LMFDB - Embedded newform 462.2.bf.a.5.14

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			5.14
Character	$\chi$	$=$	462.5
Dual form			462.2.bf.a.185.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.207912 + 0.978148i) q^{2} +(1.38379 + 1.04170i) q^{3} +(-0.913545 - 0.406737i) q^{4} +(1.51673 + 1.68449i) q^{5} +(-1.30664 + 1.13697i) q^{6} +(-2.61122 - 0.426069i) q^{7} +(0.587785 - 0.809017i) q^{8} +(0.829732 + 2.88298i) q^{9} +O(q^{10})$	\(q+(-0.207912 + 0.978148i) q^{2} +(1.38379 + 1.04170i) q^{3} +(-0.913545 - 0.406737i) q^{4} +(1.51673 + 1.68449i) q^{5} +(-1.30664 + 1.13697i) q^{6} +(-2.61122 - 0.426069i) q^{7} +(0.587785 - 0.809017i) q^{8} +(0.829732 + 2.88298i) q^{9} +(-1.96303 + 1.13336i) q^{10} +(-2.47299 + 2.21005i) q^{11} +(-0.840455 - 1.51448i) q^{12} +(-1.89961 + 0.617221i) q^{13} +(0.959661 - 2.46557i) q^{14} +(0.344091 + 3.91095i) q^{15} +(0.669131 + 0.743145i) q^{16} +(0.643670 - 0.136816i) q^{17} +(-2.99249 + 0.212196i) q^{18} +(0.628277 + 1.41113i) q^{19} +(-0.700452 - 2.15577i) q^{20} +(-3.16954 - 3.30969i) q^{21} +(-1.64759 - 2.87844i) q^{22} +(7.10475 + 4.10193i) q^{23} +(1.65612 - 0.507212i) q^{24} +(-0.0144229 + 0.137225i) q^{25} +(-0.208782 - 1.98643i) q^{26} +(-1.85502 + 4.85375i) q^{27} +(2.21217 + 1.45131i) q^{28} +(-1.91935 - 2.64176i) q^{29} +(-3.89703 - 0.476561i) q^{30} +(4.83325 + 4.35187i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-5.72429 + 0.482128i) q^{33} +0.658050i q^{34} +(-3.24279 - 5.04482i) q^{35} +(0.414614 - 2.97121i) q^{36} +(-1.00410 - 9.55336i) q^{37} +(-1.51092 + 0.321157i) q^{38} +(-3.27161 - 1.12472i) q^{39} +(2.25429 - 0.236936i) q^{40} +(-1.18003 - 0.857341i) q^{41} +(3.89635 - 2.41215i) q^{42} +9.77126 q^{43} +(3.15810 - 1.01312i) q^{44} +(-3.59788 + 5.77036i) q^{45} +(-5.48945 + 6.09665i) q^{46} +(-4.65990 + 2.07472i) q^{47} +(0.151802 + 1.72539i) q^{48} +(6.63693 + 2.22512i) q^{49} +(-0.131228 - 0.0426385i) q^{50} +(1.03322 + 0.481185i) q^{51} +(1.98643 + 0.208782i) q^{52} +(-2.77125 - 2.49524i) q^{53} +(-4.36201 - 2.82363i) q^{54} +(-7.47367 - 0.813701i) q^{55} +(-1.87953 + 1.86208i) q^{56} +(-0.600573 + 2.60718i) q^{57} +(2.98309 - 1.32816i) q^{58} +(-0.979044 - 0.435898i) q^{59} +(1.27638 - 3.71279i) q^{60} +(8.50123 - 7.65455i) q^{61} +(-5.26166 + 3.82282i) q^{62} +(-0.938265 - 7.88160i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(-3.92089 - 2.26373i) q^{65} +(0.718556 - 5.69945i) q^{66} +(0.627993 + 1.08772i) q^{67} +(-0.643670 - 0.136816i) q^{68} +(5.55848 + 13.0772i) q^{69} +(5.60879 - 2.12305i) q^{70} +(0.0302076 + 0.00981506i) q^{71} +(2.82008 + 1.02330i) q^{72} +(-2.97668 + 6.68574i) q^{73} +(9.55336 + 1.00410i) q^{74} +(-0.162905 + 0.174866i) q^{75} -1.54468i q^{76} +(7.39915 - 4.71726i) q^{77} +(1.78035 - 2.96628i) q^{78} +(-7.19247 - 1.52881i) q^{79} +(-0.236936 + 2.25429i) q^{80} +(-7.62309 + 4.78419i) q^{81} +(1.08395 - 0.975991i) q^{82} +(-1.74239 + 5.36253i) q^{83} +(1.54934 + 4.31272i) q^{84} +(1.20674 + 0.876746i) q^{85} +(-2.03156 + 9.55773i) q^{86} +(0.0959430 - 5.65502i) q^{87} +(0.334380 + 3.29973i) q^{88} +(8.15885 - 14.1315i) q^{89} +(-4.89622 - 4.71898i) q^{90} +(5.22328 - 0.802334i) q^{91} +(-4.82210 - 6.63706i) q^{92} +(2.15484 + 11.0568i) q^{93} +(-1.06054 - 4.98943i) q^{94} +(-1.42412 + 3.19863i) q^{95} +(-1.71924 - 0.210243i) q^{96} +(7.62438 - 2.47731i) q^{97} +(-3.55639 + 6.02927i) q^{98} +(-8.42343 - 5.29582i) 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
$3$	1.38379	+	1.04170i	0.798930	+	0.601424i
$3$	1.38379	+	1.04170i	0.798930	+	0.601424i
$4$	−0.913545	−	0.406737i	−0.456773	−	0.203368i
$5$	1.51673	+	1.68449i	0.678301	+	0.753329i	0.979766	−	0.200148i	$-0.0641424\pi$
$5$	1.51673	+	1.68449i	0.678301	+	0.753329i	−0.301465	+	0.953477i	$0.597476\pi$
$6$	−1.30664	+	1.13697i	−0.533433	+	0.464165i
$7$	−2.61122	−	0.426069i	−0.986948	−	0.161039i
$7$	−2.61122	−	0.426069i	−0.986948	−	0.161039i
$8$	0.587785	−	0.809017i	0.207813	−	0.286031i
$9$	0.829732	+	2.88298i	0.276577	+	0.960992i
$10$	−1.96303	+	1.13336i	−0.620765	+	0.358399i
$11$	−2.47299	+	2.21005i	−0.745635	+	0.666355i
$11$	−2.47299	+	2.21005i	−0.745635	+	0.666355i
$12$	−0.840455	−	1.51448i	−0.242619	−	0.437191i
$13$	−1.89961	+	0.617221i	−0.526857	+	0.171186i	−0.560355	−	0.828253i	$-0.689335\pi$
$13$	−1.89961	+	0.617221i	−0.526857	+	0.171186i	0.0334979	+	0.999439i	$0.489335\pi$
$14$	0.959661	−	2.46557i	0.256480	−	0.658952i
$15$	0.344091	+	3.91095i	0.0888439	+	1.00980i
$16$	0.669131	+	0.743145i	0.167283	+	0.185786i
$17$	0.643670	−	0.136816i	0.156113	−	0.0331828i	−0.129192	−	0.991620i	$-0.541238\pi$
$17$	0.643670	−	0.136816i	0.156113	−	0.0331828i	0.285305	+	0.958437i	$0.407905\pi$
$18$	−2.99249	+	0.212196i	−0.705336	+	0.0500150i
$19$	0.628277	+	1.41113i	0.144137	+	0.323736i	0.971159	−	0.238433i	$-0.0766337\pi$
$19$	0.628277	+	1.41113i	0.144137	+	0.323736i	−0.827022	+	0.562169i	$0.809967\pi$
$20$	−0.700452	−	2.15577i	−0.156626	−	0.482045i
$21$	−3.16954	−	3.30969i	−0.691649	−	0.722233i
$22$	−1.64759	−	2.87844i	−0.351267	−	0.613687i
$23$	7.10475	+	4.10193i	1.48144	+	0.855311i	0.999779	−	0.0210455i	$-0.00669948\pi$
$23$	7.10475	+	4.10193i	1.48144	+	0.855311i	0.481663	+	0.876356i	$0.340033\pi$
$24$	1.65612	−	0.507212i	0.338054	−	0.103534i
$25$	−0.0144229	+	0.137225i	−0.00288459	+	0.0274450i
$26$	−0.208782	−	1.98643i	−0.0409455	−	0.389570i
$27$	−1.85502	+	4.85375i	−0.356998	+	0.934105i
$28$	2.21217	+	1.45131i	0.418061	+	0.274272i
$29$	−1.91935	−	2.64176i	−0.356415	−	0.490563i	0.592731	−	0.805401i	$-0.298050\pi$
$29$	−1.91935	−	2.64176i	−0.356415	−	0.490563i	−0.949145	+	0.314838i	$0.898050\pi$
$30$	−3.89703	−	0.476561i	−0.711497	−	0.0870077i
$31$	4.83325	+	4.35187i	0.868077	+	0.781620i	0.977180	−	0.212411i	$-0.0681315\pi$
$31$	4.83325	+	4.35187i	0.868077	+	0.781620i	−0.109104	+	0.994030i	$0.534798\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	−5.72429	+	0.482128i	−0.996472	+	0.0839277i
$34$			0.658050i			0.112855i
$35$	−3.24279	−	5.04482i	−0.548132	−	0.852729i
$36$	0.414614	−	2.97121i	0.0691023	−	0.495202i
$37$	−1.00410	−	9.55336i	−0.165073	−	1.57056i	−0.692788	−	0.721141i	$-0.743618\pi$
$37$	−1.00410	−	9.55336i	−0.165073	−	1.57056i	0.527716	−	0.849421i	$-0.323049\pi$
$38$	−1.51092	+	0.321157i	−0.245104	+	0.0520985i
$39$	−3.27161	−	1.12472i	−0.523877	−	0.180099i
$40$	2.25429	−	0.236936i	0.356435	−	0.0374629i
$41$	−1.18003	−	0.857341i	−0.184290	−	0.133894i	0.491815	−	0.870699i	$-0.336333\pi$
$41$	−1.18003	−	0.857341i	−0.184290	−	0.133894i	−0.676105	+	0.736805i	$0.736333\pi$
$42$	3.89635	−	2.41215i	0.601220	−	0.372203i
$43$	9.77126			1.49010			0.745052	−	0.667007i	$-0.232425\pi$
$43$	9.77126			1.49010			0.745052	+	0.667007i	$0.232425\pi$
$44$	3.15810	−	1.01312i	0.476101	−	0.152734i
$45$	−3.59788	+	5.77036i	−0.536340	+	0.860195i
$46$	−5.48945	+	6.09665i	−0.809375	+	0.898902i
$47$	−4.65990	+	2.07472i	−0.679716	+	0.302629i	−0.717401	−	0.696661i	$-0.754668\pi$
$47$	−4.65990	+	2.07472i	−0.679716	+	0.302629i	0.0376849	+	0.999290i	$0.488002\pi$
$48$	0.151802	+	1.72539i	0.0219107	+	0.249038i
$49$	6.63693	+	2.22512i	0.948133	+	0.317874i
$50$	−0.131228	−	0.0426385i	−0.0185584	−	0.00602999i
$51$	1.03322	+	0.481185i	0.144680	+	0.0673794i
$52$	1.98643	+	0.208782i	0.275468	+	0.0289528i
$53$	−2.77125	−	2.49524i	−0.380660	−	0.342748i	0.456483	−	0.889732i	$-0.349109\pi$
$53$	−2.77125	−	2.49524i	−0.380660	−	0.342748i	−0.837143	+	0.546984i	$0.815776\pi$
$54$	−4.36201	−	2.82363i	−0.593594	−	0.384248i
$55$	−7.47367	−	0.813701i	−1.00775	−	0.109719i
$56$	−1.87953	+	1.86208i	−0.251163	+	0.248831i
$57$	−0.600573	+	2.60718i	−0.0795479	+	0.345330i
$58$	2.98309	−	1.32816i	0.391699	−	0.174396i
$59$	−0.979044	−	0.435898i	−0.127461	−	0.0567491i	0.342015	−	0.939694i	$-0.388891\pi$
$59$	−0.979044	−	0.435898i	−0.127461	−	0.0567491i	−0.469476	+	0.882945i	$0.655557\pi$
$60$	1.27638	−	3.71279i	0.164781	−	0.479319i
$61$	8.50123	−	7.65455i	1.08847	−	0.980064i	0.0885995	−	0.996067i	$-0.471761\pi$
$61$	8.50123	−	7.65455i	1.08847	−	0.980064i	0.999872	+	0.0160033i	$0.00509422\pi$
$62$	−5.26166	+	3.82282i	−0.668232	+	0.485499i
$63$	−0.938265	−	7.88160i	−0.118210	−	0.992989i
$64$	−0.309017	−	0.951057i	−0.0386271	−	0.118882i
$65$	−3.92089	−	2.26373i	−0.486327	−	0.280781i
$66$	0.718556	−	5.69945i	0.0884481	−	0.701553i
$67$	0.627993	+	1.08772i	0.0767216	+	0.132886i	0.901834	−	0.432083i	$-0.142221\pi$
$67$	0.627993	+	1.08772i	0.0767216	+	0.132886i	−0.825112	+	0.564969i	$0.808888\pi$
$68$	−0.643670	−	0.136816i	−0.0780565	−	0.0165914i
$69$	5.55848	+	13.0772i	0.669163	+	1.57431i
$70$	5.60879	−	2.12305i	0.670378	−	0.253754i
$71$	0.0302076	+	0.00981506i	0.00358499	+	0.00116483i	0.310809	−	0.950472i	$-0.399400\pi$
$71$	0.0302076	+	0.00981506i	0.00358499	+	0.00116483i	−0.307224	+	0.951637i	$0.599400\pi$
$72$	2.82008	+	1.02330i	0.332350	+	0.120597i
$73$	−2.97668	+	6.68574i	−0.348394	+	0.782506i	0.651325	+	0.758799i	$0.274214\pi$
$73$	−2.97668	+	6.68574i	−0.348394	+	0.782506i	−0.999719	+	0.0237071i	$0.992453\pi$
$74$	9.55336	+	1.00410i	1.11055	+	0.116724i
$75$	−0.162905	+	0.174866i	−0.0188107	+	0.0201918i
$76$		−	1.54468i		−	0.177187i
$77$	7.39915	−	4.71726i	0.843212	−	0.537581i
$78$	1.78035	−	2.96628i	0.201585	−	0.335865i
$79$	−7.19247	−	1.52881i	−0.809216	−	0.172004i	−0.215317	−	0.976544i	$-0.569079\pi$
$79$	−7.19247	−	1.52881i	−0.809216	−	0.172004i	−0.593898	+	0.804540i	$0.702412\pi$
