LMFDB - Embedded newform 462.2.j.e.421.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(169,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("462.169");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.j (of order $5$, degree $4$, 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:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.484000000.9
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + x^{6} + 16x^{4} + 66x^{2} + 121 $ x^8 + x^6 + 16x^4 + 66x^2 + 121
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			421.1
Root			$-0.476925 - 1.46782i$ of defining polynomial
Character	$\chi$	$=$	462.421
Dual form			462.2.j.e.169.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 + 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-1.52029 - 1.10455i) q^{5} +(-0.809017 - 0.587785i) q^{6} +(0.309017 - 0.951057i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(-0.809017 + 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-1.52029 - 1.10455i) q^{5} +(-0.809017 - 0.587785i) q^{6} +(0.309017 - 0.951057i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-0.809017 + 0.587785i) q^{9} +1.87918 q^{10} +(-2.97414 - 1.46782i) q^{11} +1.00000 q^{12} +(-0.748606 + 0.543894i) q^{13} +(0.309017 + 0.951057i) q^{14} +(0.580698 - 1.78720i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-3.66140 - 2.66016i) q^{17} +(0.309017 - 0.951057i) q^{18} +(-0.858891 - 2.64339i) q^{19} +(-1.52029 + 1.10455i) q^{20} +1.00000 q^{21} +(3.26889 - 0.560659i) q^{22} -4.11525 q^{23} +(-0.809017 + 0.587785i) q^{24} +(-0.453850 - 1.39681i) q^{25} +(0.285942 - 0.880039i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(-0.809017 - 0.587785i) q^{28} +(1.44131 - 4.43590i) q^{29} +(0.580698 + 1.78720i) q^{30} +(-0.635083 + 0.461415i) q^{31} +1.00000 q^{32} +(0.476925 - 3.28216i) q^{33} +4.52573 q^{34} +(-1.52029 + 1.10455i) q^{35} +(0.309017 + 0.951057i) q^{36} +(0.344630 - 1.06066i) q^{37} +(2.24861 + 1.63371i) q^{38} +(-0.748606 - 0.543894i) q^{39} +(0.580698 - 1.78720i) q^{40} +(0.146556 + 0.451054i) q^{41} +(-0.809017 + 0.587785i) q^{42} +11.0065 q^{43} +(-2.31504 + 2.37499i) q^{44} +1.87918 q^{45} +(3.32930 - 2.41888i) q^{46} +(-0.574186 - 1.76716i) q^{47} +(0.309017 - 0.951057i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(1.18820 + 0.863274i) q^{50} +(1.39853 - 4.30423i) q^{51} +(0.285942 + 0.880039i) q^{52} +(-3.70848 + 2.69437i) q^{53} +1.00000 q^{54} +(2.90025 + 5.51661i) q^{55} +1.00000 q^{56} +(2.24861 - 1.63371i) q^{57} +(1.44131 + 4.43590i) q^{58} +(-0.458940 + 1.41247i) q^{59} +(-1.52029 - 1.10455i) q^{60} +(-11.5626 - 8.40071i) q^{61} +(0.242580 - 0.746585i) q^{62} +(0.309017 + 0.951057i) q^{63} +(-0.809017 + 0.587785i) q^{64} +1.73886 q^{65} +(1.54336 + 2.93565i) q^{66} +0.676236 q^{67} +(-3.66140 + 2.66016i) q^{68} +(-1.27168 - 3.91383i) q^{69} +(0.580698 - 1.78720i) q^{70} +(4.30172 + 3.12538i) q^{71} +(-0.809017 - 0.587785i) q^{72} +(-1.08442 + 3.33751i) q^{73} +(0.344630 + 1.06066i) q^{74} +(1.18820 - 0.863274i) q^{75} -2.77943 q^{76} +(-2.31504 + 2.37499i) q^{77} +0.925328 q^{78} +(3.23004 - 2.34676i) q^{79} +(0.580698 + 1.78720i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-0.383689 - 0.278766i) q^{82} +(-2.55611 - 1.85712i) q^{83} +(0.309017 - 0.951057i) q^{84} +(2.62808 + 8.08841i) q^{85} +(-8.90443 + 6.46944i) q^{86} +4.66418 q^{87} +(0.476925 - 3.28216i) q^{88} -13.6366 q^{89} +(-1.52029 + 1.10455i) q^{90} +(0.285942 + 0.880039i) q^{91} +(-1.27168 + 3.91383i) q^{92} +(-0.635083 - 0.461415i) q^{93} +(1.50324 + 1.09217i) q^{94} +(-1.61401 + 4.96741i) q^{95} +(0.309017 + 0.951057i) q^{96} +(-3.82930 + 2.78215i) q^{97} +1.00000 q^{98} +(3.26889 - 0.560659i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 4 q^{5} - 2 q^{6} - 2 q^{7} - 2 q^{8} - 2 q^{9}+O(q^{10}) $ 8 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 + 4 * q^5 - 2 * q^6 - 2 * q^7 - 2 * q^8 - 2 * q^9	$ 8 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 4 q^{5} - 2 q^{6} - 2 q^{7} - 2 q^{8} - 2 q^{9} + 4 q^{10} + 8 q^{12} + 4 q^{13} - 2 q^{14} - 6 q^{15} - 2 q^{16} - 8 q^{17} - 2 q^{18} - 12 q^{19} + 4 q^{20} + 8 q^{21} - 4 q^{23} - 2 q^{24} + 4 q^{25} - 6 q^{26} - 2 q^{27} - 2 q^{28} - 4 q^{29} - 6 q^{30} - 14 q^{31} + 8 q^{32} + 12 q^{34} + 4 q^{35} - 2 q^{36} + 10 q^{37} + 8 q^{38} + 4 q^{39} - 6 q^{40} - 12 q^{41} - 2 q^{42} + 20 q^{43} + 4 q^{45} + 6 q^{46} + 28 q^{47} - 2 q^{48} - 2 q^{49} - 6 q^{50} + 2 q^{51} - 6 q^{52} + 2 q^{53} + 8 q^{54} + 4 q^{55} + 8 q^{56} + 8 q^{57} - 4 q^{58} + 4 q^{60} - 34 q^{61} + 6 q^{62} - 2 q^{63} - 2 q^{64} + 16 q^{65} - 24 q^{67} - 8 q^{68} - 4 q^{69} - 6 q^{70} - 2 q^{72} + 10 q^{74} - 6 q^{75} + 8 q^{76} + 4 q^{78} + 22 q^{79} - 6 q^{80} - 2 q^{81} - 2 q^{82} - 30 q^{83} - 2 q^{84} - 28 q^{85} + 36 q^{87} - 4 q^{89} + 4 q^{90} - 6 q^{91} - 4 q^{92} - 14 q^{93} - 22 q^{94} - 30 q^{95} - 2 q^{96} - 10 q^{97} + 8 q^{98}+O(q^{100}) $ 8 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 + 4 * q^5 - 2 * q^6 - 2 * q^7 - 2 * q^8 - 2 * q^9 + 4 * q^10 + 8 * q^12 + 4 * q^13 - 2 * q^14 - 6 * q^15 - 2 * q^16 - 8 * q^17 - 2 * q^18 - 12 * q^19 + 4 * q^20 + 8 * q^21 - 4 * q^23 - 2 * q^24 + 4 * q^25 - 6 * q^26 - 2 * q^27 - 2 * q^28 - 4 * q^29 - 6 * q^30 - 14 * q^31 + 8 * q^32 + 12 * q^34 + 4 * q^35 - 2 * q^36 + 10 * q^37 + 8 * q^38 + 4 * q^39 - 6 * q^40 - 12 * q^41 - 2 * q^42 + 20 * q^43 + 4 * q^45 + 6 * q^46 + 28 * q^47 - 2 * q^48 - 2 * q^49 - 6 * q^50 + 2 * q^51 - 6 * q^52 + 2 * q^53 + 8 * q^54 + 4 * q^55 + 8 * q^56 + 8 * q^57 - 4 * q^58 + 4 * q^60 - 34 * q^61 + 6 * q^62 - 2 * q^63 - 2 * q^64 + 16 * q^65 - 24 * q^67 - 8 * q^68 - 4 * q^69 - 6 * q^70 - 2 * q^72 + 10 * q^74 - 6 * q^75 + 8 * q^76 + 4 * q^78 + 22 * q^79 - 6 * q^80 - 2 * q^81 - 2 * q^82 - 30 * q^83 - 2 * q^84 - 28 * q^85 + 36 * q^87 - 4 * q^89 + 4 * q^90 - 6 * q^91 - 4 * q^92 - 14 * q^93 - 22 * q^94 - 30 * q^95 - 2 * q^96 - 10 * q^97 + 8 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$	−1.52029	−	1.10455i	−0.679893	−	0.493971i	0.193429	−	0.981114i	$-0.438039\pi$
$5$	−1.52029	−	1.10455i	−0.679893	−	0.493971i	−0.873322	+	0.487143i	$0.838039\pi$
$6$	−0.809017	−	0.587785i	−0.330280	−	0.239962i
$7$	0.309017	−	0.951057i	0.116797	−	0.359466i
$7$	0.309017	−	0.951057i	0.116797	−	0.359466i
$8$	0.309017	+	0.951057i	0.109254	+	0.336249i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$	1.87918			0.594248
$11$	−2.97414	−	1.46782i	−0.896736	−	0.442566i
$11$	−2.97414	−	1.46782i	−0.896736	−	0.442566i
$12$	1.00000			0.288675
$13$	−0.748606	+	0.543894i	−0.207626	+	0.150849i	−0.686739	−	0.726904i	$-0.740958\pi$
$13$	−0.748606	+	0.543894i	−0.207626	+	0.150849i	0.479113	+	0.877753i	$0.340958\pi$
$14$	0.309017	+	0.951057i	0.0825883	+	0.254181i
$15$	0.580698	−	1.78720i	0.149936	−	0.461454i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	−3.66140	−	2.66016i	−0.888019	−	0.645184i	0.0473418	−	0.998879i	$-0.484925\pi$
$17$	−3.66140	−	2.66016i	−0.888019	−	0.645184i	−0.935361	+	0.353695i	$0.884925\pi$
$18$	0.309017	−	0.951057i	0.0728360	−	0.224166i
$19$	−0.858891	−	2.64339i	−0.197043	−	0.606436i	−0.999947	−	0.0103274i	$-0.996713\pi$
$19$	−0.858891	−	2.64339i	−0.197043	−	0.606436i	0.802904	−	0.596109i	$-0.203287\pi$
$20$	−1.52029	+	1.10455i	−0.339947	+	0.246986i
$21$	1.00000			0.218218
$22$	3.26889	−	0.560659i	0.696930	−	0.119533i
$23$	−4.11525			−0.858088			−0.429044	−	0.903284i	$-0.641149\pi$
$23$	−4.11525			−0.858088			−0.429044	+	0.903284i	$0.641149\pi$
$24$	−0.809017	+	0.587785i	−0.165140	+	0.119981i
$25$	−0.453850	−	1.39681i	−0.0907700	−	0.279361i
$26$	0.285942	−	0.880039i	0.0560779	−	0.172590i
$27$	−0.809017	−	0.587785i	−0.155695	−	0.113119i
$28$	−0.809017	−	0.587785i	−0.152890	−	0.111081i
$29$	1.44131	−	4.43590i	0.267645	−	0.823726i	−0.723427	−	0.690401i	$-0.757434\pi$
$29$	1.44131	−	4.43590i	0.267645	−	0.823726i	0.991072	−	0.133326i	$-0.0425657\pi$
$30$	0.580698	+	1.78720i	0.106020	+	0.326297i
$31$	−0.635083	+	0.461415i	−0.114064	+	0.0828726i	−0.643355	−	0.765568i	$-0.722458\pi$
$31$	−0.635083	+	0.461415i	−0.114064	+	0.0828726i	0.529291	+	0.848441i	$0.322458\pi$
$32$	1.00000			0.176777
$33$	0.476925	−	3.28216i	0.0830220	−	0.571350i
$34$	4.52573			0.776157
$35$	−1.52029	+	1.10455i	−0.256975	+	0.186704i
$36$	0.309017	+	0.951057i	0.0515028	+	0.158509i
$37$	0.344630	−	1.06066i	0.0566568	−	0.174372i	−0.918723	−	0.394902i	$-0.870779\pi$
$37$	0.344630	−	1.06066i	0.0566568	−	0.174372i	0.975380	+	0.220530i	$0.0707787\pi$
$38$	2.24861	+	1.63371i	0.364772	+	0.265022i
$39$	−0.748606	−	0.543894i	−0.119873	−	0.0870928i
$40$	0.580698	−	1.78720i	0.0918164	−	0.282582i
$41$	0.146556	+	0.451054i	0.0228882	+	0.0704427i	0.961848	−	0.273584i	$-0.0882090\pi$
$41$	0.146556	+	0.451054i	0.0228882	+	0.0704427i	−0.938960	+	0.344026i	$0.888209\pi$
$42$	−0.809017	+	0.587785i	−0.124834	+	0.0906972i
$43$	11.0065			1.67847			0.839236	−	0.543767i	$-0.183003\pi$
$43$	11.0065			1.67847			0.839236	+	0.543767i	$0.183003\pi$
$44$	−2.31504	+	2.37499i	−0.349006	+	0.358043i
$45$	1.87918			0.280131
$46$	3.32930	−	2.41888i	0.490879	−	0.356645i
$47$	−0.574186	−	1.76716i	−0.0837536	−	0.257767i	0.900406	−	0.435050i	$-0.143269\pi$
$47$	−0.574186	−	1.76716i	−0.0837536	−	0.257767i	−0.984160	+	0.177283i	$0.943269\pi$
$48$	0.309017	−	0.951057i	0.0446028	−	0.137273i
$49$	−0.809017	−	0.587785i	−0.115574	−	0.0839693i
$50$	1.18820	+	0.863274i	0.168036	+	0.122085i
$51$	1.39853	−	4.30423i	0.195833	−	0.602713i
