LMFDB - Embedded newform 867.2.i.b.65.3

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,-8,16,0,16,0,0,-24,-32] 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			65.3
Character	$\chi$	$=$	867.65
Dual form			867.2.i.b.827.3

$q$-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} +(1.22380 + 1.22569i) q^{3} +(0.917091 - 0.917091i) q^{4} +(0.454651 + 0.680434i) q^{5} +(-0.556799 + 1.34130i) q^{6} +(0.162303 + 0.108447i) q^{7} +(2.55399 + 1.05790i) q^{8} +(-0.00463376 + 3.00000i) q^{9} +(-0.381213 + 0.570525i) q^{10} +(-0.861524 - 4.33117i) q^{11} +(2.24641 + 0.00173489i) q^{12} +(3.75023 + 3.75023i) q^{13} +(-0.0319304 + 0.160525i) q^{14} +(-0.277599 + 1.38998i) q^{15} -0.276039i q^{16} +(-2.32543 + 0.959018i) q^{18} +(-0.508991 + 0.210831i) q^{19} +(1.04098 + 0.207063i) q^{20} +(0.0657033 + 0.331651i) q^{21} +(3.07870 - 2.05712i) q^{22} +(-4.05597 + 0.806783i) q^{23} +(1.82891 + 4.42505i) q^{24} +(1.65713 - 4.00068i) q^{25} +(-1.70177 + 4.10844i) q^{26} +(-3.68274 + 3.66571i) q^{27} +(0.248303 - 0.0493905i) q^{28} +(0.514560 - 0.343818i) q^{29} +(-1.16581 + 0.230959i) q^{30} +(-0.653180 - 0.129926i) q^{31} +(5.32181 - 2.20436i) q^{32} +(4.25434 - 6.35644i) q^{33} +0.159742i q^{35} +(2.74702 + 2.75552i) q^{36} +(-0.383200 + 1.92648i) q^{37} +(-0.326640 - 0.326640i) q^{38} +(-0.00709440 + 9.18614i) q^{39} +(0.441345 + 2.21879i) q^{40} +(-4.44180 + 6.64762i) q^{41} +(-0.235831 + 0.157314i) q^{42} +(7.13212 + 2.95422i) q^{43} +(-4.76218 - 3.18198i) q^{44} +(-2.04341 + 1.36080i) q^{45} +(-1.92641 - 2.88308i) q^{46} +(-7.05884 + 7.05884i) q^{47} +(0.338339 - 0.337817i) q^{48} +(-2.66420 - 6.43195i) q^{49} +3.63084 q^{50} +6.87860 q^{52} +(-4.43410 - 10.7049i) q^{53} +(-4.02132 - 1.67661i) q^{54} +(2.55538 - 2.55538i) q^{55} +(0.299794 + 0.448673i) q^{56} +(-0.881316 - 0.365851i) q^{57} +(0.431445 + 0.288282i) q^{58} +(0.240270 + 0.0995233i) q^{59} +(1.02015 + 1.52932i) q^{60} +(5.86155 - 8.77243i) q^{61} +(-0.108939 - 0.547674i) q^{62} +(-0.326094 + 0.486406i) q^{63} +(3.02483 + 3.02483i) q^{64} +(-0.846735 + 4.25683i) q^{65} +(6.28910 + 1.25603i) q^{66} +5.40994i q^{67} +(-5.95256 - 3.98403i) q^{69} +(-0.123744 + 0.0512564i) q^{70} +(-6.38963 - 1.27098i) q^{71} +(-3.18552 + 7.65705i) q^{72} +(9.64936 - 6.44749i) q^{73} +(-1.61530 + 0.321303i) q^{74} +(6.93159 - 2.86489i) q^{75} +(-0.273440 + 0.660143i) q^{76} +(0.329876 - 0.796392i) q^{77} +(-7.11830 + 2.94206i) q^{78} +(-10.6016 + 2.10878i) q^{79} +(0.187826 - 0.125502i) q^{80} +(-8.99996 - 0.0278025i) q^{81} +(-6.57481 - 1.30781i) q^{82} +(-2.55289 + 1.05744i) q^{83} +(0.364410 + 0.243898i) q^{84} +6.47280i q^{86} +(1.05113 + 0.209927i) q^{87} +(2.38161 - 11.9732i) q^{88} +(3.69661 + 3.69661i) q^{89} +(-1.70981 - 1.14628i) q^{90} +(0.201971 + 1.01538i) q^{91} +(-2.97980 + 4.45959i) q^{92} +(-0.640112 - 0.959599i) q^{93} +(-7.73308 - 3.20315i) q^{94} +(-0.374870 - 0.250480i) q^{95} +(9.21469 + 3.82519i) q^{96} +(-1.37174 - 2.05296i) q^{97} +(4.12764 - 4.12764i) q^{98} +(12.9975 - 2.56450i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 8 q^{3} + 16 q^{4} + 16 q^{6} - 24 q^{9} - 32 q^{10} - 40 q^{12} + 16 q^{13} - 16 q^{15} + 16 q^{18} - 32 q^{19} - 16 q^{21} + 32 q^{22} - 16 q^{24} + 16 q^{27} - 32 q^{28} + 8 q^{30} + 24 q^{36}+ \cdots + 16 q^{99}+O(q^{100}) $ 32 * q - 8 * q^3 + 16 * q^4 + 16 * q^6 - 24 * q^9 - 32 * q^10 - 40 * q^12 + 16 * q^13 - 16 * q^15 + 16 * q^18 - 32 * q^19 - 16 * q^21 + 32 * q^22 - 16 * q^24 + 16 * q^27 - 32 * q^28 + 8 * q^30 + 24 * q^36 + 96 * q^37 - 48 * q^39 - 80 * q^40 + 24 * q^42 + 32 * q^43 + 40 * q^45 + 64 * q^46 - 48 * q^48 + 64 * q^49 - 96 * q^52 - 48 * q^54 + 48 * q^55 + 8 * q^57 - 48 * q^60 + 64 * q^61 - 16 * q^64 - 120 * q^66 + 80 * q^69 - 64 * q^72 + 144 * q^73 - 8 * q^75 - 32 * q^76 + 40 * q^78 - 64 * q^79 - 48 * q^81 + 32 * q^82 + 56 * q^87 - 32 * q^88 - 24 * q^90 - 48 * q^91 + 56 * q^93 + 48 * q^94 + 72 * q^96 + 32 * q^97 + 16 * q^99

Character values

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

$n$	$290$	$292$
$\chi(n)$	$-1$	$e\left(\frac{9}{16}\right)$

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	0.995796	−	0.0916024i	$-0.0291989\pi$
$2$	0.320870	+	0.774648i	0.226889	+	0.547759i	−0.768907	+	0.639361i	$0.779199\pi$
$3$	1.22380	+	1.22569i	0.706560	+	0.707653i
$3$	1.22380	+	1.22569i	0.706560	+	0.707653i
$4$	0.917091	−	0.917091i	0.458546	−	0.458546i
$5$	0.454651	+	0.680434i	0.203326	+	0.304299i	0.919093	−	0.394040i	$-0.128923\pi$
$5$	0.454651	+	0.680434i	0.203326	+	0.304299i	−0.715767	+	0.698339i	$0.753923\pi$
$6$	−0.556799	+	1.34130i	−0.227312	+	0.547583i
$7$	0.162303	+	0.108447i	0.0613448	+	0.0409893i	0.585864	−	0.810409i	$-0.300755\pi$
$7$	0.162303	+	0.108447i	0.0613448	+	0.0409893i	−0.524520	+	0.851398i	$0.675755\pi$
$8$	2.55399	+	1.05790i	0.902970	+	0.374023i
$9$	−0.00463376	+	3.00000i	−0.00154459	+	0.999999i
$10$	−0.381213	+	0.570525i	−0.120550	+	0.180416i
$11$	−0.861524	−	4.33117i	−0.259759	−	1.30590i	−0.861725	−	0.507376i	$-0.830616\pi$
$11$	−0.861524	−	4.33117i	−0.259759	−	1.30590i	0.601966	−	0.798522i	$-0.294384\pi$
$12$	2.24641	+	0.00173489i	0.648481	+	0.000500818i
$13$	3.75023	+	3.75023i	1.04013	+	1.04013i	0.999161	+	0.0409655i	$0.0130434\pi$
$13$	3.75023	+	3.75023i	1.04013	+	1.04013i	0.0409655	+	0.999161i	$0.486957\pi$
$14$	−0.0319304	+	0.160525i	−0.00853377	+	0.0429022i
$15$	−0.277599	+	1.38998i	−0.0716759	+	0.358890i
$16$		−	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	$-0.645129\pi$
$19$	−0.508991	+	0.210831i	−0.116771	+	0.0483680i	0.323533	+	0.946217i	$0.395129\pi$
$20$	1.04098	+	0.207063i	0.232769	+	0.0463007i
$21$	0.0657033	+	0.331651i	0.0143376	+	0.0723722i
$22$	3.07870	−	2.05712i	0.656380	−	0.438579i
$23$	−4.05597	+	0.806783i	−0.845729	+	0.168226i	−0.598891	−	0.800831i	$-0.704392\pi$
$23$	−4.05597	+	0.806783i	−0.845729	+	0.168226i	−0.246838	+	0.969057i	$0.579392\pi$
$24$	1.82891	+	4.42505i	0.373325	+	0.903259i
$25$	1.65713	−	4.00068i	0.331427	−	0.800136i
$26$	−1.70177	+	4.10844i	−0.333745	+	0.805732i
$27$	−3.68274	+	3.66571i	−0.708743	+	0.705467i
$28$	0.248303	−	0.0493905i	0.0469248	−	0.00933393i
$29$	0.514560	−	0.343818i	0.0955514	−	0.0638454i	−0.506877	−	0.862019i	$-0.669200\pi$
$29$	0.514560	−	0.343818i	0.0955514	−	0.0638454i	0.602428	+	0.798173i	$0.294200\pi$
$30$	−1.16581	+	0.230959i	−0.212848	+	0.0421672i
$31$	−0.653180	−	0.129926i	−0.117315	−	0.0233353i	0.136084	−	0.990697i	$-0.456548\pi$
$31$	−0.653180	−	0.129926i	−0.117315	−	0.0233353i	−0.253398	+	0.967362i	$0.581548\pi$
$32$	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
$36$	2.74702	+	2.75552i	0.457837	+	0.459253i
$37$	−0.383200	+	1.92648i	−0.0629978	+	0.316711i	−0.999416	−	0.0341751i	$-0.989120\pi$
$37$	−0.383200	+	1.92648i	−0.0629978	+	0.316711i	0.936418	+	0.350886i	$0.114120\pi$
$38$	−0.326640	−	0.326640i	−0.0529880	−	0.0529880i
$39$	−0.00709440	+	9.18614i	−0.00113601	+	1.47096i
$40$	0.441345	+	2.21879i	0.0697828	+	0.350822i
$41$	−4.44180	+	6.64762i	−0.693693	+	1.03818i	0.302680	+	0.953092i	$0.402119\pi$
$41$	−4.44180	+	6.64762i	−0.693693	+	1.03818i	−0.996373	+	0.0850923i	$0.972881\pi$
$42$	−0.235831	+	0.157314i	−0.0363895	+	0.0242740i
$43$	7.13212	+	2.95422i	1.08764	+	0.450514i	0.853182	−	0.521613i	$-0.174669\pi$
$43$	7.13212	+	2.95422i	1.08764	+	0.450514i	0.234455	+	0.972127i	$0.424669\pi$
$44$	−4.76218	−	3.18198i	−0.717925	−	0.479702i
$45$	−2.04341	+	1.36080i	−0.304613	+	0.202856i
$46$	−1.92641	−	2.88308i	−0.284034	−	0.425087i
$47$	−7.05884	+	7.05884i	−1.02964	+	1.02964i	−0.0300900	+	0.999547i	$0.509579\pi$
$47$	−7.05884	+	7.05884i	−1.02964	+	1.02964i	−0.999547	+	0.0300900i	$0.990421\pi$
$48$	0.338339	−	0.337817i	0.0488350	−	0.0487596i
$49$	−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	−0.864012	−	0.503471i	$-0.832056\pi$
$53$	−4.43410	−	10.7049i	−0.609071	−	1.47043i	0.254941	−	0.966957i	$-0.417944\pi$
$54$	−4.02132	−	1.67661i	−0.547232	−	0.228158i
$55$	2.55538	−	2.55538i	0.344568	−	0.344568i
$56$	0.299794	+	0.448673i	0.0400616	+	0.0599564i
$57$	−0.881316	−	0.365851i	−0.116733	−	0.0484581i
$58$	0.431445	+	0.288282i	0.0566514	+	0.0378533i
$59$	0.240270	+	0.0995233i	0.0312805	+	0.0129568i	0.398269	−	0.917269i	$-0.369611\pi$
$59$	0.240270	+	0.0995233i	0.0312805	+	0.0129568i	−0.366988	+	0.930226i	$0.619611\pi$
$60$	1.02015	+	1.52932i	0.131701	+	0.197434i
$61$	5.86155	−	8.77243i	0.750495	−	1.12319i	−0.237900	−	0.971290i	$-0.576459\pi$
$61$	5.86155	−	8.77243i	0.750495	−	1.12319i	0.988395	−	0.151905i	$-0.0485408\pi$
$62$	−0.108939	−	0.547674i	−0.0138353	−	0.0695546i
$63$	−0.326094	+	0.486406i	−0.0410840	+	0.0612814i
$64$	3.02483	+	3.02483i	0.378104	+	0.378104i
$65$	−0.846735	+	4.25683i	−0.105025	+	0.527994i
