LMFDB - Embedded newform 966.2.y.d.163.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(25,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([0, 44, 6]))

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

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

chi := DirichletCharacter("966.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.y (of order $33$, degree $20$, 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:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$8$ over $\Q(\zeta_{33})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			163.7
Character	$\chi$	$=$	966.163
Dual form			966.2.y.d.403.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.888835 + 0.458227i) q^{2} +(-0.786053 + 0.618159i) q^{3} +(0.580057 - 0.814576i) q^{4} +(1.27403 - 1.21479i) q^{5} +(0.415415 - 0.909632i) q^{6} +(2.64520 - 0.0541045i) q^{7} +(-0.142315 + 0.989821i) q^{8} +(0.235759 - 0.971812i) q^{9} +O(q^{10})$	\(q+(-0.888835 + 0.458227i) q^{2} +(-0.786053 + 0.618159i) q^{3} +(0.580057 - 0.814576i) q^{4} +(1.27403 - 1.21479i) q^{5} +(0.415415 - 0.909632i) q^{6} +(2.64520 - 0.0541045i) q^{7} +(-0.142315 + 0.989821i) q^{8} +(0.235759 - 0.971812i) q^{9} +(-0.575758 + 1.66354i) q^{10} +(2.70230 + 1.39313i) q^{11} +(0.0475819 + 0.998867i) q^{12} +(0.130239 + 0.150304i) q^{13} +(-2.32635 + 1.26019i) q^{14} +(-0.250526 + 1.74244i) q^{15} +(-0.327068 - 0.945001i) q^{16} +(4.44630 - 0.424570i) q^{17} +(0.235759 + 0.971812i) q^{18} +(-6.39606 - 0.610750i) q^{19} +(-0.250526 - 1.74244i) q^{20} +(-2.04582 + 1.67768i) q^{21} -3.04027 q^{22} +(2.71900 - 3.95058i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-0.0904592 + 1.89897i) q^{25} +(-0.184634 - 0.0739163i) q^{26} +(0.415415 + 0.909632i) q^{27} +(1.49029 - 2.18610i) q^{28} +(1.69278 - 3.70668i) q^{29} +(-0.575758 - 1.66354i) q^{30} +(-3.36783 + 1.34828i) q^{31} +(0.723734 + 0.690079i) q^{32} +(-2.98532 + 0.575374i) q^{33} +(-3.75748 + 2.41479i) q^{34} +(3.30435 - 3.28229i) q^{35} +(-0.654861 - 0.755750i) q^{36} +(0.992538 - 4.09130i) q^{37} +(5.96491 - 2.38799i) q^{38} +(-0.195286 - 0.0376383i) q^{39} +(1.02111 + 1.43395i) q^{40} +(8.57882 + 2.51897i) q^{41} +(1.04964 - 2.42863i) q^{42} +(-1.51738 - 10.5536i) q^{43} +(2.70230 - 1.39313i) q^{44} +(-0.880181 - 1.52452i) q^{45} +(-0.606482 + 4.75733i) q^{46} +(-3.17143 + 5.49308i) q^{47} +(0.841254 + 0.540641i) q^{48} +(6.99415 - 0.286234i) q^{49} +(-0.789756 - 1.72932i) q^{50} +(-3.23258 + 3.08226i) q^{51} +(0.197980 - 0.0189048i) q^{52} +(-5.68363 - 1.09543i) q^{53} +(-0.786053 - 0.618159i) q^{54} +(5.13518 - 1.50782i) q^{55} +(-0.322897 + 2.62597i) q^{56} +(5.40519 - 3.47370i) q^{57} +(0.193893 + 4.07031i) q^{58} +(1.63222 - 4.71598i) q^{59} +(1.27403 + 1.21479i) q^{60} +(5.75741 + 4.52767i) q^{61} +(2.37563 - 2.74162i) q^{62} +(0.571050 - 2.58339i) q^{63} +(-0.959493 - 0.281733i) q^{64} +(0.348516 + 0.0332792i) q^{65} +(2.38981 - 1.87937i) q^{66} +(-0.633288 + 13.2943i) q^{67} +(2.23326 - 3.86812i) q^{68} +(0.304808 + 4.78614i) q^{69} +(-1.43299 + 4.43155i) q^{70} +(5.27418 + 3.38951i) q^{71} +(0.928368 + 0.371662i) q^{72} +(0.144294 - 0.202632i) q^{73} +(0.992538 + 4.09130i) q^{74} +(-1.10276 - 1.54861i) q^{75} +(-4.20758 + 4.85581i) q^{76} +(7.22348 + 3.53890i) q^{77} +(0.190824 - 0.0560310i) q^{78} +(0.0836856 - 0.0161291i) q^{79} +(-1.56467 - 0.806645i) q^{80} +(-0.888835 - 0.458227i) q^{81} +(-8.77942 + 1.69209i) q^{82} +(6.52881 - 1.91703i) q^{83} +(0.179907 + 2.63963i) q^{84} +(5.14898 - 5.94223i) q^{85} +(6.18466 + 8.68514i) q^{86} +(0.960700 + 3.96006i) q^{87} +(-1.76353 + 2.47653i) q^{88} +(16.2095 + 6.48931i) q^{89} +(1.48091 + 0.951724i) q^{90} +(0.352640 + 0.390536i) q^{91} +(-1.64087 - 4.50639i) q^{92} +(1.81384 - 3.14167i) q^{93} +(0.301805 - 6.33568i) q^{94} +(-8.89073 + 6.99175i) q^{95} +(-0.995472 - 0.0950560i) q^{96} +(-13.9451 - 4.09464i) q^{97} +(-6.08548 + 3.45932i) q^{98} +(1.99095 - 2.29768i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q + 8 q^{2} + 8 q^{3} + 8 q^{4} - 2 q^{5} - 16 q^{6} + 6 q^{7} - 16 q^{8} + 8 q^{9}+O(q^{10}) $ 160 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 - 2 * q^5 - 16 * q^6 + 6 * q^7 - 16 * q^8 + 8 * q^9	\( 160 q + 8 q^{2} + 8 q^{3} + 8 q^{4} - 2 q^{5} - 16 q^{6} + 6 q^{7} - 16 q^{8} + 8 q^{9} - 2 q^{10} - 4 q^{11} + 8 q^{12} - 4 q^{13} + 5 q^{14} + 26 q^{15} + 8 q^{16} - 13 q^{17} + 8 q^{18} + 4 q^{19} + 26 q^{20} + 11 q^{21} - 124 q^{22} + 26 q^{23} - 80 q^{24} + 14 q^{25} + 2 q^{26} - 16 q^{27} - 22 q^{28} + 54 q^{29} - 2 q^{30} + 15 q^{31} + 8 q^{32} - 4 q^{33} + 4 q^{34} - 2 q^{35} - 16 q^{36} + 7 q^{37} - 7 q^{38} + 2 q^{39} + 9 q^{40} - 30 q^{41} + 6 q^{42} + 36 q^{43} - 4 q^{44} + 20 q^{45} + 4 q^{46} - 6 q^{47} - 16 q^{48} + 14 q^{49} - 28 q^{50} + 9 q^{51} + 2 q^{52} - 24 q^{53} + 8 q^{54} - 14 q^{55} + 6 q^{56} - 30 q^{57} - 5 q^{58} + 4 q^{59} - 2 q^{60} + 32 q^{61} - 8 q^{62} - 6 q^{63} - 16 q^{64} + 38 q^{65} - 4 q^{66} + 6 q^{67} + 42 q^{68} - 30 q^{69} - 8 q^{70} - 180 q^{71} + 8 q^{72} - 32 q^{73} + 7 q^{74} + 14 q^{75} - 8 q^{76} + 61 q^{77} + 18 q^{78} - 66 q^{79} - 2 q^{80} + 8 q^{81} - 7 q^{82} + 130 q^{83} + 5 q^{84} - 70 q^{85} - 40 q^{86} + 6 q^{87} - 15 q^{88} - 4 q^{89} + 4 q^{90} - 6 q^{91} + 58 q^{92} - 18 q^{93} + 16 q^{94} + 19 q^{95} + 8 q^{96} + 40 q^{97} + 43 q^{98} + 8 q^{99}+O(q^{100}) \) 160 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 - 2 * q^5 - 16 * q^6 + 6 * q^7 - 16 * q^8 + 8 * q^9 - 2 * q^10 - 4 * q^11 + 8 * q^12 - 4 * q^13 + 5 * q^14 + 26 * q^15 + 8 * q^16 - 13 * q^17 + 8 * q^18 + 4 * q^19 + 26 * q^20 + 11 * q^21 - 124 * q^22 + 26 * q^23 - 80 * q^24 + 14 * q^25 + 2 * q^26 - 16 * q^27 - 22 * q^28 + 54 * q^29 - 2 * q^30 + 15 * q^31 + 8 * q^32 - 4 * q^33 + 4 * q^34 - 2 * q^35 - 16 * q^36 + 7 * q^37 - 7 * q^38 + 2 * q^39 + 9 * q^40 - 30 * q^41 + 6 * q^42 + 36 * q^43 - 4 * q^44 + 20 * q^45 + 4 * q^46 - 6 * q^47 - 16 * q^48 + 14 * q^49 - 28 * q^50 + 9 * q^51 + 2 * q^52 - 24 * q^53 + 8 * q^54 - 14 * q^55 + 6 * q^56 - 30 * q^57 - 5 * q^58 + 4 * q^59 - 2 * q^60 + 32 * q^61 - 8 * q^62 - 6 * q^63 - 16 * q^64 + 38 * q^65 - 4 * q^66 + 6 * q^67 + 42 * q^68 - 30 * q^69 - 8 * q^70 - 180 * q^71 + 8 * q^72 - 32 * q^73 + 7 * q^74 + 14 * q^75 - 8 * q^76 + 61 * q^77 + 18 * q^78 - 66 * q^79 - 2 * q^80 + 8 * q^81 - 7 * q^82 + 130 * q^83 + 5 * q^84 - 70 * q^85 - 40 * q^86 + 6 * q^87 - 15 * q^88 - 4 * q^89 + 4 * q^90 - 6 * q^91 + 58 * q^92 - 18 * q^93 + 16 * q^94 + 19 * q^95 + 8 * q^96 + 40 * q^97 + 43 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{11}\right)$

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 $

$2$	−0.888835	+	0.458227i	−0.628502	+	0.324015i
$2$	−0.888835	+	0.458227i	−0.628502	+	0.324015i
$3$	−0.786053	+	0.618159i	−0.453828	+	0.356894i
$3$	−0.786053	+	0.618159i	−0.453828	+	0.356894i
$4$	0.580057	−	0.814576i	0.290028	−	0.407288i
$5$	1.27403	−	1.21479i	0.569765	−	0.543270i	−0.349486	−	0.936942i	$-0.613644\pi$
$5$	1.27403	−	1.21479i	0.569765	−	0.543270i	0.919251	+	0.393671i	$0.128795\pi$
$6$	0.415415	−	0.909632i	0.169592	−	0.371356i
$7$	2.64520	−	0.0541045i	0.999791	−	0.0204496i
$7$	2.64520	−	0.0541045i	0.999791	−	0.0204496i
$8$	−0.142315	+	0.989821i	−0.0503159	+	0.349955i
$9$	0.235759	−	0.971812i	0.0785863	−	0.323937i
$10$	−0.575758	+	1.66354i	−0.182071	+	0.526059i
$11$	2.70230	+	1.39313i	0.814773	+	0.420045i	0.814648	−	0.579955i	$-0.196930\pi$
$11$	2.70230	+	1.39313i	0.814773	+	0.420045i	0.000124750		1.00000i	$0.499960\pi$
$12$	0.0475819	+	0.998867i	0.0137357	+	0.288348i
$13$	0.130239	+	0.150304i	0.0361218	+	0.0416867i	0.773523	−	0.633768i	$-0.218493\pi$
$13$	0.130239	+	0.150304i	0.0361218	+	0.0416867i	−0.737401	+	0.675455i	$0.763947\pi$
$14$	−2.32635	+	1.26019i	−0.621744	+	0.336800i
$15$	−0.250526	+	1.74244i	−0.0646854	+	0.449897i
$16$	−0.327068	−	0.945001i	−0.0817670	−	0.236250i
$17$	4.44630	−	0.424570i	1.07839	−	0.102973i	0.459288	−	0.888287i	$-0.348104\pi$
$17$	4.44630	−	0.424570i	1.07839	−	0.102973i	0.619098	+	0.785314i	$0.287498\pi$
$18$	0.235759	+	0.971812i	0.0555689	+	0.229058i
$19$	−6.39606	−	0.610750i	−1.46736	−	0.140116i	−0.669433	−	0.742873i	$-0.733463\pi$
$19$	−6.39606	−	0.610750i	−1.46736	−	0.140116i	−0.797925	+	0.602757i	$0.794069\pi$
$20$	−0.250526	−	1.74244i	−0.0560192	−	0.389622i
$21$	−2.04582	+	1.67768i	−0.446435	+	0.366100i
$22$	−3.04027			−0.648187
$23$	2.71900	−	3.95058i	0.566950	−	0.823752i
$23$	2.71900	−	3.95058i	0.566950	−	0.823752i
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	−0.0904592	+	1.89897i	−0.0180918	+	0.379794i
$26$	−0.184634	−	0.0739163i	−0.0362097	−	0.0144962i
$27$	0.415415	+	0.909632i	0.0799467	+	0.175059i
$28$	1.49029	−	2.18610i	0.281639	−	0.413134i
$29$	1.69278	−	3.70668i	0.314342	−	0.688313i	−0.684842	−	0.728691i	$-0.740129\pi$
$29$	1.69278	−	3.70668i	0.314342	−	0.688313i	0.999184	+	0.0403779i	$0.0128562\pi$
$30$	−0.575758	−	1.66354i	−0.105119	−	0.303720i
$31$	−3.36783	+	1.34828i	−0.604880	+	0.242157i	−0.653827	−	0.756644i	$-0.726838\pi$
$31$	−3.36783	+	1.34828i	−0.604880	+	0.242157i	0.0489471	+	0.998801i	$0.484413\pi$
$32$	0.723734	+	0.690079i	0.127939	+	0.121990i
$33$	−2.98532	+	0.575374i	−0.519678	+	0.100160i
$34$	−3.75748	+	2.41479i	−0.644403	+	0.414132i
$35$	3.30435	−	3.28229i	0.558537	−	0.554808i
$36$	−0.654861	−	0.755750i	−0.109143	−	0.125958i
$37$	0.992538	−	4.09130i	0.163172	−	0.672605i	−0.830180	−	0.557495i	$-0.811763\pi$
$37$	0.992538	−	4.09130i	0.163172	−	0.672605i	0.993353	−	0.115110i	$-0.0367222\pi$
$38$	5.96491	−	2.38799i	0.967636	−	0.387383i
$39$	−0.195286	−	0.0376383i	−0.0312708	−	0.00602696i
$40$	1.02111	+	1.43395i	0.161452	+	0.226727i
$41$	8.57882	+	2.51897i	1.33979	+	0.393397i	0.871594	−	0.490229i	$-0.163087\pi$
$41$	8.57882	+	2.51897i	1.33979	+	0.393397i	0.468193	+	0.883626i	$0.344905\pi$
$42$	1.04964	−	2.42863i	0.161963	−	0.374746i
$43$	−1.51738	−	10.5536i	−0.231399	−	1.60941i	−0.692061	−	0.721839i	$-0.743297\pi$
$43$	−1.51738	−	10.5536i	−0.231399	−	1.60941i	0.460663	−	0.887575i	$-0.347612\pi$
$44$	2.70230	−	1.39313i	0.407387	−	0.210022i
$45$	−0.880181	−	1.52452i	−0.131210	−	0.227262i
