LMFDB - Embedded newform 160.2.z.a.29.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [160,2,Mod(29,160)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(160, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("160.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 160 = 2^{5} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	160.z (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.27760643234$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$22$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			29.14
Character	$\chi$	$=$	160.29
Dual form			160.2.z.a.149.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.425344 - 1.34873i) q^{2} +(-0.872653 + 2.10677i) q^{3} +(-1.63817 - 1.14735i) q^{4} +(-1.24656 + 1.85636i) q^{5} +(2.47030 + 2.07308i) q^{6} +(3.02408 + 3.02408i) q^{7} +(-2.24425 + 1.72143i) q^{8} +(-1.55564 - 1.55564i) q^{9} +O(q^{10})$	\(q+(0.425344 - 1.34873i) q^{2} +(-0.872653 + 2.10677i) q^{3} +(-1.63817 - 1.14735i) q^{4} +(-1.24656 + 1.85636i) q^{5} +(2.47030 + 2.07308i) q^{6} +(3.02408 + 3.02408i) q^{7} +(-2.24425 + 1.72143i) q^{8} +(-1.55564 - 1.55564i) q^{9} +(1.97353 + 2.47087i) q^{10} +(1.86770 - 0.773625i) q^{11} +(3.84676 - 2.45000i) q^{12} +(-1.07611 - 0.445737i) q^{13} +(5.36495 - 2.79241i) q^{14} +(-2.82312 - 4.24618i) q^{15} +(1.36717 + 3.75910i) q^{16} -3.22297 q^{17} +(-2.75983 + 1.43646i) q^{18} +(-1.40346 + 3.38826i) q^{19} +(4.17197 - 1.61079i) q^{20} +(-9.01002 + 3.73207i) q^{21} +(-0.249002 - 2.84808i) q^{22} +(6.24664 - 6.24664i) q^{23} +(-1.66821 - 6.23034i) q^{24} +(-1.89218 - 4.62814i) q^{25} +(-1.05890 + 1.26179i) q^{26} +(-1.68540 + 0.698114i) q^{27} +(-1.48426 - 8.42363i) q^{28} +(-2.66356 - 1.10328i) q^{29} +(-6.92776 + 2.00155i) q^{30} +6.92742 q^{31} +(5.65154 - 0.245044i) q^{32} +4.60992i q^{33} +(-1.37087 + 4.34693i) q^{34} +(-9.38349 + 1.84410i) q^{35} +(0.763532 + 4.33326i) q^{36} +(10.1503 - 4.20439i) q^{37} +(3.97291 + 3.33407i) q^{38} +(1.87813 - 1.87813i) q^{39} +(-0.398008 - 6.31202i) q^{40} +(-1.40549 - 1.40549i) q^{41} +(1.20122 + 13.7395i) q^{42} +(1.31076 + 3.16447i) q^{43} +(-3.94722 - 0.875576i) q^{44} +(4.82704 - 0.948638i) q^{45} +(-5.76809 - 11.0820i) q^{46} -2.41036 q^{47} +(-9.11263 - 0.400070i) q^{48} +11.2901i q^{49} +(-7.04695 + 0.583497i) q^{50} +(2.81254 - 6.79006i) q^{51} +(1.25142 + 1.96486i) q^{52} +(-0.510478 - 1.23240i) q^{53} +(0.224698 + 2.57009i) q^{54} +(-0.892064 + 4.43150i) q^{55} +(-11.9926 - 1.58106i) q^{56} +(-5.91355 - 5.91355i) q^{57} +(-2.62096 + 3.12316i) q^{58} +(1.03161 + 2.49053i) q^{59} +(-0.247115 + 10.1951i) q^{60} +(2.26479 + 0.938105i) q^{61} +(2.94654 - 9.34325i) q^{62} -9.40877i q^{63} +(2.07335 - 7.72666i) q^{64} +(2.16888 - 1.44201i) q^{65} +(6.21755 + 1.96080i) q^{66} +(2.43510 - 5.87886i) q^{67} +(5.27976 + 3.69788i) q^{68} +(7.70909 + 18.6114i) q^{69} +(-1.50401 + 13.4402i) q^{70} +(2.32800 - 2.32800i) q^{71} +(6.16918 + 0.813325i) q^{72} +(0.592312 - 0.592312i) q^{73} +(-1.35324 - 15.4783i) q^{74} +(11.4016 + 0.0523716i) q^{75} +(6.18663 - 3.94027i) q^{76} +(7.98757 + 3.30856i) q^{77} +(-1.73425 - 3.33195i) q^{78} +14.1092i q^{79} +(-8.68252 - 2.14797i) q^{80} -10.7600i q^{81} +(-2.49345 + 1.29781i) q^{82} +(-2.38317 - 0.987140i) q^{83} +(19.0419 + 4.22390i) q^{84} +(4.01762 - 5.98301i) q^{85} +(4.82555 - 0.421887i) q^{86} +(4.64873 - 4.64873i) q^{87} +(-2.85984 + 4.95132i) q^{88} +(6.48035 - 6.48035i) q^{89} +(0.773689 - 6.91389i) q^{90} +(-1.90628 - 4.60217i) q^{91} +(-17.4001 + 3.06595i) q^{92} +(-6.04524 + 14.5945i) q^{93} +(-1.02523 + 3.25093i) q^{94} +(-4.54035 - 6.82901i) q^{95} +(-4.41559 + 12.1204i) q^{96} +1.47782i q^{97} +(15.2274 + 4.80218i) q^{98} +(-4.10895 - 1.70198i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q - 8 q^{4} - 4 q^{5} - 8 q^{6} - 8 q^{9}+O(q^{10}) $ 88 * q - 8 * q^4 - 4 * q^5 - 8 * q^6 - 8 * q^9	$ 88 q - 8 q^{4} - 4 q^{5} - 8 q^{6} - 8 q^{9} - 4 q^{10} - 8 q^{11} - 24 q^{14} - 8 q^{16} - 8 q^{19} - 4 q^{20} - 8 q^{21} - 16 q^{24} - 4 q^{25} + 32 q^{26} - 8 q^{29} - 52 q^{30} - 64 q^{31} - 24 q^{34} + 20 q^{35} + 72 q^{36} - 8 q^{39} - 56 q^{40} - 8 q^{41} - 8 q^{44} - 16 q^{45} - 8 q^{46} - 44 q^{50} - 48 q^{51} + 24 q^{54} + 28 q^{55} - 56 q^{56} + 24 q^{59} + 32 q^{60} + 24 q^{61} + 64 q^{64} - 8 q^{65} - 8 q^{66} - 40 q^{69} + 80 q^{70} - 40 q^{71} + 128 q^{74} + 28 q^{75} - 8 q^{76} + 48 q^{80} + 200 q^{84} - 24 q^{85} + 24 q^{86} - 8 q^{89} + 80 q^{90} - 8 q^{91} + 120 q^{94} - 8 q^{95} - 56 q^{96} - 48 q^{99}+O(q^{100}) $ 88 * q - 8 * q^4 - 4 * q^5 - 8 * q^6 - 8 * q^9 - 4 * q^10 - 8 * q^11 - 24 * q^14 - 8 * q^16 - 8 * q^19 - 4 * q^20 - 8 * q^21 - 16 * q^24 - 4 * q^25 + 32 * q^26 - 8 * q^29 - 52 * q^30 - 64 * q^31 - 24 * q^34 + 20 * q^35 + 72 * q^36 - 8 * q^39 - 56 * q^40 - 8 * q^41 - 8 * q^44 - 16 * q^45 - 8 * q^46 - 44 * q^50 - 48 * q^51 + 24 * q^54 + 28 * q^55 - 56 * q^56 + 24 * q^59 + 32 * q^60 + 24 * q^61 + 64 * q^64 - 8 * q^65 - 8 * q^66 - 40 * q^69 + 80 * q^70 - 40 * q^71 + 128 * q^74 + 28 * q^75 - 8 * q^76 + 48 * q^80 + 200 * q^84 - 24 * q^85 + 24 * q^86 - 8 * q^89 + 80 * q^90 - 8 * q^91 + 120 * q^94 - 8 * q^95 - 56 * q^96 - 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/160\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$101$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{8}\right)$

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 $

$2$	0.425344	−	1.34873i	0.300763	−	0.953699i
$2$	0.425344	−	1.34873i	0.300763	−	0.953699i
$3$	−0.872653	+	2.10677i	−0.503827	+	1.21635i	0.443557	+	0.896246i	$0.353716\pi$
$3$	−0.872653	+	2.10677i	−0.503827	+	1.21635i	−0.947384	+	0.320099i	$0.896284\pi$
$4$	−1.63817	−	1.14735i	−0.819083	−	0.573675i
$5$	−1.24656	+	1.85636i	−0.557478	+	0.830191i
$5$	−1.24656	+	1.85636i	−0.557478	+	0.830191i
$6$	2.47030	+	2.07308i	1.00849	+	0.846331i
$7$	3.02408	+	3.02408i	1.14299	+	1.14299i	0.987899	+	0.155095i	$0.0495685\pi$
$7$	3.02408	+	3.02408i	1.14299	+	1.14299i	0.155095	+	0.987899i	$0.450431\pi$
$8$	−2.24425	+	1.72143i	−0.793464	+	0.608618i
$9$	−1.55564	−	1.55564i	−0.518547	−	0.518547i
$10$	1.97353	+	2.47087i	0.624084	+	0.781358i
$11$	1.86770	−	0.773625i	0.563132	−	0.233257i	−0.0829124	−	0.996557i	$-0.526422\pi$
$11$	1.86770	−	0.773625i	0.563132	−	0.233257i	0.646044	+	0.763300i	$0.276422\pi$
$12$	3.84676	−	2.45000i	1.11046	−	0.707254i
$13$	−1.07611	−	0.445737i	−0.298458	−	0.123625i	0.228429	−	0.973560i	$-0.426641\pi$
$13$	−1.07611	−	0.445737i	−0.298458	−	0.123625i	−0.526887	+	0.849935i	$0.676641\pi$
$14$	5.36495	−	2.79241i	1.43384	−	0.746302i
$15$	−2.82312	−	4.24618i	−0.728927	−	1.09636i
$16$	1.36717	+	3.75910i	0.341793	+	0.939775i
$17$	−3.22297			−0.781685			−0.390843	−	0.920458i	$-0.627816\pi$
$17$	−3.22297			−0.781685			−0.390843	+	0.920458i	$0.627816\pi$
$18$	−2.75983	+	1.43646i	−0.650498	+	0.338578i
$19$	−1.40346	+	3.38826i	−0.321977	+	0.777320i	0.677162	+	0.735834i	$0.263209\pi$
$19$	−1.40346	+	3.38826i	−0.321977	+	0.777320i	−0.999139	+	0.0414868i	$0.986791\pi$
$20$	4.17197	−	1.61079i	0.932881	−	0.360184i
$21$	−9.01002	+	3.73207i	−1.96615	+	0.814405i
$22$	−0.249002	−	2.84808i	−0.0530873	−	0.607213i
$23$	6.24664	−	6.24664i	1.30251	−	1.30251i	0.375824	−	0.926691i	$-0.377360\pi$
$23$	6.24664	−	6.24664i	1.30251	−	1.30251i	0.926691	−	0.375824i	$-0.122640\pi$
$24$	−1.66821	−	6.23034i	−0.340521	−	1.27176i
$25$	−1.89218	−	4.62814i	−0.378436	−	0.925628i
$26$	−1.05890	+	1.26179i	−0.207666	+	0.247457i
$27$	−1.68540	+	0.698114i	−0.324355	+	0.134352i
$28$	−1.48426	−	8.42363i	−0.280500	−	1.59192i
$29$	−2.66356	−	1.10328i	−0.494610	−	0.204874i	0.121413	−	0.992602i	$-0.461257\pi$
$29$	−2.66356	−	1.10328i	−0.494610	−	0.204874i	−0.616024	+	0.787728i	$0.711257\pi$
$30$	−6.92776	+	2.00155i	−1.26483	+	0.365432i
$31$	6.92742			1.24420			0.622101	−	0.782937i	$-0.286279\pi$
$31$	6.92742			1.24420			0.622101	+	0.782937i	$0.286279\pi$
$32$	5.65154	−	0.245044i	0.999061	−	0.0433180i
$33$			4.60992i			0.802483i
$34$	−1.37087	+	4.34693i	−0.235102	+	0.745492i
$35$	−9.38349	+	1.84410i	−1.58610	+	0.311710i
$36$	0.763532	+	4.33326i	0.127255	+	0.722211i
$37$	10.1503	−	4.20439i	1.66870	−	0.691197i	0.670007	−	0.742355i	$-0.266291\pi$
$37$	10.1503	−	4.20439i	1.66870	−	0.691197i	0.998691	+	0.0511583i	$0.0162913\pi$
$38$	3.97291	+	3.33407i	0.644491	+	0.540858i
$39$	1.87813	−	1.87813i	0.300742	−	0.300742i
$40$	−0.398008	−	6.31202i	−0.0629306	−	0.998018i
$41$	−1.40549	−	1.40549i	−0.219500	−	0.219500i	0.588787	−	0.808288i	$-0.299606\pi$
$41$	−1.40549	−	1.40549i	−0.219500	−	0.219500i	−0.808288	+	0.588787i	$0.799606\pi$
$42$	1.20122	+	13.7395i	0.185352	+	2.12006i
$43$	1.31076	+	3.16447i	0.199890	+	0.482576i	0.991760	−	0.128114i	$-0.0408922\pi$
$43$	1.31076	+	3.16447i	0.199890	+	0.482576i	−0.791870	+	0.610690i	$0.790892\pi$
$44$	−3.94722	−	0.875576i	−0.595065	−	0.131998i
$45$	4.82704	−	0.948638i	0.719572	−	0.141415i
$46$	−5.76809	−	11.0820i	−0.850458	−	1.63396i
$47$	−2.41036			−0.351587			−0.175793	−	0.984427i	$-0.556249\pi$
$47$	−2.41036			−0.351587			−0.175793	+	0.984427i	$0.556249\pi$
$48$	−9.11263	−	0.400070i	−1.31530	−	0.0577451i
$49$			11.2901i			1.61288i
$50$	−7.04695	+	0.583497i	−0.996590	+	0.0825189i
$51$	2.81254	−	6.79006i	0.393834	−	0.950799i
$52$	1.25142	+	1.96486i	0.173541	+	0.272477i
$53$	−0.510478	−	1.23240i	−0.0701196	−	0.169284i	0.884934	−	0.465716i	$-0.154203\pi$
$53$	−0.510478	−	1.23240i	−0.0701196	−	0.169284i	−0.955054	+	0.296432i	$0.904203\pi$
$54$	0.224698	+	2.57009i	0.0305775	+	0.349745i
