LMFDB - Embedded newform 462.2.bf.a.5.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(5,462)]

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, 25, 12]))

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

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

chi := DirichletCharacter("462.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.bf (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:	$256$
Relative dimension:	$32$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			5.3
Character	$\chi$	$=$	462.5
Dual form			462.2.bf.a.185.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.207912 + 0.978148i) q^{2} +(-1.46408 - 0.925462i) q^{3} +(-0.913545 - 0.406737i) q^{4} +(0.383830 + 0.426287i) q^{5} +(1.20964 - 1.23967i) q^{6} +(-2.12466 + 1.57664i) q^{7} +(0.587785 - 0.809017i) q^{8} +(1.28704 + 2.70989i) q^{9} +O(q^{10})$	\(q+(-0.207912 + 0.978148i) q^{2} +(-1.46408 - 0.925462i) q^{3} +(-0.913545 - 0.406737i) q^{4} +(0.383830 + 0.426287i) q^{5} +(1.20964 - 1.23967i) q^{6} +(-2.12466 + 1.57664i) q^{7} +(0.587785 - 0.809017i) q^{8} +(1.28704 + 2.70989i) q^{9} +(-0.496774 + 0.286813i) q^{10} +(-2.05262 - 2.60514i) q^{11} +(0.961081 + 1.44095i) q^{12} +(5.25730 - 1.70820i) q^{13} +(-1.10045 - 2.40604i) q^{14} +(-0.167445 - 0.979337i) q^{15} +(0.669131 + 0.743145i) q^{16} +(-1.80521 + 0.383709i) q^{17} +(-2.91827 + 0.695496i) q^{18} +(-2.38460 - 5.35590i) q^{19} +(-0.177260 - 0.545550i) q^{20} +(4.56979 - 0.342031i) q^{21} +(2.97498 - 1.46612i) q^{22} +(-6.17919 - 3.56755i) q^{23} +(-1.60928 + 0.640490i) q^{24} +(0.488248 - 4.64537i) q^{25} +(0.577817 + 5.49757i) q^{26} +(0.623580 - 5.15860i) q^{27} +(2.58226 - 0.576157i) q^{28} +(-4.25665 - 5.85878i) q^{29} +(0.992750 + 0.0398300i) q^{30} +(1.57061 + 1.41418i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(0.594229 + 5.71375i) q^{33} -1.84554i q^{34} +(-1.48761 - 0.300553i) q^{35} +(-0.0735559 - 2.99910i) q^{36} +(-0.0798338 - 0.759568i) q^{37} +(5.73465 - 1.21894i) q^{38} +(-9.27796 - 2.36449i) q^{39} +(0.570483 - 0.0599602i) q^{40} +(-1.20627 - 0.876408i) q^{41} +(-0.615557 + 4.54104i) q^{42} +7.77598 q^{43} +(0.815553 + 3.21479i) q^{44} +(-0.661188 + 1.58879i) q^{45} +(4.77432 - 5.30242i) q^{46} +(-0.407668 + 0.181505i) q^{47} +(-0.291906 - 1.70728i) q^{48} +(2.02839 - 6.69967i) q^{49} +(4.44234 + 1.44340i) q^{50} +(2.99807 + 1.10887i) q^{51} +(-5.49757 - 0.577817i) q^{52} +(-2.59005 - 2.33210i) q^{53} +(4.91622 + 1.68249i) q^{54} +(0.322681 - 1.87494i) q^{55} +(0.0266852 + 2.64562i) q^{56} +(-1.46545 + 10.0483i) q^{57} +(6.61576 - 2.94552i) q^{58} +(9.56549 + 4.25883i) q^{59} +(-0.245364 + 0.962775i) q^{60} +(-0.468853 + 0.422157i) q^{61} +(-1.70983 + 1.24226i) q^{62} +(-7.00706 - 3.72841i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(2.74609 + 1.58546i) q^{65} +(-5.71243 - 0.606711i) q^{66} +(2.30807 + 3.99770i) q^{67} +(1.80521 + 0.383709i) q^{68} +(5.74516 + 10.9418i) q^{69} +(0.603277 - 1.39262i) q^{70} +(-7.77727 - 2.52699i) q^{71} +(2.94885 + 0.551599i) q^{72} +(-5.15099 + 11.5693i) q^{73} +(0.759568 + 0.0798338i) q^{74} +(-5.01394 + 6.34932i) q^{75} +5.86276i q^{76} +(8.46850 + 2.29880i) q^{77} +(4.24182 - 8.58360i) q^{78} +(-10.3411 - 2.19806i) q^{79} +(-0.0599602 + 0.570483i) q^{80} +(-5.68706 + 6.97548i) q^{81} +(1.10805 - 0.997697i) q^{82} +(-1.54533 + 4.75602i) q^{83} +(-4.31383 - 1.54624i) q^{84} +(-0.856463 - 0.622257i) q^{85} +(-1.61672 + 7.60606i) q^{86} +(0.809986 + 12.5171i) q^{87} +(-3.31410 + 0.129338i) q^{88} +(6.63333 - 11.4893i) q^{89} +(-1.41660 - 0.977067i) q^{90} +(-8.47676 + 11.9182i) q^{91} +(4.19391 + 5.77243i) q^{92} +(-0.990718 - 3.52401i) q^{93} +(-0.0927802 - 0.436497i) q^{94} +(1.36787 - 3.07228i) q^{95} +(1.73066 + 0.0694355i) q^{96} +(3.18905 - 1.03619i) q^{97} +(6.13154 + 3.37701i) q^{98} +(4.41786 - 8.91530i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 256 q - 32 q^{4} + 4 q^{7} - 12 q^{9}+O(q^{10}) $ 256 * q - 32 * q^4 + 4 * q^7 - 12 * q^9	$ 256 q - 32 q^{4} + 4 q^{7} - 12 q^{9} + 12 q^{10} + 24 q^{15} + 32 q^{16} - 8 q^{18} - 16 q^{21} - 12 q^{22} + 48 q^{25} + 6 q^{28} + 18 q^{31} - 132 q^{33} + 16 q^{36} + 4 q^{37} - 18 q^{40} - 4 q^{42} + 64 q^{43} - 48 q^{45} + 8 q^{46} + 76 q^{49} - 8 q^{51} - 88 q^{57} + 46 q^{58} - 8 q^{60} - 12 q^{63} + 64 q^{64} - 120 q^{66} - 32 q^{67} - 58 q^{70} - 12 q^{72} - 96 q^{73} - 204 q^{75} - 32 q^{78} - 4 q^{79} - 64 q^{81} + 24 q^{82} - 36 q^{84} + 232 q^{85} - 228 q^{87} - 6 q^{88} + 40 q^{91} - 2 q^{93} - 144 q^{94} + 160 q^{99}+O(q^{100}) $ 256 * q - 32 * q^4 + 4 * q^7 - 12 * q^9 + 12 * q^10 + 24 * q^15 + 32 * q^16 - 8 * q^18 - 16 * q^21 - 12 * q^22 + 48 * q^25 + 6 * q^28 + 18 * q^31 - 132 * q^33 + 16 * q^36 + 4 * q^37 - 18 * q^40 - 4 * q^42 + 64 * q^43 - 48 * q^45 + 8 * q^46 + 76 * q^49 - 8 * q^51 - 88 * q^57 + 46 * q^58 - 8 * q^60 - 12 * q^63 + 64 * q^64 - 120 * q^66 - 32 * q^67 - 58 * q^70 - 12 * q^72 - 96 * q^73 - 204 * q^75 - 32 * q^78 - 4 * q^79 - 64 * q^81 + 24 * q^82 - 36 * q^84 + 232 * q^85 - 228 * q^87 - 6 * q^88 + 40 * q^91 - 2 * q^93 - 144 * q^94 + 160 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{5}\right)$

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 $

$2$	−0.207912	+	0.978148i	−0.147016	+	0.691655i
$2$	−0.207912	+	0.978148i	−0.147016	+	0.691655i
$3$	−1.46408	−	0.925462i	−0.845285	−	0.534316i
$3$	−1.46408	−	0.925462i	−0.845285	−	0.534316i
$4$	−0.913545	−	0.406737i	−0.456773	−	0.203368i
$5$	0.383830	+	0.426287i	0.171654	+	0.190641i	0.822833	−	0.568283i	$-0.192392\pi$
$5$	0.383830	+	0.426287i	0.171654	+	0.190641i	−0.651179	+	0.758924i	$0.725725\pi$
$6$	1.20964	−	1.23967i	0.493832	−	0.506093i
$7$	−2.12466	+	1.57664i	−0.803047	+	0.595915i
$7$	−2.12466	+	1.57664i	−0.803047	+	0.595915i
$8$	0.587785	−	0.809017i	0.207813	−	0.286031i
$9$	1.28704	+	2.70989i	0.429013	+	0.903298i
$10$	−0.496774	+	0.286813i	−0.157094	+	0.0906982i
$11$	−2.05262	−	2.60514i	−0.618887	−	0.785480i
$11$	−2.05262	−	2.60514i	−0.618887	−	0.785480i
$12$	0.961081	+	1.44095i	0.277440	+	0.415965i
$13$	5.25730	−	1.70820i	1.45811	−	0.473769i	0.530619	−	0.847611i	$-0.321960\pi$
$13$	5.25730	−	1.70820i	1.45811	−	0.473769i	0.927493	+	0.373841i	$0.121960\pi$
$14$	−1.10045	−	2.40604i	−0.294107	−	0.643041i
$15$	−0.167445	−	0.979337i	−0.0432341	−	0.252864i
$16$	0.669131	+	0.743145i	0.167283	+	0.185786i
$17$	−1.80521	+	0.383709i	−0.437827	+	0.0930630i	−0.421551	−	0.906805i	$-0.638514\pi$
$17$	−1.80521	+	0.383709i	−0.437827	+	0.0930630i	−0.0162757	+	0.999868i	$0.505181\pi$
$18$	−2.91827	+	0.695496i	−0.687842	+	0.163930i
$19$	−2.38460	−	5.35590i	−0.547065	−	1.22873i	−0.949641	−	0.313341i	$-0.898552\pi$
$19$	−2.38460	−	5.35590i	−0.547065	−	1.22873i	0.402576	−	0.915387i	$-0.368115\pi$
$20$	−0.177260	−	0.545550i	−0.0396366	−	0.121989i
$21$	4.56979	−	0.342031i	0.997211	−	0.0746372i
$22$	2.97498	−	1.46612i	0.634267	−	0.312579i
$23$	−6.17919	−	3.56755i	−1.28845	−	0.743887i	−0.310072	−	0.950713i	$-0.600353\pi$
$23$	−6.17919	−	3.56755i	−1.28845	−	0.743887i	−0.978378	+	0.206827i	$0.933686\pi$
$24$	−1.60928	+	0.640490i	−0.328492	+	0.130739i
$25$	0.488248	−	4.64537i	0.0976495	−	0.929073i
$26$	0.577817	+	5.49757i	0.113319	+	1.07816i
$27$	0.623580	−	5.15860i	0.120008	−	0.992773i
$28$	2.58226	−	0.576157i	0.488000	−	0.108883i
$29$	−4.25665	−	5.85878i	−0.790440	−	1.08795i	−0.994053	−	0.108896i	$-0.965268\pi$
$29$	−4.25665	−	5.85878i	−0.790440	−	1.08795i	0.203613	−	0.979051i	$-0.434732\pi$
$30$	0.992750	+	0.0398300i	0.181251	+	0.00727192i
$31$	1.57061	+	1.41418i	0.282089	+	0.253994i	0.798013	−	0.602640i	$-0.205885\pi$
$31$	1.57061	+	1.41418i	0.282089	+	0.253994i	−0.515924	+	0.856635i	$0.672551\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	0.594229	+	5.71375i	0.103442	+	0.994635i
$34$		−	1.84554i		−	0.316507i
$35$	−1.48761	−	0.300553i	−0.251453	−	0.0508027i
$36$	−0.0735559	−	2.99910i	−0.0122593	−	0.499850i
$37$	−0.0798338	−	0.759568i	−0.0131246	−	0.124872i	0.985998	−	0.166758i	$-0.0533300\pi$
$37$	−0.0798338	−	0.759568i	−0.0131246	−	0.124872i	−0.999122	+	0.0418862i	$0.986663\pi$
$38$	5.73465	−	1.21894i	0.930283	−	0.197738i
$39$	−9.27796	−	2.36449i	−1.48566	−	0.378622i
$40$	0.570483	−	0.0599602i	0.0902013	−	0.00948054i
$41$	−1.20627	−	0.876408i	−0.188388	−	0.136872i	0.489594	−	0.871951i	$-0.337145\pi$
$41$	−1.20627	−	0.876408i	−0.188388	−	0.136872i	−0.677982	+	0.735079i	$0.737145\pi$
$42$	−0.615557	+	4.54104i	−0.0949825	+	0.700698i
$43$	7.77598			1.18583			0.592913	−	0.805267i	$-0.297978\pi$
$43$	7.77598			1.18583			0.592913	+	0.805267i	$0.297978\pi$
$44$	0.815553	+	3.21479i	0.122949	+	0.484648i
$45$	−0.661188	+	1.58879i	−0.0985640	+	0.236843i
$46$	4.77432	−	5.30242i	0.703935	−	0.781799i
$47$	−0.407668	+	0.181505i	−0.0594645	+	0.0264753i	−0.436253	−	0.899824i	$-0.643695\pi$
$47$	−0.407668	+	0.181505i	−0.0594645	+	0.0264753i	0.376789	+	0.926299i	$0.377028\pi$
$48$	−0.291906	−	1.70728i	−0.0421330	−	0.246424i
$49$	2.02839	−	6.69967i	0.289770	−	0.957096i
$50$	4.44234	+	1.44340i	0.628242	+	0.204128i
$51$	2.99807	+	1.10887i	0.419814	+	0.155273i
$52$	−5.49757	−	0.577817i	−0.762375	−	0.0801289i
$53$	−2.59005	−	2.33210i	−0.355771	−	0.320338i	0.471792	−	0.881710i	$-0.343607\pi$
$53$	−2.59005	−	2.33210i	−0.355771	−	0.320338i	−0.827564	+	0.561372i	$0.810274\pi$
$54$	4.91622	+	1.68249i	0.669013	+	0.228957i
$55$	0.322681	−	1.87494i	0.0435103	−	0.252816i
$56$	0.0266852	+	2.64562i	0.00356596	+	0.353535i
$57$	−1.46545	+	10.0483i	−0.194103	+	1.33093i
$58$	6.61576	−	2.94552i	0.868691	−	0.386766i
$59$	9.56549	+	4.25883i	1.24532	+	0.554453i	0.920285	−	0.391249i	$-0.127957\pi$
$59$	9.56549	+	4.25883i	1.24532	+	0.554453i	0.325036	+	0.945702i	$0.394624\pi$
$60$	−0.245364	+	0.962775i	−0.0316763	+	0.124294i
