LMFDB - Embedded newform 714.2.bh.b.457.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [714,2,Mod(25,714)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(714, base_ring=CyclotomicField(24)) chi = DirichletCharacter(H, H._module([0, 16, 15])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("714.25"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 714 = 2 \cdot 3 \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	714.bh (of order $24$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [96,0,0,0,8,0,0,0,0,8] 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:	$5.70131870432$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$12$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			457.3
Character	$\chi$	$=$	714.457
Dual form			714.2.bh.b.25.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.965926 + 0.258819i) q^{2} +(-0.608761 + 0.793353i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-0.118819 + 0.902520i) q^{5} +(0.382683 - 0.923880i) q^{6} +(2.16960 - 1.51421i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.258819 - 0.965926i) q^{9} +(-0.118819 - 0.902520i) q^{10} +(-5.92170 + 0.779607i) q^{11} +(-0.130526 + 0.991445i) q^{12} +1.56173i q^{13} +(-1.70377 + 2.02415i) q^{14} +(-0.643685 - 0.643685i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-4.07091 - 0.653958i) q^{17} +(0.500000 + 0.866025i) q^{18} +(-2.11820 + 0.567569i) q^{19} +(0.348360 + 0.841015i) q^{20} +(-0.119471 + 2.64305i) q^{21} +(5.51815 - 2.28569i) q^{22} +(3.09604 + 4.03483i) q^{23} +(-0.130526 - 0.991445i) q^{24} +(4.02920 + 1.07962i) q^{25} +(-0.404204 - 1.50851i) q^{26} +(0.923880 + 0.382683i) q^{27} +(1.12183 - 2.39614i) q^{28} +(2.77654 - 1.15008i) q^{29} +(0.788350 + 0.455154i) q^{30} +(-5.33736 + 6.95578i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(2.98640 - 5.17260i) q^{33} +(4.10146 - 0.421955i) q^{34} +(1.10881 + 2.13803i) q^{35} +(-0.707107 - 0.707107i) q^{36} +(-11.3254 - 1.49102i) q^{37} +(1.89912 - 1.09646i) q^{38} +(-1.23900 - 0.950718i) q^{39} +(-0.554160 - 0.722196i) q^{40} +(-10.1130 - 4.18894i) q^{41} +(-0.568672 - 2.58391i) q^{42} +(-2.37969 + 2.37969i) q^{43} +(-4.73854 + 3.63601i) q^{44} +(0.902520 - 0.118819i) q^{45} +(-4.03483 - 3.09604i) q^{46} +(0.760894 + 0.439302i) q^{47} +(0.382683 + 0.923880i) q^{48} +(2.41436 - 6.57045i) q^{49} -4.17134 q^{50} +(2.99704 - 2.83157i) q^{51} +(0.780863 + 1.35249i) q^{52} +(-1.39067 + 5.19005i) q^{53} +(-0.991445 - 0.130526i) q^{54} -5.43709i q^{55} +(-0.463437 + 2.60485i) q^{56} +(0.839193 - 2.02599i) q^{57} +(-2.38427 + 1.82951i) q^{58} +(-11.6002 - 3.10826i) q^{59} +(-0.879290 - 0.235605i) q^{60} +(2.90496 - 2.22905i) q^{61} +(3.35520 - 8.10018i) q^{62} +(-2.02415 - 1.70377i) q^{63} -1.00000i q^{64} +(-1.40949 - 0.185563i) q^{65} +(-1.54587 + 5.76928i) q^{66} +(-2.39293 - 4.14467i) q^{67} +(-3.85249 + 1.46911i) q^{68} -5.08579 q^{69} +(-1.62439 - 1.77819i) q^{70} +(3.58894 + 8.66448i) q^{71} +(0.866025 + 0.500000i) q^{72} +(3.61307 + 2.77240i) q^{73} +(11.3254 - 1.49102i) q^{74} +(-3.30935 + 2.53935i) q^{75} +(-1.55063 + 1.55063i) q^{76} +(-11.6673 + 10.6581i) q^{77} +(1.44285 + 0.597647i) q^{78} +(-6.44842 - 8.40374i) q^{79} +(0.722196 + 0.554160i) q^{80} +(-0.866025 + 0.500000i) q^{81} +(10.8526 + 1.42877i) q^{82} +(-10.5731 - 10.5731i) q^{83} +(1.21806 + 2.34869i) q^{84} +(1.07391 - 3.59638i) q^{85} +(1.68270 - 2.91452i) q^{86} +(-0.777830 + 2.90290i) q^{87} +(3.63601 - 4.73854i) q^{88} +(12.9436 + 7.47298i) q^{89} +(-0.841015 + 0.348360i) q^{90} +(2.36477 + 3.38833i) q^{91} +(4.69866 + 1.94625i) q^{92} +(-2.26921 - 8.46882i) q^{93} +(-0.848667 - 0.227400i) q^{94} +(-0.260560 - 1.97915i) q^{95} +(-0.608761 - 0.793353i) q^{96} +(-3.27077 + 1.35480i) q^{97} +(-0.631537 + 6.97145i) q^{98} +(2.28569 + 5.51815i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 8 q^{5} + 8 q^{10} + 16 q^{14} + 16 q^{15} + 48 q^{16} + 8 q^{17} + 48 q^{18} - 8 q^{19} + 16 q^{22} + 24 q^{25} + 32 q^{28} - 32 q^{29} - 16 q^{33} - 48 q^{37} - 16 q^{39} + 128 q^{41} + 16 q^{42}+ \cdots + 160 q^{97}+O(q^{100}) $ 96 * q + 8 * q^5 + 8 * q^10 + 16 * q^14 + 16 * q^15 + 48 * q^16 + 8 * q^17 + 48 * q^18 - 8 * q^19 + 16 * q^22 + 24 * q^25 + 32 * q^28 - 32 * q^29 - 16 * q^33 - 48 * q^37 - 16 * q^39 + 128 * q^41 + 16 * q^42 + 48 * q^43 - 8 * q^44 - 8 * q^46 - 112 * q^49 + 64 * q^50 - 16 * q^52 - 40 * q^53 + 16 * q^57 + 16 * q^58 - 24 * q^59 + 8 * q^60 - 56 * q^70 + 24 * q^73 + 48 * q^74 - 16 * q^76 + 16 * q^77 + 32 * q^78 - 56 * q^79 - 8 * q^80 - 80 * q^83 + 80 * q^85 + 16 * q^86 - 24 * q^87 + 16 * q^90 - 40 * q^91 + 16 * q^92 - 8 * q^93 - 8 * q^94 + 80 * q^95 + 160 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/714\mathbb{Z}\right)^\times$.

$n$	$239$	$409$	$547$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{8}\right)$

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 $

$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i
$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i
$3$	−0.608761	+	0.793353i	−0.351469	+	0.458043i
$3$	−0.608761	+	0.793353i	−0.351469	+	0.458043i
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$	−0.118819	+	0.902520i	−0.0531375	+	0.403619i	0.944120	+	0.329603i	$0.106915\pi$
$5$	−0.118819	+	0.902520i	−0.0531375	+	0.403619i	−0.997257	+	0.0740161i	$0.976418\pi$
$6$	0.382683	−	0.923880i	0.156230	−	0.377172i
$7$	2.16960	−	1.51421i	0.820033	−	0.572316i
$7$	2.16960	−	1.51421i	0.820033	−	0.572316i
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	−0.258819	−	0.965926i	−0.0862730	−	0.321975i
$10$	−0.118819	−	0.902520i	−0.0375739	−	0.285402i
$11$	−5.92170	+	0.779607i	−1.78546	+	0.235060i	−0.949508	−	0.313742i	$-0.898417\pi$
$11$	−5.92170	+	0.779607i	−1.78546	+	0.235060i	−0.835952	+	0.548802i	$0.815084\pi$
$12$	−0.130526	+	0.991445i	−0.0376797	+	0.286205i
$13$			1.56173i			0.433145i	0.976267	+	0.216572i	$0.0694877\pi$
$13$			1.56173i			0.433145i	−0.976267	+	0.216572i	$0.930512\pi$
$14$	−1.70377	+	2.02415i	−0.455352	+	0.540976i
$15$	−0.643685	−	0.643685i	−0.166199	−	0.166199i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−4.07091	−	0.653958i	−0.987342	−	0.158608i
$17$	−4.07091	−	0.653958i	−0.987342	−	0.158608i
$18$	0.500000	+	0.866025i	0.117851	+	0.204124i
$19$	−2.11820	+	0.567569i	−0.485947	+	0.130209i	−0.493471	−	0.869762i	$-0.664272\pi$
$19$	−2.11820	+	0.567569i	−0.485947	+	0.130209i	0.00752314	+	0.999972i	$0.497605\pi$
$20$	0.348360	+	0.841015i	0.0778956	+	0.188057i
$21$	−0.119471	+	2.64305i	−0.0260707	+	0.576761i
$22$	5.51815	−	2.28569i	1.17647	−	0.487311i
$23$	3.09604	+	4.03483i	0.645568	+	0.841321i	0.995431	−	0.0954801i	$-0.0304386\pi$
$23$	3.09604	+	4.03483i	0.645568	+	0.841321i	−0.349863	+	0.936801i	$0.613772\pi$
$24$	−0.130526	−	0.991445i	−0.0266435	−	0.202378i
$25$	4.02920	+	1.07962i	0.805841	+	0.215924i
$26$	−0.404204	−	1.50851i	−0.0792710	−	0.295843i
$27$	0.923880	+	0.382683i	0.177801	+	0.0736475i
$28$	1.12183	−	2.39614i	0.212006	−	0.452828i
$29$	2.77654	−	1.15008i	0.515591	−	0.213565i	−0.109688	−	0.993966i	$-0.534985\pi$
$29$	2.77654	−	1.15008i	0.515591	−	0.213565i	0.625279	+	0.780401i	$0.284985\pi$
$30$	0.788350	+	0.455154i	0.143932	+	0.0830994i
$31$	−5.33736	+	6.95578i	−0.958618	+	1.24930i	0.00979707	+	0.999952i	$0.496881\pi$
$31$	−5.33736	+	6.95578i	−0.958618	+	1.24930i	−0.968415	+	0.249343i	$0.919785\pi$
$32$	−0.258819	+	0.965926i	−0.0457532	+	0.170753i
$33$	2.98640	−	5.17260i	0.519866	−	0.900434i
$34$	4.10146	−	0.421955i	0.703394	−	0.0723646i
$35$	1.10881	+	2.13803i	0.187423	+	0.361393i
$36$	−0.707107	−	0.707107i	−0.117851	−	0.117851i
$37$	−11.3254	−	1.49102i	−1.86189	−	0.245122i	−0.886044	−	0.463601i	$-0.846557\pi$
$37$	−11.3254	−	1.49102i	−1.86189	−	0.245122i	−0.975842	+	0.218479i	$0.929890\pi$
$38$	1.89912	−	1.09646i	0.308078	−	0.177869i
$39$	−1.23900	−	0.950718i	−0.198399	−	0.152237i
$40$	−0.554160	−	0.722196i	−0.0876204	−	0.114189i
$41$	−10.1130	−	4.18894i	−1.57939	−	0.654203i	−0.591070	−	0.806620i	$-0.701294\pi$
$41$	−10.1130	−	4.18894i	−1.57939	−	0.654203i	−0.988316	+	0.152417i	$0.951294\pi$
$42$	−0.568672	−	2.58391i	−0.0877480	−	0.398707i
$43$	−2.37969	+	2.37969i	−0.362900	+	0.362900i	−0.864880	−	0.501979i	$-0.832605\pi$
$43$	−2.37969	+	2.37969i	−0.362900	+	0.362900i	0.501979	+	0.864880i	$0.332605\pi$
$44$	−4.73854	+	3.63601i	−0.714362	+	0.548149i
$45$	0.902520	−	0.118819i	0.134540	−	0.0177125i
$46$	−4.03483	−	3.09604i	−0.594904	−	0.456486i
$47$	0.760894	+	0.439302i	0.110988	+	0.0640788i	0.554466	−	0.832206i	$-0.312922\pi$
$47$	0.760894	+	0.439302i	0.110988	+	0.0640788i	−0.443479	+	0.896285i	$0.646256\pi$
$48$	0.382683	+	0.923880i	0.0552356	+	0.133351i
$49$	2.41436	−	6.57045i	0.344909	−	0.938636i
$50$	−4.17134			−0.589916
$51$	2.99704	−	2.83157i	0.419669	−	0.396499i
$52$	0.780863	+	1.35249i	0.108286	+	0.187557i
$53$	−1.39067	+	5.19005i	−0.191023	+	0.712908i	0.802237	+	0.597005i	$0.203643\pi$
$53$	−1.39067	+	5.19005i	−0.191023	+	0.712908i	−0.993261	+	0.115903i	$0.963024\pi$
$54$	−0.991445	−	0.130526i	−0.134919	−	0.0177624i
$55$		−	5.43709i		−	0.733137i
$56$	−0.463437	+	2.60485i	−0.0619293	+	0.348087i
$57$	0.839193	−	2.02599i	0.111154	−	0.268349i
$58$	−2.38427	+	1.82951i	−0.313070	+	0.240227i
$59$	−11.6002	−	3.10826i	−1.51021	−	0.404661i	−0.593708	−	0.804680i	$-0.702337\pi$
$59$	−11.6002	−	3.10826i	−1.51021	−	0.404661i	−0.916507	+	0.400019i	$0.869003\pi$
$60$	−0.879290	−	0.235605i	−0.113516	−	0.0304165i
$61$	2.90496	−	2.22905i	0.371942	−	0.285401i	−0.405829	−	0.913949i	$-0.633017\pi$
