i	−0.00162167	−	0.00499098i
$329$		−	35.3761i		−	1.95035i
$330$	−0.286247	−	0.0441280i	−0.0157574	−	0.00242917i
$331$		−	6.48294i		−	0.356334i	−0.984000	−	0.178167i	$-0.942983\pi$
$331$		−	6.48294i		−	0.356334i	0.984000	−	0.178167i	$-0.0570168\pi$
$332$	2.75147	−	0.894008i	0.151007	−	0.0490650i
$333$	5.04929	−	6.94975i	0.276699	−	0.380844i
$334$	−5.50196	+	3.99741i	−0.301054	+	0.218728i
$335$	0.880919	+	0.286228i	0.0481297	+	0.0156383i
$336$	−2.60747	+	8.02495i	−0.142249	+	0.437797i
$337$	−19.4298	+	14.1166i	−1.05841	+	0.768979i	−0.973793	−	0.227434i	$-0.926966\pi$
$337$	−19.4298	+	14.1166i	−1.05841	+	0.768979i	−0.0846157	+	0.996414i	$0.526966\pi$
$338$	3.08883	+	2.24417i	0.168010	+	0.122067i
$339$	−5.66479	−	17.4344i	−0.307669	−	0.946909i
$340$		−	1.66460i		−	0.0902755i
$341$	−7.28675	−	7.22691i	−0.394600	−	0.391359i
$342$	1.47258	+	0.919912i	0.0796278	+	0.0497431i
$343$	−16.8722	+	5.48210i	−0.911011	+	0.296005i
$344$	−7.50238	+	10.3261i	−0.404501	+	0.556748i
$345$	−0.129912	−	0.178808i	−0.00699420	−	0.00962669i
$346$	2.73145	−	8.40655i	0.146844	−	0.451939i
$347$	−13.3547	−	4.33920i	−0.716917	−	0.232940i	−0.0722308	−	0.997388i	$-0.523012\pi$
$347$	−13.3547	−	4.33920i	−0.716917	−	0.232940i	−0.644686	+	0.764448i	$0.723012\pi$
$348$	−3.20904	−	4.41686i	−0.172022	−	0.236769i
$349$	2.60276	−	3.58239i	0.139322	−	0.191761i	−0.733654	−	0.679523i	$-0.762187\pi$
$349$	2.60276	−	3.58239i	0.139322	−	0.191761i	0.872976	+	0.487762i	$0.162187\pi$
$350$	−5.15085	+	1.67361i	−0.275325	+	0.0894584i
$351$		−	4.75236i		−	0.253662i
$352$	6.50324	+	12.6343i	0.346624	+	0.673409i
$353$	−30.9762			−1.64870			−0.824348	−	0.566084i	$-0.808458\pi$
$353$	−30.9762			−1.64870			−0.824348	+	0.566084i	$0.808458\pi$
$354$	1.17866	+	3.62754i	0.0626451	+	0.192802i
$355$	0.646211	−	0.889433i	0.0342973	−	0.0472062i
$356$	14.8653	+	20.4604i	0.787861	+	1.08440i
$357$	10.7680	+	3.49875i	0.569905	+	0.185173i
$358$	−1.75330	−	0.569682i	−0.0926649	−	0.0301087i
$359$	−13.5164	−	18.6037i	−0.713368	−	0.981867i	−0.999718	−	0.0237422i	$-0.992442\pi$
$359$	−13.5164	−	18.6037i	−0.713368	−	0.981867i	0.286350	−	0.958125i	$-0.407558\pi$
$360$	−0.271384	−	0.197172i	−0.0143032	−	0.0103919i
$361$	−13.6642	+	13.2019i	−0.719166	+	0.694838i
$362$			4.01267i			0.210901i
$363$	3.48534	+	10.4332i	0.182933	+	0.547603i
$364$		−	24.0266i		−	1.25934i
$365$	0.962410	−	0.312706i	0.0503748	−	0.0163678i
$366$	−2.63864	−	1.91708i	−0.137924	−	0.100208i
$367$	−12.1813	+	8.85022i	−0.635858	+	0.461978i	−0.858425	−	0.512940i	$-0.828557\pi$
$367$	−12.1813	+	8.85022i	−0.635858	+	0.461978i	0.222567	+	0.974917i	$0.428557\pi$
$368$	−0.957411	+	2.94661i	−0.0499085	+	0.153603i
$369$	0.0191942	−	0.0590737i	0.000999211	−	0.00307526i
$370$	0.440935	+	0.606895i	0.0229231	+	0.0315510i
$371$	12.3255	+	8.95503i	0.639910	+	0.464922i
$372$	−1.76069	−	5.41885i	−0.0912877	−	0.280955i
$373$	−13.5680			−0.702523			−0.351262	−	0.936277i	$-0.614247\pi$
$373$	−13.5680			−0.702523			−0.351262	+	0.936277i	$0.614247\pi$
$374$	4.84380	−	2.49325i	0.250467	−	0.128923i
$375$			2.18175i			0.112665i
$376$	−6.09213	−	18.7496i	−0.314178	−	0.966939i
$377$	11.3997	+	8.28233i	0.587112	+	0.426562i
$378$	0.884821	−	0.642860i	0.0455103	−	0.0330651i
$379$	−33.1002	−	10.7549i	−1.70024	−	0.552442i	−0.711581	−	0.702605i	$-0.752020\pi$
$379$	−33.1002	−	10.7549i	−1.70024	−	0.552442i	−0.988661	+	0.150162i	$0.952020\pi$
$380$	1.34777	−	1.13120i	0.0691390	−	0.0580293i
$381$	6.99722	+	9.63084i	0.358478	+	0.493403i
$382$	−0.568009	−	0.412683i	−0.0290619	−	0.0211147i
$383$	0.723206	−	0.234984i	0.0369541	−	0.0120071i	−0.290482	−	0.956881i	$-0.593816\pi$
$383$	0.723206	−	0.234984i	0.0369541	−	0.0120071i	0.327436	+	0.944873i	$0.393816\pi$
$384$			10.3373i			0.527522i
$385$	−1.41747	−	1.40583i	−0.0722409	−	0.0716477i
$386$	8.20499			0.417623
$387$	−7.93339	+	2.57771i	−0.403277	+	0.131033i
$388$	19.8345	−	27.2998i	1.00694	−	1.38594i
$389$	2.03111	−	1.47569i	0.102982	−	0.0748205i	−0.535103	−	0.844787i	$-0.679727\pi$
$389$	2.03111	−	1.47569i	0.102982	−	0.0748205i	0.638084	+	0.769967i	$0.279727\pi$
$390$	0.394694	+	0.128244i	0.0199861	+	0.00649388i
$391$	3.95382	+	1.28467i	0.199953	+	0.0649687i
$392$	0.666976	−	0.484586i	0.0336874	−	0.0244753i
$393$	10.5799	+	7.68677i	0.533687	+	0.387746i
$394$	−1.80782	+	0.587395i	−0.0910764	+	0.0295925i
$395$	0.799627			0.0402336
$396$	−0.930468	+	6.03570i	−0.0467578	+	0.303305i
$397$	15.4015			0.772980			0.386490	−	0.922294i	$-0.373687\pi$
$397$	15.4015			0.772980			0.386490	+	0.922294i	$0.373687\pi$
$398$	−1.11133	−	3.42031i	−0.0557057	−	0.171445i
$399$	4.48474	+	11.0961i	0.224518	+	0.555502i
$400$	12.3117	−	8.94497i	0.615585	−	0.447249i
$401$	21.8630	+	7.10373i	1.09179	+	0.354744i	0.798937	−	0.601414i	$-0.205396\pi$
$401$	21.8630	+	7.10373i	1.09179	+	0.354744i	0.292851	+	0.956158i	$0.405396\pi$
$402$	−0.520068	+	1.60061i	−0.0259386	+	0.0798309i
$403$	8.64366	+	11.8970i	0.430571	+	0.592631i
$404$	5.61117	−	7.72311i	0.279166	−	0.384239i
$405$	−0.0677455	−	0.208499i	−0.00336630	−	0.0103604i
$406$			3.24281i			0.160938i
$407$	12.8299	−	25.4388i	0.635953	−	1.26095i
$408$	6.30969			0.312376
$409$	0.0897564	+	0.276242i	0.00443817	+	0.0136593i	0.953251	−	0.302179i	$-0.0977142\pi$
$409$	0.0897564	+	0.276242i	0.00443817	+	0.0136593i	−0.948813	+	0.315839i	$0.897714\pi$
$410$	0.00438824	+	0.00318824i	0.000216720	+	0.000157456i
$411$	−1.51643	−	2.08719i	−0.0748002	−	0.102954i
$412$	−1.77133	−	0.575538i	−0.0872669	−	0.0283547i
$413$	−8.12443	+	25.0044i	−0.399777	+	1.23039i
$414$	0.324889	−	0.236046i	0.0159674	−	0.0116010i
$415$	−0.202462	+	0.278665i	−0.00993848	+	0.0136791i
$416$	−6.29190	−	19.3645i	−0.308486	−	0.949422i
$417$	10.2132			0.500142
$418$	5.31036	+	2.22754i	0.259738	+	0.108953i
$419$	27.1353			1.32565			0.662823	−	0.748776i	$-0.269358\pi$
$419$	27.1353			1.32565			0.662823	+	0.748776i	$0.269358\pi$
