LMFDB - Embedded newform 546.2.bv.a.515.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(317,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 4, 9]))

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

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

chi := DirichletCharacter("546.317");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bv (of order $12$, 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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$36$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			515.8
Character	$\chi$	$=$	546.515
Dual form			546.2.bv.a.317.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 - 0.258819i) q^{2} +(-0.357658 - 1.69472i) q^{3} +(0.866025 + 0.500000i) q^{4} +(3.24035 + 0.868248i) q^{5} +(-0.0931546 + 1.72954i) q^{6} +(-1.25441 - 2.32948i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.74416 + 1.21226i) q^{9} +O(q^{10})$	\(q+(-0.965926 - 0.258819i) q^{2} +(-0.357658 - 1.69472i) q^{3} +(0.866025 + 0.500000i) q^{4} +(3.24035 + 0.868248i) q^{5} +(-0.0931546 + 1.72954i) q^{6} +(-1.25441 - 2.32948i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.74416 + 1.21226i) q^{9} +(-2.90521 - 1.67733i) q^{10} +(-6.11240 + 1.63781i) q^{11} +(0.537619 - 1.64650i) q^{12} +(-0.0266902 - 3.60545i) q^{13} +(0.608755 + 2.57477i) q^{14} +(0.312501 - 5.80202i) q^{15} +(0.500000 + 0.866025i) q^{16} +(2.03425 - 3.52342i) q^{17} +(2.96441 - 0.460715i) q^{18} +(0.600144 - 2.23977i) q^{19} +(2.37210 + 2.37210i) q^{20} +(-3.49916 + 2.95903i) q^{21} +6.32802 q^{22} +(-2.74170 - 4.74876i) q^{23} +(-0.945446 + 1.45125i) q^{24} +(5.41586 + 3.12685i) q^{25} +(-0.907379 + 3.48951i) q^{26} +(3.03592 + 4.21701i) q^{27} +(0.0783861 - 2.64459i) q^{28} +0.127692i q^{29} +(-1.80353 + 5.52344i) q^{30} +(1.65420 - 0.443241i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(4.96179 + 9.77304i) q^{33} +(-2.87686 + 2.87686i) q^{34} +(-2.04216 - 8.63745i) q^{35} +(-2.98264 - 0.322230i) q^{36} +(-7.58283 - 2.03181i) q^{37} +(-1.15939 + 2.00812i) q^{38} +(-6.10069 + 1.33475i) q^{39} +(-1.67733 - 2.90521i) q^{40} +(7.12298 - 7.12298i) q^{41} +(4.14578 - 1.95256i) q^{42} +2.56093i q^{43} +(-6.11240 - 1.63781i) q^{44} +(-9.94458 + 1.54554i) q^{45} +(1.41921 + 5.29656i) q^{46} +(2.54114 - 9.48367i) q^{47} +(1.28884 - 1.15710i) q^{48} +(-3.85291 + 5.84424i) q^{49} +(-4.42203 - 4.42203i) q^{50} +(-6.69878 - 2.18730i) q^{51} +(1.77961 - 3.13576i) q^{52} +(2.68874 + 1.55235i) q^{53} +(-1.84103 - 4.85907i) q^{54} -21.2283 q^{55} +(-0.760185 + 2.53419i) q^{56} +(-4.01043 - 0.216005i) q^{57} +(0.0330492 - 0.123341i) q^{58} +(-6.18587 + 1.65750i) q^{59} +(3.17164 - 4.86845i) q^{60} +(1.79532 + 3.10959i) q^{61} -1.71255 q^{62} +(6.26624 + 4.87178i) q^{63} +1.00000i q^{64} +(3.04394 - 11.7061i) q^{65} +(-2.26327 - 10.7242i) q^{66} +(3.15651 - 0.845785i) q^{67} +(3.52342 - 2.03425i) q^{68} +(-7.06724 + 6.34485i) q^{69} +(-0.262958 + 8.87168i) q^{70} +(-8.71117 + 8.71117i) q^{71} +(2.79761 + 1.08322i) q^{72} +(1.09357 + 4.08124i) q^{73} +(6.79858 + 3.92516i) q^{74} +(3.36211 - 10.2967i) q^{75} +(1.63962 - 1.63962i) q^{76} +(11.4827 + 12.1842i) q^{77} +(6.23827 + 0.289703i) q^{78} +(3.01834 + 5.22792i) q^{79} +(0.868248 + 3.24035i) q^{80} +(6.06084 - 6.65329i) q^{81} +(-8.72383 + 5.03671i) q^{82} +(-0.395201 + 0.395201i) q^{83} +(-4.50988 + 0.813017i) q^{84} +(9.65087 - 9.65087i) q^{85} +(0.662816 - 2.47366i) q^{86} +(0.216403 - 0.0456702i) q^{87} +(5.48023 + 3.16401i) q^{88} +(-0.836494 + 3.12184i) q^{89} +(10.0057 + 1.08097i) q^{90} +(-8.36533 + 4.58489i) q^{91} -5.48340i q^{92} +(-1.34281 - 2.64487i) q^{93} +(-4.90911 + 8.50283i) q^{94} +(3.88935 - 6.73655i) q^{95} +(-1.54441 + 0.784098i) q^{96} +(2.43118 + 2.43118i) q^{97} +(5.23422 - 4.64789i) q^{98} +(14.7879 - 11.9043i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 16 q^{7}+O(q^{10}) $ 144 * q - 16 * q^7	$ 144 q - 16 q^{7} + 72 q^{16} + 16 q^{18} + 8 q^{19} + 8 q^{21} + 24 q^{27} - 8 q^{28} - 8 q^{31} + 12 q^{33} - 8 q^{37} + 16 q^{39} - 40 q^{45} + 8 q^{46} + 8 q^{52} - 12 q^{54} - 32 q^{55} + 16 q^{57} + 8 q^{58} - 32 q^{61} - 40 q^{63} - 32 q^{66} - 8 q^{67} + 16 q^{72} + 80 q^{73} - 16 q^{76} + 16 q^{78} - 112 q^{79} - 48 q^{81} + 16 q^{84} - 80 q^{85} + 96 q^{87} - 32 q^{91} + 36 q^{93} - 64 q^{94} - 144 q^{97} - 32 q^{99}+O(q^{100}) $ 144 * q - 16 * q^7 + 72 * q^16 + 16 * q^18 + 8 * q^19 + 8 * q^21 + 24 * q^27 - 8 * q^28 - 8 * q^31 + 12 * q^33 - 8 * q^37 + 16 * q^39 - 40 * q^45 + 8 * q^46 + 8 * q^52 - 12 * q^54 - 32 * q^55 + 16 * q^57 + 8 * q^58 - 32 * q^61 - 40 * q^63 - 32 * q^66 - 8 * q^67 + 16 * q^72 + 80 * q^73 - 16 * q^76 + 16 * q^78 - 112 * q^79 - 48 * q^81 + 16 * q^84 - 80 * q^85 + 96 * q^87 - 32 * q^91 + 36 * q^93 - 64 * q^94 - 144 * q^97 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$3$	−0.357658	−	1.69472i	−0.206494	−	0.978448i
$3$	−0.357658	−	1.69472i	−0.206494	−	0.978448i
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$	3.24035	+	0.868248i	1.44913	+	0.388292i	0.895720	−	0.444619i	$-0.146661\pi$
$5$	3.24035	+	0.868248i	1.44913	+	0.388292i	0.553407	+	0.832911i	$0.313327\pi$
$6$	−0.0931546	+	1.72954i	−0.0380302	+	0.706083i
$7$	−1.25441	−	2.32948i	−0.474123	−	0.880459i
$7$	−1.25441	−	2.32948i	−0.474123	−	0.880459i
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	−2.74416	+	1.21226i	−0.914720	+	0.404088i
$10$	−2.90521	−	1.67733i	−0.918710	−	0.530417i
$11$	−6.11240	+	1.63781i	−1.84296	+	0.493819i	−0.999087	−	0.0427270i	$-0.986395\pi$
$11$	−6.11240	+	1.63781i	−1.84296	+	0.493819i	−0.843871	+	0.536546i	$0.819729\pi$
$12$	0.537619	−	1.64650i	0.155197	−	0.475304i
$13$	−0.0266902	−	3.60545i	−0.00740253	−	0.999973i
$13$	−0.0266902	−	3.60545i	−0.00740253	−	0.999973i
$14$	0.608755	+	2.57477i	0.162697	+	0.688135i
$15$	0.312501	−	5.80202i	0.0806875	−	1.49808i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	2.03425	−	3.52342i	0.493377	−	0.854555i	−0.506594	−	0.862185i	$-0.669096\pi$
$17$	2.03425	−	3.52342i	0.493377	−	0.854555i	0.999971	+	0.00763036i	$0.00242884\pi$
$18$	2.96441	−	0.460715i	0.698719	−	0.108592i
$19$	0.600144	−	2.23977i	0.137683	−	0.513838i	−0.862290	−	0.506415i	$-0.830970\pi$
$19$	0.600144	−	2.23977i	0.137683	−	0.513838i	0.999972	−	0.00742326i	$-0.00236292\pi$
$20$	2.37210	+	2.37210i	0.530417	+	0.530417i
$21$	−3.49916	+	2.95903i	−0.763579	+	0.645714i
$22$	6.32802			1.34914
$23$	−2.74170	−	4.74876i	−0.571684	−	0.990185i	−0.996393	−	0.0848557i	$-0.972957\pi$
$23$	−2.74170	−	4.74876i	−0.571684	−	0.990185i	0.424709	−	0.905330i	$-0.360376\pi$
$24$	−0.945446	+	1.45125i	−0.192988	+	0.296236i
$25$	5.41586	+	3.12685i	1.08317	+	0.625370i
$26$	−0.907379	+	3.48951i	−0.177952	+	0.684349i
$27$	3.03592	+	4.21701i	0.584263	+	0.811564i
$28$	0.0783861	−	2.64459i	0.0148136	−	0.499781i
$29$			0.127692i			0.0237119i	0.999930	+	0.0118559i	$0.00377395\pi$
$29$			0.127692i			0.0237119i	−0.999930	+	0.0118559i	$0.996226\pi$
$30$	−1.80353	+	5.52344i	−0.329277	+	1.00844i
$31$	1.65420	−	0.443241i	0.297103	−	0.0796084i	−0.107189	−	0.994239i	$-0.534185\pi$
$31$	1.65420	−	0.443241i	0.297103	−	0.0796084i	0.404291	+	0.914630i	$0.367518\pi$
$32$	−0.258819	−	0.965926i	−0.0457532	−	0.170753i
$33$	4.96179	+	9.77304i	0.863736	+	1.70127i
$34$	−2.87686	+	2.87686i	−0.493377	+	0.493377i
$35$	−2.04216	−	8.63745i	−0.345188	−	1.45999i
$36$	−2.98264	−	0.322230i	−0.497107	−	0.0537050i
$37$	−7.58283	−	2.03181i	−1.24661	−	0.334028i	−0.425584	−	0.904919i	$-0.639931\pi$
$37$	−7.58283	−	2.03181i	−1.24661	−	0.334028i	−0.821026	+	0.570891i	$0.806598\pi$
$38$	−1.15939	+	2.00812i	−0.188078	+	0.325760i
$39$	−6.10069	+	1.33475i	−0.976892	+	0.213732i
$40$	−1.67733	−	2.90521i	−0.265209	−	0.459355i
$41$	7.12298	−	7.12298i	1.11242	−	1.11242i	0.119600	−	0.992822i	$-0.461839\pi$
$41$	7.12298	−	7.12298i	1.11242	−	1.11242i	0.992822	−	0.119600i	$-0.0381613\pi$
$42$	4.14578	−	1.95256i	0.639708	−	0.301286i
$43$			2.56093i			0.390538i	0.980750	+	0.195269i	$0.0625579\pi$
$43$			2.56093i			0.390538i	−0.980750	+	0.195269i	$0.937442\pi$
$44$	−6.11240	−	1.63781i	−0.921479	−	0.246910i
$45$	−9.94458	+	1.54554i	−1.48245	+	0.230395i
$46$	1.41921	+	5.29656i	0.209251	+	0.780935i
$47$	2.54114	−	9.48367i	0.370664	−	1.38334i	−0.488914	−	0.872332i	$-0.662607\pi$
$47$	2.54114	−	9.48367i	0.370664	−	1.38334i	0.859578	−	0.511004i	$-0.170726\pi$
$48$	1.28884	−	1.15710i	0.186028	−	0.167013i
$49$	−3.85291	+	5.84424i	−0.550415	+	0.834891i
$50$	−4.42203	−	4.42203i	−0.625370	−	0.625370i
$51$	−6.69878	−	2.18730i	−0.938017	−	0.306283i
$52$	1.77961	−	3.13576i	0.246788	−	0.434851i
$53$	2.68874	+	1.55235i	0.369327	+	0.213231i	0.673165	−	0.739493i	$-0.264935\pi$
$53$	2.68874	+	1.55235i	0.369327	+	0.213231i	−0.303837	+	0.952724i	$0.598268\pi$
$54$	−1.84103	−	4.85907i	−0.250533	−	0.661236i
$55$	−21.2283			−2.86243
$56$	−0.760185	+	2.53419i	−0.101584	+	0.338645i
$57$	−4.01043	−	0.216005i	−0.531195	−	0.0286106i
$58$	0.0330492	−	0.123341i	0.00433957	−	0.0161955i
$59$	−6.18587	+	1.65750i	−0.805332	+	0.215788i	−0.637924	−	0.770100i	$-0.720207\pi$
$59$	−6.18587	+	1.65750i	−0.805332	+	0.215788i	−0.167408	+	0.985888i	$0.553540\pi$
$60$	3.17164	−	4.86845i	0.409458	−	0.628514i
$61$	1.79532	+	3.10959i	0.229867	+	0.398142i	0.957769	−	0.287540i	$-0.0928374\pi$
$61$	1.79532	+	3.10959i	0.229867	+	0.398142i	−0.727901	+	0.685682i	$0.759504\pi$
$62$	−1.71255			−0.217494
$63$	6.26624	+	4.87178i	0.789472	+	0.613786i
$64$			1.00000i			0.125000i
