LMFDB - Embedded newform 309.2.i.b.100.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [309,2,Mod(13,309)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(309, base_ring=CyclotomicField(34))

chi = DirichletCharacter(H, H._module([0, 24]))

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

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

chi := DirichletCharacter("309.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 309 = 3 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	309.i (of order $17$, degree $16$, 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:	$2.46737742246$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$10$ over $\Q(\zeta_{17})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{17}]$

Embedding invariants

Embedding label			100.10
Character	$\chi$	$=$	309.100
Dual form			309.2.i.b.34.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.16143 - 1.33830i) q^{2} +(-0.273663 - 0.961826i) q^{3} +(1.98927 - 3.99498i) q^{4} +(-1.14272 + 0.442694i) q^{5} +(-1.87872 - 1.71268i) q^{6} +(-0.0140028 + 0.151114i) q^{7} +(-0.577702 - 6.23440i) q^{8} +(-0.850217 + 0.526432i) q^{9} +O(q^{10})$	\(q+(2.16143 - 1.33830i) q^{2} +(-0.273663 - 0.961826i) q^{3} +(1.98927 - 3.99498i) q^{4} +(-1.14272 + 0.442694i) q^{5} +(-1.87872 - 1.71268i) q^{6} +(-0.0140028 + 0.151114i) q^{7} +(-0.577702 - 6.23440i) q^{8} +(-0.850217 + 0.526432i) q^{9} +(-1.87746 + 2.48616i) q^{10} +(2.29432 - 1.42058i) q^{11} +(-4.38687 - 0.820048i) q^{12} +(-0.118547 + 1.27933i) q^{13} +(0.171970 + 0.345363i) q^{14} +(0.738515 + 0.977952i) q^{15} +(-4.21324 - 5.57923i) q^{16} +(-0.583492 + 0.531923i) q^{17} +(-1.13316 + 2.27570i) q^{18} +(-0.297622 + 1.04603i) q^{19} +(-0.504628 + 5.44580i) q^{20} +(0.149177 - 0.0278861i) q^{21} +(3.05785 - 6.14100i) q^{22} +(3.93308 + 2.43526i) q^{23} +(-5.83831 + 2.26177i) q^{24} +(-2.58520 + 2.35672i) q^{25} +(1.45590 + 2.92384i) q^{26} +(0.739009 + 0.673696i) q^{27} +(0.575843 + 0.356547i) q^{28} +(1.74621 - 0.676484i) q^{29} +(2.90505 + 1.12542i) q^{30} +(2.71210 + 3.59140i) q^{31} +(-4.89673 - 1.89700i) q^{32} +(-1.99422 - 1.81798i) q^{33} +(-0.549305 + 1.93061i) q^{34} +(-0.0508959 - 0.178880i) q^{35} +(0.411780 + 4.44382i) q^{36} +(6.47604 + 1.21058i) q^{37} +(0.756618 + 2.65924i) q^{38} +(1.26293 - 0.236083i) q^{39} +(3.42008 + 6.86845i) q^{40} +(-11.0291 - 4.27271i) q^{41} +(0.285117 - 0.259918i) q^{42} +(-6.98286 + 1.30532i) q^{43} +(-1.11119 - 11.9917i) q^{44} +(0.738515 - 0.977952i) q^{45} +11.7602 q^{46} -0.266802 q^{47} +(-4.21324 + 5.57923i) q^{48} +(6.85817 + 1.28201i) q^{49} +(-2.43374 + 8.55369i) q^{50} +(0.671297 + 0.415650i) q^{51} +(4.87508 + 3.01852i) q^{52} +(3.37263 - 11.8536i) q^{53} +(2.49893 + 0.467131i) q^{54} +(-1.99289 + 2.63902i) q^{55} +0.950194 q^{56} +1.08755 q^{57} +(2.86897 - 3.79913i) q^{58} +(-0.438528 - 4.73247i) q^{59} +(5.37601 - 1.00495i) q^{60} +(-8.00207 + 7.29485i) q^{61} +(10.6684 + 4.13296i) q^{62} +(-0.0676458 - 0.135851i) q^{63} +(0.621923 - 0.116258i) q^{64} +(-0.430884 - 1.51440i) q^{65} +(-6.74339 - 1.26056i) q^{66} +(0.590906 + 6.37689i) q^{67} +(0.964304 + 3.38918i) q^{68} +(1.26596 - 4.44938i) q^{69} +(-0.349404 - 0.318524i) q^{70} +(-10.5786 - 4.09816i) q^{71} +(3.77316 + 4.99647i) q^{72} +(-9.47372 - 3.67014i) q^{73} +(15.6177 - 6.05031i) q^{74} +(2.97423 + 1.84157i) q^{75} +(3.58683 + 3.26983i) q^{76} +(0.182543 + 0.366596i) q^{77} +(2.41380 - 2.20047i) q^{78} +(-4.68402 + 1.81460i) q^{79} +(7.28446 + 4.51035i) q^{80} +(0.445738 - 0.895163i) q^{81} +(-29.5569 + 5.52515i) q^{82} +(-1.09018 + 11.7649i) q^{83} +(0.185349 - 0.651434i) q^{84} +(0.431291 - 0.866149i) q^{85} +(-13.3461 + 12.1666i) q^{86} +(-1.12853 - 1.49442i) q^{87} +(-10.1819 - 13.4830i) q^{88} +(0.787694 + 1.58190i) q^{89} +(0.287455 - 3.10214i) q^{90} +(-0.191665 - 0.0358283i) q^{91} +(17.5528 - 10.8682i) q^{92} +(2.71210 - 3.59140i) q^{93} +(-0.576676 + 0.357063i) q^{94} +(-0.122972 - 1.32708i) q^{95} +(-0.484533 + 5.22894i) q^{96} +(6.38776 + 5.82322i) q^{97} +(16.5392 - 6.40733i) q^{98} +(-1.20283 + 2.41561i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q - q^{2} - 10 q^{3} - 17 q^{4} - 4 q^{5} - q^{6} - 12 q^{7} + 36 q^{8} - 10 q^{9}+O(q^{10}) $ 160 * q - q^2 - 10 * q^3 - 17 * q^4 - 4 * q^5 - q^6 - 12 * q^7 + 36 * q^8 - 10 * q^9	\( 160 q - q^{2} - 10 q^{3} - 17 q^{4} - 4 q^{5} - q^{6} - 12 q^{7} + 36 q^{8} - 10 q^{9} + 12 q^{10} + q^{11} + 17 q^{12} - 18 q^{13} + 31 q^{14} - 4 q^{15} - 39 q^{16} - 14 q^{17} - q^{18} - 11 q^{19} + 31 q^{20} + 5 q^{21} + 3 q^{23} - 15 q^{24} - 8 q^{25} - 33 q^{26} - 10 q^{27} - 2 q^{28} - 28 q^{29} + 12 q^{30} - 20 q^{31} - 46 q^{32} + 18 q^{33} + 5 q^{34} - 3 q^{35} - 17 q^{36} - 34 q^{37} - 14 q^{38} - 18 q^{39} - 56 q^{40} + 40 q^{41} + 14 q^{42} - 42 q^{43} - 26 q^{44} - 4 q^{45} + 112 q^{46} - 40 q^{47} - 39 q^{48} + 30 q^{49} - 10 q^{50} + 3 q^{51} - 58 q^{52} - 48 q^{53} - q^{54} - 64 q^{55} + 86 q^{56} + 6 q^{57} - 36 q^{58} + 76 q^{59} - 20 q^{60} - 28 q^{61} - 66 q^{62} - 12 q^{63} + 88 q^{64} - 14 q^{65} - 34 q^{66} - 84 q^{67} - 107 q^{68} - 14 q^{69} + 8 q^{70} + 41 q^{71} - 15 q^{72} - 32 q^{73} + 3 q^{74} - 42 q^{75} - 68 q^{76} + 93 q^{77} + 18 q^{78} - 100 q^{79} - 168 q^{80} - 10 q^{81} + 99 q^{82} - 28 q^{83} + 151 q^{84} + 15 q^{85} + 64 q^{86} - 11 q^{87} - 25 q^{88} - 19 q^{89} - 5 q^{90} + 122 q^{91} - 78 q^{92} - 20 q^{93} + 138 q^{94} - 15 q^{95} + 56 q^{96} + 161 q^{97} + 65 q^{98} + q^{99}+O(q^{100}) \) 160 * q - q^2 - 10 * q^3 - 17 * q^4 - 4 * q^5 - q^6 - 12 * q^7 + 36 * q^8 - 10 * q^9 + 12 * q^10 + q^11 + 17 * q^12 - 18 * q^13 + 31 * q^14 - 4 * q^15 - 39 * q^16 - 14 * q^17 - q^18 - 11 * q^19 + 31 * q^20 + 5 * q^21 + 3 * q^23 - 15 * q^24 - 8 * q^25 - 33 * q^26 - 10 * q^27 - 2 * q^28 - 28 * q^29 + 12 * q^30 - 20 * q^31 - 46 * q^32 + 18 * q^33 + 5 * q^34 - 3 * q^35 - 17 * q^36 - 34 * q^37 - 14 * q^38 - 18 * q^39 - 56 * q^40 + 40 * q^41 + 14 * q^42 - 42 * q^43 - 26 * q^44 - 4 * q^45 + 112 * q^46 - 40 * q^47 - 39 * q^48 + 30 * q^49 - 10 * q^50 + 3 * q^51 - 58 * q^52 - 48 * q^53 - q^54 - 64 * q^55 + 86 * q^56 + 6 * q^57 - 36 * q^58 + 76 * q^59 - 20 * q^60 - 28 * q^61 - 66 * q^62 - 12 * q^63 + 88 * q^64 - 14 * q^65 - 34 * q^66 - 84 * q^67 - 107 * q^68 - 14 * q^69 + 8 * q^70 + 41 * q^71 - 15 * q^72 - 32 * q^73 + 3 * q^74 - 42 * q^75 - 68 * q^76 + 93 * q^77 + 18 * q^78 - 100 * q^79 - 168 * q^80 - 10 * q^81 + 99 * q^82 - 28 * q^83 + 151 * q^84 + 15 * q^85 + 64 * q^86 - 11 * q^87 - 25 * q^88 - 19 * q^89 - 5 * q^90 + 122 * q^91 - 78 * q^92 - 20 * q^93 + 138 * q^94 - 15 * q^95 + 56 * q^96 + 161 * q^97 + 65 * q^98 + q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/309\mathbb{Z}\right)^\times$.

$n$	$104$	$211$
$\chi(n)$	$1$	$e\left(\frac{15}{17}\right)$

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 $

$2$	2.16143	−	1.33830i	1.52836	−	0.946324i	0.533426	−	0.845847i	$-0.320904\pi$
$2$	2.16143	−	1.33830i	1.52836	−	0.946324i	0.994939	−	0.100476i	$-0.0320367\pi$
$3$	−0.273663	−	0.961826i	−0.157999	−	0.555310i
$3$	−0.273663	−	0.961826i	−0.157999	−	0.555310i
$4$	1.98927	−	3.99498i	0.994633	−	1.99749i
$5$	−1.14272	+	0.442694i	−0.511042	+	0.197979i	−0.602935	−	0.797790i	$-0.706002\pi$
$5$	−1.14272	+	0.442694i	−0.511042	+	0.197979i	0.0918934	+	0.995769i	$0.470708\pi$
$6$	−1.87872	−	1.71268i	−0.766984	−	0.699198i
$7$	−0.0140028	+	0.151114i	−0.00529255	+	0.0571157i	−0.997971	−	0.0636726i	$-0.979719\pi$
$7$	−0.0140028	+	0.151114i	−0.00529255	+	0.0571157i	0.992678	+	0.120788i	$0.0385422\pi$
$8$	−0.577702	−	6.23440i	−0.204249	−	2.20419i
$9$	−0.850217	+	0.526432i	−0.283406	+	0.175477i
$10$	−1.87746	+	2.48616i	−0.593706	+	0.786194i
$11$	2.29432	−	1.42058i	0.691764	−	0.428322i	−0.135019	−	0.990843i	$-0.543110\pi$
$11$	2.29432	−	1.42058i	0.691764	−	0.428322i	0.826783	+	0.562521i	$0.190168\pi$
$12$	−4.38687	−	0.820048i	−1.26638	−	0.236727i
$13$	−0.118547	+	1.27933i	−0.0328791	+	0.354822i	0.963362	+	0.268203i	$0.0864298\pi$
$13$	−0.118547	+	1.27933i	−0.0328791	+	0.354822i	−0.996242	+	0.0866190i	$0.972394\pi$
$14$	0.171970	+	0.345363i	0.0459610	+	0.0923021i
$15$	0.738515	+	0.977952i	0.190684	+	0.252506i
$16$	−4.21324	−	5.57923i	−1.05331	−	1.39481i
$17$	−0.583492	+	0.531923i	−0.141517	+	0.129010i	−0.741359	−	0.671108i	$-0.765818\pi$
$17$	−0.583492	+	0.531923i	−0.141517	+	0.129010i	0.599842	+	0.800119i	$0.295230\pi$
$18$	−1.13316	+	2.27570i	−0.267089	+	0.536387i
$19$	−0.297622	+	1.04603i	−0.0682791	+	0.239976i	−0.988452	−	0.151537i	$-0.951578\pi$
$19$	−0.297622	+	1.04603i	−0.0682791	+	0.239976i	0.920172	+	0.391513i	$0.128048\pi$
$20$	−0.504628	+	5.44580i	−0.112838	+	1.21772i
$21$	0.149177	−	0.0278861i	0.0325532	−	0.00608524i
$22$	3.05785	−	6.14100i	0.651936	−	1.30926i
$23$	3.93308	+	2.43526i	0.820104	+	0.507787i	0.871212	−	0.490906i	$-0.163334\pi$
$23$	3.93308	+	2.43526i	0.820104	+	0.507787i	−0.0511083	+	0.998693i	$0.516275\pi$
$24$	−5.83831	+	2.26177i	−1.19174	+	0.461682i
$25$	−2.58520	+	2.35672i	−0.517041	+	0.471345i
$26$	1.45590	+	2.92384i	0.285525	+	0.573412i
$27$	0.739009	+	0.673696i	0.142222	+	0.129653i
$28$	0.575843	+	0.356547i	0.108824	+	0.0673810i
$29$	1.74621	−	0.676484i	0.324262	−	0.125620i	−0.193608	−	0.981079i	$-0.562019\pi$
$29$	1.74621	−	0.676484i	0.324262	−	0.125620i	0.517870	+	0.855459i	$0.326725\pi$
$30$	2.90505	+	1.12542i	0.530387	+	0.205473i
$31$	2.71210	+	3.59140i	0.487107	+	0.645034i	0.973495	−	0.228709i	$-0.0734503\pi$
$31$	2.71210	+	3.59140i	0.487107	+	0.645034i	−0.486387	+	0.873743i	$0.661686\pi$
$32$	−4.89673	−	1.89700i	−0.865628	−	0.335346i
$33$	−1.99422	−	1.81798i	−0.347150	−	0.316469i
$34$	−0.549305	+	1.93061i	−0.0942050	+	0.331096i
$35$	−0.0508959	−	0.178880i	−0.00860297	−	0.0302363i
$36$	0.411780	+	4.44382i	0.0686301	+	0.740636i
$37$	6.47604	+	1.21058i	1.06465	+	0.199018i	0.686800	−	0.726847i	$-0.259015\pi$
$37$	6.47604	+	1.21058i	1.06465	+	0.199018i	0.377854	+	0.925865i	$0.376662\pi$
$38$	0.756618	+	2.65924i	0.122740	+	0.431385i
$39$	1.26293	−	0.236083i	0.202231	−	0.0378036i
