LMFDB - Embedded newform 462.2.bc.a.95.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(95,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([15, 20, 21]))

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

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

chi := DirichletCharacter("462.95");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.bc (of order $30$, degree $8$, 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:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$16$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			95.1
Character	$\chi$	$=$	462.95
Dual form			462.2.bc.a.107.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.104528 - 0.994522i) q^{2} +(-1.64414 + 0.544800i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(1.25353 - 2.81547i) q^{5} +(0.369957 + 1.69208i) q^{6} +(1.28350 + 2.31358i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(2.40638 - 1.79146i) q^{9} +O(q^{10})$	\(q+(0.104528 - 0.994522i) q^{2} +(-1.64414 + 0.544800i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(1.25353 - 2.81547i) q^{5} +(0.369957 + 1.69208i) q^{6} +(1.28350 + 2.31358i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(2.40638 - 1.79146i) q^{9} +(-2.66902 - 1.54096i) q^{10} +(3.25565 - 0.633032i) q^{11} +(1.72148 - 0.191060i) q^{12} +(-1.85644 + 2.55517i) q^{13} +(2.43506 - 1.03463i) q^{14} +(-0.527105 + 5.31195i) q^{15} +(0.913545 + 0.406737i) q^{16} +(-0.684127 - 6.50903i) q^{17} +(-1.53011 - 2.58046i) q^{18} +(-0.878223 - 4.13171i) q^{19} +(-1.81151 + 2.49332i) q^{20} +(-3.37069 - 3.10459i) q^{21} +(-0.289256 - 3.30399i) q^{22} +(0.815547 - 0.470856i) q^{23} +(-0.0100692 - 1.73202i) q^{24} +(-3.00989 - 3.34282i) q^{25} +(2.34712 + 2.11336i) q^{26} +(-2.98045 + 4.25640i) q^{27} +(-0.774430 - 2.52987i) q^{28} +(-2.13594 - 6.57373i) q^{29} +(5.22775 + 1.07947i) q^{30} +(6.76396 - 3.01151i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-5.00787 + 2.81447i) q^{33} -6.54489 q^{34} +(8.12271 - 0.713516i) q^{35} +(-2.72626 + 1.25199i) q^{36} +(-0.820875 + 0.911674i) q^{37} +(-4.20088 + 0.441530i) q^{38} +(1.66019 - 5.21244i) q^{39} +(2.29031 + 2.06220i) q^{40} +(0.788646 - 2.42720i) q^{41} +(-3.43992 + 3.02770i) q^{42} +1.24741i q^{43} +(-3.31612 - 0.0576896i) q^{44} +(-2.02732 - 9.02075i) q^{45} +(-0.383029 - 0.860297i) q^{46} +(-2.14061 - 10.0708i) q^{47} +(-1.72359 - 0.171032i) q^{48} +(-3.70527 + 5.93894i) q^{49} +(-3.63913 + 2.64398i) q^{50} +(4.67092 + 10.3290i) q^{51} +(2.34712 - 2.11336i) q^{52} +(2.44967 + 5.50204i) q^{53} +(3.92154 + 3.40903i) q^{54} +(2.29877 - 9.95972i) q^{55} +(-2.59696 + 0.505744i) q^{56} +(3.69488 + 6.31466i) q^{57} +(-6.76099 + 1.43709i) q^{58} +(-2.34885 + 11.0505i) q^{59} +(1.62000 - 5.08628i) q^{60} +(3.62706 - 8.14652i) q^{61} +(-2.28798 - 7.04169i) q^{62} +(7.23326 + 3.26803i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(4.86691 + 8.42973i) q^{65} +(2.27559 + 5.27463i) q^{66} +(-3.14450 + 5.44644i) q^{67} +(-0.684127 + 6.50903i) q^{68} +(-1.08435 + 1.21846i) q^{69} +(0.139447 - 8.15279i) q^{70} +(6.06001 + 8.34089i) q^{71} +(0.960161 + 2.84220i) q^{72} +(-0.0996603 + 0.468865i) q^{73} +(0.820875 + 0.911674i) q^{74} +(6.76985 + 3.85627i) q^{75} +4.22402i q^{76} +(5.64319 + 6.71970i) q^{77} +(-5.01035 - 2.19594i) q^{78} +(16.5959 + 1.74430i) q^{79} +(2.29031 - 2.06220i) q^{80} +(2.58138 - 8.62186i) q^{81} +(-2.33147 - 1.03804i) q^{82} +(-9.93212 + 7.21611i) q^{83} +(2.65155 + 3.73755i) q^{84} +(-19.1836 - 6.23312i) q^{85} +(1.24057 + 0.130390i) q^{86} +(7.09315 + 9.64447i) q^{87} +(-0.404003 + 3.29193i) q^{88} +(-5.63638 + 3.25417i) q^{89} +(-9.18324 + 1.07329i) q^{90} +(-8.29431 - 1.01546i) q^{91} +(-0.895621 + 0.291005i) q^{92} +(-9.48021 + 8.63634i) q^{93} +(-10.2394 + 1.07620i) q^{94} +(-12.7336 - 2.70661i) q^{95} +(-0.350258 + 1.69627i) q^{96} +(7.13209 + 5.18176i) q^{97} +(5.51910 + 4.30576i) q^{98} +(6.70030 - 7.35567i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q - 16 q^{2} + 16 q^{4} + 32 q^{8} - 4 q^{9}+O(q^{10}) $ 128 * q - 16 * q^2 + 16 * q^4 + 32 * q^8 - 4 * q^9	$ 128 q - 16 q^{2} + 16 q^{4} + 32 q^{8} - 4 q^{9} + 6 q^{11} - 12 q^{15} + 16 q^{16} + 2 q^{17} + 4 q^{18} + 2 q^{22} - 12 q^{25} - 18 q^{27} - 5 q^{28} - 38 q^{29} - 6 q^{30} - 3 q^{31} + 64 q^{32} - 4 q^{33} - 16 q^{34} + 31 q^{35} + 8 q^{36} + 2 q^{37} + 22 q^{39} + 5 q^{40} - 16 q^{41} + 17 q^{42} + q^{44} + 28 q^{45} + 38 q^{49} - 34 q^{50} + 16 q^{51} - 25 q^{53} + 6 q^{54} - 42 q^{55} + 20 q^{57} - 19 q^{58} - 40 q^{59} - 4 q^{60} + 40 q^{61} + 4 q^{62} + 6 q^{63} - 32 q^{64} - 20 q^{65} - 41 q^{66} + 16 q^{67} + 2 q^{68} - 68 q^{69} - 21 q^{70} - 80 q^{71} - 16 q^{72} + 10 q^{73} - 2 q^{74} - 14 q^{75} - q^{77} - 16 q^{78} + 5 q^{80} - 88 q^{81} - 8 q^{82} + 92 q^{83} - 48 q^{84} - 100 q^{85} + 40 q^{86} + 38 q^{87} - q^{88} - 164 q^{90} + 12 q^{91} + 20 q^{92} + 47 q^{93} + 40 q^{94} - 38 q^{95} - 16 q^{97} - 18 q^{98} - 138 q^{99}+O(q^{100}) $ 128 * q - 16 * q^2 + 16 * q^4 + 32 * q^8 - 4 * q^9 + 6 * q^11 - 12 * q^15 + 16 * q^16 + 2 * q^17 + 4 * q^18 + 2 * q^22 - 12 * q^25 - 18 * q^27 - 5 * q^28 - 38 * q^29 - 6 * q^30 - 3 * q^31 + 64 * q^32 - 4 * q^33 - 16 * q^34 + 31 * q^35 + 8 * q^36 + 2 * q^37 + 22 * q^39 + 5 * q^40 - 16 * q^41 + 17 * q^42 + q^44 + 28 * q^45 + 38 * q^49 - 34 * q^50 + 16 * q^51 - 25 * q^53 + 6 * q^54 - 42 * q^55 + 20 * q^57 - 19 * q^58 - 40 * q^59 - 4 * q^60 + 40 * q^61 + 4 * q^62 + 6 * q^63 - 32 * q^64 - 20 * q^65 - 41 * q^66 + 16 * q^67 + 2 * q^68 - 68 * q^69 - 21 * q^70 - 80 * q^71 - 16 * q^72 + 10 * q^73 - 2 * q^74 - 14 * q^75 - q^77 - 16 * q^78 + 5 * q^80 - 88 * q^81 - 8 * q^82 + 92 * q^83 - 48 * q^84 - 100 * q^85 + 40 * q^86 + 38 * q^87 - q^88 - 164 * q^90 + 12 * q^91 + 20 * q^92 + 47 * q^93 + 40 * q^94 - 38 * q^95 - 16 * q^97 - 18 * q^98 - 138 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{10}\right)$

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 $

$2$	0.104528	−	0.994522i	0.0739128	−	0.703233i
$2$	0.104528	−	0.994522i	0.0739128	−	0.703233i
$3$	−1.64414	+	0.544800i	−0.949244	+	0.314541i
$3$	−1.64414	+	0.544800i	−0.949244	+	0.314541i
$4$	−0.978148	−	0.207912i	−0.489074	−	0.103956i
$5$	1.25353	−	2.81547i	0.560595	−	1.25912i	−0.381685	−	0.924292i	$-0.624656\pi$
$5$	1.25353	−	2.81547i	0.560595	−	1.25912i	0.942280	−	0.334825i	$-0.108677\pi$
$6$	0.369957	+	1.69208i	0.151034	+	0.690788i
$7$	1.28350	+	2.31358i	0.485116	+	0.874450i
$7$	1.28350	+	2.31358i	0.485116	+	0.874450i
$8$	−0.309017	+	0.951057i	−0.109254	+	0.336249i
$9$	2.40638	−	1.79146i	0.802128	−	0.597152i
$10$	−2.66902	−	1.54096i	−0.844018	−	0.487294i
$11$	3.25565	−	0.633032i	0.981616	−	0.190866i
$11$	3.25565	−	0.633032i	0.981616	−	0.190866i
$12$	1.72148	−	0.191060i	0.496949	−	0.0551541i
$13$	−1.85644	+	2.55517i	−0.514884	+	0.708676i	−0.984733	−	0.174070i	$-0.944308\pi$
$13$	−1.85644	+	2.55517i	−0.514884	+	0.708676i	0.469850	+	0.882746i	$0.344308\pi$
$14$	2.43506	−	1.03463i	0.650798	−	0.276517i
$15$	−0.527105	+	5.31195i	−0.136098	+	1.37154i
$16$	0.913545	+	0.406737i	0.228386	+	0.101684i
$17$	−0.684127	−	6.50903i	−0.165925	−	1.57867i	−0.687960	−	0.725748i	$-0.741494\pi$
$17$	−0.684127	−	6.50903i	−0.165925	−	1.57867i	0.522035	−	0.852924i	$-0.325173\pi$
$18$	−1.53011	−	2.58046i	−0.360649	−	0.608220i
$19$	−0.878223	−	4.13171i	−0.201478	−	0.947880i	−0.956399	−	0.292064i	$-0.905658\pi$
$19$	−0.878223	−	4.13171i	−0.201478	−	0.947880i	0.754921	−	0.655816i	$-0.227675\pi$
$20$	−1.81151	+	2.49332i	−0.405065	+	0.557524i
$21$	−3.37069	−	3.10459i	−0.735544	−	0.677477i
$22$	−0.289256	−	3.30399i	−0.0616695	−	0.704412i
$23$	0.815547	−	0.470856i	0.170053	−	0.0981803i	−0.412558	−	0.910931i	$-0.635364\pi$
$23$	0.815547	−	0.470856i	0.170053	−	0.0981803i	0.582611	+	0.812751i	$0.302031\pi$
$24$	−0.0100692	−	1.73202i	−0.00205536	−	0.353547i
$25$	−3.00989	−	3.34282i	−0.601978	−	0.668564i
$26$	2.34712	+	2.11336i	0.460308	+	0.414463i
$27$	−2.98045	+	4.25640i	−0.573587	+	0.819145i
$28$	−0.774430	−	2.52987i	−0.146354	−	0.478101i
$29$	−2.13594	−	6.57373i	−0.396633	−	1.22071i	−0.927682	−	0.373370i	$-0.878202\pi$
$29$	−2.13594	−	6.57373i	−0.396633	−	1.22071i	0.531049	−	0.847341i	$-0.321798\pi$
$30$	5.22775	+	1.07947i	0.954452	+	0.197083i
$31$	6.76396	−	3.01151i	1.21484	−	0.540883i	0.303618	−	0.952794i	$-0.401805\pi$
$31$	6.76396	−	3.01151i	1.21484	−	0.540883i	0.911224	+	0.411911i	$0.135139\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	−5.00787	+	2.81447i	−0.871758	+	0.489937i
$34$	−6.54489			−1.12244
$35$	8.12271	−	0.713516i	1.37299	−	0.120606i
$36$	−2.72626	+	1.25199i	−0.454377	+	0.208665i
$37$	−0.820875	+	0.911674i	−0.134951	+	0.149878i	−0.806832	−	0.590781i	$-0.798820\pi$
$37$	−0.820875	+	0.911674i	−0.134951	+	0.149878i	0.671881	+	0.740659i	$0.265487\pi$
$38$	−4.20088	+	0.441530i	−0.681473	+	0.0716257i
$39$	1.66019	−	5.21244i	0.265843	−	0.834659i
$40$	2.29031	+	2.06220i	0.362130	+	0.326063i
$41$	0.788646	−	2.42720i	0.123166	−	0.379065i	−0.870397	−	0.492351i	$-0.836138\pi$
$41$	0.788646	−	2.42720i	0.123166	−	0.379065i	0.993562	+	0.113286i	$0.0361376\pi$
$42$	−3.43992	+	3.02770i	−0.530791	+	0.467185i
$43$			1.24741i			0.190228i	0.995466	+	0.0951139i	$0.0303215\pi$
$43$			1.24741i			0.190228i	−0.995466	+	0.0951139i	$0.969678\pi$
$44$	−3.31612	−	0.0576896i	−0.499924	−	0.00869703i
$45$	−2.02732	−	9.02075i	−0.302215	−	1.34473i
$46$	−0.383029	−	0.860297i	−0.0564745	−	0.126844i
$47$	−2.14061	−	10.0708i	−0.312240	−	1.46898i	−0.802108	−	0.597179i	$-0.796288\pi$
$47$	−2.14061	−	10.0708i	−0.312240	−	1.46898i	0.489868	−	0.871797i	$-0.337045\pi$
$48$	−1.72359	−	0.171032i	−0.248778	−	0.0246863i
$49$	−3.70527	+	5.93894i	−0.529324	+	0.848420i
$50$	−3.63913	+	2.64398i	−0.514651	+	0.373916i
$51$	4.67092	+	10.3290i	0.654060	+	1.44636i
$52$	2.34712	−	2.11336i	0.325487	−	0.293070i
$53$	2.44967	+	5.50204i	0.336487	+	0.755763i	0.999971	+	0.00757264i	$0.00241047\pi$
