LMFDB - Embedded newform 195.2.bf.a.173.6

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			173.6
Character	$\chi$	$=$	195.173
Dual form			195.2.bf.a.62.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.442218 - 1.65038i) q^{2} +(1.56387 - 0.744530i) q^{3} +(-0.796141 + 0.459652i) q^{4} +(0.908487 + 2.04320i) q^{5} +(-1.92033 - 2.25172i) q^{6} +(0.0293212 - 0.109428i) q^{7} +(-1.30565 - 1.30565i) q^{8} +(1.89135 - 2.32869i) q^{9} +(2.97030 - 2.40288i) q^{10} +(2.05447 - 3.55845i) q^{11} +(-0.902832 + 1.31159i) q^{12} +(-1.57162 + 3.24500i) q^{13} -0.193564 q^{14} +(2.94197 + 2.51889i) q^{15} +(-2.49674 + 4.32449i) q^{16} +(-1.35141 + 5.04353i) q^{17} +(-4.67961 - 2.09165i) q^{18} +(-3.97662 - 6.88771i) q^{19} +(-1.66244 - 1.20908i) q^{20} +(-0.0356182 - 0.192962i) q^{21} +(-6.78132 - 1.81705i) q^{22} +(1.79398 + 6.69524i) q^{23} +(-3.01397 - 1.06977i) q^{24} +(-3.34930 + 3.71244i) q^{25} +(6.05047 + 1.15878i) q^{26} +(1.22403 - 5.04992i) q^{27} +(0.0269551 + 0.100598i) q^{28} +(2.00973 - 3.48095i) q^{29} +(2.85612 - 5.96926i) q^{30} +6.89468i q^{31} +(4.67403 + 1.25240i) q^{32} +(0.563544 - 7.09456i) q^{33} +8.92135 q^{34} +(0.250221 - 0.0395052i) q^{35} +(-0.435393 + 2.72333i) q^{36} +(-4.10339 + 1.09950i) 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} +(-0.302709 + 0.144115i) q^{42} +(1.30993 - 4.88872i) q^{43} +3.77737i q^{44} +(6.47624 + 1.74881i) q^{45} +(10.2563 - 5.92150i) q^{46} +(-0.185543 + 0.185543i) q^{47} +(-0.684859 + 8.62182i) q^{48} +(6.05106 + 3.49358i) q^{49} +(7.60804 + 3.88591i) q^{50} +(1.64164 + 8.89356i) q^{51} +(-0.240337 - 3.30587i) q^{52} +(1.94409 - 1.94409i) q^{53} +(-8.87558 + 0.213046i) q^{54} +(9.13708 + 0.964884i) q^{55} +(-0.181159 + 0.104592i) q^{56} +(-11.3470 - 7.81074i) q^{57} +(-6.63362 - 1.77747i) q^{58} +(0.619675 - 0.357770i) q^{59} +(-3.50004 - 0.653105i) q^{60} +(2.04160 + 3.53616i) q^{61} +(11.3788 - 3.04895i) q^{62} +(-0.199368 - 0.275247i) q^{63} +1.71922i q^{64} +(-8.05796 - 0.263096i) q^{65} +(-11.9579 + 2.20728i) q^{66} +(-2.85424 + 0.764792i) q^{67} +(-1.24236 - 4.63654i) q^{68} +(7.79036 + 9.13477i) q^{69} +(-0.175851 - 0.395490i) q^{70} +(-4.25380 - 7.36780i) q^{71} +(-5.50991 + 0.571017i) q^{72} +(3.00868 - 3.00868i) q^{73} +(3.62918 + 6.28592i) q^{74} +(-2.47384 + 8.29941i) q^{75} +(6.33191 + 3.65573i) q^{76} +(-0.329156 - 0.329156i) q^{77} +(10.3249 - 2.69259i) q^{78} -4.84485i q^{79} +(-11.1040 - 1.17260i) q^{80} +(-1.84560 - 8.80873i) q^{81} +(5.73743 + 1.53734i) q^{82} +(2.04442 + 2.04442i) q^{83} +(0.117052 + 0.137253i) q^{84} +(-11.5327 + 1.82079i) q^{85} -8.64751 q^{86} +(0.551270 - 6.94004i) q^{87} +(-7.32854 + 1.96368i) q^{88} +(-2.79966 - 1.61638i) q^{89} +(0.0222950 - 11.4616i) q^{90} +(0.309013 + 0.267127i) q^{91} +(-4.50574 - 4.50574i) q^{92} +(5.13330 + 10.7823i) q^{93} +(0.388267 + 0.224166i) q^{94} +(10.4602 - 14.3824i) q^{95} +(8.24201 - 1.52137i) q^{96} +(0.0386722 - 0.144327i) q^{97} +(3.08985 - 11.5315i) 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 $\left(\mathbb{Z}/195\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.442218	−	1.65038i	−0.312695	−	1.16699i	−0.926116	−	0.377238i	$-0.876874\pi$
$2$	−0.442218	−	1.65038i	−0.312695	−	1.16699i	0.613421	−	0.789756i	$-0.289793\pi$
$3$	1.56387	−	0.744530i	0.902898	−	0.429855i
$3$	1.56387	−	0.744530i	0.902898	−	0.429855i
$4$	−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
$7$	0.0293212	−	0.109428i	0.0110824	−	0.0413600i	−0.960163	−	0.279440i	$-0.909851\pi$
$7$	0.0293212	−	0.109428i	0.0110824	−	0.0413600i	0.971246	+	0.238080i	$0.0765180\pi$
$8$	−1.30565	−	1.30565i	−0.461618	−	0.461618i
$9$	1.89135	−	2.32869i	0.630450	−	0.776230i
$10$	2.97030	−	2.40288i	0.939291	−	0.759859i
$11$	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	$-0.0459766\pi$
$12$	−0.902832	+	1.31159i	−0.260625	+	0.378622i
$13$	−1.57162	+	3.24500i	−0.435890	+	0.900000i
$13$	−1.57162	+	3.24500i	−0.435890	+	0.900000i
$14$	−0.193564			−0.0517323
$15$	2.94197	+	2.51889i	0.759614	+	0.650374i
$16$	−2.49674	+	4.32449i	−0.624186	+	1.08112i
$17$	−1.35141	+	5.04353i	−0.327765	+	1.22324i	0.583738	+	0.811942i	$0.301589\pi$
$17$	−1.35141	+	5.04353i	−0.327765	+	1.22324i	−0.911503	+	0.411293i	$0.865077\pi$
$18$	−4.67961	−	2.09165i	−1.10299	−	0.493007i
$19$	−3.97662	−	6.88771i	−0.912300	−	1.58015i	−0.810807	−	0.585313i	$-0.800971\pi$
$19$	−3.97662	−	6.88771i	−0.912300	−	1.58015i	−0.101493	−	0.994836i	$-0.532362\pi$
$20$	−1.66244	−	1.20908i	−0.371734	−	0.270359i
$21$	−0.0356182	−	0.192962i	−0.00777254	−	0.0421077i
$22$	−6.78132	−	1.81705i	−1.44578	−	0.387396i
$23$	1.79398	+	6.69524i	0.374071	+	1.39605i	0.854697	+	0.519127i	$0.173743\pi$
$23$	1.79398	+	6.69524i	0.374071	+	1.39605i	−0.480625	+	0.876926i	$0.659590\pi$
$24$	−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
$27$	1.22403	−	5.04992i	0.235565	−	0.971858i
$28$	0.0269551	+	0.100598i	0.00509404	+	0.0190112i
$29$	2.00973	−	3.48095i	0.373197	−	0.646396i	−0.616858	−	0.787074i	$-0.711595\pi$
$29$	2.00973	−	3.48095i	0.373197	−	0.646396i	0.990055	+	0.140678i	$0.0449282\pi$
$30$	2.85612	−	5.96926i	0.521455	−	1.08983i
$31$			6.89468i			1.23832i	0.785265	+	0.619160i	$0.212527\pi$
$31$			6.89468i			1.23832i	−0.785265	+	0.619160i	$0.787473\pi$
$32$	4.67403	+	1.25240i	0.826260	+	0.221396i
$33$	0.563544	−	7.09456i	0.0981004	−	1.23500i
$34$	8.92135			1.53000
$35$	0.250221	−	0.0395052i	0.0422951	−	0.00667760i
$36$	−0.435393	+	2.72333i	−0.0725655	+	0.453888i
$37$	−4.10339	+	1.09950i	−0.674593	+	0.180757i	−0.579823	−	0.814743i	$-0.696878\pi$
$37$	−4.10339	+	1.09950i	−0.674593	+	0.180757i	−0.0947700	+	0.995499i	$0.530212\pi$
$38$	−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	$0.254174\pi$
$42$	−0.302709	+	0.144115i	−0.0467090	+	0.0222374i
$43$	1.30993	−	4.88872i	0.199762	−	0.745523i	−0.791220	−	0.611531i	$-0.790554\pi$
$43$	1.30993	−	4.88872i	0.199762	−	0.745523i	0.990982	−	0.133991i	$-0.0427794\pi$
$44$			3.77737i			0.569461i
$45$	6.47624	+	1.74881i	0.965421	+	0.260697i
$46$	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	$0.256092\pi$
$48$	−0.684859	+	8.62182i	−0.0988509	+	1.24445i
$49$	6.05106	+	3.49358i	0.864438	+	0.499083i
$50$	7.60804	+	3.88591i	1.07594	+	0.549551i
$51$	1.64164	+	8.89356i	0.229875	+	1.24535i
$52$	−0.240337	−	3.30587i	−0.0333287	−	0.458442i
$53$	1.94409	−	1.94409i	0.267042	−	0.267042i	−0.560865	−	0.827907i	$-0.689531\pi$
$53$	1.94409	−	1.94409i	0.267042	−	0.267042i	0.827907	+	0.560865i	$0.189531\pi$
$54$	−8.87558	+	0.213046i	−1.20781	+	0.0289919i
$55$	9.13708	+	0.964884i	1.23204	+	0.130105i
$56$	−0.181159	+	0.104592i	−0.0242084	+	0.0139767i
$57$	−11.3470	−	7.81074i	−1.50295	−	1.03456i
$58$	−6.63362	−	1.77747i	−0.871037	−	0.233394i
$59$	0.619675	−	0.357770i	0.0806749	−	0.0465777i	−0.459120	−	0.888374i	$-0.651835\pi$
$59$	0.619675	−	0.357770i	0.0806749	−	0.0465777i	0.539795	+	0.841797i	$0.318502\pi$
$60$	−3.50004	−	0.653105i	−0.451853	−	0.0843155i
$61$	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	$0.749149\pi$
$62$	11.3788	−	3.04895i	1.44511	−	0.387217i
$63$	−0.199368	−	0.275247i	−0.0251180	−	0.0346779i
$64$			1.71922i			0.214903i
$65$	−8.05796	−	0.263096i	−0.999467	−	0.0326330i
$66$	−11.9579	+	2.20728i	−1.47192	+	0.271697i
$67$	−2.85424	+	0.764792i	−0.348701	+	0.0934343i	−0.428919	−	0.903343i	$-0.641105\pi$
$67$	−2.85424	+	0.764792i	−0.348701	+	0.0934343i	0.0802172	+	0.996777i	$0.474439\pi$
$68$	−1.24236	−	4.63654i	−0.150658	−	0.562263i
$69$	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	$-0.335113\pi$
$72$	−5.50991	+	0.571017i	−0.649349	+	0.0672949i
$73$	3.00868	−	3.00868i	0.352139	−	0.352139i	−0.508766	−	0.860905i	$-0.669898\pi$
$73$	3.00868	−	3.00868i	0.352139	−	0.352139i	0.860905	+	0.508766i	$0.169898\pi$
$74$	3.62918	+	6.28592i	0.421884	+	0.730724i
$75$	−2.47384	+	8.29941i	−0.285654	+	0.958333i
$76$	6.33191	+	3.65573i	0.726319	+	0.419341i
$77$	−0.329156	−	0.329156i	−0.0375108	−	0.0375108i
$78$	10.3249	−	2.69259i	1.16906	−	0.304876i
$79$		−	4.84485i		−	0.545088i	−0.962143	−	0.272544i	$-0.912135\pi$