$40$	3.42008	+	6.86845i	0.540763	+	1.08600i
$41$	−11.0291	−	4.27271i	−1.72246	−	0.667285i	−0.722745	−	0.691115i	$-0.757120\pi$
$41$	−11.0291	−	4.27271i	−1.72246	−	0.667285i	−0.999716	+	0.0238304i	$0.992414\pi$
$42$	0.285117	−	0.259918i	0.0439945	−	0.0401063i
$43$	−6.98286	+	1.30532i	−1.06488	+	0.199060i	−0.686897	−	0.726755i	$-0.741028\pi$
$43$	−6.98286	+	1.30532i	−1.06488	+	0.199060i	−0.377979	+	0.925814i	$0.623381\pi$
$44$	−1.11119	−	11.9917i	−0.167519	−	1.80782i
$45$	0.738515	−	0.977952i	0.110091	−	0.145785i
$46$	11.7602			1.73395
$47$	−0.266802			−0.0389171			−0.0194586	−	0.999811i	$-0.506194\pi$
$47$	−0.266802			−0.0389171			−0.0194586	+	0.999811i	$0.506194\pi$
$48$	−4.21324	+	5.57923i	−0.608129	+	0.805293i
$49$	6.85817	+	1.28201i	0.979739	+	0.183145i
$50$	−2.43374	+	8.55369i	−0.344182	+	1.20968i
$51$	0.671297	+	0.415650i	0.0940004	+	0.0582026i
$52$	4.87508	+	3.01852i	0.676052	+	0.418594i
$53$	3.37263	−	11.8536i	0.463267	−	1.62821i	−0.280556	−	0.959838i	$-0.590519\pi$
$53$	3.37263	−	11.8536i	0.463267	−	1.62821i	0.743823	−	0.668376i	$-0.233010\pi$
$54$	2.49893	+	0.467131i	0.340061	+	0.0635684i
$55$	−1.99289	+	2.63902i	−0.268722	+	0.355845i
$56$	0.950194			0.126975
$57$	1.08755			0.144049
$58$	2.86897	−	3.79913i	0.376714	−	0.498850i
$59$	−0.438528	−	4.73247i	−0.0570915	−	0.616115i	−0.975429	−	0.220316i	$-0.929291\pi$
$59$	−0.438528	−	4.73247i	−0.0570915	−	0.616115i	0.918337	−	0.395799i	$-0.129532\pi$
$60$	5.37601	−	1.00495i	0.694040	−	0.129738i
$61$	−8.00207	+	7.29485i	−1.02456	+	0.934010i	−0.997844	−	0.0656327i	$-0.979093\pi$
$61$	−8.00207	+	7.29485i	−1.02456	+	0.934010i	−0.0267167	+	0.999643i	$0.508505\pi$
$62$	10.6684	+	4.13296i	1.35489	+	0.524887i
$63$	−0.0676458	−	0.135851i	−0.00852258	−	0.0171156i
$64$	0.621923	−	0.116258i	0.0777404	−	0.0145322i
$65$	−0.430884	−	1.51440i	−0.0534446	−	0.187838i
$66$	−6.74339	−	1.26056i	−0.830054	−	0.155164i
$67$	0.590906	+	6.37689i	0.0721907	+	0.779061i	0.952475	+	0.304615i	$0.0985280\pi$
$67$	0.590906	+	6.37689i	0.0721907	+	0.779061i	−0.880285	+	0.474446i	$0.842649\pi$
$68$	0.964304	+	3.38918i	0.116939	+	0.410998i
$69$	1.26596	−	4.44938i	0.152403	−	0.535642i
$70$	−0.349404	−	0.318524i	−0.0417618	−	0.0380709i
$71$	−10.5786	−	4.09816i	−1.25544	−	0.486362i	−0.360592	−	0.932724i	$-0.617425\pi$
$71$	−10.5786	−	4.09816i	−1.25544	−	0.486362i	−0.894853	+	0.446362i	$0.852719\pi$
$72$	3.77316	+	4.99647i	0.444671	+	0.588840i
$73$	−9.47372	−	3.67014i	−1.10882	−	0.429557i	−0.263950	−	0.964536i	$-0.585025\pi$
$73$	−9.47372	−	3.67014i	−1.10882	−	0.429557i	−0.844865	+	0.534979i	$0.820320\pi$
$74$	15.6177	−	6.05031i	1.81552	−	0.703334i
$75$	2.97423	+	1.84157i	0.343435	+	0.212646i
$76$	3.58683	+	3.26983i	0.411438	+	0.375075i
$77$	0.182543	+	0.366596i	0.0208027	+	0.0417775i
$78$	2.41380	−	2.20047i	0.273309	−	0.249154i
$79$	−4.68402	+	1.81460i	−0.526994	+	0.204158i	−0.610016	−	0.792389i	$-0.708837\pi$
$79$	−4.68402	+	1.81460i	−0.526994	+	0.204158i	0.0830222	+	0.996548i	$0.473543\pi$
$80$	7.28446	+	4.51035i	0.814427	+	0.504272i
$81$	0.445738	−	0.895163i	0.0495265	−	0.0994626i
$82$	−29.5569	+	5.52515i	−3.26402	+	0.610150i
$83$	−1.09018	+	11.7649i	−0.119662	+	1.29136i	0.698180	+	0.715922i	$0.253993\pi$
$83$	−1.09018	+	11.7649i	−0.119662	+	1.29136i	−0.817843	+	0.575442i	$0.804830\pi$
$84$	0.185349	−	0.651434i	0.0202232	−	0.0710773i
$85$	0.431291	−	0.866149i	0.0467801	−	0.0939471i
$86$	−13.3461	+	12.1666i	−1.43914	+	1.31195i
$87$	−1.12853	−	1.49442i	−0.120991	−	0.160218i
$88$	−10.1819	−	13.4830i	−1.08540	−	1.43730i
$89$	0.787694	+	1.58190i	0.0834954	+	0.167681i	0.932976	−	0.359938i	$-0.117202\pi$
$89$	0.787694	+	1.58190i	0.0834954	+	0.167681i	−0.849481	+	0.527620i	$0.823085\pi$
$90$	0.287455	−	3.10214i	0.0303005	−	0.326994i
$91$	−0.191665	−	0.0358283i	−0.0200919	−	0.00375583i
$92$	17.5528	−	10.8682i	1.83000	−	1.13309i
$93$	2.71210	−	3.59140i	0.281232	−	0.372411i
$94$	−0.576676	+	0.357063i	−0.0594796	+	0.0368282i
$95$	−0.122972	−	1.32708i	−0.0126167	−	0.136156i
$96$	−0.484533	+	5.22894i	−0.0494524	+	0.533676i
$97$	6.38776	+	5.82322i	0.648579	+	0.591258i	0.929657	−	0.368427i	$-0.120104\pi$
$97$	6.38776	+	5.82322i	0.648579	+	0.591258i	−0.281078	+	0.959685i	$0.590692\pi$
$98$	16.5392	−	6.40733i	1.67071	−	0.647238i
$99$	−1.20283	+	2.41561i	−0.120889	+	0.242778i
$100$	4.27242	+	15.0160i	0.427242	+	1.50160i
$101$	−2.94556	+	1.82381i	−0.293094	+	0.181476i	−0.665100	−	0.746754i	$-0.731611\pi$
$101$	−2.94556	+	1.82381i	−0.293094	+	0.181476i	0.372006	+	0.928230i	$0.378670\pi$
$102$	2.00723			0.198745
$103$	−6.57437	−	7.73160i	−0.647792	−	0.761817i
$103$	−6.57437	−	7.73160i	−0.647792	−	0.761817i
$104$	8.04433			0.788812
$105$	−0.158124	+	0.0979059i	−0.0154313	+	0.00955464i
$106$	−8.57396	−	30.1343i	−0.832776	−	2.92691i
$107$	1.49155	−	2.99543i	0.144193	−	0.289579i	−0.811280	−	0.584658i	$-0.801229\pi$
$107$	1.49155	−	2.99543i	0.144193	−	0.289579i	0.955473	+	0.295080i	$0.0953462\pi$
$108$	4.16149	−	1.61217i	0.400439	−	0.155131i
$109$	−8.83765	−	8.05658i	−0.846493	−	0.771681i	0.129015	−	0.991643i	$-0.458818\pi$
$109$	−8.83765	−	8.05658i	−0.846493	−	0.771681i	−0.975508	+	0.219962i	$0.929407\pi$
$110$	−0.775702	+	8.37116i	−0.0739603	+	0.798158i
$111$	−0.607884	−	6.56011i	−0.0576978	−	0.622658i
$112$	0.902097	−	0.558555i	0.0852401	−	0.0527784i
$113$	2.61284	−	3.45996i	0.245796	−	0.325486i	−0.658349	−	0.752713i	$-0.728745\pi$
$113$	2.61284	−	3.45996i	0.245796	−	0.325486i	0.904144	+	0.427227i	$0.140509\pi$
$114$	2.35066	−	1.45547i	0.220160	−	0.136317i
$115$	−5.57250	−	1.04168i	−0.519638	−	0.0971373i
$116$	0.771126	−	8.32177i	0.0715972	−	0.772657i
$117$	−0.572689	−	1.15011i	−0.0529451	−	0.106328i
$118$	−7.28133	−	9.64204i	−0.670301	−	0.887622i
$119$	−0.0722105	−	0.0956221i	−0.00661952	−	0.00876566i
$120$	5.67030	−	5.16916i	0.517625	−	0.471878i
$121$	−1.65727	+	3.32825i	−0.150661	+	0.302568i
$122$	−7.53323	+	26.4766i	−0.682026	+	2.39707i
$123$	−1.09134	+	11.7774i	−0.0984024	+	1.06193i
$124$	19.7427	−	3.69055i	1.77294	−	0.331421i
$125$	4.64208	−	9.32255i	0.415200	−	0.833835i
$126$	−0.328022	−	0.203103i	−0.0292225	−	0.0180938i
$127$	−1.49085	+	0.577558i	−0.132292	+	0.0512500i	−0.426477	−	0.904498i	$-0.640246\pi$
$127$	−1.49085	+	0.577558i	−0.132292	+	0.0512500i	0.294186	+	0.955748i	$0.404952\pi$
$128$	8.95024	−	8.15922i	0.791097	−	0.721180i
$129$	3.16644	+	6.35907i	0.278790	+	0.559885i
$130$	−2.95806	−	2.69662i	−0.259439	−	0.236510i
$131$	7.79571	+	4.82690i	0.681115	+	0.421728i	0.822913	−	0.568167i	$-0.192347\pi$
$131$	7.79571	+	4.82690i	0.681115	+	0.421728i	−0.141799	+	0.989896i	$0.545289\pi$
$132$	−11.2298	+	4.35046i	−0.977431	+	0.378659i
$133$	−0.153902	−	0.0596221i	−0.0133450	−	0.00516989i
$134$	9.81142	+	12.9924i	0.847578	+	1.12237i
$135$	−1.14272	−	0.442694i	−0.0983500	−	0.0381010i
$136$	3.65330	+	3.33043i	0.313268	+	0.285582i
$137$	4.31353	−	15.1605i	0.368529	−	1.29525i	−0.526856	−	0.849955i	$-0.676629\pi$
$137$	4.31353	−	15.1605i	0.368529	−	1.29525i	0.895385	−	0.445292i	$-0.146900\pi$
$138$	−3.21834	−	11.3113i	−0.273963	−	0.962880i
$139$	1.59237	+	17.1844i	0.135063	+	1.45756i	0.746035	+	0.665907i	$0.231955\pi$
$139$	1.59237	+	17.1844i	0.135063	+	1.45756i	−0.610972	+	0.791652i	$0.709221\pi$
$140$	−0.815870	−	0.152513i	−0.0689536	−	0.0128897i
$141$	0.0730139	+	0.256617i	0.00614888	+	0.0216111i
$142$	−28.3495	+	5.29943i	−2.37903	+	0.444718i
$143$	1.54541	+	3.10360i	0.129234	+	0.259536i
$144$	6.51926	+	2.52557i	0.543271	+	0.210464i
$145$	−1.69596	+	1.54607i	−0.140841	+	0.128394i
$146$	−25.3886	+	4.74595i	−2.10118	+	0.392778i
$147$	−0.643753	−	6.94721i	−0.0530959	−	0.572996i
$148$	17.7188	−	23.4635i	1.45648	−	1.92869i
$149$	−10.9984			−0.901028			−0.450514	−	0.892769i	$-0.648759\pi$
$149$	−10.9984			−0.901028			−0.450514	+	0.892769i	$0.648759\pi$
$150$	8.89319			0.726126
$151$	−7.06250	+	9.35226i	−0.574738	+	0.761076i	−0.988812	−	0.149167i	$-0.952341\pi$
$151$	−7.06250	+	9.35226i	−0.574738	+	0.761076i	0.414074	+	0.910243i	$0.364105\pi$
$152$	6.69331	+	1.25120i	0.542899	+	0.101485i
$153$	0.216073	−	0.759419i	0.0174685	−	0.0613954i
$154$	0.885172	+	0.548075i	0.0713292	+	0.0441652i
$155$	−4.68907	−	2.90335i	−0.376635	−	0.233203i
$156$	1.56916	−	5.51503i	0.125634	−	0.441556i
$157$	5.89281	+	1.10156i	0.470297	+	0.0879138i	0.413563	−	0.910475i	$-0.364284\pi$
$157$	5.89281	+	1.10156i	0.470297	+	0.0879138i	0.0567344	+	0.998389i	$0.481931\pi$
$158$	−7.69572	+	10.1908i	−0.612239	+	0.810735i
$159$	−12.3240			−0.977360
$160$	6.43540			0.508763
$161$	−0.423076	+	0.560243i	−0.0333431	+	0.0441533i
$162$	−0.234566	−	2.53137i	−0.0184292	−	0.198883i
$163$	−13.1489	+	2.45796i	−1.02990	+	0.192522i	−0.671468	−	0.741033i	$-0.734336\pi$
$163$	−13.1489	+	2.45796i	−1.02990	+	0.192522i	−0.358433	+	0.933555i	$0.616689\pi$
$164$	−39.0093	+	35.5616i	−3.04611	+	2.77690i
$165$	3.08365	+	1.19461i	0.240062	+	0.0930006i
$166$	13.3886	+	26.8880i	1.03916	+	2.08691i
$167$	1.92159	−	0.359207i	0.148697	−	0.0277963i	−0.108875	−	0.994055i	$-0.534725\pi$
$167$	1.92159	−	0.359207i	0.148697	−	0.0277963i	0.257572	+	0.966259i	$0.417078\pi$
$168$	−0.260033	−	0.913921i	−0.0200620	−	0.0705105i
$169$	11.1560	+	2.08542i	0.858155	+	0.160417i
$170$	−0.226963	−	2.44932i	−0.0174073	−	0.187854i
$171$	−0.297622	−	1.04603i	−0.0227597	−	0.0799920i
$172$	−8.67602	+	30.4930i	−0.661540	+	2.32507i
$173$	−15.2359	−	13.8893i	−1.15836	−	1.05599i	−0.997617	−	0.0689899i	$-0.978022\pi$
$173$	−15.2359	−	13.8893i	−1.15836	−	1.05599i	−0.160744	−	0.986996i	$-0.551389\pi$
$174$	−4.43923	−	1.71977i	−0.336537	−	0.130375i
$175$	−0.319934	−	0.423661i	−0.0241847	−	0.0320258i
$176$	−17.5923	−	6.81529i	−1.32607	−	0.513722i
$177$	−4.43180	+	1.71689i	−0.333115	+	0.129049i
$178$	3.81962	+	2.36501i	0.286292	+	0.177265i
$179$	11.8016	+	10.7586i	0.882095	+	0.804135i	0.981609	−	0.190901i	$-0.0611408\pi$
$179$	11.8016	+	10.7586i	0.882095	+	0.804135i	−0.0995149	+	0.995036i	$0.531729\pi$
$180$	−2.43780	−	4.89576i	−0.181703	−	0.364909i
$181$	16.0738	−	14.6532i	1.19475	−	1.08916i	0.200769	−	0.979639i	$-0.435656\pi$
