LMFDB - Embedded newform 195.2.bf.a.17.19

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [195,2,Mod(17,195)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(195, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 3, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("195.17"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 195 = 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	195.bf (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			17.19
Character	$\chi$	$=$	195.17
Dual form			195.2.bf.a.23.19

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.65038 - 0.442218i) q^{2} +(-0.744530 - 1.56387i) q^{3} +(0.796141 - 0.459652i) q^{4} +(0.908487 - 2.04320i) q^{5} +(-1.92033 - 2.25172i) q^{6} +(0.109428 + 0.0293212i) q^{7} +(-1.30565 + 1.30565i) q^{8} +(-1.89135 + 2.32869i) q^{9} +(0.595810 - 3.77380i) q^{10} +(2.05447 - 3.55845i) q^{11} +(-1.31159 - 0.902832i) q^{12} +(3.24500 + 1.57162i) q^{13} +0.193564 q^{14} +(-3.87168 + 0.100470i) q^{15} +(-2.49674 + 4.32449i) q^{16} +(-5.04353 - 1.35141i) q^{17} +(-2.09165 + 4.67961i) q^{18} +(3.97662 + 6.88771i) q^{19} +(-0.215876 - 2.04426i) q^{20} +(-0.0356182 - 0.192962i) q^{21} +(1.81705 - 6.78132i) q^{22} +(6.69524 - 1.79398i) q^{23} +(3.01397 + 1.06977i) q^{24} +(-3.34930 - 3.71244i) q^{25} +(6.05047 + 1.15878i) q^{26} +(5.04992 + 1.22403i) q^{27} +(0.100598 - 0.0269551i) q^{28} +(-2.00973 + 3.48095i) q^{29} +(-6.34531 + 1.87794i) q^{30} +6.89468i q^{31} +(-1.25240 + 4.67403i) q^{32} +(-7.09456 - 0.563544i) q^{33} -8.92135 q^{34} +(0.159323 - 0.196946i) q^{35} +(-0.435393 + 2.72333i) q^{36} +(-1.09950 - 4.10339i) q^{37} +(9.60880 + 9.60880i) q^{38} +(0.0418074 - 6.24486i) q^{39} +(1.48154 + 3.85388i) q^{40} +(-1.73822 + 3.01068i) q^{41} +(-0.144115 - 0.302709i) q^{42} +(-4.88872 - 1.30993i) q^{43} -3.77737i q^{44} +(3.03971 + 5.97998i) q^{45} +(10.2563 - 5.92150i) q^{46} +(-0.185543 - 0.185543i) q^{47} +(8.62182 + 0.684859i) q^{48} +(-6.05106 - 3.49358i) q^{49} +(-7.16932 - 4.64580i) q^{50} +(1.64164 + 8.89356i) q^{51} +(3.30587 - 0.240337i) q^{52} +(-1.94409 - 1.94409i) q^{53} +(8.87558 - 0.213046i) q^{54} +(-5.40416 - 7.43050i) q^{55} +(-0.181159 + 0.104592i) q^{56} +(7.81074 - 11.3470i) q^{57} +(-1.77747 + 6.63362i) q^{58} +(-0.619675 + 0.357770i) q^{59} +(-3.03622 + 1.85961i) q^{60} +(2.04160 + 3.53616i) q^{61} +(3.04895 + 11.3788i) q^{62} +(-0.275247 + 0.199368i) q^{63} -1.71922i q^{64} +(6.15917 - 5.20237i) q^{65} +(-11.9579 + 2.20728i) q^{66} +(-0.764792 - 2.85424i) q^{67} +(-4.63654 + 1.24236i) q^{68} +(-7.79036 - 9.13477i) q^{69} +(0.175851 - 0.395490i) q^{70} +(-4.25380 - 7.36780i) q^{71} +(-0.571017 - 5.50991i) q^{72} +(-3.00868 - 3.00868i) q^{73} +(-3.62918 - 6.28592i) q^{74} +(-3.31209 + 8.00188i) q^{75} +(6.33191 + 3.65573i) q^{76} +(0.329156 - 0.329156i) q^{77} +(-2.69259 - 10.3249i) q^{78} +4.84485i q^{79} +(6.56752 + 9.03008i) q^{80} +(-1.84560 - 8.80873i) q^{81} +(-1.53734 + 5.73743i) q^{82} +(2.04442 - 2.04442i) q^{83} +(-0.117052 - 0.137253i) q^{84} +(-7.34318 + 9.07718i) q^{85} -8.64751 q^{86} +(6.94004 + 0.551270i) q^{87} +(1.96368 + 7.32854i) q^{88} +(2.79966 + 1.61638i) q^{89} +(7.66112 + 8.52502i) q^{90} +(0.309013 + 0.267127i) q^{91} +(4.50574 - 4.50574i) q^{92} +(10.7823 - 5.13330i) q^{93} +(-0.388267 - 0.224166i) q^{94} +(17.6857 - 1.86762i) q^{95} +(8.24201 - 1.52137i) q^{96} +(0.144327 + 0.0386722i) q^{97} +(-11.5315 - 3.08985i) q^{98} +(4.40081 + 11.5145i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 2 q^{3} - 12 q^{6} - 12 q^{7} + 4 q^{10} - 12 q^{12} - 24 q^{13} - 6 q^{15} + 16 q^{16} + 20 q^{22} - 16 q^{25} - 32 q^{27} - 36 q^{28} + 30 q^{33} - 4 q^{36} - 84 q^{37} - 152 q^{40} - 48 q^{42}+ \cdots - 48 q^{97}+O(q^{100}) $ 96 * q - 2 * q^3 - 12 * q^6 - 12 * q^7 + 4 * q^10 - 12 * q^12 - 24 * q^13 - 6 * q^15 + 16 * q^16 + 20 * q^22 - 16 * q^25 - 32 * q^27 - 36 * q^28 + 30 * q^33 - 4 * q^36 - 84 * q^37 - 152 * q^40 - 48 * q^42 + 8 * q^43 + 54 * q^45 - 28 * q^48 - 16 * q^51 + 28 * q^52 - 40 * q^55 + 84 * q^58 - 32 * q^61 + 90 * q^63 + 36 * q^67 + 90 * q^72 - 20 * q^75 + 72 * q^76 + 60 * q^78 + 32 * q^81 - 68 * q^82 + 84 * q^85 - 26 * q^87 - 108 * q^88 - 20 * q^90 - 80 * q^91 + 48 * q^93 - 48 * q^97

Character values

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

$n$	$106$	$131$	$157$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	1.65038	−	0.442218i	1.16699	−	0.312695i	0.377238	−	0.926116i	$-0.376874\pi$
$2$	1.65038	−	0.442218i	1.16699	−	0.312695i	0.789756	+	0.613421i	$0.210207\pi$
$3$	−0.744530	−	1.56387i	−0.429855	−	0.902898i
$3$	−0.744530	−	1.56387i	−0.429855	−	0.902898i
$4$	0.796141	−	0.459652i	0.398071	−	0.229826i
$5$	0.908487	−	2.04320i	0.406288	−	0.913745i
$5$	0.908487	−	2.04320i	0.406288	−	0.913745i
$6$	−1.92033	−	2.25172i	−0.783970	−	0.919263i
$7$	0.109428	+	0.0293212i	0.0413600	+	0.0110824i	0.279440	−	0.960163i	$-0.409851\pi$
$7$	0.109428	+	0.0293212i	0.0413600	+	0.0110824i	−0.238080	+	0.971246i	$0.576518\pi$
$8$	−1.30565	+	1.30565i	−0.461618	+	0.461618i
$9$	−1.89135	+	2.32869i	−0.630450	+	0.776230i
$10$	0.595810	−	3.77380i	0.188412	−	1.19338i
$11$	2.05447	−	3.55845i	0.619447	−	1.07291i	−0.370139	−	0.928976i	$-0.620690\pi$
$11$	2.05447	−	3.55845i	0.619447	−	1.07291i	0.989587	−	0.143938i	$-0.0459766\pi$
$12$	−1.31159	−	0.902832i	−0.378622	−	0.260625i
$13$	3.24500	+	1.57162i	0.900000	+	0.435890i
$13$	3.24500	+	1.57162i	0.900000	+	0.435890i
$14$	0.193564			0.0517323
$15$	−3.87168	+	0.100470i	−0.999663	+	0.0259413i
$16$	−2.49674	+	4.32449i	−0.624186	+	1.08112i
$17$	−5.04353	−	1.35141i	−1.22324	−	0.327765i	−0.411293	−	0.911503i	$-0.634923\pi$
$17$	−5.04353	−	1.35141i	−1.22324	−	0.327765i	−0.811942	+	0.583738i	$0.801589\pi$
$18$	−2.09165	+	4.67961i	−0.493007	+	1.10299i
$19$	3.97662	+	6.88771i	0.912300	+	1.58015i	0.810807	+	0.585313i	$0.199029\pi$
$19$	3.97662	+	6.88771i	0.912300	+	1.58015i	0.101493	+	0.994836i	$0.467638\pi$
$20$	−0.215876	−	2.04426i	−0.0482713	−	0.457111i
$21$	−0.0356182	−	0.192962i	−0.00777254	−	0.0421077i
$22$	1.81705	−	6.78132i	0.387396	−	1.44578i
$23$	6.69524	−	1.79398i	1.39605	−	0.374071i	0.519127	−	0.854697i	$-0.326257\pi$
$23$	6.69524	−	1.79398i	1.39605	−	0.374071i	0.876926	+	0.480625i	$0.159590\pi$
$24$	3.01397	+	1.06977i	0.615223	+	0.218365i
$25$	−3.34930	−	3.71244i	−0.669860	−	0.742487i
$26$	6.05047	+	1.15878i	1.18659	+	0.227255i
$27$	5.04992	+	1.22403i	0.971858	+	0.235565i
$28$	0.100598	−	0.0269551i	0.0190112	−	0.00509404i
$29$	−2.00973	+	3.48095i	−0.373197	+	0.646396i	−0.990055	−	0.140678i	$-0.955072\pi$
$29$	−2.00973	+	3.48095i	−0.373197	+	0.646396i	0.616858	+	0.787074i	$0.288405\pi$
$30$	−6.34531	+	1.87794i	−1.15849	+	0.342863i
$31$			6.89468i			1.23832i	0.785265	+	0.619160i	$0.212527\pi$
$31$			6.89468i			1.23832i	−0.785265	+	0.619160i	$0.787473\pi$
$32$	−1.25240	+	4.67403i	−0.221396	+	0.826260i
$33$	−7.09456	−	0.563544i	−1.23500	−	0.0981004i
$34$	−8.92135			−1.53000
$35$	0.159323	−	0.196946i	0.0269305	−	0.0332899i
$36$	−0.435393	+	2.72333i	−0.0725655	+	0.453888i
$37$	−1.09950	−	4.10339i	−0.180757	−	0.674593i	−0.995499	−	0.0947700i	$-0.969788\pi$
$37$	−1.09950	−	4.10339i	−0.180757	−	0.674593i	0.814743	−	0.579823i	$-0.196878\pi$
$38$	9.60880	+	9.60880i	1.55875	+	1.55875i
$39$	0.0418074	−	6.24486i	0.00669454	−	0.999978i
$40$	1.48154	+	3.85388i	0.234252	+	0.609351i
$41$	−1.73822	+	3.01068i	−0.271464	+	0.470189i	−0.969237	−	0.246130i	$-0.920841\pi$
$41$	−1.73822	+	3.01068i	−0.271464	+	0.470189i	0.697773	+	0.716319i	$0.254174\pi$
$42$	−0.144115	−	0.302709i	−0.0222374	−	0.0467090i
$43$	−4.88872	−	1.30993i	−0.745523	−	0.199762i	−0.133991	−	0.990982i	$-0.542779\pi$
$43$	−4.88872	−	1.30993i	−0.745523	−	0.199762i	−0.611531	+	0.791220i	$0.709446\pi$
$44$		−	3.77737i		−	0.569461i
$45$	3.03971	+	5.97998i	0.453133	+	0.891443i
$46$	10.2563	−	5.92150i	1.51222	−	0.873078i
$47$	−0.185543	−	0.185543i	−0.0270642	−	0.0270642i	0.693445	−	0.720509i	$-0.256092\pi$
$47$	−0.185543	−	0.185543i	−0.0270642	−	0.0270642i	−0.720509	+	0.693445i	$0.756092\pi$
$48$	8.62182	+	0.684859i	1.24445	+	0.0988509i
$49$	−6.05106	−	3.49358i	−0.864438	−	0.499083i
$50$	−7.16932	−	4.64580i	−1.01389	−	0.657016i
$51$	1.64164	+	8.89356i	0.229875	+	1.24535i
$52$	3.30587	−	0.240337i	0.458442	−	0.0333287i
$53$	−1.94409	−	1.94409i	−0.267042	−	0.267042i	0.560865	−	0.827907i	$-0.310469\pi$
$53$	−1.94409	−	1.94409i	−0.267042	−	0.267042i	−0.827907	+	0.560865i	$0.810469\pi$
$54$	8.87558	−	0.213046i	1.20781	−	0.0289919i
$55$	−5.40416	−	7.43050i	−0.728696	−	1.00193i
$56$	−0.181159	+	0.104592i	−0.0242084	+	0.0139767i
$57$	7.81074	−	11.3470i	1.03456	−	1.50295i
$58$	−1.77747	+	6.63362i	−0.233394	+	0.871037i
$59$	−0.619675	+	0.357770i	−0.0806749	+	0.0465777i	−0.539795	−	0.841797i	$-0.681498\pi$
$59$	−0.619675	+	0.357770i	−0.0806749	+	0.0465777i	0.459120	+	0.888374i	$0.348165\pi$
$60$	−3.03622	+	1.85961i	−0.391975	+	0.240075i
$61$	2.04160	+	3.53616i	0.261400	+	0.452758i	0.966614	−	0.256236i	$-0.0824825\pi$
$61$	2.04160	+	3.53616i	0.261400	+	0.452758i	−0.705214	+	0.708994i	$0.749149\pi$
$62$	3.04895	+	11.3788i	0.387217	+	1.44511i
$63$	−0.275247	+	0.199368i	−0.0346779	+	0.0251180i
$64$		−	1.71922i		−	0.214903i
$65$	6.15917	−	5.20237i	0.763951	−	0.645274i
$66$	−11.9579	+	2.20728i	−1.47192	+	0.271697i
$67$	−0.764792	−	2.85424i	−0.0934343	−	0.348701i	0.903343	−	0.428919i	$-0.141105\pi$
$67$	−0.764792	−	2.85424i	−0.0934343	−	0.348701i	−0.996777	+	0.0802172i	$0.974439\pi$