$66$	6.28910	+	1.25603i	0.774134	+	0.154606i
$67$			5.40994i			0.660929i	0.943818	+	0.330465i	$0.107205\pi$
$67$			5.40994i			0.660929i	−0.943818	+	0.330465i	$0.892795\pi$
$68$		0			0
$69$	−5.95256	−	3.98403i	−0.716604	−	0.479621i
$70$	−0.123744	+	0.0512564i	−0.0147902	+	0.00612632i
$71$	−6.38963	−	1.27098i	−0.758309	−	0.150837i	−0.199232	−	0.979952i	$-0.563845\pi$
$71$	−6.38963	−	1.27098i	−0.758309	−	0.150837i	−0.559078	+	0.829115i	$0.688845\pi$
$72$	−3.18552	+	7.65705i	−0.375417	+	0.902392i
$73$	9.64936	−	6.44749i	1.12937	−	0.754622i	0.156894	−	0.987616i	$-0.449852\pi$
$73$	9.64936	−	6.44749i	1.12937	−	0.754622i	0.972478	+	0.232993i	$0.0748520\pi$
$74$	−1.61530	+	0.321303i	−0.187775	+	0.0373507i
$75$	6.93159	−	2.86489i	0.800391	−	0.330809i
$76$	−0.273440	+	0.660143i	−0.0313657	+	0.0757236i
$77$	0.329876	−	0.796392i	0.0375929	−	0.0907573i
$78$	−7.11830	+	2.94206i	−0.805989	+	0.333123i
$79$	−10.6016	+	2.10878i	−1.19277	+	0.237257i	−0.751264	−	0.660002i	$-0.770556\pi$
$79$	−10.6016	+	2.10878i	−1.19277	+	0.237257i	−0.441506	+	0.897258i	$0.645556\pi$
$80$	0.187826	−	0.125502i	0.0209996	−	0.0140315i
$81$	−8.99996	−	0.0278025i	−0.999995	−	0.00308917i
$82$	−6.57481	−	1.30781i	−0.726066	−	0.144424i
$83$	−2.55289	+	1.05744i	−0.280216	+	0.116069i	−0.518365	−	0.855159i	$-0.673459\pi$
$83$	−2.55289	+	1.05744i	−0.280216	+	0.116069i	0.238149	+	0.971229i	$0.423459\pi$
$84$	0.364410	+	0.243898i	0.0397604	+	0.0266115i
$85$		0			0
$86$			6.47280i			0.697980i
$87$	1.05113	+	0.209927i	0.112693	+	0.0225066i
$88$	2.38161	−	11.9732i	0.253880	−	1.27634i
$89$	3.69661	+	3.69661i	0.391839	+	0.391839i	0.875343	−	0.483503i	$-0.160636\pi$
$89$	3.69661	+	3.69661i	0.391839	+	0.391839i	−0.483503	+	0.875343i	$0.660636\pi$
$90$	−1.70981	−	1.14628i	−0.180230	−	0.120829i
$91$	0.201971	+	1.01538i	0.0211723	+	0.106440i
$92$	−2.97980	+	4.45959i	−0.310666	+	0.464945i
$93$	−0.640112	−	0.959599i	−0.0663765	−	0.0995057i
$94$	−7.73308	−	3.20315i	−0.797606	−	0.330379i
$95$	−0.374870	−	0.250480i	−0.0384609	−	0.0256987i
$96$	9.21469	+	3.82519i	0.940470	+	0.390407i
$97$	−1.37174	−	2.05296i	−0.139279	−	0.208446i	0.755272	−	0.655411i	$-0.227505\pi$
$97$	−1.37174	−	2.05296i	−0.139279	−	0.208446i	−0.894551	+	0.446965i	$0.852505\pi$
$98$	4.12764	−	4.12764i	0.416954	−	0.416954i
$99$	12.9975	−	2.56450i	1.30630	−	0.257742i
$100$	−2.14924	−	5.18873i	−0.214924	−	0.518873i
$101$	−6.79257			−0.675886			−0.337943	−	0.941167i	$-0.609731\pi$
$101$	−6.79257			−0.675886			−0.337943	+	0.941167i	$0.609731\pi$
$102$		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
$105$	−0.195794	+	0.195492i	−0.0191076	+	0.0190781i
$106$	6.86974	−	6.86974i	0.667248	−	0.667248i
$107$	−2.28563	−	3.42069i	−0.220960	−	0.330690i	0.704384	−	0.709820i	$-0.251224\pi$
$107$	−2.28563	−	3.42069i	−0.220960	−	0.330690i	−0.925344	+	0.379129i	$0.876224\pi$
$108$	−0.0156140	+	6.73920i	−0.00150245	+	0.648480i
$109$	−10.5167	−	7.02704i	−1.00732	−	0.673068i	−0.0616150	−	0.998100i	$-0.519625\pi$
$109$	−10.5167	−	7.02704i	−1.00732	−	0.673068i	−0.945703	+	0.325032i	$0.894625\pi$
$110$	2.79947	+	1.15958i	0.266919	+	0.110561i
$111$	−2.83023	+	1.88794i	−0.268633	+	0.179195i
$112$	0.0299357	−	0.0448020i	0.00282866	−	0.00423339i
$113$	−0.241188	−	1.21253i	−0.0226891	−	0.114066i	0.967781	−	0.251793i	$-0.0810202\pi$
$113$	−0.241188	−	1.21253i	−0.0226891	−	0.114066i	−0.990470	+	0.137727i	$0.956020\pi$
$114$	0.000617913	−	0.800100i	5.78728e−5	−	0.0749363i
$115$	−2.39302	−	2.39302i	−0.223150	−	0.223150i
$116$	0.156586	−	0.787211i	0.0145386	−	0.0730907i
$117$	−11.2680	+	11.2333i	−1.04173	+	1.03852i
$118$			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
$122$	8.67634	+	1.72583i	0.785519	+	0.156249i
$123$	−13.5838	+	2.69108i	−1.22481	+	0.242647i
$124$	−0.718179	+	0.479872i	−0.0644944	+	0.0430938i
$125$	7.48875	−	1.48960i	0.669814	−	0.133234i
$126$	−0.481427	−	0.0965351i	−0.0428889	−	0.00860003i
$127$	−3.38823	+	8.17992i	−0.300657	+	0.725850i	0.699282	+	0.714845i	$0.253503\pi$
$127$	−3.38823	+	8.17992i	−0.300657	+	0.725850i	−0.999939	+	0.0110047i	$0.996497\pi$
$128$	3.03612	−	7.32985i	0.268358	−	0.647873i
$129$	5.10732	+	12.3571i	0.449674	+	1.08799i
$130$	−3.56923	+	0.709965i	−0.313043	+	0.0622680i
$131$	−8.17531	+	5.46257i	−0.714280	+	0.477267i	−0.858850	−	0.512228i	$-0.828820\pi$
$131$	−8.17531	+	5.46257i	−0.714280	+	0.477267i	0.144569	+	0.989495i	$0.453820\pi$
$132$	−1.92782	−	9.73106i	−0.167795	−	0.846980i
$133$	−0.105475	−	0.0209803i	−0.00914583	−	0.00181922i
$134$	−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	$-0.181953\pi$
$138$	1.17622	−	5.88949i	0.100127	−	0.501347i
$139$	−2.32272	+	11.6771i	−0.197010	+	0.990437i	0.748075	+	0.663614i	$0.230978\pi$
$139$	−2.32272	+	11.6771i	−0.197010	+	0.990437i	−0.945085	+	0.326823i	$0.894022\pi$
$140$	0.146498	+	0.146498i	0.0123814	+	0.0123814i
$141$	−17.2905	−	0.0133534i	−1.45613	−	0.00112456i
$142$	−1.06568	−	5.35753i	−0.0894298	−	0.449594i
$143$	13.0120	−	19.4738i	1.08812	−	1.62848i
$144$	0.828117	+	0.00127910i	0.0690097	+	0.000106592i
$145$	0.467891	+	0.193807i	0.0388562	+	0.0160948i
$146$	8.09073	+	5.40605i	0.669593	+	0.447408i
$147$	4.62314	−	11.1369i	0.381310	−	0.918556i
$148$	1.41533	+	2.11819i	0.116339	+	0.174114i
$149$	8.98104	−	8.98104i	0.735756	−	0.735756i	−0.235998	−	0.971754i	$-0.575836\pi$
$149$	8.98104	−	8.98104i	0.735756	−	0.735756i	0.971754	+	0.235998i	$0.0758358\pi$
$150$	4.44342	+	4.45029i	0.362804	+	0.363364i
$151$	0.303307	+	0.732249i	0.0246828	+	0.0595895i	0.935740	−	0.352690i	$-0.114733\pi$
$151$	0.303307	+	0.732249i	0.0246828	+	0.0595895i	−0.911058	+	0.412279i	$0.864733\pi$
$152$	−1.52299			−0.123531
$153$		0			0
$154$	0.722771			0.0582426
$155$	−0.208563	−	0.503516i	−0.0167522	−	0.0404434i
$156$	8.41803	+	8.43104i	0.673981	+	0.675023i
$157$	1.66767	−	1.66767i	0.133095	−	0.133095i	−0.637421	−	0.770516i	$-0.719999\pi$
$157$	1.66767	−	1.66767i	0.133095	−	0.133095i	0.770516	+	0.637421i	$0.219999\pi$
$158$	−5.03529	−	7.53584i	−0.400586	−	0.599519i
$159$	7.69441	−	18.5354i	0.610206	−	1.46996i
$160$	3.91949	+	2.61892i	0.309863	+	0.207044i
$161$	−0.745790	−	0.308916i	−0.0587765	−	0.0243460i
$162$	−2.86628	−	6.98072i	−0.225196	−	0.548457i
$163$	8.96232	−	13.4131i	0.701983	−	1.05059i	−0.293529	−	0.955950i	$-0.594830\pi$
$163$	8.96232	−	13.4131i	0.701983	−	1.05059i	0.995511	−	0.0946411i	$-0.0301704\pi$
$164$	2.02294	+	10.1700i	0.157965	+	0.794145i
$165$	6.25938	+	0.00483408i	0.487292	+	0.000376333i
$166$	−1.63829	−	1.63829i	−0.127156	−	0.127156i
$167$	1.78848	−	8.99131i	0.138397	−	0.695769i	−0.847816	−	0.530290i	$-0.822083\pi$
$167$	1.78848	−	8.99131i	0.138397	−	0.695769i	0.986213	−	0.165479i	$-0.0529169\pi$
$168$	−0.183047	+	0.916539i	−0.0141224	+	0.0707125i
$169$			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
$173$	1.14330	+	0.227417i	0.0869239	+	0.0172902i	0.238361	−	0.971177i	$-0.423390\pi$
$173$	1.14330	+	0.227417i	0.0869239	+	0.0172902i	−0.151437	+	0.988467i	$0.548390\pi$
$174$	0.174657	+	0.881617i	0.0132407	+	0.0668352i
$175$	0.702821	−	0.469610i	0.0531283	−	0.0354992i
$176$	−1.19557	+	0.237814i	−0.0901197	+	0.0179259i
$177$	0.172058	+	0.416294i	0.0129327	+	0.0312905i
$178$	−1.67744	+	4.04970i	−0.125729	+	0.303538i
$179$	3.93697	−	9.50468i	0.294263	−	0.710413i	−0.705735	−	0.708476i	$-0.749383\pi$
$179$	3.93697	−	9.50468i	0.294263	−	0.710413i	0.999998	−	0.00193768i	$-0.000616785\pi$
$180$	−0.626012	+	3.12197i	−0.0466602	+	0.232698i
$181$	12.6336	−	2.51298i	0.939047	−	0.186788i	0.298241	−	0.954491i	$-0.403600\pi$
$181$	12.6336	−	2.51298i	0.939047	−	0.186788i	0.640806	+	0.767702i	$0.278600\pi$
$182$	−0.721753	+	0.482260i	−0.0534999	+	0.0357475i
$183$	17.9256	−	3.55124i	1.32510	−	0.262515i
$184$	−11.2124	−	2.23028i	−0.826588	−	0.164419i
$185$	−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
$189$	−0.995256	+	0.195573i	−0.0723942	+	0.0142258i
$190$	0.0737495	−	0.370764i	0.00535035	−	0.0268980i
$191$	−11.7655	−	11.7655i	−0.851319	−	0.851319i	0.138977	−	0.990296i	$-0.455619\pi$
$191$	−11.7655	−	11.7655i	−0.851319	−	0.851319i	−0.990296	+	0.138977i	$0.955619\pi$
$192$	−0.00572216	+	7.40930i	−0.000412961	+	0.534720i
$193$	0.580436	+	2.91805i	0.0417807	+	0.210046i	0.996036	−	0.0889458i	$-0.0283498\pi$
$193$	0.580436	+	2.91805i	0.0417807	+	0.210046i	−0.954256	+	0.298991i	$0.903350\pi$
$194$	1.15017	−	1.72135i	0.0825773	−	0.123586i
$195$	−6.25379	+	4.17166i	−0.447843	+	0.298739i
$196$	−8.34201	−	3.45537i	−0.595858	−	0.246812i
$197$	11.2824	+	7.53865i	0.803837	+	0.537107i	0.888270	−	0.459323i	$-0.151908\pi$
$197$	11.2824	+	7.53865i	0.803837	+	0.537107i	−0.0844326	+	0.996429i	$0.526908\pi$
$198$	6.15709	+	9.24561i	0.437565	+	0.657057i
