LMFDB - Embedded newform 462.2.bf.a.383.30

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			383.30
Character	$\chi$	$=$	462.383
Dual form			462.2.bf.a.269.30

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.743145 - 0.669131i) q^{2} +(1.41833 - 0.994157i) q^{3} +(0.104528 - 0.994522i) q^{4} +(-2.21718 - 0.471276i) q^{5} +(0.388801 - 1.68785i) q^{6} +(-0.401695 - 2.61508i) q^{7} +(-0.587785 - 0.809017i) q^{8} +(1.02330 - 2.82008i) q^{9} +O(q^{10})$	\(q+(0.743145 - 0.669131i) q^{2} +(1.41833 - 0.994157i) q^{3} +(0.104528 - 0.994522i) q^{4} +(-2.21718 - 0.471276i) q^{5} +(0.388801 - 1.68785i) q^{6} +(-0.401695 - 2.61508i) q^{7} +(-0.587785 - 0.809017i) q^{8} +(1.02330 - 2.82008i) q^{9} +(-1.96303 + 1.13336i) q^{10} +(-3.15045 + 1.03665i) q^{11} +(-0.840455 - 1.51448i) q^{12} +(1.89961 + 0.617221i) q^{13} +(-2.04835 - 1.67460i) q^{14} +(-3.61321 + 1.53580i) q^{15} +(-0.978148 - 0.207912i) q^{16} +(-0.440321 + 0.489027i) q^{17} +(-1.12654 - 2.78045i) q^{18} +(1.53622 - 0.161463i) 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} +(-1.63796 - 0.563100i) q^{24} +(0.126052 + 0.0561219i) q^{25} +(1.82469 - 0.812403i) q^{26} +(-1.35222 - 5.01712i) q^{27} +(-2.64274 + 0.126145i) q^{28} +(1.91935 - 2.64176i) q^{29} +(-1.65748 + 3.55903i) q^{30} +(-1.35221 - 6.36165i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-3.43778 + 4.60235i) q^{33} +0.658050i q^{34} +(-0.341793 + 5.98741i) q^{35} +(-2.69767 - 1.31248i) q^{36} +(8.77550 - 3.90710i) q^{37} +(1.03359 - 1.14792i) q^{38} +(3.30788 - 1.01309i) q^{39} +(0.921955 + 2.07074i) q^{40} +(-1.18003 + 0.857341i) q^{41} +(-4.57004 - 0.338746i) q^{42} +9.77126 q^{43} +(0.701657 + 3.24155i) q^{44} +(-3.59788 + 5.77036i) q^{45} +(8.02458 - 1.70568i) q^{46} +(0.533188 + 5.07295i) q^{47} +(-1.59403 + 0.677546i) q^{48} +(-6.67728 + 2.10093i) q^{49} +(0.131228 - 0.0426385i) q^{50} +(-0.138351 + 1.13135i) q^{51} +(0.812403 - 1.82469i) q^{52} +(0.775320 + 3.64759i) q^{53} +(-4.36201 - 2.82363i) q^{54} +(7.47367 - 0.813701i) q^{55} +(-1.87953 + 1.86208i) q^{56} +(2.01834 - 1.75625i) q^{57} +(-0.341327 - 3.24751i) q^{58} +(0.112023 - 1.06583i) q^{59} +(1.14970 + 3.75395i) q^{60} +(-2.37841 + 11.1896i) q^{61} +(-5.26166 - 3.82282i) q^{62} +(-7.78579 - 1.54321i) q^{63} +(-0.309017 + 0.951057i) q^{64} +(-3.92089 - 2.26373i) q^{65} +(0.524804 + 5.72054i) q^{66} +(0.627993 + 1.08772i) q^{67} +(0.440321 + 0.489027i) q^{68} +(14.1548 - 1.24536i) q^{69} +(3.75236 + 4.67821i) q^{70} +(-0.0302076 + 0.00981506i) q^{71} +(-2.88298 + 0.829732i) q^{72} +(-7.27836 - 0.764986i) q^{73} +(3.90710 - 8.77550i) q^{74} +(0.234577 - 0.0457161i) q^{75} -1.54468i q^{76} +(3.97644 + 7.82227i) q^{77} +(1.78035 - 2.96628i) q^{78} +(4.92022 + 5.46446i) q^{79} +(2.07074 + 0.921955i) q^{80} +(-6.90570 - 5.77159i) q^{81} +(-0.303259 + 1.42672i) q^{82} +(-1.74239 - 5.36253i) q^{83} +(-3.62287 + 2.80622i) q^{84} +(1.20674 - 0.876746i) q^{85} +(7.26146 - 6.53825i) q^{86} +(0.0959430 - 5.65502i) q^{87} +(2.69046 + 1.93944i) q^{88} +(8.15885 - 14.1315i) q^{89} +(1.18738 + 6.69567i) q^{90} +(0.851017 - 5.21557i) q^{91} +(4.82210 - 6.63706i) q^{92} +(-8.24236 - 7.67859i) q^{93} +(3.79070 + 3.41316i) q^{94} +(-3.48216 - 0.365990i) q^{95} +(-0.731229 + 1.57013i) q^{96} +(-7.62438 - 2.47731i) q^{97} +(-3.55639 + 6.02927i) q^{98} +(-0.300439 + 9.94534i) 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 $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.743145	−	0.669131i	0.525483	−	0.473147i
$2$	0.743145	−	0.669131i	0.525483	−	0.473147i
$3$	1.41833	−	0.994157i	0.818872	−	0.573977i
$3$	1.41833	−	0.994157i	0.818872	−	0.573977i
$4$	0.104528	−	0.994522i	0.0522642	−	0.497261i
$5$	−2.21718	−	0.471276i	−0.991552	−	0.210761i	−0.316549	−	0.948576i	$-0.602524\pi$
$5$	−2.21718	−	0.471276i	−0.991552	−	0.210761i	−0.675003	+	0.737815i	$0.735858\pi$
$6$	0.388801	−	1.68785i	0.158728	−	0.689061i
$7$	−0.401695	−	2.61508i	−0.151827	−	0.988407i
$7$	−0.401695	−	2.61508i	−0.151827	−	0.988407i
$8$	−0.587785	−	0.809017i	−0.207813	−	0.286031i
$9$	1.02330	−	2.82008i	0.341101	−	0.940027i
$10$	−1.96303	+	1.13336i	−0.620765	+	0.358399i
$11$	−3.15045	+	1.03665i	−0.949898	+	0.312561i
$11$	−3.15045	+	1.03665i	−0.949898	+	0.312561i
$12$	−0.840455	−	1.51448i	−0.242619	−	0.437191i
$13$	1.89961	+	0.617221i	0.526857	+	0.171186i	0.560355	−	0.828253i	$-0.310665\pi$
$13$	1.89961	+	0.617221i	0.526857	+	0.171186i	−0.0334979	+	0.999439i	$0.510665\pi$
$14$	−2.04835	−	1.67460i	−0.547444	−	0.447555i
$15$	−3.61321	+	1.53580i	−0.932926	+	0.396542i
$16$	−0.978148	−	0.207912i	−0.244537	−	0.0519779i
$17$	−0.440321	+	0.489027i	−0.106794	+	0.118606i	−0.794172	−	0.607693i	$-0.792095\pi$
$17$	−0.440321	+	0.489027i	−0.106794	+	0.118606i	0.687378	+	0.726300i	$0.258762\pi$
$18$	−1.12654	−	2.78045i	−0.265528	−	0.655359i
$19$	1.53622	−	0.161463i	0.352432	−	0.0370421i	0.0733416	−	0.997307i	$-0.476634\pi$
$19$	1.53622	−	0.161463i	0.352432	−	0.0370421i	0.279091	+	0.960265i	$0.409967\pi$
$20$	−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	$0.340033\pi$
$24$	−1.63796	−	0.563100i	−0.334348	−	0.114942i
$25$	0.126052	+	0.0561219i	0.0252104	+	0.0112244i
$26$	1.82469	−	0.812403i	0.357851	−	0.159325i
$27$	−1.35222	−	5.01712i	−0.260236	−	0.965545i
$28$	−2.64274	+	0.126145i	−0.499431	+	0.0238391i
$29$	1.91935	−	2.64176i	0.356415	−	0.490563i	−0.592731	−	0.805401i	$-0.701950\pi$
$29$	1.91935	−	2.64176i	0.356415	−	0.490563i	0.949145	+	0.314838i	$0.101950\pi$
$30$	−1.65748	+	3.55903i	−0.302614	+	0.649787i
$31$	−1.35221	−	6.36165i	−0.242864	−	1.14259i	−0.915408	−	0.402528i	$-0.868131\pi$
$31$	−1.35221	−	6.36165i	−0.242864	−	1.14259i	0.672543	−	0.740058i	$-0.265202\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	−3.43778	+	4.60235i	−0.598441	+	0.801167i
$34$			0.658050i			0.112855i
$35$	−0.341793	+	5.98741i	−0.0577736	+	1.01206i
$36$	−2.69767	−	1.31248i	−0.449611	−	0.218746i
$37$	8.77550	−	3.90710i	1.44268	−	0.642324i	0.471762	−	0.881726i	$-0.343618\pi$
$37$	8.77550	−	3.90710i	1.44268	−	0.642324i	0.970921	+	0.239402i	$0.0769514\pi$
$38$	1.03359	−	1.14792i	0.167671	−	0.186217i
$39$	3.30788	−	1.01309i	0.529685	−	0.162224i
$40$	0.921955	+	2.07074i	0.145774	+	0.327413i
$41$	−1.18003	+	0.857341i	−0.184290	+	0.133894i	−0.676105	−	0.736805i	$-0.736333\pi$
$41$	−1.18003	+	0.857341i	−0.184290	+	0.133894i	0.491815	+	0.870699i	$0.336333\pi$
$42$	−4.57004	−	0.338746i	−0.705172	−	0.0522696i
$43$	9.77126			1.49010			0.745052	−	0.667007i	$-0.232425\pi$
$43$	9.77126			1.49010			0.745052	+	0.667007i	$0.232425\pi$
$44$	0.701657	+	3.24155i	0.105779	+	0.488683i
$45$	−3.59788	+	5.77036i	−0.536340	+	0.860195i
$46$	8.02458	−	1.70568i	1.18316	−	0.251488i
$47$	0.533188	+	5.07295i	0.0777735	+	0.739966i	0.962026	+	0.272957i	$0.0880017\pi$
$47$	0.533188	+	5.07295i	0.0777735	+	0.739966i	−0.884253	+	0.467009i	$0.845332\pi$
$48$	−1.59403	+	0.677546i	−0.230078	+	0.0977953i
$49$	−6.67728	+	2.10093i	−0.953897	+	0.300133i
$50$	0.131228	−	0.0426385i	0.0185584	−	0.00602999i
$51$	−0.138351	+	1.13135i	−0.0193730	+	0.158420i
$52$	0.812403	−	1.82469i	0.112660	−	0.253039i
$53$	0.775320	+	3.64759i	0.106498	+	0.501036i	0.998772	+	0.0495407i	$0.0157757\pi$
$53$	0.775320	+	3.64759i	0.106498	+	0.501036i	−0.892274	+	0.451495i	$0.850891\pi$
$54$	−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
$57$	2.01834	−	1.75625i	0.267335	−	0.232621i
$58$	−0.341327	−	3.24751i	−0.0448184	−	0.426419i
$59$	0.112023	−	1.06583i	0.0145841	−	0.138759i	−0.984807	−	0.173653i	$-0.944443\pi$
$59$	0.112023	−	1.06583i	0.0145841	−	0.138759i	0.999391	+	0.0348944i	$0.0111095\pi$
$60$	1.14970	+	3.75395i	0.148426	+	0.484633i
$61$	−2.37841	+	11.1896i	−0.304525	+	1.43268i	0.513795	+	0.857913i	$0.328239\pi$
$61$	−2.37841	+	11.1896i	−0.304525	+	1.43268i	−0.818320	+	0.574763i	$0.805094\pi$
$62$	−5.26166	−	3.82282i	−0.668232	−	0.485499i
$63$	−7.78579	−	1.54321i	−0.980917	−	0.194426i
$64$	−0.309017	+	0.951057i	−0.0386271	+	0.118882i
$65$	−3.92089	−	2.26373i	−0.486327	−	0.280781i
$66$	0.524804	+	5.72054i	0.0645990	+	0.704150i
$67$	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	$0.808888\pi$
$68$	0.440321	+	0.489027i	0.0533968	+	0.0593032i
$69$	14.1548	−	1.24536i	1.70404	−	0.149924i
$70$	3.75236	+	4.67821i	0.448492	+	0.559154i
$71$	−0.0302076	+	0.00981506i	−0.00358499	+	0.00116483i	−0.310809	−	0.950472i	$-0.600600\pi$
$71$	−0.0302076	+	0.00981506i	−0.00358499	+	0.00116483i	0.307224	+	0.951637i	$0.400600\pi$
$72$	−2.88298	+	0.829732i	−0.339762	+	0.0977848i
$73$	−7.27836	−	0.764986i	−0.851867	−	0.0895349i	−0.331477	−	0.943463i	$-0.607547\pi$
$73$	−7.27836	−	0.764986i	−0.851867	−	0.0895349i	−0.520390	+	0.853928i	$0.674214\pi$
$74$	3.90710	−	8.77550i	0.454192	−	1.02013i
$75$	0.234577	−	0.0457161i	0.0270866	−	0.00527885i
$76$		−	1.54468i		−	0.177187i
$77$	3.97644	+	7.82227i	0.453157	+	0.891430i