$68$	−4.63654	+	1.24236i	−0.562263	+	0.150658i
$69$	−7.79036	−	9.13477i	−0.937849	−	1.09970i
$70$	0.175851	−	0.395490i	0.0210182	−	0.0472701i
$71$	−4.25380	−	7.36780i	−0.504833	−	0.874397i	−0.999984	−	0.00558990i	$-0.998221\pi$
$71$	−4.25380	−	7.36780i	−0.504833	−	0.874397i	0.495151	−	0.868807i	$-0.335113\pi$
$72$	−0.571017	−	5.50991i	−0.0672949	−	0.649349i
$73$	−3.00868	−	3.00868i	−0.352139	−	0.352139i	0.508766	−	0.860905i	$-0.330102\pi$
$73$	−3.00868	−	3.00868i	−0.352139	−	0.352139i	−0.860905	+	0.508766i	$0.830102\pi$
$74$	−3.62918	−	6.28592i	−0.421884	−	0.730724i
$75$	−3.31209	+	8.00188i	−0.382447	+	0.923977i
$76$	6.33191	+	3.65573i	0.726319	+	0.419341i
$77$	0.329156	−	0.329156i	0.0375108	−	0.0375108i
$78$	−2.69259	−	10.3249i	−0.304876	−	1.16906i
$79$			4.84485i			0.545088i	0.962143	+	0.272544i	$0.0878650\pi$
$79$			4.84485i			0.545088i	−0.962143	+	0.272544i	$0.912135\pi$
$80$	6.56752	+	9.03008i	0.734271	+	1.00959i
$81$	−1.84560	−	8.80873i	−0.205066	−	0.978748i
$82$	−1.53734	+	5.73743i	−0.169771	+	0.633593i
$83$	2.04442	−	2.04442i	0.224405	−	0.224405i	−0.585946	−	0.810350i	$-0.699277\pi$
$83$	2.04442	−	2.04442i	0.224405	−	0.224405i	0.810350	+	0.585946i	$0.199277\pi$
$84$	−0.117052	−	0.137253i	−0.0127715	−	0.0149755i
$85$	−7.34318	+	9.07718i	−0.796479	+	0.984558i
$86$	−8.64751			−0.932485
$87$	6.94004	+	0.551270i	0.744050	+	0.0591023i
$88$	1.96368	+	7.32854i	0.209329	+	0.781225i
$89$	2.79966	+	1.61638i	0.296763	+	0.171336i	0.640988	−	0.767551i	$-0.278525\pi$
$89$	2.79966	+	1.61638i	0.296763	+	0.171336i	−0.344225	+	0.938887i	$0.611858\pi$
$90$	7.66112	+	8.52502i	0.807553	+	0.898616i
$91$	0.309013	+	0.267127i	0.0323933	+	0.0280025i
$92$	4.50574	−	4.50574i	0.469756	−	0.469756i
$93$	10.7823	−	5.13330i	1.11808	−	0.532298i
$94$	−0.388267	−	0.224166i	−0.0400466	−	0.0231209i
$95$	17.6857	−	1.86762i	1.81451	−	0.191614i
$96$	8.24201	−	1.52137i	0.841196	−	0.155274i
$97$	0.144327	+	0.0386722i	0.0146542	+	0.00392657i	0.266139	−	0.963935i	$-0.414252\pi$
$97$	0.144327	+	0.0386722i	0.0146542	+	0.00392657i	−0.251485	+	0.967861i	$0.580919\pi$
$98$	−11.5315	−	3.08985i	−1.16485	−	0.312122i
$99$	4.40081	+	11.5145i	0.442298	+	1.15725i
$100$	−4.37295	−	1.41611i	−0.437295	−	0.141611i
$101$	−10.5103	−	6.06812i	−1.04581	−	0.603800i	−0.124339	−	0.992240i	$-0.539681\pi$
$101$	−10.5103	−	6.06812i	−1.04581	−	0.603800i	−0.921474	+	0.388440i	$0.873014\pi$
$102$	6.64221	+	13.9518i	0.657677	+	1.38143i
$103$	0.528320	−	0.528320i	0.0520569	−	0.0520569i	−0.680599	−	0.732656i	$-0.738280\pi$
$103$	0.528320	−	0.528320i	0.0520569	−	0.0520569i	0.732656	+	0.680599i	$0.238280\pi$
$104$	−6.28884	+	2.18485i	−0.616671	+	0.214242i
$105$	−0.426617	−	0.102528i	−0.0416336	−	0.0100057i
$106$	−4.06820	−	2.34878i	−0.395139	−	0.228133i
$107$	−0.427445	−	1.59525i	−0.0413227	−	0.154218i	0.942182	−	0.335102i	$-0.108771\pi$
$107$	−0.427445	−	1.59525i	−0.0413227	−	0.154218i	−0.983504	+	0.180884i	$0.942104\pi$
$108$	4.58308	−	1.34671i	0.441007	−	0.129587i
$109$	−0.638870			−0.0611926			−0.0305963	−	0.999532i	$-0.509741\pi$
$109$	−0.638870			−0.0611926			−0.0305963	+	0.999532i	$0.509741\pi$
$110$	−12.2048	−	9.87333i	−1.16368	−	0.941385i
$111$	−5.59853	+	4.77457i	−0.531389	+	0.453182i
$112$	−0.400014	+	0.400014i	−0.0377977	+	0.0377977i
$113$	−2.04834	+	7.64451i	−0.192692	+	0.719135i	0.800161	+	0.599786i	$0.204747\pi$
$113$	−2.04834	+	7.64451i	−0.192692	+	0.719135i	−0.992852	+	0.119349i	$0.961919\pi$
$114$	7.87282	−	22.1809i	0.737357	−	2.07743i
$115$	2.41708	−	15.3095i	0.225394	−	1.42762i
$116$			3.69510i			0.343082i
$117$	−9.79724	+	4.58411i	−0.905755	+	0.423801i
$118$	−0.864487	+	0.864487i	−0.0795825	+	0.0795825i
$119$	−0.512280	−	0.295765i	−0.0469606	−	0.0271127i
$120$	4.92389	−	5.18625i	0.449488	−	0.473438i
$121$	−2.94173	−	5.09522i	−0.267430	−	0.463202i
$122$	4.93316	+	4.93316i	0.446628	+	0.446628i
$123$	6.00245	+	0.476794i	0.541223	+	0.0429911i
$124$	3.16915	+	5.48913i	0.284598	+	0.492939i
$125$	−10.6280	+	3.47058i	−0.950600	+	0.310418i
$126$	−0.366098	+	0.450752i	−0.0326146	+	0.0401561i
$127$	12.3036	−	3.29674i	1.09177	−	0.292539i	0.332361	−	0.943152i	$-0.392155\pi$
$127$	12.3036	−	3.29674i	1.09177	−	0.292539i	0.759409	+	0.650614i	$0.225488\pi$
$128$	−3.26508	−	12.1854i	−0.288595	−	1.07705i
$129$	1.59125	+	8.62058i	0.140102	+	0.759000i
$130$	7.86438	−	11.3096i	0.689752	−	0.991914i
$131$			12.9569i			1.13205i	0.824390	+	0.566023i	$0.191519\pi$
$131$			12.9569i			1.13205i	−0.824390	+	0.566023i	$0.808481\pi$
$132$	−5.90731	+	2.81237i	−0.514165	+	0.244785i
$133$	0.233199	+	0.870310i	0.0202209	+	0.0754655i
$134$	−2.52439	−	4.37238i	−0.218074	−	0.377716i
$135$	7.08873	−	9.20597i	0.610101	−	0.792324i
$136$	8.34958	−	4.82063i	0.715970	−	0.413366i
$137$	3.22490	−	12.0355i	0.275522	−	1.02826i	−0.679969	−	0.733241i	$-0.738007\pi$
$137$	3.22490	−	12.0355i	0.275522	−	1.02826i	0.955491	−	0.295021i	$-0.0953267\pi$
$138$	−16.8966	−	11.6308i	−1.43833	−	0.990079i
$139$	3.31851	−	1.91594i	0.281472	−	0.162508i	−0.352618	−	0.935767i	$-0.614708\pi$
$139$	3.31851	−	1.91594i	0.281472	−	0.162508i	0.634090	+	0.773260i	$0.281375\pi$
$140$	0.0363173	−	0.230030i	0.00306937	−	0.0194411i
$141$	−0.152022	+	0.428307i	−0.0128026	+	0.0360699i
$142$	−10.2785	−	10.2785i	−0.862557	−	0.862557i
$143$	12.2593	−	8.31831i	1.02517	−	0.695612i
$144$	−5.34818	−	13.9933i	−0.445682	−	1.16610i
$145$	5.28645	+	7.26867i	0.439016	+	0.603630i
$146$	−6.29594	−	3.63496i	−0.521056	−	0.300832i
$147$	−0.958292	+	12.0641i	−0.0790386	+	0.995032i
$148$	−2.76149	−	2.76149i	−0.226993	−	0.226993i
$149$	−10.3032	+	5.94857i	−0.844073	+	0.487326i	−0.858647	−	0.512568i	$-0.828694\pi$
$149$	−10.3032	+	5.94857i	−0.844073	+	0.487326i	0.0145735	+	0.999894i	$0.495361\pi$
$150$	−1.92763	+	14.6708i	−0.157391	+	1.19786i
$151$			11.1014i			0.903416i	0.892166	+	0.451708i	$0.149185\pi$
$151$			11.1014i			0.903416i	−0.892166	+	0.451708i	$0.850815\pi$
$152$	−14.1851	−	3.80088i	−1.15056	−	0.308292i
$153$	12.6861	−	9.18883i	1.02561	−	0.742873i
$154$	0.397673	−	0.688790i	0.0320454	−	0.0555043i
$155$	14.0872	+	6.26372i	1.13151	+	0.503114i
$156$	−2.83718	−	4.99100i	−0.227156	−	0.399600i
$157$	5.53986	+	5.53986i	0.442129	+	0.442129i	0.892727	−	0.450598i	$-0.148789\pi$
$157$	5.53986	+	5.53986i	0.442129	+	0.442129i	−0.450598	+	0.892727i	$0.648789\pi$
$158$	2.14248	+	7.99583i	0.170446	+	0.636114i
$159$	−1.59286	+	4.48774i	−0.126322	+	0.355901i
$160$	8.41217	+	6.80520i	0.665041	+	0.537999i
$161$	0.785250			0.0618864
$162$	−6.94131	−	13.7216i	−0.545361	−	1.07807i
$163$	3.17233	−	11.8393i	0.248476	−	0.927326i	−0.723128	−	0.690714i	$-0.757296\pi$
$163$	3.17233	−	11.8393i	0.248476	−	0.927326i	0.971604	−	0.236612i	$-0.0760369\pi$
$164$			3.19590i			0.249558i
$165$	−7.59675	+	13.9836i	−0.591406	+	1.08862i
$166$	2.46999	−	4.27815i	0.191708	−	0.332049i
$167$	−8.61742	+	2.30903i	−0.666836	+	0.178678i	−0.576329	−	0.817218i	$-0.695515\pi$
$167$	−8.61742	+	2.30903i	−0.666836	+	0.178678i	−0.0905069	+	0.995896i	$0.528849\pi$
$168$	0.298446	+	0.205436i	0.0230256	+	0.0158497i
$169$	8.06000	+	10.1998i	0.620000	+	0.784602i
$170$	−8.10493	+	18.2281i	−0.621620	+	1.39803i
$171$	−23.5605	−	3.76674i	−1.80172	−	0.288050i
$172$	−4.49422	+	1.20422i	−0.342681	+	0.0918211i
$173$	−2.27704	+	8.49801i	−0.173120	+	0.646092i	0.823744	+	0.566961i	$0.191881\pi$
$173$	−2.27704	+	8.49801i	−0.173120	+	0.646092i	−0.996864	+	0.0791307i	$0.974786\pi$
$174$	11.6975	−	2.15920i	0.886783	−	0.163689i
$175$	−0.257655	−	0.504451i	−0.0194769	−	0.0381329i
$176$	10.2590	+	17.7691i	0.773301	+	1.33940i
$177$	1.02087	+	0.702718i	0.0767334	+	0.0528196i
$178$	5.33529	+	1.42959i	0.399897	+	0.107152i
$179$	−9.95273	+	17.2386i	−0.743902	+	1.28848i	0.206804	+	0.978382i	$0.433694\pi$
$179$	−9.95273	+	17.2386i	−0.743902	+	1.28848i	−0.950706	+	0.310094i	$0.899640\pi$
$180$	5.16875	+	3.36370i	0.385256	+	0.250716i
$181$	7.45086			0.553818			0.276909	−	0.960896i	$-0.410690\pi$
$181$	7.45086			0.553818			0.276909	+	0.960896i	$0.410690\pi$
$182$	0.628116	+	0.304210i	0.0465590	+	0.0225496i
$183$	4.01004	−	5.82556i	0.296430	−	0.430638i
$184$	−6.39934	+	11.0840i	−0.471766	+	0.817122i
$185$	−9.38291	−	1.48138i	−0.689845	−	0.108913i
$186$	15.5249	−	13.2400i	1.13834	−	0.970805i
$187$	−15.1707	+	15.1707i	−1.10939	+	1.10939i
$188$	−0.233004	−	0.0624332i	−0.0169935	−	0.00455341i
$189$	0.516714	+	0.282014i	0.0375854	+	0.0205135i
$190$	28.3621	−	10.9032i	2.05761	−	0.791001i
$191$	19.8776	−	11.4763i	1.43829	−	0.830399i	0.440562	−	0.897722i	$-0.354779\pi$
$191$	19.8776	−	11.4763i	1.43829	−	0.830399i	0.997731	+	0.0673227i	$0.0214457\pi$
$192$	−2.68863	+	1.28001i	−0.194035	+	0.0923770i
$193$	−21.1680	+	5.67196i	−1.52371	+	0.408276i	−0.920961	−	0.389655i	$-0.872594\pi$
$193$	−21.1680	+	5.67196i	−1.52371	+	0.408276i	−0.602748	+	0.797932i	$0.705928\pi$
$194$	0.255295			0.0183291
$195$	−12.7215	−	5.75879i	−0.911005	−	0.412396i
$196$	−6.42333			−0.458810
$197$	8.39781	−	2.25019i	0.598319	−	0.160319i	0.0530668	−	0.998591i	$-0.483100\pi$
$197$	8.39781	−	2.25019i	0.598319	−	0.160319i	0.545253	+	0.838272i	$0.316434\pi$
$198$	12.3549	+	17.0572i	0.878026	+	1.21220i
$199$	17.5413	−	10.1275i	1.24347	−	0.717919i	0.273673	−	0.961823i	$-0.411761\pi$
$199$	17.5413	−	10.1275i	1.24347	−	0.717919i	0.969799	+	0.243904i	$0.0784282\pi$
$200$	9.22018	+	0.474126i	0.651965	+	0.0335258i
$201$	−3.89424	+	3.32110i	−0.274679	+	0.234253i
$202$	−20.0294	−	5.36686i	−1.40926	−	0.377611i
$203$	−0.321987	+	0.321987i	−0.0225990	+	0.0225990i
