LMFDB - Embedded newform 462.2.y.b.361.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(25,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([0, 20, 24]))

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

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

chi := DirichletCharacter("462.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.y (of order $15$, 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:	$24$
Relative dimension:	$3$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			361.1
Character	$\chi$	$=$	462.361
Dual form			462.2.y.b.247.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.978148 + 0.207912i) q^{2} +(-0.104528 - 0.994522i) q^{3} +(0.913545 - 0.406737i) q^{4} +(-2.71957 + 3.02039i) q^{5} +(0.309017 + 0.951057i) q^{6} +(-1.98308 - 1.75140i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(-0.978148 + 0.207912i) q^{9} +O(q^{10})$	\(q+(-0.978148 + 0.207912i) q^{2} +(-0.104528 - 0.994522i) q^{3} +(0.913545 - 0.406737i) q^{4} +(-2.71957 + 3.02039i) q^{5} +(0.309017 + 0.951057i) q^{6} +(-1.98308 - 1.75140i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(-0.978148 + 0.207912i) q^{9} +(2.03217 - 3.51982i) q^{10} +(2.84321 - 1.70767i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(0.914136 - 2.81342i) q^{13} +(2.30388 + 1.30082i) q^{14} +(3.28812 + 2.38896i) q^{15} +(0.669131 - 0.743145i) q^{16} +(4.37242 + 0.929387i) q^{17} +(0.913545 - 0.406737i) q^{18} +(6.68049 + 2.97435i) q^{19} +(-1.25595 + 3.86542i) q^{20} +(-1.53452 + 2.15528i) q^{21} +(-2.42604 + 2.26149i) q^{22} +(1.81137 + 3.13738i) q^{23} +(0.669131 + 0.743145i) q^{24} +(-1.20405 - 11.4558i) q^{25} +(-0.309217 + 2.94200i) q^{26} +(0.309017 + 0.951057i) q^{27} +(-2.52399 - 0.793395i) q^{28} +(-0.324558 - 0.235805i) q^{29} +(-3.71296 - 1.65312i) q^{30} +(4.09580 + 4.54885i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-1.99551 - 2.64914i) q^{33} -4.47011 q^{34} +(10.6830 - 1.22660i) q^{35} +(-0.809017 + 0.587785i) q^{36} +(0.904907 - 8.60962i) q^{37} +(-7.15291 - 1.52040i) q^{38} +(-2.89356 - 0.615046i) q^{39} +(0.424839 - 4.04207i) q^{40} +(5.50197 - 3.99742i) q^{41} +(1.05288 - 2.42723i) q^{42} -1.88928 q^{43} +(1.90283 - 2.71647i) q^{44} +(2.03217 - 3.51982i) q^{45} +(-2.42408 - 2.69222i) q^{46} +(-0.119044 - 0.0530017i) q^{47} +(-0.809017 - 0.587785i) q^{48} +(0.865183 + 6.94633i) q^{49} +(3.55952 + 10.9551i) q^{50} +(0.467253 - 4.44562i) q^{51} +(-0.309217 - 2.94200i) q^{52} +(-0.0143905 - 0.0159823i) q^{53} +(-0.500000 - 0.866025i) q^{54} +(-2.57448 + 13.2318i) q^{55} +(2.63379 + 0.251291i) q^{56} +(2.25975 - 6.95480i) q^{57} +(0.366492 + 0.163173i) q^{58} +(-2.86663 + 1.27631i) q^{59} +(3.97552 + 0.845024i) q^{60} +(-5.14692 + 5.71623i) q^{61} +(-4.95205 - 3.59788i) q^{62} +(2.30388 + 1.30082i) q^{63} +(0.309017 - 0.951057i) q^{64} +(6.01158 + 10.4124i) q^{65} +(2.50269 + 2.17636i) q^{66} +(2.73153 - 4.73114i) q^{67} +(4.37242 - 0.929387i) q^{68} +(2.93085 - 2.12939i) q^{69} +(-10.1946 + 3.42093i) q^{70} +(-4.19406 - 12.9080i) q^{71} +(0.669131 - 0.743145i) q^{72} +(3.02937 - 1.34876i) q^{73} +(0.904907 + 8.60962i) q^{74} +(-11.2671 + 2.39491i) q^{75} +7.31271 q^{76} +(-8.62913 - 1.59316i) q^{77} +2.95821 q^{78} +(16.3109 - 3.46699i) q^{79} +(0.424839 + 4.04207i) q^{80} +(0.913545 - 0.406737i) q^{81} +(-4.55063 + 5.05399i) q^{82} +(2.23659 + 6.88353i) q^{83} +(-0.525220 + 2.59310i) q^{84} +(-14.6982 + 10.6789i) q^{85} +(1.84799 - 0.392802i) q^{86} +(-0.200588 + 0.347428i) q^{87} +(-1.29646 + 3.05273i) q^{88} +(-0.223374 - 0.386896i) q^{89} +(-1.25595 + 3.86542i) q^{90} +(-6.74023 + 3.97821i) q^{91} +(2.93085 + 2.12939i) q^{92} +(4.09580 - 4.54885i) q^{93} +(0.127462 + 0.0270929i) q^{94} +(-27.1518 + 12.0888i) q^{95} +(0.913545 + 0.406737i) q^{96} +(5.58811 - 17.1984i) q^{97} +(-2.29050 - 6.61465i) q^{98} +(-2.42604 + 2.26149i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 3 q^{2} + 3 q^{3} + 3 q^{4} + 5 q^{5} - 6 q^{6} - 5 q^{7} - 6 q^{8} + 3 q^{9}+O(q^{10}) $ 24 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 + 5 * q^5 - 6 * q^6 - 5 * q^7 - 6 * q^8 + 3 * q^9	\( 24 q + 3 q^{2} + 3 q^{3} + 3 q^{4} + 5 q^{5} - 6 q^{6} - 5 q^{7} - 6 q^{8} + 3 q^{9} + 10 q^{10} - 2 q^{11} - 12 q^{12} + 10 q^{13} + 7 q^{14} + 20 q^{15} + 3 q^{16} + 8 q^{17} + 3 q^{18} + 7 q^{19} - 10 q^{20} + 8 q^{21} - 6 q^{22} + 24 q^{23} + 3 q^{24} + 8 q^{25} - 6 q^{27} - 2 q^{28} + 2 q^{29} - 10 q^{30} - 19 q^{31} - 12 q^{32} - 7 q^{33} + 24 q^{34} + 14 q^{35} - 6 q^{36} - q^{37} - 8 q^{38} - 5 q^{39} - 10 q^{40} + 16 q^{41} + 10 q^{42} - 68 q^{43} - 2 q^{44} + 10 q^{45} - 6 q^{46} + 25 q^{47} - 6 q^{48} - 21 q^{49} + 14 q^{50} - 2 q^{51} - 5 q^{53} - 12 q^{54} - 10 q^{55} - 10 q^{56} + 16 q^{57} - q^{58} - 36 q^{59} + 5 q^{60} - q^{61} - 52 q^{62} + 7 q^{63} - 6 q^{64} + 6 q^{65} + 8 q^{66} + 56 q^{67} + 8 q^{68} + 12 q^{69} - 17 q^{70} - 6 q^{71} + 3 q^{72} + 35 q^{73} - q^{74} - 7 q^{75} - 4 q^{76} + 38 q^{77} - 20 q^{78} - 3 q^{79} - 10 q^{80} + 3 q^{81} + 2 q^{82} - 28 q^{83} + 7 q^{84} - 80 q^{85} - 11 q^{86} + 4 q^{87} - 7 q^{88} - 6 q^{89} - 10 q^{90} - 24 q^{91} + 12 q^{92} - 19 q^{93} - 30 q^{94} - 44 q^{95} + 3 q^{96} - 8 q^{97} - 6 q^{99}+O(q^{100}) \) 24 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 + 5 * q^5 - 6 * q^6 - 5 * q^7 - 6 * q^8 + 3 * q^9 + 10 * q^10 - 2 * q^11 - 12 * q^12 + 10 * q^13 + 7 * q^14 + 20 * q^15 + 3 * q^16 + 8 * q^17 + 3 * q^18 + 7 * q^19 - 10 * q^20 + 8 * q^21 - 6 * q^22 + 24 * q^23 + 3 * q^24 + 8 * q^25 - 6 * q^27 - 2 * q^28 + 2 * q^29 - 10 * q^30 - 19 * q^31 - 12 * q^32 - 7 * q^33 + 24 * q^34 + 14 * q^35 - 6 * q^36 - q^37 - 8 * q^38 - 5 * q^39 - 10 * q^40 + 16 * q^41 + 10 * q^42 - 68 * q^43 - 2 * q^44 + 10 * q^45 - 6 * q^46 + 25 * q^47 - 6 * q^48 - 21 * q^49 + 14 * q^50 - 2 * q^51 - 5 * q^53 - 12 * q^54 - 10 * q^55 - 10 * q^56 + 16 * q^57 - q^58 - 36 * q^59 + 5 * q^60 - q^61 - 52 * q^62 + 7 * q^63 - 6 * q^64 + 6 * q^65 + 8 * q^66 + 56 * q^67 + 8 * q^68 + 12 * q^69 - 17 * q^70 - 6 * q^71 + 3 * q^72 + 35 * q^73 - q^74 - 7 * q^75 - 4 * q^76 + 38 * q^77 - 20 * q^78 - 3 * q^79 - 10 * q^80 + 3 * q^81 + 2 * q^82 - 28 * q^83 + 7 * q^84 - 80 * q^85 - 11 * q^86 + 4 * q^87 - 7 * q^88 - 6 * q^89 - 10 * q^90 - 24 * q^91 + 12 * q^92 - 19 * q^93 - 30 * q^94 - 44 * q^95 + 3 * q^96 - 8 * q^97 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{5}\right)$

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 $

$2$	−0.978148	+	0.207912i	−0.691655	+	0.147016i
$2$	−0.978148	+	0.207912i	−0.691655	+	0.147016i
$3$	−0.104528	−	0.994522i	−0.0603495	−	0.574187i
$3$	−0.104528	−	0.994522i	−0.0603495	−	0.574187i
$4$	0.913545	−	0.406737i	0.456773	−	0.203368i
$5$	−2.71957	+	3.02039i	−1.21623	+	1.35076i	−0.298074	+	0.954543i	$0.596344\pi$
$5$	−2.71957	+	3.02039i	−1.21623	+	1.35076i	−0.918156	+	0.396218i	$0.870322\pi$
$6$	0.309017	+	0.951057i	0.126156	+	0.388267i
$7$	−1.98308	−	1.75140i	−0.749532	−	0.661968i
$7$	−1.98308	−	1.75140i	−0.749532	−	0.661968i
$8$	−0.809017	+	0.587785i	−0.286031	+	0.207813i
$9$	−0.978148	+	0.207912i	−0.326049	+	0.0693039i
$10$	2.03217	−	3.51982i	0.642629	−	1.11307i
$11$	2.84321	−	1.70767i	0.857261	−	0.514883i
$11$	2.84321	−	1.70767i	0.857261	−	0.514883i
$12$	−0.500000	−	0.866025i	−0.144338	−	0.250000i
$13$	0.914136	−	2.81342i	0.253536	−	0.780303i	−0.740579	−	0.671969i	$-0.765449\pi$
$13$	0.914136	−	2.81342i	0.253536	−	0.780303i	0.994115	−	0.108333i	$-0.0345513\pi$
$14$	2.30388	+	1.30082i	0.615737	+	0.347660i
$15$	3.28812	+	2.38896i	0.848989	+	0.616827i
$16$	0.669131	−	0.743145i	0.167283	−	0.185786i
$17$	4.37242	+	0.929387i	1.06047	+	0.225410i	0.704948	−	0.709259i	$-0.250970\pi$
$17$	4.37242	+	0.929387i	1.06047	+	0.225410i	0.355520	+	0.934669i	$0.384304\pi$
$18$	0.913545	−	0.406737i	0.215325	−	0.0958687i
$19$	6.68049	+	2.97435i	1.53261	+	0.682362i	0.987733	−	0.156153i	$-0.0499094\pi$
$19$	6.68049	+	2.97435i	1.53261	+	0.682362i	0.544878	+	0.838516i	$0.316576\pi$
$20$	−1.25595	+	3.86542i	−0.280839	+	0.864333i
$21$	−1.53452	+	2.15528i	−0.334860	+	0.470322i
$22$	−2.42604	+	2.26149i	−0.517233	+	0.482152i
$23$	1.81137	+	3.13738i	0.377696	+	0.654189i	0.990727	−	0.135870i	$-0.0433831\pi$
$23$	1.81137	+	3.13738i	0.377696	+	0.654189i	−0.613031	+	0.790059i	$0.710050\pi$
$24$	0.669131	+	0.743145i	0.136586	+	0.151694i
$25$	−1.20405	−	11.4558i	−0.240810	−	2.29115i
$26$	−0.309217	+	2.94200i	−0.0606424	+	0.576974i
$27$	0.309017	+	0.951057i	0.0594703	+	0.183031i
$28$	−2.52399	−	0.793395i	−0.476989	−	0.149938i
$29$	−0.324558	−	0.235805i	−0.0602689	−	0.0437879i	0.557243	−	0.830350i	$-0.311859\pi$
$29$	−0.324558	−	0.235805i	−0.0602689	−	0.0437879i	−0.617512	+	0.786562i	$0.711859\pi$
$30$	−3.71296	−	1.65312i	−0.677890	−	0.301816i
$31$	4.09580	+	4.54885i	0.735627	+	0.816997i	0.988614	−	0.150473i	$-0.0480796\pi$
$31$	4.09580	+	4.54885i	0.735627	+	0.816997i	−0.252987	+	0.967470i	$0.581413\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−1.99551	−	2.64914i	−0.347374	−	0.461155i
$34$	−4.47011			−0.766617
$35$	10.6830	−	1.22660i	1.80576	−	0.207334i
$36$	−0.809017	+	0.587785i	−0.134836	+	0.0979642i
$37$	0.904907	−	8.60962i	0.148766	−	1.41541i	−0.624349	−	0.781146i	$-0.714635\pi$
$37$	0.904907	−	8.60962i	0.148766	−	1.41541i	0.773114	−	0.634267i	$-0.218698\pi$
$38$	−7.15291	−	1.52040i	−1.16036	−	0.246641i
$39$	−2.89356	−	0.615046i	−0.463341	−	0.0984861i
$40$	0.424839	−	4.04207i	0.0671730	−	0.639108i
$41$	5.50197	−	3.99742i	0.859264	−	0.624292i	−0.0684209	−	0.997657i	$-0.521796\pi$
$41$	5.50197	−	3.99742i	0.859264	−	0.624292i	0.927685	+	0.373365i	$0.121796\pi$
$42$	1.05288	−	2.42723i	0.162463	−	0.374530i
$43$	−1.88928			−0.288112			−0.144056	−	0.989570i	$-0.546015\pi$
$43$	−1.88928			−0.288112			−0.144056	+	0.989570i	$0.546015\pi$
$44$	1.90283	−	2.71647i	0.286862	−	0.409524i
$45$	2.03217	−	3.51982i	0.302938	−	0.524704i
$46$	−2.42408	−	2.69222i	−0.357411	−	0.396946i
$47$	−0.119044	−	0.0530017i	−0.0173643	−	0.00773110i	0.398036	−	0.917370i	$-0.369692\pi$