$78$	1.78035	−	2.96628i	0.201585	−	0.335865i
$79$	4.92022	+	5.46446i	0.553568	+	0.614799i	0.953371	−	0.301802i	$-0.0975881\pi$
$79$	4.92022	+	5.46446i	0.553568	+	0.614799i	−0.399803	+	0.916601i	$0.630921\pi$
$80$	2.07074	+	0.921955i	0.231516	+	0.103078i
$81$	−6.90570	−	5.77159i	−0.767300	−	0.641288i
$82$	−0.303259	+	1.42672i	−0.0334894	+	0.157555i
$83$	−1.74239	−	5.36253i	−0.191252	−	0.588614i	−1.00000		0.000458022i	$-0.999854\pi$
$83$	−1.74239	−	5.36253i	−0.191252	−	0.588614i	0.808748	−	0.588156i	$-0.200146\pi$
$84$	−3.62287	+	2.80622i	−0.395287	+	0.306183i
$85$	1.20674	−	0.876746i	0.130889	−	0.0950965i
$86$	7.26146	−	6.53825i	0.783023	−	0.705037i
$87$	0.0959430	−	5.65502i	0.0102862	−	0.606282i
$88$	2.69046	+	1.93944i	0.286804	+	0.206745i
$89$	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	$-0.165911\pi$
$90$	1.18738	+	6.69567i	0.125161	+	0.705785i
$91$	0.851017	−	5.21557i	0.0892108	−	0.546740i
$92$	4.82210	−	6.63706i	0.502739	−	0.691961i
$93$	−8.24236	−	7.67859i	−0.854693	−	0.796233i
$94$	3.79070	+	3.41316i	0.390981	+	0.352041i
$95$	−3.48216	−	0.365990i	−0.357262	−	0.0375498i
$96$	−0.731229	+	1.57013i	−0.0746307	+	0.160251i
$97$	−7.62438	−	2.47731i	−0.774138	−	0.251533i	−0.104803	−	0.994493i	$-0.533421\pi$
$97$	−7.62438	−	2.47731i	−0.774138	−	0.251533i	−0.669336	+	0.742960i	$0.733421\pi$
$98$	−3.55639	+	6.02927i	−0.359250	+	0.609048i
$99$	−0.300439	+	9.94534i	−0.0301953	+	0.999544i
$100$	0.0689905	−	0.119495i	0.00689905	−	0.0119495i
$101$	−8.81620	+	1.87394i	−0.877244	+	0.186464i	−0.624458	−	0.781058i	$-0.714680\pi$
$101$	−8.81620	+	1.87394i	−0.877244	+	0.186464i	−0.252786	+	0.967522i	$0.581347\pi$
$102$	0.654205	+	0.933330i	0.0647760	+	0.0924135i
$103$	3.34471	+	7.51234i	0.329564	+	0.740213i	0.999998	−	0.00175606i	$-0.000558972\pi$
$103$	3.34471	+	7.51234i	0.329564	+	0.740213i	−0.670435	+	0.741969i	$0.733892\pi$
$104$	−0.617221	−	1.89961i	−0.0605235	−	0.186272i
$105$	5.46765	+	8.83190i	0.533588	+	0.861905i
$106$	3.01689	+	2.19190i	0.293026	+	0.212896i
$107$	0.613485	−	0.0644799i	0.0593079	−	0.00623351i	−0.0748280	−	0.997196i	$-0.523841\pi$
$107$	0.613485	−	0.0644799i	0.0593079	−	0.00623351i	0.134136	+	0.990963i	$0.457174\pi$
$108$	−5.13098	+	0.820384i	−0.493729	+	0.0789415i
$109$	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	$0.551299\pi$
$110$	5.00954	−	5.60556i	0.477641	−	0.534469i
$111$	8.56225	−	14.2658i	0.812693	−	1.35405i
$112$	−0.150788	+	2.64145i	−0.0142481	+	0.249594i
$113$	1.34470	+	1.85082i	0.126499	+	0.174111i	0.867569	−	0.497317i	$-0.165681\pi$
$113$	1.34470	+	1.85082i	0.126499	+	0.174111i	−0.741070	+	0.671428i	$0.765681\pi$
$114$	0.324758	−	2.65568i	0.0304164	−	0.248727i
$115$	−13.8193	−	12.4430i	−1.28866	−	1.16032i
$116$	−2.42666	−	2.18498i	−0.225310	−	0.202870i
$117$	3.68449	−	4.72545i	0.340631	−	0.436868i
$118$	−0.629928	−	0.867021i	−0.0579895	−	0.0798158i
$119$	1.45572	+	0.955036i	0.133445	+	0.0875480i
$120$	3.36628	+	2.02042i	0.307298	+	0.184439i
$121$	8.85072	−	6.53183i	0.804611	−	0.593802i
$122$	5.71977	+	9.90693i	0.517844	+	0.896931i
$123$	−0.821335	+	2.38912i	−0.0740573	+	0.215420i
$124$	−6.46814	+	0.679829i	−0.580857	+	0.0610505i
$125$	8.91601	+	6.47786i	0.797472	+	0.579397i
$126$	−6.81858	+	4.06288i	−0.607447	+	0.361950i
$127$	5.71627	+	17.5929i	0.507237	+	1.56112i	0.796977	+	0.604010i	$0.206431\pi$
$127$	5.71627	+	17.5929i	0.507237	+	1.56112i	−0.289740	+	0.957105i	$0.593569\pi$
$128$	0.406737	+	0.913545i	0.0359508	+	0.0807468i
$129$	13.8588	−	9.71417i	1.22020	−	0.855285i
$130$	−4.42852	+	0.941311i	−0.388407	+	0.0825585i
$131$	−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	$0.270679\pi$
$132$	4.21779	+	3.90003i	0.367112	+	0.339454i
$133$	−1.03933	−	3.95247i	−0.0901213	−	0.342723i
$134$	1.19451	+	0.388121i	0.103190	+	0.0335286i
$135$	0.633674	+	11.7611i	0.0545380	+	1.01224i
$136$	0.654445	+	0.0687850i	0.0561182	+	0.00589826i
$137$	−12.3358	−	11.1072i	−1.05391	−	0.948949i	−0.0551419	−	0.998479i	$-0.517561\pi$
$137$	−12.3358	−	11.1072i	−1.05391	−	0.948949i	−0.998773	+	0.0495296i	$0.984228\pi$
$138$	9.68577	−	10.3969i	0.824507	−	0.885043i
$139$	−11.7444	+	16.1647i	−0.996145	+	1.37108i	−0.0684836	+	0.997652i	$0.521816\pi$
$139$	−11.7444	+	16.1647i	−0.996145	+	1.37108i	−0.927661	+	0.373423i	$0.878184\pi$
$140$	5.91888	+	0.965775i	0.500237	+	0.0816229i
$141$	5.79954	+	6.66503i	0.488410	+	0.561297i
$142$	−0.0158811	+	0.0275069i	−0.00133271	+	0.00230832i
$143$	−6.62448	+	0.0247020i	−0.553966	+	0.00206568i
$144$	−1.58727	+	2.54570i	−0.132272	+	0.212141i
$145$	−5.50055	+	4.95271i	−0.456796	+	0.411301i
$146$	−5.92075	+	4.30168i	−0.490005	+	0.356009i
$147$	−7.38191	+	9.61807i	−0.608850	+	0.793285i
$148$	−2.96841	−	9.13583i	−0.244002	−	0.750960i
$149$	0.706336	−	3.32305i	0.0578653	−	0.272235i	−0.939698	−	0.342006i	$-0.888894\pi$
$149$	0.706336	−	3.32305i	0.0578653	−	0.272235i	0.997563	+	0.0697714i	$0.0222270\pi$
$150$	0.143734	−	0.190936i	0.0117359	−	0.0155899i
$151$	0.606038	+	0.269826i	0.0493187	+	0.0219581i	0.431248	−	0.902234i	$-0.358073\pi$
$151$	0.606038	+	0.269826i	0.0493187	+	0.0219581i	−0.381929	+	0.924192i	$0.624740\pi$
$152$	−1.03359	−	1.14792i	−0.0838354	−	0.0931086i
$153$	0.928511	+	1.74216i	0.0750657	+	0.140846i
$154$	8.18919	+	3.15232i	0.659904	+	0.254021i
$155$			14.7422i			1.18412i
$156$	−0.661772	−	3.39566i	−0.0529842	−	0.271870i
$157$	0.529381	−	1.18901i	0.0422492	−	0.0948933i	−0.891188	−	0.453634i	$-0.850127\pi$
$157$	0.529381	−	1.18901i	0.0422492	−	0.0948933i	0.933437	+	0.358741i	$0.116794\pi$
$158$	7.31287	+	0.768614i	0.581781	+	0.0611476i
$159$	4.72594	+	4.40269i	0.374791	+	0.349156i
$160$	2.15577	−	0.700452i	0.170429	−	0.0553756i
$161$	7.87292	−	20.2272i	0.620473	−	1.59413i
$162$	−8.99389	+	0.331686i	−0.706626	+	0.0260597i
$163$	6.67739	+	7.41599i	0.523013	+	0.580865i	0.945548	−	0.325481i	$-0.105526\pi$
$163$	6.67739	+	7.41599i	0.523013	+	0.580865i	−0.422535	+	0.906347i	$0.638860\pi$
$164$	0.729298	+	1.26318i	0.0569486	+	0.0986379i
$165$	9.79116	−	8.58409i	0.762240	−	0.668271i
$166$	−4.88308	−	2.81925i	−0.379000	−	0.218816i
$167$	−7.30133	+	22.4712i	−0.564994	+	1.73887i	0.102977	+	0.994684i	$0.467163\pi$
$167$	−7.30133	+	22.4712i	−0.564994	+	1.73887i	−0.667970	+	0.744188i	$0.732837\pi$
$168$	−0.814589	+	4.50959i	−0.0628469	+	0.347923i
$169$	−7.28966	−	5.29625i	−0.560743	−	0.407404i
$170$	0.310123	−	1.45901i	0.0237854	−	0.111901i
$171$	1.11668	−	4.49748i	0.0853945	−	0.343931i
$172$	1.02137	−	9.71773i	0.0778791	−	0.740970i
$173$	−2.32793	−	22.1488i	−0.176989	−	1.68394i	−0.617796	−	0.786338i	$-0.711974\pi$
$173$	−2.32793	−	22.1488i	−0.176989	−	1.68394i	0.440807	−	0.897602i	$-0.354692\pi$
$174$	−3.71265	−	4.26670i	−0.281455	−	0.323458i
$175$	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
$178$	−3.39264	−	15.9611i	−0.254289	−	1.19634i
$179$	−0.399912	+	0.898217i	−0.0298908	+	0.0671359i	−0.927874	−	0.372894i	$-0.878365\pi$
$179$	−0.399912	+	0.898217i	−0.0298908	+	0.0671359i	0.897983	+	0.440030i	$0.145032\pi$
$180$	5.36267	+	4.18134i	0.399710	+	0.311659i
$181$	17.5136	−	5.69051i	1.30177	−	0.422972i	0.425576	−	0.904923i	$-0.360071\pi$
$181$	17.5136	−	5.69051i	1.30177	−	0.422972i	0.876199	+	0.481950i	$0.160071\pi$
$182$	−2.85747	−	4.44536i	−0.211810	−	0.329512i
$183$	7.75081	+	18.2350i	0.572956	+	1.34797i
$184$	−0.857536	−	8.15891i	−0.0632184	−	0.601483i
$185$	−21.2982	+	4.52706i	−1.56587	+	0.332836i
$186$	−11.2632	−	0.191092i	−0.825861	−	0.0140116i
$187$	0.880264	−	1.99711i	0.0643713	−	0.146043i
$188$	5.10089			0.372021
$189$	−12.5770	+	5.55153i	−0.914841	+	0.403814i
$190$	−2.83264	+	2.05804i	−0.205502	+	0.149306i
$191$	−9.20070	−	20.6651i	−0.665740	−	1.49528i	−0.857849	−	0.513902i	$-0.828199\pi$
$191$	−9.20070	−	20.6651i	−0.665740	−	1.49528i	0.192109	−	0.981374i	$-0.438467\pi$
$192$	0.507212	+	1.65612i	0.0366049	+	0.119520i
$193$	16.2911	−	18.0931i	1.17266	−	1.30237i	0.228251	−	0.973602i	$-0.426699\pi$
$193$	16.2911	−	18.0931i	1.17266	−	1.30237i	0.944410	−	0.328770i	$-0.106634\pi$
$194$	−7.32366	+	3.26070i	−0.525808	+	0.234105i
$195$	−7.81161	+	0.687276i	−0.559401	+	0.0492169i
$196$	1.39146	+	6.86031i	0.0993897	+	0.490022i
$197$		−	10.9108i		−	0.777361i	−0.921373	−	0.388680i	$-0.872931\pi$
$197$		−	10.9108i		−	0.777361i	0.921373	−	0.388680i	$-0.127069\pi$
$198$	6.43146	+	7.59186i	0.457064	+	0.539530i
$199$	−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	$0.522977\pi$
$200$	−0.0286879	−	0.134966i	−0.00202854	−	0.00954352i
$201$	1.97206	+	0.918413i	0.139098	+	0.0647799i
$202$	−5.29780	+	7.29180i	−0.372752	+	0.513049i
$203$	−7.67941	−	3.95808i	−0.538989	−	0.277802i
$204$	1.11069	+	0.255851i	0.0777638	+	0.0179131i
$205$	3.02038	−	1.34476i	0.210952	−	0.0939221i
$206$	7.51234	+	3.34471i	0.523409	+	0.233037i
$207$	18.8381	−	15.8384i	1.30934	−	1.10085i