$420$	−0.342502	−	1.05411i	−0.0167124	−	0.0514355i
$421$	−8.96552	+	12.3400i	−0.436953	+	0.601414i	−0.969532	−	0.244966i	$-0.921223\pi$
$421$	−8.96552	+	12.3400i	−0.436953	+	0.601414i	0.532579	+	0.846381i	$0.321223\pi$
$422$	−2.44966	+	1.77978i	−0.119248	+	0.0866384i
$423$	3.98145	−	12.2536i	0.193585	−	0.595792i
$424$	8.07480	+	2.62366i	0.392147	+	0.127416i
$425$	−12.0025	−	16.5201i	−0.582209	−	0.801342i
$426$	1.61607	+	1.17415i	0.0782991	+	0.0568876i
$427$	−6.94719	−	21.3812i	−0.336198	−	1.03471i
$428$	30.5417			1.47629
$429$	−2.52986	−	15.5575i	−0.122143	−	0.751121i
$430$		−	0.728445i		−	0.0351288i
$431$	11.6034	+	35.7117i	0.558917	+	1.72017i	0.685368	+	0.728197i	$0.259641\pi$
$431$	11.6034	+	35.7117i	0.558917	+	1.72017i	−0.126451	+	0.991973i	$0.540359\pi$
$432$	−1.80636	+	2.48624i	−0.0869084	+	0.119619i
$433$	−17.4579	−	24.0287i	−0.838972	−	1.15475i	−0.986186	−	0.165641i	$-0.947031\pi$
$433$	−17.4579	−	24.0287i	−0.838972	−	1.15475i	0.147215	−	0.989105i	$-0.452969\pi$
$434$	−1.04580	+	3.21865i	−0.0502001	+	0.154500i
$435$	0.618200	+	0.200865i	0.0296404	+	0.00963075i
$436$	−4.84440	+	3.51966i	−0.232005	+	0.168561i
$437$	1.64671	+	4.07429i	0.0787729	+	0.194900i
$438$	0.568178	+	1.74867i	0.0271486	+	0.0835548i
$439$	−25.9311			−1.23763			−0.618813	−	0.785538i	$-0.712386\pi$
$439$	−25.9311			−1.23763			−0.618813	+	0.785538i	$0.712386\pi$
$440$	−0.993371	−	0.500999i	−0.0473571	−	0.0238842i
$441$	0.538796			0.0256570
$442$	−7.42407	+	2.41223i	−0.353127	+	0.114738i
$443$	10.2673	+	7.45963i	0.487814	+	0.354418i	0.804343	−	0.594165i	$-0.202517\pi$
$443$	10.2673	+	7.45963i	0.487814	+	0.354418i	−0.316529	+	0.948583i	$0.602517\pi$
$444$	12.7968	−	9.29741i	0.607309	−	0.441236i
$445$	−2.86371	−	0.930475i	−0.135753	−	0.0441087i
$446$	3.98698	+	1.29545i	0.188789	+	0.0613413i
$447$	−6.66741	+	4.84415i	−0.315357	+	0.229121i
$448$	−7.16512	+	9.86194i	−0.338520	+	0.465933i
$449$	−23.2935	+	7.56851i	−1.09929	+	0.357180i	−0.801828	−	0.597554i	$-0.796139\pi$
$449$	−23.2935	+	7.56851i	−1.09929	+	0.357180i	−0.297459	+	0.954735i	$0.596139\pi$
$450$	−1.97252			−0.0929856
$451$	0.0313876	−	0.203603i	0.00147798	−	0.00958729i
$452$		−	33.7546i		−	1.58768i
$453$	−0.808612	+	0.262734i	−0.0379919	+	0.0123443i
$454$	6.07844	+	4.41624i	0.285275	+	0.207265i
$455$	1.68142	+	2.31428i	0.0788264	+	0.108495i
$456$	4.28783	+	5.10874i	0.200796	+	0.239238i
$457$	−22.1925	−	7.21078i	−1.03812	−	0.337306i	−0.260125	−	0.965575i	$-0.583764\pi$
$457$	−22.1925	−	7.21078i	−1.03812	−	0.337306i	−0.777996	+	0.628269i	$0.783764\pi$
$458$	−8.76857	+	6.37074i	−0.409728	+	0.297685i
$459$	3.33609	+	2.42381i	0.155715	+	0.113134i
$460$	−0.125760	−	0.387050i	−0.00586360	−	0.0180463i
$461$		−	4.83351i		−	0.225119i	−0.993645	−	0.112560i	$-0.964095\pi$
$461$		−	4.83351i		−	0.225119i	0.993645	−	0.112560i	$-0.0359049\pi$
$462$	2.55435	−	2.57550i	0.118839	−	0.119823i
$463$	14.7792			0.686849			0.343425	−	0.939180i	$-0.388413\pi$
$463$	14.7792			0.686849			0.343425	+	0.939180i	$0.388413\pi$
$464$	−2.81574	−	8.66594i	−0.130717	−	0.402306i
$465$	0.548814	+	0.398737i	0.0254506	+	0.0184910i
$466$	−3.81325	−	5.24848i	−0.176645	−	0.243131i
$467$	7.76504	−	23.8983i	0.359323	−	1.10588i	−0.594137	−	0.804364i	$-0.702506\pi$
$467$	7.76504	−	23.8983i	0.359323	−	1.10588i	0.953460	−	0.301519i	$-0.0974937\pi$
$468$	2.70411	−	8.32238i	0.124997	−	0.384702i
$469$	−9.38513	+	6.81869i	−0.433365	+	0.314858i
$470$	0.910250	+	0.661336i	0.0419867	+	0.0305051i
$471$	19.5516	−	6.35271i	0.900892	−	0.292718i
$472$			14.6517i			0.674399i
$473$	−24.5987	+	12.6617i	−1.13105	+	0.582186i
$474$			1.45290i			0.0667339i
$475$	5.21927	−	20.9445i	0.239476	−	0.960999i
$476$	16.8663	+	12.2541i	0.773066	+	0.561665i
$477$	3.26149	+	4.48905i	0.149333	+	0.205540i
$478$	−0.183426	−	0.0595986i	−0.00838970	−	0.00272598i
$479$	20.9211	+	6.79767i	0.955908	+	0.310593i	0.745114	−	0.666937i	$-0.232395\pi$
$479$	20.9211	+	6.79767i	0.955908	+	0.310593i	0.210794	+	0.977530i	$0.432395\pi$
$480$	−0.552086	−	0.759882i	−0.0251992	−	0.0346837i
$481$	−23.9961	+	33.0277i	−1.09413	+	1.50593i
$482$	2.21850	+	6.82785i	0.101050	+	0.311000i
$483$	2.76810			0.125953
$484$	0.167022	+	20.2539i	0.00759192	+	0.920634i
$485$			4.01761i			0.182430i
$486$	0.378837	−	0.123092i	0.0171844	−	0.00558355i
$487$	9.51491	−	13.0961i	0.431162	−	0.593443i	−0.537058	−	0.843546i	$-0.680464\pi$
$487$	9.51491	−	13.0961i	0.431162	−	0.593443i	0.968219	+	0.250102i	$0.0804643\pi$
$488$	−7.36415	−	10.1359i	−0.333359	−	0.458830i
$489$	12.7702	+	4.14929i	0.577489	+	0.187638i
$490$	−0.0145396	+	0.0447482i	−0.000656831	+	0.00202152i
$491$	14.7133	+	20.2511i	0.664000	+	0.913918i	0.999606	−	0.0280849i	$-0.00894087\pi$
$491$	14.7133	+	20.2511i	0.664000	+	0.913918i	−0.335605	+	0.942003i	$0.608941\pi$
$492$	0.0672262	−	0.0925289i	0.00303079	−	0.00417153i
$493$	−11.6281	+	3.77821i	−0.523705	+	0.170162i
$494$	−6.99822	−	4.37175i	−0.314865	−	0.196695i
$495$	−0.332765	−	0.646485i	−0.0149567	−	0.0290573i
$496$		−	9.50943i		−	0.426986i
$497$	4.25491	+	13.0953i	0.190859	+	0.587403i
$498$	−0.506327	−	0.367868i	−0.0226891	−	0.0164846i
$499$	−1.72003	+	1.24967i	−0.0769991	+	0.0559431i	−0.625619	−	0.780129i	$-0.715153\pi$
$499$	−1.72003	+	1.24967i	−0.0769991	+	0.0559431i	0.548620	+	0.836072i	$0.315153\pi$
$500$	−1.24142	+	3.82071i	−0.0555182	+	0.170867i
$501$	−16.2375	−	5.27589i	−0.725439	−	0.235709i
$502$	4.78956	−	3.47982i	0.213768	−	0.155312i
$503$	−3.97170	+	5.46658i	−0.177090	+	0.243743i	−0.888330	−	0.459206i	$-0.848134\pi$
$503$	−3.97170	+	5.46658i	−0.177090	+	0.243743i	0.711240	+	0.702949i	$0.248134\pi$
$504$	3.99563	−	1.29826i	0.177980	−	0.0578291i
$505$			1.13658i			0.0505773i
$506$	0.937909	−	0.945675i	0.0416951	−	0.0420404i
$507$			9.58495i			0.425683i
$508$	6.77362	+	20.8471i	0.300531	+	0.924939i
