LMFDB - Embedded newform 462.2.y.a.247.1

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			247.1
Character	$\chi$	$=$	462.247
Dual form			462.2.y.a.361.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.978148 + 0.207912i) q^{2} +(0.104528 - 0.994522i) q^{3} +(0.913545 + 0.406737i) q^{4} +(-1.71977 - 1.91000i) q^{5} +(0.309017 - 0.951057i) q^{6} +(-1.36179 - 2.26838i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-0.978148 - 0.207912i) q^{9} +O(q^{10})$	\(q+(0.978148 + 0.207912i) q^{2} +(0.104528 - 0.994522i) q^{3} +(0.913545 + 0.406737i) q^{4} +(-1.71977 - 1.91000i) q^{5} +(0.309017 - 0.951057i) q^{6} +(-1.36179 - 2.26838i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-0.978148 - 0.207912i) q^{9} +(-1.28508 - 2.22582i) q^{10} +(2.50957 + 2.16842i) q^{11} +(0.500000 - 0.866025i) q^{12} +(-1.70150 - 5.23668i) q^{13} +(-0.860411 - 2.50194i) q^{14} +(-2.07930 + 1.51070i) q^{15} +(0.669131 + 0.743145i) q^{16} +(-2.14250 + 0.455403i) q^{17} +(-0.913545 - 0.406737i) q^{18} +(-2.35339 + 1.04780i) q^{19} +(-0.794222 - 2.44436i) q^{20} +(-2.39829 + 1.11722i) q^{21} +(2.00389 + 2.64281i) q^{22} +(3.88508 - 6.72915i) q^{23} +(0.669131 - 0.743145i) q^{24} +(-0.167841 + 1.59690i) q^{25} +(-0.575551 - 5.47600i) q^{26} +(-0.309017 + 0.951057i) q^{27} +(-0.321427 - 2.62615i) q^{28} +(6.36168 - 4.62203i) q^{29} +(-2.34795 + 1.04538i) q^{30} +(-3.35463 + 3.72569i) q^{31} +(0.500000 + 0.866025i) q^{32} +(2.41887 - 2.26916i) q^{33} -2.19037 q^{34} +(-1.99062 + 6.50210i) q^{35} +(-0.809017 - 0.587785i) q^{36} +(1.00823 + 9.59266i) q^{37} +(-2.51982 + 0.535603i) q^{38} +(-5.38585 + 1.14480i) q^{39} +(-0.268654 - 2.55608i) q^{40} +(5.19641 + 3.77541i) q^{41} +(-2.57817 + 0.594174i) q^{42} +2.45884 q^{43} +(1.41063 + 3.00169i) q^{44} +(1.28508 + 2.22582i) q^{45} +(5.19925 - 5.77435i) q^{46} +(11.1121 - 4.94743i) q^{47} +(0.809017 - 0.587785i) q^{48} +(-3.29105 + 6.17811i) q^{49} +(-0.496189 + 1.52711i) q^{50} +(0.228956 + 2.17837i) q^{51} +(0.575551 - 5.47600i) q^{52} +(-3.53796 + 3.92930i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(-0.174198 - 8.52246i) q^{55} +(0.231605 - 2.63559i) q^{56} +(0.796062 + 2.45003i) q^{57} +(7.18364 - 3.19836i) q^{58} +(6.30886 + 2.80889i) q^{59} +(-2.51399 + 0.534365i) q^{60} +(0.357789 + 0.397365i) q^{61} +(-4.05593 + 2.94681i) q^{62} +(0.860411 + 2.50194i) q^{63} +(0.309017 + 0.951057i) q^{64} +(-7.07585 + 12.2557i) q^{65} +(2.83779 - 1.71666i) q^{66} +(-6.99602 - 12.1175i) q^{67} +(-2.14250 - 0.455403i) q^{68} +(-6.28619 - 4.56718i) q^{69} +(-3.29899 + 5.94614i) q^{70} +(-1.58558 + 4.87991i) q^{71} +(-0.669131 - 0.743145i) q^{72} +(10.6396 + 4.73705i) q^{73} +(-1.00823 + 9.59266i) q^{74} +(1.57061 + 0.333844i) q^{75} -2.57611 q^{76} +(1.50129 - 8.64558i) q^{77} -5.50617 q^{78} +(-2.02064 - 0.429499i) q^{79} +(0.268654 - 2.55608i) q^{80} +(0.913545 + 0.406737i) q^{81} +(4.29790 + 4.77330i) q^{82} +(2.41558 - 7.43438i) q^{83} +(-2.64537 + 0.0451581i) q^{84} +(4.55443 + 3.30899i) q^{85} +(2.40511 + 0.511222i) q^{86} +(-3.93173 - 6.80996i) q^{87} +(0.755717 + 3.22938i) q^{88} +(-8.51845 + 14.7544i) q^{89} +(0.794222 + 2.44436i) q^{90} +(-9.56166 + 10.9909i) q^{91} +(6.28619 - 4.56718i) q^{92} +(3.35463 + 3.72569i) q^{93} +(11.8979 - 2.52898i) q^{94} +(6.04859 + 2.69301i) q^{95} +(0.913545 - 0.406737i) q^{96} +(-2.41490 - 7.43229i) q^{97} +(-4.50363 + 5.35885i) q^{98} +(-2.00389 - 2.64281i) 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} + 11 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 + 11 * q^7 + 6 * q^8 + 3 * q^9	\( 24 q - 3 q^{2} - 3 q^{3} + 3 q^{4} + 5 q^{5} - 6 q^{6} + 11 q^{7} + 6 q^{8} + 3 q^{9} + 10 q^{10} + 6 q^{11} + 12 q^{12} - 2 q^{13} - 5 q^{14} + 3 q^{16} - 2 q^{17} - 3 q^{18} + 7 q^{19} - 10 q^{20} - 4 q^{21} + 2 q^{22} + 24 q^{23} + 3 q^{24} + 4 q^{25} + 4 q^{26} + 6 q^{27} + 14 q^{28} - 6 q^{29} - 7 q^{31} + 12 q^{32} - q^{33} - 24 q^{34} + 4 q^{35} - 6 q^{36} - q^{37} + 8 q^{38} - q^{39} + 16 q^{41} - 4 q^{42} + 52 q^{43} - 4 q^{44} - 10 q^{45} - 4 q^{46} + 27 q^{47} + 6 q^{48} - 33 q^{49} - 22 q^{50} - 8 q^{51} - 4 q^{52} + 13 q^{53} - 12 q^{54} + 30 q^{55} + 14 q^{56} - 16 q^{57} - 3 q^{58} + 14 q^{59} - 5 q^{60} + 9 q^{61} - 4 q^{62} + 5 q^{63} - 6 q^{64} - 50 q^{65} - 4 q^{66} - 20 q^{67} - 2 q^{68} - 32 q^{69} - 17 q^{70} - 18 q^{71} - 3 q^{72} + 7 q^{73} + q^{74} + 11 q^{75} - 4 q^{76} - 34 q^{77} - 12 q^{78} + q^{79} + 3 q^{81} - 2 q^{82} - 68 q^{83} - 5 q^{84} - 19 q^{86} - 8 q^{87} - q^{88} - 42 q^{89} + 10 q^{90} - 16 q^{91} + 32 q^{92} + 7 q^{93} + 8 q^{94} + 38 q^{95} + 3 q^{96} - 80 q^{97} - 2 q^{99}+O(q^{100}) \) 24 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 + 5 * q^5 - 6 * q^6 + 11 * q^7 + 6 * q^8 + 3 * q^9 + 10 * q^10 + 6 * q^11 + 12 * q^12 - 2 * q^13 - 5 * q^14 + 3 * q^16 - 2 * q^17 - 3 * q^18 + 7 * q^19 - 10 * q^20 - 4 * q^21 + 2 * q^22 + 24 * q^23 + 3 * q^24 + 4 * q^25 + 4 * q^26 + 6 * q^27 + 14 * q^28 - 6 * q^29 - 7 * q^31 + 12 * q^32 - q^33 - 24 * q^34 + 4 * q^35 - 6 * q^36 - q^37 + 8 * q^38 - q^39 + 16 * q^41 - 4 * q^42 + 52 * q^43 - 4 * q^44 - 10 * q^45 - 4 * q^46 + 27 * q^47 + 6 * q^48 - 33 * q^49 - 22 * q^50 - 8 * q^51 - 4 * q^52 + 13 * q^53 - 12 * q^54 + 30 * q^55 + 14 * q^56 - 16 * q^57 - 3 * q^58 + 14 * q^59 - 5 * q^60 + 9 * q^61 - 4 * q^62 + 5 * q^63 - 6 * q^64 - 50 * q^65 - 4 * q^66 - 20 * q^67 - 2 * q^68 - 32 * q^69 - 17 * q^70 - 18 * q^71 - 3 * q^72 + 7 * q^73 + q^74 + 11 * q^75 - 4 * q^76 - 34 * q^77 - 12 * q^78 + q^79 + 3 * q^81 - 2 * q^82 - 68 * q^83 - 5 * q^84 - 19 * q^86 - 8 * q^87 - q^88 - 42 * q^89 + 10 * q^90 - 16 * q^91 + 32 * q^92 + 7 * q^93 + 8 * q^94 + 38 * q^95 + 3 * q^96 - 80 * q^97 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.978148	+	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
$5$	−1.71977	−	1.91000i	−0.769104	−	0.854177i	0.223609	−	0.974679i	$-0.428216\pi$
$5$	−1.71977	−	1.91000i	−0.769104	−	0.854177i	−0.992713	+	0.120502i	$0.961550\pi$
$6$	0.309017	−	0.951057i	0.126156	−	0.388267i
$7$	−1.36179	−	2.26838i	−0.514709	−	0.857365i
$7$	−1.36179	−	2.26838i	−0.514709	−	0.857365i
$8$	0.809017	+	0.587785i	0.286031	+	0.207813i
$9$	−0.978148	−	0.207912i	−0.326049	−	0.0693039i
$10$	−1.28508	−	2.22582i	−0.406377	−	0.703866i
$11$	2.50957	+	2.16842i	0.756664	+	0.653804i
$11$	2.50957	+	2.16842i	0.756664	+	0.653804i
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	−1.70150	−	5.23668i	−0.471911	−	1.45239i	−0.850079	−	0.526656i	$-0.823446\pi$
$13$	−1.70150	−	5.23668i	−0.471911	−	1.45239i	0.378168	−	0.925737i	$-0.376554\pi$
$14$	−0.860411	−	2.50194i	−0.229954	−	0.668671i
$15$	−2.07930	+	1.51070i	−0.536873	+	0.390061i
$16$	0.669131	+	0.743145i	0.167283	+	0.185786i
$17$	−2.14250	+	0.455403i	−0.519633	+	0.110451i	−0.460260	−	0.887784i	$-0.652244\pi$
$17$	−2.14250	+	0.455403i	−0.519633	+	0.110451i	−0.0593737	+	0.998236i	$0.518910\pi$
$18$	−0.913545	−	0.406737i	−0.215325	−	0.0958687i
$19$	−2.35339	+	1.04780i	−0.539906	+	0.240381i	−0.658526	−	0.752558i	$-0.728820\pi$
$19$	−2.35339	+	1.04780i	−0.539906	+	0.240381i	0.118620	+	0.992940i	$0.462153\pi$
$20$	−0.794222	−	2.44436i	−0.177593	−	0.546576i
$21$	−2.39829	+	1.11722i	−0.523351	+	0.243798i
$22$	2.00389	+	2.64281i	0.427231	+	0.563448i
$23$	3.88508	−	6.72915i	0.810095	−	1.40313i	−0.102702	−	0.994712i	$-0.532749\pi$
$23$	3.88508	−	6.72915i	0.810095	−	1.40313i	0.912797	−	0.408414i	$-0.133918\pi$
$24$	0.669131	−	0.743145i	0.136586	−	0.151694i
$25$	−0.167841	+	1.59690i	−0.0335683	+	0.319381i
$26$	−0.575551	−	5.47600i	−0.112875	−	1.07393i
$27$	−0.309017	+	0.951057i	−0.0594703	+	0.183031i
$28$	−0.321427	−	2.62615i	−0.0607439	−	0.496296i
$29$	6.36168	−	4.62203i	1.18133	−	0.858289i	0.189013	−	0.981975i	$-0.439471\pi$
$29$	6.36168	−	4.62203i	1.18133	−	0.858289i	0.992322	+	0.123685i	$0.0394713\pi$
$30$	−2.34795	+	1.04538i	−0.428676	+	0.190859i
$31$	−3.35463	+	3.72569i	−0.602509	+	0.669154i	−0.964822	−	0.262902i	$-0.915320\pi$
$31$	−3.35463	+	3.72569i	−0.602509	+	0.669154i	0.362314	+	0.932056i	$0.381987\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	2.41887	−	2.26916i	0.421071	−	0.395010i
$34$	−2.19037			−0.375645
$35$	−1.99062	+	6.50210i	−0.336477	+	1.09906i
$36$	−0.809017	−	0.587785i	−0.134836	−	0.0979642i
$37$	1.00823	+	9.59266i	0.165752	+	1.57702i	0.688948	+	0.724811i	$0.258073\pi$
$37$	1.00823	+	9.59266i	0.165752	+	1.57702i	−0.523196	+	0.852212i	$0.675260\pi$
$38$	−2.51982	+	0.535603i	−0.408768	+	0.0868864i
$39$	−5.38585	+	1.14480i	−0.862425	+	0.183314i
$40$	−0.268654	−	2.55608i	−0.0424780	−	0.404151i
$41$	5.19641	+	3.77541i	0.811542	+	0.589620i	0.914277	−	0.405089i	$-0.132759\pi$
$41$	5.19641	+	3.77541i	0.811542	+	0.589620i	−0.102735	+	0.994709i	$0.532759\pi$
$42$	−2.57817	+	0.594174i	−0.397820	+	0.0916830i
$43$	2.45884			0.374970			0.187485	−	0.982267i	$-0.439966\pi$
$43$	2.45884			0.374970			0.187485	+	0.982267i	$0.439966\pi$
$44$	1.41063	+	3.00169i	0.212660	+	0.452521i
$45$	1.28508	+	2.22582i	0.191568	+	0.331806i
$46$	5.19925	−	5.77435i	0.766588	−	0.851382i
$47$	11.1121	−	4.94743i	1.62087	−	0.721657i	0.622718	−	0.782447i	$-0.286029\pi$
$47$	11.1121	−	4.94743i	1.62087	−	0.721657i	0.998151	+	0.0607896i	$0.0193619\pi$
$48$	0.809017	−	0.587785i	0.116772	−	0.0848395i
$49$	−3.29105	+	6.17811i	−0.470150	+	0.882586i
$50$	−0.496189	+	1.52711i	−0.0701717	+	0.215966i
$51$	0.228956	+	2.17837i	0.0320602	+	0.305033i
$52$	0.575551	−	5.47600i	0.0798146	−	0.759385i
$53$	−3.53796	+	3.92930i	−0.485976	+	0.539731i	−0.935402	−	0.353586i	$-0.884962\pi$
$53$	−3.53796	+	3.92930i	−0.485976	+	0.539731i	0.449425	+	0.893318i	$0.351629\pi$
$54$	−0.500000	+	0.866025i	−0.0680414	+	0.117851i
$55$	−0.174198	−	8.52246i	−0.0234888	−	1.14917i
$56$	0.231605	−	2.63559i	0.0309496	−	0.352196i
$57$	0.796062	+	2.45003i	0.105441	+	0.324514i
