LMFDB - Embedded newform 171.2.g.c.106.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [171,2,Mod(106,171)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(171, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 4]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("171.106");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 171 = 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	171.g (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.36544187456$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			106.8
Character	$\chi$	$=$	171.106
Dual form			171.2.g.c.121.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.185445 - 0.321199i) q^{2} +(-0.894876 - 1.48297i) q^{3} +(0.931221 - 1.61292i) q^{4} -3.55521 q^{5} +(-0.310379 + 0.562442i) q^{6} +(-0.124876 + 0.216291i) q^{7} -1.43254 q^{8} +(-1.39839 + 2.65415i) q^{9} +O(q^{10})$	\(q+(-0.185445 - 0.321199i) q^{2} +(-0.894876 - 1.48297i) q^{3} +(0.931221 - 1.61292i) q^{4} -3.55521 q^{5} +(-0.310379 + 0.562442i) q^{6} +(-0.124876 + 0.216291i) q^{7} -1.43254 q^{8} +(-1.39839 + 2.65415i) q^{9} +(0.659294 + 1.14193i) q^{10} +(-0.815815 + 1.41303i) q^{11} +(-3.22524 + 0.0623929i) q^{12} +(0.662707 - 1.14784i) q^{13} +0.0926300 q^{14} +(3.18147 + 5.27227i) q^{15} +(-1.59679 - 2.76571i) q^{16} +(3.73000 - 6.46055i) q^{17} +(1.11183 - 0.0430334i) q^{18} +(-4.07660 - 1.54315i) q^{19} +(-3.31069 + 5.73428i) q^{20} +(0.432501 - 0.00836682i) q^{21} +0.605154 q^{22} +(2.24572 - 3.88969i) q^{23} +(1.28194 + 2.12441i) q^{24} +7.63952 q^{25} -0.491582 q^{26} +(5.18741 - 0.301355i) q^{27} +(0.232573 + 0.402829i) q^{28} -4.12725 q^{29} +(1.10346 - 1.99960i) q^{30} +(-4.32871 - 7.49755i) q^{31} +(-2.02477 + 3.50700i) q^{32} +(2.82554 - 0.0546606i) q^{33} -2.76683 q^{34} +(0.443959 - 0.768960i) q^{35} +(2.97872 + 4.72710i) q^{36} +3.10599 q^{37} +(0.260326 + 1.59557i) q^{38} +(-2.29526 + 0.0444022i) q^{39} +5.09297 q^{40} +5.54922 q^{41} +(-0.0828923 - 0.137367i) q^{42} +(5.02032 + 8.69544i) q^{43} +(1.51941 + 2.63169i) q^{44} +(4.97159 - 9.43605i) q^{45} -1.66582 q^{46} +3.36575 q^{47} +(-2.67254 + 4.84295i) q^{48} +(3.46881 + 6.00816i) q^{49} +(-1.41671 - 2.45381i) q^{50} +(-12.9187 + 0.249914i) q^{51} +(-1.23425 - 2.13779i) q^{52} +(0.254182 + 0.440256i) q^{53} +(-1.05877 - 1.61031i) q^{54} +(2.90039 - 5.02363i) q^{55} +(0.178889 - 0.309845i) q^{56} +(1.35962 + 7.42640i) q^{57} +(0.765376 + 1.32567i) q^{58} -10.4624 q^{59} +(11.4664 - 0.221820i) q^{60} +4.14100 q^{61} +(-1.60547 + 2.78076i) q^{62} +(-0.399442 - 0.633898i) q^{63} -4.88521 q^{64} +(-2.35606 + 4.08082i) q^{65} +(-0.541537 - 0.897424i) q^{66} +(0.399675 - 0.692257i) q^{67} +(-6.94690 - 12.0324i) q^{68} +(-7.77793 + 0.150466i) q^{69} -0.329319 q^{70} +(5.60051 - 9.70037i) q^{71} +(2.00325 - 3.80216i) q^{72} +(-1.84754 + 3.20004i) q^{73} +(-0.575989 - 0.997642i) q^{74} +(-6.83642 - 11.3292i) q^{75} +(-6.28519 + 5.13823i) q^{76} +(-0.203751 - 0.352907i) q^{77} +(0.439905 + 0.729000i) q^{78} +(-4.92764 - 8.53493i) q^{79} +(5.67691 + 9.83269i) q^{80} +(-5.08898 - 7.42309i) q^{81} +(-1.02907 - 1.78241i) q^{82} +(0.185251 - 0.320865i) q^{83} +(0.389259 - 0.705381i) q^{84} +(-13.2609 + 22.9686i) q^{85} +(1.86198 - 3.22504i) q^{86} +(3.69338 + 6.12059i) q^{87} +(1.16868 - 2.02422i) q^{88} +(4.01034 + 6.94611i) q^{89} +(-3.95281 + 0.152993i) q^{90} +(0.165512 + 0.286675i) q^{91} +(-4.18251 - 7.24433i) q^{92} +(-7.24498 + 13.1287i) q^{93} +(-0.624161 - 1.08108i) q^{94} +(14.4932 + 5.48621i) q^{95} +(7.01269 - 0.135662i) q^{96} +(-3.21577 - 5.56988i) q^{97} +(1.28654 - 2.22836i) q^{98} +(-2.60956 - 4.14127i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + q^{2} - 2 q^{3} - 17 q^{4} - 6 q^{5} + 2 q^{6} + q^{7} - 36 q^{8} - 10 q^{9}+O(q^{10}) $ 32 * q + q^2 - 2 * q^3 - 17 * q^4 - 6 * q^5 + 2 * q^6 + q^7 - 36 * q^8 - 10 * q^9	\( 32 q + q^{2} - 2 q^{3} - 17 q^{4} - 6 q^{5} + 2 q^{6} + q^{7} - 36 q^{8} - 10 q^{9} - 8 q^{10} + 7 q^{11} - 3 q^{12} - 4 q^{13} - 2 q^{14} + q^{15} - 11 q^{16} - 7 q^{17} + 6 q^{18} + 7 q^{19} - 3 q^{20} + 11 q^{21} + 16 q^{22} + 5 q^{23} + 27 q^{24} + 18 q^{25} - 4 q^{26} - 5 q^{27} - 10 q^{28} - 20 q^{29} - 5 q^{30} - 10 q^{31} + 17 q^{32} + 34 q^{33} + 26 q^{34} - 3 q^{35} - 16 q^{36} + 2 q^{37} + 38 q^{38} - 24 q^{40} - 12 q^{41} + 25 q^{42} + 7 q^{43} + 20 q^{44} - 35 q^{45} + 18 q^{47} - 33 q^{48} - 13 q^{49} + q^{50} - 28 q^{51} + 19 q^{52} + 16 q^{53} + 35 q^{54} + 15 q^{55} - 6 q^{56} + 6 q^{57} - 74 q^{59} + 50 q^{60} + 24 q^{61} + 54 q^{62} - 30 q^{63} - 64 q^{64} + 54 q^{65} + 4 q^{66} - 11 q^{67} - 2 q^{68} + 3 q^{69} - 48 q^{70} + 9 q^{71} - 10 q^{73} + 6 q^{74} - 76 q^{75} + 29 q^{76} + 46 q^{77} - 82 q^{78} - 8 q^{79} - 24 q^{80} + 26 q^{81} + 7 q^{82} + 3 q^{83} + 12 q^{84} - 27 q^{85} + 17 q^{86} - 9 q^{87} + 9 q^{88} + 30 q^{89} - 74 q^{90} - q^{91} - 17 q^{92} - 24 q^{93} - 18 q^{94} - 6 q^{95} - 5 q^{96} + 18 q^{98} - 10 q^{99}+O(q^{100}) \) 32 * q + q^2 - 2 * q^3 - 17 * q^4 - 6 * q^5 + 2 * q^6 + q^7 - 36 * q^8 - 10 * q^9 - 8 * q^10 + 7 * q^11 - 3 * q^12 - 4 * q^13 - 2 * q^14 + q^15 - 11 * q^16 - 7 * q^17 + 6 * q^18 + 7 * q^19 - 3 * q^20 + 11 * q^21 + 16 * q^22 + 5 * q^23 + 27 * q^24 + 18 * q^25 - 4 * q^26 - 5 * q^27 - 10 * q^28 - 20 * q^29 - 5 * q^30 - 10 * q^31 + 17 * q^32 + 34 * q^33 + 26 * q^34 - 3 * q^35 - 16 * q^36 + 2 * q^37 + 38 * q^38 - 24 * q^40 - 12 * q^41 + 25 * q^42 + 7 * q^43 + 20 * q^44 - 35 * q^45 + 18 * q^47 - 33 * q^48 - 13 * q^49 + q^50 - 28 * q^51 + 19 * q^52 + 16 * q^53 + 35 * q^54 + 15 * q^55 - 6 * q^56 + 6 * q^57 - 74 * q^59 + 50 * q^60 + 24 * q^61 + 54 * q^62 - 30 * q^63 - 64 * q^64 + 54 * q^65 + 4 * q^66 - 11 * q^67 - 2 * q^68 + 3 * q^69 - 48 * q^70 + 9 * q^71 - 10 * q^73 + 6 * q^74 - 76 * q^75 + 29 * q^76 + 46 * q^77 - 82 * q^78 - 8 * q^79 - 24 * q^80 + 26 * q^81 + 7 * q^82 + 3 * q^83 + 12 * q^84 - 27 * q^85 + 17 * q^86 - 9 * q^87 + 9 * q^88 + 30 * q^89 - 74 * q^90 - q^91 - 17 * q^92 - 24 * q^93 - 18 * q^94 - 6 * q^95 - 5 * q^96 + 18 * q^98 - 10 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/171\mathbb{Z}\right)^\times$.

$n$	$20$	$154$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.185445	−	0.321199i	−0.131129	−	0.227122i	0.792983	−	0.609244i	$-0.208527\pi$
$2$	−0.185445	−	0.321199i	−0.131129	−	0.227122i	−0.924112	+	0.382122i	$0.875194\pi$
$3$	−0.894876	−	1.48297i	−0.516657	−	0.856193i
$3$	−0.894876	−	1.48297i	−0.516657	−	0.856193i
$4$	0.931221	−	1.61292i	0.465610	−	0.806461i
$5$	−3.55521			−1.58994			−0.794969	−	0.606650i	$-0.792513\pi$
$5$	−3.55521			−1.58994			−0.794969	+	0.606650i	$0.792513\pi$
$6$	−0.310379	+	0.562442i	−0.126712	+	0.229616i
$7$	−0.124876	+	0.216291i	−0.0471985	+	0.0817503i	−0.888660	−	0.458568i	$-0.848363\pi$
$7$	−0.124876	+	0.216291i	−0.0471985	+	0.0817503i	0.841461	+	0.540318i	$0.181696\pi$
$8$	−1.43254			−0.506478
$9$	−1.39839	+	2.65415i	−0.466132	+	0.884715i
$10$	0.659294	+	1.14193i	0.208487	+	0.361110i
$11$	−0.815815	+	1.41303i	−0.245977	+	0.426045i	−0.962406	−	0.271615i	$-0.912442\pi$
$11$	−0.815815	+	1.41303i	−0.245977	+	0.426045i	0.716429	+	0.697660i	$0.245776\pi$
$12$	−3.22524	+	0.0623929i	−0.931046	+	0.0180113i
$13$	0.662707	−	1.14784i	0.183802	−	0.318354i	−0.759370	−	0.650659i	$-0.774493\pi$
$13$	0.662707	−	1.14784i	0.183802	−	0.318354i	0.943172	+	0.332305i	$0.107826\pi$
$14$	0.0926300			0.0247564
$15$	3.18147	+	5.27227i	0.821453	+	1.36129i
$16$	−1.59679	−	2.76571i	−0.399196	−	0.691428i
$17$	3.73000	−	6.46055i	0.904658	−	1.56691i	0.0832816	−	0.996526i	$-0.473460\pi$
$17$	3.73000	−	6.46055i	0.904658	−	1.56691i	0.821376	−	0.570387i	$-0.193207\pi$
$18$	1.11183	−	0.0430334i	0.262062	−	0.0101431i
$19$	−4.07660	−	1.54315i	−0.935237	−	0.354022i
$19$	−4.07660	−	1.54315i	−0.935237	−	0.354022i
$20$	−3.31069	+	5.73428i	−0.740292	+	1.28222i
$21$	0.432501	−	0.00836682i	0.0943794	−	0.00182579i
$22$	0.605154			0.129019
$23$	2.24572	−	3.88969i	0.468264	−	0.811057i	−0.531078	−	0.847323i	$-0.678213\pi$
$23$	2.24572	−	3.88969i	0.468264	−	0.811057i	0.999342	+	0.0362656i	$0.0115462\pi$
$24$	1.28194	+	2.12441i	0.261675	+	0.433643i
$25$	7.63952			1.52790
$26$	−0.491582			−0.0964071
$27$	5.18741	−	0.301355i	0.998317	−	0.0579958i
$28$	0.232573	+	0.402829i	0.0439522	+	0.0761275i
$29$	−4.12725			−0.766411			−0.383206	−	0.923663i	$-0.625180\pi$
$29$	−4.12725			−0.766411			−0.383206	+	0.923663i	$0.625180\pi$
$30$	1.10346	−	1.99960i	0.201464	−	0.365075i
$31$	−4.32871	−	7.49755i	−0.777460	−	1.34660i	−0.933401	−	0.358834i	$-0.883174\pi$
$31$	−4.32871	−	7.49755i	−0.777460	−	1.34660i	0.155941	−	0.987766i	$-0.450159\pi$
$32$	−2.02477	+	3.50700i	−0.357932	+	0.619956i
$33$	2.82554	−	0.0546606i	0.491863	−	0.00951519i
$34$	−2.76683			−0.474508
$35$	0.443959	−	0.768960i	0.0750428	−	0.129978i
$36$	2.97872	+	4.72710i	0.496453	+	0.787849i
$37$	3.10599			0.510622			0.255311	−	0.966859i	$-0.417822\pi$
$37$	3.10599			0.510622			0.255311	+	0.966859i	$0.417822\pi$
$38$	0.260326	+	1.59557i	0.0422305	+	0.258836i
$39$	−2.29526	+	0.0444022i	−0.367535	+	0.00711004i
$40$	5.09297			0.805269
$41$	5.54922			0.866643			0.433322	−	0.901239i	$-0.357341\pi$
$41$	5.54922			0.866643			0.433322	+	0.901239i	$0.357341\pi$
$42$	−0.0828923	−	0.137367i	−0.0127906	−	0.0211962i
$43$	5.02032	+	8.69544i	0.765591	+	1.32604i	0.939934	+	0.341358i	$0.110887\pi$
$43$	5.02032	+	8.69544i	0.765591	+	1.32604i	−0.174342	+	0.984685i	$0.555780\pi$
$44$	1.51941	+	2.63169i	0.229059	+	0.396742i