$61$	2.90496	−	2.22905i	0.371942	−	0.285401i	0.777771	+	0.628548i	$0.216350\pi$
$62$	3.35520	−	8.10018i	0.426111	−	1.02872i
$63$	−2.02415	−	1.70377i	−0.255018	−	0.214655i
$64$		−	1.00000i		−	0.125000i
$65$	−1.40949	−	0.185563i	−0.174826	−	0.0230162i
$66$	−1.54587	+	5.76928i	−0.190284	+	0.710150i
$67$	−2.39293	−	4.14467i	−0.292343	−	0.506352i	0.682021	−	0.731333i	$-0.261101\pi$
$67$	−2.39293	−	4.14467i	−0.292343	−	0.506352i	−0.974363	+	0.224981i	$0.927768\pi$
$68$	−3.85249	+	1.46911i	−0.467184	+	0.178156i
$69$	−5.08579			−0.612258
$70$	−1.62439	−	1.77819i	−0.194152	−	0.212535i
$71$	3.58894	+	8.66448i	0.425929	+	1.02828i	0.980566	+	0.196191i	$0.0628574\pi$
$71$	3.58894	+	8.66448i	0.425929	+	1.02828i	−0.554636	+	0.832093i	$0.687143\pi$
$72$	0.866025	+	0.500000i	0.102062	+	0.0589256i
$73$	3.61307	+	2.77240i	0.422877	+	0.324485i	0.798182	−	0.602416i	$-0.205795\pi$
$73$	3.61307	+	2.77240i	0.422877	+	0.324485i	−0.375305	+	0.926902i	$0.622462\pi$
$74$	11.3254	−	1.49102i	1.31655	−	0.173327i
$75$	−3.30935	+	2.53935i	−0.382130	+	0.293219i
$76$	−1.55063	+	1.55063i	−0.177869	+	0.177869i
$77$	−11.6673	+	10.6581i	−1.32961	+	1.21460i
$78$	1.44285	+	0.597647i	0.163370	+	0.0676701i
$79$	−6.44842	−	8.40374i	−0.725504	−	0.945495i	0.274366	−	0.961625i	$-0.411532\pi$
$79$	−6.44842	−	8.40374i	−0.725504	−	0.945495i	−0.999870	+	0.0161305i	$0.994865\pi$
$80$	0.722196	+	0.554160i	0.0807440	+	0.0619570i
$81$	−0.866025	+	0.500000i	−0.0962250	+	0.0555556i
$82$	10.8526	+	1.42877i	1.19847	+	0.157781i
$83$	−10.5731	−	10.5731i	−1.16055	−	1.16055i	−0.984356	−	0.176193i	$-0.943622\pi$
$83$	−10.5731	−	10.5731i	−1.16055	−	1.16055i	−0.176193	−	0.984356i	$-0.556378\pi$
$84$	1.21806	+	2.34869i	0.132901	+	0.256263i
$85$	1.07391	−	3.59638i	0.116482	−	0.390082i
$86$	1.68270	−	2.91452i	0.181450	−	0.314281i
$87$	−0.777830	+	2.90290i	−0.0833922	+	0.311224i
$88$	3.63601	−	4.73854i	0.387600	−	0.505130i
$89$	12.9436	+	7.47298i	1.37202	+	0.792134i	0.991182	−	0.132509i	$-0.0423032\pi$
$89$	12.9436	+	7.47298i	1.37202	+	0.792134i	0.380835	+	0.924643i	$0.375637\pi$
$90$	−0.841015	+	0.348360i	−0.0886508	+	0.0367203i
$91$	2.36477	+	3.38833i	0.247896	+	0.355193i
$92$	4.69866	+	1.94625i	0.489869	+	0.202911i
$93$	−2.26921	−	8.46882i	−0.235307	−	0.878176i
$94$	−0.848667	−	0.227400i	−0.0875333	−	0.0234545i
$95$	−0.260560	−	1.97915i	−0.0267329	−	0.203057i
$96$	−0.608761	−	0.793353i	−0.0621315	−	0.0809713i
$97$	−3.27077	+	1.35480i	−0.332096	+	0.137559i	−0.542500	−	0.840056i	$-0.682522\pi$
$97$	−3.27077	+	1.35480i	−0.332096	+	0.137559i	0.210404	+	0.977615i	$0.432522\pi$
$98$	−0.631537	+	6.97145i	−0.0637948	+	0.704223i
$99$	2.28569	+	5.51815i	0.229721	+	0.554595i
$100$	4.02920	−	1.07962i	0.402920	−	0.107962i
$101$	8.03698	+	13.9205i	0.799710	+	1.38514i	0.919805	+	0.392376i	$0.128347\pi$
$101$	8.03698	+	13.9205i	0.799710	+	1.38514i	−0.120095	+	0.992762i	$0.538320\pi$
$102$	−2.16205	+	3.51077i	−0.214075	+	0.347619i
$103$	−7.57744	+	13.1245i	−0.746627	+	1.29320i	0.202804	+	0.979219i	$0.434995\pi$
$103$	−7.57744	+	13.1245i	−0.746627	+	1.29320i	−0.949431	+	0.313976i	$0.898339\pi$
$104$	−1.10431	−	1.10431i	−0.108286	−	0.108286i
$105$	−2.37121	−	0.421870i	−0.231407	−	0.0411703i
$106$		−	5.37314i		−	0.521885i
$107$	0.0392690	−	0.298277i	0.00379627	−	0.0288356i	−0.989442	−	0.144930i	$-0.953704\pi$
$107$	0.0392690	−	0.298277i	0.00379627	−	0.0288356i	0.993238	+	0.116095i	$0.0370376\pi$
$108$	0.991445	−	0.130526i	0.0954018	−	0.0125599i
$109$	−0.685775	−	5.20898i	−0.0656854	−	0.498930i	−0.992390	−	0.123138i	$-0.960704\pi$
$109$	−0.685775	−	5.20898i	−0.0656854	−	0.498930i	0.926704	−	0.375792i	$-0.122629\pi$
$110$	1.40722	+	5.25182i	0.134173	+	0.500742i
$111$	8.07738	−	8.07738i	0.766671	−	0.766671i
$112$	−0.226539	−	2.63603i	−0.0214059	−	0.249082i
$113$	6.99337	−	16.8835i	0.657881	−	1.58827i	−0.143189	−	0.989695i	$-0.545736\pi$
$113$	6.99337	−	16.8835i	0.657881	−	1.58827i	0.801070	−	0.598570i	$-0.204264\pi$
$114$	−0.286233	+	2.17416i	−0.0268082	+	0.203628i
$115$	−4.00939	+	2.31482i	−0.373877	+	0.215858i
$116$	1.82951	−	2.38427i	0.169866	−	0.221374i
$117$	1.50851	−	0.404204i	0.139462	−	0.0373687i
$118$	12.0094			1.10555
$119$	−9.82250	+	4.74537i	−0.900427	+	0.435007i
$120$	0.910308			0.0830994
$121$	23.8336	−	6.38619i	2.16669	−	0.580563i
$122$	−2.22905	+	2.90496i	−0.201809	+	0.263003i
$123$	9.47972	−	5.47312i	0.854758	−	0.493494i
$124$	−1.14440	+	8.69256i	−0.102770	+	0.780615i
$125$	−3.19493	+	7.71323i	−0.285763	+	0.689893i
$126$	2.39614	+	1.12183i	0.213465	+	0.0999405i
$127$	12.2428	−	12.2428i	1.08637	−	1.08637i	0.0904751	−	0.995899i	$-0.471161\pi$
$127$	12.2428	−	12.2428i	1.08637	−	1.08637i	0.995899	−	0.0904751i	$-0.0288385\pi$
$128$	0.258819	+	0.965926i	0.0228766	+	0.0853766i
$129$	−0.439272	−	3.33661i	−0.0386758	−	0.293772i
$130$	1.40949	−	0.185563i	0.123620	−	0.0162749i
$131$	−1.88059	+	14.2845i	−0.164308	+	1.24804i	0.688274	+	0.725450i	$0.258368\pi$
$131$	−1.88059	+	14.2845i	−0.164308	+	1.24804i	−0.852582	+	0.522593i	$0.824965\pi$
$132$		−	5.97280i		−	0.519866i
$133$	−3.73623	+	4.43878i	−0.323972	+	0.384891i
$134$	3.38411	+	3.38411i	0.292343	+	0.292343i
$135$	−0.455154	+	0.788350i	−0.0391734	+	0.0678503i
$136$	3.34099	−	2.41615i	0.286487	−	0.207183i
$137$	−8.77311	−	15.1955i	−0.749537	−	1.29824i	−0.948045	−	0.318137i	$-0.896943\pi$
$137$	−8.77311	−	15.1955i	−0.749537	−	1.29824i	0.198508	−	0.980099i	$-0.436391\pi$
$138$	4.91250	−	1.31630i	0.418180	−	0.112051i
$139$	0.849047	+	2.04978i	0.0720153	+	0.173860i	0.955788	−	0.294056i	$-0.0950051\pi$
$139$	0.849047	+	2.04978i	0.0720153	+	0.173860i	−0.883773	+	0.467916i	$0.845005\pi$
$140$	2.02927	+	1.29718i	0.171505	+	0.109632i
$141$	−0.811725	+	0.336227i	−0.0683595	+	0.0283155i
$142$	−5.70918	−	7.44035i	−0.479104	−	0.624381i
$143$	−1.21753	−	9.24808i	−0.101815	−	0.773363i
$144$	−0.965926	−	0.258819i	−0.0804938	−	0.0215683i
$145$	0.708065	+	2.64253i	0.0588016	+	0.219451i
$146$	−4.20751	−	1.74281i	−0.348216	−	0.144236i
$147$	3.74292	+	5.91528i	0.308711	+	0.487884i
$148$	−10.5536	+	4.37144i	−0.867501	+	0.359330i
$149$	1.14775	+	0.662655i	0.0940276	+	0.0542868i	0.546276	−	0.837605i	$-0.316045\pi$
$149$	1.14775	+	0.662655i	0.0940276	+	0.0542868i	−0.452249	+	0.891892i	$0.649378\pi$
$150$	2.53935	−	3.30935i	0.207337	−	0.270207i
$151$	−5.80100	+	21.6496i	−0.472078	+	1.76182i	0.160205	+	0.987084i	$0.448784\pi$
$151$	−5.80100	+	21.6496i	−0.472078	+	1.76182i	−0.632283	+	0.774737i	$0.717882\pi$
$152$	1.09646	−	1.89912i	0.0889346	−	0.154039i
$153$	0.421955	+	4.10146i	0.0341130	+	0.331583i
$154$	8.51119	−	13.3147i	0.685851	−	1.07293i
$155$	−5.64355	−	5.64355i	−0.453301	−	0.453301i
$156$	−1.54836	−	0.203846i	−0.123968	−	0.0163208i
$157$	0.985415	−	0.568929i	0.0786446	−	0.0454055i	−0.460162	−	0.887835i	$-0.652209\pi$
$157$	0.985415	−	0.568929i	0.0786446	−	0.0454055i	0.538807	+	0.842429i	$0.318875\pi$
$158$	8.40374	+	6.44842i	0.668566	+	0.513009i
$159$	−3.27096	−	4.26279i	−0.259404	−	0.338062i
$160$	−0.841015	−	0.348360i	−0.0664881	−	0.0275403i
$161$	12.8267	+	4.06595i	1.01089	+	0.320442i
$162$	0.707107	−	0.707107i	0.0555556	−	0.0555556i
$163$	−14.9758	+	11.4913i	−1.17299	+	0.900068i	−0.996447	−	0.0842247i	$-0.973159\pi$
$163$	−14.9758	+	11.4913i	−1.17299	+	0.900068i	−0.176545	+	0.984293i	$0.556492\pi$
$164$	−10.8526	+	1.42877i	−0.847445	+	0.111568i
$165$	4.31353	+	3.30989i	0.335808	+	0.257675i
$166$	12.9494	+	7.47631i	1.00506	+	0.580274i
$167$	0.645002	+	1.55717i	0.0499118	+	0.120498i	0.946869	−	0.321620i	$-0.104227\pi$
$167$	0.645002	+	1.55717i	0.0499118	+	0.120498i	−0.896957	+	0.442118i	$0.854227\pi$
$168$	−1.78444	−	1.95340i	−0.137673	−	0.150708i
$169$	10.5610			0.812386
$170$	−0.106509	+	3.75178i	−0.00816883	+	0.287749i
$171$	1.09646	+	1.89912i	0.0838483	+	0.145230i
$172$	−0.871029	+	3.25072i	−0.0664153	+	0.247865i
$173$	10.8169	+	1.42407i	0.822394	+	0.108270i	0.529968	−	0.848018i	$-0.322204\pi$
$173$	10.8169	+	1.42407i	0.822394	+	0.108270i	0.292426	+	0.956288i	$0.405537\pi$
$174$		−	3.00531i		−	0.227832i
$175$	10.3765	−	3.75869i	0.784393	−	0.284130i
$176$	−2.28569	+	5.51815i	−0.172291	+	0.415946i
$177$	9.52769	−	7.31085i	0.716145	−	0.549517i
$178$	−14.4367	−	3.86830i	−1.08208	−	0.289941i
$179$	16.8013	+	4.50189i	1.25579	+	0.336487i	0.824570	−	0.565760i	$-0.191417\pi$
$179$	16.8013	+	4.50189i	1.25579	+	0.336487i	0.431218	+	0.902248i	$0.358084\pi$
$180$	0.722196	−	0.554160i	0.0538293	−	0.0413047i
$181$	−3.20873	+	7.74656i	−0.238503	+	0.575797i	−0.997128	−	0.0757300i	$-0.975871\pi$
$181$	−3.20873	+	7.74656i	−0.238503	+	0.575797i	0.758625	+	0.651527i	$0.225871\pi$
$182$	−3.16116	−	2.66082i	−0.234321	−	0.197233i
$183$			3.66162i			0.270675i
$184$	−5.04229	−	0.663829i	−0.371722	−	0.0489382i
$185$	2.69135	−	10.0442i	0.197872	−	0.738468i
$186$	4.38379	+	7.59294i	0.321435	+	0.556741i
$187$	24.6166	+	0.698834i	1.80014	+	0.0511038i
$188$	0.878604			0.0640788
$189$	2.58391	−	0.568672i	0.187952	−	0.0413648i
$190$	0.763924	+	1.84428i	0.0554209	+	0.133798i
$191$	9.70396	+	5.60258i	0.702154	+	0.405389i	0.808149	−	0.588978i	$-0.200470\pi$
$191$	9.70396	+	5.60258i	0.702154	+	0.405389i	−0.105995	+	0.994367i	$0.533803\pi$
$192$	0.793353	+	0.608761i	0.0572553	+	0.0439336i
$193$	6.68604	−	0.880234i	0.481272	−	0.0633606i	0.114013	−	0.993479i	$-0.463630\pi$
$193$	6.68604	−	0.880234i	0.481272	−	0.0633606i	0.367259	+	0.930119i	$0.380296\pi$
$194$	2.80867	−	2.15517i	0.201651	−	0.154732i
$195$	1.00526	−	1.00526i	0.0719881	−	0.0719881i
$196$	−1.19433	−	6.89736i	−0.0853091	−	0.492669i
