LMFDB - Embedded newform 195.2.bh.a.59.20

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)

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);

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")

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			59.20
Character	$\chi$	$=$	195.59
Dual form			195.2.bh.a.119.20

$q$-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} +(-0.716618 + 2.11813i) 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} +(-0.248718 + 3.85445i) q^{10} +(-1.14830 + 0.307686i) q^{11} +(0.519902 - 1.62262i) q^{12} +(1.66563 + 3.19776i) q^{13} -5.54355i q^{14} +(1.54695 + 3.55062i) 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} +(0.431321 + 2.15699i) 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} +(4.16846 + 5.23258i) 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} +(5.97080 + 3.98083i) 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} +(6.11754 + 2.75240i) 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} +(-7.98598 - 3.28899i) q^{50} +(-2.87745 + 8.98056i) q^{51} +(2.99188 + 1.90503i) q^{52} +0.952426 q^{53} +(-7.04403 - 5.56259i) q^{54} +(0.171174 - 2.65274i) 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} +(3.06434 + 2.26402i) q^{60} +(-6.49787 - 11.2546i) q^{61} +(-0.313203 - 0.180828i) q^{62} +(-9.01626 - 3.37675i) q^{63} -1.14613i q^{64} +(-7.96688 + 1.23643i) 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} +(11.7419 + 3.97261i) 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} +(-8.62925 + 0.732204i) q^{75} +(-0.469034 - 1.75046i) q^{76} +3.81522i q^{77} +(10.7420 + 0.987461i) q^{78} -0.0854873 q^{79} +(-7.37982 - 8.39792i) 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} +(-2.38719 - 11.9381i) 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} +(11.4376 + 1.85737i) q^{90} +(11.2963 - 2.50718i) q^{91} +3.88057 q^{92} +(-0.362217 - 0.0174994i) q^{93} +(7.61001 - 13.1809i) q^{94} +(3.42733 + 2.28506i) 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	0.384953	−	0.922936i	$-0.374217\pi$
$2$	1.66849	−	0.447071i	1.17980	−	0.316127i	0.794847	+	0.606809i	$0.207551\pi$
$3$	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
$5$	−0.716618	+	2.11813i	−0.320481	+	0.947255i
$5$	−0.716618	+	2.11813i	−0.320481	+	0.947255i
$6$	1.61922	−	2.51582i	0.661042	−	1.02708i
$7$	0.830623	−	3.09993i	0.313946	−	1.17166i	−0.611021	−	0.791615i	$-0.709241\pi$
$7$	0.830623	−	3.09993i	0.313946	−	1.17166i	0.924967	−	0.380048i	$-0.124093\pi$
$8$	−1.24129	+	1.24129i	−0.438862	+	0.438862i
$9$	0.289197	−	2.98603i	0.0963989	−	0.995343i
$10$	−0.248718	+	3.85445i	−0.0786516	+	1.21888i
$11$	−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
$15$	1.54695	+	3.55062i	0.399422	+	0.916767i
$16$	−2.49987	+	4.32990i	−0.624967	+	1.08247i
$17$	−4.71514	+	2.72229i	−1.14359	+	0.660251i	−0.947317	−	0.320298i	$-0.896217\pi$
$17$	−4.71514	+	2.72229i	−1.14359	+	0.660251i	−0.196272	+	0.980549i	$0.562884\pi$
$18$	−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	$0.0155597\pi$
$20$	0.431321	+	2.15699i	0.0964464	+	0.482318i
$21$	−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	0.811926	−	0.583761i	$-0.198419\pi$
$23$	3.41625	+	1.97237i	0.712337	+	0.411268i	−0.0995889	+	0.995029i	$0.531753\pi$
$24$	−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	$0.939043\pi$
$30$	4.16846	+	5.23258i	0.761053	+	0.955335i
$31$	−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
$35$	5.97080	+	3.98083i	1.00925	+	0.672883i
$36$	−1.22235	−	2.68616i	−0.203725	−	0.447693i
$37$	6.89966	−	1.84876i	1.13430	−	0.303934i	0.357642	−	0.933859i	$-0.383581\pi$
$37$	6.89966	−	1.84876i	1.13430	−	0.303934i	0.776656	+	0.629925i	$0.216914\pi$
$38$		−	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	0.894360	−	0.447348i	$-0.147631\pi$
$43$	0.391907	+	0.678803i	0.0597653	+	0.103517i	−0.834595	+	0.550864i	$0.814298\pi$
$44$	−0.826939	+	0.826939i	−0.124666	+	0.124666i
$45$	6.11754	+	2.75240i	0.911949	+	0.410303i
$46$	6.58176	+	1.76358i	0.970428	+	0.260025i
$47$	6.23046	−	6.23046i	0.908806	−	0.908806i	−0.0873702	−	0.996176i	$-0.527846\pi$
$47$	6.23046	−	6.23046i	0.908806	−	0.908806i	0.996176	+	0.0873702i	$0.0278463\pi$
$48$	1.83506	+	8.46313i	0.264869	+	1.22155i
$49$	−2.85745	−	1.64975i	−0.408207	−	0.235678i
$50$	−7.98598	−	3.28899i	−1.12939	−	0.465133i
$51$	−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	$-0.479164\pi$
$53$	0.952426			0.130826			0.0654129	+	0.997858i	$0.479164\pi$
$54$	−7.04403	−	5.56259i	−0.958571	−	0.756973i
$55$	0.171174	−	2.65274i	0.0230812	−	0.357695i
$56$	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	$-0.0935814\pi$
$60$	3.06434	+	2.26402i	0.395605	+	0.292283i
$61$	−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
$65$	−7.96688	+	1.23643i	−0.988170	+	0.153360i
$66$	−1.08526	+	3.38712i	−0.133587	+	0.416926i
$67$	−0.614925	−	2.29493i	−0.0751250	−	0.280370i	0.918137	−	0.396264i	$-0.129693\pi$
$67$	−0.614925	−	2.29493i	−0.0751250	−	0.280370i	−0.993262	+	0.115894i	$0.963027\pi$
$68$	−2.67800	+	4.63844i	−0.324756	+	0.562493i
$69$	6.67733	−	1.44785i	0.803856	−	0.174300i
$70$	11.7419	+	3.97261i	1.40343	+	0.474817i
$71$	−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	$0.0470188\pi$
