LMFDB - Embedded newform 867.2.i.f.329.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [867,2,Mod(65,867)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(867, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([8, 9])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("867.65"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 867 = 3 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	867.i (of order $16$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [32,0,0,16,0,-8,0,0,24,-16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(10)] == traces)

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

Self dual:	no
Analytic conductor:	$6.92302985525$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{16})$
Twist minimal:	no (minimal twist has level 51)
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			329.3
Character	$\chi$	$=$	867.329
Dual form			867.2.i.f.224.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.320870 - 0.774648i) q^{2} +(-0.664063 + 1.59969i) q^{3} +(0.917091 + 0.917091i) q^{4} +(0.680434 + 0.454651i) q^{5} +(1.02612 + 1.02771i) q^{6} +(0.108447 + 0.162303i) q^{7} +(2.55399 - 1.05790i) q^{8} +(-2.11804 - 2.12459i) q^{9} +(0.570525 - 0.381213i) q^{10} +(4.33117 + 0.861524i) q^{11} +(-2.07607 + 0.858059i) q^{12} +(3.75023 - 3.75023i) q^{13} +(0.160525 - 0.0319304i) q^{14} +(-1.17915 + 0.786569i) q^{15} +0.276039i q^{16} +(-2.32543 + 0.959018i) q^{18} +(0.508991 + 0.210831i) q^{19} +(0.207063 + 1.04098i) q^{20} +(-0.331651 + 0.0657033i) q^{21} +(2.05712 - 3.07870i) q^{22} +(-0.806783 + 4.05597i) q^{23} +(-0.00369783 + 4.78810i) q^{24} +(-1.65713 - 4.00068i) q^{25} +(-1.70177 - 4.10844i) q^{26} +(4.80521 - 1.97735i) q^{27} +(-0.0493905 + 0.248303i) q^{28} +(-0.343818 + 0.514560i) q^{29} +(0.230959 + 1.16581i) q^{30} +(0.129926 + 0.653180i) q^{31} +(5.32181 + 2.20436i) q^{32} +(-4.25434 + 6.35644i) q^{33} +0.159742i q^{35} +(0.00600982 - 3.89088i) q^{36} +(-1.92648 + 0.383200i) q^{37} +(0.326640 - 0.326640i) q^{38} +(3.50883 + 8.48960i) q^{39} +(2.21879 + 0.441345i) q^{40} +(-6.64762 + 4.44180i) q^{41} +(-0.0555199 + 0.277995i) q^{42} +(-7.13212 + 2.95422i) q^{43} +(3.18198 + 4.76218i) q^{44} +(-0.475237 - 2.40862i) q^{45} +(2.88308 + 1.92641i) q^{46} +(7.05884 + 7.05884i) q^{47} +(-0.441578 - 0.183307i) q^{48} +(2.66420 - 6.43195i) q^{49} -3.63084 q^{50} +6.87860 q^{52} +(-4.43410 + 10.7049i) q^{53} +(0.0100943 - 4.35682i) q^{54} +(2.55538 + 2.55538i) q^{55} +(0.448673 + 0.299794i) q^{56} +(-0.675267 + 0.674225i) q^{57} +(0.288282 + 0.431445i) q^{58} +(0.240270 - 0.0995233i) q^{59} +(-1.80275 - 0.360036i) q^{60} +(-8.77243 + 5.86155i) q^{61} +(0.547674 + 0.108939i) q^{62} +(0.115132 - 0.574171i) q^{63} +(3.02483 - 3.02483i) q^{64} +(4.25683 - 0.846735i) q^{65} +(3.55892 + 5.33521i) q^{66} -5.40994i q^{67} +(-5.95256 - 3.98403i) q^{69} +(0.123744 + 0.0512564i) q^{70} +(-1.27098 - 6.38963i) q^{71} +(-7.65705 - 3.18552i) q^{72} +(6.44749 - 9.64936i) q^{73} +(-0.321303 + 1.61530i) q^{74} +(7.50030 + 0.00579244i) q^{75} +(0.273440 + 0.660143i) q^{76} +(0.329876 + 0.796392i) q^{77} +(7.70233 + 0.00594847i) q^{78} +(2.10878 - 10.6016i) q^{79} +(-0.125502 + 0.187826i) q^{80} +(-0.0278025 + 8.99996i) q^{81} +(1.30781 + 6.57481i) q^{82} +(-2.55289 - 1.05744i) q^{83} +(-0.364410 - 0.243898i) q^{84} +6.47280i q^{86} +(-0.594822 - 0.891703i) q^{87} +(11.9732 - 2.38161i) q^{88} +(-3.69661 + 3.69661i) q^{89} +(-2.01832 - 0.404710i) q^{90} +(1.01538 + 0.201971i) q^{91} +(-4.45959 + 2.97980i) q^{92} +(-1.13117 - 0.225911i) q^{93} +(7.73308 - 3.20315i) q^{94} +(0.250480 + 0.374870i) q^{95} +(-7.06032 + 7.04942i) q^{96} +(2.05296 + 1.37174i) q^{97} +(-4.12764 - 4.12764i) q^{98} +(-7.34321 - 11.0267i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{4} - 8 q^{6} + 24 q^{9} - 16 q^{10} - 16 q^{12} + 16 q^{13} + 16 q^{15} + 16 q^{18} + 32 q^{19} - 16 q^{21} + 16 q^{22} + 24 q^{24} + 24 q^{27} + 8 q^{30} + 32 q^{31} - 24 q^{36} + 16 q^{37}+ \cdots - 96 q^{99}+O(q^{100}) $ 32 * q + 16 * q^4 - 8 * q^6 + 24 * q^9 - 16 * q^10 - 16 * q^12 + 16 * q^13 + 16 * q^15 + 16 * q^18 + 32 * q^19 - 16 * q^21 + 16 * q^22 + 24 * q^24 + 24 * q^27 + 8 * q^30 + 32 * q^31 - 24 * q^36 + 16 * q^37 - 64 * q^39 + 16 * q^40 - 24 * q^42 - 32 * q^43 + 40 * q^45 - 40 * q^48 - 64 * q^49 - 96 * q^52 - 88 * q^54 + 48 * q^55 - 24 * q^57 - 64 * q^58 + 48 * q^60 - 32 * q^61 - 80 * q^63 - 16 * q^64 + 120 * q^66 + 80 * q^69 - 64 * q^72 + 48 * q^73 + 16 * q^75 + 32 * q^76 + 88 * q^78 - 32 * q^79 - 48 * q^81 + 96 * q^82 - 56 * q^87 + 128 * q^88 + 8 * q^90 + 64 * q^91 - 56 * q^93 - 48 * q^94 + 16 * q^96 + 128 * q^97 - 96 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/867\mathbb{Z}\right)^\times$.

$n$	$290$	$292$
$\chi(n)$	$-1$	$e\left(\frac{15}{16}\right)$

Coefficient data

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

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

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

$2$	0.320870	−	0.774648i	0.226889	−	0.547759i	−0.768907	−	0.639361i	$-0.779199\pi$
$2$	0.320870	−	0.774648i	0.226889	−	0.547759i	0.995796	+	0.0916024i	$0.0291989\pi$
$3$	−0.664063	+	1.59969i	−0.383397	+	0.923584i
$3$	−0.664063	+	1.59969i	−0.383397	+	0.923584i
$4$	0.917091	+	0.917091i	0.458546	+	0.458546i
$5$	0.680434	+	0.454651i	0.304299	+	0.203326i	0.698339	−	0.715767i	$-0.253923\pi$
$5$	0.680434	+	0.454651i	0.304299	+	0.203326i	−0.394040	+	0.919093i	$0.628923\pi$
$6$	1.02612	+	1.02771i	0.418913	+	0.419560i
$7$	0.108447	+	0.162303i	0.0409893	+	0.0613448i	0.851398	−	0.524520i	$-0.175755\pi$
$7$	0.108447	+	0.162303i	0.0409893	+	0.0613448i	−0.810409	+	0.585864i	$0.800755\pi$
$8$	2.55399	−	1.05790i	0.902970	−	0.374023i
$9$	−2.11804	−	2.12459i	−0.706014	−	0.708198i
$10$	0.570525	−	0.381213i	0.180416	−	0.120550i
$11$	4.33117	+	0.861524i	1.30590	+	0.259759i	0.798522	−	0.601966i	$-0.205616\pi$
$11$	4.33117	+	0.861524i	1.30590	+	0.259759i	0.507376	+	0.861725i	$0.330616\pi$
$12$	−2.07607	+	0.858059i	−0.599310	+	0.247700i
$13$	3.75023	−	3.75023i	1.04013	−	1.04013i	0.0409655	−	0.999161i	$-0.486957\pi$
$13$	3.75023	−	3.75023i	1.04013	−	1.04013i	0.999161	−	0.0409655i	$-0.0130434\pi$
$14$	0.160525	−	0.0319304i	0.0429022	−	0.00853377i
$15$	−1.17915	+	0.786569i	−0.304456	+	0.203091i
$16$			0.276039i			0.0690098i
$17$		0			0
$17$		0			0
$18$	−2.32543	+	0.959018i	−0.548109	+	0.226043i
$19$	0.508991	+	0.210831i	0.116771	+	0.0483680i	0.440304	−	0.897849i	$-0.354871\pi$
$19$	0.508991	+	0.210831i	0.116771	+	0.0483680i	−0.323533	+	0.946217i	$0.604871\pi$
$20$	0.207063	+	1.04098i	0.0463007	+	0.232769i
$21$	−0.331651	+	0.0657033i	−0.0723722	+	0.0143376i
$22$	2.05712	−	3.07870i	0.438579	−	0.656380i
$23$	−0.806783	+	4.05597i	−0.168226	+	0.845729i	0.800831	+	0.598891i	$0.204392\pi$
$23$	−0.806783	+	4.05597i	−0.168226	+	0.845729i	−0.969057	+	0.246838i	$0.920608\pi$
$24$	−0.00369783	+	4.78810i	−0.000754815	+	0.977368i
$25$	−1.65713	−	4.00068i	−0.331427	−	0.800136i
$26$	−1.70177	−	4.10844i	−0.333745	−	0.805732i
$27$	4.80521	−	1.97735i	0.924764	−	0.380542i
$28$	−0.0493905	+	0.248303i	−0.00933393	+	0.0469248i
$29$	−0.343818	+	0.514560i	−0.0638454	+	0.0955514i	−0.862019	−	0.506877i	$-0.830800\pi$
$29$	−0.343818	+	0.514560i	−0.0638454	+	0.0955514i	0.798173	+	0.602428i	$0.205800\pi$
$30$	0.230959	+	1.16581i	0.0421672	+	0.212848i
$31$	0.129926	+	0.653180i	0.0233353	+	0.117315i	0.990697	−	0.136084i	$-0.0434517\pi$
$31$	0.129926	+	0.653180i	0.0233353	+	0.117315i	−0.967362	+	0.253398i	$0.918452\pi$
$32$	5.32181	+	2.20436i	0.940771	+	0.389680i
$33$	−4.25434	+	6.35644i	−0.740586	+	1.10651i
$34$		0			0
$35$			0.159742i			0.0270014i
$36$	0.00600982	−	3.89088i	0.00100164	−	0.648481i
$37$	−1.92648	+	0.383200i	−0.316711	+	0.0629978i	−0.350886	−	0.936418i	$-0.614120\pi$
$37$	−1.92648	+	0.383200i	−0.316711	+	0.0629978i	0.0341751	+	0.999416i	$0.489120\pi$
$38$	0.326640	−	0.326640i	0.0529880	−	0.0529880i
$39$	3.50883	+	8.48960i	0.561862	+	1.35942i
$40$	2.21879	+	0.441345i	0.350822	+	0.0697828i
$41$	−6.64762	+	4.44180i	−1.03818	+	0.693693i	−0.953092	−	0.302680i	$-0.902119\pi$
$41$	−6.64762	+	4.44180i	−1.03818	+	0.693693i	−0.0850923	+	0.996373i	$0.527119\pi$
$42$	−0.0555199	+	0.277995i	−0.00856690	+	0.0428956i
$43$	−7.13212	+	2.95422i	−1.08764	+	0.450514i	−0.853182	−	0.521613i	$-0.825331\pi$
$43$	−7.13212	+	2.95422i	−1.08764	+	0.450514i	−0.234455	+	0.972127i	$0.575331\pi$
$44$	3.18198	+	4.76218i	0.479702	+	0.717925i
$45$	−0.475237	−	2.40862i	−0.0708442	−	0.359055i
$46$	2.88308	+	1.92641i	0.425087	+	0.284034i
$47$	7.05884	+	7.05884i	1.02964	+	1.02964i	0.999547	+	0.0300900i	$0.00957939\pi$
$47$	7.05884	+	7.05884i	1.02964	+	1.02964i	0.0300900	+	0.999547i	$0.490421\pi$
$48$	−0.441578	−	0.183307i	−0.0637363	−	0.0264581i
$49$	2.66420	−	6.43195i	0.380600	−	0.918851i
$50$	−3.63084			−0.513479
$51$		0			0
$52$	6.87860			0.953891
$53$	−4.43410	+	10.7049i	−0.609071	+	1.47043i	0.254941	+	0.966957i	$0.417944\pi$
$53$	−4.43410	+	10.7049i	−0.609071	+	1.47043i	−0.864012	+	0.503471i	$0.832056\pi$
$54$	0.0100943	−	4.35682i	0.00137365	−	0.592888i
$55$	2.55538	+	2.55538i	0.344568	+	0.344568i
$56$	0.448673	+	0.299794i	0.0599564	+	0.0400616i
$57$	−0.675267	+	0.674225i	−0.0894413	+	0.0893033i
$58$	0.288282	+	0.431445i	0.0378533	+	0.0566514i
$59$	0.240270	−	0.0995233i	0.0312805	−	0.0129568i	−0.366988	−	0.930226i	$-0.619611\pi$
$59$	0.240270	−	0.0995233i	0.0312805	−	0.0129568i	0.398269	+	0.917269i	$0.369611\pi$
$60$	−1.80275	−	0.360036i	−0.232734	−	0.0464805i
$61$	−8.77243	+	5.86155i	−1.12319	+	0.750495i	−0.971290	−	0.237900i	$-0.923541\pi$
