LMFDB - Embedded newform 280.2.w.a.267.25

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [280,2,Mod(43,280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(280, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 2, 3, 0]))

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

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

chi := DirichletCharacter("280.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 280 = 2^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	280.w (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.23581125660$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			267.25
Character	$\chi$	$=$	280.267
Dual form			280.2.w.a.43.25

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.838219 - 1.13903i) q^{2} +(1.33262 - 1.33262i) q^{3} +(-0.594776 - 1.90951i) q^{4} +(-2.22159 - 0.254081i) q^{5} +(-0.400865 - 2.63492i) q^{6} +(0.707107 - 0.707107i) q^{7} +(-2.67355 - 0.923123i) q^{8} -0.551751i q^{9} +O(q^{10})$	\(q+(0.838219 - 1.13903i) q^{2} +(1.33262 - 1.33262i) q^{3} +(-0.594776 - 1.90951i) q^{4} +(-2.22159 - 0.254081i) q^{5} +(-0.400865 - 2.63492i) q^{6} +(0.707107 - 0.707107i) q^{7} +(-2.67355 - 0.923123i) q^{8} -0.551751i q^{9} +(-2.15158 + 2.31748i) q^{10} +2.64839 q^{11} +(-3.33727 - 1.75204i) q^{12} +(-0.0577942 - 0.0577942i) q^{13} +(-0.212705 - 1.39813i) q^{14} +(-3.29912 + 2.62194i) q^{15} +(-3.29248 + 2.27147i) q^{16} +(0.478637 + 0.478637i) q^{17} +(-0.628460 - 0.462488i) q^{18} -4.82978i q^{19} +(0.836177 + 4.39327i) q^{20} -1.88461i q^{21} +(2.21993 - 3.01660i) q^{22} +(4.78774 + 4.78774i) q^{23} +(-4.79299 + 2.33265i) q^{24} +(4.87089 + 1.12892i) q^{25} +(-0.114274 + 0.0173851i) q^{26} +(3.26259 + 3.26259i) q^{27} +(-1.77080 - 0.929659i) q^{28} -3.08786 q^{29} +(0.221075 + 5.95555i) q^{30} +0.226672i q^{31} +(-0.172554 + 5.65422i) q^{32} +(3.52930 - 3.52930i) q^{33} +(0.946385 - 0.143979i) q^{34} +(-1.75056 + 1.39124i) q^{35} +(-1.05358 + 0.328168i) q^{36} +(7.94914 - 7.94914i) q^{37} +(-5.50126 - 4.04841i) q^{38} -0.154035 q^{39} +(5.70496 + 2.73009i) q^{40} -0.329472 q^{41} +(-2.14663 - 1.57972i) q^{42} +(-7.87804 + 7.87804i) q^{43} +(-1.57520 - 5.05714i) q^{44} +(-0.140189 + 1.22576i) q^{45} +(9.46656 - 1.44020i) q^{46} +(-3.89166 + 3.89166i) q^{47} +(-1.36062 + 7.41463i) q^{48} -1.00000i q^{49} +(5.36875 - 4.60180i) q^{50} +1.27568 q^{51} +(-0.0759842 + 0.144733i) q^{52} +(4.03807 + 4.03807i) q^{53} +(6.45094 - 0.981419i) q^{54} +(-5.88363 - 0.672905i) q^{55} +(-2.54323 + 1.23774i) q^{56} +(-6.43625 - 6.43625i) q^{57} +(-2.58830 + 3.51716i) q^{58} -9.73780i q^{59} +(6.96886 + 4.74025i) q^{60} -7.13553i q^{61} +(0.258186 + 0.190001i) q^{62} +(-0.390147 - 0.390147i) q^{63} +(6.29569 + 4.93602i) q^{64} +(0.113710 + 0.143079i) q^{65} +(-1.06165 - 6.97830i) q^{66} +(-1.81503 - 1.81503i) q^{67} +(0.629282 - 1.19865i) q^{68} +12.7605 q^{69} +(0.117305 + 3.16010i) q^{70} +12.7101i q^{71} +(-0.509334 + 1.47513i) q^{72} +(-6.85695 + 6.85695i) q^{73} +(-2.39118 - 15.7174i) q^{74} +(7.99546 - 4.98661i) q^{75} +(-9.22252 + 2.87264i) q^{76} +(1.87270 - 1.87270i) q^{77} +(-0.129116 + 0.175451i) q^{78} +2.75146 q^{79} +(7.89167 - 4.20970i) q^{80} +10.3508 q^{81} +(-0.276170 + 0.375278i) q^{82} +(-11.0702 + 11.0702i) q^{83} +(-3.59869 + 1.12092i) q^{84} +(-0.941721 - 1.18495i) q^{85} +(2.36979 + 15.5768i) q^{86} +(-4.11494 + 4.11494i) q^{87} +(-7.08060 - 2.44479i) q^{88} +14.6461i q^{89} +(1.27867 + 1.18714i) q^{90} -0.0817334 q^{91} +(6.29462 - 11.9899i) q^{92} +(0.302068 + 0.302068i) q^{93} +(1.17065 + 7.69477i) q^{94} +(-1.22715 + 10.7298i) q^{95} +(7.30498 + 7.76488i) q^{96} +(-6.01880 - 6.01880i) q^{97} +(-1.13903 - 0.838219i) q^{98} -1.46125i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 8 q^{6}+O(q^{10}) $ 72 * q + 8 * q^6	$ 72 q + 8 q^{6} + 16 q^{10} - 16 q^{12} - 8 q^{16} + 8 q^{17} - 28 q^{18} - 20 q^{20} - 36 q^{22} - 8 q^{25} - 32 q^{26} - 4 q^{30} + 40 q^{32} + 64 q^{36} - 4 q^{40} + 20 q^{42} - 64 q^{43} + 48 q^{46} - 80 q^{48} - 32 q^{51} + 16 q^{52} - 24 q^{56} + 4 q^{58} - 80 q^{60} - 40 q^{62} - 8 q^{65} + 32 q^{66} - 24 q^{68} + 40 q^{72} - 40 q^{73} + 112 q^{75} - 8 q^{76} + 28 q^{78} - 20 q^{80} - 72 q^{81} + 24 q^{82} + 80 q^{83} + 8 q^{86} - 88 q^{88} + 136 q^{90} - 96 q^{92} - 56 q^{96} - 8 q^{97}+O(q^{100}) $ 72 * q + 8 * q^6 + 16 * q^10 - 16 * q^12 - 8 * q^16 + 8 * q^17 - 28 * q^18 - 20 * q^20 - 36 * q^22 - 8 * q^25 - 32 * q^26 - 4 * q^30 + 40 * q^32 + 64 * q^36 - 4 * q^40 + 20 * q^42 - 64 * q^43 + 48 * q^46 - 80 * q^48 - 32 * q^51 + 16 * q^52 - 24 * q^56 + 4 * q^58 - 80 * q^60 - 40 * q^62 - 8 * q^65 + 32 * q^66 - 24 * q^68 + 40 * q^72 - 40 * q^73 + 112 * q^75 - 8 * q^76 + 28 * q^78 - 20 * q^80 - 72 * q^81 + 24 * q^82 + 80 * q^83 + 8 * q^86 - 88 * q^88 + 136 * q^90 - 96 * q^92 - 56 * q^96 - 8 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/280\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$141$	$241$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$-1$	$1$

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 $

$2$	0.838219	−	1.13903i	0.592711	−	0.805415i
$2$	0.838219	−	1.13903i	0.592711	−	0.805415i
$3$	1.33262	−	1.33262i	0.769388	−	0.769388i	−0.208610	−	0.977999i	$-0.566894\pi$
$3$	1.33262	−	1.33262i	0.769388	−	0.769388i	0.977999	+	0.208610i	$0.0668941\pi$
$4$	−0.594776	−	1.90951i	−0.297388	−	0.954757i
$5$	−2.22159	−	0.254081i	−0.993523	−	0.113628i
$5$	−2.22159	−	0.254081i	−0.993523	−	0.113628i
$6$	−0.400865	−	2.63492i	−0.163653	−	1.07570i
$7$	0.707107	−	0.707107i	0.267261	−	0.267261i
$7$	0.707107	−	0.707107i	0.267261	−	0.267261i
$8$	−2.67355	−	0.923123i	−0.945241	−	0.326373i
$9$		−	0.551751i		−	0.183917i
$10$	−2.15158	+	2.31748i	−0.680390	+	0.732850i
$11$	2.64839			0.798520			0.399260	−	0.916838i	$-0.369267\pi$
$11$	2.64839			0.798520			0.399260	+	0.916838i	$0.369267\pi$
$12$	−3.33727	−	1.75204i	−0.963386	−	0.505772i
$13$	−0.0577942	−	0.0577942i	−0.0160292	−	0.0160292i	0.699047	−	0.715076i	$-0.253608\pi$
$13$	−0.0577942	−	0.0577942i	−0.0160292	−	0.0160292i	−0.715076	+	0.699047i	$0.753608\pi$
$14$	−0.212705	−	1.39813i	−0.0568478	−	0.373665i
$15$	−3.29912	+	2.62194i	−0.851830	+	0.676981i
$16$	−3.29248	+	2.27147i	−0.823120	+	0.567867i
$17$	0.478637	+	0.478637i	0.116087	+	0.116087i	0.762764	−	0.646677i	$-0.223842\pi$
$17$	0.478637	+	0.478637i	0.116087	+	0.116087i	−0.646677	+	0.762764i	$0.723842\pi$
$18$	−0.628460	−	0.462488i	−0.148129	−	0.109009i
$19$		−	4.82978i		−	1.10803i	−0.832508	−	0.554013i	$-0.813096\pi$
$19$		−	4.82978i		−	1.10803i	0.832508	−	0.554013i	$-0.186904\pi$
$20$	0.836177	+	4.39327i	0.186975	+	0.982365i
$21$		−	1.88461i		−	0.411255i
$22$	2.21993	−	3.01660i	0.473291	−	0.643141i
$23$	4.78774	+	4.78774i	0.998313	+	0.998313i	0.999999	−	0.00168512i	$-0.000536391\pi$
$23$	4.78774	+	4.78774i	0.998313	+	0.998313i	−0.00168512	+	0.999999i	$0.500536\pi$
$24$	−4.79299	+	2.33265i	−0.978365	+	0.476150i
$25$	4.87089	+	1.12892i	0.974177	+	0.225785i
$26$	−0.114274	+	0.0173851i	−0.0224109	+	0.00340950i
$27$	3.26259	+	3.26259i	0.627885	+	0.627885i
$28$	−1.77080	−	0.929659i	−0.334650	−	0.175689i
$29$	−3.08786			−0.573401			−0.286701	−	0.958020i	$-0.592558\pi$
$29$	−3.08786			−0.573401			−0.286701	+	0.958020i	$0.592558\pi$
$30$	0.221075	+	5.95555i	0.0403625	+	1.08733i
$31$			0.226672i			0.0407116i	0.999793	+	0.0203558i	$0.00647989\pi$
$31$			0.226672i			0.0407116i	−0.999793	+	0.0203558i	$0.993520\pi$
$32$	−0.172554	+	5.65422i	−0.0305035	+	0.999535i
$33$	3.52930	−	3.52930i	0.614372	−	0.614372i
$34$	0.946385	−	0.143979i	0.162304	−	0.0246922i
$35$	−1.75056	+	1.39124i	−0.295899	+	0.235162i
$36$	−1.05358	+	0.328168i	−0.175596	+	0.0546947i
$37$	7.94914	−	7.94914i	1.30683	−	1.30683i	0.383140	−	0.923690i	$-0.374843\pi$
$37$	7.94914	−	7.94914i	1.30683	−	1.30683i	0.923690	−	0.383140i	$-0.125157\pi$
$38$	−5.50126	−	4.04841i	−0.892422	−	0.656739i
$39$	−0.154035			−0.0246654
$40$	5.70496	+	2.73009i	0.902034	+	0.431666i
$41$	−0.329472			−0.0514549			−0.0257274	−	0.999669i	$-0.508190\pi$
$41$	−0.329472			−0.0514549			−0.0257274	+	0.999669i	$0.508190\pi$
$42$	−2.14663	−	1.57972i	−0.331231	−	0.243755i
$43$	−7.87804	+	7.87804i	−1.20139	+	1.20139i	−0.227646	+	0.973744i	$0.573103\pi$
$43$	−7.87804	+	7.87804i	−1.20139	+	1.20139i	−0.973744	+	0.227646i	$0.926897\pi$
$44$	−1.57520	−	5.05714i	−0.237471	−	0.762393i
$45$	−0.140189	+	1.22576i	−0.0208982	+	0.182726i
$46$	9.46656	−	1.44020i	1.39577	−	0.212346i
$47$	−3.89166	+	3.89166i	−0.567657	+	0.567657i	−0.931471	−	0.363815i	$-0.881474\pi$
$47$	−3.89166	+	3.89166i	−0.567657	+	0.567657i	0.363815	+	0.931471i	$0.381474\pi$
$48$	−1.36062	+	7.41463i	−0.196389	+	1.07021i
$49$		−	1.00000i		−	0.142857i
$50$	5.36875	−	4.60180i	0.759256	−	0.650792i
$51$	1.27568			0.178631
$52$	−0.0759842	+	0.144733i	−0.0105371	+	0.0200709i
$53$	4.03807	+	4.03807i	0.554672	+	0.554672i	0.927786	−	0.373114i	$-0.121710\pi$
$53$	4.03807	+	4.03807i	0.554672	+	0.554672i	−0.373114	+	0.927786i	$0.621710\pi$
$54$	6.45094	−	0.981419i	0.877862	−	0.133554i
$55$	−5.88363	−	0.672905i	−0.793349	−	0.0907345i
$56$	−2.54323	+	1.23774i	−0.339853	+	0.165399i
$57$	−6.43625	−	6.43625i	−0.852503	−	0.852503i