$208$	−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	0.772801	+	0.634649i	$0.218855\pi$
$211$	−3.27478	+	10.0787i	−0.225445	+	0.693849i	−0.998246	+	0.0592005i	$0.981145\pi$
$212$	3.70865	−	0.389795i	0.254711	−	0.0267713i
$213$	−0.0330866	+	0.0439521i	−0.00226706	+	0.00301155i
$214$	0.412763	−	0.458420i	0.0282159	−	0.0313369i
$215$	−21.6646	−	4.60496i	−1.47752	−	0.314056i
$216$	−3.26412	+	4.04296i	−0.222095	+	0.275089i
$217$	−16.0930	+	6.09158i	−1.09247	+	0.413524i
$218$	15.3819	+	4.99789i	1.04180	+	0.338500i
$219$	−11.0836	+	6.15083i	−0.748961	+	0.415635i
$220$	−0.0280330	−	7.51778i	−0.00188999	−	0.506849i
$221$	−1.13828	+	0.657184i	−0.0765688	+	0.0442070i
$222$	−3.18267	−	16.3308i	−0.213607	−	1.09605i
$223$	−15.4910	−	21.3216i	−1.03736	−	1.42780i	−0.899279	−	0.437376i	$-0.855908\pi$
$223$	−15.4910	−	21.3216i	−1.03736	−	1.42780i	−0.138077	−	0.990421i	$-0.544092\pi$
$224$	1.65542	+	2.06388i	0.110607	+	0.137899i
$225$	0.287258	−	0.298047i	0.0191505	−	0.0198698i
$226$	2.23775	+	0.475648i	0.148853	+	0.0316397i
$227$	−0.484673	+	4.61136i	−0.0321689	+	0.306067i	0.966593	+	0.256317i	$0.0825090\pi$
$227$	−0.484673	+	4.61136i	−0.0321689	+	0.306067i	−0.998762	+	0.0497498i	$0.984158\pi$
$228$	−1.53565	−	2.19086i	−0.101701	−	0.145093i
$229$	13.8399	−	12.4615i	0.914564	−	0.823477i	−0.0701711	−	0.997535i	$-0.522355\pi$
$229$	13.8399	−	12.4615i	0.914564	−	0.823477i	0.984735	+	0.174057i	$0.0556879\pi$
$230$	−18.5958			−1.22617
$231$	13.4165	+	7.14133i	0.882738	+	0.469865i
$232$	−3.26540			−0.214384
$233$	−11.4642	+	10.3224i	−0.751044	+	0.676243i	−0.952938	−	0.303165i	$-0.901957\pi$
$233$	−11.4642	+	10.3224i	−0.751044	+	0.676243i	0.201895	+	0.979407i	$0.435290\pi$
$234$	−0.423833	−	5.97710i	−0.0277068	−	0.390735i
$235$	1.20858	−	11.4989i	0.0788394	−	0.750106i
$236$	−1.04828	−	0.222818i	−0.0682371	−	0.0145042i
$237$	12.4110	+	2.85892i	0.806182	+	0.185707i
$238$	1.72085	−	0.264336i	0.111546	−	0.0171343i
$239$	13.0381	+	17.9453i	0.843361	+	1.16079i	0.985287	+	0.170910i	$0.0546707\pi$
$239$	13.0381	+	17.9453i	0.843361	+	1.16079i	−0.141925	+	0.989877i	$0.545329\pi$
$240$	3.85356	−	0.751012i	0.248746	−	0.0484776i
$241$	−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	$0.588111\pi$
$242$	2.20672	−	10.7764i	0.141854	−	0.692732i
$243$	−15.5324	−	1.32066i	−0.996405	−	0.0847201i
$244$	10.8796	+	3.53501i	0.696498	+	0.226306i
$245$	15.7948	−	1.51130i	1.00910	−	0.0965533i
$246$	0.988265	+	2.32505i	0.0630095	+	0.148240i
$247$	3.01787	+	0.641468i	0.192023	+	0.0408157i
$248$	−4.35187	+	4.83325i	−0.276344	+	0.306911i
$249$	−7.80247	−	5.87361i	−0.494462	−	0.372225i
$250$	10.9604	−	1.15199i	0.693198	−	0.0728580i
$251$	3.44299	−	10.5964i	0.217320	−	0.668841i	−0.781661	−	0.623703i	$-0.785627\pi$
$251$	3.44299	−	10.5964i	0.217320	−	0.668841i	0.998981	−	0.0451375i	$-0.0143726\pi$
$252$	−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
$255$	0.839925	−	2.44320i	0.0525982	−	0.152999i
$256$	0.913545	+	0.406737i	0.0570966	+	0.0254210i
$257$	−9.26911	+	4.12688i	−0.578191	+	0.257427i	−0.674929	−	0.737882i	$-0.735826\pi$
$257$	−9.26911	+	4.12688i	−0.578191	+	0.257427i	0.0967378	+	0.995310i	$0.469159\pi$
$258$	3.79908	−	16.4924i	0.236520	−	1.02677i
$259$	−13.7425	−	21.3792i	−0.853915	−	1.32844i
$260$	−2.66117	+	3.66279i	−0.165039	+	0.227157i
$261$	−5.48590	−	8.11605i	−0.339569	−	0.502371i
$262$	1.52765	+	7.18701i	0.0943783	+	0.444015i
$263$	−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	$0.476332\pi$
$264$	5.74406	+	0.0760299i	0.353522	+	0.00467931i
$265$		−	8.45276i		−	0.519249i
$266$	−3.41709	−	2.24181i	−0.209515	−	0.137454i
$267$	−2.47706	−	28.1543i	−0.151593	−	1.72302i
$268$	1.14740	−	0.510856i	0.0700886	−	0.0312055i
$269$	5.02852	−	5.58473i	0.306594	−	0.340507i	−0.570082	−	0.821587i	$-0.693089\pi$
$269$	5.02852	−	5.58473i	0.306594	−	0.340507i	0.876677	+	0.481080i	$0.159755\pi$
$270$	8.34064	+	8.31620i	0.507595	+	0.506108i
$271$	−3.01573	−	6.77345i	−0.183193	−	0.411458i	0.798483	−	0.602018i	$-0.205636\pi$
$271$	−3.01573	−	6.77345i	−0.183193	−	0.411458i	−0.981676	+	0.190560i	$0.938970\pi$
$272$	0.532374	−	0.386792i	0.0322799	−	0.0234527i
$273$	−3.97807	−	8.24342i	−0.240764	−	0.498915i
$274$	−16.5994			−1.00281
$275$	−0.455299	−	0.0461380i	−0.0274556	−	0.00278223i
$276$	0.241043	−	14.2074i	0.0145091	−	0.855188i
$277$	−2.47806	+	0.526727i	−0.148892	+	0.0316480i	−0.281755	−	0.959486i	$-0.590916\pi$
$277$	−2.47806	+	0.526727i	−0.148892	+	0.0316480i	0.132863	+	0.991134i	$0.457583\pi$
$278$	2.08855	+	19.8713i	0.125263	+	1.19180i
$279$	−19.3241	−	2.69656i	−1.15690	−	0.161439i
$280$	5.04482	−	3.24279i	0.301485	−	0.193794i
$281$	14.8499	−	4.82503i	0.885872	−	0.287837i	0.169478	−	0.985534i	$-0.445792\pi$
$281$	14.8499	−	4.82503i	0.885872	−	0.287837i	0.716393	+	0.697697i	$0.245792\pi$
$282$	8.76968	+	1.07243i	0.522227	+	0.0638622i
$283$	6.19872	−	13.9226i	0.368476	−	0.827610i	−0.630213	−	0.776422i	$-0.717033\pi$
$283$	6.19872	−	13.9226i	0.368476	−	0.827610i	0.998689	−	0.0511881i	$-0.0163008\pi$
$284$	0.00660373	+	0.0310681i	0.000391859	+	0.00184355i
$285$	−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
$288$	0.523833	+	2.95391i	0.0308672	+	0.174061i
$289$	1.73172	+	16.4762i	0.101866	+	0.969189i
$290$	−0.773690	+	7.36117i	−0.0454326	+	0.432263i
$291$	−13.2767	+	4.06619i	−0.778294	+	0.238364i
$292$	−1.52159	+	7.15852i	−0.0890444	+	0.418921i
$293$	14.9312	+	10.8482i	0.872293	+	0.633758i	0.931201	−	0.364505i	$-0.118762\pi$
$293$	14.9312	+	10.8482i	0.872293	+	0.633758i	−0.0589083	+	0.998263i	$0.518762\pi$
$294$	0.949917	+	12.0871i	0.0554003	+	0.704933i
$295$	−0.750673	+	2.31033i	−0.0437059	+	0.134513i
$296$	−8.31902	−	4.80299i	−0.483533	−	0.279168i
$297$	9.46111	+	14.4044i	0.548989	+	0.835829i
$298$	−1.69864	−	2.94214i	−0.0983998	−	0.170433i
$299$	10.9645	+	12.1773i	0.634091	+	0.704229i
$300$	−0.0209458	−	0.238070i	−0.00120930	−	0.0137450i
$301$	−3.92507	−	25.5526i	−0.226237	−	1.47283i
$302$	0.630923	−	0.204999i	0.0363055	−	0.0117964i
$303$	−10.6413	+	11.4225i	−0.611324	+	0.656208i
$304$	−1.53622	−	0.161463i	−0.0881081	−	0.00926053i
$305$	10.5467	−	23.6884i	0.603904	−	1.35639i
$306$	1.85575	+	0.673385i	0.106086	+	0.0384948i
$307$			20.3454i			1.16117i	0.814199	+	0.580586i	$0.197176\pi$
$307$			20.3454i			1.16117i	−0.814199	+	0.580586i	$0.802824\pi$
$308$	8.19507	−	3.13701i	0.466957	−	0.178748i
$309$	12.2123	+	7.32979i	0.694735	+	0.416977i
$310$	9.86444	+	10.9556i	0.560263	+	0.622235i
$311$	−7.76498	−	3.45719i	−0.440312	−	0.196039i	0.174593	−	0.984641i	$-0.444139\pi$
$311$	−7.76498	−	3.45719i	−0.440312	−	0.196039i	−0.614905	+	0.788601i	$0.710806\pi$
$312$	−2.76393	−	2.08065i	−0.156477	−	0.117794i
$313$	−4.97135	+	23.3884i	−0.280997	+	1.32199i	0.580514	+	0.814250i	$0.302852\pi$
$313$	−4.97135	+	23.3884i	−0.280997	+	1.32199i	−0.861511	+	0.507738i	$0.830482\pi$
$314$	−0.402196	−	1.23783i	−0.0226972	−	0.0698549i
$315$	16.5352	+	7.09082i	0.931653	+	0.399522i
$316$	5.94882	−	4.32207i	0.334648	−	0.243136i
$317$	−20.5296	+	18.4849i	−1.15306	+	1.03822i	−0.154318	+	0.988021i	$0.549318\pi$
$317$	−20.5296	+	18.4849i	−1.15306	+	1.03822i	−0.998739	+	0.0501968i	$0.984015\pi$
$318$	6.45803	+	0.109567i	0.362148	+	0.00614421i
$319$	−3.30825	+	10.3124i	−0.185227	+	0.577386i
$320$	1.13336	−	1.96303i	0.0633565	−	0.109737i
$321$	0.806020	−	0.701355i	0.0449876	−	0.0391458i
$322$	−7.68392	−	20.2998i	−0.428208	−	1.13126i
$323$	−0.597470	+	0.822346i	−0.0332441	+	0.0457566i
$324$	−6.46182	+	6.26457i	−0.358990	+	0.348032i
$325$	0.204810	+	0.184412i	0.0113608	+	0.0102293i
$326$	9.92453	+	1.04311i	0.549669	+	0.0577725i
$327$	25.3945	+	11.8265i	1.40432	+	0.654009i
$328$	1.38721	+	0.450731i	0.0765957	+	0.0248875i
$329$	13.0520	−	3.43211i	0.719579	−	0.189218i
$330$	1.53237	−	12.9308i	0.0843540	−	0.711816i
$331$	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	$-0.0121540\pi$
$332$	−5.51528	+	1.17231i	−0.302690	+	0.0643388i
$333$	−2.03835	−	28.7458i	−0.111701	−	1.57526i
$334$	9.61021	+	21.5849i	0.525847	+	1.18107i
$335$	−0.879759	−	2.70762i	−0.0480663	−	0.147933i
$336$	2.41215	+	3.89635i	0.131594	+	0.212563i
$337$	−6.72297	−	4.88452i	−0.366223	−	0.266077i	0.389420	−	0.921060i	$-0.372676\pi$
$337$	−6.72297	−	4.88452i	−0.366223	−	0.266077i	−0.755643	+	0.654983i	$0.772676\pi$
$338$	−8.96116	+	0.941856i	−0.487423	+	0.0512302i
$339$	3.74723	+	1.28823i	0.203522	+	0.0699669i
$340$	−0.745805	−	1.29177i	−0.0404469	−	0.0700562i
$341$	10.8549	+	18.6403i	0.587824	+	1.00943i
$342$	−2.17955	−	4.08948i	−0.117856	−	0.221134i
$343$	8.17634	+	16.6177i	0.441481	+	0.897271i
$344$	−5.74340	−	7.90511i	−0.309663	−	0.426215i
$345$	−31.9707	−	3.90964i	−1.72124	−	0.210488i
$346$	−16.5504	−	14.9021i	−0.889756	−	0.801140i
$347$	6.99637	+	6.29956i	0.375585	+	0.338178i	0.835206	−	0.549937i	$-0.185348\pi$
$347$	6.99637	+	6.29956i	0.375585	+	0.338178i	−0.459622	+	0.888115i	$0.652015\pi$