$61$	−8.77243	+	5.86155i	−1.12319	+	0.750495i	−0.151905	+	0.988395i	$0.548541\pi$
$62$	0.547674	+	0.108939i	0.0695546	+	0.0138353i
$63$	0.115132	−	0.574171i	0.0145053	−	0.0723388i
$64$	3.02483	−	3.02483i	0.378104	−	0.378104i
$65$	4.25683	−	0.846735i	0.527994	−	0.105025i
$66$	3.55892	+	5.33521i	0.438072	+	0.656719i
$67$		−	5.40994i		−	0.660929i	−0.943818	−	0.330465i	$-0.892795\pi$
$67$		−	5.40994i		−	0.660929i	0.943818	−	0.330465i	$-0.107205\pi$
$68$		0			0
$69$	−5.95256	−	3.98403i	−0.716604	−	0.479621i
$70$	0.123744	+	0.0512564i	0.0147902	+	0.00612632i
$71$	−1.27098	−	6.38963i	−0.150837	−	0.758309i	−0.979952	−	0.199232i	$-0.936155\pi$
$71$	−1.27098	−	6.38963i	−0.150837	−	0.758309i	0.829115	−	0.559078i	$-0.188845\pi$
$72$	−7.65705	−	3.18552i	−0.902392	−	0.375417i
$73$	6.44749	−	9.64936i	0.754622	−	1.12937i	−0.232993	−	0.972478i	$-0.574852\pi$
$73$	6.44749	−	9.64936i	0.754622	−	1.12937i	0.987616	−	0.156894i	$-0.0501480\pi$
$74$	−0.321303	+	1.61530i	−0.0373507	+	0.187775i
$75$	7.50030	+	0.00579244i	0.866060	+	0.000668853i
$76$	0.273440	+	0.660143i	0.0313657	+	0.0757236i
$77$	0.329876	+	0.796392i	0.0375929	+	0.0907573i
$78$	7.70233	+	0.00594847i	0.872117	+	0.000673531i
$79$	2.10878	−	10.6016i	0.237257	−	1.19277i	−0.660002	−	0.751264i	$-0.729444\pi$
$79$	2.10878	−	10.6016i	0.237257	−	1.19277i	0.897258	−	0.441506i	$-0.145556\pi$
$80$	−0.125502	+	0.187826i	−0.0140315	+	0.0209996i
$81$	−0.0278025	+	8.99996i	−0.00308917	+	0.999995i
$82$	1.30781	+	6.57481i	0.144424	+	0.726066i
$83$	−2.55289	−	1.05744i	−0.280216	−	0.116069i	0.238149	−	0.971229i	$-0.423459\pi$
$83$	−2.55289	−	1.05744i	−0.280216	−	0.116069i	−0.518365	+	0.855159i	$0.673459\pi$
$84$	−0.364410	−	0.243898i	−0.0397604	−	0.0266115i
$85$		0			0
$86$			6.47280i			0.697980i
$87$	−0.594822	−	0.891703i	−0.0637716	−	0.0956006i
$88$	11.9732	−	2.38161i	1.27634	−	0.253880i
$89$	−3.69661	+	3.69661i	−0.391839	+	0.391839i	−0.875343	−	0.483503i	$-0.839364\pi$
$89$	−3.69661	+	3.69661i	−0.391839	+	0.391839i	0.483503	+	0.875343i	$0.339364\pi$
$90$	−2.01832	−	0.404710i	−0.212749	−	0.0426602i
$91$	1.01538	+	0.201971i	0.106440	+	0.0211723i
$92$	−4.45959	+	2.97980i	−0.464945	+	0.310666i
$93$	−1.13117	−	0.225911i	−0.117296	−	0.0234259i
$94$	7.73308	−	3.20315i	0.797606	−	0.330379i
$95$	0.250480	+	0.374870i	0.0256987	+	0.0384609i
$96$	−7.06032	+	7.04942i	−0.720591	+	0.719479i
$97$	2.05296	+	1.37174i	0.208446	+	0.139279i	0.655411	−	0.755272i	$-0.272495\pi$
$97$	2.05296	+	1.37174i	0.208446	+	0.139279i	−0.446965	+	0.894551i	$0.647495\pi$
$98$	−4.12764	−	4.12764i	−0.416954	−	0.416954i
$99$	−7.34321	−	11.0267i	−0.738021	−	1.10823i
$100$	2.14924	−	5.18873i	0.214924	−	0.518873i
$101$	6.79257			0.675886			0.337943	−	0.941167i	$-0.390269\pi$
$101$	6.79257			0.675886			0.337943	+	0.941167i	$0.390269\pi$
$102$		0			0
$103$	2.47763			0.244128			0.122064	−	0.992522i	$-0.461049\pi$
$103$	2.47763			0.244128			0.122064	+	0.992522i	$0.461049\pi$
$104$	5.61068	−	13.5454i	0.550172	−	1.32823i
$105$	−0.255539	−	0.106079i	−0.0249380	−	0.0103522i
$106$	6.86974	+	6.86974i	0.667248	+	0.667248i
$107$	−3.42069	−	2.28563i	−0.330690	−	0.220960i	0.379129	−	0.925344i	$-0.376224\pi$
$107$	−3.42069	−	2.28563i	−0.330690	−	0.220960i	−0.709820	+	0.704384i	$0.751224\pi$
$108$	6.22023	+	2.59341i	0.598542	+	0.249551i
$109$	−7.02704	−	10.5167i	−0.673068	−	1.00732i	−0.998100	−	0.0616150i	$-0.980375\pi$
$109$	−7.02704	−	10.5167i	−0.673068	−	1.00732i	0.325032	−	0.945703i	$-0.394625\pi$
$110$	2.79947	−	1.15958i	0.266919	−	0.110561i
$111$	0.666299	−	3.33625i	0.0632423	−	0.316662i
$112$	−0.0448020	+	0.0299357i	−0.00423339	+	0.00282866i
$113$	1.21253	+	0.241188i	0.114066	+	0.0226891i	0.251793	−	0.967781i	$-0.418980\pi$
$113$	1.21253	+	0.241188i	0.114066	+	0.0226891i	−0.137727	+	0.990470i	$0.543980\pi$
$114$	0.305614	+	0.739433i	0.0286234	+	0.0692542i
$115$	−2.39302	+	2.39302i	−0.223150	+	0.223150i
$116$	−0.787211	+	0.156586i	−0.0730907	+	0.0145386i
$117$	−15.9108	−	0.0245757i	−1.47096	−	0.00227203i
$118$		−	0.218059i		−	0.0200740i
$119$		0			0
$120$	−2.17943	+	3.25631i	−0.198954	+	0.297259i
$121$	7.85415	+	3.25330i	0.714014	+	0.295754i
$122$	1.72583	+	8.67634i	0.156249	+	0.785519i
$123$	−2.69108	−	13.5838i	−0.242647	−	1.22481i
$124$	−0.479872	+	0.718179i	−0.0430938	+	0.0644944i
$125$	1.48960	−	7.48875i	0.133234	−	0.669814i
$126$	−0.407838	−	0.273421i	−0.0363331	−	0.0243583i
$127$	3.38823	+	8.17992i	0.300657	+	0.725850i	0.999939	+	0.0110047i	$0.00350299\pi$
$127$	3.38823	+	8.17992i	0.300657	+	0.725850i	−0.699282	+	0.714845i	$0.746497\pi$
$128$	3.03612	+	7.32985i	0.268358	+	0.647873i
$129$	0.0103263	−	13.3710i	0.000909184	−	1.17725i
$130$	0.709965	−	3.56923i	0.0622680	−	0.313043i
$131$	5.46257	−	8.17531i	0.477267	−	0.714280i	−0.512228	−	0.858850i	$-0.671180\pi$
$131$	5.46257	−	8.17531i	0.477267	−	0.714280i	0.989495	+	0.144569i	$0.0461797\pi$
$132$	−9.73106	+	1.92782i	−0.846980	+	0.167795i
$133$	0.0209803	+	0.105475i	0.00181922	+	0.00914583i
$134$	−4.19080	−	1.73589i	−0.362030	−	0.149958i
$135$	4.16863	+	0.839238i	0.358779	+	0.0722301i
$136$		0			0
$137$		−	12.6644i		−	1.08200i	−0.841024	−	0.540998i	$-0.818047\pi$
$137$		−	12.6644i		−	1.08200i	0.841024	−	0.540998i	$-0.181953\pi$
$138$	−4.99622	+	3.33279i	−0.425306	+	0.283706i
$139$	−11.6771	+	2.32272i	−0.990437	+	0.197010i	−0.663614	−	0.748075i	$-0.730978\pi$
$139$	−11.6771	+	2.32272i	−0.990437	+	0.197010i	−0.326823	+	0.945085i	$0.605978\pi$
$140$	−0.146498	+	0.146498i	−0.0123814	+	0.0123814i
$141$	−15.9795	+	6.60447i	−1.34572	+	0.556197i
$142$	−5.35753	−	1.06568i	−0.449594	−	0.0894298i
$143$	19.4738	−	13.0120i	1.62848	−	1.08812i
$144$	0.586472	−	0.584663i	0.0488726	−	0.0487219i
$145$	−0.467891	+	0.193807i	−0.0388562	+	0.0160948i
$146$	−5.40605	−	8.09073i	−0.447408	−	0.669593i
$147$	8.51996	+	8.53313i	0.702714	+	0.703801i
$148$	−2.11819	−	1.41533i	−0.174114	−	0.116339i
$149$	−8.98104	−	8.98104i	−0.735756	−	0.735756i	0.235998	−	0.971754i	$-0.424164\pi$
$149$	−8.98104	−	8.98104i	−0.735756	−	0.735756i	−0.971754	+	0.235998i	$0.924164\pi$
$150$	2.41111	−	5.80824i	0.196866	−	0.474240i
$151$	−0.303307	+	0.732249i	−0.0246828	+	0.0595895i	−0.935740	−	0.352690i	$-0.885267\pi$
$151$	−0.303307	+	0.732249i	−0.0246828	+	0.0595895i	0.911058	+	0.412279i	$0.135267\pi$
$152$	1.52299			0.123531
$153$		0			0
$154$	0.722771			0.0582426
$155$	−0.208563	+	0.503516i	−0.0167522	+	0.0404434i
$156$	−4.56782	+	11.0037i	−0.365719	+	0.880998i
$157$	1.66767	+	1.66767i	0.133095	+	0.133095i	0.770516	−	0.637421i	$-0.219999\pi$
$157$	1.66767	+	1.66767i	0.133095	+	0.133095i	−0.637421	+	0.770516i	$0.719999\pi$
$158$	−7.53584	−	5.03529i	−0.599519	−	0.400586i
$159$	−14.1800	−	14.2019i	−1.12455	−	1.12629i
$160$	2.61892	+	3.91949i	0.207044	+	0.309863i
$161$	−0.745790	+	0.308916i	−0.0587765	+	0.0243460i
$162$	6.96288	+	2.90935i	0.547055	+	0.228580i
$163$	−13.4131	+	8.96232i	−1.05059	+	0.701983i	−0.955950	−	0.293529i	$-0.905170\pi$
$163$	−13.4131	+	8.96232i	−1.05059	+	0.701983i	−0.0946411	+	0.995511i	$0.530170\pi$
$164$	−10.1700	−	2.02294i	−0.794145	−	0.157965i
$165$	−5.78476	+	2.39090i	−0.450343	+	0.186131i
$166$	−1.63829	+	1.63829i	−0.127156	+	0.127156i
$167$	−8.99131	+	1.78848i	−0.695769	+	0.138397i	−0.530290	−	0.847816i	$-0.677917\pi$
$167$	−8.99131	+	1.78848i	−0.695769	+	0.138397i	−0.165479	+	0.986213i	$0.552917\pi$
$168$	−0.777525	+	0.518657i	−0.0599873	+	0.0400153i
$169$		−	15.1284i		−	1.16372i
$170$		0			0
$171$	−0.630134	−	1.52795i	−0.0481875	−	0.116845i
$172$	−9.25009	−	3.83151i	−0.705313	−	0.292150i
$173$	0.227417	+	1.14330i	0.0172902	+	0.0869239i	0.988467	−	0.151437i	$-0.0483900\pi$
$173$	0.227417	+	1.14330i	0.0172902	+	0.0869239i	−0.971177	+	0.238361i	$0.923390\pi$
$174$	−0.881617	+	0.174657i	−0.0668352	+	0.0132407i
$175$	0.469610	−	0.702821i	0.0354992	−	0.0531283i
$176$	−0.237814	+	1.19557i	−0.0179259	+	0.0901197i
$177$	−0.000347879		0.450449i	−2.61482e−5		0.0338578i
$178$	1.67744	+	4.04970i	0.125729	+	0.303538i
$179$	3.93697	+	9.50468i	0.294263	+	0.710413i	0.999998	+	0.00193768i	$0.000616785\pi$
$179$	3.93697	+	9.50468i	0.294263	+	0.710413i	−0.705735	+	0.708476i	$0.749383\pi$
$180$	1.77308	−	2.64476i	0.132158	−	0.197129i
$181$	−2.51298	+	12.6336i	−0.186788	+	0.939047i	0.767702	+	0.640806i	$0.221400\pi$
$181$	−2.51298	+	12.6336i	−0.186788	+	0.939047i	−0.954491	+	0.298241i	$0.903600\pi$
$182$	0.482260	−	0.721753i	0.0357475	−	0.0534999i
$183$	−3.55124	−	17.9256i	−0.262515	−	1.32510i
$184$	2.23028	+	11.2124i	0.164419	+	0.826588i
$185$	−1.48506	−	0.615133i	−0.109184	−	0.0452255i
$186$	−0.537959	+	0.803768i	−0.0394450	+	0.0589351i
$187$		0			0
$188$			12.9472i			0.944271i
$189$	0.842043	+	0.565462i	0.0612496	+	0.0411313i
$190$	0.370764	−	0.0737495i	0.0268980	−	0.00535035i
$191$	11.7655	−	11.7655i	0.851319	−	0.851319i	−0.138977	−	0.990296i	$-0.544381\pi$
$191$	11.7655	−	11.7655i	0.851319	−	0.851319i	0.990296	+	0.138977i	$0.0443814\pi$
$192$	2.83013	+	6.84749i	0.204247	+	0.494175i
$193$	2.91805	+	0.580436i	0.210046	+	0.0417807i	0.298991	−	0.954256i	$-0.403350\pi$
$193$	2.91805	+	0.580436i	0.210046	+	0.0417807i	−0.0889458	+	0.996036i	$0.528350\pi$
$194$	1.72135	−	1.15017i	0.123586	−	0.0825773i
$195$	−1.47228	+	7.37191i	−0.105432	+	0.527913i
$196$	8.34201	−	3.45537i	0.595858	−	0.246812i
$197$	−7.53865	−	11.2824i	−0.537107	−	0.803837i	0.459323	−	0.888270i	$-0.348092\pi$
$197$	−7.53865	−	11.2824i	−0.537107	−	0.803837i	−0.996429	+	0.0844326i	$0.973092\pi$
$198$	−10.8980	+	2.15026i	−0.774490	+	0.152812i
$199$	−3.57679	−	2.38994i	−0.253552	−	0.169418i	0.422298	−	0.906457i	$-0.361223\pi$
