LMFDB - Embedded newform 462.2.y.d.163.3

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:	$40$
Relative dimension:	$5$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			163.3
Character	$\chi$	$=$	462.163
Dual form			462.2.y.d.445.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.669131 + 0.743145i) q^{2} +(-0.913545 - 0.406737i) q^{3} +(-0.104528 + 0.994522i) q^{4} +(-0.408781 - 0.0868890i) q^{5} +(-0.309017 - 0.951057i) q^{6} +(-2.24058 - 1.40705i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(0.669131 + 0.743145i) q^{9} +O(q^{10})$	\(q+(0.669131 + 0.743145i) q^{2} +(-0.913545 - 0.406737i) q^{3} +(-0.104528 + 0.994522i) q^{4} +(-0.408781 - 0.0868890i) q^{5} +(-0.309017 - 0.951057i) q^{6} +(-2.24058 - 1.40705i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(0.669131 + 0.743145i) q^{9} +(-0.208957 - 0.361923i) q^{10} +(-3.16457 + 0.992716i) q^{11} +(0.500000 - 0.866025i) q^{12} +(-1.95111 + 6.00490i) q^{13} +(-0.453596 - 2.60658i) q^{14} +(0.338099 + 0.245643i) q^{15} +(-0.978148 - 0.207912i) q^{16} +(-4.10002 + 4.55354i) q^{17} +(-0.104528 + 0.994522i) q^{18} +(0.354967 + 3.37729i) q^{19} +(0.129142 - 0.397459i) q^{20} +(1.47457 + 2.19673i) q^{21} +(-2.85524 - 1.68748i) q^{22} +(4.39833 - 7.61812i) q^{23} +(0.978148 - 0.207912i) q^{24} +(-4.40818 - 1.96265i) q^{25} +(-5.76806 + 2.56810i) q^{26} +(-0.309017 - 0.951057i) q^{27} +(1.63355 - 2.08123i) q^{28} +(-3.21593 - 2.33651i) q^{29} +(0.0436838 + 0.415624i) q^{30} +(2.03863 - 0.433325i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(3.29475 + 0.380256i) q^{33} -6.12739 q^{34} +(0.793649 + 0.769858i) q^{35} +(-0.809017 + 0.587785i) q^{36} +(0.784787 - 0.349410i) q^{37} +(-2.27229 + 2.52364i) q^{38} +(4.22484 - 4.69216i) q^{39} +(0.381783 - 0.169981i) q^{40} +(-3.13451 + 2.27736i) q^{41} +(-0.645810 + 2.56572i) q^{42} +2.07519 q^{43} +(-0.656490 - 3.25100i) q^{44} +(-0.208957 - 0.361923i) q^{45} +(8.60442 - 1.82893i) q^{46} +(0.0192241 + 0.182905i) q^{47} +(0.809017 + 0.587785i) q^{48} +(3.04040 + 6.30523i) q^{49} +(-1.49111 - 4.58918i) q^{50} +(5.59765 - 2.49223i) q^{51} +(-5.76806 - 2.56810i) q^{52} +(-6.25729 + 1.33003i) q^{53} +(0.500000 - 0.866025i) q^{54} +(1.37987 - 0.130837i) q^{55} +(2.63971 - 0.178650i) q^{56} +(1.04939 - 3.22968i) q^{57} +(-0.415512 - 3.95334i) q^{58} +(-0.467776 + 4.45059i) q^{59} +(-0.279639 + 0.310570i) q^{60} +(6.67528 + 1.41888i) q^{61} +(1.68614 + 1.22505i) q^{62} +(-0.453596 - 2.60658i) q^{63} +(0.309017 - 0.951057i) q^{64} +(1.31934 - 2.28516i) q^{65} +(1.92204 + 2.70292i) q^{66} +(5.77491 + 10.0024i) q^{67} +(-4.10002 - 4.55354i) q^{68} +(-7.11664 + 5.17054i) q^{69} +(-0.0410617 + 1.10493i) q^{70} +(-0.960669 - 2.95664i) q^{71} +(-0.978148 - 0.207912i) q^{72} +(0.416094 - 3.95887i) q^{73} +(0.784787 + 0.349410i) q^{74} +(3.22879 + 3.58593i) q^{75} -3.39589 q^{76} +(8.48728 + 2.22846i) q^{77} +6.31393 q^{78} +(8.97328 + 9.96584i) q^{79} +(0.381783 + 0.169981i) q^{80} +(-0.104528 + 0.994522i) q^{81} +(-3.78980 - 0.805547i) q^{82} +(-3.63374 - 11.1835i) q^{83} +(-2.33883 + 1.23687i) q^{84} +(2.07166 - 1.50515i) q^{85} +(1.38857 + 1.54216i) q^{86} +(1.98756 + 3.44255i) q^{87} +(1.97669 - 2.66321i) q^{88} +(4.82050 - 8.34936i) q^{89} +(0.129142 - 0.397459i) q^{90} +(12.8208 - 10.7091i) q^{91} +(7.11664 + 5.17054i) q^{92} +(-2.03863 - 0.433325i) q^{93} +(-0.123062 + 0.136674i) q^{94} +(0.148345 - 1.41141i) q^{95} +(0.104528 + 0.994522i) q^{96} +(2.35935 - 7.26132i) q^{97} +(-2.65128 + 6.47848i) q^{98} +(-2.85524 - 1.68748i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 5 q^{2} - 5 q^{3} + 5 q^{4} - 3 q^{5} + 10 q^{6} - 7 q^{7} - 10 q^{8} + 5 q^{9}+O(q^{10}) $ 40 * q + 5 * q^2 - 5 * q^3 + 5 * q^4 - 3 * q^5 + 10 * q^6 - 7 * q^7 - 10 * q^8 + 5 * q^9	\( 40 q + 5 q^{2} - 5 q^{3} + 5 q^{4} - 3 q^{5} + 10 q^{6} - 7 q^{7} - 10 q^{8} + 5 q^{9} + 12 q^{10} + 2 q^{11} + 20 q^{12} + 10 q^{13} + 5 q^{14} - 6 q^{15} + 5 q^{16} + 5 q^{18} - 13 q^{19} + 6 q^{20} - 2 q^{21} - 4 q^{22} - 20 q^{23} - 5 q^{24} + 12 q^{25} + 10 q^{27} - 3 q^{28} + 12 q^{29} + 3 q^{30} - 10 q^{31} - 20 q^{32} + 8 q^{33} - 13 q^{35} - 10 q^{36} + 3 q^{37} + 2 q^{38} + 5 q^{39} - 3 q^{40} - 44 q^{41} - 3 q^{42} + 36 q^{43} - 3 q^{44} + 12 q^{45} + 11 q^{47} + 10 q^{48} + 33 q^{49} - 4 q^{50} + 26 q^{53} + 20 q^{54} - 20 q^{55} + 8 q^{56} + 4 q^{57} - 6 q^{58} + 4 q^{59} + 3 q^{60} - 23 q^{61} + 5 q^{63} - 10 q^{64} - 50 q^{65} - 7 q^{66} - 108 q^{67} + 20 q^{69} - 86 q^{71} + 5 q^{72} - 35 q^{73} + 3 q^{74} - 2 q^{75} - 44 q^{76} - 37 q^{77} + 20 q^{78} + 3 q^{79} - 3 q^{80} + 5 q^{81} - 28 q^{82} - 88 q^{83} - 5 q^{84} + 96 q^{85} - 13 q^{86} + 6 q^{87} - 8 q^{88} + 6 q^{89} + 6 q^{90} + 40 q^{91} - 20 q^{92} + 10 q^{93} - 24 q^{94} + 36 q^{95} - 5 q^{96} + 60 q^{97} + 2 q^{98} - 4 q^{99}+O(q^{100}) \) 40 * q + 5 * q^2 - 5 * q^3 + 5 * q^4 - 3 * q^5 + 10 * q^6 - 7 * q^7 - 10 * q^8 + 5 * q^9 + 12 * q^10 + 2 * q^11 + 20 * q^12 + 10 * q^13 + 5 * q^14 - 6 * q^15 + 5 * q^16 + 5 * q^18 - 13 * q^19 + 6 * q^20 - 2 * q^21 - 4 * q^22 - 20 * q^23 - 5 * q^24 + 12 * q^25 + 10 * q^27 - 3 * q^28 + 12 * q^29 + 3 * q^30 - 10 * q^31 - 20 * q^32 + 8 * q^33 - 13 * q^35 - 10 * q^36 + 3 * q^37 + 2 * q^38 + 5 * q^39 - 3 * q^40 - 44 * q^41 - 3 * q^42 + 36 * q^43 - 3 * q^44 + 12 * q^45 + 11 * q^47 + 10 * q^48 + 33 * q^49 - 4 * q^50 + 26 * q^53 + 20 * q^54 - 20 * q^55 + 8 * q^56 + 4 * q^57 - 6 * q^58 + 4 * q^59 + 3 * q^60 - 23 * q^61 + 5 * q^63 - 10 * q^64 - 50 * q^65 - 7 * q^66 - 108 * q^67 + 20 * q^69 - 86 * q^71 + 5 * q^72 - 35 * q^73 + 3 * q^74 - 2 * q^75 - 44 * q^76 - 37 * q^77 + 20 * q^78 + 3 * q^79 - 3 * q^80 + 5 * q^81 - 28 * q^82 - 88 * q^83 - 5 * q^84 + 96 * q^85 - 13 * q^86 + 6 * q^87 - 8 * q^88 + 6 * q^89 + 6 * q^90 + 40 * q^91 - 20 * q^92 + 10 * q^93 - 24 * q^94 + 36 * q^95 - 5 * q^96 + 60 * q^97 + 2 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	0.669131	+	0.743145i	0.473147	+	0.525483i
$2$	0.669131	+	0.743145i	0.473147	+	0.525483i
$3$	−0.913545	−	0.406737i	−0.527436	−	0.234830i
$3$	−0.913545	−	0.406737i	−0.527436	−	0.234830i
$4$	−0.104528	+	0.994522i	−0.0522642	+	0.497261i
$5$	−0.408781	−	0.0868890i	−0.182812	−	0.0388580i	0.115596	−	0.993296i	$-0.463122\pi$
$5$	−0.408781	−	0.0868890i	−0.182812	−	0.0388580i	−0.298408	+	0.954438i	$0.596456\pi$
$6$	−0.309017	−	0.951057i	−0.126156	−	0.388267i
$7$	−2.24058	−	1.40705i	−0.846860	−	0.531816i
$7$	−2.24058	−	1.40705i	−0.846860	−	0.531816i
$8$	−0.809017	+	0.587785i	−0.286031	+	0.207813i
$9$	0.669131	+	0.743145i	0.223044	+	0.247715i
$10$	−0.208957	−	0.361923i	−0.0660779	−	0.114450i
$11$	−3.16457	+	0.992716i	−0.954154	+	0.299315i
$11$	−3.16457	+	0.992716i	−0.954154	+	0.299315i
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	−1.95111	+	6.00490i	−0.541141	+	1.66546i	0.188853	+	0.982005i	$0.439523\pi$
$13$	−1.95111	+	6.00490i	−0.541141	+	1.66546i	−0.729993	+	0.683454i	$0.760477\pi$
$14$	−0.453596	−	2.60658i	−0.121229	−	0.696637i
$15$	0.338099	+	0.245643i	0.0872968	+	0.0634248i
$16$	−0.978148	−	0.207912i	−0.244537	−	0.0519779i
$17$	−4.10002	+	4.55354i	−0.994401	+	1.10439i	0.000134548		1.00000i	$0.499957\pi$
$17$	−4.10002	+	4.55354i	−0.994401	+	1.10439i	−0.994536	+	0.104395i	$0.966709\pi$
$18$	−0.104528	+	0.994522i	−0.0246376	+	0.234411i
$19$	0.354967	+	3.37729i	0.0814351	+	0.774803i	0.956684	+	0.291129i	$0.0940310\pi$
$19$	0.354967	+	3.37729i	0.0814351	+	0.774803i	−0.875249	+	0.483673i	$0.839302\pi$
$20$	0.129142	−	0.397459i	0.0288771	−	0.0888746i
$21$	1.47457	+	2.19673i	0.321778	+	0.479367i
$22$	−2.85524	−	1.68748i	−0.608740	−	0.359772i
$23$	4.39833	−	7.61812i	0.917114	−	1.58849i	0.113338	−	0.993556i	$-0.463846\pi$
$23$	4.39833	−	7.61812i	0.917114	−	1.58849i	0.803776	−	0.594932i	$-0.202821\pi$
$24$	0.978148	−	0.207912i	0.199664	−	0.0424398i
$25$	−4.40818	−	1.96265i	−0.881635	−	0.392529i
$26$	−5.76806	+	2.56810i	−1.13121	+	0.503647i
$27$	−0.309017	−	0.951057i	−0.0594703	−	0.183031i
$28$	1.63355	−	2.08123i	0.308712	−	0.393315i
$29$	−3.21593	−	2.33651i	−0.597184	−	0.433880i	0.247694	−	0.968838i	$-0.420327\pi$
$29$	−3.21593	−	2.33651i	−0.597184	−	0.433880i	−0.844878	+	0.534959i	$0.820327\pi$
$30$	0.0436838	+	0.415624i	0.00797554	+	0.0758822i
$31$	2.03863	−	0.433325i	0.366150	−	0.0778275i	−0.0211628	−	0.999776i	$-0.506737\pi$
$31$	2.03863	−	0.433325i	0.366150	−	0.0778275i	0.387312	+	0.921949i	$0.373403\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	3.29475	+	0.380256i	0.573543	+	0.0661940i
$34$	−6.12739			−1.05084
$35$	0.793649	+	0.769858i	0.134151	+	0.130130i
$36$	−0.809017	+	0.587785i	−0.134836	+	0.0979642i
$37$	0.784787	−	0.349410i	0.129018	−	0.0574426i	−0.341212	−	0.939986i	$-0.610837\pi$
$37$	0.784787	−	0.349410i	0.129018	−	0.0574426i	0.470230	+	0.882544i	$0.344171\pi$
$38$	−2.27229	+	2.52364i	−0.368615	+	0.409388i
$39$	4.22484	−	4.69216i	0.676516	−	0.751347i
$40$	0.381783	−	0.169981i	0.0603651	−	0.0268763i
$41$	−3.13451	+	2.27736i	−0.489528	+	0.355663i	−0.805003	−	0.593271i	$-0.797836\pi$
$41$	−3.13451	+	2.27736i	−0.489528	+	0.355663i	0.315475	+	0.948934i	$0.397836\pi$
$42$	−0.645810	+	2.56572i	−0.0996507	+	0.395899i
$43$	2.07519			0.316463			0.158231	−	0.987402i	$-0.449421\pi$
$43$	2.07519			0.316463			0.158231	+	0.987402i	$0.449421\pi$
$44$	−0.656490	−	3.25100i	−0.0989697	−	0.490107i
$45$	−0.208957	−	0.361923i	−0.0311494	−	0.0539524i
$46$	8.60442	−	1.82893i	1.26865	−	0.269660i
$47$	0.0192241	+	0.182905i	0.00280413	+	0.0266795i	0.995834	−	0.0911793i	$-0.0290636\pi$
$47$	0.0192241	+	0.182905i	0.00280413	+	0.0266795i	−0.993030	+	0.117859i	$0.962397\pi$
$48$	0.809017	+	0.587785i	0.116772	+	0.0848395i
$49$	3.04040	+	6.30523i	0.434343	+	0.900748i
$50$	−1.49111	−	4.58918i	−0.210875	−	0.649008i
$51$	5.59765	−	2.49223i	0.783827	−	0.348982i
$52$	−5.76806	−	2.56810i	−0.799886	−	0.356132i
$53$	−6.25729	+	1.33003i	−0.859505	+	0.182694i	−0.616523	−	0.787337i	$-0.711459\pi$