$73$	9.70845	+	9.70845i	1.13629	+	1.13629i	0.147177	+	0.989110i	$0.452981\pi$
$74$	10.6855	−	6.16928i	1.24216	−	0.717164i
$75$	−8.62925	+	0.732204i	−0.996419	+	0.0845476i
$76$	−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	$0.501531\pi$
$80$	−7.37982	−	8.39792i	−0.825089	−	0.938916i
$81$	−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	0.909276	−	0.416194i	$-0.136636\pi$
$83$	4.49219	+	4.49219i	0.493082	+	0.493082i	−0.416194	+	0.909276i	$0.636636\pi$
$84$	−4.59816	−	2.95944i	−0.501701	−	0.322902i
$85$	−2.38719	−	11.9381i	−0.258927	−	1.29487i
$86$	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	$0.507119\pi$
$90$	11.4376	+	1.85737i	1.20563	+	0.195784i
$91$	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
$95$	3.42733	+	2.28506i	0.351637	+	0.234442i
$96$	4.06255	+	7.89332i	0.414633	+	0.805609i
$97$	1.85928	+	0.498193i	0.188781	+	0.0505838i	0.351971	−	0.936011i	$-0.385512\pi$
$97$	1.85928	+	0.498193i	0.188781	+	0.0505838i	−0.163190	+	0.986595i	$0.552178\pi$
$98$	−5.50517	−	1.47511i	−0.556107	−	0.149008i
$99$	0.586675	+	3.51784i	0.0589630	+	0.353556i
$100$	−4.87787	−	0.632146i	−0.487787	−	0.0632146i
$101$	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	$-0.608346\pi$
$103$	−6.77628			−0.667686			−0.333843	+	0.942629i	$0.608346\pi$
$104$	−6.03687	−	1.90183i	−0.591964	−	0.186489i
$105$	12.2916	−	1.84622i	1.19954	−	0.180172i
$106$	1.58911	−	0.425802i	0.154348	−	0.0413575i
$107$	2.61134	−	4.52298i	0.252448	−	0.437253i	−0.711751	−	0.702432i	$-0.752098\pi$
$107$	2.61134	−	4.52298i	0.252448	−	0.437253i	0.964199	+	0.265179i	$0.0854309\pi$
$108$	−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	$0.784119\pi$
$110$	−0.900358	−	4.50259i	−0.0858458	−	0.429306i
$111$	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	0.734477	−	0.678634i	$-0.237428\pi$
$113$	−2.34369	−	4.05939i	−0.220476	−	0.381875i	−0.954953	+	0.296759i	$0.904094\pi$
$114$	−3.70463	−	4.08076i	−0.346971	−	0.382198i
$115$	−6.62587	+	5.82261i	−0.617866	+	0.542961i
$116$	−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
$120$	−6.32757	−	2.48713i	−0.577625	−	0.227043i
$121$	−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
$125$	9.27722	−	6.23965i	0.829780	−	0.558091i
$126$	−16.5532	−	1.60318i	−1.47468	−	0.142822i
$127$	−7.95071	+	13.7710i	−0.705512	+	1.22198i	0.260995	+	0.965340i	$0.415949\pi$
$127$	−7.95071	+	13.7710i	−0.705512	+	1.22198i	−0.966507	+	0.256642i	$0.917384\pi$
$128$	−3.16550	−	11.8138i	−0.279793	−	1.04420i
$129$	1.29286	+	0.414245i	0.113830	+	0.0364722i
$130$	−12.7399	+	5.62473i	−1.11736	+	0.493322i
$131$		−	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
$135$	11.0496	−	3.59242i	0.951001	−	0.309186i
$136$	2.47370	−	9.23199i	0.212118	−	0.791637i
$137$	3.68153	+	0.986463i	0.314534	+	0.0842792i	0.412633	−	0.910898i	$-0.364609\pi$
$137$	3.68153	+	0.986463i	0.314534	+	0.0842792i	−0.0980984	+	0.995177i	$0.531276\pi$
$138$	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	$0.508775\pi$
$140$	7.04479	+	0.454582i	0.595393	+	0.0384192i
$141$	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
$145$	13.6589	−	12.0030i	1.13431	−	0.996796i
$146$	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	$0.616197\pi$
$150$	−14.0705	+	5.07956i	−1.14885	+	0.414744i
$151$	−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	$0.0689709\pi$
$157$			5.38756i			0.429974i	−0.976617	+	0.214987i	$0.931029\pi$
$158$	−0.142635	+	0.0382189i	−0.0113474	+	0.00304053i
$159$	1.22141	−	1.10883i	0.0968641	−	0.0879360i
$160$	−9.53568	−	6.35759i	−0.753862	−	0.502612i
$161$	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	$-0.754340\pi$
$163$	3.22604	−	12.0398i	0.252683	−	0.943027i	0.969365	−	0.245626i	$-0.0789935\pi$
$164$	6.36068	+	6.36068i	0.496686	+	0.496686i
$165$	−2.86884	−	3.60120i	−0.223339	−	0.280353i
$166$	9.50350	+	5.48685i	0.737615	+	0.425862i
$167$	2.71716	+	10.1406i	0.210260	+	0.784702i	0.987781	+	0.155845i	$0.0498102\pi$
$167$	2.71716	+	10.1406i	0.210260	+	0.784702i	−0.777521	+	0.628857i	$0.783523\pi$
$168$	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	0.169772	−	0.985483i	$-0.445697\pi$
$173$	14.5749	−	8.41484i	1.10811	−	0.639768i	0.938340	+	0.345715i	$0.112364\pi$
$174$	−21.6324	+	11.1338i	−1.63995	+	0.844052i
$175$	−12.7107	+	9.79418i	−0.960837	+	0.740370i
$176$	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	$0.929791\pi$
$180$	6.56558	−	0.664143i	0.489369	−	0.0495023i
$181$			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
$185$	−1.02852	+	15.9392i	−0.0756181	+	1.17187i
$186$	−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
$190$	6.74005	+	2.28034i	0.488975	+	0.165433i
$191$	−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	−0.0171925	−	0.999852i	$-0.505473\pi$
$193$	6.49950	−	1.74154i	0.467845	−	0.125359i	0.485037	+	0.874494i	$0.338806\pi$
$194$	3.32492			0.238715
$195$	−8.77741	+	10.8608i	−0.628563	+	0.777758i
$196$	−3.24582			−0.231844
$197$	−15.8690	+	4.25210i	−1.13062	+	0.302949i	−0.775175	−	0.631747i	$-0.782338\pi$
$197$	−15.8690	+	4.25210i	−1.13062	+	0.302949i	−0.355447	+	0.934696i	$0.615672\pi$
$198$	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	$0.250030\pi$
$200$	8.69981	−	1.16326i	0.615170	−	0.0822552i
$201$	−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