$80$	−0.236936	+	2.25429i	−0.0264902	+	0.252038i
$81$	−7.62309	+	4.78419i	−0.847010	+	0.531577i
$82$	1.08395	−	0.975991i	0.119702	−	0.107780i
$83$	−1.74239	+	5.36253i	−0.191252	+	0.588614i	0.808748	+	0.588156i	$0.200146\pi$
$83$	−1.74239	+	5.36253i	−0.191252	+	0.588614i	−1.00000		0.000458022i	$0.999854\pi$
$84$	1.54934	+	4.31272i	0.169047	+	0.470556i
$85$	1.20674	+	0.876746i	0.130889	+	0.0950965i
$86$	−2.03156	+	9.55773i	−0.219069	+	1.03064i
$87$	0.0959430	−	5.65502i	0.0102862	−	0.606282i
$88$	0.334380	+	3.29973i	0.0356450	+	0.351752i
$89$	8.15885	−	14.1315i	0.864836	−	1.49794i	−0.00237382	−	0.999997i	$-0.500756\pi$
$89$	8.15885	−	14.1315i	0.864836	−	1.49794i	0.867210	−	0.497943i	$-0.165911\pi$
$90$	−4.89622	−	4.71898i	−0.516107	−	0.497425i
$91$	5.22328	−	0.802334i	0.547548	−	0.0841074i
$92$	−4.82210	−	6.63706i	−0.502739	−	0.691961i
$93$	2.15484	+	11.0568i	0.223447	+	1.14654i
$94$	−1.06054	−	4.98943i	−0.109386	−	0.514620i
$95$	−1.42412	+	3.19863i	−0.146112	+	0.328173i
$96$	−1.71924	−	0.210243i	−0.175470	−	0.0214579i
$97$	7.62438	−	2.47731i	0.774138	−	0.251533i	0.104803	−	0.994493i	$-0.466579\pi$
$97$	7.62438	−	2.47731i	0.774138	−	0.251533i	0.669336	+	0.742960i	$0.266579\pi$
$98$	−3.55639	+	6.02927i	−0.359250	+	0.609048i
$99$	−8.42343	−	5.29582i	−0.846587	−	0.532250i
$100$	0.0689905	−	0.119495i	0.00689905	−	0.0119495i
$101$	6.03098	−	6.69808i	0.600105	−	0.666484i	−0.364187	−	0.931326i	$-0.618653\pi$
$101$	6.03098	−	6.69808i	0.600105	−	0.666484i	0.964292	+	0.264842i	$0.0853198\pi$
$102$	−0.685489	+	0.910601i	−0.0678736	+	0.0901629i
$103$	8.17823	−	0.859566i	0.805825	−	0.0846956i	0.307346	−	0.951598i	$-0.400559\pi$
$103$	8.17823	−	0.859566i	0.805825	−	0.0846956i	0.498478	+	0.866902i	$0.333892\pi$
$104$	−0.617221	+	1.89961i	−0.0605235	+	0.186272i
$105$	0.767838	−	10.3590i	0.0749334	−	1.01093i
$106$	3.01689	−	2.19190i	0.293026	−	0.212896i
$107$	0.250901	+	0.563534i	0.0242556	+	0.0544789i	0.925267	−	0.379316i	$-0.123841\pi$
$107$	0.250901	+	0.563534i	0.0242556	+	0.0544789i	−0.901011	+	0.433795i	$0.857174\pi$
$108$	3.66884	−	3.67962i	0.353034	−	0.354072i
$109$	8.08676	+	14.0067i	0.774571	+	1.34160i	0.935035	+	0.354554i	$0.115367\pi$
$109$	8.08676	+	14.0067i	0.774571	+	1.34160i	−0.160465	+	0.987042i	$0.551299\pi$
$110$	2.34978	−	7.14117i	0.224043	−	0.680884i
$111$	8.56225	−	14.2658i	0.812693	−	1.35405i
$112$	−1.43062	−	2.22561i	−0.135180	−	0.210300i
$113$	−1.34470	+	1.85082i	−0.126499	+	0.174111i	−0.867569	−	0.497317i	$-0.834319\pi$
$113$	−1.34470	+	1.85082i	−0.126499	+	0.174111i	0.741070	+	0.671428i	$0.234319\pi$
$114$	−2.42534	−	1.12951i	−0.227154	−	0.105789i
$115$	3.86628	+	18.1894i	0.360532	+	1.69617i
$116$	0.678914	+	3.19404i	0.0630356	+	0.296559i
$117$	−3.35560	−	4.96440i	−0.310225	−	0.458959i
$118$	0.629928	−	0.867021i	0.0579895	−	0.0798158i
$119$	−1.73906	+	0.0830095i	−0.159419	+	0.00760947i
$120$	3.36628	+	2.02042i	0.307298	+	0.184439i
$121$	1.23137	−	10.9309i	0.111942	−	0.993715i
$122$	5.71977	+	9.90693i	0.517844	+	0.896931i
$123$	−0.739818	−	2.41561i	−0.0667071	−	0.217808i
$124$	−2.64532	−	5.94149i	−0.237557	−	0.533562i
$125$	8.91601	−	6.47786i	0.797472	−	0.579397i
$126$	7.90445	+	0.720916i	0.704184	+	0.0642243i
$127$	5.71627	−	17.5929i	0.507237	−	1.56112i	−0.289740	−	0.957105i	$-0.593569\pi$
$127$	5.71627	−	17.5929i	0.507237	−	1.56112i	0.796977	−	0.604010i	$-0.206431\pi$
$128$	0.994522	−	0.104528i	0.0879041	−	0.00923910i
$129$	13.5213	+	10.1787i	1.19049	+	0.896184i
$130$	3.02946	−	3.36456i	0.265701	−	0.295091i
$131$	−3.67379	+	6.36319i	−0.320980	+	0.555954i	−0.980691	−	0.195566i	$-0.937346\pi$
$131$	−3.67379	+	6.36319i	−0.320980	+	0.555954i	0.659710	+	0.751520i	$0.270679\pi$
$132$	5.42550	+	1.88783i	0.472229	+	0.164315i
$133$	−1.03933	−	3.95247i	−0.0901213	−	0.342723i
$134$	−1.19451	+	0.388121i	−0.103190	+	0.0335286i
$135$	−10.9897	+	4.23705i	−0.945841	+	0.364667i
$136$	0.267653	−	0.601159i	0.0229511	−	0.0515489i
$137$	3.45121	+	16.2367i	0.294857	+	1.38719i	0.837137	+	0.546994i	$0.184228\pi$
$137$	3.45121	+	16.2367i	0.294857	+	1.38719i	−0.542280	+	0.840198i	$0.682439\pi$
$138$	−13.9471	+	2.71812i	−1.18726	+	0.231382i
$139$	11.7444	+	16.1647i	0.996145	+	1.37108i	0.927661	+	0.373423i	$0.121816\pi$
$139$	11.7444	+	16.1647i	0.996145	+	1.37108i	0.0684836	+	0.997652i	$0.478184\pi$
$140$	0.910528	+	5.92763i	0.0769536	+	0.500976i
$141$	−8.60954	−	1.98323i	−0.725054	−	0.167018i
$142$	−0.0158811	+	0.0275069i	−0.00133271	+	0.00230832i
$143$	3.33363	−	5.72461i	0.278772	−	0.478716i
$144$	−1.58727	+	2.54570i	−0.132272	+	0.212141i
$145$	1.53890	−	7.23997i	0.127799	−	0.601247i
$146$	−5.92075	−	4.30168i	−0.490005	−	0.356009i
$147$	6.86620	+	9.99277i	0.566314	+	0.824189i
$148$	−2.96841	+	9.13583i	−0.244002	+	0.750960i
$149$	−2.52468	+	2.27323i	−0.206830	+	0.186230i	−0.766035	−	0.642799i	$-0.777773\pi$
$149$	−2.52468	+	2.27323i	−0.206830	+	0.186230i	0.559205	+	0.829029i	$0.311106\pi$
$150$	−0.137175	−	0.195702i	−0.0112003	−	0.0159790i
$151$	−0.0693433	+	0.659757i	−0.00564308	+	0.0536903i	−0.996981	−	0.0776452i	$-0.975260\pi$
$151$	−0.0693433	+	0.659757i	−0.00564308	+	0.0536903i	0.991338	+	0.131336i	$0.0419265\pi$
$152$	1.51092	+	0.321157i	0.122552	+	0.0260493i
$153$	0.928511	+	1.74216i	0.0750657	+	0.140846i
$154$	3.07580	+	8.21824i	0.247855	+	0.662244i
$155$			14.7422i			1.18412i
$156$	2.53130	+	2.35817i	0.202666	+	0.188804i
$157$	1.29440	+	0.136047i	0.103305	+	0.0108578i	0.156040	−	0.987751i	$-0.450127\pi$
$157$	1.29440	+	0.136047i	0.103305	+	0.0108578i	−0.0527351	+	0.998609i	$0.516794\pi$
$158$	2.99080	−	6.71744i	0.237935	−	0.534411i
$159$	−1.23553	−	6.33969i	−0.0979837	−	0.502770i
$160$	−2.15577	−	0.700452i	−0.170429	−	0.0553756i
$161$	−16.8043	−	13.7381i	−1.32437	−	1.08272i
$162$	−3.09472	−	8.45120i	−0.243144	−	0.663989i
$163$	−9.76113	−	2.07479i	−0.764551	−	0.162510i	−0.190899	−	0.981610i	$-0.561140\pi$
$163$	−9.76113	−	2.07479i	−0.764551	−	0.162510i	−0.573652	+	0.819099i	$0.694474\pi$
$164$	0.729298	+	1.26318i	0.0569486	+	0.0986379i
$165$	−9.49433	−	8.91129i	−0.739133	−	0.693743i
$166$	−4.88308	−	2.81925i	−0.379000	−	0.218816i
$167$	−7.30133	−	22.4712i	−0.564994	−	1.73887i	−0.667970	−	0.744188i	$-0.732837\pi$
$167$	−7.30133	−	22.4712i	−0.564994	−	1.73887i	0.102977	−	0.994684i	$-0.467163\pi$
$168$	−4.54060	+	0.618821i	−0.350315	+	0.0477431i
$169$	−7.28966	+	5.29625i	−0.560743	+	0.407404i
$170$	−1.10848	+	0.998082i	−0.0850167	+	0.0765494i
$171$	−3.54696	+	2.98217i	−0.271243	+	0.228052i
$172$	−8.92649	−	3.97433i	−0.680638	−	0.303040i
$173$	20.3454	−	9.05834i	1.54683	−	0.688693i	0.556943	−	0.830551i	$-0.311974\pi$
$173$	20.3454	−	9.05834i	1.54683	−	0.688693i	0.989887	+	0.141858i	$0.0453077\pi$
$174$	5.51150	+	1.26959i	0.417826	+	0.0962475i
$175$	0.0961288	−	0.352180i	0.00726665	−	0.0266223i
$176$	−3.29714	−	0.358979i	−0.248531	−	0.0270590i
$177$	−0.900714	−	1.62306i	−0.0677018	−	0.121997i
$178$	12.1264	+	10.9187i	0.908913	+	0.818389i
$179$	−0.977835	−	0.102775i	−0.0730868	−	0.00768173i	0.0679145	−	0.997691i	$-0.478365\pi$
$179$	−0.977835	−	0.102775i	−0.0730868	−	0.00768173i	−0.141001	+	0.990009i	$0.545032\pi$
$180$	5.63385	−	3.80810i	0.419922	−	0.283839i
$181$	−17.5136	−	5.69051i	−1.30177	−	0.422972i	−0.425576	−	0.904923i	$-0.639929\pi$
$181$	−17.5136	−	5.69051i	−1.30177	−	0.422972i	−0.876199	+	0.481950i	$0.839929\pi$
$182$	−0.301179	+	5.27595i	−0.0223249	+	0.391079i
$183$	19.7376	−	1.73654i	1.45905	−	0.128369i
$184$	7.49459	−	3.33681i	0.552509	−	0.245993i
$185$	14.5696	−	16.1812i	1.07118	−	1.18967i
$186$	−11.2632	−	0.191092i	−0.825861	−	0.0140116i
$187$	−1.28942	+	1.76089i	−0.0942917	+	0.128769i
$188$	5.10089			0.372021
$189$	6.91189	−	11.8838i	0.502766	−	0.864423i
$190$	−2.83264	−	2.05804i	−0.205502	−	0.149306i
$191$	−22.4969	+	2.36452i	−1.62782	+	0.171090i	−0.873977	−	0.485968i	$-0.838467\pi$
$191$	−22.4969	+	2.36452i	−1.62782	+	0.171090i	−0.753840	+	0.657058i	$0.771801\pi$
$192$	0.563100	−	1.63796i	0.0406382	−	0.118210i
$193$	−23.8147	+	5.06197i	−1.71422	+	0.364368i	−0.957290	−	0.289130i	$-0.906634\pi$
$193$	−23.8147	+	5.06197i	−1.71422	+	0.364368i	−0.756928	+	0.653498i	$0.773301\pi$
$194$	0.837978	+	7.97283i	0.0601633	+	0.572416i
$195$	−3.06756	−	7.21690i	−0.219672	−	0.516813i
$196$	−5.15810	−	4.73223i	−0.368436	−	0.338016i
$197$		−	10.9108i		−	0.777361i	−0.921373	−	0.388680i	$-0.872931\pi$
$197$		−	10.9108i		−	0.777361i	0.921373	−	0.388680i	$-0.127069\pi$
$198$	6.93143	−	7.13830i	0.492595	−	0.507297i
$199$	−13.7111	+	7.91610i	−0.971954	+	0.561158i	−0.899831	−	0.436238i	$-0.856311\pi$
$199$	−13.7111	+	7.91610i	−0.971954	+	0.561158i	−0.0721223	+	0.997396i	$0.522977\pi$
$200$	0.102540	+	0.0923273i	0.00725066	+	0.00652852i
$201$	−0.264063	+	2.15935i	−0.0186256	+	0.152309i
$202$	5.29780	+	7.29180i	0.372752	+	0.513049i
$203$	3.88628	+	7.71600i	0.272763	+	0.541557i
$204$	−0.748181	−	0.859834i	−0.0523831	−	0.0602004i
$205$	−0.345594	−	3.28810i	−0.0241373	−	0.229651i
$206$	−0.859566	+	8.17823i	−0.0598888	+	0.569804i
$207$	−5.93072	+	23.8863i	−0.412214	+	1.66021i
$208$	−1.72977	−	0.998684i	−0.119938	−	0.0692463i
$209$	−4.67240	−	2.10120i	−0.323197	−	0.145343i
$210$	9.97295	+	2.90481i	0.688199	+	0.200451i
$211$	−3.27478	−	10.0787i	−0.225445	−	0.693849i	−0.998246	−	0.0592005i	$-0.981145\pi$
$211$	−3.27478	−	10.0787i	−0.225445	−	0.693849i	0.772801	−	0.634649i	$-0.218855\pi$