$53$	−6.25729	+	1.33003i	−0.859505	+	0.182694i	−0.242983	+	0.970031i	$0.578126\pi$
$54$	0.500000	−	0.866025i	0.0680414	−	0.117851i
$55$	1.37987	−	0.130837i	0.186062	−	0.0176420i
$56$	2.63971	−	0.178650i	0.352746	−	0.0238731i
$57$	1.04939	−	3.22968i	0.138995	−	0.427782i
$58$	−0.415512	−	3.95334i	−0.0545595	−	0.519099i
$59$	−0.467776	+	4.45059i	−0.0608992	+	0.579417i	0.920940	+	0.389704i	$0.127423\pi$
$59$	−0.467776	+	4.45059i	−0.0608992	+	0.579417i	−0.981839	+	0.189714i	$0.939244\pi$
$60$	−0.279639	+	0.310570i	−0.0361012	+	0.0400944i
$61$	6.67528	+	1.41888i	0.854682	+	0.181668i	0.614361	−	0.789025i	$-0.289414\pi$
$61$	6.67528	+	1.41888i	0.854682	+	0.181668i	0.240321	+	0.970693i	$0.422747\pi$
$62$	1.68614	+	1.22505i	0.214140	+	0.155581i
$63$	−0.453596	−	2.60658i	−0.0571478	−	0.328398i
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	1.31934	−	2.28516i	0.163644	−	0.283439i
$66$	1.92204	+	2.70292i	0.236586	+	0.332706i
$67$	5.77491	+	10.0024i	0.705517	+	1.22199i	0.966505	+	0.256649i	$0.0826185\pi$
$67$	5.77491	+	10.0024i	0.705517	+	1.22199i	−0.260988	+	0.965342i	$0.584048\pi$
$68$	−4.10002	−	4.55354i	−0.497201	−	0.552197i
$69$	−7.11664	+	5.17054i	−0.856743	+	0.622460i
$70$	−0.0410617	+	1.10493i	−0.00490781	+	0.132065i
$71$	−0.960669	−	2.95664i	−0.114010	−	0.350888i	0.877729	−	0.479158i	$-0.159058\pi$
$71$	−0.960669	−	2.95664i	−0.114010	−	0.350888i	−0.991739	+	0.128269i	$0.959058\pi$
$72$	−0.978148	−	0.207912i	−0.115276	−	0.0245026i
$73$	0.416094	−	3.95887i	0.0487001	−	0.463351i	−0.942811	−	0.333328i	$-0.891828\pi$
$73$	0.416094	−	3.95887i	0.0487001	−	0.463351i	0.991511	−	0.130023i	$-0.0415050\pi$
$74$	0.784787	+	0.349410i	0.0912296	+	0.0406180i
$75$	3.22879	+	3.58593i	0.372828	+	0.414068i
$76$	−3.39589			−0.389535
$77$	8.48728	+	2.22846i	0.967216	+	0.253957i
$78$	6.31393			0.714911
$79$	8.97328	+	9.96584i	1.00957	+	1.12124i	0.992605	+	0.121389i	$0.0387347\pi$
$79$	8.97328	+	9.96584i	1.00957	+	1.12124i	0.0169681	+	0.999856i	$0.494599\pi$
$80$	0.381783	+	0.169981i	0.0426846	+	0.0190044i
$81$	−0.104528	+	0.994522i	−0.0116143	+	0.110502i
$82$	−3.78980	−	0.805547i	−0.418514	−	0.0889578i
$83$	−3.63374	−	11.1835i	−0.398855	−	1.22755i	−0.925919	−	0.377723i	$-0.876707\pi$
$83$	−3.63374	−	11.1835i	−0.398855	−	1.22755i	0.527064	−	0.849825i	$-0.323293\pi$
$84$	−2.33883	+	1.23687i	−0.255188	+	0.134954i
$85$	2.07166	−	1.50515i	0.224703	−	0.163257i
$86$	1.38857	+	1.54216i	0.149733	+	0.166296i
$87$	1.98756	+	3.44255i	0.213088	+	0.369080i
$88$	1.97669	−	2.66321i	0.210716	−	0.283899i
$89$	4.82050	−	8.34936i	0.510972	−	0.885030i	−0.488947	−	0.872314i	$-0.662619\pi$
$89$	4.82050	−	8.34936i	0.510972	−	0.885030i	0.999919	−	0.0127163i	$-0.00404784\pi$
$90$	0.129142	−	0.397459i	0.0136128	−	0.0418959i
$91$	12.8208	−	10.7091i	1.34399	−	1.12262i
$92$	7.11664	+	5.17054i	0.741961	+	0.539066i
$93$	−2.03863	−	0.433325i	−0.211397	−	0.0449337i
$94$	−0.123062	+	0.136674i	−0.0126928	+	0.0140968i
$95$	0.148345	−	1.41141i	0.0152199	−	0.144808i
$96$	0.104528	+	0.994522i	0.0106684	+	0.101503i
$97$	2.35935	−	7.26132i	0.239555	−	0.737275i	−0.756929	−	0.653497i	$-0.773301\pi$
$97$	2.35935	−	7.26132i	0.239555	−	0.737275i	0.996484	−	0.0837783i	$-0.0266988\pi$
$98$	−2.65128	+	6.47848i	−0.267819	+	0.654426i
$99$	−2.85524	−	1.68748i	−0.286963	−	0.169598i
$100$	2.41267	−	4.17887i	0.241267	−	0.417887i
$101$	−0.439248	+	0.0933651i	−0.0437068	+	0.00929017i	−0.229713	−	0.973258i	$-0.573779\pi$
$101$	−0.439248	+	0.0933651i	−0.0437068	+	0.00929017i	0.186006	+	0.982549i	$0.440445\pi$
$102$	5.59765	+	2.49223i	0.554250	+	0.246768i
$103$	−16.7883	+	7.47461i	−1.65420	+	0.736495i	−0.999807	−	0.0196624i	$-0.993741\pi$
$103$	−16.7883	+	7.47461i	−1.65420	+	0.736495i	−0.654389	+	0.756158i	$0.727074\pi$
$104$	−1.95111	−	6.00490i	−0.191322	−	0.588829i
$105$	−0.411905	−	1.02611i	−0.0401978	−	0.100138i
$106$	−5.17535	−	3.76011i	−0.502675	−	0.365214i
$107$	−1.82738	−	17.3864i	−0.176660	−	1.68081i	−0.620116	−	0.784510i	$-0.712914\pi$
$107$	−1.82738	−	17.3864i	−0.176660	−	1.68081i	0.443456	−	0.896296i	$-0.353752\pi$
$108$	0.978148	−	0.207912i	0.0941223	−	0.0200063i
$109$	10.1073	+	17.5063i	0.968102	+	1.67680i	0.701040	+	0.713122i	$0.252719\pi$
$109$	10.1073	+	17.5063i	0.968102	+	1.67680i	0.267062	+	0.963679i	$0.413947\pi$
$110$	1.02055	+	0.937898i	0.0973052	+	0.0894251i
$111$	−0.859056			−0.0815380
$112$	1.89908	+	1.84215i	0.179446	+	0.174067i
$113$	−7.45386	+	5.41554i	−0.701200	+	0.509451i	−0.880323	−	0.474375i	$-0.842674\pi$
$113$	−7.45386	+	5.41554i	−0.701200	+	0.509451i	0.179123	+	0.983827i	$0.442674\pi$
$114$	3.10230	−	1.38123i	0.290557	−	0.129364i
$115$	−2.45988	+	2.73198i	−0.229385	+	0.254758i
$116$	2.65987	−	2.95408i	0.246963	−	0.274280i
$117$	−5.76806	+	2.56810i	−0.533257	+	0.237421i
$118$	−3.62044	+	2.63040i	−0.333288	+	0.242148i
$119$	15.5935	−	4.43361i	1.42945	−	0.406429i
$120$	−0.417913			−0.0381501
$121$	9.02903	−	6.28304i	0.820821	−	0.571186i
$122$	3.41221	+	5.91011i	0.308927	+	0.535077i
$123$	3.78980	−	0.805547i	0.341715	−	0.0726337i
$124$	0.217856	+	2.07276i	0.0195641	+	0.186140i
$125$	3.32194	+	2.41353i	0.297123	+	0.215873i
$126$	1.63355	−	2.08123i	0.145528	−	0.185411i
$127$	0.647857	+	1.99390i	0.0574880	+	0.176930i	0.975677	−	0.219212i	$-0.0703487\pi$
$127$	0.647857	+	1.99390i	0.0574880	+	0.176930i	−0.918189	+	0.396142i	$0.870349\pi$
$128$	0.913545	−	0.406737i	0.0807468	−	0.0359508i
$129$	−1.89578	−	0.844054i	−0.166914	−	0.0743148i
$130$	2.58101	−	0.548611i	0.226370	−	0.0481164i
$131$	−10.9750	+	19.0093i	−0.958892	+	1.66085i	−0.233694	+	0.972310i	$0.575081\pi$
$131$	−10.9750	+	19.0093i	−0.958892	+	1.66085i	−0.725198	+	0.688540i	$0.758252\pi$
$132$	−0.722568	+	3.23696i	−0.0628915	+	0.281741i
$133$	3.95669	−	8.06654i	0.343089	−	0.699458i
$134$	−3.56909	+	10.9845i	−0.308322	+	0.948918i
$135$	0.0436838	+	0.415624i	0.00375971	+	0.0357712i
$136$	0.640486	−	6.09382i	0.0549212	−	0.522541i
$137$	−10.4145	+	11.5664i	−0.889769	+	0.988188i	−0.999984	−	0.00571962i	$-0.998179\pi$
$137$	−10.4145	+	11.5664i	−0.889769	+	0.988188i	0.110215	+	0.993908i	$0.464846\pi$
$138$	−8.60442	−	1.82893i	−0.732457	−	0.155689i
$139$	4.53733	+	3.29656i	0.384851	+	0.279611i	0.763342	−	0.645994i	$-0.223557\pi$
$139$	4.53733	+	3.29656i	0.384851	+	0.279611i	−0.378491	+	0.925605i	$0.623557\pi$
$140$	−0.848600	+	0.708829i	−0.0717198	+	0.0599070i
$141$	0.0568322	−	0.174911i	0.00478613	−	0.0147302i
$142$	1.55440	−	2.69229i	0.130442	−	0.225932i
$143$	0.213265	−	20.9398i	0.0178341	−	1.75108i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	1.11159	+	1.23455i	0.0923129	+	0.102524i
$146$	3.22044	−	2.33978i	0.266525	−	0.193642i
$147$	−0.212974	−	6.99676i	−0.0175658	−	0.577083i
$148$	0.265463	+	0.817011i	0.0218209	+	0.0671579i
$149$	−7.79853	−	1.65763i	−0.638880	−	0.135798i	−0.122928	−	0.992416i	$-0.539228\pi$
$149$	−7.79853	−	1.65763i	−0.638880	−	0.135798i	−0.515952	+	0.856617i	$0.672562\pi$
$150$	−0.504386	+	4.79891i	−0.0411830	+	0.391830i
$151$	−6.12577	−	2.72737i	−0.498508	−	0.221950i	0.142050	−	0.989859i	$-0.454631\pi$
$151$	−6.12577	−	2.72737i	−0.498508	−	0.221950i	−0.640559	+	0.767909i	$0.721297\pi$
$152$	−2.27229	−	2.52364i	−0.184307	−	0.204694i
$153$	−6.12739			−0.495370
$154$	4.02303	+	7.79841i	0.324185	+	0.628414i
$155$	−0.871006			−0.0699609
$156$	4.22484	+	4.69216i	0.338258	+	0.375674i
$157$	3.33046	+	1.48282i	0.265800	+	0.118342i	0.535309	−	0.844656i	$-0.320195\pi$
$157$	3.33046	+	1.48282i	0.265800	+	0.118342i	−0.269510	+	0.962998i	$0.586862\pi$
$158$	−1.40176	+	13.3369i	−0.111518	+	1.06103i
$159$	6.25729	+	1.33003i	0.496236	+	0.105478i
$160$	0.129142	+	0.397459i	0.0102096	+	0.0314219i
$161$	−20.5739	+	10.8803i	−1.62145	+	0.857491i
$162$	−0.809017	+	0.587785i	−0.0635624	+	0.0461808i
$163$	−9.53803	−	10.5931i	−0.747076	−	0.829712i	0.243032	−	0.970018i	$-0.421858\pi$
$163$	−9.53803	−	10.5931i	−0.747076	−	0.829712i	−0.990108	+	0.140306i	$0.955191\pi$
$164$	−1.93723	−	3.35539i	−0.151273	−	0.262012i
$165$	−1.31379	−	0.441719i	−0.102279	−	0.0343878i
$166$	5.87951	−	10.1836i	0.456339	−	0.790402i
$167$	−3.89279	+	11.9808i	−0.301233	+	0.927101i	0.679823	+	0.733376i	$0.262057\pi$
$167$	−3.89279	+	11.9808i	−0.301233	+	0.927101i	−0.981056	+	0.193724i	$0.937943\pi$
$168$	−2.48416	−	0.910463i	−0.191657	−	0.0702438i
$169$	−21.7348	−	15.7912i	−1.67191	−	1.21471i
$170$	2.50476	+	0.532403i	0.192106	+	0.0408334i
$171$	−2.27229	+	2.52364i	−0.173767	+	0.192987i
$172$	−0.216916	+	2.06382i	−0.0165397	+	0.157365i
$173$	1.33465	+	12.6983i	0.101471	+	0.965434i	0.920252	+	0.391327i	$0.127984\pi$
$173$	1.33465	+	12.6983i	0.101471	+	0.965434i	−0.818780	+	0.574107i	$0.805349\pi$
$174$	−1.22838	+	3.78056i	−0.0931231	+	0.286603i
$175$	7.11532	+	10.6000i	0.537868	+	0.801285i
$176$	3.30182	−	0.313072i	0.248884	−	0.0235987i
$177$	2.23755	−	3.87555i	0.168185	−	0.291305i
$178$	9.43033	−	2.00448i	0.706833	−	0.150242i
$179$	11.0932	+	4.93902i	0.829147	+	0.369160i	0.777016	−	0.629480i	$-0.216732\pi$
$179$	11.0932	+	4.93902i	0.829147	+	0.369160i	0.0521304	+	0.998640i	$0.483399\pi$
$180$	0.381783	−	0.169981i	0.0284564	−	0.0126696i
$181$	4.27025	+	13.1425i	0.317405	+	0.976873i	0.974753	+	0.223286i	$0.0716782\pi$
$181$	4.27025	+	13.1425i	0.317405	+	0.976873i	−0.657348	+	0.753587i	$0.728322\pi$
$182$	16.5373	+	2.36192i	1.22582	+	0.175077i
$183$	−5.52107	−	4.01129i	−0.408129	−	0.296523i
$184$	0.919500	+	8.74846i	0.0677865	+	0.644945i
$185$	−0.351166	+	0.0746426i	−0.0258182	+	0.00548783i
$186$	−1.04209	−	1.80495i	−0.0764097	−	0.132346i
$187$	8.45444	−	18.4801i	0.618250	−	1.35140i
$188$	−0.183913			−0.0134132
$189$	−0.645810	+	2.56572i	−0.0469758	+	0.186629i
$190$	1.14815	−	0.834177i	0.0832953	−	0.0605176i
$191$	4.68500	−	2.08590i	0.338995	−	0.150930i	−0.230177	−	0.973149i	$-0.573931\pi$
$191$	4.68500	−	2.08590i	0.338995	−	0.150930i	0.569172	+	0.822219i	$0.307264\pi$
$192$	−0.669131	+	0.743145i	−0.0482903	+	0.0536319i