$61$	−0.468853	+	0.422157i	−0.0600304	+	0.0540516i	−0.698600	−	0.715513i	$-0.746193\pi$
$61$	−0.468853	+	0.422157i	−0.0600304	+	0.0540516i	0.638569	+	0.769564i	$0.279527\pi$
$62$	−1.70983	+	1.24226i	−0.217148	+	0.157767i
$63$	−7.00706	−	3.72841i	−0.882807	−	0.469736i
$64$	−0.309017	−	0.951057i	−0.0386271	−	0.118882i
$65$	2.74609	+	1.58546i	0.340611	+	0.196652i
$66$	−5.71243	−	0.606711i	−0.703152	−	0.0746810i
$67$	2.30807	+	3.99770i	0.281976	+	0.488396i	0.971871	−	0.235513i	$-0.0756769\pi$
$67$	2.30807	+	3.99770i	0.281976	+	0.488396i	−0.689896	+	0.723909i	$0.742344\pi$
$68$	1.80521	+	0.383709i	0.218913	+	0.0465315i
$69$	5.74516	+	10.9418i	0.691637	+	1.31724i
$70$	0.603277	−	1.39262i	0.0721054	−	0.166450i
$71$	−7.77727	−	2.52699i	−0.922992	−	0.299898i	−0.191299	−	0.981532i	$-0.561270\pi$
$71$	−7.77727	−	2.52699i	−0.922992	−	0.299898i	−0.731694	+	0.681634i	$0.761270\pi$
$72$	2.94885	+	0.551599i	0.347526	+	0.0650066i
$73$	−5.15099	+	11.5693i	−0.602878	+	1.35409i	0.311895	+	0.950117i	$0.399036\pi$
$73$	−5.15099	+	11.5693i	−0.602878	+	1.35409i	−0.914773	+	0.403969i	$0.867630\pi$
$74$	0.759568	+	0.0798338i	0.0882979	+	0.00928049i
$75$	−5.01394	+	6.34932i	−0.578960	+	0.733156i
$76$			5.86276i			0.672505i
$77$	8.46850	+	2.29880i	0.965075	+	0.261973i
$78$	4.24182	−	8.58360i	0.480291	−	0.971902i
$79$	−10.3411	−	2.19806i	−1.16346	−	0.247301i	−0.414584	−	0.910011i	$-0.636073\pi$
$79$	−10.3411	−	2.19806i	−1.16346	−	0.247301i	−0.748876	+	0.662710i	$0.769406\pi$
$80$	−0.0599602	+	0.570483i	−0.00670376	+	0.0637820i
$81$	−5.68706	+	6.97548i	−0.631895	+	0.775054i
$82$	1.10805	−	0.997697i	0.122364	−	0.110177i
$83$	−1.54533	+	4.75602i	−0.169622	+	0.522041i	−0.999347	−	0.0361301i	$-0.988497\pi$
$83$	−1.54533	+	4.75602i	−0.169622	+	0.522041i	0.829726	+	0.558172i	$0.188497\pi$
$84$	−4.31383	−	1.54624i	−0.470678	−	0.168709i
$85$	−0.856463	−	0.622257i	−0.0928965	−	0.0674933i
$86$	−1.61672	+	7.60606i	−0.174335	+	0.820182i
$87$	0.809986	+	12.5171i	0.0868396	+	1.34197i
$88$	−3.31410	+	0.129338i	−0.353284	+	0.0137875i
$89$	6.63333	−	11.4893i	0.703132	−	1.21786i	−0.264229	−	0.964460i	$-0.585118\pi$
$89$	6.63333	−	11.4893i	0.703132	−	1.21786i	0.967361	−	0.253401i	$-0.0815491\pi$
$90$	−1.41660	−	0.977067i	−0.149323	−	0.102992i
$91$	−8.47676	+	11.9182i	−0.888606	+	1.24937i
$92$	4.19391	+	5.77243i	0.437246	+	0.601817i
$93$	−0.990718	−	3.52401i	−0.102733	−	0.365422i
$94$	−0.0927802	−	0.436497i	−0.00956955	−	0.0450212i
$95$	1.36787	−	3.07228i	0.140340	−	0.315210i
$96$	1.73066	+	0.0694355i	0.176635	+	0.00708673i
$97$	3.18905	−	1.03619i	0.323799	−	0.105209i	−0.142607	−	0.989779i	$-0.545549\pi$
$97$	3.18905	−	1.03619i	0.323799	−	0.105209i	0.466406	+	0.884571i	$0.345549\pi$
$98$	6.13154	+	3.37701i	0.619379	+	0.341129i
$99$	4.41786	−	8.91530i	0.444012	−	0.896021i
$100$	−2.33548	+	4.04516i	−0.233548	+	0.404516i
$101$	−11.5500	+	12.8275i	−1.14926	+	1.27639i	−0.193878	+	0.981026i	$0.562107\pi$
$101$	−11.5500	+	12.8275i	−1.14926	+	1.27639i	−0.955386	+	0.295361i	$0.904560\pi$
$102$	−1.70797	+	2.70201i	−0.169115	+	0.267538i
$103$	8.74670	−	0.919315i	0.861838	−	0.0905828i	0.336712	−	0.941608i	$-0.390685\pi$
$103$	8.74670	−	0.919315i	0.861838	−	0.0905828i	0.525125	+	0.851025i	$0.324018\pi$
$104$	1.70820	−	5.25730i	0.167503	−	0.515520i
$105$	1.89983	+	1.81676i	0.185404	+	0.177298i
$106$	2.81964	−	2.04859i	0.273867	−	0.198976i
$107$	−6.01554	−	13.5111i	−0.581544	−	1.30617i	−0.929557	−	0.368680i	$-0.879810\pi$
$107$	−6.01554	−	13.5111i	−0.581544	−	1.30617i	0.348012	−	0.937490i	$-0.386857\pi$
$108$	−2.66786	+	4.45898i	−0.256715	+	0.429066i
$109$	−8.50953	−	14.7389i	−0.815065	−	1.41173i	−0.909281	−	0.416182i	$-0.863368\pi$
$109$	−8.50953	−	14.7389i	−0.815065	−	1.41173i	0.0942163	−	0.995552i	$-0.469965\pi$
$110$	1.76688	+	0.705451i	0.168465	+	0.0672621i
$111$	−0.586068	+	1.18595i	−0.0556271	+	0.112565i
$112$	−2.59335	−	0.523953i	−0.245049	−	0.0495089i
$113$	3.84599	−	5.29355i	0.361800	−	0.497975i	−0.588849	−	0.808243i	$-0.700419\pi$
$113$	3.84599	−	5.29355i	0.361800	−	0.497975i	0.950649	+	0.310268i	$0.100419\pi$
$114$	−9.52404	−	3.52258i	−0.892008	−	0.329920i
$115$	−0.850958	−	4.00344i	−0.0793522	−	0.373323i
$116$	1.50566	+	7.08359i	0.139797	+	0.657695i
$117$	11.3954	+	12.0482i	1.05350	+	1.11386i
$118$	−6.15454	+	8.47100i	−0.566572	+	0.779819i
$119$	3.23049	−	3.66142i	0.296138	−	0.335642i
$120$	−0.890722	−	0.440174i	−0.0813114	−	0.0401822i
$121$	−2.57352	+	10.6947i	−0.233957	+	0.972247i
$122$	−0.315452	−	0.546378i	−0.0285597	−	0.0494668i
$123$	0.954992	+	2.39949i	0.0861087	+	0.216354i
$124$	−0.859622	−	1.93074i	−0.0771963	−	0.173386i
$125$	4.48803	−	3.26074i	0.401421	−	0.291650i
$126$	5.10379	−	6.07876i	0.454682	−	0.541539i
$127$	−3.76408	+	11.5846i	−0.334008	+	1.02797i	0.633201	+	0.773987i	$0.281741\pi$
$127$	−3.76408	+	11.5846i	−0.334008	+	1.02797i	−0.967209	+	0.253983i	$0.918259\pi$
$128$	0.994522	−	0.104528i	0.0879041	−	0.00923910i
$129$	−11.3846	−	7.19637i	−1.00236	−	0.633605i
$130$	−2.12176	+	2.35645i	−0.186090	+	0.206674i
$131$	−1.36096	+	2.35725i	−0.118908	+	0.205954i	−0.919335	−	0.393476i	$-0.871273\pi$
$131$	−1.36096	+	2.35725i	−0.118908	+	0.205954i	0.800427	+	0.599430i	$0.204606\pi$
$132$	1.78113	−	5.46146i	0.155028	−	0.475359i
$133$	13.5108	+	7.61982i	1.17154	+	0.660723i
$134$	−4.39021	+	1.42647i	−0.379256	+	0.123228i
$135$	2.43839	−	1.71420i	0.209863	−	0.147535i
$136$	−0.750647	+	1.68598i	−0.0643675	+	0.144572i
$137$	1.48542	+	6.98837i	0.126908	+	0.597057i	0.994933	+	0.100537i	$0.0320559\pi$
$137$	1.48542	+	6.98837i	0.126908	+	0.597057i	−0.868025	+	0.496521i	$0.834611\pi$
$138$	−11.8972	+	3.34470i	−1.01275	+	0.284719i
$139$	−4.87086	−	6.70416i	−0.413141	−	0.568639i	0.550840	−	0.834611i	$-0.314307\pi$
$139$	−4.87086	−	6.70416i	−0.413141	−	0.568639i	−0.963981	+	0.265971i	$0.914307\pi$
$140$	1.23676	+	0.879635i	0.104525	+	0.0743428i
$141$	0.764833	+	0.111543i	0.0644106	+	0.00939364i
$142$	4.08875	−	7.08193i	0.343121	−	0.594302i
$143$	−15.2413	−	10.1897i	−1.27454	−	0.852107i
$144$	−1.15265	+	2.76973i	−0.0960539	+	0.230811i
$145$	0.863688	−	4.06333i	0.0717254	−	0.337441i
$146$	−10.2455	−	7.44382i	−0.847927	−	0.616055i
$147$	−9.17001	+	7.93163i	−0.756330	+	0.654190i
$148$	−0.236012	+	0.726371i	−0.0194001	+	0.0597073i
$149$	−9.17923	+	8.26501i	−0.751991	+	0.677096i	−0.953162	−	0.302460i	$-0.902192\pi$
$149$	−9.17923	+	8.26501i	−0.751991	+	0.677096i	0.201171	+	0.979556i	$0.435525\pi$
$150$	−5.16811	−	6.22447i	−0.421974	−	0.508226i
$151$	2.43691	−	23.1856i	0.198313	−	1.88682i	−0.215567	−	0.976489i	$-0.569160\pi$
$151$	2.43691	−	23.1856i	0.198313	−	1.88682i	0.413880	−	0.910331i	$-0.364173\pi$
$152$	−5.73465	−	1.21894i	−0.465141	−	0.0988689i
$153$	−3.36318	−	4.39807i	−0.271897	−	0.355563i
$154$	−4.00927	+	7.80549i	−0.323076	+	0.628985i
$155$			1.21234i			0.0973771i
$156$	7.51411	+	5.93376i	0.601610	+	0.475081i
$157$	10.9913	+	1.15523i	0.877201	+	0.0921975i	0.532415	−	0.846484i	$-0.321285\pi$
$157$	10.9913	+	1.15523i	0.877201	+	0.0921975i	0.344786	+	0.938681i	$0.387951\pi$
$158$	4.30005	−	9.65808i	0.342094	−	0.768355i
$159$	1.63377	+	5.81136i	0.129567	+	0.460871i
$160$	−0.545550	−	0.177260i	−0.0431295	−	0.0140136i
$161$	18.7535	−	2.16252i	1.47798	−	0.170430i
$162$	−5.64065	−	7.01307i	−0.443171	−	0.550999i
$163$	7.47060	+	1.58793i	0.585143	+	0.124376i	0.490965	−	0.871179i	$-0.336644\pi$
$163$	7.47060	+	1.58793i	0.585143	+	0.124376i	0.0941779	+	0.995555i	$0.469978\pi$
$164$	0.745517	+	1.29127i	0.0582151	+	0.100832i
$165$	−2.20761	+	2.44642i	−0.171862	+	0.190454i
$166$	−4.33080	−	2.50039i	−0.336135	−	0.194068i
$167$	4.73526	+	14.5736i	0.366425	+	1.12774i	0.949084	+	0.315024i	$0.102012\pi$
$167$	4.73526	+	14.5736i	0.366425	+	1.12774i	−0.582659	+	0.812717i	$0.697988\pi$
$168$	2.40935	−	3.89808i	0.185885	−	0.300744i
$169$	14.2040	−	10.3198i	1.09261	−	0.793831i
$170$	0.786728	−	0.708373i	0.0603393	−	0.0543297i
$171$	11.4449	−	13.3553i	0.875210	−	1.02130i
$172$	−7.10371	−	3.16278i	−0.541653	−	0.241159i
$173$	7.41533	−	3.30152i	0.563777	−	0.251010i	−0.105001	−	0.994472i	$-0.533484\pi$
$173$	7.41533	−	3.30152i	0.563777	−	0.251010i	0.668778	+	0.743462i	$0.266818\pi$
$174$	−12.4119	−	1.81016i	−0.940947	−	0.137228i
$175$	6.28672	+	10.6396i	0.475232	+	0.804281i
$176$	0.562528	−	3.26857i	0.0424022	−	0.246378i
$177$	−10.0632	−	15.0878i	−0.756398	−	1.13407i
$178$	9.85906	+	8.87713i	0.738968	+	0.665369i
$179$	−10.7035	−	1.12498i	−0.800016	−	0.0840851i	−0.304307	−	0.952574i	$-0.598425\pi$
$179$	−10.7035	−	1.12498i	−0.800016	−	0.0840851i	−0.495709	+	0.868489i	$0.665092\pi$
$180$	1.25024	−	1.18250i	0.0931876	−	0.0881384i
$181$	0.702191	+	0.228156i	0.0521934	+	0.0169587i	0.334997	−	0.942219i	$-0.391265\pi$
$181$	0.702191	+	0.228156i	0.0521934	+	0.0169587i	−0.282804	+	0.959178i	$0.591265\pi$
$182$	−9.89537	−	10.7695i	−0.733493	−	0.798286i
$183$	1.07713	−	0.184165i	0.0796235	−	0.0136138i
$184$	−6.51825	+	2.90211i	−0.480532	+	0.213946i
$185$	0.293151	−	0.325577i	0.0215529	−	0.0239369i
$186$	3.65298	−	0.236386i	0.267850	−	0.0173327i
$187$	4.70501	+	3.91521i	0.344065	+	0.286309i
$188$	0.446248			0.0325460
$189$	6.80837	+	11.9435i	0.495236	+	0.868758i
$190$	2.72075	+	1.97674i	0.197384	+	0.143408i
$191$	20.5339	−	2.15820i	1.48578	−	0.156162i	0.673395	−	0.739282i	$-0.264835\pi$
$191$	20.5339	−	2.15820i	1.48578	−	0.156162i	0.812386	+	0.583121i	$0.198168\pi$
$192$	−0.427742	+	1.67840i	−0.0308696	+	0.121128i
$193$	−7.45383	+	1.58436i	−0.536539	+	0.114045i	−0.468209	−	0.883618i	$-0.655100\pi$
$193$	−7.45383	+	1.58436i	−0.536539	+	0.114045i	−0.0683300	+	0.997663i	$0.521767\pi$
$194$	0.350501	+	3.33480i	0.0251645	+	0.239425i
$195$	−2.55321	−	4.86264i	−0.182839	−	0.348221i
$196$	−4.57803	+	5.29543i	−0.327002	+	0.378245i