$205$	−20.4044	−	1.31665i	−1.42511	−	0.0919586i
$206$	−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
$210$	19.6831	−	8.57562i	1.35826	−	0.591774i
$211$	−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
$215$	−1.71864	+	0.343666i	−0.117210	+	0.0234378i
$216$	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	0.989189	−	0.146643i	$-0.0468470\pi$
$223$	0.884112	+	3.29955i	0.0592045	+	0.220954i	−0.929985	+	0.367598i	$0.880180\pi$
$224$	14.2451	+	8.22441i	0.951791	+	0.549517i
$225$	−10.2139	+	10.9853i	−0.680924	+	0.732354i
$226$	−5.72526	−	5.72526i	−0.380838	−	0.380838i
$227$	−3.18305	+	11.8793i	−0.211266	+	0.788456i	0.776181	+	0.630510i	$0.217154\pi$
$227$	−3.18305	+	11.8793i	−0.211266	+	0.788456i	−0.987448	+	0.157947i	$0.949513\pi$
$228$	−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	$0.183201\pi$
$230$	−8.45209	+	12.6772i	−0.557314	+	0.835910i
$231$	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	$0.0783930\pi$
$233$			7.44279i			0.487594i	−0.969826	+	0.243797i	$0.921607\pi$
$234$	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	$0.0405358\pi$
$240$	−19.2410	−	2.17794i	−1.24200	−	0.140585i
$241$	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
$245$	5.54207	−	4.87019i	0.354070	−	0.311145i
$246$	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
$250$	12.6894	−	14.5584i	0.802547	−	0.920752i
$251$	−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
$255$	−16.9599	−	12.5304i	−1.06207	−	0.784686i
$256$	−9.41708	−	16.3109i	−0.588568	−	1.01943i
$257$	−5.59821	−	3.23213i	−0.349207	−	0.201615i	0.315129	−	0.949049i	$-0.397952\pi$
$257$	−5.59821	−	3.23213i	−0.349207	−	0.201615i	−0.664336	+	0.747434i	$0.731286\pi$
$258$	2.34233	+	0.113162i	0.145827	+	0.00704518i
$259$		−	22.9241i		−	1.42443i
$260$	−6.17913	+	4.97200i	−0.383213	+	0.308351i
$261$	−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	−0.505342	−	0.862919i	$-0.668634\pi$
$263$	8.02170	−	13.8940i	0.494639	−	0.856740i	0.999981	+	0.00617933i	$0.00196695\pi$
$264$	−0.765955	−	3.53251i	−0.0471413	−	0.217411i
$265$	−0.682526	+	2.01736i	−0.0419272	+	0.123925i
$266$	−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	$0.447260\pi$
$270$	16.8302	−	10.9339i	1.02425	−	0.665415i
$271$	−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
$275$	5.49617	+	2.26357i	0.331431	+	0.136498i
$276$	4.97652	−	4.51783i	0.299551	−	0.271941i
$277$	−9.87847	−	17.1100i	−0.593540	−	1.02804i	−0.993751	−	0.111618i	$-0.964397\pi$
$277$	−9.87847	−	17.1100i	−0.593540	−	1.02804i	0.400211	−	0.916423i	$-0.368937\pi$
$278$	24.5357	+	24.5357i	1.47155	+	1.47155i
$279$	−0.484887	+	0.399258i	−0.0290294	+	0.0239029i
$280$	−12.3528	+	2.47013i	−0.738224	+	0.147618i
$281$	−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	−0.737496	−	0.675352i	$-0.763992\pi$
$283$	3.63577	−	6.29734i	0.216124	−	0.374338i	0.953620	+	0.301014i	$0.0973251\pi$
$284$	−1.69768	+	0.454891i	−0.100739	+	0.0269928i
$285$	7.05557	−	1.05976i	0.417936	−	0.0627746i
$286$	−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
$290$	17.4236	−	26.1334i	1.02315	−	1.53461i
$291$	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	0.317777	−	0.948165i	$-0.397064\pi$
$293$	2.03520	+	0.545330i	0.118898	+	0.0318585i	−0.198880	+	0.980024i	$0.563730\pi$
$294$	−8.77729	+	4.51751i	−0.511902	+	0.263467i
$295$	15.0800	+	10.0541i	0.877989	+	0.585370i
$296$	−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
$300$	−6.99143	+	4.86823i	−0.403651	+	0.281067i
$301$	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
$305$	28.4952	−	5.69803i	1.63163	−	0.326268i
$306$	17.9342	+	21.7806i	1.02523	+	1.24511i
$307$	9.18929	+	9.18929i	0.524461	+	0.524461i	0.918915	−	0.394455i	$-0.129066\pi$
$307$	9.18929	+	9.18929i	0.524461	+	0.524461i	−0.394455	+	0.918915i	$0.629066\pi$
$308$	1.87658	+	3.25033i	0.106928	+	0.185205i
$309$	−8.69003	+	7.88906i	−0.494358	+	0.448793i
$310$	0.607462	−	0.533818i	0.0345015	−	0.0303188i
$311$	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	$0.255326\pi$
$313$			25.4351i			1.43768i	−0.695178	+	0.718838i	$0.744674\pi$
$314$	2.40862	+	8.98909i	0.135926	+	0.507284i
$315$	13.6136	−	16.6777i	0.767040	−	0.939684i
$316$	−0.0728298	+	0.0420483i	−0.00409700	+	0.00236540i
$317$	−3.36120	−	3.36120i	−0.188784	−	0.188784i	0.606386	−	0.795170i	$-0.292618\pi$
$317$	−3.36120	−	3.36120i	−0.188784	−	0.188784i	−0.795170	+	0.606386i	$0.792618\pi$
$318$	1.54218	−	2.39613i	0.0864814	−	0.134368i
$319$	9.33785	+	2.50207i	0.522819	+	0.140089i
$320$	2.42766	+	0.821341i	0.135710	+	0.0459143i
$321$	−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
$325$	3.09030	−	17.7609i	0.171419	−	0.985198i
$326$		−	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
$330$	−6.39663	−	4.72600i	−0.352123	−	0.260158i
$331$	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
$335$	5.30162	+	0.342100i	0.289658	+	0.0186909i
$336$	27.7594	+	1.34111i	1.51440	+	0.0731635i
$337$	−23.0073			−1.25329			−0.626644	−	0.779305i	$-0.715572\pi$
$337$	−23.0073			−1.25329			−0.626644	+	0.779305i	$0.715572\pi$
$338$	−7.67012	+	21.1050i	−0.417199	+	1.14796i
$339$	−7.73160	−	2.47727i	−0.419923	−	0.134547i
$340$	−7.90569	−	8.99634i	−0.428746	−	0.487895i
$341$	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