$47$	−0.119044	−	0.0530017i	−0.0173643	−	0.00773110i	−0.415400	+	0.909639i	$0.636359\pi$
$48$	−0.809017	−	0.587785i	−0.116772	−	0.0848395i
$49$	0.865183	+	6.94633i	0.123598	+	0.992332i
$50$	3.55952	+	10.9551i	0.503393	+	1.54928i
$51$	0.467253	−	4.44562i	0.0654285	−	0.622511i
$52$	−0.309217	−	2.94200i	−0.0428806	−	0.407982i
$53$	−0.0143905	−	0.0159823i	−0.00197669	−	0.00219534i	0.742156	−	0.670228i	$-0.233803\pi$
$53$	−0.0143905	−	0.0159823i	−0.00197669	−	0.00219534i	−0.744132	+	0.668032i	$0.767137\pi$
$54$	−0.500000	−	0.866025i	−0.0680414	−	0.117851i
$55$	−2.57448	+	13.2318i	−0.347143	+	1.78417i
$56$	2.63379	+	0.251291i	0.351955	+	0.0335802i
$57$	2.25975	−	6.95480i	0.299311	−	0.921186i
$58$	0.366492	+	0.163173i	0.0481228	+	0.0214256i
$59$	−2.86663	+	1.27631i	−0.373204	+	0.166161i	−0.584763	−	0.811204i	$-0.698812\pi$
$59$	−2.86663	+	1.27631i	−0.373204	+	0.166161i	0.211559	+	0.977365i	$0.432146\pi$
$60$	3.97552	+	0.845024i	0.513238	+	0.109092i
$61$	−5.14692	+	5.71623i	−0.658995	+	0.731889i	−0.976297	−	0.216436i	$-0.930557\pi$
$61$	−5.14692	+	5.71623i	−0.658995	+	0.731889i	0.317301	+	0.948325i	$0.397223\pi$
$62$	−4.95205	−	3.59788i	−0.628911	−	0.456931i
$63$	2.30388	+	1.30082i	0.290261	+	0.163889i
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	6.01158	+	10.4124i	0.745644	+	1.29149i
$66$	2.50269	+	2.17636i	0.308060	+	0.267891i
$67$	2.73153	−	4.73114i	0.333709	−	0.578001i	−0.649527	−	0.760339i	$-0.725033\pi$
$67$	2.73153	−	4.73114i	0.333709	−	0.578001i	0.983236	+	0.182337i	$0.0583663\pi$
$68$	4.37242	−	0.929387i	0.530234	−	0.112705i
$69$	2.93085	−	2.12939i	0.352833	−	0.256348i
$70$	−10.1946	+	3.42093i	−1.21848	+	0.408879i
$71$	−4.19406	−	12.9080i	−0.497743	−	1.53190i	−0.812638	−	0.582769i	$-0.801969\pi$
$71$	−4.19406	−	12.9080i	−0.497743	−	1.53190i	0.314895	−	0.949127i	$-0.398031\pi$
$72$	0.669131	−	0.743145i	0.0788578	−	0.0875805i
$73$	3.02937	−	1.34876i	0.354561	−	0.157861i	−0.221724	−	0.975109i	$-0.571168\pi$
$73$	3.02937	−	1.34876i	0.354561	−	0.157861i	0.576285	+	0.817249i	$0.304502\pi$
$74$	0.904907	+	8.60962i	0.105193	+	1.00085i
$75$	−11.2671	+	2.39491i	−1.30102	+	0.276540i
$76$	7.31271			0.838826
$77$	−8.62913	−	1.59316i	−0.983380	−	0.181558i
$78$	2.95821			0.334951
$79$	16.3109	−	3.46699i	1.83512	−	0.390066i	0.845522	−	0.533940i	$-0.179289\pi$
$79$	16.3109	−	3.46699i	1.83512	−	0.390066i	0.989596	+	0.143874i	$0.0459560\pi$
$80$	0.424839	+	4.04207i	0.0474985	+	0.451918i
$81$	0.913545	−	0.406737i	0.101505	−	0.0451930i
$82$	−4.55063	+	5.05399i	−0.502533	+	0.558120i
$83$	2.23659	+	6.88353i	0.245498	+	0.755565i	0.995554	+	0.0941910i	$0.0300264\pi$
$83$	2.23659	+	6.88353i	0.245498	+	0.755565i	−0.750056	+	0.661374i	$0.769974\pi$
$84$	−0.525220	+	2.59310i	−0.0573062	+	0.282930i
$85$	−14.6982	+	10.6789i	−1.59425	+	1.15829i
$86$	1.84799	−	0.392802i	0.199274	−	0.0423570i
$87$	−0.200588	+	0.347428i	−0.0215053	+	0.0372482i
$88$	−1.29646	+	3.05273i	−0.138203	+	0.325423i
$89$	−0.223374	−	0.386896i	−0.0236776	−	0.0410109i	0.853944	−	0.520365i	$-0.174204\pi$
$89$	−0.223374	−	0.386896i	−0.0236776	−	0.0410109i	−0.877621	+	0.479354i	$0.840871\pi$
$90$	−1.25595	+	3.86542i	−0.132389	+	0.407451i
$91$	−6.74023	+	3.97821i	−0.706568	+	0.417030i
$92$	2.93085	+	2.12939i	0.305563	+	0.222004i
$93$	4.09580	−	4.54885i	0.424715	−	0.471693i
$94$	0.127462	+	0.0270929i	0.0131467	+	0.00279442i
$95$	−27.1518	+	12.0888i	−2.78572	+	1.24028i
$96$	0.913545	+	0.406737i	0.0932383	+	0.0415124i
$97$	5.58811	−	17.1984i	0.567386	−	1.74624i	−0.0933667	−	0.995632i	$-0.529763\pi$
$97$	5.58811	−	17.1984i	0.567386	−	1.74624i	0.660753	−	0.750603i	$-0.270237\pi$
$98$	−2.29050	−	6.61465i	−0.231375	−	0.668181i
$99$	−2.42604	+	2.26149i	−0.243826	+	0.227289i
$100$	−5.75943	−	9.97562i	−0.575943	−	0.997562i
$101$	4.87292	+	5.41193i	0.484874	+	0.538507i	0.935089	−	0.354413i	$-0.115319\pi$
$101$	4.87292	+	5.41193i	0.484874	+	0.538507i	−0.450215	+	0.892920i	$0.648653\pi$
$102$	0.467253	+	4.44562i	0.0462650	+	0.440182i
$103$	−0.338420	+	3.21986i	−0.0333456	+	0.317262i	0.965116	+	0.261821i	$0.0843230\pi$
$103$	−0.338420	+	3.21986i	−0.0333456	+	0.317262i	−0.998462	+	0.0554407i	$0.982344\pi$
$104$	0.914136	+	2.81342i	0.0896384	+	0.275879i
$105$	−2.33657	−	10.4963i	−0.228025	−	1.02433i
$106$	0.0173990	+	0.0126411i	0.00168994	+	0.00122781i
$107$	−7.22304	−	3.21590i	−0.698278	−	0.310893i	0.0267216	−	0.999643i	$-0.491493\pi$
$107$	−7.22304	−	3.21590i	−0.698278	−	0.310893i	−0.724999	+	0.688750i	$0.758160\pi$
$108$	0.669131	+	0.743145i	0.0643871	+	0.0715091i
$109$	−7.28717	+	12.6217i	−0.697984	+	1.20894i	0.271180	+	0.962529i	$0.412586\pi$
$109$	−7.28717	+	12.6217i	−0.697984	+	1.20894i	−0.969164	+	0.246415i	$0.920747\pi$
$110$	−0.232813	−	13.4779i	−0.0221978	−	1.28507i
$111$	−8.65704			−0.821690
$112$	−2.62848	+	0.301796i	−0.248368	+	0.0285171i
$113$	−4.69137	+	3.40848i	−0.441327	+	0.320643i	−0.786162	−	0.618021i	$-0.787935\pi$
$113$	−4.69137	+	3.40848i	−0.441327	+	0.320643i	0.344835	+	0.938663i	$0.387935\pi$
$114$	−0.764386	+	7.27265i	−0.0715914	+	0.681146i
$115$	−14.4023	−	3.06130i	−1.34302	−	0.285467i
$116$	−0.392409	−	0.0834091i	−0.0364343	−	0.00774434i
$117$	−0.309217	+	2.94200i	−0.0285871	+	0.271988i
$118$	2.53863	−	1.84442i	0.233700	−	0.169793i
$119$	−7.04312	−	9.50092i	−0.645642	−	0.870948i
$120$	−4.06434			−0.371022
$121$	5.16771	−	9.71055i	0.469792	−	0.882777i
$122$	3.84597	−	6.66142i	0.348198	−	0.603097i
$123$	−4.55063	−	5.05399i	−0.410317	−	0.455703i
$124$	5.59188	+	2.48967i	0.502166	+	0.223579i
$125$	21.4348	+	15.5733i	1.91719	+	1.39292i
$126$	−2.52399	−	0.793395i	−0.224855	−	0.0706813i
$127$	3.93222	+	12.1021i	0.348928	+	1.07389i	0.959447	+	0.281889i	$0.0909610\pi$
$127$	3.93222	+	12.1021i	0.348928	+	1.07389i	−0.610519	+	0.792002i	$0.709039\pi$
$128$	−0.104528	+	0.994522i	−0.00923910	+	0.0879041i
$129$	0.197483	+	1.87893i	0.0173874	+	0.165430i
$130$	−8.04506	−	8.93494i	−0.705598	−	0.783646i
$131$	0.728040	+	1.26100i	0.0636092	+	0.110174i	0.896076	−	0.443900i	$-0.146406\pi$
$131$	0.728040	+	1.26100i	0.0636092	+	0.110174i	−0.832467	+	0.554075i	$0.813072\pi$
$132$	−2.90049	−	1.60846i	−0.252456	−	0.139998i
$133$	−8.03865	−	17.5986i	−0.697039	−	1.52599i
$134$	−1.68818	+	5.19567i	−0.145836	+	0.448838i
$135$	−3.71296	−	1.65312i	−0.319561	−	0.142278i
$136$	−4.08364	+	1.81816i	−0.350170	+	0.155906i
$137$	−13.7552	−	2.92376i	−1.17519	−	0.249793i	−0.421376	−	0.906886i	$-0.638453\pi$
$137$	−13.7552	−	2.92376i	−1.17519	−	0.249793i	−0.753810	+	0.657093i	$0.771786\pi$
$138$	−2.42408	+	2.69222i	−0.206352	+	0.229177i
$139$	12.6023	+	9.15613i	1.06892	+	0.776613i	0.975717	−	0.219035i	$-0.0702907\pi$
$139$	12.6023	+	9.15613i	1.06892	+	0.776613i	0.0931989	+	0.995648i	$0.470291\pi$
$140$	9.26054	−	5.46574i	0.782659	−	0.461940i
$141$	−0.0402679	+	0.123932i	−0.00339117	+	0.0104369i
$142$	6.78613	+	11.7539i	0.569479	+	0.986367i
$143$	−2.20532	−	9.56020i	−0.184418	−	0.799464i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	1.59488	−	0.339003i	0.132448	−	0.0281527i
$146$	−2.68275	+	1.94913i	−0.222026	+	0.161311i
$147$	6.81784	−	1.58653i	0.562326	−	0.130855i
$148$	−2.67517	−	8.23334i	−0.219898	−	0.676776i
$149$	4.20195	−	4.66674i	0.344237	−	0.382314i	−0.546020	−	0.837772i	$-0.683858\pi$
$149$	4.20195	−	4.66674i	0.344237	−	0.382314i	0.890257	+	0.455458i	$0.150524\pi$
$150$	10.5230	−	4.68514i	0.859199	−	0.382540i
$151$	−1.22051	−	11.6124i	−0.0993235	−	0.945000i	−0.924772	−	0.380522i	$-0.875744\pi$
$151$	−1.22051	−	11.6124i	−0.0993235	−	0.945000i	0.825448	−	0.564478i	$-0.190922\pi$
$152$	−7.15291	+	1.52040i	−0.580178	+	0.123321i
$153$	−4.47011			−0.361387
$154$	8.77180	−	0.235749i	0.706852	−	0.0189972i
$155$	−24.8781			−1.99826
$156$	−2.89356	+	0.615046i	−0.231670	+	0.0492431i
$157$	−0.650097	−	6.18526i	−0.0518834	−	0.493638i	−0.989349	−	0.145561i	$-0.953501\pi$
$157$	−0.650097	−	6.18526i	−0.0518834	−	0.493638i	0.937466	−	0.348077i	$-0.113165\pi$
$158$	−15.2336	+	6.78245i	−1.21192	+	0.539583i
$159$	−0.0143905	+	0.0159823i	−0.00114124	+	0.00126748i
$160$	−1.25595	−	3.86542i	−0.0992916	−	0.305588i
$161$	1.90273	−	9.39409i	0.149956	−	0.740358i
$162$	−0.809017	+	0.587785i	−0.0635624	+	0.0461808i
$163$	5.89158	−	1.25230i	0.461465	−	0.0980873i	0.0286877	−	0.999588i	$-0.490867\pi$
$163$	5.89158	−	1.25230i	0.461465	−	0.0980873i	0.432777	+	0.901501i	$0.357534\pi$
$164$	3.40041	−	5.88968i	0.265527	−	0.459906i
$165$	13.4284	+	1.17728i	1.04540	+	0.0916515i
$166$	−3.61888	−	6.26809i	−0.280880	−	0.486498i
$167$	−0.622218	+	1.91499i	−0.0481487	+	0.148186i	−0.972240	−	0.233985i	$-0.924823\pi$
$167$	−0.622218	+	1.91499i	−0.0481487	+	0.148186i	0.924092	+	0.382171i	$0.124823\pi$
$168$	−0.0253917	−	2.64563i	−0.00195902	−	0.204115i
$169$	3.43753	+	2.49751i	0.264425	+	0.192116i
$170$	12.1568	−	13.5015i	0.932383	−	1.03552i
$171$	−7.15291	−	1.52040i	−0.546997	−	0.116268i
$172$	−1.72594	+	0.768438i	−0.131602	+	0.0585928i
$173$	−8.77337	−	3.90616i	−0.667027	−	0.296980i	0.0451491	−	0.998980i	$-0.485624\pi$
$173$	−8.77337	−	3.90616i	−0.667027	−	0.296980i	−0.712176	+	0.702001i	$0.752290\pi$
$174$	0.123970	−	0.381541i	0.00939815	−	0.0289245i
$175$	−17.6759	+	24.8264i	−1.33617	+	1.87670i
$176$	0.633432	−	3.25557i	0.0477467	−	0.245398i
$177$	1.56896	+	2.71752i	0.117930	+	0.204261i
$178$	0.298933	+	0.331999i	0.0224060	+	0.0248844i
$179$	1.61585	+	15.3738i	0.120774	+	1.14909i	0.872158	+	0.489224i	$0.162720\pi$
$179$	1.61585	+	15.3738i	0.120774	+	1.14909i	−0.751384	+	0.659865i	$0.770613\pi$
$180$	0.424839	−	4.04207i	0.0316656	−	0.301278i
$181$	5.33243	+	16.4115i	0.396356	+	1.21986i	0.927900	+	0.372828i	$0.121612\pi$
$181$	5.33243	+	16.4115i	0.396356	+	1.21986i	−0.531544	+	0.847031i	$0.678388\pi$
$182$	5.76583	−	5.29265i	0.427391	−	0.392317i
$183$	6.22292	+	4.52121i	0.460011	+	0.334218i
$184$	−3.30953	−	1.47350i	−0.243982	−	0.108628i
$185$	23.5435	+	26.1477i	1.73095	+	1.92241i
$186$	−3.06054	+	5.30101i	−0.224410	+	0.388689i
$187$	14.0188	−	4.82422i	1.02516	−	0.352782i