$197$	3.25433	+	1.34799i	0.231861	+	0.0960402i	0.495589	−	0.868557i	$-0.334952\pi$
$197$	3.25433	+	1.34799i	0.231861	+	0.0960402i	−0.263728	+	0.964597i	$0.584952\pi$
$198$	−3.63601	−	4.73854i	−0.258400	−	0.336753i
$199$	9.85449	+	7.56162i	0.698566	+	0.536029i	0.895871	−	0.444313i	$-0.146552\pi$
$199$	9.85449	+	7.56162i	0.698566	+	0.536029i	−0.197305	+	0.980342i	$0.563219\pi$
$200$	−3.61249	+	2.08567i	−0.255441	+	0.147479i
$201$	4.74491	+	0.624680i	0.334680	+	0.0440615i
$202$	−11.3660	−	11.3660i	−0.799710	−	0.799710i
$203$	4.28253	−	6.69947i	0.300575	−	0.470211i
$204$	1.17972	−	3.95073i	0.0825972	−	0.276606i
$205$	4.98222	−	8.62946i	0.347974	−	0.602708i
$206$	3.92237	−	14.6385i	0.273284	−	1.01991i
$207$	3.09604	−	4.03483i	0.215189	−	0.280440i
$208$	1.35249	+	0.780863i	0.0937786	+	0.0541431i
$209$	12.1008	−	5.01233i	0.837033	−	0.346710i
$210$	2.39960	−	0.206220i	0.165588	−	0.0142305i
$211$	−10.5263	−	4.36015i	−0.724663	−	0.300165i	−0.0103061	−	0.999947i	$-0.503281\pi$
$211$	−10.5263	−	4.36015i	−0.724663	−	0.300165i	−0.714357	+	0.699782i	$0.753281\pi$
$212$	1.39067	+	5.19005i	0.0955116	+	0.356454i
$213$	−9.05880	−	2.42730i	−0.620699	−	0.166316i
$214$	0.0392690	+	0.298277i	0.00268437	+	0.0203898i
$215$	−1.86497	−	2.43048i	−0.127190	−	0.165757i
$216$	−0.923880	+	0.382683i	−0.0628620	+	0.0260383i
$217$	−1.04747	+	23.1732i	−0.0711070	+	1.57310i
$218$	2.01059	+	4.85400i	0.136174	+	0.328754i
$219$	−4.39899	+	1.17871i	−0.297256	+	0.0796496i
$220$	−2.71854	−	4.70866i	−0.183284	−	0.317458i
$221$	1.02130	−	6.35765i	0.0687003	−	0.427662i
$222$	−5.71157	+	9.89272i	−0.383335	+	0.663956i
$223$	−3.51036	−	3.51036i	−0.235071	−	0.235071i	0.579735	−	0.814805i	$-0.303156\pi$
$223$	−3.51036	−	3.51036i	−0.235071	−	0.235071i	−0.814805	+	0.579735i	$0.803156\pi$
$224$	0.901076	+	2.48758i	0.0602056	+	0.166209i
$225$		−	4.17134i		−	0.278089i
$226$	−2.38531	+	18.1182i	−0.158668	+	1.20521i
$227$	−8.39884	+	1.10573i	−0.557450	+	0.0733897i	−0.403987	−	0.914765i	$-0.632376\pi$
$227$	−8.39884	+	1.10573i	−0.557450	+	0.0733897i	−0.153463	+	0.988154i	$0.549043\pi$
$228$	−0.286233	−	2.17416i	−0.0189563	−	0.143987i
$229$	3.87925	+	14.4776i	0.256348	+	0.956705i	0.967335	+	0.253500i	$0.0815817\pi$
$229$	3.87925	+	14.4776i	0.256348	+	0.956705i	−0.710987	+	0.703205i	$0.751752\pi$
$230$	3.27365	−	3.27365i	0.215858	−	0.215858i
$231$	−1.35307	−	15.7445i	−0.0890255	−	1.03591i
$232$	−1.15008	+	2.77654i	−0.0755065	+	0.182289i
$233$	0.409439	−	3.11000i	0.0268232	−	0.203743i	−0.972786	−	0.231707i	$-0.925569\pi$
$233$	0.409439	−	3.11000i	0.0268232	−	0.203743i	0.999609	+	0.0279640i	$0.00890239\pi$
$234$	−1.35249	+	0.780863i	−0.0884153	+	0.0510466i
$235$	−0.486888	+	0.634525i	−0.0317611	+	0.0413918i
$236$	−11.6002	+	3.10826i	−0.755107	+	0.202330i
$237$	10.5927			0.688069
$238$	8.25961	−	7.12592i	0.535391	−	0.461905i
$239$	2.41992			0.156532			0.0782659	−	0.996933i	$-0.475062\pi$
$239$	2.41992			0.156532			0.0782659	+	0.996933i	$0.475062\pi$
$240$	−0.879290	+	0.235605i	−0.0567579	+	0.0152082i
$241$	3.20277	−	4.17393i	0.206309	−	0.268867i	−0.678726	−	0.734391i	$-0.737468\pi$
$241$	3.20277	−	4.17393i	0.206309	−	0.268867i	0.885035	+	0.465525i	$0.154134\pi$
$242$	−21.3686	+	12.3372i	−1.37363	+	0.793064i
$243$	0.130526	−	0.991445i	0.00837326	−	0.0636012i
$244$	1.40124	−	3.38290i	0.0897053	−	0.216568i
$245$	5.64309	+	2.95971i	0.360524	+	0.189089i
$246$	−7.74016	+	7.74016i	−0.493494	+	0.493494i
$247$	−0.886387	−	3.30804i	−0.0563994	−	0.210486i
$248$	−1.14440	−	8.69256i	−0.0726693	−	0.551978i
$249$	14.8247	−	1.95171i	0.939477	−	0.123685i
$250$	1.08973	−	8.27732i	0.0689206	−	0.523504i
$251$			8.39038i			0.529596i	0.964304	+	0.264798i	$0.0853053\pi$
$251$			8.39038i			0.529596i	−0.964304	+	0.264798i	$0.914695\pi$
$252$	−2.60485	−	0.463437i	−0.164090	−	0.0291938i
$253$	−21.4794	−	21.4794i	−1.35040	−	1.35040i
$254$	−8.65697	+	14.9943i	−0.543187	+	0.940827i
$255$	2.19944	+	3.04133i	0.137734	+	0.190455i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	9.20411	−	2.46623i	0.574136	−	0.153839i	0.0399434	−	0.999202i	$-0.487282\pi$
$257$	9.20411	−	2.46623i	0.574136	−	0.153839i	0.534193	+	0.845363i	$0.320616\pi$
$258$	1.28788	+	3.10922i	0.0801800	+	0.193572i
$259$	−26.8294	+	13.9141i	−1.66710	+	0.864579i
$260$	−1.31343	+	0.544042i	−0.0814558	+	0.0337401i
$261$	−1.82951	−	2.38427i	−0.113244	−	0.147583i
$262$	−1.88059	−	14.2845i	−0.116183	−	0.882500i
$263$	1.62086	+	0.434309i	0.0999467	+	0.0267806i	0.308446	−	0.951242i	$-0.400191\pi$
$263$	1.62086	+	0.434309i	0.0999467	+	0.0267806i	−0.208499	+	0.978023i	$0.566858\pi$
$264$	1.54587	+	5.76928i	0.0951420	+	0.355075i
$265$	−4.51889	−	1.87178i	−0.277593	−	0.114983i
$266$	2.46008	−	5.25454i	0.150837	−	0.322177i
$267$	−13.8083	+	5.71957i	−0.845052	+	0.350032i
$268$	−4.14467	−	2.39293i	−0.253176	−	0.146171i
$269$	7.96951	−	10.3861i	0.485909	−	0.633249i	−0.484478	−	0.874803i	$-0.660990\pi$
$269$	7.96951	−	10.3861i	0.485909	−	0.633249i	0.970387	+	0.241554i	$0.0776571\pi$
$270$	0.235605	−	0.879290i	0.0143385	−	0.0535119i
$271$	−2.77523	+	4.80684i	−0.168583	+	0.291995i	−0.937922	−	0.346846i	$-0.887253\pi$
$271$	−2.77523	+	4.80684i	−0.168583	+	0.291995i	0.769339	+	0.638841i	$0.220586\pi$
$272$	−2.60180	+	3.19854i	−0.157757	+	0.193940i
$273$	−4.12772	−	0.186581i	−0.249821	−	0.0112924i
$274$	12.4070	+	12.4070i	0.749537	+	0.749537i
$275$	−24.7014	−	3.25201i	−1.48955	−	0.196103i
$276$	−4.40443	+	2.54290i	−0.265115	+	0.153064i
$277$	−0.488590	−	0.374908i	−0.0293565	−	0.0225261i	0.593979	−	0.804481i	$-0.297556\pi$
$277$	−0.488590	−	0.374908i	−0.0293565	−	0.0225261i	−0.623335	+	0.781955i	$0.714223\pi$
$278$	−1.35064	−	1.76019i	−0.0810060	−	0.105569i
$279$	8.10018	+	3.35520i	0.484945	+	0.200871i
$280$	−2.29586	−	0.727766i	−0.137204	−	0.0434924i
$281$	13.4090	−	13.4090i	0.799915	−	0.799915i	−0.183167	−	0.983082i	$-0.558635\pi$
$281$	13.4090	−	13.4090i	0.799915	−	0.799915i	0.983082	+	0.183167i	$0.0586348\pi$
$282$	0.697044	−	0.534861i	0.0415084	−	0.0318505i
$283$	−15.8839	+	2.09116i	−0.944201	+	0.124306i	−0.586879	−	0.809675i	$-0.699644\pi$
$283$	−15.8839	+	2.09116i	−0.944201	+	0.124306i	−0.357322	+	0.933981i	$0.616310\pi$
$284$	7.44035	+	5.70918i	0.441504	+	0.338778i
$285$	1.72879	+	0.998115i	0.102404	+	0.0591232i
$286$	3.56962	+	8.61783i	0.211076	+	0.509583i
$287$	−28.2841	+	6.22482i	−1.66956	+	0.367439i
$288$	1.00000			0.0589256
$289$	16.1447	+	5.32442i	0.949687	+	0.313201i
$290$	−1.36788	−	2.36923i	−0.0803245	−	0.139126i
$291$	0.916286	−	3.41963i	0.0537136	−	0.200462i
$292$	4.51521	+	0.594439i	0.264233	+	0.0347869i
$293$		−	9.20694i		−	0.537875i	−0.963158	−	0.268938i	$-0.913327\pi$
$293$		−	9.20694i		−	0.537875i	0.963158	−	0.268938i	$-0.0866726\pi$
$294$	−5.14637	−	4.74498i	−0.300142	−	0.276733i
$295$	4.18359	−	10.1001i	0.243578	−	0.588049i
$296$	9.06258	−	6.95396i	0.526752	−	0.404191i
$297$	−5.76928	−	1.54587i	−0.334768	−	0.0897007i
$298$	−1.28015	−	0.343016i	−0.0741572	−	0.0198704i
$299$	−6.30130	+	4.83516i	−0.364414	+	0.279624i
$300$	−1.59630	+	3.85382i	−0.0921626	+	0.222500i
$301$	−1.55965	+	8.76634i	−0.0898966	+	0.505284i
$302$		−	22.4133i		−	1.28974i
$303$	−15.9365	−	2.09807i	−0.915525	−	0.120531i
$304$	−0.567569	+	2.11820i	−0.0325523	+	0.121487i
$305$	1.66660	+	2.88664i	0.0954293	+	0.165288i
$306$	−1.46911	−	3.85249i	−0.0839836	−	0.220232i
$307$	8.68607			0.495740			0.247870	−	0.968793i	$-0.420269\pi$
$307$	8.68607			0.495740			0.247870	+	0.968793i	$0.420269\pi$
$308$	−4.77509	+	15.0638i	−0.272086	+	0.858341i
$309$	−5.79952	−	14.0013i	−0.329923	−	0.796505i
$310$	6.91191	+	3.99060i	0.392570	+	0.226651i
$311$	5.32526	+	4.08622i	0.301968	+	0.231708i	0.748620	−	0.663000i	$-0.230717\pi$
$311$	5.32526	+	4.08622i	0.301968	+	0.231708i	−0.446652	+	0.894708i	$0.647384\pi$
$312$	1.54836	−	0.203846i	0.0876589	−	0.0115405i
$313$	−24.6748	+	18.9337i	−1.39470	+	1.07019i	−0.407075	+	0.913395i	$0.633451\pi$
$313$	−24.6748	+	18.9337i	−1.39470	+	1.07019i	−0.987630	+	0.156800i	$0.949882\pi$
$314$	−0.804588	+	0.804588i	−0.0454055	+	0.0454055i
$315$	1.77819	−	1.62439i	0.100190	−	0.0915241i
$316$	−9.78636	−	4.05364i	−0.550526	−	0.228035i
$317$	−16.3927	−	21.3634i	−0.920706	−	1.19989i	−0.979465	−	0.201615i	$-0.935381\pi$
$317$	−16.3927	−	21.3634i	−0.920706	−	1.19989i	0.0587587	−	0.998272i	$-0.481286\pi$
$318$	4.26279	+	3.27096i	0.239046	+	0.183426i
$319$	−15.5452	+	8.97504i	−0.870366	+	0.502506i
$320$	0.902520	+	0.118819i	0.0504524	+	0.00664219i
$321$	0.212734	+	0.212734i	0.0118736	+	0.0118736i
$322$	−13.4420	−	0.607605i	−0.749095	−	0.0338605i
$323$	8.99416	−	0.925312i	0.500448	−	0.0514857i
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	−1.68607	+	6.29251i	−0.0935265	+	0.349046i
$326$	11.4913	−	14.9758i	0.636444	−	0.829430i
$327$	4.55004	+	2.62696i	0.251618	+	0.145271i
$328$	10.1130	−	4.18894i	0.558397	−	0.231296i
$329$	2.31603	−	0.199038i	0.127687	−	0.0109733i
$330$	−5.02321	−	2.08068i	−0.276519	−	0.114538i
$331$	−3.49646	−	13.0490i	−0.192183	−	0.717236i	−0.992978	−	0.118298i	$-0.962256\pi$
$331$	−3.49646	−	13.0490i	−0.192183	−	0.717236i	0.800795	−	0.598938i	$-0.204410\pi$
$332$	−14.4431	−	3.87002i	−0.792669	−	0.212395i
$333$	1.49102	+	11.3254i	0.0817073	+	0.620628i
$334$	−1.02605	−	1.33717i	−0.0561430	−	0.0731669i
$335$	4.02498	−	1.66720i	0.219908	−	0.0910889i
$336$	2.22922	+	1.42499i	0.121614	+	0.0777396i
$337$	−3.25800	−	7.86550i	−0.177474	−	0.428461i	0.809961	−	0.586484i	$-0.199488\pi$
$337$	−3.25800	−	7.86550i	−0.177474	−	0.428461i	−0.987436	+	0.158022i	$0.949488\pi$
$338$	−10.2012	+	2.73339i	−0.554870	+	0.148677i