$53$	2.44967	+	5.50204i	0.336487	+	0.755763i	−0.663484	+	0.748191i	$0.730923\pi$
$54$	3.92154	+	3.40903i	0.533654	+	0.463911i
$55$	2.29877	−	9.95972i	0.309966	−	1.34297i
$56$	−2.59696	+	0.505744i	−0.347034	+	0.0675829i
$57$	3.69488	+	6.31466i	0.489399	+	0.836397i
$58$	−6.76099	+	1.43709i	−0.887761	+	0.188699i
$59$	−2.34885	+	11.0505i	−0.305795	+	1.43865i	0.509932	+	0.860215i	$0.329670\pi$
$59$	−2.34885	+	11.0505i	−0.305795	+	1.43865i	−0.815727	+	0.578437i	$0.803663\pi$
$60$	1.62000	−	5.08628i	0.209141	−	0.656636i
$61$	3.62706	−	8.14652i	0.464398	−	1.04306i	−0.517851	−	0.855471i	$-0.673268\pi$
$61$	3.62706	−	8.14652i	0.464398	−	1.04306i	0.982249	−	0.187584i	$-0.0600657\pi$
$62$	−2.28798	−	7.04169i	−0.290574	−	0.894295i
$63$	7.23326	+	3.26803i	0.911305	+	0.411733i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	4.86691	+	8.42973i	0.603665	+	1.04558i
$66$	2.27559	+	5.27463i	0.280106	+	0.649262i
$67$	−3.14450	+	5.44644i	−0.384162	+	0.665388i	−0.991653	−	0.128939i	$-0.958843\pi$
$67$	−3.14450	+	5.44644i	−0.384162	+	0.665388i	0.607491	+	0.794327i	$0.292176\pi$
$68$	−0.684127	+	6.50903i	−0.0829626	+	0.789336i
$69$	−1.08435	+	1.21846i	−0.130540	+	0.146686i
$70$	0.139447	−	8.15279i	0.0166671	−	0.974445i
$71$	6.06001	+	8.34089i	0.719191	+	0.989881i	0.999550	+	0.0299863i	$0.00954636\pi$
$71$	6.06001	+	8.34089i	0.719191	+	0.989881i	−0.280359	+	0.959895i	$0.590454\pi$
$72$	0.960161	+	2.84220i	0.113156	+	0.334956i
$73$	−0.0996603	+	0.468865i	−0.0116644	+	0.0548765i	−0.983595	−	0.180392i	$-0.942263\pi$
$73$	−0.0996603	+	0.468865i	−0.0116644	+	0.0548765i	0.971931	+	0.235268i	$0.0755968\pi$
$74$	0.820875	+	0.911674i	0.0954248	+	0.105980i
$75$	6.76985	+	3.85627i	0.781715	+	0.445284i
$76$			4.22402i			0.484528i
$77$	5.64319	+	6.71970i	0.643101	+	0.765781i
$78$	−5.01035	−	2.19594i	−0.567311	−	0.248641i
$79$	16.5959	+	1.74430i	1.86719	+	0.196249i	0.969618	−	0.244624i	$-0.0786647\pi$
$79$	16.5959	+	1.74430i	1.86719	+	0.196249i	0.897569	+	0.440874i	$0.145331\pi$
$80$	2.29031	−	2.06220i	0.256065	−	0.230562i
$81$	2.58138	−	8.62186i	0.286820	−	0.957985i
$82$	−2.33147	−	1.03804i	−0.257468	−	0.114632i
$83$	−9.93212	+	7.21611i	−1.09019	+	0.792071i	−0.979432	−	0.201777i	$-0.935329\pi$
$83$	−9.93212	+	7.21611i	−1.09019	+	0.792071i	−0.110760	+	0.993847i	$0.535329\pi$
$84$	2.65155	+	3.73755i	0.289307	+	0.407800i
$85$	−19.1836	−	6.23312i	−2.08075	−	0.676077i
$86$	1.24057	+	0.130390i	0.133775	+	0.0140603i
$87$	7.09315	+	9.64447i	0.760465	+	1.03400i
$88$	−0.404003	+	3.29193i	−0.0430668	+	0.350921i
$89$	−5.63638	+	3.25417i	−0.597455	+	0.344941i	−0.768040	−	0.640402i	$-0.778768\pi$
$89$	−5.63638	+	3.25417i	−0.597455	+	0.344941i	0.170585	+	0.985343i	$0.445434\pi$
$90$	−9.18324	+	1.07329i	−0.967999	+	0.113134i
$91$	−8.29431	−	1.01546i	−0.869480	−	0.106449i
$92$	−0.895621	+	0.291005i	−0.0933750	+	0.0303394i
$93$	−9.48021	+	8.63634i	−0.983052	+	0.895547i
$94$	−10.2394	+	1.07620i	−1.05611	+	0.111002i
$95$	−12.7336	−	2.70661i	−1.30644	−	0.277692i
$96$	−0.350258	+	1.69627i	−0.0357481	+	0.173124i
$97$	7.13209	+	5.18176i	0.724154	+	0.526128i	0.887709	−	0.460406i	$-0.152296\pi$
$97$	7.13209	+	5.18176i	0.724154	+	0.526128i	−0.163555	+	0.986534i	$0.552296\pi$
$98$	5.51910	+	4.30576i	0.557513	+	0.434947i
$99$	6.70030	−	7.35567i	0.673406	−	0.739273i
$100$	2.24911	+	3.89557i	0.224911	+	0.389557i
$101$	−9.79140	+	4.35941i	−0.974281	+	0.433778i	−0.831225	−	0.555937i	$-0.812360\pi$
$101$	−9.79140	+	4.35941i	−0.974281	+	0.433778i	−0.143056	+	0.989715i	$0.545693\pi$
$102$	10.7607	−	3.56566i	1.06547	−	0.353053i
$103$	0.440469	−	0.489190i	0.0434007	−	0.0482014i	−0.721054	−	0.692879i	$-0.756342\pi$
$103$	0.440469	−	0.489190i	0.0434007	−	0.0482014i	0.764454	+	0.644678i	$0.223009\pi$
$104$	−1.85644	−	2.55517i	−0.182039	−	0.250555i
$105$	−12.9661	+	5.59837i	−1.26537	+	0.546345i
$106$	5.72796	−	1.86113i	0.556349	−	0.180769i
$107$	6.46092	−	1.37331i	0.624600	−	0.132763i	0.115270	−	0.993334i	$-0.463227\pi$
$107$	6.46092	−	1.37331i	0.624600	−	0.132763i	0.509330	+	0.860571i	$0.329893\pi$
$108$	3.80027	−	3.54372i	0.365681	−	0.340994i
$109$	−7.42308	−	4.28572i	−0.711003	−	0.410498i	0.100430	−	0.994944i	$-0.467978\pi$
$109$	−7.42308	−	4.28572i	−0.711003	−	0.410498i	−0.811432	+	0.584447i	$0.801312\pi$
$110$	−9.66487	−	3.32725i	−0.921509	−	0.317241i
$111$	0.852952	−	1.94613i	0.0809586	−	0.184719i
$112$	0.231517	+	2.63560i	0.0218763	+	0.249041i
$113$	6.35140	+	2.06370i	0.597490	+	0.194136i	0.592121	−	0.805849i	$-0.298291\pi$
$113$	6.35140	+	2.06370i	0.597490	+	0.194136i	0.00536916	+	0.999986i	$0.498291\pi$
$114$	6.66628	−	3.01458i	0.624355	−	0.282341i
$115$	−0.303371	−	2.88638i	−0.0282895	−	0.269156i
$116$	0.722504	+	6.87417i	0.0670828	+	0.638250i
$117$	0.110164	+	9.47445i	0.0101846	+	0.875913i
$118$	10.7444	+	3.49108i	0.989105	+	0.321380i
$119$	14.1811	−	9.93711i	1.29998	−	0.910933i
$120$	−4.88908	−	2.14279i	−0.446310	−	0.195609i
$121$	10.1985	−	4.12186i	0.927140	−	0.374715i
$122$	−7.72276	−	4.45874i	−0.699186	−	0.403675i
$123$	0.0256976	+	4.42031i	0.00231708	+	0.398566i
$124$	−7.24227	+	1.53939i	−0.650375	+	0.138242i
$125$	1.47078	−	0.477886i	0.131551	−	0.0427434i
$126$	4.00621	−	6.85203i	0.356901	−	0.610427i
$127$	−1.28837	−	1.77329i	−0.114324	−	0.157354i	0.748020	−	0.663676i	$-0.231005\pi$
$127$	−1.28837	−	1.77329i	−0.114324	−	0.157354i	−0.862344	+	0.506322i	$0.831005\pi$
$128$	−0.669131	+	0.743145i	−0.0591433	+	0.0656853i
$129$	−0.679588	−	2.05091i	−0.0598344	−	0.180573i
$130$	8.89228	−	3.95910i	0.779905	−	0.347236i
$131$	−5.63954	−	9.76796i	−0.492729	−	0.853431i	0.507236	−	0.861807i	$-0.330667\pi$
$131$	−5.63954	−	9.76796i	−0.492729	−	0.853431i	−0.999965	+	0.00837614i	$0.997334\pi$
$132$	5.48360	−	1.71178i	0.477286	−	0.148991i
$133$	8.43184	−	7.33488i	0.731133	−	0.636015i
$134$	5.08791	+	3.69658i	0.439529	+	0.319336i
$135$	8.24770	+	13.7269i	0.709849	+	1.18142i
$136$	6.40187	+	1.36076i	0.548955	+	0.116684i
$137$	13.8537	−	1.45608i	1.18360	−	0.124402i	0.507793	−	0.861479i	$-0.330461\pi$
$137$	13.8537	−	1.45608i	1.18360	−	0.124402i	0.675808	+	0.737077i	$0.263795\pi$
$138$	1.09844	+	1.20577i	0.0935056	+	0.102642i
$139$	15.1592	−	4.92553i	1.28579	−	0.417778i	0.415172	−	0.909743i	$-0.363721\pi$
$139$	15.1592	−	4.92553i	1.28579	−	0.417778i	0.870615	+	0.491965i	$0.163721\pi$
$140$	−8.09355	−	0.990882i	−0.684030	−	0.0837448i
$141$	9.00603	+	15.3916i	0.758445	+	1.29620i
$142$	8.92864	−	5.15495i	0.749275	−	0.432594i
$143$	−4.42642	+	9.49393i	−0.370156	+	0.793922i
$144$	2.92699	−	0.657811i	0.243916	−	0.0548176i
$145$	−21.1856	−	2.22670i	−1.75937	−	0.184917i
$146$	0.455879	+	0.148124i	0.0377288	+	0.0122588i
$147$	2.85644	−	11.7831i	0.235595	−	0.971851i
$148$	0.992484	−	0.721082i	0.0815817	−	0.0592726i
$149$	8.47818	+	3.77473i	0.694560	+	0.309238i	0.723481	−	0.690344i	$-0.242541\pi$
$149$	8.47818	+	3.77473i	0.694560	+	0.309238i	−0.0289218	+	0.999582i	$0.509207\pi$
$150$	4.54279	−	6.32967i	0.370917	−	0.516816i
$151$	−9.98655	+	8.99193i	−0.812694	+	0.731753i	−0.966588	−	0.256334i	$-0.917485\pi$
$151$	−9.98655	+	8.99193i	−0.812694	+	0.731753i	0.153894	+	0.988087i	$0.450818\pi$
$152$	4.20088	+	0.441530i	0.340736	+	0.0358128i
$153$	−13.3069	−	14.4377i	−1.07580	−	1.16722i
$154$	7.27277	−	4.90987i	0.586056	−	0.395649i
$155$		−	22.8187i		−	1.83284i
$156$	−2.70763	+	4.75337i	−0.216784	+	0.380574i
$157$	5.24970	+	5.83038i	0.418971	+	0.465315i	0.915272	−	0.402836i	$-0.131975\pi$
$157$	5.24970	+	5.83038i	0.418971	+	0.465315i	−0.496301	+	0.868151i	$0.665309\pi$
$158$	3.46949	−	16.3227i	0.276018	−	1.29856i
$159$	−7.02510	−	7.71154i	−0.557127	−	0.611565i
$160$	−1.81151	−	2.49332i	−0.143212	−	0.197114i
$161$	2.13611	+	1.28249i	0.168349	+	0.101074i
$162$	−8.30480	−	3.46847i	−0.652487	−	0.272508i
$163$	−1.58467	+	15.0772i	−0.124121	+	1.18094i	0.738203	+	0.674579i	$0.235675\pi$
$163$	−1.58467	+	15.0772i	−0.124121	+	1.18094i	−0.862324	+	0.506356i	$0.830992\pi$
$164$	−1.27606	+	2.21019i	−0.0996432	+	0.172587i
$165$	1.64656	+	17.6275i	0.128185	+	1.37230i
$166$	6.13839	+	10.6320i	0.476431	+	0.825203i
$167$	−6.50759	−	4.72804i	−0.503572	−	0.365867i	0.306807	−	0.951772i	$-0.400739\pi$
$167$	−6.50759	−	4.72804i	−0.503572	−	0.365867i	−0.810380	+	0.585905i	$0.800739\pi$
$168$	3.99424	−	2.24634i	0.308162	−	0.173309i
$169$	0.934697	+	2.87670i	0.0718998	+	0.221285i
$170$	−8.20420	+	18.4269i	−0.629234	+	1.41328i
$171$	−9.51512	−	8.36920i	−0.727640	−	0.640009i
$172$	0.259351	−	1.22015i	0.0197753	−	0.0930355i
$173$	−13.5630	+	2.88292i	−1.03118	+	0.219184i	−0.692273	−	0.721636i	$-0.743390\pi$
$173$	−13.5630	+	2.88292i	−1.03118	+	0.219184i	−0.338907	+	0.940820i	$0.610057\pi$
$174$	10.3331	−	6.04617i	0.783348	−	0.458359i
$175$	3.87069	−	11.2541i	0.292596	−	0.850731i
$176$	3.23166	+	0.745890i	0.243596	+	0.0562235i
$177$	−2.15847	−	19.4482i	−0.162241	−	1.46182i
$178$	2.64718	+	5.94566i	0.198414	+	0.445646i
$179$	0.0930807	−	0.0838102i	0.00695718	−	0.00626427i	−0.665645	−	0.746269i	$-0.731843\pi$
$179$	0.0930807	−	0.0838102i	0.00695718	−	0.00626427i	0.672602	+	0.740005i	$0.265177\pi$
$180$	0.107497	+	9.24513i	0.00801238	+	0.689091i
$181$	−9.06514	+	6.58621i	−0.673806	+	0.489549i	−0.871297	−	0.490756i	$-0.836721\pi$
$181$	−9.06514	+	6.58621i	−0.673806	+	0.489549i	0.197491	+	0.980305i	$0.436721\pi$
$182$	−1.87689	+	8.14273i	−0.139124	+	0.603579i
$183$	−1.52517	+	15.3700i	−0.112744	+	1.13619i
$184$	0.195793	+	0.921133i	0.0144340	+	0.0679069i
$185$	1.53780	+	3.45396i	0.113061	+	0.253940i
$186$	7.59808	+	10.3310i	0.557118	+	0.757507i
$187$	−6.34771	−	20.7581i	−0.464190	−	1.51798i
$188$			10.2958i			0.750897i
$189$	−13.6729	−	1.43241i	−0.994557	−	0.104192i
$190$	−4.02281	+	12.3809i	−0.291845	+	0.898207i
$191$	−11.9706	−	10.7784i	−0.866160	−	0.779894i	0.110682	−	0.993856i	$-0.464697\pi$
$191$	−11.9706	−	10.7784i	−0.866160	−	0.779894i	−0.976842	+	0.213962i	$0.931363\pi$
