LMFDB - Embedded newform 462.2.ba.a.19.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(19,462)]

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([0, 25, 9]))

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

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

chi := DirichletCharacter("462.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.ba (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:	$64$
Relative dimension:	$8$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			19.3
Character	$\chi$	$=$	462.19
Dual form			462.2.ba.a.73.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.994522 + 0.104528i) q^{2} +(0.743145 + 0.669131i) q^{3} +(0.978148 - 0.207912i) q^{4} +(-0.281694 - 0.632696i) q^{5} +(-0.809017 - 0.587785i) q^{6} +(-2.57173 - 0.621464i) q^{7} +(-0.951057 + 0.309017i) q^{8} +(0.104528 + 0.994522i) q^{9} +O(q^{10})$	\(q+(-0.994522 + 0.104528i) q^{2} +(0.743145 + 0.669131i) q^{3} +(0.978148 - 0.207912i) q^{4} +(-0.281694 - 0.632696i) q^{5} +(-0.809017 - 0.587785i) q^{6} +(-2.57173 - 0.621464i) q^{7} +(-0.951057 + 0.309017i) q^{8} +(0.104528 + 0.994522i) q^{9} +(0.346286 + 0.599785i) q^{10} +(0.415101 - 3.29055i) q^{11} +(0.866025 + 0.500000i) q^{12} +(5.05619 - 3.67354i) q^{13} +(2.62260 + 0.349240i) q^{14} +(0.214016 - 0.658675i) q^{15} +(0.913545 - 0.406737i) q^{16} +(0.110806 - 1.05425i) q^{17} +(-0.207912 - 0.978148i) q^{18} +(5.00902 + 1.06470i) q^{19} +(-0.407083 - 0.560302i) q^{20} +(-1.49533 - 2.18266i) q^{21} +(-0.0688715 + 3.31591i) q^{22} +(0.216245 - 0.374548i) q^{23} +(-0.913545 - 0.406737i) q^{24} +(3.02470 - 3.35927i) q^{25} +(-4.64450 + 4.18193i) q^{26} +(-0.587785 + 0.809017i) q^{27} +(-2.64474 - 0.0731908i) q^{28} +(-4.28660 - 1.39280i) q^{29} +(-0.143994 + 0.677437i) q^{30} +(-1.05414 + 2.36763i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(2.51029 - 2.16760i) q^{33} +1.06005i q^{34} +(0.331244 + 1.80218i) q^{35} +(0.309017 + 0.951057i) q^{36} +(6.04090 + 6.70910i) q^{37} +(-5.09287 - 0.535283i) q^{38} +(6.21556 + 0.653282i) q^{39} +(0.463421 + 0.514681i) q^{40} +(-3.40498 - 10.4795i) q^{41} +(1.71528 + 2.01440i) q^{42} -7.26185i q^{43} +(-0.278113 - 3.30494i) q^{44} +(0.599785 - 0.346286i) q^{45} +(-0.175910 + 0.395100i) q^{46} +(-2.14989 + 10.1144i) q^{47} +(0.951057 + 0.309017i) q^{48} +(6.22757 + 3.19647i) q^{49} +(-2.65699 + 3.65704i) q^{50} +(0.787774 - 0.709315i) q^{51} +(4.18193 - 4.64450i) q^{52} +(6.44459 + 2.86932i) q^{53} +(0.500000 - 0.866025i) q^{54} +(-2.19885 + 0.664295i) q^{55} +(2.63790 - 0.203661i) q^{56} +(3.01001 + 4.14292i) q^{57} +(4.40871 + 0.937100i) q^{58} +(-2.12421 - 9.99360i) q^{59} +(0.0723934 - 0.688778i) q^{60} +(6.97447 - 3.10523i) q^{61} +(0.800876 - 2.46484i) q^{62} +(0.349240 - 2.62260i) q^{63} +(0.809017 - 0.587785i) q^{64} +(-3.74853 - 2.16422i) q^{65} +(-2.26996 + 2.41812i) q^{66} +(-3.08471 - 5.34288i) q^{67} +(-0.110806 - 1.05425i) q^{68} +(0.411323 - 0.133647i) q^{69} +(-0.517808 - 1.75769i) q^{70} +(4.86924 + 3.53771i) q^{71} +(-0.406737 - 0.913545i) q^{72} +(-15.2813 + 3.24814i) q^{73} +(-6.70910 - 6.04090i) q^{74} +(4.49558 - 0.472505i) q^{75} +5.12093 q^{76} +(-3.11248 + 8.20442i) q^{77} -6.24980 q^{78} +(-4.63722 + 0.487392i) q^{79} +(-0.514681 - 0.463421i) q^{80} +(-0.978148 + 0.207912i) q^{81} +(4.48173 + 10.0661i) q^{82} +(-3.66608 - 2.66357i) q^{83} +(-1.91645 - 1.82407i) q^{84} +(-0.698231 + 0.226869i) q^{85} +(0.759070 + 7.22207i) q^{86} +(-2.25360 - 3.90335i) q^{87} +(0.622050 + 3.25777i) q^{88} +(-4.61490 - 2.66441i) q^{89} +(-0.560302 + 0.407083i) q^{90} +(-15.2861 + 6.30510i) q^{91} +(0.133647 - 0.411323i) q^{92} +(-2.36763 + 1.05414i) q^{93} +(1.08086 - 10.2837i) q^{94} +(-0.737381 - 3.46911i) q^{95} +(-0.978148 - 0.207912i) q^{96} +(0.312328 + 0.429883i) q^{97} +(-6.52757 - 2.52800i) q^{98} +(3.31591 + 0.0688715i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 8 q^{4} - 22 q^{5} - 16 q^{6} + 4 q^{7} - 8 q^{9}+O(q^{10}) $ 64 * q - 8 * q^4 - 22 * q^5 - 16 * q^6 + 4 * q^7 - 8 * q^9	$ 64 q - 8 q^{4} - 22 q^{5} - 16 q^{6} + 4 q^{7} - 8 q^{9} + 2 q^{10} + 4 q^{11} + 2 q^{14} - 6 q^{15} + 8 q^{16} + 30 q^{17} + 10 q^{19} + 20 q^{20} - 4 q^{21} - 2 q^{22} + 4 q^{23} - 8 q^{24} - 12 q^{26} - 10 q^{28} - 20 q^{29} + 18 q^{30} - 16 q^{31} - 14 q^{33} + 42 q^{35} - 16 q^{36} - 14 q^{37} + 12 q^{38} + 18 q^{39} + 18 q^{40} - 28 q^{41} - 6 q^{42} + 6 q^{44} - 12 q^{45} - 42 q^{46} + 24 q^{47} + 116 q^{49} + 26 q^{51} + 32 q^{54} - 14 q^{55} - 4 q^{56} + 20 q^{58} + 30 q^{59} + 2 q^{60} - 32 q^{61} - 8 q^{62} + 4 q^{63} + 16 q^{64} + 12 q^{65} + 4 q^{66} + 16 q^{67} - 30 q^{68} - 20 q^{70} - 24 q^{71} - 64 q^{73} + 4 q^{74} + 12 q^{75} - 48 q^{77} - 60 q^{79} - 18 q^{80} + 8 q^{81} - 68 q^{82} + 8 q^{83} + 2 q^{84} - 80 q^{85} - 18 q^{86} + 10 q^{87} - 8 q^{88} - 24 q^{89} + 4 q^{90} - 172 q^{91} + 8 q^{92} - 104 q^{93} - 6 q^{94} - 118 q^{95} + 8 q^{96} + 120 q^{97} + 40 q^{98} + 8 q^{99}+O(q^{100}) $ 64 * q - 8 * q^4 - 22 * q^5 - 16 * q^6 + 4 * q^7 - 8 * q^9 + 2 * q^10 + 4 * q^11 + 2 * q^14 - 6 * q^15 + 8 * q^16 + 30 * q^17 + 10 * q^19 + 20 * q^20 - 4 * q^21 - 2 * q^22 + 4 * q^23 - 8 * q^24 - 12 * q^26 - 10 * q^28 - 20 * q^29 + 18 * q^30 - 16 * q^31 - 14 * q^33 + 42 * q^35 - 16 * q^36 - 14 * q^37 + 12 * q^38 + 18 * q^39 + 18 * q^40 - 28 * q^41 - 6 * q^42 + 6 * q^44 - 12 * q^45 - 42 * q^46 + 24 * q^47 + 116 * q^49 + 26 * q^51 + 32 * q^54 - 14 * q^55 - 4 * q^56 + 20 * q^58 + 30 * q^59 + 2 * q^60 - 32 * q^61 - 8 * q^62 + 4 * q^63 + 16 * q^64 + 12 * q^65 + 4 * q^66 + 16 * q^67 - 30 * q^68 - 20 * q^70 - 24 * q^71 - 64 * q^73 + 4 * q^74 + 12 * q^75 - 48 * q^77 - 60 * q^79 - 18 * q^80 + 8 * q^81 - 68 * q^82 + 8 * q^83 + 2 * q^84 - 80 * q^85 - 18 * q^86 + 10 * q^87 - 8 * q^88 - 24 * q^89 + 4 * q^90 - 172 * q^91 + 8 * q^92 - 104 * q^93 - 6 * q^94 - 118 * q^95 + 8 * q^96 + 120 * q^97 + 40 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{10}\right)$

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 $

$2$	−0.994522	+	0.104528i	−0.703233	+	0.0739128i
$2$	−0.994522	+	0.104528i	−0.703233	+	0.0739128i
$3$	0.743145	+	0.669131i	0.429055	+	0.386323i
$3$	0.743145	+	0.669131i	0.429055	+	0.386323i
$4$	0.978148	−	0.207912i	0.489074	−	0.103956i
$5$	−0.281694	−	0.632696i	−0.125977	−	0.282950i	0.839536	−	0.543305i	$-0.182827\pi$
$5$	−0.281694	−	0.632696i	−0.125977	−	0.282950i	−0.965513	+	0.260355i	$0.916161\pi$
$6$	−0.809017	−	0.587785i	−0.330280	−	0.239962i
$7$	−2.57173	−	0.621464i	−0.972022	−	0.234891i
$7$	−2.57173	−	0.621464i	−0.972022	−	0.234891i
$8$	−0.951057	+	0.309017i	−0.336249	+	0.109254i
$9$	0.104528	+	0.994522i	0.0348428	+	0.331507i
$10$	0.346286	+	0.599785i	0.109505	+	0.189669i
$11$	0.415101	−	3.29055i	0.125158	−	0.992137i
$11$	0.415101	−	3.29055i	0.125158	−	0.992137i
$12$	0.866025	+	0.500000i	0.250000	+	0.144338i
$13$	5.05619	−	3.67354i	1.40234	−	1.01886i	0.407953	−	0.913003i	$-0.366243\pi$
$13$	5.05619	−	3.67354i	1.40234	−	1.01886i	0.994382	−	0.105853i	$-0.0337574\pi$
$14$	2.62260	+	0.349240i	0.700919	+	0.0933384i
$15$	0.214016	−	0.658675i	0.0552588	−	0.170069i
$16$	0.913545	−	0.406737i	0.228386	−	0.101684i
$17$	0.110806	−	1.05425i	0.0268744	−	0.255693i	−0.972833	−	0.231507i	$-0.925634\pi$
$17$	0.110806	−	1.05425i	0.0268744	−	0.255693i	0.999707	−	0.0241851i	$-0.00769910\pi$
$18$	−0.207912	−	0.978148i	−0.0490053	−	0.230552i
$19$	5.00902	+	1.06470i	1.14915	+	0.244259i	0.742835	−	0.669475i	$-0.233481\pi$
$19$	5.00902	+	1.06470i	1.14915	+	0.244259i	0.406314	+	0.913734i	$0.366814\pi$
$20$	−0.407083	−	0.560302i	−0.0910266	−	0.125287i
$21$	−1.49533	−	2.18266i	−0.326307	−	0.476295i
$22$	−0.0688715	+	3.31591i	−0.0146835	+	0.706954i
$23$	0.216245	−	0.374548i	0.0450903	−	0.0780986i	−0.842599	−	0.538541i	$-0.818976\pi$
$23$	0.216245	−	0.374548i	0.0450903	−	0.0780986i	0.887690	+	0.460442i	$0.152309\pi$
$24$	−0.913545	−	0.406737i	−0.186477	−	0.0830248i
$25$	3.02470	−	3.35927i	0.604940	−	0.671854i
$26$	−4.64450	+	4.18193i	−0.910862	+	0.820144i
$27$	−0.587785	+	0.809017i	−0.113119	+	0.155695i
$28$	−2.64474	−	0.0731908i	−0.499809	−	0.0138318i
$29$	−4.28660	−	1.39280i	−0.796002	−	0.258637i	−0.117344	−	0.993091i	$-0.537438\pi$
$29$	−4.28660	−	1.39280i	−0.796002	−	0.258637i	−0.678658	+	0.734454i	$0.737438\pi$
$30$	−0.143994	+	0.677437i	−0.0262895	+	0.123683i
$31$	−1.05414	+	2.36763i	−0.189328	+	0.425238i	−0.983123	−	0.182948i	$-0.941436\pi$
$31$	−1.05414	+	2.36763i	−0.189328	+	0.425238i	0.793794	+	0.608186i	$0.208103\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	2.51029	−	2.16760i	0.436985	−	0.377330i
$34$			1.06005i			0.181798i
$35$	0.331244	+	1.80218i	0.0559904	+	0.304625i
$36$	0.309017	+	0.951057i	0.0515028	+	0.158509i
$37$	6.04090	+	6.70910i	0.993118	+	1.10297i	0.994684	+	0.102971i	$0.0328348\pi$
$37$	6.04090	+	6.70910i	0.993118	+	1.10297i	−0.00156617	+	0.999999i	$0.500499\pi$
$38$	−5.09287	−	0.535283i	−0.826173	−	0.0868343i
$39$	6.21556	+	0.653282i	0.995286	+	0.104609i
$40$	0.463421	+	0.514681i	0.0732733	+	0.0813782i
$41$	−3.40498	−	10.4795i	−0.531769	−	1.63662i	−0.750529	−	0.660837i	$-0.770201\pi$
$41$	−3.40498	−	10.4795i	−0.531769	−	1.63662i	0.218761	−	0.975779i	$-0.429799\pi$
$42$	1.71528	+	2.01440i	0.264674	+	0.310828i
$43$		−	7.26185i		−	1.10742i	−0.832709	−	0.553711i	$-0.813211\pi$
$43$		−	7.26185i		−	1.10742i	0.832709	−	0.553711i	$-0.186789\pi$
$44$	−0.278113	−	3.30494i	−0.0419271	−	0.498239i
$45$	0.599785	−	0.346286i	0.0894106	−	0.0516212i
$46$	−0.175910	+	0.395100i	−0.0259365	+	0.0582543i
$47$	−2.14989	+	10.1144i	−0.313593	+	1.47534i	0.485556	+	0.874206i	$0.338617\pi$
$47$	−2.14989	+	10.1144i	−0.313593	+	1.47534i	−0.799149	+	0.601133i	$0.794716\pi$
$48$	0.951057	+	0.309017i	0.137273	+	0.0446028i
$49$	6.22757	+	3.19647i	0.889652	+	0.456639i
$50$	−2.65699	+	3.65704i	−0.375755	+	0.517183i
$51$	0.787774	−	0.709315i	0.110310	−	0.0993239i
$52$	4.18193	−	4.64450i	0.579929	−	0.644077i