$58$	7.18364	−	3.19836i	0.943257	−	0.419965i
$59$	6.30886	+	2.80889i	0.821344	+	0.365686i	0.773994	−	0.633192i	$-0.218256\pi$
$59$	6.30886	+	2.80889i	0.821344	+	0.365686i	0.0473497	+	0.998878i	$0.484922\pi$
$60$	−2.51399	+	0.534365i	−0.324555	+	0.0689863i
$61$	0.357789	+	0.397365i	0.0458101	+	0.0508773i	0.765614	−	0.643300i	$-0.222435\pi$
$61$	0.357789	+	0.397365i	0.0458101	+	0.0508773i	−0.719804	+	0.694177i	$0.755768\pi$
$62$	−4.05593	+	2.94681i	−0.515104	+	0.374245i
$63$	0.860411	+	2.50194i	0.108402	+	0.315215i
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	−7.07585	+	12.2557i	−0.877652	+	1.52014i
$66$	2.83779	−	1.71666i	0.349308	−	0.211307i
$67$	−6.99602	−	12.1175i	−0.854700	−	1.48038i	−0.876923	−	0.480630i	$-0.840408\pi$
$67$	−6.99602	−	12.1175i	−0.854700	−	1.48038i	0.0222237	−	0.999753i	$-0.492925\pi$
$68$	−2.14250	−	0.455403i	−0.259817	−	0.0552257i
$69$	−6.28619	−	4.56718i	−0.756768	−	0.549824i
$70$	−3.29899	+	5.94614i	−0.394304	+	0.710700i
$71$	−1.58558	+	4.87991i	−0.188174	+	0.579139i	−0.999989	−	0.00477590i	$-0.998480\pi$
$71$	−1.58558	+	4.87991i	−0.188174	+	0.579139i	0.811815	+	0.583915i	$0.198480\pi$
$72$	−0.669131	−	0.743145i	−0.0788578	−	0.0875805i
$73$	10.6396	+	4.73705i	1.24527	+	0.554430i	0.920270	−	0.391284i	$-0.127969\pi$
$73$	10.6396	+	4.73705i	1.24527	+	0.554430i	0.325000	+	0.945714i	$0.394636\pi$
$74$	−1.00823	+	9.59266i	−0.117204	+	1.11512i
$75$	1.57061	+	0.333844i	0.181359	+	0.0385490i
$76$	−2.57611			−0.295500
$77$	1.50129	−	8.64558i	0.171088	−	0.985256i
$78$	−5.50617			−0.623451
$79$	−2.02064	−	0.429499i	−0.227339	−	0.0483225i	0.0928334	−	0.995682i	$-0.470408\pi$
$79$	−2.02064	−	0.429499i	−0.227339	−	0.0483225i	−0.320173	+	0.947359i	$0.603741\pi$
$80$	0.268654	−	2.55608i	0.0300365	−	0.285778i
$81$	0.913545	+	0.406737i	0.101505	+	0.0451930i
$82$	4.29790	+	4.77330i	0.474624	+	0.527123i
$83$	2.41558	−	7.43438i	0.265144	−	0.816030i	−0.726516	−	0.687149i	$-0.758862\pi$
$83$	2.41558	−	7.43438i	0.265144	−	0.816030i	0.991660	−	0.128880i	$-0.0411383\pi$
$84$	−2.64537	+	0.0451581i	−0.288633	+	0.00492715i
$85$	4.55443	+	3.30899i	0.493998	+	0.358910i
$86$	2.40511	+	0.511222i	0.259350	+	0.0551265i
$87$	−3.93173	−	6.80996i	−0.421526	−	0.730105i
$88$	0.755717	+	3.22938i	0.0805597	+	0.344253i
$89$	−8.51845	+	14.7544i	−0.902954	+	1.56396i	−0.0793127	+	0.996850i	$0.525273\pi$
$89$	−8.51845	+	14.7544i	−0.902954	+	1.56396i	−0.823641	+	0.567112i	$0.808061\pi$
$90$	0.794222	+	2.44436i	0.0837183	+	0.257659i
$91$	−9.56166	+	10.9909i	−1.00233	+	1.15216i
$92$	6.28619	−	4.56718i	0.655381	−	0.476162i
$93$	3.35463	+	3.72569i	0.347859	+	0.386336i
$94$	11.8979	−	2.52898i	1.22718	−	0.260844i
$95$	6.04859	+	2.69301i	0.620572	+	0.276297i
$96$	0.913545	−	0.406737i	0.0932383	−	0.0415124i
$97$	−2.41490	−	7.43229i	−0.245196	−	0.754634i	−0.995604	−	0.0936602i	$-0.970143\pi$
$97$	−2.41490	−	7.43229i	−0.245196	−	0.754634i	0.750409	−	0.660974i	$-0.229857\pi$
$98$	−4.50363	+	5.35885i	−0.454936	+	0.541326i
$99$	−2.00389	−	2.64281i	−0.201398	−	0.265612i
$100$	−0.802850	+	1.39058i	−0.0802850	+	0.139058i
$101$	6.31297	−	7.01126i	0.628164	−	0.697647i	−0.342109	−	0.939660i	$-0.611141\pi$
$101$	6.31297	−	7.01126i	0.628164	−	0.697647i	0.970273	+	0.242014i	$0.0778079\pi$
$102$	−0.228956	+	2.17837i	−0.0226700	+	0.215691i
$103$	0.516946	+	4.91841i	0.0509362	+	0.484625i	0.990019	+	0.140934i	$0.0450106\pi$
$103$	0.516946	+	4.91841i	0.0509362	+	0.484625i	−0.939083	+	0.343691i	$0.888323\pi$
$104$	1.70150	−	5.23668i	0.166846	−	0.513498i
$105$	6.25841	+	2.65937i	0.610758	+	0.259528i
$106$	−4.27760	+	3.10786i	−0.415477	+	0.301862i
$107$	4.43061	−	1.97263i	0.428323	−	0.190702i	−0.181241	−	0.983439i	$-0.558011\pi$
$107$	4.43061	−	1.97263i	0.428323	−	0.190702i	0.609564	+	0.792737i	$0.291345\pi$
$108$	−0.669131	+	0.743145i	−0.0643871	+	0.0715091i
$109$	−8.73389	−	15.1275i	−0.836555	−	1.44896i	−0.892758	−	0.450537i	$-0.851233\pi$
$109$	−8.73389	−	15.1275i	−0.836555	−	1.44896i	0.0562025	−	0.998419i	$-0.482101\pi$
$110$	1.60153	−	8.37244i	0.152700	−	0.798281i
$111$	9.64550			0.915510
$112$	0.774515	−	2.52985i	0.0731848	−	0.239048i
$113$	9.19937	+	6.68373i	0.865404	+	0.628752i	0.929350	−	0.369201i	$-0.120369\pi$
$113$	9.19937	+	6.68373i	0.865404	+	0.628752i	−0.0639461	+	0.997953i	$0.520369\pi$
$114$	0.269277	+	2.56200i	0.0252201	+	0.239953i
$115$	−19.5341	+	4.15210i	−1.82157	+	0.387186i
$116$	7.69163	−	1.63491i	0.714150	−	0.151797i
$117$	0.575551	+	5.47600i	0.0532097	+	0.506257i
$118$	5.58700	+	4.05919i	0.514325	+	0.373679i
$119$	3.95067	+	4.23984i	0.362157	+	0.388665i
$120$	−2.57016			−0.234622
$121$	1.59588	+	10.8836i	0.145080	+	0.989420i
$122$	0.267353	+	0.463070i	0.0242050	+	0.0419244i
$123$	4.29790	−	4.77330i	0.387529	−	0.430394i
$124$	−4.57998	+	2.03914i	−0.411294	+	0.183120i
$125$	−7.05777	+	5.12777i	−0.631266	+	0.458641i
$126$	0.321427	+	2.62615i	0.0286350	+	0.233956i
$127$	0.855155	−	2.63190i	0.0758827	−	0.233543i	−0.905919	−	0.423450i	$-0.860819\pi$
$127$	0.855155	−	2.63190i	0.0758827	−	0.233543i	0.981802	+	0.189907i	$0.0608188\pi$
$128$	0.104528	+	0.994522i	0.00923910	+	0.0879041i
$129$	0.257019	−	2.44537i	0.0226293	−	0.215303i
$130$	−9.46934	+	10.5168i	−0.830516	+	0.922382i
$131$	−0.397950	+	0.689269i	−0.0347690	+	0.0602217i	−0.882886	−	0.469587i	$-0.844403\pi$
$131$	−0.397950	+	0.689269i	−0.0347690	+	0.0602217i	0.848117	+	0.529809i	$0.177736\pi$
$132$	3.13269	−	1.08914i	0.272666	−	0.0947974i
$133$	5.58163	+	3.91150i	0.483989	+	0.339170i
$134$	−4.32378	−	13.3072i	−0.373517	−	1.14957i
$135$	2.34795	−	1.04538i	0.202080	−	0.0899717i
$136$	−2.00100	−	0.890903i	−0.171584	−	0.0763943i
$137$	−13.9753	+	2.97055i	−1.19399	+	0.253791i	−0.761692	−	0.647939i	$-0.775631\pi$
$137$	−13.9753	+	2.97055i	−1.19399	+	0.253791i	−0.432300	+	0.901730i	$0.642298\pi$
$138$	−5.19925	−	5.77435i	−0.442590	−	0.491546i
$139$	0.462004	−	0.335665i	0.0391866	−	0.0284708i	−0.568020	−	0.823015i	$-0.692290\pi$
$139$	0.462004	−	0.335665i	0.0391866	−	0.0284708i	0.607206	+	0.794544i	$0.292290\pi$
$140$	−4.46317	+	5.13031i	−0.377207	+	0.433590i
$141$	−3.75880	−	11.5684i	−0.316548	−	0.974234i
$142$	−2.56552	+	4.44361i	−0.215294	+	0.372900i
$143$	7.08530	−	16.8314i	0.592503	−	1.40751i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	−19.7687	−	4.20197i	−1.64170	−	0.348954i
$146$	9.42220	+	6.84563i	0.779787	+	0.566548i
$147$	5.80025	+	3.91881i	0.478397	+	0.323218i
$148$	−2.98062	+	9.17341i	−0.245006	+	0.754050i
$149$	7.64783	+	8.49377i	0.626534	+	0.695837i	0.969938	−	0.243351i	$-0.0782466\pi$
$149$	7.64783	+	8.49377i	0.626534	+	0.695837i	−0.343404	+	0.939188i	$0.611580\pi$
$150$	1.46688	+	0.653097i	0.119770	+	0.0533252i
$151$	0.482316	−	4.58893i	0.0392503	−	0.373442i	−0.957211	−	0.289391i	$-0.906547\pi$
$151$	0.482316	−	4.58893i	0.0392503	−	0.373442i	0.996461	−	0.0840513i	$-0.0267860\pi$
$152$	−2.51982	−	0.535603i	−0.204384	−	0.0434432i
$153$	2.19037			0.177081
$154$	3.26600	−	8.14452i	0.263182	−	0.656304i
$155$	12.8852			1.03497
$156$	−5.38585	−	1.14480i	−0.431213	−	0.0916571i
$157$	−1.42469	+	13.5551i	−0.113703	+	1.08181i	0.777711	+	0.628622i	$0.216381\pi$
$157$	−1.42469	+	13.5551i	−0.113703	+	1.08181i	−0.891414	+	0.453189i	$0.850286\pi$
$158$	−1.88718	−	0.840228i	−0.150136	−	0.0668449i
$159$	3.53796	+	3.92930i	0.280579	+	0.311614i
$160$	0.794222	−	2.44436i	0.0627887	−	0.193244i
$161$	−20.5549	+	0.350886i	−1.61995	+	0.0276537i
$162$	0.809017	+	0.587785i	0.0635624	+	0.0461808i
$163$	10.7757	+	2.29045i	0.844019	+	0.179402i	0.609576	−	0.792728i	$-0.291340\pi$
$163$	10.7757	+	2.29045i	0.844019	+	0.179402i	0.234444	+	0.972130i	$0.424673\pi$
$164$	3.21156	+	5.56258i	0.250780	+	0.434364i
$165$	−8.49398	−	0.717597i	−0.661256	−	0.0558648i
$166$	3.90849	−	6.76970i	0.303357	−	0.525430i
$167$	−2.99719	−	9.22439i	−0.231929	−	0.713805i	−0.997514	−	0.0704698i	$-0.977550\pi$
$167$	−2.99719	−	9.22439i	−0.231929	−	0.713805i	0.765585	−	0.643335i	$-0.222450\pi$
$168$	−2.59695	−	0.505831i	−0.200359	−	0.0390257i
$169$	−14.0105	+	10.1792i	−1.07773	+	0.783015i
$170$	3.76693	+	4.18360i	0.288910	+	0.320867i
$171$	2.51982	−	0.535603i	0.192695	−	0.0409586i
$172$	2.24627	+	1.00010i	0.171276	+	0.0762571i
$173$	4.64594	−	2.06850i	0.353224	−	0.157265i	−0.222451	−	0.974944i	$-0.571406\pi$
$173$	4.64594	−	2.06850i	0.353224	−	0.157265i	0.575675	+	0.817678i	$0.304739\pi$
$174$	−2.42995	−	7.47860i	−0.184214	−	0.566951i
$175$	3.85094	−	1.79392i	0.291104	−	0.135608i
$176$	0.0677770	+	3.31593i	0.00510889	+	0.249948i
$177$	3.45296	−	5.98069i	0.259540	−	0.449537i
$178$	−11.3999	+	12.6609i	−0.854459	+	0.948973i
$179$	1.88689	−	17.9526i	0.141033	−	1.34184i	−0.663610	−	0.748078i	$-0.730977\pi$
$179$	1.88689	−	17.9526i	0.141033	−	1.34184i	0.804643	−	0.593759i	$-0.202357\pi$
$180$	0.268654	+	2.55608i	0.0200243	+	0.190519i
$181$	4.82282	−	14.8431i	0.358478	−	1.10328i	−0.595488	−	0.803364i	$-0.703041\pi$
$181$	4.82282	−	14.8431i	0.358478	−	1.10328i	0.953966	−	0.299916i	$-0.0969587\pi$
$182$	−11.6379	+	8.76274i	−0.862655	+	0.649538i
$183$	0.432587	−	0.314293i	0.0319777	−	0.0232332i
$184$	7.09839	−	3.16041i	0.523300	−	0.232988i
$185$	16.5880	−	18.4229i	1.21958	−	1.35448i
$186$	2.50671	+	4.34174i	0.183801	+	0.318352i
$187$	−6.36427	−	3.50299i	−0.465401	−	0.256164i
$188$	12.1637			0.887131
$189$	2.57817	−	0.594174i	0.187534	−	0.0432198i
$190$	5.35651	+	3.89173i	0.388602	+	0.282336i
$191$	0.619757	+	5.89660i	0.0448441	+	0.426663i	0.993794	+	0.111236i	$0.0354810\pi$
$191$	0.619757	+	5.89660i	0.0448441	+	0.426663i	−0.948950	+	0.315427i	$0.897852\pi$
$192$	0.978148	−	0.207912i	0.0705917	−	0.0150047i
$193$	−8.78073	+	1.86640i	−0.632051	+	0.134347i	−0.512787	−	0.858516i	$-0.671387\pi$
$193$	−8.78073	+	1.86640i	−0.632051	+	0.134347i	−0.119264	+	0.992863i	$0.538054\pi$
$194$	−0.816866	−	7.77196i	−0.0586475	−	0.557994i
