LMFDB - Embedded newform 195.2.bh.a.59.19

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			59.19
Character	$\chi$	$=$	195.59
Dual form			195.2.bh.a.119.19

$q$-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} +(0.367032 - 1.69272i) q^{3} +(0.851938 - 0.491866i) q^{4} +(2.11813 - 0.716618i) q^{5} +(-0.144374 - 2.98837i) q^{6} +(-0.830623 + 3.09993i) q^{7} +(-1.24129 + 1.24129i) q^{8} +(-2.73057 - 1.24256i) 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} +(-0.435610 - 3.84841i) q^{15} +(-2.49987 + 4.32990i) q^{16} +(-4.71514 + 2.72229i) q^{17} +(-5.11145 - 0.852444i) q^{18} +(0.476790 - 1.77941i) q^{19} +(1.45203 - 1.65235i) q^{20} +(4.94243 + 2.54378i) q^{21} +(1.77837 - 1.02674i) q^{22} +(3.41625 + 1.97237i) q^{23} +(1.64556 + 2.55674i) 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} +(-2.44732 - 6.22628i) q^{30} +(-0.148047 - 0.148047i) q^{31} +(-1.32655 + 4.95075i) q^{32} +(-0.0993620 - 2.05668i) q^{33} +(-6.65011 + 6.65011i) q^{34} +(0.462099 + 7.16128i) q^{35} +(-2.93745 + 0.284492i) q^{36} +(-6.89966 + 1.84876i) q^{37} -3.18208i q^{38} +(-6.02424 + 1.64575i) q^{39} +(-1.73968 + 3.51874i) q^{40} +(-2.36667 - 8.83254i) q^{41} +(9.38365 + 2.03466i) q^{42} +(-0.391907 - 0.678803i) q^{43} +(0.826939 - 0.826939i) q^{44} +(-6.67414 - 0.675125i) q^{45} +(6.58176 + 1.76358i) q^{46} +(6.23046 - 6.23046i) q^{47} +(6.41176 + 5.82078i) 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} +(-3.31901 + 8.33936i) q^{54} +(2.21175 - 1.47461i) q^{55} +(-2.81686 - 4.87895i) q^{56} +(-2.83703 - 1.46017i) q^{57} +(13.5680 + 3.63553i) q^{58} +(-2.09784 + 7.82924i) q^{59} +(-2.26402 - 3.06434i) q^{60} +(-6.49787 - 11.2546i) q^{61} +(-0.313203 - 0.180828i) q^{62} +(6.11993 - 7.43249i) 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} +(4.59254 - 5.05881i) q^{69} +(3.97261 + 11.7419i) q^{70} +(1.72575 + 0.462414i) q^{71} +(4.93181 - 1.84705i) q^{72} +(-9.70845 - 9.70845i) q^{73} +(-10.6855 + 6.16928i) q^{74} +(-3.68052 - 7.83925i) q^{75} +(-0.469034 - 1.75046i) q^{76} +3.81522i q^{77} +(-9.31563 + 5.43918i) q^{78} -0.0854873 q^{79} +(-2.19215 + 10.9627i) q^{80} +(5.91208 + 6.78582i) q^{81} +(-7.89754 - 13.6789i) q^{82} +(4.49219 + 4.49219i) q^{83} +(5.46185 - 0.263872i) q^{84} +(-8.03642 + 9.14510i) q^{85} +(-0.957366 - 0.957366i) q^{86} +(9.46729 - 10.4285i) 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} +(-0.304940 + 0.196264i) q^{93} +(7.61001 - 13.1809i) q^{94} +(-0.265252 - 4.11068i) q^{95} +(7.89332 + 4.06255i) q^{96} +(-1.85928 - 0.498193i) q^{97} +(-5.50517 - 1.47511i) q^{98} +(-3.51784 - 0.586675i) 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	$0.207551\pi$
$3$	0.367032	−	1.69272i	0.211906	−	0.977290i
$3$	0.367032	−	1.69272i	0.211906	−	0.977290i
$4$	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
$6$	−0.144374	−	2.98837i	−0.0589404	−	1.22000i
$7$	−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
$9$	−2.73057	−	1.24256i	−0.910192	−	0.414188i
$10$	3.21369	−	2.14262i	1.01626	−	0.677557i
$11$	1.14830	−	0.307686i	0.346225	−	0.0927708i	−0.0815158	−	0.996672i	$-0.525976\pi$
$11$	1.14830	−	0.307686i	0.346225	−	0.0927708i	0.427741	+	0.903901i	$0.359309\pi$
$12$	−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
$15$	−0.435610	−	3.84841i	−0.112474	−	0.993655i
$16$	−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	$0.562884\pi$
$18$	−5.11145	−	0.852444i	−1.20478	−	0.200923i
$19$	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
$21$	4.94243	+	2.54378i	1.07853	+	0.555099i
$22$	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	$0.531753\pi$
$24$	1.64556	+	2.55674i	0.335898	+	0.521893i
$25$	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	0.981720	−	0.190333i	$-0.0609569\pi$
$29$	7.04243	+	4.06595i	1.30775	+	0.755027i	0.326026	+	0.945361i	$0.394290\pi$
$30$	−2.44732	−	6.22628i	−0.446818	−	1.13676i
$31$	−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
$33$	−0.0993620	−	2.05668i	−0.0172967	−	0.358021i
$34$	−6.65011	+	6.65011i	−1.14048	+	1.14048i
$35$	0.462099	+	7.16128i	0.0781091	+	1.21048i
$36$	−2.93745	+	0.284492i	−0.489576	+	0.0474154i
$37$	−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
$39$	−6.02424	+	1.64575i	−0.964651	+	0.263531i
$40$	−1.73968	+	3.51874i	−0.275067	+	0.556361i
$41$	−2.36667	−	8.83254i	−0.369612	−	1.37941i	−0.861060	−	0.508504i	$-0.830199\pi$
$41$	−2.36667	−	8.83254i	−0.369612	−	1.37941i	0.491448	−	0.870907i	$-0.336468\pi$
$42$	9.38365	+	2.03466i	1.44793	+	0.313955i
$43$	−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
$45$	−6.67414	−	0.675125i	−0.994923	−	0.100642i
$46$	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	$0.0278463\pi$
$48$	6.41176	+	5.82078i	0.925457	+	0.840157i
$49$	−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	$-0.479164\pi$
$53$	0.952426			0.130826			0.0654129	+	0.997858i	$0.479164\pi$
$54$	−3.31901	+	8.33936i	−0.451660	+	1.13484i
$55$	2.21175	−	1.47461i	0.298232	−	0.198836i
$56$	−2.81686	−	4.87895i	−0.376419	−	0.651977i
$57$	−2.83703	−	1.46017i	−0.375774	−	0.193404i
$58$	13.5680	+	3.63553i	1.78156	+	0.477369i
$59$	−2.09784	+	7.82924i	−0.273115	+	1.01928i	0.683979	+	0.729502i	$0.260248\pi$
$59$	−2.09784	+	7.82924i	−0.273115	+	1.01928i	−0.957094	+	0.289778i	$0.906419\pi$
$60$	−2.26402	−	3.06434i	−0.292283	−	0.395605i
$61$	−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
$63$	6.11993	−	7.43249i	0.771039	−	0.936405i
$64$		−	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
$69$	4.59254	−	5.05881i	0.552876	−	0.609009i
$70$	3.97261	+	11.7419i	0.474817	+	1.40343i
$71$	1.72575	+	0.462414i	0.204809	+	0.0548784i	0.359765	−	0.933043i	$-0.382857\pi$
$71$	1.72575	+	0.462414i	0.204809	+	0.0548784i	−0.154956	+	0.987921i	$0.549524\pi$
$72$	4.93181	−	1.84705i	0.581219	−	0.217677i
$73$	−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
$75$	−3.68052	−	7.83925i	−0.424989	−	0.905198i
$76$	−0.469034	−	1.75046i	−0.0538019	−	0.200792i