$53$	6.44459	+	2.86932i	0.885233	+	0.394131i	0.798425	−	0.602094i	$-0.205667\pi$
$53$	6.44459	+	2.86932i	0.885233	+	0.394131i	0.0868077	+	0.996225i	$0.472333\pi$
$54$	0.500000	−	0.866025i	0.0680414	−	0.117851i
$55$	−2.19885	+	0.664295i	−0.296492	+	0.0895735i
$56$	2.63790	−	0.203661i	0.352504	−	0.0272153i
$57$	3.01001	+	4.14292i	0.398685	+	0.548743i
$58$	4.40871	+	0.937100i	0.578892	+	0.123047i
$59$	−2.12421	−	9.99360i	−0.276548	−	1.30106i	−0.868744	−	0.495262i	$-0.835072\pi$
$59$	−2.12421	−	9.99360i	−0.276548	−	1.30106i	0.592195	−	0.805794i	$-0.298261\pi$
$60$	0.0723934	−	0.688778i	0.00934595	−	0.0889208i
$61$	6.97447	−	3.10523i	0.892989	−	0.397584i	0.0916475	−	0.995792i	$-0.470787\pi$
$61$	6.97447	−	3.10523i	0.892989	−	0.397584i	0.801341	+	0.598207i	$0.204120\pi$
$62$	0.800876	−	2.46484i	0.101711	−	0.313036i
$63$	0.349240	−	2.62260i	0.0440002	−	0.330417i
$64$	0.809017	−	0.587785i	0.101127	−	0.0734732i
$65$	−3.74853	−	2.16422i	−0.464948	−	0.268438i
$66$	−2.26996	+	2.41812i	−0.279413	+	0.297650i
$67$	−3.08471	−	5.34288i	−0.376858	−	0.652736i	0.613746	−	0.789504i	$-0.289662\pi$
$67$	−3.08471	−	5.34288i	−0.376858	−	0.652736i	−0.990603	+	0.136767i	$0.956329\pi$
$68$	−0.110806	−	1.05425i	−0.0134372	−	0.127846i
$69$	0.411323	−	0.133647i	0.0495175	−	0.0160892i
$70$	−0.517808	−	1.75769i	−0.0618899	−	0.210084i
$71$	4.86924	+	3.53771i	0.577873	+	0.419849i	0.837957	−	0.545737i	$-0.183750\pi$
$71$	4.86924	+	3.53771i	0.577873	+	0.419849i	−0.260084	+	0.965586i	$0.583750\pi$
$72$	−0.406737	−	0.913545i	−0.0479344	−	0.107662i
$73$	−15.2813	+	3.24814i	−1.78854	+	0.380166i	−0.978506	−	0.206216i	$-0.933885\pi$
$73$	−15.2813	+	3.24814i	−1.78854	+	0.380166i	−0.810034	+	0.586382i	$0.800552\pi$
$74$	−6.70910	−	6.04090i	−0.779917	−	0.702241i
$75$	4.49558	−	0.472505i	0.519105	−	0.0545601i
$76$	5.12093			0.587411
$77$	−3.11248	+	8.20442i	−0.354700	+	0.934980i
$78$	−6.24980			−0.707650
$79$	−4.63722	+	0.487392i	−0.521728	+	0.0548358i	−0.361733	−	0.932282i	$-0.617815\pi$
$79$	−4.63722	+	0.487392i	−0.521728	+	0.0548358i	−0.159996	+	0.987118i	$0.551148\pi$
$80$	−0.514681	−	0.463421i	−0.0575431	−	0.0518120i
$81$	−0.978148	+	0.207912i	−0.108683	+	0.0231013i
$82$	4.48173	+	10.0661i	0.494924	+	1.11162i
$83$	−3.66608	−	2.66357i	−0.402405	−	0.292364i	0.368115	−	0.929780i	$-0.380003\pi$
$83$	−3.66608	−	2.66357i	−0.402405	−	0.292364i	−0.770520	+	0.637416i	$0.780003\pi$
$84$	−1.91645	−	1.82407i	−0.209102	−	0.199022i
$85$	−0.698231	+	0.226869i	−0.0757338	+	0.0246074i
$86$	0.759070	+	7.22207i	0.0818526	+	0.778776i
$87$	−2.25360	−	3.90335i	−0.241611	−	0.418483i
$88$	0.622050	+	3.25777i	0.0663107	+	0.347279i
$89$	−4.61490	−	2.66441i	−0.489179	−	0.282427i	0.235055	−	0.971982i	$-0.424473\pi$
$89$	−4.61490	−	2.66441i	−0.489179	−	0.282427i	−0.724234	+	0.689555i	$0.757806\pi$
$90$	−0.560302	+	0.407083i	−0.0590610	+	0.0429104i
$91$	−15.2861	+	6.30510i	−1.60242	+	0.660954i
$92$	0.133647	−	0.411323i	0.0139337	−	0.0428834i
$93$	−2.36763	+	1.05414i	−0.245512	+	0.109309i
$94$	1.08086	−	10.2837i	0.111483	−	1.06069i
$95$	−0.737381	−	3.46911i	−0.0756537	−	0.355923i
$96$	−0.978148	−	0.207912i	−0.0998318	−	0.0212199i
$97$	0.312328	+	0.429883i	0.0317121	+	0.0436480i	0.824579	−	0.565747i	$-0.191412\pi$
$97$	0.312328	+	0.429883i	0.0317121	+	0.0436480i	−0.792867	+	0.609395i	$0.791412\pi$
$98$	−6.52757	−	2.52800i	−0.659384	−	0.255367i
$99$	3.31591	+	0.0688715i	0.333261	+	0.00692185i
$100$	2.26017	−	3.91473i	0.226017	−	0.391473i
$101$	7.47963	+	3.33015i	0.744251	+	0.331362i	0.743588	−	0.668638i	$-0.233122\pi$
$101$	7.47963	+	3.33015i	0.744251	+	0.331362i	0.000662720		1.00000i	$0.499789\pi$
$102$	−0.709315	+	0.787774i	−0.0702326	+	0.0780012i
$103$	−9.25423	+	8.33255i	−0.911846	+	0.821030i	−0.984329	−	0.176339i	$-0.943574\pi$
$103$	−9.25423	+	8.33255i	−0.911846	+	0.821030i	0.0724830	+	0.997370i	$0.476908\pi$
$104$	−3.67354	+	5.05619i	−0.360220	+	0.495800i
$105$	−0.959734	+	1.56093i	−0.0936605	+	0.152331i
$106$	−6.70921	−	2.17996i	−0.651657	−	0.211736i
$107$	−3.31799	+	15.6099i	−0.320762	+	1.50907i	0.462074	+	0.886841i	$0.347105\pi$
$107$	−3.31799	+	15.6099i	−0.320762	+	1.50907i	−0.782837	+	0.622227i	$0.786228\pi$
$108$	−0.406737	+	0.913545i	−0.0391383	+	0.0879060i
$109$	10.2451	−	5.91499i	0.981299	−	0.566553i	0.0786369	−	0.996903i	$-0.474943\pi$
$109$	10.2451	−	5.91499i	0.981299	−	0.566553i	0.902662	+	0.430350i	$0.141610\pi$
$110$	2.11736	−	0.890498i	0.201883	−	0.0849056i
$111$			9.02799i			0.856899i
$112$	−2.60216	+	0.478281i	−0.245881	+	0.0451933i
$113$	4.51202	+	13.8866i	0.424456	+	1.30634i	0.903515	+	0.428557i	$0.140978\pi$
$113$	4.51202	+	13.8866i	0.424456	+	1.30634i	−0.479059	+	0.877783i	$0.659022\pi$
$114$	−3.42657	−	3.80559i	−0.320928	−	0.356426i
$115$	−0.297890	−	0.0313095i	−0.0277784	−	0.00291962i
$116$	−4.48251	−	0.471131i	−0.416191	−	0.0437434i
$117$	4.18193	+	4.64450i	0.386620	+	0.429385i
$118$	3.15719	+	9.71682i	0.290643	+	0.894506i
$119$	−0.940139	+	2.64238i	−0.0861824	+	0.242226i
$120$			0.692572i			0.0632228i
$121$	−10.6554	−	2.73182i	−0.968671	−	0.248347i
$122$	−6.61168	+	3.81725i	−0.598593	+	0.345598i
$123$	4.48173	−	10.0661i	0.404104	−	0.907632i
$124$	−0.538843	+	2.53506i	−0.0483895	+	0.227655i
$125$	−6.27081	−	2.03751i	−0.560878	−	0.182240i
$126$	−0.0731908	+	2.64474i	−0.00652036	+	0.235612i
$127$	−8.16001	+	11.2313i	−0.724084	+	0.996616i	0.275295	+	0.961360i	$0.411225\pi$
$127$	−8.16001	+	11.2313i	−0.724084	+	0.996616i	−0.999378	+	0.0352558i	$0.988775\pi$
$128$	−0.743145	+	0.669131i	−0.0656853	+	0.0591433i
$129$	4.85913	−	5.39661i	0.427822	−	0.475145i
$130$	3.95422	+	1.76053i	0.346808	+	0.154409i
$131$	4.77062	−	8.26296i	0.416811	−	0.721938i	−0.578806	−	0.815466i	$-0.696481\pi$
$131$	4.77062	−	8.26296i	0.416811	−	0.721938i	0.995617	+	0.0935275i	$0.0298143\pi$
$132$	2.00476	−	2.64215i	0.174492	−	0.229969i
$133$	−12.2202	−	5.85104i	−1.05962	−	0.507350i
$134$	3.62630	+	4.99117i	0.313264	+	0.431171i
$135$	0.677437	+	0.143994i	0.0583045	+	0.0123930i
$136$	0.220398	+	1.03689i	0.0188989	+	0.0889126i
$137$	0.485559	−	4.61979i	0.0414841	−	0.394695i	−0.954003	−	0.299797i	$-0.903081\pi$
$137$	0.485559	−	4.61979i	0.0414841	−	0.394695i	0.995487	−	0.0948977i	$-0.0302524\pi$
$138$	−0.395100	+	0.175910i	−0.0336331	+	0.0149744i
$139$	−4.49981	+	13.8490i	−0.381669	+	1.17466i	0.557199	+	0.830379i	$0.311876\pi$
$139$	−4.49981	+	13.8490i	−0.381669	+	1.17466i	−0.938868	+	0.344278i	$0.888124\pi$
$140$	0.698700	+	1.69393i	0.0590509	+	0.143163i
$141$	−8.36554	+	6.07792i	−0.704506	+	0.511853i
$142$	−5.21236	−	3.00936i	−0.437412	−	0.252540i
$143$	−9.98911	−	18.1625i	−0.835332	−	1.51883i
$144$	0.500000	+	0.866025i	0.0416667	+	0.0721688i
$145$	0.326292	+	3.10446i	0.0270971	+	0.257811i
$146$	14.8581	−	4.82768i	1.22966	−	0.399541i
$147$	2.48913	+	6.54250i	0.205300	+	0.539616i
$148$	7.30379	+	5.30652i	0.600368	+	0.436193i
$149$	2.38977	+	5.36752i	0.195778	+	0.439724i	0.984583	−	0.174919i	$-0.0559665\pi$
$149$	2.38977	+	5.36752i	0.195778	+	0.439724i	−0.788805	+	0.614644i	$0.789300\pi$
$150$	−4.42156	+	0.939833i	−0.361019	+	0.0767370i
$151$	−0.515989	−	0.464599i	−0.0419906	−	0.0378085i	0.647868	−	0.761752i	$-0.275661\pi$
$151$	−0.515989	−	0.464599i	−0.0419906	−	0.0378085i	−0.689859	+	0.723944i	$0.742327\pi$
$152$	−5.09287	+	0.535283i	−0.413087	+	0.0434172i
$153$	1.06005			0.0857003
$154$	2.23784	−	8.48482i	0.180330	−	0.683726i
$155$	1.79493			0.144172
$156$	6.21556	−	0.653282i	0.497643	−	0.0523044i
$157$	−0.0895886	−	0.0806660i	−0.00714995	−	0.00643784i	0.665548	−	0.746355i	$-0.268198\pi$
$157$	−0.0895886	−	0.0806660i	−0.00714995	−	0.00643784i	−0.672698	+	0.739917i	$0.734865\pi$
$158$	4.56087	−	0.969443i	0.362844	−	0.0771248i
$159$	2.86932	+	6.44459i	0.227552	+	0.511089i
$160$	0.560302	+	0.407083i	0.0442958	+	0.0321828i
$161$	−0.788892	+	0.828846i	−0.0621734	+	0.0653223i
$162$	0.951057	−	0.309017i	0.0747221	−	0.0242787i
$163$	−0.140825	−	1.33986i	−0.0110303	−	0.104946i	0.987621	−	0.156856i	$-0.0501359\pi$
$163$	−0.140825	−	1.33986i	−0.0110303	−	0.104946i	−0.998652	+	0.0519097i	$0.983469\pi$
$164$	−5.50937	−	9.54252i	−0.430210	−	0.745145i
$165$	−2.07856	−	0.977647i	−0.161816	−	0.0761097i
$166$	3.92442	+	2.26576i	0.304594	+	0.175857i
$167$	−2.27940	+	1.65608i	−0.176385	+	0.128151i	−0.672475	−	0.740120i	$-0.734769\pi$
$167$	−2.27940	+	1.65608i	−0.176385	+	0.128151i	0.496090	+	0.868271i	$0.334769\pi$
$168$	2.09662	+	1.61375i	0.161758	+	0.124504i
$169$	8.05297	−	24.7845i	0.619459	−	1.90650i
$170$	0.670692	−	0.298611i	0.0514397	−	0.0229024i
$171$	−0.535283	+	5.09287i	−0.0409341	+	0.389462i
$172$	−1.50982	−	7.10316i	−0.115123	−	0.541611i
$173$	−10.5327	−	2.23879i	−0.800786	−	0.170212i	−0.210698	−	0.977551i	$-0.567574\pi$
$173$	−10.5327	−	2.23879i	−0.800786	−	0.170212i	−0.590088	+	0.807339i	$0.700907\pi$
$174$	2.64927	+	3.64640i	0.200840	+	0.276433i
$175$	−9.86637	+	6.75939i	−0.745828	+	0.510962i
$176$	−0.959172	−	3.17490i	−0.0723003	−	0.239317i
$177$	5.10843	−	8.84807i	0.383973	−	0.665061i
$178$	4.86813	+	2.16743i	0.364882	+	0.162456i
$179$	−5.67566	+	6.30346i	−0.424219	+	0.471142i	−0.916929	−	0.399051i	$-0.869340\pi$
$179$	−5.67566	+	6.30346i	−0.424219	+	0.471142i	0.492710	+	0.870193i	$0.336006\pi$
$180$	0.514681	−	0.463421i	0.0383621	−	0.0345413i
$181$	15.1335	−	20.8295i	1.12486	−	1.54824i	0.327390	−	0.944889i	$-0.393831\pi$
$181$	15.1335	−	20.8295i	1.12486	−	1.54824i	0.797474	−	0.603353i	$-0.206169\pi$
$182$	14.5433	−	7.86840i	1.07802	−	0.583244i
$183$	7.26085	+	2.35919i	0.536737	+	0.174396i
$184$	−0.0899199	+	0.423040i	−0.00662898	+	0.0311869i
$185$	2.54313	−	5.71197i	0.186975	−	0.419952i
$186$	2.24447	−	1.29585i	0.164573	−	0.0950160i
$187$	−3.42305	−	0.802231i	−0.250318	−	0.0586649i
$188$			10.3404i			0.754150i
$189$	2.01440	−	1.71528i	0.146526	−	0.124769i
$190$	1.09596	+	3.37302i	0.0795094	+	0.244705i
