LMFDB - Embedded newform 720.2.cf.a.11.28

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [720,2,Mod(11,720)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(720, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 3, 2, 0]))

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

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

chi := DirichletCharacter("720.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 720 = 2^{4} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	720.cf (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.74922894553$
Analytic rank:	$0$
Dimension:	$384$
Relative dimension:	$96$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			11.28
Character	$\chi$	$=$	720.11
Dual form			720.2.cf.a.131.28

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.887969 - 1.10069i) q^{2} +(-1.65828 + 0.500091i) q^{3} +(-0.423021 + 1.95475i) q^{4} +(-0.965926 - 0.258819i) q^{5} +(2.02295 + 1.38119i) q^{6} +(0.167388 - 0.289924i) q^{7} +(2.52720 - 1.27015i) q^{8} +(2.49982 - 1.65859i) q^{9} +O(q^{10})$	\(q+(-0.887969 - 1.10069i) q^{2} +(-1.65828 + 0.500091i) q^{3} +(-0.423021 + 1.95475i) q^{4} +(-0.965926 - 0.258819i) q^{5} +(2.02295 + 1.38119i) q^{6} +(0.167388 - 0.289924i) q^{7} +(2.52720 - 1.27015i) q^{8} +(2.49982 - 1.65859i) q^{9} +(0.572834 + 1.29300i) q^{10} +(1.91715 - 0.513699i) q^{11} +(-0.276066 - 3.45308i) q^{12} +(-5.28283 - 1.41553i) q^{13} +(-0.467750 + 0.0732022i) q^{14} +(1.73121 - 0.0538554i) q^{15} +(-3.64211 - 1.65380i) q^{16} +7.27766i q^{17} +(-4.04535 - 1.27874i) q^{18} +(-4.21365 - 4.21365i) q^{19} +(0.914533 - 1.77866i) q^{20} +(-0.132588 + 0.564485i) q^{21} +(-2.26779 - 1.65403i) q^{22} +(-0.951548 + 0.549377i) q^{23} +(-3.55562 + 3.37009i) q^{24} +(0.866025 + 0.500000i) q^{25} +(3.13293 + 7.07168i) q^{26} +(-3.31596 + 4.00055i) q^{27} +(0.495920 + 0.449845i) q^{28} +(9.15214 - 2.45231i) q^{29} +(-1.59654 - 1.85770i) q^{30} +(2.90498 - 1.67719i) q^{31} +(1.41376 + 5.47734i) q^{32} +(-2.92229 + 1.81061i) q^{33} +(8.01043 - 6.46234i) q^{34} +(-0.236722 + 0.236722i) q^{35} +(2.18465 + 5.58814i) q^{36} +(3.53467 + 3.53467i) q^{37} +(-0.896314 + 8.37949i) q^{38} +(9.46832 - 0.294545i) q^{39} +(-2.76982 + 0.572781i) q^{40} +(5.26639 + 9.12165i) q^{41} +(0.739055 - 0.355308i) q^{42} +(0.369014 + 1.37718i) q^{43} +(0.193160 + 3.96486i) q^{44} +(-2.84391 + 0.955072i) q^{45} +(1.44964 + 0.559526i) q^{46} +(-0.299135 + 0.518117i) q^{47} +(6.86670 + 0.921085i) q^{48} +(3.44396 + 5.96512i) q^{49} +(-0.218661 - 1.39721i) q^{50} +(-3.63950 - 12.0684i) q^{51} +(5.00175 - 9.72781i) q^{52} +(6.50107 - 6.50107i) q^{53} +(7.34782 + 0.0974717i) q^{54} -1.98478 q^{55} +(0.0547757 - 0.945301i) q^{56} +(9.09463 + 4.88022i) q^{57} +(-10.8260 - 7.89606i) q^{58} +(-0.848686 + 3.16734i) q^{59} +(-0.627065 + 3.40687i) q^{60} +(3.20249 + 11.9518i) q^{61} +(-4.42559 - 1.70817i) q^{62} +(-0.0624257 - 1.00238i) q^{63} +(4.77345 - 6.41982i) q^{64} +(4.73645 + 2.73459i) q^{65} +(4.58781 + 1.60875i) q^{66} +(-1.10610 + 4.12803i) q^{67} +(-14.2260 - 3.07860i) q^{68} +(1.30320 - 1.38688i) q^{69} +(0.470758 + 0.0503547i) q^{70} +11.4257i q^{71} +(4.21088 - 7.36671i) q^{72} +7.36140i q^{73} +(0.751884 - 7.02924i) q^{74} +(-1.68616 - 0.396051i) q^{75} +(10.0191 - 6.45417i) q^{76} +(0.171974 - 0.641814i) q^{77} +(-8.73178 - 10.1601i) q^{78} +(-9.23438 - 5.33147i) q^{79} +(3.08997 + 2.54009i) q^{80} +(3.49817 - 8.29233i) q^{81} +(5.36369 - 13.8964i) q^{82} +(-1.90977 - 7.12734i) q^{83} +(-1.04734 - 0.497965i) q^{84} +(1.88360 - 7.02968i) q^{85} +(1.18817 - 1.62906i) q^{86} +(-13.9505 + 8.64353i) q^{87} +(4.19255 - 3.73328i) q^{88} -5.17730 q^{89} +(3.57654 + 2.28218i) q^{90} +(-1.29467 + 1.29467i) q^{91} +(-0.671370 - 2.09244i) q^{92} +(-3.97853 + 4.23401i) q^{93} +(0.835907 - 0.130818i) q^{94} +(2.97950 + 5.16064i) q^{95} +(-5.08360 - 8.37598i) q^{96} +(0.513631 - 0.889636i) q^{97} +(3.50759 - 9.08757i) q^{98} +(3.94051 - 4.46392i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 384 q - 12 q^{6}+O(q^{10}) $ 384 * q - 12 * q^6	$ 384 q - 12 q^{6} + 24 q^{12} + 20 q^{18} - 24 q^{24} + 24 q^{27} - 12 q^{36} + 48 q^{39} - 80 q^{42} + 24 q^{46} - 40 q^{48} - 192 q^{49} + 40 q^{51} + 12 q^{54} - 36 q^{58} + 72 q^{59} - 28 q^{60} + 72 q^{64} - 72 q^{66} - 156 q^{68} - 112 q^{72} - 168 q^{74} + 12 q^{76} - 116 q^{78} + 72 q^{82} - 120 q^{83} - 116 q^{84} - 36 q^{90} + 48 q^{93} + 20 q^{96} - 32 q^{99}+O(q^{100}) $ 384 * q - 12 * q^6 + 24 * q^12 + 20 * q^18 - 24 * q^24 + 24 * q^27 - 12 * q^36 + 48 * q^39 - 80 * q^42 + 24 * q^46 - 40 * q^48 - 192 * q^49 + 40 * q^51 + 12 * q^54 - 36 * q^58 + 72 * q^59 - 28 * q^60 + 72 * q^64 - 72 * q^66 - 156 * q^68 - 112 * q^72 - 168 * q^74 + 12 * q^76 - 116 * q^78 + 72 * q^82 - 120 * q^83 - 116 * q^84 - 36 * q^90 + 48 * q^93 + 20 * q^96 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/720\mathbb{Z}\right)^\times$.

$n$	$181$	$271$	$577$	$641$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.887969	−	1.10069i	−0.627889	−	0.778303i
$2$	−0.887969	−	1.10069i	−0.627889	−	0.778303i
$3$	−1.65828	+	0.500091i	−0.957411	+	0.288728i
$3$	−1.65828	+	0.500091i	−0.957411	+	0.288728i
$4$	−0.423021	+	1.95475i	−0.211510	+	0.977376i
$5$	−0.965926	−	0.258819i	−0.431975	−	0.115747i
$5$	−0.965926	−	0.258819i	−0.431975	−	0.115747i
$6$	2.02295	+	1.38119i	0.825866	+	0.563867i
$7$	0.167388	−	0.289924i	0.0632665	−	0.109581i	−0.832657	−	0.553789i	$-0.813182\pi$
$7$	0.167388	−	0.289924i	0.0632665	−	0.109581i	0.895924	+	0.444208i	$0.146515\pi$
$8$	2.52720	−	1.27015i	0.893499	−	0.449065i
$9$	2.49982	−	1.65859i	0.833272	−	0.552863i
$10$	0.572834	+	1.29300i	0.181146	+	0.408884i
$11$	1.91715	−	0.513699i	0.578043	−	0.154886i	0.0420601	−	0.999115i	$-0.486608\pi$
$11$	1.91715	−	0.513699i	0.578043	−	0.154886i	0.535983	+	0.844229i	$0.319941\pi$
$12$	−0.276066	−	3.45308i	−0.0796933	−	0.996819i
$13$	−5.28283	−	1.41553i	−1.46519	−	0.392597i	−0.563912	−	0.825835i	$-0.690704\pi$
$13$	−5.28283	−	1.41553i	−1.46519	−	0.392597i	−0.901280	+	0.433238i	$0.857371\pi$
$14$	−0.467750	+	0.0732022i	−0.125011	+	0.0195641i
$15$	1.73121	−	0.0538554i	0.446997	−	0.0139054i
$16$	−3.64211	−	1.65380i	−0.910527	−	0.413450i
$17$			7.27766i			1.76509i	0.470225	+	0.882546i	$0.344173\pi$
$17$			7.27766i			1.76509i	−0.470225	+	0.882546i	$0.655827\pi$
$18$	−4.04535	−	1.27874i	−0.953497	−	0.301402i
$19$	−4.21365	−	4.21365i	−0.966677	−	0.966677i	0.0327856	−	0.999462i	$-0.489562\pi$
$19$	−4.21365	−	4.21365i	−0.966677	−	0.966677i	−0.999462	+	0.0327856i	$0.989562\pi$
$20$	0.914533	−	1.77866i	0.204496	−	0.397720i
$21$	−0.132588	+	0.564485i	−0.0289330	+	0.123181i
$22$	−2.26779	−	1.65403i	−0.483495	−	0.352641i
$23$	−0.951548	+	0.549377i	−0.198412	+	0.114553i	−0.595914	−	0.803048i	$-0.703210\pi$
$23$	−0.951548	+	0.549377i	−0.198412	+	0.114553i	0.397503	+	0.917601i	$0.369877\pi$
$24$	−3.55562	+	3.37009i	−0.725789	+	0.687918i
$25$	0.866025	+	0.500000i	0.173205	+	0.100000i
$26$	3.13293	+	7.07168i	0.614419	+	1.38687i
$27$	−3.31596	+	4.00055i	−0.638158	+	0.769906i
$28$	0.495920	+	0.449845i	0.0937202	+	0.0850127i
$29$	9.15214	−	2.45231i	1.69951	−	0.455382i	0.726694	−	0.686962i	$-0.241056\pi$
$29$	9.15214	−	2.45231i	1.69951	−	0.455382i	0.972816	+	0.231580i	$0.0743894\pi$
$30$	−1.59654	−	1.85770i	−0.291487	−	0.339168i
$31$	2.90498	−	1.67719i	0.521749	−	0.301232i	−0.215901	−	0.976415i	$-0.569269\pi$
$31$	2.90498	−	1.67719i	0.521749	−	0.301232i	0.737650	+	0.675183i	$0.235936\pi$
$32$	1.41376	+	5.47734i	0.249921	+	0.968266i
$33$	−2.92229	+	1.81061i	−0.508705	+	0.315187i
$34$	8.01043	−	6.46234i	1.37378	−	1.10828i
$35$	−0.236722	+	0.236722i	−0.0400133	+	0.0400133i
$36$	2.18465	+	5.58814i	0.364109	+	0.931356i
$37$	3.53467	+	3.53467i	0.581096	+	0.581096i	0.935204	−	0.354108i	$-0.115216\pi$
$37$	3.53467	+	3.53467i	0.581096	+	0.581096i	−0.354108	+	0.935204i	$0.615216\pi$
$38$	−0.896314	+	8.37949i	−0.145401	+	1.35933i
$39$	9.46832	−	0.294545i	1.51615	−	0.0471650i
$40$	−2.76982	+	0.572781i	−0.437948	+	0.0905646i
$41$	5.26639	+	9.12165i	0.822472	+	1.42456i	0.903836	+	0.427879i	$0.140739\pi$
$41$	5.26639	+	9.12165i	0.822472	+	1.42456i	−0.0813644	+	0.996684i	$0.525928\pi$
$42$	0.739055	−	0.355308i	0.114039	−	0.0548252i
$43$	0.369014	+	1.37718i	0.0562741	+	0.210018i	0.988338	−	0.152276i	$-0.0486603\pi$
$43$	0.369014	+	1.37718i	0.0562741	+	0.210018i	−0.932064	+	0.362294i	$0.881994\pi$
$44$	0.193160	+	3.96486i	0.0291199	+	0.597725i
$45$	−2.84391	+	0.955072i	−0.423945	+	0.142374i
$46$	1.44964	+	0.559526i	0.213737	+	0.0824977i
$47$	−0.299135	+	0.518117i	−0.0436333	+	0.0755751i	−0.887017	−	0.461736i	$-0.847227\pi$
$47$	−0.299135	+	0.518117i	−0.0436333	+	0.0755751i	0.843384	+	0.537311i	$0.180560\pi$
$48$	6.86670	+	0.921085i	0.991123	+	0.132947i
$49$	3.44396	+	5.96512i	0.491995	+	0.852160i
$50$	−0.218661	−	1.39721i	−0.0309233	−	0.197595i
$51$	−3.63950	−	12.0684i	−0.509631	−	1.68992i
$52$	5.00175	−	9.72781i	0.693618	−	1.34900i
$53$	6.50107	−	6.50107i	0.892991	−	0.892991i	−0.101813	−	0.994804i	$-0.532464\pi$
$53$	6.50107	−	6.50107i	0.892991	−	0.892991i	0.994804	+	0.101813i	$0.0324643\pi$
$54$	7.34782	+	0.0974717i	0.999912	+	0.0132642i
$55$	−1.98478			−0.267628
$56$	0.0547757	−	0.945301i	0.00731971	−	0.126321i
$57$	9.09463	+	4.88022i	1.20461	+	0.646401i
$58$	−10.8260	−	7.89606i	−1.42153	−	1.03680i
$59$	−0.848686	+	3.16734i	−0.110490	+	0.412352i	−0.998910	−	0.0466781i	$-0.985136\pi$
$59$	−0.848686	+	3.16734i	−0.110490	+	0.412352i	0.888420	+	0.459031i	$0.151803\pi$