$345$	−1.71837	+	15.1810i	−0.0925139	+	0.817316i
$346$	20.5561	−	20.5561i	1.10510	−	1.10510i
$347$	2.50750	+	4.34312i	0.134610	+	0.233151i	0.925448	−	0.378874i	$-0.123689\pi$
$347$	2.50750	+	4.34312i	0.134610	+	0.233151i	−0.790839	+	0.612025i	$0.790355\pi$
$348$	−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	−0.391999	−	0.919965i	$-0.628216\pi$
$353$	−5.10099	+	1.36681i	−0.271498	+	0.0727477i	0.120501	+	0.992713i	$0.461550\pi$
$354$	−16.3001	−	17.9550i	−0.866339	−	0.954298i
$355$	2.21615	−	3.32398i	0.117621	−	0.176419i
$356$	−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	$0.569307\pi$
$360$	−11.0102	+	4.17712i	−0.580286	+	0.220153i
$361$	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	0.775441	−	0.631420i	$-0.217527\pi$
$367$	11.8073	+	6.81696i	0.616337	+	0.355842i	−0.159105	+	0.987262i	$0.550861\pi$
$368$	−17.0803	+	9.86133i	−0.890374	+	0.514058i
$369$	27.0586	−	4.51261i	1.40862	−	0.234917i
$370$	5.40988	+	27.0542i	0.281246	+	1.40648i
$371$	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	0.191169	−	0.981557i	$-0.438772\pi$
$373$	21.9554	−	12.6759i	1.13681	−	0.656335i	0.945638	+	0.325222i	$0.105439\pi$
$374$	5.59017	−	9.68247i	0.289061	−	0.500668i
$375$	4.63297	−	18.8025i	0.239246	−	0.970959i
$376$			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	$0.650495\pi$
$380$	4.04381	+	0.260937i	0.207443	+	0.0133858i
$381$	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	$-0.808761\pi$
$383$	3.36875	−	12.5724i	0.172135	−	0.642417i	0.997022	−	0.0771191i	$-0.0245722\pi$
$384$	−17.8133	−	11.4649i	−0.909033	−	0.585067i
$385$	−8.08112	−	2.73405i	−0.411852	−	0.139340i
$386$	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	$0.658174\pi$
$390$	−9.78948	+	22.0453i	−0.495709	+	1.11631i
$391$	−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
$395$	0.0612617	−	0.181073i	0.00308241	−	0.00911076i
$396$	2.23012	+	2.70841i	0.112068	+	0.136103i
$397$	−2.40525	+	8.97652i	−0.120716	+	0.450519i	−0.999651	−	0.0264234i	$-0.991588\pi$
$397$	−2.40525	+	8.97652i	−0.120716	+	0.450519i	0.878935	+	0.476942i	$0.158255\pi$
$398$	8.91594	−	8.91594i	0.446916	−	0.446916i
$399$	−10.0074	+	2.16992i	−0.500999	+	0.108632i
$400$	23.0764	−	9.61329i	1.15382	−	0.480665i
$401$	−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
$405$	9.98791	−	17.4712i	0.496303	−	0.868149i
$406$	−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	$0.149354\pi$
$410$	−34.6332	+	6.92541i	−1.71041	+	0.342022i
$411$	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	$0.678465\pi$
$420$	9.56360	−	7.61870i	0.466656	−	0.371754i
$421$	−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
$425$	26.9971	+	3.49868i	1.30955	+	0.169711i
$426$	−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	$-0.822574\pi$
$433$	−18.3621	−	31.8042i	−0.882428	−	1.52841i	−0.0337954	−	0.999429i	$-0.510759\pi$
$434$	−0.820706	+	0.820706i	−0.0393952	+	0.0393952i
$435$	3.54234	−	31.2948i	0.169842	−	1.50047i
$436$	−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	$0.617021\pi$
$440$	3.08034	+	3.50529i	0.146849	+	0.167108i
$441$	−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	$-0.365387\pi$
$443$	17.2761			0.820814			0.410407	+	0.911902i	$0.365387\pi$
$444$	0.587314	−	12.1567i	0.0278727	−	0.576932i
$445$	0.761663	−	11.8037i	0.0361063	−	0.559549i
$446$	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	$-0.0509687\pi$
$450$	−12.1305	+	22.8952i	−0.571838	+	1.07929i
$451$	−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
$455$	−2.78463	+	25.7238i	−0.130546	+	1.20595i
$456$	5.33407	+	1.70908i	0.249791	+	0.0800351i
$457$	5.66785	+	21.1527i	0.265131	+	0.989481i	0.962170	+	0.272449i	$0.0878335\pi$
$457$	5.66785	+	21.1527i	0.265131	+	0.989481i	−0.697040	+	0.717033i	$0.745500\pi$
$458$	5.44537	−	9.43166i	0.254446	−	0.440713i
$459$	25.9840	+	11.1893i	1.21283	+	0.522272i
$460$	−2.78089	+	8.21954i	−0.129660	+	0.383238i
$461$	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	0.624836	−	0.780756i	$-0.285166\pi$
$463$	−3.35500	−	3.35500i	−0.155920	−	0.155920i	−0.780756	+	0.624836i	$0.785166\pi$
$464$	35.2103	−	20.3287i	1.63460	−	0.943734i
$465$	0.296637	−	0.754681i	0.0137562	−	0.0349975i
$466$	3.32745	+	12.4182i	0.154141	+	0.575263i
$467$		−	16.4147i		−	0.759584i	−0.925072	−	0.379792i	$-0.875996\pi$
$467$		−	16.4147i		−	0.759584i	0.925072	−	0.379792i	$-0.124004\pi$
$468$	6.55372	−	8.38292i	0.302946	−	0.387500i
$469$	−7.62489			−0.352085
$470$	22.4654	+	25.5646i	1.03625	+	1.17921i
$471$	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
$475$	−7.29612	+	5.62200i	−0.334769	+	0.257955i
$476$	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	$0.396898\pi$
$480$	−19.6304	+	2.94850i	−0.895999	+	0.134580i
$481$	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
$485$	−2.38763	+	3.58118i	−0.108417	+	0.162613i
$486$	−18.6472	+	19.4250i	−0.845853	+	0.881135i
$487$	13.2878	+	3.56046i	0.602129	+	0.161340i	0.546990	−	0.837139i	$-0.315773\pi$
$487$	13.2878	+	3.56046i	0.602129	+	0.161340i	0.0551382	+	0.998479i	$0.482440\pi$
$488$	22.0360	+	5.90453i	0.997523	+	0.267285i
$489$	−9.87975	−	19.1958i	−0.446778	−	0.868065i
$490$	7.06957	−	10.6036i	0.319371	−	0.479020i
$491$	−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