$199$	−3.57679	−	2.38994i	−0.253552	−	0.169418i	−0.675850	+	0.737039i	$0.736223\pi$
$200$	−8.46460	−	8.46460i	−0.598538	−	0.598538i
$201$	8.65425	+	3.59254i	0.610424	+	0.253398i
$202$	2.17953	−	5.26185i	0.153351	−	0.370223i
$203$	−0.120801			−0.00847855
$204$		0			0
$205$	−6.54274			−0.456965
$206$	0.794996	−	1.91929i	0.0553900	−	0.133723i
$207$	10.3261	−	6.87663i	0.717713	−	0.477959i
$208$	1.03521	+	1.03521i	0.0717789	+	0.0717789i
$209$	2.02289	+	1.35165i	0.139926	+	0.0934958i
$210$	−0.164168	+	0.163915i	−0.0113287	+	0.0113112i
$211$	−8.62651	−	12.9105i	−0.593873	−	0.888794i	0.405810	−	0.913957i	$-0.366989\pi$
$211$	−8.62651	−	12.9105i	−0.593873	−	0.888794i	−0.999683	+	0.0251632i	$0.991989\pi$
$212$	−13.8838	+	5.75087i	−0.953545	+	0.394971i
$213$	11.0655	+	2.20994i	0.758193	+	0.151423i
$214$	−2.86815	+	1.91644i	−0.196063	+	0.131005i
$215$	−6.19607	−	1.23248i	−0.422569	−	0.0840541i
$216$	10.1806	−	10.1335i	0.692703	−	0.689501i
$217$	−0.0919229	+	0.0919229i	−0.00624014	+	0.00624014i
$218$	−10.4015	+	2.06899i	−0.704479	+	0.140130i
$219$	11.1545	+	16.7218i	0.753750	+	1.12995i
$220$			4.68704i			0.316000i
$221$		0			0
$222$	−2.37062	−	1.58665i	−0.159106	−	0.106489i
$223$	15.3941	+	6.37645i	1.03087	+	0.426999i	0.833025	−	0.553235i	$-0.186607\pi$
$223$	15.3941	+	6.37645i	1.03087	+	0.426999i	0.197841	+	0.980234i	$0.436607\pi$
$224$	0.219361	+	1.10280i	0.0146567	+	0.0736841i
$225$	−4.98994	+	11.9943i	−0.332662	+	0.799623i
$226$	0.575901	−	0.861897i	0.0383084	−	0.0573325i
$227$	3.75522	−	18.8788i	0.249243	−	1.25303i	−0.629978	−	0.776613i	$-0.716936\pi$
$227$	3.75522	−	18.8788i	0.249243	−	1.25303i	0.879221	−	0.476415i	$-0.158064\pi$
$228$	−1.23761		0.000955797i	−0.0819626		6.32992e-5i
$229$	−4.20213	−	10.1448i	−0.277685	−	0.670391i	0.722086	−	0.691803i	$-0.243184\pi$
$229$	−4.20213	−	10.1448i	−0.277685	−	0.670391i	−0.999771	+	0.0214129i	$0.993184\pi$
$230$	1.08590	+	2.62159i	0.0716020	+	0.172863i
$231$	−1.49304	−	0.00115307i	−0.0982350	−	7.58663e-5i
$232$	−0.333755	+	1.67790i	−0.0219121	+	0.110160i
$233$	−13.0485	+	19.5285i	−0.854837	+	1.27935i	0.103765	+	0.994602i	$0.466911\pi$
$233$	−13.0485	+	19.5285i	−0.854837	+	1.27935i	−0.958601	+	0.284752i	$0.908089\pi$
$234$	−5.12435	+	12.3174i	−0.334989	+	0.805215i
$235$	1.59376	+	8.01238i	0.103966	+	0.522670i
$236$	0.311622	+	0.129078i	0.0202849	+	0.00840226i
$237$	15.5589	+	10.4135i	1.01066	+	0.676431i
$238$		0			0
$239$		−	13.7217i		−	0.887582i	−0.896130	−	0.443791i	$-0.853633\pi$
$239$		−	13.7217i		−	0.887582i	0.896130	−	0.443791i	$-0.146367\pi$
$240$	−0.217124	−	0.325493i	−0.0140153	−	0.0210105i
$241$	−4.19398	+	0.834235i	−0.270158	+	0.0537378i	−0.328310	−	0.944570i	$-0.606479\pi$
$241$	−4.19398	+	0.834235i	−0.270158	+	0.0537378i	0.0581522	+	0.998308i	$0.481479\pi$
$242$	5.04032	−	5.04032i	0.324004	−	0.324004i
$243$	−14.3787	−	6.02101i	−0.922395	−	0.386248i
$244$	−13.4207	−	2.66954i	−0.859172	−	0.170900i
$245$	4.73711	−	3.16523i	0.302643	−	0.202219i
$246$	−11.3861	−	2.27399i	−0.725954	−	0.144984i
$247$	2.69950	−	1.11817i	0.171765	−	0.0711474i
$248$	1.02282	+	1.53076i	0.0649494	+	0.0972036i
$249$	3.38686	−	3.38163i	0.214633	−	0.214302i
$250$	−5.32317	−	3.55683i	−0.336667	−	0.224954i
$251$	6.57161	+	6.57161i	0.414796	+	0.414796i	0.883406	−	0.468609i	$-0.155245\pi$
$251$	6.57161	+	6.57161i	0.414796	+	0.414796i	−0.468609	+	0.883406i	$0.655245\pi$
$252$	0.632154	−	0.420981i	0.0398220	−	0.0265193i
$253$	−6.98863	+	16.8721i	−0.439372	+	1.06074i
$254$	7.42374			0.465807
$255$		0			0
$256$	15.2078			0.950486
$257$	−6.01912	+	14.5315i	−0.375463	+	0.906447i	0.617341	+	0.786696i	$0.288210\pi$
$257$	−6.01912	+	14.5315i	−0.375463	+	0.906447i	−0.992804	+	0.119752i	$0.961790\pi$
$258$	−10.3545	−	4.29835i	−0.644643	−	0.267603i
$259$	−0.271116	−	0.271116i	−0.0168463	−	0.0168463i
$260$	4.68043	+	3.12737i	0.290268	+	0.193951i
$261$	1.82145	−	0.359385i	0.112745	−	0.0222454i
$262$	−4.58021	−	6.85478i	−0.282967	−	0.423489i
$263$	−14.2664	+	5.90932i	−0.879701	+	0.364384i	−0.776381	−	0.630264i	$-0.782947\pi$
$263$	−14.2664	+	5.90932i	−0.879701	+	0.364384i	−0.103320	+	0.994648i	$0.532947\pi$
$264$	−4.14108	+	20.7349i	−0.254866	+	1.27615i
$265$	−7.88410	+	5.26799i	−0.484316	+	0.323610i
$266$	0.0884379	+	0.0175914i	0.00542247	+	0.00107860i
$267$	−3.45866	−	8.36821i	−0.211666	−	0.512126i
$268$	4.96141	−	4.96141i	0.303066	−	0.303066i
$269$	23.8706	−	4.74815i	1.45541	−	0.289500i	0.596911	−	0.802307i	$-0.296395\pi$
$269$	23.8706	−	4.74815i	1.45541	−	0.289500i	0.858504	+	0.512807i	$0.171395\pi$
$270$	1.98770	−	2.95994i	0.120968	−	0.180136i
$271$			5.62528i			0.341711i	0.985296	+	0.170856i	$0.0546532\pi$
$271$			5.62528i			0.341711i	−0.985296	+	0.170856i	$0.945347\pi$
$272$		0			0
$273$	−0.997365	+	1.49017i	−0.0603633	+	0.0901891i
$274$	−9.81047	−	4.06363i	−0.592672	−	0.245493i
$275$	−3.73066	−	18.7553i	−0.224967	−	1.13099i
$276$	−1.80533	−	9.11276i	−0.108668	−	0.548524i
$277$	−4.92476	+	7.37043i	−0.295900	+	0.442846i	−0.949395	−	0.314085i	$-0.898302\pi$
$277$	−4.92476	+	7.37043i	−0.295900	+	0.442846i	0.653495	+	0.756931i	$0.273302\pi$
$278$	−1.94753	+	9.79092i	−0.116805	+	0.587220i
$279$	1.11255	−	1.65950i	0.0666069	−	0.0993517i
$280$	0.168991	+	0.407979i	0.0100991	+	0.0243814i
$281$	−2.76232	−	6.66883i	−0.164786	−	0.397829i	0.819819	−	0.572623i	$-0.194074\pi$
$281$	−2.76232	−	6.66883i	−0.164786	−	0.397829i	−0.984605	+	0.174794i	$0.944074\pi$
$282$	−0.0111965	+	14.4977i	−0.000666739	+	0.863323i
$283$	0.964082	−	4.84677i	0.0573087	−	0.288110i	−0.941494	−	0.337030i	$-0.890578\pi$
$283$	0.964082	−	4.84677i	0.0573087	−	0.288110i	0.998803	+	0.0489193i	$0.0155777\pi$
$284$	4.69427	−	7.02547i	0.278554	−	0.416885i
$285$	−0.766012	+	0.151754i	−0.0453746	+	0.00898915i
$286$	−3.83115	−	19.2605i	−0.226541	−	1.13890i
$287$	−1.44184	−	0.597228i	−0.0851088	−	0.0352532i
$288$	−6.58842	−	15.9756i	−0.388227	−	0.941372i
$289$		0			0
$290$			0.424637i			0.0249356i
$291$	−3.55766	+	2.37318i	−0.208554	+	0.139118i
$292$	14.7623	−	2.93640i	0.863897	−	0.171840i
$293$	−13.5083	+	13.5083i	−0.789165	+	0.789165i	−0.981357	−	0.192192i	$-0.938440\pi$
$293$	−13.5083	+	13.5083i	−0.789165	+	0.789165i	0.192192	+	0.981357i	$0.438440\pi$
$294$	9.34397	−	3.86195i	0.544951	−	0.225233i
$295$	0.208736	+	0.0415203i	0.0121531	+	0.00241740i
$296$	−4.51481	+	3.01670i	−0.262418	+	0.175342i
$297$	22.5157	−	4.42445i	1.30650	−	0.256733i
$298$	−9.83889	+	4.07540i	−0.569952	+	0.236082i
$299$	12.1852	+	18.2364i	0.704688	+	1.05464i
$300$	6.87315	+	6.88377i	0.396821	+	0.397435i
$301$	−1.25294	−	0.837187i	−0.0722182	−	0.0482546i
$302$	0.469913	+	0.469913i	0.0270404	+	0.0270404i
$303$	−4.51069	+	10.8660i	−0.259133	+	0.624237i
$304$	−0.0581977	+	0.140502i	−0.00333786	+	0.00805832i
$305$	−8.63402			−0.494382
$306$		0			0
$307$	−4.98811			−0.284687			−0.142343	−	0.989817i	$-0.545464\pi$
$307$	−4.98811			−0.284687			−0.142343	+	0.989817i	$0.545464\pi$
$308$	−0.427838	+	1.03289i	−0.0243783	+	0.0588544i
$309$	−1.64530	+	3.96345i	−0.0935979	+	0.225473i
$310$	0.323126	+	0.323126i	0.0183523	+	0.0183523i
$311$	8.70232	+	5.81470i	0.493463	+	0.329722i	0.777278	−	0.629158i	$-0.216600\pi$
$311$	8.70232	+	5.81470i	0.493463	+	0.329722i	−0.283814	+	0.958879i	$0.591600\pi$
$312$	17.9426	+	17.9704i	1.01580	+	1.01737i
$313$	13.3418	+	19.9675i	0.754125	+	1.12863i	0.987711	+	0.156292i	$0.0499541\pi$
$313$	13.3418	+	19.9675i	0.754125	+	1.12863i	−0.233586	+	0.972336i	$0.575046\pi$
$314$	1.82697	−	0.756754i	0.103102	−	0.0427061i
$315$	0.339387	−	0.338341i	0.0191223	−	0.0190633i
$316$	11.6566	−	7.78866i	0.655732	−	0.438146i
$317$	−9.64699	−	1.91890i	−0.541829	−	0.107776i	−0.0834143	−	0.996515i	$-0.526582\pi$
$317$	−9.64699	−	1.91890i	−0.541829	−	0.107776i	−0.458414	+	0.888739i	$0.651582\pi$
$318$	−15.5514	+	6.42754i	−0.872080	+	0.360439i
$319$	−1.93244	+	1.93244i	−0.108196	+	0.108196i
$320$	3.43344	−	0.682954i	0.191935	−	0.0381783i
$321$	5.92786	−	3.95425i	0.330861	−	0.220705i
$322$			0.676847i			0.0377192i
$323$		0			0
$324$	−8.27928	+	8.22829i	−0.459960	+	0.457127i
$325$	−21.2181	−	8.78882i	−1.17697	−	0.487516i
$326$	2.63880	+	13.2661i	0.146149	+	0.734743i
$327$	21.4899	−	4.25736i	1.18839	−	0.235432i
$328$	−12.2790	+	18.3768i	−0.677993	+	1.01469i
$329$	−0.380158	+	1.91118i	−0.0209588	+	0.105367i
$330$	−0.00405325	+	5.24832i	−0.000223124	+	0.288911i
$331$	1.60689	+	3.87936i	0.0883224	+	0.213229i	0.961869	−	0.273512i	$-0.0881854\pi$
$331$	1.60689	+	3.87936i	0.0883224	+	0.213229i	−0.873546	+	0.486741i	$0.838185\pi$
$332$	−1.37146	−	3.31100i	−0.0752687	−	0.181715i
$333$	4.89451	+	3.28135i	0.268217	+	0.179817i
$334$	−1.49959	+	7.53897i	−0.0820542	+	0.412514i
$335$	2.45964	−	3.68110i	0.134384	−	0.201120i
$336$	−0.0181367	−	0.0915487i	−0.000989437	−	0.00499439i
$337$	−1.12873	−	5.67449i	−0.0614856	−	0.309109i	0.937788	−	0.347207i	$-0.112870\pi$
$337$	−1.12873	−	5.67449i	−0.0614856	−	0.309109i	−0.999274	+	0.0380983i	$0.987870\pi$
$338$	−11.7192	−	4.85425i	−0.637440	−	0.264036i
$339$	−1.19103	+	1.77952i	−0.0646876	+	0.0966502i
$340$		0			0
$341$			2.94097i			0.159262i
$342$	−1.38581	−	0.00214051i	−0.0749362	−	0.000115746i
$343$	2.67300	−	0.531692i	0.144328	−	0.0287087i
$344$	−15.0901	+	15.0901i	−0.813602	+	0.813602i
$345$	−2.23898	−	5.41721i	−0.120543	−	0.291653i
$346$	0.958630	+	0.190683i	0.0515363	+	0.0102512i
$347$	−0.0157453	+	0.0105207i	−0.000845252	+	0.000564779i	−0.555993	−	0.831187i	$-0.687662\pi$
$347$	−0.0157453	+	0.0105207i	−0.000845252	+	0.000564779i	0.555148	+	0.831752i	$0.312662\pi$