$339$	9.13728	+	15.8262i	0.496269	+	0.859563i
$340$	−0.868154	−	3.65151i	−0.0470823	−	0.198031i
$341$	26.1835	−	45.3511i	1.41791	−	2.45590i
$342$	−1.55063	−	1.55063i	−0.0838483	−	0.0838483i
$343$	−4.71081	−	17.9111i	−0.254360	−	0.967110i
$344$		−	3.36540i		−	0.181450i
$345$	0.604289	−	4.59003i	0.0325338	−	0.247119i
$346$	−10.8169	+	1.42407i	−0.581520	+	0.0765586i
$347$	4.36088	+	33.1241i	0.234104	+	1.77820i	0.555763	+	0.831341i	$0.312426\pi$
$347$	4.36088	+	33.1241i	0.234104	+	1.77820i	−0.321659	+	0.946856i	$0.604240\pi$
$348$	0.777830	+	2.90290i	0.0416961	+	0.155612i
$349$	6.62858	−	6.62858i	0.354820	−	0.354820i	−0.507079	−	0.861899i	$-0.669275\pi$
$349$	6.62858	−	6.62858i	0.354820	−	0.354820i	0.861899	+	0.507079i	$0.169275\pi$
$350$	−9.05015	+	6.31627i	−0.483751	+	0.337619i
$351$	−0.597647	+	1.44285i	−0.0319000	+	0.0770134i
$352$	0.779607	−	5.92170i	0.0415532	−	0.315628i
$353$	−16.1961	+	9.35081i	−0.862030	+	0.497693i	−0.864691	−	0.502303i	$-0.832486\pi$
$353$	−16.1961	+	9.35081i	−0.862030	+	0.497693i	0.00266170	+	0.999996i	$0.499153\pi$
$354$	−7.31085	+	9.52769i	−0.388568	+	0.506391i
$355$	−8.24630	+	2.20959i	−0.437668	+	0.117273i
$356$	14.9460			0.792134
$357$	2.21480	−	10.6815i	0.117220	−	0.565325i
$358$	−17.3940			−0.919300
$359$	5.90781	−	1.58299i	0.311803	−	0.0835472i	−0.0995244	−	0.995035i	$-0.531732\pi$
$359$	5.90781	−	1.58299i	0.311803	−	0.0835472i	0.411327	+	0.911488i	$0.365065\pi$
$360$	−0.554160	+	0.722196i	−0.0292068	+	0.0380631i
$361$	−12.2899	+	7.09556i	−0.646835	+	0.373450i
$362$	1.09444	−	8.31308i	0.0575224	−	0.436926i
$363$	−9.44247	+	22.7961i	−0.495601	+	1.19649i
$364$	3.74212	+	1.75199i	0.196140	+	0.0918292i
$365$	−2.93145	+	2.93145i	−0.153439	+	0.153439i
$366$	−0.947697	−	3.53685i	−0.0495369	−	0.184874i
$367$	−0.537805	−	4.08503i	−0.0280732	−	0.213237i	0.971659	−	0.236388i	$-0.0759636\pi$
$367$	−0.537805	−	4.08503i	−0.0280732	−	0.213237i	−0.999732	+	0.0231508i	$0.992630\pi$
$368$	5.04229	−	0.663829i	0.262847	−	0.0346045i
$369$	−1.42877	+	10.8526i	−0.0743788	+	0.564963i
$370$			10.3986i			0.540596i
$371$	4.84160	+	13.3661i	0.251363	+	0.693934i
$372$	−6.19961	−	6.19961i	−0.321435	−	0.321435i
$373$	1.21526	−	2.10490i	0.0629239	−	0.108987i	−0.832847	−	0.553503i	$-0.813291\pi$
$373$	1.21526	−	2.10490i	0.0629239	−	0.108987i	0.895771	+	0.444515i	$0.146624\pi$
$374$	−23.9587	+	5.69622i	−1.23887	+	0.294544i
$375$	−4.17437	−	7.23022i	−0.215564	−	0.373367i
$376$	−0.848667	+	0.227400i	−0.0437666	+	0.0117272i
$377$	1.79611	+	4.33619i	0.0925044	+	0.223325i
$378$	−2.34869	+	1.21806i	−0.120803	+	0.0626503i
$379$	14.5028	−	6.00727i	0.744960	−	0.308573i	0.0222769	−	0.999752i	$-0.492908\pi$
$379$	14.5028	−	6.00727i	0.744960	−	0.308573i	0.722683	+	0.691179i	$0.242908\pi$
$380$	−1.21523	−	1.58372i	−0.0623399	−	0.0812429i
$381$	2.25992	+	17.1658i	0.115779	+	0.879432i
$382$	−10.8234	−	2.90011i	−0.553771	−	0.148383i
$383$	−5.01301	−	18.7088i	−0.256153	−	0.955975i	−0.967446	−	0.253079i	$-0.918557\pi$
$383$	−5.01301	−	18.7088i	−0.256153	−	0.955975i	0.711293	−	0.702896i	$-0.248110\pi$
$384$	−0.923880	−	0.382683i	−0.0471465	−	0.0195287i
$385$	−8.23287	−	11.7963i	−0.419586	−	0.601197i
$386$	−6.23040	+	2.58071i	−0.317119	+	0.131355i
$387$	2.91452	+	1.68270i	0.148153	+	0.0855364i
$388$	−2.15517	+	2.80867i	−0.109412	+	0.142589i
$389$	7.39899	−	27.6134i	0.375144	−	1.40006i	−0.477991	−	0.878365i	$-0.658635\pi$
$389$	7.39899	−	27.6134i	0.375144	−	1.40006i	0.853135	−	0.521691i	$-0.174699\pi$
$390$	−0.710826	+	1.23119i	−0.0359941	+	0.0623435i
$391$	−9.96508	−	18.4501i	−0.503956	−	0.933063i
$392$	2.93880	+	6.35322i	0.148432	+	0.320886i
$393$	−10.1878	−	10.1878i	−0.513908	−	0.513908i
$394$	−3.49233	−	0.459774i	−0.175941	−	0.0231631i
$395$	8.35074	−	4.82130i	0.420171	−	0.242586i
$396$	4.73854	+	3.63601i	0.238121	+	0.182716i
$397$	22.4807	+	29.2974i	1.12827	+	1.47040i	0.862288	+	0.506418i	$0.169031\pi$
$397$	22.4807	+	29.2974i	1.12827	+	1.47040i	0.265986	+	0.963977i	$0.414302\pi$
$398$	−11.4758	−	4.75343i	−0.575230	−	0.238268i
$399$	−1.24705	−	5.66631i	−0.0624306	−	0.283670i
$400$	2.94958	−	2.94958i	0.147479	−	0.147479i
$401$	−24.7861	+	19.0190i	−1.23776	+	0.949766i	−0.999769	−	0.0215018i	$-0.993155\pi$
$401$	−24.7861	+	19.0190i	−1.23776	+	0.949766i	−0.237990	+	0.971268i	$0.576489\pi$
$402$	−4.74491	+	0.624680i	−0.236655	+	0.0311562i
$403$	−10.8630	−	8.33549i	−0.541126	−	0.415220i
$404$	13.9205	+	8.03698i	0.692569	+	0.399855i
$405$	−0.348360	−	0.841015i	−0.0173101	−	0.0417904i
$406$	−2.40266	+	7.57959i	−0.119242	+	0.376169i
$407$	68.2281			3.38194
$408$	−0.117003	+	4.12145i	−0.00579250	+	0.204042i
$409$	14.2527	+	24.6865i	0.704753	+	1.22067i	0.966781	+	0.255607i	$0.0822753\pi$
$409$	14.2527	+	24.6865i	0.704753	+	1.22067i	−0.262028	+	0.965060i	$0.584391\pi$
$410$	−2.57899	+	9.62492i	−0.127367	+	0.475341i
$411$	17.3961	+	2.29024i	0.858086	+	0.112969i
$412$			15.1549i			0.746627i
$413$	−29.8743	+	10.8214i	−1.47002	+	0.532485i
$414$	−1.94625	+	4.69866i	−0.0956529	+	0.230927i
$415$	10.7987	−	8.28615i	0.530088	−	0.406751i
$416$	−1.50851	−	0.404204i	−0.0739608	−	0.0198177i
$417$	−2.14307	−	0.574233i	−0.104947	−	0.0281203i
$418$	−10.3912	+	7.97347i	−0.508252	+	0.389995i
$419$	−1.55342	+	3.75029i	−0.0758896	+	0.183214i	−0.957271	−	0.289191i	$-0.906614\pi$
$419$	−1.55342	+	3.75029i	−0.0758896	+	0.183214i	0.881382	+	0.472404i	$0.156614\pi$
$420$	−2.26447	+	0.820256i	−0.110495	+	0.0400244i
$421$			32.6771i			1.59259i	0.604911	+	0.796293i	$0.293209\pi$
$421$			32.6771i			1.59259i	−0.604911	+	0.796293i	$0.706791\pi$
$422$	11.2961	+	1.48717i	0.549888	+	0.0723941i
$423$	0.227400	−	0.848667i	0.0110565	−	0.0412636i
$424$	−2.68657	−	4.65327i	−0.130471	−	0.225983i
$425$	−15.6965	−	7.02998i	−0.761393	−	0.341004i
$426$	9.37836			0.454383
$427$	2.92737	−	9.23487i	0.141665	−	0.446907i
$428$	−0.115131	−	0.277950i	−0.00556505	−	0.0134352i
$429$	8.07818	+	4.66394i	0.390018	+	0.225177i
$430$	2.43048	+	1.86497i	0.117208	+	0.0899368i
$431$	−7.65229	+	1.00744i	−0.368598	+	0.0485269i	−0.312550	−	0.949901i	$-0.601183\pi$
$431$	−7.65229	+	1.00744i	−0.368598	+	0.0485269i	−0.0560478	+	0.998428i	$0.517850\pi$
$432$	0.793353	−	0.608761i	0.0381702	−	0.0292890i
$433$	−17.3263	+	17.3263i	−0.832648	+	0.832648i	−0.987878	−	0.155230i	$-0.950388\pi$
$433$	−17.3263	+	17.3263i	−0.832648	+	0.832648i	0.155230	+	0.987878i	$0.450388\pi$
$434$	−4.98587	−	22.6547i	−0.239330	−	1.08746i
$435$	−2.52751	−	1.04693i	−0.121185	−	0.0501963i
$436$	−3.19839	−	4.16822i	−0.153175	−	0.199622i
$437$	−8.84806	−	6.78935i	−0.423260	−	0.324779i
$438$	3.94403	−	2.27709i	0.188453	−	0.108803i
$439$	−39.8987	−	5.25276i	−1.90426	−	0.250701i	−0.915738	−	0.401776i	$-0.868393\pi$
$439$	−39.8987	−	5.25276i	−1.90426	−	0.250701i	−0.988522	+	0.151076i	$0.951726\pi$
$440$	3.84460	+	3.84460i	0.183284	+	0.183284i
$441$	−6.97145	−	0.631537i	−0.331974	−	0.0300732i
$442$	0.658978	+	6.40535i	0.0313444	+	0.304672i
$443$	−3.87336	+	6.70885i	−0.184029	+	0.318747i	−0.943249	−	0.332087i	$-0.892247\pi$
$443$	−3.87336	+	6.70885i	−0.184029	+	0.318747i	0.759220	+	0.650834i	$0.225581\pi$
$444$	2.95652	−	11.0339i	0.140310	−	0.523646i
$445$	−8.28246	+	10.7939i	−0.392626	+	0.511680i
$446$	4.29929	+	2.48220i	0.203577	+	0.117535i
$447$	−1.22443	+	0.507174i	−0.0579134	+	0.0239885i
$448$	−1.51421	−	2.16960i	−0.0715395	−	0.102504i
$449$	3.27775	+	1.35769i	0.154687	+	0.0640734i	0.458683	−	0.888600i	$-0.348321\pi$
$449$	3.27775	+	1.35769i	0.154687	+	0.0640734i	−0.303997	+	0.952673i	$0.598321\pi$
$450$	1.07962	+	4.02920i	0.0508939	+	0.189939i
$451$	63.1519	+	16.9215i	2.97371	+	0.796803i
$452$	−2.38531	−	18.1182i	−0.112196	−	0.852209i
$453$	−13.6444	−	17.7817i	−0.641069	−	0.835457i
$454$	7.82647	−	3.24183i	0.367315	−	0.152147i
$455$	−3.33901	+	1.73166i	−0.156535	+	0.0811814i
$456$	0.839193	+	2.02599i	0.0392988	+	0.0948758i
$457$	−3.04728	+	0.816516i	−0.142546	+	0.0381950i	−0.329386	−	0.944195i	$-0.606842\pi$
$457$	−3.04728	+	0.816516i	−0.142546	+	0.0381950i	0.186841	+	0.982390i	$0.440175\pi$
$458$	−7.49414	−	12.9802i	−0.350178	−	0.606527i
$459$	−3.51077	−	2.16205i	−0.163869	−	0.100916i
$460$	−2.31482	+	4.00939i	−0.107929	+	0.186939i
$461$	2.05772	+	2.05772i	0.0958374	+	0.0958374i	0.753400	−	0.657563i	$-0.228412\pi$
$461$	2.05772	+	2.05772i	0.0958374	+	0.0958374i	−0.657563	+	0.753400i	$0.728412\pi$
$462$	5.38194	+	14.8578i	0.250391	+	0.691249i
$463$		−	17.9524i		−	0.834320i	−0.908833	−	0.417160i	$-0.863025\pi$
$463$		−	17.9524i		−	0.834320i	0.908833	−	0.417160i	$-0.136975\pi$
$464$	0.392271	−	2.97959i	0.0182107	−	0.138324i
$465$	7.91291	−	1.04175i	0.366952	−	0.0483102i
$466$	0.409439	+	3.11000i	0.0189669	+	0.144068i
$467$	1.14159	+	4.26045i	0.0528263	+	0.197150i	0.987296	−	0.158893i	$-0.0507924\pi$
$467$	1.14159	+	4.26045i	0.0528263	+	0.197150i	−0.934470	+	0.356043i	$0.884126\pi$
$468$	1.10431	−	1.10431i	0.0510466	−	0.0510466i
$469$	−11.4676	−	5.36891i	−0.529524	−	0.247913i
$470$	0.306070	−	0.738919i	0.0141180	−	0.0340838i
$471$	−0.148520	+	1.12812i	−0.00684346	+	0.0519812i
$472$	10.4004	−	6.00470i	0.478719	−	0.276389i
$473$	12.2366	−	15.9471i	0.562640	−	0.733247i
$474$	−10.2317	+	2.74159i	−0.469960	+	0.125925i
$475$	−9.14740			−0.419712
$476$	−6.13385	+	9.02086i	−0.281144	+	0.413470i
$477$	5.37314			0.246019
$478$	−2.33747	+	0.626322i	−0.106913	+	0.0286473i
$479$	0.608641	−	0.793196i	0.0278095	−	0.0362421i	−0.779242	−	0.626724i	$-0.784395\pi$
$479$	0.608641	−	0.793196i	0.0278095	−	0.0362421i	0.807051	+	0.590482i	$0.201062\pi$