$495$	−7.87165	−	1.27829i	−0.353804	−	0.0574551i
$496$	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	$0.952369\pi$
$500$	4.83454	−	9.87895i	0.216207	−	0.441800i
$501$	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	$-0.822132\pi$
$503$	−19.8054	−	34.3040i	−0.883081	−	1.52954i	−0.0351832	−	0.999381i	$-0.511201\pi$
$504$	15.3833	−	7.00026i	0.685227	−	0.311816i
$505$	17.4716	+	19.8819i	0.777476	+	0.884735i
$506$	−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	$-0.256093\pi$
$510$	−33.8995	−	13.3246i	−1.50109	−	0.590024i
$511$	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
$515$	4.85600	−	14.3530i	0.213981	−	0.632469i
$516$	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
$520$	8.35444	−	11.4240i	0.366366	−	0.500974i
$521$			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	0.842415	−	0.538829i	$-0.181133\pi$
$523$	18.2263	+	10.5230i	0.796983	+	0.460138i	−0.0454324	+	0.998967i	$0.514467\pi$
$524$	−1.25195	−	2.16845i	−0.0546918	−	0.0947290i
$525$	−4.89787	+	27.3582i	−0.213761	+	1.19401i
$526$	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
$530$	−0.236886	+	3.67108i	−0.0102897	+	0.159462i
$531$	−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
$535$	7.70891	+	8.77241i	0.333285	+	0.379264i
$536$	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
$540$	7.64661	−	8.49547i	0.329058	−	0.365587i
$541$	−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	$-0.797673\pi$
$547$		−	27.7702i		−	1.18737i	0.804698	−	0.593685i	$-0.202327\pi$
$548$	3.62164	−	0.970416i	0.154709	−	0.0414541i
$549$	−35.4858	+	16.1480i	−1.51450	+	0.689181i
$550$	10.1823	+	1.31957i	0.434174	+	0.0562666i
$551$	−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
$555$	17.2377	+	21.6382i	0.731700	+	0.918489i
$556$	17.1136	+	9.88054i	0.725778	+	0.419028i
$557$	−5.53600	−	20.6607i	−0.234568	−	0.875420i	−0.978343	−	0.206990i	$-0.933633\pi$
$557$	−5.53600	−	20.6607i	−0.234568	−	0.875420i	0.743775	−	0.668430i	$-0.233033\pi$
$558$	−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	−0.529894	−	0.848064i	$-0.677768\pi$
$563$	−1.43304	+	0.827364i	−0.0603953	+	0.0348692i	0.469498	+	0.882933i	$0.344435\pi$
$564$	−6.87044	−	13.3489i	−0.289298	−	0.562090i
$565$	10.2778	−	2.05520i	0.432391	−	0.0864629i
$566$	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	$-0.0667391\pi$
$570$	11.2984	−	4.92253i	0.473237	−	0.206182i
$571$			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
$575$	−7.58479	−	18.2070i	−0.316308	−	0.759285i
$576$	−3.42239	−	0.331458i	−0.142600	−	0.0138108i
$577$	−13.0485	+	13.0485i	−0.543215	+	0.543215i	−0.924470	−	0.381255i	$-0.875492\pi$
$577$	−13.0485	+	13.0485i	−0.543215	+	0.543215i	0.381255	+	0.924470i	$0.375492\pi$
$578$	5.65248	−	21.0953i	0.235112	−	0.877451i
$579$	6.30756	−	9.80021i	0.262133	−	0.407283i
$580$	5.73267	−	16.9442i	0.238036	−	0.703569i
$581$	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
$585$	1.38802	+	24.1469i	0.0573876	+	0.998352i
$586$	3.63951			0.150347
$587$	−33.8321	+	9.06530i	−1.39640	+	0.374165i	−0.877052	−	0.480396i	$-0.840493\pi$
$587$	−33.8321	+	9.06530i	−1.39640	+	0.374165i	−0.519351	+	0.854561i	$0.673826\pi$
$588$	−4.16250	+	3.77884i	−0.171659	+	0.155837i
$589$	−0.334023	+	0.192848i	−0.0137632	+	0.00794618i
$590$	29.6556	+	10.0333i	1.22090	+	0.413064i
$591$	−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	−0.995194	−	0.0979268i	$-0.968779\pi$
$593$	−21.8499	+	21.8499i	−0.897267	+	0.897267i	0.0979268	+	0.995194i	$0.468779\pi$
$594$	9.80019	+	4.22017i	0.402107	+	0.173156i
$595$	−38.9901	−	2.51593i	−1.59844	−	0.103143i
$596$	−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	$-0.227082\pi$
$600$	9.80251	−	11.6203i	0.400186	−	0.474395i
$601$	−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
$605$	−4.20334	−	21.0205i	−0.170890	−	0.854603i
$606$	−16.2064	−	31.4881i	−0.658340	−	1.27912i
$607$	42.5887	−	24.5886i	1.72862	−	0.998020i	0.832862	−	0.553480i	$-0.186701\pi$
$607$	42.5887	−	24.5886i	1.72862	−	0.998020i	0.895759	−	0.444540i	$-0.146633\pi$
$608$	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	$-0.959091\pi$
$613$	−4.87630	−	18.1986i	−0.196952	−	0.735035i	0.794801	−	0.606870i	$-0.207575\pi$
$614$	19.4405	+	11.2240i	0.784555	+	0.452963i
$615$	−27.6999	+	22.0667i	−1.11697	+	0.889815i
$616$	−4.73579	−	4.73579i	−0.190810	−	0.190810i
$617$	−4.04209	+	15.0853i	−0.162728	+	0.607310i	0.835591	+	0.549352i	$0.185126\pi$
$617$	−4.04209	+	15.0853i	−0.162728	+	0.607310i	−0.998319	+	0.0579578i	$0.981541\pi$
$618$	−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	$-0.0766304\pi$
$620$	0.255480	−	0.383192i	0.0102603	−	0.0153894i
$621$	−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
$630$	15.2580	−	33.9129i	0.607895	−	1.35112i
$631$	−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
$635$	−23.4712	−	26.7092i	−0.931425	−	1.05992i
$636$	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
$640$	27.2916	+	1.76106i	1.07879	+	0.0696119i
$641$	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	0.679203	−	0.733950i	$-0.262325\pi$
$643$	22.8328	+	6.11802i	0.900436	+	0.241271i	0.221232	+	0.975221i	$0.428992\pi$
$644$	3.22329	−	12.0295i	0.127016	−	0.474029i
$645$	−1.80391	+	2.44159i	−0.0710290	+	0.0961376i