$52$	0.285942	+	0.880039i	0.0396530	+	0.122039i
$53$	−3.70848	+	2.69437i	−0.509399	+	0.370100i	−0.812596	−	0.582828i	$-0.801946\pi$
$53$	−3.70848	+	2.69437i	−0.509399	+	0.370100i	0.303196	+	0.952928i	$0.401946\pi$
$54$	1.00000			0.136083
$55$	2.90025	+	5.51661i	0.391070	+	0.743859i
$56$	1.00000			0.133631
$57$	2.24861	−	1.63371i	0.297835	−	0.216390i
$58$	1.44131	+	4.43590i	0.189254	+	0.582463i
$59$	−0.458940	+	1.41247i	−0.0597489	+	0.183888i	−0.976476	−	0.215625i	$-0.930821\pi$
$59$	−0.458940	+	1.41247i	−0.0597489	+	0.183888i	0.916727	+	0.399514i	$0.130821\pi$
$60$	−1.52029	−	1.10455i	−0.196268	−	0.142597i
$61$	−11.5626	−	8.40071i	−1.48044	−	1.07560i	−0.977415	−	0.211327i	$-0.932222\pi$
$61$	−11.5626	−	8.40071i	−1.48044	−	1.07560i	−0.503022	−	0.864274i	$-0.667778\pi$
$62$	0.242580	−	0.746585i	0.0308077	−	0.0948164i
$63$	0.309017	+	0.951057i	0.0389325	+	0.119822i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	1.73886			0.215679
$66$	1.54336	+	2.93565i	0.189975	+	0.361353i
$67$	0.676236			0.0826153			0.0413077	−	0.999146i	$-0.486848\pi$
$67$	0.676236			0.0826153			0.0413077	+	0.999146i	$0.486848\pi$
$68$	−3.66140	+	2.66016i	−0.444009	+	0.322592i
$69$	−1.27168	−	3.91383i	−0.153092	−	0.471170i
$70$	0.580698	−	1.78720i	0.0694067	−	0.213612i
$71$	4.30172	+	3.12538i	0.510520	+	0.370914i	0.813021	−	0.582235i	$-0.197821\pi$
$71$	4.30172	+	3.12538i	0.510520	+	0.370914i	−0.302501	+	0.953149i	$0.597821\pi$
$72$	−0.809017	−	0.587785i	−0.0953436	−	0.0692712i
$73$	−1.08442	+	3.33751i	−0.126922	+	0.390626i	−0.994246	−	0.107118i	$-0.965838\pi$
$73$	−1.08442	+	3.33751i	−0.126922	+	0.390626i	0.867324	+	0.497743i	$0.165838\pi$
$74$	0.344630	+	1.06066i	0.0400624	+	0.123299i
$75$	1.18820	−	0.863274i	0.137201	−	0.0996823i
$76$	−2.77943			−0.318822
$77$	−2.31504	+	2.37499i	−0.263824	+	0.270655i
$78$	0.925328			0.104773
$79$	3.23004	−	2.34676i	0.363408	−	0.264031i	−0.391064	−	0.920363i	$-0.627893\pi$
$79$	3.23004	−	2.34676i	0.363408	−	0.264031i	0.754472	+	0.656332i	$0.227893\pi$
$80$	0.580698	+	1.78720i	0.0649240	+	0.199816i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	−0.383689	−	0.278766i	−0.0423714	−	0.0307846i
$83$	−2.55611	−	1.85712i	−0.280569	−	0.203846i	0.438596	−	0.898684i	$-0.355476\pi$
$83$	−2.55611	−	1.85712i	−0.280569	−	0.203846i	−0.719166	+	0.694839i	$0.755476\pi$
$84$	0.309017	−	0.951057i	0.0337165	−	0.103769i
$85$	2.62808	+	8.08841i	0.285056	+	0.877312i
$86$	−8.90443	+	6.46944i	−0.960189	+	0.697618i
$87$	4.66418			0.500053
$88$	0.476925	−	3.28216i	0.0508404	−	0.349879i
$89$	−13.6366			−1.44547			−0.722736	−	0.691124i	$-0.757116\pi$
$89$	−13.6366			−1.44547			−0.722736	+	0.691124i	$0.757116\pi$
$90$	−1.52029	+	1.10455i	−0.160252	+	0.116430i
$91$	0.285942	+	0.880039i	0.0299749	+	0.0922532i
$92$	−1.27168	+	3.91383i	−0.132582	+	0.408045i
$93$	−0.635083	−	0.461415i	−0.0658550	−	0.0478465i
$94$	1.50324	+	1.09217i	0.155047	+	0.112648i
$95$	−1.61401	+	4.96741i	−0.165594	+	0.509645i
$96$	0.309017	+	0.951057i	0.0315389	+	0.0970668i
$97$	−3.82930	+	2.78215i	−0.388807	+	0.282485i	−0.764966	−	0.644070i	$-0.777244\pi$
$97$	−3.82930	+	2.78215i	−0.388807	+	0.282485i	0.376160	+	0.926555i	$0.377244\pi$
$98$	1.00000			0.101015
$99$	3.26889	−	0.560659i	0.328536	−	0.0563484i
$100$	−1.46869			−0.146869
$101$	5.06365	−	3.67896i	0.503852	−	0.366070i	−0.306634	−	0.951827i	$-0.599203\pi$
$101$	5.06365	−	3.67896i	0.503852	−	0.366070i	0.810486	+	0.585758i	$0.199203\pi$
$102$	1.39853	+	4.30423i	0.138475	+	0.426182i
$103$	−4.53070	+	13.9440i	−0.446423	+	1.37395i	0.434493	+	0.900675i	$0.356927\pi$
$103$	−4.53070	+	13.9440i	−0.446423	+	1.37395i	−0.880916	+	0.473273i	$0.843073\pi$
$104$	−0.748606	−	0.543894i	−0.0734069	−	0.0533332i
$105$	−1.52029	−	1.10455i	−0.148365	−	0.107793i
$106$	1.41651	−	4.35958i	0.137584	−	0.423440i
$107$	−2.00479	−	6.17011i	−0.193810	−	0.596487i	−0.999988	−	0.00481381i	$-0.998468\pi$
$107$	−2.00479	−	6.17011i	−0.193810	−	0.596487i	0.806178	−	0.591673i	$-0.201532\pi$
$108$	−0.809017	+	0.587785i	−0.0778477	+	0.0565597i
$109$	−4.20197			−0.402476			−0.201238	−	0.979542i	$-0.564496\pi$
$109$	−4.20197			−0.402476			−0.201238	+	0.979542i	$0.564496\pi$
$110$	−5.58893	−	2.75830i	−0.532884	−	0.262994i
$111$	1.11525			0.105854
$112$	−0.809017	+	0.587785i	−0.0764449	+	0.0555405i
$113$	6.10577	+	18.7916i	0.574383	+	1.76777i	0.638271	+	0.769812i	$0.279650\pi$
$113$	6.10577	+	18.7916i	0.574383	+	1.76777i	−0.0638881	+	0.997957i	$0.520350\pi$
$114$	−0.858891	+	2.64339i	−0.0804425	+	0.247577i
$115$	6.25635	+	4.54551i	0.583408	+	0.423871i
$116$	−3.77340	−	2.74154i	−0.350352	−	0.254545i
$117$	0.285942	−	0.880039i	0.0264354	−	0.0813596i
$118$	−0.458940	−	1.41247i	−0.0422488	−	0.130029i
$119$	−3.66140	+	2.66016i	−0.335640	+	0.243856i
$120$	1.87918			0.171545
$121$	6.69098	+	8.73102i	0.608271	+	0.793729i
$122$	14.2921			1.29395
$123$	−0.383689	+	0.278766i	−0.0345961	+	0.0251355i
$124$	0.242580	+	0.746585i	0.0217843	+	0.0670453i
$125$	−3.75635	+	11.5609i	−0.335979	+	1.03404i
$126$	−0.809017	−	0.587785i	−0.0720730	−	0.0523641i
$127$	−0.493038	−	0.358213i	−0.0437500	−	0.0317863i	0.565695	−	0.824614i	$-0.308608\pi$
$127$	−0.493038	−	0.358213i	−0.0437500	−	0.0317863i	−0.609445	+	0.792828i	$0.708608\pi$
$128$	0.309017	−	0.951057i	0.0273135	−	0.0840623i
$129$	3.40119	+	10.4678i	0.299458	+	0.921637i
$130$	−1.40676	+	1.02207i	−0.123381	+	0.0896418i
$131$	16.7829			1.46633			0.733163	−	0.680053i	$-0.238043\pi$
$131$	16.7829			1.46633			0.733163	+	0.680053i	$0.238043\pi$
$132$	−2.97414	−	1.46782i	−0.258865	−	0.127758i
$133$	−2.77943			−0.241007
$134$	−0.547086	+	0.397481i	−0.0472610	+	0.0343372i
$135$	0.580698	+	1.78720i	0.0499785	+	0.153818i
$136$	1.39853	−	4.30423i	0.119923	−	0.369085i
$137$	17.7337	+	12.8843i	1.51509	+	1.10078i	0.963853	+	0.266435i	$0.0858459\pi$
$137$	17.7337	+	12.8843i	1.51509	+	1.10078i	0.551242	+	0.834345i	$0.314154\pi$
$138$	3.32930	+	2.41888i	0.283409	+	0.205909i
$139$	−1.72849	+	5.31975i	−0.146609	+	0.451215i	−0.997214	−	0.0745890i	$-0.976236\pi$
$139$	−1.72849	+	5.31975i	−0.146609	+	0.451215i	0.850606	+	0.525804i	$0.176236\pi$
$140$	0.580698	+	1.78720i	0.0490779	+	0.151046i
$141$	1.50324	−	1.09217i	0.126595	−	0.0919770i
$142$	−5.31722			−0.446211
$143$	3.02480	−	0.518793i	0.252946	−	0.0433837i
$144$	1.00000			0.0833333
$145$	−7.09090	+	5.15184i	−0.588867	+	0.427837i
$146$	−1.08442	−	3.33751i	−0.0897474	−	0.276214i
$147$	0.309017	−	0.951057i	0.0254873	−	0.0784418i
$148$	−0.902253	−	0.655525i	−0.0741647	−	0.0538838i
$149$	−17.3172	−	12.5817i	−1.41868	−	1.03073i	−0.991987	−	0.126337i	$-0.959678\pi$
$149$	−17.3172	−	12.5817i	−1.41868	−	1.03073i	−0.426694	−	0.904396i	$-0.640322\pi$
$150$	−0.453850	+	1.39681i	−0.0370567	+	0.114049i
$151$	−3.30357	−	10.1673i	−0.268841	−	0.827407i	−0.990784	−	0.135454i	$-0.956751\pi$
$151$	−3.30357	−	10.1673i	−0.268841	−	0.827407i	0.721943	−	0.691953i	$-0.243249\pi$
$152$	2.24861	−	1.63371i	0.182386	−	0.132511i
$153$	4.52573			0.365884
$154$	0.476925	−	3.28216i	0.0384317	−	0.264484i
$155$	1.47517			0.118488
$156$	−0.748606	+	0.543894i	−0.0599364	+	0.0435464i
$157$	−1.44114	−	4.43537i	−0.115016	−	0.353981i	0.876935	−	0.480609i	$-0.159585\pi$
$157$	−1.44114	−	4.43537i	−0.115016	−	0.353981i	−0.991950	+	0.126628i	$0.959585\pi$
$158$	−1.23377	+	3.79714i	−0.0981532	+	0.302084i
$159$	−3.70848	−	2.69437i	−0.294102	−	0.213677i
$160$	−1.52029	−	1.10455i	−0.120189	−	0.0873226i
$161$	−1.27168	+	3.91383i	−0.100222	+	0.308453i
$162$	0.309017	+	0.951057i	0.0242787	+	0.0747221i
$163$	8.37081	−	6.08175i	0.655653	−	0.476360i	−0.209539	−	0.977800i	$-0.567196\pi$
$163$	8.37081	−	6.08175i	0.655653	−	0.476360i	0.865192	+	0.501441i	$0.167196\pi$
$164$	0.474266			0.0370339
$165$	−4.35038	+	4.46303i	−0.338676	+	0.347446i
$166$	3.15952			0.245227
$167$	8.26159	−	6.00240i	0.639301	−	0.464480i	−0.220309	−	0.975430i	$-0.570706\pi$
$167$	8.26159	−	6.00240i	0.639301	−	0.464480i	0.859610	+	0.510951i	$0.170706\pi$
$168$	0.309017	+	0.951057i	0.0238412	+	0.0733756i
$169$	−3.75263	+	11.5494i	−0.288664	+	0.888416i
$170$	−6.88041	−	4.99891i	−0.527704	−	0.383399i
$171$	2.24861	+	1.63371i	0.171955	+	0.124933i
$172$	3.40119	−	10.4678i	0.259338	−	0.798161i
$173$	−3.11056	−	9.57333i	−0.236492	−	0.727847i	−0.996920	−	0.0784248i	$-0.975011\pi$
$173$	−3.11056	−	9.57333i	−0.236492	−	0.727847i	0.760428	−	0.649422i	$-0.224989\pi$
$174$	−3.77340	+	2.74154i	−0.286061	+	0.207835i
$175$	−1.46869			−0.111023
$176$	1.54336	+	2.93565i	0.116335	+	0.221283i
$177$	−1.48516			−0.111631
$178$	11.0322	−	8.01537i	0.826899	−	0.600777i
$179$	−0.505748	−	1.55653i	−0.0378014	−	0.116341i	0.930375	−	0.366609i	$-0.119481\pi$
$179$	−0.505748	−	1.55653i	−0.0378014	−	0.116341i	−0.968177	+	0.250268i	$0.919481\pi$
$180$	0.580698	−	1.78720i	0.0432827	−	0.133210i
$181$	−17.3675	−	12.6183i	−1.29092	−	0.937908i	−0.291096	−	0.956694i	$-0.594020\pi$
$181$	−17.3675	−	12.6183i	−1.29092	−	0.937908i	−0.999824	+	0.0187864i	$0.994020\pi$
$182$	−0.748606	−	0.543894i	−0.0554904	−	0.0403161i
$183$	4.41651	−	13.5926i	0.326478	−	1.00480i
$184$	−1.27168	−	3.91383i	−0.0937496	−	0.288531i
$185$	−1.69549	+	1.23185i	−0.124655	+	0.0905673i
$186$	0.785006			0.0575594
$187$	6.98485	+	13.2860i	0.510783	+	0.971566i
$188$	−1.85810			−0.135516
$189$	−0.809017	+	0.587785i	−0.0588473	+	0.0427551i
$190$	−1.61401	−	4.96741i	−0.117093	−	0.360374i
$191$	2.08979	−	6.43171i	0.151212	−	0.465382i	−0.846546	−	0.532316i	$-0.821322\pi$