$58$	−2.58830	+	3.51716i	−0.339861	+	0.461826i
$59$		−	9.73780i		−	1.26775i	−0.773434	−	0.633877i	$-0.781463\pi$
$59$		−	9.73780i		−	1.26775i	0.773434	−	0.633877i	$-0.218537\pi$
$60$	6.96886	+	4.74025i	0.899676	+	0.611964i
$61$		−	7.13553i		−	0.913612i	−0.889566	−	0.456806i	$-0.848993\pi$
$61$		−	7.13553i		−	0.913612i	0.889566	−	0.456806i	$-0.151007\pi$
$62$	0.258186	+	0.190001i	0.0327897	+	0.0241302i
$63$	−0.390147	−	0.390147i	−0.0491538	−	0.0491538i
$64$	6.29569	+	4.93602i	0.786961	+	0.617003i
$65$	0.113710	+	0.143079i	0.0141040	+	0.0177468i
$66$	−1.06165	−	6.97830i	−0.130680	−	0.858970i
$67$	−1.81503	−	1.81503i	−0.221741	−	0.221741i	0.587490	−	0.809231i	$-0.300116\pi$
$67$	−1.81503	−	1.81503i	−0.221741	−	0.221741i	−0.809231	+	0.587490i	$0.800116\pi$
$68$	0.629282	−	1.19865i	0.0763117	−	0.145357i
$69$	12.7605			1.53618
$70$	0.117305	+	3.16010i	0.0140207	+	0.377704i
$71$			12.7101i			1.50841i	0.656640	+	0.754204i	$0.271977\pi$
$71$			12.7101i			1.50841i	−0.656640	+	0.754204i	$0.728023\pi$
$72$	−0.509334	+	1.47513i	−0.0600256	+	0.173846i
$73$	−6.85695	+	6.85695i	−0.802546	+	0.802546i	−0.983493	−	0.180947i	$-0.942084\pi$
$73$	−6.85695	+	6.85695i	−0.802546	+	0.802546i	0.180947	+	0.983493i	$0.442084\pi$
$74$	−2.39118	−	15.7174i	−0.277969	−	1.82711i
$75$	7.99546	−	4.98661i	0.923237	−	0.575804i
$76$	−9.22252	+	2.87264i	−1.05790	+	0.329514i
$77$	1.87270	−	1.87270i	0.213414	−	0.213414i
$78$	−0.129116	+	0.175451i	−0.0146195	+	0.0198659i
$79$	2.75146			0.309564			0.154782	−	0.987949i	$-0.450533\pi$
$79$	2.75146			0.309564			0.154782	+	0.987949i	$0.450533\pi$
$80$	7.89167	−	4.20970i	0.882315	−	0.470659i
$81$	10.3508			1.15009
$82$	−0.276170	+	0.375278i	−0.0304979	+	0.0414426i
$83$	−11.0702	+	11.0702i	−1.21511	+	1.21511i	−0.245784	+	0.969325i	$0.579045\pi$
$83$	−11.0702	+	11.0702i	−1.21511	+	1.21511i	−0.969325	+	0.245784i	$0.920955\pi$
$84$	−3.59869	+	1.12092i	−0.392649	+	0.122303i
$85$	−0.941721	−	1.18495i	−0.102144	−	0.128525i
$86$	2.36979	+	15.5768i	0.255541	+	1.67969i
$87$	−4.11494	+	4.11494i	−0.441168	+	0.441168i
$88$	−7.08060	−	2.44479i	−0.754794	−	0.260616i
$89$			14.6461i			1.55248i	0.630436	+	0.776241i	$0.282876\pi$
$89$			14.6461i			1.55248i	−0.630436	+	0.776241i	$0.717124\pi$
$90$	1.27867	+	1.18714i	0.134784	+	0.125135i
$91$	−0.0817334			−0.00856799
$92$	6.29462	−	11.9899i	0.656260	−	1.25003i
$93$	0.302068	+	0.302068i	0.0313230	+	0.0313230i
$94$	1.17065	+	7.69477i	0.120743	+	0.793655i
$95$	−1.22715	+	10.7298i	−0.125903	+	1.10085i
$96$	7.30498	+	7.76488i	0.745561	+	0.792499i
$97$	−6.01880	−	6.01880i	−0.611116	−	0.611116i	0.332121	−	0.943237i	$-0.392236\pi$
$97$	−6.01880	−	6.01880i	−0.611116	−	0.611116i	−0.943237	+	0.332121i	$0.892236\pi$
$98$	−1.13903	−	0.838219i	−0.115059	−	0.0846729i
$99$		−	1.46125i		−	0.146861i
$100$	−0.741393	−	9.97248i	−0.0741393	−	0.997248i
$101$		−	10.1979i		−	1.01473i	−0.861730	−	0.507366i	$-0.830619\pi$
$101$		−	10.1979i		−	1.01473i	0.861730	−	0.507366i	$-0.169381\pi$
$102$	1.06930	−	1.45304i	0.105877	−	0.143872i
$103$	−2.26559	−	2.26559i	−0.223235	−	0.223235i	0.586624	−	0.809859i	$-0.300457\pi$
$103$	−2.26559	−	2.26559i	−0.223235	−	0.223235i	−0.809859	+	0.586624i	$0.800457\pi$
$104$	0.101164	+	0.207867i	0.00991998	+	0.0203830i
$105$	−0.478843	+	4.18682i	−0.0467303	+	0.408592i
$106$	7.98427	−	1.21469i	0.775501	−	0.117981i
$107$	12.3108	+	12.3108i	1.19013	+	1.19013i	0.977030	+	0.213101i	$0.0683564\pi$
$107$	12.3108	+	12.3108i	1.19013	+	1.19013i	0.213101	+	0.977030i	$0.431644\pi$
$108$	4.28944	−	8.17046i	0.412752	−	0.786203i
$109$	6.02035			0.576645			0.288323	−	0.957533i	$-0.406902\pi$
$109$	6.02035			0.576645			0.288323	+	0.957533i	$0.406902\pi$
$110$	−5.69823	+	6.13759i	−0.543305	+	0.585196i
$111$		−	21.1864i		−	2.01092i
$112$	−0.721966	+	3.93431i	−0.0682194	+	0.371757i
$113$	1.61929	−	1.61929i	0.152330	−	0.152330i	−0.626828	−	0.779158i	$-0.715647\pi$
$113$	1.61929	−	1.61929i	0.152330	−	0.152330i	0.779158	+	0.626828i	$0.215647\pi$
$114$	−12.7261	+	1.93609i	−1.19191	+	0.181331i
$115$	−9.41991	−	11.8529i	−0.878411	−	1.10528i
$116$	1.83659	+	5.89631i	0.170523	+	0.547459i
$117$	−0.0318880	+	0.0318880i	−0.00294805	+	0.00294805i
$118$	−11.0916	−	8.16241i	−1.02107	−	0.751411i
$119$	0.676895			0.0620509
$120$	11.2407	−	3.96437i	1.02613	−	0.361896i
$121$	−3.98602			−0.362365
$122$	−8.12758	−	5.98114i	−0.735837	−	0.541507i
$123$	−0.439061	+	0.439061i	−0.0395888	+	0.0395888i
$124$	0.432834	−	0.134819i	0.0388696	−	0.0121071i
$125$	−10.5343	−	3.74560i	−0.942212	−	0.335017i
$126$	−0.771417	+	0.117360i	−0.0687233	+	0.0104553i
$127$	−4.51305	+	4.51305i	−0.400469	+	0.400469i	−0.878398	−	0.477930i	$-0.841387\pi$
$127$	−4.51305	+	4.51305i	−0.400469	+	0.400469i	0.477930	+	0.878398i	$0.341387\pi$
$128$	10.8994	−	3.03350i	0.963384	−	0.268126i
$129$			20.9969i			1.84867i
$130$	0.258286	−	0.00958776i	0.0226532	−	0.000840902i
$131$	−8.17119			−0.713920			−0.356960	−	0.934120i	$-0.616187\pi$
$131$	−8.17119			−0.713920			−0.356960	+	0.934120i	$0.616187\pi$
$132$	−8.83839	−	4.64010i	−0.769283	−	0.403869i
$133$	−3.41517	−	3.41517i	−0.296133	−	0.296133i
$134$	−3.58876	+	0.545978i	−0.310021	+	0.0471653i
$135$	−6.41915	−	8.07707i	−0.552473	−	0.695164i
$136$	−0.837817	−	1.72150i	−0.0718422	−	0.147617i
$137$	−13.8922	−	13.8922i	−1.18689	−	1.18689i	−0.977923	−	0.208968i	$-0.932990\pi$
$137$	−13.8922	−	13.8922i	−1.18689	−	1.18689i	−0.208968	−	0.977923i	$-0.567010\pi$
$138$	10.6961	−	14.5346i	0.910511	−	1.23726i
$139$		−	3.37104i		−	0.285928i	−0.989728	−	0.142964i	$-0.954337\pi$
$139$		−	3.37104i		−	0.285928i	0.989728	−	0.142964i	$-0.0456633\pi$
$140$	3.69778	+	2.51524i	0.312519	+	0.212577i
$141$			10.3722i			0.873497i
$142$	14.4771	+	10.6538i	1.21490	+	0.894050i
$143$	−0.153062	−	0.153062i	−0.0127997	−	0.0127997i
$144$	1.25328	+	1.81663i	0.104440	+	0.151386i
$145$	6.85995	+	0.784565i	0.569687	+	0.0651546i
$146$	2.06264	+	13.5579i	0.170705	+	1.12206i
$147$	−1.33262	−	1.33262i	−0.109913	−	0.109913i
$148$	−19.9069	−	10.4510i	−1.63634	−	0.859069i
$149$	−11.8653			−0.972044			−0.486022	−	0.873947i	$-0.661553\pi$
$149$	−11.8653			−0.972044			−0.486022	+	0.873947i	$0.661553\pi$
$150$	1.02205	−	13.2869i	0.0834504	−	1.08487i
$151$		−	10.3384i		−	0.841324i	−0.907217	−	0.420662i	$-0.861798\pi$
$151$		−	10.3384i		−	0.841324i	0.907217	−	0.420662i	$-0.138202\pi$
$152$	−4.45848	+	12.9126i	−0.361630	+	1.04735i
$153$	0.264088	−	0.264088i	0.0213503	−	0.0213503i
$154$	−0.563326	−	3.70279i	−0.0453941	−	0.298379i
$155$	0.0575931	−	0.503572i	0.00462599	−	0.0404479i
$156$	0.0916167	+	0.294133i	0.00733520	+	0.0235495i
$157$	−13.3999	+	13.3999i	−1.06943	+	1.06943i	−0.0720223	+	0.997403i	$0.522945\pi$
$157$	−13.3999	+	13.3999i	−1.06943	+	1.06943i	−0.997403	+	0.0720223i	$0.977055\pi$
$158$	2.30633	−	3.13400i	0.183482	−	0.249327i
$159$	10.7624			0.853516
$160$	1.81997	−	12.5175i	0.143881	−	0.989595i
$161$	6.77089			0.533621
$162$	8.67626	−	11.7899i	0.681671	−	0.926301i
$163$	0.711190	−	0.711190i	0.0557047	−	0.0557047i	−0.678706	−	0.734410i	$-0.737459\pi$
$163$	0.711190	−	0.711190i	0.0557047	−	0.0557047i	0.734410	+	0.678706i	$0.237459\pi$
$164$	0.195962	+	0.629131i	0.0153021	+	0.0491269i
$165$	−8.73737	+	6.94392i	−0.680203	+	0.540583i
$166$	3.33002	+	21.8885i	0.258459	+	1.69887i
$167$	3.39520	−	3.39520i	0.262729	−	0.262729i	−0.563433	−	0.826162i	$-0.690520\pi$
$167$	3.39520	−	3.39520i	0.262729	−	0.262729i	0.826162	+	0.563433i	$0.190520\pi$
$168$	−1.73973	+	5.03859i	−0.134223	+	0.388735i
$169$		−	12.9933i		−	0.999486i
$170$	−2.13906	+	0.0794034i	−0.164058	+	0.00608997i
$171$	−2.66483			−0.203785
$172$	19.7289	+	10.3575i	1.50431	+	0.789756i
$173$	−5.16118	−	5.16118i	−0.392397	−	0.392397i	0.483144	−	0.875541i	$-0.339495\pi$
$173$	−5.16118	−	5.16118i	−0.392397	−	0.392397i	−0.875541	+	0.483144i	$0.839495\pi$
$174$	1.23782	+	8.13627i	0.0938386	+	0.616809i
$175$	4.24251	−	2.64597i	0.320703	−	0.200016i
$176$	−8.71978	+	6.01574i	−0.657278	+	0.453453i
$177$	−12.9768	−	12.9768i	−0.975395	−	0.975395i
$178$	16.6823	+	12.2766i	1.25039	+	0.920173i
$179$			3.91894i			0.292916i	0.989217	+	0.146458i	$0.0467873\pi$
$179$			3.91894i			0.292916i	−0.989217	+	0.146458i	$0.953213\pi$
$180$	2.42399	−	0.461361i	0.180673	−	0.0343878i
$181$		−	6.18531i		−	0.459750i	−0.973220	−	0.229875i	$-0.926168\pi$
$181$		−	6.18531i		−	0.459750i	0.973220	−	0.229875i	$-0.0738318\pi$
$182$	−0.0685105	+	0.0930967i	−0.00507834	+	0.00690079i
$183$	−9.50895	−	9.50895i	−0.702922	−	0.702922i
$184$	−8.38057	−	17.2199i	−0.617824	−	1.26947i
$185$	−19.6794	+	15.6400i	−1.44686	+	1.14987i
$186$	0.597264	−	0.0908651i	0.0437935	−	0.00666255i
$187$	1.26762	+	1.26762i	0.0926975	+	0.0926975i
$188$	9.74584	+	5.11650i	0.710788	+	0.373159i
$189$	4.61399			0.335619
$190$	11.1929	+	10.3917i	0.812018	+	0.753890i
$191$		−	1.94576i		−	0.140790i	−0.997519	−	0.0703950i	$-0.977574\pi$
$191$		−	1.94576i		−	0.140790i	0.997519	−	0.0703950i	$-0.0224260\pi$
$192$	14.9676	−	1.81192i	1.08019	−	0.130764i
$193$	10.8892	−	10.8892i	0.783821	−	0.783821i	−0.196652	−	0.980473i	$-0.563007\pi$
$193$	10.8892	−	10.8892i	0.783821	−	0.783821i	0.980473	+	0.196652i	$0.0630069\pi$