$480$	0.788350	−	0.455154i	0.0359831	−	0.0207748i
$481$	2.32856	−	17.6872i	0.106173	−	0.806466i
$482$	−2.01335	+	4.86065i	−0.0917054	+	0.221396i
$483$	−11.0342	+	7.70094i	−0.502072	+	0.350405i
$484$	17.4474	−	17.4474i	0.793064	−	0.793064i
$485$	−0.834102	−	3.11291i	−0.0378746	−	0.141350i
$486$	0.130526	+	0.991445i	0.00592079	+	0.0449729i
$487$	22.5228	−	2.96518i	1.02060	−	0.134365i	0.398393	−	0.917215i	$-0.369568\pi$
$487$	22.5228	−	2.96518i	1.02060	−	0.134365i	0.622211	+	0.782850i	$0.286235\pi$
$488$	−0.477937	+	3.63029i	−0.0216352	+	0.164336i
$489$		−	18.8765i		−	0.853626i
$490$	−6.21684	−	1.39832i	−0.280848	−	0.0631695i
$491$	−4.89469	−	4.89469i	−0.220894	−	0.220894i	0.587981	−	0.808875i	$-0.299923\pi$
$491$	−4.89469	−	4.89469i	−0.220894	−	0.220894i	−0.808875	+	0.587981i	$0.799923\pi$
$492$	5.47312	−	9.47972i	0.246747	−	0.427379i
$493$	−12.0552	+	2.86614i	−0.542937	+	0.129084i
$494$	1.71237	+	2.96591i	0.0770431	+	0.133443i
$495$	−5.25182	+	1.40722i	−0.236052	+	0.0632499i
$496$	3.35520	+	8.10018i	0.150653	+	0.363709i
$497$	20.9064	+	13.3641i	0.937780	+	0.599461i
$498$	−13.8144	+	5.72212i	−0.619039	+	0.256414i
$499$	8.76522	+	11.4231i	0.392385	+	0.511366i	0.947216	−	0.320597i	$-0.103884\pi$
$499$	8.76522	+	11.4231i	0.392385	+	0.511366i	−0.554831	+	0.831963i	$0.687217\pi$
$500$	1.08973	+	8.27732i	0.0487342	+	0.370173i
$501$	−1.62804	−	0.436232i	−0.0727355	−	0.0194894i
$502$	−2.17159	−	8.10448i	−0.0969228	−	0.361721i
$503$	−6.58617	−	2.72808i	−0.293663	−	0.121639i	0.230988	−	0.972957i	$-0.425804\pi$
$503$	−6.58617	−	2.72808i	−0.293663	−	0.121639i	−0.524651	+	0.851317i	$0.675804\pi$
$504$	2.63603	−	0.226539i	0.117418	−	0.0100908i
$505$	−13.5184	+	5.59952i	−0.601563	+	0.249176i
$506$	26.3068	+	15.1882i	1.16948	+	0.675199i
$507$	−6.42914	+	8.37861i	−0.285528	+	0.372107i
$508$	4.48118	−	16.7240i	0.198820	−	0.742007i
$509$	15.1828	−	26.2974i	0.672966	−	1.16561i	−0.304094	−	0.952642i	$-0.598354\pi$
$509$	15.1828	−	26.2974i	0.672966	−	1.16561i	0.977059	−	0.212968i	$-0.0683131\pi$
$510$	−2.91165	−	2.36844i	−0.128930	−	0.104876i
$511$	12.0369	+	0.544092i	0.532482	+	0.0240692i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−2.17416	−	0.286233i	−0.0959914	−	0.0126375i
$514$	−8.25218	+	4.76440i	−0.363988	+	0.210148i
$515$	−10.9448	−	8.39823i	−0.482285	−	0.370070i
$516$	−2.04872	−	2.66995i	−0.0901900	−	0.117538i
$517$	−4.84827	−	2.00822i	−0.213227	−	0.0883214i
$518$	22.3139	−	20.3839i	0.980418	−	0.895618i
$519$	−7.71471	+	7.71471i	−0.338638	+	0.338638i
$520$	1.12787	−	0.865446i	0.0494605	−	0.0379523i
$521$	−23.3851	+	3.07871i	−1.02452	+	0.134881i	−0.624013	−	0.781414i	$-0.714499\pi$
$521$	−23.3851	+	3.07871i	−1.02452	+	0.134881i	−0.400506	+	0.916294i	$0.631166\pi$
$522$	2.38427	+	1.82951i	0.104357	+	0.0800756i
$523$	−2.21336	−	1.27788i	−0.0967835	−	0.0558780i	0.450827	−	0.892611i	$-0.351129\pi$
$523$	−2.21336	−	1.27788i	−0.0967835	−	0.0558780i	−0.547611	+	0.836733i	$0.684462\pi$
$524$	5.51361	+	13.3110i	0.240863	+	0.581496i
$525$	−3.33487	+	10.5204i	−0.145546	+	0.459149i
$526$	−1.67804			−0.0731661
$527$	26.2767	−	24.8260i	1.14463	−	1.08144i
$528$	−2.98640	−	5.17260i	−0.129966	−	0.225108i
$529$	−0.741597	+	2.76768i	−0.0322433	+	0.120334i
$530$	4.84936	+	0.638431i	0.210643	+	0.0277317i
$531$			12.0094i			0.521163i
$532$	−1.01628	+	5.71221i	−0.0440613	+	0.247656i
$533$	6.54198	−	15.7937i	0.283365	−	0.684103i
$534$	11.8574	−	9.09852i	0.513121	−	0.393732i
$535$	0.264535	+	0.0708820i	0.0114369	+	0.00306450i
$536$	4.62278	+	1.23867i	0.199674	+	0.0535024i
$537$	−13.7996	+	10.5888i	−0.595495	+	0.456940i
$538$	−5.00984	+	12.0948i	−0.215990	+	0.521445i
$539$	−9.17477	+	40.7905i	−0.395185	+	1.75697i
$540$			0.910308i			0.0391734i
$541$	22.4078	+	2.95004i	0.963387	+	0.126832i	0.595779	−	0.803149i	$-0.296844\pi$
$541$	22.4078	+	2.95004i	0.963387	+	0.126832i	0.367608	+	0.929981i	$0.380177\pi$
$542$	1.43657	−	5.36134i	0.0617058	−	0.230289i
$543$	−4.19241	−	7.26146i	−0.179913	−	0.311619i
$544$	1.68531	−	3.76294i	0.0722569	−	0.161335i
$545$	4.78269			0.204868
$546$	4.03536	−	0.888110i	0.172698	−	0.0380076i
$547$	−4.66489	−	11.2621i	−0.199457	−	0.481531i	0.792228	−	0.610226i	$-0.208921\pi$
$547$	−4.66489	−	11.2621i	−0.199457	−	0.481531i	−0.991684	+	0.128695i	$0.958921\pi$
$548$	−15.1955	−	8.77311i	−0.649118	−	0.374769i
$549$	−2.90496	−	2.22905i	−0.123981	−	0.0951337i
$550$	24.7014	−	3.25201i	1.05327	−	0.138666i
$551$	−5.22851	+	4.01197i	−0.222742	+	0.170916i
$552$	3.59620	−	3.59620i	0.153064	−	0.153064i
$553$	−26.7155	−	8.46856i	−1.13606	−	0.360120i
$554$	0.568975	+	0.235677i	0.0241734	+	0.0100130i
$555$	6.33025	+	8.24974i	0.268704	+	0.350182i
$556$	1.76019	+	1.35064i	0.0746486	+	0.0572799i
$557$	17.1148	−	9.88121i	0.725176	−	0.418680i	−0.0914789	−	0.995807i	$-0.529159\pi$
$557$	17.1148	−	9.88121i	0.725176	−	0.418680i	0.816655	+	0.577127i	$0.195826\pi$
$558$	−8.69256	−	1.14440i	−0.367986	−	0.0484462i
$559$	−3.71643	−	3.71643i	−0.157188	−	0.157188i
$560$	2.40599	+	0.108755i	0.101672	+	0.00459576i
$561$	−15.5400	+	19.1042i	−0.656101	+	0.806581i
$562$	−9.48161	+	16.4226i	−0.399958	+	0.692747i
$563$	8.29208	−	30.9465i	0.349470	−	1.30424i	−0.537833	−	0.843051i	$-0.680757\pi$
$563$	8.29208	−	30.9465i	0.349470	−	1.30424i	0.887303	−	0.461187i	$-0.152576\pi$
$564$	−0.534861	+	0.697044i	−0.0225217	+	0.0293508i
$565$	14.4067	+	8.31774i	0.606096	+	0.349930i
$566$	14.8015	−	6.13097i	0.622152	−	0.257704i
$567$	−1.12183	+	2.39614i	−0.0471124	+	0.100629i
$568$	−8.66448	−	3.58894i	−0.363553	−	0.150589i
$569$	−5.04916	−	18.8437i	−0.211672	−	0.789969i	−0.987312	−	0.158794i	$-0.949239\pi$
$569$	−5.04916	−	18.8437i	−0.211672	−	0.789969i	0.775640	−	0.631175i	$-0.217427\pi$
$570$	−1.92821	−	0.516662i	−0.0807639	−	0.0216406i
$571$	−5.44591	−	41.3658i	−0.227904	−	1.73111i	−0.597462	−	0.801898i	$-0.703824\pi$
$571$	−5.44591	−	41.3658i	−0.227904	−	1.73111i	0.369557	−	0.929208i	$-0.379509\pi$
$572$	−5.67845	−	7.40030i	−0.237428	−	0.309422i
$573$	−10.3522	+	4.28803i	−0.432470	+	0.179135i
$574$	25.7093	−	13.3332i	1.07308	−	0.556516i
$575$	8.11847	+	19.5997i	0.338563	+	0.817365i
$576$	−0.965926	+	0.258819i	−0.0402469	+	0.0107841i
$577$	−13.8237	−	23.9433i	−0.575486	−	0.996772i	−0.995989	−	0.0894803i	$-0.971479\pi$
$577$	−13.8237	−	23.9433i	−0.575486	−	0.996772i	0.420502	−	0.907292i	$-0.361854\pi$
$578$	−16.9726	−	0.964441i	−0.705968	−	0.0401155i
$579$	−3.37187	+	5.84024i	−0.140130	+	0.242712i
$580$	1.93447	+	1.93447i	0.0803245	+	0.0803245i
$581$	−38.9493	−	6.92959i	−1.61589	−	0.287488i
$582$			3.54026i			0.146748i
$583$	4.18893	−	31.8181i	0.173488	−	1.31777i
$584$	−4.51521	+	0.594439i	−0.186841	+	0.0245980i
$585$	0.185563	+	1.40949i	0.00767207	+	0.0582752i
$586$	2.38293	+	8.89322i	0.0984380	+	0.367376i
$587$	1.19937	−	1.19937i	0.0495032	−	0.0495032i	−0.681922	−	0.731425i	$-0.738856\pi$
$587$	1.19937	−	1.19937i	0.0495032	−	0.0495032i	0.731425	+	0.681922i	$0.238856\pi$
$588$	6.19910	+	3.25132i	0.255647	+	0.134082i
$589$	7.35769	−	17.7630i	0.303168	−	0.731913i
$590$	−1.42694	+	10.8387i	−0.0587464	+	0.446223i
$591$	−3.05054	+	1.76123i	−0.125483	+	0.0724474i
$592$	−6.95396	+	9.06258i	−0.285806	+	0.372470i
$593$	31.4052	−	8.41499i	1.28966	−	0.345562i	0.452126	−	0.891954i	$-0.350666\pi$
$593$	31.4052	−	8.41499i	1.28966	−	0.345562i	0.837530	+	0.546392i	$0.183999\pi$
$594$	5.97280			0.245067
$595$	−3.11569	−	9.42884i	−0.127731	−	0.386545i
$596$	1.32531			0.0542868
$597$	−11.9981	+	3.21487i	−0.491048	+	0.131576i
$598$	4.83516	−	6.30130i	0.197724	−	0.257679i
$599$	−15.3612	+	8.86882i	−0.627644	+	0.362370i	−0.779839	−	0.625980i	$-0.784699\pi$
$599$	−15.3612	+	8.86882i	−0.627644	+	0.362370i	0.152195	+	0.988350i	$0.451366\pi$
$600$	0.544469	−	4.13565i	0.0222279	−	0.168837i
$601$	−3.31741	+	8.00894i	−0.135320	+	0.326691i	−0.976985	−	0.213309i	$-0.931576\pi$
$601$	−3.31741	+	8.00894i	−0.135320	+	0.326691i	0.841665	+	0.540000i	$0.181576\pi$
$602$	−0.762392	−	8.87130i	−0.0310728	−	0.361567i
$603$	−3.38411	+	3.38411i	−0.137812	+	0.137812i
$604$	5.80100	+	21.6496i	0.236039	+	0.880910i
$605$	2.93178	+	22.2691i	0.119194	+	0.905368i
$606$	15.9365	−	2.09807i	0.647374	−	0.0852284i
$607$	−1.17118	+	8.89601i	−0.0475368	+	0.361078i	0.951100	+	0.308883i	$0.0999551\pi$
$607$	−1.17118	+	8.89601i	−0.0475368	+	0.361078i	−0.998637	+	0.0521951i	$0.983378\pi$
$608$		−	2.19292i		−	0.0889346i
$609$	2.70801	+	7.47594i	0.109734	+	0.302940i
$610$	−2.35693	−	2.35693i	−0.0954293	−	0.0954293i
$611$	−0.686070	+	1.18831i	−0.0277554	+	0.0480738i
$612$	2.41615	+	3.34099i	0.0976672	+	0.135051i
$613$	4.40300	+	7.62622i	0.177835	+	0.308020i	0.941139	−	0.338020i	$-0.109757\pi$
$613$	4.40300	+	7.62622i	0.177835	+	0.308020i	−0.763303	+	0.646040i	$0.776424\pi$
$614$	−8.39010	+	2.24812i	−0.338597	+	0.0907267i
$615$	3.81323	+	9.20595i	0.153764	+	0.371220i
$616$	0.713577	−	15.7864i	0.0287508	−	0.636053i
$617$	10.4127	−	4.31309i	0.419200	−	0.173638i	−0.163105	−	0.986609i	$-0.552151\pi$
$617$	10.4127	−	4.31309i	0.419200	−	0.173638i	0.582305	+	0.812970i	$0.302151\pi$
$618$	9.22570	+	12.0232i	0.371112	+	0.483643i
$619$	0.442379	+	3.36020i	0.0177807	+	0.135058i	0.998033	−	0.0626941i	$-0.0199693\pi$
$619$	0.442379	+	3.36020i	0.0177807	+	0.135058i	−0.980252	+	0.197752i	$0.936636\pi$
$620$	−7.70924	−	2.06568i	−0.309610	−	0.0829599i
$621$	1.31630	+	4.91250i	0.0528213	+	0.197132i
$622$	−6.20140	−	2.56870i	−0.248653	−	0.102996i
$623$	39.3981	−	3.38584i	1.57845	−	0.135651i
$624$	−1.44285	+	0.597647i	−0.0577601	+	0.0239250i
$625$	11.4807	+	6.62838i	0.459228	+	0.265135i