$509$	14.9357	−	20.5572i	0.662011	−	0.911180i	−0.337535	−	0.941313i	$-0.609593\pi$
$509$	14.9357	−	20.5572i	0.662011	−	0.911180i	0.999546	+	0.0301328i	$0.00959303\pi$
$510$	−0.291328	+	0.211662i	−0.0129002	+	0.00937255i
$511$	−3.91642	+	12.0535i	−0.173252	+	0.533215i
$512$	−6.97492	+	21.4666i	−0.308251	+	0.948698i
$513$	0.304605	+	4.34824i	0.0134486	+	0.191980i
$514$	1.24115	−	1.70830i	0.0547449	−	0.0753499i
$515$	0.210894	−	0.0685237i	0.00929311	−	0.00301951i
$516$	−15.3597			−0.676175
$517$	6.51071	−	42.2333i	0.286340	−	1.85742i
$518$	−9.39527			−0.412804
$519$	21.1043	−	6.85721i	0.926376	−	0.300998i
$520$	1.28971	+	0.937033i	0.0565577	+	0.0410916i
$521$	20.3997	+	28.0778i	0.893727	+	1.23011i	0.972426	+	0.233212i	$0.0749235\pi$
$521$	20.3997	+	28.0778i	0.893727	+	1.23011i	−0.0786986	+	0.996898i	$0.525076\pi$
$522$	−0.364967	+	1.12325i	−0.0159742	+	0.0491634i
$523$	12.5179	−	38.5262i	0.547370	−	1.68463i	−0.167917	−	0.985801i	$-0.553704\pi$
$523$	12.5179	−	38.5262i	0.547370	−	1.68463i	0.715287	−	0.698831i	$-0.246296\pi$
$524$	14.1539	+	19.4812i	0.618315	+	0.851038i
$525$	−10.9998	−	7.99181i	−0.480070	−	0.348791i
$526$	−9.13863	+	2.96932i	−0.398463	+	0.129469i
$527$	−12.7599			−0.555832
$528$	−4.58982	+	9.10060i	−0.199746	+	0.396053i
$529$	−21.9836			−0.955809
$530$	−0.460838	+	0.149735i	−0.0200175	+	0.00650409i
$531$	−5.62832	+	7.74671i	−0.244248	+	0.336179i
$532$	1.54000	+	21.9835i	0.0667673	+	0.953105i
$533$	−0.0912179	+	0.280740i	−0.00395109	+	0.0121602i
$534$	1.69065	−	5.20328i	0.0731615	−	0.225168i
$535$	−2.94183	+	2.13736i	−0.127186	+	0.0924063i
$536$	−3.79995	+	5.23019i	−0.164133	+	0.225910i
$537$	−1.43017	−	4.40160i	−0.0617162	−	0.189943i
$538$			4.02552i			0.173553i
$539$	1.76382	−	0.286821i	0.0759729	−	0.0123542i
$540$		−	0.403673i		−	0.0173713i
$541$	−12.9320	+	4.20186i	−0.555990	+	0.180652i	−0.573516	−	0.819194i	$-0.694421\pi$
$541$	−12.9320	+	4.20186i	−0.555990	+	0.180652i	0.0175260	+	0.999846i	$0.494421\pi$
$542$	1.35648	−	1.86703i	0.0582658	−	0.0801960i
$543$	−8.14975	+	5.92114i	−0.349739	+	0.254100i
$544$	16.8026	+	5.45949i	0.720405	+	0.234074i
$545$	0.220309	−	0.678040i	0.00943698	−	0.0290440i
$546$	−4.20499	+	3.05510i	−0.179957	+	0.130746i
$547$	9.14201	+	6.64206i	0.390884	+	0.283994i	0.765818	−	0.643058i	$-0.222334\pi$
$547$	9.14201	+	6.64206i	0.390884	+	0.283994i	−0.374934	+	0.927052i	$0.622334\pi$
$548$	−1.46798	−	4.51797i	−0.0627088	−	0.192998i
$549$		−	8.18796i		−	0.349454i
$550$	−6.45730	+	1.05005i	−0.275340	+	0.0447741i
$551$	−10.9611	−	6.84737i	−0.466960	−	0.291708i
$552$	1.46712	−	0.476696i	0.0624447	−	0.0202895i
$553$	−5.88653	+	8.10211i	−0.250321	+	0.344537i
$554$	−4.97007	−	6.84071i	−0.211158	−	0.290634i
$555$	−0.581959	+	1.79108i	−0.0247028	+	0.0760273i
$556$	17.8854	+	5.81133i	0.758512	+	0.246455i
$557$	8.15115	+	11.2191i	0.345375	+	0.475368i	0.946002	−	0.324162i	$-0.105082\pi$
$557$	8.15115	+	11.2191i	0.345375	+	0.475368i	−0.600627	+	0.799530i	$0.705082\pi$
$558$	−0.724494	+	0.997180i	−0.0306703	+	0.0422140i
$559$	37.7023	−	12.2502i	1.59464	−	0.518130i
$560$		−	1.84984i		−	0.0781700i
$561$	12.2114	+	6.15872i	0.515565	+	0.260021i
$562$	−1.65493			−0.0698090
$563$	−7.71743	−	23.7518i	−0.325251	−	1.00102i	−0.971327	−	0.237747i	$-0.923591\pi$
$563$	−7.71743	−	23.7518i	−0.325251	−	1.00102i	0.646076	−	0.763273i	$-0.276409\pi$
$564$	13.9447	−	19.1932i	0.587177	−	0.808180i
$565$	2.36221	+	3.25130i	0.0993789	+	0.136783i
$566$	10.2836	+	3.34133i	0.432250	+	0.140447i
$567$	2.61130	+	0.848464i	0.109664	+	0.0356321i
$568$	4.51029	+	6.20788i	0.189247	+	0.260477i
$569$	29.3149	+	21.2985i	1.22894	+	0.892880i	0.996811	−	0.0798038i	$-0.0254294\pi$
$569$	29.3149	+	21.2985i	1.22894	+	0.892880i	0.232133	+	0.972684i	$0.425429\pi$
$570$	−0.369351	−	0.0920405i	−0.0154704	−	0.00385515i
$571$		−	9.93710i		−	0.415855i	−0.978144	−	0.207927i	$-0.933328\pi$
$571$		−	9.93710i		−	0.415855i	0.978144	−	0.207927i	$-0.0666717\pi$
$572$	4.42192	−	28.6839i	0.184890	−	1.19933i
$573$		−	1.76259i		−	0.0736333i
$574$	−0.0646089	+	0.0209927i	−0.00269672	+	0.000876218i
$575$	−4.03891	−	2.93444i	−0.168434	−	0.122374i
$576$	−3.59179	+	2.60959i	−0.149658	+	0.108733i
$577$	0.0335817	−	0.103354i	0.00139802	−	0.00430268i	−0.950355	−	0.311168i	$-0.899280\pi$
$577$	0.0335817	−	0.103354i	0.00139802	−	0.00430268i	0.951753	+	0.306865i	$0.0992800\pi$
$578$	0.000530342	−	0.00163222i	2.20593e−5	−	6.78916e-5i
$579$	12.1074	+	16.6644i	0.503166	+	0.692548i
$580$	0.968305	+	0.703514i	0.0402067	+	0.0292118i
$581$	−1.33309	−	4.10284i	−0.0553060	−	0.170214i
$582$	−7.29990			−0.302590
$583$	13.0666	+	12.9593i	0.541162	+	0.536718i
$584$			7.06291i			0.292265i
$585$	0.321951	+	0.990864i	0.0133110	+	0.0409672i
$586$	−9.02557	−	6.55746i	−0.372843	−	0.270886i
$587$	13.7509	−	9.99059i	0.567559	−	0.412356i	−0.266659	−	0.963791i	$-0.585920\pi$
$587$	13.7509	−	9.99059i	0.567559	−	0.412356i	0.834218	+	0.551435i	$0.185920\pi$
$588$	0.943545	+	0.306576i	0.0389111	+	0.0126430i
$589$	−8.67118	−	10.3313i	−0.357290	−	0.425693i
$590$	−0.491500	−	0.676491i	−0.0202347	−	0.0278507i
$591$	−3.86064	−	2.80492i	−0.158805	−	0.115379i
$592$	25.1075	−	8.15791i	1.03191	−	0.335288i
$593$			24.6617i			1.01274i	0.862318	+	0.506368i	$0.169012\pi$
$593$			24.6617i			1.01274i	−0.862318	+	0.506368i	$0.830988\pi$
$594$	1.17465	−	0.604625i	0.0481963	−	0.0248081i
$595$	−2.48215			−0.101758
$596$	−14.4324	+	4.68936i	−0.591173	+	0.192084i
$597$	5.30678	−	7.30416i	0.217192	−	0.298939i
$598$	−1.54399	+	1.12177i	−0.0631385	+	0.0458728i
$599$	−18.2714	−	5.93672i	−0.746547	−	0.242568i	−0.0890523	−	0.996027i	$-0.528384\pi$
$599$	−18.2714	−	5.93672i	−0.746547	−	0.242568i	−0.657495	+	0.753459i	$0.728384\pi$
$600$	−7.20626	−	2.34146i	−0.294194	−	0.0955895i
$601$	20.5506	−	14.9309i	0.838278	−	0.609045i	−0.0836110	−	0.996498i	$-0.526645\pi$