$77$			3.81522i			0.434785i
$78$	−9.31563	+	5.43918i	−1.05479	+	0.615866i
$79$	−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
$81$	5.91208	+	6.78582i	0.656897	+	0.753980i
$82$	−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	$0.636636\pi$
$84$	5.46185	−	0.263872i	0.595936	−	0.0287908i
$85$	−8.03642	+	9.14510i	−0.871672	+	0.991925i
$86$	−0.957366	−	0.957366i	−0.103235	−	0.103235i
$87$	9.46729	−	10.4285i	1.01500	−	1.11805i
$88$	−1.04344	+	1.80730i	−0.111232	+	0.192659i
$89$	5.10951	−	1.36909i	0.541607	−	0.145123i	0.0223639	−	0.999750i	$-0.492881\pi$
$89$	5.10951	−	1.36909i	0.541607	−	0.145123i	0.519243	+	0.854627i	$0.326214\pi$
$90$	−11.4376	+	1.85737i	−1.20563	+	0.195784i
$91$	11.2963	−	2.50718i	1.18418	−	0.262824i
$92$	3.88057			0.404578
$93$	−0.304940	+	0.196264i	−0.0316208	+	0.0203516i
$94$	7.61001	−	13.1809i	0.784912	−	1.35951i
$95$	−0.265252	−	4.11068i	−0.0272143	−	0.421747i
$96$	7.89332	+	4.06255i	0.805609	+	0.414633i
$97$	−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
$99$	−3.51784	−	0.586675i	−0.353556	−	0.0589630i
$100$	1.89148	−	4.54044i	0.189148	−	0.454044i
$101$	−5.91840	+	10.2510i	−0.588903	+	1.02001i	0.405474	+	0.914107i	$0.367107\pi$
$101$	−5.91840	+	10.2510i	−0.588903	+	1.02001i	−0.994377	+	0.105903i	$0.966227\pi$
$102$	8.81594	+	13.6976i	0.872908	+	1.35626i
$103$	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
$105$	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	$0.0854309\pi$
$108$	−0.596576	+	5.07669i	−0.0574055	+	0.488505i
$109$	−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
$111$	0.597026	+	12.3577i	0.0566672	+	1.17294i
$112$	−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	$0.904094\pi$
$114$	−5.38636	−	1.16793i	−0.504479	−	0.109386i
$115$	8.64948	+	1.72959i	0.806568	+	0.161285i
$116$	7.99961			0.742745
$117$	0.574694	+	10.8014i	0.0531305	+	0.998588i
$118$			14.0009i			1.28889i
$119$	−4.52239	−	16.8778i	−0.414567	−	1.54718i
$120$	5.31770	+	4.23627i	0.485438	+	0.386717i
$121$	−8.30236	+	4.79337i	−0.754760	+	0.435761i
$122$	−15.8733	−	15.8733i	−1.43710	−	1.43710i
$123$	−15.8196	+	0.764277i	−1.42641	+	0.0689125i
$124$	−0.198946	−	0.0533075i	−0.0178659	−	0.00478715i
$125$	6.23965	−	9.27722i	0.558091	−	0.829780i
$126$	6.88821	−	15.1371i	0.613650	−	1.34852i
$127$	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	$0.0354670\pi$
$131$			2.54531i			0.222385i	−0.993799	+	0.111192i	$0.964533\pi$
$132$	−1.09626	−	1.70329i	−0.0954172	−	0.148252i
$133$	5.12000	+	2.95603i	0.443960	+	0.256321i
$134$	2.05199	+	3.55415i	0.177265	+	0.307032i
$135$	−3.59242	+	11.0496i	−0.309186	+	0.951001i
$136$	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	$0.531276\pi$
$138$	5.40096	−	10.4938i	0.459760	−	0.893289i
$139$	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
$141$	−8.25962	−	12.8332i	−0.695585	−	1.08075i
$142$	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
$147$	−3.84133	+	4.23133i	−0.316827	+	0.348995i
$148$	−4.96874	+	4.96874i	−0.408428	+	0.408428i
$149$	2.43030	+	0.651196i	0.199098	+	0.0533481i	0.356990	−	0.934108i	$-0.383803\pi$
$149$	2.43030	+	0.651196i	0.199098	+	0.0533481i	−0.157892	+	0.987456i	$0.550470\pi$
$150$	−9.64560	−	11.4343i	−0.787560	−	0.933603i
$151$	−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
$153$	16.2576	−	1.57455i	1.31435	−	0.127295i
$154$	1.70567	+	6.36566i	0.137447	+	0.512959i
$155$	−0.419675	−	0.207489i	−0.0337091	−	0.0166659i
$156$	−4.32279	+	4.36520i	−0.346100	+	0.349496i
$157$		−	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
$159$	0.349571	−	1.61219i	0.0277228	−	0.127855i
$160$	0.737997	+	11.4369i	0.0583438	+	0.904169i
$161$	−8.95182	+	8.95182i	−0.705503	+	0.705503i
$162$	12.8980	+	8.67896i	1.01336	+	0.681883i
$163$	−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
$165$	−1.68431	−	4.28510i	−0.131124	−	0.333594i
$166$	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
$171$	−3.51293	+	4.26636i	−0.268641	+	0.326257i
$172$	−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	$0.112364\pi$
$174$	11.1338	−	21.6324i	0.844052	−	1.63995i
$175$	6.11069	+	14.8373i	0.461925	+	1.12160i
$176$	−1.53835	+	5.74120i	−0.115957	+	0.432759i
$177$	12.4827	+	6.42462i	0.938257	+	0.482904i
$178$	7.91308	−	4.56862i	0.593111	−	0.342433i
$179$	9.06243	−	15.6966i	0.677358	−	1.17322i	−0.298415	−	0.954436i	$-0.596458\pi$
$179$	9.06243	−	15.6966i	0.677358	−	1.17322i	0.975774	−	0.218783i	$-0.0702086\pi$
$180$	−6.01803	+	2.70762i	−0.448557	+	0.201814i
$181$			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
$186$	−0.421045	+	0.463793i	−0.0308725	+	0.0340070i
$187$	−4.57678	+	4.57678i	−0.334688	+	0.334688i
$188$	2.24341	−	8.37252i	0.163617	−	0.610628i
$189$	−10.3349	−	13.0873i	−0.751751	−	0.951959i
$190$	−2.28034	−	6.74005i	−0.165433	−	0.488975i
$191$	10.9457	−	6.31949i	0.792001	−	0.457262i	−0.0486655	−	0.998815i	$-0.515497\pi$
$191$	10.9457	−	6.31949i	0.792001	−	0.457262i	0.840667	+	0.541553i	$0.182163\pi$
$192$	−1.94008	−	0.420668i	−0.140013	−	0.0303591i
$193$	−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
$195$	−11.5807	+	7.80299i	−0.829314	+	0.558783i
$196$	−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	$0.615672\pi$
$198$	−6.13176	+	0.593861i	−0.435765	+	0.0422039i
$199$	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
$201$	4.11036	−	0.198580i	0.289923	−	0.0140067i
$202$	−5.29188	+	19.7496i	−0.372336	+	1.38958i
$203$	−18.4538	+	18.4538i	−1.29520	+	1.29520i
$204$	6.86864	+	6.23555i	0.480901	+	0.436576i
$205$	−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
$210$	21.3338	−	2.41483i	1.47217	−	0.166639i
$211$	−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
$213$	1.41614	−	2.75149i	0.0970324	−	0.188529i
$214$	2.33491	−	8.71401i	0.159611	−	0.595677i
$215$	−1.31655	−	1.15694i	−0.0897881	−	0.0789029i
$216$	−1.31640	−	9.02608i	−0.0895698	−	0.614147i
$217$	0.581907	−	0.335964i	0.0395024	−	0.0228067i
$218$	−3.34174	−	1.92936i	−0.226331	−	0.130672i