$204$	5.39492	+	6.32595i	0.377720	+	0.442905i
$205$	4.57226	+	6.28668i	0.319341	+	0.439081i
$206$	0.638295	−	1.10556i	0.0444721	−	0.0770280i
$207$	−8.48540	+	18.9842i	−0.589776	+	1.31949i
$208$	−14.8984	+	10.1090i	−1.03302	+	0.700934i
$209$	32.6795			2.26049
$210$	−0.749420	+	0.0194475i	−0.0517149	+	0.00134200i
$211$	3.64767	−	6.31794i	0.251116	−	0.434945i	−0.712718	−	0.701451i	$-0.752536\pi$
$211$	3.64767	−	6.31794i	0.251116	−	0.434945i	0.963833	+	0.266506i	$0.0858692\pi$
$212$	−2.44138	−	0.654166i	−0.167675	−	0.0449283i
$213$	−8.35516	+	12.1379i	−0.572486	+	0.831677i
$214$	−1.41089	−	2.44374i	−0.0964466	−	0.167050i
$215$	−7.11778	+	8.79856i	−0.485428	+	0.600057i
$216$	−8.19162	+	4.99529i	−0.557369	+	0.339886i
$217$	−0.202160	+	0.754473i	−0.0137235	+	0.0512169i
$218$	−1.05438	+	0.282519i	−0.0714114	+	0.0191346i
$219$	−2.46511	+	6.94521i	−0.166577	+	0.469314i
$220$	−7.71792	−	3.43170i	−0.520342	−	0.231365i
$221$	−14.2423	−	12.3118i	−0.958043	−	0.828184i
$222$	−7.12830	+	10.3556i	−0.478420	+	0.695023i
$223$	−11.7287	+	3.14269i	−0.785411	+	0.210450i	−0.629169	−	0.777268i	$-0.716605\pi$
$223$	−11.7287	+	3.14269i	−0.785411	+	0.210450i	−0.156242	+	0.987719i	$0.549938\pi$
$224$	−0.274097	+	0.474749i	−0.0183139	+	0.0317205i
$225$	14.9798	−	0.777977i	0.998654	−	0.0518651i
$226$			13.5221i			0.899479i
$227$	−3.58919	+	13.3950i	−0.238223	+	0.889061i	0.738446	+	0.674312i	$0.235560\pi$
$227$	−3.58919	+	13.3950i	−0.238223	+	0.889061i	−0.976669	+	0.214748i	$0.931107\pi$
$228$	1.00277	−	12.6240i	0.0664100	−	0.836048i
$229$	−8.51901			−0.562952			−0.281476	−	0.959568i	$-0.590824\pi$
$229$	−8.51901			−0.562952			−0.281476	+	0.959568i	$0.590824\pi$
$230$	−2.78104	−	26.3353i	−0.183376	−	1.73650i
$231$	−0.759822	−	0.269689i	−0.0499926	−	0.0177442i
$232$	−1.92091	−	7.16892i	−0.126114	−	0.470663i
$233$	8.61258	+	8.61258i	0.564229	+	0.564229i	0.930506	−	0.366277i	$-0.119368\pi$
$233$	8.61258	+	8.61258i	0.564229	+	0.564229i	−0.366277	+	0.930506i	$0.619368\pi$
$234$	−14.1420	+	11.8980i	−0.924490	+	0.777798i
$235$	−0.547664	+	0.210537i	−0.0357257	+	0.0137339i
$236$	−0.328899	+	0.569670i	−0.0214095	+	0.0370824i
$237$	7.57669	−	3.60714i	0.492159	−	0.234309i
$238$	−0.976248	−	0.261585i	−0.0632807	−	0.0169560i
$239$		−	11.5531i		−	0.747310i	−0.927568	−	0.373655i	$-0.878104\pi$
$239$		−	11.5531i		−	0.747310i	0.927568	−	0.373655i	$-0.121896\pi$
$240$	9.23211	−	16.9939i	0.595930	−	1.09695i
$241$	12.0934	−	6.98212i	0.779004	−	0.449758i	−0.0570731	−	0.998370i	$-0.518177\pi$
$241$	12.0934	−	6.98212i	0.779004	−	0.449758i	0.836077	+	0.548612i	$0.184843\pi$
$242$	−7.10816	−	7.10816i	−0.456930	−	0.456930i
$243$	−12.4016	+	9.44464i	−0.795561	+	0.605874i
$244$	3.25080	+	1.87685i	0.208111	+	0.120153i
$245$	−12.6354	+	9.18963i	−0.807245	+	0.587104i
$246$	10.1172	−	1.86750i	0.645047	−	0.119067i
$247$	2.07924	+	28.6004i	0.132299	+	1.81980i
$248$	−9.00206	−	9.00206i	−0.571631	−	0.571631i
$249$	−4.71934	−	1.67507i	−0.299076	−	0.106153i
$250$	−16.0055	+	10.4277i	−1.01228	+	0.659504i
$251$	14.9246	−	8.61672i	0.942032	−	0.543882i	0.0514354	−	0.998676i	$-0.483620\pi$
$251$	14.9246	−	8.61672i	0.942032	−	0.543882i	0.890597	+	0.454794i	$0.150287\pi$
$252$	−0.127496	+	0.285243i	−0.00803147	+	0.0179686i
$253$	7.37138	−	27.5104i	0.463435	−	1.72956i
$254$	18.8477	−	10.8818i	1.18261	−	0.682782i
$255$	19.6627	+	4.72550i	1.23133	+	0.295922i
$256$	−9.05800	−	15.6889i	−0.566125	−	0.980557i
$257$	0.108348	+	0.404361i	0.00675857	+	0.0252233i	0.969223	−	0.246185i	$-0.0791772\pi$
$257$	0.108348	+	0.404361i	0.00675857	+	0.0252233i	−0.962464	+	0.271409i	$0.912511\pi$
$258$	6.43833	+	13.5235i	0.400833	+	0.841939i
$259$		−	0.481265i		−	0.0299044i
$260$	2.51229	−	6.97289i	0.155806	−	0.432441i
$261$	−4.30496	−	11.2637i	−0.266470	−	0.697207i
$262$	5.72975	+	21.3837i	0.353985	+	1.32109i
$263$	−12.6393	+	3.38670i	−0.779374	+	0.208833i	−0.626509	−	0.779414i	$-0.715517\pi$
$263$	−12.6393	+	3.38670i	−0.779374	+	0.208833i	−0.152865	+	0.988247i	$0.548850\pi$
$264$	9.99883	−	8.52725i	0.615386	−	0.524816i
$265$	−5.73835	+	2.20598i	−0.352504	+	0.135512i
$266$	0.769733	+	1.33322i	0.0471953	+	0.0817447i
$267$	0.443375	−	5.58173i	0.0271341	−	0.341597i
$268$	−1.92084	−	1.92084i	−0.117334	−	0.117334i
$269$	−0.403612	−	0.699076i	−0.0246086	−	0.0426234i	0.853459	−	0.521160i	$-0.174501\pi$
$269$	−0.403612	−	0.699076i	−0.0246086	−	0.0426234i	−0.878067	+	0.478537i	$0.841167\pi$
$270$	7.62805	−	18.3281i	0.464228	−	1.11541i
$271$	−9.22378	−	5.32535i	−0.560305	−	0.323492i	0.192963	−	0.981206i	$-0.438190\pi$
$271$	−9.22378	−	5.32535i	−0.560305	−	0.323492i	−0.753268	+	0.657714i	$0.771524\pi$
$272$	18.4366	−	18.4366i	1.11788	−	1.11788i
$273$	0.187682	−	0.682138i	0.0113590	−	0.0412849i
$274$		−	21.2892i		−	1.28613i
$275$	−20.0916	+	4.29123i	−1.21157	+	0.258771i
$276$	−10.4010	−	3.69171i	−0.626069	−	0.222215i
$277$	7.38713	−	27.5691i	0.443849	−	1.65647i	−0.275107	−	0.961414i	$-0.588713\pi$
$277$	7.38713	−	27.5691i	0.443849	−	1.65647i	0.718957	−	0.695055i	$-0.244620\pi$
$278$	4.62953	−	4.62953i	0.277661	−	0.277661i
$279$	−16.0556	−	13.0402i	−0.961222	−	0.780699i
$280$	0.0491217	+	0.465164i	0.00293558	+	0.0277988i
$281$	13.4870			0.804568			0.402284	−	0.915515i	$-0.368216\pi$
$281$	13.4870			0.804568			0.402284	+	0.915515i	$0.368216\pi$
$282$	−0.0614889	+	0.774095i	−0.00366161	+	0.0460967i
$283$	0.294869	+	1.10046i	0.0175281	+	0.0654158i	0.974136	−	0.225963i	$-0.0725528\pi$
$283$	0.294869	+	1.10046i	0.0175281	+	0.0654158i	−0.956608	+	0.291379i	$0.905886\pi$
$284$	−6.77325	−	3.91054i	−0.401918	−	0.232048i
$285$	−16.0882	−	26.2675i	−0.952984	−	1.55595i
$286$	16.5540	−	19.1496i	0.978858	−	1.13234i
$287$	−0.278487	+	0.278487i	−0.0164386	+	0.0164386i
$288$	−8.51564	−	11.7567i	−0.501789	−	0.692769i
$289$	8.88844	+	5.13174i	0.522850	+	0.301867i
$290$	11.9390	+	9.65829i	0.701081	+	0.567154i
$291$	−0.0469775	−	0.254500i	−0.00275387	−	0.0149191i
$292$	−3.77827	−	1.01239i	−0.221107	−	0.0592454i
$293$	−7.29093	−	1.95360i	−0.425941	−	0.114130i	0.0394794	−	0.999220i	$-0.487430\pi$
$293$	−7.29093	−	1.95360i	−0.425941	−	0.114130i	−0.465420	+	0.885090i	$0.654097\pi$
$294$	3.75342	+	20.3341i	0.218904	+	1.18591i
$295$	0.168027	+	1.59115i	0.00978289	+	0.0926402i
$296$	6.79317	+	3.92204i	0.394845	+	0.227964i
$297$	14.7306	−	15.4552i	0.854757	−	0.896800i
$298$	−14.3737	+	14.3737i	−0.832644	+	0.832644i
$299$	24.5455	+	4.70092i	1.41950	+	0.271861i
$300$	1.04119	+	7.89303i	0.0601131	+	0.455705i
$301$	−0.496555	−	0.286686i	−0.0286210	−	0.0165243i
$302$	4.90922	+	18.3214i	0.282494	+	1.05428i
$303$	−1.66449	+	20.9546i	−0.0956224	+	1.20381i
$304$	−39.7144			−2.27778
$305$	9.07983	−	0.958838i	0.519909	−	0.0549029i
$306$	16.8734	−	20.7751i	0.964587	−	1.18763i
$307$	−5.28300	+	5.28300i	−0.301517	+	0.301517i	−0.841607	−	0.540090i	$-0.818390\pi$
$307$	−5.28300	+	5.28300i	−0.301517	+	0.301517i	0.540090	+	0.841607i	$0.318390\pi$
$308$	0.110757	−	0.413352i	0.00631098	−	0.0235529i
$309$	−1.21957	−	0.432871i	−0.0693790	−	0.0246252i
$310$	26.0191	+	4.10792i	1.47779	+	0.233314i
$311$			2.37607i			0.134735i	0.997728	+	0.0673674i	$0.0214599\pi$
$311$			2.37607i			0.134735i	−0.997728	+	0.0673674i	$0.978540\pi$
$312$	8.09904	+	8.20821i	0.458518	+	0.464698i
$313$	20.5099	−	20.5099i	1.15929	−	1.15929i	0.174659	−	0.984629i	$-0.444118\pi$
$313$	20.5099	−	20.5099i	1.15929	−	1.15929i	0.984629	−	0.174659i	$-0.0558822\pi$
$314$	11.5927	+	6.69304i	0.654213	+	0.377710i
$315$	0.157289	+	0.743507i	0.00886225	+	0.0418919i
$316$	2.22694	+	3.85718i	0.125275	+	0.216983i
$317$	−23.9045	−	23.9045i	−1.34261	−	1.34261i	−0.893450	−	0.449162i	$-0.851723\pi$
$317$	−23.9045	−	23.9045i	−1.34261	−	1.34261i	−0.449162	−	0.893450i	$-0.648277\pi$
$318$	−0.644271	+	8.11085i	−0.0361289	+	0.454834i
$319$	8.25787	+	14.3030i	0.462352	+	0.800817i
$320$	−3.51271	−	1.56189i	−0.196366	−	0.0873124i
$321$	−2.17651	+	1.85618i	−0.121481	+	0.103602i
$322$	1.29596	−	0.347251i	0.0722210	−	0.0193516i
$323$	−10.7481	−	40.1124i	−0.598040	−	2.23191i
$324$	−5.51831	−	6.16466i	−0.306573	−	0.342481i
$325$	−5.03393	−	17.3107i	−0.279232	−	0.960224i
$326$		−	20.9422i		−	1.15988i
$327$	0.475658	+	0.999106i	0.0263039	+	0.0552507i
$328$	−1.66140	−	6.20041i	−0.0917352	−	0.342361i
$329$	−0.0148633	−	0.0257440i	−0.000819441	−	0.00141931i
$330$	−6.35371	+	26.4377i	−0.349760	+	1.45535i
$331$	12.0767	−	6.97251i	0.663798	−	0.383244i	−0.129925	−	0.991524i	$-0.541474\pi$
$331$	12.0767	−	6.97251i	0.663798	−	0.383244i	0.793722	+	0.608280i	$0.208140\pi$
$332$	0.687925	−	2.56737i	0.0377548	−	0.140903i
$333$	11.6351	+	5.20054i	0.637597	+	0.284988i
$334$	−13.2009	+	7.62155i	−0.722322	+	0.417033i
$335$	−6.52659	−	1.03042i	−0.356585	−	0.0562980i
$336$	0.923390	+	0.327745i	0.0503750	+	0.0178800i
$337$	−2.58183	−	2.58183i	−0.140641	−	0.140641i	0.633281	−	0.773922i	$-0.281708\pi$
$337$	−2.58183	−	2.58183i	−0.140641	−	0.140641i	−0.773922	+	0.633281i	$0.781708\pi$
$338$	17.8126	+	13.2693i	0.968877	+	0.721754i
$339$	13.4800	−	2.48824i	0.732135	−	0.135143i
$340$	−1.67386	+	10.6020i	−0.0907777	+	0.574975i
$341$	24.5344	+	14.1649i	1.32861	+	0.767074i
$342$	−40.5495	+	4.20233i	−2.19267	+	0.227236i
$343$	−1.12047	−	1.12047i	−0.0604997	−	0.0604997i
$344$	8.09329	−	4.67266i	0.436361	−	0.251933i
$345$	−25.7416	+	7.61840i	−1.38588	+	0.410161i
$346$			15.0319i			0.808119i
$347$	15.4146	+	4.13034i	0.827500	+	0.221728i	0.647623	−	0.761961i	$-0.275763\pi$
$347$	15.4146	+	4.13034i	0.827500	+	0.221728i	0.179877	+	0.983689i	$0.442430\pi$