$601$	20.5506	−	14.9309i	0.838278	−	0.609045i	0.921889	+	0.387454i	$0.126645\pi$
$602$	7.38087	+	5.36252i	0.300822	+	0.218560i
$603$	−4.01826	+	1.30561i	−0.163636	+	0.0531686i
$604$	−1.56555			−0.0637012
$605$	−1.43350	−	1.93921i	−0.0582799	−	0.0788399i
$606$	−2.06514			−0.0838905
$607$	12.9255	+	39.7804i	0.524628	+	1.61464i	0.765051	+	0.643970i	$0.222714\pi$
$607$	12.9255	+	39.7804i	0.524628	+	1.61464i	−0.240423	+	0.970668i	$0.577286\pi$
$608$	6.99804	+	17.3145i	0.283808	+	0.702197i
$609$	−6.58617	+	4.78513i	−0.266885	+	0.193903i
$610$	0.680028	+	0.220954i	0.0275335	+	0.00894618i
$611$	−18.9213	+	58.2337i	−0.765473	+	2.35588i
$612$	4.46303	+	6.14284i	0.180407	+	0.248309i
$613$	−18.4224	+	25.3563i	−0.744075	+	1.02413i	0.254299	+	0.967126i	$0.418155\pi$
$613$	−18.4224	+	25.3563i	−0.744075	+	1.02413i	−0.998374	+	0.0570053i	$0.981845\pi$
$614$	0.566068	+	1.74218i	0.0228447	+	0.0703086i
$615$			0.0136172i			0.000549097i
$616$	12.3891	−	6.37704i	0.499171	−	0.256938i
$617$	−47.0927			−1.89588			−0.947939	−	0.318451i	$-0.896837\pi$
$617$	−47.0927			−1.89588			−0.947939	+	0.318451i	$0.896837\pi$
$618$	0.124506	+	0.383189i	0.00500835	+	0.0154141i
$619$	16.2907	+	11.8359i	0.654779	+	0.475725i	0.864896	−	0.501951i	$-0.167384\pi$
$619$	16.2907	+	11.8359i	0.654779	+	0.475725i	−0.210117	+	0.977676i	$0.567384\pi$
$620$	0.734206	+	1.01055i	0.0294864	+	0.0405846i
$621$	0.958820	+	0.311540i	0.0384761	+	0.0125017i
$622$	0.562812	−	1.73216i	0.0225667	−	0.0694532i
$623$	30.5093	−	22.1663i	1.22233	−	0.888075i
$624$	8.58447	−	11.8155i	0.343654	−	0.472999i
$625$	7.50336	+	23.0930i	0.300134	+	0.923719i
$626$	1.59959			0.0639323
$627$	3.31189	+	14.0724i	0.132264	+	0.561996i
$628$	37.8537			1.51053
$629$	−10.9465	−	33.6897i	−0.436464	−	1.34330i
$630$	−0.140934	+	0.193978i	−0.00561493	+	0.00772828i
$631$	0.141741	−	0.102981i	0.00564260	−	0.00409959i	−0.584960	−	0.811062i	$-0.698890\pi$
$631$	0.141741	−	0.102981i	0.00564260	−	0.00409959i	0.590603	+	0.806962i	$0.298890\pi$
$632$	−1.72465	+	5.30792i	−0.0686027	+	0.211138i
$633$	−7.22949	−	2.34900i	−0.287347	−	0.0933646i
$634$	5.93544	+	8.16943i	0.235726	+	0.324450i
$635$	−2.11136	−	1.53399i	−0.0837868	−	0.0608747i
$636$	3.15727	+	9.71707i	0.125194	+	0.385307i
$637$	−2.56055			−0.101453
$638$	−0.596816	+	3.87139i	−0.0236282	+	0.153270i
$639$			5.01484i			0.198384i
$640$	−0.700305	−	2.15532i	−0.0276820	−	0.0851963i
$641$	19.3874	−	26.6844i	0.765755	−	1.05397i	−0.230958	−	0.972964i	$-0.574186\pi$
$641$	19.3874	−	26.6844i	0.765755	−	1.05397i	0.996713	−	0.0810082i	$-0.0258140\pi$
$642$	−3.88353	−	5.34522i	−0.153271	−	0.210959i
$643$	−0.928099	+	2.85640i	−0.0366007	+	0.112645i	−0.967688	−	0.252152i	$-0.918862\pi$
$643$	−0.928099	+	2.85640i	−0.0366007	+	0.112645i	0.931087	+	0.364797i	$0.118862\pi$
$644$	4.84752	+	1.57506i	0.191019	+	0.0620659i
$645$	1.47948	−	1.07490i	0.0582543	−	0.0423243i
$646$	6.63815	−	2.68295i	0.261174	−	0.105559i
$647$	12.8363	+	39.5062i	0.504648	+	1.55315i	0.801361	+	0.598181i	$0.204110\pi$
$647$	12.8363	+	39.5062i	0.504648	+	1.55315i	−0.296713	+	0.954967i	$0.595890\pi$
$648$	1.53013			0.0601092
$649$	−14.3011	+	28.3560i	−0.561369	+	1.11307i
$650$	9.37414			0.367684
$651$	−8.08029	+	2.62544i	−0.316691	+	0.102899i
$652$	20.0024	+	14.5326i	0.783353	+	0.569139i
$653$	−28.1549	+	20.4557i	−1.10179	+	0.800494i	−0.981350	−	0.192227i	$-0.938429\pi$
$653$	−28.1549	+	20.4557i	−1.10179	+	0.800494i	−0.120435	+	0.992721i	$0.538429\pi$
$654$	1.23198	+	0.400295i	0.0481742	+	0.0156528i
$655$	−2.72665	−	0.885943i	−0.106539	−	0.0346167i
$656$	0.154430	−	0.112200i	0.00602947	−	0.00438067i
$657$	−2.71315	+	3.73433i	−0.105850	+	0.145690i
$658$	−13.4018	+	4.35450i	−0.522456	+	0.169756i
$659$	16.7671			0.653152			0.326576	−	0.945171i	$-0.394105\pi$
$659$	16.7671			0.653152			0.326576	+	0.945171i	$0.394105\pi$
$660$	−0.214890	−	1.32147i	−0.00836458	−	0.0514383i
$661$		−	28.7453i		−	1.11806i	−0.829147	−	0.559031i	$-0.811173\pi$
$661$		−	28.7453i		−	1.11806i	0.829147	−	0.559031i	$-0.188827\pi$
$662$	−2.45598	+	0.797996i	−0.0954543	+	0.0310150i
$663$	−15.8543	−	11.5188i	−0.615729	−	0.447354i
$664$	−1.41310	−	1.94497i	−0.0548390	−	0.0754795i
$665$	−1.68678	−	2.00971i	−0.0654105	−	0.0779334i
$666$	−3.25435	−	1.05740i	−0.126104	−	0.0409735i
$667$	−2.41832	+	1.75701i	−0.0936375	+	0.0680317i
$668$	−25.4333	−	18.4784i	−0.984044	−	0.714950i
$669$	3.25217	+	10.0092i	0.125736	+	0.386977i
$670$		−	0.368957i		−	0.0142541i
$671$	−4.35875	−	26.8043i	−0.168268	−	1.03477i
$672$	11.7636			0.453792
$673$	0.349266	+	1.07493i	0.0134632	+	0.0414355i	0.957562	−	0.288226i	$-0.0930654\pi$
$673$	0.349266	+	1.07493i	0.0134632	+	0.0414355i	−0.944099	+	0.329661i	$0.893065\pi$
$674$	7.73954	+	5.62310i	0.298116	+	0.216594i
$675$	−2.91068	−	4.00620i	−0.112032	−	0.154199i
$676$	−5.45386	+	16.7853i	−0.209764	+	0.645587i
$677$	−1.50308	+	4.62600i	−0.0577679	+	0.177791i	−0.975777	−	0.218768i	$-0.929796\pi$
$677$	−1.50308	+	4.62600i	−0.0577679	+	0.177791i	0.918009	+	0.396560i	$0.129796\pi$
$678$	−5.90753	+	4.29207i	−0.226877	+	0.164836i
$679$	−40.7079	−	29.5760i	−1.56223	−	1.13502i
$680$	−1.31556	+	0.427453i	−0.0504496	+	0.0163921i
$681$			18.8620i			0.722793i
$682$	−1.84089	+	3.65007i	−0.0704911	+	0.139768i
$683$		−	0.0517566i		−	0.00198041i	−1.00000		0.000990206i	$-0.999685\pi$
$683$		−	0.0517566i		−	0.00198041i	1.00000		0.000990206i	$-0.000315192\pi$
$684$	−1.94073	+	7.78801i	−0.0742058	+	0.297782i
$685$	0.457573	+	0.332446i	0.0174830	+	0.0127021i
$686$	4.15365	+	5.71701i	0.158587	+	0.218276i
$687$	−25.8780	−	8.40827i	−0.987307	−	0.320796i
$688$	−24.3806	−	7.92173i	−0.929500	−	0.302013i
$689$	−15.4998	−	21.3336i	−0.590494	−	0.812746i
$690$	−0.0517481	+	0.0712251i	−0.00197002	+	0.00271149i
$691$	5.97879	+	18.4008i	0.227444	+	0.700001i	0.998034	+	0.0626700i	$0.0199615\pi$
$691$	5.97879	+	18.4008i	0.227444	+	0.700001i	−0.770590	+	0.637331i	$0.780038\pi$