$65$	3.04394	−	11.7061i	0.377555	−	1.45196i
$66$	−2.26327	−	10.7242i	−0.278589	−	1.32006i
$67$	3.15651	−	0.845785i	0.385629	−	0.103329i	−0.0607954	−	0.998150i	$-0.519364\pi$
$67$	3.15651	−	0.845785i	0.385629	−	0.103329i	0.446425	+	0.894821i	$0.352697\pi$
$68$	3.52342	−	2.03425i	0.427277	−	0.246689i
$69$	−7.06724	+	6.34485i	−0.850795	+	0.763830i
$70$	−0.262958	+	8.87168i	−0.0314295	+	1.06037i
$71$	−8.71117	+	8.71117i	−1.03383	+	1.03383i	−0.0344187	+	0.999408i	$0.510958\pi$
$71$	−8.71117	+	8.71117i	−1.03383	+	1.03383i	−0.999408	+	0.0344187i	$0.989042\pi$
$72$	2.79761	+	1.08322i	0.329702	+	0.127658i
$73$	1.09357	+	4.08124i	0.127992	+	0.477673i	0.999929	−	0.0119458i	$-0.00380255\pi$
$73$	1.09357	+	4.08124i	0.127992	+	0.477673i	−0.871937	+	0.489619i	$0.837136\pi$
$74$	6.79858	+	3.92516i	0.790319	+	0.456291i
$75$	3.36211	−	10.2967i	0.388223	−	1.18896i
$76$	1.63962	−	1.63962i	0.188078	−	0.188078i
$77$	11.4827	+	12.1842i	1.30858	+	1.38852i
$78$	6.23827	+	0.289703i	0.706346	+	0.0328024i
$79$	3.01834	+	5.22792i	0.339590	+	0.588187i	0.984356	−	0.176193i	$-0.0563784\pi$
$79$	3.01834	+	5.22792i	0.339590	+	0.588187i	−0.644766	+	0.764380i	$0.723045\pi$
$80$	0.868248	+	3.24035i	0.0970731	+	0.362282i
$81$	6.06084	−	6.65329i	0.673426	−	0.739254i
$82$	−8.72383	+	5.03671i	−0.963386	+	0.556211i
$83$	−0.395201	+	0.395201i	−0.0433790	+	0.0433790i	−0.728464	−	0.685085i	$-0.759765\pi$
$83$	−0.395201	+	0.395201i	−0.0433790	+	0.0433790i	0.685085	+	0.728464i	$0.259765\pi$
$84$	−4.50988	+	0.813017i	−0.492068	+	0.0887075i
$85$	9.65087	−	9.65087i	1.04678	−	1.04678i
$86$	0.662816	−	2.47366i	0.0714733	−	0.266742i
$87$	0.216403	−	0.0456702i	0.0232008	−	0.00489636i
$88$	5.48023	+	3.16401i	0.584194	+	0.337285i
$89$	−0.836494	+	3.12184i	−0.0886682	+	0.330914i	−0.995984	−	0.0895366i	$-0.971461\pi$
$89$	−0.836494	+	3.12184i	−0.0886682	+	0.330914i	0.907315	+	0.420451i	$0.138128\pi$
$90$	10.0057	+	1.08097i	1.05470	+	0.113944i
$91$	−8.36533	+	4.58489i	−0.876925	+	0.480627i
$92$		−	5.48340i		−	0.571684i
$93$	−1.34281	−	2.64487i	−0.139243	−	0.274261i
$94$	−4.90911	+	8.50283i	−0.506336	+	0.877000i
$95$	3.88935	−	6.73655i	0.399039	−	0.691156i
$96$	−1.54441	+	0.784098i	−0.157625	+	0.0800266i
$97$	2.43118	+	2.43118i	0.246849	+	0.246849i	0.819676	−	0.572827i	$-0.194153\pi$
$97$	2.43118	+	2.43118i	0.246849	+	0.246849i	−0.572827	+	0.819676i	$0.694153\pi$
$98$	5.23422	−	4.64789i	0.528736	−	0.469508i
$99$	14.7879	−	11.9043i	1.48624	−	1.19642i
$100$	3.12685	+	5.41586i	0.312685	+	0.541586i
$101$	0.867612	−	1.50275i	0.0863306	−	0.149529i	−0.819627	−	0.572898i	$-0.805819\pi$
$101$	0.867612	−	1.50275i	0.0863306	−	0.149529i	0.905957	+	0.423369i	$0.139153\pi$
$102$	5.90441	+	3.84654i	0.584624	+	0.380864i
$103$	11.0778	−	6.39579i	1.09153	−	0.630196i	0.157548	−	0.987511i	$-0.449641\pi$
$103$	11.0778	−	6.39579i	1.09153	−	0.630196i	0.933984	+	0.357315i	$0.116308\pi$
$104$	−2.53057	+	2.56831i	−0.248143	+	0.251844i
$105$	−13.9077	+	6.55015i	−1.35725	+	0.639229i
$106$	−2.19535	−	2.19535i	−0.213231	−	0.213231i
$107$	15.1052	−	8.72097i	1.46027	−	0.843088i	0.461248	−	0.887271i	$-0.347402\pi$
$107$	15.1052	−	8.72097i	1.46027	−	0.843088i	0.999023	+	0.0441826i	$0.0140683\pi$
$108$	0.520678	+	5.17000i	0.0501022	+	0.497483i
$109$	5.10102	−	1.36681i	0.488589	−	0.130917i	−0.00611014	−	0.999981i	$-0.501945\pi$
$109$	5.10102	−	1.36681i	0.488589	−	0.130917i	0.494699	+	0.869064i	$0.335278\pi$
$110$	20.5050	+	5.49429i	1.95507	+	0.523860i
$111$	−0.731294	+	13.5775i	−0.0694114	+	1.28872i
$112$	1.39018	−	2.25109i	0.131360	−	0.212708i
$113$		−	0.606621i		−	0.0570661i	−0.999593	−	0.0285331i	$-0.990916\pi$
$113$		−	0.606621i		−	0.0570661i	0.999593	−	0.0285331i	$-0.00908359\pi$
$114$	3.81787	+	1.24662i	0.357577	+	0.116757i
$115$	−4.76095	−	17.7681i	−0.443961	−	1.65688i
$116$	−0.0638462	+	0.110585i	−0.00592797	+	0.0102675i
$117$	4.44400	+	9.86159i	0.410848	+	0.911704i
$118$	6.40409			0.589544
$119$	−10.7595	−	0.318913i	−0.986322	−	0.0292347i
$120$	−4.32362	+	3.88168i	−0.394691	+	0.354347i
$121$	25.1527	−	14.5219i	2.28661	−	1.32018i
$122$	−0.929327	−	3.46830i	−0.0841373	−	0.314005i
$123$	−14.6191	−	9.52387i	−1.31816	−	0.858738i
$124$	1.65420	+	0.443241i	0.148551	+	0.0398042i
$125$	2.97389	+	2.97389i	0.265993	+	0.265993i
$126$	−4.79181	−	6.32760i	−0.426889	−	0.563707i
$127$			20.5110i			1.82006i	0.414543	+	0.910030i	$0.363941\pi$
$127$			20.5110i			1.82006i	−0.414543	+	0.910030i	$0.636059\pi$
$128$	0.258819	−	0.965926i	0.0228766	−	0.0853766i
$129$	4.34006	−	0.915937i	0.382121	−	0.0806437i
$130$	−5.96998	+	10.5194i	−0.523602	+	0.922611i
$131$	−3.33860	+	1.92754i	−0.291695	+	0.168410i	−0.638706	−	0.769451i	$-0.720530\pi$
$131$	−3.33860	+	1.92754i	−0.291695	+	0.168410i	0.347011	+	0.937861i	$0.387197\pi$
$132$	−0.589485	+	10.9446i	−0.0513080	+	0.952604i
$133$	−5.97031	+	1.41157i	−0.517692	+	0.122399i
$134$	−3.26786			−0.282300
$135$	6.17602	+	16.3005i	0.531547	+	1.40292i
$136$	−3.92986	+	1.05300i	−0.336983	+	0.0902943i
$137$	−2.36895	+	0.634758i	−0.202393	+	0.0542311i	−0.358591	−	0.933495i	$-0.616743\pi$
$137$	−2.36895	+	0.634758i	−0.202393	+	0.0542311i	0.156198	+	0.987726i	$0.450076\pi$
$138$	8.46860	−	4.29952i	0.720895	−	0.365999i
$139$	17.2879			1.46634			0.733171	−	0.680044i	$-0.238039\pi$
$139$	17.2879			1.46634			0.733171	+	0.680044i	$0.238039\pi$
$140$	2.55016	−	8.50133i	0.215528	−	0.718493i
$141$	−16.9810	−	0.914613i	−1.43006	−	0.0770243i
$142$	10.6690	−	6.15973i	0.895320	−	0.516913i
$143$	6.06820	+	21.9943i	0.507448	+	1.83925i
$144$	−2.42193	−	1.77038i	−0.201828	−	0.147532i
$145$	−0.110869	+	0.413767i	−0.00920714	+	0.0343615i
$146$		−	4.22521i		−	0.349681i
$147$	11.2824	+	4.43937i	0.930555	+	0.366153i
$148$	−5.55102	−	5.55102i	−0.456291	−	0.456291i
$149$	5.67339	+	1.52018i	0.464783	+	0.124538i	0.483608	−	0.875285i	$-0.339326\pi$
$149$	5.67339	+	1.52018i	0.464783	+	0.124538i	−0.0188255	+	0.999823i	$0.505993\pi$
$150$	−5.91254	+	9.07569i	−0.482756	+	0.741027i
$151$	−2.81919	−	10.5214i	−0.229423	−	0.856217i	−0.980584	−	0.196098i	$-0.937173\pi$
$151$	−2.81919	−	10.5214i	−0.229423	−	0.856217i	0.751162	−	0.660118i	$-0.229494\pi$
$152$	−2.00812	+	1.15939i	−0.162880	+	0.0940389i
$153$	−1.31099	+	12.1349i	−0.105987	+	0.981046i
$154$	−7.93794	−	14.7410i	−0.639657	−	1.18786i
$155$	5.74501			0.461451
$156$	−5.95073	−	1.89442i	−0.476440	−	0.151675i
$157$	−3.72889	+	6.45864i	−0.297598	+	0.515455i	−0.975586	−	0.219618i	$-0.929519\pi$
$157$	−3.72889	+	6.45864i	−0.297598	+	0.515455i	0.677988	+	0.735073i	$0.262852\pi$
$158$	−1.56241	−	5.83099i	−0.124298	−	0.463888i
$159$	1.66914	−	5.11188i	0.132372	−	0.405398i
$160$		−	3.35465i		−	0.265209i
$161$	−7.62291	+	12.3436i	−0.600769	+	0.972813i
$162$	−7.57632	+	4.85792i	−0.595252	+	0.381674i
$163$	−8.96107	−	2.40111i	−0.701885	−	0.188070i	−0.109810	−	0.993953i	$-0.535024\pi$
$163$	−8.96107	−	2.40111i	−0.701885	−	0.188070i	−0.592075	+	0.805883i	$0.701691\pi$
$164$	9.73017	−	2.60719i	0.759799	−	0.203587i
$165$	7.59249	+	35.9761i	0.591074	+	2.80073i
$166$	0.484021	−	0.279450i	0.0375673	−	0.0216895i
$167$	7.85626	+	7.85626i	0.607935	+	0.607935i	0.942406	−	0.334471i	$-0.108558\pi$
$167$	7.85626	+	7.85626i	0.607935	+	0.607935i	−0.334471	+	0.942406i	$0.608558\pi$
$168$	4.56663	+	0.381928i	0.352323	+	0.0294664i
$169$	−12.9986	+	0.192461i	−0.999890	+	0.0148047i
$170$	−11.8198	+	6.82419i	−0.906541	+	0.523392i
$171$	1.06830	+	6.87382i	0.0816946	+	0.525654i
$172$	−1.28046	+	2.21783i	−0.0976344	+	0.169108i
$173$	−7.45262	−	12.9083i	−0.566612	−	0.981401i	−0.996898	−	0.0787079i	$-0.974921\pi$
$173$	−7.45262	−	12.9083i	−0.566612	−	0.981401i	0.430286	−	0.902693i	$-0.358413\pi$
$174$	−0.220850	−	0.0118951i	−0.0167426	−	0.000901768i
$175$	0.490203	−	16.5385i	0.0370559	−	1.25019i
$176$	−4.47459	−	4.47459i	−0.337285	−	0.337285i
$177$	5.02143	+	9.89051i	0.377434	+	0.743417i
$178$	1.61598	−	2.79896i	0.121123	−	0.209791i
$179$	4.86804	−	8.43169i	0.363854	−	0.630214i	−0.624737	−	0.780835i	$-0.714794\pi$
$179$	4.86804	−	8.43169i	0.363854	−	0.630214i	0.988592	+	0.150621i	$0.0481272\pi$
$180$	−9.38502	−	3.63381i	−0.699518	−	0.270848i
$181$		−	0.413098i		−	0.0307053i	−0.999882	−	0.0153527i	$-0.995113\pi$
$181$		−	0.413098i		−	0.0307053i	0.999882	−	0.0153527i	$-0.00488710\pi$
$182$	9.26695	−	2.26356i	0.686912	−	0.167786i
$183$	4.62777	−	4.15474i	0.342095	−	0.307127i
$184$	−1.41921	+	5.29656i	−0.104625	+	0.390467i
$185$	−22.8069	−	13.1676i	−1.67679	−	0.968098i
$186$	0.612508	+	2.90230i	0.0449113	+	0.212807i
$187$	−6.66343	+	24.8683i	−0.487278	+	1.81855i
$188$	6.94253	−	6.94253i	0.506336	−	0.506336i
$189$	6.01513	−	12.3620i	0.437537	−	0.899201i
$190$	−5.50037	+	5.50037i	−0.399039	+	0.399039i
$191$	21.0580	−	12.1578i	1.52370	−	0.879711i	0.524098	−	0.851658i	$-0.324403\pi$
$191$	21.0580	−	12.1578i	1.52370	−	0.879711i	0.999606	−	0.0280531i	$-0.00893076\pi$
$192$	1.69472	−	0.357658i	0.122306	−	0.0258118i
$193$	0.225659	+	0.842169i	0.0162433	+	0.0606207i	0.973572	−	0.228381i	$-0.0733433\pi$
$193$	0.225659	+	0.842169i	0.0162433	+	0.0606207i	−0.957329	+	0.289002i	$0.906677\pi$
$194$	−1.71910	−	2.97758i	−0.123424	−	0.213777i
$195$	−20.9272	−	0.971852i	−1.49863	−	0.0695958i
$196$	−6.25883	+	3.13480i	−0.447060	+	0.223915i
$197$	−3.35030	+	3.35030i	−0.238699	+	0.238699i	−0.816311	−	0.577612i	$-0.803985\pi$
$197$	−3.35030	+	3.35030i	−0.238699	+	0.238699i	0.577612	+	0.816311i	$0.303985\pi$
$198$	−17.3651	+	7.67123i	−1.23408	+	0.545170i