$348$	5.77864	−	2.75112i	0.309768	−	0.147475i
$349$	−2.98342	+	5.16743i	−0.159699	+	0.276606i	−0.934760	−	0.355280i	$-0.884386\pi$
$349$	−2.98342	+	5.16743i	−0.159699	+	0.276606i	0.775061	+	0.631886i	$0.217719\pi$
$350$	−0.648306	−	0.718595i	−0.0346534	−	0.0384105i
$351$	14.4633	+	11.9086i	0.771992	+	0.635632i
$352$	14.0593	+	14.0593i	0.749363	+	0.749363i
$353$	−3.22389	−	12.0317i	−0.171590	−	0.640383i	−0.997107	−	0.0760061i	$-0.975783\pi$
$353$	−3.22389	−	12.0317i	−0.171590	−	0.640383i	0.825517	−	0.564377i	$-0.190884\pi$
$354$	1.99558	+	0.708304i	0.106064	+	0.0376459i
$355$	−18.9184	+	1.99780i	−1.00408	+	0.106032i
$356$	2.97190			0.157510
$357$	−0.0811285	+	1.02134i	−0.00429378	+	0.0540552i
$358$	−8.80254	+	32.8515i	−0.465229	+	1.73626i
$359$		−	29.8863i		−	1.57734i	−0.614816	−	0.788671i	$-0.710770\pi$
$359$		−	29.8863i		−	1.57734i	0.614816	−	0.788671i	$-0.289230\pi$
$360$	−11.7766	−	3.83898i	−0.620681	−	0.202332i
$361$	−22.1271	+	38.3252i	−1.16458	+	2.01712i
$362$	12.2967	−	3.29490i	0.646302	−	0.173176i
$363$	−5.77804	+	8.39402i	−0.303268	+	0.440572i
$364$	0.368803	+	0.0706327i	0.0193305	+	0.00370216i
$365$	−8.88066	+	3.41397i	−0.464835	+	0.178695i
$366$	4.04191	−	11.3877i	0.211274	−	0.595244i
$367$	12.9762	−	3.47695i	0.677351	−	0.181496i	0.0962869	−	0.995354i	$-0.469303\pi$
$367$	12.9762	−	3.47695i	0.677351	−	0.181496i	0.581064	+	0.813858i	$0.302637\pi$
$368$	−8.95823	+	33.4326i	−0.466980	+	1.74279i
$369$	−3.72337	−	9.74201i	−0.193831	−	0.507149i
$370$	−16.1404	+	1.70445i	−0.839102	+	0.0886099i
$371$	−0.155736	−	0.269742i	−0.00808539	−	0.0140043i
$372$	6.22474	−	9.04296i	0.322738	−	0.468855i
$373$	19.2834	+	5.16696i	0.998455	+	0.267535i	0.720798	−	0.693145i	$-0.243776\pi$
$373$	19.2834	+	5.16696i	0.998455	+	0.267535i	0.277657	+	0.960680i	$0.410442\pi$
$374$	−18.3287	+	31.7462i	−0.947753	+	1.64156i
$375$	13.3404	+	14.0369i	0.688896	+	0.724860i
$376$	0.484510			0.0249867
$377$	−11.9923	+	8.13714i	−0.617635	+	0.419084i
$378$	0.977486	+	0.236929i	0.0502764	+	0.0121863i
$379$	16.7541	−	29.0190i	0.860601	−	1.49061i	−0.0107483	−	0.999942i	$-0.503421\pi$
$379$	16.7541	−	29.0190i	0.860601	−	1.49061i	0.871350	−	0.490663i	$-0.163245\pi$
$380$	13.2218	−	9.61614i	0.678265	−	0.493298i
$381$	−14.3161	−	16.7867i	−0.733435	−	0.860007i
$382$	27.7305	−	27.7305i	1.41882	−	1.41882i
$383$	−2.60975	−	0.699279i	−0.133352	−	0.0357315i	0.191526	−	0.981488i	$-0.438656\pi$
$383$	−2.60975	−	0.699279i	−0.133352	−	0.0357315i	−0.324878	+	0.945756i	$0.605323\pi$
$384$	−16.6254	+	14.1786i	−0.848412	+	0.723547i
$385$	−0.373496	−	0.971564i	−0.0190351	−	0.0495155i
$386$	−32.4270	+	18.7218i	−1.65049	+	0.952912i
$387$	12.2967	−	8.90678i	0.625076	−	0.452757i
$388$	0.132680	−	0.0355516i	0.00673582	−	0.00180486i
$389$	−38.6182			−1.95802			−0.979011	−	0.203807i	$-0.934668\pi$
$389$	−38.6182			−1.95802			−0.979011	+	0.203807i	$0.934668\pi$
$390$	−23.5419	−	3.87852i	−1.19209	−	0.196397i
$391$	−36.1920			−1.83031
$392$	12.4620	−	3.33918i	0.629426	−	0.168654i
$393$	20.2628	−	9.64677i	1.02212	−	0.486615i
$394$	12.8645	−	7.42732i	0.648104	−	0.374183i
$395$	9.89897	+	4.40148i	0.498071	+	0.221463i
$396$	8.79634	+	7.14433i	0.442033	+	0.359016i
$397$	−10.9688	−	2.93908i	−0.550509	−	0.147508i	−0.0271666	−	0.999631i	$-0.508648\pi$
$397$	−10.9688	−	2.93908i	−0.550509	−	0.147508i	−0.523342	+	0.852122i	$0.675315\pi$
$398$	24.4713	−	24.4713i	1.22663	−	1.22663i
$399$	1.18742	−	1.01266i	0.0594456	−	0.0506966i
$400$	24.4167	−	5.21501i	1.22084	−	0.260751i
$401$	−15.5856	+	26.9950i	−0.778307	+	1.34807i	0.154611	+	0.987975i	$0.450588\pi$
$401$	−15.5856	+	26.9950i	−0.778307	+	1.34807i	−0.932917	+	0.360091i	$0.882746\pi$
$402$	−4.95832	+	7.20318i	−0.247299	+	0.359262i
$403$	−10.8358	+	22.3732i	−0.539771	+	1.11449i
$404$	−11.1569			−0.555076
$405$	−19.6747	−	4.23170i	−0.977642	−	0.210275i
$406$	−0.389012	+	0.673788i	−0.0193063	+	0.0334395i
$407$	−16.8606	−	4.51779i	−0.835749	−	0.223938i
$408$	−13.7553	−	9.46851i	−0.680990	−	0.468761i
$409$	5.22725	+	9.05386i	0.258471	+	0.447685i	0.965832	−	0.259167i	$-0.0834481\pi$
$409$	5.22725	+	9.05386i	0.258471	+	0.447685i	−0.707362	+	0.706852i	$0.750115\pi$
$410$	10.3260	+	8.35347i	0.509967	+	0.412548i
$411$	−21.2229	+	3.91748i	−1.04685	+	0.193235i
$412$	0.177774	−	0.663461i	0.00875828	−	0.0326864i
$413$	−0.0783003	+	0.0209805i	−0.00385290	+	0.00103238i
$414$	−5.60898	+	35.0835i	−0.275666	+	1.72426i
$415$	−2.31982	−	6.03449i	−0.113876	−	0.296221i
$416$	−11.4099	+	13.1989i	−0.559414	+	0.647130i
$417$	−5.46700	−	3.76322i	−0.267720	−	0.184286i
$418$	53.9335	−	14.4514i	2.63797	−	0.706843i
$419$	10.9200	−	18.9139i	0.533476	−	0.924007i	−0.465760	−	0.884911i	$-0.654219\pi$
$419$	10.9200	−	18.9139i	0.533476	−	0.924007i	0.999235	−	0.0390956i	$-0.0124477\pi$
$420$	−0.386775	+	0.114469i	−0.0188727	+	0.00558550i
$421$		−	11.3030i		−	0.550876i	−0.961319	−	0.275438i	$-0.911177\pi$
$421$		−	11.3030i		−	0.550876i	0.961319	−	0.275438i	$-0.0888229\pi$
$422$	3.22612	−	12.0401i	0.157045	−	0.586101i
$423$	0.782999	−	0.0811457i	0.0380707	−	0.00394544i
$424$	5.07663			0.246543
$425$	11.8753	+	23.2501i	0.576036	+	1.12779i
$426$	−8.42157	+	23.7270i	−0.408027	+	1.14957i
$427$	0.119724	+	0.446818i	0.00579387	+	0.0216230i
$428$	−1.07357	−	1.07357i	−0.0518927	−	0.0518927i
$429$	−22.1361	−	12.9787i	−1.06874	−	0.626616i
$430$	−7.85615	+	17.6686i	−0.378857	+	0.852053i
$431$	−1.35987	+	2.35537i	−0.0655028	+	0.113454i	−0.896917	−	0.442199i	$-0.854198\pi$
$431$	−1.35987	+	2.35537i	−0.0655028	+	0.113454i	0.831414	+	0.555653i	$0.187532\pi$
$432$	−17.9017	+	18.7822i	−0.861295	+	0.903661i
$433$	13.6874	+	3.66753i	0.657775	+	0.176250i	0.572242	−	0.820085i	$-0.306074\pi$
$433$	13.6874	+	3.66753i	0.657775	+	0.176250i	0.0855335	+	0.996335i	$0.472741\pi$
$434$			1.33456i			0.0640611i
$435$	7.43129	−	13.6790i	0.356303	−	0.655860i
$436$	−0.508630	+	0.293658i	−0.0243590	+	0.0140637i
$437$	38.9809	+	38.9809i	1.86471	+	1.86471i
$438$	−0.997073	+	12.5523i	−0.0476420	+	0.599774i
$439$	−8.10140	−	4.67735i	−0.386659	−	0.223237i	0.294053	−	0.955789i	$-0.404996\pi$
$439$	−8.10140	−	4.67735i	−0.386659	−	0.223237i	−0.680711	+	0.732552i	$0.738329\pi$
$440$	16.7576	+	2.64571i	0.798888	+	0.126129i
$441$	19.5801	−	7.48347i	0.932388	−	0.356356i
$442$	−28.9497	−	14.0210i	−1.37700	−	0.666910i
$443$	−5.74199	−	5.74199i	−0.272810	−	0.272810i	0.557420	−	0.830230i	$-0.311791\pi$
$443$	−5.74199	−	5.74199i	−0.272810	−	0.272810i	−0.830230	+	0.557420i	$0.811791\pi$
$444$	−2.26258	+	6.37461i	−0.107377	+	0.302525i
$445$	5.84604	−	4.25179i	0.277129	−	0.201554i
$446$	−17.9670	+	10.3733i	−0.850763	+	0.491188i
$447$	16.9738	+	11.6840i	0.802835	+	0.552633i
$448$	0.0504097	−	0.188132i	0.00238163	−	0.00888838i
$449$	23.4891	−	13.5614i	1.10852	−	0.640004i	0.170074	−	0.985431i	$-0.445599\pi$
$449$	23.4891	−	13.5614i	1.10852	−	0.640004i	0.938446	+	0.345427i	$0.112266\pi$
$450$	24.3783	−	7.90829i	1.14920	−	0.372800i
$451$	7.14224	+	12.3707i	0.336315	+	0.582515i
$452$	1.88305	+	7.02763i	0.0885711	+	0.330552i
$453$	17.3610	−	8.26530i	0.815693	−	0.388338i
$454$			23.6941i			1.11202i
$455$	0.826527	−	0.388692i	0.0387482	−	0.0182221i
$456$	4.61715	+	25.0134i	0.216218	+	1.17136i
$457$	3.46105	+	12.9168i	0.161901	+	0.604224i	0.998415	+	0.0562781i	$0.0179233\pi$
$457$	3.46105	+	12.9168i	0.161901	+	0.604224i	−0.836514	+	0.547946i	$0.815410\pi$
$458$	−14.0596	+	3.76726i	−0.656962	+	0.176032i
$459$	−23.8153	−	12.9980i	−1.11160	−	0.606693i
$460$	−5.11271	−	13.2995i	−0.238381	−	0.620094i
$461$	17.1508	+	29.7061i	0.798792	+	1.38355i	0.920403	+	0.390971i	$0.127861\pi$
$461$	17.1508	+	29.7061i	0.798792	+	1.38355i	−0.121611	+	0.992578i	$0.538806\pi$
$462$	−1.37325	−	0.109082i	−0.0638896	−	0.00507496i
$463$	−19.4344	−	19.4344i	−0.903191	−	0.903191i	0.0925195	−	0.995711i	$-0.470508\pi$
$463$	−19.4344	−	19.4344i	−0.903191	−	0.903191i	−0.995711	+	0.0925195i	$0.970508\pi$
$464$	−10.0356	−	17.3821i	−0.465889	−	0.806943i
$465$	−0.692709	−	26.6940i	−0.0321236	−	1.23790i
$466$	18.0226	+	10.4054i	0.834883	+	0.482020i
$467$	−19.6345	+	19.6345i	−0.908575	+	0.908575i	−0.996157	−	0.0875827i	$-0.972086\pi$
$467$	−19.6345	+	19.6345i	−0.908575	+	0.908575i	0.0875827	+	0.996157i	$0.472086\pi$
$468$	−5.69289	+	8.15292i	−0.263154	+	0.376869i
$469$		−	0.334760i		−	0.0154578i
$470$	−0.810750	+	0.589653i	−0.0373971	+	0.0271987i
$471$	4.53900	−	12.7882i	0.209146	−	0.589249i
$472$	0.341958	−	1.27621i	0.0157399	−	0.0587421i
$473$	−14.7051	+	14.7051i	−0.676140	+	0.676140i
$474$	10.9093	−	9.30368i	0.501079	−	0.427332i
$475$	12.2513	−	37.8320i	0.562127	−	1.73585i
$476$	−0.543796			−0.0249248
$477$	8.20415	−	0.850233i	0.375642	−	0.0389295i
$478$	−5.10900	−	19.0670i	−0.233680	−	0.872107i
$479$	−1.49161	−	0.861181i	−0.0681534	−	0.0393484i	0.465536	−	0.885029i	$-0.345862\pi$
$479$	−1.49161	−	0.861181i	−0.0681534	−	0.0393484i	−0.533689	+	0.845681i	$0.679195\pi$
$480$	4.37930	−	18.2222i	0.199887	−	0.831725i
$481$	2.88111	−	15.0435i	0.131367	−	0.685924i
$482$	16.8711	−	16.8711i	0.768456	−	0.768456i
$483$	−0.584643	−	1.22803i	−0.0266022	−	0.0558771i
$484$	−4.68406	−	2.70434i	−0.212912	−	0.122925i
$485$	0.210134	−	0.259755i	0.00954169	−	0.0117948i
$486$	−16.2907	+	21.0714i	−0.738961	+	0.955819i
$487$	−20.1087	−	5.38812i	−0.911213	−	0.244159i	−0.227388	−	0.973804i	$-0.573018\pi$
$487$	−20.1087	−	5.38812i	−0.911213	−	0.244159i	−0.683826	+	0.729645i	$0.739685\pi$
$488$	−7.28262	−	1.95137i	−0.329669	−	0.0883344i