$60$	−0.627065	+	3.40687i	−0.0809537	+	0.439826i
$61$	3.20249	+	11.9518i	0.410037	+	1.53028i	0.794574	+	0.607168i	$0.207694\pi$
$61$	3.20249	+	11.9518i	0.410037	+	1.53028i	−0.384537	+	0.923110i	$0.625639\pi$
$62$	−4.42559	−	1.70817i	−0.562050	−	0.216938i
$63$	−0.0624257	−	1.00238i	−0.00786489	−	0.126288i
$64$	4.77345	−	6.41982i	0.596682	−	0.802478i
$65$	4.73645	+	2.73459i	0.587484	+	0.339184i
$66$	4.58781	+	1.60875i	0.564721	+	0.198024i
$67$	−1.10610	+	4.12803i	−0.135132	+	0.504320i	0.864865	+	0.502004i	$0.167404\pi$
$67$	−1.10610	+	4.12803i	−0.135132	+	0.504320i	−0.999997	+	0.00231557i	$0.999263\pi$
$68$	−14.2260	−	3.07860i	−1.72516	−	0.373335i
$69$	1.30320	−	1.38688i	0.156887	−	0.166961i
$70$	0.470758	+	0.0503547i	0.0562663	+	0.00601854i
$71$			11.4257i			1.35598i	0.735069	+	0.677992i	$0.237150\pi$
$71$			11.4257i			1.35598i	−0.735069	+	0.677992i	$0.762850\pi$
$72$	4.21088	−	7.36671i	0.496257	−	0.868176i
$73$			7.36140i			0.861586i	0.902451	+	0.430793i	$0.141766\pi$
$73$			7.36140i			0.861586i	−0.902451	+	0.430793i	$0.858234\pi$
$74$	0.751884	−	7.02924i	0.0874047	−	0.817133i
$75$	−1.68616	−	0.396051i	−0.194701	−	0.0457320i
$76$	10.0191	−	6.45417i	1.14927	−	0.740344i
$77$	0.171974	−	0.641814i	0.0195982	−	0.0731415i
$78$	−8.73178	−	10.1601i	−0.988680	−	1.15041i
$79$	−9.23438	−	5.33147i	−1.03895	−	0.599837i	−0.119413	−	0.992845i	$-0.538101\pi$
$79$	−9.23438	−	5.33147i	−1.03895	−	0.599837i	−0.919535	+	0.393007i	$0.871435\pi$
$80$	3.08997	+	2.54009i	0.345469	+	0.283991i
$81$	3.49817	−	8.29233i	0.388686	−	0.921370i
$82$	5.36369	−	13.8964i	0.592320	−	1.53460i
$83$	−1.90977	−	7.12734i	−0.209624	−	0.782327i	−0.987990	−	0.154517i	$-0.950618\pi$
$83$	−1.90977	−	7.12734i	−0.209624	−	0.782327i	0.778366	−	0.627811i	$-0.216049\pi$
$84$	−1.04734	−	0.497965i	−0.114274	−	0.0543325i
$85$	1.88360	−	7.02968i	0.204305	−	0.762476i
$86$	1.18817	−	1.62906i	0.128124	−	0.175666i
$87$	−13.9505	+	8.64353i	−1.49565	+	0.926684i
$88$	4.19255	−	3.73328i	0.446927	−	0.397969i
$89$	−5.17730			−0.548793			−0.274396	−	0.961617i	$-0.588478\pi$
$89$	−5.17730			−0.548793			−0.274396	+	0.961617i	$0.588478\pi$
$90$	3.57654	+	2.28218i	0.377001	+	0.240563i
$91$	−1.29467	+	1.29467i	−0.135719	+	0.135719i
$92$	−0.671370	−	2.09244i	−0.0699952	−	0.218152i
$93$	−3.97853	+	4.23401i	−0.412554	+	0.439046i
$94$	0.835907	−	0.130818i	0.0862172	−	0.0134929i
$95$	2.97950	+	5.16064i	0.305690	+	0.529471i
$96$	−5.08360	−	8.37598i	−0.518842	−	0.854870i
$97$	0.513631	−	0.889636i	0.0521514	−	0.0903288i	−0.838771	−	0.544484i	$-0.816726\pi$
$97$	0.513631	−	0.889636i	0.0521514	−	0.0903288i	0.890923	+	0.454155i	$0.150059\pi$
$98$	3.50759	−	9.08757i	0.354320	−	0.917983i
$99$	3.94051	−	4.46392i	0.396036	−	0.448640i
$100$	−1.34372	+	1.48135i	−0.134372	+	0.148135i
$101$	0.647879	+	2.41792i	0.0644664	+	0.240592i	0.990639	−	0.136508i	$-0.0435880\pi$
$101$	0.647879	+	2.41792i	0.0644664	+	0.240592i	−0.926173	+	0.377100i	$0.876921\pi$
$102$	−10.0518	+	14.7224i	−0.995277	+	1.45773i
$103$	7.12362	+	12.3385i	0.701911	+	1.21575i	0.967795	+	0.251740i	$0.0810029\pi$
$103$	7.12362	+	12.3385i	0.701911	+	1.21575i	−0.265884	+	0.964005i	$0.585664\pi$
$104$	−15.1487	+	3.13264i	−1.48545	+	0.307181i
$105$	0.274170	−	0.510935i	0.0267562	−	0.0498621i
$106$	−12.9284	−	1.38289i	−1.25572	−	0.134318i
$107$	12.4564	+	12.4564i	1.20420	+	1.20420i	0.972876	+	0.231328i	$0.0743072\pi$
$107$	12.4564	+	12.4564i	1.20420	+	1.20420i	0.231328	+	0.972876i	$0.425693\pi$
$108$	−6.41736	−	8.17420i	−0.617510	−	0.786563i
$109$	3.29577	−	3.29577i	0.315678	−	0.315678i	−0.531427	−	0.847104i	$-0.678344\pi$
$109$	3.29577	−	3.29577i	0.315678	−	0.315678i	0.847104	+	0.531427i	$0.178344\pi$
$110$	1.76242	+	2.18462i	0.168041	+	0.208295i
$111$	−7.62915	−	4.09383i	−0.724127	−	0.388569i
$112$	−1.08912	+	0.779108i	−0.102912	+	0.0736188i
$113$	11.3961	−	6.57951i	1.07205	−	0.618949i	0.143309	−	0.989678i	$-0.454226\pi$
$113$	11.3961	−	6.57951i	1.07205	−	0.618949i	0.928741	+	0.370729i	$0.120892\pi$
$114$	−2.70417	−	14.3438i	−0.253269	−	1.34342i
$115$	1.06131	−	0.284378i	0.0989680	−	0.0265184i
$116$	0.922110	+	18.9275i	0.0856158	+	1.75738i
$117$	−15.5539	+	5.22347i	−1.43796	+	0.482910i
$118$	4.23985	−	1.87836i	0.390310	−	0.172917i
$119$	2.10997	+	1.21819i	0.193420	+	0.111671i
$120$	4.30671	−	2.33500i	0.393147	−	0.213155i
$121$	−6.11470	+	3.53032i	−0.555882	+	0.320938i
$122$	10.3115	−	14.1378i	0.933562	−	1.27998i
$123$	−13.2948	−	12.4926i	−1.19875	−	1.12642i
$124$	2.04962	+	6.38799i	0.184061	+	0.573658i
$125$	−0.707107	−	0.707107i	−0.0632456	−	0.0632456i
$126$	−1.04788	+	0.958797i	−0.0933523	+	0.0854164i
$127$		−	8.82802i		−	0.783360i	−0.920102	−	0.391680i	$-0.871894\pi$
$127$		−	8.82802i		−	0.783360i	0.920102	−	0.391680i	$-0.128106\pi$
$128$	−11.3049	+	0.446531i	−0.999221	+	0.0394681i
$129$	−1.30065	−	2.09922i	−0.114516	−	0.184826i
$130$	−1.19590	−	7.64158i	−0.104887	−	0.670211i
$131$	6.76816	+	1.81352i	0.591337	+	0.158448i	0.542064	−	0.840337i	$-0.317643\pi$
$131$	6.76816	+	1.81352i	0.591337	+	0.158448i	0.0492728	+	0.998785i	$0.484310\pi$
$132$	−2.30311	−	6.47827i	−0.200460	−	0.563861i
$133$	−1.92695	+	0.516324i	−0.167088	+	0.0447710i
$134$	5.52586	−	2.44809i	0.477361	−	0.211483i
$135$	4.23839	−	3.00600i	0.364783	−	0.258715i
$136$	9.24370	+	18.3921i	0.792641	+	1.57711i
$137$	−1.93108	+	3.34473i	−0.164984	+	0.285760i	−0.936649	−	0.350268i	$-0.886090\pi$
$137$	−1.93108	+	3.34473i	−0.164984	+	0.285760i	0.771666	+	0.636028i	$0.219424\pi$
$138$	−2.68373	−	0.202903i	−0.228454	−	0.0172723i
$139$	4.75217	+	1.27334i	0.403074	+	0.108003i	0.454660	−	0.890665i	$-0.349761\pi$
$139$	4.75217	+	1.27334i	0.403074	+	0.108003i	−0.0515860	+	0.998669i	$0.516428\pi$
$140$	−0.362594	−	0.562870i	−0.0306448	−	0.0475712i
$141$	0.236945	−	1.00878i	0.0199544	−	0.0849546i
$142$	12.5761	−	10.1457i	1.05537	−	0.851408i
$143$	−10.8551			−0.907751
$144$	−11.8476	+	1.90656i	−0.987298	+	0.158880i
$145$	−9.47499			−0.786855
$146$	8.10259	−	6.53669i	0.670575	−	0.540981i
$147$	−8.69418	−	8.16957i	−0.717084	−	0.673815i
$148$	−8.40464	+	5.41416i	−0.690857	+	0.445041i
$149$	−1.55367	−	0.416305i	−0.127282	−	0.0341050i	0.194616	−	0.980880i	$-0.437654\pi$
$149$	−1.55367	−	0.416305i	−0.127282	−	0.0341050i	−0.321897	+	0.946775i	$0.604321\pi$
$150$	1.06133	+	2.20762i	0.0866575	+	0.180251i
$151$	8.52872	−	14.7722i	0.694057	−	1.20214i	−0.276440	−	0.961031i	$-0.589155\pi$
$151$	8.52872	−	14.7722i	0.694057	−	1.20214i	0.970497	−	0.241111i	$-0.0775119\pi$
$152$	−16.0007	−	5.29677i	−1.29783	−	0.429625i
$153$	12.0706	+	18.1928i	0.975854	+	1.47080i
$154$	−0.859143	+	0.380622i	−0.0692318	+	0.0306714i
$155$	−3.24008	+	0.868176i	−0.260249	+	0.0697336i
$156$	−3.42953	+	18.6328i	−0.274582	+	1.49182i
$157$	−9.64863	−	2.58534i	−0.770045	−	0.206333i	−0.147653	−	0.989039i	$-0.547172\pi$
$157$	−9.64863	−	2.58534i	−0.770045	−	0.206333i	−0.622391	+	0.782706i	$0.713839\pi$
$158$	2.33157	+	14.8983i	0.185490	+	1.18525i
$159$	−7.52950	+	14.0318i	−0.597128	+	1.11279i
$160$	0.0520483	−	5.65661i	0.00411478	−	0.447195i
$161$			0.367835i			0.0289895i
$162$	−12.2335	+	3.51295i	−0.961157	+	0.276003i
$163$	−17.3084	−	17.3084i	−1.35570	−	1.35570i	−0.879147	−	0.476551i	$-0.841887\pi$
$163$	−17.3084	−	17.3084i	−1.35570	−	1.35570i	−0.476551	−	0.879147i	$-0.658113\pi$
$164$	−20.0584	+	6.43584i	−1.56629	+	0.502554i
$165$	3.29133	−	0.992572i	0.256230	−	0.0772716i
$166$	−6.14915	+	8.43091i	−0.477267	+	0.654366i
$167$	19.6229	−	11.3293i	1.51847	−	0.876689i	0.518705	−	0.854953i	$-0.326414\pi$
$167$	19.6229	−	11.3293i	1.51847	−	0.876689i	0.999764	−	0.0217356i	$-0.00691919\pi$
$168$	0.381903	+	1.59497i	0.0294645	+	0.123055i
$169$	14.6462	+	8.45598i	1.12663	+	0.650460i
$170$	−9.41005	+	4.16889i	−0.721718	+	0.319740i
$171$	−17.5220	−	3.54464i	−1.33994	−	0.271066i
$172$	−2.84814	+	0.138756i	−0.217169	+	0.0105800i
$173$	−13.4721	+	3.60984i	−1.02427	+	0.274451i	−0.731579	−	0.681757i	$-0.761216\pi$
$173$	−13.4721	+	3.60984i	−1.02427	+	0.274451i	−0.292687	+	0.956208i	$0.594550\pi$
$174$	21.9014	+	7.67991i	1.66034	+	0.582212i
$175$	0.289924	−	0.167388i	0.0219162	−	0.0126533i
$176$	−7.83202	−	1.29964i	−0.590361	−	0.0979639i
$177$	−0.176596	−	5.67677i	−0.0132737	−	0.426692i
$178$	4.59729	+	5.69858i	0.344581	+	0.427127i
$179$	−17.5193	+	17.5193i	−1.30946	+	1.30946i	−0.387650	+	0.921807i	$0.626713\pi$
$179$	−17.5193	+	17.5193i	−1.30946	+	1.30946i	−0.921807	+	0.387650i	$0.873287\pi$
$180$	−0.663896	−	5.96316i	−0.0494839	−	0.444467i
$181$	6.17494	+	6.17494i	0.458980	+	0.458980i	0.898321	−	0.439341i	$-0.144788\pi$
$181$	6.17494	+	6.17494i	0.458980	+	0.458980i	−0.439341	+	0.898321i	$0.644788\pi$
$182$	2.57466	+	0.275399i	0.190847	+	0.0204139i
$183$	−11.2877	−	18.2180i	−0.834407	−	1.34672i
$184$	−1.70696	+	2.59699i	−0.125839	+	0.191453i
$185$	−2.49939	−	4.32907i	−0.183759	−	0.318279i
$186$	8.19313	+	0.619442i	0.600749	+	0.0454197i
$187$	3.73853	+	13.9524i	0.273388	+	1.02030i
$188$	−0.886250	−	0.803909i	−0.0646364	−	0.0586311i
$189$	0.604803	+	1.63102i	0.0439929	+	0.118639i
$190$	3.03454	−	7.86198i	0.220149	−	0.570368i
$191$	1.74091	−	3.01534i	0.125968	−	0.218182i	−0.796143	−	0.605108i	$-0.793130\pi$
$191$	1.74091	−	3.01534i	0.125968	−	0.218182i	0.922111	+	0.386926i	$0.126463\pi$
$192$	−4.70525	+	13.0331i	−0.339572	+	0.940580i
$193$	4.44376	+	7.69682i	0.319869	+	0.554029i	0.980460	−	0.196716i	$-0.0630278\pi$
$193$	4.44376	+	7.69682i	0.319869	+	0.554029i	−0.660591	+	0.750746i	$0.729694\pi$
$194$	−1.43530	+	0.224622i	−0.103048	+	0.0161269i
$195$	−9.22193	−	2.16607i	−0.660396	−	0.155116i