$45$	4.97159	−	9.43605i	0.741121	−	1.40664i
$46$	−1.66582			−0.245612
$47$	3.36575			0.490946			0.245473	−	0.969403i	$-0.421057\pi$
$47$	3.36575			0.490946			0.245473	+	0.969403i	$0.421057\pi$
$48$	−2.67254	+	4.84295i	−0.385748	+	0.699020i
$49$	3.46881	+	6.00816i	0.495545	+	0.858308i
$50$	−1.41671	−	2.45381i	−0.200353	−	0.347021i
$51$	−12.9187	+	0.249914i	−1.80898	+	0.0349950i
$52$	−1.23425	−	2.13779i	−0.171160	−	0.296458i
$53$	0.254182	+	0.440256i	0.0349146	+	0.0604739i	0.882955	−	0.469458i	$-0.155551\pi$
$53$	0.254182	+	0.440256i	0.0349146	+	0.0604739i	−0.848040	+	0.529932i	$0.822217\pi$
$54$	−1.05877	−	1.61031i	−0.144080	−	0.219135i
$55$	2.90039	−	5.02363i	0.391089	−	0.677386i
$56$	0.178889	−	0.309845i	0.0239050	−	0.0414047i
$57$	1.35962	+	7.42640i	0.180085	+	0.983651i
$58$	0.765376	+	1.32567i	0.100499	+	0.174069i
$59$	−10.4624			−1.36209			−0.681045	−	0.732242i	$-0.738474\pi$
$59$	−10.4624			−1.36209			−0.681045	+	0.732242i	$0.738474\pi$
$60$	11.4664	−	0.221820i	1.48031	−	0.0286368i
$61$	4.14100			0.530201			0.265100	−	0.964221i	$-0.414595\pi$
$61$	4.14100			0.530201			0.265100	+	0.964221i	$0.414595\pi$
$62$	−1.60547	+	2.78076i	−0.203895	+	0.353157i
$63$	−0.399442	−	0.633898i	−0.0503250	−	0.0798636i
$64$	−4.88521			−0.610652
$65$	−2.35606	+	4.08082i	−0.292234	+	0.506164i
$66$	−0.541537	−	0.897424i	−0.0666586	−	0.110465i
$67$	0.399675	−	0.692257i	0.0488281	−	0.0845727i	−0.840578	−	0.541690i	$-0.817785\pi$
$67$	0.399675	−	0.692257i	0.0488281	−	0.0845727i	0.889406	+	0.457117i	$0.151118\pi$
$68$	−6.94690	−	12.0324i	−0.842436	−	1.45914i
$69$	−7.77793	+	0.150466i	−0.936353	+	0.0181139i
$70$	−0.329319			−0.0393612
$71$	5.60051	−	9.70037i	0.664658	−	1.15122i	−0.314719	−	0.949185i	$-0.601910\pi$
$71$	5.60051	−	9.70037i	0.664658	−	1.15122i	0.979378	−	0.202037i	$-0.0647563\pi$
$72$	2.00325	−	3.80216i	0.236086	−	0.448089i
$73$	−1.84754	+	3.20004i	−0.216239	+	0.374537i	−0.953655	−	0.300902i	$-0.902712\pi$
$73$	−1.84754	+	3.20004i	−0.216239	+	0.374537i	0.737416	+	0.675439i	$0.236046\pi$
$74$	−0.575989	−	0.997642i	−0.0669573	−	0.115974i
$75$	−6.83642	−	11.3292i	−0.789402	−	1.30818i
$76$	−6.28519	+	5.13823i	−0.720961	+	0.589396i
$77$	−0.203751	−	0.352907i	−0.0232195	−	0.0402174i
$78$	0.439905	+	0.729000i	0.0498094	+	0.0825430i
$79$	−4.92764	−	8.53493i	−0.554403	−	0.960255i	−0.997950	−	0.0640032i	$-0.979613\pi$
$79$	−4.92764	−	8.53493i	−0.554403	−	0.960255i	0.443546	−	0.896251i	$-0.353720\pi$
$80$	5.67691	+	9.83269i	0.634698	+	1.09933i
$81$	−5.08898	−	7.42309i	−0.565443	−	0.824788i
$82$	−1.02907	−	1.78241i	−0.113642	−	0.196834i
$83$	0.185251	−	0.320865i	0.0203340	−	0.0352195i	−0.855679	−	0.517506i	$-0.826860\pi$
$83$	0.185251	−	0.320865i	0.0203340	−	0.0352195i	0.876013	+	0.482287i	$0.160194\pi$
$84$	0.389259	−	0.705381i	0.0424716	−	0.0769634i
$85$	−13.2609	+	22.9686i	−1.43835	+	2.49130i
$86$	1.86198	−	3.22504i	0.200782	−	0.347765i
$87$	3.69338	+	6.12059i	0.395972	+	0.656196i
$88$	1.16868	−	2.02422i	0.124582	−	0.215783i
$89$	4.01034	+	6.94611i	0.425095	+	0.736286i	0.996429	−	0.0844315i	$-0.0269074\pi$
$89$	4.01034	+	6.94611i	0.425095	+	0.736286i	−0.571334	+	0.820717i	$0.693574\pi$
$90$	−3.95281	+	0.152993i	−0.416662	+	0.0161269i
$91$	0.165512	+	0.286675i	0.0173504	+	0.0300517i
$92$	−4.18251	−	7.24433i	−0.436057	−	0.755273i
$93$	−7.24498	+	13.1287i	−0.751269	+	1.36139i
$94$	−0.624161	−	1.08108i	−0.0643772	−	0.111505i
$95$	14.4932	+	5.48621i	1.48697	+	0.562873i
$96$	7.01269	−	0.135662i	0.715729	−	0.0138459i
$97$	−3.21577	−	5.56988i	−0.326512	−	0.565536i	0.655305	−	0.755364i	$-0.272540\pi$
$97$	−3.21577	−	5.56988i	−0.326512	−	0.565536i	−0.981817	+	0.189829i	$0.939207\pi$
$98$	1.28654	−	2.22836i	0.129961	−	0.225098i
$99$	−2.60956	−	4.14127i	−0.262271	−	0.416213i
$100$	7.11408	−	12.3220i	0.711408	−	1.23220i
$101$	7.56353			0.752600			0.376300	−	0.926498i	$-0.377196\pi$
$101$	7.56353			0.752600			0.376300	+	0.926498i	$0.377196\pi$
$102$	2.47597	+	4.10313i	0.245158	+	0.406270i
$103$	−6.90927	−	11.9672i	−0.680791	−	1.17916i	−0.974740	−	0.223343i	$-0.928303\pi$
$103$	−6.90927	−	11.9672i	−0.680791	−	1.17916i	0.293949	−	0.955821i	$-0.405030\pi$
$104$	−0.949353	+	1.64433i	−0.0930917	+	0.161240i
$105$	−1.53763	+	0.0297458i	−0.150057	+	0.00290289i
$106$	0.0942734	−	0.163286i	0.00915664	−	0.0158598i
$107$	12.0119			1.16123			0.580616	−	0.814177i	$-0.302812\pi$
$107$	12.0119			1.16123			0.580616	+	0.814177i	$0.302812\pi$
$108$	4.34456	−	8.64751i	0.418055	−	0.832107i
$109$	−7.62598	+	13.2086i	−0.730436	+	1.26515i	0.226261	+	0.974067i	$0.427350\pi$
$109$	−7.62598	+	13.2086i	−0.730436	+	1.26515i	−0.956697	+	0.291086i	$0.905984\pi$
$110$	−2.15145			−0.205133
$111$	−2.77948	−	4.60609i	−0.263816	−	0.437191i
$112$	0.797598			0.0753659
$113$	−1.46481	−	2.53713i	−0.137798	−	0.238673i	0.788865	−	0.614567i	$-0.210669\pi$
$113$	−1.46481	−	2.53713i	−0.137798	−	0.238673i	−0.926663	+	0.375894i	$0.877336\pi$
$114$	2.13322	−	1.81389i	0.199795	−	0.169887i
$115$	−7.98399	+	13.8287i	−0.744511	+	1.28953i
$116$	−3.84338	+	6.65693i	−0.356849	+	0.618081i
$117$	2.11982	+	3.36406i	0.195977	+	0.311007i
$118$	1.94020	+	3.36052i	0.178610	+	0.309361i
$119$	0.931572	+	1.61353i	0.0853970	+	0.147912i
$120$	−4.55758	−	7.55272i	−0.416048	−	0.689466i
$121$	4.16889	+	7.22073i	0.378990	+	0.656430i
$122$	−0.767926	−	1.33009i	−0.0695248	−	0.120420i
$123$	−4.96587	−	8.22933i	−0.447757	−	0.742014i
$124$	−16.1240			−1.44797
$125$	−9.38406			−0.839336
$126$	−0.129533	+	0.245853i	−0.0115397	+	0.0219024i
$127$	−0.949181	−	1.64403i	−0.0842262	−	0.145884i	0.820835	−	0.571165i	$-0.193509\pi$
$127$	−0.949181	−	1.64403i	−0.0842262	−	0.145884i	−0.905061	+	0.425281i	$0.860175\pi$
$128$	4.95547	+	8.58313i	0.438006	+	0.758648i
$129$	8.40251	−	15.2263i	0.739800	−	1.34060i
$130$	1.74768			0.153281
$131$	−3.02889			−0.264636			−0.132318	−	0.991207i	$-0.542242\pi$
$131$	−3.02889			−0.264636			−0.132318	+	0.991207i	$0.542242\pi$
$132$	2.54304	−	4.60827i	0.221343	−	0.401098i
$133$	0.842837	−	0.689031i	0.0730832	−	0.0597465i
$134$	−0.296470			−0.0256111
$135$	−18.4423	+	1.07138i	−1.58726	+	0.0922098i
$136$	−5.34336	+	9.25497i	−0.458190	+	0.793608i
$137$	4.25747			0.363741			0.181870	−	0.983323i	$-0.441785\pi$
$137$	4.25747			0.363741			0.181870	+	0.983323i	$0.441785\pi$
$138$	1.49070	+	2.47036i	0.126897	+	0.210291i
$139$	8.63607	−	14.9581i	0.732502	−	1.26873i	−0.223308	−	0.974748i	$-0.571686\pi$
$139$	8.63607	−	14.9581i	0.732502	−	1.26873i	0.955811	−	0.293983i	$-0.0949809\pi$
$140$	−0.826848	−	1.43214i	−0.0698814	−	0.121038i
$141$	−3.01193	−	4.99131i	−0.253650	−	0.420344i
$142$	−4.15434			−0.348624
$143$	1.08129	+	1.87285i	0.0904222	+	0.156616i
$144$	9.57354	−	0.370543i	0.797795	−	0.0308786i
$145$	14.6732			1.21855
$146$	1.37047			0.113421
$147$	5.80576	−	10.5207i	0.478851	−	0.867732i
$148$	2.89236	−	5.00972i	0.237751	−	0.411796i
$149$	1.84615			0.151242			0.0756211	−	0.997137i	$-0.475906\pi$
$149$	1.84615			0.151242			0.0756211	+	0.997137i	$0.475906\pi$
$150$	−2.37115	+	4.29679i	−0.193603	+	0.350831i
$151$	−5.59926	+	9.69820i	−0.455661	+	0.789228i	−0.998726	−	0.0504626i	$-0.983930\pi$
$151$	−5.59926	+	9.69820i	−0.455661	+	0.789228i	0.543065	+	0.839691i	$0.317264\pi$
$152$	5.83989	+	2.21061i	0.473677	+	0.179305i
$153$	11.9312	+	18.9344i	0.964583	+	1.53075i
$154$	−0.0755689	+	0.130889i	−0.00608952	+	0.0105473i
$155$	15.3895	+	26.6554i	1.23611	+	2.14101i
$156$	−2.06577	+	3.74342i	−0.165394	+	0.299713i
$157$	20.7711			1.65772			0.828858	−	0.559459i	$-0.188991\pi$
$157$	20.7711			1.65772			0.828858	+	0.559459i	$0.188991\pi$
$158$	−1.82761	+	3.16551i	−0.145397	+	0.251835i
$159$	0.425425	−	0.770919i	0.0337384	−	0.0611379i
$160$	7.19847	−	12.4681i	0.569089	−	0.985692i
$161$	0.560870	+	0.971456i	0.0442028	+	0.0765614i
$162$	−1.44057	+	3.01115i	−0.113182	+	0.236578i
$163$	−5.41671			−0.424269			−0.212135	−	0.977240i	$-0.568042\pi$
$163$	−5.41671			−0.424269			−0.212135	+	0.977240i	$0.568042\pi$
$164$	5.16755	−	8.95046i	0.403518	−	0.698914i
$165$	−10.0454	+	0.194330i	−0.782032	+	0.0151286i
$166$	−0.137415			−0.0106655
$167$	0.750032	−	1.29909i	0.0580392	−	0.100527i	−0.835546	−	0.549421i	$-0.814848\pi$
$167$	0.750032	−	1.29909i	0.0580392	−	0.100527i	0.893585	+	0.448894i	$0.148182\pi$
$168$	−0.619573	+	0.0119858i	−0.0478011	+	0.000924723i
$169$	5.62164	+	9.73696i	0.432434	+	0.748997i
$170$	9.83667			0.754438
$171$	9.79644	−	8.66197i	0.749152	−	0.662398i
$172$	18.7001			1.42587
$173$	−11.2067	−	19.4106i	−0.852031	−	1.47576i	−0.879372	−	0.476135i	$-0.842037\pi$
$173$	−11.2067	−	19.4106i	−0.852031	−	1.47576i	0.0273414	−	0.999626i	$-0.491296\pi$
$174$	1.28101	−	2.32134i	0.0971132	−	0.175980i
$175$	−0.953990	+	1.65236i	−0.0721149	+	0.124907i
$176$	5.21072			0.392773
$177$	9.36256	+	15.5154i	0.703733	+	1.16621i
$178$	1.48739	−	2.57623i	0.111485	−	0.193097i
$179$	−12.7134			−0.950242			−0.475121	−	0.879920i	$-0.657596\pi$
$179$	−12.7134			−0.950242			−0.475121	+	0.879920i	$0.657596\pi$
$180$	−10.5900	−	16.8058i	−0.789329	−	1.25263i
$181$	1.31157	+	2.27170i	0.0974880	+	0.168854i	0.910644	−	0.413191i	$-0.135586\pi$
$181$	1.31157	+	2.27170i	0.0974880	+	0.168854i	−0.813156	+	0.582045i	$0.802253\pi$
$182$	0.0613866	−	0.106325i	0.00455027	−	0.00788131i
$183$	−3.70568	−	6.14098i	−0.273932	−	0.453954i
$184$	−3.21707	+	5.57213i	−0.237166	+	0.410783i
$185$	−11.0425			−0.811857
$186$	5.56048	−	0.107569i	0.407714	−	0.00788731i