$489$	−20.8770	+	3.85362i	−0.944089	+	0.174267i
$490$	−16.7894	+	20.7540i	−0.758466	+	0.937568i
$491$	−19.5711	−	11.2994i	−0.883233	−	0.509935i	−0.0115102	−	0.999934i	$-0.503664\pi$
$491$	−19.5711	−	11.2994i	−0.883233	−	0.509935i	−0.871723	+	0.489999i	$0.836997\pi$
$492$	4.99796	−	2.37945i	0.225325	−	0.107274i
$493$	14.8403	−	14.8403i	0.668374	−	0.668374i
$494$	16.0791	+	46.2819i	0.723434	+	2.08232i
$495$	27.5245	+	1.46907i	1.23713	+	0.0660298i
$496$	−29.8159	−	17.2142i	−1.33878	−	0.772942i
$497$	−0.249453	−	0.930972i	−0.0111895	−	0.0417598i
$498$	−8.52943	−	0.677520i	−0.382213	−	0.0303604i
$499$	35.8828			1.60634			0.803168	−	0.595753i	$-0.203146\pi$
$499$	35.8828			1.60634			0.803168	+	0.595753i	$0.203146\pi$
$500$	−6.86615	+	7.64827i	−0.307064	+	0.342041i
$501$	10.0269	+	11.7573i	0.447971	+	0.525279i
$502$	20.8208	−	20.8208i	0.929276	−	0.929276i
$503$	8.55700	−	31.9352i	0.381538	−	1.42392i	−0.462015	−	0.886872i	$-0.652873\pi$
$503$	8.55700	−	31.9352i	0.381538	−	1.42392i	0.843553	−	0.537047i	$-0.180460\pi$
$504$	0.0990719	−	0.619683i	0.00441302	−	0.0276029i
$505$	−21.9468	+	15.9618i	−0.976621	+	0.710290i
$506$		−	48.6623i		−	2.16330i
$507$	9.95022	−	20.1988i	0.441905	−	0.897062i
$508$	8.28006	−	8.28006i	0.367368	−	0.367368i
$509$	−5.25012	−	3.03116i	−0.232707	−	0.134354i	0.379113	−	0.925350i	$-0.376229\pi$
$509$	−5.25012	−	3.03116i	−0.232707	−	0.134354i	−0.611820	+	0.790997i	$0.709562\pi$
$510$	34.5406	−	0.896329i	1.52948	−	0.0396901i
$511$	−0.241016	−	0.417452i	−0.0106619	−	0.0184670i
$512$	−4.04633	−	4.04633i	−0.178824	−	0.178824i
$513$	11.6509	+	39.6500i	0.514398	+	1.75059i
$514$	0.357631	+	0.619435i	0.0157744	+	0.0273221i
$515$	−0.599489	−	1.55943i	−0.0264167	−	0.0687168i
$516$	5.22933	+	6.13178i	0.230208	+	0.269936i
$517$	−1.04144	+	0.279053i	−0.0458025	+	0.0122727i
$518$	−0.212824	−	0.794270i	−0.00935095	−	0.0348982i
$519$	14.9851	−	2.76605i	0.657772	−	0.121416i
$520$	−1.24926	+	14.8342i	−0.0547835	+	0.650524i
$521$		−	23.5394i		−	1.03128i	−0.856805	−	0.515640i	$-0.827554\pi$
$521$		−	23.5394i		−	1.03128i	0.856805	−	0.515640i	$-0.172446\pi$
$522$	−12.0858	−	16.6857i	−0.528982	−	0.730312i
$523$	8.20158	+	30.6087i	0.358630	+	1.33843i	0.875854	+	0.482575i	$0.160299\pi$
$523$	8.20158	+	30.6087i	0.358630	+	1.33843i	−0.517225	+	0.855850i	$0.673035\pi$
$524$	5.95565	+	10.3155i	0.260174	+	0.450634i
$525$	−0.597061	+	0.778517i	−0.0260579	+	0.0339773i
$526$	−19.3620	+	11.1787i	−0.844224	+	0.487413i
$527$	9.31753	−	34.7735i	0.405878	−	1.51476i
$528$	20.1503	−	29.2733i	0.876931	−	1.27396i
$529$	21.6892	−	12.5223i	0.943010	−	0.544447i
$530$	−8.49492	+	6.17830i	−0.368996	+	0.268368i
$531$	0.338887	−	2.11970i	0.0147065	−	0.0919871i
$532$	0.585699	+	0.585699i	0.0253933	+	0.0253933i
$533$	−10.3722	+	7.03782i	−0.449268	+	0.304842i
$534$	−1.73660	−	9.40804i	−0.0751502	−	0.407126i
$535$	−3.64773	−	0.575907i	−0.157705	−	0.0248986i
$536$	4.72521	+	2.72810i	0.204098	+	0.117836i
$537$	34.3690	+	2.73004i	1.48313	+	0.117810i
$538$	−0.975256	−	0.975256i	−0.0420463	−	0.0420463i
$539$	−24.8635	+	14.3550i	−1.07095	+	0.618312i
$540$	1.41209	−	10.5876i	0.0607666	−	0.455618i
$541$			26.7974i			1.15211i	0.817411	+	0.576055i	$0.195409\pi$
$541$			26.7974i			1.15211i	−0.817411	+	0.576055i	$0.804591\pi$
$542$	−17.5777	−	4.70993i	−0.755027	−	0.202309i
$543$	−5.54739	−	11.6521i	−0.238061	−	0.500041i
$544$	12.6331	−	21.8811i	0.541638	−	0.938145i
$545$	−0.580405	+	1.30534i	−0.0248618	+	0.0559144i
$546$	0.00809242	−	1.20878i	0.000346324	−	0.0517311i
$547$	6.51421	+	6.51421i	0.278528	+	0.278528i	0.832521	−	0.553993i	$-0.186897\pi$
$547$	6.51421	+	6.51421i	0.278528	+	0.278528i	−0.553993	+	0.832521i	$0.686897\pi$
$548$	−2.96467	−	11.0643i	−0.126644	−	0.472643i
$549$	−12.0960	−	1.93385i	−0.516244	−	0.0825347i
$550$	−31.2611	+	15.9670i	−1.33298	+	0.680836i
$551$	−31.9677			−1.36187
$552$	22.0984	+	1.75534i	0.940569	+	0.0747124i
$553$	−0.142057	+	0.530163i	−0.00604087	+	0.0225448i
$554$		−	48.7662i		−	2.07188i
$555$	4.66918	+	15.7765i	0.198196	+	0.669677i
$556$	1.76133	−	3.05072i	0.0746971	−	0.129379i
$557$	−22.7031	+	6.08328i	−0.961962	+	0.257757i	−0.705431	−	0.708779i	$-0.749246\pi$
$557$	−22.7031	+	6.08328i	−0.961962	+	0.257757i	−0.256531	+	0.966536i	$0.582580\pi$
$558$	−32.2644	−	14.4213i	−1.36586	−	0.610501i
$559$	−13.8052	−	11.9339i	−0.583896	−	0.504752i
$560$	0.453899	+	1.18071i	0.0191807	+	0.0498943i
$561$	35.0200	+	12.4299i	1.47855	+	0.524791i
$562$	22.2587	−	5.96419i	0.938926	−	0.251584i
$563$	−9.60782	+	35.8569i	−0.404921	+	1.51119i	0.399279	+	0.916829i	$0.369260\pi$
$563$	−9.60782	+	35.8569i	−0.404921	+	1.51119i	−0.804201	+	0.594358i	$0.797406\pi$
$564$	0.0758413	+	0.410870i	0.00319350	+	0.0173007i
$565$	13.7583	+	11.1301i	0.578818	+	0.468247i
$566$	0.973289	+	1.68579i	0.0409104	+	0.0708589i
$567$	0.0563221	−	1.01804i	0.00236531	−	0.0427537i
$568$	15.1738	+	4.06580i	0.636678	+	0.170597i
$569$	−6.61515	+	11.4578i	−0.277322	+	0.480335i	−0.970718	−	0.240221i	$-0.922780\pi$
$569$	−6.61515	+	11.4578i	−0.277322	+	0.480335i	0.693397	+	0.720556i	$0.256113\pi$
$570$	−38.1676	−	36.2368i	−1.59866	−	1.51779i
$571$	16.3611			0.684690			0.342345	−	0.939574i	$-0.388779\pi$
$571$	16.3611			0.684690			0.342345	+	0.939574i	$0.388779\pi$
$572$	5.93661	−	12.2576i	0.248222	−	0.512515i
$573$	−32.7469	−	22.5414i	−1.36802	−	0.941681i
$574$	−0.336457	+	0.582760i	−0.0140434	+	0.0243240i
$575$	−29.0844	−	18.8470i	−1.21290	−	0.785976i
$576$	4.00354	+	3.25165i	0.166814	+	0.135485i
$577$	1.55067	−	1.55067i	0.0645553	−	0.0645553i	−0.674092	−	0.738647i	$-0.735465\pi$
$577$	1.55067	−	1.55067i	0.0645553	−	0.0645553i	0.738647	+	0.674092i	$0.235465\pi$
$578$	16.9386	+	4.53869i	0.704554	+	0.188785i
$579$	24.6304	+	28.8810i	1.02361	+	1.20025i
$580$	7.54982	+	3.35695i	0.313489	+	0.139390i
$581$	0.283663	−	0.163773i	0.0117683	−	0.00679444i
$582$	−0.190075	−	0.399247i	−0.00787886	−	0.0165493i
$583$	−10.9121	+	2.92388i	−0.451931	+	0.121095i
$584$	7.85658			0.325107
$585$	0.465557	+	24.1823i	0.0192484	+	0.999815i
$586$	−12.8967			−0.532758
$587$	19.5193	−	5.23017i	0.805646	−	0.215872i	0.167585	−	0.985858i	$-0.446403\pi$
$587$	19.5193	−	5.23017i	0.805646	−	0.215872i	0.638061	+	0.769986i	$0.279737\pi$
$588$	4.78237	+	10.0452i	0.197221	+	0.414258i
$589$	−47.4885	+	27.4175i	−1.95673	+	1.12972i
$590$	0.980941	+	2.55169i	0.0403847	+	0.105051i
$591$	−9.77142	−	11.4577i	−0.401942	−	0.471307i
$592$	20.4902	+	5.49034i	0.842143	+	0.225651i
$593$	3.08282	−	3.08282i	0.126596	−	0.126596i	−0.640970	−	0.767566i	$-0.721468\pi$
$593$	3.08282	−	3.08282i	0.126596	−	0.126596i	0.767566	+	0.640970i	$0.221468\pi$
$594$	17.4765	−	32.0210i	0.717071	−	1.31384i
$595$	−1.06971	+	0.777989i	−0.0438536	+	0.0318945i
$596$	−5.46855	+	9.47180i	−0.224000	+	0.387980i
$597$	−28.8981	−	19.8921i	−1.18272	−	0.814128i
$598$	42.5882	−	3.09615i	1.74156	−	0.126611i
$599$	−17.9813			−0.734698			−0.367349	−	0.930083i	$-0.619734\pi$
$599$	−17.9813			−0.734698			−0.367349	+	0.930083i	$0.619734\pi$
$600$	−6.12324	−	14.7721i	−0.249980	−	0.603070i
$601$	−4.18909	+	7.25572i	−0.170877	+	0.295967i	−0.938727	−	0.344663i	$-0.887993\pi$
$601$	−4.18909	+	7.25572i	−0.170877	+	0.295967i	0.767850	+	0.640630i	$0.221327\pi$
$602$	−0.946282	−	0.253555i	−0.0385676	−	0.0103341i
$603$	8.09314	+	3.61741i	0.329578	+	0.147312i
$604$	5.10277	+	8.83825i	0.207629	+	0.359623i
$605$	−13.0831	+	1.38158i	−0.531902	+	0.0561694i
$606$	6.51944	+	35.3190i	0.264834	+	1.43474i
$607$	−4.58950	+	17.1283i	−0.186282	+	0.695214i	0.808070	+	0.589086i	$0.200512\pi$
$607$	−4.58950	+	17.1283i	−0.186282	+	0.695214i	−0.994352	+	0.106128i	$0.966155\pi$
$608$	−37.1737	+	9.96067i	−1.50759	+	0.403958i
$609$	0.743273	+	0.263815i	0.0301189	+	0.0106903i
$610$	14.5611	−	5.59770i	0.589563	−	0.226644i
$611$	−0.310483	−	0.893690i	−0.0125608	−	0.0361548i
$612$	5.87625	−	13.1468i	0.237533	−	0.531428i
$613$	−36.8917	+	9.88511i	−1.49004	+	0.399256i	−0.909752	−	0.415153i	$-0.863728\pi$
$613$	−36.8917	+	9.88511i	−1.49004	+	0.399256i	−0.580291	+	0.814409i	$0.697061\pi$
$614$	−6.38272	+	11.0552i	−0.257585	+	0.446151i
$615$	6.42733	−	11.8310i	0.259175	−	0.477073i
$616$			0.859527i			0.0346313i
$617$	−7.27686	+	27.1576i	−0.292955	+	1.09332i	0.649872	+	0.760043i	$0.274822\pi$
$617$	−7.27686	+	27.1576i	−0.292955	+	1.09332i	−0.942828	+	0.333281i	$0.891844\pi$
$618$	−2.20418	−	0.175085i	−0.0886650	−	0.00704295i
$619$	−34.9871			−1.40625			−0.703125	−	0.711066i	$-0.748213\pi$
$619$	−34.9871			−1.40625			−0.703125	+	0.711066i	$0.748213\pi$
$620$	14.0945	−	1.48839i	0.566049	−	0.0597753i
$621$	36.0063	−	0.864283i	1.44488	−	0.0346825i
$622$	1.05074	+	3.92142i	0.0421309	+	0.157235i
$623$	0.258967	+	0.258967i	0.0103753	+	0.0103753i
$624$	26.9014	+	15.7726i	1.07692	+	0.631410i
$625$	−2.56435	+	24.8681i	−0.102574	+	0.994725i
$626$	24.7792	−	42.9189i	0.990378	−	1.71538i
$627$	−24.3309	−	51.1063i	−0.971681	−	2.04099i
$628$	6.95692	+	1.86410i	0.277611	+	0.0743857i
$629$			22.1814i			0.884431i
$630$	0.588379	+	1.15751i	0.0234416	+	0.0461164i
$631$	−10.8292	+	6.25222i	−0.431102	+	0.248897i	−0.699816	−	0.714323i	$-0.746735\pi$
$631$	−10.8292	+	6.25222i	−0.431102	+	0.248897i	0.268714	+	0.963220i	$0.413401\pi$
$632$	−6.32569	−	6.32569i	−0.251623	−	0.251623i
$633$	−12.5962	−	1.00056i	−0.500654	−	0.0397686i
$634$	−50.0225	−	28.8805i	−1.98665	−	1.14699i
$635$	4.44178	−	28.1338i	0.176267	−	1.11645i
$636$	0.794654	+	4.30503i	0.0315101	+	0.170706i
$637$	−14.1451	−	20.8467i	−0.560449	−	0.825974i