$196$	−13.1172	+	4.20872i	−0.936942	+	0.300623i
$197$	−8.32127	+	8.32127i	−0.592866	+	0.592866i	−0.938405	−	0.345539i	$-0.887696\pi$
$197$	−8.32127	+	8.32127i	−0.592866	+	0.592866i	0.345539	+	0.938405i	$0.387696\pi$
$198$	−8.41243	−	0.373446i	−0.597845	−	0.0265396i
$199$	17.1997			1.21926			0.609629	−	0.792687i	$-0.291319\pi$
$199$	17.1997			1.21926			0.609629	+	0.792687i	$0.291319\pi$
$200$	2.82369	+	0.163619i	0.199665	+	0.0115696i
$201$	−0.230159	−	7.39861i	−0.0162342	−	0.521858i
$202$	2.08607	−	2.86015i	0.146775	−	0.201239i
$203$	0.820972	−	3.06391i	0.0576209	−	0.215044i
$204$	25.1304	−	2.00911i	1.75948	−	0.140666i
$205$	−2.72608	−	10.1739i	−0.190398	−	0.710575i
$206$	7.25523	−	18.7970i	0.505496	−	1.30965i
$207$	−1.46751	+	2.95157i	−0.101999	+	0.205148i
$208$	16.8996	+	13.8922i	1.17178	+	0.963254i
$209$	−10.2427	−	5.91365i	−0.708505	−	0.409056i
$210$	−0.805833	+	0.151920i	−0.0556077	+	0.0104834i
$211$	−1.85287	+	6.91502i	−0.127557	+	0.476049i	−0.999918	−	0.0128131i	$-0.995921\pi$
$211$	−1.85287	+	6.91502i	−0.127557	+	0.476049i	0.872361	+	0.488862i	$0.162588\pi$
$212$	9.95789	+	15.4581i	0.683911	+	1.06166i
$213$	−5.71390	−	18.9471i	−0.391510	−	1.29823i
$214$	2.64968	−	24.7715i	0.181129	−	1.69334i
$215$		−	1.42576i		−	0.0972361i
$216$	−3.29881	+	14.3219i	−0.224456	+	0.974484i
$217$		−	1.12296i		−	0.0762316i
$218$	−6.55416	−	0.701066i	−0.443904	−	0.0474822i
$219$	−3.68137	−	12.2073i	−0.248764	−	0.824892i
$220$	0.839603	−	3.87975i	0.0566060	−	0.261573i
$221$	10.3017	−	38.4466i	0.692970	−	2.58620i
$222$	2.26842	+	12.0325i	0.152247	+	0.807568i
$223$	−15.4354	−	8.91165i	−1.03363	−	0.596768i	−0.115609	−	0.993295i	$-0.536882\pi$
$223$	−15.4354	−	8.91165i	−1.03363	−	0.596768i	−0.918023	+	0.396527i	$0.870215\pi$
$224$	1.82466	+	0.506955i	0.121915	+	0.0338723i
$225$	2.99420	−	0.186470i	0.199613	−	0.0124314i
$226$	−17.3613	−	6.70107i	−1.15486	−	0.445749i
$227$	2.23177	+	8.32910i	0.148128	+	0.552822i	0.999596	+	0.0284152i	$0.00904605\pi$
$227$	2.23177	+	8.32910i	0.148128	+	0.552822i	−0.851468	+	0.524406i	$0.824287\pi$
$228$	−13.3868	+	15.7133i	−0.886565	+	1.04064i
$229$	−2.93828	+	10.9658i	−0.194167	+	0.724640i	0.798314	+	0.602241i	$0.205725\pi$
$229$	−2.93828	+	10.9658i	−0.194167	+	0.724640i	−0.992481	+	0.122399i	$0.960941\pi$
$230$	−1.25543	−	0.915655i	−0.0827803	−	0.0603765i
$231$	0.0357845	+	1.15031i	0.00235445	+	0.0756851i
$232$	20.0145	−	17.8220i	1.31401	−	1.17007i
$233$	6.72592			0.440630			0.220315	−	0.975429i	$-0.429292\pi$
$233$	6.72592			0.440630			0.220315	+	0.975429i	$0.429292\pi$
$234$	19.5608	+	12.4817i	1.27873	+	0.815952i
$235$	0.423041	−	0.423041i	0.0275961	−	0.0275961i
$236$	−5.83235	−	2.99882i	−0.379654	−	0.195207i
$237$	17.9795	+	4.22307i	1.16789	+	0.274318i
$238$	−0.532741	−	3.40413i	−0.0345325	−	0.220657i
$239$	4.19258	+	7.26176i	0.271195	+	0.469724i	0.969168	−	0.246400i	$-0.0792477\pi$
$239$	4.19258	+	7.26176i	0.271195	+	0.469724i	−0.697973	+	0.716124i	$0.745914\pi$
$240$	−6.39433	−	2.66693i	−0.412752	−	0.172150i
$241$	−4.88011	+	8.45260i	−0.314356	+	0.544480i	−0.979300	−	0.202413i	$-0.935122\pi$
$241$	−4.88011	+	8.45260i	−0.314356	+	0.544480i	0.664945	+	0.746893i	$0.268455\pi$
$242$	9.31544	+	3.59555i	0.598819	+	0.231130i
$243$	−1.65404	+	15.5005i	−0.106107	+	0.994355i
$244$	−24.7176	+	1.20419i	−1.58238	+	0.0770904i
$245$	−1.78273	−	6.65323i	−0.113894	−	0.425059i
$246$	−1.94505	+	25.7265i	−0.124012	+	1.64026i
$247$	16.2954	+	28.2245i	1.03685	+	1.79588i
$248$	5.21117	−	7.92833i	0.330910	−	0.503449i
$249$	6.73126	+	10.8641i	0.426576	+	0.688485i
$250$	−0.150414	+	1.40619i	−0.00951299	+	0.0889354i
$251$	−10.4975	−	10.4975i	−0.662593	−	0.662593i	0.293397	−	0.955991i	$-0.405214\pi$
$251$	−10.4975	−	10.4975i	−0.662593	−	0.662593i	−0.955991	+	0.293397i	$0.905214\pi$
$252$	1.98582	+	0.302002i	0.125095	+	0.0190243i
$253$	−1.54205	+	1.54205i	−0.0969477	+	0.0969477i
$254$	−9.71688	+	7.83901i	−0.609691	+	0.491863i
$255$	0.391942	+	12.5992i	0.0245443	+	0.788992i
$256$	10.5299	+	12.0466i	0.658118	+	0.752915i
$257$	8.94188	−	5.16260i	0.557779	−	0.322034i	−0.194474	−	0.980908i	$-0.562300\pi$
$257$	8.94188	−	5.16260i	0.557779	−	0.322034i	0.752254	+	0.658874i	$0.228967\pi$
$258$	−1.15564	+	3.29564i	−0.0719472	+	0.205178i
$259$	1.61644	−	0.433125i	0.100441	−	0.0269131i
$260$	−7.34906	+	8.10180i	−0.455770	+	0.502452i
$261$	18.8113	−	21.3099i	1.16439	−	1.31905i
$262$	−4.01380	−	9.05997i	−0.247973	−	0.559727i
$263$	−6.87765	−	3.97081i	−0.424094	−	0.244851i	0.272734	−	0.962090i	$-0.412072\pi$
$263$	−6.87765	−	3.97081i	−0.424094	−	0.244851i	−0.696827	+	0.717239i	$0.745406\pi$
$264$	−5.08545	+	8.28750i	−0.312988	+	0.510060i
$265$	−7.96215	+	4.59695i	−0.489111	+	0.282388i
$266$	2.27938	+	1.66248i	0.139758	+	0.101933i
$267$	8.58544	−	2.58912i	0.525420	−	0.158452i
$268$	−7.60138	−	3.90840i	−0.464328	−	0.238744i
$269$	3.01231	+	3.01231i	0.183664	+	0.183664i	0.792950	−	0.609287i	$-0.208544\pi$
$269$	3.01231	+	3.01231i	0.183664	+	0.183664i	−0.609287	+	0.792950i	$0.708544\pi$
$270$	−7.07222	−	1.99591i	−0.430402	−	0.121467i
$271$		−	22.2234i		−	1.34997i	−0.737830	−	0.674987i	$-0.764149\pi$
$271$		−	22.2234i		−	1.34997i	0.737830	−	0.674987i	$-0.235851\pi$
$272$	12.0358	−	26.5060i	0.729778	−	1.60716i
$273$	1.49948	−	2.79439i	0.0907529	−	0.169124i
$274$	5.39625	−	0.844505i	0.325999	−	0.0510184i
$275$	1.91715	+	0.513699i	0.115609	+	0.0309772i
$276$	2.15973	+	3.13411i	0.130001	+	0.188651i
$277$	4.80586	−	1.28773i	0.288756	−	0.0773720i	−0.111533	−	0.993761i	$-0.535576\pi$
$277$	4.80586	−	1.28773i	0.288756	−	0.0773720i	0.400290	+	0.916389i	$0.368910\pi$
$278$	−2.81823	−	6.36133i	−0.169026	−	0.381527i
$279$	4.48014	−	9.01082i	0.268219	−	0.539464i
$280$	−0.297571	+	0.898914i	−0.0177833	+	0.0537204i
$281$	2.44465	−	4.23426i	0.145836	−	0.252595i	−0.783849	−	0.620952i	$-0.786746\pi$
$281$	2.44465	−	4.23426i	0.145836	−	0.252595i	0.929684	+	0.368357i	$0.120080\pi$
$282$	−1.32075	+	0.634964i	−0.0786496	+	0.0378115i
$283$	11.7306	+	3.14320i	0.697311	+	0.186844i	0.590026	−	0.807384i	$-0.299118\pi$
$283$	11.7306	+	3.14320i	0.697311	+	0.186844i	0.107285	+	0.994228i	$0.465784\pi$
$284$	−22.3344	−	4.83332i	−1.32531	−	0.286804i
$285$	−7.52165	−	7.06779i	−0.445544	−	0.418660i
$286$	9.63902	+	11.9481i	0.569967	+	0.706505i
$287$	3.52611			0.208140
$288$	12.6188	+	11.3475i	0.743570	+	0.668658i
$289$	−35.9644			−2.11555
$290$	8.41350	+	10.4290i	0.494058	+	0.612412i
$291$	−0.406848	+	1.73213i	−0.0238499	+	0.101539i
$292$	−14.3897	−	3.11402i	−0.842093	−	0.182234i
$293$	6.55348	+	1.75600i	0.382858	+	0.102587i	0.445115	−	0.895474i	$-0.353163\pi$
$293$	6.55348	+	1.75600i	0.382858	+	0.102587i	−0.0622562	+	0.998060i	$0.519830\pi$
$294$	−1.27197	+	16.8239i	−0.0741829	+	0.981189i
$295$	1.63954	−	2.83976i	0.0954574	−	0.165337i
$296$	13.4224	+	4.44326i	0.780159	+	0.258259i
$297$	−4.30213	+	9.37306i	−0.249635	+	0.543880i
$298$	0.921390	+	2.07977i	0.0533747	+	0.120478i
$299$	5.80452	−	1.55532i	0.335684	−	0.0899463i
$300$	1.48746	−	3.12849i	0.0858787	−	0.180624i
$301$	0.461045	+	0.123537i	0.0265742	+	0.00712054i
$302$	−23.8328	+	3.72980i	−1.37142	+	0.214626i
$303$	−2.28355	−	3.68560i	−0.131186	−	0.211732i
$304$	8.37802	+	22.3151i	0.480513	+	1.27986i
$305$		−	12.3735i		−	0.708503i
$306$	9.30624	−	29.4407i	0.532002	−	1.68301i
$307$	−4.35025	−	4.35025i	−0.248282	−	0.248282i	0.571983	−	0.820265i	$-0.306174\pi$
$307$	−4.35025	−	4.35025i	−0.248282	−	0.248282i	−0.820265	+	0.571983i	$0.806174\pi$
$308$	1.18184	+	0.607666i	0.0673415	+	0.0346250i
$309$	−17.9833	−	16.8982i	−1.02304	−	0.961307i
$310$	3.83268	+	2.79540i	0.217682	+	0.158768i
$311$	6.01271	−	3.47144i	0.340949	−	0.196847i	−0.319742	−	0.947505i	$-0.603596\pi$
$311$	6.01271	−	3.47144i	0.340949	−	0.196847i	0.660692	+	0.750657i	$0.270263\pi$
$312$	23.5542	−	12.7705i	1.33349	−	0.722989i
$313$	−16.8649	−	9.73697i	−0.953262	−	0.550366i	−0.0591691	−	0.998248i	$-0.518845\pi$
$313$	−16.8649	−	9.73697i	−0.953262	−	0.550366i	−0.894093	+	0.447882i	$0.852178\pi$
$314$	5.72204	+	12.9158i	0.322913	+	0.728882i
$315$	−0.199137	+	0.984385i	−0.0112201	+	0.0554638i
$316$	14.3280	−	15.7956i	0.806015	−	0.888572i
$317$	21.2290	−	5.68831i	1.19234	−	0.319487i	0.392531	−	0.919739i	$-0.371600\pi$
$317$	21.2290	−	5.68831i	1.19234	−	0.319487i	0.799811	+	0.600252i	$0.204933\pi$
$318$	22.1305	−	4.17216i	1.24102	−	0.233963i
$319$	16.2863	−	9.40289i	0.911857	−	0.526461i
$320$	−6.27238	+	4.96561i	−0.350636	+	0.277586i
$321$	−26.8856	−	14.4269i	−1.50061	−	0.805231i
$322$	0.404871	−	0.326626i	0.0225626	−	0.0182022i
$323$	30.6655	−	30.6655i	1.70627	−	1.70627i
$324$	14.7297	+	10.3459i	0.818314	+	0.574772i
$325$	−3.86730	−	3.86730i	−0.214519	−	0.214519i
$326$	−3.68179	+	34.4204i	−0.203915	+	1.90637i
$327$	−3.81714	+	7.11352i	−0.211088	+	0.393378i
$328$	24.8950	+	16.3631i	1.37460	+	0.903503i
$329$	0.100143	+	0.173453i	0.00552106	+	0.00956275i
$330$	−4.01511	−	2.74135i	−0.221025	−	0.150906i
$331$	−1.30769	−	4.88037i	−0.0718772	−	0.268249i	0.920630	−	0.390436i	$-0.127676\pi$
$331$	−1.30769	−	4.88037i	−0.0718772	−	0.268249i	−0.992507	+	0.122187i	$0.961009\pi$
$332$	14.7400	−	0.718105i	0.808965	−	0.0394111i
$333$	14.6986	+	2.97347i	0.805478	+	0.162945i
$334$	−29.8946	−	11.5386i	−1.63576	−	0.631365i
$335$	2.13683	−	3.70109i	0.116747	−	0.202212i
$336$	1.41644	−	1.83664i	0.0772734	−	0.100197i
$337$	−6.21391	−	10.7628i	−0.338493	−	0.586288i	0.645656	−	0.763628i	$-0.276584\pi$
$337$	−6.21391	−	10.7628i	−0.338493	−	0.586288i	−0.984150	+	0.177341i	$0.943251\pi$