$348$	−5.61401	−	0.686528i	−0.300943	−	0.0368018i
$349$	−8.94246	−	12.3082i	−0.478679	−	0.658845i	0.499572	−	0.866273i	$-0.333491\pi$
$349$	−8.94246	−	12.3082i	−0.478679	−	0.658845i	−0.978250	+	0.207428i	$0.933491\pi$
$350$	−0.164217	−	0.326043i	−0.00877774	−	0.0174277i
$351$	0.527973	−	10.3652i	0.0281811	−	0.553253i
$352$	2.21005	−	2.47299i	0.117796	−	0.131811i
$353$	−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	$-0.342350\pi$
$354$	−1.75540	−	0.603472i	−0.0932984	−	0.0320742i
$355$	0.0716013	−	0.00752560i	0.00380020	−	0.000399417i
$356$	−13.2013	−	9.59130i	−0.699667	−	0.508338i
$357$	3.01414	−	0.0926595i	0.159525	−	0.00490406i
$358$	0.303832	+	0.935099i	0.0160580	+	0.0494215i
$359$	1.81505	+	4.07668i	0.0957949	+	0.215159i	0.955086	−	0.296327i	$-0.0957619\pi$
$359$	1.81505	+	4.07668i	0.0957949	+	0.215159i	−0.859292	+	0.511486i	$0.829095\pi$
$360$	6.78310	−	0.480987i	0.357501	−	0.0253502i
$361$	−16.2509	+	3.45424i	−0.855311	+	0.181802i
$362$	9.20744	−	15.9478i	0.483932	−	0.838195i
$363$	6.05956	−	18.0633i	0.318044	−	0.948076i
$364$	−5.09804	−	1.39153i	−0.267210	−	0.0729360i
$365$	15.7769	+	5.12623i	0.825801	+	0.268319i
$366$	17.9615	+	8.36492i	0.938865	+	0.437241i
$367$	1.49462	+	0.157091i	0.0780184	+	0.00820006i	0.143457	−	0.989657i	$-0.454178\pi$
$367$	1.49462	+	0.157091i	0.0780184	+	0.00820006i	−0.0654388	+	0.997857i	$0.520845\pi$
$368$	−6.09665	−	5.48945i	−0.317810	−	0.286157i
$369$	1.21024	+	4.20510i	0.0630027	+	0.218909i
$370$	−12.7984	+	17.6155i	−0.665358	+	0.915787i
$371$	9.22731	−	3.49275i	0.479058	−	0.181334i
$372$	−8.49809	+	7.39457i	−0.440605	+	0.383391i
$373$	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	$0.158394\pi$
$374$	−0.682166	−	2.07316i	−0.0352740	−	0.107200i
$375$	19.0858	+	0.323810i	0.985588	+	0.0167215i
$376$	3.79070	−	3.41316i	0.195491	−	0.176020i
$377$	5.27657	−	3.83365i	0.271757	−	0.197443i
$378$	−5.63182	+	12.5412i	−0.289670	+	0.645051i
$379$	4.17801	+	12.8586i	0.214610	+	0.660501i	0.999181	+	0.0404625i	$0.0128831\pi$
$379$	4.17801	+	12.8586i	0.214610	+	0.660501i	−0.784571	+	0.620039i	$0.787117\pi$
$380$	−0.727970	+	3.42483i	−0.0373441	+	0.175690i
$381$	25.5976	+	19.2696i	1.31141	+	0.987210i
$382$	−20.6651	−	9.20070i	−1.05732	−	0.470749i
$383$	2.65189	+	2.94522i	0.135505	+	0.150494i	0.807078	−	0.590445i	$-0.201048\pi$
$383$	2.65189	+	2.94522i	0.135505	+	0.150494i	−0.671573	+	0.740938i	$0.734381\pi$
$384$	1.48509	+	0.891346i	0.0757858	+	0.0454863i
$385$	−5.13003	−	19.2174i	−0.261451	−	0.979408i
$386$		−	24.3467i		−	1.23922i
$387$	9.99896	−	27.5557i	0.508276	−	1.40074i
$388$	−3.26070	+	7.32366i	−0.165537	+	0.371803i
$389$	13.8026	+	1.45071i	0.699819	+	0.0735539i	0.447754	−	0.894157i	$-0.352224\pi$
$389$	13.8026	+	1.45071i	0.699819	+	0.0735539i	0.252064	+	0.967710i	$0.418891\pi$
$390$	−5.34528	+	5.73773i	−0.270669	+	0.290541i
$391$	−5.13432	+	1.66824i	−0.259654	+	0.0843667i
$392$	5.62450	+	4.16714i	0.284080	+	0.210472i
$393$	1.11538	+	12.6774i	0.0562632	+	0.639490i
$394$	−7.30073	−	8.10829i	−0.367806	−	0.408490i
$395$	−8.33374	−	14.4345i	−0.419316	−	0.726276i
$396$	9.85945	+	1.33836i	0.495456	+	0.0672553i
$397$	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
$399$	−5.40349	−	4.57264i	−0.270513	−	0.228918i
$400$	−0.111629	−	0.0811032i	−0.00558145	−	0.00405516i
$401$	7.42319	−	34.9234i	0.370697	−	1.74399i	−0.257819	−	0.966193i	$-0.583004\pi$
$401$	7.42319	−	34.9234i	0.370697	−	1.74399i	0.628516	−	0.777797i	$-0.283663\pi$
$402$	2.08006	−	0.637052i	0.103744	−	0.0317733i
$403$	1.35787	−	12.9193i	0.0676403	−	0.643555i
$404$	0.942131	+	8.96378i	0.0468728	+	0.445965i
$405$	12.5912	+	16.0511i	0.625660	+	0.797588i
$406$	−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
$409$	1.78349	+	8.39068i	0.0881881	+	0.414892i	0.999991	+	0.00426401i	$0.00135728\pi$
$409$	1.78349	+	8.39068i	0.0881881	+	0.414892i	−0.911803	+	0.410628i	$0.865309\pi$
$410$	1.34476	−	3.02038i	0.0664129	−	0.149166i
$411$	−28.5384	−	3.48991i	−1.40770	−	0.172145i
$412$	7.82080	−	2.54113i	0.385303	−	0.125193i
$413$	−2.83222	+	0.135189i	−0.139364	+	0.00665221i
$414$	3.40143	−	24.3754i	0.167171	−	1.19798i
$415$	1.33596	+	12.7108i	0.0655798	+	0.623950i
$416$	−1.95372	+	0.415276i	−0.0957891	+	0.0203606i
$417$	−0.587068	+	34.6026i	−0.0287489	+	1.69450i
$418$	−2.06629	+	4.68794i	−0.101066	+	0.229295i
$419$	31.3649			1.53228			0.766138	−	0.642677i	$-0.222176\pi$
$419$	31.3649			1.53228			0.766138	+	0.642677i	$0.222176\pi$
$420$	9.35504	−	4.51451i	0.456479	−	0.220286i
$421$	21.7386	−	15.7940i	1.05947	−	0.769753i	0.0854826	−	0.996340i	$-0.472757\pi$
$421$	21.7386	−	15.7940i	1.05947	−	0.769753i	0.973991	+	0.226587i	$0.0727568\pi$
$422$	4.31036	+	9.68122i	0.209825	+	0.471274i
$423$	14.8517	+	3.68753i	0.722116	+	0.179294i
$424$	2.49524	−	2.77125i	0.121180	−	0.134584i
$425$	−0.0829485	+	0.0369310i	−0.00402359	+	0.00179142i
$426$	0.00482156	+	0.0548020i	0.000233605	+	0.00265517i
$427$	30.2170	+	1.72495i	1.46230	+	0.0834760i
$428$		−	0.616865i		−	0.0298173i
$429$	−9.37111	+	6.62080i	−0.452442	+	0.319655i
$430$	−19.1813	+	11.0743i	−0.925003	+	0.534051i
$431$	7.55880	+	35.5614i	0.364095	+	1.71293i	0.654531	+	0.756036i	$0.272866\pi$
$431$	7.55880	+	35.5614i	0.364095	+	1.71293i	−0.290436	+	0.956894i	$0.593800\pi$
$432$	0.279556	+	5.18863i	0.0134502	+	0.249638i
$433$	−0.0880414	+	0.121179i	−0.00423100	+	0.00582347i	−0.811127	−	0.584870i	$-0.801146\pi$
$433$	−0.0880414	+	0.121179i	−0.00423100	+	0.00582347i	0.806896	+	0.590693i	$0.201146\pi$
$434$	−7.88340	+	15.2953i	−0.378415	+	0.734197i
$435$	−2.87780	+	12.4930i	−0.137980	+	0.598992i
$436$	14.7752	−	6.57836i	0.707606	−	0.315046i
$437$	11.5767	+	5.15430i	0.553791	+	0.246563i
$438$	−4.12102	+	11.9873i	−0.196910	+	0.572777i
$439$	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
$443$	−19.2482	+	2.02306i	−0.914508	+	0.0961186i	−0.550079	−	0.835113i	$-0.685402\pi$
$443$	−19.2482	+	2.02306i	−0.914508	+	0.0961186i	−0.364429	+	0.931231i	$0.618736\pi$
$444$	−13.2926	−	10.0065i	−0.630840	−	0.474889i
$445$	−24.7495	+	27.4871i	−1.17324	+	1.30301i
$446$	−25.7790	−	5.47949i	−1.22067	−	0.259462i
$447$	−2.30182	−	5.41538i	−0.108872	−	0.256139i
$448$	2.61122	+	0.426069i	0.123369	+	0.0201299i
$449$	−6.09453	−	1.98023i	−0.287619	−	0.0934530i	0.161654	−	0.986847i	$-0.448317\pi$
$449$	−6.09453	−	1.98023i	−0.287619	−	0.0934530i	−0.449273	+	0.893394i	$0.648317\pi$
$450$	0.0140419	−	0.413705i	0.000661940	−	0.0195022i
$451$	2.82887	−	3.92429i	0.133206	−	0.184788i
$452$	1.98124	−	1.14387i	0.0931898	−	0.0538032i
$453$	1.12781	−	0.219796i	0.0529891	−	0.0103269i
$454$	2.72542	+	3.75122i	0.127910	+	0.176053i
$455$	−4.34483	+	11.1628i	−0.203689	+	0.523319i
$456$	−2.60718	−	0.600573i	−0.122093	−	0.0281244i
$457$	−6.67684	−	1.41921i	−0.312329	−	0.0663876i	0.0490802	−	0.998795i	$-0.484371\pi$
$457$	−6.67684	−	1.41921i	−0.312329	−	0.0663876i	−0.361409	+	0.932407i	$0.617704\pi$
$458$	1.94667	−	18.5214i	0.0909621	−	0.865446i
$459$	3.04892	+	1.54787i	0.142311	+	0.0722485i
$460$	−13.8193	+	12.4430i	−0.644330	+	0.580158i
$461$	18.1166			0.843773			0.421886	−	0.906649i	$-0.361368\pi$
$461$	18.1166			0.843773			0.421886	+	0.906649i	$0.361368\pi$
$462$	14.7489	−	3.67032i	0.686179	−	0.170759i
$463$	13.7420			0.638647			0.319323	−	0.947646i	$-0.396544\pi$
$463$	13.7420			0.638647			0.319323	+	0.947646i	$0.396544\pi$
$464$	−2.42666	+	2.18498i	−0.112655	+	0.101435i
$465$	14.6560	+	20.9092i	0.679658	+	0.969642i
$466$	−1.61252	+	15.3421i	−0.0746984	+	0.710708i
$467$	22.6987	+	4.82475i	1.05037	+	0.223263i	0.700586	−	0.713568i	$-0.252922\pi$
$467$	22.6987	+	4.82475i	1.05037	+	0.223263i	0.349783	+	0.936831i	$0.386255\pi$
$468$	−4.31443	−	4.15825i	−0.199434	−	0.192215i
$469$	2.59220	−	2.07918i	0.119697	−	0.0960077i
$470$	−6.79612	−	9.35406i	−0.313482	−	0.431471i
$471$	−0.431227	−	2.21269i	−0.0198699	−	0.101955i
$472$	−0.928117	+	0.535848i	−0.0427200	+	0.0246644i
$473$	−30.7839	+	10.1294i	−1.41545	+	0.465748i
$474$	11.1362	−	6.18000i	0.511501	−	0.283857i
$475$	0.202705	+	0.0658627i	0.00930073	+	0.00302199i
$476$	1.10197	−	1.34792i	0.0505086	−	0.0617816i
$477$	11.0799	+	1.54613i	0.507313	+	0.0707924i
$478$	21.6969	+	4.61183i	0.992395	+	0.210940i
$479$	10.9029	−	12.1089i	0.498165	−	0.553269i	−0.440655	−	0.897677i	$-0.645254\pi$
$479$	10.9029	−	12.1089i	0.498165	−	0.553269i	0.938820	+	0.344408i	$0.111920\pi$
$480$	2.36123	−	3.13665i	0.107775	−	0.143168i
$481$	19.0816	−	2.00555i	0.870045	−	0.0914454i
$482$	−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
$486$	−12.4265	+	9.41177i	−0.563679	+	0.426927i
$487$	−6.81486	−	3.03417i	−0.308811	−	0.137491i	0.246480	−	0.969148i	$-0.420726\pi$
$487$	−6.81486	−	3.03417i	−0.308811	−	0.137491i	−0.555290	+	0.831657i	$0.687393\pi$
$488$	10.4505	−	4.65288i	0.473074	−	0.210626i
$489$	16.8434	+	3.87993i	0.761684	+	0.175456i