$192$	1.65036	+	0.525648i	0.119105	+	0.0379354i
$193$	5.35261	−	0.562582i	0.385289	−	0.0404955i	0.0900958	−	0.995933i	$-0.471283\pi$
$193$	5.35261	−	0.562582i	0.385289	−	0.0404955i	0.295193	+	0.955438i	$0.404616\pi$
$194$	5.89888	−	6.55137i	0.423515	−	0.470361i
$195$	−12.5944	−	11.2082i	−0.901903	−	0.802632i
$196$	4.85907	−	5.03879i	0.347077	−	0.359913i
$197$	−21.1572			−1.50739			−0.753694	−	0.657226i	$-0.771730\pi$
$197$	−21.1572			−1.50739			−0.753694	+	0.657226i	$0.771730\pi$
$198$	−6.61501	−	7.43248i	−0.470108	−	0.528203i
$199$	−9.58513	+	16.6019i	−0.679472	+	1.17688i	0.295668	+	0.955291i	$0.404458\pi$
$199$	−9.58513	+	16.6019i	−0.679472	+	1.17688i	−0.975140	+	0.221589i	$0.928876\pi$
$200$	4.10932	−	1.82959i	0.290573	−	0.129371i
$201$	2.20278	−	10.6678i	0.155372	−	0.752450i
$202$	3.31205	+	10.1934i	0.233035	+	0.717209i
$203$	12.4674	−	13.3790i	0.875037	−	0.939023i
$204$	−2.42132	−	11.0745i	−0.169527	−	0.775368i
$205$	−5.84513	−	5.26298i	−0.408241	−	0.367582i
$206$	−0.440469	−	0.489190i	−0.0306889	−	0.0340835i
$207$	1.11900	−	2.59408i	0.0777760	−	0.180301i
$208$	−2.73522	+	1.57918i	−0.189654	+	0.109497i
$209$	−5.47470	−	12.8955i	−0.378693	−	0.891999i
$210$	4.21237	+	13.4803i	0.290681	+	0.930229i
$211$	−7.30474	+	10.0541i	−0.502879	+	0.692154i	−0.982698	−	0.185213i	$-0.940702\pi$
$211$	−7.30474	+	10.0541i	−0.502879	+	0.692154i	0.479819	+	0.877368i	$0.340702\pi$
$212$	−1.25220	−	5.89112i	−0.0860012	−	0.404604i
$213$	−14.5076	−	10.4121i	−0.994046	−	0.713424i
$214$	−0.690437	−	6.56907i	−0.0471973	−	0.449053i
$215$	3.51204	+	1.56366i	0.239519	+	0.106641i
$216$	−3.12707	−	4.14987i	−0.212770	−	0.282363i
$217$	15.6489	+	11.7837i	1.06231	+	0.799927i
$218$	−5.03817	+	6.93444i	−0.341228	+	0.469660i
$219$	−0.0915824	−	0.825174i	−0.00618857	−	0.0557601i
$220$	−4.31928	+	9.26413i	−0.291206	+	0.624588i
$221$	17.9017	+	10.3356i	1.20420	+	0.695245i
$222$	−1.84631	−	1.05171i	−0.123916	−	0.0705859i
$223$	−4.44688	+	13.6861i	−0.297785	+	0.916489i	0.684486	+	0.729026i	$0.260027\pi$
$223$	−4.44688	+	13.6861i	−0.297785	+	0.916489i	−0.982272	+	0.187463i	$0.939973\pi$
$224$	2.64536	+	0.0452468i	0.176751	+	0.00302318i
$225$	−13.2315	−	2.65203i	−0.882098	−	0.176802i
$226$	2.71629	−	6.10089i	0.180685	−	0.405825i
$227$	15.8516	+	3.36935i	1.05210	+	0.223632i	0.701336	−	0.712831i	$-0.252587\pi$
$227$	15.8516	+	3.36935i	1.05210	+	0.223632i	0.350768	+	0.936462i	$0.385921\pi$
$228$	−2.30125	−	6.94487i	−0.152404	−	0.459936i
$229$	0.825233	−	7.85157i	0.0545329	−	0.518846i	−0.932824	−	0.360333i	$-0.882663\pi$
$229$	0.825233	−	7.85157i	0.0545329	−	0.518846i	0.987357	−	0.158514i	$-0.0506702\pi$
$230$	−2.90228			−0.191371
$231$	−12.9391	−	7.97372i	−0.851329	−	0.524632i
$232$	6.91203			0.453797
$233$	−1.54271	+	14.6779i	−0.101067	+	0.961584i	0.820049	+	0.572294i	$0.193946\pi$
$233$	−1.54271	+	14.6779i	−0.101067	+	0.961584i	−0.921115	+	0.389290i	$0.872720\pi$
$234$	9.43406	+	0.880789i	0.616724	+	0.0575790i
$235$	−31.0373	−	6.59719i	−2.02465	−	0.430353i
$236$	4.59505	−	10.3207i	0.299112	−	0.671818i
$237$	−28.2363	+	6.17359i	−1.83414	+	0.401018i
$238$	−8.40035	−	15.1421i	−0.544514	−	0.981516i
$239$	−0.406865	+	1.25220i	−0.0263179	+	0.0809981i	−0.963353	−	0.268238i	$-0.913559\pi$
$239$	−0.406865	+	1.25220i	−0.0263179	+	0.0809981i	0.937035	+	0.349236i	$0.113559\pi$
$240$	−2.64210	+	4.63831i	−0.170547	+	0.299402i
$241$	−14.9809	−	8.64925i	−0.965007	−	0.557147i	−0.0672967	−	0.997733i	$-0.521437\pi$
$241$	−14.9809	−	8.64925i	−0.965007	−	0.557147i	−0.897710	+	0.440586i	$0.854771\pi$
$242$	−3.03324	−	10.5735i	−0.194984	−	0.679692i
$243$	0.453051	+	15.5819i	0.0290632	+	0.999578i
$244$	−5.24156	+	7.21439i	−0.335557	+	0.461854i
$245$	12.0762	+	17.8767i	0.771523	+	1.14210i
$246$	4.39878	+	0.436492i	0.280456	+	0.0278297i
$247$	12.1876	+	5.42627i	0.775478	+	0.345265i
$248$	0.773936	+	7.36351i	0.0491450	+	0.467583i
$249$	12.3984	−	17.2753i	0.785719	−	1.09478i
$250$	−0.321529	−	1.51268i	−0.0203353	−	0.0956701i
$251$	−3.11981	+	4.29405i	−0.196921	+	0.271038i	−0.896046	−	0.443961i	$-0.853573\pi$
$251$	−3.11981	+	4.29405i	−0.196921	+	0.271038i	0.699126	+	0.714999i	$0.253573\pi$
$252$	−6.39573	−	4.70049i	−0.402893	−	0.296103i
$253$	2.35707	−	2.04921i	0.148188	−	0.128833i
$254$	−1.89824	+	1.09595i	−0.119106	+	0.0687661i
$255$	34.9363	−	0.203103i	2.18779	−	0.0127188i
$256$	0.669131	+	0.743145i	0.0418207	+	0.0464466i
$257$	5.27859	+	4.75286i	0.329269	+	0.296475i	0.817139	−	0.576441i	$-0.195559\pi$
$257$	5.27859	+	4.75286i	0.329269	+	0.296475i	−0.487869	+	0.872917i	$0.662226\pi$
$258$	−2.11071	+	0.461487i	−0.131407	+	0.0287309i
$259$	−3.16282	−	0.729026i	−0.196528	−	0.0452994i
$260$	−3.00791	−	9.25741i	−0.186543	−	0.574120i
$261$	−16.9164	−	11.9925i	−1.04710	−	0.742317i
$262$	−10.3039	+	4.58761i	−0.636580	+	0.283424i
$263$	−3.24743	+	5.62471i	−0.200245	+	0.346835i	−0.948607	−	0.316456i	$-0.897507\pi$
$263$	−3.24743	+	5.62471i	−0.200245	+	0.346835i	0.748362	+	0.663290i	$0.230841\pi$
$264$	−1.12921	−	5.63249i	−0.0694979	−	0.346656i
$265$	18.5616			1.14023
$266$	−6.41333	−	9.15235i	−0.393227	−	0.561167i
$267$	7.49412	−	8.42100i	0.458633	−	0.515357i
$268$	4.20816	−	4.67364i	0.257055	−	0.285488i
$269$	21.2008	−	2.22830i	1.29264	−	0.135862i	0.566873	−	0.823805i	$-0.308153\pi$
$269$	21.2008	−	2.22830i	1.29264	−	0.135862i	0.725764	+	0.687944i	$0.241486\pi$
$270$	14.5138	−	6.76767i	0.883282	−	0.411867i
$271$	11.6244	+	10.4666i	0.706132	+	0.635804i	0.941856	−	0.336016i	$-0.109080\pi$
$271$	11.6244	+	10.4666i	0.706132	+	0.635804i	−0.235725	+	0.971820i	$0.575746\pi$
$272$	2.02248	−	6.22456i	0.122631	−	0.377419i
$273$	14.1902	−	2.84919i	0.858832	−	0.172441i
$274$		−	13.9300i		−	0.841543i
$275$	−11.9153	−	8.97771i	−0.718518	−	0.541376i
$276$	1.31399	−	0.966388i	0.0790927	−	0.0581697i
$277$	2.05477	+	4.61509i	0.123459	+	0.277294i	0.964693	−	0.263378i	$-0.0848366\pi$
$277$	2.05477	+	4.61509i	0.123459	+	0.277294i	−0.841233	+	0.540672i	$0.818170\pi$
$278$	−3.31397	−	15.5910i	−0.198759	−	0.935087i
$279$	10.8817	−	19.3642i	0.651470	−	1.15930i
$280$	−1.83146	+	7.94564i	−0.109451	+	0.474843i
$281$	6.05472	−	4.39901i	0.361195	−	0.262423i	−0.392356	−	0.919814i	$-0.628340\pi$
$281$	6.05472	−	4.39901i	0.361195	−	0.262423i	0.753550	+	0.657390i	$0.228340\pi$
$282$	16.2486	−	7.34784i	0.967592	−	0.437558i
$283$	7.05404	−	6.35148i	0.419319	−	0.377557i	−0.432290	−	0.901735i	$-0.642294\pi$
$283$	7.05404	−	6.35148i	0.419319	−	0.377557i	0.851609	+	0.524178i	$0.175627\pi$
$284$	−4.19342	−	9.41857i	−0.248833	−	0.558889i
$285$	22.4104	−	2.48723i	1.32748	−	0.147331i
$286$	8.97923	+	5.39455i	0.530953	+	0.318987i
$287$	6.62774	−	1.29072i	0.391223	−	0.0761885i
$288$	−0.348253	−	2.97972i	−0.0205210	−	0.175582i
$289$	−25.2710	+	5.37151i	−1.48653	+	0.315971i
$290$	−4.42900	+	20.8368i	−0.260080	+	1.22358i
$291$	−14.5492	−	4.63398i	−0.852887	−	0.271648i
$292$	0.194965	−	0.437899i	0.0114095	−	0.0256261i
$293$	−7.22868	−	22.2476i	−0.422304	−	1.29972i	−0.905552	−	0.424234i	$-0.860543\pi$
$293$	−7.22868	−	22.2476i	−0.422304	−	1.29972i	0.483249	−	0.875483i	$-0.339457\pi$
$294$	−11.4199	−	4.07246i	−0.666025	−	0.237511i
$295$	28.1680	+	20.4652i	1.64000	+	1.19153i
$296$	−0.613389	−	1.06242i	−0.0356525	−	0.0617520i
$297$	−7.00886	+	15.7441i	−0.406695	+	0.913564i
$298$	4.64026	−	8.03717i	0.268803	−	0.465581i
$299$	−0.310896	+	2.95798i	−0.0179796	+	0.171064i
$300$	−5.82015	−	5.17954i	−0.336026	−	0.299041i
$301$	−2.88597	+	1.60104i	−0.166345	+	0.0922826i
$302$	7.89879	+	10.8718i	0.454524	+	0.625599i
$303$	13.7234	−	12.5018i	0.788390	−	0.718212i
$304$	0.878223	−	4.13171i	0.0503695	−	0.236970i
$305$	−18.3897	−	20.4238i	−1.05299	−	1.16946i
$306$	−15.7495	+	11.7249i	−0.900340	+	0.670266i
$307$			32.9371i			1.87982i	0.341425	+	0.939909i	$0.389090\pi$
$307$			32.9371i			1.87982i	−0.341425	+	0.939909i	$0.610910\pi$
$308$	−4.12277	−	7.74615i	−0.234916	−	0.441378i
$309$	−0.457681	+	1.04426i	−0.0260366	+	0.0594061i
$310$	−22.6937	−	2.38521i	−1.28892	−	0.135471i
$311$	−22.4324	+	20.1982i	−1.27202	+	1.14534i	−0.289909	+	0.957054i	$0.593625\pi$
$311$	−22.4324	+	20.1982i	−1.27202	+	1.14534i	−0.982115	+	0.188281i	$0.939708\pi$
$312$	4.44430	+	3.18966i	0.251609	+	0.180579i
$313$	6.72088	+	2.99233i	0.379886	+	0.169136i	0.587791	−	0.809013i	$-0.299998\pi$
$313$	6.72088	+	2.99233i	0.379886	+	0.169136i	−0.207905	+	0.978149i	$0.566664\pi$
$314$	6.34718	−	4.61150i	0.358192	−	0.260242i
$315$	18.2681	−	16.2685i	1.02929	−	0.916624i
$316$	−15.8706	−	5.15667i	−0.892791	−	0.290085i
$317$	−5.07186	−	0.533074i	−0.284864	−	0.0299404i	−0.0389811	−	0.999240i	$-0.512411\pi$
$317$	−5.07186	−	0.533074i	−0.284864	−	0.0299404i	−0.245883	+	0.969300i	$0.579078\pi$
$318$	−8.40362	+	6.18054i	−0.471251	+	0.346588i
$319$	−11.1152	−	20.0497i	−0.622334	−	1.12257i
$320$	−2.66902	+	1.54096i	−0.149203	+	0.0861422i
$321$	−9.87446	+	5.77782i	−0.551139	+	0.322487i
$322$	1.49875	−	1.99035i	0.0835218	−	0.110918i
$323$	−26.2927	+	8.54300i	−1.46296	+	0.475345i
$324$	−4.31755	+	7.89675i	−0.239864	+	0.438709i
$325$	14.1292	−	1.48503i	0.783745	−	0.0823749i
$326$	14.8289	+	3.15199i	0.821299	+	0.174572i
$327$	14.5394	+	3.00222i	0.804033	+	0.166023i
$328$	2.06470	+	1.50009i	0.114004	+	0.0828288i
$329$	20.5521	−	17.8783i	1.13307	−	0.985663i
$330$	17.7031	+	0.205037i	0.974522	+	0.0112869i
$331$	−11.3458	−	19.6515i	−0.623621	−	1.08014i	−0.988806	−	0.149208i	$-0.952328\pi$
$331$	−11.3458	−	19.6515i	−0.623621	−	1.08014i	0.365185	−	0.930935i	$-0.381006\pi$
$332$	11.2154	−	4.99341i	0.615525	−	0.274049i
$333$	−0.342118	+	3.66440i	−0.0187480	+	0.200808i
$334$	−5.38237	+	5.97773i	−0.294510	+	0.327087i
$335$	11.3926	+	15.6805i	0.622442	+	0.856718i
$336$	−1.81652	−	4.20717i	−0.0990995	−	0.229520i
$337$	19.9563	−	6.48418i	1.08709	−	0.353216i	0.289967	−	0.957037i	$-0.406356\pi$
$337$	19.9563	−	6.48418i	1.08709	−	0.353216i	0.797120	+	0.603821i	$0.206356\pi$