$193$	−11.8734	+	13.1868i	−0.854668	+	0.949205i	−0.999188	−	0.0402967i	$-0.987170\pi$
$193$	−11.8734	+	13.1868i	−0.854668	+	0.949205i	0.144520	+	0.989502i	$0.453836\pi$
$194$	6.97492	−	3.10544i	0.500770	−	0.222957i
$195$	−2.13473	+	1.55097i	−0.152871	+	0.111067i
$196$	−6.58850	+	2.36467i	−0.470607	+	0.168905i
$197$	8.14631			0.580400			0.290200	−	0.956966i	$-0.406278\pi$
$197$	8.14631			0.580400			0.290200	+	0.956966i	$0.406278\pi$
$198$	−0.656490	−	3.25100i	−0.0466547	−	0.231039i
$199$	−8.80153	−	15.2447i	−0.623924	−	1.08067i	−0.988748	−	0.149592i	$-0.952204\pi$
$199$	−8.80153	−	15.2447i	−0.623924	−	1.08067i	0.364824	−	0.931077i	$-0.381129\pi$
$200$	4.71990	−	1.00325i	0.333748	−	0.0709402i
$201$	−1.20728	−	11.4865i	−0.0851552	−	0.810198i
$202$	−0.363298	−	0.263952i	−0.0255616	−	0.0185716i
$203$	3.91796	+	9.76014i	0.274987	+	0.685027i
$204$	1.89347	+	5.82749i	0.132569	+	0.408006i
$205$	1.47920	−	0.658584i	0.103312	−	0.0459975i
$206$	−16.7883	−	7.47461i	−1.16969	−	0.520781i
$207$	8.60442	−	1.82893i	0.598049	−	0.127119i
$208$	3.15696	−	5.46802i	0.218896	−	0.379139i
$209$	−4.47601	−	10.3353i	−0.309612	−	0.714907i
$210$	0.486928	−	0.992704i	0.0336012	−	0.0685031i
$211$	6.94769	−	21.3828i	0.478299	−	1.47205i	−0.363158	−	0.931727i	$-0.618302\pi$
$211$	6.94769	−	21.3828i	0.478299	−	1.47205i	0.841457	−	0.540324i	$-0.181698\pi$
$212$	−0.668678	−	6.36204i	−0.0459250	−	0.436947i
$213$	−0.324957	+	3.09176i	−0.0222657	+	0.211844i
$214$	11.6979	−	12.9918i	0.799649	−	0.888100i
$215$	−0.848296	−	0.180311i	−0.0578533	−	0.0122971i
$216$	0.809017	+	0.587785i	0.0550466	+	0.0399937i
$217$	−5.17744	−	1.89757i	−0.351467	−	0.128815i
$218$	−6.24664	+	19.2252i	−0.423076	+	1.30209i
$219$	−1.99034	+	3.44737i	−0.134495	+	0.232952i
$220$	−0.0141158	+	1.38599i	−0.000951690	+	0.0934434i
$221$	−19.3439	−	33.5047i	−1.30121	−	2.25377i
$222$	−0.574821	−	0.638403i	−0.0385794	−	0.0428468i
$223$	−18.1913	+	13.2168i	−1.21818	+	0.885062i	−0.995948	−	0.0899315i	$-0.971335\pi$
$223$	−18.1913	+	13.2168i	−1.21818	+	0.885062i	−0.222235	+	0.974993i	$0.571335\pi$
$224$	−0.0982540	+	2.64393i	−0.00656487	+	0.176655i
$225$	−1.49111	−	4.58918i	−0.0994076	−	0.305945i
$226$	−9.01214	−	1.91559i	−0.599478	−	0.127423i
$227$	1.55526	−	14.7973i	0.103226	−	0.982133i	−0.813215	−	0.581964i	$-0.802285\pi$
$227$	1.55526	−	14.7973i	0.103226	−	0.982133i	0.916441	−	0.400169i	$-0.131049\pi$
$228$	3.10230	+	1.38123i	0.205455	+	0.0914744i
$229$	8.61834	+	9.57163i	0.569516	+	0.632511i	0.957251	−	0.289260i	$-0.0934091\pi$
$229$	8.61834	+	9.57163i	0.569516	+	0.632511i	−0.387735	+	0.921771i	$0.626742\pi$
$230$	−3.67624			−0.242404
$231$	−6.84712	−	5.48789i	−0.450508	−	0.361077i
$232$	3.97511			0.260979
$233$	−0.315461	−	0.350355i	−0.0206665	−	0.0229525i	0.732723	−	0.680527i	$-0.238249\pi$
$233$	−0.315461	−	0.350355i	−0.0206665	−	0.0229525i	−0.753389	+	0.657575i	$0.771582\pi$
$234$	−5.76806	−	2.56810i	−0.377070	−	0.167882i
$235$	0.00803401	−	0.0764385i	0.000524081	−	0.00498630i
$236$	−4.37731	−	0.930427i	−0.284939	−	0.0605656i
$237$	−4.14403	−	12.7540i	−0.269184	−	0.828462i
$238$	13.7289	+	8.62156i	0.889913	+	0.558853i
$239$	4.66922	−	3.39238i	0.302026	−	0.219435i	−0.426441	−	0.904515i	$-0.640233\pi$
$239$	4.66922	−	3.39238i	0.302026	−	0.219435i	0.728468	+	0.685080i	$0.240233\pi$
$240$	−0.279639	−	0.310570i	−0.0180506	−	0.0200472i
$241$	0.196880	+	0.341006i	0.0126821	+	0.0219661i	0.872297	−	0.488977i	$-0.162630\pi$
$241$	0.196880	+	0.341006i	0.0126821	+	0.0219661i	−0.859615	+	0.510943i	$0.829296\pi$
$242$	10.7108	+	2.50570i	0.688517	+	0.161072i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−2.10886	+	6.49040i	−0.135006	+	0.415505i
$245$	−0.695002	−	2.84164i	−0.0444020	−	0.181545i
$246$	3.13451	+	2.27736i	0.199849	+	0.145199i
$247$	−20.9729	−	4.45792i	−1.33447	−	0.283650i
$248$	−1.39459	+	1.54885i	−0.0885564	+	0.0983519i
$249$	−1.22915	+	11.6946i	−0.0778944	+	0.741115i
$250$	0.429209	+	4.08365i	0.0271455	+	0.258273i
$251$	4.18524	−	12.8808i	0.264170	−	0.813031i	−0.727714	−	0.685881i	$-0.759417\pi$
$251$	4.18524	−	12.8808i	0.264170	−	0.813031i	0.991884	−	0.127150i	$-0.0405829\pi$
$252$	2.63971	−	0.178650i	0.166286	−	0.0112539i
$253$	−6.35618	+	28.4744i	−0.399610	+	1.79017i
$254$	−1.04826	+	1.81563i	−0.0657734	+	0.113923i
$255$	−2.50476	+	0.532403i	−0.156854	+	0.0333404i
$256$	0.913545	+	0.406737i	0.0570966	+	0.0254210i
$257$	11.2647	−	5.01535i	0.702670	−	0.312849i	−0.0241193	−	0.999709i	$-0.507678\pi$
$257$	11.2647	−	5.01535i	0.702670	−	0.312849i	0.726790	+	0.686860i	$0.241011\pi$
$258$	−0.641268	−	1.97362i	−0.0399236	−	0.122872i
$259$	−2.25002	−	0.321357i	−0.139809	−	0.0199681i
$260$	2.13473	+	1.55097i	0.132390	+	0.0961873i
$261$	−0.415512	−	3.95334i	−0.0257196	−	0.244705i
$262$	−21.4704	+	4.56367i	−1.32645	+	0.281945i
$263$	−1.17681	−	2.03830i	−0.0725654	−	0.125687i	0.827460	−	0.561525i	$-0.189785\pi$
$263$	−1.17681	−	2.03830i	−0.0725654	−	0.125687i	−0.900025	+	0.435838i	$0.856452\pi$
$264$	−2.88902	+	1.62897i	−0.177807	+	0.100256i
$265$	2.67343			0.164227
$266$	8.64215	−	2.45717i	0.529884	−	0.150659i
$267$	−7.79974	+	5.66684i	−0.477336	+	0.346805i
$268$	−10.5513	+	4.69773i	−0.644522	+	0.286960i
$269$	−10.6544	+	11.8329i	−0.649611	+	0.721466i	−0.974525	−	0.224277i	$-0.927998\pi$
$269$	−10.6544	+	11.8329i	−0.649611	+	0.721466i	0.324914	+	0.945744i	$0.394665\pi$
$270$	−0.279639	+	0.310570i	−0.0170183	+	0.0189007i
$271$	−7.84885	+	3.49453i	−0.476784	+	0.212278i	−0.631036	−	0.775754i	$-0.717370\pi$
$271$	−7.84885	+	3.49453i	−0.476784	+	0.212278i	0.154252	+	0.988032i	$0.450703\pi$
$272$	4.95716	−	3.60159i	0.300572	−	0.218378i
$273$	−16.0682	+	4.56859i	−0.972493	+	0.276503i
$274$	−15.5642			−0.940267
$275$	15.8983	+	1.83487i	0.958706	+	0.110647i
$276$	−4.39833	−	7.61812i	−0.264748	−	0.458557i
$277$	0.915309	−	0.194555i	0.0549956	−	0.0116897i	−0.180332	−	0.983606i	$-0.557717\pi$
$277$	0.915309	−	0.194555i	0.0549956	−	0.0116897i	0.235327	+	0.971916i	$0.424384\pi$
$278$	0.586242	+	5.57772i	0.0351605	+	0.334530i
$279$	1.68614	+	1.22505i	0.100946	+	0.0733418i
$280$	−1.09459	−	0.156334i	−0.0654141	−	0.00934272i
$281$	3.13550	+	9.65007i	0.187048	+	0.575675i	0.999978	−	0.00668710i	$-0.00212859\pi$
$281$	3.13550	+	9.65007i	0.187048	+	0.575675i	−0.812929	+	0.582362i	$0.802129\pi$
$282$	0.168013	−	0.0748041i	0.0100050	−	0.00445452i
$283$	−7.89428	−	3.51476i	−0.469267	−	0.208931i	0.158459	−	0.987366i	$-0.449347\pi$
$283$	−7.89428	−	3.51476i	−0.469267	−	0.208931i	−0.627726	+	0.778435i	$0.716014\pi$
$284$	3.04086	−	0.646354i	0.180442	−	0.0383541i
$285$	−0.709594	+	1.22905i	−0.0420327	+	0.0728028i
$286$	15.7040	−	13.8530i	0.928599	−	0.819145i
$287$	10.2275	−	0.692173i	0.603709	−	0.0408577i
$288$	0.309017	−	0.951057i	0.0182090	−	0.0560415i
$289$	−2.14752	−	20.4323i	−0.126325	−	1.20190i
$290$	−0.173648	+	1.65215i	−0.0101970	+	0.0970177i
$291$	−5.10881	+	5.67391i	−0.299484	+	0.332611i
$292$	3.89369	+	0.827629i	0.227861	+	0.0484334i
$293$	−3.96425	−	2.88020i	−0.231594	−	0.168263i	0.465936	−	0.884818i	$-0.345718\pi$
$293$	−3.96425	−	2.88020i	−0.231594	−	0.168263i	−0.697530	+	0.716555i	$0.745718\pi$
$294$	5.05710	−	4.84002i	0.294936	−	0.282276i
$295$	0.577925	−	1.77867i	0.0336481	−	0.103558i
$296$	−0.429528	+	0.743964i	−0.0249658	+	0.0432421i
$297$	1.92204	+	2.70292i	0.111528	+	0.156839i
$298$	−3.98638	−	6.90461i	−0.230925	−	0.399973i
$299$	37.1644	+	41.2753i	2.14928	+	2.38701i
$300$	−3.90379	+	2.83627i	−0.225385	+	0.163752i
$301$	−4.64962	−	2.91990i	−0.268000	−	0.168300i
$302$	−2.07211	−	6.37730i	−0.119237	−	0.366973i
$303$	0.439248	+	0.0933651i	0.0252342	+	0.00536368i
$304$	0.354967	−	3.37729i	0.0203588	−	0.193701i
$305$	−2.60544	−	1.16002i	−0.149187	−	0.0664224i
$306$	−4.10002	−	4.55354i	−0.234383	−	0.260308i
$307$	−20.4366			−1.16638			−0.583189	−	0.812337i	$-0.698195\pi$
$307$	−20.4366			−1.16638			−0.583189	+	0.812337i	$0.698195\pi$
$308$	−3.10342	+	8.20785i	−0.176834	+	0.467686i
$309$	18.3770			1.04543
$310$	−0.582817	−	0.647284i	−0.0331018	−	0.0367632i
$311$	20.0976	+	8.94802i	1.13963	+	0.507396i	0.887733	−	0.460358i	$-0.152279\pi$
$311$	20.0976	+	8.94802i	1.13963	+	0.507396i	0.251896	+	0.967754i	$0.418946\pi$
$312$	−0.659985	+	6.27934i	−0.0373643	+	0.355497i
$313$	−28.4252	−	6.04197i	−1.60669	−	0.341512i	−0.684729	−	0.728797i	$-0.740080\pi$
$313$	−28.4252	−	6.04197i	−1.60669	−	0.341512i	−0.921960	+	0.387285i	$0.873413\pi$
$314$	1.12657	+	3.46721i	0.0635757	+	0.195666i
$315$	−0.0410617	+	1.10493i	−0.00231356	+	0.0622559i
$316$	−10.8492	+	7.88241i	−0.610316	+	0.443420i
$317$	15.5660	+	17.2878i	0.874276	+	0.970982i	0.999777	−	0.0211116i	$-0.00672054\pi$
$317$	15.5660	+	17.2878i	0.874276	+	0.970982i	−0.125501	+	0.992093i	$0.540054\pi$
$318$	3.19854	+	5.54004i	0.179365	+	0.310670i
$319$	12.4965	+	4.20155i	0.699672	+	0.235242i
$320$	−0.208957	+	0.361923i	−0.0116810	+	0.0202321i
$321$	−5.40229	+	16.6265i	−0.301526	+	0.928002i
$322$	−21.8523	−	8.00903i	−1.21778	−	0.446326i
$323$	−16.8340	−	12.2306i	−0.936667	−	0.680529i
$324$	−0.978148	−	0.207912i	−0.0543415	−	0.0115506i
$325$	20.3863	−	22.6413i	1.13083	−	1.25591i
$326$	1.48999	−	14.1763i	0.0825227	−	0.785151i
$327$	−2.11300	−	20.1038i	−0.116849	−	1.11174i
$328$	1.19728	−	3.68484i	0.0661085	−	0.203461i
$329$	0.214284	−	0.436863i	0.0118139	−	0.0240851i
$330$	−0.550837	−	1.27191i	−0.0303226	−	0.0700161i
$331$	−17.3175	+	29.9948i	−0.951857	+	1.64866i	−0.210454	+	0.977604i	$0.567494\pi$
$331$	−17.3175	+	29.9948i	−0.951857	+	1.64866i	−0.741403	+	0.671060i	$0.765839\pi$
$332$	11.5021	−	2.44484i	0.631258	−	0.134178i
$333$	0.784787	+	0.349410i	0.0430061	+	0.0191475i
$334$	−11.5082	+	5.12380i	−0.629703	+	0.280362i
$335$	−1.49157	−	4.59058i	−0.0814931	−	0.250810i
$336$	−0.985622	−	2.45531i	−0.0537701	−	0.133948i
$337$	26.8016	+	19.4725i	1.45998	+	1.06074i	0.983369	+	0.181620i	$0.0581341\pi$
$337$	26.8016	+	19.4725i	1.45998	+	1.06074i	0.476609	+	0.879116i	$0.341866\pi$
$338$	−2.80823	−	26.7185i	−0.152747	−	1.45329i