$490$	10.7266	−	11.6919i	0.484578	−	0.528187i
$491$	−11.5506	+	15.8981i	−0.521273	+	0.717471i	−0.985769	−	0.168104i	$-0.946236\pi$
$491$	−11.5506	+	15.8981i	−0.521273	+	0.717471i	0.464496	+	0.885575i	$0.346236\pi$
$492$	2.29018	+	1.06657i	0.103249	+	0.0480846i
$493$	0.446760	+	2.10184i	0.0201210	+	0.0946621i
$494$	2.67194	−	1.54265i	0.120216	−	0.0694069i
$495$	5.35312	−	21.9090i	0.240605	−	0.984736i
$496$			6.50377i			0.292028i
$497$	0.0378014	+	0.0750527i	0.00169563	+	0.00336657i
$498$	−9.72858	+	0.855933i	−0.435948	+	0.0383553i
$499$	−26.8679	+	11.9624i	−1.20277	+	0.535509i	−0.907560	−	0.419922i	$-0.862057\pi$
$499$	−26.8679	+	11.9624i	−1.20277	+	0.535509i	−0.295213	+	0.955431i	$0.595391\pi$
$500$	7.37435	−	8.19005i	0.329791	−	0.366270i
$501$	11.9842	+	39.1301i	0.535415	+	1.74821i
$502$	−4.53176	−	10.1785i	−0.202262	−	0.454288i
$503$	17.2348	−	12.5218i	0.768462	−	0.558320i	−0.133032	−	0.991112i	$-0.542471\pi$
$503$	17.2348	−	12.5218i	0.768462	−	0.558320i	0.901494	+	0.432792i	$0.142471\pi$
$504$	3.32789	+	7.20591i	0.148236	+	0.320977i
$505$	20.4302			0.909133
$506$	−23.5129	+	13.6923i	−1.04528	+	0.608698i
$507$	−15.6044	−	0.264745i	−0.693017	−	0.0117577i
$508$	18.0940	−	3.84600i	0.802792	−	0.170639i
$509$	0.741346	+	7.05344i	0.0328596	+	0.312638i	0.998590	+	0.0530900i	$0.0169070\pi$
$509$	0.741346	+	7.05344i	0.0328596	+	0.312638i	−0.965730	+	0.259548i	$0.916426\pi$
$510$	−1.01063	−	2.37767i	−0.0447516	−	0.105285i
$511$	0.923183	+	19.3408i	0.0408392	+	0.855586i
$512$	0.951057	−	0.309017i	0.0420312	−	0.0136568i
$513$	−2.88739	−	7.48905i	−0.127481	−	0.330650i
$514$	−4.12688	+	9.26911i	−0.182029	+	0.408843i
$515$	−3.87543	−	18.2325i	−0.170772	−	0.803419i
$516$	−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
$519$	−25.3211	−	29.0999i	−1.11147	−	1.27734i
$520$	0.473248	+	4.50266i	0.0207533	+	0.197455i
$521$	−0.778982	+	7.41151i	−0.0341278	+	0.324704i	0.964117	+	0.265478i	$0.0855299\pi$
$521$	−0.778982	+	7.41151i	−0.0341278	+	0.324704i	−0.998245	+	0.0592259i	$0.981137\pi$
$522$	−9.50752	−	2.36062i	−0.416133	−	0.103321i
$523$	−2.26472	+	10.6547i	−0.0990293	+	0.465896i	0.900490	+	0.434878i	$0.143208\pi$
$523$	−2.26472	+	10.6547i	−0.0990293	+	0.465896i	−0.999519	+	0.0310184i	$0.990125\pi$
$524$	5.94431	+	4.31880i	0.259679	+	0.188668i
$525$	−0.213780	−	0.595073i	−0.00933011	−	0.0259711i
$526$	−4.35275	+	13.3964i	−0.189789	+	0.584110i
$527$	3.70642	+	2.13990i	0.161454	+	0.0932157i
$528$	4.31954	−	3.78702i	0.187984	−	0.164809i
$529$	22.1516	+	38.3677i	0.963113	+	1.66816i
$530$	−5.65600	−	6.28162i	−0.245681	−	0.272856i
$531$	−2.89108	−	1.40658i	−0.125462	−	0.0610402i
$532$	−4.03946	+	0.620490i	−0.175133	+	0.0269017i
$533$	−2.77076	+	0.900276i	−0.120015	+	0.0389953i
$534$	−20.6797	−	19.2653i	−0.894899	−	0.833689i
$535$	−1.39059	−	0.146157i	−0.0601206	−	0.00631893i
$536$	0.510856	−	1.14740i	0.0220656	−	0.0495602i
$537$	0.325763	+	1.67154i	0.0140577	+	0.0721323i
$538$		−	7.51500i		−	0.323995i
$539$	18.8585	−	13.5409i	0.812295	−	0.583247i
$540$	11.7629	+	0.599169i	0.506196	+	0.0257841i
$541$	12.0491	+	13.3818i	0.518029	+	0.575330i	0.944225	−	0.329301i	$-0.106813\pi$
$541$	12.0491	+	13.3818i	0.518029	+	0.575330i	−0.426195	+	0.904631i	$0.640146\pi$
$542$	−6.77345	−	3.01573i	−0.290944	−	0.129537i
$543$	19.1827	−	25.4823i	0.823210	−	1.09355i
$544$	0.136816	−	0.643670i	0.00586595	−	0.0275971i
$545$	−11.3288	−	34.8664i	−0.485271	−	1.49351i
$546$	−8.47221	−	3.46421i	−0.362577	−	0.148254i
$547$	−7.71964	+	5.60865i	−0.330068	+	0.239808i	−0.740460	−	0.672101i	$-0.765392\pi$
$547$	−7.71964	+	5.60865i	−0.330068	+	0.239808i	0.410391	+	0.911909i	$0.365392\pi$
$548$	−12.3358	+	11.1072i	−0.526957	+	0.474474i
$549$	29.1216	+	18.1576i	1.24288	+	0.774949i
$550$	−0.369226	+	0.270367i	−0.0157438	+	0.0115285i
$551$	2.52200	−	4.36822i	0.107441	−	0.186093i
$552$	−9.32751	−	10.7195i	−0.397005	−	0.456251i
$553$	12.3136	−	15.0618i	0.523626	−	0.640493i
$554$	−1.48911	+	2.04958i	−0.0632660	+	0.0870782i
$555$	−25.7072	+	27.5946i	−1.09121	+	1.17132i
$556$	14.8486	+	13.3697i	0.629720	+	0.567002i
$557$	−34.7083	−	3.64799i	−1.47064	−	0.154570i	−0.664940	−	0.746897i	$-0.731543\pi$
$557$	−34.7083	−	3.64799i	−1.47064	−	0.154570i	−0.805698	+	0.592327i	$0.798210\pi$
$558$	−16.1649	+	10.9264i	−0.684317	+	0.462552i
$559$	18.5616	+	6.03102i	0.785071	+	0.255085i
$560$	1.57918	−	5.78551i	0.0667324	−	0.244482i
$561$	−0.736943	−	3.70768i	−0.0311138	−	0.156538i
$562$	7.80706	−	13.5222i	0.329321	−	0.570401i
$563$	36.6832	−	7.79725i	1.54601	−	0.328615i	0.645607	−	0.763670i	$-0.276604\pi$
$563$	36.6832	−	7.79725i	1.54601	−	0.328615i	0.900404	+	0.435055i	$0.143271\pi$
$564$	7.23473	−	5.07109i	0.304637	−	0.213531i
$565$	−2.10919	−	4.73733i	−0.0887345	−	0.199301i
$566$	−4.70946	−	14.4942i	−0.197953	−	0.609238i
$567$	−12.3192	+	20.3774i	−0.517357	+	0.855770i
$568$	0.0256961	+	0.0186693i	0.00107819	+	0.000783348i
$569$	21.6500	−	2.27550i	0.907614	−	0.0953941i	0.360795	−	0.932645i	$-0.382505\pi$
$569$	21.6500	−	2.27550i	0.907614	−	0.0953941i	0.546819	+	0.837251i	$0.315839\pi$
$570$	−1.97160	+	5.73506i	−0.0825814	+	0.240215i
$571$	−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	$-0.366356\pi$
$572$	−0.667880	+	6.59077i	−0.0279254	+	0.275574i
$573$	−33.5940	−	20.1630i	−1.40341	−	0.842319i
$574$	3.85281	+	0.219939i	0.160813	+	0.00918008i
$575$	0.665359	+	0.915788i	0.0277474	+	0.0381910i
$576$	2.36584	+	1.84467i	0.0985766	+	0.0768613i
$577$	9.83914	+	8.85920i	0.409609	+	0.368813i	0.848023	−	0.529960i	$-0.177793\pi$
$577$	9.83914	+	8.85920i	0.409609	+	0.368813i	−0.438414	+	0.898773i	$0.644460\pi$
$578$	12.3117	+	11.0855i	0.512097	+	0.461095i
$579$	5.11873	−	41.8579i	0.212727	−	1.73956i
$580$	4.35062	+	5.98811i	0.180650	+	0.248643i
$581$	−13.3235	+	6.71059i	−0.552753	+	0.278402i
$582$	−7.14570	+	11.9056i	−0.296199	+	0.493504i
$583$	−6.22388	−	10.6878i	−0.257767	−	0.442645i
$584$	3.65922	+	6.33796i	0.151420	+	0.262267i
$585$	−10.3962	+	8.74075i	−0.429828	+	0.361386i
$586$	18.3549	−	1.92918i	0.758235	−	0.0796938i
$587$	28.8123	+	20.9334i	1.18921	+	0.864012i	0.993181	−	0.116586i	$-0.0371951\pi$
$587$	28.8123	+	20.9334i	1.18921	+	0.864012i	0.196030	+	0.980598i	$0.437195\pi$
$588$	8.79377	+	8.34684i	0.362649	+	0.344218i
$589$	−3.10446	−	9.55454i	−0.127917	−	0.393688i
$590$	0.988056	+	2.21921i	0.0406776	+	0.0913634i
$591$	−10.8470	−	15.4750i	−0.446187	−	0.636558i
$592$	−9.39606	+	1.99720i	−0.386176	+	0.0820842i
$593$	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	$0.163144\pi$
$594$	16.6694	+	4.37386i	0.683954	+	0.179462i
$595$	−2.77750	−	2.80353i	−0.113866	−	0.114934i
$596$	−3.23101	−	1.04982i	−0.132347	−	0.0430023i
$597$	−11.5770	+	24.8586i	−0.473814	+	1.01739i
$598$	16.2964	+	1.71282i	0.666407	+	0.0700422i
$599$	33.5697	+	30.2263i	1.37162	+	1.23501i	0.943534	+	0.331276i	$0.107479\pi$
$599$	33.5697	+	30.2263i	1.37162	+	1.23501i	0.428087	+	0.903737i	$0.359188\pi$
$600$	−0.174866	−	0.162905i	−0.00713887	−	0.00665058i
$601$	−12.2760	+	16.8964i	−0.500748	+	0.689220i	−0.982325	−	0.187184i	$-0.940064\pi$
$601$	−12.2760	+	16.8964i	−0.500748	+	0.689220i	0.481577	+	0.876404i	$0.340064\pi$
$602$	−20.0149	−	16.3629i	−0.815748	−	0.666903i
$603$	3.71007	−	0.657927i	0.151086	−	0.0267929i
$604$	0.331696	−	0.574514i	0.0134965	−	0.0233766i
$605$	−22.7019	+	10.3111i	−0.922964	+	0.419205i
$606$	−0.264822	+	15.6090i	−0.0107577	+	0.634072i
$607$	−19.3371	+	17.4112i	−0.784867	+	0.706697i	−0.960659	−	0.277730i	$-0.910418\pi$
$607$	−19.3371	+	17.4112i	−0.784867	+	0.706697i	0.175792	+	0.984427i	$0.443751\pi$
$608$	−1.24967	+	0.907939i	−0.0506809	+	0.0368218i
$609$	−14.8269	+	2.02070i	−0.600815	+	0.0818828i
$610$	−8.01285	−	24.6610i	−0.324431	−	0.998496i
$611$	−2.11828	+	9.96572i	−0.0856964	+	0.403170i
$612$	1.82968	−	0.741319i	0.0739603	−	0.0299661i
$613$	−17.9002	−	7.96968i	−0.722982	−	0.321892i	0.0120473	−	0.999927i	$-0.496165\pi$
$613$	−17.9002	−	7.96968i	−0.722982	−	0.321892i	−0.735030	+	0.678035i	$0.762832\pi$
$614$	13.6137	+	15.1196i	0.549405	+	0.610176i
$615$	2.94698	−	4.91004i	0.118834	−	0.197992i
$616$	3.99106	−	7.81482i	0.160804	−	0.314868i
$617$		−	17.6927i		−	0.712282i	−0.934432	−	0.356141i	$-0.884092\pi$
$617$		−	17.6927i		−	0.712282i	0.934432	−	0.356141i	$-0.115908\pi$
$618$	13.9801	−	2.72455i	0.562363	−	0.109598i
$619$	−4.13230	+	9.28129i	−0.166091	+	0.373046i	−0.977347	−	0.211645i	$-0.932118\pi$
$619$	−4.13230	+	9.28129i	−0.166091	+	0.373046i	0.811256	+	0.584692i	$0.198785\pi$
$620$	14.6614	+	1.54098i	0.588817	+	0.0618871i
$621$	10.9727	−	41.1921i	0.440317	−	1.65298i
$622$	−8.08382	+	2.62659i	−0.324132	+	0.105317i
$623$	−40.2325	−	15.6595i	−1.61188	−	0.627383i
$624$	−3.44623	+	0.303204i	−0.137960	+	0.0121379i
$625$	−17.1772	−	19.0772i	−0.687086	−	0.763087i
$626$	11.9554	+	20.7074i	0.477835	+	0.827635i