$195$	11.4490	+	8.31817i	0.819878	+	0.595676i
$196$	−5.51939	+	4.30539i	−0.394242	+	0.307528i
$197$	−12.4856			−0.889559			−0.444780	−	0.895640i	$-0.646718\pi$
$197$	−12.4856			−0.889559			−0.444780	+	0.895640i	$0.646718\pi$
$198$	−1.41063	−	3.00169i	−0.100249	−	0.213321i
$199$	−1.71286	−	2.96677i	−0.121422	−	0.210309i	0.798907	−	0.601455i	$-0.205412\pi$
$199$	−1.71286	−	2.96677i	−0.121422	−	0.210309i	−0.920329	+	0.391146i	$0.872079\pi$
$200$	−1.07442	+	1.19327i	−0.0759732	+	0.0843768i
$201$	−12.7824	+	5.69107i	−0.901598	+	0.401417i
$202$	7.63274	−	5.54551i	0.537038	−	0.390181i
$203$	−19.1478	−	8.13643i	−1.34391	−	0.571066i
$204$	−0.676861	+	2.08316i	−0.0473898	+	0.145851i
$205$	−1.72560	−	16.4180i	−0.120521	−	1.14668i
$206$	−0.516946	+	4.91841i	−0.0360173	+	0.342682i
$207$	−5.19925	+	5.77435i	−0.361373	+	0.401345i
$208$	2.75308	−	4.76848i	0.190892	−	0.330635i
$209$	−8.17808	−	2.47363i	−0.565689	−	0.171105i
$210$	5.56873	+	3.90246i	0.384279	+	0.269295i
$211$	−6.61610	−	20.3623i	−0.455471	−	1.40180i	−0.870581	−	0.492025i	$-0.836257\pi$
$211$	−6.61610	−	20.3623i	−0.455471	−	1.40180i	0.415110	−	0.909771i	$-0.363743\pi$
$212$	−4.83028	+	2.15058i	−0.331745	+	0.147702i
$213$	4.68744	+	2.08698i	0.321178	+	0.142998i
$214$	4.74392	−	1.00835i	0.324288	−	0.0689295i
$215$	−4.22865	−	4.69639i	−0.288391	−	0.320291i
$216$	−0.809017	+	0.587785i	−0.0550466	+	0.0399937i
$217$	13.0196	+	2.53594i	0.883826	+	0.172151i
$218$	−5.39784	−	16.6129i	−0.365588	−	1.12516i
$219$	5.82324	−	10.0861i	0.393498	−	0.681559i
$220$	3.30726	−	7.85651i	0.222975	−	0.529686i
$221$	6.03027	+	10.4447i	0.405640	+	0.702589i
$222$	9.43472	+	2.00541i	0.633217	+	0.134594i
$223$	−4.45454	−	3.23641i	−0.298298	−	0.216726i	0.428561	−	0.903513i	$-0.359021\pi$
$223$	−4.45454	−	3.23641i	−0.298298	−	0.216726i	−0.726859	+	0.686787i	$0.759021\pi$
$224$	1.28357	−	2.31353i	0.0857625	−	0.154579i
$225$	0.496189	−	1.52711i	0.0330793	−	0.101807i
$226$	7.60871	+	8.45033i	0.506124	+	0.562108i
$227$	6.75748	+	3.00862i	0.448509	+	0.199689i	0.618546	−	0.785748i	$-0.287722\pi$
$227$	6.75748	+	3.00862i	0.448509	+	0.199689i	−0.170037	+	0.985438i	$0.554389\pi$
$228$	−0.269277	+	2.56200i	−0.0178333	+	0.169672i
$229$	25.9920	+	5.52478i	1.71760	+	0.365087i	0.958325	−	0.285681i	$-0.0922197\pi$
$229$	25.9920	+	5.52478i	1.71760	+	0.365087i	0.759277	+	0.650768i	$0.225553\pi$
$230$	−19.9705			−1.31682
$231$	−8.44130	−	2.39677i	−0.555396	−	0.157696i
$232$	7.86347			0.516262
$233$	−2.08468	−	0.443112i	−0.136572	−	0.0290293i	0.139118	−	0.990276i	$-0.455573\pi$
$233$	−2.08468	−	0.443112i	−0.136572	−	0.0290293i	−0.275690	+	0.961246i	$0.588906\pi$
$234$	−0.575551	+	5.47600i	−0.0376250	+	0.357978i
$235$	−28.5599	−	12.7157i	−1.86304	−	0.829479i
$236$	4.62096	+	5.13209i	0.300799	+	0.334071i
$237$	−0.638361	+	1.96467i	−0.0414660	+	0.127619i
$238$	2.98282	+	4.96858i	0.193348	+	0.322065i
$239$	5.25010	+	3.81442i	0.339601	+	0.246734i	0.744493	−	0.667630i	$-0.232691\pi$
$239$	5.25010	+	3.81442i	0.339601	+	0.246734i	−0.404893	+	0.914364i	$0.632691\pi$
$240$	−2.51399	−	0.534365i	−0.162277	−	0.0344931i
$241$	6.82424	+	11.8199i	0.439588	+	0.761389i	0.997658	−	0.0684055i	$-0.0217912\pi$
$241$	6.82424	+	11.8199i	0.439588	+	0.761389i	−0.558070	+	0.829794i	$0.688458\pi$
$242$	−0.701827	+	10.9776i	−0.0451151	+	0.705666i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	0.165233	+	0.508536i	0.0105780	+	0.0325557i
$245$	17.4600	−	4.33902i	1.11548	−	0.277210i
$246$	5.19641	−	3.77541i	0.331311	−	0.240711i
$247$	9.49128	+	10.5411i	0.603916	+	0.670716i
$248$	−4.90386	+	1.04235i	−0.311395	+	0.0661891i
$249$	−7.14116	−	3.17945i	−0.452553	−	0.201489i
$250$	−7.96966	+	3.54832i	−0.504045	+	0.224416i
$251$	3.30374	+	10.1679i	0.208530	+	0.641789i	0.999550	+	0.0299990i	$0.00955042\pi$
$251$	3.30374	+	10.1679i	0.208530	+	0.641789i	−0.791020	+	0.611790i	$0.790450\pi$
$252$	−0.231605	+	2.63559i	−0.0145898	+	0.166027i
$253$	24.3415	−	8.46278i	1.53034	−	0.532051i
$254$	1.38367	−	2.39659i	0.0868192	−	0.150375i
$255$	3.76693	−	4.18360i	0.235894	−	0.261987i
$256$	−0.104528	+	0.994522i	−0.00653303	+	0.0621576i
$257$	−0.709544	−	6.75086i	−0.0442601	−	0.421107i	−0.994108	−	0.108395i	$-0.965429\pi$
$257$	−0.709544	−	6.75086i	−0.0442601	−	0.421107i	0.949848	−	0.312712i	$-0.101238\pi$
$258$	0.759825	−	2.33850i	0.0473046	−	0.145589i
$259$	20.3868	−	15.3502i	1.26677	−	0.953817i
$260$	−11.4490	+	8.31817i	−0.710035	+	0.515871i
$261$	−7.18364	+	3.19836i	−0.444656	+	0.197974i
$262$	−0.532561	+	0.591469i	−0.0329017	+	0.0365411i
$263$	−2.14469	−	3.71471i	−0.132247	−	0.229059i	0.792295	−	0.610138i	$-0.208886\pi$
$263$	−2.14469	−	3.71471i	−0.132247	−	0.229059i	−0.924543	+	0.381079i	$0.875553\pi$
$264$	3.29068	−	0.414015i	0.202528	−	0.0254809i
$265$	13.5894			0.834793
$266$	4.64641	+	4.98651i	0.284890	+	0.305742i
$267$	13.7831	+	10.0140i	0.843514	+	0.612849i
$268$	−1.46257	−	13.9154i	−0.0893404	−	0.850018i
$269$	−2.37022	+	0.503806i	−0.144515	+	0.0307176i	−0.279601	−	0.960116i	$-0.590202\pi$
$269$	−2.37022	+	0.503806i	−0.144515	+	0.0307176i	0.135086	+	0.990834i	$0.456869\pi$
$270$	2.51399	−	0.534365i	0.152997	−	0.0325204i
$271$	−0.544917	−	5.18454i	−0.0331013	−	0.314938i	−0.998527	−	0.0542593i	$-0.982720\pi$
$271$	−0.544917	−	5.18454i	−0.0331013	−	0.314938i	0.965426	−	0.260679i	$-0.0839464\pi$
$272$	−1.77205	−	1.28747i	−0.107446	−	0.0780641i
$273$	9.93122	+	10.6581i	0.601065	+	0.645060i
$274$	−14.2875			−0.863142
$275$	−3.88398	+	3.64359i	−0.234213	+	0.219717i
$276$	−3.88508	−	6.72915i	−0.233854	−	0.405048i
$277$	−14.6458	+	16.2658i	−0.879980	+	0.977317i	−0.999880	−	0.0154694i	$-0.995076\pi$
$277$	−14.6458	+	16.2658i	−0.879980	+	0.977317i	0.119901	+	0.992786i	$0.461742\pi$
$278$	0.521696	−	0.232274i	0.0312893	−	0.0139309i
$279$	4.05593	−	2.94681i	0.242822	−	0.176421i
$280$	−5.43229	+	4.09025i	−0.324641	+	0.244439i
$281$	4.46129	−	13.7304i	0.266138	−	0.819089i	−0.725291	−	0.688443i	$-0.758295\pi$
$281$	4.46129	−	13.7304i	0.266138	−	0.819089i	0.991429	−	0.130646i	$-0.0417053\pi$
$282$	−1.27146	−	12.0971i	−0.0757141	−	0.720371i
$283$	1.56701	−	14.9091i	0.0931491	−	0.886255i	−0.843769	−	0.536706i	$-0.819668\pi$
$283$	1.56701	−	14.9091i	0.0931491	−	0.886255i	0.936918	−	0.349548i	$-0.113665\pi$
$284$	−3.43334	+	3.81311i	−0.203731	+	0.226266i
$285$	3.31050	−	5.73396i	0.196097	−	0.339650i
$286$	10.4299	−	14.9905i	0.616734	−	0.886404i
$287$	1.48763	−	16.9287i	0.0878118	−	0.999270i
$288$	−0.309017	−	0.951057i	−0.0182090	−	0.0560415i
$289$	−11.1473	+	4.96312i	−0.655726	+	0.291948i
$290$	−18.4631	−	8.22028i	−1.08419	−	0.482712i
$291$	−7.64400	+	1.62478i	−0.448099	+	0.0952464i
$292$	7.79302	+	8.65502i	0.456052	+	0.506497i
$293$	−14.8674	+	10.8018i	−0.868564	+	0.631049i	−0.930201	−	0.367050i	$-0.880368\pi$
$293$	−14.8674	+	10.8018i	−0.868564	+	0.631049i	0.0616373	+	0.998099i	$0.480368\pi$
$294$	4.85874	+	5.03911i	0.283367	+	0.293887i
$295$	−5.48483	−	16.8806i	−0.319339	−	0.982824i
$296$	−4.82275	+	8.35325i	−0.280317	+	0.485523i
$297$	−2.83779	+	1.71666i	−0.164665	+	0.0996109i
$298$	5.71475	+	9.89824i	0.331047	+	0.573389i
$299$	−41.8489	−	8.89525i	−2.42018	−	0.514426i
$300$	1.29904	+	0.943807i	0.0750001	+	0.0544907i
$301$	−3.34843	−	5.57758i	−0.193000	−	0.321486i
$302$	1.42587	−	4.38837i	0.0820495	−	0.252522i
$303$	−6.31297	−	7.01126i	−0.362671	−	0.402786i
$304$	−2.35339	−	1.04780i	−0.134976	−	0.0600954i
$305$	0.143651	−	1.36675i	0.00822545	−	0.0782600i
$306$	2.14250	+	0.455403i	0.122479	+	0.0260337i
$307$	−1.82124			−0.103943			−0.0519717	−	0.998649i	$-0.516551\pi$
$307$	−1.82124			−0.103943			−0.0519717	+	0.998649i	$0.516551\pi$
$308$	4.88797	−	7.28751i	0.278518	−	0.415244i
$309$	4.94550			0.281340
$310$	12.6037	+	2.67899i	0.715841	+	0.152157i
$311$	−1.89629	+	18.0420i	−0.107529	+	1.02307i	0.799117	+	0.601176i	$0.205301\pi$
$311$	−1.89629	+	18.0420i	−0.107529	+	1.02307i	−0.906646	+	0.421893i	$0.861366\pi$
$312$	−5.03013	−	2.23956i	−0.284775	−	0.126790i
$313$	5.67963	+	6.30787i	0.321032	+	0.356542i	0.881961	−	0.471322i	$-0.156223\pi$
$313$	5.67963	+	6.30787i	0.321032	+	0.356542i	−0.560930	+	0.827863i	$0.689556\pi$
$314$	−4.21181	+	12.9626i	−0.237686	+	0.731524i
$315$	3.29899	−	5.94614i	0.185877	−	0.335027i
$316$	−1.67125	−	1.21423i	−0.0940151	−	0.0683060i
$317$	−11.5245	−	2.44961i	−0.647280	−	0.137584i	−0.127439	−	0.991846i	$-0.540676\pi$
$317$	−11.5245	−	2.44961i	−0.647280	−	0.137584i	−0.519841	+	0.854263i	$0.674009\pi$
$318$	2.64370	+	4.57902i	0.148251	+	0.256779i
$319$	25.9876	+	2.19551i	1.45503	+	0.122925i
$320$	1.28508	−	2.22582i	0.0718380	−	0.124427i
$321$	−1.49870	−	4.61253i	−0.0836494	−	0.257446i
$322$	−20.1787	−	3.93039i	−1.12451	−	0.219032i
$323$	4.56498	−	3.31665i	0.254002	−	0.184544i
$324$	0.669131	+	0.743145i	0.0371739	+	0.0412858i
$325$	8.64806	−	1.83820i	0.479708	−	0.101965i
$326$	10.0640	+	4.48079i	0.557395	+	0.248168i
$327$	−15.9576	+	7.10479i	−0.882458	+	0.392896i
$328$	1.98485	+	6.10874i	0.109595	+	0.337299i
$329$	−26.3550	−	18.4691i	−1.45300	−	1.01823i
$330$	−8.15917	−	2.46791i	−0.449148	−	0.135854i
$331$	14.8051	−	25.6432i	0.813762	−	1.40948i	−0.0964521	−	0.995338i	$-0.530749\pi$
$331$	14.8051	−	25.6432i	0.813762	−	1.40948i	0.910214	−	0.414139i	$-0.135917\pi$
$332$	5.23058	−	5.80914i	0.287065	−	0.318818i
$333$	1.00823	−	9.59266i	0.0552506	−	0.525674i
$334$	−1.01383	−	9.64597i	−0.0554744	−	0.527804i
$335$	−11.1128	+	34.2016i	−0.607156	+	1.86863i
$336$	−2.43503	−	1.03471i	−0.132842	−	0.0564482i
$337$	−19.4715	+	14.1468i	−1.06068	+	0.770628i	−0.974214	−	0.225627i	$-0.927557\pi$
$337$	−19.4715	+	14.1468i	−1.06068	+	0.770628i	−0.0864643	+	0.996255i	$0.527557\pi$
$338$	−15.8207	+	7.04382i	−0.860531	+	0.383133i
$339$	7.60871	−	8.45033i	0.413248	−	0.458959i
$340$	2.81479	+	4.87537i	0.152654	+	0.264404i
$341$	−16.4975	+	2.07563i	−0.893392	+	0.112402i