$46$	−0.606482	+	4.75733i	−0.0894209	+	0.701430i
$47$	−3.17143	+	5.49308i	−0.462601	+	0.801248i	−0.999090	−	0.0426596i	$-0.986417\pi$
$47$	−3.17143	+	5.49308i	−0.462601	+	0.801248i	0.536489	+	0.843907i	$0.319750\pi$
$48$	0.841254	+	0.540641i	0.121424	+	0.0780348i
$49$	6.99415	−	0.286234i	0.999164	−	0.0408906i
$50$	−0.789756	−	1.72932i	−0.111688	−	0.244563i
$51$	−3.23258	+	3.08226i	−0.452651	+	0.431602i
$52$	0.197980	−	0.0189048i	0.0274548	−	0.00262162i
$53$	−5.68363	−	1.09543i	−0.780707	−	0.150469i	−0.216699	−	0.976238i	$-0.569529\pi$
$53$	−5.68363	−	1.09543i	−0.780707	−	0.150469i	−0.564008	+	0.825769i	$0.690741\pi$
$54$	−0.786053	−	0.618159i	−0.106968	−	0.0841208i
$55$	5.13518	−	1.50782i	0.692427	−	0.203315i
$56$	−0.322897	+	2.62597i	−0.0431489	+	0.350910i
$57$	5.40519	−	3.47370i	0.715934	−	0.460103i
$58$	0.193893	+	4.07031i	0.0254594	+	0.534458i
$59$	1.63222	−	4.71598i	0.212496	−	0.613968i	−0.787501	−	0.616314i	$-0.788625\pi$
$59$	1.63222	−	4.71598i	0.212496	−	0.613968i	0.999997	+	0.00234543i	$0.000746575\pi$
$60$	1.27403	+	1.21479i	0.164477	+	0.156829i
$61$	5.75741	+	4.52767i	0.737160	+	0.579709i	0.914570	−	0.404428i	$-0.132529\pi$
$61$	5.75741	+	4.52767i	0.737160	+	0.579709i	−0.177410	+	0.984137i	$0.556772\pi$
$62$	2.37563	−	2.74162i	0.301705	−	0.348187i
$63$	0.571050	−	2.58339i	0.0719455	−	0.325477i
$64$	−0.959493	−	0.281733i	−0.119937	−	0.0352166i
$65$	0.348516	+	0.0332792i	0.0432281	+	0.00412778i
$66$	2.38981	−	1.87937i	0.294165	−	0.231334i
$67$	−0.633288	+	13.2943i	−0.0773684	+	1.62416i	0.542917	+	0.839786i	$0.317320\pi$
$67$	−0.633288	+	13.2943i	−0.0773684	+	1.62416i	−0.620285	+	0.784376i	$0.712983\pi$
$68$	2.23326	−	3.86812i	0.270823	−	0.469079i
$69$	0.304808	+	4.78614i	0.0366946	+	0.576183i
$70$	−1.43299	+	4.43155i	−0.171275	+	0.529672i
$71$	5.27418	+	3.38951i	0.625930	+	0.402261i	0.814801	−	0.579741i	$-0.196846\pi$
$71$	5.27418	+	3.38951i	0.625930	+	0.402261i	−0.188871	+	0.982002i	$0.560483\pi$
$72$	0.928368	+	0.371662i	0.109409	+	0.0438008i
$73$	0.144294	−	0.202632i	0.0168883	−	0.0237163i	−0.806045	−	0.591854i	$-0.798396\pi$
$73$	0.144294	−	0.202632i	0.0168883	−	0.0237163i	0.822934	+	0.568137i	$0.192336\pi$
$74$	0.992538	+	4.09130i	0.115380	+	0.475604i
$75$	−1.10276	−	1.54861i	−0.127336	−	0.178818i
$76$	−4.20758	+	4.85581i	−0.482643	+	0.556999i
$77$	7.22348	+	3.53890i	0.823192	+	0.403295i
$78$	0.190824	−	0.0560310i	0.0216066	−	0.00634427i
$79$	0.0836856	−	0.0161291i	0.00941536	−	0.00181466i	−0.184541	−	0.982825i	$-0.559080\pi$
$79$	0.0836856	−	0.0161291i	0.00941536	−	0.00181466i	0.193957	+	0.981010i	$0.437868\pi$
$80$	−1.56467	−	0.806645i	−0.174936	−	0.0901856i
$81$	−0.888835	−	0.458227i	−0.0987595	−	0.0509141i
$82$	−8.77942	+	1.69209i	−0.969525	+	0.186861i
$83$	6.52881	−	1.91703i	0.716630	−	0.210422i	0.0969648	−	0.995288i	$-0.469087\pi$
$83$	6.52881	−	1.91703i	0.716630	−	0.210422i	0.619665	+	0.784866i	$0.287268\pi$
$84$	0.179907	+	2.63963i	0.0196294	+	0.288007i
$85$	5.14898	−	5.94223i	0.558485	−	0.644526i
$86$	6.18466	+	8.68514i	0.666909	+	0.936543i
$87$	0.960700	+	3.96006i	0.102998	+	0.424563i
$88$	−1.76353	+	2.47653i	−0.187993	+	0.263999i
$89$	16.2095	+	6.48931i	1.71820	+	0.687865i	0.999969	−	0.00793377i	$-0.00252542\pi$
$89$	16.2095	+	6.48931i	1.71820	+	0.687865i	0.718236	+	0.695799i	$0.244950\pi$
$90$	1.48091	+	0.951724i	0.156102	+	0.100320i
$91$	0.352640	+	0.390536i	0.0369667	+	0.0409393i
$92$	−1.64087	−	4.50639i	−0.171073	−	0.469824i
$93$	1.81384	−	3.14167i	0.188087	−	0.325776i
$94$	0.301805	−	6.33568i	0.0311289	−	0.653475i
$95$	−8.89073	+	6.99175i	−0.912170	+	0.717338i
$96$	−0.995472	−	0.0950560i	−0.101600	−	0.00970162i
$97$	−13.9451	−	4.09464i	−1.41591	−	0.415748i	−0.517791	−	0.855507i	$-0.673245\pi$
$97$	−13.9451	−	4.09464i	−1.41591	−	0.415748i	−0.898115	+	0.439760i	$0.855064\pi$
$98$	−6.08548	+	3.45932i	−0.614727	+	0.349444i
$99$	1.99095	−	2.29768i	0.200098	−	0.230926i
$100$	1.49438	+	1.17520i	0.149438	+	0.117520i
$101$	−8.04988	−	7.67555i	−0.800993	−	0.763746i	0.174292	−	0.984694i	$-0.444236\pi$
$101$	−8.04988	−	7.67555i	−0.800993	−	0.763746i	−0.975286	+	0.220948i	$0.929085\pi$
$102$	1.46086	−	4.22087i	0.144646	−	0.417928i
$103$	0.278704	+	5.85071i	0.0274615	+	0.576487i	0.970105	+	0.242686i	$0.0780284\pi$
$103$	0.278704	+	5.85071i	0.0274615	+	0.576487i	−0.942643	+	0.333801i	$0.891669\pi$
$104$	−0.167309	+	0.107523i	−0.0164060	+	0.0105435i
$105$	−0.568416	+	4.62266i	−0.0554717	+	0.451126i
$106$	5.55377	−	1.63073i	0.539430	−	0.158391i
$107$	13.1851	+	10.3689i	1.27465	+	1.00240i	0.999155	+	0.0410961i	$0.0130850\pi$
$107$	13.1851	+	10.3689i	1.27465	+	1.00240i	0.275497	+	0.961302i	$0.411157\pi$
$108$	0.981929	+	0.189251i	0.0944861	+	0.0182107i
$109$	20.0720	−	1.91665i	1.92255	−	0.183582i	0.936576	−	0.350464i	$-0.113976\pi$
$109$	20.0720	−	1.91665i	1.92255	−	0.183582i	0.985977	+	0.166883i	$0.0533701\pi$
$110$	−3.87340	+	3.69328i	−0.369314	+	0.352141i
$111$	1.74888	+	3.82952i	0.165997	+	0.363482i
$112$	−0.916288	−	2.48202i	−0.0865811	−	0.234529i
$113$	3.29637	+	2.11845i	0.310097	+	0.199287i	0.686427	−	0.727198i	$-0.259178\pi$
$113$	3.29637	+	2.11845i	0.310097	+	0.199287i	−0.376331	+	0.926485i	$0.622814\pi$
$114$	−3.21258	+	5.56435i	−0.300885	+	0.521149i
$115$	−1.33502	−	8.33618i	−0.124491	−	0.777353i
$116$	−2.03746	−	3.52899i	−0.189174	−	0.327658i
$117$	0.176772	−	0.0911322i	0.0163426	−	0.00842517i
$118$	0.710215	+	4.93965i	0.0653806	+	0.454732i
$119$	11.7384	−	1.36364i	1.07606	−	0.125004i
$120$	−1.68906	−	0.495951i	−0.154189	−	0.0452740i
$121$	−1.01903	−	1.43103i	−0.0926393	−	0.130094i
$122$	−7.19209	−	1.38616i	−0.651141	−	0.125497i
$123$	−8.30053	+	3.32303i	−0.748434	+	0.299628i
$124$	−0.855260	+	3.52543i	−0.0768046	+	0.316593i
$125$	7.95556	+	9.18121i	0.711567	+	0.821192i
$126$	0.676208	+	2.55788i	0.0602414	+	0.227874i
$127$	−2.48074	+	1.59427i	−0.220130	+	0.141469i	−0.646059	−	0.763288i	$-0.723584\pi$
$127$	−2.48074	+	1.59427i	−0.220130	+	0.141469i	0.425929	+	0.904757i	$0.359947\pi$
$128$	0.981929	−	0.189251i	0.0867911	−	0.0167276i
$129$	7.71657	+	7.35773i	0.679406	+	0.647812i
$130$	−0.325023	+	0.130119i	−0.0285064	+	0.0114122i
$131$	−4.32937	−	12.5089i	−0.378259	−	1.09291i	−0.960112	−	0.279614i	$-0.909793\pi$
$131$	−4.32937	−	12.5089i	−0.378259	−	1.09291i	0.581853	−	0.813294i	$-0.302328\pi$
$132$	−1.26297	+	2.76552i	−0.109928	+	0.240708i
$133$	−16.9519	−	1.26950i	−1.46992	−	0.110079i
$134$	−5.52893	−	12.1067i	−0.477627	−	1.04586i
$135$	1.63426	+	0.654261i	0.140655	+	0.0563098i
$136$	−0.212526	+	4.46147i	−0.0182239	+	0.382568i
$137$	−5.22459	−	9.04925i	−0.446367	−	0.773130i	0.551780	−	0.833990i	$-0.313949\pi$
$137$	−5.22459	−	9.04925i	−0.446367	−	0.773130i	−0.998146	+	0.0608602i	$0.980616\pi$
$138$	−2.46406	−	4.11442i	−0.209755	−	0.350242i
$139$	−14.3758			−1.21934			−0.609670	−	0.792655i	$-0.708698\pi$
$139$	−14.3758			−1.21934			−0.609670	+	0.792655i	$0.708698\pi$
$140$	−0.756964	−	4.59556i	−0.0639751	−	0.388395i
$141$	−0.902683	−	6.27830i	−0.0760196	−	0.528728i
$142$	−6.24104	−	0.595947i	−0.523737	−	0.0500108i
$143$	0.142551	+	0.587605i	0.0119207	+	0.0491380i
$144$	−0.995472	+	0.0950560i	−0.0829560	+	0.00792134i
$145$	−2.34617	−	6.77881i	−0.194839	−	0.562950i
$146$	−0.0354019	+	0.246226i	−0.00292988	+	0.0203778i
$147$	−5.32083	+	4.54849i	−0.438855	+	0.375153i
$148$	−2.75694	−	3.18168i	−0.226619	−	0.261533i
$149$	−0.765489	−	16.0696i	−0.0627113	−	1.31647i	−0.782662	−	0.622447i	$-0.786139\pi$
$149$	−0.765489	−	16.0696i	−0.0627113	−	1.31647i	0.719950	−	0.694025i	$-0.244165\pi$
$150$	1.68979	+	0.871146i	0.137971	+	0.0711288i
$151$	−4.73971	+	13.6945i	−0.385712	+	1.11444i	0.570382	+	0.821380i	$0.306795\pi$
$151$	−4.73971	+	13.6945i	−0.385712	+	1.11444i	−0.956094	+	0.293061i	$0.905326\pi$
$152$	1.51479	−	6.24404i	0.122866	−	0.506459i
$153$	0.635653	−	4.42106i	0.0513895	−	0.357422i
$154$	−8.04211	+	0.164492i	−0.648051	+	0.0132552i
$155$	−2.65286	+	5.80895i	−0.213083	+	0.466586i
$156$	−0.143936	+	0.137243i	−0.0115241	+	0.0109882i
$157$	−6.69578	+	9.40291i	−0.534382	+	0.750434i	−0.990203	−	0.139638i	$-0.955406\pi$
$157$	−6.69578	+	9.40291i	−0.534382	+	0.750434i	0.455821	+	0.890071i	$0.349346\pi$
$158$	−0.0669919	+	0.0526830i	−0.00532959	+	0.00419124i
$159$	5.14479	−	2.65232i	0.408008	−	0.210343i
$160$	1.76036			0.139169
$161$	6.97854	−	10.5972i	0.549986	−	0.835174i
$162$	1.00000			0.0785674
$163$	12.7286	−	6.56206i	0.996982	−	0.513980i	0.119113	−	0.992881i	$-0.461995\pi$
$163$	12.7286	−	6.56206i	0.996982	−	0.513980i	0.877869	+	0.478901i	$0.158965\pi$
$164$	7.02810	−	5.52696i	0.548802	−	0.431583i
$165$	−3.10445	+	4.35959i	−0.241681	+	0.339393i
$166$	−4.92460	+	4.69560i	−0.382223	+	0.364449i
$167$	−3.20925	+	7.02728i	−0.248339	+	0.543787i	−0.992216	−	0.124530i	$-0.960258\pi$
$167$	−3.20925	+	7.02728i	−0.248339	+	0.543787i	0.743877	+	0.668317i	$0.232985\pi$
$168$	−1.36945	−	2.26376i	−0.105656	−	0.174653i
$169$	1.84446	−	12.8285i	0.141882	−	0.986810i
$170$	−1.85370	+	7.64107i	−0.142172	+	0.586043i
$171$	−2.10146	+	6.07178i	−0.160703	+	0.464320i
$172$	−9.47690	−	4.88568i	−0.722607	−	0.372530i
$173$	0.579606	+	12.1674i	0.0440666	+	0.925072i	0.907356	+	0.420363i	$0.138097\pi$
$173$	0.579606	+	12.1674i	0.0440666	+	0.925072i	−0.863289	+	0.504709i	$0.831600\pi$
$174$	−2.66851	−	3.07962i	−0.202299	−	0.233466i
$175$	−0.136539	+	5.02805i	−0.0103214	+	0.380085i
$176$	0.432675	−	3.00932i	0.0326141	−	0.226836i
$177$	1.63222	+	4.71598i	0.122685	+	0.354475i
$178$	−17.3812	+	1.65970i	−1.30277	+	0.124400i
$179$	−3.14475	−	12.9628i	−0.235050	−	0.968888i	−0.959981	−	0.280066i	$-0.909644\pi$
$179$	−3.14475	−	12.9628i	−0.235050	−	0.968888i	0.724931	−	0.688821i	$-0.241872\pi$
$180$	−1.75239	−	0.167333i	−0.130616	−	0.0124723i
$181$	−1.27049	−	8.83647i	−0.0944349	−	0.656809i	−0.980972	−	0.194151i	$-0.937805\pi$
$181$	−1.27049	−	8.83647i	−0.0944349	−	0.656809i	0.886537	−	0.462658i	$-0.153104\pi$
$182$	−0.492393	−	0.185534i	−0.0364986	−	0.0137527i
$183$	−7.32445			−0.541439
$184$	3.52341	+	3.25355i	0.259749	+	0.239855i
$185$	−3.70554	−	6.41818i	−0.272436	−	0.471874i
$186$	−0.172612	+	3.62358i	−0.0126566	+	0.265694i
$187$	12.6067	+	5.04696i	0.921894	+	0.369071i