$627$	−4.53807	+	7.62529i	−0.181233	+	0.304525i
$628$	−1.12716	−	0.650766i	−0.0449786	−	0.0259684i
$629$	−1.95336	+	6.01183i	−0.0778857	+	0.239707i
$630$	17.0327	−	5.79471i	0.678601	−	0.230867i
$631$	−34.5856	−	25.1279i	−1.37683	−	1.00033i	−0.997168	−	0.0752036i	$-0.976039\pi$
$631$	−34.5856	−	25.1279i	−1.37683	−	1.00033i	−0.379665	−	0.925124i	$-0.623961\pi$
$632$	1.52881	−	7.19247i	0.0608126	−	0.286101i
$633$	5.37514	+	17.5506i	0.213643	+	0.697574i
$634$	−2.88763	+	27.4740i	−0.114683	+	1.09113i
$635$	−4.38290	−	41.7005i	−0.173930	−	1.65483i
$636$	4.87257	−	4.23984i	0.193210	−	0.168121i
$637$	−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
$640$	−0.471276	−	2.21718i	−0.0186288	−	0.0876417i
$641$	−14.8840	+	33.4299i	−0.587881	+	1.32040i	0.337487	+	0.941330i	$0.390423\pi$
$641$	−14.8840	+	33.4299i	−0.587881	+	1.32040i	−0.925367	+	0.379071i	$0.876243\pi$
$642$	0.129692	−	1.06054i	0.00511852	−	0.0418562i
$643$	0.0480928	−	0.0156263i	0.00189660	−	0.000616242i	−0.308069	−	0.951364i	$-0.599683\pi$
$643$	0.0480928	−	0.0156263i	0.00189660	−	0.000616242i	0.309965	+	0.950748i	$0.399683\pi$
$644$	−19.2934	−	9.94411i	−0.760268	−	0.391853i
$645$	−35.3056	+	15.0067i	−1.39016	+	0.590888i
$646$	0.106251	+	1.01091i	0.00418038	+	0.0397736i
$647$	38.2372	−	8.12758i	1.50326	−	0.319528i	0.618579	−	0.785723i	$-0.287709\pi$
$647$	38.2372	−	8.12758i	1.50326	−	0.319528i	0.884682	+	0.466195i	$0.154375\pi$
$648$	−0.610249	+	8.97929i	−0.0239728	+	0.352740i
$649$	0.751964	+	3.47396i	0.0295172	+	0.136365i
$650$	0.275599			0.0108099
$651$	−16.7692	+	24.6389i	−0.657237	+	0.965674i
$652$	8.07334	−	5.86563i	0.316176	−	0.229716i
$653$	−12.7539	−	28.6457i	−0.499098	−	1.12099i	−0.970943	−	0.239311i	$-0.923078\pi$
$653$	−12.7539	−	28.6457i	−0.499098	−	1.12099i	0.471845	−	0.881682i	$-0.343588\pi$
$654$	26.7853	−	8.20341i	1.04739	−	0.320779i
$655$	11.1443	−	12.3770i	0.435442	−	0.483608i
$656$	1.33249	−	0.593264i	0.0520251	−	0.0231631i
$657$	−9.60529	+	19.7427i	−0.374738	+	0.770238i
$658$	7.40299	−	11.2840i	0.288598	−	0.439898i
$659$		−	2.23889i		−	0.0872149i	−0.999049	−	0.0436074i	$-0.986115\pi$
$659$		−	2.23889i		−	0.0872149i	0.999049	−	0.0436074i	$-0.0138851\pi$
$660$	−7.51361	−	10.6348i	−0.292467	−	0.413959i
$661$	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	$0.208510\pi$
$662$	−4.02997	−	18.9595i	−0.156629	−	0.736882i
$663$	−0.961104	+	2.06373i	−0.0373262	+	0.0801485i
$664$	−3.31422	+	4.56164i	−0.128617	+	0.177026i
$665$	0.441676	+	9.25314i	0.0171274	+	0.358821i
$666$	−20.7495	−	19.9983i	−0.804025	−	0.774920i
$667$	24.4728	−	10.8960i	0.947592	−	0.421895i
$668$	21.5849	+	9.61021i	0.835144	+	0.371830i
$669$	−43.1683	−	14.8404i	−1.66898	−	0.573765i
$670$	−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	0.00792622	−	0.999969i	$-0.497477\pi$
$673$	15.2873	−	47.0493i	0.589281	−	1.81362i	0.581354	−	0.813650i	$-0.302523\pi$
$674$	−8.26452	+	0.868636i	−0.318338	+	0.0334586i
$675$	0.111120	−	0.708307i	0.00427701	−	0.0272627i
$676$	−6.02921	+	6.69612i	−0.231893	+	0.257543i
$677$	−19.8265	−	4.21426i	−0.761996	−	0.161967i	−0.189506	−	0.981879i	$-0.560689\pi$
$677$	−19.8265	−	4.21426i	−0.761996	−	0.161967i	−0.572489	+	0.819912i	$0.694022\pi$
$678$	3.64673	−	1.55005i	0.140052	−	0.0595293i
$679$	−3.41569	+	20.9335i	−0.131082	+	0.803353i
$680$	−1.41861	−	0.460933i	−0.0544010	−	0.0176760i
$681$	3.89699	+	7.02226i	0.149333	+	0.269093i
$682$	20.5395	+	6.58913i	0.786500	+	0.252311i
$683$	−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	$0.371074\pi$
$684$	−4.35612	−	1.58067i	−0.166560	−	0.0604386i
$685$	22.1160	+	30.4401i	0.845010	+	1.16306i
$686$	17.1956	+	6.87831i	0.656531	+	0.262615i
$687$	7.24080	−	31.4335i	0.276254	−	1.19926i
$688$	−9.55773	−	2.03156i	−0.364385	−	0.0774525i
$689$	−0.778565	+	7.40755i	−0.0296610	+	0.282205i
$690$	−26.3749	+	18.4871i	−1.00407	+	0.703792i
$691$	−2.73233	+	2.46020i	−0.103943	+	0.0935904i	−0.719464	−	0.694530i	$-0.755612\pi$
$691$	−2.73233	+	2.46020i	−0.103943	+	0.0935904i	0.615521	+	0.788121i	$0.288946\pi$
$692$	−22.2708			−0.846608
$693$	26.1285	−	3.20932i	0.992541	−	0.121912i
$694$	9.41454			0.357371
$695$	33.6574	−	30.3053i	1.27670	−	1.14954i
$696$	−4.63140	+	3.24632i	−0.175553	+	0.123051i
$697$	0.100329	−	0.954571i	0.00380025	−	0.0361570i
$698$	−14.8814	−	3.16313i	−0.563268	−	0.119726i
$699$	−5.99788	+	26.0377i	−0.226861	+	0.984838i
$700$	−0.340202	−	0.132415i	−0.0128584	−	0.00500482i
$701$	−8.92178	−	12.2798i	−0.336971	−	0.463801i	0.606583	−	0.795020i	$-0.292540\pi$
$701$	−8.92178	−	12.2798i	−0.336971	−	0.463801i	−0.943554	+	0.331219i	$0.892540\pi$
$702$	−6.54331	−	8.05612i	−0.246961	−	0.304059i
$703$	12.8502	−	7.41907i	0.484655	−	0.279816i
$704$	−0.0123673	−	3.31660i	−0.000466109	−	0.124999i
$705$	−9.71756	−	17.5107i	−0.365984	−	0.659493i
$706$	−18.7381	−	6.08839i	−0.705219	−	0.229140i
$707$	8.44193	+	22.3023i	0.317491	+	0.838764i
$708$	−1.70832	+	0.726124i	−0.0642025	+	0.0272894i
$709$	13.2534	+	2.81709i	0.497741	+	0.105798i	0.449940	−	0.893059i	$-0.351445\pi$
$709$	13.2534	+	2.81709i	0.497741	+	0.105798i	0.0478011	+	0.998857i	$0.484779\pi$
$710$	0.0481745	−	0.0535032i	0.00180796	−	0.00200794i
$711$	20.4451	−	8.28361i	0.766750	−	0.310660i
$712$	−16.2283	+	1.70566i	−0.608181	+	0.0639224i
$713$	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
$717$	36.3327	+	12.4905i	1.35687	+	0.466466i
$718$	4.07668	+	1.81505i	0.152140	+	0.0677372i
$719$	−28.6400	+	12.7514i	−1.06809	+	0.475545i	−0.864044	−	0.503416i	$-0.832076\pi$
$719$	−28.6400	+	12.7514i	−1.06809	+	0.475545i	−0.204048	+	0.978961i	$0.565410\pi$
$720$	4.71898	−	4.89622i	0.175866	−	0.182472i
$721$	18.3018	−	11.7643i	0.681595	−	0.438127i
$722$	−9.76545	+	13.4410i	−0.363432	+	0.500222i
$723$	−16.2929	+	34.9848i	−0.605939	+	1.30110i
$724$	−3.82867	−	18.0125i	−0.142291	−	0.669428i
$725$	0.390199	−	0.225281i	0.0144916	−	0.00836674i
$726$	−7.58356	−	17.4783i	−0.281452	−	0.648679i
$727$		−	46.3995i		−	1.72086i	−0.509565	−	0.860432i	$-0.670194\pi$
$727$		−	46.3995i		−	1.72086i	0.509565	−	0.860432i	$-0.329806\pi$
$728$	−4.71970	+	2.37715i	−0.174924	+	0.0881029i
$729$	−23.3430	+	13.5685i	−0.864555	+	0.502538i
$730$	15.1546	−	6.74728i	0.560898	−	0.249728i
$731$	−4.30250	+	4.77840i	−0.159134	+	0.176736i
$732$	18.9453	−	5.80228i	0.700237	−	0.214458i
$733$	−1.77886	−	3.99538i	−0.0657036	−	0.147573i	0.877709	−	0.479194i	$-0.159071\pi$
$733$	−1.77886	−	3.99538i	−0.0657036	−	0.147573i	−0.943413	+	0.331621i	$0.892404\pi$
$734$	1.21583	−	0.883353i	0.0448771	−	0.0326052i
$735$	20.8998	−	17.8461i	0.770900	−	0.658262i
$736$	−8.20385			−0.302398
$737$	−3.10604	−	2.77579i	−0.114413	−	0.102248i
$738$	3.71314	+	2.31518i	0.136683	+	0.0852231i
$739$	13.4468	−	2.85821i	0.494649	−	0.105141i	0.0461687	−	0.998934i	$-0.485299\pi$
$739$	13.4468	−	2.85821i	0.494649	−	0.105141i	0.448480	+	0.893793i	$0.351965\pi$
$740$	2.27600	+	21.6547i	0.0836674	+	0.796043i
$741$	4.91805	−	2.09043i	0.180669	−	0.0767937i
$742$	4.52012	−	8.76989i	0.165939	−	0.321953i
$743$	−23.9706	+	7.78852i	−0.879396	+	0.285733i	−0.713706	−	0.700445i	$-0.752985\pi$
$743$	−23.9706	+	7.78852i	−0.879396	+	0.285733i	−0.165689	+	0.986178i	$0.552985\pi$
$744$	−1.36737	+	11.1816i	−0.0501304	+	0.409936i
$745$	−3.13214	+	7.03491i	−0.114753	+	0.257739i
$746$	−0.208691	−	0.981814i	−0.00764072	−	0.0359468i
$747$	−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
$750$	14.4002	−	12.5303i	0.525821	−	0.457541i
$751$	−3.13617	−	29.8387i	−0.114440	−	1.08883i	−0.889498	−	0.456938i	$-0.848946\pi$
$751$	−3.13617	−	29.8387i	−0.114440	−	1.08883i	0.775058	−	0.631890i	$-0.217721\pi$
$752$	0.533188	−	5.07295i	0.0194434	−	0.184991i
$753$	−5.65123	−	18.4521i	−0.205942	−	0.672431i
$754$	1.35604	−	6.37968i	0.0493841	−	0.232334i
$755$	−1.21653	−	0.883863i	−0.0442742	−	0.0321671i
$756$	4.20646	+	13.0884i	0.152988	+	0.476020i
$757$	6.06780	−	18.6748i	0.220538	−	0.678745i	−0.778176	−	0.628046i	$-0.783855\pi$
$757$	6.06780	−	18.6748i	0.220538	−	0.678745i	0.998714	−	0.0506994i	$-0.0161451\pi$
$758$	11.7089	+	6.76016i	0.425288	+	0.245540i
$759$	−43.3031	+	18.5970i	−1.57180	+	0.675029i
$760$	1.75067	+	3.03225i	0.0635035	+	0.109991i
$761$	−22.2731	−	24.7368i	−0.807399	−	0.896707i	0.188958	−	0.981985i	$-0.439489\pi$
$761$	−22.2731	−	24.7368i	−0.807399	−	0.896707i	−0.996357	+	0.0852779i	$0.972822\pi$
$762$	31.9166	−	2.80807i	1.15622	−	0.101726i
$763$	33.3802	−	26.7739i	1.20844	−	0.969281i
$764$	−21.5136	+	6.99021i	−0.778337	+	0.252897i
$765$	−1.23764	−	4.30027i	−0.0447468	−	0.155477i
$766$	3.94147	+	0.414265i	0.142411	+	0.0149680i
$767$	0.870650	−	1.95551i	0.0314373	−	0.0706094i
$768$	1.70007	−	0.331322i	0.0613459	−	0.0119556i
$769$			28.5406i			1.02920i	0.857430	+	0.514601i	$0.172060\pi$
$769$			28.5406i			1.02920i	−0.857430	+	0.514601i	$0.827940\pi$
$770$	−16.6713	−	10.8486i	−0.600791	−	0.390957i