$188$	−0.130310			−0.00950381
$189$	1.05288	−	2.42723i	0.0765856	−	0.176555i
$190$	24.0451	−	17.4698i	1.74441	−	1.26739i
$191$	−0.0366510	+	0.348711i	−0.00265197	+	0.0252318i	−0.995768	−	0.0919041i	$-0.970705\pi$
$191$	−0.0366510	+	0.348711i	−0.00265197	+	0.0252318i	0.993116	+	0.117136i	$0.0373713\pi$
$192$	−0.978148	−	0.207912i	−0.0705917	−	0.0150047i
$193$	20.9549	+	4.45410i	1.50837	+	0.320613i	0.886580	−	0.462575i	$-0.153074\pi$
$193$	20.9549	+	4.45410i	1.50837	+	0.320613i	0.621785	+	0.783188i	$0.286408\pi$
$194$	−1.89024	+	17.9844i	−0.135711	+	1.29121i
$195$	9.72694	−	7.06703i	0.696560	−	0.506081i
$196$	3.61571	+	5.99388i	0.258265	+	0.428135i
$197$	8.00492			0.570327			0.285163	−	0.958479i	$-0.407952\pi$
$197$	8.00492			0.570327			0.285163	+	0.958479i	$0.407952\pi$
$198$	1.90283	−	2.71647i	0.135228	−	0.193051i
$199$	0.404168	−	0.700040i	0.0286507	−	0.0496245i	−0.851345	−	0.524607i	$-0.824212\pi$
$199$	0.404168	−	0.700040i	0.0286507	−	0.0496245i	0.879995	+	0.474982i	$0.157546\pi$
$200$	7.70762	+	8.56018i	0.545011	+	0.605296i
$201$	−4.99075	−	2.22202i	−0.352020	−	0.156730i
$202$	−5.89164	−	4.28053i	−0.414534	−	0.301177i
$203$	0.230634	+	1.03605i	0.0161873	+	0.0727165i
$204$	−1.38134	−	4.25132i	−0.0967131	−	0.297652i
$205$	−2.88925	+	27.4894i	−0.201794	+	1.91994i
$206$	−0.338420	−	3.21986i	−0.0235789	−	0.224338i
$207$	−2.42408	−	2.69222i	−0.168485	−	0.187122i
$208$	−1.47910	−	2.56188i	−0.102557	−	0.177635i
$209$	24.0733	−	2.95140i	1.66518	−	0.204152i
$210$	4.46781	+	9.78114i	0.308308	+	0.674963i
$211$	−4.04478	+	12.4486i	−0.278454	+	0.856994i	0.709831	+	0.704373i	$0.248772\pi$
$211$	−4.04478	+	12.4486i	−0.278454	+	0.856994i	−0.988285	+	0.152621i	$0.951228\pi$
$212$	−0.0196470	−	0.00874740i	−0.00134936	−	0.000600774i
$213$	−12.3989	+	5.52033i	−0.849557	+	0.378247i
$214$	7.73382	+	1.64387i	0.528673	+	0.112373i
$215$	5.13802	−	5.70635i	0.350410	−	0.389170i
$216$	−0.809017	−	0.587785i	−0.0550466	−	0.0399937i
$217$	−0.155425	−	16.1941i	−0.0105509	−	1.09933i
$218$	4.50372	−	13.8610i	0.305030	−	0.938787i
$219$	−1.65803	−	2.87180i	−0.112039	−	0.194058i
$220$	3.02993	+	13.1350i	0.204278	+	0.885558i
$221$	6.61175	−	11.4519i	0.444754	−	0.770337i
$222$	8.46787	−	1.79990i	0.568326	−	0.120801i
$223$	−20.8590	+	15.1549i	−1.39682	+	1.01485i	−0.401743	+	0.915752i	$0.631596\pi$
$223$	−20.8590	+	15.1549i	−1.39682	+	1.01485i	−0.995078	+	0.0990974i	$0.968404\pi$
$224$	2.50830	−	0.841693i	0.167593	−	0.0562380i
$225$	3.55952	+	10.9551i	0.237302	+	0.730339i
$226$	3.88019	−	4.30938i	0.258106	−	0.286656i
$227$	21.4801	−	9.56356i	1.42568	−	0.634756i	0.458468	−	0.888711i	$-0.348398\pi$
$227$	21.4801	−	9.56356i	1.42568	−	0.634756i	0.967216	+	0.253955i	$0.0817316\pi$
$228$	−0.764386	−	7.27265i	−0.0506227	−	0.481643i
$229$	1.56805	−	0.333300i	0.103620	−	0.0220251i	−0.155810	−	0.987787i	$-0.549799\pi$
$229$	1.56805	−	0.333300i	0.103620	−	0.0220251i	0.259430	+	0.965762i	$0.416465\pi$
$230$	14.7240			0.970873
$231$	−0.682445	+	8.74839i	−0.0449016	+	0.575602i
$232$	0.401176			0.0263385
$233$	−0.176446	+	0.0375047i	−0.0115593	+	0.00245702i	−0.213688	−	0.976902i	$-0.568548\pi$
$233$	−0.176446	+	0.0375047i	−0.0115593	+	0.00245702i	0.202128	+	0.979359i	$0.435214\pi$
$234$	−0.309217	−	2.94200i	−0.0202141	−	0.192325i
$235$	0.483835	−	0.215417i	0.0315619	−	0.0140523i
$236$	−2.09968	+	2.33193i	−0.136677	+	0.151796i
$237$	−5.15295	−	15.8591i	−0.334720	−	1.03016i
$238$	8.86456	+	7.82895i	0.574604	+	0.507476i
$239$	2.64083	−	1.91868i	0.170821	−	0.124109i	−0.499090	−	0.866550i	$-0.666332\pi$
$239$	2.64083	−	1.91868i	0.170821	−	0.124109i	0.669911	+	0.742441i	$0.266332\pi$
$240$	3.97552	−	0.845024i	0.256619	−	0.0545460i
$241$	12.0102	−	20.8022i	0.773643	−	1.33999i	−0.161912	−	0.986805i	$-0.551766\pi$
$241$	12.0102	−	20.8022i	0.773643	−	1.33999i	0.935554	−	0.353183i	$-0.114901\pi$
$242$	−3.03585	+	10.5728i	−0.195152	+	0.679644i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	−2.37694	+	7.31548i	−0.152168	+	0.468326i
$245$	−23.3336	−	16.2779i	−1.49073	−	1.03995i
$246$	5.50197	+	3.99742i	0.350793	+	0.254866i
$247$	14.4750	−	16.0761i	0.921020	−	1.02290i
$248$	−5.98732	−	1.27264i	−0.380195	−	0.0808129i
$249$	6.61203	−	2.94387i	0.419020	−	0.186560i
$250$	−24.2043	−	10.7764i	−1.53081	−	0.681561i
$251$	−4.74905	+	14.6161i	−0.299757	+	0.922558i	0.681825	+	0.731516i	$0.261187\pi$
$251$	−4.74905	+	14.6161i	−0.299757	+	0.922558i	−0.981582	+	0.191042i	$0.938813\pi$
$252$	2.63379	+	0.251291i	0.165913	+	0.0158298i
$253$	10.5077	+	5.82701i	0.660614	+	0.366341i
$254$	−6.36247	−	11.0201i	−0.399217	−	0.691464i
$255$	12.1568	+	13.5015i	0.761287	+	0.845495i
$256$	−0.104528	−	0.994522i	−0.00653303	−	0.0621576i
$257$	1.59171	−	15.1441i	0.0992884	−	0.944666i	−0.825556	−	0.564320i	$-0.809138\pi$
$257$	1.59171	−	15.1441i	0.0992884	−	0.944666i	0.924844	−	0.380346i	$-0.124195\pi$
$258$	−0.583818	−	1.79681i	−0.0363469	−	0.111864i
$259$	−16.8734	+	15.4887i	−1.04846	+	0.962419i
$260$	9.72694	+	7.06703i	0.603239	+	0.438279i
$261$	0.366492	+	0.163173i	0.0226853	+	0.0101001i
$262$	−0.974308	−	1.08208i	−0.0601929	−	0.0668510i
$263$	8.45781	−	14.6494i	0.521531	−	0.903318i	−0.478155	−	0.878275i	$-0.658694\pi$
$263$	8.45781	−	14.6494i	0.521531	−	0.903318i	0.999686	−	0.0250431i	$-0.00797230\pi$
$264$	3.17153	+	0.970262i	0.195194	+	0.0597155i
$265$	0.0874089			0.00536949
$266$	11.5219	+	15.5427i	0.706455	+	0.952983i
$267$	−0.361427	+	0.262592i	−0.0221190	+	0.0160704i
$268$	0.571045	−	5.43313i	0.0348821	−	0.331881i
$269$	−25.9827	−	5.52279i	−1.58419	−	0.336731i	−0.670111	−	0.742261i	$-0.733754\pi$
$269$	−25.9827	−	5.52279i	−1.58419	−	0.336731i	−0.914082	+	0.405530i	$0.867087\pi$
$270$	3.97552	+	0.845024i	0.241943	+	0.0514265i
$271$	−0.761147	+	7.24183i	−0.0462364	+	0.439910i	0.946775	+	0.321895i	$0.104320\pi$
$271$	−0.761147	+	7.24183i	−0.0462364	+	0.439910i	−0.993012	+	0.118015i	$0.962347\pi$
$272$	3.61639	−	2.62746i	0.219276	−	0.159313i
$273$	4.66096	+	6.28747i	0.282094	+	0.380535i
$274$	14.0625			0.849546
$275$	−22.9860	−	30.5150i	−1.38611	−	1.84013i
$276$	1.81137	−	3.13738i	0.109031	−	0.188848i
$277$	−6.62668	−	7.35967i	−0.398158	−	0.442200i	0.510413	−	0.859929i	$-0.329493\pi$
$277$	−6.62668	−	7.35967i	−0.398158	−	0.442200i	−0.908571	+	0.417730i	$0.862826\pi$
$278$	−14.2306	−	6.33588i	−0.853495	−	0.380001i
$279$	−4.95205	−	3.59788i	−0.296472	−	0.215399i
$280$	−7.92179	+	7.27168i	−0.473417	+	0.434566i
$281$	−8.41388	−	25.8953i	−0.501930	−	1.54478i	−0.805871	−	0.592091i	$-0.798303\pi$
$281$	−8.41388	−	25.8953i	−0.501930	−	1.54478i	0.303941	−	0.952691i	$-0.401697\pi$
$282$	0.0136211	−	0.129596i	0.000811123	−	0.00771732i
$283$	2.58399	+	24.5851i	0.153603	+	1.46143i	0.751434	+	0.659808i	$0.229363\pi$
$283$	2.58399	+	24.5851i	0.153603	+	1.46143i	−0.597831	+	0.801622i	$0.703971\pi$
$284$	−9.08161	−	10.0862i	−0.538895	−	0.598503i
$285$	14.8607	+	25.7394i	0.880270	+	1.52467i
$286$	4.14480	+	8.89277i	0.245087	+	0.525841i
$287$	−17.9119	−	1.70898i	−1.05731	−	0.100878i
$288$	0.309017	−	0.951057i	0.0182090	−	0.0560415i
$289$	2.72405	+	1.21283i	0.160238	+	0.0713427i
$290$	−1.48955	+	0.663190i	−0.0874693	+	0.0389438i
$291$	−17.6883	−	3.75977i	−1.03691	−	0.220402i
$292$	2.21888	−	2.46432i	0.129850	−	0.144213i
$293$	−10.8830	−	7.90697i	−0.635793	−	0.461930i	0.222610	−	0.974908i	$-0.428542\pi$
$293$	−10.8830	−	7.90697i	−0.635793	−	0.461930i	−0.858402	+	0.512977i	$0.828542\pi$
$294$	−6.33899	+	2.96937i	−0.369698	+	0.173177i
$295$	3.94107	−	12.1294i	0.229458	−	0.706199i
$296$	4.32852	+	7.49722i	0.251590	+	0.435767i
$297$	2.50269	+	2.17636i	0.145221	+	0.126285i
$298$	−3.13986	+	5.43840i	−0.181887	+	0.315038i
$299$	10.4826	−	2.22815i	0.606225	−	0.128857i
$300$	−9.31895	+	6.77061i	−0.538030	+	0.390902i
$301$	3.74658	+	3.30888i	0.215949	+	0.190721i
$302$	3.60818	+	11.1048i	0.207627	+	0.639012i
$303$	4.87292	−	5.41193i	0.279942	−	0.310907i
$304$	6.68049	−	2.97435i	0.383153	−	0.170591i
$305$	−3.26784	−	31.0914i	−0.187116	−	1.78029i
$306$	4.37242	−	0.929387i	0.249955	−	0.0531295i
$307$	−17.0794			−0.974775			−0.487387	−	0.873186i	$-0.662050\pi$
$307$	−17.0794			−0.974775			−0.487387	+	0.873186i	$0.662050\pi$
$308$	−8.53110	+	2.05436i	−0.486104	+	0.117058i
$309$	3.23759			0.184180
$310$	24.3345	−	5.17245i	1.38211	−	0.293776i
$311$	−2.70840	−	25.7687i	−0.153579	−	1.46121i	−0.751541	−	0.659686i	$-0.770689\pi$
$311$	−2.70840	−	25.7687i	−0.153579	−	1.46121i	0.597962	−	0.801525i	$-0.295977\pi$
$312$	2.70246	−	1.20321i	0.152996	−	0.0681184i
$313$	−9.94008	+	11.0396i	−0.561847	+	0.623994i	−0.955403	−	0.295307i	$-0.904578\pi$
$313$	−9.94008	+	11.0396i	−0.561847	+	0.623994i	0.393556	+	0.919301i	$0.371245\pi$
$314$	1.92188	+	5.91494i	0.108458	+	0.333799i
$315$	−10.1946	+	3.42093i	−0.574399	+	0.192747i
$316$	13.4906	−	9.80149i	0.758905	−	0.551377i
$317$	1.74382	−	0.370660i	0.0979427	−	0.0208184i	−0.158680	−	0.987330i	$-0.550724\pi$
$317$	1.74382	−	0.370660i	0.0979427	−	0.0208184i	0.256622	+	0.966512i	$0.417390\pi$
$318$	0.0107532	−	0.0186250i	0.000603007	−	0.00104444i
$319$	−1.32546	−	0.116205i	−0.0742118	−	0.00650625i
$320$	2.03217	+	3.51982i	0.113602	+	0.196764i
$321$	−2.44327	+	7.51962i	−0.136370	+	0.419705i
$322$	0.0919875	+	9.58441i	0.00512626	+	0.534118i
$323$	26.4456	+	19.2139i	1.47147	+	1.06909i
$324$	0.669131	−	0.743145i	0.0371739	−	0.0412858i
$325$	−33.3305	−	7.08462i	−1.84884	−	0.392984i
$326$	−5.50247	+	2.44986i	−0.304754	+	0.135685i
$327$	13.3143	+	5.92792i	0.736284	+	0.327815i
$328$	−2.10157	+	6.46796i	−0.116040	+	0.357133i
$329$	0.143246	+	0.313600i	0.00789739	+	0.0172893i
$330$	−13.3797	+	1.64036i	−0.736529	+	0.0902988i
$331$	−12.7836	−	22.1418i	−0.702650	−	1.21703i	−0.967533	−	0.252745i	$-0.918667\pi$
$331$	−12.7836	−	22.1418i	−0.702650	−	1.21703i	0.264883	−	0.964281i	$-0.414667\pi$
$332$	4.84301	+	5.37871i	0.265795	+	0.295195i
$333$	0.904907	+	8.60962i	0.0495886	+	0.471804i
$334$	0.210472	−	2.00251i	0.0115165	−	0.109572i
$335$	6.86132	+	21.1170i	0.374874	+	1.15374i