$194$	−11.9007	+	1.81051i	−0.854417	+	0.129987i
$195$	0.342203	+	0.0391374i	0.0245057	+	0.00280269i
$196$	−1.90951	+	0.594776i	−0.136394	+	0.0424840i
$197$	−16.3183	+	16.3183i	−1.16263	+	1.16263i	−0.178733	+	0.983898i	$0.557200\pi$
$197$	−16.3183	+	16.3183i	−1.16263	+	1.16263i	−0.983898	+	0.178733i	$0.942800\pi$
$198$	−1.66441	−	1.22485i	−0.118284	−	0.0870463i
$199$	13.3897			0.949174			0.474587	−	0.880209i	$-0.342597\pi$
$199$	13.3897			0.949174			0.474587	+	0.880209i	$0.342597\pi$
$200$	−11.9804	−	7.51466i	−0.847142	−	0.531366i
$201$	−4.83748			−0.341209
$202$	−11.6158	−	8.54811i	−0.817281	−	0.601443i
$203$	−2.18345	+	2.18345i	−0.153248	+	0.153248i
$204$	−0.758746	−	2.43593i	−0.0531229	−	0.170549i
$205$	0.731950	+	0.0837125i	0.0511216	+	0.00584673i
$206$	−4.47963	+	0.681511i	−0.312110	+	0.0474831i
$207$	2.64164	−	2.64164i	0.183607	−	0.183607i
$208$	0.321564	+	0.0590088i	0.0222965	+	0.00409152i
$209$		−	12.7911i		−	0.884782i
$210$	4.36754	+	4.05489i	0.301389	+	0.279814i
$211$	−12.3951			−0.853313			−0.426656	−	0.904414i	$-0.640309\pi$
$211$	−12.3951			−0.853313			−0.426656	+	0.904414i	$0.640309\pi$
$212$	5.30900	−	10.1125i	0.364624	−	0.694529i
$213$	16.9377	+	16.9377i	1.16055	+	1.16055i
$214$	24.3415	−	3.70322i	1.66395	−	0.253147i
$215$	19.5034	−	15.5001i	1.33012	−	1.05710i
$216$	−5.71090	−	11.7344i	−0.388578	−	0.798427i
$217$	0.160282	+	0.160282i	0.0108806	+	0.0108806i
$218$	5.04638	−	6.85736i	0.341784	−	0.464439i
$219$			18.2754i			1.23494i
$220$	2.21452	+	11.6351i	0.149303	+	0.784438i
$221$		−	0.0553250i		−	0.00372156i
$222$	−24.1319	−	17.7588i	−1.61963	−	1.19189i
$223$	11.8727	+	11.8727i	0.795053	+	0.795053i	0.982311	−	0.187258i	$-0.0599600\pi$
$223$	11.8727	+	11.8727i	0.795053	+	0.795053i	−0.187258	+	0.982311i	$0.559960\pi$
$224$	3.87612	+	4.12015i	0.258984	+	0.275289i
$225$	0.622884	−	2.68751i	0.0415256	−	0.179168i
$226$	−0.487098	−	3.20174i	−0.0324013	−	0.212976i
$227$	−1.38932	−	1.38932i	−0.0922124	−	0.0922124i	0.659496	−	0.751708i	$-0.270770\pi$
$227$	−1.38932	−	1.38932i	−0.0922124	−	0.0922124i	−0.751708	+	0.659496i	$0.770770\pi$
$228$	−8.46198	+	16.1182i	−0.560408	+	1.06746i
$229$	14.6410			0.967502			0.483751	−	0.875206i	$-0.339274\pi$
$229$	14.6410			0.967502			0.483751	+	0.875206i	$0.339274\pi$
$230$	−21.3967	+	0.794262i	−1.41086	+	0.0523721i
$231$		−	4.99118i		−	0.328396i
$232$	8.25553	+	2.85047i	0.542002	+	0.187143i
$233$	18.1628	−	18.1628i	1.18988	−	1.18988i	0.212786	−	0.977099i	$-0.431746\pi$
$233$	18.1628	−	18.1628i	1.18988	−	1.18988i	0.977099	−	0.212786i	$-0.0682536\pi$
$234$	0.00959223	+	0.0630505i	0.000627064	+	0.00412174i
$235$	9.63444	−	7.65685i	0.628482	−	0.499478i
$236$	−18.5945	+	5.79181i	−1.21040	+	0.377015i
$237$	3.66665	−	3.66665i	0.238175	−	0.238175i
$238$	0.567387	−	0.771004i	0.0367782	−	0.0499768i
$239$	6.91467			0.447273			0.223636	−	0.974673i	$-0.428207\pi$
$239$	6.91467			0.447273			0.223636	+	0.974673i	$0.428207\pi$
$240$	4.90666	−	16.1265i	0.316723	−	1.04096i
$241$	13.7124			0.883293			0.441647	−	0.897189i	$-0.354394\pi$
$241$	13.7124			0.883293			0.441647	+	0.897189i	$0.354394\pi$
$242$	−3.34116	+	4.54019i	−0.214778	+	0.291855i
$243$	4.00595	−	4.00595i	0.256982	−	0.256982i
$244$	−13.6254	+	4.24405i	−0.872277	+	0.271697i
$245$	−0.254081	+	2.22159i	−0.0162326	+	0.141932i
$246$	0.132074	+	0.868133i	0.00842073	+	0.0553501i
$247$	−0.279133	+	0.279133i	−0.0177608	+	0.0177608i
$248$	0.209246	−	0.606019i	0.0132872	−	0.0384822i
$249$			29.5046i			1.86978i
$250$	−13.0964	+	8.85919i	−0.828287	+	0.560304i
$251$	15.3645			0.969801			0.484901	−	0.874569i	$-0.338856\pi$
$251$	15.3645			0.969801			0.484901	+	0.874569i	$0.338856\pi$
$252$	−0.512940	+	0.977040i	−0.0323122	+	0.0615477i
$253$	12.6798	+	12.6798i	0.797174	+	0.797174i
$254$	1.35757	+	8.92343i	0.0851816	+	0.559906i
$255$	−2.83404	−	0.324126i	−0.177474	−	0.0202976i
$256$	5.68087	−	14.9575i	0.355055	−	0.934846i
$257$	15.5167	+	15.5167i	0.967902	+	0.967902i	0.999501	−	0.0315982i	$-0.0100597\pi$
$257$	15.5167	+	15.5167i	0.967902	+	0.967902i	−0.0315982	+	0.999501i	$0.510060\pi$
$258$	23.9160	+	17.6000i	1.48895	+	1.09573i
$259$		−	11.2418i		−	0.698530i
$260$	0.205579	−	0.302232i	0.0127495	−	0.0187436i
$261$			1.70373i			0.105458i
$262$	−6.84925	+	9.30722i	−0.423148	+	0.575002i
$263$	8.97878	+	8.97878i	0.553655	+	0.553655i	0.927494	−	0.373838i	$-0.121959\pi$
$263$	8.97878	+	8.97878i	0.553655	+	0.553655i	−0.373838	+	0.927494i	$0.621959\pi$
$264$	−12.6937	+	6.17776i	−0.781245	+	0.380215i
$265$	−7.94492	−	9.99691i	−0.488053	−	0.614106i
$266$	−6.75264	+	1.02732i	−0.414031	+	0.0629888i
$267$	19.5177	+	19.5177i	1.19446	+	1.19446i
$268$	−2.38628	+	4.54535i	−0.145765	+	0.277651i
$269$	−29.0906			−1.77368			−0.886841	−	0.462074i	$-0.847105\pi$
$269$	−29.0906			−1.77368			−0.886841	+	0.462074i	$0.847105\pi$
$270$	−14.5807	+	0.541246i	−0.887352	+	0.0329392i
$271$		−	19.9916i		−	1.21440i	−0.794548	−	0.607201i	$-0.792292\pi$
$271$		−	19.9916i		−	1.21440i	0.794548	−	0.607201i	$-0.207708\pi$
$272$	−2.66311	−	0.488696i	−0.161475	−	0.0296315i
$273$	−0.108920	+	0.108920i	−0.00659211	+	0.00659211i
$274$	−27.4683	+	4.17891i	−1.65942	+	0.252457i
$275$	12.9000	+	2.98983i	0.777900	+	0.180294i
$276$	−7.58963	−	24.3663i	−0.456842	−	1.46668i
$277$	−13.5683	+	13.5683i	−0.815241	+	0.815241i	−0.985414	−	0.170173i	$-0.945567\pi$
$277$	−13.5683	+	13.5683i	−0.815241	+	0.815241i	0.170173	+	0.985414i	$0.445567\pi$
$278$	−3.83971	−	2.82567i	−0.230291	−	0.169472i
$279$	0.125067			0.00748754
$280$	5.96448	−	2.10355i	0.356446	−	0.125711i
$281$	−6.32922			−0.377569			−0.188785	−	0.982018i	$-0.560455\pi$
$281$	−6.32922			−0.377569			−0.188785	+	0.982018i	$0.560455\pi$
$282$	11.8142	+	8.69418i	0.703528	+	0.517731i
$283$	14.4224	−	14.4224i	0.857323	−	0.857323i	−0.133699	−	0.991022i	$-0.542685\pi$
$283$	14.4224	−	14.4224i	0.857323	−	0.857323i	0.991022	+	0.133699i	$0.0426855\pi$
$284$	24.2701	−	7.55965i	1.44016	−	0.448583i
$285$	12.6634	+	15.9340i	0.750113	+	0.943850i
$286$	−0.302641	+	0.0460425i	−0.0178956	+	0.00272255i
$287$	−0.232972	+	0.232972i	−0.0137519	+	0.0137519i
$288$	3.11972	+	0.0952068i	0.183831	+	0.00561011i
$289$		−	16.5418i		−	0.973048i
$290$	6.64378	−	7.15604i	0.390136	−	0.420217i
$291$	−16.0415			−0.940371
$292$	17.1718	+	9.01509i	1.00490	+	0.527568i
$293$	−5.05393	−	5.05393i	−0.295254	−	0.295254i	0.543898	−	0.839151i	$-0.316948\pi$
$293$	−5.05393	−	5.05393i	−0.295254	−	0.295254i	−0.839151	+	0.543898i	$0.816948\pi$
$294$	−2.63492	+	0.400865i	−0.153672	+	0.0233790i
$295$	−2.47419	+	21.6334i	−0.144053	+	1.25954i
$296$	−28.5904	+	13.9143i	−1.66178	+	0.808755i
$297$	8.64061	+	8.64061i	0.501379	+	0.501379i
$298$	−9.94573	+	13.5149i	−0.576141	+	0.782899i
$299$		−	0.553408i		−	0.0320044i
$300$	−14.2775	−	12.3015i	−0.824313	−	0.710229i
$301$			11.1412i			0.642170i
$302$	−11.7757	−	8.66582i	−0.677616	−	0.498662i
$303$	−13.5900	−	13.5900i	−0.780724	−	0.780724i
$304$	10.9707	+	15.9019i	0.629212	+	0.912039i
$305$	−1.81300	+	15.8522i	−0.103812	+	0.907694i
$306$	−0.0794405	−	0.522169i	−0.00454131	−	0.0298504i
$307$	20.9729	+	20.9729i	1.19699	+	1.19699i	0.975064	+	0.221924i	$0.0712337\pi$
$307$	20.9729	+	20.9729i	1.19699	+	1.19699i	0.221924	+	0.975064i	$0.428766\pi$
$308$	−4.68977	−	2.46210i	−0.267225	−	0.140291i
$309$	−6.03833			−0.343509
$310$	−0.525308	−	0.487704i	−0.0298355	−	0.0276997i
$311$			1.02430i			0.0580825i	0.999578	+	0.0290413i	$0.00924542\pi$
$311$			1.02430i			0.0580825i	−0.999578	+	0.0290413i	$0.990755\pi$
$312$	0.411821	+	0.142194i	0.0233148	+	0.00805013i
$313$	−12.8405	+	12.8405i	−0.725786	+	0.725786i	−0.969777	−	0.243991i	$-0.921543\pi$
$313$	−12.8405	+	12.8405i	−0.725786	+	0.725786i	0.243991	+	0.969777i	$0.421543\pi$
$314$	4.03081	+	26.4949i	0.227472	+	1.49519i
$315$	0.767615	+	0.965873i	0.0432502	+	0.0544208i
$316$	−1.63651	−	5.25395i	−0.0920606	−	0.295558i
$317$	6.97845	−	6.97845i	0.391949	−	0.391949i	−0.483433	−	0.875382i	$-0.660610\pi$
$317$	6.97845	−	6.97845i	0.391949	−	0.391949i	0.875382	+	0.483433i	$0.160610\pi$
$318$	9.02127	−	12.2587i	0.505888	−	0.687435i
$319$	−8.17786			−0.457873
$320$	−12.7323	−	12.5654i	−0.711755	−	0.702428i
$321$	32.8113			1.83135
$322$	5.67549	−	7.71225i	0.316283	−	0.429787i
$323$	2.31171	−	2.31171i	0.128627	−	0.128627i
$324$	−6.15643	−	19.7650i	−0.342024	−	1.09806i
$325$	−0.216264	−	0.346754i	−0.0119962	−	0.0192345i
$326$	−0.213933	−	1.40620i	−0.0118487	−	0.0778822i
$327$	8.02284	−	8.02284i	0.443664	−	0.443664i
$328$	0.880858	+	0.304143i	0.0486373	+	0.0167935i
$329$			5.50363i			0.303425i
$330$	0.585492	+	15.7726i	0.0322303	+	0.868256i
$331$	−1.22021			−0.0670688			−0.0335344	−	0.999438i	$-0.510676\pi$
$331$	−1.22021			−0.0670688			−0.0335344	+	0.999438i	$0.510676\pi$
$332$	27.7229	+	14.5544i	1.52149	+	0.798774i
$333$	−4.38594	−	4.38594i	−0.240348	−	0.240348i
$334$	−1.02131	−	6.71316i	−0.0558837	−	0.367328i
$335$	3.57107	+	4.49340i	0.195108	+	0.245501i
$336$	4.28083	+	6.20504i	0.233538	+	0.338513i
$337$	3.94802	+	3.94802i	0.215062	+	0.215062i	0.806414	−	0.591352i	$-0.201405\pi$
$337$	3.94802	+	3.94802i	0.215062	+	0.215062i	−0.591352	+	0.806414i	$0.701405\pi$