$338$	−3.69799	−	23.6295i	−0.201144	−	1.28528i
$339$	−15.6075	+	16.6098i	−0.847685	+	0.902119i
$340$	12.9445	+	6.65567i	0.702013	+	0.360954i
$341$	4.70771	−	4.70771i	0.254937	−	0.254937i
$342$	11.6575	+	22.4338i	0.630366	+	1.21308i
$343$	4.64933			0.251040
$344$	2.68179	+	3.01170i	0.144593	+	0.162380i
$345$	−1.61775	+	1.00233i	−0.0870965	+	0.0539639i
$346$	15.9361	+	11.6231i	0.856732	+	0.624864i
$347$	−4.44529	+	16.5900i	−0.238635	+	0.890600i	0.737841	+	0.674975i	$0.235845\pi$
$347$	−4.44529	+	16.5900i	−0.238635	+	0.890600i	−0.976476	+	0.215625i	$0.930821\pi$
$348$	−10.9946	−	30.9261i	−0.589373	−	1.65781i
$349$	−3.16002	−	11.7934i	−0.169152	−	0.631285i	−0.997474	−	0.0710321i	$-0.977371\pi$
$349$	−3.16002	−	11.7934i	−0.169152	−	0.631285i	0.828322	−	0.560253i	$-0.189296\pi$
$350$	−0.441685	−	0.170480i	−0.0236090	−	0.00911254i
$351$	23.1805	−	16.4404i	1.23729	−	0.877521i
$352$	5.52410	+	9.77464i	0.294436	+	0.520990i
$353$	19.4127	+	11.2079i	1.03323	+	0.596537i	0.917909	−	0.396791i	$-0.129876\pi$
$353$	19.4127	+	11.2079i	1.03323	+	0.596537i	0.115323	+	0.993328i	$0.463210\pi$
$354$	−6.09153	+	5.23518i	−0.323761	+	0.278246i
$355$	2.95719	−	11.0364i	0.156952	−	0.585751i
$356$	2.19010	−	10.1203i	0.116075	−	0.536377i
$357$	−4.10813	−	0.964930i	−0.217425	−	0.0510695i
$358$	34.8399	+	3.72666i	1.84135	+	0.196960i
$359$		−	22.3469i		−	1.17942i	−0.807614	−	0.589711i	$-0.799242\pi$
$359$		−	22.3469i		−	1.17942i	0.807614	−	0.589711i	$-0.200758\pi$
$360$	−5.97405	+	6.02584i	−0.314860	+	0.317590i
$361$			16.5096i			0.868928i
$362$	1.31351	−	12.2798i	0.0690368	−	0.645414i
$363$	8.37443	−	8.91219i	0.439544	−	0.467769i
$364$	−1.98309	−	3.07844i	−0.103942	−	0.161354i
$365$	1.90527	−	7.11056i	0.0997264	−	0.372184i
$366$	−10.0292	+	28.6012i	−0.524237	+	1.49501i
$367$	20.0857	+	11.5965i	1.04847	+	0.605333i	0.922220	−	0.386666i	$-0.126373\pi$
$367$	20.0857	+	11.5965i	1.04847	+	0.605333i	0.126247	+	0.991999i	$0.459707\pi$
$368$	4.37420	−	0.427218i	0.228021	−	0.0222703i
$369$	28.2941	+	14.0677i	1.47293	+	0.732335i
$370$	−2.54557	+	6.59512i	−0.132338	+	0.342864i
$371$	−0.796616	−	2.97301i	−0.0413583	−	0.154351i
$372$	−6.59344	−	9.56811i	−0.341854	−	0.496083i
$373$	−6.70036	+	25.0061i	−0.346932	+	1.29477i	0.543408	+	0.839469i	$0.317134\pi$
$373$	−6.70036	+	25.0061i	−0.346932	+	1.29477i	−0.890339	+	0.455297i	$0.849533\pi$
$374$	12.0375	−	16.5042i	0.622444	−	0.853414i
$375$	1.52620	+	0.818967i	0.0788128	+	0.0422912i
$376$	−0.0978886	+	1.68933i	−0.00504822	+	0.0871205i
$377$	−51.8205			−2.66889
$378$	1.25819	−	2.11399i	0.0647145	−	0.108732i
$379$	−25.2061	+	25.2061i	−1.29475	+	1.29475i	−0.362934	+	0.931815i	$0.618225\pi$
$379$	−25.2061	+	25.2061i	−1.29475	+	1.29475i	−0.931815	+	0.362934i	$0.881775\pi$
$380$	−11.3482	+	3.64112i	−0.582148	+	0.186786i
$381$	4.41481	+	14.6394i	0.226178	+	0.749997i
$382$	−4.86482	+	0.761337i	−0.248906	+	0.0389534i
$383$	7.08461	+	12.2709i	0.362007	+	0.627014i	0.988291	−	0.152581i	$-0.0487584\pi$
$383$	7.08461	+	12.2709i	0.362007	+	0.627014i	−0.626284	+	0.779595i	$0.715425\pi$
$384$	18.5234	−	6.39395i	0.945270	−	0.326290i
$385$	−0.332228	+	0.575435i	−0.0169319	+	0.0293269i
$386$	4.52586	−	11.7257i	0.230360	−	0.596824i
$387$	3.20664	+	2.83066i	0.163003	+	0.143890i
$388$	1.52174	+	1.38036i	0.0772546	+	0.0700770i
$389$	−6.72338	−	25.0920i	−0.340889	−	1.27222i	−0.897342	−	0.441336i	$-0.854505\pi$
$389$	−6.72338	−	25.0920i	−0.340889	−	1.27222i	0.556453	−	0.830879i	$-0.312162\pi$
$390$	5.80463	+	12.0739i	0.293929	+	0.611384i
$391$	−3.99818	−	6.92505i	−0.202197	−	0.350215i
$392$	16.2802	+	10.7007i	0.822272	+	0.540467i
$393$	−12.1305	+	0.377360i	−0.611901	+	0.0190353i
$394$	16.5481	+	1.77007i	0.833683	+	0.0891751i
$395$	7.53984	+	7.53984i	0.379370	+	0.379370i
$396$	7.05893	+	9.59105i	0.354725	+	0.481968i
$397$	4.85238	−	4.85238i	0.243534	−	0.243534i	−0.574777	−	0.818310i	$-0.694911\pi$
$397$	4.85238	−	4.85238i	0.243534	−	0.243534i	0.818310	+	0.574777i	$0.194911\pi$
$398$	−15.2728	−	18.9315i	−0.765559	−	0.948951i
$399$	2.93722	−	1.81986i	0.147045	−	0.0911071i
$400$	−2.32726	−	3.25329i	−0.116363	−	0.162664i
$401$	16.6567	−	9.61674i	0.831795	−	0.480237i	−0.0226716	−	0.999743i	$-0.507217\pi$
$401$	16.6567	−	9.61674i	0.831795	−	0.480237i	0.854467	+	0.519506i	$0.173884\pi$
$402$	−7.93917	+	6.82307i	−0.395970	+	0.340304i
$403$	−17.7206	+	4.74822i	−0.882725	+	0.236525i
$404$	−5.00049	+	0.243614i	−0.248784	+	0.0121202i
$405$	−5.52519	+	7.10438i	−0.274549	+	0.353020i
$406$	−4.10140	+	1.81702i	−0.203549	+	0.0901774i
$407$	8.59225	+	4.96074i	0.425902	+	0.245895i
$408$	−24.5264	−	25.8766i	−1.21424	−	1.28108i
$409$	13.5094	−	7.79966i	0.667997	−	0.385668i	−0.127320	−	0.991862i	$-0.540638\pi$
$409$	13.5094	−	7.79966i	0.667997	−	0.385668i	0.795317	+	0.606193i	$0.207304\pi$
$410$	−8.77757	+	12.0347i	−0.433493	+	0.594349i
$411$	1.52961	−	6.51224i	0.0754503	−	0.321225i
$412$	−27.1321	+	8.70548i	−1.33670	+	0.428888i
$413$	0.776227	+	0.776227i	0.0381956	+	0.0381956i
$414$	4.55185	−	1.00564i	0.223711	−	0.0494243i
$415$			7.37877i			0.362209i
$416$	0.284662	−	30.9371i	0.0139567	−	1.51681i
$417$	−8.51723	+	0.264958i	−0.417091	+	0.0129751i
$418$	2.58617	+	16.5252i	0.126494	+	0.808273i
$419$	−18.3921	−	4.92814i	−0.898512	−	0.240756i	−0.220135	−	0.975469i	$-0.570650\pi$
$419$	−18.3921	−	4.92814i	−0.898512	−	0.240756i	−0.678377	+	0.734714i	$0.737316\pi$
$420$	0.882771	+	0.752069i	0.0430748	+	0.0366972i
$421$	10.9346	−	2.92992i	0.532920	−	0.142796i	0.0176838	−	0.999844i	$-0.494371\pi$
$421$	10.9346	−	2.92992i	0.532920	−	0.142796i	0.515236	+	0.857048i	$0.327704\pi$
$422$	9.25656	−	4.10089i	0.450602	−	0.199628i
$423$	0.111560	+	1.79134i	0.00542422	+	0.0870979i
$424$	8.17218	−	24.6868i	0.396876	−	1.19890i
$425$	−3.63883	+	6.30264i	−0.176509	+	0.305723i
$426$	−15.7810	+	23.1137i	−0.764594	+	1.11986i
$427$	4.00118	+	1.07211i	0.193631	+	0.0518832i
$428$	−29.6184	+	19.0798i	−1.43166	+	0.922258i
$429$	18.0009	−	5.42856i	0.869091	−	0.262093i
$430$	−1.56932	+	1.26603i	−0.0756791	+	0.0610535i
$431$	−16.9710			−0.817462			−0.408731	−	0.912655i	$-0.634029\pi$
$431$	−16.9710			−0.817462			−0.408731	+	0.912655i	$0.634029\pi$
$432$	18.6932	−	9.08648i	0.899377	−	0.437174i
$433$	6.17424			0.296715			0.148358	−	0.988934i	$-0.452601\pi$
$433$	6.17424			0.296715			0.148358	+	0.988934i	$0.452601\pi$
$434$	−1.23603	+	0.997156i	−0.0593313	+	0.0478650i
$435$	15.7122	−	4.73836i	0.753344	−	0.227187i
$436$	5.04824	+	7.83660i	0.241767	+	0.375305i
$437$	6.32437	+	1.69461i	0.302535	+	0.0810641i
$438$	−10.1675	+	14.8917i	−0.485820	+	0.711555i
$439$	−3.64144	+	6.30716i	−0.173796	+	0.301024i	−0.939744	−	0.341879i	$-0.888937\pi$
$439$	−3.64144	+	6.30716i	−0.173796	+	0.301024i	0.765948	+	0.642903i	$0.222270\pi$
$440$	−5.01593	+	2.52096i	−0.239125	+	0.120182i
$441$	18.5030	+	9.19959i	0.881093	+	0.438076i
$442$	−51.4653	+	22.8004i	−2.44796	+	1.08451i
$443$	14.7533	−	3.95313i	0.700950	−	0.187819i	0.109294	−	0.994009i	$-0.465141\pi$
$443$	14.7533	−	3.95313i	0.700950	−	0.187819i	0.591656	+	0.806191i	$0.298474\pi$
$444$	11.2297	−	13.1813i	0.532938	−	0.625557i
$445$	5.00089	+	1.33998i	0.237065	+	0.0635213i
$446$	3.89726	+	24.9028i	0.184541	+	1.17918i
$447$	2.78462	−	0.0866252i	0.131708	−	0.00409723i
$448$	−1.06224	−	2.45854i	−0.0501862	−	0.116155i
$449$			31.8667i			1.50388i	0.659229	+	0.751942i	$0.270883\pi$
$449$			31.8667i			1.50388i	−0.659229	+	0.751942i	$0.729117\pi$
$450$	−2.86400	−	3.13009i	−0.135010	−	0.147554i
$451$	14.7822	+	14.7822i	0.696069	+	0.696069i
$452$	8.04055	+	25.0597i	0.378196	+	1.17871i
$453$	−6.75561	+	28.7616i	−0.317406	+	1.35134i
$454$	7.18597	−	9.85247i	0.337255	−	0.462399i
$455$	1.58565	−	0.915473i	0.0743362	−	0.0429180i
$456$	29.1825	+	0.781755i	1.36660	+	0.0366090i
$457$	−5.20961	−	3.00777i	−0.243695	−	0.140697i	0.373179	−	0.927759i	$-0.378268\pi$
$457$	−5.20961	−	3.00777i	−0.243695	−	0.140697i	−0.616874	+	0.787062i	$0.711601\pi$
$458$	14.6790	−	6.50317i	0.685904	−	0.303873i
$459$	−29.1146	−	24.1325i	−1.35896	−	1.12641i
$460$	0.106931	+	2.19490i	0.00498569	+	0.102338i
$461$	−10.9587	+	2.93638i	−0.510398	+	0.136761i	−0.504821	−	0.863224i	$-0.668442\pi$
$461$	−10.9587	+	2.93638i	−0.510398	+	0.136761i	−0.00557624	+	0.999984i	$0.501775\pi$
$462$	1.23436	−	1.06083i	0.0574276	−	0.0493543i
$463$	−10.5721	+	6.10381i	−0.491328	+	0.283668i	−0.725125	−	0.688617i	$-0.758218\pi$
$463$	−10.5721	+	6.10381i	−0.491328	+	0.283668i	0.233797	+	0.972285i	$0.424885\pi$
$464$	−37.3887	−	6.20424i	−1.73573	−	0.288025i
$465$	4.93881	−	3.06002i	0.229032	−	0.141905i
$466$	−5.97241	−	7.40313i	−0.276667	−	0.342943i
$467$	−11.6183	+	11.6183i	−0.537633	+	0.537633i	−0.922833	−	0.385200i	$-0.874132\pi$
$467$	−11.6183	+	11.6183i	−0.537633	+	0.537633i	0.385200	+	0.922833i	$0.374132\pi$
$468$	−3.63097	−	32.6136i	−0.167842	−	1.50756i
$469$	1.01167	+	1.01167i	0.0467144	+	0.0467144i
$470$	−0.841282	−	0.0899879i	−0.0388055	−	0.00415083i
$471$	17.2931	−	0.537962i	0.796823	−	0.0247880i
$472$	1.87819	+	9.08245i	0.0864506	+	0.418054i
$473$	1.41491	+	2.45070i	0.0650577	+	0.112683i
$474$	−11.3169	−	23.5397i	−0.519804	−	1.08121i
$475$	−1.54230	−	5.75595i	−0.0707657	−	0.264101i
$476$	−3.27382	+	3.60914i	−0.150055	+	0.165425i
$477$	5.46889	−	27.0341i	0.250403	−	1.23781i
$478$	4.27004	−	11.0629i	0.195307	−	0.506007i
$479$	−9.39801	+	16.2778i	−0.429406	+	0.743753i	−0.996821	−	0.0796793i	$-0.974610\pi$
$479$	−9.39801	+	16.2778i	−0.429406	+	0.743753i	0.567415	+	0.823432i	$0.307944\pi$
$480$	2.74251	+	9.40631i	0.125178	+	0.429337i