$191$	14.6730	+	16.2960i	1.06170	+	1.17914i	0.983258	+	0.182217i	$0.0583273\pi$
$191$	14.6730	+	16.2960i	1.06170	+	1.17914i	0.0784401	+	0.996919i	$0.475006\pi$
$192$	0.994522	+	0.104528i	0.0717734	+	0.00754369i
$193$	5.68195	+	0.597197i	0.408995	+	0.0429872i	0.306793	−	0.951776i	$-0.400744\pi$
$193$	5.68195	+	0.597197i	0.408995	+	0.0429872i	0.102203	+	0.994764i	$0.467411\pi$
$194$	−0.355553	−	0.394881i	−0.0255272	−	0.0283508i
$195$	−1.33756	−	4.11658i	−0.0957846	−	0.294795i
$196$	6.75606	+	1.83184i	0.482576	+	0.130845i
$197$			6.81931i			0.485856i	0.970044	+	0.242928i	$0.0781078\pi$
$197$			6.81931i			0.485856i	−0.970044	+	0.242928i	$0.921892\pi$
$198$	−3.30494	+	0.278113i	−0.234872	+	0.0197646i
$199$	−6.16050	+	3.55677i	−0.436706	+	0.252133i	−0.702200	−	0.711980i	$-0.747799\pi$
$199$	−6.16050	+	3.55677i	−0.436706	+	0.252133i	0.265493	+	0.964113i	$0.414465\pi$
$200$	−1.83859	+	4.12954i	−0.130008	+	0.292003i
$201$	1.28270	−	6.03461i	0.0904743	−	0.425648i
$202$	−7.78675	−	2.53007i	−0.547874	−	0.178015i
$203$	10.1584	+	6.24588i	0.712980	+	0.438375i
$204$	0.623084	−	0.857602i	0.0436246	−	0.0600442i
$205$	−5.67114	+	5.10632i	−0.396090	+	0.356641i
$206$	8.33255	−	9.25423i	0.580556	−	0.644773i
$207$	0.395100	+	0.175910i	0.0274613	+	0.0122266i
$208$	3.12490	−	5.41248i	0.216673	−	0.375288i
$209$	5.58270	−	16.0405i	0.386163	−	1.10954i
$210$	0.791315	−	1.65270i	0.0546059	−	0.114047i
$211$	8.50904	+	11.7117i	0.585786	+	0.806266i	0.994315	−	0.106480i	$-0.0339580\pi$
$211$	8.50904	+	11.7117i	0.585786	+	0.806266i	−0.408529	+	0.912746i	$0.633958\pi$
$212$	6.90033	+	1.46671i	0.473916	+	0.100734i
$213$	1.25136	+	5.88719i	0.0857419	+	0.403384i
$214$	1.66813	−	15.8712i	0.114031	−	1.08494i
$215$	−4.59454	+	2.04562i	−0.313345	+	0.139510i
$216$	0.309017	−	0.951057i	0.0210259	−	0.0647112i
$217$	4.18234	−	5.43379i	0.283916	−	0.368869i
$218$	−9.57065	+	6.95349i	−0.648206	+	0.470950i
$219$	−13.5296	−	7.81135i	−0.914249	−	0.527842i
$220$	−2.01268	+	1.10694i	−0.135695	+	0.0746302i
$221$	−3.31256	−	5.73753i	−0.222827	−	0.385948i
$222$	−0.943682	−	8.97853i	−0.0633358	−	0.602600i
$223$	0.724432	−	0.235382i	0.0485116	−	0.0157624i	−0.284661	−	0.958628i	$-0.591881\pi$
$223$	0.724432	−	0.235382i	0.0485116	−	0.0157624i	0.333172	+	0.942866i	$0.391881\pi$
$224$	2.53791	−	0.747661i	0.169571	−	0.0499552i
$225$	3.65704	+	2.65699i	0.243802	+	0.177133i
$226$	−5.93885	−	13.3389i	−0.395046	−	0.887289i
$227$	−8.44525	+	1.79509i	−0.560531	+	0.119144i	−0.479460	−	0.877564i	$-0.659167\pi$
$227$	−8.44525	+	1.79509i	−0.560531	+	0.119144i	−0.0810710	+	0.996708i	$0.525834\pi$
$228$	3.80559	+	3.42657i	0.252031	+	0.226930i
$229$	−19.6150	+	2.06162i	−1.29619	+	0.136235i	−0.727382	−	0.686233i	$-0.759263\pi$
$229$	−19.6150	+	2.06162i	−1.29619	+	0.136235i	−0.568811	+	0.822468i	$0.692597\pi$
$230$	0.299531			0.0197505
$231$	−7.80285	+	4.01441i	−0.513390	+	0.264129i
$232$	4.50720			0.295912
$233$	29.0515	−	3.05344i	1.90323	−	0.200037i	0.921242	−	0.388989i	$-0.127176\pi$
$233$	29.0515	−	3.05344i	1.90323	−	0.200037i	0.981986	+	0.188952i	$0.0605089\pi$
$234$	−4.64450	−	4.18193i	−0.303621	−	0.273381i
$235$	7.00496	−	1.48895i	0.456953	−	0.0971284i
$236$	−4.15557	−	9.33357i	−0.270505	−	0.607564i
$237$	−3.77226	−	2.74070i	−0.245034	−	0.178028i
$238$	0.658785	−	2.72617i	0.0427027	−	0.176711i
$239$	13.0728	−	4.24760i	0.845608	−	0.274755i	0.146003	−	0.989284i	$-0.453359\pi$
$239$	13.0728	−	4.24760i	0.845608	−	0.274755i	0.699605	+	0.714530i	$0.253359\pi$
$240$	−0.0723934	−	0.688778i	−0.00467298	−	0.0444604i
$241$	6.31530	+	10.9384i	0.406804	+	0.704606i	0.994530	−	0.104455i	$-0.0333097\pi$
$241$	6.31530	+	10.9384i	0.406804	+	0.704606i	−0.587725	+	0.809061i	$0.699976\pi$
$242$	10.8826	+	1.60306i	0.699558	+	0.103049i
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	6.17644	−	4.48745i	0.395406	−	0.287280i
$245$	0.268123	−	4.84058i	0.0171298	−	0.309253i
$246$	−3.40498	+	10.4795i	−0.217094	+	0.668146i
$247$	29.2378	−	13.0175i	1.86036	−	0.828284i
$248$	0.270905	−	2.57749i	0.0172025	−	0.163671i
$249$	−0.942158	−	4.43251i	−0.0597068	−	0.280899i
$250$	6.44944	+	1.37087i	0.407898	+	0.0867014i
$251$	8.84785	+	12.1780i	0.558472	+	0.768670i	0.991131	−	0.132887i	$-0.0424248\pi$
$251$	8.84785	+	12.1780i	0.558472	+	0.768670i	−0.432660	+	0.901557i	$0.642425\pi$
$252$	−0.203661	−	2.63790i	−0.0128294	−	0.166172i
$253$	−1.14270	−	0.867040i	−0.0718411	−	0.0545104i
$254$	6.94132	−	12.0227i	0.435537	−	0.754372i
$255$	−0.670692	−	0.298611i	−0.0420003	−	0.0186998i
$256$	0.669131	−	0.743145i	0.0418207	−	0.0464466i
$257$	2.35419	−	2.11973i	0.146851	−	0.132225i	−0.592431	−	0.805621i	$-0.701832\pi$
$257$	2.35419	−	2.11973i	0.146851	−	0.132225i	0.739282	+	0.673396i	$0.235165\pi$
$258$	−4.26841	+	5.87496i	−0.265740	+	0.365759i
$259$	−11.3661	−	21.0082i	−0.706255	−	1.30538i
$260$	−4.11658	−	1.33756i	−0.255300	−	0.0829519i
$261$	0.937100	−	4.40871i	0.0580050	−	0.272892i
$262$	−3.88077	+	8.71636i	−0.239755	+	0.538499i
$263$	23.1461	−	13.3634i	1.42725	−	0.824025i	0.430349	−	0.902663i	$-0.358390\pi$
$263$	23.1461	−	13.3634i	1.42725	−	0.824025i	0.996903	+	0.0786380i	$0.0250571\pi$
$264$	−1.71760	+	2.83723i	−0.105711	+	0.174619i
$265$		−	4.88574i		−	0.300128i
$266$	12.7648	+	4.54164i	0.782662	+	0.278466i
$267$	−1.64670	−	5.06802i	−0.100776	−	0.310158i
$268$	−4.12815	−	4.58478i	−0.252167	−	0.280060i
$269$	1.37366	+	0.144378i	0.0837535	+	0.00880285i	0.146313	−	0.989238i	$-0.453259\pi$
$269$	1.37366	+	0.144378i	0.0837535	+	0.00880285i	−0.0625590	+	0.998041i	$0.519926\pi$
$270$	−0.688778	−	0.0723934i	−0.0419177	−	0.00440572i
$271$	−1.14501	−	1.27167i	−0.0695546	−	0.0772482i	0.707363	−	0.706850i	$-0.249885\pi$
$271$	−1.14501	−	1.27167i	−0.0695546	−	0.0772482i	−0.776918	+	0.629602i	$0.783218\pi$
$272$	−0.327575	−	1.00817i	−0.0198621	−	0.0611294i
$273$	−15.5787	−	5.54281i	−0.942868	−	0.335466i
$274$			4.64523i			0.280629i
$275$	−9.79828	−	11.3474i	−0.590858	−	0.684271i
$276$	0.374548	−	0.216245i	0.0225451	−	0.0130164i
$277$	−8.96318	+	20.1316i	−0.538545	+	1.20959i	0.415407	+	0.909636i	$0.363639\pi$
$277$	−8.96318	+	20.1316i	−0.538545	+	1.20959i	−0.953953	+	0.299957i	$0.903028\pi$
$278$	3.02755	−	14.2435i	0.181580	−	0.854268i
$279$	−2.46484	−	0.800876i	−0.147566	−	0.0479472i
$280$	−0.871937	−	1.61162i	−0.0521082	−	0.0963126i
$281$	13.4789	−	18.5521i	0.804085	−	1.10673i	−0.188125	−	0.982145i	$-0.560241\pi$
$281$	13.4789	−	18.5521i	0.804085	−	1.10673i	0.992209	−	0.124582i	$-0.0397591\pi$
$282$	7.68440	−	6.91906i	0.457599	−	0.412024i
$283$	−18.6517	+	20.7148i	−1.10873	+	1.23137i	−0.138192	+	0.990405i	$0.544129\pi$
$283$	−18.6517	+	20.7148i	−1.10873	+	1.23137i	−0.970535	+	0.240961i	$0.922538\pi$
$284$	5.49837	+	2.44803i	0.326268	+	0.145264i
$285$	1.77330	−	3.07145i	0.105041	−	0.181937i
$286$	11.8329	+	17.0189i	0.699694	+	1.00635i
$287$	2.24408	+	29.0664i	0.132464	+	1.71573i
$288$	−0.587785	−	0.809017i	−0.0346356	−	0.0476718i
$289$	15.5293	+	3.30087i	0.913491	+	0.194169i
$290$	−0.649009	−	3.05335i	−0.0381111	−	0.179299i
$291$	−0.0555428	+	0.528454i	−0.00325597	+	0.0309785i
$292$	−14.2720	+	6.35432i	−0.835208	+	0.371859i
$293$	−5.02911	+	15.4780i	−0.293804	+	0.904235i	0.689817	+	0.723984i	$0.257691\pi$
$293$	−5.02911	+	15.4780i	−0.293804	+	0.904235i	−0.983621	+	0.180251i	$0.942309\pi$
$294$	−3.15937	−	6.24647i	−0.184258	−	0.364302i
$295$	−5.72453	+	4.15912i	−0.333295	+	0.242153i
$296$	−7.81847	−	4.51399i	−0.454439	−	0.262371i
$297$	2.41812	+	2.26996i	0.140313	+	0.131716i
$298$	−2.93774	−	5.08831i	−0.170179	−	0.294758i
$299$	−0.282538	−	2.68817i	−0.0163396	−	0.155461i
$300$	4.29910	−	1.39686i	0.248209	−	0.0806479i
$301$	−4.51298	+	18.6755i	−0.260124	+	1.07644i
$302$	0.561726	+	0.408118i	0.0323237	+	0.0234846i
$303$	3.33015	+	7.47963i	0.191312	+	0.429693i
$304$	5.00902	−	1.06470i	0.287287	−	0.0610648i
$305$	−3.92933	−	3.53799i	−0.224993	−	0.202585i
$306$	−1.05425	+	0.110806i	−0.0602673	+	0.00633435i
$307$	−6.03348			−0.344349			−0.172174	−	0.985066i	$-0.555079\pi$
$307$	−6.03348			−0.344349			−0.172174	+	0.985066i	$0.555079\pi$
$308$	−1.33867	+	8.67225i	−0.0762779	+	0.494147i
$309$	−12.4528			−0.708415
$310$	−1.78510	+	0.187621i	−0.101387	+	0.0106562i
$311$	2.27766	+	2.05081i	0.129154	+	0.116291i	0.731177	−	0.682188i	$-0.238972\pi$
$311$	2.27766	+	2.05081i	0.129154	+	0.116291i	−0.602022	+	0.798479i	$0.705638\pi$
$312$	−6.11322	+	1.29941i	−0.346093	+	0.0735644i
$313$	−4.19135	−	9.41393i	−0.236909	−	0.532107i	0.755491	−	0.655159i	$-0.227398\pi$
$313$	−4.19135	−	9.41393i	−0.236909	−	0.532107i	−0.992400	+	0.123052i	$0.960732\pi$
$314$	0.0975297	+	0.0708595i	0.00550392	+	0.00399883i
$315$	−1.75769	+	0.517808i	−0.0990344	+	0.0291752i
$316$	−4.43455	+	1.44087i	−0.249463	+	0.0810555i
$317$	2.48612	+	23.6539i	0.139635	+	1.32854i	0.809968	+	0.586475i	$0.199485\pi$
$317$	2.48612	+	23.6539i	0.139635	+	1.32854i	−0.670333	+	0.742061i	$0.733849\pi$
$318$	−3.52724	−	6.10936i	−0.197798	−	0.342596i
$319$	−6.36245	+	13.5271i	−0.356229	+	0.757373i
$320$	−0.599785	−	0.346286i	−0.0335290	−	0.0193580i
$321$	−12.9108	+	9.38026i	−0.720612	+	0.523555i
$322$	0.697932	−	0.906768i	0.0388942	−	0.0505322i
$323$	1.67749	−	5.16277i	0.0933379	−	0.287264i
$324$	−0.913545	+	0.406737i	−0.0507525	+	0.0225965i
$325$	2.95306	−	28.0965i	0.163806	−	1.55851i
$326$	0.280108	+	1.31780i	0.0155137	+	0.0729865i
$327$	11.5715	+	2.45959i	0.639903	+	0.136016i
$328$	6.47666	+	8.91436i	0.357614	+	0.492213i
$329$	11.8147	−	24.6754i	0.651363	−	1.36040i
$330$	2.16937	+	0.755023i	0.119420	+	0.0415626i
$331$	−0.489695	+	0.848176i	−0.0269161	+	0.0466200i	−0.879170	−	0.476509i	$-0.841902\pi$
$331$	−0.489695	+	0.848176i	−0.0269161	+	0.0466200i	0.852254	+	0.523129i	$0.175235\pi$
$332$	−4.13976	−	1.84314i	−0.227199	−	0.101155i
$333$	−6.04090	+	6.70910i	−0.331039	+	0.367657i
$334$	2.09380	−	1.88527i	0.114568	−	0.103157i
$335$	−2.51147	+	3.45674i	−0.137216	+	0.188862i
$336$	−2.25382	−	1.38575i	−0.122956	−	0.0755991i