$55$	−0.892064	+	4.43150i	−0.120286	+	0.597543i
$56$	−11.9926	−	1.58106i	−1.60257	−	0.211278i
$57$	−5.91355	−	5.91355i	−0.783269	−	0.783269i
$58$	−2.62096	+	3.12316i	−0.344149	+	0.410091i
$59$	1.03161	+	2.49053i	0.134304	+	0.324239i	0.976696	−	0.214626i	$-0.0688533\pi$
$59$	1.03161	+	2.49053i	0.134304	+	0.324239i	−0.842392	+	0.538865i	$0.818853\pi$
$60$	−0.247115	+	10.1951i	−0.0319024	+	1.31618i
$61$	2.26479	+	0.938105i	0.289976	+	0.120112i	0.522930	−	0.852376i	$-0.324839\pi$
$61$	2.26479	+	0.938105i	0.289976	+	0.120112i	−0.232954	+	0.972488i	$0.574839\pi$
$62$	2.94654	−	9.34325i	0.374210	−	1.18659i
$63$		−	9.40877i		−	1.18539i
$64$	2.07335	−	7.72666i	0.259169	−	0.965832i
$65$	2.16888	−	1.44201i	0.269016	−	0.178859i
$66$	6.21755	+	1.96080i	0.765328	+	0.241358i
$67$	2.43510	−	5.87886i	0.297495	−	0.718217i	−0.702484	−	0.711700i	$-0.747926\pi$
$67$	2.43510	−	5.87886i	0.297495	−	0.718217i	0.999979	−	0.00651672i	$-0.00207435\pi$
$68$	5.27976	+	3.69788i	0.640265	+	0.448433i
$69$	7.70909	+	18.6114i	0.928066	+	2.24055i
$70$	−1.50401	+	13.4402i	−0.179763	+	1.60641i
$71$	2.32800	−	2.32800i	0.276283	−	0.276283i	−0.555340	−	0.831623i	$-0.687412\pi$
$71$	2.32800	−	2.32800i	0.276283	−	0.276283i	0.831623	+	0.555340i	$0.187412\pi$
$72$	6.16918	+	0.813325i	0.727045	+	0.0958512i
$73$	0.592312	−	0.592312i	0.0693249	−	0.0693249i	−0.671594	−	0.740919i	$-0.734390\pi$
$73$	0.592312	−	0.592312i	0.0693249	−	0.0693249i	0.740919	+	0.671594i	$0.234390\pi$
$74$	−1.35324	−	15.4783i	−0.157311	−	1.79932i
$75$	11.4016	+	0.0523716i	1.31655	+	0.00604735i
$76$	6.18663	−	3.94027i	0.709655	−	0.451980i
$77$	7.98757	+	3.30856i	0.910268	+	0.377045i
$78$	−1.73425	−	3.33195i	−0.196365	−	0.377269i
$79$			14.1092i			1.58741i	0.608301	+	0.793707i	$0.291851\pi$
$79$			14.1092i			1.58741i	−0.608301	+	0.793707i	$0.708149\pi$
$80$	−8.68252	−	2.14797i	−0.970736	−	0.240150i
$81$		−	10.7600i		−	1.19555i
$82$	−2.49345	+	1.29781i	−0.275355	+	0.143320i
$83$	−2.38317	−	0.987140i	−0.261586	−	0.108353i	0.248036	−	0.968751i	$-0.420215\pi$
$83$	−2.38317	−	0.987140i	−0.261586	−	0.108353i	−0.509622	+	0.860398i	$0.670215\pi$
$84$	19.0419	+	4.22390i	2.07764	+	0.460865i
$85$	4.01762	−	5.98301i	0.435773	−	0.648948i
$86$	4.82555	−	0.421887i	0.520352	−	0.0454933i
$87$	4.64873	−	4.64873i	0.498396	−	0.498396i
$88$	−2.85984	+	4.95132i	−0.304860	+	0.527813i
$89$	6.48035	−	6.48035i	0.686916	−	0.686916i	−0.274633	−	0.961549i	$-0.588556\pi$
$89$	6.48035	−	6.48035i	0.686916	−	0.686916i	0.961549	+	0.274633i	$0.0885563\pi$
$90$	0.773689	−	6.91389i	0.0815540	−	0.728788i
$91$	−1.90628	−	4.60217i	−0.199833	−	0.482439i
$92$	−17.4001	+	3.06595i	−1.81409	+	0.319647i
$93$	−6.04524	+	14.5945i	−0.626862	+	1.51338i
$94$	−1.02523	+	3.25093i	−0.105744	+	0.335308i
$95$	−4.54035	−	6.82901i	−0.465830	−	0.700642i
$96$	−4.41559	+	12.1204i	−0.450664	+	1.23703i
$97$			1.47782i			0.150050i	0.997182	+	0.0750249i	$0.0239036\pi$
$97$			1.47782i			0.150050i	−0.997182	+	0.0750249i	$0.976096\pi$
$98$	15.2274	+	4.80218i	1.53820	+	0.485094i
$99$	−4.10895	−	1.70198i	−0.412965	−	0.171056i
$100$	−2.21039	+	9.75265i	−0.221039	+	0.975265i
$101$	−4.43262	−	10.7013i	−0.441062	−	1.06482i	−0.975577	−	0.219658i	$-0.929506\pi$
$101$	−4.43262	−	10.7013i	−0.441062	−	1.06482i	0.534515	−	0.845159i	$-0.320494\pi$
$102$	−7.96169	−	6.68147i	−0.788325	−	0.661564i
$103$	−4.04340	−	4.04340i	−0.398408	−	0.398408i	0.479263	−	0.877671i	$-0.340904\pi$
$103$	−4.04340	−	4.04340i	−0.398408	−	0.398408i	−0.877671	+	0.479263i	$0.840904\pi$
$104$	3.18236	−	0.852093i	0.312056	−	0.0835546i
$105$	4.30344	−	21.3781i	0.419973	−	2.08629i
$106$	−1.87931	+	0.164304i	−0.182535	+	0.0159586i
$107$	2.78394	+	6.72104i	0.269134	+	0.649747i	0.999443	−	0.0333698i	$-0.0106239\pi$
$107$	2.78394	+	6.72104i	0.269134	+	0.649747i	−0.730309	+	0.683117i	$0.760624\pi$
$108$	3.56194	+	0.790114i	0.342748	+	0.0760288i
$109$	2.60118	−	6.27980i	0.249148	−	0.601496i	−0.748984	−	0.662588i	$-0.769458\pi$
$109$	2.60118	−	6.27980i	0.249148	−	0.601496i	0.998132	+	0.0610919i	$0.0194583\pi$
$110$	5.59747	+	3.08807i	0.533698	+	0.294436i
$111$			25.0533i			2.37795i
$112$	−7.23338	+	15.5023i	−0.683490	+	1.46483i
$113$	−10.9167			−1.02695			−0.513477	−	0.858104i	$-0.671643\pi$
$113$	−10.9167			−1.02695			−0.513477	+	0.858104i	$0.671643\pi$
$114$	−10.4911	+	5.46052i	−0.982582	+	0.511424i
$115$	3.80923	+	19.3829i	0.355213	+	1.80746i
$116$	3.09750	+	4.86339i	0.287596	+	0.451555i
$117$	0.980626	+	2.36744i	0.0906589	+	0.218870i
$118$	3.79785	−	0.332038i	0.349620	−	0.0305665i
$119$	−9.74652	−	9.74652i	−0.893462	−	0.893462i
$120$	13.6453	+	4.66969i	1.24564	+	0.426283i
$121$	−4.88838	+	4.88838i	−0.444398	+	0.444398i
$122$	2.22857	−	2.65558i	0.201765	−	0.240425i
$123$	4.18755	−	1.73454i	0.377579	−	0.156398i
$124$	−11.3483	−	7.94818i	−1.01910	−	0.713768i
$125$	10.9502	+	2.25668i	0.979418	+	0.201843i
$126$	−12.6899	−	4.00196i	−1.13051	−	0.356523i
$127$			19.2892i			1.71164i	0.517276	+	0.855819i	$0.326946\pi$
$127$			19.2892i			1.71164i	−0.517276	+	0.855819i	$0.673054\pi$
$128$	−9.53932	−	6.08288i	−0.843164	−	0.537656i
$129$	−7.81065			−0.687689
$130$	−1.02236	−	3.53859i	−0.0896671	−	0.310355i
$131$	−13.8960	−	5.75592i	−1.21410	−	0.502897i	−0.318571	−	0.947899i	$-0.603203\pi$
$131$	−13.8960	−	5.75592i	−1.21410	−	0.502897i	−0.895529	+	0.445002i	$0.853203\pi$
$132$	5.28919	−	7.55181i	0.460365	−	0.657300i
$133$	−14.4906	+	6.00219i	−1.25649	+	0.520456i
$134$	−6.89326	−	5.78484i	−0.595487	−	0.499734i
$135$	0.804993	−	3.99895i	0.0692828	−	0.344175i
$136$	7.23316	−	5.54812i	0.620239	−	0.475748i
$137$	−7.40594	+	7.40594i	−0.632732	+	0.632732i	−0.948752	−	0.316020i	$-0.897653\pi$
$137$	−7.40594	+	7.40594i	−0.632732	+	0.632732i	0.316020	+	0.948752i	$0.397653\pi$
$138$	28.3808	−	2.48128i	2.41594	−	0.211220i
$139$	−8.30668	+	3.44074i	−0.704564	+	0.291840i	−0.706053	−	0.708159i	$-0.749526\pi$
$139$	−8.30668	+	3.44074i	−0.704564	+	0.291840i	0.00148919	+	0.999999i	$0.499526\pi$
$140$	17.4875	+	7.74521i	1.47797	+	0.654590i
$141$	2.10341	−	5.07807i	0.177139	−	0.427651i
$142$	−2.14966	−	4.13006i	−0.180395	−	0.346587i
$143$	−2.35467			−0.196908
$144$	3.72098	−	7.97465i	0.310082	−	0.664554i
$145$	5.36838	−	3.56923i	0.445820	−	0.296408i
$146$	−0.546935	−	1.05081i	−0.0452647	−	0.0869654i
$147$	−23.7857	−	9.85236i	−1.96181	−	0.812609i
$148$	−21.4518	−	4.75846i	−1.76332	−	0.391143i
$149$	3.11949	−	1.29214i	0.255559	−	0.105856i	−0.251226	−	0.967928i	$-0.580834\pi$
$149$	3.11949	−	1.29214i	0.255559	−	0.105856i	0.506785	+	0.862072i	$0.330834\pi$
$150$	4.92025	−	15.3555i	0.401737	−	1.25377i
$151$	−3.00768	−	3.00768i	−0.244761	−	0.244761i	0.574055	−	0.818817i	$-0.305369\pi$
$151$	−3.00768	−	3.00768i	−0.244761	−	0.244761i	−0.818817	+	0.574055i	$0.805369\pi$
$152$	−2.68293	−	10.0201i	−0.217614	−	0.812736i
$153$	5.01379	+	5.01379i	0.405341	+	0.405341i
$154$	7.85983	−	9.36583i	0.633363	−	0.754720i
$155$	−8.63545	+	12.8598i	−0.693616	+	1.03293i
$156$	−5.23157	+	0.921816i	−0.418861	+	0.0738044i
$157$	6.43281	−	15.5302i	0.513394	−	1.23944i	−0.428503	−	0.903540i	$-0.640959\pi$
$157$	6.43281	−	15.5302i	0.513394	−	1.23944i	0.941897	−	0.335902i	$-0.109041\pi$
$158$	19.0296	+	6.00127i	1.51391	+	0.477436i
$159$	3.04186			0.241235
$160$	−6.59010	+	10.7968i	−0.520993	+	0.853561i
$161$	37.7807			2.97754
$162$	−14.5124	−	4.57669i	−1.14020	−	0.359579i
$163$	7.32080	−	17.6740i	0.573410	−	1.38433i	−0.325226	−	0.945636i	$-0.605440\pi$
$163$	7.32080	−	17.6740i	0.573410	−	1.38433i	0.898635	−	0.438697i	$-0.144560\pi$
$164$	0.689835	+	3.91501i	0.0538671	+	0.305711i
$165$	−8.55769	−	5.74654i	−0.666215	−	0.447367i
$166$	−2.34505	+	2.79438i	−0.182011	+	0.216886i
$167$	3.45376	+	3.45376i	0.267260	+	0.267260i	0.827995	−	0.560735i	$-0.189481\pi$
$167$	3.45376	+	3.45376i	0.267260	+	0.267260i	−0.560735	+	0.827995i	$0.689481\pi$
$168$	13.7963	−	23.8858i	1.06440	−	1.84283i
$169$	−8.23307	−	8.23307i	−0.633313	−	0.633313i
$170$	−6.36061	−	7.96354i	−0.487837	−	0.610776i
$171$	7.45421	−	3.08763i	0.570037	−	0.236117i
$172$	1.48350	−	6.68782i	0.113116	−	0.509942i
$173$	20.3437	+	8.42665i	1.54671	+	0.640667i	0.982717	−	0.185115i	$-0.0592658\pi$
$173$	20.3437	+	8.42665i	1.54671	+	0.640667i	0.563989	+	0.825782i	$0.309266\pi$
$174$	−4.29259	−	8.24720i	−0.325420	−	0.625219i
$175$	8.27376	−	19.7180i	0.625437	−	1.49054i
$176$	5.46160	+	5.96318i	0.411684	+	0.449492i
$177$	−6.14721			−0.462053
$178$	−5.98390	−	11.4967i	−0.448512	−	0.861710i
$179$	−1.10130	+	2.65878i	−0.0823152	+	0.198726i	−0.959678	−	0.281101i	$-0.909301\pi$
$179$	−1.10130	+	2.65878i	−0.0823152	+	0.198726i	0.877363	+	0.479827i	$0.159301\pi$
$180$	−8.99591	−	3.98428i	−0.670515	−	0.296971i
$181$	−15.8975	+	6.58497i	−1.18165	+	0.489457i	−0.885029	−	0.465537i	$-0.845861\pi$
$181$	−15.8975	+	6.58497i	−1.18165	+	0.489457i	−0.296626	+	0.954994i	$0.595861\pi$
$182$	−7.01793	+	0.613563i	−0.520204	+	0.0454803i
$183$	−3.95274	+	3.95274i	−0.292195	+	0.292195i
$184$	−3.26589	+	24.7722i	−0.240764	+	1.82623i
$185$	−4.84806	+	24.0837i	−0.356437	+	1.77067i
$186$	17.1128	+	14.3611i	1.25477	+	1.05301i
$187$	−6.01953	+	2.49337i	−0.440192	+	0.182333i
$188$	3.94857	+	2.76553i	0.287979	+	0.201697i
$189$	−7.20793	−	2.98562i	−0.524300	−	0.217172i
$190$	−11.1417	+	3.21904i	−0.808306	+	0.233534i
$191$	−15.4539			−1.11821			−0.559103	−	0.829099i	$-0.688854\pi$
$191$	−15.4539			−1.11821			−0.559103	+	0.829099i	$0.688854\pi$
$192$	14.4690	+	11.1108i	1.04421	+	0.801850i
$193$			6.67958i			0.480807i	0.970673	+	0.240403i	$0.0772797\pi$