$646$	8.66254	+	15.0040i	0.340823	+	0.590323i
$647$	22.6540	+	13.0793i	0.890620	+	0.514200i	0.874145	−	0.485664i	$-0.161422\pi$
$647$	22.6540	+	13.0793i	0.890620	+	0.514200i	0.0164751	+	0.999864i	$0.494756\pi$
$648$	13.1078	−	8.82014i	0.514923	−	0.346488i
$649$			9.63578i			0.378238i
$650$	−2.78425	−	31.0155i	−0.109207	−	1.21653i
$651$	−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	−0.929190	−	0.369602i	$-0.879494\pi$
$653$	−3.69279	+	6.39610i	−0.144510	+	0.250299i	0.784680	+	0.619901i	$0.212827\pi$
$654$	−6.53170	+	1.41627i	−0.255410	+	0.0553806i
$655$	5.39129	+	1.82401i	0.210655	+	0.0712701i
$656$	−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	$0.324512\pi$
$660$	−4.21539	−	1.65691i	−0.164084	−	0.0644953i
$661$	−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
$665$	9.93033	−	8.72646i	0.385082	−	0.338397i
$666$	−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
$670$	8.99864	−	1.79941i	0.347648	−	0.0695172i
$671$	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	$0.390476\pi$
$673$	−16.7742	+	29.0538i	−0.646599	+	1.11994i	−0.983930	+	0.178556i	$0.942857\pi$
$674$	−38.3875	+	10.2859i	−1.47863	+	0.396198i
$675$	−0.309167	+	25.9789i	−0.0118999	+	0.999929i
$676$	−1.10848	+	12.7404i	−0.0426338	+	0.490015i
$677$	−7.62559			−0.293075			−0.146538	−	0.989205i	$-0.546813\pi$
$677$	−7.62559			−0.293075			−0.146538	+	0.989205i	$0.546813\pi$
$678$	−14.0076	−	0.676735i	−0.537959	−	0.0259899i
$679$	3.08872	−	5.34983i	0.118534	−	0.205307i
$680$	17.7818	+	11.8554i	0.681902	+	0.454635i
$681$	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	0.617133	−	0.786859i	$-0.288294\pi$
$683$	19.8139	+	5.30911i	0.758157	+	0.203147i	0.141024	+	0.990006i	$0.454961\pi$
$684$	−5.36257	+	0.894323i	−0.205043	+	0.0341953i
$685$	−4.72770	+	7.09103i	−0.180636	+	0.270934i
$686$	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
$690$	3.91989	+	26.0975i	0.149228	+	0.993517i
$691$	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
$695$	−44.0458	+	8.80759i	−1.67075	+	0.334091i
$696$	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
$700$	−6.01128	+	14.5960i	−0.227205	+	0.551676i
$701$	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
$705$	31.7603	+	12.4838i	1.19616	+	0.470166i
$706$	−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	$0.579758\pi$
$710$	2.21158	−	6.53681i	0.0829990	−	0.245322i
$711$	−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
$715$	8.76794	−	3.87109i	0.327902	−	0.144771i
$716$			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	$0.573345\pi$
$720$	−27.2106	+	19.6077i	−1.01408	+	0.730736i
$721$	−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
$725$	15.6357	+	37.5329i	0.580695	+	1.39394i
$726$	−1.38408	+	28.6487i	−0.0513678	+	1.06325i
$727$	−0.507235			−0.0188123			−0.00940616	−	0.999956i	$-0.502994\pi$
$727$	−0.507235			−0.0188123			−0.00940616	+	0.999956i	$0.502994\pi$
$728$	−10.9099	+	17.1342i	−0.404347	+	0.635035i
$729$	−7.71156	+	25.8753i	−0.285613	+	0.958345i
$730$	−39.8354	+	35.0061i	−1.47437	+	1.29563i
$731$	−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	$0.601387\pi$
$733$	−34.1906	+	34.1906i	−1.26286	+	1.26286i	−0.949701	+	0.313158i	$0.898613\pi$
$734$	22.7481	+	6.09532i	0.839646	+	0.224982i
$735$	1.43729	−	12.6978i	0.0530154	−	0.468365i
$736$	−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	0.541493	−	0.840705i	$-0.317859\pi$
$743$	39.0006	−	10.4502i	1.43079	−	0.383380i	0.889299	+	0.457326i	$0.151193\pi$
$744$	0.471338	−	0.427894i	0.0172801	−	0.0156874i
$745$	3.12091	−	4.68102i	0.114341	−	0.171499i
$746$	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
$750$	−0.675995	−	33.4431i	−0.0246838	−	1.22117i
$751$	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	0.350366	−	0.936613i	$-0.386057\pi$
$757$	−7.85737	−	4.53645i	−0.285581	−	0.164880i	−0.635947	+	0.771733i	$0.719390\pi$
$758$	−39.0410	+	22.5403i	−1.41803	+	0.818701i
$759$	−7.22209	+	3.71708i	−0.262145	+	0.134922i
$760$	−7.09072	+	1.41789i	−0.257207	+	0.0514323i
$761$	−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
$765$	−36.3379	+	3.67577i	−1.31380	+	0.132898i
$766$		−	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	$0.730781\pi$
$770$	−14.7056	−	0.948914i	−0.529952	−	0.0341965i
$771$	−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	$-0.616123\pi$
$773$	11.6577	−	43.5070i	0.419297	−	1.56484i	0.776069	−	0.630647i	$-0.217211\pi$
$774$	3.13559	−	2.58186i	0.112706	−	0.0928029i
$775$	0.138741	+	1.03762i	0.00498373	+	0.0372723i
$776$	−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
$780$	−2.13574	+	13.5700i	−0.0764717	+	0.485885i
$781$	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
$785$	−11.4115	−	3.86082i	−0.407295	−	0.137799i
$786$	−6.40353	−	4.12141i	−0.228406	−	0.147006i
$787$	10.6722	−	39.8293i	0.380424	−	1.41976i	−0.464831	−	0.885399i	$-0.653885\pi$
$787$	10.6722	−	39.8293i	0.380424	−	1.41976i	0.845255	−	0.534362i	$-0.179448\pi$
$788$	−11.4280	+	11.4280i	−0.407105	+	0.407105i
$789$	−5.88844	−	27.1569i	−0.209634	−	0.966812i
$790$	0.0212622	−	0.329507i	0.000756476	−	0.0117233i
$791$	−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
$795$	1.47336	+	3.38171i	0.0522547	+	0.119937i