$187$	6.08598	+	10.5412i	0.445051	+	0.770850i
$188$	3.13426	−	5.42870i	0.228589	−	0.395928i
$189$	−0.582600	+	1.15962i	−0.0423779	+	0.0843500i
$190$	−0.925514	−	5.67259i	−0.0671439	−	0.411533i
$191$	−1.70417	+	2.95170i	−0.123309	+	0.213578i	−0.921071	−	0.389395i	$-0.872684\pi$
$191$	−1.70417	+	2.95170i	−0.123309	+	0.213578i	0.797762	+	0.602973i	$0.206017\pi$
$192$	4.37166	+	7.24462i	0.315497	+	0.522835i
$193$	0.497765			0.0358299			0.0179150	−	0.999840i	$-0.494297\pi$
$193$	0.497765			0.0358299			0.0179150	+	0.999840i	$0.494297\pi$
$194$	−1.19269	+	2.06581i	−0.0856305	+	0.148316i
$195$	8.16012	−	0.157859i	0.584358	−	0.0113045i
$196$	12.9209			0.922923
$197$	−2.64398			−0.188376			−0.0941880	−	0.995554i	$-0.530025\pi$
$197$	−2.64398			−0.188376			−0.0941880	+	0.995554i	$0.530025\pi$
$198$	−0.846243	+	1.60617i	−0.0601399	+	0.114145i
$199$	0.106311	+	0.184136i	0.00753617	+	0.0130530i	0.869769	−	0.493459i	$-0.164268\pi$
$199$	0.106311	+	0.184136i	0.00753617	+	0.0130530i	−0.862233	+	0.506512i	$0.830934\pi$
$200$	−10.9439			−0.773851
$201$	−1.38426	+	0.0267787i	−0.0976379	+	0.00188882i
$202$	−1.40262	−	2.42940i	−0.0986877	−	0.170932i
$203$	0.515393	−	0.892687i	0.0361735	−	0.0626543i
$204$	−11.6270	+	21.0695i	−0.814056	+	1.47516i
$205$	−19.7287			−1.37791
$206$	−2.56257	+	4.43851i	−0.178543	+	0.309245i
$207$	7.18342	+	11.3998i	0.499282	+	0.792340i
$208$	−4.23280			−0.293492
$209$	5.50627	−	4.50145i	0.380877	−	0.311372i
$210$	0.294700	+	0.488370i	0.0203362	+	0.0337007i
$211$	−8.52375			−0.586799			−0.293400	−	0.955990i	$-0.594787\pi$
$211$	−8.52375			−0.586799			−0.293400	+	0.955990i	$0.594787\pi$
$212$	0.946799			0.0650264
$213$	−19.3971	+	0.375241i	−1.32907	+	0.0257111i
$214$	−2.22754	−	3.85821i	−0.152271	−	0.263742i
$215$	−17.8483	−	30.9141i	−1.21724	−	2.10833i
$216$	−7.43115	+	0.431702i	−0.505626	+	0.0293736i
$217$	2.16220			0.146780
$218$	5.65678			0.383126
$219$	6.39889	−	0.123788i	0.432397	−	0.00836480i
$220$	−5.40181	−	9.35621i	−0.364190	−	0.630796i
$221$	−4.94380	−	8.56290i	−0.332556	−	0.576003i
$222$	−0.964034	+	1.74694i	−0.0647017	+	0.117247i
$223$	−7.80159	−	13.5127i	−0.522433	−	0.904880i	−0.999659	−	0.0260998i	$-0.991691\pi$
$223$	−7.80159	−	13.5127i	−0.522433	−	0.904880i	0.477227	−	0.878780i	$-0.341642\pi$
$224$	−0.505688	−	0.875877i	−0.0337877	−	0.0585220i
$225$	−10.6831	+	20.2764i	−0.712205	+	1.35176i
$226$	−0.543283	+	0.940994i	−0.0361386	+	0.0625940i
$227$	−0.595426	+	1.03131i	−0.0395198	+	0.0684503i	−0.885109	−	0.465384i	$-0.845916\pi$
$227$	−0.595426	+	1.03131i	−0.0395198	+	0.0684503i	0.845589	+	0.533835i	$0.179249\pi$
$228$	13.2443	+	4.72267i	0.877126	+	0.312766i
$229$	−9.98443	−	17.2935i	−0.659790	−	1.14279i	−0.980670	−	0.195669i	$-0.937312\pi$
$229$	−9.98443	−	17.2935i	−0.659790	−	1.14279i	0.320880	−	0.947120i	$-0.396021\pi$
$230$	5.92235			0.390508
$231$	−0.341018	+	0.617964i	−0.0224373	+	0.0406590i
$232$	5.91244			0.388171
$233$	6.18432	−	10.7115i	0.405148	−	0.701737i	−0.589191	−	0.807994i	$-0.700553\pi$
$233$	6.18432	−	10.7115i	0.405148	−	0.701737i	0.994339	+	0.106257i	$0.0338867\pi$
$234$	0.687425	−	1.30473i	0.0449384	−	0.0852928i
$235$	−11.9660			−0.780573
$236$	−9.74281	+	16.8750i	−0.634203	+	1.09847i
$237$	−8.24741	+	14.9452i	−0.535727	+	0.970798i
$238$	0.345510	−	0.598440i	0.0223961	−	0.0387911i
$239$	8.11631	+	14.0579i	0.525000	+	0.909327i	0.999576	+	0.0291128i	$0.00926819\pi$
$239$	8.11631	+	14.0579i	0.525000	+	0.909327i	−0.474576	+	0.880215i	$0.657398\pi$
$240$	9.50145	−	17.2177i	0.613316	−	1.11140i
$241$	10.4869			0.675523			0.337762	−	0.941232i	$-0.390330\pi$
$241$	10.4869			0.675523			0.337762	+	0.941232i	$0.390330\pi$
$242$	1.54620	−	2.67809i	0.0993933	−	0.172154i
$243$	−6.45420	+	14.1895i	−0.414037	+	0.910260i
$244$	3.85619	−	6.67911i	0.246867	−	0.427586i
$245$	−12.3324	−	21.3603i	−0.787885	−	1.36466i
$246$	−1.72236	+	3.12112i	−0.109814	+	0.198995i
$247$	−4.47288	+	3.65665i	−0.284603	+	0.232667i
$248$	6.20104	+	10.7405i	0.393767	+	0.682024i
$249$	−0.641609	+	0.0124121i	−0.0406603	+	0.000786583i
$250$	1.74022	+	3.01415i	0.110061	+	0.190632i
$251$	−7.02198	−	12.1624i	−0.443223	−	0.767685i	0.554703	−	0.832048i	$-0.312832\pi$
$251$	−7.02198	−	12.1624i	−0.443223	−	0.767685i	−0.997927	+	0.0643630i	$0.979498\pi$
$252$	−1.39440	+	0.0539700i	−0.0878387	+	0.00339979i
$253$	3.66418	+	6.34654i	0.230365	+	0.399004i
$254$	−0.352041	+	0.609753i	−0.0220890	+	0.0382593i
$255$	45.9286	−	0.888499i	2.87616	−	0.0556399i
$256$	−3.04728	+	5.27805i	−0.190455	+	0.329878i
$257$	−8.58033	+	14.8616i	−0.535227	+	0.927040i	0.463926	+	0.885874i	$0.346440\pi$
$257$	−8.58033	+	14.8616i	−0.535227	+	0.927040i	−0.999152	+	0.0411655i	$0.986893\pi$
$258$	−6.44888	+	0.124755i	−0.401490	+	0.00776690i
$259$	−0.387862	+	0.671797i	−0.0241006	+	0.0417435i
$260$	4.38803	+	7.60029i	0.272134	+	0.471350i
$261$	5.77153	−	10.9543i	0.357249	−	0.678056i
$262$	0.561691	+	0.972878i	0.0347014	+	0.0601046i
$263$	−9.74973	−	16.8870i	−0.601194	−	1.04130i	−0.992641	−	0.121098i	$-0.961358\pi$
$263$	−9.74973	−	16.8870i	−0.601194	−	1.04130i	0.391446	−	0.920201i	$-0.371975\pi$
$264$	−4.04769	+	0.0783033i	−0.249118	+	0.00481924i
$265$	−0.903671	−	1.56520i	−0.0555121	−	0.0961498i
$266$	−0.377616	−	0.142942i	−0.0231531	−	0.00876431i
$267$	6.71211	−	12.1631i	0.410774	−	0.744370i
$268$	−0.744371	−	1.28929i	−0.0454697	−	0.0787558i
$269$	−11.5796	+	20.0564i	−0.706020	+	1.22286i	0.260303	+	0.965527i	$0.416178\pi$
$269$	−11.5796	+	20.0564i	−0.706020	+	1.22286i	−0.966322	+	0.257335i	$0.917156\pi$
$270$	3.76415	+	5.72498i	0.229079	+	0.348411i
$271$	−11.0388	+	19.1197i	−0.670557	+	1.16144i	0.307190	+	0.951648i	$0.400611\pi$
$271$	−11.0388	+	19.1197i	−0.670557	+	1.16144i	−0.977746	+	0.209790i	$0.932722\pi$
$272$	−23.8240			−1.44454
$273$	0.277018	−	0.501988i	0.0167659	−	0.0303817i
$274$	−0.789525	−	1.36750i	−0.0476970	−	0.0826136i
$275$	−6.23244	+	10.7949i	−0.375830	+	0.650957i
$276$	−7.00028	+	12.6853i	−0.421368	+	0.763566i
$277$	14.7992	−	25.6330i	0.889199	−	1.54014i	0.0483752	−	0.998829i	$-0.484596\pi$
$277$	14.7992	−	25.6330i	0.889199	−	1.54014i	0.840824	−	0.541309i	$-0.182071\pi$
$278$	−6.40605			−0.384209
$279$	25.9529	−	1.00450i	1.55376	−	0.0601380i
$280$	−0.635988	+	1.10156i	−0.0380075	+	0.0658310i
$281$	28.8083			1.71856			0.859280	−	0.511506i	$-0.170912\pi$
$281$	28.8083			1.71856			0.859280	+	0.511506i	$0.170912\pi$
$282$	−1.04466	+	1.89304i	−0.0622085	+	0.112729i
$283$	16.0204			0.952314			0.476157	−	0.879360i	$-0.342029\pi$
$283$	16.0204			0.952314			0.476157	+	0.879360i	$0.342029\pi$
$284$	−10.4306	−	18.0664i	−0.618944	−	1.07204i
$285$	−4.83372	−	26.4024i	−0.286325	−	1.56394i
$286$	0.401040	−	0.694621i	0.0237140	−	0.0410738i
$287$	−0.692963	+	1.20025i	−0.0409043	+	0.0708483i
$288$	−6.47667	−	10.2782i	−0.381641	−	0.605649i
$289$	−19.3258	−	33.4732i	−1.13681	−	1.96901i
$290$	−2.72107	−	4.71304i	−0.159787	−	0.276759i
$291$	−5.38225	+	9.75324i	−0.315513	+	0.571745i
$292$	3.44094	+	5.95989i	0.201366	+	0.348776i
$293$	−0.400378	−	0.693475i	−0.0233903	−	0.0405132i	0.854093	−	0.520120i	$-0.174113\pi$
$293$	−0.400378	−	0.693475i	−0.0233903	−	0.0405132i	−0.877484	+	0.479607i	$0.840779\pi$
$294$	−4.45589	+	0.0862000i	−0.259873	+	0.00502729i
$295$	37.1961			2.16564
$296$	−4.44945			−0.258619
$297$	−3.80614	+	7.57582i	−0.220855	+	0.439594i
$298$	−0.342358	−	0.592981i	−0.0198322	−	0.0343504i
$299$	−2.97650	−	5.15546i	−0.172136	−	0.298148i
$300$	−24.6393	+	0.476652i	−1.42255	+	0.0275195i
$301$	−2.50766			−0.144539
$302$	4.15341			0.239002
$303$	−6.76842	−	11.2165i	−0.388836	−	0.644370i
$304$	2.24156	+	13.7388i	0.128562	+	0.787974i
$305$	−14.7221			−0.842987
$306$	3.86912	−	7.34358i	0.221183	−	0.419804i
$307$	2.29987	−	3.98349i	0.131260	−	0.227350i	−0.792902	−	0.609349i	$-0.791431\pi$
$307$	2.29987	−	3.98349i	0.131260	−	0.227350i	0.924163	+	0.381999i	$0.124764\pi$
$308$	−0.758947			−0.0432450
$309$	−11.5641	+	20.9554i	−0.657856	+	1.19211i
$310$	5.70779	−	9.88619i	0.324181	−	0.561498i
$311$	16.4116	+	28.4257i	0.930615	+	1.61187i	0.782273	+	0.622936i	$0.214060\pi$
$311$	16.4116	+	28.4257i	0.930615	+	1.61187i	0.148342	+	0.988936i	$0.452606\pi$
$312$	3.28804	−	0.0636078i	0.186149	−	0.00360108i
$313$	−18.3876			−1.03933			−0.519664	−	0.854371i	$-0.673943\pi$
$313$	−18.3876			−1.03933			−0.519664	+	0.854371i	$0.673943\pi$
$314$	−3.85189	−	6.67167i	−0.217375	−	0.376504i
$315$	1.42010	+	2.25364i	0.0800136	+	0.126978i
$316$	−18.3549			−1.03254
$317$	1.35820			0.0762844			0.0381422	−	0.999272i	$-0.487856\pi$
$317$	1.35820			0.0762844			0.0381422	+	0.999272i	$0.487856\pi$
$318$	−0.326511	+	0.00631643i	−0.0183099	+	0.000354208i
$319$	3.36707	−	5.83194i	0.188520	−	0.326526i
$320$	17.3680			0.970899
$321$	−10.7491	−	17.8133i	−0.599959	−	0.994239i
$322$	0.208021	−	0.360302i	0.0115925	−	0.0200789i
$323$	−25.1753	+	20.5812i	−1.40079	+	1.14517i
$324$	−16.7118	+	1.29560i	−0.928435	+	0.0719778i
$325$	5.06277	−	8.76897i	0.280832	−	0.486415i
$326$	1.00450	+	1.73984i	0.0556341	+	0.0963610i
$327$	26.4122	−	0.510950i	1.46060	−	0.0282556i
$328$	−7.94947			−0.438936
$329$	−0.420300	+	0.727982i	−0.0231719	+	0.0401349i
$330$	1.92528	+	3.19053i	0.105983	+	0.175633i
$331$	8.39869	−	14.5470i	0.461634	−	0.799573i	−0.537409	−	0.843322i	$-0.680597\pi$
$331$	8.39869	−	14.5470i	0.461634	−	0.799573i	0.999043	+	0.0437490i	$0.0139302\pi$
$332$	−0.345020	−	0.597592i	−0.0189354	−	0.0327971i
$333$	−4.34340	+	8.24375i	−0.238017	+	0.451755i
