LMFDB - Embedded newform 195.2.bh.a.59.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [195,2,Mod(59,195)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(195, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 6, 11])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("195.59"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 195 = 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	195.bh (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$1.55708283941$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$24$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			59.5
Character	$\chi$	$=$	195.59
Dual form			195.2.bh.a.119.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.66849 + 0.447071i) q^{2} +(-1.28242 + 1.16422i) q^{3} +(0.851938 - 0.491866i) q^{4} +(-2.11813 + 0.716618i) q^{5} +(1.61922 - 2.51582i) q^{6} +(-0.830623 + 3.09993i) q^{7} +(1.24129 - 1.24129i) q^{8} +(0.289197 - 2.98603i) q^{9} +(3.21369 - 2.14262i) q^{10} +(-1.14830 + 0.307686i) q^{11} +(-0.519902 + 1.62262i) q^{12} +(-1.66563 - 3.19776i) q^{13} -5.54355i q^{14} +(1.88203 - 3.38496i) q^{15} +(-2.49987 + 4.32990i) q^{16} +(4.71514 - 2.72229i) q^{17} +(0.852444 + 5.11145i) q^{18} +(0.476790 - 1.77941i) q^{19} +(-1.45203 + 1.65235i) q^{20} +(-2.54378 - 4.94243i) q^{21} +(1.77837 - 1.02674i) q^{22} +(-3.41625 - 1.97237i) q^{23} +(-0.146722 + 3.03698i) q^{24} +(3.97292 - 3.03577i) q^{25} +(4.20871 + 4.59079i) q^{26} +(3.10551 + 4.16603i) q^{27} +(0.817112 + 3.04950i) q^{28} +(-7.04243 - 4.06595i) q^{29} +(-1.62682 + 6.48918i) q^{30} +(-0.148047 - 0.148047i) q^{31} +(1.32655 - 4.95075i) q^{32} +(1.11439 - 1.73145i) q^{33} +(-6.65011 + 6.65011i) q^{34} +(-0.462099 - 7.16128i) q^{35} +(-1.22235 - 2.68616i) q^{36} +(-6.89966 + 1.84876i) q^{37} +3.18208i q^{38} +(5.85892 + 2.16172i) q^{39} +(-1.73968 + 3.51874i) q^{40} +(2.36667 + 8.83254i) q^{41} +(6.45390 + 7.10915i) q^{42} +(-0.391907 - 0.678803i) q^{43} +(-0.826939 + 0.826939i) q^{44} +(1.52729 + 6.53203i) q^{45} +(6.58176 + 1.76358i) q^{46} +(-6.23046 + 6.23046i) q^{47} +(-1.83506 - 8.46313i) q^{48} +(-2.85745 - 1.64975i) q^{49} +(-5.27157 + 6.84134i) q^{50} +(-2.87745 + 8.98056i) q^{51} +(-2.99188 - 1.90503i) q^{52} -0.952426 q^{53} +(-7.04403 - 5.56259i) q^{54} +(2.21175 - 1.47461i) q^{55} +(2.81686 + 4.87895i) q^{56} +(1.46017 + 2.83703i) q^{57} +(13.5680 + 3.63553i) q^{58} +(2.09784 - 7.82924i) q^{59} +(-0.0615809 - 3.80948i) q^{60} +(-6.49787 - 11.2546i) q^{61} +(0.313203 + 0.180828i) q^{62} +(9.01626 + 3.37675i) q^{63} -1.14613i q^{64} +(5.81958 + 5.57965i) q^{65} +(-1.08526 + 3.38712i) q^{66} +(0.614925 + 2.29493i) q^{67} +(2.67800 - 4.63844i) q^{68} +(6.67733 - 1.44785i) q^{69} +(3.97261 + 11.7419i) q^{70} +(-1.72575 - 0.462414i) q^{71} +(-3.34755 - 4.06550i) q^{72} +(-9.70845 - 9.70845i) q^{73} +(10.6855 - 6.16928i) q^{74} +(-1.56064 + 8.51847i) q^{75} +(-0.469034 - 1.75046i) q^{76} -3.81522i q^{77} +(-10.7420 - 0.987461i) q^{78} -0.0854873 q^{79} +(2.19215 - 10.9627i) q^{80} +(-8.83273 - 1.72710i) q^{81} +(-7.89754 - 13.6789i) q^{82} +(-4.49219 - 4.49219i) q^{83} +(-4.59816 - 2.95944i) q^{84} +(-8.03642 + 9.14510i) q^{85} +(0.957366 + 0.957366i) q^{86} +(13.7650 - 2.98467i) q^{87} +(-1.04344 + 1.80730i) q^{88} +(-5.10951 + 1.36909i) q^{89} +(-5.46854 - 10.2158i) q^{90} +(11.2963 - 2.50718i) q^{91} -3.88057 q^{92} +(0.362217 + 0.0174994i) q^{93} +(7.61001 - 13.1809i) q^{94} +(0.265252 + 4.11068i) q^{95} +(4.06255 + 7.89332i) q^{96} +(-1.85928 - 0.498193i) q^{97} +(5.50517 + 1.47511i) q^{98} +(0.586675 + 3.51784i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 24 q^{4} - 4 q^{9} - 36 q^{10} + 10 q^{15} - 16 q^{21} - 28 q^{24} + 18 q^{30} - 40 q^{31} - 32 q^{34} - 60 q^{36} - 4 q^{39} + 40 q^{40} + 4 q^{45} - 128 q^{46} + 60 q^{54} + 28 q^{55} + 20 q^{60}+ \cdots - 48 q^{99}+O(q^{100}) $ 96 * q - 24 * q^4 - 4 * q^9 - 36 * q^10 + 10 * q^15 - 16 * q^21 - 28 * q^24 + 18 * q^30 - 40 * q^31 - 32 * q^34 - 60 * q^36 - 4 * q^39 + 40 * q^40 + 4 * q^45 - 128 * q^46 + 60 * q^54 + 28 * q^55 + 20 * q^60 - 48 * q^61 - 8 * q^66 + 72 * q^69 + 168 * q^70 + 66 * q^75 - 80 * q^76 - 80 * q^79 + 48 * q^81 - 132 * q^84 - 20 * q^85 - 56 * q^91 + 72 * q^94 + 204 * q^96 - 48 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/195\mathbb{Z}\right)^\times$.

$n$	$106$	$131$	$157$
$\chi(n)$	$e\left(\frac{11}{12}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.66849	+	0.447071i	−1.17980	+	0.316127i	−0.794847	−	0.606809i	$-0.792449\pi$
$2$	−1.66849	+	0.447071i	−1.17980	+	0.316127i	−0.384953	+	0.922936i	$0.625783\pi$
$3$	−1.28242	+	1.16422i	−0.740405	+	0.672161i
$3$	−1.28242	+	1.16422i	−0.740405	+	0.672161i
$4$	0.851938	−	0.491866i	0.425969	−	0.245933i
$5$	−2.11813	+	0.716618i	−0.947255	+	0.320481i
$5$	−2.11813	+	0.716618i	−0.947255	+	0.320481i
$6$	1.61922	−	2.51582i	0.661042	−	1.02708i
$7$	−0.830623	+	3.09993i	−0.313946	+	1.17166i	0.611021	+	0.791615i	$0.290759\pi$
$7$	−0.830623	+	3.09993i	−0.313946	+	1.17166i	−0.924967	+	0.380048i	$0.875907\pi$
$8$	1.24129	−	1.24129i	0.438862	−	0.438862i
$9$	0.289197	−	2.98603i	0.0963989	−	0.995343i
$10$	3.21369	−	2.14262i	1.01626	−	0.677557i
$11$	−1.14830	+	0.307686i	−0.346225	+	0.0927708i	−0.427741	−	0.903901i	$-0.640691\pi$
$11$	−1.14830	+	0.307686i	−0.346225	+	0.0927708i	0.0815158	+	0.996672i	$0.474024\pi$
$12$	−0.519902	+	1.62262i	−0.150083	+	0.468410i
$13$	−1.66563	−	3.19776i	−0.461961	−	0.886900i
$13$	−1.66563	−	3.19776i	−0.461961	−	0.886900i
$14$		−	5.54355i		−	1.48158i
$15$	1.88203	−	3.38496i	0.485937	−	0.873994i
$16$	−2.49987	+	4.32990i	−0.624967	+	1.08247i
$17$	4.71514	−	2.72229i	1.14359	−	0.660251i	0.196272	−	0.980549i	$-0.437116\pi$
$17$	4.71514	−	2.72229i	1.14359	−	0.660251i	0.947317	+	0.320298i	$0.103783\pi$
$18$	0.852444	+	5.11145i	0.200923	+	1.20478i
$19$	0.476790	−	1.77941i	0.109383	−	0.408224i	−0.889422	−	0.457086i	$-0.848893\pi$
$19$	0.476790	−	1.77941i	0.109383	−	0.408224i	0.998806	+	0.0488627i	$0.0155597\pi$
$20$	−1.45203	+	1.65235i	−0.324684	+	0.369476i
$21$	−2.54378	−	4.94243i	−0.555099	−	1.07853i
$22$	1.77837	−	1.02674i	0.379150	−	0.218902i
$23$	−3.41625	−	1.97237i	−0.712337	−	0.411268i	0.0995889	−	0.995029i	$-0.468247\pi$
$23$	−3.41625	−	1.97237i	−0.712337	−	0.411268i	−0.811926	+	0.583761i	$0.801581\pi$
$24$	−0.146722	+	3.03698i	−0.0299496	+	0.619921i
$25$	3.97292	−	3.03577i	0.794583	−	0.607155i
$26$	4.20871	+	4.59079i	0.825395	+	0.900327i
$27$	3.10551	+	4.16603i	0.597657	+	0.801752i
$28$	0.817112	+	3.04950i	0.154420	+	0.576302i
$29$	−7.04243	−	4.06595i	−1.30775	−	0.755027i	−0.326026	−	0.945361i	$-0.605710\pi$
$29$	−7.04243	−	4.06595i	−1.30775	−	0.755027i	−0.981720	+	0.190333i	$0.939043\pi$
$30$	−1.62682	+	6.48918i	−0.297016	+	1.18476i
$31$	−0.148047	−	0.148047i	−0.0265900	−	0.0265900i	0.693687	−	0.720277i	$-0.255985\pi$
$31$	−0.148047	−	0.148047i	−0.0265900	−	0.0265900i	−0.720277	+	0.693687i	$0.755985\pi$
$32$	1.32655	−	4.95075i	0.234503	−	0.875177i
$33$	1.11439	−	1.73145i	0.193990	−	0.301407i
$34$	−6.65011	+	6.65011i	−1.14048	+	1.14048i
$35$	−0.462099	−	7.16128i	−0.0781091	−	1.21048i
$36$	−1.22235	−	2.68616i	−0.203725	−	0.447693i
$37$	−6.89966	+	1.84876i	−1.13430	+	0.303934i	−0.776656	−	0.629925i	$-0.783086\pi$
$37$	−6.89966	+	1.84876i	−1.13430	+	0.303934i	−0.357642	+	0.933859i	$0.616419\pi$
$38$			3.18208i			0.516202i
$39$	5.85892	+	2.16172i	0.938178	+	0.346153i
$40$	−1.73968	+	3.51874i	−0.275067	+	0.556361i
$41$	2.36667	+	8.83254i	0.369612	+	1.37941i	0.861060	+	0.508504i	$0.169801\pi$
$41$	2.36667	+	8.83254i	0.369612	+	1.37941i	−0.491448	+	0.870907i	$0.663532\pi$
$42$	6.45390	+	7.10915i	0.995858	+	1.09697i
$43$	−0.391907	−	0.678803i	−0.0597653	−	0.103517i	0.834595	−	0.550864i	$-0.185702\pi$
$43$	−0.391907	−	0.678803i	−0.0597653	−	0.103517i	−0.894360	+	0.447348i	$0.852369\pi$
$44$	−0.826939	+	0.826939i	−0.124666	+	0.124666i
$45$	1.52729	+	6.53203i	0.227674	+	0.973737i
$46$	6.58176	+	1.76358i	0.970428	+	0.260025i
$47$	−6.23046	+	6.23046i	−0.908806	+	0.908806i	−0.996176	−	0.0873702i	$-0.972154\pi$
$47$	−6.23046	+	6.23046i	−0.908806	+	0.908806i	0.0873702	+	0.996176i	$0.472154\pi$
$48$	−1.83506	−	8.46313i	−0.264869	−	1.22155i
$49$	−2.85745	−	1.64975i	−0.408207	−	0.235678i
$50$	−5.27157	+	6.84134i	−0.745512	+	0.967511i
$51$	−2.87745	+	8.98056i	−0.402924	+	1.25753i
$52$	−2.99188	−	1.90503i	−0.414899	−	0.264180i
$53$	−0.952426			−0.130826			−0.0654129	−	0.997858i	$-0.520836\pi$
$53$	−0.952426			−0.130826			−0.0654129	+	0.997858i	$0.520836\pi$
$54$	−7.04403	−	5.56259i	−0.958571	−	0.756973i
$55$	2.21175	−	1.47461i	0.298232	−	0.198836i
$56$	2.81686	+	4.87895i	0.376419	+	0.651977i
$57$	1.46017	+	2.83703i	0.193404	+	0.375774i
$58$	13.5680	+	3.63553i	1.78156	+	0.477369i
$59$	2.09784	−	7.82924i	0.273115	−	1.01928i	−0.683979	−	0.729502i	$-0.739752\pi$
$59$	2.09784	−	7.82924i	0.273115	−	1.01928i	0.957094	−	0.289778i	$-0.0935814\pi$
$60$	−0.0615809	−	3.80948i	−0.00795006	−	0.491802i
$61$	−6.49787	−	11.2546i	−0.831967	−	1.44101i	−0.896476	−	0.443092i	$-0.853881\pi$
$61$	−6.49787	−	11.2546i	−0.831967	−	1.44101i	0.0645090	−	0.997917i	$-0.479452\pi$
$62$	0.313203	+	0.180828i	0.0397768	+	0.0229651i
$63$	9.01626	+	3.37675i	1.13594	+	0.425431i
$64$		−	1.14613i		−	0.143267i
$65$	5.81958	+	5.57965i	0.721830	+	0.692070i
$66$	−1.08526	+	3.38712i	−0.133587	+	0.416926i
$67$	0.614925	+	2.29493i	0.0751250	+	0.280370i	0.993262	−	0.115894i	$-0.0369732\pi$