$181$	16.0738	−	14.6532i	1.19475	−	1.08916i	0.993984	−	0.109523i	$-0.0349324\pi$
$182$	−0.462219	+	0.179065i	−0.0342620	+	0.0132732i
$183$	9.20625	+	5.70027i	0.680546	+	0.421376i
$184$	12.9102	−	25.9273i	0.951755	−	1.91138i
$185$	−7.93624	+	1.48354i	−0.583484	+	0.109072i
$186$	1.05564	−	11.3922i	0.0774034	−	0.835316i
$187$	−0.583076	+	2.04930i	−0.0426388	+	0.149860i
$188$	−0.530741	+	1.06587i	−0.0387083	+	0.0777367i
$189$	−0.112153	+	0.102241i	−0.00815793	+	0.00743693i
$190$	−2.04183	−	2.70382i	−0.148130	−	0.196156i
$191$	−14.2087	−	18.8154i	−1.02811	−	1.36144i	−0.930533	−	0.366208i	$-0.880656\pi$
$191$	−14.2087	−	18.8154i	−1.02811	−	1.36144i	−0.0975758	−	0.995228i	$-0.531109\pi$
$192$	−0.282017	−	0.566367i	−0.0203528	−	0.0408740i
$193$	0.323138	−	3.48721i	0.0232600	−	0.251015i	−0.976163	−	0.217040i	$-0.930360\pi$
$193$	0.323138	−	3.48721i	0.0232600	−	0.251015i	0.999423	−	0.0339750i	$-0.0108167\pi$
$194$	21.6000	+	4.03773i	1.55079	+	0.289892i
$195$	−1.33867	+	0.828871i	−0.0958643	+	0.0593567i
$196$	18.7644	−	24.8480i	1.34031	−	1.77486i
$197$	18.1498	−	11.2379i	1.29312	−	0.800665i	0.304705	−	0.952447i	$-0.401442\pi$
$197$	18.1498	−	11.2379i	1.29312	−	0.800665i	0.988414	+	0.151782i	$0.0485011\pi$
$198$	0.632979	+	6.83093i	0.0449839	+	0.485453i
$199$	0.997283	−	10.7624i	0.0706955	−	0.762926i	−0.884420	−	0.466692i	$-0.845446\pi$
$199$	0.997283	−	10.7624i	0.0706955	−	0.762926i	0.955115	−	0.296234i	$-0.0957308\pi$
$200$	16.1862	+	14.7557i	1.14454	+	1.04339i
$201$	5.97175	−	2.31347i	0.421215	−	0.163179i
$202$	−3.92582	+	7.88410i	−0.276220	+	0.554724i
$203$	0.0777744	+	0.273349i	0.00545869	+	0.0191853i
$204$	2.99590	−	1.85498i	0.209755	−	0.129875i
$205$	14.4948			1.01236
$206$	−24.5573	−	7.91285i	−1.71099	−	0.551314i
$207$	−4.62597			−0.321527
$208$	7.63714	−	4.72872i	0.529541	−	0.327878i
$209$	0.803136	+	2.82273i	0.0555541	+	0.195252i
$210$	−0.210746	+	0.423234i	−0.0145428	+	0.0292060i
$211$	12.1040	−	4.68910i	0.833270	−	0.322811i	0.0934575	−	0.995623i	$-0.470208\pi$
$211$	12.1040	−	4.68910i	0.833270	−	0.322811i	0.739813	+	0.672813i	$0.234914\pi$
$212$	−40.6458	−	37.0535i	−2.79156	−	2.54485i
$213$	−1.04675	+	11.2962i	−0.0717222	+	0.774006i
$214$	−0.784913	−	8.47056i	−0.0536555	−	0.579035i
$215$	7.40162	−	4.58289i	0.504786	−	0.312551i
$216$	3.77316	−	4.99647i	0.256731	−	0.339967i
$217$	−0.580688	+	0.359546i	−0.0394196	+	0.0244076i
$218$	−29.8842	−	5.58632i	−2.02401	−	0.378353i
$219$	−0.937427	+	10.1165i	−0.0633455	+	0.683607i
$220$	6.57844	+	13.2113i	0.443518	+	0.890704i
$221$	−0.611333	−	0.809536i	−0.0411227	−	0.0544553i
$222$	−10.0933	−	13.3657i	−0.677419	−	0.897048i
$223$	6.19706	−	5.64937i	0.414986	−	0.378310i	−0.439103	−	0.898437i	$-0.644704\pi$
$223$	6.19706	−	5.64937i	0.414986	−	0.378310i	0.854089	+	0.520127i	$0.174115\pi$
$224$	0.355231	−	0.713401i	0.0237349	−	0.0476661i
$225$	0.957329	−	3.36466i	0.0638219	−	0.224311i
$226$	1.01701	−	10.9753i	0.0676504	−	0.730064i
$227$	16.3454	−	3.05549i	1.08489	−	0.202800i	0.389205	−	0.921151i	$-0.372750\pi$
$227$	16.3454	−	3.05549i	1.08489	−	0.202800i	0.695681	+	0.718351i	$0.255103\pi$
$228$	2.16342	−	4.34474i	0.143276	−	0.287737i
$229$	0.243858	+	0.150990i	0.0161146	+	0.00997772i	0.534466	−	0.845190i	$-0.320513\pi$
$229$	0.243858	+	0.150990i	0.0161146	+	0.00997772i	−0.518351	+	0.855168i	$0.673454\pi$
$230$	−13.4387	+	5.20617i	−0.886120	+	0.343285i
$231$	0.302646	−	0.275898i	0.0199127	−	0.0181528i
$232$	−5.22626	−	10.4957i	−0.343120	−	0.689079i
$233$	−14.2247	−	12.9676i	−0.931894	−	0.849533i	0.0569671	−	0.998376i	$-0.481857\pi$
$233$	−14.2247	−	12.9676i	−0.931894	−	0.849533i	−0.988861	+	0.148843i	$0.952445\pi$
$234$	−2.77703	−	1.71947i	−0.181540	−	0.112405i
$235$	0.304881	−	0.118112i	0.0198883	−	0.00770476i
$236$	−19.7785	−	7.66223i	−1.28747	−	0.498769i
$237$	3.02717	+	4.00862i	0.196636	+	0.260388i
$238$	−0.284050	−	0.110041i	−0.0184122	−	0.00713292i
$239$	12.7227	+	11.5983i	0.822962	+	0.750229i	0.971083	−	0.238740i	$-0.0767344\pi$
$239$	12.7227	+	11.5983i	0.822962	+	0.750229i	−0.148121	+	0.988969i	$0.547323\pi$
$240$	2.34468	−	8.24070i	0.151348	−	0.531935i
$241$	−7.57907	−	26.6377i	−0.488211	−	1.71588i	−0.678898	−	0.734232i	$-0.737542\pi$
$241$	−7.57907	−	26.6377i	−0.488211	−	1.71588i	0.190688	−	0.981651i	$-0.438928\pi$
$242$	0.872124	+	9.41172i	0.0560623	+	0.605008i
$243$	−0.982973	−	0.183750i	−0.0630578	−	0.0117875i
$244$	13.2246	+	46.4796i	0.846617	+	2.97555i
$245$	−8.40454	+	1.57108i	−0.536946	+	0.100373i
$246$	13.4029	+	26.9166i	0.854535	+	1.71614i
$247$	−1.30294	−	0.504760i	−0.0829039	−	0.0321171i
$248$	20.8234	−	18.9831i	1.32229	−	1.20543i
$249$	11.6141	−	2.17105i	0.736014	−	0.137585i
$250$	−2.44285	−	26.3626i	−0.154500	−	1.66732i
$251$	−9.10641	+	12.0588i	−0.574792	+	0.761147i	−0.988820	−	0.149117i	$-0.952357\pi$
$251$	−9.10641	+	12.0588i	−0.574792	+	0.761147i	0.414028	+	0.910264i	$0.364122\pi$
$252$	−0.677289			−0.0426652
$253$	12.4832			0.784815
$254$	−2.44943	+	3.24357i	−0.153691	+	0.203519i
$255$	−0.951113	−	0.177794i	−0.0595610	−	0.0111339i
$256$	8.07955	−	28.3967i	0.504972	−	1.77479i
$257$	3.57266	+	2.21210i	0.222857	+	0.137987i	0.633320	−	0.773890i	$-0.281692\pi$
$257$	3.57266	+	2.21210i	0.222857	+	0.137987i	−0.410463	+	0.911877i	$0.634633\pi$
$258$	15.3544	+	9.50706i	0.955925	+	0.591884i
$259$	−0.273618	+	0.961668i	−0.0170018	+	0.0597551i
$260$	−6.90715	−	1.29117i	−0.428363	−	0.0800750i
$261$	−1.12853	+	1.49442i	−0.0698543	+	0.0925021i
$262$	23.3098			1.44008
$263$	−0.858063			−0.0529105			−0.0264552	−	0.999650i	$-0.508422\pi$
$263$	−0.858063			−0.0529105			−0.0264552	+	0.999650i	$0.508422\pi$
$264$	−10.1819	+	13.4830i	−0.626654	+	0.829824i
$265$	1.39351	+	15.0384i	0.0856029	+	0.923802i
$266$	−0.412443	+	0.0770989i	−0.0252885	+	0.00472724i
$267$	1.30595	−	1.19053i	0.0799230	−	0.0728594i
$268$	26.6510	+	10.3247i	1.62797	+	0.630680i
$269$	0.427940	+	0.859420i	0.0260920	+	0.0523997i	0.907826	−	0.419348i	$-0.137741\pi$
$269$	0.427940	+	0.859420i	0.0260920	+	0.0523997i	−0.881734	+	0.471747i	$0.843623\pi$
$270$	−3.06238	+	0.572458i	−0.186371	+	0.0348387i
$271$	3.82283	+	13.4359i	0.232221	+	0.816171i	0.987072	+	0.160275i	$0.0512382\pi$
$271$	3.82283	+	13.4359i	0.232221	+	0.816171i	−0.754852	+	0.655895i	$0.772291\pi$
$272$	5.42611	+	1.01432i	0.329006	+	0.0615019i
$273$	0.0179909	+	0.194153i	0.00108886	+	0.0117507i
$274$	−10.9659	−	38.5412i	−0.662475	−	2.32836i
$275$	−2.58336	+	9.07958i	−0.155783	+	0.547519i
$276$	−15.2569	−	13.9085i	−0.918356	−	0.837192i
$277$	18.9012	+	7.32236i	1.13566	+	0.439958i	0.854371	−	0.519664i	$-0.173943\pi$
$277$	18.9012	+	7.32236i	1.13566	+	0.439958i	0.281292	+	0.959622i	$0.409237\pi$
$278$	26.4397	+	35.0118i	1.58575	+	2.09987i
$279$	−4.19650	−	1.62573i	−0.251238	−	0.0973301i
$280$	−1.08581	+	0.420645i	−0.0648895	+	0.0251383i
$281$	19.1331	+	11.8467i	1.14138	+	0.706714i	0.960909	−	0.276865i	$-0.0892956\pi$
$281$	19.1331	+	11.8467i	1.14138	+	0.706714i	0.180474	+	0.983580i	$0.442237\pi$
$282$	0.501247	+	0.456947i	0.0298488	+	0.0272108i
$283$	−0.0667697	−	0.134092i	−0.00396905	−	0.00797092i	0.893170	−	0.449719i	$-0.148476\pi$
$283$	−0.0667697	−	0.134092i	−0.00396905	−	0.00797092i	−0.897139	+	0.441748i	$0.854358\pi$
$284$	−37.4157	+	34.1089i	−2.22021	+	2.02399i
$285$	−1.24277	+	0.481451i	−0.0736152	+	0.0285187i
$286$	7.49386	+	4.64000i	0.443121	+	0.274369i
$287$	0.800104	−	1.60683i	0.0472286	−	0.0948479i
$288$	5.16193	−	0.964931i	0.304169	−	0.0568591i
$289$	−1.51104	+	16.3067i	−0.0888848	+	0.959220i
$290$	−1.59659	+	5.61143i	−0.0937550	+	0.329514i
$291$	3.85282	−	7.73751i	0.225857	−	0.453581i
$292$	−33.5079	+	30.5465i	−1.96090	+	1.78760i
$293$	12.0461	+	15.9516i	0.703739	+	0.931901i	0.999729	−	0.0232898i	$-0.00741406\pi$
$293$	12.0461	+	15.9516i	0.703739	+	0.931901i	−0.295990	+	0.955191i	$0.595649\pi$
$294$	−10.6889	−	14.1544i	−0.623389	−	0.825501i
$295$	2.59615	+	5.21377i	0.151154	+	0.303558i
$296$	3.80602	−	41.0735i	0.221221	−	2.38735i
$297$	2.65256	+	0.495850i	0.153917	+	0.0287722i
$298$	−23.7724	+	14.7193i	−1.37710	+	0.852664i
$299$	−3.58176	+	4.74301i	−0.207138	+	0.274296i
$300$	13.2736	−	8.21865i	0.766350	−	0.474504i
$301$	−0.0994731	−	1.07349i	−0.00573353	−	0.0618747i
$302$	−2.74896	+	29.6660i	−0.158185	+	1.70709i
$303$	2.56028	+	2.33400i	0.147084	+	0.134085i
$304$	7.09000	−	2.74668i	0.406640	−	0.157533i
$305$	5.91478	−	11.8785i	0.338679	−	0.680159i
$306$	−0.549305	−	1.93061i	−0.0314017	−	0.110365i
$307$	7.70534	−	4.77094i	0.439767	−	0.272292i	−0.288639	−	0.957438i	$-0.593203\pi$
$307$	7.70534	−	4.77094i	0.439767	−	0.272292i	0.728406	+	0.685146i	$0.240262\pi$
$308$	1.82767			0.104141
$309$	−5.63729	+	8.43925i	−0.320694	+	0.480092i
$310$	−14.0207			−0.796321
$311$	−17.0429	+	10.5525i	−0.966412	+	0.598377i	−0.916354	−	0.400369i	$-0.868882\pi$
$311$	−17.0429	+	10.5525i	−0.966412	+	0.598377i	−0.0500585	+	0.998746i	$0.515941\pi$
$312$	−2.20144	−	7.73725i	−0.124632	−	0.438035i
$313$	4.33918	−	8.71425i	0.245265	−	0.492558i	−0.737986	−	0.674816i	$-0.764223\pi$
$313$	4.33918	−	8.71425i	0.245265	−	0.492558i	0.983251	+	0.182258i	$0.0583405\pi$
$314$	14.2111	−	5.50543i	0.801981	−	0.310689i
$315$	0.137441	+	0.125294i	0.00774392	+	0.00705952i
$316$	−2.06847	+	22.3223i	−0.116360	+	1.25573i
$317$	−0.650750	−	7.02271i	−0.0365497	−	0.394435i	−0.994283	−	0.106777i	$-0.965947\pi$
$317$	−0.650750	−	7.02271i	−0.0365497	−	0.394435i	0.957733	−	0.287658i	$-0.0928766\pi$
$318$	−26.6376	+	16.4933i	−1.49376	+	0.924899i
$319$	3.04536	−	4.03270i	0.170507	−	0.225788i
$320$	−0.659220	+	0.408172i	−0.0368515	+	0.0228175i
$321$	−3.28926	−	0.614869i	−0.183589	−	0.0343186i
$322$	−0.164676	+	1.77713i	−0.00917701	+	0.0990357i
$323$	−0.382748	−	0.768662i	−0.0212967	−	0.0427695i
$324$	−2.68947	−	3.56144i	−0.149415	−	0.197858i
$325$	−2.70856	−	3.58671i	−0.150244	−	0.198955i
$326$	−25.1310	+	22.9099i	−1.39188	+	1.26886i
$327$	−5.33049	+	10.7051i	−0.294777	+	0.591992i
$328$	−20.2662	+	71.2283i	−1.11901	+	3.93293i
$329$	0.00373597	−	0.0403176i	0.000205971	−	0.00222278i
$330$	8.26387	−	1.54479i	0.454911	−	0.0850377i