$339$	9.01214	−	1.91559i	0.489472	−	0.104041i
$340$	1.28036	+	2.21765i	0.0694372	+	0.120269i
$341$	−6.02124	+	3.39508i	−0.326068	+	0.183854i
$342$	−3.39589			−0.183629
$343$	2.05954	−	18.4054i	0.111205	−	0.993798i
$344$	−1.67886	+	1.21976i	−0.0905181	+	0.0657652i
$345$	3.35841	−	1.49526i	0.180811	−	0.0805021i
$346$	−8.54363	+	9.48866i	−0.459308	+	0.510113i
$347$	−7.36242	+	8.17680i	−0.395235	+	0.438953i	−0.907614	−	0.419807i	$-0.862098\pi$
$347$	−7.36242	+	8.17680i	−0.395235	+	0.438953i	0.512378	+	0.858760i	$0.328765\pi$
$348$	−3.63145	+	1.61682i	−0.194666	+	0.0866709i
$349$	−0.168009	+	0.122065i	−0.00899329	+	0.00653401i	−0.592273	−	0.805737i	$-0.701769\pi$
$349$	−0.168009	+	0.122065i	−0.00899329	+	0.00653401i	0.583280	+	0.812272i	$0.301769\pi$
$350$	−3.11626	+	12.3805i	−0.166571	+	0.661766i
$351$	6.31393			0.337012
$352$	2.44200	+	2.24424i	0.130159	+	0.119618i
$353$	−2.02883	−	3.51404i	−0.107984	−	0.187033i	0.806970	−	0.590593i	$-0.201106\pi$
$353$	−2.02883	−	3.51404i	−0.107984	−	0.187033i	−0.914953	+	0.403560i	$0.867773\pi$
$354$	4.37731	−	0.930427i	0.232652	−	0.0494516i
$355$	0.135804	+	1.29209i	0.00720772	+	0.0685769i
$356$	7.79974	+	5.66684i	0.413385	+	0.300342i
$357$	−16.0487	−	2.29214i	−0.849386	−	0.121313i
$358$	3.75241	+	11.5487i	0.198321	+	0.610369i
$359$	−13.4643	+	5.99467i	−0.710616	+	0.316387i	−0.730021	−	0.683425i	$-0.760490\pi$
$359$	−13.4643	+	5.99467i	−0.710616	+	0.316387i	0.0194047	+	0.999812i	$0.493823\pi$
$360$	0.381783	+	0.169981i	0.0201217	+	0.00895877i
$361$	7.30474	−	1.55267i	0.384460	−	0.0817195i
$362$	−6.90941	+	11.9674i	−0.363151	+	0.628995i
$363$	−10.8040	+	2.06741i	−0.567061	+	0.108511i
$364$	9.31034	+	13.8700i	0.487994	+	0.726986i
$365$	−0.514074	+	1.58216i	−0.0269079	+	0.0828139i
$366$	−0.713345	−	6.78703i	−0.0372872	−	0.354764i
$367$	1.74815	−	16.6326i	0.0912528	−	0.868213i	−0.849150	−	0.528151i	$-0.822885\pi$
$367$	1.74815	−	16.6326i	0.0912528	−	0.868213i	0.940403	−	0.340061i	$-0.110448\pi$
$368$	−5.88611	+	6.53718i	−0.306835	+	0.340774i
$369$	−3.78980	−	0.805547i	−0.197289	−	0.0419351i
$370$	−0.290446	−	0.211021i	−0.0150996	−	0.0109705i
$371$	15.8914	+	5.82431i	0.825040	+	0.302383i
$372$	0.644047	−	1.98217i	0.0333923	−	0.102771i
$373$	−6.55254	+	11.3493i	−0.339278	+	0.587647i	−0.984297	−	0.176520i	$-0.943516\pi$
$373$	−6.55254	+	11.3493i	−0.339278	+	0.587647i	0.645019	+	0.764166i	$0.276849\pi$
$374$	19.3906	−	6.08276i	1.00266	−	0.314532i
$375$	−2.05307	−	3.55602i	−0.106020	−	0.183632i
$376$	−0.123062	−	0.136674i	−0.00634642	−	0.00704842i
$377$	20.3052	−	14.7526i	1.04577	−	0.759796i
$378$	−2.33883	+	1.23687i	−0.120297	+	0.0636179i
$379$	2.14179	+	6.59176i	0.110016	+	0.338596i	0.990875	−	0.134784i	$-0.0430340\pi$
$379$	2.14179	+	6.59176i	0.110016	+	0.338596i	−0.880859	+	0.473379i	$0.843034\pi$
$380$	1.38817	+	0.295066i	0.0712119	+	0.0151365i
$381$	0.219145	−	2.08503i	0.0112271	−	0.106819i
$382$	4.68500	+	2.08590i	0.239705	+	0.106724i
$383$	−6.78587	−	7.53647i	−0.346742	−	0.385096i	0.544396	−	0.838828i	$-0.316759\pi$
$383$	−6.78587	−	7.53647i	−0.346742	−	0.385096i	−0.891138	+	0.453732i	$0.850092\pi$
$384$	−1.00000			−0.0510310
$385$	−3.27581	−	1.64840i	−0.166951	−	0.0840104i
$386$	−17.7446			−0.903175
$387$	1.38857	+	1.54216i	0.0705850	+	0.0783926i
$388$	6.97492	+	3.10544i	0.354098	+	0.157655i
$389$	−0.471055	+	4.48179i	−0.0238835	+	0.227236i	0.976069	+	0.217462i	$0.0697778\pi$
$389$	−0.471055	+	4.48179i	−0.0238835	+	0.227236i	−0.999952	+	0.00977384i	$0.996889\pi$
$390$	−2.58101	−	0.548611i	−0.130695	−	0.0277800i
$391$	16.6562	+	51.2624i	0.842338	+	2.59245i
$392$	−6.16586	−	3.31394i	−0.311423	−	0.167379i
$393$	17.7580	−	12.9019i	0.895771	−	0.650816i
$394$	5.45094	+	6.05388i	0.274615	+	0.304990i
$395$	−2.80218	−	4.85352i	−0.140993	−	0.244207i
$396$	1.97669	−	2.66321i	0.0993323	−	0.133831i
$397$	−4.83950	+	8.38226i	−0.242888	+	0.420694i	−0.961536	−	0.274680i	$-0.911428\pi$
$397$	−4.83950	+	8.38226i	−0.242888	+	0.420694i	0.718648	+	0.695374i	$0.244761\pi$
$398$	5.43965	−	16.7415i	0.272665	−	0.839176i
$399$	−6.89558	+	5.75982i	−0.345211	+	0.288352i
$400$	3.90379	+	2.83627i	0.195189	+	0.141813i
$401$	−6.89961	−	1.46656i	−0.344550	−	0.0732363i	0.0323867	−	0.999475i	$-0.489689\pi$
$401$	−6.89961	−	1.46656i	−0.344550	−	0.0732363i	−0.376937	+	0.926239i	$0.623023\pi$
$402$	7.72833	−	8.58318i	0.385454	−	0.428090i
$403$	−1.37553	+	13.0873i	−0.0685199	+	0.651923i
$404$	−0.0469397	−	0.446601i	−0.00233534	−	0.0222192i
$405$	0.129142	−	0.397459i	0.00641713	−	0.0197499i
$406$	−4.63157	+	9.44242i	−0.229861	+	0.468619i
$407$	−2.13665	+	1.88480i	−0.105910	+	0.0934262i
$408$	−3.06369	+	5.30647i	−0.151675	+	0.262710i
$409$	−3.24158	+	0.689020i	−0.160286	+	0.0340698i	−0.287356	−	0.957824i	$-0.592776\pi$
$409$	−3.24158	+	0.689020i	−0.160286	+	0.0340698i	0.127070	+	0.991894i	$0.459443\pi$
$410$	1.47920	+	0.658584i	0.0730527	+	0.0325252i
$411$	14.2186	−	6.33053i	0.701351	−	0.312262i
$412$	−5.67882	−	17.4776i	−0.279775	−	0.861059i
$413$	7.31031	−	9.31372i	0.359717	−	0.458298i
$414$	7.11664	+	5.17054i	0.349764	+	0.254118i
$415$	0.513679	+	4.88733i	0.0252155	+	0.239910i
$416$	6.17595	−	1.31274i	0.302801	−	0.0643623i
$417$	−2.80422	−	4.85706i	−0.137323	−	0.237851i
$418$	4.68558	−	10.2420i	0.229179	−	0.500951i
$419$	−2.28522			−0.111640			−0.0558202	−	0.998441i	$-0.517777\pi$
$419$	−2.28522			−0.111640			−0.0558202	+	0.998441i	$0.517777\pi$
$420$	1.06354	−	0.302391i	0.0518955	−	0.0147552i
$421$	19.0722	−	13.8567i	0.929521	−	0.675336i	−0.0163547	−	0.999866i	$-0.505206\pi$
$421$	19.0722	−	13.8567i	0.929521	−	0.675336i	0.945875	+	0.324530i	$0.105206\pi$
$422$	20.5394	−	9.14474i	0.999843	−	0.445159i
$423$	−0.123062	+	0.136674i	−0.00598346	+	0.00664531i
$424$	4.28049	−	4.75396i	0.207879	−	0.230873i
$425$	27.0106	−	12.0259i	1.31021	−	0.583341i
$426$	−2.51506	+	1.82730i	−0.121855	+	0.0885330i
$427$	−12.9601	−	12.5716i	−0.627182	−	0.608382i
$428$	17.4822			0.845032
$429$	−8.71183	+	19.0427i	−0.420611	+	0.919393i
$430$	−0.433624	−	0.751058i	−0.0209112	−	0.0362193i
$431$	−22.7119	+	4.82757i	−1.09399	+	0.232536i	−0.719360	−	0.694637i	$-0.755565\pi$
$431$	−22.7119	+	4.82757i	−1.09399	+	0.232536i	−0.374634	+	0.927173i	$0.622232\pi$
$432$	0.104528	+	0.994522i	0.00502913	+	0.0478490i
$433$	−14.2517	−	10.3544i	−0.684891	−	0.497602i	0.190086	−	0.981767i	$-0.439123\pi$
$433$	−14.2517	−	10.3544i	−0.684891	−	0.497602i	−0.874977	+	0.484165i	$0.839123\pi$
$434$	−2.05421	−	5.11731i	−0.0986054	−	0.245639i
$435$	−0.513355	−	1.57994i	−0.0246135	−	0.0757526i
$436$	−18.4669	+	8.22200i	−0.884405	+	0.393762i
$437$	27.2898	+	12.1502i	1.30545	+	0.581224i
$438$	−3.89369	+	0.827629i	−0.186048	+	0.0395457i
$439$	6.10353	−	10.5716i	0.291305	−	0.504556i	−0.682813	−	0.730593i	$-0.739244\pi$
$439$	6.10353	−	10.5716i	0.291305	−	0.504556i	0.974119	+	0.226037i	$0.0725771\pi$
$440$	−1.03944	+	0.916918i	−0.0495532	+	0.0437123i
$441$	−2.65128	+	6.47848i	−0.126251	+	0.308499i
$442$	11.9552	−	36.7943i	0.568651	−	1.75013i
$443$	−3.32960	−	31.6790i	−0.158194	−	1.50512i	−0.729275	−	0.684221i	$-0.760142\pi$
$443$	−3.32960	−	31.6790i	−0.158194	−	1.50512i	0.571081	−	0.820894i	$-0.306524\pi$
$444$	0.0897958	−	0.854350i	0.00426152	−	0.0405457i
$445$	−2.69600	+	2.99421i	−0.127802	+	0.141939i
$446$	−21.9944	−	4.67505i	−1.04146	−	0.221370i
$447$	6.45009	+	4.68627i	0.305079	+	0.221653i
$448$	−2.03056	+	1.69612i	−0.0959352	+	0.0801339i
$449$	3.33501	−	10.2641i	0.157389	−	0.484393i	−0.841006	−	0.541025i	$-0.818036\pi$
$449$	3.33501	−	10.2641i	0.157389	−	0.484393i	0.998395	+	0.0566324i	$0.0180363\pi$
$450$	2.41267	−	4.17887i	0.113735	−	0.196994i
$451$	7.65861	−	10.3185i	0.360630	−	0.485881i
$452$	−4.60674	−	7.97910i	−0.216683	−	0.375305i
$453$	4.48685	+	4.98315i	0.210811	+	0.234129i
$454$	12.0372	−	8.74556i	0.564935	−	0.410449i
$455$	−6.17142	+	3.26370i	−0.289321	+	0.153005i
$456$	1.04939	+	3.22968i	0.0491421	+	0.151244i
$457$	31.4906	+	6.69353i	1.47307	+	0.313110i	0.873346	−	0.487099i	$-0.161945\pi$
$457$	31.4906	+	6.69353i	1.47307	+	0.313110i	0.599721	+	0.800210i	$0.295278\pi$
$458$	−1.34632	+	12.8093i	−0.0629092	+	0.598542i
$459$	5.59765	+	2.49223i	0.261276	+	0.116327i
$460$	−2.45988	−	2.73198i	−0.114693	−	0.127379i
$461$	29.1559			1.35792			0.678962	−	0.734173i	$-0.262430\pi$
$461$	29.1559			1.35792			0.678962	+	0.734173i	$0.262430\pi$
$462$	−0.503322	−	8.76052i	−0.0234167	−	0.407576i
$463$	2.99596			0.139234			0.0696171	−	0.997574i	$-0.477822\pi$
$463$	2.99596			0.139234			0.0696171	+	0.997574i	$0.477822\pi$
$464$	2.65987	+	2.95408i	0.123481	+	0.137140i
$465$	0.795704	+	0.354270i	0.0368999	+	0.0164289i
$466$	0.0492798	−	0.468866i	0.00228284	−	0.0217198i
$467$	33.5653	+	7.13452i	1.55322	+	0.330146i	0.903013	−	0.429614i	$-0.141350\pi$
$467$	33.5653	+	7.13452i	1.55322	+	0.330146i	0.650203	+	0.759760i	$0.274684\pi$
$468$	−1.95111	−	6.00490i	−0.0901901	−	0.277577i
$469$	1.13482	−	30.5368i	0.0524009	−	1.41006i
$470$	0.0621807	−	0.0451769i	0.00286818	−	0.00208386i
$471$	−2.43941	−	2.70924i	−0.112402	−	0.124835i
$472$	−2.23755	−	3.87555i	−0.102992	−	0.178387i
$473$	−6.56707	+	2.06007i	−0.301954	+	0.0947222i
$474$	6.70518	−	11.6137i	0.307979	−	0.533435i
$475$	5.06366	−	15.5843i	0.232337	−	0.715059i
$476$	2.77936	+	15.9715i	0.127392	+	0.732053i
$477$	−5.17535	−	3.76011i	−0.236963	−	0.172164i
$478$	5.64535	+	1.19996i	0.258212	+	0.0548847i
$479$	−10.1989	+	11.3270i	−0.465997	+	0.517543i	−0.929635	−	0.368483i	$-0.879877\pi$
$479$	−10.1989	+	11.3270i	−0.465997	+	0.517543i	0.463637	+	0.886025i	$0.346544\pi$
$480$	0.0436838	−	0.415624i	0.00199388	−	0.0189705i
$481$	0.566964	+	5.39430i	0.0258513	+	0.245959i
$482$	−0.121678	+	0.374487i	−0.00554230	+	0.0170574i
$483$	23.2206	−	1.57152i	1.05658	−	0.0715066i
$484$	5.30484	+	9.63632i	0.241129	+	0.438015i
$485$	−1.59538	+	2.76329i	−0.0724427	+	0.125474i
$486$	0.978148	−	0.207912i	0.0443697	−	0.00943107i