$336$	0.574894	+	2.58254i	0.0313630	+	0.140889i
$337$	−7.50201	−	5.45053i	−0.408660	−	0.296909i	0.364399	−	0.931243i	$-0.381274\pi$
$337$	−7.50201	−	5.45053i	−0.408660	−	0.296909i	−0.773059	+	0.634334i	$0.781274\pi$
$338$	−3.88167	−	1.72823i	−0.211135	−	0.0940034i
$339$	3.88019	+	4.30938i	0.210743	+	0.234054i
$340$	−9.08401	+	15.7340i	−0.492650	+	0.853295i
$341$	19.4132	+	5.93905i	1.05128	+	0.321618i
$342$	7.31271			0.395426
$343$	10.4501	−	15.2904i	0.564252	−	0.825603i
$344$	1.52846	−	1.11049i	0.0824088	−	0.0598735i
$345$	−1.53908	+	14.6434i	−0.0828612	+	0.788372i
$346$	9.39379	+	1.99671i	0.505013	+	0.107344i
$347$	18.6944	+	3.97361i	1.00357	+	0.213315i	0.680253	−	0.732977i	$-0.261870\pi$
$347$	18.6944	+	3.97361i	1.00357	+	0.213315i	0.323313	+	0.946292i	$0.395203\pi$
$348$	−0.0419343	+	0.398978i	−0.00224791	+	0.0213875i
$349$	−19.9574	+	14.4999i	−1.06830	+	0.776163i	−0.975605	−	0.219532i	$-0.929547\pi$
$349$	−19.9574	+	14.4999i	−1.06830	+	0.776163i	−0.0926912	+	0.995695i	$0.529547\pi$
$350$	12.1280	−	27.9589i	0.648266	−	1.49447i
$351$	2.95821			0.157897
$352$	0.0572818	+	3.31613i	0.00305313	+	0.176750i
$353$	10.9310	−	18.9331i	0.581799	−	1.00771i	−0.413467	−	0.910519i	$-0.635682\pi$
$353$	10.9310	−	18.9331i	0.581799	−	1.00771i	0.995266	−	0.0971866i	$-0.0309844\pi$
$354$	−2.09968	−	2.33193i	−0.111597	−	0.123941i
$355$	50.3932	+	22.4365i	2.67460	+	1.19081i
$356$	−0.361427	−	0.262592i	−0.0191556	−	0.0139174i
$357$	−8.71266	+	7.99765i	−0.461123	+	0.423281i
$358$	−4.77692	−	14.7019i	−0.252468	−	0.777018i
$359$	−1.21162	+	11.5278i	−0.0639468	+	0.608413i	0.914880	+	0.403725i	$0.132285\pi$
$359$	−1.21162	+	11.5278i	−0.0639468	+	0.608413i	−0.978827	+	0.204688i	$0.934382\pi$
$360$	0.424839	+	4.04207i	0.0223910	+	0.213036i
$361$	23.0688	+	25.6205i	1.21415	+	1.34845i
$362$	−8.62805	−	14.9442i	−0.453480	−	0.785451i
$363$	−10.1975	−	4.12437i	−0.535231	−	0.216473i
$364$	−4.53942	+	6.37577i	−0.237931	+	0.334181i
$365$	−4.16481	+	12.8180i	−0.217996	+	0.670923i
$366$	−7.02695	−	3.12860i	−0.367304	−	0.163534i
$367$	−15.6383	+	6.96264i	−0.816315	+	0.363447i	−0.772041	−	0.635573i	$-0.780764\pi$
$367$	−15.6383	+	6.96264i	−0.816315	+	0.363447i	−0.0442737	+	0.999019i	$0.514097\pi$
$368$	3.54357	+	0.753209i	0.184721	+	0.0392637i
$369$	−4.55063	+	5.05399i	−0.236896	+	0.263100i
$370$	−28.4654	−	20.6813i	−1.47985	−	1.07517i
$371$	0.000546083		0.0568977i	2.83512e−5		0.00295398i
$372$	1.89152	−	5.82149i	0.0980706	−	0.301830i
$373$	−9.79539	−	16.9661i	−0.507186	−	0.878472i	−0.999965	−	0.00831777i	$-0.997352\pi$
$373$	−9.79539	−	16.9661i	−0.507186	−	0.878472i	0.492779	−	0.870154i	$-0.335981\pi$
$374$	−12.7095	+	7.63348i	−0.657190	+	0.394718i
$375$	13.2474	−	22.9452i	0.684094	−	1.18489i
$376$	0.127462	−	0.0270929i	0.00657336	−	0.00139721i
$377$	−0.960109	+	0.697560i	−0.0494481	+	0.0359262i
$378$	−0.525220	+	2.59310i	−0.0270144	+	0.133374i
$379$	−9.13488	−	28.1143i	−0.469227	−	1.44413i	−0.853587	−	0.520950i	$-0.825578\pi$
$379$	−9.13488	−	28.1143i	−0.469227	−	1.44413i	0.384360	−	0.923183i	$-0.374422\pi$
$380$	−19.8875	+	22.0873i	−1.02021	+	1.13305i
$381$	11.6248	−	5.17570i	0.595557	−	0.265159i
$382$	−0.0366510	−	0.348711i	−0.00187523	−	0.0178416i
$383$	−11.1720	+	2.37469i	−0.570864	+	0.121341i	−0.484295	−	0.874905i	$-0.660924\pi$
$383$	−11.1720	+	2.37469i	−0.570864	+	0.121341i	−0.0865693	+	0.996246i	$0.527590\pi$
$384$	1.00000			0.0510310
$385$	28.2795	−	21.7306i	1.44126	−	1.10750i
$386$	−21.4230			−1.09040
$387$	1.84799	−	0.392802i	0.0939386	−	0.0199673i
$388$	−1.89024	−	17.9844i	−0.0959624	−	0.913021i
$389$	−14.3732	+	6.39937i	−0.728752	+	0.324461i	−0.737358	−	0.675502i	$-0.763927\pi$
$389$	−14.3732	+	6.39937i	−0.728752	+	0.324461i	0.00860667	+	0.999963i	$0.497260\pi$
$390$	−8.04506	+	8.93494i	−0.407377	+	0.452438i
$391$	5.00422	+	15.4014i	0.253074	+	0.778883i
$392$	−4.78290	−	5.11115i	−0.241573	−	0.258152i
$393$	1.17799	−	0.855863i	0.0594219	−	0.0431726i
$394$	−7.82999	+	1.66432i	−0.394469	+	0.0838470i
$395$	−33.8870	+	58.6940i	−1.70504	+	2.95322i
$396$	−1.29646	+	3.05273i	−0.0651497	+	0.153406i
$397$	5.52663	+	9.57241i	0.277374	+	0.480425i	0.970731	−	0.240168i	$-0.0772027\pi$
$397$	5.52663	+	9.57241i	0.277374	+	0.480425i	−0.693358	+	0.720594i	$0.743869\pi$
$398$	−0.249790	+	0.768774i	−0.0125208	+	0.0385351i
$399$	−16.6619	+	9.83417i	−0.834139	+	0.492324i
$400$	−9.31895	−	6.77061i	−0.465948	−	0.338531i
$401$	−18.4674	+	20.5102i	−0.922220	+	1.02423i	0.0774089	+	0.996999i	$0.475335\pi$
$401$	−18.4674	+	20.5102i	−0.922220	+	1.02423i	−0.999629	+	0.0272300i	$0.991331\pi$
$402$	5.34367	+	1.13583i	0.266518	+	0.0566502i
$403$	16.5419	−	7.36494i	0.824012	−	0.366874i
$404$	6.65286	+	2.96205i	0.330992	+	0.147367i
$405$	−1.25595	+	3.86542i	−0.0624087	+	0.192074i
$406$	−0.441001	−	0.965459i	−0.0218865	−	0.0479149i
$407$	−12.1296	−	26.0243i	−0.601240	−	1.28997i
$408$	2.23505	+	3.87123i	0.110652	+	0.191654i
$409$	−3.79285	−	4.21239i	−0.187544	−	0.208289i	0.642039	−	0.766672i	$-0.278089\pi$
$409$	−3.79285	−	4.21239i	−0.187544	−	0.208289i	−0.829583	+	0.558383i	$0.811422\pi$
$410$	−2.88925	−	27.4894i	−0.142690	−	1.35760i
$411$	−1.46993	+	13.9855i	−0.0725063	+	0.689852i
$412$	1.00047	+	3.07913i	0.0492897	+	0.151698i
$413$	7.92007	+	2.48961i	0.389721	+	0.122506i
$414$	2.93085	+	2.12939i	0.144044	+	0.104654i
$415$	−26.8735	−	11.9649i	−1.31917	−	0.587332i
$416$	1.97943	+	2.19838i	0.0970493	+	0.107784i
$417$	7.78867	−	13.4904i	0.381413	−	0.660626i
$418$	−22.9336	+	7.89202i	−1.12172	+	0.386011i
$419$	22.9429			1.12083			0.560417	−	0.828210i	$-0.310641\pi$
$419$	22.9429			1.12083			0.560417	+	0.828210i	$0.310641\pi$
$420$	−6.40379	−	8.63849i	−0.312473	−	0.421515i
$421$	24.3997	−	17.7275i	1.18917	−	0.863983i	0.195994	−	0.980605i	$-0.437207\pi$
$421$	24.3997	−	17.7275i	1.18917	−	0.863983i	0.993176	+	0.116622i	$0.0372065\pi$
$422$	1.36819	−	13.0175i	0.0666026	−	0.633681i
$423$	0.127462	+	0.0270929i	0.00619742	+	0.00131730i
$424$	0.0210363	+	0.00447141i	0.00102162	+	0.000217151i
$425$	5.38222	−	51.2084i	0.261076	−	2.48397i
$426$	10.9802	−	7.97757i	0.531992	−	0.386515i
$427$	20.2182	−	2.32140i	0.978425	−	0.112340i
$428$	−7.90660			−0.382180
$429$	−9.27731	+	3.19255i	−0.447913	+	0.154138i
$430$	−3.83933	+	6.64991i	−0.185149	+	0.320687i
$431$	−8.79386	−	9.76657i	−0.423585	−	0.470439i	0.493144	−	0.869948i	$-0.335847\pi$
$431$	−8.79386	−	9.76657i	−0.423585	−	0.470439i	−0.916730	+	0.399508i	$0.869181\pi$
$432$	0.913545	+	0.406737i	0.0439530	+	0.0195691i
$433$	−22.1364	−	16.0830i	−1.06381	−	0.772901i	−0.0890180	−	0.996030i	$-0.528373\pi$
$433$	−22.1364	−	16.0830i	−1.06381	−	0.772901i	−0.974789	+	0.223129i	$0.928373\pi$
$434$	3.51897	+	15.8079i	0.168916	+	0.758804i
$435$	−0.503857	−	1.55071i	−0.0241581	−	0.0743509i
$436$	−1.52343	+	14.4945i	−0.0729592	+	0.694161i
$437$	2.76917	+	26.3469i	0.132467	+	1.26034i
$438$	2.21888	+	2.46432i	0.106022	+	0.117750i
$439$	13.3724	+	23.1617i	0.638231	+	1.10545i	0.985821	+	0.167802i	$0.0536669\pi$
$439$	13.3724	+	23.1617i	0.638231	+	1.10545i	−0.347590	+	0.937647i	$0.613000\pi$
$440$	−5.69463	−	12.2180i	−0.271481	−	0.582468i
$441$	−2.29050	−	6.61465i	−0.109071	−	0.314983i
$442$	−4.08628	+	12.5763i	−0.194365	+	0.598193i
$443$	3.93479	+	1.75188i	0.186947	+	0.0832343i	0.498076	−	0.867134i	$-0.334040\pi$
$443$	3.93479	+	1.75188i	0.186947	+	0.0832343i	−0.311128	+	0.950368i	$0.600707\pi$
$444$	−7.90860	+	3.52114i	−0.375326	+	0.167106i
$445$	1.77606	+	0.377513i	0.0841933	+	0.0178958i
$446$	17.2523	−	19.1606i	0.816919	−	0.907280i
$447$	−5.08040	−	3.69113i	−0.240295	−	0.174584i
$448$	−2.27849	+	1.34480i	−0.107648	+	0.0635360i
$449$	−11.7771	+	36.2461i	−0.555795	+	1.71056i	0.138041	+	0.990427i	$0.455920\pi$
$449$	−11.7771	+	36.2461i	−0.555795	+	1.71056i	−0.693835	+	0.720134i	$0.744080\pi$
$450$	−5.75943	−	9.97562i	−0.271502	−	0.470255i
$451$	8.81699	−	20.7611i	0.415176	−	0.977601i
$452$	−2.89942	+	5.02195i	−0.136377	+	0.236213i
$453$	−11.4212	+	2.42764i	−0.536613	+	0.114061i
$454$	−19.0223	+	13.8205i	−0.892762	+	0.648630i
$455$	6.31481	−	31.1772i	0.296043	−	1.46161i
$456$	2.25975	+	6.95480i	0.105823	+	0.325688i
$457$	−2.53191	+	2.81198i	−0.118438	+	0.131539i	−0.799448	−	0.600736i	$-0.794874\pi$
$457$	−2.53191	+	2.81198i	−0.118438	+	0.131539i	0.681010	+	0.732274i	$0.261541\pi$
$458$	−1.46449	+	0.652033i	−0.0684312	+	0.0304675i
$459$	0.467253	+	4.44562i	0.0218095	+	0.207504i
$460$	−14.4023	+	3.06130i	−0.671509	+	0.142734i
$461$	−12.9291			−0.602168			−0.301084	−	0.953598i	$-0.597349\pi$
$461$	−12.9291			−0.602168			−0.301084	+	0.953598i	$0.597349\pi$
$462$	−1.15136	−	8.69910i	−0.0535661	−	0.404719i
$463$	0.102436			0.00476060			0.00238030	−	0.999997i	$-0.499242\pi$
$463$	0.102436			0.00476060			0.00238030	+	0.999997i	$0.499242\pi$
$464$	−0.392409	+	0.0834091i	−0.0182171	+	0.00387217i
$465$	2.60047	+	24.7418i	0.120594	+	1.14738i
$466$	0.164792	−	0.0733703i	0.00763386	−	0.00339881i
$467$	−20.4786	+	22.7438i	−0.947637	+	1.05246i	0.0509167	+	0.998703i	$0.483786\pi$
$467$	−20.4786	+	22.7438i	−0.947637	+	1.05246i	−0.998554	+	0.0537551i	$0.982881\pi$
$468$	0.914136	+	2.81342i	0.0422559	+	0.130050i
$469$	−13.7030	+	4.59822i	−0.632744	+	0.212326i
$470$	−0.428474	+	0.311305i	−0.0197640	+	0.0143594i
$471$	−6.08343	+	1.29307i	−0.280310	+	0.0595816i
$472$	1.56896	−	2.71752i	0.0722172	−	0.125084i
$473$	−5.37161	+	3.22626i	−0.246987	+	0.148344i
$474$	8.33764	+	14.4412i	0.382961	+	0.663307i
$475$	26.0298	−	80.1114i	1.19433	−	3.67576i
$476$	−10.2986	−	5.81482i	−0.472035	−	0.266522i
$477$	0.0173990	+	0.0126411i	0.000796644	+	0.000578796i
$478$	−2.18421	+	2.42581i	−0.0999033	+	0.110954i
$479$	7.36243	+	1.56493i	0.336398	+	0.0715036i	0.373014	−	0.927826i	$-0.378324\pi$
$479$	7.36243	+	1.56493i	0.336398	+	0.0715036i	−0.0366157	+	0.999329i	$0.511658\pi$
$480$	−3.71296	+	1.65312i	−0.169473	+	0.0754541i
$481$	−23.3953	−	10.4162i	−1.06673	−	0.474940i
$482$	−7.42269	+	22.8447i	−0.338094	+	1.04055i