$188$	2.63492	+	5.76967i	0.192171	+	0.420796i
$189$	1.14807	+	2.38368i	0.0835098	+	0.173387i
$190$	4.69859	−	10.2885i	0.340872	−	0.746405i
$191$	1.89051	+	5.46227i	0.136793	+	0.395236i	0.992503	−	0.122218i	$-0.0390008\pi$
$191$	1.89051	+	5.46227i	0.136793	+	0.395236i	−0.855711	+	0.517455i	$0.826880\pi$
$192$	0.928368	−	0.371662i	0.0669992	−	0.0268224i
$193$	−8.40659	−	8.01566i	−0.605119	−	0.576980i	0.324324	−	0.945946i	$-0.394863\pi$
$193$	−8.40659	−	8.01566i	−0.605119	−	0.576980i	−0.929443	+	0.368966i	$0.879712\pi$
$194$	14.2711	−	2.75054i	1.02461	−	0.197477i
$195$	−0.294524	+	0.189279i	−0.0210913	+	0.0135546i
$196$	3.82384	−	5.86329i	0.273132	−	0.418807i
$197$	−9.68905	−	11.1818i	−0.690316	−	0.796667i	0.297094	−	0.954848i	$-0.403982\pi$
$197$	−9.68905	−	11.1818i	−0.690316	−	0.796667i	−0.987410	+	0.158181i	$0.949437\pi$
$198$	−0.716770	+	2.95457i	−0.0509386	+	0.209972i
$199$	−17.8532	+	7.14734i	−1.26558	+	0.506661i	−0.904739	−	0.425967i	$-0.859934\pi$
$199$	−17.8532	+	7.14734i	−1.26558	+	0.506661i	−0.360840	+	0.932628i	$0.617510\pi$
$200$	−1.86677	−	0.359790i	−0.132000	−	0.0254410i
$201$	−7.72022	−	10.8415i	−0.544542	−	0.764703i
$202$	10.6722	+	3.13363i	0.750891	+	0.220481i
$203$	4.27720	−	9.89649i	0.300201	−	0.694598i
$204$	0.635653	+	4.42106i	0.0445046	+	0.309536i
$205$	13.9897	−	7.21221i	0.977085	−	0.503722i
$206$	−2.92867	−	5.07261i	−0.204050	−	0.353425i
$207$	−3.19819	−	3.57374i	−0.222289	−	0.248392i
$208$	0.0994401	−	0.172235i	0.00689493	−	0.0119424i
$209$	−16.4332	−	10.5610i	−1.13671	−	0.730518i
$210$	−1.61300	−	4.36925i	−0.111308	−	0.301507i
$211$	3.03673	+	6.64951i	0.209057	+	0.457771i	0.984893	−	0.173163i	$-0.0553988\pi$
$211$	3.03673	+	6.64951i	0.209057	+	0.457771i	−0.775836	+	0.630935i	$0.782672\pi$
$212$	−4.18914	+	3.99434i	−0.287712	+	0.274332i
$213$	−6.24104	+	0.595947i	−0.427629	+	0.0408336i
$214$	−16.4707	−	3.17447i	−1.12591	−	0.217002i
$215$	−14.7536	−	11.6024i	−1.00619	−	0.791276i
$216$	−0.959493	+	0.281733i	−0.0652852	+	0.0191695i
$217$	−8.83563	+	3.74867i	−0.599802	+	0.254476i
$218$	−16.9625	+	10.9011i	−1.14884	+	0.738317i
$219$	0.0118364	+	0.248476i	0.000799827	+	0.0167904i
$220$	1.75046	−	5.05762i	0.118016	−	0.340984i
$221$	0.642896	+	0.613000i	0.0432458	+	0.0412348i
$222$	−3.30926	−	2.60243i	−0.222103	−	0.174664i
$223$	−4.02541	+	4.64557i	−0.269561	+	0.311090i	−0.874350	−	0.485296i	$-0.838712\pi$
$223$	−4.02541	+	4.64557i	−0.269561	+	0.311090i	0.604789	+	0.796386i	$0.293257\pi$
$224$	1.95176	+	1.78624i	0.130407	+	0.119348i
$225$	1.82412	+	0.535609i	0.121608	+	0.0357072i
$226$	−3.90066	−	0.372468i	−0.259468	−	0.0247762i
$227$	−19.3074	+	15.1835i	−1.28148	+	1.00776i	−0.282656	+	0.959221i	$0.591216\pi$
$227$	−19.3074	+	15.1835i	−1.28148	+	1.00776i	−0.998821	+	0.0485437i	$0.984542\pi$
$228$	0.305721	−	6.41788i	0.0202469	−	0.425034i
$229$	10.7276	−	18.5808i	0.708903	−	1.22786i	−0.256362	−	0.966581i	$-0.582524\pi$
$229$	10.7276	−	18.5808i	0.708903	−	1.22786i	0.965264	−	0.261275i	$-0.0841429\pi$
$230$	5.00647	+	6.79775i	0.330117	+	0.448230i
$231$	−7.86564	+	1.68350i	−0.517521	+	0.110766i
$232$	3.42804	+	2.20307i	0.225062	+	0.144639i
$233$	−5.68330	−	2.27525i	−0.372325	−	0.149057i	0.177951	−	0.984039i	$-0.443053\pi$
$233$	−5.68330	−	2.27525i	−0.372325	−	0.149057i	−0.550276	+	0.834983i	$0.685477\pi$
$234$	−0.115362	+	0.162003i	−0.00754144	+	0.0105905i
$235$	2.63242	+	10.8510i	0.171720	+	0.707840i
$236$	−2.89475	−	4.06510i	−0.188432	−	0.264616i
$237$	−0.0558110	+	0.0644093i	−0.00362531	+	0.00418383i
$238$	−9.80863	+	6.59088i	−0.635799	+	0.427224i
$239$	7.02126	−	2.06163i	0.454168	−	0.133356i	−0.0466447	−	0.998912i	$-0.514853\pi$
$239$	7.02126	−	2.06163i	0.454168	−	0.133356i	0.500812	+	0.865556i	$0.333035\pi$
$240$	1.72855	−	0.333151i	0.111577	−	0.0215048i
$241$	12.0144	+	6.19387i	0.773918	+	0.398982i	0.799481	−	0.600691i	$-0.205108\pi$
$241$	12.0144	+	6.19387i	0.773918	+	0.398982i	−0.0255635	+	0.999673i	$0.508138\pi$
$242$	1.56149	+	0.805003i	0.100376	+	0.0517476i
$243$	0.981929	−	0.189251i	0.0629908	−	0.0121405i
$244$	7.02776	−	2.06354i	0.449906	−	0.132104i
$245$	8.56307	−	8.86108i	0.547074	−	0.566114i
$246$	5.85511	−	6.75715i	0.373308	−	0.430820i
$247$	−0.741218	−	1.04089i	−0.0471626	−	0.0662306i
$248$	−0.855260	−	3.52543i	−0.0543091	−	0.223865i
$249$	−3.94696	+	5.54273i	−0.250129	+	0.351256i
$250$	−11.2783	−	4.51513i	−0.713300	−	0.285562i
$251$	4.24463	+	2.72786i	0.267919	+	0.172181i	0.667702	−	0.744429i	$-0.267278\pi$
$251$	4.24463	+	2.72786i	0.267919	+	0.172181i	−0.399783	+	0.916610i	$0.630915\pi$
$252$	−1.77313	−	1.96368i	−0.111696	−	0.123700i
$253$	12.8512	−	6.88771i	0.807948	−	0.433027i
$254$	1.47443	−	2.55379i	0.0925140	−	0.160239i
$255$	−0.374122	+	7.85380i	−0.0234285	+	0.491824i
$256$	−0.786053	+	0.618159i	−0.0491283	+	0.0386349i
$257$	10.2361	+	0.977427i	0.638509	+	0.0609702i	0.409290	−	0.912404i	$-0.365777\pi$
$257$	10.2361	+	0.977427i	0.638509	+	0.0609702i	0.229220	+	0.973375i	$0.426383\pi$
$258$	−10.2303	−	3.00388i	−0.636909	−	0.187013i
$259$	2.40410	−	10.8760i	0.149384	−	0.675801i
$260$	0.229268	−	0.264589i	0.0142186	−	0.0164091i
$261$	−3.20311	−	2.51895i	−0.198267	−	0.155919i
$262$	9.58001	+	9.13452i	0.591855	+	0.564333i
$263$	−8.51297	+	24.5966i	−0.524932	+	1.51669i	0.301394	+	0.953500i	$0.402548\pi$
$263$	−8.51297	+	24.5966i	−0.524932	+	1.51669i	−0.826326	+	0.563192i	$0.809573\pi$
$264$	−0.144662	−	3.03682i	−0.00890331	−	0.186904i
$265$	−8.57186	+	5.50880i	−0.526565	+	0.338403i
$266$	15.6492	−	6.63943i	0.959512	−	0.407090i
$267$	−16.7530	+	4.91911i	−1.02526	+	0.301045i
$268$	10.4619	+	8.22734i	0.639063	+	0.502565i
$269$	−22.9500	−	4.42325i	−1.39929	−	0.269690i	−0.566855	−	0.823818i	$-0.691840\pi$
$269$	−22.9500	−	4.42325i	−1.39929	−	0.269690i	−0.832432	+	0.554127i	$0.813052\pi$
$270$	−1.75239	+	0.167333i	−0.106647	+	0.0101836i
$271$	−7.93270	+	7.56382i	−0.481877	+	0.459469i	−0.891654	−	0.452717i	$-0.850455\pi$
$271$	−7.93270	+	7.56382i	−0.481877	+	0.459469i	0.409777	+	0.912186i	$0.365606\pi$
$272$	−1.85546	−	4.06289i	−0.112504	−	0.246349i
$273$	−0.518607	−	0.0889950i	−0.0313875	−	0.00538622i
$274$	8.79041	+	5.64925i	0.531048	+	0.341284i
$275$	−2.88996	+	5.00556i	−0.174271	+	0.301847i
$276$	4.07548	+	2.52794i	0.245315	+	0.152164i
$277$	−3.36133	−	5.82199i	−0.201963	−	0.349809i	0.747198	−	0.664601i	$-0.231399\pi$
$277$	−3.36133	−	5.82199i	−0.201963	−	0.349809i	−0.949161	+	0.314792i	$0.898065\pi$
$278$	12.7777	−	6.58738i	0.766357	−	0.395085i
$279$	0.516274	+	3.59076i	0.0309085	+	0.214973i
$280$	2.77862	+	3.73783i	0.166054	+	0.223378i
$281$	−5.80703	−	1.70510i	−0.346419	−	0.101718i	0.103895	−	0.994588i	$-0.466870\pi$
$281$	−5.80703	−	1.70510i	−0.346419	−	0.101718i	−0.450313	+	0.892871i	$0.648688\pi$
$282$	3.67922	+	5.16674i	0.219094	+	0.307675i
$283$	−27.5581	−	5.31138i	−1.63816	−	0.315729i	−0.714700	−	0.699431i	$-0.753437\pi$
$283$	−27.5581	−	5.31138i	−1.63816	−	0.315729i	−0.923457	+	0.383702i	$0.874649\pi$
$284$	5.82034	−	2.33011i	0.345373	−	0.138267i
$285$	2.66658	−	10.9918i	0.157954	−	0.651096i
$286$	−0.395961	−	0.456963i	−0.0234137	−	0.0270208i
$287$	22.8290	+	6.19902i	1.34755	+	0.365917i
$288$	0.841254	−	0.540641i	0.0495713	−	0.0318576i
$289$	2.89654	−	0.558263i	0.170385	−	0.0328390i
$290$	5.19159	+	4.95017i	0.304861	+	0.290684i
$291$	13.4927	−	5.40166i	0.790956	−	0.316651i
$292$	−0.0813606	−	0.235076i	−0.00476127	−	0.0137568i
$293$	−4.74885	+	10.3985i	−0.277431	+	0.607489i	−0.996136	−	0.0878265i	$-0.972008\pi$
$293$	−4.74885	+	10.3985i	−0.277431	+	0.607489i	0.718705	+	0.695315i	$0.244735\pi$
$294$	2.64511	−	6.48100i	0.154266	−	0.377980i
$295$	−3.64942	−	7.99112i	−0.212477	−	0.465261i
$296$	3.90840	+	1.56469i	0.227171	+	0.0909456i
$297$	−0.144662	+	3.03682i	−0.00839412	+	0.176214i
$298$	8.04391	+	13.9325i	0.465971	+	0.807086i
$299$	0.947905	−	0.105843i	0.0548188	−	0.00612108i
$300$	−1.90112			−0.109761
$301$	−4.58478	−	27.8344i	−0.264262	−	1.60435i
$302$	−2.06236	−	14.3440i	−0.118675	−	0.825404i
$303$	11.0723	+	1.05728i	0.636090	+	0.0607392i
$304$	1.51479	+	6.24404i	0.0868790	+	0.358120i
$305$	12.8353	−	1.22562i	0.734947	−	0.0701790i
$306$	1.46086	+	4.22087i	0.0835117	+	0.241291i
$307$	−3.93082	+	27.3394i	−0.224344	+	1.56034i	0.496990	+	0.867756i	$0.334439\pi$
$307$	−3.93082	+	27.3394i	−0.224344	+	1.56034i	−0.721334	+	0.692588i	$0.756471\pi$
$308$	7.07273	−	3.83131i	0.403006	−	0.218309i
$309$	−3.83574	−	4.42668i	−0.218208	−	0.251825i
$310$	−0.303860	−	6.37881i	−0.0172581	−	0.362292i
$311$	−15.4737	−	7.97726i	−0.877434	−	0.452349i	−0.0401988	−	0.999192i	$-0.512799\pi$
$311$	−15.4737	−	7.97726i	−0.877434	−	0.452349i	−0.837235	+	0.546843i	$0.815829\pi$
$312$	0.0650474	−	0.187942i	0.00368258	−	0.0106401i
$313$	−5.72113	+	23.5828i	−0.323377	+	1.33298i	0.545566	+	0.838068i	$0.316315\pi$
$313$	−5.72113	+	23.5828i	−0.323377	+	1.33298i	−0.868943	+	0.494912i	$0.835200\pi$
$314$	1.64279	−	11.4258i	0.0927077	−	0.644797i
$315$	−2.41074	−	3.98503i	−0.135830	−	0.224531i
$316$	0.0354040	−	0.0775240i	0.00199163	−	0.00436107i
$317$	−12.3196	+	11.7467i	−0.691937	+	0.659761i	−0.952094	−	0.305805i	$-0.901074\pi$
$317$	−12.3196	+	11.7467i	−0.691937	+	0.659761i	0.260157	+	0.965566i	$0.416226\pi$
$318$	−3.35751	+	4.71496i	−0.188280	+	0.264402i
$319$	9.73830	−	7.65828i	0.545240	−	0.428781i
$320$	−1.56467	+	0.806645i	−0.0874678	+	0.0450928i
$321$	−16.7738			−0.936223
$322$	−1.34687	+	12.6169i	−0.0750582	+	0.703112i
$323$	−28.6981			−1.59681
$324$	−0.888835	+	0.458227i	−0.0493797	+	0.0254570i
$325$	−0.297204	+	0.233724i	−0.0164859	+	0.0129646i
$326$	−8.30674	+	11.6652i	−0.460068	+	0.646075i
$327$	−14.5929	+	13.9143i	−0.806989	+	0.769463i
$328$	−3.71422	+	8.13301i	−0.205084	+	0.449071i
$329$	−8.09186	+	14.7019i	−0.446119	+	0.810540i
$330$	0.761665	−	5.29749i	0.0419283	−	0.291617i
$331$	4.65797	−	19.2004i	0.256025	−	1.05535i	−0.688062	−	0.725652i	$-0.741538\pi$
$331$	4.65797	−	19.2004i	0.256025	−	1.05535i	0.944087	−	0.329697i	$-0.106947\pi$
$332$	2.22551	−	6.43020i	0.122141	−	0.352903i
$333$	−3.74197	−	1.92912i	−0.205059	−	0.105715i
$334$	−0.367590	−	7.71666i	−0.0201136	−	0.422237i