$197$			24.7824i			1.76567i	0.469683	+	0.882835i	$0.344368\pi$
$197$			24.7824i			1.76567i	−0.469683	+	0.882835i	$0.655632\pi$
$198$	7.80195	+	6.17491i	0.554461	+	0.438832i
$199$	−22.2678	+	12.8563i	−1.57852	+	0.911360i	−0.583456	+	0.812144i	$0.698300\pi$
$199$	−22.2678	+	12.8563i	−1.57852	+	0.911360i	−0.995066	+	0.0992159i	$0.968367\pi$
$200$	−3.47119	−	3.12548i	−0.245451	−	0.221005i
$201$	0.320524	−	7.98896i	0.0226080	−	0.563498i
$202$	−10.1458	−	13.9646i	−0.713859	−	0.982543i
$203$	18.2812	+	5.73671i	1.28309	+	0.402638i
$204$	−2.28785	−	2.23243i	−0.160182	−	0.156301i
$205$	−0.0894027	−	0.850610i	−0.00624416	−	0.0594092i
$206$	−0.919315	+	8.74670i	−0.0640517	+	0.609411i
$207$	1.71484	−	21.3365i	0.119190	−	1.48299i
$208$	4.78726	+	2.76392i	0.331937	+	0.191644i
$209$	−9.05821	+	17.2058i	−0.626569	+	1.19015i
$210$	−2.17206	+	1.48059i	−0.149886	+	0.102170i
$211$	1.12878	+	3.47402i	0.0777082	+	0.239161i	0.982363	−	0.186984i	$-0.0598713\pi$
$211$	1.12878	+	3.47402i	0.0777082	+	0.239161i	−0.904655	+	0.426145i	$0.859871\pi$
$212$	1.41758	+	3.18395i	0.0973600	+	0.218674i
$213$	9.04789	+	10.8973i	0.619951	+	0.746669i
$214$	14.4666	−	3.07497i	0.988915	−	0.210200i
$215$	2.98466	+	3.31480i	0.203552	+	0.226067i
$216$	−3.80686	−	3.53664i	−0.259024	−	0.240638i
$217$	−5.56667	−	0.528372i	−0.377890	−	0.0358682i
$218$	16.1861	−	5.25918i	1.09626	−	0.356196i
$219$	18.2484	−	12.1713i	1.23311	−	0.822461i
$220$	−1.05739	+	1.58159i	−0.0712892	+	0.106631i
$221$	−8.83506	+	5.10092i	−0.594310	+	0.343125i
$222$	−1.03818	−	0.819834i	−0.0696782	−	0.0550236i
$223$	7.56718	−	10.4153i	0.506736	−	0.697462i	−0.476629	−	0.879105i	$-0.658141\pi$
$223$	7.56718	−	10.4153i	0.506736	−	0.697462i	0.983365	+	0.181643i	$0.0581414\pi$
$224$	1.05169	−	2.42774i	0.0702691	−	0.162211i
$225$	13.2168	−	4.65567i	0.881123	−	0.310378i
$226$	4.37825	+	4.86254i	0.291237	+	0.323451i
$227$	8.77515	+	3.90695i	0.582427	+	0.259313i	0.676731	−	0.736230i	$-0.263396\pi$
$227$	8.77515	+	3.90695i	0.582427	+	0.259313i	−0.0943042	+	0.995543i	$0.530063\pi$
$228$	5.42577	−	8.58353i	0.359330	−	0.568458i
$229$	3.22100	−	15.1536i	0.212850	−	1.00138i	−0.733862	−	0.679298i	$-0.762284\pi$
$229$	3.22100	−	15.1536i	0.212850	−	1.00138i	0.946712	−	0.322081i	$-0.104382\pi$
$230$	4.09288			0.269877
$231$	−10.2711	−	11.2029i	−0.675787	−	0.737097i
$232$	−7.24185			−0.475450
$233$	3.82624	−	18.0010i	0.250665	−	1.17929i	−0.655112	−	0.755532i	$-0.727378\pi$
$233$	3.82624	−	18.0010i	0.250665	−	1.17929i	0.905777	−	0.423755i	$-0.139288\pi$
$234$	−14.1541	+	8.64141i	−0.925286	+	0.564907i
$235$	−0.233849	−	0.104116i	−0.0152546	−	0.00679179i
$236$	−7.00629	−	7.78127i	−0.456071	−	0.506518i
$237$	13.1059	+	12.7884i	0.851318	+	0.830695i
$238$	2.90975	+	3.92114i	0.188611	+	0.254170i
$239$	−1.03027	+	1.41805i	−0.0666429	+	0.0917261i	−0.841037	−	0.540977i	$-0.818055\pi$
$239$	−1.03027	+	1.41805i	−0.0666429	+	0.0917261i	0.774394	+	0.632703i	$0.218055\pi$
$240$	0.615747	−	0.779740i	0.0397463	−	0.0503320i
$241$	6.56869	−	3.79244i	0.423127	−	0.244292i	−0.273287	−	0.961932i	$-0.588111\pi$
$241$	6.56869	−	3.79244i	0.423127	−	0.244292i	0.696414	+	0.717640i	$0.254778\pi$
$242$	−9.92595	−	4.74084i	−0.638064	−	0.304753i
$243$	14.7818	−	4.94949i	0.948255	−	0.317510i
$244$	0.600025	−	0.194960i	0.0384127	−	0.0124810i
$245$	3.63454	−	1.70686i	0.232202	−	0.109047i
$246$	−2.54561	+	0.435242i	−0.162302	+	0.0277500i
$247$	−21.6855	−	24.0842i	−1.37982	−	1.53244i
$248$	2.06728	−	0.439413i	0.131272	−	0.0279028i
$249$	6.66400	−	5.53304i	0.422314	−	0.350642i
$250$	2.25637	+	5.06790i	0.142706	+	0.320522i
$251$	−2.79881	−	8.61385i	−0.176659	−	0.543701i	0.823046	−	0.567975i	$-0.192273\pi$
$251$	−2.79881	−	8.61385i	−0.176659	−	0.543701i	−0.999705	+	0.0242733i	$0.992273\pi$
$252$	4.88479	+	6.25610i	0.307713	+	0.394097i
$253$	3.38952	+	23.4205i	0.213097	+	1.47243i
$254$	−10.5489	−	6.09040i	−0.661896	−	0.382146i
$255$	0.678053	+	1.70366i	0.0424613	+	0.106687i
$256$	−0.104528	+	0.994522i	−0.00653303	+	0.0621576i
$257$	−2.55936	−	24.3507i	−0.159649	−	1.51896i	−0.721904	−	0.691993i	$-0.756733\pi$
$257$	−2.55936	−	24.3507i	−0.159649	−	1.51896i	0.562256	−	0.826964i	$-0.309934\pi$
$258$	9.40611	−	9.63964i	0.585599	−	0.600138i
$259$	1.36719	+	1.48796i	0.0849529	+	0.0924571i
$260$	−1.86382	−	2.56532i	−0.115589	−	0.159095i
$261$	10.3982	−	19.0756i	0.643632	−	1.18075i
$262$	−2.02278	−	1.82132i	−0.124968	−	0.112522i
$263$	6.50504	−	3.75568i	0.401118	−	0.231585i	−0.285848	−	0.958275i	$-0.592275\pi$
$263$	6.50504	−	3.75568i	0.401118	−	0.231585i	0.686966	+	0.726689i	$0.258942\pi$
$264$	4.97180	+	2.87771i	0.305993	+	0.177111i
$265$		−	1.99924i		−	0.122812i
$266$	−10.2624	+	11.6313i	−0.629226	+	0.713162i
$267$	−20.3446	+	10.6823i	−1.24507	+	0.653745i
$268$	−0.482518	−	4.59085i	−0.0294745	−	0.280431i
$269$	0.526248	−	0.111857i	0.0320859	−	0.00682007i	−0.191841	−	0.981426i	$-0.561446\pi$
$269$	0.526248	−	0.111857i	0.0320859	−	0.00682007i	0.223927	+	0.974606i	$0.428112\pi$
$270$	1.16977	+	2.74151i	0.0711902	+	0.166843i
$271$	−10.0781	+	1.05925i	−0.612202	+	0.0643450i	−0.405555	−	0.914071i	$-0.632922\pi$
$271$	−10.0781	+	1.05925i	−0.612202	+	0.0643450i	−0.206647	+	0.978416i	$0.566255\pi$
$272$	−1.49307	−	1.08478i	−0.0905307	−	0.0657744i
$273$	23.4405	−	9.60427i	1.41868	−	0.581277i
$274$	−7.14450			−0.431615
$275$	−13.1040	+	8.26320i	−0.790202	+	0.498290i
$276$	−0.798048	−	12.3326i	−0.0480368	−	0.742334i
$277$	1.54921	−	1.72058i	0.0930833	−	0.103379i	−0.694803	−	0.719200i	$-0.744509\pi$
$277$	1.54921	−	1.72058i	0.0930833	−	0.103379i	0.787887	+	0.615820i	$0.211175\pi$
$278$	7.57037	−	3.37054i	0.454040	−	0.202152i
$279$	−1.81085	+	6.07629i	−0.108413	+	0.363778i
$280$	−1.11755	+	1.02684i	−0.0667863	+	0.0613657i
$281$	−8.20269	−	2.66521i	−0.489331	−	0.158993i	0.0539508	−	0.998544i	$-0.482819\pi$
$281$	−8.20269	−	2.66521i	−0.489331	−	0.158993i	−0.543282	+	0.839550i	$0.682819\pi$
$282$	−0.268124	+	0.724929i	−0.0159665	+	0.0431689i
$283$	18.0712	+	1.89936i	1.07422	+	0.112905i	0.625085	−	0.780557i	$-0.285064\pi$
$283$	18.0712	+	1.89936i	1.07422	+	0.112905i	0.449139	+	0.893462i	$0.351731\pi$
$284$	6.07707	+	5.47182i	0.360608	+	0.324693i
$285$	−4.84594	+	3.23215i	−0.287049	+	0.191456i
$286$	13.1359	−	12.7897i	0.776742	−	0.756270i
$287$	3.94471	−	0.0397885i	0.232849	−	0.00234864i
$288$	−2.46956	−	1.70332i	−0.145520	−	0.100369i
$289$	−12.4187	+	5.52918i	−0.730514	+	0.325246i
$290$	3.79497	+	1.68963i	0.222848	+	0.0992184i
$291$	−5.62797	−	1.43429i	−0.329917	−	0.0840797i
$292$	9.41132	−	8.47400i	0.550756	−	0.495903i
$293$	−16.5539	+	12.0271i	−0.967088	+	0.702630i	−0.954786	−	0.297294i	$-0.903916\pi$
$293$	−16.5539	+	12.0271i	−0.967088	+	0.702630i	−0.0123016	+	0.999924i	$0.503916\pi$
$294$	−5.85176	−	10.6187i	−0.341281	−	0.619296i
$295$	1.85604	+	5.71231i	0.108063	+	0.332584i
$296$	−0.661428	−	0.381876i	−0.0384447	−	0.0221961i
$297$	−14.7189	+	8.96412i	−0.854074	+	0.520151i
$298$	−6.17593	−	10.6970i	−0.357762	−	0.619662i
$299$	−38.5799	−	8.20041i	−2.23113	−	0.474242i
$300$	7.16296	−	3.76103i	0.413554	−	0.217143i
$301$	−16.5213	+	12.2599i	−0.952274	+	0.706651i
$302$	22.1723	+	7.20422i	1.27587	+	0.414556i
$303$	28.7814	−	8.09143i	1.65345	−	0.464841i
$304$	2.38460	−	5.35590i	0.136766	−	0.307182i
$305$	−0.359920	−	0.0378291i	−0.0206090	−	0.00216609i
$306$	5.00121	−	2.37528i	0.285900	−	0.135786i
$307$		−	12.1207i		−	0.691765i	−0.938278	−	0.345882i	$-0.887580\pi$
$307$		−	12.1207i		−	0.691765i	0.938278	−	0.345882i	$-0.112420\pi$
$308$	−6.80135	−	5.54451i	−0.387543	−	0.315928i
$309$	−13.6566	−	6.74879i	−0.776898	−	0.383925i
$310$	−1.18584	−	0.252059i	−0.0673513	−	0.0143160i
$311$	3.41274	−	32.4701i	0.193519	−	1.84121i	−0.279486	−	0.960150i	$-0.590164\pi$
$311$	3.41274	−	32.4701i	0.193519	−	1.84121i	0.473005	−	0.881060i	$-0.343169\pi$
$312$	−7.36636	+	6.11621i	−0.417038	+	0.346262i
$313$	−12.7162	+	11.4497i	−0.718761	+	0.647175i	−0.945065	−	0.326881i	$-0.894002\pi$
$313$	−12.7162	+	11.4497i	−0.718761	+	0.647175i	0.226304	+	0.974057i	$0.427336\pi$
$314$	−3.41521	+	10.5109i	−0.192731	+	0.593166i
$315$	−1.10015	−	4.41810i	−0.0619865	−	0.248932i
$316$	8.55299	+	6.21411i	0.481143	+	0.349571i
$317$	0.777025	−	3.65561i	0.0436421	−	0.205320i	−0.950924	−	0.309423i	$-0.899864\pi$
$317$	0.777025	−	3.65561i	0.0436421	−	0.205320i	0.994566	+	0.104104i	$0.0331973\pi$
$318$	−6.02405	+	0.389820i	−0.337812	+	0.0218600i
$319$	−6.52567	+	23.1150i	−0.365367	+	1.29419i
$320$	0.286813	−	0.496774i	0.0160333	−	0.0277705i
$321$	−3.69682	+	25.3485i	−0.206337	+	1.41481i
$322$	−1.78380	+	18.7933i	−0.0994073	+	1.04731i
$323$	6.35980	+	8.75352i	0.353869	+	0.487059i
$324$	8.03257	−	4.05929i	0.446254	−	0.225516i
$325$	−5.36835	−	25.2561i	−0.297782	−	1.40096i
$326$	−3.10645	+	6.97720i	−0.172050	+	0.386431i
$327$	−1.18173	+	29.4542i	−0.0653496	+	1.62882i
$328$	−1.41806	+	0.460755i	−0.0782991	+	0.0254409i
$329$	0.579988	−	1.02838i	0.0319758	−	0.0566967i
$330$	−1.93397	−	2.66801i	−0.106462	−	0.146869i
$331$	−1.63784	+	2.83683i	−0.0900240	+	0.155926i	−0.907521	−	0.420007i	$-0.862028\pi$
$331$	−1.63784	+	2.83683i	−0.0900240	+	0.155926i	0.817497	+	0.575933i	$0.195361\pi$
$332$	3.34617	−	3.71630i	0.183645	−	0.203959i
$333$	1.95560	−	1.19393i	0.107166	−	0.0654272i
$334$	−15.2397	+	1.60175i	−0.833878	+	0.0876441i
$335$	−0.818258	+	2.51834i	−0.0447062	+	0.137591i
$336$	3.31197	+	3.16716i	0.180683	+	0.172782i
$337$	8.60418	−	6.25130i	0.468699	−	0.340530i	−0.328235	−	0.944596i	$-0.606454\pi$
$337$	8.60418	−	6.25130i	0.468699	−	0.340530i	0.796934	+	0.604066i	$0.206454\pi$
$338$	7.14111	+	16.0392i	0.388425	+	0.872418i
$339$	−10.5298	+	4.19085i	−0.571900	+	0.227615i
$340$	0.529323	+	0.916815i	0.0287066	+	0.0497213i
$341$	0.460286	−	6.99443i	0.0249259	−	0.378769i