$338$	−14.7998	−	10.8913i	−0.805002	−	0.592406i
$339$		−	4.31579i		−	0.234402i
$340$	−1.70256	+	2.50301i	−0.0923341	+	0.135745i
$341$			0.600317i			0.0325090i
$342$	−2.23371	+	3.03532i	−0.120785	+	0.164131i
$343$	−0.707107	−	0.707107i	−0.0381802	−	0.0381802i
$344$	28.3347	−	13.7899i	1.52770	−	0.743501i
$345$	−28.3485	−	3.24219i	−1.52623	−	0.174554i
$346$	−10.2049	+	1.55254i	−0.548621	+	0.0834649i
$347$	−22.9658	−	22.9658i	−1.23287	−	1.23287i	−0.962857	−	0.270013i	$-0.912972\pi$
$347$	−22.9658	−	22.9658i	−1.23287	−	1.23287i	−0.270013	−	0.962857i	$-0.587028\pi$
$348$	10.3050	+	5.41007i	0.552406	+	0.290010i
$349$	25.8750			1.38506			0.692529	−	0.721390i	$-0.256497\pi$
$349$	25.8750			1.38506			0.692529	+	0.721390i	$0.256497\pi$
$350$	0.542317	−	7.05024i	0.0289880	−	0.376851i
$351$		−	0.377117i		−	0.0201290i
$352$	−0.456991	+	14.9746i	−0.0243577	+	0.798149i
$353$	26.3973	−	26.3973i	1.40498	−	1.40498i	0.621839	−	0.783145i	$-0.286386\pi$
$353$	26.3973	−	26.3973i	1.40498	−	1.40498i	0.783145	−	0.621839i	$-0.213614\pi$
$354$	−25.6583	+	3.90355i	−1.36372	+	0.207471i
$355$	3.22938	−	28.2365i	0.171398	−	1.49864i
$356$	27.9669	−	8.71115i	1.48224	−	0.461690i
$357$	0.902044	−	0.902044i	0.0477412	−	0.0477412i
$358$	4.46379	+	3.28494i	0.235919	+	0.173614i
$359$	−25.2088			−1.33047			−0.665234	−	0.746635i	$-0.731668\pi$
$359$	−25.2088			−1.33047			−0.665234	+	0.746635i	$0.731668\pi$
$360$	1.50633	−	3.14772i	0.0793906	−	0.165899i
$361$	−4.32674			−0.227723
$362$	−7.04525	−	5.18464i	−0.370290	−	0.272499i
$363$	−5.31185	+	5.31185i	−0.278800	+	0.278800i
$364$	0.0486131	+	0.156071i	0.00254802	+	0.00818034i
$365$	16.9755	−	13.4911i	0.888540	−	0.706156i
$366$	−18.8016	+	2.86039i	−0.982774	+	0.149515i
$367$	−16.7304	+	16.7304i	−0.873321	+	0.873321i	−0.992833	−	0.119512i	$-0.961867\pi$
$367$	−16.7304	+	16.7304i	−0.873321	+	0.873321i	0.119512	+	0.992833i	$0.461867\pi$
$368$	−26.6388	−	4.88836i	−1.38864	−	0.254823i
$369$			0.181786i			0.00946342i
$370$	1.31872	+	35.5252i	0.0685570	+	1.84687i
$371$	5.71069			0.296484
$372$	0.397140	−	0.756466i	0.0205907	−	0.0392209i
$373$	6.54312	+	6.54312i	0.338790	+	0.338790i	0.855912	−	0.517122i	$-0.172997\pi$
$373$	6.54312	+	6.54312i	0.338790	+	0.338790i	−0.517122	+	0.855912i	$0.672997\pi$
$374$	2.50640	−	0.381313i	0.129603	−	0.0197172i
$375$	−19.0296	+	9.04669i	−0.982685	+	0.467169i
$376$	13.9970	−	6.81204i	0.721840	−	0.351304i
$377$	0.178460	+	0.178460i	0.00919118	+	0.00919118i
$378$	3.86754	−	5.25547i	0.198925	−	0.270312i
$379$		−	11.9272i		−	0.612658i	−0.951926	−	0.306329i	$-0.900899\pi$
$379$		−	11.9272i		−	0.612658i	0.951926	−	0.306329i	$-0.0991007\pi$
$380$	21.2185	−	4.03855i	1.08849	−	0.207173i
$381$			12.0284i			0.616232i
$382$	−2.21627	−	1.63097i	−0.113394	−	0.0834477i
$383$	8.23642	+	8.23642i	0.420861	+	0.420861i	0.885500	−	0.464639i	$-0.153816\pi$
$383$	8.23642	+	8.23642i	0.420861	+	0.420861i	−0.464639	+	0.885500i	$0.653816\pi$
$384$	10.4823	−	18.5673i	0.534923	−	0.947510i
$385$	−4.63617	+	3.68454i	−0.236281	+	0.187782i
$386$	−3.27558	−	21.5306i	−0.166723	−	1.09588i
$387$	4.34671	+	4.34671i	0.220956	+	0.220956i
$388$	−7.91313	+	15.0728i	−0.401728	+	0.765206i
$389$	−15.1127			−0.766246			−0.383123	−	0.923697i	$-0.625152\pi$
$389$	−15.1127			−0.766246			−0.383123	+	0.923697i	$0.625152\pi$
$390$	0.331420	−	0.356974i	0.0167821	−	0.0180761i
$391$			4.58319i			0.231782i
$392$	−0.923123	+	2.67355i	−0.0466248	+	0.135034i
$393$	−10.8891	+	10.8891i	−0.549282	+	0.549282i
$394$	4.90871	+	32.2653i	0.247297	+	1.62550i
$395$	−6.11261	−	0.699093i	−0.307559	−	0.0351752i
$396$	−2.79028	+	0.869118i	−0.140217	+	0.0436748i
$397$	18.4293	−	18.4293i	0.924942	−	0.924942i	−0.0724317	−	0.997373i	$-0.523076\pi$
$397$	18.4293	−	18.4293i	0.924942	−	0.924942i	0.997373	+	0.0724317i	$0.0230759\pi$
$398$	11.2235	−	15.2513i	0.562585	−	0.764479i
$399$	−9.10224			−0.455682
$400$	−18.6016	+	7.34710i	−0.930081	+	0.367355i
$401$	0.565845			0.0282569			0.0141285	−	0.999900i	$-0.495503\pi$
$401$	0.565845			0.0282569			0.0141285	+	0.999900i	$0.495503\pi$
$402$	−4.05487	+	5.51003i	−0.202238	+	0.274815i
$403$	0.0131004	−	0.0131004i	0.000652575	−	0.000652575i
$404$	−19.4731	+	6.06549i	−0.968823	+	0.301770i
$405$	−22.9952	−	2.62994i	−1.14264	−	0.130683i
$406$	0.656803	+	4.31722i	0.0325966	+	0.214260i
$407$	21.0524	−	21.0524i	1.04353	−	1.04353i
$408$	−3.41060	−	1.17761i	−0.168850	−	0.0583005i
$409$		−	17.7186i		−	0.876130i	−0.898943	−	0.438065i	$-0.855664\pi$
$409$		−	17.7186i		−	0.876130i	0.898943	−	0.438065i	$-0.144336\pi$
$410$	0.708886	−	0.763544i	0.0350094	−	0.0377087i
$411$	−37.0260			−1.82636
$412$	−2.97865	+	5.67368i	−0.146748	+	0.279522i
$413$	−6.88566	−	6.88566i	−0.338821	−	0.338821i
$414$	−0.794632	−	5.22318i	−0.0390540	−	0.256705i
$415$	27.4060	−	21.7806i	1.34531	−	1.06917i
$416$	0.336754	−	0.316809i	0.0165107	−	0.0155328i
$417$	−4.49231	−	4.49231i	−0.219989	−	0.219989i
$418$	−14.5695	−	10.7218i	−0.712617	−	0.524420i
$419$			19.0533i			0.930814i	0.885097	+	0.465407i	$0.154092\pi$
$419$			19.0533i			0.930814i	−0.885097	+	0.465407i	$0.845908\pi$
$420$	8.27959	−	1.57587i	0.404003	−	0.0768944i
$421$			7.21586i			0.351680i	0.984419	+	0.175840i	$0.0562641\pi$
$421$			7.21586i			0.351680i	−0.984419	+	0.175840i	$0.943736\pi$
$422$	−10.3898	+	14.1184i	−0.505767	+	0.687271i
$423$	2.14722	+	2.14722i	0.104402	+	0.104402i
$424$	−7.06833	−	14.5236i	−0.343268	−	0.705328i
$425$	1.79104	+	2.87173i	0.0868783	+	0.139300i
$426$	33.4900	−	5.09503i	1.62260	−	0.246855i
$427$	−5.04558	−	5.04558i	−0.244173	−	0.244173i
$428$	16.1855	−	30.8298i	0.782355	−	1.49022i
$429$	−0.407946			−0.0196958
$430$	−1.30693	−	35.2074i	−0.0630256	−	1.69785i
$431$		−	0.570407i		−	0.0274755i	−0.999906	−	0.0137378i	$-0.995627\pi$
$431$		−	0.570407i		−	0.0274755i	0.999906	−	0.0137378i	$-0.00437300\pi$
$432$	−18.1529	−	3.33115i	−0.873380	−	0.160270i
$433$	−4.37133	+	4.37133i	−0.210073	+	0.210073i	−0.804298	−	0.594226i	$-0.797459\pi$
$433$	−4.37133	+	4.37133i	−0.210073	+	0.210073i	0.594226	+	0.804298i	$0.297459\pi$
$434$	0.316916	−	0.0482143i	0.0152125	−	0.00231436i
$435$	10.1872	−	8.09617i	0.488440	−	0.388182i
$436$	−3.58077	−	11.4959i	−0.171488	−	0.550556i
$437$	23.1237	−	23.1237i	1.10616	−	1.10616i
$438$	20.8162	+	15.3188i	0.994638	+	0.731961i
$439$	−31.9198			−1.52345			−0.761723	−	0.647902i	$-0.775647\pi$
$439$	−31.9198			−1.52345			−0.761723	+	0.647902i	$0.775647\pi$
$440$	15.1090	+	7.23036i	0.720292	+	0.344694i
$441$	−0.551751			−0.0262738
$442$	−0.0630168	−	0.0463744i	−0.00299740	−	0.00220581i
$443$	−10.7226	+	10.7226i	−0.509445	+	0.509445i	−0.914356	−	0.404911i	$-0.867303\pi$
$443$	−10.7226	+	10.7226i	−0.509445	+	0.509445i	0.404911	+	0.914356i	$0.367303\pi$
$444$	−40.4556	+	12.6011i	−1.91994	+	0.598024i
$445$	3.72129	−	32.5375i	0.176406	−	1.54243i
$446$	23.4752	−	3.57142i	1.11158	−	0.169112i
$447$	−15.8119	+	15.8119i	−0.747879	+	0.747879i
$448$	7.94202	−	0.961428i	0.375225	−	0.0454232i
$449$		−	23.8974i		−	1.12779i	−0.825846	−	0.563895i	$-0.809302\pi$
$449$		−	23.8974i		−	1.12779i	0.825846	−	0.563895i	$-0.190698\pi$
$450$	−2.53904	−	2.96221i	−0.119692	−	0.139640i
$451$	−0.872571			−0.0410878
$452$	−4.05517	−	2.12894i	−0.190739	−	0.100137i
$453$	−13.7771	−	13.7771i	−0.647305	−	0.647305i
$454$	−2.74703	+	0.417922i	−0.128925	+	0.0196140i
$455$	0.181578	+	0.0207669i	0.00851249	+	0.000973566i
$456$	11.2662	+	23.1491i	0.527586	+	1.08405i
$457$	−25.9126	−	25.9126i	−1.21214	−	1.21214i	−0.970321	−	0.241822i	$-0.922255\pi$
$457$	−25.9126	−	25.9126i	−1.21214	−	1.21214i	−0.241822	−	0.970321i	$-0.577745\pi$
$458$	12.2723	−	16.6765i	0.573448	−	0.779241i
$459$			3.12319i			0.145778i
$460$	−17.0304	+	25.0372i	−0.794048	+	1.16737i
$461$		−	6.92170i		−	0.322376i	−0.986924	−	0.161188i	$-0.948468\pi$
$461$		−	6.92170i		−	0.322376i	0.986924	−	0.161188i	$-0.0515325\pi$
$462$	−5.68511	−	4.18371i	−0.264495	−	0.194644i
$463$	−21.1905	−	21.1905i	−0.984807	−	0.984807i	0.0150795	−	0.999886i	$-0.495200\pi$
$463$	−21.1905	−	21.1905i	−0.984807	−	0.984807i	−0.999886	+	0.0150795i	$0.995200\pi$
$464$	10.1667	−	7.01397i	0.471978	−	0.325615i
$465$	−0.594320	−	0.747820i	−0.0275609	−	0.0346793i
$466$	−5.46355	−	35.9124i	−0.253094	−	1.66361i
$467$	15.5251	+	15.5251i	0.718417	+	0.718417i	0.968281	−	0.249864i	$-0.0803860\pi$
$467$	15.5251	+	15.5251i	0.718417	+	0.718417i	−0.249864	+	0.968281i	$0.580386\pi$
$468$	0.0798568	+	0.0419243i	0.00369138	+	0.00193795i
$469$	−2.56683			−0.118525
$470$	−0.645606	−	17.3920i	−0.0297796	−	0.802235i
$471$			35.7138i			1.64561i
$472$	−8.98919	+	26.0344i	−0.413761	+	1.19833i
$473$	−20.8641	+	20.8641i	−0.959334	+	0.959334i
$474$	−1.10297	−	7.24989i	−0.0506609	−	0.332998i
$475$	5.45245	−	23.5253i	0.250176	−	1.07941i
$476$	−0.402601	−	1.29254i	−0.0184532	−	0.0592435i
$477$	2.22801	−	2.22801i	0.102013	−	0.102013i
$478$	5.79601	−	7.87601i	0.265103	−	0.360240i
$479$	26.4751			1.20968			0.604840	−	0.796347i	$-0.293237\pi$
$479$	26.4751			1.20968			0.604840	+	0.796347i	$0.293237\pi$
$480$	−14.2557	−	19.1064i	−0.650682	−	0.872083i
$481$	−0.918829			−0.0418950
$482$	11.4940	−	15.6188i	0.523537	−	0.711418i
$483$	9.02302	−	9.02302i	0.410562	−	0.410562i