$219$	−19.9970	+	12.8703i	−1.35127	+	0.869696i
$220$	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
$225$	−14.6205	+	3.35281i	−0.974699	+	0.223521i
$226$	−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	$0.949513\pi$
$228$	−3.13518	+	0.151467i	−0.207633	+	0.0100311i
$229$	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
$231$	6.45808	+	1.40031i	0.424911	+	0.0921335i
$232$	−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	$0.921607\pi$
$234$	5.78785	+	17.7651i	0.378364	+	1.16134i
$235$	8.73204	−	17.6618i	0.569615	−	1.15213i
$236$	2.06371	+	7.70188i	0.134336	+	0.501349i
$237$	−0.0313766	+	0.144706i	−0.00203813	+	0.00939964i
$238$	−15.0911	−	26.1386i	−0.978213	−	1.69431i
$239$	−13.3710	+	13.3710i	−0.864899	+	0.864899i	−0.991902	−	0.127003i	$-0.959464\pi$
$239$	−13.3710	+	13.3710i	−0.864899	+	0.864899i	0.127003	+	0.991902i	$0.459464\pi$
$240$	17.7522	+	7.73436i	1.14590	+	0.499251i
$241$	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
$243$	13.6564	−	7.51685i	0.876058	−	0.482206i
$244$	−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
$249$	9.25278	−	5.95522i	0.586371	−	0.377397i
$250$	6.26322	−	18.2685i	0.396121	−	1.15540i
$251$	12.0103	+	20.8025i	0.758085	+	1.31304i	0.943826	+	0.330443i	$0.107198\pi$
$251$	12.0103	+	20.8025i	0.758085	+	1.31304i	−0.185741	+	0.982599i	$0.559468\pi$
$252$	1.55801	−	9.34221i	0.0981456	−	0.588504i
$253$	4.52975	+	1.21374i	0.284783	+	0.0763073i
$254$	7.10906	−	26.5314i	0.446062	−	1.66473i
$255$	12.5304	+	16.9599i	0.784686	+	1.06207i
$256$	−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	$0.731286\pi$
$258$	−1.97193	+	1.26917i	−0.122767	+	0.0790148i
$259$		−	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	−0.505342	−	0.862919i	$-0.668634\pi$
$263$	8.02170	−	13.8940i	0.494639	−	0.856740i	0.999981	+	0.00617933i	$0.00196695\pi$
$264$	2.67627	+	2.42959i	0.164713	+	0.149531i
$265$	2.01736	−	0.682526i	0.123925	−	0.0419272i
$266$	9.86422	+	2.64311i	0.604814	+	0.162060i
$267$	−0.442124	−	9.15144i	−0.0270575	−	0.560059i
$268$	1.65268	+	1.65268i	0.100953	+	0.100953i
$269$	9.95173	−	5.74563i	0.606767	−	0.350317i	−0.164932	−	0.986305i	$-0.552740\pi$
$269$	9.95173	−	5.74563i	0.606767	−	0.350317i	0.771699	+	0.635988i	$0.219407\pi$
$270$	−1.05395	+	20.0423i	−0.0641415	+	1.21973i
$271$	−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
$273$	−0.0978270	−	20.0417i	−0.00592076	−	1.21298i
$274$	6.58362			0.397731
$275$	3.62803	−	4.70839i	0.218779	−	0.283927i
$276$	1.42430	−	6.56871i	0.0857325	−	0.395390i
$277$	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
$279$	0.220296	+	0.588211i	0.0131888	+	0.0352153i
$280$	−9.46282	−	8.31562i	−0.565511	−	0.496953i
$281$	1.76652	+	1.76652i	0.105382	+	0.105382i	0.757832	−	0.652450i	$-0.226259\pi$
$281$	1.76652	+	1.76652i	0.105382	+	0.105382i	−0.652450	+	0.757832i	$0.726259\pi$
$282$	−19.5184	−	17.7194i	−1.16231	−	1.05517i
$283$	−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
$285$	−7.05557	−	1.05976i	−0.417936	−	0.0627746i
$286$	−6.24538	−	3.97664i	−0.369297	−	0.235144i
$287$	29.3460			1.73224
$288$	9.77385	−	11.8701i	0.575930	−	0.699450i
$289$	6.32169	−	10.9495i	0.371864	−	0.644087i
$290$	31.3440	−	2.02255i	1.84058	−	0.118768i
$291$	−1.52571	+	2.96438i	−0.0894390	+	0.173775i
$292$	−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	$0.563730\pi$
$294$	−4.51751	+	8.77729i	−0.263467	+	0.511902i
$295$	1.16709	+	18.0867i	0.0679504	+	1.05305i
$296$	6.26963	−	10.8593i	0.364415	−	0.631185i
$297$	−2.28423	+	5.73937i	−0.132545	+	0.333032i
$298$	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
$303$	15.1797	+	13.7806i	0.872053	+	0.791675i
$304$	6.51273	+	6.51273i	0.373531	+	0.373531i
$305$	−21.8286	−	19.1823i	−1.24990	−	1.09837i
$306$	26.4218	−	9.89544i	1.51043	−	0.565685i
$307$	−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
$309$	2.48711	−	11.4703i	0.141487	−	0.652523i
$310$	−0.792987	−	0.158569i	−0.0450386	−	0.00900612i
$311$	−12.7422			−0.722542			−0.361271	−	0.932461i	$-0.617657\pi$
$311$	−12.7422			−0.722542			−0.361271	+	0.932461i	$0.617657\pi$
$312$	5.43498	−	9.52068i	0.307695	−	0.539002i
$313$		−	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
$315$	7.63654	−	20.1286i	0.430270	−	1.13412i
$316$	−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	$0.792618\pi$
$318$	−0.137506	−	2.84620i	−0.00771093	−	0.159607i
$319$	9.33785	+	2.50207i	0.522819	+	0.140089i
$320$	−0.821341	−	2.42766i	−0.0459143	−	0.135710i
$321$	−6.69767	−	6.08034i	−0.373828	−	0.339372i
$322$	−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
$327$	−3.25358	+	2.09405i	−0.179923	+	0.115801i
$328$	13.9015	+	8.02601i	0.767579	+	0.443162i
$329$	14.1388	+	24.4891i	0.779498	+	1.35013i
$330$	−4.72600	−	6.39663i	−0.260158	−	0.352123i
$331$	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
$333$	21.1372	+	3.52509i	1.15831	+	0.193174i
$334$	9.06712	+	15.7047i	0.496131	+	0.859324i
$335$	2.94708	+	4.42029i	0.161016	+	0.241506i
$336$	−23.3698	+	15.0411i	−1.27492	+	0.820560i
$337$	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
$342$	−3.95393	+	8.68891i	−0.213804	+	0.469842i
$343$	−8.39758	+	8.39758i	−0.453427	+	0.453427i
$344$	1.32906	+	0.356121i	0.0716581	+	0.0192007i
$345$	6.10234	−	14.0063i	0.328539	−	0.754074i
$346$	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	$0.790355\pi$
$348$	2.93612	−	13.5411i	0.157392	−	0.725878i
$349$	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
$351$	18.4946	+	2.99166i	0.987168	+	0.159683i
$352$			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	$0.461550\pi$
$354$	23.6995	+	5.13878i	1.25962	+	0.273123i
$355$	3.98673	−	0.257254i	0.211594	−	0.0136536i
$356$	3.67957	−	3.67957i	0.195017	−	0.195017i
$357$	−30.2292	+	1.46043i	−1.59990	+	0.0772941i
$358$	8.10310	−	30.2412i	0.428262	−	1.59830i
$359$	−14.4070	−	14.4070i	−0.760371	−	0.760371i	0.216018	−	0.976389i	$-0.430693\pi$