$626$	18.9337	−	24.6748i	0.756742	−	0.986205i
$627$	−3.38998	+	12.6516i	−0.135383	+	0.505255i
$628$	0.568929	−	0.985415i	0.0227028	−	0.0393223i
$629$	45.1297	+	13.4762i	1.79944	+	0.537329i
$630$	−1.29718	+	2.02927i	−0.0516809	+	0.0808481i
$631$	33.9715	+	33.9715i	1.35238	+	1.35238i	0.882989	+	0.469394i	$0.155528\pi$
$631$	33.9715	+	33.9715i	1.35238	+	1.35238i	0.469394	+	0.882989i	$0.344472\pi$
$632$	10.5021	+	1.38262i	0.417750	+	0.0549978i
$633$	9.86717	−	5.69681i	0.392185	−	0.226428i
$634$	21.3634	+	16.3927i	0.848449	+	0.651038i
$635$	9.59470	+	12.5041i	0.380754	+	0.496209i
$636$	−4.96413	−	2.05621i	−0.196841	−	0.0815340i
$637$	10.2612	+	3.77057i	0.406565	+	0.149395i
$638$	12.6926	−	12.6926i	0.502506	−	0.502506i
$639$	7.44035	−	5.70918i	0.294336	−	0.225852i
$640$	−0.902520	+	0.118819i	−0.0356752	+	0.00469673i
$641$	4.87487	+	3.74062i	0.192546	+	0.147745i	0.700535	−	0.713618i	$-0.252945\pi$
$641$	4.87487	+	3.74062i	0.192546	+	0.147745i	−0.507990	+	0.861363i	$0.669611\pi$
$642$	−0.260545	−	0.150426i	−0.0102829	−	0.00593682i
$643$	7.83094	+	18.9056i	0.308822	+	0.745563i	0.999744	+	0.0226332i	$0.00720500\pi$
$643$	7.83094	+	18.9056i	0.308822	+	0.745563i	−0.690922	+	0.722930i	$0.742795\pi$
$644$	13.1413	−	2.89215i	0.517838	−	0.113967i
$645$	3.06355			0.120627
$646$	−8.44820	+	3.22164i	−0.332390	+	0.126754i
$647$	−6.02296	−	10.4321i	−0.236787	−	0.410127i	0.723004	−	0.690844i	$-0.242761\pi$
$647$	−6.02296	−	10.4321i	−0.236787	−	0.410127i	−0.959790	+	0.280717i	$0.909428\pi$
$648$	0.258819	−	0.965926i	0.0101674	−	0.0379452i
$649$	71.1160	+	9.36260i	2.79155	+	0.367514i
$650$		−	6.51449i		−	0.255519i
$651$	−17.7468	−	14.9379i	−0.695553	−	0.585464i
$652$	−7.22373	+	17.4396i	−0.282903	+	0.682989i
$653$	−22.4840	+	17.2526i	−0.879868	+	0.675146i	−0.946525	−	0.322630i	$-0.895433\pi$
$653$	−22.4840	+	17.2526i	−0.879868	+	0.675146i	0.0666576	+	0.997776i	$0.478766\pi$
$654$	−5.07491	−	1.35982i	−0.198445	−	0.0531731i
$655$	−12.6686	−	3.39454i	−0.495003	−	0.132636i
$656$	−8.68423	+	6.66365i	−0.339062	+	0.260172i
$657$	1.74281	−	4.20751i	0.0679933	−	0.164150i
$658$	−2.18560	+	0.791689i	−0.0852036	+	0.0308632i
$659$			24.8763i			0.969043i	0.874779	+	0.484521i	$0.161006\pi$
$659$			24.8763i			0.969043i	−0.874779	+	0.484521i	$0.838994\pi$
$660$	5.39057	+	0.709682i	0.209828	+	0.0276244i
$661$	8.84048	−	32.9931i	0.343855	−	1.28328i	−0.550090	−	0.835106i	$-0.685406\pi$
$661$	8.84048	−	32.9931i	0.343855	−	1.28328i	0.893944	−	0.448178i	$-0.147927\pi$
$662$	6.75464	+	11.6994i	0.262527	+	0.454710i
$663$	4.42213	+	4.68055i	0.171741	+	0.181777i
$664$	14.9526			0.580274
$665$	−3.56216	−	3.89944i	−0.138135	−	0.151214i
$666$	−4.37144	−	10.5536i	−0.169390	−	0.408944i
$667$	13.2366	+	7.64218i	0.512525	+	0.295906i
$668$	1.33717	+	1.02605i	0.0517368	+	0.0396991i
$669$	4.92192	−	0.647984i	0.190293	−	0.0250525i
$670$	−3.45633	+	2.65213i	−0.133530	+	0.102461i
$671$	−15.4645	+	15.4645i	−0.597001	+	0.597001i
$672$	−2.52207	−	0.799473i	−0.0972910	−	0.0308403i
$673$	−22.1263	−	9.16501i	−0.852906	−	0.353285i	−0.0869770	−	0.996210i	$-0.527721\pi$
$673$	−22.1263	−	9.16501i	−0.852906	−	0.353285i	−0.765929	+	0.642925i	$0.777721\pi$
$674$	5.18272	+	6.75426i	0.199631	+	0.260164i
$675$	3.30935	+	2.53935i	0.127377	+	0.0977396i
$676$	9.14611	−	5.28051i	0.351773	−	0.203096i
$677$	−26.1504	−	3.44276i	−1.00504	−	0.132316i	−0.390003	−	0.920814i	$-0.627526\pi$
$677$	−26.1504	−	3.44276i	−1.00504	−	0.132316i	−0.615038	+	0.788497i	$0.710859\pi$
$678$	−12.9221	−	12.9221i	−0.496269	−	0.496269i
$679$	−5.04484	+	7.89199i	−0.193603	+	0.302867i
$680$	1.78365	+	3.30239i	0.0684000	+	0.126641i
$681$	4.23566	−	7.33637i	0.162311	−	0.281130i
$682$	−13.5536	+	50.5826i	−0.518993	+	1.93691i
$683$	6.71518	−	8.75140i	0.256949	−	0.334863i	−0.647010	−	0.762482i	$-0.723981\pi$
$683$	6.71518	−	8.75140i	0.256949	−	0.334863i	0.903959	+	0.427619i	$0.140647\pi$
$684$	1.89912	+	1.09646i	0.0726148	+	0.0419242i
$685$	14.7566	−	6.11239i	0.563822	−	0.233543i
$686$	9.18603	+	16.0816i	0.350724	+	0.613997i
$687$	−13.8474	−	5.73577i	−0.528310	−	0.218833i
$688$	0.871029	+	3.25072i	0.0332077	+	0.123933i
$689$	−8.10543	−	2.17184i	−0.308792	−	0.0827407i
$690$	0.604289	+	4.59003i	0.0230049	+	0.174740i
$691$	−19.7491	−	25.7375i	−0.751289	−	0.979099i	−0.999945	−	0.0105074i	$-0.996655\pi$
$691$	−19.7491	−	25.7375i	−0.751289	−	0.979099i	0.248655	−	0.968592i	$-0.420011\pi$
$692$	10.0798	−	4.17517i	0.383175	−	0.158716i
$693$	13.3147	+	8.51119i	0.505782	+	0.323313i
$694$	−12.7854	−	30.8668i	−0.485329	−	1.17169i
$695$	−1.95085	+	0.522729i	−0.0740000	+	0.0198283i
$696$	−1.50265	−	2.60267i	−0.0569579	−	0.0986540i
$697$	38.4298	+	23.6663i	1.45563	+	0.896425i
$698$	−4.68711	+	8.11832i	−0.177410	+	0.307283i
$699$	2.21808	+	2.21808i	0.0838953	+	0.0838953i
$700$	7.10701	−	8.44340i	0.268620	−	0.319130i
$701$		−	12.9515i		−	0.489170i	−0.969628	−	0.244585i	$-0.921348\pi$
$701$		−	12.9515i		−	0.489170i	0.969628	−	0.244585i	$-0.0786517\pi$
$702$	0.203846	−	1.54836i	0.00769368	−	0.0584393i
$703$	24.8357	−	3.26968i	0.936696	−	0.123318i
$704$	0.779607	+	5.92170i	0.0293825	+	0.223183i
$705$	−0.207004	−	0.772548i	−0.00779621	−	0.0290958i
$706$	13.2240	−	13.2240i	0.497693	−	0.497693i
$707$	38.5155	+	18.0322i	1.44853	+	0.678172i
$708$	4.59580	−	11.0952i	0.172721	−	0.416984i
$709$	1.10827	−	8.41817i	0.0416221	−	0.316151i	−0.957951	−	0.286932i	$-0.907365\pi$
$709$	1.10827	−	8.41817i	0.0416221	−	0.316151i	0.999573	−	0.0292191i	$-0.00930206\pi$
$710$	7.39343	−	4.26860i	0.277470	−	0.160198i
$711$	−6.44842	+	8.40374i	−0.241835	+	0.315165i
$712$	−14.4367	+	3.86830i	−0.541038	+	0.144971i
$713$	−44.5901			−1.66991
$714$	0.625243	+	10.8908i	0.0233991	+	0.407577i
$715$	8.49124			0.317554
$716$	16.8013	−	4.50189i	0.627894	−	0.168244i
$717$	−1.47316	+	1.91985i	−0.0550160	+	0.0716983i
$718$	−5.29680	+	3.05811i	−0.197675	+	0.114128i
$719$	−0.903429	+	6.86223i	−0.0336922	+	0.255918i	−0.999999	−	0.00147557i	$-0.999530\pi$
$719$	−0.903429	+	6.86223i	−0.0336922	+	0.255918i	0.966307	+	0.257393i	$0.0828636\pi$
$720$	0.348360	−	0.841015i	0.0129826	−	0.0313428i
$721$	3.43316	+	39.9488i	0.127858	+	1.48777i
$722$	10.0346	−	10.0346i	0.373450	−	0.373450i
$723$	1.36168	+	5.08186i	0.0506414	+	0.188996i
$724$	1.09444	+	8.31308i	0.0406745	+	0.308953i
$725$	12.4289	−	1.63630i	0.461598	−	0.0607705i
$726$	3.22065	−	24.4633i	0.119529	−	0.907917i
$727$			22.7580i			0.844048i	0.906585	+	0.422024i	$0.138680\pi$
$727$			22.7580i			0.844048i	−0.906585	+	0.422024i	$0.861320\pi$
$728$	−4.06806	−	0.723761i	−0.150772	−	0.0268244i
$729$	0.707107	+	0.707107i	0.0261891	+	0.0261891i
$730$	2.07285	−	3.59028i	0.0767196	−	0.132882i
$731$	11.2438	−	8.13131i	0.415865	−	0.300747i
$732$	1.83081	+	3.17106i	0.0676687	+	0.117206i
$733$	−21.5222	+	5.76686i	−0.794941	+	0.213004i	−0.633362	−	0.773856i	$-0.718325\pi$
$733$	−21.5222	+	5.76686i	−0.794941	+	0.213004i	−0.161580	+	0.986860i	$0.551659\pi$
$734$	1.57676	+	3.80664i	0.0581994	+	0.140506i
$735$	−5.78339	+	2.67521i	−0.213324	+	0.0986767i
$736$	−4.69866	+	1.94625i	−0.173195	+	0.0717397i
$737$	17.4014	+	22.6780i	0.640990	+	0.835354i
$738$	−1.42877	−	10.8526i	−0.0525938	−	0.399489i
$739$	2.55633	+	0.684967i	0.0940362	+	0.0251969i	0.305530	−	0.952182i	$-0.401166\pi$
$739$	2.55633	+	0.684967i	0.0940362	+	0.0251969i	−0.211494	+	0.977379i	$0.567833\pi$
$740$	−2.69135	−	10.0442i	−0.0989359	−	0.369234i
$741$	3.16404	+	1.31059i	0.116234	+	0.0481457i
$742$	−8.13603	−	11.6576i	−0.298683	−	0.427963i
$743$	−36.0704	+	14.9408i	−1.32329	+	0.548127i	−0.928735	−	0.370744i	$-0.879103\pi$
$743$	−36.0704	+	14.9408i	−1.32329	+	0.548127i	−0.394560	+	0.918870i	$0.629103\pi$
$744$	7.59294	+	4.38379i	0.278371	+	0.160717i
$745$	−0.734435	+	0.957134i	−0.0269076	+	0.0350667i
$746$	−0.629066	+	2.34771i	−0.0230318	+	0.0859557i
$747$	−7.47631	+	12.9494i	−0.273544	+	0.473792i
$748$	21.6680	−	11.7031i	0.792260	−	0.427907i
$749$	−0.366455	−	0.706605i	−0.0133900	−	0.0258188i
$750$	5.90345	+	5.90345i	0.215564	+	0.215564i
$751$	−22.5867	−	2.97359i	−0.824199	−	0.108508i	−0.293383	−	0.955995i	$-0.594781\pi$
$751$	−22.5867	−	2.97359i	−0.824199	−	0.108508i	−0.530816	+	0.847487i	$0.678115\pi$
$752$	0.760894	−	0.439302i	0.0277469	−	0.0160197i
$753$	−6.65653	−	5.10774i	−0.242578	−	0.186136i
$754$	−2.85720	−	3.72357i	−0.104053	−	0.135605i
$755$	−18.8499	−	7.80790i	−0.686020	−	0.284159i
$756$	1.95340	−	1.78444i	0.0710444	−	0.0648995i
$757$	−18.3933	+	18.3933i	−0.668516	+	0.668516i	−0.957372	−	0.288857i	$-0.906725\pi$
$757$	−18.3933	+	18.3933i	−0.668516	+	0.668516i	0.288857	+	0.957372i	$0.406725\pi$
$758$	−12.4539	+	9.55618i	−0.452345	+	0.347096i
$759$	30.1166	−	3.96492i	1.09316	−	0.143918i
$760$	1.58372	+	1.21523i	0.0574474	+	0.0440810i
$761$	−42.5473	−	24.5647i	−1.54234	−	0.890470i	−0.998691	−	0.0511580i	$-0.983709\pi$
$761$	−42.5473	−	24.5647i	−1.54234	−	0.890470i	−0.543649	−	0.839312i	$-0.682958\pi$
$762$	−6.62576	−	15.9960i	−0.240026	−	0.579474i
$763$	−9.37533	−	10.2630i	−0.339410	−	0.371546i
$764$	11.2052			0.405389
$765$	−3.75178	−	0.106509i	−0.135646	−	0.00385082i
$766$	9.68439	+	16.7739i	0.349911	+	0.606064i
$767$	4.85425	−	18.1163i	0.175277	−	0.654142i
$768$	0.991445	+	0.130526i	0.0357757	+	0.00470996i
$769$			2.54964i			0.0919425i	0.998943	+	0.0459712i	$0.0146383\pi$
$769$			2.54964i			0.0919425i	−0.998943	+	0.0459712i	$0.985362\pi$
$770$	11.0055	+	9.26355i	0.396609	+	0.333835i
$771$	−3.64651	+	8.80346i	−0.131326	+	0.317049i
$772$	5.35016	−	4.10532i	0.192557	−	0.147754i