$796$	3.59045	−	6.21885i	0.127260	−	0.220421i
$797$	−17.4955	+	10.1010i	−0.619721	+	0.357796i	−0.776761	−	0.629796i	$-0.783138\pi$
$797$	−17.4955	+	10.1010i	−0.619721	+	0.357796i	0.157039	+	0.987592i	$0.449805\pi$
$798$	−15.7272	+	8.09452i	−0.556738	+	0.286543i
$799$	−12.4164	+	46.3386i	−0.439260	+	1.63934i
$800$	20.2996	−	15.6418i	0.717700	−	0.553021i
$801$	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	$0.556883\pi$
$810$	8.85388	−	33.6158i	0.311094	−	1.18114i
$811$	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
$815$	23.1899	+	15.4611i	0.812306	+	0.541578i
$816$	−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	0.908270	−	0.418385i	$-0.137404\pi$
$823$	2.63365	+	4.56162i	0.0918034	+	0.159008i	−0.816467	+	0.577393i	$0.804070\pi$
$824$	8.41132	−	8.41132i	0.293022	−	0.293022i
$825$	9.68367	−	3.49589i	0.337142	−	0.121711i
$826$	−43.4018	−	11.6295i	−1.51014	−	0.404641i
$827$	−7.14407	+	7.14407i	−0.248424	+	0.248424i	−0.820323	−	0.571900i	$-0.806207\pi$
$827$	−7.14407	+	7.14407i	−0.248424	+	0.248424i	0.571900	+	0.820323i	$0.306207\pi$
$828$	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	$0.537260\pi$
$830$	−18.4322	+	16.1976i	−0.639792	+	0.562228i
$831$	−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
$835$	−23.4262	−	1.51163i	−0.810697	−	0.0523123i
$836$	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	$0.153445\pi$
$840$	−12.9658	+	17.5491i	−0.447361	+	0.605503i
$841$	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
$845$	−17.2237	−	23.4168i	−0.592512	−	0.805562i
$846$	−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
$850$	46.6086	−	6.23210i	1.59866	−	0.213759i
$851$	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	0.827916	−	0.560852i	$-0.189526\pi$
$853$	7.79992	+	7.79992i	0.267064	+	0.267064i	−0.560852	+	0.827916i	$0.689526\pi$
$854$	−62.3907	+	36.0213i	−2.13496	+	1.23262i
$855$	7.81441	−	9.57327i	0.267247	−	0.327399i
$856$	2.37289	+	8.85576i	0.0811038	+	0.302684i
$857$			20.1264i			0.687503i	0.939061	+	0.343752i	$0.111698\pi$
$857$			20.1264i			0.687503i	−0.939061	+	0.343752i	$0.888302\pi$
$858$	−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	$0.377913\pi$
$860$	−1.29513	+	1.13812i	−0.0441637	+	0.0388097i
$861$	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	0.990480	−	0.137658i	$-0.0439573\pi$
$863$	25.0532	+	25.0532i	0.852822	+	0.852822i	−0.137658	+	0.990480i	$0.543957\pi$
$864$	24.7446	−	9.84818i	0.841827	−	0.335042i
$865$	7.37903	+	36.9018i	0.250895	+	1.25470i
$866$	−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
$870$	−8.08066	−	53.7988i	−0.273960	−	1.82395i
$871$	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
$875$	−11.6366	−	33.9415i	−0.393389	−	1.14743i
$876$	20.8005	−	10.7057i	0.702785	−	0.361711i
$877$	−16.2264	−	4.34785i	−0.547926	−	0.146816i	−0.0257727	−	0.999668i	$-0.508205\pi$
$877$	−16.2264	−	4.34785i	−0.547926	−	0.146816i	−0.522154	+	0.852851i	$0.674871\pi$
$878$	10.8606	+	2.91009i	0.366528	+	0.0982109i
$879$	3.24486	−	1.67007i	0.109446	−	0.0563301i
$880$	11.0582	+	7.37266i	0.372771	+	0.248532i
$881$	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	$-0.581406\pi$
$883$	−15.0338			−0.505929			−0.252964	+	0.967476i	$0.581406\pi$
$884$	−19.2932	−	0.837720i	−0.648900	−	0.0281756i
$885$	31.0439	−	4.66284i	1.04353	−	0.156740i
$886$	28.8251	−	7.72365i	0.968397	−	0.259481i
$887$	7.59276	−	13.1511i	0.254940	−	0.441569i	−0.709939	−	0.704263i	$-0.751278\pi$
$887$	7.59276	−	13.1511i	0.254940	−	0.441569i	0.964879	+	0.262694i	$0.0846109\pi$
$888$	4.60231	+	21.2254i	0.154444	+	0.712278i
$889$	36.0852	+	36.0852i	1.21026	+	1.21026i
$890$	−4.00626	−	20.0349i	−0.134290	−	0.671570i
$891$	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
$895$	−26.7531	−	30.4438i	−0.894256	−	1.01763i
$896$	−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
$900$	−3.29827	+	14.3827i	−0.109942	+	0.479422i
$901$	−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
$905$	−0.700800	−	0.237099i	−0.0232954	−	0.00788145i
$906$	12.2453	+	56.4743i	0.406824	+	1.87623i
$907$	7.51117	−	13.0097i	0.249404	−	0.431981i	−0.713956	−	0.700190i	$-0.753099\pi$
$907$	7.51117	−	13.0097i	0.249404	−	0.431981i	0.963361	+	0.268209i	$0.0864319\pi$
$908$	3.13127	+	11.6860i	0.103915	+	0.387815i
$909$	−28.8981	−	20.6370i	−0.958489	−	0.684488i
$910$	6.85421	+	44.1648i	0.227215	+	1.46405i
$911$			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
$915$	29.9091	−	40.4819i	0.988764	−	1.33829i
$916$	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	$-0.521115\pi$
$920$	0.997089	−	15.4522i	0.0328731	−	0.509443i
$921$	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
$925$	−33.0242	−	13.6009i	−1.08583	−	0.447193i
$926$	−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	$0.726615\pi$
$930$	0.157541	−	1.39180i	0.00516596	−	0.0456388i
$931$	−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	$0.0663123\pi$
$937$			12.6619i			0.413645i	−0.978378	+	0.206822i	$0.933688\pi$
$938$	−12.7221	+	3.40887i	−0.415390	+	0.111303i
$939$	29.6119	+	32.6184i	0.966349	+	1.06446i
$940$	16.1264	+	10.7517i	0.525984	+	0.350682i
$941$	−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
$945$	−1.95816	−	37.2370i	−0.0636990	−	1.21132i
$946$	−1.39391	−	0.804775i	−0.0453200	−	0.0261655i