$342$	10.6839	+	13.9715i	0.577720	+	0.755491i
$343$	6.25334	+	17.4326i	0.337649	+	0.941272i
$344$	4.57061	−	6.29090i	0.246431	−	0.339183i
$345$	−2.45917	+	6.64888i	−0.132397	+	0.357963i
$346$	1.68764	+	7.93971i	0.0907279	+	0.426841i
$347$	5.41764	+	25.4880i	0.290834	+	1.36827i	0.844513	+	0.535536i	$0.179890\pi$
$347$	5.41764	+	25.4880i	0.290834	+	1.36827i	−0.553679	+	0.832730i	$0.686776\pi$
$348$	4.35119	−	11.7644i	0.233248	−	0.630636i
$349$	−8.75870	+	12.0553i	−0.468843	+	0.645307i	−0.976313	−	0.216363i	$-0.930581\pi$
$349$	−8.75870	+	12.0553i	−0.468843	+	0.645307i	0.507470	+	0.861669i	$0.330581\pi$
$350$	−11.7142	+	3.93724i	−0.626151	+	0.210454i
$351$	−5.53357	−	28.1855i	−0.295360	−	1.50443i
$352$	3.08019	+	1.22981i	0.164175	+	0.0655491i
$353$	−9.61706	−	16.6572i	−0.511864	−	0.886575i	−0.999905	−	0.0137543i	$-0.995622\pi$
$353$	−9.61706	−	16.6572i	−0.511864	−	0.886575i	0.488041	−	0.872821i	$-0.337712\pi$
$354$	16.8503	−	6.70640i	0.895584	−	0.356441i
$355$	−1.90793	−	4.28528i	−0.101262	−	0.227439i
$356$	−10.7330	+	7.79795i	−0.568846	+	0.413291i
$357$	−8.11818	+	2.37090i	−0.429660	+	0.125482i
$358$	3.32578	−	10.2357i	0.175773	−	0.540973i
$359$	−5.17692	+	0.544117i	−0.273228	+	0.0287174i	−0.240151	−	0.970735i	$-0.577197\pi$
$359$	−5.17692	+	0.544117i	−0.273228	+	0.0287174i	−0.0330762	+	0.999453i	$0.510530\pi$
$360$	0.896721	+	1.46878i	0.0472613	+	0.0774114i
$361$	−10.2859	+	11.4236i	−0.541362	+	0.601243i
$362$	−0.369163	+	0.639410i	−0.0194028	+	0.0336066i
$363$	13.6654	−	13.2762i	0.717247	−	0.696819i
$364$	12.5915	−	7.44003i	0.659973	−	0.389964i
$365$	−6.90895	+	2.24485i	−0.361631	+	0.117501i
$366$	−0.0438071	+	1.09188i	−0.00228983	+	0.0570734i
$367$	4.49807	−	10.1028i	0.234797	−	0.527363i	−0.757266	−	0.653107i	$-0.773465\pi$
$367$	4.49807	−	10.1028i	0.234797	−	0.527363i	0.992063	+	0.125744i	$0.0401318\pi$
$368$	−1.48347	−	6.97919i	−0.0773314	−	0.363815i
$369$	0.822453	−	4.39684i	0.0428152	−	0.228890i
$370$	0.257513	+	0.354436i	0.0133875	+	0.0184263i
$371$	9.17988	+	0.871327i	0.476595	+	0.0452370i
$372$	−0.528277	+	3.62230i	−0.0273899	+	0.187808i
$373$	−7.93738	+	13.7479i	−0.410982	+	0.711842i	−0.994997	−	0.0999008i	$-0.968147\pi$
$373$	−7.93738	+	13.7479i	−0.410982	+	0.711842i	0.584015	+	0.811743i	$0.301481\pi$
$374$	−4.80788	+	3.78818i	−0.248610	+	0.195882i
$375$	−9.58851	+	0.620478i	−0.495149	+	0.0320413i
$376$	−0.0927802	+	0.436497i	−0.00478477	+	0.0225106i
$377$	−32.3864	−	23.5301i	−1.66799	−	1.21186i
$378$	−13.0980	+	4.17641i	−0.673688	+	0.214811i
$379$	1.08677	−	3.34472i	0.0558235	−	0.171807i	−0.919257	−	0.393657i	$-0.871210\pi$
$379$	1.08677	−	3.34472i	0.0558235	−	0.171807i	0.975081	+	0.221850i	$0.0712097\pi$
$380$	−2.49922	+	2.25031i	−0.128207	+	0.115438i
$381$	16.2320	−	13.4773i	0.831592	−	0.690462i
$382$	−2.15820	+	20.5339i	−0.110423	+	1.05061i
$383$	0.670465	+	0.142512i	0.0342591	+	0.00728201i	0.225009	−	0.974357i	$-0.427759\pi$
$383$	0.670465	+	0.142512i	0.0342591	+	0.00728201i	−0.190750	+	0.981639i	$0.561092\pi$
$384$	−1.55279	−	0.767355i	−0.0792406	−	0.0391589i
$385$	2.27052	+	4.49236i	0.115716	+	0.228952i
$386$		−	7.62036i		−	0.387866i
$387$	10.0080	+	21.0721i	0.508735	+	1.07115i
$388$	−3.33480	−	0.350501i	−0.169299	−	0.0177940i
$389$	0.975881	−	2.19186i	0.0494791	−	0.111132i	−0.887114	−	0.461550i	$-0.847294\pi$
$389$	0.975881	−	2.19186i	0.0494791	−	0.111132i	0.936594	+	0.350418i	$0.113960\pi$
$390$	5.28722	−	1.48642i	0.267729	−	0.0752676i
$391$	12.5236	+	4.06917i	0.633346	+	0.205787i
$392$	−4.22789	−	5.57897i	−0.213541	−	0.281781i
$393$	4.17410	−	2.19168i	0.210555	−	0.110556i
$394$	−24.2408	−	5.15254i	−1.22123	−	0.259581i
$395$	−3.03221	−	5.25194i	−0.152567	−	0.264254i
$396$	−7.66209	+	6.34762i	−0.385035	+	0.318980i
$397$	−14.0038	−	8.08509i	−0.702830	−	0.405779i	0.105570	−	0.994412i	$-0.466333\pi$
$397$	−14.0038	−	8.08509i	−0.702830	−	0.405779i	−0.808401	+	0.588633i	$0.799667\pi$
$398$	−7.94564	−	24.4542i	−0.398279	−	1.22578i
$399$	−12.7290	−	23.6598i	−0.637248	−	1.18447i
$400$	3.77888	−	2.74552i	0.188944	−	0.137276i
$401$	26.1642	−	23.5583i	1.30658	−	1.17645i	0.334338	−	0.942453i	$-0.391487\pi$
$401$	26.1642	−	23.5583i	1.30658	−	1.17645i	0.972238	−	0.233994i	$-0.0751795\pi$
$402$	7.74774	+	1.97452i	0.386422	+	0.0984800i
$403$	10.6728	+	4.75186i	0.531652	+	0.236707i
$404$	15.7688	−	7.02074i	0.784529	−	0.349295i
$405$	−5.15642	+	0.253085i	−0.256225	+	0.0125759i
$406$	−9.41222	+	16.6889i	−0.467120	+	0.828258i
$407$	−1.81491	+	1.76708i	−0.0899619	+	0.0875909i
$408$	2.65932	−	1.77371i	0.131656	−	0.0878117i
$409$	2.70993	+	2.44003i	0.133998	+	0.120652i	0.733404	−	0.679793i	$-0.237930\pi$
$409$	2.70993	+	2.44003i	0.133998	+	0.120652i	−0.599407	+	0.800444i	$0.704597\pi$
$410$	0.850610	+	0.0894027i	0.0420086	+	0.00441529i
$411$	4.29270	−	11.6062i	0.211743	−	0.572493i
$412$	−8.36443	−	2.71777i	−0.412086	−	0.133895i
$413$	−27.0381	+	6.03278i	−1.33046	+	0.296854i
$414$	20.5137	+	6.11348i	1.00820	+	0.300461i
$415$	−2.62057	+	1.16675i	−0.128639	+	0.0572737i
$416$	−3.69885	+	4.10799i	−0.181351	+	0.201411i
$417$	0.926862	+	14.3232i	0.0453886	+	0.701410i
$418$	−14.9465	−	12.4376i	−0.731059	−	0.608341i
$419$	23.5510			1.15054			0.575271	−	0.817963i	$-0.304897\pi$
$419$	23.5510			1.15054			0.575271	+	0.817963i	$0.304897\pi$
$420$	−0.996637	−	2.43242i	−0.0486309	−	0.118690i
$421$	16.0972	+	11.6953i	0.784527	+	0.569993i	0.906334	−	0.422561i	$-0.138869\pi$
$421$	16.0972	+	11.6953i	0.784527	+	0.569993i	−0.121807	+	0.992554i	$0.538869\pi$
$422$	−3.63279	+	0.381821i	−0.176841	+	0.0185868i
$423$	−1.01655	−	0.871132i	−0.0494261	−	0.0423559i
$424$	−3.40910	+	0.724627i	−0.165561	+	0.0351910i
$425$	0.901079	+	8.57319i	0.0437087	+	0.415861i
$426$	−12.5403	+	6.58450i	−0.607580	+	0.319020i
$427$	0.330564	−	1.63615i	0.0159971	−	0.0791791i
$428$			14.7898i			0.714890i
$429$	12.8843	+	29.0238i	0.622057	+	1.40128i
$430$	−3.86291	+	2.23025i	−0.186286	+	0.107552i
$431$	24.1786	+	21.7705i	1.16464	+	1.04865i	0.998037	+	0.0626232i	$0.0199466\pi$
$431$	24.1786	+	21.7705i	1.16464	+	1.04865i	0.166603	+	0.986024i	$0.446720\pi$
$432$	4.25084	−	2.98837i	0.204519	−	0.143778i
$433$	18.8256	+	25.9113i	0.904702	+	1.24522i	0.968944	+	0.247281i	$0.0795371\pi$
$433$	18.8256	+	25.9113i	0.904702	+	1.24522i	−0.0642418	+	0.997934i	$0.520463\pi$
$434$	1.67420	−	5.33517i	0.0803643	−	0.256096i
$435$	−5.02496	+	5.14972i	−0.240929	+	0.246910i
$436$	1.77898	+	16.9258i	0.0851975	+	0.810600i
$437$	−4.37258	+	41.6023i	−0.209169	+	1.99011i
$438$	8.11128	+	20.3802i	0.387572	+	0.973803i
$439$	0.295939	+	0.170861i	0.0141244	+	0.00815473i	0.507046	−	0.861919i	$-0.330738\pi$
$439$	0.295939	+	0.170861i	0.0141244	+	0.00815473i	−0.492921	+	0.870074i	$0.664071\pi$
$440$	−1.32719	−	1.36311i	−0.0632712	−	0.0649839i
$441$	20.7660	−	3.12602i	0.988859	−	0.148858i
$442$	−3.15254	−	9.70253i	−0.149951	−	0.461502i
$443$	11.6830	+	26.2405i	0.555078	+	1.24673i	0.945359	+	0.326030i	$0.105711\pi$
$443$	11.6830	+	26.2405i	0.555078	+	1.24673i	−0.390281	+	0.920696i	$0.627622\pi$
$444$	1.01777	−	0.845042i	0.0483012	−	0.0401039i
$445$	7.44380	−	1.58223i	0.352870	−	0.0750049i
$446$	8.61443	+	9.56729i	0.407905	+	0.453024i
$447$	21.0880	−	3.60558i	0.997430	−	0.170538i
$448$	2.15603	+	1.53347i	0.101863	+	0.0724494i
$449$	13.1851	−	4.28409i	0.622242	−	0.202179i	0.0191065	−	0.999817i	$-0.493918\pi$
$449$	13.1851	−	4.28409i	0.622242	−	0.202179i	0.603135	+	0.797639i	$0.293918\pi$
$450$	1.80600	+	13.8960i	0.0851355	+	0.655063i
$451$	0.192848	+	4.94144i	0.00908086	+	0.232683i
$452$	−5.66657	+	3.27159i	−0.266533	+	0.153883i
$453$	−25.0253	+	31.6903i	−1.17579	+	1.48894i
$454$	−5.64603	+	7.77109i	−0.264981	+	0.364715i
$455$	−8.33423	+	0.961045i	−0.390715	+	0.0450545i
$456$	7.26788	+	7.09182i	0.340350	+	0.332105i
$457$	−17.1929	−	19.0946i	−0.804248	−	0.893208i	0.191854	−	0.981424i	$-0.438550\pi$
$457$	−17.1929	−	19.0946i	−0.804248	−	0.893208i	−0.996101	+	0.0882159i	$0.971883\pi$
$458$	14.1528	+	6.30123i	0.661317	+	0.294437i
$459$	0.853708	+	9.55161i	0.0398477	+	0.445831i
$460$	−0.850958	+	4.00344i	−0.0396761	+	0.186661i
$461$	38.8494			1.80940			0.904699	−	0.426050i	$-0.140095\pi$
$461$	38.8494			1.80940			0.904699	+	0.426050i	$0.140095\pi$
$462$	13.0936	−	7.71741i	0.609168	−	0.359047i
$463$	−36.2859			−1.68635			−0.843175	−	0.537639i	$-0.819316\pi$
$463$	−36.2859			−1.68635			−0.843175	+	0.537639i	$0.819316\pi$
$464$	1.50566	−	7.08359i	0.0698987	−	0.328848i
$465$	1.12197	−	1.77495i	0.0520301	−	0.0823114i
$466$	16.8122	+	7.48525i	0.778808	+	0.346748i
$467$	1.81869	+	2.01986i	0.0841590	+	0.0934680i	0.783753	−	0.621072i	$-0.213303\pi$
$467$	1.81869	+	2.01986i	0.0841590	+	0.0934680i	−0.699594	+	0.714540i	$0.746636\pi$
$468$	−5.50976	−	15.6415i	−0.254689	−	0.723028i
$469$	−11.2068	−	4.85475i	−0.517483	−	0.224172i
$470$	0.150461	−	0.207092i	0.00694024	−	0.00955243i
$471$	−15.0230	−	11.8634i	−0.692222	−	0.546636i
$472$	9.06792	−	5.23537i	0.417385	−	0.240977i
$473$	−15.9611	−	20.2575i	−0.733893	−	0.931442i
$474$	−15.2338	+	10.1606i	−0.699711	+	0.466693i
$475$	−26.0444	+	8.46234i	−1.19500	+	0.388279i
$476$	−4.44043	+	2.03092i	−0.203527	+	0.0930869i
$477$	2.98623	−	10.0203i	0.136730	−	0.458797i
$478$	−1.17286	−	1.30259i	−0.0536452	−	0.0595791i
$479$	−5.60978	+	1.19239i	−0.256317	+	0.0544819i	−0.334278	−	0.942475i	$-0.608492\pi$
$479$	−5.60978	+	1.19239i	−0.256317	+	0.0544819i	0.0779608	+	0.996956i	$0.475159\pi$
$480$	0.634680	+	0.764409i	0.0289690	+	0.0348903i
$481$	−1.71720	−	3.85690i	−0.0782977	−	0.175859i
$482$	2.34386	+	7.21364i	0.106760	+	0.328573i
$483$	−29.4578	−	14.1895i	−1.34038	−	0.645646i
$484$	6.70097	−	8.72336i	0.304589	−	0.396517i
$485$	1.66577	+	0.961731i	0.0756386	+	0.0436700i
$486$	1.76801	+	15.4879i	0.0801987	+	0.702544i