$483$	−9.54152	−	0.910360i	−0.434154	−	0.0414228i
$484$	0.771301	−	10.9729i	0.0350591	−	0.498769i
$485$	36.7487	+	63.6507i	1.66867	+	2.89023i
$486$	0.669131	+	0.743145i	0.0303524	+	0.0337097i
$487$	2.52561	+	24.0295i	0.114446	+	1.08888i	0.889484	+	0.456967i	$0.151064\pi$
$487$	2.52561	+	24.0295i	0.114446	+	1.08888i	−0.775038	+	0.631915i	$0.782269\pi$
$488$	0.804028	−	7.64981i	0.0363966	−	0.346291i
$489$	−1.86127	−	5.72841i	−0.0841697	−	0.259048i
$490$	26.2080	+	11.0708i	1.18396	+	0.500129i
$491$	−6.64020	−	4.82439i	−0.299668	−	0.217722i	0.427782	−	0.903882i	$-0.359295\pi$
$491$	−6.64020	−	4.82439i	−0.299668	−	0.217722i	−0.727451	+	0.686160i	$0.759295\pi$
$492$	−6.21285	−	2.76614i	−0.280097	−	0.124707i
$493$	−1.19995	−	1.33268i	−0.0540430	−	0.0600209i
$494$	−10.8163	+	18.7343i	−0.486646	+	0.842896i
$495$	−0.232813	−	13.4779i	−0.0104641	−	0.605786i
$496$	6.12108			0.274844
$497$	−14.2899	+	32.9430i	−0.640991	+	1.47770i
$498$	−5.85548	+	4.25425i	−0.262390	+	0.190638i
$499$	−2.02233	+	19.2411i	−0.0905317	+	0.861352i	0.851167	+	0.524895i	$0.175895\pi$
$499$	−2.02233	+	19.2411i	−0.0905317	+	0.861352i	−0.941699	+	0.336457i	$0.890771\pi$
$500$	25.9159	+	5.50859i	1.15899	+	0.246352i
$501$	1.96954	+	0.418639i	0.0879926	+	0.0187034i
$502$	1.60642	−	15.2840i	0.0716980	−	0.682160i
$503$	21.3373	−	15.5024i	0.951383	−	0.691220i	0.000249069	−	1.00000i	$-0.499921\pi$
$503$	21.3373	−	15.5024i	0.951383	−	0.691220i	0.951133	+	0.308780i	$0.0999207\pi$
$504$	−2.62848	+	0.301796i	−0.117082	+	0.0134431i
$505$	−29.5984			−1.31711
$506$	−11.4896	−	3.51500i	−0.510775	−	0.156261i
$507$	2.12451	−	3.67976i	0.0943528	−	0.163424i
$508$	8.51464	+	9.45647i	0.377776	+	0.419563i
$509$	21.7115	+	9.66659i	0.962347	+	0.428464i	0.826918	−	0.562323i	$-0.190092\pi$
$509$	21.7115	+	9.66659i	0.962347	+	0.428464i	0.135429	+	0.990787i	$0.456759\pi$
$510$	−14.6982	−	10.6789i	−0.650849	−	0.472870i
$511$	−8.36971	−	2.63095i	−0.370254	−	0.116386i
$512$	0.309017	+	0.951057i	0.0136568	+	0.0420312i
$513$	−0.764386	+	7.27265i	−0.0337485	+	0.321095i
$514$	1.59171	+	15.1441i	0.0702075	+	0.667980i
$515$	−8.80487	−	9.77880i	−0.387989	−	0.430905i
$516$	0.944638	+	1.63616i	0.0415854	+	0.0720280i
$517$	−0.428976	+	0.0525927i	−0.0188664	+	0.00231303i
$518$	13.2844	−	18.6584i	0.583683	−	0.819802i
$519$	−2.96769	+	9.13362i	−0.130267	+	0.400921i
$520$	−10.9837	−	4.89026i	−0.481667	−	0.214452i
$521$	−9.57018	+	4.26092i	−0.419277	+	0.186674i	−0.605521	−	0.795829i	$-0.707035\pi$
$521$	−9.57018	+	4.26092i	−0.419277	+	0.186674i	0.186244	+	0.982504i	$0.440369\pi$
$522$	−0.392409	−	0.0834091i	−0.0171753	−	0.00365072i
$523$	−14.8236	+	16.4633i	−0.648190	+	0.719888i	−0.974252	−	0.225460i	$-0.927611\pi$
$523$	−14.8236	+	16.4633i	−0.648190	+	0.719888i	0.326062	+	0.945348i	$0.394278\pi$
$524$	1.17799	+	0.855863i	0.0514609	+	0.0373885i
$525$	26.5380	+	14.9840i	1.15822	+	0.653956i
$526$	−5.22722	+	16.0877i	−0.227917	+	0.701458i
$527$	13.6809	+	23.6961i	0.595951	+	1.03222i
$528$	−3.30395	−	0.289662i	−0.143786	−	0.0126059i
$529$	4.93790	−	8.55270i	0.214691	−	0.371856i
$530$	−0.0854988	+	0.0181733i	−0.00371383	+	0.000789399i
$531$	2.53863	−	1.84442i	0.110167	−	0.0800411i
$532$	−14.5017	−	12.8075i	−0.628727	−	0.555275i
$533$	−6.21687	−	19.1335i	−0.269282	−	0.828766i
$534$	0.298933	−	0.331999i	0.0129361	−	0.0143670i
$535$	29.3569	−	13.0705i	1.26921	−	0.565088i
$536$	0.571045	+	5.43313i	0.0246654	+	0.234675i
$537$	15.1206	−	3.21399i	0.652504	−	0.138694i
$538$	26.5632			1.14522
$539$	14.3219	+	18.2724i	0.616890	+	0.787049i
$540$	−4.06434			−0.174901
$541$	10.9665	−	2.33101i	0.471489	−	0.100218i	0.0339614	−	0.999423i	$-0.489188\pi$
$541$	10.9665	−	2.33101i	0.471489	−	0.100218i	0.437527	+	0.899205i	$0.355854\pi$
$542$	−0.761147	−	7.24183i	−0.0326941	−	0.311063i
$543$	15.7642	−	7.01869i	0.676508	−	0.301201i
$544$	−2.99108	+	3.32194i	−0.128242	+	0.142427i
$545$	−18.3046	−	56.3359i	−0.784085	−	2.41316i
$546$	−5.86635	−	5.18101i	−0.251057	−	0.221727i
$547$	−2.13798	+	1.55333i	−0.0914134	+	0.0664157i	−0.632553	−	0.774517i	$-0.717993\pi$
$547$	−2.13798	+	1.55333i	−0.0914134	+	0.0664157i	0.541140	+	0.840933i	$0.317993\pi$
$548$	−13.7552	+	2.92376i	−0.587593	+	0.124897i
$549$	3.84597	−	6.66142i	0.164142	−	0.284303i
$550$	28.8282	+	25.0691i	1.22924	+	1.06895i
$551$	−1.46684	−	2.54064i	−0.0624895	−	0.108235i
$552$	−1.11949	+	3.44542i	−0.0476485	+	0.146647i
$553$	−38.4178	−	21.6916i	−1.63369	−	0.922422i
$554$	8.01203	+	5.82108i	0.340399	+	0.247314i
$555$	23.5435	−	26.1477i	0.999365	−	1.10991i
$556$	15.2369	+	3.23871i	0.646190	+	0.137352i
$557$	−8.94754	+	3.98370i	−0.379119	+	0.168795i	−0.587444	−	0.809265i	$-0.699866\pi$
$557$	−8.94754	+	3.98370i	−0.379119	+	0.168795i	0.208324	+	0.978060i	$0.433199\pi$
$558$	5.59188	+	2.48967i	0.236723	+	0.105396i
$559$	−1.72705	+	5.31533i	−0.0730466	+	0.224814i
$560$	6.23681	−	8.75981i	0.263553	−	0.370169i
$561$	−6.26316	−	13.4378i	−0.264431	−	0.567342i
$562$	13.6139	+	23.5800i	0.574270	+	0.994664i
$563$	−8.10641	−	9.00308i	−0.341645	−	0.379435i	0.547698	−	0.836676i	$-0.315504\pi$
$563$	−8.10641	−	9.00308i	−0.341645	−	0.379435i	−0.889343	+	0.457241i	$0.848838\pi$
$564$	0.0136211	+	0.129596i	0.000573551	+	0.00545697i
$565$	2.46358	−	23.4394i	0.103644	−	0.986102i
$566$	−7.63905	−	23.5106i	−0.321093	−	0.988223i
$567$	−2.52399	−	0.793395i	−0.105998	−	0.0333195i
$568$	10.9802	+	7.97757i	0.460718	+	0.334732i
$569$	30.8458	+	13.7334i	1.29312	+	0.575736i	0.933906	−	0.357518i	$-0.116377\pi$
$569$	30.8458	+	13.7334i	1.29312	+	0.575736i	0.359218	+	0.933254i	$0.383043\pi$
$570$	−19.8875	−	22.0873i	−0.832994	−	0.925134i
$571$	−2.40510	+	4.16576i	−0.100650	+	0.174332i	−0.911953	−	0.410295i	$-0.865426\pi$
$571$	−2.40510	+	4.16576i	−0.100650	+	0.174332i	0.811302	+	0.584627i	$0.198759\pi$
$572$	−5.90314	−	7.83669i	−0.246823	−	0.327668i
$573$	0.350632			0.0146478
$574$	17.8758	−	2.05246i	0.746122	−	0.0856680i
$575$	33.7601	−	24.5281i	1.40789	−	1.02289i
$576$	−0.104528	+	0.994522i	−0.00435535	+	0.0414384i
$577$	−25.3173	−	5.38136i	−1.05397	−	0.224029i	−0.351829	−	0.936064i	$-0.614440\pi$
$577$	−25.3173	−	5.38136i	−1.05397	−	0.224029i	−0.702144	+	0.712035i	$0.747774\pi$
$578$	−2.91669	−	0.619961i	−0.121318	−	0.0257870i
$579$	2.23932	−	21.3057i	0.0930628	−	0.885433i
$580$	1.31911	−	0.958392i	0.0547732	−	0.0397951i
$581$	7.62049	−	17.5677i	0.316151	−	0.728832i
$582$	18.0835			0.749585
$583$	−0.0682079	−	0.0208668i	−0.00282488	−	0.000864213i
$584$	−1.65803	+	2.87180i	−0.0686098	+	0.118836i
$585$	−8.04506	−	8.93494i	−0.332622	−	0.369414i
$586$	12.2891	+	5.47148i	0.507660	+	0.226025i
$587$	33.5882	+	24.4033i	1.38633	+	1.00723i	0.996256	+	0.0864480i	$0.0275516\pi$
$587$	33.5882	+	24.4033i	1.38633	+	1.00723i	0.390077	+	0.920782i	$0.372448\pi$
$588$	5.58310	−	4.22243i	0.230243	−	0.174130i
$589$	13.8321	+	42.5709i	0.569942	+	1.75410i
$590$	−1.33311	+	12.6837i	−0.0548833	+	0.522180i
$591$	−0.836742	−	7.96107i	−0.0344190	−	0.327475i
$592$	−5.79269	−	6.43344i	−0.238078	−	0.264413i
$593$	−4.19594	−	7.26757i	−0.172306	−	0.298443i	0.766919	−	0.641743i	$-0.221789\pi$
$593$	−4.19594	−	7.26757i	−0.172306	−	0.298443i	−0.939226	+	0.343300i	$0.888455\pi$
$594$	−2.90049	−	1.60846i	−0.119009	−	0.0659958i
$595$	47.8508	+	4.56546i	1.96169	+	0.187166i
$596$	1.94054	−	5.97237i	0.0794876	−	0.244638i
$597$	−0.738452	−	0.328780i	−0.0302228	−	0.0134561i
$598$	−9.79028	+	4.35891i	−0.400354	+	0.178249i
$599$	28.6991	+	6.10018i	1.17261	+	0.249247i	0.752728	−	0.658331i	$-0.228737\pi$
$599$	28.6991	+	6.10018i	1.17261	+	0.249247i	0.419884	+	0.907578i	$0.362071\pi$
$600$	7.70762	−	8.56018i	0.314662	−	0.349468i
$601$	−21.3292	−	15.4966i	−0.870037	−	0.632119i	0.0605601	−	0.998165i	$-0.480711\pi$
$601$	−21.3292	−	15.4966i	−0.870037	−	0.632119i	−0.930597	+	0.366046i	$0.880711\pi$
$602$	−4.35266	−	2.45762i	−0.177401	−	0.100165i
$603$	−1.68818	+	5.19567i	−0.0687479	+	0.211584i
$604$	−5.83816	−	10.1120i	−0.237551	−	0.411451i
$605$	15.2757	+	42.0171i	0.621046	+	1.70824i
$606$	−3.64123	+	6.30680i	−0.147915	+	0.256196i
$607$	−2.50148	+	0.531707i	−0.101532	+	0.0215813i	−0.258398	−	0.966039i	$-0.583194\pi$
$607$	−2.50148	+	0.531707i	−0.101532	+	0.0215813i	0.156865	+	0.987620i	$0.449861\pi$
$608$	−5.91611	+	4.29830i	−0.239930	+	0.174319i
$609$	1.00627	−	0.337667i	0.0407760	−	0.0136830i
$610$	9.66070	+	29.7326i	0.391150	+	1.20384i
$611$	−0.257938	+	0.286470i	−0.0104351	+	0.0115893i
$612$	−4.08364	+	1.81816i	−0.165072	+	0.0734946i
$613$	1.61880	+	15.4018i	0.0653826	+	0.622073i	0.977323	+	0.211752i	$0.0679169\pi$
$613$	1.61880	+	15.4018i	0.0653826	+	0.622073i	−0.911941	+	0.410322i	$0.865416\pi$
$614$	16.7062	−	3.55101i	0.674208	−	0.143307i
$615$	27.6408			1.11458
$616$	7.91755	−	3.78318i	0.319007	−	0.152429i
$617$	−14.0324			−0.564923			−0.282461	−	0.959279i	$-0.591151\pi$
$617$	−14.0324			−0.564923			−0.282461	+	0.959279i	$0.591151\pi$
$618$	−3.16684	+	0.673133i	−0.127389	+	0.0270774i
$619$	2.13190	+	20.2837i	0.0856885	+	0.815271i	0.949986	+	0.312291i	$0.101096\pi$
$619$	2.13190	+	20.2837i	0.0856885	+	0.815271i	−0.864298	+	0.502980i	$0.832237\pi$
$620$	−22.7273	+	10.1188i	−0.912750	+	0.406383i
$621$	−2.42408	+	2.69222i	−0.0972751	+	0.108035i
$622$	8.00684	+	24.6425i	0.321045	+	0.988075i
$623$	−0.234642	+	1.15846i	−0.00940071	+	0.0464128i
$624$	−2.39324	+	1.73879i	−0.0958062	+	0.0696073i
$625$	−48.9952	+	10.4143i	−1.95981	+	0.416570i
$626$	7.42761	−	12.8650i	0.296867	−	0.514189i
$627$	−5.45157	−	23.6329i	−0.217715	−	0.943807i
$628$	−3.10967	−	5.38610i	−0.124089	−	0.214929i
$629$	11.9583	−	36.8039i	0.476809	−	1.46747i
$630$	9.26054	−	5.46574i	0.368949	−	0.217760i
$631$	−19.8470	−	14.4197i	−0.790095	−	0.574038i	0.117896	−	0.993026i	$-0.462385\pi$
$631$	−19.8470	−	14.4197i	−0.790095	−	0.574038i	−0.907992	+	0.418988i	$0.862385\pi$
$632$	−11.1579	+	12.3921i	−0.443839	+	0.492933i
$633$	12.8032	+	2.72139i	0.508880	+	0.108166i
$634$	−1.62865	+	0.725121i	−0.0646819	+	0.0287982i
$635$	−47.2472	−	21.0358i	−1.87495	−	0.834780i