$67$	0.614925	+	2.29493i	0.0751250	+	0.280370i	−0.918137	+	0.396264i	$0.870307\pi$
$68$	2.67800	−	4.63844i	0.324756	−	0.562493i
$69$	6.67733	−	1.44785i	0.803856	−	0.174300i
$70$	3.97261	+	11.7419i	0.474817	+	1.40343i
$71$	−1.72575	−	0.462414i	−0.204809	−	0.0548784i	0.154956	−	0.987921i	$-0.450476\pi$
$71$	−1.72575	−	0.462414i	−0.204809	−	0.0548784i	−0.359765	+	0.933043i	$0.617143\pi$
$72$	−3.34755	−	4.06550i	−0.394512	−	0.479124i
$73$	−9.70845	−	9.70845i	−1.13629	−	1.13629i	−0.989110	−	0.147177i	$-0.952981\pi$
$73$	−9.70845	−	9.70845i	−1.13629	−	1.13629i	−0.147177	−	0.989110i	$-0.547019\pi$
$74$	10.6855	−	6.16928i	1.24216	−	0.717164i
$75$	−1.56064	+	8.51847i	−0.180208	+	0.983629i
$76$	−0.469034	−	1.75046i	−0.0538019	−	0.200792i
$77$		−	3.81522i		−	0.434785i
$78$	−10.7420	−	0.987461i	−1.21629	−	0.111808i
$79$	−0.0854873			−0.00961807			−0.00480903	−	0.999988i	$-0.501531\pi$
$79$	−0.0854873			−0.00961807			−0.00480903	+	0.999988i	$0.501531\pi$
$80$	2.19215	−	10.9627i	0.245090	−	1.22567i
$81$	−8.83273	−	1.72710i	−0.981415	−	0.191900i
$82$	−7.89754	−	13.6789i	−0.872137	−	1.51059i
$83$	−4.49219	−	4.49219i	−0.493082	−	0.493082i	0.416194	−	0.909276i	$-0.363364\pi$
$83$	−4.49219	−	4.49219i	−0.493082	−	0.493082i	−0.909276	+	0.416194i	$0.863364\pi$
$84$	−4.59816	−	2.95944i	−0.501701	−	0.322902i
$85$	−8.03642	+	9.14510i	−0.871672	+	0.991925i
$86$	0.957366	+	0.957366i	0.103235	+	0.103235i
$87$	13.7650	−	2.98467i	1.47576	−	0.319990i
$88$	−1.04344	+	1.80730i	−0.111232	+	0.192659i
$89$	−5.10951	+	1.36909i	−0.541607	+	0.145123i	−0.519243	−	0.854627i	$-0.673786\pi$
$89$	−5.10951	+	1.36909i	−0.541607	+	0.145123i	−0.0223639	+	0.999750i	$0.507119\pi$
$90$	−5.46854	−	10.2158i	−0.576435	−	1.07684i
$91$	11.2963	−	2.50718i	1.18418	−	0.262824i
$92$	−3.88057			−0.404578
$93$	0.362217	+	0.0174994i	0.0375602	+	0.00181461i
$94$	7.61001	−	13.1809i	0.784912	−	1.35951i
$95$	0.265252	+	4.11068i	0.0272143	+	0.421747i
$96$	4.06255	+	7.89332i	0.414633	+	0.805609i
$97$	−1.85928	−	0.498193i	−0.188781	−	0.0505838i	0.163190	−	0.986595i	$-0.447822\pi$
$97$	−1.85928	−	0.498193i	−0.188781	−	0.0505838i	−0.351971	+	0.936011i	$0.614488\pi$
$98$	5.50517	+	1.47511i	0.556107	+	0.149008i
$99$	0.586675	+	3.51784i	0.0589630	+	0.353556i
$100$	1.89148	−	4.54044i	0.189148	−	0.454044i
$101$	5.91840	−	10.2510i	0.588903	−	1.02001i	−0.405474	−	0.914107i	$-0.632893\pi$
$101$	5.91840	−	10.2510i	0.588903	−	1.02001i	0.994377	−	0.105903i	$-0.0337732\pi$
$102$	0.786054	−	16.2704i	0.0778310	−	1.61101i
$103$	6.77628			0.667686			0.333843	−	0.942629i	$-0.391654\pi$
$103$	6.77628			0.667686			0.333843	+	0.942629i	$0.391654\pi$
$104$	−6.03687	−	1.90183i	−0.591964	−	0.186489i
$105$	8.92989	+	8.64578i	0.871468	+	0.843741i
$106$	1.58911	−	0.425802i	0.154348	−	0.0413575i
$107$	−2.61134	+	4.52298i	−0.252448	+	0.437253i	−0.964199	−	0.265179i	$-0.914569\pi$
$107$	−2.61134	+	4.52298i	−0.252448	+	0.437253i	0.711751	+	0.702432i	$0.247902\pi$
$108$	4.69483	+	2.02170i	0.451761	+	0.194538i
$109$	−1.57960	−	1.57960i	−0.151298	−	0.151298i	0.627399	−	0.778698i	$-0.284119\pi$
$109$	−1.57960	−	1.57960i	−0.151298	−	0.151298i	−0.778698	+	0.627399i	$0.784119\pi$
$110$	−3.03103	+	3.44918i	−0.288997	+	0.328867i
$111$	6.69590	−	10.4036i	0.635547	−	0.987465i
$112$	−11.3459	−	11.3459i	−1.07209	−	1.07209i
$113$	2.34369	+	4.05939i	0.220476	+	0.381875i	0.954953	−	0.296759i	$-0.0959057\pi$
$113$	2.34369	+	4.05939i	0.220476	+	0.381875i	−0.734477	+	0.678634i	$0.762572\pi$
$114$	−3.70463	−	4.08076i	−0.346971	−	0.382198i
$115$	8.64948	+	1.72959i	0.806568	+	0.161285i
$116$	−7.99961			−0.742745
$117$	−10.0303	+	4.04882i	−0.927302	+	0.374314i
$118$			14.0009i			1.28889i
$119$	4.52239	+	16.8778i	0.414567	+	1.54718i
$120$	−1.86558	−	6.53786i	−0.170303	−	0.596822i
$121$	−8.30236	+	4.79337i	−0.754760	+	0.435761i
$122$	15.8733	+	15.8733i	1.43710	+	1.43710i
$123$	−13.3181	−	8.57169i	−1.20085	−	0.772884i
$124$	−0.198946	−	0.0533075i	−0.0178659	−	0.00478715i
$125$	−6.23965	+	9.27722i	−0.558091	+	0.829780i
$126$	−16.5532	−	1.60318i	−1.47468	−	0.142822i
$127$	7.95071	−	13.7710i	0.705512	−	1.22198i	−0.260995	−	0.965340i	$-0.584051\pi$
$127$	7.95071	−	13.7710i	0.705512	−	1.22198i	0.966507	−	0.256642i	$-0.0826160\pi$
$128$	3.16550	+	11.8138i	0.279793	+	1.04420i
$129$	1.29286	+	0.414245i	0.113830	+	0.0364722i
$130$	−12.2044	−	6.70783i	−1.07040	−	0.588315i
$131$		−	2.54531i		−	0.222385i	−0.993799	−	0.111192i	$-0.964533\pi$
$131$		−	2.54531i		−	0.222385i	0.993799	−	0.111192i	$-0.0354670\pi$
$132$	0.0977457	−	2.02322i	0.00850767	−	0.176099i
$133$	5.12000	+	2.95603i	0.443960	+	0.256321i
$134$	−2.05199	−	3.55415i	−0.177265	−	0.307032i
$135$	−9.56332	−	6.59870i	−0.823080	−	0.567926i
$136$	2.47370	−	9.23199i	0.212118	−	0.791637i
$137$	−3.68153	−	0.986463i	−0.314534	−	0.0842792i	0.0980984	−	0.995177i	$-0.468724\pi$
$137$	−3.68153	−	0.986463i	−0.314534	−	0.0842792i	−0.412633	+	0.910898i	$0.635391\pi$
$138$	−10.4938	+	5.40096i	−0.893289	+	0.459760i
$139$	10.0439	+	17.3966i	0.851915	+	1.47556i	0.879478	+	0.475939i	$0.157892\pi$
$139$	10.0439	+	17.3966i	0.851915	+	1.47556i	−0.0275635	+	0.999620i	$0.508775\pi$
$140$	−3.91607	−	5.87367i	−0.330969	−	0.496416i
$141$	0.736451	−	15.2437i	0.0620204	−	1.28375i
$142$	3.08613			0.258982
$143$	2.89654	+	3.15950i	0.242221	+	0.264211i
$144$	12.2062	+	8.71687i	1.01719	+	0.726406i
$145$	17.8305	+	3.56546i	1.48074	+	0.296095i
$146$	20.5388	+	11.8581i	1.69980	+	0.981382i
$147$	5.58511	−	1.21102i	0.460652	−	0.0998833i
$148$	−4.96874	+	4.96874i	−0.408428	+	0.408428i
$149$	−2.43030	−	0.651196i	−0.199098	−	0.0533481i	0.157892	−	0.987456i	$-0.449530\pi$
$149$	−2.43030	−	0.651196i	−0.199098	−	0.0533481i	−0.356990	+	0.934108i	$0.616197\pi$
$150$	−1.20444	−	14.9107i	−0.0983422	−	1.21745i
$151$	−13.6575	+	13.6575i	−1.11143	+	1.11143i	−0.118477	+	0.992957i	$0.537801\pi$
$151$	−13.6575	+	13.6575i	−1.11143	+	1.11143i	−0.992957	+	0.118477i	$0.962199\pi$
$152$	−1.61692	−	2.80059i	−0.131150	−	0.227158i
$153$	−6.76522	−	14.8668i	−0.546936	−	1.20191i
$154$	1.70567	+	6.36566i	0.137447	+	0.512959i
$155$	0.419675	+	0.207489i	0.0337091	+	0.0166659i
$156$	6.05471	−	1.04015i	0.484765	−	0.0832790i
$157$		−	5.38756i		−	0.429974i	−0.976617	−	0.214987i	$-0.931029\pi$
$157$		−	5.38756i		−	0.429974i	0.976617	−	0.214987i	$-0.0689709\pi$
$158$	0.142635	−	0.0382189i	0.0113474	−	0.00304053i
$159$	1.22141	−	1.10883i	0.0968641	−	0.0879360i
$160$	0.737997	+	11.4369i	0.0583438	+	0.904169i
$161$	8.95182	−	8.95182i	0.705503	−	0.705503i
$162$	15.5095	−	1.06721i	1.21854	−	0.0838477i
$163$	−3.22604	+	12.0398i	−0.252683	+	0.943027i	0.716681	+	0.697401i	$0.245660\pi$
$163$	−3.22604	+	12.0398i	−0.252683	+	0.943027i	−0.969365	+	0.245626i	$0.921007\pi$
$164$	6.36068	+	6.36068i	0.496686	+	0.496686i
$165$	−1.11962	+	4.46603i	−0.0871626	+	0.347680i
$166$	9.50350	+	5.48685i	0.737615	+	0.425862i
$167$	−2.71716	−	10.1406i	−0.210260	−	0.784702i	−0.987781	−	0.155845i	$-0.950190\pi$
$167$	−2.71716	−	10.1406i	−0.210260	−	0.784702i	0.777521	−	0.628857i	$-0.216477\pi$
$168$	−9.29256	−	2.97742i	−0.716936	−	0.229713i
$169$	−7.45138	+	10.6526i	−0.573183	+	0.819427i
$170$	9.32018	−	18.8514i	0.714825	−	1.44583i
$171$	−5.17547	−	1.93831i	−0.395778	−	0.148226i
$172$	−0.667761	−	0.385532i	−0.0509163	−	0.0293965i
$173$	−14.5749	+	8.41484i	−1.10811	+	0.639768i	−0.938340	−	0.345715i	$-0.887636\pi$
$173$	−14.5749	+	8.41484i	−1.10811	+	0.639768i	−0.169772	+	0.985483i	$0.554303\pi$
$174$	−21.6324	+	11.1338i	−1.63995	+	0.844052i
$175$	6.11069	+	14.8373i	0.461925	+	1.12160i
$176$	1.53835	−	5.74120i	0.115957	−	0.432759i
$177$	6.42462	+	12.4827i	0.482904	+	0.938257i
$178$	7.91308	−	4.56862i	0.593111	−	0.342433i
$179$	−9.06243	+	15.6966i	−0.677358	+	1.17322i	0.298415	+	0.954436i	$0.403542\pi$
$179$	−9.06243	+	15.6966i	−0.677358	+	1.17322i	−0.975774	+	0.218783i	$0.929791\pi$
$180$	4.51404	+	4.81366i	0.336457	+	0.358789i
$181$			0.330859i			0.0245925i	0.999924	+	0.0122963i	$0.00391412\pi$
$181$			0.330859i			0.0245925i	−0.999924	+	0.0122963i	$0.996086\pi$
$182$	−17.7270	+	9.23348i	−1.31401	+	0.684431i
$183$	21.4358	+	6.86823i	1.58458	+	0.507714i
$184$	−6.68883	+	1.79227i	−0.493107	+	0.132128i
$185$	13.2895	−	8.86033i	0.977064	−	0.651424i
$186$	−0.612180	+	0.132739i	−0.0448872	+	0.00973290i
$187$	−4.57678	+	4.57678i	−0.334688	+	0.334688i
$188$	−2.24341	+	8.37252i	−0.163617	+	0.610628i
$189$	−15.4939	+	6.16647i	−1.12702	+	0.448545i
$190$	−2.28034	−	6.74005i	−0.165433	−	0.488975i
$191$	−10.9457	+	6.31949i	−0.792001	+	0.457262i	−0.840667	−	0.541553i	$-0.817837\pi$
$191$	−10.9457	+	6.31949i	−0.792001	+	0.457262i	0.0486655	+	0.998815i	$0.484503\pi$
$192$	1.33435	+	1.46982i	0.0962984	+	0.106075i
$193$	−6.49950	+	1.74154i	−0.467845	+	0.125359i	−0.485037	−	0.874494i	$-0.661194\pi$
$193$	−6.49950	+	1.74154i	−0.467845	+	0.125359i	0.0171925	+	0.999852i	$0.494527\pi$
$194$	3.32492			0.238715
$195$	−13.9591	−	0.380193i	−0.999629	−	0.0272262i
$196$	−3.24582			−0.231844
$197$	15.8690	−	4.25210i	1.13062	−	0.302949i	0.355447	−	0.934696i	$-0.384328\pi$
$197$	15.8690	−	4.25210i	1.13062	−	0.302949i	0.775175	+	0.631747i	$0.217662\pi$
$198$	−2.55158	−	5.60719i	−0.181333	−	0.398486i
$199$	6.32168	−	3.64982i	0.448132	−	0.258729i	−0.258909	−	0.965902i	$-0.583363\pi$
$199$	6.32168	−	3.64982i	0.448132	−	0.258729i	0.707041	+	0.707173i	$0.250030\pi$
$200$	1.16326	−	8.69981i	0.0822552	−	0.615170i
$201$	−3.46039	−	2.22716i	−0.244077	−	0.157091i