$191$	2.08979	−	6.43171i	0.151212	−	0.465382i	0.997757	+	0.0669340i	$0.0213217\pi$
$192$	−0.809017	−	0.587785i	−0.0583858	−	0.0424197i
$193$	−12.5857	−	9.14402i	−0.905936	−	0.658201i	0.0340481	−	0.999420i	$-0.489160\pi$
$193$	−12.5857	−	9.14402i	−0.905936	−	0.658201i	−0.939984	+	0.341219i	$0.889160\pi$
$194$	1.46266	−	4.50162i	0.105013	−	0.323197i
$195$	0.537336	+	1.65375i	0.0384794	+	0.118428i
$196$	−0.809017	+	0.587785i	−0.0577869	+	0.0419847i
$197$	19.3367			1.37768			0.688842	−	0.724912i	$-0.258119\pi$
$197$	19.3367			1.37768			0.688842	+	0.724912i	$0.258119\pi$
$198$	−2.31504	+	2.37499i	−0.164523	+	0.168783i
$199$	12.1723			0.862871			0.431435	−	0.902144i	$-0.358007\pi$
$199$	12.1723			0.862871			0.431435	+	0.902144i	$0.358007\pi$
$200$	1.18820	−	0.863274i	0.0840181	−	0.0610427i
$201$	0.208968	+	0.643138i	0.0147395	+	0.0453635i
$202$	−1.93414	+	5.95268i	−0.136086	+	0.418829i
$203$	−3.77340	−	2.74154i	−0.264841	−	0.192418i
$204$	−3.66140	−	2.66016i	−0.256349	−	0.186248i
$205$	0.275405	−	0.847610i	0.0192351	−	0.0591996i
$206$	−4.53070	−	13.9440i	−0.315668	−	0.971528i
$207$	3.32930	−	2.41888i	0.231403	−	0.168124i
$208$	0.925328			0.0641599
$209$	−1.32558	+	9.12252i	−0.0916923	+	0.631018i
$210$	1.87918			0.129676
$211$	14.8910	−	10.8189i	1.02514	−	0.744804i	0.0578061	−	0.998328i	$-0.481589\pi$
$211$	14.8910	−	10.8189i	1.02514	−	0.744804i	0.967329	+	0.253523i	$0.0815895\pi$
$212$	1.41651	+	4.35958i	0.0972866	+	0.299417i
$213$	−1.64311	+	5.05697i	−0.112584	+	0.346498i
$214$	5.24861	+	3.81334i	0.358787	+	0.260674i
$215$	−16.7330	−	12.1572i	−1.14118	−	0.829117i
$216$	0.309017	−	0.951057i	0.0210259	−	0.0647112i
$217$	0.242580	+	0.746585i	0.0164674	+	0.0506815i
$218$	3.39947	−	2.46986i	0.230241	−	0.167280i
$219$	−3.50926			−0.237134
$220$	6.14283	−	1.05358i	0.414150	−	0.0710322i
$221$	4.18779			0.281701
$222$	−0.902253	+	0.655525i	−0.0605553	+	0.0439960i
$223$	−7.34291	−	22.5991i	−0.491717	−	1.51335i	−0.822011	−	0.569472i	$-0.807148\pi$
$223$	−7.34291	−	22.5991i	−0.491717	−	1.51335i	0.330293	−	0.943878i	$-0.392852\pi$
$224$	0.309017	−	0.951057i	0.0206471	−	0.0635451i
$225$	1.18820	+	0.863274i	0.0792130	+	0.0575516i
$226$	−15.9851	−	11.6139i	−1.06331	−	0.772543i
$227$	5.64470	−	17.3726i	0.374652	−	1.15306i	−0.569061	−	0.822295i	$-0.692693\pi$
$227$	5.64470	−	17.3726i	0.374652	−	1.15306i	0.943713	−	0.330765i	$-0.107307\pi$
$228$	−0.858891	−	2.64339i	−0.0568815	−	0.175063i
$229$	−21.2156	+	15.4140i	−1.40197	+	1.01859i	−0.407538	+	0.913188i	$0.633612\pi$
$229$	−21.2156	+	15.4140i	−1.40197	+	1.01859i	−0.994430	+	0.105400i	$0.966388\pi$
$230$	−7.73328			−0.509917
$231$	−2.97414	−	1.46782i	−0.195684	−	0.0965758i
$232$	4.66418			0.306219
$233$	21.8239	−	15.8560i	1.42973	−	1.03876i	0.439665	−	0.898162i	$-0.355097\pi$
$233$	21.8239	−	15.8560i	1.42973	−	1.03876i	0.990067	−	0.140598i	$-0.0449027\pi$
$234$	0.285942	+	0.880039i	0.0186926	+	0.0575300i
$235$	−1.07900	+	3.32081i	−0.0703860	+	0.216626i
$236$	1.20152	+	0.872955i	0.0782123	+	0.0568246i
$237$	3.23004	+	2.34676i	0.209814	+	0.152439i
$238$	1.39853	−	4.30423i	0.0906532	−	0.279002i
$239$	−2.35036	−	7.23365i	−0.152032	−	0.467906i	0.845816	−	0.533474i	$-0.179114\pi$
$239$	−2.35036	−	7.23365i	−0.152032	−	0.467906i	−0.997848	+	0.0655685i	$0.979114\pi$
$240$	−1.52029	+	1.10455i	−0.0981341	+	0.0712986i
$241$	−17.5282			−1.12909			−0.564546	−	0.825402i	$-0.690949\pi$
$241$	−17.5282			−1.12909			−0.564546	+	0.825402i	$0.690949\pi$
$242$	−10.5451	−	3.13068i	−0.677864	−	0.201248i
$243$	1.00000			0.0641500
$244$	−11.5626	+	8.40071i	−0.740219	+	0.537800i
$245$	0.580698	+	1.78720i	0.0370994	+	0.114180i
$246$	0.146556	−	0.451054i	0.00934408	−	0.0287581i
$247$	2.08070	+	1.51172i	0.132392	+	0.0961882i
$248$	−0.635083	−	0.461415i	−0.0403278	−	0.0292999i
$249$	0.976346	−	3.00489i	0.0618734	−	0.190427i
$250$	−3.75635	−	11.5609i	−0.237573	−	0.731174i
$251$	11.3761	−	8.26523i	0.718054	−	0.521697i	−0.167708	−	0.985837i	$-0.553637\pi$
$251$	11.3761	−	8.26523i	0.718054	−	0.521697i	0.885762	+	0.464140i	$0.153637\pi$
$252$	1.00000			0.0629941
$253$	12.2393	+	6.04046i	0.769479	+	0.379760i
$254$	0.609428			0.0382389
$255$	−6.88041	+	4.99891i	−0.430868	+	0.313044i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	−2.65009	+	8.15615i	−0.165308	+	0.508767i	−0.999059	−	0.0433745i	$-0.986189\pi$
$257$	−2.65009	+	8.15615i	−0.165308	+	0.508767i	0.833751	+	0.552141i	$0.186189\pi$
$258$	−8.90443	−	6.46944i	−0.554365	−	0.402770i
$259$	−0.902253	−	0.655525i	−0.0560633	−	0.0407324i
$260$	0.537336	−	1.65375i	0.0333242	−	0.102561i
$261$	1.44131	+	4.43590i	0.0892150	+	0.274575i
$262$	−13.5776	+	9.86473i	−0.838829	+	0.609445i
$263$	24.1884			1.49152			0.745760	−	0.666215i	$-0.232087\pi$
$263$	24.1884			1.49152			0.745760	+	0.666215i	$0.232087\pi$
$264$	3.26889	−	0.560659i	0.201186	−	0.0345062i
$265$	8.61403			0.529156
$266$	2.24861	−	1.63371i	0.137871	−	0.100169i
$267$	−4.21393	−	12.9691i	−0.257888	−	0.793699i
$268$	0.208968	−	0.643138i	0.0127648	−	0.0392859i
$269$	−13.4039	−	9.73853i	−0.817253	−	0.593769i	0.0986716	−	0.995120i	$-0.468541\pi$
$269$	−13.4039	−	9.73853i	−0.817253	−	0.593769i	−0.915924	+	0.401351i	$0.868541\pi$
$270$	−1.52029	−	1.10455i	−0.0925217	−	0.0672210i
$271$	−8.90924	+	27.4198i	−0.541198	+	1.66564i	0.188665	+	0.982041i	$0.439584\pi$
$271$	−8.90924	+	27.4198i	−0.541198	+	1.66564i	−0.729863	+	0.683594i	$0.760416\pi$
$272$	1.39853	+	4.30423i	0.0847983	+	0.260982i
$273$	−0.748606	+	0.543894i	−0.0453077	+	0.0329180i
$274$	−21.9201			−1.32424
$275$	−0.700455	+	4.82047i	−0.0422390	+	0.290685i
$276$	−4.11525			−0.247709
$277$	13.5410	−	9.83813i	0.813601	−	0.591116i	−0.101271	−	0.994859i	$-0.532291\pi$
$277$	13.5410	−	9.83813i	0.813601	−	0.591116i	0.914872	+	0.403743i	$0.132291\pi$
$278$	−1.72849	−	5.31975i	−0.103668	−	0.319057i
$279$	0.242580	−	0.746585i	0.0145229	−	0.0446969i
$280$	−1.52029	−	1.10455i	−0.0908545	−	0.0660097i
$281$	1.02783	+	0.746761i	0.0613151	+	0.0445480i	0.618021	−	0.786162i	$-0.287935\pi$
$281$	1.02783	+	0.746761i	0.0613151	+	0.0445480i	−0.556706	+	0.830710i	$0.687935\pi$
$282$	−0.574186	+	1.76716i	−0.0341923	+	0.105233i
$283$	7.31983	+	22.5281i	0.435119	+	1.33916i	0.892965	+	0.450127i	$0.148621\pi$
$283$	7.31983	+	22.5281i	0.435119	+	1.33916i	−0.457846	+	0.889032i	$0.651379\pi$
$284$	4.30172	−	3.12538i	0.255260	−	0.185457i
$285$	−5.22304			−0.309386
$286$	−2.14217	+	2.19764i	−0.126669	+	0.129949i
$287$	0.474266			0.0279950
$288$	−0.809017	+	0.587785i	−0.0476718	+	0.0346356i
$289$	1.07608	+	3.31184i	0.0632989	+	0.194814i
$290$	2.70848	−	8.33585i	0.159048	−	0.489498i
$291$	−3.82930	−	2.78215i	−0.224478	−	0.163093i
$292$	2.83905	+	2.06269i	0.166143	+	0.120710i
$293$	4.10856	−	12.6449i	0.240025	−	0.738720i	−0.756390	−	0.654121i	$-0.773039\pi$
$293$	4.10856	−	12.6449i	0.240025	−	0.738720i	0.996415	−	0.0845996i	$-0.0269611\pi$
$294$	0.309017	+	0.951057i	0.0180222	+	0.0554667i
$295$	2.25787	−	1.64044i	0.131458	−	0.0955100i
$296$	1.11525			0.0648224
$297$	1.54336	+	2.93565i	0.0895549	+	0.170344i
$298$	21.4053			1.23997
$299$	3.08070	−	2.23826i	0.178161	−	0.129442i
$300$	−0.453850	−	1.39681i	−0.0262030	−	0.0806447i
$301$	3.40119	−	10.4678i	0.196041	−	0.603353i
$302$	8.64886	+	6.28376i	0.497686	+	0.361590i
$303$	5.06365	+	3.67896i	0.290899	+	0.211351i
$304$	−0.858891	+	2.64339i	−0.0492608	+	0.151609i
$305$	8.29942	+	25.5430i	0.475223	+	1.46259i
$306$	−3.66140	+	2.66016i	−0.209308	+	0.152071i
$307$	−11.9130			−0.679912			−0.339956	−	0.940441i	$-0.610412\pi$
$307$	−11.9130			−0.679912			−0.339956	+	0.940441i	$0.610412\pi$
$308$	1.54336	+	2.93565i	0.0879412	+	0.167274i
$309$	−14.6616			−0.834071
$310$	−1.19343	+	0.867081i	−0.0677825	+	0.0492469i
$311$	−9.20339	−	28.3251i	−0.521877	−	1.60617i	−0.770411	−	0.637548i	$-0.779949\pi$
$311$	−9.20339	−	28.3251i	−0.521877	−	1.60617i	0.248534	−	0.968623i	$-0.420051\pi$
$312$	0.285942	−	0.880039i	0.0161883	−	0.0498224i
$313$	−0.497212	−	0.361246i	−0.0281041	−	0.0204188i	0.573645	−	0.819104i	$-0.305529\pi$
$313$	−0.497212	−	0.361246i	−0.0281041	−	0.0204188i	−0.601749	+	0.798686i	$0.705529\pi$
$314$	3.77295	+	2.74121i	0.212920	+	0.154696i
$315$	0.580698	−	1.78720i	0.0327186	−	0.100698i
$316$	−1.23377	−	3.79714i	−0.0694048	−	0.213606i
$317$	20.7646	−	15.0863i	1.16625	−	0.847333i	0.175698	−	0.984444i	$-0.443782\pi$
$317$	20.7646	−	15.0863i	1.16625	−	0.847333i	0.990556	+	0.137111i	$0.0437818\pi$
$318$	4.58394			0.257054
$319$	−10.7978	+	11.0774i	−0.604560	+	0.620215i
$320$	1.87918			0.105049
$321$	5.24861	−	3.81334i	0.292949	−	0.212840i
$322$	−1.27168	−	3.91383i	−0.0708680	−	0.218109i
$323$	−3.88711	+	11.9633i	−0.216285	+	0.665656i
$324$	−0.809017	−	0.587785i	−0.0449454	−	0.0326547i
$325$	1.09947	+	0.798812i	0.0609876	+	0.0443101i
$326$	−3.19737	+	9.84048i	−0.177086	+	0.545014i
$327$	−1.29848	−	3.99631i	−0.0718061	−	0.220996i
$328$	−0.383689	+	0.278766i	−0.0211857	+	0.0153923i
$329$	−1.85810			−0.102441
$330$	0.896227	−	6.16775i	0.0493357	−	0.339524i
$331$	32.4433			1.78324			0.891622	−	0.452780i	$-0.149568\pi$
$331$	32.4433			1.78324			0.891622	+	0.452780i	$0.149568\pi$
$332$	−2.55611	+	1.85712i	−0.140285	+	0.101923i
$333$	0.344630	+	1.06066i	0.0188856	+	0.0581239i
$334$	−3.15565	+	9.71209i	−0.172669	+	0.531422i
$335$	−1.02807	−	0.746938i	−0.0561696	−	0.0408096i
$336$	−0.809017	−	0.587785i	−0.0441355	−	0.0320663i