$337$	−14.7549	−	4.79416i	−0.803751	−	0.261155i	−0.121802	−	0.992554i	$-0.538867\pi$
$337$	−14.7549	−	4.79416i	−0.803751	−	0.261155i	−0.681949	+	0.731400i	$0.738867\pi$
$338$	−5.41817	+	25.4905i	−0.294710	+	1.38650i
$339$	−5.93885	+	13.3389i	−0.322554	+	0.724468i
$340$	−0.635804	+	0.367082i	−0.0344813	+	0.0199078i
$341$	7.35321	+	4.45149i	0.398199	+	0.241061i
$342$		−	5.12093i		−	0.276908i
$343$	−14.0291	−	12.0907i	−0.757501	−	0.652834i
$344$	2.24404	+	6.90643i	0.120990	+	0.372370i
$345$	−0.200425	−	0.222595i	−0.0107905	−	0.0119841i
$346$	10.7090	+	1.12556i	0.575720	+	0.0605106i
$347$	14.2265	+	1.49526i	0.763716	+	0.0802698i	0.478374	−	0.878156i	$-0.341226\pi$
$347$	14.2265	+	1.49526i	0.763716	+	0.0802698i	0.285342	+	0.958426i	$0.407893\pi$
$348$	−3.01591	−	3.34950i	−0.161670	−	0.179552i
$349$	−1.36691	−	4.20691i	−0.0731689	−	0.225191i	0.907783	−	0.419439i	$-0.137773\pi$
$349$	−1.36691	−	4.20691i	−0.0731689	−	0.225191i	−0.980952	+	0.194248i	$0.937773\pi$
$350$	9.10577	−	7.75368i	0.486724	−	0.414451i
$351$			6.24980i			0.333589i
$352$	1.28578	+	3.05725i	0.0685326	+	0.162952i
$353$	22.1877	−	12.8101i	1.18093	−	0.681811i	0.224702	−	0.974428i	$-0.427859\pi$
$353$	22.1877	−	12.8101i	1.18093	−	0.681811i	0.956230	+	0.292616i	$0.0945258\pi$
$354$	−4.15557	+	9.33357i	−0.220866	+	0.496074i
$355$	0.866657	−	4.07730i	0.0459974	−	0.216401i
$356$	−5.06802	−	1.64670i	−0.268604	−	0.0872749i
$357$	−2.46675	+	1.33459i	−0.130554	+	0.0706341i
$358$	4.98567	−	6.86219i	0.263501	−	0.362678i
$359$	−10.4481	+	9.40755i	−0.551432	+	0.496511i	−0.897089	−	0.441849i	$-0.854323\pi$
$359$	−10.4481	+	9.40755i	−0.551432	+	0.496511i	0.345658	+	0.938361i	$0.387656\pi$
$360$	−0.463421	+	0.514681i	−0.0244244	+	0.0271261i
$361$	6.59935	+	2.93822i	0.347334	+	0.154643i
$362$	−12.8733	+	22.2973i	−0.676607	+	1.17192i
$363$	−6.09055	−	9.15998i	−0.319671	−	0.480774i
$364$	−13.6412	+	9.34548i	−0.714992	+	0.489836i
$365$	6.35974	+	8.75343i	0.332884	+	0.458175i
$366$	−7.46767	−	1.58730i	−0.390341	−	0.0829696i
$367$	−1.44335	−	6.79044i	−0.0753424	−	0.354458i	0.924287	−	0.381699i	$-0.124661\pi$
$367$	−1.44335	−	6.79044i	−0.0753424	−	0.354458i	−0.999629	+	0.0272414i	$0.991328\pi$
$368$	0.0452076	−	0.430121i	0.00235661	−	0.0224216i
$369$	10.0661	−	4.48173i	0.524022	−	0.233310i
$370$	−1.93214	+	5.94651i	−0.100447	+	0.309144i
$371$	−14.7906	−	11.3842i	−0.767888	−	0.591037i
$372$	−2.09672	+	1.52336i	−0.108710	+	0.0789824i
$373$	25.4149	+	14.6733i	1.31593	+	0.759754i	0.983071	−	0.183223i	$-0.0586529\pi$
$373$	25.4149	+	14.6733i	1.31593	+	0.759754i	0.332860	+	0.942976i	$0.391986\pi$
$374$	3.48816	+	0.440030i	0.180368	+	0.0227534i
$375$	−3.29676	−	5.71016i	−0.170244	−	0.294871i
$376$	−1.08086	−	10.2837i	−0.0557413	−	0.530343i
$377$	−26.7904	+	8.70473i	−1.37978	+	0.448316i
$378$	−1.82407	+	1.91645i	−0.0938199	+	0.0985715i
$379$	8.16381	+	5.93135i	0.419347	+	0.304673i	0.777375	−	0.629038i	$-0.216551\pi$
$379$	8.16381	+	5.93135i	0.419347	+	0.304673i	−0.358028	+	0.933711i	$0.616551\pi$
$380$	−1.44254	−	3.23999i	−0.0740005	−	0.166208i
$381$	−13.5793	+	2.88636i	−0.695687	+	0.147873i
$382$	−16.2960	−	14.6730i	−0.833775	−	0.750734i
$383$	−36.8093	+	3.86881i	−1.88087	+	0.197687i	−0.974436	−	0.224665i	$-0.927871\pi$
$383$	−36.8093	+	3.86881i	−1.88087	+	0.197687i	−0.906432	+	0.422352i	$0.861205\pi$
$384$	−1.00000			−0.0510310
$385$	6.06767	−	0.341884i	0.309237	−	0.0174240i
$386$	−5.71324			−0.290796
$387$	7.22207	−	0.759070i	0.367118	−	0.0385857i
$388$	0.394881	+	0.355553i	0.0200470	+	0.0180504i
$389$	13.0656	−	2.77717i	0.662451	−	0.140808i	0.135597	−	0.990764i	$-0.456705\pi$
$389$	13.0656	−	2.77717i	0.662451	−	0.140808i	0.526854	+	0.849956i	$0.323371\pi$
$390$	1.76053	+	3.95422i	0.0891480	+	0.200230i
$391$	−0.370905	−	0.269478i	−0.0187575	−	0.0136281i
$392$	−6.91053	−	1.11560i	−0.349035	−	0.0563463i
$393$	9.07426	−	2.94841i	0.457736	−	0.148727i
$394$	−0.712812	−	6.78195i	−0.0359110	−	0.341670i
$395$	1.61465	+	2.79665i	0.0812418	+	0.140715i
$396$	3.25777	−	0.622050i	0.163709	−	0.0312592i
$397$	7.20181	+	4.15797i	0.361448	+	0.208682i	0.669716	−	0.742617i	$-0.266416\pi$
$397$	7.20181	+	4.15797i	0.361448	+	0.208682i	−0.308268	+	0.951300i	$0.599749\pi$
$398$	5.75497	−	4.18123i	0.288471	−	0.209586i
$399$	−5.16624	−	12.5251i	−0.258636	−	0.627037i
$400$	1.39686	−	4.29910i	0.0698432	−	0.214955i
$401$	−34.2639	+	15.2553i	−1.71106	+	0.761813i	−0.712894	+	0.701272i	$0.752616\pi$
$401$	−34.2639	+	15.2553i	−1.71106	+	0.761813i	−0.998166	+	0.0605414i	$0.980717\pi$
$402$	−0.644880	+	6.13563i	−0.0321637	+	0.306017i
$403$	3.36766	+	15.8436i	0.167755	+	0.789225i
$404$	8.00856	+	1.70227i	0.398441	+	0.0846912i
$405$	0.407083	+	0.560302i	0.0202281	+	0.0278416i
$406$	−10.7556	−	5.14982i	−0.533793	−	0.255581i
$407$	24.5842	−	17.0929i	1.21859	−	0.847264i
$408$	−0.530027	+	0.918034i	−0.0262403	+	0.0454495i
$409$	14.6519	+	6.52346i	0.724491	+	0.322564i	0.735639	−	0.677374i	$-0.236882\pi$
$409$	14.6519	+	6.52346i	0.724491	+	0.322564i	−0.0111479	+	0.999938i	$0.503549\pi$
$410$	5.10632	−	5.67114i	0.252183	−	0.280078i
$411$	3.45208	−	3.10827i	0.170279	−	0.153320i
$412$	−7.31957	+	10.0745i	−0.360609	+	0.496336i
$413$	−0.747781	+	27.0209i	−0.0367959	+	1.32961i
$414$	−0.411323	−	0.133647i	−0.0202154	−	0.00656839i
$415$	−0.652512	+	3.06983i	−0.0320305	+	0.150692i
$416$	−2.54202	+	5.70947i	−0.124633	+	0.279930i
$417$	−12.6108	+	7.28085i	−0.617554	+	0.356545i
$418$	−3.87543	+	16.5361i	−0.189553	+	0.808809i
$419$		−	17.3641i		−	0.848292i	−0.905594	−	0.424146i	$-0.860574\pi$
$419$		−	17.3641i		−	0.848292i	0.905594	−	0.424146i	$-0.139426\pi$
$420$	−0.614226	+	1.72636i	−0.0299712	+	0.0842377i
$421$	−3.58883	−	11.0453i	−0.174909	−	0.538315i	0.824720	−	0.565541i	$-0.191333\pi$
$421$	−3.58883	−	11.0453i	−0.174909	−	0.538315i	−0.999629	+	0.0272263i	$0.991333\pi$
$422$	−9.68663	−	10.7581i	−0.471538	−	0.523696i
$423$	−10.2837	−	1.08086i	−0.500012	−	0.0525534i
$424$	−7.01584	−	0.737395i	−0.340719	−	0.0358110i
$425$	−3.20635	−	3.56101i	−0.155531	−	0.172734i
$426$	−1.85989	−	5.72414i	−0.0901118	−	0.277335i
$427$	−19.8662	+	3.65144i	−0.961394	+	0.176705i
$428$			15.9587i			0.771391i
$429$	4.72974	−	20.1814i	0.228354	−	0.974367i
$430$	4.35555	−	2.51468i	0.210043	−	0.121268i
$431$	−7.27908	+	16.3491i	−0.350621	+	0.787507i	0.649022	+	0.760770i	$0.275178\pi$
$431$	−7.27908	+	16.3491i	−0.350621	+	0.787507i	−0.999642	+	0.0267374i	$0.991488\pi$
$432$	−0.207912	+	0.978148i	−0.0100032	+	0.0470611i
$433$	−6.59219	−	2.14193i	−0.316800	−	0.102935i	0.146301	−	0.989240i	$-0.453263\pi$
$433$	−6.59219	−	2.14193i	−0.316800	−	0.102935i	−0.463101	+	0.886305i	$0.653263\pi$
$434$	−3.59145	+	5.84119i	−0.172395	+	0.280386i
$435$	−1.83481	+	2.52540i	−0.0879723	+	0.121083i
$436$	8.79139	−	7.91580i	0.421031	−	0.379098i
$437$	1.48196	−	1.64588i	0.0708917	−	0.0787332i
$438$	14.2720	+	6.35432i	0.681944	+	0.303621i
$439$	6.57364	−	11.3859i	0.313743	−	0.543418i	−0.665427	−	0.746463i	$-0.731750\pi$
$439$	6.57364	−	11.3859i	0.313743	−	0.543418i	0.979169	+	0.203045i	$0.0650838\pi$
$440$	1.88595	−	1.31126i	0.0899090	−	0.0625120i
$441$	−2.52800	+	6.52757i	−0.120381	+	0.310837i
$442$	3.89415	+	5.35984i	0.185226	+	0.254942i
$443$	9.48004	+	2.01504i	0.450410	+	0.0957377i	0.427531	−	0.904001i	$-0.359383\pi$
$443$	9.48004	+	2.01504i	0.450410	+	0.0957377i	0.0228791	+	0.999738i	$0.492717\pi$
$444$	1.87702	+	8.83070i	0.0890796	+	0.419087i
$445$	−0.385772	+	3.67038i	−0.0182874	+	0.173993i
$446$	−0.695860	+	0.309817i	−0.0329499	+	0.0146702i
$447$	−1.81562	+	5.58791i	−0.0858760	+	0.264299i
$448$	−2.44586	+	1.00885i	−0.115556	+	0.0476636i
$449$	20.8277	−	15.1322i	0.982921	−	0.714134i	0.0245618	−	0.999698i	$-0.492181\pi$
$449$	20.8277	−	15.1322i	0.982921	−	0.714134i	0.958360	+	0.285564i	$0.0921810\pi$
$450$	−3.91473	−	2.26017i	−0.184542	−	0.106546i
$451$	−35.8965	+	6.85421i	−1.69030	+	0.322752i
$452$	7.30061	+	12.6450i	0.343392	+	0.594772i
$453$	−0.0725775	−	0.690528i	−0.00340999	−	0.0324439i
$454$	8.21135	−	2.66803i	0.385378	−	0.125217i
$455$	8.29522	+	7.89535i	0.388886	+	0.370140i
$456$	−4.14292	−	3.01001i	−0.194010	−	0.140956i
$457$	−14.0430	−	31.5411i	−0.656905	−	1.47543i	−0.867285	−	0.497813i	$-0.834137\pi$
$457$	−14.0430	−	31.5411i	−0.656905	−	1.47543i	0.210380	−	0.977620i	$-0.432530\pi$
$458$	19.2920	−	4.10065i	0.901457	−	0.191611i
$459$	0.787774	+	0.709315i	0.0367701	+	0.0331080i
$460$	−0.297890	+	0.0313095i	−0.0138892	+	0.00145981i
$461$	−28.5964			−1.33187			−0.665935	−	0.746010i	$-0.731967\pi$
$461$	−28.5964			−1.33187			−0.665935	+	0.746010i	$0.731967\pi$
$462$	7.34049	−	4.80804i	0.341510	−	0.223690i
$463$	12.8000			0.594865			0.297433	−	0.954743i	$-0.403870\pi$
$463$	12.8000			0.594865			0.297433	+	0.954743i	$0.403870\pi$
$464$	−4.48251	+	0.471131i	−0.208095	+	0.0218717i
$465$	1.33389	+	1.20104i	0.0618578	+	0.0556971i
$466$	−28.5732	+	6.07342i	−1.32363	+	0.281346i
$467$	2.80010	+	6.28913i	0.129573	+	0.291026i	0.966669	−	0.256031i	$-0.0824148\pi$
$467$	2.80010	+	6.28913i	0.129573	+	0.291026i	−0.837096	+	0.547057i	$0.815748\pi$
$468$	5.05619	+	3.67354i	0.233723	+	0.169809i
$469$	4.61263	+	15.6575i	0.212992	+	0.722994i
$470$	−6.81095	+	2.21301i	−0.314165	+	0.102079i
$471$	−0.0126013	−	0.119893i	−0.000580635	−	0.00552438i
$472$	5.10843	+	8.84807i	0.235135	+	0.407265i
$473$	−23.8955	−	3.01440i	−1.09871	−	0.138602i
$474$	4.03807	+	2.33138i	0.185475	+	0.107084i
$475$	18.7274	−	13.6063i	0.859273	−	0.624298i
$476$	−0.370214	+	2.78010i	−0.0169687	+	0.127426i
$477$	−2.17996	+	6.70921i	−0.0998133	+	0.307194i
$478$	−12.5572	+	5.59081i	−0.574352	+	0.255718i
$479$	2.96473	−	28.2075i	0.135462	−	1.28884i	−0.689765	−	0.724034i	$-0.742286\pi$
$479$	2.96473	−	28.2075i	0.135462	−	1.28884i	0.825227	−	0.564802i	$-0.191047\pi$
$480$	0.143994	+	0.677437i	0.00657238	+	0.0309206i
$481$	55.1901	+	11.7310i	2.51645	+	0.534888i