$193$			6.67958i			0.480807i	−0.970673	+	0.240403i	$0.922720\pi$
$194$	1.99318	+	0.628581i	0.143102	+	0.0451295i
$195$	1.14530	+	5.82770i	0.0820163	+	0.417331i
$196$	12.9537	−	18.4951i	0.925267	−	1.32108i
$197$	−7.69762	+	3.18846i	−0.548432	+	0.227168i	−0.639655	−	0.768662i	$-0.720923\pi$
$197$	−7.69762	+	3.18846i	−0.548432	+	0.227168i	0.0912223	+	0.995831i	$0.470923\pi$
$198$	−4.04324	+	4.81795i	−0.287340	+	0.342397i
$199$	13.1455	−	13.1455i	0.931861	−	0.931861i	−0.0659608	−	0.997822i	$-0.521011\pi$
$199$	13.1455	−	13.1455i	0.931861	−	0.931861i	0.997822	+	0.0659608i	$0.0210112\pi$
$200$	12.2135	+	7.12946i	0.863628	+	0.504129i
$201$	10.2604	+	10.2604i	0.723713	+	0.723713i
$202$	−16.3186	+	1.42670i	−1.14817	+	0.100382i
$203$	−4.71840	−	11.3912i	−0.331167	−	0.799508i
$204$	−12.3980	+	7.89628i	−0.868032	+	0.552850i
$205$	4.36113	−	0.857074i	0.304594	−	0.0598607i
$206$	−7.17330	+	3.73363i	−0.499787	+	0.260135i
$207$	−19.4351			−1.35083
$208$	0.204349	−	4.65459i	0.0141691	−	0.322738i
$209$			7.41400i			0.512837i
$210$	−27.0030	−	14.8972i	−1.86338	−	1.02801i
$211$	−0.219322	+	0.529490i	−0.0150987	+	0.0364516i	−0.931249	−	0.364383i	$-0.881280\pi$
$211$	−0.219322	+	0.529490i	−0.0150987	+	0.0364516i	0.916150	+	0.400835i	$0.131280\pi$
$212$	−0.577751	+	2.60458i	−0.0396801	+	0.178883i
$213$	2.87303	+	6.93611i	0.196857	+	0.475255i
$214$	10.2490	−	0.896050i	0.700609	−	0.0612527i
$215$	−7.50835	−	1.51144i	−0.512065	−	0.103079i
$216$	2.58070	−	4.46804i	0.175595	−	0.304012i
$217$	20.9491	+	20.9491i	1.42212	+	1.42212i
$218$	−7.36338	−	6.17937i	−0.498711	−	0.418520i
$219$	0.730983	+	1.76475i	0.0493952	+	0.119251i
$220$	6.54583	−	6.23601i	0.441320	−	0.420432i
$221$	3.46826	+	1.43660i	0.233300	+	0.0966361i
$222$	33.7902	+	10.6563i	2.26785	+	0.715202i
$223$		−	0.594430i		−	0.0398060i	−0.999802	−	0.0199030i	$-0.993664\pi$
$223$		−	0.594430i		−	0.0398060i	0.999802	−	0.0199030i	$-0.00633573\pi$
$224$	17.8318	+	16.3497i	1.19143	+	1.09241i
$225$	−4.25617	+	10.1433i	−0.283745	+	0.676218i
$226$	−4.64333	+	14.7237i	−0.308870	+	0.979404i
$227$	4.10177	−	9.90254i	0.272244	−	0.657255i	−0.727335	−	0.686283i	$-0.759241\pi$
$227$	4.10177	−	9.90254i	0.272244	−	0.657255i	0.999579	+	0.0290280i	$0.00924119\pi$
$228$	2.90246	+	16.4723i	0.192220	+	1.09090i
$229$	−5.23542	−	12.6394i	−0.345966	−	0.835237i	−0.997088	−	0.0762632i	$-0.975701\pi$
$229$	−5.23542	−	12.6394i	−0.345966	−	0.835237i	0.651121	−	0.758974i	$-0.274299\pi$
$230$	27.7625	+	3.10673i	1.83061	+	0.204852i
$231$	−13.9408	+	13.9408i	−0.917235	+	0.917235i
$232$	7.87693	−	2.10909i	0.517146	−	0.138468i
$233$	−2.22105	+	2.22105i	−0.145506	+	0.145506i	−0.776107	−	0.630601i	$-0.782808\pi$
$233$	−2.22105	+	2.22105i	−0.145506	+	0.145506i	0.630601	+	0.776107i	$0.282808\pi$
$234$	3.61015	−	0.315628i	0.236003	−	0.0206332i
$235$	3.00465	−	4.47450i	0.196002	−	0.291884i
$236$	1.16756	−	5.26352i	0.0760017	−	0.342626i
$237$	−29.7249	−	12.3125i	−1.93084	−	0.799781i
$238$	−17.2911	+	8.99984i	−1.12081	+	0.583373i
$239$			8.94076i			0.578329i	0.957279	+	0.289165i	$0.0933775\pi$
$239$			8.94076i			0.578329i	−0.957279	+	0.289165i	$0.906622\pi$
$240$	12.1021	−	16.4177i	0.781188	−	1.05976i
$241$			13.0409i			0.840037i	0.907515	+	0.420019i	$0.137977\pi$
$241$			13.0409i			0.840037i	−0.907515	+	0.420019i	$0.862023\pi$
$242$	4.51388	+	8.67236i	0.290163	+	0.557481i
$243$	17.6126	+	7.29539i	1.12985	+	0.468000i
$244$	−2.63376	−	4.13527i	−0.168609	−	0.264734i
$245$	−20.9586	−	14.0738i	−1.33900	−	0.899143i
$246$	−0.558285	−	6.38566i	−0.0355949	−	0.407135i
$247$	3.02055	−	3.02055i	0.192193	−	0.192193i
$248$	−15.5469	+	11.9251i	−0.987229	+	0.757244i
$249$	4.15935	−	4.15935i	0.263588	−	0.263588i
$250$	7.70126	−	13.8091i	0.487071	−	0.873363i
$251$	−2.54944	−	6.15488i	−0.160919	−	0.388493i	0.822769	−	0.568376i	$-0.192428\pi$
$251$	−2.54944	−	6.15488i	−0.160919	−	0.388493i	−0.983688	+	0.179883i	$0.942428\pi$
$252$	−10.7952	+	15.4131i	−0.680031	+	0.970936i
$253$	6.83427	−	16.4994i	0.429667	−	1.03731i
$254$	26.0160	+	8.20453i	1.63239	+	0.514798i
$255$	9.09884	+	13.6853i	0.569791	+	0.857007i
$256$	−12.2617	+	10.2787i	−0.766355	+	0.642418i
$257$		−	30.8764i		−	1.92602i	−0.269471	−	0.963009i	$-0.586849\pi$
$257$		−	30.8764i		−	1.92602i	0.269471	−	0.963009i	$-0.413151\pi$
$258$	−3.32221	+	10.5345i	−0.206832	+	0.655848i
$259$	43.4097	+	17.9809i	2.69735	+	1.11728i
$260$	−5.20747	−	0.126222i	−0.322954	−	0.00782797i
$261$	2.42723	+	5.85985i	0.150242	+	0.362716i
$262$	−13.6738	+	16.2938i	−0.844769	+	1.00663i
$263$	2.53924	+	2.53924i	0.156576	+	0.156576i	0.781048	−	0.624471i	$-0.214686\pi$
$263$	2.53924	+	2.53924i	0.156576	+	0.156576i	−0.624471	+	0.781048i	$0.714686\pi$
$264$	−7.93565	−	10.3458i	−0.488406	−	0.636741i
$265$	2.92413	+	0.588631i	0.179628	+	0.0361593i
$266$	1.93189	+	22.0969i	0.118451	+	1.35485i
$267$	7.99752	+	19.3077i	0.489440	+	1.18161i
$268$	−10.7342	+	6.83662i	−0.655696	+	0.417613i
$269$	4.28118	−	10.3357i	0.261028	−	0.630178i	−0.737974	−	0.674829i	$-0.764217\pi$
$269$	4.28118	−	10.3357i	0.261028	−	0.630178i	0.999003	+	0.0446505i	$0.0142174\pi$
$270$	−5.05112	−	2.78665i	−0.307402	−	0.169590i
$271$		−	21.4288i		−	1.30171i	−0.759203	−	0.650854i	$-0.774411\pi$
$271$		−	21.4288i		−	1.30171i	0.759203	−	0.650854i	$-0.225589\pi$
$272$	−4.40636	−	12.1155i	−0.267175	−	0.734608i
$273$	11.3593			0.687493
$274$	6.83857	+	13.1387i	0.413133	+	0.793738i
$275$	−7.11446	−	7.18012i	−0.429018	−	0.432978i
$276$	8.72503	−	39.3336i	0.525185	−	2.36760i
$277$	−2.72558	−	6.58014i	−0.163765	−	0.395363i	0.820601	−	0.571502i	$-0.193639\pi$
$277$	−2.72558	−	6.58014i	−0.163765	−	0.395363i	−0.984365	+	0.176139i	$0.943639\pi$
$278$	1.10745	+	12.6670i	0.0664204	+	0.759716i
$279$	−10.7766	−	10.7766i	−0.645178	−	0.645178i
$280$	17.8844	−	20.2917i	1.06880	−	1.21266i
$281$	12.1526	−	12.1526i	0.724962	−	0.724962i	−0.244650	−	0.969612i	$-0.578673\pi$
$281$	12.1526	−	12.1526i	0.724962	−	0.724962i	0.969612	+	0.244650i	$0.0786729\pi$
$282$	−5.95430	−	4.99686i	−0.354573	−	0.297559i
$283$	10.6888	−	4.42746i	0.635386	−	0.263185i	−0.0416537	−	0.999132i	$-0.513263\pi$
$283$	10.6888	−	4.42746i	0.635386	−	0.263185i	0.677039	+	0.735947i	$0.263263\pi$
$284$	−6.48469	+	1.14262i	−0.384796	+	0.0678020i
$285$	18.3493	−	3.60612i	1.08692	−	0.213608i
$286$	−1.00154	+	3.17582i	−0.0592226	+	0.187790i
$287$		−	8.50062i		−	0.501776i
$288$	−9.17298	−	8.41058i	−0.540523	−	0.495598i
$289$	−6.61246			−0.388968
$290$	−2.53053	−	8.75866i	−0.148598	−	0.514326i
$291$	−3.11343	−	1.28962i	−0.182512	−	0.0755990i
$292$	−1.64989	+	0.290716i	−0.0965528	+	0.0170128i
$293$	−6.01561	+	2.49175i	−0.351435	+	0.145569i	−0.551416	−	0.834231i	$-0.685912\pi$
$293$	−6.01561	+	2.49175i	−0.351435	+	0.145569i	0.199980	+	0.979800i	$0.435912\pi$
$294$	−23.4053	+	27.8900i	−1.36503	+	1.62658i
$295$	−5.90929	−	1.18955i	−0.344052	−	0.0692580i
$296$	−15.5423	+	26.9087i	−0.903375	+	1.56404i
$297$	−2.60773	+	2.60773i	−0.151316	+	0.151316i
$298$	−0.415891	−	4.75697i	−0.0240919	−	0.275564i
$299$	−9.50640	+	3.93768i	−0.549770	+	0.227722i
$300$	−18.6177	−	13.1675i	−1.07489	−	0.760225i
$301$	−5.60574	+	13.5335i	−0.323109	+	0.780055i
$302$	−5.33586	+	2.77726i	−0.307044	+	0.159813i
$303$	26.4133			1.51740
$304$	−14.6556	−	0.643421i	−0.840556	−	0.0369027i
$305$	−4.56465	+	3.03486i	−0.261371	+	0.173776i
$306$	8.89485	−	4.62968i	0.508485	−	0.264661i
$307$	9.33139	+	3.86519i	0.532570	+	0.220598i	0.632729	−	0.774374i	$-0.281935\pi$
$307$	9.33139	+	3.86519i	0.532570	+	0.220598i	−0.100158	+	0.994972i	$0.531935\pi$
$308$	−9.28888	−	14.5845i	−0.529283	−	0.831030i
$309$	12.0470	−	4.99003i	0.685330	−	0.283873i
$310$	13.6714	+	17.1168i	0.776486	+	0.972167i
$311$	18.9201	+	18.9201i	1.07286	+	1.07286i	0.997128	+	0.0757301i	$0.0241287\pi$
$311$	18.9201	+	18.9201i	1.07286	+	1.07286i	0.0757301	+	0.997128i	$0.475871\pi$
$312$	−0.981930	+	7.44808i	−0.0555909	+	0.421665i
$313$	−15.2959	−	15.2959i	−0.864573	−	0.864573i	0.127292	−	0.991865i	$-0.459371\pi$
$313$	−15.2959	−	15.2959i	−0.864573	−	0.864573i	−0.991865	+	0.127292i	$0.959371\pi$
$314$	−18.2099	−	15.2818i	−1.02764	−	0.862402i
$315$	17.4661	+	11.7286i	0.984104	+	0.660831i
$316$	16.1882	−	23.1133i	0.910660	−	1.30022i
$317$	−12.5020	+	30.1826i	−0.702185	+	1.69522i	0.0164778	+	0.999864i	$0.494755\pi$
$317$	−12.5020	+	30.1826i	−0.702185	+	1.69522i	−0.718662	+	0.695359i	$0.755245\pi$
$318$	1.29384	−	4.10266i	0.0725548	−	0.230066i
$319$	−5.82825			−0.326319
$320$	11.7589	+	13.4806i	0.657345	+	0.753590i
$321$	−16.5891			−0.925914
$322$	16.0698	−	50.9561i	0.895534	−	2.83967i
$323$	4.52332	−	10.9203i	0.251684	−	0.607620i
$324$	−12.3455	+	17.6266i	−0.685860	+	0.979258i
$325$	−0.0267506	+	5.82378i	−0.00148385	+	0.323045i
$326$	−20.7236	−	17.3913i	−1.14778	−	0.963217i
$327$	10.9602	+	10.9602i	0.606099	+	0.606099i
$328$	5.57373	+	0.734821i	0.307758	+	0.0405737i
$329$	−7.28912	−	7.28912i	−0.401862	−	0.401862i
$330$	−11.3905	+	9.09779i	−0.627027	+	0.500817i
$331$	12.6176	−	5.22637i	0.693525	−	0.287267i	−0.00794292	−	0.999968i	$-0.502528\pi$
$331$	12.6176	−	5.22637i	0.693525	−	0.287267i	0.701468	+	0.712701i	$0.252528\pi$
$332$	2.77143	+	4.35142i	0.152102	+	0.238815i
$333$	−22.3307	−	9.24969i	−1.22372	−	0.506880i
$334$	6.12724	−	3.18917i	0.335268	−	0.174504i
$335$	7.87780	+	11.8488i	0.430410	+	0.647368i
$336$	−26.3475	−	28.7672i	−1.43737	−	1.56938i
$337$	33.2022			1.80864			0.904320	−	0.426854i	$-0.140378\pi$
$337$	33.2022			1.80864			0.904320	+	0.426854i	$0.140378\pi$
$338$	−14.6061	+	7.60233i	−0.794467	+	0.413512i
