LMFDB - Embedded newform 195.2.bf.a.23.19

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			23.19
Character	$\chi$	$=$	195.23
Dual form			195.2.bf.a.17.19

$q$-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 $\left(\mathbb{Z}/195\mathbb{Z}\right)^\times$.

$n$	$106$	$131$	$157$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{3}{4}\right)$

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	0.789756	−	0.613421i	$-0.210207\pi$
$2$	1.65038	+	0.442218i	1.16699	+	0.312695i	0.377238	+	0.926116i	$0.376874\pi$
$3$	−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	−0.238080	−	0.971246i	$-0.576518\pi$
$7$	0.109428	−	0.0293212i	0.0413600	−	0.0110824i	0.279440	+	0.960163i	$0.409851\pi$
$8$	−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	0.989587	+	0.143938i	$0.0459766\pi$
$11$	2.05447	+	3.55845i	0.619447	+	1.07291i	−0.370139	+	0.928976i	$0.620690\pi$
$12$	−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	−0.811942	−	0.583738i	$-0.801589\pi$
$17$	−5.04353	+	1.35141i	−1.22324	+	0.327765i	−0.411293	+	0.911503i	$0.634923\pi$
$18$	−2.09165	−	4.67961i	−0.493007	−	1.10299i
$19$	3.97662	−	6.88771i	0.912300	−	1.58015i	0.101493	−	0.994836i	$-0.467638\pi$
$19$	3.97662	−	6.88771i	0.912300	−	1.58015i	0.810807	−	0.585313i	$-0.199029\pi$
$20$	−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	0.876926	−	0.480625i	$-0.159590\pi$
$23$	6.69524	+	1.79398i	1.39605	+	0.374071i	0.519127	+	0.854697i	$0.326257\pi$
$24$	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	0.616858	−	0.787074i	$-0.288405\pi$
$29$	−2.00973	−	3.48095i	−0.373197	−	0.646396i	−0.990055	+	0.140678i	$0.955072\pi$
$30$	−6.34531	−	1.87794i	−1.15849	−	0.342863i
$31$		−	6.89468i		−	1.23832i	−0.785265	−	0.619160i	$-0.787473\pi$
$31$		−	6.89468i		−	1.23832i	0.785265	−	0.619160i	$-0.212527\pi$
$32$	−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	0.814743	+	0.579823i	$0.196878\pi$
$37$	−1.09950	+	4.10339i	−0.180757	+	0.674593i	−0.995499	+	0.0947700i	$0.969788\pi$
$38$	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	0.697773	−	0.716319i	$-0.254174\pi$
$41$	−1.73822	−	3.01068i	−0.271464	−	0.470189i	−0.969237	+	0.246130i	$0.920841\pi$
$42$	−0.144115	+	0.302709i	−0.0222374	+	0.0467090i
$43$	−4.88872	+	1.30993i	−0.745523	+	0.199762i	−0.611531	−	0.791220i	$-0.709446\pi$
$43$	−4.88872	+	1.30993i	−0.745523	+	0.199762i	−0.133991	+	0.990982i	$0.542779\pi$
$44$			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	−0.720509	−	0.693445i	$-0.756092\pi$
$47$	−0.185543	+	0.185543i	−0.0270642	+	0.0270642i	0.693445	+	0.720509i	$0.256092\pi$
$48$	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	−0.827907	−	0.560865i	$-0.810469\pi$
$53$	−1.94409	+	1.94409i	−0.267042	+	0.267042i	0.560865	+	0.827907i	$0.310469\pi$
$54$	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	0.459120	−	0.888374i	$-0.348165\pi$
$59$	−0.619675	−	0.357770i	−0.0806749	−	0.0465777i	−0.539795	+	0.841797i	$0.681498\pi$
$60$	−3.03622	−	1.85961i	−0.391975	−	0.240075i
$61$	2.04160	−	3.53616i	0.261400	−	0.452758i	−0.705214	−	0.708994i	$-0.749149\pi$
$61$	2.04160	−	3.53616i	0.261400	−	0.452758i	0.966614	+	0.256236i	$0.0824825\pi$
$62$	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	−0.996777	−	0.0802172i	$-0.974439\pi$
$67$	−0.764792	+	2.85424i	−0.0934343	+	0.348701i	0.903343	+	0.428919i	$0.141105\pi$
$68$	−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	0.495151	+	0.868807i	$0.335113\pi$
$71$	−4.25380	+	7.36780i	−0.504833	+	0.874397i	−0.999984	+	0.00558990i	$0.998221\pi$
$72$	−0.571017	+	5.50991i	−0.0672949	+	0.649349i
$73$	−3.00868	+	3.00868i	−0.352139	+	0.352139i	−0.860905	−	0.508766i	$-0.830102\pi$
$73$	−3.00868	+	3.00868i	−0.352139	+	0.352139i	0.508766	+	0.860905i	$0.330102\pi$
$74$	−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	$-0.912135\pi$