$692$	40.8598			1.55326
$693$	9.00009	+	1.38746i	0.341885	+	0.0527053i
$694$			5.59337i			0.212321i
$695$	−2.12944	+	0.691898i	−0.0807744	+	0.0262452i
$696$	−2.66668	+	3.67037i	−0.101080	+	0.139125i
$697$	−0.150552	−	0.207217i	−0.00570256	−	0.00784890i
$698$	−1.67752	−	0.545059i	−0.0634951	−	0.0206308i
$699$	5.03283	−	15.4895i	0.190359	−	0.585865i
$700$	−14.7156	−	20.2542i	−0.556196	−	0.765538i
$701$	9.99521	−	13.7572i	0.377514	−	0.519603i	−0.577410	−	0.816454i	$-0.695937\pi$
$701$	9.99521	−	13.7572i	0.377514	−	0.519603i	0.954924	+	0.296851i	$0.0959366\pi$
$702$	−1.80037	+	0.584977i	−0.0679507	+	0.0220785i
$703$	19.8386	−	31.7572i	0.748227	−	1.19775i
$704$	−10.3690	+	10.4549i	−0.390796	+	0.394032i
$705$			2.82460i			0.106381i
$706$	3.81291	+	11.7349i	0.143501	+	0.441650i
$707$	−11.5163	−	8.36705i	−0.433113	−	0.314675i
$708$	−14.2643	+	10.3636i	−0.536084	+	0.389488i
$709$	8.87613	−	27.3179i	0.333350	−	1.02595i	−0.634179	−	0.773186i	$-0.718662\pi$
$709$	8.87613	−	27.3179i	0.333350	−	1.02595i	0.967529	−	0.252760i	$-0.0813383\pi$
$710$	−0.416494	−	0.135327i	−0.0156307	−	0.00507873i
$711$	−2.95085	+	2.14392i	−0.110666	+	0.0804032i
$712$	12.3530	−	17.0024i	0.462947	−	0.637191i
$713$	−2.96693	+	0.964012i	−0.111112	+	0.0361026i
$714$		−	4.51000i		−	0.168783i
$715$	1.58142	+	3.07233i	0.0591418	+	0.114899i
$716$		−	8.52189i		−	0.318478i
$717$	−0.149620	−	0.460483i	−0.00558766	−	0.0171971i
$718$	−5.38403	+	7.41048i	−0.200930	+	0.276557i
$719$	30.7326	−	22.3286i	1.14613	−	0.832715i	0.158172	−	0.987412i	$-0.449440\pi$
$719$	30.7326	−	22.3286i	1.14613	−	0.832715i	0.987962	+	0.154697i	$0.0494401\pi$
$720$	0.208193	−	0.640752i	0.00775889	−	0.0238794i
$721$	−0.858210	+	2.64130i	−0.0319614	+	0.0983671i
$722$	6.68333	+	3.55145i	0.248728	+	0.132171i
$723$	−10.5937	+	14.5810i	−0.393986	+	0.542275i
$724$	−17.6411	+	5.73193i	−0.655625	+	0.213025i
$725$	14.6825			0.545294
$726$	3.52348	−	2.60462i	0.130769	−	0.0966666i
$727$	17.3222			0.642446			0.321223	−	0.947004i	$-0.395906\pi$
$727$	17.3222			0.642446			0.321223	+	0.947004i	$0.395906\pi$
$728$	−18.9887	+	6.16980i	−0.703768	+	0.228668i
$729$	0.809017	+	0.587785i	0.0299636	+	0.0217698i
$730$	−0.236929	−	0.326105i	−0.00876915	−	0.0120697i
$731$	−10.6295	+	32.7143i	−0.393147	+	1.20998i
$732$	4.65897	−	14.3388i	0.172200	−	0.529978i
$733$	2.62843	+	3.61773i	0.0970835	+	0.133624i	0.854795	−	0.518965i	$-0.173683\pi$
$733$	2.62843	+	3.61773i	0.0970835	+	0.133624i	−0.757712	+	0.652589i	$0.773683\pi$
$734$	4.85221	+	3.52534i	0.179098	+	0.130123i
$735$	−0.112339	+	0.0365010i	−0.00414367	+	0.00134636i
$736$	4.31938			0.159214
$737$	−12.4592	+	6.41315i	−0.458942	+	0.236231i
$738$	−0.0247420			−0.000910765
$739$	24.5491	−	7.97648i	0.903053	−	0.293420i	0.179556	−	0.983748i	$-0.442534\pi$
$739$	24.5491	−	7.97648i	0.903053	−	0.293420i	0.723497	+	0.690328i	$0.242534\pi$
$740$	−2.03826	+	2.80543i	−0.0749280	+	0.103130i
$741$	−1.44759	−	20.6644i	−0.0531787	−	0.759127i
$742$	1.87533	−	5.77166i	0.0688454	−	0.211884i
$743$	−4.85608	+	14.9455i	−0.178152	+	0.548297i	−0.999763	−	0.0217518i	$-0.993076\pi$
$743$	−4.85608	+	14.9455i	−0.178152	+	0.548297i	0.821611	+	0.570049i	$0.193076\pi$
$744$	−3.83050	+	2.78302i	−0.140433	+	0.102030i
$745$	1.06198	−	1.46169i	0.0389079	−	0.0535522i
$746$	1.67011	+	5.14006i	0.0611469	+	0.188191i
$747$		−	1.57118i		−	0.0574866i
$748$	17.8803	+	17.7335i	0.653770	+	0.648401i
$749$		−	45.5420i		−	1.66407i
$750$	0.826530	−	0.268556i	0.0301806	−	0.00980628i
$751$	1.48807	−	2.04816i	0.0543005	−	0.0747383i	−0.781003	−	0.624527i	$-0.785292\pi$
$751$	1.48807	−	2.04816i	0.0543005	−	0.0747383i	0.835304	+	0.549789i	$0.185292\pi$
$752$	32.0333	−	23.2735i	1.16813	−	0.848698i
$753$	14.1351	+	4.59276i	0.515110	+	0.167369i
$754$	1.73445	−	5.33810i	0.0631651	−	0.194402i
$755$	0.150796	−	0.109560i	0.00548803	−	0.00398729i
$756$	4.09016	+	2.97168i	0.148758	+	0.108079i
$757$	2.82767	+	8.70266i	0.102773	+	0.316304i	0.989201	−	0.146563i	$-0.0468210\pi$
$757$	2.82767	+	8.70266i	0.102773	+	0.316304i	−0.886428	+	0.462866i	$0.846821\pi$
$758$			13.8634i			0.503542i
$759$	3.30466	+	0.509449i	0.119952	+	0.0184918i
$760$	−1.24010	−	0.774687i	−0.0449832	−	0.0281008i
$761$	−8.83005	+	2.86906i	−0.320089	+	0.104003i	−0.464655	−	0.885492i	$-0.653822\pi$
$761$	−8.83005	+	2.86906i	−0.320089	+	0.104003i	0.144566	+	0.989495i	$0.453822\pi$
$762$	2.78722	−	3.83628i	0.100970	−	0.138974i
$763$	5.24832	+	7.22369i	0.190002	+	0.261515i
$764$	1.00292	−	3.08666i	0.0362843	−	0.111672i
$765$	−0.859773	−	0.279357i	−0.0310852	−	0.0101002i
$766$	−0.178041	−	0.245053i	−0.00643290	−	0.00885412i
$767$	26.7478	−	36.8152i	0.965807	−	1.32932i
$768$	−4.52866	+	1.47145i	−0.163414	+	0.0530964i
$769$		−	19.1309i		−	0.689879i	−0.938625	−	0.344939i	$-0.887899\pi$
$769$		−	19.1309i		−	0.689879i	0.938625	−	0.344939i	$-0.112101\pi$
$770$	−0.358102	+	0.710037i	−0.0129051	+	0.0255879i
$771$	5.30103			0.190912
$772$	11.7205	+	36.0720i	0.421830	+	1.29826i
$773$	−29.3086	+	40.3399i	−1.05416	+	1.45092i	−0.169010	+	0.985614i	$0.554057\pi$
$773$	−29.3086	+	40.3399i	−1.05416	+	1.45092i	−0.885148	+	0.465310i	$0.845943\pi$
$774$	1.95307	+	2.68817i	0.0702016	+	0.0966242i
$775$	14.5731	+	4.73508i	0.523480	+	0.170089i
$776$	−26.6689	−	8.66524i	−0.957357	−	0.311064i
$777$	−13.8638	−	19.0818i	−0.497360	−	0.684557i
$778$	−0.809060	−	0.587816i	−0.0290062	−	0.0210742i
$779$	0.0654670	−	0.262714i	0.00234560	−	0.00941269i
$780$			1.91840i			0.0686898i
$781$	2.66958	+	16.4167i	0.0955252	+	0.587436i
$782$		−	1.65599i		−	0.0592180i
$783$	−2.81988	+	0.916235i	−0.100774	+	0.0327436i
$784$	1.33958	+	0.973258i	0.0478420	+	0.0347592i
$785$	−3.64613	+	2.64907i	−0.130136	+	0.0945494i
$786$	1.60973	−	4.95425i	0.0574173	−	0.176712i
$787$	6.89178	−	21.2107i	0.245665	−	0.756080i	−0.749861	−	0.661595i	$-0.769880\pi$