$348$	0.272268	−	1.36328i	0.0145951	−	0.0730794i
$349$	5.74159	−	2.37825i	0.307340	−	0.127305i	−0.223682	−	0.974662i	$-0.571808\pi$
$349$	5.74159	−	2.37825i	0.307340	−	0.127305i	0.531023	+	0.847358i	$0.321808\pi$
$350$	−0.393755	−	0.589297i	−0.0210471	−	0.0314992i
$351$	10.6051	−	25.4362i	0.566059	−	1.35768i
$352$	21.1505	+	14.1323i	1.12733	+	0.753256i
$353$	8.61113	+	8.61113i	0.458324	+	0.458324i	0.898105	−	0.439781i	$-0.144944\pi$
$353$	8.61113	+	8.61113i	0.458324	+	0.458324i	−0.439781	+	0.898105i	$0.644944\pi$
$354$	0.348828	+	0.144805i	0.0185400	+	0.00769629i
$355$	2.04024	−	4.92557i	0.108285	−	0.261422i
$356$	−6.78025			−0.359352
$357$		0			0
$358$	8.62604			0.455900
$359$	12.1801	−	29.4053i	0.642840	−	1.55195i	−0.179992	−	0.983668i	$-0.557607\pi$
$359$	12.1801	−	29.4053i	0.642840	−	1.55195i	0.822832	−	0.568284i	$-0.192393\pi$
$360$	−3.76181	−	5.64882i	−0.198265	−	0.297719i
$361$	−13.2204	−	13.2204i	−0.695811	−	0.695811i
$362$	8.98025	+	6.00041i	0.471991	+	0.315375i
$363$	−10.4199	+	10.4038i	−0.546904	+	0.546060i
$364$	0.745967	+	1.11642i	0.0390993	+	0.0585162i
$365$	8.77418	−	3.63439i	0.459262	−	0.190232i
$366$	−15.0255	−	3.00083i	−0.785398	−	0.156856i
$367$	27.9587	−	18.6814i	1.45943	−	0.975161i	0.463401	−	0.886149i	$-0.346629\pi$
$367$	27.9587	−	18.6814i	1.45943	−	0.975161i	0.996031	−	0.0890125i	$-0.0283711\pi$
$368$	−1.11961	−	0.222704i	−0.0583636	−	0.0116092i
$369$	23.5170	+	4.71559i	1.22424	+	0.245484i
$370$	−0.953024	+	0.953024i	−0.0495453	+	0.0495453i
$371$	−2.21830	+	0.441247i	−0.115168	+	0.0229084i
$372$	−0.830202	−	1.24456i	−0.0430439	−	0.0645276i
$373$		−	15.2764i		−	0.790981i	−0.918470	−	0.395490i	$-0.870575\pi$
$373$		−	15.2764i		−	0.790981i	0.918470	−	0.395490i	$-0.129425\pi$
$374$		0			0
$375$	10.9905	+	7.35591i	0.567547	+	0.379857i
$376$	25.4957	+	10.5607i	1.31484	+	0.544624i
$377$	0.640321	+	3.21911i	0.0329782	+	0.165793i
$378$	0.708220	−	0.470848i	0.0364269	−	0.0242178i
$379$	21.1206	−	31.6091i	1.08489	−	1.62365i	0.362779	−	0.931875i	$-0.381828\pi$
$379$	21.1206	−	31.6091i	1.08489	−	1.62365i	0.722111	−	0.691778i	$-0.243172\pi$
$380$	−0.114077	+	0.573503i	−0.00585202	+	0.0294201i
$381$	−15.3354	−	0.0118434i	−0.785654	−	0.000606756i
$382$	−5.33891	−	12.8893i	−0.273162	−	0.659472i
$383$	−13.1831	−	31.8268i	−0.673624	−	1.62627i	−0.775404	−	0.631465i	$-0.782454\pi$
$383$	−13.1831	−	31.8268i	−0.673624	−	1.62627i	0.101781	−	0.994807i	$-0.467546\pi$
$384$	−13.7417	−	0.0106126i	−0.701253	−	0.000541574i
$385$	−0.137622	+	0.691871i	−0.00701385	+	0.0352610i
$386$	1.38595	−	2.07422i	0.0705428	−	0.105575i
$387$	21.3826	+	8.89570i	1.08694	+	0.452194i
$388$	0.624737	+	3.14076i	0.0317162	+	0.159448i
$389$	0.697275	+	0.288821i	0.0353532	+	0.0146438i	0.400290	−	0.916389i	$-0.368909\pi$
$389$	0.697275	+	0.288821i	0.0353532	+	0.0146438i	−0.364937	+	0.931032i	$0.618909\pi$
$390$	5.23822	+	3.50592i	0.265248	+	0.177529i
$391$		0			0
$392$		−	19.2456i		−	0.972048i
$393$	9.45050	+	14.1674i	0.476715	+	0.714648i
$394$	−11.1588	+	2.21962i	−0.562172	+	0.111823i
$395$	6.25490	−	6.25490i	0.314718	−	0.314718i
$396$	3.37812	−	16.8469i	0.169757	−	0.846589i
$397$	19.7598	+	3.93046i	0.991713	+	0.197264i	0.664178	−	0.747575i	$-0.268782\pi$
$397$	19.7598	+	3.93046i	0.991713	+	0.197264i	0.327536	+	0.944839i	$0.393782\pi$
$398$	−2.99904	+	2.00390i	−0.150329	+	0.100446i
$399$	−0.182660	−	0.0364800i	−0.00914443	−	0.00182628i
$400$	1.10434	−	0.457434i	0.0552172	−	0.0228717i
$401$	−8.76056	−	13.1111i	−0.437481	−	0.654737i	0.545570	−	0.838065i	$-0.316313\pi$
$401$	−8.76056	−	13.1111i	−0.437481	−	0.654737i	−0.983052	+	0.183328i	$0.941313\pi$
$402$	5.55984	−	5.55126i	0.277300	−	0.276872i
$403$	2.93682	+	1.96232i	0.146294	+	0.0977502i
$404$	6.22941	+	6.22941i	0.309925	+	0.309925i
$405$	−4.11076	+	6.11123i	−0.204265	+	0.303670i
$406$	−0.0387613	+	0.0935781i	−0.00192369	+	0.00464420i
$407$	−8.67405			−0.429957
$408$		0			0
$409$	−28.3555			−1.40209			−0.701045	−	0.713117i	$-0.747283\pi$
$409$	−28.3555			−1.40209			−0.701045	+	0.713117i	$0.747283\pi$
$410$	−2.09937	+	5.06832i	−0.103680	+	0.250306i
$411$	20.2592	+	8.40997i	0.999313	+	0.414833i
$412$	2.27221	+	2.27221i	0.111944	+	0.111944i
$413$	0.0422096	+	0.0282036i	0.00207700	+	0.00138781i
$414$	−2.01364	−	10.2056i	−0.0989649	−	0.501578i
$415$	−1.25630	−	1.88019i	−0.0616695	−	0.0922950i
$416$	28.2248	−	11.6911i	1.38384	−	0.573204i
$417$	4.03868	−	20.2222i	0.197775	−	0.990285i
$418$	1.69614	−	1.13332i	0.0829610	−	0.0554327i
$419$	34.5545	+	6.87332i	1.68810	+	0.335784i	0.943410	−	0.331628i	$-0.107598\pi$
$419$	34.5545	+	6.87332i	1.68810	+	0.335784i	0.744689	+	0.667412i	$0.232598\pi$
$420$	−0.137068	−	0.331636i	−0.00668825	−	0.0161822i
$421$	0.00892902	−	0.00892902i	0.000435174	−	0.000435174i	−0.706889	−	0.707324i	$-0.749902\pi$
$421$	0.00892902	−	0.00892902i	0.000435174	−	0.000435174i	0.707324	+	0.706889i	$0.249902\pi$
$422$	−12.7691	+	2.53992i	−0.621588	+	0.123642i
$423$	0.0462575	−	29.9481i	0.00224912	−	1.45613i
$424$			32.0309i			1.55556i
$425$		0			0
$426$	5.26250	−	7.86273i	0.254969	−	0.380951i
$427$	−1.90269	−	0.788122i	−0.0920779	−	0.0381399i
$428$	−1.04095	−	5.23321i	−0.0503163	−	0.252957i
$429$	7.88335	+	39.7929i	0.380612	+	1.92122i
$430$	−2.94287	+	4.40431i	−0.141918	+	0.212395i
$431$	−2.31319	+	11.6292i	−0.111422	+	0.560159i	0.884233	+	0.467046i	$0.154682\pi$
$431$	−2.31319	+	11.6292i	−0.111422	+	0.560159i	−0.995656	+	0.0931127i	$0.970318\pi$
$432$	0.545827	+	1.32643i	0.0262611	+	0.0638178i
$433$	0.207692	+	0.501414i	0.00998106	+	0.0240964i	0.928791	−	0.370603i	$-0.120849\pi$
$433$	0.207692	+	0.501414i	0.00998106	+	0.0240964i	−0.918810	+	0.394699i	$0.870849\pi$
$434$	0.0417126	+	0.100703i	0.00200227	+	0.00483391i
$435$	0.000677442	−	0.877181i	3.24809e−5	−	0.0420576i
$436$	3.20035	−	16.0892i	0.153269	−	0.770534i
$437$	−1.26577	+	1.89436i	−0.0605500	+	0.0906195i
$438$	16.5326	−	3.27528i	0.789960	−	0.156499i
$439$	−5.94070	−	29.8659i	−0.283534	−	1.42542i	−0.815550	−	0.578687i	$-0.803565\pi$
$439$	−5.94070	−	29.8659i	−0.283534	−	1.42542i	0.532016	−	0.846734i	$-0.321435\pi$
$440$	9.22974	+	3.82308i	0.440010	+	0.182258i
$441$	−19.3082	+	7.96279i	−0.919437	+	0.379181i
$442$		0			0
$443$			40.2451i			1.91210i	0.293203	+	0.956050i	$0.405279\pi$
$443$			40.2451i			1.91210i	−0.293203	+	0.956050i	$0.594721\pi$
$444$	3.67070	−	2.44858i	0.174204	−	0.116205i
$445$	−4.19596	+	0.834628i	−0.198908	+	0.0395652i
$446$	9.87902	−	9.87902i	0.467785	−	0.467785i
$447$	20.3309	−	8.40294i	0.961618	−	0.397446i
$448$	0.818975	+	0.162904i	0.0386929	+	0.00769650i
$449$	−30.2957	+	20.2429i	−1.42974	+	0.955323i	−0.431150	+	0.902280i	$0.641892\pi$
$449$	−30.2957	+	20.2429i	−1.42974	+	0.955323i	−0.998592	+	0.0530433i	$0.983108\pi$
$450$	7.69027	+	7.71407i	0.362523	+	0.363645i
$451$	−32.6187	+	13.5111i	−1.53596	+	0.636214i
$452$	0.890813	+	1.33320i	0.0419003	+	0.0627082i
$453$	−0.969959	−	0.971458i	−0.0455726	−	0.0456431i
$454$	−13.4195	−	8.96660i	−0.629807	−	0.420823i
$455$	0.599070	+	0.599070i	0.0280848	+	0.0280848i
$456$	−1.01136	+	2.43632i	−0.0473614	+	0.114091i
$457$	8.15675	−	19.6921i	0.381557	−	0.921160i	−0.610108	−	0.792318i	$-0.708874\pi$
$457$	8.15675	−	19.6921i	0.381557	−	0.921160i	0.991665	−	0.128842i	$-0.0411259\pi$
$458$	−9.20703			−0.430216
$459$		0			0
$460$	−4.38923			−0.204649
$461$	2.35253	−	5.67952i	0.109568	−	0.264521i	−0.859579	−	0.511002i	$-0.829274\pi$
$461$	2.35253	−	5.67952i	0.109568	−	0.264521i	0.969148	+	0.246481i	$0.0792743\pi$
$462$	−0.479965	+	1.15621i	−0.0223300	+	0.0537919i
$463$	−25.6637	−	25.6637i	−1.19270	−	1.19270i	−0.976307	−	0.216388i	$-0.930572\pi$
$463$	−25.6637	−	25.6637i	−1.19270	−	1.19270i	−0.216388	−	0.976307i	$-0.569428\pi$
$464$	−0.142039	−	0.0949073i	−0.00659398	−	0.00440596i
$465$	−0.666973	−	0.668004i	−0.0309301	−	0.0309779i
$466$	10.9408	+	16.3741i	0.506824	+	0.758516i
$467$	7.10485	−	2.94293i	0.328773	−	0.136182i	−0.212190	−	0.977228i	$-0.568060\pi$
$467$	7.10485	−	2.94293i	0.328773	−	0.136182i	0.540964	+	0.841046i	$0.318060\pi$
$468$	−14.5692	−	14.6142i	−0.673460	−	0.675544i
$469$	0.878050	−	0.586694i	0.0405446	−	0.0270910i
$470$	6.71816	+	1.33633i	0.309886	+	0.0616401i
$471$	−3.77521	+	1.56033i	−0.173952	+	0.0718961i
$472$	0.508362	−	0.508362i	0.0233993	−	0.0233993i
$473$	−33.4356	+	6.65075i	−1.53737	+	0.305802i
$474$	13.0592	−	8.71129i	0.599828	−	0.400123i
$475$		−	2.38569i		−	0.109463i
$476$		0			0
$477$	32.1351	−	13.2527i	1.47137	−	0.606799i
$478$	−10.6295	−	4.40287i	−0.486181	−	0.201383i
$479$	0.447923	+	2.25186i	0.0204661	+	0.102890i	0.989668	−	0.143377i	$-0.0457960\pi$
$479$	0.447923	+	2.25186i	0.0204661	+	0.102890i	−0.969202	+	0.246267i	$0.920796\pi$
$480$	−8.00911	+	1.58668i	−0.365564	+	0.0724218i
$481$	−5.78764	+	8.66182i	−0.263894	+	0.394945i
$482$	−0.699483	+	3.51654i	−0.0318606	+	0.160174i
$483$	0.00107980	−	1.39818i	4.91327e−5	−	0.0636192i
$484$	4.21940	+	10.1865i	0.191791	+	0.463025i
$485$	0.773237	+	1.86676i	0.0351109	+	0.0847652i
$486$	−9.27786	+	9.20648i	−0.420852	+	0.417615i
$487$	−5.47752	+	27.5373i	−0.248210	+	1.24784i	0.632642	+	0.774444i	$0.281970\pi$
$487$	−5.47752	+	27.5373i	−0.248210	+	1.24784i	−0.880852	+	0.473392i	$0.843030\pi$
$488$	−16.2038	+	24.2506i	−0.733510	+	1.09777i
$489$	−5.42985	−	27.4083i	−0.245546	−	1.23945i
$490$	−0.931948	−	4.68522i	−0.0421011	−	0.211657i
$491$	12.4942	+	5.17526i	0.563854	+	0.233556i	0.646357	−	0.763035i	$-0.276291\pi$
$491$	12.4942	+	5.17526i	0.563854	+	0.233556i	−0.0825033	+	0.996591i	$0.526291\pi$
$492$	9.98962	−	14.9256i	0.450367	−	0.672896i
$493$		0			0
$494$		−	2.44995i		−	0.110228i