$202$	−5.29188	+	19.7496i	−0.372336	+	1.38958i
$203$	18.4538	−	18.4538i	1.29520	−	1.29520i
$204$	1.96583	+	9.06620i	0.137635	+	0.634761i
$205$	−11.3425	−	17.0124i	−0.792192	−	1.18820i
$206$	−11.3062	+	3.02948i	−0.787737	+	0.211074i
$207$	−6.87752	+	9.63061i	−0.478021	+	0.669373i
$208$	18.0098	+	0.781997i	1.24876	+	0.0542217i
$209$			2.18999i			0.151485i
$210$	−18.7647	−	10.4331i	−1.29489	−	0.719953i
$211$	−13.1703	+	22.8117i	−0.906684	+	1.57042i	−0.0880423	+	0.996117i	$0.528061\pi$
$211$	−13.1703	+	22.8117i	−0.906684	+	1.57042i	−0.818641	+	0.574305i	$0.805272\pi$
$212$	−0.811408	+	0.468467i	−0.0557277	+	0.0321744i
$213$	2.75149	−	1.41614i	0.188529	−	0.0970324i
$214$	2.33491	−	8.71401i	0.159611	−	0.595677i
$215$	1.31655	+	1.15694i	0.0897881	+	0.0789029i
$216$	9.02608	+	1.31640i	0.614147	+	0.0895698i
$217$	0.581907	−	0.335964i	0.0395024	−	0.0228067i
$218$	3.34174	+	1.92936i	0.226331	+	0.130672i
$219$	23.7530	+	1.14756i	1.60508	+	0.0775446i
$220$	1.15896	−	2.34416i	0.0781372	−	0.158043i
$221$	−16.5589	−	10.5436i	−1.11387	−	0.709238i
$222$	−6.52091	+	20.3518i	−0.437655	+	1.36593i
$223$	−0.884112	−	3.29955i	−0.0592045	−	0.220954i	0.929985	−	0.367598i	$-0.119820\pi$
$223$	−0.884112	−	3.29955i	−0.0592045	−	0.220954i	−0.989189	+	0.146643i	$0.953153\pi$
$224$	14.2451	+	8.22441i	0.951791	+	0.549517i
$225$	−7.91595	−	12.7412i	−0.527730	−	0.849412i
$226$	−5.72526	−	5.72526i	−0.380838	−	0.380838i
$227$	3.18305	−	11.8793i	0.211266	−	0.788456i	−0.776181	−	0.630510i	$-0.782846\pi$
$227$	3.18305	−	11.8793i	0.211266	−	0.788456i	0.987448	−	0.157947i	$-0.0504874\pi$
$228$	2.63941	+	1.69877i	0.174799	+	0.112503i
$229$	4.45823	−	4.45823i	0.294608	−	0.294608i	−0.544289	−	0.838898i	$-0.683201\pi$
$229$	4.45823	−	4.45823i	0.294608	−	0.294608i	0.838898	+	0.544289i	$0.183201\pi$
$230$	−15.2048	+	0.981129i	−1.00258	+	0.0646937i
$231$	4.44174	+	4.89271i	0.292245	+	0.321917i
$232$	−13.7887	+	3.69467i	−0.905273	+	0.242567i
$233$		−	7.44279i		−	0.487594i	−0.969826	−	0.243797i	$-0.921607\pi$
$233$		−	7.44279i		−	0.487594i	0.969826	−	0.243797i	$-0.0783930\pi$
$234$	14.9254	−	11.2397i	0.975701	−	0.734761i
$235$	8.73204	−	17.6618i	0.569615	−	1.15213i
$236$	−2.06371	−	7.70188i	−0.134336	−	0.501349i
$237$	0.109630	−	0.0995257i	0.00712127	−	0.00646489i
$238$	−15.0911	−	26.1386i	−0.978213	−	1.69431i
$239$	13.3710	−	13.3710i	0.864899	−	0.864899i	−0.127003	−	0.991902i	$-0.540536\pi$
$239$	13.3710	−	13.3710i	0.864899	−	0.864899i	0.991902	+	0.127003i	$0.0405358\pi$
$240$	9.95173	+	16.6109i	0.642381	+	1.07223i
$241$	28.0098	+	7.50522i	1.80427	+	0.483453i	0.994632	−	0.103473i	$-0.0329955\pi$
$241$	28.0098	+	7.50522i	1.80427	+	0.483453i	0.809640	+	0.586926i	$0.199662\pi$
$242$	11.7094	−	11.7094i	0.752711	−	0.752711i
$243$	13.3380	−	8.06835i	0.855632	−	0.517585i
$244$	−11.0716	−	6.39217i	−0.708784	−	0.409217i
$245$	7.23467	+	1.44668i	0.462206	+	0.0924247i
$246$	26.0532	+	8.34768i	1.66109	+	0.532228i
$247$	−6.48427	+	1.43916i	−0.412584	+	0.0915716i
$248$	−0.367538			−0.0233387
$249$	10.9908	+	0.530985i	0.696511	+	0.0336498i
$250$	6.26322	−	18.2685i	0.396121	−	1.15540i
$251$	−12.0103	−	20.8025i	−0.758085	−	1.31304i	−0.943826	−	0.330443i	$-0.892802\pi$
$251$	−12.0103	−	20.8025i	−0.758085	−	1.31304i	0.185741	−	0.982599i	$-0.440532\pi$
$252$	9.34221	−	1.55801i	0.588504	−	0.0981456i
$253$	4.52975	+	1.21374i	0.284783	+	0.0763073i
$254$	−7.10906	+	26.5314i	−0.446062	+	1.66473i
$255$	−0.340826	−	21.0840i	−0.0213434	−	1.32033i
$256$	−9.41708	−	16.3109i	−0.588568	−	1.01943i
$257$	5.59821	+	3.23213i	0.349207	+	0.201615i	0.664336	−	0.747434i	$-0.268714\pi$
$257$	5.59821	+	3.23213i	0.349207	+	0.201615i	−0.315129	+	0.949049i	$0.602048\pi$
$258$	−2.34233	−	0.113162i	−0.145827	−	0.00704518i
$259$		−	22.9241i		−	1.42443i
$260$	7.70236	+	1.89106i	0.477680	+	0.117278i
$261$	−14.1777	+	19.8530i	−0.877576	+	1.22887i
$262$	1.13793	+	4.24682i	0.0703018	+	0.262370i
$263$	−8.02170	+	13.8940i	−0.494639	+	0.856740i	−0.999981	−	0.00617933i	$-0.998033\pi$
$263$	−8.02170	+	13.8940i	−0.494639	+	0.856740i	0.505342	+	0.862919i	$0.331366\pi$
$264$	−0.765955	−	3.53251i	−0.0471413	−	0.217411i
$265$	2.01736	−	0.682526i	0.123925	−	0.0419272i
$266$	−9.86422	−	2.64311i	−0.604814	−	0.162060i
$267$	4.95861	−	7.70432i	0.303462	−	0.471497i
$268$	1.65268	+	1.65268i	0.100953	+	0.100953i
$269$	−9.95173	+	5.74563i	−0.606767	+	0.350317i	−0.771699	−	0.635988i	$-0.780593\pi$
$269$	−9.95173	+	5.74563i	−0.606767	+	0.350317i	0.164932	+	0.986305i	$0.447260\pi$
$270$	18.9064	+	6.73439i	1.15061	+	0.409842i
$271$	−3.04037	−	11.3468i	−0.184690	−	0.689271i	−0.994697	−	0.102851i	$-0.967204\pi$
$271$	−3.04037	−	11.3468i	−0.184690	−	0.689271i	0.810007	−	0.586420i	$-0.199463\pi$
$272$			27.2214i			1.65054i
$273$	−11.5677	+	16.3667i	−0.700112	+	0.990555i
$274$	6.58362			0.397731
$275$	−3.62803	+	4.70839i	−0.218779	+	0.283927i
$276$	4.97652	−	4.51783i	0.299551	−	0.271941i
$277$	9.87847	+	17.1100i	0.593540	+	1.02804i	0.993751	+	0.111618i	$0.0356034\pi$
$277$	9.87847	+	17.1100i	0.593540	+	1.02804i	−0.400211	+	0.916423i	$0.631063\pi$
$278$	−24.5357	−	24.5357i	−1.47155	−	1.47155i
$279$	−0.484887	+	0.399258i	−0.0290294	+	0.0239029i
$280$	−9.46282	−	8.31562i	−0.565511	−	0.496953i
$281$	−1.76652	−	1.76652i	−0.105382	−	0.105382i	0.652450	−	0.757832i	$-0.273741\pi$
$281$	−1.76652	−	1.76652i	−0.105382	−	0.105382i	−0.757832	+	0.652450i	$0.773741\pi$
$282$	5.58623	+	25.7632i	0.332655	+	1.53417i
$283$	−3.63577	+	6.29734i	−0.216124	+	0.374338i	−0.953620	−	0.301014i	$-0.902675\pi$
$283$	−3.63577	+	6.29734i	−0.216124	+	0.374338i	0.737496	+	0.675352i	$0.236008\pi$
$284$	−1.69768	+	0.454891i	−0.100739	+	0.0269928i
$285$	−5.12589	−	4.96281i	−0.303632	−	0.293971i
$286$	−6.24538	−	3.97664i	−0.369297	−	0.235144i
$287$	−29.3460			−1.73224
$288$	−14.3994	−	5.39285i	−0.848495	−	0.317777i
$289$	6.32169	−	10.9495i	0.371864	−	0.644087i
$290$	−31.3440	+	2.02255i	−1.84058	+	0.118768i
$291$	2.96438	−	1.52571i	0.173775	−	0.0894390i
$292$	−13.0462	−	3.49573i	−0.763474	−	0.204572i
$293$	−2.03520	−	0.545330i	−0.118898	−	0.0318585i	0.198880	−	0.980024i	$-0.436270\pi$
$293$	−2.03520	−	0.545330i	−0.118898	−	0.0318585i	−0.317777	+	0.948165i	$0.602936\pi$
$294$	−8.77729	+	4.51751i	−0.511902	+	0.263467i
$295$	1.16709	+	18.0867i	0.0679504	+	1.05305i
$296$	−6.26963	+	10.8593i	−0.364415	+	0.631185i
$297$	−4.84789	−	3.82832i	−0.281303	−	0.222142i
$298$	4.34606			0.251760
$299$	−0.616988	+	14.2096i	−0.0356813	+	0.821761i
$300$	2.86038	+	8.02484i	0.165144	+	0.463314i
$301$	2.42977	−	0.651055i	0.140050	−	0.0375262i
$302$	16.6816	−	28.8933i	0.959917	−	1.66262i
$303$	4.34449	+	20.0363i	0.249584	+	1.15106i
$304$	6.51273	+	6.51273i	0.373531	+	0.373531i
$305$	21.8286	+	19.1823i	1.24990	+	1.09837i
$306$	17.9342	+	21.7806i	1.02523	+	1.24511i
$307$	−9.18929	−	9.18929i	−0.524461	−	0.524461i	0.394455	−	0.918915i	$-0.370934\pi$
$307$	−9.18929	−	9.18929i	−0.524461	−	0.524461i	−0.918915	+	0.394455i	$0.870934\pi$
$308$	−1.87658	−	3.25033i	−0.106928	−	0.185205i
$309$	−8.69003	+	7.88906i	−0.494358	+	0.448793i
$310$	−0.792987	−	0.158569i	−0.0450386	−	0.00900612i
$311$	12.7422			0.722542			0.361271	−	0.932461i	$-0.382343\pi$
$311$	12.7422			0.722542			0.361271	+	0.932461i	$0.382343\pi$
$312$	9.95593	−	4.58929i	0.563644	−	0.259817i
$313$		−	25.4351i		−	1.43768i	−0.695178	−	0.718838i	$-0.744674\pi$
$313$		−	25.4351i		−	1.43768i	0.695178	−	0.718838i	$-0.255326\pi$
$314$	2.40862	+	8.98909i	0.135926	+	0.507284i
$315$	−21.5174	−	0.691176i	−1.21237	−	0.0389434i
$316$	−0.0728298	+	0.0420483i	−0.00409700	+	0.00236540i
$317$	3.36120	+	3.36120i	0.188784	+	0.188784i	0.795170	−	0.606386i	$-0.207382\pi$
$317$	3.36120	+	3.36120i	0.188784	+	0.188784i	−0.606386	+	0.795170i	$0.707382\pi$
$318$	−1.54218	+	2.39613i	−0.0864814	+	0.134368i
$319$	9.33785	+	2.50207i	0.522819	+	0.140089i
$320$	0.821341	+	2.42766i	0.0459143	+	0.135710i
$321$	−1.91689	−	8.84053i	−0.106991	−	0.493430i
$322$	−10.9339	+	18.9381i	−0.609324	+	1.05538i
$323$	−2.59592	−	9.68810i	−0.144441	−	0.539061i
$324$	−8.37444	+	2.87314i	−0.465247	+	0.159619i
$325$	−16.3251	−	7.64799i	−0.905553	−	0.424234i
$326$		−	21.5305i		−	1.19246i
$327$	3.86471	+	0.186712i	0.213719	+	0.0103252i
$328$	13.9015	+	8.02601i	0.767579	+	0.443162i
$329$	−14.1388	−	24.4891i	−0.779498	−	1.35013i
$330$	−0.128547	−	7.95207i	−0.00707625	−	0.437747i
$331$	5.30136	−	19.7850i	0.291389	−	1.08748i	−0.652653	−	0.757657i	$-0.726344\pi$
$331$	5.30136	−	19.7850i	0.291389	−	1.08748i	0.944043	−	0.329823i	$-0.106989\pi$
$332$	−6.03662	−	1.61751i	−0.331303	−	0.0887723i
$333$	3.52509	+	21.1372i	0.193174	+	1.15831i
$334$	9.06712	+	15.7047i	0.496131	+	0.859324i
$335$	−2.94708	−	4.42029i	−0.161016	−	0.241506i
$336$	27.7594	+	1.34111i	1.51440	+	0.0731635i
$337$	23.0073			1.25329			0.626644	−	0.779305i	$-0.284428\pi$
$337$	23.0073			1.25329			0.626644	+	0.779305i	$0.284428\pi$
$338$	7.67012	−	21.1050i	0.417199	−	1.14796i
$339$	−7.73160	−	2.47727i	−0.419923	−	0.134547i
$340$	−2.34836	+	11.7439i	−0.127358	+	0.636902i
$341$	0.215554	+	0.124450i	0.0116729	+	0.00673937i
$342$	9.50178	+	0.920247i	0.513798	+	0.0497613i
$343$	−8.39758	+	8.39758i	−0.453427	+	0.453427i
$344$	−1.32906	−	0.356121i	−0.0716581	−	0.0192007i
$345$	−13.1059	+	7.85182i	−0.705596	+	0.422728i
$346$	20.5561	−	20.5561i	1.10510	−	1.10510i
$347$	−2.50750	−	4.34312i	−0.134610	−	0.233151i	0.790839	−	0.612025i	$-0.209645\pi$