$638$	19.9537	+	19.9537i	0.789973	+	0.789973i
$639$	25.2027	+	4.02929i	0.997005	+	0.159396i
$640$	−27.8635	−	4.39912i	−1.10140	−	0.173890i
$641$	−3.54806	+	2.04848i	−0.140140	+	0.0809099i	−0.568431	−	0.822731i	$-0.692449\pi$
$641$	−3.54806	+	2.04848i	−0.140140	+	0.0809099i	0.428291	+	0.903641i	$0.359116\pi$
$642$	−2.77122	+	4.02588i	−0.109371	+	0.158889i
$643$	−10.8144	+	40.3600i	−0.426479	+	1.59164i	0.334192	+	0.942505i	$0.391536\pi$
$643$	−10.8144	+	40.3600i	−0.426479	+	1.59164i	−0.760672	+	0.649137i	$0.775130\pi$
$644$	0.625170	−	0.360942i	0.0246351	−	0.0142231i
$645$	19.0592	+	4.58045i	0.750454	+	0.180355i
$646$	−35.4768	−	61.4477i	−1.39582	−	2.41763i
$647$	−1.68818	−	6.30036i	−0.0663691	−	0.247693i	0.924769	−	0.380529i	$-0.124258\pi$
$647$	−1.68818	−	6.30036i	−0.0663691	−	0.247693i	−0.991138	+	0.132836i	$0.957591\pi$
$648$	13.9109	+	9.09144i	0.546470	+	0.357146i
$649$			2.94012i			0.115410i
$650$	−15.9630	−	26.3431i	−0.626119	−	1.03326i
$651$	1.33041	−	0.245576i	0.0521428	−	0.00962489i
$652$	−2.91634	−	10.8839i	−0.114213	−	0.426247i
$653$	44.7451	−	11.9894i	1.75101	−	0.469182i	0.766171	−	0.642637i	$-0.222160\pi$
$653$	44.7451	−	11.9894i	1.75101	−	0.469182i	0.984842	+	0.173454i	$0.0554929\pi$
$654$	1.22684	+	1.43856i	0.0479731	+	0.0562521i
$655$	26.4734	+	11.7711i	1.03440	+	0.459936i
$656$	−8.67976	−	15.0338i	−0.338888	−	0.586971i
$657$	12.6967	−	1.31582i	0.495347	−	0.0513350i
$658$	−0.0359145	−	0.0359145i	−0.00140009	−	0.00140009i
$659$	12.0799	+	20.9230i	0.470566	+	0.815045i	0.999433	−	0.0336601i	$-0.0107164\pi$
$659$	12.0799	+	20.9230i	0.470566	+	0.815045i	−0.528867	+	0.848705i	$0.677383\pi$
$660$	0.379514	+	14.6248i	0.0147725	+	0.569269i
$661$	35.3712	+	20.4215i	1.37578	+	0.794306i	0.991648	−	0.128973i	$-0.0411680\pi$
$661$	35.3712	+	20.4215i	1.37578	+	0.794306i	0.384130	+	0.923279i	$0.374501\pi$
$662$	16.8478	−	16.8478i	0.654809	−	0.654809i
$663$	−8.65022	+	31.4396i	−0.335947	+	1.22101i
$664$			5.33862i			0.207178i
$665$	1.99007	+	0.314194i	0.0771717	+	0.0121839i
$666$	21.5020	+	3.43764i	0.833186	+	0.133206i
$667$	−7.21084	+	26.9112i	−0.279205	+	1.04201i
$668$	−5.79933	+	5.79933i	−0.224383	+	0.224383i
$669$	13.6471	+	16.0023i	0.527628	+	0.618683i
$670$	−11.2270	+	1.18558i	−0.433737	+	0.0458030i
$671$	16.7777			0.647694
$672$	0.946517	+	0.0751849i	0.0365127	+	0.00290032i
$673$	−3.20311	−	11.9542i	−0.123471	−	0.460799i	0.876310	−	0.481748i	$-0.159998\pi$
$673$	−3.20311	−	11.9542i	−0.123471	−	0.460799i	−0.999781	+	0.0209488i	$0.993331\pi$
$674$	−5.40272	−	3.11926i	−0.208105	−	0.120150i
$675$	−12.3696	−	22.8472i	−0.476105	−	0.879388i
$676$	11.1053	+	4.41570i	0.427126	+	0.169834i
$677$	−17.7462	+	17.7462i	−0.682043	+	0.682043i	−0.960460	−	0.278418i	$-0.910190\pi$
$677$	−17.7462	+	17.7462i	−0.682043	+	0.682043i	0.278418	+	0.960460i	$0.410190\pi$
$678$	21.1468	−	10.0676i	0.812138	−	0.386645i
$679$	0.0146595	+	0.00846367i	0.000562580	+	0.000324806i
$680$	−2.26401	−	21.4393i	−0.0868208	−	0.822160i
$681$	23.6203	−	4.36001i	0.905132	−	0.167076i
$682$	46.7550	+	12.5280i	1.79034	+	0.479721i
$683$	21.3203	+	5.71276i	0.815798	+	0.218593i	0.642509	−	0.766278i	$-0.277894\pi$
$683$	21.3203	+	5.71276i	0.815798	+	0.218593i	0.173290	+	0.984871i	$0.444560\pi$
$684$	−20.4889	+	7.83079i	−0.783413	+	0.299418i
$685$	−21.6611	−	17.5232i	−0.827628	−	0.669527i
$686$	−2.34469	−	1.35371i	−0.0895208	−	0.0516848i
$687$	6.34267	+	13.3226i	0.241988	+	0.508289i
$688$	17.8706	−	17.8706i	0.681312	−	0.681312i
$689$	−3.25319	−	9.36396i	−0.123937	−	0.356738i
$690$	−39.1143	+	23.9566i	−1.48906	+	0.912013i
$691$	−7.86173	−	4.53897i	−0.299074	−	0.172671i	0.342953	−	0.939353i	$-0.388573\pi$
$691$	−7.86173	−	4.53897i	−0.299074	−	0.172671i	−0.642027	+	0.766682i	$0.721906\pi$
$692$	2.09329	+	7.81226i	0.0795749	+	0.296978i
$693$	0.143953	+	1.38905i	0.00546834	+	0.0527657i
$694$	27.2665			1.03502
$695$	−0.899822	−	8.52096i	−0.0341322	−	0.323219i
$696$	−9.78106	+	8.34152i	−0.370750	+	0.316185i
$697$	12.8354	−	12.8354i	0.486176	−	0.486176i
$698$	−2.63864	+	9.84754i	−0.0998740	+	0.372735i
$699$	7.05659	−	19.8812i	0.266905	−	0.751977i
$700$	−0.437002	−	0.283182i	−0.0165171	−	0.0107033i
$701$		−	31.3445i		−	1.18386i	−0.805988	−	0.591932i	$-0.798365\pi$
$701$		−	31.3445i		−	1.18386i	0.805988	−	0.591932i	$-0.201635\pi$
$702$	29.1360	+	13.2577i	1.09967	+	0.500380i
$703$	23.8907	−	23.8907i	0.901053	−	0.901053i
$704$	−6.11777	−	3.53210i	−0.230572	−	0.133121i
$705$	0.737005	+	0.699722i	0.0277572	+	0.0263530i
$706$	−10.6413	−	18.4312i	−0.400489	−	0.693667i
$707$	−0.972198	−	0.972198i	−0.0365633	−	0.0365633i
$708$	1.13576	+	0.0902174i	0.0426846	+	0.00339058i
$709$	−16.2682	−	28.1774i	−0.610967	−	1.05823i	−0.991078	−	0.133285i	$-0.957448\pi$
$709$	−16.2682	−	28.1774i	−0.610967	−	1.05823i	0.380111	−	0.924941i	$-0.375886\pi$
$710$	−30.3390	+	11.6632i	−1.13860	+	0.437711i
$711$	−11.2821	−	9.16330i	−0.423114	−	0.343650i
$712$	−5.76582	+	1.54495i	−0.216083	+	0.0578993i
$713$	12.3689	+	46.1615i	0.463220	+	1.72876i
$714$	0.317763	+	1.72148i	0.0118920	+	0.0644247i
$715$	−5.85852	−	32.6053i	−0.219096	−	1.21937i
$716$			18.2992i			0.683873i
$717$	−18.0676	+	8.60166i	−0.674745	+	0.321235i
$718$	−13.2163	−	49.3238i	−0.493227	−	1.84075i
$719$	14.5548	+	25.2096i	0.542802	+	0.940160i	0.998742	+	0.0501495i	$0.0159698\pi$
$719$	14.5548	+	25.2096i	0.542802	+	0.940160i	−0.455940	+	0.890010i	$0.650697\pi$
$720$	−33.4497	−	1.78532i	−1.24660	−	0.0665349i
$721$	0.0733041	−	0.0423222i	0.00272999	−	0.00157616i
$722$	−19.5699	+	73.0360i	−0.728318	+	2.71812i
$723$	−19.9230	−	13.7140i	−0.740944	−	0.510030i
$724$	5.93194	−	3.42480i	0.220459	−	0.127282i
$725$	19.6540	−	4.19777i	0.729931	−	0.155901i
$726$	−5.82396	+	16.4084i	−0.216148	+	0.608975i
$727$	12.8617	+	12.8617i	0.477014	+	0.477014i	0.904175	−	0.427161i	$-0.140486\pi$
$727$	12.8617	+	12.8617i	0.477014	+	0.477014i	−0.427161	+	0.904175i	$0.640486\pi$
$728$	−0.752239	+	0.0546877i	−0.0278798	+	0.00202686i
$729$	24.0035	+	12.3626i	0.889018	+	0.457873i
$730$	−13.1467	+	9.56153i	−0.486582	+	0.353888i
$731$	22.8861	+	13.2133i	0.846475	+	0.488712i
$732$	0.514822	−	6.48119i	0.0190284	−	0.239552i
$733$	9.86693	+	9.86693i	0.364443	+	0.364443i	0.865446	−	0.501003i	$-0.167035\pi$
$733$	9.86693	+	9.86693i	0.364443	+	0.364443i	−0.501003	+	0.865446i	$0.667035\pi$
$734$	19.8780	−	11.4766i	0.733711	−	0.423608i
$735$	23.7788	+	12.9181i	0.877094	+	0.476491i
$736$			33.5405i			1.23632i
$737$	−11.7279	−	3.14249i	−0.432004	−	0.115755i
$738$	−10.4531	−	14.4315i	−0.384782	−	0.531230i
$739$	12.6022	−	21.8276i	0.463578	−	0.802941i	−0.535558	−	0.844498i	$-0.679899\pi$
$739$	12.6022	−	21.8276i	0.463578	−	0.802941i	0.999136	+	0.0415576i	$0.0132320\pi$
$740$	−8.15104	+	3.13349i	−0.299638	+	0.115189i
$741$	43.1790	−	24.5455i	1.58622	−	0.901701i
$742$	−0.376307	−	0.376307i	−0.0138147	−	0.0138147i
$743$	9.73165	+	36.3190i	0.357020	+	1.33242i	0.877924	+	0.478801i	$0.158928\pi$
$743$	9.73165	+	36.3190i	0.357020	+	1.33242i	−0.520904	+	0.853615i	$0.674405\pi$
$744$	−7.37570	+	20.7803i	−0.270406	+	0.761843i
$745$	2.79375	+	26.4557i	0.102355	+	0.969262i
$746$	34.1098			1.24885
$747$	0.894111	+	8.62754i	0.0327138	+	0.315665i
$748$	−5.10478	+	19.0513i	−0.186649	+	0.696584i
$749$		−	0.187098i		−	0.00683642i
$750$	28.2241	+	17.2668i	1.03060	+	0.630493i
$751$	14.1002	−	24.4223i	0.514524	−	0.891182i	−0.485334	−	0.874329i	$-0.661302\pi$
$751$	14.1002	−	24.4223i	0.514524	−	0.891182i	0.999858	−	0.0168530i	$-0.00536474\pi$
$752$	1.26563	−	0.339125i	0.0461529	−	0.0123666i
$753$	−24.5872	−	16.9246i	−0.896007	−	0.616768i
$754$	−16.1934	+	18.7326i	−0.589730	+	0.682200i
$755$	22.6823	+	10.0854i	0.825492	+	0.367047i
$756$	0.541006	−	0.0129861i	0.0196762	−	0.000472300i
$757$	−29.1397	+	7.80797i	−1.05910	+	0.283785i	−0.746008	−	0.665937i	$-0.768032\pi$
$757$	−29.1397	+	7.80797i	−1.05910	+	0.283785i	−0.313093	+	0.949722i	$0.601365\pi$
$758$	14.8179	−	55.3013i	0.538211	−	2.00863i
$759$	−48.5108	+	8.95446i	−1.76083	+	0.325026i
$760$	−20.6529	+	25.5298i	−0.749159	+	0.926064i
$761$	14.3226	+	24.8075i	0.519195	+	0.899272i	0.999751	+	0.0223082i	$0.00710150\pi$
$761$	14.3226	+	24.8075i	0.519195	+	0.899272i	−0.480556	+	0.876964i	$0.659565\pi$
$762$	−31.0503	−	21.3735i	−1.12483	−	0.774282i
$763$	−0.0699104	−	0.0187324i	−0.00253093	−	0.000678160i
$764$	10.5503	−	18.2736i	0.381695	−	0.661115i
$765$	−7.24944	−	34.2681i	−0.262104	−	1.23897i
$766$	−4.61630			−0.166794
$767$	−2.57312	+	0.187066i	−0.0929101	+	0.00675455i
$768$	−17.7914	+	25.8464i	−0.641992	+	0.932650i
$769$	26.5529	−	45.9910i	0.957522	−	1.65848i	0.229035	−	0.973418i	$-0.426443\pi$
$769$	26.5529	−	45.9910i	0.957522	−	1.65848i	0.728488	−	0.685059i	$-0.240224\pi$
$770$	−1.04605	−	1.43828i	−0.0376971	−	0.0518321i
$771$	0.551697	−	0.470501i	0.0198689	−	0.0169447i
$772$	−14.2456	+	14.2456i	−0.512711	+	0.512711i
$773$	−34.1355	−	9.14659i	−1.22777	−	0.328980i	−0.414059	−	0.910250i	$-0.635889\pi$
$773$	−34.1355	−	9.14659i	−1.22777	−	0.328980i	−0.813711	+	0.581270i	$0.802556\pi$
$774$	16.3555	−	20.1374i	0.587885	−	0.723823i
$775$	25.5960	−	23.0924i	0.919437	−	0.829502i
$776$	−0.238933	+	0.137948i	−0.00857720	+	0.00495205i
$777$	−0.752634	+	0.358317i	−0.0270006	+	0.0128545i
$778$	−63.7347	+	17.0777i	−2.28500	+	0.612264i
$779$	−27.6489			−0.990626
$780$	−12.7751	+	1.26265i	−0.457423	+	0.0452101i
$781$	−34.9573			−1.25087
$782$	−59.7305	+	16.0047i	−2.13596	+	0.572329i
$783$	−14.4098	+	15.1186i	−0.514963	+	0.540293i