$212$	1.51675	+	3.40669i	0.104171	+	0.233972i
$213$	0.0315766	+	0.0450492i	0.00216359	+	0.00308672i
$214$	−0.603385	+	0.128253i	−0.0412465	+	0.00876722i
$215$	14.8203	+	16.4596i	1.01074	+	1.12254i
$216$	2.83642	+	4.35370i	0.192994	+	0.296232i
$217$	−10.7665	−	13.4230i	−0.730875	−	0.911212i
$218$	−15.3819	+	4.99789i	−1.04180	+	0.338500i
$219$	−11.0836	+	6.15083i	−0.748961	+	0.415635i
$220$	6.49657	+	3.78317i	0.437999	+	0.255061i
$221$	−1.13828	+	0.657184i	−0.0765688	+	0.0442070i
$222$	12.1738	+	11.3412i	0.817055	+	0.761169i
$223$	15.4910	−	21.3216i	1.03736	−	1.42780i	0.138077	−	0.990421i	$-0.455908\pi$
$223$	15.4910	−	21.3216i	1.03736	−	1.42780i	0.899279	−	0.437376i	$-0.144092\pi$
$224$	2.47442	−	0.936623i	0.165329	−	0.0625808i
$225$	−0.407584	+	0.0722790i	−0.0271722	+	0.00481860i
$226$	−1.53080	−	1.70012i	−0.101827	−	0.113091i
$227$	4.23589	+	1.88594i	0.281146	+	0.125174i	0.542465	−	0.840078i	$-0.317491\pi$
$227$	4.23589	+	1.88594i	0.281146	+	0.125174i	−0.261320	+	0.965252i	$0.584158\pi$
$228$	1.60909	−	2.13751i	0.106564	−	0.141560i
$229$	−3.87202	+	18.2164i	−0.255870	+	1.20377i	0.643106	+	0.765777i	$0.277645\pi$
$229$	−3.87202	+	18.2164i	−0.255870	+	1.20377i	−0.898976	+	0.437998i	$0.855688\pi$
$230$	−18.5958			−1.22617
$231$	15.1528	+	1.18000i	0.996982	+	0.0776385i
$232$	−3.26540			−0.214384
$233$	3.20737	−	15.0895i	0.210122	−	0.988544i	−0.739017	−	0.673686i	$-0.764710\pi$
$233$	3.20737	−	15.0895i	0.210122	−	0.988544i	0.949139	−	0.314858i	$-0.101957\pi$
$234$	5.55359	−	2.25011i	0.363049	−	0.147095i
$235$	−10.5626	−	4.70279i	−0.689031	−	0.306776i
$236$	0.717105	+	0.796426i	0.0466796	+	0.0518429i
$237$	−8.36029	−	9.60792i	−0.543059	−	0.624101i
$238$	0.280375	−	1.71831i	0.0181740	−	0.111382i
$239$	−13.0381	+	17.9453i	−0.843361	+	1.16079i	0.141925	+	0.989877i	$0.454671\pi$
$239$	−13.0381	+	17.9453i	−0.843361	+	1.16079i	−0.985287	+	0.170910i	$0.945329\pi$
$240$	−2.67616	+	2.87265i	−0.172746	+	0.185429i
$241$	−19.2963	+	11.1408i	−1.24299	+	0.717639i	−0.969701	−	0.244294i	$-0.921444\pi$
$241$	−19.2963	+	11.1408i	−1.24299	+	0.717639i	−0.273286	+	0.961933i	$0.588111\pi$
$242$	10.4360	+	3.47711i	0.670850	+	0.223517i
$243$	−15.5324	−	1.32066i	−0.996405	−	0.0847201i
$244$	−10.8796	+	3.53501i	−0.696498	+	0.226306i
$245$	6.31820	+	14.5548i	0.403655	+	0.929870i
$246$	2.51664	−	0.221417i	0.160455	−	0.0141171i
$247$	−2.06446	−	2.29282i	−0.131359	−	0.145889i
$248$	6.36165	−	1.35221i	0.403965	−	0.0858655i
$249$	−7.99723	+	5.60555i	−0.506804	+	0.355237i
$250$	4.48256	+	10.0680i	0.283502	+	0.636756i
$251$	3.44299	+	10.5964i	0.217320	+	0.668841i	0.998981	+	0.0451375i	$0.0143726\pi$
$251$	3.44299	+	10.5964i	0.217320	+	0.668841i	−0.781661	+	0.623703i	$0.785627\pi$
$252$	−2.34859	+	7.58183i	−0.147947	+	0.477610i
$253$	−26.6354	+	5.55781i	−1.67456	+	0.349416i
$254$	16.0199	+	9.24912i	1.00518	+	0.580341i
$255$	0.756563	+	2.47029i	0.0473778	+	0.154695i
$256$	−0.104528	+	0.994522i	−0.00653303	+	0.0621576i
$257$	1.06058	+	10.0907i	0.0661570	+	0.629442i	0.976490	+	0.215565i	$0.0691592\pi$
$257$	1.06058	+	10.0907i	0.0661570	+	0.629442i	−0.910333	+	0.413878i	$0.864174\pi$
$258$	−12.7675	+	11.1096i	−0.794871	+	0.691653i
$259$	−1.44847	+	25.3737i	−0.0900034	+	1.57665i
$260$	2.66117	+	3.66279i	0.165039	+	0.227157i
$261$	6.02359	−	7.72540i	0.372851	−	0.478190i
$262$	−5.46031	−	4.91649i	−0.337339	−	0.303742i
$263$	−12.1987	+	7.04290i	−0.752201	+	0.434284i	−0.826489	−	0.562953i	$-0.809665\pi$
$263$	−12.1987	+	7.04290i	−0.752201	+	0.434284i	0.0742874	+	0.997237i	$0.476332\pi$
$264$	−2.97461	+	4.91444i	−0.183074	+	0.302463i
$265$		−	8.45276i		−	0.519249i
$266$	4.08219	−	0.194853i	0.250295	−	0.0119472i
$267$	26.0109	−	11.0560i	1.59184	−	0.676615i
$268$	−0.131286	−	1.24911i	−0.00801959	−	0.0763013i
$269$	−7.35078	+	1.56246i	−0.448185	+	0.0952647i	−0.426474	−	0.904500i	$-0.640245\pi$
$269$	−7.35078	+	1.56246i	−0.448185	+	0.0952647i	−0.0217106	+	0.999764i	$0.506911\pi$
$270$	−1.85957	−	11.6305i	−0.113170	−	0.707807i
$271$	−7.37384	+	0.775022i	−0.447929	+	0.0470792i	−0.325808	−	0.945436i	$-0.605636\pi$
$271$	−7.37384	+	0.775022i	−0.447929	+	0.0470792i	−0.122121	+	0.992515i	$0.538970\pi$
$272$	0.532374	+	0.386792i	0.0322799	+	0.0234527i
$273$	8.06369	+	4.33082i	0.488037	+	0.262113i
$274$	−16.5994			−1.00281
$275$	−0.267606	−	0.371232i	−0.0161373	−	0.0223861i
$276$	0.241043	−	14.2074i	0.0145091	−	0.855188i
$277$	1.69519	−	1.88270i	0.101854	−	0.113120i	−0.690062	−	0.723750i	$-0.742417\pi$
$277$	1.69519	−	1.88270i	0.101854	−	0.113120i	0.791916	+	0.610630i	$0.209084\pi$
$278$	−18.2533	+	8.12689i	−1.09476	+	0.487419i
$279$	−8.53605	+	17.5450i	−0.511040	+	1.05039i
$280$	−5.98741	−	0.341793i	−0.357816	−	0.0204261i
$281$	−14.8499	−	4.82503i	−0.885872	−	0.287837i	−0.169478	−	0.985534i	$-0.554208\pi$
$281$	−14.8499	−	4.82503i	−0.885872	−	0.287837i	−0.716393	+	0.697697i	$0.754208\pi$
$282$	3.72992	−	8.00906i	0.222113	−	0.476932i
$283$	15.1566	+	1.59303i	0.900969	+	0.0946957i	0.543675	−	0.839296i	$-0.317033\pi$
$283$	15.1566	+	1.59303i	0.900969	+	0.0946957i	0.357295	+	0.933992i	$0.383699\pi$
$284$	−0.0236039	−	0.0212531i	−0.00140063	−	0.00126114i
$285$	−5.30269	+	2.94272i	−0.314104	+	0.174312i
$286$	4.90642	+	4.45100i	0.290122	+	0.263193i
$287$	2.71603	+	2.74148i	0.160322	+	0.161824i
$288$	−2.16006	−	2.08186i	−0.127283	−	0.122675i
$289$	−15.1347	+	6.73839i	−0.890275	+	0.396376i
$290$	6.76180	+	3.01055i	0.397067	+	0.176786i
$291$	13.1311	+	4.51423i	0.769760	+	0.264629i
$292$	5.43867	−	4.89700i	0.318274	−	0.286575i
$293$	14.9312	−	10.8482i	0.872293	−	0.633758i	−0.0589083	−	0.998263i	$-0.518762\pi$
$293$	14.9312	−	10.8482i	0.872293	−	0.633758i	0.931201	+	0.364505i	$0.118762\pi$
$294$	−11.2020	+	4.63854i	−0.653312	+	0.270525i
$295$	−0.750673	−	2.31033i	−0.0437059	−	0.134513i
$296$	−8.31902	−	4.80299i	−0.483533	−	0.279168i
$297$	−6.13959	−	16.1030i	−0.356255	−	0.934389i
$298$	−1.69864	−	2.94214i	−0.0983998	−	0.170433i
$299$	−16.0280	−	3.40687i	−0.926926	−	0.197024i
$300$	0.219946	−	0.0934884i	0.0126986	−	0.00539756i
$301$	−25.5149	−	4.16323i	−1.47065	−	0.239965i
$302$	−0.630923	−	0.204999i	−0.0363055	−	0.0117964i
$303$	15.3230	−	2.98626i	0.880281	−	0.171556i
$304$	−0.628277	+	1.41113i	−0.0360342	+	0.0809341i
$305$	25.7881	+	2.71044i	1.47662	+	0.155199i
$306$	−1.89714	+	0.546005i	−0.108452	+	0.0312130i
$307$			20.3454i			1.16117i	0.814199	+	0.580586i	$0.197176\pi$
$307$			20.3454i			1.16117i	−0.814199	+	0.580586i	$0.802824\pi$
$308$	−8.67815	+	1.29992i	−0.494483	+	0.0740700i
$309$	12.2123	+	7.32979i	0.694735	+	0.416977i
$310$	−14.4200	−	3.06507i	−0.819002	−	0.174084i
$311$	0.888474	−	8.45326i	0.0503807	−	0.479341i	−0.940020	−	0.341118i	$-0.889194\pi$
$311$	0.888474	−	8.45326i	0.0503807	−	0.479341i	0.990401	−	0.138223i	$-0.0441389\pi$
$312$	−2.83292	+	1.98570i	−0.160383	+	0.112418i
$313$	17.7692	−	15.9995i	1.00438	−	0.904345i	0.00895865	−	0.999960i	$-0.497148\pi$
$313$	17.7692	−	15.9995i	1.00438	−	0.904345i	0.995418	+	0.0956147i	$0.0304817\pi$
$314$	−0.402196	+	1.23783i	−0.0226972	+	0.0698549i
$315$	11.8534	−	13.5347i	0.667865	−	0.762596i
$316$	5.94882	+	4.32207i	0.334648	+	0.243136i
$317$	5.74363	−	27.0216i	0.322594	−	1.51769i	−0.455898	−	0.890032i	$-0.650682\pi$
$317$	5.74363	−	27.0216i	0.322594	−	1.51769i	0.778492	−	0.627654i	$-0.215985\pi$
$318$	6.45803	+	0.109567i	0.362148	+	0.00614421i
$319$	10.5850	+	2.29119i	0.592644	+	0.128282i
$320$	1.13336	−	1.96303i	0.0633565	−	0.109737i
$321$	−0.239838	+	1.04117i	−0.0133864	+	0.0581127i
$322$	16.9317	−	13.5808i	0.943569	−	0.756829i
$323$	0.597470	+	0.822346i	0.0332441	+	0.0457566i
$324$	8.90995	−	1.26999i	0.494997	−	0.0705548i
$325$	−0.0573002	−	0.269576i	−0.00317844	−	0.0149534i
$326$	4.05891	−	9.11645i	0.224802	−	0.504914i
$327$	−3.40037	+	27.8062i	−0.188041	+	1.53769i
$328$	−1.38721	+	0.450731i	−0.0765957	+	0.0248875i
$329$	13.0520	−	3.43211i	0.719579	−	0.189218i
$330$	10.6905	−	7.43409i	0.588495	−	0.409233i
$331$	9.69153	−	16.7862i	0.532695	−	0.922655i	−0.466576	−	0.884481i	$-0.654513\pi$
$331$	9.69153	−	16.7862i	0.532695	−	0.922655i	0.999271	−	0.0381737i	$-0.0121540\pi$
$332$	3.77289	−	4.19022i	0.207064	−	0.229968i
$333$	26.7090	−	10.8215i	1.46364	−	0.593015i
$334$	23.4982	−	2.46976i	1.28576	−	0.135139i
$335$	−0.879759	+	2.70762i	−0.0480663	+	0.147933i
$336$	0.338746	−	4.57004i	0.0184801	−	0.249316i
$337$	−6.72297	+	4.88452i	−0.366223	+	0.266077i	−0.755643	−	0.654983i	$-0.772676\pi$
$337$	−6.72297	+	4.88452i	−0.366223	+	0.266077i	0.389420	+	0.921060i	$0.372676\pi$
$338$	−3.66491	−	8.23152i	−0.199345	−	0.447736i
$339$	−3.78878	+	1.16037i	−0.205778	+	0.0630227i
$340$	−0.745805	−	1.29177i	−0.0404469	−	0.0700562i
$341$	−21.5704	−	0.0804339i	−1.16810	−	0.00435574i
$342$	−2.17955	−	4.08948i	−0.117856	−	0.221134i
$343$	−16.3824	−	8.63806i	−0.884568	−	0.466412i
$344$	5.74340	−	7.90511i	0.309663	−	0.426215i
$345$	−13.5978	+	29.1978i	−0.732079	+	1.57195i
$346$	4.63035	+	21.7841i	0.248929	+	1.17112i
$347$	−1.95739	−	9.20881i	−0.105078	−	0.494355i	−0.998941	−	0.0460135i	$-0.985348\pi$
$347$	−1.95739	−	9.20881i	−0.105078	−	0.494355i	0.893862	−	0.448341i	$-0.147985\pi$
$348$	−2.38775	+	5.12710i	−0.127997	+	0.274841i
$349$	8.94246	−	12.3082i	0.478679	−	0.658845i	−0.499572	−	0.866273i	$-0.666509\pi$
$349$	8.94246	−	12.3082i	0.478679	−	0.658845i	0.978250	+	0.207428i	$0.0665092\pi$
$350$	0.324497	+	0.167250i	0.0173451	+	0.00893991i