$342$	2.57611			0.139300
$343$	18.4960	−	0.947952i	0.998689	−	0.0511846i
$344$	1.98925	+	1.44527i	0.107253	+	0.0779239i
$345$	2.08749	+	19.8611i	0.112387	+	1.06929i
$346$	4.97448	−	1.05736i	0.267430	−	0.0568439i
$347$	6.76539	−	1.43803i	0.363185	−	0.0771974i	−0.0227047	−	0.999742i	$-0.507228\pi$
$347$	6.76539	−	1.43803i	0.363185	−	0.0771974i	0.385890	+	0.922545i	$0.373894\pi$
$348$	−0.821956	−	7.82039i	−0.0440615	−	0.419217i
$349$	−4.06684	−	2.95473i	−0.217693	−	0.158163i	0.473595	−	0.880743i	$-0.342956\pi$
$349$	−4.06684	−	2.95473i	−0.217693	−	0.158163i	−0.691287	+	0.722580i	$0.742956\pi$
$350$	4.13977	−	0.954065i	0.221280	−	0.0509969i
$351$	5.50617			0.293898
$352$	−0.623125	+	3.25756i	−0.0332127	+	0.173629i
$353$	11.4142	+	19.7700i	0.607518	+	1.05225i	0.991648	+	0.128973i	$0.0411682\pi$
$353$	11.4142	+	19.7700i	0.607518	+	1.05225i	−0.384130	+	0.923279i	$0.625498\pi$
$354$	4.62096	−	5.13209i	0.245601	−	0.272768i
$355$	12.0475	−	5.36387i	0.639412	−	0.284685i
$356$	−13.7831	+	10.0140i	−0.730505	+	0.530743i
$357$	4.62957	−	3.48584i	0.245023	−	0.184490i
$358$	5.57820	−	17.1679i	0.294817	−	0.907354i
$359$	1.54431	+	14.6931i	0.0815055	+	0.775473i	0.956577	+	0.291479i	$0.0941475\pi$
$359$	1.54431	+	14.6931i	0.0815055	+	0.775473i	−0.875072	+	0.483993i	$0.839186\pi$
$360$	−0.268654	+	2.55608i	−0.0141593	+	0.134717i
$361$	−8.27290	+	9.18799i	−0.435416	+	0.483578i
$362$	7.80349	−	13.5160i	0.410142	−	0.710387i
$363$	10.9908	−	0.449488i	0.576868	−	0.0235920i
$364$	−13.2054	+	6.15161i	−0.692152	+	0.322432i
$365$	−9.24989	−	28.4682i	−0.484161	−	1.49010i
$366$	0.488479	−	0.217485i	0.0255332	−	0.0113681i
$367$	−0.409478	−	0.182311i	−0.0213746	−	0.00951657i	0.396022	−	0.918241i	$-0.370391\pi$
$367$	−0.409478	−	0.182311i	−0.0213746	−	0.00951657i	−0.417396	+	0.908725i	$0.637057\pi$
$368$	7.60036	−	1.61551i	0.396196	−	0.0842141i
$369$	−4.29790	−	4.77330i	−0.223740	−	0.248488i
$370$	20.0559	−	14.5715i	1.04266	−	0.757534i
$371$	13.7311	+	2.67453i	0.712883	+	0.138855i
$372$	1.54923	+	4.76804i	0.0803238	+	0.247211i
$373$	11.4865	−	19.8952i	0.594750	−	1.03014i	−0.398832	−	0.917024i	$-0.630584\pi$
$373$	11.4865	−	19.8952i	0.594750	−	1.03014i	0.993582	−	0.113113i	$-0.0360822\pi$
$374$	−5.49688	−	4.74965i	−0.284237	−	0.245598i
$375$	4.36194	+	7.55510i	0.225250	+	0.390144i
$376$	11.8979	+	2.52898i	0.613588	+	0.130422i
$377$	−35.0285	−	25.4497i	−1.80406	−	1.31073i
$378$	2.64537	−	0.0451581i	0.136063	−	0.00232268i
$379$	−5.91148	+	18.1937i	−0.303652	+	0.934546i	0.676524	+	0.736420i	$0.263485\pi$
$379$	−5.91148	+	18.1937i	−0.303652	+	0.934546i	−0.980177	+	0.198126i	$0.936515\pi$
$380$	4.43032	+	4.92037i	0.227270	+	0.252409i
$381$	−2.52809	−	1.12558i	−0.129518	−	0.0576651i
$382$	−0.619757	+	5.89660i	−0.0317095	+	0.301696i
$383$	2.63953	+	0.561049i	0.134873	+	0.0286682i	0.274854	−	0.961486i	$-0.411371\pi$
$383$	2.63953	+	0.561049i	0.134873	+	0.0286682i	−0.139980	+	0.990154i	$0.544704\pi$
$384$	1.00000			0.0510310
$385$	−19.0949	+	12.0010i	−0.973167	+	0.611625i
$386$	−8.97690			−0.456912
$387$	−2.40511	−	0.511222i	−0.122259	−	0.0259869i
$388$	0.816866	−	7.77196i	0.0414701	−	0.394561i
$389$	14.0144	+	6.23962i	0.710560	+	0.316362i	0.729998	−	0.683450i	$-0.239521\pi$
$389$	14.0144	+	6.23962i	0.710560	+	0.316362i	−0.0194381	+	0.999811i	$0.506188\pi$
$390$	9.46934	+	10.5168i	0.479499	+	0.532537i
$391$	−5.25932	+	16.1865i	−0.265975	+	0.818587i
$392$	−6.29392	+	3.06376i	−0.317891	+	0.154743i
$393$	0.643896	+	0.467818i	0.0324803	+	0.0235983i
$394$	−12.2127	−	2.59589i	−0.615268	−	0.130779i
$395$	2.65469	+	4.59805i	0.133572	+	0.231353i
$396$	−0.755717	−	3.22938i	−0.0379762	−	0.162282i
$397$	−9.53844	+	16.5211i	−0.478721	+	0.829168i	−0.999702	−	0.0243994i	$-0.992233\pi$
$397$	−9.53844	+	16.5211i	−0.478721	+	0.829168i	0.520982	+	0.853568i	$0.325566\pi$
$398$	−1.05861	−	3.25806i	−0.0530632	−	0.163312i
$399$	4.47351	−	5.14219i	0.223956	−	0.257432i
$400$	−1.29904	+	0.943807i	−0.0649520	+	0.0471904i
$401$	18.8640	+	20.9506i	0.942022	+	1.04622i	0.998855	+	0.0478378i	$0.0152330\pi$
$401$	18.8640	+	20.9506i	0.942022	+	1.04622i	−0.0568331	+	0.998384i	$0.518100\pi$
$402$	−13.6863	+	2.90911i	−0.682609	+	0.145093i
$403$	25.2181	+	11.2278i	1.25620	+	0.559298i
$404$	8.61892	−	3.83739i	0.428807	−	0.190917i
$405$	−0.794222	−	2.44436i	−0.0394652	−	0.121461i
$406$	−17.0377	−	11.9397i	−0.845566	−	0.592556i
$407$	−18.2707	+	26.2597i	−0.905646	+	1.30165i
$408$	−1.09518	+	1.89691i	−0.0542197	+	0.0939113i
$409$	−6.27448	+	6.96851i	−0.310253	+	0.344571i	−0.878025	−	0.478615i	$-0.841139\pi$
$409$	−6.27448	+	6.96851i	−0.310253	+	0.344571i	0.567772	+	0.823186i	$0.307806\pi$
$410$	1.72560	−	16.4180i	0.0852212	−	0.810825i
$411$	1.49345	+	14.2093i	0.0736667	+	0.700891i
$412$	−1.52824	+	4.70345i	−0.0752912	+	0.231722i
$413$	−2.21974	−	18.1360i	−0.109226	−	0.892414i
$414$	−6.28619	+	4.56718i	−0.308949	+	0.224465i
$415$	−18.3539	+	8.17168i	−0.900957	+	0.401132i
$416$	3.68435	−	4.09188i	0.180640	−	0.200621i
$417$	−0.285534	−	0.494559i	−0.0139827	−	0.0242187i
$418$	−7.48507	−	4.11989i	−0.366107	−	0.201511i
$419$	−33.0616			−1.61516			−0.807582	−	0.589756i	$-0.799224\pi$
$419$	−33.0616			−1.61516			−0.807582	+	0.589756i	$0.799224\pi$
$420$	4.63567	+	4.97498i	0.226198	+	0.242754i
$421$	20.6547	+	15.0065i	1.00665	+	0.731373i	0.963503	−	0.267696i	$-0.0862623\pi$
$421$	20.6547	+	15.0065i	1.00665	+	0.731373i	0.0431448	+	0.999069i	$0.486262\pi$
$422$	−2.23797	−	21.2929i	−0.108943	−	1.03652i
$423$	−11.8979	+	2.52898i	−0.578496	+	0.122963i
$424$	−5.17186	+	1.09931i	−0.251168	+	0.0533873i
$425$	−0.367635	−	3.49781i	−0.0178329	−	0.169669i
$426$	4.15110	+	3.01595i	0.201121	+	0.146123i
$427$	0.414138	−	1.35273i	0.0200416	−	0.0654630i
$428$	4.84990			0.234429
$429$	−15.9986	−	8.80585i	−0.772418	−	0.425150i
$430$	−3.15981	−	5.47294i	−0.152379	−	0.263929i
$431$	5.98389	−	6.64578i	0.288234	−	0.320116i	−0.581587	−	0.813484i	$-0.697568\pi$
$431$	5.98389	−	6.64578i	0.288234	−	0.320116i	0.869820	+	0.493368i	$0.164235\pi$
$432$	−0.913545	+	0.406737i	−0.0439530	+	0.0195691i
$433$	−3.52418	+	2.56047i	−0.169361	+	0.123048i	−0.669237	−	0.743049i	$-0.733379\pi$
$433$	−3.52418	+	2.56047i	−0.169361	+	0.123048i	0.499876	+	0.866097i	$0.333379\pi$
$434$	12.2078	+	5.18744i	0.585993	+	0.249005i
$435$	−6.24534	+	19.2212i	−0.299441	+	0.921585i
$436$	−1.82588	−	17.3721i	−0.0874438	−	0.831973i
$437$	−2.09232	+	19.9071i	−0.100089	+	0.952287i
$438$	7.79302	−	8.65502i	0.372365	−	0.413553i
$439$	−17.3144	+	29.9894i	−0.826370	+	1.43132i	0.0744974	+	0.997221i	$0.476265\pi$
$439$	−17.3144	+	29.9894i	−0.826370	+	1.43132i	−0.900868	+	0.434094i	$0.857069\pi$
$440$	4.86845	−	6.99721i	0.232094	−	0.333579i
$441$	4.50363	−	5.35885i	0.214459	−	0.255183i
$442$	3.72691	+	11.4703i	0.177271	+	0.545584i
$443$	20.7247	−	9.22723i	0.984660	−	0.438399i	0.149713	−	0.988729i	$-0.452165\pi$
$443$	20.7247	−	9.22723i	0.984660	−	0.438399i	0.834947	+	0.550330i	$0.185498\pi$
$444$	8.81160	+	3.92318i	0.418180	+	0.186186i
$445$	42.8306	−	9.10393i	2.03037	−	0.431568i
$446$	−3.68431	−	4.09184i	−0.174457	−	0.193754i
$447$	9.24666	−	6.71809i	0.437352	−	0.317755i
$448$	1.73654	−	1.99611i	0.0820436	−	0.0943072i
$449$	5.99195	+	18.4413i	0.282778	+	0.870301i	0.987056	+	0.160376i	$0.0512708\pi$
$449$	5.99195	+	18.4413i	0.282778	+	0.870301i	−0.704278	+	0.709924i	$0.748729\pi$
$450$	0.802850	−	1.39058i	0.0378467	−	0.0655525i
$451$	4.85405	+	20.7427i	0.228568	+	0.976734i
$452$	5.68552	+	9.84761i	0.267424	+	0.463193i
$453$	−4.51338	−	0.959348i	−0.212057	−	0.0450741i
$454$	5.98428	+	4.34783i	0.280856	+	0.204054i
$455$	37.4365	−	0.639064i	1.75505	−	0.0299598i
$456$	−0.796062	+	2.45003i	−0.0372790	+	0.114733i
$457$	5.74845	+	6.38430i	0.268901	+	0.298645i	0.862439	−	0.506161i	$-0.168936\pi$
$457$	5.74845	+	6.38430i	0.268901	+	0.298645i	−0.593538	+	0.804806i	$0.702269\pi$
$458$	24.2754	+	10.8081i	1.13431	+	0.505029i
$459$	0.228956	−	2.17837i	0.0106867	−	0.101678i
$460$	−19.5341	−	4.15210i	−0.910783	−	0.193593i
$461$	25.6335			1.19387			0.596936	−	0.802289i	$-0.296385\pi$
$461$	25.6335			1.19387			0.596936	+	0.802289i	$0.296385\pi$
$462$	−7.75852	−	4.09944i	−0.360959	−	0.190723i
$463$	15.7912			0.733880			0.366940	−	0.930245i	$-0.380405\pi$
$463$	15.7912			0.733880			0.366940	+	0.930245i	$0.380405\pi$
$464$	7.69163	+	1.63491i	0.357075	+	0.0758986i
$465$	1.34688	−	12.8147i	0.0624598	−	0.594266i
$466$	−1.94700	−	0.866859i	−0.0901929	−	0.0401565i
$467$	5.06616	+	5.62654i	0.234434	+	0.260365i	0.848870	−	0.528601i	$-0.177283\pi$
$467$	5.06616	+	5.62654i	0.234434	+	0.260365i	−0.614436	+	0.788966i	$0.710617\pi$
$468$	−1.70150	+	5.23668i	−0.0786518	+	0.242065i
$469$	−17.9598	+	32.3710i	−0.829308	+	1.49476i
$470$	−25.2920	−	18.3757i	−1.16663	−	0.847609i
$471$	13.3319	+	2.83378i	0.614300	+	0.130574i
$472$	3.45296	+	5.98069i	0.158935	+	0.275284i
$473$	6.17064	+	5.33182i	0.283726	+	0.245157i
$474$	−1.03289	+	1.78902i	−0.0474422	+	0.0821722i
$475$	−1.27824	−	3.93401i	−0.0586495	−	0.180505i
$476$	1.88462	+	5.48017i	0.0863813	+	0.251183i
$477$	4.27760	−	3.10786i	0.195858	−	0.142299i
$478$	4.34231	+	4.82262i	0.198613	+	0.220582i
$479$	−35.9962	+	7.65123i	−1.64471	+	0.349594i	−0.934930	−	0.354831i	$-0.884538\pi$
$479$	−35.9962	+	7.65123i	−1.64471	+	0.349594i	−0.709779	+	0.704425i	$0.751205\pi$
$480$	−2.34795	−	1.04538i	−0.107169	−	0.0477147i
$481$	48.5182	−	21.6017i	2.21224	−	0.984952i
$482$	4.21761	+	12.9805i	0.192107	+	0.591244i
$483$	−1.79961	+	20.4790i	−0.0818851	+	0.931826i
$484$	−2.96886	+	10.5918i	−0.134948	+	0.481445i
$485$	−10.0426	+	17.3943i	−0.456010	+	0.789833i
$486$	0.669131	−	0.743145i	0.0303524	−	0.0337097i
$487$	−4.21352	+	40.0889i	−0.190933	+	1.81660i	0.309580	+	0.950873i	$0.399811\pi$
$487$	−4.21352	+	40.0889i	−0.190933	+	1.81660i	−0.500513	+	0.865729i	$0.666855\pi$