$773$	35.6041	+	9.54010i	1.28059	+	0.343133i	0.834079	−	0.551644i	$-0.185999\pi$
$773$	35.6041	+	9.54010i	1.28059	+	0.343133i	0.446512	+	0.894778i	$0.352666\pi$
$774$	−3.25072	−	0.871029i	−0.116845	−	0.0313085i
$775$	−29.0149	+	22.2639i	−1.04225	+	0.799744i
$776$	1.35480	−	3.27077i	0.0486344	−	0.117414i
$777$	5.29390	−	29.7555i	0.189918	−	1.06747i
$778$			28.5875i			1.02491i
$779$	23.7988	+	3.13318i	0.852682	+	0.112258i
$780$	0.367950	−	1.37321i	0.0131747	−	0.0491688i
$781$	−28.0075	−	48.5105i	−1.00219	−	1.73584i
$782$	14.4008	+	15.2423i	0.514971	+	0.545064i
$783$	3.00531			0.107401
$784$	−4.48300	−	5.37613i	−0.160107	−	0.192004i
$785$	0.396384	+	0.956956i	0.0141476	+	0.0341552i
$786$	12.4775	+	7.20388i	0.445057	+	0.256954i
$787$	0.578014	+	0.443526i	0.0206040	+	0.0158100i	0.619012	−	0.785381i	$-0.287533\pi$
$787$	0.578014	+	0.443526i	0.0206040	+	0.0158100i	−0.598408	+	0.801191i	$0.704200\pi$
$788$	3.49233	−	0.459774i	0.124409	−	0.0163788i
$789$	−1.33128	+	1.02153i	−0.0473948	+	0.0363673i
$790$	−6.81835	+	6.81835i	−0.242586	+	0.242586i
$791$	−10.3922	−	47.2199i	−0.369505	−	1.67895i
$792$	−5.51815	−	2.28569i	−0.196079	−	0.0812185i
$793$	3.48117	+	4.53675i	0.123620	+	0.161105i
$794$	−29.2974	−	22.4807i	−1.03973	−	0.797810i
$795$	4.23591	−	2.44560i	0.150232	−	0.0867366i
$796$	12.3150	+	1.62131i	0.436495	+	0.0574657i
$797$	−20.8204	−	20.8204i	−0.737495	−	0.737495i	0.234597	−	0.972093i	$-0.424623\pi$
$797$	−20.8204	−	20.8204i	−0.737495	−	0.737495i	−0.972093	+	0.234597i	$0.924623\pi$
$798$	2.67111	+	5.15048i	0.0945562	+	0.182325i
$799$	−2.81025	−	2.28595i	−0.0994194	−	0.0808712i
$800$	−2.08567	+	3.61249i	−0.0737396	+	0.127721i
$801$	3.86830	−	14.4367i	0.136680	−	0.510095i
$802$	19.0190	−	24.7861i	0.671586	−	0.875228i
$803$	−23.5569	−	13.6006i	−0.831305	−	0.479954i
$804$	4.42155	−	1.83147i	0.155936	−	0.0645909i
$805$	−5.19367	+	11.0933i	−0.183053	+	0.390987i
$806$	12.6503	+	5.23991i	0.445586	+	0.184568i
$807$	3.38829	+	12.6453i	0.119273	+	0.445135i
$808$	−15.5263	−	4.16025i	−0.546212	−	0.146357i
$809$	1.88967	+	14.3535i	0.0664374	+	0.504642i	0.992018	+	0.126093i	$0.0402437\pi$
$809$	1.88967	+	14.3535i	0.0664374	+	0.504642i	−0.925581	+	0.378549i	$0.876423\pi$
$810$	0.554160	+	0.722196i	0.0194712	+	0.0253754i
$811$	−25.4657	+	10.5482i	−0.894220	+	0.370398i	−0.781995	−	0.623285i	$-0.785798\pi$
$811$	−25.4657	+	10.5482i	−0.894220	+	0.370398i	−0.112225	+	0.993683i	$0.535798\pi$
$812$	0.359047	−	7.94318i	0.0126001	−	0.278751i
$813$	−2.12407	−	5.12796i	−0.0744944	−	0.179845i
$814$	−65.9033	+	17.6587i	−2.30991	+	0.618938i
$815$	−8.59172	−	14.8813i	−0.300955	−	0.521269i
$816$	−0.953693	−	4.01129i	−0.0333859	−	0.140423i
$817$	3.69002	−	6.39130i	0.129097	−	0.223603i
$818$	−20.1564	−	20.1564i	−0.704753	−	0.704753i
$819$	2.66082	−	3.16116i	0.0929767	−	0.110460i
$820$		−	9.96445i		−	0.347974i
$821$	−6.62339	+	50.3096i	−0.231158	+	1.75582i	0.345114	+	0.938561i	$0.387840\pi$
$821$	−6.62339	+	50.3096i	−0.231158	+	1.75582i	−0.576272	+	0.817258i	$0.695493\pi$
$822$	−17.3961	+	2.29024i	−0.606759	+	0.0798813i
$823$	−2.52138	−	19.1518i	−0.0878899	−	0.667590i	−0.977510	−	0.210889i	$-0.932364\pi$
$823$	−2.52138	−	19.1518i	−0.0878899	−	0.667590i	0.889620	−	0.456701i	$-0.150969\pi$
$824$	−3.92237	−	14.6385i	−0.136642	−	0.509956i
$825$	17.6173	−	17.6173i	0.613355	−	0.613355i
$826$	26.0556	−	18.1847i	0.906591	−	0.632726i
$827$	−11.5724	+	27.9382i	−0.402410	+	0.971505i	0.584669	+	0.811272i	$0.301224\pi$
$827$	−11.5724	+	27.9382i	−0.402410	+	0.971505i	−0.987079	+	0.160233i	$0.948776\pi$
$828$	0.663829	−	5.04229i	0.0230697	−	0.175232i
$829$	−31.3037	+	18.0732i	−1.08722	+	0.627708i	−0.932835	−	0.360303i	$-0.882673\pi$
$829$	−31.3037	+	18.0732i	−1.08722	+	0.627708i	−0.154386	+	0.988011i	$0.549340\pi$
$830$	−8.28615	+	10.7987i	−0.287617	+	0.374829i
$831$	0.594870	−	0.159395i	0.0206358	−	0.00552934i
$832$	1.56173			0.0541431
$833$	−14.1255	+	25.1689i	−0.489418	+	0.872049i
$834$	2.21867			0.0768262
$835$	−1.48202	+	0.397106i	−0.0512874	+	0.0137424i
$836$	7.97347	−	10.3912i	0.275768	−	0.359388i
$837$	−7.59294	+	4.38379i	−0.262450	+	0.151526i
$838$	0.529843	−	4.02456i	0.0183031	−	0.139026i
$839$	−3.24888	+	7.84350i	−0.112164	+	0.270788i	−0.969987	−	0.243158i	$-0.921817\pi$
$839$	−3.24888	+	7.84350i	−0.112164	+	0.270788i	0.857823	+	0.513946i	$0.171817\pi$
$840$	1.97501	−	1.37839i	0.0681442	−	0.0475591i
$841$	−14.1196	+	14.1196i	−0.486883	+	0.486883i
$842$	−8.45746	−	31.5637i	−0.291463	−	1.08776i
$843$	2.47520	+	18.8010i	0.0852503	+	0.647541i
$844$	−11.2961	+	1.48717i	−0.388830	+	0.0511904i
$845$	−1.25485	+	9.53153i	−0.0431681	+	0.327894i
$846$			0.878604i			0.0302070i
$847$	42.0394	−	49.9445i	1.44449	−	1.71611i
$848$	3.79938	+	3.79938i	0.130471	+	0.130471i
$849$	8.01049	−	13.8746i	0.274919	−	0.476174i
$850$	16.9812	+	2.72788i	0.582449	+	0.0935656i
$851$	−29.0479	−	50.3124i	−0.995748	−	1.72469i
$852$	−9.05880	+	2.42730i	−0.310349	+	0.0831579i
$853$	−4.86332	−	11.7411i	−0.166517	−	0.402008i	0.818490	−	0.574520i	$-0.194811\pi$
$853$	−4.86332	−	11.7411i	−0.166517	−	0.402008i	−0.985007	+	0.172513i	$0.944811\pi$
$854$	−0.437458	+	9.67786i	−0.0149695	+	0.331169i
$855$	−1.84428	+	0.763924i	−0.0630729	+	0.0261257i
$856$	0.183147	+	0.238681i	0.00625982	+	0.00815796i
$857$	0.771552	+	5.86052i	0.0263557	+	0.200192i	0.999557	−	0.0297635i	$-0.00947542\pi$
$857$	0.771552	+	5.86052i	0.0263557	+	0.200192i	−0.973201	+	0.229955i	$0.926142\pi$
$858$	−9.01004	−	2.41423i	−0.307598	−	0.0824205i
$859$	−3.01970	−	11.2697i	−0.103031	−	0.384517i	0.895083	−	0.445899i	$-0.147116\pi$
$859$	−3.01970	−	11.2697i	−0.103031	−	0.384517i	−0.998114	+	0.0613820i	$0.980449\pi$
$860$	−2.83035	−	1.17237i	−0.0965141	−	0.0399774i
$861$	12.2798	−	26.2287i	0.418495	−	0.893873i
$862$	7.13080	−	2.95368i	0.242876	−	0.100603i
$863$	−34.4855	−	19.9102i	−1.17390	−	0.677752i	−0.219305	−	0.975656i	$-0.570379\pi$
$863$	−34.4855	−	19.9102i	−1.17390	−	0.677752i	−0.954596	+	0.297905i	$0.903712\pi$
$864$	−0.608761	+	0.793353i	−0.0207105	+	0.0269904i
$865$	−2.57051	+	9.59327i	−0.0873999	+	0.326181i
$866$	12.2515	−	21.2203i	0.416324	−	0.721095i
$867$	−14.0524	+	9.56713i	−0.477245	+	0.324917i
$868$	10.6794	+	20.5923i	0.362484	+	0.698947i
$869$	44.7372	+	44.7372i	1.51761	+	1.51761i
$870$	2.71235	+	0.357087i	0.0919572	+	0.0121064i
$871$	6.47284	−	3.73710i	0.219324	−	0.126627i
$872$	4.16822	+	3.19839i	0.141154	+	0.108311i
$873$	2.15517	+	2.80867i	0.0729415	+	0.0950592i
$874$	10.3038	+	4.26796i	0.348531	+	0.144366i
$875$	4.74770	+	21.5724i	0.160501	+	0.729281i
$876$	−3.22029	+	3.22029i	−0.108803	+	0.108803i
$877$	43.4823	−	33.3651i	1.46829	−	1.12666i	0.503387	−	0.864061i	$-0.332087\pi$
$877$	43.4823	−	33.3651i	1.46829	−	1.12666i	0.964905	−	0.262599i	$-0.0845795\pi$
$878$	39.8987	−	5.25276i	1.34652	−	0.177272i
$879$	7.30436	+	5.60483i	0.246370	+	0.189046i
$880$	−4.70866	−	2.71854i	−0.158729	−	0.0916421i
$881$	21.3661	+	51.5824i	0.719843	+	1.73785i	0.673799	+	0.738915i	$0.264661\pi$
$881$	21.3661	+	51.5824i	0.719843	+	1.73785i	0.0460440	+	0.998939i	$0.485339\pi$
$882$	6.89736	−	1.19433i	0.232246	−	0.0402151i
$883$	−17.6814			−0.595027			−0.297513	−	0.954718i	$-0.596157\pi$
$883$	−17.6814			−0.595027			−0.297513	+	0.954718i	$0.596157\pi$
$884$	−2.29435	−	6.01654i	−0.0771674	−	0.202358i
$885$	5.46612	+	9.46760i	0.183742	+	0.318250i
$886$	2.00500	−	7.48275i	0.0673592	−	0.251388i
$887$	−25.2341	−	3.32214i	−0.847279	−	0.111546i	−0.305629	−	0.952151i	$-0.598867\pi$
$887$	−25.2341	−	3.32214i	−0.847279	−	0.111546i	−0.541650	+	0.840604i	$0.682200\pi$
$888$			11.4231i			0.383335i
$889$	8.02392	−	45.1002i	0.269114	−	1.51261i
$890$	5.20657	−	12.5698i	0.174525	−	0.421340i
$891$	4.73854	−	3.63601i	0.158747	−	0.121811i
$892$	−4.79524	−	1.28488i	−0.160556	−	0.0430210i
$893$	−1.86106	−	0.498669i	−0.0622779	−	0.0166873i
$894$	1.05144	−	0.806798i	0.0351654	−	0.0269834i
$895$	−6.05936	+	14.6286i	−0.202542	+	0.488980i
$896$	2.02415	+	1.70377i	0.0676219	+	0.0569190i
$897$		−	7.94262i		−	0.265196i
$898$	−3.51746	−	0.463083i	−0.117379	−	0.0154533i
$899$	−6.81968	+	25.4514i	−0.227449	+	0.848852i
$900$	−2.08567	−	3.61249i	−0.0695223	−	0.120416i
$901$	9.05537	−	20.2188i	0.301678	−	0.673586i
$902$	−65.3797			−2.17691
$903$	−6.00535	−	6.57396i	−0.199846	−	0.218768i
$904$	6.99337	+	16.8835i	0.232596	+	0.561537i
$905$	−6.61017	−	3.81638i	−0.219729	−	0.126861i
$906$	17.7817	+	13.6444i	0.590757	+	0.453304i
$907$	−20.9526	+	2.75846i	−0.695719	+	0.0915932i	−0.470088	−	0.882620i	$-0.655778\pi$
$907$	−20.9526	+	2.75846i	−0.695719	+	0.0915932i	−0.225631	+	0.974213i	$0.572444\pi$
$908$	−6.72074	+	5.15701i	−0.223036	+	0.171141i
$909$	11.3660	−	11.3660i	0.376987	−	0.376987i
$910$	2.77705	−	2.53685i	0.0920584	−	0.0840959i
$911$	3.43380	+	1.42233i	0.113767	+	0.0471238i	0.438841	−	0.898565i	$-0.355389\pi$
$911$	3.43380	+	1.42233i	0.113767	+	0.0471238i	−0.325074	+	0.945689i	$0.605389\pi$
$912$	−1.33496	−	1.73976i	−0.0442051	−	0.0576092i
$913$	70.8536	+	54.3679i	2.34491	+	1.79931i
$914$	2.73212	−	1.57739i	0.0903704	−	0.0521754i
$915$	−3.30469	−	0.435070i	−0.109250	−	0.0143830i
$916$	10.5983	+	10.5983i	0.350178	+	0.350178i
$917$	17.5495	+	33.8393i	0.579537	+	1.11747i
$918$	3.95073	+	1.17972i	0.130393	+	0.0389367i
$919$	23.1479	−	40.0933i	0.763577	−	1.32255i	−0.177418	−	0.984136i	$-0.556775\pi$
$919$	23.1479	−	40.0933i	0.763577	−	1.32255i	0.940996	−	0.338419i	$-0.109892\pi$
$920$	1.19824	−	4.47189i	0.0395048	−	0.147434i
$921$	−5.28774	+	6.89112i	−0.174237	+	0.227070i
$922$	−2.52018	−	1.45502i	−0.0829976	−	0.0479187i