$636$	−0.00664581	+	0.0204537i	−0.000263524	+	0.000811042i
$637$	20.3338	+	3.91576i	0.805656	+	0.155148i
$638$	1.32066	−	0.161914i	0.0522855	−	0.00641022i
$639$	6.78613	+	11.7539i	0.268455	+	0.464978i
$640$	−2.71957	−	3.02039i	−0.107501	−	0.119392i
$641$	1.58308	+	15.0620i	0.0625279	+	0.594913i	0.980260	+	0.197713i	$0.0633514\pi$
$641$	1.58308	+	15.0620i	0.0625279	+	0.594913i	−0.917732	+	0.397200i	$0.869982\pi$
$642$	0.826465	−	7.86329i	0.0326180	−	0.310339i
$643$	7.55820	+	23.2617i	0.298066	+	0.917353i	0.982174	+	0.187973i	$0.0601916\pi$
$643$	7.55820	+	23.2617i	0.298066	+	0.917353i	−0.684108	+	0.729381i	$0.739808\pi$
$644$	−2.08269	−	9.35584i	−0.0820694	−	0.368672i
$645$	−6.21216	−	4.51340i	−0.244604	−	0.177715i
$646$	−29.8625	−	13.2956i	−1.17492	−	0.523110i
$647$	−26.3879	−	29.3068i	−1.03742	−	1.15217i	−0.988167	−	0.153381i	$-0.950984\pi$
$647$	−26.3879	−	29.3068i	−1.03742	−	1.15217i	−0.0492494	−	0.998787i	$-0.515683\pi$
$648$	−0.500000	+	0.866025i	−0.0196419	+	0.0340207i
$649$	−5.97093	+	8.52408i	−0.234379	+	0.334599i
$650$	34.0752			1.33654
$651$	−16.0891	+	1.84732i	−0.630583	+	0.0724021i
$652$	4.87288	−	3.54035i	0.190837	−	0.138651i
$653$	3.43824	−	32.7126i	0.134549	−	1.28014i	−0.693897	−	0.720074i	$-0.744108\pi$
$653$	3.43824	−	32.7126i	0.134549	−	1.28014i	0.828446	−	0.560070i	$-0.189226\pi$
$654$	−14.2559	−	3.03018i	−0.557448	−	0.118489i
$655$	−5.78868	−	1.23042i	−0.226183	−	0.0480766i
$656$	0.710878	−	6.76356i	0.0277551	−	0.264072i
$657$	−2.68275	+	1.94913i	−0.104664	+	0.0760429i
$658$	−0.205317	−	0.276965i	−0.00800407	−	0.0107972i
$659$	−13.0332			−0.507703			−0.253851	−	0.967243i	$-0.581697\pi$
$659$	−13.0332			−0.507703			−0.253851	+	0.967243i	$0.581697\pi$
$660$	12.7463	−	4.38631i	0.496148	−	0.170737i
$661$	10.8593	−	18.8088i	0.422377	−	0.731578i	−0.573795	−	0.818999i	$-0.694529\pi$
$661$	10.8593	−	18.8088i	0.422377	−	0.731578i	0.996171	+	0.0874215i	$0.0278627\pi$
$662$	17.1078	+	19.0001i	0.664913	+	0.738461i
$663$	−12.0803	−	5.37848i	−0.469159	−	0.208883i
$664$	−5.85548	−	4.25425i	−0.227237	−	0.165097i
$665$	75.0164	+	23.5808i	2.90901	+	0.914423i
$666$	−2.67517	−	8.23334i	−0.103661	−	0.319035i
$667$	0.151917	−	1.44539i	0.00588224	−	0.0559658i
$668$	0.210472	+	2.00251i	0.00814342	+	0.0774795i
$669$	17.2523	+	19.1606i	0.667012	+	0.740791i
$670$	−11.1019	−	19.2290i	−0.428902	−	0.742880i
$671$	−4.87233	+	25.0417i	−0.188094	+	0.966725i
$672$	−1.09927	−	2.40658i	−0.0424053	−	0.0928356i
$673$	−1.67545	+	5.15650i	−0.0645837	+	0.198768i	−0.978141	−	0.207941i	$-0.933324\pi$
$673$	−1.67545	+	5.15650i	−0.0645837	+	0.198768i	0.913558	+	0.406709i	$0.133324\pi$
$674$	8.47130	+	3.77166i	0.326302	+	0.145279i
$675$	10.5230	−	4.68514i	0.405030	−	0.180331i
$676$	4.15617	+	0.883421i	0.159853	+	0.0339777i
$677$	0.788163	−	0.875344i	0.0302916	−	0.0336422i	−0.727809	−	0.685780i	$-0.759461\pi$
$677$	0.788163	−	0.875344i	0.0302916	−	0.0336422i	0.758100	+	0.652138i	$0.226128\pi$
$678$	−4.69137	−	3.40848i	−0.180171	−	0.130902i
$679$	−41.2030	+	24.3188i	−1.58123	+	0.933268i
$680$	5.61423	−	17.2788i	0.215296	−	0.662613i
$681$	−11.7564	−	20.3628i	−0.450508	−	0.780303i
$682$	−20.2237	−	1.77304i	−0.774407	−	0.0678933i
$683$	−9.54445	+	16.5315i	−0.365208	+	0.632559i	−0.988810	−	0.149183i	$-0.952336\pi$
$683$	−9.54445	+	16.5315i	−0.365208	+	0.632559i	0.623601	+	0.781743i	$0.285669\pi$
$684$	−7.15291	+	1.52040i	−0.273498	+	0.0581339i
$685$	46.2391	−	33.5947i	1.76671	−	1.28359i
$686$	−7.04268	+	17.1289i	−0.268891	+	0.653986i
$687$	−0.495381	−	1.52462i	−0.0188999	−	0.0581681i
$688$	−1.26417	+	1.40401i	−0.0481961	+	0.0535272i
$689$	−0.0581198	+	0.0258766i	−0.00221419	+	0.000985821i
$690$	−1.53908	−	14.6434i	−0.0585917	−	0.557463i
$691$	−18.7277	+	3.98069i	−0.712434	+	0.151433i	−0.549852	−	0.835262i	$-0.685316\pi$
$691$	−18.7277	+	3.98069i	−0.712434	+	0.151433i	−0.162583	+	0.986695i	$0.551982\pi$
$692$	−9.60365			−0.365076
$693$	8.77180	−	0.235749i	0.333213	−	0.00895535i
$694$	−19.1120			−0.725482
$695$	−61.9281	+	13.1632i	−2.34907	+	0.499310i
$696$	−0.0419343	−	0.398978i	−0.00158951	−	0.0151232i
$697$	27.7721	−	12.3649i	1.05194	−	0.468355i
$698$	16.5066	−	18.3324i	0.624784	−	0.693893i
$699$	0.0557429	+	0.171559i	0.00210839	+	0.00648895i
$700$	−6.04994	+	29.8695i	−0.228666	+	1.12896i
$701$	−1.40062	+	1.01761i	−0.0529005	+	0.0384345i	−0.613921	−	0.789367i	$-0.710409\pi$
$701$	−1.40062	+	1.01761i	−0.0529005	+	0.0384345i	0.561021	+	0.827802i	$0.310409\pi$
$702$	−2.89356	+	0.615046i	−0.109210	+	0.0232134i
$703$	31.6532	−	54.8250i	1.19382	−	2.06776i
$704$	−0.745492	−	3.23176i	−0.0280968	−	0.121801i
$705$	−0.264811	−	0.458667i	−0.00997338	−	0.0172744i
$706$	−6.75574	+	20.7920i	−0.254256	+	0.782518i
$707$	−0.184915	−	19.2667i	−0.00695443	−	0.724599i
$708$	2.53863	+	1.84442i	0.0954075	+	0.0693176i
$709$	−35.5372	+	39.4680i	−1.33463	+	1.48225i	−0.612583	+	0.790406i	$0.709870\pi$
$709$	−35.5372	+	39.4680i	−1.33463	+	1.48225i	−0.722044	+	0.691847i	$0.756797\pi$
$710$	−53.9568	−	11.4689i	−2.02496	−	0.430419i
$711$	−15.2336	+	6.78245i	−0.571306	+	0.254362i
$712$	0.408125	+	0.181709i	0.0152951	+	0.00680984i
$713$	−6.85246	+	21.0897i	−0.256627	+	0.789816i
$714$	6.85947	−	9.63435i	0.256709	−	0.360556i
$715$	34.8731	+	19.3387i	1.30418	+	0.723228i
$716$	7.72923	+	13.3874i	0.288855	+	0.500311i
$717$	−2.18421	−	2.42581i	−0.0815707	−	0.0905934i
$718$	−1.21162	−	11.5278i	−0.0452172	−	0.430213i
$719$	−2.99219	+	28.4688i	−0.111590	+	1.06171i	0.785198	+	0.619245i	$0.212561\pi$
$719$	−2.99219	+	28.4688i	−0.111590	+	1.06171i	−0.896788	+	0.442461i	$0.854106\pi$
$720$	−1.25595	−	3.86542i	−0.0468065	−	0.144056i
$721$	6.31038	−	5.79251i	0.235011	−	0.215724i
$722$	−27.8915	−	20.2643i	−1.03801	−	0.754160i
$723$	−21.9437	−	9.76995i	−0.816094	−	0.363348i
$724$	11.5466	+	12.8238i	0.429125	+	0.476592i
$725$	−2.31054	+	4.00198i	−0.0858114	+	0.148630i
$726$	10.8322	+	1.91406i	0.402020	+	0.0710374i
$727$	−31.2356			−1.15846			−0.579232	−	0.815163i	$-0.696647\pi$
$727$	−31.2356			−1.15846			−0.579232	+	0.815163i	$0.696647\pi$
$728$	3.11463	−	7.18025i	0.115436	−	0.266118i
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$	1.40879	−	13.4038i	0.0521418	−	0.496096i
$731$	−8.26071	−	1.75587i	−0.305533	−	0.0649431i
$732$	7.52386	+	1.59925i	0.278090	+	0.0591098i
$733$	1.80463	−	17.1699i	0.0666554	−	0.634184i	−0.909289	−	0.416165i	$-0.863374\pi$
$733$	1.80463	−	17.1699i	0.0666554	−	0.634184i	0.975945	−	0.218019i	$-0.0699595\pi$
$734$	13.8490	−	10.0619i	0.511176	−	0.371391i
$735$	−13.7497	+	24.9072i	−0.507164	+	0.918717i
$736$	−3.62273			−0.133536
$737$	−0.312933	−	18.1162i	−0.0115270	−	0.667319i
$738$	3.40041	−	5.88968i	0.125171	−	0.216802i
$739$	−31.3798	−	34.8508i	−1.15432	−	1.28201i	−0.953166	−	0.302448i	$-0.902196\pi$
$739$	−31.3798	−	34.8508i	−1.15432	−	1.28201i	−0.201158	−	0.979559i	$-0.564470\pi$
$740$	32.1432	+	14.3111i	1.18161	+	0.526086i
$741$	−17.5011	−	12.7153i	−0.642918	−	0.467107i
$742$	−0.0123638	−	0.0555408i	−0.000453891	−	0.00203897i
$743$	1.88720	+	5.80819i	0.0692345	+	0.213082i	0.979687	−	0.200531i	$-0.0642667\pi$
$743$	1.88720	+	5.80819i	0.0692345	+	0.213082i	−0.910453	+	0.413613i	$0.864267\pi$
$744$	−0.639827	+	6.08754i	−0.0234572	+	0.223180i
$745$	2.66787	+	25.3831i	0.0977432	+	0.929965i
$746$	13.1088	+	14.5588i	0.479947	+	0.533035i
$747$	−3.61888	−	6.26809i	−0.132408	−	0.229337i
$748$	10.8446	−	10.1091i	0.396519	−	0.369626i
$749$	8.69150	+	19.0278i	0.317580	+	0.695262i
$750$	−8.18736	+	25.1981i	−0.298960	+	0.920105i
$751$	20.7378	+	9.23304i	0.756731	+	0.336918i	0.748577	−	0.663048i	$-0.230738\pi$
$751$	20.7378	+	9.23304i	0.756731	+	0.336918i	0.00815463	+	0.999967i	$0.497404\pi$
$752$	−0.119044	+	0.0530017i	−0.00434108	+	0.00193277i
$753$	15.0324	+	3.19524i	0.547811	+	0.116441i
$754$	0.794097	−	0.881935i	0.0289193	−	0.0321182i
$755$	38.3931	+	27.8942i	1.39727	+	1.01518i
$756$	−0.0253917	−	2.64563i	−0.000923489	−	0.0962206i
$757$	1.17325	−	3.61089i	0.0426424	−	0.131240i	−0.927469	−	0.373901i	$-0.878020\pi$
$757$	1.17325	−	3.61089i	0.0426424	−	0.131240i	0.970111	+	0.242661i	$0.0780201\pi$
$758$	14.7805	+	25.6007i	0.536854	+	0.929858i
$759$	4.69674	−	11.0592i	0.170481	−	0.401425i
$760$	14.8607	−	25.7394i	0.539053	−	0.933668i
$761$	0.0798684	−	0.0169766i	0.00289523	−	0.000615400i	−0.206464	−	0.978454i	$-0.566196\pi$
$761$	0.0798684	−	0.0169766i	0.00289523	−	0.000615400i	0.209359	+	0.977839i	$0.432862\pi$
$762$	−10.2947	+	7.47953i	−0.372937	+	0.270955i
$763$	36.5568	−	12.2671i	1.32344	−	0.444100i
$764$	0.108351	+	0.333471i	0.00392001	+	0.0120645i
$765$	12.1568	−	13.5015i	0.439529	−	0.488147i
$766$	10.4342	−	4.64559i	0.377002	−	0.167852i
$767$	0.970297	+	9.23176i	0.0350354	+	0.333339i
$768$	−0.978148	+	0.207912i	−0.0352959	+	0.00750237i
$769$	−38.2744			−1.38021			−0.690105	−	0.723710i	$-0.742436\pi$
$769$	−38.2744			−1.38021			−0.690105	+	0.723710i	$0.742436\pi$
$770$	−23.1435	+	27.1354i	−0.834034	+	0.977892i
$771$	−15.2276			−0.548407
$772$	20.9549	−	4.45410i	0.754183	−	0.160306i
$773$	1.80545	+	17.1777i	0.0649374	+	0.617838i	0.977796	+	0.209561i	$0.0672036\pi$
$773$	1.80545	+	17.1777i	0.0649374	+	0.617838i	−0.912858	+	0.408277i	$0.866130\pi$
$774$	−1.72594	+	0.768438i	−0.0620376	+	0.0276209i
$775$	47.1789	−	52.3975i	1.69472	−	1.88217i
$776$	5.58811	+	17.1984i	0.200601	+	0.617387i
$777$	17.1676	+	15.1620i	0.615883	+	0.543932i
$778$	12.7286	−	9.24789i	0.456344	−	0.331553i
$779$	48.6456	−	10.3399i	1.74291	−	0.370467i
$780$	6.01158	−	10.4124i	0.215249	−	0.372822i
$781$	−33.9672	−	29.5381i	−1.21544	−	1.05695i
$782$	−8.09700	−	14.0244i	−0.289548	−	0.501512i
$783$	0.123970	−	0.381541i	0.00443033	−	0.0136352i
$784$	5.74105	+	4.00504i	0.205037	+	0.143037i
$785$	20.4499	+	14.8577i	0.729889	+	0.530295i
$786$	−0.974308	+	1.08208i	−0.0347524	+	0.0385965i
$787$	−5.65034	−	1.20102i	−0.201413	−	0.0428117i	0.106100	−	0.994355i	$-0.466164\pi$
$787$	−5.65034	−	1.20102i	−0.201413	−	0.0428117i	−0.307513	+	0.951544i	$0.599497\pi$