$339$	9.52646	−	22.9989i	0.517406	−	1.24913i
$340$	−13.4461	+	5.19154i	−0.729220	+	0.281551i
$341$	12.9383	−	5.35923i	0.700650	−	0.290219i
$342$	−0.993797	−	11.3670i	−0.0537384	−	0.614659i
$343$	−12.9737	+	12.9737i	−0.700513	+	0.700513i
$344$	−8.38910	−	4.84547i	−0.452310	−	0.261250i
$345$	−44.1594	−	8.88933i	−2.37746	−	0.478585i
$346$	20.0184	−	23.8541i	1.07620	−	1.28240i
$347$	15.1496	−	6.27516i	0.813272	−	0.336868i	0.0630131	−	0.998013i	$-0.479929\pi$
$347$	15.1496	−	6.27516i	0.813272	−	0.336868i	0.750259	+	0.661145i	$0.229929\pi$
$348$	−12.9491	+	2.28167i	−0.694145	+	0.122310i
$349$	−2.79425	−	1.15742i	−0.149573	−	0.0619551i	0.306641	−	0.951825i	$-0.400795\pi$
$349$	−2.79425	−	1.15742i	−0.149573	−	0.0619551i	−0.456214	+	0.889870i	$0.650795\pi$
$350$	−23.0751	−	19.5460i	−1.23342	−	1.04478i
$351$	2.12484			0.113416
$352$	10.3658	−	4.82984i	0.552499	−	0.257432i
$353$			24.1150i			1.28351i	0.766910	+	0.641755i	$0.221793\pi$
$353$			24.1150i			1.28351i	−0.766910	+	0.641755i	$0.778207\pi$
$354$	−2.61468	+	8.29095i	−0.138968	+	0.440659i
$355$	1.41963	+	7.22362i	0.0753461	+	0.383390i
$356$	−18.0511	+	3.18066i	−0.956708	+	0.168574i
$357$	29.0390	−	12.0284i	1.53691	−	0.636608i
$358$	3.11755	+	2.61626i	0.164768	+	0.138274i
$359$	14.7355	−	14.7355i	0.777709	−	0.777709i	−0.201732	−	0.979441i	$-0.564657\pi$
$359$	14.7355	−	14.7355i	0.777709	−	0.777709i	0.979441	+	0.201732i	$0.0646570\pi$
$360$	−9.20008	+	10.4384i	−0.484887	+	0.550152i
$361$	3.92443	+	3.92443i	0.206549	+	0.206549i
$362$	2.11946	+	24.2424i	0.111396	+	1.27415i
$363$	−6.03284	−	14.5646i	−0.316642	−	0.764441i
$364$	−2.15750	+	9.72630i	−0.113084	+	0.509797i
$365$	0.361195	+	1.83790i	0.0189058	+	0.0962000i
$366$	3.64993	+	7.01248i	0.190785	+	0.366548i
$367$	−12.8233			−0.669370			−0.334685	−	0.942330i	$-0.608630\pi$
$367$	−12.8233			−0.669370			−0.334685	+	0.942330i	$0.608630\pi$
$368$	32.0220	+	14.9415i	1.66926	+	0.778880i
$369$			4.37287i			0.227643i
$370$	30.4203	+	16.7826i	1.58148	+	0.872484i
$371$	2.18316	−	5.27061i	0.113344	−	0.273637i
$372$	26.6481	−	16.9722i	1.38164	−	0.879967i
$373$	−7.75298	−	18.7174i	−0.401434	−	0.969148i	−0.987318	−	0.158753i	$-0.949253\pi$
$373$	−7.75298	−	18.7174i	−0.401434	−	0.969148i	0.585884	−	0.810395i	$-0.300747\pi$
$374$	0.802525	+	9.17929i	0.0414976	+	0.474650i
$375$	−14.3100	+	21.1003i	−0.738968	+	1.08962i
$376$	5.40945	−	4.14927i	0.278971	−	0.213982i
$377$	2.37450	+	2.37450i	0.122293	+	0.122293i
$378$	−7.09266	+	8.45166i	−0.364807	+	0.434707i
$379$	−4.85167	−	11.7130i	−0.249213	−	0.601654i	0.748924	−	0.662656i	$-0.230571\pi$
$379$	−4.85167	−	11.7130i	−0.249213	−	0.601654i	−0.998138	+	0.0610012i	$0.980571\pi$
$380$	−0.397428	+	16.3964i	−0.0203876	+	0.841119i
$381$	−40.6379	−	16.8328i	−2.08194	−	0.862368i
$382$	−6.57322	+	20.8432i	−0.336315	+	1.06643i
$383$			15.4184i			0.787843i	0.919144	+	0.393922i	$0.128882\pi$
$383$			15.4184i			0.787843i	−0.919144	+	0.393922i	$0.871118\pi$
$384$	21.1398	−	14.7889i	1.07878	−	0.754694i
$385$	−16.0989	+	10.7035i	−0.820475	+	0.545502i
$386$	9.00897	+	2.84112i	0.458545	+	0.144609i
$387$	2.88369	−	6.96185i	0.146586	−	0.353891i
$388$	1.69558	−	2.42091i	0.0860798	−	0.122903i
$389$	4.57635	+	11.0483i	0.232030	+	0.560170i	0.996416	−	0.0845889i	$-0.0269577\pi$
$389$	4.57635	+	11.0483i	0.232030	+	0.560170i	−0.764386	+	0.644759i	$0.776958\pi$
$390$	8.34717	+	0.934079i	0.422675	+	0.0472989i
$391$	−20.1327	+	20.1327i	−1.01816	+	1.01816i
$392$	−19.4352	−	25.3379i	−0.981624	−	1.27976i
$393$	24.2528	−	24.2528i	1.22339	−	1.22339i
$394$	1.02625	+	11.7382i	0.0517016	+	0.591363i
$395$	−26.1919	−	17.5880i	−1.31786	−	0.884949i
$396$	4.77837	+	7.50254i	0.240122	+	0.377017i
$397$	−20.2417	−	8.38440i	−1.01590	−	0.420801i	−0.188298	−	0.982112i	$-0.560297\pi$
$397$	−20.2417	−	8.38440i	−1.01590	−	0.420801i	−0.827605	+	0.561311i	$0.810297\pi$
$398$	−12.1384	−	23.3212i	−0.608445	−	1.16898i
$399$		−	35.7661i		−	1.79055i
$400$	14.8107	−	13.4404i	0.740535	−	0.672018i
$401$			16.8722i			0.842558i	0.906931	+	0.421279i	$0.138419\pi$
$401$			16.8722i			0.842558i	−0.906931	+	0.421279i	$0.861581\pi$
$402$	18.2028	−	9.47436i	0.907871	−	0.472538i
$403$	−7.45464	−	3.08781i	−0.371342	−	0.153815i
$404$	−5.01676	+	22.6162i	−0.249593	+	1.12520i
$405$	19.9745	+	13.4130i	0.992539	+	0.666496i
$406$	−17.3707	+	1.51868i	−0.862092	+	0.0753709i
$407$	15.7050	−	15.7050i	0.778470	−	0.778470i
$408$	5.37658	+	20.0802i	0.266180	+	0.994119i
$409$	−15.4111	+	15.4111i	−0.762029	+	0.762029i	−0.976689	−	0.214660i	$-0.931136\pi$
$409$	−15.4111	+	15.4111i	−0.762029	+	0.762029i	0.214660	+	0.976689i	$0.431136\pi$
$410$	0.699012	−	6.24655i	0.0345217	−	0.308495i
$411$	−9.13980	−	22.0654i	−0.450833	−	1.08841i
$412$	1.98456	+	11.2629i	0.0977723	+	0.554886i
$413$	−4.41188	+	10.6512i	−0.217095	+	0.524113i
$414$	−8.26658	+	26.2127i	−0.406280	+	1.28829i
$415$	4.80325	−	3.19350i	0.235782	−	0.156763i
$416$	−6.19088	−	2.25541i	−0.303533	−	0.110581i
$417$		−	20.5029i		−	1.00403i
$418$	9.99951	+	3.15350i	0.489092	+	0.154243i
$419$	−24.7884	−	10.2677i	−1.21099	−	0.501611i	−0.316459	−	0.948606i	$-0.602494\pi$
$419$	−24.7884	−	10.2677i	−1.21099	−	0.501611i	−0.894536	+	0.446996i	$0.852494\pi$
$420$	−31.5780	+	30.0834i	−1.54085	+	1.46792i
$421$	−0.698888	−	1.68727i	−0.0340617	−	0.0822323i	0.905933	−	0.423420i	$-0.139171\pi$
$421$	−0.698888	−	1.68727i	−0.0340617	−	0.0822323i	−0.939995	+	0.341188i	$0.889171\pi$
$422$	0.620854	+	0.521022i	0.0302227	+	0.0253630i
$423$	3.74965	+	3.74965i	0.182314	+	0.182314i
$424$	3.26714	+	1.88707i	0.158666	+	0.0916444i
$425$	6.09844	+	14.9164i	0.295818	+	0.723549i
$426$	10.5770	−	0.924724i	0.512457	−	0.0448030i
$427$	4.01199	+	9.68580i	0.194154	+	0.468729i
$428$	3.15082	−	14.2043i	0.152301	−	0.686592i
$429$	2.05481	−	4.96075i	0.0992072	−	0.239507i
$430$	−5.23215	+	9.48388i	−0.252317	+	0.457353i
$431$			9.32379i			0.449111i	0.974461	+	0.224556i	$0.0720931\pi$
$431$			9.32379i			0.449111i	−0.974461	+	0.224556i	$0.927907\pi$
$432$	−4.92851	−	5.38113i	−0.237123	−	0.258900i
$433$	1.29230			0.0621039			0.0310519	−	0.999518i	$-0.490114\pi$
$433$	1.29230			0.0621039			0.0310519	+	0.999518i	$0.490114\pi$
$434$	37.1653	−	19.3442i	1.78399	−	0.928550i
$435$	2.83482	+	14.4246i	0.135919	+	0.691609i
$436$	−11.4663	+	7.30289i	−0.549136	+	0.349745i
$437$	12.3983	+	29.9322i	0.593092	+	1.43185i
$438$	2.69109	−	0.235277i	0.128585	−	0.0112420i
$439$	−9.73766	−	9.73766i	−0.464753	−	0.464753i	0.435457	−	0.900210i	$-0.356587\pi$
$439$	−9.73766	−	9.73766i	−0.464753	−	0.464753i	−0.900210	+	0.435457i	$0.856587\pi$
$440$	−5.62650	−	11.4810i	−0.268233	−	0.547337i
$441$	17.5634	−	17.5634i	0.836352	−	0.836352i
$442$	3.41279	−	4.06671i	0.162330	−	0.193433i
$443$	−26.5769	+	11.0085i	−1.26271	+	0.523031i	−0.910739	−	0.412981i	$-0.864487\pi$
$443$	−26.5769	+	11.0085i	−1.26271	+	0.523031i	−0.351968	+	0.936012i	$0.614487\pi$
$444$	28.7449	−	41.0415i	1.36417	−	1.94774i
$445$	3.95175	+	20.1080i	0.187331	+	0.953213i
$446$	−0.801727	−	0.252837i	−0.0379629	−	0.0119722i
$447$			7.69964i			0.364181i
$448$	29.6360	−	17.0961i	1.40017	−	0.807713i
$449$	−30.6675			−1.44729			−0.723644	−	0.690173i	$-0.757534\pi$
$449$	−30.6675			−1.44729			−0.723644	+	0.690173i	$0.757534\pi$
$450$	11.8702	+	10.0548i	0.559569	+	0.473989i
$451$	−3.71235	−	1.53771i	−0.174808	−	0.0724077i
$452$	17.8833	+	12.5252i	0.841160	+	0.589138i
$453$	8.96115	−	3.71183i	0.421032	−	0.174397i
$454$	−11.6112	−	9.74418i	−0.544942	−	0.457317i
$455$	10.9196	+	2.19813i	0.511919	+	0.103050i
$456$	23.4513	+	3.09174i	1.09821	+	0.144784i
$457$	−14.0159	+	14.0159i	−0.655637	+	0.655637i	−0.954345	−	0.298708i	$-0.903444\pi$
$457$	−14.0159	+	14.0159i	−0.655637	+	0.655637i	0.298708	+	0.954345i	$0.403444\pi$
$458$	−19.2741	+	1.68509i	−0.900619	+	0.0787392i
$459$	5.43199	−	2.25000i	0.253543	−	0.105021i
$460$	15.9988	−	36.1229i	0.745947	−	1.68424i
$461$	−5.57556	+	13.4606i	−0.259680	+	0.626922i	−0.998917	−	0.0465225i	$-0.985186\pi$
$461$	−5.57556	+	13.4606i	−0.259680	+	0.626922i	0.739238	+	0.673445i	$0.235186\pi$
$462$	12.8728	+	24.7320i	0.598895	+	1.15064i
$463$	−23.6735			−1.10020			−0.550100	−	0.835098i	$-0.685411\pi$
$463$	−23.6735			−1.10020			−0.550100	+	0.835098i	$0.685411\pi$
$464$	0.505802	−	11.5210i	0.0234813	−	0.534847i
$465$	−19.5570	−	29.4151i	−0.906932	−	1.36409i
$466$	2.05089	+	3.94031i	0.0950058	+	0.182531i
$467$	1.43351	+	0.593779i	0.0663350	+	0.0274768i	0.415604	−	0.909546i	$-0.363570\pi$
$467$	1.43351	+	0.593779i	0.0663350	+	0.0274768i	−0.349269	+	0.937022i	$0.613570\pi$
$468$	1.10986	−	5.00338i	0.0513031	−	0.231281i
$469$	25.1421	−	10.4142i	1.16095	−	0.480883i
$470$	−4.75690	−	5.95568i	−0.219420	−	0.274715i
$471$	27.1049	+	27.1049i	1.24893	+	1.24893i
$472$	−6.60247	−	3.81353i	−0.303903	−	0.175532i
$473$	4.89622	+	4.89622i	0.225128	+	0.225128i
$474$	−29.2496	+	34.8540i	−1.34348	+	1.60090i
$475$	18.3369	+	0.0842277i	0.841357	+	0.00386463i
$476$	4.78374	+	27.1491i	0.219262	+	1.24438i
$477$	−1.12306	+	2.71130i	−0.0514212	+	0.124142i
$478$	12.0587	+	3.80289i	0.551552	+	0.173940i
$479$	11.3138			0.516939			0.258469	−	0.966019i	$-0.416782\pi$
$479$	11.3138			0.516939			0.258469	+	0.966019i	$0.416782\pi$
$480$	−16.9955	−	23.3057i	−0.775735	−	1.06375i
$481$	−12.7968			−0.583485
$482$	17.5887	+	5.54686i	0.801143	+	0.252652i
$483$	−32.9694	+	79.5953i	−1.50016	+	3.62171i
$484$	13.6167	−	2.39929i	0.618939	−	0.109059i
$485$	−2.74337	−	1.84219i	−0.124570	−	0.0836495i
$486$	17.3310	−	20.6517i	0.786149	−	0.936781i