$351$	0.527973	−	10.3652i	0.0281811	−	0.553253i
$352$	1.03665	−	3.15045i	0.0552535	−	0.167920i
$353$	−9.85122	−	17.0628i	−0.524328	−	0.908162i	−0.999599	−	0.0283228i	$-0.990983\pi$
$353$	−9.85122	−	17.0628i	−0.524328	−	0.908162i	0.475271	−	0.879839i	$-0.342350\pi$
$354$	1.77486	−	0.543578i	0.0943327	−	0.0288908i
$355$	0.0292833	+	0.0657714i	0.00155420	+	0.00349078i
$356$	−13.2013	+	9.59130i	−0.699667	+	0.508338i
$357$	−2.49295	−	1.69670i	−0.131941	−	0.0897991i
$358$	0.303832	−	0.935099i	0.0160580	−	0.0494215i
$359$	4.43803	−	0.466456i	0.234230	−	0.0246186i	0.0133140	−	0.999911i	$-0.495762\pi$
$359$	4.43803	−	0.466456i	0.234230	−	0.0246186i	0.220916	+	0.975293i	$0.429095\pi$
$360$	2.55354	+	6.30248i	0.134583	+	0.332170i
$361$	11.1169	−	12.3466i	0.585101	−	0.649820i
$362$	9.20744	−	15.9478i	0.483932	−	0.838195i
$363$	13.0906	−	13.8433i	0.687078	−	0.726583i
$364$	−5.09804	−	1.39153i	−0.267210	−	0.0729360i
$365$	−15.7769	+	5.12623i	−0.825801	+	0.268319i
$366$	−2.40509	+	19.6673i	−0.125716	+	1.02803i
$367$	0.611264	−	1.37292i	0.0319077	−	0.0716659i	−0.896889	−	0.442257i	$-0.854178\pi$
$367$	0.611264	−	1.37292i	0.0319077	−	0.0716659i	0.928796	+	0.370591i	$0.120845\pi$
$368$	1.70568	+	8.02458i	0.0889146	+	0.418310i
$369$	1.49259	−	4.11336i	0.0777009	−	0.214133i
$370$	12.7984	+	17.6155i	0.665358	+	0.915787i
$371$	6.17319	+	7.69637i	0.320496	+	0.399576i
$372$	2.52868	−	10.9774i	0.131106	−	0.569151i
$373$	0.501874	−	0.869272i	0.0259861	−	0.0450092i	−0.852740	−	0.522336i	$-0.825061\pi$
$373$	0.501874	−	0.869272i	0.0259861	−	0.0450092i	0.878726	+	0.477327i	$0.158394\pi$
$374$	−1.45432	−	1.62735i	−0.0752013	−	0.0841484i
$375$	19.0858	+	0.323810i	0.985588	+	0.0167215i
$376$	−1.06054	+	4.98943i	−0.0546929	+	0.257310i
$377$	5.27657	+	3.83365i	0.271757	+	0.197443i
$378$	10.1871	+	9.23164i	0.523968	+	0.474824i
$379$	4.17801	−	12.8586i	0.214610	−	0.660501i	−0.784571	−	0.620039i	$-0.787117\pi$
$379$	4.17801	−	12.8586i	0.214610	−	0.660501i	0.999181	−	0.0404625i	$-0.0128831\pi$
$380$	2.60200	−	2.34285i	0.133480	−	0.120186i
$381$	26.2366	−	18.3902i	1.34414	−	0.942156i
$382$	2.36452	−	22.4969i	0.120979	−	1.15104i
$383$	−3.87658	−	0.823992i	−0.198084	−	0.0421040i	0.107801	−	0.994172i	$-0.465619\pi$
$383$	−3.87658	−	0.823992i	−0.198084	−	0.0421040i	−0.305885	+	0.952068i	$0.598952\pi$
$384$	1.48509	+	0.891346i	0.0757858	+	0.0454863i
$385$	19.1687	+	5.30905i	0.976927	+	0.270574i
$386$		−	24.3467i		−	1.23922i
$387$	8.10752	+	28.1703i	0.412129	+	1.43198i
$388$	−7.97283	−	0.837978i	−0.404759	−	0.0425419i
$389$	5.64494	−	12.6787i	0.286210	−	0.642838i	−0.712030	−	0.702149i	$-0.752224\pi$
$389$	5.64494	−	12.6787i	0.286210	−	0.642838i	0.998240	+	0.0593116i	$0.0188906\pi$
$390$	7.69698	−	1.50005i	0.389752	−	0.0759578i
$391$	5.13432	+	1.66824i	0.259654	+	0.0843667i
$392$	5.70125	−	4.06150i	0.287957	−	0.205137i
$393$	−11.7123	+	4.97832i	−0.590805	+	0.251123i
$394$	10.6723	+	2.26848i	0.537665	+	0.114284i
$395$	−8.33374	−	14.4345i	−0.419316	−	0.726276i
$396$	5.54119	+	8.26409i	0.278455	+	0.415286i
$397$	2.71436	+	1.56714i	0.136230	+	0.0786524i	0.566566	−	0.824016i	$-0.308272\pi$
$397$	2.71436	+	1.56714i	0.136230	+	0.0786524i	−0.430336	+	0.902669i	$0.641605\pi$
$398$	−4.89242	−	15.0573i	−0.245235	−	0.754755i
$399$	2.67907	−	6.55204i	0.134121	−	0.328012i
$400$	−0.111629	+	0.0811032i	−0.00558145	+	0.00405516i
$401$	−26.5329	+	23.8904i	−1.32499	+	1.19303i	−0.359334	+	0.933209i	$0.616996\pi$
$401$	−26.5329	+	23.8904i	−1.32499	+	1.19303i	−0.965657	+	0.259819i	$0.916337\pi$
$402$	−2.05726	−	0.707246i	−0.102607	−	0.0352742i
$403$	−11.8673	−	5.28368i	−0.591155	−	0.263199i
$404$	−8.23393	+	3.66598i	−0.409653	+	0.182389i
$405$	−19.6211	−	5.58475i	−0.974980	−	0.277508i
$406$	−8.35539	+	2.19711i	−0.414671	+	0.109041i
$407$	23.5965	+	21.4063i	1.16964	+	1.06107i
$408$	0.996600	−	0.553062i	0.0493391	−	0.0273806i
$409$	−6.37479	−	5.73989i	−0.315213	−	0.283819i	0.496303	−	0.868150i	$-0.334691\pi$
$409$	−6.37479	−	5.73989i	−0.315213	−	0.283819i	−0.811516	+	0.584330i	$0.801357\pi$
$410$	3.28810	+	0.345594i	0.162388	+	0.0170677i
$411$	−12.1380	+	26.0632i	−0.598721	+	1.28560i
$412$	−7.82080	−	2.54113i	−0.385303	−	0.125193i
$413$	2.37078	+	1.55537i	0.116658	+	0.0765346i
$414$	−22.1313	−	10.7674i	−1.08769	−	0.529187i
$415$	−11.6759	+	5.19844i	−0.573146	+	0.255181i
$416$	1.33650	−	1.48433i	0.0655273	−	0.0727755i
$417$	−0.587068	+	34.6026i	−0.0287489	+	1.69450i
$418$	3.02673	−	4.13343i	0.148042	−	0.202173i
$419$	31.3649			1.53228			0.766138	−	0.642677i	$-0.222176\pi$
$419$	31.3649			1.53228			0.766138	+	0.642677i	$0.222176\pi$
$420$	−4.91482	+	9.15107i	−0.239819	+	0.446527i
$421$	21.7386	+	15.7940i	1.05947	+	0.769753i	0.973991	−	0.226587i	$-0.0727568\pi$
$421$	21.7386	+	15.7940i	1.05947	+	0.769753i	0.0854826	+	0.996340i	$0.472757\pi$
$422$	10.5394	−	1.10773i	0.513048	−	0.0539235i
$423$	−9.84783	−	11.7129i	−0.478818	−	0.569501i
$424$	−3.64759	+	0.775320i	−0.177143	+	0.0376529i
$425$	0.00949102	+	0.0903010i	0.000460382	+	0.00438024i
$426$	−0.0506299	+	0.0215203i	−0.00245303	+	0.00104266i
$427$	−25.4599	+	16.3656i	−1.23209	+	0.791986i
$428$		−	0.616865i		−	0.0298173i
$429$	10.5763	−	4.44901i	0.510631	−	0.214800i
$430$	−19.1813	+	11.0743i	−0.925003	+	0.534051i
$431$	−27.0176	−	24.3268i	−1.30139	−	1.17178i	−0.973913	−	0.226922i	$-0.927134\pi$
$431$	−27.0176	−	24.3268i	−1.30139	−	1.17178i	−0.327481	−	0.944858i	$-0.606200\pi$
$432$	−4.84829	+	1.86925i	−0.233263	+	0.0899342i
$433$	0.0880414	+	0.121179i	0.00423100	+	0.00582347i	0.811127	−	0.584870i	$-0.198854\pi$
$433$	0.0880414	+	0.121179i	0.00423100	+	0.00582347i	−0.806896	+	0.590693i	$0.798854\pi$
$434$	15.3681	−	7.74039i	0.737694	−	0.371551i
$435$	9.67137	−	8.41550i	0.463707	−	0.403492i
$436$	−1.69059	−	16.0849i	−0.0809647	−	0.770328i
$437$	−1.32462	+	12.6029i	−0.0633651	+	0.602878i
$438$	−3.71201	−	12.1202i	−0.177367	−	0.579127i
$439$	15.8549	+	9.15382i	0.756712	+	0.436888i	0.828114	−	0.560560i	$-0.189414\pi$
$439$	15.8549	+	9.15382i	0.756712	+	0.436888i	−0.0714019	+	0.997448i	$0.522747\pi$
$440$	−5.05121	+	5.56804i	−0.240807	+	0.265446i
$441$	−0.908091	+	20.9804i	−0.0432424	+	0.999065i
$442$	−0.406162	−	1.25004i	−0.0193192	−	0.0594583i
$443$	−7.87206	−	17.6809i	−0.374013	−	0.840046i	−0.998268	−	0.0588260i	$-0.981264\pi$
$443$	−7.87206	−	17.6809i	−0.374013	−	0.840046i	0.624256	−	0.781220i	$-0.285402\pi$
$444$	−13.6244	+	9.54985i	−0.646586	+	0.453216i
$445$	36.1792	−	7.69013i	1.71506	−	0.364547i
$446$	17.6349	+	19.5855i	0.835035	+	0.927401i
$447$	−5.86163	+	0.515714i	−0.277246	+	0.0243924i
$448$	0.401695	+	2.61508i	0.0189783	+	0.123551i
$449$	6.09453	−	1.98023i	0.287619	−	0.0934530i	−0.161654	−	0.986847i	$-0.551683\pi$
$449$	6.09453	−	1.98023i	0.287619	−	0.0934530i	0.449273	+	0.893394i	$0.351683\pi$
$450$	0.0140419	−	0.413705i	0.000661940	−	0.0195022i
$451$	4.81297	−	0.487725i	0.226634	−	0.0229661i
$452$	1.98124	−	1.14387i	0.0931898	−	0.0538032i
$453$	−0.783224	+	0.840729i	−0.0367991	+	0.0395009i
$454$	−2.72542	+	3.75122i	−0.127910	+	0.176053i
$455$	9.27381	+	7.58166i	0.434763	+	0.355434i
$456$	1.75625	+	2.01834i	0.0822439	+	0.0945174i
$457$	4.56749	+	5.07271i	0.213658	+	0.237291i	0.840442	−	0.541902i	$-0.182296\pi$
$457$	4.56749	+	5.07271i	0.213658	+	0.237291i	−0.626784	+	0.779193i	$0.715629\pi$
$458$	−17.0133	−	7.57481i	−0.794980	−	0.353948i
$459$	−0.529947	+	3.37801i	−0.0247358	+	0.157672i
$460$	3.86628	−	18.1894i	0.180266	−	0.848085i
$461$	18.1166			0.843773			0.421886	−	0.906649i	$-0.361368\pi$
$461$	18.1166			0.843773			0.421886	+	0.906649i	$0.361368\pi$
$462$	−4.30466	+	14.5763i	−0.200271	+	0.678153i
$463$	13.7420			0.638647			0.319323	−	0.947646i	$-0.396544\pi$
$463$	13.7420			0.638647			0.319323	+	0.947646i	$0.396544\pi$
$464$	0.678914	−	3.19404i	0.0315178	−	0.148280i
$465$	−15.3569	+	20.4000i	−0.712159	+	0.946029i
$466$	14.0929	+	6.27456i	0.652840	+	0.290663i
$467$	−15.5277	−	17.2452i	−0.718536	−	0.798015i	0.267675	−	0.963509i	$-0.413745\pi$
$467$	−15.5277	−	17.2452i	−0.718536	−	0.798015i	−0.986211	+	0.165494i	$0.947078\pi$
$468$	1.04629	+	5.90005i	0.0483647	+	0.272730i
$469$	−1.17639	−	3.10783i	−0.0543204	−	0.143506i
$470$	6.79612	−	9.35406i	0.313482	−	0.431471i
$471$	1.64946	+	1.53664i	0.0760030	+	0.0708045i
$472$	−0.928117	+	0.535848i	−0.0427200	+	0.0246644i
$473$	−24.1642	+	21.5950i	−1.11107	+	0.992937i
$474$	11.1362	−	6.18000i	0.511501	−	0.283857i
$475$	−0.202705	+	0.0658627i	−0.00930073	+	0.00302199i
$476$	1.62247	+	0.631505i	0.0743658	+	0.0289450i
$477$	4.89433	−	10.0598i	0.224096	−	0.460608i
$478$	−14.8424	−	16.4842i	−0.678877	−	0.753969i
$479$	−15.9380	+	3.38773i	−0.728228	+	0.154790i	−0.557083	−	0.830456i	$-0.688080\pi$
$479$	−15.9380	+	3.38773i	−0.728228	+	0.154790i	−0.171144	+	0.985246i	$0.554746\pi$
$480$	−2.25347	−	3.21494i	−0.102856	−	0.146741i
$481$	7.80392	+	17.5279i	0.355828	+	0.799203i
$482$	−6.88536	−	21.1910i	−0.313620	−	0.965222i
$483$	−8.94264	−	36.5157i	−0.406904	−	1.66152i
$484$	−5.57089	+	9.48500i	−0.253222	+	0.431136i
$485$	15.7371	+	9.08583i	0.714585	+	0.412566i
$486$	4.52117	−	14.9184i	0.205084	−	0.676713i
$487$	0.779761	−	7.41893i	0.0353343	−	0.336184i	−0.962547	−	0.271116i	$-0.912607\pi$
$487$	0.779761	−	7.41893i	0.0353343	−	0.336184i	0.997881	−	0.0650672i	$-0.0207262\pi$
$488$	−1.19576	−	11.3769i	−0.0541294	−	0.515007i
$489$	−11.3460	−	13.0392i	−0.513085	−	0.589654i