$788$	7.31286	−	3.25589i	0.260510	−	0.115986i
$789$	−15.4532	−	6.88021i	−0.550148	−	0.244942i
$790$	20.9433	−	64.4569i	0.745130	−	2.29327i
$791$	15.2730	+	1.45720i	0.543044	+	0.0518120i
$792$	0.633432	−	3.25557i	0.0225080	−	0.115682i
$793$	11.3772	+	19.7059i	0.404016	+	0.699776i
$794$	−7.39608	−	8.21417i	−0.262477	−	0.291510i
$795$	−0.00913672	−	0.0869301i	−0.000324046	−	0.00308309i
$796$	0.0844942	−	0.803908i	0.00299482	−	0.0284938i
$797$	−6.68440	−	20.5725i	−0.236774	−	0.728714i	−0.996881	−	0.0789169i	$-0.974854\pi$
$797$	−6.68440	−	20.5725i	−0.236774	−	0.728714i	0.760108	−	0.649797i	$-0.225146\pi$
$798$	14.2532	−	13.0835i	0.504557	−	0.463150i
$799$	−0.471251	−	0.342384i	−0.0166717	−	0.0121127i
$800$	10.5230	+	4.68514i	0.372044	+	0.165645i
$801$	0.298933	+	0.331999i	0.0105623	+	0.0117306i
$802$	13.7996	−	23.9016i	0.487280	−	0.843994i
$803$	6.30991	−	9.00800i	0.222672	−	0.317886i
$804$	−5.46305			−0.192667
$805$	23.1992	+	31.2949i	0.817665	+	1.10300i
$806$	−14.6492	+	10.6433i	−0.515996	+	0.374893i
$807$	−2.77661	+	26.4176i	−0.0977412	+	0.929945i
$808$	−7.12333	−	1.51411i	−0.250598	−	0.0532662i
$809$	6.22184	+	1.32249i	0.218748	+	0.0464963i	0.315982	−	0.948765i	$-0.397666\pi$
$809$	6.22184	+	1.32249i	0.218748	+	0.0464963i	−0.0972338	+	0.995262i	$0.530999\pi$
$810$	0.424839	−	4.04207i	0.0149273	−	0.142024i
$811$	12.7288	−	9.24803i	0.446970	−	0.324742i	−0.341429	−	0.939908i	$-0.610911\pi$
$811$	12.7288	−	9.24803i	0.446970	−	0.324742i	0.788398	+	0.615165i	$0.210911\pi$
$812$	0.632094	+	0.852672i	0.0221822	+	0.0299229i
$813$	7.28172			0.255381
$814$	17.2753	+	22.9337i	0.605497	+	0.803825i
$815$	−12.2402	+	21.2006i	−0.428755	+	0.742625i
$816$	−2.99108	−	3.32194i	−0.104709	−	0.116291i
$817$	−12.6213	−	5.61936i	−0.441563	−	0.196597i
$818$	4.58577	+	3.33176i	0.160338	+	0.116492i
$819$	5.76583	−	5.29265i	0.201474	−	0.184940i
$820$	8.54148	+	26.2880i	0.298281	+	0.918016i
$821$	−5.03117	+	47.8684i	−0.175589	+	1.67062i	0.451957	+	0.892040i	$0.350726\pi$
$821$	−5.03117	+	47.8684i	−0.175589	+	1.67062i	−0.627546	+	0.778580i	$0.715941\pi$
$822$	−1.46993	−	13.9855i	−0.0512697	−	0.487799i
$823$	13.4192	+	14.9036i	0.467765	+	0.519506i	0.930153	−	0.367172i	$-0.119674\pi$
$823$	13.4192	+	14.9036i	0.467765	+	0.519506i	−0.462388	+	0.886678i	$0.653007\pi$
$824$	−1.61880	−	2.80384i	−0.0563934	−	0.0976763i
$825$	−27.9452	+	26.0498i	−0.972926	+	0.906938i
$826$	−8.26462	−	0.788530i	−0.287563	−	0.0274365i
$827$	−15.7004	+	48.3210i	−0.545958	+	1.68029i	0.172744	+	0.984967i	$0.444737\pi$
$827$	−15.7004	+	48.3210i	−0.545958	+	1.68029i	−0.718702	+	0.695319i	$0.755263\pi$
$828$	−3.30953	−	1.47350i	−0.115014	−	0.0512076i
$829$	−17.3581	+	7.72834i	−0.602873	+	0.268416i	−0.685393	−	0.728173i	$-0.740370\pi$
$829$	−17.3581	+	7.72834i	−0.602873	+	0.268416i	0.0825205	+	0.996589i	$0.473703\pi$
$830$	28.7739	+	6.11609i	0.998757	+	0.212292i
$831$	−6.62668	+	7.35967i	−0.229877	+	0.255304i
$832$	−2.39324	−	1.73879i	−0.0829706	−	0.0602817i
$833$	−2.67288	+	31.1764i	−0.0926099	+	1.08020i
$834$	−4.81366	+	14.8149i	−0.166684	+	0.512999i
$835$	−4.09186	−	7.08730i	−0.141605	−	0.245266i
$836$	20.7916	−	12.4877i	0.719092	−	0.431897i
$837$	−3.06054	+	5.30101i	−0.105788	+	0.183230i
$838$	−22.4416	+	4.77010i	−0.775231	+	0.164780i
$839$	29.5513	−	21.4703i	1.02022	−	0.741236i	0.0538950	−	0.998547i	$-0.482836\pi$
$839$	29.5513	−	21.4703i	1.02022	−	0.741236i	0.966329	+	0.257311i	$0.0828364\pi$
$840$	8.05990	+	7.11829i	0.278093	+	0.245604i
$841$	−8.91176	−	27.4276i	−0.307302	−	0.945778i
$842$	−20.1808	+	22.4131i	−0.695477	+	0.772405i
$843$	−24.8739	+	11.0746i	−0.856703	+	0.381429i
$844$	1.36819	+	13.0175i	0.0470951	+	0.448080i
$845$	−16.8921	+	3.59052i	−0.581105	+	0.123518i
$846$	−0.130310			−0.00448014
$847$	−27.2550	+	10.2060i	−0.936494	+	0.350683i
$848$	−0.0215063			−0.000738530
$849$	24.1803	−	5.13968i	0.829865	−	0.176393i
$850$	5.38222	+	51.2084i	0.184609	+	1.75644i
$851$	28.6508	−	12.7561i	0.982135	−	0.437275i
$852$	−9.08161	+	10.0862i	−0.311131	+	0.345546i
$853$	−2.27483	−	7.00119i	−0.0778885	−	0.239716i	0.904529	−	0.426411i	$-0.140222\pi$
$853$	−2.27483	−	7.00119i	−0.0778885	−	0.239716i	−0.982418	+	0.186695i	$0.940222\pi$
$854$	−19.2937	+	6.47426i	−0.660216	+	0.221545i
$855$	24.0451	−	17.4698i	0.822324	−	0.597453i
$856$	7.73382	−	1.64387i	0.264337	−	0.0561865i
$857$	0.292421	−	0.506487i	0.00998890	−	0.0173013i	−0.860988	−	0.508626i	$-0.830154\pi$
$857$	0.292421	−	0.506487i	0.00998890	−	0.0173013i	0.870977	+	0.491324i	$0.163487\pi$
$858$	8.41081	−	5.05165i	0.287140	−	0.172460i
$859$	16.2903	+	28.2157i	0.555819	+	0.962706i	0.997839	+	0.0657012i	$0.0209284\pi$
$859$	16.2903	+	28.2157i	0.555819	+	0.962706i	−0.442021	+	0.897005i	$0.645738\pi$
$860$	2.37284	−	7.30284i	0.0809130	−	0.249025i
$861$	0.172684	+	17.9924i	0.00588507	+	0.613180i
$862$	10.6323	+	7.72480i	0.362137	+	0.263108i
$863$	14.9298	−	16.5812i	0.508215	−	0.564430i	−0.433366	−	0.901218i	$-0.642674\pi$
$863$	14.9298	−	16.5812i	0.508215	−	0.564430i	0.941580	+	0.336789i	$0.109341\pi$
$864$	−0.978148	−	0.207912i	−0.0332773	−	0.00707330i
$865$	35.6580	−	15.8760i	1.21241	−	0.539799i
$866$	24.9965	+	11.1292i	0.849416	+	0.378184i
$867$	0.921441	−	2.83590i	0.0312938	−	0.0963124i
$868$	−6.72872	−	14.7308i	−0.228388	−	0.499997i
$869$	40.4548	−	37.7110i	1.37234	−	1.27926i
$870$	0.815257	+	1.41207i	0.0276398	+	0.0478735i
$871$	−10.8137	−	12.0098i	−0.366409	−	0.406938i
$872$	−1.52343	−	14.4945i	−0.0515900	−	0.490846i
$873$	−1.89024	+	17.9844i	−0.0639749	+	0.608681i
$874$	−8.18648	−	25.1954i	−0.276912	−	0.852247i
$875$	−15.2317	−	68.4239i	−0.514927	−	2.31315i
$876$	−2.68275	−	1.94913i	−0.0906418	−	0.0658551i
$877$	27.3128	+	12.1605i	0.922289	+	0.410629i	0.812258	−	0.583299i	$-0.198238\pi$
$877$	27.3128	+	12.1605i	0.922289	+	0.410629i	0.110031	+	0.993928i	$0.464905\pi$
$878$	−17.8958	−	19.8753i	−0.603954	−	0.670759i
$879$	−6.72607	+	11.6499i	−0.226865	+	0.392941i
$880$	8.11045	+	10.7670i	0.273403	+	0.362955i
$881$	−26.6847			−0.899032			−0.449516	−	0.893272i	$-0.648403\pi$
$881$	−26.6847			−0.899032			−0.449516	+	0.893272i	$0.648403\pi$
$882$	3.61571	+	5.99388i	0.121747	+	0.201825i
$883$	−13.0138	+	9.45509i	−0.437950	+	0.318189i	−0.784820	−	0.619724i	$-0.787245\pi$
$883$	−13.0138	+	9.45509i	−0.437950	+	0.318189i	0.346870	+	0.937913i	$0.387245\pi$
$884$	1.38223	−	13.1511i	0.0464895	−	0.442318i
$885$	−12.4749	−	2.65162i	−0.419338	−	0.0891331i
$886$	−4.21304	−	0.895509i	−0.141540	−	0.0300852i
$887$	−0.0985935	+	0.938054i	−0.00331044	+	0.0314968i	−0.996052	−	0.0887670i	$-0.971707\pi$
$887$	−0.0985935	+	0.938054i	−0.00331044	+	0.0314968i	0.992742	+	0.120264i	$0.0383740\pi$
$888$	7.00369	−	5.08848i	0.235029	−	0.170758i
$889$	13.3978	−	30.8864i	0.449348	−	1.03590i
$890$	−1.81574			−0.0608637
$891$	1.90283	−	2.71647i	0.0637472	−	0.0910053i
$892$	−12.8916	+	22.3288i	−0.431641	+	0.747625i
$893$	−0.637626	−	0.708155i	−0.0213373	−	0.0236975i
$894$	5.73681	+	2.55419i	0.191868	+	0.0854250i
$895$	−50.8292	−	36.9296i	−1.69903	−	1.23442i
$896$	1.94910	−	1.78914i	0.0651147	−	0.0597710i
$897$	−3.31167	−	10.1923i	−0.110573	−	0.340310i
$898$	3.98373	−	37.9027i	0.132939	−	1.26483i
$899$	−0.256683	−	2.44217i	−0.00856085	−	0.0814511i
$900$	7.70762	+	8.56018i	0.256921	+	0.285339i
$901$	−0.0480677	−	0.0832558i	−0.00160137	−	0.00277365i
$902$	−4.30785	+	22.1405i	−0.143436	+	0.737200i
$903$	2.89913	−	4.07193i	0.0964770	−	0.135505i
$904$	1.79194	−	5.51503i	0.0595991	−	0.183427i
$905$	−64.0712	−	28.5263i	−2.12980	−	0.948247i
$906$	10.6668	−	4.74919i	0.354382	−	0.157781i
$907$	3.18031	+	0.675995i	0.105600	+	0.0224461i	0.260409	−	0.965498i	$-0.416143\pi$
$907$	3.18031	+	0.675995i	0.105600	+	0.0224461i	−0.154808	+	0.987945i	$0.549476\pi$
$908$	15.7332	−	17.4735i	0.522125	−	0.579878i
$909$	−5.89164	−	4.28053i	−0.195413	−	0.141976i
$910$	0.305289	+	31.8088i	0.0101202	+	1.05445i
$911$	6.52812	−	20.0915i	0.216286	−	0.665660i	−0.782774	−	0.622307i	$-0.786196\pi$
$911$	6.52812	−	20.0915i	0.216286	−	0.665660i	0.999060	−	0.0433539i	$-0.0138043\pi$
$912$	−3.65636	−	6.33299i	−0.121074	−	0.209706i
$913$	18.1139	+	15.7520i	0.599483	+	0.521314i
$914$	1.89194	−	3.27694i	0.0625799	−	0.108392i
$915$	−30.5795	+	6.49988i	−1.01093	+	0.214879i
$916$	1.29692	−	0.942270i	0.0428515	−	0.0311335i
$917$	0.764763	−	3.77576i	0.0252547	−	0.124686i
$918$	−1.38134	−	4.25132i	−0.0455910	−	0.140315i
$919$	11.3930	−	12.6532i	0.375820	−	0.417390i	−0.525330	−	0.850899i	$-0.676058\pi$
$919$	11.3930	−	12.6532i	0.375820	−	0.417390i	0.901149	+	0.433509i	$0.142725\pi$
$920$	13.4511	−	5.98880i	0.443468	−	0.197445i
$921$	1.78529	+	16.9859i	0.0588272	+	0.559703i
$922$	12.6466	−	2.68811i	0.416493	−	0.0885282i
$923$	−40.1495			−1.32154
$924$	2.93484	+	8.26962i	0.0965493	+	0.272051i
$925$	−99.7192			−3.27875
$926$	−0.100198	+	0.0212976i	−0.00329270	+	0.000699884i
$927$	−0.338420	−	3.21986i	−0.0111152	−	0.105754i
$928$	0.366492	−	0.163173i	0.0120307	−	0.00535641i
$929$	13.6166	−	15.1228i	0.446746	−	0.496162i	−0.477141	−	0.878827i	$-0.658327\pi$
$929$	13.6166	−	15.1228i	0.446746	−	0.496162i	0.923887	+	0.382665i	$0.124994\pi$
$930$	−7.68776	−	23.6605i	−0.252092	−	0.775859i
$931$	−14.8809	+	48.9783i	−0.487703	+	1.60520i
$932$	−0.145937	+	0.106029i	−0.00478032	+	0.00347310i
$933$	−25.3445	+	5.38713i	−0.829740	+	0.176367i
$934$	15.3024	−	26.5045i	0.500710	−	0.867255i
$935$	−23.5542	+	55.4622i	−0.770303	+	1.81381i
$936$	−1.47910	−	2.56188i	−0.0483460	−	0.0837377i
$937$	−12.4307	+	38.2577i	−0.406093	+	1.24982i	0.513887	+	0.857858i	$0.328205\pi$
$937$	−12.4307	+	38.2577i	−0.406093	+	1.24982i	−0.919979	+	0.391967i	$0.871795\pi$
$938$	12.4475	−	7.34674i	0.406425	−	0.239880i
$939$	12.0181	+	8.73168i	0.392197	+	0.284948i
$940$	0.354387	−	0.393586i	0.0115588	−	0.0128374i
$941$	−23.7522	−	5.04868i	−0.774299	−	0.164582i	−0.196216	−	0.980561i	$-0.562865\pi$
$941$	−23.7522	−	5.04868i	−0.774299	−	0.164582i	−0.578082	+	0.815978i	$0.696199\pi$