$338$	2.95865	−	0.628880i	0.160929	−	0.0342065i
$339$	−11.5669	+	0.0672445i	−0.628227	+	0.00365222i
$340$	17.4684	+	10.0854i	0.947358	+	0.546958i
$341$	20.1147	−	14.0862i	1.08927	−	0.762811i
$342$	−9.31795	+	8.58818i	−0.503857	+	0.464396i
$343$	−18.4959	−	0.949813i	−0.998684	−	0.0512851i
$344$	−1.18636	−	0.385470i	−0.0639640	−	0.0207832i
$345$	2.07128	+	4.58033i	0.111514	+	0.246597i
$346$	1.44940	+	13.7901i	0.0779201	+	0.741360i
$347$	−0.0103379	−	0.0983583i	−0.000554966	−	0.00528015i	0.994241	−	0.107168i	$-0.0341783\pi$
$347$	−0.0103379	−	0.0983583i	−0.000554966	−	0.00528015i	−0.994796	+	0.101888i	$0.967512\pi$
$348$	−4.93295	−	10.9085i	−0.264434	−	0.584755i
$349$	3.52948	+	1.14680i	0.188928	+	0.0613866i	0.401953	−	0.915660i	$-0.368331\pi$
$349$	3.52948	+	1.14680i	0.188928	+	0.0613866i	−0.213025	+	0.977047i	$0.568331\pi$
$350$	−10.7879	−	5.02586i	−0.576636	−	0.268643i
$351$	−5.34281	−	15.5173i	−0.285178	−	0.828252i
$352$	1.07960	−	3.13599i	0.0575431	−	0.167149i
$353$	−6.79914	−	3.92549i	−0.361882	−	0.208933i	0.308024	−	0.951379i	$-0.400332\pi$
$353$	−6.79914	−	3.92549i	−0.361882	−	0.208933i	−0.669906	+	0.742446i	$0.733666\pi$
$354$	−19.5673	+	0.113755i	−1.03999	+	0.00604601i
$355$	31.0799	−	6.60624i	1.64955	−	0.350623i
$356$	6.18979	−	2.01119i	0.328058	−	0.106593i
$357$	−17.9019	+	24.0638i	−0.947469	+	1.27359i
$358$	−0.0736215	−	0.101331i	−0.00389102	−	0.00535553i
$359$	−23.8912	+	26.5339i	−1.26093	+	1.40040i	−0.381503	+	0.924368i	$0.624593\pi$
$359$	−23.8912	+	26.5339i	−1.26093	+	1.40040i	−0.879426	+	0.476036i	$0.842073\pi$
$360$	9.20572	+	0.859470i	0.485184	+	0.0452981i
$361$	1.05757	−	0.470861i	0.0556617	−	0.0247822i
$362$	5.60256	+	9.70392i	0.294464	+	0.510027i
$363$	−14.5222	+	12.3331i	−0.762219	+	0.647319i
$364$	7.90194	+	2.71775i	0.414174	+	0.142449i
$365$	1.19515	+	0.868326i	0.0625569	+	0.0454503i
$366$	15.1264	+	3.12342i	0.790670	+	0.163264i
$367$	28.2753	+	6.01010i	1.47596	+	0.313725i	0.874440	−	0.485133i	$-0.161229\pi$
$367$	28.2753	+	6.01010i	1.47596	+	0.313725i	0.601519	+	0.798858i	$0.294562\pi$
$368$	0.936553	−	0.0984357i	0.0488212	−	0.00513132i
$369$	−2.45044	−	7.25361i	−0.127565	−	0.377608i
$370$	3.59578	−	1.16834i	0.186936	−	0.0607391i
$371$	−9.58525	+	12.7293i	−0.497641	+	0.660874i
$372$	11.0686	−	6.47657i	0.573882	−	0.335794i
$373$	−22.2105	+	12.8232i	−1.15001	+	0.663961i	−0.948891	−	0.315605i	$-0.897793\pi$
$373$	−22.2105	+	12.8232i	−1.15001	+	0.663961i	−0.201124	+	0.979566i	$0.564459\pi$
$374$	−21.3079	+	4.14312i	−1.10180	+	0.214236i
$375$	−2.15782	+	1.58699i	−0.111429	+	0.0819520i
$376$	10.2394	+	1.07620i	0.528055	+	0.0555009i
$377$	20.7622	+	6.74606i	1.06931	+	0.347440i
$378$	−2.85377	+	13.4483i	−0.146782	+	0.691704i
$379$	−0.104403	+	0.0758535i	−0.00536284	+	0.00389633i	−0.590463	−	0.807064i	$-0.701055\pi$
$379$	−0.104403	+	0.0758535i	−0.00536284	+	0.00389633i	0.585101	+	0.810961i	$0.301055\pi$
$380$	11.8926	+	5.29493i	0.610078	+	0.271624i
$381$	3.08434	+	2.21363i	0.158016	+	0.113408i
$382$	−11.9706	+	10.7784i	−0.612468	+	0.551468i
$383$	20.7093	+	2.17664i	1.05820	+	0.111221i	0.617607	−	0.786487i	$-0.288102\pi$
$383$	20.7093	+	2.17664i	1.05820	+	0.111221i	0.440591	+	0.897708i	$0.354769\pi$
$384$	0.695278	−	1.58638i	0.0354808	−	0.0809544i
$385$	25.9930	−	7.46489i	1.32473	−	0.380446i
$386$		−	5.38209i		−	0.273941i
$387$	2.23467	+	3.00174i	0.113595	+	0.152587i
$388$	−5.89888	−	6.55137i	−0.299470	−	0.332596i
$389$	3.69086	−	17.3642i	0.187134	−	0.880397i	−0.779930	−	0.625866i	$-0.784746\pi$
$389$	3.69086	−	17.3642i	0.187134	−	0.880397i	0.967065	−	0.254531i	$-0.0819211\pi$
$390$	−12.4632	+	11.3538i	−0.631100	+	0.574923i
$391$	−3.62276	−	4.98629i	−0.183211	−	0.252168i
$392$	−4.50327	−	5.35915i	−0.227450	−	0.270678i
$393$	14.5938	+	12.9875i	0.736158	+	0.655131i
$394$	−2.21153	+	21.0413i	−0.111415	+	1.06005i
$395$	25.7145	−	44.5388i	1.29384	−	2.24099i
$396$	−8.08322	+	5.80186i	−0.406197	+	0.291555i
$397$	−6.68970	−	11.5869i	−0.335746	−	0.581530i	0.647882	−	0.761741i	$-0.275655\pi$
$397$	−6.68970	−	11.5869i	−0.335746	−	0.581530i	−0.983628	+	0.180211i	$0.942322\pi$
$398$	15.5091	+	11.2680i	0.777399	+	0.564814i
$399$	−9.86707	+	16.6532i	−0.493971	+	0.833704i
$400$	−1.39002	−	4.27805i	−0.0695012	−	0.213903i
$401$	9.46995	−	21.2698i	0.472907	−	1.06217i	−0.506861	−	0.862028i	$-0.669194\pi$
$401$	9.46995	−	21.2698i	0.472907	−	1.06217i	0.979768	−	0.200138i	$-0.0641390\pi$
$402$	−10.3791	−	3.30580i	−0.517664	−	0.164878i
$403$	−4.86196	+	22.8737i	−0.242192	+	1.13942i
$404$	10.4838	−	2.22840i	0.521589	−	0.110867i
$405$	−21.0388	−	18.0755i	−1.04542	−	0.898181i
$406$	−12.0025	−	13.7976i	−0.595676	−	0.684761i
$407$	−2.09536	+	3.48773i	−0.103863	+	0.172881i
$408$	−11.2669	+	1.25046i	−0.557795	+	0.0619072i
$409$	3.11517	+	6.99678i	0.154035	+	0.345969i	0.974036	−	0.226394i	$-0.0726937\pi$
$409$	3.11517	+	6.99678i	0.154035	+	0.345969i	−0.820001	+	0.572363i	$0.806027\pi$
$410$	−5.84513	+	5.26298i	−0.288670	+	0.259920i
$411$	−21.9841	+	9.94150i	−1.08440	+	0.490378i
$412$	−0.532552	+	0.386922i	−0.0262370	+	0.0190623i
$413$	−28.5809	+	8.74902i	−1.40637	+	0.430511i
$414$	−2.46290	−	1.38403i	−0.121045	−	0.0680212i
$415$	7.86655	+	37.0092i	0.386154	+	1.81671i
$416$	1.28462	+	2.88531i	0.0629838	+	0.141464i
$417$	−22.2404	+	16.3570i	−1.08912	+	0.801005i
$418$	−13.3971	+	4.09676i	−0.655274	+	0.200379i
$419$			1.41006i			0.0688859i	0.999407	+	0.0344430i	$0.0109657\pi$
$419$			1.41006i			0.0688859i	−0.999407	+	0.0344430i	$0.989034\pi$
$420$	13.8468	−	2.78022i	0.675653	−	0.135661i
$421$	8.76429	−	26.9737i	0.427145	−	1.31462i	−0.473780	−	0.880643i	$-0.657111\pi$
$421$	8.76429	−	26.9737i	0.427145	−	1.31462i	0.900925	−	0.433975i	$-0.142889\pi$
$422$	9.23549	+	8.31567i	0.449577	+	0.404801i
$423$	−23.1925	−	20.3994i	−1.12766	−	0.991852i
$424$	−5.98974	+	0.629547i	−0.290887	+	0.0305735i
$425$	−19.6994	+	21.8784i	−0.955561	+	1.06126i
$426$	−11.8715	+	13.3398i	−0.575176	+	0.646315i
$427$	23.5029	−	2.06455i	1.13739	−	0.0999104i
$428$	−6.60526			−0.319277
$429$	2.10535	−	18.0208i	0.101647	−	0.870055i
$430$	1.92220	−	3.32935i	0.0926969	−	0.160556i
$431$	−2.29839	+	1.02331i	−0.110710	+	0.0492911i	−0.461344	−	0.887221i	$-0.652633\pi$
$431$	−2.29839	+	1.02331i	−0.110710	+	0.0492911i	0.350634	+	0.936512i	$0.385966\pi$
$432$	−4.45401	+	2.67616i	−0.214293	+	0.128757i
$433$	4.56670	+	14.0549i	0.219462	+	0.675433i	0.998807	+	0.0488383i	$0.0155519\pi$
$433$	4.56670	+	14.0549i	0.219462	+	0.675433i	−0.779345	+	0.626595i	$0.784448\pi$
$434$	13.3549	−	14.3314i	0.641054	−	0.687930i
$435$	36.0452	−	7.88093i	1.72823	−	0.377862i
$436$	6.36982	+	5.73541i	0.305059	+	0.274676i
$437$	−2.66167	−	2.95609i	−0.127325	−	0.141409i
$438$	−0.830227	+	0.00482655i	−0.0396698	+	0.000230621i
$439$	29.7430	−	17.1721i	1.41956	−	0.819581i	0.423296	−	0.905991i	$-0.360873\pi$
$439$	29.7430	−	17.1721i	1.41956	−	0.819581i	0.996260	+	0.0864107i	$0.0275397\pi$
$440$	8.76190	+	5.26398i	0.417707	+	0.250951i
$441$	1.72304	+	20.9292i	0.0820493	+	0.996628i
$442$	12.1502	−	16.7233i	0.577925	−	0.795446i
$443$	0.0902981	+	0.424819i	0.00429019	+	0.0201838i	0.980241	−	0.197809i	$-0.0633825\pi$
$443$	0.0902981	+	0.424819i	0.00429019	+	0.0201838i	−0.975950	+	0.217993i	$0.930049\pi$
$444$	−1.23894	+	1.72627i	−0.0587973	+	0.0819249i
$445$	2.09665	+	19.9483i	0.0993906	+	0.945638i
$446$	13.1463	+	5.85311i	0.622495	+	0.277153i
$447$	−15.9958	−	1.58726i	−0.756574	−	0.0750749i
$448$	0.321515	−	2.62614i	0.0151901	−	0.124074i
$449$	14.0701	−	19.3658i	0.664008	−	0.913928i	−0.335598	−	0.942005i	$-0.608938\pi$
$449$	14.0701	−	19.3658i	0.664008	−	0.913928i	0.999606	+	0.0280772i	$0.00893843\pi$
$450$	−4.02057	+	12.8818i	−0.189532	+	0.607253i
$451$	1.03106	−	8.40136i	0.0485507	−	0.395605i
$452$	−5.78354	−	3.33913i	−0.272035	−	0.157059i
$453$	11.5205	−	20.2247i	0.541279	−	0.950237i
$454$	5.00783	−	15.4125i	0.235029	−	0.723345i
$455$	−13.2562	+	22.0795i	−0.621458	+	1.03510i
$456$	−7.14738	+	1.56270i	−0.334707	+	0.0731803i
$457$	−0.625599	+	1.40512i	−0.0292643	+	0.0657287i	−0.927586	−	0.373609i	$-0.878120\pi$
$457$	−0.625599	+	1.40512i	−0.0292643	+	0.0657287i	0.898322	+	0.439338i	$0.144787\pi$
$458$	−7.72230	−	1.64142i	−0.360839	−	0.0766987i
$459$	29.7441	+	16.4879i	1.38833	+	0.769589i
$460$	−0.303371	+	2.88638i	−0.0141447	+	0.134578i
$461$	26.6732			1.24229			0.621147	−	0.783694i	$-0.286667\pi$
$461$	26.6732			1.24229			0.621147	+	0.783694i	$0.286667\pi$
$462$	−9.28254	+	12.0347i	−0.431863	+	0.559906i
$463$	−21.7003			−1.00850			−0.504250	−	0.863557i	$-0.668231\pi$
$463$	−21.7003			−1.00850			−0.504250	+	0.863557i	$0.668231\pi$
$464$	0.722504	−	6.87417i	0.0335414	−	0.319125i
$465$	12.4317	+	37.5172i	0.576504	+	1.73982i
$466$	14.4363	+	3.06853i	0.668748	+	0.142147i
$467$	−14.7550	+	33.1404i	−0.682782	+	1.53355i	0.155217	+	0.987880i	$0.450392\pi$
$467$	−14.7550	+	33.1404i	−0.682782	+	1.53355i	−0.837998	+	0.545673i	$0.816274\pi$
$468$	1.86209	−	9.29031i	0.0860752	−	0.429445i
$469$	−16.6367	−	0.284557i	−0.768212	−	0.0131396i
$470$	−9.80533	+	30.1777i	−0.452286	+	1.39199i
$471$	−11.8076	−	6.72591i	−0.544066	−	0.309914i
$472$	−9.78381	−	5.64868i	−0.450336	−	0.260002i
$473$	0.789649	+	4.06112i	0.0363081	+	0.186731i
$474$	3.18828	+	28.7269i	0.146442	+	1.31947i
$475$	−11.1682	+	15.3718i	−0.512434	+	0.705304i
$476$	−15.9372	+	6.77155i	−0.730481	+	0.310373i
$477$	15.7515	+	8.85156i	0.721211	+	0.405285i
$478$	1.20281	+	0.535526i	0.0550153	+	0.0244944i
$479$	−0.618868	−	5.88814i	−0.0282768	−	0.269036i	−0.999521	−	0.0309500i	$-0.990147\pi$
$479$	−0.618868	−	5.88814i	−0.0282768	−	0.269036i	0.971244	−	0.238086i	$-0.0765199\pi$
$480$	4.33673	+	3.11246i	0.197944	+	0.142064i
$481$	−0.805577	−	3.78994i	−0.0367311	−	0.172806i
$482$	−10.1678	+	13.9948i	−0.463131	+	0.637445i
$483$	−4.21077	−	0.944831i	−0.191596	−	0.0429913i
$484$	−10.8327	+	1.91139i	−0.492394	+	0.0868816i