$199$	−19.7369	−	11.3951i	−1.39911	−	0.807778i	−0.404813	−	0.914400i	$-0.632663\pi$
$199$	−19.7369	−	11.3951i	−1.39911	−	0.807778i	−0.994300	+	0.106622i	$0.965997\pi$
$200$	−1.61858	−	6.04061i	−0.114451	−	0.427135i
$201$	−2.56232	−	5.04691i	−0.180732	−	0.355981i
$202$	−1.22699	+	1.22699i	−0.0863306	+	0.0863306i
$203$	0.297456	−	0.160179i	0.0208773	−	0.0112423i
$204$	−4.70766	−	5.24365i	−0.329602	−	0.367129i
$205$	29.2654	−	16.8964i	2.04399	−	1.18010i
$206$	−12.3557	+	3.31071i	−0.860864	+	0.230668i
$207$	13.2804	+	9.70771i	0.923052	+	0.674732i
$208$	3.10907	−	1.82584i	0.215575	−	0.126599i
$209$			14.6733i			1.01497i
$210$	15.1291	−	2.72739i	1.04401	−	0.188208i
$211$	13.7192			0.944470			0.472235	−	0.881473i	$-0.343447\pi$
$211$	13.7192			0.944470			0.472235	+	0.881473i	$0.343447\pi$
$212$	1.55235	+	2.68874i	0.106616	+	0.184664i
$213$	17.8786	+	11.6474i	1.22502	+	0.798066i
$214$	−16.8476	+	4.51431i	−1.15168	+	0.308592i
$215$	−2.22352	+	8.29829i	−0.151643	+	0.565938i
$216$	0.835158	−	5.12860i	0.0568253	−	0.348957i
$217$	−3.10756	−	3.29740i	−0.210955	−	0.223842i
$218$	−5.28096			−0.357672
$219$	6.52544	−	3.31298i	0.440949	−	0.223870i
$220$	−18.3843	−	10.6142i	−1.23947	−	0.715606i
$221$	−12.7578	−	7.24034i	−0.858183	−	0.487038i
$222$	4.22049	−	12.9256i	0.283260	−	0.867507i
$223$	−4.07576	−	4.07576i	−0.272933	−	0.272933i	0.557347	−	0.830280i	$-0.311819\pi$
$223$	−4.07576	−	4.07576i	−0.272933	−	0.272933i	−0.830280	+	0.557347i	$0.811819\pi$
$224$	−1.92543	+	1.81458i	−0.128649	+	0.121242i
$225$	−18.6526	−	2.01513i	−1.24350	−	0.134342i
$226$	−0.157005	+	0.585951i	−0.0104438	+	0.0389769i
$227$	4.41341	+	16.4711i	0.292928	+	1.09322i	0.942849	+	0.333221i	$0.108135\pi$
$227$	4.41341	+	16.4711i	0.292928	+	1.09322i	−0.649921	+	0.760002i	$0.725198\pi$
$228$	−3.36513	−	2.19228i	−0.222861	−	0.145187i
$229$	9.59834	+	2.57187i	0.634276	+	0.169954i	0.561609	−	0.827403i	$-0.310182\pi$
$229$	9.59834	+	2.57187i	0.634276	+	0.169954i	0.0726666	+	0.997356i	$0.476849\pi$
$230$			18.3949i			1.21292i
$231$	16.5419	−	23.8178i	1.08838	−	1.56709i
$232$	0.0902921	−	0.0902921i	0.00592797	−	0.00592797i
$233$	−9.19291	−	15.9226i	−0.602248	−	1.04312i	−0.992480	−	0.122407i	$-0.960939\pi$
$233$	−9.19291	−	15.9226i	−0.602248	−	1.04312i	0.390232	−	0.920716i	$-0.372395\pi$
$234$	−1.74021	−	10.6758i	−0.113761	−	0.697896i
$235$	16.4684	−	28.5240i	1.07428	−	1.86070i
$236$	−6.18587	−	1.65750i	−0.402666	−	0.107894i
$237$	7.78033	−	6.98505i	0.505387	−	0.453728i
$238$	10.3103	+	3.09281i	0.668320	+	0.200477i
$239$	3.07854	−	3.07854i	0.199134	−	0.199134i	−0.600495	−	0.799629i	$-0.705030\pi$
$239$	3.07854	−	3.07854i	0.199134	−	0.199134i	0.799629	+	0.600495i	$0.205030\pi$
$240$	5.18095	−	2.63038i	0.334429	−	0.169790i
$241$	−4.61685	−	17.2303i	−0.297397	−	1.10990i	−0.939295	−	0.343112i	$-0.888519\pi$
$241$	−4.61685	−	17.2303i	−0.297397	−	1.10990i	0.641897	−	0.766791i	$-0.278148\pi$
$242$	−28.0542	+	7.51710i	−1.80339	+	0.483218i
$243$	−13.4432	−	7.89183i	−0.862380	−	0.506261i
$244$			3.59064i			0.229867i
$245$	−17.5590	+	15.5921i	−1.12180	+	0.996141i
$246$	11.6560	+	12.9830i	0.743157	+	0.827769i
$247$	−8.09140	−	2.10401i	−0.514843	−	0.133875i
$248$	−1.48311	−	0.856275i	−0.0941777	−	0.0543735i
$249$	0.811103	+	0.528409i	0.0514016	+	0.0334866i
$250$	−2.10286	−	3.64226i	−0.132997	−	0.230357i
$251$	25.3659			1.60108			0.800542	−	0.599276i	$-0.204545\pi$
$251$	25.3659			1.60108			0.800542	+	0.599276i	$0.204545\pi$
$252$	2.99083	+	7.35220i	0.188405	+	0.463145i
$253$	24.5359	+	24.5359i	1.54256	+	1.54256i
$254$	5.30864	−	19.8121i	0.333094	−	1.24312i
$255$	−19.8072	−	12.9038i	−1.24038	−	0.808068i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	11.3035	+	19.5783i	0.705096	+	1.22126i	0.966657	+	0.256075i	$0.0824294\pi$
$257$	11.3035	+	19.5783i	0.705096	+	1.22126i	−0.261561	+	0.965187i	$0.584237\pi$
$258$	−4.42923	−	0.238562i	−0.275752	−	0.0148522i
$259$	4.77892	+	20.2127i	0.296948	+	1.25596i
$260$	8.48917	−	8.61580i	0.526476	−	0.534329i
$261$	−0.154797	−	0.350408i	−0.00958167	−	0.0216897i
$262$	3.72373	−	0.997770i	0.230053	−	0.0616424i
$263$	16.2993	+	9.41043i	1.00506	+	0.580272i	0.909742	−	0.415175i	$-0.136280\pi$
$263$	16.2993	+	9.41043i	1.00506	+	0.580272i	0.0953187	+	0.995447i	$0.469613\pi$
$264$	3.40207	−	10.4191i	0.209383	−	0.641251i
$265$	7.36464	+	7.36464i	0.452406	+	0.452406i
$266$	6.13222	+	0.181760i	0.375991	+	0.0111444i
$267$	5.58982	+	0.301072i	0.342092	+	0.0184253i
$268$	3.15651	+	0.845785i	0.192815	+	0.0516645i
$269$	−4.49802	−	2.59693i	−0.274249	−	0.158338i	0.356568	−	0.934269i	$-0.383947\pi$
$269$	−4.49802	−	2.59693i	−0.274249	−	0.158338i	−0.630817	+	0.775932i	$0.717280\pi$
$270$	−1.74669	−	17.3436i	−0.106300	−	1.05550i
$271$	−4.20199	−	1.12592i	−0.255253	−	0.0683948i	0.128923	−	0.991655i	$-0.458848\pi$
$271$	−4.20199	−	1.12592i	−0.255253	−	0.0683948i	−0.384176	+	0.923260i	$0.625515\pi$
$272$	4.06849			0.246689
$273$	10.7620	+	12.5371i	0.651349	+	0.758779i
$274$	2.45252			0.148162
$275$	−38.2251	−	10.2424i	−2.30506	−	0.617639i
$276$	−9.29283	+	1.96118i	−0.559363	+	0.118049i
$277$	−6.13780	−	3.54366i	−0.368785	−	0.212918i	0.304143	−	0.952627i	$-0.401630\pi$
$277$	−6.13780	−	3.54366i	−0.368785	−	0.212918i	−0.672928	+	0.739708i	$0.734963\pi$
$278$	−16.6989	−	4.47444i	−1.00153	−	0.268359i
$279$	−4.00206	+	3.22165i	−0.239597	+	0.192875i
$280$	−4.66357	+	7.55162i	−0.278702	+	0.451296i
$281$	7.47121	+	7.47121i	0.445695	+	0.445695i	0.893920	−	0.448226i	$-0.147944\pi$
$281$	7.47121	+	7.47121i	0.445695	+	0.445695i	−0.448226	+	0.893920i	$0.647944\pi$
$282$	16.1657	+	5.27847i	0.962654	+	0.314328i
$283$	10.1109	+	5.83755i	0.601033	+	0.347006i	0.769448	−	0.638710i	$-0.220532\pi$
$283$	10.1109	+	5.83755i	0.601033	+	0.347006i	−0.168415	+	0.985716i	$0.553865\pi$
$284$	−11.8997	+	3.18851i	−0.706116	+	0.189203i
$285$	−12.8076	−	4.18198i	−0.758659	−	0.247719i
$286$	−0.168896	−	22.8154i	−0.00998704	−	1.34910i
$287$	−25.5279	−	7.65766i	−1.50687	−	0.452017i
$288$	1.88120	+	2.33690i	0.110851	+	0.137703i
$289$	0.223679	+	0.387423i	0.0131576	+	0.0227896i
$290$	0.214182	−	0.370974i	0.0125772	−	0.0217843i
$291$	3.25064	−	4.98970i	0.190556	−	0.292502i
$292$	−1.09357	+	4.08124i	−0.0639961	+	0.238837i
$293$	−11.5897	−	11.5897i	−0.677076	−	0.677076i	0.282261	−	0.959338i	$-0.408916\pi$
$293$	−11.5897	−	11.5897i	−0.677076	−	0.677076i	−0.959338	+	0.282261i	$0.908916\pi$
$294$	−9.74895	−	7.20819i	−0.568570	−	0.420390i
$295$	−21.4835			−1.25082
$296$	3.92516	+	6.79858i	0.228145	+	0.395159i
$297$	−25.4634	−	20.8038i	−1.47754	−	1.20716i
$298$	−5.08663	−	2.93676i	−0.294660	−	0.170122i
$299$	−17.0483	+	10.0118i	−0.985926	+	0.578998i
$300$	8.06003	−	7.23617i	0.465346	−	0.417780i
$301$	5.96561	−	3.21245i	0.343852	−	0.185163i
$302$			10.8925i			0.626794i
$303$	−2.85705	−	0.932890i	−0.164133	−	0.0535931i
$304$	2.23977	−	0.600144i	0.128460	−	0.0344206i
$305$	3.11757	+	11.6349i	0.178512	+	0.666214i
$306$	4.40706	−	11.3821i	0.251935	−	0.650670i
$307$	−18.6550	+	18.6550i	−1.06469	+	1.06469i	−0.0669373	+	0.997757i	$0.521323\pi$
$307$	−18.6550	+	18.6550i	−1.06469	+	1.06469i	−0.997757	+	0.0669373i	$0.978677\pi$
$308$	3.85222	+	16.2932i	0.219500	+	0.928390i
$309$	−14.8012	−	16.4863i	−0.842009	−	0.937875i
$310$	−5.54926	−	1.48692i	−0.315177	−	0.0844513i
$311$	6.40089	−	11.0867i	0.362961	−	0.628667i	−0.625486	−	0.780236i	$-0.715099\pi$
$311$	6.40089	−	11.0867i	0.362961	−	0.628667i	0.988447	+	0.151569i	$0.0484325\pi$
$312$	5.25765	+	3.37003i	0.297656	+	0.190790i
$313$	−8.15974	−	14.1331i	−0.461216	−	0.798849i	0.537806	−	0.843069i	$-0.319253\pi$
$313$	−8.15974	−	14.1331i	−0.461216	−	0.798849i	−0.999022	+	0.0442193i	$0.985920\pi$
$314$	5.27345	−	5.27345i	0.297598	−	0.297598i
$315$	16.0749	+	21.2269i	0.905717	+	1.19600i
$316$			6.03668i			0.339590i
$317$	0.351074	+	0.0940699i	0.0197183	+	0.00528349i	0.268665	−	0.963234i	$-0.413418\pi$
$317$	0.351074	+	0.0940699i	0.0197183	+	0.00528349i	−0.248946	+	0.968517i	$0.580084\pi$
$318$	−2.93532	+	4.50569i	−0.164605	+	0.252667i
$319$	−0.209136	−	0.780507i	−0.0117094	−	0.0437000i
$320$	−0.868248	+	3.24035i	−0.0485365	+	0.181141i
$321$	−20.1821	−	22.4799i	−1.12646	−	1.25471i
$322$	10.5579	−	9.95007i	0.588370	−	0.554496i
$323$	−6.67080	−	6.67080i	−0.371173	−	0.371173i
$324$	8.57548	−	2.73150i	0.476416	−	0.151750i
$325$	11.1292	−	19.6101i	0.617334	−	1.08777i
$326$	8.03428	+	4.63859i	0.444977	+	0.256908i
$327$	−4.14079	−	8.15595i	−0.228986	−	0.451025i
$328$	−10.0734			−0.556211
$329$	−25.2796	+	5.97689i	−1.39371	+	0.329517i
$330$	1.97752	−	36.7153i	0.108859	−	2.02111i
$331$	−3.54154	+	13.2172i	−0.194661	+	0.726484i	0.797694	+	0.603063i	$0.206053\pi$
$331$	−3.54154	+	13.2172i	−0.194661	+	0.726484i	−0.992354	+	0.123421i	$0.960613\pi$
$332$	−0.539855	+	0.144654i	−0.0296284	+	0.00793891i
$333$	23.2716	−	3.61676i	1.27528	−	0.198197i
$334$	−5.55521	−	9.62191i	−0.303968	−	0.526487i
$335$	10.9625			0.598948
$336$	−4.31218	−	1.55085i	−0.235249	−	0.0846056i
$337$		−	6.55986i		−	0.357338i	−0.983909	−	0.178669i	$-0.942821\pi$
$337$		−	6.55986i		−	0.357338i	0.983909	−	0.178669i	$-0.0571792\pi$
$338$	12.6055	+	3.17838i	0.685647	+	0.172881i
$339$	−1.02805	+	0.216963i	−0.0558362	+	0.0117838i
$340$	13.1833	−	3.53246i	0.714966	−	0.191575i
$341$	−9.38517	+	5.41853i	−0.508235	+	0.293430i
$342$	0.747180	−	6.91609i	0.0404029	−	0.373980i
$343$	18.4471	+	1.64418i	0.996051	+	0.0887774i
$344$	1.81085	−	1.81085i	0.0976344	−	0.0976344i
$345$	−28.4092	+	14.4234i	−1.52950	+	0.776530i