$771$	−9.04387	+	15.0682i	−0.325707	+	0.542668i
$772$	−16.2911	−	18.0931i	−0.586331	−	0.651186i
$773$	−6.75491	−	3.00748i	−0.242957	−	0.108172i	0.281646	−	0.959518i	$-0.409120\pi$
$773$	−6.75491	−	3.00748i	−0.242957	−	0.108172i	−0.524603	+	0.851347i	$0.675786\pi$
$774$	−11.0077	−	27.1685i	−0.395664	−	0.976552i
$775$	0.186579	−	0.877787i	0.00670213	−	0.0315310i
$776$	2.47731	+	7.62438i	0.0889303	+	0.273699i
$777$	−40.7455	−	16.6605i	−1.46174	−	0.597691i
$778$	11.2280	−	8.15764i	0.402544	−	0.292466i
$779$	−1.67435	+	1.50759i	−0.0599899	+	0.0540151i
$780$	−0.133025	+	7.84066i	−0.00476304	+	0.280741i
$781$	0.0849930	−	0.0622366i	0.00304129	−	0.00222700i
$782$	−2.69927	+	4.67528i	−0.0965258	+	0.167188i
$783$	−15.8494	−	6.05737i	−0.566413	−	0.216473i
$784$	6.96818	−	0.666736i	0.248863	−	0.0238120i
$785$	−1.73408	+	2.38676i	−0.0618921	+	0.0851872i
$786$	9.31172	+	8.67481i	0.332138	+	0.309420i
$787$	−17.9932	−	16.2012i	−0.641390	−	0.577510i	0.282924	−	0.959142i	$-0.408695\pi$
$787$	−17.9932	−	16.2012i	−0.641390	−	0.577510i	−0.924314	+	0.381632i	$0.875362\pi$
$788$	−10.8510	−	1.14049i	−0.386551	−	0.0406282i
$789$	−10.2999	+	22.1165i	−0.366687	+	0.787369i
$790$	−15.8517	−	5.15053i	−0.563978	−	0.183248i
$791$	4.29989	−	4.25997i	0.152886	−	0.151467i
$792$	8.22254	−	5.60266i	0.292175	−	0.199082i
$793$	−11.4245	+	19.7878i	−0.405695	+	0.702685i
$794$	3.06579	−	0.651653i	0.108801	−	0.0231263i
$795$	−8.40337	−	11.9888i	−0.298037	−	0.425198i
$796$	6.43954	+	14.4634i	0.228243	+	0.512643i
$797$	10.9797	+	33.7920i	0.388920	+	1.19697i	0.933596	+	0.358327i	$0.116653\pi$
$797$	10.9797	+	33.7920i	0.388920	+	1.19697i	−0.544676	+	0.838647i	$0.683347\pi$
$798$	−7.07527	+	0.217505i	−0.250462	+	0.00769959i
$799$	−2.71558	−	1.97299i	−0.0960704	−	0.0697992i
$800$	−0.137225	+	0.0144229i	−0.00485164	+	0.000509928i
$801$	−31.5031	−	37.4694i	−1.11311	−	1.32392i
$802$	−17.8518	−	30.9202i	−0.630369	−	1.09183i
$803$	23.7232	−	5.13504i	0.837172	−	0.181212i
$804$	1.11952	−	1.86526i	0.0394824	−	0.0657825i
$805$	−26.9883	+	41.1370i	−0.951211	+	1.44989i
$806$	−7.63558	−	10.5095i	−0.268952	−	0.370181i
$807$	1.57998	−	12.9201i	0.0556179	−	0.454810i
$808$	6.69808	+	6.03098i	0.235638	+	0.212169i
$809$	−21.3736	−	19.2449i	−0.751456	−	0.676614i	0.201579	−	0.979472i	$-0.435393\pi$
$809$	−21.3736	−	19.2449i	−0.751456	−	0.676614i	−0.953036	+	0.302858i	$0.902059\pi$
$810$	20.0974	+	3.50319i	0.706149	+	0.123090i
$811$	27.7819	+	38.2386i	0.975556	+	1.34274i	0.939189	+	0.343399i	$0.111578\pi$
$811$	27.7819	+	38.2386i	0.975556	+	1.34274i	0.0363667	+	0.999339i	$0.488422\pi$
$812$	−4.73911	+	7.22361i	−0.166310	+	0.253499i
$813$	−11.0112	−	6.60885i	−0.386178	−	0.231783i
$814$	−3.21204	+	31.6971i	−0.112582	+	1.11098i
$815$	−11.3100	−	19.5895i	−0.396171	−	0.686189i
$816$	0.370548	−	1.07786i	0.0129718	−	0.0377327i
$817$	15.0108	−	1.57770i	0.525160	−	0.0551966i
$818$	6.93985	+	5.04210i	0.242646	+	0.176293i
$819$	−13.8375	−	7.73704i	−0.483520	−	0.270354i
$820$	−1.02168	−	3.14440i	−0.0356785	−	0.109807i
$821$	11.8043	+	26.5129i	0.411973	+	0.925307i	0.993716	+	0.111934i	$0.0357044\pi$
$821$	11.8043	+	26.5129i	0.411973	+	0.925307i	−0.581743	+	0.813373i	$0.697629\pi$
$822$	−23.5434	+	16.5024i	−0.821169	+	0.575587i
$823$	−19.8946	+	4.22873i	−0.693482	+	0.147404i	−0.541151	−	0.840925i	$-0.682011\pi$
$823$	−19.8946	+	4.22873i	−0.693482	+	0.147404i	−0.152331	+	0.988330i	$0.548678\pi$
$824$	4.11164	−	7.12157i	0.143236	−	0.248092i
$825$	−0.691632	+	0.387200i	−0.0240795	+	0.0134806i
$826$	−2.01429	+	1.99559i	−0.0700861	+	0.0694354i
$827$	−33.7377	−	10.9621i	−1.17318	−	0.381188i	−0.343348	−	0.939208i	$-0.611561\pi$
$827$	−33.7377	−	10.9621i	−1.17318	−	0.381188i	−0.829827	+	0.558020i	$0.811561\pi$
$828$	−13.7826	−	20.3904i	−0.478977	−	0.708617i
$829$	50.5257	+	5.31047i	1.75483	+	0.184440i	0.926626	−	0.375985i	$-0.122695\pi$
$829$	50.5257	+	5.31047i	1.75483	+	0.184440i	0.828205	+	0.560425i	$0.189362\pi$
$830$	9.49801	+	8.55205i	0.329681	+	0.296846i
$831$	−2.99105	+	3.21065i	−0.103758	+	0.111376i
$832$	−1.17402	+	1.61590i	−0.0407019	+	0.0560214i
$833$	1.91274	−	4.19045i	0.0662725	−	0.145191i
$834$	22.7174	+	26.1076i	0.786640	+	0.904032i
$835$	26.7785	−	46.3817i	0.926707	−	1.60510i
$836$	1.60129	+	4.86644i	0.0553817	+	0.168309i
$837$	−30.0887	+	15.3866i	−1.04002	+	0.531838i
$838$	23.3087	−	20.9872i	0.805184	−	0.724991i
$839$	−32.4160	+	23.5516i	−1.11913	+	0.813093i	−0.984076	−	0.177746i	$-0.943119\pi$
$839$	−32.4160	+	23.5516i	−1.11913	+	0.813093i	−0.135050	+	0.990839i	$0.543119\pi$
$840$	3.93135	−	9.61468i	0.135645	−	0.331738i
$841$	5.66650	+	17.4397i	0.195397	+	0.601369i
$842$	5.58666	−	26.2832i	0.192529	−	0.905778i
$843$	16.2652	−	21.6066i	0.560203	−	0.744172i
$844$	9.68122	+	4.31036i	0.333241	+	0.148369i
$845$	13.6665	+	15.1782i	0.470142	+	0.522145i
$846$	13.5044	−	7.19738i	0.464292	−	0.247451i
$847$	−20.6365	−	20.5215i	−0.709080	−	0.705128i
$848$		−	3.72908i		−	0.128057i
$849$	−5.04939	−	25.9092i	−0.173295	−	0.889203i
$850$	−0.0369310	+	0.0829485i	−0.00126672	+	0.00284511i
$851$	78.3743	+	8.23747i	2.68664	+	0.282377i
$852$	0.0402528	+	0.0374996i	0.00137904	+	0.00128471i
$853$	−11.9648	+	3.88761i	−0.409668	+	0.133109i	−0.506599	−	0.862182i	$-0.669097\pi$
$853$	−11.9648	+	3.88761i	−0.409668	+	0.133109i	0.0969310	+	0.995291i	$0.469097\pi$
$854$	23.6098	−	18.9372i	0.807911	−	0.648018i
$855$	−4.59543	+	9.44545i	−0.157160	+	0.323028i
$856$	−0.412763	−	0.458420i	−0.0141080	−	0.0156685i
$857$	−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	$0.892753\pi$
$858$	−2.53391	+	11.1907i	−0.0865063	+	0.382045i
$859$	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
$861$	6.57768	+	1.18816i	0.224167	+	0.0404923i
$862$	29.4125	+	21.3694i	1.00179	+	0.727845i
$863$	−5.32327	+	25.0440i	−0.181206	+	0.852509i	0.789783	+	0.613386i	$0.210193\pi$
$863$	−5.32327	+	25.0440i	−0.181206	+	0.852509i	−0.970989	+	0.239122i	$0.923140\pi$
$864$	3.67962	+	3.66884i	0.125183	+	0.124817i
$865$	−5.27675	+	50.2049i	−0.179415	+	1.70702i
$866$	0.0156568	+	0.148964i	0.000532039	+	0.00506202i
$867$	18.8361	+	21.6471i	0.639707	+	0.735173i
$868$	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
$871$	0.521581	+	2.45385i	0.0176731	+	0.0831454i
$872$	6.57836	−	14.7752i	0.222771	−	0.500353i
$873$	−14.7883	+	18.9663i	−0.500507	+	0.641913i
$874$	12.0521	−	3.91596i	0.407668	−	0.132459i
$875$	13.3586	−	25.9182i	0.451603	−	0.876195i
$876$	4.95858	+	11.6658i	0.167535	+	0.394152i
$877$	−0.175229	−	1.66719i	−0.00591705	−	0.0562970i	0.991165	−	0.132635i	$-0.0423438\pi$
$877$	−0.175229	−	1.66719i	−0.00591705	−	0.0562970i	−0.997082	+	0.0763381i	$0.975677\pi$
$878$	17.9076	−	3.80637i	0.604351	−	0.128459i
$879$	31.9622	+	0.542270i	1.07806	+	0.0182903i
$880$	−7.47953	−	0.757942i	−0.252135	−	0.0255502i
$881$	−51.3749			−1.73086			−0.865432	−	0.501026i	$-0.832956\pi$
$881$	−51.3749			−1.73086			−0.865432	+	0.501026i	$0.832956\pi$
$882$	13.3638	+	16.1991i	0.449981	+	0.545451i
$883$	−2.11708	+	1.53815i	−0.0712456	+	0.0517629i	−0.622838	−	0.782351i	$-0.714020\pi$
$883$	−2.11708	+	1.53815i	−0.0712456	+	0.0517629i	0.551592	+	0.834114i	$0.314020\pi$
$884$	0.534602	+	1.20074i	0.0179806	+	0.0403851i
$885$	1.23213	+	4.02309i	0.0414177	+	0.135235i
$886$	−12.9505	+	14.3830i	−0.435080	+	0.483205i
$887$	20.2640	−	9.02214i	0.680400	−	0.302934i	−0.0372817	−	0.999305i	$-0.511870\pi$
$887$	20.2640	−	9.02214i	0.680400	−	0.302934i	0.717682	+	0.696371i	$0.245203\pi$
$888$	−16.5740	+	1.45820i	−0.556188	+	0.0489341i
$889$	43.7106	−	22.0155i	1.46601	−	0.738376i
$890$			36.9875i			1.23982i
$891$	27.7392	+	11.0244i	0.929298	+	0.369330i
$892$	−22.8240	+	13.1775i	−0.764205	+	0.441214i
$893$	1.63819	+	7.70706i	0.0548198	+	0.257907i
$894$	−5.33418	−	2.48419i	−0.178402	−	0.0830839i
$895$	1.30998	−	1.80304i	0.0437879	−	0.0602689i
$896$	2.22561	−	1.43062i	0.0743524	−	0.0477935i
$897$	27.6573	+	6.37095i	0.923450	+	0.212720i
$898$	−5.85415	+	2.60644i	−0.195356	+	0.0869780i
$899$	−19.4013	−	8.63803i	−0.647071	−	0.288095i
$900$	−0.266387	−	0.316838i	−0.00887958	−	0.0105613i
$901$	−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
$905$	−41.5125	+	4.36314i	−1.37992	+	0.145036i
$906$	0.691054	−	0.917992i	0.0229587	−	0.0304983i
$907$	−13.3428	+	14.8187i	−0.443041	+	0.492047i	−0.922760	−	0.385376i	$-0.874072\pi$
$907$	−13.3428	+	14.8187i	−0.443041	+	0.492047i	0.479719	+	0.877422i	$0.340739\pi$
$908$	4.53543	+	0.964036i	0.150514	+	0.0319927i
$909$	−3.73698	+	26.7800i	−0.123948	+	0.888236i
$910$	4.24052	+	11.2028i	0.140572	+	0.371370i
$911$	22.2862	+	7.24122i	0.738375	+	0.239912i	0.653971	−	0.756519i	$-0.273102\pi$
$911$	22.2862	+	7.24122i	0.738375	+	0.239912i	0.0844032	+	0.996432i	$0.473102\pi$
$912$	−2.33938	+	1.29823i	−0.0774645	+	0.0429888i
$913$	11.0484	+	15.0881i	0.365648	+	0.499345i