$485$	23.5294	−	13.5847i	1.06841	−	0.616849i
$486$	15.5439	+	1.17818i	0.705084	+	0.0534433i
$487$	1.22064	+	1.35566i	0.0553125	+	0.0614308i	0.770166	−	0.637843i	$-0.220173\pi$
$487$	1.22064	+	1.35566i	0.0553125	+	0.0614308i	−0.714854	+	0.699274i	$0.753507\pi$
$488$	6.62698	+	5.96696i	0.299989	+	0.270111i
$489$	−5.60862	−	25.6523i	−0.253631	−	1.16004i
$490$	19.0411	−	10.1415i	0.860189	−	0.458145i
$491$	−4.72757	−	14.5500i	−0.213352	−	0.656631i	−0.999266	−	0.0382954i	$-0.987807\pi$
$491$	−4.72757	−	14.5500i	−0.213352	−	0.656631i	0.785914	−	0.618336i	$-0.212193\pi$
$492$	0.893898	−	4.32906i	0.0403001	−	0.195169i
$493$	−41.3274	+	18.4001i	−1.86129	+	0.828701i
$494$	6.67049	−	11.5536i	0.300120	−	0.519823i
$495$	−12.3107	−	28.0851i	−0.553323	−	1.26233i
$496$	7.40407			0.332453
$497$	−11.5193	+	24.7258i	−0.516710	+	1.10910i
$498$	−15.8847	−	14.1363i	−0.711809	−	0.633462i
$499$	27.6948	−	30.7582i	1.23979	−	1.37693i	0.340104	−	0.940388i	$-0.389538\pi$
$499$	27.6948	−	30.7582i	1.23979	−	1.37693i	0.899686	−	0.436538i	$-0.143796\pi$
$500$	−1.53800	+	0.161650i	−0.0687814	+	0.00722922i
$501$	13.2752	+	4.22822i	0.593093	+	0.188903i
$502$	3.94442	+	3.55157i	0.176048	+	0.158514i
$503$	0.145451	−	0.447653i	0.00648535	−	0.0199599i	−0.947761	−	0.318980i	$-0.896660\pi$
$503$	0.145451	−	0.447653i	0.00648535	−	0.0199599i	0.954247	+	0.299020i	$0.0966597\pi$
$504$	−5.34328	+	5.86936i	−0.238009	+	0.261442i
$505$			33.0321i			1.46991i
$506$	−1.79160	−	2.55836i	−0.0796465	−	0.113733i
$507$	−3.10400	−	4.22047i	−0.137854	−	0.187438i
$508$	0.891528	+	2.00240i	0.0395551	+	0.0888423i
$509$	7.92969	+	37.3063i	0.351478	+	1.65357i	0.698422	+	0.715686i	$0.253886\pi$
$509$	7.92969	+	37.3063i	0.351478	+	1.65357i	−0.346945	+	0.937886i	$0.612781\pi$
$510$	3.44984	−	34.7661i	0.152762	−	1.53947i
$511$	−1.21267	+	0.371215i	−0.0536453	+	0.0164216i
$512$	0.809017	−	0.587785i	0.0357538	−	0.0259767i
$513$	20.2037	+	8.57628i	0.892016	+	0.378652i
$514$	5.27859	−	4.75286i	0.232829	−	0.209640i
$515$	−0.825161	−	1.85334i	−0.0363609	−	0.0816680i
$516$	0.238329	+	2.14739i	0.0104919	+	0.0945335i
$517$	−13.3442	−	31.4319i	−0.586878	−	1.38237i
$518$	−1.05564	+	3.06929i	−0.0463820	+	0.134857i
$519$	20.7289	−	12.1291i	0.909899	−	0.532407i
$520$	−9.52110	+	2.02377i	−0.417528	+	0.0887483i
$521$	−6.77646	+	31.8807i	−0.296882	+	1.39672i	0.536442	+	0.843937i	$0.319768\pi$
$521$	−6.77646	+	31.8807i	−0.296882	+	1.39672i	−0.833325	+	0.552784i	$0.813565\pi$
$522$	−13.6951	+	15.5702i	−0.599416	+	0.681489i
$523$	−8.05494	+	18.0917i	−0.352218	+	0.791094i	0.647364	+	0.762181i	$0.275871\pi$
$523$	−8.05494	+	18.0917i	−0.352218	+	0.791094i	−0.999582	+	0.0289133i	$0.990795\pi$
$524$	3.48542	+	10.7270i	0.152261	+	0.468613i
$525$	−0.232701	+	20.6121i	−0.0101559	+	0.899585i
$526$	5.25445	+	3.81758i	0.229105	+	0.166455i
$527$	−24.2294	−	41.9666i	−1.05545	−	1.82809i
$528$	−5.71966	+	0.534265i	−0.248916	+	0.0232509i
$529$	−11.0566	+	19.1506i	−0.480721	+	0.832634i
$530$	1.94021	−	18.4599i	0.0842774	−	0.801846i
$531$	14.1442	+	30.7996i	0.613806	+	1.33659i
$532$	−9.77259	+	5.42152i	−0.423696	+	0.235053i
$533$	4.73784	+	6.52108i	0.205219	+	0.282459i
$534$	−7.59152	−	8.33330i	−0.328517	−	0.360617i
$535$	4.23243	−	19.9120i	0.182984	−	0.860871i
$536$	−4.20816	−	4.67364i	−0.181765	−	0.201871i
$537$	−0.107378	+	0.188506i	−0.00463369	+	0.00813464i
$538$		−	21.3176i		−	0.919067i
$539$	−8.30353	+	21.6807i	−0.357658	+	0.933852i
$540$	−5.21349	−	15.1417i	−0.224353	−	0.651595i
$541$	−27.3195	−	2.87140i	−1.17456	−	0.123451i	−0.502922	−	0.864332i	$-0.667742\pi$
$541$	−27.3195	−	2.87140i	−1.17456	−	0.123451i	−0.671637	+	0.740881i	$0.734408\pi$
$542$	11.6244	−	10.4666i	0.499310	−	0.449581i
$543$	11.3162	−	15.7673i	0.485623	−	0.676641i
$544$	−5.97905	−	2.66205i	−0.256350	−	0.114134i
$545$	−21.3714	+	15.5272i	−0.915449	+	0.665113i
$546$	−1.35030	−	14.4103i	−0.0577874	−	0.616704i
$547$	−12.5373	−	4.07360i	−0.536055	−	0.174175i	0.0284643	−	0.999595i	$-0.490938\pi$
$547$	−12.5373	−	4.07360i	−0.536055	−	0.174175i	−0.564519	+	0.825420i	$0.690938\pi$
$548$	−13.8537	−	1.45608i	−0.591801	−	0.0622008i
$549$	−5.86601	−	26.1014i	−0.250355	−	1.11398i
$550$	−10.1740	+	10.9116i	−0.433821	+	0.465271i
$551$	−25.2850	+	14.5983i	−1.07718	+	0.621908i
$552$	−0.823745	−	1.40780i	−0.0350609	−	0.0599201i
$553$	17.2652	+	40.6347i	0.734193	+	1.72796i
$554$	4.80459	−	1.56111i	0.204128	−	0.0663251i
$555$	−4.41008	−	4.84099i	−0.187197	−	0.205489i
$556$	−15.8520	+	1.66611i	−0.672275	+	0.0706590i
$557$	−10.0877	−	2.14421i	−0.427431	−	0.0908532i	−0.0108270	−	0.999941i	$-0.503446\pi$
$557$	−10.0877	−	2.14421i	−0.427431	−	0.0908532i	−0.416604	+	0.909088i	$0.636780\pi$
$558$	−18.1206	−	12.8462i	−0.767108	−	0.543823i
$559$	−3.18734	−	2.31574i	−0.134810	−	0.0979452i
$560$	7.71068	+	2.65197i	0.325836	+	0.112066i
$561$	21.7455	+	30.6709i	0.918096	+	1.29493i
$562$	−3.74202	−	6.48138i	−0.157848	−	0.273400i
$563$	−5.76820	+	2.56817i	−0.243101	+	0.108235i	−0.524671	−	0.851305i	$-0.675812\pi$
$563$	−5.76820	+	2.56817i	−0.243101	+	0.108235i	0.281570	+	0.959541i	$0.409145\pi$
$564$	−5.60914	−	16.9277i	−0.236188	−	0.712784i
$565$	13.7719	−	15.2953i	0.579390	−	0.643478i
$566$	−5.57934	−	7.67931i	−0.234517	−	0.322785i
$567$	23.2605	−	5.09392i	0.976850	−	0.213925i
$568$	−9.80530	+	3.18594i	−0.411421	+	0.133679i
$569$	29.7627	−	6.32627i	1.24772	−	0.265211i	0.463725	−	0.885979i	$-0.346513\pi$
$569$	29.7627	−	6.32627i	1.24772	−	0.265211i	0.783994	+	0.620768i	$0.213179\pi$
$570$	−0.131081	−	22.5476i	−0.00549039	−	0.944415i
$571$	−11.8491	−	6.84107i	−0.495868	−	0.286290i	0.231137	−	0.972921i	$-0.425755\pi$
$571$	−11.8491	−	6.84107i	−0.495868	−	0.286290i	−0.727006	+	0.686631i	$0.759089\pi$
$572$	6.30359	−	8.36616i	0.263566	−	0.349807i
$573$	25.5533	+	11.1995i	1.06751	+	0.467867i
$574$	−0.590857	−	6.72635i	−0.0246619	−	0.280752i
$575$	−4.02869	−	1.30900i	−0.168008	−	0.0545892i
$576$	−2.99980	+	0.0348800i	−0.124992	+	0.00145333i
$577$	−4.06452	−	38.6714i	−0.169208	−	1.60991i	−0.668660	−	0.743568i	$-0.733132\pi$
$577$	−4.06452	−	38.6714i	−0.169208	−	1.60991i	0.499452	−	0.866342i	$-0.333535\pi$
$578$	2.70055	+	25.6940i	0.112328	+	1.06873i
$579$	−8.49393	+	3.84106i	−0.352996	+	0.159629i
$580$	20.2597	+	6.58277i	0.841238	+	0.273335i
$581$	−29.4429	−	13.7169i	−1.22150	−	0.569071i
$582$	−6.12939	+	13.9851i	−0.254071	+	0.579700i
$583$	11.4582	+	16.3620i	0.474551	+	0.677645i
$584$	−0.415120	−	0.239670i	−0.0171778	−	0.00991761i
$585$	26.8131	+	11.5663i	1.10859	+	0.478209i
$586$	−22.8813	+	4.86357i	−0.945218	+	0.200912i
$587$	−3.93016	+	1.27698i	−0.162215	+	0.0527068i	−0.388999	−	0.921238i	$-0.627179\pi$
$587$	−3.93016	+	1.27698i	−0.162215	+	0.0527068i	0.226784	+	0.973945i	$0.427179\pi$
$588$	−5.24386	+	10.9317i	−0.216253	+	0.450815i
$589$	−18.3829	−	25.3020i	−0.757456	−	1.04255i
$590$	23.2975	−	25.8745i	0.959142	−	1.06524i
$591$	34.7854	−	11.5264i	1.43088	−	0.474135i
$592$	−1.12072	+	0.498976i	−0.0460612	+	0.0205078i
$593$	−11.9654	−	20.7247i	−0.491359	−	0.851060i	0.508591	−	0.861008i	$-0.330167\pi$
$593$	−11.9654	−	20.7247i	−0.491359	−	0.851060i	−0.999951	+	0.00994862i	$0.996833\pi$
$594$	14.9252	+	8.61617i	0.612389	+	0.353526i
$595$	−10.2013	−	52.3828i	−0.418211	−	2.14749i
$596$	−7.50810	−	5.45496i	−0.307544	−	0.223444i
$597$	6.71454	−	32.5179i	0.274808	−	1.33087i
$598$	2.90927	+	0.618385i	0.118969	+	0.0252877i
$599$	−20.9951	+	2.20667i	−0.857835	+	0.0901621i	−0.523225	−	0.852195i	$-0.675271\pi$
$599$	−20.9951	+	2.20667i	−0.857835	+	0.0901621i	−0.334610	+	0.942357i	$0.608605\pi$
$600$	−5.75953	+	5.24686i	−0.235132	+	0.214202i
$601$	25.8399	−	8.39589i	1.05403	−	0.342475i	0.269782	−	0.962921i	$-0.413048\pi$
$601$	25.8399	−	8.39589i	1.05403	−	0.342475i	0.784249	+	0.620446i	$0.213048\pi$
$602$	1.29061	+	3.03752i	0.0526012	+	0.123800i
$603$	2.19017	+	18.7395i	0.0891904	+	0.763130i
$604$	11.6378	−	6.71911i	0.473537	−	0.273397i
$605$	1.17918	−	33.8806i	0.0479404	−	1.37744i
$606$	−10.9989	−	14.9550i	−0.446799	−	0.607507i
$607$	−8.36565	−	0.879265i	−0.339551	−	0.0356883i	−0.0667815	−	0.997768i	$-0.521273\pi$
$607$	−8.36565	−	0.879265i	−0.339551	−	0.0356883i	−0.272770	+	0.962079i	$0.587940\pi$
$608$	−4.01728	−	1.30529i	−0.162922	−	0.0529367i
$609$	−13.2092	+	28.7892i	−0.535263	+	1.16660i
$610$	−22.2342	+	16.1541i	−0.900234	+	0.654059i
$611$	29.7065	+	13.2262i	1.20180	+	0.535074i
$612$	10.0144	+	16.8888i	0.404807	+	0.682690i
$613$	2.54581	−	2.29226i	0.102824	−	0.0925835i	−0.616115	−	0.787656i	$-0.711294\pi$
$613$	2.54581	−	2.29226i	0.102824	−	0.0925835i	0.718940	+	0.695073i	$0.244628\pi$
$614$	32.7566	+	3.44286i	1.32195	+	0.138943i
$615$	12.4775	+	5.46864i	0.503140	+	0.220517i
$616$	−8.13466	+	3.29049i	−0.327755	+	0.132578i
$617$			3.55740i			0.143215i	0.997433	+	0.0716077i	$0.0228130\pi$
$617$			3.55740i			0.143215i	−0.997433	+	0.0716077i	$0.977187\pi$
$618$	0.990703	+	0.564329i	0.0398519	+	0.0227006i
$619$	16.3170	+	18.1219i	0.655837	+	0.728380i	0.975707	−	0.219081i	$-0.0703059\pi$
$619$	16.3170	+	18.1219i	0.655837	+	0.728380i	−0.319870	+	0.947461i	$0.603639\pi$
$620$	−4.74428	+	22.3201i	−0.190535	+	0.896396i
$621$	−0.426540	+	4.87465i	−0.0171165	+	0.195613i
$622$	17.7427	+	24.4208i	0.711419	+	0.979184i
$623$	−14.7630	−	8.86348i	−0.591469	−	0.355108i
$624$	3.63675	−	4.08654i	0.145586	−	0.163593i
$625$	2.84915	−	27.1078i	0.113966	−	1.08431i
$626$	3.67846	−	6.37128i	0.147021	−	0.254647i
$627$	16.0266	+	18.2193i	0.640042	+	0.727611i
$628$	−3.92277	−	6.79444i	−0.156536	−	0.271128i
$629$	6.49570	+	4.71940i	0.259000	+	0.188175i
$630$	−14.2698	−	19.8686i	−0.568522	−	0.791583i
$631$	4.73303	+	14.5668i	0.188419	+	0.579894i	0.999990	−	0.00435903i	$-0.00138753\pi$
$631$	4.73303	+	14.5668i	0.188419	+	0.579894i	−0.811571	+	0.584253i	$0.801388\pi$
$632$	−6.78735	+	15.2446i	−0.269986	+	0.606399i
$633$	6.53253	−	20.5100i	0.259645	−	0.815199i
$634$	−1.06031	+	4.98836i	−0.0421102	+	0.198113i