$490$	−15.5503	+	3.15403i	−0.702493	+	0.142485i
$491$	11.5506	+	15.8981i	0.521273	+	0.717471i	0.985769	−	0.168104i	$-0.0537644\pi$
$491$	11.5506	+	15.8981i	0.521273	+	0.717471i	−0.464496	+	0.885575i	$0.653764\pi$
$492$	−0.306660	+	2.50768i	−0.0138253	+	0.113055i
$493$	−1.59687	−	1.43782i	−0.0719192	−	0.0647564i
$494$	2.67194	−	1.54265i	0.120216	−	0.0694069i
$495$	−3.85526	−	22.2215i	−0.173281	−	0.998784i
$496$			6.50377i			0.292028i
$497$	−0.0746969	−	0.0384998i	−0.00335061	−	0.00172695i
$498$	−3.82034	−	8.98793i	−0.171193	−	0.402759i
$499$	3.07424	+	29.2495i	0.137622	+	1.30939i	0.817443	+	0.576009i	$0.195391\pi$
$499$	3.07424	+	29.2495i	0.137622	+	1.30939i	−0.679821	+	0.733378i	$0.737943\pi$
$500$	−10.7800	+	2.29135i	−0.482095	+	0.102472i
$501$	13.3047	−	38.7011i	0.594410	−	1.72904i
$502$	−11.0807	+	1.16463i	−0.494556	+	0.0519800i
$503$	17.2348	+	12.5218i	0.768462	+	0.558320i	0.901494	−	0.432792i	$-0.142471\pi$
$503$	17.2348	+	12.5218i	0.768462	+	0.558320i	−0.133032	+	0.991112i	$0.542471\pi$
$504$	−6.92785	−	3.87362i	−0.308591	−	0.172545i
$505$	20.4302			0.909133
$506$	0.101459	−	27.2089i	0.00451041	−	1.20958i
$507$	−15.6044	−	0.264745i	−0.693017	−	0.0117577i
$508$	−12.3777	+	13.7469i	−0.549173	+	0.609919i
$509$	−6.47913	+	2.88470i	−0.287182	+	0.127862i	−0.545272	−	0.838259i	$-0.683574\pi$
$509$	−6.47913	+	2.88470i	−0.287182	+	0.127862i	0.258090	+	0.966121i	$0.416907\pi$
$510$	−2.57360	+	0.226429i	−0.113961	+	0.0100264i
$511$	10.6214	−	16.1897i	0.469861	−	0.716188i
$512$	−0.951057	−	0.309017i	−0.0420312	−	0.0136568i
$513$	−8.01476	+	0.431825i	−0.353860	+	0.0190655i
$514$	−10.0907	−	1.06058i	−0.445083	−	0.0467801i
$515$	13.8521	+	12.4725i	0.610395	+	0.549602i
$516$	−8.21231	−	14.7983i	−0.361527	−	0.651460i
$517$	6.93865	−	15.4294i	0.305161	−	0.678583i
$518$	−24.5181	−	6.69231i	−1.07726	−	0.294043i
$519$	37.5897	+	8.65891i	1.65000	+	0.380084i
$520$	−4.13604	+	1.84148i	−0.181377	+	0.0807544i
$521$	6.80805	+	3.03114i	0.298266	+	0.132797i	0.550413	−	0.834892i	$-0.314470\pi$
$521$	6.80805	+	3.03114i	0.298266	+	0.132797i	−0.252147	+	0.967689i	$0.581137\pi$
$522$	6.30421	+	7.49816i	0.275928	+	0.328185i
$523$	8.09485	−	7.28864i	0.353963	−	0.318710i	−0.472897	−	0.881118i	$-0.656792\pi$
$523$	8.09485	−	7.28864i	0.353963	−	0.318710i	0.826860	+	0.562408i	$0.190125\pi$
$524$	5.94431	−	4.31880i	0.259679	−	0.188668i
$525$	0.499886	−	0.387204i	0.0218168	−	0.0168990i
$526$	−4.35275	−	13.3964i	−0.189789	−	0.584110i
$527$	3.70642	+	2.13990i	0.161454	+	0.0932157i
$528$	−4.18859	−	3.93137i	−0.182285	−	0.171091i
$529$	22.1516	+	38.3677i	0.963113	+	1.66816i
$530$	8.26804	+	1.75743i	0.359141	+	0.0763377i
$531$	0.444341	−	3.18424i	0.0192827	−	0.138184i
$532$	−0.658140	+	4.03349i	−0.0285340	+	0.174874i
$533$	2.77076	+	0.900276i	0.120015	+	0.0389953i
$534$	5.40641	+	27.7412i	0.233958	+	1.20048i
$535$	−0.568721	+	1.27737i	−0.0245880	+	0.0552255i
$536$	1.24911	+	0.131286i	0.0539532	+	0.00567071i
$537$	−1.24605	−	1.16083i	−0.0537712	−	0.0500934i
$538$		−	7.51500i		−	0.323995i
$539$	−21.3307	+	9.16524i	−0.918778	+	0.394775i
$540$	11.7629	+	0.599169i	0.506196	+	0.0257841i
$541$	−17.6135	−	3.74387i	−0.757265	−	0.160962i	−0.186929	−	0.982373i	$-0.559854\pi$
$541$	−17.6135	−	3.74387i	−0.757265	−	0.160962i	−0.570336	+	0.821412i	$0.693187\pi$
$542$	0.775022	−	7.37384i	0.0332901	−	0.316734i
$543$	−18.3073	−	26.1183i	−0.785641	−	1.12084i
$544$	−0.489027	+	0.440321i	−0.0209668	+	0.0188786i
$545$	−11.3288	+	34.8664i	−0.485271	+	1.49351i
$546$	−5.91271	+	6.98705i	−0.253041	+	0.299018i
$547$	−7.71964	−	5.60865i	−0.330068	−	0.239808i	0.410391	−	0.911909i	$-0.365392\pi$
$547$	−7.71964	−	5.60865i	−0.330068	−	0.239808i	−0.740460	+	0.672101i	$0.765392\pi$
$548$	3.45121	−	16.2367i	0.147428	−	0.693596i
$549$	29.1216	+	18.1576i	1.24288	+	0.774949i
$550$	0.418758	−	0.184575i	0.0178559	−	0.00787031i
$551$	2.52200	−	4.36822i	0.107441	−	0.186093i
$552$	13.8469	+	3.18967i	0.589362	+	0.135761i
$553$	18.1297	+	7.05653i	0.770955	+	0.300074i
$554$	1.48911	+	2.04958i	0.0632660	+	0.0870782i
$555$	37.0172	−	7.21420i	1.57129	−	0.306226i
$556$	−4.15423	−	19.5441i	−0.176178	−	0.828854i
$557$	−14.1949	+	31.8823i	−0.601457	+	1.35089i	0.314362	+	0.949303i	$0.398210\pi$
$557$	−14.1949	+	31.8823i	−0.601457	+	1.35089i	−0.915819	+	0.401592i	$0.868457\pi$
$558$	−15.3869	−	11.9973i	−0.651378	−	0.507887i
$559$	−18.5616	+	6.03102i	−0.785071	+	0.255085i
$560$	1.57918	−	5.78551i	0.0667324	−	0.244482i
$561$	−3.61859	+	1.09351i	−0.152777	+	0.0461679i
$562$	7.80706	−	13.5222i	0.329321	−	0.570401i
$563$	−25.0942	+	27.8699i	−1.05759	+	1.17458i	−0.0734334	+	0.997300i	$0.523396\pi$
$563$	−25.0942	+	27.8699i	−1.05759	+	1.17458i	−0.984161	+	0.177277i	$0.943271\pi$
$564$	7.05855	+	5.31359i	0.297218	+	0.223742i
$565$	−5.15724	+	0.542048i	−0.216967	+	0.0228041i
$566$	−4.70946	+	14.4942i	−0.197953	+	0.609238i
$567$	21.9440	−	9.24461i	0.921560	−	0.388237i
$568$	0.0256961	−	0.0186693i	0.00107819	−	0.000783348i
$569$	8.85434	+	19.8872i	0.371193	+	0.833714i	0.998490	+	0.0549337i	$0.0174947\pi$
$569$	8.85434	+	19.8872i	0.371193	+	0.833714i	−0.627297	+	0.778780i	$0.715839\pi$
$570$	−1.77592	−	5.79864i	−0.0743853	−	0.242878i
$571$	−14.0266	−	24.2948i	−0.586994	−	1.01670i	−0.994624	−	0.103556i	$-0.966978\pi$
$571$	−14.0266	−	24.2948i	−0.586994	−	1.01670i	0.407629	−	0.913148i	$-0.366356\pi$
$572$	−5.37383	+	3.87378i	−0.224691	+	0.161971i
$573$	−33.5940	−	20.1630i	−1.40341	−	0.842319i
$574$	−3.24627	+	2.08669i	−0.135497	+	0.0870968i
$575$	−0.665359	+	0.915788i	−0.0277474	+	0.0381910i
$576$	2.48547	−	1.68001i	0.103561	−	0.0700004i
$577$	−2.75272	−	12.9505i	−0.114597	−	0.539138i	−0.997567	−	0.0697089i	$-0.977793\pi$
$577$	−2.75272	−	12.9505i	−0.114597	−	0.539138i	0.882970	−	0.469429i	$-0.155540\pi$
$578$	−3.44447	−	16.2049i	−0.143271	−	0.674037i
$579$	−38.2275	−	17.8030i	−1.58868	−	0.739868i
$580$	−4.35062	+	5.98811i	−0.180650	+	0.248643i
$581$	6.83457	−	13.2604i	0.283546	−	0.550132i
$582$	−7.14570	+	11.9056i	−0.296199	+	0.493504i
$583$	12.3679	+	0.0461186i	0.512225	+	0.00191004i
$584$	3.65922	+	6.33796i	0.151420	+	0.262267i
$585$	3.27298	−	13.1821i	0.135321	−	0.545014i
$586$	7.50675	+	16.8604i	0.310101	+	0.696498i
$587$	28.8123	−	20.9334i	1.18921	−	0.864012i	0.196030	−	0.980598i	$-0.437195\pi$
$587$	28.8123	−	20.9334i	1.18921	−	0.864012i	0.993181	+	0.116586i	$0.0371951\pi$
$588$	−2.20816	−	11.9216i	−0.0910629	−	0.491638i
$589$	−3.10446	+	9.55454i	−0.127917	+	0.393688i
$590$	2.41592	−	0.253923i	0.0994619	−	0.0104539i
$591$	11.3657	−	15.0982i	0.467524	−	0.621056i
$592$	6.42765	−	7.13863i	0.264175	−	0.293396i
$593$	0.269484	−	0.466759i	0.0110664	−	0.0191675i	−0.860439	−	0.509553i	$-0.829811\pi$
$593$	0.269484	−	0.466759i	0.0110664	−	0.0191675i	0.871506	+	0.490386i	$0.163144\pi$
$594$	17.0276	−	2.65743i	0.698650	−	0.109036i
$595$	−2.77750	−	2.80353i	−0.113866	−	0.114934i
$596$	3.23101	−	1.04982i	0.132347	−	0.0430023i
$597$	−27.2194	−	3.32862i	−1.11402	−	0.136231i
$598$	6.66483	−	14.9695i	0.272545	−	0.612147i
$599$	−9.39189	−	44.1854i	−0.383742	−	1.80537i	−0.568616	−	0.822603i	$-0.692521\pi$
$599$	−9.39189	−	44.1854i	−0.383742	−	1.80537i	0.184873	−	0.982762i	$-0.440812\pi$
$600$	0.0457161	+	0.234577i	0.00186635	+	0.00957656i
$601$	12.2760	+	16.8964i	0.500748	+	0.689220i	0.982325	−	0.187184i	$-0.0599359\pi$
$601$	12.2760	+	16.8964i	0.500748	+	0.689220i	−0.481577	+	0.876404i	$0.659936\pi$
$602$	9.37710	−	24.0918i	0.382182	−	0.981907i
$603$	−2.61479	+	2.71300i	−0.106483	+	0.110482i
$604$	0.331696	−	0.574514i	0.0134965	−	0.0233766i
$605$	20.2806	−	14.5049i	0.824525	−	0.589708i
$606$	−0.264822	+	15.6090i	−0.0107577	+	0.634072i
$607$	5.40998	−	25.4520i	0.219584	−	1.03306i	−0.720851	−	0.693090i	$-0.756249\pi$
$607$	5.40998	−	25.4520i	0.219584	−	1.03306i	0.940435	−	0.339973i	$-0.110418\pi$
$608$	−1.24967	−	0.907939i	−0.0506809	−	0.0368218i
$609$	−2.65996	+	14.7256i	−0.107787	+	0.596712i
$610$	−8.01285	+	24.6610i	−0.324431	+	0.998496i
$611$	7.57143	−	6.81734i	0.306307	−	0.275800i
$612$	−0.139635	−	1.96921i	−0.00564443	−	0.0796004i
$613$	2.04815	−	19.4869i	0.0827241	−	0.787067i	−0.871986	−	0.489530i	$-0.837168\pi$
$613$	2.04815	−	19.4869i	0.0827241	−	0.787067i	0.954710	−	0.297537i	$-0.0961651\pi$
$614$	−19.9008	−	4.23004i	−0.803130	−	0.170711i
$615$	2.94698	−	4.91004i	0.118834	−	0.197992i
$616$	0.532772	−	8.75878i	0.0214660	−	0.352901i
$617$		−	17.6927i		−	0.712282i	−0.934432	−	0.356141i	$-0.884092\pi$
$617$		−	17.6927i		−	0.712282i	0.934432	−	0.356141i	$-0.115908\pi$
$618$	−9.70870	+	10.4215i	−0.390541	+	0.419215i
$619$	−10.1040	−	1.06197i	−0.406113	−	0.0426842i	−0.100730	−	0.994914i	$-0.532118\pi$
$619$	−10.1040	−	1.06197i	−0.406113	−	0.0426842i	−0.305383	+	0.952230i	$0.598785\pi$
$620$	5.99618	−	13.4676i	0.240813	−	0.540874i
$621$	−33.0892	+	26.8755i	−1.32782	+	1.07848i
$622$	8.08382	+	2.62659i	0.324132	+	0.105317i
$623$	−27.3255	+	33.4243i	−1.09477	+	1.33912i
$624$	−1.35331	−	3.18387i	−0.0541757	−	0.127457i
$625$	25.1099	+	5.33727i	1.00440	+	0.213491i
$626$	11.9554	+	20.7074i	0.477835	+	0.827635i
$627$	−4.27679	−	7.77484i	−0.170799	−	0.310497i
$628$	−1.12716	−	0.650766i	−0.0449786	−	0.0259684i
$629$	−1.95336	−	6.01183i	−0.0778857	−	0.239707i
$630$	10.7745	+	14.4084i	0.429266	+	0.574046i
$631$	−34.5856	+	25.1279i	−1.37683	+	1.00033i	−0.379665	+	0.925124i	$0.623961\pi$