$334$	−0.556357			−0.0304425
$335$	−1.42093	+	2.46112i	−0.0776336	+	0.134465i
$336$	−0.713751	−	1.18281i	−0.0389383	−	0.0645277i
$337$	36.5224			1.98950			0.994750	−	0.102335i	$-0.0326312\pi$
$337$	36.5224			1.98950			0.994750	+	0.102335i	$0.0326312\pi$
$338$	2.08500	−	3.61133i	0.113409	−	0.196431i
$339$	−2.45166	+	4.44269i	−0.133156	+	0.241294i
$340$	24.6977	+	42.7777i	1.33942	+	2.31995i
$341$	14.1257			0.764951
$342$	−4.59892	−	1.54029i	−0.248681	−	0.0832895i
$343$	−3.48094			−0.187953
$344$	−7.19179	−	12.4565i	−0.387755	−	0.671612i
$345$	27.6522	−	0.534937i	1.48874	−	0.0288001i
$346$	−4.15645	+	7.19918i	−0.223452	+	0.387030i
$347$	−10.1508			−0.544926			−0.272463	−	0.962166i	$-0.587838\pi$
$347$	−10.1508			−0.544926			−0.272463	+	0.962166i	$0.587838\pi$
$348$	13.3114	−	0.257511i	0.713565	−	0.0138041i
$349$	8.63614	−	14.9582i	0.462282	−	0.800696i	−0.536792	−	0.843715i	$-0.680364\pi$
$349$	8.63614	−	14.9582i	0.462282	−	0.800696i	0.999074	+	0.0430183i	$0.0136974\pi$
$350$	0.707649			0.0378254
$351$	3.09182	−	6.15404i	0.165029	−	0.328478i
$352$	−3.30367	−	5.72212i	−0.176086	−	0.304990i
$353$	−8.45158	+	14.6386i	−0.449832	+	0.779132i	−0.998375	−	0.0569905i	$-0.981850\pi$
$353$	−8.45158	+	14.6386i	−0.449832	+	0.779132i	0.548543	+	0.836123i	$0.315183\pi$
$354$	3.24731	−	5.88450i	0.172593	−	0.312758i
$355$	−19.9110	+	34.4869i	−1.05677	+	1.83037i
$356$	14.9380			0.791714
$357$	1.55917	−	2.82540i	0.0825202	−	0.149536i
$358$	2.35762	+	4.08353i	0.124604	+	0.215821i
$359$	3.82747	−	6.62938i	0.202006	−	0.349885i	−0.747168	−	0.664635i	$-0.768587\pi$
$359$	3.82747	−	6.62938i	0.202006	−	0.349885i	0.949175	+	0.314750i	$0.101921\pi$
$360$	−7.12198	+	13.5175i	−0.375361	+	0.712434i
$361$	14.2374	+	12.5816i	0.749337	+	0.662189i
$362$	0.486446	−	0.842549i	0.0255670	−	0.0442834i
$363$	6.97748	−	12.6440i	0.366223	−	0.663638i
$364$	0.616512			0.0323140
$365$	6.56841	−	11.3768i	0.343806	−	0.595490i
$366$	−1.28528	+	2.32907i	−0.0671826	+	0.121743i
$367$	−24.7775			−1.29338			−0.646688	−	0.762755i	$-0.723846\pi$
$367$	−24.7775			−1.29338			−0.646688	+	0.762755i	$0.723846\pi$
$368$	−14.3437			−0.747717
$369$	−7.76001	+	14.7285i	−0.403970	+	0.766733i
$370$	2.04776	+	3.54683i	0.106458	+	0.184391i
$371$	−0.126965			−0.00659167
$372$	14.4289	+	23.9113i	0.748105	+	1.23974i
$373$	11.5863	+	20.0681i	0.599917	+	1.03909i	0.992833	+	0.119512i	$0.0381330\pi$
$373$	11.5863	+	20.0681i	0.599917	+	1.03909i	−0.392916	+	0.919574i	$0.628534\pi$
$374$	2.25722	−	3.90962i	0.116718	−	0.202162i
$375$	8.39757	+	13.9163i	0.433649	+	0.718633i
$376$	−4.82157			−0.248653
$377$	−2.73516	+	4.73744i	−0.140868	+	0.243990i
$378$	0.480509	−	0.0279145i	0.0247147	−	0.00143577i
$379$	29.0801			1.49374			0.746871	−	0.664969i	$-0.231555\pi$
$379$	29.0801			1.49374			0.746871	+	0.664969i	$0.231555\pi$
$380$	22.3452	−	18.2675i	1.14628	−	0.937103i
$381$	−1.58865	+	2.87881i	−0.0813888	+	0.147486i
$382$	1.26411			0.0646777
$383$	−2.82855			−0.144532			−0.0722662	−	0.997385i	$-0.523023\pi$
$383$	−2.82855			−0.144532			−0.0722662	+	0.997385i	$0.523023\pi$
$384$	8.29398	−	15.0296i	0.423250	−	0.766978i
$385$	0.724377	+	1.25466i	0.0369177	+	0.0639433i
$386$	−0.0923078	−	0.159882i	−0.00469834	−	0.00813777i
$387$	−30.0994	+	1.16499i	−1.53004	+	0.0592199i
$388$	−11.9784			−0.608110
$389$	19.1659			0.971750			0.485875	−	0.874028i	$-0.338501\pi$
$389$	19.1659			0.971750			0.485875	+	0.874028i	$0.338501\pi$
$390$	−1.56395	−	2.59175i	−0.0791939	−	0.131238i
$391$	−16.7530	−	29.0171i	−0.847238	−	1.46746i
$392$	−4.96920	−	8.60691i	−0.250983	−	0.434715i
$393$	2.71048	+	4.49175i	0.136726	+	0.226579i
$394$	0.490312	+	0.849245i	0.0247016	+	0.0427844i
$395$	17.5188	+	30.3435i	0.881467	+	1.52675i
$396$	−9.10962	+	0.352587i	−0.457776	+	0.0177182i
$397$	15.9590	−	27.6417i	0.800958	−	1.38730i	−0.118029	−	0.993010i	$-0.537658\pi$
$397$	15.9590	−	27.6417i	0.800958	−	1.38730i	0.918986	−	0.394289i	$-0.129009\pi$
$398$	0.0394295	−	0.0682939i	0.00197642	−	0.00342326i
$399$	−1.77605	−	0.633304i	−0.0889135	−	0.0317049i
$400$	−12.1987	−	21.1287i	−0.609934	−	1.05644i
$401$	38.3406			1.91464			0.957320	−	0.289030i	$-0.0933328\pi$
$401$	38.3406			1.91464			0.957320	+	0.289030i	$0.0933328\pi$
$402$	0.265304	+	0.439656i	0.0132322	+	0.0219280i
$403$	−11.4747			−0.571595
$404$	7.04332	−	12.1994i	0.350418	−	0.606942i
$405$	18.0924	+	26.3906i	0.899019	+	1.31136i
$406$	−0.382307			−0.0189736
$407$	−2.53391	+	4.38887i	−0.125601	+	0.217548i
$408$	18.5065	−	0.358012i	0.916208	−	0.0177242i
$409$	−1.14644	+	1.98569i	−0.0566877	+	0.0981860i	−0.892977	−	0.450103i	$-0.851387\pi$
$409$	−1.14644	+	1.98569i	−0.0566877	+	0.0981860i	0.836289	+	0.548289i	$0.184721\pi$
$410$	3.65857	+	6.33683i	0.180684	+	0.312954i
$411$	−3.80991	−	6.31370i	−0.187929	−	0.311432i
$412$	−25.7362			−1.26793
$413$	1.30650	−	2.26292i	0.0642886	−	0.111351i
$414$	2.32948	−	4.42134i	0.114488	−	0.217297i
$415$	−0.658608	+	1.14074i	−0.0323298	+	0.0559968i
$416$	2.68366	+	4.64823i	0.131577	+	0.227898i
$417$	−29.9106	+	0.578627i	−1.46473	+	0.0283355i
$418$	−2.46697	−	0.933841i	−0.120663	−	0.0456756i
$419$	5.32211	+	9.21817i	0.260002	+	0.450337i	0.966242	−	0.257636i	$-0.0829434\pi$
$419$	5.32211	+	9.21817i	0.260002	+	0.450337i	−0.706240	+	0.707972i	$0.749610\pi$
$420$	−1.38390	+	2.50778i	−0.0675272	+	0.122367i
$421$	−12.9323	−	22.3994i	−0.630280	−	1.09168i	−0.987494	−	0.157655i	$-0.949607\pi$
$421$	−12.9323	−	22.3994i	−0.630280	−	1.09168i	0.357214	−	0.934023i	$-0.383727\pi$
$422$	1.58068	+	2.73782i	0.0769464	+	0.133275i
$423$	−4.70665	+	8.93320i	−0.228845	+	0.434347i
$424$	−0.364125	−	0.630684i	−0.0176835	−	0.0306287i
$425$	28.4954	−	49.3555i	1.38223	−	2.39409i
$426$	3.71762	+	6.16075i	0.180119	+	0.298489i
$427$	−0.517110	+	0.895661i	−0.0250247	+	0.0433441i
$428$	11.1857	−	19.3742i	0.540682	−	0.936489i
$429$	1.80976	−	3.27950i	0.0873761	−	0.158336i
$430$	−6.61973	+	11.4657i	−0.319232	+	0.552926i
$431$	−9.52984	−	16.5062i	−0.459036	−	0.795074i	0.539874	−	0.841746i	$-0.318472\pi$
$431$	−9.52984	−	16.5062i	−0.459036	−	0.795074i	−0.998910	+	0.0466716i	$0.985139\pi$
$432$	−9.11664	−	13.8657i	−0.438624	−	0.667113i
$433$	13.3288	+	23.0861i	0.640540	+	1.10945i	0.985312	+	0.170761i	$0.0546226\pi$
$433$	13.3288	+	23.0861i	0.640540	+	1.10945i	−0.344773	+	0.938686i	$0.612044\pi$
$434$	−0.400969	−	0.694498i	−0.0192471	−	0.0333370i
$435$	−13.1307	−	21.7600i	−0.629571	−	1.04331i
$436$	14.2029	+	24.6002i	0.680197	+	1.17814i
$437$	−15.1573	+	12.3913i	−0.725070	+	0.592755i
$438$	−1.22640	−	2.03236i	−0.0585996	−	0.0971100i
$439$	0.973523	+	1.68619i	0.0464637	+	0.0804775i	0.888322	−	0.459221i	$-0.151871\pi$
$439$	0.973523	+	1.68619i	0.0464637	+	0.0804775i	−0.841858	+	0.539699i	$0.818538\pi$
$440$	−4.15492	+	7.19653i	−0.198078	+	0.343081i
$441$	−20.7973	+	0.804957i	−0.990348	+	0.0383313i
$442$	−1.83360	+	3.17589i	−0.0872154	+	0.151062i
$443$	6.56230			0.311784			0.155892	−	0.987774i	$-0.450175\pi$
$443$	6.56230			0.311784			0.155892	+	0.987774i	$0.450175\pi$
$444$	−10.0176	+	0.193792i	−0.475413	+	0.00919695i
$445$	−14.2576	−	24.6949i	−0.675875	−	1.17065i
$446$	−2.89352	+	5.01173i	−0.137012	+	0.237312i
$447$	−1.65207	−	2.73778i	−0.0781403	−	0.129492i
$448$	0.610044	−	1.05663i	0.0288219	−	0.0499209i
$449$	−35.5348			−1.67699			−0.838495	−	0.544910i	$-0.816564\pi$
$449$	−35.5348			−1.67699			−0.838495	+	0.544910i	$0.816564\pi$
$450$	8.49389	−	0.328755i	0.400406	−	0.0154977i
$451$	−4.52714	+	7.84124i	−0.213175	+	0.369229i
$452$	−5.45626			−0.256641
$453$	19.3928	−	0.375157i	0.911152	−	0.0176264i
$454$	0.441674			0.0207288
$455$	−0.588430	−	1.01919i	−0.0275860	−	0.0477804i
$456$	−1.94770	−	10.6386i	−0.0912094	−	0.498198i
$457$	−3.32444	+	5.75809i	−0.155511	+	0.269352i	−0.933245	−	0.359241i	$-0.883036\pi$
$457$	−3.32444	+	5.75809i	−0.155511	+	0.269352i	0.777734	+	0.628593i	$0.216369\pi$
$458$	−3.70311	+	6.41398i	−0.173035	+	0.299706i
$459$	17.4021	−	34.6375i	0.812261	−	1.61674i
$460$	14.8697	+	25.7551i	0.693304	+	1.20084i
$461$	3.48590	+	6.03776i	0.162355	+	0.281207i	0.935713	−	0.352763i	$-0.114758\pi$
$461$	3.48590	+	6.03776i	0.162355	+	0.281207i	−0.773358	+	0.633970i	$0.781424\pi$
$462$	0.261729	−	0.00506321i	0.0121768	−	0.000235562i
$463$	8.59691	+	14.8903i	0.399532	+	0.692010i	0.993668	−	0.112354i	$-0.0358392\pi$
$463$	8.59691	+	14.8903i	0.399532	+	0.692010i	−0.594136	+	0.804365i	$0.702506\pi$
$464$	6.59033	+	11.4148i	0.305949	+	0.529919i
$465$	25.7574	−	46.6754i	1.19447	−	2.16452i
$466$	−4.58739			−0.212507
$467$	36.5485			1.69126			0.845632	−	0.533766i	$-0.179224\pi$
$467$	36.5485			1.69126			0.845632	+	0.533766i	$0.179224\pi$
$468$	7.39998	−	0.286415i	0.342064	−	0.0132396i
$469$	0.0998193	+	0.172892i	0.00460923	+	0.00798341i
$470$	2.21902	+	3.84346i	0.102356	+	0.177286i
$471$	−18.5876	−	30.8029i	−0.856470	−	1.41932i
$472$	14.9878			0.689869
$473$	−16.3826			−0.753272
$474$	6.32984	−	0.122452i	0.290739	−	0.00562441i
$475$	−31.1433	−	11.7889i	−1.42895	−	0.540912i
$476$	3.47000			0.159047
$477$	−1.52395	+	0.0589844i	−0.0697770	+	0.00270071i
$478$	3.01025	−	5.21391i	0.137686	−	0.238479i
$479$	−19.9654			−0.912242			−0.456121	−	0.889918i	$-0.650762\pi$
$479$	−19.9654			−0.912242			−0.456121	+	0.889918i	$0.650762\pi$
$480$	−24.9316	+	0.482306i	−1.13797	+	0.0220142i
$481$	2.05836	−	3.56519i	0.0938533	−	0.162559i
$482$	−1.94475	−	3.36840i	−0.0885807	−	0.153426i
$483$	0.938730	−	1.70109i	0.0427137	−	0.0774021i