$488$	0.0558921	+	0.531778i	0.00253012	+	0.0240724i
$489$	3.40427	−	10.4773i	0.153946	−	0.473798i
$490$	17.9806	−	0.614060i	0.812281	−	0.0277404i
$491$	−10.4090	+	7.56261i	−0.469753	+	0.341296i	−0.797345	−	0.603524i	$-0.793763\pi$
$491$	−10.4090	+	7.56261i	−0.469753	+	0.341296i	0.327592	+	0.944819i	$0.393763\pi$
$492$	5.86780	−	2.61251i	0.264541	−	0.117781i
$493$	−11.5250	+	12.7998i	−0.519061	+	0.576476i
$494$	7.09225	+	12.2841i	0.319095	+	0.552689i
$495$	−1.60153	+	8.37244i	−0.0719834	+	0.376313i
$496$	−5.01341			−0.225109
$497$	13.2287	−	3.04873i	0.593388	−	0.136754i
$498$	−6.32406	−	4.59470i	−0.283388	−	0.205894i
$499$	2.83565	+	26.9794i	0.126941	+	1.20776i	0.853661	+	0.520830i	$0.174377\pi$
$499$	2.83565	+	26.9794i	0.126941	+	1.20776i	−0.726720	+	0.686934i	$0.758956\pi$
$500$	−8.53324	+	1.81380i	−0.381618	+	0.0811154i
$501$	−9.48715	+	2.01656i	−0.423855	+	0.0900931i
$502$	1.11753	+	10.6326i	0.0498776	+	0.474554i
$503$	19.7965	+	14.3830i	0.882684	+	0.641307i	0.933960	−	0.357377i	$-0.116329\pi$
$503$	19.7965	+	14.3830i	0.882684	+	0.641307i	−0.0512764	+	0.998684i	$0.516329\pi$
$504$	−0.774515	+	2.52985i	−0.0344996	+	0.112688i
$505$	−24.2484			−1.07904
$506$	25.5691	−	3.21696i	1.13669	−	0.143011i
$507$	8.65894	+	14.9977i	0.384557	+	0.666073i
$508$	1.85171	−	2.05653i	0.0821564	−	0.0912440i
$509$	18.7297	−	8.33901i	0.830181	−	0.369620i	0.0527647	−	0.998607i	$-0.483197\pi$
$509$	18.7297	−	8.33901i	0.830181	−	0.369620i	0.777416	+	0.628987i	$0.216530\pi$
$510$	4.55443	−	3.30899i	0.201674	−	0.146524i
$511$	−3.74349	−	30.5854i	−0.165602	−	1.35302i
$512$	−0.309017	+	0.951057i	−0.0136568	+	0.0420312i
$513$	−0.269277	−	2.56200i	−0.0118889	−	0.113115i
$514$	0.709544	−	6.75086i	0.0312966	−	0.297768i
$515$	8.50512	−	9.44590i	0.374781	−	0.416236i
$516$	1.22942	−	2.12942i	0.0541223	−	0.0937426i
$517$	38.6147	+	11.6798i	1.69827	+	0.513679i
$518$	23.1327	−	10.7762i	1.01639	−	0.473477i
$519$	−1.57154	−	4.83670i	−0.0689830	−	0.212308i
$520$	−12.9282	+	5.75602i	−0.566940	+	0.252418i
$521$	−16.4954	−	7.34421i	−0.722675	−	0.321756i	0.0122303	−	0.999925i	$-0.496107\pi$
$521$	−16.4954	−	7.34421i	−0.722675	−	0.321756i	−0.734906	+	0.678169i	$0.762774\pi$
$522$	−7.69163	+	1.63491i	−0.336654	+	0.0715579i
$523$	15.7038	+	17.4409i	0.686681	+	0.762636i	0.981197	−	0.193010i	$-0.0618251\pi$
$523$	15.7038	+	17.4409i	0.686681	+	0.762636i	−0.294516	+	0.955647i	$0.595158\pi$
$524$	−0.643896	+	0.467818i	−0.0281287	+	0.0204367i
$525$	−1.38156	−	4.01736i	−0.0602963	−	0.175332i
$526$	−1.32549	−	4.07944i	−0.0577942	−	0.177872i
$527$	5.49061	−	9.51001i	0.239175	−	0.414263i
$528$	3.30485	+	0.279204i	0.143825	+	0.0121508i
$529$	−18.6877	−	32.3680i	−0.812508	−	1.40731i
$530$	13.2925	+	2.82540i	0.577389	+	0.122728i
$531$	−5.58700	−	4.05919i	−0.242455	−	0.176154i
$532$	3.50812	+	5.84358i	0.152096	+	0.253352i
$533$	10.9289	−	33.6358i	0.473384	−	1.45693i
$534$	11.3999	+	12.6609i	0.493322	+	0.547890i
$535$	−11.3873	−	5.06997i	−0.492318	−	0.219194i
$536$	1.46257	−	13.9154i	0.0631732	−	0.601053i
$537$	−17.6570	−	3.75311i	−0.761955	−	0.161958i
$538$	−2.42318			−0.104471
$539$	−21.6559	+	8.36799i	−0.932784	+	0.360435i
$540$	2.57016			0.110602
$541$	−14.6346	−	3.11068i	−0.629191	−	0.133739i	−0.117731	−	0.993046i	$-0.537562\pi$
$541$	−14.6346	−	3.11068i	−0.629191	−	0.133739i	−0.511460	+	0.859307i	$0.670895\pi$
$542$	0.544917	−	5.18454i	0.0234062	−	0.222695i
$543$	−14.2577	−	6.34793i	−0.611856	−	0.272416i
$544$	−1.46564	−	1.62776i	−0.0628389	−	0.0697897i
$545$	−13.8733	+	42.6976i	−0.594267	+	1.82897i
$546$	7.49825	+	12.4901i	0.320895	+	0.534525i
$547$	−32.3415	−	23.4974i	−1.38282	−	1.00468i	−0.996610	−	0.0822677i	$-0.973784\pi$
$547$	−32.3415	−	23.4974i	−1.38282	−	1.00468i	−0.386211	−	0.922411i	$-0.626216\pi$
$548$	−13.9753	−	2.97055i	−0.596996	−	0.126895i
$549$	−0.267353	−	0.463070i	−0.0114104	−	0.0197633i
$550$	−4.55665	+	2.75645i	−0.194296	+	0.117535i
$551$	−10.1286	+	17.5432i	−0.431492	+	0.747366i
$552$	−2.40111	−	7.38986i	−0.102198	−	0.314533i
$553$	1.77742	+	5.16845i	0.0755835	+	0.219785i
$554$	−17.7076	+	12.8653i	−0.752323	+	0.546595i
$555$	−16.5880	−	18.4229i	−0.704123	−	0.782008i
$556$	0.558589	−	0.118732i	0.0236894	−	0.00503534i
$557$	6.83898	+	3.04491i	0.289777	+	0.129017i	0.546477	−	0.837474i	$-0.315969\pi$
$557$	6.83898	+	3.04491i	0.289777	+	0.129017i	−0.256700	+	0.966491i	$0.582635\pi$
$558$	4.57998	−	2.03914i	0.193886	−	0.0863236i
$559$	−4.18372	−	12.8762i	−0.176953	−	0.544604i
$560$	−6.16399	+	2.87143i	−0.260476	+	0.121340i
$561$	−4.14905	+	5.96324i	−0.175173	+	0.251768i
$562$	7.21852	−	12.5028i	0.304495	−	0.527400i
$563$	−20.7572	+	23.0532i	−0.874810	+	0.971575i	−0.999788	−	0.0205842i	$-0.993447\pi$
$563$	−20.7572	+	23.0532i	−0.874810	+	0.971575i	0.124978	+	0.992160i	$0.460114\pi$
$564$	1.27146	−	12.0971i	0.0535379	−	0.509379i
$565$	−3.05488	−	29.0652i	−0.128520	−	1.22278i
$566$	4.63255	−	14.2575i	0.194720	−	0.599288i
$567$	−0.321427	−	2.62615i	−0.0134987	−	0.110288i
$568$	−4.15110	+	3.01595i	−0.174176	+	0.126546i
$569$	−12.0426	+	5.36171i	−0.504852	+	0.224775i	−0.643327	−	0.765591i	$-0.722446\pi$
$569$	−12.0426	+	5.36171i	−0.504852	+	0.224775i	0.138475	+	0.990366i	$0.455780\pi$
$570$	4.43032	−	4.92037i	0.185566	−	0.206091i
$571$	−17.8562	−	30.9279i	−0.747260	−	1.29429i	−0.949131	−	0.314880i	$-0.898036\pi$
$571$	−17.8562	−	30.9279i	−0.747260	−	1.29429i	0.201871	−	0.979412i	$-0.435298\pi$
$572$	13.3187	−	12.4944i	0.556882	−	0.522416i
$573$	5.92908			0.247691
$574$	4.97480	−	16.2495i	0.207644	−	0.678240i
$575$	10.0937	+	7.33353i	0.420938	+	0.305829i
$576$	−0.104528	−	0.994522i	−0.00435535	−	0.0414384i
$577$	−19.6707	+	4.18114i	−0.818902	+	0.174063i	−0.598270	−	0.801294i	$-0.704145\pi$
$577$	−19.6707	+	4.18114i	−0.818902	+	0.174063i	−0.220632	+	0.975357i	$0.570812\pi$
$578$	−11.9356	+	2.53700i	−0.496457	+	0.105525i
$579$	0.938341	+	8.92772i	0.0389961	+	0.371023i
$580$	−16.3505	−	11.8793i	−0.678918	−	0.493263i
$581$	−20.1535	+	4.64464i	−0.836107	+	0.192692i
$582$	−7.81477			−0.323933
$583$	−17.3992	+	2.18906i	−0.720599	+	0.0906617i
$584$	5.82324	+	10.0861i	0.240967	+	0.417368i
$585$	9.46934	−	10.5168i	0.391509	−	0.434815i
$586$	−16.7884	+	7.47466i	−0.693520	+	0.308775i
$587$	−14.3894	+	10.4545i	−0.593914	+	0.431504i	−0.843714	−	0.536794i	$-0.819635\pi$
$587$	−14.3894	+	10.4545i	−0.593914	+	0.431504i	0.249799	+	0.968298i	$0.419635\pi$
$588$	3.70487	+	5.93919i	0.152786	+	0.244928i
$589$	3.99099	−	12.2830i	0.164446	−	0.506112i
$590$	−1.85530	−	17.6520i	−0.0763816	−	0.726723i
$591$	−1.30510	+	12.4172i	−0.0536845	+	0.510774i
$592$	−6.45410	+	7.16800i	−0.265262	+	0.294603i
$593$	10.1873	−	17.6449i	0.418341	−	0.724588i	−0.577431	−	0.816439i	$-0.695945\pi$
$593$	10.1873	−	17.6449i	0.418341	−	0.724588i	0.995773	+	0.0918508i	$0.0292783\pi$
$594$	−3.13269	+	1.08914i	−0.128536	+	0.0446879i
$595$	1.30384	−	14.8373i	0.0534523	−	0.608270i
$596$	3.53191	+	10.8701i	0.144673	+	0.445257i
$597$	−3.12956	+	1.39337i	−0.128084	+	0.0570268i
$598$	−39.0849	−	17.4017i	−1.59830	−	0.711610i
$599$	7.04264	−	1.49696i	0.287755	−	0.0611641i	−0.0617730	−	0.998090i	$-0.519675\pi$
$599$	7.04264	−	1.49696i	0.287755	−	0.0611641i	0.349527	+	0.936926i	$0.386342\pi$
$600$	1.07442	+	1.19327i	0.0438632	+	0.0487150i
$601$	0.316670	−	0.230074i	0.0129172	−	0.00938492i	−0.581308	−	0.813684i	$-0.697459\pi$
$601$	0.316670	−	0.230074i	0.0129172	−	0.00938492i	0.594225	+	0.804299i	$0.297459\pi$
$602$	−2.11562	−	6.15188i	−0.0862261	−	0.250732i
$603$	4.32378	+	13.3072i	0.176078	+	0.541912i
$604$	2.30710	−	3.99602i	0.0938747	−	0.162596i
$605$	18.0431	−	21.7654i	0.733558	−	0.884891i
$606$	−4.71729	−	8.17059i	−0.191627	−	0.331908i
$607$	24.8832	+	5.28908i	1.00998	+	0.214677i	0.683050	−	0.730372i	$-0.260653\pi$
$607$	24.8832	+	5.28908i	1.00998	+	0.214677i	0.326928	+	0.945049i	$0.393987\pi$
$608$	−2.08412	−	1.51420i	−0.0845221	−	0.0614089i
$609$	−10.0933	+	18.1924i	−0.409003	+	0.737193i
$610$	0.424676	−	1.30702i	0.0171946	−	0.0529196i
$611$	−44.8154	−	49.7725i	−1.81304	−	2.01358i
$612$	2.00100	+	0.890903i	0.0808857	+	0.0360126i
$613$	3.73082	−	35.4964i	0.150687	−	1.43369i	−0.614011	−	0.789297i	$-0.710445\pi$
$613$	3.73082	−	35.4964i	0.150687	−	1.43369i	0.764698	−	0.644389i	$-0.222888\pi$
$614$	−1.78144	−	0.378656i	−0.0718929	−	0.0152813i
$615$	−16.5084			−0.665683
$616$	6.29632	−	6.11199i	0.253686	−	0.246259i
$617$	11.5520			0.465067			0.232534	−	0.972588i	$-0.425298\pi$
$617$	11.5520			0.465067			0.232534	+	0.972588i	$0.425298\pi$
$618$	4.83743	+	1.02823i	0.194590	+	0.0413614i
$619$	0.788427	−	7.50138i	0.0316896	−	0.301506i	−0.967185	−	0.254074i	$-0.918229\pi$
$619$	0.788427	−	7.50138i	0.0316896	−	0.301506i	0.998874	−	0.0474324i	$-0.0151039\pi$
$620$	11.7713	+	5.24090i	0.472745	+	0.210480i
$621$	5.19925	+	5.77435i	0.208639	+	0.231717i
$622$	−5.60600	+	17.2535i	−0.224780	+	0.691802i
$623$	45.0688	−	0.769354i	1.80564	−	0.0308235i
$624$	−4.45458	−	3.23644i	−0.178326	−	0.129561i
$625$	29.7848	+	6.33096i	1.19139	+	0.253238i
$626$	4.24404	+	7.35089i	0.169626	+	0.293801i
$627$	−3.31492	+	7.87471i	−0.132385	+	0.314486i
$628$	−6.81486	+	11.8037i	−0.271942	+	0.471018i
$629$	−6.52866	−	20.0932i	−0.260315	−	0.801167i
$630$	4.46317	−	5.13031i	0.177817	−	0.204396i
$631$	15.0689	−	10.9482i	0.599883	−	0.435841i	−0.245954	−	0.969281i	$-0.579101\pi$
$631$	15.0689	−	10.9482i	0.599883	−	0.435841i	0.845837	+	0.533441i	$0.179101\pi$
$632$	−1.38228	−	1.53517i	−0.0549840	−	0.0610659i
$633$	−20.9423	+	4.45142i	−0.832381	+	0.176928i
$634$	−10.7634	−	4.79215i	−0.427467	−	0.190321i
$635$	−6.49759	+	2.89291i	−0.257849	+	0.114802i
$636$	1.63390	+	5.02862i	0.0647882	+	0.199398i
$637$	37.9525	+	6.72213i	1.50373	+	0.266340i
$638$	24.9632	+	7.55066i	0.988304	+	0.298933i
$639$	2.56552	−	4.44361i	0.101490	−	0.175787i