$346$	3.85776	+	14.3973i	0.207394	+	0.774006i
$347$	18.0884	+	10.4434i	0.971038	+	0.560629i	0.899553	−	0.436812i	$-0.143893\pi$
$347$	18.0884	+	10.4434i	0.971038	+	0.560629i	0.0714856	+	0.997442i	$0.477226\pi$
$348$	0.210246	+	0.0686499i	0.0112703	+	0.00368002i
$349$	3.21831	−	3.21831i	0.172272	−	0.172272i	−0.615705	−	0.787977i	$-0.711129\pi$
$349$	3.21831	−	3.21831i	0.172272	−	0.172272i	0.787977	+	0.615705i	$0.211129\pi$
$350$	−4.75397	+	15.8481i	−0.254110	+	0.847114i
$351$	15.1232	−	11.0584i	0.807217	−	0.590255i
$352$	3.16401	+	5.48023i	0.168642	+	0.292097i
$353$	−4.76936	−	17.7995i	−0.253848	−	0.947372i	−0.968728	−	0.248125i	$-0.920185\pi$
$353$	−4.76936	−	17.7995i	−0.253848	−	0.947372i	0.714880	−	0.699247i	$-0.246481\pi$
$354$	−2.29048	−	10.8531i	−0.121737	−	0.576838i
$355$	−35.7907	+	20.6638i	−1.89957	+	1.09672i
$356$	−2.28534	+	2.28534i	−0.121123	+	0.121123i
$357$	3.30776	+	18.3484i	0.175065	+	0.971101i
$358$	−6.88445	+	6.88445i	−0.363854	+	0.363854i
$359$	2.23711	−	8.34901i	0.118070	−	0.440644i	−0.881428	−	0.472318i	$-0.843417\pi$
$359$	2.23711	−	8.34901i	0.118070	−	0.440644i	0.999498	+	0.0316744i	$0.0100840\pi$
$360$	8.12474	+	5.93902i	0.428211	+	0.313014i
$361$	11.7981	+	6.81163i	0.620952	+	0.358507i
$362$	−0.106918	+	0.399022i	−0.00561947	+	0.0209721i
$363$	−33.6067	−	37.4330i	−1.76389	−	1.96472i
$364$	−9.53704	−	0.212033i	−0.499876	−	0.0111135i
$365$			14.1741i			0.741907i
$366$	−5.54541	+	2.81542i	−0.289863	+	0.147164i
$367$	12.2707	−	21.2535i	0.640527	−	1.10943i	−0.344788	−	0.938680i	$-0.612049\pi$
$367$	12.2707	−	21.2535i	0.640527	−	1.10943i	0.985315	−	0.170745i	$-0.0546174\pi$
$368$	2.74170	−	4.74876i	0.142921	−	0.247546i
$369$	−10.9117	+	28.1815i	−0.568039	+	1.46707i
$370$	18.6217	+	18.6217i	0.968098	+	0.968098i
$371$	0.243365	−	8.21064i	0.0126349	−	0.426275i
$372$	0.159532	−	2.96193i	0.00827135	−	0.153569i
$373$	0.647930	+	1.12225i	0.0335485	+	0.0581078i	0.882312	−	0.470665i	$-0.155986\pi$
$373$	0.647930	+	1.12225i	0.0335485	+	0.0581078i	−0.848764	+	0.528772i	$0.822652\pi$
$374$	12.8728	−	22.2963i	0.665635	−	1.15291i
$375$	3.97628	−	6.10356i	0.205334	−	0.315186i
$376$	−8.50283	+	4.90911i	−0.438500	+	0.253168i
$377$	0.460389	−	0.00340814i	0.0237112	−	0.000175528i
$378$	−9.00969	+	10.3839i	−0.463408	+	0.534091i
$379$	−20.8376	−	20.8376i	−1.07035	−	1.07035i	−0.997330	−	0.0730241i	$-0.976735\pi$
$379$	−20.8376	−	20.8376i	−1.07035	−	1.07035i	−0.0730241	−	0.997330i	$-0.523265\pi$
$380$	6.73655	−	3.88935i	0.345578	−	0.199519i
$381$	34.7605	−	7.33594i	1.78083	−	0.375832i
$382$	−23.4872	+	6.29337i	−1.20171	+	0.321997i
$383$	−8.85758	−	2.37338i	−0.452601	−	0.121274i	0.0253151	−	0.999680i	$-0.491941\pi$
$383$	−8.85758	−	2.37338i	−0.452601	−	0.121274i	−0.477916	+	0.878405i	$0.658608\pi$
$384$	−1.72954	−	0.0931546i	−0.0882604	−	0.00475378i
$385$	26.6290	+	49.4508i	1.35714	+	2.52025i
$386$		−	0.871878i		−	0.0443774i
$387$	−3.10451	−	7.02759i	−0.157811	−	0.357233i
$388$	0.889874	+	3.32105i	0.0451765	+	0.168601i
$389$	−17.7461	+	30.7371i	−0.899761	+	1.55843i	−0.0719626	+	0.997407i	$0.522926\pi$
$389$	−17.7461	+	30.7371i	−0.899761	+	1.55843i	−0.827799	+	0.561025i	$0.810407\pi$
$390$	19.9626	+	6.35511i	1.01085	+	0.321803i
$391$	−22.3092			−1.12822
$392$	6.85692	−	1.40808i	0.346327	−	0.0711189i
$393$	4.46073	+	4.96860i	0.225014	+	0.250633i
$394$	4.10326	−	2.36902i	0.206719	−	0.119349i
$395$	5.24134	+	19.5609i	0.263720	+	0.984217i
$396$	18.7589	−	2.91541i	0.942669	−	0.146505i
$397$	32.5233	+	8.71460i	1.63230	+	0.437373i	0.954582	−	0.297949i	$-0.0963026\pi$
$397$	32.5233	+	8.71460i	1.63230	+	0.437373i	0.677718	+	0.735322i	$0.262969\pi$
$398$	16.1151	+	16.1151i	0.807778	+	0.807778i
$399$	4.52755	+	9.61316i	0.226661	+	0.481260i
$400$			6.25370i			0.312685i
$401$	−3.88669	+	14.5053i	−0.194092	+	0.724362i	0.798408	+	0.602117i	$0.205676\pi$
$401$	−3.88669	+	14.5053i	−0.194092	+	0.724362i	−0.992500	+	0.122245i	$0.960991\pi$
$402$	1.16878	+	5.53812i	0.0582934	+	0.276216i
$403$	−1.64223	−	5.95230i	−0.0818055	−	0.296505i
$404$	1.50275	−	0.867612i	0.0747645	−	0.0431653i
$405$	25.4159	−	16.2966i	1.26293	−	0.809787i
$406$	−0.328778	+	0.0777334i	−0.0163170	+	0.00385784i
$407$	49.6770			2.46240
$408$	3.19010	+	6.28341i	0.157933	+	0.311075i
$409$	−27.2465	+	7.30067i	−1.34725	+	0.360995i	−0.859119	−	0.511775i	$-0.828988\pi$
$409$	−27.2465	+	7.30067i	−1.34725	+	0.360995i	−0.488131	+	0.872770i	$0.662321\pi$
$410$	−32.6413	+	8.74622i	−1.61204	+	0.431945i
$411$	1.92301	+	3.78768i	0.0948553	+	0.186833i
$412$	12.7916			0.630196
$413$	11.6207	+	12.3307i	0.571819	+	0.606752i
$414$	−10.3154	−	12.8141i	−0.506972	−	0.629781i
$415$	−1.62372	+	0.937456i	−0.0797054	+	0.0460179i
$416$	−3.47569	+	0.958941i	−0.170410	+	0.0470159i
$417$	−6.18317	−	29.2982i	−0.302791	−	1.43474i
$418$	3.79773	−	14.1733i	0.185753	−	0.693239i
$419$			22.9443i			1.12090i	0.828187	+	0.560451i	$0.189372\pi$
$419$			22.9443i			1.12090i	−0.828187	+	0.560451i	$0.810628\pi$
$420$	−15.3195	−	1.28124i	−0.747513	−	0.0625179i
$421$	−17.8994	−	17.8994i	−0.872363	−	0.872363i	0.120367	−	0.992729i	$-0.461593\pi$
$421$	−17.8994	−	17.8994i	−0.872363	−	0.872363i	−0.992729	+	0.120367i	$0.961593\pi$
$422$	−13.2518	−	3.55080i	−0.645085	−	0.172850i
$423$	4.52340	+	29.1053i	0.219935	+	1.41515i
$424$	−0.803554	−	2.99890i	−0.0390240	−	0.145640i
$425$	22.0344	−	12.7216i	1.06883	−	0.617087i
$426$	−14.2549	−	15.8778i	−0.690651	−	0.769284i
$427$	4.99164	−	8.08286i	0.241562	−	0.391157i
$428$	17.4419			0.843088
$429$	35.1038	−	18.1503i	1.69483	−	0.876306i
$430$	4.29551	−	7.44004i	0.207148	−	0.358791i
$431$	−2.78931	−	10.4099i	−0.134356	−	0.501425i	−1.00000		0.000763751i	$-0.999757\pi$
$431$	−2.78931	−	10.4099i	−0.134356	−	0.501425i	0.865643	−	0.500661i	$-0.166910\pi$
$432$	−2.13408	+	4.73769i	−0.102676	+	0.227942i
$433$		−	30.1662i		−	1.44970i	−0.688909	−	0.724848i	$-0.741910\pi$
$433$		−	30.1662i		−	1.44970i	0.688909	−	0.724848i	$-0.258090\pi$
$434$	2.14824	+	3.98934i	0.103119	+	0.191495i
$435$	0.740874	+	0.0399040i	0.0355222	+	0.00191325i
$436$	5.10102	+	1.36681i	0.244294	+	0.0654585i
$437$	−12.2815	+	3.29083i	−0.587506	+	0.157422i
$438$	−7.16056	+	1.51118i	−0.342145	+	0.0722071i
$439$	25.2577	−	14.5825i	1.20548	−	0.695986i	0.243714	−	0.969847i	$-0.421634\pi$
$439$	25.2577	−	14.5825i	1.20548	−	0.695986i	0.961769	+	0.273861i	$0.0883007\pi$
$440$	15.0107	+	15.0107i	0.715606	+	0.715606i
$441$	3.48825	−	20.7083i	0.166107	−	0.986108i
$442$	10.4492	+	10.2956i	0.497016	+	0.489712i
$443$	−12.2531	+	7.07436i	−0.582165	+	0.336113i	−0.761993	−	0.647585i	$-0.775779\pi$
$443$	−12.2531	+	7.07436i	−0.582165	+	0.336113i	0.179828	+	0.983698i	$0.442446\pi$
$444$	−7.42206	+	11.3928i	−0.352235	+	0.540678i
$445$	−5.42106	+	9.38955i	−0.256983	+	0.445107i
$446$	2.88200	+	4.99176i	0.136466	+	0.236367i
$447$	0.547147	−	10.1585i	0.0258791	−	0.480482i
$448$	2.32948	−	1.25441i	0.110057	−	0.0592653i
$449$	16.7895	+	16.7895i	0.792348	+	0.792348i	0.981875	−	0.189528i	$-0.0606957\pi$
$449$	16.7895	+	16.7895i	0.792348	+	0.792348i	−0.189528	+	0.981875i	$0.560696\pi$
$450$	17.4954	+	6.77410i	0.824743	+	0.319334i
$451$	−31.8724	+	55.2046i	−1.50081	+	2.59948i
$452$	0.303311	−	0.525349i	0.0142665	−	0.0247104i
$453$	−16.8225	+	8.54080i	−0.790389	+	0.401282i
$454$		−	17.0521i		−	0.800295i
$455$	−31.0874	+	7.59345i	−1.45740	+	0.355987i
$456$	2.68306	+	2.98854i	0.125646	+	0.139951i
$457$	−9.97842	+	37.2400i	−0.466771	+	1.74201i	0.184179	+	0.982893i	$0.441037\pi$
$457$	−9.97842	+	37.2400i	−0.466771	+	1.74201i	−0.650950	+	0.759120i	$0.725629\pi$
$458$	−8.60563	−	4.96846i	−0.402115	−	0.232161i
$459$	21.0341	−	2.11837i	0.981788	−	0.0988773i
$460$	4.76095	−	17.7681i	0.221980	−	0.828442i
$461$	−2.27891	+	2.27891i	−0.106140	+	0.106140i	−0.758182	−	0.652043i	$-0.773912\pi$
$461$	−2.27891	+	2.27891i	−0.106140	+	0.106140i	0.652043	+	0.758182i	$0.273912\pi$
$462$	−22.1428	+	18.7248i	−1.03017	+	0.871158i
$463$	10.4036	−	10.4036i	0.483497	−	0.483497i	−0.422749	−	0.906247i	$-0.638935\pi$
$463$	10.4036	−	10.4036i	0.483497	−	0.483497i	0.906247	+	0.422749i	$0.138935\pi$
$464$	−0.110585	+	0.0638462i	−0.00513377	+	0.00296398i
$465$	−2.05475	−	9.73620i	−0.0952869	−	0.451505i
$466$	4.75860	+	17.7593i	0.220438	+	0.822685i
$467$	−0.964739	−	1.67098i	−0.0446428	−	0.0773236i	0.842841	−	0.538163i	$-0.180882\pi$
$467$	−0.964739	−	1.67098i	−0.0446428	−	0.0773236i	−0.887483	+	0.460840i	$0.847548\pi$
$468$	−1.08218	+	10.7624i	−0.0500237	+	0.497491i
$469$	−5.92980	−	6.29206i	−0.273813	−	0.290540i
$470$	−23.2898	+	23.2898i	−1.07428	+	1.07428i
$471$	12.2793	+	4.00945i	0.565798	+	0.184746i
$472$	5.54610	+	3.20204i	0.255280	+	0.147386i
$473$	−4.19432	−	15.6534i	−0.192855	−	0.719744i
$474$	−9.32309	+	4.73335i	−0.428224	+	0.217410i
$475$	10.2537	−	10.2537i	0.470473	−	0.470473i
$476$	−9.15854	−	5.65594i	−0.419781	−	0.259239i
$477$	−9.26020	−	1.00043i	−0.423995	−	0.0458063i
$478$	−3.77043	+	2.17686i	−0.172455	+	0.0995672i
$479$	4.55727	−	1.22112i	0.208227	−	0.0557942i	−0.153198	−	0.988196i	$-0.548957\pi$
$479$	4.55727	−	1.22112i	0.208227	−	0.0557942i	0.361425	+	0.932401i	$0.382290\pi$
$480$	−5.68520	+	1.19982i	−0.259493	+	0.0547640i
$481$	−7.12322	+	27.3938i	−0.324791	+	1.24905i
$482$			17.8381i			0.812505i
$483$	23.6454	+	8.50390i	1.07590	+	0.386941i
$484$	29.0439			1.32018
$485$	5.76700	+	9.98873i	0.261866	+	0.453565i
$486$	10.9426	+	11.1023i	0.496365	+	0.503609i