$337$	−2.55147	+	7.85261i	−0.138987	+	0.427759i	−0.996189	−	0.0872220i	$-0.972201\pi$
$337$	−2.55147	+	7.85261i	−0.138987	+	0.427759i	0.857202	+	0.514981i	$0.172201\pi$
$338$	−3.75263	−	11.5494i	−0.204116	−	0.628205i
$339$	−15.9851	+	11.6139i	−0.868193	+	0.630779i
$340$	8.50466			0.461230
$341$	2.56610	−	0.440121i	0.138962	−	0.0238339i
$342$	−2.77943			−0.150294
$343$	−0.809017	+	0.587785i	−0.0436828	+	0.0317374i
$344$	3.40119	+	10.4678i	0.183380	+	0.564385i
$345$	−2.38971	+	7.35479i	−0.128658	+	0.395968i
$346$	8.14356	+	5.91664i	0.437801	+	0.318081i
$347$	1.23880	+	0.900039i	0.0665021	+	0.0483166i	0.620540	−	0.784175i	$-0.286914\pi$
$347$	1.23880	+	0.900039i	0.0665021	+	0.0483166i	−0.554038	+	0.832492i	$0.686914\pi$
$348$	1.44131	−	4.43590i	0.0772624	−	0.237789i
$349$	−5.55443	−	17.0948i	−0.297322	−	0.915062i	−0.982432	−	0.186623i	$-0.940246\pi$
$349$	−5.55443	−	17.0948i	−0.297322	−	0.915062i	0.685110	−	0.728440i	$-0.259754\pi$
$350$	1.18820	−	0.863274i	0.0635117	−	0.0461439i
$351$	0.925328			0.0493904
$352$	−2.97414	−	1.46782i	−0.158522	−	0.0782353i
$353$	−3.36131			−0.178904			−0.0894522	−	0.995991i	$-0.528512\pi$
$353$	−3.36131			−0.178904			−0.0894522	+	0.995991i	$0.528512\pi$
$354$	1.20152	−	0.872955i	0.0638601	−	0.0463971i
$355$	−3.08770	−	9.50295i	−0.163878	−	0.504364i
$356$	−4.21393	+	12.9691i	−0.223338	+	0.687363i
$357$	−3.66140	−	2.66016i	−0.193782	−	0.140791i
$358$	1.32406	+	0.961989i	0.0699790	+	0.0508427i
$359$	−6.26897	+	19.2939i	−0.330864	+	1.01829i	0.637860	+	0.770152i	$0.279820\pi$
$359$	−6.26897	+	19.2939i	−0.330864	+	1.01829i	−0.968724	+	0.248142i	$0.920180\pi$
$360$	0.580698	+	1.78720i	0.0306055	+	0.0941939i
$361$	9.12148	−	6.62714i	0.480078	−	0.348797i
$362$	21.4675			1.12830
$363$	−6.23607	+	9.06154i	−0.327309	+	0.475607i
$364$	0.925328			0.0485004
$365$	5.33509	−	3.87617i	0.279251	−	0.202888i
$366$	4.41651	+	13.5926i	0.230855	+	0.710498i
$367$	1.66725	−	5.13127i	0.0870297	−	0.267850i	−0.898065	−	0.439863i	$-0.855027\pi$
$367$	1.66725	−	5.13127i	0.0870297	−	0.267850i	0.985095	+	0.172013i	$0.0550271\pi$
$368$	3.32930	+	2.41888i	0.173552	+	0.126093i
$369$	−0.383689	−	0.278766i	−0.0199741	−	0.0145120i
$370$	0.647621	−	1.99317i	0.0336682	−	0.103620i
$371$	1.41651	+	4.35958i	0.0735417	+	0.226338i
$372$	−0.635083	+	0.461415i	−0.0329275	+	0.0239232i
$373$	−27.5943			−1.42878			−0.714389	−	0.699749i	$-0.753295\pi$
$373$	−27.5943			−1.42878			−0.714389	+	0.699749i	$0.753295\pi$
$374$	−13.4602	−	6.64298i	−0.696008	−	0.343500i
$375$	−12.1558			−0.627724
$376$	1.50324	−	1.09217i	0.0775236	−	0.0563242i
$377$	1.33369	+	4.10466i	0.0686883	+	0.211401i
$378$	0.309017	−	0.951057i	0.0158941	−	0.0489171i
$379$	−6.20152	−	4.50567i	−0.318551	−	0.231441i	0.417006	−	0.908904i	$-0.363079\pi$
$379$	−6.20152	−	4.50567i	−0.318551	−	0.231441i	−0.735557	+	0.677463i	$0.763079\pi$
$380$	4.22553	+	3.07003i	0.216765	+	0.157489i
$381$	0.188324	−	0.579601i	0.00964812	−	0.0296938i
$382$	2.08979	+	6.43171i	0.106923	+	0.329075i
$383$	4.62451	−	3.35990i	0.236301	−	0.171683i	−0.463333	−	0.886185i	$-0.653346\pi$
$383$	4.62451	−	3.35990i	0.236301	−	0.171683i	0.699634	+	0.714501i	$0.253346\pi$
$384$	1.00000			0.0510310
$385$	6.14283	−	1.05358i	0.313068	−	0.0536953i
$386$	15.5567			0.791817
$387$	−8.90443	+	6.46944i	−0.452637	+	0.328860i
$388$	1.46266	+	4.50162i	0.0742555	+	0.228535i
$389$	−3.32996	+	10.2486i	−0.168836	+	0.519623i	−0.999298	−	0.0374512i	$-0.988076\pi$
$389$	−3.32996	+	10.2486i	−0.168836	+	0.519623i	0.830463	+	0.557074i	$0.188076\pi$
$390$	−1.40676	−	1.02207i	−0.0712343	−	0.0517547i
$391$	15.0675	+	10.9472i	0.761999	+	0.553624i
$392$	0.309017	−	0.951057i	0.0156077	−	0.0480356i
$393$	5.18619	+	15.9615i	0.261609	+	0.805149i
$394$	−15.6437	+	11.3658i	−0.788120	+	0.572603i
$395$	−7.50272			−0.377503
$396$	0.476925	−	3.28216i	0.0239664	−	0.164935i
$397$	18.7092			0.938987			0.469493	−	0.882936i	$-0.344437\pi$
$397$	18.7092			0.938987			0.469493	+	0.882936i	$0.344437\pi$
$398$	−9.84759	+	7.15469i	−0.493615	+	0.358632i
$399$	−0.858891	−	2.64339i	−0.0429983	−	0.132335i
$400$	−0.453850	+	1.39681i	−0.0226925	+	0.0698404i
$401$	−0.0994701	−	0.0722692i	−0.00496730	−	0.00360895i	0.585299	−	0.810818i	$-0.300977\pi$
$401$	−0.0994701	−	0.0722692i	−0.00496730	−	0.00360895i	−0.590266	+	0.807209i	$0.700977\pi$
$402$	−0.547086	−	0.397481i	−0.0272862	−	0.0198246i
$403$	0.224466	−	0.690836i	0.0111815	−	0.0344130i
$404$	−1.93414	−	5.95268i	−0.0962271	−	0.296157i
$405$	−1.52029	+	1.10455i	−0.0755437	+	0.0548857i
$406$	4.66418			0.231480
$407$	−2.58184	+	2.64870i	−0.127977	+	0.131291i
$408$	4.52573			0.224057
$409$	−11.8550	+	8.61316i	−0.586192	+	0.425894i	−0.840951	−	0.541111i	$-0.818004\pi$
$409$	−11.8550	+	8.61316i	−0.586192	+	0.425894i	0.254759	+	0.967005i	$0.418004\pi$
$410$	0.275405	+	0.847610i	0.0136013	+	0.0418605i
$411$	−6.77368	+	20.8472i	−0.334121	+	1.02832i
$412$	11.8615	+	8.61789i	0.584375	+	0.424573i
$413$	1.20152	+	0.872955i	0.0591229	+	0.0429553i
$414$	−1.27168	+	3.91383i	−0.0624997	+	0.192354i
$415$	1.83473	+	5.64671i	0.0900633	+	0.277186i
$416$	−0.748606	+	0.543894i	−0.0367034	+	0.0266666i
$417$	−5.59351			−0.273916
$418$	−4.28967	−	8.15943i	−0.209814	−	0.399091i
$419$	−6.44949			−0.315078			−0.157539	−	0.987513i	$-0.550356\pi$
$419$	−6.44949			−0.315078			−0.157539	+	0.987513i	$0.550356\pi$
$420$	−1.52029	+	1.10455i	−0.0741824	+	0.0538967i
$421$	−7.96927	−	24.5269i	−0.388398	−	1.19537i	−0.933985	−	0.357313i	$-0.883693\pi$
$421$	−7.96927	−	24.5269i	−0.388398	−	1.19537i	0.545586	−	0.838055i	$-0.316307\pi$
$422$	−5.68784	+	17.5054i	−0.276880	+	0.852148i
$423$	1.50324	+	1.09217i	0.0730899	+	0.0531029i
$424$	−3.70848	−	2.69437i	−0.180100	−	0.130850i
$425$	−2.05401	+	6.32158i	−0.0996339	+	0.306642i
$426$	−1.64311	−	5.05697i	−0.0796089	−	0.245011i
$427$	−11.5626	+	8.40071i	−0.559553	+	0.406539i
$428$	−6.48763			−0.313592
$429$	1.42812	+	2.71644i	0.0689501	+	0.131151i
$430$	20.6831			0.997429
$431$	−19.2466	+	13.9835i	−0.927075	+	0.673559i	−0.945275	−	0.326275i	$-0.894206\pi$
$431$	−19.2466	+	13.9835i	−0.927075	+	0.673559i	0.0182002	+	0.999834i	$0.494206\pi$
$432$	0.309017	+	0.951057i	0.0148676	+	0.0457577i
$433$	7.93826	−	24.4314i	0.381488	−	1.17410i	−0.557507	−	0.830172i	$-0.688242\pi$
$433$	7.93826	−	24.4314i	0.381488	−	1.17410i	0.938996	−	0.343929i	$-0.111758\pi$
$434$	−0.635083	−	0.461415i	−0.0304850	−	0.0221486i
$435$	−7.09090	−	5.15184i	−0.339983	−	0.247012i
$436$	−1.29848	+	3.99631i	−0.0621859	+	0.191389i
$437$	3.53455	+	10.8782i	0.169080	+	0.520376i
$438$	2.83905	−	2.06269i	0.135655	−	0.0985593i
$439$	31.8712			1.52113			0.760565	−	0.649262i	$-0.224922\pi$
$439$	31.8712			1.52113			0.760565	+	0.649262i	$0.224922\pi$
$440$	−4.35038	+	4.46303i	−0.207396	+	0.212767i
$441$	1.00000			0.0476190
$442$	−3.38799	+	2.46152i	−0.161150	+	0.117083i
$443$	4.04349	+	12.4446i	0.192112	+	0.591260i	0.999998	+	0.00192142i	$0.000611607\pi$
$443$	4.04349	+	12.4446i	0.192112	+	0.591260i	−0.807886	+	0.589339i	$0.799388\pi$
$444$	0.344630	−	1.06066i	0.0163554	−	0.0503368i
$445$	20.7315	+	15.0623i	0.982767	+	0.714022i
$446$	19.2240	+	13.9670i	0.910282	+	0.661358i
$447$	6.61459	−	20.3576i	0.312859	−	0.962882i
$448$	0.309017	+	0.951057i	0.0145997	+	0.0449332i
$449$	−28.7467	+	20.8857i	−1.35664	+	0.985656i	−0.357989	+	0.933726i	$0.616538\pi$
$449$	−28.7467	+	20.8857i	−1.35664	+	0.985656i	−0.998651	+	0.0519307i	$0.983462\pi$
$450$	−1.46869			−0.0692347
$451$	0.226189	−	1.55661i	0.0106508	−	0.0732981i
$452$	19.7587			0.929371
$453$	8.64886	−	6.28376i	0.406359	−	0.295237i
$454$	5.64470	+	17.3726i	0.264919	+	0.815337i
$455$	0.537336	−	1.65375i	0.0251907	−	0.0775290i
$456$	2.24861	+	1.63371i	0.105301	+	0.0765054i
$457$	−12.9573	−	9.41403i	−0.606117	−	0.440370i	0.241928	−	0.970294i	$-0.422220\pi$
$457$	−12.9573	−	9.41403i	−0.606117	−	0.440370i	−0.848045	+	0.529925i	$0.822220\pi$
$458$	8.10364	−	24.9405i	0.378658	−	1.16539i
$459$	1.39853	+	4.30423i	0.0652777	+	0.200904i
$460$	6.25635	−	4.54551i	0.291704	−	0.211935i
$461$	−4.43314			−0.206472			−0.103236	−	0.994657i	$-0.532920\pi$
$461$	−4.43314			−0.206472			−0.103236	+	0.994657i	$0.532920\pi$
$462$	3.26889	−	0.560659i	0.152083	−	0.0260842i
$463$	−24.2555			−1.12725			−0.563624	−	0.826031i	$-0.690593\pi$
$463$	−24.2555			−1.12725			−0.563624	+	0.826031i	$0.690593\pi$
$464$	−3.77340	+	2.74154i	−0.175176	+	0.127273i
$465$	0.455851	+	1.40297i	0.0211396	+	0.0650610i
$466$	−8.33599	+	25.6555i	−0.386157	+	1.18847i
$467$	6.12054	+	4.44684i	0.283225	+	0.205775i	0.720323	−	0.693639i	$-0.243994\pi$
$467$	6.12054	+	4.44684i	0.283225	+	0.205775i	−0.437098	+	0.899414i	$0.643994\pi$
$468$	−0.748606	−	0.543894i	−0.0346043	−	0.0251415i
$469$	0.208968	−	0.643138i	0.00964926	−	0.0296974i
$470$	−1.07900	−	3.32081i	−0.0497704	−	0.153178i
$471$	3.77295	−	2.74121i	0.173849	−	0.126308i
$472$	−1.48516			−0.0683600
$473$	−32.7348	−	16.1556i	−1.50515	−	0.742834i
$474$	−3.99255			−0.183384
$475$	−3.30250	+	2.39941i	−0.151529	+	0.110092i
$476$	1.39853	+	4.30423i	0.0641015	+	0.197284i
$477$	1.41651	−	4.35958i	0.0648577	−	0.199612i
$478$	6.15331	+	4.47064i	0.281446	+	0.204482i
$479$	−14.3237	−	10.4068i	−0.654466	−	0.475498i	0.210323	−	0.977632i	$-0.432548\pi$
$479$	−14.3237	−	10.4068i	−0.654466	−	0.475498i	−0.864790	+	0.502134i	$0.832548\pi$
$480$	0.580698	−	1.78720i	0.0265051	−	0.0815744i
$481$	0.318896	+	0.981460i	0.0145404	+	0.0447507i
$482$	14.1806	−	10.3028i	0.645909	−	0.469281i