$359$	−14.4070	−	14.4070i	−0.760371	−	0.760371i	−0.976389	+	0.216018i	$0.930693\pi$
$360$	9.12257	−	7.44652i	0.480801	−	0.392466i
$361$	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
$366$	−32.6949	+	21.0429i	−1.70899	+	1.09993i
$367$	−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
$369$	−4.51261	+	27.0586i	−0.234917	+	1.40862i
$370$	−18.2122	+	20.7247i	−0.946808	+	1.07743i
$371$	−0.791108	+	2.95245i	−0.0410723	+	0.153284i
$372$	−0.163254	+	0.317194i	−0.00846433	+	0.0164457i
$373$	−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
$375$	−13.4135	−	13.9670i	−0.692672	−	0.721252i
$376$			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
$381$	−20.3923	−	18.5127i	−1.04473	−	0.948435i
$382$	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	$-0.0245722\pi$
$384$	−21.1593	+	1.02225i	−1.07978	+	0.0521662i
$385$	2.73405	+	8.08112i	0.139340	+	0.411852i
$386$	−10.0658	+	5.81148i	−0.512334	+	0.295796i
$387$	0.226676	+	2.34049i	0.0115226	+	0.118974i
$388$	−1.82904	+	0.490089i	−0.0928552	+	0.0248805i
$389$	18.8047			0.953438			0.476719	−	0.879056i	$-0.341826\pi$
$389$	18.8047			0.953438			0.476719	+	0.879056i	$0.341826\pi$
$390$	−15.8339	+	18.1966i	−0.801779	+	0.921421i
$391$	−21.4774			−1.08616
$392$	5.59473	−	1.49910i	0.282576	−	0.0757161i
$393$	4.30849	+	0.934211i	0.217334	+	0.0471247i
$394$	−24.5764	+	14.1892i	−1.23814	+	0.714840i
$395$	−0.181073	+	0.0612617i	−0.00911076	+	0.00308241i
$396$	−3.28554	+	1.23050i	−0.165105	+	0.0618348i
$397$	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
$399$	6.88293	−	7.58174i	0.344577	−	0.379562i
$400$	3.21283	+	24.7914i	0.160641	+	1.23957i
$401$	24.4394	−	6.54850i	1.22044	−	0.327017i	0.409592	−	0.912269i	$-0.365671\pi$
$401$	24.4394	−	6.54850i	1.22044	−	0.327017i	0.810851	+	0.585252i	$0.199005\pi$
$402$	6.76932	−	2.16895i	0.337623	−	0.108177i
$403$	−0.226828	+	0.720010i	−0.0112991	+	0.0358663i
$404$			11.6442i			0.579323i
$405$	17.3854	+	10.1365i	0.863886	+	0.503688i
$406$	−22.5398	+	39.0400i	−1.11863	+	1.93752i
$407$	−7.35405	+	4.24586i	−0.364527	+	0.210459i
$408$	−14.7192	−	7.57572i	−0.728710	−	0.375054i
$409$	−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
$411$	3.02104	−	5.86972i	0.149017	−	0.289532i
$412$	5.77297	−	3.33302i	0.284414	−	0.164206i
$413$	−22.5276	−	13.0063i	−1.10851	−	0.639998i
$414$	−15.7806	−	12.9938i	−0.775576	−	0.638612i
$415$	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	0.531748	−	0.846902i	$-0.321535\pi$
$419$	1.31380	+	0.758522i	0.0641833	+	0.0370562i	−0.467565	+	0.883959i	$0.654869\pi$
$420$	11.3798	−	4.47297i	0.555277	−	0.218259i
$421$	−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
$423$	−24.7545	+	9.27100i	−1.20360	+	0.450771i
$424$	−1.18224	+	1.18224i	−0.0574145	+	0.0574145i
$425$	−10.4686	+	25.1295i	−0.507802	+	1.21896i
$426$	1.13271	−	5.22394i	0.0548799	−	0.253101i
$427$	40.2859	−	10.7946i	1.94957	−	0.522386i
$428$		−	5.13773i		−	0.248342i
$429$	−6.41126	+	3.74339i	−0.309539	+	0.180733i
$430$	−2.71389	−	1.34176i	−0.130875	−	0.0647053i
$431$	2.61881	+	9.77353i	0.126144	+	0.470775i	0.999878	−	0.0156291i	$-0.00497511\pi$
$431$	2.61881	+	9.77353i	0.126144	+	0.470775i	−0.873734	+	0.486404i	$0.838308\pi$
$432$	−10.2751	−	23.8611i	−0.494361	−	1.14802i
$433$	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
$435$	12.5797	−	28.8733i	0.603149	−	1.38437i
$436$	−2.12267	−	0.568769i	−0.101658	−	0.0272391i
$437$	5.13848	−	5.13848i	0.245807	−	0.245807i
$438$	−27.6108	+	30.4141i	−1.31929	+	1.45324i
$439$	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	$-0.365387\pi$
$443$	17.2761			0.820814			0.410407	+	0.911902i	$0.365387\pi$
$444$	6.58698	+	10.2344i	0.312604	+	0.485701i
$445$	9.84146	−	6.56146i	0.466530	−	0.311043i
$446$	−2.95026	−	5.11001i	−0.139699	−	0.241966i
$447$	1.99429	−	3.87479i	0.0943266	−	0.183271i
$448$	3.55294	+	0.952006i	0.167860	+	0.0449781i
$449$	−4.49179	+	16.7636i	−0.211980	+	0.791122i	0.775227	+	0.631682i	$0.217635\pi$
$449$	−4.49179	+	16.7636i	−0.211980	+	0.791122i	−0.987208	+	0.159439i	$0.949031\pi$
$450$	−22.8952	+	12.1305i	−1.07929	+	0.571838i
$451$	−5.43530	−	9.41421i	−0.255938	−	0.443298i
$452$	−3.99335	−	2.30556i	−0.187832	−	0.108445i
$453$	18.1056	+	28.1311i	0.850673	+	1.32171i
$454$			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
$459$	3.30181	−	28.0975i	0.154115	−	1.31148i
$460$	8.21954	−	2.78089i	0.383238	−	0.129660i
$461$	−31.4414	−	8.42468i	−1.46437	−	0.392377i	−0.563373	−	0.826203i	$-0.690497\pi$
$461$	−31.4414	−	8.42468i	−1.46437	−	0.392377i	−0.900997	+	0.433826i	$0.857163\pi$
$462$	11.4013	−	0.550818i	0.530436	−	0.0256264i
$463$	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
$465$	−0.505255	+	0.634236i	−0.0234306	+	0.0294120i
$466$	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	$-0.124004\pi$
$468$	5.80244	+	8.91943i	0.268218	+	0.412301i
$469$	−7.62489			−0.352085
$470$	6.67327	−	33.3723i	0.307815	−	1.53935i
$471$	−9.11961	−	1.97741i	−0.420209	−	0.0911142i
$472$	−7.11432	−	12.3224i	−0.327463	−	0.567183i
$473$	−0.658885	−	0.658885i	−0.0302956	−	0.0302956i
$474$	0.0123421	+	0.255468i	0.000566893	+	0.0117340i
$475$	−3.50763	−	8.51686i	−0.160941	−	0.390780i
$476$	−12.1544	−	12.1544i	−0.557097	−	0.557097i
$477$	−2.60067	−	1.18345i	−0.119077	−	0.0541864i
$478$	−16.3316	+	28.2872i	−0.746991	+	1.29383i
$479$	−2.62410	+	0.703124i	−0.119898	+	0.0321266i	−0.318269	−	0.948000i	$-0.603102\pi$
$479$	−2.62410	+	0.703124i	−0.119898	+	0.0321266i	0.198371	+	0.980127i	$0.436435\pi$
$480$	19.6304	+	2.94850i	0.895999	+	0.134580i
$481$	17.4042	+	18.9842i	0.793561	+	0.865603i
$482$	50.0895			2.28152
$483$	11.8673	+	18.4385i	0.539980	+	0.838981i
$484$	−4.71539	+	8.16730i	−0.214336	+	0.371241i
$485$	−4.29520	+	0.277159i	−0.195035	+	0.0125851i
$486$	19.4250	−	18.6472i	0.881135	−	0.845853i
$487$	−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
$489$	19.1958	+	9.87975i	0.868065	+	0.446778i
$490$	−12.7177	+	0.820644i	−0.574529	+	0.0370729i