$481$	−13.6696	−	23.6765i	−0.623281	−	1.07955i
$482$	13.6371	−	2.13418i	0.621151	−	0.0972092i
$483$	−0.183951	−	0.609975i	−0.00837007	−	0.0277548i
$484$	−4.31426	−	13.4461i	−0.196103	−	0.611187i
$485$	−0.726384	+	0.726384i	−0.0329834	+	0.0329834i
$486$	18.5299	−	11.9433i	0.840532	−	0.541761i
$487$	−23.5372			−1.06657			−0.533287	−	0.845935i	$-0.679043\pi$
$487$	−23.5372			−1.06657			−0.533287	+	0.845935i	$0.679043\pi$
$488$	23.2739	+	26.1371i	1.05356	+	1.18317i
$489$	37.3580	+	20.0465i	1.68939	+	0.906533i
$490$	−5.74011	+	7.87008i	−0.259312	+	0.355534i
$491$	−10.3834	+	38.7514i	−0.468597	+	1.74883i	0.176083	+	0.984375i	$0.443657\pi$
$491$	−10.3834	+	38.7514i	−0.468597	+	1.74883i	−0.644680	+	0.764452i	$0.723009\pi$
$492$	30.0440	−	20.7035i	1.35449	−	0.933384i
$493$	17.8471	+	66.6062i	0.803792	+	2.99979i
$494$	16.5965	−	42.9986i	0.746711	−	1.93460i
$495$	−4.96159	+	3.29193i	−0.223007	+	0.147961i
$496$	−13.3540	+	1.30425i	−0.599611	+	0.0585626i
$497$	3.31259	+	1.91252i	0.148590	+	0.0857884i
$498$	5.98082	−	17.0560i	0.268007	−	0.764297i
$499$	−0.149600	+	0.558314i	−0.00669700	+	0.0249935i	−0.969193	−	0.246301i	$-0.920785\pi$
$499$	−0.149600	+	0.558314i	−0.00669700	+	0.0249935i	0.962496	+	0.271294i	$0.0874516\pi$
$500$	1.68134	−	1.08310i	0.0751918	−	0.0484376i
$501$	−26.8747	+	28.6005i	−1.20067	+	1.27778i
$502$	−2.23299	+	20.8758i	−0.0996630	+	0.931733i
$503$		−	14.6115i		−	0.651496i	−0.945457	−	0.325748i	$-0.894384\pi$
$503$		−	14.6115i		−	0.651496i	0.945457	−	0.325748i	$-0.105616\pi$
$504$	−1.43094	−	2.45393i	−0.0637389	−	0.109307i
$505$		−	2.50321i		−	0.111391i
$506$	3.06660	+	0.328019i	0.136327	+	0.0145822i
$507$	−28.5163	−	6.69799i	−1.26645	−	0.297468i
$508$	17.2566	+	3.73443i	0.765637	+	0.165689i
$509$	2.03299	−	7.58723i	0.0901108	−	0.336298i	−0.906122	−	0.423016i	$-0.860971\pi$
$509$	2.03299	−	7.58723i	0.0901108	−	0.336298i	0.996233	+	0.0867182i	$0.0276380\pi$
$510$	13.5197	−	11.6191i	0.598663	−	0.514502i
$511$	2.13424	+	1.23221i	0.0944134	+	0.0545096i
$512$	3.90934	−	22.2871i	0.172770	−	0.984962i
$513$	30.8292	−	2.88459i	1.36114	−	0.127358i
$514$	−13.6225	−	5.25798i	−0.600864	−	0.231920i
$515$	−3.68746	−	13.7618i	−0.162489	−	0.606416i
$516$	4.65364	−	1.65443i	0.204865	−	0.0728322i
$517$	−0.307331	+	1.14697i	−0.0135164	+	0.0504438i
$518$	−1.91209	−	1.39460i	−0.0840123	−	0.0612750i
$519$	20.5354	−	12.7234i	0.901402	−	0.558497i
$520$	15.4433	+	0.894865i	0.677233	+	0.0392424i
$521$	−25.2662			−1.10693			−0.553467	−	0.832871i	$-0.686695\pi$
$521$	−25.2662			−1.10693			−0.553467	+	0.832871i	$0.686695\pi$
$522$	−40.1594	−	1.78276i	−1.75773	−	0.0780295i
$523$	−8.31046	+	8.31046i	−0.363391	+	0.363391i	−0.865060	−	0.501669i	$-0.832720\pi$
$523$	−8.31046	+	8.31046i	−0.363391	+	0.363391i	0.501669	+	0.865060i	$0.332720\pi$
$524$	−6.40806	+	12.4629i	−0.279937	+	0.544445i
$525$	−0.397067	+	0.422565i	−0.0173294	+	0.0184422i
$526$	1.73652	+	11.0961i	0.0757160	+	0.483812i
$527$	12.2060	+	21.1414i	0.531702	+	0.920935i
$528$	13.6377	−	1.76156i	0.593503	−	0.0766620i
$529$	−10.8964	+	18.8731i	−0.473755	+	0.820568i
$530$	12.1299	+	4.68188i	0.526891	+	0.203368i
$531$	3.13175	+	9.32539i	0.135906	+	0.404687i
$532$	−0.194147	−	3.98512i	−0.00841733	−	0.172777i
$533$	−14.9095	−	55.6428i	−0.645800	−	2.41016i
$534$	−10.4734	−	7.15081i	−0.453229	−	0.309446i
$535$	−8.80799	−	15.2559i	−0.380803	−	0.659570i
$536$	2.44787	+	11.8373i	0.105732	+	0.511292i
$537$	20.2908	−	37.8133i	0.875612	−	1.63176i
$538$	0.640769	−	5.99044i	0.0276255	−	0.258266i
$539$	9.66687	+	9.66687i	0.416382	+	0.416382i
$540$	4.08305	+	9.55660i	0.175707	+	0.411251i
$541$	−3.14916	+	3.14916i	−0.135393	+	0.135393i	−0.771555	−	0.636162i	$-0.780521\pi$
$541$	−3.14916	+	3.14916i	−0.135393	+	0.135393i	0.636162	+	0.771555i	$0.280521\pi$
$542$	−24.4610	+	19.7337i	−1.05069	+	0.847634i
$543$	−13.3279	−	7.15178i	−0.571953	−	0.306912i
$544$	−39.8623	+	10.2889i	−1.70908	+	0.441133i
$545$	−4.03648	+	2.33046i	−0.172904	+	0.0998261i
$546$	−4.40725	+	0.830876i	−0.188613	+	0.0355582i
$547$	13.8787	−	3.71878i	0.593409	−	0.159003i	0.0503983	−	0.998729i	$-0.483951\pi$
$547$	13.8787	−	3.71878i	0.593409	−	0.159003i	0.543011	+	0.839726i	$0.317284\pi$
$548$	−5.72124	−	5.18968i	−0.244399	−	0.221692i
$549$	27.8288	+	24.5658i	1.18771	+	1.04844i
$550$	−1.13695	−	2.56633i	−0.0484797	−	0.109429i
$551$	−48.8970	−	28.2307i	−2.08308	−	1.20267i
$552$	1.53190	−	5.16018i	0.0652018	−	0.219632i
$553$	−3.09144	+	1.78484i	−0.131461	+	0.0758993i
$554$	−5.68484	−	4.14628i	−0.241526	−	0.176159i
$555$	6.30963	+	5.92891i	0.267829	+	0.251668i
$556$	−4.49933	+	8.75066i	−0.190814	+	0.371111i
$557$	−15.7001	−	15.7001i	−0.665233	−	0.665233i	0.291375	−	0.956609i	$-0.405887\pi$
$557$	−15.7001	−	15.7001i	−0.665233	−	0.665233i	−0.956609	+	0.291375i	$0.905887\pi$
$558$	−13.8963	+	3.07010i	−0.588278	+	0.129968i
$559$		−	7.79775i		−	0.329810i
$560$	1.25366	−	0.470675i	0.0529766	−	0.0198897i
$561$	−13.1770	−	21.2674i	−0.556334	−	0.897911i
$562$	−6.83136	+	1.06910i	−0.288164	+	0.0450972i
$563$	31.9400	+	8.55829i	1.34611	+	0.360689i	0.858697	−	0.512483i	$-0.171274\pi$
$563$	31.9400	+	8.55829i	1.34611	+	0.360689i	0.487412	+	0.873172i	$0.337941\pi$
$564$	1.87168	+	0.889904i	0.0788120	+	0.0374717i
$565$	−12.7106	+	3.40581i	−0.534741	+	0.143283i
$566$	−6.95673	−	15.7028i	−0.292413	−	0.660037i
$567$	−1.81859	−	2.40224i	−0.0763737	−	0.100884i
$568$	14.5123	+	28.8751i	0.608924	+	1.21157i
$569$	−21.3049	+	36.9011i	−0.893146	+	1.54697i	−0.0570642	+	0.998371i	$0.518174\pi$
$569$	−21.3049	+	36.9011i	−0.893146	+	1.54697i	−0.836082	+	0.548604i	$0.815159\pi$
$570$	−1.10043	+	14.5550i	−0.0460919	+	0.609640i
$571$	1.11611	+	0.299061i	0.0467078	+	0.0125153i	0.282097	−	0.959386i	$-0.408970\pi$
$571$	1.11611	+	0.299061i	0.0467078	+	0.0125153i	−0.235389	+	0.971901i	$0.575637\pi$
$572$	4.59194	−	21.2191i	0.191999	−	0.887214i
$573$	−1.37898	+	5.87091i	−0.0576075	+	0.245261i
$574$	−3.13108	−	3.88114i	−0.130689	−	0.161996i
$575$	−1.09875			−0.0458212
$576$	1.28492	−	23.9656i	0.0535385	−	0.998566i
$577$	−2.76466			−0.115094			−0.0575472	−	0.998343i	$-0.518328\pi$
$577$	−2.76466			−0.115094			−0.0575472	+	0.998343i	$0.518328\pi$
$578$	31.9353	+	39.5855i	1.32833	+	1.64654i
$579$	−11.2181	−	10.5412i	−0.466210	−	0.438079i
$580$	4.00812	−	18.5213i	0.166428	−	0.769053i
$581$	−2.38606	−	0.639342i	−0.0989903	−	0.0265244i
$582$	2.26780	−	1.09027i	0.0940034	−	0.0451931i
$583$	9.12394	−	15.8031i	0.377875	−	0.654499i
$584$	9.35005	+	18.6037i	0.386908	+	0.769827i
$585$	16.3758	−	1.01984i	0.677057	−	0.0421652i
$586$	−3.88648	−	8.77260i	−0.160549	−	0.362393i
$587$	11.3697	−	3.04651i	0.469279	−	0.125743i	−0.0164272	−	0.999865i	$-0.505229\pi$
$587$	11.3697	−	3.04651i	0.469279	−	0.125743i	0.485706	+	0.874122i	$0.338563\pi$
$588$	19.6473	−	13.5391i	0.810241	−	0.558341i
$589$	−19.3076	−	5.17346i	−0.795556	−	0.213169i
$590$	−4.58154	+	0.717005i	−0.188619	+	0.0295186i
$591$	9.63764	−	17.9604i	0.396440	−	0.738794i
$592$	−7.02801	−	18.7193i	−0.288849	−	0.769358i
$593$		−	37.8177i		−	1.55299i	−0.630125	−	0.776494i	$-0.716996\pi$
$593$		−	37.8177i		−	1.55299i	0.630125	−	0.776494i	$-0.283004\pi$
$594$	14.1370	−	3.58770i	0.580046	−	0.147205i
$595$	−1.72278	−	1.72278i	−0.0706271	−	0.0706271i
$596$	1.47101	−	2.86093i	0.0602548	−	0.117188i
$597$	−28.5221	+	8.60144i	−1.16733	+	0.352034i
$598$	−6.86615	−	5.00788i	−0.280778	−	0.204788i
$599$	−18.5961	+	10.7365i	−0.759816	+	0.438680i	−0.829230	−	0.558908i	$-0.811221\pi$
$599$	−18.5961	+	10.7365i	−0.759816	+	0.438680i	0.0694135	+	0.997588i	$0.477887\pi$
$600$	−4.76431	+	1.14078i	−0.194502	+	0.0465720i
$601$	−6.00991	−	3.46983i	−0.245150	−	0.141537i	0.372392	−	0.928076i	$-0.378538\pi$
$601$	−6.00991	−	3.46983i	−0.245150	−	0.141537i	−0.617541	+	0.786539i	$0.711871\pi$
$602$	−0.273419	−	0.617163i	−0.0111437	−	0.0251537i
$603$	4.08165	+	12.1539i	0.166218	+	0.494945i
$604$	25.2681	+	22.9205i	1.02814	+	0.932620i
$605$	6.82006	−	1.82743i	0.277275	−	0.0742956i
$606$	−2.02897	+	5.78617i	−0.0824211	+	0.235047i
$607$	31.2602	−	18.0481i	1.26881	−	0.732549i	0.294050	−	0.955790i	$-0.404997\pi$
$607$	31.2602	−	18.0481i	1.26881	−	0.732549i	0.974763	+	0.223241i	$0.0716636\pi$
$608$	17.1225	−	29.0367i	0.694408	−	1.17759i
$609$	0.170829	+	5.49139i	0.00692234	+	0.222522i
$610$	−13.6193	+	10.9873i	−0.551429	+	0.444861i
$611$	2.31369	−	2.31369i	0.0936018	−	0.0936018i
$612$	−40.6686	+	15.8992i	−1.64393	+	0.642686i
$613$	−7.63448	−	7.63448i	−0.308354	−	0.308354i	0.535917	−	0.844271i	$-0.319966\pi$
$613$	−7.63448	−	7.63448i	−0.308354	−	0.308354i	−0.844271	+	0.535917i	$0.819966\pi$
$614$	−0.925371	+	8.65114i	−0.0373449	+	0.349132i
$615$	9.60849	+	15.5079i	0.387452	+	0.625339i
$616$	−0.380587	−	1.84042i	−0.0153343	−	0.0741528i
$617$	−1.19748	−	2.07410i	−0.0482088	−	0.0835001i	0.840914	−	0.541169i	$-0.182018\pi$
$617$	−1.19748	−	2.07410i	−0.0482088	−	0.0835001i	−0.889123	+	0.457669i	$0.848685\pi$
$618$	−2.63099	+	34.7991i	−0.105834	+	1.39983i
$619$	−2.10184	−	7.84418i	−0.0844802	−	0.315284i	0.910735	−	0.412991i	$-0.135516\pi$
$619$	−2.10184	−	7.84418i	−0.0844802	−	0.315284i	−0.995215	+	0.0977068i	$0.968849\pi$
$620$	−0.326449	−	6.70081i	−0.0131105	−	0.269111i
$621$	0.957492	−	5.62843i	0.0384228	−	0.225861i
$622$	−9.16007	−	3.53557i	−0.367285	−	0.141764i
$623$	−0.866616	+	1.50102i	−0.0347202	+	0.0601372i
$624$	−34.9718	−	14.5859i	−1.39999	−	0.583905i
$625$	0.500000	+	0.866025i	0.0200000	+	0.0346410i
$626$	4.25819	+	27.2091i	0.170191	+	1.08750i