$199$	2.38994	+	3.57679i	0.169418	+	0.253552i	0.906457	−	0.422298i	$-0.138777\pi$
$199$	2.38994	+	3.57679i	0.169418	+	0.253552i	−0.737039	+	0.675850i	$0.763777\pi$
$200$	8.46460	−	8.46460i	0.598538	−	0.598538i
$201$	−6.63091	+	6.62068i	−0.467708	+	0.466987i
$202$	−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
$207$	−2.40155	−	12.1716i	−0.166919	−	0.845988i
$208$	1.03521	−	1.03521i	0.0717789	−	0.0717789i
$209$	1.35165	+	2.02289i	0.0934958	+	0.139926i
$210$	−0.214262	−	0.0889442i	−0.0147855	−	0.00613774i
$211$	−12.9105	−	8.62651i	−0.888794	−	0.593873i	0.0251632	−	0.999683i	$-0.491989\pi$
$211$	−12.9105	−	8.62651i	−0.888794	−	0.593873i	−0.913957	+	0.405810i	$0.866989\pi$
$212$	−13.8838	−	5.75087i	−0.953545	−	0.394971i
$213$	−6.26179	−	9.38712i	−0.429051	−	0.643195i
$214$	1.91644	−	2.86815i	0.131005	−	0.196063i
$215$	1.23248	+	6.19607i	0.0840541	+	0.422569i
$216$	−13.2836	+	5.46623i	−0.903835	+	0.371930i
$217$	−0.0919229	−	0.0919229i	−0.00624014	−	0.00624014i
$218$	2.06899	−	10.4015i	0.140130	−	0.704479i
$219$	19.7115	+	3.93669i	1.33198	+	0.266017i
$220$		−	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	$-0.813393\pi$
$223$	−15.3941	+	6.37645i	−1.03087	+	0.426999i	−0.197841	+	0.980234i	$0.563393\pi$
$224$	1.10280	+	0.219361i	0.0736841	+	0.0146567i
$225$	11.9943	+	4.98994i	0.799623	+	0.332662i
$226$	0.861897	−	0.575901i	0.0573325	−	0.0383084i
$227$	18.8788	−	3.75522i	1.25303	−	0.249243i	0.476415	−	0.879221i	$-0.341936\pi$
$227$	18.8788	−	3.75522i	1.25303	−	0.249243i	0.776613	+	0.629978i	$0.216936\pi$
$228$	−1.14377	+	0.472729i	−0.0757478	+	0.0313072i
$229$	4.20213	−	10.1448i	0.277685	−	0.670391i	−0.722086	−	0.691803i	$-0.756816\pi$
$229$	4.20213	−	10.1448i	0.277685	−	0.670391i	0.999771	+	0.0214129i	$0.00681647\pi$
$230$	1.08590	−	2.62159i	0.0716020	−	0.172863i
$231$	1.37983	−	0.570297i	0.0907863	−	0.0375228i
$232$	1.67790	−	0.333755i	0.110160	−	0.0219121i
$233$	19.5285	−	13.0485i	1.27935	−	0.854837i	0.284752	−	0.958601i	$-0.408089\pi$
$233$	19.5285	−	13.0485i	1.27935	−	0.854837i	0.994602	+	0.103765i	$0.0330889\pi$
$234$	−12.3174	−	5.12435i	−0.805215	−	0.334989i
$235$	−8.01238	−	1.59376i	−0.522670	−	0.103966i
$236$	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	$-0.146367\pi$
$240$	0.383688	+	0.0766283i	0.0247669	+	0.00494634i
$241$	−0.834235	+	4.19398i	−0.0537378	+	0.270158i	−0.998308	−	0.0581522i	$-0.981479\pi$
$241$	−0.834235	+	4.19398i	−0.0537378	+	0.270158i	0.944570	+	0.328310i	$0.106479\pi$
$242$	−5.04032	−	5.04032i	−0.324004	−	0.324004i
$243$	−10.9801	−	11.0652i	−0.704371	−	0.709832i
$244$	−2.66954	−	13.4207i	−0.170900	−	0.859172i
$245$	3.16523	−	4.73711i	0.202219	−	0.302643i
$246$	−6.44327	−	9.65918i	−0.410808	−	0.615847i
$247$	−2.69950	−	1.11817i	−0.171765	−	0.0711474i
$248$	−1.53076	−	1.02282i	−0.0972036	−	0.0649494i
$249$	−4.42032	−	1.83496i	−0.280126	−	0.116286i
$250$	3.55683	+	5.32317i	0.224954	+	0.336667i
$251$	−6.57161	+	6.57161i	−0.414796	+	0.414796i	−0.883406	−	0.468609i	$-0.844755\pi$
$251$	−6.57161	+	6.57161i	−0.414796	+	0.414796i	0.468609	+	0.883406i	$0.344755\pi$
$252$	0.147021	+	0.745137i	0.00926144	+	0.0469392i
$253$	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	−0.992804	−	0.119752i	$-0.961790\pi$
$257$	−6.01912	−	14.5315i	−0.375463	−	0.906447i	0.617341	−	0.786696i	$-0.288210\pi$
$258$	−7.93365	+	7.92141i	−0.493927	+	0.493165i
$259$	−0.271116	+	0.271116i	−0.0168463	+	0.0168463i
$260$	3.12737	+	4.68043i	0.193951	+	0.290268i
$261$	1.02907	+	1.54527i	0.0636977	+	0.0956499i
$262$	−6.85478	−	4.58021i	−0.423489	−	0.282967i
$263$	−14.2664	−	5.90932i	−0.879701	−	0.364384i	−0.103320	−	0.994648i	$-0.532947\pi$
$263$	−14.2664	−	5.90932i	−0.879701	−	0.364384i	−0.776381	+	0.630264i	$0.782947\pi$
$264$	17.5900	−	11.7336i	1.08259	−	0.722154i
$265$	5.26799	−	7.88410i	0.323610	−	0.484316i
$266$	−0.0175914	−	0.0884379i	−0.00107860	−	0.00542247i
$267$	−0.00699296	+	9.05479i	−0.000427962	+	0.554144i
$268$	4.96141	+	4.96141i	0.303066	+	0.303066i
$269$	−4.74815	+	23.8706i	−0.289500	+	1.45541i	0.512807	+	0.858504i	$0.328605\pi$
$269$	−4.74815	+	23.8706i	−0.289500	+	1.45541i	−0.802307	+	0.596911i	$0.796395\pi$
$270$	−0.687475	−	3.49851i	−0.0418384	−	0.212913i
$271$		−	5.62528i		−	0.341711i	−0.985296	−	0.170856i	$-0.945347\pi$
$271$		−	5.62528i		−	0.341711i	0.985296	−	0.170856i	$-0.0546532\pi$
$272$		0			0
$273$	−0.997365	+	1.49017i	−0.0603633	+	0.0901891i
$274$	9.81047	−	4.06363i	0.592672	−	0.245493i
$275$	−18.7553	−	3.73066i	−1.13099	−	0.224967i
$276$	−9.11276	+	1.80533i	−0.548524	+	0.108668i
$277$	−7.37043	+	4.92476i	−0.442846	+	0.295900i	−0.756931	−	0.653495i	$-0.773302\pi$
$277$	−7.37043	+	4.92476i	−0.442846	+	0.295900i	0.314085	+	0.949395i	$0.398302\pi$
$278$	−9.79092	+	1.94753i	−0.587220	+	0.116805i
$279$	0.392803	−	1.95893i	0.0235165	−	0.117278i
$280$	−0.168991	+	0.407979i	−0.0100991	+	0.0243814i
$281$	−2.76232	+	6.66883i	−0.164786	+	0.397829i	−0.984605	−	0.174794i	$-0.944074\pi$
$281$	−2.76232	+	6.66883i	−0.164786	+	0.397829i	0.819819	+	0.572623i	$0.194074\pi$
$282$	−5.53767	−	13.3984i	−0.329763	−	0.797861i
$283$	−4.84677	+	0.964082i	−0.288110	+	0.0573087i	−0.337030	−	0.941494i	$-0.609422\pi$
$283$	−4.84677	+	0.964082i	−0.288110	+	0.0573087i	0.0489193	+	0.998803i	$0.484422\pi$
$284$	−7.02547	+	4.69427i	−0.416885	+	0.278554i
$285$	−0.151754	−	0.766012i	−0.00898915	−	0.0453746i
$286$	19.2605	+	3.83115i	1.13890	+	0.226541i
$287$	−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
$291$	0.837554	−	4.19374i	0.0490983	−	0.245841i
$292$	2.93640	−	14.7623i	0.171840	−	0.863897i
$293$	13.5083	+	13.5083i	0.789165	+	0.789165i	0.981357	−	0.192192i	$-0.0615598\pi$
$293$	13.5083	+	13.5083i	0.789165	+	0.789165i	−0.192192	+	0.981357i	$0.561560\pi$
$294$	10.1106	+	0.00780836i	0.589662	+	0.000455393i
$295$	0.0415203	+	0.208736i	0.00241740	+	0.0121531i
$296$	−3.01670	+	4.51481i	−0.175342	+	0.262418i
$297$	19.0496	+	12.7925i	1.10537	+	0.742294i
$298$	9.83889	+	4.07540i	0.569952	+	0.236082i
$299$	−18.2364	−	12.1852i	−1.05464	−	0.704688i
$300$	3.72954	−	8.98427i	0.215325	−	0.518707i
$301$	0.837187	+	1.25294i	0.0482546	+	0.0722182i
$302$	−0.469913	+	0.469913i	−0.0270404	+	0.0270404i
$303$	−8.31274	−	8.32559i	−0.477554	−	0.478293i
$304$	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
$309$	3.03212	+	3.03681i	0.172491	+	0.172758i
$310$	0.323126	−	0.323126i	0.0183523	−	0.0183523i
$311$	5.81470	+	8.70232i	0.329722	+	0.493463i	0.958879	−	0.283814i	$-0.0916000\pi$
$311$	5.81470	+	8.70232i	0.329722	+	0.493463i	−0.629158	+	0.777278i	$0.716600\pi$
$312$	−9.73610	+	23.4538i	−0.551198	+	1.32781i
$313$	19.9675	+	13.3418i	1.12863	+	0.754125i	0.972336	−	0.233586i	$-0.0750459\pi$
$313$	19.9675	+	13.3418i	1.12863	+	0.754125i	0.156292	+	0.987711i	$0.450046\pi$
$314$	1.82697	+	0.756754i	0.103102	+	0.0427061i
$315$	−0.479226		0.000740207i	−0.0270013		4.17060e-5i
$316$	−7.78866	+	11.6566i	−0.438146	+	0.655732i
$317$	1.91890	+	9.64699i	0.107776	+	0.541829i	0.996515	+	0.0834143i	$0.0265825\pi$
$317$	1.91890	+	9.64699i	0.107776	+	0.541829i	−0.888739	+	0.458414i	$0.848418\pi$
$318$	16.8274	+	0.0129957i	0.943631	+	0.000728761i
$319$	−1.93244	−	1.93244i	−0.108196	−	0.108196i
$320$	−0.682954	+	3.43344i	−0.0381783	+	0.191935i
$321$	1.39555	−	6.98771i	0.0778921	−	0.390016i
$322$		−	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
$326$	13.2661	+	2.63880i	0.734743	+	0.146149i
$327$	−4.25736	−	21.4899i	−0.235432	−	1.18839i
$328$	−18.3768	+	12.2790i	−1.01469	+	0.677993i
$329$	−1.91118	+	0.380158i	−0.105367	+	0.0209588i
$330$	2.00470	+	4.85037i	0.110355	+	0.267004i
$331$	−1.60689	+	3.87936i	−0.0883224	+	0.213229i	−0.961869	−	0.273512i	$-0.911815\pi$
$331$	−1.60689	+	3.87936i	−0.0883224	+	0.213229i	0.873546	+	0.486741i	$0.161815\pi$
$332$	−1.37146	+	3.31100i	−0.0752687	+	0.181715i
$333$	−5.77765	−	1.15853i	−0.316613	−	0.0634869i
$334$	7.53897	−	1.49959i	0.412514	−	0.0820542i
$335$	−3.68110	+	2.45964i	−0.201120	+	0.134384i
$336$	0.0915487	−	0.0181367i	0.00499439	−	0.000989437i
$337$	5.67449	+	1.12873i	0.309109	+	0.0614856i	0.347207	−	0.937788i	$-0.387130\pi$
$337$	5.67449	+	1.12873i	0.309109	+	0.0614856i	−0.0380983	+	0.999274i	$0.512130\pi$
$338$	−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
$342$	0.981432	−	0.978404i	0.0530697	−	0.0529061i
$343$	0.531692	−	2.67300i	0.0287087	−	0.144328i
$344$	15.0901	+	15.0901i	0.813602	+	0.813602i
$345$	0.00452693	−	5.86167i	0.000243722	−	0.315581i
$346$	0.190683	+	0.958630i	0.0102512	+	0.0515363i
$347$	−0.0105207	+	0.0157453i	−0.000564779	+	0.000845252i	−0.831752	−	0.555148i	$-0.812662\pi$
$347$	−0.0105207	+	0.0157453i	−0.000564779	+	0.000845252i	0.831187	+	0.555993i	$0.187662\pi$