$79$		−	4.84485i		−	0.545088i	0.962143	−	0.272544i	$-0.0878650\pi$
$80$	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	0.810350	−	0.585946i	$-0.199277\pi$
$83$	2.04442	+	2.04442i	0.224405	+	0.224405i	−0.585946	+	0.810350i	$0.699277\pi$
$84$	−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	−0.344225	−	0.938887i	$-0.611858\pi$
$89$	2.79966	−	1.61638i	0.296763	−	0.171336i	0.640988	+	0.767551i	$0.278525\pi$
$90$	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	−0.251485	−	0.967861i	$-0.580919\pi$
$97$	0.144327	−	0.0386722i	0.0146542	−	0.00392657i	0.266139	+	0.963935i	$0.414252\pi$
$98$	−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	−0.921474	−	0.388440i	$-0.873014\pi$
$101$	−10.5103	+	6.06812i	−1.04581	+	0.603800i	−0.124339	+	0.992240i	$0.539681\pi$
$102$	6.64221	−	13.9518i	0.657677	−	1.38143i
$103$	0.528320	+	0.528320i	0.0520569	+	0.0520569i	0.732656	−	0.680599i	$-0.238280\pi$
$103$	0.528320	+	0.528320i	0.0520569	+	0.0520569i	−0.680599	+	0.732656i	$0.738280\pi$
$104$	−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	−0.983504	−	0.180884i	$-0.942104\pi$
$107$	−0.427445	+	1.59525i	−0.0413227	+	0.154218i	0.942182	+	0.335102i	$0.108771\pi$
$108$	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	−0.992852	−	0.119349i	$-0.961919\pi$
$113$	−2.04834	−	7.64451i	−0.192692	−	0.719135i	0.800161	−	0.599786i	$-0.204747\pi$
$114$	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	0.759409	−	0.650614i	$-0.225488\pi$
$127$	12.3036	+	3.29674i	1.09177	+	0.292539i	0.332361	+	0.943152i	$0.392155\pi$
$128$	−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	$-0.808481\pi$
$131$		−	12.9569i		−	1.13205i	0.824390	−	0.566023i	$-0.191519\pi$
$132$	−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	0.955491	+	0.295021i	$0.0953267\pi$
$137$	3.22490	+	12.0355i	0.275522	+	1.02826i	−0.679969	+	0.733241i	$0.738007\pi$
$138$	−16.8966	+	11.6308i	−1.43833	+	0.990079i
$139$	3.31851	+	1.91594i	0.281472	+	0.162508i	0.634090	−	0.773260i	$-0.281375\pi$
$139$	3.31851	+	1.91594i	0.281472	+	0.162508i	−0.352618	+	0.935767i	$0.614708\pi$
$140$	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	0.0145735	−	0.999894i	$-0.495361\pi$
$149$	−10.3032	−	5.94857i	−0.844073	−	0.487326i	−0.858647	+	0.512568i	$0.828694\pi$
$150$	−1.92763	−	14.6708i	−0.157391	−	1.19786i
$151$		−	11.1014i		−	0.903416i	−0.892166	−	0.451708i	$-0.850815\pi$
$151$		−	11.1014i		−	0.903416i	0.892166	−	0.451708i	$-0.149185\pi$
$152$	−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	−0.450598	−	0.892727i	$-0.648789\pi$
$157$	5.53986	−	5.53986i	0.442129	−	0.442129i	0.892727	+	0.450598i	$0.148789\pi$
$158$	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	0.971604	+	0.236612i	$0.0760369\pi$
$163$	3.17233	+	11.8393i	0.248476	+	0.927326i	−0.723128	+	0.690714i	$0.757296\pi$
$164$		−	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	−0.0905069	−	0.995896i	$-0.528849\pi$
$167$	−8.61742	−	2.30903i	−0.666836	−	0.178678i	−0.576329	+	0.817218i	$0.695515\pi$
$168$	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	−0.996864	−	0.0791307i	$-0.974786\pi$
$173$	−2.27704	−	8.49801i	−0.173120	−	0.646092i	0.823744	−	0.566961i	$-0.191881\pi$
$174$	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	−0.950706	−	0.310094i	$-0.899640\pi$
$179$	−9.95273	−	17.2386i	−0.743902	−	1.28848i	0.206804	−	0.978382i	$-0.433694\pi$
$180$	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	0.997731	−	0.0673227i	$-0.0214457\pi$
$191$	19.8776	+	11.4763i	1.43829	+	0.830399i	0.440562	+	0.897722i	$0.354779\pi$
$192$	−2.68863	−	1.28001i	−0.194035	−	0.0923770i
$193$	−21.1680	−	5.67196i	−1.52371	−	0.408276i	−0.602748	−	0.797932i	$-0.705928\pi$
$193$	−21.1680	−	5.67196i	−1.52371	−	0.408276i	−0.920961	+	0.389655i	$0.872594\pi$