$635$	−6.60765	+	1.40450i	−0.262216	+	0.0557358i
$636$	5.26827	+	9.00362i	0.208900	+	0.357017i
$637$	−8.29638	−	20.4929i	−0.328715	−	0.811957i
$638$	−21.1017	+	8.95859i	−0.835424	+	0.354674i
$639$	29.5250	+	9.21515i	1.16799	+	0.364546i
$640$	1.25353	+	2.81547i	0.0495501	+	0.111291i
$641$	11.6753	−	10.5125i	0.461148	−	0.415220i	−0.405534	−	0.914080i	$-0.632915\pi$
$641$	11.6753	−	10.5125i	0.461148	−	0.415220i	0.866683	+	0.498860i	$0.166248\pi$
$642$	4.71401	+	10.4243i	0.186047	+	0.411415i
$643$	23.3131	−	16.9380i	0.919379	−	0.667968i	−0.0239904	−	0.999712i	$-0.507637\pi$
$643$	23.3131	−	16.9380i	0.919379	−	0.667968i	0.943369	+	0.331744i	$0.107637\pi$
$644$	−1.82279	−	1.69858i	−0.0718280	−	0.0669336i
$645$	−6.62616	−	0.657515i	−0.260905	−	0.0258896i
$646$	5.74787	+	27.0416i	0.226147	+	1.06394i
$647$	13.9072	+	31.2360i	0.546747	+	1.22801i	0.949806	+	0.312841i	$0.101281\pi$
$647$	13.9072	+	31.2360i	0.546747	+	1.22801i	−0.403058	+	0.915174i	$0.632053\pi$
$648$	7.40219	+	5.11934i	0.290785	+	0.201107i
$649$	−0.651740	+	37.4635i	−0.0255830	+	1.47057i
$650$		−	14.2070i		−	0.557244i
$651$	−32.1487	−	10.8485i	−1.26001	−	0.425185i
$652$	4.68477	−	14.4182i	0.183470	−	0.564661i
$653$	−16.5847	−	14.9329i	−0.649008	−	0.584369i	0.277463	−	0.960736i	$-0.410506\pi$
$653$	−16.5847	−	14.9329i	−0.649008	−	0.584369i	−0.926471	+	0.376367i	$0.877173\pi$
$654$	4.50556	−	14.1460i	0.176181	−	0.553152i
$655$	−34.5707	+	3.63353i	−1.35079	+	0.141974i
$656$	1.70770	−	1.89659i	0.0666743	−	0.0740493i
$657$	0.600129	+	1.30681i	0.0234133	+	0.0509834i
$658$	−15.6321	−	22.3083i	−0.609402	−	0.869667i
$659$	25.6988			1.00108			0.500541	−	0.865713i	$-0.333135\pi$
$659$	25.6988			1.00108			0.500541	+	0.865713i	$0.333135\pi$
$660$	2.05439	−	17.5847i	0.0799670	−	0.684482i
$661$	−3.56073	+	6.16737i	−0.138496	+	0.239883i	−0.926928	−	0.375240i	$-0.877560\pi$
$661$	−3.56073	+	6.16737i	−0.138496	+	0.239883i	0.788431	+	0.615123i	$0.210894\pi$
$662$	−20.7298	+	9.22949i	−0.805686	+	0.358714i
$663$	−35.0637	−	7.24024i	−1.36176	−	0.281187i
$664$	−3.79373	−	11.6759i	−0.147225	−	0.453113i
$665$	−10.0816	−	32.9341i	−0.390947	−	1.27713i
$666$	3.60856	+	0.723278i	0.139829	+	0.0280265i
$667$	−4.83724	−	4.35547i	−0.187299	−	0.168644i
$668$	5.38237	+	5.97773i	0.208250	+	0.231285i
$669$	−0.144900	−	24.9245i	−0.00560214	−	0.963637i
$670$	16.7855	−	9.69109i	0.648479	−	0.374400i
$671$	6.65145	−	28.8183i	0.256777	−	1.11252i
$672$	−4.37400	+	1.36680i	−0.168731	+	0.0527256i
$673$	22.0224	−	30.3112i	0.848901	−	1.16841i	−0.135203	−	0.990818i	$-0.543169\pi$
$673$	22.0224	−	30.3112i	0.848901	−	1.16841i	0.984104	−	0.177594i	$-0.0568313\pi$
$674$	−4.36266	−	20.5247i	−0.168044	−	0.790583i
$675$	23.1992	−	2.84820i	0.892938	−	0.109627i
$676$	−0.316172	−	3.00817i	−0.0121605	−	0.115699i
$677$	−20.1849	−	8.98688i	−0.775767	−	0.345394i	−0.0196304	−	0.999807i	$-0.506249\pi$
$677$	−20.1849	−	8.98688i	−0.775767	−	0.345394i	−0.756137	+	0.654413i	$0.772916\pi$
$678$	−1.14219	+	11.5106i	−0.0438657	+	0.442060i
$679$	−2.83439	+	23.1514i	−0.108774	+	0.888469i
$680$	11.8561	−	16.3185i	0.454661	−	0.625787i
$681$	−27.8978	+	3.09625i	−1.06904	+	0.118649i
$682$	−11.9065	−	21.4769i	−0.455923	−	0.822394i
$683$	26.0305	+	15.0287i	0.996031	+	0.575059i	0.907071	−	0.420977i	$-0.138313\pi$
$683$	26.0305	+	15.0287i	0.996031	+	0.575059i	0.0889592	+	0.996035i	$0.471646\pi$
$684$	7.56714	+	10.1646i	0.289337	+	0.388654i
$685$	13.2665	−	40.8299i	0.506885	−	1.56003i
$686$	−2.87796	+	18.2953i	−0.109881	+	0.698517i
$687$	2.92074	+	13.3587i	0.111433	+	0.509665i
$688$	−0.507366	+	1.13956i	−0.0193432	+	0.0434454i
$689$	−18.6063	−	3.95489i	−0.708843	−	0.150669i
$690$	4.77175	−	1.58116i	0.181657	−	0.0601938i
$691$	3.91547	−	37.2532i	0.148951	−	1.41718i	−0.623360	−	0.781935i	$-0.714233\pi$
$691$	3.91547	−	37.2532i	0.148951	−	1.41718i	0.772312	−	0.635244i	$-0.219100\pi$
$692$	13.8661			0.527108
$693$	25.6177	+	6.06068i	0.973137	+	0.230226i
$694$	−0.0989001			−0.00375420
$695$	5.13483	−	48.8546i	0.194775	−	1.85316i
$696$	−11.3643	+	3.76568i	−0.430764	+	0.142738i
$697$	−16.3383	−	3.47281i	−0.618856	−	0.131542i
$698$	1.50944	−	3.39027i	0.0571333	−	0.128324i
$699$	−5.46011	−	24.9731i	−0.206521	−	0.944568i
$700$	−6.12597	+	10.2034i	−0.231540	+	0.385653i
$701$	2.35501	−	7.24797i	0.0889474	−	0.273752i	−0.896682	−	0.442676i	$-0.854029\pi$
$701$	2.35501	−	7.24797i	0.0889474	−	0.273752i	0.985629	+	0.168924i	$0.0540292\pi$
$702$	−15.9908	+	3.69154i	−0.603532	+	0.139328i
$703$	4.48769	+	2.59097i	0.169256	+	0.0977202i
$704$	−3.00596	−	1.40149i	−0.113292	−	0.0528207i
$705$	54.6238	−	6.06246i	2.05725	−	0.228325i
$706$	−4.61468	+	6.35157i	−0.173676	+	0.239044i
$707$	−22.6531	−	17.0579i	−0.851957	−	0.641527i
$708$	−1.93221	+	19.4720i	−0.0726167	+	0.731802i
$709$	24.0158	+	10.6925i	0.901933	+	0.401566i	0.804691	−	0.593694i	$-0.202331\pi$
$709$	24.0158	+	10.6925i	0.901933	+	0.401566i	0.0972421	+	0.995261i	$0.468998\pi$
$710$	−3.32132	−	31.6002i	−0.124647	−	1.18593i
$711$	43.0610	−	25.5334i	1.61491	−	0.957577i
$712$	−1.35316	−	6.36611i	−0.0507118	−	0.238580i
$713$	4.09833	−	5.64087i	0.153484	−	0.211252i
$714$	22.0608	+	20.3192i	0.825603	+	0.760427i
$715$	21.1812	+	24.3634i	0.792133	+	0.911138i
$716$	−0.108472	+	0.0626262i	−0.00405378	+	0.00234045i
$717$	−0.0132575	−	2.28045i	−0.000495110	−	0.0851650i
$718$	23.8912	+	26.5339i	0.891611	+	0.990235i
$719$	−10.0853	−	9.08084i	−0.376118	−	0.338658i	0.459292	−	0.888285i	$-0.348103\pi$
$719$	−10.0853	−	9.08084i	−0.376118	−	0.338658i	−0.835410	+	0.549627i	$0.814770\pi$
$720$	1.81702	−	9.06545i	0.0677164	−	0.337849i
$721$	1.69712	+	0.391184i	0.0632040	+	0.0145685i
$722$	−0.357736	−	1.10100i	−0.0133135	−	0.0409749i
$723$	29.3429	+	6.05894i	1.09127	+	0.225335i
$724$	10.2364	−	4.55753i	0.380432	−	0.169379i
$725$	−15.5459	+	26.9263i	−0.577360	+	1.00002i
$726$	10.7475	+	15.7318i	0.398878	+	0.583863i
$727$	−9.71879			−0.360450			−0.180225	−	0.983625i	$-0.557683\pi$
$727$	−9.71879			−0.360450			−0.180225	+	0.983625i	$0.557683\pi$
$728$	3.52884	−	7.57457i	0.130788	−	0.280732i
$729$	−9.23389	−	25.3719i	−0.341996	−	0.939701i
$730$	0.988496	−	1.09784i	0.0365859	−	0.0406328i
$731$	8.11942	−	0.853385i	0.300308	−	0.0315636i
$732$	4.68745	−	14.7171i	0.173253	−	0.543958i
$733$	4.26339	+	3.83878i	0.157472	+	0.141789i	0.744100	−	0.668068i	$-0.232878\pi$
$733$	4.26339	+	3.83878i	0.157472	+	0.141789i	−0.586628	+	0.809856i	$0.699545\pi$
$734$	8.93276	−	27.4922i	0.329714	−	1.01476i
$735$	−29.5943	−	22.8126i	−1.09160	−	0.841457i
$736$		−	0.941712i		−	0.0347120i
$737$	−6.78964	+	19.7223i	−0.250099	+	0.726479i
$738$	−7.47001	+	1.67881i	−0.274975	+	0.0617977i
$739$	−4.39103	−	9.86241i	−0.161527	−	0.362794i	0.814592	−	0.580035i	$-0.196961\pi$
$739$	−4.39103	−	9.86241i	−0.161527	−	0.362794i	−0.976118	+	0.217240i	$0.930294\pi$
$740$	−0.786078	−	3.69821i	−0.0288968	−	0.135949i
$741$	−22.9943	−	2.28173i	−0.844718	−	0.0838214i
$742$	11.6577	+	10.8633i	0.427967	+	0.398805i
$743$	−17.7155	+	12.8711i	−0.649918	+	0.472193i	−0.863243	−	0.504788i	$-0.831571\pi$
$743$	−17.7155	+	12.8711i	−0.649918	+	0.472193i	0.213325	+	0.976981i	$0.431571\pi$
$744$	−5.28410	−	11.6850i	−0.193725	−	0.428393i
$745$	21.2553	−	19.1383i	0.778733	−	0.701175i
$746$	10.4313	+	23.4292i	0.381919	+	0.857804i
$747$	−10.9732	+	35.1577i	−0.401487	+	1.28635i
$748$	1.89315	+	21.6242i	0.0692203	+	0.790660i
$749$	11.4698	+	13.1852i	0.419098	+	0.481776i
$750$	1.35275	+	2.31188i	0.0493953	+	0.0844180i
$751$	−50.8622	+	10.8111i	−1.85599	+	0.394503i	−0.993715	−	0.111939i	$-0.964294\pi$
$751$	−50.8622	+	10.8111i	−1.85599	+	0.394503i	−0.862274	+	0.506442i	$0.830961\pi$
$752$	2.14061	−	10.0708i	0.0780601	−	0.367244i
$753$	2.79000	−	8.75968i	0.101673	−	0.319221i
$754$	8.87935	−	19.9433i	0.323367	−	0.726294i
$755$	12.7981	+	39.3885i	0.465770	+	1.43349i
$756$	13.0763	+	4.24386i	0.475580	+	0.154348i
$757$	−16.4528	−	11.9537i	−0.597988	−	0.434464i	0.247176	−	0.968971i	$-0.420497\pi$
$757$	−16.4528	−	11.9537i	−0.597988	−	0.434464i	−0.845164	+	0.534507i	$0.820497\pi$
$758$	0.0645249	+	0.111760i	0.00234365	+	0.00405932i
$759$	−2.75894	+	4.65332i	−0.100143	+	0.168905i
$760$	6.50904	−	11.2740i	0.236108	−	0.408950i
$761$	0.528610	−	5.02939i	0.0191621	−	0.182315i	−0.980754	−	0.195246i	$-0.937449\pi$
$761$	0.528610	−	5.02939i	0.0191621	−	0.182315i	0.999916	+	0.0129308i	$0.00411611\pi$
$762$	2.52390	−	2.83606i	0.0914313	−	0.102740i
$763$	0.387830	−	22.6746i	0.0140404	−	0.820875i
$764$	9.46804	+	13.0316i	0.342542	+	0.471468i
$765$	−57.3294	+	19.3672i	−2.07275	+	0.700223i
$766$	4.32943	−	20.3684i	0.156429	−	0.735939i
$767$	−23.8754	−	26.5163i	−0.862090	−	0.957448i
$768$	−1.50501	−	0.857291i	−0.0543073	−	0.0309348i
$769$			30.0408i			1.08330i	0.840605	+	0.541649i	$0.182200\pi$
$769$			30.0408i			1.08330i	−0.840605	+	0.541649i	$0.817800\pi$
$770$	−4.70699	−	26.6309i	−0.169628	−	0.959712i
$771$	−11.2681	−	4.93859i	−0.405811	−	0.177859i
$772$	−5.35261	−	0.562582i	−0.192645	−	0.0202478i
$773$	21.0556	−	18.9586i	0.757319	−	0.681893i	−0.197094	−	0.980385i	$-0.563150\pi$
$773$	21.0556	−	18.9586i	0.757319	−	0.681893i	0.954412	+	0.298492i	$0.0964836\pi$
$774$	3.21889	−	1.90867i	0.115700	−	0.0686056i
$775$	−30.4257	−	13.5464i	−1.09292	−	0.486601i
$776$	−7.13209	+	5.18176i	−0.256027	+	0.186014i
$777$	5.59728	−	0.524485i	0.200801	−	0.0188158i
$778$	−16.8832	−	5.48569i	−0.605293	−	0.196672i
$779$	−10.7211	−	1.12683i	−0.384124	−	0.0403730i
$780$	9.98887	+	13.5817i	0.357659	+	0.486305i
$781$	25.0093	+	23.3189i	0.894904	+	0.834414i
$782$	−5.33766	+	3.08170i	−0.190874	+	0.110201i
$783$	34.3465	+	10.5013i	1.22744	+	0.375284i
$784$	−5.80052	+	3.91842i	−0.207161	+	0.139944i
$785$	22.9959	−	7.47182i	0.820759	−	0.266681i
$786$	14.4418	−	13.1563i	0.515121	−	0.469268i
$787$	−21.4385	+	2.25328i	−0.764201	+	0.0803208i	−0.478606	−	0.878030i	$-0.658858\pi$