$787$	6.89178	−	21.2107i	0.245665	−	0.756080i	0.995526	−	0.0944847i	$-0.0301204\pi$
$788$	−5.16478	−	7.10871i	−0.183988	−	0.253237i
$789$	−19.5158	−	14.1790i	−0.694780	−	0.504787i
$790$	−0.0984275	−	0.302929i	−0.00350189	−	0.0107777i
$791$	−50.3330			−1.78964
$792$	5.00907	−	0.814544i	0.177990	−	0.0289436i
$793$			38.9121i			1.38181i
$794$	−1.89580	−	5.83467i	−0.0672794	−	0.207065i
$795$	−0.984131	−	0.715013i	−0.0349035	−	0.0253589i
$796$	13.4494	−	9.77154i	0.476700	−	0.346343i
$797$	−50.3062	−	16.3455i	−1.78194	−	0.578986i	−0.782870	−	0.622185i	$-0.786245\pi$
$797$	−50.3062	−	16.3455i	−1.78194	−	0.578986i	−0.999067	+	0.0431984i	$0.986245\pi$
$798$	3.65160	−	3.06483i	0.129265	−	0.108494i
$799$	−31.2289	−	42.9829i	−1.10480	−	1.52063i
$800$	−17.1642	−	12.4705i	−0.606845	−	0.440899i
$801$	13.0626	−	4.24430i	0.461545	−	0.149965i
$802$		−	9.15695i		−	0.323343i
$803$	−6.89392	+	13.6691i	−0.243281	+	0.482373i
$804$	−7.77971			−0.274369
$805$	−0.577147	+	0.187526i	−0.0203418	+	0.00660944i
$806$	3.44306	−	4.73896i	0.121277	−	0.166923i
$807$	−8.17586	+	5.94011i	−0.287804	+	0.209102i
$808$	−7.54462	−	2.45140i	−0.265419	−	0.0862398i
$809$	48.5917	+	15.7884i	1.70839	+	0.555090i	0.990064	−	0.140614i	$-0.0449078\pi$
$809$	48.5917	+	15.7884i	1.70839	+	0.555090i	0.718328	+	0.695705i	$0.244908\pi$
$810$	−0.0706484	+	0.0513291i	−0.00248233	+	0.00180352i
$811$	33.8934	+	24.6250i	1.19016	+	0.864701i	0.993281	−	0.115727i	$-0.0369199\pi$
$811$	33.8934	+	24.6250i	1.19016	+	0.864701i	0.196877	+	0.980428i	$0.436920\pi$
$812$	−14.2565	+	4.63222i	−0.500306	+	0.162559i
$813$	5.79360			0.203190
$814$	−11.2164	−	1.72913i	−0.393135	−	0.0606060i
$815$	−2.94368			−0.103112
$816$	3.91604	+	12.0523i	0.137089	+	0.421916i
$817$	−33.7111	+	13.6251i	−1.17940	+	0.476681i
$818$	0.0936025	−	0.0680062i	0.00327273	−	0.00237778i
$819$	−12.4099	−	4.03221i	−0.433636	−	0.140897i
$820$	−0.00774819	+	0.0238465i	−0.000270579	+	0.000832756i
$821$	−20.8036	−	28.6337i	−0.726052	−	0.999324i	−0.999301	−	0.0373811i	$-0.988098\pi$
$821$	−20.8036	−	28.6337i	−0.726052	−	0.999324i	0.273250	−	0.961943i	$-0.411902\pi$
$822$	−0.604046	+	0.831398i	−0.0210685	+	0.0289983i
$823$	5.60429	+	17.2482i	0.195353	+	0.601236i	0.999972	+	0.00744419i	$0.00236958\pi$
$823$	5.60429	+	17.2482i	0.195353	+	0.601236i	−0.804619	+	0.593791i	$0.797630\pi$
$824$			1.54771i			0.0539169i
$825$	−11.6611	−	11.5653i	−0.405988	−	0.402654i
$826$	10.4727			0.364391
$827$	−3.45802	−	10.6427i	−0.120247	−	0.370082i	0.872758	−	0.488153i	$-0.162329\pi$
$827$	−3.45802	−	10.6427i	−0.120247	−	0.370082i	−0.993005	+	0.118071i	$0.962329\pi$
$828$	1.50183	+	1.09114i	0.0521921	+	0.0379198i
$829$	−2.51048	−	3.45538i	−0.0871925	−	0.120010i	0.763192	−	0.646171i	$-0.223631\pi$
$829$	−2.51048	−	3.45538i	−0.0871925	−	0.120010i	−0.850385	+	0.526161i	$0.823631\pi$
$830$	0.130490	+	0.0423989i	0.00452938	+	0.00147169i
$831$	6.55963	−	20.1885i	0.227551	−	0.700330i
$832$	17.0695	−	12.4017i	0.591779	−	0.429952i
$833$	1.30594	−	1.79747i	0.0452481	−	0.0622786i
$834$	−1.25716	−	3.86914i	−0.0435319	−	0.133977i
$835$	3.74293			0.129529
$836$	−2.20739	+	26.5281i	−0.0763443	+	0.917495i
$837$	−3.09435			−0.106956
$838$	−3.34013	−	10.2799i	−0.115383	−	0.355112i
$839$	−14.7723	+	20.3323i	−0.509996	+	0.701949i	−0.983919	−	0.178617i	$-0.942838\pi$
$839$	−14.7723	+	20.3323i	−0.509996	+	0.701949i	0.473923	+	0.880566i	$0.342838\pi$
$840$	−0.745135	+	0.541372i	−0.0257096	+	0.0186791i
$841$	−6.24486	+	19.2197i	−0.215340	+	0.662748i
$842$	5.77843	+	1.87753i	0.199138	+	0.0647038i
$843$	−2.44203	−	3.36117i	−0.0841081	−	0.115765i
$844$	−11.3238	−	8.22720i	−0.389780	−	0.283192i
$845$	−0.649337	−	1.99846i	−0.0223379	−	0.0687489i
$846$	−5.13222			−0.176449
$847$	30.2015	−	0.249054i	1.03774	−	0.00855760i
$848$			17.0523i			0.585577i
$849$	8.38828	+	25.8165i	0.287885	+	0.886019i
$850$	−4.78101	+	6.58050i	−0.163987	+	0.225709i
$851$	−5.09051	−	7.00648i	−0.174500	−	0.240179i
$852$	−2.85346	+	8.78204i	−0.0977578	+	0.300868i
$853$	46.1817	+	15.0053i	1.58123	+	0.513773i	0.962374	−	0.271730i	$-0.0875957\pi$
$853$	46.1817	+	15.0053i	1.58123	+	0.513773i	0.618858	+	0.785503i	$0.287596\pi$
$854$	−7.24487	+	5.26371i	−0.247914	+	0.180120i
$855$	−0.358084	−	0.885970i	−0.0122462	−	0.0302995i
$856$	−7.84281	−	24.1377i	−0.268062	−	0.825010i
$857$	22.9262			0.783145			0.391573	−	0.920147i	$-0.371931\pi$
$857$	22.9262			0.783145			0.391573	+	0.920147i	$0.371931\pi$
$858$	−5.58234	+	2.87340i	−0.190578	+	0.0980962i
$859$	−41.2181			−1.40634			−0.703172	−	0.711019i	$-0.748234\pi$
$859$	−41.2181			−1.40634			−0.703172	+	0.711019i	$0.748234\pi$
$860$	3.20250	−	1.04055i	0.109204	−	0.0354826i
$861$	−0.137974	−	0.100244i	−0.00470214	−	0.00341630i
$862$	12.1006	−	8.79162i	0.412149	−	0.299444i
$863$	1.07848	+	0.350420i	0.0367119	+	0.0119284i	0.327315	−	0.944915i	$-0.393856\pi$
$863$	1.07848	+	0.350420i	0.0367119	+	0.0119284i	−0.290603	+	0.956844i	$0.593856\pi$
$864$	4.07471	+	1.32395i	0.138624	+	0.0450418i
$865$	−3.93569	+	2.85945i	−0.133817	+	0.0972240i
$866$	−6.95405	+	9.57143i	−0.236308	+	0.325250i
$867$	0.00409763	−	0.00133140i	0.000139163	−	4.52168e-5i
$868$	−15.6442			−0.530997
$869$	−8.51869	+	8.58923i	−0.288977	+	0.291370i
$870$		−	0.258922i		−	0.00877828i
$871$	19.0962	−	6.20474i	0.647051	−	0.210239i
$872$	4.02566	+	2.92481i	0.136326	+	0.0990466i
$873$	−10.7718	−	14.8261i	−0.364571	−	0.501788i
$874$	1.34080	−	1.12535i	0.0453531	−	0.0380654i
$875$	5.69722	+	1.85114i	0.192601	+	0.0625799i
$876$	−6.87614	+	4.99581i	−0.232323	+	0.168793i
$877$	−7.41783	−	5.38937i	−0.250482	−	0.181986i	0.455458	−	0.890257i	$-0.349475\pi$
$877$	−7.41783	−	5.38937i	−0.250482	−	0.181986i	−0.705941	+	0.708271i	$0.749475\pi$
$878$	3.19191	+	9.82369i	0.107722	+	0.331533i
$879$		−	28.0072i		−	0.944661i
$880$	0.340450	−	2.20841i	0.0114766	−	0.0744454i