$487$	−1.87629	+	17.8517i	−0.0850228	+	0.808938i	0.866047	+	0.499962i	$0.166653\pi$
$487$	−1.87629	+	17.8517i	−0.0850228	+	0.808938i	−0.951070	+	0.308976i	$0.900014\pi$
$488$	0.0659474	+	0.627447i	0.00298530	+	0.0284032i
$489$	−9.46797	−	9.23860i	−0.428156	−	0.417784i
$490$	0.913899	+	3.91000i	0.0412858	+	0.176636i
$491$	−7.86498	−	10.8252i	−0.354942	−	0.488535i	0.593789	−	0.804621i	$-0.297631\pi$
$491$	−7.86498	−	10.8252i	−0.354942	−	0.488535i	−0.948731	+	0.316085i	$0.897631\pi$
$492$	0.103531	−	2.58047i	0.00466752	−	0.116337i
$493$	9.93220	+	8.94299i	0.447324	+	0.402772i
$494$	28.0666	−	16.2042i	1.26277	−	0.729063i
$495$	5.49618	−	1.53869i	0.247035	−	0.0691589i
$496$			2.11346i			0.0948972i
$497$	20.5082	−	6.89298i	0.919921	−	0.309192i
$498$	4.02661	+	7.66876i	0.180437	+	0.343645i
$499$	−0.100890	−	0.959905i	−0.00451646	−	0.0429712i	0.992032	−	0.125990i	$-0.0402106\pi$
$499$	−0.100890	−	0.959905i	−0.00451646	−	0.0429712i	−0.996548	+	0.0830184i	$0.973544\pi$
$500$	−5.42628	+	1.15339i	−0.242671	+	0.0515812i
$501$	6.55456	−	25.7192i	0.292836	−	1.14905i
$502$	9.00752	−	0.946728i	0.402025	−	0.0422546i
$503$	11.2682	+	8.18686i	0.502426	+	0.365034i	0.809943	−	0.586509i	$-0.199498\pi$
$503$	11.2682	+	8.18686i	0.502426	+	0.365034i	−0.307517	+	0.951543i	$0.599498\pi$
$504$	−7.13500	+	3.47733i	−0.317818	+	0.154893i
$505$	−9.90144			−0.440608
$506$	−23.6134	−	1.55394i	−1.04974	−	0.0690811i
$507$	−30.3463	+	1.96373i	−1.34773	+	0.0872121i
$508$	8.15055	−	9.05210i	0.361622	−	0.401622i
$509$	8.78650	−	3.91200i	0.389455	−	0.173396i	−0.202662	−	0.979249i	$-0.564959\pi$
$509$	8.78650	−	3.91200i	0.389455	−	0.173396i	0.592116	+	0.805852i	$0.298293\pi$
$510$	−1.80740	+	0.309025i	−0.0800331	+	0.0136839i
$511$	−7.29656	−	32.7022i	−0.322781	−	1.44666i
$512$	−0.951057	−	0.309017i	−0.0420312	−	0.0136568i
$513$	−29.1159	+	8.96137i	−1.28550	+	0.395654i
$514$	24.3507	+	2.55936i	1.07406	+	0.112889i
$515$	3.74914	+	3.37574i	0.165207	+	0.148753i
$516$	7.47335	+	11.2048i	0.328996	+	0.493262i
$517$	1.30963	+	0.689471i	0.0575976	+	0.0303229i
$518$	−1.73970	+	1.02795i	−0.0764378	+	0.0451654i
$519$	−13.9120	−	2.02893i	−0.610671	−	0.0890602i
$520$	2.89678	−	1.28973i	0.127032	−	0.0565583i
$521$	13.3346	+	5.93696i	0.584201	+	0.260103i	0.677485	−	0.735537i	$-0.263070\pi$
$521$	13.3346	+	5.93696i	0.584201	+	0.260103i	−0.0932842	+	0.995640i	$0.529737\pi$
$522$	16.4968	+	14.1370i	0.722045	+	0.618759i
$523$	−15.8982	+	14.3148i	−0.695181	+	0.625944i	−0.939016	−	0.343873i	$-0.888261\pi$
$523$	−15.8982	+	14.3148i	−0.695181	+	0.625944i	0.243835	+	0.969817i	$0.421594\pi$
$524$	2.20208	−	1.59990i	0.0961983	−	0.0698922i
$525$	0.642334	−	21.3954i	0.0280338	−	0.933770i
$526$	2.32114	+	7.14374i	0.101207	+	0.311482i
$527$	−3.37790	−	1.95023i	−0.147144	−	0.0849535i
$528$	−3.84852	+	4.26484i	−0.167486	+	0.185603i
$529$	13.9549	+	24.1706i	0.606735	+	1.05090i
$530$	1.95555	+	0.415664i	0.0849436	+	0.0180553i
$531$	0.770185	+	31.4028i	0.0334232	+	1.36276i
$532$	−9.24349	−	12.4564i	−0.400756	−	0.540054i
$533$	−7.83881	−	2.54698i	−0.339536	−	0.110322i
$534$	−6.21896	−	22.1210i	−0.269121	−	0.957269i
$535$	3.45067	−	7.75033i	0.149185	−	0.335076i
$536$	4.59085	+	0.482518i	0.198295	+	0.0208416i
$537$	14.6296	+	11.5527i	0.631314	+	0.498537i
$538$			0.538005i			0.0231950i
$539$	−21.6171	+	8.46762i	−0.931115	+	0.364726i
$540$	−2.92481	+	0.574219i	−0.125864	+	0.0247105i
$541$	−7.99242	−	1.69884i	−0.343621	−	0.0730389i	0.0328688	−	0.999460i	$-0.489536\pi$
$541$	−7.99242	−	1.69884i	−0.343621	−	0.0730389i	−0.376490	+	0.926421i	$0.622869\pi$
$542$	1.05925	−	10.0781i	0.0454988	−	0.432892i
$543$	−0.816911	−	0.983888i	−0.0350570	−	0.0422227i
$544$	1.37150	−	1.23490i	0.0588026	−	0.0529461i
$545$	3.01680	−	9.28475i	0.129225	−	0.397715i
$546$	4.52084	+	24.9251i	0.193474	+	1.06670i
$547$	13.6251	+	9.89924i	0.582569	+	0.423261i	0.839649	−	0.543129i	$-0.182761\pi$
$547$	13.6251	+	9.89924i	0.582569	+	0.423261i	−0.257081	+	0.966390i	$0.582761\pi$
$548$	1.48542	−	6.98837i	0.0634542	−	0.298529i
$549$	−1.74743	−	0.727209i	−0.0745786	−	0.0310365i
$550$	−5.35815	−	14.5357i	−0.228472	−	0.619804i
$551$	−21.2286	+	36.7690i	−0.904370	+	1.56641i
$552$	12.2290	+	1.78348i	0.520501	+	0.0759099i
$553$	25.4368	−	11.6340i	1.08168	−	0.494729i
$554$	1.36088	+	1.87309i	0.0578182	+	0.0795799i
$555$	−0.730505	+	0.205370i	−0.0310082	+	0.00871746i
$556$	1.72292	+	8.10571i	0.0730682	+	0.343759i
$557$	14.5394	−	32.6559i	0.616053	−	1.38368i	−0.288568	−	0.957459i	$-0.593179\pi$
$557$	14.5394	−	32.6559i	0.616053	−	1.38368i	0.904621	−	0.426217i	$-0.140154\pi$
$558$	−5.56701	−	3.03461i	−0.235670	−	0.128465i
$559$	40.8806	−	13.2829i	1.72907	−	0.561808i
$560$	−0.772053	−	1.30662i	−0.0326252	−	0.0552148i
$561$	−3.26512	−	10.0865i	−0.137853	−	0.425852i
$562$	4.31241	−	7.46931i	0.181908	−	0.315074i
$563$	20.5504	−	22.8235i	0.866097	−	0.961898i	−0.133478	−	0.991052i	$-0.542615\pi$
$563$	20.5504	−	22.8235i	0.866097	−	0.961898i	0.999575	+	0.0291539i	$0.00928128\pi$
$564$	−0.653341	−	0.412986i	−0.0275106	−	0.0173898i
$565$	3.73278	−	0.392331i	0.157039	−	0.0165055i
$566$	−5.61508	+	17.2814i	−0.236019	+	0.726393i
$567$	1.08523	−	23.7870i	0.0455755	−	0.998961i
$568$	−6.61574	+	4.80662i	−0.277590	+	0.201681i
$569$	−1.49417	−	3.35596i	−0.0626389	−	0.140689i	0.879514	−	0.475874i	$-0.157868\pi$
$569$	−1.49417	−	3.35596i	−0.0626389	−	0.140689i	−0.942153	+	0.335184i	$0.891201\pi$
$570$	−2.15399	−	5.41205i	−0.0902206	−	0.226686i
$571$	−11.4258	−	19.7901i	−0.478157	−	0.828192i	0.521530	−	0.853233i	$-0.325362\pi$
$571$	−11.4258	−	19.7901i	−0.478157	−	0.828192i	−0.999686	+	0.0250415i	$0.992028\pi$
$572$	9.77910	+	15.5080i	0.408885	+	0.648421i
$573$	−32.0605	−	15.8436i	−1.33935	−	0.661875i
$574$	−0.781231	+	3.86678i	−0.0326080	+	0.161396i
$575$	−19.5896	+	26.9627i	−0.816942	+	1.12442i
$576$	2.17955	−	2.06145i	0.0908144	−	0.0858938i
$577$	7.86768	+	37.0145i	0.327536	+	1.54094i	0.766389	+	0.642376i	$0.222051\pi$
$577$	7.86768	+	37.0145i	0.327536	+	1.54094i	−0.438853	+	0.898559i	$0.644615\pi$
$578$	−2.82635	−	13.2969i	−0.117561	−	0.553080i
$579$	12.3792	+	4.57861i	0.514464	+	0.190281i
$580$	−2.44172	+	3.36074i	−0.101387	+	0.139547i
$581$	−4.21526	−	12.5414i	−0.174878	−	0.520304i
$582$	2.57307	−	5.20678i	0.106657	−	0.215828i
$583$	−0.759048	+	11.5344i	−0.0314366	+	0.477704i
$584$	6.33209	+	10.9675i	0.262024	+	0.453839i
$585$	−0.762092	+	9.48217i	−0.0315086	+	0.392039i
$586$	−8.32253	−	18.6927i	−0.343800	−	0.772188i
$587$	5.50217	−	3.99756i	0.227099	−	0.164997i	−0.468417	−	0.883507i	$-0.655176\pi$
$587$	5.50217	−	3.99756i	0.227099	−	0.164997i	0.695516	+	0.718510i	$0.255176\pi$
$588$	11.6033	−	3.51613i	0.478513	−	0.145003i
$589$	3.82894	−	11.7843i	0.157769	−	0.485563i
$590$	−5.97338	+	0.627827i	−0.245920	+	0.0258472i
$591$	22.9351	−	36.2833i	0.943426	−	1.49249i
$592$	0.511050	−	0.567578i	0.0210040	−	0.0233273i
$593$	−6.60072	+	11.4328i	−0.271059	+	0.469488i	−0.969133	−	0.246537i	$-0.920707\pi$
$593$	−6.60072	+	11.4328i	−0.271059	+	0.469488i	0.698074	+	0.716025i	$0.254041\pi$
$594$	−5.70801	−	16.2610i	−0.234202	−	0.667195i
$595$	2.80077	−	0.0282502i	0.114821	−	0.00115814i
$596$	11.7473	−	3.81694i	0.481189	−	0.156348i
$597$	44.4998	+	1.78537i	1.82126	+	0.0730703i
$598$	16.0424	−	36.0319i	0.656024	−	1.47345i
$599$	4.50314	+	21.1856i	0.183993	+	0.865621i	0.969179	+	0.246360i	$0.0792344\pi$
$599$	4.50314	+	21.1856i	0.183993	+	0.865621i	−0.785185	+	0.619261i	$0.787432\pi$
$600$	2.18958	+	7.78840i	0.0893894	+	0.317960i
$601$	−16.6129	−	22.8657i	−0.677655	−	0.932712i	0.322248	−	0.946655i	$-0.395561\pi$
$601$	−16.6129	−	22.8657i	−0.677655	−	0.932712i	−0.999903	+	0.0139435i	$0.995561\pi$
$602$	−8.55706	−	18.7093i	−0.348760	−	0.762534i
$603$	−7.86275	+	11.3998i	−0.320196	+	0.464237i
$604$	−11.6567	+	20.1900i	−0.474303	+	0.821518i
$605$	−5.54682	+	3.00790i	−0.225510	+	0.122288i
$606$	1.93062	+	29.8348i	0.0784262	+	1.21195i
$607$	3.93471	−	18.5114i	0.159705	−	0.751353i	−0.823275	−	0.567642i	$-0.807856\pi$
$607$	3.93471	−	18.5114i	0.159705	−	0.751353i	0.982980	−	0.183711i	$-0.0588109\pi$
$608$	4.74308	+	3.44605i	0.192357	+	0.139756i
$609$	−21.4559	−	25.3175i	−0.869437	−	1.02592i
$610$	0.111834	−	0.344190i	0.00452803	−	0.0139358i
$611$	−1.83318	+	1.65061i	−0.0741627	+	0.0667764i
$612$	1.28356	+	5.38577i	0.0518850	+	0.217707i
$613$	2.29983	−	21.8815i	0.0928894	−	0.883784i	−0.844513	−	0.535535i	$-0.820110\pi$
$613$	2.29983	−	21.8815i	0.0928894	−	0.883784i	0.937402	−	0.348249i	$-0.113224\pi$
$614$	11.8558	+	2.52003i	0.478462	+	0.101700i
$615$	−0.656315	+	1.32810i	−0.0264652	+	0.0535540i
$616$	6.83743	−	5.49996i	0.275488	−	0.221600i
$617$		−	24.4514i		−	0.984375i	−0.870489	−	0.492187i	$-0.836197\pi$
$617$		−	24.4514i		−	0.984375i	0.870489	−	0.492187i	$-0.163803\pi$
$618$	9.44068	−	11.9550i	0.379760	−	0.480902i
$619$	10.3453	+	1.08734i	0.415813	+	0.0437037i	0.310125	−	0.950696i	$-0.399629\pi$
$619$	10.3453	+	1.08734i	0.415813	+	0.0437037i	0.105688	+	0.994399i	$0.466296\pi$
$620$	0.493101	−	1.10752i	0.0198034	−	0.0444792i
$621$	−22.2568	+	29.6513i	−0.893135	+	1.18987i
$622$	31.0510	+	10.0891i	1.24503	+	0.404535i
$623$	4.02088	+	34.8692i	0.161093	+	1.39701i
$624$	−4.45100	−	8.47702i	−0.178183	−	0.339352i
$625$	−19.7318	−	4.19411i	−0.789270	−	0.167765i
$626$	−8.55565	−	14.8188i	−0.341953	−	0.592279i
$627$	29.1853	−	16.8076i	1.16555	−	0.671232i
$628$	−9.57117	−	5.52592i	−0.381931	−	0.220508i
$629$	0.435569	+	1.34054i	0.0173673	+	0.0534510i
$630$	4.55029	−	0.157536i	0.181288	−	0.00627639i
$631$	−10.0220	+	7.28140i	−0.398969	+	0.289868i	−0.769121	−	0.639103i	$-0.779306\pi$
$631$	−10.0220	+	7.28140i	−0.398969	+	0.289868i	0.370152	+	0.928971i	$0.379306\pi$
$632$	−7.85659	+	7.07410i	−0.312518	+	0.281393i