$484$	15.5286			0.705847
$485$	11.4327	+	19.8021i	0.519134	+	0.899167i
$486$	5.75457	−	0.558289i	0.261033	−	0.0253245i
$487$	0.541412			0.0245337			0.0122669	−	0.999925i	$-0.496095\pi$
$487$	0.541412			0.0245337			0.0122669	+	0.999925i	$0.496095\pi$
$488$	−5.93214			−0.268535
$489$	4.84728	+	8.03281i	0.219202	+	0.363256i
$490$	−4.57394	+	7.92229i	−0.206629	+	0.357893i
$491$	−7.34369			−0.331416			−0.165708	−	0.986175i	$-0.552991\pi$
$491$	−7.34369			−0.331416			−0.165708	+	0.986175i	$0.552991\pi$
$492$	−17.8976	+	0.346232i	−0.806885	+	0.0156094i
$493$	−15.3946	+	26.6643i	−0.693340	+	1.20090i
$494$	2.00398	+	0.758583i	0.0901635	+	0.0341302i
$495$	9.27755	+	14.7231i	0.416995	+	0.661753i
$496$	−13.8241	+	23.9440i	−0.620718	+	1.07512i
$497$	1.39873	+	2.42268i	0.0627418	+	0.108672i
$498$	0.122970	+	0.203783i	0.00551040	+	0.00913172i
$499$	−11.9475			−0.534842			−0.267421	−	0.963580i	$-0.586171\pi$
$499$	−11.9475			−0.534842			−0.267421	+	0.963580i	$0.586171\pi$
$500$	−8.73863	+	15.1358i	−0.390803	+	0.676891i
$501$	−2.59770	+	0.0502530i	−0.116057	+	0.00224514i
$502$	−2.60437	+	4.51091i	−0.116239	+	0.201332i
$503$	14.7358	+	25.5232i	0.657038	+	1.13802i	0.981379	+	0.192083i	$0.0615242\pi$
$503$	14.7358	+	25.5232i	0.657038	+	1.13802i	−0.324341	+	0.945940i	$0.605142\pi$
$504$	0.572216	+	0.908082i	0.0254885	+	0.0404492i
$505$	−26.8900			−1.19659
$506$	1.35900	−	2.35386i	0.0604151	−	0.104642i
$507$	9.40895	−	17.0501i	0.417866	−	0.757221i
$508$	−3.53559			−0.156866
$509$	−8.95222	+	15.5057i	−0.396800	+	0.687278i	−0.993329	−	0.115314i	$-0.963213\pi$
$509$	−8.95222	+	15.5057i	−0.396800	+	0.687278i	0.596529	+	0.802592i	$0.296546\pi$
$510$	−8.80260	−	14.5875i	−0.389786	−	0.645944i
$511$	−0.461426	−	0.799214i	−0.0204123	−	0.0353552i
$512$	22.0823			0.975909
$513$	−21.6120	−	6.77642i	−0.954195	−	0.299186i
$514$	6.36470			0.280735
$515$	24.5639	+	42.5459i	1.08242	+	1.87480i
$516$	−16.7343	−	27.7317i	−0.736685	−	1.22082i
$517$	−2.74583	+	4.75592i	−0.120762	+	0.209165i
$518$	0.287708			0.0126412
$519$	−18.7567	+	33.9893i	−0.823328	+	1.49196i
$520$	3.37515	−	5.84593i	0.148010	−	0.256361i
$521$	−27.8411			−1.21974			−0.609871	−	0.792501i	$-0.708779\pi$
$521$	−27.8411			−1.21974			−0.609871	+	0.792501i	$0.708779\pi$
$522$	−4.58882	+	0.177610i	−0.200847	+	0.00777377i
$523$	−12.9624	−	22.4515i	−0.566805	−	0.981735i	−0.996879	−	0.0789417i	$-0.974846\pi$
$523$	−12.9624	−	22.4515i	−0.566805	−	0.981735i	0.430074	−	0.902794i	$-0.358487\pi$
$524$	−2.82057	+	4.88537i	−0.123217	+	0.213418i
$525$	3.30410	−	0.0639185i	0.144203	−	0.00278963i
$526$	−3.61607	+	6.26321i	−0.157668	+	0.273089i
$527$	−64.5844			−2.81334
$528$	−4.66295	−	7.72734i	−0.202929	−	0.336289i
$529$	1.41352	+	2.44829i	0.0614573	+	0.106447i
$530$	−0.335162	+	0.580517i	−0.0145585	+	0.0252161i
$531$	14.6306	−	27.7688i	0.634913	−	1.20506i
$532$	−0.326485	−	2.00107i	−0.0141549	−	0.0867574i
$533$	3.67751	−	6.36964i	0.159291	−	0.275900i
$534$	−5.15151	+	0.0996569i	−0.222927	+	0.00431258i
$535$	−42.7048			−1.84629
$536$	−0.572549	+	0.991684i	−0.0247304	+	0.0428342i
$537$	11.3769	+	18.8535i	0.490949	+	0.813590i
$538$	8.58948			0.370319
$539$	−11.3196			−0.487571
$540$	−15.4458	+	30.7437i	−0.664682	+	1.32300i
$541$	−12.3043	−	21.3116i	−0.529001	−	0.916257i	−0.999428	−	0.0338181i	$-0.989233\pi$
$541$	−12.3043	−	21.3116i	−0.529001	−	0.916257i	0.470427	−	0.882439i	$-0.344100\pi$
$542$	8.18831			0.351718
$543$	2.19517	−	3.97790i	0.0942038	−	0.170708i
$544$	15.1048	+	26.1622i	0.647611	+	1.12170i
$545$	27.1120	−	46.9593i	1.16135	−	2.01151i
$546$	−0.212609	+	0.00411297i	−0.00909885	+	0.000176019i
$547$	12.8871			0.551014			0.275507	−	0.961299i	$-0.411154\pi$
$547$	12.8871			0.551014			0.275507	+	0.961299i	$0.411154\pi$
$548$	3.96465	−	6.86697i	0.169361	−	0.293343i
$549$	−5.79076	+	10.9908i	−0.247143	+	0.469077i
$550$	4.62308			0.197129
$551$	16.8252	+	6.36895i	0.716776	+	0.271327i
$552$	11.1422	−	0.215548i	0.474243	−	0.00917432i
$553$	2.46137			0.104668
$554$	−10.9777			−0.466399
$555$	9.88162	+	16.3756i	0.419451	+	0.695106i
$556$	−16.0842	−	27.8586i	−0.682121	−	1.18147i
$557$	−11.8767	−	20.5710i	−0.503231	−	0.871622i	−0.999993	−	0.00373498i	$-0.998811\pi$
$557$	−11.8767	−	20.5710i	−0.503231	−	0.871622i	0.496762	−	0.867887i	$-0.334522\pi$
$558$	−5.13546	−	8.14976i	−0.217401	−	0.345007i
$559$	13.3080			0.562868
$560$	−2.83563			−0.119827
$561$	10.1861	−	18.4584i	0.430058	−	0.779314i
$562$	−5.34234	−	9.25321i	−0.225353	−	0.390323i
$563$	13.3440	+	23.1125i	0.562383	+	0.974077i	0.997288	+	0.0735999i	$0.0234488\pi$
$563$	13.3440	+	23.1125i	0.562383	+	0.974077i	−0.434904	+	0.900477i	$0.643218\pi$
$564$	−10.8554	+	0.209999i	−0.457093	+	0.00884256i
$565$	5.20772	+	9.02003i	0.219090	+	0.379476i
$566$	−2.97090	−	5.14574i	−0.124876	−	0.216292i
$567$	2.24104	−	0.173738i	0.0941147	−	0.00729633i
$568$	−8.02294	+	13.8961i	−0.336635	+	0.583069i
$569$	6.57047	−	11.3804i	0.275448	−	0.477090i	−0.694800	−	0.719203i	$-0.744507\pi$
$569$	6.57047	−	11.3804i	0.275448	−	0.477090i	0.970248	+	0.242113i	$0.0778404\pi$
$570$	−7.58405	+	6.44877i	−0.317661	+	0.270109i
$571$	−1.08070	−	1.87182i	−0.0452258	−	0.0783333i	0.842526	−	0.538655i	$-0.181067\pi$
$571$	−1.08070	−	1.87182i	−0.0452258	−	0.0783333i	−0.887752	+	0.460322i	$0.847734\pi$
$572$	4.02769			0.168406
$573$	5.90230	−	0.114181i	0.246572	−	0.00476999i
$574$	0.514024			0.0214550
$575$	17.1562	−	29.7154i	0.715463	−	1.23922i
$576$	6.83146	−	12.9661i	0.284644	−	0.540253i
$577$	4.53956			0.188985			0.0944923	−	0.995526i	$-0.469877\pi$
$577$	4.53956			0.188985			0.0944923	+	0.995526i	$0.469877\pi$
$578$	−7.16772	+	12.4149i	−0.298138	+	0.516390i
$579$	−0.445438	−	0.738170i	−0.0185118	−	0.0306773i
$580$	13.6640	−	23.6668i	0.567368	−	0.982710i
$581$	0.0462667	+	0.0801364i	0.00191947	+	0.00332462i
$582$	4.13084	−	0.0799120i	0.171229	−	0.00331246i
$583$	−0.829462			−0.0343528
$584$	2.64668	−	4.58418i	0.109520	−	0.189695i
$585$	−7.53639	−	11.9599i	−0.311591	−	0.494483i
$586$	−0.148496	+	0.257202i	−0.00613430	+	0.0106249i
$587$	−12.1339	−	21.0165i	−0.500819	−	0.867444i	−1.00000		0.000946197i	$-0.999699\pi$
$587$	−12.1339	−	21.0165i	−0.500819	−	0.867444i	0.499180	−	0.866498i	$-0.333635\pi$
$588$	−11.5626	−	19.1613i	−0.476834	−	0.790200i
$589$	6.07663	+	37.2444i	0.250383	+	1.53463i
$590$	−6.89781	−	11.9474i	−0.283978	−	0.491865i
$591$	2.36604	+	3.92094i	0.0973257	+	0.161286i
$592$	−4.95960	−	8.59028i	−0.203838	−	0.353058i
$593$	16.5350	+	28.6395i	0.679013	+	1.17608i	0.975279	+	0.220979i	$0.0709252\pi$
$593$	16.5350	+	28.6395i	0.679013	+	1.17608i	−0.296266	+	0.955106i	$0.595741\pi$
$594$	3.13918	−	0.182366i	0.128802	−	0.00748257i
$595$	−3.31193	−	5.73644i	−0.135776	−	0.235171i
$596$	1.71917	−	2.97769i	0.0704199	−	0.121971i
$597$	0.177932	−	0.322434i	0.00728229	−	0.0131963i
$598$	−1.10395	+	1.91210i	−0.0451440	+	0.0781917i
$599$	6.64241	−	11.5050i	0.271401	−	0.470081i	−0.697820	−	0.716274i	$-0.745846\pi$
$599$	6.64241	−	11.5050i	0.271401	−	0.470081i	0.969221	+	0.246193i	$0.0791796\pi$
$600$	9.79343	+	16.2295i	0.399815	+	0.662565i
$601$	−7.35146	+	12.7331i	−0.299872	+	0.519394i	−0.976106	−	0.217293i	$-0.930277\pi$
$601$	−7.35146	+	12.7331i	−0.299872	+	0.519394i	0.676234	+	0.736687i	$0.263611\pi$
$602$	0.465032	+	0.805459i	0.0189533	+	0.0328280i
$603$	1.27845	+	2.02884i	0.0520625	+	0.0826209i
$604$	10.4283	+	18.0623i	0.424321	+	0.734946i
$605$	−14.8213	−	25.6712i	−0.602571	−	1.04368i
$606$	−2.34756	+	4.25405i	−0.0953632	+	0.172809i
$607$	−1.19304	−	2.06641i	−0.0484241	−	0.0838729i	0.840797	−	0.541350i	$-0.182087\pi$
$607$	−1.19304	−	2.06641i	−0.0484241	−	0.0838729i	−0.889221	+	0.457477i	$0.848753\pi$
$608$	13.6660	−	11.1721i	0.554229	−	0.453090i
$609$	−1.78504	+	0.0345320i	−0.0723335	+	0.00139931i
$610$	2.73014	+	4.72874i	0.110540	+	0.191461i
$611$	2.23051	−	3.86336i	0.0902368	−	0.156295i
$612$	41.6502	−	1.61207i	1.68361	−	0.0651640i
$613$	2.16079	−	3.74260i	0.0872736	−	0.151162i	−0.819084	−	0.573673i	$-0.805518\pi$
$613$	2.16079	−	3.74260i	0.0872736	−	0.151162i	0.906358	+	0.422511i	$0.138851\pi$
$614$	−1.70599			−0.0688482
$615$	17.6547	+	29.2570i	0.711906	+	1.17976i
$616$	0.291880	+	0.505552i	0.0117602	+	0.0203693i
$617$	4.80522	−	8.32289i	0.193451	−	0.335067i	−0.752941	−	0.658088i	$-0.771365\pi$
$617$	4.80522	−	8.32289i	0.193451	−	0.335067i	0.946392	+	0.323021i	$0.104699\pi$
$618$	8.87535	−	0.171695i	0.357019	−	0.00690661i
$619$	−1.79677	+	3.11209i	−0.0722182	+	0.125086i	−0.899873	−	0.436152i	$-0.856341\pi$
$619$	−1.79677	+	3.11209i	−0.0722182	+	0.125086i	0.827655	+	0.561237i	$0.189674\pi$
$620$	57.3241			2.30219
$621$	10.4773	−	20.8542i	0.420438	−	0.836850i
$622$	6.08687	−	10.5428i	0.244061	−	0.422727i
$623$	−2.00317			−0.0802554
$624$	3.78783	+	6.27712i	0.151635	+	0.251286i
$625$	−4.83530			−0.193412
$626$	3.40988	+	5.90608i	0.136286	+	0.236055i
$627$	−11.6029	−	4.13739i	−0.463377	−	0.165231i
$628$	19.3425	−	33.5022i	0.771850	−	1.33688i
$629$	11.5853	−	20.0664i	0.461938	−	0.800100i
$630$	0.460518	−	0.874061i	0.0183475	−	0.0348234i
$631$	12.6319	+	21.8792i	0.502870	+	0.870996i	0.999994	+	0.00331669i	$0.00105574\pi$
$631$	12.6319	+	21.8792i	0.502870	+	0.870996i	−0.497125	+	0.867679i	$0.665611\pi$
$632$	7.05903	+	12.2266i	0.280793	+	0.486348i
$633$	7.62770	+	12.6405i	0.303174	+	0.502413i
$634$	−0.251872	−	0.436254i	−0.0100031	−	0.0173259i
$635$	3.37454	+	5.84487i	0.133915	+	0.231947i
$636$	−0.847267	−	1.40407i	−0.0335963	−	0.0556751i