$335$	15.3430	+	17.7068i	0.838277	+	0.967424i
$336$	2.25453	+	1.38459i	0.122995	+	0.0755354i
$337$	2.14475	−	14.9171i	0.116832	−	0.812584i	−0.844177	−	0.536065i	$-0.819910\pi$
$337$	2.14475	−	14.9171i	0.116832	−	0.812584i	0.961009	−	0.276519i	$-0.0891807\pi$
$338$	4.23895	+	12.2476i	0.230568	+	0.666183i
$339$	−3.90066	+	0.372468i	−0.211855	+	0.0202297i
$340$	−1.85370	−	7.64107i	−0.100531	−	0.414395i
$341$	−10.9792	−	1.04839i	−0.594557	−	0.0567733i
$342$	−0.914395	−	6.35976i	−0.0494448	−	0.343896i
$343$	18.4854	−	1.13556i	0.998118	−	0.0613146i
$344$	10.6622			0.574865
$345$	6.20248	+	5.72742i	0.333930	+	0.308354i
$346$	−6.09061	−	10.5492i	−0.327433	−	0.567131i
$347$	0.686935	−	14.4205i	0.0368766	−	0.774136i	−0.902384	−	0.430932i	$-0.858185\pi$
$347$	0.686935	−	14.4205i	0.0368766	−	0.774136i	0.939261	−	0.343204i	$-0.111512\pi$
$348$	3.78303	+	1.51450i	0.202792	+	0.0811855i
$349$	8.37687	+	18.3428i	0.448404	+	0.981867i	0.989979	+	0.141215i	$0.0451008\pi$
$349$	8.37687	+	18.3428i	0.448404	+	0.981867i	−0.541575	+	0.840652i	$0.682172\pi$
$350$	−2.18262	−	4.53167i	−0.116666	−	0.242228i
$351$	−0.0826178	+	0.180908i	−0.00440981	+	0.00965615i
$352$	0.994374	+	2.87305i	0.0530003	+	0.153134i
$353$	6.91474	−	2.76824i	0.368035	−	0.147339i	−0.180271	−	0.983617i	$-0.557697\pi$
$353$	6.91474	−	2.76824i	0.368035	−	0.147339i	0.548305	+	0.836278i	$0.315273\pi$
$354$	−3.61176	−	3.44380i	−0.191963	−	0.183036i
$355$	10.8370	−	2.08867i	0.575170	−	0.110855i
$356$	14.6885	−	9.43971i	0.778488	−	0.500304i
$357$	−8.38404	+	8.32807i	−0.443731	+	0.440768i
$358$	8.73508	+	10.0808i	0.461663	+	0.532788i
$359$	−3.64717	+	15.0338i	−0.192490	+	0.793456i	0.790899	+	0.611947i	$0.209613\pi$
$359$	−3.64717	+	15.0338i	−0.192490	+	0.793456i	−0.983389	+	0.181509i	$0.941902\pi$
$360$	1.63426	−	0.654261i	0.0861333	−	0.0344826i
$361$	21.8800	+	4.21702i	1.15158	+	0.221948i
$362$	5.17836	+	7.27199i	0.272169	+	0.382207i
$363$	1.68562	+	0.494942i	0.0884720	+	0.0259777i
$364$	0.522673	−	0.0607185i	0.0273955	−	0.00318251i
$365$	−0.0623202	−	0.433446i	−0.00326199	−	0.0226876i
$366$	6.51023	−	3.35626i	0.340295	−	0.175434i
$367$	−6.12929	−	10.6162i	−0.319946	−	0.554163i	0.660530	−	0.750800i	$-0.270332\pi$
$367$	−6.12929	−	10.6162i	−0.319946	−	0.554163i	−0.980477	+	0.196636i	$0.936998\pi$
$368$	−4.62259	−	1.27735i	−0.240969	−	0.0665863i
$369$	4.47050	−	7.74313i	0.232725	−	0.403091i
$370$	6.23459	+	4.00673i	0.324121	+	0.208300i
$371$	−15.0936	−	2.59012i	−0.783621	−	0.134472i
$372$	−1.50700	−	3.29986i	−0.0781341	−	0.171090i
$373$	−9.78058	+	9.32577i	−0.506419	+	0.482870i	−0.899676	−	0.436559i	$-0.856197\pi$
$373$	−9.78058	+	9.32577i	−0.506419	+	0.482870i	0.393256	+	0.919429i	$0.371349\pi$
$374$	−13.5179	+	1.29081i	−0.698996	+	0.0667460i
$375$	−11.9289	−	2.29911i	−0.616008	−	0.118726i
$376$	−4.98582	−	3.92090i	−0.257124	−	0.202205i
$377$	0.777594	−	0.228322i	0.0400481	−	0.0117592i
$378$	−2.11271	−	1.59262i	−0.108666	−	0.0819157i
$379$	16.7988	−	10.7959i	0.862894	−	0.554548i	−0.0326776	−	0.999466i	$-0.510403\pi$
$379$	16.7988	−	10.7959i	0.862894	−	0.554548i	0.895571	+	0.444918i	$0.146767\pi$
$380$	0.538180	+	11.2978i	0.0276081	+	0.579564i
$381$	0.964478	−	2.78668i	0.0494117	−	0.142766i
$382$	−4.18331	−	3.98878i	−0.214037	−	0.204084i
$383$	−22.2149	−	17.4700i	−1.13513	−	0.892673i	−0.139890	−	0.990167i	$-0.544675\pi$
$383$	−22.2149	−	17.4700i	−1.13513	−	0.892673i	−0.995236	+	0.0974939i	$0.968917\pi$
$384$	−0.654861	+	0.755750i	−0.0334182	+	0.0385667i
$385$	13.5020	−	4.26633i	0.688125	−	0.217432i
$386$	11.1451	+	3.27249i	0.567269	+	0.166565i
$387$	−10.6139	−	1.01350i	−0.539534	−	0.0515192i
$388$	−11.4243	+	8.98419i	−0.579982	+	0.456103i
$389$	−1.26008	+	26.4523i	−0.0638885	+	1.34119i	0.708354	+	0.705857i	$0.249438\pi$
$389$	−1.26008	+	26.4523i	−0.0638885	+	1.34119i	−0.772242	+	0.635328i	$0.780865\pi$
$390$	0.175051	−	0.303197i	0.00886403	−	0.0153530i
$391$	10.4122	−	18.7199i	0.526567	−	0.946704i
$392$	−0.712050	+	6.96369i	−0.0359639	+	0.351719i
$393$	11.1356	+	7.15642i	0.561717	+	0.360994i
$394$	13.7357	+	5.49896i	0.691997	+	0.277034i
$395$	0.0870248	−	0.122209i	0.00437870	−	0.00614902i
$396$	−0.716770	−	2.95457i	−0.0360190	−	0.148473i
$397$	10.5079	+	14.7562i	0.527374	+	0.740594i	0.989231	−	0.146361i	$-0.0467560\pi$
$397$	10.5079	+	14.7562i	0.527374	+	0.740594i	−0.461857	+	0.886954i	$0.652817\pi$
$398$	12.5934	−	14.5336i	0.631252	−	0.728504i
$399$	14.1098	−	9.48107i	0.706376	−	0.474647i
$400$	1.82412	−	0.535609i	0.0912058	−	0.0267804i
$401$	9.53588	−	1.83789i	0.476199	−	0.0917799i	0.0544963	−	0.998514i	$-0.482645\pi$
$401$	9.53588	−	1.83789i	0.476199	−	0.0917799i	0.421703	+	0.906734i	$0.361433\pi$
$402$	11.8299	+	6.09873i	0.590021	+	0.304177i
$403$	−0.641273	−	0.330599i	−0.0319441	−	0.0164683i
$404$	−10.9217	+	2.10499i	−0.543375	+	0.104727i
$405$	−1.68906	+	0.495951i	−0.0839298	+	0.0246440i
$406$	0.733107	+	10.7563i	0.0363835	+	0.533825i
$407$	8.38185	−	9.67316i	0.415473	−	0.479481i
$408$	−2.59084	−	3.63832i	−0.128266	−	0.180124i
$409$	0.786148	+	3.24055i	0.0388725	+	0.160235i	0.987940	−	0.154839i	$-0.0494859\pi$
$409$	0.786148	+	3.24055i	0.0388725	+	0.160235i	−0.949067	+	0.315074i	$0.897971\pi$
$410$	−9.12974	+	12.8209i	−0.450886	+	0.633180i
$411$	9.70068	+	3.88357i	0.478499	+	0.191562i
$412$	4.92751	+	3.16672i	0.242761	+	0.156013i
$413$	4.06238	−	12.5630i	0.199897	−	0.618185i
$414$	4.48024	+	1.71097i	0.220192	+	0.0840895i
$415$	5.98914	−	10.3735i	0.293995	−	0.509215i
$416$	−0.00946310	+	0.198655i	−0.000463967	+	0.00973986i
$417$	11.3001	−	8.88653i	0.553371	−	0.435175i
$418$	19.4457	+	1.85684i	0.951122	+	0.0908211i
$419$	−15.0111	−	4.40765i	−0.733339	−	0.215328i	−0.106320	−	0.994332i	$-0.533907\pi$
$419$	−15.0111	−	4.40765i	−0.733339	−	0.215328i	−0.627019	+	0.779004i	$0.715725\pi$
$420$	3.43580	+	3.14443i	0.167650	+	0.153432i
$421$	−5.95799	+	6.87589i	−0.290375	+	0.335110i	−0.882129	−	0.471008i	$-0.843890\pi$
$421$	−5.95799	+	6.87589i	−0.290375	+	0.335110i	0.591754	+	0.806119i	$0.298436\pi$
$422$	−5.74614	−	4.51881i	−0.279718	−	0.219972i
$423$	4.59054	+	4.37707i	0.223200	+	0.212821i
$424$	1.89315	−	5.46989i	0.0919393	−	0.265641i
$425$	0.404038	+	8.48180i	0.0195987	+	0.411428i
$426$	5.27418	−	3.38951i	0.255535	−	0.164222i
$427$	15.4744	+	11.6651i	0.748861	+	0.564513i
$428$	16.0944	−	4.72573i	0.777950	−	0.228427i
$429$	−0.475286	−	0.373769i	−0.0229470	−	0.0180457i
$430$	18.4301	+	3.55211i	0.888777	+	0.171298i
$431$	10.3586	−	0.989129i	0.498958	−	0.0476447i	0.157456	−	0.987526i	$-0.449671\pi$
$431$	10.3586	−	0.989129i	0.498958	−	0.0476447i	0.341501	+	0.939881i	$0.389065\pi$
$432$	0.723734	−	0.690079i	0.0348207	−	0.0332014i
$433$	−4.55043	−	9.96405i	−0.218680	−	0.478842i	0.768218	−	0.640188i	$-0.221144\pi$
$433$	−4.55043	−	9.96405i	−0.218680	−	0.478842i	−0.986898	+	0.161346i	$0.948416\pi$
$434$	6.13568	−	7.38067i	0.294522	−	0.354284i
$435$	6.03460	+	3.87820i	0.289337	+	0.185946i
$436$	10.0817	−	17.4620i	0.482824	−	0.836277i
$437$	−19.8037	+	23.6075i	−0.947339	+	1.12930i
$438$	−0.124379	−	0.215430i	−0.00594305	−	0.0102937i
$439$	−3.15202	+	1.62498i	−0.150438	+	0.0775561i	−0.531802	−	0.846869i	$-0.678485\pi$
$439$	−3.15202	+	1.62498i	−0.150438	+	0.0775561i	0.381364	+	0.924425i	$0.375455\pi$
$440$	0.761665	+	5.29749i	0.0363109	+	0.252548i
$441$	1.37077	−	6.86447i	0.0652746	−	0.326880i
$442$	−0.852321	−	0.250264i	−0.0405408	−	0.0119038i
$443$	14.2042	+	19.9470i	0.674862	+	0.947712i	0.999998	+	0.00204418i	$0.000650682\pi$
$443$	14.2042	+	19.9470i	0.674862	+	0.947712i	−0.325136	+	0.945667i	$0.605410\pi$
$444$	4.13389	+	0.796742i	0.196186	+	0.0378117i
$445$	28.5346	−	11.4235i	1.35267	−	0.541528i
$446$	1.44920	−	5.97369i	0.0686217	−	0.282863i
$447$	10.5353	+	12.1584i	0.498302	+	0.575071i
$448$	−2.55329	−	0.693325i	−0.120632	−	0.0327566i
$449$	−10.1303	+	6.51033i	−0.478077	+	0.307241i	−0.757395	−	0.652957i	$-0.773528\pi$
$449$	−10.1303	+	6.51033i	−0.478077	+	0.307241i	0.279318	+	0.960199i	$0.409892\pi$
$450$	−1.86677	+	0.359790i	−0.0880003	+	0.0169607i
$451$	19.6733	+	18.7584i	0.926378	+	0.883300i
$452$	3.63772	−	1.45633i	0.171104	−	0.0684998i
$453$	−4.73971	−	13.6945i	−0.222691	−	0.643423i
$454$	10.2036	−	22.3428i	0.478880	−	1.04860i
$455$	0.923694	+	0.0691739i	0.0433035	+	0.00324292i
$456$	2.66911	+	5.84453i	0.124992	+	0.273695i
$457$	−14.5637	−	5.83042i	−0.681261	−	0.272736i	0.00511065	−	0.999987i	$-0.498373\pi$
$457$	−14.5637	−	5.83042i	−0.681261	−	0.272736i	−0.686371	+	0.727251i	$0.740797\pi$
$458$	−1.02088	+	21.4310i	−0.0477028	+	1.00140i
$459$	2.23326	+	3.86812i	0.104240	+	0.180549i
$460$	−7.56484	−	3.74798i	−0.352712	−	0.174750i
$461$	2.34997			0.109449			0.0547245	−	0.998501i	$-0.482572\pi$
$461$	2.34997			0.109449			0.0547245	+	0.998501i	$0.482572\pi$
$462$	6.21984	−	5.10060i	0.289373	−	0.237301i
$463$	−1.82418	−	12.6875i	−0.0847771	−	0.589637i	−0.987285	−	0.158963i	$-0.949185\pi$
$463$	−1.82418	−	12.6875i	−0.0847771	−	0.589637i	0.902507	−	0.430674i	$-0.141724\pi$
$464$	−4.05647	−	0.387346i	−0.188317	−	0.0179821i
$465$	−1.50557	−	6.20603i	−0.0698190	−	0.287798i
$466$	6.09410	−	0.581916i	0.282304	−	0.0269567i
$467$	4.27609	+	12.3550i	0.197874	+	0.571720i	0.999665	−	0.0258852i	$-0.00824043\pi$
$467$	4.27609	+	12.3550i	0.197874	+	0.571720i	−0.801791	+	0.597605i	$0.796119\pi$
$468$	0.0283036	−	0.196856i	0.00130833	−	0.00909967i
$469$	−0.955887	+	35.2004i	−0.0441388	+	1.62541i
$470$	−7.31200	−	8.43850i	−0.337277	−	0.389239i
$471$	−0.549253	−	11.5302i	−0.0253083	−	0.531286i
$472$	4.43569	+	2.28676i	0.204169	+	0.105257i
$473$	10.6022	−	30.6330i	0.487488	−	1.40851i
$474$	0.0200927	−	0.0828233i	0.000922889	−	0.00380420i
$475$	1.73838	−	12.0907i	0.0797623	−	0.554759i
$476$	5.69814	−	10.3528i	0.261174	−	0.474519i
$477$	−2.40452	+	5.26516i	−0.110095	+	0.241075i
$478$	−5.29605	+	5.04978i	−0.242236	+	0.230971i
$479$	−7.70813	+	10.8246i	−0.352194	+	0.494587i	−0.952228	−	0.305387i	$-0.901214\pi$
$479$	−7.70813	+	10.8246i	−0.352194	+	0.494587i	0.600035	+	0.799974i	$0.295153\pi$
$480$	−1.38374	+	1.08818i	−0.0631587	+	0.0496686i
$481$	0.744204	−	0.383664i	0.0339328	−	0.0174936i
$482$	−13.5171			−0.615685