$348$	1.15651	−	0.771462i	0.0619953	−	0.0413547i
$349$	−5.74159	−	2.37825i	−0.307340	−	0.127305i	0.223682	−	0.974662i	$-0.428192\pi$
$349$	−5.74159	−	2.37825i	−0.307340	−	0.127305i	−0.531023	+	0.847358i	$0.678192\pi$
$350$	0.589297	+	0.393755i	0.0314992	+	0.0210471i
$351$	−27.5584	−	0.0638496i	−1.47096	−	0.00340804i
$352$	−14.1323	−	21.1505i	−0.753256	−	1.12733i
$353$	−8.61113	+	8.61113i	−0.458324	+	0.458324i	−0.898105	−	0.439781i	$-0.855056\pi$
$353$	−8.61113	+	8.61113i	−0.458324	+	0.458324i	0.439781	+	0.898105i	$0.355056\pi$
$354$	−0.267273	+	0.266860i	−0.0142054	+	0.0141835i
$355$	−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	0.822832	+	0.568284i	$0.192393\pi$
$359$	12.1801	+	29.4053i	0.642840	+	1.55195i	−0.179992	+	0.983668i	$0.557607\pi$
$360$	−6.65841	+	1.31375i	−0.350929	+	0.0692408i
$361$	−13.2204	+	13.2204i	−0.695811	+	0.695811i
$362$	6.00041	+	8.98025i	0.315375	+	0.471991i
$363$	−13.5994	−	5.64538i	−0.713785	−	0.296306i
$364$	1.11642	+	0.745967i	0.0585162	+	0.0390993i
$365$	8.77418	+	3.63439i	0.459262	+	0.190232i
$366$	8.50276	+	12.7466i	0.444446	+	0.666274i
$367$	−18.6814	+	27.9587i	−0.975161	+	1.45943i	−0.0890125	+	0.996031i	$0.528371\pi$
$367$	−18.6814	+	27.9587i	−0.975161	+	1.45943i	−0.886149	+	0.463401i	$0.846629\pi$
$368$	0.222704	+	1.11961i	0.0116092	+	0.0583636i
$369$	−19.9223	−	13.3562i	−1.03711	−	0.695295i
$370$	−0.953024	−	0.953024i	−0.0495453	−	0.0495453i
$371$	0.441247	−	2.21830i	0.0229084	−	0.115168i
$372$	−1.46708	−	0.292999i	−0.0760646	−	0.0151913i
$373$			15.2764i			0.790981i	0.918470	+	0.395490i	$0.129425\pi$
$373$			15.2764i			0.790981i	−0.918470	+	0.395490i	$0.870575\pi$
$374$		0			0
$375$	10.9905	+	7.35591i	0.567547	+	0.379857i
$376$	−25.4957	+	10.5607i	−1.31484	+	0.544624i
$377$	3.21911	+	0.640321i	0.165793	+	0.0329782i
$378$	−0.470848	−	0.708220i	−0.0242178	−	0.0364269i
$379$	31.6091	−	21.1206i	1.62365	−	1.08489i	0.691778	−	0.722111i	$-0.256828\pi$
$379$	31.6091	−	21.1206i	1.62365	−	1.08489i	0.931875	−	0.362779i	$-0.118172\pi$
$380$	−0.573503	+	0.114077i	−0.0294201	+	0.00585202i
$381$	−14.1726	+	5.85765i	−0.726082	+	0.300096i
$382$	5.33891	−	12.8893i	0.273162	−	0.659472i
$383$	−13.1831	+	31.8268i	−0.673624	+	1.62627i	0.101781	+	0.994807i	$0.467546\pi$
$383$	−13.1831	+	31.8268i	−0.673624	+	1.62627i	−0.775404	+	0.631465i	$0.782454\pi$
$384$	12.6997	−	5.24891i	0.648080	−	0.267858i
$385$	0.691871	−	0.137622i	0.0352610	−	0.00701385i
$386$	−2.07422	+	1.38595i	−0.105575	+	0.0705428i
$387$	−8.89570	+	21.3826i	−0.452194	+	1.08694i
$388$	−3.14076	−	0.624737i	−0.159448	−	0.0317162i
$389$	0.697275	−	0.288821i	0.0353532	−	0.0146438i	−0.364937	−	0.931032i	$-0.618909\pi$
$389$	0.697275	−	0.288821i	0.0353532	−	0.0146438i	0.400290	+	0.916389i	$0.368909\pi$
$390$	−5.23822	−	3.50592i	−0.265248	−	0.177529i
$391$		0			0
$392$		−	19.2456i		−	0.972048i
$393$	−16.7003	−	3.33532i	−0.842421	−	0.168244i
$394$	−2.21962	+	11.1588i	−0.111823	+	0.562172i
$395$	−6.25490	−	6.25490i	−0.314718	−	0.314718i
$396$	9.56801	−	14.2718i	0.480811	−	0.717183i
$397$	3.93046	+	19.7598i	0.197264	+	0.991713i	0.944839	+	0.327536i	$0.106218\pi$
$397$	3.93046	+	19.7598i	0.197264	+	0.991713i	−0.747575	+	0.664178i	$0.768782\pi$
$398$	−2.00390	+	2.99904i	−0.100446	+	0.150329i
$399$	−0.103365	−	0.154955i	−0.00517471	−	0.00775746i
$400$	−1.10434	−	0.457434i	−0.0552172	−	0.0228717i
$401$	13.1111	+	8.76056i	0.654737	+	0.437481i	0.838065	−	0.545570i	$-0.183687\pi$
$401$	13.1111	+	8.76056i	0.654737	+	0.437481i	−0.183328	+	0.983052i	$0.558687\pi$
$402$	−7.25635	−	3.01225i	−0.361914	−	0.150237i
$403$	−1.96232	−	2.93682i	−0.0977502	−	0.146294i
$404$	−6.22941	+	6.22941i	−0.309925	+	0.309925i
$405$	−4.07292	−	6.13651i	−0.202385	−	0.304926i
$406$	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
$411$	15.5227	−	15.4987i	0.765677	−	0.764495i
$412$	2.27221	−	2.27221i	0.111944	−	0.111944i
$413$	0.0282036	+	0.0422096i	0.00138781	+	0.00207700i
$414$	8.65815	−	5.76587i	0.425525	−	0.283377i
$415$	−1.88019	−	1.25630i	−0.0922950	−	0.0616695i
$416$	28.2248	+	11.6911i	1.38384	+	0.573204i
$417$	−17.1550	+	11.4435i	−0.840085	+	0.560389i
$418$	−1.13332	+	1.69614i	−0.0554327	+	0.0829610i
$419$	−6.87332	−	34.5545i	−0.335784	−	1.68810i	−0.667412	−	0.744689i	$-0.732598\pi$
$419$	−6.87332	−	34.5545i	−0.335784	−	1.68810i	0.331628	−	0.943410i	$-0.392402\pi$
$420$	−0.000277134		0.358846i	−1.35228e−5		0.0175099i
$421$	0.00892902	+	0.00892902i	0.000435174	+	0.000435174i	0.707324	−	0.706889i	$-0.249902\pi$
$421$	0.00892902	+	0.00892902i	0.000435174	+	0.000435174i	−0.706889	+	0.707324i	$0.749902\pi$
$422$	2.53992	−	12.7691i	0.123642	−	0.621588i
$423$	−21.1438	−	21.2092i	−1.02805	−	1.03123i
$424$		−	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
$428$	−5.23321	−	1.04095i	−0.252957	−	0.0503163i
$429$	39.7929	−	7.88335i	1.92122	−	0.380612i
$430$	−4.40431	+	2.94287i	−0.212395	+	0.141918i
$431$	−11.6292	+	2.31319i	−0.560159	+	0.111422i	−0.467046	−	0.884233i	$-0.654682\pi$
$431$	−11.6292	+	2.31319i	−0.560159	+	0.111422i	−0.0931127	+	0.995656i	$0.529682\pi$
$432$	1.01188	+	1.01658i	0.0486841	+	0.0489102i
$433$	−0.207692	+	0.501414i	−0.00998106	+	0.0240964i	−0.928791	−	0.370603i	$-0.879151\pi$
$433$	−0.207692	+	0.501414i	−0.00998106	+	0.0240964i	0.918810	+	0.394699i	$0.129151\pi$
$434$	0.0417126	−	0.100703i	0.00200227	−	0.00483391i
$435$	0.335057	+	0.810669i	0.0160647	+	0.0388686i
$436$	−16.0892	+	3.20035i	−0.770534	+	0.153269i
$437$	1.89436	−	1.26577i	0.0906195	−	0.0605500i
$438$	3.27528	+	16.5326i	0.156499	+	0.789960i
$439$	29.8659	+	5.94070i	1.42542	+	0.283534i	0.846734	−	0.532016i	$-0.178565\pi$
$439$	29.8659	+	5.94070i	1.42542	+	0.283534i	0.578687	+	0.815550i	$0.303565\pi$
$440$	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	$0.594721\pi$
$444$	−0.864166	+	4.32699i	−0.0410115	+	0.205350i
$445$	−0.834628	+	4.19596i	−0.0395652	+	0.198908i
$446$	−9.87902	−	9.87902i	−0.467785	−	0.467785i
$447$	21.9990	+	0.0169897i	1.04052	+	0.000803584i
$448$	0.162904	+	0.818975i	0.00769650	+	0.0386929i
$449$	−20.2429	+	30.2957i	−0.955323	+	1.42974i	−0.0530433	+	0.998592i	$0.516892\pi$
$449$	−20.2429	+	30.2957i	−0.955323	+	1.42974i	−0.902280	+	0.431150i	$0.858108\pi$
$450$	−0.0168245	+	10.8925i	−0.000793112	+	0.513478i
$451$	32.6187	+	13.5111i	1.53596	+	0.636214i
$452$	−1.33320	−	0.890813i	−0.0627082	−	0.0419003i
$453$	−0.526323	+	1.26789i	−0.0247288	+	0.0595705i
$454$	8.96660	+	13.4195i	0.420823	+	0.629807i
$455$	−0.599070	+	0.599070i	−0.0280848	+	0.0280848i
$456$	−1.86384	−	1.86672i	−0.0872822	−	0.0874171i
$457$	−8.15675	−	19.6921i	−0.381557	−	0.921160i	−0.991665	−	0.128842i	$-0.958874\pi$
$457$	−8.15675	−	19.6921i	−0.381557	−	0.921160i	0.610108	−	0.792318i	$-0.291126\pi$
$458$	9.20703			0.430216
$459$		0			0
$460$	−4.38923			−0.204649
$461$	2.35253	+	5.67952i	0.109568	+	0.264521i	0.969148	−	0.246481i	$-0.0792743\pi$
$461$	2.35253	+	5.67952i	0.109568	+	0.264521i	−0.859579	+	0.511002i	$0.829274\pi$
$462$	0.884526	+	0.885894i	0.0411519	+	0.0412155i
$463$	−25.6637	+	25.6637i	−1.19270	+	1.19270i	−0.216388	+	0.976307i	$0.569428\pi$
$463$	−25.6637	+	25.6637i	−1.19270	+	1.19270i	−0.976307	+	0.216388i	$0.930572\pi$
$464$	−0.0949073	−	0.142039i	−0.00440596	−	0.00659398i
$465$	0.361916	−	0.871836i	0.0167834	−	0.0404304i
$466$	16.3741	+	10.9408i	0.758516	+	0.506824i
$467$	7.10485	+	2.94293i	0.328773	+	0.136182i	0.540964	−	0.841046i	$-0.318060\pi$
$467$	7.10485	+	2.94293i	0.328773	+	0.136182i	−0.212190	+	0.977228i	$0.568060\pi$
$468$	−0.0318738	+	20.6358i	−0.00147337	+	0.953889i
$469$	−0.586694	+	0.878050i	−0.0270910	+	0.0405446i
$470$	−1.33633	−	6.71816i	−0.0616401	−	0.309886i
$471$	4.08495	+	0.00315478i	0.188224	+	0.000145365i
$472$	0.508362	+	0.508362i	0.0233993	+	0.0233993i
$473$	6.65075	−	33.4356i	0.305802	−	1.53737i
$474$	3.07443	−	15.3941i	0.141213	−	0.707072i
$475$			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
$479$	2.25186	+	0.447923i	0.102890	+	0.0204661i	0.246267	−	0.969202i	$-0.420796\pi$
$479$	2.25186	+	0.447923i	0.102890	+	0.0204661i	−0.143377	+	0.989668i	$0.545796\pi$
$480$	1.58668	+	8.00911i	0.0724218	+	0.365564i
$481$	−8.66182	+	5.78764i	−0.394945	+	0.263894i
$482$	−3.51654	+	0.699483i	−0.160174	+	0.0318606i
$483$	−0.534061	−	1.29216i	−0.0243006	−	0.0587953i
$484$	−4.21940	+	10.1865i	−0.191791	+	0.463025i
$485$	0.773237	−	1.86676i	0.0351109	−	0.0847652i
$486$	5.04846	−	12.0562i	0.229003	−	0.546879i
$487$	27.5373	−	5.47752i	1.24784	−	0.248210i	0.473392	−	0.880852i	$-0.343030\pi$
$487$	27.5373	−	5.47752i	1.24784	−	0.248210i	0.774444	+	0.632642i	$0.218030\pi$
$488$	24.2506	−	16.2038i	1.09777	−	0.733510i
$489$	27.4083	−	5.42985i	1.23945	−	0.245546i