$331$	−9.35585	+	18.7891i	−0.514244	+	1.03274i	0.474095	+	0.880474i	$0.342775\pi$
$331$	−9.35585	+	18.7891i	−0.514244	+	1.03274i	−0.988339	+	0.152268i	$0.951342\pi$
$332$	44.8319	+	27.7587i	2.46047	+	1.52346i
$333$	−6.14333	+	2.37994i	−0.336652	+	0.130420i
$334$	3.67265	−	3.34807i	0.200959	−	0.183198i
$335$	−3.49825	−	7.02544i	−0.191130	−	0.383841i
$336$	−0.784103	−	0.714804i	−0.0427763	−	0.0389958i
$337$	−28.0768	−	17.3844i	−1.52944	−	0.946989i	−0.994793	−	0.101912i	$-0.967504\pi$
$337$	−28.0768	−	17.3844i	−1.52944	−	0.946989i	−0.534646	−	0.845076i	$-0.679555\pi$
$338$	26.9039	−	10.4226i	1.46338	−	0.566917i
$339$	−4.04292	−	1.56624i	−0.219581	−	0.0850663i
$340$	−2.60230	−	3.44600i	−0.141129	−	0.186886i
$341$	11.3243	+	4.38706i	0.613246	+	0.237573i
$342$	−2.04320	−	1.86262i	−0.110483	−	0.100719i
$343$	−0.580484	+	2.04019i	−0.0313432	+	0.110160i
$344$	12.1719	+	42.7798i	0.656265	+	2.30653i
$345$	0.523072	+	5.64484i	0.0281612	+	0.303908i
$346$	−51.5195	−	9.63066i	−2.76970	−	0.517747i
$347$	−0.728235	−	2.55948i	−0.0390937	−	0.137400i	0.939822	−	0.341664i	$-0.110990\pi$
$347$	−0.728235	−	2.55948i	−0.0390937	−	0.137400i	−0.978916	+	0.204264i	$0.934520\pi$
$348$	−8.21512	+	1.53567i	−0.440377	+	0.0823207i
$349$	3.86013	+	7.75218i	0.206628	+	0.414965i	0.974100	−	0.226118i	$-0.0726033\pi$
$349$	3.86013	+	7.75218i	0.206628	+	0.414965i	−0.767472	+	0.641082i	$0.778486\pi$
$350$	−1.25850	−	0.487547i	−0.0672698	−	0.0260605i
$351$	−0.949486	+	0.865571i	−0.0506798	+	0.0462008i
$352$	−13.9295	+	2.60388i	−0.742446	+	0.138787i
$353$	0.698613	+	7.53923i	0.0371834	+	0.401273i	0.993903	+	0.110261i	$0.0351685\pi$
$353$	0.698613	+	7.53923i	0.0371834	+	0.401273i	−0.956719	+	0.291012i	$0.906008\pi$
$354$	−7.28133	+	9.64204i	−0.386998	+	0.512469i
$355$	13.9026			0.737874
$356$	7.88661			0.417990
$357$	−0.0722105	+	0.0956221i	−0.00382178	+	0.00506086i
$358$	39.9067	+	7.45985i	2.10913	+	0.394266i
$359$	0.0673081	−	0.236563i	0.00355239	−	0.0124853i	−0.960029	−	0.279900i	$-0.909699\pi$
$359$	0.0673081	−	0.236563i	0.00355239	−	0.0124853i	0.963582	+	0.267415i	$0.0861693\pi$
$360$	−6.52359	−	4.03923i	−0.343823	−	0.212886i
$361$	15.1485	+	9.37957i	0.797291	+	0.493661i
$362$	15.1320	−	53.1835i	0.795320	−	2.79526i
$363$	3.65473	+	0.683187i	0.191823	+	0.0358580i
$364$	−0.524405	+	0.694425i	−0.0274863	+	0.0363977i
$365$	12.4506			0.651694
$366$	27.5274			1.43888
$367$	8.44944	−	11.1889i	0.441057	−	0.584054i	−0.522137	−	0.852862i	$-0.674865\pi$
$367$	8.44944	−	11.1889i	0.441057	−	0.584054i	0.963194	+	0.268808i	$0.0866297\pi$
$368$	−2.98413	−	32.2039i	−0.155559	−	1.67874i
$369$	11.6264	−	2.17336i	0.605249	−	0.113141i
$370$	−15.1682	+	13.8277i	−0.788559	+	0.718866i
$371$	1.74401	+	0.675635i	0.0905447	+	0.0350772i
$372$	−8.95250	−	17.9790i	−0.464166	−	0.932170i
$373$	7.36672	−	1.37708i	0.381434	−	0.0713024i	0.0104593	−	0.999945i	$-0.496671\pi$
$373$	7.36672	−	1.37708i	0.381434	−	0.0713024i	0.370975	+	0.928643i	$0.379024\pi$
$374$	1.48230	+	5.20976i	0.0766482	+	0.269390i
$375$	−10.2370	−	1.91363i	−0.528638	−	0.0988196i
$376$	0.154132	+	1.66335i	0.00794877	+	0.0857808i
$377$	0.658437	+	2.31417i	0.0339113	+	0.119186i
$378$	−0.105582	+	0.371082i	−0.00543055	+	0.0190864i
$379$	9.30380	+	8.48154i	0.477904	+	0.435667i	0.876458	−	0.481478i	$-0.159900\pi$
$379$	9.30380	+	8.48154i	0.477904	+	0.435667i	−0.398554	+	0.917145i	$0.630488\pi$
$380$	−5.54629	−	2.14864i	−0.284519	−	0.110223i
$381$	0.963501	+	1.27588i	0.0493617	+	0.0653654i
$382$	−55.8920	−	21.6527i	−2.85968	−	1.10785i
$383$	19.8431	−	7.68728i	1.01394	−	0.392801i	0.203782	−	0.979016i	$-0.434677\pi$
$383$	19.8431	−	7.68728i	1.01394	−	0.392801i	0.810156	+	0.586215i	$0.199383\pi$
$384$	−10.2971	−	6.37569i	−0.525471	−	0.325358i
$385$	−0.370886	−	0.338107i	−0.0189021	−	0.0172315i
$386$	−3.96851	−	7.96984i	−0.201992	−	0.405654i
$387$	5.24978	−	4.78581i	0.266861	−	0.243276i
$388$	35.9706	−	13.9351i	1.82613	−	0.707447i
$389$	15.6168	+	9.66949i	0.791802	+	0.490263i	0.861778	−	0.507286i	$-0.169351\pi$
$389$	15.6168	+	9.66949i	0.791802	+	0.490263i	−0.0699762	+	0.997549i	$0.522292\pi$
$390$	−1.78417	+	3.58310i	−0.0903450	+	0.181437i
$391$	−3.59029	+	0.671142i	−0.181569	+	0.0339411i
$392$	4.03061	−	43.4972i	0.203576	−	2.19694i
$393$	2.50924	−	8.81906i	0.126574	−	0.444863i
$394$	24.1899	−	48.5798i	1.21867	−	2.44742i
$395$	4.54923	−	4.14717i	0.228897	−	0.208667i
$396$	7.25757	+	9.61058i	0.364707	+	0.482950i
$397$	−13.3371	−	17.6612i	−0.669370	−	0.886389i	0.328949	−	0.944348i	$-0.393305\pi$
$397$	−13.3371	−	17.6612i	−0.669370	−	0.886389i	−0.998319	+	0.0579590i	$0.981541\pi$
$398$	−12.2478	−	24.5969i	−0.613926	−	1.23293i
$399$	−0.0152287	+	0.164344i	−0.000762388	+	0.00822747i
$400$	24.0408	+	4.49400i	1.20204	+	0.224700i
$401$	−22.2999	+	13.8075i	−1.11360	+	0.689514i	−0.954637	−	0.297771i	$-0.903757\pi$
$401$	−22.2999	+	13.8075i	−1.11360	+	0.689514i	−0.158965	+	0.987284i	$0.550816\pi$
$402$	9.81142	−	12.9924i	0.489349	−	0.648003i
$403$	−4.91610	+	3.04392i	−0.244888	+	0.151628i
$404$	1.42660	+	15.3955i	0.0709762	+	0.765955i
$405$	−0.113073	+	1.22025i	−0.00561863	+	0.0606347i
$406$	0.533928	+	0.486739i	0.0264984	+	0.0241565i
$407$	16.5778	−	6.42229i	0.821733	−	0.318341i
$408$	2.20352	−	4.42525i	0.109090	−	0.219083i
$409$	3.16654	+	11.1292i	0.156575	+	0.550305i	0.999916	+	0.0129265i	$0.00411475\pi$
$409$	3.16654	+	11.1292i	0.156575	+	0.550305i	−0.843341	+	0.537379i	$0.819415\pi$
$410$	31.3295	−	19.3984i	1.54725	−	0.958018i
$411$	−15.7622			−0.777491
$412$	−43.9658	+	10.8843i	−2.16604	+	0.536230i
$413$	0.721283			0.0354920
$414$	−9.99874	+	6.19096i	−0.491411	+	0.304269i
$415$	−3.96247	−	13.9266i	−0.194510	−	0.683631i
$416$	3.00739	−	6.03965i	0.147449	−	0.296118i
$417$	16.0926	−	6.23430i	0.788058	−	0.305295i
$418$	5.51359	+	5.02630i	0.269679	+	0.245845i
$419$	−3.13163	+	33.7957i	−0.152990	+	1.65103i	0.480294	+	0.877107i	$0.340530\pi$
$419$	−3.13163	+	33.7957i	−0.152990	+	1.65103i	−0.633285	+	0.773919i	$0.718294\pi$
$420$	0.0765830	+	0.826462i	0.00373687	+	0.0403272i
$421$	14.0801	−	8.71802i	0.686221	−	0.424890i	−0.138551	−	0.990355i	$-0.544244\pi$
$421$	14.0801	−	8.71802i	0.686221	−	0.424890i	0.824772	+	0.565465i	$0.191303\pi$
$422$	19.8865	−	26.3339i	0.968058	−	1.28192i
$423$	0.226840	−	0.140453i	0.0110293	−	0.00682908i
$424$	−75.8483	−	14.1785i	−3.68352	−	0.688569i
$425$	0.254849	−	2.75026i	0.0123620	−	0.133407i
$426$	12.8553	+	25.8170i	0.622843	+	1.25084i
$427$	−0.990303	−	1.31137i	−0.0479241	−	0.0634618i
$428$	−8.99960	−	11.9174i	−0.435012	−	0.576049i
$429$	2.56220	−	2.33575i	0.123704	−	0.112771i
$430$	9.86482	−	19.8112i	0.475724	−	0.955382i
$431$	−4.76155	+	16.7351i	−0.229356	+	0.806101i	0.758625	+	0.651527i	$0.225871\pi$
$431$	−4.76155	+	16.7351i	−0.229356	+	0.806101i	−0.987981	+	0.154575i	$0.950599\pi$
$432$	0.645082	−	6.96154i	0.0310365	−	0.334937i
$433$	28.1150	−	5.25560i	1.35112	−	0.252568i	0.542083	−	0.840325i	$-0.317636\pi$
$433$	28.1150	−	5.25560i	1.35112	−	0.252568i	0.809038	+	0.587757i	$0.199989\pi$
$434$	−0.773936	+	1.55427i	−0.0371501	+	0.0746075i
$435$	1.95117	+	1.20811i	0.0935514	+	0.0579246i
$436$	−49.7664	+	19.2796i	−2.38338	+	0.923325i
$437$	−3.71793	+	3.38934i	−0.177853	+	0.162134i
$438$	11.5127	+	23.1206i	0.550098	+	1.10475i
$439$	−17.7879	−	16.2158i	−0.848969	−	0.773937i	0.126987	−	0.991904i	$-0.459469\pi$
$439$	−17.7879	−	16.2158i	−0.848969	−	0.773937i	−0.975956	+	0.217967i	$0.930057\pi$
$440$	17.6040	+	10.8999i	0.839237	+	0.519633i
$441$	−6.50583	+	2.52037i	−0.309801	+	0.120018i
$442$	−2.40476	−	0.931610i	−0.114383	−	0.0443121i
$443$	9.93718	+	13.1590i	0.472130	+	0.625201i	0.970308	−	0.241874i	$-0.0777620\pi$
$443$	9.93718	+	13.1590i	0.472130	+	0.625201i	−0.498178	+	0.867075i	$0.665997\pi$
$444$	−27.4168	−	10.6213i	−1.30114	−	0.504065i
$445$	−1.60042	−	1.45897i	−0.0758670	−	0.0691619i
$446$	5.83397	−	20.5043i	0.276247	−	0.970906i
$447$	3.00987	+	10.5786i	0.142362	+	0.500350i
$448$	0.00885950	+	0.0956092i	0.000418572	+	0.00451711i
$449$	−22.8510	−	4.27158i	−1.07840	−	0.201588i	−0.385564	−	0.922681i	$-0.625993\pi$
$449$	−22.8510	−	4.27158i	−1.07840	−	0.201588i	−0.692839	+	0.721092i	$0.743640\pi$
$450$	−2.43374	−	8.55369i	−0.114727	−	0.403225i
$451$	−31.3741	+	5.86484i	−1.47735	+	0.276164i
$452$	−8.62486	−	17.3211i	−0.405679	−	0.814714i
$453$	10.9280	+	4.23352i	0.513441	+	0.198908i
$454$	31.2404	−	28.4794i	1.46619	−	1.33661i
$455$	0.234881	−	0.0439068i	0.0110114	−	0.00205838i
$456$	−0.628279	−	6.78021i	−0.0294218	−	0.317512i
$457$	18.5100	−	24.5112i	0.865862	−	1.14659i	−0.122196	−	0.992506i	$-0.538994\pi$
$457$	18.5100	−	24.5112i	0.865862	−	1.14659i	0.988058	−	0.154081i	$-0.0492416\pi$
$458$	0.729153			0.0340711
$459$	−0.789560			−0.0368535
$460$	−15.2467	+	20.1899i	−0.710880	+	0.941358i
$461$	−23.7008	−	4.43044i	−1.10386	−	0.206346i	−0.399878	−	0.916568i	$-0.630947\pi$
$461$	−23.7008	−	4.43044i	−1.10386	−	0.206346i	−0.703978	+	0.710222i	$0.748595\pi$
$462$	0.284914	−	1.00137i	0.0132554	−	0.0465879i
$463$	−9.47822	−	5.86867i	−0.440490	−	0.272740i	0.288217	−	0.957565i	$-0.406937\pi$
$463$	−9.47822	−	5.86867i	−0.440490	−	0.272740i	−0.728708	+	0.684825i	$0.759879\pi$
$464$	−11.1314	−	6.89230i	−0.516764	−	0.319967i
$465$	−1.50929	+	5.30461i	−0.0699917	+	0.245995i
$466$	−48.1004	−	8.99152i	−2.22821	−	0.416524i
$467$	3.86542	−	5.11865i	0.178871	−	0.236863i	−0.699745	−	0.714393i	$-0.746703\pi$
$467$	3.86542	−	5.11865i	0.178871	−	0.236863i	0.878616	+	0.477530i	$0.158468\pi$
$468$	−5.73392			−0.265051
$469$	−0.971911			−0.0448787
$470$	0.500912	−	0.663315i	0.0231053	−	0.0305964i
$471$	−0.553138	−	5.96931i	−0.0254873	−	0.275051i
$472$	−29.2508	+	5.46791i	−1.34638	+	0.251681i
$473$	−14.1666	+	12.9146i	−0.651381	+	0.593812i
$474$	11.9078	+	4.61310i	0.546943	+	0.211887i
$475$	−1.69580	−	3.40562i	−0.0778085	−	0.156260i
$476$	−0.525655	+	0.0982619i	−0.0240933	+	0.00450383i
$477$	3.37263	+	11.8536i	0.154422	+	0.542738i
$478$	43.0212	+	8.04206i	1.96775	+	0.367835i
$479$	−1.49757	−	16.1613i	−0.0684256	−	0.738429i	−0.958965	−	0.283524i	$-0.908497\pi$