$194$	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	0.545253	−	0.838272i	$-0.316434\pi$
$197$	8.39781	+	2.25019i	0.598319	+	0.160319i	0.0530668	+	0.998591i	$0.483100\pi$
$198$	12.3549	−	17.0572i	0.878026	−	1.21220i
$199$	17.5413	+	10.1275i	1.24347	+	0.717919i	0.969799	−	0.243904i	$-0.0784282\pi$
$199$	17.5413	+	10.1275i	1.24347	+	0.717919i	0.273673	+	0.961823i	$0.411761\pi$
$200$	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	0.963833	−	0.266506i	$-0.0858692\pi$
$211$	3.64767	+	6.31794i	0.251116	+	0.434945i	−0.712718	+	0.701451i	$0.752536\pi$
$212$	−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	−0.156242	−	0.987719i	$-0.549938\pi$
$223$	−11.7287	−	3.14269i	−0.785411	−	0.210450i	−0.629169	+	0.777268i	$0.716605\pi$
$224$	−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	−0.976669	−	0.214748i	$-0.931107\pi$
$227$	−3.58919	−	13.3950i	−0.238223	−	0.889061i	0.738446	−	0.674312i	$-0.235560\pi$
$228$	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	−0.366277	−	0.930506i	$-0.619368\pi$
$233$	8.61258	−	8.61258i	0.564229	−	0.564229i	0.930506	+	0.366277i	$0.119368\pi$
$234$	−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	$0.121896\pi$
$239$			11.5531i			0.747310i	−0.927568	+	0.373655i	$0.878104\pi$
$240$	9.23211	+	16.9939i	0.595930	+	1.09695i
$241$	12.0934	+	6.98212i	0.779004	+	0.449758i	0.836077	−	0.548612i	$-0.184843\pi$
$241$	12.0934	+	6.98212i	0.779004	+	0.449758i	−0.0570731	+	0.998370i	$0.518177\pi$
$242$	−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	0.890597	−	0.454794i	$-0.150287\pi$
$251$	14.9246	+	8.61672i	0.942032	+	0.543882i	0.0514354	+	0.998676i	$0.483620\pi$
$252$	−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	−0.962464	−	0.271409i	$-0.912511\pi$
$257$	0.108348	−	0.404361i	0.00675857	−	0.0252233i	0.969223	+	0.246185i	$0.0791772\pi$
$258$	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	−0.152865	−	0.988247i	$-0.548850\pi$
$263$	−12.6393	−	3.38670i	−0.779374	−	0.208833i	−0.626509	+	0.779414i	$0.715517\pi$
$264$	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	−0.878067	−	0.478537i	$-0.841167\pi$
$269$	−0.403612	+	0.699076i	−0.0246086	+	0.0426234i	0.853459	+	0.521160i	$0.174501\pi$
$270$	7.62805	+	18.3281i	0.464228	+	1.11541i
$271$	−9.22378	+	5.32535i	−0.560305	+	0.323492i	−0.753268	−	0.657714i	$-0.771524\pi$
$271$	−9.22378	+	5.32535i	−0.560305	+	0.323492i	0.192963	+	0.981206i	$0.438190\pi$
$272$	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	0.718957	+	0.695055i	$0.244620\pi$
$277$	7.38713	+	27.5691i	0.443849	+	1.65647i	−0.275107	+	0.961414i	$0.588713\pi$
$278$	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	−0.956608	−	0.291379i	$-0.905886\pi$
$283$	0.294869	−	1.10046i	0.0175281	−	0.0654158i	0.974136	+	0.225963i	$0.0725528\pi$
$284$	−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	−0.465420	−	0.885090i	$-0.654097\pi$
$293$	−7.29093	+	1.95360i	−0.425941	+	0.114130i	0.0394794	+	0.999220i	$0.487430\pi$
$294$	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	0.540090	−	0.841607i	$-0.318390\pi$
$307$	−5.28300	−	5.28300i	−0.301517	−	0.301517i	−0.841607	+	0.540090i	$0.818390\pi$
$308$	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	$-0.978540\pi$
$311$		−	2.37607i		−	0.134735i	0.997728	−	0.0673674i	$-0.0214599\pi$
$312$	8.09904	−	8.20821i	0.458518	−	0.464698i
$313$	20.5099	+	20.5099i	1.15929	+	1.15929i	0.984629	+	0.174659i	$0.0558822\pi$
$313$	20.5099	+	20.5099i	1.15929	+	1.15929i	0.174659	+	0.984629i	$0.444118\pi$
$314$	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	−0.449162	+	0.893450i	$0.648277\pi$
$317$	−23.9045	+	23.9045i	−1.34261	+	1.34261i	−0.893450	+	0.449162i	$0.851723\pi$
$318$	−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	0.793722	−	0.608280i	$-0.208140\pi$