$637$	9.19523			0.364328
$638$	−2.49762			−0.0988818
$639$	17.9145	+	28.4295i	0.708686	+	1.12465i
$640$	−17.6177	−	30.5148i	−0.696402	−	1.20620i
$641$	11.6521	+	20.1821i	0.460231	+	0.797144i	0.998972	−	0.0453273i	$-0.0144331\pi$
$641$	11.6521	+	20.1821i	0.460231	+	0.797144i	−0.538741	+	0.842472i	$0.681100\pi$
$642$	−3.72824	+	6.75599i	−0.147142	+	0.266638i
$643$	17.2596			0.680651			0.340325	−	0.940308i	$-0.389463\pi$
$643$	17.2596			0.680651			0.340325	+	0.940308i	$0.389463\pi$
$644$	2.08918			0.0823251
$645$	−29.8727	+	54.1328i	−1.17624	+	2.13148i
$646$	11.2793	+	4.26963i	0.443777	+	0.167986i
$647$	−35.6673			−1.40223			−0.701114	−	0.713049i	$-0.747314\pi$
$647$	−35.6673			−1.40223			−0.701114	+	0.713049i	$0.747314\pi$
$648$	7.29016	+	10.6338i	0.286384	+	0.417737i
$649$	8.53539	−	14.7837i	0.335043	−	0.580312i
$650$	−3.75545			−0.147301
$651$	−1.93490	−	3.20648i	−0.0758348	−	0.125672i
$652$	−5.04415	+	8.73673i	−0.197544	+	0.342157i
$653$	−8.46548	−	14.6626i	−0.331280	−	0.573794i	0.651483	−	0.758663i	$-0.274147\pi$
$653$	−8.46548	−	14.6626i	−0.331280	−	0.573794i	−0.982763	+	0.184869i	$0.940814\pi$
$654$	−5.06212	−	8.38883i	−0.197944	−	0.328029i
$655$	10.7684			0.420754
$656$	−8.86092	−	15.3476i	−0.345961	−	0.599222i
$657$	−5.90978	−	9.37858i	−0.230563	−	0.365893i
$658$	0.311770			0.0121540
$659$	−4.52365			−0.176216			−0.0881082	−	0.996111i	$-0.528082\pi$
$659$	−4.52365			−0.176216			−0.0881082	+	0.996111i	$0.528082\pi$
$660$	−9.04103	+	16.3834i	−0.351921	+	0.637722i
$661$	−10.0400	+	17.3898i	−0.390510	+	0.676384i	−0.992517	−	0.122107i	$-0.961035\pi$
$661$	−10.0400	+	17.3898i	−0.390510	+	0.676384i	0.602007	+	0.798491i	$0.294368\pi$
$662$	−6.22996			−0.242134
$663$	−8.27444	+	14.9942i	−0.321353	+	0.582328i
$664$	−0.265379	+	0.459651i	−0.0102987	+	0.0178379i
$665$	−2.99646	+	2.44965i	−0.116198	+	0.0949933i
$666$	3.45335	−	0.133661i	0.133815	−	0.00517928i
$667$	−9.26864	+	16.0537i	−0.358883	+	0.621604i
$668$	−1.39689	−	2.41948i	−0.0540473	−	0.0936127i
$669$	−13.0575	+	23.6617i	−0.504833	+	0.914816i
$670$	1.05401			0.0407201
$671$	−3.37829	+	5.85137i	−0.130417	+	0.225890i
$672$	−0.846371	+	1.53372i	−0.0326495	+	0.0591646i
$673$	8.72911	−	15.1193i	0.336482	−	0.582805i	−0.647286	−	0.762247i	$-0.724096\pi$
$673$	8.72911	−	15.1193i	0.336482	−	0.582805i	0.983768	+	0.179443i	$0.0574294\pi$
$674$	−6.77287	−	11.7310i	−0.260881	−	0.451860i
$675$	39.6293	−	2.30221i	1.52533	−	0.0886121i
$676$	20.9399			0.805382
$677$	−20.4904	+	35.4905i	−0.787511	+	1.36401i	0.139976	+	0.990155i	$0.455297\pi$
$677$	−20.4904	+	35.4905i	−0.787511	+	1.36401i	−0.927487	+	0.373854i	$0.878036\pi$
$678$	1.88164	−	0.0364006i	0.0722638	−	0.00139796i
$679$	1.60629			0.0616436
$680$	18.9968	−	32.9034i	0.728493	−	1.26179i
$681$	2.06223	−	0.0398942i	0.0790248	−	0.00152875i
$682$	−2.61954	−	4.53717i	−0.100307	−	0.173737i
$683$	20.9461			0.801480			0.400740	−	0.916192i	$-0.368753\pi$
$683$	20.9461			0.801480			0.400740	+	0.916192i	$0.368753\pi$
$684$	−4.84844	−	23.8671i	−0.185385	−	0.912581i
$685$	−15.1362			−0.578325
$686$	0.645521	+	1.11807i	0.0246461	+	0.0426883i
$687$	−16.7110	+	30.2822i	−0.637563	+	1.15534i
$688$	16.0327	−	27.7695i	0.611242	−	1.05870i
$689$	0.673794			0.0256695
$690$	−5.29977	−	8.78266i	−0.201759	−	0.334350i
$691$	−10.5768	+	18.3195i	−0.402359	+	0.696907i	−0.994010	−	0.109288i	$-0.965143\pi$
$691$	−10.5768	+	18.3195i	−0.402359	+	0.696907i	0.591651	+	0.806194i	$0.298476\pi$
$692$	−41.7437			−1.58686
$693$	1.22159	−	0.0472815i	0.0464043	−	0.00179608i
$694$	1.88242	+	3.26044i	0.0714556	+	0.123765i
$695$	−30.7031	+	53.1793i	−1.16463	+	2.01720i
$696$	−5.29090	−	8.76797i	−0.200551	−	0.332349i
$697$	20.6986	−	35.8510i	0.784015	−	1.35795i
$698$	−6.40610			−0.242475
$699$	−21.4191	+	0.414357i	−0.810144	+	0.0156724i
$700$	1.77675	+	3.07742i	0.0671548	+	0.116316i
$701$	−1.32346	+	2.29231i	−0.0499865	+	0.0865792i	−0.889936	−	0.456085i	$-0.849251\pi$
$701$	−1.32346	+	2.29231i	−0.0499865	+	0.0865792i	0.839950	+	0.542665i	$0.182585\pi$
$702$	−2.55003	+	0.148141i	−0.0962448	+	0.00559121i
$703$	−12.6619	−	4.79300i	−0.477552	−	0.180771i
$704$	3.98543	−	6.90297i	0.150207	−	0.260165i
$705$	10.7081	+	17.7452i	0.403289	+	0.668321i
$706$	6.26920			0.235944
$707$	−0.944501	+	1.63592i	−0.0355216	+	0.0615252i
$708$	33.7438	−	0.652780i	1.26817	−	0.0245330i
$709$	26.8452			1.00819			0.504097	−	0.863647i	$-0.331825\pi$
$709$	26.8452			1.00819			0.504097	+	0.863647i	$0.331825\pi$
$710$	14.7695			0.554291
$711$	29.5437	−	1.14349i	1.10798	−	0.0428841i
$712$	−5.74496	−	9.95056i	−0.215301	−	0.372913i
$713$	−38.8843			−1.45623
$714$	−1.19666	+	0.0231496i	−0.0447838	+	0.000866351i
$715$	−3.84422	−	6.65839i	−0.143766	−	0.249010i
$716$	−11.8390	+	20.5057i	−0.442442	+	0.766333i
$717$	13.5843	−	24.6163i	0.507314	−	0.919312i
$718$	−2.83914			−0.105956
$719$	1.94193	−	3.36352i	0.0724217	−	0.125438i	−0.827540	−	0.561406i	$-0.810261\pi$
$719$	1.94193	−	3.36352i	0.0724217	−	0.125438i	0.899962	+	0.435968i	$0.143594\pi$
$720$	−34.0360	+	1.31736i	−1.26845	+	0.0490950i
$721$	3.45120			0.128529
$722$	1.40095	−	6.90623i	0.0521381	−	0.257023i
$723$	−9.38451	−	15.5518i	−0.349014	−	0.578378i
$724$	4.88543			0.181566
$725$	−31.5302			−1.17100
$726$	−5.35518	+	0.103597i	−0.198749	+	0.00384485i
$727$	26.1519	+	45.2965i	0.969922	+	1.67995i	0.695766	+	0.718269i	$0.255065\pi$
$727$	26.1519	+	45.2965i	0.969922	+	1.67995i	0.274156	+	0.961685i	$0.411602\pi$
$728$	−0.237102	−	0.410673i	−0.00878758	−	0.0152205i
$729$	26.8184	−	3.12650i	0.993273	−	0.115796i
$730$	−4.87230			−0.180332
$731$	74.9031			2.77039
$732$	−13.3557	+	0.258369i	−0.493642	+	0.00954960i
$733$	3.06517	+	5.30902i	0.113215	+	0.196093i	0.917065	−	0.398739i	$-0.130552\pi$
$733$	3.06517	+	5.30902i	0.113215	+	0.196093i	−0.803850	+	0.594832i	$0.797219\pi$
$734$	4.59485	+	7.95852i	0.169599	+	0.293754i
$735$	−20.6407	+	37.4033i	−0.761343	+	1.37964i
$736$	9.09410	+	15.7515i	0.335213	+	0.580606i
$737$	0.652121	+	1.12951i	0.0240212	+	0.0416059i
$738$	6.16982	−	0.238802i	0.227114	−	0.00879043i
$739$	−6.68714	+	11.5825i	−0.245990	+	0.426068i	−0.962410	−	0.271602i	$-0.912447\pi$
$739$	−6.68714	+	11.5825i	−0.245990	+	0.426068i	0.716419	+	0.697670i	$0.245780\pi$
$740$	−10.2830	+	17.8106i	−0.378009	+	0.654731i
$741$	9.42537	+	3.36091i	0.346250	+	0.123466i
$742$	0.0235449	+	0.0407809i	0.000864360	+	0.00149712i
$743$	−2.74391			−0.100664			−0.0503321	−	0.998733i	$-0.516028\pi$
$743$	−2.74391			−0.100664			−0.0503321	+	0.998733i	$0.516028\pi$
$744$	10.3787	−	18.8074i	0.380502	−	0.689512i
$745$	−6.56344			−0.240466
$746$	4.29724	−	7.44304i	0.157333	−	0.272509i
$747$	0.592568	+	0.940380i	0.0216809	+	0.0344067i
$748$	22.6696			0.828881
$749$	−1.49999	+	2.59806i	−0.0548085	+	0.0949311i
$750$	2.91261	−	5.27799i	0.106354	−	0.192725i
$751$	10.4736	−	18.1408i	0.382187	−	0.661967i	−0.609188	−	0.793026i	$-0.708504\pi$
$751$	10.4736	−	18.1408i	0.382187	−	0.661967i	0.991375	+	0.131059i	$0.0418377\pi$
$752$	−5.37439	−	9.30871i	−0.195984	−	0.339454i
$753$	−11.7527	+	21.2972i	−0.428292	+	0.776114i
$754$	2.02888			0.0738875
$755$	19.9065	−	34.4791i	0.724473	−	1.25482i
$756$	1.32785	+	2.01955i	0.0482933	+	0.0734503i
$757$	3.65990	−	6.33913i	0.133021	−	0.230400i	−0.791819	−	0.610756i	$-0.790865\pi$
$757$	3.65990	−	6.33913i	0.133021	−	0.230400i	0.924840	+	0.380357i	$0.124199\pi$
$758$	−5.39274	−	9.34049i	−0.195873	−	0.339262i
$759$	6.13274	−	11.1132i	0.222604	−	0.403385i
$760$	−20.7620	−	7.85920i	−0.753118	−	0.285083i
$761$	6.05266	+	10.4835i	0.219409	+	0.380027i	0.954627	−	0.297803i	$-0.0962539\pi$
$761$	6.05266	+	10.4835i	0.219409	+	0.380027i	−0.735219	+	0.677830i	$0.762921\pi$
$762$	1.21928	−	0.0235872i	0.0441698	−	0.000854473i
$763$	−1.90460	−	3.29886i	−0.0689510	−	0.119427i
$764$	3.17391	+	5.49737i	0.114828	+	0.198888i
$765$	−42.4180	−	67.3156i	−1.53363	−	2.43380i
$766$	0.524540	+	0.908530i	0.0189524	+	0.0328265i
$767$	−6.93352	+	12.0092i	−0.250355	+	0.433627i
$768$	10.5541	−	0.204172i	0.380839	−	0.00736741i
$769$	14.4830	−	25.0852i	0.522269	−	0.904597i	−0.477395	−	0.878689i	$-0.658419\pi$
$769$	14.4830	−	25.0852i	0.522269	−	0.904597i	0.999664	−	0.0259081i	$-0.00824772\pi$
$770$	0.268663	−	0.465339i	0.00968195	−	0.0167696i
$771$	29.7176	−	0.574893i	1.07025	−	0.0207043i
$772$	0.463529	−	0.802856i	0.0166828	−	0.0288954i
$773$	21.7876	+	37.7372i	0.783645	+	1.35731i	0.929805	+	0.368052i	$0.119975\pi$
$773$	21.7876	+	37.7372i	0.783645	+	1.35731i	−0.146160	+	0.989261i	$0.546691\pi$
$774$	5.95596	+	9.45185i	0.214082	+	0.339740i
$775$	−33.0693	−	57.2777i	−1.18788	−	2.05748i
$776$	4.60671	+	7.97906i	0.165371	+	0.286432i
$777$	1.34334	−	0.0259873i	0.0481922	−	0.000932287i
$778$	−3.55421	−	6.15608i	−0.127425	−	0.220706i
$779$	−22.6220	−	8.56327i	−0.810517	−	0.306811i
$780$	7.34426	−	13.3086i	0.262967	−	0.476525i
$781$	9.13796	+	15.8274i	0.326982	+	0.566349i
$782$	−6.21352	+	10.7621i	−0.222195	+	0.384853i
$783$	−21.4097	+	1.24377i	−0.765121	+	0.0444487i
$784$	11.0779	−	19.1875i	0.395639	−	0.685267i
$785$	−73.8457			−2.63567
$786$	0.940104	−	1.70358i	0.0335324	−	0.0607645i
$787$	3.10060	+	5.37040i	0.110525	+	0.191434i	0.915982	−	0.401220i	$-0.131414\pi$
$787$	3.10060	+	5.37040i	0.110525	+	0.191434i	−0.805457	+	0.592654i	$0.798080\pi$
$788$	−2.46213	+	4.26454i	−0.0877098	+	0.151918i
$789$	−16.3181	+	29.5703i	−0.580941	+	1.05273i
$790$	6.49754	−	11.2541i	0.231172	−	0.400402i