$490$	4.68522	+	0.931948i	0.211657	+	0.0421011i
$491$	12.4942	−	5.17526i	0.563854	−	0.233556i	−0.0825033	−	0.996591i	$-0.526291\pi$
$491$	12.4942	−	5.17526i	0.563854	−	0.233556i	0.646357	+	0.763035i	$0.276291\pi$
$492$	−9.98962	+	14.9256i	−0.450367	+	0.672896i
$493$		0			0
$494$		−	2.44995i		−	0.110228i
$495$	7.65430	+	7.67798i	0.344035	+	0.345099i
$496$	−0.0358645	+	0.180303i	−0.00161037	+	0.00809585i
$497$	−0.899222	−	0.899222i	−0.0403356	−	0.0403356i
$498$	0.00309919	−	4.01297i	0.000138878	−	0.179825i
$499$	2.97184	+	14.9405i	0.133038	+	0.668827i	0.988532	+	0.151014i	$0.0482538\pi$
$499$	2.97184	+	14.9405i	0.133038	+	0.668827i	−0.855494	+	0.517813i	$0.826746\pi$
$500$	5.50176	−	8.23397i	0.246046	−	0.368234i
$501$	13.2093	−	8.81143i	0.590148	−	0.393666i
$502$	−7.19931	−	2.98205i	−0.321321	−	0.133096i
$503$	−20.2838	−	13.5532i	−0.904408	−	0.604306i	0.0140169	−	0.999902i	$-0.495538\pi$
$503$	−20.2838	−	13.5532i	−0.904408	−	0.604306i	−0.918425	+	0.395596i	$0.870538\pi$
$504$	−1.34741	+	0.897301i	−0.0600182	+	0.0399689i
$505$	−3.08825	−	4.62189i	−0.137425	−	0.205672i
$506$	−10.8275	+	10.8275i	−0.481339	+	0.481339i
$507$	−18.5428	+	18.5141i	−0.823513	+	0.822242i
$508$	4.39441	+	10.6090i	0.194971	+	0.470700i
$509$	18.8631			0.836090			0.418045	−	0.908426i	$-0.362715\pi$
$509$	18.8631			0.836090			0.418045	+	0.908426i	$0.362715\pi$
$510$		0			0
$511$	2.26533			0.100212
$512$	−1.19253	−	2.87903i	−0.0527030	−	0.127236i
$513$	1.10164	−	2.64225i	0.0486384	−	0.116658i
$514$	9.32541	−	9.32541i	0.411326	−	0.411326i
$515$	1.12646	+	1.68586i	0.0496376	+	0.0742880i
$516$	16.0165	+	6.64875i	0.705087	+	0.292695i
$517$	36.6544	+	24.4917i	1.61206	+	1.07714i
$518$	−0.297013	−	0.123027i	−0.0130500	−	0.00540548i
$519$	1.12043	+	1.67965i	0.0491815	+	0.0737285i
$520$	−6.66583	+	9.97612i	−0.292316	+	0.437482i
$521$	6.43336	+	32.3427i	0.281851	+	1.41696i	0.819156	+	0.573571i	$0.194442\pi$
$521$	6.43336	+	32.3427i	0.281851	+	1.41696i	−0.537305	+	0.843388i	$0.680558\pi$
$522$	−0.866844	+	1.29300i	−0.0379407	+	0.0565929i
$523$	−9.24397	−	9.24397i	−0.404211	−	0.404211i	0.475503	−	0.879714i	$-0.342266\pi$
$523$	−9.24397	−	9.24397i	−0.404211	−	0.404211i	−0.879714	+	0.475503i	$0.842266\pi$
$524$	−2.48783	+	12.5072i	−0.108681	+	0.546379i
$525$	1.43571	+	0.286733i	0.0626594	+	0.0125141i
$526$		−	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
$530$	7.79774	+	1.55107i	0.338712	+	0.0673740i
$531$	−0.299683	+	0.720349i	−0.0130051	+	0.0312605i
$532$	−0.115971	+	0.0774893i	−0.00502798	+	0.00335959i
$533$	−41.5879	+	8.27234i	−1.80137	+	0.358315i
$534$	−7.01652	+	2.89999i	−0.303635	+	0.125495i
$535$	1.28839	−	3.11044i	0.0557018	−	0.134476i
$536$	−5.72315	+	13.8169i	−0.247202	+	0.596800i
$537$	16.4679	−	6.80631i	0.710640	−	0.293714i
$538$	−20.0148	+	3.98120i	−0.862901	+	0.171642i
$539$	−25.5626	+	17.0804i	−1.10106	+	0.735705i
$540$	−4.59268	+	3.05336i	−0.197637	+	0.131396i
$541$	−16.3632	−	3.25485i	−0.703511	−	0.139937i	−0.169644	−	0.985505i	$-0.554262\pi$
$541$	−16.3632	−	3.25485i	−0.703511	−	0.139937i	−0.533867	+	0.845568i	$0.679262\pi$
$542$	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
$546$	−1.47438	−	0.294456i	−0.0630977	−	0.0126016i
$547$	−2.11537	+	10.6347i	−0.0904466	+	0.454706i	0.908847	+	0.417129i	$0.136964\pi$
$547$	−2.11537	+	10.6347i	−0.0904466	+	0.454706i	−0.999294	+	0.0375766i	$0.988036\pi$
$548$	−11.6144	−	11.6144i	−0.496144	−	0.496144i
$549$	26.2901	+	17.6253i	1.12203	+	0.752229i
$550$	−3.12806	−	15.7258i	−0.133381	−	0.670550i
$551$	−0.189419	+	0.283486i	−0.00806952	+	0.0120769i
$552$	−10.9881	−	16.4723i	−0.467683	−	0.701109i
$553$	−1.94936	−	0.807451i	−0.0828952	−	0.0343363i
$554$	−6.17990	−	4.12928i	−0.262559	−	0.175436i
$555$	−2.57138	−	1.06743i	−0.109149	−	0.0453098i
$556$	8.57881	+	12.8391i	0.363822	+	0.544499i
$557$	−8.63556	+	8.63556i	−0.365900	+	0.365900i	−0.865980	−	0.500079i	$-0.833304\pi$
$557$	−8.63556	+	8.63556i	−0.365900	+	0.365900i	0.500079	+	0.865980i	$0.333304\pi$
$558$	1.64352	−	0.324279i	0.0695759	−	0.0137278i
$559$	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	−0.992052	−	0.125830i	$-0.959841\pi$
$563$	−9.00559	−	21.7414i	−0.379541	−	0.916292i	0.612511	−	0.790462i	$-0.290159\pi$
$564$	−15.8693	+	15.8448i	−0.668216	+	0.667185i
$565$	0.715392	−	0.715392i	0.0300968	−	0.0300968i
$566$	−2.30200	−	3.44519i	−0.0967605	−	0.144812i
$567$	−1.45771	−	0.980534i	−0.0612179	−	0.0411786i
$568$	−14.9745	−	10.0056i	−0.628314	−	0.419826i
$569$	1.73268	+	0.717701i	0.0726379	+	0.0300876i	0.418707	−	0.908122i	$-0.362484\pi$
$569$	1.73268	+	0.717701i	0.0726379	+	0.0300876i	−0.346069	+	0.938209i	$0.612484\pi$
$570$	0.544696	−	0.363346i	0.0228148	−	0.0152189i
$571$	−22.2530	+	33.3039i	−0.931258	+	1.39373i	−0.0120616	+	0.999927i	$0.503839\pi$
$571$	−22.2530	+	33.3039i	−0.931258	+	1.39373i	−0.919197	+	0.393799i	$0.871161\pi$
$572$	−5.92608	−	29.7924i	−0.247782	−	1.24568i
$573$	0.0222570	−	28.8194i	0.000929801	−	1.20395i
$574$	−0.925283	−	0.925283i	−0.0386205	−	0.0386205i
$575$	−3.49362	+	17.5636i	−0.145694	+	0.732452i
$576$	−9.08851	+	9.06047i	−0.378688	+	0.377520i
$577$		−	31.8433i		−	1.32565i	−0.748773	−	0.662826i	$-0.769357\pi$
$577$		−	31.8433i		−	1.32565i	0.748773	−	0.662826i	$-0.230643\pi$
$578$		0			0
$579$	−2.86629	+	4.28254i	−0.119119	+	0.177976i
$580$	0.606837	−	0.251360i	0.0251975	−	0.0104372i
$581$	−0.529018	−	0.105228i	−0.0219474	−	0.00436560i
$582$	3.51742	−	0.696834i	0.145802	−	0.0288847i
$583$	−42.5446	+	28.4274i	−1.76202	+	1.17734i
$584$	31.4651	−	6.25880i	1.30204	−	0.258991i
$585$	−12.7665	−	2.55993i	−0.527832	−	0.105840i
$586$	−6.12978	+	14.7986i	−0.253219	+	0.611325i
$587$	4.81996	−	11.6364i	0.198941	−	0.480286i	−0.792653	−	0.609673i	$-0.791301\pi$
$587$	4.81996	−	11.6364i	0.198941	−	0.480286i	0.991594	+	0.129387i	$0.0413008\pi$
$588$	−5.97372	−	14.4534i	−0.246352	−	0.596048i
$589$	0.359855	−	0.0715796i	0.0148276	−	0.00294939i
$590$	−0.148375	+	0.0991408i	−0.00610849	+	0.00408156i
$591$	4.56732	+	23.0545i	0.187874	+	0.948336i
$592$	0.531784	+	0.105778i	0.0218562	+	0.00434746i
$593$	17.0275	−	7.05301i	0.699234	−	0.289632i	−0.00460731	−	0.999989i	$-0.501467\pi$
$593$	17.0275	−	7.05301i	0.699234	−	0.289632i	0.703841	+	0.710357i	$0.251467\pi$
$594$	−3.79722	+	18.8614i	−0.155802	+	0.773895i
$595$		0			0
$596$		−	16.4729i		−	0.674755i
$597$	−1.45924	+	7.30660i	−0.0597227	+	0.299039i
$598$	3.58772	−	18.0367i	0.146713	−	0.737575i
$599$	12.3968	+	12.3968i	0.506519	+	0.506519i	0.913456	−	0.406937i	$-0.133403\pi$
$599$	12.3968	+	12.3968i	0.506519	+	0.506519i	−0.406937	+	0.913456i	$0.633403\pi$
$600$	20.7339	+	0.0160127i	0.846460	+	0.000653716i
$601$	2.64838	+	13.3143i	0.108030	+	0.543102i	0.996458	+	0.0840872i	$0.0267974\pi$
$601$	2.64838	+	13.3143i	0.108030	+	0.543102i	−0.888429	+	0.459015i	$0.848203\pi$
$602$	−0.701959	+	1.05056i	−0.0286097	+	0.0428174i
$603$	−16.2298	−	0.0250684i	−0.660929	−	0.00102086i
$604$	0.949699	+	0.393378i	0.0386427	+	0.0160063i
$605$	−5.78455	−	3.86511i	−0.235175	−	0.157139i
$606$	3.78209	−	9.11088i	0.153637	−	0.370104i
$607$	2.29815	+	3.43942i	0.0932790	+	0.139602i	0.875174	−	0.483808i	$-0.160747\pi$
$607$	2.29815	+	3.43942i	0.0932790	+	0.139602i	−0.781895	+	0.623410i	$0.785747\pi$
$608$	−2.24400	+	2.24400i	−0.0910064	+	0.0910064i
$609$	0.147836	+	0.148064i	0.00599061	+	0.00599987i
$610$	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
$615$	−8.00699	−	8.01937i	−0.322873	−	0.323372i
$616$	1.68500	−	1.68500i	0.0678906	−	0.0678906i
$617$	−7.08791	−	10.6078i	−0.285349	−	0.427054i	0.660910	−	0.750465i	$-0.270170\pi$
$617$	−7.08791	−	10.6078i	−0.285349	−	0.427054i	−0.946259	+	0.323411i	$0.895170\pi$
$618$	−1.37954	+	3.32324i	−0.0554933	+	0.133680i
$619$	−3.23219	−	2.15968i	−0.129913	−	0.0868049i	0.488916	−	0.872331i	$-0.337392\pi$
$619$	−3.23219	−	2.15968i	−0.129913	−	0.0868049i	−0.618829	+	0.785526i	$0.712392\pi$
$620$	−0.653042	−	0.270499i	−0.0262268	−	0.0108635i
$621$	11.9797	−	17.8392i	0.480727	−	0.715863i
$622$	−4.87547	+	7.29666i	−0.195489	+	0.292569i
$623$	0.199083	+	1.00086i	0.00797609	+	0.0400985i
$624$	2.53574	+	0.00195833i	0.101511	+	7.83961e-5i
$625$	−10.8916	−	10.8916i	−0.435663	−	0.435663i
$626$	−3.92827	+	19.7488i	−0.157005	+	0.789319i
$627$	−0.825288	+	4.13232i	−0.0329588	+	0.165029i
$628$		−	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	$-0.379069\pi$
$631$	32.3983	−	13.4198i	1.28976	−	0.534234i	0.918913	+	0.394461i	$0.129069\pi$
$632$	−29.3071	−	5.82955i	−1.16578	−	0.231887i
$633$	−5.22640	−	26.3814i	−0.207731	−	1.04857i
$634$	−6.85730	+	4.58190i	−0.272338	+	0.181971i
$635$	−7.10635	+	1.41354i	−0.282007	+	0.0560947i
$636$	−9.94222	−	24.0552i	−0.394235	−	0.953850i