$914$	−5.91149	+	3.41300i	−0.195535	+	0.112892i
$915$	−8.59123	−	44.0829i	−0.284017	−	1.45734i
$916$	−10.9465	−	15.0666i	−0.361684	−	0.497816i
$917$	18.1160	+	7.05118i	0.598242	+	0.232851i
$918$	3.30152	−	0.889831i	0.108966	−	0.0293688i
$919$	−7.42793	−	1.57886i	−0.245025	−	0.0520816i	0.0837621	−	0.996486i	$-0.473306\pi$
$919$	−7.42793	−	1.57886i	−0.245025	−	0.0520816i	−0.328787	+	0.944404i	$0.606640\pi$
$920$	−1.94379	+	18.4939i	−0.0640848	+	0.609726i
$921$	20.2265	+	28.8564i	0.666486	+	0.950851i
$922$	13.4632	−	12.1224i	0.443388	−	0.399228i
$923$	−0.0634408			−0.00208818
$924$	8.50461	−	12.5965i	0.279781	−	0.414394i
$925$	1.32544			0.0435803
$926$	10.2123	−	9.19522i	0.335598	−	0.302174i
$927$	24.6080	−	1.74494i	0.808234	−	0.0573115i
$928$	−0.341327	+	3.24751i	−0.0112046	+	0.106605i
$929$	−17.0401	−	3.62198i	−0.559067	−	0.118833i	−0.0802926	−	0.996771i	$-0.525585\pi$
$929$	−17.0401	−	3.62198i	−0.559067	−	0.118833i	−0.478774	+	0.877938i	$0.658919\pi$
$930$	24.8826	+	5.73178i	0.815931	+	0.187952i
$931$	−9.91853	+	4.30562i	−0.325067	+	0.141111i
$932$	9.06752	+	12.4804i	0.297016	+	0.408808i
$933$	−14.4503	+	2.81618i	−0.473081	+	0.0921976i
$934$	20.0968	−	11.6029i	0.657587	−	0.379658i
$935$	−2.89289	+	4.01311i	−0.0946077	+	0.131243i
$936$	−5.98866	−	0.203266i	−0.195745	−	0.00664394i
$937$	−52.3891	−	17.0222i	−1.71148	−	0.556092i	−0.720898	−	0.693041i	$-0.756270\pi$
$937$	−52.3891	−	17.0222i	−1.71148	−	0.556092i	−0.990578	+	0.136949i	$0.956270\pi$
$938$	0.535137	−	3.27966i	0.0174728	−	0.107085i
$939$	16.2007	+	38.1147i	0.528690	+	1.24382i
$940$	−11.3096	−	2.40393i	−0.368878	−	0.0784075i
$941$	−6.84171	+	7.59849i	−0.223033	+	0.247704i	−0.844268	−	0.535921i	$-0.819965\pi$
$941$	−6.84171	+	7.59849i	−0.223033	+	0.247704i	0.621235	+	0.783624i	$0.286631\pi$
$942$	−1.80104	−	1.35580i	−0.0586812	−	0.0441745i
$943$	−11.9006	+	1.25080i	−0.387535	+	0.0407316i
$944$	−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	$0.514687\pi$
$948$	4.14056	−	12.0442i	0.134479	−	0.391177i
$949$	−13.3539	−	5.94553i	−0.433485	−	0.193000i
$950$	0.194710	−	0.0866903i	0.00631722	−	0.00281261i
$951$	−10.7408	+	46.6274i	−0.348293	+	1.51200i
$952$	−0.0830095	−	1.73906i	−0.00269035	−	0.0563632i
$953$	15.8738	−	21.8485i	0.514204	−	0.707741i	−0.470417	−	0.882444i	$-0.655897\pi$
$953$	15.8738	−	21.8485i	0.514204	−	0.707741i	0.984621	+	0.174703i	$0.0558965\pi$
$954$	9.26853	−	6.26490i	0.300080	−	0.202834i
$955$	10.6606	+	50.1543i	0.344970	+	1.62296i
$956$	19.2099	−	11.0908i	0.621292	−	0.358703i
$957$	5.56000	+	17.9153i	0.179729	+	0.579121i
$958$		−	16.2941i		−	0.526439i
$959$	−24.0909	+	36.7207i	−0.777936	+	1.18577i
$960$	−0.344091	−	3.91095i	−0.0111055	−	0.126225i
$961$	−10.3222	+	4.59574i	−0.332975	+	0.148250i
$962$	12.8384	−	14.2585i	0.413926	−	0.459712i
$963$	0.445943	−	1.79606i	0.0143703	−	0.0578772i
$964$	9.06270	+	20.3552i	0.291890	+	0.655596i
$965$	−44.6472	+	32.4381i	−1.43724	+	1.04422i
$966$	−31.0795	−	21.1527i	−0.999965	−	0.680576i
$967$	−25.6470			−0.824753			−0.412376	−	0.911014i	$-0.635301\pi$
$967$	−25.6470			−0.824753			−0.412376	+	0.911014i	$0.635301\pi$
$968$	−10.4867	−	3.32107i	−0.337055	−	0.106743i
$969$	−0.0298658	+	1.76033i	−0.000959429	+	0.0565501i
$970$	17.7746	−	3.77810i	0.570707	−	0.121307i
$971$	2.42407	+	23.0635i	0.0777922	+	0.740144i	0.962000	+	0.273050i	$0.0880323\pi$
$971$	2.42407	+	23.0635i	0.0777922	+	0.740144i	−0.884208	+	0.467094i	$0.845301\pi$
$972$	−2.93700	+	15.3093i	−0.0942044	+	0.491045i
$973$	46.9897	+	24.2192i	1.50642	+	0.776431i
$974$	−7.09469	+	2.30520i	−0.227328	+	0.0738635i
$975$	0.473821	+	0.0579428i	0.0151744	+	0.00185566i
$976$	4.65288	−	10.4505i	0.148935	−	0.334514i
$977$	10.0966	+	47.5005i	0.323017	+	1.51968i	0.777478	+	0.628910i	$0.216499\pi$
$977$	10.0966	+	47.5005i	0.323017	+	1.51968i	−0.454461	+	0.890767i	$0.650168\pi$
$978$	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
$981$	47.7751	−	8.47222i	1.52534	−	0.270497i
$982$	2.05410	+	19.5435i	0.0655491	+	0.623658i
$983$	0.550470	−	5.23737i	0.0175573	−	0.167046i	−0.982230	−	0.187682i	$-0.939902\pi$
$983$	0.550470	−	5.23737i	0.0175573	−	0.167046i	0.999787	+	0.0206361i	$0.00656913\pi$
$984$	2.41561	−	0.739818i	0.0770069	−	0.0235845i
$985$	−5.14198	+	24.1911i	−0.163837	+	0.770794i
$986$	1.73841	+	1.26303i	0.0553623	+	0.0402231i
$987$	15.0999	−	17.8436i	0.480636	−	0.567967i
$988$	0.953408	−	2.93429i	0.0303319	−	0.0933521i
$989$	69.4223	+	40.0810i	2.20750	+	1.27450i
$990$	−10.6818	−	19.8635i	−0.339491	−	0.631303i
$991$	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	$0.508038\pi$
$992$	4.35187	+	4.83325i	0.138172	+	0.153456i
$993$	−2.94238	−	33.4433i	−0.0933737	−	1.06129i
$994$	0.0783120	+	0.0304809i	0.00248391	+	0.000966797i
$995$	34.1306	−	11.0897i	1.08201	−	0.351567i
$996$	−6.65701	+	7.14577i	−0.210935	+	0.226422i
$997$	−19.7249	−	2.07317i	−0.624692	−	0.0656578i	−0.213107	−	0.977029i	$-0.568358\pi$
$997$	−19.7249	−	2.07317i	−0.624692	−	0.0656578i	−0.411586	+	0.911371i	$0.635025\pi$
$998$	−11.9624	+	26.8679i	−0.378662	+	0.850489i
$999$	−31.4688	−	38.7444i	−0.995630	−	1.22582i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.bf.a.5.14	✓	256	11.5	even	5	inner
462.2.bf.a.5.30	yes	256	33.5	odd	10	inner
462.2.bf.a.185.14	yes	256	21.17	even	6	inner
462.2.bf.a.185.30	yes	256	7.3	odd	6	inner
462.2.bf.a.269.8	yes	256	77.38	odd	30	inner
462.2.bf.a.269.30	yes	256	231.38	even	30	inner
462.2.bf.a.383.8	yes	256	3.2	odd	2	inner
462.2.bf.a.383.30	yes	256	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(0.743145 - 0.669131i) q^{2} +(1.41833 - 0.994157i) q^{3} +(0.104528 - 0.994522i) q^{4} +(-2.21718 - 0.471276i) q^{5} +(0.388801 - 1.68785i) q^{6} +(-0.401695 - 2.61508i) q^{7} +(-0.587785 - 0.809017i) q^{8} +(1.02330 - 2.82008i) q^{9} +O(q^{10})\)	\(q+(0.743145 - 0.669131i) q^{2} +(1.41833 - 0.994157i) q^{3} +(0.104528 - 0.994522i) q^{4} +(-2.21718 - 0.471276i) q^{5} +(0.388801 - 1.68785i) q^{6} +(-0.401695 - 2.61508i) q^{7} +(-0.587785 - 0.809017i) q^{8} +(1.02330 - 2.82008i) q^{9} +(-1.96303 + 1.13336i) q^{10} +(-3.15045 + 1.03665i) q^{11} +(-0.840455 - 1.51448i) q^{12} +(1.89961 + 0.617221i) q^{13} +(-2.04835 - 1.67460i) q^{14} +(-3.61321 + 1.53580i) q^{15} +(-0.978148 - 0.207912i) q^{16} +(-0.440321 + 0.489027i) q^{17} +(-1.12654 - 2.78045i) q^{18} +(1.53622 - 0.161463i) 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} +(-1.63796 - 0.563100i) q^{24} +(0.126052 + 0.0561219i) q^{25} +(1.82469 - 0.812403i) q^{26} +(-1.35222 - 5.01712i) q^{27} +(-2.64274 + 0.126145i) q^{28} +(1.91935 - 2.64176i) q^{29} +(-1.65748 + 3.55903i) q^{30} +(-1.35221 - 6.36165i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-3.43778 + 4.60235i) q^{33} +0.658050i q^{34} +(-0.341793 + 5.98741i) q^{35} +(-2.69767 - 1.31248i) q^{36} +(8.77550 - 3.90710i) q^{37} +(1.03359 - 1.14792i) q^{38} +(3.30788 - 1.01309i) q^{39} +(0.921955 + 2.07074i) q^{40} +(-1.18003 + 0.857341i) q^{41} +(-4.57004 - 0.338746i) q^{42} +9.77126 q^{43} +(0.701657 + 3.24155i) q^{44} +(-3.59788 + 5.77036i) q^{45} +(8.02458 - 1.70568i) q^{46} +(0.533188 + 5.07295i) q^{47} +(-1.59403 + 0.677546i) q^{48} +(-6.67728 + 2.10093i) q^{49} +(0.131228 - 0.0426385i) q^{50} +(-0.138351 + 1.13135i) q^{51} +(0.812403 - 1.82469i) q^{52} +(0.775320 + 3.64759i) q^{53} +(-4.36201 - 2.82363i) q^{54} +(7.47367 - 0.813701i) q^{55} +(-1.87953 + 1.86208i) q^{56} +(2.01834 - 1.75625i) q^{57} +(-0.341327 - 3.24751i) q^{58} +(0.112023 - 1.06583i) q^{59} +(1.14970 + 3.75395i) q^{60} +(-2.37841 + 11.1896i) q^{61} +(-5.26166 - 3.82282i) q^{62} +(-7.78579 - 1.54321i) q^{63} +(-0.309017 + 0.951057i) q^{64} +(-3.92089 - 2.26373i) q^{65} +(0.524804 + 5.72054i) q^{66} +(0.627993 + 1.08772i) q^{67} +(0.440321 + 0.489027i) q^{68} +(14.1548 - 1.24536i) q^{69} +(3.75236 + 4.67821i) q^{70} +(-0.0302076 + 0.00981506i) q^{71} +(-2.88298 + 0.829732i) q^{72} +(-7.27836 - 0.764986i) q^{73} +(3.90710 - 8.77550i) q^{74} +(0.234577 - 0.0457161i) q^{75} -1.54468i q^{76} +(3.97644 + 7.82227i) q^{77} +(1.78035 - 2.96628i) q^{78} +(4.92022 + 5.46446i) q^{79} +(2.07074 + 0.921955i) q^{80} +(-6.90570 - 5.77159i) q^{81} +(-0.303259 + 1.42672i) q^{82} +(-1.74239 - 5.36253i) q^{83} +(-3.62287 + 2.80622i) q^{84} +(1.20674 - 0.876746i) q^{85} +(7.26146 - 6.53825i) q^{86} +(0.0959430 - 5.65502i) q^{87} +(2.69046 + 1.93944i) q^{88} +(8.15885 - 14.1315i) q^{89} +(1.18738 + 6.69567i) q^{90} +(0.851017 - 5.21557i) q^{91} +(4.82210 - 6.63706i) q^{92} +(-8.24236 - 7.67859i) q^{93} +(3.79070 + 3.41316i) q^{94} +(-3.48216 - 0.365990i) q^{95} +(-0.731229 + 1.57013i) q^{96} +(-7.62438 - 2.47731i) q^{97} +(-3.55639 + 6.02927i) q^{98} +(-0.300439 + 9.94534i) 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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Database

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