$787$	−21.4385	+	2.25328i	−0.764201	+	0.0803208i	−0.285595	+	0.958350i	$0.592191\pi$
$788$	20.6949	+	4.39883i	0.737224	+	0.156702i
$789$	2.27488	−	11.0170i	0.0809878	−	0.392216i
$790$	−41.6069	−	30.2292i	−1.48031	−	1.07551i
$791$	3.37749	+	17.3432i	0.120090	+	0.616653i
$792$	4.92515	+	8.64540i	0.175008	+	0.307201i
$793$	14.0823	+	24.3913i	0.500078	+	0.866160i
$794$	−12.2227	+	5.44189i	−0.433767	+	0.193126i
$795$	−30.5178	+	10.1123i	−1.08235	+	0.358648i
$796$	12.8274	−	14.2463i	0.454655	−	0.504946i
$797$	6.90639	+	9.50583i	0.244637	+	0.336714i	0.913624	−	0.406560i	$-0.133272\pi$
$797$	6.90639	+	9.50583i	0.244637	+	0.336714i	−0.668987	+	0.743274i	$0.733272\pi$
$798$	15.5306	+	11.5538i	0.549778	+	0.408998i
$799$	−64.0867	+	20.8230i	−2.26722	+	0.736665i
$800$	−4.39991	+	0.935231i	−0.155560	+	0.0330654i
$801$	−7.73361	+	17.9281i	−0.273254	+	0.633458i
$802$	−20.1635	−	11.6414i	−0.711996	−	0.411071i
$803$	−0.0276529	+	1.58955i	−0.000975850	+	0.0560940i
$804$	−4.37261	+	9.97672i	−0.154210	+	0.351852i
$805$	6.28848	−	4.40653i	0.221640	−	0.155310i
$806$	22.2402	+	7.22628i	0.783378	+	0.254535i
$807$	−33.6431	+	15.2138i	−1.18429	+	0.535553i
$808$	−1.12034	−	10.6593i	−0.0394134	−	0.374993i
$809$	4.24113	+	40.3516i	0.149110	+	1.41869i	0.771624	+	0.636079i	$0.219445\pi$
$809$	4.24113	+	40.3516i	0.149110	+	1.41869i	−0.622514	+	0.782609i	$0.713889\pi$
$810$	−20.1757	+	19.0341i	−0.708901	+	0.668790i
$811$	−35.8012	−	11.6325i	−1.25715	−	0.408473i	−0.396672	−	0.917961i	$-0.629835\pi$
$811$	−35.8012	−	11.6325i	−1.25715	−	0.408473i	−0.860478	+	0.509488i	$0.829835\pi$
$812$	−14.9766	+	10.4945i	−0.525575	+	0.368286i
$813$	−24.8144	−	10.8757i	−0.870277	−	0.381426i
$814$	3.24960	+	2.44845i	0.113898	+	0.0858182i
$815$	40.4629	+	23.3613i	1.41735	+	0.818310i
$816$	0.0659016	+	11.3359i	0.00230702	+	0.396835i
$817$	5.15393	−	1.09550i	0.180313	−	0.0383268i
$818$	7.28408	−	2.36674i	0.254682	−	0.0827511i
$819$	−21.7785	+	12.4153i	−0.761001	+	0.433826i
$820$	4.62316	+	6.36324i	0.161448	+	0.222214i
$821$	−23.0487	+	25.5982i	−0.804406	+	0.893383i	−0.996114	−	0.0880689i	$-0.971930\pi$
$821$	−23.0487	+	25.5982i	−0.804406	+	0.893383i	0.191709	+	0.981452i	$0.438597\pi$
$822$	7.58908	+	22.9029i	0.264699	+	0.798829i
$823$	21.7047	−	9.66356i	0.756579	−	0.336851i	0.00806310	−	0.999967i	$-0.497433\pi$
$823$	21.7047	−	9.66356i	0.756579	−	0.336851i	0.748516	+	0.663117i	$0.230767\pi$
$824$	0.329135	+	0.570079i	0.0114660	+	0.0198596i
$825$	24.4814	+	8.26916i	0.852334	+	0.287895i
$826$	5.71358	+	29.3389i	0.198801	+	1.02083i
$827$	−16.7875	−	12.1969i	−0.583760	−	0.424126i	0.256318	−	0.966593i	$-0.417491\pi$
$827$	−16.7875	−	12.1969i	−0.583760	−	0.424126i	−0.840078	+	0.542466i	$0.817491\pi$
$828$	−1.63389	+	2.30474i	−0.0567815	+	0.0800951i
$829$	−44.6026	−	9.48057i	−1.54911	−	0.329274i	−0.647584	−	0.761994i	$-0.724220\pi$
$829$	−44.6026	−	9.48057i	−1.54911	−	0.329274i	−0.901528	+	0.432721i	$0.857554\pi$
$830$	37.6287	−	3.95494i	1.30611	−	0.137278i
$831$	−5.89264	−	6.46841i	−0.204413	−	0.224387i
$832$	3.00378	−	0.975988i	0.104137	−	0.0338363i
$833$	41.1916	+	20.0547i	1.42721	+	0.694855i
$834$	13.9426	+	23.8284i	0.482794	+	0.825108i
$835$	−21.4691	+	12.3952i	−0.742969	+	0.428954i
$836$	2.67394	+	13.7519i	0.0924801	+	0.475621i
$837$	−7.34142	+	37.7657i	−0.253757	+	1.30537i
$838$	1.40234	+	0.147391i	0.0484429	+	0.00509155i
$839$	−11.1698	−	3.62928i	−0.385624	−	0.125297i	0.109788	−	0.993955i	$-0.464983\pi$
$839$	−11.1698	−	3.62928i	−0.385624	−	0.125297i	−0.495412	+	0.868658i	$0.664983\pi$
$840$	−1.31761	−	14.0615i	−0.0454620	−	0.485169i
$841$	−15.1902	+	11.0364i	−0.523802	+	0.380564i
$842$	−25.9098	−	11.5358i	−0.892912	−	0.397550i
$843$	−7.55822	+	10.5312i	−0.260319	+	0.362714i
$844$	9.23549	−	8.31567i	0.317899	−	0.286237i
$845$	9.27094	+	0.974415i	0.318930	+	0.0335209i
$846$	−22.7119	+	20.9331i	−0.780852	+	0.719696i
$847$	22.6260	+	18.3047i	0.777440	+	0.628957i
$848$			6.02273i			0.206821i
$849$	−8.13753	+	14.2858i	−0.279279	+	0.490286i
$850$	19.6994	+	21.8784i	0.675684	+	0.750423i
$851$	−0.240195	+	1.13003i	−0.00823376	+	0.0387368i
$852$	12.0258	+	13.2009i	0.411997	+	0.452254i
$853$	20.6310	+	28.3961i	0.706391	+	0.972264i	0.999867	+	0.0162977i	$0.00518794\pi$
$853$	20.6310	+	28.3961i	0.706391	+	0.972264i	−0.293476	+	0.955966i	$0.594812\pi$
$854$	0.403488	−	23.5900i	0.0138071	−	0.807232i
$855$	−35.4907	+	16.2985i	−1.21376	+	0.557398i
$856$	−0.690437	+	6.56907i	−0.0235987	+	0.224526i
$857$	12.2401	−	21.2004i	0.418112	−	0.724192i	−0.577637	−	0.816293i	$-0.696025\pi$
$857$	12.2401	−	21.2004i	0.418112	−	0.724192i	0.995750	+	0.0921019i	$0.0293585\pi$
$858$	−17.7021	−	3.97751i	−0.604338	−	0.135790i
$859$	−14.9776	−	25.9419i	−0.511028	−	0.885126i	−0.999918	−	0.0127809i	$-0.995932\pi$
$859$	−14.9776	−	25.9419i	−0.511028	−	0.885126i	0.488891	−	0.872345i	$-0.337402\pi$
$860$	−3.11019	−	2.25969i	−0.106057	−	0.0770546i
$861$	−10.1937	+	5.73291i	−0.347402	+	0.195377i
$862$	0.777457	+	2.39277i	0.0264803	+	0.0814980i
$863$	10.5892	−	23.7838i	0.360462	−	0.809611i	−0.638730	−	0.769431i	$-0.720540\pi$
$863$	10.5892	−	23.7838i	0.360462	−	0.809611i	0.999192	−	0.0401804i	$-0.0127933\pi$
$864$	2.19593	+	4.70934i	0.0747070	+	0.160215i
$865$	−8.88490	+	41.8002i	−0.302096	+	1.42125i
$866$	14.4552	−	3.07255i	0.491208	−	0.104409i
$867$	38.6226	−	22.5992i	1.31169	−	0.767508i
$868$	−12.8569	−	14.7797i	−0.436393	−	0.501657i
$869$	55.1347	−	4.82691i	1.87032	−	0.163742i
$870$	−4.07001	−	36.6715i	−0.137986	−	1.24328i
$871$	−8.07899	−	18.1457i	−0.273746	−	0.614844i
$872$	6.36982	−	5.73541i	0.215709	−	0.194226i
$873$	26.4454	−	0.307493i	0.895043	−	0.0104071i
$874$	−3.21812	+	2.33810i	−0.108854	+	0.0790874i
$875$	2.99337	+	2.78940i	0.101194	+	0.0942989i
$876$	−0.0819822	+	0.826183i	−0.00276992	+	0.0279141i
$877$	−4.67127	−	21.9766i	−0.157737	−	0.742096i	−0.983908	−	0.178676i	$-0.942819\pi$
$877$	−4.67127	−	21.9766i	−0.157737	−	0.742096i	0.826171	−	0.563420i	$-0.190515\pi$
$878$	−13.9691	−	31.3750i	−0.471433	−	1.05886i
$879$	24.0054	+	32.6399i	0.809683	+	1.10092i
$880$	6.15101	−	8.16366i	0.207351	−	0.275197i
$881$			7.69766i			0.259341i	0.991557	+	0.129670i	$0.0413919\pi$
$881$			7.69766i			0.259341i	−0.991557	+	0.129670i	$0.958608\pi$
$882$	20.9946	+	0.474100i	0.706927	+	0.0159638i
$883$	15.7346	−	48.4262i	0.529512	−	1.62967i	−0.225705	−	0.974196i	$-0.572468\pi$
$883$	15.7346	−	48.4262i	0.529512	−	1.62967i	0.755217	−	0.655475i	$-0.227532\pi$
$884$	−15.3616	−	13.8317i	−0.516668	−	0.465210i
$885$	−57.4615	−	18.3018i	−1.93155	−	0.615207i
$886$	0.431931	−	0.0453978i	0.0145110	−	0.00152517i
$887$	−31.6616	+	35.1638i	−1.06309	+	1.18069i	−0.0801494	+	0.996783i	$0.525540\pi$
$887$	−31.6616	+	35.1638i	−1.06309	+	1.18069i	−0.982944	+	0.183903i	$0.941127\pi$
$888$	1.58730	+	1.41259i	0.0532664	+	0.0474035i
$889$	2.44902	−	5.25675i	0.0821374	−	0.176306i
$890$	20.0581			0.672350
$891$	2.94615	−	29.7039i	0.0986999	−	0.995117i
$892$	7.19521	−	12.4625i	0.240913	−	0.417274i
$893$	−39.7297	+	17.6888i	−1.32950	+	0.591933i
$894$	−3.25058	+	15.7422i	−0.108716	+	0.526499i
$895$	−0.119286	−	0.367124i	−0.00398729	−	0.0122716i
$896$	−2.57815	−	0.594260i	−0.0861299	−	0.0198528i
$897$	−1.10035	−	5.03270i	−0.0367396	−	0.168037i
$898$	−17.7890	−	16.0173i	−0.593626	−	0.534503i
$899$	−34.2442	−	38.0320i	−1.14211	−	1.26844i
$900$	12.3909	+	5.34506i	0.413031	+	0.178169i
$901$	34.1371	−	19.7091i	1.13727	−	0.656604i
$902$	−8.24756	−	1.90359i	−0.274614	−	0.0633827i
$903$	3.87269	−	4.20462i	0.128875	−	0.139921i
$904$	−3.92538	+	5.40283i	−0.130556	+	0.179695i
$905$	7.17987	+	33.7786i	0.238667	+	1.12284i
$906$	−18.9096	−	13.5714i	−0.628231	−	0.450880i
$907$	−6.08487	−	57.8937i	−0.202045	−	1.92233i	−0.356440	−	0.934318i	$-0.616010\pi$
$907$	−6.08487	−	57.8937i	−0.202045	−	1.92233i	0.154396	−	0.988009i	$-0.450657\pi$
$908$	−14.8046	−	6.59145i	−0.491309	−	0.218745i
$909$	−15.7522	+	28.0313i	−0.522467	+	0.929739i
$910$	20.5729	+	15.4915i	0.681985	+	0.513537i
$911$	−12.1683	+	16.7483i	−0.403154	+	0.554894i	−0.961532	−	0.274692i	$-0.911424\pi$
$911$	−12.1683	+	16.7483i	−0.403154	+	0.554894i	0.558378	+	0.829587i	$0.311424\pi$
$912$	0.807039	+	7.27157i	0.0267237	+	0.240786i
$913$	−27.7675	+	29.7805i	−0.918970	+	0.985590i
$914$	1.33203	+	0.769047i	0.0440596	+	0.0254378i
$915$	41.3621	+	23.5609i	1.36739	+	0.778898i
$916$	−2.43963	+	7.50842i	−0.0806077	+	0.248085i
$917$	15.3606	−	25.5846i	0.507252	−	0.844880i
$918$	19.5067	−	27.8577i	0.643816	−	0.919440i
$919$	4.11659	−	9.24602i	0.135794	−	0.304998i	−0.832830	−	0.553529i	$-0.813281\pi$
$919$	4.11659	−	9.24602i	0.135794	−	0.304998i	0.968624	+	0.248531i	$0.0799476\pi$
$920$	2.83886	+	0.603418i	0.0935943	+	0.0198941i
$921$	−17.9441	−	54.1531i	−0.591279	−	1.78441i
$922$	2.78811	−	26.5270i	0.0918214	−	0.873622i
$923$	−32.5624			−1.07181
$924$	10.9985	+	10.4897i	0.361824	+	0.345084i
$925$	5.51831			0.181441
$926$	−2.26830	+	21.5815i	−0.0745411	+	0.709211i
$927$	0.183575	−	1.96626i	0.00602941	−	0.0645805i
$928$	−6.76099	−	1.43709i	−0.221940	−	0.0471749i
$929$	21.6246	−	48.5696i	0.709480	−	1.59352i	−0.0921829	−	0.995742i	$-0.529384\pi$
$929$	21.6246	−	48.5696i	0.709480	−	1.59352i	0.801663	−	0.597776i	$-0.203949\pi$
$930$	38.6111	−	8.44194i	1.26611	−	0.276822i
$931$	27.7920	+	10.0934i	0.910848	+	0.330798i
$932$	4.56072	−	14.0364i	0.149391	−	0.459779i
$933$	25.8780	−	45.4298i	0.847206	−	1.48731i
$934$	31.4165	+	18.1383i	1.02798	+	0.593504i
$935$	−66.4008	−	8.14906i	−2.17154	−	0.266503i
$936$	−9.04478	−	2.82299i	−0.295638	−	0.0922724i
$937$	18.8079	−	25.8869i	0.614428	−	0.845688i	−0.382504	−	0.923954i	$-0.624938\pi$
$937$	18.8079	−	25.8869i	0.614428	−	0.845688i	0.996933	+	0.0782658i	$0.0249383\pi$
$938$	−2.02201	+	16.5158i	−0.0660209	+	0.539261i
$939$	−12.6803	−	1.25826i	−0.413805	−	0.0410619i
$940$	28.9875	+	12.9060i	0.945467	+	0.420949i
$941$	2.16084	+	20.5590i	0.0704414	+	0.670205i	0.971586	+	0.236686i	$0.0760614\pi$