$79$		−	4.84485i		−	0.545088i	0.962143	−	0.272544i	$-0.0878650\pi$
$80$	−11.1040	−	1.17260i	−1.24147	−	0.131100i
$81$	−1.84560	−	8.80873i	−0.205066	−	0.978748i
$82$	5.73743	+	1.53734i	0.633593	+	0.169771i
$83$	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
$85$	−11.5327	+	1.82079i	−1.25089	+	0.197492i
$86$	−8.64751			−0.932485
$87$	0.551270	−	6.94004i	0.0591023	−	0.744050i
$88$	−7.32854	+	1.96368i	−0.781225	+	0.209329i
$89$	−2.79966	−	1.61638i	−0.296763	−	0.171336i	0.344225	−	0.938887i	$-0.388142\pi$
$89$	−2.79966	−	1.61638i	−0.296763	−	0.171336i	−0.640988	+	0.767551i	$0.721475\pi$
$90$	0.0222950	−	11.4616i	0.00235009	−	1.20816i
$91$	0.309013	+	0.267127i	0.0323933	+	0.0280025i
$92$	−4.50574	−	4.50574i	−0.469756	−	0.469756i
$93$	5.13330	+	10.7823i	0.532298	+	1.11808i
$94$	0.388267	+	0.224166i	0.0400466	+	0.0231209i
$95$	10.4602	−	14.3824i	1.07320	−	1.47561i
$96$	8.24201	−	1.52137i	0.841196	−	0.155274i
$97$	0.0386722	−	0.144327i	0.00392657	−	0.0146542i	−0.963935	−	0.266139i	$-0.914252\pi$
$97$	0.0386722	−	0.144327i	0.00392657	−	0.0146542i	0.967861	+	0.251485i	$0.0809188\pi$
$98$	3.08985	−	11.5315i	0.312122	−	1.16485i
$99$	−4.40081	−	11.5145i	−0.442298	−	1.15725i
$100$	0.960088	−	4.49514i	0.0960088	−	0.449514i
$101$	−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	$0.873014\pi$
$102$	13.9518	−	6.64221i	1.38143	−	0.657677i
$103$	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
$105$	0.361900	−	0.248078i	0.0353178	−	0.0242100i
$106$	−4.06820	−	2.34878i	−0.395139	−	0.228133i
$107$	−1.59525	+	0.427445i	−0.154218	+	0.0413227i	−0.335102	−	0.942182i	$-0.608771\pi$
$107$	−1.59525	+	0.427445i	−0.154218	+	0.0413227i	0.180884	+	0.983504i	$0.442104\pi$
$108$	1.34671	+	4.58308i	0.129587	+	0.441007i
$109$	0.638870			0.0611926			0.0305963	−	0.999532i	$-0.490259\pi$
$109$	0.638870			0.0611926			0.0305963	+	0.999532i	$0.490259\pi$
$110$	−2.44815	−	15.5063i	−0.233422	−	1.47847i
$111$	−5.59853	+	4.77457i	−0.531389	+	0.453182i
$112$	0.400014	+	0.400014i	0.0377977	+	0.0377977i
$113$	−7.64451	−	2.04834i	−0.719135	−	0.192692i	−0.119349	−	0.992852i	$-0.538081\pi$
$113$	−7.64451	−	2.04834i	−0.719135	−	0.192692i	−0.599786	+	0.800161i	$0.704747\pi$
$114$	−7.87282	+	22.1809i	−0.737357	+	2.07743i
$115$	−12.0499	+	9.74800i	−1.12366	+	0.909005i
$116$			3.69510i			0.343082i
$117$	4.58411	+	9.79724i	0.423801	+	0.905755i
$118$	−0.864487	−	0.864487i	−0.0795825	−	0.0795825i
$119$	0.512280	+	0.295765i	0.0469606	+	0.0271127i
$120$	−0.552404	−	7.12999i	−0.0504273	−	0.650876i
$121$	−2.94173	−	5.09522i	−0.267430	−	0.463202i
$122$	4.93316	−	4.93316i	0.446628	−	0.446628i
$123$	−0.476794	+	6.00245i	−0.0429911	+	0.541223i
$124$	−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
$127$	−3.29674	−	12.3036i	−0.292539	−	1.09177i	−0.943152	−	0.332361i	$-0.892155\pi$
$127$	−3.29674	−	12.3036i	−0.292539	−	1.09177i	0.650614	−	0.759409i	$-0.274512\pi$
$128$	12.1854	−	3.26508i	1.07705	−	0.288595i
$129$	−1.59125	−	8.62058i	−0.140102	−	0.759000i
$130$	3.12917	+	13.4150i	0.274446	+	1.17658i
$131$			12.9569i			1.13205i	0.824390	+	0.566023i	$0.191519\pi$
$131$			12.9569i			1.13205i	−0.824390	+	0.566023i	$0.808481\pi$
$132$	2.81237	+	5.90731i	0.244785	+	0.514165i
$133$	−0.870310	+	0.233199i	−0.0754655	+	0.0202209i
$134$	2.52439	+	4.37238i	0.218074	+	0.377716i
$135$	11.4300	−	2.08685i	0.983738	−	0.179607i
$136$	8.34958	−	4.82063i	0.715970	−	0.413366i
$137$	−12.0355	−	3.22490i	−1.02826	−	0.275522i	−0.295021	−	0.955491i	$-0.595327\pi$
$137$	−12.0355	−	3.22490i	−1.02826	−	0.275522i	−0.733241	+	0.679969i	$0.761993\pi$
$138$	11.6308	−	16.8966i	0.990079	−	1.43833i
$139$	−3.31851	+	1.91594i	−0.281472	+	0.162508i	−0.634090	−	0.773260i	$-0.718625\pi$
$139$	−3.31851	+	1.91594i	−0.281472	+	0.162508i	0.352618	+	0.935767i	$0.385292\pi$
$140$	−0.181053	+	0.146467i	−0.0153018	+	0.0123787i
$141$	−0.152022	+	0.428307i	−0.0128026	+	0.0360699i
$142$	−10.2785	+	10.2785i	−0.862557	+	0.862557i
$143$	8.31831	+	12.2593i	0.695612	+	1.02517i
$144$	5.34818	+	13.9933i	0.445682	+	1.16610i
$145$	8.93808	+	0.943869i	0.742267	+	0.0783841i
$146$	−6.29594	−	3.63496i	−0.521056	−	0.300832i
$147$	12.0641	+	0.958292i	0.995032	+	0.0790386i
$148$	2.76149	−	2.76149i	0.226993	−	0.226993i
$149$	10.3032	−	5.94857i	0.844073	−	0.487326i	−0.0145735	−	0.999894i	$-0.504639\pi$
$149$	10.3032	−	5.94857i	0.844073	−	0.487326i	0.858647	+	0.512568i	$0.171306\pi$
$150$	14.7911	+	0.412623i	1.20769	+	0.0336905i
$151$			11.1014i			0.903416i	0.892166	+	0.451708i	$0.149185\pi$
$151$			11.1014i			0.903416i	−0.892166	+	0.451708i	$0.850815\pi$
$152$	−3.80088	+	14.1851i	−0.308292	+	1.15056i
$153$	9.18883	+	12.6861i	0.742873	+	1.02561i
$154$	−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	$0.148789\pi$
$158$	−7.99583	+	2.14248i	−0.636114	+	0.170446i
$159$	1.59286	−	4.48774i	0.126322	−	0.355901i
$160$	1.68739	+	10.6878i	0.133400	+	0.844941i
$161$	0.785250			0.0618864
$162$	−13.7216	+	6.94131i	−1.07807	+	0.545361i
$163$	11.8393	+	3.17233i	0.927326	+	0.248476i	0.690714	−	0.723128i	$-0.257296\pi$
$163$	11.8393	+	3.17233i	0.927326	+	0.248476i	0.236612	+	0.971604i	$0.423963\pi$
$164$		−	3.19590i		−	0.249558i
$165$	15.0076	−	5.29389i	1.16834	−	0.412129i
$166$	2.46999	−	4.27815i	0.191708	−	0.332049i
$167$	2.30903	+	8.61742i	0.178678	+	0.666836i	0.995896	+	0.0905069i	$0.0288487\pi$
$167$	2.30903	+	8.61742i	0.178678	+	0.666836i	−0.817218	+	0.576329i	$0.804485\pi$
$168$	−0.205436	+	0.298446i	−0.0158497	+	0.0230256i
$169$	−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
$172$	1.20422	+	4.49422i	0.0918211	+	0.342681i
$173$	−8.49801	−	2.27704i	−0.646092	−	0.173120i	−0.0791307	−	0.996864i	$-0.525214\pi$
$173$	−8.49801	−	2.27704i	−0.646092	−	0.173120i	−0.566961	+	0.823744i	$0.691881\pi$
$174$	−11.6975	+	2.15920i	−0.886783	+	0.163689i
$175$	0.308040	+	0.475362i	0.0232856	+	0.0359340i
$176$	10.2590	+	17.7691i	0.773301	+	1.33940i
$177$	0.702718	−	1.02087i	0.0528196	−	0.0767334i
$178$	−1.42959	+	5.33529i	−0.107152	+	0.399897i
$179$	9.95273	−	17.2386i	0.743902	−	1.28848i	−0.206804	−	0.978382i	$-0.566306\pi$
$179$	9.95273	−	17.2386i	0.743902	−	1.28848i	0.950706	−	0.310094i	$-0.100360\pi$
$180$	−5.95984	+	1.58452i	−0.444221	+	0.118103i
$181$	7.45086			0.553818			0.276909	−	0.960896i	$-0.410690\pi$
$181$	7.45086			0.553818			0.276909	+	0.960896i	$0.410690\pi$
$182$	0.304210	−	0.628116i	0.0225496	−	0.0465590i
$183$	5.82556	+	4.01004i	0.430638	+	0.296430i
$184$	6.39934	−	11.0840i	0.471766	−	0.817122i
$185$	−5.97437	−	7.38515i	−0.439244	−	0.542967i
$186$	15.5249	−	13.2400i	1.13834	−	0.970805i
$187$	15.1707	+	15.1707i	1.10939	+	1.10939i
$188$	0.0624332	−	0.233004i	0.00455341	−	0.0169935i
$189$	−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	$0.0214457\pi$
$192$	1.28001	+	2.68863i	0.0923770	+	0.194035i
$193$	−5.67196	−	21.1680i	−0.408276	−	1.52371i	−0.797932	−	0.602748i	$-0.794072\pi$
$193$	−5.67196	−	21.1680i	−0.408276	−	1.52371i	0.389655	−	0.920961i	$-0.372594\pi$
$194$	−0.255295			−0.0183291
$195$	−12.7975	+	5.58795i	−0.916445	+	0.400162i
$196$	−6.42333			−0.458810
$197$	−2.25019	−	8.39781i	−0.160319	−	0.598319i	−0.998591	−	0.0530668i	$-0.983100\pi$
$197$	−2.25019	−	8.39781i	−0.160319	−	0.598319i	0.838272	−	0.545253i	$-0.183566\pi$
$198$	−17.0572	+	12.3549i	−1.21220	+	0.878026i
$199$	−17.5413	+	10.1275i	−1.24347	+	0.717919i	−0.969799	−	0.243904i	$-0.921572\pi$
$199$	−17.5413	+	10.1275i	−1.24347	+	0.717919i	−0.273673	+	0.961823i	$0.588239\pi$
$200$	9.22018	−	0.474126i	0.651965	−	0.0335258i
$201$	−3.89424	+	3.32110i	−0.274679	+	0.234253i
$202$	−5.36686	+	20.0294i	−0.377611	+	1.40926i
$203$	−0.321987	−	0.321987i	−0.0225990	−	0.0225990i
$204$	−5.39492	−	6.32595i	−0.377720	−	0.442905i
$205$	−7.73056	−	0.816354i	−0.539925	−	0.0570166i
$206$	0.638295	−	1.10556i	0.0444721	−	0.0770280i
$207$	18.9842	+	8.48540i	1.31949	+	0.589776i
$208$	−10.1090	−	14.8984i	−0.700934	−	1.03302i
$209$	−32.6795			−2.26049
$210$	−0.569461	−	0.487567i	−0.0392966	−	0.0336453i
$211$	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	$0.0858692\pi$