$347$	−2.50750	−	4.34312i	−0.134610	−	0.233151i	−0.925448	+	0.378874i	$0.876311\pi$
$348$	10.2589	−	9.31329i	0.549932	−	0.499245i
$349$	0.823955	+	3.07504i	0.0441053	+	0.164603i	0.984466	−	0.175576i	$-0.0561789\pi$
$349$	0.823955	+	3.07504i	0.0441053	+	0.164603i	−0.940361	+	0.340179i	$0.889512\pi$
$350$	−16.8290	−	22.0241i	−0.899546	−	1.17724i
$351$	8.14934	−	16.8697i	0.434980	−	0.900440i
$352$			6.09310i			0.324763i
$353$	5.10099	−	1.36681i	0.271498	−	0.0727477i	−0.120501	−	0.992713i	$-0.538450\pi$
$353$	5.10099	−	1.36681i	0.271498	−	0.0727477i	0.391999	+	0.919965i	$0.371784\pi$
$354$	−16.3001	−	17.9550i	−0.866339	−	0.954298i
$355$	3.98673	−	0.257254i	0.211594	−	0.0136536i
$356$	−3.67957	+	3.67957i	−0.195017	+	0.195017i
$357$	−25.4490	−	16.3794i	−1.34690	−	0.866887i
$358$	8.10310	−	30.2412i	0.428262	−	1.59830i
$359$	14.4070	+	14.4070i	0.760371	+	0.760371i	0.976389	−	0.216018i	$-0.0693070\pi$
$359$	14.4070	+	14.4070i	0.760371	+	0.760371i	−0.216018	+	0.976389i	$0.569307\pi$
$360$	10.0039	+	6.21233i	0.527254	+	0.327419i
$361$	13.5155	+	7.80319i	0.711344	+	0.410694i
$362$	−0.147917	−	0.552035i	−0.00777436	−	0.0290143i
$363$	5.06658	−	15.8129i	0.265926	−	0.829960i
$364$	8.39058	−	7.69226i	0.439786	−	0.403184i
$365$	27.5210	+	13.6065i	1.44051	+	0.712195i
$366$	−38.8361	−	1.87625i	−2.02999	−	0.0980730i
$367$	−11.8073	−	6.81696i	−0.616337	−	0.355842i	0.159105	−	0.987262i	$-0.449139\pi$
$367$	−11.8073	−	6.81696i	−0.616337	−	0.355842i	−0.775441	+	0.631420i	$0.782473\pi$
$368$	17.0803	−	9.86133i	0.890374	−	0.514058i
$369$	27.0586	−	4.51261i	1.40862	−	0.234917i
$370$	−18.2122	+	20.7247i	−0.946808	+	1.07743i
$371$	0.791108	−	2.95245i	0.0410723	−	0.153284i
$372$	0.317194	−	0.163254i	0.0164457	−	0.00846433i
$373$	−21.9554	+	12.6759i	−1.13681	+	0.656335i	−0.945638	−	0.325222i	$-0.894561\pi$
$373$	−21.9554	+	12.6759i	−1.13681	+	0.656335i	−0.191169	+	0.981557i	$0.561228\pi$
$374$	5.59017	−	9.68247i	0.289061	−	0.500668i
$375$	−2.79885	−	19.1616i	−0.144532	−	0.989500i
$376$			15.4676i			0.797680i
$377$	−1.27189	+	29.2924i	−0.0655057	+	1.50863i
$378$	23.0946	−	17.2156i	1.18786	−	0.885473i
$379$	−25.2089	+	6.75470i	−1.29489	+	0.346966i	−0.839517	−	0.543333i	$-0.817162\pi$
$379$	−25.2089	+	6.75470i	−1.29489	+	0.346966i	−0.455376	+	0.890299i	$0.650495\pi$
$380$	2.24789	+	3.37158i	0.115314	+	0.172958i
$381$	5.83633	+	26.9166i	0.299004	+	1.37898i
$382$	15.4375	−	15.4375i	0.789851	−	0.789851i
$383$	−3.36875	+	12.5724i	−0.172135	+	0.642417i	0.824887	+	0.565298i	$0.191239\pi$
$383$	−3.36875	+	12.5724i	−0.172135	+	0.642417i	−0.997022	+	0.0771191i	$0.975428\pi$
$384$	−17.8133	−	11.4649i	−0.909033	−	0.585067i
$385$	2.73405	+	8.08112i	0.139340	+	0.411852i
$386$	10.0658	−	5.81148i	0.512334	−	0.295796i
$387$	−2.14026	+	0.973938i	−0.108796	+	0.0495081i
$388$	−1.82904	+	0.490089i	−0.0928552	+	0.0248805i
$389$	−18.8047			−0.953438			−0.476719	−	0.879056i	$-0.658174\pi$
$389$	−18.8047			−0.953438			−0.476719	+	0.879056i	$0.658174\pi$
$390$	23.4605	−	5.60634i	1.18797	−	0.283888i
$391$	−21.4774			−1.08616
$392$	−5.59473	+	1.49910i	−0.282576	+	0.0757161i
$393$	2.96329	+	3.26415i	0.149478	+	0.164655i
$394$	−24.5764	+	14.1892i	−1.23814	+	0.714840i
$395$	0.181073	−	0.0612617i	0.00911076	−	0.00308241i
$396$	2.23012	+	2.70841i	0.112068	+	0.136103i
$397$	2.40525	−	8.97652i	0.120716	−	0.450519i	−0.878935	−	0.476942i	$-0.841745\pi$
$397$	2.40525	−	8.97652i	0.120716	−	0.450519i	0.999651	+	0.0264234i	$0.00841181\pi$
$398$	−8.91594	+	8.91594i	−0.446916	+	0.446916i
$399$	−10.0074	+	2.16992i	−0.500999	+	0.108632i
$400$	3.21283	+	24.7914i	0.160641	+	1.23957i
$401$	−24.4394	+	6.54850i	−1.22044	+	0.327017i	−0.810851	−	0.585252i	$-0.800995\pi$
$401$	−24.4394	+	6.54850i	−1.22044	+	0.327017i	−0.409592	+	0.912269i	$0.634329\pi$
$402$	6.76932	+	2.16895i	0.337623	+	0.108177i
$403$	−0.226828	+	0.720010i	−0.0112991	+	0.0358663i
$404$		−	11.6442i		−	0.579323i
$405$	19.9465	−	2.67148i	0.991150	−	0.132747i
$406$	−22.5398	+	39.0400i	−1.11863	+	1.93752i
$407$	7.35405	−	4.24586i	0.364527	−	0.210459i
$408$	7.57572	+	14.7192i	0.375054	+	0.728710i
$409$	−2.15574	+	8.04533i	−0.106595	+	0.397816i	−0.998521	−	0.0543639i	$-0.982687\pi$
$409$	−2.15574	+	8.04533i	−0.106595	+	0.397816i	0.891927	+	0.452180i	$0.149354\pi$
$410$	26.5305	+	23.3142i	1.31025	+	1.15141i
$411$	5.86972	−	3.02104i	0.289532	−	0.149017i
$412$	5.77297	−	3.33302i	0.284414	−	0.164206i
$413$	22.5276	+	13.0063i	1.10851	+	0.639998i
$414$	7.16952	−	19.1433i	0.352363	−	0.940843i
$415$	12.7342	+	6.29584i	0.625098	+	0.309051i
$416$	−18.0409	+	4.00410i	−0.884526	+	0.196317i
$417$	−33.1339	−	10.6164i	−1.62258	−	0.519888i
$418$	−0.979082	−	3.65398i	−0.0478885	−	0.178722i
$419$	−1.31380	−	0.758522i	−0.0641833	−	0.0370562i	0.467565	−	0.883959i	$-0.345131\pi$
$419$	−1.31380	−	0.758522i	−0.0641833	−	0.0370562i	−0.531748	+	0.846902i	$0.678465\pi$
$420$	11.8603	+	2.97335i	0.578722	+	0.145085i
$421$	−12.6589	−	12.6589i	−0.616955	−	0.616955i	0.327794	−	0.944749i	$-0.393695\pi$
$421$	−12.6589	−	12.6589i	−0.616955	−	0.616955i	−0.944749	+	0.327794i	$0.893695\pi$
$422$	11.7761	−	43.9492i	0.573254	−	2.13941i
$423$	16.8025	+	20.4062i	0.816965	+	0.992181i
$424$	−1.18224	+	1.18224i	−0.0574145	+	0.0574145i
$425$	10.4686	−	25.1295i	0.507802	−	1.21896i
$426$	−3.95771	+	3.59293i	−0.191752	+	0.174078i
$427$	40.2859	−	10.7946i	1.94957	−	0.522386i
$428$			5.13773i			0.248342i
$429$	−7.39293	−	0.679597i	−0.356934	−	0.0328113i
$430$	−2.71389	−	1.34176i	−0.130875	−	0.0647053i
$431$	−2.61881	−	9.77353i	−0.126144	−	0.470775i	0.873734	−	0.486404i	$-0.161692\pi$
$431$	−2.61881	−	9.77353i	−0.126144	−	0.470775i	−0.999878	+	0.0156291i	$0.995025\pi$
$432$	−25.8018	+	3.03204i	−1.24139	+	0.145879i
$433$	18.3621	+	31.8042i	0.882428	+	1.52841i	0.848633	+	0.528982i	$0.177426\pi$
$433$	18.3621	+	31.8042i	0.882428	+	1.52841i	0.0337954	+	0.999429i	$0.489241\pi$
$434$	−0.820706	+	0.820706i	−0.0393952	+	0.0393952i
$435$	−27.0171	+	16.1861i	−1.29537	+	0.776066i
$436$	−2.12267	−	0.568769i	−0.101658	−	0.0272391i
$437$	−5.13848	+	5.13848i	−0.245807	+	0.245807i
$438$	−40.1447	+	8.70460i	−1.91819	+	0.415922i
$439$	5.63717	+	3.25462i	0.269048	+	0.155335i	0.628455	−	0.777846i	$-0.283688\pi$
$439$	5.63717	+	3.25462i	0.269048	+	0.155335i	−0.359407	+	0.933181i	$0.617021\pi$
$440$	0.915004	−	4.57584i	0.0436211	−	0.218145i
$441$	−5.75256	+	8.05531i	−0.273931	+	0.383586i
$442$	32.3421	+	10.1889i	1.53836	+	0.484636i
$443$	−17.2761			−0.820814			−0.410407	−	0.911902i	$-0.634613\pi$
$443$	−17.2761			−0.820814			−0.410407	+	0.911902i	$0.634613\pi$
$444$	0.587314	−	12.1567i	0.0278727	−	0.576932i
$445$	9.84146	−	6.56146i	0.466530	−	0.311043i
$446$	2.95026	+	5.11001i	0.139699	+	0.241966i
$447$	3.87479	−	1.99429i	0.183271	−	0.0943266i
$448$	3.55294	+	0.952006i	0.167860	+	0.0449781i
$449$	4.49179	−	16.7636i	0.211980	−	0.791122i	−0.775227	−	0.631682i	$-0.782365\pi$
$449$	4.49179	−	16.7636i	0.211980	−	0.791122i	0.987208	−	0.159439i	$-0.0509687\pi$
$450$	18.9039	+	17.7195i	0.891139	+	0.835307i
$451$	−5.43530	−	9.41421i	−0.255938	−	0.443298i
$452$	3.99335	+	2.30556i	0.187832	+	0.108445i
$453$	1.61434	−	33.4150i	0.0758485	−	1.56997i
$454$			21.2435i			0.997008i
$455$	−22.1304	+	13.4057i	−1.03749	+	0.628469i
$456$	5.33407	+	1.70908i	0.249791	+	0.0800351i
$457$	−5.66785	−	21.1527i	−0.265131	−	0.989481i	−0.962170	−	0.272449i	$-0.912167\pi$
$457$	−5.66785	−	21.1527i	−0.265131	−	0.989481i	0.697040	−	0.717033i	$-0.254500\pi$
$458$	−5.44537	+	9.43166i	−0.254446	+	0.440713i
$459$	25.9840	+	11.1893i	1.21283	+	0.522272i
$460$	8.21954	−	2.78089i	0.383238	−	0.129660i
$461$	31.4414	+	8.42468i	1.46437	+	0.392377i	0.900997	−	0.433826i	$-0.142837\pi$
$461$	31.4414	+	8.42468i	1.46437	+	0.392377i	0.563373	+	0.826203i	$0.309503\pi$
$462$	−9.59839	−	6.17767i	−0.446558	−	0.287411i
$463$	3.35500	+	3.35500i	0.155920	+	0.155920i	0.780756	−	0.624836i	$-0.214834\pi$
$463$	3.35500	+	3.35500i	0.155920	+	0.155920i	−0.624836	+	0.780756i	$0.714834\pi$
$464$	35.2103	−	20.3287i	1.63460	−	0.943734i
$465$	−0.779762	+	0.222505i	−0.0361606	+	0.0103184i
$466$	3.32745	+	12.4182i	0.154141	+	0.575263i
$467$			16.4147i			0.759584i	0.925072	+	0.379792i	$0.124004\pi$
$467$			16.4147i			0.759584i	−0.925072	+	0.379792i	$0.875996\pi$
$468$	−6.55372	+	8.38292i	−0.302946	+	0.387500i
$469$	−7.62489			−0.352085
$470$	−6.67327	+	33.3723i	−0.307815	+	1.53935i
$471$	6.27229	+	6.90911i	0.289012	+	0.318355i
$472$	−7.11432	−	12.3224i	−0.327463	−	0.567183i
$473$	0.658885	+	0.658885i	0.0302956	+	0.0302956i
$474$	−0.138422	+	0.215070i	−0.00635795	+	0.00987851i
$475$	−3.50763	−	8.51686i	−0.160941	−	0.390780i
$476$	12.1544	+	12.1544i	0.557097	+	0.557097i
$477$	−0.275438	+	2.84397i	−0.0126115	+	0.130217i
$478$	−16.3316	+	28.2872i	−0.746991	+	1.29383i
$479$	2.62410	−	0.703124i	0.119898	−	0.0321266i	−0.198371	−	0.980127i	$-0.563565\pi$
$479$	2.62410	−	0.703124i	0.119898	−	0.0321266i	0.318269	+	0.948000i	$0.396898\pi$
$480$	−14.2615	−	13.8078i	−0.650945	−	0.630235i
$481$	17.4042	+	18.9842i	0.793561	+	0.865603i
$482$	−50.0895			−2.28152
$483$	−1.05812	+	21.9019i	−0.0481462	+	0.996569i
$484$	−4.71539	+	8.16730i	−0.214336	+	0.371241i
$485$	4.29520	−	0.277159i	0.195035	−	0.0125851i
$486$	−18.6472	+	19.4250i	−0.845853	+	0.881135i
$487$	−13.2878	−	3.56046i	−0.602129	−	0.161340i	−0.0551382	−	0.998479i	$-0.517560\pi$
$487$	−13.2878	−	3.56046i	−0.602129	−	0.161340i	−0.546990	+	0.837139i	$0.684227\pi$