$637$	14.1299	−	34.1127i	0.559848	−	1.35159i
$638$	0.876899	−	2.11702i	0.0347168	−	0.0838137i
$639$	3.84253	−	19.1630i	0.152008	−	0.758075i
$640$	6.36785	−	1.26665i	0.251712	−	0.0500685i
$641$	1.85961	−	1.24255i	0.0734500	−	0.0490777i	−0.518303	−	0.855197i	$-0.673436\pi$
$641$	1.85961	−	1.24255i	0.0734500	−	0.0490777i	0.591753	+	0.806119i	$0.298436\pi$
$642$	5.86080	−	1.16108i	0.231307	−	0.0458242i
$643$	−3.58974	−	0.714043i	−0.141565	−	0.0281591i	0.123799	−	0.992307i	$-0.460492\pi$
$643$	−3.58974	−	0.714043i	−0.141565	−	0.0281591i	−0.265364	+	0.964148i	$0.585492\pi$
$644$	−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	$0.811928\pi$
$648$	−22.9564	−	9.59202i	−0.901811	−	0.376810i
$649$	0.224054	−	1.12639i	0.00879488	−	0.0442148i
$650$	13.6165	+	13.6165i	0.534082	+	0.534082i
$651$	0.000173893	−	0.225164i	6.81540e−6	−	0.00882488i
$652$	−4.08173	−	20.5203i	−0.159853	−	0.803635i
$653$	−5.66385	+	8.47655i	−0.221644	+	0.331713i	−0.925581	−	0.378548i	$-0.876423\pi$
$653$	−5.66385	+	8.47655i	−0.221644	+	0.331713i	0.703938	+	0.710262i	$0.251423\pi$
$654$	15.2811	−	10.1934i	0.597537	−	0.398594i
$655$	−7.43383	−	3.07919i	−0.290464	−	0.120314i
$656$	1.83501	+	1.22611i	0.0716449	+	0.0478716i
$657$	19.2977	+	28.9779i	0.752877	+	1.13054i
$658$	−0.907729	−	1.35851i	−0.0353870	−	0.0529604i
$659$	27.6176	−	27.6176i	1.07583	−	1.07583i	0.0789501	−	0.996879i	$-0.474843\pi$
$659$	27.6176	−	27.6176i	1.07583	−	1.07583i	0.996879	−	0.0789501i	$-0.0251568\pi$
$660$	5.74486	−	5.73599i	0.223618	−	0.223273i
$661$	0.783917	+	1.89254i	0.0304909	+	0.0736114i	0.938392	−	0.345574i	$-0.112316\pi$
$661$	0.783917	+	1.89254i	0.0304909	+	0.0736114i	−0.907901	+	0.419185i	$0.862316\pi$
$662$	−3.52074			−0.136838
$663$		0			0
$664$	−7.63870			−0.296439
$665$	−0.0336786	−	0.0813074i	−0.00130600	−	0.00315296i
$666$	−0.956424	−	4.84738i	−0.0370607	−	0.187832i
$667$	−1.80965	+	1.80965i	−0.0700701	+	0.0700701i
$668$	−6.60565	−	9.88606i	−0.255580	−	0.382503i
$669$	−26.6549	−	11.0649i	−1.03054	−	0.427795i
$670$	−3.08651	−	2.06234i	−0.119242	−	0.0796751i
$671$	−43.0448	−	17.8297i	−1.66172	−	0.688309i
$672$	1.08074	+	1.62015i	0.0416904	+	0.0624986i
$673$	9.44730	−	14.1389i	0.364167	−	0.545014i	−0.603462	−	0.797392i	$-0.706213\pi$
$673$	9.44730	−	14.1389i	0.364167	−	0.545014i	0.967629	+	0.252378i	$0.0812126\pi$
$674$	0.946406	+	4.75791i	0.0364542	+	0.183268i
$675$	8.56254	+	20.8080i	0.329572	+	0.800901i
$676$	13.8741	+	13.8741i	0.533621	+	0.533621i
$677$	−4.27498	+	21.4918i	−0.164301	+	0.825995i	0.807441	+	0.589948i	$0.200852\pi$
$677$	−4.27498	+	21.4918i	−0.164301	+	0.825995i	−0.971742	+	0.236047i	$0.924148\pi$
$678$	1.76066	+	0.351632i	0.0676179	+	0.0135043i
$679$		−	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
$683$	35.6104	+	7.08334i	1.36259	+	0.271036i	0.821635	−	0.570014i	$-0.193062\pi$
$683$	35.6104	+	7.08334i	1.36259	+	0.271036i	0.540957	+	0.841050i	$0.318062\pi$
$684$	−1.97916	−	0.823378i	−0.0756750	−	0.0314827i
$685$	8.61730	−	5.75790i	0.329250	−	0.219998i
$686$	2.24124	−	0.445810i	0.0855708	−	0.0170211i
$687$	17.5770	−	7.26474i	0.670605	−	0.277167i
$688$	0.815481	−	1.96874i	0.0310899	−	0.0750577i
$689$	23.5168	−	56.7746i	0.895919	−	2.16294i
$690$	4.54218	−	1.87732i	0.172918	−	0.0714685i
$691$	−2.81905	+	0.560744i	−0.107242	+	0.0213317i	−0.248419	−	0.968653i	$-0.579911\pi$
$691$	−2.81905	+	0.560744i	−0.107242	+	0.0213317i	0.141178	+	0.989984i	$0.454911\pi$
$692$	1.25708	−	0.839952i	0.0477869	−	0.0319302i
$693$	2.38765	+	0.993319i	0.0906991	+	0.0377331i
$694$	−0.0155728	−	0.00309763i	−0.000591136	−	0.000117584i
$695$	−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
$699$	39.8924	+	7.96712i	1.50887	+	0.301344i
$700$	0.213876	−	1.07523i	0.00808375	−	0.0406397i
$701$	3.87452	+	3.87452i	0.146339	+	0.146339i	0.776480	−	0.630142i	$-0.217003\pi$
$701$	3.87452	+	3.87452i	0.146339	+	0.146339i	−0.630142	+	0.776480i	$0.717003\pi$
$702$	−8.79318	−	21.3685i	−0.331877	−	0.806503i
$703$	−0.211116	−	1.06135i	−0.00796239	−	0.0400296i
$704$	10.4951	−	15.7070i	0.395549	−	0.591981i
$705$	−7.85208	−	11.7711i	−0.295726	−	0.443327i
$706$	−9.43364	−	3.90754i	−0.355040	−	0.147062i
$707$	−1.10245	−	0.736637i	−0.0414621	−	0.0277041i
$708$	0.539572	+	0.223986i	0.0202784	+	0.00841793i
$709$	20.8730	+	31.2387i	0.783903	+	1.17319i	0.981227	+	0.192856i	$0.0617749\pi$
$709$	20.8730	+	31.2387i	0.783903	+	1.17319i	−0.197324	+	0.980338i	$0.563225\pi$
$710$	3.16093	−	3.16093i	0.118628	−	0.118628i
$711$	−6.27722	−	31.8144i	−0.235414	−	1.19313i
$712$	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
$717$	16.8185	−	16.7926i	0.628100	−	0.627130i
$718$	−18.8705	+	18.8705i	−0.704242	+	0.704242i
$719$	13.6583	+	20.4411i	0.509370	+	0.762326i	0.993641	−	0.112592i	$-0.0359152\pi$
$719$	13.6583	+	20.4411i	0.509370	+	0.762326i	−0.484271	+	0.874918i	$0.660915\pi$
$720$	0.375634	+	0.564060i	0.0139991	+	0.0210213i
$721$	0.402127	+	0.268692i	0.0149760	+	0.0100066i
$722$	−14.4832	−	5.99913i	−0.539009	−	0.223265i
$723$	−6.16146	+	4.11008i	−0.229147	+	0.152855i
$724$	9.28153	−	13.8908i	0.344945	−	0.516247i
$725$	−0.522810	−	2.62834i	−0.0194167	−	0.0976141i
$726$	0.00953490	−	12.3462i	0.000353873	−	0.458211i
$727$	−26.6720	−	26.6720i	−0.989211	−	0.989211i	0.0107310	−	0.999942i	$-0.496584\pi$
$727$	−26.6720	−	26.6720i	−0.989211	−	0.989211i	−0.999942	+	0.0107310i	$0.996584\pi$
$728$	−0.558331	+	2.80692i	−0.0206931	+	0.104031i
$729$	0.125111	−	26.9997i	0.00463375	−	0.999989i
$730$			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	$-0.739173\pi$
$733$	−17.5613	+	7.27415i	−0.648643	+	0.268677i	0.0340076	+	0.999422i	$0.489173\pi$
$734$	−27.6524	−	5.50041i	−1.02067	−	0.203024i
$735$	9.67984	−	1.91767i	0.357046	−	0.0707343i
$736$	−19.8067	+	13.2344i	−0.730083	+	0.487826i
$737$	23.4314	−	4.66079i	0.863106	−	0.171682i
$738$	3.95389	−	19.7183i	0.145545	−	0.725842i
$739$	−13.8881	+	33.5289i	−0.510884	+	1.23338i	0.432487	+	0.901640i	$0.357636\pi$
$739$	−13.8881	+	33.5289i	−0.510884	+	1.23338i	−0.943370	+	0.331742i	$0.892364\pi$
$740$	−0.797805	+	1.92607i	−0.0293279	+	0.0708038i
$741$	−1.93311	−	4.67716i	−0.0710147	−	0.171820i
$742$	1.85998	−	0.369974i	0.0682822	−	0.0135822i
$743$	−0.148245	+	0.0990543i	−0.00543859	+	0.00363395i	−0.558287	−	0.829648i	$-0.688541\pi$
$743$	−0.148245	+	0.0990543i	−0.00543859	+	0.00363395i	0.552848	+	0.833282i	$0.313541\pi$
$744$	−0.619682	−	3.12797i	−0.0227186	−	0.114677i
$745$	10.1942	+	2.02776i	0.373488	+	0.0742914i
$746$	−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
$750$	−2.17172	+	10.8741i	−0.0792999	+	0.397065i
$751$	−7.41046	+	37.2549i	−0.270412	+	1.35945i	0.571840	+	0.820365i	$0.306230\pi$
$751$	−7.41046	+	37.2549i	−0.270412	+	1.35945i	−0.842251	+	0.539085i	$0.818770\pi$
$752$	1.94852	+	1.94852i	0.0710551	+	0.0710551i
$753$	−16.0971	−	0.0124317i	−0.586610	−	0.000453036i
$754$	0.536892	+	2.69914i	0.0195525	+	0.0982968i
$755$	−0.360348	+	0.539298i	−0.0131144	+	0.0196271i
$756$	−0.733383	+	1.09210i	−0.0266729	+	0.0397193i
$757$	17.7157	+	7.33808i	0.643888	+	0.266707i	0.680641	−	0.732617i	$-0.261701\pi$
$757$	17.7157	+	7.33808i	0.643888	+	0.266707i	−0.0367531	+	0.999324i	$0.511701\pi$
$758$	26.5034	+	17.7090i	0.962647	+	0.643220i
$759$	−12.1272	+	29.2139i	−0.440191	+	1.06040i
$760$	−0.692431	−	1.03630i	−0.0251171	−	0.0375904i
$761$	21.9157	−	21.9157i	0.794443	−	0.794443i	−0.187770	−	0.982213i	$-0.560126\pi$
$761$	21.9157	−	21.9157i	0.794443	−	0.794443i	0.982213	+	0.187770i	$0.0601259\pi$
$762$	−9.08516	−	9.09920i	−0.329121	−	0.329629i
$763$	−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
$768$	18.6113	+	18.6400i	0.671576	+	0.672614i
$769$	13.1164	−	13.1164i	0.472990	−	0.472990i	−0.429891	−	0.902881i	$-0.641448\pi$
$769$	13.1164	−	13.1164i	0.472990	−	0.472990i	0.902881	+	0.429891i	$0.141448\pi$
$770$	0.328609	+	0.491798i	0.0118422	+	0.0177232i
$771$	10.4449	−	25.1612i	0.376163	−	0.906157i
$772$	3.20843	+	2.14380i	0.115474	+	0.0771572i
$773$	37.8763	+	15.6889i	1.36232	+	0.564289i	0.939694	−	0.342017i	$-0.111110\pi$
$773$	37.8763	+	15.6889i	1.36232	+	0.564289i	0.422621	+	0.906306i	$0.361110\pi$
$774$	−19.4184	−	0.0299934i	−0.697979	−	0.00107809i
$775$	−1.60220	+	2.39786i	−0.0575526	+	0.0861336i
$776$	−1.33160	−	6.69439i	−0.0478015	−	0.240314i
$777$	−0.664096		0.000512878i	−0.0238243		1.83994e-5i
$778$	0.447469	+	0.447469i	0.0160425	+	0.0160425i
$779$	0.859312	−	4.32005i	0.0307880	−	0.154782i
$780$	−1.90950	+	9.56109i	−0.0683709	+	0.342342i
$781$			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
$785$	1.89295	+	0.376531i	0.0675623	+	0.0134390i
$786$	−2.77494	−	14.0071i	−0.0989788	−	0.499616i