$484$	2.37079	+	7.61135i	0.107763	+	0.345971i
$485$	11.8420	+	14.9005i	0.537718	+	0.676598i
$486$	−1.20503	−	7.92077i	−0.0546613	−	0.359293i
$487$	16.7006	−	16.7006i	0.756776	−	0.756776i	−0.218958	−	0.975734i	$-0.570266\pi$
$487$	16.7006	−	16.7006i	0.756776	−	0.756776i	0.975734	+	0.218958i	$0.0702659\pi$
$488$	−6.58698	+	19.0772i	−0.298178	+	0.863583i
$489$		−	1.89549i		−	0.0857171i
$490$	2.31748	+	2.15158i	0.104693	+	0.0971985i
$491$	−12.3883			−0.559078			−0.279539	−	0.960134i	$-0.590182\pi$
$491$	−12.3883			−0.559078			−0.279539	+	0.960134i	$0.590182\pi$
$492$	1.09954	+	0.577250i	0.0495709	+	0.0260244i
$493$	−1.47796	−	1.47796i	−0.0665642	−	0.0665642i
$494$	0.0839661	+	0.551916i	0.00377781	+	0.0248319i
$495$	−0.371276	+	3.24630i	−0.0166876	+	0.145910i
$496$	−0.514879	−	0.746315i	−0.0231187	−	0.0335105i
$497$	8.98738	+	8.98738i	0.403139	+	0.403139i
$498$	33.6067	+	24.7314i	1.50595	+	1.10824i
$499$			38.3536i			1.71694i	0.512862	+	0.858471i	$0.328585\pi$
$499$			38.3536i			1.71694i	−0.512862	+	0.858471i	$0.671415\pi$
$500$	−0.886745	+	22.3431i	−0.0396564	+	0.999213i
$501$		−	9.04903i		−	0.404281i
$502$	12.8789	−	17.5007i	0.574811	−	0.781093i
$503$	15.2581	+	15.2581i	0.680327	+	0.680327i	0.960074	−	0.279747i	$-0.0902506\pi$
$503$	15.2581	+	15.2581i	0.680327	+	0.680327i	−0.279747	+	0.960074i	$0.590251\pi$
$504$	0.682921	+	1.40323i	0.0304197	+	0.0625047i
$505$	−2.59110	+	22.6556i	−0.115302	+	1.00816i
$506$	25.0712	−	3.81422i	1.11455	−	0.169563i
$507$	−17.3152	−	17.3152i	−0.768993	−	0.768993i
$508$	11.3020	+	5.93348i	0.501445	+	0.263255i
$509$	−41.9526			−1.85952			−0.929758	−	0.368172i	$-0.879984\pi$
$509$	−41.9526			−1.85952			−0.929758	+	0.368172i	$0.879984\pi$
$510$	−2.74474	+	2.95637i	−0.121539	+	0.130910i
$511$			9.69719i			0.428979i
$512$	−12.2752	−	19.0084i	−0.542494	−	0.840059i
$513$	15.7576	−	15.7576i	0.695713	−	0.695713i
$514$	30.6803	−	4.66757i	1.35325	−	0.205878i
$515$	4.45755	+	5.60884i	0.196423	+	0.247155i
$516$	40.0938	−	12.4884i	1.76503	−	0.549773i
$517$	−10.3066	+	10.3066i	−0.453285	+	0.453285i
$518$	−12.8047	−	9.42308i	−0.562607	−	0.414026i
$519$	−13.7558			−0.603812
$520$	−0.171930	−	0.487498i	−0.00753964	−	0.0213782i
$521$	27.2979			1.19594			0.597971	−	0.801517i	$-0.295974\pi$
$521$	27.2979			1.19594			0.597971	+	0.801517i	$0.295974\pi$
$522$	1.94060	+	1.42810i	0.0849376	+	0.0625062i
$523$	−15.8639	+	15.8639i	−0.693682	+	0.693682i	−0.963040	−	0.269358i	$-0.913188\pi$
$523$	−15.8639	+	15.8639i	−0.693682	+	0.693682i	0.269358	+	0.963040i	$0.413188\pi$
$524$	4.86003	+	15.6030i	0.212311	+	0.681620i
$525$	2.12758	−	9.17972i	0.0928552	−	0.400636i
$526$	17.7533	−	2.70091i	0.774080	−	0.117765i
$527$	−0.108494	+	0.108494i	−0.00472607	+	0.00472607i
$528$	−3.60347	+	19.6368i	−0.156821	+	0.854584i
$529$			22.8450i			0.993260i
$530$	−18.0464	+	0.669895i	−0.783884	+	0.0290984i
$531$	−5.37284			−0.233161
$532$	−4.49005	+	8.55257i	−0.194668	+	0.370801i
$533$	0.0190416	+	0.0190416i	0.000824782	+	0.000824782i
$534$	38.5913	−	5.87111i	1.67001	−	0.254068i
$535$	−24.2216	−	30.4775i	−1.04719	−	1.31766i
$536$	3.17706	+	6.52804i	0.137228	+	0.281969i
$537$	5.22246	+	5.22246i	0.225366	+	0.225366i
$538$	−24.3843	+	33.1350i	−1.05128	+	1.42855i
$539$		−	2.64839i		−	0.114074i
$540$	−11.6053	+	17.0615i	−0.499413	+	0.734211i
$541$			21.0896i			0.906712i	0.891330	+	0.453356i	$0.149773\pi$
$541$			21.0896i			0.906712i	−0.891330	+	0.453356i	$0.850227\pi$
$542$	−22.7710	−	16.7573i	−0.978098	−	0.719789i
$543$	−8.24266	−	8.24266i	−0.353727	−	0.353727i
$544$	−2.78891	+	2.62373i	−0.119574	+	0.112492i
$545$	−13.3747	−	1.52966i	−0.572911	−	0.0655232i
$546$	0.0327641	+	0.215361i	0.00140217	+	0.00921660i
$547$	13.1374	+	13.1374i	0.561715	+	0.561715i	0.929794	−	0.368079i	$-0.119985\pi$
$547$	13.1374	+	13.1374i	0.561715	+	0.561715i	−0.368079	+	0.929794i	$0.619985\pi$
$548$	−18.2646	+	34.7901i	−0.780224	+	1.48616i
$549$	−3.93704			−0.168029
$550$	14.2186	−	12.1874i	0.606281	−	0.519671i
$551$			14.9137i			0.635344i
$552$	−34.1157	−	11.7795i	−1.45206	−	0.501369i
$553$	1.94558	−	1.94558i	0.0827344	−	0.0827344i
$554$	4.08149	+	26.8279i	0.173406	+	1.13981i
$555$	−5.38304	+	47.0673i	−0.228497	+	1.99790i
$556$	−6.43704	+	2.00501i	−0.272991	+	0.0850315i
$557$	16.7058	−	16.7058i	0.707849	−	0.707849i	−0.258233	−	0.966083i	$-0.583140\pi$
$557$	16.7058	−	16.7058i	0.707849	−	0.707849i	0.966083	+	0.258233i	$0.0831404\pi$
$558$	0.104833	−	0.142455i	0.00443794	−	0.00603058i
$559$	0.910611			0.0385147
$560$	2.60354	−	8.55696i	0.110020	−	0.361598i
$561$	3.37851			0.142641
$562$	−5.30527	+	7.20917i	−0.223789	+	0.304100i
$563$	−12.6206	+	12.6206i	−0.531893	+	0.531893i	−0.921135	−	0.389242i	$-0.872737\pi$
$563$	−12.6206	+	12.6206i	−0.531893	+	0.531893i	0.389242	+	0.921135i	$0.372737\pi$
$564$	19.8058	−	6.16914i	0.833977	−	0.259768i
$565$	−4.00882	+	3.18596i	−0.168652	+	0.134034i
$566$	−4.33841	−	28.5167i	−0.182357	−	1.19865i
$567$	7.31914	−	7.31914i	0.307375	−	0.307375i
$568$	11.7330	−	33.9810i	0.492304	−	1.42581i
$569$			4.24450i			0.177939i	0.996034	+	0.0889694i	$0.0283573\pi$
$569$			4.24450i			0.177939i	−0.996034	+	0.0889694i	$0.971643\pi$
$570$	28.7640	−	1.06774i	1.20479	−	0.0447228i
$571$	−4.34540			−0.181850			−0.0909248	−	0.995858i	$-0.528982\pi$
$571$	−4.34540			−0.181850			−0.0909248	+	0.995858i	$0.528982\pi$
$572$	−0.201236	+	0.383311i	−0.00841410	+	0.0160270i
$573$	−2.59295	−	2.59295i	−0.108322	−	0.108322i
$574$	0.0700803	+	0.460643i	0.00292510	+	0.0192269i
$575$	17.9156	+	28.7255i	0.747130	+	1.19794i
$576$	2.72345	−	3.47365i	0.113477	−	0.144735i
$577$	−1.96400	−	1.96400i	−0.0817624	−	0.0817624i	0.665043	−	0.746805i	$-0.268413\pi$
$577$	−1.96400	−	1.96400i	−0.0817624	−	0.0817624i	−0.746805	+	0.665043i	$0.768413\pi$
$578$	−18.8416	−	13.8657i	−0.783708	−	0.576736i
$579$		−	29.0223i		−	1.20613i
$580$	−2.58200	−	13.5658i	−0.107212	−	0.563289i
$581$			15.6556i			0.649503i
$582$	−13.4463	+	18.2718i	−0.557368	+	0.757390i
$583$	10.6944	+	10.6944i	0.442917	+	0.442917i
$584$	24.6622	−	12.0026i	1.02053	−	0.496669i
$585$	0.0789440	−	0.0627398i	0.00326393	−	0.00259397i
$586$	−9.99288	+	1.52027i	−0.412802	+	0.0628019i
$587$	−1.99108	−	1.99108i	−0.0821807	−	0.0821807i	0.664822	−	0.747002i	$-0.268508\pi$
$587$	−1.99108	−	1.99108i	−0.0821807	−	0.0821807i	−0.747002	+	0.664822i	$0.768508\pi$
$588$	−1.75204	+	3.33727i	−0.0722531	+	0.137627i
$589$	1.09478			0.0451095
$590$	22.5671	+	20.9517i	0.929073	+	0.862566i
$591$			43.4922i			1.78903i
$592$	−8.11619	+	44.2286i	−0.333573	+	1.81778i
$593$	−2.87371	+	2.87371i	−0.118009	+	0.118009i	−0.763645	−	0.645636i	$-0.776592\pi$
$593$	−2.87371	+	2.87371i	−0.118009	+	0.118009i	0.645636	+	0.763645i	$0.276592\pi$
$594$	17.0846	−	2.59918i	0.700991	−	0.106646i
$595$	−1.50378	−	0.171986i	−0.0616490	−	0.00705074i
$596$	7.05721	+	22.6570i	0.289074	+	0.928066i
$597$	17.8434	−	17.8434i	0.730283	−	0.730283i
$598$	−0.630348	−	0.463877i	−0.0257768	−	0.0189693i
$599$	9.22171			0.376789			0.188394	−	0.982093i	$-0.439672\pi$
$599$	9.22171			0.376789			0.188394	+	0.982093i	$0.439672\pi$
$600$	−25.9795	+	5.95114i	−1.06061	+	0.242954i
$601$	−41.3086			−1.68501			−0.842507	−	0.538686i	$-0.818921\pi$
$601$	−41.3086			−1.68501			−0.842507	+	0.538686i	$0.818921\pi$
$602$	12.6902	+	9.33880i	0.517214	+	0.380621i
$603$	−1.00144	+	1.00144i	−0.0407818	+	0.0407818i
$604$	−19.7412	+	6.14902i	−0.803260	+	0.250200i
$605$	8.85528	+	1.01277i	0.360018	+	0.0411750i
$606$	−26.8708	+	4.08800i	−1.09155	+	0.166064i
$607$	−30.1959	+	30.1959i	−1.22562	+	1.22562i	−0.260009	+	0.965606i	$0.583726\pi$
$607$	−30.1959	+	30.1959i	−1.22562	+	1.22562i	−0.965606	+	0.260009i	$0.916274\pi$
$608$	27.3086	+	0.833397i	1.10751	+	0.0337987i
$609$			5.81941i			0.235814i
$610$	16.5364	+	15.3527i	0.669541	+	0.621612i
$611$	0.449831			0.0181982
$612$	−0.661354	−	0.347207i	−0.0267336	−	0.0140350i
$613$	2.93355	+	2.93355i	0.118485	+	0.118485i	0.763863	−	0.645378i	$-0.223300\pi$
$613$	2.93355	+	2.93355i	0.118485	+	0.118485i	−0.645378	+	0.763863i	$0.723300\pi$
$614$	41.4687	−	6.30887i	1.67354	−	0.254605i
$615$	1.08697	−	0.863855i	0.0438308	−	0.0348340i
$616$	−6.73547	+	3.27801i	−0.271380	+	0.132075i
$617$	11.6600	+	11.6600i	0.469415	+	0.469415i	0.901725	−	0.432310i	$-0.142301\pi$
$617$	11.6600	+	11.6600i	0.469415	+	0.469415i	−0.432310	+	0.901725i	$0.642301\pi$
$618$	−5.06145	+	6.87784i	−0.203601	+	0.276667i
$619$			21.9496i			0.882228i	0.897451	+	0.441114i	$0.145417\pi$
$619$			21.9496i			0.882228i	−0.897451	+	0.441114i	$0.854583\pi$
$620$	−0.995832	+	0.189538i	−0.0399936	+	0.00761203i
$621$			31.2408i			1.25365i
$622$	1.16670	+	0.858586i	0.0467806	+	0.0344261i
$623$	10.3563	+	10.3563i	0.414918	+	0.414918i
$624$	0.507159	−	0.349886i	0.0203026	−	0.0140067i
$625$	22.4511	+	10.9977i	0.898042	+	0.439909i
$626$	3.86254	+	25.3888i	0.154378	+	1.01474i
$627$	−17.0457	−	17.0457i	−0.680741	−	0.680741i
$628$	33.5571	+	17.6173i	1.33908	+	0.703006i
$629$	7.60951			0.303411
$630$	1.74359	−	0.0647233i	0.0694662	−	0.00257864i
$631$			21.1003i			0.839989i	0.907527	+	0.419994i	$0.137968\pi$
$631$			21.1003i			0.839989i	−0.907527	+	0.419994i	$0.862032\pi$