$881$	−36.9298			−1.24420			−0.622099	−	0.782938i	$-0.713720\pi$
$881$	−36.9298			−1.24420			−0.622099	+	0.782938i	$0.713720\pi$
$882$	−0.0663213	−	0.204116i	−0.00223316	−	0.00687295i
$883$	−29.2417	−	21.2453i	−0.984060	−	0.714962i	−0.0254479	−	0.999676i	$-0.508101\pi$
$883$	−29.2417	−	21.2453i	−0.984060	−	0.714962i	−0.958612	+	0.284715i	$0.908101\pi$
$884$	−21.2099	−	29.1930i	−0.713368	−	0.981866i
$885$	0.648695	−	1.99648i	0.0218056	−	0.0671108i
$886$	1.56217	−	4.80786i	0.0524820	−	0.161523i
$887$	9.50868	−	6.90846i	0.319270	−	0.231963i	−0.416594	−	0.909093i	$-0.636776\pi$
$887$	9.50868	−	6.90846i	0.319270	−	0.231963i	0.735864	+	0.677129i	$0.236776\pi$
$888$	−10.6340	−	7.72607i	−0.356854	−	0.259270i
$889$	31.0859	−	10.1004i	1.04259	−	0.338758i
$890$			1.19941i			0.0402044i
$891$	2.96132	+	1.49352i	0.0992079	+	0.0500348i
$892$			19.3786i			0.648845i
$893$	13.5798	−	54.4945i	0.454430	−	1.82359i
$894$	2.65585	+	1.92959i	0.0888249	+	0.0645351i
$895$	0.596377	+	0.820842i	0.0199347	+	0.0274377i
$896$	26.9938	+	8.77081i	0.901799	+	0.293012i
$897$	−4.55666	−	1.48055i	−0.152143	−	0.0494341i
$898$	5.73447	+	7.89282i	0.191362	+	0.263387i
$899$	5.39278	−	7.42252i	0.179859	−	0.247555i
$900$	−2.81767	−	8.67188i	−0.0939222	−	0.289063i
$901$	22.8811			0.762279
$902$	−0.0809960	+	0.0131711i	−0.00269687	+	0.000438549i
$903$			22.9036i			0.762183i
$904$	−26.6770	+	8.66787i	−0.887262	+	0.288289i
$905$	1.29809	−	1.78666i	0.0431498	−	0.0593907i
$906$	0.199067	+	0.273992i	0.00661356	+	0.00910278i
$907$	−22.3214	−	7.25267i	−0.741170	−	0.240821i	−0.0859928	−	0.996296i	$-0.527406\pi$
$907$	−22.3214	−	7.25267i	−0.741170	−	0.240821i	−0.655178	+	0.755475i	$0.727406\pi$
$908$	−10.7325	+	33.0313i	−0.356171	+	1.09618i
$909$	−3.04734	−	4.19431i	−0.101074	−	0.139116i
$910$	0.669767	−	0.921856i	0.0222026	−	0.0305592i
$911$	−2.19806	+	0.714192i	−0.0728249	+	0.0236622i	−0.345203	−	0.938528i	$-0.612190\pi$
$911$	−2.19806	+	0.714192i	−0.0728249	+	0.0236622i	0.272378	+	0.962190i	$0.412190\pi$
$912$	−7.09716	+	11.3610i	−0.235011	+	0.376200i
$913$	−0.836398	−	5.14347i	−0.0276807	−	0.170224i
$914$			9.29494i			0.307449i
$915$	0.554697	+	1.70718i	0.0183377	+	0.0564377i
$916$	−40.5335	−	29.4493i	−1.33926	−	0.973032i
$917$	29.0492	−	21.1055i	0.959288	−	0.696964i
$918$	0.507585	−	1.56218i	0.0167528	−	0.0515598i
$919$	13.3975	+	4.35311i	0.441942	+	0.143596i	0.521532	−	0.853232i	$-0.325361\pi$
$919$	13.3975	+	4.35311i	0.441942	+	0.143596i	−0.0795893	+	0.996828i	$0.525361\pi$
$920$	−0.273599	+	0.198782i	−0.00902030	+	0.00655363i
$921$	−2.70308	+	3.72047i	−0.0890695	+	0.122594i
$922$	−1.83112	+	0.594965i	−0.0603046	+	0.0195941i
$923$		−	23.8323i		−	0.784451i
$924$	14.9716	+	7.55081i	0.492529	+	0.248403i
$925$			42.5390i			1.39867i
$926$	−1.81920	−	5.59893i	−0.0597827	−	0.183992i
$927$	−0.594537	+	0.818310i	−0.0195272	+	0.0268768i
$928$	−10.2771	+	7.46678i	−0.337364	+	0.245109i
$929$	9.42869	−	29.0185i	0.309345	−	0.952067i	−0.668675	−	0.743555i	$-0.733138\pi$
$929$	9.42869	−	29.0185i	0.309345	−	0.952067i	0.978020	−	0.208512i	$-0.0668619\pi$
$930$	0.0835019	−	0.256992i	0.00273814	−	0.00842712i
$931$	2.34282	−	0.164120i	0.0767827	−	0.00537882i
$932$	17.6271	−	24.2616i	0.577394	−	0.794715i
$933$	4.34851	−	1.41292i	0.142364	−	0.0462568i
$934$	−10.0094			−0.327517
$935$	−2.96329	−	0.456822i	−0.0969099	−	0.0149397i
$936$	−7.27173			−0.237684
$937$	1.01301	−	0.329147i	0.0330936	−	0.0107528i	−0.292423	−	0.956289i	$-0.594462\pi$
$937$	1.01301	−	0.329147i	0.0330936	−	0.0107528i	0.325517	+	0.945536i	$0.394462\pi$
$938$	3.73841	+	2.71611i	0.122063	+	0.0886842i
$939$	2.36037	+	3.24877i	0.0770277	+	0.106019i
$940$	−1.60720	+	4.94646i	−0.0524212	+	0.161336i
$941$	17.1292	−	52.7184i	0.558397	−	1.71857i	−0.128402	−	0.991722i	$-0.540985\pi$
$941$	17.1292	−	52.7184i	0.558397	−	1.71857i	0.686799	−	0.726848i	$-0.259015\pi$
$942$	−4.81329	−	6.62493i	−0.156826	−	0.215852i
$943$	−0.0506613	−	0.0368076i	−0.00164976	−	0.00119862i
$944$	−27.9867	+	9.09342i	−0.910888	+	0.295966i
$945$	−0.601934			−0.0195809
$946$	7.82462	+	7.76037i	0.254400	+	0.252311i
$947$	−23.1612			−0.752639			−0.376319	−	0.926490i	$-0.622810\pi$
$947$	−23.1612			−0.752639			−0.376319	+	0.926490i	$0.622810\pi$
$948$	−6.38745	+	2.07541i	−0.207455	+	0.0674061i
$949$	12.8939	−	17.7469i	0.418553	−	0.576089i
$950$	−8.57700	+	0.600840i	−0.278275	+	0.0194938i
$951$	−7.83376	+	24.1098i	−0.254027	+	0.781814i
$952$	5.35354	−	16.4765i	0.173509	−	0.534007i
$953$	26.1462	−	18.9963i	0.846957	−	0.615351i	−0.0773481	−	0.997004i	$-0.524645\pi$
$953$	26.1462	−	18.9963i	0.846957	−	0.615351i	0.924305	+	0.381654i	$0.124645\pi$
$954$	1.29916	−	1.78814i	0.0420618	−	0.0578931i
$955$	0.119408	+	0.367499i	0.00386394	+	0.0118920i
$956$		−	0.891537i		−	0.0288344i
$957$	−8.74348	+	4.50053i	−0.282637	+	0.145482i
$958$		−	8.76242i		−	0.283101i
$959$	−6.73693	+	2.18896i	−0.217547	+	0.0706853i
$960$	0.572098	−	0.787426i	0.0184644	−	0.0254140i
$961$	−17.3332	+	12.5933i	−0.559135	+	0.406235i
$962$	15.4659	+	5.02516i	0.498639	+	0.162018i
$963$	5.12559	−	15.7749i	0.165170	−	0.508340i
$964$	−26.8485	+	19.5066i	−0.864732	+	0.628265i
$965$	−3.65332	−	2.65429i	−0.117604	−	0.0854447i
$966$	−0.340730	−	1.04866i	−0.0109628	−	0.0337401i
$967$			6.54951i			0.210618i	0.994440	+	0.105309i	$0.0335832\pi$
$967$			6.54951i			0.210618i	−0.994440	+	0.105309i	$0.966417\pi$
$968$	15.9642	−	5.33302i	0.513109	−	0.171410i
$969$	15.2444	+	9.52312i	0.489721	+	0.305927i
$970$	1.52202	−	0.494535i	0.0488692	−	0.0158786i
$971$	−16.8012	+	23.1249i	−0.539177	+	0.742113i	−0.988494	−	0.151259i	$-0.951667\pi$
$971$	−16.8012	+	23.1249i	−0.539177	+	0.742113i	0.449317	+	0.893372i	$0.351667\pi$
$972$	1.08231	+	1.48967i	0.0347150	+	0.0477811i
$973$	8.66553	−	26.6698i	0.277804	−	0.854993i
$974$	−6.13252	−	1.99258i	−0.196499	−	0.0638462i
$975$	13.8326	+	19.0389i	0.442997	+	0.609734i