$483$	1.06523	+	12.6438i	0.0484697	+	0.575312i
$484$	−1.75678			−0.0798537
$485$	−22.7406	+	11.7236i	−1.03260	+	0.532341i
$486$	−0.786053	+	0.618159i	−0.0356561	+	0.0280403i
$487$	3.04717	−	4.27915i	0.138081	−	0.193907i	−0.739745	−	0.672887i	$-0.765054\pi$
$487$	3.04717	−	4.27915i	0.138081	−	0.193907i	0.877826	+	0.478980i	$0.158993\pi$
$488$	−5.30095	+	5.05445i	−0.239963	+	0.228804i
$489$	−5.94897	+	13.0264i	−0.269022	+	0.589076i
$490$	−3.55077	+	11.7999i	−0.160408	+	0.533064i
$491$	−0.759670	+	5.28362i	−0.0342834	+	0.238447i	−0.999757	−	0.0220554i	$-0.992979\pi$
$491$	−0.759670	+	5.28362i	−0.0342834	+	0.238447i	0.965473	+	0.260502i	$0.0838881\pi$
$492$	−2.10792	+	8.68896i	−0.0950323	+	0.391729i
$493$	5.95288	−	17.1997i	0.268104	−	0.774637i
$494$	1.13579	+	0.585539i	0.0511014	+	0.0263446i
$495$	−0.254657	−	5.34591i	−0.0114460	−	0.240281i
$496$	2.37563	+	2.74162i	0.106669	+	0.123103i
$497$	14.1346	+	8.68057i	0.634025	+	0.389377i
$498$	0.968372	−	6.73518i	0.0433938	−	0.301811i
$499$	−3.98693	−	11.5195i	−0.178480	−	0.515683i	0.819905	−	0.572499i	$-0.194026\pi$
$499$	−3.98693	−	11.5195i	−0.178480	−	0.515683i	−0.998385	+	0.0568168i	$0.981905\pi$
$500$	12.0935	−	1.15479i	0.540836	−	0.0516436i
$501$	−1.82133	−	7.50764i	−0.0813712	−	0.335417i
$502$	−5.02276	−	0.479615i	−0.224177	−	0.0214063i
$503$	−0.795766	−	5.53467i	−0.0354814	−	0.246779i	0.964360	−	0.264594i	$-0.0852380\pi$
$503$	−0.795766	−	5.53467i	−0.0354814	−	0.246779i	−0.999841	+	0.0178153i	$0.994329\pi$
$504$	2.47583	+	0.932892i	0.110282	+	0.0415543i
$505$	−19.5800			−0.871299
$506$	−8.26648	+	12.0108i	−0.367490	+	0.533945i
$507$	6.48022	+	11.2241i	0.287797	+	0.498479i
$508$	−0.140312	+	2.94552i	−0.00622536	+	0.130686i
$509$	−18.8986	−	7.56584i	−0.837664	−	0.335350i	−0.0871424	−	0.996196i	$-0.527774\pi$
$509$	−18.8986	−	7.56584i	−0.837664	−	0.335350i	−0.750522	+	0.660846i	$0.770198\pi$
$510$	−3.26628	−	7.15217i	−0.144634	−	0.316703i
$511$	0.370722	−	0.543809i	0.0163998	−	0.0240567i
$512$	0.415415	−	0.909632i	0.0183589	−	0.0402004i
$513$	−2.10146	−	6.07178i	−0.0927818	−	0.268076i
$514$	−9.54608	+	3.82167i	−0.421059	+	0.168567i
$515$	7.46245	+	7.11543i	0.328835	+	0.313543i
$516$	10.4695	−	2.01783i	0.460893	−	0.0888299i
$517$	−16.2227	+	10.4257i	−0.713474	+	0.458522i
$518$	2.84682	+	10.7686i	0.125082	+	0.473145i
$519$	−7.97700	−	9.20595i	−0.350152	−	0.404096i
$520$	−0.0825395	+	0.340232i	−0.00361960	+	0.0149202i
$521$	6.09218	−	2.43894i	0.266903	−	0.106852i	−0.234351	−	0.972152i	$-0.575296\pi$
$521$	6.09218	−	2.43894i	0.266903	−	0.106852i	0.501254	+	0.865300i	$0.332872\pi$
$522$	4.00128	+	0.771184i	0.175131	+	0.0337538i
$523$	−19.6936	−	27.6558i	−0.861141	−	1.20930i	−0.976400	−	0.215968i	$-0.930709\pi$
$523$	−19.6936	−	27.6558i	−0.861141	−	1.20930i	0.115260	−	0.993335i	$-0.463230\pi$
$524$	−12.7007	−	3.72927i	−0.554834	−	0.162914i
$525$	−3.00081	−	4.03672i	−0.130966	−	0.176177i
$526$	−3.70419	−	25.7632i	−0.161510	−	1.12333i
$527$	−14.4019	+	7.42472i	−0.627359	+	0.323426i
$528$	1.52013	+	2.63295i	0.0661553	+	0.114584i
$529$	−8.21411	−	21.4832i	−0.357135	−	0.934053i
$530$	5.09470	−	8.82427i	0.221299	−	0.383302i
$531$	−4.19823	−	2.69804i	−0.182188	−	0.117085i
$532$	−10.8672	+	13.0722i	−0.471151	+	0.566753i
$533$	0.738686	+	1.61750i	0.0319960	+	0.0700615i
$534$	12.6366	−	12.0489i	0.546837	−	0.521408i
$535$	29.3943	−	2.80681i	1.27083	−	0.121349i
$536$	−13.0689	−	2.51882i	−0.564491	−	0.108797i
$537$	10.4850	+	8.24552i	0.452463	+	0.355821i
$538$	22.4256	−	6.58476i	0.966838	−	0.283889i
$539$	19.2990	+	8.97027i	0.831267	+	0.386377i
$540$	1.48091	−	0.951724i	0.0637283	−	0.0409557i
$541$	1.87251	+	39.3087i	0.0805053	+	1.69001i	0.572886	+	0.819635i	$0.305824\pi$
$541$	1.87251	+	39.3087i	0.0805053	+	1.69001i	−0.492381	+	0.870380i	$0.663873\pi$
$542$	3.58493	−	10.3580i	0.153986	−	0.444913i
$543$	6.46102	+	6.16057i	0.277269	+	0.264375i
$544$	3.51093	+	2.76102i	0.150530	+	0.118378i
$545$	23.2441	−	26.8252i	0.995670	−	1.14906i
$546$	0.501736	−	0.158538i	0.0214723	−	0.00678478i
$547$	−27.0067	−	7.92987i	−1.15472	−	0.339057i	−0.352342	−	0.935871i	$-0.614615\pi$
$547$	−27.0067	−	7.92987i	−1.15472	−	0.339057i	−0.802379	+	0.596814i	$0.796433\pi$
$548$	−10.4019	−	0.993257i	−0.444345	−	0.0424298i
$549$	5.75741	−	4.52767i	0.245720	−	0.193236i
$550$	0.275020	−	5.77338i	0.0117269	−	0.246178i
$551$	−13.0910	+	22.6743i	−0.557696	+	0.965957i
$552$	−4.78080	−	0.379432i	−0.203484	−	0.0161497i
$553$	0.220492	−	0.0471924i	0.00937628	−	0.00200682i
$554$	5.65545	+	3.63454i	0.240277	+	0.154417i
$555$	6.88020	+	2.75442i	0.292048	+	0.116919i
$556$	−8.33879	+	11.7102i	−0.353643	+	0.496623i
$557$	−4.95400	−	20.4207i	−0.209908	−	0.865251i	−0.975157	−	0.221517i	$-0.928899\pi$
$557$	−4.95400	−	20.4207i	−0.209908	−	0.865251i	0.765249	−	0.643734i	$-0.222616\pi$
$558$	−2.10427	−	2.95503i	−0.0890807	−	0.125096i
$559$	1.38863	−	1.60256i	0.0587327	−	0.0677811i
$560$	−4.18251	−	2.04908i	−0.176743	−	0.0865894i
$561$	−13.0294	+	3.82577i	−0.550100	+	0.161524i
$562$	5.94282	−	1.14538i	0.250683	−	0.0483151i
$563$	27.2186	+	14.0322i	1.14713	+	0.591385i	0.923617	−	0.383317i	$-0.125218\pi$
$563$	27.2186	+	14.0322i	1.14713	+	0.591385i	0.223510	+	0.974702i	$0.428249\pi$
$564$	−5.63776	−	2.90647i	−0.237392	−	0.122384i
$565$	6.77316	−	1.30542i	0.284949	−	0.0549195i
$566$	26.9284	−	7.90689i	1.13189	−	0.332351i
$567$	−2.37594	−	1.16401i	−0.0997800	−	0.0488838i
$568$	−4.10560	+	4.73812i	−0.172267	+	0.198807i
$569$	22.3771	+	31.4243i	0.938098	+	1.31737i	0.948283	+	0.317426i	$0.102819\pi$
$569$	22.3771	+	31.4243i	0.938098	+	1.31737i	−0.0101848	+	0.999948i	$0.503242\pi$
$570$	2.66658	+	10.9918i	0.111691	+	0.460395i
$571$	7.51961	−	10.5598i	0.314686	−	0.441914i	−0.626693	−	0.779266i	$-0.715592\pi$
$571$	7.51961	−	10.5598i	0.314686	−	0.441914i	0.941379	+	0.337352i	$0.109531\pi$
$572$	0.561337	+	0.224725i	0.0234707	+	0.00939624i
$573$	−4.86260	−	3.12500i	−0.203138	−	0.130549i
$574$	−23.1318	+	4.95093i	−0.965501	+	0.206648i
$575$	7.25607	+	5.52066i	0.302599	+	0.230228i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−1.02314	+	21.4784i	−0.0425940	+	0.894159i	0.871931	+	0.489629i	$0.162868\pi$
$577$	−1.02314	+	21.4784i	−0.0425940	+	0.894159i	−0.914525	+	0.404530i	$0.867435\pi$
$578$	−2.31874	+	1.82348i	−0.0964469	+	0.0758467i
$579$	11.5630	+	1.10413i	0.480541	+	0.0458861i
$580$	−6.88277	−	2.02096i	−0.285792	−	0.0839160i
$581$	17.1663	−	5.42417i	0.712177	−	0.225032i
$582$	−9.51760	+	10.9839i	−0.394517	+	0.455297i
$583$	−13.8328	−	10.8782i	−0.572896	−	0.450530i
$584$	0.180034	+	0.171662i	0.00744987	+	0.00710344i
$585$	0.114507	−	0.330846i	0.00473428	−	0.0136788i
$586$	−0.543936	−	11.4186i	−0.0224698	−	0.471699i
$587$	−13.6592	+	8.77821i	−0.563774	+	0.362315i	−0.791273	−	0.611463i	$-0.790581\pi$
$587$	−13.6592	+	8.77821i	−0.563774	+	0.362315i	0.227499	+	0.973778i	$0.426945\pi$
$588$	0.618705	+	6.97260i	0.0255150	+	0.287545i
$589$	22.3643	−	6.56675i	0.921505	−	0.270578i
$590$	6.90548	+	5.43053i	0.284294	+	0.223571i
$591$	14.5282	+	2.80008i	0.597611	+	0.115180i
$592$	−4.19091	+	0.400183i	−0.172245	+	0.0164474i
$593$	4.39570	−	4.19129i	0.180510	−	0.172116i	−0.594437	−	0.804142i	$-0.702625\pi$
$593$	4.39570	−	4.19129i	0.180510	−	0.172116i	0.774947	+	0.632026i	$0.217777\pi$
$594$	−1.26297	−	2.76552i	−0.0518204	−	0.113471i
$595$	13.2986	−	15.9970i	0.545188	−	0.655812i
$596$	−13.5339	−	8.69773i	−0.554372	−	0.356273i
$597$	9.61536	−	16.6543i	0.393530	−	0.681615i
$598$	−0.794031	+	0.528433i	−0.0324704	+	0.0216092i
$599$	11.3161	+	19.6001i	0.462365	+	0.800839i	0.999078	−	0.0429252i	$-0.0136677\pi$
$599$	11.3161	+	19.6001i	0.462365	+	0.800839i	−0.536713	+	0.843765i	$0.680334\pi$
$600$	1.68979	−	0.871146i	0.0689853	−	0.0355644i
$601$	4.82097	+	33.5306i	0.196651	+	1.36774i	0.813915	+	0.580984i	$0.197332\pi$
$601$	4.82097	+	33.5306i	0.196651	+	1.36774i	−0.617264	+	0.786756i	$0.711759\pi$
$602$	16.8296	+	22.6393i	0.685921	+	0.922709i
$603$	12.7703	+	3.74970i	0.520047	+	0.152699i
$604$	8.40589	+	11.8044i	0.342031	+	0.480315i
$605$	−3.03668	−	0.585273i	−0.123459	−	0.0237947i
$606$	−10.3260	+	4.13389i	−0.419464	+	0.167928i
$607$	−6.65726	+	27.4416i	−0.270210	+	1.11382i	0.661305	+	0.750117i	$0.270003\pi$
$607$	−6.65726	+	27.4416i	−0.270210	+	1.11382i	−0.931515	+	0.363703i	$0.881512\pi$
$608$	−4.20758	−	4.85581i	−0.170640	−	0.196929i
$609$	2.75550	+	10.4232i	0.111658	+	0.422368i
$610$	−10.8469	+	6.97085i	−0.439176	+	0.282242i
$611$	−1.23867	+	0.238735i	−0.0501113	+	0.00965817i
$612$	−3.23258	−	3.08226i	−0.130669	−	0.124593i
$613$	−31.0009	+	12.4109i	−1.25211	+	0.501271i	−0.900492	−	0.434872i	$-0.856794\pi$
$613$	−31.0009	+	12.4109i	−1.25211	+	0.501271i	−0.351621	+	0.936142i	$0.614370\pi$
$614$	−9.03380	−	26.1015i	−0.364575	−	1.05337i
$615$	−6.53838	+	14.3171i	−0.263653	+	0.577319i
$616$	−4.53089	+	6.64632i	−0.182555	+	0.267788i
$617$	−16.0588	−	35.1638i	−0.646501	−	1.41564i	−0.894583	−	0.446901i	$-0.852528\pi$
$617$	−16.0588	−	35.1638i	−0.646501	−	1.41564i	0.248082	−	0.968739i	$-0.420200\pi$
$618$	5.43777	+	2.17695i	0.218739	+	0.0875699i
$619$	−1.05721	+	22.1935i	−0.0424927	+	0.892031i	0.872513	+	0.488590i	$0.162489\pi$
$619$	−1.05721	+	22.1935i	−0.0424927	+	0.892031i	−0.915006	+	0.403440i	$0.867814\pi$
$620$	3.19302	+	5.53048i	0.128235	+	0.222109i
$621$	4.72308	+	0.832158i	0.189531	+	0.0333933i
$622$	17.4090			0.698036
$623$	43.2285	+	16.2885i	1.73191	+	0.652585i
$624$	0.0283036	+	0.196856i	0.00113305	+	0.00788054i
$625$	11.8263	+	1.12928i	0.473052	+	0.0451710i
$626$	−5.72113	−	23.5828i	−0.228662	−	0.942559i
$627$	19.4457	−	1.85684i	0.776588	−	0.0741551i
$628$	3.77545	+	10.9084i	0.150657	+	0.435294i
$629$	2.67608	−	18.6125i	0.106702	−	0.742131i
$630$	3.96880	+	2.43737i	0.158121	+	0.0971073i
$631$	14.2855	+	16.4863i	0.568695	+	0.656309i	0.965135	−	0.261751i	$-0.0843000\pi$
$631$	14.2855	+	16.4863i	0.568695	+	0.656309i	−0.396440	+	0.918061i	$0.629755\pi$
$632$	0.00405520	+	0.0851292i	0.000161307	+	0.00338626i
$633$	−6.49749	−	3.34969i	−0.258252	−	0.133138i
$634$	5.56744	−	16.0861i	0.221111	−	0.638859i
$635$	−1.22384	+	5.04473i	−0.0485666	+	0.200194i