$942$	5.68164	−	2.52963i	0.185118	−	0.0824198i
$943$	22.5075	+	10.0210i	0.732945	+	0.326328i
$944$	−0.969670	+	2.98434i	−0.0315601	+	0.0971319i
$945$	4.46781	+	9.78114i	0.145338	+	0.318180i
$946$	4.58345	−	4.27258i	0.149021	−	0.138914i
$947$	−9.26207	−	16.0424i	−0.300977	−	0.521307i	0.675381	−	0.737469i	$-0.263979\pi$
$947$	−9.26207	−	16.0424i	−0.300977	−	0.521307i	−0.976357	+	0.216162i	$0.930646\pi$
$948$	−11.1579	−	12.3921i	−0.362393	−	0.402478i
$949$	−1.02538	−	9.75586i	−0.0332853	−	0.316689i
$950$	−8.80486	+	83.7726i	−0.285667	+	2.71794i
$951$	−0.550908	−	1.69552i	−0.0178644	−	0.0549811i
$952$	11.2825	+	3.54656i	0.365668	+	0.114945i
$953$	17.2917	+	12.5632i	0.560133	+	0.406960i	0.831508	−	0.555513i	$-0.187478\pi$
$953$	17.2917	+	12.5632i	0.560133	+	0.406960i	−0.271375	+	0.962474i	$0.587478\pi$
$954$	−0.0196470	−	0.00874740i	−0.000636095	−	0.000283208i
$955$	−0.953569	−	1.05905i	−0.0308568	−	0.0342699i
$956$	1.63212	−	2.82692i	0.0527866	−	0.0914291i
$957$	0.0229800	+	1.33035i	0.000742839	+	0.0430041i
$958$	−7.52691			−0.243183
$959$	22.1569	+	29.8889i	0.715484	+	0.965163i
$960$	3.28812	−	2.38896i	0.106124	−	0.0771033i
$961$	−0.676044	+	6.43213i	−0.0218079	+	0.207488i
$962$	25.0497	+	5.32448i	0.807634	+	0.171668i
$963$	7.73382	+	1.64387i	0.249219	+	0.0529731i
$964$	2.51081	−	23.8887i	0.0808677	−	0.769405i
$965$	−70.4415	+	51.1787i	−2.26759	+	1.64750i
$966$	9.52229	−	1.09333i	0.306375	−	0.0351772i
$967$	17.9898			0.578514			0.289257	−	0.957251i	$-0.406592\pi$
$967$	17.9898			0.578514			0.289257	+	0.957251i	$0.406592\pi$
$968$	1.52695	+	10.8935i	0.0490781	+	0.350130i
$969$	16.3443	−	28.3092i	0.525054	−	0.909421i
$970$	−49.1794	−	54.6193i	−1.57906	−	1.75372i
$971$	−51.2891	−	22.8354i	−1.64594	−	0.732822i	−0.646400	−	0.762999i	$-0.723726\pi$
$971$	−51.2891	−	22.8354i	−1.64594	−	0.732822i	−0.999545	+	0.0301767i	$0.990393\pi$
$972$	−0.809017	−	0.587785i	−0.0259492	−	0.0188532i
$973$	−8.95532	−	40.2291i	−0.287094	−	1.28968i
$974$	−7.46644	−	22.9793i	−0.239240	−	0.736305i
$975$	−3.56182	+	33.8885i	−0.114070	+	1.08530i
$976$	0.804028	+	7.64981i	0.0257363	+	0.244865i
$977$	−13.5594	−	15.0592i	−0.433802	−	0.481786i	0.486117	−	0.873894i	$-0.338413\pi$
$977$	−13.5594	−	15.0592i	−0.433802	−	0.481786i	−0.919919	+	0.392108i	$0.871746\pi$
$978$	3.01160	+	5.21625i	0.0963005	+	0.166797i
$979$	−1.29579	−	0.718576i	−0.0414137	−	0.0229658i
$980$	−27.9371	−	5.37995i	−0.892417	−	0.171856i
$981$	4.50372	−	13.8610i	0.143793	−	0.442548i
$982$	7.49815	+	3.33839i	0.239276	+	0.106532i
$983$	29.6017	−	13.1795i	0.944149	−	0.420362i	0.123852	−	0.992301i	$-0.460475\pi$
$983$	29.6017	−	13.1795i	0.944149	−	0.420362i	0.820296	+	0.571939i	$0.193808\pi$
$984$	6.65220	+	1.41397i	0.212064	+	0.0450757i
$985$	−21.7700	+	24.1780i	−0.693649	+	0.770375i
$986$	1.45081	+	1.05407i	0.0462031	+	0.0335685i
$987$	0.296909	−	0.175241i	0.00945071	−	0.00557799i
$988$	6.68481	−	20.5737i	0.212672	−	0.654538i
$989$	−3.42217	−	5.92737i	−0.108819	−	0.188480i
$990$	3.02993	+	13.1350i	0.0962976	+	0.417456i
$991$	18.8938	−	32.7251i	0.600182	−	1.03955i	−0.392611	−	0.919705i	$-0.628428\pi$
$991$	18.8938	−	32.7251i	0.600182	−	1.03955i	0.992793	−	0.119841i	$-0.0382385\pi$
$992$	−5.98732	+	1.27264i	−0.190097	+	0.0404065i
$993$	−20.6843	+	15.0280i	−0.656396	+	0.476900i
$994$	7.12843	−	35.1942i	0.226100	−	1.11629i
$995$	1.01523	+	3.12456i	0.0321850	+	0.0990551i
$996$	4.84301	−	5.37871i	0.153457	−	0.170431i
$997$	−32.0181	+	14.2554i	−1.01402	+	0.451472i	−0.845357	−	0.534201i	$-0.820613\pi$
$997$	−32.0181	+	14.2554i	−1.01402	+	0.451472i	−0.168666	+	0.985673i	$0.553946\pi$
$998$	−2.02233	−	19.2411i	−0.0640156	−	0.609068i
$999$	8.46787	−	1.79990i	0.267911	−	0.0569463i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.y.b.361.1	yes	24
7.2	even	3	inner	462.2.y.b.163.3	✓	24
11.5	even	5	inner	462.2.y.b.445.3	yes	24
77.16	even	15	inner	462.2.y.b.247.1	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.y.b.163.3	✓	24	7.2	even	3	inner
462.2.y.b.247.1	yes	24	77.16	even	15	inner
462.2.y.b.361.1	yes	24	1.1	even	1	trivial
462.2.y.b.445.3	yes	24	11.5	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.y (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.978148 + 0.207912i) q^{2} +(-0.104528 - 0.994522i) q^{3} +(0.913545 - 0.406737i) q^{4} +(-2.71957 + 3.02039i) q^{5} +(0.309017 + 0.951057i) q^{6} +(-1.98308 - 1.75140i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(-0.978148 + 0.207912i) q^{9} +O(q^{10})\)	\(q+(-0.978148 + 0.207912i) q^{2} +(-0.104528 - 0.994522i) q^{3} +(0.913545 - 0.406737i) q^{4} +(-2.71957 + 3.02039i) q^{5} +(0.309017 + 0.951057i) q^{6} +(-1.98308 - 1.75140i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(-0.978148 + 0.207912i) q^{9} +(2.03217 - 3.51982i) q^{10} +(2.84321 - 1.70767i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(0.914136 - 2.81342i) q^{13} +(2.30388 + 1.30082i) q^{14} +(3.28812 + 2.38896i) q^{15} +(0.669131 - 0.743145i) q^{16} +(4.37242 + 0.929387i) q^{17} +(0.913545 - 0.406737i) q^{18} +(6.68049 + 2.97435i) q^{19} +(-1.25595 + 3.86542i) q^{20} +(-1.53452 + 2.15528i) q^{21} +(-2.42604 + 2.26149i) q^{22} +(1.81137 + 3.13738i) q^{23} +(0.669131 + 0.743145i) q^{24} +(-1.20405 - 11.4558i) q^{25} +(-0.309217 + 2.94200i) q^{26} +(0.309017 + 0.951057i) q^{27} +(-2.52399 - 0.793395i) q^{28} +(-0.324558 - 0.235805i) q^{29} +(-3.71296 - 1.65312i) q^{30} +(4.09580 + 4.54885i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-1.99551 - 2.64914i) q^{33} -4.47011 q^{34} +(10.6830 - 1.22660i) q^{35} +(-0.809017 + 0.587785i) q^{36} +(0.904907 - 8.60962i) q^{37} +(-7.15291 - 1.52040i) q^{38} +(-2.89356 - 0.615046i) q^{39} +(0.424839 - 4.04207i) q^{40} +(5.50197 - 3.99742i) q^{41} +(1.05288 - 2.42723i) q^{42} -1.88928 q^{43} +(1.90283 - 2.71647i) q^{44} +(2.03217 - 3.51982i) q^{45} +(-2.42408 - 2.69222i) q^{46} +(-0.119044 - 0.0530017i) q^{47} +(-0.809017 - 0.587785i) q^{48} +(0.865183 + 6.94633i) q^{49} +(3.55952 + 10.9551i) q^{50} +(0.467253 - 4.44562i) q^{51} +(-0.309217 - 2.94200i) q^{52} +(-0.0143905 - 0.0159823i) q^{53} +(-0.500000 - 0.866025i) q^{54} +(-2.57448 + 13.2318i) q^{55} +(2.63379 + 0.251291i) q^{56} +(2.25975 - 6.95480i) q^{57} +(0.366492 + 0.163173i) q^{58} +(-2.86663 + 1.27631i) q^{59} +(3.97552 + 0.845024i) q^{60} +(-5.14692 + 5.71623i) q^{61} +(-4.95205 - 3.59788i) q^{62} +(2.30388 + 1.30082i) q^{63} +(0.309017 - 0.951057i) q^{64} +(6.01158 + 10.4124i) q^{65} +(2.50269 + 2.17636i) q^{66} +(2.73153 - 4.73114i) q^{67} +(4.37242 - 0.929387i) q^{68} +(2.93085 - 2.12939i) q^{69} +(-10.1946 + 3.42093i) q^{70} +(-4.19406 - 12.9080i) q^{71} +(0.669131 - 0.743145i) q^{72} +(3.02937 - 1.34876i) q^{73} +(0.904907 + 8.60962i) q^{74} +(-11.2671 + 2.39491i) q^{75} +7.31271 q^{76} +(-8.62913 - 1.59316i) q^{77} +2.95821 q^{78} +(16.3109 - 3.46699i) q^{79} +(0.424839 + 4.04207i) q^{80} +(0.913545 - 0.406737i) q^{81} +(-4.55063 + 5.05399i) q^{82} +(2.23659 + 6.88353i) q^{83} +(-0.525220 + 2.59310i) q^{84} +(-14.6982 + 10.6789i) q^{85} +(1.84799 - 0.392802i) q^{86} +(-0.200588 + 0.347428i) q^{87} +(-1.29646 + 3.05273i) q^{88} +(-0.223374 - 0.386896i) q^{89} +(-1.25595 + 3.86542i) q^{90} +(-6.74023 + 3.97821i) q^{91} +(2.93085 + 2.12939i) q^{92} +(4.09580 - 4.54885i) q^{93} +(0.127462 + 0.0270929i) q^{94} +(-27.1518 + 12.0888i) q^{95} +(0.913545 + 0.406737i) q^{96} +(5.58811 - 17.1984i) q^{97} +(-2.29050 - 6.61465i) q^{98} +(-2.42604 + 2.26149i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 3 q^{2} + 3 q^{3} + 3 q^{4} + 5 q^{5} - 6 q^{6} - 5 q^{7} - 6 q^{8} + 3 q^{9}+O(q^{10}) \) 24 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 + 5 * q^5 - 6 * q^6 - 5 * q^7 - 6 * q^8 + 3 * q^9	\( 24 q + 3 q^{2} + 3 q^{3} + 3 q^{4} + 5 q^{5} - 6 q^{6} - 5 q^{7} - 6 q^{8} + 3 q^{9} + 10 q^{10} - 2 q^{11} - 12 q^{12} + 10 q^{13} + 7 q^{14} + 20 q^{15} + 3 q^{16} + 8 q^{17} + 3 q^{18} + 7 q^{19} - 10 q^{20} + 8 q^{21} - 6 q^{22} + 24 q^{23} + 3 q^{24} + 8 q^{25} - 6 q^{27} - 2 q^{28} + 2 q^{29} - 10 q^{30} - 19 q^{31} - 12 q^{32} - 7 q^{33} + 24 q^{34} + 14 q^{35} - 6 q^{36} - q^{37} - 8 q^{38} - 5 q^{39} - 10 q^{40} + 16 q^{41} + 10 q^{42} - 68 q^{43} - 2 q^{44} + 10 q^{45} - 6 q^{46} + 25 q^{47} - 6 q^{48} - 21 q^{49} + 14 q^{50} - 2 q^{51} - 5 q^{53} - 12 q^{54} - 10 q^{55} - 10 q^{56} + 16 q^{57} - q^{58} - 36 q^{59} + 5 q^{60} - q^{61} - 52 q^{62} + 7 q^{63} - 6 q^{64} + 6 q^{65} + 8 q^{66} + 56 q^{67} + 8 q^{68} + 12 q^{69} - 17 q^{70} - 6 q^{71} + 3 q^{72} + 35 q^{73} - q^{74} - 7 q^{75} - 4 q^{76} + 38 q^{77} - 20 q^{78} - 3 q^{79} - 10 q^{80} + 3 q^{81} + 2 q^{82} - 28 q^{83} + 7 q^{84} - 80 q^{85} - 11 q^{86} + 4 q^{87} - 7 q^{88} - 6 q^{89} - 10 q^{90} - 24 q^{91} + 12 q^{92} - 19 q^{93} - 30 q^{94} - 44 q^{95} + 3 q^{96} - 8 q^{97} - 6 q^{99}+O(q^{100}) \) 24 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 + 5 * q^5 - 6 * q^6 - 5 * q^7 - 6 * q^8 + 3 * q^9 + 10 * q^10 - 2 * q^11 - 12 * q^12 + 10 * q^13 + 7 * q^14 + 20 * q^15 + 3 * q^16 + 8 * q^17 + 3 * q^18 + 7 * q^19 - 10 * q^20 + 8 * q^21 - 6 * q^22 + 24 * q^23 + 3 * q^24 + 8 * q^25 - 6 * q^27 - 2 * q^28 + 2 * q^29 - 10 * q^30 - 19 * q^31 - 12 * q^32 - 7 * q^33 + 24 * q^34 + 14 * q^35 - 6 * q^36 - q^37 - 8 * q^38 - 5 * q^39 - 10 * q^40 + 16 * q^41 + 10 * q^42 - 68 * q^43 - 2 * q^44 + 10 * q^45 - 6 * q^46 + 25 * q^47 - 6 * q^48 - 21 * q^49 + 14 * q^50 - 2 * q^51 - 5 * q^53 - 12 * q^54 - 10 * q^55 - 10 * q^56 + 16 * q^57 - q^58 - 36 * q^59 + 5 * q^60 - q^61 - 52 * q^62 + 7 * q^63 - 6 * q^64 + 6 * q^65 + 8 * q^66 + 56 * q^67 + 8 * q^68 + 12 * q^69 - 17 * q^70 - 6 * q^71 + 3 * q^72 + 35 * q^73 - q^74 - 7 * q^75 - 4 * q^76 + 38 * q^77 - 20 * q^78 - 3 * q^79 - 10 * q^80 + 3 * q^81 + 2 * q^82 - 28 * q^83 + 7 * q^84 - 80 * q^85 - 11 * q^86 + 4 * q^87 - 7 * q^88 - 6 * q^89 - 10 * q^90 - 24 * q^91 + 12 * q^92 - 19 * q^93 - 30 * q^94 - 44 * q^95 + 3 * q^96 - 8 * q^97 - 6 * q^99

Introduction

L-functions

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