$488$	−22.0360	−	5.90453i	−0.997523	−	0.267285i
$489$	−9.87975	−	19.1958i	−0.446778	−	0.868065i
$490$	−12.7177	+	0.820644i	−0.574529	+	0.0370729i
$491$	−9.72844	+	16.8501i	−0.439038	+	0.760436i	−0.997616	−	0.0690160i	$-0.978014\pi$
$491$	−9.72844	+	16.8501i	−0.439038	+	0.760436i	0.558577	+	0.829452i	$0.311347\pi$
$492$	−15.5623	−	0.751844i	−0.701602	−	0.0338957i
$493$	−44.2747			−1.99403
$494$	10.1755	−	5.30016i	0.457819	−	0.238465i
$495$	−3.76360	−	7.03080i	−0.169161	−	0.316011i
$496$	1.01113	−	0.270931i	0.0454009	−	0.0121651i
$497$	2.86690	−	4.96561i	0.128598	−	0.222738i
$498$	−18.5754	+	4.02770i	−0.832382	+	0.180486i
$499$	−18.7585	−	18.7585i	−0.839745	−	0.839745i	0.149080	−	0.988825i	$-0.452369\pi$
$499$	−18.7585	−	18.7585i	−0.839745	−	0.839745i	−0.988825	+	0.149080i	$0.952369\pi$
$500$	−0.752641	+	10.9727i	−0.0336591	+	0.490713i
$501$	15.2904	+	9.84111i	0.683124	+	0.439669i
$502$	29.3393	+	29.3393i	1.30948	+	1.30948i
$503$	19.8054	+	34.3040i	0.883081	+	1.52954i	0.847898	+	0.530160i	$0.177868\pi$
$503$	19.8054	+	34.3040i	0.883081	+	1.52954i	0.0351832	+	0.999381i	$0.488799\pi$
$504$	15.3833	−	7.00026i	0.685227	−	0.311816i
$505$	−5.18989	+	25.9541i	−0.230947	+	1.15494i
$506$	−8.10047			−0.360110
$507$	−2.84609	−	22.3361i	−0.126399	−	0.991979i
$508$		−	15.6428i		−	0.694035i
$509$	−6.03174	−	22.5108i	−0.267352	−	0.997772i	−0.960795	−	0.277260i	$-0.910574\pi$
$509$	−6.03174	−	22.5108i	−0.267352	−	0.997772i	0.693442	−	0.720512i	$-0.256093\pi$
$510$	9.99470	+	35.0261i	0.442573	+	1.55098i
$511$	38.1596	−	22.0314i	1.68808	−	0.974613i
$512$	5.70780	+	5.70780i	0.252252	+	0.252252i
$513$	8.89373	−	3.53965i	0.392668	−	0.156279i
$514$	−10.7856	−	2.88998i	−0.475730	−	0.127472i
$515$	−14.3530	+	4.85600i	−0.632469	+	0.213981i
$516$	1.30519	−	0.283005i	0.0574579	−	0.0124586i
$517$	5.23741	−	9.07146i	0.230341	−	0.398962i
$518$	10.2487	+	38.2486i	0.450302	+	1.68055i
$519$	8.89446	−	27.7597i	0.390424	−	1.21852i
$520$	14.1497	−	0.297823i	0.620507	−	0.0130604i
$521$			0.498625i			0.0218452i	0.999940	+	0.0109226i	$0.00347683\pi$
$521$			0.498625i			0.0218452i	−0.999940	+	0.0109226i	$0.996523\pi$
$522$	14.7796	−	39.4630i	0.646886	−	1.72725i
$523$	−18.2263	−	10.5230i	−0.796983	−	0.460138i	0.0454324	−	0.998967i	$-0.485533\pi$
$523$	−18.2263	−	10.5230i	−0.796983	−	0.460138i	−0.842415	+	0.538829i	$0.818867\pi$
$524$	−1.25195	−	2.16845i	−0.0546918	−	0.0947290i
$525$	−25.1104	−	11.9135i	−1.09591	−	0.519949i
$526$	7.17253	−	26.7682i	0.312737	−	1.16715i
$527$	−1.10109	−	0.295036i	−0.0479642	−	0.0128520i
$528$	4.71119	+	9.15359i	0.205028	+	0.398359i
$529$	−3.71951	−	6.44237i	−0.161718	−	0.280103i
$530$	−3.06081	+	2.04069i	−0.132953	+	0.0886419i
$531$	−22.7716	−	8.52839i	−0.988205	−	0.370101i
$532$	5.81589			0.252151
$533$	24.3024	−	22.2798i	1.05265	−	0.965043i
$534$	−4.82902	+	15.0714i	−0.208972	+	0.652205i
$535$	2.28991	−	11.4516i	0.0990013	−	0.495095i
$536$	3.61197	+	2.08537i	0.156013	+	0.0900744i
$537$	−6.65241	−	30.6803i	−0.287073	−	1.32395i
$538$	14.0357	−	14.0357i	0.605120	−	0.605120i
$539$	3.78881	+	1.01521i	0.163196	+	0.0437281i
$540$	−11.3930	−	0.917807i	−0.490278	−	0.0394961i
$541$	−9.37270	+	9.37270i	−0.402964	+	0.402964i	−0.879276	−	0.476312i	$-0.841973\pi$
$541$	−9.37270	+	9.37270i	−0.402964	+	0.402964i	0.476312	+	0.879276i	$0.341973\pi$
$542$	10.1457	+	17.5728i	0.435794	+	0.754817i
$543$	−0.385191	−	0.424299i	−0.0165301	−	0.0182084i
$544$	−7.22249	−	26.9547i	−0.309662	−	1.15567i
$545$	4.47776	+	2.21382i	0.191806	+	0.0948298i
$546$	11.9836	−	32.4792i	0.512851	−	1.38998i
$547$			27.7702i			1.18737i	0.804698	+	0.593685i	$0.202327\pi$
$547$			27.7702i			1.18737i	−0.804698	+	0.593685i	$0.797673\pi$
$548$	−3.62164	+	0.970416i	−0.154709	+	0.0414541i
$549$	−35.4858	+	16.1480i	−1.51450	+	0.689181i
$550$	3.94836	−	9.47789i	0.168359	−	0.404139i
$551$	−10.5927	+	10.5927i	−0.451266	+	0.451266i
$552$	6.49130	−	10.0857i	0.276288	−	0.429275i
$553$	0.0710077	−	0.265004i	0.00301956	−	0.0112691i
$554$	−24.1315	−	24.1315i	−1.02525	−	1.02525i
$555$	−6.72737	+	26.8345i	−0.285561	+	1.13906i
$556$	17.1136	+	9.88054i	0.725778	+	0.419028i
$557$	5.53600	+	20.6607i	0.234568	+	0.875420i	0.978343	+	0.206990i	$0.0663667\pi$
$557$	5.53600	+	20.6607i	0.234568	+	0.875420i	−0.743775	+	0.668430i	$0.766967\pi$
$558$	0.630533	−	0.882937i	0.0266926	−	0.0373777i
$559$	−1.51788	+	2.38386i	−0.0641995	+	0.100826i
$560$	32.1628	+	15.9014i	1.35913	+	0.671957i
$561$	0.540984	−	11.1977i	0.0228404	−	0.472768i
$562$	3.73718	+	2.15766i	0.157643	+	0.0910154i
$563$	1.43304	−	0.827364i	0.0603953	−	0.0348692i	−0.469498	−	0.882933i	$-0.655565\pi$
$563$	1.43304	−	0.827364i	0.0603953	−	0.0348692i	0.529894	+	0.848064i	$0.322232\pi$
$564$	−6.87044	−	13.3489i	−0.289298	−	0.562090i
$565$	−7.87326	−	6.91877i	−0.331231	−	0.291075i
$566$	3.25089	−	12.1325i	0.136645	−	0.509967i
$567$	12.6906	−	25.9463i	0.532953	−	1.08964i
$568$	−2.71614	+	1.56817i	−0.113967	+	0.0657988i
$569$	15.9653	−	27.6527i	0.669300	−	1.15926i	−0.308800	−	0.951127i	$-0.599928\pi$
$569$	15.9653	−	27.6527i	0.669300	−	1.15926i	0.978100	−	0.208134i	$-0.0667391\pi$
$570$	10.7712	+	5.98876i	0.451157	+	0.250842i
$571$			2.79633i			0.117023i	0.998287	+	0.0585113i	$0.0186354\pi$
$571$			2.79633i			0.117023i	−0.998287	+	0.0585113i	$0.981365\pi$
$572$	4.02173	+	1.26699i	0.168157	+	0.0529753i
$573$	6.67968	−	20.8474i	0.279048	−	0.870911i
$574$	48.9636	−	13.1198i	2.04370	−	0.547608i
$575$	−19.5601	+	2.53489i	−0.815714	+	0.105712i
$576$	−3.42239	−	0.331458i	−0.142600	−	0.0138108i
$577$	13.0485	−	13.0485i	0.543215	−	0.543215i	−0.381255	−	0.924470i	$-0.624508\pi$
$577$	13.0485	−	13.0485i	0.543215	−	0.543215i	0.924470	+	0.381255i	$0.124508\pi$
$578$	−5.65248	+	21.0953i	−0.235112	+	0.877451i
$579$	6.30756	−	9.80021i	0.262133	−	0.407283i
$580$	16.9442	−	5.73267i	0.703569	−	0.238036i
$581$	17.6568	−	10.1942i	0.732527	−	0.422925i
$582$	−4.26394	+	3.87093i	−0.176746	+	0.160455i
$583$	1.09367	−	0.293048i	0.0452952	−	0.0121368i
$584$	−24.1020			−0.997347
$585$	18.3440	−	15.7638i	0.758431	−	0.651754i
$586$	3.63951			0.150347
$587$	33.8321	−	9.06530i	1.39640	−	0.374165i	0.519351	−	0.854561i	$-0.326174\pi$
$587$	33.8321	−	9.06530i	1.39640	−	0.374165i	0.877052	+	0.480396i	$0.159507\pi$
$588$	4.16250	−	3.77884i	0.171659	−	0.155837i
$589$	−0.334023	+	0.192848i	−0.0137632	+	0.00794618i
$590$	−10.0333	−	29.6556i	−0.413064	−	1.22090i
$591$	−15.4004	+	23.9280i	−0.633487	+	0.984265i
$592$	9.24331	−	34.4965i	0.379898	−	1.41780i
$593$	21.8499	−	21.8499i	0.897267	−	0.897267i	−0.0979268	−	0.995194i	$-0.531221\pi$
$593$	21.8499	−	21.8499i	0.897267	−	0.897267i	0.995194	+	0.0979268i	$0.0312211\pi$
$594$	9.80019	+	4.22017i	0.402107	+	0.173156i
$595$	−21.6739	−	32.5085i	−0.888544	−	1.33272i
$596$	−2.39076	+	0.640603i	−0.0979295	+	0.0262401i
$597$	−3.85786	+	12.0404i	−0.157892	+	0.492781i
$598$	−5.32325	−	23.9844i	−0.217684	−	0.980795i
$599$		−	32.0326i		−	1.30882i	−0.756142	−	0.654408i	$-0.772918\pi$
$599$		−	32.0326i		−	1.30882i	0.756142	−	0.654408i	$-0.227082\pi$
$600$	8.63668	+	12.5111i	0.352591	+	0.510763i
$601$	−1.29184	+	2.23753i	−0.0526953	+	0.0912709i	−0.891170	−	0.453670i	$-0.850115\pi$
$601$	−1.29184	+	2.23753i	−0.0526953	+	0.0912709i	0.838475	+	0.544941i	$0.183448\pi$
$602$	−3.76298	+	2.17256i	−0.153368	+	0.0885468i
$603$	7.03056	−	1.17250i	0.286307	−	0.0477477i
$604$	−4.91768	+	18.3530i	−0.200098	+	0.746775i
$605$	14.1504	−	16.1026i	0.575297	−	0.654663i
$606$	−16.2064	−	31.4881i	−0.658340	−	1.27912i
$607$	−42.5887	+	24.5886i	−1.72862	+	0.998020i	−0.832862	+	0.553480i	$0.813299\pi$
$607$	−42.5887	+	24.5886i	−1.72862	+	0.998020i	−0.895759	+	0.444540i	$0.853367\pi$
$608$	−8.17690	−	4.72094i	−0.331617	−	0.191459i
$609$	−2.18127	+	45.1496i	−0.0883893	+	1.82955i
$610$	−44.9966	−	22.2465i	−1.82186	−	0.900734i
$611$	30.3011	+	9.54592i	1.22585	+	0.386187i
$612$	−13.0760	−	9.33801i	−0.528567	−	0.377467i
$613$	4.87630	+	18.1986i	0.196952	+	0.735035i	0.991753	+	0.128165i	$0.0409086\pi$
$613$	4.87630	+	18.1986i	0.196952	+	0.735035i	−0.794801	+	0.606870i	$0.792425\pi$
$614$	19.4405	+	11.2240i	0.784555	+	0.452963i
$615$	34.3520	+	8.61197i	1.38520	+	0.347268i
$616$	−4.73579	−	4.73579i	−0.190810	−	0.190810i
$617$	4.04209	−	15.0853i	0.162728	−	0.607310i	−0.835591	−	0.549352i	$-0.814874\pi$
$617$	4.04209	−	15.0853i	0.162728	−	0.607310i	0.998319	−	0.0579578i	$-0.0184589\pi$
$618$	10.9723	−	17.0479i	0.441369	−	0.685766i
$619$	30.0941	−	30.0941i	1.20958	−	1.20958i	0.238423	−	0.971161i	$-0.423370\pi$
$619$	30.0941	−	30.0941i	1.20958	−	1.20958i	0.971161	−	0.238423i	$-0.0766304\pi$
$620$	0.459594	−	0.0296565i	0.0184578	−	0.00119103i
$621$	−2.39225	−	20.3574i	−0.0959978	−	0.816914i
$622$	−21.2602	+	5.69665i	−0.852455	+	0.228415i
$623$		−	16.9763i		−	0.680141i
$624$	−24.0066	+	19.9645i	−0.961032	+	0.799220i
$625$	6.56814	−	24.1218i	0.262726	−	0.964871i
$626$	11.3713	+	42.4382i	0.454488	+	1.69617i
$627$	−2.54963	−	2.80849i	−0.101822	−	0.112160i
$628$	−2.64996	−	4.58987i	−0.105745	−	0.183156i
$629$	−27.5000	+	27.5000i	−1.09650	+	1.09650i
$630$	36.2106	−	8.46659i	1.44267	−	0.337317i
$631$	−46.4467	−	12.4453i	−1.84901	−	0.495441i	−0.849527	−	0.527545i	$-0.823113\pi$
$631$	−46.4467	−	12.4453i	−1.84901	−	0.495441i	−0.999485	+	0.0321033i	$0.989779\pi$
$632$	−0.106114	+	0.106114i	−0.00422100	+	0.00422100i
$633$	−9.66788	−	44.5873i	−0.384264	−	1.77219i
$634$	−7.11082	−	4.10543i	−0.282407	−	0.163048i