$212$	−0.654166	+	2.44138i	−0.0449283	+	0.167675i
$213$	−12.1379	−	8.35516i	−0.831677	−	0.572486i
$214$	1.41089	+	2.44374i	0.0964466	+	0.167050i
$215$	11.1787	−	1.76490i	0.762379	−	0.120365i
$216$	−8.19162	+	4.99529i	−0.557369	+	0.339886i
$217$	0.754473	+	0.202160i	0.0512169	+	0.0137235i
$218$	−0.282519	−	1.05438i	−0.0191346	−	0.0714114i
$219$	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
$222$	10.3556	+	7.12830i	0.695023	+	0.478420i
$223$	−3.14269	−	11.7287i	−0.210450	−	0.785411i	−0.987719	−	0.156242i	$-0.950062\pi$
$223$	−3.14269	−	11.7287i	−0.210450	−	0.785411i	0.777268	−	0.629169i	$-0.216605\pi$
$224$	0.274097	−	0.474749i	0.0183139	−	0.0317205i
$225$	2.31041	+	14.8210i	0.154028	+	0.988067i
$226$			13.5221i			0.899479i
$227$	13.3950	+	3.58919i	0.889061	+	0.238223i	0.674312	−	0.738446i	$-0.264440\pi$
$227$	13.3950	+	3.58919i	0.889061	+	0.238223i	0.214748	+	0.976669i	$0.431107\pi$
$228$	12.6240	+	1.00277i	0.836048	+	0.0664100i
$229$	8.51901			0.562952			0.281476	−	0.959568i	$-0.409176\pi$
$229$	8.51901			0.562952			0.281476	+	0.959568i	$0.409176\pi$
$230$	21.4165	+	15.5761i	1.41217	+	1.02706i
$231$	−0.759822	−	0.269689i	−0.0499926	−	0.0177442i
$232$	−7.16892	+	1.92091i	−0.470663	+	0.126114i
$233$	−8.61258	+	8.61258i	−0.564229	+	0.564229i	−0.930506	−	0.366277i	$-0.880632\pi$
$233$	−8.61258	+	8.61258i	−0.564229	+	0.564229i	0.366277	+	0.930506i	$0.380632\pi$
$234$	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
$237$	−3.60714	−	7.57669i	−0.234309	−	0.492159i
$238$	0.261585	−	0.976248i	0.0169560	−	0.0632807i
$239$			11.5531i			0.747310i	0.927568	+	0.373655i	$0.121896\pi$
$239$			11.5531i			0.747310i	−0.927568	+	0.373655i	$0.878104\pi$
$240$	−18.2383	+	6.43351i	−1.17727	+	0.415281i
$241$	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
$243$	−9.44464	−	12.4016i	−0.605874	−	0.795561i
$244$	−3.25080	−	1.87685i	−0.208111	−	0.120153i
$245$	−1.64076	+	15.5374i	−0.104824	+	0.992647i
$246$	10.1172	−	1.86750i	0.645047	−	0.119067i
$247$	28.6004	−	2.07924i	1.81980	−	0.132299i
$248$	9.00206	−	9.00206i	0.571631	−	0.571631i
$249$	4.71934	+	1.67507i	0.299076	+	0.106153i
$250$	−1.02787	+	19.0750i	−0.0650082	+	1.20641i
$251$	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	$0.150287\pi$
$252$	0.285243	+	0.127496i	0.0179686	+	0.00803147i
$253$	27.5104	+	7.37138i	1.72956	+	0.463435i
$254$	−18.8477	+	10.8818i	−1.18261	+	0.682782i
$255$	−16.6799	+	11.4339i	−1.04454	+	0.716017i
$256$	−9.05800	−	15.6889i	−0.566125	−	0.980557i
$257$	0.404361	−	0.108348i	0.0252233	−	0.00675857i	−0.246185	−	0.969223i	$-0.579177\pi$
$257$	0.404361	−	0.108348i	0.0252233	−	0.00675857i	0.271409	+	0.962464i	$0.412511\pi$
$258$	−13.5235	+	6.43833i	−0.841939	+	0.400833i
$259$			0.481265i			0.0299044i
$260$	6.53621	−	3.49440i	0.405358	−	0.216713i
$261$	−4.30496	−	11.2637i	−0.266470	−	0.697207i
$262$	21.3837	−	5.72975i	1.32109	−	0.353985i
$263$	−3.38670	−	12.6393i	−0.208833	−	0.779374i	−0.988247	−	0.152865i	$-0.951150\pi$
$263$	−3.38670	−	12.6393i	−0.208833	−	0.779374i	0.779414	−	0.626509i	$-0.215517\pi$
$264$	−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
$267$	−5.58173	−	0.443375i	−0.341597	−	0.0271341i
$268$	1.92084	−	1.92084i	0.117334	−	0.117334i
$269$	0.403612	+	0.699076i	0.0246086	+	0.0426234i	0.878067	−	0.478537i	$-0.158833\pi$
$269$	0.403612	+	0.699076i	0.0246086	+	0.0426234i	−0.853459	+	0.521160i	$0.825499\pi$
$270$	−8.49864	−	17.9410i	−0.517211	−	1.09185i
$271$	−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
$273$	0.682138	+	0.187682i	0.0412849	+	0.0113590i
$274$			21.2892i			1.28613i
$275$	6.32947	+	19.5454i	0.381682	+	1.17863i
$276$	−10.4010	−	3.69171i	−0.626069	−	0.222215i
$277$	−27.5691	−	7.38713i	−1.65647	−	0.443849i	−0.695055	−	0.718957i	$-0.744620\pi$
$277$	−27.5691	−	7.38713i	−1.65647	−	0.443849i	−0.961414	+	0.275107i	$0.911287\pi$
$278$	4.62953	+	4.62953i	0.277661	+	0.277661i
$279$	16.0556	+	13.0402i	0.961222	+	0.780699i
$280$	−0.378283	−	0.275122i	−0.0226067	−	0.0164417i
$281$	13.4870			0.804568			0.402284	−	0.915515i	$-0.368216\pi$
$281$	13.4870			0.804568			0.402284	+	0.915515i	$0.368216\pi$
$282$	0.774095	+	0.0614889i	0.0460967	+	0.00366161i
$283$	−1.10046	+	0.294869i	−0.0654158	+	0.0175281i	−0.291379	−	0.956608i	$-0.594114\pi$
$283$	−1.10046	+	0.294869i	−0.0654158	+	0.0175281i	0.225963	+	0.974136i	$0.427447\pi$
$284$	6.77325	+	3.91054i	0.401918	+	0.232048i
$285$	5.65025	−	30.2801i	0.334692	−	1.79364i
$286$	16.5540	−	19.1496i	0.978858	−	1.13234i
$287$	0.278487	+	0.278487i	0.0164386	+	0.0164386i
$288$	11.7567	−	8.51564i	0.692769	−	0.501789i
$289$	−8.88844	−	5.13174i	−0.522850	−	0.301867i
$290$	−2.39483	−	15.1686i	−0.140629	−	0.890731i
$291$	−0.0469775	−	0.254500i	−0.00275387	−	0.0149191i
$292$	−1.01239	+	3.77827i	−0.0592454	+	0.221107i
$293$	1.95360	−	7.29093i	0.114130	−	0.425941i	−0.885090	−	0.465420i	$-0.845903\pi$
$293$	1.95360	−	7.29093i	0.114130	−	0.425941i	0.999220	+	0.0394794i	$0.0125700\pi$
$294$	−3.75342	−	20.3341i	−0.218904	−	1.18591i
$295$	1.29396	+	0.941089i	0.0753373	+	0.0547923i
$296$	6.79317	+	3.92204i	0.394845	+	0.227964i
$297$	−15.4552	−	14.7306i	−0.896800	−	0.854757i
$298$	−14.3737	−	14.3737i	−0.832644	−	0.832644i
$299$	−24.5455	−	4.70092i	−1.41950	−	0.271861i
$300$	−1.84532	−	7.74460i	−0.106539	−	0.447135i
$301$	−0.496555	−	0.286686i	−0.0286210	−	0.0165243i
$302$	18.3214	−	4.90922i	1.05428	−	0.282494i
$303$	−20.9546	−	1.66449i	−1.20381	−	0.0956224i
$304$	39.7144			2.27778
$305$	−5.37029	+	7.38394i	−0.307502	+	0.422803i
$306$	16.8734	−	20.7751i	0.964587	−	1.18763i
$307$	5.28300	+	5.28300i	0.301517	+	0.301517i	0.841607	−	0.540090i	$-0.181610\pi$
$307$	5.28300	+	5.28300i	0.301517	+	0.301517i	−0.540090	+	0.841607i	$0.681610\pi$
$308$	0.413352	+	0.110757i	0.0235529	+	0.00631098i
$309$	1.21957	+	0.432871i	0.0693790	+	0.0246252i
$310$	16.5671	+	20.4792i	0.940949	+	1.16314i
$311$			2.37607i			0.134735i	0.997728	+	0.0673674i	$0.0214599\pi$
$311$			2.37607i			0.134735i	−0.997728	+	0.0673674i	$0.978540\pi$
$312$	8.20821	−	8.09904i	0.464698	−	0.458518i
$313$	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
$315$	0.381261	−	0.657406i	0.0214816	−	0.0370407i
$316$	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	$0.851723\pi$
$318$	−8.11085	−	0.644271i	−0.454834	−	0.0361289i
$319$	−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
$322$	−0.347251	−	1.29596i	−0.0193516	−	0.0722210i
$323$	40.1124	−	10.7481i	2.23191	−	0.598040i
$324$	5.51831	+	6.16466i	0.306573	+	0.342481i
$325$	−6.78300	−	16.7030i	−0.376253	−	0.926517i
$326$		−	20.9422i		−	1.15988i
$327$	0.999106	−	0.475658i	0.0552507	−	0.0263039i
$328$	6.20041	−	1.66140i	0.342361	−	0.0917352i
$329$	0.0148633	+	0.0257440i	0.000819441	+	0.00141931i
$330$	−15.3735	−	22.4271i	−0.846284	−	1.23457i
$331$	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	$0.208140\pi$
$332$	−2.56737	−	0.687925i	−0.140903	−	0.0377548i
$333$	−5.20054	+	11.6351i	−0.284988	+	0.637597i
$334$	13.2009	−	7.62155i	0.722322	−	0.417033i
$335$	−4.15567	−	5.13698i	−0.227048	−	0.280663i
$336$	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	$0.281708\pi$
$338$	−13.2693	+	17.8126i	−0.721754	+	0.968877i
$339$	−13.4800	+	2.48824i	−0.732135	+	0.135143i
$340$	8.34469	−	6.75061i	0.452555	−	0.366103i
$341$	24.5344	+	14.1649i	1.32861	+	0.767074i
$342$	4.20233	+	40.5495i	0.227236	+	2.19267i
$343$	1.12047	−	1.12047i	0.0604997	−	0.0604997i
$344$	−8.09329	+	4.67266i	−0.436361	+	0.251933i
$345$	−11.5867	+	24.2160i	−0.623807	+	1.30375i
$346$			15.0319i			0.808119i
$347$	4.13034	−	15.4146i	0.221728	−	0.827500i	−0.761961	−	0.647623i	$-0.775763\pi$
$347$	4.13034	−	15.4146i	0.221728	−	0.827500i	0.983689	−	0.179877i	$-0.0575701\pi$
$348$	2.75112	+	5.77864i	0.147475	+	0.309768i
$349$	2.98342	−	5.16743i	0.159699	−	0.276606i	−0.775061	−	0.631886i	$-0.782281\pi$
$349$	2.98342	−	5.16743i	0.159699	−	0.276606i	0.934760	+	0.355280i	$0.115614\pi$
$350$	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
$353$	12.0317	−	3.22389i	0.640383	−	0.171590i	0.0760061	−	0.997107i	$-0.475783\pi$