$491$	9.72844	−	16.8501i	0.439038	−	0.760436i	−0.558577	−	0.829452i	$-0.688653\pi$
$491$	9.72844	−	16.8501i	0.439038	−	0.760436i	0.997616	+	0.0690160i	$0.0219860\pi$
$492$	−13.1014	+	8.43226i	−0.590657	+	0.380155i
$493$	−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
$498$	12.7758	−	14.0729i	0.572496	−	0.630621i
$499$	−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
$501$	18.1624	−	0.877462i	0.811437	−	0.0392021i
$502$	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	$-0.511201\pi$
$504$	1.62925	+	16.8225i	0.0725728	+	0.749332i
$505$	−5.18989	+	25.9541i	−0.230947	+	1.15494i
$506$	8.10047			0.360110
$507$	15.2969	+	16.5229i	0.679357	+	0.733808i
$508$		−	15.6428i		−	0.694035i
$509$	6.03174	+	22.5108i	0.267352	+	0.997772i	0.960795	+	0.277260i	$0.0894265\pi$
$509$	6.03174	+	22.5108i	0.267352	+	0.997772i	−0.693442	+	0.720512i	$0.743907\pi$
$510$	28.4892	+	22.6955i	1.26152	+	1.00497i
$511$	38.1596	−	22.0314i	1.68808	−	0.974613i
$512$	−5.70780	−	5.70780i	−0.252252	−	0.252252i
$513$	5.93237	+	7.51229i	0.261921	+	0.331676i
$514$	−10.7856	−	2.88998i	−0.475730	−	0.127472i
$515$	14.3530	−	4.85600i	0.632469	−	0.213981i
$516$	−0.897686	+	0.988827i	−0.0395184	+	0.0435307i
$517$	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	$-0.996523\pi$
$521$		−	0.498625i		−	0.0218452i	0.999940	−	0.0109226i	$-0.00347683\pi$
$522$	−32.5310	−	26.7862i	−1.42384	−	1.17240i
$523$	−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
$525$	27.3582	−	4.89787i	1.19401	−	0.213761i
$526$	7.17253	−	26.7682i	0.312737	−	1.16715i
$527$	1.10109	+	0.295036i	0.0479642	+	0.0128520i
$528$	9.15359	+	4.71119i	0.398359	+	0.205028i
$529$	−3.71951	−	6.44237i	−0.161718	−	0.280103i
$530$	3.06081	−	2.04069i	0.132953	−	0.0886419i
$531$	15.4566	−	18.7716i	0.670760	−	0.814619i
$532$	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
$537$	−23.2437	−	21.1013i	−1.00304	−	0.910588i
$538$	14.0357	−	14.0357i	0.605120	−	0.605120i
$539$	−3.78881	−	1.01521i	−0.163196	−	0.0437281i
$540$	2.37443	+	11.1806i	0.102179	+	0.481136i
$541$	−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
$543$	0.560050	+	0.121436i	0.0240340	+	0.00521131i
$544$	−7.22249	−	26.9547i	−0.309662	−	1.15567i
$545$	−4.47776	−	2.21382i	−0.191806	−	0.0948298i
$546$	−9.12329	−	33.3957i	−0.390441	−	1.42920i
$547$			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
$549$	3.75832	+	38.8057i	0.160401	+	1.65618i
$550$	3.94836	−	9.47789i	0.168359	−	0.404139i
$551$	10.5927	−	10.5927i	0.451266	−	0.451266i
$552$	0.578782	+	11.9801i	0.0246346	+	0.509907i
$553$	0.0710077	−	0.265004i	0.00301956	−	0.0112691i
$554$	24.1315	+	24.1315i	1.02525	+	1.02525i
$555$	10.1203	+	25.7474i	0.429585	+	1.09292i
$556$	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
$561$	6.06737	+	9.42702i	0.256164	+	0.398009i
$562$	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	$0.344435\pi$
$564$	−13.3489	−	6.87044i	−0.562090	−	0.289298i
$565$	−7.87326	−	6.91877i	−0.331231	−	0.291075i
$566$	−3.25089	+	12.1325i	−0.136645	+	0.509967i
$567$	−25.9463	+	12.6906i	−1.08964	+	0.532953i
$568$	−2.71614	+	1.56817i	−0.113967	+	0.0657988i
$569$	−15.9653	+	27.6527i	−0.669300	+	1.15926i	0.308800	+	0.951127i	$0.400072\pi$
$569$	−15.9653	+	27.6527i	−0.669300	+	1.15926i	−0.978100	+	0.208134i	$0.933261\pi$
$570$	−12.2459	+	1.38615i	−0.512926	+	0.0580593i
$571$			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
$576$	−1.42414	+	3.12961i	−0.0593393	+	0.130400i
$577$	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
$579$	0.562400	+	11.6410i	0.0233725	+	0.483784i
$580$	16.9442	−	5.73267i	0.703569	−	0.238036i
$581$	−17.6568	+	10.1942i	−0.732527	+	0.422925i
$582$	−1.22035	+	5.62814i	−0.0505852	+	0.233294i
$583$	1.09367	−	0.293048i	0.0452952	−	0.0121368i
$584$	24.1020			0.997347
$585$	8.95774	+	22.4668i	0.370357	+	0.928890i
$586$	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	$0.673826\pi$
$588$	−1.19132	+	5.49425i	−0.0491292	+	0.226579i
$589$	−0.334023	+	0.192848i	−0.0137632	+	0.00794618i
$590$	10.0333	+	29.6556i	0.413064	+	1.22090i
$591$	1.37314	+	28.4224i	0.0564835	+	1.16914i
$592$	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	$0.468779\pi$
$594$	−1.24532	+	10.5973i	−0.0510960	+	0.434813i
$595$	−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	$0.227082\pi$
$599$			32.0326i			1.30882i	−0.756142	+	0.654408i	$0.772918\pi$
$600$	14.2994	+	5.16219i	0.583769	+	0.210745i
$601$	−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
$603$	1.17250	−	7.03056i	0.0477477	−	0.286307i
$604$	−4.91768	+	18.3530i	−0.200098	+	0.746775i
$605$	−14.1504	+	16.1026i	−0.575297	+	0.654663i
$606$	31.4881	+	16.2064i	1.27912	+	0.658340i
$607$	−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
$609$	24.4638	+	38.0101i	0.991325	+	1.54025i
$610$	−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
$615$	−32.9603	+	12.9555i	−1.32909	+	0.522414i
$616$	−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	$0.981541\pi$
$618$	−0.978318	−	20.2500i	−0.0393537	−	0.814575i
$619$	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
$621$	−18.8262	+	8.10695i	−0.755468	+	0.325321i
$622$	−21.2602	+	5.69665i	−0.852455	+	0.228415i
$623$			16.9763i			0.680141i
$624$	7.93389	−	30.1985i	0.317610	−	1.20891i
$625$	6.56814	−	24.1218i	0.262726	−	0.964871i
$626$	−11.3713	−	42.4382i	−0.454488	−	1.69617i
$627$	−3.70704	−	0.803798i	−0.148045	−	0.0321006i
$628$	−2.64996	−	4.58987i	−0.105745	−	0.183156i
$629$	27.5000	−	27.5000i	1.09650	−	1.09650i
$630$	3.74259	−	36.9984i	0.149108	−	1.47405i
$631$	−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
$633$	33.7798	+	30.6663i	1.34263	+	1.21887i
$634$	−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
$639$	−4.13771	−	3.40701i	−0.163685	−	0.134779i
$640$	−15.1709	−	22.7547i	−0.599683	−	0.899458i
$641$	−5.90025	−	10.2195i	−0.233046	−	0.403647i	0.725657	−	0.688057i	$-0.241536\pi$
$641$	−5.90025	−	10.2195i	−0.233046	−	0.403647i	−0.958703	+	0.284409i	$0.908203\pi$