$487$	−1.43540	−	0.639080i	−0.0650440	−	0.0289595i	0.373957	−	0.927446i	$-0.378001\pi$
$487$	−1.43540	−	0.639080i	−0.0650440	−	0.0289595i	−0.439001	+	0.898487i	$0.644667\pi$
$488$	−6.23441	+	2.77574i	−0.282219	+	0.125652i
$489$	4.40484	+	13.5567i	0.199194	+	0.613055i
$490$	1.64670	−	2.41791i	0.0743903	−	0.109230i
$491$	15.8840	+	11.5404i	0.716833	+	0.520810i	0.885371	−	0.464885i	$-0.153904\pi$
$491$	15.8840	+	11.5404i	0.716833	+	0.520810i	−0.168538	+	0.985695i	$0.553904\pi$
$492$	0.404992	+	3.85324i	0.0182585	+	0.173718i
$493$	23.8248	−	5.06412i	1.07301	−	0.228076i
$494$	−10.7207	−	18.5688i	−0.482347	−	0.835450i
$495$	1.02055	+	0.937898i	0.0458701	+	0.0421554i
$496$	−2.08418			−0.0935824
$497$	−2.00769	+	7.97629i	−0.0900571	+	0.357786i
$498$	−9.51325	+	6.91178i	−0.426299	+	0.309724i
$499$	11.2143	−	4.99295i	0.502023	−	0.223515i	−0.140070	−	0.990142i	$-0.544733\pi$
$499$	11.2143	−	4.99295i	0.502023	−	0.223515i	0.642093	+	0.766626i	$0.278066\pi$
$500$	−2.74755	+	3.05146i	−0.122874	+	0.136465i
$501$	8.42927	−	9.36165i	0.376592	−	0.418248i
$502$	12.3728	−	5.50872i	0.552225	−	0.245866i
$503$	30.5400	−	22.1886i	1.36171	−	0.989340i	0.363376	−	0.931643i	$-0.381624\pi$
$503$	30.5400	−	22.1886i	1.36171	−	0.989340i	0.998334	−	0.0576975i	$-0.0183759\pi$
$504$	1.89908	+	1.84215i	0.0845915	+	0.0820558i
$505$	0.187669			0.00835115
$506$	−25.4137	+	14.3295i	−1.12978	+	0.637025i
$507$	13.4328	+	23.2663i	0.596573	+	1.03329i
$508$	−2.05070	+	0.435889i	−0.0909850	+	0.0193395i
$509$	3.56959	+	33.9624i	0.158219	+	1.50536i	0.729147	+	0.684357i	$0.239917\pi$
$509$	3.56959	+	33.9624i	0.158219	+	1.50536i	−0.570928	+	0.821000i	$0.693416\pi$
$510$	−2.07166	−	1.50515i	−0.0917348	−	0.0666492i
$511$	−6.50264	+	8.28470i	−0.287660	+	0.366494i
$512$	0.309017	+	0.951057i	0.0136568	+	0.0420312i
$513$	3.10230	−	1.38123i	0.136970	−	0.0609829i
$514$	11.2647	+	5.01535i	0.496863	+	0.221218i
$515$	7.51218	−	1.59676i	0.331026	−	0.0703618i
$516$	1.03759	−	1.79716i	0.0456775	−	0.0791157i
$517$	−0.242409	−	0.559733i	−0.0106611	−	0.0246170i
$518$	−1.26674	−	1.88712i	−0.0556574	−	0.0829152i
$519$	3.94561	−	12.1433i	0.173193	−	0.533033i
$520$	0.275816	+	2.62422i	0.0120954	+	0.115080i
$521$	−2.74385	+	26.1060i	−0.120210	+	1.14373i	0.753557	+	0.657382i	$0.228336\pi$
$521$	−2.74385	+	26.1060i	−0.120210	+	1.14373i	−0.873768	+	0.486343i	$0.838330\pi$
$522$	2.65987	−	2.95408i	0.116419	−	0.129297i
$523$	−12.7408	−	2.70813i	−0.557115	−	0.118418i	−0.0792549	−	0.996854i	$-0.525254\pi$
$523$	−12.7408	−	2.70813i	−0.557115	−	0.118418i	−0.477860	+	0.878436i	$0.658587\pi$
$524$	−17.7580	−	12.9019i	−0.775760	−	0.563623i
$525$	−2.18876	−	12.5776i	−0.0955253	−	0.548934i
$526$	0.727310	−	2.23843i	0.0317122	−	0.0976002i
$527$	−6.38529	+	11.0596i	−0.278147	+	0.481765i
$528$	−3.14370	−	1.05696i	−0.136812	−	0.0459985i
$529$	−27.1905	−	47.0954i	−1.18220	−	2.04762i
$530$	1.78887	+	1.98674i	0.0777036	+	0.0862986i
$531$	−3.62044	+	2.63040i	−0.157114	+	0.114150i
$532$	7.60876	+	4.77820i	0.329882	+	0.207161i
$533$	−7.55951	−	23.2658i	−0.327439	−	1.00775i
$534$	−9.43033	−	2.00448i	−0.408090	−	0.0867422i
$535$	−0.763688	+	7.26601i	−0.0330171	+	0.314137i
$536$	−10.5513	−	4.69773i	−0.455746	−	0.202911i
$537$	−8.12529	−	9.02405i	−0.350632	−	0.389416i
$538$	−15.9228			−0.686480
$539$	−15.8809	−	16.9351i	−0.684038	−	0.729447i
$540$	−0.417913			−0.0179841
$541$	11.2410	+	12.4844i	0.483289	+	0.536747i	0.934638	−	0.355601i	$-0.115724\pi$
$541$	11.2410	+	12.4844i	0.483289	+	0.536747i	−0.451349	+	0.892348i	$0.649057\pi$
$542$	−7.84885	−	3.49453i	−0.337137	−	0.150103i
$543$	1.44446	−	13.7431i	0.0619877	−	0.589774i
$544$	5.99349	+	1.27396i	0.256969	+	0.0546204i
$545$	−2.61055	−	8.03446i	−0.111824	−	0.344158i
$546$	−14.1469	−	8.88403i	−0.605430	−	0.380201i
$547$	−13.2517	+	9.62789i	−0.566600	+	0.411659i	−0.833869	−	0.551963i	$-0.813879\pi$
$547$	−13.2517	+	9.62789i	−0.566600	+	0.411659i	0.267269	+	0.963622i	$0.413879\pi$
$548$	−10.4145	−	11.5664i	−0.444884	−	0.494094i
$549$	3.41221	+	5.91011i	0.145629	+	0.252238i
$550$	9.27449	+	13.0425i	0.395466	+	0.556135i
$551$	6.74952	−	11.6905i	0.287539	−	0.498033i
$552$	2.71831	−	8.36611i	0.115699	−	0.356085i
$553$	−6.08289	−	34.9552i	−0.258671	−	1.48644i
$554$	0.757044	+	0.550025i	0.0321637	+	0.0233683i
$555$	0.351166	+	0.0746426i	0.0149062	+	0.00316840i
$556$	−3.75278	+	4.16789i	−0.159153	+	0.176758i
$557$	−1.45104	+	13.8057i	−0.0614825	+	0.584967i	0.919799	+	0.392389i	$0.128351\pi$
$557$	−1.45104	+	13.8057i	−0.0614825	+	0.584967i	−0.981282	+	0.192578i	$0.938315\pi$
$558$	0.217856	+	2.07276i	0.00922258	+	0.0877470i
$559$	−4.04892	+	12.4613i	−0.171251	+	0.527056i
$560$	−0.616243	−	0.918044i	−0.0260410	−	0.0387944i
$561$	−15.2401	+	13.4437i	−0.643436	+	0.567595i
$562$	−5.07334	+	8.78729i	−0.214006	+	0.370669i
$563$	−44.8624	+	9.53581i	−1.89073	+	0.401886i	−0.998740	−	0.0501759i	$-0.984022\pi$
$563$	−44.8624	+	9.53581i	−1.89073	+	0.401886i	−0.891986	+	0.452062i	$0.850688\pi$
$564$	0.168013	+	0.0748041i	0.00707461	+	0.00314982i
$565$	3.51754	−	1.56611i	0.147984	−	0.0658868i
$566$	−2.67033	−	8.21843i	−0.112242	−	0.345446i
$567$	1.63355	−	2.08123i	0.0686027	−	0.0874034i
$568$	2.51506	+	1.82730i	0.105530	+	0.0766719i
$569$	2.06857	+	19.6811i	0.0867190	+	0.825076i	0.948283	+	0.317427i	$0.102819\pi$
$569$	2.06857	+	19.6811i	0.0867190	+	0.825076i	−0.861564	+	0.507649i	$0.830515\pi$
$570$	−1.38817	+	0.295066i	−0.0581442	+	0.0123589i
$571$	10.5072	+	18.1989i	0.439711	+	0.761601i	0.997667	−	0.0682691i	$-0.0217476\pi$
$571$	10.5072	+	18.1989i	0.439711	+	0.761601i	−0.557956	+	0.829870i	$0.688414\pi$
$572$	20.8028	+	2.40091i	0.869810	+	0.100387i
$573$	−5.12837			−0.214241
$574$	7.35791	+	7.13735i	0.307113	+	0.297907i
$575$	−34.3403	+	24.9497i	−1.43209	+	1.04047i
$576$	0.913545	−	0.406737i	0.0380644	−	0.0169474i
$577$	6.58628	−	7.31481i	0.274191	−	0.304520i	−0.590284	−	0.807195i	$-0.700984\pi$
$577$	6.58628	−	7.31481i	0.274191	−	0.304520i	0.864475	+	0.502676i	$0.167651\pi$
$578$	13.7472	−	15.2678i	0.571808	−	0.635057i
$579$	16.2105	−	7.21736i	0.673684	−	0.299943i
$580$	−1.34398	+	0.976460i	−0.0558058	+	0.0405453i
$581$	−7.59410	+	30.1704i	−0.315056	+	1.25168i
$582$	−7.63500			−0.316481
$583$	18.4813	−	10.4207i	0.765418	−	0.431581i
$584$	1.99034	+	3.44737i	0.0823608	+	0.142653i
$585$	2.58101	−	0.548611i	0.106712	−	0.0226823i
$586$	−0.512198	−	4.87324i	−0.0211587	−	0.201312i
$587$	30.6558	+	22.2728i	1.26530	+	0.919295i	0.999005	−	0.0445960i	$-0.0142001\pi$
$587$	30.6558	+	22.2728i	1.26530	+	0.919295i	0.266296	+	0.963891i	$0.414200\pi$
$588$	6.98069	+	0.519553i	0.287879	+	0.0214260i
$589$	2.18711	+	6.73124i	0.0901184	+	0.277356i
$590$	1.70852	−	0.760681i	0.0703386	−	0.0313167i
$591$	−7.44202	−	3.31340i	−0.306124	−	0.136295i
$592$	−0.840284	+	0.178608i	−0.0345354	+	0.00734074i
$593$	5.28653	−	9.15654i	0.217092	−	0.376014i	−0.736826	−	0.676083i	$-0.763676\pi$
$593$	5.28653	−	9.15654i	0.217092	−	0.376014i	0.953918	+	0.300069i	$0.0970096\pi$
$594$	−0.722568	+	3.23696i	−0.0296473	+	0.132814i
$595$	−6.75955	+	0.457471i	−0.277115	+	0.0187545i
$596$	2.46372	−	7.58254i	0.100918	−	0.310593i
$597$	1.84002	+	17.5066i	0.0753071	+	0.716499i
$598$	−5.80566	+	55.2371i	−0.237411	+	2.25881i
$599$	17.1786	−	19.0787i	0.701898	−	0.779536i	−0.281779	−	0.959479i	$-0.590925\pi$
$599$	17.1786	−	19.0787i	0.701898	−	0.779536i	0.983677	+	0.179943i	$0.0575913\pi$
$600$	−4.71990	−	1.00325i	−0.192689	−	0.0409574i
$601$	−13.7091	−	9.96022i	−0.559204	−	0.406286i	0.271963	−	0.962308i	$-0.412327\pi$
$601$	−13.7091	−	9.96022i	−0.559204	−	0.406286i	−0.831168	+	0.556022i	$0.812327\pi$
$602$	−0.941297	−	5.40913i	−0.0383644	−	0.220460i
$603$	−3.56909	+	10.9845i	−0.145344	+	0.447324i
$604$	3.35275	−	5.80713i	0.136421	−	0.236289i
$605$	−4.23682	+	1.78386i	−0.172251	+	0.0725244i
$606$	0.224531	+	0.388898i	0.00912093	+	0.0157979i
$607$	−8.36516	−	9.29045i	−0.339531	−	0.377088i	0.549064	−	0.835781i	$-0.314984\pi$
$607$	−8.36516	−	9.29045i	−0.339531	−	0.377088i	−0.888595	+	0.458693i	$0.848318\pi$
$608$	2.74733	−	1.99605i	0.111419	−	0.0809507i
$609$	0.390571	−	10.5099i	0.0158267	−	0.425883i
$610$	−0.881320	−	2.71242i	−0.0356836	−	0.109823i
$611$	−1.13584	−	0.241429i	−0.0459510	−	0.00976719i
$612$	0.640486	−	6.09382i	0.0258901	−	0.246328i
$613$	−8.37427	−	3.72846i	−0.338233	−	0.150591i	0.230590	−	0.973051i	$-0.425934\pi$
$613$	−8.37427	−	3.72846i	−0.338233	−	0.150591i	−0.568823	+	0.822460i	$0.692601\pi$
$614$	−13.6747	−	15.1873i	−0.551868	−	0.612911i
$615$	−1.61919			−0.0652921
$616$	−8.17621	+	3.18584i	−0.329429	+	0.128361i
$617$	15.3923			0.619671			0.309836	−	0.950790i	$-0.399726\pi$
$617$	15.3923			0.619671			0.309836	+	0.950790i	$0.399726\pi$
$618$	12.2966	+	13.6568i	0.494643	+	0.549357i
$619$	27.3874	+	12.1936i	1.10079	+	0.490104i	0.875025	−	0.484078i	$-0.160845\pi$
$619$	27.3874	+	12.1936i	1.10079	+	0.490104i	0.225766	+	0.974182i	$0.427511\pi$
$620$	0.0910449	−	0.866235i	0.00365645	−	0.0347888i
$621$	−8.60442	−	1.82893i	−0.345284	−	0.0733923i
$622$	6.79823	+	20.9228i	0.272584	+	0.838928i
$623$	−22.5487	+	11.9247i	−0.903395	+	0.477753i
$624$	−5.10807	+	3.71123i	−0.204487	+	0.148568i
$625$	14.9957	+	16.6544i	0.599828	+	0.666177i
$626$	−14.5301	−	25.1669i	−0.580741	−	1.00587i
$627$	−0.114703	+	11.2623i	−0.00458079	+	0.449773i
$628$	−1.82282	+	3.15722i	−0.0727385	+	0.125987i
$629$	−1.62659	+	5.00614i	−0.0648566	+	0.199608i
$630$	−0.848600	+	0.708829i	−0.0338090	+	0.0282404i
$631$	5.49787	+	3.99443i	0.218867	+	0.159016i	0.691816	−	0.722074i	$-0.256811\pi$
$631$	5.49787	+	3.99443i	0.218867	+	0.159016i	−0.472950	+	0.881089i	$0.656811\pi$
$632$	−13.1173	−	2.78817i	−0.521779	−	0.110907i
$633$	−15.0442	+	16.7083i	−0.597953	+	0.664094i
$634$	−2.43165	+	23.1356i	−0.0965733	+	0.918834i
$635$	−0.0915836	−	0.871360i	−0.00363438	−	0.0345789i
$636$	−1.97681	+	6.08399i	−0.0783855	+	0.241246i
$637$	−43.7945	+	5.95509i	−1.73520	+	0.235949i