$627$	19.9427	+	4.68421i	0.796437	+	0.187069i
$628$	9.13527	−	17.7670i	0.364537	−	0.708982i
$629$	−25.7241	+	25.7241i	−1.02569	+	1.02569i
$630$	1.26033	−	0.654916i	0.0502126	−	0.0260925i
$631$	42.6408			1.69750			0.848751	−	0.528792i	$-0.177355\pi$
$631$	42.6408			1.69750			0.848751	+	0.528792i	$0.177355\pi$
$632$	−30.1089	−	1.74466i	−1.19767	−	0.0693990i
$633$	−0.385548	−	12.3937i	−0.0153242	−	0.492604i
$634$	−25.1118	−	18.3155i	−0.997316	−	0.727400i
$635$	−2.28486	+	8.52721i	−0.0906719	+	0.338392i
$636$	−24.2435	−	20.6540i	−0.961316	−	0.818985i
$637$	−9.75006	−	36.3877i	−0.386311	−	1.44173i
$638$	−24.8114	−	9.57661i	−0.982291	−	0.379142i
$639$	18.9506	+	28.5622i	0.749673	+	1.12990i
$640$	11.0353	+	2.49461i	0.436207	+	0.0986080i
$641$	20.9026	+	12.0681i	0.825602	+	0.476661i	0.852344	−	0.522981i	$-0.175180\pi$
$641$	20.9026	+	12.0681i	0.825602	+	0.476661i	−0.0267425	+	0.999642i	$0.508513\pi$
$642$	7.99406	+	42.4032i	0.315501	+	1.67352i
$643$	−4.73495	+	17.6711i	−0.186728	+	0.696880i	0.807526	+	0.589832i	$0.200806\pi$
$643$	−4.73495	+	17.6711i	−0.186728	+	0.696880i	−0.994254	+	0.107047i	$0.965860\pi$
$644$	−0.719026	−	0.155602i	−0.0283336	−	0.00613157i
$645$	0.713011	+	2.36432i	0.0280748	+	0.0930949i
$646$	−60.9831	−	6.52307i	−2.39935	−	0.256647i
$647$			18.7427i			0.736850i	0.929657	+	0.368425i	$0.120103\pi$
$647$			18.7427i			0.736850i	−0.929657	+	0.368425i	$0.879897\pi$
$648$	−1.69190	−	25.3996i	−0.0664643	−	0.997789i
$649$			6.50824i			0.255471i
$650$	−0.822639	+	7.69072i	−0.0322666	+	0.301655i
$651$	0.561583	+	1.86219i	0.0220102	+	0.0729850i
$652$	41.1554	−	26.5118i	1.61177	−	1.03828i
$653$	1.39892	−	5.22086i	0.0547441	−	0.204308i	−0.933137	−	0.359522i	$-0.882940\pi$
$653$	1.39892	−	5.22086i	0.0547441	−	0.204308i	0.987881	+	0.155214i	$0.0496066\pi$
$654$	11.2193	−	2.11511i	0.438708	−	0.0827073i
$655$	−6.06817	−	3.50346i	−0.237103	−	0.136891i
$656$	−4.09536	−	41.9316i	−0.159897	−	1.63715i
$657$	12.2095	+	18.4021i	0.476339	+	0.717936i
$658$	0.101993	−	0.264247i	0.00397610	−	0.0103014i
$659$	3.61565	+	13.4938i	0.140846	+	0.525643i	0.999905	+	0.0137677i	$0.00438253\pi$
$659$	3.61565	+	13.4938i	0.140846	+	0.525643i	−0.859059	+	0.511876i	$0.828951\pi$
$660$	0.547930	+	6.85361i	0.0213281	+	0.266777i
$661$	−2.61958	+	9.77639i	−0.101890	+	0.380258i	−0.997974	−	0.0636268i	$-0.979733\pi$
$661$	−2.61958	+	9.77639i	−0.101890	+	0.380258i	0.896084	+	0.443884i	$0.146400\pi$
$662$	−4.21057	+	5.77298i	−0.163648	+	0.224373i
$663$	2.14360	+	68.9073i	0.0832506	+	2.67614i
$664$	−13.8791	−	15.5865i	−0.538614	−	0.604874i
$665$	1.99492			0.0773598
$666$	−9.77904	−	18.8189i	−0.378930	−	0.729217i
$667$	−7.36146	+	7.36146i	−0.285037	+	0.285037i
$668$	13.8451	+	43.1505i	0.535682	+	1.66954i
$669$	30.0530	+	7.05893i	1.16192	+	0.272914i
$670$	−5.97118	+	0.934481i	−0.230687	+	0.0361022i
$671$	12.2793	+	21.2684i	0.474037	+	0.821057i
$672$	−3.27933	+	0.0718202i	−0.126503	+	0.00277052i
$673$	−8.41380	+	14.5731i	−0.324328	+	0.561753i	−0.981376	−	0.192096i	$-0.938472\pi$
$673$	−8.41380	+	14.5731i	−0.324328	+	0.561753i	0.657048	+	0.753849i	$0.271805\pi$
$674$	−6.32872	+	16.3966i	−0.243773	+	0.631574i
$675$	−4.87198	+	1.80659i	−0.187523	+	0.0695358i
$676$	−22.7250	+	25.0526i	−0.874038	+	0.963562i
$677$	−10.8991	−	40.6759i	−0.418885	−	1.56330i	−0.776924	−	0.629595i	$-0.783221\pi$
$677$	−10.8991	−	40.6759i	−0.418885	−	1.56330i	0.358038	−	0.933707i	$-0.383446\pi$
$678$	32.1412	+	2.43004i	1.23437	+	0.0933250i
$679$	−0.171951	−	0.297828i	−0.00659887	−	0.0114296i
$680$	−4.16851	−	20.1578i	−0.159855	−	0.773018i
$681$	−7.86623	−	12.6959i	−0.301434	−	0.486509i
$682$	−9.36200	−	1.00141i	−0.358490	−	0.0383459i
$683$	33.6594	+	33.6594i	1.28794	+	1.28794i	0.936035	+	0.351906i	$0.114466\pi$
$683$	33.6594	+	33.6594i	1.28794	+	1.28794i	0.351906	+	0.936035i	$0.385534\pi$
$684$	14.3411	−	32.7518i	0.548345	−	1.25230i
$685$	2.73096	−	2.73096i	0.104345	−	0.104345i
$686$	−4.12846	−	5.11746i	−0.157625	−	0.195385i
$687$	−0.611400	−	19.6538i	−0.0233264	−	0.749840i
$688$	0.933591	−	5.62611i	0.0355928	−	0.214493i
$689$	−43.5465	+	25.1416i	−1.65899	+	0.957817i
$690$	2.53976	+	0.890589i	0.0966872	+	0.0339041i
$691$	40.1291	−	10.7526i	1.52658	−	0.409047i	0.604680	−	0.796469i	$-0.293301\pi$
$691$	40.1291	−	10.7526i	1.52658	−	0.409047i	0.921902	+	0.387422i	$0.126634\pi$
$692$	−1.35736	−	27.8617i	−0.0515992	−	1.05914i
$693$	−0.634603	−	1.88965i	−0.0241066	−	0.0717819i
$694$	22.2077	−	9.83858i	0.842993	−	0.373467i
$695$	−4.26068	−	2.45990i	−0.161617	−	0.0933094i
$696$	−24.2771	+	39.5631i	−0.920219	+	1.49963i
$697$	−66.3843	+	38.3270i	−2.51449	+	1.45174i
$698$	−10.1748	+	13.9503i	−0.385122	+	0.528029i
$699$	−11.1535	+	3.36357i	−0.421864	+	0.127222i
$700$	0.204557	+	0.637537i	0.00773154	+	0.0240966i
$701$	6.48209	+	6.48209i	0.244825	+	0.244825i	0.818843	−	0.574018i	$-0.194616\pi$
$701$	6.48209	+	6.48209i	0.244825	+	0.244825i	−0.574018	+	0.818843i	$0.694616\pi$
$702$	−38.6793	−	10.9160i	−1.45986	−	0.411997i
$703$		−	29.7877i		−	1.12346i
$704$	5.85358	−	14.7599i	0.220615	−	0.556284i
$705$	−0.489963	+	0.913081i	−0.0184531	+	0.0343886i
$706$	−4.90146	−	31.3195i	−0.184469	−	1.17873i
$707$	0.809458	+	0.216894i	0.0304428	+	0.00815713i
$708$	11.1714	+	2.05619i	0.419846	+	0.0772764i
$709$	33.6477	−	9.01588i	1.26367	−	0.338598i	0.436065	−	0.899915i	$-0.356372\pi$
$709$	33.6477	−	9.01588i	1.26367	−	0.338598i	0.827601	+	0.561316i	$0.189705\pi$
$710$	−14.7735	+	6.54504i	−0.554440	+	0.245631i
$711$	−31.9270	+	1.98832i	−1.19736	+	0.0745680i
$712$	−13.0841	+	6.57593i	−0.490346	+	0.246444i
$713$	−1.84282	+	3.19185i	−0.0690140	+	0.119536i
$714$	2.58581	+	5.37859i	0.0967716	+	0.201289i
$715$	10.4852	+	2.80951i	0.392126	+	0.105070i
$716$	−26.8349	−	41.6570i	−1.00287	−	1.55679i
$717$	−10.5840	−	9.94540i	−0.395268	−	0.371418i
$718$	−24.5969	+	19.8433i	−0.917948	+	0.740547i
$719$	−6.41197			−0.239126			−0.119563	−	0.992827i	$-0.538149\pi$
$719$	−6.41197			−0.239126			−0.119563	+	0.992827i	$0.538149\pi$
$720$	11.9373	+	1.22479i	0.444878	+	0.0456451i
$721$	4.76962			0.177630
$722$	18.1719	−	14.6600i	0.676289	−	0.545590i
$723$	3.86554	−	16.4573i	0.143761	−	0.612054i
$724$	−14.6826	+	9.45835i	−0.545675	+	0.351517i
$725$	9.15214	+	2.45231i	0.339902	+	0.0910764i
$726$	−17.2458	−	1.30387i	−0.640050	−	0.0483910i
$727$	12.3697	−	21.4249i	0.458765	−	0.794605i	−0.540131	−	0.841581i	$-0.681625\pi$
$727$	12.3697	−	21.4249i	0.458765	−	0.794605i	0.998896	+	0.0469765i	$0.0149586\pi$
$728$	−1.62747	+	4.91632i	−0.0603181	+	0.182211i
$729$	−5.00877	−	26.5313i	−0.185510	−	0.982642i
$730$	−9.51832	+	4.21686i	−0.352289	+	0.156073i
$731$	−10.0227	+	2.68556i	−0.370701	+	0.0993291i
$732$	40.3866	−	14.3580i	1.49273	−	0.530685i
$733$	−31.8992	−	8.54735i	−1.17822	−	0.315704i	−0.384001	−	0.923333i	$-0.625454\pi$
$733$	−31.8992	−	8.54735i	−1.17822	−	0.315704i	−0.794221	+	0.607629i	$0.792121\pi$
$734$	−5.07141	−	32.4054i	−0.187189	−	1.19611i
$735$	6.28349	+	10.1414i	0.231770	+	0.374072i
$736$	−4.35439	−	4.43526i	−0.160505	−	0.163486i
$737$			8.48227i			0.312448i
$738$	−9.64015	−	43.6346i	−0.354859	−	1.60621i
$739$	−33.2406	−	33.2406i	−1.22278	−	1.22278i	−0.966641	−	0.256136i	$-0.917551\pi$
$739$	−33.2406	−	33.2406i	−1.22278	−	1.22278i	−0.256136	−	0.966641i	$-0.582449\pi$
$740$	9.51955	−	3.05440i	0.349945	−	0.112282i
$741$	−41.1373	−	38.6551i	−1.51122	−	1.42003i
$742$	−2.56498	+	3.51677i	−0.0941635	+	0.129105i
$743$	−8.70783	+	5.02747i	−0.319459	+	0.184440i	−0.651152	−	0.758948i	$-0.725714\pi$
$743$	−8.70783	+	5.02747i	−0.319459	+	0.184440i	0.331692	+	0.943388i	$0.392380\pi$
$744$	−4.67672	+	15.7535i	−0.171457	+	0.577551i
$745$	1.39298	+	0.804239i	0.0510349	+	0.0294650i
$746$	33.4736	−	14.8296i	1.22555	−	0.542952i
$747$	−16.5954	−	14.6495i	−0.607193	−	0.535998i
$748$	−28.8549	+	1.40575i	−1.05504	+	0.0513994i
$749$	5.69644	−	1.52636i	0.208144	−	0.0557719i
$750$	−0.453796	−	2.40709i	−0.0165703	−	0.0878944i
$751$	−4.25960	+	2.45928i	−0.155435	+	0.0897404i	−0.575700	−	0.817661i	$-0.695270\pi$
$751$	−4.25960	+	2.45928i	−0.155435	+	0.0897404i	0.420265	+	0.907401i	$0.361937\pi$
$752$	1.94634	−	1.39233i	0.0709758	−	0.0507730i
$753$	22.6575	+	12.1581i	0.825684	+	0.443065i
$754$	46.0150	+	57.0381i	1.67577	+	2.07720i
$755$	−12.0614	+	12.0614i	−0.438960	+	0.438960i
$756$	−3.44408	+	0.492285i	−0.125260	+	0.0179042i
$757$	17.3471	+	17.3471i	0.630490	+	0.630490i	0.948191	−	0.317701i	$-0.102911\pi$
$757$	17.3471	+	17.3471i	0.630490	+	0.630490i	−0.317701	+	0.948191i	$0.602911\pi$
$758$	50.1262	+	5.36176i	1.82067	+	0.194748i
$759$	1.78599	−	3.32832i	0.0648273	−	0.120810i
$760$	14.0846	+	9.25756i	0.510900	+	0.335807i
$761$	−18.4037	−	31.8761i	−0.667133	−	1.15551i	−0.978702	−	0.205285i	$-0.934188\pi$
$761$	−18.4037	−	31.8761i	−0.667133	−	1.15551i	0.311569	−	0.950224i	$-0.399146\pi$
$762$	12.1931	−	17.8586i	0.441710	−	0.646950i
$763$	−0.403851	−	1.50719i	−0.0146204	−	0.0545641i
$764$	5.15780	+	4.67859i	0.186603	+	0.169266i
$765$	−6.95070	−	20.6970i	−0.251303	−	0.748303i
$766$	7.21550	−	18.6941i	0.260707	−	0.675446i
$767$	8.96692	−	15.5312i	0.323777	−	0.560798i
$768$	−23.4860	−	14.7108i	−0.847477	−	0.530832i
$769$	−23.9236	−	41.4369i	−0.862707	−	1.49425i	−0.869306	−	0.494274i	$-0.835434\pi$
$769$	−23.9236	−	41.4369i	−0.862707	−	1.49425i	0.00659884	−	0.999978i	$-0.497900\pi$
$770$	0.928381	−	0.145290i	0.0334565	−	0.00523590i
$771$	−12.2464	+	13.0328i	−0.441044	+	0.469366i
$772$	−16.9252	+	5.43054i	−0.609150	+	0.195449i
$773$	16.4912	−	16.4912i	0.593148	−	0.593148i	−0.345333	−	0.938480i	$-0.612234\pi$