$331$	12.0767	+	6.97251i	0.663798	+	0.383244i	−0.129925	+	0.991524i	$0.541474\pi$
$332$	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	−0.773922	−	0.633281i	$-0.781708\pi$
$337$	−2.58183	+	2.58183i	−0.140641	+	0.140641i	0.633281	+	0.773922i	$0.281708\pi$
$338$	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	0.179877	−	0.983689i	$-0.442430\pi$
$347$	15.4146	−	4.13034i	0.827500	−	0.221728i	0.647623	+	0.761961i	$0.275763\pi$
$348$	5.77864	+	2.75112i	0.309768	+	0.147475i
$349$	−2.98342	−	5.16743i	−0.159699	−	0.276606i	0.775061	−	0.631886i	$-0.217719\pi$
$349$	−2.98342	−	5.16743i	−0.159699	−	0.276606i	−0.934760	+	0.355280i	$0.884386\pi$
$350$	−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	0.825517	+	0.564377i	$0.190884\pi$
$353$	−3.22389	+	12.0317i	−0.171590	+	0.640383i	−0.997107	+	0.0760061i	$0.975783\pi$
$354$	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	$0.289230\pi$
$359$			29.8863i			1.57734i	−0.614816	+	0.788671i	$0.710770\pi$
$360$	−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	0.581064	−	0.813858i	$-0.302637\pi$
$367$	12.9762	+	3.47695i	0.677351	+	0.181496i	0.0962869	+	0.995354i	$0.469303\pi$
$368$	−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	0.277657	−	0.960680i	$-0.410442\pi$
$373$	19.2834	−	5.16696i	0.998455	−	0.267535i	0.720798	+	0.693145i	$0.243776\pi$
$374$	−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	0.871350	+	0.490663i	$0.163245\pi$
$379$	16.7541	+	29.0190i	0.860601	+	1.49061i	−0.0107483	+	0.999942i	$0.503421\pi$
$380$	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	−0.324878	−	0.945756i	$-0.605323\pi$
$383$	−2.60975	+	0.699279i	−0.133352	+	0.0357315i	0.191526	+	0.981488i	$0.438656\pi$
$384$	−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	−0.523342	−	0.852122i	$-0.675315\pi$
$397$	−10.9688	+	2.93908i	−0.550509	+	0.147508i	−0.0271666	+	0.999631i	$0.508648\pi$
$398$	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	−0.932917	−	0.360091i	$-0.882746\pi$
$401$	−15.5856	−	26.9950i	−0.778307	−	1.34807i	0.154611	−	0.987975i	$-0.450588\pi$
$402$	−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	−0.707362	−	0.706852i	$-0.750115\pi$
$409$	5.22725	−	9.05386i	0.258471	−	0.447685i	0.965832	+	0.259167i	$0.0834481\pi$
$410$	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	0.999235	+	0.0390956i	$0.0124477\pi$
$419$	10.9200	+	18.9139i	0.533476	+	0.924007i	−0.465760	+	0.884911i	$0.654219\pi$
$420$	−0.386775	−	0.114469i	−0.0188727	−	0.00558550i
$421$			11.3030i			0.550876i	0.961319	+	0.275438i	$0.0888229\pi$
$421$			11.3030i			0.550876i	−0.961319	+	0.275438i	$0.911177\pi$
$422$	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	0.831414	−	0.555653i	$-0.187532\pi$
$431$	−1.35987	−	2.35537i	−0.0655028	−	0.113454i	−0.896917	+	0.442199i	$0.854198\pi$
$432$	−17.9017	−	18.7822i	−0.861295	−	0.903661i
$433$	13.6874	−	3.66753i	0.657775	−	0.176250i	0.0855335	−	0.996335i	$-0.472741\pi$
$433$	13.6874	−	3.66753i	0.657775	−	0.176250i	0.572242	+	0.820085i	$0.306074\pi$
$434$		−	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	−0.680711	−	0.732552i	$-0.738329\pi$
$439$	−8.10140	+	4.67735i	−0.386659	+	0.223237i	0.294053	+	0.955789i	$0.404996\pi$
$440$	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	−0.830230	−	0.557420i	$-0.811791\pi$
$443$	−5.74199	+	5.74199i	−0.272810	+	0.272810i	0.557420	+	0.830230i	$0.311791\pi$
$444$	−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	0.938446	−	0.345427i	$-0.112266\pi$
$449$	23.4891	+	13.5614i	1.10852	+	0.640004i	0.170074	+	0.985431i	$0.445599\pi$
$450$	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	−0.836514	−	0.547946i	$-0.815410\pi$
$457$	3.46105	−	12.9168i	0.161901	−	0.604224i	0.998415	−	0.0562781i	$-0.0179233\pi$
$458$	−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	−0.121611	−	0.992578i	$-0.538806\pi$