$784$	30.2159	−	17.4452i	1.07914	−	0.623042i
$785$	16.3519	−	6.28613i	0.583625	−	0.224362i
$786$	29.1753	−	24.8814i	1.04065	−	0.887489i
$787$	18.5304	+	4.96521i	0.660539	+	0.176991i	0.573489	−	0.819213i	$-0.305590\pi$
$787$	18.5304	+	4.96521i	0.660539	+	0.176991i	0.0870495	+	0.996204i	$0.472256\pi$
$788$	5.65154	−	5.65154i	0.201328	−	0.201328i
$789$	14.7067	+	17.2447i	0.523572	+	0.613928i
$790$	18.2835	+	2.88661i	0.650496	+	0.102701i
$791$	−0.448293	+	0.776465i	−0.0159394	+	0.0276079i
$792$	−20.7799	−	9.28803i	−0.738382	−	0.330036i
$793$	1.06748	+	14.6834i	0.0379075	+	0.521424i
$794$	−19.4024			−0.688566
$795$	7.72223	+	7.33158i	0.273879	+	0.260024i
$796$	9.31025	−	16.1258i	0.329993	−	0.571565i
$797$	15.1753	+	4.06620i	0.537535	+	0.144032i	0.517366	−	0.855764i	$-0.326913\pi$
$797$	15.1753	+	4.06620i	0.537535	+	0.144032i	0.0201695	+	0.999797i	$0.493579\pi$
$798$	1.51188	−	2.19638i	0.0535200	−	0.0777509i
$799$	0.685047	+	1.18654i	0.0242352	+	0.0419766i
$800$	21.5467	−	11.0053i	0.761791	−	0.389095i
$801$	−9.05919	+	3.46239i	−0.320091	+	0.122338i
$802$	−13.7844	+	51.4442i	−0.486745	+	1.81656i
$803$	−16.8875	+	4.52499i	−0.595946	+	0.159683i
$804$	−1.57381	+	4.43406i	−0.0555041	+	0.156377i
$805$	0.713390	−	1.60442i	0.0251437	−	0.0565484i
$806$	−7.98939	+	41.7160i	−0.281414	+	1.46938i
$807$	−0.792760	+	1.15168i	−0.0279065	+	0.0405410i
$808$	21.6457	−	5.79994i	0.761492	−	0.204041i
$809$	9.50547	−	16.4640i	0.334195	−	0.578842i	−0.649135	−	0.760673i	$-0.724869\pi$
$809$	9.50547	−	16.4640i	0.334195	−	0.578842i	0.983330	+	0.181831i	$0.0582024\pi$
$810$	−34.3420	+	1.71658i	−1.20665	+	0.0603144i
$811$		−	18.8816i		−	0.663023i	−0.943451	−	0.331512i	$-0.892441\pi$
$811$		−	18.8816i		−	0.663023i	0.943451	−	0.331512i	$-0.107559\pi$
$812$	−0.108345	+	0.404349i	−0.00380216	+	0.0141899i
$813$	−1.46075	+	18.3896i	−0.0512307	+	0.644953i
$814$	−29.8242			−1.04534
$815$	−21.3080	−	17.2375i	−0.746386	−	0.603805i
$816$	−42.5589	−	15.1057i	−1.48986	−	0.528806i
$817$	−10.4182	−	38.8812i	−0.364486	−	1.36028i
$818$	12.6307	+	12.6307i	0.441623	+	0.441623i
$819$	−1.20651	+	0.214364i	−0.0421588	+	0.00749047i
$820$	6.52985	+	2.90343i	0.228032	+	0.101392i
$821$	−0.931007	+	1.61255i	−0.0324924	+	0.0562784i	−0.881814	−	0.471597i	$-0.843678\pi$
$821$	−0.931007	+	1.61255i	−0.0324924	+	0.0562784i	0.849322	+	0.527875i	$0.177011\pi$
$822$	−33.2935	+	15.8505i	−1.16124	+	0.552849i
$823$	−21.4397	−	5.74475i	−0.747341	−	0.200249i	−0.135003	−	0.990845i	$-0.543104\pi$
$823$	−21.4397	−	5.74475i	−0.747341	−	0.200249i	−0.612338	+	0.790596i	$0.709771\pi$
$824$			1.37961i			0.0480608i
$825$	21.6697	+	28.2256i	0.754442	+	0.982688i
$826$	−0.119947	+	0.0692515i	−0.00417349	+	0.00240957i
$827$	5.90430	+	5.90430i	0.205313	+	0.205313i	0.802272	−	0.596959i	$-0.203625\pi$
$827$	5.90430	+	5.90430i	0.205313	+	0.205313i	−0.596959	+	0.802272i	$0.703625\pi$
$828$	1.97055	+	19.0144i	0.0684813	+	0.660797i
$829$	27.7895	+	16.0443i	0.965168	+	0.557240i	0.897760	−	0.440485i	$-0.145194\pi$
$829$	27.7895	+	16.0443i	0.965168	+	0.557240i	0.0674084	+	0.997725i	$0.478527\pi$
$830$	−6.49714	−	8.93332i	−0.225519	−	0.310080i
$831$	−48.6143	+	8.97358i	−1.68641	+	0.311290i
$832$	2.70197	−	5.57887i	0.0936739	−	0.193412i
$833$	25.7974	+	25.7974i	0.893829	+	0.893829i
$834$	−10.6868	−	3.79313i	−0.370053	−	0.131345i
$835$	−3.11101	+	19.7048i	−0.107661	+	0.681913i
$836$	26.0175	−	15.0212i	0.899833	−	0.519519i
$837$	−8.43932	+	34.8176i	−0.291706	+	1.20347i
$838$	9.65801	−	36.0442i	0.333630	−	1.24513i
$839$	−6.21211	+	3.58656i	−0.214466	+	0.123822i	−0.603385	−	0.797450i	$-0.706182\pi$
$839$	−6.21211	+	3.58656i	−0.214466	+	0.123822i	0.388919	+	0.921272i	$0.372848\pi$
$840$	0.690881	−	0.423148i	0.0238376	−	0.0146000i
$841$	6.42199	+	11.1232i	0.221448	+	0.383559i
$842$	−4.99840	−	18.6543i	−0.172256	−	0.642869i
$843$	−10.0415	−	21.0919i	−0.345847	−	0.726443i
$844$		−	6.70663i		−	0.230852i
$845$	28.1626	−	7.20177i	0.968824	−	0.247748i
$846$	1.25636	−	0.480177i	0.0431946	−	0.0165088i
$847$	−0.172510	−	0.643817i	−0.00592752	−	0.0221218i
$848$	13.2611	−	3.55330i	0.455388	−	0.122021i
$849$	1.50144	−	1.28046i	0.0515293	−	0.0439454i
$850$	29.8803	+	33.1199i	1.02489	+	1.13600i
$851$	−14.7228	−	25.5007i	−0.504692	−	0.874152i
$852$	−1.07266	+	13.5040i	−0.0367488	+	0.462638i
$853$	26.8806	+	26.8806i	0.920373	+	0.920373i	0.997056	−	0.0766825i	$-0.0244328\pi$
$853$	26.8806	+	26.8806i	0.920373	+	0.920373i	−0.0766825	+	0.997056i	$0.524433\pi$
$854$	0.395181	+	0.684474i	0.0135228	+	0.0234222i
$855$	−29.1006	+	44.7168i	−0.995221	+	1.52928i
$856$	2.64094	+	1.52474i	0.0902653	+	0.0521147i
$857$	31.5042	−	31.5042i	1.07616	−	1.07616i	0.0793118	−	0.996850i	$-0.474728\pi$
$857$	31.5042	−	31.5042i	1.07616	−	1.07616i	0.996850	−	0.0793118i	$-0.0252723\pi$
$858$	−42.2724	−	11.6307i	−1.44316	−	0.397066i
$859$			29.9066i			1.02040i	0.860055	+	0.510201i	$0.170429\pi$
$859$			29.9066i			1.02040i	−0.860055	+	0.510201i	$0.829571\pi$
$860$	−1.62248	+	10.2766i	−0.0553261	+	0.350429i
$861$	0.642858	+	0.228174i	0.0219085	+	0.00777615i
$862$	−1.20272	+	4.48861i	−0.0409648	+	0.152883i
$863$	9.69182	−	9.69182i	0.329913	−	0.329913i	−0.522640	−	0.852553i	$-0.675053\pi$
$863$	9.69182	−	9.69182i	0.329913	−	0.329913i	0.852553	+	0.522640i	$0.175053\pi$
$864$	−12.0457	+	22.0705i	−0.409804	+	0.750854i
$865$	15.2945	+	12.3728i	0.520027	+	0.420687i
$866$	24.2113			0.822732
$867$	1.40764	−	17.7211i	0.0478060	−	0.601839i
$868$	0.185847	+	0.693590i	0.00630806	+	0.0235420i
$869$	17.2402	+	9.95361i	0.584832	+	0.337653i
$870$	6.21533	−	25.8618i	0.210719	−	0.876799i
$871$	2.00405	−	10.4640i	0.0679045	−	0.354558i
$872$	0.834142	−	0.834142i	0.0282476	−	0.0282476i
$873$	−0.363028	+	0.262950i	−0.0122866	+	0.00889949i
$874$	81.5712	+	47.0952i	2.75919	+	1.59302i
$875$	−1.26477	+	0.0681529i	−0.0427570	+	0.00230399i
$876$	1.22981	+	6.66246i	0.0415513	+	0.225104i
$877$	−34.0942	−	9.13551i	−1.15128	−	0.308484i	−0.367801	−	0.929904i	$-0.619889\pi$
$877$	−34.0942	−	9.13551i	−1.15128	−	0.308484i	−0.783478	+	0.621420i	$0.786556\pi$
$878$	−15.4388	−	4.13681i	−0.521033	−	0.139610i
$879$	2.37315	+	12.8565i	0.0800445	+	0.433640i
$880$	45.6259	−	4.81814i	1.53805	−	0.162419i
$881$	0.0237715	+	0.0137245i	0.000800881	+	0.000462389i	0.500400	−	0.865794i	$-0.333186\pi$
$881$	0.0237715	+	0.0137245i	0.000800881	+	0.000462389i	−0.499600	+	0.866257i	$0.666519\pi$
$882$	29.0053	−	21.0092i	0.976660	−	0.707418i
$883$	−12.5285	+	12.5285i	−0.421617	+	0.421617i	−0.885760	−	0.464143i	$-0.846362\pi$
$883$	−12.5285	+	12.5285i	−0.421617	+	0.421617i	0.464143	+	0.885760i	$0.346362\pi$
$884$	−16.9981	−	3.25545i	−0.571707	−	0.109492i
$885$	2.36324	−	1.44743i	0.0794394	−	0.0486548i
$886$	−12.0157	−	6.93725i	−0.403674	−	0.233061i
$887$	−0.784839	−	2.92906i	−0.0263523	−	0.0983482i	0.951497	−	0.307658i	$-0.0995451\pi$
$887$	−0.784839	−	2.92906i	−0.0263523	−	0.0983482i	−0.977849	+	0.209309i	$0.932878\pi$
$888$	1.07582	−	13.5437i	0.0361021	−	0.454496i
$889$	1.44303			0.0483976
$890$	7.76796	−	9.60228i	0.260383	−	0.321869i
$891$	−35.1372	−	11.5298i	−1.17714	−	0.386264i
$892$	−7.89315	+	7.89315i	−0.264282	+	0.264282i
$893$	0.540132	−	2.01580i	0.0180748	−	0.0674562i
$894$	33.1801	+	11.7768i	1.10971	+	0.393876i
$895$	26.1800	+	35.9965i	0.875100	+	1.20323i
$896$		−	1.42917i		−	0.0477451i
$897$	−10.9233	−	41.8858i	−0.364717	−	1.39853i
$898$	32.7688	−	32.7688i	1.09351	−	1.09351i
$899$	−24.0000	−	13.8564i	−0.800446	−	0.462138i
$900$	11.5684	−	7.50488i	0.385615	−	0.250163i
$901$	7.17782	+	12.4324i	0.239128	+	0.414182i
$902$	17.2580	+	17.2580i	0.574627	+	0.574627i
$903$	−0.0786383	+	0.989992i	−0.00261692	+	0.0329449i
$904$	−7.30666	−	12.6555i	−0.243016	−	0.420916i
$905$	6.76901	−	15.2236i	0.225010	−	0.506049i
$906$	24.9972	−	21.3182i	0.830477	−	0.708251i
$907$	−16.8138	+	4.50525i	−0.558294	+	0.149594i	−0.526922	−	0.849913i	$-0.676654\pi$
$907$	−16.8138	+	4.50525i	−0.558294	+	0.149594i	−0.0313715	+	0.999508i	$0.509988\pi$
$908$	3.29956	+	12.3141i	0.109500	+	0.408659i
$909$	34.0094	−	12.9983i	1.12802	−	0.431126i
$910$	1.19220	−	1.00699i	0.0395209	−	0.0333815i
$911$			4.78351i			0.158485i	0.996855	+	0.0792423i	$0.0252501\pi$
$911$			4.78351i			0.158485i	−0.996855	+	0.0792423i	$0.974750\pi$
$912$	29.5686	+	62.1080i	0.979114	+	2.05660i
$913$	−3.07477	−	11.4752i	−0.101760	−	0.379774i
$914$	11.4241	+	19.7871i	0.377876	+	0.654500i
$915$	−8.25970	−	13.4857i	−0.273057	−	0.445825i
$916$	−6.78234	+	3.91578i	−0.224095	+	0.129381i
$917$	−0.379911	+	1.41785i	−0.0125458	+	0.0468214i
$918$	−45.0521	−	10.9200i	−1.48694	−	0.360415i
$919$	20.5581	−	11.8693i	0.678151	−	0.391530i	−0.121007	−	0.992652i	$-0.538612\pi$
$919$	20.5581	−	11.8693i	0.678151	−	0.391530i	0.799158	+	0.601121i	$0.205279\pi$
$920$	16.8330	+	23.1448i	0.554969	+	0.763060i
$921$	12.1953	+	4.32855i	0.401848	+	0.142631i
$922$	41.4418	+	41.4418i	1.36481	+	1.36481i
$923$	−2.22417	−	30.5938i	−0.0732094	−	1.00701i
$924$	−0.728888	+	0.134543i	−0.0239787	+	0.00442616i
$925$	−11.5510	+	17.8253i	−0.379795	+	0.586092i
$926$	−40.6683	−	23.4798i	−1.33644	−	0.771595i
$927$	0.231056	+	2.22953i	0.00758888	+	0.0732274i
$928$	−13.7531	−	13.7531i	−0.451467	−	0.451467i
$929$	27.3742	−	15.8045i	0.898117	−	0.518528i	0.0215282	−	0.999768i	$-0.493147\pi$
$929$	27.3742	−	15.8045i	0.898117	−	0.518528i	0.876589	+	0.481240i	$0.159814\pi$
$930$	−12.9478	−	43.7488i	−0.424574	−	1.43458i
$931$		−	55.5706i		−	1.82125i
$932$	10.8156	+	2.89804i	0.354277	+	0.0949283i