$640$	1.71977	−	1.91000i	0.0679799	−	0.0754993i
$641$	0.337438	−	3.21051i	0.0133280	−	0.126808i	−0.985835	−	0.167720i	$-0.946360\pi$
$641$	0.337438	−	3.21051i	0.0133280	−	0.126808i	0.999163	+	0.0409121i	$0.0130264\pi$
$642$	−0.506953	−	4.82333i	−0.0200078	−	0.190362i
$643$	−4.92364	+	15.1534i	−0.194169	+	0.597592i	0.805816	+	0.592166i	$0.201727\pi$
$643$	−4.92364	+	15.1534i	−0.194169	+	0.597592i	−0.999985	+	0.00542559i	$0.998273\pi$
$644$	−18.9206	−	8.03989i	−0.745575	−	0.316816i
$645$	−5.11267	+	3.71457i	−0.201311	+	0.146261i
$646$	5.15480	−	2.29506i	0.202813	−	0.0902981i
$647$	14.0218	−	15.5728i	0.551254	−	0.612230i	−0.401542	−	0.915841i	$-0.631526\pi$
$647$	14.0218	−	15.5728i	0.551254	−	0.612230i	0.952796	+	0.303611i	$0.0981923\pi$
$648$	0.500000	+	0.866025i	0.0196419	+	0.0340207i
$649$	9.74168	+	20.7294i	0.382394	+	0.813700i
$650$	8.84126			0.346783
$651$	3.88296	−	12.6832i	0.152185	−	0.497092i
$652$	8.91250	+	6.47531i	0.349040	+	0.253593i
$653$	1.60473	+	15.2679i	0.0627977	+	0.597481i	0.979992	+	0.199039i	$0.0637821\pi$
$653$	1.60473	+	15.2679i	0.0627977	+	0.597481i	−0.917194	+	0.398441i	$0.869551\pi$
$654$	−17.0861	+	3.63176i	−0.668118	+	0.142013i
$655$	2.00088	−	0.425301i	0.0781810	−	0.0166179i
$656$	0.671398	+	6.38792i	0.0262137	+	0.249407i
$657$	−9.42220	−	6.84563i	−0.367595	−	0.267073i
$658$	−21.9391	−	23.5450i	−0.855277	−	0.917879i
$659$	36.6357			1.42712			0.713562	−	0.700592i	$-0.247081\pi$
$659$	36.6357			1.42712			0.713562	+	0.700592i	$0.247081\pi$
$660$	−7.46777	−	4.11037i	−0.290682	−	0.159996i
$661$	11.5300	+	19.9705i	0.448465	+	0.776764i	0.998286	−	0.0585183i	$-0.0186376\pi$
$661$	11.5300	+	19.9705i	0.448465	+	0.776764i	−0.549821	+	0.835282i	$0.685304\pi$
$662$	19.8131	−	22.0047i	0.770057	−	0.855235i
$663$	11.0178	−	4.90546i	0.427898	−	0.190512i
$664$	6.32406	−	4.59470i	0.245421	−	0.178309i
$665$	−2.12817	−	17.3878i	−0.0825268	−	0.674269i
$666$	2.98062	−	9.17341i	0.115497	−	0.355463i
$667$	−6.38673	−	60.7657i	−0.247295	−	2.35286i
$668$	1.01383	−	9.64597i	0.0392263	−	0.373214i
$669$	−3.68431	+	4.09184i	−0.142444	+	0.158200i
$670$	−17.9809	+	31.1438i	−0.694661	+	1.20319i
$671$	0.0362408	+	1.77305i	0.00139906	+	0.0684479i
$672$	−2.16669	−	1.51837i	−0.0835819	−	0.0585725i
$673$	−0.730761	−	2.24905i	−0.0281688	−	0.0866946i	0.935984	−	0.352043i	$-0.114513\pi$
$673$	−0.730761	−	2.24905i	−0.0281688	−	0.0866946i	−0.964153	+	0.265349i	$0.914513\pi$
$674$	−21.9873	+	9.78936i	−0.846917	+	0.377072i
$675$	−1.46688	−	0.653097i	−0.0564603	−	0.0251377i
$676$	−16.9395	+	3.60059i	−0.651517	+	0.138484i
$677$	−26.9812	−	29.9656i	−1.03697	−	1.15167i	−0.988248	−	0.152861i	$-0.951151\pi$
$677$	−26.9812	−	29.9656i	−1.03697	−	1.15167i	−0.0487232	−	0.998812i	$-0.515515\pi$
$678$	9.19937	−	6.68373i	0.353300	−	0.256687i
$679$	−13.5706	+	15.5991i	−0.520793	+	0.598639i
$680$	1.73964	+	5.35406i	0.0667121	+	0.205319i
$681$	3.69849	−	6.40597i	0.141726	−	0.245477i
$682$	−16.5686	−	1.39976i	−0.634444	−	0.0535997i
$683$	13.4560	+	23.3065i	0.514879	+	0.891797i	0.999851	+	0.0172674i	$0.00549664\pi$
$683$	13.4560	+	23.3065i	0.514879	+	0.891797i	−0.484971	+	0.874530i	$0.661170\pi$
$684$	2.51982	+	0.535603i	0.0963476	+	0.0204793i
$685$	29.7081	+	21.5842i	1.13509	+	0.824689i
$686$	18.2889	+	2.91829i	0.698273	+	0.111421i
$687$	8.21142	−	25.2721i	0.313285	−	0.964192i
$688$	1.64529	+	1.82728i	0.0627260	+	0.0696643i
$689$	26.5963	+	11.8415i	1.01324	+	0.451123i
$690$	−2.08749	+	19.8611i	−0.0794693	+	0.756100i
$691$	4.99171	+	1.06102i	0.189893	+	0.0403631i	0.301877	−	0.953347i	$-0.402387\pi$
$691$	4.99171	+	1.06102i	0.189893	+	0.0403631i	−0.111983	+	0.993710i	$0.535720\pi$
$692$	5.08561			0.193326
$693$	−3.26600	+	8.14452i	−0.124065	+	0.309385i
$694$	6.91653			0.262548
$695$	−1.43566	−	0.305159i	−0.0544577	−	0.0115753i
$696$	0.821956	−	7.82039i	0.0311562	−	0.296431i
$697$	−12.8526	−	5.72237i	−0.486829	−	0.216750i
$698$	−3.36364	−	3.73570i	−0.127316	−	0.141398i
$699$	−0.658593	+	2.02694i	−0.0249103	+	0.0766660i
$700$	4.24767	−	0.0725104i	0.160547	−	0.00274064i
$701$	31.1517	+	22.6330i	1.17658	+	0.854838i	0.991782	−	0.127938i	$-0.0408359\pi$
$701$	31.1517	+	22.6330i	1.17658	+	0.854838i	0.184801	+	0.982776i	$0.440836\pi$
$702$	5.38585	+	1.14480i	0.203276	+	0.0432076i
$703$	−12.4239	−	21.5189i	−0.468578	−	0.811600i
$704$	−1.28679	+	3.05682i	−0.0484979	+	0.115208i
$705$	−15.6313	+	27.0743i	−0.588710	+	1.01968i
$706$	7.05438	+	21.7112i	0.265495	+	0.817110i
$707$	−24.5011	−	4.77231i	−0.921459	−	0.179481i
$708$	5.58700	−	4.05919i	0.209972	−	0.152554i
$709$	−21.2123	−	23.5586i	−0.796644	−	0.884763i	0.198806	−	0.980039i	$-0.436293\pi$
$709$	−21.2123	−	23.5586i	−0.796644	−	0.884763i	−0.995451	+	0.0952755i	$0.969627\pi$
$710$	12.8994	−	2.74185i	0.484106	−	0.102900i
$711$	1.88718	+	0.840228i	0.0707749	+	0.0315110i
$712$	−15.5640	+	6.92953i	−0.583285	+	0.259695i
$713$	12.0378	+	37.0484i	0.450818	+	1.38747i
$714$	5.25315	−	2.44713i	0.196594	−	0.0915814i
$715$	−44.3330	+	15.4132i	−1.65796	+	0.576420i
$716$	9.02572	−	15.6330i	0.337307	−	0.584233i
$717$	4.34231	−	4.82262i	0.162167	−	0.180104i
$718$	−1.54431	+	14.6931i	−0.0576331	+	0.548342i
$719$	−1.98244	−	18.8617i	−0.0739325	−	0.703421i	−0.967221	−	0.253937i	$-0.918274\pi$
$719$	−1.98244	−	18.8617i	−0.0739325	−	0.703421i	0.893288	−	0.449484i	$-0.148392\pi$
$720$	−0.794222	+	2.44436i	−0.0295989	+	0.0910960i
$721$	10.4528	−	7.87047i	0.389284	−	0.293112i
$722$	−10.0024	+	7.26717i	−0.372251	+	0.270456i
$723$	12.4685	−	5.55134i	0.463709	−	0.206456i
$724$	10.4431	−	11.5982i	0.388115	−	0.431045i
$725$	6.31319	+	10.9348i	0.234466	+	0.406107i
$726$	10.8441	+	1.84545i	0.402462	+	0.0684912i
$727$	−41.9184			−1.55467			−0.777334	−	0.629088i	$-0.783429\pi$
$727$	−41.9184			−1.55467			−0.777334	+	0.629088i	$0.783429\pi$
$728$	−14.1958	+	3.27162i	−0.526133	+	0.121254i
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$	−3.12888	−	29.7693i	−0.115805	−	1.10181i
$731$	−5.26808	+	1.11977i	−0.194847	+	0.0414160i
$732$	0.523022	−	0.111172i	0.0193315	−	0.00410903i
$733$	−0.453695	−	4.31662i	−0.0167576	−	0.159438i	0.982943	−	0.183911i	$-0.0588759\pi$
$733$	−0.453695	−	4.31662i	−0.0167576	−	0.159438i	−0.999700	+	0.0244731i	$0.992209\pi$
$734$	−0.362625	−	0.263463i	−0.0133847	−	0.00972458i
$735$	−2.49018	−	17.8179i	−0.0918517	−	0.657224i
$736$	7.77016			0.286412
$737$	8.71879	−	45.5799i	0.321161	−	1.67896i
$738$	−3.21156	−	5.56258i	−0.118219	−	0.204761i
$739$	17.6715	−	19.6262i	0.650058	−	0.721963i	−0.324553	−	0.945868i	$-0.605214\pi$
$739$	17.6715	−	19.6262i	0.650058	−	0.721963i	0.974611	+	0.223905i	$0.0718804\pi$
$740$	22.6472	−	10.0832i	0.832527	−	0.370665i
$741$	11.4755	−	8.33744i	0.421563	−	0.306283i
$742$	12.8750	+	5.47094i	0.472655	+	0.200845i
$743$	6.13132	−	18.8703i	0.224936	−	0.692283i	−0.773362	−	0.633965i	$-0.781426\pi$
$743$	6.13132	−	18.8703i	0.224936	−	0.692283i	0.998298	−	0.0583180i	$-0.0185737\pi$
$744$	0.524044	+	4.98595i	0.0192124	+	0.182794i
$745$	3.07059	−	29.2147i	0.112498	−	1.07034i
$746$	15.3720	−	17.0723i	0.562808	−	0.625062i
$747$	−3.90849	+	6.76970i	−0.143004	+	0.247690i
$748$	−4.38925	−	5.78872i	−0.160487	−	0.211657i
$749$	−10.5082	−	7.36396i	−0.383962	−	0.269073i
$750$	2.69583	+	8.29690i	0.0984377	+	0.302960i
$751$	−31.5942	+	14.0667i	−1.15289	+	0.513300i	−0.891985	−	0.452065i	$-0.850688\pi$
$751$	−31.5942	+	14.0667i	−1.15289	+	0.513300i	−0.260905	+	0.965365i	$0.584021\pi$
$752$	11.1121	+	4.94743i	0.405217	+	0.180414i
$753$	10.4575	−	2.22281i	0.381092	−	0.0810036i
$754$	−28.9717	−	32.1764i	−1.05509	−	1.17179i
$755$	−9.59432	+	6.97068i	−0.349173	+	0.253689i
$756$	2.59695	+	0.505831i	0.0944501	+	0.0183969i
$757$	6.66932	+	20.5261i	0.242401	+	0.746033i	0.996053	+	0.0887595i	$0.0282902\pi$
$757$	6.66932	+	20.5261i	0.242401	+	0.746033i	−0.753652	+	0.657273i	$0.771710\pi$
$758$	−9.56498	+	16.5670i	−0.347416	+	0.601742i
$759$	−5.87204	−	25.0928i	−0.213142	−	0.910811i
$760$	3.31050	+	5.73396i	0.120085	+	0.207993i
$761$	26.1684	+	5.56226i	0.948603	+	0.201632i	0.656135	−	0.754643i	$-0.272190\pi$
$761$	26.1684	+	5.56226i	0.948603	+	0.201632i	0.292468	+	0.956275i	$0.405523\pi$
$762$	−2.23883	−	1.62660i	−0.0811041	−	0.0589256i
$763$	−22.4212	+	40.4123i	−0.811702	+	1.46302i
$764$	−1.83219	+	5.63889i	−0.0662861	+	0.204008i
$765$	−3.76693	−	4.18360i	−0.136194	−	0.151258i
$766$	2.46520	+	1.09758i	0.0890712	+	0.0396571i
$767$	3.97471	−	37.8168i	0.143518	−	1.36549i
$768$	0.978148	+	0.207912i	0.0352959	+	0.00750237i
$769$	30.8545			1.11264			0.556320	−	0.830968i	$-0.312213\pi$
$769$	30.8545			1.11264			0.556320	+	0.830968i	$0.312213\pi$
$770$	−21.1728	+	7.76865i	−0.763014	+	0.279963i
$771$	−6.78804			−0.244465
$772$	−8.78073	−	1.86640i	−0.316025	−	0.0671733i
$773$	2.38283	−	22.6711i	0.0857044	−	0.815423i	−0.864256	−	0.503052i	$-0.832210\pi$
$773$	2.38283	−	22.6711i	0.0857044	−	0.815423i	0.949960	−	0.312370i	$-0.101123\pi$
$774$	−2.24627	−	1.00010i	−0.0807404	−	0.0359479i
$775$	−5.38653	−	5.98234i	−0.193490	−	0.214892i
$776$	2.41490	−	7.43229i	0.0866897	−	0.266804i
$777$	−13.1352	−	21.8796i	−0.471221	−	0.784927i
$778$	12.4109	+	9.01704i	0.444952	+	0.323276i
$779$	−16.1851	−	3.44024i	−0.579890	−	0.123259i
$780$	7.07585	+	12.2557i	0.253356	+	0.438826i
$781$	−14.5608	+	8.80827i	−0.521028	+	0.315185i
$782$	−8.50975	+	14.7393i	−0.304308	+	0.527077i
$783$	2.42995	+	7.47860i	0.0868392	+	0.267263i
$784$	−6.79337	+	1.68823i	−0.242620	+	0.0602940i
$785$	28.3403	−	20.5904i	1.01151	−	0.734903i
$786$	0.532561	+	0.591469i	0.0189958	+	0.0210970i
$787$	42.7975	−	9.09689i	1.52557	−	0.324269i	0.632631	−	0.774454i	$-0.281975\pi$
$787$	42.7975	−	9.09689i	1.52557	−	0.324269i	0.892936	+	0.450185i	$0.148642\pi$
$788$	−11.4061	−	5.07834i	−0.406326	−	0.180908i
$789$	−3.91854	+	1.74465i	−0.139504	+	0.0621111i