$636$	0.823752	−	5.72932i	0.0326639	−	0.227182i
$637$	0.953932	+	1.01397i	0.0377961	+	0.0401748i
$638$	−5.14652	+	11.2693i	−0.203753	+	0.446156i
$639$	4.53740	−	4.32640i	0.179497	−	0.171150i
$640$	1.02111	−	1.43395i	0.0403629	−	0.0566818i
$641$	−17.9036	+	14.0796i	−0.707151	+	0.556109i	−0.905668	−	0.423988i	$-0.860630\pi$
$641$	−17.9036	+	14.0796i	−0.707151	+	0.556109i	0.198517	+	0.980097i	$0.436387\pi$
$642$	14.9092	−	7.68621i	0.588418	−	0.303350i
$643$	−20.8105			−0.820685			−0.410343	−	0.911931i	$-0.634591\pi$
$643$	−20.8105			−0.820685			−0.410343	+	0.911931i	$0.634591\pi$
$644$	−4.58425	−	11.8315i	−0.180645	−	0.466227i
$645$	18.7693			0.739039
$646$	25.5079	−	13.1502i	1.00360	−	0.517389i
$647$	0.667857	−	0.525208i	0.0262562	−	0.0206481i	−0.604945	−	0.796267i	$-0.706805\pi$
$647$	0.667857	−	0.525208i	0.0262562	−	0.0206481i	0.631201	+	0.775619i	$0.282562\pi$
$648$	0.580057	−	0.814576i	0.0227868	−	0.0319996i
$649$	10.9807	−	10.4701i	0.431030	−	0.410987i
$650$	0.157067	−	0.343928i	0.00616067	−	0.0134900i
$651$	4.62800	−	8.40848i	0.181386	−	0.329554i
$652$	2.03803	−	14.1748i	0.0798153	−	0.555128i
$653$	11.2796	−	46.4951i	0.441404	−	1.81949i	−0.121027	−	0.992649i	$-0.538619\pi$
$653$	11.2796	−	46.4951i	0.441404	−	1.81949i	0.562431	−	0.826844i	$-0.309866\pi$
$654$	6.59478	−	19.0544i	0.257876	−	0.745085i
$655$	−20.7115	−	10.6775i	−0.809263	−	0.417204i
$656$	−0.425430	−	8.93087i	−0.0166102	−	0.348692i
$657$	−0.162902	−	0.187998i	−0.00635540	−	0.00733452i
$658$	0.455546	−	16.7754i	0.0177590	−	0.653975i
$659$	5.94790	−	41.3686i	0.231697	−	1.61149i	−0.459061	−	0.888405i	$-0.651814\pi$
$659$	5.94790	−	41.3686i	0.231697	−	1.61149i	0.690758	−	0.723086i	$-0.257277\pi$
$660$	1.75046	+	5.05762i	0.0681365	+	0.196867i
$661$	−9.68674	+	0.924971i	−0.376770	+	0.0359772i	−0.281724	−	0.959496i	$-0.590906\pi$
$661$	−9.68674	+	0.924971i	−0.376770	+	0.0359772i	−0.0950467	+	0.995473i	$0.530300\pi$
$662$	4.65797	+	19.2004i	0.181037	+	0.746245i
$663$	−0.884281	−	0.0844386i	−0.0343426	−	0.00327932i
$664$	0.968372	+	6.73518i	0.0375801	+	0.261376i
$665$	−23.1395	+	18.9756i	−0.897310	+	0.735842i
$666$	4.20997			0.163133
$667$	−10.0409	−	16.7659i	−0.388783	−	0.649179i
$668$	3.86270	+	6.69040i	0.149453	+	0.258859i
$669$	0.292484	−	6.14000i	0.0113081	−	0.237386i
$670$	−21.7511	−	8.70783i	−0.840318	−	0.336413i
$671$	9.25058	+	20.2559i	0.357115	+	0.781972i
$672$	−2.63836	−	0.197583i	−0.101777	−	0.00762191i
$673$	12.8673	−	28.1755i	0.495999	−	1.08609i	−0.481751	−	0.876308i	$-0.659999\pi$
$673$	12.8673	−	28.1755i	0.495999	−	1.08609i	0.977749	−	0.209777i	$-0.0672738\pi$
$674$	4.92906	+	14.2416i	0.189860	+	0.548565i
$675$	−1.76494	+	0.706577i	−0.0679327	+	0.0271961i
$676$	−9.37992	−	8.94373i	−0.360766	−	0.343990i
$677$	−24.5342	+	4.72858i	−0.942927	+	0.181734i	−0.637473	−	0.770473i	$-0.720020\pi$
$677$	−24.5342	+	4.72858i	−0.942927	+	0.181734i	−0.305454	+	0.952207i	$0.598808\pi$
$678$	3.29637	−	2.11845i	0.126596	−	0.0813586i
$679$	−37.1090	−	10.0766i	−1.42411	−	0.386706i
$680$	5.14898	+	5.94223i	0.197454	+	0.227874i
$681$	5.79082	−	23.8701i	0.221905	−	0.914704i
$682$	10.2391	−	4.09912i	0.392075	−	0.156963i
$683$	−6.66550	−	1.28467i	−0.255048	−	0.0491565i	0.0601243	−	0.998191i	$-0.480850\pi$
$683$	−6.66550	−	1.28467i	−0.255048	−	0.0491565i	−0.315173	+	0.949034i	$0.602062\pi$
$684$	3.72696	+	5.23378i	0.142504	+	0.200118i
$685$	−17.6492	−	5.18228i	−0.674343	−	0.198005i
$686$	−15.9101	+	9.47983i	−0.607452	+	0.361942i
$687$	3.05341	+	21.2369i	0.116495	+	0.810239i
$688$	−9.47690	+	4.88568i	−0.361304	+	0.186265i
$689$	−0.575583	−	0.996939i	−0.0219280	−	0.0379803i
$690$	−8.13744	−	2.24859i	−0.309787	−	0.0856025i
$691$	9.79117	−	16.9588i	0.372473	−	0.645143i	−0.617472	−	0.786593i	$-0.711843\pi$
$691$	9.79117	−	16.9588i	0.372473	−	0.645143i	0.989945	+	0.141450i	$0.0451764\pi$
$692$	10.2475	+	6.58567i	0.389551	+	0.250349i
$693$	5.14214	−	6.18554i	0.195334	−	0.234969i
$694$	5.99731	+	13.1323i	0.227655	+	0.498494i
$695$	−18.3153	+	17.4636i	−0.694738	+	0.662431i
$696$	−4.05647	+	0.387346i	−0.153760	+	0.0146823i
$697$	39.2135	+	7.55778i	1.48532	+	0.286271i
$698$	−15.8508	−	12.4652i	−0.599962	−	0.471815i
$699$	5.87384	−	1.72472i	0.222169	−	0.0652347i
$700$	4.01653	+	3.02778i	0.151810	+	0.114439i
$701$	4.60818	−	2.96149i	0.174048	−	0.111854i	−0.450716	−	0.892667i	$-0.648831\pi$
$701$	4.60818	−	2.96149i	0.174048	−	0.111854i	0.624765	+	0.780813i	$0.285195\pi$
$702$	−0.00946310	−	0.198655i	−0.000357162	−	0.00749775i
$703$	−8.84710	+	25.5620i	−0.333675	+	0.964089i
$704$	−2.20034	−	2.09802i	−0.0829286	−	0.0790723i
$705$	−8.77686	−	6.90220i	−0.330556	−	0.259952i
$706$	−4.87758	+	5.62903i	−0.183570	+	0.211851i
$707$	−21.7088	−	19.8678i	−0.816444	−	0.747206i
$708$	4.78830	+	1.40597i	0.179955	+	0.0528397i
$709$	6.09130	+	0.581649i	0.228764	+	0.0218443i	0.208808	−	0.977957i	$-0.433042\pi$
$709$	6.09130	+	0.581649i	0.228764	+	0.0218443i	0.0199554	+	0.999801i	$0.493648\pi$
$710$	−8.67525	+	6.82229i	−0.325576	+	0.256036i
$711$	0.00405520	−	0.0851292i	0.000152082	−	0.00319259i
$712$	−8.73011	+	15.1210i	−0.327175	+	0.566683i
$713$	−3.83065	+	16.9708i	−0.143459	+	0.635562i
$714$	3.63589	−	11.2441i	0.136070	−	0.420799i
$715$	0.895431	+	0.575459i	0.0334872	+	0.0215209i
$716$	−12.3833	−	4.95754i	−0.462787	−	0.185272i
$717$	−4.24467	+	5.96081i	−0.158520	+	0.222610i
$718$	−3.64717	−	15.0338i	−0.136111	−	0.561058i
$719$	0.219077	+	0.307651i	0.00817021	+	0.0114734i	0.818641	−	0.574306i	$-0.194728\pi$
$719$	0.219077	+	0.307651i	0.00817021	+	0.0114734i	−0.810471	+	0.585779i	$0.800789\pi$
$720$	−1.15279	+	1.33039i	−0.0429620	+	0.0495808i
$721$	1.05378	+	15.4612i	0.0392447	+	0.575805i
$722$	−21.3800	+	6.27774i	−0.795682	+	0.233633i
$723$	−13.2728	+	2.55812i	−0.493620	+	0.0951375i
$724$	−7.93493	−	4.09074i	−0.294899	−	0.152031i
$725$	6.88575	+	3.54985i	0.255730	+	0.131838i
$726$	−1.72503	+	0.332473i	−0.0640220	+	0.0123392i
$727$	−6.64805	+	1.95204i	−0.246563	+	0.0723973i	−0.402679	−	0.915341i	$-0.631921\pi$
$727$	−6.64805	+	1.95204i	−0.246563	+	0.0723973i	0.156116	+	0.987739i	$0.450103\pi$
$728$	−0.436747	+	0.293471i	−0.0161869	+	0.0108768i
$729$	−0.654861	+	0.755750i	−0.0242541	+	0.0279907i
$730$	0.254009	+	0.356706i	0.00940129	+	0.0132023i
$731$	−11.2275	−	46.2804i	−0.415264	−	1.71174i
$732$	−4.24860	+	5.96632i	−0.157033	+	0.220522i
$733$	14.5101	+	5.80895i	0.535941	+	0.214558i	0.623813	−	0.781573i	$-0.285583\pi$
$733$	14.5101	+	5.80895i	0.535941	+	0.214558i	−0.0878724	+	0.996132i	$0.528007\pi$
$734$	10.3126	+	6.62749i	0.380644	+	0.244625i
$735$	−1.25347	+	12.2586i	−0.0462348	+	0.452166i
$736$	4.69404	−	0.982844i	0.173025	−	0.0362281i
$737$	−20.2321	+	35.0430i	−0.745259	+	1.29083i
$738$	−0.425430	+	8.93087i	−0.0156603	+	0.328750i
$739$	−23.8103	+	18.7247i	−0.875877	+	0.688797i	−0.951271	−	0.308356i	$-0.900221\pi$
$739$	−23.8103	+	18.7247i	−0.875877	+	0.688797i	0.0753937	+	0.997154i	$0.475979\pi$
$740$	−7.37752	−	0.704467i	−0.271203	−	0.0258967i
$741$	1.22608	+	0.360008i	0.0450410	+	0.0132252i
$742$	14.6026	−	4.61410i	0.536078	−	0.169389i
$743$	−28.1738	+	32.5142i	−1.03359	+	1.19283i	−0.0526365	+	0.998614i	$0.516762\pi$
$743$	−28.1738	+	32.5142i	−1.03359	+	1.19283i	−0.980958	+	0.194218i	$0.937783\pi$
$744$	2.85156	+	2.24249i	0.104543	+	0.0822136i
$745$	−20.4964	−	19.5433i	−0.750931	−	0.716011i
$746$	4.42002	−	12.7708i	0.161828	−	0.467572i
$747$	−0.323768	−	6.79673i	−0.0118461	−	0.248679i
$748$	11.4237	−	7.34159i	0.417693	−	0.268435i
$749$	35.4382	+	26.7144i	1.29488	+	0.976122i
$750$	11.6564	−	3.42262i	0.425631	−	0.124976i
$751$	−31.5880	−	24.8411i	−1.15266	−	0.906463i	−0.155972	−	0.987761i	$-0.549851\pi$
$751$	−31.5880	−	24.8411i	−1.15266	−	0.906463i	−0.996690	+	0.0812980i	$0.974093\pi$
$752$	6.22824	+	1.20039i	0.227120	+	0.0437739i
$753$	−5.02276	+	0.479615i	−0.183039	+	0.0174781i
$754$	−0.586530	+	0.559255i	−0.0213602	+	0.0203669i
$755$	10.5974	+	23.2050i	0.385677	+	0.844516i
$756$	2.60764	+	0.447480i	0.0948388	+	0.0162747i
$757$	39.2442	+	25.2207i	1.42636	+	0.916663i	0.999926	+	0.0121424i	$0.00386514\pi$
$757$	39.2442	+	25.2207i	1.42636	+	0.916663i	0.426429	+	0.904521i	$0.359771\pi$
$758$	−9.98436	+	17.2934i	−0.362648	+	0.628125i
$759$	−5.84403	+	13.3582i	−0.212125	+	0.484872i
$760$	−5.65530	−	9.79527i	−0.205139	−	0.355312i
$761$	28.5130	−	14.6995i	1.03360	−	0.532856i	0.143987	−	0.989580i	$-0.454008\pi$
$761$	28.5130	−	14.6995i	1.03360	−	0.532856i	0.889608	+	0.456724i	$0.150977\pi$
$762$	0.419667	+	2.91885i	0.0152029	+	0.105739i
$763$	52.9908	−	6.15590i	1.91840	−	0.222859i
$764$	5.54604	+	1.62846i	0.200649	+	0.0589158i
$765$	−4.56082	−	6.40477i	−0.164897	−	0.231565i
$766$	27.7506	+	5.34848i	1.00267	+	0.193248i
$767$	0.921407	−	0.368876i	0.0332701	−	0.0133193i
$768$	0.235759	−	0.971812i	0.00850722	−	0.0350672i
$769$	−12.6690	−	14.6208i	−0.456856	−	0.527239i	0.479853	−	0.877349i	$-0.340690\pi$
$769$	−12.6690	−	14.6208i	−0.456856	−	0.527239i	−0.936709	+	0.350109i	$0.886144\pi$
$770$	−10.0461	+	9.97903i	−0.362036	+	0.359619i
$771$	−8.65031	+	5.55922i	−0.311533	+	0.200210i
$772$	−11.4057	+	2.19826i	−0.410499	+	0.0791172i
$773$	−36.6782	−	34.9726i	−1.31922	−	1.25788i	−0.943593	−	0.331107i	$-0.892578\pi$
$773$	−36.6782	−	34.9726i	−1.31922	−	1.25788i	−0.375630	−	0.926770i	$-0.622574\pi$
$774$	9.89841	−	3.96272i	0.355791	−	0.142437i
$775$	−2.25569	−	6.51738i	−0.0810266	−	0.234111i
$776$	6.03755	−	13.2204i	0.216735	−	0.474584i
$777$	4.83334	+	10.0352i	0.173395	+	0.360012i
$778$	−11.0011	−	24.0892i	−0.394410	−	0.863638i
$779$	−53.3322	−	21.3510i	−1.91082	−	0.764979i
$780$	−0.0166585	+	0.349705i	−0.000596470	+	0.0125214i
$781$	9.53037	+	16.5071i	0.341023	+	0.590670i
$782$	−0.676781	+	21.4100i	−0.0242016	+	0.765620i
$783$	4.07492			0.145626
$784$	−2.55805	−	6.51586i	−0.0913590	−	0.232709i
$785$	2.89190	+	20.1136i	0.103216	+	0.717885i
$786$	−13.1770	−	1.25825i	−0.470008	−	0.0448803i
$787$	−2.56330	−	10.5661i	−0.0913716	−	0.376639i	0.907705	−	0.419610i	$-0.137833\pi$
$787$	−2.56330	−	10.5661i	−0.0913716	−	0.376639i	−0.999076	+	0.0429705i	$0.986318\pi$
$788$	−14.7286	+	1.40641i	−0.524684	+	0.0501013i