$487$	−21.8553	−	21.8553i	−0.990356	−	0.990356i	0.00959773	−	0.999954i	$-0.496945\pi$
$487$	−21.8553	−	21.8553i	−0.990356	−	0.990356i	−0.999954	+	0.00959773i	$0.996945\pi$
$488$	−6.69764	+	1.79333i	−0.303188	+	0.0811801i
$489$	30.8465	+	30.8465i	1.39493	+	1.39493i
$490$	−27.8964	+	22.2813i	−1.26023	+	1.00657i
$491$	25.7307	−	10.6580i	1.16121	−	0.480990i	0.282934	−	0.959139i	$-0.408692\pi$
$491$	25.7307	−	10.6580i	1.16121	−	0.480990i	0.878278	+	0.478149i	$0.158692\pi$
$492$	−8.85002	−	1.96312i	−0.398990	−	0.0885044i
$493$	8.58457	+	3.55585i	0.386630	+	0.160147i
$494$	−2.78915	−	5.35869i	−0.125490	−	0.241099i
$495$	8.28155	−	5.50609i	0.372228	−	0.247480i
$496$	9.47099	+	26.0409i	0.425260	+	1.16927i
$497$	14.0801			0.631581
$498$	−3.84071	−	7.37902i	−0.172106	−	0.330662i
$499$	0.975369	−	2.35475i	0.0436635	−	0.105413i	−0.900543	−	0.434767i	$-0.856831\pi$
$499$	0.975369	−	2.35475i	0.0436635	−	0.105413i	0.944207	+	0.329354i	$0.106831\pi$
$500$	−15.3491	−	16.2606i	−0.686432	−	0.727194i
$501$	−10.2902	+	4.26235i	−0.459734	+	0.190428i
$502$	−9.38568	+	0.820570i	−0.418904	+	0.0366238i
$503$	−5.99082	+	5.99082i	−0.267117	+	0.267117i	−0.827938	−	0.560820i	$-0.810486\pi$
$503$	−5.99082	+	5.99082i	−0.267117	+	0.267117i	0.560820	+	0.827938i	$0.310486\pi$
$504$	16.1966	+	21.1157i	0.721452	+	0.940567i
$505$	25.3910	+	5.11123i	1.12988	+	0.227447i
$506$	−19.3464	−	16.2355i	−0.860051	−	0.721757i
$507$	24.5298	−	10.1606i	1.08941	−	0.451247i
$508$	22.1314	−	31.5989i	0.981924	−	1.40197i
$509$	16.3456	+	6.77056i	0.724505	+	0.300100i	0.714292	−	0.699848i	$-0.246749\pi$
$509$	16.3456	+	6.77056i	0.724505	+	0.300100i	0.0102130	+	0.999948i	$0.496749\pi$
$510$	22.3280	−	6.45095i	0.988699	−	0.285653i
$511$	3.58240			0.158476
$512$	8.64778	+	20.9097i	0.382182	+	0.924087i
$513$		−	6.69034i		−	0.295386i
$514$	−41.6441	−	13.1331i	−1.83684	−	0.579275i
$515$	12.5464	−	2.46568i	0.552858	−	0.108651i
$516$	12.7951	+	8.96155i	0.563274	+	0.394510i
$517$	−4.50182	+	1.86471i	−0.197990	+	0.0820100i
$518$	42.7155	−	50.9001i	1.87681	−	2.23642i
$519$	−35.5061	+	35.5061i	−1.55854	+	1.55854i
$520$	−2.38520	+	6.96980i	−0.104598	+	0.305646i
$521$	−1.73731	−	1.73731i	−0.0761131	−	0.0761131i	0.668025	−	0.744138i	$-0.267140\pi$
$521$	−1.73731	−	1.73731i	−0.0761131	−	0.0761131i	−0.744138	+	0.668025i	$0.767140\pi$
$522$	8.93579	−	0.781237i	0.391109	−	0.0341938i
$523$	−6.89338	−	16.6421i	−0.301426	−	0.727708i	−0.999927	−	0.0120981i	$-0.996149\pi$
$523$	−6.89338	−	16.6421i	−0.301426	−	0.727708i	0.698500	−	0.715610i	$-0.253851\pi$
$524$	16.1599	+	25.3727i	0.705949	+	1.10841i
$525$	34.3211	+	34.6379i	1.49790	+	1.51172i
$526$	4.50481	−	2.34471i	0.196419	−	0.102234i
$527$	−22.3269			−0.972574
$528$	−17.3291	+	6.30256i	−0.754154	+	0.274284i
$529$		−	55.0411i		−	2.39309i
$530$	2.03767	−	3.69350i	0.0885106	−	0.160436i
$531$	2.26955	−	5.47918i	0.0984902	−	0.237776i
$532$	30.6246	+	6.79318i	1.32774	+	0.294522i
$533$	0.885975	+	2.13893i	0.0383758	+	0.0926475i
$534$	29.4427	−	2.57411i	1.27411	−	0.111393i
$535$	−15.9470	−	3.21016i	−0.689451	−	0.138787i
$536$	4.65506	+	17.3855i	0.201068	+	0.750939i
$537$	−4.64038	−	4.64038i	−0.200247	−	0.200247i
$538$	−12.1191	−	10.1704i	−0.522493	−	0.438477i
$539$	8.73433	+	21.0865i	0.376214	+	0.908261i
$540$	−5.90691	+	5.62734i	−0.254193	+	0.242162i
$541$	−20.1097	−	8.32972i	−0.864584	−	0.358123i	−0.0940857	−	0.995564i	$-0.529993\pi$
$541$	−20.1097	−	8.32972i	−0.864584	−	0.358123i	−0.770499	+	0.637442i	$0.779993\pi$
$542$	−28.9018	−	9.11461i	−1.24144	−	0.391506i
$543$		−	39.2389i		−	1.68390i
$544$	−18.2148	+	0.789768i	−0.780951	+	0.0338610i
$545$	8.41507	+	12.6569i	0.360462	+	0.542161i
$546$	4.83159	−	15.3206i	0.206773	−	0.655661i
$547$	−13.1139	+	31.6598i	−0.560711	+	1.35368i	0.348488	+	0.937313i	$0.386695\pi$
$547$	−13.1139	+	31.6598i	−0.560711	+	1.35368i	−0.909199	+	0.416362i	$0.863305\pi$
$548$	20.6294	−	3.63495i	0.881243	−	0.155277i
$549$	−2.06384	−	4.98255i	−0.0880825	−	0.212650i
$550$	−12.7102	+	6.54149i	−0.541963	+	0.278930i
$551$	7.47642	−	7.47642i	0.318506	−	0.318506i
$552$	−49.3394	−	28.4980i	−2.10002	−	1.21296i
$553$	−42.6675	+	42.6675i	−1.81441	+	1.81441i
$554$	−10.0342	+	0.877266i	−0.426311	+	0.0372715i
$555$	−46.5081	−	31.2304i	−1.97416	−	1.32566i
$556$	17.5555	+	3.89417i	0.744517	+	0.165150i
$557$	−25.3123	−	10.4847i	−1.07251	−	0.444250i	−0.224637	−	0.974442i	$-0.572120\pi$
$557$	−25.3123	−	10.4847i	−1.07251	−	0.444250i	−0.847877	+	0.530192i	$0.822120\pi$
$558$	−19.1185	+	9.95100i	−0.809351	+	0.421259i
$559$		−	3.98955i		−	0.168740i
$560$	−19.7610	−	32.7523i	−0.835055	−	1.38404i
$561$		−	14.8576i		−	0.627289i
$562$	−11.2216	−	21.5596i	−0.473353	−	0.909437i
$563$	11.4048	+	4.72403i	0.480656	+	0.199094i	0.609837	−	0.792527i	$-0.291235\pi$
$563$	11.4048	+	4.72403i	0.480656	+	0.199094i	−0.129181	+	0.991621i	$0.541235\pi$
$564$	−9.27206	+	5.90538i	−0.390424	+	0.248661i
$565$	13.6083	−	20.2653i	0.572504	−	0.852568i
$566$	−1.42504	−	16.2996i	−0.0598989	−	0.685123i
$567$	32.5391	−	32.5391i	1.36651	−	1.36651i
$568$	−1.21713	+	9.23213i	−0.0510698	+	0.387372i
$569$	21.4772	−	21.4772i	0.900369	−	0.900369i	−0.0950987	−	0.995468i	$-0.530317\pi$
$569$	21.4772	−	21.4772i	0.900369	−	0.900369i	0.995468	+	0.0950987i	$0.0303167\pi$
$570$	2.94107	−	26.2822i	0.123188	−	1.10084i
$571$	8.22145	+	19.8483i	0.344057	+	0.830627i	0.997297	+	0.0734760i	$0.0234092\pi$
$571$	8.22145	+	19.8483i	0.344057	+	0.830627i	−0.653240	+	0.757151i	$0.726591\pi$
$572$	3.85734	+	2.70163i	0.161284	+	0.112961i
$573$	13.4859	−	32.5578i	0.563381	−	1.36012i
$574$	−11.4651	−	3.61569i	−0.478543	−	0.150916i
$575$	−40.7301	−	17.0906i	−1.69856	−	0.712725i
$576$	−15.2453	+	8.79452i	−0.635221	+	0.366438i
$577$		−	3.00769i		−	0.125212i	−0.998038	−	0.0626059i	$-0.980059\pi$
$577$		−	3.00769i		−	0.125212i	0.998038	−	0.0626059i	$-0.0199411\pi$
$578$	−2.81257	+	8.91845i	−0.116987	+	0.370959i
$579$	−14.0723	−	5.82896i	−0.584827	−	0.242243i
$580$	−12.8895	−	0.312423i	−0.535205	−	0.0129727i
$581$	−4.22170	−	10.1921i	−0.175145	−	0.422838i
$582$	−3.06363	+	3.65065i	−0.126992	+	0.151324i
$583$	−1.90684	−	1.90684i	−0.0789731	−	0.0789731i
$584$	−0.309674	+	2.34892i	−0.0128144	+	0.0971991i
$585$	−5.61724	−	1.13076i	−0.232244	−	0.0467510i
$586$	0.802002	+	9.17330i	0.0331304	+	0.378945i
$587$	12.2402	+	29.5504i	0.505206	+	1.21968i	0.946614	+	0.322369i	$0.104479\pi$
$587$	12.2402	+	29.5504i	0.505206	+	1.21968i	−0.441408	+	0.897306i	$0.645521\pi$
$588$	27.6608	+	43.4304i	1.14071	+	1.79104i
$589$	−9.72239	+	23.4719i	−0.400604	+	0.967144i
$590$	−4.11786	+	7.46409i	−0.169530	+	0.307292i
$591$		−	18.9995i		−	0.781536i
$592$	29.6819	+	32.4078i	1.21992	+	1.33195i
$593$	−12.0472			−0.494718			−0.247359	−	0.968924i	$-0.579563\pi$
$593$	−12.0472			−0.494718			−0.247359	+	0.968924i	$0.579563\pi$
$594$	2.40795	+	4.62632i	0.0987995	+	0.189820i
$595$	30.2427	−	5.94348i	1.23983	−	0.243659i
$596$	−6.59278	−	1.46242i	−0.270051	−	0.0599030i
$597$	16.2231	+	39.1661i	0.663968	+	1.60296i
$598$	1.26740	+	14.4965i	0.0518277	+	0.592805i
$599$	28.6405	+	28.6405i	1.17022	+	1.17022i	0.982158	+	0.188060i	$0.0602198\pi$
$599$	28.6405	+	28.6405i	1.17022	+	1.17022i	0.188060	+	0.982158i	$0.439780\pi$
$600$	−25.6783	+	19.5096i	−1.04831	+	0.796477i
$601$	−6.80046	+	6.80046i	−0.277396	+	0.277396i	−0.832069	−	0.554672i	$-0.812844\pi$
$601$	−6.80046	+	6.80046i	−0.277396	+	0.277396i	0.554672	+	0.832069i	$0.312844\pi$
$602$	15.8687	+	13.3170i	0.646758	+	0.542761i
$603$	−12.9335	+	5.35725i	−0.526694	+	0.218164i
$604$	1.47621	+	8.37794i	0.0600663	+	0.340893i
$605$	−2.98096	−	15.1683i	−0.121193	−	0.616678i
$606$	11.2347	−	35.6245i	0.456380	−	1.44715i
$607$		−	12.0006i		−	0.487091i	−0.969889	−	0.243545i	$-0.921690\pi$
$607$		−	12.0006i		−	0.487091i	0.969889	−	0.243545i	$-0.0783105\pi$
$608$	−7.10147	+	19.4928i	−0.288002	+	0.790538i
$609$	28.1162			1.13933
$610$	2.15168	+	7.44736i	0.0871189	+	0.301535i
$611$	2.59380	+	1.07439i	0.104934	+	0.0434650i
$612$	−2.46084	−	13.9660i	−0.0994737	−	0.564542i
$613$	13.7408	−	5.69161i	0.554984	−	0.229882i	−0.0875220	−	0.996163i	$-0.527895\pi$
$613$	13.7408	−	5.69161i	0.554984	−	0.229882i	0.642506	+	0.766281i	$0.277895\pi$
$614$	9.18215	−	10.9415i	0.370562	−	0.441564i
$615$	−2.00009	+	9.93582i	−0.0806515	+	0.400651i
$616$	−23.6216	+	6.32480i	−0.951741	+	0.254834i
$617$	10.5851	−	10.5851i	0.426140	−	0.426140i	−0.461171	−	0.887311i	$-0.652571\pi$
$617$	10.5851	−	10.5851i	0.426140	−	0.426140i	0.887311	+	0.461171i	$0.152571\pi$
$618$	−1.60611	−	18.3707i	−0.0646072	−	0.738977i
$619$	−25.2044	+	10.4400i	−1.01305	+	0.419620i	−0.826567	−	0.562838i	$-0.809710\pi$
$619$	−25.2044	+	10.4400i	−1.01305	+	0.419620i	−0.186485	+	0.982458i	$0.559710\pi$
$620$	28.9010	−	11.1586i	1.16069	−	0.448142i
$621$	−6.16720	+	14.8889i	−0.247481	+	0.597473i
$622$	33.5657	−	17.4706i	1.34586	−	0.700507i
$623$	39.1942			1.57028
$624$	9.62783	+	4.49236i	0.385421	+	0.179838i
$625$	−17.8393	+	17.5145i	−0.713573	+	0.700581i
$626$	−27.1360	+	14.1240i	−1.08457	+	0.564510i
$627$	−15.6196	−	6.46985i	−0.623787	−	0.258381i
$628$	−28.3566	+	18.0603i	−1.13155	+	0.720685i
$629$	−32.7141	+	13.5506i	−1.30440	+	0.540298i
$630$	23.2478	−	18.5684i	0.926216	−	0.739785i
$631$	5.83586	+	5.83586i	0.232322	+	0.232322i	0.813661	−	0.581339i	$-0.197471\pi$
$631$	5.83586	+	5.83586i	0.232322	+	0.232322i	−0.581339	+	0.813661i	$0.697471\pi$
$632$	−24.2881	−	31.6647i	−0.966128	−	1.25955i
$633$	−0.924123	−	0.924123i	−0.0367306	−	0.0367306i
$634$	35.3906	+	29.6999i	1.40554	+	1.17953i