$631$	−34.5856	+	25.1279i	−1.37683	+	1.00033i	−0.997168	+	0.0752036i	$0.976039\pi$
$632$	−5.46446	+	4.92022i	−0.217364	+	0.195716i
$633$	5.96740	−	17.3582i	0.237183	−	0.689925i
$634$	25.2370	+	11.2362i	1.00229	+	0.446248i
$635$	38.3051	−	17.0545i	1.52009	−	0.676789i
$636$	−1.44987	+	6.29413i	−0.0574912	+	0.249578i
$637$	−13.9810	−	0.130407i	−0.553946	−	0.00516690i
$638$	−4.44186	+	9.87729i	−0.175855	+	0.391046i
$639$	−0.00323233	+	0.0952317i	−0.000127869	+	0.00376731i
$640$	1.68449	+	1.51673i	0.0665855	+	0.0599539i
$641$	−36.3931	−	3.82507i	−1.43744	−	0.151081i	−0.646473	−	0.762937i	$-0.723757\pi$
$641$	−36.3931	−	3.82507i	−1.43744	−	0.151081i	−0.790969	+	0.611856i	$0.790423\pi$
$642$	−0.968557	−	0.451069i	−0.0382259	−	0.0178023i
$643$	−0.0480928	−	0.0156263i	−0.00189660	−	0.000616242i	0.308069	−	0.951364i	$-0.400317\pi$
$643$	−0.0480928	−	0.0156263i	−0.00189660	−	0.000616242i	−0.309965	+	0.950748i	$0.600317\pi$
$644$	9.76373	+	19.3854i	0.384745	+	0.763890i
$645$	3.36220	+	38.2149i	0.132387	+	1.50471i
$646$	−0.928597	+	0.413438i	−0.0365352	+	0.0162665i
$647$	−26.1573	+	29.0506i	−1.02835	+	1.14210i	−0.0386047	+	0.999255i	$0.512291\pi$
$647$	−26.1573	+	29.0506i	−1.02835	+	1.14210i	−0.989745	+	0.142844i	$0.954375\pi$
$648$	−0.610249	+	8.97929i	−0.0239728	+	0.352740i
$649$	3.38452	−	1.08576i	0.132854	−	0.0426199i
$650$	0.275599			0.0108099
$651$	−0.915791	−	29.7900i	−0.0358927	−	1.16756i
$652$	8.07334	+	5.86563i	0.316176	+	0.229716i
$653$	−31.1848	+	3.27766i	−1.22036	+	0.128265i	−0.692721	−	0.721206i	$-0.743588\pi$
$653$	−31.1848	+	3.27766i	−1.22036	+	0.128265i	−0.527636	+	0.849471i	$0.676922\pi$
$654$	−26.4916	−	9.10730i	−1.03590	−	0.356124i
$655$	−16.2909	+	3.46273i	−0.636538	+	0.135300i
$656$	−0.152465	−	1.45061i	−0.00595275	−	0.0566366i
$657$	−21.7447	−	3.03433i	−0.848340	−	0.118381i
$658$	0.643450	+	13.4803i	0.0250843	+	0.525519i
$659$		−	2.23889i		−	0.0872149i	−0.999049	−	0.0436074i	$-0.986115\pi$
$659$		−	2.23889i		−	0.0872149i	0.999049	−	0.0436074i	$-0.0138851\pi$
$660$	5.04895	+	12.0026i	0.196530	+	0.467199i
$661$	17.0184	−	9.82555i	0.661937	−	0.382170i	−0.131077	−	0.991372i	$-0.541844\pi$
$661$	17.0184	−	9.82555i	0.661937	−	0.382170i	0.793015	+	0.609202i	$0.208510\pi$
$662$	14.4044	+	12.9698i	0.559844	+	0.504086i
$663$	−2.25972	−	0.276337i	−0.0877602	−	0.0107320i
$664$	3.31422	+	4.56164i	0.128617	+	0.177026i
$665$	5.08154	−	7.74556i	0.197054	−	0.300360i
$666$	5.03193	+	28.3752i	0.194983	+	1.09952i
$667$	−2.80020	−	26.6421i	−0.108424	−	1.03159i
$668$	−2.46976	+	23.4982i	−0.0955577	+	0.909171i
$669$	43.6469	−	13.3675i	1.68749	−	0.516819i
$670$	−2.46554	−	1.42348i	−0.0952521	−	0.0549938i
$671$	−4.10655	+	37.7178i	−0.158532	+	1.45608i
$672$	4.39974	+	1.28151i	0.169724	+	0.0494352i
$673$	15.2873	+	47.0493i	0.589281	+	1.81362i	0.581354	+	0.813650i	$0.302523\pi$
$673$	15.2873	+	47.0493i	0.589281	+	1.81362i	0.00792622	+	0.999969i	$0.497477\pi$
$674$	−3.38000	−	7.59161i	−0.130193	−	0.292418i
$675$	−0.639302	−	0.324560i	−0.0246067	−	0.0124923i
$676$	8.81362	−	1.87339i	0.338985	−	0.0720536i
$677$	13.5629	+	15.0632i	0.521265	+	0.578924i	0.945086	−	0.326822i	$-0.105978\pi$
$677$	13.5629	+	15.0632i	0.521265	+	0.578924i	−0.423820	+	0.905746i	$0.639311\pi$
$678$	−0.347283	−	3.94724i	−0.0133373	−	0.151593i
$679$	−20.9644	+	3.22029i	−0.804541	+	0.123583i
$680$	1.41861	−	0.460933i	0.0544010	−	0.0176760i
$681$	3.89699	+	7.02226i	0.149333	+	0.269093i
$682$	4.56342	−	21.0823i	0.174742	−	0.807284i
$683$	−5.35436	+	3.09134i	−0.204879	+	0.118287i	−0.598929	−	0.800802i	$-0.704407\pi$
$683$	−5.35436	+	3.09134i	−0.204879	+	0.118287i	0.394050	+	0.919089i	$0.371074\pi$
$684$	4.45327	−	1.28167i	0.170275	−	0.0490058i
$685$	−22.1160	+	30.4401i	−0.845010	+	1.16306i
$686$	11.8554	−	14.2285i	0.452641	−	0.543246i
$687$	−24.3340	+	21.1742i	−0.928402	+	0.807845i
$688$	6.53825	+	7.26146i	0.249268	+	0.276841i
$689$	6.80441	+	3.02952i	0.259227	+	0.115415i
$690$	−25.7326	−	19.3712i	−0.979623	−	0.737448i
$691$	0.764431	−	3.59637i	0.0290803	−	0.136812i	−0.961213	−	0.275809i	$-0.911054\pi$
$691$	0.764431	−	3.59637i	0.0290803	−	0.136812i	0.990293	+	0.138997i	$0.0443877\pi$
$692$	−22.2708			−0.846608
$693$	19.7390	+	17.4175i	0.749824	+	0.661637i
$694$	9.41454			0.357371
$695$	−9.41643	+	44.3008i	−0.357186	+	1.68043i
$696$	−4.51861	−	3.40156i	−0.171278	−	0.128936i
$697$	−0.876848	−	0.390398i	−0.0332130	−	0.0147874i
$698$	10.1800	+	11.3061i	0.385320	+	0.427941i
$699$	20.1570	−	17.5395i	0.762407	−	0.663405i
$700$	−0.231062	+	0.282633i	−0.00873334	+	0.0106825i
$701$	8.92178	−	12.2798i	0.336971	−	0.463801i	−0.606583	−	0.795020i	$-0.707460\pi$
$701$	8.92178	−	12.2798i	0.336971	−	0.463801i	0.943554	+	0.331219i	$0.107460\pi$
$702$	10.0289	+	2.67148i	0.378517	+	0.100829i
$703$	12.8502	−	7.41907i	0.484655	−	0.279816i
$704$	2.86608	+	1.66901i	0.108019	+	0.0629032i
$705$	−9.71756	−	17.5107i	−0.365984	−	0.659493i
$706$	18.7381	−	6.08839i	0.705219	−	0.229140i
$707$	−18.6020	+	14.9205i	−0.699602	+	0.561145i
$708$	0.162686	+	1.84909i	0.00611410	+	0.0694931i
$709$	−9.06637	−	10.0692i	−0.340495	−	0.378158i	0.548441	−	0.836189i	$-0.315221\pi$
$709$	−9.06637	−	10.0692i	−0.340495	−	0.378158i	−0.888936	+	0.458031i	$0.848555\pi$
$710$	−0.0704224	+	0.0149688i	−0.00264291	+	0.000561767i
$711$	−1.56031	−	22.0042i	−0.0585161	−	0.825222i
$712$	−6.63700	−	14.9070i	−0.248732	−	0.558662i
$713$	16.4879	+	50.7446i	0.617477	+	1.90040i
$714$	2.17794	−	2.08571i	0.0815074	−	0.0780558i
$715$	14.6993	−	3.06719i	0.549722	−	0.114706i
$716$	0.851494	+	0.491611i	0.0318218	+	0.0183723i
$717$	−36.7355	+	11.2508i	−1.37191	+	0.420169i
$718$	−0.466456	+	4.43803i	−0.0174080	+	0.165626i
$719$	3.27701	+	31.1787i	0.122212	+	1.16277i	0.867993	+	0.496577i	$0.165410\pi$
$719$	3.27701	+	31.1787i	0.122212	+	1.16277i	−0.745781	+	0.666191i	$0.767924\pi$
$720$	−6.69567	+	1.18738i	−0.249533	+	0.0442510i
$721$	−21.7214	−	1.23997i	−0.808947	−	0.0461790i
$722$	9.76545	+	13.4410i	0.363432	+	0.500222i
$723$	−38.3073	−	4.68454i	−1.42466	−	0.174220i
$724$	13.6849	+	12.3220i	0.508596	+	0.457942i
$725$	0.390199	−	0.225281i	0.0144916	−	0.00836674i
$726$	10.8191	+	15.6827i	0.401533	+	0.582040i
$727$		−	46.3995i		−	1.72086i	−0.509565	−	0.860432i	$-0.670194\pi$
$727$		−	46.3995i		−	1.72086i	0.509565	−	0.860432i	$-0.329806\pi$
$728$	2.42106	−	4.69732i	0.0897306	−	0.174094i
$729$	−20.1178	−	18.0076i	−0.745105	−	0.666948i
$730$	−1.73400	−	16.4979i	−0.0641783	−	0.610616i
$731$	6.28947	−	1.33687i	0.232624	−	0.0494458i
$732$	−18.7375	−	6.44160i	−0.692559	−	0.238088i
$733$	−4.34953	+	0.457154i	−0.160654	+	0.0168854i	−0.184514	−	0.982830i	$-0.559071\pi$
$733$	−4.34953	+	0.457154i	−0.160654	+	0.0168854i	0.0238602	+	0.999715i	$0.492404\pi$
$734$	1.21583	+	0.883353i	0.0448771	+	0.0326052i
$735$	−6.41862	+	26.7224i	−0.236755	+	0.985669i
$736$	−8.20385			−0.302398
$737$	−3.95693	−	1.30202i	−0.145755	−	0.0479604i
$738$	3.71314	+	2.31518i	0.136683	+	0.0852231i
$739$	−9.19869	+	10.2162i	−0.338379	+	0.375808i	−0.888186	−	0.459484i	$-0.848035\pi$
$739$	−9.19869	+	10.2162i	−0.338379	+	0.375808i	0.549807	+	0.835292i	$0.314701\pi$
$740$	−19.8915	+	8.85628i	−0.731227	+	0.325563i
$741$	−0.468353	−	5.32332i	−0.0172054	−	0.195557i
$742$	−8.81167	+	4.43813i	−0.323486	+	0.162929i
$743$	23.9706	+	7.78852i	0.879396	+	0.285733i	0.713706	−	0.700445i	$-0.247015\pi$
$743$	23.9706	+	7.78852i	0.879396	+	0.285733i	0.165689	+	0.986178i	$0.447015\pi$
$744$	10.2118	+	4.75575i	0.374381	+	0.174354i
$745$	−7.65849	−	0.804939i	−0.280585	−	0.0294907i
$746$	0.745930	+	0.671639i	0.0273105	+	0.0245904i
$747$	−16.9057	−	0.573811i	−0.618549	−	0.0209946i
$748$	1.89416	−	1.08420i	0.0692574	−	0.0396422i
$749$	−0.415054	−	1.57841i	−0.0151658	−	0.0576739i
$750$	−4.28490	+	18.6014i	−0.156462	+	0.679228i
$751$	27.4091	−	12.2033i	1.00017	−	0.445306i	0.159704	−	0.987165i	$-0.448946\pi$
$751$	27.4091	−	12.2033i	1.00017	−	0.445306i	0.840469	+	0.541859i	$0.182279\pi$
$752$	−4.65990	−	2.07472i	−0.169929	−	0.0756573i
$753$	−6.27391	+	18.2498i	−0.228634	+	0.665058i
$754$	−4.84694	+	4.36421i	−0.176515	+	0.158935i
$755$	−1.21653	+	0.883863i	−0.0442742	+	0.0321671i
$756$	−11.1479	+	8.04511i	−0.405446	+	0.292598i
$757$	6.06780	+	18.6748i	0.220538	+	0.678745i	0.998714	+	0.0506994i	$0.0161451\pi$
$757$	6.06780	+	18.6748i	0.220538	+	0.678745i	−0.778176	+	0.628046i	$0.783855\pi$
$758$	11.7089	+	6.76016i	0.425288	+	0.245540i
$759$	−42.6473	−	20.0552i	−1.54800	−	0.727959i
$760$	1.75067	+	3.03225i	0.0635035	+	0.109991i
$761$	32.5592	+	6.92067i	1.18027	+	0.250874i	0.755945	−	0.654635i	$-0.227178\pi$
$761$	32.5592	+	6.92067i	1.18027	+	0.250874i	0.424326	+	0.905510i	$0.360511\pi$
$762$	12.5334	+	29.4868i	0.454037	+	1.06819i
$763$	−15.1485	−	40.0200i	−0.548412	−	1.44882i
$764$	21.5136	+	6.99021i	0.778337	+	0.252897i
$765$	−1.52637	+	4.20646i	−0.0551860	+	0.152085i
$766$	1.61197	−	3.62055i	0.0582429	−	0.130816i
$767$	2.12885	+	0.223751i	0.0768682	+	0.00807918i
$768$	−1.18064	+	1.26732i	−0.0426025	+	0.0457304i
$769$			28.5406i			1.02920i	0.857430	+	0.514601i	$0.172060\pi$
$769$			28.5406i			1.02920i	−0.857430	+	0.514601i	$0.827940\pi$
$770$	−9.17843	+	17.6460i	−0.330768	+	0.635917i
$771$	−9.04387	+	15.0682i	−0.325707	+	0.542668i
$772$	23.8147	+	5.06197i	0.857109	+	0.182184i
$773$	0.772901	−	7.35366i	0.0277993	−	0.264493i	−0.971790	−	0.235847i	$-0.924214\pi$