$495$	0.0167457	−	10.8416i	0.000752665	−	0.487292i
$496$	−0.180303	+	0.0358645i	−0.00809585	+	0.00161037i
$497$	0.899222	−	0.899222i	0.0403356	−	0.0403356i
$498$	−1.53283	−	3.70869i	−0.0686879	−	0.166190i
$499$	14.9405	+	2.97184i	0.668827	+	0.133038i	0.517813	−	0.855494i	$-0.326746\pi$
$499$	14.9405	+	2.97184i	0.668827	+	0.133038i	0.151014	+	0.988532i	$0.451746\pi$
$500$	8.23397	−	5.50176i	0.368234	−	0.246046i
$501$	3.10977	−	15.5710i	0.138934	−	0.695661i
$502$	7.19931	−	2.98205i	0.321321	−	0.133096i
$503$	13.5532	+	20.2838i	0.604306	+	0.904408i	0.999902	−	0.0140169i	$-0.00446188\pi$
$503$	13.5532	+	20.2838i	0.604306	+	0.904408i	−0.395596	+	0.918425i	$0.629462\pi$
$504$	−0.313368	−	1.58822i	−0.0139585	−	0.0707451i
$505$	4.62189	+	3.08825i	0.205672	+	0.137425i
$506$	10.8275	+	10.8275i	0.481339	+	0.481339i
$507$	24.2008	+	10.0462i	1.07480	+	0.446168i
$508$	−4.39441	+	10.6090i	−0.194971	+	0.470700i
$509$	−18.8631			−0.836090			−0.418045	−	0.908426i	$-0.637285\pi$
$509$	−18.8631			−0.836090			−0.418045	+	0.908426i	$0.637285\pi$
$510$		0			0
$511$	2.26533			0.100212
$512$	−1.19253	+	2.87903i	−0.0527030	+	0.127236i
$513$	2.86270	+	0.00663255i	0.126391	+	0.000292834i
$514$	9.32541	+	9.32541i	0.411326	+	0.411326i
$515$	1.68586	+	1.12646i	0.0742880	+	0.0496376i
$516$	12.2719	−	12.2530i	0.540240	−	0.539406i
$517$	24.4917	+	36.6544i	1.07714	+	1.61206i
$518$	−0.297013	+	0.123027i	−0.0130500	+	0.00540548i
$519$	−1.97996	−	0.395428i	−0.0869105	−	0.0173574i
$520$	9.97612	−	6.66583i	0.437482	−	0.292316i
$521$	−32.3427	−	6.43336i	−1.41696	−	0.281851i	−0.573571	−	0.819156i	$-0.694442\pi$
$521$	−32.3427	−	6.43336i	−1.41696	−	0.281851i	−0.843388	+	0.537305i	$0.819442\pi$
$522$	0.306051	−	1.52630i	0.0133955	−	0.0668043i
$523$	−9.24397	+	9.24397i	−0.404211	+	0.404211i	−0.879714	−	0.475503i	$-0.842266\pi$
$523$	−9.24397	+	9.24397i	−0.404211	+	0.404211i	0.475503	+	0.879714i	$0.342266\pi$
$524$	12.5072	−	2.48783i	0.546379	−	0.108681i
$525$	0.812448	+	1.21795i	0.0354581	+	0.0531557i
$526$			12.9475i			0.564539i
$527$		0			0
$528$	−1.75463	−	1.17437i	−0.0763604	−	0.0511077i
$529$	5.44921	+	2.25714i	0.236922	+	0.0981363i
$530$	1.55107	+	7.79774i	0.0673740	+	0.338712i
$531$	−0.720349	−	0.299683i	−0.0312605	−	0.0130051i
$532$	−0.0774893	+	0.115971i	−0.00335959	+	0.00502798i
$533$	−8.27234	+	41.5879i	−0.358315	+	1.80137i
$534$	−7.59220	−	0.00586341i	−0.328547	−	0.000253735i
$535$	−1.28839	−	3.11044i	−0.0557018	−	0.134476i
$536$	−5.72315	−	13.8169i	−0.247202	−	0.596800i
$537$	−17.8190	−	0.0137615i	−0.768946	−	0.000593852i
$538$	3.98120	−	20.0148i	0.171642	−	0.862901i
$539$	17.0804	−	25.5626i	0.735705	−	1.10106i
$540$	3.05336	+	4.59268i	0.131396	+	0.197637i
$541$	3.25485	+	16.3632i	0.139937	+	0.703511i	0.985505	+	0.169644i	$0.0542617\pi$
$541$	3.25485	+	16.3632i	0.139937	+	0.703511i	−0.845568	+	0.533867i	$0.820738\pi$
$542$	4.35761	+	1.80498i	0.187176	+	0.0775306i
$543$	−18.5411	−	12.4095i	−0.795675	−	0.532542i
$544$		0			0
$545$		−	10.3508i		−	0.443379i
$546$	0.834332	+	1.25076i	0.0357061	+	0.0535274i
$547$	−10.6347	+	2.11537i	−0.454706	+	0.0904466i	−0.417129	−	0.908847i	$-0.636964\pi$
$547$	−10.6347	+	2.11537i	−0.454706	+	0.0904466i	−0.0375766	+	0.999294i	$0.511964\pi$
$548$	11.6144	−	11.6144i	0.496144	−	0.496144i
$549$	31.0338	+	6.22285i	1.32449	+	0.265585i
$550$	−15.7258	−	3.12806i	−0.670550	−	0.133381i
$551$	−0.283486	+	0.189419i	−0.0120769	+	0.00806952i
$552$	−19.4174	−	3.87796i	−0.826461	−	0.165057i
$553$	1.94936	−	0.807451i	0.0828952	−	0.0343363i
$554$	4.12928	+	6.17990i	0.175436	+	0.262559i
$555$	1.97020	−	1.96716i	0.0836304	−	0.0835013i
$556$	−12.8391	−	8.57881i	−0.544499	−	0.363822i
$557$	8.63556	+	8.63556i	0.365900	+	0.365900i	0.865980	−	0.500079i	$-0.166696\pi$
$557$	8.63556	+	8.63556i	0.365900	+	0.365900i	−0.500079	+	0.865980i	$0.666696\pi$
$558$	−0.928544	−	1.39432i	−0.0393084	−	0.0590263i
$559$	−15.6681	+	37.8261i	−0.662689	+	1.59987i
$560$	−0.0440951			−0.00186336
$561$		0			0
$562$	−6.05234			−0.255302
$563$	−9.00559	+	21.7414i	−0.379541	+	0.916292i	0.612511	+	0.790462i	$0.290159\pi$
$563$	−9.00559	+	21.7414i	−0.379541	+	0.916292i	−0.992052	+	0.125830i	$0.959841\pi$
$564$	−20.7116	−	8.59775i	−0.872114	−	0.362031i
$565$	0.715392	+	0.715392i	0.0300968	+	0.0300968i
$566$	−3.44519	−	2.30200i	−0.144812	−	0.0967605i
$567$	−1.46374	+	0.971510i	−0.0614711	+	0.0407996i
$568$	−10.0056	−	14.9745i	−0.419826	−	0.628314i
$569$	1.73268	−	0.717701i	0.0726379	−	0.0300876i	−0.346069	−	0.938209i	$-0.612484\pi$
$569$	1.73268	−	0.717701i	0.0726379	−	0.0300876i	0.418707	+	0.908122i	$0.362484\pi$
$570$	−0.128234	+	0.642083i	−0.00537112	+	0.0268939i
$571$	33.3039	−	22.2530i	1.39373	−	0.931258i	0.393799	−	0.919197i	$-0.371161\pi$
$571$	33.3039	−	22.2530i	1.39373	−	0.931258i	0.999927	−	0.0120616i	$-0.00383943\pi$
$572$	29.7924	+	5.92608i	1.24568	+	0.247782i
$573$	11.0081	+	26.6341i	0.459871	+	1.11266i
$574$	−0.925283	+	0.925283i	−0.0386205	+	0.0386205i
$575$	17.5636	−	3.49362i	0.732452	−	0.145694i
$576$	−12.8333	−	0.0198221i	−0.534719	−	0.000825922i
$577$			31.8433i			1.32565i	0.748773	+	0.662826i	$0.230643\pi$
$577$			31.8433i			1.32565i	−0.748773	+	0.662826i	$0.769357\pi$
$578$		0			0
$579$	−2.86629	+	4.28254i	−0.119119	+	0.177976i
$580$	−0.606837	−	0.251360i	−0.0251975	−	0.0104372i
$581$	−0.105228	−	0.529018i	−0.00436560	−	0.0219474i
$582$	0.696834	+	3.51742i	0.0288847	+	0.145802i
$583$	−28.4274	+	42.5446i	−1.17734	+	1.76202i
$584$	6.25880	−	31.4651i	0.258991	−	1.30204i
$585$	−10.8151	−	7.25061i	−0.447150	−	0.299776i
$586$	6.12978	+	14.7986i	0.253219	+	0.611325i
$587$	4.81996	+	11.6364i	0.198941	+	0.480286i	0.991594	−	0.129387i	$-0.0413008\pi$
$587$	4.81996	+	11.6364i	0.198941	+	0.480286i	−0.792653	+	0.609673i	$0.791301\pi$
$588$	−0.0120781	+	15.6392i	−0.000498092	+	0.644951i
$589$	−0.0715796	+	0.359855i	−0.00294939	+	0.0148276i
$590$	0.0991408	−	0.148375i	0.00408156	−	0.00610849i
$591$	23.0545	−	4.56732i	0.948336	−	0.187874i
$592$	−0.105778	−	0.531784i	−0.00434746	−	0.0218562i
$593$	17.0275	+	7.05301i	0.699234	+	0.289632i	0.703841	−	0.710357i	$-0.251467\pi$
$593$	17.0275	+	7.05301i	0.699234	+	0.289632i	−0.00460731	+	0.999989i	$0.501467\pi$
$594$	3.79722	−	18.8614i	0.155802	−	0.773895i
$595$		0			0
$596$		−	16.4729i		−	0.674755i
$597$	6.19838	−	4.13471i	0.253683	−	0.169222i
$598$	18.0367	−	3.58772i	0.737575	−	0.146713i
$599$	−12.3968	+	12.3968i	−0.506519	+	0.506519i	−0.913456	−	0.406937i	$-0.866597\pi$
$599$	−12.3968	+	12.3968i	−0.506519	+	0.506519i	0.406937	+	0.913456i	$0.366597\pi$
$600$	19.1618	−	7.91974i	0.782277	−	0.323322i
$601$	13.3143	+	2.64838i	0.543102	+	0.108030i	0.459015	−	0.888429i	$-0.348203\pi$
$601$	13.3143	+	2.64838i	0.543102	+	0.108030i	0.0840872	+	0.996458i	$0.473203\pi$
$602$	−1.05056	+	0.701959i	−0.0428174	+	0.0286097i
$603$	−11.4939	+	11.4585i	−0.468069	+	0.466625i
$604$	−0.949699	+	0.393378i	−0.0386427	+	0.0160063i
$605$	3.86511	+	5.78455i	0.157139	+	0.235175i
$606$	6.97001	+	6.98078i	0.283137	+	0.283575i
$607$	−3.43942	−	2.29815i	−0.139602	−	0.0932790i	0.483808	−	0.875174i	$-0.339253\pi$
$607$	−3.43942	−	2.29815i	−0.139602	−	0.0932790i	−0.623410	+	0.781895i	$0.714253\pi$
$608$	2.24400	+	2.24400i	0.0910064	+	0.0910064i
$609$	0.0802193	−	0.193244i	0.00325065	−	0.00783065i
$610$	−2.77040	+	6.68833i	−0.112170	+	0.270802i
$611$	52.9445			2.14190
$612$		0			0
$613$	−27.1330			−1.09589			−0.547947	−	0.836513i	$-0.684590\pi$
$613$	−27.1330			−1.09589			−0.547947	+	0.836513i	$0.684590\pi$
$614$	−1.60053	+	3.86403i	−0.0645923	+	0.155940i
$615$	4.34479	−	10.4664i	0.175199	−	0.422045i
$616$	1.68500	+	1.68500i	0.0678906	+	0.0678906i
$617$	−10.6078	−	7.08791i	−0.427054	−	0.285349i	0.323411	−	0.946259i	$-0.395170\pi$
$617$	−10.6078	−	7.08791i	−0.427054	−	0.285349i	−0.750465	+	0.660910i	$0.770170\pi$
$618$	2.54235	+	2.54628i	0.102268	+	0.102426i
$619$	−2.15968	−	3.23219i	−0.0868049	−	0.129913i	0.785526	−	0.618829i	$-0.212392\pi$
$619$	−2.15968	−	3.23219i	−0.0868049	−	0.129913i	−0.872331	+	0.488916i	$0.837392\pi$
$620$	−0.653042	+	0.270499i	−0.0262268	+	0.0108635i
$621$	4.14333	+	21.0851i	0.166266	+	0.846116i
$622$	7.29666	−	4.87547i	0.292569	−	0.195489i
$623$	−1.00086	−	0.199083i	−0.0400985	−	0.00797609i
$624$	−2.34346	+	0.968575i	−0.0938136	+	0.0387740i
$625$	−10.8916	+	10.8916i	−0.435663	+	0.435663i
$626$	19.7488	−	3.92827i	0.789319	−	0.157005i
$627$	−3.50556	+	2.33843i	−0.139999	+	0.0933877i
$628$			3.05882i			0.122060i
$629$		0			0
$630$	−0.153196	−	0.371469i	−0.00610346	−	0.0147997i
$631$	−32.3983	−	13.4198i	−1.28976	−	0.534234i	−0.370843	−	0.928696i	$-0.620931\pi$
$631$	−32.3983	−	13.4198i	−1.28976	−	0.534234i	−0.918913	+	0.394461i	$0.870931\pi$
$632$	−5.82955	−	29.3071i	−0.231887	−	1.16578i
$633$	26.3814	−	5.22640i	1.04857	−	0.207731i
$634$	−4.58190	+	6.85730i	−0.181971	+	0.272338i
$635$	−1.41354	+	7.10635i	−0.0560947	+	0.282007i
$636$	0.0201019	−	26.0288i	0.000797092	−	1.03211i
$637$	−14.1299	−	34.1127i	−0.559848	−	1.35159i
$638$	0.876899	+	2.11702i	0.0347168	+	0.0838137i
$639$	−10.8834	+	16.2338i	−0.430540	+	0.642199i
$640$	−1.26665	+	6.36785i	−0.0500685	+	0.251712i
$641$	−1.24255	+	1.85961i	−0.0490777	+	0.0734500i	−0.855197	−	0.518303i	$-0.826564\pi$
$641$	−1.24255	+	1.85961i	−0.0490777	+	0.0734500i	0.806119	+	0.591753i	$0.201564\pi$
$642$	−1.16108	−	5.86080i	−0.0458242	−	0.231307i
$643$	0.714043	+	3.58974i	0.0281591	+	0.141565i	0.992307	−	0.123799i	$-0.0395078\pi$
$643$	0.714043	+	3.58974i	0.0281591	+	0.141565i	−0.964148	+	0.265364i	$0.914508\pi$
$644$	−0.967262	−	0.400653i	−0.0381155	−	0.0157879i