$632$	−7.35616	−	2.53994i	−0.292612	−	0.101033i
$633$	−16.5179	+	16.5179i	−0.656529	+	0.656529i
$634$	−2.09919	−	13.7981i	−0.0833695	−	0.547994i
$635$	11.1728	−	8.87945i	0.443379	−	0.352370i
$636$	−6.40124	−	20.5510i	−0.253826	−	0.814900i
$637$	−0.0577942	+	0.0577942i	−0.00228989	+	0.00228989i
$638$	−6.85484	+	9.31483i	−0.271386	+	0.368778i
$639$	7.01279			0.277422
$640$	−24.9848	+	3.96985i	−0.987611	+	0.156922i
$641$	−12.9036			−0.509660			−0.254830	−	0.966986i	$-0.582019\pi$
$641$	−12.9036			−0.509660			−0.254830	+	0.966986i	$0.582019\pi$
$642$	27.5030	−	37.3730i	1.08546	−	1.47499i
$643$	−1.64441	+	1.64441i	−0.0648494	+	0.0648494i	−0.738788	−	0.673938i	$-0.764601\pi$
$643$	−1.64441	+	1.64441i	−0.0648494	+	0.0648494i	0.673938	+	0.738788i	$0.264601\pi$
$644$	−4.02717	−	12.9291i	−0.158693	−	0.509478i
$645$	5.33490	−	46.6463i	0.210061	−	1.83670i
$646$	−0.695386	−	4.57083i	−0.0273596	−	0.179837i
$647$	23.8181	−	23.8181i	0.936387	−	0.936387i	−0.0617077	−	0.998094i	$-0.519655\pi$
$647$	23.8181	−	23.8181i	0.936387	−	0.936387i	0.998094	+	0.0617077i	$0.0196546\pi$
$648$	−27.6734	−	9.55508i	−1.08711	−	0.375359i
$649$		−	25.7895i		−	1.01233i
$650$	−0.576240	−	0.0443254i	−0.0226020	−	0.00173858i
$651$	0.427189			0.0167428
$652$	−1.78103	−	0.935028i	−0.0697504	−	0.0366185i
$653$	−31.0162	−	31.0162i	−1.21376	−	1.21376i	−0.969781	−	0.243977i	$-0.921548\pi$
$653$	−31.0162	−	31.0162i	−1.21376	−	1.21376i	−0.243977	−	0.969781i	$-0.578452\pi$
$654$	−2.41335	−	15.8632i	−0.0943695	−	0.620299i
$655$	18.1530	+	2.07614i	0.709296	+	0.0811215i
$656$	1.08478	−	0.748385i	0.0423536	−	0.0292195i
$657$	3.78333	+	3.78333i	0.147602	+	0.147602i
$658$	6.26880	+	4.61325i	0.244383	+	0.179843i
$659$		−	24.3781i		−	0.949634i	−0.880085	−	0.474817i	$-0.842514\pi$
$659$		−	24.3781i		−	0.949634i	0.880085	−	0.474817i	$-0.157486\pi$
$660$	18.4563	+	12.5540i	0.718410	+	0.488666i
$661$		−	42.3178i		−	1.64597i	−0.568062	−	0.822986i	$-0.692307\pi$
$661$		−	42.3178i		−	1.64597i	0.568062	−	0.822986i	$-0.307693\pi$
$662$	−1.02280	+	1.38986i	−0.0397524	+	0.0540183i
$663$	−0.0737271	−	0.0737271i	−0.00286332	−	0.00286332i
$664$	39.8157	−	19.3775i	1.54515	−	0.751991i
$665$	6.71936	+	8.45481i	0.260566	+	0.327864i
$666$	−8.67210	+	1.31934i	−0.336037	+	0.0511232i
$667$	−14.7839	−	14.7839i	−0.572434	−	0.572434i
$668$	−8.50257	−	4.46380i	−0.328974	−	0.172710i
$669$	31.6435			1.22341
$670$	8.11145	−	0.301103i	0.313373	−	0.0116326i
$671$		−	18.8977i		−	0.729537i
$672$	10.6560	+	0.325197i	0.411064	+	0.0125447i
$673$	−5.39981	+	5.39981i	−0.208147	+	0.208147i	−0.803480	−	0.595332i	$-0.797020\pi$
$673$	−5.39981	+	5.39981i	−0.208147	+	0.208147i	0.595332	+	0.803480i	$0.297020\pi$
$674$	7.80621	−	1.18760i	0.300684	−	0.0457448i
$675$	12.2085	+	19.5749i	0.469904	+	0.753438i
$676$	−24.8109	+	7.72812i	−0.954266	+	0.297235i
$677$	−8.53369	+	8.53369i	−0.327976	+	0.327976i	−0.851817	−	0.523840i	$-0.824499\pi$
$677$	−8.53369	+	8.53369i	−0.327976	+	0.327976i	0.523840	+	0.851817i	$0.324499\pi$
$678$	−4.91581	−	3.61758i	−0.188791	−	0.138932i
$679$	−8.51186			−0.326655
$680$	1.42388	+	4.03733i	0.0546034	+	0.154825i
$681$	−3.70287			−0.141894
$682$	0.683779	+	0.503198i	0.0261833	+	0.0192684i
$683$	25.0104	−	25.0104i	0.956998	−	0.956998i	−0.0421149	−	0.999113i	$-0.513410\pi$
$683$	25.0104	−	25.0104i	0.956998	−	0.956998i	0.999113	+	0.0421149i	$0.0134095\pi$
$684$	1.58498	+	5.08853i	0.0606032	+	0.194565i
$685$	27.3330	+	34.3924i	1.04434	+	1.31407i
$686$	−1.39813	+	0.212705i	−0.0533807	+	0.00812111i
$687$	19.5108	−	19.5108i	0.744384	−	0.744384i
$688$	8.04359	−	43.8330i	0.306659	−	1.67112i
$689$		−	0.466754i		−	0.0177819i
$690$	−27.4552	+	29.5721i	−1.04520	+	1.12579i
$691$	−17.9294			−0.682065			−0.341033	−	0.940051i	$-0.610777\pi$
$691$	−17.9294			−0.682065			−0.341033	+	0.940051i	$0.610777\pi$
$692$	−6.78560	+	12.9251i	−0.257950	+	0.491338i
$693$	−1.03326	−	1.03326i	−0.0392503	−	0.0392503i
$694$	−45.4091	+	6.90835i	−1.72371	+	0.262237i
$695$	−0.856516	+	7.48905i	−0.0324895	+	0.284076i
$696$	14.8001	−	7.20289i	0.560996	−	0.273025i
$697$	−0.157698	−	0.157698i	−0.00597322	−	0.00597322i
$698$	21.6889	−	29.4724i	0.820938	−	1.11555i
$699$		−	48.4082i		−	1.83097i
$700$	−7.57585	−	6.52736i	−0.286340	−	0.246711i
$701$		−	22.0532i		−	0.832938i	−0.909150	−	0.416469i	$-0.863267\pi$
$701$		−	22.0532i		−	0.832938i	0.909150	−	0.416469i	$-0.136733\pi$
$702$	−0.429548	−	0.316107i	−0.0162122	−	0.0119307i
$703$	−38.3926	−	38.3926i	−1.44800	−	1.44800i
$704$	16.6735	+	13.0725i	0.628404	+	0.492689i
$705$	2.63537	−	23.0427i	0.0992540	−	0.867839i
$706$	−7.94056	−	52.1939i	−0.298847	−	1.96435i
$707$	−7.21103	−	7.21103i	−0.271199	−	0.271199i
$708$	−17.0611	+	32.4976i	−0.641194	+	1.22134i
$709$	35.0814			1.31751			0.658755	−	0.752357i	$-0.271083\pi$
$709$	35.0814			1.31751			0.658755	+	0.752357i	$0.271083\pi$
$710$	−29.4553	−	27.3468i	−1.10544	−	1.02631i
$711$		−	1.51812i		−	0.0569340i
$712$	13.5201	−	39.1570i	0.506689	−	1.46747i
$713$	−1.08525	+	1.08525i	−0.0406429	+	0.0406429i
$714$	−0.271344	−	1.78357i	−0.0101548	−	0.0667483i
$715$	0.301150	+	0.378930i	0.0112624	+	0.0141712i
$716$	7.48328	−	2.33090i	0.279663	−	0.0871097i
$717$	9.21462	−	9.21462i	0.344126	−	0.344126i
$718$	−21.1305	+	28.7136i	−0.788583	+	1.07158i
$719$	−15.2445			−0.568525			−0.284262	−	0.958747i	$-0.591749\pi$
$719$	−15.2445			−0.568525			−0.284262	+	0.958747i	$0.591749\pi$
$720$	−2.32271	−	4.35423i	−0.0865621	−	0.162273i
$721$	−3.20402			−0.119324
$722$	−3.62675	+	4.92828i	−0.134974	+	0.183412i
$723$	18.2734	−	18.2734i	0.679596	−	0.679596i
$724$	−11.8109	+	3.67888i	−0.438950	+	0.136724i
$725$	−15.0406	−	3.48596i	−0.558594	−	0.129465i
$726$	1.59786	+	10.5028i	0.0593020	+	0.389797i
$727$	−22.9669	+	22.9669i	−0.851794	+	0.851794i	−0.990354	−	0.138560i	$-0.955753\pi$
$727$	−22.9669	+	22.9669i	−0.851794	+	0.851794i	0.138560	+	0.990354i	$0.455753\pi$
$728$	0.218518	+	0.0754500i	0.00809881	+	0.00279636i
$729$			20.3756i			0.754653i
$730$	−1.13753	−	30.6441i	−0.0421020	−	1.13419i
$731$	−7.54145			−0.278931
$732$	−12.5018	+	23.8132i	−0.462079	+	0.880160i
$733$	−16.1458	−	16.1458i	−0.596358	−	0.596358i	0.342983	−	0.939341i	$-0.388563\pi$
$733$	−16.1458	−	16.1458i	−0.596358	−	0.596358i	−0.939341	+	0.342983i	$0.888563\pi$
$734$	5.03268	+	33.0802i	0.185760	+	1.22101i
$735$	2.62194	+	3.29912i	0.0967116	+	0.121690i
$736$	−27.8971	+	26.2448i	−1.02830	+	0.967397i
$737$	−4.80690	−	4.80690i	−0.177064	−	0.177064i
$738$	0.207060	+	0.152377i	0.00762199	+	0.00560907i
$739$			13.1771i			0.484727i	0.970186	+	0.242363i	$0.0779226\pi$
$739$			13.1771i			0.484727i	−0.970186	+	0.242363i	$0.922077\pi$
$740$	41.5696	+	28.2758i	1.52813	+	1.03944i
$741$			0.743957i			0.0273299i
$742$	4.78681	−	6.50465i	0.175729	−	0.238793i
$743$	−6.76978	−	6.76978i	−0.248359	−	0.248359i	0.571938	−	0.820297i	$-0.306192\pi$
$743$	−6.76978	−	6.76978i	−0.248359	−	0.248359i	−0.820297	+	0.571938i	$0.806192\pi$
$744$	−0.528747	−	1.08644i	−0.0193848	−	0.0398308i
$745$	26.3598	+	3.01475i	0.965749	+	0.110452i
$746$	12.9374	−	1.96824i	0.473671	−	0.0720622i
$747$	6.10797	+	6.10797i	0.223479	+	0.223479i
$748$	1.66659	−	3.17449i	0.0609364	−	0.116071i
$749$	17.4101			0.636152
$750$	−5.64654	+	29.2584i	−0.206182	+	1.06837i
$751$			2.58086i			0.0941768i	0.998891	+	0.0470884i	$0.0149942\pi$
$751$			2.58086i			0.0941768i	−0.998891	+	0.0470884i	$0.985006\pi$
$752$	3.97344	−	21.6530i	0.144896	−	0.789603i
$753$	20.4751	−	20.4751i	0.746154	−	0.746154i
$754$	0.352861	−	0.0536827i	0.0128504	−	0.00195501i
$755$	−2.62678	+	22.9676i	−0.0955983	+	0.835875i
$756$	−2.74429	−	8.81048i	−0.0998090	−	0.320434i
$757$	−15.7122	+	15.7122i	−0.571070	+	0.571070i	−0.932427	−	0.361357i	$-0.882313\pi$
$757$	−15.7122	+	15.7122i	−0.571070	+	0.571070i	0.361357	+	0.932427i	$0.382313\pi$
$758$	−13.5854	−	9.99759i	−0.493444	−	0.363129i
$759$	33.7948			1.22667
$760$	13.1857	−	27.5537i	0.478297	−	0.999477i
$761$	−31.8223			−1.15356			−0.576778	−	0.816901i	$-0.695690\pi$
$761$	−31.8223			−1.15356			−0.576778	+	0.816901i	$0.695690\pi$
$762$	13.7007	+	10.0824i	0.496323	+	0.365247i
$763$	4.25703	−	4.25703i	0.154115	−	0.154115i
$764$	−3.71545	+	1.15729i	−0.134420	+	0.0418693i
$765$	−0.653795	+	0.519595i	−0.0236380	+	0.0187860i
$766$	16.2854	−	2.47760i	0.588417	−	0.0895192i
$767$	−0.562788	+	0.562788i	−0.0203211	+	0.0203211i
$768$	−12.3623	−	27.5031i	−0.446084	−	0.992434i
$769$		−	4.37567i		−	0.157791i	−0.996883	−	0.0788954i	$-0.974861\pi$
$769$		−	4.37567i		−	0.157791i	0.996883	−	0.0788954i	$-0.0251393\pi$
$770$	0.310671	+	8.36919i	0.0111958	+	0.301605i
$771$	41.3556			1.48939
$772$	−27.2697	−	14.3164i	−0.981458	−	0.515259i
$773$	26.9983	+	26.9983i	0.971062	+	0.971062i	0.999593	−	0.0285308i	$-0.00908286\pi$
$773$	26.9983	+	26.9983i	0.971062	+	0.971062i	−0.0285308	+	0.999593i	$0.509083\pi$
$774$	8.59453	−	1.30754i	0.308924	−	0.0469984i
$775$	−0.255896	+	1.10410i	−0.00919205	+	0.0396603i
$776$	10.5354	+	21.6476i	0.378200	+	0.777104i
$777$	−14.9810	−	14.9810i	−0.537441	−	0.537441i
$778$	−12.6678	+	17.2139i	−0.454162	+	0.617147i
$779$			1.59128i			0.0570134i
$780$	−0.128801	−	0.676719i	−0.00461181	−	0.0242304i