$791$	0.731677			0.0260155
$792$	3.73830	+	5.93252i	0.132835	+	0.210803i
$793$	2.74427	−	4.75322i	0.0974520	−	0.168792i
$794$	−11.8380			−0.420115
$795$	−1.51248	+	2.74078i	−0.0536420	+	0.0972055i
$796$	0.395995			0.0140357
$797$	−19.1606	−	33.1871i	−0.678702	−	1.17555i	−0.975372	−	0.220566i	$-0.929210\pi$
$797$	−19.1606	−	33.1871i	−0.678702	−	1.17555i	0.296671	−	0.954980i	$-0.404124\pi$
$798$	0.125941	+	0.687907i	0.00445827	+	0.0243517i
$799$	12.5543	−	21.7446i	0.444138	−	0.769269i
$800$	−15.4683	+	26.7918i	−0.546885	+	0.947233i
$801$	−24.0440	+	0.930621i	−0.849554	+	0.0328819i
$802$	−7.11006	−	12.3150i	−0.251065	−	0.434857i
$803$	−3.01451	−	5.22128i	−0.106380	−	0.184255i
$804$	−1.24586	+	2.25763i	−0.0439379	+	0.0796206i
$805$	−1.99401	−	3.45373i	−0.0702797	−	0.121728i
$806$	2.12792	+	3.68566i	0.0749527	+	0.129822i
$807$	40.1053	−	0.775846i	1.41177	−	0.0273111i
$808$	−10.8350			−0.381175
$809$	−36.9557			−1.29929			−0.649647	−	0.760236i	$-0.725083\pi$
$809$	−36.9557			−1.29929			−0.649647	+	0.760236i	$0.725083\pi$
$810$	5.12152	−	10.7053i	0.179952	−	0.376145i
$811$	21.0016	+	36.3759i	0.737467	+	1.27733i	0.953632	+	0.300974i	$0.0973118\pi$
$811$	21.0016	+	36.3759i	0.737467	+	1.27733i	−0.216165	+	0.976357i	$0.569355\pi$
$812$	−0.959889	−	1.66258i	−0.0336855	−	0.0583450i
$813$	38.2322	−	0.739610i	1.34086	−	0.0259393i
$814$	1.87960			0.0658800
$815$	19.2575			0.674562
$816$	21.3195	+	35.3303i	0.746333	+	1.23681i
$817$	−7.04750	−	43.1950i	−0.246561	−	1.51120i
$818$	0.850402			0.0297336
$819$	−0.992328	+	0.0384080i	−0.0346748	+	0.00134208i
$820$	−18.3717	+	31.8208i	−0.641569	+	1.11123i
$821$	−17.7203			−0.618444			−0.309222	−	0.950990i	$-0.600069\pi$
$821$	−17.7203			−0.618444			−0.309222	+	0.950990i	$0.600069\pi$
$822$	−1.32143	+	2.39458i	−0.0460902	+	0.0835207i
$823$	14.6013	−	25.2903i	0.508971	−	0.881563i	−0.490975	−	0.871174i	$-0.663359\pi$
$823$	14.6013	−	25.2903i	0.508971	−	0.881563i	0.999946	−	0.0103898i	$-0.00330724\pi$
$824$	9.89779	+	17.1435i	0.344806	+	0.597221i
$825$	21.5858	−	0.417581i	0.751519	−	0.0145383i
$826$	−0.969133			−0.0337204
$827$	7.34515	+	12.7222i	0.255416	+	0.442393i	0.965008	−	0.262219i	$-0.0844543\pi$
$827$	7.34515	+	12.7222i	0.255416	+	0.442393i	−0.709593	+	0.704612i	$0.751121\pi$
$828$	25.0763	−	0.970576i	0.871462	−	0.0337298i
$829$	−2.88680			−0.100263			−0.0501314	−	0.998743i	$-0.515964\pi$
$829$	−2.88680			−0.100263			−0.0501314	+	0.998743i	$0.515964\pi$
$830$	0.488541			0.0169575
$831$	−51.2564	+	0.991566i	−1.77807	+	0.0343970i
$832$	−3.23747	+	5.60746i	−0.112239	+	0.194404i
$833$	51.7547			1.79319
$834$	5.73262	+	9.49997i	0.198504	+	0.328957i
$835$	−2.66652	+	4.61855i	−0.0922788	+	0.159831i
$836$	−2.13294	−	13.0730i	−0.0737692	−	0.452140i
$837$	−24.7142	−	37.5884i	−0.854249	−	1.29924i
$838$	1.97391	−	3.41892i	0.0681877	−	0.118105i
$839$	7.55921	+	13.0929i	0.260973	+	0.452019i	0.966501	−	0.256664i	$-0.0826233\pi$
$839$	7.55921	+	13.0929i	0.260973	+	0.452019i	−0.705528	+	0.708682i	$0.749290\pi$
$840$	2.20271	−	0.0426119i	0.0760009	−	0.00147025i
$841$	−11.9658			−0.412614
$842$	−4.79644	+	8.30768i	−0.165296	+	0.286301i
$843$	−25.7799	−	42.7218i	−0.887906	−	1.47142i
$844$	−7.93749	+	13.7481i	−0.273220	+	0.473230i
$845$	−19.9861	−	34.6170i	−0.687543	−	1.19086i
$846$	3.74216	−	0.144840i	0.128658	−	0.00497970i
$847$	−2.08237			−0.0715511
$848$	0.811749	−	1.40599i	0.0278756	−	0.0482819i
$849$	−14.3363	−	23.7578i	−0.492019	−	0.815364i
$850$	−21.1373			−0.725002
$851$	6.97517	−	12.0814i	0.239106	−	0.414143i
$852$	−17.4578	+	31.6355i	−0.598093	+	1.08381i
$853$	−13.0507	−	22.6045i	−0.446848	−	0.773964i	0.551331	−	0.834287i	$-0.314120\pi$
$853$	−13.0507	−	22.6045i	−0.446848	−	0.773964i	−0.998179	+	0.0603231i	$0.980787\pi$
$854$	0.383581			0.0131259
$855$	−34.8284	+	30.7951i	−1.19111	+	1.05317i
$856$	−17.2075			−0.588139
$857$	−20.8227	−	36.0660i	−0.711291	−	1.23199i	−0.964373	−	0.264547i	$-0.914778\pi$
$857$	−20.8227	−	36.0660i	−0.711291	−	1.23199i	0.253082	−	0.967445i	$-0.418556\pi$
$858$	−1.38898	+	0.0268701i	−0.0474191	+	0.000917332i
$859$	−4.72015	+	8.17554i	−0.161049	+	0.278946i	−0.935245	−	0.354000i	$-0.884821\pi$
$859$	−4.72015	+	8.17554i	−0.161049	+	0.278946i	0.774196	+	0.632946i	$0.218155\pi$
$860$	−66.4828			−2.26704
$861$	2.40004	−	0.0464293i	0.0817933	−	0.00158231i
$862$	−3.53451	+	6.12196i	−0.120386	+	0.208515i
$863$	31.0403			1.05662			0.528311	−	0.849051i	$-0.322825\pi$
$863$	31.0403			1.05662			0.528311	+	0.849051i	$0.322825\pi$
$864$	−9.44644	+	18.8024i	−0.321374	+	0.639671i
$865$	39.8422	+	69.0088i	1.35468	+	2.34637i
$866$	4.94349	−	8.56238i	0.167987	−	0.290962i
$867$	−32.3456	+	58.6139i	−1.09851	+	1.99063i
$868$	2.01349	−	3.48746i	0.0683422	−	0.118372i
$869$	16.0802			0.545483
$870$	−4.55427	+	8.25285i	−0.154404	+	0.279798i
$871$	−0.529735	−	0.917528i	−0.0179494	−	0.0310892i
$872$	10.9245	−	18.9218i	0.369950	−	0.640772i
$873$	19.2802	−	0.746238i	0.652536	−	0.0252563i
$874$	6.79090	+	2.57061i	0.229706	+	0.0869522i
$875$	1.17184	−	2.02969i	0.0396154	−	0.0686159i
$876$	5.75912	−	10.4362i	0.194582	−	0.352606i
$877$	−41.4554			−1.39985			−0.699924	−	0.714217i	$-0.746783\pi$
$877$	−41.4554			−1.39985			−0.699924	+	0.714217i	$0.746783\pi$
$878$	0.361069	−	0.625390i	0.0121855	−	0.0211059i
$879$	−0.670113	+	1.21432i	−0.0226024	+	0.0409580i
$880$	−18.5252			−0.624485
$881$	15.2233			0.512886			0.256443	−	0.966559i	$-0.417449\pi$
$881$	15.2233			0.512886			0.256443	+	0.966559i	$0.417449\pi$
$882$	4.11530	+	6.53080i	0.138569	+	0.219904i
$883$	−0.314882	−	0.545392i	−0.0105966	−	0.0183539i	0.860678	−	0.509149i	$-0.170040\pi$
$883$	−0.314882	−	0.545392i	−0.0105966	−	0.0183539i	−0.871275	+	0.490795i	$0.836706\pi$
$884$	−18.4151			−0.619365
$885$	−33.2859	−	55.1606i	−1.11889	−	1.85420i
$886$	−1.21694	−	2.10781i	−0.0408840	−	0.0708132i
$887$	0.563597	−	0.976178i	0.0189237	−	0.0327769i	−0.856408	−	0.516299i	$-0.827309\pi$
$887$	0.563597	−	0.976178i	0.0189237	−	0.0327769i	0.875332	+	0.483522i	$0.160643\pi$
$888$	3.98170	+	6.59839i	0.133617	+	0.221428i
$889$	0.474118			0.0159014
$890$	−5.28798	+	9.15906i	−0.177254	+	0.307012i
$891$	14.6407	−	1.13504i	0.490483	−	0.0380252i
$892$	−29.0600			−0.973000
$893$	−13.7208	−	5.19385i	−0.459151	−	0.173806i
$894$	−0.573004	+	1.03835i	−0.0191641	+	0.0347276i
$895$	45.1987			1.51083
$896$	−2.47527			−0.0826929
$897$	−4.98178	+	9.02756i	−0.166337	+	0.301421i
$898$	6.58973	+	11.4137i	0.219902	+	0.380881i
$899$	17.8657	+	30.9443i	0.595854	+	1.03205i
$900$	22.7560	+	36.1128i	0.758532	+	1.20376i
$901$	3.79240			0.126343
$902$	3.35813			0.111814
$903$	2.24404	+	3.71878i	0.0746771	+	0.123753i
$904$	2.09840	+	3.63453i	0.0697917	+	0.120883i
$905$	−4.66290	−	8.07637i	−0.155000	−	0.268468i
$906$	−3.71678	−	6.15937i	−0.123482	−	0.204631i
$907$	−14.3660	−	24.8826i	−0.477014	−	0.826213i	0.522639	−	0.852554i	$-0.324948\pi$
$907$	−14.3660	−	24.8826i	−0.477014	−	0.826213i	−0.999653	+	0.0263414i	$0.991614\pi$
$908$	1.10895	+	1.92075i	0.0368016	+	0.0637423i
$909$	−10.5768	+	20.0747i	−0.350811	+	0.665837i
$910$	−0.218242	+	0.378006i	−0.00723466	+	0.0125308i
$911$	−19.6724	+	34.0735i	−0.651774	+	1.12891i	0.330918	+	0.943660i	$0.392642\pi$
$911$	−19.6724	+	34.0735i	−0.651774	+	1.12891i	−0.982692	+	0.185246i	$0.940692\pi$
$912$	18.3683	−	15.6187i	0.608235	−	0.517186i
$913$	0.302262	+	0.523532i	0.0100034	+	0.0173264i
$914$	2.46599			0.0815678
$915$	13.1745	+	21.8325i	0.435535	+	0.721759i
$916$	−37.1908			−1.22882
$917$	0.378235	−	0.655122i	0.0124904	−	0.0216340i
$918$	−14.3527	+	0.833799i	−0.473709	+	0.0275195i
$919$	14.3218			0.472433			0.236217	−	0.971700i	$-0.424093\pi$
$919$	14.3218			0.472433			0.236217	+	0.971700i	$0.424093\pi$
$920$	11.4374	−	19.8101i	0.377079	−	0.653120i
$921$	−7.96549	+	0.154094i	−0.262472	+	0.00507757i
$922$	1.29288	−	2.23934i	0.0425788	−	0.0737487i
$923$	−7.42300	−	12.8570i	−0.244331	−	0.423194i
$924$	0.679164	+	1.12550i	0.0223428	+	0.0370261i
$925$	23.7283			0.780181
$926$	3.18850	−	5.52264i	0.104781	−	0.181485i
$927$	41.4246	−	1.60334i	1.36056	−	0.0526604i
$928$	8.35672	−	14.4743i	0.274323	−	0.475141i
$929$	−0.893942	−	1.54835i	−0.0293293	−	0.0507998i	0.850988	−	0.525185i	$-0.176004\pi$
$929$	−0.893942	−	1.54835i	−0.0293293	−	0.0507998i	−0.880317	+	0.474385i	$0.842670\pi$
$930$	−19.7687	+	0.382429i	−0.648240	+	0.0125403i
$931$	−4.86950	−	29.8458i	−0.159591	−	0.978156i
$932$	−11.5179	−	19.9496i	−0.377282	−	0.653472i
$933$	27.4681	−	49.7753i	0.899265	−	1.62957i
$934$	−6.77773	−	11.7394i	−0.221774	−	0.384124i
$935$	−21.6369	−	37.4763i	−0.707603	−	1.22560i
$936$	−3.03671	−	4.81914i	−0.0992581	−	0.157518i
$937$	6.96721	+	12.0676i	0.227609	+	0.394230i	0.957099	−	0.289761i	$-0.0935759\pi$
$937$	6.96721	+	12.0676i	0.227609	+	0.394230i	−0.729490	+	0.683991i	$0.760243\pi$
$938$	0.0370219	−	0.0641238i	0.00120881	−	0.00209372i
$939$	16.4546	+	27.2682i	0.536976	+	0.889866i
$940$	−11.1430	+	19.3002i	−0.363443	+	0.629502i
$941$	22.7165	−	39.3461i	0.740535	−	1.28264i	−0.211717	−	0.977331i	$-0.567905\pi$
$941$	22.7165	−	39.3461i	0.740535	−	1.28264i	0.952252	−	0.305314i	$-0.0987613\pi$
$942$	−6.44692	+	11.6826i	−0.210052	+	0.380638i
$943$	12.4620	−	21.5848i	0.405818	−	0.702897i
$944$	16.7062	+	28.9360i	0.543741	+	0.941787i
$945$	2.07127	−	4.12269i	0.0673783	−	0.134111i
$946$	3.03806	+	5.26208i	0.0987759	+	0.171085i
$947$	2.58749	+	4.48167i	0.0840823	+	0.145635i	0.905000	−	0.425412i	$-0.139871\pi$