$353$	12.0317	−	3.22389i	0.640383	−	0.171590i	0.564377	+	0.825517i	$0.309116\pi$
$354$	−1.99558	−	0.708304i	−0.106064	−	0.0376459i
$355$	11.1893	−	15.3849i	0.593868	−	0.816546i
$356$	2.97190			0.157510
$357$	1.02134	+	0.0811285i	0.0540552	+	0.00429378i
$358$	−32.8515	−	8.80254i	−1.73626	−	0.465229i
$359$			29.8863i			1.57734i	0.614816	+	0.788671i	$0.289230\pi$
$359$			29.8863i			1.57734i	−0.614816	+	0.788671i	$0.710770\pi$
$360$	−6.17238	−	10.7391i	−0.325313	−	0.565999i
$361$	−22.1271	+	38.3252i	−1.16458	+	2.01712i
$362$	−3.29490	−	12.2967i	−0.173176	−	0.646302i
$363$	−8.39402	−	5.77804i	−0.440572	−	0.303268i
$364$	−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
$367$	−3.47695	−	12.9762i	−0.181496	−	0.677351i	−0.995354	−	0.0962869i	$-0.969303\pi$
$367$	−3.47695	−	12.9762i	−0.181496	−	0.677351i	0.813858	−	0.581064i	$-0.197363\pi$
$368$	−33.4326	−	8.95823i	−1.74279	−	0.466980i
$369$	3.72337	+	9.74201i	0.193831	+	0.507149i
$370$	−9.54631	+	13.1258i	−0.496289	+	0.682378i
$371$	−0.155736	−	0.269742i	−0.00808539	−	0.0140043i
$372$	−9.04296	−	6.22474i	−0.468855	−	0.322738i
$373$	−5.16696	+	19.2834i	−0.267535	+	0.998455i	0.693145	+	0.720798i	$0.256224\pi$
$373$	−5.16696	+	19.2834i	−0.267535	+	0.998455i	−0.960680	+	0.277657i	$0.910442\pi$
$374$	18.3287	−	31.7462i	0.947753	−	1.64156i
$375$	−19.2048	+	2.48537i	−0.991730	+	0.128344i
$376$	0.484510			0.0249867
$377$	8.13714	+	11.9923i	0.419084	+	0.617635i
$378$	−0.236929	+	0.977486i	−0.0121863	+	0.0502764i
$379$	−16.7541	+	29.0190i	−0.860601	+	1.49061i	0.0107483	+	0.999942i	$0.496579\pi$
$379$	−16.7541	+	29.0190i	−0.860601	+	1.49061i	−0.871350	+	0.490663i	$0.836755\pi$
$380$	−1.71691	+	16.2585i	−0.0880758	+	0.834044i
$381$	−14.3161	−	16.7867i	−0.733435	−	0.860007i
$382$	−27.7305	−	27.7305i	−1.41882	−	1.41882i
$383$	0.699279	−	2.60975i	0.0357315	−	0.133352i	−0.945756	−	0.324878i	$-0.894677\pi$
$383$	0.699279	−	2.60975i	0.0357315	−	0.133352i	0.981488	+	0.191526i	$0.0613436\pi$
$384$	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
$387$	−8.90678	−	12.2967i	−0.452757	−	0.625076i
$388$	0.0355516	+	0.132680i	0.00180486	+	0.00673582i
$389$	38.6182			1.95802			0.979011	−	0.203807i	$-0.0653316\pi$
$389$	38.6182			1.95802			0.979011	+	0.203807i	$0.0653316\pi$
$390$	14.8815	+	18.6495i	0.753554	+	0.944356i
$391$	−36.1920			−1.83031
$392$	−3.33918	−	12.4620i	−0.168654	−	0.629426i
$393$	9.64677	+	20.2628i	0.486615	+	1.02212i
$394$	−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
$397$	−2.93908	+	10.9688i	−0.147508	+	0.550509i	0.852122	+	0.523342i	$0.175315\pi$
$397$	−2.93908	+	10.9688i	−0.147508	+	0.550509i	−0.999631	+	0.0271666i	$0.991352\pi$
$398$	24.4713	+	24.4713i	1.22663	+	1.22663i
$399$	−1.18742	+	1.01266i	−0.0594456	+	0.0506966i
$400$	−7.69203	−	23.7530i	−0.384602	−	1.18765i
$401$	−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	$0.882746\pi$
$402$	7.20318	+	4.95832i	0.359262	+	0.247299i
$403$	−22.3732	−	10.8358i	−1.11449	−	0.539771i
$404$	11.1569			0.555076
$405$	16.3213	−	11.7735i	0.811010	−	0.585032i
$406$	−0.389012	+	0.673788i	−0.0193063	+	0.0334395i
$407$	−4.51779	+	16.8606i	−0.223938	+	0.835749i
$408$	9.46851	−	13.7553i	0.468761	−	0.680990i
$409$	−5.22725	−	9.05386i	−0.258471	−	0.447685i	0.707362	−	0.706852i	$-0.249885\pi$
$409$	−5.22725	−	9.05386i	−0.258471	−	0.447685i	−0.965832	+	0.259167i	$0.916552\pi$
$410$	2.07129	+	13.1193i	0.102294	+	0.647918i
$411$	−21.2229	+	3.91748i	−1.04685	+	0.193235i
$412$	−0.663461	−	0.177774i	−0.0326864	−	0.00875828i
$413$	−0.0209805	−	0.0783003i	−0.00103238	−	0.00385290i
$414$	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
$417$	−3.76322	+	5.46700i	−0.184286	+	0.267720i
$418$	14.4514	+	53.9335i	0.706843	+	2.63797i
$419$	−10.9200	+	18.9139i	−0.533476	+	0.924007i	0.465760	+	0.884911i	$0.345781\pi$
$419$	−10.9200	+	18.9139i	−0.533476	+	0.924007i	−0.999235	+	0.0390956i	$0.987552\pi$
$420$	−0.174094	+	0.363853i	−0.00849490	+	0.0177542i
$421$		−	11.3030i		−	0.550876i	−0.961319	−	0.275438i	$-0.911177\pi$
$421$		−	11.3030i		−	0.550876i	0.961319	−	0.275438i	$-0.0888229\pi$
$422$	−12.0401	−	3.22612i	−0.586101	−	0.157045i
$423$	0.0811457	+	0.782999i	0.00394544	+	0.0380707i
$424$	−5.07663			−0.246543
$425$	−14.1975	−	21.9093i	−0.688680	−	1.06276i
$426$	−8.42157	+	23.7270i	−0.408027	+	1.14957i
$427$	0.446818	−	0.119724i	0.0216230	−	0.00579387i
$428$	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	$0.187532\pi$
$432$	18.7822	+	17.9017i	0.903661	+	0.861295i
$433$	−3.66753	+	13.6874i	−0.176250	+	0.657775i	0.820085	+	0.572242i	$0.193926\pi$
$433$	−3.66753	+	13.6874i	−0.176250	+	0.657775i	−0.996335	+	0.0855335i	$0.972741\pi$
$434$		−	1.33456i		−	0.0640611i
$435$	14.6807	−	5.17859i	0.703885	−	0.248294i
$436$	−0.508630	+	0.293658i	−0.0243590	+	0.0140637i
$437$	38.9809	−	38.9809i	1.86471	−	1.86471i
$438$	−12.5523	−	0.997073i	−0.599774	−	0.0476420i
$439$	8.10140	+	4.67735i	0.386659	+	0.223237i	0.680711	−	0.732552i	$-0.261671\pi$
$439$	8.10140	+	4.67735i	0.386659	+	0.223237i	−0.294053	+	0.955789i	$0.595004\pi$
$440$	−10.6701	−	13.1897i	−0.508675	−	0.628793i
$441$	19.5801	−	7.48347i	0.932388	−	0.356356i
$442$	−14.0210	+	28.9497i	−0.666910	+	1.37700i
$443$	5.74199	−	5.74199i	0.272810	−	0.272810i	−0.557420	−	0.830230i	$-0.688209\pi$
$443$	5.74199	−	5.74199i	0.272810	−	0.272810i	0.830230	+	0.557420i	$0.188209\pi$
$444$	2.26258	−	6.37461i	0.107377	−	0.302525i
$445$	0.759135	−	7.18871i	0.0359864	−	0.340778i
$446$	−17.9670	+	10.3733i	−0.850763	+	0.491188i
$447$	11.6840	−	16.9738i	0.552633	−	0.802835i
$448$	0.188132	+	0.0504097i	0.00888838	+	0.00238163i
$449$	−23.4891	+	13.5614i	−1.10852	+	0.640004i	−0.938446	−	0.345427i	$-0.887734\pi$
$449$	−23.4891	+	13.5614i	−1.10852	+	0.640004i	−0.170074	+	0.985431i	$0.554401\pi$
$450$	23.4385	−	10.3672i	1.10490	−	0.488713i
$451$	7.14224	+	12.3707i	0.336315	+	0.582515i
$452$	7.02763	−	1.88305i	0.330552	−	0.0885711i
$453$	8.26530	+	17.3610i	0.388338	+	0.815693i
$454$		−	23.6941i		−	1.11202i
$455$	−0.265059	+	0.874055i	−0.0124262	+	0.0409763i
$456$	4.61715	+	25.0134i	0.216218	+	1.17136i
$457$	12.9168	−	3.46105i	0.604224	−	0.161901i	0.0562781	−	0.998415i	$-0.482077\pi$
$457$	12.9168	−	3.46105i	0.604224	−	0.161901i	0.547946	+	0.836514i	$0.315410\pi$
$458$	−3.76726	−	14.0596i	−0.176032	−	0.656962i
$459$	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	$0.538806\pi$
$462$	−0.109082	+	1.37325i	−0.00507496	+	0.0638896i
$463$	19.4344	−	19.4344i	0.903191	−	0.903191i	−0.0925195	−	0.995711i	$-0.529492\pi$
$463$	19.4344	−	19.4344i	0.903191	−	0.903191i	0.995711	+	0.0925195i	$0.0294920\pi$
$464$	10.0356	+	17.3821i	0.465889	+	0.806943i
$465$	−17.3669	+	20.2840i	−0.805371	+	0.940646i
$466$	18.0226	+	10.4054i	0.834883	+	0.482020i
$467$	19.6345	+	19.6345i	0.908575	+	0.908575i	0.996157	−	0.0875827i	$-0.0279142\pi$
$467$	19.6345	+	19.6345i	0.908575	+	0.908575i	−0.0875827	+	0.996157i	$0.527914\pi$
$468$	−8.15292	−	5.69289i	−0.376869	−	0.263154i
$469$			0.334760i			0.0154578i
$470$	−0.105280	+	0.996957i	−0.00485618	+	0.0459862i
$471$	4.53900	−	12.7882i	0.209146	−	0.589249i
$472$	−1.27621	−	0.341958i	−0.0587421	−	0.0157399i
$473$	−14.7051	−	14.7051i	−0.676140	−	0.676140i
$474$	−10.9093	+	9.30368i	−0.501079	+	0.427332i
$475$	38.8891	+	8.30608i	1.78435	+	0.381109i
$476$	−0.543796			−0.0249248
$477$	−0.850233	−	8.20415i	−0.0389295	−	0.375642i
$478$	19.0670	−	5.10900i	0.872107	−	0.233680i
$479$	1.49161	+	0.861181i	0.0681534	+	0.0393484i	0.533689	−	0.845681i	$-0.320805\pi$
$479$	1.49161	+	0.861181i	0.0681534	+	0.0393484i	−0.465536	+	0.885029i	$0.654138\pi$
$480$	10.5962	+	15.4579i	0.483649	+	0.705553i
$481$	2.88111	−	15.0435i	0.131367	−	0.685924i
$482$	−16.8711	−	16.8711i	−0.768456	−	0.768456i
$483$	1.22803	−	0.584643i	0.0558771	−	0.0266022i
$484$	4.68406	+	2.70434i	0.212912	+	0.122925i
$485$	0.330021	−	0.0521040i	0.0149855	−	0.00236592i
$486$	−16.2907	+	21.0714i	−0.738961	+	0.955819i
$487$	−5.38812	+	20.1087i	−0.244159	+	0.911213i	0.729645	+	0.683826i	$0.239685\pi$