$483$	−4.11525			−0.187250
$484$	10.3713	−	3.66547i	0.471424	−	0.166612i
$485$	8.89468			0.403886
$486$	−0.809017	+	0.587785i	−0.0366978	+	0.0266625i
$487$	−8.04047	−	24.7460i	−0.364348	−	1.12135i	−0.950388	−	0.311067i	$-0.899314\pi$
$487$	−8.04047	−	24.7460i	−0.364348	−	1.12135i	0.586040	−	0.810282i	$-0.300686\pi$
$488$	4.41651	−	13.5926i	0.199926	−	0.615310i
$489$	8.37081	+	6.08175i	0.378541	+	0.275026i
$490$	−1.52029	−	1.10455i	−0.0686796	−	0.0498986i
$491$	10.9992	−	33.8521i	0.496388	−	1.52772i	−0.318396	−	0.947958i	$-0.603144\pi$
$491$	10.9992	−	33.8521i	0.496388	−	1.52772i	0.814783	−	0.579766i	$-0.196856\pi$
$492$	0.146556	+	0.451054i	0.00660726	+	0.0203351i
$493$	−17.0774	+	12.4075i	−0.769128	+	0.558805i
$494$	−2.57188			−0.115715
$495$	−5.58893	−	2.75830i	−0.251204	−	0.123977i
$496$	0.785006			0.0352478
$497$	4.30172	−	3.12538i	0.192958	−	0.140193i
$498$	0.976346	+	3.00489i	0.0437511	+	0.134652i
$499$	−4.54496	+	13.9879i	−0.203460	+	0.626186i	0.796313	+	0.604885i	$0.206781\pi$
$499$	−4.54496	+	13.9879i	−0.203460	+	0.626186i	−0.999773	+	0.0213012i	$0.993219\pi$
$500$	9.83426	+	7.14501i	0.439802	+	0.319535i
$501$	8.26159	+	6.00240i	0.369101	+	0.268167i
$502$	−4.34529	+	13.3734i	−0.193940	+	0.596885i
$503$	13.2446	+	40.7626i	0.590546	+	1.81751i	0.575753	+	0.817623i	$0.304709\pi$
$503$	13.2446	+	40.7626i	0.590546	+	1.81751i	0.0147926	+	0.999891i	$0.495291\pi$
$504$	−0.809017	+	0.587785i	−0.0360365	+	0.0261820i
$505$	−11.7618			−0.523393
$506$	−13.4523	+	2.30725i	−0.598028	+	0.102570i
$507$	−12.1438			−0.539324
$508$	−0.493038	+	0.358213i	−0.0218750	+	0.0158931i
$509$	−8.08783	−	24.8918i	−0.358487	−	1.10331i	−0.953960	−	0.299934i	$-0.903035\pi$
$509$	−8.08783	−	24.8918i	−0.358487	−	1.10331i	0.595473	−	0.803375i	$-0.296965\pi$
$510$	2.62808	−	8.08841i	0.116374	−	0.358161i
$511$	2.83905	+	2.06269i	0.125592	+	0.0912482i
$512$	−0.809017	−	0.587785i	−0.0357538	−	0.0259767i
$513$	−0.858891	+	2.64339i	−0.0379210	+	0.116709i
$514$	−2.65009	−	8.15615i	−0.116891	−	0.359752i
$515$	22.2899	−	16.1946i	0.982210	−	0.713617i
$516$	11.0065			0.484533
$517$	−0.886176	+	6.09859i	−0.0389740	+	0.268216i
$518$	1.11525			0.0490011
$519$	8.14356	−	5.91664i	0.357463	−	0.259712i
$520$	0.537336	+	1.65375i	0.0235637	+	0.0725217i
$521$	0.887886	−	2.73263i	0.0388990	−	0.119719i	−0.929721	−	0.368264i	$-0.879952\pi$
$521$	0.887886	−	2.73263i	0.0388990	−	0.119719i	0.968620	+	0.248545i	$0.0799524\pi$
$522$	−3.77340	−	2.74154i	−0.165157	−	0.119994i
$523$	18.1287	+	13.1713i	0.792712	+	0.575939i	0.908767	−	0.417304i	$-0.137025\pi$
$523$	18.1287	+	13.1713i	0.792712	+	0.575939i	−0.116055	+	0.993243i	$0.537025\pi$
$524$	5.18619	−	15.9615i	0.226560	−	0.697280i
$525$	−0.453850	−	1.39681i	−0.0198076	−	0.0609617i
$526$	−19.5688	+	14.2176i	−0.853241	+	0.619916i
$527$	3.55273			0.154759
$528$	−2.31504	+	2.37499i	−0.100749	+	0.103358i
$529$	−6.06475			−0.263685
$530$	−6.96890	+	5.06320i	−0.302710	+	0.219931i
$531$	−0.458940	−	1.41247i	−0.0199163	−	0.0612960i
$532$	−0.858891	+	2.64339i	−0.0372377	+	0.114606i
$533$	−0.355038	−	0.257950i	−0.0153784	−	0.0111731i
$534$	11.0322	+	8.01537i	0.477410	+	0.346859i
$535$	−3.76736	+	11.5947i	−0.162877	+	0.501284i
$536$	0.208968	+	0.643138i	0.00902606	+	0.0277793i
$537$	1.32406	−	0.961989i	0.0571376	−	0.0415129i
$538$	16.5682			0.714305
$539$	1.54336	+	2.93565i	0.0664773	+	0.126447i
$540$	1.87918			0.0808669
$541$	23.1086	−	16.7894i	0.993515	−	0.721831i	0.0328269	−	0.999461i	$-0.489549\pi$
$541$	23.1086	−	16.7894i	0.993515	−	0.721831i	0.960688	+	0.277630i	$0.0895490\pi$
$542$	−8.90924	−	27.4198i	−0.382685	−	1.17778i
$543$	6.63381	−	20.4168i	0.284684	−	0.876167i
$544$	−3.66140	−	2.66016i	−0.156981	−	0.114053i
$545$	6.38820	+	4.64130i	0.273640	+	0.198811i
$546$	0.285942	−	0.880039i	0.0122372	−	0.0376622i
$547$	−6.80194	−	20.9342i	−0.290830	−	0.895082i	−0.984590	−	0.174877i	$-0.944047\pi$
$547$	−6.80194	−	20.9342i	−0.290830	−	0.895082i	0.693760	−	0.720206i	$-0.255953\pi$
$548$	17.7337	−	12.8843i	0.757547	−	0.550390i
$549$	14.2921			0.609974
$550$	−2.26672	−	4.31156i	−0.0966533	−	0.183845i
$551$	−12.9638			−0.552275
$552$	3.32930	−	2.41888i	0.141705	−	0.102954i
$553$	−1.23377	−	3.79714i	−0.0524651	−	0.161471i
$554$	−5.17221	+	15.9184i	−0.219746	+	0.676309i
$555$	−1.69549	−	1.23185i	−0.0719697	−	0.0522891i
$556$	4.52525	+	3.28779i	0.191913	+	0.139433i
$557$	−9.27072	+	28.5323i	−0.392813	+	1.20895i	0.537838	+	0.843048i	$0.319241\pi$
$557$	−9.27072	+	28.5323i	−0.392813	+	1.20895i	−0.930652	+	0.365907i	$0.880759\pi$
$558$	0.242580	+	0.746585i	0.0102692	+	0.0316055i
$559$	−8.23951	+	5.98636i	−0.348494	+	0.253196i
$560$	1.87918			0.0794098
$561$	−10.4773	+	10.7486i	−0.442351	+	0.453805i
$562$	−1.27046			−0.0535913
$563$	−11.0797	+	8.04991i	−0.466956	+	0.339263i	−0.796254	−	0.604963i	$-0.793188\pi$
$563$	−11.0797	+	8.04991i	−0.466956	+	0.339263i	0.329298	+	0.944226i	$0.393188\pi$
$564$	−0.574186	−	1.76716i	−0.0241776	−	0.0744110i
$565$	11.4738	−	35.3128i	0.482708	−	1.48562i
$566$	−19.1636	−	13.9231i	−0.805505	−	0.585234i
$567$	−0.809017	−	0.587785i	−0.0339755	−	0.0246847i
$568$	−1.64311	+	5.05697i	−0.0689434	+	0.212186i
$569$	−4.79962	−	14.7717i	−0.201211	−	0.619263i	−0.999848	−	0.0174499i	$-0.994445\pi$
$569$	−4.79962	−	14.7717i	−0.201211	−	0.619263i	0.798637	−	0.601813i	$-0.205555\pi$
$570$	4.22553	−	3.07003i	0.176988	−	0.128589i
$571$	0.403940			0.0169044			0.00845218	−	0.999964i	$-0.497310\pi$
$571$	0.403940			0.0169044			0.00845218	+	0.999964i	$0.497310\pi$
$572$	0.441312	−	3.03707i	0.0184522	−	0.126986i
$573$	6.76270			0.282516
$574$	−0.383689	+	0.278766i	−0.0160149	+	0.0116355i
$575$	1.86770	+	5.74820i	0.0778887	+	0.239717i
$576$	0.309017	−	0.951057i	0.0128757	−	0.0396274i
$577$	14.6103	+	10.6150i	0.608235	+	0.441909i	0.848792	−	0.528726i	$-0.177330\pi$
$577$	14.6103	+	10.6150i	0.608235	+	0.441909i	−0.240557	+	0.970635i	$0.577330\pi$
$578$	−2.81722	−	2.04683i	−0.117181	−	0.0851368i
$579$	4.80729	−	14.7953i	0.199784	−	0.614873i
$580$	2.70848	+	8.33585i	0.112464	+	0.346127i
$581$	−2.55611	+	1.85712i	−0.106045	+	0.0770464i
$582$	4.73328			0.196201
$583$	14.9844	−	2.57003i	0.620590	−	0.106440i
$584$	−3.50926			−0.145214
$585$	−1.40676	+	1.02207i	−0.0581625	+	0.0422576i
$586$	4.10856	+	12.6449i	0.169723	+	0.522354i
$587$	−0.361493	+	1.11256i	−0.0149204	+	0.0459203i	−0.958240	−	0.285967i	$-0.907685\pi$
$587$	−0.361493	+	1.11256i	−0.0149204	+	0.0459203i	0.943319	+	0.331887i	$0.107685\pi$
$588$	−0.809017	−	0.587785i	−0.0333633	−	0.0242399i
$589$	1.76517	+	1.28247i	0.0727325	+	0.0528433i
$590$	−0.862430	+	2.65429i	−0.0355057	+	0.109275i
$591$	5.97537	+	18.3903i	0.245794	+	0.756476i
$592$	−0.902253	+	0.655525i	−0.0370824	+	0.0269419i
$593$	20.2877			0.833117			0.416558	−	0.909109i	$-0.363236\pi$
$593$	20.2877			0.833117			0.416558	+	0.909109i	$0.363236\pi$
$594$	−2.97414	−	1.46782i	−0.122030	−	0.0602256i
$595$	8.50466			0.348657
$596$	−17.3172	+	12.5817i	−0.709341	+	0.515366i
$597$	3.76144	+	11.5765i	0.153946	+	0.473796i
$598$	−1.17672	+	3.62158i	−0.0481197	+	0.148097i
$599$	−5.44110	−	3.95319i	−0.222317	−	0.161523i	0.471052	−	0.882106i	$-0.343874\pi$
$599$	−5.44110	−	3.95319i	−0.222317	−	0.161523i	−0.693369	+	0.720582i	$0.743874\pi$
$600$	1.18820	+	0.863274i	0.0485079	+	0.0352430i
$601$	10.9414	−	33.6741i	0.446308	−	1.37360i	−0.434734	−	0.900559i	$-0.643158\pi$
$601$	10.9414	−	33.6741i	0.446308	−	1.37360i	0.881043	−	0.473037i	$-0.156842\pi$
$602$	3.40119	+	10.4678i	0.138622	+	0.426635i
$603$	−0.547086	+	0.397481i	−0.0222791	+	0.0161867i
$604$	−10.6906			−0.434993
$605$	−0.528336	−	20.6642i	−0.0214799	−	0.840119i
$606$	−6.25901			−0.254255
$607$	−21.6961	+	15.7632i	−0.880618	+	0.639807i	−0.933415	−	0.358799i	$-0.883186\pi$
$607$	−21.6961	+	15.7632i	−0.880618	+	0.639807i	0.0527968	+	0.998605i	$0.483186\pi$
$608$	−0.858891	−	2.64339i	−0.0348326	−	0.107204i
$609$	1.44131	−	4.43590i	0.0584049	−	0.179752i
$610$	−21.7282	−	15.7864i	−0.879747	−	0.639174i
$611$	1.39099	+	1.01061i	0.0562734	+	0.0408850i
$612$	1.39853	−	4.30423i	0.0565322	−	0.173988i
$613$	−9.20392	−	28.3268i	−0.371743	−	1.14411i	−0.945650	−	0.325187i	$-0.894573\pi$
$613$	−9.20392	−	28.3268i	−0.371743	−	1.14411i	0.573907	−	0.818920i	$-0.305427\pi$
$614$	9.63783	−	7.00230i	0.388951	−	0.282590i
$615$	0.891230			0.0359379
$616$	−2.97414	−	1.46782i	−0.119831	−	0.0591403i
$617$	−21.7810			−0.876870			−0.438435	−	0.898763i	$-0.644467\pi$
$617$	−21.7810			−0.876870			−0.438435	+	0.898763i	$0.644467\pi$
$618$	11.8615	−	8.61789i	0.477140	−	0.346663i
$619$	−10.0918	−	31.0594i	−0.405624	−	1.24838i	−0.920373	−	0.391042i	$-0.872115\pi$
$619$	−10.0918	−	31.0594i	−0.405624	−	1.24838i	0.514749	−	0.857341i	$-0.327885\pi$
$620$	0.455851	−	1.40297i	0.0183074	−	0.0563445i
$621$	3.32930	+	2.41888i	0.133600	+	0.0970663i
$622$	24.0948	+	17.5059i	0.966113	+	0.701922i
$623$	−4.21393	+	12.9691i	−0.168828	+	0.519598i
$624$	0.285942	+	0.880039i	0.0114468	+	0.0352298i
$625$	12.5394	−	9.11038i	0.501574	−	0.364415i
$626$	0.614588			0.0245639
$627$	−9.08566	+	1.55831i	−0.362846	+	0.0622330i
$628$	−4.66363			−0.186099
$629$	−4.08336	+	2.96673i	−0.162814	+	0.118291i
$630$	0.580698	+	1.78720i	0.0231356	+	0.0712039i
$631$	1.84535	−	5.67939i	0.0734620	−	0.226093i	−0.907583	−	0.419873i	$-0.862075\pi$
$631$	1.84535	−	5.67939i	0.0734620	−	0.226093i	0.981045	+	0.193780i	$0.0620747\pi$
$632$	3.23004	+	2.34676i	0.128484	+	0.0933492i