$933$	3.71586	−	1.76906i	0.121652	−	0.0579164i
$934$	−23.7216	+	41.0870i	−0.776194	+	1.34441i
$935$	17.2144	+	44.7792i	0.562970	+	1.46444i
$936$	6.80655	−	18.7771i	0.222479	−	0.613747i
$937$	−12.6526	−	12.6526i	−0.413344	−	0.413344i	0.469558	−	0.882902i	$-0.344413\pi$
$937$	−12.6526	−	12.6526i	−0.413344	−	0.413344i	−0.882902	+	0.469558i	$0.844413\pi$
$938$	−0.148037	−	0.552480i	−0.00483357	−	0.0180391i
$939$	−47.3449	−	16.8045i	−1.54504	−	0.548393i
$940$	−0.339244	+	0.419353i	−0.0110649	+	0.0136778i
$941$	−49.4334			−1.61148			−0.805741	−	0.592268i	$-0.798233\pi$
$941$	−49.4334			−1.61148			−0.805741	+	0.592268i	$0.798233\pi$
$942$	1.83591	−	23.1126i	0.0598171	−	0.753048i
$943$	−6.23666	+	23.2755i	−0.203094	+	0.757956i
$944$		−	3.57304i		−	0.116293i
$945$	1.04564	−	0.799543i	0.0340146	−	0.0260091i
$946$	−17.7661	+	30.7718i	−0.577625	+	1.00048i
$947$	−23.6300	+	6.33163i	−0.767871	+	0.205750i	−0.621431	−	0.783469i	$-0.713448\pi$
$947$	−23.6300	+	6.33163i	−0.767871	+	0.205750i	−0.146440	+	0.989220i	$0.546782\pi$
$948$	4.37408	−	6.35443i	0.142064	−	0.206382i
$949$	−5.03464	−	14.4916i	−0.163431	−	0.470419i
$950$	3.48927	−	67.8548i	0.113207	−	2.20150i
$951$	−19.5858	+	55.1811i	−0.635114	+	1.78937i
$952$	1.05503	−	0.282693i	0.0341936	−	0.00916215i
$953$	11.1821	−	41.7321i	0.362223	−	1.35184i	−0.508923	−	0.860812i	$-0.669956\pi$
$953$	11.1821	−	41.7321i	0.362223	−	1.35184i	0.871146	−	0.491024i	$-0.163377\pi$
$954$	13.1640	−	5.03122i	0.426199	−	0.162892i
$955$	−5.38987	−	51.0400i	−0.174412	−	1.65162i
$956$	−5.31043	−	9.19793i	−0.171751	−	0.297482i
$957$	16.2198	−	23.5632i	0.524312	−	0.761691i
$958$	−2.84255	−	0.761659i	−0.0918386	−	0.0246081i
$959$	0.705791	−	1.22247i	0.0227912	−	0.0394755i
$960$	0.172731	+	6.65628i	0.00557486	+	0.214830i
$961$	−16.5366			−0.533437
$962$	−1.89758	−	26.1015i	−0.0611803	−	0.841546i
$963$	4.52328	+	2.02178i	0.145761	+	0.0651510i
$964$	6.41870	−	11.1175i	0.206732	−	0.358071i
$965$	−7.64197	+	48.4034i	−0.246004	+	1.55816i
$966$	−1.50794	−	1.76817i	−0.0485170	−	0.0568898i
$967$	−4.55251	+	4.55251i	−0.146399	+	0.146399i	−0.776507	−	0.630108i	$-0.783010\pi$
$967$	−4.55251	+	4.55251i	−0.146399	+	0.146399i	0.630108	+	0.776507i	$0.283010\pi$
$968$	10.4935	+	2.81172i	0.337273	+	0.0903721i
$969$	−54.7281	+	46.6735i	−1.75812	+	1.49937i
$970$	0.231932	−	0.521618i	0.00744690	−	0.0167482i
$971$	51.2257	−	29.5752i	1.64391	−	0.949113i	0.664488	−	0.747299i	$-0.268650\pi$
$971$	51.2257	−	29.5752i	1.64391	−	0.949113i	0.979424	−	0.201814i	$-0.0646838\pi$
$972$	−5.53215	+	13.2197i	−0.177444	+	0.424021i
$973$	0.419316	−	0.112355i	0.0134427	−	0.00360195i
$974$	−35.5697			−1.13973
$975$	−23.3237	+	20.7607i	−0.746955	+	0.664875i
$976$	−20.3894			−0.652649
$977$	55.9598	−	14.9944i	1.79031	−	0.479713i	0.797914	−	0.602772i	$-0.205937\pi$
$977$	55.9598	−	14.9944i	1.79031	−	0.479713i	0.992399	+	0.123059i	$0.0392703\pi$
$978$	−32.7508	+	15.5921i	−1.04725	+	0.498580i
$979$	11.5036	−	6.64164i	0.367658	−	0.212268i
$980$	−5.83552	+	13.1241i	−0.186409	+	0.419235i
$981$	1.20833	−	1.48773i	0.0385789	−	0.0474995i
$982$	−37.2966	−	9.99359i	−1.19018	−	0.318908i
$983$	−17.2893	+	17.2893i	−0.551443	+	0.551443i	−0.926857	−	0.375414i	$-0.877500\pi$
$983$	−17.2893	+	17.2893i	−0.551443	+	0.551443i	0.375414	+	0.926857i	$0.377500\pi$
$984$	−8.45965	+	7.21460i	−0.269684	+	0.229993i
$985$	3.03173	−	19.2026i	0.0965990	−	0.611847i
$986$	17.9295	−	31.0548i	0.570991	−	0.988985i
$987$	−0.0291940	+	0.0424114i	−0.000929254	+	0.00134997i
$988$	14.8016	+	21.8142i	0.470901	+	0.694002i
$989$	−35.0811			−1.11551
$990$	46.0755	−	9.74729i	1.46437	−	0.309789i
$991$	6.95908	−	12.0535i	0.221063	−	0.382892i	−0.734068	−	0.679076i	$-0.762381\pi$
$991$	6.95908	−	12.0535i	0.221063	−	0.382892i	0.955131	+	0.296184i	$0.0957142\pi$
$992$	−32.2259	−	8.63491i	−1.02317	−	0.274159i
$993$	−19.8956	−	13.6952i	−0.631367	−	0.434602i
$994$	−0.823384	−	1.42614i	−0.0261162	−	0.0452345i
$995$	−4.75638	−	45.0411i	−0.150787	−	1.42790i
$996$	−4.52721	+	0.835664i	−0.143450	+	0.0264790i
$997$	−12.5004	+	46.6520i	−0.395891	+	1.47748i	0.424367	+	0.905490i	$0.360497\pi$
$997$	−12.5004	+	46.6520i	−0.395891	+	1.47748i	−0.820258	+	0.571994i	$0.806170\pi$
$998$	59.2202	−	15.8680i	1.87458	−	0.502293i
$999$	−0.529703	−	22.0676i	−0.0167591	−	0.698189i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	195.2.bf.a.17.19	yes	96
3.2	odd	2	inner	195.2.bf.a.17.6	✓	96
5.2	odd	4		975.2.bn.d.368.19		96
5.3	odd	4	inner	195.2.bf.a.173.6	yes	96
5.4	even	2		975.2.bn.d.407.6		96
13.10	even	6	inner	195.2.bf.a.62.19	yes	96
15.2	even	4		975.2.bn.d.368.6		96
15.8	even	4	inner	195.2.bf.a.173.19	yes	96
15.14	odd	2		975.2.bn.d.407.19		96
39.23	odd	6	inner	195.2.bf.a.62.6	yes	96
65.23	odd	12	inner	195.2.bf.a.23.6	yes	96
65.49	even	6		975.2.bn.d.257.6		96
65.62	odd	12		975.2.bn.d.218.19		96
195.23	even	12	inner	195.2.bf.a.23.19	yes	96
195.62	even	12		975.2.bn.d.218.6		96
195.179	odd	6		975.2.bn.d.257.19		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.bf.a.17.6	✓	96	3.2	odd	2	inner
195.2.bf.a.17.19	yes	96	1.1	even	1	trivial
195.2.bf.a.23.6	yes	96	65.23	odd	12	inner
195.2.bf.a.23.19	yes	96	195.23	even	12	inner
195.2.bf.a.62.6	yes	96	39.23	odd	6	inner
195.2.bf.a.62.19	yes	96	13.10	even	6	inner
195.2.bf.a.173.6	yes	96	5.3	odd	4	inner
195.2.bf.a.173.19	yes	96	15.8	even	4	inner
975.2.bn.d.218.6		96	195.62	even	12
975.2.bn.d.218.19		96	65.62	odd	12
975.2.bn.d.257.6		96	65.49	even	6
975.2.bn.d.257.19		96	195.179	odd	6
975.2.bn.d.368.6		96	15.2	even	4
975.2.bn.d.368.19		96	5.2	odd	4
975.2.bn.d.407.6		96	5.4	even	2
975.2.bn.d.407.19		96	15.14	odd	2

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.bf (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.65038 - 0.442218i) q^{2} +(-0.744530 - 1.56387i) q^{3} +(0.796141 - 0.459652i) q^{4} +(0.908487 - 2.04320i) q^{5} +(-1.92033 - 2.25172i) q^{6} +(0.109428 + 0.0293212i) q^{7} +(-1.30565 + 1.30565i) q^{8} +(-1.89135 + 2.32869i) q^{9} +(0.595810 - 3.77380i) q^{10} +(2.05447 - 3.55845i) q^{11} +(-1.31159 - 0.902832i) q^{12} +(3.24500 + 1.57162i) q^{13} +0.193564 q^{14} +(-3.87168 + 0.100470i) q^{15} +(-2.49674 + 4.32449i) q^{16} +(-5.04353 - 1.35141i) q^{17} +(-2.09165 + 4.67961i) q^{18} +(3.97662 + 6.88771i) q^{19} +(-0.215876 - 2.04426i) q^{20} +(-0.0356182 - 0.192962i) q^{21} +(1.81705 - 6.78132i) q^{22} +(6.69524 - 1.79398i) q^{23} +(3.01397 + 1.06977i) q^{24} +(-3.34930 - 3.71244i) q^{25} +(6.05047 + 1.15878i) q^{26} +(5.04992 + 1.22403i) q^{27} +(0.100598 - 0.0269551i) q^{28} +(-2.00973 + 3.48095i) q^{29} +(-6.34531 + 1.87794i) q^{30} +6.89468i q^{31} +(-1.25240 + 4.67403i) q^{32} +(-7.09456 - 0.563544i) q^{33} -8.92135 q^{34} +(0.159323 - 0.196946i) q^{35} +(-0.435393 + 2.72333i) q^{36} +(-1.09950 - 4.10339i) q^{37} +(9.60880 + 9.60880i) q^{38} +(0.0418074 - 6.24486i) q^{39} +(1.48154 + 3.85388i) q^{40} +(-1.73822 + 3.01068i) q^{41} +(-0.144115 - 0.302709i) q^{42} +(-4.88872 - 1.30993i) q^{43} -3.77737i q^{44} +(3.03971 + 5.97998i) q^{45} +(10.2563 - 5.92150i) q^{46} +(-0.185543 - 0.185543i) q^{47} +(8.62182 + 0.684859i) q^{48} +(-6.05106 - 3.49358i) q^{49} +(-7.16932 - 4.64580i) q^{50} +(1.64164 + 8.89356i) q^{51} +(3.30587 - 0.240337i) q^{52} +(-1.94409 - 1.94409i) q^{53} +(8.87558 - 0.213046i) q^{54} +(-5.40416 - 7.43050i) q^{55} +(-0.181159 + 0.104592i) q^{56} +(7.81074 - 11.3470i) q^{57} +(-1.77747 + 6.63362i) q^{58} +(-0.619675 + 0.357770i) q^{59} +(-3.03622 + 1.85961i) q^{60} +(2.04160 + 3.53616i) q^{61} +(3.04895 + 11.3788i) q^{62} +(-0.275247 + 0.199368i) q^{63} -1.71922i q^{64} +(6.15917 - 5.20237i) q^{65} +(-11.9579 + 2.20728i) q^{66} +(-0.764792 - 2.85424i) q^{67} +(-4.63654 + 1.24236i) q^{68} +(-7.79036 - 9.13477i) q^{69} +(0.175851 - 0.395490i) q^{70} +(-4.25380 - 7.36780i) q^{71} +(-0.571017 - 5.50991i) q^{72} +(-3.00868 - 3.00868i) q^{73} +(-3.62918 - 6.28592i) q^{74} +(-3.31209 + 8.00188i) q^{75} +(6.33191 + 3.65573i) q^{76} +(0.329156 - 0.329156i) q^{77} +(-2.69259 - 10.3249i) q^{78} +4.84485i q^{79} +(6.56752 + 9.03008i) q^{80} +(-1.84560 - 8.80873i) q^{81} +(-1.53734 + 5.73743i) q^{82} +(2.04442 - 2.04442i) q^{83} +(-0.117052 - 0.137253i) q^{84} +(-7.34318 + 9.07718i) q^{85} -8.64751 q^{86} +(6.94004 + 0.551270i) q^{87} +(1.96368 + 7.32854i) q^{88} +(2.79966 + 1.61638i) q^{89} +(7.66112 + 8.52502i) q^{90} +(0.309013 + 0.267127i) q^{91} +(4.50574 - 4.50574i) q^{92} +(10.7823 - 5.13330i) q^{93} +(-0.388267 - 0.224166i) q^{94} +(17.6857 - 1.86762i) q^{95} +(8.24201 - 1.52137i) q^{96} +(0.144327 + 0.0386722i) q^{97} +(-11.5315 - 3.08985i) q^{98} +(4.40081 + 11.5145i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 2 q^{3} - 12 q^{6} - 12 q^{7} + 4 q^{10} - 12 q^{12} - 24 q^{13} - 6 q^{15} + 16 q^{16} + 20 q^{22} - 16 q^{25} - 32 q^{27} - 36 q^{28} + 30 q^{33} - 4 q^{36} - 84 q^{37} - 152 q^{40} - 48 q^{42}+ \cdots - 48 q^{97}+O(q^{100}) \) 96 * q - 2 * q^3 - 12 * q^6 - 12 * q^7 + 4 * q^10 - 12 * q^12 - 24 * q^13 - 6 * q^15 + 16 * q^16 + 20 * q^22 - 16 * q^25 - 32 * q^27 - 36 * q^28 + 30 * q^33 - 4 * q^36 - 84 * q^37 - 152 * q^40 - 48 * q^42 + 8 * q^43 + 54 * q^45 - 28 * q^48 - 16 * q^51 + 28 * q^52 - 40 * q^55 + 84 * q^58 - 32 * q^61 + 90 * q^63 + 36 * q^67 + 90 * q^72 - 20 * q^75 + 72 * q^76 + 60 * q^78 + 32 * q^81 - 68 * q^82 + 84 * q^85 - 26 * q^87 - 108 * q^88 - 20 * q^90 - 80 * q^91 + 48 * q^93 - 48 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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