$790$	1.64069	+	5.04951i	0.0583730	+	0.179654i
$791$	2.63359	−	29.9695i	0.0936398	−	1.06559i
$792$	−0.0677770	−	3.31593i	−0.00240835	−	0.117827i
$793$	1.47209	−	2.54974i	0.0522755	−	0.0905439i
$794$	−12.7649	+	14.1769i	−0.453010	+	0.503119i
$795$	1.42048	−	13.5150i	0.0503794	−	0.479328i
$796$	−0.358086	−	3.40696i	−0.0126920	−	0.120757i
$797$	8.16433	−	25.1272i	0.289195	−	0.890051i	−0.695914	−	0.718125i	$-0.745001\pi$
$797$	8.16433	−	25.1272i	0.289195	−	0.890051i	0.985110	−	0.171927i	$-0.0549993\pi$
$798$	5.44487	−	4.09973i	0.192746	−	0.145129i
$799$	−21.5547	+	15.6604i	−0.762549	+	0.554024i
$800$	−1.46688	+	0.653097i	−0.0518621	+	0.0230905i
$801$	11.3999	−	12.6609i	0.402796	−	0.447350i
$802$	14.0959	+	24.4148i	0.497743	+	0.862116i
$803$	16.4289	+	34.9591i	0.579762	+	1.23368i
$804$	−13.9920			−0.493461
$805$	36.0199	+	38.6564i	1.26954	+	1.36246i
$806$	22.3327	+	16.2256i	0.786634	+	0.571523i
$807$	0.253291	+	2.40990i	0.00891626	+	0.0848325i
$808$	9.22842	−	1.96156i	0.324655	−	0.0690074i
$809$	−21.7572	+	4.62464i	−0.764943	+	0.162594i	−0.573830	−	0.818975i	$-0.694543\pi$
$809$	−21.7572	+	4.62464i	−0.764943	+	0.162594i	−0.191113	+	0.981568i	$0.561210\pi$
$810$	−0.268654	−	2.55608i	−0.00943955	−	0.0898114i
$811$	−30.8235	−	22.3946i	−1.08236	−	0.786379i	−0.104266	−	0.994549i	$-0.533249\pi$
$811$	−30.8235	−	22.3946i	−1.08236	−	0.786379i	−0.978093	+	0.208170i	$0.933249\pi$
$812$	−14.1830	−	15.2211i	−0.497725	−	0.534156i
$813$	−5.21310			−0.182831
$814$	−23.3312	+	21.8872i	−0.817757	+	0.767145i
$815$	−14.1570	−	24.5206i	−0.495898	−	0.858921i
$816$	−1.46564	+	1.62776i	−0.0513077	+	0.0569830i
$817$	−5.78663	+	2.57637i	−0.202449	+	0.0901359i
$818$	−7.58620	+	5.51170i	−0.265245	+	0.192712i
$819$	11.6379	−	8.76274i	0.406659	−	0.306195i
$820$	5.10137	−	15.7004i	0.178148	−	0.548282i
$821$	−2.81617	−	26.7941i	−0.0982851	−	0.935120i	−0.926902	−	0.375304i	$-0.877538\pi$
$821$	−2.81617	−	26.7941i	−0.0982851	−	0.935120i	0.828617	−	0.559816i	$-0.189128\pi$
$822$	−1.49345	+	14.2093i	−0.0520902	+	0.495605i
$823$	−15.5200	+	17.2367i	−0.540992	+	0.600833i	−0.950212	−	0.311603i	$-0.899134\pi$
$823$	−15.5200	+	17.2367i	−0.540992	+	0.600833i	0.409220	+	0.912436i	$0.365801\pi$
$824$	−2.47275	+	4.28293i	−0.0861424	+	0.149203i
$825$	3.21765	+	4.24356i	0.112024	+	0.147742i
$826$	1.59945	−	18.2012i	0.0556518	−	0.633300i
$827$	8.17060	+	25.1465i	0.284120	+	0.874431i	0.986661	+	0.162788i	$0.0520486\pi$
$827$	8.17060	+	25.1465i	0.284120	+	0.874431i	−0.702541	+	0.711643i	$0.747951\pi$
$828$	−7.09839	+	3.16041i	−0.246686	+	0.109832i
$829$	−16.3466	−	7.27798i	−0.567741	−	0.252775i	0.102731	−	0.994709i	$-0.467242\pi$
$829$	−16.3466	−	7.27798i	−0.567741	−	0.252775i	−0.670472	+	0.741934i	$0.733909\pi$
$830$	−19.6518	+	4.17712i	−0.682124	+	0.144990i
$831$	14.6458	+	16.2658i	0.508057	+	0.564254i
$832$	4.45458	−	3.23644i	0.154435	−	0.112204i
$833$	4.23756	−	14.7354i	0.146823	−	0.510550i
$834$	−0.176470	−	0.543118i	−0.00611064	−	0.0188066i
$835$	−12.4641	+	21.5885i	−0.431338	+	0.747099i
$836$	−6.46493	−	5.58610i	−0.223594	−	0.193199i
$837$	−2.50671	−	4.34174i	−0.0866444	−	0.150073i
$838$	−32.3391	−	6.87389i	−1.11714	−	0.237455i
$839$	−18.7443	−	13.6185i	−0.647123	−	0.470163i	0.215167	−	0.976577i	$-0.430971\pi$
$839$	−18.7443	−	13.6185i	−0.647123	−	0.470163i	−0.862290	+	0.506415i	$0.830971\pi$
$840$	3.50002	+	5.83008i	0.120762	+	0.201157i
$841$	10.1463	−	31.2271i	0.349872	−	1.07680i
$842$	17.0833	+	18.9729i	0.588730	+	0.653851i
$843$	−13.1889	−	5.87207i	−0.454249	−	0.202245i
$844$	2.23797	−	21.2929i	0.0770341	−	0.732931i
$845$	43.5370	+	9.25408i	1.49772	+	0.318350i
$846$	−12.1637			−0.418197
$847$	22.5149	−	18.4413i	0.773620	−	0.633649i
$848$	−5.28740			−0.181570
$849$	−14.6636	−	3.11685i	−0.503255	−	0.106970i
$850$	0.367635	−	3.49781i	0.0126098	−	0.119974i
$851$	68.4675	+	30.4837i	2.34704	+	1.04497i
$852$	3.43334	+	3.81311i	0.117624	+	0.130635i
$853$	0.671406	−	2.06638i	0.0229885	−	0.0707514i	−0.938904	−	0.344179i	$-0.888157\pi$
$853$	0.671406	−	2.06638i	0.0229885	−	0.0707514i	0.961893	+	0.273427i	$0.0881573\pi$
$854$	0.686336	−	1.23706i	0.0234859	−	0.0423314i
$855$	−5.35651	−	3.89173i	−0.183189	−	0.133094i
$856$	4.74392	+	1.00835i	0.162144	+	0.0344647i
$857$	−7.08993	−	12.2801i	−0.242188	−	0.419481i	0.719150	−	0.694855i	$-0.244532\pi$
$857$	−7.08993	−	12.2801i	−0.242188	−	0.419481i	−0.961337	+	0.275374i	$0.911198\pi$
$858$	−13.8181	−	11.9397i	−0.471743	−	0.407615i
$859$	3.13713	−	5.43366i	0.107037	−	0.185394i	−0.807531	−	0.589825i	$-0.799197\pi$
$859$	3.13713	−	5.43366i	0.107037	−	0.185394i	0.914569	+	0.404430i	$0.132530\pi$
$860$	−1.95287	−	6.01031i	−0.0665922	−	0.204950i
$861$	−16.6805	−	3.24901i	−0.568469	−	0.110726i
$862$	7.23486	−	5.25643i	0.246420	−	0.179035i
$863$	28.9670	+	32.1711i	0.986047	+	1.09512i	0.995462	+	0.0951600i	$0.0303363\pi$
$863$	28.9670	+	32.1711i	0.986047	+	1.09512i	−0.00941538	+	0.999956i	$0.502997\pi$
$864$	−0.978148	+	0.207912i	−0.0332773	+	0.00707330i
$865$	−11.9408	−	5.31638i	−0.405999	−	0.180762i
$866$	−3.97952	+	1.77180i	−0.135230	+	0.0602081i
$867$	3.77071	+	11.6051i	0.128060	+	0.394129i
$868$	10.8625	+	7.61223i	0.368697	+	0.258376i
$869$	−4.13959	−	5.45945i	−0.140426	−	0.185199i
$870$	−10.1052	+	17.5027i	−0.342597	+	0.593396i
$871$	−51.5515	+	57.2537i	−1.74676	+	1.93997i
$872$	1.82588	−	17.3721i	0.0618321	−	0.588293i
$873$	0.816866	+	7.77196i	0.0276467	+	0.263041i
$874$	−6.18553	+	19.0371i	−0.209229	+	0.643939i
$875$	21.2429	+	9.02671i	0.718141	+	0.305159i
$876$	9.42220	−	6.84563i	0.318347	−	0.231292i
$877$	−18.3885	+	8.18707i	−0.620934	+	0.276458i	−0.692995	−	0.720943i	$-0.743709\pi$
$877$	−18.3885	+	8.18707i	−0.620934	+	0.276458i	0.0720608	+	0.997400i	$0.477042\pi$
$878$	−23.1712	+	25.7342i	−0.781989	+	0.868487i
$879$	9.18857	+	15.9151i	0.309923	+	0.536802i
$880$	6.21686	−	5.83209i	0.209570	−	0.196600i
$881$	−13.4156			−0.451985			−0.225992	−	0.974129i	$-0.572562\pi$
$881$	−13.4156			−0.451985			−0.225992	+	0.974129i	$0.572562\pi$
$882$	5.51939	−	4.30539i	0.185847	−	0.144970i
$883$	27.0987	+	19.6884i	0.911944	+	0.662566i	0.941506	−	0.336997i	$-0.109411\pi$
$883$	27.0987	+	19.6884i	0.911944	+	0.662566i	−0.0295618	+	0.999563i	$0.509411\pi$
$884$	1.26067	+	11.9945i	0.0424009	+	0.403418i
$885$	−17.3614	+	3.69028i	−0.583597	+	0.124047i
$886$	22.1903	−	4.71669i	0.745497	−	0.158460i
$887$	−4.37408	−	41.6166i	−0.146867	−	1.39735i	−0.781197	−	0.624285i	$-0.785391\pi$
$887$	−4.37408	−	41.6166i	−0.146867	−	1.39735i	0.634330	−	0.773063i	$-0.281276\pi$
$888$	7.80337	+	5.66948i	0.261864	+	0.190255i
$889$	−7.13467	+	1.64428i	−0.239289	+	0.0551474i
$890$	43.7875			1.46776
$891$	1.41063	+	3.00169i	0.0472578	+	0.100560i
$892$	−2.75306	−	4.76843i	−0.0921791	−	0.159659i
$893$	−20.9673	+	23.2865i	−0.701643	+	0.779253i
$894$	10.4414	−	4.64880i	0.349212	−	0.155479i
$895$	−37.5344	+	27.2703i	−1.25464	+	0.911546i
$896$	2.11360	−	1.59144i	0.0706105	−	0.0531663i
$897$	−13.2209	+	40.6898i	−0.441434	+	1.35859i
$898$	2.02685	+	19.2841i	0.0676367	+	0.643520i
$899$	−4.12080	+	39.2068i	−0.137437	+	1.30762i
$900$	1.07442	−	1.19327i	0.0358141	−	0.0397756i
$901$	5.79068	−	10.0297i	0.192915	−	0.334139i
$902$	0.435339	+	21.2986i	0.0144952	+	0.709166i
$903$	−5.89703	+	2.74707i	−0.196241	+	0.0914169i
$904$	3.51384	+	10.8145i	0.116869	+	0.359685i
$905$	−36.6445	+	16.3152i	−1.21810	+	0.542335i
$906$	−4.21529	−	1.87677i	−0.140044	−	0.0623514i
$907$	30.9211	−	6.57248i	1.02672	−	0.218236i	0.336383	−	0.941725i	$-0.390796\pi$
$907$	30.9211	−	6.57248i	1.02672	−	0.218236i	0.690335	+	0.723490i	$0.257463\pi$
$908$	4.94954	+	5.49703i	0.164256	+	0.182425i
$909$	−7.63274	+	5.54551i	−0.253162	+	0.183933i
$910$	36.7512	+	7.15838i	1.21829	+	0.237298i
$911$	−13.6183	−	41.9129i	−0.451195	−	1.38864i	−0.875545	−	0.483137i	$-0.839497\pi$
$911$	−13.6183	−	41.9129i	−0.451195	−	1.38864i	0.424350	−	0.905498i	$-0.360503\pi$
$912$	−1.28806	+	2.23098i	−0.0426518	+	0.0738750i
$913$	22.1830	−	13.4191i	0.734149	−	0.444108i
$914$	4.29546	+	7.43996i	0.142081	+	0.246092i
$915$	−1.34425	−	0.285729i	−0.0444395	−	0.00944590i
$916$	21.4978	+	15.6190i	0.710306	+	0.516068i
$917$	2.10545	−	0.0359413i	0.0695279	−	0.00118689i
$918$	0.676861	−	2.08316i	0.0223397	−	0.0687547i
$919$	−11.1731	−	12.4090i	−0.368568	−	0.409336i	0.530122	−	0.847922i	$-0.322146\pi$
$919$	−11.1731	−	12.4090i	−0.368568	−	0.409336i	−0.898689	+	0.438586i	$0.855480\pi$
$920$	−18.2440	−	8.12274i	−0.601486	−	0.267799i
$921$	−0.190371	+	1.81126i	−0.00627293	+	0.0596830i
$922$	25.0734	+	5.32951i	0.825748	+	0.175518i
$923$	28.2524			0.929938
$924$	−6.73665	−	5.62295i	−0.221620	−	0.184981i
$925$	−15.4878			−0.509235
$926$	15.4461	+	3.28318i	0.507592	+	0.107892i
$927$	0.516946	−	4.91841i	0.0169787	−	0.161542i
$928$	7.18364	+	3.19836i	0.235814	+	0.104991i
$929$	−20.1864	−	22.4192i	−0.662293	−	0.735551i	0.314613	−	0.949220i	$-0.398125\pi$
$929$	−20.1864	−	22.4192i	−0.662293	−	0.735551i	−0.976906	+	0.213669i	$0.931459\pi$
$930$	3.98176	−	12.2546i	0.130567	−	0.401844i
$931$	1.27173	−	17.9879i	0.0416792	−	0.589529i
$932$	−1.72422	−	1.25272i	−0.0564787	−	0.0410342i
$933$	17.7450	+	3.77181i	0.580944	+	0.123483i
$934$	3.78563	+	6.55690i	0.123870	+	0.214548i
$935$	4.25438	+	18.1801i	0.139133	+	0.594552i
$936$	−2.75308	+	4.76848i	−0.0899874	+	0.155863i
$937$	15.9343	+	49.0406i	0.520550	+	1.60209i	0.772952	+	0.634465i	$0.218779\pi$
$937$	15.9343	+	49.0406i	0.520550	+	1.60209i	−0.252402	+	0.967622i	$0.581221\pi$
$938$	−24.2977	+	27.9296i	−0.793347	+	0.911934i
$939$	6.86700	−	4.98916i	0.224096	−	0.162815i
$940$	−20.9188	−	23.2327i	−0.682296	−	0.757767i
$941$	2.85828	−	0.607547i	0.0931774	−	0.0198055i	−0.161087	−	0.986940i	$-0.551500\pi$
$941$	2.85828	−	0.607547i	0.0931774	−	0.0198055i	0.254264	+	0.967135i	$0.418167\pi$
$942$	12.4514	+	5.54370i	0.405687	+	0.180624i