$633$	14.8910	+	10.8189i	0.591862	+	0.430013i
$634$	−7.93135	+	24.4102i	−0.314994	+	0.969453i
$635$	0.353894	+	1.08917i	0.0140438	+	0.0432225i
$636$	−3.70848	+	2.69437i	−0.147051	+	0.106839i
$637$	0.925328			0.0366628
$638$	2.22447	−	15.3086i	0.0880675	−	0.606072i
$639$	−5.31722			−0.210346
$640$	−1.52029	+	1.10455i	−0.0600946	+	0.0436613i
$641$	13.1962	+	40.6138i	0.521219	+	1.60415i	0.771673	+	0.636020i	$0.219420\pi$
$641$	13.1962	+	40.6138i	0.521219	+	1.60415i	−0.250453	+	0.968129i	$0.580580\pi$
$642$	−2.00479	+	6.17011i	−0.0791227	+	0.243515i
$643$	13.6064	+	9.88563i	0.536584	+	0.389851i	0.822815	−	0.568310i	$-0.192402\pi$
$643$	13.6064	+	9.88563i	0.536584	+	0.389851i	−0.286231	+	0.958161i	$0.592402\pi$
$644$	3.32930	+	2.41888i	0.131193	+	0.0953173i
$645$	6.39144	−	19.6708i	0.251663	−	0.774538i
$646$	−3.88711	−	11.9633i	−0.152936	−	0.470690i
$647$	11.4531	−	8.32115i	0.450267	−	0.327138i	−0.339434	−	0.940630i	$-0.610236\pi$
$647$	11.4531	−	8.32115i	0.450267	−	0.327138i	0.789701	+	0.613492i	$0.210236\pi$
$648$	1.00000			0.0392837
$649$	3.43821	−	3.52724i	0.134962	−	0.138456i
$650$	−1.35902			−0.0533051
$651$	−0.635083	+	0.461415i	−0.0248909	+	0.0180843i
$652$	−3.19737	−	9.84048i	−0.125219	−	0.385383i
$653$	9.21659	−	28.3657i	0.360673	−	1.11004i	−0.591974	−	0.805957i	$-0.701651\pi$
$653$	9.21659	−	28.3657i	0.360673	−	1.11004i	0.952647	−	0.304080i	$-0.0983490\pi$
$654$	3.39947	+	2.46986i	0.132930	+	0.0965790i
$655$	−25.5148	−	18.5376i	−0.996945	−	0.724323i
$656$	0.146556	−	0.451054i	0.00572206	−	0.0176107i
$657$	−1.08442	−	3.33751i	−0.0423073	−	0.130209i
$658$	1.50324	−	1.09217i	0.0586023	−	0.0425771i
$659$	−37.3447			−1.45474			−0.727371	−	0.686244i	$-0.759258\pi$
$659$	−37.3447			−1.45474			−0.727371	+	0.686244i	$0.759258\pi$
$660$	2.90025	+	5.51661i	0.112892	+	0.214734i
$661$	−16.1887			−0.629667			−0.314833	−	0.949147i	$-0.601949\pi$
$661$	−16.1887			−0.629667			−0.314833	+	0.949147i	$0.601949\pi$
$662$	−26.2472	+	19.0697i	−1.02013	+	0.741164i
$663$	1.29410	+	3.98282i	0.0502586	+	0.154680i
$664$	0.976346	−	3.00489i	0.0378896	−	0.116612i
$665$	4.22553	+	3.07003i	0.163859	+	0.119051i
$666$	−0.902253	−	0.655525i	−0.0349616	−	0.0254011i
$667$	−5.93135	+	18.2548i	−0.229663	+	0.706830i
$668$	−3.15565	−	9.71209i	−0.122096	−	0.375772i
$669$	19.2240	−	13.9670i	0.743242	−	0.539997i
$670$	1.27077			0.0490940
$671$	22.0579	+	41.9567i	0.851537	+	1.61972i
$672$	1.00000			0.0385758
$673$	10.4650	−	7.60326i	0.403396	−	0.293084i	−0.367527	−	0.930013i	$-0.619795\pi$
$673$	10.4650	−	7.60326i	0.403396	−	0.293084i	0.770923	+	0.636929i	$0.219795\pi$
$674$	−2.55147	−	7.85261i	−0.0982789	−	0.302471i
$675$	−0.453850	+	1.39681i	−0.0174687	+	0.0537631i
$676$	9.82451	+	7.13793i	0.377866	+	0.274536i
$677$	−25.0430	−	18.1948i	−0.962483	−	0.699284i	−0.00875653	−	0.999962i	$-0.502787\pi$
$677$	−25.0430	−	18.1948i	−0.962483	−	0.699284i	−0.953726	+	0.300677i	$0.902787\pi$
$678$	6.10577	−	18.7916i	0.234491	−	0.721689i
$679$	1.46266	+	4.50162i	0.0561319	+	0.172756i
$680$	−6.88041	+	4.99891i	−0.263852	+	0.191700i
$681$	18.2666			0.699979
$682$	−1.81732	+	1.86438i	−0.0695889	+	0.0713908i
$683$	−46.0524			−1.76215			−0.881073	−	0.472980i	$-0.843178\pi$
$683$	−46.0524			−1.76215			−0.881073	+	0.472980i	$0.843178\pi$
$684$	2.24861	−	1.63371i	0.0859776	−	0.0624664i
$685$	−12.7290	−	39.1757i	−0.486348	−	1.49683i
$686$	0.309017	−	0.951057i	0.0117983	−	0.0363115i
$687$	−21.2156	−	15.4140i	−0.809426	−	0.588083i
$688$	−8.90443	−	6.46944i	−0.339478	−	0.246645i
$689$	1.31074	−	4.03404i	0.0499352	−	0.153685i
$690$	−2.38971	−	7.35479i	−0.0909749	−	0.279992i
$691$	29.3220	−	21.3037i	1.11546	−	0.810432i	0.131948	−	0.991257i	$-0.457877\pi$
$691$	29.3220	−	21.3037i	1.11546	−	0.810432i	0.983515	+	0.180825i	$0.0578768\pi$
$692$	−10.0660			−0.382652
$693$	0.476925	−	3.28216i	0.0181169	−	0.124679i
$694$	−1.53124			−0.0581250
$695$	8.50375	−	6.17833i	0.322565	−	0.234358i
$696$	1.44131	+	4.43590i	0.0546328	+	0.168142i
$697$	0.663274	−	2.04135i	0.0251233	−	0.0773216i
$698$	14.5417	+	10.5652i	0.550411	+	0.399897i
$699$	21.8239	+	15.8560i	0.825456	+	0.599729i
$700$	−0.453850	+	1.39681i	−0.0171539	+	0.0527943i
$701$	5.47700	+	16.8565i	0.206864	+	0.636661i	0.999632	+	0.0271374i	$0.00863915\pi$
$701$	5.47700	+	16.8565i	0.206864	+	0.636661i	−0.792768	+	0.609523i	$0.791361\pi$
$702$	−0.748606	+	0.543894i	−0.0282543	+	0.0205280i
$703$	−3.09975			−0.116909
$704$	3.26889	−	0.560659i	0.123201	−	0.0211306i
$705$	−3.49171			−0.131505
$706$	2.71936	−	1.97573i	0.102344	−	0.0743575i
$707$	−1.93414	−	5.95268i	−0.0727409	−	0.223873i
$708$	−0.458940	+	1.41247i	−0.0172480	+	0.0530839i
$709$	9.18489	+	6.67321i	0.344946	+	0.250618i	0.746746	−	0.665110i	$-0.231615\pi$
$709$	9.18489	+	6.67321i	0.344946	+	0.250618i	−0.401800	+	0.915727i	$0.631615\pi$
$710$	8.08369	+	5.87315i	0.303376	+	0.220415i
$711$	−1.23377	+	3.79714i	−0.0462699	+	0.142404i
$712$	−4.21393	−	12.9691i	−0.157924	−	0.486039i
$713$	2.61352	−	1.89884i	0.0978772	−	0.0711120i
$714$	4.52573			0.169371
$715$	−5.17160	−	2.55234i	−0.193407	−	0.0954519i
$716$	−1.63663			−0.0611639
$717$	6.15331	−	4.47064i	0.229800	−	0.166959i
$718$	−6.26897	−	19.2939i	−0.233956	−	0.720042i
$719$	−5.52218	+	16.9955i	−0.205943	+	0.633826i	0.793731	+	0.608269i	$0.208136\pi$
$719$	−5.52218	+	16.9955i	−0.205943	+	0.633826i	−0.999673	+	0.0255570i	$0.991864\pi$
$720$	−1.52029	−	1.10455i	−0.0566578	−	0.0411643i
$721$	11.8615	+	8.61789i	0.441746	+	0.320947i
$722$	−3.48410	+	10.7229i	−0.129665	+	0.399067i
$723$	−5.41651	−	16.6703i	−0.201442	−	0.619976i
$724$	−17.3675	+	12.6183i	−0.645460	+	0.468954i
$725$	−6.85024			−0.254412
$726$	−0.281153	−	10.9964i	−0.0104346	−	0.408115i
$727$	2.31474			0.0858490			0.0429245	−	0.999078i	$-0.486333\pi$
$727$	2.31474			0.0858490			0.0429245	+	0.999078i	$0.486333\pi$
$728$	−0.748606	+	0.543894i	−0.0277452	+	0.0201581i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	−2.03782	+	6.27177i	−0.0754232	+	0.232129i
$731$	−40.2991	−	29.2790i	−1.49051	−	1.08292i
$732$	−11.5626	−	8.40071i	−0.427365	−	0.310499i
$733$	−6.09213	+	18.7496i	−0.225018	+	0.692534i	0.773272	+	0.634075i	$0.218619\pi$
$733$	−6.09213	+	18.7496i	−0.225018	+	0.692534i	−0.998290	+	0.0584593i	$0.981381\pi$
$734$	1.66725	+	5.13127i	0.0615393	+	0.189399i
$735$	−1.52029	+	1.10455i	−0.0560766	+	0.0407421i
$736$	−4.11525			−0.151690
$737$	−2.01122	−	0.992595i	−0.0740841	−	0.0365627i
$738$	0.474266			0.0174580
$739$	−25.3919	+	18.4483i	−0.934056	+	0.678631i	−0.946982	−	0.321285i	$-0.895885\pi$
$739$	−25.3919	+	18.4483i	−0.934056	+	0.678631i	0.0129268	+	0.999916i	$0.495885\pi$
$740$	0.647621	+	1.99317i	0.0238070	+	0.0732705i
$741$	−0.794756	+	2.44601i	−0.0291961	+	0.0898563i
$742$	−3.70848	−	2.69437i	−0.136143	−	0.0989134i
$743$	7.25656	+	5.27220i	0.266217	+	0.193418i	0.712884	−	0.701282i	$-0.247389\pi$
$743$	7.25656	+	5.27220i	0.266217	+	0.193418i	−0.446666	+	0.894701i	$0.647389\pi$
$744$	0.242580	−	0.746585i	0.00889342	−	0.0273711i
$745$	12.4300	+	38.2556i	0.455400	+	1.40158i
$746$	22.3242	−	16.2195i	0.817348	−	0.593838i
$747$	3.15952			0.115601
$748$	14.7941	−	2.53739i	0.540927	−	0.0927763i
$749$	−6.48763			−0.237053
$750$	9.83426	−	7.14501i	0.359097	−	0.260899i
$751$	3.72495	+	11.4642i	0.135925	+	0.418336i	0.995733	−	0.0922830i	$-0.0294165\pi$
$751$	3.72495	+	11.4642i	0.135925	+	0.418336i	−0.859807	+	0.510619i	$0.829416\pi$
$752$	−0.574186	+	1.76716i	−0.0209384	+	0.0644418i
$753$	11.3761	+	8.26523i	0.414569	+	0.301202i
$754$	−3.49164	−	2.53682i	−0.127158	−	0.0923856i
$755$	−6.20800	+	19.1062i	−0.225932	+	0.695347i
$756$	0.309017	+	0.951057i	0.0112388	+	0.0345896i
$757$	3.56307	−	2.58872i	0.129502	−	0.0940887i	−0.521149	−	0.853466i	$-0.674496\pi$
$757$	3.56307	−	2.58872i	0.129502	−	0.0940887i	0.650651	+	0.759377i	$0.274496\pi$
$758$	7.66550			0.278424
$759$	−1.96266	+	13.5069i	−0.0712402	+	0.490269i
$760$	−5.22304			−0.189460
$761$	10.1558	−	7.37864i	0.368148	−	0.267475i	−0.388294	−	0.921535i	$-0.626936\pi$
$761$	10.1558	−	7.37864i	0.368148	−	0.267475i	0.756443	+	0.654060i	$0.226936\pi$
$762$	0.188324	+	0.579601i	0.00682225	+	0.0209967i
$763$	−1.29848	+	3.99631i	−0.0470081	+	0.144676i
$764$	−5.47114	−	3.97502i	−0.197939	−	0.143811i
$765$	−6.88041	−	4.99891i	−0.248762	−	0.180736i
$766$	−1.76641	+	5.43644i	−0.0638228	+	0.196426i
$767$	−0.424670	−	1.30700i	−0.0153339	−	0.0471930i
$768$	−0.809017	+	0.587785i	−0.0291929	+	0.0212099i
$769$	−37.9619			−1.36894			−0.684471	−	0.729041i	$-0.739967\pi$
$769$	−37.9619			−1.36894			−0.684471	+	0.729041i	$0.739967\pi$
$770$	−4.35038	+	4.46303i	−0.156777	+	0.160836i
$771$	−8.57589			−0.308853
$772$	−12.5857	+	9.14402i	−0.452968	+	0.329100i
$773$	12.8817	+	39.6456i	0.463321	+	1.42595i	0.861082	+	0.508466i	$0.169787\pi$
$773$	12.8817	+	39.6456i	0.463321	+	1.42595i	−0.397761	+	0.917489i	$0.630213\pi$
$774$	3.40119	−	10.4678i	0.122253	−	0.376257i
$775$	0.932740	+	0.677675i	0.0335050	+	0.0243428i
$776$	−3.82930	−	2.78215i	−0.137464	−	0.0998734i
$777$	0.344630	−	1.06066i	0.0123635	−	0.0380510i
$778$	−3.32996	−	10.2486i	−0.119385	−	0.367429i
$779$	1.06644	−	0.774812i	0.0382091	−	0.0277605i
$780$	1.73886			0.0622610
$781$	−8.20639	−	15.6095i	−0.293648	−	0.558551i
$782$	−18.6245			−0.666011
$783$	−3.77340	+	2.74154i	−0.134850	+	0.0979746i
$784$	0.309017	+	0.951057i	0.0110363	+	0.0339663i
$785$	−2.70816	+	8.33486i	−0.0966583	+	0.297484i
$786$	−13.5776	−	9.86473i	−0.484298	−	0.351863i