$642$	−13.8933	−	7.15066i	−0.548327	−	0.282214i
$643$	−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
$645$	−2.44159	+	1.80391i	−0.0961376	+	0.0710290i
$646$	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	$0.494756\pi$
$648$	−15.7618	−	1.08457i	−0.619180	−	0.0426058i
$649$			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	−0.929190	−	0.369602i	$-0.879494\pi$
$653$	−3.69279	+	6.39610i	−0.144510	+	0.250299i	0.784680	+	0.619901i	$0.212827\pi$
$654$	−4.49238	+	4.94848i	−0.175666	+	0.193501i
$655$	1.82401	+	5.39129i	0.0712701	+	0.210655i
$656$	44.1603	+	11.8327i	1.72417	+	0.461990i
$657$	14.4463	+	38.5730i	0.563603	+	1.50488i
$658$	34.5389	+	34.5389i	1.34646	+	1.34646i
$659$	−1.23199	+	0.711291i	−0.0479916	+	0.0277079i	−0.523804	−	0.851839i	$-0.675488\pi$
$659$	−1.23199	+	0.711291i	−0.0479916	+	0.0277079i	0.475812	+	0.879547i	$0.342154\pi$
$660$	−3.54262	−	2.82218i	−0.137896	−	0.109853i
$661$	−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
$663$	23.9249	−	24.1597i	0.929168	−	0.938283i
$664$	−11.1522			−0.432790
$665$	12.9631	+	2.59217i	0.502689	+	0.100520i
$666$	36.8433	−	3.56827i	1.42765	−	0.138268i
$667$	16.0391	+	27.7806i	0.621037	+	1.07567i
$668$	7.30267	+	7.30267i	0.282549	+	0.282549i
$669$	−5.90970	+	0.285509i	−0.228482	+	0.0110384i
$670$	6.89335	+	6.05765i	0.266313	+	0.234028i
$671$	−10.9244	−	10.9244i	−0.421732	−	0.421732i
$672$	−19.1500	+	21.0943i	−0.738728	+	0.813730i
$673$	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
$675$	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	$0.546813\pi$
$678$	−11.7926	+	7.58988i	−0.452892	+	0.291488i
$679$	3.08872	−	5.34983i	0.118534	−	0.205307i
$680$	−1.37619	−	21.3272i	−0.0527746	−	0.817862i
$681$	18.9400	+	9.74807i	0.725782	+	0.373547i
$682$	−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	$0.454961\pi$
$684$	−0.894323	+	5.36257i	−0.0341953	+	0.205043i
$685$	8.50486	−	0.548797i	0.324954	−	0.0209685i
$686$	−10.2570	+	17.7656i	−0.391613	+	0.678293i
$687$	−5.91020	−	9.18283i	−0.225488	−	0.350347i
$688$	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
$693$	4.74065	−	10.4177i	0.180082	−	0.395737i
$694$	6.12543	+	6.12543i	0.232518	+	0.232518i
$695$	33.7410	+	29.6505i	1.27987	+	1.12471i
$696$	1.19313	+	24.6964i	0.0452255	+	0.936115i
$697$	35.2039	+	35.2039i	1.33344	+	1.33344i
$698$	2.74952	+	4.76231i	0.104071	+	0.180256i
$699$	12.5985	+	2.73174i	0.476520	+	0.103324i
$700$	12.5039	+	9.63485i	0.472604	+	0.364163i
$701$	−38.7093			−1.46203			−0.731016	−	0.682360i	$-0.760954\pi$
$701$	−38.7093			−1.46203			−0.731016	+	0.682360i	$0.760954\pi$
$702$	32.1955	−	3.27684i	1.21514	−	0.123676i
$703$			13.1588i			0.496293i
$704$	−0.352650	−	1.31611i	−0.0132910	−	0.0496026i
$705$	−26.6914	−	21.2633i	−1.00526	−	0.800822i
$706$	−7.89989	+	4.56100i	−0.297316	+	0.171656i
$707$	−26.8613	−	26.8613i	−1.01022	−	1.01022i
$708$	13.7945	−	0.666441i	0.518430	−	0.0250464i
$709$	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
$711$	0.233429	+	0.106223i	0.00875428	+	0.00398368i
$712$	−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
$717$	17.7257	+	27.5409i	0.661980	+	1.02853i
$718$	−30.4788	−	17.5970i	−1.13746	−	0.656713i
$719$	−19.5460	−	33.8547i	−0.728944	−	1.26257i	−0.957330	−	0.288998i	$-0.906678\pi$
$719$	−19.5460	−	33.8547i	−0.728944	−	1.26257i	0.228385	−	0.973571i	$-0.426655\pi$
$720$	19.6077	−	27.2106i	0.730736	−	1.01408i
$721$	−5.62853	+	21.0060i	−0.209618	+	0.782304i
$722$	26.0391	+	6.97716i	0.969075	+	0.259663i
$723$	22.9847	−	44.6581i	0.854811	−	1.66085i
$724$	0.162738	+	0.281871i	0.00604812	+	0.0104757i
$725$	40.3223	−	5.22555i	1.49753	−	0.194072i
$726$	15.5230	+	24.1185i	0.576113	+	0.895121i
$727$	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
$732$	−14.8837	+	16.3949i	−0.550119	+	0.605972i
$733$	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
$735$	−5.10417	+	11.7153i	−0.188270	+	0.432124i
$736$	−14.2965	+	14.2965i	−0.526977	+	0.526977i
$737$	1.41224	+	2.44606i	0.0520204	+	0.0901019i
$738$	4.56788	+	47.1645i	0.168146	+	1.73615i
$739$	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
$741$	0.0561542	+	11.5043i	0.00206288	+	0.422619i
$742$			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	$0.151193\pi$
$744$	0.134898	−	0.622138i	0.00494561	−	0.0228087i
$745$	5.61434	−	0.362279i	0.205693	−	0.0132729i
$746$	−30.9653	+	30.9653i	−1.13372	+	1.13372i
$747$	−6.68443	−	17.8481i	−0.244571	−	0.653027i
$748$	−1.64797	+	6.15030i	−0.0602557	+	0.224877i
$749$	11.8519	+	11.8519i	0.433058	+	0.433058i
$750$	−28.6246	−	17.3070i	−1.04522	−	0.631962i
$751$	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
$756$	−15.2419	−	6.06616i	−0.554341	−	0.220624i
$757$	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
$759$	3.71708	−	7.22209i	0.134922	−	0.262145i
$760$	5.43180	+	4.77329i	0.197032	+	0.173145i
$761$	3.24132	−	12.0968i	0.117498	−	0.438507i	−0.881964	−	0.471317i	$-0.843779\pi$
$761$	3.24132	−	12.0968i	0.117498	−	0.438507i	0.999462	+	0.0328095i	$0.0104455\pi$
$762$	−42.3008	−	21.7715i	−1.53240	−	0.788698i
$763$	6.20870	−	3.58460i	0.224770	−	0.129771i
$764$	6.21669	−	10.7676i	0.224912	−	0.389559i
$765$	33.3074	−	14.9856i	1.20423	−	0.541806i
$766$		−	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
$771$	−7.52580	+	8.28989i	−0.271035	+	0.298553i
$772$	−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	$-0.217211\pi$
$774$	1.42457	+	3.80375i	0.0512052	+	0.136723i
$775$	−1.03762	−	0.138741i	−0.0372723	−	0.00498373i
$776$	2.92630	−	1.68950i	0.105048	−	0.0606496i
$777$	−38.8040	−	8.41388i	−1.39208	−	0.301846i
$778$	31.3755	−	8.40705i	1.12487	−	0.301407i
$779$	−16.8451			−0.603537
$780$	−6.02804	+	12.3438i	−0.215838	+	0.441980i
$781$	2.12396			0.0760012
$782$	−35.8349	+	9.60193i	−1.28145	+	0.343364i
$783$	−38.8092	+	16.7121i	−1.38693	+	0.597241i
$784$	14.2865	−	8.24830i	0.510231	−	0.294582i
$785$	−3.86082	−	11.4115i	−0.137799	−	0.407295i
$786$	7.60633	−	0.367476i	0.271309	−	0.0131074i