$645$	6.08617	−	9.09338i	0.239643	−	0.358051i
$646$		0			0
$647$			28.3391i			1.11413i	0.830470	+	0.557063i	$0.188072\pi$
$647$			28.3391i			1.11413i	−0.830470	+	0.557063i	$0.811928\pi$
$648$	9.45001	+	23.0152i	0.371231	+	0.904121i
$649$	1.12639	−	0.224054i	0.0442148	−	0.00879488i
$650$	−13.6165	+	13.6165i	−0.534082	+	0.534082i
$651$	−0.0860060	−	0.208091i	−0.00337084	−	0.00815574i
$652$	−20.5203	−	4.08173i	−0.803635	−	0.159853i
$653$	−8.47655	+	5.66385i	−0.331713	+	0.221644i	−0.710262	−	0.703938i	$-0.751423\pi$
$653$	−8.47655	+	5.66385i	−0.331713	+	0.221644i	0.378548	+	0.925581i	$0.376423\pi$
$654$	3.59751	−	18.0132i	0.140674	−	0.704371i
$655$	7.43383	−	3.07919i	0.290464	−	0.120314i
$656$	−1.22611	−	1.83501i	−0.0478716	−	0.0716449i
$657$	−34.1570	+	6.73943i	−1.33259	+	0.262930i
$658$	1.35851	+	0.907729i	0.0529604	+	0.0353870i
$659$	−27.6176	−	27.6176i	−1.07583	−	1.07583i	−0.996879	−	0.0789501i	$-0.974843\pi$
$659$	−27.6176	−	27.6176i	−1.07583	−	1.07583i	−0.0789501	−	0.996879i	$-0.525157\pi$
$660$	−7.49783	−	3.11249i	−0.291852	−	0.121153i
$661$	−0.783917	+	1.89254i	−0.0304909	+	0.0736114i	−0.938392	−	0.345574i	$-0.887684\pi$
$661$	−0.783917	+	1.89254i	−0.0304909	+	0.0736114i	0.907901	+	0.419185i	$0.137684\pi$
$662$	3.52074			0.136838
$663$		0			0
$664$	−7.63870			−0.296439
$665$	−0.0336786	+	0.0813074i	−0.00130600	+	0.00315296i
$666$	4.11239	−	2.73863i	0.159352	−	0.106120i
$667$	−1.80965	−	1.80965i	−0.0700701	−	0.0700701i
$668$	−9.88606	−	6.60565i	−0.382503	−	0.255580i
$669$	−20.4230	+	20.3915i	−0.789600	+	0.788382i
$670$	−2.06234	−	3.08651i	−0.0796751	−	0.119242i
$671$	−43.0448	+	17.8297i	−1.66172	+	0.688309i
$672$	−1.90982	−	0.381420i	−0.0736728	−	0.0147136i
$673$	−14.1389	+	9.44730i	−0.545014	+	0.364167i	−0.797392	−	0.603462i	$-0.793787\pi$
$673$	−14.1389	+	9.44730i	−0.545014	+	0.364167i	0.252378	+	0.967629i	$0.418787\pi$
$674$	−4.75791	−	0.946406i	−0.183268	−	0.0364542i
$675$	−15.8736	−	15.9474i	−0.610977	−	0.613814i
$676$	13.8741	−	13.8741i	0.533621	−	0.533621i
$677$	21.4918	−	4.27498i	0.825995	−	0.164301i	0.236047	−	0.971742i	$-0.424148\pi$
$677$	21.4918	−	4.27498i	0.825995	−	0.164301i	0.589948	+	0.807441i	$0.299148\pi$
$678$	0.996337	+	1.49362i	0.0382641	+	0.0573621i
$679$			0.481963i			0.0184960i
$680$		0			0
$681$	27.7066	+	18.5439i	1.06172	+	0.710603i
$682$	2.27821	+	0.943667i	0.0872373	+	0.0361349i
$683$	7.08334	+	35.6104i	0.271036	+	1.36259i	0.841050	+	0.540957i	$0.181938\pi$
$683$	7.08334	+	35.6104i	0.271036	+	1.36259i	−0.570014	+	0.821635i	$0.693062\pi$
$684$	0.823378	−	1.97916i	0.0314827	−	0.0756750i
$685$	5.75790	−	8.61730i	0.219998	−	0.329250i
$686$	0.445810	−	2.24124i	0.0170211	−	0.0855708i
$687$	19.0191	+	0.0146884i	0.725625	+	0.000560396i
$688$	−0.815481	−	1.96874i	−0.0310899	−	0.0750577i
$689$	23.5168	+	56.7746i	0.895919	+	2.16294i
$690$	−4.91485	−	0.00379571i	−0.187105	−	0.000144500i
$691$	0.560744	−	2.81905i	0.0213317	−	0.107242i	−0.968653	−	0.248419i	$-0.920089\pi$
$691$	0.560744	−	2.81905i	0.0213317	−	0.107242i	0.989984	+	0.141178i	$0.0450889\pi$
$692$	−0.839952	+	1.25708i	−0.0319302	+	0.0477869i
$693$	0.993319	−	2.38765i	0.0377331	−	0.0906991i
$694$	0.00309763	+	0.0155728i	0.000117584	+	0.000591136i
$695$	−9.00150	−	3.72855i	−0.341447	−	0.141432i
$696$	−2.46250	−	1.64814i	−0.0933406	−	0.0624725i
$697$		0			0
$698$		−	5.21082i		−	0.197232i
$699$	−22.5746	−	33.8418i	−0.853848	−	1.28001i
$700$	1.07523	−	0.213876i	0.0406397	−	0.00808375i
$701$	−3.87452	+	3.87452i	−0.146339	+	0.146339i	−0.776480	−	0.630142i	$-0.782997\pi$
$701$	−3.87452	+	3.87452i	−0.146339	+	0.146339i	0.630142	+	0.776480i	$0.282997\pi$
$702$	−16.3012	−	16.3769i	−0.615250	−	0.618107i
$703$	−1.06135	−	0.211116i	−0.0400296	−	0.00796239i
$704$	15.7070	−	10.4951i	0.591981	−	0.395549i
$705$	−13.8757	−	2.77119i	−0.522590	−	0.104369i
$706$	9.43364	−	3.90754i	0.355040	−	0.147062i
$707$	0.736637	+	1.10245i	0.0277041	+	0.0414621i
$708$	−0.413422	+	0.412784i	−0.0155373	+	0.0155134i
$709$	−31.2387	−	20.8730i	−1.17319	−	0.783903i	−0.192856	−	0.981227i	$-0.561775\pi$
$709$	−31.2387	−	20.8730i	−1.17319	−	0.783903i	−0.980338	+	0.197324i	$0.936775\pi$
$710$	−3.16093	−	3.16093i	−0.118628	−	0.118628i
$711$	−26.9905	+	17.9743i	−1.01222	+	0.674087i
$712$	−5.53046	+	13.3517i	−0.207263	+	0.500376i
$713$	−2.75410			−0.103142
$714$		0			0
$715$	19.1665			0.716788
$716$	−5.10610	+	12.3272i	−0.190824	+	0.460690i
$717$	21.9505	+	9.11206i	0.819756	+	0.340296i
$718$	−18.8705	−	18.8705i	−0.704242	−	0.704242i
$719$	20.4411	+	13.6583i	0.762326	+	0.509370i	0.874918	−	0.484271i	$-0.160915\pi$
$719$	20.4411	+	13.6583i	0.762326	+	0.509370i	−0.112592	+	0.993641i	$0.535915\pi$
$720$	0.664873	−	0.131184i	0.0247783	−	0.00488894i
$721$	0.268692	+	0.402127i	0.0100066	+	0.0149760i
$722$	−14.4832	+	5.99913i	−0.539009	+	0.223265i
$723$	1.45055	−	7.26307i	0.0539464	−	0.270117i
$724$	−13.8908	+	9.28153i	−0.516247	+	0.344945i
$725$	2.62834	+	0.522810i	0.0976141	+	0.0194167i
$726$	4.71588	+	11.4101i	0.175023	+	0.423467i
$727$	−26.6720	+	26.6720i	−0.989211	+	0.989211i	−0.999942	−	0.0107310i	$-0.996584\pi$
$727$	−26.6720	+	26.6720i	−0.989211	+	0.989211i	0.0107310	+	0.999942i	$0.496584\pi$
$728$	2.80692	−	0.558331i	0.104031	−	0.0206931i
$729$	19.1801	−	19.0032i	0.710376	−	0.703823i
$730$		−	7.96307i		−	0.294726i
$731$		0			0
$732$	13.1826	−	19.6963i	0.487244	−	0.727995i
$733$	17.5613	+	7.27415i	0.648643	+	0.268677i	0.682651	−	0.730745i	$-0.260827\pi$
$733$	17.5613	+	7.27415i	0.648643	+	0.268677i	−0.0340076	+	0.999422i	$0.510827\pi$
$734$	−5.50041	−	27.6524i	−0.203024	−	1.02067i
$735$	1.91767	+	9.67984i	0.0707343	+	0.357046i
$736$	−13.2344	+	19.8067i	−0.487826	+	0.730083i
$737$	4.66079	−	23.4314i	0.171682	−	0.863106i
$738$	11.1988	−	16.7043i	0.412234	−	0.614893i
$739$	13.8881	+	33.5289i	0.510884	+	1.23338i	0.943370	+	0.331742i	$0.107636\pi$
$739$	13.8881	+	33.5289i	0.510884	+	1.23338i	−0.432487	+	0.901640i	$0.642364\pi$
$740$	−0.797805	−	1.92607i	−0.0293279	−	0.0708038i
$741$	−0.00390851	+	5.06090i	−0.000143583	+	0.185917i
$742$	−0.369974	+	1.85998i	−0.0135822	+	0.0682822i
$743$	0.0990543	−	0.148245i	0.00363395	−	0.00543859i	−0.829648	−	0.558287i	$-0.811459\pi$
$743$	0.0990543	−	0.148245i	0.00363395	−	0.00543859i	0.833282	+	0.552848i	$0.186459\pi$
$744$	−3.12797	+	0.619682i	−0.114677	+	0.0227186i
$745$	−2.02776	−	10.1942i	−0.0742914	−	0.373488i
$746$	−11.8338	−	4.90173i	−0.433267	−	0.179465i
$747$	3.16049	+	7.66355i	0.115636	+	0.280395i
$748$		0			0
$749$		−	0.803058i		−	0.0293431i
$750$	9.22476	−	6.15349i	0.336841	−	0.224694i
$751$	−37.2549	+	7.41046i	−1.35945	+	0.270412i	−0.820365	−	0.571840i	$-0.806230\pi$
$751$	−37.2549	+	7.41046i	−1.35945	+	0.270412i	−0.539085	+	0.842251i	$0.681230\pi$
$752$	−1.94852	+	1.94852i	−0.0710551	+	0.0710551i
$753$	−14.8765	+	6.14860i	−0.542131	+	0.224067i
$754$	2.69914	+	0.536892i	0.0982968	+	0.0195525i
$755$	−0.539298	+	0.360348i	−0.0196271	+	0.0131144i
$756$	0.253651	+	1.29081i	0.00922519	+	0.0469463i
$757$	−17.7157	+	7.33808i	−0.643888	+	0.266707i	−0.680641	−	0.732617i	$-0.738299\pi$
$757$	−17.7157	+	7.33808i	−0.643888	+	0.266707i	0.0367531	+	0.999324i	$0.488299\pi$
$758$	−17.7090	−	26.5034i	−0.643220	−	0.962647i
$759$	−22.3492	−	22.3838i	−0.811226	−	0.812480i
$760$	1.03630	+	0.692431i	0.0375904	+	0.0251171i
$761$	−21.9157	−	21.9157i	−0.794443	−	0.794443i	0.187770	−	0.982213i	$-0.439874\pi$
$761$	−21.9157	−	21.9157i	−0.794443	−	0.794443i	−0.982213	+	0.187770i	$0.939874\pi$
$762$	−4.92983	+	11.8757i	−0.178589	+	0.430211i
$763$	0.944829	−	2.28102i	0.0342051	−	0.0825785i
$764$	21.5800			0.780737
$765$		0			0
$766$	−28.8846			−1.04364
$767$	0.527834	−	1.27430i	0.0190590	−	0.0460124i
$768$	−10.0989	+	24.3278i	−0.364413	+	0.877853i
$769$	13.1164	+	13.1164i	0.472990	+	0.472990i	0.902881	−	0.429891i	$-0.141448\pi$
$769$	13.1164	+	13.1164i	0.472990	+	0.472990i	−0.429891	+	0.902881i	$0.641448\pi$
$770$	0.491798	+	0.328609i	0.0177232	+	0.0118422i
$771$	−19.2488	−	19.2786i	−0.693229	−	0.694300i
$772$	2.14380	+	3.20843i	0.0771572	+	0.115474i
$773$	37.8763	−	15.6889i	1.36232	−	0.564289i	0.422621	−	0.906306i	$-0.361110\pi$
$773$	37.8763	−	15.6889i	1.36232	−	0.564289i	0.939694	+	0.342017i	$0.111110\pi$
$774$	13.7521	−	13.7097i	0.494308	−	0.492784i
$775$	2.39786	−	1.60220i	0.0861336	−	0.0575526i
$776$	6.69439	+	1.33160i	0.240314	+	0.0478015i
$777$	0.613741	−	0.253665i	0.0220178	−	0.00910017i
$778$	0.447469	−	0.447469i	0.0160425	−	0.0160425i
$779$	−4.32005	+	0.859312i	−0.154782	+	0.0307880i
$780$	−8.11093	+	5.41049i	−0.290418	+	0.193727i
$781$		−	28.7696i		−	1.02946i
$782$		0			0
$783$	−0.634651	+	3.15242i	−0.0226806	+	0.112658i
$784$	1.77547	+	0.735425i	0.0634097	+	0.0262652i
$785$	0.376531	+	1.89295i	0.0134390	+	0.0675623i
$786$	14.0071	−	2.77494i	0.499616	−	0.0989788i
$787$	−8.35391	+	12.5025i	−0.297785	+	0.445667i	−0.949946	−	0.312414i	$-0.898862\pi$
$787$	−8.35391	+	12.5025i	−0.297785	+	0.445667i	0.652161	+	0.758080i	$0.273862\pi$
$788$	3.43335	−	17.2606i	0.122308	−	0.614884i
$789$	0.0206557	−	26.7460i	0.000735364	−	0.952181i
$790$	−2.83834	−	6.85236i	−0.100984	−	0.243796i
$791$	0.0923506	+	0.222954i	0.00328361	+	0.00792734i
$792$	−30.4196	−	20.3938i	−1.08091	−	0.724660i
$793$	−10.9165	+	54.8808i	−0.387655	+	1.94887i
$794$	9.38503	−	14.0457i	0.333062	−	0.498463i
$795$	−3.19163	−	16.1104i	−0.113195	−	0.571378i
$796$	−1.08846	−	5.47204i	−0.0385793	−	0.193951i
$797$	−14.9967	−	6.21185i	−0.531211	−	0.220035i	0.100922	−	0.994894i	$-0.467821\pi$
$797$	−14.9967	−	6.21185i	−0.531211	−	0.220035i	−0.632134	+	0.774859i	$0.717821\pi$