$482$	−7.42408	−	10.2184i	−0.338158	−	0.465434i
$483$	−1.14087	+	0.0880813i	−0.0519113	+	0.00400784i
$484$	−10.9905	−	0.456744i	−0.499569	−	0.0207611i
$485$	0.184004	−	0.318704i	0.00835520	−	0.0144716i
$486$	0.913545	+	0.406737i	0.0414393	+	0.0184499i
$487$	−0.0458826	+	0.0509578i	−0.00207914	+	0.00230912i	−0.744183	−	0.667975i	$-0.767161\pi$
$487$	−0.0458826	+	0.0509578i	−0.00207914	+	0.00230912i	0.742104	+	0.670284i	$0.233828\pi$
$488$	−5.67354	+	5.10848i	−0.256829	+	0.231250i
$489$	0.791891	−	1.08994i	0.0358105	−	0.0492890i
$490$	0.239324	+	4.84209i	0.0108116	+	0.218743i
$491$	6.40103	+	2.07982i	0.288875	+	0.0938611i	0.449870	−	0.893094i	$-0.351470\pi$
$491$	6.40103	+	2.07982i	0.288875	+	0.0938611i	−0.160995	+	0.986955i	$0.551470\pi$
$492$	2.29093	−	10.7780i	0.103283	−	0.485908i
$493$	−1.94334	+	4.36481i	−0.0875236	+	0.196581i
$494$	−27.7169	+	16.0024i	−1.24704	+	0.719981i
$495$	−0.890498	−	2.11736i	−0.0400249	−	0.0951683i
$496$			2.59169i			0.116370i
$497$	−10.3238	−	12.1241i	−0.463086	−	0.543840i
$498$	1.40032	+	4.30974i	0.0627498	+	0.193124i
$499$	−15.8194	−	17.5693i	−0.708175	−	0.786508i	0.276480	−	0.961020i	$-0.410832\pi$
$499$	−15.8194	−	17.5693i	−0.708175	−	0.786508i	−0.984655	+	0.174512i	$0.944165\pi$
$500$	−6.55740	−	0.689210i	−0.293256	−	0.0308224i
$501$	−2.80206	−	0.294508i	−0.125187	−	0.0131577i
$502$	−10.0723	−	11.1865i	−0.449550	−	0.499276i
$503$	−1.71294	−	5.27188i	−0.0763761	−	0.235061i	0.905578	−	0.424179i	$-0.139437\pi$
$503$	−1.71294	−	5.27188i	−0.0763761	−	0.235061i	−0.981954	+	0.189118i	$0.939437\pi$
$504$	0.478281	+	2.60216i	0.0213043	+	0.115910i
$505$		−	5.67041i		−	0.252330i
$506$	1.22707	+	0.742846i	0.0545501	+	0.0330235i
$507$	22.5686	−	13.0300i	1.00231	−	0.578682i
$508$	−5.64658	+	12.6824i	−0.250526	+	0.562691i
$509$	3.23443	−	15.2168i	0.143364	−	0.674473i	−0.846493	−	0.532400i	$-0.821290\pi$
$509$	3.23443	−	15.2168i	0.143364	−	0.674473i	0.989856	−	0.142072i	$-0.0453766\pi$
$510$	0.698231	+	0.226869i	0.0309182	+	0.0100459i
$511$	41.3179	+	1.14344i	1.82780	+	0.0505827i
$512$	−0.587785	+	0.809017i	−0.0259767	+	0.0357538i
$513$	−3.80559	+	3.42657i	−0.168021	+	0.151287i
$514$	−2.11973	+	2.35419i	−0.0934971	+	0.103839i
$515$	7.87883	+	3.50788i	0.347183	+	0.154576i
$516$	3.63093	−	6.28895i	0.159843	−	0.276855i
$517$	32.3895	+	11.2728i	1.42449	+	0.495777i
$518$	13.4998	+	19.7050i	0.593146	+	0.865789i
$519$	−6.32927	−	8.71150i	−0.277824	−	0.382392i
$520$	4.23384	+	0.899931i	0.185666	+	0.0394646i
$521$	5.44049	+	25.5955i	0.238352	+	1.12136i	0.920682	+	0.390314i	$0.127634\pi$
$521$	5.44049	+	25.5955i	0.238352	+	1.12136i	−0.682330	+	0.731045i	$0.739033\pi$
$522$	−0.471131	+	4.48251i	−0.0206208	+	0.196194i
$523$	14.0483	−	6.25470i	0.614289	−	0.273499i	−0.0759146	−	0.997114i	$-0.524188\pi$
$523$	14.0483	−	6.25470i	0.614289	−	0.273499i	0.690204	+	0.723615i	$0.257521\pi$
$524$	2.94841	−	9.07426i	0.128802	−	0.396411i
$525$	−11.8551	−	1.57869i	−0.517397	−	0.0688995i
$526$	−21.6225	+	15.7097i	−0.942785	+	0.684974i
$527$	2.37926	+	1.37367i	0.103642	+	0.0598379i
$528$	1.41162	−	3.00122i	0.0614328	−	0.130611i
$529$	11.4065	+	19.7566i	0.495934	+	0.858982i
$530$	0.510698	+	4.85897i	0.0221833	+	0.211060i
$531$	9.71682	−	3.15719i	0.421674	−	0.137010i
$532$	−13.1696	−	3.18247i	−0.570976	−	0.137978i
$533$	−55.7129	−	40.4778i	−2.41319	−	1.75329i
$534$	2.16743	+	4.86813i	0.0937939	+	0.210665i
$535$	10.8110	−	2.29795i	0.467400	−	0.0993489i
$536$	4.58478	+	4.12815i	0.198032	+	0.178309i
$537$	−8.43567	+	0.886625i	−0.364026	+	0.0382607i
$538$	−1.38123			−0.0595489
$539$	13.1032	−	19.1652i	0.564395	−	0.825505i
$540$	0.692572			0.0298035
$541$	−19.6392	+	2.06416i	−0.844354	+	0.0887452i	−0.516820	−	0.856094i	$-0.672884\pi$
$541$	−19.6392	+	2.06416i	−0.844354	+	0.0887452i	−0.327534	+	0.944839i	$0.606218\pi$
$542$	1.27167	+	1.14501i	0.0546228	+	0.0491825i
$543$	25.1840	−	5.35303i	1.08075	−	0.229720i
$544$	0.431163	+	0.968408i	0.0184860	+	0.0415201i
$545$	−6.62836	−	4.81579i	−0.283928	−	0.206286i
$546$	16.0728	+	3.88402i	0.687851	+	0.166221i
$547$	3.37424	−	1.09636i	0.144272	−	0.0468768i	−0.235991	−	0.971755i	$-0.575834\pi$
$547$	3.37424	−	1.09636i	0.144272	−	0.0468768i	0.380263	+	0.924878i	$0.375834\pi$
$548$	−0.485559	−	4.61979i	−0.0207421	−	0.197348i
$549$	3.81725	+	6.61168i	0.162916	+	0.282179i
$550$	10.9307	+	10.2610i	0.466088	+	0.437530i
$551$	−19.9888	−	11.5405i	−0.851551	−	0.491643i
$552$	−0.349892	+	0.254212i	−0.0148924	+	0.0108200i
$553$	12.2286	+	1.62843i	0.520012	+	0.0692477i
$554$	6.80975	−	20.9583i	0.289319	−	0.890431i
$555$	5.71197	−	2.54313i	0.242460	−	0.107950i
$556$	−1.52211	+	14.4819i	−0.0645519	+	0.614171i
$557$	−1.68750	−	7.93905i	−0.0715016	−	0.336388i	0.927828	−	0.373009i	$-0.121674\pi$
$557$	−1.68750	−	7.93905i	−0.0715016	−	0.336388i	−0.999329	+	0.0366207i	$0.988341\pi$
$558$	2.53506	+	0.538843i	0.107317	+	0.0228110i
$559$	−26.6767	−	36.7173i	−1.12830	−	1.55298i
$560$	1.03562	+	1.51165i	0.0437629	+	0.0638788i
$561$	−2.00703	−	2.88664i	−0.0847367	−	0.121874i
$562$	−11.4658	+	19.8594i	−0.483658	+	0.837720i
$563$	18.5609	+	8.26383i	0.782247	+	0.348279i	0.758697	−	0.651444i	$-0.225836\pi$
$563$	18.5609	+	8.26383i	0.782247	+	0.348279i	0.0235504	+	0.999723i	$0.492503\pi$
$564$	−6.91906	+	7.68440i	−0.291345	+	0.323572i
$565$	7.51497	−	6.76651i	0.316157	−	0.284669i
$566$	16.3842	−	22.5509i	0.688680	−	0.947887i
$567$	2.64474	+	0.0731908i	0.111069	+	0.00307373i
$568$	−5.72414	−	1.85989i	−0.240180	−	0.0780391i
$569$	−1.19149	+	5.60552i	−0.0499499	+	0.234996i	−0.996040	−	0.0889083i	$-0.971662\pi$
$569$	−1.19149	+	5.60552i	−0.0499499	+	0.234996i	0.946090	+	0.323904i	$0.104996\pi$
$570$	−1.44254	+	3.23999i	−0.0604212	+	0.135708i
$571$	−25.8875	+	14.9461i	−1.08336	+	0.625476i	−0.931800	−	0.362973i	$-0.881762\pi$
$571$	−25.8875	+	14.9461i	−1.08336	+	0.625476i	−0.151556	+	0.988449i	$0.548429\pi$
$572$	−13.5470	−	15.6888i	−0.566430	−	0.655980i
$573$			21.9284i			0.916072i
$574$	−5.27005	−	28.6726i	−0.219968	−	1.19677i
$575$	−0.604130	−	1.85932i	−0.0251940	−	0.0775391i
$576$	0.669131	+	0.743145i	0.0278804	+	0.0309644i
$577$	27.6490	+	2.90603i	1.15104	+	0.120980i	0.660770	−	0.750588i	$-0.270230\pi$
$577$	27.6490	+	2.90603i	1.15104	+	0.120980i	0.490275	+	0.871568i	$0.336896\pi$
$578$	−15.7893	−	1.65952i	−0.656749	−	0.0690271i
$579$	3.82291	+	4.24577i	0.158875	+	0.176448i
$580$	0.964615	+	2.96878i	0.0400535	+	0.123272i
$581$	7.77286	+	9.12831i	0.322473	+	0.378706i
$582$		−	0.531365i		−	0.0220258i
$583$	12.1168	−	20.0152i	0.501826	−	0.828944i
$584$	13.5296	−	7.81135i	0.559861	−	0.323236i
$585$	1.76053	−	3.95422i	0.0727890	−	0.163487i
$586$	3.38367	−	15.9189i	0.139778	−	0.657604i
$587$	10.6552	+	3.46207i	0.439785	+	0.142895i	0.520537	−	0.853839i	$-0.325732\pi$
$587$	10.6552	+	3.46207i	0.439785	+	0.142895i	−0.0807512	+	0.996734i	$0.525732\pi$
$588$	3.79500	+	5.88201i	0.156503	+	0.242570i
$589$	−7.80100	+	10.7372i	−0.321435	+	0.442417i
$590$	5.25843	−	4.73471i	0.216486	−	0.194925i
$591$	−4.56301	+	5.06774i	−0.187697	+	0.208459i
$592$	8.24748	+	3.67201i	0.338969	+	0.150919i
$593$	−14.7764	+	25.5934i	−0.606792	+	1.05100i	0.384973	+	0.922928i	$0.374211\pi$
$593$	−14.7764	+	25.5934i	−0.606792	+	1.05100i	−0.991765	+	0.128068i	$0.959123\pi$
$594$	−2.64215	−	2.00476i	−0.108409	−	0.0822563i
$595$	1.93665	−	0.149520i	0.0793949	−	0.00612973i
$596$	3.45352	+	4.75336i	0.141462	+	0.194705i
$597$	−6.95809	−	1.47899i	−0.284776	−	0.0605309i
$598$	0.561981	+	2.64391i	0.0229811	+	0.108118i
$599$	1.19751	−	11.3936i	0.0489291	−	0.465529i	−0.942435	−	0.334390i	$-0.891470\pi$
$599$	1.19751	−	11.3936i	0.0489291	−	0.465529i	0.991364	−	0.131139i	$-0.0418635\pi$
$600$	−4.12954	+	1.83859i	−0.168588	+	0.0750601i
$601$	−10.8046	+	33.2531i	−0.440728	+	1.35642i	0.446374	+	0.894846i	$0.352715\pi$
$601$	−10.8046	+	33.2531i	−0.440728	+	1.35642i	−0.887102	+	0.461574i	$0.847285\pi$
$602$	2.53613	−	19.0449i	0.103365	−	0.776213i
$603$	4.99117	−	3.62630i	0.203256	−	0.147674i
$604$	−0.601309	−	0.347166i	−0.0244669	−	0.0141260i
$605$	1.27315	+	7.51115i	0.0517609	+	0.305372i
$606$	−4.09374	−	7.09056i	−0.166297	−	0.288034i
$607$	0.879468	+	8.36758i	0.0356965	+	0.339630i	0.997765	+	0.0668214i	$0.0212858\pi$
$607$	0.879468	+	8.36758i	0.0356965	+	0.339630i	−0.962068	+	0.272808i	$0.912048\pi$
$608$	−4.87029	+	1.58245i	−0.197516	+	0.0641770i
$609$	3.36986	+	11.4389i	0.136554	+	0.463527i
$610$	4.27763	+	3.10788i	0.173196	+	0.125834i
$611$	26.2855	+	59.0381i	1.06340	+	2.38843i
$612$	1.03689	−	0.220398i	0.0419138	−	0.00890905i
$613$	20.3312	+	18.3063i	0.821168	+	0.739383i	0.968315	−	0.249732i	$-0.0803425\pi$
$613$	20.3312	+	18.3063i	0.821168	+	0.739383i	−0.147147	+	0.989115i	$0.547009\pi$
$614$	6.00042	−	0.630670i	0.242157	−	0.0254518i
$615$	−7.63127			−0.307723
$616$	0.424841	−	8.76467i	0.0171174	−	0.353139i
$617$	−3.60763			−0.145238			−0.0726189	−	0.997360i	$-0.523136\pi$
$617$	−3.60763			−0.145238			−0.0726189	+	0.997360i	$0.523136\pi$
$618$	12.3846	−	1.30167i	0.498181	−	0.0523609i
$619$	−21.4651	−	19.3272i	−0.862754	−	0.776827i	0.113482	−	0.993540i	$-0.463800\pi$
$619$	−21.4651	−	19.3272i	−0.862754	−	0.776827i	−0.976235	+	0.216713i	$0.930466\pi$
$620$	1.75571	−	0.373187i	0.0705109	−	0.0149876i
$621$	0.175910	+	0.395100i	0.00705902	+	0.0158548i
$622$	−2.47955	−	1.80150i	−0.0994208	−	0.0722335i
$623$	10.2124	+	9.72014i	0.409153	+	0.389429i
$624$	5.94391	−	1.93129i	0.237947	−	0.0773136i
$625$	−1.88520	−	17.9364i	−0.0754078	−	0.717458i
$626$	5.15241	+	8.92424i	0.205932	+	0.356684i
$627$	14.8819	−	8.18483i	0.594326	−	0.326871i
$628$	−0.104402	−	0.0602767i	−0.00416611	−	0.00240530i
$629$	7.74242	−	5.62520i	0.308711	−	0.224291i
$630$	1.69393	−	0.698700i	0.0674879	−	0.0278369i
$631$	12.8875	−	39.6635i	0.513041	−	1.57898i	−0.273776	−	0.961793i	$-0.588273\pi$
$631$	12.8875	−	39.6635i	0.513041	−	1.57898i	0.786818	−	0.617186i	$-0.211727\pi$