$479$	−1.49757	−	16.1613i	−0.0684256	−	0.738429i	0.890540	−	0.454906i	$-0.150327\pi$
$480$	−1.76113	−	6.18974i	−0.0803843	−	0.282521i
$481$	−2.31645	+	8.14147i	−0.105621	+	0.371219i
$482$	−52.0309	−	47.4325i	−2.36994	−	2.16049i
$483$	0.654636	+	0.253607i	0.0297870	+	0.0115395i
$484$	9.99954	+	13.2415i	0.454525	+	0.601888i
$485$	−9.87735	−	3.82651i	−0.448507	−	0.173753i
$486$	−2.37054	+	0.918354i	−0.107530	+	0.0416574i
$487$	−30.1597	−	18.6741i	−1.36667	−	0.846204i	−0.370099	−	0.928992i	$-0.620676\pi$
$487$	−30.1597	−	18.6741i	−1.36667	−	0.846204i	−0.996567	+	0.0827881i	$0.973618\pi$
$488$	50.1018	+	45.6739i	2.26800	+	2.06756i
$489$	5.96249	+	11.9743i	0.269633	+	0.541496i
$490$	−16.0633	+	14.6436i	−0.725665	+	0.661531i
$491$	16.0974	−	6.23618i	0.726467	−	0.281435i	0.0305265	−	0.999534i	$-0.490282\pi$
$491$	16.0974	−	6.23618i	0.726467	−	0.281435i	0.695941	+	0.718099i	$0.254987\pi$
$492$	44.8795	+	27.7882i	2.02332	+	1.25279i
$493$	−0.659059	+	1.32357i	−0.0296825	+	0.0596106i
$494$	−3.49173	+	0.652718i	−0.157101	+	0.0293672i
$495$	0.305128	−	3.29286i	0.0137145	−	0.148003i
$496$	8.61053	−	30.2629i	0.386624	−	1.35884i
$497$	0.767418	−	1.54118i	0.0344234	−	0.0691315i
$498$	22.1976	−	20.2358i	0.994698	−	0.906787i
$499$	9.42846	+	12.4853i	0.422076	+	0.558919i	0.958523	−	0.285015i	$-0.0919986\pi$
$499$	9.42846	+	12.4853i	0.422076	+	0.558919i	−0.536447	+	0.843934i	$0.680234\pi$
$500$	−28.0091	−	37.0901i	−1.25261	−	1.65872i
$501$	−0.871361	−	1.74993i	−0.0389295	−	0.0781811i
$502$	−3.54453	+	38.2515i	−0.158200	+	1.70725i
$503$	−34.7703	−	6.49969i	−1.55033	−	0.289807i	−0.662174	−	0.749350i	$-0.730366\pi$
$503$	−34.7703	−	6.49969i	−1.55033	−	0.289807i	−0.888155	+	0.459543i	$0.848013\pi$
$504$	−0.807871	+	0.500213i	−0.0359854	+	0.0222812i
$505$	2.55857	−	3.38809i	0.113855	−	0.150768i
$506$	26.9817	−	16.7064i	1.19948	−	0.742689i
$507$	−1.04718	−	11.3008i	−0.0465068	−	0.501888i
$508$	−0.658360	+	7.10484i	−0.0292100	+	0.315226i
$509$	2.33538	+	2.12898i	0.103514	+	0.0943653i	0.723798	−	0.690012i	$-0.242395\pi$
$509$	2.33538	+	2.12898i	0.103514	+	0.0943653i	−0.620284	+	0.784377i	$0.712983\pi$
$510$	−2.29371	+	0.888588i	−0.101567	+	0.0393473i
$511$	0.687268	−	1.38022i	0.0304029	−	0.0610573i
$512$	−13.9112	−	48.8928i	−0.614794	−	2.16078i
$513$	−0.924652	+	0.572520i	−0.0408244	+	0.0252774i
$514$	10.6825			0.471186
$515$	10.9354	+	5.92466i	0.481872	+	0.261072i
$516$	31.7033			1.39566
$517$	−0.612130	+	0.379015i	−0.0269215	+	0.0166691i
$518$	0.695596	+	2.44477i	0.0305627	+	0.107417i
$519$	−9.18962	+	18.4552i	−0.403379	+	0.810095i
$520$	−9.19245	+	3.56118i	−0.403116	+	0.156168i
$521$	−29.3315	−	26.7392i	−1.28503	−	1.17146i	−0.975360	−	0.220621i	$-0.929192\pi$
$521$	−29.3315	−	26.7392i	−1.28503	−	1.17146i	−0.309675	−	0.950842i	$-0.600220\pi$
$522$	−0.439263	+	4.74040i	−0.0192260	+	0.207482i
$523$	−1.77569	−	19.1628i	−0.0776455	−	0.837929i	−0.942125	−	0.335261i	$-0.891175\pi$
$523$	−1.77569	−	19.1628i	−0.0776455	−	0.837929i	0.864480	−	0.502668i	$-0.167648\pi$
$524$	34.7911	−	21.5418i	1.51986	−	0.941056i
$525$	−0.319934	+	0.423661i	−0.0139631	+	0.0184901i
$526$	−1.85465	+	1.14835i	−0.0808665	+	0.0500704i
$527$	−3.49283	−	0.652924i	−0.152150	−	0.0284418i
$528$	−1.74076	+	18.7858i	−0.0757569	+	0.817547i
$529$	−0.713347	−	1.43259i	−0.0310151	−	0.0622867i
$530$	23.1379	+	30.6396i	1.00505	+	1.33090i
$531$	2.86417	+	3.79277i	0.124294	+	0.164592i
$532$	−0.544342	+	0.496234i	−0.0236002	+	0.0215145i
$533$	6.77367	−	13.6034i	0.293400	−	0.589227i
$534$	1.22944	−	4.32102i	0.0532029	−	0.186989i
$535$	−0.378368	+	4.08324i	−0.0163583	+	0.176534i
$536$	39.4147	−	7.36789i	1.70246	−	0.318244i
$537$	7.11823	−	14.2953i	0.307174	−	0.616889i
$538$	2.07513	+	1.28487i	0.0894652	+	0.0553945i
$539$	17.5561	−	6.80125i	0.756193	−	0.292951i
$540$	−4.04174	+	3.68453i	−0.173929	+	0.158557i
$541$	−5.85756	−	11.7636i	−0.251836	−	0.505756i	0.732784	−	0.680461i	$-0.238220\pi$
$541$	−5.85756	−	11.7636i	−0.251836	−	0.505756i	−0.984621	+	0.174705i	$0.944103\pi$
$542$	26.2441	+	23.9246i	1.12728	+	1.02765i
$543$	−18.4926	−	11.4501i	−0.793593	−	0.491372i
$544$	3.86626	−	1.49780i	0.165765	−	0.0642175i
$545$	13.6656	+	5.29408i	0.585370	+	0.226773i
$546$	0.298721	+	0.395571i	0.0127841	+	0.0169289i
$547$	41.1740	+	15.9509i	1.76047	+	0.682011i	0.999446	+	0.0332916i	$0.0105990\pi$
$547$	41.1740	+	15.9509i	1.76047	+	0.682011i	0.761028	+	0.648719i	$0.224695\pi$
$548$	−51.9851	−	47.3907i	−2.22069	−	2.02443i
$549$	2.96325	−	10.4148i	0.126469	−	0.444491i
$550$	6.56747	+	23.0822i	0.280038	+	0.984230i
$551$	0.187915	+	2.02792i	0.00800544	+	0.0863924i
$552$	−28.4705	−	5.32207i	−1.21179	−	0.226522i
$553$	−0.208622	−	0.733230i	−0.00887151	−	0.0311801i
$554$	50.6532	−	9.46873i	2.15205	−	0.402288i
$555$	3.59876	+	7.22729i	0.152759	+	0.306781i
$556$	71.8189	+	27.8228i	3.04580	+	1.17995i
$557$	−10.3603	+	9.44466i	−0.438980	+	0.400183i	−0.862785	−	0.505570i	$-0.831282\pi$
$557$	−10.3603	+	9.44466i	−0.438980	+	0.400183i	0.423806	+	0.905753i	$0.360694\pi$
$558$	−11.2462	+	2.10228i	−0.476089	+	0.0889965i
$559$	−0.842138	−	9.08812i	−0.0356186	−	0.384386i
$560$	−0.783579	+	1.03763i	−0.0331123	+	0.0438477i
$561$	2.13064			0.0899555
$562$	57.2093			2.41323
$563$	4.51939	−	5.98463i	0.190469	−	0.252222i	−0.692755	−	0.721173i	$-0.743603\pi$
$563$	4.51939	−	5.98463i	0.190469	−	0.252222i	0.883224	+	0.468951i	$0.155368\pi$
$564$	1.17043	+	0.218791i	0.0492838	+	0.00921275i
$565$	−1.45406	+	5.11047i	−0.0611726	+	0.214999i
$566$	−0.323774	−	0.200472i	−0.0136092	−	0.00842648i
$567$	0.129030	+	0.0798920i	0.00541875	+	0.00335515i
$568$	−19.4383	+	68.3185i	−0.815612	+	2.86658i
$569$	−42.5349	−	7.95114i	−1.78315	−	0.333329i	−0.814203	−	0.580581i	$-0.802826\pi$
$569$	−42.5349	−	7.95114i	−1.78315	−	0.333329i	−0.968951	+	0.247252i	$0.920473\pi$
$570$	−2.04183	+	2.70382i	−0.0855230	+	0.113251i
$571$	−32.4399			−1.35757			−0.678785	−	0.734337i	$-0.737493\pi$
$571$	−32.4399			−1.35757			−0.678785	+	0.734337i	$0.737493\pi$
$572$	15.4731			0.646961
$573$	−14.2087	+	18.8154i	−0.593579	+	0.786026i
$574$	−0.421048	−	4.54383i	−0.0175742	−	0.189656i
$575$	−15.9071	+	2.97354i	−0.663370	+	0.124005i
$576$	−0.467568	+	0.426245i	−0.0194820	+	0.0177602i
$577$	−28.0023	−	10.8482i	−1.16575	−	0.451615i	−0.300907	−	0.953654i	$-0.597289\pi$
$577$	−28.0023	−	10.8482i	−1.16575	−	0.451615i	−0.864845	+	0.502039i	$0.832583\pi$
$578$	18.5573	+	37.2682i	0.771884	+	1.55015i
$579$	−3.44252	+	0.643519i	−0.143066	+	0.0267437i
$580$	2.80281	+	9.85086i	0.116380	+	0.409035i
$581$	−1.76257	−	0.329482i	−0.0731238	−	0.0136692i
$582$	−2.02752	−	21.8804i	−0.0840432	−	0.906971i
$583$	−9.10109	−	31.9870i	−0.376929	−	1.32477i
$584$	−17.4081	+	61.1832i	−0.720353	+	2.53178i
$585$	1.16357	+	1.06074i	0.0481079	+	0.0438561i
$586$	47.3849	+	18.3570i	1.95745	+	0.758320i
$587$	12.6483	+	16.7490i	0.522049	+	0.691305i	0.980299	−	0.197518i	$-0.0632882\pi$
$587$	12.6483	+	16.7490i	0.522049	+	0.691305i	−0.458250	+	0.888823i	$0.651524\pi$
$588$	−29.0346	−	11.2481i	−1.19737	−	0.463862i
$589$	−4.56390	+	1.76806i	−0.188052	+	0.0728518i
$590$	12.5890	+	7.79479i	0.518282	+	0.320906i
$591$	−15.7758	−	14.3815i	−0.648930	−	0.591578i
$592$	−20.5310	−	41.2318i	−0.843818	−	1.69462i
$593$	−20.9395	+	19.0889i	−0.859883	+	0.783887i	−0.977889	−	0.209126i	$-0.932938\pi$
$593$	−20.9395	+	19.0889i	−0.859883	+	0.783887i	0.118005	+	0.993013i	$0.462350\pi$
$594$	6.39694	−	2.47819i	0.262470	−	0.101681i
$595$	0.124848	+	0.0773026i	0.00511827	+	0.00316910i
$596$	−21.8788	+	43.9386i	−0.896192	+	1.79980i
$597$	−10.6245	+	1.98606i	−0.434831	+	0.0812839i
$598$	−1.39414	+	15.0452i	−0.0570107	+	0.615244i
$599$	−0.0682246	+	0.239785i	−0.00278758	+	0.00979734i	−0.963207	−	0.268761i	$-0.913386\pi$
$599$	−0.0682246	+	0.239785i	−0.00278758	+	0.00979734i	0.960419	+	0.278558i	$0.0898565\pi$
$600$	9.76284	−	19.6064i	0.398566	−	0.800429i
$601$	−22.1959	+	20.2343i	−0.905391	+	0.825373i	−0.985195	−	0.171438i	$-0.945159\pi$
$601$	−22.1959	+	20.2343i	−0.905391	+	0.825373i	0.0798040	+	0.996811i	$0.474571\pi$
$602$	−1.65165	−	2.18714i	−0.0673164	−	0.0891413i
$603$	−3.85940	−	5.11067i	−0.157167	−	0.208123i
$604$	23.3129	+	46.8187i	0.948590	+	1.90503i
$605$	0.420408	−	4.53693i	0.0170920	−	0.184452i
$606$	8.65748	+	1.61836i	0.351686	+	0.0657416i
$607$	12.6313	−	7.82094i	0.512687	−	0.317442i	−0.245591	−	0.969373i	$-0.578982\pi$
$607$	12.6313	−	7.82094i	0.512687	−	0.317442i	0.758278	+	0.651931i	$0.226041\pi$
$608$	3.44170	−	4.55755i	0.139579	−	0.184833i
$609$	0.241630	−	0.149611i	0.00979133	−	0.00606254i
$610$	−3.11260	−	33.5903i	−0.126025	−	1.36003i
$611$	0.0316287	−	0.341328i	0.00127956	−	0.0138087i
$612$	−2.60404	−	2.37389i	−0.105262	−	0.0959590i
$613$	−15.4003	+	5.96611i	−0.622012	+	0.240969i	−0.651563	−	0.758594i	$-0.725886\pi$
$613$	−15.4003	+	5.96611i	−0.622012	+	0.240969i	0.0295508	+	0.999563i	$0.490592\pi$
$614$	10.2696	−	20.6242i	0.414448	−	0.832323i
$615$	−3.96668	−	13.9414i	−0.159952	−	0.562172i
$616$	2.18005	−	1.34983i	0.0878367	−	0.0543862i
$617$	−14.9384			−0.601398			−0.300699	−	0.953719i	$-0.597220\pi$
$617$	−14.9384			−0.601398			−0.300699	+	0.953719i	$0.597220\pi$
$618$	−0.890358	+	25.7853i	−0.0358155	+	1.03724i
$619$	−0.643032			−0.0258457			−0.0129228	−	0.999916i	$-0.504114\pi$
$619$	−0.643032			−0.0258457			−0.0129228	+	0.999916i	$0.504114\pi$
$620$	−20.9266	+	12.9572i	−0.840434	+	0.520375i
$621$	1.26596	+	4.44938i	0.0508011	+	0.178547i
$622$	−22.7146	+	45.6171i	−0.910772	+	1.82908i
$623$	−0.250078	+	0.0968806i	−0.0100191	+	0.00388144i
$624$	−6.63821	−	6.05152i	−0.265741	−	0.242255i
$625$	0.436287	−	4.70828i	0.0174515	−	0.188331i
$626$	−2.28346	−	24.6424i	−0.0912653	−	0.984909i
$627$	2.49518	−	1.54495i	0.0996481	−	0.0616995i
$628$	16.1231	−	21.3504i	0.643381	−	0.851974i
$629$	−4.42265	+	2.73839i	−0.176343	+	0.109187i
$630$	0.464751	+	0.0868770i	0.0185161	+	0.00346126i
$631$	1.26015	−	13.5992i	0.0501657	−	0.541374i	−0.933153	−	0.359481i	$-0.882954\pi$