$923$	−13.5315	+	5.60495i	−0.445396	+	0.184489i
$924$	−9.04405	−	12.9586i	−0.297527	−	0.426307i
$925$	−44.0226	−	18.2348i	−1.44746	−	0.599556i
$926$	4.64643	+	17.3407i	0.152691	+	0.569851i
$927$	14.6385	+	3.92237i	0.480791	+	0.128828i
$928$	0.392271	+	2.97959i	0.0128769	+	0.0978100i
$929$	−2.07672	−	2.70643i	−0.0681350	−	0.0887952i	0.758043	−	0.652205i	$-0.226156\pi$
$929$	−2.07672	−	2.70643i	−0.0681350	−	0.0887952i	−0.826178	+	0.563410i	$0.809489\pi$
$930$	−7.37366	+	3.05427i	−0.241792	+	0.100153i
$931$	−1.38491	+	15.2878i	−0.0453885	+	0.501038i
$932$	−1.20041	−	2.89805i	−0.0393209	−	0.0949289i
$933$	−6.48363	+	1.73728i	−0.212264	+	0.0568761i
$934$	−2.20537	−	3.81982i	−0.0721620	−	0.124988i
$935$	−3.55563	+	22.1339i	−0.116282	+	0.723856i
$936$	−0.780863	+	1.35249i	−0.0255233	+	0.0442077i
$937$	−11.2287	−	11.2287i	−0.366826	−	0.366826i	0.499492	−	0.866318i	$-0.333520\pi$
$937$	−11.2287	−	11.2287i	−0.366826	−	0.366826i	−0.866318	+	0.499492i	$0.833520\pi$
$938$	12.4664	+	2.21794i	0.407043	+	0.0724183i
$939$		−	31.1020i		−	1.01497i
$940$	−0.104395	+	0.792958i	−0.00340499	+	0.0258634i
$941$	−25.8198	+	3.39924i	−0.841700	+	0.110812i	−0.539033	−	0.842285i	$-0.681210\pi$
$941$	−25.8198	+	3.39924i	−0.841700	+	0.110812i	−0.302667	+	0.953096i	$0.597877\pi$
$942$	−0.148520	−	1.12812i	−0.00483906	−	0.0367563i
$943$	−14.4085	−	53.7734i	−0.469207	−	1.75110i
$944$	−8.49192	+	8.49192i	−0.276389	+	0.276389i
$945$	0.206220	+	2.39960i	0.00670833	+	0.0780591i
$946$	−7.69226	+	18.5708i	−0.250097	+	0.603787i
$947$	−3.64199	+	27.6637i	−0.118349	+	0.898949i	0.824531	+	0.565816i	$0.191439\pi$
$947$	−3.64199	+	27.6637i	−0.118349	+	0.898949i	−0.942880	+	0.333132i	$0.891894\pi$
$948$	9.17353	−	5.29634i	0.297943	−	0.172017i
$949$	−4.32973	+	5.64262i	−0.140549	+	0.183167i
$950$	8.83571	−	2.36752i	0.286668	−	0.0768126i
$951$	26.9280			0.873199
$952$	3.59007	−	10.3010i	0.116355	−	0.333859i
$953$	−3.32853			−0.107822			−0.0539109	−	0.998546i	$-0.517169\pi$
$953$	−3.32853			−0.107822			−0.0539109	+	0.998546i	$0.517169\pi$
$954$	−5.19005	+	1.39067i	−0.168034	+	0.0450246i
$955$	−6.20946	+	8.09232i	−0.200933	+	0.261861i
$956$	2.09572	−	1.20996i	0.0677803	−	0.0391330i
$957$	2.34296	−	17.7965i	0.0757370	−	0.575280i
$958$	−0.382608	+	0.923697i	−0.0123615	+	0.0298433i
$959$	−42.0432	−	19.6839i	−1.35765	−	0.635625i
$960$	−0.643685	+	0.643685i	−0.0207748	+	0.0207748i
$961$	−11.8721	−	44.3073i	−0.382971	−	1.42927i
$962$	2.32856	+	17.6872i	0.0750758	+	0.570258i
$963$	−0.298277	+	0.0392690i	−0.00961185	+	0.00126542i
$964$	0.686715	−	5.21612i	0.0221176	−	0.168000i
$965$			6.13887i			0.197617i
$966$	8.66503	−	10.2944i	0.278793	−	0.331216i
$967$	24.5551	+	24.5551i	0.789640	+	0.789640i	0.981435	−	0.191795i	$-0.0614308\pi$
$967$	24.5551	+	24.5551i	0.789640	+	0.789640i	−0.191795	+	0.981435i	$0.561431\pi$
$968$	−12.3372	+	21.3686i	−0.396532	+	0.686813i
$969$	−4.74120	+	7.69884i	−0.152309	+	0.247322i
$970$	1.61136	+	2.79096i	0.0517377	+	0.0896124i
$971$	19.7534	−	5.29292i	0.633918	−	0.169858i	0.0724710	−	0.997371i	$-0.476912\pi$
$971$	19.7534	−	5.29292i	0.633918	−	0.169858i	0.561447	+	0.827513i	$0.310245\pi$
$972$	−0.382683	−	0.923880i	−0.0122746	−	0.0296334i
$973$	4.94589	+	3.16158i	0.158558	+	0.101356i
$974$	−20.9879	+	8.69347i	−0.672495	+	0.278557i
$975$	−3.96577	−	5.16829i	−0.127006	−	0.165518i
$976$	−0.477937	−	3.63029i	−0.0152984	−	0.116203i
$977$	−4.08982	−	1.09586i	−0.130845	−	0.0350598i	0.192802	−	0.981238i	$-0.438242\pi$
$977$	−4.08982	−	1.09586i	−0.130845	−	0.0350598i	−0.323647	+	0.946178i	$0.604909\pi$
$978$	4.88560	+	18.2333i	0.156224	+	0.583037i
$979$	−82.4740	−	34.1619i	−2.63588	−	1.09182i
$980$	6.36692	−	0.258367i	0.203384	−	0.00825322i
$981$	−4.85400	+	2.01059i	−0.154976	+	0.0641933i
$982$	5.99474	+	3.46107i	0.191300	+	0.110447i
$983$	19.3585	−	25.2285i	0.617440	−	0.804664i	−0.375048	−	0.927006i	$-0.622374\pi$
$983$	19.3585	−	25.2285i	0.617440	−	0.804664i	0.992488	+	0.122342i	$0.0390403\pi$
$984$	−2.83309	+	10.5733i	−0.0903158	+	0.337063i
$985$	−1.60326	+	2.77693i	−0.0510842	+	0.0884804i
$986$	10.9026	−	5.88858i	0.347209	−	0.187531i
$987$	−1.25200	+	1.95860i	−0.0398517	+	0.0623429i
$988$	−2.42165	−	2.42165i	−0.0770431	−	0.0770431i
$989$	−16.9693	−	2.23405i	−0.539592	−	0.0710386i
$990$	4.70866	−	2.71854i	0.149651	−	0.0864010i
$991$	−16.0774	−	12.3366i	−0.510716	−	0.391886i	0.321007	−	0.947077i	$-0.395979\pi$
$991$	−16.0774	−	12.3366i	−0.510716	−	0.391886i	−0.831723	+	0.555191i	$0.812645\pi$
$992$	−5.33736	−	6.95578i	−0.169461	−	0.220846i
$993$	12.4810	+	5.16978i	0.396071	+	0.164058i
$994$	−23.6529	−	7.49774i	−0.750224	−	0.237814i
$995$	−7.99541	+	7.99541i	−0.253472	+	0.253472i
$996$	11.8627	−	9.10258i	0.375884	−	0.288426i
$997$	−4.97312	+	0.654724i	−0.157500	+	0.0207353i	−0.208864	−	0.977945i	$-0.566977\pi$
$997$	−4.97312	+	0.654724i	−0.157500	+	0.0207353i	0.0513636	+	0.998680i	$0.483643\pi$
$998$	−11.4231	−	8.76522i	−0.361590	−	0.277458i
$999$	−9.89272	−	5.71157i	−0.312992	−	0.180706i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	714.2.bh.b.457.3	yes	96
7.4	even	3	inner	714.2.bh.b.151.9	yes	96
17.8	even	8	inner	714.2.bh.b.331.9	yes	96
119.25	even	24	inner	714.2.bh.b.25.3	✓	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
714.2.bh.b.25.3	✓	96	119.25	even	24	inner
714.2.bh.b.151.9	yes	96	7.4	even	3	inner
714.2.bh.b.331.9	yes	96	17.8	even	8	inner
714.2.bh.b.457.3	yes	96	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 714 = 2 \cdot 3 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	714.bh (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.965926 + 0.258819i) q^{2} +(-0.608761 + 0.793353i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-0.118819 + 0.902520i) q^{5} +(0.382683 - 0.923880i) q^{6} +(2.16960 - 1.51421i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.258819 - 0.965926i) q^{9} +(-0.118819 - 0.902520i) q^{10} +(-5.92170 + 0.779607i) q^{11} +(-0.130526 + 0.991445i) q^{12} +1.56173i q^{13} +(-1.70377 + 2.02415i) q^{14} +(-0.643685 - 0.643685i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-4.07091 - 0.653958i) q^{17} +(0.500000 + 0.866025i) q^{18} +(-2.11820 + 0.567569i) q^{19} +(0.348360 + 0.841015i) q^{20} +(-0.119471 + 2.64305i) q^{21} +(5.51815 - 2.28569i) q^{22} +(3.09604 + 4.03483i) q^{23} +(-0.130526 - 0.991445i) q^{24} +(4.02920 + 1.07962i) q^{25} +(-0.404204 - 1.50851i) q^{26} +(0.923880 + 0.382683i) q^{27} +(1.12183 - 2.39614i) q^{28} +(2.77654 - 1.15008i) q^{29} +(0.788350 + 0.455154i) q^{30} +(-5.33736 + 6.95578i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(2.98640 - 5.17260i) q^{33} +(4.10146 - 0.421955i) q^{34} +(1.10881 + 2.13803i) q^{35} +(-0.707107 - 0.707107i) q^{36} +(-11.3254 - 1.49102i) q^{37} +(1.89912 - 1.09646i) q^{38} +(-1.23900 - 0.950718i) q^{39} +(-0.554160 - 0.722196i) q^{40} +(-10.1130 - 4.18894i) q^{41} +(-0.568672 - 2.58391i) q^{42} +(-2.37969 + 2.37969i) q^{43} +(-4.73854 + 3.63601i) q^{44} +(0.902520 - 0.118819i) q^{45} +(-4.03483 - 3.09604i) q^{46} +(0.760894 + 0.439302i) q^{47} +(0.382683 + 0.923880i) q^{48} +(2.41436 - 6.57045i) q^{49} -4.17134 q^{50} +(2.99704 - 2.83157i) q^{51} +(0.780863 + 1.35249i) q^{52} +(-1.39067 + 5.19005i) q^{53} +(-0.991445 - 0.130526i) q^{54} -5.43709i q^{55} +(-0.463437 + 2.60485i) q^{56} +(0.839193 - 2.02599i) q^{57} +(-2.38427 + 1.82951i) q^{58} +(-11.6002 - 3.10826i) q^{59} +(-0.879290 - 0.235605i) q^{60} +(2.90496 - 2.22905i) q^{61} +(3.35520 - 8.10018i) q^{62} +(-2.02415 - 1.70377i) q^{63} -1.00000i q^{64} +(-1.40949 - 0.185563i) q^{65} +(-1.54587 + 5.76928i) q^{66} +(-2.39293 - 4.14467i) q^{67} +(-3.85249 + 1.46911i) q^{68} -5.08579 q^{69} +(-1.62439 - 1.77819i) q^{70} +(3.58894 + 8.66448i) q^{71} +(0.866025 + 0.500000i) q^{72} +(3.61307 + 2.77240i) q^{73} +(11.3254 - 1.49102i) q^{74} +(-3.30935 + 2.53935i) q^{75} +(-1.55063 + 1.55063i) q^{76} +(-11.6673 + 10.6581i) q^{77} +(1.44285 + 0.597647i) q^{78} +(-6.44842 - 8.40374i) q^{79} +(0.722196 + 0.554160i) q^{80} +(-0.866025 + 0.500000i) q^{81} +(10.8526 + 1.42877i) q^{82} +(-10.5731 - 10.5731i) q^{83} +(1.21806 + 2.34869i) q^{84} +(1.07391 - 3.59638i) q^{85} +(1.68270 - 2.91452i) q^{86} +(-0.777830 + 2.90290i) q^{87} +(3.63601 - 4.73854i) q^{88} +(12.9436 + 7.47298i) q^{89} +(-0.841015 + 0.348360i) q^{90} +(2.36477 + 3.38833i) q^{91} +(4.69866 + 1.94625i) q^{92} +(-2.26921 - 8.46882i) q^{93} +(-0.848667 - 0.227400i) q^{94} +(-0.260560 - 1.97915i) q^{95} +(-0.608761 - 0.793353i) q^{96} +(-3.27077 + 1.35480i) q^{97} +(-0.631537 + 6.97145i) q^{98} +(2.28569 + 5.51815i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 8 q^{5} + 8 q^{10} + 16 q^{14} + 16 q^{15} + 48 q^{16} + 8 q^{17} + 48 q^{18} - 8 q^{19} + 16 q^{22} + 24 q^{25} + 32 q^{28} - 32 q^{29} - 16 q^{33} - 48 q^{37} - 16 q^{39} + 128 q^{41} + 16 q^{42}+ \cdots + 160 q^{97}+O(q^{100}) \) 96 * q + 8 * q^5 + 8 * q^10 + 16 * q^14 + 16 * q^15 + 48 * q^16 + 8 * q^17 + 48 * q^18 - 8 * q^19 + 16 * q^22 + 24 * q^25 + 32 * q^28 - 32 * q^29 - 16 * q^33 - 48 * q^37 - 16 * q^39 + 128 * q^41 + 16 * q^42 + 48 * q^43 - 8 * q^44 - 8 * q^46 - 112 * q^49 + 64 * q^50 - 16 * q^52 - 40 * q^53 + 16 * q^57 + 16 * q^58 - 24 * q^59 + 8 * q^60 - 56 * q^70 + 24 * q^73 + 48 * q^74 - 16 * q^76 + 16 * q^77 + 32 * q^78 - 56 * q^79 - 8 * q^80 - 80 * q^83 + 80 * q^85 + 16 * q^86 - 24 * q^87 + 16 * q^90 - 40 * q^91 + 16 * q^92 - 8 * q^93 - 8 * q^94 + 80 * q^95 + 160 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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