$789$	−8.51297	−	24.5966i	−0.303070	−	0.875662i
$790$	−0.0213512	+	0.148501i	−0.000759643	+	0.00528343i
$791$	8.83418	+	5.42537i	0.314107	+	0.192904i
$792$	1.99095	+	2.29768i	0.0707454	+	0.0816445i
$793$	0.0693120	+	1.45504i	0.00246134	+	0.0516699i
$794$	−16.1015	−	8.30088i	−0.571419	−	0.294587i
$795$	3.33262	−	9.62898i	0.118196	−	0.341505i
$796$	−4.53381	+	18.6886i	−0.160697	+	0.662401i
$797$	0.723583	−	5.03263i	0.0256306	−	0.178265i	−0.972985	−	0.230869i	$-0.925843\pi$
$797$	0.723583	−	5.03263i	0.0256306	−	0.178265i	0.998615	+	0.0526041i	$0.0167522\pi$
$798$	−8.19685	+	14.8926i	−0.290165	+	0.527193i
$799$	−11.7689	+	25.7704i	−0.416355	+	0.911690i
$800$	−1.37591	+	1.31193i	−0.0486457	+	0.0463836i
$801$	10.1279	−	14.2227i	0.357853	−	0.502534i
$802$	−7.63366	+	6.00318i	−0.269554	+	0.211980i
$803$	0.672217	−	0.346552i	0.0237220	−	0.0122295i
$804$	−13.3094			−0.469387
$805$	−3.98242	−	21.9786i	−0.140362	−	0.774644i
$806$	0.721476			0.0254129
$807$	20.7742	−	10.7098i	0.731286	−	0.377004i
$808$	8.74304	−	6.87560i	0.307579	−	0.241883i
$809$	−11.6175	+	16.3145i	−0.408449	+	0.573586i	−0.966644	−	0.256124i	$-0.917555\pi$
$809$	−11.6175	+	16.3145i	−0.408449	+	0.573586i	0.558195	+	0.829710i	$0.311494\pi$
$810$	1.27403	−	1.21479i	0.0447650	−	0.0426833i
$811$	−0.0677318	+	0.148312i	−0.00237839	+	0.00520794i	−0.910817	−	0.412809i	$-0.864548\pi$
$811$	−0.0677318	+	0.148312i	−0.00237839	+	0.00520794i	0.908439	+	0.418017i	$0.137275\pi$
$812$	−5.58042	−	9.22464i	−0.195835	−	0.323721i
$813$	1.55988	−	10.8492i	0.0547075	−	0.380499i
$814$	−3.01758	+	12.4386i	−0.105766	+	0.435974i
$815$	8.24518	−	23.8229i	0.288816	−	0.834479i
$816$	3.97001	+	2.04668i	0.138978	+	0.0716481i
$817$	3.25965	+	68.4284i	0.114041	+	2.39401i
$818$	−2.18366	−	2.52008i	−0.0763499	−	0.0881124i
$819$	0.462666	−	0.250627i	0.0161669	−	0.00875761i
$820$	2.23995	−	15.5792i	0.0782224	−	0.544049i
$821$	−14.7398	−	42.5878i	−0.514422	−	1.48632i	−0.840938	−	0.541132i	$-0.817996\pi$
$821$	−14.7398	−	42.5878i	−0.514422	−	1.48632i	0.326516	−	0.945192i	$-0.394125\pi$
$822$	−10.4019	+	0.993257i	−0.362807	+	0.0346438i
$823$	−8.21516	−	33.8634i	−0.286363	−	1.18040i	−0.915244	−	0.402901i	$-0.868002\pi$
$823$	−8.21516	−	33.8634i	−0.286363	−	1.18040i	0.628881	−	0.777501i	$-0.283513\pi$
$824$	−5.83082	−	0.556776i	−0.203126	−	0.0193962i
$825$	−0.822569	−	5.72109i	−0.0286382	−	0.199183i
$826$	2.14592	+	13.0279i	0.0746660	+	0.453300i
$827$	−46.8080			−1.62767			−0.813837	−	0.581093i	$-0.802625\pi$
$827$	−46.8080			−1.62767			−0.813837	+	0.581093i	$0.802625\pi$
$828$	−4.76621	+	0.532197i	−0.165637	+	0.0184951i
$829$	−20.5856	−	35.6552i	−0.714966	−	1.23836i	−0.962973	−	0.269599i	$-0.913109\pi$
$829$	−20.5856	−	35.6552i	−0.714966	−	1.23836i	0.248006	−	0.968758i	$-0.420225\pi$
$830$	−0.569949	+	11.9647i	−0.0197832	+	0.415301i
$831$	6.24109	+	2.49856i	0.216501	+	0.0866740i
$832$	−0.0826178	−	0.180908i	−0.00286426	−	0.00627185i
$833$	30.9765	−	4.24219i	1.07327	−	0.146983i
$834$	−5.97193	+	13.0767i	−0.206791	+	0.452809i
$835$	4.44797	+	12.8516i	0.153928	+	0.444746i
$836$	−18.1349	+	7.26012i	−0.627209	+	0.251097i
$837$	−2.62548	−	2.50339i	−0.0907499	−	0.0865299i
$838$	15.3621	−	2.96080i	0.530674	−	0.102279i
$839$	10.3819	−	6.67205i	0.358424	−	0.230345i	−0.349019	−	0.937116i	$-0.613485\pi$
$839$	10.3819	−	6.67205i	0.358424	−	0.230345i	0.707443	+	0.706771i	$0.249849\pi$
$840$	−4.49472	−	1.22050i	−0.155083	−	0.0421114i
$841$	8.11700	+	9.36751i	0.279896	+	0.323018i
$842$	2.14496	−	8.84164i	0.0739202	−	0.304703i
$843$	5.61866	−	2.24937i	0.193517	−	0.0774725i
$844$	7.17801	+	1.38345i	0.247077	+	0.0476203i
$845$	−13.2340	−	18.5846i	−0.455265	−	0.639330i
$846$	−6.08593	−	1.78699i	−0.209239	−	0.0614380i
$847$	−2.77297	−	3.73023i	−0.0952803	−	0.128172i
$848$	0.823752	+	5.72932i	0.0282878	+	0.196746i
$849$	24.9454	−	12.8602i	0.856123	−	0.441362i
$850$	−4.24571	−	7.35379i	−0.145627	−	0.252233i
$851$	−13.4643	−	15.0453i	−0.461549	−	0.515747i
$852$	−3.13471	+	5.42949i	−0.107394	+	0.186011i
$853$	−35.3056	−	22.6895i	−1.20884	−	0.776874i	−0.228376	−	0.973573i	$-0.573342\pi$
$853$	−35.3056	−	22.6895i	−1.20884	−	0.776874i	−0.980464	+	0.196699i	$0.936978\pi$
$854$	−19.0995	−	3.27755i	−0.653571	−	0.112155i
$855$	4.69859	+	10.2885i	0.160689	+	0.351859i
$856$	−12.1398	+	11.5753i	−0.414929	+	0.395634i
$857$	−12.3198	+	1.17640i	−0.420837	+	0.0401851i	−0.303327	−	0.952887i	$-0.598097\pi$
$857$	−12.3198	+	1.17640i	−0.420837	+	0.0401851i	−0.117510	+	0.993072i	$0.537491\pi$
$858$	0.593722	+	0.114431i	0.0202693	+	0.00390659i
$859$	−17.7796	−	13.9821i	−0.606633	−	0.477062i	0.266967	−	0.963706i	$-0.413978\pi$
$859$	−17.7796	−	13.9821i	−0.606633	−	0.477062i	−0.873600	+	0.486644i	$0.838221\pi$
$860$	−18.0090	+	5.28791i	−0.614101	+	0.180316i
$861$	−21.7768	+	9.23917i	−0.742150	+	0.314870i
$862$	−8.75387	+	5.62577i	−0.298158	+	0.191615i
$863$	0.147822	+	3.10317i	0.00503192	+	0.105633i	0.999986	+	0.00530119i	$0.00168743\pi$
$863$	0.147822	+	3.10317i	0.00503192	+	0.105633i	−0.994954	+	0.100332i	$0.968010\pi$
$864$	−0.327068	+	0.945001i	−0.0111271	+	0.0321496i
$865$	15.5193	+	14.7976i	0.527672	+	0.503134i
$866$	8.61038	+	6.77128i	0.292593	+	0.230097i
$867$	−1.93174	+	2.22935i	−0.0656054	+	0.0757127i
$868$	−2.07159	+	9.37173i	−0.0703144	+	0.318097i
$869$	0.248613	+	0.0729994i	0.00843362	+	0.00247633i
$870$	−7.14086	−	0.681870i	−0.242098	−	0.0231175i
$871$	−2.08067	+	1.63625i	−0.0705007	+	0.0554424i
$872$	−0.959410	+	20.1405i	−0.0324897	+	0.682044i
$873$	−7.26689	+	12.5866i	−0.245947	+	0.425993i
$874$	6.78463	−	30.0578i	0.229494	−	1.01672i
$875$	21.5408	+	23.8557i	0.728211	+	0.806469i
$876$	0.209268	+	0.134489i	0.00707052	+	0.00454395i
$877$	36.0501	+	14.4323i	1.21732	+	0.487343i	0.889299	−	0.457325i	$-0.151193\pi$
$877$	36.0501	+	14.4323i	1.21732	+	0.487343i	0.328026	+	0.944669i	$0.393617\pi$
$878$	2.05702	−	2.88868i	0.0694211	−	0.0974883i
$879$	−2.69510	−	11.1093i	−0.0909034	−	0.374709i
$880$	−3.10445	−	4.35959i	−0.104651	−	0.146962i
$881$	−21.8097	+	25.1698i	−0.734788	+	0.847991i	−0.993002	−	0.118097i	$-0.962321\pi$
$881$	−21.8097	+	25.1698i	−0.734788	+	0.847991i	0.258214	+	0.966088i	$0.416866\pi$
$882$	1.92710	+	6.72951i	0.0648888	+	0.226594i
$883$	46.4505	−	13.6391i	1.56318	−	0.458992i	0.618176	−	0.786039i	$-0.287872\pi$
$883$	46.4505	−	13.6391i	1.56318	−	0.458992i	0.945008	+	0.327047i	$0.106054\pi$
$884$	0.872251	−	0.168113i	0.0293370	−	0.00565424i
$885$	7.80842	+	4.02552i	0.262477	+	0.135316i
$886$	−21.7655	−	11.2209i	−0.731225	−	0.376973i
$887$	−31.8057	+	6.13004i	−1.06793	+	0.205827i	−0.692788	−	0.721141i	$-0.743618\pi$
$887$	−31.8057	+	6.13004i	−1.06793	+	0.205827i	−0.375142	+	0.926968i	$0.622406\pi$
$888$	−4.03944	+	1.18609i	−0.135555	+	0.0398024i
$889$	−6.47579	+	4.35139i	−0.217191	+	0.145941i
$890$	−20.1280	+	23.2290i	−0.674692	+	0.778637i
$891$	−1.76353	−	2.47653i	−0.0590804	−	0.0829668i
$892$	1.44920	+	5.97369i	0.0485229	+	0.200014i
$893$	23.6396	−	33.1971i	0.791068	−	1.11090i
$894$	−14.9354	−	5.97924i	−0.499515	−	0.199976i
$895$	−19.7536	−	12.6949i	−0.660291	−	0.424343i
$896$	2.58716	−	0.553734i	0.0864308	−	0.0184989i
$897$	−0.679676	+	0.669155i	−0.0226937	+	0.0223424i
$898$	6.02093	−	10.4286i	0.200921	−	0.348006i
$899$	−0.703382	+	14.7658i	−0.0234591	+	0.492467i
$900$	1.49438	−	1.17520i	0.0498128	−	0.0391732i
$901$	−25.7362	−	2.45751i	−0.857398	−	0.0818716i
$902$	−26.0819	−	7.65834i	−0.868432	−	0.254995i
$903$	20.8099	+	19.0452i	0.692511	+	0.633783i
$904$	−2.56601	+	2.96133i	−0.0853443	+	0.0984925i
$905$	−12.3531	−	9.71458i	−0.410631	−	0.322924i
$906$	10.4880	+	10.0003i	0.348440	+	0.332237i
$907$	−10.8066	+	31.2237i	−0.358828	+	1.03677i	0.610716	+	0.791850i	$0.290882\pi$
$907$	−10.8066	+	31.2237i	−0.358828	+	1.03677i	−0.969544	+	0.244916i	$0.921239\pi$
$908$	1.16873	+	24.5346i	0.0387856	+	0.814211i
$909$	−9.35702	+	6.01339i	−0.310353	+	0.199452i
$910$	−0.852710	+	0.361777i	−0.0282670	+	0.0119928i
$911$	4.73504	−	1.39033i	0.156879	−	0.0460638i	−0.202350	−	0.979313i	$-0.564858\pi$
$911$	4.73504	−	1.39033i	0.156879	−	0.0460638i	0.359229	+	0.933249i	$0.383040\pi$
$912$	−5.05051	−	3.97177i	−0.167239	−	0.131518i
$913$	20.3135	+	3.91510i	0.672277	+	0.129571i
$914$	15.6164	−	1.49118i	0.516544	−	0.0493240i
$915$	−9.33160	+	8.89766i	−0.308493	+	0.294148i
$916$	−8.91285	−	19.5164i	−0.294489	−	0.644841i
$917$	−12.1288	−	32.8543i	−0.400530	−	1.08494i
$918$	−3.75748	−	2.41479i	−0.124015	−	0.0796998i
$919$	25.2594	−	43.7505i	0.833230	−	1.44320i	−0.0622328	−	0.998062i	$-0.519822\pi$
$919$	25.2594	−	43.7505i	0.833230	−	1.44320i	0.895463	−	0.445136i	$-0.146845\pi$
$920$	8.44132	−	0.135072i	0.278302	−	0.00445320i
$921$	−13.8103	−	23.9201i	−0.455064	−	0.788195i
$922$	−2.08874	+	1.07682i	−0.0687889	+	0.0354631i
$923$	0.177447	+	1.23417i	0.00584076	+	0.0406233i
$924$	−3.19118	+	7.38369i	−0.104982	+	0.242906i
$925$	7.67947	+	2.25490i	0.252500	+	0.0741406i
$926$	7.43514	+	10.4412i	0.244334	+	0.343119i
$927$	5.75149	+	1.10851i	0.188904	+	0.0364082i
$928$	3.78303	−	1.51450i	0.124184	−	0.0497158i
$929$	2.35462	−	9.70587i	0.0772525	−	0.318439i	−0.920053	−	0.391793i	$-0.871855\pi$
$929$	2.35462	−	9.70587i	0.0772525	−	0.318439i	0.997306	+	0.0733536i	$0.0233702\pi$
$930$	4.18197	+	4.82625i	0.137132	+	0.158259i
$931$	−44.9098	−	2.44090i	−1.47186	−	0.0799973i
$932$	−5.15000	+	3.30970i	−0.168694	+	0.108413i
$933$	17.0944	−	3.29467i	0.559645	−	0.107863i
$934$	−9.46212	−	9.02211i	−0.309610	−	0.295212i
$935$	22.1924	−	8.88448i	0.725768	−	0.290554i
$936$	0.0650474	+	0.187942i	0.00212614	+	0.00614308i
$937$	−1.64503	+	3.60210i	−0.0537406	+	0.117676i	−0.934597	−	0.355707i	$-0.884240\pi$
$937$	−1.64503	+	3.60210i	−0.0537406	+	0.117676i	0.880857	+	0.473383i	$0.156967\pi$
$938$	−15.2801	−	31.7254i	−0.498915	−	1.03587i
$939$	−10.0808	−	22.0739i	−0.328975	−	0.720355i
$940$	10.3659	+	4.14988i	0.338099	+	0.135354i
$941$	2.21162	−	46.4276i	0.0720968	−	1.51350i	−0.615923	−	0.787806i	$-0.711217\pi$
$941$	2.21162	−	46.4276i	0.0720968	−	1.51350i	0.688020	−	0.725692i	$-0.258480\pi$
$942$	5.77166	+	9.99681i	0.188051	+	0.325714i
$943$	33.2772	−	27.0422i	1.08365	−	0.880616i