$461$	17.1508	−	29.7061i	0.798792	−	1.38355i	0.920403	−	0.390971i	$-0.127861\pi$
$462$	−1.37325	+	0.109082i	−0.0638896	+	0.00507496i
$463$	−19.4344	+	19.4344i	−0.903191	+	0.903191i	−0.995711	−	0.0925195i	$-0.970508\pi$
$463$	−19.4344	+	19.4344i	−0.903191	+	0.903191i	0.0925195	+	0.995711i	$0.470508\pi$
$464$	−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	0.0875827	−	0.996157i	$-0.472086\pi$
$467$	−19.6345	−	19.6345i	−0.908575	−	0.908575i	−0.996157	+	0.0875827i	$0.972086\pi$
$468$	−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	−0.533689	−	0.845681i	$-0.679195\pi$
$479$	−1.49161	+	0.861181i	−0.0681534	+	0.0393484i	0.465536	+	0.885029i	$0.345862\pi$
$480$	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	−0.683826	−	0.729645i	$-0.739685\pi$
$487$	−20.1087	+	5.38812i	−0.911213	+	0.244159i	−0.227388	+	0.973804i	$0.573018\pi$
$488$	−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	−0.871723	−	0.489999i	$-0.836997\pi$
$491$	−19.5711	+	11.2994i	−0.883233	+	0.509935i	−0.0115102	+	0.999934i	$0.503664\pi$
$492$	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	0.843553	+	0.537047i	$0.180460\pi$
$503$	8.55700	+	31.9352i	0.381538	+	1.42392i	−0.462015	+	0.886872i	$0.652873\pi$
$504$	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	−0.611820	−	0.790997i	$-0.709562\pi$
$509$	−5.25012	+	3.03116i	−0.232707	+	0.134354i	0.379113	+	0.925350i	$0.376229\pi$
$510$	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	$0.172446\pi$
$521$			23.5394i			1.03128i	−0.856805	+	0.515640i	$0.827554\pi$
$522$	−12.0858	+	16.6857i	−0.528982	+	0.730312i
$523$	8.20158	−	30.6087i	0.358630	−	1.33843i	−0.517225	−	0.855850i	$-0.673035\pi$
$523$	8.20158	−	30.6087i	0.358630	−	1.33843i	0.875854	−	0.482575i	$-0.160299\pi$
$524$	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	$-0.804591\pi$
$541$		−	26.7974i		−	1.15211i	0.817411	−	0.576055i	$-0.195409\pi$
$542$	−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	−0.553993	−	0.832521i	$-0.686897\pi$
$547$	6.51421	−	6.51421i	0.278528	−	0.278528i	0.832521	+	0.553993i	$0.186897\pi$
$548$	−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	−0.256531	−	0.966536i	$-0.582580\pi$
$557$	−22.7031	−	6.08328i	−0.961962	−	0.257757i	−0.705431	+	0.708779i	$0.749246\pi$
$558$	−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	−0.804201	−	0.594358i	$-0.797406\pi$
$563$	−9.60782	−	35.8569i	−0.404921	−	1.51119i	0.399279	−	0.916829i	$-0.369260\pi$
$564$	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	0.693397	−	0.720556i	$-0.256113\pi$
$569$	−6.61515	−	11.4578i	−0.277322	−	0.480335i	−0.970718	+	0.240221i	$0.922780\pi$
$570$	−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	0.738647	−	0.674092i	$-0.235465\pi$
$577$	1.55067	+	1.55067i	0.0645553	+	0.0645553i	−0.674092	+	0.738647i	$0.735465\pi$
$578$	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	0.638061	−	0.769986i	$-0.279737\pi$
$587$	19.5193	+	5.23017i	0.805646	+	0.215872i	0.167585	+	0.985858i	$0.446403\pi$
$588$	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	0.767566	−	0.640970i	$-0.221468\pi$
$593$	3.08282	+	3.08282i	0.126596	+	0.126596i	−0.640970	+	0.767566i	$0.721468\pi$
$594$	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	0.767850	−	0.640630i	$-0.221327\pi$
$601$	−4.18909	−	7.25572i	−0.170877	−	0.295967i	−0.938727	+	0.344663i	$0.887993\pi$
$602$	−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	−0.994352	−	0.106128i	$-0.966155\pi$
$607$	−4.58950	−	17.1283i	−0.186282	−	0.695214i	0.808070	−	0.589086i	$-0.200512\pi$
$608$	−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	−0.580291	−	0.814409i	$-0.697061\pi$
$613$	−36.8917	−	9.88511i	−1.49004	−	0.399256i	−0.909752	+	0.415153i	$0.863728\pi$