$487$	−16.5087	+	4.42349i	−0.748081	+	0.200448i	−0.612667	−	0.790342i	$-0.709903\pi$
$487$	−16.5087	+	4.42349i	−0.748081	+	0.200448i	−0.135414	+	0.990789i	$0.543236\pi$
$488$	0.929327	−	3.46830i	0.0420687	−	0.157002i
$489$	−0.864212	+	16.0453i	−0.0390810	+	0.725593i
$490$	20.9962	−	10.5162i	0.948512	−	0.475072i
$491$	−24.8371			−1.12088			−0.560442	−	0.828194i	$-0.689369\pi$
$491$	−24.8371			−1.12088			−0.560442	+	0.828194i	$0.689369\pi$
$492$	−7.89854	−	15.5574i	−0.356094	−	0.701384i
$493$	0.449914	+	0.259758i	0.0202631	+	0.0116989i
$494$	7.27113	+	4.12653i	0.327144	+	0.185661i
$495$	58.2539	−	25.7343i	2.61832	−	1.15667i
$496$	1.21096	+	1.21096i	0.0543735	+	0.0543735i
$497$	31.2199	+	9.36507i	1.40040	+	0.420081i
$498$	−0.646703	−	0.720333i	−0.0289795	−	0.0322789i
$499$	7.15652	−	26.7085i	0.320370	−	1.19564i	−0.598516	−	0.801111i	$-0.704243\pi$
$499$	7.15652	−	26.7085i	0.320370	−	1.19564i	0.918885	−	0.394525i	$-0.129091\pi$
$500$	1.08852	+	4.06241i	0.0486801	+	0.181677i
$501$	10.5043	−	16.1240i	0.469298	−	0.720368i
$502$	−24.5016	−	6.56519i	−1.09356	−	0.293019i
$503$		−	27.6359i		−	1.23222i	−0.787658	−	0.616112i	$-0.788707\pi$
$503$		−	27.6359i		−	1.23222i	0.787658	−	0.616112i	$-0.211293\pi$
$504$	−0.986033	−	7.87577i	−0.0439214	−	0.350815i
$505$	4.11612	−	4.11612i	0.183165	−	0.183165i
$506$	−17.3495	−	30.0503i	−0.771281	−	1.33590i
$507$	4.97522	+	21.9601i	0.220957	+	0.975284i
$508$	−10.2555	+	17.7631i	−0.455015	+	0.788109i
$509$	3.42423	+	0.917520i	0.151776	+	0.0406684i	0.333907	−	0.942606i	$-0.391633\pi$
$509$	3.42423	+	0.917520i	0.151776	+	0.0406684i	−0.182131	+	0.983274i	$0.558299\pi$
$510$	15.7926	+	17.5906i	0.699307	+	0.778926i
$511$	8.13537	−	7.66699i	0.359888	−	0.339167i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	11.2671	−	4.26894i	0.497456	−	0.188478i
$514$	−5.85115	−	21.8368i	−0.258083	−	0.963179i
$515$	41.4492	−	11.1063i	1.82647	−	0.489401i
$516$	4.21657	+	1.37680i	0.185624	+	0.0606104i
$517$			62.1299i			2.73247i
$518$	0.615356	−	20.7609i	0.0270372	−	0.912181i
$519$	−19.2105	+	17.2469i	−0.843247	+	0.757054i
$520$	−10.4298	+	6.12506i	−0.457379	+	0.268602i
$521$	4.31187	+	2.48946i	0.188906	+	0.109065i	0.591471	−	0.806327i	$-0.298548\pi$
$521$	4.31187	+	2.48946i	0.188906	+	0.109065i	−0.402564	+	0.915392i	$0.631881\pi$
$522$	0.0588298	+	0.378533i	0.00257491	+	0.0165679i
$523$	−0.204767	−	0.354667i	−0.00895385	−	0.0155085i	0.861514	−	0.507734i	$-0.169517\pi$
$523$	−0.204767	−	0.354667i	−0.00895385	−	0.0155085i	−0.870468	+	0.492226i	$0.836183\pi$
$524$	−3.85509			−0.168410
$525$	−28.2034	+	5.08436i	−1.23090	+	0.221900i
$526$	−13.3084	−	13.3084i	−0.580272	−	0.580272i
$527$	1.80332	−	6.73009i	0.0785540	−	0.293167i
$528$	−5.98280	+	9.18355i	−0.260368	+	0.399663i
$529$	−3.53383	+	6.12077i	−0.153645	+	0.266121i
$530$	−5.20758	−	9.01980i	−0.226203	−	0.391795i
$531$	14.9657	−	12.0474i	0.649456	−	0.522810i
$532$	−5.87623	−	1.76270i	−0.254767	−	0.0764228i
$533$	−25.8717	−	25.4914i	−1.12063	−	1.10416i
$534$	−5.32143	−	1.73757i	−0.230281	−	0.0751919i
$535$	56.5179	−	15.1439i	2.44348	−	0.654730i
$536$	−2.83005	−	1.63393i	−0.122240	−	0.0705751i
$537$	−16.0305	−	5.23431i	−0.691766	−	0.225877i
$538$	3.67262	+	3.67262i	0.158338	+	0.158338i
$539$	13.9787	−	42.0326i	0.602107	−	1.81047i
$540$	−2.80167	+	17.2047i	−0.120565	+	0.740371i
$541$	−29.7273	−	7.96540i	−1.27807	−	0.342459i	−0.444956	−	0.895553i	$-0.646781\pi$
$541$	−29.7273	−	7.96540i	−1.27807	−	0.342459i	−0.833119	+	0.553094i	$0.813447\pi$
$542$	3.76740	+	2.17511i	0.161824	+	0.0934290i
$543$	−0.700086	+	0.147748i	−0.0300436	+	0.00634047i
$544$	−3.92986	−	1.05300i	−0.168492	−	0.0451472i
$545$	17.7158			0.758862
$546$	−7.15050	−	14.8953i	−0.306013	−	0.637460i
$547$	11.8216			0.505453			0.252727	−	0.967538i	$-0.418673\pi$
$547$	11.8216			0.505453			0.252727	+	0.967538i	$0.418673\pi$
$548$	−2.36895	−	0.634758i	−0.101197	−	0.0271155i
$549$	−8.69629	−	6.35681i	−0.371149	−	0.271302i
$550$	34.2717	+	19.7868i	1.46135	+	0.843711i
$551$	0.286001	+	0.0766338i	0.0121841	+	0.00326471i
$552$	9.48378	+	0.510804i	0.403656	+	0.0217413i
$553$	8.39207	−	13.5891i	0.356867	−	0.577867i
$554$	5.01150	+	5.01150i	0.212918	+	0.212918i
$555$	−14.1583	+	43.3608i	−0.600985	+	1.84056i
$556$	14.9718	+	8.64396i	0.634945	+	0.366586i
$557$	10.5106	−	2.81630i	0.445347	−	0.119330i	−0.0291745	−	0.999574i	$-0.509288\pi$
$557$	10.5106	−	2.81630i	0.445347	−	0.119330i	0.474521	+	0.880244i	$0.342621\pi$
$558$	4.69951	−	2.07606i	0.198946	−	0.0878867i
$559$	9.23330	−	0.0683516i	0.390527	−	0.00289097i
$560$	6.45917	−	6.08729i	0.272950	−	0.257235i
$561$	44.5280	+	2.39831i	1.87997	+	0.101257i
$562$	−5.28294	−	9.15032i	−0.222847	−	0.385983i
$563$	−10.7017	+	18.5359i	−0.451024	+	0.781196i	−0.998450	−	0.0556577i	$-0.982274\pi$
$563$	−10.7017	+	18.5359i	−0.451024	+	0.781196i	0.547426	+	0.836854i	$0.315608\pi$
$564$	−14.2487	−	9.28260i	−0.599979	−	0.390868i
$565$	0.526698	−	1.96566i	0.0221583	−	0.0826961i
$566$	−8.25554	−	8.25554i	−0.347006	−	0.347006i
$567$	−23.1014	−	5.77262i	−0.970170	−	0.242427i
$568$	12.3195			0.516913
$569$	−6.50476	−	11.2666i	−0.272694	−	0.472319i	0.696857	−	0.717210i	$-0.254581\pi$
$569$	−6.50476	−	11.2666i	−0.272694	−	0.472319i	−0.969551	+	0.244891i	$0.921248\pi$
$570$	11.2889	+	7.35434i	0.472838	+	0.308040i
$571$	−30.0569	−	17.3534i	−1.25784	−	0.726216i	−0.285188	−	0.958472i	$-0.592056\pi$
$571$	−30.0569	−	17.3534i	−1.25784	−	0.726216i	−0.972655	+	0.232256i	$0.925389\pi$
$572$	−5.74191	+	22.0817i	−0.240081	+	0.923281i
$573$	−28.1357	−	31.3391i	−1.17539	−	1.30921i
$574$	22.6761	+	14.0038i	0.946484	+	0.584509i
$575$		−	34.2915i		−	1.43006i
$576$	−1.21226	−	2.74416i	−0.0505109	−	0.114340i
$577$	−39.1973	+	10.5029i	−1.63180	+	0.437240i	−0.954439	−	0.298407i	$-0.903545\pi$
$577$	−39.1973	+	10.5029i	−1.63180	+	0.437240i	−0.677364	+	0.735648i	$0.736878\pi$
$578$	−0.115785	−	0.432114i	−0.00481600	−	0.0179736i
$579$	1.34653	−	0.683637i	0.0559600	−	0.0284110i
$580$	−0.302899	+	0.302899i	−0.0125772	+	0.0125772i
$581$	1.41636	+	0.424867i	0.0587604	+	0.0176265i
$582$	−4.43131	+	3.97836i	−0.183684	+	0.164908i
$583$	−18.9771	−	5.08491i	−0.785952	−	0.210595i
$584$	2.11261	−	3.65914i	0.0874203	−	0.151416i
$585$	5.83779	+	35.8134i	0.241363	+	1.48070i
$586$	8.19514	+	14.1944i	0.338538	+	0.586365i
$587$	11.6106	−	11.6106i	0.479223	−	0.479223i	−0.425660	−	0.904883i	$-0.639958\pi$
$587$	11.6106	−	11.6106i	0.479223	−	0.479223i	0.904883	+	0.425660i	$0.139958\pi$
$588$	7.55114	+	9.48579i	0.311404	+	0.391187i
$589$		−	3.97103i		−	0.163623i
$590$	20.7515	+	5.56034i	0.854324	+	0.228915i
$591$	6.87609	+	4.47956i	0.282844	+	0.184265i
$592$	−2.03181	−	7.58283i	−0.0835070	−	0.311652i
$593$	9.64729	−	36.0042i	0.396167	−	1.47851i	−0.423617	−	0.905841i	$-0.639240\pi$
$593$	9.64729	−	36.0042i	0.396167	−	1.47851i	0.819784	−	0.572673i	$-0.194094\pi$
$594$	19.2114	+	26.6853i	0.788252	+	1.09491i
$595$	−34.5876	−	10.3753i	−1.41795	−	0.425346i
$596$	4.15321	+	4.15321i	0.170122	+	0.170122i
$597$	−12.2525	+	37.5241i	−0.501460	+	1.53576i
$598$	19.0586	−	5.25825i	0.779364	−	0.215026i
$599$	−36.8375	−	21.2681i	−1.50514	−	0.868993i	−0.999982	−	0.00596522i	$-0.998101\pi$
$599$	−36.8375	−	21.2681i	−1.50514	−	0.868993i	−0.505157	−	0.863027i	$-0.668565\pi$
$600$	−9.65825	+	4.90351i	−0.394296	+	0.200185i
$601$	−16.3118			−0.665372			−0.332686	−	0.943038i	$-0.607955\pi$
$601$	−16.3118			−0.665372			−0.332686	+	0.943038i	$0.607955\pi$
$602$	−6.59378	+	1.55898i	−0.268743	+	0.0635391i
$603$	−7.63666	+	6.14749i	−0.310989	+	0.250345i
$604$	2.81919	−	10.5214i	0.114711	−	0.428108i
$605$	94.1122	−	25.2173i	3.82620	−	1.02523i
$606$	2.51825	+	1.64056i	0.102297	+	0.0666433i
$607$	−1.43203	−	2.48035i	−0.0581243	−	0.100674i	0.835499	−	0.549492i	$-0.185179\pi$
$607$	−1.43203	−	2.48035i	−0.0581243	−	0.100674i	−0.893623	+	0.448818i	$0.851845\pi$
$608$	−2.31878			−0.0940389
$609$	−0.377846	−	0.446816i	−0.0153111	−	0.0181059i
$610$		−	12.0454i		−	0.487703i
$611$	−34.2608	−	8.90885i	−1.38604	−	0.360413i
$612$	−7.20279	+	9.85361i	−0.291155	+	0.398309i
$613$	−19.0273	+	5.09834i	−0.768504	+	0.205920i	−0.621711	−	0.783247i	$-0.713562\pi$
$613$	−19.0273	+	5.09834i	−0.768504	+	0.205920i	−0.146794	+	0.989167i	$0.546895\pi$
$614$	22.8476	−	13.1910i	0.922052	−	0.532347i
$615$	−39.1017	−	43.5536i	−1.57673	−	1.75625i
$616$	0.496029	−	16.7350i	0.0199856	−	0.674273i
$617$	24.8368	−	24.8368i	0.999893	−	0.999893i	−0.000106988	−	1.00000i	$-0.500034\pi$
$617$	24.8368	−	24.8368i	0.999893	−	0.999893i	1.00000		0.000106988i	$3.40553e-5\pi$
$618$	10.0299	+	19.7554i	0.403460	+	0.794679i
$619$	10.4779	+	39.1040i	0.421142	+	1.57172i	0.772206	+	0.635373i	$0.219153\pi$
$619$	10.4779	+	39.1040i	0.421142	+	1.57172i	−0.351063	+	0.936352i	$0.614180\pi$
$620$	4.97533	+	2.87251i	0.199814	+	0.115363i
$621$	11.7020	−	25.9786i	0.469585	−	1.04249i
$622$	−9.05222	+	9.05222i	−0.362961	+	0.362961i
$623$	8.32155	−	1.96747i	0.333396	−	0.0788252i
$624$	−4.20628	−	4.61598i	−0.168386	−	0.184787i
$625$	−8.57988	−	14.8608i	−0.343195	−	0.594431i
$626$	4.22379	+	15.7634i	0.168817	+	0.630033i
$627$	24.8671	−	5.24802i	0.993098	−	0.209586i
$628$	−6.45864	+	3.72889i	−0.257728	+	0.148799i
$629$	−22.5843	+	22.5843i	−0.900494	+	0.900494i
$630$	−10.0332	−	24.6641i	−0.399733	−	0.982641i
$631$	−12.0035	+	12.0035i	−0.477850	+	0.477850i	−0.904444	−	0.426593i	$-0.859714\pi$
$631$	−12.0035	+	12.0035i	−0.477850	+	0.477850i	0.426593	+	0.904444i	$0.359714\pi$
$632$	1.56241	−	5.83099i	0.0621492	−	0.231944i