$635$	−6.97204	+	34.8664i	−0.276677	+	1.38363i
$636$	0.495168	−	1.54543i	0.0196347	−	0.0612801i
$637$	−0.516066	+	11.8853i	−0.0204473	+	0.470913i
$638$	−16.6987			−0.661109
$639$	−1.87986	+	5.01941i	−0.0743662	+	0.198565i
$640$	−15.1709	−	22.7547i	−0.599683	−	0.899458i
$641$	5.90025	+	10.2195i	0.233046	+	0.403647i	0.958703	−	0.284409i	$-0.0917974\pi$
$641$	5.90025	+	10.2195i	0.233046	+	0.403647i	−0.725657	+	0.688057i	$0.758464\pi$
$642$	7.15066	+	13.8933i	0.282214	+	0.548327i
$643$	−22.8328	−	6.11802i	−0.900436	−	0.241271i	−0.221232	−	0.975221i	$-0.571008\pi$
$643$	−22.8328	−	6.11802i	−0.900436	−	0.241271i	−0.679203	+	0.733950i	$0.737675\pi$
$644$	3.22329	−	12.0295i	0.127016	−	0.474029i
$645$	−3.03530	+	0.0490662i	−0.119515	+	0.00193198i
$646$	8.66254	+	15.0040i	0.340823	+	0.590323i
$647$	−22.6540	−	13.0793i	−0.890620	−	0.514200i	−0.0164751	−	0.999864i	$-0.505244\pi$
$647$	−22.6540	−	13.0793i	−0.890620	−	0.514200i	−0.874145	+	0.485664i	$0.838578\pi$
$648$	−13.1078	+	8.82014i	−0.514923	+	0.346488i
$649$			9.63578i			0.378238i
$650$	30.6574	+	5.46213i	1.20248	+	0.214242i
$651$	−0.355113	+	1.10831i	−0.0139180	+	0.0434382i
$652$	3.17356	+	11.8439i	0.124286	+	0.463843i
$653$	3.69279	−	6.39610i	0.144510	−	0.250299i	−0.784680	−	0.619901i	$-0.787173\pi$
$653$	3.69279	−	6.39610i	0.144510	−	0.250299i	0.929190	+	0.369602i	$0.120506\pi$
$654$	−6.53170	+	1.41627i	−0.255410	+	0.0553806i
$655$	1.82401	+	5.39129i	0.0712701	+	0.210655i
$656$	−44.1603	−	11.8327i	−1.72417	−	0.461990i
$657$	−31.7973	+	26.1820i	−1.24053	+	1.02146i
$658$	34.5389	+	34.5389i	1.34646	+	1.34646i
$659$	1.23199	−	0.711291i	0.0479916	−	0.0277079i	−0.475812	−	0.879547i	$-0.657846\pi$
$659$	1.23199	−	0.711291i	0.0479916	−	0.0277079i	0.523804	+	0.851839i	$0.324512\pi$
$660$	1.24284	+	4.35548i	0.0483774	+	0.169537i
$661$	−6.72014	−	25.0799i	−0.261383	−	0.975496i	−0.964427	−	0.264349i	$-0.914843\pi$
$661$	−6.72014	−	25.0799i	−0.261383	−	0.975496i	0.703044	−	0.711147i	$-0.251824\pi$
$662$			35.3811i			1.37513i
$663$	33.5105	−	5.75684i	1.30144	−	0.223577i
$664$	−11.1522			−0.432790
$665$	−12.9631	−	2.59217i	−0.502689	−	0.100520i
$666$	−15.3314	−	33.6913i	−0.594080	−	1.30551i
$667$	16.0391	+	27.7806i	0.621037	+	1.07567i
$668$	−7.30267	−	7.30267i	−0.282549	−	0.282549i
$669$	4.97520	+	3.20211i	0.192352	+	0.123801i
$670$	6.89335	+	6.05765i	0.266313	+	0.234028i
$671$	10.9244	+	10.9244i	0.421732	+	0.421732i
$672$	−27.8432	+	6.03725i	−1.07407	+	0.232892i
$673$	16.7742	−	29.0538i	0.646599	−	1.11994i	−0.337331	−	0.941386i	$-0.609524\pi$
$673$	16.7742	−	29.0538i	0.646599	−	1.11994i	0.983930	−	0.178556i	$-0.0571426\pi$
$674$	−38.3875	+	10.2859i	−1.47863	+	0.396198i
$675$	24.9851	+	7.12364i	0.961676	+	0.274189i
$676$	−1.10848	+	12.7404i	−0.0426338	+	0.490015i
$677$	7.62559			0.293075			0.146538	−	0.989205i	$-0.453187\pi$
$677$	7.62559			0.293075			0.146538	+	0.989205i	$0.453187\pi$
$678$	14.0076	+	0.676735i	0.537959	+	0.0259899i
$679$	3.08872	−	5.34983i	0.118534	−	0.205307i
$680$	1.37619	+	21.3272i	0.0527746	+	0.817862i
$681$	9.74807	+	18.9400i	0.373547	+	0.725782i
$682$	−0.415289	−	0.111276i	−0.0159022	−	0.00426099i
$683$	−19.8139	−	5.30911i	−0.758157	−	0.203147i	−0.141024	−	0.990006i	$-0.545039\pi$
$683$	−19.8139	−	5.30911i	−0.758157	−	0.203147i	−0.617133	+	0.786859i	$0.711706\pi$
$684$	−5.36257	+	0.894323i	−0.205043	+	0.0341953i
$685$	8.50486	−	0.548797i	0.324954	−	0.0209685i
$686$	10.2570	−	17.7656i	0.391613	−	0.678293i
$687$	−0.526971	+	10.9077i	−0.0201052	+	0.416154i
$688$	3.91886			0.149405
$689$	1.58639	+	3.04563i	0.0604365	+	0.116029i
$690$	18.3567	−	18.9599i	0.698828	−	0.721792i
$691$	9.87914	−	2.64711i	0.375820	−	0.100701i	−0.0659642	−	0.997822i	$-0.521012\pi$
$691$	9.87914	−	2.64711i	0.375820	−	0.100701i	0.441784	+	0.897121i	$0.354346\pi$
$692$	−8.27795	+	14.3378i	−0.314681	+	0.545043i
$693$	−11.3924	−	1.10335i	−0.432760	−	0.0419127i
$694$	6.12543	+	6.12543i	0.232518	+	0.232518i
$695$	−33.7410	−	29.6505i	−1.27987	−	1.12471i
$696$	13.3815	−	20.7912i	0.507224	−	0.788087i
$697$	35.2039	+	35.2039i	1.33344	+	1.33344i
$698$	−2.74952	−	4.76231i	−0.104071	−	0.180256i
$699$	8.66503	+	9.54478i	0.327741	+	0.361017i
$700$	12.5039	+	9.63485i	0.472604	+	0.364163i
$701$	38.7093			1.46203			0.731016	−	0.682360i	$-0.239046\pi$
$701$	38.7093			1.46203			0.731016	+	0.682360i	$0.239046\pi$
$702$	−6.05514	+	31.7903i	−0.228536	+	1.19985i
$703$			13.1588i			0.496293i
$704$	0.352650	+	1.31611i	0.0132910	+	0.0496026i
$705$	9.36399	+	32.8158i	0.352668	+	1.23591i
$706$	−7.89989	+	4.56100i	−0.297316	+	0.171656i
$707$	26.8613	+	26.8613i	1.01022	+	1.01022i
$708$	11.6132	+	7.47442i	0.436451	+	0.280906i
$709$	0.577806	+	0.154823i	0.0216999	+	0.00581448i	0.269653	−	0.962958i	$-0.413091\pi$
$709$	0.577806	+	0.154823i	0.0216999	+	0.00581448i	−0.247953	+	0.968772i	$0.579758\pi$
$710$	−6.53681	+	2.21158i	−0.245322	+	0.0829990i
$711$	−0.0247226	+	0.255267i	−0.000927171	+	0.00957328i
$712$	−4.64294	+	8.04181i	−0.174001	+	0.301379i
$713$	0.213762	+	0.797769i	0.00800543	+	0.0298767i
$714$	49.7842	+	15.9513i	1.86313	+	0.596962i
$715$	−8.39940	−	4.61651i	−0.314120	−	0.172648i
$716$			17.8300i			0.666340i
$717$	−1.58048	+	32.7140i	−0.0590240	+	1.22173i
$718$	−30.4788	−	17.5970i	−1.13746	−	0.656713i
$719$	19.5460	+	33.8547i	0.728944	+	1.26257i	0.957330	+	0.288998i	$0.0933221\pi$
$719$	19.5460	+	33.8547i	0.728944	+	1.26257i	−0.228385	+	0.973571i	$0.573345\pi$
$720$	−32.1010	−	9.71621i	−1.19633	−	0.362102i
$721$	−5.62853	+	21.0060i	−0.209618	+	0.782304i
$722$	−26.0391	−	6.97716i	−0.969075	−	0.259663i
$723$	−44.6581	+	22.9847i	−1.66085	+	0.854811i
$724$	0.162738	+	0.281871i	0.00604812	+	0.0104757i
$725$	−40.3223	+	5.22555i	−1.49753	+	0.194072i
$726$	−1.38408	+	28.6487i	−0.0513678	+	1.06325i
$727$	0.507235			0.0188123			0.00940616	−	0.999956i	$-0.497006\pi$
$727$	0.507235			0.0188123			0.00940616	+	0.999956i	$0.497006\pi$
$728$	10.9099	−	17.1342i	0.404347	−	0.635035i
$729$	−7.71156	+	25.8753i	−0.285613	+	0.958345i
$730$	−52.0015	−	10.3984i	−1.92466	−	0.384864i
$731$	−3.69579	−	2.13377i	−0.136694	−	0.0789202i
$732$	21.6403	−	4.69226i	0.799847	−	0.173431i
$733$	34.1906	−	34.1906i	1.26286	−	1.26286i	0.313158	−	0.949701i	$-0.398613\pi$
$733$	34.1906	−	34.1906i	1.26286	−	1.26286i	0.949701	−	0.313158i	$-0.101387\pi$
$734$	22.7481	+	6.09532i	0.839646	+	0.224982i
$735$	−10.9621	+	6.56748i	−0.404344	+	0.242245i
$736$	−14.2965	+	14.2965i	−0.526977	+	0.526977i
$737$	−1.41224	−	2.44606i	−0.0520204	−	0.0901019i
$738$	−43.1296	+	19.6264i	−1.58762	+	0.722457i
$739$	3.71733	+	13.8733i	0.136744	+	0.510337i	0.999985	+	0.00554351i	$0.00176456\pi$
$739$	3.71733	+	13.8733i	0.136744	+	0.510337i	−0.863240	+	0.504793i	$0.831569\pi$
$740$	6.96373	−	14.0851i	0.255992	−	0.517779i
$741$	6.64006	−	9.39471i	0.243929	−	0.345123i
$742$			5.27982i			0.193828i
$743$	−39.0006	+	10.4502i	−1.43079	+	0.383380i	−0.889299	−	0.457326i	$-0.848807\pi$
$743$	−39.0006	+	10.4502i	−1.43079	+	0.383380i	−0.541493	+	0.840705i	$0.682141\pi$
$744$	0.471338	−	0.427894i	0.0172801	−	0.0156874i
$745$	5.61434	−	0.362279i	0.205693	−	0.0132729i
$746$	30.9653	−	30.9653i	1.13372	−	1.13372i
$747$	−14.7129	+	12.1147i	−0.538318	+	0.443253i
$748$	−1.64797	+	6.15030i	−0.0602557	+	0.224877i
$749$	−11.8519	−	11.8519i	−0.433058	−	0.433058i
$750$	13.2364	+	30.7196i	0.483327	+	1.12172i
$751$	11.0569	+	6.38370i	0.403472	+	0.232945i	0.687981	−	0.725729i	$-0.258497\pi$
$751$	11.0569	+	6.38370i	0.403472	+	0.232945i	−0.284509	+	0.958673i	$0.591831\pi$
$752$	−11.4019	−	42.5526i	−0.415785	−	1.55173i
$753$	39.6209	+	12.6949i	1.44387	+	0.462627i
$754$	−10.9736	−	49.4427i	−0.399636	−	1.80060i
$755$	19.1411	−	38.7156i	0.696617	−	1.40900i
$756$	−10.1668	+	12.8744i	−0.369761	+	0.468237i
$757$	7.85737	+	4.53645i	0.285581	+	0.164880i	0.635947	−	0.771733i	$-0.280610\pi$
$757$	7.85737	+	4.53645i	0.285581	+	0.164880i	−0.350366	+	0.936613i	$0.613943\pi$
$758$	39.0410	−	22.5403i	1.41803	−	0.818701i
$759$	−7.22209	+	3.71708i	−0.262145	+	0.134922i
$760$	5.43180	+	4.77329i	0.197032	+	0.173145i
$761$	−3.24132	+	12.0968i	−0.117498	+	0.438507i	−0.999462	−	0.0328095i	$-0.989555\pi$
$761$	−3.24132	+	12.0968i	−0.117498	+	0.438507i	0.881964	+	0.471317i	$0.156221\pi$
$762$	−21.7715	−	42.3008i	−0.788698	−	1.53240i
$763$	6.20870	−	3.58460i	0.224770	−	0.129771i
$764$	−6.21669	+	10.7676i	−0.224912	+	0.389559i
$765$	24.9834	+	26.6417i	0.903277	+	0.963233i
$766$		−	22.4829i		−	0.812341i
$767$	−28.5303	+	6.33219i	−1.03017	+	0.228642i
$768$	31.0660	+	9.95383i	1.12100	+	0.359178i
$769$	−44.6938	+	11.9757i	−1.61170	+	0.431854i	−0.948548	−	0.316632i	$-0.897448\pi$
$769$	−44.6938	+	11.9757i	−1.61170	+	0.431854i	−0.663151	+	0.748486i	$0.730781\pi$
$770$	−8.17457	−	12.2609i	−0.294591	−	0.441854i
$771$	−10.9422	+	2.37259i	−0.394072	+	0.0854468i
$772$	−4.68057	+	4.68057i	−0.168457	+	0.168457i
$773$	−11.6577	+	43.5070i	−0.419297	+	1.56484i	0.356772	+	0.934191i	$0.383877\pi$
$773$	−11.6577	+	43.5070i	−0.419297	+	1.56484i	−0.776069	+	0.630647i	$0.782789\pi$
$774$	3.13559	−	2.58186i	0.112706	−	0.0928029i
$775$	−1.03762	−	0.138741i	−0.0372723	−	0.00498373i
$776$	−2.92630	+	1.68950i	−0.105048	+	0.0606496i
$777$	26.6886	+	29.3983i	0.957449	+	1.05466i
$778$	31.3755	−	8.40705i	1.12487	−	0.301407i
$779$	16.8451			0.603537
$780$	−12.0793	+	6.54209i	−0.432507	+	0.234245i
$781$	2.12396			0.0760012
$782$	35.8349	−	9.60193i	1.28145	−	0.343364i