$787$	−12.5025	+	8.35391i	−0.445667	+	0.297785i	−0.758080	−	0.652161i	$-0.773862\pi$
$787$	−12.5025	+	8.35391i	−0.445667	+	0.297785i	0.312414	+	0.949946i	$0.398862\pi$
$788$	17.2606	−	3.43335i	0.614884	−	0.122308i
$789$	−10.2161	−	24.7179i	−0.363705	−	0.879982i
$790$	2.83834	−	6.85236i	0.100984	−	0.243796i
$791$	0.0923506	−	0.222954i	0.00328361	−	0.00792734i
$792$	35.9084	+	7.20030i	1.27595	+	0.255851i
$793$	54.8808	−	10.9165i	1.94887	−	0.387655i
$794$	−14.0457	+	9.38503i	−0.498463	+	0.333062i
$795$	16.1104	−	3.19163i	0.571378	−	0.113195i
$796$	5.47204	+	1.08846i	0.193951	+	0.0385793i
$797$	−14.9967	+	6.21185i	−0.531211	+	0.220035i	−0.632134	−	0.774859i	$-0.717821\pi$
$797$	−14.9967	+	6.21185i	−0.531211	+	0.220035i	0.100922	+	0.994894i	$0.467821\pi$
$798$	0.0868691	−	0.129792i	0.00307513	−	0.00459458i
$799$		0			0
$800$		−	24.9438i		−	0.881895i
$801$	−11.1069	+	11.0727i	−0.392444	+	0.391234i
$802$	−2.57939	+	12.9675i	−0.0910815	+	0.457898i
$803$	−36.2384	−	36.2384i	−1.27882	−	1.27882i
$804$	−0.00938563	+	12.1529i	−0.000331006	+	0.428600i
$805$	−0.128877	−	0.647910i	−0.00454233	−	0.0228358i
$806$	1.64535	−	2.46245i	0.0579551	−	0.0867360i
$807$	−35.0687	+	23.3930i	−1.23448	+	0.823473i
$808$	−17.3481	−	7.18583i	−0.610305	−	0.252797i
$809$	31.4493	+	21.0138i	1.10570	+	0.738804i	0.967820	−	0.251645i	$-0.0809715\pi$
$809$	31.4493	+	21.0138i	1.10570	+	0.738804i	0.137879	+	0.990449i	$0.455972\pi$
$810$	3.44676	−	5.12410i	0.121107	−	0.180043i
$811$	−19.2151	−	28.7574i	−0.674733	−	1.00981i	−0.997982	−	0.0634956i	$-0.979775\pi$
$811$	−19.2151	−	28.7574i	−0.674733	−	1.00981i	0.323249	−	0.946314i	$-0.395225\pi$
$812$	0.110785	−	0.110785i	0.00388780	−	0.00388780i
$813$	6.89485	−	6.88421i	0.241813	−	0.241440i
$814$	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
$819$	−3.04706	+	0.601207i	−0.106473	+	0.0210079i
$820$	−6.00029	+	6.00029i	−0.209539	+	0.209539i
$821$	−27.9751	−	41.8677i	−0.976339	−	1.46119i	−0.885120	−	0.465363i	$-0.845924\pi$
$821$	−27.9751	−	41.8677i	−0.976339	−	1.46119i	−0.0912190	−	0.995831i	$-0.529076\pi$
$822$	16.9868	+	7.05154i	0.592483	+	0.245951i
$823$	−19.8619	−	13.2713i	−0.692343	−	0.462609i	0.158959	−	0.987285i	$-0.449186\pi$
$823$	−19.8619	−	13.2713i	−0.692343	−	0.462609i	−0.851302	+	0.524676i	$0.824186\pi$
$824$	6.32783	+	2.62107i	0.220440	+	0.0913094i
$825$	−18.3801	−	27.5537i	−0.639912	−	0.959298i
$826$	−0.0236479	+	0.0353916i	−0.000822817	+	0.00123143i
$827$	−1.31023	−	6.58698i	−0.0455612	−	0.229052i	0.951295	−	0.308282i	$-0.0997539\pi$
$827$	−1.31023	−	6.58698i	−0.0455612	−	0.229052i	−0.996856	+	0.0792299i	$0.974754\pi$
$828$	−13.3650	−	8.96007i	−0.464464	−	0.311384i
$829$	−17.6880	−	17.6880i	−0.614331	−	0.614331i	0.329741	−	0.944072i	$-0.393039\pi$
$829$	−17.6880	−	17.6880i	−0.614331	−	0.614331i	−0.944072	+	0.329741i	$0.893039\pi$
$830$	0.369897	−	1.85960i	0.0128393	−	0.0645475i
$831$	−15.0562	−	3.00694i	−0.522292	−	0.104310i
$832$			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
$836$	3.09477	+	0.615587i	0.107035	+	0.0212905i
$837$	2.88176	−	1.91589i	0.0996082	−	0.0662227i
$838$	24.5622	−	16.4119i	0.848485	−	0.566940i
$839$	43.1914	−	8.59130i	1.49113	−	0.296604i	0.618811	−	0.785540i	$-0.287615\pi$
$839$	43.1914	−	8.59130i	1.49113	−	0.296604i	0.872320	+	0.488935i	$0.162615\pi$
$840$	−0.706867	+	0.292154i	−0.0243892	+	0.0100803i
$841$	−10.9513	+	26.4387i	−0.377630	+	0.911679i
$842$	−0.00405180	+	0.00978190i	−0.000139634	+	0.000337107i
$843$	−11.5544	+	4.77555i	−0.397956	+	0.164479i
$844$	−19.7514	+	3.92880i	−0.679871	+	0.135235i
$845$	−10.2939	+	6.87815i	−0.354120	+	0.236616i
$846$	9.64526	−	23.1844i	0.331611	−	0.797095i
$847$	−1.62756	−	0.323743i	−0.0559238	−	0.0111239i
$848$	−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
$852$	−14.3515	−	2.86621i	−0.491674	−	0.0981948i
$853$	6.31373	−	31.7413i	0.216178	−	1.08680i	−0.708401	−	0.705810i	$-0.750583\pi$
$853$	6.31373	−	31.7413i	0.216178	−	1.08680i	0.924579	−	0.380990i	$-0.124417\pi$
$854$	1.22103	+	1.22103i	0.0417829	+	0.0417829i
$855$	0.753177	−	1.12345i	0.0257581	−	0.0384211i
$856$	−2.21874	−	11.1543i	−0.0758349	−	0.381248i
$857$	13.7775	−	20.6196i	0.470632	−	0.704351i	−0.517887	−	0.855449i	$-0.673281\pi$
$857$	13.7775	−	20.6196i	0.470632	−	0.704351i	0.988519	+	0.151099i	$0.0482811\pi$
$858$	18.8751	+	28.2959i	0.644387	+	0.966007i
$859$	−38.7830	−	16.0644i	−1.32326	−	0.548112i	−0.394534	−	0.918881i	$-0.629094\pi$
$859$	−38.7830	−	16.0644i	−1.32326	−	0.548112i	−0.928725	+	0.370770i	$0.879094\pi$
$860$	6.81266	+	4.55207i	0.232310	+	0.155224i
$861$	−2.49653	−	1.03636i	−0.0850816	−	0.0353190i
$862$	−5.52336	−	8.26630i	−0.188127	−	0.281551i
$863$	0.148288	−	0.148288i	0.00504779	−	0.00504779i	−0.704578	−	0.709626i	$-0.748864\pi$
$863$	0.148288	−	0.148288i	0.00504779	−	0.00504779i	0.709626	+	0.704578i	$0.248864\pi$
$864$	−11.5182	+	27.6263i	−0.391859	+	0.939866i
$865$	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
$870$	−0.520474	+	0.519670i	−0.0176457	+	0.0176185i
$871$	−20.2885	+	20.2885i	−0.687450	+	0.687450i
$872$	−19.4257	−	29.0725i	−0.657836	−	0.984521i
$873$	6.16522	−	4.10571i	0.208661	−	0.138957i
$874$	1.58837	+	1.06131i	0.0537274	+	0.0358995i
$875$	1.37699	+	0.570368i	0.0465507	+	0.0192820i
$876$	21.6876	−	14.4669i	0.732755	−	0.488793i
$877$	−4.10835	+	6.14858i	−0.138729	+	0.207623i	−0.894328	−	0.447412i	$-0.852346\pi$
$877$	−4.10835	+	6.14858i	−0.138729	+	0.207623i	0.755599	+	0.655034i	$0.227346\pi$
$878$	4.98111	+	25.0417i	0.168104	+	0.845118i
$879$	−0.0255540	+	33.0885i	−0.000861917	+	1.11605i
$880$	−0.705386	−	0.705386i	−0.0237786	−	0.0237786i
$881$	9.71313	−	48.8312i	0.327244	−	1.64516i	−0.370511	−	0.928828i	$-0.620817\pi$
$881$	9.71313	−	48.8312i	0.327244	−	1.64516i	0.697755	−	0.716337i	$-0.254183\pi$
$882$	12.3638	+	12.4020i	0.416310	+	0.417598i
$883$		−	28.6327i		−	0.963566i	−0.876291	−	0.481783i	$-0.839989\pi$
$883$		−	28.6327i		−	0.963566i	0.876291	−	0.481783i	$-0.160011\pi$
$884$		0			0
$885$	−0.205034	+	0.306342i	−0.00689214	+	0.0102976i
$886$	−31.1758	+	12.9134i	−1.04737	+	0.433835i
$887$	41.9468	+	8.34375i	1.40844	+	0.280156i	0.840007	−	0.542576i	$-0.182551\pi$
$887$	41.9468	+	8.34375i	1.40844	+	0.280156i	0.568430	+	0.822731i	$0.307551\pi$
$888$	−9.22560	+	1.82768i	−0.309591	+	0.0613329i
$889$	−1.43701	+	0.960180i	−0.0481958	+	0.0322034i
$890$	−3.51820	+	0.699813i	−0.117930	+	0.0234578i
$891$	7.63326	+	39.0043i	0.255724	+	1.30669i
$892$	−8.27003	+	19.9656i	−0.276901	+	0.668498i
$893$	2.10466	−	5.08111i	0.0704299	−	0.170033i
$894$	7.04564	+	17.0469i	0.235642	+	0.570134i
$895$	8.25725	−	1.64247i	0.276010	−	0.0549017i
$896$	1.28768	−	0.860397i	0.0430182	−	0.0287439i
$897$	−7.38245	−	37.2645i	−0.246493	−	1.24422i
$898$	−29.9639	−	5.96018i	−0.999907	−	0.198894i
$899$	−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
$903$	−0.511167	+	2.55948i	−0.0170106	+	0.0851740i
$904$	0.666743	−	3.35195i	0.0221756	−	0.111484i
$905$	7.45379	+	7.45379i	0.247772	+	0.247772i
$906$	−1.15105		0.000888946i	−0.0382409		2.95333e-5i
$907$	−1.58718	−	7.97928i	−0.0527013	−	0.264948i	0.945447	−	0.325776i	$-0.105626\pi$
$907$	−1.58718	−	7.97928i	−0.0527013	−	0.264948i	−0.998148	+	0.0608288i	$0.980626\pi$
$908$	13.8697	−	20.7574i	0.460281	−	0.688860i
$909$	0.0314752	−	20.3777i	0.00104396	−	0.675885i
$910$	−0.656291	−	0.271845i	−0.0217558	−	0.00901157i
$911$	2.46522	+	1.64721i	0.0816765	+	0.0545745i	0.595738	−	0.803179i	$-0.296860\pi$
$911$	2.46522	+	1.64721i	0.0816765	+	0.0545745i	−0.514061	+	0.857753i	$0.671860\pi$
$912$	−0.100989	+	0.243278i	−0.00334409	+	0.00805574i
$913$	6.77933	+	10.1460i	0.224363	+	0.335783i
$914$	12.6372	−	12.6372i	0.418002	−	0.418002i
$915$	10.5663	+	10.5826i	0.349311	+	0.349851i
$916$	−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
$921$	−6.10445	−	6.11388i	−0.201148	−	0.201459i
$922$	−3.64477	+	3.64477i	−0.120034	+	0.120034i
$923$	−19.1961	−	28.7290i	−0.631848	−	0.945627i
$924$	0.742418	−	1.78845i	0.0244238	−	0.0588356i
$925$	7.07221	+	4.72550i	0.232533	+	0.155373i
$926$	−28.1151	−	11.6457i	−0.923919	−	0.382700i
$927$	−0.0114807	+	7.43288i	−0.000377077	+	0.244128i
$928$	1.98049	−	2.96401i	0.0650127	−	0.0972984i
$929$	5.49193	+	27.6098i	0.180184	+	0.905849i	0.960034	+	0.279882i	$0.0902954\pi$
$929$	5.49193	+	27.6098i	0.180184	+	0.905849i	−0.779850	+	0.625967i	$0.784705\pi$
$930$	0.791494		0.000611266i	0.0259541		2.00442e-5i
$931$	2.71211	+	2.71211i	0.0888859	+	0.0888859i
$932$	5.94272	−	29.8761i	0.194660	−	0.978624i
$933$	−3.55032	+	17.7769i	−0.116232	+	0.581990i
$934$			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	$-0.416887\pi$
$937$	34.4010	−	14.2493i	1.12383	−	0.465506i	0.865679	+	0.500599i	$0.166887\pi$