$787$	−4.37209	−	3.17651i	−0.155848	−	0.113230i	0.507128	−	0.861871i	$-0.330707\pi$
$787$	−4.37209	−	3.17651i	−0.155848	−	0.113230i	−0.662976	+	0.748640i	$0.730707\pi$
$788$	5.97537	−	18.3903i	0.212864	−	0.655128i
$789$	7.47462	+	23.0045i	0.266104	+	0.818983i
$790$	6.06982	−	4.40999i	0.215955	−	0.156900i
$791$	19.7587			0.702538
$792$	1.54336	+	2.93565i	0.0548410	+	0.104314i
$793$	13.2249			0.469631
$794$	−15.1360	+	10.9970i	−0.537158	+	0.390268i
$795$	2.66188	+	8.19243i	0.0944072	+	0.290556i
$796$	3.76144	−	11.5765i	0.133321	−	0.410319i
$797$	1.60888	+	1.16892i	0.0569896	+	0.0414053i	0.615915	−	0.787812i	$-0.288786\pi$
$797$	1.60888	+	1.16892i	0.0569896	+	0.0414053i	−0.558926	+	0.829218i	$0.688786\pi$
$798$	2.24861	+	1.63371i	0.0795998	+	0.0578326i
$799$	−2.59861	+	7.99771i	−0.0919323	+	0.282939i
$800$	−0.453850	−	1.39681i	−0.0160460	−	0.0493846i
$801$	11.0322	−	8.01537i	0.389804	−	0.283209i
$802$	0.122952			0.00434158
$803$	8.12410	−	8.33447i	0.286693	−	0.294117i
$804$	0.676236			0.0238490
$805$	6.25635	−	4.54551i	0.220508	−	0.160208i
$806$	0.224466	+	0.690836i	0.00790648	+	0.0243337i
$807$	5.11985	−	15.7573i	0.180227	−	0.554682i
$808$	5.06365	+	3.67896i	0.178139	+	0.129425i
$809$	−23.2682	−	16.9053i	−0.818067	−	0.594360i	0.0980914	−	0.995177i	$-0.468726\pi$
$809$	−23.2682	−	16.9053i	−0.818067	−	0.594360i	−0.916158	+	0.400817i	$0.868726\pi$
$810$	0.580698	−	1.78720i	0.0204036	−	0.0627960i
$811$	−15.3327	−	47.1892i	−0.538404	−	1.65704i	−0.736176	−	0.676790i	$-0.763370\pi$
$811$	−15.3327	−	47.1892i	−0.538404	−	1.65704i	0.197772	−	0.980248i	$-0.436630\pi$
$812$	−3.77340	+	2.74154i	−0.132421	+	0.0962091i
$813$	−28.8309			−1.01114
$814$	0.531889	−	3.66041i	0.0186427	−	0.128297i
$815$	−19.4437			−0.681082
$816$	−3.66140	+	2.66016i	−0.128174	+	0.0931242i
$817$	−9.45336	−	29.0945i	−0.330731	−	1.01789i
$818$	4.52821	−	13.9364i	0.158325	−	0.487274i
$819$	−0.748606	−	0.543894i	−0.0261584	−	0.0190052i
$820$	−0.721020	−	0.523852i	−0.0251791	−	0.0182937i
$821$	8.94597	−	27.5329i	0.312217	−	0.960904i	−0.664668	−	0.747138i	$-0.731427\pi$
$821$	8.94597	−	27.5329i	0.312217	−	0.960904i	0.976885	−	0.213765i	$-0.0685728\pi$
$822$	−6.77368	−	20.8472i	−0.236259	−	0.727131i
$823$	21.4122	−	15.5569i	0.746384	−	0.542279i	−0.148320	−	0.988939i	$-0.547387\pi$
$823$	21.4122	−	15.5569i	0.746384	−	0.542279i	0.894704	+	0.446660i	$0.147387\pi$
$824$	−14.6616			−0.510762
$825$	−4.80099	+	0.823434i	−0.167149	+	0.0286683i
$826$	−1.48516			−0.0516753
$827$	3.69477	−	2.68440i	0.128480	−	0.0933459i	−0.521689	−	0.853135i	$-0.674698\pi$
$827$	3.69477	−	2.68440i	0.128480	−	0.0933459i	0.650169	+	0.759790i	$0.274698\pi$
$828$	−1.27168	−	3.91383i	−0.0441940	−	0.136015i
$829$	15.5139	−	47.7467i	0.538818	−	1.65831i	−0.196432	−	0.980517i	$-0.562936\pi$
$829$	15.5139	−	47.7467i	0.538818	−	1.65831i	0.735251	−	0.677795i	$-0.237064\pi$
$830$	−4.80338	−	3.48986i	−0.166728	−	0.121135i
$831$	13.5410	+	9.83813i	0.469733	+	0.341281i
$832$	0.285942	−	0.880039i	0.00991326	−	0.0305099i
$833$	1.39853	+	4.30423i	0.0484562	+	0.149133i
$834$	4.52525	−	3.28779i	0.156697	−	0.113847i
$835$	−19.1900			−0.664096
$836$	8.26641	+	4.07972i	0.285900	+	0.141100i
$837$	0.785006			0.0271338
$838$	5.21775	−	3.79091i	0.180244	−	0.130955i
$839$	2.37859	+	7.32053i	0.0821179	+	0.252733i	0.983683	−	0.179911i	$-0.0575809\pi$
$839$	2.37859	+	7.32053i	0.0821179	+	0.252733i	−0.901565	+	0.432644i	$0.857581\pi$
$840$	0.580698	−	1.78720i	0.0200360	−	0.0616644i
$841$	5.86164	+	4.25873i	0.202126	+	0.146853i
$842$	20.8638	+	15.1584i	0.719015	+	0.522395i
$843$	−0.392595	+	1.20828i	−0.0135217	+	0.0416155i
$844$	−5.68784	−	17.5054i	−0.195783	−	0.602559i
$845$	18.4620	−	13.4134i	0.635113	−	0.461436i
$846$	−1.85810			−0.0638829
$847$	10.3713	−	3.66547i	0.356363	−	0.125947i
$848$	4.58394			0.157413
$849$	−19.1636	+	13.9231i	−0.657692	+	0.477841i
$850$	−2.05401	−	6.32158i	−0.0704518	−	0.216828i
$851$	−1.41824	+	4.36489i	−0.0486165	+	0.149626i
$852$	4.30172	+	3.12538i	0.147374	+	0.107074i
$853$	31.0499	+	22.5591i	1.06313	+	0.772409i	0.974665	−	0.223670i	$-0.0718039\pi$
$853$	31.0499	+	22.5591i	1.06313	+	0.772409i	0.0884648	+	0.996079i	$0.471804\pi$
$854$	4.41651	−	13.5926i	0.151130	−	0.465130i
$855$	−1.61401	−	4.96741i	−0.0551980	−	0.169882i
$856$	5.24861	−	3.81334i	0.179394	−	0.130337i
$857$	14.1029			0.481747			0.240874	−	0.970557i	$-0.422566\pi$
$857$	14.1029			0.481747			0.240874	+	0.970557i	$0.422566\pi$
$858$	−2.75205	−	1.35822i	−0.0939535	−	0.0463688i
$859$	53.5036			1.82552			0.912760	−	0.408496i	$-0.133947\pi$
$859$	53.5036			1.82552			0.912760	+	0.408496i	$0.133947\pi$
$860$	−16.7330	+	12.1572i	−0.570591	+	0.414558i
$861$	0.146556	+	0.451054i	0.00499462	+	0.0153719i
$862$	7.35154	−	22.6257i	0.250394	−	0.770634i
$863$	−40.7757	−	29.6253i	−1.38802	−	1.00846i	−0.996079	−	0.0884682i	$-0.971803\pi$
$863$	−40.7757	−	29.6253i	−1.38802	−	1.00846i	−0.391944	−	0.919989i	$-0.628197\pi$
$864$	−0.809017	−	0.587785i	−0.0275233	−	0.0199969i
$865$	−5.84530	+	17.9900i	−0.198746	+	0.611678i
$866$	7.93826	+	24.4314i	0.269753	+	0.830214i
$867$	−2.81722	+	2.04683i	−0.0956777	+	0.0695139i
$868$	0.785006			0.0266448
$869$	−13.0512	+	2.23846i	−0.442732	+	0.0759346i
$870$	8.76483			0.297156
$871$	−0.506234	+	0.367801i	−0.0171531	+	0.0124624i
$872$	−1.29848	−	3.99631i	−0.0439721	−	0.135332i
$873$	1.46266	−	4.50162i	0.0495037	−	0.152357i
$874$	−9.25357	−	6.72311i	−0.313007	−	0.227413i
$875$	9.83426	+	7.14501i	0.332459	+	0.241545i
$876$	−1.08442	+	3.33751i	−0.0366392	+	0.112764i
$877$	4.55852	+	14.0297i	0.153930	+	0.473748i	0.998051	−	0.0624048i	$-0.0198770\pi$
$877$	4.55852	+	14.0297i	0.153930	+	0.473748i	−0.844121	+	0.536153i	$0.819877\pi$
$878$	−25.7844	+	18.7334i	−0.870180	+	0.632223i
$879$	13.2956			0.448449
$880$	0.896227	−	6.16775i	0.0302118	−	0.207915i
$881$	38.4292			1.29471			0.647356	−	0.762188i	$-0.275875\pi$
$881$	38.4292			1.29471			0.647356	+	0.762188i	$0.275875\pi$
$882$	−0.809017	+	0.587785i	−0.0272410	+	0.0197918i
$883$	4.05289	+	12.4735i	0.136391	+	0.419767i	0.995804	−	0.0915146i	$-0.0291708\pi$
$883$	4.05289	+	12.4735i	0.136391	+	0.419767i	−0.859413	+	0.511282i	$0.829171\pi$
$884$	1.29410	−	3.98282i	0.0435252	−	0.133957i
$885$	2.25787	+	1.64044i	0.0758975	+	0.0551427i
$886$	−10.5860	−	7.69118i	−0.355643	−	0.258390i
$887$	−9.73558	+	29.9630i	−0.326889	+	1.00606i	0.643692	+	0.765285i	$0.277402\pi$
$887$	−9.73558	+	29.9630i	−0.326889	+	1.00606i	−0.970581	+	0.240776i	$0.922598\pi$
$888$	0.344630	+	1.06066i	0.0115650	+	0.0355935i
$889$	−0.493038	+	0.358213i	−0.0165360	+	0.0120141i
$890$	−25.6255			−0.858970
$891$	−2.31504	+	2.37499i	−0.0775569	+	0.0795652i
$892$	−23.7621			−0.795615
$893$	−4.17814	+	3.03560i	−0.139816	+	0.101582i
$894$	6.61459	+	20.3576i	0.221225	+	0.680860i
$895$	−0.950390	+	2.92500i	−0.0317680	+	0.0977720i
$896$	−0.809017	−	0.587785i	−0.0270274	−	0.0196365i
$897$	3.08070	+	2.23826i	0.102862	+	0.0747333i
$898$	10.9803	−	33.7938i	0.366416	−	1.12771i
$899$	1.13144	+	3.48221i	0.0377356	+	0.116138i
$900$	1.18820	−	0.863274i	0.0396065	−	0.0287758i
$901$	20.7457			0.691139
$902$	0.731964	+	1.39228i	0.0243717	+	0.0463578i
$903$	11.0065			0.366273
$904$	−15.9851	+	11.6139i	−0.531657	+	0.386272i
$905$	12.4661	+	38.3667i	0.414388	+	1.27535i
$906$	−3.30357	+	10.1673i	−0.109754	+	0.337787i
$907$	47.7435	+	34.6877i	1.58530	+	1.15179i	0.910286	+	0.413981i	$0.135862\pi$
$907$	47.7435	+	34.6877i	1.58530	+	1.15179i	0.675013	+	0.737806i	$0.264138\pi$
$908$	−14.7780	−	10.7369i	−0.490426	−	0.356315i
$909$	−1.93414	+	5.95268i	−0.0641514	+	0.197438i
$910$	0.537336	+	1.65375i	0.0178125	+	0.0548213i
$911$	−20.2420	+	14.7067i	−0.670647	+	0.487254i	−0.870242	−	0.492625i	$-0.836037\pi$
$911$	−20.2420	+	14.7067i	−0.670647	+	0.487254i	0.199595	+	0.979879i	$0.436037\pi$
$912$	−2.77943			−0.0920361
$913$	4.87629	+	9.27525i	0.161382	+	0.306966i
$914$	16.0161			0.529765
$915$	−21.7282	+	15.7864i	−0.718311	+	0.521883i
$916$	8.10364	+	24.9405i	0.267752	+	0.824056i
$917$	5.18619	−	15.9615i	0.171263	−	0.527094i
$918$	−3.66140	−	2.66016i	−0.120844	−	0.0877984i
$919$	43.2550	+	31.4266i	1.42685	+	1.03667i	0.990593	+	0.136845i	$0.0436961\pi$
$919$	43.2550	+	31.4266i	1.42685	+	1.03667i	0.436257	+	0.899822i	$0.356304\pi$
$920$	−2.38971	+	7.35479i	−0.0787866	+	0.242480i
$921$	−3.68133	−	11.3300i	−0.121304	−	0.373335i
$922$	3.58648	−	2.60573i	0.118114	−	0.0858152i
$923$	−4.92017			−0.161949
$924$	−2.31504	+	2.37499i	−0.0761593	+	0.0781314i
$925$	−1.63795			−0.0538555
$926$	19.6231	−	14.2570i	0.644855	−	0.468515i
$927$	−4.53070	−	13.9440i	−0.148808	−	0.457983i
$928$	1.44131	−	4.43590i	0.0473134	−	0.145616i
$929$	38.1776	+	27.7376i	1.25256	+	0.910042i	0.998368	−	0.0571108i	$-0.0181888\pi$
$929$	38.1776	+	27.7376i	1.25256	+	0.910042i	0.254197	+	0.967152i	$0.418189\pi$
$930$	−1.19343	−	0.867081i	−0.0391342	−	0.0284327i
$931$	−0.858891	+	2.64339i	−0.0281490	+	0.0866338i
$932$	−8.33599	−	25.6555i	−0.273054	−	0.840375i
$933$	24.0948	−	17.5059i	0.788828	−	0.573117i
$934$	−7.56541			−0.247548
$935$	4.05609	−	27.9136i	0.132648	−	0.912873i
$936$	0.925328			0.0302453
$937$	10.6396	−	7.73009i	0.347579	−	0.252531i	−0.400274	−	0.916396i	$-0.631085\pi$
$937$	10.6396	−	7.73009i	0.347579	−	0.252531i	0.747853	+	0.663865i	$0.231085\pi$
$938$	0.208968	+	0.643138i	0.00682306	+	0.0209992i
$939$	0.189918	−	0.584508i	0.00619774	−	0.0190747i
$940$	2.82485	+	2.05237i	0.0921365	+	0.0669411i