$633$	−4.90680	−	23.2503i	−0.195028	−	0.924115i
$634$	−0.314764	−	0.181729i	−0.0125009	−	0.00721738i
$635$	−17.8087	+	66.4628i	−0.706715	+	2.63750i
$636$	4.00146	−	3.59245i	0.158668	−	0.142450i
$637$	21.1740	+	13.7355i	0.838943	+	0.544220i
$638$			0.808040i			0.0319906i
$639$	13.3446	−	34.4651i	0.527905	−	1.36342i
$640$	1.67733	−	2.90521i	0.0663022	−	0.114839i
$641$	−12.8018	+	22.1734i	−0.505641	+	0.875795i	0.494338	+	0.869270i	$0.335411\pi$
$641$	−12.8018	+	22.1734i	−0.505641	+	0.875795i	−0.999979	+	0.00652568i	$0.997923\pi$
$642$	13.6762	+	26.9375i	0.539756	+	1.06314i
$643$	0.384715	+	0.384715i	0.0151717	+	0.0151717i	0.714652	−	0.699480i	$-0.246585\pi$
$643$	0.384715	+	0.384715i	0.0151717	+	0.0151717i	−0.699480	+	0.714652i	$0.746585\pi$
$644$	−12.7734	+	6.87843i	−0.503344	+	0.271048i
$645$	14.8585	+	0.800293i	0.585055	+	0.0315115i
$646$	4.71697	+	8.17003i	0.185587	+	0.321446i
$647$	0.186170	−	0.322457i	0.00731911	−	0.0126771i	−0.862343	−	0.506325i	$-0.831004\pi$
$647$	0.186170	−	0.322457i	0.00731911	−	0.0126771i	0.869662	+	0.493648i	$0.164337\pi$
$648$	−8.99024	+	0.418926i	−0.353170	+	0.0164570i
$649$	35.0959	−	20.2626i	1.37763	−	0.795377i
$650$	−15.8254	+	16.0615i	−0.620723	+	0.629982i
$651$	−4.47674	+	6.44579i	−0.175457	+	0.252631i
$652$	−6.55996	−	6.55996i	−0.256908	−	0.256908i
$653$	−6.47137	+	3.73625i	−0.253244	+	0.146211i	−0.621249	−	0.783613i	$-0.713374\pi$
$653$	−6.47137	+	3.73625i	−0.253244	+	0.146211i	0.368005	+	0.929824i	$0.380041\pi$
$654$	1.88878	+	8.94976i	0.0738572	+	0.349963i
$655$	−12.4918	+	3.34717i	−0.488096	+	0.130785i
$656$	9.73017	+	2.60719i	0.379899	+	0.101794i
$657$	−7.94846	−	9.87389i	−0.310099	−	0.385217i
$658$	25.9652	+	0.769612i	1.01223	+	0.0300026i
$659$			32.4190i			1.26286i	0.775431	+	0.631432i	$0.217532\pi$
$659$			32.4190i			1.26286i	−0.775431	+	0.631432i	$0.782468\pi$
$660$	−11.4128	+	34.9524i	−0.444241	+	1.36052i
$661$	5.61492	+	20.9552i	0.218395	+	0.815061i	0.984944	+	0.172875i	$0.0553057\pi$
$661$	5.61492	+	20.9552i	0.218395	+	0.815061i	−0.766549	+	0.642186i	$0.778028\pi$
$662$	6.84173	−	11.8502i	0.265911	−	0.460572i
$663$	−7.70742	+	24.2105i	−0.299331	+	0.940258i
$664$	0.558899			0.0216895
$665$	−20.5715	−	0.609742i	−0.797727	−	0.0236448i
$666$	−23.4147	−	2.52961i	−0.907302	−	0.0980204i
$667$	0.606381	−	0.350094i	0.0234792	−	0.0135557i
$668$	2.87559	+	10.7318i	0.111260	+	0.415228i
$669$	−5.44954	+	8.36500i	−0.210692	+	0.323410i
$670$	−10.5890	−	2.83732i	−0.409089	−	0.109615i
$671$	−16.0666	−	16.0666i	−0.620246	−	0.620246i
$672$	3.76386	+	2.61408i	0.145194	+	0.100840i
$673$		−	22.3366i		−	0.861014i	−0.902587	−	0.430507i	$-0.858335\pi$
$673$		−	22.3366i		−	0.861014i	0.902587	−	0.430507i	$-0.141665\pi$
$674$	−1.69782	+	6.33634i	−0.0653975	+	0.244067i
$675$	3.25616	+	32.3316i	0.125330	+	1.24444i
$676$	−11.3533	−	6.33261i	−0.436666	−	0.243562i
$677$	−21.2839	+	12.2883i	−0.818006	+	0.472276i	−0.849728	−	0.527221i	$-0.823234\pi$
$677$	−21.2839	+	12.2883i	−0.818006	+	0.472276i	0.0317225	+	0.999497i	$0.489901\pi$
$678$	1.04918	+	0.0565096i	0.0402934	+	0.00217024i
$679$	2.61368	−	8.71307i	0.100304	−	0.334377i
$680$	−13.6484			−0.523392
$681$	26.3354	−	13.3705i	1.00917	−	0.512359i
$682$	10.4678	−	2.80484i	0.400833	−	0.107403i
$683$	−30.6088	+	8.20161i	−1.17121	+	0.313826i	−0.791436	−	0.611252i	$-0.790666\pi$
$683$	−30.6088	+	8.20161i	−1.17121	+	0.313826i	−0.379778	+	0.925078i	$0.624000\pi$
$684$	−2.51174	+	6.48705i	−0.0960387	+	0.248039i
$685$	−8.22735			−0.314351
$686$	−17.3930	−	6.36263i	−0.664068	−	0.242926i
$687$	0.925671	−	17.1864i	0.0353165	−	0.655700i
$688$	−2.21783	+	1.28046i	−0.0845539	+	0.0488172i
$689$	5.52515	−	9.73557i	0.210491	−	0.370896i
$690$	31.1742	−	6.57909i	1.18678	−	0.250462i
$691$	−2.97064	+	11.0866i	−0.113008	+	0.421753i	−0.999130	−	0.0416992i	$-0.986723\pi$
$691$	−2.97064	+	11.0866i	−0.113008	+	0.421753i	0.886122	+	0.463453i	$0.153390\pi$
$692$		−	14.9052i		−	0.566612i
$693$	−46.2808	−	19.5153i	−1.75806	−	0.741326i
$694$	−14.7691	−	14.7691i	−0.560629	−	0.560629i
$695$	56.0189	+	15.0102i	2.12492	+	0.569370i
$696$	−0.185314	−	0.120726i	−0.00702430	−	0.00457612i
$697$	−10.6073	−	39.5871i	−0.401782	−	1.49947i
$698$	−3.94161	+	2.27569i	−0.149192	+	0.0861360i
$699$	−23.6964	+	21.2743i	−0.896281	+	0.804667i
$700$	8.69376	−	14.0776i	0.328593	−	0.532084i
$701$	10.1192			0.382196			0.191098	−	0.981571i	$-0.438795\pi$
$701$	10.1192			0.382196			0.191098	+	0.981571i	$0.438795\pi$
$702$	−17.4700	+	6.76744i	−0.659364	+	0.255420i
$703$	−9.10158	+	15.7644i	−0.343273	+	0.594566i
$704$	−1.63781	−	6.11240i	−0.0617274	−	0.230370i
$705$	−54.2304	−	17.7074i	−2.04243	−	0.666900i
$706$			18.4274i			0.693525i
$707$	−4.58896	−	0.136017i	−0.172585	−	0.00511546i
$708$	−0.596570	+	11.0762i	−0.0224205	+	0.416267i
$709$	28.3531	+	7.59719i	1.06482	+	0.285318i	0.748364	−	0.663288i	$-0.230840\pi$
$709$	28.3531	+	7.59719i	1.06482	+	0.285318i	0.316459	+	0.948606i	$0.397506\pi$
$710$	39.9193	−	10.6963i	1.49815	−	0.401427i
$711$	−14.6204	−	10.6872i	−0.548309	−	0.400802i
$712$	2.79896	−	1.61598i	0.104896	−	0.0605615i
$713$	−6.64016	−	6.64016i	−0.248676	−	0.248676i
$714$	1.55387	−	18.5793i	0.0581522	−	0.695313i
$715$	0.566588	+	76.5377i	0.0211892	+	2.86235i
$716$	8.43169	−	4.86804i	0.315107	−	0.181927i
$717$	−6.31834	−	4.11620i	−0.235963	−	0.153722i
$718$	−4.32177	+	7.48552i	−0.161287	+	0.279357i
$719$	20.6861	+	35.8293i	0.771460	+	1.33621i	0.936763	+	0.349966i	$0.113807\pi$
$719$	20.6861	+	35.8293i	0.771460	+	1.33621i	−0.165302	+	0.986243i	$0.552860\pi$
$720$	−6.31076	−	7.83949i	−0.235188	−	0.292160i
$721$	−28.7950	−	17.7826i	−1.07238	−	0.662259i
$722$	−9.63310	−	9.63310i	−0.358507	−	0.358507i
$723$	−27.5493	+	13.9868i	−1.02457	+	0.520176i
$724$	0.206549	−	0.357753i	0.00767633	−	0.0132958i
$725$	−0.399275	+	0.691564i	−0.0148287	+	0.0256840i
$726$	22.7732	+	44.8555i	0.845194	+	1.66474i
$727$			3.12755i			0.115995i	0.998317	+	0.0579973i	$0.0184715\pi$
$727$			3.12755i			0.115995i	−0.998317	+	0.0579973i	$0.981529\pi$
$728$	9.15719	+	2.67317i	0.339388	+	0.0990744i
$729$	−8.56638	+	25.6050i	−0.317273	+	0.948334i
$730$	3.66853	−	13.6911i	0.135778	−	0.506732i
$731$	9.02321	+	5.20956i	0.333736	+	0.192682i
$732$	6.08514	−	1.28422i	0.224913	−	0.0474663i
$733$	2.38043	−	8.88387i	0.0879230	−	0.328133i	−0.907929	−	0.419125i	$-0.862337\pi$
$733$	2.38043	−	8.88387i	0.0879230	−	0.328133i	0.995852	+	0.0909916i	$0.0290036\pi$
$734$	−17.3534	+	17.3534i	−0.640527	+	0.640527i
$735$	32.7043	+	24.1810i	1.20632	+	0.891929i
$736$	−3.87735	+	3.87735i	−0.142921	+	0.142921i
$737$	−17.9086	+	10.3396i	−0.659673	+	0.380862i
$738$	17.8338	−	24.3971i	0.656471	−	0.898070i
$739$	9.16774	+	34.2145i	0.337241	+	1.25860i	0.901420	+	0.432947i	$0.142526\pi$
$739$	9.16774	+	34.2145i	0.337241	+	1.25860i	−0.564179	+	0.825653i	$0.690807\pi$
$740$	−13.1676	−	22.8069i	−0.484049	−	0.838397i
$741$	−0.671757	+	14.4652i	−0.0246776	+	0.531392i
$742$	−2.36014	+	7.86788i	−0.0866435	+	0.288839i
$743$	1.93223	−	1.93223i	0.0708866	−	0.0708866i	−0.670775	−	0.741661i	$-0.734038\pi$
$743$	1.93223	−	1.93223i	0.0708866	−	0.0708866i	0.741661	+	0.670775i	$0.234038\pi$
$744$	−0.920700	+	2.81972i	−0.0337545	+	0.103376i
$745$	17.0639	+	9.85183i	0.625172	+	0.360943i
$746$	−0.335393	−	1.25170i	−0.0122796	−	0.0458282i
$747$	0.605408	−	1.56358i	0.0221507	−	0.0572086i
$748$	−18.2048	+	18.2048i	−0.665635	+	0.665635i
$749$	−39.2634	−	24.2474i	−1.43465	−	0.885982i
$750$	−5.42051	+	4.86645i	−0.197929	+	0.177698i
$751$	−44.5053	+	25.6951i	−1.62402	+	0.937628i	−0.638190	+	0.769879i	$0.720317\pi$
$751$	−44.5053	+	25.6951i	−1.62402	+	0.937628i	−0.985830	+	0.167750i	$0.946350\pi$
$752$	9.48367	−	2.54114i	0.345834	−	0.0926659i
$753$	−9.07234	−	42.9882i	−0.330615	−	1.56658i
$754$	−0.445583	−	0.115865i	−0.0162272	−	0.00421957i
$755$		−	36.5406i		−	1.32985i
$756$	11.3902	−	7.69821i	0.414259	−	0.279981i
$757$	10.1111			0.367493			0.183746	−	0.982974i	$-0.441178\pi$
$757$	10.1111			0.367493			0.183746	+	0.982974i	$0.441178\pi$
$758$	14.7344	+	25.5207i	0.535177	+	0.926954i
$759$	32.8061	−	50.3571i	1.19079	−	1.82785i
$760$	−7.51365	+	2.01328i	−0.272549	+	0.0730292i
$761$	8.27536	−	30.8841i	0.299981	−	1.11955i	−0.637198	−	0.770700i	$-0.719907\pi$
$761$	8.27536	−	30.8841i	0.299981	−	1.11955i	0.937180	−	0.348846i	$-0.113427\pi$
$762$	−35.4747	−	1.91070i	−1.28511	−	0.0692173i
$763$	−9.58273	−	10.1682i	−0.346918	−	0.368112i
$764$	24.3157			0.879711
$765$	−14.7841	+	38.1829i	−0.534522	+	1.38051i
$766$	7.94149	+	4.58502i	0.286938	+	0.165664i
$767$	6.14114	+	22.2586i	0.221744	+	0.803713i
$768$	1.64650	+	0.537619i	0.0594130	+	0.0193997i
$769$	−15.3274	−	15.3274i	−0.552718	−	0.552718i	0.374506	−	0.927224i	$-0.377812\pi$
$769$	−15.3274	−	15.3274i	−0.552718	−	0.552718i	−0.927224	+	0.374506i	$0.877812\pi$
$770$	−12.9228	−	54.6579i	−0.465707	−	1.96974i
$771$	29.1370	−	26.1587i	1.04934	−	0.942083i
$772$	−0.225659	+	0.842169i	−0.00812163	+	0.0303103i
$773$	−5.09546	−	19.0165i	−0.183271	−	0.683977i	−0.994994	−	0.0999342i	$-0.968137\pi$
$773$	−5.09546	−	19.0165i	−0.183271	−	0.683977i	0.811723	−	0.584043i	$-0.198530\pi$
$774$	1.17986	+	7.59164i	0.0424091	+	0.272876i
$775$	10.3448	+	2.77189i	0.371598	+	0.0995694i
$776$		−	3.43821i		−	0.123424i
$777$	32.5457	−	15.3282i	1.16757	−	0.549896i
$778$	25.0967	−	25.0967i	0.899761	−	0.899761i
$779$	−11.6790	−	20.2286i	−0.418444	−	0.724766i
$780$	−17.6376	−	11.3053i	−0.631527	−	0.404794i