$631$	1.26015	−	13.5992i	0.0501657	−	0.541374i	0.983318	−	0.181893i	$-0.0582226\pi$
$632$	14.0189	+	28.1538i	0.557642	+	1.11990i
$633$	−7.82250	−	10.3587i	−0.310916	−	0.411720i
$634$	−10.8051	−	14.3082i	−0.429124	−	0.568252i
$635$	1.44795	−	1.31998i	0.0574601	−	0.0523818i
$636$	−24.5158	+	49.2343i	−0.972114	+	1.95227i
$637$	−2.45314	+	8.62188i	−0.0971968	+	0.341611i
$638$	1.18536	−	12.7920i	0.0469287	−	0.506441i
$639$	11.1515	−	2.08457i	0.441146	−	0.0824644i
$640$	−6.61561	+	13.2859i	−0.261505	+	0.525173i
$641$	10.0171	+	6.20231i	0.395651	+	0.244977i	0.709809	−	0.704394i	$-0.248781\pi$
$641$	10.0171	+	6.20231i	0.395651	+	0.244977i	−0.314158	+	0.949371i	$0.601722\pi$
$642$	−7.93240	+	3.07303i	−0.313067	+	0.121283i
$643$	4.79275	−	4.36917i	0.189008	−	0.172303i	−0.573661	−	0.819093i	$-0.694477\pi$
$643$	4.79275	−	4.36917i	0.189008	−	0.172303i	0.762668	+	0.646790i	$0.223889\pi$
$644$	1.39655	+	2.80465i	0.0550318	+	0.110519i
$645$	−6.43349	−	5.86490i	−0.253318	−	0.230930i
$646$	−1.85599	−	1.14918i	−0.0730229	−	0.0452139i
$647$	43.8162	−	16.9745i	1.72259	−	0.667337i	0.722874	−	0.690980i	$-0.242821\pi$
$647$	43.8162	−	16.9745i	1.72259	−	0.667337i	0.999720	+	0.0236435i	$0.00752665\pi$
$648$	−5.83831	−	2.26177i	−0.229350	−	0.0888508i
$649$	−7.72899	−	10.2348i	−0.303389	−	0.401753i
$650$	−10.6545	−	4.12757i	−0.417903	−	0.161897i
$651$	0.504734	+	0.460126i	0.0197821	+	0.0180337i
$652$	−16.3372	+	57.4192i	−0.639813	+	2.24871i
$653$	6.04774	+	21.2556i	0.236666	+	0.831796i	0.985592	+	0.169142i	$0.0540995\pi$
$653$	6.04774	+	21.2556i	0.236666	+	0.831796i	−0.748925	+	0.662654i	$0.769430\pi$
$654$	2.80512	+	30.2721i	0.109689	+	1.18373i
$655$	−11.0452	−	2.06470i	−0.431571	−	0.0806746i
$656$	22.6299	+	79.5360i	0.883551	+	3.10536i
$657$	9.98680	−	1.86686i	0.389622	−	0.0728330i
$658$	−0.0458821	−	0.0921436i	−0.00178867	−	0.00359213i
$659$	−23.4782	−	9.09550i	−0.914580	−	0.354310i	−0.142470	−	0.989799i	$-0.545505\pi$
$659$	−23.4782	−	9.09550i	−0.914580	−	0.354310i	−0.772110	+	0.635489i	$0.780799\pi$
$660$	10.9067	−	9.94275i	0.424542	−	0.387021i
$661$	11.6506	−	2.17788i	0.453157	−	0.0847097i	0.0477771	−	0.998858i	$-0.484786\pi$
$661$	11.6506	−	2.17788i	0.453157	−	0.0847097i	0.405380	+	0.914148i	$0.367139\pi$
$662$	4.92344	+	53.1323i	0.191355	+	2.06505i
$663$	−0.611333	+	0.809536i	−0.0237422	+	0.0314398i
$664$	73.9767			2.87085
$665$	0.202262			0.00784340
$666$	−10.0933	+	13.3657i	−0.391108	+	0.517911i
$667$	8.51538	+	1.59180i	0.329717	+	0.0616348i
$668$	2.38752	−	8.39126i	0.0923759	−	0.324668i
$669$	−7.12961	−	4.41447i	−0.275647	−	0.170673i
$670$	−16.9634	−	10.5033i	−0.655354	−	0.405778i
$671$	−7.99638	+	28.1044i	−0.308697	+	1.08496i
$672$	−0.783381	−	0.146439i	−0.0302196	−	0.00564902i
$673$	−10.8371	+	14.3506i	−0.417739	+	0.553175i	−0.957422	−	0.288693i	$-0.906779\pi$
$673$	−10.8371	+	14.3506i	−0.417739	+	0.553175i	0.539683	+	0.841868i	$0.318544\pi$
$674$	−83.9517			−3.23370
$675$	−3.49820			−0.134646
$676$	30.5235	−	40.4197i	1.17398	−	1.55460i
$677$	−4.71726	−	50.9073i	−0.181299	−	1.95653i	−0.276358	−	0.961055i	$-0.589128\pi$
$677$	−4.71726	−	50.9073i	−0.181299	−	1.95653i	0.0950594	−	0.995472i	$-0.469696\pi$
$678$	−10.8346	+	2.02534i	−0.416101	+	0.0777827i
$679$	−0.969416	+	0.883739i	−0.0372028	+	0.0339148i
$680$	−5.64908	−	2.18846i	−0.216632	−	0.0839237i
$681$	−7.41200	−	14.8853i	−0.284028	−	0.570406i
$682$	30.3480	−	5.67302i	1.16208	−	0.217231i
$683$	8.70551	+	30.5967i	0.333107	+	1.17075i	0.929734	+	0.368231i	$0.120037\pi$
$683$	8.70551	+	30.5967i	0.333107	+	1.17075i	−0.596627	+	0.802519i	$0.703493\pi$
$684$	−4.77093	−	0.891841i	−0.182421	−	0.0341004i
$685$	1.78227	+	19.2338i	0.0680972	+	0.734886i
$686$	1.47571	+	5.18660i	0.0563430	+	0.198025i
$687$	0.0784915	−	0.275869i	0.00299464	−	0.0105251i
$688$	36.7032	+	33.4593i	1.39929	+	1.27563i
$689$	14.7648	+	5.71992i	0.562495	+	0.217912i
$690$	8.68510	+	11.5009i	0.330636	+	0.437833i
$691$	−14.4466	−	5.59666i	−0.549576	−	0.212907i	0.0704122	−	0.997518i	$-0.477569\pi$
$691$	−14.4466	−	5.59666i	−0.549576	−	0.212907i	−0.619988	+	0.784611i	$0.712863\pi$
$692$	−85.7958	+	33.2375i	−3.26147	+	1.26350i
$693$	−0.348189	−	0.215590i	−0.0132266	−	0.00818957i
$694$	−4.99939	−	4.55755i	−0.189774	−	0.173002i
$695$	−9.42704	−	18.9321i	−0.357588	−	0.718134i
$696$	−8.66483	+	7.89904i	−0.328440	+	0.299412i
$697$	8.70815	−	3.37356i	0.329845	−	0.127783i
$698$	18.7182	+	11.5898i	0.708494	+	0.438681i
$699$	−8.57975	+	17.2305i	−0.324516	+	0.651716i
$700$	−2.32895	+	0.435357i	−0.0880261	+	0.0164549i
$701$	−0.642157	+	6.92998i	−0.0242539	+	0.261742i	0.974969	+	0.222339i	$0.0713691\pi$
$701$	−0.642157	+	6.92998i	−0.0242539	+	0.261742i	−0.999223	+	0.0394029i	$0.987454\pi$
$702$	−0.893855	+	3.14158i	−0.0337364	+	0.118571i
$703$	−3.19371	+	6.41384i	−0.120453	+	0.241903i
$704$	1.26174	−	1.15023i	0.0475536	−	0.0433508i
$705$	−0.197038	−	0.260920i	−0.00742087	−	0.00982682i
$706$	11.5998	+	15.3606i	0.436564	+	0.578104i
$707$	−0.234358	−	0.470653i	−0.00881392	−	0.0177007i
$708$	−1.95709	+	21.1203i	−0.0735518	+	0.793751i
$709$	−18.8009	−	3.51450i	−0.706084	−	0.131990i	−0.181553	−	0.983381i	$-0.558112\pi$
$709$	−18.8009	−	3.51450i	−0.706084	−	0.131990i	−0.524531	+	0.851391i	$0.675759\pi$
$710$	30.0496	−	18.6059i	1.12774	−	0.698267i
$711$	3.02717	−	4.00862i	0.113528	−	0.150335i
$712$	9.40716	−	5.82467i	0.352548	−	0.218289i
$713$	1.92091	+	20.7299i	0.0719387	+	0.776342i
$714$	−0.0281068	+	0.303320i	−0.00105187	+	0.0113515i
$715$	−3.13992	−	2.86241i	−0.117426	−	0.107048i
$716$	66.4570	−	25.7456i	2.48361	−	0.962157i
$717$	7.67378	−	15.4110i	0.286582	−	0.575535i
$718$	−0.171112	−	0.601395i	−0.00638583	−	0.0224439i
$719$	14.4236	−	8.93069i	0.537908	−	0.333058i	−0.230445	−	0.973085i	$-0.574018\pi$
$719$	14.4236	−	8.93069i	0.537908	−	0.333058i	0.768352	+	0.640027i	$0.221077\pi$
$720$	−8.56776			−0.319302
$721$	1.26041	−	0.885215i	0.0469402	−	0.0329671i
$722$	45.2952			1.68571
$723$	−23.5467	+	14.5795i	−0.875710	+	0.542217i
$724$	−26.5642	−	93.3635i	−0.987251	−	3.46983i
$725$	−2.92001	+	5.86417i	−0.108447	+	0.217790i
$726$	8.81376	−	3.41447i	0.327109	−	0.126723i
$727$	29.8735	+	27.2333i	1.10795	+	1.01003i	0.999874	+	0.0158835i	$0.00505609\pi$
$727$	29.8735	+	27.2333i	1.10795	+	1.01003i	0.108072	+	0.994143i	$0.465532\pi$
$728$	−0.112643	+	1.21561i	−0.00417483	+	0.0450535i
$729$	0.0922684	+	0.995734i	0.00341735	+	0.0368790i
$730$	26.9112	−	16.6627i	0.996027	−	0.616714i
$731$	3.38011	−	4.47599i	0.125018	−	0.165550i
$732$	41.0862	−	25.4395i	1.51859	−	0.940270i
$733$	−20.0179	−	3.74200i	−0.739379	−	0.138214i	−0.199431	−	0.979912i	$-0.563909\pi$
$733$	−20.0179	−	3.74200i	−0.739379	−	0.138214i	−0.539949	+	0.841698i	$0.681556\pi$
$734$	3.28881	−	35.4919i	0.121392	−	1.31003i
$735$	3.81112	+	7.65375i	0.140575	+	0.282313i
$736$	−14.6395	−	19.3859i	−0.539621	−	0.714573i
$737$	10.4146	+	13.7912i	0.383628	+	0.508006i
$738$	22.2212	−	20.2573i	0.817973	−	0.745681i
$739$	20.6533	−	41.4775i	0.759745	−	1.52577i	−0.0884452	−	0.996081i	$-0.528190\pi$
$739$	20.6533	−	41.4775i	0.759745	−	1.52577i	0.848190	−	0.529692i	$-0.177693\pi$
$740$	−9.86057	+	34.6563i	−0.362482	+	1.27399i
$741$	−0.128926	+	1.39133i	−0.00473621	+	0.0511119i
$742$	4.67378	−	0.873680i	0.171580	−	0.0320738i
$743$	−12.6705	+	25.4457i	−0.464834	+	0.933513i	0.531426	+	0.847105i	$0.321656\pi$
$743$	−12.6705	+	25.4457i	−0.464834	+	0.933513i	−0.996260	+	0.0864078i	$0.972461\pi$
$744$	−23.9570	−	14.8335i	−0.878306	−	0.543824i
$745$	12.5682	−	4.86894i	0.460463	−	0.178384i
$746$	14.0797	−	12.8354i	0.515496	−	0.469936i
$747$	−5.26652	−	10.5766i	−0.192692	−	0.386978i
$748$	7.02703	+	6.40598i	0.256934	+	0.234226i
$749$	0.431765	+	0.267338i	0.0157763	+	0.00976830i
$750$	−24.6877	+	9.56407i	−0.901468	+	0.349230i
$751$	13.9995	+	5.42344i	0.510850	+	0.197904i	0.602850	−	0.797855i	$-0.294032\pi$
$751$	13.9995	+	5.42344i	0.510850	+	0.197904i	−0.0919999	+	0.995759i	$0.529326\pi$
$752$	1.12410	+	1.48855i	0.0409918	+	0.0542819i
$753$	14.0906	+	5.45872i	0.513489	+	0.198927i
$754$	4.52023	+	4.12073i	0.164617	+	0.150068i
$755$	3.93030	−	13.8136i	0.143038	−	0.502727i
$756$	0.185349	+	0.651434i	0.00674107	+	0.0236924i
$757$	2.85650	+	30.8266i	0.103821	+	1.12041i	0.875109	+	0.483925i	$0.160789\pi$
$757$	2.85650	+	30.8266i	0.103821	+	1.12041i	−0.771288	+	0.636486i	$0.780387\pi$
$758$	31.4604	+	5.88097i	1.14269	+	0.213607i
$759$	−3.41620	−	12.0067i	−0.124000	−	0.435816i
$760$	−8.20251	+	1.53331i	−0.297536	+	0.0556192i
$761$	0.628163	+	1.26152i	0.0227709	+	0.0457301i	0.906257	−	0.422728i	$-0.138927\pi$
$761$	0.628163	+	1.26152i	0.0227709	+	0.0457301i	−0.883486	+	0.468458i	$0.844810\pi$
$762$	3.79006	+	1.46828i	0.137299	+	0.0531901i
$763$	1.34121	−	1.22268i	0.0485552	−	0.0442639i
$764$	−103.432	+	19.3348i	−3.74205	+	0.699510i
$765$	0.0892777	+	0.963460i	0.00322784	+	0.0348340i
$766$	32.6018	−	43.1717i	1.17795	−	1.55986i
$767$	6.10637			0.220488
$768$	−29.5237			−1.06535
$769$	28.3266	−	37.5105i	1.02148	−	1.35266i	0.0871771	−	0.996193i	$-0.472215\pi$
$769$	28.3266	−	37.5105i	1.02148	−	1.35266i	0.934307	−	0.356470i	$-0.116020\pi$
$770$	−1.25414	−	0.234439i	−0.0451959	−	0.00844859i
$771$	1.14995	−	4.04165i	0.0414144	−	0.145556i
$772$	−13.2885	−	8.22792i	−0.478265	−	0.296129i
$773$	−5.40596	−	3.34723i	−0.194439	−	0.120391i	0.425760	−	0.904836i	$-0.360007\pi$
$773$	−5.40596	−	3.34723i	−0.194439	−	0.120391i	−0.620199	+	0.784445i	$0.712948\pi$
$774$	4.94219	−	17.3700i	0.177644	−	0.624352i
$775$	−15.4753	−	2.89283i	−0.555888	−	0.103914i
$776$	32.6140	−	43.1879i	1.17078	−	1.55036i
$777$	0.999836			0.0358689
$778$	46.6953			1.67411
$779$	7.75190	−	10.2652i	0.277740	−	0.367788i
$780$	0.648351	+	6.99682i	0.0232147	+	0.250526i
$781$	−30.0924	+	5.62524i	−1.07679	+	0.201287i
$782$	−6.86199	+	6.25553i	−0.245384	+	0.223697i
$783$	1.74621	+	0.676484i	0.0624043	+	0.0241756i
$784$	−21.7425	−	43.6648i	−0.776517	−	1.55946i
$785$	−7.22151	+	1.34993i	−0.257747	+	0.0481812i
$786$	−6.37902	−	22.4199i	−0.227532	−	0.799693i
$787$	−14.9041	−	2.78605i	−0.531273	−	0.0993121i	−0.0887234	−	0.996056i	$-0.528279\pi$