$638$	5.23946	+	12.0981i	0.207432	+	0.478970i
$639$	1.55440	−	2.69229i	0.0614909	−	0.106505i
$640$	−0.408781	+	0.0868890i	−0.0161585	+	0.00343459i
$641$	−43.0515	−	19.1678i	−1.70043	−	0.757081i	−0.999017	−	0.0443274i	$-0.985886\pi$
$641$	−43.0515	−	19.1678i	−1.70043	−	0.757081i	−0.701415	−	0.712754i	$-0.747448\pi$
$642$	−15.9708	+	7.11064i	−0.630315	+	0.280634i
$643$	−1.87575	−	5.77295i	−0.0739722	−	0.227663i	0.907234	−	0.420627i	$-0.138190\pi$
$643$	−1.87575	−	5.77295i	−0.0739722	−	0.227663i	−0.981206	+	0.192964i	$0.938190\pi$
$644$	−8.67017	−	21.5985i	−0.341653	−	0.851100i
$645$	0.701618	+	0.509755i	0.0276262	+	0.0200716i
$646$	−2.17502	−	20.6939i	−0.0855751	−	0.814192i
$647$	−22.3330	+	4.74703i	−0.878002	+	0.186625i	−0.624797	−	0.780788i	$-0.714818\pi$
$647$	−22.3330	+	4.74703i	−0.878002	+	0.186625i	−0.253205	+	0.967413i	$0.581485\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$	−2.93786	−	14.5486i	−0.115321	−	0.571082i
$650$	30.4669			1.19501
$651$	3.95801	+	3.83937i	0.155127	+	0.150477i
$652$	11.5320	−	8.37851i	0.451629	−	0.328128i
$653$	−26.3060	+	11.7122i	−1.02943	+	0.458334i	−0.850749	−	0.525572i	$-0.823851\pi$
$653$	−26.3060	+	11.7122i	−1.02943	+	0.458334i	−0.178686	+	0.983906i	$0.557185\pi$
$654$	13.5262	−	15.0223i	0.528915	−	0.587420i
$655$	6.13808	−	6.81703i	0.239835	−	0.266363i
$656$	3.53950	−	1.57589i	0.138194	−	0.0615281i
$657$	3.22044	−	2.33978i	0.125641	−	0.0912837i
$658$	0.468037	−	0.133074i	0.0182460	−	0.00518778i
$659$	−10.5554			−0.411180			−0.205590	−	0.978638i	$-0.565911\pi$
$659$	−10.5554			−0.411180			−0.205590	+	0.978638i	$0.565911\pi$
$660$	0.576628	−	1.26042i	0.0224452	−	0.0490619i
$661$	13.4052	+	23.2184i	0.521401	+	0.903092i	0.999690	+	0.0248903i	$0.00792363\pi$
$661$	13.4052	+	23.2184i	0.521401	+	0.903092i	−0.478290	+	0.878202i	$0.658743\pi$
$662$	−33.8782	+	7.20103i	−1.31671	+	0.279876i
$663$	4.04398	+	38.4759i	0.157055	+	1.49428i
$664$	9.51325	+	6.91178i	0.369186	+	0.268229i
$665$	−2.31831	+	2.95365i	−0.0899003	+	0.114538i
$666$	0.265463	+	0.817011i	0.0102865	+	0.0316585i
$667$	−31.9446	+	14.2226i	−1.23690	+	0.550703i
$668$	−11.5082	−	5.12380i	−0.445267	−	0.198246i
$669$	21.9944	−	4.67505i	0.850352	−	0.180748i
$670$	2.41341	−	4.18015i	0.0932381	−	0.161493i
$671$	−22.5329	+	2.13653i	−0.869875	+	0.0824799i
$672$	1.16514	−	2.37538i	0.0449463	−	0.0916324i
$673$	4.58631	−	14.1152i	0.176789	−	0.544101i	−0.822922	−	0.568155i	$-0.807657\pi$
$673$	4.58631	−	14.1152i	0.176789	−	0.544101i	0.999711	+	0.0240540i	$0.00765738\pi$
$674$	3.46288	+	32.9471i	0.133385	+	1.26908i
$675$	−0.504386	+	4.79891i	−0.0194138	+	0.184710i
$676$	17.9766	−	19.9651i	0.691409	−	0.767887i
$677$	−41.2112	−	8.75972i	−1.58388	−	0.336663i	−0.669907	−	0.742445i	$-0.733666\pi$
$677$	−41.2112	−	8.75972i	−1.58388	−	0.336663i	−0.913970	+	0.405782i	$0.866999\pi$
$678$	7.45386	+	5.41554i	0.286264	+	0.207983i
$679$	−15.5034	+	12.9498i	−0.594965	+	0.496969i
$680$	−0.791305	+	2.43539i	−0.0303452	+	0.0933928i
$681$	−7.43942	+	12.8854i	−0.285079	+	0.493771i
$682$	−6.55203	−	2.20290i	−0.250890	−	0.0843535i
$683$	−8.91415	−	15.4398i	−0.341091	−	0.590786i	0.643545	−	0.765408i	$-0.277463\pi$
$683$	−8.91415	−	15.4398i	−0.341091	−	0.590786i	−0.984636	+	0.174622i	$0.944130\pi$
$684$	−2.27229	−	2.52364i	−0.0868833	−	0.0964937i
$685$	5.26223	−	3.82324i	0.201060	−	0.146078i
$686$	15.0560	−	10.7851i	0.574840	−	0.411776i
$687$	−3.98011	−	12.2495i	−0.151851	−	0.467348i
$688$	−2.02984	−	0.431455i	−0.0773869	−	0.0164491i
$689$	4.22198	−	40.1695i	0.160845	−	1.53033i
$690$	3.35841	+	1.49526i	0.127852	+	0.0569236i
$691$	−26.2437	−	29.1466i	−0.998357	−	1.10879i	−0.994064	−	0.108797i	$-0.965300\pi$
$691$	−26.2437	−	29.1466i	−0.998357	−	1.10879i	−0.00429268	−	0.999991i	$-0.501366\pi$
$692$	−12.7682			−0.485376
$693$	4.02303	+	7.79841i	0.152822	+	0.296237i
$694$	−11.0030			−0.417667
$695$	−1.56834	−	1.74182i	−0.0594904	−	0.0660708i
$696$	−3.63145	−	1.61682i	−0.137650	−	0.0612856i
$697$	2.48154	−	23.6103i	0.0939952	−	0.894304i
$698$	−0.203132	−	0.0431770i	−0.00768866	−	0.00163427i
$699$	0.145686	+	0.448374i	0.00551034	+	0.0169591i
$700$	−11.2857	+	5.96834i	−0.426559	+	0.225582i
$701$	29.8242	−	21.6686i	1.12645	−	0.818411i	0.141272	−	0.989971i	$-0.454881\pi$
$701$	29.8242	−	21.6686i	1.12645	−	0.818411i	0.985174	+	0.171560i	$0.0548807\pi$
$702$	4.22484	+	4.69216i	0.159456	+	0.177094i
$703$	1.45863	+	2.52642i	0.0550133	+	0.0952858i
$704$	−0.0337770	+	3.31645i	−0.00127302	+	0.124994i
$705$	−0.0384298	+	0.0665624i	−0.00144735	+	0.00250688i
$706$	1.25389	−	3.85907i	0.0471906	−	0.145238i
$707$	1.11554	+	0.408854i	0.0419542	+	0.0153765i
$708$	3.62044	+	2.63040i	0.136064	+	0.0988565i
$709$	33.3236	+	7.08316i	1.25150	+	0.266014i	0.785549	−	0.618799i	$-0.212381\pi$
$709$	33.3236	+	7.08316i	1.25150	+	0.266014i	0.465947	+	0.884813i	$0.345714\pi$
$710$	−0.869338	+	0.965497i	−0.0326257	+	0.0362345i
$711$	−1.40176	+	13.3369i	−0.0525703	+	0.500173i
$712$	1.00776	+	9.58819i	0.0377674	+	0.359333i
$713$	5.66545	−	17.4365i	0.212173	−	0.653001i
$714$	−9.03527	−	13.4602i	−0.338137	−	0.503737i
$715$	−1.90662	+	8.54127i	−0.0713036	+	0.319425i
$716$	−6.07153	+	10.5162i	−0.226904	+	0.393008i
$717$	−5.64535	+	1.19996i	−0.210829	+	0.0448132i
$718$	−13.4643	−	5.99467i	−0.502481	−	0.223719i
$719$	−11.8069	+	5.25677i	−0.440323	+	0.196044i	−0.614910	−	0.788597i	$-0.710808\pi$
$719$	−11.8069	+	5.25677i	−0.440323	+	0.196044i	0.174587	+	0.984642i	$0.444141\pi$
$720$	0.129142	+	0.397459i	0.00481285	+	0.0148124i
$721$	48.1326	+	6.87450i	1.79255	+	0.256020i
$722$	6.04168	+	4.38954i	0.224848	+	0.163362i
$723$	−0.0411591	−	0.391602i	−0.00153072	−	0.0145638i
$724$	−13.5168	+	2.87309i	−0.502350	+	0.106778i
$725$	9.59065	+	16.6115i	0.356188	+	0.616936i
$726$	−8.76565	−	6.64555i	−0.325324	−	0.246639i
$727$	−15.6572			−0.580695			−0.290347	−	0.956921i	$-0.593771\pi$
$727$	−15.6572			−0.580695			−0.290347	+	0.956921i	$0.593771\pi$
$728$	−4.07760	+	16.1998i	−0.151126	+	0.600404i
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$	−1.51975	+	0.676638i	−0.0562486	+	0.0250435i
$731$	−8.50831	+	9.44943i	−0.314691	+	0.349500i
$732$	4.56642	−	5.07153i	0.168780	−	0.187449i
$733$	31.9828	−	14.2396i	1.18131	−	0.525953i	0.280368	−	0.959892i	$-0.409543\pi$
$733$	31.9828	−	14.2396i	1.18131	−	0.525953i	0.900942	+	0.433939i	$0.142877\pi$
$734$	13.5301	−	9.83022i	0.499407	−	0.362840i
$735$	−0.520882	+	2.87865i	−0.0192130	+	0.106180i
$736$	−8.79665			−0.324249
$737$	−28.2047	−	25.9206i	−1.03893	−	0.954796i
$738$	−1.93723	−	3.35539i	−0.0713106	−	0.123514i
$739$	−44.5127	+	9.46147i	−1.63743	+	0.348046i	−0.932482	−	0.361217i	$-0.882361\pi$
$739$	−44.5127	+	9.46147i	−1.63743	+	0.348046i	−0.704944	+	0.709263i	$0.749028\pi$
$740$	−0.0375269	−	0.357044i	−0.00137951	−	0.0131252i
$741$	17.3465	+	12.6029i	0.637238	+	0.462980i
$742$	6.30511	+	15.7068i	0.231468	+	0.576616i
$743$	6.74844	+	20.7696i	0.247576	+	0.761961i	0.995202	+	0.0978412i	$0.0311937\pi$
$743$	6.74844	+	20.7696i	0.247576	+	0.761961i	−0.747626	+	0.664120i	$0.768806\pi$
$744$	1.90399	−	0.847712i	0.0698037	−	0.0310786i
$745$	3.04386	+	1.35521i	0.111518	+	0.0496512i
$746$	−12.8187	+	2.72470i	−0.469326	+	0.0997584i
$747$	5.87951	−	10.1836i	0.215120	−	0.372599i
$748$	17.4952	+	10.3398i	0.639687	+	0.378062i
$749$	−20.3692	+	41.5268i	−0.744274	+	1.51736i
$750$	1.26887	−	3.90517i	0.0463325	−	0.142597i
$751$	−2.93474	−	27.9222i	−0.107090	−	1.01889i	−0.907675	−	0.419674i	$-0.862144\pi$
$751$	−2.93474	−	27.9222i	−0.107090	−	1.01889i	0.800585	−	0.599220i	$-0.204522\pi$
$752$	0.0192241	−	0.182905i	0.000701032	−	0.00666987i
$753$	−9.06251	+	10.0649i	−0.330256	+	0.366787i
$754$	24.5501	+	5.21829i	0.894062	+	0.190039i
$755$	2.26712	+	1.64716i	0.0825090	+	0.0599463i
$756$	−2.48416	−	0.910463i	−0.0903481	−	0.0331132i
$757$	−2.62226	+	8.07050i	−0.0953078	+	0.293327i	−0.987334	−	0.158657i	$-0.949284\pi$
$757$	−2.62226	+	8.07050i	−0.0953078	+	0.293327i	0.892026	+	0.451984i	$0.149284\pi$
$758$	−3.46549	+	6.00241i	−0.125872	+	0.218017i
$759$	17.3882	−	23.4274i	0.631153	−	0.850359i
$760$	0.709594	+	1.22905i	0.0257397	+	0.0445824i
$761$	−32.9534	−	36.5984i	−1.19456	−	1.32669i	−0.932296	−	0.361695i	$-0.882198\pi$
$761$	−32.9534	−	36.5984i	−1.19456	−	1.32669i	−0.262263	−	0.964997i	$-0.584469\pi$
$762$	1.69611	−	1.23230i	0.0614437	−	0.0446414i
$763$	1.98616	−	53.4458i	0.0719039	−	1.93487i
$764$	1.58475	+	4.87737i	0.0573344	+	0.176457i
$765$	2.50476	+	0.532403i	0.0905597	+	0.0192491i
$766$	1.06006	−	10.0858i	0.0383014	−	0.364414i
$767$	−25.8127	−	11.4925i	−0.932041	−	0.414972i
$768$	−0.669131	−	0.743145i	−0.0241452	−	0.0268159i
$769$	42.4983			1.53253			0.766264	−	0.642526i	$-0.222114\pi$
$769$	42.4983			1.53253			0.766264	+	0.642526i	$0.222114\pi$
$770$	−0.966941	−	3.53740i	−0.0348461	−	0.127479i
$771$	−12.3307			−0.444080
$772$	−11.8734	−	13.1868i	−0.427334	−	0.474603i
$773$	28.3901	+	12.6401i	1.02112	+	0.454633i	0.847847	−	0.530241i	$-0.177899\pi$
$773$	28.3901	+	12.6401i	1.02112	+	0.454633i	0.173275	+	0.984874i	$0.444565\pi$
$774$	−0.216916	+	2.06382i	−0.00779688	+	0.0741824i
$775$	−9.83712	−	2.09095i	−0.353360	−	0.0751090i
$776$	2.35935	+	7.26132i	0.0846956	+	0.260666i
$777$	1.92478	+	1.20874i	0.0690513	+	0.0433632i
$778$	−3.64582	+	2.64884i	−0.130709	+	0.0949656i
$779$	−8.80393	−	9.77775i	−0.315434	−	0.350324i
$780$	−1.31934	−	2.28516i	−0.0472398	−	0.0818218i
$781$	5.97521	+	8.40281i	0.213810	+	0.300676i
$782$	−26.9502	+	46.6792i	−0.963739	+	1.66924i
$783$	−1.22838	+	3.78056i	−0.0438986	+	0.135106i
$784$	−1.66303	−	6.79958i	−0.0593939	−	0.242842i
$785$	−1.23259	−	0.895527i	−0.0439929	−	0.0319627i
$786$	21.4704	+	4.56367i	0.765823	+	0.162781i
$787$	−17.7609	+	19.7255i	−0.633108	+	0.703138i	−0.971278	−	0.237947i	$-0.923526\pi$
$787$	−17.7609	+	19.7255i	−0.633108	+	0.703138i	0.338170	+	0.941085i	$0.390192\pi$
$788$	−0.851521	+	8.10168i	−0.0303342	+	0.288610i