$632$	4.25965	−	1.89652i	0.169440	−	0.0754394i
$633$	−1.51320	+	14.3971i	−0.0601443	+	0.572235i
$634$	−4.94501	−	23.2644i	−0.196391	−	0.923949i
$635$	9.40461	+	1.99901i	0.373211	+	0.0793284i
$636$	4.14652	+	5.70720i	0.164420	+	0.226305i
$637$	43.2301	−	6.71524i	1.71284	−	0.266067i
$638$	4.91363	−	14.1181i	0.194533	−	0.558940i
$639$	−3.00936	+	5.21236i	−0.119048	+	0.206198i
$640$	0.632696	+	0.281694i	0.0250095	+	0.0111349i
$641$	−27.1068	+	30.1051i	−1.07065	+	1.18908i	−0.0894719	+	0.995989i	$0.528518\pi$
$641$	−27.1068	+	30.1051i	−1.07065	+	1.18908i	−0.981181	+	0.193091i	$0.938149\pi$
$642$	11.8596	−	10.6784i	0.468061	−	0.421444i
$643$	10.4689	−	14.4092i	0.412852	−	0.568242i	−0.551059	−	0.834466i	$-0.685776\pi$
$643$	10.4689	−	14.4092i	0.412852	−	0.568242i	0.963911	+	0.266224i	$0.0857762\pi$
$644$	−0.599326	+	0.974754i	−0.0236167	+	0.0384107i
$645$	−4.78320	−	1.55416i	−0.188338	−	0.0611948i
$646$	−1.12864	+	5.30984i	−0.0444058	+	0.208913i
$647$	1.19537	−	2.68484i	0.0469947	−	0.105552i	−0.888522	−	0.458833i	$-0.848268\pi$
$647$	1.19537	−	2.68484i	0.0469947	−	0.105552i	0.935517	+	0.353281i	$0.114934\pi$
$648$	0.866025	−	0.500000i	0.0340207	−	0.0196419i
$649$	−33.7662	+	2.84144i	−1.32544	+	0.111536i
$650$			28.2512i			1.10810i
$651$	6.74400	−	1.23956i	0.264318	−	0.0485820i
$652$	−0.416322	−	1.28131i	−0.0163044	−	0.0501798i
$653$	−4.66598	−	5.18210i	−0.182594	−	0.202791i	0.644898	−	0.764269i	$-0.276900\pi$
$653$	−4.66598	−	5.18210i	−0.182594	−	0.202791i	−0.827492	+	0.561477i	$0.810233\pi$
$654$	−11.7652	−	1.23657i	−0.460055	−	0.0483537i
$655$	−6.57179	−	0.690723i	−0.256781	−	0.0269888i
$656$	−7.37298	−	8.18853i	−0.287867	−	0.319708i
$657$	−4.82768	−	14.8581i	−0.188346	−	0.579668i
$658$	−9.17065	+	25.7752i	−0.357509	+	1.00482i
$659$			13.2471i			0.516033i	0.966140	+	0.258017i	$0.0830690\pi$
$659$			13.2471i			0.516033i	−0.966140	+	0.258017i	$0.916931\pi$
$660$	−2.23640	−	0.524126i	−0.0870519	−	0.0204016i
$661$	−10.7466	+	6.20456i	−0.417995	+	0.241329i	−0.694219	−	0.719764i	$-0.744250\pi$
$661$	−10.7466	+	6.20456i	−0.417995	+	0.241329i	0.276224	+	0.961093i	$0.410917\pi$
$662$	0.398354	−	0.894717i	0.0154825	−	0.0347742i
$663$	1.37744	−	6.48035i	0.0534954	−	0.251676i
$664$	4.30974	+	1.40032i	0.167250	+	0.0543429i
$665$	−0.259579	+	9.37985i	−0.0100661	+	0.363735i
$666$	5.30652	−	7.30379i	0.205623	−	0.283016i
$667$	−1.44863	+	1.30435i	−0.0560911	+	0.0505047i
$668$	−1.88527	+	2.09380i	−0.0729433	+	0.0810117i
$669$	0.695860	+	0.309817i	0.0269035	+	0.0119782i
$670$	2.13638	−	3.70032i	0.0825357	−	0.142956i
$671$	−7.32280	−	24.2388i	−0.282694	−	0.935728i
$672$	2.38632	+	1.14258i	0.0920543	+	0.0440758i
$673$	−21.5411	−	29.6487i	−0.830347	−	1.14287i	−0.987858	−	0.155357i	$-0.950347\pi$
$673$	−21.5411	−	29.6487i	−0.830347	−	1.14287i	0.157512	−	0.987517i	$-0.449653\pi$
$674$	15.1752	+	3.22559i	0.584527	+	0.124245i
$675$	0.939833	+	4.42156i	0.0361742	+	0.170186i
$676$	2.72401	−	25.9172i	0.104769	−	0.996815i
$677$	−18.2340	+	8.11831i	−0.700791	+	0.312012i	−0.726024	−	0.687669i	$-0.758634\pi$
$677$	−18.2340	+	8.11831i	−0.700791	+	0.312012i	0.0252332	+	0.999682i	$0.491967\pi$
$678$	4.51202	−	13.8866i	0.173283	−	0.533311i
$679$	−0.536067	−	1.29964i	−0.0205724	−	0.0498757i
$680$	0.593951	−	0.431530i	0.0227770	−	0.0165484i
$681$	−7.47719	−	4.31696i	−0.286527	−	0.165426i
$682$	−7.77824	−	3.65848i	−0.297844	−	0.140090i
$683$	−21.5068	−	37.2509i	−0.822936	−	1.42537i	−0.903486	−	0.428617i	$-0.859001\pi$
$683$	−21.5068	−	37.2509i	−0.822936	−	1.42537i	0.0805497	−	0.996751i	$-0.474332\pi$
$684$	0.535283	+	5.09287i	0.0204670	+	0.194731i
$685$	−3.05970	+	0.994156i	−0.116905	+	0.0379848i
$686$	15.2161	+	10.5580i	0.580953	+	0.403106i
$687$	−15.9563	−	11.5929i	−0.608769	−	0.442297i
$688$	−2.95366	−	6.63403i	−0.112607	−	0.252920i
$689$	43.1256	−	9.16664i	1.64296	−	0.349221i
$690$	0.222595	+	0.200425i	0.00847403	+	0.00763005i
$691$	9.47925	−	0.996310i	0.360608	−	0.0379014i	0.0775076	−	0.996992i	$-0.475304\pi$
$691$	9.47925	−	0.996310i	0.360608	−	0.0379014i	0.283100	+	0.959090i	$0.408637\pi$
$692$	−10.7680			−0.409338
$693$	−8.48482	−	2.23784i	−0.322311	−	0.0850084i
$694$	−14.3048			−0.543004
$695$	10.0298	−	1.05417i	0.380451	−	0.0399870i
$696$	3.34950	+	3.01591i	0.126963	+	0.114318i
$697$	−11.4252	+	2.42851i	−0.432761	+	0.0919863i
$698$	1.79916	+	4.04098i	0.0680992	+	0.152953i
$699$	23.6326	+	17.1701i	0.893869	+	0.649434i
$700$	−8.24541	+	8.66301i	−0.311647	+	0.327431i
$701$	−21.6093	+	7.02129i	−0.816172	+	0.265190i	−0.687210	−	0.726459i	$-0.741165\pi$
$701$	−21.6093	+	7.02129i	−0.816172	+	0.265190i	−0.128963	+	0.991649i	$0.541165\pi$
$702$	−0.653282	−	6.21556i	−0.0246565	−	0.234591i
$703$	23.1158	+	40.0378i	0.871830	+	1.51005i
$704$	−1.59831	−	2.90610i	−0.0602386	−	0.109528i
$705$	6.20200	+	3.58073i	0.233581	+	0.134858i
$706$	−20.7271	+	15.0591i	−0.780076	+	0.566758i
$707$	−17.1660	−	13.2125i	−0.645594	−	0.496909i
$708$	3.15719	−	9.71682i	0.118654	−	0.365180i
$709$	−39.2952	+	17.4954i	−1.47576	+	0.657052i	−0.977684	−	0.210079i	$-0.932628\pi$
$709$	−39.2952	+	17.4954i	−1.47576	+	0.657052i	−0.498079	+	0.867132i	$0.665961\pi$
$710$	−0.435716	+	4.14556i	−0.0163521	+	0.155580i
$711$	−0.969443	−	4.56087i	−0.0363570	−	0.171046i
$712$	5.21238	+	1.10793i	0.195342	+	0.0415213i
$713$	0.658838	+	0.906812i	0.0246737	+	0.0339604i
$714$	2.31374	−	1.58513i	0.0865894	−	0.0593219i
$715$	−8.67747	+	11.4363i	−0.324519	+	0.427695i
$716$	−4.24107	+	7.34575i	−0.158496	+	0.274523i
$717$	12.5572	+	5.59081i	0.468956	+	0.208793i
$718$	9.40755	−	10.4481i	0.351086	−	0.389921i
$719$	16.0528	−	14.4540i	0.598670	−	0.539045i	−0.313114	−	0.949716i	$-0.601372\pi$
$719$	16.0528	−	14.4540i	0.598670	−	0.539045i	0.911784	+	0.410671i	$0.134705\pi$
$720$	0.407083	−	0.560302i	0.0151711	−	0.0208812i
$721$	28.9777	−	15.6779i	1.07919	−	0.583874i
$722$	−6.87033	−	2.23230i	−0.255687	−	0.0830778i
$723$	−2.62605	+	12.3546i	−0.0976639	+	0.459472i
$724$	10.4721	−	23.5207i	0.389193	−	0.874141i
$725$	−17.6445	+	10.1871i	−0.655300	+	0.378338i
$726$	7.01466	+	8.47316i	0.260339	+	0.314469i
$727$			16.4491i			0.610064i	0.952342	+	0.305032i	$0.0986672\pi$
$727$			16.4491i			0.610064i	−0.952342	+	0.305032i	$0.901333\pi$
$728$	12.5896	−	10.7202i	0.466601	−	0.397316i
$729$	−0.309017	−	0.951057i	−0.0114451	−	0.0352243i
$730$	−7.23988	−	8.04070i	−0.267960	−	0.297600i
$731$	−7.65579	−	0.804656i	−0.283160	−	0.0297613i
$732$	7.59268	+	0.798023i	0.280634	+	0.0294958i
$733$	7.28628	+	8.09223i	0.269125	+	0.298893i	0.862525	−	0.506014i	$-0.168882\pi$
$733$	7.28628	+	8.09223i	0.269125	+	0.298893i	−0.593400	+	0.804907i	$0.702215\pi$
$734$	2.14524	+	6.60237i	0.0791822	+	0.243698i
$735$	3.43823	−	3.41784i	0.126821	−	0.126069i
$736$			0.432491i			0.0159418i
$737$	−18.8614	+	7.93255i	−0.694770	+	0.292199i
$738$	−9.54252	+	5.50937i	−0.351265	+	0.202803i
$739$	−0.677735	+	1.52222i	−0.0249309	+	0.0559957i	−0.925582	−	0.378548i	$-0.876424\pi$
$739$	−0.677735	+	1.52222i	−0.0249309	+	0.0559957i	0.900651	+	0.434543i	$0.143090\pi$
$740$	1.29997	−	6.11589i	0.0477880	−	0.224825i
$741$	30.4383	+	9.89001i	1.11818	+	0.363319i
$742$	15.8995	+	9.77579i	0.583689	+	0.358880i
$743$	−25.4214	+	34.9896i	−0.932622	+	1.28364i	0.0262055	+	0.999657i	$0.491658\pi$
$743$	−25.4214	+	34.9896i	−0.932622	+	1.28364i	−0.958828	+	0.283988i	$0.908342\pi$
$744$	1.92600	−	1.73418i	0.0706106	−	0.0635781i
$745$	2.72282	−	3.02400i	0.0997564	−	0.110791i
$746$	−26.8094	−	11.9363i	−0.981562	−	0.437020i
$747$	2.26576	−	3.92442i	0.0829000	−	0.143587i
$748$	−3.51504	−	0.0730076i	−0.128523	−	0.00266942i
$749$	18.2340	−	38.0825i	0.666255	−	1.39150i
$750$	3.87557	+	5.33427i	0.141516	+	0.194780i
$751$	22.4431	+	4.77043i	0.818961	+	0.174076i	0.598297	−	0.801274i	$-0.295844\pi$
$751$	22.4431	+	4.77043i	0.818961	+	0.174076i	0.220664	+	0.975350i	$0.429178\pi$
$752$	2.14989	+	10.1144i	0.0783983	+	0.368835i
$753$	−1.57345	+	14.9704i	−0.0573398	+	0.545552i
$754$	25.7338	−	11.4574i	0.937168	−	0.417254i
$755$	−0.148598	+	0.457339i	−0.00540805	+	0.0166443i
$756$	1.61375	−	2.09662i	0.0586916	−	0.0762533i
$757$	7.17282	−	5.21136i	0.260701	−	0.189410i	−0.449755	−	0.893152i	$-0.648489\pi$
$757$	7.17282	−	5.21136i	0.260701	−	0.189410i	0.710456	+	0.703742i	$0.248489\pi$
$758$	−8.73908	−	5.04551i	−0.317418	−	0.183261i
$759$	−0.269031	−	1.40895i	−0.00976520	−	0.0511418i
$760$	1.77330	+	3.07145i	0.0643245	+	0.111413i
$761$	−3.13877	−	29.8634i	−0.113780	−	1.08255i	−0.891214	−	0.453584i	$-0.850145\pi$
$761$	−3.13877	−	29.8634i	−0.113780	−	1.08255i	0.777433	−	0.628965i	$-0.216521\pi$
$762$	13.2032	−	4.28997i	0.478300	−	0.155409i
$763$	−30.0235	+	8.84481i	−1.08692	+	0.320204i
$764$	17.7404	+	12.8892i	0.641827	+	0.466315i
$765$	−0.298611	−	0.670692i	−0.0107963	−	0.0242489i
$766$	36.2033	−	7.69524i	1.30808	−	0.278040i
$767$	−47.4523	−	42.7262i	−1.71340	−	1.54275i
$768$	0.994522	−	0.104528i	0.0358867	−	0.00377185i
$769$	9.84182			0.354905			0.177453	−	0.984129i	$-0.443214\pi$
$769$	9.84182			0.354905			0.177453	+	0.984129i	$0.443214\pi$
$770$	−5.99869	+	0.974255i	−0.216178	+	0.0351097i
$771$	3.16788			0.114088
$772$	5.68195	−	0.597197i	0.204498	−	0.0214936i
$773$	26.5471	+	23.9031i	0.954834	+	0.859736i	0.990203	−	0.139638i	$-0.0445939\pi$
$773$	26.5471	+	23.9031i	0.954834	+	0.859736i	−0.0353686	+	0.999374i	$0.511261\pi$
$774$	−7.10316	+	1.50982i	−0.255318	+	0.0542695i
$775$	4.76506	+	10.7025i	0.171166	+	0.384445i
$776$	−0.429883	−	0.312328i	−0.0154319	−	0.0112119i
$777$	5.61056	−	23.2175i	0.201278	−	0.832924i
$778$	−12.7037	+	4.12768i	−0.455450	+	0.147985i
$779$	−5.89814	−	56.1171i	−0.211323	−	2.01060i
$780$	−2.16422	−	3.74853i	−0.0774913	−	0.134219i
$781$	13.6622	−	14.5540i	0.488873	−	0.520782i
$782$	0.397041	+	0.229232i	0.0141982	+	0.00819731i
$783$	3.64640	−	2.64927i	0.130312	−	0.0946771i
$784$	6.98929	+	0.387141i	0.249617	+	0.0138265i
$785$	−0.0258004	+	0.0794055i	−0.000920856	+	0.00283410i