$944$	−4.99045			−0.162425
$945$	4.35835	+	1.64223i	0.141777	+	0.0534217i
$946$	4.61325	+	32.0859i	0.149990	+	1.04320i
$947$	−7.41283	−	0.707839i	−0.240884	−	0.0230017i	−0.0260845	−	0.999660i	$-0.508304\pi$
$947$	−7.41283	−	0.707839i	−0.240884	−	0.0230017i	−0.214800	+	0.976658i	$0.568910\pi$
$948$	0.0200927	+	0.0828233i	0.000652581	+	0.00268998i
$949$	0.0492490	−	0.00470270i	0.00159869	−	0.000152656i
$950$	3.99514	+	11.5432i	0.129620	+	0.374511i
$951$	2.42252	−	16.8490i	0.0785556	−	0.546367i
$952$	−0.320787	+	11.8130i	−0.0103968	+	0.382860i
$953$	7.77664	+	8.97472i	0.251910	+	0.290720i	0.867594	−	0.497274i	$-0.165666\pi$
$953$	7.77664	+	8.97472i	0.251910	+	0.290720i	−0.615684	+	0.787993i	$0.711120\pi$
$954$	−0.275415	−	5.78168i	−0.00891690	−	0.187189i
$955$	9.04409	+	4.66255i	0.292660	+	0.150877i
$956$	2.39338	−	6.91521i	0.0774074	−	0.223654i
$957$	−2.92078	+	12.0396i	−0.0944155	+	0.389186i
$958$	1.89116	−	13.1533i	0.0611007	−	0.424964i
$959$	−14.3097	−	23.6544i	−0.462083	−	0.763840i
$960$	0.731281	−	1.60128i	0.0236020	−	0.0516811i
$961$	−12.9113	+	12.3109i	−0.416494	+	0.397127i
$962$	−0.485670	+	0.682028i	−0.0156586	+	0.0219895i
$963$	13.1851	−	10.3689i	0.424884	−	0.334133i
$964$	12.0144	−	6.19387i	0.386959	−	0.199491i
$965$	−20.4476			−0.658232
$966$	−6.74053	−	10.7501i	−0.216873	−	0.345880i
$967$	−36.0234			−1.15844			−0.579218	−	0.815173i	$-0.696642\pi$
$967$	−36.0234			−1.15844			−0.579218	+	0.815173i	$0.696642\pi$
$968$	1.56149	−	0.805003i	0.0501881	−	0.0258738i
$969$	22.5582	−	17.7400i	0.724675	−	0.569891i
$970$	14.8406	−	20.8407i	0.476503	−	0.669154i
$971$	−4.13227	+	3.94011i	−0.132611	+	0.126444i	−0.753482	−	0.657468i	$-0.771627\pi$
$971$	−4.13227	+	3.94011i	−0.132611	+	0.126444i	0.620871	+	0.783912i	$0.286779\pi$
$972$	0.415415	−	0.909632i	0.0133244	−	0.0291765i
$973$	−38.0269	+	0.777796i	−1.21909	+	0.0249350i
$974$	−0.747613	+	5.19976i	−0.0239551	+	0.166611i
$975$	0.0891395	−	0.367438i	0.00285475	−	0.0117674i
$976$	2.39559	−	6.92161i	0.0766811	−	0.221555i
$977$	35.2140	+	18.1541i	1.12660	+	0.580801i	0.917754	−	0.397149i	$-0.130000\pi$
$977$	35.2140	+	18.1541i	1.12660	+	0.580801i	0.208842	+	0.977949i	$0.433031\pi$
$978$	−0.681400	−	14.3043i	−0.0217888	−	0.457402i
$979$	34.7625	+	40.1180i	1.11101	+	1.28218i
$980$	−2.25096	−	12.1152i	−0.0719043	−	0.387006i
$981$	2.86954	−	19.9581i	0.0916175	−	0.637213i
$982$	−1.74587	−	5.04437i	−0.0557131	−	0.160972i
$983$	−12.9208	+	1.23378i	−0.412108	+	0.0393516i	−0.299051	−	0.954237i	$-0.596670\pi$
$983$	−12.9208	+	1.23378i	−0.412108	+	0.0393516i	−0.113057	+	0.993589i	$0.536064\pi$
$984$	−2.10792	−	8.68896i	−0.0671980	−	0.276994i
$985$	−25.9277	−	2.47579i	−0.826124	−	0.0788852i
$986$	2.59024	+	18.0155i	0.0824900	+	0.573730i
$987$	−2.72746	−	16.5585i	−0.0868160	−	0.527063i
$988$	−1.27784			−0.0406534
$989$	−45.8187	−	22.7008i	−1.45695	−	0.721842i
$990$	2.67599	+	4.63494i	0.0850484	+	0.147308i
$991$	−0.940542	+	19.7444i	−0.0298773	+	0.627202i	0.933423	+	0.358777i	$0.116806\pi$
$991$	−0.940542	+	19.7444i	−0.0298773	+	0.627202i	−0.963301	+	0.268425i	$0.913497\pi$
$992$	−3.36783	−	1.34828i	−0.106929	−	0.0428078i
$993$	8.20749	+	17.9719i	0.260457	+	0.570321i
$994$	−16.5410	−	1.23873i	−0.524650	−	0.0392901i
$995$	−14.0631	+	30.7938i	−0.445829	+	0.976229i
$996$	2.22551	+	6.43020i	0.0705181	+	0.203749i
$997$	−13.1285	+	5.25584i	−0.415782	+	0.166454i	−0.570115	−	0.821565i	$-0.693101\pi$
$997$	−13.1285	+	5.25584i	−0.415782	+	0.166454i	0.154333	+	0.988019i	$0.450677\pi$
$998$	8.82226	+	8.41200i	0.279264	+	0.266277i
$999$	4.13389	−	0.796742i	0.130791	−	0.0252078i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.y.d.163.7	yes	160
7.4	even	3	inner	966.2.y.d.25.7	✓	160
23.12	even	11	inner	966.2.y.d.541.7	yes	160
161.81	even	33	inner	966.2.y.d.403.7	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.y.d.25.7	✓	160	7.4	even	3	inner
966.2.y.d.163.7	yes	160	1.1	even	1	trivial
966.2.y.d.403.7	yes	160	161.81	even	33	inner
966.2.y.d.541.7	yes	160	23.12	even	11	inner

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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.y (of order \(33\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.888835 + 0.458227i) q^{2} +(-0.786053 + 0.618159i) q^{3} +(0.580057 - 0.814576i) q^{4} +(1.27403 - 1.21479i) q^{5} +(0.415415 - 0.909632i) q^{6} +(2.64520 - 0.0541045i) q^{7} +(-0.142315 + 0.989821i) q^{8} +(0.235759 - 0.971812i) q^{9} +O(q^{10})\)	\(q+(-0.888835 + 0.458227i) q^{2} +(-0.786053 + 0.618159i) q^{3} +(0.580057 - 0.814576i) q^{4} +(1.27403 - 1.21479i) q^{5} +(0.415415 - 0.909632i) q^{6} +(2.64520 - 0.0541045i) q^{7} +(-0.142315 + 0.989821i) q^{8} +(0.235759 - 0.971812i) q^{9} +(-0.575758 + 1.66354i) q^{10} +(2.70230 + 1.39313i) q^{11} +(0.0475819 + 0.998867i) q^{12} +(0.130239 + 0.150304i) q^{13} +(-2.32635 + 1.26019i) q^{14} +(-0.250526 + 1.74244i) q^{15} +(-0.327068 - 0.945001i) q^{16} +(4.44630 - 0.424570i) q^{17} +(0.235759 + 0.971812i) q^{18} +(-6.39606 - 0.610750i) q^{19} +(-0.250526 - 1.74244i) q^{20} +(-2.04582 + 1.67768i) q^{21} -3.04027 q^{22} +(2.71900 - 3.95058i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-0.0904592 + 1.89897i) q^{25} +(-0.184634 - 0.0739163i) q^{26} +(0.415415 + 0.909632i) q^{27} +(1.49029 - 2.18610i) q^{28} +(1.69278 - 3.70668i) q^{29} +(-0.575758 - 1.66354i) q^{30} +(-3.36783 + 1.34828i) q^{31} +(0.723734 + 0.690079i) q^{32} +(-2.98532 + 0.575374i) q^{33} +(-3.75748 + 2.41479i) q^{34} +(3.30435 - 3.28229i) q^{35} +(-0.654861 - 0.755750i) q^{36} +(0.992538 - 4.09130i) q^{37} +(5.96491 - 2.38799i) q^{38} +(-0.195286 - 0.0376383i) q^{39} +(1.02111 + 1.43395i) q^{40} +(8.57882 + 2.51897i) q^{41} +(1.04964 - 2.42863i) q^{42} +(-1.51738 - 10.5536i) q^{43} +(2.70230 - 1.39313i) q^{44} +(-0.880181 - 1.52452i) q^{45} +(-0.606482 + 4.75733i) q^{46} +(-3.17143 + 5.49308i) q^{47} +(0.841254 + 0.540641i) q^{48} +(6.99415 - 0.286234i) q^{49} +(-0.789756 - 1.72932i) q^{50} +(-3.23258 + 3.08226i) q^{51} +(0.197980 - 0.0189048i) q^{52} +(-5.68363 - 1.09543i) q^{53} +(-0.786053 - 0.618159i) q^{54} +(5.13518 - 1.50782i) q^{55} +(-0.322897 + 2.62597i) q^{56} +(5.40519 - 3.47370i) q^{57} +(0.193893 + 4.07031i) q^{58} +(1.63222 - 4.71598i) q^{59} +(1.27403 + 1.21479i) q^{60} +(5.75741 + 4.52767i) q^{61} +(2.37563 - 2.74162i) q^{62} +(0.571050 - 2.58339i) q^{63} +(-0.959493 - 0.281733i) q^{64} +(0.348516 + 0.0332792i) q^{65} +(2.38981 - 1.87937i) q^{66} +(-0.633288 + 13.2943i) q^{67} +(2.23326 - 3.86812i) q^{68} +(0.304808 + 4.78614i) q^{69} +(-1.43299 + 4.43155i) q^{70} +(5.27418 + 3.38951i) q^{71} +(0.928368 + 0.371662i) q^{72} +(0.144294 - 0.202632i) q^{73} +(0.992538 + 4.09130i) q^{74} +(-1.10276 - 1.54861i) q^{75} +(-4.20758 + 4.85581i) q^{76} +(7.22348 + 3.53890i) q^{77} +(0.190824 - 0.0560310i) q^{78} +(0.0836856 - 0.0161291i) q^{79} +(-1.56467 - 0.806645i) q^{80} +(-0.888835 - 0.458227i) q^{81} +(-8.77942 + 1.69209i) q^{82} +(6.52881 - 1.91703i) q^{83} +(0.179907 + 2.63963i) q^{84} +(5.14898 - 5.94223i) q^{85} +(6.18466 + 8.68514i) q^{86} +(0.960700 + 3.96006i) q^{87} +(-1.76353 + 2.47653i) q^{88} +(16.2095 + 6.48931i) q^{89} +(1.48091 + 0.951724i) q^{90} +(0.352640 + 0.390536i) q^{91} +(-1.64087 - 4.50639i) q^{92} +(1.81384 - 3.14167i) q^{93} +(0.301805 - 6.33568i) q^{94} +(-8.89073 + 6.99175i) q^{95} +(-0.995472 - 0.0950560i) q^{96} +(-13.9451 - 4.09464i) q^{97} +(-6.08548 + 3.45932i) q^{98} +(1.99095 - 2.29768i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q + 8 q^{2} + 8 q^{3} + 8 q^{4} - 2 q^{5} - 16 q^{6} + 6 q^{7} - 16 q^{8} + 8 q^{9}+O(q^{10}) \) 160 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 - 2 * q^5 - 16 * q^6 + 6 * q^7 - 16 * q^8 + 8 * q^9	\( 160 q + 8 q^{2} + 8 q^{3} + 8 q^{4} - 2 q^{5} - 16 q^{6} + 6 q^{7} - 16 q^{8} + 8 q^{9} - 2 q^{10} - 4 q^{11} + 8 q^{12} - 4 q^{13} + 5 q^{14} + 26 q^{15} + 8 q^{16} - 13 q^{17} + 8 q^{18} + 4 q^{19} + 26 q^{20} + 11 q^{21} - 124 q^{22} + 26 q^{23} - 80 q^{24} + 14 q^{25} + 2 q^{26} - 16 q^{27} - 22 q^{28} + 54 q^{29} - 2 q^{30} + 15 q^{31} + 8 q^{32} - 4 q^{33} + 4 q^{34} - 2 q^{35} - 16 q^{36} + 7 q^{37} - 7 q^{38} + 2 q^{39} + 9 q^{40} - 30 q^{41} + 6 q^{42} + 36 q^{43} - 4 q^{44} + 20 q^{45} + 4 q^{46} - 6 q^{47} - 16 q^{48} + 14 q^{49} - 28 q^{50} + 9 q^{51} + 2 q^{52} - 24 q^{53} + 8 q^{54} - 14 q^{55} + 6 q^{56} - 30 q^{57} - 5 q^{58} + 4 q^{59} - 2 q^{60} + 32 q^{61} - 8 q^{62} - 6 q^{63} - 16 q^{64} + 38 q^{65} - 4 q^{66} + 6 q^{67} + 42 q^{68} - 30 q^{69} - 8 q^{70} - 180 q^{71} + 8 q^{72} - 32 q^{73} + 7 q^{74} + 14 q^{75} - 8 q^{76} + 61 q^{77} + 18 q^{78} - 66 q^{79} - 2 q^{80} + 8 q^{81} - 7 q^{82} + 130 q^{83} + 5 q^{84} - 70 q^{85} - 40 q^{86} + 6 q^{87} - 15 q^{88} - 4 q^{89} + 4 q^{90} - 6 q^{91} + 58 q^{92} - 18 q^{93} + 16 q^{94} + 19 q^{95} + 8 q^{96} + 40 q^{97} + 43 q^{98} + 8 q^{99}+O(q^{100}) \) 160 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 - 2 * q^5 - 16 * q^6 + 6 * q^7 - 16 * q^8 + 8 * q^9 - 2 * q^10 - 4 * q^11 + 8 * q^12 - 4 * q^13 + 5 * q^14 + 26 * q^15 + 8 * q^16 - 13 * q^17 + 8 * q^18 + 4 * q^19 + 26 * q^20 + 11 * q^21 - 124 * q^22 + 26 * q^23 - 80 * q^24 + 14 * q^25 + 2 * q^26 - 16 * q^27 - 22 * q^28 + 54 * q^29 - 2 * q^30 + 15 * q^31 + 8 * q^32 - 4 * q^33 + 4 * q^34 - 2 * q^35 - 16 * q^36 + 7 * q^37 - 7 * q^38 + 2 * q^39 + 9 * q^40 - 30 * q^41 + 6 * q^42 + 36 * q^43 - 4 * q^44 + 20 * q^45 + 4 * q^46 - 6 * q^47 - 16 * q^48 + 14 * q^49 - 28 * q^50 + 9 * q^51 + 2 * q^52 - 24 * q^53 + 8 * q^54 - 14 * q^55 + 6 * q^56 - 30 * q^57 - 5 * q^58 + 4 * q^59 - 2 * q^60 + 32 * q^61 - 8 * q^62 - 6 * q^63 - 16 * q^64 + 38 * q^65 - 4 * q^66 + 6 * q^67 + 42 * q^68 - 30 * q^69 - 8 * q^70 - 180 * q^71 + 8 * q^72 - 32 * q^73 + 7 * q^74 + 14 * q^75 - 8 * q^76 + 61 * q^77 + 18 * q^78 - 66 * q^79 - 2 * q^80 + 8 * q^81 - 7 * q^82 + 130 * q^83 + 5 * q^84 - 70 * q^85 - 40 * q^86 + 6 * q^87 - 15 * q^88 - 4 * q^89 + 4 * q^90 - 6 * q^91 + 58 * q^92 - 18 * q^93 + 16 * q^94 + 19 * q^95 + 8 * q^96 + 40 * q^97 + 43 * q^98 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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