$976$	14.7904	−	20.3572i	0.473429	−	0.651619i
$977$	−1.21207	+	0.393825i	−0.0387775	+	0.0125996i	−0.328342	−	0.944559i	$-0.606490\pi$
$977$	−1.21207	+	0.393825i	−0.0387775	+	0.0125996i	0.289564	+	0.957159i	$0.406490\pi$
$978$		−	5.34858i		−	0.171029i
$979$	40.5027	−	20.8480i	1.29447	−	0.666304i
$980$	−0.217498			−0.00694770
$981$	1.00492	+	3.09284i	0.0320847	+	0.0987467i
$982$	5.86078	−	8.06667i	0.187025	−	0.257418i
$983$	25.5542	+	35.1723i	0.815053	+	1.12182i	0.990524	+	0.137339i	$0.0438550\pi$
$983$	25.5542	+	35.1723i	0.815053	+	1.12182i	−0.175472	+	0.984485i	$0.556145\pi$
$984$	−0.0903905	−	0.0293697i	−0.00288154	−	0.000936270i
$985$	0.994960	+	0.323282i	0.0317021	+	0.0103006i
$986$	2.86266	+	3.94011i	0.0911655	+	0.125479i
$987$	−28.6198	−	20.7935i	−0.910979	−	0.661865i
$988$	9.22307	−	37.0114i	0.293425	−	1.17749i
$989$			8.40975i			0.267415i
$990$	−0.203952	+	0.205641i	−0.00648202	+	0.00653569i
$991$			15.8162i			0.502417i	0.967933	+	0.251208i	$0.0808279\pi$
$991$			15.8162i			0.502417i	−0.967933	+	0.251208i	$0.919172\pi$
$992$	−12.6086	+	4.09677i	−0.400322	+	0.130073i
$993$	−5.24481	−	3.81057i	−0.166439	−	0.120925i
$994$	4.43723	−	3.22384i	0.140741	−	0.102254i
$995$	−0.611636	+	1.88242i	−0.0193902	+	0.0596768i
$996$	0.894008	−	2.75147i	0.0283277	−	0.0871837i
$997$	−6.24589	−	8.59673i	−0.197809	−	0.272261i	0.698577	−	0.715535i	$-0.253817\pi$
$997$	−6.24589	−	8.59673i	−0.197809	−	0.272261i	−0.896386	+	0.443274i	$0.853817\pi$
$998$	0.685145	+	0.497787i	0.0216879	+	0.0157572i
$999$	−2.65457	−	8.16992i	−0.0839868	−	0.258485i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	627.2.s.a.94.19	✓	160
11.2	odd	10	inner	627.2.s.a.607.22	yes	160
19.18	odd	2	inner	627.2.s.a.94.22	yes	160
209.189	even	10	inner	627.2.s.a.607.19	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
627.2.s.a.94.19	✓	160	1.1	even	1	trivial
627.2.s.a.94.22	yes	160	19.18	odd	2	inner
627.2.s.a.607.19	yes	160	209.189	even	10	inner
627.2.s.a.607.22	yes	160	11.2	odd	10	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 627 = 3 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	627.s (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.123092 - 0.378837i) q^{2} +(0.587785 - 0.809017i) q^{3} +(1.48967 - 1.08231i) q^{4} +(-0.0677455 + 0.208499i) q^{5} +(-0.378837 - 0.123092i) q^{6} +(-1.61387 - 2.22131i) q^{7} +(-1.23790 - 0.899388i) q^{8} +(-0.309017 - 0.951057i) q^{9} +0.0873262 q^{10} +(-1.51789 - 2.94890i) q^{11} -1.84133i q^{12} +(1.46856 + 4.51977i) q^{13} +(-0.642860 + 0.884821i) q^{14} +(0.128860 + 0.177360i) q^{15} +(0.949659 - 2.92275i) q^{16} +(-3.92180 - 1.27427i) q^{17} +(-0.322258 + 0.234134i) q^{18} +(-1.63338 - 4.04130i) q^{19} +(0.124742 + 0.383916i) q^{20} -2.74569 q^{21} +(-0.930315 + 0.938018i) q^{22} -1.00816 q^{23} +(-1.45524 + 0.472836i) q^{24} +(4.00620 + 2.91068i) q^{25} +(1.53149 - 1.11269i) q^{26} +(-0.951057 - 0.309017i) q^{27} +(-4.80827 - 1.56230i) q^{28} +(2.39873 - 1.74278i) q^{29} +(0.0513291 - 0.0706484i) q^{30} +(2.94290 - 0.956207i) q^{31} -4.28440 q^{32} +(-3.27790 - 0.505324i) q^{33} +1.64258i q^{34} +(0.572474 - 0.186008i) q^{35} +(-1.48967 - 1.08231i) q^{36} +(5.04929 + 6.94975i) q^{37} +(-1.32994 + 1.11623i) q^{38} +(4.51977 + 1.46856i) q^{39} +(0.271384 - 0.197172i) q^{40} +(0.0502511 + 0.0365096i) q^{41} +(0.337971 + 1.04017i) q^{42} -8.34166i q^{43} +(-5.45276 - 2.75006i) q^{44} +0.219229 q^{45} +(0.124097 + 0.381930i) q^{46} +(10.4236 + 7.57316i) q^{47} +(-1.80636 - 2.48624i) q^{48} +(-0.166497 + 0.512425i) q^{49} +(0.609543 - 1.87598i) q^{50} +(-3.33609 + 2.42381i) q^{51} +(7.07944 + 5.14352i) q^{52} +(-5.27720 + 1.71467i) q^{53} +0.398333i q^{54} +(0.717674 - 0.116704i) q^{55} +4.20126i q^{56} +(-4.22955 - 1.05398i) q^{57} +(-0.955495 - 0.694208i) q^{58} +(-5.62832 - 7.74671i) q^{59} +(0.383916 + 0.124742i) q^{60} +(7.78721 + 2.53022i) q^{61} +(-0.724494 - 0.997180i) q^{62} +(-1.61387 + 2.22131i) q^{63} +(-1.37194 - 4.22241i) q^{64} -1.04186 q^{65} +(0.212047 + 1.30399i) q^{66} -4.22505i q^{67} +(-7.22134 + 2.34635i) q^{68} +(-0.592584 + 0.815621i) q^{69} +(-0.140934 - 0.193978i) q^{70} +(-4.76940 - 1.54967i) q^{71} +(-0.472836 + 1.45524i) q^{72} +(-2.71315 - 3.73433i) q^{73} +(2.01130 - 2.76832i) q^{74} +(4.70957 - 1.53023i) q^{75} +(-6.80711 - 4.25237i) q^{76} +(-4.10074 + 8.13085i) q^{77} -1.89302i q^{78} +(-1.12712 - 3.46893i) q^{79} +(0.545056 + 0.396006i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(0.00764570 - 0.0235310i) q^{82} +(1.49428 + 0.485523i) q^{83} +(-4.09016 + 2.97168i) q^{84} +(0.531369 - 0.731367i) q^{85} +(-3.16013 + 1.02679i) q^{86} -2.96500i q^{87} +(-0.773211 + 5.01562i) q^{88} +13.7349i q^{89} +(-0.0269853 - 0.0830522i) q^{90} +(7.66972 - 10.5565i) q^{91} +(-1.50183 + 1.09114i) q^{92} +(0.956207 - 2.94290i) q^{93} +(1.58594 - 4.88103i) q^{94} +(0.953261 - 0.0667783i) q^{95} +(-2.51831 + 3.46615i) q^{96} +(17.4292 - 5.66308i) q^{97} +0.214620 q^{98} +(-2.33552 + 2.35486i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q - 40 q^{4} + 4 q^{5} - 10 q^{7} + 40 q^{9} + 10 q^{11} - 40 q^{16} - 50 q^{17} + 76 q^{20} + 16 q^{23} - 80 q^{25} - 68 q^{26} - 40 q^{35} + 40 q^{36} - 62 q^{38} + 8 q^{42} + 40 q^{44} - 4 q^{45}+ \cdots - 10 q^{99}+O(q^{100}) \) 160 * q - 40 * q^4 + 4 * q^5 - 10 * q^7 + 40 * q^9 + 10 * q^11 - 40 * q^16 - 50 * q^17 + 76 * q^20 + 16 * q^23 - 80 * q^25 - 68 * q^26 - 40 * q^35 + 40 * q^36 - 62 * q^38 + 8 * q^42 + 40 * q^44 - 4 * q^45 + 20 * q^47 + 110 * q^49 - 18 * q^55 - 20 * q^57 - 24 * q^58 + 10 * q^61 + 120 * q^62 - 10 * q^63 - 136 * q^64 - 12 * q^66 + 160 * q^68 + 20 * q^73 - 100 * q^74 + 90 * q^77 - 156 * q^80 - 40 * q^81 + 68 * q^82 - 200 * q^83 + 30 * q^85 - 84 * q^92 - 96 * q^93 - 60 * q^95 + 100 * q^96 - 10 * q^99

Introduction

L-functions

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