$947$	8.08395	+	30.1697i	0.262693	+	0.980384i	0.963647	+	0.267178i	$0.0860911\pi$
$947$	8.08395	+	30.1697i	0.262693	+	0.980384i	−0.700954	+	0.713206i	$0.747242\pi$
$948$	−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	0.388957	−	0.921256i	$-0.372835\pi$
$953$	42.6407	−	24.6186i	1.38127	−	0.797475i	0.992310	+	0.123781i	$0.0395021\pi$
$954$	−0.811890	−	4.86828i	−0.0262859	−	0.157616i
$955$	−5.54161	−	27.7130i	−0.179322	−	0.896771i
$956$	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
$960$	4.06949	−	1.77302i	0.131342	−	0.0572239i
$961$		−	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
$965$	−0.968866	+	15.0148i	−0.0311889	+	0.483343i
$966$	−8.02621	−	37.0161i	−0.258239	−	1.19097i
$967$	−21.5311	+	21.5311i	−0.692393	+	0.692393i	−0.962758	−	0.270365i	$-0.912856\pi$
$967$	−21.5311	+	21.5311i	−0.692393	+	0.692393i	0.270365	+	0.962758i	$0.412856\pi$
$968$	4.35567	−	16.2556i	0.139997	−	0.522474i
$969$	14.6081	+	9.40199i	0.469280	+	0.302036i
$970$	−2.38270	+	7.04260i	−0.0765038	+	0.226124i
$971$	−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
$975$	−16.7145	−	26.3747i	−0.535293	−	0.844667i
$976$	64.9753			2.07981
$977$	10.2928	−	2.75795i	0.329297	−	0.0882347i	−0.0903830	−	0.995907i	$-0.528809\pi$
$977$	10.2928	−	2.75795i	0.329297	−	0.0882347i	0.419680	+	0.907672i	$0.362142\pi$
$978$	−25.0662	−	27.6111i	−0.801528	−	0.882906i
$979$	5.44600	−	3.14425i	0.174055	−	0.100491i
$980$	2.32601	−	6.87506i	0.0743018	−	0.219616i
$981$	−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	−0.969205	−	0.246254i	$-0.920800\pi$
$983$	−22.6666	+	22.6666i	−0.722952	+	0.722952i	0.246254	+	0.969205i	$0.420800\pi$
$984$	−27.1715	+	5.89161i	−0.866196	+	0.187818i
$985$	2.36556	−	36.6598i	0.0753731	−	1.16808i
$986$	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
$990$	−13.7053	+	1.38636i	−0.435582	+	0.0440614i
$991$	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
$995$	3.20056	+	16.0056i	0.101465	+	0.507413i
$996$	9.62461	−	4.95362i	0.304967	−	0.156961i
$997$	−50.8556	+	29.3615i	−1.61061	+	0.929888i	−0.621386	+	0.783505i	$0.713430\pi$
$997$	−50.8556	+	29.3615i	−1.61061	+	0.929888i	−0.989228	+	0.146383i	$0.953237\pi$
$998$	−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.59.20	yes	96
3.2	odd	2	inner	195.2.bh.a.59.6	yes	96
5.2	odd	4		975.2.bo.h.176.20		96
5.3	odd	4		975.2.bo.h.176.5		96
5.4	even	2	inner	195.2.bh.a.59.5	✓	96
13.2	odd	12	inner	195.2.bh.a.119.19	yes	96
15.2	even	4		975.2.bo.h.176.6		96
15.8	even	4		975.2.bo.h.176.19		96
15.14	odd	2	inner	195.2.bh.a.59.19	yes	96
39.2	even	12	inner	195.2.bh.a.119.5	yes	96
65.2	even	12		975.2.bo.h.626.6		96
65.28	even	12		975.2.bo.h.626.19		96
65.54	odd	12	inner	195.2.bh.a.119.6	yes	96
195.2	odd	12		975.2.bo.h.626.20		96
195.119	even	12	inner	195.2.bh.a.119.20	yes	96
195.158	odd	12		975.2.bo.h.626.5		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.bh.a.59.5	✓	96	5.4	even	2	inner
195.2.bh.a.59.6	yes	96	3.2	odd	2	inner
195.2.bh.a.59.19	yes	96	15.14	odd	2	inner
195.2.bh.a.59.20	yes	96	1.1	even	1	trivial
195.2.bh.a.119.5	yes	96	39.2	even	12	inner
195.2.bh.a.119.6	yes	96	65.54	odd	12	inner
195.2.bh.a.119.19	yes	96	13.2	odd	12	inner
195.2.bh.a.119.20	yes	96	195.119	even	12	inner
975.2.bo.h.176.5		96	5.3	odd	4
975.2.bo.h.176.6		96	15.2	even	4
975.2.bo.h.176.19		96	15.8	even	4
975.2.bo.h.176.20		96	5.2	odd	4
975.2.bo.h.626.5		96	195.158	odd	12
975.2.bo.h.626.6		96	65.2	even	12
975.2.bo.h.626.19		96	65.28	even	12
975.2.bo.h.626.20		96	195.2	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} +(-0.716618 + 2.11813i) 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} +(-0.248718 + 3.85445i) q^{10} +(-1.14830 + 0.307686i) q^{11} +(0.519902 - 1.62262i) q^{12} +(1.66563 + 3.19776i) q^{13} -5.54355i q^{14} +(1.54695 + 3.55062i) 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} +(0.431321 + 2.15699i) 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} +(4.16846 + 5.23258i) 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} +(5.97080 + 3.98083i) 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} +(6.11754 + 2.75240i) 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} +(-7.98598 - 3.28899i) q^{50} +(-2.87745 + 8.98056i) q^{51} +(2.99188 + 1.90503i) q^{52} +0.952426 q^{53} +(-7.04403 - 5.56259i) q^{54} +(0.171174 - 2.65274i) 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} +(3.06434 + 2.26402i) q^{60} +(-6.49787 - 11.2546i) q^{61} +(-0.313203 - 0.180828i) q^{62} +(-9.01626 - 3.37675i) q^{63} -1.14613i q^{64} +(-7.96688 + 1.23643i) 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} +(11.7419 + 3.97261i) 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} +(-8.62925 + 0.732204i) q^{75} +(-0.469034 - 1.75046i) q^{76} +3.81522i q^{77} +(10.7420 + 0.987461i) q^{78} -0.0854873 q^{79} +(-7.37982 - 8.39792i) 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} +(-2.38719 - 11.9381i) 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} +(11.4376 + 1.85737i) q^{90} +(11.2963 - 2.50718i) q^{91} +3.88057 q^{92} +(-0.362217 - 0.0174994i) q^{93} +(7.61001 - 13.1809i) q^{94} +(3.42733 + 2.28506i) 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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