$941$	35.2047	+	25.5777i	1.14764	+	0.833808i	0.988165	−	0.153394i	$-0.0490203\pi$
$941$	35.2047	+	25.5777i	1.14764	+	0.833808i	0.159474	+	0.987202i	$0.449020\pi$
$942$	−1.44114	+	4.43537i	−0.0469549	+	0.144512i
$943$	−0.603115	−	1.85620i	−0.0196401	−	0.0604461i
$944$	1.20152	−	0.872955i	0.0391061	−	0.0284123i
$945$	1.87918			0.0611297
$946$	35.9790	−	6.17088i	1.16978	−	0.200633i
$947$	−60.4254			−1.96356			−0.981780	−	0.190020i	$-0.939145\pi$
$947$	−60.4254			−1.96356			−0.981780	+	0.190020i	$0.939145\pi$
$948$	3.23004	−	2.34676i	0.104907	−	0.0762193i
$949$	−1.00345	−	3.08829i	−0.0325732	−	0.100250i
$950$	1.26144	−	3.88233i	0.0409267	−	0.125959i
$951$	20.7646	+	15.0863i	0.673337	+	0.489208i
$952$	−3.66140	−	2.66016i	−0.118667	−	0.0862163i
$953$	1.81298	−	5.57979i	0.0587283	−	0.180747i	−0.917389	−	0.397992i	$-0.869707\pi$
$953$	1.81298	−	5.57979i	0.0587283	−	0.180747i	0.976117	+	0.217245i	$0.0697071\pi$
$954$	1.41651	+	4.35958i	0.0458613	+	0.141147i
$955$	−10.2812	+	7.46976i	−0.332693	+	0.241716i
$956$	−7.60591			−0.245993
$957$	−13.8719	−	6.84620i	−0.448416	−	0.221306i
$958$	17.7051			0.572024
$959$	17.7337	−	12.8843i	0.572652	−	0.416056i
$960$	0.580698	+	1.78720i	0.0187419	+	0.0576818i
$961$	−9.38910	+	28.8967i	−0.302874	+	0.932151i
$962$	−0.834880	−	0.606576i	−0.0269176	−	0.0195568i
$963$	5.24861	+	3.81334i	0.169134	+	0.122883i
$964$	−5.41651	+	16.6703i	−0.174454	+	0.536915i
$965$	9.03376	+	27.8031i	0.290807	+	0.895012i
$966$	3.32930	−	2.41888i	0.107119	−	0.0778262i
$967$	13.8068			0.443998			0.221999	−	0.975047i	$-0.428742\pi$
$967$	13.8068			0.443998			0.221999	+	0.975047i	$0.428742\pi$
$968$	−6.23607	+	9.06154i	−0.200435	+	0.291249i
$969$	−12.5790			−0.404094
$970$	−7.19594	+	5.22816i	−0.231048	+	0.167866i
$971$	10.3446	+	31.8374i	0.331974	+	1.02171i	0.968194	+	0.250202i	$0.0804972\pi$
$971$	10.3446	+	31.8374i	0.331974	+	1.02171i	−0.636220	+	0.771508i	$0.719503\pi$
$972$	0.309017	−	0.951057i	0.00991172	−	0.0305052i
$973$	4.52525	+	3.28779i	0.145073	+	0.105402i
$974$	21.0502	+	15.2939i	0.674492	+	0.490047i
$975$	−0.419960	+	1.29250i	−0.0134495	+	0.0413933i
$976$	4.41651	+	13.5926i	0.141369	+	0.435090i
$977$	33.0618	−	24.0208i	1.05774	−	0.768495i	0.0840727	−	0.996460i	$-0.473207\pi$
$977$	33.0618	−	24.0208i	1.05774	−	0.768495i	0.973669	+	0.227965i	$0.0732072\pi$
$978$	−10.3469			−0.330857
$979$	40.5570	+	20.0161i	1.29621	+	0.639717i
$980$	1.87918			0.0600281
$981$	3.39947	−	2.46986i	0.108537	−	0.0788564i
$982$	10.9992	+	33.8521i	0.350999	+	1.08026i
$983$	4.75567	−	14.6364i	0.151682	−	0.466830i	−0.846127	−	0.532981i	$-0.821072\pi$
$983$	4.75567	−	14.6364i	0.151682	−	0.466830i	0.997810	+	0.0661506i	$0.0210718\pi$
$984$	−0.383689	−	0.278766i	−0.0122316	−	0.00888675i
$985$	−29.3974	−	21.3584i	−0.936678	−	0.680536i
$986$	6.52300	−	20.0757i	0.207734	−	0.639341i
$987$	−0.574186	−	1.76716i	−0.0182765	−	0.0562494i
$988$	2.08070	−	1.51172i	0.0661958	−	0.0480941i
$989$	−45.2944			−1.44028
$990$	6.14283	−	1.05358i	0.195232	−	0.0334849i
$991$	−48.7434			−1.54839			−0.774193	−	0.632950i	$-0.781844\pi$
$991$	−48.7434			−1.54839			−0.774193	+	0.632950i	$0.781844\pi$
$992$	−0.635083	+	0.461415i	−0.0201639	+	0.0146499i
$993$	10.0255	+	30.8554i	0.318150	+	0.979166i
$994$	−1.64311	+	5.05697i	−0.0521163	+	0.160397i
$995$	−18.5054	−	13.4449i	−0.586660	−	0.426233i
$996$	−2.55611	−	1.85712i	−0.0809934	−	0.0588451i
$997$	−0.710162	+	2.18565i	−0.0224911	+	0.0692203i	−0.961672	−	0.274202i	$-0.911586\pi$
$997$	−0.710162	+	2.18565i	−0.0224911	+	0.0692203i	0.939181	+	0.343422i	$0.111586\pi$
$998$	−4.54496	−	13.9879i	−0.143868	−	0.442780i
$999$	−0.902253	+	0.655525i	−0.0285460	+	0.0207399i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.j.e.421.1	yes	8
11.2	odd	10		5082.2.a.ca.1.3		4
11.4	even	5	inner	462.2.j.e.169.1	✓	8
11.9	even	5		5082.2.a.cf.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.j.e.169.1	✓	8	11.4	even	5	inner
462.2.j.e.421.1	yes	8	1.1	even	1	trivial
5082.2.a.ca.1.3		4	11.2	odd	10
5082.2.a.cf.1.3		4	11.9	even	5

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.j (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 + 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-1.52029 - 1.10455i) q^{5} +(-0.809017 - 0.587785i) q^{6} +(0.309017 - 0.951057i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(-0.809017 + 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-1.52029 - 1.10455i) q^{5} +(-0.809017 - 0.587785i) q^{6} +(0.309017 - 0.951057i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-0.809017 + 0.587785i) q^{9} +1.87918 q^{10} +(-2.97414 - 1.46782i) q^{11} +1.00000 q^{12} +(-0.748606 + 0.543894i) q^{13} +(0.309017 + 0.951057i) q^{14} +(0.580698 - 1.78720i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-3.66140 - 2.66016i) q^{17} +(0.309017 - 0.951057i) q^{18} +(-0.858891 - 2.64339i) q^{19} +(-1.52029 + 1.10455i) q^{20} +1.00000 q^{21} +(3.26889 - 0.560659i) q^{22} -4.11525 q^{23} +(-0.809017 + 0.587785i) q^{24} +(-0.453850 - 1.39681i) q^{25} +(0.285942 - 0.880039i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(-0.809017 - 0.587785i) q^{28} +(1.44131 - 4.43590i) q^{29} +(0.580698 + 1.78720i) q^{30} +(-0.635083 + 0.461415i) q^{31} +1.00000 q^{32} +(0.476925 - 3.28216i) q^{33} +4.52573 q^{34} +(-1.52029 + 1.10455i) q^{35} +(0.309017 + 0.951057i) q^{36} +(0.344630 - 1.06066i) q^{37} +(2.24861 + 1.63371i) q^{38} +(-0.748606 - 0.543894i) q^{39} +(0.580698 - 1.78720i) q^{40} +(0.146556 + 0.451054i) q^{41} +(-0.809017 + 0.587785i) q^{42} +11.0065 q^{43} +(-2.31504 + 2.37499i) q^{44} +1.87918 q^{45} +(3.32930 - 2.41888i) q^{46} +(-0.574186 - 1.76716i) q^{47} +(0.309017 - 0.951057i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(1.18820 + 0.863274i) q^{50} +(1.39853 - 4.30423i) q^{51} +(0.285942 + 0.880039i) q^{52} +(-3.70848 + 2.69437i) q^{53} +1.00000 q^{54} +(2.90025 + 5.51661i) q^{55} +1.00000 q^{56} +(2.24861 - 1.63371i) q^{57} +(1.44131 + 4.43590i) q^{58} +(-0.458940 + 1.41247i) q^{59} +(-1.52029 - 1.10455i) q^{60} +(-11.5626 - 8.40071i) q^{61} +(0.242580 - 0.746585i) q^{62} +(0.309017 + 0.951057i) q^{63} +(-0.809017 + 0.587785i) q^{64} +1.73886 q^{65} +(1.54336 + 2.93565i) q^{66} +0.676236 q^{67} +(-3.66140 + 2.66016i) q^{68} +(-1.27168 - 3.91383i) q^{69} +(0.580698 - 1.78720i) q^{70} +(4.30172 + 3.12538i) q^{71} +(-0.809017 - 0.587785i) q^{72} +(-1.08442 + 3.33751i) q^{73} +(0.344630 + 1.06066i) q^{74} +(1.18820 - 0.863274i) q^{75} -2.77943 q^{76} +(-2.31504 + 2.37499i) q^{77} +0.925328 q^{78} +(3.23004 - 2.34676i) q^{79} +(0.580698 + 1.78720i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-0.383689 - 0.278766i) q^{82} +(-2.55611 - 1.85712i) q^{83} +(0.309017 - 0.951057i) q^{84} +(2.62808 + 8.08841i) q^{85} +(-8.90443 + 6.46944i) q^{86} +4.66418 q^{87} +(0.476925 - 3.28216i) q^{88} -13.6366 q^{89} +(-1.52029 + 1.10455i) q^{90} +(0.285942 + 0.880039i) q^{91} +(-1.27168 + 3.91383i) q^{92} +(-0.635083 - 0.461415i) q^{93} +(1.50324 + 1.09217i) q^{94} +(-1.61401 + 4.96741i) q^{95} +(0.309017 + 0.951057i) q^{96} +(-3.82930 + 2.78215i) q^{97} +1.00000 q^{98} +(3.26889 - 0.560659i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 4 q^{5} - 2 q^{6} - 2 q^{7} - 2 q^{8} - 2 q^{9}+O(q^{10}) \) 8 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 + 4 * q^5 - 2 * q^6 - 2 * q^7 - 2 * q^8 - 2 * q^9	\( 8 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 4 q^{5} - 2 q^{6} - 2 q^{7} - 2 q^{8} - 2 q^{9} + 4 q^{10} + 8 q^{12} + 4 q^{13} - 2 q^{14} - 6 q^{15} - 2 q^{16} - 8 q^{17} - 2 q^{18} - 12 q^{19} + 4 q^{20} + 8 q^{21} - 4 q^{23} - 2 q^{24} + 4 q^{25} - 6 q^{26} - 2 q^{27} - 2 q^{28} - 4 q^{29} - 6 q^{30} - 14 q^{31} + 8 q^{32} + 12 q^{34} + 4 q^{35} - 2 q^{36} + 10 q^{37} + 8 q^{38} + 4 q^{39} - 6 q^{40} - 12 q^{41} - 2 q^{42} + 20 q^{43} + 4 q^{45} + 6 q^{46} + 28 q^{47} - 2 q^{48} - 2 q^{49} - 6 q^{50} + 2 q^{51} - 6 q^{52} + 2 q^{53} + 8 q^{54} + 4 q^{55} + 8 q^{56} + 8 q^{57} - 4 q^{58} + 4 q^{60} - 34 q^{61} + 6 q^{62} - 2 q^{63} - 2 q^{64} + 16 q^{65} - 24 q^{67} - 8 q^{68} - 4 q^{69} - 6 q^{70} - 2 q^{72} + 10 q^{74} - 6 q^{75} + 8 q^{76} + 4 q^{78} + 22 q^{79} - 6 q^{80} - 2 q^{81} - 2 q^{82} - 30 q^{83} - 2 q^{84} - 28 q^{85} + 36 q^{87} - 4 q^{89} + 4 q^{90} - 6 q^{91} - 4 q^{92} - 14 q^{93} - 22 q^{94} - 30 q^{95} - 2 q^{96} - 10 q^{97} + 8 q^{98}+O(q^{100}) \) 8 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 + 4 * q^5 - 2 * q^6 - 2 * q^7 - 2 * q^8 - 2 * q^9 + 4 * q^10 + 8 * q^12 + 4 * q^13 - 2 * q^14 - 6 * q^15 - 2 * q^16 - 8 * q^17 - 2 * q^18 - 12 * q^19 + 4 * q^20 + 8 * q^21 - 4 * q^23 - 2 * q^24 + 4 * q^25 - 6 * q^26 - 2 * q^27 - 2 * q^28 - 4 * q^29 - 6 * q^30 - 14 * q^31 + 8 * q^32 + 12 * q^34 + 4 * q^35 - 2 * q^36 + 10 * q^37 + 8 * q^38 + 4 * q^39 - 6 * q^40 - 12 * q^41 - 2 * q^42 + 20 * q^43 + 4 * q^45 + 6 * q^46 + 28 * q^47 - 2 * q^48 - 2 * q^49 - 6 * q^50 + 2 * q^51 - 6 * q^52 + 2 * q^53 + 8 * q^54 + 4 * q^55 + 8 * q^56 + 8 * q^57 - 4 * q^58 + 4 * q^60 - 34 * q^61 + 6 * q^62 - 2 * q^63 - 2 * q^64 + 16 * q^65 - 24 * q^67 - 8 * q^68 - 4 * q^69 - 6 * q^70 - 2 * q^72 + 10 * q^74 - 6 * q^75 + 8 * q^76 + 4 * q^78 + 22 * q^79 - 6 * q^80 - 2 * q^81 - 2 * q^82 - 30 * q^83 - 2 * q^84 - 28 * q^85 + 36 * q^87 - 4 * q^89 + 4 * q^90 - 6 * q^91 - 4 * q^92 - 14 * q^93 - 22 * q^94 - 30 * q^95 - 2 * q^96 - 10 * q^97 + 8 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more