$635$	−35.8077	−	24.0451i	−1.42099	−	0.954201i
$636$	−4.98308	−	3.49008i	−0.197592	−	0.138391i
$637$	5.03243	−	12.1494i	0.199392	−	0.481375i
$638$	−2.47901	+	7.86075i	−0.0981448	+	0.311210i
$639$	−7.24308			−0.286532
$640$	23.1834	−	10.1258i	0.916403	−	0.400256i
$641$	5.31745			0.210027			0.105013	−	0.994471i	$-0.466511\pi$
$641$	5.31745			0.210027			0.105013	+	0.994471i	$0.466511\pi$
$642$	−7.05607	+	22.3743i	−0.278481	+	0.883043i
$643$	5.26853	−	12.7194i	0.207771	−	0.501602i	−0.785301	−	0.619114i	$-0.787492\pi$
$643$	5.26853	−	12.7194i	0.207771	−	0.501602i	0.993071	+	0.117512i	$0.0374918\pi$
$644$	−61.8910	−	43.3477i	−2.43885	−	1.70814i
$645$	9.73644	−	14.4994i	0.383372	−	0.570914i
$646$	−12.8046	−	10.7456i	−0.503789	−	0.422781i
$647$	−17.3149	−	17.3149i	−0.680719	−	0.680719i	0.279443	−	0.960162i	$-0.409850\pi$
$647$	−17.3149	−	17.3149i	−0.680719	−	0.680719i	−0.960162	+	0.279443i	$0.909850\pi$
$648$	18.5226	+	24.1481i	0.727636	+	0.948629i
$649$	3.85347	+	3.85347i	0.151262	+	0.151262i
$650$	7.84335	+	2.51319i	0.307641	+	0.0985753i
$651$	−62.4162	+	25.8536i	−2.44628	+	1.01328i
$652$	−32.2709	+	20.5534i	−1.26383	+	0.804933i
$653$	12.0053	+	4.97274i	0.469802	+	0.194598i	0.605008	−	0.796219i	$-0.293170\pi$
$653$	12.0053	+	4.97274i	0.469802	+	0.194598i	−0.135206	+	0.990817i	$0.543170\pi$
$654$	19.4442	−	10.1205i	0.760328	−	0.395744i
$655$	28.0073	−	18.6210i	1.09434	−	0.727582i
$656$	3.36183	−	7.20492i	0.131257	−	0.281305i
$657$	−1.84285			−0.0718964
$658$	−12.9315	+	6.73070i	−0.504121	+	0.262390i
$659$	−15.5655	+	37.5784i	−0.606345	+	1.46385i	0.260602	+	0.965446i	$0.416079\pi$
$659$	−15.5655	+	37.5784i	−0.606345	+	1.46385i	−0.866947	+	0.498400i	$0.833921\pi$
$660$	7.42562	+	19.2324i	0.289042	+	0.748622i
$661$	32.6180	−	13.5108i	1.26869	−	0.525510i	0.356127	−	0.934437i	$-0.384097\pi$
$661$	32.6180	−	13.5108i	1.26869	−	0.525510i	0.912567	+	0.408927i	$0.134097\pi$
$662$	−1.68218	−	19.2408i	−0.0653797	−	0.747814i
$663$	−6.05317	+	6.05317i	−0.235086	+	0.235086i
$664$	7.04772	−	1.88706i	0.273505	−	0.0732323i
$665$	6.92110	−	34.3818i	0.268389	−	1.33327i
$666$	−21.9736	+	26.1839i	−0.851460	+	1.01461i
$667$	−23.5301	+	9.74649i	−0.911089	+	0.377386i
$668$	−1.69516	−	9.62051i	−0.0655877	−	0.372229i
$669$	1.25233	+	0.518731i	0.0484178	+	0.0200553i
$670$	19.3316	−	5.58525i	0.746846	−	0.215777i
$671$	4.95567			0.191312
$672$	−50.0060	+	23.2998i	−1.92902	+	0.898810i
$673$		−	40.4407i		−	1.55888i	−0.626480	−	0.779438i	$-0.715505\pi$
$673$		−	40.4407i		−	1.55888i	0.626480	−	0.779438i	$-0.284495\pi$
$674$	14.1224	−	44.7810i	0.543973	−	1.72490i
$675$	6.42004	+	6.47929i	0.247108	+	0.249388i
$676$	4.04091	+	22.9333i	0.155420	+	0.882052i
$677$	15.8703	−	6.57369i	0.609945	−	0.252647i	−0.0562602	−	0.998416i	$-0.517918\pi$
$677$	15.8703	−	6.57369i	0.609945	−	0.252647i	0.666205	+	0.745769i	$0.267918\pi$
$678$	−26.9674	−	22.6311i	−1.03568	−	0.869142i
$679$	−4.46904	+	4.46904i	−0.171506	+	0.171506i
$680$	1.28277	+	20.3435i	0.0491919	+	0.780136i
$681$	17.2830	+	17.2830i	0.662285	+	0.662285i
$682$	−1.72494	−	19.7299i	−0.0660514	−	0.755496i
$683$	5.96174	+	14.3929i	0.228120	+	0.550730i	0.995949	−	0.0899254i	$-0.0286629\pi$
$683$	5.96174	+	14.3929i	0.228120	+	0.550730i	−0.767829	+	0.640655i	$0.778663\pi$
$684$	−15.7538	−	3.49453i	−0.602363	−	0.133617i
$685$	−4.51618	−	22.9801i	−0.172554	−	0.878023i
$686$	11.9798	+	23.0163i	0.457390	+	0.878767i
$687$	31.1971			1.19024
$688$	−10.1035	+	9.25367i	−0.385192	+	0.352793i
$689$			1.55373i			0.0591926i
$690$	−30.7722	+	55.7782i	−1.17148	+	2.12344i
$691$	−6.78837	+	16.3886i	−0.258242	+	0.623451i	−0.998822	−	0.0485166i	$-0.984551\pi$
$691$	−6.78837	+	16.3886i	−0.258242	+	0.623451i	0.740580	+	0.671968i	$0.234551\pi$
$692$	−23.6581	−	37.1457i	−0.899346	−	1.41207i
$693$	−7.27886	−	17.5727i	−0.276501	−	0.667533i
$694$	−2.01974	−	23.1018i	−0.0766684	−	0.876934i
$695$	3.96751	−	19.7093i	0.150496	−	0.747617i
$696$	−2.43046	+	18.4354i	−0.0921263	+	0.698791i
$697$	4.52985	+	4.52985i	0.171580	+	0.171580i
$698$	−2.74957	+	3.27640i	−0.104073	+	0.124014i
$699$	−2.74104	−	6.61744i	−0.103675	−	0.250295i
$700$	−36.1772	+	22.8084i	−1.36737	+	0.862076i
$701$	22.1202	+	9.16247i	0.835467	+	0.346062i	0.759065	−	0.651015i	$-0.225657\pi$
$701$	22.1202	+	9.16247i	0.835467	+	0.346062i	0.0764026	+	0.997077i	$0.475657\pi$
$702$	0.903787	−	2.86584i	0.0341112	−	0.108164i
$703$			40.2925i			1.51966i
$704$	−2.10515	−	16.0350i	−0.0793408	−	0.604344i
$705$	6.80473	+	10.2348i	0.256281	+	0.385465i
$706$	32.5247	+	10.2571i	1.22408	+	0.386033i
$707$	18.9570	−	45.7661i	0.712950	−	1.72121i
$708$	10.0701	+	7.05301i	0.378459	+	0.265068i
$709$	−16.1729	−	39.0447i	−0.607384	−	1.46636i	−0.865834	−	0.500331i	$-0.833212\pi$
$709$	−16.1729	−	39.0447i	−0.607384	−	1.46636i	0.258450	−	0.966025i	$-0.416788\pi$
$710$	10.3466	+	1.15782i	0.388300	+	0.0434522i
$711$	21.9489	−	21.9489i	0.823149	−	0.823149i
$712$	−3.38808	+	25.6990i	−0.126974	+	0.963112i
$713$	43.2731	−	43.2731i	1.62059	−	1.62059i
$714$	−3.87149	−	44.2821i	−0.144887	−	1.65722i
$715$	2.93524	−	4.37113i	0.109772	−	0.163471i
$716$	4.85467	−	3.09194i	0.181427	−	0.115551i
$717$	−18.8361	−	7.80218i	−0.703448	−	0.291378i
$718$	−13.6066	−	26.1419i	−0.507794	−	0.975606i
$719$		−	1.69729i		−	0.0632983i	−0.999499	−	0.0316492i	$-0.989924\pi$
$719$		−	1.69729i		−	0.0632983i	0.999499	−	0.0316492i	$-0.0100759\pi$
$720$	10.1654	+	16.8484i	0.378843	+	0.627902i
$721$		−	24.4551i		−	0.910756i
$722$	6.96223	−	3.62378i	0.259108	−	0.134863i
$723$	−27.4742	−	11.3802i	−1.02178	−	0.423233i
$724$	33.5981	+	7.45276i	1.24866	+	0.276980i
$725$	−0.0662126	+	14.4149i	−0.00245907	+	0.535357i
$726$	−22.2097	+	1.94175i	−0.824281	+	0.0720651i
$727$	−10.4678	+	10.4678i	−0.388230	+	0.388230i	−0.874056	−	0.485826i	$-0.838519\pi$
$727$	−10.4678	+	10.4678i	−0.388230	+	0.388230i	0.485826	+	0.874056i	$0.338519\pi$
$728$	12.2005	+	7.04691i	0.452181	+	0.261176i
$729$	−7.91408	+	7.91408i	−0.293114	+	0.293114i
$730$	2.63247	+	0.294583i	0.0974320	+	0.0109030i
$731$	−4.22456	−	10.1990i	−0.156251	−	0.377223i
$732$	11.0104	−	1.94007i	0.406957	−	0.0717069i
$733$	0.587974	−	1.41950i	0.0217173	−	0.0524303i	−0.912649	−	0.408744i	$-0.865967\pi$
$733$	0.587974	−	1.41950i	0.0217173	−	0.0524303i	0.934366	+	0.356314i	$0.115967\pi$
$734$	−5.45430	+	17.2952i	−0.201322	+	0.638377i
$735$	47.9399	−	31.8734i	1.76829	−	1.17567i
$736$	33.7725	−	36.8339i	1.24487	−	1.35771i
$737$		−	12.8638i		−	0.473843i
$738$	5.89784	+	1.85997i	0.217103	+	0.0684666i
$739$	20.8137	+	8.62132i	0.765645	+	0.317140i	0.731107	−	0.682263i	$-0.239004\pi$
$739$	20.8137	+	8.62132i	0.765645	+	0.317140i	0.0345378	+	0.999403i	$0.489004\pi$
$740$	35.5743	−	33.8906i	1.30774	−	1.24584i
$741$	3.72771	+	8.99950i	0.136941	+	0.330605i
$742$	−6.18006	−	5.18632i	−0.226877	−	0.190396i
$743$	−4.05453	−	4.05453i	−0.148746	−	0.148746i	0.628811	−	0.777558i	$-0.283542\pi$
$743$	−4.05453	−	4.05453i	−0.148746	−	0.148746i	−0.777558	+	0.628811i	$0.783542\pi$
$744$	−11.5564	−	43.1602i	−0.423677	−	1.58233i
$745$	−1.48996	+	7.40164i	−0.0545878	+	0.271175i
$746$	−28.5424	+	2.49540i	−1.04501	+	0.0913632i
$747$	2.17172	+	5.24299i	0.0794589	+	0.191831i
$748$	12.7218	+	2.82196i	0.465154	+	0.103181i
$749$	−11.9061	+	28.7438i	−0.435039	+	1.05028i
$750$	22.3720	+	28.2753i	0.816911	+	1.03247i
$751$			12.6228i			0.460612i	0.973118	+	0.230306i	$0.0739727\pi$
$751$			12.6228i			0.460612i	−0.973118	+	0.230306i	$0.926027\pi$
$752$	−3.29538	−	9.06078i	−0.120170	−	0.330413i
$753$	15.1917			0.553616
$754$	4.21254	−	2.19259i	0.153412	−	0.0798493i
$755$	9.33260	−	1.83410i	0.339648	−	0.0667497i
$756$	8.38223	+	13.1610i	0.304859	+	0.478660i
$757$	7.03754	+	16.9901i	0.255784	+	0.617517i	0.998651	−	0.0519220i	$-0.0165347\pi$
$757$	7.03754	+	16.9901i	0.255784	+	0.617517i	−0.742867	+	0.669439i	$0.766535\pi$
$758$	−17.8613	+	1.56157i	−0.648751	+	0.0567189i
$759$	28.7965	+	28.7965i	1.04525	+	1.04525i
$760$	21.9454	+	7.51014i	0.796042	+	0.272421i
$761$	2.27570	−	2.27570i	0.0824941	−	0.0824941i	−0.664656	−	0.747150i	$-0.731422\pi$
$761$	2.27570	−	2.27570i	0.0824941	−	0.0824941i	0.747150	+	0.664656i	$0.231422\pi$
$762$	−39.9880	+	47.6500i	−1.44861	+	1.72618i
$763$	26.8568	−	11.1244i	0.972281	−	0.402732i
$764$	25.3161	+	17.7310i	0.915903	+	0.641487i
$765$	−15.5574	+	3.05743i	−0.562479	+	0.110542i
$766$	20.7953	+	6.55812i	0.751365	+	0.236954i
$767$		−	3.13990i		−	0.113375i
$768$	−10.9546	−	34.8023i	−0.395292	−	1.25582i
$769$	42.4200			1.52970			0.764852	−	0.644206i	$-0.222812\pi$
$769$	42.4200			1.52970			0.764852	+	0.644206i	$0.222812\pi$
$770$	7.58865	+	26.2658i	0.273476	+	0.946553i
$771$	65.0495	+	26.9444i	2.34270	+	0.970379i
$772$	7.66382	−	10.9423i	0.275827	−	0.393820i
$773$	42.0471	−	17.4165i	1.51233	−	0.626427i	0.536291	−	0.844033i	$-0.319825\pi$
$773$	42.0471	−	17.4165i	1.51233	−	0.626427i	0.976037	+	0.217607i	$0.0698250\pi$
$774$	−8.16313	−	6.85052i	−0.293418	−	0.246237i
$775$	−13.1079	−	32.0611i	−0.470851	−	1.15167i
$776$	−2.54396	−	3.31660i	−0.0913229	−	0.119059i
$777$	−75.7632	+	75.7632i	−2.71799	+	2.71799i
$778$	16.8477	−	1.47296i	0.604020	−	0.0528082i
$779$	6.73472	−	2.78961i	0.241296	−	0.0999482i
$780$	4.81024	−	10.8608i	0.172234	−	0.388879i
$781$	2.54700	−	6.14901i	0.0911389	−	0.220029i
$782$	18.5904	+	35.7170i	0.664791	+	1.27724i
$783$	5.25937			0.187955
$784$	−42.4407	+	15.4356i	−1.51574	+	0.551270i
$785$	20.8108	+	31.3009i	0.742769	+	1.11718i
$786$	−22.3948	−	43.0264i	−0.798796	−	1.53470i
$787$	−37.4146	−	15.4976i	−1.33369	−	0.552431i	−0.401982	−	0.915647i	$-0.631679\pi$