$633$	1.56246	−	6.13087i	0.0621021	−	0.243680i
$634$	3.41418	+	1.52009i	0.135594	+	0.0603705i
$635$	−6.38315	+	2.84196i	−0.253307	+	0.112780i
$636$	0.871170	−	5.97346i	0.0345441	−	0.236863i
$637$	−0.780519	−	38.6871i	−0.0309253	−	1.53284i
$638$	−21.2531	−	11.1889i	−0.841419	−	0.442975i
$639$	−3.16178	−	24.3279i	−0.125078	−	0.962398i
$640$	0.426287	+	0.383830i	0.0168505	+	0.0151722i
$641$	−26.7676	−	2.81338i	−1.05726	−	0.111122i	−0.440089	−	0.897954i	$-0.645053\pi$
$641$	−26.7676	−	2.81338i	−1.05726	−	0.111122i	−0.617167	+	0.786832i	$0.711720\pi$
$642$	−24.0259	−	8.88628i	−0.948228	−	0.350714i
$643$	19.9480	+	6.48148i	0.786670	+	0.255605i	0.674686	−	0.738105i	$-0.264279\pi$
$643$	19.9480	+	6.48148i	0.786670	+	0.255605i	0.111985	+	0.993710i	$0.464279\pi$
$644$	−18.0117	−	5.65216i	−0.709761	−	0.222726i
$645$	−1.30205	−	7.61531i	−0.0512681	−	0.299852i
$646$	−9.88451	+	4.40087i	−0.388901	+	0.173150i
$647$	−14.0408	+	15.5939i	−0.552001	+	0.613059i	−0.952982	−	0.303027i	$-0.902003\pi$
$647$	−14.0408	+	15.5939i	−0.552001	+	0.613059i	0.400981	+	0.916086i	$0.368669\pi$
$648$	2.30052	+	8.70101i	0.0903728	+	0.341808i
$649$	−8.53944	−	33.6612i	−0.335202	−	1.32132i
$650$	25.8203			1.01276
$651$	7.66104	+	5.92532i	0.300260	+	0.232232i
$652$	−6.17887	−	4.48921i	−0.241983	−	0.175811i
$653$	36.6591	−	3.85303i	1.43458	−	0.150781i	0.644886	−	0.764279i	$-0.276905\pi$
$653$	36.6591	−	3.85303i	1.43458	−	0.150781i	0.789696	+	0.613499i	$0.210238\pi$
$654$	−28.5648	−	7.27977i	−1.11697	−	0.284662i
$655$	−1.52724	+	0.324626i	−0.0596744	+	0.0126842i
$656$	−0.155856	−	1.48287i	−0.00608514	−	0.0578962i
$657$	−37.9811	+	0.931526i	−1.48179	+	0.0363423i
$658$	0.885326	+	0.781127i	0.0345136	+	0.0304515i
$659$			1.19425i			0.0465212i	0.999729	+	0.0232606i	$0.00740475\pi$
$659$			1.19425i			0.0465212i	−0.999729	+	0.0232606i	$0.992595\pi$
$660$	3.01180	−	1.33700i	0.117234	−	0.0520427i
$661$	39.1889	−	22.6257i	1.52427	−	0.880038i	0.524684	−	0.851297i	$-0.324184\pi$
$661$	39.1889	−	22.6257i	1.52427	−	0.880038i	0.999587	−	0.0287410i	$-0.00914982\pi$
$662$	−2.43431	−	2.19186i	−0.0946121	−	0.0851892i
$663$	17.6559	+	0.708370i	0.685699	+	0.0275108i
$664$	2.93938	+	4.04572i	0.114070	+	0.157004i
$665$	1.93763	+	8.68421i	0.0751382	+	0.336759i
$666$	0.761253	+	2.16110i	0.0294979	+	0.0837408i
$667$	5.40113	+	51.3883i	0.209133	+	1.98976i
$668$	1.60175	−	15.2397i	0.0619737	−	0.589640i
$669$	−20.7179	+	8.24570i	−0.801001	+	0.318797i
$670$	−2.29318	−	1.32397i	−0.0885933	−	0.0511494i
$671$	2.06215	+	0.354901i	0.0796085	+	0.0137008i
$672$	−3.78654	+	2.58110i	−0.146069	+	0.0995682i
$673$	−13.3737	−	41.1600i	−0.515518	−	1.58660i	−0.782338	−	0.622854i	$-0.785973\pi$
$673$	−13.3737	−	41.1600i	−0.515518	−	1.58660i	0.266820	−	0.963746i	$-0.414027\pi$
$674$	4.32578	+	9.71587i	0.166623	+	0.374241i
$675$	−23.6591	−	5.41543i	−0.910640	−	0.208440i
$676$	−17.1734	+	3.65033i	−0.660517	+	0.140397i
$677$	−7.58063	−	8.41914i	−0.291347	−	0.323574i	0.579647	−	0.814868i	$-0.303191\pi$
$677$	−7.58063	−	8.41914i	−0.291347	−	0.323574i	−0.870994	+	0.491294i	$0.836524\pi$
$678$	−1.91000	−	11.1710i	−0.0733530	−	0.429021i
$679$	−5.14197	+	7.22954i	−0.197331	+	0.277444i
$680$	−1.00683	+	0.327140i	−0.0386103	+	0.0125452i
$681$	−9.23176	−	13.8411i	−0.353762	−	0.530393i
$682$	6.74588	+	1.90445i	0.258313	+	0.0729252i
$683$	−3.95212	+	2.28176i	−0.151224	+	0.0873091i	−0.573703	−	0.819064i	$-0.694493\pi$
$683$	−3.95212	+	2.28176i	−0.151224	+	0.0873091i	0.422479	+	0.906373i	$0.361160\pi$
$684$	−15.8875	+	7.54561i	−0.607473	+	0.288514i
$685$	−2.40890	+	3.31557i	−0.0920394	+	0.126681i
$686$	−18.3518	+	2.49225i	−0.700675	+	0.0951546i
$687$	−18.7399	+	19.2051i	−0.714972	+	0.732722i
$688$	5.20315	+	5.77868i	0.198368	+	0.220310i
$689$	−17.6004	−	7.83619i	−0.670520	−	0.298535i
$690$	−5.99229	−	3.78781i	−0.228123	−	0.144199i
$691$	5.64101	−	26.5389i	0.214594	−	1.00959i	−0.730532	−	0.682879i	$-0.760728\pi$
$691$	5.64101	−	26.5389i	0.214594	−	1.00959i	0.945126	−	0.326707i	$-0.105939\pi$
$692$	−8.11709			−0.308565
$693$	4.66978	+	25.9074i	0.177390	+	0.984141i
$694$	−26.0574			−0.989125
$695$	0.988312	−	4.64964i	0.0374888	−	0.176371i
$696$	10.6026	+	6.70205i	0.401891	+	0.254041i
$697$	2.51386	+	1.11924i	0.0952191	+	0.0423943i
$698$	−9.97085	−	11.0737i	−0.377402	−	0.419147i
$699$	−22.2612	+	22.8139i	−0.841995	+	0.862899i
$700$	−1.41568	−	12.2768i	−0.0535076	−	0.464020i
$701$	−14.6754	+	20.1989i	−0.554281	+	0.762903i	−0.990585	−	0.136897i	$-0.956287\pi$
$701$	−14.6754	+	20.1989i	−0.554281	+	0.762903i	0.436304	+	0.899799i	$0.356287\pi$
$702$	28.7201	+	0.447444i	1.08397	+	0.0168877i
$703$	−3.87780	+	2.23885i	−0.146254	+	0.0844397i
$704$	−1.84334	+	2.75719i	−0.0694736	+	0.103915i
$705$	0.246017	+	0.368852i	0.00926553	+	0.0138918i
$706$	18.2927	−	5.94367i	0.688456	−	0.223693i
$707$	4.31534	−	45.4644i	0.162295	−	1.70986i
$708$	3.05647	+	17.8764i	0.114869	+	0.671837i
$709$	23.7216	+	26.3455i	0.890882	+	0.989424i	0.999989	−	0.00460566i	$-0.00146603\pi$
$709$	23.7216	+	26.3455i	0.890882	+	0.989424i	−0.109108	+	0.994030i	$0.534799\pi$
$710$	4.58832	−	0.975278i	0.172197	−	0.0366015i
$711$	−7.35284	−	30.8522i	−0.275753	−	1.15705i
$712$	−5.39604	−	12.1197i	−0.202225	−	0.454205i
$713$	−4.65991	−	14.3417i	−0.174515	−	0.537101i
$714$	−0.631230	−	8.43372i	−0.0236232	−	0.315624i
$715$	−1.50634	−	10.4083i	−0.0563338	−	0.389248i
$716$	9.32055	+	5.38122i	0.348325	+	0.201106i
$717$	2.82075	−	1.12266i	0.105343	−	0.0419263i
$718$	0.544117	−	5.17692i	0.0203063	−	0.193201i
$719$	−0.463987	−	4.41454i	−0.0173038	−	0.164634i	0.982457	−	0.186487i	$-0.0597102\pi$
$719$	−0.463987	−	4.41454i	−0.0173038	−	0.164634i	−0.999761	+	0.0218525i	$0.993044\pi$
$720$	−1.62312	+	0.571749i	−0.0604901	+	0.0213078i
$721$	−17.1344	+	15.7437i	−0.638117	+	0.586324i
$722$	−9.03544	−	12.4362i	−0.336264	−	0.462828i
$723$	−13.1268	−	0.526659i	−0.488192	−	0.0195867i
$724$	−0.548684	−	0.494037i	−0.0203917	−	0.0183607i
$725$	−29.2945	+	16.9132i	−1.08797	+	0.628139i
$726$	10.1449	+	16.1270i	0.376512	+	0.598531i
$727$		−	8.22143i		−	0.304916i	−0.988310	−	0.152458i	$-0.951281\pi$
$727$		−	8.22143i		−	0.304916i	0.988310	−	0.152458i	$-0.0487189\pi$
$728$	4.65953	+	13.8632i	0.172694	+	0.513805i
$729$	−26.2223	−	6.43360i	−0.971196	−	0.238281i
$730$	−0.759347	−	7.22471i	−0.0281047	−	0.267398i
$731$	−14.0373	+	2.98371i	−0.519186	+	0.110356i
$732$	−1.05891	−	0.269864i	−0.0391384	−	0.00997446i
$733$	20.0982	−	2.11241i	0.742344	−	0.0780235i	0.274197	−	0.961674i	$-0.411588\pi$
$733$	20.0982	−	2.11241i	0.742344	−	0.0780235i	0.468148	+	0.883650i	$0.344921\pi$
$734$	8.94685	+	6.50027i	0.330234	+	0.239929i
$735$	−6.90088	−	0.864655i	−0.254543	−	0.0318933i
$736$	7.13511			0.263004
$737$	5.67698	−	14.2186i	0.209114	−	0.523748i
$738$	4.12976	+	1.71864i	0.152019	+	0.0632638i
$739$	8.64362	−	9.59971i	0.317961	−	0.353131i	−0.562884	−	0.826536i	$-0.690308\pi$
$739$	8.64362	−	9.59971i	0.317961	−	0.353131i	0.880845	+	0.473404i	$0.156975\pi$
$740$	−0.400231	+	0.178194i	−0.0147128	+	0.00655056i
$741$	9.46023	+	55.3302i	0.347530	+	2.03261i
$742$	−2.76089	+	8.79812i	−0.101355	+	0.322989i
$743$	8.24475	+	2.67888i	0.302471	+	0.0982787i	0.456320	−	0.889816i	$-0.349167\pi$
$743$	8.24475	+	2.67888i	0.302471	+	0.0982787i	−0.153850	+	0.988094i	$0.549167\pi$
$744$	−3.43331	−	1.26985i	−0.125871	−	0.0465550i
$745$	−7.04653	−	0.740620i	−0.258165	−	0.0271342i
$746$	−11.7972	−	10.6223i	−0.431928	−	0.388910i
$747$	−14.8772	+	1.93352i	−0.544329	+	0.0707439i
$748$	−2.70578	−	5.49043i	−0.0989332	−	0.200750i
$749$	34.0832	+	19.2222i	1.24537	+	0.702365i
$750$	1.38664	−	9.50798i	0.0506331	−	0.347182i
$751$	30.5349	−	13.5950i	1.11424	−	0.496090i	0.234770	−	0.972051i	$-0.424566\pi$
$751$	30.5349	−	13.5950i	1.11424	−	0.496090i	0.879466	+	0.475961i	$0.157900\pi$
$752$	−0.407668	−	0.181505i	−0.0148661	−	0.00661882i
$753$	−3.87412	+	15.2015i	−0.141181	+	0.553974i
$754$	29.7494	−	26.7865i	1.08341	−	0.975507i
$755$	10.8191	−	7.86053i	0.393747	−	0.286074i
$756$	−1.36192	−	13.6801i	−0.0495325	−	0.497540i
$757$	3.45829	+	10.6435i	0.125694	+	0.386845i	0.994027	−	0.109136i	$-0.0348084\pi$
$757$	3.45829	+	10.6435i	0.125694	+	0.386845i	−0.868333	+	0.495981i	$0.834808\pi$
$758$	3.04568	+	1.75843i	0.110624	+	0.0638689i
$759$	16.7123	−	37.4262i	0.606616	−	1.35849i
$760$	−1.68152	−	2.91247i	−0.0609950	−	0.105646i
$761$	−7.20633	−	1.53175i	−0.261229	−	0.0555260i	0.0754351	−	0.997151i	$-0.475965\pi$
$761$	−7.20633	−	1.53175i	−0.261229	−	0.0555260i	−0.336664	+	0.941625i	$0.609299\pi$
$762$	9.80794	+	18.6794i	0.355304	+	0.676684i
$763$	41.3179	+	17.8988i	1.49581	+	0.647980i
$764$	−19.6365	−	6.38028i	−0.710423	−	0.230830i
$765$	0.583949	−	3.12180i	0.0211127	−	0.112869i
$766$	−0.278795	+	0.626184i	−0.0100733	+	0.0226249i
$767$	57.5635	+	6.05017i	2.07850	+	0.218459i
$768$	1.07343	−	1.35932i	0.0387341	−	0.0490502i
$769$		−	15.1564i		−	0.546554i	−0.961935	−	0.273277i	$-0.911892\pi$
$769$		−	15.1564i		−	0.546554i	0.961935	−	0.273277i	$-0.0881075\pi$
$770$	−4.86626	+	1.28689i	−0.175368	+	0.0463762i
$771$	−18.7886	+	38.0199i	−0.676654	+	1.36925i
$772$	7.45383	+	1.58436i	0.268269	+	0.0570224i
$773$	−1.29864	+	12.3557i	−0.0467088	+	0.444405i	0.946027	+	0.324089i	$0.105058\pi$
$773$	−1.29864	+	12.3557i	−0.0467088	+	0.444405i	−0.992736	+	0.120316i	$0.961609\pi$
$774$	−22.6924	+	5.40816i	−0.815661	+	0.194392i
$775$	7.33623	−	6.60557i	0.263525	−	0.237279i
$776$	1.03619	−	3.18905i	0.0371969	−	0.114480i
$777$	−0.624619	−	3.44376i	−0.0224081	−	0.123544i
$778$	1.94107	+	1.41027i	0.0695907	+	0.0505606i
$779$	−1.81748	+	8.55056i	−0.0651179	+	0.306356i
$780$	0.354660	+	5.48072i	0.0126989	+	0.196241i
$781$	9.38060	+	25.4478i	0.335664	+	0.910595i
$782$	−6.58405	+	11.4039i	−0.235445	+	0.407803i