$798$	−0.0868691	+	0.129792i	−0.00307513	+	0.00459458i
$799$		0			0
$800$		−	24.9438i		−	0.881895i
$801$	15.6833	+	0.0242243i	0.554144	+	0.000855925i
$802$	−12.9675	+	2.57939i	−0.457898	+	0.0910815i
$803$	36.2384	−	36.2384i	1.27882	−	1.27882i
$804$	4.64205	+	11.2314i	0.163712	+	0.396102i
$805$	−0.647910	−	0.128877i	−0.0228358	−	0.00454233i
$806$	2.46245	−	1.64535i	0.0867360	−	0.0579551i
$807$	−8.25597	+	41.3387i	−0.290624	+	1.45519i
$808$	17.3481	−	7.18583i	0.610305	−	0.252797i
$809$	−21.0138	−	31.4493i	−0.738804	−	1.10570i	−0.990449	−	0.137879i	$-0.955972\pi$
$809$	−21.0138	−	31.4493i	−0.738804	−	1.10570i	0.251645	−	0.967820i	$-0.419028\pi$
$810$	3.41504	+	5.14530i	0.119992	+	0.180787i
$811$	28.7574	+	19.2151i	1.00981	+	0.674733i	0.946314	−	0.323249i	$-0.104775\pi$
$811$	28.7574	+	19.2151i	1.00981	+	0.674733i	0.0634956	+	0.997982i	$0.479775\pi$
$812$	−0.110785	−	0.110785i	−0.00388780	−	0.00388780i
$813$	−8.99873	−	3.73554i	−0.315599	−	0.131011i
$814$	−2.78324	+	6.71933i	−0.0975525	+	0.235513i
$815$	−13.2014			−0.462426
$816$		0			0
$817$	−4.25303			−0.148795
$818$	−9.09843	+	21.9656i	−0.318119	+	0.768007i
$819$	−1.72150	−	2.58504i	−0.0601541	−	0.0903288i
$820$	−6.00029	−	6.00029i	−0.209539	−	0.209539i
$821$	−41.8677	−	27.9751i	−1.46119	−	0.976339i	−0.995831	−	0.0912190i	$-0.970924\pi$
$821$	−41.8677	−	27.9751i	−1.46119	−	0.976339i	−0.465363	−	0.885120i	$-0.654076\pi$
$822$	13.0153	−	12.9952i	0.453962	−	0.453261i
$823$	−13.2713	−	19.8619i	−0.462609	−	0.692343i	0.524676	−	0.851302i	$-0.324186\pi$
$823$	−13.2713	−	19.8619i	−0.462609	−	0.692343i	−0.987285	+	0.158959i	$0.949186\pi$
$824$	6.32783	−	2.62107i	0.220440	−	0.0913094i
$825$	32.4801	+	6.48677i	1.13081	+	0.225841i
$826$	0.0353916	−	0.0236479i	0.00123143	−	0.000822817i
$827$	6.58698	+	1.31023i	0.229052	+	0.0455612i	0.308282	−	0.951295i	$-0.400246\pi$
$827$	6.58698	+	1.31023i	0.229052	+	0.0455612i	−0.0792299	+	0.996856i	$0.525246\pi$
$828$	15.7765	+	3.16348i	0.548270	+	0.109938i
$829$	−17.6880	+	17.6880i	−0.614331	+	0.614331i	−0.944072	−	0.329741i	$-0.893039\pi$
$829$	−17.6880	+	17.6880i	−0.614331	+	0.614331i	0.329741	+	0.944072i	$0.393039\pi$
$830$	−1.85960	+	0.369897i	−0.0645475	+	0.0128393i
$831$	−8.52008	−	12.7725i	−0.295558	−	0.443074i
$832$		−	22.6876i		−	0.786552i
$833$		0			0
$834$	−14.3692	−	9.61724i	−0.497564	−	0.333018i
$835$	−6.93113	−	2.87097i	−0.239862	−	0.0993539i
$836$	0.615587	+	3.09477i	0.0212905	+	0.107035i
$837$	1.91589	+	2.88176i	0.0662227	+	0.0996082i
$838$	16.4119	−	24.5622i	0.566940	−	0.848485i
$839$	8.59130	−	43.1914i	0.296604	−	1.49113i	−0.488935	−	0.872320i	$-0.662615\pi$
$839$	8.59130	−	43.1914i	0.296604	−	1.49113i	0.785540	−	0.618811i	$-0.212385\pi$
$840$	−0.764862		0.000590699i	−0.0263903		2.03810e-5i
$841$	10.9513	+	26.4387i	0.377630	+	0.911679i
$842$	−0.00405180	−	0.00978190i	−0.000139634	−	0.000337107i
$843$	12.5024	+	0.00965556i	0.430607	+	0.000332555i
$844$	3.92880	−	19.7514i	0.135235	−	0.679871i
$845$	6.87815	−	10.2939i	0.236616	−	0.354120i
$846$	−23.1844	−	9.64526i	−0.797095	−	0.331611i
$847$	0.323743	+	1.62756i	0.0111239	+	0.0559238i
$848$	−2.95497	−	1.22399i	−0.101474	−	0.0420319i
$849$	7.11313	+	4.76079i	0.244122	+	0.163390i
$850$		0			0
$851$		−	8.12291i		−	0.278450i
$852$	8.12132	+	12.1748i	0.278232	+	0.417100i
$853$	31.7413	−	6.31373i	1.08680	−	0.216178i	0.380990	−	0.924579i	$-0.375583\pi$
$853$	31.7413	−	6.31373i	1.08680	−	0.216178i	0.705810	+	0.708401i	$0.250583\pi$
$854$	−1.22103	+	1.22103i	−0.0417829	+	0.0417829i
$855$	0.265919	−	1.32616i	0.00909425	−	0.0453537i
$856$	−11.1543	−	2.21874i	−0.381248	−	0.0758349i
$857$	20.6196	−	13.7775i	0.704351	−	0.470632i	−0.151099	−	0.988519i	$-0.548281\pi$
$857$	20.6196	−	13.7775i	0.704351	−	0.470632i	0.855449	+	0.517887i	$0.173281\pi$
$858$	33.3550	+	6.66150i	1.13872	+	0.227420i
$859$	38.7830	−	16.0644i	1.32326	−	0.548112i	0.394534	−	0.918881i	$-0.370906\pi$
$859$	38.7830	−	16.0644i	1.32326	−	0.548112i	0.928725	+	0.370770i	$0.120906\pi$
$860$	−4.55207	−	6.81266i	−0.155224	−	0.232310i
$861$	1.91285	−	1.90990i	0.0651898	−	0.0650892i
$862$	8.26630	+	5.52336i	0.281551	+	0.188127i
$863$	−0.148288	−	0.148288i	−0.00504779	−	0.00504779i	0.704578	−	0.709626i	$-0.251136\pi$
$863$	−0.148288	−	0.148288i	−0.00504779	−	0.00504779i	−0.709626	+	0.704578i	$0.751136\pi$
$864$	29.9312	+	0.0693472i	1.01828	+	0.00235924i
$865$	−0.365062	+	0.881339i	−0.0124125	+	0.0299664i
$866$	0.455061			0.0154636
$867$		0			0
$868$	−0.168603			−0.00572278
$869$	18.2670	−	44.1005i	0.619666	−	1.49601i
$870$	−0.679289	−	0.281986i	−0.0230301	−	0.00956021i
$871$	−20.2885	−	20.2885i	−0.687450	−	0.687450i
$872$	−29.0725	−	19.4257i	−0.984521	−	0.657836i
$873$	−1.43385	−	7.26711i	−0.0485286	−	0.245954i
$874$	1.06131	+	1.58837i	0.0358995	+	0.0537274i
$875$	1.37699	−	0.570368i	0.0465507	−	0.0192820i
$876$	−5.10574	+	25.5651i	−0.172507	+	0.863764i
$877$	6.14858	−	4.10835i	0.207623	−	0.138729i	−0.447412	−	0.894328i	$-0.647654\pi$
$877$	6.14858	−	4.10835i	0.207623	−	0.138729i	0.655034	+	0.755599i	$0.272654\pi$
$878$	−25.0417	−	4.98111i	−0.845118	−	0.168104i
$879$	−12.6388	−	30.5796i	−0.426296	−	1.03142i
$880$	−0.705386	+	0.705386i	−0.0237786	+	0.0237786i
$881$	−48.8312	+	9.71313i	−1.64516	+	0.327244i	−0.928828	−	0.370511i	$-0.879183\pi$
$881$	−48.8312	+	9.71313i	−1.64516	+	0.327244i	−0.716337	+	0.697755i	$0.754183\pi$
$882$	−0.0270489	+	17.5121i	−0.000910785	+	0.589662i
$883$			28.6327i			0.963566i	0.876291	+	0.481783i	$0.160011\pi$
$883$			28.6327i			0.963566i	−0.876291	+	0.481783i	$0.839989\pi$
$884$		0			0
$885$	−0.205034	+	0.306342i	−0.00689214	+	0.0102976i
$886$	31.1758	+	12.9134i	1.04737	+	0.433835i
$887$	8.34375	+	41.9468i	0.280156	+	1.40844i	0.822731	+	0.568430i	$0.192449\pi$
$887$	8.34375	+	41.9468i	0.280156	+	1.40844i	−0.542576	+	0.840007i	$0.682551\pi$
$888$	−1.82768	−	9.22560i	−0.0613329	−	0.309591i
$889$	−0.960180	+	1.43701i	−0.0322034	+	0.0481958i
$890$	−0.699813	+	3.51820i	−0.0234578	+	0.117930i
$891$	−7.87409	+	38.9564i	−0.263792	+	1.30509i
$892$	8.27003	+	19.9656i	0.276901	+	0.668498i
$893$	2.10466	+	5.08111i	0.0704299	+	0.170033i
$894$	0.0142454	−	18.4455i	0.000476437	−	0.616911i
$895$	−1.64247	+	8.25725i	−0.0549017	+	0.276010i
$896$	−0.860397	+	1.28768i	−0.0287439	+	0.0430182i
$897$	−37.2645	+	7.38245i	−1.24422	+	0.246493i
$898$	5.96018	+	29.9639i	0.198894	+	0.999907i
$899$	−0.380771	−	0.157720i	−0.0126994	−	0.00526027i
$900$	−15.5761	+	6.42368i	−0.519204	+	0.214123i
$901$		0			0
$902$			29.6033i			0.985683i
$903$	2.17127	−	1.44837i	0.0722554	−	0.0481989i
$904$	3.35195	−	0.666743i	0.111484	−	0.0221756i
$905$	−7.45379	+	7.45379i	−0.247772	+	0.247772i
$906$	−1.06377	+	0.439665i	−0.0353413	+	0.0146069i
$907$	−7.97928	−	1.58718i	−0.264948	−	0.0527013i	0.0608288	−	0.998148i	$-0.480626\pi$
$907$	−7.97928	−	1.58718i	−0.264948	−	0.0527013i	−0.325776	+	0.945447i	$0.605626\pi$
$908$	20.7574	−	13.8697i	0.688860	−	0.460281i
$909$	−14.3869	−	14.4315i	−0.477185	−	0.478661i
$910$	0.656291	−	0.271845i	0.0217558	−	0.00901157i
$911$	−1.64721	−	2.46522i	−0.0545745	−	0.0816765i	0.803179	−	0.595738i	$-0.203140\pi$
$911$	−1.64721	−	2.46522i	−0.0545745	−	0.0816765i	−0.857753	+	0.514061i	$0.828140\pi$
$912$	−0.186113	−	0.186400i	−0.00616280	−	0.00617233i
$913$	−10.1460	−	6.77933i	−0.335783	−	0.224363i
$914$	−12.6372	−	12.6372i	−0.418002	−	0.418002i
$915$	5.73353	−	13.8118i	0.189545	−	0.456604i
$916$	5.45001	−	13.1575i	0.180073	−	0.434736i
$917$	1.91928			0.0633802
$918$		0			0
$919$	36.7672			1.21284			0.606418	−	0.795146i	$-0.292606\pi$
$919$	36.7672			1.21284			0.606418	+	0.795146i	$0.292606\pi$
$920$	−3.58017	+	8.64329i	−0.118035	+	0.284961i
$921$	3.31242	−	7.97945i	0.109148	−	0.262932i
$922$	−3.64477	−	3.64477i	−0.120034	−	0.120034i
$923$	−28.7290	−	19.1961i	−0.945627	−	0.631848i
$924$	−1.36820	−	1.37031i	−0.0450104	−	0.0450800i
$925$	4.72550	+	7.07221i	0.155373	+	0.232533i
$926$	−28.1151	+	11.6457i	−0.923919	+	0.382700i
$927$	−5.24772	−	5.26396i	−0.172358	−	0.172891i
$928$	−2.96401	+	1.98049i	−0.0972984	+	0.0650127i
$929$	−27.6098	−	5.49193i	−0.905849	−	0.180184i	−0.279882	−	0.960034i	$-0.590295\pi$
$929$	−27.6098	−	5.49193i	−0.905849	−	0.180184i	−0.625967	+	0.779850i	$0.715295\pi$
$930$	−0.731479	+	0.302327i	−0.0239861	+	0.00991369i
$931$	2.71211	−	2.71211i	0.0888859	−	0.0888859i
$932$	−29.8761	+	5.94272i	−0.978624	+	0.194660i
$933$	−15.0806	+	10.0597i	−0.493718	+	0.329340i
$934$		−	6.44805i		−	0.210987i
$935$		0			0
$936$	−40.6621	+	16.7693i	−1.32908	+	0.548120i
$937$	−34.4010	−	14.2493i	−1.12383	−	0.465506i	−0.258151	−	0.966105i	$-0.583113\pi$
$937$	−34.4010	−	14.2493i	−1.12383	−	0.465506i	−0.865679	+	0.500599i	$0.833113\pi$
$938$	−0.172742	−	0.868432i	−0.00564022	−	0.0283553i
$939$	−40.8017	+	8.08320i	−1.33151	+	0.263785i
$940$	−5.88646	+	8.80971i	−0.191995	+	0.287341i
$941$	−8.87241	+	44.6046i	−0.289232	+	1.45407i	0.513686	+	0.857979i	$0.328280\pi$
$941$	−8.87241	+	44.6046i	−0.289232	+	1.45407i	−0.802918	+	0.596090i	$0.796720\pi$
$942$	−0.00264520	+	3.42512i	−8.61852e−5	+	0.111596i
$943$	−12.6526	−	30.5462i	−0.412026	−	0.994720i
$944$	0.0274723	+	0.0663241i	0.000894148	+	0.00215867i
$945$	0.315867	+	0.767595i	0.0102751	+	0.0249699i
$946$	−5.57647	+	28.0348i	−0.181307	+	0.911490i
$947$	−9.13749	+	13.6752i	−0.296929	+	0.444385i	−0.949696	−	0.313173i	$-0.898608\pi$
$947$	−9.13749	+	13.6752i	−0.296929	+	0.444385i	0.652767	+	0.757558i	$0.273608\pi$
$948$	4.71879	+	23.8191i	0.153259	+	0.773608i
$949$	−12.0077	−	60.3669i	−0.389787	−	1.95959i