$787$	−14.9041	−	2.78605i	−0.531273	−	0.0993121i	−0.442549	+	0.896744i	$0.645926\pi$
$788$	−8.79037	−	94.8632i	−0.313144	−	3.37936i
$789$	0.234820	+	0.825307i	0.00835982	+	0.0293817i
$790$	4.28269	−	15.0521i	0.152371	−	0.535529i
$791$	0.486262	+	0.443286i	0.0172895	+	0.0157614i
$792$	15.7547	+	6.10342i	0.559820	+	0.216876i
$793$	−8.38390	−	11.1021i	−0.297721	−	0.394246i
$794$	−52.4633	−	20.3244i	−1.86185	−	0.721285i
$795$	14.0830	−	5.45577i	0.499472	−	0.193496i
$796$	−41.0117	−	25.3934i	−1.45362	−	0.900045i
$797$	9.18187	+	8.37038i	0.325238	+	0.296494i	0.819802	−	0.572648i	$-0.194084\pi$
$797$	9.18187	+	8.37038i	0.325238	+	0.296494i	−0.494563	+	0.869142i	$0.664672\pi$
$798$	0.187026	+	0.375599i	0.00662065	+	0.0132960i
$799$	0.155677	−	0.141918i	0.00550745	−	0.00502071i
$800$	17.1298	−	6.63611i	0.605629	−	0.234622i
$801$	−1.50248	−	0.930294i	−0.0530874	−	0.0328703i
$802$	−29.7211	+	59.6880i	−1.04949	+	2.10766i
$803$	−26.9495	+	5.03774i	−0.951028	+	0.177778i
$804$	2.63713	−	28.4591i	0.0930043	−	1.00368i
$805$	0.235443	−	0.827496i	0.00829827	−	0.0291654i
$806$	−6.55213	+	13.1585i	−0.230789	+	0.463487i
$807$	0.709501	−	0.646795i	0.0249756	−	0.0227683i
$808$	13.0720	+	17.3102i	0.459872	+	0.608970i
$809$	21.7554	+	28.8088i	0.764879	+	1.01286i	0.999172	+	0.0406968i	$0.0129578\pi$
$809$	21.7554	+	28.8088i	0.764879	+	1.01286i	−0.234293	+	0.972166i	$0.575278\pi$
$810$	1.38867	+	2.78882i	0.0487927	+	0.0979890i
$811$	−2.54556	+	27.4710i	−0.0893869	+	0.964638i	0.826429	+	0.563040i	$0.190368\pi$
$811$	−2.54556	+	27.4710i	−0.0893869	+	0.964638i	−0.915816	+	0.401597i	$0.868455\pi$
$812$	1.24674	+	0.233056i	0.0437519	+	0.00817865i
$813$	11.8768	−	7.35380i	0.416537	−	0.257909i
$814$	27.2369	−	36.0675i	0.954654	−	1.26417i
$815$	13.9374	−	8.62970i	0.488207	−	0.302285i
$816$	−0.509331	−	5.49655i	−0.0178301	−	0.192418i
$817$	0.712841	−	7.69278i	0.0249392	−	0.269136i
$818$	21.7386	+	19.8173i	0.760071	+	0.692896i
$819$	0.181818	−	0.0704365i	0.00635322	−	0.00246125i
$820$	28.8339	−	57.9063i	1.00692	−	2.02218i
$821$	−8.36301	−	29.3929i	−0.291871	−	1.02582i	−0.959589	−	0.281406i	$-0.909199\pi$
$821$	−8.36301	−	29.3929i	−0.291871	−	1.02582i	0.667718	−	0.744415i	$-0.267271\pi$
$822$	−34.0689	+	21.0946i	−1.18829	+	0.735758i
$823$	33.0061			1.15052			0.575260	−	0.817970i	$-0.304901\pi$
$823$	33.0061			1.15052			0.575260	+	0.817970i	$0.304901\pi$
$824$	−44.4039	+	45.4538i	−1.54688	+	1.58346i
$825$	9.43995			0.328657
$826$	1.55901	−	0.965295i	0.0542447	−	0.0335869i
$827$	−3.43658	−	12.0783i	−0.119502	−	0.420004i	0.878869	−	0.477063i	$-0.158299\pi$
$827$	−3.43658	−	12.0783i	−0.119502	−	0.420004i	−0.998371	+	0.0570582i	$0.981828\pi$
$828$	−9.20229	+	18.4807i	−0.319802	+	0.642248i
$829$	−6.19256	+	2.39901i	−0.215077	+	0.0833211i	−0.466370	−	0.884590i	$-0.654438\pi$
$829$	−6.19256	+	2.39901i	−0.215077	+	0.0833211i	0.251293	+	0.967911i	$0.419144\pi$
$830$	−27.2027	−	24.7985i	−0.944218	−	0.860769i
$831$	1.87028	−	20.1835i	0.0648792	−	0.700158i
$832$	0.0750045	+	0.809427i	0.00260031	+	0.0280618i
$833$	−4.68362	+	2.89997i	−0.162278	+	0.100478i
$834$	26.4397	−	35.0118i	0.915532	−	1.21236i
$835$	−2.03682	+	1.26115i	−0.0704872	+	0.0436438i
$836$	12.8744	+	2.40664i	0.445271	+	0.0832355i
$837$	−0.415245	+	4.48121i	−0.0143530	+	0.154893i
$838$	38.4600	+	77.2382i	1.32858	+	2.66815i
$839$	5.02734	+	6.65727i	0.173563	+	0.229835i	0.876481	−	0.481436i	$-0.159885\pi$
$839$	5.02734	+	6.65727i	0.173563	+	0.229835i	−0.702918	+	0.711271i	$0.748120\pi$
$840$	0.701733	+	0.929244i	0.0242121	+	0.0320620i
$841$	−18.8397	+	17.1746i	−0.649643	+	0.592228i
$842$	18.7658	−	37.6869i	0.646713	−	1.29877i
$843$	6.15844	−	21.6447i	0.212108	−	0.745482i
$844$	5.34511	−	57.6830i	0.183986	−	1.98553i
$845$	−13.6715	+	2.55564i	−0.470312	+	0.0879166i
$846$	0.302330	−	0.607161i	0.0103943	−	0.0208746i
$847$	−0.479738	−	0.297041i	−0.0164840	−	0.0102065i
$848$	−80.3436	+	31.1253i	−2.75901	+	1.06885i
$849$	−0.110700	+	0.100917i	−0.00379923	+	0.00346345i
$850$	−3.12984	−	6.28557i	−0.107353	−	0.215593i
$851$	22.5227	+	20.5322i	0.772068	+	0.703833i
$852$	43.0461	+	26.6530i	1.47473	+	0.913117i
$853$	46.2372	−	17.9124i	1.58313	−	0.613308i	0.600624	−	0.799532i	$-0.294919\pi$
$853$	46.2372	−	17.9124i	1.58313	−	0.613308i	0.982507	+	0.186224i	$0.0596249\pi$
$854$	−3.89549	−	1.50912i	−0.133301	−	0.0516411i
$855$	0.803171	+	1.06357i	0.0274679	+	0.0363733i
$856$	−19.5363	−	7.56842i	−0.667739	−	0.258683i
$857$	1.93828	+	1.76698i	0.0662104	+	0.0603588i	0.706125	−	0.708088i	$-0.250442\pi$
$857$	1.93828	+	1.76698i	0.0662104	+	0.0603588i	−0.639914	+	0.768446i	$0.721030\pi$
$858$	2.41208	−	8.47758i	0.0823470	−	0.289420i
$859$	9.52723	+	33.4847i	0.325065	+	1.14248i	0.936348	+	0.351073i	$0.114183\pi$
$859$	9.52723	+	33.4847i	0.325065	+	1.14248i	−0.611283	+	0.791412i	$0.709346\pi$
$860$	−3.58478	−	38.6859i	−0.122240	−	1.31918i
$861$	−1.76444	−	0.329832i	−0.0601321	−	0.0112406i
$862$	12.1049	+	42.5442i	0.412294	+	1.44906i
$863$	40.7970	−	7.62629i	1.38875	−	0.259602i	0.564314	−	0.825560i	$-0.309141\pi$
$863$	40.7970	−	7.62629i	1.38875	−	0.259602i	0.824434	+	0.565959i	$0.191494\pi$
$864$	−2.34072	−	4.70081i	−0.0796331	−	0.159925i
$865$	23.5591	+	9.12685i	0.801034	+	0.310322i
$866$	53.7351	−	48.9860i	1.82599	−	1.66461i
$867$	16.0978	−	3.00919i	0.546708	−	0.102198i
$868$	0.281241	+	3.03507i	0.00954593	+	0.103017i
$869$	−8.16886	+	10.8173i	−0.277110	+	0.366952i
$870$	5.83414			0.197796
$871$	−8.22819			−0.278802
$872$	−45.1224	+	59.7517i	−1.52804	+	2.02345i
$873$	−8.49651	−	1.58827i	−0.287563	−	0.0537549i
$874$	−3.50010	+	12.3016i	−0.118392	+	0.416106i
$875$	1.34377	+	0.832025i	0.0454276	+	0.0281276i
$876$	38.5503	+	23.8693i	1.30249	+	0.806470i
$877$	−3.49378	+	12.2794i	−0.117977	+	0.414645i	−0.998204	−	0.0599076i	$-0.980919\pi$
$877$	−3.49378	+	12.2794i	−0.117977	+	0.414645i	0.880227	+	0.474552i	$0.157390\pi$
$878$	−60.1490	−	11.2438i	−2.02993	−	0.379459i
$879$	12.0461	−	15.9516i	0.406304	−	0.538033i
$880$	23.1202			0.779382
$881$	−36.5037			−1.22984			−0.614920	−	0.788590i	$-0.710812\pi$
$881$	−36.5037			−1.22984			−0.614920	+	0.788590i	$0.710812\pi$
$882$	−10.6889	+	14.1544i	−0.359914	+	0.476603i
$883$	−1.07785	−	11.6319i	−0.0362726	−	0.391443i	−0.994445	−	0.105253i	$-0.966435\pi$
$883$	−1.07785	−	11.6319i	−0.0362726	−	0.391443i	0.958173	−	0.286190i	$-0.0923889\pi$
$884$	−4.45019	+	0.831884i	−0.149676	+	0.0279793i
$885$	4.30427	−	3.92386i	0.144686	−	0.131899i
$886$	39.0893	+	15.1433i	1.31323	+	0.508748i
$887$	12.8479	+	25.8020i	0.431389	+	0.866346i	0.999071	+	0.0430980i	$0.0137228\pi$
$887$	12.8479	+	25.8020i	0.431389	+	0.866346i	−0.567682	+	0.823248i	$0.692160\pi$
$888$	−40.5472	+	7.57958i	−1.36067	+	0.254354i
$889$	−0.0664011	−	0.233376i	−0.00222702	−	0.00782717i
$890$	−5.41174	−	1.01163i	−0.181402	−	0.0339099i
$891$	−0.248987	−	2.68700i	−0.00834139	−	0.0900179i
$892$	−10.2415	−	35.9953i	−0.342912	−	1.20521i
$893$	0.0794062	−	0.279084i	0.00265723	−	0.00933918i
$894$	20.6630	+	18.8368i	0.691074	+	0.629997i
$895$	−18.2488	−	7.06961i	−0.609989	−	0.236311i
$896$	1.10764	+	1.46676i	0.0370038	+	0.0490009i
$897$	5.54215	+	2.14704i	0.185047	+	0.0716875i
$898$	−55.1075	+	21.3488i	−1.83896	+	0.712417i
$899$	7.16541	+	4.43663i	0.238980	+	0.147970i
$900$	−11.5374	−	10.5177i	−0.384580	−	0.350591i
$901$	4.33729	+	8.71044i	0.144496	+	0.290187i
$902$	−59.9641	+	54.6645i	−1.99659	+	1.82013i
$903$	−1.00528	+	0.389449i	−0.0334537	+	0.0129600i
$904$	−23.0802	−	14.2907i	−0.767637	−	0.475301i
$905$	−11.8810	+	23.8603i	−0.394938	+	0.793143i
$906$	29.2859	−	5.47448i	0.972957	−	0.181877i
$907$	−4.88492	+	52.7167i	−0.162201	+	1.75043i	0.393753	+	0.919216i	$0.371177\pi$
$907$	−4.88492	+	52.7167i	−0.162201	+	1.75043i	−0.555954	+	0.831213i	$0.687647\pi$
$908$	20.3088	−	71.3780i	0.673971	−	2.36876i
$909$	1.54425	−	3.10127i	0.0512196	−	0.102863i
$910$	0.448918	−	0.409243i	0.0148815	−	0.0135663i
$911$	−24.8541	−	32.9121i	−0.823452	−	1.09043i	−0.994456	−	0.105156i	$-0.966466\pi$
$911$	−24.8541	−	32.9121i	−0.823452	−	1.09043i	0.171004	−	0.985270i	$-0.445299\pi$
$912$	−4.58210	−	6.06768i	−0.151729	−	0.200921i
$913$	14.2118	+	28.5411i	0.470341	+	0.944573i
$914$	7.20473	−	77.7514i	0.238311	−	2.57179i
$915$	−13.0437	−	2.43829i	−0.431211	−	0.0806072i
$916$	1.08830	−	0.673848i	0.0359585	−	0.0222646i
$917$	−0.838574	+	1.11045i	−0.0276921	+	0.0366703i
$918$	−1.70658	+	1.05667i	−0.0563256	+	0.0348753i
$919$	2.38151	+	25.7006i	0.0785587	+	0.847784i	0.940280	+	0.340402i	$0.110563\pi$
$919$	2.38151	+	25.7006i	0.0785587	+	0.847784i	−0.861721	+	0.507382i	$0.830613\pi$
$920$	−3.27501	+	35.3430i	−0.107974	+	1.16522i
$921$	−6.69748	−	6.10556i	−0.220689	−	0.201185i
$922$	−57.1570	+	22.1427i	−1.88236	+	0.729232i
$923$	6.49695	−	13.0476i	0.213850	−	0.429468i
$924$	−0.500166	−	1.75790i	−0.0164543	−	0.0578307i
$925$	−19.5949	+	12.1326i	−0.644276	+	0.398919i
$926$	−28.3406			−0.931330
$927$	9.65981	+	3.11258i	0.317270	+	0.102231i
$928$	−9.83399			−0.322817
$929$	1.71228	−	1.06020i	0.0561780	−	0.0347839i	−0.498056	−	0.867145i	$-0.665953\pi$
$929$	1.71228	−	1.06020i	0.0561780	−	0.0347839i	0.554234	+	0.832361i	$0.313011\pi$
$930$	3.83694	+	13.4855i	0.125818	+	0.442205i
$931$	−3.38217	+	6.79231i	−0.110846	+	0.222609i
$932$	−80.1020	+	31.0317i	−2.62383	+	1.01648i
$933$	14.8137	+	13.5044i	0.484978	+	0.442116i
$934$	1.50456	−	16.2367i	0.0492305	−	0.531282i
$935$	−0.240917	−	2.59991i	−0.00787883	−	0.0850261i
$936$	−6.83943	+	4.23480i	−0.223554	+	0.138419i
$937$	−14.2449	+	18.8633i	−0.465361	+	0.616237i	−0.968815	−	0.247785i	$-0.920297\pi$
$937$	−14.2449	+	18.8633i	−0.465361	+	0.616237i	0.503455	+	0.864022i	$0.332062\pi$
$938$	−2.10072	+	1.30071i	−0.0685910	+	0.0424698i
$939$	−9.56906	−	1.78877i	−0.312275	−	0.0583742i
$940$	0.134636	−	1.45295i	0.00439134	−	0.0473901i
$941$	−8.55800	−	17.1868i	−0.278983	−	0.560273i	0.710709	−	0.703486i	$-0.248374\pi$
$941$	−8.55800	−	17.1868i	−0.278983	−	0.560273i	−0.989692	+	0.143213i	$0.954257\pi$
$942$	−9.18432	−	12.1620i	−0.299241	−	0.396260i