$781$			33.6613i			1.20449i
$782$	5.22038	+	3.84171i	0.186681	+	0.137379i
$783$	−10.0744	−	10.0744i	−0.360030	−	0.360030i
$784$	2.27147	+	3.29248i	0.0811238	+	0.117589i
$785$	33.1736	−	26.3643i	1.18402	−	0.940982i
$786$	3.27555	+	21.5304i	0.116835	+	0.767965i
$787$	9.92719	+	9.92719i	0.353866	+	0.353866i	0.861546	−	0.507680i	$-0.169497\pi$
$787$	9.92719	+	9.92719i	0.353866	+	0.353866i	−0.507680	+	0.861546i	$0.669497\pi$
$788$	40.8657	+	21.4543i	1.45578	+	0.764277i
$789$	23.9306			0.851952
$790$	−5.92000	+	6.37645i	−0.210624	+	0.226864i
$791$		−	2.29002i		−	0.0814237i
$792$	−1.34892	+	3.90672i	−0.0479316	+	0.138819i
$793$	−0.412393	+	0.412393i	−0.0146445	+	0.0146445i
$794$	−5.54373	−	36.4394i	−0.196740	−	1.29319i
$795$	−23.9096	−	2.73452i	−0.847988	−	0.0969835i
$796$	−7.96391	−	25.5679i	−0.282273	−	0.906230i
$797$	−5.05324	+	5.05324i	−0.178995	+	0.178995i	−0.790918	−	0.611923i	$-0.790396\pi$
$797$	−5.05324	+	5.05324i	−0.178995	+	0.178995i	0.611923	+	0.790918i	$0.290396\pi$
$798$	−7.62967	+	10.3677i	−0.270087	+	0.367013i
$799$	−3.72538			−0.131795
$800$	−7.22368	+	27.3463i	−0.255396	+	0.966837i
$801$	8.08099			0.285528
$802$	0.474302	−	0.644514i	0.0167482	−	0.0227586i
$803$	−18.1599	+	18.1599i	−0.640849	+	0.640849i
$804$	2.87722	+	9.23723i	0.101472	+	0.325772i
$805$	−15.0421	−	1.72035i	−0.530165	−	0.0606345i
$806$	−0.00394072	−	0.0259027i	−0.000138806	−	0.000912382i
$807$	−38.7666	+	38.7666i	−1.36465	+	1.36465i
$808$	−9.41395	+	27.2646i	−0.331182	+	0.959167i
$809$		−	10.8908i		−	0.382900i	−0.981502	−	0.191450i	$-0.938681\pi$
$809$		−	10.8908i		−	0.382900i	0.981502	−	0.191450i	$-0.0613190\pi$
$810$	−22.2706	+	23.9878i	−0.782511	+	0.842845i
$811$	8.39576			0.294815			0.147408	−	0.989076i	$-0.452907\pi$
$811$	8.39576			0.294815			0.147408	+	0.989076i	$0.452907\pi$
$812$	5.46798	+	2.87066i	0.191889	+	0.100740i
$813$	−26.6412	−	26.6412i	−0.934347	−	0.934347i
$814$	−6.33279	−	41.6259i	−0.221964	−	1.45899i
$815$	−1.76067	+	1.39927i	−0.0616736	+	0.0490143i
$816$	−4.20016	+	2.89767i	−0.147035	+	0.101439i
$817$	38.0492	+	38.0492i	1.33117	+	1.33117i
$818$	−20.1821	−	14.8521i	−0.705649	−	0.519292i
$819$			0.0450964i			0.00157580i
$820$	−0.275497	−	1.44746i	−0.00962076	−	0.0505475i
$821$		−	27.4298i		−	0.957307i	−0.878004	−	0.478653i	$-0.841125\pi$
$821$		−	27.4298i		−	0.957307i	0.878004	−	0.478653i	$-0.158875\pi$
$822$	−31.0359	+	42.1737i	−1.08250	+	1.47098i
$823$	−0.449275	−	0.449275i	−0.0156607	−	0.0156607i	0.699233	−	0.714894i	$-0.253525\pi$
$823$	−0.449275	−	0.449275i	−0.0156607	−	0.0156607i	−0.714894	+	0.699233i	$0.753525\pi$
$824$	3.96573	+	8.14856i	0.138153	+	0.283869i
$825$	21.1751	−	13.2065i	0.737223	−	0.459792i
$826$	−13.6147	+	2.07128i	−0.473715	+	0.0720689i
$827$	−9.24540	−	9.24540i	−0.321494	−	0.321494i	0.527846	−	0.849340i	$-0.323000\pi$
$827$	−9.24540	−	9.24540i	−0.321494	−	0.321494i	−0.849340	+	0.527846i	$0.823000\pi$
$828$	−6.61543	−	3.47306i	−0.229902	−	0.120697i
$829$	−54.1348			−1.88018			−0.940090	−	0.340925i	$-0.889260\pi$
$829$	−54.1348			−1.88018			−0.940090	+	0.340925i	$0.889260\pi$
$830$	−1.83648	−	49.4732i	−0.0637452	−	1.71724i
$831$			36.1628i			1.25447i
$832$	−0.0785808	−	0.649128i	−0.00272430	−	0.0225045i
$833$	0.478637	−	0.478637i	0.0165838	−	0.0165838i
$834$	−8.88242	+	1.35133i	−0.307573	+	0.0467928i
$835$	−8.40539	+	6.68008i	−0.290881	+	0.231174i
$836$	−24.4249	+	7.60787i	−0.844751	+	0.263124i
$837$	−0.739538	+	0.739538i	−0.0255622	+	0.0255622i
$838$	21.7023	+	15.9708i	0.749692	+	0.551704i
$839$	−43.6223			−1.50601			−0.753005	−	0.658015i	$-0.771396\pi$
$839$	−43.6223			−1.50601			−0.753005	+	0.658015i	$0.771396\pi$
$840$	5.14516	−	10.7516i	0.177525	−	0.370966i
$841$	−19.4651			−0.671211
$842$	8.21908	+	6.04848i	0.283248	+	0.208444i
$843$	−8.43444	+	8.43444i	−0.290498	+	0.290498i
$844$	7.37230	+	23.6686i	0.253765	+	0.814706i
$845$	−3.30135	+	28.8658i	−0.113570	+	0.993013i
$846$	4.24560	−	0.645907i	0.145967	−	0.0222067i
$847$	−2.81854	+	2.81854i	−0.0968462	+	0.0968462i
$848$	−22.4676	−	4.12293i	−0.771541	−	0.141582i
$849$		−	38.4392i		−	1.31923i
$850$	4.77228	+	0.367092i	0.163688	+	0.0125911i
$851$	76.1169			2.60925
$852$	22.2686	−	42.4169i	0.762910	−	1.45318i
$853$	−0.921445	−	0.921445i	−0.0315497	−	0.0315497i	0.691156	−	0.722706i	$-0.257102\pi$
$853$	−0.921445	−	0.921445i	−0.0315497	−	0.0315497i	−0.722706	+	0.691156i	$0.757102\pi$
$854$	−9.97638	+	1.51776i	−0.341385	+	0.0519368i
$855$	5.92015	+	0.677082i	0.202465	+	0.0231557i
$856$	−21.5491	−	44.2779i	−0.736534	−	1.51339i
$857$	−9.22846	−	9.22846i	−0.315238	−	0.315238i	0.531697	−	0.846935i	$-0.321555\pi$
$857$	−9.22846	−	9.22846i	−0.315238	−	0.315238i	−0.846935	+	0.531697i	$0.821555\pi$
$858$	−0.341949	+	0.464663i	−0.0116739	+	0.0158633i
$859$		−	29.4069i		−	1.00335i	−0.865056	−	0.501675i	$-0.832717\pi$
$859$		−	29.4069i		−	1.00335i	0.865056	−	0.501675i	$-0.167283\pi$
$860$	−41.1978	−	28.0229i	−1.40483	−	0.955573i
$861$			0.620926i			0.0211611i
$862$	−0.649710	−	0.478126i	−0.0221292	−	0.0162850i
$863$	−15.1799	−	15.1799i	−0.516730	−	0.516730i	0.399850	−	0.916580i	$-0.369062\pi$
$863$	−15.1799	−	15.1799i	−0.516730	−	0.516730i	−0.916580	+	0.399850i	$0.869062\pi$
$864$	−19.0104	+	17.8844i	−0.646745	+	0.608440i
$865$	10.1547	+	12.7774i	0.345269	+	0.434443i
$866$	1.31494	+	8.64320i	0.0446834	+	0.293708i
$867$	−22.0439	−	22.0439i	−0.748652	−	0.748652i
$868$	0.210728	−	0.401391i	0.00715258	−	0.0136241i
$869$	7.28695			0.247193
$870$	−0.682648	−	18.3899i	−0.0231439	−	0.623477i
$871$			0.209796i			0.00710867i
$872$	−16.0957	−	5.55753i	−0.545069	−	0.188202i
$873$	−3.32087	+	3.32087i	−0.112395	+	0.112395i
$874$	−6.95585	−	45.7214i	−0.235285	−	1.54655i
$875$	−10.0974	+	4.80030i	−0.341354	+	0.162280i
$876$	34.8972	−	10.8698i	1.17907	−	0.367256i
$877$	−19.4166	+	19.4166i	−0.655653	+	0.655653i	−0.954348	−	0.298696i	$-0.903448\pi$
$877$	−19.4166	+	19.4166i	−0.655653	+	0.655653i	0.298696	+	0.954348i	$0.403448\pi$
$878$	−26.7558	+	36.3575i	−0.902963	+	1.22701i
$879$	−13.4699			−0.454329
$880$	20.9002	−	11.1489i	0.704547	−	0.375831i
$881$	10.0672			0.339172			0.169586	−	0.985515i	$-0.445757\pi$
$881$	10.0672			0.339172			0.169586	+	0.985515i	$0.445757\pi$
$882$	−0.462488	+	0.628460i	−0.0155728	+	0.0211614i
$883$	13.7390	−	13.7390i	0.462355	−	0.462355i	−0.437072	−	0.899427i	$-0.643984\pi$
$883$	13.7390	−	13.7390i	0.462355	−	0.462355i	0.899427	+	0.437072i	$0.143984\pi$
$884$	−0.105644	+	0.0329060i	−0.00355318	+	0.00110675i
$885$	25.5319	+	32.1262i	0.858245	+	1.07991i
$886$	3.22546	+	21.2012i	0.108362	+	0.712269i
$887$	0.403834	−	0.403834i	0.0135594	−	0.0135594i	−0.700295	−	0.713854i	$-0.746948\pi$
$887$	0.403834	−	0.403834i	0.0135594	−	0.0135594i	0.713854	+	0.700295i	$0.246948\pi$
$888$	−19.5576	+	56.6427i	−0.656311	+	1.90080i
$889$			6.38242i			0.214059i
$890$	−33.9420	−	31.5123i	−1.13774	−	1.05629i
$891$	27.4130			0.918371
$892$	15.6094	−	29.7326i	0.522643	−	0.995522i
$893$	18.7958	+	18.7958i	0.628979	+	0.628979i
$894$	4.75639	+	31.2642i	0.159078	+	1.04563i
$895$	0.995728	−	8.70627i	0.0332835	−	0.291019i
$896$	5.56206	−	9.85208i	0.185815	−	0.329135i
$897$	−0.737482	−	0.737482i	−0.0246238	−	0.0246238i
$898$	−27.2199	−	20.0313i	−0.908340	−	0.668453i
$899$		−	0.699932i		−	0.0233441i
$900$	−5.50232	+	0.409064i	−0.183411	+	0.0136355i
$901$			3.86554i			0.128780i
$902$	−0.731406	+	0.993884i	−0.0243532	+	0.0330927i
$903$	14.8470	+	14.8470i	0.494078	+	0.494078i
$904$	−5.82404	+	2.83444i	−0.193705	+	0.0942720i
$905$	−1.57157	+	13.7412i	−0.0522407	+	0.456773i
$906$	−27.2408	+	4.14429i	−0.905014	+	0.137685i
$907$	26.2041	+	26.2041i	0.870094	+	0.870094i	0.992482	−	0.122389i	$-0.0390555\pi$
$907$	26.2041	+	26.2041i	0.870094	+	0.870094i	−0.122389	+	0.992482i	$0.539055\pi$
$908$	−1.82659	+	3.47926i	−0.0606175	+	0.115463i
$909$	−5.62672			−0.186626
$910$	0.175856	−	0.189415i	0.00582957	−	0.00627905i
$911$		−	54.4168i		−	1.80291i	−0.432873	−	0.901455i	$-0.642500\pi$
$911$		−	54.4168i		−	1.80291i	0.432873	−	0.901455i	$-0.357500\pi$
$912$	35.8110	+	6.57151i	1.18582	+	0.217604i
$913$	−29.3181	+	29.3181i	−0.970289	+	0.970289i
$914$	−51.2357	+	7.79479i	−1.69473	+	0.257829i
$915$	18.7089	+	23.5410i	0.618498	+	0.778241i
$916$	−8.70810	−	27.9571i	−0.287724	−	0.923729i
$917$	−5.77790	+	5.77790i	−0.190803	+	0.190803i
$918$	3.55741	+	2.61792i	0.117412	+	0.0864042i
$919$	23.6892			0.781434			0.390717	−	0.920511i	$-0.372227\pi$
$919$	23.6892			0.781434			0.390717	+	0.920511i	$0.372227\pi$
$920$	14.2429	+	40.3849i	0.469575	+	1.33145i
$921$	55.8979			1.84190
$922$	−7.88402	−	5.80190i	−0.259646	−	0.191075i
$923$	0.734569	−	0.734569i	0.0241786	−	0.0241786i
$924$	−9.53073	+	2.96864i	−0.313538	+	0.0976610i
$925$	47.6933	−	29.7454i	1.56815	−	0.978022i
$926$	−41.8989	+	6.37432i	−1.37688	+	0.209473i
$927$	−1.25004	+	1.25004i	−0.0410567	+	0.0410567i
$928$	0.532822	−	17.4594i	0.0174908	−	0.573134i
$929$		−	14.7866i		−	0.485132i	−0.970135	−	0.242566i	$-0.922011\pi$
$929$		−	14.7866i		−	0.485132i	0.970135	−	0.242566i	$-0.0779891\pi$
$930$	−1.34996	+	0.0501115i	−0.0442669	+	0.00164322i
$931$	−4.82978			−0.158290
$932$	−45.4849	−	23.8793i	−1.48991	−	0.782192i