$787$	−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
$789$	−20.5744	−	18.6780i	−0.732466	−	0.664954i
$790$	−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
$795$	−0.414887	−	3.66532i	−0.0147145	−	0.129996i
$796$	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	$0.449805\pi$
$798$	8.09452	−	15.7272i	0.286543	−	0.556738i
$799$	−12.4164	+	46.3386i	−0.439260	+	1.63934i
$800$	9.75908	+	23.6960i	0.345036	+	0.837781i
$801$	−15.6531	−	2.61048i	−0.553074	−	0.0922369i
$802$	37.8492	−	21.8522i	1.33650	−	0.771629i
$803$	−14.1354	−	8.16105i	−0.498826	−	0.287997i
$804$	3.40410	−	2.19093i	0.120053	−	0.0772680i
$805$	−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	0.177753	−	0.984075i	$-0.443117\pi$
$809$	−16.6563	−	9.61653i	−0.585605	−	0.338099i	−0.763358	+	0.645976i	$0.776451\pi$
$810$	33.5391	+	9.14020i	1.17844	+	0.321154i
$811$	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
$813$	−20.3229	+	0.981838i	−0.712755	+	0.0344346i
$814$	−10.3720	+	10.3720i	−0.363537	+	0.363537i
$815$	1.79474	+	27.8136i	0.0628670	+	0.974267i
$816$	−46.0781	−	9.99114i	−1.61306	−	0.349760i
$817$	−1.39472	+	0.373715i	−0.0487952	+	0.0130746i
$818$			14.3873i			0.503041i
$819$	−33.9609	−	7.19036i	−1.18669	−	0.251252i
$820$	−18.0309	−	8.91455i	−0.629667	−	0.311310i
$821$	−9.41992	−	35.1556i	−0.328757	−	1.22694i	−0.910480	−	0.413553i	$-0.864288\pi$
$821$	−9.41992	−	35.1556i	−0.328757	−	1.22694i	0.581723	−	0.813387i	$-0.302379\pi$
$822$	2.41640	−	11.1442i	0.0842816	−	0.388698i
$823$	−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
$825$	−6.63836	−	7.86936i	−0.231118	−	0.273976i
$826$	−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	$0.306207\pi$
$828$	−10.5962	−	4.82185i	−0.368243	−	0.167571i
$829$	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
$834$	50.5374	−	32.5266i	1.74997	−	1.12630i
$835$	13.0222	+	19.5319i	0.450653	+	0.675928i
$836$	−1.07718	−	1.86574i	−0.0372552	−	0.0645279i
$837$	1.07653	−	0.157006i	0.0372103	−	0.00542691i
$838$	2.53118	+	0.678226i	0.0874380	+	0.0234289i
$839$	3.27587	−	12.2257i	0.113096	−	0.422079i	−0.886042	−	0.463606i	$-0.846555\pi$
$839$	3.27587	−	12.2257i	0.113096	−	0.422079i	0.999137	+	0.0415267i	$0.0132222\pi$
$840$	−17.5491	+	12.9658i	−0.605503	+	0.447361i
$841$	18.5639	+	32.1535i	0.640133	+	1.10874i
$842$	−26.7806	−	15.4618i	−0.922920	−	0.532848i
$843$	3.63858	−	2.34184i	0.125319	−	0.0806574i
$844$			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
$849$	9.32516	+	8.46565i	0.320039	+	0.290540i
$850$	−6.23210	+	46.6086i	−0.213759	+	1.59866i
$851$	−27.2174	−	7.29288i	−0.933000	−	0.249997i
$852$	−0.146900	−	3.04065i	−0.00503269	−	0.104171i
$853$	−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
$855$	−4.38349	+	11.5541i	−0.149912	+	0.395143i
$856$	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	$0.888302\pi$
$858$	−9.02357	+	9.11210i	−0.308060	+	0.311082i
$859$	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
$861$	10.7709	−	49.6745i	0.367073	−	1.69290i
$862$	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	$0.543957\pi$
$864$	−16.5053	−	20.9011i	−0.561523	−	0.711068i
$865$	24.8413	−	28.2683i	0.844630	−	0.961152i
$866$	44.8558	+	44.8558i	1.52426	+	1.52426i
$867$	−16.2141	−	14.7196i	−0.550660	−	0.499905i
$868$	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
$873$	4.45787	+	3.67062i	0.150876	+	0.124232i
$874$	6.27624	−	10.8708i	0.212297	−	0.367709i
$875$	23.5759	+	27.0483i	0.797011	+	0.914401i
$876$	−10.7057	+	20.8005i	−0.361711	+	0.702785i
$877$	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
$879$	1.67007	−	3.24486i	0.0563301	−	0.109446i
$880$	0.855827	+	13.2630i	0.0288499	+	0.447095i
$881$	−16.3359	+	28.2946i	−0.550370	+	0.953269i	0.447878	+	0.894095i	$0.352180\pi$
$881$	−16.3359	+	28.2946i	−0.550370	+	0.953269i	−0.998248	+	0.0591738i	$0.981153\pi$
$882$	13.1994	+	10.8684i	0.444446	+	0.365959i
$883$	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
$885$	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	$0.0846109\pi$
$888$	−16.0806	−	14.5984i	−0.539629	−	0.489891i
$889$	36.0852	+	36.0852i	1.21026	+	1.21026i
$890$	13.4870	−	15.3476i	0.452084	−	0.514452i
$891$	8.87674	+	5.97309i	0.297382	+	0.200106i
$892$	−2.37615	−	2.37615i	−0.0795593	−	0.0795593i
$893$	−8.11589	−	14.0571i	−0.271588	−	0.470404i
$894$	1.59514	−	7.35664i	0.0533496	−	0.246043i
$895$	7.94692	−	39.7417i	0.265636	−	1.32842i
$896$	39.2513			1.31129
$897$	−23.8263	−	6.25976i	−0.795538	−	0.209007i
$898$			29.9780i			1.00038i
$899$	−0.440659	−	1.64456i	−0.0146968	−	0.0548492i
$900$	−10.8066	+	10.0477i	−0.360220	+	0.334924i
$901$	−4.49082	+	2.59278i	−0.149611	+	0.0863779i
$902$	−13.2776	−	13.2776i	−0.442094	−	0.442094i
$903$	−0.210247	−	4.35187i	−0.00699658	−	0.144821i
$904$	7.94807	+	2.12968i	0.264349	+	0.0708321i
$905$	0.237099	+	0.700800i	0.00788145	+	0.0232954i
$906$	42.7855	+	38.8419i	1.42145	+	1.29044i
$907$	−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	$-0.888371\pi$
$911$		−	20.7385i		−	0.687097i	0.939135	−	0.343548i	$-0.111629\pi$
$912$	13.4146	−	8.63382i	0.444201	−	0.285894i
$913$	6.54057	+	3.77620i	0.216461	+	0.124974i
$914$	−18.9135	−	32.7591i	−0.625603	−	1.08358i
$915$	−40.4819	+	29.9091i	−1.33829	+	0.988764i
$916$	1.60528	−	5.99099i	0.0530400	−	0.197948i
$917$	−7.89028	−	2.11419i	−0.260560	−	0.0698168i
$918$	−7.05253	−	48.3565i	−0.232768	−	1.59600i
$919$	−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
$921$	−18.9276	+	12.1821i	−0.623687	+	0.401414i
$922$	−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
$927$	−18.5031	−	8.41995i	−0.607723	−	0.276547i
$928$	−29.4716	+	29.4716i	−0.967453	+	0.967453i
$929$	25.6186	+	6.86447i	0.840518	+	0.225216i	0.653297	−	0.757102i	$-0.273385\pi$
$929$	25.6186	+	6.86447i	0.840518	+	0.225216i	0.187221	+	0.982318i	$0.440052\pi$
$930$	−0.559464	+	1.28410i	−0.0183456	+	0.0421074i
$931$	−4.29797	+	4.29797i	−0.140860	+	0.140860i