$938$	−0.868432	−	0.172742i	−0.0283553	−	0.00564022i
$939$	8.08320	+	40.8017i	0.263785	+	1.33151i
$940$	−8.80971	+	5.88646i	−0.287341	+	0.191995i
$941$	−44.6046	+	8.87241i	−1.45407	+	0.289232i	−0.857979	−	0.513686i	$-0.828280\pi$
$941$	−44.6046	+	8.87241i	−1.45407	+	0.289232i	−0.596090	+	0.802918i	$0.703280\pi$
$942$	1.30829	+	3.16541i	0.0426265	+	0.103135i
$943$	12.6526	−	30.5462i	0.412026	−	0.994720i
$944$	0.0274723	−	0.0663241i	0.000894148	−	0.00215867i
$945$	−0.585569	−	0.588289i	−0.0190486	−	0.0191370i
$946$	28.0348	−	5.57647i	0.911490	−	0.181307i
$947$	13.6752	−	9.13749i	0.444385	−	0.296929i	−0.313173	−	0.949696i	$-0.601392\pi$
$947$	13.6752	−	9.13749i	0.444385	−	0.296929i	0.757558	+	0.652767i	$0.226392\pi$
$948$	−23.8191	+	4.71879i	−0.773608	+	0.153259i
$949$	60.3669	+	12.0077i	1.95959	+	0.389787i
$950$	−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	$-0.0797593\pi$
$954$	20.5774	+	20.6410i	0.666217	+	0.668278i
$955$	2.65643	−	13.3548i	0.0859602	−	0.432151i
$956$	−12.5840	−	12.5840i	−0.406997	−	0.406997i
$957$	0.00365565	−	4.73349i	0.000118170	−	0.153012i
$958$	0.375571	+	1.88812i	0.0121342	+	0.0610025i
$959$	1.37342	−	2.05547i	0.0443502	−	0.0663747i
$960$	−5.04414	+	3.36475i	−0.162799	+	0.108597i
$961$	−28.2305	−	11.6935i	−0.910661	−	0.377208i
$962$	−7.26270	−	4.85278i	−0.234159	−	0.156460i
$963$	10.2726	−	6.84103i	0.331031	−	0.220449i
$964$	3.08119	+	4.61133i	0.0992386	+	0.148521i
$965$	−1.72164	+	1.72164i	−0.0554216	+	0.0554216i
$966$	0.829605	−	0.828324i	0.0266921	−	0.0266509i
$967$	−18.4809	−	44.6169i	−0.594306	−	1.43478i	−0.879307	−	0.476255i	$-0.841994\pi$
$967$	−18.4809	−	44.6169i	−0.594306	−	1.43478i	0.285001	−	0.958527i	$-0.408006\pi$
$968$	−23.5010			−0.755352
$969$		0			0
$970$	1.69419			0.0543972
$971$	−1.27013	−	3.06636i	−0.0407603	−	0.0984041i	0.902188	−	0.431342i	$-0.141960\pi$
$971$	−1.27013	−	3.06636i	−0.0407603	−	0.0984041i	−0.942949	+	0.332938i	$0.891960\pi$
$972$	−20.2175	−	0.0780697i	−0.648477	−	0.00250409i
$973$	−1.64333	+	1.64333i	−0.0526828	+	0.0526828i
$974$	13.0790	+	19.5742i	0.419080	+	0.627197i
$975$	36.7390	+	15.2511i	1.17659	+	0.488425i
$976$	−2.42154	−	1.61802i	−0.0775115	−	0.0517915i
$977$	27.3947	+	11.3473i	0.876434	+	0.363031i	0.775113	−	0.631823i	$-0.217693\pi$
$977$	27.3947	+	11.3473i	0.876434	+	0.363031i	0.101321	+	0.994854i	$0.467693\pi$
$978$	13.0007	+	19.4895i	0.415717	+	0.623206i
$979$	12.8259	−	19.1953i	0.409918	−	0.613486i
$980$	−1.44155	−	7.24717i	−0.0460487	−	0.231502i
$981$	21.1298	−	31.5175i	0.674624	−	1.00628i
$982$	8.01800	+	8.01800i	0.255865	+	0.255865i
$983$	−0.487844	+	2.45256i	−0.0155598	+	0.0782245i	−0.987785	−	0.155823i	$-0.950197\pi$
$983$	−0.487844	+	2.45256i	−0.0155598	+	0.0782245i	0.972225	+	0.234047i	$0.0751971\pi$
$984$	−37.5397	−	7.49726i	−1.19672	−	0.239004i
$985$			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
$989$	−31.3111	−	6.22816i	−0.995635	−	0.198044i
$990$	−3.49170	+	8.39302i	−0.110973	+	0.266748i
$991$	31.7268	−	21.1992i	1.00784	−	0.673414i	0.0620049	−	0.998076i	$-0.480251\pi$
$991$	31.7268	−	21.1992i	1.00784	−	0.673414i	0.945830	+	0.324662i	$0.105251\pi$
$992$	−3.76250	+	0.748407i	−0.119459	+	0.0237620i
$993$	−6.72140	+	2.77802i	−0.213297	+	0.0881577i
$994$	0.408047	−	0.985113i	0.0129425	−	0.0312459i
$995$	−1.34718	+	3.25239i	−0.0427086	+	0.103108i
$996$	−5.73665	+	2.37101i	−0.181773	+	0.0751284i
$997$	−43.8361	+	8.71954i	−1.38830	+	0.276151i	−0.831975	−	0.554813i	$-0.812790\pi$
$997$	−43.8361	+	8.71954i	−1.38830	+	0.276151i	−0.556327	+	0.830963i	$0.687790\pi$
$998$	−10.6200	+	7.09608i	−0.336171	+	0.224622i
$999$	−5.65069	−	8.49942i	−0.178780	−	0.268910i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.2.i.a.29.2	✓	32	51.8	odd	8
51.2.i.a.29.3	yes	32	17.8	even	8
51.2.i.a.44.2	yes	32	17.12	odd	16
51.2.i.a.44.3	yes	32	51.29	even	16
816.2.cj.c.401.1		32	68.63	even	16
816.2.cj.c.401.2		32	204.131	odd	16
816.2.cj.c.641.1		32	204.59	even	8
816.2.cj.c.641.2		32	68.59	odd	8
867.2.i.b.65.2		32	3.2	odd	2	inner
867.2.i.b.65.3		32	1.1	even	1	trivial
867.2.i.b.827.2		32	17.11	odd	16	inner
867.2.i.b.827.3		32	51.11	even	16	inner
867.2.i.c.158.2		32	17.2	even	8
867.2.i.c.158.3		32	51.2	odd	8
867.2.i.c.653.2		32	51.14	even	16
867.2.i.c.653.3		32	17.14	odd	16
867.2.i.d.158.2		32	17.15	even	8
867.2.i.d.158.3		32	51.32	odd	8
867.2.i.d.653.2		32	51.20	even	16
867.2.i.d.653.3		32	17.3	odd	16
867.2.i.f.224.2		32	17.13	even	4
867.2.i.f.224.3		32	51.47	odd	4
867.2.i.f.329.2		32	51.44	even	16
867.2.i.f.329.3		32	17.10	odd	16
867.2.i.g.224.2		32	17.4	even	4
867.2.i.g.224.3		32	51.38	odd	4
867.2.i.g.329.2		32	51.41	even	16
867.2.i.g.329.3		32	17.7	odd	16
867.2.i.h.131.2		32	51.26	odd	8
867.2.i.h.131.3		32	17.9	even	8
867.2.i.h.503.2		32	17.5	odd	16
867.2.i.h.503.3		32	51.5	even	16
867.2.i.i.65.2		32	51.50	odd	2
867.2.i.i.65.3		32	17.16	even	2
867.2.i.i.827.2		32	17.6	odd	16
867.2.i.i.827.3		32	51.23	even	16

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} +(1.22380 + 1.22569i) q^{3} +(0.917091 - 0.917091i) q^{4} +(0.454651 + 0.680434i) q^{5} +(-0.556799 + 1.34130i) q^{6} +(0.162303 + 0.108447i) q^{7} +(2.55399 + 1.05790i) q^{8} +(-0.00463376 + 3.00000i) q^{9} +(-0.381213 + 0.570525i) q^{10} +(-0.861524 - 4.33117i) q^{11} +(2.24641 + 0.00173489i) q^{12} +(3.75023 + 3.75023i) q^{13} +(-0.0319304 + 0.160525i) q^{14} +(-0.277599 + 1.38998i) q^{15} -0.276039i q^{16} +(-2.32543 + 0.959018i) q^{18} +(-0.508991 + 0.210831i) q^{19} +(1.04098 + 0.207063i) q^{20} +(0.0657033 + 0.331651i) q^{21} +(3.07870 - 2.05712i) q^{22} +(-4.05597 + 0.806783i) q^{23} +(1.82891 + 4.42505i) q^{24} +(1.65713 - 4.00068i) q^{25} +(-1.70177 + 4.10844i) q^{26} +(-3.68274 + 3.66571i) q^{27} +(0.248303 - 0.0493905i) q^{28} +(0.514560 - 0.343818i) q^{29} +(-1.16581 + 0.230959i) q^{30} +(-0.653180 - 0.129926i) q^{31} +(5.32181 - 2.20436i) q^{32} +(4.25434 - 6.35644i) q^{33} +0.159742i q^{35} +(2.74702 + 2.75552i) q^{36} +(-0.383200 + 1.92648i) q^{37} +(-0.326640 - 0.326640i) q^{38} +(-0.00709440 + 9.18614i) q^{39} +(0.441345 + 2.21879i) q^{40} +(-4.44180 + 6.64762i) q^{41} +(-0.235831 + 0.157314i) q^{42} +(7.13212 + 2.95422i) q^{43} +(-4.76218 - 3.18198i) q^{44} +(-2.04341 + 1.36080i) q^{45} +(-1.92641 - 2.88308i) q^{46} +(-7.05884 + 7.05884i) q^{47} +(0.338339 - 0.337817i) q^{48} +(-2.66420 - 6.43195i) q^{49} +3.63084 q^{50} +6.87860 q^{52} +(-4.43410 - 10.7049i) q^{53} +(-4.02132 - 1.67661i) q^{54} +(2.55538 - 2.55538i) q^{55} +(0.299794 + 0.448673i) q^{56} +(-0.881316 - 0.365851i) q^{57} +(0.431445 + 0.288282i) q^{58} +(0.240270 + 0.0995233i) q^{59} +(1.02015 + 1.52932i) q^{60} +(5.86155 - 8.77243i) q^{61} +(-0.108939 - 0.547674i) q^{62} +(-0.326094 + 0.486406i) q^{63} +(3.02483 + 3.02483i) q^{64} +(-0.846735 + 4.25683i) q^{65} +(6.28910 + 1.25603i) q^{66} +5.40994i q^{67} +(-5.95256 - 3.98403i) q^{69} +(-0.123744 + 0.0512564i) q^{70} +(-6.38963 - 1.27098i) q^{71} +(-3.18552 + 7.65705i) q^{72} +(9.64936 - 6.44749i) q^{73} +(-1.61530 + 0.321303i) q^{74} +(6.93159 - 2.86489i) q^{75} +(-0.273440 + 0.660143i) q^{76} +(0.329876 - 0.796392i) q^{77} +(-7.11830 + 2.94206i) q^{78} +(-10.6016 + 2.10878i) q^{79} +(0.187826 - 0.125502i) q^{80} +(-8.99996 - 0.0278025i) q^{81} +(-6.57481 - 1.30781i) q^{82} +(-2.55289 + 1.05744i) q^{83} +(0.364410 + 0.243898i) q^{84} +6.47280i q^{86} +(1.05113 + 0.209927i) q^{87} +(2.38161 - 11.9732i) q^{88} +(3.69661 + 3.69661i) q^{89} +(-1.70981 - 1.14628i) q^{90} +(0.201971 + 1.01538i) q^{91} +(-2.97980 + 4.45959i) q^{92} +(-0.640112 - 0.959599i) q^{93} +(-7.73308 - 3.20315i) q^{94} +(-0.374870 - 0.250480i) q^{95} +(9.21469 + 3.82519i) q^{96} +(-1.37174 - 2.05296i) q^{97} +(4.12764 - 4.12764i) q^{98} +(12.9975 - 2.56450i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 8 q^{3} + 16 q^{4} + 16 q^{6} - 24 q^{9} - 32 q^{10} - 40 q^{12} + 16 q^{13} - 16 q^{15} + 16 q^{18} - 32 q^{19} - 16 q^{21} + 32 q^{22} - 16 q^{24} + 16 q^{27} - 32 q^{28} + 8 q^{30} + 24 q^{36}+ \cdots + 16 q^{99}+O(q^{100}) \) 32 * q - 8 * q^3 + 16 * q^4 + 16 * q^6 - 24 * q^9 - 32 * q^10 - 40 * q^12 + 16 * q^13 - 16 * q^15 + 16 * q^18 - 32 * q^19 - 16 * q^21 + 32 * q^22 - 16 * q^24 + 16 * q^27 - 32 * q^28 + 8 * q^30 + 24 * q^36 + 96 * q^37 - 48 * q^39 - 80 * q^40 + 24 * q^42 + 32 * q^43 + 40 * q^45 + 64 * q^46 - 48 * q^48 + 64 * q^49 - 96 * q^52 - 48 * q^54 + 48 * q^55 + 8 * q^57 - 48 * q^60 + 64 * q^61 - 16 * q^64 - 120 * q^66 + 80 * q^69 - 64 * q^72 + 144 * q^73 - 8 * q^75 - 32 * q^76 + 40 * q^78 - 64 * q^79 - 48 * q^81 + 32 * q^82 + 56 * q^87 - 32 * q^88 - 24 * q^90 - 48 * q^91 + 56 * q^93 + 48 * q^94 + 72 * q^96 + 32 * q^97 + 16 * q^99

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