$487$	−5.38812	+	20.1087i	−0.244159	+	0.911213i	−0.973804	+	0.227388i	$0.926982\pi$
$488$	1.95137	−	7.28262i	0.0883344	−	0.329669i
$489$	20.8770	−	3.85362i	0.944089	−	0.174267i
$490$	26.3681	−	4.16303i	1.19119	−	0.188066i
$491$	−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	$0.836997\pi$
$492$	−2.37945	−	4.99796i	−0.107274	−	0.225325i
$493$	14.8403	+	14.8403i	0.668374	+	0.668374i
$494$	−16.0791	−	46.2819i	−0.723434	−	2.08232i
$495$	19.5283	−	19.4525i	0.877733	−	0.874325i
$496$	−29.8159	−	17.2142i	−1.33878	−	0.772942i
$497$	−0.930972	+	0.249453i	−0.0417598	+	0.0111895i
$498$	0.677520	−	8.52943i	0.0303604	−	0.382213i
$499$	−35.8828			−1.60634			−0.803168	−	0.595753i	$-0.796854\pi$
$499$	−35.8828			−1.60634			−0.803168	+	0.595753i	$0.796854\pi$
$500$	10.0567	−	2.12213i	0.449748	−	0.0949044i
$501$	10.0269	+	11.7573i	0.447971	+	0.525279i
$502$	−20.8208	−	20.8208i	−0.929276	−	0.929276i
$503$	31.9352	+	8.55700i	1.42392	+	0.381538i	0.886872	−	0.462015i	$-0.152873\pi$
$503$	31.9352	+	8.55700i	1.42392	+	0.381538i	0.537047	+	0.843553i	$0.319540\pi$
$504$	−0.0990719	+	0.619683i	−0.00441302	+	0.0276029i
$505$	2.84989	−	26.9874i	0.126819	−	1.20092i
$506$		−	48.6623i		−	2.16330i
$507$	−20.1988	−	9.95022i	−0.897062	−	0.441905i
$508$	8.28006	+	8.28006i	0.367368	+	0.367368i
$509$	5.25012	+	3.03116i	0.232707	+	0.134354i	0.611820	−	0.790997i	$-0.290438\pi$
$509$	5.25012	+	3.03116i	0.232707	+	0.134354i	−0.379113	+	0.925350i	$0.623771\pi$
$510$	26.2464	+	22.4719i	1.16221	+	0.995071i
$511$	−0.241016	−	0.417452i	−0.0106619	−	0.0184670i
$512$	−4.04633	+	4.04633i	−0.178824	+	0.178824i
$513$	−39.6500	+	11.6509i	−1.75059	+	0.514398i
$514$	−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
$517$	0.279053	+	1.04144i	0.0122727	+	0.0458025i
$518$	0.794270	−	0.212824i	0.0348982	−	0.00935095i
$519$	−14.9851	+	2.76605i	−0.657772	+	0.121416i
$520$	10.1774	+	10.8644i	0.446308	+	0.476436i
$521$		−	23.5394i		−	1.03128i	−0.856805	−	0.515640i	$-0.827554\pi$
$521$		−	23.5394i		−	1.03128i	0.856805	−	0.515640i	$-0.172446\pi$
$522$	−16.6857	+	12.0858i	−0.730312	+	0.528982i
$523$	−30.6087	+	8.20158i	−1.33843	+	0.358630i	−0.855850	−	0.517225i	$-0.826965\pi$
$523$	−30.6087	+	8.20158i	−1.33843	+	0.358630i	−0.482575	+	0.875854i	$0.660299\pi$
$524$	−5.95565	−	10.3155i	−0.260174	−	0.450634i
$525$	0.835654	+	0.514056i	0.0364709	+	0.0224353i
$526$	−19.3620	+	11.1787i	−0.844224	+	0.487413i
$527$	−34.7735	−	9.31753i	−1.51476	−	0.405878i
$528$	29.2733	+	20.1503i	1.27396	+	0.876931i
$529$	−21.6892	+	12.5223i	−0.943010	+	0.544447i
$530$	1.10310	−	10.4460i	0.0479158	−	0.453744i
$531$	0.338887	−	2.11970i	0.0147065	−	0.0919871i
$532$	0.585699	−	0.585699i	0.0253933	−	0.0253933i
$533$	−7.03782	−	10.3722i	−0.304842	−	0.449268i
$534$	1.73660	+	9.40804i	0.0751502	+	0.407126i
$535$	−2.32262	−	2.87107i	−0.100415	−	0.124127i
$536$	4.72521	+	2.72810i	0.204098	+	0.117836i
$537$	2.73004	−	34.3690i	0.117810	−	1.48313i
$538$	0.975256	−	0.975256i	0.0420463	−	0.0420463i
$539$	24.8635	−	14.3550i	1.07095	−	0.618312i
$540$	−8.14067	+	6.91526i	−0.350319	+	0.297585i
$541$			26.7974i			1.15211i	0.817411	+	0.576055i	$0.195409\pi$
$541$			26.7974i			1.15211i	−0.817411	+	0.576055i	$0.804591\pi$
$542$	−4.70993	+	17.5777i	−0.202309	+	0.755027i
$543$	11.6521	−	5.54739i	0.500041	−	0.238061i
$544$	−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	$0.186897\pi$
$548$	11.0643	−	2.96467i	0.472643	−	0.126644i
$549$	12.0960	+	1.93385i	0.516244	+	0.0825347i
$550$	29.4584	−	19.0894i	1.25611	−	0.813973i
$551$	−31.9677			−1.36187
$552$	1.75534	−	22.0984i	0.0747124	−	0.940569i
$553$	−0.530163	−	0.142057i	−0.0225448	−	0.00604087i
$554$			48.7662i			2.07188i
$555$	−14.8416	−	7.10127i	−0.629990	−	0.301432i
$556$	1.76133	−	3.05072i	0.0746971	−	0.129379i
$557$	6.08328	+	22.7031i	0.257757	+	0.961962i	0.966536	+	0.256531i	$0.0825797\pi$
$557$	6.08328	+	22.7031i	0.257757	+	0.961962i	−0.708779	+	0.705431i	$0.750754\pi$
$558$	14.4213	−	32.2644i	0.610501	−	1.36586i
$559$	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
$562$	−5.96419	−	22.2587i	−0.251584	−	0.938926i
$563$	−35.8569	−	9.60782i	−1.51119	−	0.404921i	−0.594358	−	0.804201i	$-0.702594\pi$
$563$	−35.8569	−	9.60782i	−1.51119	−	0.404921i	−0.916829	+	0.399279i	$0.869260\pi$
$564$	−0.0758413	−	0.410870i	−0.00319350	−	0.0173007i
$565$	−2.75978	−	17.4801i	−0.116105	−	0.735394i
$566$	0.973289	+	1.68579i	0.0409104	+	0.0708589i
$567$	−1.01804	−	0.0563221i	−0.0427537	−	0.00236531i
$568$	−4.06580	+	15.1738i	−0.170597	+	0.636678i
$569$	6.61515	−	11.4578i	0.277322	−	0.480335i	−0.693397	−	0.720556i	$-0.743887\pi$
$569$	6.61515	−	11.4578i	0.277322	−	0.480335i	0.970718	+	0.240221i	$0.0772199\pi$
$570$	−52.4723	+	4.06535i	−2.19782	+	0.170279i
$571$	16.3611			0.684690			0.342345	−	0.939574i	$-0.388779\pi$
$571$	16.3611			0.684690			0.342345	+	0.939574i	$0.388779\pi$
$572$	−12.2576	−	5.93661i	−0.512515	−	0.248222i
$573$	22.5414	−	32.7469i	0.941681	−	1.36802i
$574$	0.336457	−	0.582760i	0.0140434	−	0.0243240i
$575$	−30.8642	−	15.7643i	−1.28713	−	0.657418i
$576$	4.00354	+	3.25165i	0.166814	+	0.135485i
$577$	−1.55067	−	1.55067i	−0.0645553	−	0.0645553i	0.674092	−	0.738647i	$-0.264535\pi$
$577$	−1.55067	−	1.55067i	−0.0645553	−	0.0645553i	−0.738647	+	0.674092i	$0.764535\pi$
$578$	−4.53869	+	16.9386i	−0.188785	+	0.704554i
$579$	−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
$582$	−0.399247	+	0.190075i	−0.0165493	+	0.00787886i
$583$	−2.92388	−	10.9121i	−0.121095	−	0.451931i
$584$	−7.85658			−0.325107
$585$	−15.8531	+	18.2669i	−0.655445	+	0.755243i
$586$	−12.8967			−0.532758
$587$	−5.23017	−	19.5193i	−0.215872	−	0.805646i	−0.985858	−	0.167585i	$-0.946403\pi$
$587$	−5.23017	−	19.5193i	−0.215872	−	0.805646i	0.769986	−	0.638061i	$-0.220263\pi$
$588$	−10.0452	+	4.78237i	−0.414258	+	0.197221i
$589$	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
$592$	5.49034	−	20.4902i	0.225651	−	0.842143i
$593$	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
$595$	−0.138906	+	1.31539i	−0.00569459	+	0.0539256i
$596$	−5.46855	+	9.47180i	−0.224000	+	0.387980i
$597$	−19.8921	+	28.8981i	−0.814128	+	1.18272i
$598$	3.09615	+	42.5882i	0.126611	+	1.74156i
$599$	17.9813			0.734698			0.367349	−	0.930083i	$-0.380266\pi$
$599$	17.9813			0.734698			0.367349	+	0.930083i	$0.380266\pi$
$600$	14.0661	−	7.60618i	0.574247	−	0.310521i
$601$	−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	$0.221327\pi$
$602$	−0.253555	+	0.946282i	−0.0103341	+	0.0385676i
$603$	−3.61741	+	8.09314i	−0.147312	+	0.329578i
$604$	−5.10277	−	8.83825i	−0.207629	−	0.359623i
$605$	7.73802	−	10.6395i	0.314595	−	0.432556i
$606$	6.51944	+	35.3190i	0.264834	+	1.43474i
$607$	17.1283	+	4.58950i	0.695214	+	0.186282i	0.589086	−	0.808070i	$-0.299488\pi$
$607$	17.1283	+	4.58950i	0.695214	+	0.186282i	0.106128	+	0.994352i	$0.466155\pi$
$608$	−9.96067	−	37.1737i	−0.403958	−	1.50759i
$609$	−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
$612$	−13.1468	−	5.87625i	−0.531428	−	0.237533i
$613$	−9.88511	−	36.8917i	−0.399256	−	1.49004i	−0.814409	−	0.580291i	$-0.802939\pi$
$613$	−9.88511	−	36.8917i	−0.399256	−	1.49004i	0.415153	−	0.909752i	$-0.363728\pi$
$614$	6.38272	−	11.0552i	0.257585	−	0.446151i
$615$	−12.6973	+	4.47897i	−0.512007	+	0.180609i
$616$			0.859527i			0.0346313i
$617$	27.1576	+	7.27686i	1.09332	+	0.292955i	0.760043	−	0.649872i	$-0.225178\pi$
$617$	27.1576	+	7.27686i	1.09332	+	0.292955i	0.333281	+	0.942828i	$0.391844\pi$
$618$	0.175085	−	2.20418i	0.00704295	−	0.0886650i
$619$	34.9871			1.40625			0.703125	−	0.711066i	$-0.251787\pi$
$619$	34.9871			1.40625			0.703125	+	0.711066i	$0.251787\pi$
$620$	8.33624	−	11.4620i	0.334792	−	0.460325i
$621$	36.0063	−	0.864283i	1.44488	−	0.0346825i
$622$	3.92142	−	1.05074i	0.157235	−	0.0421309i
$623$	−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
$627$	−51.1063	+	24.3309i	−2.04099	+	0.971681i
$628$	−1.86410	+	6.95692i	−0.0743857	+	0.277611i
$629$		−	22.1814i		−	0.884431i
$630$	−1.25357	−	0.338508i	−0.0499434	−	0.0134865i
$631$	−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