$783$	−4.93151	−	41.9658i	−0.176238	−	1.49974i
$784$	14.2865	−	8.24830i	0.510231	−	0.294582i
$785$	3.86082	+	11.4115i	0.137799	+	0.407295i
$786$	−6.40353	−	4.12141i	−0.228406	−	0.147006i
$787$	−10.6722	+	39.8293i	−0.380424	+	1.41976i	0.464831	+	0.885399i	$0.346115\pi$
$787$	−10.6722	+	39.8293i	−0.380424	+	1.41976i	−0.845255	+	0.534362i	$0.820552\pi$
$788$	11.4280	−	11.4280i	0.407105	−	0.407105i
$789$	−5.88844	−	27.1569i	−0.209634	−	0.966812i
$790$	−0.274730	+	0.183167i	−0.00977445	+	0.00651679i
$791$	−14.5305	+	3.89345i	−0.516646	+	0.138435i
$792$	5.09489	+	3.63842i	0.181039	+	0.129286i
$793$	−25.1667	+	39.5247i	−0.893694	+	1.40356i
$794$			16.0526i			0.569684i
$795$	−1.79249	+	3.22393i	−0.0635731	+	0.114341i
$796$	3.59045	−	6.21885i	0.127260	−	0.220421i
$797$	17.4955	−	10.1010i	0.619721	−	0.357796i	−0.157039	−	0.987592i	$-0.550195\pi$
$797$	17.4955	−	10.1010i	0.619721	−	0.357796i	0.776761	+	0.629796i	$0.216862\pi$
$798$	15.7272	−	8.09452i	0.556738	−	0.286543i
$799$	−12.4164	+	46.3386i	−0.439260	+	1.63934i
$800$	−9.75908	−	23.6960i	−0.345036	−	0.837781i
$801$	2.61048	+	15.6531i	0.0922369	+	0.553074i
$802$	37.8492	−	21.8522i	1.33650	−	0.771629i
$803$	14.1354	+	8.16105i	0.498826	+	0.287997i
$804$	−4.04350	−	0.195349i	−0.142603	−	0.00688944i
$805$	−12.5461	+	25.3761i	−0.442190	+	0.894391i
$806$	0.0565656	−	1.30274i	0.00199244	−	0.0458870i
$807$	6.07312	−	18.9543i	0.213784	−	0.667222i
$808$	−5.37797	−	20.0708i	−0.189196	−	0.706090i
$809$	16.6563	+	9.61653i	0.585605	+	0.338099i	0.763358	−	0.645976i	$-0.223549\pi$
$809$	16.6563	+	9.61653i	0.585605	+	0.338099i	−0.177753	+	0.984075i	$0.556883\pi$
$810$	−32.0862	+	13.3748i	−1.12739	+	0.469944i
$811$	6.34354	+	6.34354i	0.222752	+	0.222752i	0.809656	−	0.586904i	$-0.199654\pi$
$811$	6.34354	+	6.34354i	0.222752	+	0.222752i	−0.586904	+	0.809656i	$0.699654\pi$
$812$	6.64467	−	24.7982i	0.233182	−	0.870247i
$813$	17.1092	+	11.0117i	0.600046	+	0.386198i
$814$	−10.3720	+	10.3720i	−0.363537	+	0.363537i
$815$	−1.79474	−	27.8136i	−0.0628670	−	0.974267i
$816$	−31.6916	−	34.9093i	−1.10943	−	1.22207i
$817$	−1.39472	+	0.373715i	−0.0487952	+	0.0130746i
$818$		−	14.3873i		−	0.503041i
$819$	−4.21966	−	34.4563i	−0.147447	−	1.20400i
$820$	−18.0309	−	8.91455i	−0.629667	−	0.311310i
$821$	9.41992	+	35.1556i	0.328757	+	1.22694i	0.910480	+	0.413553i	$0.135712\pi$
$821$	9.41992	+	35.1556i	0.328757	+	1.22694i	−0.581723	+	0.813387i	$0.697621\pi$
$822$	−8.44295	+	7.66476i	−0.294482	+	0.267339i
$823$	−2.63365	−	4.56162i	−0.0918034	−	0.159008i	0.816467	−	0.577393i	$-0.195930\pi$
$823$	−2.63365	−	4.56162i	−0.0918034	−	0.159008i	−0.908270	+	0.418385i	$0.862596\pi$
$824$	8.41132	−	8.41132i	0.293022	−	0.293022i
$825$	−0.828929	−	10.2619i	−0.0288596	−	0.357275i
$826$	−43.4018	−	11.6295i	−1.51014	−	0.404641i
$827$	7.14407	−	7.14407i	0.248424	−	0.248424i	−0.571900	−	0.820323i	$-0.693793\pi$
$827$	7.14407	−	7.14407i	0.248424	−	0.248424i	0.820323	+	0.571900i	$0.193793\pi$
$828$	−1.12225	+	11.5875i	−0.0390008	+	0.402693i
$829$	19.7203	+	11.3855i	0.684915	+	0.395436i	0.801704	−	0.597721i	$-0.203927\pi$
$829$	19.7203	+	11.3855i	0.684915	+	0.395436i	−0.116789	+	0.993157i	$0.537260\pi$
$830$	−24.0616	−	4.81146i	−0.835190	−	0.167008i
$831$	−32.5881	−	10.4415i	−1.13047	−	0.362212i
$832$	−3.66507	+	1.90903i	−0.127063	+	0.0661838i
$833$	−17.9643			−0.622427
$834$	60.0299	+	2.90016i	2.07867	+	0.100424i
$835$	13.0222	+	19.5319i	0.450653	+	0.675928i
$836$	1.07718	+	1.86574i	0.0372552	+	0.0645279i
$837$	0.157006	−	1.07653i	0.00542691	−	0.0372103i
$838$	2.53118	+	0.678226i	0.0874380	+	0.0234289i
$839$	−3.27587	+	12.2257i	−0.113096	+	0.422079i	−0.999137	−	0.0415267i	$-0.986778\pi$
$839$	−3.27587	+	12.2257i	−0.113096	+	0.422079i	0.886042	+	0.463606i	$0.153445\pi$
$840$	21.8165	−	0.352667i	0.752740	−	0.0121682i
$841$	18.5639	+	32.1535i	0.640133	+	1.10874i
$842$	26.7806	+	15.4618i	0.922920	+	0.532848i
$843$	4.32203	+	0.208805i	0.148858	+	0.00719164i
$844$			25.9122i			0.891934i
$845$	8.14916	−	27.9032i	0.280340	−	0.959901i
$846$	−37.1578	−	26.5356i	−1.27751	−	0.912312i
$847$	−7.96297	−	29.7182i	−0.273611	−	1.02113i
$848$	2.38094	−	4.12391i	0.0817618	−	0.141616i
$849$	−2.66889	−	12.3086i	−0.0915960	−	0.422432i
$850$	−6.23210	+	46.6086i	−0.213759	+	1.59866i
$851$	27.2174	+	7.29288i	0.933000	+	0.249997i
$852$	1.64754	−	2.55983i	0.0564439	−	0.0876982i
$853$	−7.79992	−	7.79992i	−0.267064	−	0.267064i	0.560852	−	0.827916i	$-0.310474\pi$
$853$	−7.79992	−	7.79992i	−0.267064	−	0.267064i	−0.827916	+	0.560852i	$0.810474\pi$
$854$	−62.3907	+	36.0213i	−2.13496	+	1.23262i
$855$	12.3513	+	0.396745i	0.422406	+	0.0135684i
$856$	2.37289	+	8.85576i	0.0811038	+	0.302684i
$857$		−	20.1264i		−	0.687503i	−0.939061	−	0.343752i	$-0.888302\pi$
$857$		−	20.1264i		−	0.687503i	0.939061	−	0.343752i	$-0.111698\pi$
$858$	12.6389	−	2.17126i	0.431484	−	0.0741256i
$859$	21.9355			0.748428			0.374214	−	0.927342i	$-0.377913\pi$
$859$	21.9355			0.748428			0.374214	+	0.927342i	$0.377913\pi$
$860$	1.69068	+	0.338076i	0.0576517	+	0.0115283i
$861$	37.6339	−	34.1652i	1.28256	−	1.16435i
$862$	8.73892	+	15.1363i	0.297649	+	0.515543i
$863$	−25.0532	−	25.0532i	−0.852822	−	0.852822i	0.137658	−	0.990480i	$-0.456043\pi$
$863$	−25.0532	−	25.0532i	−0.852822	−	0.852822i	−0.990480	+	0.137658i	$0.956043\pi$
$864$	24.7446	−	9.84818i	0.841827	−	0.335042i
$865$	24.8413	−	28.2683i	0.844630	−	0.961152i
$866$	−44.8558	−	44.8558i	−1.52426	−	1.52426i
$867$	4.64053	+	21.4016i	0.157601	+	0.726838i
$868$	0.330499	−	0.572441i	0.0112179	−	0.0194299i
$869$	0.0981650	−	0.0263032i	0.00333002	−	0.000892276i
$870$	37.8415	−	39.0850i	1.28295	−	1.32510i
$871$	6.31441	−	5.78888i	0.213956	−	0.196149i
$872$	−3.92148			−0.132798
$873$	−2.02532	+	5.40779i	−0.0685465	+	0.183026i
$874$	6.27624	−	10.8708i	0.212297	−	0.367709i
$875$	−23.5759	−	27.0483i	−0.797011	−	0.914401i
$876$	20.8005	−	10.7057i	0.702785	−	0.361711i
$877$	16.2264	+	4.34785i	0.547926	+	0.146816i	0.522154	−	0.852851i	$-0.325129\pi$
$877$	16.2264	+	4.34785i	0.547926	+	0.146816i	0.0257727	+	0.999668i	$0.491795\pi$
$878$	−10.8606	−	2.91009i	−0.366528	−	0.0982109i
$879$	3.24486	−	1.67007i	0.109446	−	0.0563301i
$880$	0.855827	+	13.2630i	0.0288499	+	0.447095i
$881$	16.3359	−	28.2946i	0.550370	−	0.953269i	−0.447878	−	0.894095i	$-0.647820\pi$
$881$	16.3359	−	28.2946i	0.550370	−	0.953269i	0.998248	−	0.0591738i	$-0.0188466\pi$
$882$	5.99679	−	16.0120i	0.201922	−	0.539152i
$883$	15.0338			0.505929			0.252964	−	0.967476i	$-0.418594\pi$
$883$	15.0338			0.505929			0.252964	+	0.967476i	$0.418594\pi$
$884$	−19.2932	−	0.837720i	−0.648900	−	0.0281756i
$885$	−22.5535	−	21.8359i	−0.758127	−	0.734007i
$886$	28.8251	−	7.72365i	0.968397	−	0.259481i
$887$	−7.59276	+	13.1511i	−0.254940	+	0.441569i	−0.964879	−	0.262694i	$-0.915389\pi$
$887$	−7.59276	+	13.1511i	−0.254940	+	0.441569i	0.709939	+	0.704263i	$0.248722\pi$
$888$	−4.60231	−	21.2254i	−0.154444	−	0.712278i
$889$	36.0852	+	36.0852i	1.21026	+	1.21026i
$890$	−13.4870	+	15.3476i	−0.452084	+	0.514452i
$891$	10.6740	−	0.734481i	0.357593	−	0.0246060i
$892$	−2.37615	−	2.37615i	−0.0795593	−	0.0795593i
$893$	8.11589	+	14.0571i	0.271588	+	0.470404i
$894$	−5.57347	+	5.05976i	−0.186405	+	0.169224i
$895$	7.94692	−	39.7417i	0.265636	−	1.32842i
$896$	−39.2513			−1.31129
$897$	−15.7518	−	18.9409i	−0.525937	−	0.632420i
$898$			29.9780i			1.00038i
$899$	0.440659	+	1.64456i	0.0146968	+	0.0548492i
$900$	−13.0109	−	6.96110i	−0.433695	−	0.232037i
$901$	−4.49082	+	2.59278i	−0.149611	+	0.0863779i
$902$	13.2776	+	13.2776i	0.442094	+	0.442094i
$903$	−2.35801	+	3.66370i	−0.0784697	+	0.121920i
$904$	7.94807	+	2.12968i	0.264349	+	0.0708321i
$905$	−0.237099	−	0.700800i	−0.00788145	−	0.0232954i
$906$	12.2453	+	56.4743i	0.406824	+	1.87623i
$907$	−7.51117	+	13.0097i	−0.249404	+	0.431981i	−0.963361	−	0.268209i	$-0.913568\pi$
$907$	−7.51117	+	13.0097i	−0.249404	+	0.431981i	0.713956	+	0.700190i	$0.246901\pi$
$908$	−3.13127	−	11.6860i	−0.103915	−	0.387815i
$909$	−28.8981	−	20.6370i	−0.958489	−	0.684488i
$910$	30.9311	−	32.2611i	1.02535	−	1.06945i
$911$			20.7385i			0.687097i	0.939135	+	0.343548i	$0.111629\pi$
$911$			20.7385i			0.687097i	−0.939135	+	0.343548i	$0.888371\pi$
$912$	−15.9343	−	0.769816i	−0.527637	−	0.0254912i
$913$	6.54057	+	3.77620i	0.216461	+	0.124974i
$914$	18.9135	+	32.7591i	0.625603	+	1.08358i
$915$	−50.3257	+	0.813523i	−1.66372	+	0.0268942i
$916$	1.60528	−	5.99099i	0.0530400	−	0.197948i
$917$	7.89028	+	2.11419i	0.260560	+	0.0698168i
$918$	−48.3565	−	7.05253i	−1.59600	−	0.232768i
$919$	−27.2006	−	47.1128i	−0.897264	−	1.55411i	−0.830977	−	0.556306i	$-0.812218\pi$
$919$	−27.2006	−	47.1128i	−0.897264	−	1.55411i	−0.0662866	−	0.997801i	$-0.521115\pi$
$920$	12.8834	−	8.58958i	0.424754	−	0.283190i
$921$	22.4829	+	1.08619i	0.740835	+	0.0357912i
$922$	−56.2260			−1.85171
$923$	1.39577	+	6.28875i	0.0459422	+	0.206997i
$924$	6.19065	+	1.98354i	0.203657	+	0.0652536i
$925$	−21.7994	+	28.2908i	−0.716759	+	0.930196i
$926$	−7.09771	−	4.09787i	−0.233245	−	0.134664i
$927$	1.95968	−	20.2342i	0.0643642	−	0.664577i
$928$	−29.4716	+	29.4716i	−0.967453	+	0.967453i
$929$	−25.6186	−	6.86447i	−0.840518	−	0.225216i	−0.187221	−	0.982318i	$-0.559948\pi$
$929$	−25.6186	−	6.86447i	−0.840518	−	0.225216i	−0.653297	+	0.757102i	$0.726615\pi$
$930$	1.20155	−	0.719857i	0.0394004	−	0.0236050i
$931$	−4.29797	+	4.29797i	−0.140860	+	0.140860i
$932$	−3.66086	−	6.34080i	−0.119915	−	0.207700i