$614$	−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	−0.942828	−	0.333281i	$-0.891844\pi$
$617$	−7.27686	−	27.1576i	−0.292955	−	1.09332i	0.649872	−	0.760043i	$-0.274822\pi$
$618$	−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	0.268714	−	0.963220i	$-0.413401\pi$
$631$	−10.8292	−	6.25222i	−0.431102	−	0.248897i	−0.699816	+	0.714323i	$0.746735\pi$
$632$	−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	0.428291	−	0.903641i	$-0.359116\pi$
$641$	−3.54806	−	2.04848i	−0.140140	−	0.0809099i	−0.568431	+	0.822731i	$0.692449\pi$
$642$	−2.77122	−	4.02588i	−0.109371	−	0.158889i
$643$	−10.8144	−	40.3600i	−0.426479	−	1.59164i	−0.760672	−	0.649137i	$-0.775130\pi$
$643$	−10.8144	−	40.3600i	−0.426479	−	1.59164i	0.334192	−	0.942505i	$-0.391536\pi$
$644$	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	−0.991138	−	0.132836i	$-0.957591\pi$
$647$	−1.68818	+	6.30036i	−0.0663691	+	0.247693i	0.924769	+	0.380529i	$0.124258\pi$
$648$	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	0.984842	−	0.173454i	$-0.0554929\pi$
$653$	44.7451	+	11.9894i	1.75101	+	0.469182i	0.766171	+	0.642637i	$0.222160\pi$
$654$	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	−0.528867	−	0.848705i	$-0.677383\pi$
$659$	12.0799	−	20.9230i	0.470566	−	0.815045i	0.999433	+	0.0336601i	$0.0107164\pi$
$660$	0.379514	−	14.6248i	0.0147725	−	0.569269i
$661$	35.3712	−	20.4215i	1.37578	−	0.794306i	0.384130	−	0.923279i	$-0.374501\pi$
$661$	35.3712	−	20.4215i	1.37578	−	0.794306i	0.991648	+	0.128973i	$0.0411680\pi$
$662$	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	−0.999781	−	0.0209488i	$-0.993331\pi$
$673$	−3.20311	+	11.9542i	−0.123471	+	0.460799i	0.876310	+	0.481748i	$0.159998\pi$
$674$	−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	0.278418	−	0.960460i	$-0.410190\pi$
$677$	−17.7462	−	17.7462i	−0.682043	−	0.682043i	−0.960460	+	0.278418i	$0.910190\pi$
$678$	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	0.173290	−	0.984871i	$-0.444560\pi$
$683$	21.3203	−	5.71276i	0.815798	−	0.218593i	0.642509	+	0.766278i	$0.277894\pi$
$684$	−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	−0.642027	−	0.766682i	$-0.721906\pi$
$691$	−7.86173	+	4.53897i	−0.299074	+	0.172671i	0.342953	+	0.939353i	$0.388573\pi$
$692$	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	$0.201635\pi$
$701$			31.3445i			1.18386i	−0.805988	+	0.591932i	$0.798365\pi$
$702$	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	0.380111	+	0.924941i	$0.375886\pi$
$709$	−16.2682	+	28.1774i	−0.610967	+	1.05823i	−0.991078	+	0.133285i	$0.957448\pi$
$710$	−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	−0.455940	−	0.890010i	$-0.650697\pi$
$719$	14.5548	−	25.2096i	0.542802	−	0.940160i	0.998742	−	0.0501495i	$-0.0159698\pi$
$720$	−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	−0.427161	−	0.904175i	$-0.640486\pi$
$727$	12.8617	−	12.8617i	0.477014	−	0.477014i	0.904175	+	0.427161i	$0.140486\pi$
$728$	−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	−0.501003	−	0.865446i	$-0.667035\pi$
$733$	9.86693	−	9.86693i	0.364443	−	0.364443i	0.865446	+	0.501003i	$0.167035\pi$
$734$	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	0.999136	−	0.0415576i	$-0.0132320\pi$
$739$	12.6022	+	21.8276i	0.463578	+	0.802941i	−0.535558	+	0.844498i	$0.679899\pi$
$740$	−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	−0.520904	−	0.853615i	$-0.674405\pi$
$743$	9.73165	−	36.3190i	0.357020	−	1.33242i	0.877924	−	0.478801i	$-0.158928\pi$
$744$	−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	0.999858	+	0.0168530i	$0.00536474\pi$
$751$	14.1002	+	24.4223i	0.514524	+	0.891182i	−0.485334	+	0.874329i	$0.661302\pi$
$752$	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	−0.313093	−	0.949722i	$-0.601365\pi$
$757$	−29.1397	−	7.80797i	−1.05910	−	0.283785i	−0.746008	+	0.665937i	$0.768032\pi$