$789$	0.246021	+	2.34073i	0.00875857	+	0.0833323i
$790$	1.73184	−	5.33007i	0.0616163	−	0.189635i
$791$	24.3209	−	1.64598i	0.864753	−	0.0585245i
$792$	3.30182	−	0.313072i	0.117325	−	0.0111245i
$793$	−21.5444	+	37.3160i	−0.765065	+	1.32513i
$794$	−9.46749	+	2.01238i	−0.335989	+	0.0714166i
$795$	−2.44230	−	1.08738i	−0.0866193	−	0.0385654i
$796$	16.0812	−	7.15981i	0.569983	−	0.253773i
$797$	−0.551135	−	1.69622i	−0.0195222	−	0.0600832i	0.940821	−	0.338904i	$-0.110056\pi$
$797$	−0.551135	−	1.69622i	−0.0195222	−	0.0600832i	−0.960343	+	0.278821i	$0.910056\pi$
$798$	−8.89442	−	1.27034i	−0.314859	−	0.0449695i
$799$	−0.911685	−	0.662378i	−0.0322531	−	0.0234333i
$800$	0.504386	+	4.79891i	0.0178327	+	0.169667i
$801$	9.43033	−	2.00448i	0.333204	−	0.0708247i
$802$	−3.52687	−	6.10872i	−0.124538	−	0.215707i
$803$	2.61328	+	12.9412i	0.0922205	+	0.456685i
$804$	11.5498			0.407330
$805$	9.35560	−	2.66003i	0.329742	−	0.0937536i
$806$	−10.6461	+	7.73487i	−0.374994	+	0.272449i
$807$	14.5462	−	6.47638i	0.512050	−	0.227979i
$808$	0.300481	−	0.333718i	0.0105709	−	0.0117401i
$809$	−6.10318	+	6.77826i	−0.214576	+	0.238311i	−0.840818	−	0.541318i	$-0.817926\pi$
$809$	−6.10318	+	6.77826i	−0.214576	+	0.238311i	0.626242	+	0.779629i	$0.284592\pi$
$810$	0.381783	−	0.169981i	0.0134145	−	0.00597251i
$811$	−1.52060	+	1.10478i	−0.0533954	+	0.0387940i	−0.614163	−	0.789179i	$-0.710506\pi$
$811$	−1.52060	+	1.10478i	−0.0533954	+	0.0387940i	0.560767	+	0.827973i	$0.310506\pi$
$812$	−10.1162	+	2.87628i	−0.355009	+	0.100938i
$813$	8.59164			0.301322
$814$	−2.83038	−	0.326661i	−0.0992047	−	0.0114495i
$815$	2.97854	+	5.15899i	0.104334	+	0.180712i
$816$	−5.99349	+	1.27396i	−0.209814	+	0.0445974i
$817$	0.736623	+	7.00850i	0.0257712	+	0.245196i
$818$	−2.68108	−	1.94792i	−0.0937419	−	0.0681075i
$819$	16.5373	+	2.36192i	0.577859	+	0.0825322i
$820$	0.500358	+	1.53994i	0.0174732	+	0.0537771i
$821$	5.51692	−	2.45629i	0.192542	−	0.0857252i	−0.308201	−	0.951321i	$-0.599727\pi$
$821$	5.51692	−	2.45629i	0.192542	−	0.0857252i	0.500743	+	0.865596i	$0.333060\pi$
$822$	14.2186	+	6.33053i	0.495930	+	0.220802i
$823$	32.8459	−	6.98161i	1.14494	−	0.243364i	0.403883	−	0.914811i	$-0.367660\pi$
$823$	32.8459	−	6.98161i	1.14494	−	0.243364i	0.741053	+	0.671447i	$0.234327\pi$
$824$	9.18852	−	15.9150i	0.320097	−	0.554424i
$825$	−13.7775	−	8.14267i	−0.479673	−	0.283491i
$826$	11.8130	−	0.799477i	0.411027	−	0.0278173i
$827$	6.20745	−	19.1046i	0.215854	−	0.664331i	−0.783238	−	0.621723i	$-0.786433\pi$
$827$	6.20745	−	19.1046i	0.215854	−	0.664331i	0.999092	−	0.0426086i	$-0.0135669\pi$
$828$	0.919500	+	8.74846i	0.0319548	+	0.304030i
$829$	−0.208666	+	1.98533i	−0.00724728	+	0.0689533i	−0.997548	−	0.0699890i	$-0.977704\pi$
$829$	−0.208666	+	1.98533i	−0.00724728	+	0.0689533i	0.990300	+	0.138942i	$0.0443702\pi$
$830$	−3.28828	+	3.65200i	−0.114138	+	0.126763i
$831$	−0.915309	−	0.194555i	−0.0317517	−	0.00674904i
$832$	5.10807	+	3.71123i	0.177091	+	0.128664i
$833$	−41.1768	−	12.0070i	−1.42669	−	0.416019i
$834$	1.73311	−	5.33395i	0.0600125	−	0.184700i
$835$	2.63230	−	4.55927i	0.0910944	−	0.157780i
$836$	10.7465	−	3.37116i	0.371677	−	0.116594i
$837$	−1.04209	−	1.80495i	−0.0360199	−	0.0623883i
$838$	−1.52911	−	1.69825i	−0.0528223	−	0.0586651i
$839$	7.01572	−	5.09722i	0.242209	−	0.175975i	−0.460058	−	0.887889i	$-0.652171\pi$
$839$	7.01572	−	5.09722i	0.242209	−	0.175975i	0.702267	+	0.711914i	$0.252171\pi$
$840$	0.936368	+	0.588026i	0.0323078	+	0.0202888i
$841$	−4.07855	−	12.5525i	−0.140640	−	0.432845i
$842$	23.0593	+	4.90141i	0.794677	+	0.168914i
$843$	1.06062	−	10.0911i	0.0365296	−	0.347556i
$844$	20.5394	+	9.14474i	0.706996	+	0.314775i
$845$	7.51267	+	8.34367i	0.258444	+	0.287031i
$846$	−0.183913			−0.00632305
$847$	−29.0708	+	1.37334i	−0.998886	+	0.0471885i
$848$	6.39709			0.219677
$849$	5.78221	+	6.42179i	0.198445	+	0.220395i
$850$	27.0106	+	12.0259i	0.926456	+	0.412485i
$851$	0.789902	−	7.51542i	0.0270775	−	0.257625i
$852$	−3.04086	−	0.646354i	−0.104178	−	0.0221437i
$853$	−3.92934	−	12.0933i	−0.134538	−	0.414066i	0.860980	−	0.508639i	$-0.169851\pi$
$853$	−3.92934	−	12.0933i	−0.134538	−	0.414066i	−0.995518	+	0.0945733i	$0.969851\pi$
$854$	0.670526	−	18.0432i	0.0229449	−	0.617427i
$855$	1.14815	−	0.834177i	0.0392658	−	0.0285283i
$856$	11.6979	+	12.9918i	0.399824	+	0.444050i
$857$	1.40133	+	2.42717i	0.0478684	+	0.0829104i	0.888967	−	0.457972i	$-0.151424\pi$
$857$	1.40133	+	2.42717i	0.0478684	+	0.0829104i	−0.841098	+	0.540882i	$0.818091\pi$
$858$	−19.9809	+	6.26794i	−0.682136	+	0.213984i
$859$	0.776539	−	1.34501i	0.0264952	−	0.0458910i	−0.852474	−	0.522770i	$-0.824899\pi$
$859$	0.776539	−	1.34501i	0.0264952	−	0.0458910i	0.878969	+	0.476879i	$0.158232\pi$
$860$	0.267994	−	0.824801i	0.00913853	−	0.0281255i
$861$	−9.62480	−	3.52756i	−0.328012	−	0.120219i
$862$	−18.7848	−	13.6480i	−0.639813	−	0.464852i
$863$	−15.0353	−	3.19586i	−0.511808	−	0.108788i	−0.0552340	−	0.998473i	$-0.517590\pi$
$863$	−15.0353	−	3.19586i	−0.511808	−	0.108788i	−0.456574	+	0.889685i	$0.650924\pi$
$864$	−0.669131	+	0.743145i	−0.0227643	+	0.0252823i
$865$	0.557766	−	5.30679i	0.0189646	−	0.180436i
$866$	−1.84137	−	17.5195i	−0.0625725	−	0.595337i
$867$	−6.34871	+	19.5393i	−0.215614	+	0.663590i
$868$	2.42836	−	4.95072i	0.0824240	−	0.168039i
$869$	−38.2898	−	22.6297i	−1.29889	−	0.767660i
$870$	0.830626	−	1.43869i	0.0281609	−	0.0487760i
$871$	−71.3311	+	15.1619i	−2.41696	+	0.513741i
$872$	−18.4669	−	8.22200i	−0.625369	−	0.278432i
$873$	6.97492	−	3.10544i	0.236065	−	0.105103i
$874$	9.23110	+	28.4104i	0.312247	+	0.960996i
$875$	−4.04711	−	10.0819i	−0.136817	−	0.340829i
$876$	−3.22044	−	2.33978i	−0.108808	−	0.0790540i
$877$	5.19471	+	49.4244i	0.175413	+	1.66894i	0.628753	+	0.777605i	$0.283566\pi$
$877$	5.19471	+	49.4244i	0.175413	+	1.66894i	−0.453340	+	0.891338i	$0.649768\pi$
$878$	11.9403	−	2.53799i	0.402966	−	0.0856530i
$879$	2.45004	+	4.24360i	0.0826379	+	0.143133i
$880$	−1.37692	−	0.158914i	−0.0464160	−	0.00535699i
$881$	1.92884			0.0649844			0.0324922	−	0.999472i	$-0.489656\pi$
$881$	1.92884			0.0649844			0.0324922	+	0.999472i	$0.489656\pi$
$882$	−6.58850	+	2.36467i	−0.221846	+	0.0796225i
$883$	−9.11868	+	6.62511i	−0.306868	+	0.222953i	−0.730551	−	0.682858i	$-0.760737\pi$
$883$	−9.11868	+	6.62511i	−0.306868	+	0.222953i	0.423683	+	0.905810i	$0.360737\pi$
$884$	35.3431	−	15.7358i	1.18872	−	0.529251i
$885$	−1.25141	+	1.38983i	−0.0420657	+	0.0467187i
$886$	21.3142	−	23.6718i	0.716063	−	0.795269i
$887$	18.3273	−	8.15985i	0.615371	−	0.273981i	−0.0752875	−	0.997162i	$-0.523987\pi$
$887$	18.3273	−	8.15985i	0.615371	−	0.273981i	0.690659	+	0.723181i	$0.257321\pi$
$888$	0.694991	−	0.504941i	0.0233224	−	0.0169447i
$889$	1.35395	−	5.37906i	0.0454100	−	0.180408i
$890$	−4.02910			−0.135056
$891$	−0.656490	−	3.25100i	−0.0219933	−	0.108913i
$892$	−11.2429	−	19.4732i	−0.376439	−	0.652012i
$893$	−0.610900	+	0.129851i	−0.0204430	+	0.00434529i
$894$	0.833380	+	7.92908i	0.0278724	+	0.265188i
$895$	−4.10555	−	2.98286i	−0.137233	−	0.0997060i
$896$	−2.61917	−	0.374081i	−0.0875004	−	0.0124972i
$897$	−17.1632	−	52.8230i	−0.573064	−	1.76371i
$898$	9.85927	−	4.38963i	0.329008	−	0.146484i
$899$	−7.56859	−	3.36975i	−0.252426	−	0.112387i
$900$	4.71990	−	1.00325i	0.157330	−	0.0334415i
$901$	19.5987	−	33.9460i	0.652928	−	1.13090i
$902$	12.7928	−	1.21299i	0.425953	−	0.0403880i
$903$	3.06001	+	4.55863i	0.101831	+	0.151702i
$904$	2.84712	−	8.76253i	0.0946938	−	0.291438i
$905$	−0.603659	−	5.74343i	−0.0200663	−	0.190918i
$906$	−0.700915	+	6.66876i	−0.0232863	+	0.221555i
$907$	18.0086	−	20.0006i	0.597966	−	0.664108i	−0.365851	−	0.930673i	$-0.619222\pi$
$907$	18.0086	−	20.0006i	0.597966	−	0.664108i	0.963817	+	0.266565i	$0.0858887\pi$
$908$	14.5537	+	3.09348i	0.482981	+	0.102661i
$909$	−0.363298	−	0.263952i	−0.0120498	−	0.00875472i
$910$	−6.55489	−	2.40241i	−0.217292	−	0.0796393i
$911$	4.76967	−	14.6795i	0.158026	−	0.486354i	−0.840429	−	0.541922i	$-0.817697\pi$
$911$	4.76967	−	14.6795i	0.158026	−	0.486354i	0.998455	+	0.0555676i	$0.0176968\pi$
$912$	−1.69795	+	2.94093i	−0.0562246	+	0.0973838i
$913$	22.6013	+	31.7837i	0.747993	+	1.05189i
$914$	16.0970	+	27.8809i	0.532443	+	0.922218i
$915$	1.90837	+	2.11946i	0.0630887	+	0.0700671i
$916$	−10.4201	+	7.57062i	−0.344289	+	0.250140i
$917$	51.3375	−	27.1494i	1.69531	−	0.896553i
$918$	1.89347	+	5.82749i	0.0624937	+	0.192336i
$919$	36.7724	+	7.81621i	1.21301	+	0.257833i	0.769624	−	0.638498i	$-0.220444\pi$
$919$	36.7724	+	7.81621i	1.21301	+	0.257833i	0.443386	+	0.896331i	$0.353777\pi$
$920$	0.384271	−	3.65610i	0.0126691	−	0.120538i
$921$	18.6698	+	8.31231i	0.615189	+	0.273900i
$922$	19.5091	+	21.6670i	0.642498	+	0.713566i
$923$	19.6287			0.646086
$924$	6.17355	−	6.23597i	0.203095	−	0.205148i
$925$	−4.14525			−0.136295
$926$	2.00469	+	2.22643i	0.0658782	+	0.0731652i
$927$	−16.7883	−	7.47461i	−0.551399	−	0.245498i
$928$	−0.415512	+	3.95334i	−0.0136399	+	0.129775i
$929$	6.00094	+	1.27554i	0.196885	+	0.0418491i	0.305298	−	0.952257i	$-0.401244\pi$
$929$	6.00094	+	1.27554i	0.196885	+	0.0418491i	−0.108414	+	0.994106i	$0.534577\pi$
$930$	0.269156	+	0.828376i	0.00882596	+	0.0271635i
$931$	−20.2153	+	12.5065i	−0.662531	+	0.409883i
$932$	0.381410	−	0.277111i	0.0124935	−	0.00907706i
$933$	−14.7206	−	16.3488i	−0.481930	−	0.535237i
$934$	17.1576	+	29.7178i	0.561413	+	0.972396i
$935$	−5.06174	+	6.81973i	−0.165536	+	0.223029i
$936$	3.15696	−	5.46802i	0.103189	−	0.178728i
$937$	9.70401	−	29.8659i	0.317016	−	0.975675i	−0.657901	−	0.753105i	$-0.728555\pi$
$937$	9.70401	−	29.8659i	0.317016	−	0.975675i	0.974917	−	0.222570i	$-0.0714447\pi$
$938$	23.4526	−	19.5898i	0.765756	−	0.639630i
$939$	23.5103	+	17.0812i	0.767228	+	0.557424i
$940$	0.0751800	+	0.0159800i	0.00245210	+	0.000521210i
$941$	−11.4338	+	12.6986i	−0.372733	+	0.413961i	−0.900105	−	0.435673i	$-0.856511\pi$
$941$	−11.4338	+	12.6986i	−0.372733	+	0.413961i	0.527373	+	0.849634i	$0.323177\pi$
$942$	0.381073	−	3.62567i	0.0124160	−	0.118131i