$933$	−16.3408	+	14.8346i	−0.534973	+	0.485664i
$934$	−7.33855	−	27.3879i	−0.240125	−	0.896158i
$935$	6.41440	−	12.9740i	0.209773	−	0.424295i
$936$	−7.42475	+	17.4763i	−0.242685	+	0.571230i
$937$		−	12.6619i		−	0.413645i	−0.978378	−	0.206822i	$-0.933688\pi$
$937$		−	12.6619i		−	0.413645i	0.978378	−	0.206822i	$-0.0663123\pi$
$938$	12.7221	−	3.40887i	0.415390	−	0.111303i
$939$	29.6119	+	32.6184i	0.966349	+	1.06446i
$940$	−1.24807	−	19.3417i	−0.0407076	−	0.630857i
$941$	−35.2291	+	35.2291i	−1.14844	+	1.14844i	−0.161576	+	0.986860i	$0.551658\pi$
$941$	−35.2291	+	35.2291i	−1.14844	+	1.14844i	−0.986860	+	0.161576i	$0.948342\pi$
$942$	−13.5541	−	8.72363i	−0.441617	−	0.284231i
$943$	9.33591	−	34.8421i	0.304019	−	1.13461i
$944$	28.6555	+	28.6555i	0.932656	+	0.932656i
$945$	28.3990	−	24.1646i	0.923821	−	0.786074i
$946$	−1.39391	−	0.804775i	−0.0453200	−	0.0261655i
$947$	−8.08395	−	30.1697i	−0.262693	−	0.980384i	−0.963647	−	0.267178i	$-0.913909\pi$
$947$	−8.08395	−	30.1697i	−0.262693	−	0.980384i	0.700954	−	0.713206i	$-0.252758\pi$
$948$	0.0444450	−	0.138713i	0.00144351	−	0.00450520i
$949$	−14.8747	+	47.2159i	−0.482852	+	1.53269i
$950$	9.66008	+	12.6421i	0.313414	+	0.410165i
$951$	−8.22363	−	0.397299i	−0.266669	−	0.0128833i
$952$	26.5638	+	15.3366i	0.860938	+	0.497063i
$953$	−42.6407	+	24.6186i	−1.38127	+	0.797475i	−0.992310	−	0.123781i	$-0.960498\pi$
$953$	−42.6407	+	24.6186i	−1.38127	+	0.797475i	−0.388957	+	0.921256i	$0.627165\pi$
$954$	−0.811890	−	4.86828i	−0.0262859	−	0.157616i
$955$	18.6557	−	21.2293i	0.603683	−	0.686965i
$956$	4.81452	−	17.9680i	0.155713	−	0.581128i
$957$	−14.8880	+	7.66259i	−0.481260	+	0.247696i
$958$	−4.06393	+	2.34631i	−0.131300	+	0.0758059i
$959$	6.11593	−	10.5931i	0.197494	−	0.342069i
$960$	−3.87962	−	2.15706i	−0.125214	−	0.0696187i
$961$		−	30.9562i		−	0.998586i
$962$	−37.5259	−	23.8940i	−1.20988	−	0.770373i
$963$	12.7506	+	9.10558i	0.410881	+	0.293423i
$964$	27.5542	−	7.38313i	0.887461	−	0.237795i
$965$	12.5188	−	8.34646i	0.402993	−	0.268682i
$966$	−8.02621	−	37.0161i	−0.258239	−	1.19097i
$967$	21.5311	−	21.5311i	0.692393	−	0.692393i	−0.270365	−	0.962758i	$-0.587144\pi$
$967$	21.5311	−	21.5311i	0.692393	−	0.692393i	0.962758	+	0.270365i	$0.0871444\pi$
$968$	−4.35567	+	16.2556i	−0.139997	+	0.522474i
$969$	14.6081	+	9.40199i	0.469280	+	0.302036i
$970$	−7.04260	+	2.38270i	−0.226124	+	0.0765038i
$971$	−5.70966	+	3.29647i	−0.183232	+	0.105789i	−0.588810	−	0.808271i	$-0.700403\pi$
$971$	−5.70966	+	3.29647i	−0.183232	+	0.105789i	0.405578	+	0.914060i	$0.367070\pi$
$972$	7.39458	−	13.4342i	0.237181	−	0.430903i
$973$	−62.2709	+	16.6854i	−1.99631	+	0.534911i
$974$	23.7624			0.761396
$975$	29.8395	−	9.19802i	0.955629	−	0.294572i
$976$	64.9753			2.07981
$977$	−10.2928	+	2.75795i	−0.329297	+	0.0882347i	−0.419680	−	0.907672i	$-0.637858\pi$
$977$	−10.2928	+	2.75795i	−0.329297	+	0.0882347i	0.0903830	+	0.995907i	$0.471191\pi$
$978$	25.0662	+	27.6111i	0.801528	+	0.882906i
$979$	5.44600	−	3.14425i	0.174055	−	0.100491i
$980$	6.87506	−	2.32601i	0.219616	−	0.0743018i
$981$	−5.17355	+	4.25992i	−0.165179	+	0.136009i
$982$	8.69860	−	32.4636i	0.277583	−	1.03596i
$983$	22.6666	−	22.6666i	0.722952	−	0.722952i	−0.246254	−	0.969205i	$-0.579200\pi$
$983$	22.6666	−	22.6666i	0.722952	−	0.722952i	0.969205	+	0.246254i	$0.0791996\pi$
$984$	−27.1715	+	5.89161i	−0.866196	+	0.187818i
$985$	−30.5655	+	20.3785i	−0.973898	+	0.649313i
$986$	73.8719	−	19.7939i	2.35256	−	0.630367i
$987$	46.6426	+	14.9447i	1.48465	+	0.475695i
$988$	−4.81632	+	4.41547i	−0.153228	+	0.140475i
$989$			3.09195i			0.0983181i
$990$	9.42279	+	10.0482i	0.299476	+	0.319354i
$991$	10.6554	−	18.4558i	0.338481	−	0.586266i	−0.645666	−	0.763620i	$-0.723420\pi$
$991$	10.6554	−	18.4558i	0.338481	−	0.586266i	0.984147	+	0.177353i	$0.0567536\pi$
$992$	−0.929335	+	0.536552i	−0.0295064	+	0.0170355i
$993$	16.2354	+	31.5446i	0.515216	+	1.00104i
$994$	−2.56341	+	9.56678i	−0.0813065	+	0.303440i
$995$	−10.7746	+	12.2610i	−0.341577	+	0.388700i
$996$	9.62461	−	4.95362i	0.304967	−	0.156961i
$997$	50.8556	−	29.3615i	1.61061	−	0.929888i	0.621386	−	0.783505i	$-0.286570\pi$
$997$	50.8556	−	29.3615i	1.61061	−	0.929888i	0.989228	−	0.146383i	$-0.0467633\pi$
$998$	39.6847	+	22.9120i	1.25620	+	0.725266i
$999$	−29.1290	−	23.0028i	−0.921600	−	0.727778i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	195.2.bh.a.59.5	✓	96
3.2	odd	2	inner	195.2.bh.a.59.19	yes	96
5.2	odd	4		975.2.bo.h.176.5		96
5.3	odd	4		975.2.bo.h.176.20		96
5.4	even	2	inner	195.2.bh.a.59.20	yes	96
13.2	odd	12	inner	195.2.bh.a.119.6	yes	96
15.2	even	4		975.2.bo.h.176.19		96
15.8	even	4		975.2.bo.h.176.6		96
15.14	odd	2	inner	195.2.bh.a.59.6	yes	96
39.2	even	12	inner	195.2.bh.a.119.20	yes	96
65.2	even	12		975.2.bo.h.626.19		96
65.28	even	12		975.2.bo.h.626.6		96
65.54	odd	12	inner	195.2.bh.a.119.19	yes	96
195.2	odd	12		975.2.bo.h.626.5		96
195.119	even	12	inner	195.2.bh.a.119.5	yes	96
195.158	odd	12		975.2.bo.h.626.20		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.bh.a.59.5	✓	96	1.1	even	1	trivial
195.2.bh.a.59.6	yes	96	15.14	odd	2	inner
195.2.bh.a.59.19	yes	96	3.2	odd	2	inner
195.2.bh.a.59.20	yes	96	5.4	even	2	inner
195.2.bh.a.119.5	yes	96	195.119	even	12	inner
195.2.bh.a.119.6	yes	96	13.2	odd	12	inner
195.2.bh.a.119.19	yes	96	65.54	odd	12	inner
195.2.bh.a.119.20	yes	96	39.2	even	12	inner
975.2.bo.h.176.5		96	5.2	odd	4
975.2.bo.h.176.6		96	15.8	even	4
975.2.bo.h.176.19		96	15.2	even	4
975.2.bo.h.176.20		96	5.3	odd	4
975.2.bo.h.626.5		96	195.2	odd	12
975.2.bo.h.626.6		96	65.28	even	12
975.2.bo.h.626.19		96	65.2	even	12
975.2.bo.h.626.20		96	195.158	odd	12

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:	\( N \)	\(=\)	\( 195 = 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	195.bh (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.66849 + 0.447071i) q^{2} +(-1.28242 + 1.16422i) q^{3} +(0.851938 - 0.491866i) q^{4} +(-2.11813 + 0.716618i) q^{5} +(1.61922 - 2.51582i) q^{6} +(-0.830623 + 3.09993i) q^{7} +(1.24129 - 1.24129i) q^{8} +(0.289197 - 2.98603i) q^{9} +(3.21369 - 2.14262i) q^{10} +(-1.14830 + 0.307686i) q^{11} +(-0.519902 + 1.62262i) q^{12} +(-1.66563 - 3.19776i) q^{13} -5.54355i q^{14} +(1.88203 - 3.38496i) q^{15} +(-2.49987 + 4.32990i) q^{16} +(4.71514 - 2.72229i) q^{17} +(0.852444 + 5.11145i) q^{18} +(0.476790 - 1.77941i) q^{19} +(-1.45203 + 1.65235i) q^{20} +(-2.54378 - 4.94243i) q^{21} +(1.77837 - 1.02674i) q^{22} +(-3.41625 - 1.97237i) q^{23} +(-0.146722 + 3.03698i) q^{24} +(3.97292 - 3.03577i) q^{25} +(4.20871 + 4.59079i) q^{26} +(3.10551 + 4.16603i) q^{27} +(0.817112 + 3.04950i) q^{28} +(-7.04243 - 4.06595i) q^{29} +(-1.62682 + 6.48918i) q^{30} +(-0.148047 - 0.148047i) q^{31} +(1.32655 - 4.95075i) q^{32} +(1.11439 - 1.73145i) q^{33} +(-6.65011 + 6.65011i) q^{34} +(-0.462099 - 7.16128i) q^{35} +(-1.22235 - 2.68616i) q^{36} +(-6.89966 + 1.84876i) q^{37} +3.18208i q^{38} +(5.85892 + 2.16172i) q^{39} +(-1.73968 + 3.51874i) q^{40} +(2.36667 + 8.83254i) q^{41} +(6.45390 + 7.10915i) q^{42} +(-0.391907 - 0.678803i) q^{43} +(-0.826939 + 0.826939i) q^{44} +(1.52729 + 6.53203i) q^{45} +(6.58176 + 1.76358i) q^{46} +(-6.23046 + 6.23046i) q^{47} +(-1.83506 - 8.46313i) q^{48} +(-2.85745 - 1.64975i) q^{49} +(-5.27157 + 6.84134i) q^{50} +(-2.87745 + 8.98056i) q^{51} +(-2.99188 - 1.90503i) q^{52} -0.952426 q^{53} +(-7.04403 - 5.56259i) q^{54} +(2.21175 - 1.47461i) q^{55} +(2.81686 + 4.87895i) q^{56} +(1.46017 + 2.83703i) q^{57} +(13.5680 + 3.63553i) q^{58} +(2.09784 - 7.82924i) q^{59} +(-0.0615809 - 3.80948i) q^{60} +(-6.49787 - 11.2546i) q^{61} +(0.313203 + 0.180828i) q^{62} +(9.01626 + 3.37675i) q^{63} -1.14613i q^{64} +(5.81958 + 5.57965i) q^{65} +(-1.08526 + 3.38712i) q^{66} +(0.614925 + 2.29493i) q^{67} +(2.67800 - 4.63844i) q^{68} +(6.67733 - 1.44785i) q^{69} +(3.97261 + 11.7419i) q^{70} +(-1.72575 - 0.462414i) q^{71} +(-3.34755 - 4.06550i) q^{72} +(-9.70845 - 9.70845i) q^{73} +(10.6855 - 6.16928i) q^{74} +(-1.56064 + 8.51847i) q^{75} +(-0.469034 - 1.75046i) q^{76} -3.81522i q^{77} +(-10.7420 - 0.987461i) q^{78} -0.0854873 q^{79} +(2.19215 - 10.9627i) q^{80} +(-8.83273 - 1.72710i) q^{81} +(-7.89754 - 13.6789i) q^{82} +(-4.49219 - 4.49219i) q^{83} +(-4.59816 - 2.95944i) q^{84} +(-8.03642 + 9.14510i) q^{85} +(0.957366 + 0.957366i) q^{86} +(13.7650 - 2.98467i) q^{87} +(-1.04344 + 1.80730i) q^{88} +(-5.10951 + 1.36909i) q^{89} +(-5.46854 - 10.2158i) q^{90} +(11.2963 - 2.50718i) q^{91} -3.88057 q^{92} +(0.362217 + 0.0174994i) q^{93} +(7.61001 - 13.1809i) q^{94} +(0.265252 + 4.11068i) q^{95} +(4.06255 + 7.89332i) q^{96} +(-1.85928 - 0.498193i) q^{97} +(5.50517 + 1.47511i) q^{98} +(0.586675 + 3.51784i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 24 q^{4} - 4 q^{9} - 36 q^{10} + 10 q^{15} - 16 q^{21} - 28 q^{24} + 18 q^{30} - 40 q^{31} - 32 q^{34} - 60 q^{36} - 4 q^{39} + 40 q^{40} + 4 q^{45} - 128 q^{46} + 60 q^{54} + 28 q^{55} + 20 q^{60}+ \cdots - 48 q^{99}+O(q^{100}) \) 96 * q - 24 * q^4 - 4 * q^9 - 36 * q^10 + 10 * q^15 - 16 * q^21 - 28 * q^24 + 18 * q^30 - 40 * q^31 - 32 * q^34 - 60 * q^36 - 4 * q^39 + 40 * q^40 + 4 * q^45 - 128 * q^46 + 60 * q^54 + 28 * q^55 + 20 * q^60 - 48 * q^61 - 8 * q^66 + 72 * q^69 + 168 * q^70 + 66 * q^75 - 80 * q^76 - 80 * q^79 + 48 * q^81 - 132 * q^84 - 20 * q^85 - 56 * q^91 + 72 * q^94 + 204 * q^96 - 48 * q^99

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