$943$	45.5938	−	20.2996i	1.48474	−	0.661048i
$944$	2.13404	+	6.56791i	0.0694572	+	0.213767i
$945$	−5.56873	−	3.90246i	−0.181151	−	0.126947i
$946$	4.92725	+	6.49825i	0.160199	+	0.211276i
$947$	−7.71273	+	13.3588i	−0.250630	+	0.434104i	−0.963699	−	0.266989i	$-0.913971\pi$
$947$	−7.71273	+	13.3588i	−0.250630	+	0.434104i	0.713069	+	0.701094i	$0.247304\pi$
$948$	−1.38228	+	1.53517i	−0.0448942	+	0.0498601i
$949$	6.70315	−	63.7762i	0.217593	−	2.07026i
$950$	−0.432378	−	4.11380i	−0.0140282	−	0.133469i
$951$	−3.64083	+	11.2053i	−0.118062	+	0.363357i
$952$	0.704043	+	5.75224i	0.0228182	+	0.186431i
$953$	−38.7196	+	28.1315i	−1.25425	+	0.911267i	−0.998461	−	0.0554646i	$-0.982336\pi$
$953$	−38.7196	+	28.1315i	−1.25425	+	0.911267i	−0.255791	+	0.966732i	$0.582336\pi$
$954$	4.83028	−	2.15058i	0.156386	−	0.0696276i
$955$	10.1966	−	11.3245i	0.329956	−	0.366453i
$956$	3.24474	+	5.62006i	0.104942	+	0.181766i
$957$	4.89992	−	25.6157i	0.158392	−	0.828039i
$958$	−36.8004			−1.18897
$959$	25.7698	+	27.6560i	0.832149	+	0.893059i
$960$	−2.07930	−	1.51070i	−0.0671091	−	0.0487576i
$961$	0.613134	+	5.83358i	0.0197785	+	0.188180i
$962$	51.9492	−	11.0421i	1.67491	−	0.356013i
$963$	−4.74392	+	1.00835i	−0.152871	+	0.0324937i
$964$	1.42665	+	13.5737i	0.0459494	+	0.437180i
$965$	18.6657	+	13.5614i	0.600869	+	0.436557i
$966$	−6.01811	+	19.6573i	−0.193629	+	0.632464i
$967$	−15.8477			−0.509628			−0.254814	−	0.966990i	$-0.582014\pi$
$967$	−15.8477			−0.509628			−0.254814	+	0.966990i	$0.582014\pi$
$968$	−5.10614	+	9.74307i	−0.164117	+	0.313154i
$969$	−2.82132	−	4.88666i	−0.0906337	−	0.156982i
$970$	−13.4396	+	14.9262i	−0.431520	+	0.479251i
$971$	−0.290135	+	0.129176i	−0.00931087	+	0.00414547i	−0.411387	−	0.911461i	$-0.634955\pi$
$971$	−0.290135	+	0.129176i	−0.00931087	+	0.00414547i	0.402076	+	0.915606i	$0.368289\pi$
$972$	0.809017	−	0.587785i	0.0259492	−	0.0188532i
$973$	−1.39057	−	0.590891i	−0.0445795	−	0.0189431i
$974$	−12.4564	+	38.3368i	−0.399129	+	1.22839i
$975$	−0.924163	−	8.79282i	−0.0295969	−	0.281596i
$976$	−0.0558921	+	0.531778i	−0.00178906	+	0.0170218i
$977$	6.26527	−	6.95829i	0.200444	−	0.222615i	−0.634540	−	0.772890i	$-0.718810\pi$
$977$	6.26527	−	6.95829i	0.200444	−	0.222615i	0.834984	+	0.550275i	$0.185477\pi$
$978$	5.50823	−	9.54053i	0.176134	−	0.305072i
$979$	−53.3714	+	18.5555i	−1.70576	+	0.593038i
$980$	17.7154	+	3.13774i	0.565896	+	0.100231i
$981$	5.39784	+	16.6129i	0.172340	+	0.530408i
$982$	−11.7539	+	5.23319i	−0.375083	+	0.166998i
$983$	−49.3358	−	21.9657i	−1.57357	−	0.700597i	−0.580082	−	0.814558i	$-0.696979\pi$
$983$	−49.3358	−	21.9657i	−1.57357	−	0.700597i	−0.993485	+	0.113961i	$0.963646\pi$
$984$	6.28275	−	1.33544i	0.200287	−	0.0425723i
$985$	21.4723	+	23.8474i	0.684164	+	0.759841i
$986$	−13.9344	+	10.1239i	−0.443762	+	0.322412i
$987$	−21.1227	+	24.2801i	−0.672344	+	0.772844i
$988$	4.38325	+	13.4903i	0.139450	+	0.429182i
$989$	9.55280	−	16.5459i	0.303762	−	0.526130i
$990$	−3.30726	+	7.85651i	−0.105112	+	0.249696i
$991$	14.5813	+	25.2555i	0.463190	+	0.802269i	0.999118	−	0.0419952i	$-0.0133714\pi$
$991$	14.5813	+	25.2555i	0.463190	+	0.802269i	−0.535928	+	0.844264i	$0.680038\pi$
$992$	−4.90386	−	1.04235i	−0.155698	−	0.0330945i
$993$	−23.9551	−	17.4044i	−0.760194	−	0.552313i
$994$	13.5735	−	0.231708i	0.430525	−	0.00734933i
$995$	−2.72079	+	8.37372i	−0.0862547	+	0.265465i
$996$	−5.23058	−	5.80914i	−0.165737	−	0.184070i
$997$	43.2394	+	19.2514i	1.36940	+	0.609698i	0.953964	−	0.299922i	$-0.0969607\pi$
$997$	43.2394	+	19.2514i	1.36940	+	0.609698i	0.415441	+	0.909620i	$0.363627\pi$
$998$	−2.83565	+	26.9794i	−0.0897609	+	0.854018i
$999$	−9.43472	−	2.00541i	−0.298501	−	0.0634484i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.y.a.247.1	yes	24
7.4	even	3	inner	462.2.y.a.445.3	yes	24
11.9	even	5	inner	462.2.y.a.163.3	✓	24
77.53	even	15	inner	462.2.y.a.361.1	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.y.a.163.3	✓	24	11.9	even	5	inner
462.2.y.a.247.1	yes	24	1.1	even	1	trivial
462.2.y.a.361.1	yes	24	77.53	even	15	inner
462.2.y.a.445.3	yes	24	7.4	even	3	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)

\(f(q)\)	\(=\)	\(q+(0.978148 + 0.207912i) q^{2} +(0.104528 - 0.994522i) q^{3} +(0.913545 + 0.406737i) q^{4} +(-1.71977 - 1.91000i) q^{5} +(0.309017 - 0.951057i) q^{6} +(-1.36179 - 2.26838i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-0.978148 - 0.207912i) q^{9} +O(q^{10})\)	\(q+(0.978148 + 0.207912i) q^{2} +(0.104528 - 0.994522i) q^{3} +(0.913545 + 0.406737i) q^{4} +(-1.71977 - 1.91000i) q^{5} +(0.309017 - 0.951057i) q^{6} +(-1.36179 - 2.26838i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-0.978148 - 0.207912i) q^{9} +(-1.28508 - 2.22582i) q^{10} +(2.50957 + 2.16842i) q^{11} +(0.500000 - 0.866025i) q^{12} +(-1.70150 - 5.23668i) q^{13} +(-0.860411 - 2.50194i) q^{14} +(-2.07930 + 1.51070i) q^{15} +(0.669131 + 0.743145i) q^{16} +(-2.14250 + 0.455403i) q^{17} +(-0.913545 - 0.406737i) q^{18} +(-2.35339 + 1.04780i) q^{19} +(-0.794222 - 2.44436i) q^{20} +(-2.39829 + 1.11722i) q^{21} +(2.00389 + 2.64281i) q^{22} +(3.88508 - 6.72915i) q^{23} +(0.669131 - 0.743145i) q^{24} +(-0.167841 + 1.59690i) q^{25} +(-0.575551 - 5.47600i) q^{26} +(-0.309017 + 0.951057i) q^{27} +(-0.321427 - 2.62615i) q^{28} +(6.36168 - 4.62203i) q^{29} +(-2.34795 + 1.04538i) q^{30} +(-3.35463 + 3.72569i) q^{31} +(0.500000 + 0.866025i) q^{32} +(2.41887 - 2.26916i) q^{33} -2.19037 q^{34} +(-1.99062 + 6.50210i) q^{35} +(-0.809017 - 0.587785i) q^{36} +(1.00823 + 9.59266i) q^{37} +(-2.51982 + 0.535603i) q^{38} +(-5.38585 + 1.14480i) q^{39} +(-0.268654 - 2.55608i) q^{40} +(5.19641 + 3.77541i) q^{41} +(-2.57817 + 0.594174i) q^{42} +2.45884 q^{43} +(1.41063 + 3.00169i) q^{44} +(1.28508 + 2.22582i) q^{45} +(5.19925 - 5.77435i) q^{46} +(11.1121 - 4.94743i) q^{47} +(0.809017 - 0.587785i) q^{48} +(-3.29105 + 6.17811i) q^{49} +(-0.496189 + 1.52711i) q^{50} +(0.228956 + 2.17837i) q^{51} +(0.575551 - 5.47600i) q^{52} +(-3.53796 + 3.92930i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(-0.174198 - 8.52246i) q^{55} +(0.231605 - 2.63559i) q^{56} +(0.796062 + 2.45003i) q^{57} +(7.18364 - 3.19836i) q^{58} +(6.30886 + 2.80889i) q^{59} +(-2.51399 + 0.534365i) q^{60} +(0.357789 + 0.397365i) q^{61} +(-4.05593 + 2.94681i) q^{62} +(0.860411 + 2.50194i) q^{63} +(0.309017 + 0.951057i) q^{64} +(-7.07585 + 12.2557i) q^{65} +(2.83779 - 1.71666i) q^{66} +(-6.99602 - 12.1175i) q^{67} +(-2.14250 - 0.455403i) q^{68} +(-6.28619 - 4.56718i) q^{69} +(-3.29899 + 5.94614i) q^{70} +(-1.58558 + 4.87991i) q^{71} +(-0.669131 - 0.743145i) q^{72} +(10.6396 + 4.73705i) q^{73} +(-1.00823 + 9.59266i) q^{74} +(1.57061 + 0.333844i) q^{75} -2.57611 q^{76} +(1.50129 - 8.64558i) q^{77} -5.50617 q^{78} +(-2.02064 - 0.429499i) q^{79} +(0.268654 - 2.55608i) q^{80} +(0.913545 + 0.406737i) q^{81} +(4.29790 + 4.77330i) q^{82} +(2.41558 - 7.43438i) q^{83} +(-2.64537 + 0.0451581i) q^{84} +(4.55443 + 3.30899i) q^{85} +(2.40511 + 0.511222i) q^{86} +(-3.93173 - 6.80996i) q^{87} +(0.755717 + 3.22938i) q^{88} +(-8.51845 + 14.7544i) q^{89} +(0.794222 + 2.44436i) q^{90} +(-9.56166 + 10.9909i) q^{91} +(6.28619 - 4.56718i) q^{92} +(3.35463 + 3.72569i) q^{93} +(11.8979 - 2.52898i) q^{94} +(6.04859 + 2.69301i) q^{95} +(0.913545 - 0.406737i) q^{96} +(-2.41490 - 7.43229i) q^{97} +(-4.50363 + 5.35885i) q^{98} +(-2.00389 - 2.64281i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 3 q^{2} - 3 q^{3} + 3 q^{4} + 5 q^{5} - 6 q^{6} + 11 q^{7} + 6 q^{8} + 3 q^{9}+O(q^{10}) \) 24 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 + 5 * q^5 - 6 * q^6 + 11 * q^7 + 6 * q^8 + 3 * q^9	\( 24 q - 3 q^{2} - 3 q^{3} + 3 q^{4} + 5 q^{5} - 6 q^{6} + 11 q^{7} + 6 q^{8} + 3 q^{9} + 10 q^{10} + 6 q^{11} + 12 q^{12} - 2 q^{13} - 5 q^{14} + 3 q^{16} - 2 q^{17} - 3 q^{18} + 7 q^{19} - 10 q^{20} - 4 q^{21} + 2 q^{22} + 24 q^{23} + 3 q^{24} + 4 q^{25} + 4 q^{26} + 6 q^{27} + 14 q^{28} - 6 q^{29} - 7 q^{31} + 12 q^{32} - q^{33} - 24 q^{34} + 4 q^{35} - 6 q^{36} - q^{37} + 8 q^{38} - q^{39} + 16 q^{41} - 4 q^{42} + 52 q^{43} - 4 q^{44} - 10 q^{45} - 4 q^{46} + 27 q^{47} + 6 q^{48} - 33 q^{49} - 22 q^{50} - 8 q^{51} - 4 q^{52} + 13 q^{53} - 12 q^{54} + 30 q^{55} + 14 q^{56} - 16 q^{57} - 3 q^{58} + 14 q^{59} - 5 q^{60} + 9 q^{61} - 4 q^{62} + 5 q^{63} - 6 q^{64} - 50 q^{65} - 4 q^{66} - 20 q^{67} - 2 q^{68} - 32 q^{69} - 17 q^{70} - 18 q^{71} - 3 q^{72} + 7 q^{73} + q^{74} + 11 q^{75} - 4 q^{76} - 34 q^{77} - 12 q^{78} + q^{79} + 3 q^{81} - 2 q^{82} - 68 q^{83} - 5 q^{84} - 19 q^{86} - 8 q^{87} - q^{88} - 42 q^{89} + 10 q^{90} - 16 q^{91} + 32 q^{92} + 7 q^{93} + 8 q^{94} + 38 q^{95} + 3 q^{96} - 80 q^{97} - 2 q^{99}+O(q^{100}) \) 24 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 + 5 * q^5 - 6 * q^6 + 11 * q^7 + 6 * q^8 + 3 * q^9 + 10 * q^10 + 6 * q^11 + 12 * q^12 - 2 * q^13 - 5 * q^14 + 3 * q^16 - 2 * q^17 - 3 * q^18 + 7 * q^19 - 10 * q^20 - 4 * q^21 + 2 * q^22 + 24 * q^23 + 3 * q^24 + 4 * q^25 + 4 * q^26 + 6 * q^27 + 14 * q^28 - 6 * q^29 - 7 * q^31 + 12 * q^32 - q^33 - 24 * q^34 + 4 * q^35 - 6 * q^36 - q^37 + 8 * q^38 - q^39 + 16 * q^41 - 4 * q^42 + 52 * q^43 - 4 * q^44 - 10 * q^45 - 4 * q^46 + 27 * q^47 + 6 * q^48 - 33 * q^49 - 22 * q^50 - 8 * q^51 - 4 * q^52 + 13 * q^53 - 12 * q^54 + 30 * q^55 + 14 * q^56 - 16 * q^57 - 3 * q^58 + 14 * q^59 - 5 * q^60 + 9 * q^61 - 4 * q^62 + 5 * q^63 - 6 * q^64 - 50 * q^65 - 4 * q^66 - 20 * q^67 - 2 * q^68 - 32 * q^69 - 17 * q^70 - 18 * q^71 - 3 * q^72 + 7 * q^73 + q^74 + 11 * q^75 - 4 * q^76 - 34 * q^77 - 12 * q^78 + q^79 + 3 * q^81 - 2 * q^82 - 68 * q^83 - 5 * q^84 - 19 * q^86 - 8 * q^87 - q^88 - 42 * q^89 + 10 * q^90 - 16 * q^91 + 32 * q^92 + 7 * q^93 + 8 * q^94 + 38 * q^95 + 3 * q^96 - 80 * q^97 - 2 * q^99

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