$950$	−1.84807	−	0.765494i	−0.0599592	−	0.0248359i
$951$	9.47587	−	14.1580i	0.307276	−	0.459103i
$952$		0			0
$953$		−	15.3092i		−	0.495915i	−0.968771	−	0.247958i	$-0.920241\pi$
$953$		−	15.3092i		−	0.495915i	0.968771	−	0.247958i	$-0.0797593\pi$
$954$	0.0450183	−	29.1458i	0.00145752	−	0.943630i
$955$	13.3548	−	2.65643i	0.432151	−	0.0859602i
$956$	12.5840	−	12.5840i	0.406997	−	0.406997i
$957$	−1.80805	−	4.37457i	−0.0584460	−	0.141410i
$958$	1.88812	+	0.375571i	0.0610025	+	0.0121342i
$959$	2.05547	−	1.37342i	0.0663747	−	0.0443502i
$960$	−1.18750	+	5.94598i	−0.0383265	+	0.191906i
$961$	28.2305	−	11.6935i	0.910661	−	0.377208i
$962$	4.85278	+	7.26270i	0.156460	+	0.234159i
$963$	2.38912	+	12.1086i	0.0769883	+	0.390195i
$964$	−4.61133	−	3.08119i	−0.148521	−	0.0992386i
$965$	1.72164	+	1.72164i	0.0554216	+	0.0554216i
$966$	−1.08275	−	0.449469i	−0.0348368	−	0.0144614i
$967$	18.4809	−	44.6169i	0.594306	−	1.43478i	−0.285001	−	0.958527i	$-0.591994\pi$
$967$	18.4809	−	44.6169i	0.594306	−	1.43478i	0.879307	−	0.476255i	$-0.158006\pi$
$968$	23.5010			0.755352
$969$		0			0
$970$	1.69419			0.0543972
$971$	−1.27013	+	3.06636i	−0.0407603	+	0.0984041i	−0.942949	−	0.332938i	$-0.891960\pi$
$971$	−1.27013	+	3.06636i	−0.0407603	+	0.0984041i	0.902188	+	0.431342i	$0.141960\pi$
$972$	−7.66478	−	18.7084i	−0.245848	−	0.600073i
$973$	−1.64333	−	1.64333i	−0.0526828	−	0.0526828i
$974$	19.5742	+	13.0790i	0.627197	+	0.419080i
$975$	28.1496	−	28.1061i	0.901507	−	0.900116i
$976$	−1.61802	−	2.42154i	−0.0517915	−	0.0775115i
$977$	27.3947	−	11.3473i	0.876434	−	0.363031i	0.101321	−	0.994854i	$-0.467693\pi$
$977$	27.3947	−	11.3473i	0.876434	−	0.363031i	0.775113	+	0.631823i	$0.217693\pi$
$978$	−22.9741	−	4.58828i	−0.734630	−	0.146717i
$979$	−19.1953	+	12.8259i	−0.613486	+	0.409918i
$980$	7.24717	+	1.44155i	0.231502	+	0.0460487i
$981$	−7.46018	+	37.2044i	−0.238185	+	1.18785i
$982$	8.01800	−	8.01800i	0.255865	−	0.255865i
$983$	2.45256	−	0.487844i	0.0782245	−	0.0155598i	−0.155823	−	0.987785i	$-0.549803\pi$
$983$	2.45256	−	0.487844i	0.0782245	−	0.0155598i	0.234047	+	0.972225i	$0.424803\pi$
$984$	−21.2432	−	31.8459i	−0.677209	−	1.01521i
$985$		−	11.1044i		−	0.353815i
$986$		0			0
$987$	−2.80486	−	1.87728i	−0.0892797	−	0.0597545i
$988$	3.50115	+	1.45022i	0.111386	+	0.0461377i
$989$	−6.22816	−	31.3111i	−0.198044	−	0.995635i
$990$	−8.39302	−	3.49170i	−0.266748	−	0.110973i
$991$	21.1992	−	31.7268i	0.673414	−	1.00784i	−0.324662	−	0.945830i	$-0.605251\pi$
$991$	21.1992	−	31.7268i	0.673414	−	1.00784i	0.998076	−	0.0620049i	$-0.0197495\pi$
$992$	−0.748407	+	3.76250i	−0.0237620	+	0.119459i
$993$	−7.27287	−	0.00561679i	−0.230798	−	0.000178244i
$994$	−0.408047	−	0.985113i	−0.0129425	−	0.0312459i
$995$	−1.34718	−	3.25239i	−0.0427086	−	0.103108i
$996$	6.20732	+	0.00479388i	0.196687	+	0.000151900i
$997$	8.71954	−	43.8361i	0.276151	−	1.38830i	−0.554813	−	0.831975i	$-0.687210\pi$
$997$	8.71954	−	43.8361i	0.276151	−	1.38830i	0.830963	−	0.556327i	$-0.187790\pi$
$998$	7.09608	−	10.6200i	0.224622	−	0.336171i
$999$	−8.49942	+	5.65069i	−0.268910	+	0.178780i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	867.2.i.f.329.3		32
3.2	odd	2	inner	867.2.i.f.329.2		32
17.2	even	8		867.2.i.d.653.3		32
17.3	odd	16	inner	867.2.i.f.224.2		32
17.4	even	4		867.2.i.i.827.2		32
17.5	odd	16		867.2.i.i.65.3		32
17.6	odd	16		867.2.i.h.131.3		32
17.7	odd	16		867.2.i.c.158.2		32
17.8	even	8		51.2.i.a.44.2	yes	32
17.9	even	8		867.2.i.h.503.2		32
17.10	odd	16		867.2.i.d.158.2		32
17.11	odd	16		51.2.i.a.29.3	yes	32
17.12	odd	16		867.2.i.b.65.3		32
17.13	even	4		867.2.i.b.827.2		32
17.14	odd	16		867.2.i.g.224.2		32
17.15	even	8		867.2.i.c.653.3		32
17.16	even	2		867.2.i.g.329.3		32
51.2	odd	8		867.2.i.d.653.2		32
51.5	even	16		867.2.i.i.65.2		32
51.8	odd	8		51.2.i.a.44.3	yes	32
51.11	even	16		51.2.i.a.29.2	✓	32
51.14	even	16		867.2.i.g.224.3		32
51.20	even	16	inner	867.2.i.f.224.3		32
51.23	even	16		867.2.i.h.131.2		32
51.26	odd	8		867.2.i.h.503.3		32
51.29	even	16		867.2.i.b.65.2		32
51.32	odd	8		867.2.i.c.653.2		32
51.38	odd	4		867.2.i.i.827.3		32
51.41	even	16		867.2.i.c.158.3		32
51.44	even	16		867.2.i.d.158.3		32
51.47	odd	4		867.2.i.b.827.3		32
51.50	odd	2		867.2.i.g.329.2		32
68.11	even	16		816.2.cj.c.641.2		32
68.59	odd	8		816.2.cj.c.401.1		32
204.11	odd	16		816.2.cj.c.641.1		32
204.59	even	8		816.2.cj.c.401.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.2.i.a.29.2	✓	32	51.11	even	16
51.2.i.a.29.3	yes	32	17.11	odd	16
51.2.i.a.44.2	yes	32	17.8	even	8
51.2.i.a.44.3	yes	32	51.8	odd	8
816.2.cj.c.401.1		32	68.59	odd	8
816.2.cj.c.401.2		32	204.59	even	8
816.2.cj.c.641.1		32	204.11	odd	16
816.2.cj.c.641.2		32	68.11	even	16
867.2.i.b.65.2		32	51.29	even	16
867.2.i.b.65.3		32	17.12	odd	16
867.2.i.b.827.2		32	17.13	even	4
867.2.i.b.827.3		32	51.47	odd	4
867.2.i.c.158.2		32	17.7	odd	16
867.2.i.c.158.3		32	51.41	even	16
867.2.i.c.653.2		32	51.32	odd	8
867.2.i.c.653.3		32	17.15	even	8
867.2.i.d.158.2		32	17.10	odd	16
867.2.i.d.158.3		32	51.44	even	16
867.2.i.d.653.2		32	51.2	odd	8
867.2.i.d.653.3		32	17.2	even	8
867.2.i.f.224.2		32	17.3	odd	16	inner
867.2.i.f.224.3		32	51.20	even	16	inner
867.2.i.f.329.2		32	3.2	odd	2	inner
867.2.i.f.329.3		32	1.1	even	1	trivial
867.2.i.g.224.2		32	17.14	odd	16
867.2.i.g.224.3		32	51.14	even	16
867.2.i.g.329.2		32	51.50	odd	2
867.2.i.g.329.3		32	17.16	even	2
867.2.i.h.131.2		32	51.23	even	16
867.2.i.h.131.3		32	17.6	odd	16
867.2.i.h.503.2		32	17.9	even	8
867.2.i.h.503.3		32	51.26	odd	8
867.2.i.i.65.2		32	51.5	even	16
867.2.i.i.65.3		32	17.5	odd	16
867.2.i.i.827.2		32	17.4	even	4
867.2.i.i.827.3		32	51.38	odd	4

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:	\( N \)	\(=\)	\( 867 = 3 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	867.i (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.320870 - 0.774648i) q^{2} +(-0.664063 + 1.59969i) q^{3} +(0.917091 + 0.917091i) q^{4} +(0.680434 + 0.454651i) q^{5} +(1.02612 + 1.02771i) q^{6} +(0.108447 + 0.162303i) q^{7} +(2.55399 - 1.05790i) q^{8} +(-2.11804 - 2.12459i) q^{9} +(0.570525 - 0.381213i) q^{10} +(4.33117 + 0.861524i) q^{11} +(-2.07607 + 0.858059i) q^{12} +(3.75023 - 3.75023i) q^{13} +(0.160525 - 0.0319304i) q^{14} +(-1.17915 + 0.786569i) q^{15} +0.276039i q^{16} +(-2.32543 + 0.959018i) q^{18} +(0.508991 + 0.210831i) q^{19} +(0.207063 + 1.04098i) q^{20} +(-0.331651 + 0.0657033i) q^{21} +(2.05712 - 3.07870i) q^{22} +(-0.806783 + 4.05597i) q^{23} +(-0.00369783 + 4.78810i) q^{24} +(-1.65713 - 4.00068i) q^{25} +(-1.70177 - 4.10844i) q^{26} +(4.80521 - 1.97735i) q^{27} +(-0.0493905 + 0.248303i) q^{28} +(-0.343818 + 0.514560i) q^{29} +(0.230959 + 1.16581i) q^{30} +(0.129926 + 0.653180i) q^{31} +(5.32181 + 2.20436i) q^{32} +(-4.25434 + 6.35644i) q^{33} +0.159742i q^{35} +(0.00600982 - 3.89088i) q^{36} +(-1.92648 + 0.383200i) q^{37} +(0.326640 - 0.326640i) q^{38} +(3.50883 + 8.48960i) q^{39} +(2.21879 + 0.441345i) q^{40} +(-6.64762 + 4.44180i) q^{41} +(-0.0555199 + 0.277995i) q^{42} +(-7.13212 + 2.95422i) q^{43} +(3.18198 + 4.76218i) q^{44} +(-0.475237 - 2.40862i) q^{45} +(2.88308 + 1.92641i) q^{46} +(7.05884 + 7.05884i) q^{47} +(-0.441578 - 0.183307i) q^{48} +(2.66420 - 6.43195i) q^{49} -3.63084 q^{50} +6.87860 q^{52} +(-4.43410 + 10.7049i) q^{53} +(0.0100943 - 4.35682i) q^{54} +(2.55538 + 2.55538i) q^{55} +(0.448673 + 0.299794i) q^{56} +(-0.675267 + 0.674225i) q^{57} +(0.288282 + 0.431445i) q^{58} +(0.240270 - 0.0995233i) q^{59} +(-1.80275 - 0.360036i) q^{60} +(-8.77243 + 5.86155i) q^{61} +(0.547674 + 0.108939i) q^{62} +(0.115132 - 0.574171i) q^{63} +(3.02483 - 3.02483i) q^{64} +(4.25683 - 0.846735i) q^{65} +(3.55892 + 5.33521i) q^{66} -5.40994i q^{67} +(-5.95256 - 3.98403i) q^{69} +(0.123744 + 0.0512564i) q^{70} +(-1.27098 - 6.38963i) q^{71} +(-7.65705 - 3.18552i) q^{72} +(6.44749 - 9.64936i) q^{73} +(-0.321303 + 1.61530i) q^{74} +(7.50030 + 0.00579244i) q^{75} +(0.273440 + 0.660143i) q^{76} +(0.329876 + 0.796392i) q^{77} +(7.70233 + 0.00594847i) q^{78} +(2.10878 - 10.6016i) q^{79} +(-0.125502 + 0.187826i) q^{80} +(-0.0278025 + 8.99996i) q^{81} +(1.30781 + 6.57481i) q^{82} +(-2.55289 - 1.05744i) q^{83} +(-0.364410 - 0.243898i) q^{84} +6.47280i q^{86} +(-0.594822 - 0.891703i) q^{87} +(11.9732 - 2.38161i) q^{88} +(-3.69661 + 3.69661i) q^{89} +(-2.01832 - 0.404710i) q^{90} +(1.01538 + 0.201971i) q^{91} +(-4.45959 + 2.97980i) q^{92} +(-1.13117 - 0.225911i) q^{93} +(7.73308 - 3.20315i) q^{94} +(0.250480 + 0.374870i) q^{95} +(-7.06032 + 7.04942i) q^{96} +(2.05296 + 1.37174i) q^{97} +(-4.12764 - 4.12764i) q^{98} +(-7.34321 - 11.0267i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{4} - 8 q^{6} + 24 q^{9} - 16 q^{10} - 16 q^{12} + 16 q^{13} + 16 q^{15} + 16 q^{18} + 32 q^{19} - 16 q^{21} + 16 q^{22} + 24 q^{24} + 24 q^{27} + 8 q^{30} + 32 q^{31} - 24 q^{36} + 16 q^{37}+ \cdots - 96 q^{99}+O(q^{100}) \) 32 * q + 16 * q^4 - 8 * q^6 + 24 * q^9 - 16 * q^10 - 16 * q^12 + 16 * q^13 + 16 * q^15 + 16 * q^18 + 32 * q^19 - 16 * q^21 + 16 * q^22 + 24 * q^24 + 24 * q^27 + 8 * q^30 + 32 * q^31 - 24 * q^36 + 16 * q^37 - 64 * q^39 + 16 * q^40 - 24 * q^42 - 32 * q^43 + 40 * q^45 - 40 * q^48 - 64 * q^49 - 96 * q^52 - 88 * q^54 + 48 * q^55 - 24 * q^57 - 64 * q^58 + 48 * q^60 - 32 * q^61 - 80 * q^63 - 16 * q^64 + 120 * q^66 + 80 * q^69 - 64 * q^72 + 48 * q^73 + 16 * q^75 + 32 * q^76 + 88 * q^78 - 32 * q^79 - 48 * q^81 + 96 * q^82 - 56 * q^87 + 128 * q^88 + 8 * q^90 + 64 * q^91 - 56 * q^93 - 48 * q^94 + 16 * q^96 + 128 * q^97 - 96 * q^99

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