$783$	−32.8774	+	18.3049i	−1.17494	+	0.654165i
$784$	6.33609	−	2.97557i	0.226289	−	0.106270i
$785$	3.72633	+	5.12886i	0.132999	+	0.183057i
$786$	1.27594	+	4.53856i	0.0455114	+	0.161885i
$787$	−11.1937	−	52.6621i	−0.399011	−	1.87720i	−0.474827	−	0.880079i	$-0.657489\pi$
$787$	−11.1937	−	52.6621i	−0.399011	−	1.87720i	0.0758157	−	0.997122i	$-0.475844\pi$
$788$	10.0799	−	22.6398i	0.359081	−	0.806510i
$789$	−12.9996	−	0.521555i	−0.462799	−	0.0185679i
$790$	5.76760	−	1.87401i	0.205202	−	0.0666742i
$791$	0.174606	+	17.3108i	0.00620828	+	0.615500i
$792$	−4.61587	−	8.81440i	−0.164018	−	0.313206i
$793$	−1.74377	+	3.02030i	−0.0619231	+	0.107254i
$794$	10.8200	−	12.0168i	0.383986	−	0.426460i
$795$	−1.85022	+	2.92703i	−0.0656204	+	0.103811i
$796$	25.5718	−	2.68770i	0.906368	−	0.0952631i
$797$	10.4230	−	32.0786i	0.369201	−	1.13628i	−0.578108	−	0.815960i	$-0.696209\pi$
$797$	10.4230	−	32.0786i	0.369201	−	1.13628i	0.947308	−	0.320323i	$-0.103791\pi$
$798$	25.7892	−	7.53172i	0.912929	−	0.266620i
$799$	0.666280	−	0.484081i	0.0235713	−	0.0171255i
$800$	1.89985	+	4.26713i	0.0671698	+	0.150866i
$801$	39.6721	+	3.18849i	1.40174	+	0.112660i
$802$	17.6037	+	30.4905i	0.621608	+	1.07666i
$803$	40.7127	−	10.3283i	1.43672	−	0.364478i
$804$	−3.54222	+	7.16791i	−0.124924	+	0.252793i
$805$	8.12000	+	7.16431i	0.286192	+	0.252509i
$806$	−6.86703	+	9.45165i	−0.241881	+	0.332920i
$807$	−0.873987	−	0.323255i	−0.0307658	−	0.0113791i
$808$	3.58879	+	16.8839i	0.126253	+	0.593975i
$809$	3.35620	+	15.7897i	0.117998	+	0.555136i	0.996937	+	0.0782031i	$0.0249183\pi$
$809$	3.35620	+	15.7897i	0.117998	+	0.555136i	−0.878940	+	0.476933i	$0.841748\pi$
$810$	0.824526	−	5.09636i	0.0289709	−	0.179068i
$811$	13.6610	−	18.8028i	0.479704	−	0.660256i	−0.498744	−	0.866749i	$-0.666205\pi$
$811$	13.6610	−	18.8028i	0.479704	−	0.660256i	0.978448	+	0.206493i	$0.0662052\pi$
$812$	−14.3673	−	12.6764i	−0.504195	−	0.444853i
$813$	15.7354	+	7.77609i	0.551866	+	0.272719i
$814$	−1.35112	−	2.14265i	−0.0473568	−	0.0750998i
$815$	2.19053	+	3.79411i	0.0767310	+	0.132902i
$816$	1.18205	+	2.96998i	0.0413799	+	0.103970i
$817$	−18.5426	−	41.6474i	−0.648724	−	1.45706i
$818$	−2.95014	+	2.14340i	−0.103149	+	0.0749423i
$819$	−43.2071	−	7.63191i	−1.50978	−	0.266680i
$820$	−0.264301	+	0.813434i	−0.00922979	+	0.0284064i
$821$	−18.6031	+	1.95526i	−0.649252	+	0.0682391i	−0.423429	−	0.905929i	$-0.639174\pi$
$821$	−18.6031	+	1.95526i	−0.649252	+	0.0682391i	−0.225823	+	0.974168i	$0.572507\pi$
$822$	10.4601	+	6.61196i	0.364838	+	0.230619i
$823$	5.16585	−	5.73725i	0.180070	−	0.199988i	−0.646352	−	0.763040i	$-0.723706\pi$
$823$	5.16585	−	5.73725i	0.180070	−	0.199988i	0.826422	+	0.563052i	$0.190373\pi$
$824$	4.39744	−	7.61659i	0.153192	−	0.265336i
$825$	26.8326	+	0.0293126i	0.934190	+	0.00102053i
$826$	−0.279414	−	27.7016i	−0.00972204	−	0.963860i
$827$	54.5386	−	17.7206i	1.89649	−	0.616207i	0.924505	−	0.381170i	$-0.124479\pi$
$827$	54.5386	−	17.7206i	1.89649	−	0.616207i	0.971986	−	0.235037i	$-0.0755212\pi$
$828$	−10.2449	+	18.7944i	−0.356036	+	0.653151i
$829$	4.16299	−	9.35023i	0.144587	−	0.324747i	−0.826706	−	0.562634i	$-0.809788\pi$
$829$	4.16299	−	9.35023i	0.144587	−	0.324747i	0.971293	+	0.237887i	$0.0764548\pi$
$830$	−0.596410	−	2.80589i	−0.0207017	−	0.0973939i
$831$	−3.86050	+	1.08532i	−0.133919	+	0.0376492i
$832$	−3.24919	−	4.47212i	−0.112645	−	0.155043i
$833$	−1.09095	+	12.8726i	−0.0377990	+	0.446009i
$834$	−14.2029	−	2.07135i	−0.491806	−	0.0717251i
$835$	−4.39501	+	7.61238i	−0.152096	+	0.263437i
$836$	15.2733	−	12.0340i	0.528239	−	0.416205i
$837$	8.27459	−	7.22028i	0.286012	−	0.249569i
$838$	−4.89653	+	23.0363i	−0.169148	+	0.795777i
$839$	−7.93550	−	5.76548i	−0.273964	−	0.199046i	0.442316	−	0.896859i	$-0.354157\pi$
$839$	−7.93550	−	5.76548i	−0.273964	−	0.199046i	−0.716280	+	0.697813i	$0.754157\pi$
$840$	2.58648	−	0.469128i	0.0892421	−	0.0161865i
$841$	−7.24470	+	22.2969i	−0.249817	+	0.768858i
$842$	−14.7865	+	13.3138i	−0.509576	+	0.458824i
$843$	9.54280	+	11.4934i	0.328672	+	0.395852i
$844$	0.381821	−	3.63279i	0.0131428	−	0.125046i
$845$	9.85112	+	2.09392i	0.338889	+	0.0720331i
$846$	1.06345	−	0.813213i	0.0365621	−	0.0279588i
$847$	−11.3939	−	26.7802i	−0.391498	−	0.920179i
$848$		−	3.48526i		−	0.119684i
$849$	−24.6999	−	19.5051i	−0.847698	−	0.669412i
$850$	−8.57319	−	0.901079i	−0.294058	−	0.0309067i
$851$	−2.21649	+	4.97832i	−0.0759804	+	0.170655i
$852$	−3.83334	−	13.6353i	−0.131328	−	0.467136i
$853$	35.1011	+	11.4050i	1.20184	+	0.390501i	0.840437	−	0.541910i	$-0.182299\pi$
$853$	35.1011	+	11.4050i	1.20184	+	0.390501i	0.361401	+	0.932411i	$0.382299\pi$
$854$	1.53167	+	0.663516i	0.0524128	+	0.0227050i
$855$	10.0861	−	0.247371i	0.344936	−	0.00845991i
$856$	−14.4666	−	3.07497i	−0.494457	−	0.105100i
$857$	−14.4523	−	25.0321i	−0.493682	−	0.855081i	0.506292	−	0.862362i	$-0.331016\pi$
$857$	−14.4523	−	25.0321i	−0.493682	−	0.855081i	−0.999973	+	0.00728067i	$0.997682\pi$
$858$	−31.0683	+	6.56831i	−1.06066	+	0.224239i
$859$	18.6851	+	10.7878i	0.637527	+	0.368076i	0.783661	−	0.621188i	$-0.213350\pi$
$859$	18.6851	+	10.7878i	0.637527	+	0.368076i	−0.146134	+	0.989265i	$0.546683\pi$
$860$	−1.37837	−	4.24219i	−0.0470021	−	0.144657i
$861$	−5.81217	−	3.59242i	−0.198078	−	0.122429i
$862$	−26.3218	+	19.1239i	−0.896522	+	0.651362i
$863$	−36.4741	+	32.8415i	−1.24159	+	1.11794i	−0.252979	+	0.967472i	$0.581410\pi$
$863$	−36.4741	+	32.8415i	−1.24159	+	1.11794i	−0.988615	+	0.150465i	$0.951923\pi$
$864$	2.03926	+	4.77927i	0.0693772	+	0.162594i
$865$	4.25362	+	1.89383i	0.144627	+	0.0643923i
$866$	−29.2591	+	13.0270i	−0.994265	+	0.442675i
$867$	23.2990	+	3.39793i	0.791276	+	0.115400i
$868$	4.87050	+	2.74686i	0.165316	+	0.0932345i
$869$	15.5000	+	31.4517i	0.525801	+	1.06693i
$870$	−3.99244	−	5.98584i	−0.135356	−	0.202939i
$871$	18.9631	+	17.0744i	0.642539	+	0.578545i
$872$	−16.9258	−	1.77898i	−0.573181	−	0.0602437i
$873$	6.91239	+	7.30838i	0.233949	+	0.247351i
$874$	−39.7841	−	12.9266i	−1.34572	−	0.437250i
$875$	−4.39452	+	14.0040i	−0.148562	+	0.473422i
$876$	−21.6213	+	3.69675i	−0.730515	+	0.124902i
$877$	−9.65588	+	4.29907i	−0.326056	+	0.145169i	−0.563236	−	0.826296i	$-0.690444\pi$
$877$	−9.65588	+	4.29907i	−0.326056	+	0.145169i	0.237180	+	0.971466i	$0.423777\pi$
$878$	−0.228656	+	0.253948i	−0.00771677	+	0.00857034i
$879$	35.3668	−	2.28860i	1.19289	−	0.0771926i
$880$	1.60927	−	1.01478i	0.0542483	−	0.0342082i
$881$	46.2099			1.55685			0.778425	−	0.627738i	$-0.216019\pi$
$881$	46.2099			1.55685			0.778425	+	0.627738i	$0.216019\pi$
$882$	−1.25979	+	20.9622i	−0.0424195	+	0.705833i
$883$	−38.3024	−	27.8283i	−1.28898	−	0.936498i	−0.289195	−	0.957270i	$-0.593388\pi$
$883$	−38.3024	−	27.8283i	−1.28898	−	0.936498i	−0.999784	+	0.0207721i	$0.993388\pi$
$884$	10.1460	−	1.06638i	0.341245	−	0.0358663i
$885$	2.56914	−	10.0810i	0.0863607	−	0.338868i
$886$	−28.0962	+	5.97202i	−0.943909	+	0.200634i
$887$	6.17824	+	58.7820i	0.207445	+	1.97371i	0.226988	+	0.973898i	$0.427112\pi$
$887$	6.17824	+	58.7820i	0.207445	+	1.97371i	−0.0195430	+	0.999809i	$0.506221\pi$
$888$	0.614970	+	1.17122i	0.0206370	+	0.0393036i
$889$	−10.2674	−	30.5481i	−0.344359	−	1.02455i
$890$			7.61010i			0.255091i
$891$	29.8455	+	0.497589i	0.999861	+	0.0166699i
$892$	−11.1493	+	6.43703i	−0.373305	+	0.215528i
$893$	1.94425	+	1.75061i	0.0650619	+	0.0585820i
$894$	−0.857657	+	21.3769i	−0.0286844	+	0.714949i
$895$	−3.62876	−	4.99456i	−0.121296	−	0.166950i
$896$	−1.94822	+	1.79009i	−0.0650855	+	0.0598028i
$897$	48.8948	+	47.7103i	1.63255	+	1.59300i
$898$	1.44914	+	13.7877i	0.0483585	+	0.460100i
$899$	1.59985	−	15.2215i	0.0533578	−	0.507666i
$900$	−13.9678	−	1.12261i	−0.465594	−	0.0374203i
$901$	5.57043	+	3.21609i	0.185578	+	0.107143i
$902$	−4.87355	−	0.838749i	−0.162272	−	0.0279273i
$903$	35.5346	−	2.65962i	1.18252	−	0.0885067i
$904$	−2.02196	−	6.22294i	−0.0672493	−	0.206972i
$905$	0.172262	+	0.386908i	0.00572620	+	0.0128612i
$906$	−25.7947	−	31.0672i	−0.856972	−	1.03214i
$907$	26.2737	−	5.58465i	0.872405	−	0.185435i	0.250109	−	0.968218i	$-0.419533\pi$
$907$	26.2737	−	5.58465i	0.872405	−	0.185435i	0.622296	+	0.782782i	$0.286200\pi$
$908$	−6.42740	−	7.13835i	−0.213301	−	0.236894i
$909$	−49.6265	−	14.7896i	−1.64601	−	0.490541i
$910$	0.792739	−	8.35192i	0.0262790	−	0.276863i
$911$	−6.76232	+	2.19721i	−0.224046	+	0.0727968i	−0.418889	−	0.908038i	$-0.637580\pi$
$911$	−6.76232	+	2.19721i	−0.224046	+	0.0727968i	0.194843	+	0.980834i	$0.437580\pi$
$912$	−8.44792	+	5.63459i	−0.279739	+	0.186580i
$913$	15.5621	−	5.73650i	0.515030	−	0.189851i
$914$	22.2519	−	12.8472i	0.736028	−	0.424946i
$915$	0.491941	+	0.388477i	0.0162631	+	0.0128427i
$916$	−9.10607	+	12.5334i	−0.300873	+	0.414116i
$917$	−0.824963	−	7.15412i	−0.0272427	−	0.236250i
$918$	−9.52038	−	1.15084i	−0.314219	−	0.0379834i
$919$	5.04750	+	5.60582i	0.166502	+	0.184919i	0.820621	−	0.571472i	$-0.193627\pi$
$919$	5.04750	+	5.60582i	0.166502	+	0.184919i	−0.654120	+	0.756391i	$0.726961\pi$
$920$	−3.73903	−	1.66473i	−0.123272	−	0.0548844i
$921$	−11.2172	+	17.7456i	−0.369621	+	0.584738i
$922$	−8.07725	+	38.0005i	−0.266010	+	1.25148i
$923$	−45.2040			−1.48791
$924$	4.82646	+	14.4120i	0.158779	+	0.474119i
$925$	−3.56745			−0.117297
$926$	7.54427	−	35.4930i	0.247920	−	1.16637i
$927$	13.7486	+	22.5194i	0.451563	+	0.739635i
$928$	6.61576	+	2.94552i	0.217173	+	0.0966916i
$929$	2.06133	+	2.28934i	0.0676302	+	0.0751109i	0.776010	−	0.630720i	$-0.217240\pi$
$929$	2.06133	+	2.28934i	0.0676302	+	0.0751109i	−0.708380	+	0.705831i	$0.750574\pi$
$930$	1.50289	+	1.46649i	0.0492818	+	0.0480880i
$931$	−40.7197	+	5.11218i	−1.33453	+	0.167545i
$932$	−10.8171	+	14.8885i	−0.354327	+	0.487689i
$933$	−35.0464	+	44.3803i	−1.14737	+	1.45295i
$934$	−2.35385	+	1.35900i	−0.0770203	+	0.0444677i