$773$	16.4912	−	16.4912i	0.593148	−	0.593148i	0.938480	+	0.345333i	$0.112234\pi$
$774$	0.268264	−	6.04304i	0.00964254	−	0.217213i
$775$	3.35438			0.120493
$776$	0.168080	−	2.90067i	0.00603373	−	0.104128i
$777$	−2.46392	+	1.52661i	−0.0883927	+	0.0547670i
$778$	−21.6483	+	29.6813i	−0.776128	+	1.06413i
$779$	16.2447	−	60.6261i	0.582028	−	2.17216i
$780$	8.13520	−	17.1103i	0.291287	−	0.612647i
$781$	5.86938	+	21.9048i	0.210023	+	0.783816i
$782$	−4.07205	+	10.5500i	−0.145616	+	0.377266i
$783$	−20.5376	+	44.7453i	−0.733953	+	1.59907i
$784$	−2.67817	−	27.4212i	−0.0956489	−	0.979330i
$785$	8.65073	+	4.99450i	0.308758	+	0.178261i
$786$	11.1868	+	13.0168i	0.399021	+	0.464292i
$787$	−4.35797	+	16.2642i	−0.155345	+	0.579755i	0.843731	+	0.536767i	$0.180355\pi$
$787$	−4.35797	+	16.2642i	−0.155345	+	0.579755i	−0.999076	+	0.0429884i	$0.986312\pi$
$788$	−12.7459	−	19.7861i	−0.454056	−	0.704850i
$789$	13.3909	+	3.14528i	0.476727	+	0.111975i
$790$	1.60385	−	14.9941i	0.0570624	−	0.533468i
$791$		−	4.40531i		−	0.156635i
$792$	4.28862	−	16.2862i	0.152390	−	0.578706i
$793$		−	67.6727i		−	2.40313i
$794$	−9.64971	−	1.03218i	−0.342455	−	0.0366308i
$795$	10.9046	−	11.6049i	0.386747	−	0.411582i
$796$	−7.27584	+	33.6212i	−0.257885	+	1.19167i
$797$	−6.82456	+	25.4696i	−0.241738	+	0.902180i	0.733256	+	0.679952i	$0.238000\pi$
$797$	−6.82456	+	25.4696i	−0.241738	+	0.902180i	−0.974995	+	0.222228i	$0.928667\pi$
$798$	−4.61126	−	1.61697i	−0.163237	−	0.0572403i
$799$	−3.77068	−	2.17700i	−0.133397	−	0.0770169i
$800$	−1.51431	+	5.45040i	−0.0535391	+	0.192701i
$801$	−12.9423	+	8.58701i	−0.457294	+	0.303407i
$802$	−25.3756	−	9.79441i	−0.896045	−	0.345853i
$803$	3.78154	+	14.1129i	0.133448	+	0.498034i
$804$	14.5598	+	2.67986i	0.513485	+	0.0945113i
$805$	0.0952027	−	0.355301i	0.00335546	−	0.0125227i
$806$	20.9616	+	15.2885i	0.738342	+	0.538516i
$807$	−6.50169	−	3.48884i	−0.228870	−	0.122813i
$808$	4.70843	+	5.28765i	0.165642	+	0.186019i
$809$	40.8161			1.43502			0.717510	−	0.696549i	$-0.245282\pi$
$809$	40.8161			1.43502			0.717510	+	0.696549i	$0.245282\pi$
$810$	12.7259	−	0.226976i	0.447142	−	0.00797512i
$811$	−24.6994	+	24.6994i	−0.867315	+	0.867315i	−0.992174	−	0.124860i	$-0.960152\pi$
$811$	−24.6994	+	24.6994i	−0.867315	+	0.867315i	0.124860	+	0.992174i	$0.460152\pi$
$812$	5.64189	+	2.90089i	0.197992	+	0.101801i
$813$	11.1137	+	36.8527i	0.389775	+	1.29248i
$814$	−2.16944	−	13.8624i	−0.0760388	−	0.485875i
$815$	12.2389	+	21.1984i	0.428709	+	0.742546i
$816$	−6.70335	+	49.9736i	−0.234664	+	1.74942i
$817$	4.24805	−	7.35784i	0.148621	−	0.257418i
$818$	−20.5809	−	7.94376i	−0.719595	−	0.277747i
$819$	−1.08912	+	5.38378i	−0.0380569	+	0.188125i
$820$	21.0406	−	1.02505i	0.734770	−	0.0357965i
$821$	−2.64038	−	9.85403i	−0.0921499	−	0.343908i	0.904422	−	0.426639i	$-0.140302\pi$
$821$	−2.64038	−	9.85403i	−0.0921499	−	0.343908i	−0.996572	+	0.0827309i	$0.973636\pi$
$822$	−8.52618	+	4.09905i	−0.297385	+	0.142971i
$823$	19.1397	+	33.1510i	0.667170	+	1.15557i	0.978692	+	0.205333i	$0.0658277\pi$
$823$	19.1397	+	33.1510i	0.667170	+	1.15557i	−0.311523	+	0.950239i	$0.600839\pi$
$824$	33.6745	+	22.1337i	1.17311	+	0.771064i
$825$	−3.43608	+	0.106891i	−0.119629	+	0.00372147i
$826$	0.165117	−	1.54365i	0.00574514	−	0.0537104i
$827$	15.3131	+	15.3131i	0.532487	+	0.532487i	0.921312	−	0.388824i	$-0.127119\pi$
$827$	15.3131	+	15.3131i	0.532487	+	0.532487i	−0.388824	+	0.921312i	$0.627119\pi$
$828$	−5.14879	−	4.11719i	−0.178933	−	0.143082i
$829$	−5.28644	+	5.28644i	−0.183606	+	0.183606i	−0.792925	−	0.609319i	$-0.791443\pi$
$829$	−5.28644	+	5.28644i	−0.183606	+	0.183606i	0.609319	+	0.792925i	$0.291443\pi$
$830$	8.12171	−	6.55212i	0.281909	−	0.227427i
$831$	−7.32550	+	4.53879i	−0.254119	+	0.157449i
$832$	−34.3048	+	27.1578i	−1.18930	+	0.941529i
$833$	−43.4121	+	25.0640i	−1.50414	+	0.868416i
$834$	7.85468	+	9.13953i	0.271985	+	0.316476i
$835$	−21.8866	+	5.86448i	−0.757415	+	0.202949i
$836$	15.8926	−	17.5204i	0.549657	−	0.605956i
$837$	−2.92312	+	17.1830i	−0.101038	+	0.593931i
$838$	10.9073	+	24.6200i	0.376785	+	0.850482i
$839$	4.48304	+	2.58829i	0.154772	+	0.0893576i	0.575386	−	0.817882i	$-0.304852\pi$
$839$	4.48304	+	2.58829i	0.154772	+	0.0893576i	−0.420614	+	0.907240i	$0.638185\pi$
$840$	0.0439188	−	1.63947i	0.00151534	−	0.0565670i
$841$	52.6331	−	30.3877i	1.81493	−	1.04785i
$842$	−12.9345	−	9.43390i	−0.445753	−	0.325113i
$843$	−1.93641	+	8.24415i	−0.0666935	+	0.283944i
$844$	−12.7333	−	6.54710i	−0.438299	−	0.225360i
$845$	−11.9586	−	11.9586i	−0.411387	−	0.411387i
$846$	1.87264	−	1.71345i	0.0643827	−	0.0589095i
$847$			2.36373i			0.0812187i
$848$	−34.4291	+	12.9261i	−1.18230	+	0.443885i
$849$	−21.0245	+	0.654042i	−0.721561	+	0.0224467i
$850$	10.1684	−	1.59134i	0.348773	−	0.0545825i
$851$	−5.30527	−	1.42154i	−0.181862	−	0.0487299i
$852$	39.4540	−	3.15425i	1.35167	−	0.108063i
$853$	0.294984	−	0.0790408i	0.0101001	−	0.00270630i	−0.253765	−	0.967266i	$-0.581669\pi$
$853$	0.294984	−	0.0790408i	0.0101001	−	0.00270630i	0.263866	+	0.964559i	$0.415002\pi$
$854$	−2.37287	−	5.35605i	−0.0811978	−	0.183280i
$855$	16.0076	+	7.95890i	0.547448	+	0.272189i
$856$	47.3012	+	15.6583i	1.61672	+	0.535190i
$857$	23.6925	−	41.0365i	0.809319	−	1.40178i	−0.104017	−	0.994575i	$-0.533170\pi$
$857$	23.6925	−	41.0365i	0.809319	−	1.40178i	0.913336	−	0.407206i	$-0.133497\pi$
$858$	−21.9594	−	14.9929i	−0.749681	−	0.511851i
$859$	6.37604	+	1.70845i	0.217548	+	0.0582917i	0.365946	−	0.930636i	$-0.380745\pi$
$859$	6.37604	+	1.70845i	0.217548	+	0.0582917i	−0.148399	+	0.988928i	$0.547412\pi$
$860$	2.78701	+	0.603126i	0.0950362	+	0.0205664i
$861$	−5.84730	+	1.76338i	−0.199275	+	0.0600958i
$862$	15.0697	+	18.6797i	0.513276	+	0.636233i
$863$	−10.3087			−0.350913			−0.175457	−	0.984487i	$-0.556140\pi$
$863$	−10.3087			−0.350913			−0.175457	+	0.984487i	$0.556140\pi$
$864$	−26.6004	−	12.5068i	−0.904963	−	0.425491i
$865$	13.9474			0.474225
$866$	−5.48254	−	6.79590i	−0.186304	−	0.230934i
$867$	59.6392	−	17.9855i	2.02545	−	0.610819i
$868$	2.19511	+	0.475036i	0.0745069	+	0.0161238i
$869$	−20.4425	−	5.47754i	−0.693463	−	0.185813i
$870$	−19.1674	−	13.0867i	−0.649837	−	0.443681i
$871$	11.6867	−	20.2420i	0.395989	−	0.685873i
$872$	4.14295	−	12.5152i	0.140298	−	0.423818i
$873$	−0.191554	−	3.07583i	−0.00648313	−	0.104101i
$874$	−3.75061	−	8.46590i	−0.126866	−	0.286363i
$875$	−0.323368	+	0.0866462i	−0.0109318	+	0.00292917i
$876$	25.4195	−	2.03223i	0.858846	−	0.0686627i
$877$	9.65113	+	2.58601i	0.325895	+	0.0873234i	0.418057	−	0.908421i	$-0.362711\pi$
$877$	9.65113	+	2.58601i	0.325895	+	0.0873234i	−0.0921620	+	0.995744i	$0.529378\pi$
$878$	10.1757	−	1.59248i	0.343413	−	0.0537436i
$879$	−11.7457	+	0.365391i	−0.396172	+	0.0123243i
$880$	7.22878	+	3.28243i	0.243682	+	0.110651i
$881$			1.18887i			0.0400540i	0.999799	+	0.0200270i	$0.00637521\pi$
$881$			1.18887i			0.0400540i	−0.999799	+	0.0200270i	$0.993625\pi$
$882$	−6.30419	−	28.5349i	−0.212273	−	0.960820i
$883$	18.2393	+	18.2393i	0.613802	+	0.613802i	0.943935	−	0.330133i	$-0.107093\pi$
$883$	18.2393	+	18.2393i	0.613802	+	0.613802i	−0.330133	+	0.943935i	$0.607093\pi$
$884$	70.7958	+	36.4011i	2.38112	+	1.22430i
$885$	−1.29868	+	5.52905i	−0.0436546	+	0.185857i
$886$	−17.4516	−	12.7285i	−0.586299	−	0.427622i
$887$	−13.6504	+	7.88107i	−0.458336	+	0.264620i	−0.711344	−	0.702844i	$-0.751913\pi$
$887$	−13.6504	+	7.88107i	−0.458336	+	0.264620i	0.253008	+	0.967464i	$0.418580\pi$
$888$	−24.4801	−	0.655785i	−0.821499	−	0.0220067i
$889$	−2.55945	−	1.47770i	−0.0858412	−	0.0495605i
$890$	−2.96573	−	6.69428i	−0.0994117	−	0.224393i
$891$	2.44676	−	17.6947i	0.0819696	−	0.592793i
$892$	23.9496	−	26.4026i	0.801891	−	0.884025i
$893$	3.44361	−	0.922713i	0.115236	−	0.0308774i
$894$	−2.56800	−	2.98807i	−0.0858868	−	0.0999360i
$895$	21.4567	−	12.3880i	0.717219	−	0.414086i
$896$	−1.76284	+	3.35230i	−0.0588923	+	0.111992i
$897$	−8.84775	+	5.48195i	−0.295418	+	0.183037i
$898$	35.0753	−	28.2967i	1.17048	−	0.944273i
$899$	22.4738	−	22.4738i	0.749542	−	0.749542i
$900$	−0.902104	+	5.93180i	−0.0300701	+	0.197727i
$901$	47.3126	+	47.3126i	1.57621	+	1.57621i
$902$	3.14443	−	29.3968i	0.104698	−	0.978806i
$903$	−0.826324	+	0.0257057i	−0.0274983	+	0.000855432i
$904$	20.4431	−	31.1024i	0.679928	−	1.03445i
$905$	−4.36634	−	7.56273i	−0.145142	−	0.251394i
$906$	37.6563	−	18.1036i	1.25105	−	0.601453i
$907$	13.7462	+	51.3015i	0.456435	+	1.70344i	0.683835	+	0.729637i	$0.260311\pi$
$907$	13.7462	+	51.3015i	0.456435	+	1.70344i	−0.227400	+	0.973801i	$0.573022\pi$
$908$	−17.2254	+	0.839186i	−0.571645	+	0.0278494i
$909$	5.62991	+	4.96979i	0.186732	+	0.164837i
$910$	−2.41565	−	0.932387i	−0.0800781	−	0.0309083i
$911$	−17.0413	+	29.5165i	−0.564605	+	0.977924i	0.432481	+	0.901643i	$0.357638\pi$
$911$	−17.0413	+	29.5165i	−0.564605	+	0.977924i	−0.997086	+	0.0762816i	$0.975695\pi$
$912$	−25.0527	−	32.8150i	−0.829579	−	1.08661i
$913$	−7.32262	−	12.6831i	−0.242343	−	0.419751i
$914$	1.31536	+	8.40495i	0.0435083	+	0.278011i
$915$	6.18786	+	20.5187i	0.204564	+	0.678328i
$916$	−20.1925	−	10.3824i	−0.667177	−	0.343043i
$917$	1.65869	−	1.65869i	0.0547747	−	0.0547747i
$918$	−0.709366	+	53.4750i	−0.0234126	+	1.76494i
$919$	49.9333			1.64715			0.823575	−	0.567208i	$-0.191976\pi$
$919$	49.9333			1.64715			0.823575	+	0.567208i	$0.191976\pi$
$920$	2.32095	−	2.06670i	0.0765194	−	0.0681372i
$921$	9.38947	+	5.03843i	0.309393	+	0.166022i
$922$	12.9630	+	9.45468i	0.426914	+	0.311373i
$923$	16.1734	−	60.3601i	0.532355	−	1.98678i
$924$	−2.26371	−	0.416656i	−0.0744707	−	0.0137070i