$633$	1.00056	−	12.5962i	0.0397686	−	0.500654i
$634$	50.0225	+	28.8805i	1.98665	+	1.14699i
$635$	22.1437	−	17.9136i	0.878744	−	0.710879i
$636$	0.794654	+	4.30503i	0.0315101	+	0.170706i
$637$	−20.8467	+	14.1451i	−0.825974	+	0.560449i
$638$	−19.9537	+	19.9537i	−0.789973	+	0.789973i
$639$	−25.2027	−	4.02929i	−0.997005	−	0.159396i
$640$	17.7415	+	21.9309i	0.701294	+	0.866897i
$641$	−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	$0.359116\pi$
$642$	4.02588	+	2.77122i	0.158889	+	0.109371i
$643$	−40.3600	−	10.8144i	−1.59164	−	0.426479i	−0.649137	−	0.760672i	$-0.724870\pi$
$643$	−40.3600	−	10.8144i	−1.59164	−	0.426479i	−0.942505	+	0.334192i	$0.891536\pi$
$644$	−0.625170	+	0.360942i	−0.0246351	+	0.0142231i
$645$	16.1679	−	11.0829i	0.636611	−	0.436389i
$646$	−35.4768	−	61.4477i	−1.39582	−	2.41763i
$647$	−6.30036	+	1.68818i	−0.247693	+	0.0663691i	−0.380529	−	0.924769i	$-0.624258\pi$
$647$	−6.30036	+	1.68818i	−0.247693	+	0.0663691i	0.132836	+	0.991138i	$0.457591\pi$
$648$	−9.09144	+	13.9109i	−0.357146	+	0.546470i
$649$		−	2.94012i		−	0.115410i
$650$	−24.5667	+	18.5809i	−0.963587	+	0.728802i
$651$	1.33041	−	0.245576i	0.0521428	−	0.00962489i
$652$	−10.8839	+	2.91634i	−0.426247	+	0.114213i
$653$	11.9894	+	44.7451i	0.469182	+	1.75101i	0.642637	+	0.766171i	$0.277840\pi$
$653$	11.9894	+	44.7451i	0.469182	+	1.75101i	−0.173454	+	0.984842i	$0.555493\pi$
$654$	−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
$657$	−1.31582	−	12.6967i	−0.0513350	−	0.495347i
$658$	0.0359145	−	0.0359145i	0.00140009	−	0.00140009i
$659$	−12.0799	−	20.9230i	−0.470566	−	0.815045i	0.528867	−	0.848705i	$-0.322617\pi$
$659$	−12.0799	−	20.9230i	−0.470566	−	0.815045i	−0.999433	+	0.0336601i	$0.989284\pi$
$660$	−9.51478	+	11.1129i	−0.370362	+	0.432570i
$661$	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
$663$	−31.4396	−	8.65022i	−1.22101	−	0.335947i
$664$		−	5.33862i		−	0.207178i
$665$	−1.26714	−	1.56636i	−0.0491375	−	0.0607407i
$666$	21.5020	+	3.43764i	0.833186	+	0.133206i
$667$	26.9112	+	7.21084i	1.04201	+	0.279205i
$668$	−5.79933	−	5.79933i	−0.224383	−	0.224383i
$669$	−13.6471	−	16.0023i	−0.527628	−	0.618683i
$670$	−6.64025	+	9.13008i	−0.256535	+	0.352726i
$671$	16.7777			0.647694
$672$	0.0751849	−	0.946517i	0.00290032	−	0.0365127i
$673$	11.9542	−	3.20311i	0.460799	−	0.123471i	−0.0209488	−	0.999781i	$-0.506669\pi$
$673$	11.9542	−	3.20311i	0.460799	−	0.123471i	0.481748	+	0.876310i	$0.340002\pi$
$674$	5.40272	+	3.11926i	0.208105	+	0.120150i
$675$	14.6479	+	21.4579i	0.563796	+	0.825914i
$676$	11.1053	+	4.41570i	0.427126	+	0.169834i
$677$	17.7462	+	17.7462i	0.682043	+	0.682043i	0.960460	−	0.278418i	$-0.0898099\pi$
$677$	17.7462	+	17.7462i	0.682043	+	0.682043i	−0.278418	+	0.960460i	$0.589810\pi$
$678$	10.0676	+	21.1468i	0.386645	+	0.812138i
$679$	−0.0146595	−	0.00846367i	−0.000562580	−	0.000324806i
$680$	17.4350	+	12.6803i	0.668601	+	0.486269i
$681$	23.6203	−	4.36001i	0.905132	−	0.167076i
$682$	12.5280	−	46.7550i	0.479721	−	1.79034i
$683$	−5.71276	+	21.3203i	−0.218593	+	0.815798i	0.766278	+	0.642509i	$0.222106\pi$
$683$	−5.71276	+	21.3203i	−0.218593	+	0.815798i	−0.984871	+	0.173290i	$0.944560\pi$
$684$	20.4889	−	7.83079i	0.783413	−	0.299418i
$685$	−4.34499	−	27.5207i	−0.166013	−	1.05151i
$686$	−2.34469	−	1.35371i	−0.0895208	−	0.0516848i
$687$	13.3226	−	6.34267i	0.508289	−	0.241988i
$688$	17.8706	+	17.8706i	0.681312	+	0.681312i
$689$	3.25319	+	9.36396i	0.123937	+	0.356738i
$690$	45.0895	+	8.41367i	1.71653	+	0.320303i
$691$	−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	$0.721906\pi$
$692$	7.81226	−	2.09329i	0.296978	−	0.0795749i
$693$	−1.38905	+	0.143953i	−0.0527657	+	0.00546834i
$694$	−27.2665			−1.03502
$695$	−6.92946	−	5.03975i	−0.262849	−	0.191169i
$696$	−9.78106	+	8.34152i	−0.370750	+	0.316185i
$697$	−12.8354	−	12.8354i	−0.486176	−	0.486176i
$698$	−9.84754	−	2.63864i	−0.372735	−	0.0998740i
$699$	−7.05659	+	19.8812i	−0.266905	+	0.751977i
$700$	−0.463744	−	0.236864i	−0.0175279	−	0.00895260i
$701$		−	31.3445i		−	1.18386i	−0.805988	−	0.591932i	$-0.798365\pi$
$701$		−	31.3445i		−	1.18386i	0.805988	−	0.591932i	$-0.201635\pi$
$702$	13.2577	−	29.1360i	0.500380	−	1.09967i
$703$	23.8907	+	23.8907i	0.901053	+	0.901053i
$704$	6.11777	+	3.53210i	0.230572	+	0.133121i
$705$	−1.01322	+	0.0785007i	−0.0381603	+	0.00295651i
$706$	−10.6413	−	18.4312i	−0.400489	−	0.693667i
$707$	−0.972198	+	0.972198i	−0.0365633	+	0.0365633i
$708$	−0.0902174	+	1.13576i	−0.00339058	+	0.0426846i
$709$	16.2682	+	28.1774i	0.610967	+	1.05823i	0.991078	+	0.133285i	$0.0425524\pi$
$709$	16.2682	+	28.1774i	0.610967	+	1.05823i	−0.380111	+	0.924941i	$0.624114\pi$
$710$	−30.3390	−	11.6632i	−1.13860	−	0.437711i
$711$	−11.2821	−	9.16330i	−0.423114	−	0.343650i
$712$	1.54495	+	5.76582i	0.0578993	+	0.216083i
$713$	−46.1615	+	12.3689i	−1.72876	+	0.463220i
$714$	−0.317763	−	1.72148i	−0.0118920	−	0.0644247i
$715$	−17.4911	+	28.1334i	−0.654130	+	1.05213i
$716$			18.2992i			0.683873i
$717$	8.60166	+	18.0676i	0.321235	+	0.674745i
$718$	49.3238	−	13.2163i	1.84075	−	0.493227i
$719$	−14.5548	−	25.2096i	−0.542802	−	0.940160i	−0.998742	−	0.0501495i	$-0.984030\pi$
$719$	−14.5548	−	25.2096i	−0.542802	−	0.940160i	0.455940	−	0.890010i	$-0.349303\pi$
$720$	−23.7322	+	23.6401i	−0.884448	+	0.881014i
$721$	0.0733041	−	0.0423222i	0.00272999	−	0.00157616i
$722$	73.0360	+	19.5699i	2.71812	+	0.728318i
$723$	13.7140	−	19.9230i	0.510030	−	0.740944i
$724$	−5.93194	+	3.42480i	−0.220459	+	0.127282i
$725$	6.19162	+	19.1197i	0.229951	+	0.710089i
$726$	−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	$0.140486\pi$
$728$	−0.0546877	−	0.752239i	−0.00202686	−	0.0278798i
$729$	−24.0035	−	12.3626i	−0.889018	−	0.457873i
$730$	1.70716	−	16.1662i	0.0631849	−	0.598337i
$731$	22.8861	+	13.2133i	0.846475	+	0.488712i
$732$	−6.48119	−	0.514822i	−0.239552	−	0.0190284i
$733$	−9.86693	+	9.86693i	−0.364443	+	0.364443i	−0.865446	−	0.501003i	$-0.832965\pi$
$733$	−9.86693	+	9.86693i	−0.364443	+	0.364443i	0.501003	+	0.865446i	$0.332965\pi$
$734$	−19.8780	+	11.4766i	−0.733711	+	0.423608i
$735$	9.00212	+	25.5200i	0.332048	+	0.941318i
$736$			33.5405i			1.23632i
$737$	−3.14249	+	11.7279i	−0.115755	+	0.432004i
$738$	14.4315	−	10.4531i	0.531230	−	0.384782i
$739$	−12.6022	+	21.8276i	−0.463578	+	0.802941i	−0.999136	−	0.0415576i	$-0.986768\pi$
$739$	−12.6022	+	21.8276i	−0.463578	+	0.802941i	0.535558	+	0.844498i	$0.320101\pi$
$740$	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
$743$	−36.3190	+	9.73165i	−1.33242	+	0.357020i	−0.853615	−	0.520904i	$-0.825595\pi$
$743$	−36.3190	+	9.73165i	−1.33242	+	0.357020i	−0.478801	+	0.877924i	$0.658928\pi$
$744$	7.37570	−	20.7803i	0.270406	−	0.761843i
$745$	21.5144	+	15.6473i	0.788228	+	0.573273i
$746$	34.1098			1.24885
$747$	8.62754	−	0.894111i	0.315665	−	0.0327138i
$748$	−19.0513	−	5.10478i	−0.696584	−	0.186649i
$749$			0.187098i			0.00683642i
$750$	12.5945	+	30.5960i	0.459886	+	1.11721i
$751$	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	$-0.00536474\pi$
$752$	−0.339125	−	1.26563i	−0.0123666	−	0.0461529i
$753$	16.9246	−	24.5872i	0.616768	−	0.896007i
$754$	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
$757$	7.80797	+	29.1397i	0.283785	+	1.05910i	0.949722	+	0.313093i	$0.101365\pi$
$757$	7.80797	+	29.1397i	0.283785	+	1.05910i	−0.665937	+	0.746008i	$0.731968\pi$
$758$	55.3013	+	14.8179i	2.00863	+	0.538211i
$759$	48.5108	−	8.95446i	1.76083	−	0.325026i
$760$	−32.4359	+	5.12101i	−1.17657	+	0.185759i
$761$	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	$0.659565\pi$
$762$	−21.3735	+	31.0503i	−0.774282	+	1.12483i
$763$	0.0187324	−	0.0699104i	0.000678160	−	0.00253093i
$764$	−10.5503	+	18.2736i	−0.381695	+	0.661115i
$765$	−17.5722	+	30.2997i	−0.635325	+	1.09549i
$766$	−4.61630			−0.166794
$767$	0.187066	+	2.57312i	0.00675455	+	0.0929101i
$768$	−25.8464	−	17.7914i	−0.932650	−	0.641992i
$769$	−26.5529	+	45.9910i	−0.957522	+	1.65848i	−0.229035	+	0.973418i	$0.573557\pi$
$769$	−26.5529	+	45.9910i	−0.957522	+	1.65848i	−0.728488	+	0.685059i	$0.759776\pi$