$943$	3.56257	+	33.8956i	0.116013	+	1.10379i
$944$	1.38288	−	4.25608i	0.0450090	−	0.138524i
$945$	0.486928	−	0.992704i	0.0158398	−	0.0322927i
$946$	−5.92516	−	3.50183i	−0.192644	−	0.113854i
$947$	−7.03433	+	12.1838i	−0.228585	+	0.395921i	−0.957389	−	0.288802i	$-0.906743\pi$
$947$	−7.03433	+	12.1838i	−0.228585	+	0.395921i	0.728804	+	0.684722i	$0.240077\pi$
$948$	13.1173	−	2.78817i	0.426030	−	0.0905556i
$949$	22.9608	+	10.2228i	0.745338	+	0.331846i
$950$	14.9697	−	6.66493i	0.485681	−	0.216239i
$951$	−7.18869	−	22.1245i	−0.233109	−	0.717436i
$952$	−10.0094	+	12.7525i	−0.324406	+	0.413311i
$953$	−28.0752	−	20.3979i	−0.909446	−	0.660751i	0.0314284	−	0.999506i	$-0.489994\pi$
$953$	−28.0752	−	20.3979i	−0.909446	−	0.660751i	−0.940875	+	0.338755i	$0.889994\pi$
$954$	−0.668678	−	6.36204i	−0.0216492	−	0.205979i
$955$	−2.09638	+	0.445599i	−0.0678373	+	0.0144193i
$956$	2.88573	+	4.99824i	0.0933313	+	0.161655i
$957$	−9.70724	−	8.92111i	−0.313791	−	0.288379i
$958$	−15.2419			−0.492445
$959$	39.6091	−	11.2618i	1.27904	−	0.363663i
$960$	0.338099	−	0.245643i	0.0109121	−	0.00792810i
$961$	−24.3516	+	10.8421i	−0.785537	+	0.349744i
$962$	−3.62938	+	4.03083i	−0.117016	+	0.129959i
$963$	11.6979	−	12.9918i	0.376958	−	0.418654i
$964$	−0.359717	+	0.160156i	−0.0115857	+	0.00515829i
$965$	5.99942	−	4.35883i	0.193128	−	0.140316i
$966$	16.7055	+	16.2047i	0.537491	+	0.521379i
$967$	29.1565			0.937608			0.468804	−	0.883302i	$-0.344685\pi$
$967$	29.1565			0.937608			0.468804	+	0.883302i	$0.344685\pi$
$968$	−3.61156	+	10.3902i	−0.116080	+	0.333954i
$969$	10.4040	+	18.0202i	0.334224	+	0.578892i
$970$	−3.12104	+	0.663398i	−0.100211	+	0.0213004i
$971$	0.0969529	+	0.922445i	0.00311137	+	0.0296027i	0.995967	−	0.0897156i	$-0.0285958\pi$
$971$	0.0969529	+	0.922445i	0.00311137	+	0.0296027i	−0.992856	+	0.119318i	$0.961929\pi$
$972$	0.809017	+	0.587785i	0.0259492	+	0.0188532i
$973$	−5.52781	−	13.7705i	−0.177213	−	0.441461i
$974$	−0.485539	−	1.49433i	−0.0155577	−	0.0478816i
$975$	−27.8329	+	12.3920i	−0.891366	+	0.396862i
$976$	−6.23441	−	2.77574i	−0.199559	−	0.0888492i
$977$	16.4072	−	3.48745i	0.524912	−	0.111573i	0.0621682	−	0.998066i	$-0.480198\pi$
$977$	16.4072	−	3.48745i	0.524912	−	0.111573i	0.462743	+	0.886492i	$0.346865\pi$
$978$	−7.12718	+	12.3446i	−0.227902	+	0.394738i
$979$	−6.96628	+	31.2075i	−0.222643	+	0.997397i
$980$	2.89872	−	0.394162i	0.0925961	−	0.0125911i
$981$	−6.24664	+	19.2252i	−0.199440	+	0.613813i
$982$	2.05228	+	19.5261i	0.0654908	+	0.623103i
$983$	1.41130	−	13.4276i	0.0450135	−	0.428275i	−0.948688	−	0.316214i	$-0.897588\pi$
$983$	1.41130	−	13.4276i	0.0450135	−	0.428275i	0.993701	−	0.112061i	$-0.0357452\pi$
$984$	−2.59253	+	2.87929i	−0.0826467	+	0.0917884i
$985$	−3.33005	−	0.707825i	−0.106104	−	0.0225532i
$986$	19.7053	+	14.3167i	0.627544	+	0.455937i
$987$	−0.373447	+	0.311937i	−0.0118869	+	0.00992907i
$988$	6.62576	−	20.3920i	0.210793	−	0.648755i
$989$	9.12734	−	15.8090i	0.290233	−	0.502698i
$990$	−0.0141158	+	1.38599i	−0.000448631	+	0.0440496i
$991$	17.6081	+	30.4981i	0.559339	+	0.968804i	0.997552	+	0.0699324i	$0.0222784\pi$
$991$	17.6081	+	30.4981i	0.559339	+	0.968804i	−0.438213	+	0.898871i	$0.644388\pi$
$992$	−1.39459	−	1.54885i	−0.0442782	−	0.0491759i
$993$	28.0203	−	20.3580i	0.889198	−	0.646040i
$994$	−7.27095	+	3.84518i	−0.230620	+	0.121962i
$995$	2.27330	+	6.99650i	0.0720685	+	0.221804i
$996$	−11.5021	−	2.44484i	−0.364457	−	0.0774677i
$997$	5.87755	−	55.9212i	0.186144	−	1.77104i	−0.359616	−	0.933100i	$-0.617092\pi$
$997$	5.87755	−	55.9212i	0.186144	−	1.77104i	0.545760	−	0.837942i	$-0.316241\pi$
$998$	11.2143	+	4.99295i	0.354984	+	0.158049i
$999$	−0.574821	−	0.638403i	−0.0181865	−	0.0201982i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.y.d.163.3	✓	40
7.4	even	3	inner	462.2.y.d.361.3	yes	40
11.5	even	5	inner	462.2.y.d.247.3	yes	40
77.60	even	15	inner	462.2.y.d.445.3	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.y.d.163.3	✓	40	1.1	even	1	trivial
462.2.y.d.247.3	yes	40	11.5	even	5	inner
462.2.y.d.361.3	yes	40	7.4	even	3	inner
462.2.y.d.445.3	yes	40	77.60	even	15	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)

\(f(q)\)	\(=\)	\(q+(0.669131 + 0.743145i) q^{2} +(-0.913545 - 0.406737i) q^{3} +(-0.104528 + 0.994522i) q^{4} +(-0.408781 - 0.0868890i) q^{5} +(-0.309017 - 0.951057i) q^{6} +(-2.24058 - 1.40705i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(0.669131 + 0.743145i) q^{9} +O(q^{10})\)	\(q+(0.669131 + 0.743145i) q^{2} +(-0.913545 - 0.406737i) q^{3} +(-0.104528 + 0.994522i) q^{4} +(-0.408781 - 0.0868890i) q^{5} +(-0.309017 - 0.951057i) q^{6} +(-2.24058 - 1.40705i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(0.669131 + 0.743145i) q^{9} +(-0.208957 - 0.361923i) q^{10} +(-3.16457 + 0.992716i) q^{11} +(0.500000 - 0.866025i) q^{12} +(-1.95111 + 6.00490i) q^{13} +(-0.453596 - 2.60658i) q^{14} +(0.338099 + 0.245643i) q^{15} +(-0.978148 - 0.207912i) q^{16} +(-4.10002 + 4.55354i) q^{17} +(-0.104528 + 0.994522i) q^{18} +(0.354967 + 3.37729i) q^{19} +(0.129142 - 0.397459i) q^{20} +(1.47457 + 2.19673i) q^{21} +(-2.85524 - 1.68748i) q^{22} +(4.39833 - 7.61812i) q^{23} +(0.978148 - 0.207912i) q^{24} +(-4.40818 - 1.96265i) q^{25} +(-5.76806 + 2.56810i) q^{26} +(-0.309017 - 0.951057i) q^{27} +(1.63355 - 2.08123i) q^{28} +(-3.21593 - 2.33651i) q^{29} +(0.0436838 + 0.415624i) q^{30} +(2.03863 - 0.433325i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(3.29475 + 0.380256i) q^{33} -6.12739 q^{34} +(0.793649 + 0.769858i) q^{35} +(-0.809017 + 0.587785i) q^{36} +(0.784787 - 0.349410i) q^{37} +(-2.27229 + 2.52364i) q^{38} +(4.22484 - 4.69216i) q^{39} +(0.381783 - 0.169981i) q^{40} +(-3.13451 + 2.27736i) q^{41} +(-0.645810 + 2.56572i) q^{42} +2.07519 q^{43} +(-0.656490 - 3.25100i) q^{44} +(-0.208957 - 0.361923i) q^{45} +(8.60442 - 1.82893i) q^{46} +(0.0192241 + 0.182905i) q^{47} +(0.809017 + 0.587785i) q^{48} +(3.04040 + 6.30523i) q^{49} +(-1.49111 - 4.58918i) q^{50} +(5.59765 - 2.49223i) q^{51} +(-5.76806 - 2.56810i) q^{52} +(-6.25729 + 1.33003i) q^{53} +(0.500000 - 0.866025i) q^{54} +(1.37987 - 0.130837i) q^{55} +(2.63971 - 0.178650i) q^{56} +(1.04939 - 3.22968i) q^{57} +(-0.415512 - 3.95334i) q^{58} +(-0.467776 + 4.45059i) q^{59} +(-0.279639 + 0.310570i) q^{60} +(6.67528 + 1.41888i) q^{61} +(1.68614 + 1.22505i) q^{62} +(-0.453596 - 2.60658i) q^{63} +(0.309017 - 0.951057i) q^{64} +(1.31934 - 2.28516i) q^{65} +(1.92204 + 2.70292i) q^{66} +(5.77491 + 10.0024i) q^{67} +(-4.10002 - 4.55354i) q^{68} +(-7.11664 + 5.17054i) q^{69} +(-0.0410617 + 1.10493i) q^{70} +(-0.960669 - 2.95664i) q^{71} +(-0.978148 - 0.207912i) q^{72} +(0.416094 - 3.95887i) q^{73} +(0.784787 + 0.349410i) q^{74} +(3.22879 + 3.58593i) q^{75} -3.39589 q^{76} +(8.48728 + 2.22846i) q^{77} +6.31393 q^{78} +(8.97328 + 9.96584i) q^{79} +(0.381783 + 0.169981i) q^{80} +(-0.104528 + 0.994522i) q^{81} +(-3.78980 - 0.805547i) q^{82} +(-3.63374 - 11.1835i) q^{83} +(-2.33883 + 1.23687i) q^{84} +(2.07166 - 1.50515i) q^{85} +(1.38857 + 1.54216i) q^{86} +(1.98756 + 3.44255i) q^{87} +(1.97669 - 2.66321i) q^{88} +(4.82050 - 8.34936i) q^{89} +(0.129142 - 0.397459i) q^{90} +(12.8208 - 10.7091i) q^{91} +(7.11664 + 5.17054i) q^{92} +(-2.03863 - 0.433325i) q^{93} +(-0.123062 + 0.136674i) q^{94} +(0.148345 - 1.41141i) q^{95} +(0.104528 + 0.994522i) q^{96} +(2.35935 - 7.26132i) q^{97} +(-2.65128 + 6.47848i) q^{98} +(-2.85524 - 1.68748i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 5 q^{2} - 5 q^{3} + 5 q^{4} - 3 q^{5} + 10 q^{6} - 7 q^{7} - 10 q^{8} + 5 q^{9}+O(q^{10}) \) 40 * q + 5 * q^2 - 5 * q^3 + 5 * q^4 - 3 * q^5 + 10 * q^6 - 7 * q^7 - 10 * q^8 + 5 * q^9	\( 40 q + 5 q^{2} - 5 q^{3} + 5 q^{4} - 3 q^{5} + 10 q^{6} - 7 q^{7} - 10 q^{8} + 5 q^{9} + 12 q^{10} + 2 q^{11} + 20 q^{12} + 10 q^{13} + 5 q^{14} - 6 q^{15} + 5 q^{16} + 5 q^{18} - 13 q^{19} + 6 q^{20} - 2 q^{21} - 4 q^{22} - 20 q^{23} - 5 q^{24} + 12 q^{25} + 10 q^{27} - 3 q^{28} + 12 q^{29} + 3 q^{30} - 10 q^{31} - 20 q^{32} + 8 q^{33} - 13 q^{35} - 10 q^{36} + 3 q^{37} + 2 q^{38} + 5 q^{39} - 3 q^{40} - 44 q^{41} - 3 q^{42} + 36 q^{43} - 3 q^{44} + 12 q^{45} + 11 q^{47} + 10 q^{48} + 33 q^{49} - 4 q^{50} + 26 q^{53} + 20 q^{54} - 20 q^{55} + 8 q^{56} + 4 q^{57} - 6 q^{58} + 4 q^{59} + 3 q^{60} - 23 q^{61} + 5 q^{63} - 10 q^{64} - 50 q^{65} - 7 q^{66} - 108 q^{67} + 20 q^{69} - 86 q^{71} + 5 q^{72} - 35 q^{73} + 3 q^{74} - 2 q^{75} - 44 q^{76} - 37 q^{77} + 20 q^{78} + 3 q^{79} - 3 q^{80} + 5 q^{81} - 28 q^{82} - 88 q^{83} - 5 q^{84} + 96 q^{85} - 13 q^{86} + 6 q^{87} - 8 q^{88} + 6 q^{89} + 6 q^{90} + 40 q^{91} - 20 q^{92} + 10 q^{93} - 24 q^{94} + 36 q^{95} - 5 q^{96} + 60 q^{97} + 2 q^{98} - 4 q^{99}+O(q^{100}) \) 40 * q + 5 * q^2 - 5 * q^3 + 5 * q^4 - 3 * q^5 + 10 * q^6 - 7 * q^7 - 10 * q^8 + 5 * q^9 + 12 * q^10 + 2 * q^11 + 20 * q^12 + 10 * q^13 + 5 * q^14 - 6 * q^15 + 5 * q^16 + 5 * q^18 - 13 * q^19 + 6 * q^20 - 2 * q^21 - 4 * q^22 - 20 * q^23 - 5 * q^24 + 12 * q^25 + 10 * q^27 - 3 * q^28 + 12 * q^29 + 3 * q^30 - 10 * q^31 - 20 * q^32 + 8 * q^33 - 13 * q^35 - 10 * q^36 + 3 * q^37 + 2 * q^38 + 5 * q^39 - 3 * q^40 - 44 * q^41 - 3 * q^42 + 36 * q^43 - 3 * q^44 + 12 * q^45 + 11 * q^47 + 10 * q^48 + 33 * q^49 - 4 * q^50 + 26 * q^53 + 20 * q^54 - 20 * q^55 + 8 * q^56 + 4 * q^57 - 6 * q^58 + 4 * q^59 + 3 * q^60 - 23 * q^61 + 5 * q^63 - 10 * q^64 - 50 * q^65 - 7 * q^66 - 108 * q^67 + 20 * q^69 - 86 * q^71 + 5 * q^72 - 35 * q^73 + 3 * q^74 - 2 * q^75 - 44 * q^76 - 37 * q^77 + 20 * q^78 + 3 * q^79 - 3 * q^80 + 5 * q^81 - 28 * q^82 - 88 * q^83 - 5 * q^84 + 96 * q^85 - 13 * q^86 + 6 * q^87 - 8 * q^88 + 6 * q^89 + 6 * q^90 + 40 * q^91 - 20 * q^92 + 10 * q^93 - 24 * q^94 + 36 * q^95 - 5 * q^96 + 60 * q^97 + 2 * q^98 - 4 * q^99

Introduction

L-functions

Modular forms

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Database

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