$941$	2.16084	+	20.5590i	0.0704414	+	0.670205i	−0.901145	+	0.433518i	$0.857272\pi$
$942$	−7.92330	+	11.0399i	−0.258155	+	0.359699i
$943$	−0.499685	−	2.35083i	−0.0162720	−	0.0765537i
$944$	−6.64043	+	9.13976i	−0.216127	+	0.297474i
$945$	−21.1723	+	36.7001i	−0.688734	+	1.19385i
$946$	4.12142	−	0.360820i	0.133999	−	0.0117313i
$947$	−12.8536	+	7.42105i	−0.417687	+	0.241152i	−0.694087	−	0.719891i	$-0.744192\pi$
$947$	−12.8536	+	7.42105i	−0.417687	+	0.241152i	0.276400	+	0.961043i	$0.410858\pi$
$948$	28.9028	−	0.168028i	0.938720	−	0.00545728i
$949$	−1.01302	−	1.12507i	−0.0328839	−	0.0365213i
$950$	14.1201	+	12.7138i	0.458118	+	0.412491i
$951$	8.62926	−	1.88670i	0.279823	−	0.0611806i
$952$	5.06856	+	16.5577i	0.164273	+	0.536639i
$953$	−2.80251	−	8.62523i	−0.0907822	−	0.279399i	0.895349	−	0.445364i	$-0.146926\pi$
$953$	−2.80251	−	8.62523i	−0.0907822	−	0.279399i	−0.986132	+	0.165966i	$0.946926\pi$
$954$	10.4495	−	14.7400i	0.338317	−	0.477224i
$955$	−45.3516	+	20.1918i	−1.46754	+	0.653392i
$956$	0.658321	−	1.14024i	0.0212916	−	0.0368782i
$957$	29.1981	+	26.9089i	0.943840	+	0.869840i
$958$	−5.92057			−0.191285
$959$	21.1499	+	30.1827i	0.682967	+	0.974651i
$960$	3.54872	−	3.98763i	0.114535	−	0.128700i
$961$	15.9389	−	17.7019i	0.514157	−	0.571029i
$962$	−3.85339	+	0.405007i	−0.124238	+	0.0130580i
$963$	13.0872	−	14.8792i	0.421730	−	0.479474i
$964$	12.8553	+	11.5750i	0.414041	+	0.372804i
$965$	5.12571	−	15.7753i	0.165003	−	0.507826i
$966$	−1.37980	+	4.08894i	−0.0443943	+	0.131559i
$967$		−	20.1273i		−	0.647250i	−0.946185	−	0.323625i	$-0.895098\pi$
$967$		−	20.1273i		−	0.647250i	0.946185	−	0.323625i	$-0.104902\pi$
$968$	0.768602	+	10.9731i	0.0247038	+	0.352689i
$969$	38.5745	−	28.3701i	1.23919	−	0.911380i
$970$	−11.0508	−	24.8205i	−0.354819	−	0.796937i
$971$	−3.99296	−	18.7854i	−0.128140	−	0.602851i	−0.994616	−	0.103632i	$-0.966954\pi$
$971$	−3.99296	−	18.7854i	−0.128140	−	0.602851i	0.866476	−	0.499219i	$-0.166380\pi$
$972$	2.79650	−	15.3356i	0.0896979	−	0.491888i
$973$	30.8524	+	28.7501i	0.989082	+	0.921685i
$974$	1.47582	−	1.07225i	0.0472885	−	0.0343571i
$975$	−22.4212	+	10.1392i	−0.718055	+	0.324713i
$976$	6.62698	−	5.96696i	0.212124	−	0.190998i
$977$	11.3042	+	25.3896i	0.361653	+	0.812286i	0.999125	+	0.0418131i	$0.0133134\pi$
$977$	11.3042	+	25.3896i	0.361653	+	0.812286i	−0.637472	+	0.770473i	$0.720020\pi$
$978$	−26.0980	+	2.89650i	−0.834523	+	0.0926200i
$979$	−16.2901	+	14.1624i	−0.520634	+	0.452634i
$980$	−8.09557	−	19.9969i	−0.258604	−	0.638776i
$981$	−25.5405	+	2.98503i	−0.815445	+	0.0953047i
$982$	−14.9644	+	3.18079i	−0.477534	+	0.101503i
$983$	4.58218	−	21.5574i	0.146149	−	0.687576i	−0.842667	−	0.538435i	$-0.819016\pi$
$983$	4.58218	−	21.5574i	0.146149	−	0.687576i	0.988816	−	0.149141i	$-0.0476508\pi$
$984$	−4.21191	−	1.34151i	−0.134271	−	0.0427658i
$985$	−26.5211	+	59.5675i	−0.845034	+	1.89798i
$986$	13.9795	+	43.0243i	0.445197	+	1.37017i
$987$	−24.0503	+	40.5912i	−0.765531	+	1.29203i
$988$	−10.7931	−	7.84164i	−0.343374	−	0.249476i
$989$	0.587349	+	1.01732i	0.0186766	+	0.0323489i
$990$	−29.2180	+	9.30753i	−0.928610	+	0.295813i
$991$	23.8211	−	41.2593i	0.756701	−	1.31065i	−0.187823	−	0.982203i	$-0.560143\pi$
$991$	23.8211	−	41.2593i	0.756701	−	1.31065i	0.944524	−	0.328442i	$-0.106524\pi$
$992$	0.773936	−	7.36351i	0.0245725	−	0.233792i
$993$	29.3602	+	26.1286i	0.931717	+	0.829165i
$994$	23.3863	+	14.0407i	0.741767	+	0.445345i
$995$	34.7270	+	47.7976i	1.10092	+	1.51529i
$996$	−15.7192	+	14.3200i	−0.498083	+	0.453747i
$997$	−0.0746478	+	0.351190i	−0.00236412	+	0.0111223i	−0.979314	−	0.202347i	$-0.935143\pi$
$997$	−0.0746478	+	0.351190i	−0.00236412	+	0.0111223i	0.976950	+	0.213469i	$0.0684764\pi$
$998$	−27.6948	−	30.7582i	−0.876664	−	0.973634i
$999$	−1.43388	−	6.21117i	−0.0453658	−	0.196513i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.bc.a.95.1	✓	128
3.2	odd	2		462.2.bc.b.95.10	yes	128
7.2	even	3	inner	462.2.bc.a.359.9	yes	128
11.8	odd	10		462.2.bc.b.305.13	yes	128
21.2	odd	6		462.2.bc.b.359.13	yes	128
33.8	even	10	inner	462.2.bc.a.305.9	yes	128
77.30	odd	30		462.2.bc.b.107.10	yes	128
231.107	even	30	inner	462.2.bc.a.107.1	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.bc.a.95.1	✓	128	1.1	even	1	trivial
462.2.bc.a.107.1	yes	128	231.107	even	30	inner
462.2.bc.a.305.9	yes	128	33.8	even	10	inner
462.2.bc.a.359.9	yes	128	7.2	even	3	inner
462.2.bc.b.95.10	yes	128	3.2	odd	2
462.2.bc.b.107.10	yes	128	77.30	odd	30
462.2.bc.b.305.13	yes	128	11.8	odd	10
462.2.bc.b.359.13	yes	128	21.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.bc (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.104528 - 0.994522i) q^{2} +(-1.64414 + 0.544800i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(1.25353 - 2.81547i) q^{5} +(0.369957 + 1.69208i) q^{6} +(1.28350 + 2.31358i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(2.40638 - 1.79146i) q^{9} +O(q^{10})\)	\(q+(0.104528 - 0.994522i) q^{2} +(-1.64414 + 0.544800i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(1.25353 - 2.81547i) q^{5} +(0.369957 + 1.69208i) q^{6} +(1.28350 + 2.31358i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(2.40638 - 1.79146i) q^{9} +(-2.66902 - 1.54096i) q^{10} +(3.25565 - 0.633032i) q^{11} +(1.72148 - 0.191060i) q^{12} +(-1.85644 + 2.55517i) q^{13} +(2.43506 - 1.03463i) q^{14} +(-0.527105 + 5.31195i) q^{15} +(0.913545 + 0.406737i) q^{16} +(-0.684127 - 6.50903i) q^{17} +(-1.53011 - 2.58046i) q^{18} +(-0.878223 - 4.13171i) q^{19} +(-1.81151 + 2.49332i) q^{20} +(-3.37069 - 3.10459i) q^{21} +(-0.289256 - 3.30399i) q^{22} +(0.815547 - 0.470856i) q^{23} +(-0.0100692 - 1.73202i) q^{24} +(-3.00989 - 3.34282i) q^{25} +(2.34712 + 2.11336i) q^{26} +(-2.98045 + 4.25640i) q^{27} +(-0.774430 - 2.52987i) q^{28} +(-2.13594 - 6.57373i) q^{29} +(5.22775 + 1.07947i) q^{30} +(6.76396 - 3.01151i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-5.00787 + 2.81447i) q^{33} -6.54489 q^{34} +(8.12271 - 0.713516i) q^{35} +(-2.72626 + 1.25199i) q^{36} +(-0.820875 + 0.911674i) q^{37} +(-4.20088 + 0.441530i) q^{38} +(1.66019 - 5.21244i) q^{39} +(2.29031 + 2.06220i) q^{40} +(0.788646 - 2.42720i) q^{41} +(-3.43992 + 3.02770i) q^{42} +1.24741i q^{43} +(-3.31612 - 0.0576896i) q^{44} +(-2.02732 - 9.02075i) q^{45} +(-0.383029 - 0.860297i) q^{46} +(-2.14061 - 10.0708i) q^{47} +(-1.72359 - 0.171032i) q^{48} +(-3.70527 + 5.93894i) q^{49} +(-3.63913 + 2.64398i) q^{50} +(4.67092 + 10.3290i) q^{51} +(2.34712 - 2.11336i) q^{52} +(2.44967 + 5.50204i) q^{53} +(3.92154 + 3.40903i) q^{54} +(2.29877 - 9.95972i) q^{55} +(-2.59696 + 0.505744i) q^{56} +(3.69488 + 6.31466i) q^{57} +(-6.76099 + 1.43709i) q^{58} +(-2.34885 + 11.0505i) q^{59} +(1.62000 - 5.08628i) q^{60} +(3.62706 - 8.14652i) q^{61} +(-2.28798 - 7.04169i) q^{62} +(7.23326 + 3.26803i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(4.86691 + 8.42973i) q^{65} +(2.27559 + 5.27463i) q^{66} +(-3.14450 + 5.44644i) q^{67} +(-0.684127 + 6.50903i) q^{68} +(-1.08435 + 1.21846i) q^{69} +(0.139447 - 8.15279i) q^{70} +(6.06001 + 8.34089i) q^{71} +(0.960161 + 2.84220i) q^{72} +(-0.0996603 + 0.468865i) q^{73} +(0.820875 + 0.911674i) q^{74} +(6.76985 + 3.85627i) q^{75} +4.22402i q^{76} +(5.64319 + 6.71970i) q^{77} +(-5.01035 - 2.19594i) q^{78} +(16.5959 + 1.74430i) q^{79} +(2.29031 - 2.06220i) q^{80} +(2.58138 - 8.62186i) q^{81} +(-2.33147 - 1.03804i) q^{82} +(-9.93212 + 7.21611i) q^{83} +(2.65155 + 3.73755i) q^{84} +(-19.1836 - 6.23312i) q^{85} +(1.24057 + 0.130390i) q^{86} +(7.09315 + 9.64447i) q^{87} +(-0.404003 + 3.29193i) q^{88} +(-5.63638 + 3.25417i) q^{89} +(-9.18324 + 1.07329i) q^{90} +(-8.29431 - 1.01546i) q^{91} +(-0.895621 + 0.291005i) q^{92} +(-9.48021 + 8.63634i) q^{93} +(-10.2394 + 1.07620i) q^{94} +(-12.7336 - 2.70661i) q^{95} +(-0.350258 + 1.69627i) q^{96} +(7.13209 + 5.18176i) q^{97} +(5.51910 + 4.30576i) q^{98} +(6.70030 - 7.35567i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q - 16 q^{2} + 16 q^{4} + 32 q^{8} - 4 q^{9}+O(q^{10}) \) 128 * q - 16 * q^2 + 16 * q^4 + 32 * q^8 - 4 * q^9	\( 128 q - 16 q^{2} + 16 q^{4} + 32 q^{8} - 4 q^{9} + 6 q^{11} - 12 q^{15} + 16 q^{16} + 2 q^{17} + 4 q^{18} + 2 q^{22} - 12 q^{25} - 18 q^{27} - 5 q^{28} - 38 q^{29} - 6 q^{30} - 3 q^{31} + 64 q^{32} - 4 q^{33} - 16 q^{34} + 31 q^{35} + 8 q^{36} + 2 q^{37} + 22 q^{39} + 5 q^{40} - 16 q^{41} + 17 q^{42} + q^{44} + 28 q^{45} + 38 q^{49} - 34 q^{50} + 16 q^{51} - 25 q^{53} + 6 q^{54} - 42 q^{55} + 20 q^{57} - 19 q^{58} - 40 q^{59} - 4 q^{60} + 40 q^{61} + 4 q^{62} + 6 q^{63} - 32 q^{64} - 20 q^{65} - 41 q^{66} + 16 q^{67} + 2 q^{68} - 68 q^{69} - 21 q^{70} - 80 q^{71} - 16 q^{72} + 10 q^{73} - 2 q^{74} - 14 q^{75} - q^{77} - 16 q^{78} + 5 q^{80} - 88 q^{81} - 8 q^{82} + 92 q^{83} - 48 q^{84} - 100 q^{85} + 40 q^{86} + 38 q^{87} - q^{88} - 164 q^{90} + 12 q^{91} + 20 q^{92} + 47 q^{93} + 40 q^{94} - 38 q^{95} - 16 q^{97} - 18 q^{98} - 138 q^{99}+O(q^{100}) \) 128 * q - 16 * q^2 + 16 * q^4 + 32 * q^8 - 4 * q^9 + 6 * q^11 - 12 * q^15 + 16 * q^16 + 2 * q^17 + 4 * q^18 + 2 * q^22 - 12 * q^25 - 18 * q^27 - 5 * q^28 - 38 * q^29 - 6 * q^30 - 3 * q^31 + 64 * q^32 - 4 * q^33 - 16 * q^34 + 31 * q^35 + 8 * q^36 + 2 * q^37 + 22 * q^39 + 5 * q^40 - 16 * q^41 + 17 * q^42 + q^44 + 28 * q^45 + 38 * q^49 - 34 * q^50 + 16 * q^51 - 25 * q^53 + 6 * q^54 - 42 * q^55 + 20 * q^57 - 19 * q^58 - 40 * q^59 - 4 * q^60 + 40 * q^61 + 4 * q^62 + 6 * q^63 - 32 * q^64 - 20 * q^65 - 41 * q^66 + 16 * q^67 + 2 * q^68 - 68 * q^69 - 21 * q^70 - 80 * q^71 - 16 * q^72 + 10 * q^73 - 2 * q^74 - 14 * q^75 - q^77 - 16 * q^78 + 5 * q^80 - 88 * q^81 - 8 * q^82 + 92 * q^83 - 48 * q^84 - 100 * q^85 + 40 * q^86 + 38 * q^87 - q^88 - 164 * q^90 + 12 * q^91 + 20 * q^92 + 47 * q^93 + 40 * q^94 - 38 * q^95 - 16 * q^97 - 18 * q^98 - 138 * q^99

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