$773$	0.772901	−	7.35366i	0.0277993	−	0.264493i	0.999590	−	0.0286462i	$-0.00911963\pi$
$774$	−29.2404	+	2.07342i	−1.05102	+	0.0745275i
$775$	−0.666896	+	0.600476i	−0.0239556	+	0.0215697i
$776$	2.47731	−	7.62438i	0.0889303	−	0.273699i
$777$	−28.4361	+	33.6029i	−1.02014	+	1.20550i
$778$	11.2280	+	8.15764i	0.402544	+	0.292466i
$779$	0.468438	−	2.20383i	0.0167835	−	0.0789603i
$780$	−0.133025	+	7.84066i	−0.00476304	+	0.280741i
$781$	−0.0963950	+	0.0424878i	−0.00344928	+	0.00152033i
$782$	−2.69927	+	4.67528i	−0.0965258	+	0.167188i
$783$	16.3829	−	4.41555i	0.585477	−	0.157799i
$784$	2.78739	+	6.42110i	0.0995496	+	0.229325i
$785$	1.73408	+	2.38676i	0.0618921	+	0.0851872i
$786$	−2.43441	−	12.4914i	−0.0868327	−	0.445552i
$787$	5.03402	+	23.6832i	0.179443	+	0.844215i	0.972104	+	0.234551i	$0.0753621\pi$
$787$	5.03402	+	23.6832i	0.179443	+	0.844215i	−0.792660	+	0.609664i	$0.791305\pi$
$788$	−4.43781	+	9.96749i	−0.158091	+	0.355077i
$789$	−24.2169	−	2.96144i	−0.862145	−	0.105430i
$790$	15.8517	−	5.15053i	0.563978	−	0.183248i
$791$	4.29989	−	4.25997i	0.152886	−	0.151467i
$792$	−9.23558	+	3.70190i	−0.328172	+	0.131541i
$793$	−11.4245	+	19.7878i	−0.405695	+	0.702685i
$794$	−2.09724	+	2.32922i	−0.0744283	+	0.0826610i
$795$	8.80522	−	11.6968i	0.312289	−	0.414843i
$796$	15.7455	−	1.65492i	0.558084	−	0.0586569i
$797$	10.9797	−	33.7920i	0.388920	−	1.19697i	−0.544676	−	0.838647i	$-0.683347\pi$
$797$	10.9797	−	33.7920i	0.388920	−	1.19697i	0.933596	−	0.358327i	$-0.116653\pi$
$798$	5.85186	+	3.98277i	0.207153	+	0.140989i
$799$	−2.71558	+	1.97299i	−0.0960704	+	0.0697992i
$800$	−0.0561219	−	0.126052i	−0.00198421	−	0.00445661i
$801$	47.5105	+	11.7964i	1.67870	+	0.416804i
$802$	−17.8518	−	30.9202i	−0.630369	−	1.09183i
$803$	−7.41450	−	23.1124i	−0.261652	−	0.815618i
$804$	1.11952	−	1.86526i	0.0394824	−	0.0657825i
$805$	−2.34576	−	49.1438i	−0.0826771	−	1.73209i
$806$	7.63558	−	10.5095i	0.268952	−	0.370181i
$807$	−11.7995	−	5.49518i	−0.415363	−	0.193440i
$808$	−1.87394	−	8.81620i	−0.0659250	−	0.310153i
$809$	5.97976	+	28.1325i	0.210237	+	0.989087i	0.949037	+	0.315163i	$0.102059\pi$
$809$	5.97976	+	28.1325i	0.210237	+	0.989087i	−0.738800	+	0.673924i	$0.764607\pi$
$810$	9.54216	−	18.0312i	0.335277	−	0.633551i
$811$	−27.7819	+	38.2386i	−0.975556	+	1.34274i	−0.0363667	+	0.999339i	$0.511578\pi$
$811$	−27.7819	+	38.2386i	−0.975556	+	1.34274i	−0.939189	+	0.343399i	$0.888422\pi$
$812$	−0.411913	−	8.62961i	−0.0144553	−	0.302840i
$813$	−11.0112	−	6.60885i	−0.386178	−	0.231783i
$814$	−25.8445	+	18.6303i	−0.905848	+	0.652990i
$815$	−11.3100	−	19.5895i	−0.396171	−	0.686189i
$816$	0.333771	+	1.08981i	0.0116843	+	0.0381510i
$817$	6.13906	+	13.7886i	0.214779	+	0.482401i
$818$	6.93985	−	5.04210i	0.242646	−	0.176293i
$819$	6.64703	+	14.3929i	0.232266	+	0.502927i
$820$	−1.02168	+	3.14440i	−0.0356785	+	0.109807i
$821$	28.8630	−	3.03362i	1.00733	−	0.105874i	0.413530	−	0.910490i	$-0.364296\pi$
$821$	28.8630	−	3.03362i	1.00733	−	0.105874i	0.593795	+	0.804616i	$0.297629\pi$
$822$	−22.9700	−	17.2916i	−0.801172	−	0.603112i
$823$	13.6095	−	15.1149i	0.474397	−	0.526871i	−0.457687	−	0.889113i	$-0.651322\pi$
$823$	13.6095	−	15.1149i	0.474397	−	0.526871i	0.932084	+	0.362242i	$0.117989\pi$
$824$	4.11164	−	7.12157i	0.143236	−	0.248092i
$825$	0.0164011	−	0.792471i	0.000571014	−	0.0275903i
$826$	−2.01429	+	1.99559i	−0.0700861	+	0.0694354i
$827$	33.7377	−	10.9621i	1.17318	−	0.381188i	0.343348	−	0.939208i	$-0.388439\pi$
$827$	33.7377	−	10.9621i	1.17318	−	0.381188i	0.829827	+	0.558020i	$0.188439\pi$
$828$	15.1334	−	19.4090i	0.525923	−	0.674509i
$829$	20.6639	−	46.4118i	0.717686	−	1.61195i	−0.0712396	−	0.997459i	$-0.522695\pi$
$829$	20.6639	−	46.4118i	0.717686	−	1.61195i	0.788925	−	0.614489i	$-0.210638\pi$
$830$	−2.65729	−	12.5015i	−0.0922357	−	0.433935i
$831$	4.30698	−	0.839377i	0.149407	−	0.0291177i
$832$	1.17402	+	1.61590i	0.0407019	+	0.0560214i
$833$	4.57643	+	0.524202i	0.158564	+	0.0181625i
$834$	−33.7244	−	7.76853i	−1.16778	−	0.269002i
$835$	26.7785	−	46.3817i	0.926707	−	1.60510i
$836$	3.41382	+	3.81998i	0.118069	+	0.132117i
$837$	−30.0887	+	15.3866i	−1.04002	+	0.531838i
$838$	−6.52113	+	30.6795i	−0.225269	+	1.05981i
$839$	−32.4160	−	23.5516i	−1.11913	−	0.813093i	−0.135050	−	0.990839i	$-0.543119\pi$
$839$	−32.4160	−	23.5516i	−1.11913	−	0.813093i	−0.984076	+	0.177746i	$0.943119\pi$
$840$	−7.92925	−	6.71004i	−0.273585	−	0.231518i
$841$	5.66650	−	17.4397i	0.195397	−	0.601369i
$842$	−19.9686	+	17.9798i	−0.688162	+	0.619624i
$843$	−15.5229	−	22.1459i	−0.534637	−	0.762747i
$844$	−1.10773	+	10.5394i	−0.0381297	+	0.362780i
$845$	−19.9779	−	4.24644i	−0.687262	−	0.146082i
$846$	13.5044	−	7.19738i	0.464292	−	0.247451i
$847$	−7.87267	+	28.0182i	−0.270508	+	0.962718i
$848$		−	3.72908i		−	0.128057i
$849$	19.3141	+	17.9931i	0.662859	+	0.617520i
$850$	−0.0903010	−	0.00949102i	−0.00309730	−	0.000325539i
$851$	32.0533	−	71.9929i	1.09877	−	2.46788i
$852$	−0.0105235	−	0.0539978i	−0.000360530	−	0.00184994i
$853$	11.9648	+	3.88761i	0.409668	+	0.133109i	0.506599	−	0.862182i	$-0.330903\pi$
$853$	11.9648	+	3.88761i	0.409668	+	0.133109i	−0.0969310	+	0.995291i	$0.530903\pi$
$854$	−10.7145	−	28.3062i	−0.366644	−	0.968618i
$855$	−10.4032	−	1.45171i	−0.355783	−	0.0496473i
$856$	0.603385	+	0.128253i	0.0206233	+	0.00438361i
$857$	−5.43310	−	9.41040i	−0.185591	−	0.321453i	0.758184	−	0.652040i	$-0.226087\pi$
$857$	−5.43310	−	9.41040i	−0.185591	−	0.321453i	−0.943776	+	0.330587i	$0.892753\pi$
$858$	2.15284	+	11.2702i	0.0734968	+	0.384759i
$859$	17.0477	+	9.84252i	0.581661	+	0.335822i	0.761793	−	0.647820i	$-0.224319\pi$
$859$	17.0477	+	9.84252i	0.581661	+	0.335822i	−0.180132	+	0.983642i	$0.557652\pi$
$860$	−6.84430	−	21.0646i	−0.233389	−	0.718297i
$861$	0.902610	+	6.62290i	0.0307609	+	0.225708i
$862$	29.4125	−	21.3694i	1.00179	−	0.727845i
$863$	19.0271	−	17.1321i	0.647691	−	0.583183i	−0.278409	−	0.960463i	$-0.589807\pi$
$863$	19.0271	−	17.1321i	0.647691	−	0.583183i	0.926100	+	0.377279i	$0.123140\pi$
$864$	−0.820384	−	5.13098i	−0.0279100	−	0.174560i
$865$	46.1171	+	20.5326i	1.56803	+	0.698131i
$866$	−0.136835	+	0.0609230i	−0.00464985	+	0.00207025i
$867$	−27.9625	−	6.44126i	−0.949658	−	0.218757i
$868$	4.37603	+	16.6416i	0.148532	+	0.564854i
$869$	21.1656	−	12.1150i	0.717995	−	0.410973i
$870$	6.22081	+	11.2097i	0.210905	+	0.380045i
$871$	−1.86430	−	1.67863i	−0.0631695	−	0.0568781i
$872$	16.0849	+	1.69059i	0.544704	+	0.0572507i
$873$	13.4682	+	19.9254i	0.455830	+	0.674372i
$874$	−12.0521	−	3.91596i	−0.407668	−	0.132459i
$875$	−26.0417	+	13.1163i	−0.880369	+	0.443411i
$876$	12.6271	−	1.11095i	0.426632	−	0.0375356i
$877$	1.53144	−	0.681842i	0.0517132	−	0.0230242i	−0.380717	−	0.924692i	$-0.624323\pi$
$877$	1.53144	−	0.681842i	0.0517132	−	0.0230242i	0.432430	+	0.901667i	$0.357656\pi$
$878$	−12.2502	+	13.6052i	−0.413424	+	0.459154i
$879$	31.9622	+	0.542270i	1.07806	+	0.0182903i
$880$	−4.39616	−	6.09849i	−0.148195	−	0.205580i
$881$	−51.3749			−1.73086			−0.865432	−	0.501026i	$-0.832956\pi$
$881$	−51.3749			−1.73086			−0.865432	+	0.501026i	$0.832956\pi$
$882$	−20.3331	−	5.25031i	−0.684651	−	0.176787i
$883$	−2.11708	−	1.53815i	−0.0712456	−	0.0517629i	0.551592	−	0.834114i	$-0.314020\pi$
$883$	−2.11708	−	1.53815i	−0.0712456	−	0.0517629i	−0.622838	+	0.782351i	$0.714020\pi$
$884$	1.30717	−	0.137389i	0.0439648	−	0.00462089i
$885$	1.36790	−	3.97898i	0.0459814	−	0.133752i
$886$	18.9312	−	4.02396i	0.636008	−	0.135188i
$887$	−2.31863	−	22.0602i	−0.0778518	−	0.740711i	−0.961916	−	0.273345i	$-0.911870\pi$
$887$	−2.31863	−	22.0602i	−0.0778518	−	0.740711i	0.884064	−	0.467365i	$-0.154797\pi$
$888$	−6.50849	−	15.3122i	−0.218411	−	0.513844i
$889$	−22.4222	+	43.5033i	−0.752017	+	1.45905i
$890$			36.9875i			1.23982i
$891$	8.27854	−	28.6787i	0.277341	−	0.960771i
$892$	−22.8240	+	13.1775i	−0.764205	+	0.441214i
$893$	−5.85542	−	5.27224i	−0.195944	−	0.176429i
$894$	0.714257	−	5.84076i	0.0238883	−	0.195344i
$895$	−1.30998	−	1.80304i	−0.0437879	−	0.0602689i
$896$	−2.64145	−	0.150788i	−0.0882447	−	0.00503748i
$897$	−18.6305	−	21.4107i	−0.622053	−	0.714884i
$898$	0.669836	+	6.37307i	0.0223527	+	0.212672i
$899$	2.21991	−	21.1211i	0.0740383	−	0.704427i
$900$	0.401745	+	0.0997490i	0.0133915	+	0.00332497i
$901$	−2.12516	−	1.22696i	−0.0707993	−	0.0408760i
$902$	−0.523605	+	4.80920i	−0.0174341	+	0.160129i
$903$	−30.9704	−	32.3398i	−1.03063	−	1.07620i
$904$	0.706951	+	2.17577i	0.0235128	+	0.0723651i
$905$	−16.9777	−	38.1325i	−0.564357	−	1.26757i
$906$	−0.659515	−	0.940906i	−0.0219109	−	0.0312595i
$907$	19.5048	−	4.14587i	0.647645	−	0.137661i	0.127635	−	0.991821i	$-0.459261\pi$
$907$	19.5048	−	4.14587i	0.647645	−	0.137661i	0.520010	+	0.854160i	$0.325928\pi$
$908$	−3.10260	−	3.44578i	−0.102963	−	0.114352i
$909$	24.3145	+	11.8296i	0.806461	+	0.392361i
$910$	−9.34412	+	7.49484i	−0.309755	+	0.248451i
$911$	−22.2862	+	7.24122i	−0.738375	+	0.239912i	−0.653971	−	0.756519i	$-0.726898\pi$
$911$	−22.2862	+	7.24122i	−0.738375	+	0.239912i	−0.0844032	+	0.996432i	$0.526898\pi$
$912$	−2.33938	+	1.29823i	−0.0774645	+	0.0429888i
$913$	−7.54253	−	17.1122i	−0.249621	−	0.566333i
$914$	−5.91149	+	3.41300i	−0.195535	+	0.112892i
$915$	32.8618	+	30.6141i	1.08638	+	1.01207i
$916$	10.9465	−	15.0666i	0.361684	−	0.497816i
$917$	12.3042	−	15.0504i	0.406321	−	0.497008i
$918$	−3.19401	−	1.22069i	−0.105418	−	0.0402889i
$919$	5.08129	+	5.64335i	0.167616	+	0.186157i	0.821101	−	0.570783i	$-0.193360\pi$