$786$	−8.71636	+	3.88077i	−0.310902	+	0.138423i
$787$	−4.33907	+	41.2835i	−0.154671	+	1.47160i	0.591748	+	0.806123i	$0.298438\pi$
$787$	−4.33907	+	41.2835i	−0.154671	+	1.47160i	−0.746420	+	0.665476i	$0.768229\pi$
$788$	1.41781	+	6.67029i	0.0505075	+	0.237619i
$789$	26.1428	+	5.55683i	0.930709	+	0.197828i
$790$	−1.89813	−	2.61256i	−0.0675326	−	0.0929506i
$791$	−2.97369	−	38.5166i	−0.105732	−	1.36949i
$792$	−3.17490	+	0.959172i	−0.112815	+	0.0340827i
$793$	23.8570	−	41.3216i	0.847189	−	1.46737i
$794$	−7.59698	−	3.38239i	−0.269607	−	0.120037i
$795$	3.26920	−	3.63081i	0.115946	−	0.128772i
$796$	−5.28639	+	4.75988i	−0.187371	+	0.168710i
$797$	−16.0647	+	22.1111i	−0.569039	+	0.783216i	−0.992440	−	0.122727i	$-0.960836\pi$
$797$	−16.0647	+	22.1111i	−0.569039	+	0.783216i	0.423401	+	0.905942i	$0.360836\pi$
$798$	6.44717	+	11.9164i	0.228227	+	0.421837i
$799$	10.4249	+	3.38725i	0.368806	+	0.119832i
$800$	−0.939833	+	4.42156i	−0.0332281	+	0.156326i
$801$	2.16743	−	4.86813i	0.0765824	−	0.172007i
$802$	32.4816	−	18.7533i	1.14697	−	0.662201i
$803$	4.34487	+	51.6321i	0.153327	+	1.82206i
$804$		−	6.16942i		−	0.217579i
$805$	0.746634	+	0.265647i	0.0263154	+	0.00936283i
$806$	−5.00531	−	15.4048i	−0.176305	−	0.542610i
$807$	0.924221	+	1.02645i	0.0325341	+	0.0361328i
$808$	−8.14262	−	0.855824i	−0.286456	−	0.0301078i
$809$	6.42325	+	0.675111i	0.225829	+	0.0237356i	0.216767	−	0.976223i	$-0.430449\pi$
$809$	6.42325	+	0.675111i	0.225829	+	0.0237356i	0.00906211	+	0.999959i	$0.497115\pi$
$810$	−0.463421	−	0.514681i	−0.0162829	−	0.0180840i
$811$	−5.86994	−	18.0658i	−0.206121	−	0.634377i	−0.999665	−	0.0258638i	$-0.991766\pi$
$811$	−5.86994	−	18.0658i	−0.206121	−	0.634377i	0.793544	−	0.608513i	$-0.208234\pi$
$812$	11.2350	+	3.99734i	0.394272	+	0.140279i
$813$		−	1.71120i		−	0.0600143i
$814$	−22.6628	+	19.5690i	−0.794331	+	0.685894i
$815$	−0.808057	+	0.466532i	−0.0283050	+	0.0163419i
$816$	0.431163	−	0.968408i	0.0150937	−	0.0339011i
$817$	7.73170	−	36.3748i	0.270498	−	1.27259i
$818$	−15.2536	−	4.95618i	−0.533328	−	0.173289i
$819$	−7.86840	−	14.5433i	−0.274944	−	0.508185i
$820$	−4.48555	+	6.17383i	−0.156642	+	0.215599i
$821$	−3.82648	+	3.44538i	−0.133545	+	0.120245i	−0.733197	−	0.680017i	$-0.761973\pi$
$821$	−3.82648	+	3.44538i	−0.133545	+	0.120245i	0.599651	+	0.800261i	$0.295306\pi$
$822$	−3.10827	+	3.45208i	−0.108413	+	0.120405i
$823$	23.9892	+	10.6807i	0.836211	+	0.372305i	0.779743	−	0.626099i	$-0.215350\pi$
$823$	23.9892	+	10.6807i	0.836211	+	0.372305i	0.0564676	+	0.998404i	$0.482016\pi$
$824$	6.22640	−	10.7844i	0.216907	−	0.375694i
$825$	0.311323	−	14.9891i	0.0108389	−	0.521852i
$826$	−2.08077	−	26.9511i	−0.0723994	−	0.937748i
$827$	−7.77375	−	10.6996i	−0.270320	−	0.372063i	0.652178	−	0.758066i	$-0.273855\pi$
$827$	−7.77375	−	10.6996i	−0.270320	−	0.372063i	−0.922498	+	0.386003i	$0.873855\pi$
$828$	0.423040	+	0.0899199i	0.0147016	+	0.00312493i
$829$	5.95807	+	28.0305i	0.206932	+	0.973540i	0.951893	+	0.306432i	$0.0991351\pi$
$829$	5.95807	+	28.0305i	0.206932	+	0.973540i	−0.744960	+	0.667109i	$0.767532\pi$
$830$	0.328053	−	3.12122i	0.0113869	−	0.108339i
$831$	−20.1316	+	8.96318i	−0.698359	+	0.310929i
$832$	1.93129	−	5.94391i	0.0669555	−	0.206068i
$833$	4.05992	−	6.21121i	0.140668	−	0.215206i
$834$	11.7807	−	8.55915i	0.407931	−	0.296379i
$835$	1.68989	+	0.975657i	0.0584810	+	0.0337640i
$836$	2.12570	−	16.8506i	0.0735190	−	0.582792i
$837$	−1.29585	−	2.24447i	−0.0447910	−	0.0775802i
$838$	1.81504	+	17.2690i	0.0626996	+	0.596547i
$839$	−13.1051	+	4.25809i	−0.452437	+	0.147006i	−0.526366	−	0.850258i	$-0.676446\pi$
$839$	−13.1051	+	4.25809i	−0.452437	+	0.147006i	0.0739297	+	0.997263i	$0.476446\pi$
$840$	0.430408	−	1.78111i	0.0148505	−	0.0614540i
$841$	−7.02641	−	5.10499i	−0.242290	−	0.176034i
$842$	4.72372	+	10.6096i	0.162790	+	0.365633i
$843$	22.4306	−	4.76777i	0.772550	−	0.164211i
$844$	10.7581	+	9.68663i	0.370309	+	0.333427i
$845$	−17.9495	+	1.88657i	−0.617482	+	0.0649000i
$846$	10.3404			0.355510
$847$	25.7050	+	13.6474i	0.883235	+	0.468931i
$848$	7.05449			0.242252
$849$	−27.7218	+	2.91368i	−0.951409	+	0.0999972i
$850$	3.56101	+	3.20635i	0.122142	+	0.109977i
$851$	3.81920	−	0.811795i	0.130920	−	0.0278280i
$852$	2.44803	+	5.49837i	0.0838682	+	0.188371i
$853$	−20.3748	−	14.8031i	−0.697619	−	0.506850i	0.181537	−	0.983384i	$-0.441893\pi$
$853$	−20.3748	−	14.8031i	−0.697619	−	0.506850i	−0.879156	+	0.476534i	$0.841893\pi$
$854$	19.3757	−	5.70802i	0.663023	−	0.195324i
$855$	3.37302	−	1.09596i	0.115355	−	0.0374811i
$856$	−1.66813	−	15.8712i	−0.0570157	−	0.542468i
$857$	7.28367	+	12.6157i	0.248806	+	0.430944i	0.963195	−	0.268805i	$-0.0866287\pi$
$857$	7.28367	+	12.6157i	0.248806	+	0.430944i	−0.714389	+	0.699749i	$0.753295\pi$
$858$	−2.59430	+	20.5652i	−0.0885679	+	0.702086i
$859$	−6.27200	−	3.62114i	−0.213998	−	0.123552i	0.389170	−	0.921166i	$-0.372762\pi$
$859$	−6.27200	−	3.62114i	−0.213998	−	0.123552i	−0.603168	+	0.797614i	$0.706095\pi$
$860$	−4.06883	+	2.95618i	−0.138746	+	0.100805i
$861$	−17.7815	+	23.1021i	−0.605993	+	0.787318i
$862$	5.53026	−	17.0204i	0.188361	−	0.579717i
$863$	−16.8834	+	7.51699i	−0.574719	+	0.255881i	−0.673450	−	0.739233i	$-0.735188\pi$
$863$	−16.8834	+	7.51699i	−0.574719	+	0.255881i	0.0987309	+	0.995114i	$0.468522\pi$
$864$	0.104528	−	0.994522i	0.00355613	−	0.0338343i
$865$	1.55052	+	7.29465i	0.0527194	+	0.248025i
$866$	6.77997	+	1.44113i	0.230393	+	0.0489715i
$867$	9.33185	+	12.8442i	0.316926	+	0.436211i
$868$	2.96120	−	6.18460i	0.100510	−	0.209919i
$869$	−0.321132	+	15.4613i	−0.0108937	+	0.524489i
$870$	1.56078	−	2.70335i	0.0529154	−	0.0916522i
$871$	−35.2242	−	15.6828i	−1.19352	−	0.531392i
$872$	−7.91580	+	8.79139i	−0.268063	+	0.297714i
$873$	−0.394881	+	0.355553i	−0.0133647	+	0.0120336i
$874$	−1.30180	+	1.79177i	−0.0440340	+	0.0606076i
$875$	14.8606	+	9.13700i	0.502379	+	0.308887i
$876$	−14.8581	−	4.82768i	−0.502007	−	0.163112i
$877$	−11.2399	+	52.8796i	−0.379545	+	1.78562i	0.209809	+	0.977742i	$0.432716\pi$
$877$	−11.2399	+	52.8796i	−0.379545	+	1.78562i	−0.589354	+	0.807875i	$0.700618\pi$
$878$	−5.34748	+	12.0106i	−0.180469	+	0.405339i
$879$	−14.0942	+	8.13727i	−0.475385	+	0.274463i
$880$	−1.73855	+	1.50121i	−0.0586066	+	0.0506059i
$881$		−	22.5310i		−	0.759088i	−0.925174	−	0.379544i	$-0.876081\pi$
$881$		−	22.5310i		−	0.759088i	0.925174	−	0.379544i	$-0.123919\pi$
$882$	1.83184	−	6.75606i	0.0616811	−	0.227488i
$883$	4.31623	+	13.2840i	0.145253	+	0.447042i	0.997043	−	0.0768402i	$-0.0244831\pi$
$883$	4.31623	+	13.2840i	0.145253	+	0.447042i	−0.851791	+	0.523882i	$0.824483\pi$
$884$	−4.43307	−	4.92343i	−0.149100	−	0.165593i
$885$	−7.03715	−	0.739634i	−0.236551	−	0.0248625i
$886$	−9.63874	−	1.01307i	−0.323820	−	0.0340348i
$887$	−14.5141	−	16.1196i	−0.487337	−	0.541242i	0.448450	−	0.893808i	$-0.351976\pi$
$887$	−14.5141	−	16.1196i	−0.487337	−	0.541242i	−0.935787	+	0.352565i	$0.885309\pi$
$888$	−2.78980	−	8.58613i	−0.0936196	−	0.288132i
$889$	27.9652	−	23.8127i	0.937921	−	0.798651i
$890$		−	3.69060i		−	0.123709i
$891$	0.278113	+	3.30494i	0.00931713	+	0.110720i
$892$	0.659663	−	0.380857i	0.0220871	−	0.0127520i
$893$	−21.5376	+	48.3743i	−0.720730	+	1.61879i
$894$	1.22158	−	5.74709i	0.0408558	−	0.192211i
$895$	5.58697	+	1.81532i	0.186752	+	0.0606793i
$896$	2.32701	−	1.25898i	0.0777398	−	0.0420597i
$897$	1.58877	−	2.18676i	0.0530475	−	0.0730136i
$898$	−19.1319	+	17.2264i	−0.638439	+	0.574853i
$899$	7.81630	−	8.68088i	0.260688	−	0.289524i
$900$	4.12954	+	1.83859i	0.137651	+	0.0612863i
$901$	3.73907	−	6.47626i	0.124566	−	0.215755i
$902$	34.9834	−	10.5689i	1.16482	−	0.351905i
$903$	−15.8501	+	10.8588i	−0.527460	+	0.361359i
$904$	−8.58238	−	11.8126i	−0.285446	−	0.392882i
$905$	−17.4417	−	3.70736i	−0.579783	−	0.123237i
$906$	0.144360	+	0.679159i	0.00479603	+	0.0225636i
$907$	4.97968	−	47.3785i	0.165348	−	1.57318i	−0.525891	−	0.850552i	$-0.676268\pi$
$907$	4.97968	−	47.3785i	0.165348	−	1.57318i	0.691239	−	0.722626i	$-0.257065\pi$
$908$	−7.88748	+	3.51173i	−0.261755	+	0.116541i
$909$	−2.53007	+	7.78675i	−0.0839171	+	0.258270i
$910$	−9.07507	−	6.98501i	−0.300836	−	0.231551i
$911$	13.1407	−	9.54730i	0.435372	−	0.316316i	−0.348421	−	0.937338i	$-0.613282\pi$
$911$	13.1407	−	9.54730i	0.435372	−	0.316316i	0.783793	+	0.621022i	$0.213282\pi$
$912$	4.43485	+	2.56046i	0.146853	+	0.0847854i
$913$	−10.2864	+	10.9578i	−0.340430	+	0.362649i
$914$	17.2630	+	29.9005i	0.571011	+	0.989019i
$915$	−0.552688	−	5.25848i	−0.0182713	−	0.173840i
$916$	−18.7577	+	6.09475i	−0.619772	+	0.201376i
$917$	−17.4039	+	18.2853i	−0.574726	+	0.603834i
$918$	−0.857602	−	0.623084i	−0.0283051	−	0.0205648i
$919$	−16.0367	−	36.0190i	−0.529001	−	1.18816i	−0.958501	−	0.285089i	$-0.907977\pi$
$919$	−16.0367	−	36.0190i	−0.529001	−	1.18816i	0.429500	−	0.903067i	$-0.358690\pi$
$920$	0.292985	−	0.0622759i	0.00965944	−	0.00205318i
$921$	−4.48375	−	4.03718i	−0.147744	−	0.133030i
$922$	28.4398	−	2.98914i	0.936615	−	0.0984422i
$923$	37.6158			1.23814
$924$	−6.79770	+	5.54899i	−0.223628	+	0.182548i
$925$	40.8096			1.34181
$926$	−12.7299	+	1.33796i	−0.418329	+	0.0439682i
$927$	−9.25423	−	8.33255i	−0.303949	−	0.273677i
$928$	4.40871	−	0.937100i	0.144723	−	0.0307618i
$929$	16.5216	+	37.1080i	0.542055	+	1.21748i	0.952206	+	0.305457i	$0.0988094\pi$
$929$	16.5216	+	37.1080i	0.542055	+	1.21748i	−0.410151	+	0.912018i	$0.634524\pi$
$930$	−1.45213	−	1.05503i	−0.0476172	−	0.0345959i
$931$	27.7907	+	22.6417i	0.910804	+	0.742051i
$932$	27.7818	−	9.02687i	0.910024	−	0.295685i
$933$	0.320368	+	3.04810i	0.0104884	+	0.0997903i
$934$	−3.44215	−	5.96198i	−0.112631	−	0.195082i
$935$	0.456686	+	2.39173i	0.0149352	+	0.0782181i
$936$	−5.41248	−	3.12490i	−0.176913	−	0.102140i
$937$	−8.90883	+	6.47264i	−0.291039	+	0.211452i	−0.723718	−	0.690096i	$-0.757568\pi$
$937$	−8.90883	+	6.47264i	−0.291039	+	0.211452i	0.432679	+	0.901548i	$0.357568\pi$