$770$	−1.76861	−	0.186767i	−0.0637364	−	0.00673063i
$771$	0.551697	−	0.470501i	0.0198689	−	0.0169447i
$772$	14.2456	+	14.2456i	0.512711	+	0.512711i
$773$	9.14659	−	34.1355i	0.328980	−	1.22777i	−0.581270	−	0.813711i	$-0.697444\pi$
$773$	9.14659	−	34.1355i	0.328980	−	1.22777i	0.910250	−	0.414059i	$-0.135889\pi$
$774$	−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
$777$	0.358317	+	0.752634i	0.0128545	+	0.0270006i
$778$	−17.0777	−	63.7347i	−0.612264	−	2.28500i
$779$	27.6489			0.990626
$780$	7.62006	−	10.3312i	0.272842	−	0.369915i
$781$	−34.9573			−1.25087
$782$	16.0047	+	59.7305i	0.572329	+	2.13596i
$783$	−15.1186	−	14.4098i	−0.540293	−	0.514963i
$784$	−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
$787$	4.96521	−	18.5304i	0.176991	−	0.660539i	−0.819213	−	0.573489i	$-0.805590\pi$
$787$	4.96521	−	18.5304i	0.176991	−	0.660539i	0.996204	−	0.0870495i	$-0.0277438\pi$
$788$	5.65154	+	5.65154i	0.201328	+	0.201328i
$789$	−14.7067	−	17.2447i	−0.523572	−	0.613928i
$790$	−11.6416	−	14.3906i	−0.414190	−	0.511996i
$791$	−0.448293	+	0.776465i	−0.0159394	+	0.0276079i
$792$	−9.28803	+	20.7799i	−0.330036	+	0.738382i
$793$	−14.6834	+	1.06748i	−0.521424	+	0.0379075i
$794$	19.4024			0.688566
$795$	10.6164	−	0.822519i	0.376526	−	0.0291717i
$796$	9.31025	−	16.1258i	0.329993	−	0.571565i
$797$	4.06620	−	15.1753i	0.144032	−	0.537535i	−0.855764	−	0.517366i	$-0.826913\pi$
$797$	4.06620	−	15.1753i	0.144032	−	0.537535i	0.999797	−	0.0201695i	$-0.00642060\pi$
$798$	2.19638	+	1.51188i	0.0777509	+	0.0535200i
$799$	−0.685047	−	1.18654i	−0.0242352	−	0.0419766i
$800$	−20.3042	+	13.1574i	−0.717862	+	0.465183i
$801$	−9.05919	+	3.46239i	−0.320091	+	0.122338i
$802$	51.4442	+	13.7844i	1.81656	+	0.486745i
$803$	−4.52499	−	16.8875i	−0.159683	−	0.595946i
$804$	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
$807$	1.15168	+	0.792760i	0.0405410	+	0.0279065i
$808$	5.79994	+	21.6457i	0.204041	+	0.761492i
$809$	−9.50547	+	16.4640i	−0.334195	+	0.578842i	−0.983330	−	0.181831i	$-0.941798\pi$
$809$	−9.50547	+	16.4640i	−0.334195	+	0.578842i	0.649135	+	0.760673i	$0.275131\pi$
$810$	−26.6483	−	21.7298i	−0.936327	−	0.763507i
$811$		−	18.8816i		−	0.663023i	−0.943451	−	0.331512i	$-0.892441\pi$
$811$		−	18.8816i		−	0.663023i	0.943451	−	0.331512i	$-0.107559\pi$
$812$	0.404349	+	0.108345i	0.0141899	+	0.00380216i
$813$	−18.3896	−	1.46075i	−0.644953	−	0.0512307i
$814$	29.8242			1.04534
$815$	4.27416	+	27.0720i	0.149717	+	0.948292i
$816$	−42.5589	−	15.1057i	−1.48986	−	0.528806i
$817$	−38.8812	+	10.4182i	−1.36028	+	0.364486i
$818$	−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	$0.177011\pi$
$822$	15.8505	+	33.2935i	0.552849	+	1.16124i
$823$	5.74475	−	21.4397i	0.200249	−	0.747341i	−0.790596	−	0.612338i	$-0.790229\pi$
$823$	5.74475	−	21.4397i	0.200249	−	0.747341i	0.990845	−	0.135003i	$-0.0431043\pi$
$824$		−	1.37961i		−	0.0480608i
$825$	24.4506	+	25.8539i	0.851261	+	0.900119i
$826$	−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	$0.203625\pi$
$828$	−19.0144	+	1.97055i	−0.660797	+	0.0684813i
$829$	−27.7895	−	16.0443i	−0.965168	−	0.557240i	−0.0674084	−	0.997725i	$-0.521473\pi$
$829$	−27.7895	−	16.0443i	−0.965168	−	0.557240i	−0.897760	+	0.440485i	$0.854806\pi$
$830$	10.9851	+	1.16003i	0.381297	+	0.0402653i
$831$	−48.6143	+	8.97358i	−1.68641	+	0.311290i
$832$	−5.57887	−	2.70197i	−0.193412	−	0.0936739i
$833$	−25.7974	+	25.7974i	−0.893829	+	0.893829i
$834$	10.6868	+	3.79313i	0.370053	+	0.131345i
$835$	−15.5094	+	12.5466i	−0.536723	+	0.434194i
$836$	26.0175	−	15.0212i	0.899833	−	0.519519i
$837$	34.8176	+	8.43932i	1.20347	+	0.291706i
$838$	36.0442	+	9.65801i	1.24513	+	0.333630i
$839$	6.21211	−	3.58656i	0.214466	−	0.123822i	−0.388919	−	0.921272i	$-0.627152\pi$
$839$	6.21211	−	3.58656i	0.214466	−	0.123822i	0.603385	+	0.797450i	$0.293818\pi$
$840$	−0.796420	−	0.148612i	−0.0274791	−	0.00512758i
$841$	6.42199	+	11.1232i	0.221448	+	0.383559i
$842$	−18.6543	+	4.99840i	−0.642869	+	0.172256i
$843$	21.0919	−	10.0415i	0.726443	−	0.345847i
$844$			6.70663i			0.230852i
$845$	13.5178	−	25.7346i	0.465027	−	0.885296i
$846$	1.25636	−	0.480177i	0.0431946	−	0.0165088i
$847$	−0.643817	+	0.172510i	−0.0221218	+	0.00592752i
$848$	3.55330	+	13.2611i	0.122021	+	0.455388i
$849$	−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
$852$	13.5040	+	1.07266i	0.462638	+	0.0367488i
$853$	−26.8806	+	26.8806i	−0.920373	+	0.920373i	−0.997056	−	0.0766825i	$-0.975567\pi$
$853$	−26.8806	+	26.8806i	−0.920373	+	0.920373i	0.0766825	+	0.997056i	$0.475567\pi$
$854$	−0.395181	−	0.684474i	−0.0135228	−	0.0234222i
$855$	−13.7082	−	51.5608i	−0.468812	−	1.76334i
$856$	2.64094	+	1.52474i	0.0902653	+	0.0521147i
$857$	−31.5042	−	31.5042i	−1.07616	−	1.07616i	−0.996850	−	0.0793118i	$-0.974728\pi$
$857$	−31.5042	−	31.5042i	−1.07616	−	1.07616i	−0.0793118	−	0.996850i	$-0.525272\pi$
$858$	11.6307	−	42.2724i	0.397066	−	1.44316i
$859$		−	29.9066i		−	1.02040i	−0.860055	−	0.510201i	$-0.829571\pi$
$859$		−	29.9066i		−	1.02040i	0.860055	−	0.510201i	$-0.170429\pi$
$860$	−8.08855	+	6.54341i	−0.275817	+	0.223128i
$861$	0.642858	+	0.228174i	0.0219085	+	0.00777615i
$862$	4.48861	+	1.20272i	0.152883	+	0.0409648i
$863$	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
$865$	−3.06791	−	19.4318i	−0.104312	−	0.660700i
$866$	24.2113			0.822732
$867$	−17.7211	−	1.40764i	−0.601839	−	0.0478060i
$868$	−0.693590	+	0.185847i	−0.0235420	+	0.00630806i
$869$	−17.2402	−	9.95361i	−0.584832	−	0.337653i
$870$	−15.0387	−	21.9386i	−0.509859	−	0.743789i
$871$	2.00405	−	10.4640i	0.0679045	−	0.354558i
$872$	−0.834142	−	0.834142i	−0.0282476	−	0.0282476i
$873$	−0.262950	−	0.363028i	−0.00889949	−	0.0122866i
$874$	−81.5712	−	47.0952i	−2.75919	−	1.59302i
$875$	−0.691407	+	1.06125i	−0.0233738	+	0.0358767i
$876$	1.22981	+	6.66246i	0.0415513	+	0.225104i
$877$	−9.13551	+	34.0942i	−0.308484	+	1.15128i	0.621420	+	0.783478i	$0.286556\pi$
$877$	−9.13551	+	34.0942i	−0.308484	+	1.15128i	−0.929904	+	0.367801i	$0.880111\pi$
$878$	4.13681	−	15.4388i	0.139610	−	0.521033i
$879$	−2.37315	−	12.8565i	−0.0800445	−	0.433640i
$880$	−26.9856	+	37.1041i	−0.909684	+	1.25078i
$881$	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	$0.666519\pi$
$882$	−21.0092	−	29.0053i	−0.707418	−	0.976660i
$883$	−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
$885$	2.72425	+	0.508343i	0.0915747	+	0.0170878i
$886$	−12.0157	−	6.93725i	−0.403674	−	0.233061i
$887$	−2.92906	+	0.784839i	−0.0983482	+	0.0263523i	−0.307658	−	0.951497i	$-0.599545\pi$
$887$	−2.92906	+	0.784839i	−0.0983482	+	0.0263523i	0.209309	+	0.977849i	$0.432878\pi$
$888$	13.5437	+	1.07582i	0.454496	+	0.0361021i
$889$	−1.44303			−0.0483976
$890$	−12.1998	+	1.92612i	−0.408938	+	0.0645635i
$891$	−35.1372	−	11.5298i	−1.17714	−	0.386264i
$892$	7.89315	+	7.89315i	0.264282	+	0.264282i
$893$	2.01580	+	0.540132i	0.0674562	+	0.0180748i
$894$	−33.1801	−	11.7768i	−1.10971	−	0.393876i
$895$	44.2638	+	4.67430i	1.47958	+	0.156245i
$896$		−	1.42917i		−	0.0477451i
$897$	−41.8858	+	10.9233i	−1.39853	+	0.364717i
$898$	32.7688	+	32.7688i	1.09351	+	1.09351i
$899$	24.0000	+	13.8564i	0.800446	+	0.462138i
$900$	−8.65192	−	10.7376i	−0.288397	−	0.357921i
$901$	7.17782	+	12.4324i	0.239128	+	0.414182i
$902$	17.2580	−	17.2580i	0.574627	−	0.574627i
$903$	−0.989992	−	0.0786383i	−0.0329449	−	0.00261692i
$904$	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
$907$	4.50525	+	16.8138i	0.149594	+	0.558294i	0.999508	+	0.0313715i	$0.00998751\pi$
$907$	4.50525	+	16.8138i	0.149594	+	0.558294i	−0.849913	+	0.526922i	$0.823346\pi$
$908$	−12.3141	+	3.29956i	−0.408659	+	0.109500i
$909$	−34.0094	+	12.9983i	−1.12802	+	0.431126i
$910$	1.55974	+	0.0509260i	0.0517047	+	0.00168818i
$911$			4.78351i			0.158485i	0.996855	+	0.0792423i	$0.0252501\pi$
$911$			4.78351i			0.158485i	−0.996855	+	0.0792423i	$0.974750\pi$
$912$	62.1080	−	29.5686i	2.05660	−	0.979114i
$913$	11.4752	−	3.07477i	0.379774	−	0.101760i
$914$	−11.4241	−	19.7871i	−0.377876	−	0.654500i
$915$	−2.90084	+	15.5458i	−0.0958989	+	0.513930i
$916$	−6.78234	+	3.91578i	−0.224095	+	0.129381i