$947$	2.58749	+	4.48167i	0.0840823	+	0.145635i	−0.820918	+	0.571047i	$0.806537\pi$
$948$	16.4254	+	27.2197i	0.533471	+	0.884056i
$949$	2.44876	+	4.24138i	0.0794902	+	0.137681i
$950$	1.98877	+	12.1894i	0.0645241	+	0.395476i
$951$	−1.21542	−	2.01418i	−0.0394128	−	0.0653141i
$952$	−1.33451	−	2.31144i	−0.0432517	−	0.0749142i
$953$	12.9234	−	22.3840i	0.418630	−	0.725088i	−0.577172	−	0.816622i	$-0.695844\pi$
$953$	12.9234	−	22.3840i	0.418630	−	0.725088i	0.995802	+	0.0915347i	$0.0291772\pi$
$954$	0.301554	+	0.478554i	0.00976318	+	0.0154938i
$955$	6.05867	−	10.4939i	0.196054	−	0.339575i
$956$	30.2323			0.977783
$957$	−11.6617	+	0.225598i	−0.376969	+	0.00729255i
$958$	3.70247	+	6.41287i	0.119621	+	0.207190i
$959$	−0.531655	+	0.920853i	−0.0171680	+	0.0297359i
$960$	−15.5422	−	25.7562i	−0.501621	−	0.831276i
$961$	−21.9755	+	38.0628i	−0.708888	+	1.22783i
$962$	−1.52685			−0.0492276
$963$	−16.7974	+	31.8813i	−0.541287	+	1.02736i
$964$	9.76565	−	16.9146i	0.314531	−	0.544783i
$965$	−1.76966			−0.0569674
$966$	−0.720470	+	0.0139376i	−0.0231807	+	0.000448436i
$967$	26.1397			0.840597			0.420299	−	0.907386i	$-0.361925\pi$
$967$	26.1397			0.840597			0.420299	+	0.907386i	$0.361925\pi$
$968$	−5.97209	−	10.3440i	−0.191950	−	0.332468i
$969$	53.0500	+	18.9166i	1.70421	+	0.607689i
$970$	4.24028	−	7.34438i	0.136147	−	0.235814i
$971$	6.28902	−	10.8929i	0.201824	−	0.349570i	−0.747292	−	0.664496i	$-0.768646\pi$
$971$	6.28902	−	10.8929i	0.201824	−	0.349570i	0.949116	+	0.314926i	$0.101980\pi$
$972$	16.8763	+	23.6237i	0.541309	+	0.757731i
$973$	2.15687	+	3.73581i	0.0691461	+	0.119764i
$974$	−0.100402	−	0.173901i	−0.00321708	−	0.00557215i
$975$	−17.5347	+	0.339212i	−0.561559	+	0.0108635i
$976$	−6.61229	−	11.4528i	−0.211654	−	0.366596i
$977$	18.8495	+	32.6483i	0.603050	+	1.04451i	0.992356	+	0.123405i	$0.0393813\pi$
$977$	18.8495	+	32.6483i	0.603050	+	1.04451i	−0.389307	+	0.921108i	$0.627285\pi$
$978$	1.68123	−	3.04658i	0.0537599	−	0.0974190i
$979$	−13.0868			−0.418255
$980$	−45.9366			−1.46739
$981$	−24.3934	−	38.7113i	−0.778821	−	1.23596i
$982$	1.36185	+	2.35879i	0.0434583	+	0.0752719i
$983$	11.6223	+	20.1305i	0.370695	+	0.642063i	0.989673	−	0.143346i	$-0.0457861\pi$
$983$	11.6223	+	20.1305i	0.370695	+	0.642063i	−0.618977	+	0.785409i	$0.712453\pi$
$984$	7.11379	+	11.7888i	0.226779	+	0.375814i
$985$	9.39991			0.299506
$986$	11.4194			0.363668
$987$	1.45569	−	0.0281606i	0.0463352	−	0.000896363i
$988$	1.73264	+	10.6196i	0.0551226	+	0.337853i
$989$	45.0968			1.43400
$990$	3.00857	−	5.71026i	0.0956188	−	0.181484i
$991$	−11.8484	+	20.5220i	−0.376376	+	0.651903i	−0.990532	−	0.137282i	$-0.956163\pi$
$991$	−11.8484	+	20.5220i	−0.376376	+	0.651903i	0.614156	+	0.789185i	$0.289497\pi$
$992$	35.0586			1.11311
$993$	−29.0885	+	0.562722i	−0.923094	+	0.0178574i
$994$	0.518775	−	0.898545i	0.0164545	−	0.0285001i
$995$	−0.377957	−	0.654641i	−0.0119820	−	0.0207535i
$996$	−0.577460	+	1.04642i	−0.0182975	+	0.0331572i
$997$	−18.9313			−0.599559			−0.299780	−	0.954008i	$-0.596913\pi$
$997$	−18.9313			−0.599559			−0.299780	+	0.954008i	$0.596913\pi$
$998$	2.21559	+	3.83752i	0.0701333	+	0.121475i
$999$	16.1120	−	0.936006i	0.509762	−	0.0296139i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	171.2.g.c.106.8	✓	32
3.2	odd	2		513.2.g.c.505.9		32
9.4	even	3		171.2.h.c.49.9	yes	32
9.5	odd	6		513.2.h.c.334.8		32
19.7	even	3		171.2.h.c.7.9	yes	32
57.26	odd	6		513.2.h.c.235.8		32
171.121	even	3	inner	171.2.g.c.121.8	yes	32
171.140	odd	6		513.2.g.c.64.9		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
171.2.g.c.106.8	✓	32	1.1	even	1	trivial
171.2.g.c.121.8	yes	32	171.121	even	3	inner
171.2.h.c.7.9	yes	32	19.7	even	3
171.2.h.c.49.9	yes	32	9.4	even	3
513.2.g.c.64.9		32	171.140	odd	6
513.2.g.c.505.9		32	3.2	odd	2
513.2.h.c.235.8		32	57.26	odd	6
513.2.h.c.334.8		32	9.5	odd	6

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 171 = 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	171.g (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.185445 - 0.321199i) q^{2} +(-0.894876 - 1.48297i) q^{3} +(0.931221 - 1.61292i) q^{4} -3.55521 q^{5} +(-0.310379 + 0.562442i) q^{6} +(-0.124876 + 0.216291i) q^{7} -1.43254 q^{8} +(-1.39839 + 2.65415i) q^{9} +O(q^{10})\)	\(q+(-0.185445 - 0.321199i) q^{2} +(-0.894876 - 1.48297i) q^{3} +(0.931221 - 1.61292i) q^{4} -3.55521 q^{5} +(-0.310379 + 0.562442i) q^{6} +(-0.124876 + 0.216291i) q^{7} -1.43254 q^{8} +(-1.39839 + 2.65415i) q^{9} +(0.659294 + 1.14193i) q^{10} +(-0.815815 + 1.41303i) q^{11} +(-3.22524 + 0.0623929i) q^{12} +(0.662707 - 1.14784i) q^{13} +0.0926300 q^{14} +(3.18147 + 5.27227i) q^{15} +(-1.59679 - 2.76571i) q^{16} +(3.73000 - 6.46055i) q^{17} +(1.11183 - 0.0430334i) q^{18} +(-4.07660 - 1.54315i) q^{19} +(-3.31069 + 5.73428i) q^{20} +(0.432501 - 0.00836682i) q^{21} +0.605154 q^{22} +(2.24572 - 3.88969i) q^{23} +(1.28194 + 2.12441i) q^{24} +7.63952 q^{25} -0.491582 q^{26} +(5.18741 - 0.301355i) q^{27} +(0.232573 + 0.402829i) q^{28} -4.12725 q^{29} +(1.10346 - 1.99960i) q^{30} +(-4.32871 - 7.49755i) q^{31} +(-2.02477 + 3.50700i) q^{32} +(2.82554 - 0.0546606i) q^{33} -2.76683 q^{34} +(0.443959 - 0.768960i) q^{35} +(2.97872 + 4.72710i) q^{36} +3.10599 q^{37} +(0.260326 + 1.59557i) q^{38} +(-2.29526 + 0.0444022i) q^{39} +5.09297 q^{40} +5.54922 q^{41} +(-0.0828923 - 0.137367i) q^{42} +(5.02032 + 8.69544i) q^{43} +(1.51941 + 2.63169i) q^{44} +(4.97159 - 9.43605i) q^{45} -1.66582 q^{46} +3.36575 q^{47} +(-2.67254 + 4.84295i) q^{48} +(3.46881 + 6.00816i) q^{49} +(-1.41671 - 2.45381i) q^{50} +(-12.9187 + 0.249914i) q^{51} +(-1.23425 - 2.13779i) q^{52} +(0.254182 + 0.440256i) q^{53} +(-1.05877 - 1.61031i) q^{54} +(2.90039 - 5.02363i) q^{55} +(0.178889 - 0.309845i) q^{56} +(1.35962 + 7.42640i) q^{57} +(0.765376 + 1.32567i) q^{58} -10.4624 q^{59} +(11.4664 - 0.221820i) q^{60} +4.14100 q^{61} +(-1.60547 + 2.78076i) q^{62} +(-0.399442 - 0.633898i) q^{63} -4.88521 q^{64} +(-2.35606 + 4.08082i) q^{65} +(-0.541537 - 0.897424i) q^{66} +(0.399675 - 0.692257i) q^{67} +(-6.94690 - 12.0324i) q^{68} +(-7.77793 + 0.150466i) q^{69} -0.329319 q^{70} +(5.60051 - 9.70037i) q^{71} +(2.00325 - 3.80216i) q^{72} +(-1.84754 + 3.20004i) q^{73} +(-0.575989 - 0.997642i) q^{74} +(-6.83642 - 11.3292i) q^{75} +(-6.28519 + 5.13823i) q^{76} +(-0.203751 - 0.352907i) q^{77} +(0.439905 + 0.729000i) q^{78} +(-4.92764 - 8.53493i) q^{79} +(5.67691 + 9.83269i) q^{80} +(-5.08898 - 7.42309i) q^{81} +(-1.02907 - 1.78241i) q^{82} +(0.185251 - 0.320865i) q^{83} +(0.389259 - 0.705381i) q^{84} +(-13.2609 + 22.9686i) q^{85} +(1.86198 - 3.22504i) q^{86} +(3.69338 + 6.12059i) q^{87} +(1.16868 - 2.02422i) q^{88} +(4.01034 + 6.94611i) q^{89} +(-3.95281 + 0.152993i) q^{90} +(0.165512 + 0.286675i) q^{91} +(-4.18251 - 7.24433i) q^{92} +(-7.24498 + 13.1287i) q^{93} +(-0.624161 - 1.08108i) q^{94} +(14.4932 + 5.48621i) q^{95} +(7.01269 - 0.135662i) q^{96} +(-3.21577 - 5.56988i) q^{97} +(1.28654 - 2.22836i) q^{98} +(-2.60956 - 4.14127i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + q^{2} - 2 q^{3} - 17 q^{4} - 6 q^{5} + 2 q^{6} + q^{7} - 36 q^{8} - 10 q^{9}+O(q^{10}) \) 32 * q + q^2 - 2 * q^3 - 17 * q^4 - 6 * q^5 + 2 * q^6 + q^7 - 36 * q^8 - 10 * q^9	\( 32 q + q^{2} - 2 q^{3} - 17 q^{4} - 6 q^{5} + 2 q^{6} + q^{7} - 36 q^{8} - 10 q^{9} - 8 q^{10} + 7 q^{11} - 3 q^{12} - 4 q^{13} - 2 q^{14} + q^{15} - 11 q^{16} - 7 q^{17} + 6 q^{18} + 7 q^{19} - 3 q^{20} + 11 q^{21} + 16 q^{22} + 5 q^{23} + 27 q^{24} + 18 q^{25} - 4 q^{26} - 5 q^{27} - 10 q^{28} - 20 q^{29} - 5 q^{30} - 10 q^{31} + 17 q^{32} + 34 q^{33} + 26 q^{34} - 3 q^{35} - 16 q^{36} + 2 q^{37} + 38 q^{38} - 24 q^{40} - 12 q^{41} + 25 q^{42} + 7 q^{43} + 20 q^{44} - 35 q^{45} + 18 q^{47} - 33 q^{48} - 13 q^{49} + q^{50} - 28 q^{51} + 19 q^{52} + 16 q^{53} + 35 q^{54} + 15 q^{55} - 6 q^{56} + 6 q^{57} - 74 q^{59} + 50 q^{60} + 24 q^{61} + 54 q^{62} - 30 q^{63} - 64 q^{64} + 54 q^{65} + 4 q^{66} - 11 q^{67} - 2 q^{68} + 3 q^{69} - 48 q^{70} + 9 q^{71} - 10 q^{73} + 6 q^{74} - 76 q^{75} + 29 q^{76} + 46 q^{77} - 82 q^{78} - 8 q^{79} - 24 q^{80} + 26 q^{81} + 7 q^{82} + 3 q^{83} + 12 q^{84} - 27 q^{85} + 17 q^{86} - 9 q^{87} + 9 q^{88} + 30 q^{89} - 74 q^{90} - q^{91} - 17 q^{92} - 24 q^{93} - 18 q^{94} - 6 q^{95} - 5 q^{96} + 18 q^{98} - 10 q^{99}+O(q^{100}) \) 32 * q + q^2 - 2 * q^3 - 17 * q^4 - 6 * q^5 + 2 * q^6 + q^7 - 36 * q^8 - 10 * q^9 - 8 * q^10 + 7 * q^11 - 3 * q^12 - 4 * q^13 - 2 * q^14 + q^15 - 11 * q^16 - 7 * q^17 + 6 * q^18 + 7 * q^19 - 3 * q^20 + 11 * q^21 + 16 * q^22 + 5 * q^23 + 27 * q^24 + 18 * q^25 - 4 * q^26 - 5 * q^27 - 10 * q^28 - 20 * q^29 - 5 * q^30 - 10 * q^31 + 17 * q^32 + 34 * q^33 + 26 * q^34 - 3 * q^35 - 16 * q^36 + 2 * q^37 + 38 * q^38 - 24 * q^40 - 12 * q^41 + 25 * q^42 + 7 * q^43 + 20 * q^44 - 35 * q^45 + 18 * q^47 - 33 * q^48 - 13 * q^49 + q^50 - 28 * q^51 + 19 * q^52 + 16 * q^53 + 35 * q^54 + 15 * q^55 - 6 * q^56 + 6 * q^57 - 74 * q^59 + 50 * q^60 + 24 * q^61 + 54 * q^62 - 30 * q^63 - 64 * q^64 + 54 * q^65 + 4 * q^66 - 11 * q^67 - 2 * q^68 + 3 * q^69 - 48 * q^70 + 9 * q^71 - 10 * q^73 + 6 * q^74 - 76 * q^75 + 29 * q^76 + 46 * q^77 - 82 * q^78 - 8 * q^79 - 24 * q^80 + 26 * q^81 + 7 * q^82 + 3 * q^83 + 12 * q^84 - 27 * q^85 + 17 * q^86 - 9 * q^87 + 9 * q^88 + 30 * q^89 - 74 * q^90 - q^91 - 17 * q^92 - 24 * q^93 - 18 * q^94 - 6 * q^95 - 5 * q^96 + 18 * q^98 - 10 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more