$938$	−6.22402	−	15.0895i	−0.203221	−	0.492691i
$939$	3.18437	−	9.80047i	0.103918	−	0.319826i
$940$	6.54231	−	2.91282i	0.213387	−	0.0950059i
$941$	1.68344	−	16.0169i	0.0548787	−	0.522136i	−0.932205	−	0.361931i	$-0.882118\pi$
$941$	1.68344	−	16.0169i	0.0548787	−	0.522136i	0.987084	−	0.160205i	$-0.0512156\pi$
$942$	0.0250645	+	0.117919i	0.000816644	+	0.00384201i
$943$	−4.66137	−	0.990804i	−0.151795	−	0.0322650i
$944$	−6.00532	−	8.26562i	−0.195457	−	0.269023i
$945$	−1.65270	−	0.791315i	−0.0537622	−	0.0257415i
$946$	24.0796	+	0.500135i	0.782897	+	0.0162608i
$947$	−10.4323	+	18.0692i	−0.339003	+	0.587170i	−0.984245	−	0.176808i	$-0.943423\pi$
$947$	−10.4323	+	18.0692i	−0.339003	+	0.587170i	0.645243	+	0.763978i	$0.276756\pi$
$948$	−4.25965	−	1.89652i	−0.138347	−	0.0615960i
$949$	−65.3330	+	72.5597i	−2.12080	+	2.35539i
$950$	−17.2026	+	15.4893i	−0.558125	+	0.502538i
$951$	−13.9800	+	19.2418i	−0.453332	+	0.623959i
$952$	0.0775863	−	2.80357i	0.00251459	−	0.0908641i
$953$	−12.7967	−	4.15790i	−0.414526	−	0.134688i	0.0943268	−	0.995541i	$-0.469930\pi$
$953$	−12.7967	−	4.15790i	−0.414526	−	0.134688i	−0.508852	+	0.860854i	$0.669930\pi$
$954$	1.46671	−	6.90033i	0.0474865	−	0.223406i
$955$	6.17710	−	13.8740i	0.199886	−	0.448952i
$956$	11.9040	−	6.87277i	0.385002	−	0.222281i
$957$	−13.7796	+	5.79529i	−0.445432	+	0.187335i
$958$			28.3629i			0.916364i
$959$	−4.11976	+	11.5791i	−0.133034	+	0.373908i
$960$	−0.214016	−	0.658675i	−0.00690735	−	0.0212586i
$961$	16.2486	+	18.0459i	0.524148	+	0.582125i
$962$	−56.1140	−	5.89782i	−1.80919	−	0.190153i
$963$	−15.8712	−	1.66813i	−0.511443	−	0.0537549i
$964$	8.45152	+	9.38637i	0.272205	+	0.302315i
$965$	−1.22273	−	3.76317i	−0.0393610	−	0.121141i
$966$	1.12541	−	0.206852i	0.0362095	−	0.00665535i
$967$			47.9124i			1.54076i	0.637585	+	0.770380i	$0.279933\pi$
$967$			47.9124i			1.54076i	−0.637585	+	0.770380i	$0.720067\pi$
$968$	10.9780	−	0.694580i	0.352848	−	0.0223246i
$969$	4.70119	−	2.71423i	0.151024	−	0.0871936i
$970$	−0.149682	+	0.336192i	−0.00480601	+	0.0107945i
$971$	−2.27667	+	10.7109i	−0.0730617	+	0.343728i	−0.999462	−	0.0328132i	$-0.989553\pi$
$971$	−2.27667	+	10.7109i	−0.0730617	+	0.343728i	0.926400	+	0.376541i	$0.122887\pi$
$972$	−0.951057	−	0.309017i	−0.0305052	−	0.00991172i
$973$	20.1789	−	32.8194i	0.646907	−	1.05214i
$974$	0.0403047	−	0.0554747i	0.00129145	−	0.00177752i
$975$	20.9948	−	18.9038i	0.672370	−	0.605405i
$976$	5.10848	−	5.67354i	0.163518	−	0.181606i
$977$	26.3766	+	11.7436i	0.843862	+	0.375712i	0.782687	−	0.622416i	$-0.213849\pi$
$977$	26.3766	+	11.7436i	0.843862	+	0.375712i	0.0611749	+	0.998127i	$0.480515\pi$
$978$	−0.673623	+	1.16675i	−0.0215401	+	0.0373085i
$979$	−10.6830	+	14.0795i	−0.341431	+	0.449984i
$980$	−0.744149	−	4.79055i	−0.0237710	−	0.153028i
$981$	6.95349	+	9.57065i	0.222008	+	0.305567i
$982$	−6.58337	−	1.39934i	−0.210084	−	0.0446547i
$983$	−2.36021	−	11.1039i	−0.0752790	−	0.354160i	0.924346	−	0.381556i	$-0.124612\pi$
$983$	−2.36021	−	11.1039i	−0.0752790	−	0.354160i	−0.999625	+	0.0273964i	$0.991278\pi$
$984$	−1.15177	+	10.9584i	−0.0367172	+	0.349341i
$985$	4.31455	−	1.92096i	0.137473	−	0.0612069i
$986$	1.47645	−	4.54403i	0.0470196	−	0.144712i
$987$	25.2911	−	10.4319i	0.805025	−	0.332050i
$988$	25.8924	−	18.8119i	0.823746	−	0.598487i
$989$	−2.71991	−	1.57034i	−0.0864881	−	0.0499339i
$990$	1.10694	+	2.01268i	0.0351810	+	0.0639672i
$991$	1.88563	+	3.26601i	0.0598991	+	0.103748i	0.894420	−	0.447228i	$-0.147589\pi$
$991$	1.88563	+	3.26601i	0.0598991	+	0.103748i	−0.834521	+	0.550976i	$0.814255\pi$
$992$	−0.270905	−	2.57749i	−0.00860126	−	0.0818355i
$993$	−0.931455	+	0.302648i	−0.0295588	+	0.00960424i
$994$	11.5346	+	10.9785i	0.365854	+	0.348218i
$995$	3.98573	+	2.89580i	0.126356	+	0.0918031i
$996$	−1.84314	−	4.13976i	−0.0584021	−	0.131173i
$997$	−38.5156	+	8.18674i	−1.21980	+	0.259277i	−0.772446	−	0.635080i	$-0.780967\pi$
$997$	−38.5156	+	8.18674i	−1.21980	+	0.259277i	−0.447355	+	0.894357i	$0.647634\pi$
$998$	17.5693	+	15.8194i	0.556145	+	0.500755i
$999$	−8.97853	+	0.943682i	−0.284068	+	0.0298568i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.ba.a.19.3	✓	64
7.3	odd	6		462.2.ba.b.283.7	yes	64
11.7	odd	10		462.2.ba.b.271.7	yes	64
77.73	even	30	inner	462.2.ba.a.73.3	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.ba.a.19.3	✓	64	1.1	even	1	trivial
462.2.ba.a.73.3	yes	64	77.73	even	30	inner
462.2.ba.b.271.7	yes	64	11.7	odd	10
462.2.ba.b.283.7	yes	64	7.3	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.ba (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.994522 + 0.104528i) q^{2} +(0.743145 + 0.669131i) q^{3} +(0.978148 - 0.207912i) q^{4} +(-0.281694 - 0.632696i) q^{5} +(-0.809017 - 0.587785i) q^{6} +(-2.57173 - 0.621464i) q^{7} +(-0.951057 + 0.309017i) q^{8} +(0.104528 + 0.994522i) q^{9} +O(q^{10})\)	\(q+(-0.994522 + 0.104528i) q^{2} +(0.743145 + 0.669131i) q^{3} +(0.978148 - 0.207912i) q^{4} +(-0.281694 - 0.632696i) q^{5} +(-0.809017 - 0.587785i) q^{6} +(-2.57173 - 0.621464i) q^{7} +(-0.951057 + 0.309017i) q^{8} +(0.104528 + 0.994522i) q^{9} +(0.346286 + 0.599785i) q^{10} +(0.415101 - 3.29055i) q^{11} +(0.866025 + 0.500000i) q^{12} +(5.05619 - 3.67354i) q^{13} +(2.62260 + 0.349240i) q^{14} +(0.214016 - 0.658675i) q^{15} +(0.913545 - 0.406737i) q^{16} +(0.110806 - 1.05425i) q^{17} +(-0.207912 - 0.978148i) q^{18} +(5.00902 + 1.06470i) q^{19} +(-0.407083 - 0.560302i) q^{20} +(-1.49533 - 2.18266i) q^{21} +(-0.0688715 + 3.31591i) q^{22} +(0.216245 - 0.374548i) q^{23} +(-0.913545 - 0.406737i) q^{24} +(3.02470 - 3.35927i) q^{25} +(-4.64450 + 4.18193i) q^{26} +(-0.587785 + 0.809017i) q^{27} +(-2.64474 - 0.0731908i) q^{28} +(-4.28660 - 1.39280i) q^{29} +(-0.143994 + 0.677437i) q^{30} +(-1.05414 + 2.36763i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(2.51029 - 2.16760i) q^{33} +1.06005i q^{34} +(0.331244 + 1.80218i) q^{35} +(0.309017 + 0.951057i) q^{36} +(6.04090 + 6.70910i) q^{37} +(-5.09287 - 0.535283i) q^{38} +(6.21556 + 0.653282i) q^{39} +(0.463421 + 0.514681i) q^{40} +(-3.40498 - 10.4795i) q^{41} +(1.71528 + 2.01440i) q^{42} -7.26185i q^{43} +(-0.278113 - 3.30494i) q^{44} +(0.599785 - 0.346286i) q^{45} +(-0.175910 + 0.395100i) q^{46} +(-2.14989 + 10.1144i) q^{47} +(0.951057 + 0.309017i) q^{48} +(6.22757 + 3.19647i) q^{49} +(-2.65699 + 3.65704i) q^{50} +(0.787774 - 0.709315i) q^{51} +(4.18193 - 4.64450i) q^{52} +(6.44459 + 2.86932i) q^{53} +(0.500000 - 0.866025i) q^{54} +(-2.19885 + 0.664295i) q^{55} +(2.63790 - 0.203661i) q^{56} +(3.01001 + 4.14292i) q^{57} +(4.40871 + 0.937100i) q^{58} +(-2.12421 - 9.99360i) q^{59} +(0.0723934 - 0.688778i) q^{60} +(6.97447 - 3.10523i) q^{61} +(0.800876 - 2.46484i) q^{62} +(0.349240 - 2.62260i) q^{63} +(0.809017 - 0.587785i) q^{64} +(-3.74853 - 2.16422i) q^{65} +(-2.26996 + 2.41812i) q^{66} +(-3.08471 - 5.34288i) q^{67} +(-0.110806 - 1.05425i) q^{68} +(0.411323 - 0.133647i) q^{69} +(-0.517808 - 1.75769i) q^{70} +(4.86924 + 3.53771i) q^{71} +(-0.406737 - 0.913545i) q^{72} +(-15.2813 + 3.24814i) q^{73} +(-6.70910 - 6.04090i) q^{74} +(4.49558 - 0.472505i) q^{75} +5.12093 q^{76} +(-3.11248 + 8.20442i) q^{77} -6.24980 q^{78} +(-4.63722 + 0.487392i) q^{79} +(-0.514681 - 0.463421i) q^{80} +(-0.978148 + 0.207912i) q^{81} +(4.48173 + 10.0661i) q^{82} +(-3.66608 - 2.66357i) q^{83} +(-1.91645 - 1.82407i) q^{84} +(-0.698231 + 0.226869i) q^{85} +(0.759070 + 7.22207i) q^{86} +(-2.25360 - 3.90335i) q^{87} +(0.622050 + 3.25777i) q^{88} +(-4.61490 - 2.66441i) q^{89} +(-0.560302 + 0.407083i) q^{90} +(-15.2861 + 6.30510i) q^{91} +(0.133647 - 0.411323i) q^{92} +(-2.36763 + 1.05414i) q^{93} +(1.08086 - 10.2837i) q^{94} +(-0.737381 - 3.46911i) q^{95} +(-0.978148 - 0.207912i) q^{96} +(0.312328 + 0.429883i) q^{97} +(-6.52757 - 2.52800i) q^{98} +(3.31591 + 0.0688715i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 8 q^{4} - 22 q^{5} - 16 q^{6} + 4 q^{7} - 8 q^{9}+O(q^{10}) \) 64 * q - 8 * q^4 - 22 * q^5 - 16 * q^6 + 4 * q^7 - 8 * q^9	\( 64 q - 8 q^{4} - 22 q^{5} - 16 q^{6} + 4 q^{7} - 8 q^{9} + 2 q^{10} + 4 q^{11} + 2 q^{14} - 6 q^{15} + 8 q^{16} + 30 q^{17} + 10 q^{19} + 20 q^{20} - 4 q^{21} - 2 q^{22} + 4 q^{23} - 8 q^{24} - 12 q^{26} - 10 q^{28} - 20 q^{29} + 18 q^{30} - 16 q^{31} - 14 q^{33} + 42 q^{35} - 16 q^{36} - 14 q^{37} + 12 q^{38} + 18 q^{39} + 18 q^{40} - 28 q^{41} - 6 q^{42} + 6 q^{44} - 12 q^{45} - 42 q^{46} + 24 q^{47} + 116 q^{49} + 26 q^{51} + 32 q^{54} - 14 q^{55} - 4 q^{56} + 20 q^{58} + 30 q^{59} + 2 q^{60} - 32 q^{61} - 8 q^{62} + 4 q^{63} + 16 q^{64} + 12 q^{65} + 4 q^{66} + 16 q^{67} - 30 q^{68} - 20 q^{70} - 24 q^{71} - 64 q^{73} + 4 q^{74} + 12 q^{75} - 48 q^{77} - 60 q^{79} - 18 q^{80} + 8 q^{81} - 68 q^{82} + 8 q^{83} + 2 q^{84} - 80 q^{85} - 18 q^{86} + 10 q^{87} - 8 q^{88} - 24 q^{89} + 4 q^{90} - 172 q^{91} + 8 q^{92} - 104 q^{93} - 6 q^{94} - 118 q^{95} + 8 q^{96} + 120 q^{97} + 40 q^{98} + 8 q^{99}+O(q^{100}) \) 64 * q - 8 * q^4 - 22 * q^5 - 16 * q^6 + 4 * q^7 - 8 * q^9 + 2 * q^10 + 4 * q^11 + 2 * q^14 - 6 * q^15 + 8 * q^16 + 30 * q^17 + 10 * q^19 + 20 * q^20 - 4 * q^21 - 2 * q^22 + 4 * q^23 - 8 * q^24 - 12 * q^26 - 10 * q^28 - 20 * q^29 + 18 * q^30 - 16 * q^31 - 14 * q^33 + 42 * q^35 - 16 * q^36 - 14 * q^37 + 12 * q^38 + 18 * q^39 + 18 * q^40 - 28 * q^41 - 6 * q^42 + 6 * q^44 - 12 * q^45 - 42 * q^46 + 24 * q^47 + 116 * q^49 + 26 * q^51 + 32 * q^54 - 14 * q^55 - 4 * q^56 + 20 * q^58 + 30 * q^59 + 2 * q^60 - 32 * q^61 - 8 * q^62 + 4 * q^63 + 16 * q^64 + 12 * q^65 + 4 * q^66 + 16 * q^67 - 30 * q^68 - 20 * q^70 - 24 * q^71 - 64 * q^73 + 4 * q^74 + 12 * q^75 - 48 * q^77 - 60 * q^79 - 18 * q^80 + 8 * q^81 - 68 * q^82 + 8 * q^83 + 2 * q^84 - 80 * q^85 - 18 * q^86 + 10 * q^87 - 8 * q^88 - 24 * q^89 + 4 * q^90 - 172 * q^91 + 8 * q^92 - 104 * q^93 - 6 * q^94 - 118 * q^95 + 8 * q^96 + 120 * q^97 + 40 * q^98 + 8 * q^99

Introduction

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