$781$	38.9789	−	67.5134i	1.39477	−	2.41582i
$782$	21.5490	+	5.77404i	0.770591	+	0.206479i
$783$	−0.538480	+	0.387664i	−0.0192437	+	0.0138540i
$784$	−6.98771	−	0.414598i	−0.249561	−	0.0148071i
$785$	−17.6906	+	17.6906i	−0.631405	+	0.631405i
$786$	−3.02277	−	5.95382i	−0.107818	−	0.212366i
$787$	1.07436	+	4.00955i	0.0382966	+	0.142925i	0.982427	−	0.186647i	$-0.0597621\pi$
$787$	1.07436	+	4.00955i	0.0382966	+	0.142925i	−0.944130	+	0.329572i	$0.893095\pi$
$788$	−4.57659	+	1.22629i	−0.163034	+	0.0436849i
$789$	10.1185	−	30.9886i	0.360227	−	1.10322i
$790$		−	20.2510i		−	0.720497i
$791$	−1.41311	+	0.760952i	−0.0502444	+	0.0270563i
$792$	−18.8742	−	2.03908i	−0.670667	−	0.0724555i
$793$	11.1636	−	6.55594i	0.396430	−	0.232808i
$794$	−29.1596	−	16.8353i	−1.03484	−	0.597463i
$795$	9.84698	−	15.1150i	0.349236	−	0.536075i
$796$	−11.3951	−	19.7369i	−0.403889	−	0.699556i
$797$	21.8139			0.772687			0.386344	−	0.922355i	$-0.373738\pi$
$797$	21.8139			0.772687			0.386344	+	0.922355i	$0.373738\pi$
$798$	−1.88521	−	10.4574i	−0.0667356	−	0.370188i
$799$	−28.2456	−	28.2456i	−0.999259	−	0.999259i
$800$	1.61858	−	6.04061i	0.0572253	−	0.213568i
$801$	−1.48901	−	9.58088i	−0.0526117	−	0.338524i
$802$	7.50852	−	13.0051i	0.265135	−	0.459227i
$803$	−13.3686	−	23.1551i	−0.471768	−	0.817127i
$804$	0.304416	−	5.65191i	0.0107359	−	0.199328i
$805$	−35.4182	+	33.3790i	−1.24833	+	1.17646i
$806$	0.0457083	+	6.17452i	0.00161001	+	0.217488i
$807$	−2.79232	+	8.55170i	−0.0982944	+	0.301034i
$808$	−1.67610	+	0.449109i	−0.0589649	+	0.0157996i
$809$	−8.41983	−	4.86119i	−0.296026	−	0.170910i	0.344631	−	0.938738i	$-0.388004\pi$
$809$	−8.41983	−	4.86119i	−0.296026	−	0.170910i	−0.640656	+	0.767828i	$0.721338\pi$
$810$	−28.7678	+	9.16323i	−1.01080	+	0.321963i
$811$	20.2937	+	20.2937i	0.712607	+	0.712607i	0.967080	−	0.254473i	$-0.0819020\pi$
$811$	20.2937	+	20.2937i	0.712607	+	0.712607i	−0.254473	+	0.967080i	$0.581902\pi$
$812$	0.337694	+	0.0100093i	0.0118507	+	0.000351258i
$813$	−0.405243	+	7.52390i	−0.0142125	+	0.263875i
$814$	−47.9843	−	12.8574i	−1.68185	−	0.450650i
$815$	−26.9522	−	15.5609i	−0.944095	−	0.545073i
$816$	−1.45513	−	6.89496i	−0.0509398	−	0.241372i
$817$	5.73588	+	1.53692i	0.200673	+	0.0537702i
$818$	28.2076			0.986256
$819$	17.3977	−	22.7227i	0.607926	−	0.793994i
$820$	33.7928			1.18010
$821$	47.1195	+	12.6256i	1.64448	+	0.440638i	0.958060	−	0.286566i	$-0.0925139\pi$
$821$	47.1195	+	12.6256i	1.64448	+	0.440638i	0.686421	+	0.727204i	$0.259181\pi$
$822$	−0.877164	−	4.15633i	−0.0305946	−	0.144969i
$823$	18.1900	+	10.5020i	0.634062	+	0.366076i	0.782323	−	0.622872i	$-0.214034\pi$
$823$	18.1900	+	10.5020i	0.634062	+	0.366076i	−0.148262	+	0.988948i	$0.547368\pi$
$824$	−12.3557	−	3.31071i	−0.430432	−	0.115334i
$825$	−3.68646	+	68.4442i	−0.128346	+	2.38292i
$826$	−8.03336	−	14.9182i	−0.279516	−	0.519069i
$827$	22.1257	+	22.1257i	0.769387	+	0.769387i	0.977999	−	0.208612i	$-0.0668945\pi$
$827$	22.1257	+	22.1257i	0.769387	+	0.769387i	−0.208612	+	0.977999i	$0.566895\pi$
$828$	6.64732	+	15.0473i	0.231010	+	0.522931i
$829$	−7.06627	−	4.07971i	−0.245422	−	0.141694i	0.372244	−	0.928135i	$-0.378588\pi$
$829$	−7.06627	−	4.07971i	−0.245422	−	0.141694i	−0.617666	+	0.786440i	$0.711922\pi$
$830$	1.81103	−	0.485263i	0.0628617	−	0.0168437i
$831$	−3.81028	+	11.6693i	−0.132177	+	0.404803i
$832$	3.60545	−	0.0266902i	0.124997	−	0.000925316i
$833$	12.7539	+	25.4640i	0.441897	+	0.882276i
$834$	−1.61045	+	29.9002i	−0.0557653	+	1.03536i
$835$	18.6358	+	32.2782i	0.644919	+	1.11703i
$836$	−7.33664	+	12.7074i	−0.253743	+	0.439496i
$837$	6.89116	+	5.63013i	0.238193	+	0.194606i
$838$	5.93842	−	22.1625i	0.205139	−	0.765591i
$839$	−35.7272	−	35.7272i	−1.23344	−	1.23344i	−0.962634	−	0.270806i	$-0.912710\pi$
$839$	−35.7272	−	35.7272i	−1.23344	−	1.23344i	−0.270806	−	0.962634i	$-0.587290\pi$
$840$	14.4659	+	5.20255i	0.499120	+	0.179505i
$841$	28.9837			0.999438
$842$	12.6568	+	21.9222i	0.436181	+	0.755488i
$843$	9.98948	−	15.3338i	0.344056	−	0.528123i
$844$	11.8812	+	6.85961i	0.408968	+	0.236118i
$845$	−42.2870	−	10.6623i	−1.45472	−	0.366796i
$846$	3.16373	−	29.2843i	0.108771	−	1.00681i
$847$	−65.3803	−	40.3762i	−2.24649	−	1.38734i
$848$			3.10469i			0.106616i
$849$	6.27676	−	19.2231i	0.215418	−	0.659734i
$850$	−24.5762	+	6.58517i	−0.842956	+	0.225869i
$851$	11.1412	+	41.5797i	0.381917	+	1.42533i
$852$	9.65966	+	19.0263i	0.330935	+	0.651829i
$853$	32.5674	−	32.5674i	1.11509	−	1.11509i	0.122634	−	0.992452i	$-0.460866\pi$
$853$	32.5674	−	32.5674i	1.11509	−	1.11509i	0.992452	−	0.122634i	$-0.0391343\pi$
$854$	−6.91355	+	6.51551i	−0.236577	+	0.222956i
$855$	−2.50653	+	23.2011i	−0.0857216	+	0.793461i
$856$	−16.8476	−	4.51431i	−0.575840	−	0.154296i
$857$	9.66161	−	16.7344i	0.330034	−	0.571636i	−0.652484	−	0.757803i	$-0.726273\pi$
$857$	9.66161	−	16.7344i	0.330034	−	0.571636i	0.982518	+	0.186166i	$0.0596063\pi$
$858$	−38.6053	+	8.44635i	−1.31796	+	0.288353i
$859$	23.7519	+	41.1395i	0.810404	+	1.40366i	0.912582	+	0.408895i	$0.134086\pi$
$859$	23.7519	+	41.1395i	0.810404	+	1.40366i	−0.102178	+	0.994766i	$0.532581\pi$
$860$	−6.07477	+	6.07477i	−0.207148	+	0.207148i
$861$	−3.84732	+	46.0016i	−0.131116	+	1.56773i
$862$			10.7771i			0.367069i
$863$	7.73101	+	2.07152i	0.263167	+	0.0705153i	0.387990	−	0.921664i	$-0.373170\pi$
$863$	7.73101	+	2.07152i	0.263167	+	0.0705153i	−0.124823	+	0.992179i	$0.539836\pi$
$864$	3.28757	−	4.02392i	0.111845	−	0.136896i
$865$	−12.9414	−	48.2981i	−0.440022	−	1.64219i
$866$	−7.80759	+	29.1383i	−0.265313	+	0.990160i
$867$	0.576573	−	0.517638i	0.0195814	−	0.0175799i
$868$	−1.04252	−	4.40942i	−0.0353856	−	0.149665i
$869$	−27.0116	−	27.0116i	−0.916307	−	0.916307i
$870$	−0.705301	−	0.230297i	−0.0239119	−	0.00780778i
$871$	−3.13369	−	11.3581i	−0.106181	−	0.384854i
$872$	−4.57345	−	2.64048i	−0.154877	−	0.0894180i
$873$	−9.61878	−	3.72432i	−0.325546	−	0.126049i
$874$	12.7148			0.430084
$875$	3.19713	−	10.6581i	0.108083	−	0.360309i
$876$	7.30769	+	0.393598i	0.246904	+	0.0132984i
$877$	6.00003	−	22.3924i	0.202607	−	0.756138i	−0.787559	−	0.616239i	$-0.788655\pi$
$877$	6.00003	−	22.3924i	0.202607	−	0.756138i	0.990166	−	0.139899i	$-0.0446778\pi$
$878$	−28.1713	+	7.54848i	−0.950735	+	0.254749i
$879$	−15.4961	+	23.7864i	−0.522672	+	0.802296i
$880$	−10.6142	−	18.3843i	−0.357803	−	0.619733i
$881$	−17.8123			−0.600111			−0.300056	−	0.953922i	$-0.597005\pi$
$881$	−17.8123			−0.600111			−0.300056	+	0.953922i	$0.597005\pi$
$882$	−8.72908	+	19.0998i	−0.293923	+	0.643124i
$883$			13.4521i			0.452701i	0.974046	+	0.226350i	$0.0726794\pi$
$883$			13.4521i			0.452701i	−0.974046	+	0.226350i	$0.927321\pi$
$884$	−7.42842	−	12.6492i	−0.249845	−	0.425439i
$885$	7.68375	+	36.4085i	0.258287	+	1.22386i
$886$	13.6666	−	3.66196i	0.459139	−	0.123026i
$887$	13.0811	−	7.55237i	0.439220	−	0.253584i	−0.264047	−	0.964510i	$-0.585057\pi$
$887$	13.0811	−	7.55237i	0.439220	−	0.253584i	0.703267	+	0.710926i	$0.251724\pi$
$888$	10.1178	−	9.08362i	0.339532	−	0.304826i
$889$	47.7799	−	25.7292i	1.60249	−	0.862931i
$890$	7.66654	−	7.66654i	0.256983	−	0.256983i
$891$	−26.1494	+	50.5941i	−0.876039	+	1.69497i
$892$	−1.49183	−	5.56759i	−0.0499502	−	0.186417i
$893$	−19.7162	−	11.3831i	−0.659777	−	0.380922i
$894$	−3.15772	+	9.67077i	−0.105610	+	0.323439i
$895$	23.0949	−	23.0949i	0.771979	−	0.771979i
$896$	−2.57477	+	0.608755i	−0.0860169	+	0.0203371i
$897$	23.0647	+	25.3112i	0.770107	+	0.845118i
$898$	−11.8720	−	20.5629i	−0.396174	−	0.686193i
$899$	0.0565985	+	0.211228i	0.00188766	+	0.00704486i
$900$	−15.1460	−	11.0714i	−0.504867	−	0.369048i
$901$	10.9391	−	6.31571i	0.364435	−	0.210407i
$902$	45.0744	−	45.0744i	1.50081	−	1.50081i
$903$	−7.57786	−	8.96109i	−0.252176	−	0.298206i
$904$	−0.428946	+	0.428946i	−0.0142665	+	0.0142665i
$905$	0.358672	−	1.33858i	0.0119226	−	0.0444959i
$906$	18.4598	−	3.89580i	0.613285	−	0.129429i
$907$	−25.5184	−	14.7331i	−0.847326	−	0.489204i	0.0124219	−	0.999923i	$-0.496046\pi$
$907$	−25.5184	−	14.7331i	−0.847326	−	0.489204i	−0.859748	+	0.510719i	$0.829379\pi$
$908$	−4.41341	+	16.4711i	−0.146464	+	0.546611i
$909$	−0.559141	+	5.17556i	−0.0185456	+	0.171662i
$910$	31.9934	+	0.711296i	1.06057	+	0.0235792i
$911$			43.7241i			1.44864i	0.689462	+	0.724322i	$0.257847\pi$
$911$			43.7241i			1.44864i	−0.689462	+	0.724322i	$0.742153\pi$
$912$	−1.81815	−	3.58114i	−0.0602049	−	0.118583i
$913$	1.76836	−	3.06289i	0.0585243	−	0.101367i
$914$	19.2768	−	33.3885i	0.637621	−	1.10439i
$915$	18.6029	−	9.44474i	0.614994	−	0.312234i
$916$	7.02647	+	7.02647i	0.232161	+	0.232161i
$917$	8.67814	+	5.35926i	0.286578	+	0.176978i
$918$	−20.8657	−	3.39784i	−0.688670	−	0.112145i
$919$	5.43311	+	9.41042i	0.179222	+	0.310421i	0.941614	−	0.336694i	$-0.109309\pi$
$919$	5.43311	+	9.41042i	0.179222	+	0.310421i	−0.762392	+	0.647115i	$0.775975\pi$
$920$	−9.19745	+	15.9305i	−0.303231	+	0.525211i
$921$	38.2871	+	24.9428i	1.26160	+	0.821895i
$922$	2.79109	−	1.61144i	0.0919196	−	0.0530698i
$923$	31.6402	+	31.1752i	1.04145	+	1.02614i
$924$	26.2346	−	12.3558i	0.863055	−	0.406477i
$925$	−34.7144	−	34.7144i	−1.14140	−	1.14140i
$926$	−12.7418	+	7.35647i	−0.418721	+	0.241749i
$927$	−22.6460	+	30.9803i	−0.743792	+	1.01753i
$928$	0.123341	−	0.0330492i	0.00404888	−	0.00108489i
$929$	20.3377	+	5.44946i	0.667257	+	0.178791i	0.576519	−	0.817084i	$-0.304411\pi$
$929$	20.3377	+	5.44946i	0.667257	+	0.178791i	0.0907383	+	0.995875i	$0.471077\pi$
$930$	−0.535175	+	9.93625i	−0.0175491	+	0.325823i