$943$	−32.9733	−	43.6637i	−1.07376	−	1.42189i
$944$	−24.5559	+	22.3857i	−0.799227	+	0.728592i
$945$	0.0828985	−	0.166483i	0.00269669	−	0.00541568i
$946$	−13.3366	+	46.8732i	−0.433609	+	1.52398i
$947$	1.26873	−	13.6918i	0.0412282	−	0.444923i	−0.949951	−	0.312398i	$-0.898868\pi$
$947$	1.26873	−	13.6918i	0.0412282	−	0.444923i	0.991180	−	0.132526i	$-0.0423087\pi$
$948$	22.0362	−	4.11929i	0.715704	−	0.133788i
$949$	5.81840	−	11.6849i	0.188873	−	0.379309i
$950$	−8.22310	−	5.09153i	−0.266793	−	0.165191i
$951$	−6.57653	+	2.54776i	−0.213259	+	0.0826169i
$952$	−0.554430	+	0.505430i	−0.0179692	+	0.0163811i
$953$	15.9104	+	31.9523i	0.515387	+	1.03504i	0.988099	+	0.153820i	$0.0491576\pi$
$953$	15.9104	+	31.9523i	0.515387	+	1.03504i	−0.472712	+	0.881217i	$0.656725\pi$
$954$	23.1534	+	21.1071i	0.749619	+	0.683368i
$955$	24.5661	+	15.2107i	0.794942	+	0.492207i
$956$	71.6437	−	27.7549i	2.31712	−	0.897658i
$957$	−4.71216	−	1.82550i	−0.152322	−	0.0590100i
$958$	−24.8656	−	32.9274i	−0.803372	−	1.06384i
$959$	2.23056	+	0.864123i	0.0720285	+	0.0279040i
$960$	0.572994	+	0.522353i	0.0184933	+	0.0168589i
$961$	2.94088	−	10.3361i	0.0948672	−	0.333423i
$962$	5.88891	+	20.6974i	0.189866	+	0.667310i
$963$	0.308752	+	3.33196i	0.00994938	+	0.107371i
$964$	−121.494	−	22.7111i	−3.91305	−	0.731476i
$965$	1.17451	+	4.12797i	0.0378088	+	0.132884i
$966$	1.75436	−	0.327946i	0.0564455	−	0.0105515i
$967$	5.89004	+	11.8288i	0.189411	+	0.380388i	0.969430	−	0.245367i	$-0.0789085\pi$
$967$	5.89004	+	11.8288i	0.189411	+	0.380388i	−0.780019	+	0.625755i	$0.784791\pi$
$968$	21.7070	+	8.40935i	0.697690	+	0.270287i
$969$	−0.634575	+	0.578492i	−0.0203855	+	0.0185838i
$970$	−26.4703	+	4.94815i	−0.849909	+	0.158876i
$971$	4.43039	+	47.8115i	0.142178	+	1.53434i	0.705859	+	0.708352i	$0.250561\pi$
$971$	4.43039	+	47.8115i	0.142178	+	1.53434i	−0.563681	+	0.825992i	$0.690615\pi$
$972$	−2.68947	+	3.56144i	−0.0862648	+	0.114233i
$973$	−2.61909			−0.0839643
$974$	−90.1798			−2.88955
$975$	−2.70856	+	3.58671i	−0.0867433	+	0.114867i
$976$	74.4143	+	13.9104i	2.38194	+	0.445263i
$977$	−5.14416	+	18.0798i	−0.164576	+	0.578426i	0.835026	+	0.550211i	$0.185453\pi$
$977$	−5.14416	+	18.0798i	−0.164576	+	0.578426i	−0.999602	+	0.0282146i	$0.991018\pi$
$978$	28.9128	+	17.9020i	0.924529	+	0.572444i
$979$	4.05445	+	2.51041i	0.129581	+	0.0802330i
$980$	−10.4424	+	36.7013i	−0.333571	+	1.17238i
$981$	11.7552	+	2.19742i	0.375314	+	0.0701583i
$982$	26.4477	−	35.0224i	0.843979	−	1.11761i
$983$	−13.2637			−0.423046			−0.211523	−	0.977373i	$-0.567842\pi$
$983$	−13.2637			−0.423046			−0.211523	+	0.977373i	$0.567842\pi$
$984$	74.0554			2.36080
$985$	−15.7653	+	20.8766i	−0.502323	+	0.665183i
$986$	0.346824	+	3.74283i	0.0110451	+	0.119196i
$987$	−0.0398009	+	0.00744007i	−0.00126688	+	0.000236820i
$988$	−4.60840	+	4.20111i	−0.146613	+	0.133655i
$989$	−30.6430	−	11.8711i	−0.974389	−	0.377480i
$990$	−3.74733	−	7.52565i	−0.119098	−	0.239181i
$991$	−29.4905	+	5.51274i	−0.936798	+	0.175118i	−0.629945	−	0.776639i	$-0.716923\pi$
$991$	−29.4905	+	5.51274i	−0.936798	+	0.175118i	−0.306852	+	0.951757i	$0.599276\pi$
$992$	−6.46752	−	22.7310i	−0.205344	−	0.721709i
$993$	20.6322	+	3.85682i	0.654742	+	0.122393i
$994$	−0.403847	−	4.35820i	−0.0128093	−	0.138234i
$995$	3.62483	+	12.7399i	0.114915	+	0.403883i
$996$	14.4302	−	50.7170i	0.457239	−	1.60703i
$997$	37.6768	+	34.3469i	1.19323	+	1.08778i	0.994174	+	0.107790i	$0.0343774\pi$
$997$	37.6768	+	34.3469i	1.19323	+	1.08778i	0.199061	+	0.979987i	$0.436211\pi$
$998$	37.0881	+	14.3680i	1.17400	+	0.454812i
$999$	3.97029	+	5.25751i	0.125614	+	0.166340i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	309.2.i.b.100.10	yes	160
3.2	odd	2		927.2.u.c.100.1		160
103.34	even	17	inner	309.2.i.b.34.10	✓	160
309.137	odd	34		927.2.u.c.343.1		160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
309.2.i.b.34.10	✓	160	103.34	even	17	inner
309.2.i.b.100.10	yes	160	1.1	even	1	trivial
927.2.u.c.100.1		160	3.2	odd	2
927.2.u.c.343.1		160	309.137	odd	34

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:	\( N \)	\(=\)	\( 309 = 3 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	309.i (of order \(17\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(2.16143 - 1.33830i) q^{2} +(-0.273663 - 0.961826i) q^{3} +(1.98927 - 3.99498i) q^{4} +(-1.14272 + 0.442694i) q^{5} +(-1.87872 - 1.71268i) q^{6} +(-0.0140028 + 0.151114i) q^{7} +(-0.577702 - 6.23440i) q^{8} +(-0.850217 + 0.526432i) q^{9} +O(q^{10})\)	\(q+(2.16143 - 1.33830i) q^{2} +(-0.273663 - 0.961826i) q^{3} +(1.98927 - 3.99498i) q^{4} +(-1.14272 + 0.442694i) q^{5} +(-1.87872 - 1.71268i) q^{6} +(-0.0140028 + 0.151114i) q^{7} +(-0.577702 - 6.23440i) q^{8} +(-0.850217 + 0.526432i) q^{9} +(-1.87746 + 2.48616i) q^{10} +(2.29432 - 1.42058i) q^{11} +(-4.38687 - 0.820048i) q^{12} +(-0.118547 + 1.27933i) q^{13} +(0.171970 + 0.345363i) q^{14} +(0.738515 + 0.977952i) q^{15} +(-4.21324 - 5.57923i) q^{16} +(-0.583492 + 0.531923i) q^{17} +(-1.13316 + 2.27570i) q^{18} +(-0.297622 + 1.04603i) q^{19} +(-0.504628 + 5.44580i) q^{20} +(0.149177 - 0.0278861i) q^{21} +(3.05785 - 6.14100i) q^{22} +(3.93308 + 2.43526i) q^{23} +(-5.83831 + 2.26177i) q^{24} +(-2.58520 + 2.35672i) q^{25} +(1.45590 + 2.92384i) q^{26} +(0.739009 + 0.673696i) q^{27} +(0.575843 + 0.356547i) q^{28} +(1.74621 - 0.676484i) q^{29} +(2.90505 + 1.12542i) q^{30} +(2.71210 + 3.59140i) q^{31} +(-4.89673 - 1.89700i) q^{32} +(-1.99422 - 1.81798i) q^{33} +(-0.549305 + 1.93061i) q^{34} +(-0.0508959 - 0.178880i) q^{35} +(0.411780 + 4.44382i) q^{36} +(6.47604 + 1.21058i) q^{37} +(0.756618 + 2.65924i) q^{38} +(1.26293 - 0.236083i) q^{39} +(3.42008 + 6.86845i) q^{40} +(-11.0291 - 4.27271i) q^{41} +(0.285117 - 0.259918i) q^{42} +(-6.98286 + 1.30532i) q^{43} +(-1.11119 - 11.9917i) q^{44} +(0.738515 - 0.977952i) q^{45} +11.7602 q^{46} -0.266802 q^{47} +(-4.21324 + 5.57923i) q^{48} +(6.85817 + 1.28201i) q^{49} +(-2.43374 + 8.55369i) q^{50} +(0.671297 + 0.415650i) q^{51} +(4.87508 + 3.01852i) q^{52} +(3.37263 - 11.8536i) q^{53} +(2.49893 + 0.467131i) q^{54} +(-1.99289 + 2.63902i) q^{55} +0.950194 q^{56} +1.08755 q^{57} +(2.86897 - 3.79913i) q^{58} +(-0.438528 - 4.73247i) q^{59} +(5.37601 - 1.00495i) q^{60} +(-8.00207 + 7.29485i) q^{61} +(10.6684 + 4.13296i) q^{62} +(-0.0676458 - 0.135851i) q^{63} +(0.621923 - 0.116258i) q^{64} +(-0.430884 - 1.51440i) q^{65} +(-6.74339 - 1.26056i) q^{66} +(0.590906 + 6.37689i) q^{67} +(0.964304 + 3.38918i) q^{68} +(1.26596 - 4.44938i) q^{69} +(-0.349404 - 0.318524i) q^{70} +(-10.5786 - 4.09816i) q^{71} +(3.77316 + 4.99647i) q^{72} +(-9.47372 - 3.67014i) q^{73} +(15.6177 - 6.05031i) q^{74} +(2.97423 + 1.84157i) q^{75} +(3.58683 + 3.26983i) q^{76} +(0.182543 + 0.366596i) q^{77} +(2.41380 - 2.20047i) q^{78} +(-4.68402 + 1.81460i) q^{79} +(7.28446 + 4.51035i) q^{80} +(0.445738 - 0.895163i) q^{81} +(-29.5569 + 5.52515i) q^{82} +(-1.09018 + 11.7649i) q^{83} +(0.185349 - 0.651434i) q^{84} +(0.431291 - 0.866149i) q^{85} +(-13.3461 + 12.1666i) q^{86} +(-1.12853 - 1.49442i) q^{87} +(-10.1819 - 13.4830i) q^{88} +(0.787694 + 1.58190i) q^{89} +(0.287455 - 3.10214i) q^{90} +(-0.191665 - 0.0358283i) q^{91} +(17.5528 - 10.8682i) q^{92} +(2.71210 - 3.59140i) q^{93} +(-0.576676 + 0.357063i) q^{94} +(-0.122972 - 1.32708i) q^{95} +(-0.484533 + 5.22894i) q^{96} +(6.38776 + 5.82322i) q^{97} +(16.5392 - 6.40733i) q^{98} +(-1.20283 + 2.41561i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q - q^{2} - 10 q^{3} - 17 q^{4} - 4 q^{5} - q^{6} - 12 q^{7} + 36 q^{8} - 10 q^{9}+O(q^{10}) \) 160 * q - q^2 - 10 * q^3 - 17 * q^4 - 4 * q^5 - q^6 - 12 * q^7 + 36 * q^8 - 10 * q^9	\( 160 q - q^{2} - 10 q^{3} - 17 q^{4} - 4 q^{5} - q^{6} - 12 q^{7} + 36 q^{8} - 10 q^{9} + 12 q^{10} + q^{11} + 17 q^{12} - 18 q^{13} + 31 q^{14} - 4 q^{15} - 39 q^{16} - 14 q^{17} - q^{18} - 11 q^{19} + 31 q^{20} + 5 q^{21} + 3 q^{23} - 15 q^{24} - 8 q^{25} - 33 q^{26} - 10 q^{27} - 2 q^{28} - 28 q^{29} + 12 q^{30} - 20 q^{31} - 46 q^{32} + 18 q^{33} + 5 q^{34} - 3 q^{35} - 17 q^{36} - 34 q^{37} - 14 q^{38} - 18 q^{39} - 56 q^{40} + 40 q^{41} + 14 q^{42} - 42 q^{43} - 26 q^{44} - 4 q^{45} + 112 q^{46} - 40 q^{47} - 39 q^{48} + 30 q^{49} - 10 q^{50} + 3 q^{51} - 58 q^{52} - 48 q^{53} - q^{54} - 64 q^{55} + 86 q^{56} + 6 q^{57} - 36 q^{58} + 76 q^{59} - 20 q^{60} - 28 q^{61} - 66 q^{62} - 12 q^{63} + 88 q^{64} - 14 q^{65} - 34 q^{66} - 84 q^{67} - 107 q^{68} - 14 q^{69} + 8 q^{70} + 41 q^{71} - 15 q^{72} - 32 q^{73} + 3 q^{74} - 42 q^{75} - 68 q^{76} + 93 q^{77} + 18 q^{78} - 100 q^{79} - 168 q^{80} - 10 q^{81} + 99 q^{82} - 28 q^{83} + 151 q^{84} + 15 q^{85} + 64 q^{86} - 11 q^{87} - 25 q^{88} - 19 q^{89} - 5 q^{90} + 122 q^{91} - 78 q^{92} - 20 q^{93} + 138 q^{94} - 15 q^{95} + 56 q^{96} + 161 q^{97} + 65 q^{98} + q^{99}+O(q^{100}) \) 160 * q - q^2 - 10 * q^3 - 17 * q^4 - 4 * q^5 - q^6 - 12 * q^7 + 36 * q^8 - 10 * q^9 + 12 * q^10 + q^11 + 17 * q^12 - 18 * q^13 + 31 * q^14 - 4 * q^15 - 39 * q^16 - 14 * q^17 - q^18 - 11 * q^19 + 31 * q^20 + 5 * q^21 + 3 * q^23 - 15 * q^24 - 8 * q^25 - 33 * q^26 - 10 * q^27 - 2 * q^28 - 28 * q^29 + 12 * q^30 - 20 * q^31 - 46 * q^32 + 18 * q^33 + 5 * q^34 - 3 * q^35 - 17 * q^36 - 34 * q^37 - 14 * q^38 - 18 * q^39 - 56 * q^40 + 40 * q^41 + 14 * q^42 - 42 * q^43 - 26 * q^44 - 4 * q^45 + 112 * q^46 - 40 * q^47 - 39 * q^48 + 30 * q^49 - 10 * q^50 + 3 * q^51 - 58 * q^52 - 48 * q^53 - q^54 - 64 * q^55 + 86 * q^56 + 6 * q^57 - 36 * q^58 + 76 * q^59 - 20 * q^60 - 28 * q^61 - 66 * q^62 - 12 * q^63 + 88 * q^64 - 14 * q^65 - 34 * q^66 - 84 * q^67 - 107 * q^68 - 14 * q^69 + 8 * q^70 + 41 * q^71 - 15 * q^72 - 32 * q^73 + 3 * q^74 - 42 * q^75 - 68 * q^76 + 93 * q^77 + 18 * q^78 - 100 * q^79 - 168 * q^80 - 10 * q^81 + 99 * q^82 - 28 * q^83 + 151 * q^84 + 15 * q^85 + 64 * q^86 - 11 * q^87 - 25 * q^88 - 19 * q^89 - 5 * q^90 + 122 * q^91 - 78 * q^92 - 20 * q^93 + 138 * q^94 - 15 * q^95 + 56 * q^96 + 161 * q^97 + 65 * q^98 + q^99

Introduction

L-functions

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