$933$	1.36500	+	1.36500i	0.0446880	+	0.0446880i
$934$	30.6970	−	4.67011i	1.00444	−	0.152811i
$935$	−2.49405	−	3.13820i	−0.0815641	−	0.102630i
$936$	0.114691	−	0.0558175i	0.00374878	−	0.00182445i
$937$	4.45187	+	4.45187i	0.145436	+	0.145436i	0.776076	−	0.630640i	$-0.217207\pi$
$937$	4.45187	+	4.45187i	0.145436	+	0.145436i	−0.630640	+	0.776076i	$0.717207\pi$
$938$	−2.15157	+	2.92370i	−0.0702512	+	0.0954622i
$939$			34.2229i			1.11682i
$940$	−20.3512	−	13.8430i	−0.663783	−	0.451508i
$941$		−	1.71086i		−	0.0557725i	−0.999611	−	0.0278863i	$-0.991122\pi$
$941$		−	1.71086i		−	0.0557725i	0.999611	−	0.0278863i	$-0.00887763\pi$
$942$	40.6791	+	29.9360i	1.32540	+	0.975369i
$943$	−1.57743	−	1.57743i	−0.0513681	−	0.0513681i
$944$	22.1191	+	32.0615i	0.719915	+	1.04351i
$945$	−10.2504	−	1.17233i	−0.333445	−	0.0381358i
$946$	6.27615	+	41.2536i	0.204055	+	1.34127i
$947$	−15.6339	−	15.6339i	−0.508033	−	0.508033i	0.405889	−	0.913922i	$-0.366962\pi$
$947$	−15.6339	−	15.6339i	−0.508033	−	0.508033i	−0.913922	+	0.405889i	$0.866962\pi$
$948$	−9.18236	−	4.82068i	−0.298229	−	0.156569i
$949$	0.792584			0.0257284
$950$	−22.2256	−	25.9299i	−0.721095	−	0.841276i
$951$		−	18.5993i		−	0.603122i
$952$	−1.80971	−	0.624858i	−0.0586531	−	0.0202518i
$953$	17.9987	−	17.9987i	0.583034	−	0.583034i	−0.352702	−	0.935736i	$-0.614737\pi$
$953$	17.9987	−	17.9987i	0.583034	−	0.583034i	0.935736	+	0.352702i	$0.114737\pi$
$954$	−0.670207	−	4.40533i	−0.0216988	−	0.142628i
$955$	−0.494379	+	4.32266i	−0.0159977	+	0.139878i
$956$	−4.11268	−	13.2037i	−0.133014	−	0.427037i
$957$	−10.8980	+	10.8980i	−0.352282	+	0.352282i
$958$	22.1920	−	30.1560i	0.716990	−	0.974295i
$959$	−19.6465			−0.634420
$960$	−33.7122	+	0.222351i	−1.08806	+	0.00717633i
$961$	30.9486			0.998343
$962$	−0.770180	+	1.04657i	−0.0248316	+	0.0337429i
$963$	6.79250	−	6.79250i	0.218885	−	0.218885i
$964$	−8.15581	−	26.1840i	−0.262681	−	0.843330i
$965$	−26.9580	+	21.4245i	−0.867809	+	0.689680i
$966$	−2.71422	−	17.8408i	−0.0873285	−	0.574017i
$967$	26.3108	−	26.3108i	0.846097	−	0.846097i	−0.143547	−	0.989644i	$-0.545851\pi$
$967$	26.3108	−	26.3108i	0.846097	−	0.846097i	0.989644	+	0.143547i	$0.0458507\pi$
$968$	10.6568	+	3.67958i	0.342522	+	0.118266i
$969$		−	6.16126i		−	0.197928i
$970$	26.8983	−	0.998487i	0.863654	−	0.0320595i
$971$	31.2431			1.00264			0.501320	−	0.865262i	$-0.332848\pi$
$971$	31.2431			1.00264			0.501320	+	0.865262i	$0.332848\pi$
$972$	−10.0321	−	5.26678i	−0.321779	−	0.168932i
$973$	−2.38368	−	2.38368i	−0.0764174	−	0.0764174i
$974$	−5.02370	−	33.0212i	−0.160970	−	1.05807i
$975$	−0.750289	−	0.173894i	−0.0240285	−	0.00556907i
$976$	16.2081	+	23.4936i	0.518810	+	0.752012i
$977$	−12.3486	−	12.3486i	−0.395068	−	0.395068i	0.481422	−	0.876489i	$-0.340121\pi$
$977$	−12.3486	−	12.3486i	−0.395068	−	0.395068i	−0.876489	+	0.481422i	$0.840121\pi$
$978$	−2.15902	−	1.58884i	−0.0690379	−	0.0508055i
$979$			38.7886i			1.23969i
$980$	4.39327	−	0.836177i	0.140338	−	0.0267107i
$981$		−	3.32173i		−	0.106055i
$982$	−10.3841	+	14.1107i	−0.331371	+	0.450290i
$983$	−16.3704	−	16.3704i	−0.522133	−	0.522133i	0.396082	−	0.918215i	$-0.370370\pi$
$983$	−16.3704	−	16.3704i	−0.522133	−	0.522133i	−0.918215	+	0.396082i	$0.870370\pi$
$984$	1.57916	−	0.768542i	0.0503417	−	0.0245002i
$985$	40.3987	−	32.1063i	1.28721	−	1.02299i
$986$	−2.92230	+	0.444587i	−0.0930651	+	0.0141585i
$987$	7.33425	+	7.33425i	0.233452	+	0.233452i
$988$	0.699030	+	0.366987i	0.0222391	+	0.0116754i
$989$	−75.4361			−2.39873
$990$	3.38642	+	3.14400i	0.107627	+	0.0999230i
$991$		−	9.56890i		−	0.303966i	−0.988383	−	0.151983i	$-0.951434\pi$
$991$		−	9.56890i		−	0.303966i	0.988383	−	0.151983i	$-0.0485659\pi$
$992$	−1.28166	−	0.0391132i	−0.0406926	−	0.00124185i
$993$	−1.62608	+	1.62608i	−0.0516020	+	0.0516020i
$994$	17.7703	−	2.70349i	0.563639	−	0.0857496i
$995$	−29.7465	−	3.40207i	−0.943026	−	0.107853i
$996$	56.3395	−	17.5487i	1.78519	−	0.556051i
$997$	30.3108	−	30.3108i	0.959952	−	0.959952i	−0.0392759	−	0.999228i	$-0.512505\pi$
$997$	30.3108	−	30.3108i	0.959952	−	0.959952i	0.999228	+	0.0392759i	$0.0125051\pi$
$998$	43.6858	+	32.1487i	1.38285	+	1.01765i
$999$	51.8695			1.64108

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.w.a.267.25	yes	72
4.3	odd	2		1120.2.bi.a.687.9		72
5.3	odd	4	inner	280.2.w.a.43.9	✓	72
8.3	odd	2	inner	280.2.w.a.267.9	yes	72
8.5	even	2		1120.2.bi.a.687.10		72
20.3	even	4		1120.2.bi.a.463.10		72
40.3	even	4	inner	280.2.w.a.43.25	yes	72
40.13	odd	4		1120.2.bi.a.463.9		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.w.a.43.9	✓	72	5.3	odd	4	inner
280.2.w.a.43.25	yes	72	40.3	even	4	inner
280.2.w.a.267.9	yes	72	8.3	odd	2	inner
280.2.w.a.267.25	yes	72	1.1	even	1	trivial
1120.2.bi.a.463.9		72	40.13	odd	4
1120.2.bi.a.463.10		72	20.3	even	4
1120.2.bi.a.687.9		72	4.3	odd	2
1120.2.bi.a.687.10		72	8.5	even	2

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:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	280.w (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.838219 - 1.13903i) q^{2} +(1.33262 - 1.33262i) q^{3} +(-0.594776 - 1.90951i) q^{4} +(-2.22159 - 0.254081i) q^{5} +(-0.400865 - 2.63492i) q^{6} +(0.707107 - 0.707107i) q^{7} +(-2.67355 - 0.923123i) q^{8} -0.551751i q^{9} +O(q^{10})\)	\(q+(0.838219 - 1.13903i) q^{2} +(1.33262 - 1.33262i) q^{3} +(-0.594776 - 1.90951i) q^{4} +(-2.22159 - 0.254081i) q^{5} +(-0.400865 - 2.63492i) q^{6} +(0.707107 - 0.707107i) q^{7} +(-2.67355 - 0.923123i) q^{8} -0.551751i q^{9} +(-2.15158 + 2.31748i) q^{10} +2.64839 q^{11} +(-3.33727 - 1.75204i) q^{12} +(-0.0577942 - 0.0577942i) q^{13} +(-0.212705 - 1.39813i) q^{14} +(-3.29912 + 2.62194i) q^{15} +(-3.29248 + 2.27147i) q^{16} +(0.478637 + 0.478637i) q^{17} +(-0.628460 - 0.462488i) q^{18} -4.82978i q^{19} +(0.836177 + 4.39327i) q^{20} -1.88461i q^{21} +(2.21993 - 3.01660i) q^{22} +(4.78774 + 4.78774i) q^{23} +(-4.79299 + 2.33265i) q^{24} +(4.87089 + 1.12892i) q^{25} +(-0.114274 + 0.0173851i) q^{26} +(3.26259 + 3.26259i) q^{27} +(-1.77080 - 0.929659i) q^{28} -3.08786 q^{29} +(0.221075 + 5.95555i) q^{30} +0.226672i q^{31} +(-0.172554 + 5.65422i) q^{32} +(3.52930 - 3.52930i) q^{33} +(0.946385 - 0.143979i) q^{34} +(-1.75056 + 1.39124i) q^{35} +(-1.05358 + 0.328168i) q^{36} +(7.94914 - 7.94914i) q^{37} +(-5.50126 - 4.04841i) q^{38} -0.154035 q^{39} +(5.70496 + 2.73009i) q^{40} -0.329472 q^{41} +(-2.14663 - 1.57972i) q^{42} +(-7.87804 + 7.87804i) q^{43} +(-1.57520 - 5.05714i) q^{44} +(-0.140189 + 1.22576i) q^{45} +(9.46656 - 1.44020i) q^{46} +(-3.89166 + 3.89166i) q^{47} +(-1.36062 + 7.41463i) q^{48} -1.00000i q^{49} +(5.36875 - 4.60180i) q^{50} +1.27568 q^{51} +(-0.0759842 + 0.144733i) q^{52} +(4.03807 + 4.03807i) q^{53} +(6.45094 - 0.981419i) q^{54} +(-5.88363 - 0.672905i) q^{55} +(-2.54323 + 1.23774i) q^{56} +(-6.43625 - 6.43625i) q^{57} +(-2.58830 + 3.51716i) q^{58} -9.73780i q^{59} +(6.96886 + 4.74025i) q^{60} -7.13553i q^{61} +(0.258186 + 0.190001i) q^{62} +(-0.390147 - 0.390147i) q^{63} +(6.29569 + 4.93602i) q^{64} +(0.113710 + 0.143079i) q^{65} +(-1.06165 - 6.97830i) q^{66} +(-1.81503 - 1.81503i) q^{67} +(0.629282 - 1.19865i) q^{68} +12.7605 q^{69} +(0.117305 + 3.16010i) q^{70} +12.7101i q^{71} +(-0.509334 + 1.47513i) q^{72} +(-6.85695 + 6.85695i) q^{73} +(-2.39118 - 15.7174i) q^{74} +(7.99546 - 4.98661i) q^{75} +(-9.22252 + 2.87264i) q^{76} +(1.87270 - 1.87270i) q^{77} +(-0.129116 + 0.175451i) q^{78} +2.75146 q^{79} +(7.89167 - 4.20970i) q^{80} +10.3508 q^{81} +(-0.276170 + 0.375278i) q^{82} +(-11.0702 + 11.0702i) q^{83} +(-3.59869 + 1.12092i) q^{84} +(-0.941721 - 1.18495i) q^{85} +(2.36979 + 15.5768i) q^{86} +(-4.11494 + 4.11494i) q^{87} +(-7.08060 - 2.44479i) q^{88} +14.6461i q^{89} +(1.27867 + 1.18714i) q^{90} -0.0817334 q^{91} +(6.29462 - 11.9899i) q^{92} +(0.302068 + 0.302068i) q^{93} +(1.17065 + 7.69477i) q^{94} +(-1.22715 + 10.7298i) q^{95} +(7.30498 + 7.76488i) q^{96} +(-6.01880 - 6.01880i) q^{97} +(-1.13903 - 0.838219i) q^{98} -1.46125i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 8 q^{6}+O(q^{10}) \) 72 * q + 8 * q^6	\( 72 q + 8 q^{6} + 16 q^{10} - 16 q^{12} - 8 q^{16} + 8 q^{17} - 28 q^{18} - 20 q^{20} - 36 q^{22} - 8 q^{25} - 32 q^{26} - 4 q^{30} + 40 q^{32} + 64 q^{36} - 4 q^{40} + 20 q^{42} - 64 q^{43} + 48 q^{46} - 80 q^{48} - 32 q^{51} + 16 q^{52} - 24 q^{56} + 4 q^{58} - 80 q^{60} - 40 q^{62} - 8 q^{65} + 32 q^{66} - 24 q^{68} + 40 q^{72} - 40 q^{73} + 112 q^{75} - 8 q^{76} + 28 q^{78} - 20 q^{80} - 72 q^{81} + 24 q^{82} + 80 q^{83} + 8 q^{86} - 88 q^{88} + 136 q^{90} - 96 q^{92} - 56 q^{96} - 8 q^{97}+O(q^{100}) \) 72 * q + 8 * q^6 + 16 * q^10 - 16 * q^12 - 8 * q^16 + 8 * q^17 - 28 * q^18 - 20 * q^20 - 36 * q^22 - 8 * q^25 - 32 * q^26 - 4 * q^30 + 40 * q^32 + 64 * q^36 - 4 * q^40 + 20 * q^42 - 64 * q^43 + 48 * q^46 - 80 * q^48 - 32 * q^51 + 16 * q^52 - 24 * q^56 + 4 * q^58 - 80 * q^60 - 40 * q^62 - 8 * q^65 + 32 * q^66 - 24 * q^68 + 40 * q^72 - 40 * q^73 + 112 * q^75 - 8 * q^76 + 28 * q^78 - 20 * q^80 - 72 * q^81 + 24 * q^82 + 80 * q^83 + 8 * q^86 - 88 * q^88 + 136 * q^90 - 96 * q^92 - 56 * q^96 - 8 * q^97

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