$917$	1.41785	+	0.379911i	0.0468214	+	0.0125458i
$918$	10.9200	−	45.0521i	0.360415	−	1.48694i
$919$	−20.5581	+	11.8693i	−0.678151	+	0.391530i	−0.799158	−	0.601121i	$-0.794721\pi$
$919$	−20.5581	+	11.8693i	−0.678151	+	0.391530i	0.121007	+	0.992652i	$0.461388\pi$
$920$	28.4605	+	3.00545i	0.938314	+	0.0990868i
$921$	12.1953	+	4.32855i	0.401848	+	0.142631i
$922$	41.4418	−	41.4418i	1.36481	−	1.36481i
$923$	30.5938	−	2.22417i	1.00701	−	0.0732094i
$924$	0.728888	−	0.134543i	0.0239787	−	0.00442616i
$925$	9.66166	−	18.9161i	0.317674	−	0.621958i
$926$	−40.6683	−	23.4798i	−1.33644	−	0.771595i
$927$	2.22953	−	0.231056i	0.0732274	−	0.00758888i
$928$	13.7531	−	13.7531i	0.451467	−	0.451467i
$929$	−27.3742	+	15.8045i	−0.898117	+	0.518528i	−0.876589	−	0.481240i	$-0.840186\pi$
$929$	−27.3742	+	15.8045i	−0.898117	+	0.518528i	−0.0215282	+	0.999768i	$0.506853\pi$
$930$	41.1561	+	19.6921i	1.34956	+	0.645728i
$931$		−	55.5706i		−	1.82125i
$932$	2.89804	−	10.8156i	0.0949283	−	0.354277i
$933$	1.76906	+	3.71586i	0.0579164	+	0.121652i
$934$	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	$0.344413\pi$
$938$	0.552480	−	0.148037i	0.0180391	−	0.00483357i
$939$	47.3449	+	16.8045i	1.54504	+	0.548393i
$940$	0.532792	−	0.0841177i	0.0173778	−	0.00274362i
$941$	−49.4334			−1.61148			−0.805741	−	0.592268i	$-0.798233\pi$
$941$	−49.4334			−1.61148			−0.805741	+	0.592268i	$0.798233\pi$
$942$	−23.1126	−	1.83591i	−0.753048	−	0.0598171i
$943$	−23.2755	−	6.23666i	−0.757956	−	0.203094i
$944$			3.57304i			0.116293i
$945$	0.106781	−	1.31196i	0.00347360	−	0.0426779i
$946$	−17.7661	+	30.7718i	−0.577625	+	1.00048i
$947$	6.33163	+	23.6300i	0.205750	+	0.767871i	0.989220	+	0.146440i	$0.0467815\pi$
$947$	6.33163	+	23.6300i	0.205750	+	0.767871i	−0.783469	+	0.621431i	$0.786552\pi$
$948$	6.35443	+	4.37408i	0.206382	+	0.142064i
$949$	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
$952$	−0.282693	−	1.05503i	−0.00916215	−	0.0341936i
$953$	41.7321	+	11.1821i	1.35184	+	0.362223i	0.860812	−	0.508923i	$-0.169956\pi$
$953$	41.7321	+	11.1821i	1.35184	+	0.362223i	0.491024	+	0.871146i	$0.336623\pi$
$954$	−13.1640	+	5.03122i	−0.426199	+	0.162892i
$955$	41.5070	+	30.1878i	1.34313	+	0.976853i
$956$	−5.31043	−	9.19793i	−0.171751	−	0.297482i
$957$	−23.5632	−	16.2198i	−0.761691	−	0.524312i
$958$	0.761659	−	2.84255i	0.0246081	−	0.0918386i
$959$	−0.705791	+	1.22247i	−0.0227912	+	0.0394755i
$960$	−4.33053	+	5.05791i	−0.139767	+	0.163243i
$961$	−16.5366			−0.533437
$962$	−26.1015	+	1.89758i	−0.841546	+	0.0611803i
$963$	−2.02178	+	4.52328i	−0.0651510	+	0.145761i
$964$	−6.41870	+	11.1175i	−0.206732	+	0.358071i
$965$	38.0976	−	30.8198i	1.22640	−	0.992125i
$966$	−1.50794	−	1.76817i	−0.0485170	−	0.0568898i
$967$	4.55251	+	4.55251i	0.146399	+	0.146399i	0.776507	−	0.630108i	$-0.216990\pi$
$967$	4.55251	+	4.55251i	0.146399	+	0.146399i	−0.630108	+	0.776507i	$0.716990\pi$
$968$	−2.81172	+	10.4935i	−0.0903721	+	0.337273i
$969$	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	$-0.0646838\pi$
$972$	13.2197	+	5.53215i	0.424021	+	0.177444i
$973$	0.112355	+	0.419316i	0.00360195	+	0.0134427i
$974$	35.5697			1.13973
$975$	−23.0436	−	21.0711i	−0.737986	−	0.674816i
$976$	−20.3894			−0.652649
$977$	−14.9944	−	55.9598i	−0.479713	−	1.79031i	−0.602772	−	0.797914i	$-0.705937\pi$
$977$	−14.9944	−	55.9598i	−0.479713	−	1.79031i	0.123059	−	0.992399i	$-0.460730\pi$
$978$	−15.5921	−	32.7508i	−0.498580	−	1.04725i
$979$	−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
$982$	−9.99359	+	37.2966i	−0.318908	+	1.19018i
$983$	−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
$985$	15.1141	−	12.2269i	0.481576	−	0.389581i
$986$	17.9295	−	31.0548i	0.570991	−	0.988985i
$987$	0.0424114	+	0.0291940i	0.00134997	+	0.000929254i
$988$	−21.8142	+	14.8016i	−0.694002	+	0.470901i
$989$	35.0811			1.11551
$990$	−40.7398	−	23.6269i	−1.29479	−	0.750912i
$991$	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	$0.0957142\pi$
$992$	−8.63491	+	32.2259i	−0.274159	+	1.02317i
$993$	13.6952	−	19.8956i	0.434602	−	0.631367i
$994$	0.823384	+	1.42614i	0.0261162	+	0.0452345i
$995$	−36.6285	−	26.6397i	−1.16120	−	0.844535i
$996$	−4.52721	+	0.835664i	−0.143450	+	0.0264790i
$997$	46.6520	+	12.5004i	1.47748	+	0.395891i	0.905490	−	0.424367i	$-0.139503\pi$
$997$	46.6520	+	12.5004i	1.47748	+	0.395891i	0.571994	+	0.820258i	$0.306170\pi$
$998$	15.8680	+	59.2202i	0.502293	+	1.87458i
$999$	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.173.6	yes	96
3.2	odd	2	inner	195.2.bf.a.173.19	yes	96
5.2	odd	4	inner	195.2.bf.a.17.19	yes	96
5.3	odd	4		975.2.bn.d.407.6		96
5.4	even	2		975.2.bn.d.368.19		96
13.10	even	6	inner	195.2.bf.a.23.6	yes	96
15.2	even	4	inner	195.2.bf.a.17.6	✓	96
15.8	even	4		975.2.bn.d.407.19		96
15.14	odd	2		975.2.bn.d.368.6		96
39.23	odd	6	inner	195.2.bf.a.23.19	yes	96
65.23	odd	12		975.2.bn.d.257.6		96
65.49	even	6		975.2.bn.d.218.19		96
65.62	odd	12	inner	195.2.bf.a.62.19	yes	96
195.23	even	12		975.2.bn.d.257.19		96
195.62	even	12	inner	195.2.bf.a.62.6	yes	96
195.179	odd	6		975.2.bn.d.218.6		96

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

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+(-0.442218 - 1.65038i) q^{2} +(1.56387 - 0.744530i) q^{3} +(-0.796141 + 0.459652i) q^{4} +(0.908487 + 2.04320i) q^{5} +(-1.92033 - 2.25172i) q^{6} +(0.0293212 - 0.109428i) q^{7} +(-1.30565 - 1.30565i) q^{8} +(1.89135 - 2.32869i) q^{9} +(2.97030 - 2.40288i) q^{10} +(2.05447 - 3.55845i) q^{11} +(-0.902832 + 1.31159i) q^{12} +(-1.57162 + 3.24500i) q^{13} -0.193564 q^{14} +(2.94197 + 2.51889i) q^{15} +(-2.49674 + 4.32449i) q^{16} +(-1.35141 + 5.04353i) q^{17} +(-4.67961 - 2.09165i) q^{18} +(-3.97662 - 6.88771i) q^{19} +(-1.66244 - 1.20908i) q^{20} +(-0.0356182 - 0.192962i) q^{21} +(-6.78132 - 1.81705i) q^{22} +(1.79398 + 6.69524i) q^{23} +(-3.01397 - 1.06977i) q^{24} +(-3.34930 + 3.71244i) q^{25} +(6.05047 + 1.15878i) q^{26} +(1.22403 - 5.04992i) q^{27} +(0.0269551 + 0.100598i) q^{28} +(2.00973 - 3.48095i) q^{29} +(2.85612 - 5.96926i) q^{30} +6.89468i q^{31} +(4.67403 + 1.25240i) q^{32} +(0.563544 - 7.09456i) q^{33} +8.92135 q^{34} +(0.250221 - 0.0395052i) q^{35} +(-0.435393 + 2.72333i) q^{36} +(-4.10339 + 1.09950i) 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} +(-0.302709 + 0.144115i) q^{42} +(1.30993 - 4.88872i) q^{43} +3.77737i q^{44} +(6.47624 + 1.74881i) q^{45} +(10.2563 - 5.92150i) q^{46} +(-0.185543 + 0.185543i) q^{47} +(-0.684859 + 8.62182i) q^{48} +(6.05106 + 3.49358i) q^{49} +(7.60804 + 3.88591i) q^{50} +(1.64164 + 8.89356i) q^{51} +(-0.240337 - 3.30587i) q^{52} +(1.94409 - 1.94409i) q^{53} +(-8.87558 + 0.213046i) q^{54} +(9.13708 + 0.964884i) q^{55} +(-0.181159 + 0.104592i) q^{56} +(-11.3470 - 7.81074i) q^{57} +(-6.63362 - 1.77747i) q^{58} +(0.619675 - 0.357770i) q^{59} +(-3.50004 - 0.653105i) q^{60} +(2.04160 + 3.53616i) q^{61} +(11.3788 - 3.04895i) q^{62} +(-0.199368 - 0.275247i) q^{63} +1.71922i q^{64} +(-8.05796 - 0.263096i) q^{65} +(-11.9579 + 2.20728i) q^{66} +(-2.85424 + 0.764792i) q^{67} +(-1.24236 - 4.63654i) q^{68} +(7.79036 + 9.13477i) q^{69} +(-0.175851 - 0.395490i) q^{70} +(-4.25380 - 7.36780i) q^{71} +(-5.50991 + 0.571017i) q^{72} +(3.00868 - 3.00868i) q^{73} +(3.62918 + 6.28592i) q^{74} +(-2.47384 + 8.29941i) q^{75} +(6.33191 + 3.65573i) q^{76} +(-0.329156 - 0.329156i) q^{77} +(10.3249 - 2.69259i) q^{78} -4.84485i q^{79} +(-11.1040 - 1.17260i) q^{80} +(-1.84560 - 8.80873i) q^{81} +(5.73743 + 1.53734i) q^{82} +(2.04442 + 2.04442i) q^{83} +(0.117052 + 0.137253i) q^{84} +(-11.5327 + 1.82079i) q^{85} -8.64751 q^{86} +(0.551270 - 6.94004i) q^{87} +(-7.32854 + 1.96368i) q^{88} +(-2.79966 - 1.61638i) q^{89} +(0.0222950 - 11.4616i) q^{90} +(0.309013 + 0.267127i) q^{91} +(-4.50574 - 4.50574i) q^{92} +(5.13330 + 10.7823i) q^{93} +(0.388267 + 0.224166i) q^{94} +(10.4602 - 14.3824i) q^{95} +(8.24201 - 1.52137i) q^{96} +(0.0386722 - 0.144327i) q^{97} +(3.08985 - 11.5315i) 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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