$787$	−37.4146	−	15.4976i	−1.33369	−	0.552431i	−0.931705	+	0.363216i	$0.881679\pi$
$788$	16.2682	+	3.60864i	0.579532	+	0.128553i
$789$	−7.56548	+	3.13373i	−0.269338	+	0.111564i
$790$	−34.8621	+	27.8449i	−1.24034	+	0.990679i
$791$	−33.0129	−	33.0129i	−1.17380	−	1.17380i
$792$	12.1514	−	3.25359i	0.431780	−	0.115611i
$793$	−2.01900	−	2.01900i	−0.0716967	−	0.0716967i
$794$	−19.9180	+	23.7344i	−0.706864	+	0.842304i
$795$	−3.79186	+	5.64681i	−0.134484	+	0.200272i
$796$	−36.6171	+	6.45202i	−1.29786	+	0.228686i
$797$	−9.32457	+	22.5115i	−0.330293	+	0.797398i	0.668276	+	0.743914i	$0.267033\pi$
$797$	−9.32457	+	22.5115i	−0.330293	+	0.797398i	−0.998569	+	0.0534843i	$0.982967\pi$
$798$	−48.2390	−	15.2129i	−1.70764	−	0.538531i
$799$	7.76851			0.274830
$800$	−11.8278	−	25.6925i	−0.418177	−	0.908366i
$801$	−20.1622			−0.712397
$802$	22.7561	+	7.17649i	0.803547	+	0.253411i
$803$	0.648031	−	1.56449i	0.0228685	−	0.0552095i
$804$	−5.03596	−	28.5805i	−0.177605	−	1.00796i
$805$	−47.0959	+	70.1347i	−1.65991	+	2.47192i
$806$	−7.33542	+	8.74094i	−0.258379	+	0.307886i
$807$	18.0390	+	18.0390i	0.635001	+	0.635001i
$808$	28.3694	+	16.3860i	0.998033	+	0.576456i
$809$	−32.3653	−	32.3653i	−1.13790	−	1.13790i	−0.988825	−	0.149078i	$-0.952369\pi$
$809$	−32.3653	−	32.3653i	−1.13790	−	1.13790i	−0.149078	−	0.988825i	$-0.547631\pi$
$810$	26.5865	−	21.2351i	0.934155	−	0.746126i
$811$	−23.2335	+	9.62364i	−0.815840	+	0.337932i	−0.751281	−	0.659982i	$-0.770564\pi$
$811$	−23.2335	+	9.62364i	−0.815840	+	0.337932i	−0.0645583	+	0.997914i	$0.520564\pi$
$812$	−5.34021	+	24.0744i	−0.187405	+	0.844845i
$813$	45.1456	+	18.6999i	1.58333	+	0.655835i
$814$	−14.5019	−	27.8620i	−0.508291	−	0.976561i
$815$	23.6835	+	35.6217i	0.829598	+	1.24778i
$816$	29.3698	+	1.28941i	1.02815	+	0.0451385i
$817$	−12.5616			−0.439476
$818$	14.2304	+	27.3404i	0.497556	+	0.955936i
$819$	−4.19384	+	10.1248i	−0.146545	+	0.353790i
$820$	−8.12761	−	3.59971i	−0.283828	−	0.125707i
$821$	−24.1730	+	10.0128i	−0.843645	+	0.349449i	−0.762290	−	0.647236i	$-0.775925\pi$
$821$	−24.1730	+	10.0128i	−0.843645	+	0.349449i	−0.0813552	+	0.996685i	$0.525925\pi$
$822$	−33.6480	+	2.94177i	−1.17361	+	0.102606i
$823$	−13.3174	+	13.3174i	−0.464214	+	0.464214i	−0.900034	−	0.435820i	$-0.856458\pi$
$823$	−13.3174	+	13.3174i	−0.464214	+	0.464214i	0.435820	+	0.900034i	$0.356458\pi$
$824$	16.0348	+	2.11398i	0.558600	+	0.0736440i
$825$	21.3353	−	8.72279i	0.742801	−	0.303688i
$826$	12.4891	+	10.4809i	0.434552	+	0.364677i
$827$	−44.3056	+	18.3520i	−1.54066	+	0.638161i	−0.981597	−	0.190966i	$-0.938838\pi$
$827$	−44.3056	+	18.3520i	−1.54066	+	0.638161i	−0.559061	+	0.829127i	$0.688838\pi$
$828$	31.8379	+	22.2988i	1.10644	+	0.774938i
$829$	21.7557	+	9.01150i	0.755606	+	0.312982i	0.727027	−	0.686609i	$-0.240902\pi$
$829$	21.7557	+	9.01150i	0.755606	+	0.312982i	0.0285795	+	0.999592i	$0.490902\pi$
$830$	−2.26415	−	7.83664i	−0.0785896	−	0.272014i
$831$	16.2414			0.563406
$832$	−5.67520	+	7.39053i	−0.196752	+	0.256220i
$833$		−	36.3877i		−	1.26076i
$834$	−27.6529	−	8.72076i	−0.957542	−	0.301975i
$835$	−10.7168	+	2.10612i	−0.370869	+	0.0728854i
$836$	8.50646	−	12.1454i	0.294202	−	0.420056i
$837$	−11.6755	+	4.83613i	−0.403563	+	0.167161i
$838$	−24.3920	+	29.0657i	−0.842608	+	1.00406i
$839$	0.354193	−	0.354193i	0.0122281	−	0.0122281i	−0.700966	−	0.713194i	$-0.747248\pi$
$839$	0.354193	−	0.354193i	0.0122281	−	0.0122281i	0.713194	+	0.700966i	$0.247248\pi$
$840$	27.1430	+	55.3860i	0.936522	+	1.91100i
$841$	−14.6288	−	14.6288i	−0.504441	−	0.504441i
$842$	−2.57294	+	0.224947i	−0.0886694	+	0.00775217i
$843$	14.9977	+	36.2077i	0.516549	+	1.24706i
$844$	0.966797	−	0.615753i	0.0332785	−	0.0211951i
$845$	25.5466	−	5.02057i	0.878829	−	0.172713i
$846$	6.65217	−	3.46239i	0.228706	−	0.119040i
$847$	−29.5657			−1.01589
$848$	3.93482	−	3.60385i	0.135122	−	0.123757i
$849$			26.3826i			0.905448i
$850$	22.7121	−	1.88059i	0.779019	−	0.0645038i
$851$	37.1419	−	89.6685i	1.27321	−	3.07380i
$852$	3.25165	−	14.6589i	0.111400	−	0.502205i
$853$	15.3915	+	37.1585i	0.526996	+	1.27228i	0.933482	+	0.358624i	$0.116754\pi$
$853$	15.3915	+	37.1585i	0.526996	+	1.27228i	−0.406486	+	0.913657i	$0.633246\pi$
$854$	14.7700	−	1.29131i	0.505420	−	0.0441878i
$855$	−3.56034	+	17.6866i	−0.121761	+	0.604870i
$856$	−17.8177	−	10.2913i	−0.608996	−	0.351751i
$857$	8.31418	+	8.31418i	0.284007	+	0.284007i	0.834705	−	0.550698i	$-0.185638\pi$
$857$	8.31418	+	8.31418i	0.284007	+	0.284007i	−0.550698	+	0.834705i	$0.685638\pi$
$858$	−5.81674	−	4.88142i	−0.198580	−	0.166649i
$859$	−11.2667	−	27.2001i	−0.384413	−	0.928056i	−0.991101	−	0.133115i	$-0.957502\pi$
$859$	−11.2667	−	27.2001i	−0.384413	−	0.928056i	0.606687	−	0.794941i	$-0.292498\pi$
$860$	10.5658	+	11.0907i	0.360290	+	0.378189i
$861$	17.9089	+	7.41810i	0.610333	+	0.252808i
$862$	12.5753	+	3.96582i	0.428317	+	0.135076i
$863$			10.7554i			0.366118i	0.983102	+	0.183059i	$0.0586000\pi$
$863$			10.7554i			0.366118i	−0.983102	+	0.183059i	$0.941400\pi$
$864$	−9.35403	+	4.35842i	−0.318231	+	0.148276i
$865$	−41.0026	+	27.2611i	−1.39413	+	0.926905i
$866$	0.549671	−	1.74297i	0.0186786	−	0.0592284i
$867$	5.77038	−	13.9309i	0.195973	−	0.473120i
$868$	−10.2821	−	58.3540i	−0.348998	−	1.98066i
$869$	10.9153	+	26.3518i	0.370275	+	0.893923i
$870$	20.6608	+	2.31202i	0.700466	+	0.0783847i
$871$	−5.24085	+	5.24085i	−0.177579	+	0.177579i
$872$	4.97254	+	18.5712i	0.168391	+	0.628901i
$873$	2.29896	−	2.29896i	0.0778079	−	0.0778079i
$874$	45.6441	−	3.99057i	1.54393	−	0.134983i
$875$	26.2900	+	39.9387i	0.888764	+	1.35018i
$876$	0.827314	−	3.72964i	0.0279524	−	0.126013i
$877$	12.4540	+	5.15862i	0.420542	+	0.174194i	0.582911	−	0.812536i	$-0.301914\pi$
$877$	12.4540	+	5.15862i	0.420542	+	0.174194i	−0.162369	+	0.986730i	$0.551914\pi$
$878$	−17.2754	+	8.99166i	−0.583015	+	0.303454i
$879$		−	14.8479i		−	0.500808i
$880$	−17.8780	+	2.70526i	−0.602669	+	0.0911944i
$881$		−	25.9843i		−	0.875434i	−0.899113	−	0.437717i	$-0.855787\pi$
$881$		−	25.9843i		−	0.875434i	0.899113	−	0.437717i	$-0.144213\pi$
$882$	−16.2179	−	31.1588i	−0.546084	−	1.04917i
$883$	43.3370	+	17.9508i	1.45841	+	0.604092i	0.964182	−	0.265241i	$-0.0854517\pi$
$883$	43.3370	+	17.9508i	1.45841	+	0.604092i	0.494226	+	0.869334i	$0.335452\pi$
$884$	−4.03329	−	6.33269i	−0.135654	−	0.212991i
$885$	7.66286	−	11.4115i	0.257584	−	0.383592i
$886$	3.54324	+	40.5276i	0.119037	+	1.36155i
$887$	5.98529	−	5.98529i	0.200966	−	0.200966i	−0.599448	−	0.800414i	$-0.704613\pi$
$887$	5.98529	−	5.98529i	0.200966	−	0.200966i	0.800414	+	0.599448i	$0.204613\pi$
$888$	−43.1275	−	56.2260i	−1.44727	−	1.88682i
$889$	−58.3320	+	58.3320i	−1.95639	+	1.95639i
$890$	28.8013	+	3.22297i	0.965420	+	0.108034i
$891$	−8.32420	−	20.0964i	−0.278871	−	0.673254i
$892$	−0.682019	+	0.973774i	−0.0228357	+	0.0326044i
$893$	3.38285	−	8.16692i	0.113203	−	0.273296i
$894$	10.3848	+	3.27499i	0.347319	+	0.109532i
$895$	−3.56282	−	5.35874i	−0.119092	−	0.179123i
$896$	−10.4525	−	47.2428i	−0.349195	−	1.57827i
$897$		−	23.4641i		−	0.783442i
$898$	−13.0442	+	41.3623i	−0.435291	+	1.38028i
$899$	−18.4516	−	7.64290i	−0.615395	−	0.254905i
$900$	18.6102	−	11.7330i	0.620340	−	0.391101i
$901$	1.64526	+	3.97200i	0.0548114	+	0.132327i
$902$	−3.65298	+	4.35292i	−0.121631	+	0.144936i
$903$	−23.6200	−	23.6200i	−0.786025	−	0.786025i
$904$	24.4998	−	18.7923i	0.814850	−	0.625022i
$905$	7.59311	−	37.7202i	0.252403	−	1.25386i
$906$	−1.19470	−	13.6650i	−0.0396913	−	0.453990i
$907$	−1.22547	−	2.95856i	−0.0406912	−	0.0982372i	0.902227	−	0.431261i	$-0.141931\pi$
$907$	−1.22547	−	2.95856i	−0.0406912	−	0.0982372i	−0.942918	+	0.333024i	$0.891931\pi$
$908$	−18.0811	+	11.5158i	−0.600041	+	0.382167i
$909$	−9.75180	+	23.5429i	−0.323447	+	0.780870i
$910$	7.60927	−	13.7927i	0.252245	−	0.457223i
$911$			20.6726i			0.684913i	0.939534	+	0.342456i	$0.111259\pi$
$911$			20.6726i			0.684913i	−0.939534	+	0.342456i	$0.888741\pi$
$912$	14.1448	−	30.3145i	0.468381	−	1.00381i
$913$	−5.21471			−0.172582
$914$	12.9422	+	24.8653i	0.428089	+	0.822472i
$915$	−2.41040	−	12.2651i	−0.0796855	−	0.405471i
$916$	−5.92537	+	26.7123i	−0.195780	+	0.882601i
$917$	−24.6163	−	59.4290i	−0.812902	−	1.96252i
$918$	−0.724194	−	8.28333i	−0.0239019	−	0.273391i
$919$	17.3138	+	17.3138i	0.571130	+	0.571130i	0.932444	−	0.361314i	$-0.117672\pi$
$919$	17.3138	+	17.3138i	0.571130	+	0.571130i	−0.361314	+	0.932444i	$0.617672\pi$
$920$	−41.9151	−	36.9427i	−1.38190	−	1.21797i
$921$	−16.2861	+	16.2861i	−0.536646	+	0.536646i
$922$	15.7832	+	13.2453i	0.519793	+	0.436211i
$923$	−3.54285	+	1.46750i	−0.116614	+	0.0483033i
$924$	38.8322	−	6.84233i	1.27749	−	0.225096i
$925$	−38.6646	−	39.0215i	−1.27129	−	1.28302i
$926$	−10.0694	+	31.9293i	−0.330900	+	1.04926i
$927$			12.5802i			0.413186i
$928$	−15.3236	−	5.58256i	−0.503021	−	0.183257i
$929$	−32.1362			−1.05435			−0.527177	−	0.849755i	$-0.676750\pi$
$929$	−32.1362			−1.05435			−0.527177	+	0.849755i	$0.676750\pi$
$930$	−47.9915	+	13.8656i	−1.57370	+	0.454671i
$931$	−38.2539	−	15.8453i	−1.25372	−	0.519308i
$932$	6.18676	−	1.09012i	0.202654	−	0.0357082i
$933$	−56.3709	+	23.3496i	−1.84550	+	0.764431i
$934$	1.41058	−	1.68086i	0.0461557	−	0.0549995i
$935$	2.87510	−	14.2826i	0.0940257	−	0.467090i
$936$	−6.27616	−	3.62506i	−0.205143	−	0.118489i
$937$	27.8397	−	27.8397i	0.909482	−	0.909482i	−0.0867483	−	0.996230i	$-0.527648\pi$
$937$	27.8397	−	27.8397i	0.909482	−	0.909482i	0.996230	+	0.0867483i	$0.0276476\pi$
$938$	−3.35195	−	38.3396i	−0.109445	−	1.25183i