$758$	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	−0.480556	−	0.876964i	$-0.659565\pi$
$761$	14.3226	−	24.8075i	0.519195	−	0.899272i	0.999751	−	0.0223082i	$-0.00710150\pi$
$762$	−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	0.728488	+	0.685059i	$0.240224\pi$
$769$	26.5529	+	45.9910i	0.957522	+	1.65848i	0.229035	+	0.973418i	$0.426443\pi$
$770$	−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	−0.813711	−	0.581270i	$-0.802556\pi$
$773$	−34.1355	+	9.14659i	−1.22777	+	0.328980i	−0.414059	+	0.910250i	$0.635889\pi$
$774$	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	0.0870495	−	0.996204i	$-0.472256\pi$
$787$	18.5304	−	4.96521i	0.660539	−	0.176991i	0.573489	+	0.819213i	$0.305590\pi$
$788$	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	0.0201695	−	0.999797i	$-0.493579\pi$
$797$	15.1753	−	4.06620i	0.537535	−	0.144032i	0.517366	+	0.855764i	$0.326913\pi$
$798$	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	0.983330	−	0.181831i	$-0.0582024\pi$
$809$	9.50547	+	16.4640i	0.334195	+	0.578842i	−0.649135	+	0.760673i	$0.724869\pi$
$810$	−34.3420	−	1.71658i	−1.20665	−	0.0603144i
$811$			18.8816i			0.663023i	0.943451	+	0.331512i	$0.107559\pi$
$811$			18.8816i			0.663023i	−0.943451	+	0.331512i	$0.892441\pi$
$812$	−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	0.849322	−	0.527875i	$-0.177011\pi$
$821$	−0.931007	−	1.61255i	−0.0324924	−	0.0562784i	−0.881814	+	0.471597i	$0.843678\pi$
$822$	−33.2935	−	15.8505i	−1.16124	−	0.552849i
$823$	−21.4397	+	5.74475i	−0.747341	+	0.200249i	−0.612338	−	0.790596i	$-0.709771\pi$
$823$	−21.4397	+	5.74475i	−0.747341	+	0.200249i	−0.135003	+	0.990845i	$0.543104\pi$
$824$		−	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	−0.596959	−	0.802272i	$-0.703625\pi$
$827$	5.90430	−	5.90430i	0.205313	−	0.205313i	0.802272	+	0.596959i	$0.203625\pi$
$828$	1.97055	−	19.0144i	0.0684813	−	0.660797i
$829$	27.7895	−	16.0443i	0.965168	−	0.557240i	0.0674084	−	0.997725i	$-0.478527\pi$
$829$	27.7895	−	16.0443i	0.965168	−	0.557240i	0.897760	+	0.440485i	$0.145194\pi$
$830$	−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	0.388919	−	0.921272i	$-0.372848\pi$
$839$	−6.21211	−	3.58656i	−0.214466	−	0.123822i	−0.603385	+	0.797450i	$0.706182\pi$
$840$	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	−0.0766825	−	0.997056i	$-0.524433\pi$
$853$	26.8806	−	26.8806i	0.920373	−	0.920373i	0.997056	+	0.0766825i	$0.0244328\pi$
$854$	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	0.996850	+	0.0793118i	$0.0252723\pi$
$857$	31.5042	+	31.5042i	1.07616	+	1.07616i	0.0793118	+	0.996850i	$0.474728\pi$
$858$	−42.2724	+	11.6307i	−1.44316	+	0.397066i
$859$		−	29.9066i		−	1.02040i	−0.860055	−	0.510201i	$-0.829571\pi$
$859$		−	29.9066i		−	1.02040i	0.860055	−	0.510201i	$-0.170429\pi$
$860$	−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	0.852553	−	0.522640i	$-0.175053\pi$
$863$	9.69182	+	9.69182i	0.329913	+	0.329913i	−0.522640	+	0.852553i	$0.675053\pi$
$864$	−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	−0.783478	−	0.621420i	$-0.786556\pi$
$877$	−34.0942	+	9.13551i	−1.15128	+	0.308484i	−0.367801	+	0.929904i	$0.619889\pi$
$878$	−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	−0.499600	−	0.866257i	$-0.666519\pi$
$881$	0.0237715	−	0.0137245i	0.000800881	−	0.000462389i	0.500400	+	0.865794i	$0.333186\pi$
$882$	29.0053	+	21.0092i	0.976660	+	0.707418i
$883$	−12.5285	−	12.5285i	−0.421617	−	0.421617i	0.464143	−	0.885760i	$-0.346362\pi$
$883$	−12.5285	−	12.5285i	−0.421617	−	0.421617i	−0.885760	+	0.464143i	$0.846362\pi$
$884$	−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	−0.977849	−	0.209309i	$-0.932878\pi$
$887$	−0.784839	+	2.92906i	−0.0263523	+	0.0983482i	0.951497	+	0.307658i	$0.0995451\pi$
$888$	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	−0.0313715	−	0.999508i	$-0.509988\pi$