$919$	5.08129	+	5.64335i	0.167616	+	0.186157i	−0.653485	+	0.756940i	$0.726694\pi$
$920$	16.9881	+	7.56358i	0.560080	+	0.249364i
$921$	−21.1937	+	28.1537i	−0.698357	+	0.927695i
$922$	−3.76665	+	17.7207i	−0.124048	+	0.583600i
$923$	−0.0634408			−0.00208818
$924$	−13.3628	−	7.24119i	−0.439605	−	0.238218i
$925$	1.32544			0.0435803
$926$	−2.85713	+	13.4417i	−0.0938911	+	0.441723i
$927$	9.26384	+	22.8644i	0.304265	+	0.750966i
$928$	2.98309	+	1.32816i	0.0979247	+	0.0435989i
$929$	11.6568	+	12.9462i	0.382446	+	0.424750i	0.903376	−	0.428850i	$-0.141081\pi$
$929$	11.6568	+	12.9462i	0.382446	+	0.424750i	−0.520929	+	0.853600i	$0.674415\pi$
$930$	−16.7614	−	19.2627i	−0.549627	−	0.631649i
$931$	1.02989	+	10.7636i	0.0337534	+	0.352762i
$932$	−9.06752	+	12.4804i	−0.297016	+	0.408808i
$933$	10.0352	−	10.7720i	0.328538	−	0.352659i
$934$	20.0968	−	11.6029i	0.657587	−	0.379658i
$935$	−4.92190	+	0.498764i	−0.160963	+	0.0163113i
$936$	−5.98866	−	0.203266i	−0.195745	−	0.00664394i
$937$	52.3891	−	17.0222i	1.71148	−	0.556092i	0.720898	−	0.693041i	$-0.243730\pi$
$937$	52.3891	−	17.0222i	1.71148	−	0.556092i	0.990578	+	0.136949i	$0.0437297\pi$
$938$	3.28450	−	0.504524i	0.107243	−	0.0164733i
$939$	41.2555	−	3.62971i	1.34632	−	0.118451i
$940$	7.73666	+	8.59243i	0.252342	+	0.280254i
$941$	10.0013	−	2.12585i	0.326035	−	0.0693008i	−0.0419867	−	0.999118i	$-0.513369\pi$
$941$	10.0013	−	2.12585i	0.326035	−	0.0693008i	0.368021	+	0.929817i	$0.380035\pi$
$942$	−1.84600	+	1.29393i	−0.0601459	+	0.0421585i
$943$	−4.86705	−	10.9316i	−0.158493	−	0.355981i
$944$	−0.331173	−	1.01924i	−0.0107787	−	0.0331736i
$945$	30.5017	−	6.38150i	0.992221	−	0.207590i
$946$	−16.0990	−	28.1260i	−0.523425	−	0.914456i
$947$	24.4930	+	14.1410i	0.795916	+	0.459522i	0.842041	−	0.539414i	$-0.181354\pi$
$947$	24.4930	+	14.1410i	0.795916	+	0.459522i	−0.0461253	+	0.998936i	$0.514687\pi$
$948$	3.72961	+	12.1777i	0.121132	+	0.395513i
$949$	1.52796	−	14.5376i	0.0495997	−	0.471909i
$950$	−0.0222788	−	0.211969i	−0.000722820	−	0.00687717i
$951$	36.0963	−	31.4091i	1.17050	−	1.01851i
$952$	−0.955036	+	1.45572i	−0.0309529	+	0.0471801i
$953$	−15.8738	−	21.8485i	−0.514204	−	0.707741i	0.470417	−	0.882444i	$-0.344103\pi$
$953$	−15.8738	−	21.8485i	−0.514204	−	0.707741i	−0.984621	+	0.174703i	$0.944103\pi$
$954$	8.82240	+	6.87893i	0.285636	+	0.222714i
$955$	−38.1046	−	34.3095i	−1.23304	−	1.11023i
$956$	19.2099	−	11.0908i	0.621292	−	0.358703i
$957$	12.2606	+	14.1969i	0.396329	+	0.458919i
$958$		−	16.2941i		−	0.526439i
$959$	−2.09393	−	43.8679i	−0.0676164	−	1.41657i
$960$	3.61321	−	1.53580i	0.116616	−	0.0495677i
$961$	1.18107	+	11.2372i	0.0380992	+	0.362489i
$962$	−18.7674	+	3.98913i	−0.605085	+	0.128615i
$963$	−1.41647	+	1.19092i	−0.0456452	+	0.0383770i
$964$	22.1594	−	2.32905i	0.713708	−	0.0750137i
$965$	−44.6472	−	32.4381i	−1.43724	−	1.04422i
$966$	37.5770	−	1.15518i	1.20902	−	0.0371672i
$967$	−25.6470			−0.824753			−0.412376	−	0.911014i	$-0.635301\pi$
$967$	−25.6470			−0.824753			−0.412376	+	0.911014i	$0.635301\pi$
$968$	−8.11947	−	7.42120i	−0.260970	−	0.238526i
$969$	−0.0298658	+	1.76033i	−0.000959429	+	0.0565501i
$970$	−12.1592	+	13.5042i	−0.390409	+	0.433593i
$971$	−21.1856	+	9.43245i	−0.679879	+	0.302702i	−0.717468	−	0.696592i	$-0.754699\pi$
$971$	−21.1856	+	9.43245i	−0.679879	+	0.302702i	0.0375886	+	0.999293i	$0.488032\pi$
$972$	13.6524	+	7.52408i	0.437901	+	0.241335i
$973$	−23.7798	−	47.2136i	−0.762347	−	1.51360i
$974$	7.09469	+	2.30520i	0.227328	+	0.0738635i
$975$	0.201526	−	0.432726i	0.00645399	−	0.0138583i
$976$	11.3769	+	1.19576i	0.364165	+	0.0382753i
$977$	−36.0884	−	32.4941i	−1.15457	−	1.03958i	−0.998657	−	0.0518088i	$-0.983501\pi$
$977$	−36.0884	−	32.4941i	−1.15457	−	1.03958i	−0.155913	−	0.987771i	$-0.549832\pi$
$978$	15.1132	−	8.38707i	0.483268	−	0.268189i
$979$	11.0546	+	52.9786i	0.353308	+	1.69320i
$980$	0.147992	−	15.8663i	0.00472743	−	0.506830i
$981$	−33.6711	+	34.9357i	−1.07503	+	1.11541i
$982$	−17.9522	+	7.99284i	−0.572878	+	0.255062i
$983$	−4.81093	−	2.14197i	−0.153445	−	0.0683181i	0.328577	−	0.944477i	$-0.393431\pi$
$983$	−4.81093	−	2.14197i	−0.153445	−	0.0683181i	−0.482022	+	0.876159i	$0.660098\pi$
$984$	−2.38912	−	0.821335i	−0.0761625	−	0.0261832i
$985$	18.3791	−	16.5487i	0.585608	−	0.527284i
$986$	1.73841	−	1.26303i	0.0553623	−	0.0402231i
$987$	21.6364	+	8.84692i	0.688694	+	0.281600i
$988$	0.953408	+	2.93429i	0.0303319	+	0.0933521i
$989$	69.4223	+	40.0810i	2.20750	+	1.27450i
$990$	22.5375	+	0.849110i	0.716289	+	0.0269865i
$991$	26.8565	+	46.5168i	0.853124	+	1.47765i	0.878374	+	0.477973i	$0.158628\pi$
$991$	26.8565	+	46.5168i	0.853124	+	1.47765i	−0.0252502	+	0.999681i	$0.508038\pi$
$992$	−6.36165	−	1.35221i	−0.201983	−	0.0429327i
$993$	30.8972	−	13.1329i	0.980493	−	0.416760i
$994$	0.0531888	−	0.0650600i	0.00168705	−	0.00206358i
$995$	−34.1306	−	11.0897i	−1.08201	−	0.351567i
$996$	9.58581	−	1.86816i	0.303738	−	0.0591948i
$997$	−8.06701	+	18.1188i	−0.255485	+	0.573828i	−0.995063	−	0.0992419i	$-0.968358\pi$
$997$	−8.06701	+	18.1188i	−0.255485	+	0.573828i	0.739578	+	0.673070i	$0.235025\pi$
$998$	−29.2495	−	3.07424i	−0.925876	−	0.0973135i
$999$	48.2322	+	12.8480i	1.52600	+	0.406493i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.bf.a.5.14	✓	256
3.2	odd	2	inner	462.2.bf.a.5.30	yes	256
7.3	odd	6	inner	462.2.bf.a.269.8	yes	256
11.9	even	5	inner	462.2.bf.a.383.30	yes	256
21.17	even	6	inner	462.2.bf.a.269.30	yes	256
33.20	odd	10	inner	462.2.bf.a.383.8	yes	256
77.31	odd	30	inner	462.2.bf.a.185.30	yes	256
231.185	even	30	inner	462.2.bf.a.185.14	yes	256

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.bf.a.5.14	✓	256	1.1	even	1	trivial
462.2.bf.a.5.30	yes	256	3.2	odd	2	inner
462.2.bf.a.185.14	yes	256	231.185	even	30	inner
462.2.bf.a.185.30	yes	256	77.31	odd	30	inner
462.2.bf.a.269.8	yes	256	7.3	odd	6	inner
462.2.bf.a.269.30	yes	256	21.17	even	6	inner
462.2.bf.a.383.8	yes	256	33.20	odd	10	inner
462.2.bf.a.383.30	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)

\(f(q)\)	\(=\)	\(q+(-0.207912 + 0.978148i) q^{2} +(1.38379 + 1.04170i) q^{3} +(-0.913545 - 0.406737i) q^{4} +(1.51673 + 1.68449i) q^{5} +(-1.30664 + 1.13697i) q^{6} +(-2.61122 - 0.426069i) q^{7} +(0.587785 - 0.809017i) q^{8} +(0.829732 + 2.88298i) q^{9} +O(q^{10})\)	\(q+(-0.207912 + 0.978148i) q^{2} +(1.38379 + 1.04170i) q^{3} +(-0.913545 - 0.406737i) q^{4} +(1.51673 + 1.68449i) q^{5} +(-1.30664 + 1.13697i) q^{6} +(-2.61122 - 0.426069i) q^{7} +(0.587785 - 0.809017i) q^{8} +(0.829732 + 2.88298i) q^{9} +(-1.96303 + 1.13336i) q^{10} +(-2.47299 + 2.21005i) q^{11} +(-0.840455 - 1.51448i) q^{12} +(-1.89961 + 0.617221i) q^{13} +(0.959661 - 2.46557i) q^{14} +(0.344091 + 3.91095i) q^{15} +(0.669131 + 0.743145i) q^{16} +(0.643670 - 0.136816i) q^{17} +(-2.99249 + 0.212196i) q^{18} +(0.628277 + 1.41113i) q^{19} +(-0.700452 - 2.15577i) q^{20} +(-3.16954 - 3.30969i) q^{21} +(-1.64759 - 2.87844i) q^{22} +(7.10475 + 4.10193i) q^{23} +(1.65612 - 0.507212i) q^{24} +(-0.0144229 + 0.137225i) q^{25} +(-0.208782 - 1.98643i) q^{26} +(-1.85502 + 4.85375i) q^{27} +(2.21217 + 1.45131i) q^{28} +(-1.91935 - 2.64176i) q^{29} +(-3.89703 - 0.476561i) q^{30} +(4.83325 + 4.35187i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-5.72429 + 0.482128i) q^{33} +0.658050i q^{34} +(-3.24279 - 5.04482i) q^{35} +(0.414614 - 2.97121i) q^{36} +(-1.00410 - 9.55336i) q^{37} +(-1.51092 + 0.321157i) q^{38} +(-3.27161 - 1.12472i) q^{39} +(2.25429 - 0.236936i) q^{40} +(-1.18003 - 0.857341i) q^{41} +(3.89635 - 2.41215i) q^{42} +9.77126 q^{43} +(3.15810 - 1.01312i) q^{44} +(-3.59788 + 5.77036i) q^{45} +(-5.48945 + 6.09665i) q^{46} +(-4.65990 + 2.07472i) q^{47} +(0.151802 + 1.72539i) q^{48} +(6.63693 + 2.22512i) q^{49} +(-0.131228 - 0.0426385i) q^{50} +(1.03322 + 0.481185i) q^{51} +(1.98643 + 0.208782i) q^{52} +(-2.77125 - 2.49524i) q^{53} +(-4.36201 - 2.82363i) q^{54} +(-7.47367 - 0.813701i) q^{55} +(-1.87953 + 1.86208i) q^{56} +(-0.600573 + 2.60718i) q^{57} +(2.98309 - 1.32816i) q^{58} +(-0.979044 - 0.435898i) q^{59} +(1.27638 - 3.71279i) q^{60} +(8.50123 - 7.65455i) q^{61} +(-5.26166 + 3.82282i) q^{62} +(-0.938265 - 7.88160i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(-3.92089 - 2.26373i) q^{65} +(0.718556 - 5.69945i) q^{66} +(0.627993 + 1.08772i) q^{67} +(-0.643670 - 0.136816i) q^{68} +(5.55848 + 13.0772i) q^{69} +(5.60879 - 2.12305i) q^{70} +(0.0302076 + 0.00981506i) q^{71} +(2.82008 + 1.02330i) q^{72} +(-2.97668 + 6.68574i) q^{73} +(9.55336 + 1.00410i) q^{74} +(-0.162905 + 0.174866i) q^{75} -1.54468i q^{76} +(7.39915 - 4.71726i) q^{77} +(1.78035 - 2.96628i) q^{78} +(-7.19247 - 1.52881i) q^{79} +(-0.236936 + 2.25429i) q^{80} +(-7.62309 + 4.78419i) q^{81} +(1.08395 - 0.975991i) q^{82} +(-1.74239 + 5.36253i) q^{83} +(1.54934 + 4.31272i) q^{84} +(1.20674 + 0.876746i) q^{85} +(-2.03156 + 9.55773i) q^{86} +(0.0959430 - 5.65502i) q^{87} +(0.334380 + 3.29973i) q^{88} +(8.15885 - 14.1315i) q^{89} +(-4.89622 - 4.71898i) q^{90} +(5.22328 - 0.802334i) q^{91} +(-4.82210 - 6.63706i) q^{92} +(2.15484 + 11.0568i) q^{93} +(-1.06054 - 4.98943i) q^{94} +(-1.42412 + 3.19863i) q^{95} +(-1.71924 - 0.210243i) q^{96} +(7.62438 - 2.47731i) q^{97} +(-3.55639 + 6.02927i) q^{98} +(-8.42343 - 5.29582i) 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

Modular forms

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