$935$	0.136924	+	3.50846i	0.00447789	+	0.114739i
$936$	16.4452	−	2.13731i	0.537529	−	0.0698602i
$937$	−48.7972	+	15.8552i	−1.59414	+	0.517966i	−0.965648	−	0.259854i	$-0.916326\pi$
$937$	−48.7972	+	15.8552i	−1.59414	+	0.517966i	−0.628487	+	0.777820i	$0.716326\pi$
$938$	7.07869	−	9.95256i	0.231128	−	0.324963i
$939$	29.2137	−	4.99489i	0.953354	−	0.163002i
$940$	0.171284	+	0.190230i	0.00558666	+	0.00620461i
$941$	−7.36912	+	1.56635i	−0.240226	+	0.0510617i	−0.326451	−	0.945214i	$-0.605853\pi$
$941$	−7.36912	+	1.56635i	−0.240226	+	0.0510617i	0.0862250	+	0.996276i	$0.472520\pi$
$942$	14.7276	−	12.2282i	0.479851	−	0.398415i
$943$	4.32715	+	9.71893i	0.140911	+	0.316492i
$944$	3.23563	+	9.95826i	0.105311	+	0.324114i
$945$	−2.47808	+	7.48658i	−0.0806118	+	0.243539i
$946$	23.1334	−	11.4005i	0.752130	−	0.370664i
$947$	22.7672	+	13.1446i	0.739834	+	0.427143i	0.822009	−	0.569475i	$-0.192853\pi$
$947$	22.7672	+	13.1446i	0.739834	+	0.427143i	−0.0821750	+	0.996618i	$0.526187\pi$
$948$	−6.77131	−	17.0134i	−0.219922	−	0.552570i
$949$	−7.31759	+	69.6222i	−0.237539	+	2.26003i
$950$	−2.86248	−	27.2347i	−0.0928711	−	0.883610i
$951$	−4.52076	+	4.63299i	−0.146596	+	0.150235i
$952$	−1.06332	−	4.76565i	−0.0344623	−	0.154455i
$953$	−31.2377	−	42.9950i	−1.01189	−	1.39275i	−0.917737	−	0.397188i	$-0.869986\pi$
$953$	−31.2377	−	42.9950i	−1.01189	−	1.39275i	−0.0941521	−	0.995558i	$-0.530014\pi$
$954$	9.18043	+	5.00431i	0.297228	+	0.162020i
$955$	8.80155	+	7.92495i	0.284811	+	0.256445i
$956$	1.51798	−	0.876404i	0.0490949	−	0.0283449i
$957$	30.9461	−	27.8029i	1.00035	−	0.898739i
$958$		−	5.73510i		−	0.185293i
$959$	−14.1742	−	12.5060i	−0.457709	−	0.403838i
$960$	−0.879662	+	0.461881i	−0.0283910	+	0.0149072i
$961$	−2.77348	−	26.3879i	−0.0894672	−	0.851224i
$962$	4.12964	−	0.877783i	0.133145	−	0.0283009i
$963$	28.8715	−	33.6908i	0.930370	−	1.08567i
$964$	−7.54332	+	0.792835i	−0.242954	+	0.0255355i
$965$	−3.53640	−	2.56935i	−0.113841	−	0.0827102i
$966$	20.0041	−	25.8639i	0.643620	−	0.832158i
$967$	28.6148			0.920191			0.460096	−	0.887869i	$-0.347815\pi$
$967$	28.6148			0.920191			0.460096	+	0.887869i	$0.347815\pi$
$968$	7.13953	+	8.36822i	0.229473	+	0.268965i
$969$	−1.21019	−	18.7016i	−0.0388769	−	0.600781i
$970$	−1.28705	+	1.42941i	−0.0413246	+	0.0458956i
$971$	44.7759	−	19.9355i	1.43693	−	0.639761i	0.467244	−	0.884129i	$-0.345247\pi$
$971$	44.7759	−	19.9355i	1.43693	−	0.639761i	0.969683	+	0.244368i	$0.0785804\pi$
$972$	−15.5170	−	1.49073i	−0.497708	−	0.0478153i
$973$	20.9190	+	6.56448i	0.670632	+	0.210448i
$974$	−17.0715	−	5.54687i	−0.547006	−	0.177733i
$975$	−15.5139	+	41.9450i	−0.496842	+	1.34332i
$976$	−0.627447	−	0.0659474i	−0.0200841	−	0.00211092i
$977$	−22.9222	−	20.6393i	−0.733347	−	0.660309i	0.215335	−	0.976540i	$-0.430916\pi$
$977$	−22.9222	−	20.6393i	−0.733347	−	0.660309i	−0.948682	+	0.316231i	$0.897582\pi$
$978$	11.0052	−	7.34025i	0.351908	−	0.234715i
$979$	−43.5469	+	6.30230i	−1.39176	+	0.201422i
$980$	−4.01456	+	0.0809945i	−0.128241	+	0.00258728i
$981$	28.9889	−	42.0295i	0.925543	−	1.34190i
$982$	12.2239	−	5.44243i	0.390080	−	0.173675i
$983$	35.8825	+	15.9759i	1.14447	+	0.509553i	0.889292	−	0.457340i	$-0.151198\pi$
$983$	35.8825	+	15.9759i	1.14447	+	0.509553i	0.255182	+	0.966893i	$0.417864\pi$
$984$	2.50256	+	0.637778i	0.0797786	+	0.0203316i
$985$	−10.5644	+	9.51223i	−0.336610	+	0.303085i
$986$	−10.8126	+	7.85580i	−0.344343	+	0.250180i
$987$	−1.80088	+	0.968877i	−0.0573226	+	0.0308397i
$988$	10.0148	+	30.8223i	0.318612	+	0.980587i
$989$	−48.0492	−	27.7412i	−1.52788	−	0.882120i
$990$	0.362342	+	5.69599i	0.0115160	+	0.181030i
$991$	1.31178	+	2.27207i	0.0416701	+	0.0721748i	0.886108	−	0.463478i	$-0.153399\pi$
$991$	1.31178	+	2.27207i	0.0416701	+	0.0721748i	−0.844438	+	0.535653i	$0.820065\pi$
$992$	−2.06728	−	0.439413i	−0.0656361	−	0.0139514i
$993$	5.02331	−	2.63757i	0.159410	−	0.0837008i
$994$	2.47845	+	21.4932i	0.0786116	+	0.681724i
$995$	−14.0275	−	4.55782i	−0.444703	−	0.144493i
$996$	−8.33835	+	2.34419i	−0.264211	+	0.0742786i
$997$	1.73262	−	3.89152i	0.0548725	−	0.123246i	−0.884028	−	0.467433i	$-0.845179\pi$
$997$	1.73262	−	3.89152i	0.0548725	−	0.123246i	0.938901	+	0.344187i	$0.111846\pi$
$998$	0.959905	+	0.100890i	0.0303853	+	0.00319362i
$999$	−3.96809	−	0.0618208i	−0.125545	−	0.00195592i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.bf.a.5.3	✓	256
3.2	odd	2	inner	462.2.bf.a.5.18	yes	256
7.3	odd	6	inner	462.2.bf.a.269.9	yes	256
11.9	even	5	inner	462.2.bf.a.383.20	yes	256
21.17	even	6	inner	462.2.bf.a.269.20	yes	256
33.20	odd	10	inner	462.2.bf.a.383.9	yes	256
77.31	odd	30	inner	462.2.bf.a.185.18	yes	256
231.185	even	30	inner	462.2.bf.a.185.3	yes	256

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.bf.a.5.3	✓	256	1.1	even	1	trivial
462.2.bf.a.5.18	yes	256	3.2	odd	2	inner
462.2.bf.a.185.3	yes	256	231.185	even	30	inner
462.2.bf.a.185.18	yes	256	77.31	odd	30	inner
462.2.bf.a.269.9	yes	256	7.3	odd	6	inner
462.2.bf.a.269.20	yes	256	21.17	even	6	inner
462.2.bf.a.383.9	yes	256	33.20	odd	10	inner
462.2.bf.a.383.20	yes	256	11.9	even	5	inner

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.bf (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.207912 + 0.978148i) q^{2} +(-1.46408 - 0.925462i) q^{3} +(-0.913545 - 0.406737i) q^{4} +(0.383830 + 0.426287i) q^{5} +(1.20964 - 1.23967i) q^{6} +(-2.12466 + 1.57664i) q^{7} +(0.587785 - 0.809017i) q^{8} +(1.28704 + 2.70989i) q^{9} +O(q^{10})\)	\(q+(-0.207912 + 0.978148i) q^{2} +(-1.46408 - 0.925462i) q^{3} +(-0.913545 - 0.406737i) q^{4} +(0.383830 + 0.426287i) q^{5} +(1.20964 - 1.23967i) q^{6} +(-2.12466 + 1.57664i) q^{7} +(0.587785 - 0.809017i) q^{8} +(1.28704 + 2.70989i) q^{9} +(-0.496774 + 0.286813i) q^{10} +(-2.05262 - 2.60514i) q^{11} +(0.961081 + 1.44095i) q^{12} +(5.25730 - 1.70820i) q^{13} +(-1.10045 - 2.40604i) q^{14} +(-0.167445 - 0.979337i) q^{15} +(0.669131 + 0.743145i) q^{16} +(-1.80521 + 0.383709i) q^{17} +(-2.91827 + 0.695496i) q^{18} +(-2.38460 - 5.35590i) q^{19} +(-0.177260 - 0.545550i) q^{20} +(4.56979 - 0.342031i) q^{21} +(2.97498 - 1.46612i) q^{22} +(-6.17919 - 3.56755i) q^{23} +(-1.60928 + 0.640490i) q^{24} +(0.488248 - 4.64537i) q^{25} +(0.577817 + 5.49757i) q^{26} +(0.623580 - 5.15860i) q^{27} +(2.58226 - 0.576157i) q^{28} +(-4.25665 - 5.85878i) q^{29} +(0.992750 + 0.0398300i) q^{30} +(1.57061 + 1.41418i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(0.594229 + 5.71375i) q^{33} -1.84554i q^{34} +(-1.48761 - 0.300553i) q^{35} +(-0.0735559 - 2.99910i) q^{36} +(-0.0798338 - 0.759568i) q^{37} +(5.73465 - 1.21894i) q^{38} +(-9.27796 - 2.36449i) q^{39} +(0.570483 - 0.0599602i) q^{40} +(-1.20627 - 0.876408i) q^{41} +(-0.615557 + 4.54104i) q^{42} +7.77598 q^{43} +(0.815553 + 3.21479i) q^{44} +(-0.661188 + 1.58879i) q^{45} +(4.77432 - 5.30242i) q^{46} +(-0.407668 + 0.181505i) q^{47} +(-0.291906 - 1.70728i) q^{48} +(2.02839 - 6.69967i) q^{49} +(4.44234 + 1.44340i) q^{50} +(2.99807 + 1.10887i) q^{51} +(-5.49757 - 0.577817i) q^{52} +(-2.59005 - 2.33210i) q^{53} +(4.91622 + 1.68249i) q^{54} +(0.322681 - 1.87494i) q^{55} +(0.0266852 + 2.64562i) q^{56} +(-1.46545 + 10.0483i) q^{57} +(6.61576 - 2.94552i) q^{58} +(9.56549 + 4.25883i) q^{59} +(-0.245364 + 0.962775i) q^{60} +(-0.468853 + 0.422157i) q^{61} +(-1.70983 + 1.24226i) q^{62} +(-7.00706 - 3.72841i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(2.74609 + 1.58546i) q^{65} +(-5.71243 - 0.606711i) q^{66} +(2.30807 + 3.99770i) q^{67} +(1.80521 + 0.383709i) q^{68} +(5.74516 + 10.9418i) q^{69} +(0.603277 - 1.39262i) q^{70} +(-7.77727 - 2.52699i) q^{71} +(2.94885 + 0.551599i) q^{72} +(-5.15099 + 11.5693i) q^{73} +(0.759568 + 0.0798338i) q^{74} +(-5.01394 + 6.34932i) q^{75} +5.86276i q^{76} +(8.46850 + 2.29880i) q^{77} +(4.24182 - 8.58360i) q^{78} +(-10.3411 - 2.19806i) q^{79} +(-0.0599602 + 0.570483i) q^{80} +(-5.68706 + 6.97548i) q^{81} +(1.10805 - 0.997697i) q^{82} +(-1.54533 + 4.75602i) q^{83} +(-4.31383 - 1.54624i) q^{84} +(-0.856463 - 0.622257i) q^{85} +(-1.61672 + 7.60606i) q^{86} +(0.809986 + 12.5171i) q^{87} +(-3.31410 + 0.129338i) q^{88} +(6.63333 - 11.4893i) q^{89} +(-1.41660 - 0.977067i) q^{90} +(-8.47676 + 11.9182i) q^{91} +(4.19391 + 5.77243i) q^{92} +(-0.990718 - 3.52401i) q^{93} +(-0.0927802 - 0.436497i) q^{94} +(1.36787 - 3.07228i) q^{95} +(1.73066 + 0.0694355i) q^{96} +(3.18905 - 1.03619i) q^{97} +(6.13154 + 3.37701i) q^{98} +(4.41786 - 8.91530i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 256 q - 32 q^{4} + 4 q^{7} - 12 q^{9}+O(q^{10}) \) 256 * q - 32 * q^4 + 4 * q^7 - 12 * q^9	\( 256 q - 32 q^{4} + 4 q^{7} - 12 q^{9} + 12 q^{10} + 24 q^{15} + 32 q^{16} - 8 q^{18} - 16 q^{21} - 12 q^{22} + 48 q^{25} + 6 q^{28} + 18 q^{31} - 132 q^{33} + 16 q^{36} + 4 q^{37} - 18 q^{40} - 4 q^{42} + 64 q^{43} - 48 q^{45} + 8 q^{46} + 76 q^{49} - 8 q^{51} - 88 q^{57} + 46 q^{58} - 8 q^{60} - 12 q^{63} + 64 q^{64} - 120 q^{66} - 32 q^{67} - 58 q^{70} - 12 q^{72} - 96 q^{73} - 204 q^{75} - 32 q^{78} - 4 q^{79} - 64 q^{81} + 24 q^{82} - 36 q^{84} + 232 q^{85} - 228 q^{87} - 6 q^{88} + 40 q^{91} - 2 q^{93} - 144 q^{94} + 160 q^{99}+O(q^{100}) \) 256 * q - 32 * q^4 + 4 * q^7 - 12 * q^9 + 12 * q^10 + 24 * q^15 + 32 * q^16 - 8 * q^18 - 16 * q^21 - 12 * q^22 + 48 * q^25 + 6 * q^28 + 18 * q^31 - 132 * q^33 + 16 * q^36 + 4 * q^37 - 18 * q^40 - 4 * q^42 + 64 * q^43 - 48 * q^45 + 8 * q^46 + 76 * q^49 - 8 * q^51 - 88 * q^57 + 46 * q^58 - 8 * q^60 - 12 * q^63 + 64 * q^64 - 120 * q^66 - 32 * q^67 - 58 * q^70 - 12 * q^72 - 96 * q^73 - 204 * q^75 - 32 * q^78 - 4 * q^79 - 64 * q^81 + 24 * q^82 - 36 * q^84 + 232 * q^85 - 228 * q^87 - 6 * q^88 + 40 * q^91 - 2 * q^93 - 144 * q^94 + 160 * q^99

Introduction

L-functions

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