$925$	1.29378	+	4.82845i	0.0425392	+	0.158758i
$926$	16.1061	+	6.21658i	0.529279	+	0.204290i
$927$	38.2722	+	19.0288i	1.25702	+	0.624987i
$928$	26.3711	+	46.6624i	0.865674	+	1.53177i
$929$	27.8938	+	16.1045i	0.915166	+	0.528371i	0.882090	−	0.471082i	$-0.156136\pi$
$929$	27.8938	+	16.1045i	0.915166	+	0.528371i	0.0330760	+	0.999453i	$0.489470\pi$
$930$	−7.75363	−	2.71887i	−0.254252	−	0.0891553i
$931$	10.6233	−	39.6465i	0.348163	−	1.29936i
$932$	−2.84520	+	13.1475i	−0.0931977	+	0.430661i
$933$	−8.23475	+	8.76354i	−0.269594	+	0.286905i
$934$	23.1049	+	2.47142i	0.756015	+	0.0808672i
$935$		−	14.4446i		−	0.472388i
$936$	−32.6731	+	32.9564i	−1.06796	+	1.07721i
$937$		−	45.0999i		−	1.47335i	−0.676248	−	0.736674i	$-0.736395\pi$
$937$		−	45.0999i		−	1.47335i	0.676248	−	0.736674i	$-0.263605\pi$
$938$	0.215199	−	2.01186i	0.00702648	−	0.0656895i
$939$	32.8362	+	7.71266i	1.07157	+	0.251693i
$940$	0.647985	+	1.00589i	0.0211349	+	0.0328087i
$941$	−10.1412	+	37.8475i	−0.330594	+	1.23379i	0.577973	+	0.816056i	$0.303844\pi$
$941$	−10.1412	+	37.8475i	−0.330594	+	1.23379i	−0.908567	+	0.417738i	$0.862823\pi$
$942$	−15.9479	−	18.5566i	−0.519609	−	0.604606i
$943$	−10.0224	−	5.78646i	−0.326376	−	0.188433i
$944$	8.32915	−	10.1322i	0.271091	−	0.329776i
$945$	−0.162056	−	1.73198i	−0.00527168	−	0.0563412i
$946$	1.44105	−	3.73352i	0.0468526	−	0.121387i
$947$	−3.65939	−	13.6570i	−0.118914	−	0.443794i	0.880636	−	0.473794i	$-0.157116\pi$
$947$	−3.65939	−	13.6570i	−0.118914	−	0.443794i	−0.999550	+	0.0300003i	$0.990449\pi$
$948$	−15.8607	+	33.3589i	−0.515132	+	1.08345i
$949$	10.4203	−	38.8890i	0.338256	−	1.26239i
$950$	−4.96598	+	6.80870i	−0.161118	+	0.220903i
$951$	−32.3591	+	20.0493i	−1.04932	+	0.650143i
$952$	6.87958	+	0.398639i	0.222969	+	0.0129200i
$953$	29.6663			0.960987			0.480493	−	0.876998i	$-0.340458\pi$
$953$	29.6663			0.960987			0.480493	+	0.876998i	$0.340458\pi$
$954$	−34.6123	+	17.9859i	−1.12061	+	0.582315i
$955$	−2.46202	+	2.46202i	−0.0796690	+	0.0796690i
$956$	−15.9685	+	5.12358i	−0.516458	+	0.165708i
$957$	−22.3050	+	23.7373i	−0.721018	+	0.767318i
$958$	26.2619	−	4.10995i	0.848484	−	0.132787i
$959$	0.646478	+	1.11973i	0.0208759	+	0.0361581i
$960$	7.91813	−	11.3712i	0.255556	−	0.367003i
$961$	−9.87408	+	17.1024i	−0.318519	+	0.551691i
$962$	−13.9222	+	36.0699i	−0.448869	+	1.16294i
$963$	51.7987	+	10.4787i	1.66919	+	0.337671i
$964$	−14.4583	−	13.1150i	−0.465672	−	0.422407i
$965$	−2.30026	−	8.58469i	−0.0740480	−	0.276351i
$966$	−0.508049	+	0.744112i	−0.0163462	+	0.0239414i
$967$	−0.142127	−	0.246172i	−0.00457051	−	0.00791635i	0.863731	−	0.503953i	$-0.168122\pi$
$967$	−0.142127	−	0.246172i	−0.00457051	−	0.00791635i	−0.868302	+	0.496037i	$0.834788\pi$
$968$	−10.9690	+	16.6884i	−0.352558	+	0.536385i
$969$	−35.5166	+	66.1877i	−1.14096	+	2.12626i
$970$	1.44453	+	0.154514i	0.0463810	+	0.00496115i
$971$	15.3598	+	15.3598i	0.492919	+	0.492919i	0.909225	−	0.416306i	$-0.136675\pi$
$971$	15.3598	+	15.3598i	0.492919	+	0.492919i	−0.416306	+	0.909225i	$0.636675\pi$
$972$	−29.5998	−	9.79026i	−0.949415	−	0.314023i
$973$	1.16462	−	1.16462i	0.0373362	−	0.0373362i
$974$	20.9003	+	25.9071i	0.669690	+	0.830117i
$975$	8.34708	+	4.47908i	0.267321	+	0.143445i
$976$	8.10216	−	48.8262i	0.259344	−	1.56289i
$977$	−8.98116	+	5.18528i	−0.287333	+	0.165892i	−0.636738	−	0.771080i	$-0.719717\pi$
$977$	−8.98116	+	5.18528i	−0.287333	+	0.165892i	0.349406	+	0.936972i	$0.386384\pi$
$978$	−11.1079	−	58.9201i	−0.355192	−	1.88406i
$979$	−9.92567	+	2.65957i	−0.317226	+	0.0850004i
$980$	13.7595	−	0.670336i	0.439532	−	0.0214131i
$981$	2.77250	−	13.7052i	0.0885192	−	0.437572i
$982$	51.8733	−	22.9812i	1.65534	−	0.733360i
$983$	−25.0907	−	14.4861i	−0.800270	−	0.462036i	0.0432956	−	0.999062i	$-0.486214\pi$
$983$	−25.0907	−	14.4861i	−0.800270	−	0.462036i	−0.843566	+	0.537026i	$0.819548\pi$
$984$	−49.4661	−	14.6849i	−1.57692	−	0.468139i
$985$	10.1914	−	5.88403i	0.324726	−	0.187481i
$986$	57.4649	−	78.7883i	1.83005	−	2.50913i
$987$	−0.252808	−	0.237553i	−0.00804696	−	0.00756140i
$988$	−62.0652	+	19.9140i	−1.97456	+	0.633547i
$989$	−1.10772	−	1.10772i	−0.0352236	−	0.0352236i
$990$	8.02912	+	2.53802i	0.255182	+	0.0806635i
$991$			15.8863i			0.504646i	0.967643	+	0.252323i	$0.0811945\pi$
$991$			15.8863i			0.504646i	−0.967643	+	0.252323i	$0.918806\pi$
$992$	13.2935	+	13.5404i	0.422069	+	0.429908i
$993$	4.60916	+	7.43908i	0.146267	+	0.236072i
$994$	−0.836388	−	5.34438i	−0.0265286	−	0.169514i
$995$	−16.6137	−	4.45162i	−0.526689	−	0.141126i
$996$	−24.0841	+	8.56219i	−0.763133	+	0.271303i
$997$	11.6446	−	3.12015i	0.368787	−	0.0988163i	−0.0696656	−	0.997570i	$-0.522193\pi$
$997$	11.6446	−	3.12015i	0.368787	−	0.0988163i	0.438453	+	0.898754i	$0.355527\pi$
$998$	0.747368	−	0.331103i	0.0236575	−	0.0104809i
$999$	−25.8615	+	2.41978i	−0.818220	+	0.0765584i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	720.2.cf.a.11.28	✓	384
9.5	odd	6	inner	720.2.cf.a.491.2	yes	384
16.3	odd	4	inner	720.2.cf.a.371.2	yes	384
144.131	even	12	inner	720.2.cf.a.131.28	yes	384

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
720.2.cf.a.11.28	✓	384	1.1	even	1	trivial
720.2.cf.a.131.28	yes	384	144.131	even	12	inner
720.2.cf.a.371.2	yes	384	16.3	odd	4	inner
720.2.cf.a.491.2	yes	384	9.5	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	720.cf (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.887969 - 1.10069i) q^{2} +(-1.65828 + 0.500091i) q^{3} +(-0.423021 + 1.95475i) q^{4} +(-0.965926 - 0.258819i) q^{5} +(2.02295 + 1.38119i) q^{6} +(0.167388 - 0.289924i) q^{7} +(2.52720 - 1.27015i) q^{8} +(2.49982 - 1.65859i) q^{9} +O(q^{10})\)	\(q+(-0.887969 - 1.10069i) q^{2} +(-1.65828 + 0.500091i) q^{3} +(-0.423021 + 1.95475i) q^{4} +(-0.965926 - 0.258819i) q^{5} +(2.02295 + 1.38119i) q^{6} +(0.167388 - 0.289924i) q^{7} +(2.52720 - 1.27015i) q^{8} +(2.49982 - 1.65859i) q^{9} +(0.572834 + 1.29300i) q^{10} +(1.91715 - 0.513699i) q^{11} +(-0.276066 - 3.45308i) q^{12} +(-5.28283 - 1.41553i) q^{13} +(-0.467750 + 0.0732022i) q^{14} +(1.73121 - 0.0538554i) q^{15} +(-3.64211 - 1.65380i) q^{16} +7.27766i q^{17} +(-4.04535 - 1.27874i) q^{18} +(-4.21365 - 4.21365i) q^{19} +(0.914533 - 1.77866i) q^{20} +(-0.132588 + 0.564485i) q^{21} +(-2.26779 - 1.65403i) q^{22} +(-0.951548 + 0.549377i) q^{23} +(-3.55562 + 3.37009i) q^{24} +(0.866025 + 0.500000i) q^{25} +(3.13293 + 7.07168i) q^{26} +(-3.31596 + 4.00055i) q^{27} +(0.495920 + 0.449845i) q^{28} +(9.15214 - 2.45231i) q^{29} +(-1.59654 - 1.85770i) q^{30} +(2.90498 - 1.67719i) q^{31} +(1.41376 + 5.47734i) q^{32} +(-2.92229 + 1.81061i) q^{33} +(8.01043 - 6.46234i) q^{34} +(-0.236722 + 0.236722i) q^{35} +(2.18465 + 5.58814i) q^{36} +(3.53467 + 3.53467i) q^{37} +(-0.896314 + 8.37949i) q^{38} +(9.46832 - 0.294545i) q^{39} +(-2.76982 + 0.572781i) q^{40} +(5.26639 + 9.12165i) q^{41} +(0.739055 - 0.355308i) q^{42} +(0.369014 + 1.37718i) q^{43} +(0.193160 + 3.96486i) q^{44} +(-2.84391 + 0.955072i) q^{45} +(1.44964 + 0.559526i) q^{46} +(-0.299135 + 0.518117i) q^{47} +(6.86670 + 0.921085i) q^{48} +(3.44396 + 5.96512i) q^{49} +(-0.218661 - 1.39721i) q^{50} +(-3.63950 - 12.0684i) q^{51} +(5.00175 - 9.72781i) q^{52} +(6.50107 - 6.50107i) q^{53} +(7.34782 + 0.0974717i) q^{54} -1.98478 q^{55} +(0.0547757 - 0.945301i) q^{56} +(9.09463 + 4.88022i) q^{57} +(-10.8260 - 7.89606i) q^{58} +(-0.848686 + 3.16734i) q^{59} +(-0.627065 + 3.40687i) q^{60} +(3.20249 + 11.9518i) q^{61} +(-4.42559 - 1.70817i) q^{62} +(-0.0624257 - 1.00238i) q^{63} +(4.77345 - 6.41982i) q^{64} +(4.73645 + 2.73459i) q^{65} +(4.58781 + 1.60875i) q^{66} +(-1.10610 + 4.12803i) q^{67} +(-14.2260 - 3.07860i) q^{68} +(1.30320 - 1.38688i) q^{69} +(0.470758 + 0.0503547i) q^{70} +11.4257i q^{71} +(4.21088 - 7.36671i) q^{72} +7.36140i q^{73} +(0.751884 - 7.02924i) q^{74} +(-1.68616 - 0.396051i) q^{75} +(10.0191 - 6.45417i) q^{76} +(0.171974 - 0.641814i) q^{77} +(-8.73178 - 10.1601i) q^{78} +(-9.23438 - 5.33147i) q^{79} +(3.08997 + 2.54009i) q^{80} +(3.49817 - 8.29233i) q^{81} +(5.36369 - 13.8964i) q^{82} +(-1.90977 - 7.12734i) q^{83} +(-1.04734 - 0.497965i) q^{84} +(1.88360 - 7.02968i) q^{85} +(1.18817 - 1.62906i) q^{86} +(-13.9505 + 8.64353i) q^{87} +(4.19255 - 3.73328i) q^{88} -5.17730 q^{89} +(3.57654 + 2.28218i) q^{90} +(-1.29467 + 1.29467i) q^{91} +(-0.671370 - 2.09244i) q^{92} +(-3.97853 + 4.23401i) q^{93} +(0.835907 - 0.130818i) q^{94} +(2.97950 + 5.16064i) q^{95} +(-5.08360 - 8.37598i) q^{96} +(0.513631 - 0.889636i) q^{97} +(3.50759 - 9.08757i) q^{98} +(3.94051 - 4.46392i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 384 q - 12 q^{6}+O(q^{10}) \) 384 * q - 12 * q^6	\( 384 q - 12 q^{6} + 24 q^{12} + 20 q^{18} - 24 q^{24} + 24 q^{27} - 12 q^{36} + 48 q^{39} - 80 q^{42} + 24 q^{46} - 40 q^{48} - 192 q^{49} + 40 q^{51} + 12 q^{54} - 36 q^{58} + 72 q^{59} - 28 q^{60} + 72 q^{64} - 72 q^{66} - 156 q^{68} - 112 q^{72} - 168 q^{74} + 12 q^{76} - 116 q^{78} + 72 q^{82} - 120 q^{83} - 116 q^{84} - 36 q^{90} + 48 q^{93} + 20 q^{96} - 32 q^{99}+O(q^{100}) \) 384 * q - 12 * q^6 + 24 * q^12 + 20 * q^18 - 24 * q^24 + 24 * q^27 - 12 * q^36 + 48 * q^39 - 80 * q^42 + 24 * q^46 - 40 * q^48 - 192 * q^49 + 40 * q^51 + 12 * q^54 - 36 * q^58 + 72 * q^59 - 28 * q^60 + 72 * q^64 - 72 * q^66 - 156 * q^68 - 112 * q^72 - 168 * q^74 + 12 * q^76 - 116 * q^78 + 72 * q^82 - 120 * q^83 - 116 * q^84 - 36 * q^90 + 48 * q^93 + 20 * q^96 - 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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