$907$	−16.8138	−	4.50525i	−0.558294	−	0.149594i	−0.526922	+	0.849913i	$0.676654\pi$
$908$	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	$-0.974750\pi$
$911$		−	4.78351i		−	0.158485i	0.996855	−	0.0792423i	$-0.0252501\pi$
$912$	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	0.799158	−	0.601121i	$-0.205279\pi$
$919$	20.5581	+	11.8693i	0.678151	+	0.391530i	−0.121007	+	0.992652i	$0.538612\pi$
$920$	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	0.876589	−	0.481240i	$-0.159814\pi$
$929$	27.3742	+	15.8045i	0.898117	+	0.518528i	0.0215282	+	0.999768i	$0.493147\pi$
$930$	−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	−0.882902	−	0.469558i	$-0.844413\pi$
$937$	−12.6526	+	12.6526i	−0.413344	+	0.413344i	0.469558	+	0.882902i	$0.344413\pi$
$938$	−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	−0.146440	−	0.989220i	$-0.546782\pi$
$947$	−23.6300	−	6.33163i	−0.767871	−	0.205750i	−0.621431	+	0.783469i	$0.713448\pi$
$948$	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	0.871146	+	0.491024i	$0.163377\pi$
$953$	11.1821	+	41.7321i	0.362223	+	1.35184i	−0.508923	+	0.860812i	$0.669956\pi$
$954$	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	0.630108	−	0.776507i	$-0.283010\pi$
$967$	−4.55251	−	4.55251i	−0.146399	−	0.146399i	−0.776507	+	0.630108i	$0.783010\pi$
$968$	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	0.979424	+	0.201814i	$0.0646838\pi$
$971$	51.2257	+	29.5752i	1.64391	+	0.949113i	0.664488	+	0.747299i	$0.268650\pi$
$972$	−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	0.992399	−	0.123059i	$-0.0392703\pi$
$977$	55.9598	+	14.9944i	1.79031	+	0.479713i	0.797914	+	0.602772i	$0.205937\pi$
$978$	−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	0.375414	−	0.926857i	$-0.377500\pi$
$983$	−17.2893	−	17.2893i	−0.551443	−	0.551443i	−0.926857	+	0.375414i	$0.877500\pi$
$984$	−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	0.955131	−	0.296184i	$-0.0957142\pi$
$991$	6.95908	+	12.0535i	0.221063	+	0.382892i	−0.734068	+	0.679076i	$0.762381\pi$
$992$	−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	−0.820258	−	0.571994i	$-0.806170\pi$
$997$	−12.5004	−	46.6520i	−0.395891	−	1.47748i	0.424367	−	0.905490i	$-0.360497\pi$
$998$	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.23.19	yes	96
3.2	odd	2	inner	195.2.bf.a.23.6	yes	96
5.2	odd	4	inner	195.2.bf.a.62.6	yes	96
5.3	odd	4		975.2.bn.d.257.19		96
5.4	even	2		975.2.bn.d.218.6		96
13.4	even	6	inner	195.2.bf.a.173.19	yes	96
15.2	even	4	inner	195.2.bf.a.62.19	yes	96
15.8	even	4		975.2.bn.d.257.6		96
15.14	odd	2		975.2.bn.d.218.19		96
39.17	odd	6	inner	195.2.bf.a.173.6	yes	96
65.4	even	6		975.2.bn.d.368.6		96
65.17	odd	12	inner	195.2.bf.a.17.6	✓	96
65.43	odd	12		975.2.bn.d.407.19		96
195.17	even	12	inner	195.2.bf.a.17.19	yes	96
195.134	odd	6		975.2.bn.d.368.19		96
195.173	even	12		975.2.bn.d.407.6		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.bf.a.17.6	✓	96	65.17	odd	12	inner
195.2.bf.a.17.19	yes	96	195.17	even	12	inner
195.2.bf.a.23.6	yes	96	3.2	odd	2	inner
195.2.bf.a.23.19	yes	96	1.1	even	1	trivial
195.2.bf.a.62.6	yes	96	5.2	odd	4	inner
195.2.bf.a.62.19	yes	96	15.2	even	4	inner
195.2.bf.a.173.6	yes	96	39.17	odd	6	inner
195.2.bf.a.173.19	yes	96	13.4	even	6	inner
975.2.bn.d.218.6		96	5.4	even	2
975.2.bn.d.218.19		96	15.14	odd	2
975.2.bn.d.257.6		96	15.8	even	4
975.2.bn.d.257.19		96	5.3	odd	4
975.2.bn.d.368.6		96	65.4	even	6
975.2.bn.d.368.19		96	195.134	odd	6
975.2.bn.d.407.6		96	195.173	even	12
975.2.bn.d.407.19		96	65.43	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 195 = 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	195.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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