$931$	10.7774	+	12.1370i	0.353216	+	0.397774i
$932$		−	18.3858i		−	0.602248i
$933$	−21.0781	−	6.88248i	−0.690067	−	0.225322i
$934$	0.499386	+	1.86373i	0.0163404	+	0.0609832i
$935$	−43.1836	+	74.7963i	−1.41226	+	2.44610i
$936$	3.83081	−	10.1156i	0.125214	−	0.330638i
$937$	40.3453			1.31802			0.659012	−	0.752133i	$-0.270975\pi$
$937$	40.3453			1.31802			0.659012	+	0.752133i	$0.270975\pi$
$938$	4.09924	+	7.61240i	0.133845	+	0.248554i
$939$	−21.0332	+	18.8833i	−0.686394	+	0.616233i
$940$	28.5240	−	16.4684i	0.930352	−	0.537139i
$941$	−4.03518	−	15.0595i	−0.131543	−	0.490926i	0.868445	−	0.495786i	$-0.165120\pi$
$941$	−4.03518	−	15.0595i	−0.131543	−	0.490926i	−0.999988	+	0.00485964i	$0.998453\pi$
$942$	−10.8231	−	7.05094i	−0.352637	−	0.229732i
$943$	−53.3544	−	14.2963i	−1.73746	−	0.465551i
$944$	−4.52837	−	4.52837i	−0.147386	−	0.147386i
$945$	30.2244	−	34.8344i	0.983199	−	1.13316i
$946$			16.2056i			0.526889i
$947$	11.0500	−	41.2392i	0.359077	−	1.34009i	−0.516198	−	0.856469i	$-0.672653\pi$
$947$	11.0500	−	41.2392i	0.359077	−	1.34009i	0.875275	−	0.483625i	$-0.160680\pi$
$948$	10.2305	−	2.15907i	0.332271	−	0.0701233i
$949$	14.6855	−	4.05173i	0.476713	−	0.131525i
$950$	−12.5582	+	7.25047i	−0.407441	+	0.235236i
$951$	0.0338578	−	0.628617i	0.00109791	−	0.0203843i
$952$	7.38261	+	7.83362i	0.239272	+	0.253889i
$953$	24.5509			0.795283			0.397641	−	0.917541i	$-0.369829\pi$
$953$	24.5509			0.795283			0.397641	+	0.917541i	$0.369829\pi$
$954$	8.68573	+	3.36305i	0.281211	+	0.108883i
$955$	78.7913	−	21.1121i	2.54963	−	0.683170i
$956$	4.20537	−	1.12682i	0.136011	−	0.0364441i
$957$	−1.24794	+	0.633582i	−0.0403402	+	0.0204808i
$958$	−4.71803			−0.152433
$959$	4.45029	+	4.72216i	0.143707	+	0.152487i
$960$	5.80202	+	0.312501i	0.187259	+	0.0100859i
$961$	−24.3069	+	14.0336i	−0.784093	+	0.452696i
$962$	13.9705	−	24.6167i	0.450428	−	0.793675i
$963$	−30.8789	+	42.2432i	−0.995059	+	1.36127i
$964$	4.61685	−	17.2303i	0.148699	−	0.554951i
$965$			2.92485i			0.0941542i
$966$	−20.6387	−	14.3340i	−0.664040	−	0.461189i
$967$	2.78613	+	2.78613i	0.0895958	+	0.0895958i	0.750484	−	0.660888i	$-0.229820\pi$
$967$	2.78613	+	2.78613i	0.0895958	+	0.0895958i	−0.660888	+	0.750484i	$0.729820\pi$
$968$	−28.0542	−	7.51710i	−0.901697	−	0.241609i
$969$	−8.91928	+	13.6910i	−0.286529	+	0.439819i
$970$	−2.98522	−	11.1410i	−0.0958496	−	0.357715i
$971$	−17.9367	+	10.3557i	−0.575615	+	0.332332i	−0.759389	−	0.650637i	$-0.774502\pi$
$971$	−17.9367	+	10.3557i	−0.575615	+	0.332332i	0.183774	+	0.982969i	$0.441169\pi$
$972$	−7.69622	−	13.5561i	−0.246856	−	0.434812i
$973$	−21.6862	−	40.2718i	−0.695226	−	1.29105i
$974$	17.0911			0.547633
$975$	−37.2141	−	11.8471i	−1.19180	−	0.379411i
$976$	−1.79532	+	3.10959i	−0.0574669	+	0.0995355i
$977$	−4.50162	−	16.8003i	−0.144020	−	0.537489i	−0.999797	−	0.0201445i	$-0.993587\pi$
$977$	−4.50162	−	16.8003i	−0.144020	−	0.537489i	0.855777	−	0.517344i	$-0.173079\pi$
$978$	4.98759	−	15.2749i	0.159486	−	0.488437i
$979$		−	20.4519i		−	0.653647i
$980$	−23.0026	+	4.72363i	−0.734790	+	0.150891i
$981$	−12.3411	+	9.93453i	−0.394020	+	0.317185i
$982$	23.9908	+	6.42832i	0.765578	+	0.205136i
$983$	13.4884	−	3.61420i	0.430212	−	0.115275i	−0.0372135	−	0.999307i	$-0.511848\pi$
$983$	13.4884	−	3.61420i	0.430212	−	0.115275i	0.467426	+	0.884032i	$0.345181\pi$
$984$	3.60284	+	17.0716i	0.114854	+	0.544224i
$985$	−13.7650	+	7.94724i	−0.438590	+	0.253220i
$986$	−0.367353	−	0.367353i	−0.0116989	−	0.0116989i
$987$	19.1706	+	40.7042i	0.610208	+	1.29563i
$988$	−5.95535	−	5.86783i	−0.189465	−	0.186680i
$989$	12.1612	−	7.02129i	0.386705	−	0.223264i
$990$	−62.9295	+	9.78020i	−2.00003	+	0.310835i
$991$	1.69315	−	2.93263i	0.0537848	−	0.0931580i	−0.837879	−	0.545855i	$-0.816205\pi$
$991$	1.69315	−	2.93263i	0.0537848	−	0.0931580i	0.891664	+	0.452697i	$0.149538\pi$
$992$	−0.856275	−	1.48311i	−0.0271868	−	0.0470889i
$993$	23.6662	+	1.27468i	0.751023	+	0.0404507i
$994$	−27.7322	−	17.1263i	−0.879612	−	0.543212i
$995$	−54.0606	−	54.0606i	−1.71384	−	1.71384i
$996$	0.438232	+	0.863167i	0.0138859	+	0.0273505i
$997$	−18.3914	+	31.8548i	−0.582461	+	1.00885i	0.412725	+	0.910855i	$0.364577\pi$
$997$	−18.3914	+	31.8548i	−0.582461	+	1.00885i	−0.995187	+	0.0979970i	$0.968756\pi$
$998$	−13.8253	+	23.9462i	−0.437633	+	0.758003i
$999$	−14.4527	−	38.1453i	−0.457263	−	1.20686i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bv.a.515.8	yes	144
3.2	odd	2	inner	546.2.bv.a.515.35	yes	144
7.2	even	3	inner	546.2.bv.a.359.35	yes	144
13.5	odd	4	inner	546.2.bv.a.473.8	yes	144
21.2	odd	6	inner	546.2.bv.a.359.8	yes	144
39.5	even	4	inner	546.2.bv.a.473.35	yes	144
91.44	odd	12	inner	546.2.bv.a.317.35	yes	144
273.44	even	12	inner	546.2.bv.a.317.8	✓	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bv.a.317.8	✓	144	273.44	even	12	inner
546.2.bv.a.317.35	yes	144	91.44	odd	12	inner
546.2.bv.a.359.8	yes	144	21.2	odd	6	inner
546.2.bv.a.359.35	yes	144	7.2	even	3	inner
546.2.bv.a.473.8	yes	144	13.5	odd	4	inner
546.2.bv.a.473.35	yes	144	39.5	even	4	inner
546.2.bv.a.515.8	yes	144	1.1	even	1	trivial
546.2.bv.a.515.35	yes	144	3.2	odd	2	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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bv (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.965926 - 0.258819i) q^{2} +(-0.357658 - 1.69472i) q^{3} +(0.866025 + 0.500000i) q^{4} +(3.24035 + 0.868248i) q^{5} +(-0.0931546 + 1.72954i) q^{6} +(-1.25441 - 2.32948i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.74416 + 1.21226i) q^{9} +O(q^{10})\)	\(q+(-0.965926 - 0.258819i) q^{2} +(-0.357658 - 1.69472i) q^{3} +(0.866025 + 0.500000i) q^{4} +(3.24035 + 0.868248i) q^{5} +(-0.0931546 + 1.72954i) q^{6} +(-1.25441 - 2.32948i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.74416 + 1.21226i) q^{9} +(-2.90521 - 1.67733i) q^{10} +(-6.11240 + 1.63781i) q^{11} +(0.537619 - 1.64650i) q^{12} +(-0.0266902 - 3.60545i) q^{13} +(0.608755 + 2.57477i) q^{14} +(0.312501 - 5.80202i) q^{15} +(0.500000 + 0.866025i) q^{16} +(2.03425 - 3.52342i) q^{17} +(2.96441 - 0.460715i) q^{18} +(0.600144 - 2.23977i) q^{19} +(2.37210 + 2.37210i) q^{20} +(-3.49916 + 2.95903i) q^{21} +6.32802 q^{22} +(-2.74170 - 4.74876i) q^{23} +(-0.945446 + 1.45125i) q^{24} +(5.41586 + 3.12685i) q^{25} +(-0.907379 + 3.48951i) q^{26} +(3.03592 + 4.21701i) q^{27} +(0.0783861 - 2.64459i) q^{28} +0.127692i q^{29} +(-1.80353 + 5.52344i) q^{30} +(1.65420 - 0.443241i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(4.96179 + 9.77304i) q^{33} +(-2.87686 + 2.87686i) q^{34} +(-2.04216 - 8.63745i) q^{35} +(-2.98264 - 0.322230i) q^{36} +(-7.58283 - 2.03181i) q^{37} +(-1.15939 + 2.00812i) q^{38} +(-6.10069 + 1.33475i) q^{39} +(-1.67733 - 2.90521i) q^{40} +(7.12298 - 7.12298i) q^{41} +(4.14578 - 1.95256i) q^{42} +2.56093i q^{43} +(-6.11240 - 1.63781i) q^{44} +(-9.94458 + 1.54554i) q^{45} +(1.41921 + 5.29656i) q^{46} +(2.54114 - 9.48367i) q^{47} +(1.28884 - 1.15710i) q^{48} +(-3.85291 + 5.84424i) q^{49} +(-4.42203 - 4.42203i) q^{50} +(-6.69878 - 2.18730i) q^{51} +(1.77961 - 3.13576i) q^{52} +(2.68874 + 1.55235i) q^{53} +(-1.84103 - 4.85907i) q^{54} -21.2283 q^{55} +(-0.760185 + 2.53419i) q^{56} +(-4.01043 - 0.216005i) q^{57} +(0.0330492 - 0.123341i) q^{58} +(-6.18587 + 1.65750i) q^{59} +(3.17164 - 4.86845i) q^{60} +(1.79532 + 3.10959i) q^{61} -1.71255 q^{62} +(6.26624 + 4.87178i) q^{63} +1.00000i q^{64} +(3.04394 - 11.7061i) q^{65} +(-2.26327 - 10.7242i) q^{66} +(3.15651 - 0.845785i) q^{67} +(3.52342 - 2.03425i) q^{68} +(-7.06724 + 6.34485i) q^{69} +(-0.262958 + 8.87168i) q^{70} +(-8.71117 + 8.71117i) q^{71} +(2.79761 + 1.08322i) q^{72} +(1.09357 + 4.08124i) q^{73} +(6.79858 + 3.92516i) q^{74} +(3.36211 - 10.2967i) q^{75} +(1.63962 - 1.63962i) q^{76} +(11.4827 + 12.1842i) q^{77} +(6.23827 + 0.289703i) q^{78} +(3.01834 + 5.22792i) q^{79} +(0.868248 + 3.24035i) q^{80} +(6.06084 - 6.65329i) q^{81} +(-8.72383 + 5.03671i) q^{82} +(-0.395201 + 0.395201i) q^{83} +(-4.50988 + 0.813017i) q^{84} +(9.65087 - 9.65087i) q^{85} +(0.662816 - 2.47366i) q^{86} +(0.216403 - 0.0456702i) q^{87} +(5.48023 + 3.16401i) q^{88} +(-0.836494 + 3.12184i) q^{89} +(10.0057 + 1.08097i) q^{90} +(-8.36533 + 4.58489i) q^{91} -5.48340i q^{92} +(-1.34281 - 2.64487i) q^{93} +(-4.90911 + 8.50283i) q^{94} +(3.88935 - 6.73655i) q^{95} +(-1.54441 + 0.784098i) q^{96} +(2.43118 + 2.43118i) q^{97} +(5.23422 - 4.64789i) q^{98} +(14.7879 - 11.9043i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 16 q^{7}+O(q^{10}) \) 144 * q - 16 * q^7	\( 144 q - 16 q^{7} + 72 q^{16} + 16 q^{18} + 8 q^{19} + 8 q^{21} + 24 q^{27} - 8 q^{28} - 8 q^{31} + 12 q^{33} - 8 q^{37} + 16 q^{39} - 40 q^{45} + 8 q^{46} + 8 q^{52} - 12 q^{54} - 32 q^{55} + 16 q^{57} + 8 q^{58} - 32 q^{61} - 40 q^{63} - 32 q^{66} - 8 q^{67} + 16 q^{72} + 80 q^{73} - 16 q^{76} + 16 q^{78} - 112 q^{79} - 48 q^{81} + 16 q^{84} - 80 q^{85} + 96 q^{87} - 32 q^{91} + 36 q^{93} - 64 q^{94} - 144 q^{97} - 32 q^{99}+O(q^{100}) \) 144 * q - 16 * q^7 + 72 * q^16 + 16 * q^18 + 8 * q^19 + 8 * q^21 + 24 * q^27 - 8 * q^28 - 8 * q^31 + 12 * q^33 - 8 * q^37 + 16 * q^39 - 40 * q^45 + 8 * q^46 + 8 * q^52 - 12 * q^54 - 32 * q^55 + 16 * q^57 + 8 * q^58 - 32 * q^61 - 40 * q^63 - 32 * q^66 - 8 * q^67 + 16 * q^72 + 80 * q^73 - 16 * q^76 + 16 * q^78 - 112 * q^79 - 48 * q^81 + 16 * q^84 - 80 * q^85 + 96 * q^87 - 32 * q^91 + 36 * q^93 - 64 * q^94 - 144 * q^97 - 32 * q^99

Introduction

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