$939$	45.5729	−	18.8769i	1.48721	−	0.616024i
$940$	−10.0559	+	3.88258i	−0.327989	+	0.126636i
$941$	13.2710	−	32.0390i	0.432622	−	1.04444i	−0.545817	−	0.837905i	$-0.683781\pi$
$941$	13.2710	−	32.0390i	0.432622	−	1.04444i	0.978439	−	0.206537i	$-0.0662195\pi$
$942$	48.0862	−	25.0284i	1.56673	−	0.815470i
$943$	−17.5592			−0.571805
$944$	−7.95175	+	7.28291i	−0.258808	+	0.237039i
$945$	14.5275	−	9.65879i	0.472580	−	0.314200i
$946$	8.68627	−	4.52112i	0.282415	−	0.146994i
$947$	24.1491	+	10.0029i	0.784740	+	0.325050i	0.738827	−	0.673895i	$-0.235380\pi$
$947$	24.1491	+	10.0029i	0.784740	+	0.325050i	0.0459135	+	0.998945i	$0.485380\pi$
$948$	34.5677	+	54.2748i	1.12271	+	1.76276i
$949$	−0.901405	+	0.373374i	−0.0292609	+	0.0121202i
$950$	7.91310	−	24.6958i	0.256735	−	0.801239i
$951$	−52.6779	−	52.6779i	−1.70820	−	1.70820i
$952$	38.6516	+	5.09570i	1.25271	+	0.165153i
$953$	−22.3009	−	22.3009i	−0.722397	−	0.722397i	0.246696	−	0.969093i	$-0.420655\pi$
$953$	−22.3009	−	22.3009i	−0.722397	−	0.722397i	−0.969093	+	0.246696i	$0.920655\pi$
$954$	3.17914	+	2.66794i	0.102928	+	0.0863777i
$955$	19.2642	−	28.6881i	0.623375	−	0.928324i
$956$	10.2582	−	14.6464i	0.331773	−	0.473700i
$957$	5.08604	−	12.2788i	0.164408	−	0.396917i
$958$	4.81223	−	15.2592i	0.155476	−	0.493004i
$959$	−44.7923			−1.44642
$960$	−38.6621	+	13.0095i	−1.24781	+	0.419879i
$961$	16.9892			0.548039
$962$	−5.44305	+	17.2595i	−0.175491	+	0.556469i
$963$	6.12470	−	14.7863i	0.197366	−	0.476483i
$964$	14.9625	−	21.3631i	0.481909	−	0.688060i
$965$	−12.3997	−	8.32649i	−0.399161	−	0.268039i
$966$	93.3295	+	78.3223i	3.00283	+	2.51998i
$967$	4.15118	+	4.15118i	0.133493	+	0.133493i	0.770696	−	0.637203i	$-0.219909\pi$
$967$	4.15118	+	4.15118i	0.133493	+	0.133493i	−0.637203	+	0.770696i	$0.719909\pi$
$968$	2.55576	−	19.3858i	0.0821451	−	0.623082i
$969$	19.0592	+	19.0592i	0.612270	+	0.612270i
$970$	−3.65150	+	2.91651i	−0.117242	+	0.0936436i
$971$	3.22862	−	1.33734i	0.103611	−	0.0429172i	−0.330276	−	0.943885i	$-0.607142\pi$
$971$	3.22862	−	1.33734i	0.103611	−	0.0429172i	0.433887	+	0.900967i	$0.357142\pi$
$972$	−20.4820	−	32.1589i	−0.656962	−	1.03150i
$973$	−35.5252	−	14.7150i	−1.13888	−	0.471741i
$974$	−38.7729	+	20.1809i	−1.24236	+	0.646639i
$975$	−12.2460	−	5.13850i	−0.392187	−	0.164564i
$976$	−0.430076	+	9.79611i	−0.0137664	+	0.313566i
$977$	−50.5646			−1.61770			−0.808852	−	0.588012i	$-0.799911\pi$
$977$	−50.5646			−1.61770			−0.808852	+	0.588012i	$0.799911\pi$
$978$	54.7241	−	28.4834i	1.74988	−	0.910798i
$979$	7.08997	−	17.1167i	0.226596	−	0.547052i
$980$	18.1860	+	47.1021i	0.580932	+	1.50462i
$981$	−13.8156	+	5.72262i	−0.441099	+	0.182709i
$982$	−3.43043	−	39.2373i	−0.109469	−	1.25211i
$983$	−24.4999	+	24.4999i	−0.781427	+	0.781427i	−0.980072	−	0.198645i	$-0.936346\pi$
$983$	−24.4999	+	24.4999i	−0.781427	+	0.781427i	0.198645	+	0.980072i	$0.436346\pi$
$984$	−6.41203	+	11.1013i	−0.204408	+	0.353897i
$985$	3.67660	−	18.2642i	0.117146	−	0.581945i
$986$	8.44728	−	10.0658i	0.269016	−	0.320562i
$987$	21.7174	−	8.99563i	0.691272	−	0.286334i
$988$	−8.41379	+	1.48253i	−0.267678	+	0.0471656i
$989$	27.9552	+	11.5794i	0.888922	+	0.368204i
$990$	−3.90374	−	13.5116i	−0.124069	−	0.429426i
$991$	−34.7483			−1.10381			−0.551907	−	0.833905i	$-0.686100\pi$
$991$	−34.7483			−1.10381			−0.551907	+	0.833905i	$0.686100\pi$
$992$	39.1506	−	1.69752i	1.24303	−	0.0538963i
$993$			31.1432i			0.988299i
$994$	5.98890	−	18.9904i	0.189956	−	0.602338i
$995$	8.01621	+	40.7896i	0.254131	+	1.29312i
$996$	−11.5860	+	2.04147i	−0.367115	+	0.0646866i
$997$	41.1175	−	17.0314i	1.30220	−	0.539391i	0.379604	−	0.925149i	$-0.376060\pi$
$997$	41.1175	−	17.0314i	1.30220	−	0.539391i	0.922600	+	0.385758i	$0.126060\pi$
$998$	−2.76106	−	2.31709i	−0.0873999	−	0.0733462i
$999$	−14.1721	+	14.1721i	−0.448386	+	0.448386i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	160.2.z.a.29.14	yes	88
4.3	odd	2		640.2.z.a.209.19		88
5.2	odd	4		800.2.y.f.701.20		88
5.3	odd	4		800.2.y.f.701.3		88
5.4	even	2	inner	160.2.z.a.29.9	✓	88
20.19	odd	2		640.2.z.a.209.4		88
32.11	odd	8		640.2.z.a.49.4		88
32.21	even	8	inner	160.2.z.a.149.9	yes	88
160.53	odd	8		800.2.y.f.501.3		88
160.117	odd	8		800.2.y.f.501.20		88
160.139	odd	8		640.2.z.a.49.19		88
160.149	even	8	inner	160.2.z.a.149.14	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
160.2.z.a.29.9	✓	88	5.4	even	2	inner
160.2.z.a.29.14	yes	88	1.1	even	1	trivial
160.2.z.a.149.9	yes	88	32.21	even	8	inner
160.2.z.a.149.14	yes	88	160.149	even	8	inner
640.2.z.a.49.4		88	32.11	odd	8
640.2.z.a.49.19		88	160.139	odd	8
640.2.z.a.209.4		88	20.19	odd	2
640.2.z.a.209.19		88	4.3	odd	2
800.2.y.f.501.3		88	160.53	odd	8
800.2.y.f.501.20		88	160.117	odd	8
800.2.y.f.701.3		88	5.3	odd	4
800.2.y.f.701.20		88	5.2	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 160 = 2^{5} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	160.z (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.425344 - 1.34873i) q^{2} +(-0.872653 + 2.10677i) q^{3} +(-1.63817 - 1.14735i) q^{4} +(-1.24656 + 1.85636i) q^{5} +(2.47030 + 2.07308i) q^{6} +(3.02408 + 3.02408i) q^{7} +(-2.24425 + 1.72143i) q^{8} +(-1.55564 - 1.55564i) q^{9} +O(q^{10})\)	\(q+(0.425344 - 1.34873i) q^{2} +(-0.872653 + 2.10677i) q^{3} +(-1.63817 - 1.14735i) q^{4} +(-1.24656 + 1.85636i) q^{5} +(2.47030 + 2.07308i) q^{6} +(3.02408 + 3.02408i) q^{7} +(-2.24425 + 1.72143i) q^{8} +(-1.55564 - 1.55564i) q^{9} +(1.97353 + 2.47087i) q^{10} +(1.86770 - 0.773625i) q^{11} +(3.84676 - 2.45000i) q^{12} +(-1.07611 - 0.445737i) q^{13} +(5.36495 - 2.79241i) q^{14} +(-2.82312 - 4.24618i) q^{15} +(1.36717 + 3.75910i) q^{16} -3.22297 q^{17} +(-2.75983 + 1.43646i) q^{18} +(-1.40346 + 3.38826i) q^{19} +(4.17197 - 1.61079i) q^{20} +(-9.01002 + 3.73207i) q^{21} +(-0.249002 - 2.84808i) q^{22} +(6.24664 - 6.24664i) q^{23} +(-1.66821 - 6.23034i) q^{24} +(-1.89218 - 4.62814i) q^{25} +(-1.05890 + 1.26179i) q^{26} +(-1.68540 + 0.698114i) q^{27} +(-1.48426 - 8.42363i) q^{28} +(-2.66356 - 1.10328i) q^{29} +(-6.92776 + 2.00155i) q^{30} +6.92742 q^{31} +(5.65154 - 0.245044i) q^{32} +4.60992i q^{33} +(-1.37087 + 4.34693i) q^{34} +(-9.38349 + 1.84410i) q^{35} +(0.763532 + 4.33326i) q^{36} +(10.1503 - 4.20439i) q^{37} +(3.97291 + 3.33407i) q^{38} +(1.87813 - 1.87813i) q^{39} +(-0.398008 - 6.31202i) q^{40} +(-1.40549 - 1.40549i) q^{41} +(1.20122 + 13.7395i) q^{42} +(1.31076 + 3.16447i) q^{43} +(-3.94722 - 0.875576i) q^{44} +(4.82704 - 0.948638i) q^{45} +(-5.76809 - 11.0820i) q^{46} -2.41036 q^{47} +(-9.11263 - 0.400070i) q^{48} +11.2901i q^{49} +(-7.04695 + 0.583497i) q^{50} +(2.81254 - 6.79006i) q^{51} +(1.25142 + 1.96486i) q^{52} +(-0.510478 - 1.23240i) q^{53} +(0.224698 + 2.57009i) q^{54} +(-0.892064 + 4.43150i) q^{55} +(-11.9926 - 1.58106i) q^{56} +(-5.91355 - 5.91355i) q^{57} +(-2.62096 + 3.12316i) q^{58} +(1.03161 + 2.49053i) q^{59} +(-0.247115 + 10.1951i) q^{60} +(2.26479 + 0.938105i) q^{61} +(2.94654 - 9.34325i) q^{62} -9.40877i q^{63} +(2.07335 - 7.72666i) q^{64} +(2.16888 - 1.44201i) q^{65} +(6.21755 + 1.96080i) q^{66} +(2.43510 - 5.87886i) q^{67} +(5.27976 + 3.69788i) q^{68} +(7.70909 + 18.6114i) q^{69} +(-1.50401 + 13.4402i) q^{70} +(2.32800 - 2.32800i) q^{71} +(6.16918 + 0.813325i) q^{72} +(0.592312 - 0.592312i) q^{73} +(-1.35324 - 15.4783i) q^{74} +(11.4016 + 0.0523716i) q^{75} +(6.18663 - 3.94027i) q^{76} +(7.98757 + 3.30856i) q^{77} +(-1.73425 - 3.33195i) q^{78} +14.1092i q^{79} +(-8.68252 - 2.14797i) q^{80} -10.7600i q^{81} +(-2.49345 + 1.29781i) q^{82} +(-2.38317 - 0.987140i) q^{83} +(19.0419 + 4.22390i) q^{84} +(4.01762 - 5.98301i) q^{85} +(4.82555 - 0.421887i) q^{86} +(4.64873 - 4.64873i) q^{87} +(-2.85984 + 4.95132i) q^{88} +(6.48035 - 6.48035i) q^{89} +(0.773689 - 6.91389i) q^{90} +(-1.90628 - 4.60217i) q^{91} +(-17.4001 + 3.06595i) q^{92} +(-6.04524 + 14.5945i) q^{93} +(-1.02523 + 3.25093i) q^{94} +(-4.54035 - 6.82901i) q^{95} +(-4.41559 + 12.1204i) q^{96} +1.47782i q^{97} +(15.2274 + 4.80218i) q^{98} +(-4.10895 - 1.70198i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 8 q^{4} - 4 q^{5} - 8 q^{6} - 8 q^{9}+O(q^{10}) \) 88 * q - 8 * q^4 - 4 * q^5 - 8 * q^6 - 8 * q^9	\( 88 q - 8 q^{4} - 4 q^{5} - 8 q^{6} - 8 q^{9} - 4 q^{10} - 8 q^{11} - 24 q^{14} - 8 q^{16} - 8 q^{19} - 4 q^{20} - 8 q^{21} - 16 q^{24} - 4 q^{25} + 32 q^{26} - 8 q^{29} - 52 q^{30} - 64 q^{31} - 24 q^{34} + 20 q^{35} + 72 q^{36} - 8 q^{39} - 56 q^{40} - 8 q^{41} - 8 q^{44} - 16 q^{45} - 8 q^{46} - 44 q^{50} - 48 q^{51} + 24 q^{54} + 28 q^{55} - 56 q^{56} + 24 q^{59} + 32 q^{60} + 24 q^{61} + 64 q^{64} - 8 q^{65} - 8 q^{66} - 40 q^{69} + 80 q^{70} - 40 q^{71} + 128 q^{74} + 28 q^{75} - 8 q^{76} + 48 q^{80} + 200 q^{84} - 24 q^{85} + 24 q^{86} - 8 q^{89} + 80 q^{90} - 8 q^{91} + 120 q^{94} - 8 q^{95} - 56 q^{96} - 48 q^{99}+O(q^{100}) \) 88 * q - 8 * q^4 - 4 * q^5 - 8 * q^6 - 8 * q^9 - 4 * q^10 - 8 * q^11 - 24 * q^14 - 8 * q^16 - 8 * q^19 - 4 * q^20 - 8 * q^21 - 16 * q^24 - 4 * q^25 + 32 * q^26 - 8 * q^29 - 52 * q^30 - 64 * q^31 - 24 * q^34 + 20 * q^35 + 72 * q^36 - 8 * q^39 - 56 * q^40 - 8 * q^41 - 8 * q^44 - 16 * q^45 - 8 * q^46 - 44 * q^50 - 48 * q^51 + 24 * q^54 + 28 * q^55 - 56 * q^56 + 24 * q^59 + 32 * q^60 + 24 * q^61 + 64 * q^64 - 8 * q^65 - 8 * q^66 - 40 * q^69 + 80 * q^70 - 40 * q^71 + 128 * q^74 + 28 * q^75 - 8 * q^76 + 48 * q^80 + 200 * q^84 - 24 * q^85 + 24 * q^86 - 8 * q^89 + 80 * q^90 - 8 * q^91 + 120 * q^94 - 8 * q^95 - 56 * q^96 - 48 * q^99

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