$932$	3.66086	+	6.34080i	0.119915	+	0.207700i
$933$	−4.67678	+	21.5689i	−0.153111	+	0.706133i
$934$	−7.33855	−	27.3879i	−0.240125	−	0.896158i
$935$	−6.41440	+	12.9740i	−0.209773	+	0.424295i
$936$	−14.1210	−	12.6943i	−0.461559	−	0.414925i
$937$		−	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
$939$	−43.0544	−	9.33549i	−1.40503	−	0.304652i
$940$	−1.24807	−	19.3417i	−0.0407076	−	0.630857i
$941$	35.2291	−	35.2291i	1.14844	−	1.14844i	0.161576	−	0.986860i	$-0.448342\pi$
$941$	35.2291	−	35.2291i	1.14844	−	1.14844i	0.986860	−	0.161576i	$-0.0516576\pi$
$942$	−16.1000	+	0.777823i	−0.524567	+	0.0253429i
$943$	9.33591	−	34.8421i	0.304019	−	1.13461i
$944$	−28.6555	−	28.6555i	−0.932656	−	0.932656i
$945$	−31.2691	−	20.3143i	−1.01719	−	0.660826i
$946$	−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
$951$	−6.92322	+	4.45588i	−0.224501	+	0.144492i
$952$	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	$0.0395021\pi$
$954$	−4.86828	−	0.811890i	−0.157616	−	0.0262859i
$955$	18.6557	−	21.2293i	0.603683	−	0.686965i
$956$	−4.81452	+	17.9680i	−0.155713	+	0.581128i
$957$	7.66259	−	14.8880i	0.247696	−	0.481260i
$958$	−4.06393	+	2.34631i	−0.131300	+	0.0758059i
$959$	−6.11593	+	10.5931i	−0.197494	+	0.342069i
$960$	−4.41079	+	0.499268i	−0.142358	+	0.0161138i
$961$		−	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
$966$	28.0438	+	25.4590i	0.902294	+	0.819128i
$967$	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
$969$	17.3520	−	0.838309i	0.557426	−	0.0269304i
$970$	−7.04260	+	2.38270i	−0.226124	+	0.0765038i
$971$	5.70966	−	3.29647i	0.183232	−	0.105789i	−0.405578	−	0.914060i	$-0.632930\pi$
$971$	5.70966	−	3.29647i	0.183232	−	0.105789i	0.588810	+	0.808271i	$0.299597\pi$
$972$	7.93710	−	13.1210i	0.254583	−	0.420857i
$973$	−62.2709	+	16.6854i	−1.99631	+	0.534911i
$974$	−23.7624			−0.761396
$975$	−18.9377	+	24.8267i	−0.606492	+	0.795090i
$976$	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	$0.362142\pi$
$978$	36.4450	+	7.90238i	1.16538	+	0.252690i
$979$	5.44600	−	3.14425i	0.174055	−	0.100491i
$980$	−6.87506	+	2.32601i	−0.219616	+	0.0743018i
$981$	2.35047	+	6.27597i	0.0750446	+	0.200376i
$982$	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	$0.420800\pi$
$984$	18.6880	−	20.5854i	0.595753	−	0.656239i
$985$	−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
$990$	−12.5623	+	5.65200i	−0.399255	+	0.179632i
$991$	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
$993$	−31.5446	−	16.2354i	−1.00104	−	0.515216i
$994$	−2.56341	+	9.56678i	−0.0813065	+	0.303440i
$995$	10.7746	−	12.2610i	0.341577	−	0.388700i
$996$	4.95362	−	9.62461i	0.156961	−	0.304967i
$997$	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
$999$	13.7250	−	34.4855i	0.434241	−	1.09107i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.bh.a.59.5	✓	96	3.2	odd	2	inner
195.2.bh.a.59.6	yes	96	5.4	even	2	inner
195.2.bh.a.59.19	yes	96	1.1	even	1	trivial
195.2.bh.a.59.20	yes	96	15.14	odd	2	inner
195.2.bh.a.119.5	yes	96	65.54	odd	12	inner
195.2.bh.a.119.6	yes	96	39.2	even	12	inner
195.2.bh.a.119.19	yes	96	195.119	even	12	inner
195.2.bh.a.119.20	yes	96	13.2	odd	12	inner
975.2.bo.h.176.5		96	15.2	even	4
975.2.bo.h.176.6		96	5.3	odd	4
975.2.bo.h.176.19		96	5.2	odd	4
975.2.bo.h.176.20		96	15.8	even	4
975.2.bo.h.626.5		96	65.2	even	12
975.2.bo.h.626.6		96	195.158	odd	12
975.2.bo.h.626.19		96	195.2	odd	12
975.2.bo.h.626.20		96	65.28	even	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} +(0.367032 - 1.69272i) q^{3} +(0.851938 - 0.491866i) q^{4} +(2.11813 - 0.716618i) q^{5} +(-0.144374 - 2.98837i) q^{6} +(-0.830623 + 3.09993i) q^{7} +(-1.24129 + 1.24129i) q^{8} +(-2.73057 - 1.24256i) 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} +(-0.435610 - 3.84841i) q^{15} +(-2.49987 + 4.32990i) q^{16} +(-4.71514 + 2.72229i) q^{17} +(-5.11145 - 0.852444i) q^{18} +(0.476790 - 1.77941i) q^{19} +(1.45203 - 1.65235i) q^{20} +(4.94243 + 2.54378i) q^{21} +(1.77837 - 1.02674i) q^{22} +(3.41625 + 1.97237i) q^{23} +(1.64556 + 2.55674i) 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} +(-2.44732 - 6.22628i) q^{30} +(-0.148047 - 0.148047i) q^{31} +(-1.32655 + 4.95075i) q^{32} +(-0.0993620 - 2.05668i) q^{33} +(-6.65011 + 6.65011i) q^{34} +(0.462099 + 7.16128i) q^{35} +(-2.93745 + 0.284492i) q^{36} +(-6.89966 + 1.84876i) q^{37} -3.18208i q^{38} +(-6.02424 + 1.64575i) q^{39} +(-1.73968 + 3.51874i) q^{40} +(-2.36667 - 8.83254i) q^{41} +(9.38365 + 2.03466i) q^{42} +(-0.391907 - 0.678803i) q^{43} +(0.826939 - 0.826939i) q^{44} +(-6.67414 - 0.675125i) q^{45} +(6.58176 + 1.76358i) q^{46} +(6.23046 - 6.23046i) q^{47} +(6.41176 + 5.82078i) 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} +(-3.31901 + 8.33936i) q^{54} +(2.21175 - 1.47461i) q^{55} +(-2.81686 - 4.87895i) q^{56} +(-2.83703 - 1.46017i) q^{57} +(13.5680 + 3.63553i) q^{58} +(-2.09784 + 7.82924i) q^{59} +(-2.26402 - 3.06434i) q^{60} +(-6.49787 - 11.2546i) q^{61} +(-0.313203 - 0.180828i) q^{62} +(6.11993 - 7.43249i) 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} +(4.59254 - 5.05881i) q^{69} +(3.97261 + 11.7419i) q^{70} +(1.72575 + 0.462414i) q^{71} +(4.93181 - 1.84705i) q^{72} +(-9.70845 - 9.70845i) q^{73} +(-10.6855 + 6.16928i) q^{74} +(-3.68052 - 7.83925i) q^{75} +(-0.469034 - 1.75046i) q^{76} +3.81522i q^{77} +(-9.31563 + 5.43918i) q^{78} -0.0854873 q^{79} +(-2.19215 + 10.9627i) q^{80} +(5.91208 + 6.78582i) q^{81} +(-7.89754 - 13.6789i) q^{82} +(4.49219 + 4.49219i) q^{83} +(5.46185 - 0.263872i) q^{84} +(-8.03642 + 9.14510i) q^{85} +(-0.957366 - 0.957366i) q^{86} +(9.46729 - 10.4285i) 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} +(-0.304940 + 0.196264i) q^{93} +(7.61001 - 13.1809i) q^{94} +(-0.265252 - 4.11068i) q^{95} +(7.89332 + 4.06255i) q^{96} +(-1.85928 - 0.498193i) q^{97} +(-5.50517 - 1.47511i) q^{98} +(-3.51784 - 0.586675i) 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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