LMFDB - Embedded newform 546.2.bv.a.515.35

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			515.35
Character	$\chi$	$=$	546.515
Dual form			546.2.bv.a.317.35

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.965926 + 0.258819i) q^{2} +(1.64650 - 0.537619i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-3.24035 - 0.868248i) q^{5} +(1.72954 - 0.0931546i) q^{6} +(-1.25441 - 2.32948i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.42193 - 1.77038i) q^{9} +O(q^{10})$	\(q+(0.965926 + 0.258819i) q^{2} +(1.64650 - 0.537619i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-3.24035 - 0.868248i) q^{5} +(1.72954 - 0.0931546i) q^{6} +(-1.25441 - 2.32948i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.42193 - 1.77038i) q^{9} +(-2.90521 - 1.67733i) q^{10} +(6.11240 - 1.63781i) q^{11} +(1.69472 + 0.357658i) q^{12} +(-0.0266902 - 3.60545i) q^{13} +(-0.608755 - 2.57477i) q^{14} +(-5.80202 + 0.312501i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-2.03425 + 3.52342i) q^{17} +(2.79761 - 1.08322i) q^{18} +(0.600144 - 2.23977i) q^{19} +(-2.37210 - 2.37210i) q^{20} +(-3.31776 - 3.16109i) q^{21} +6.32802 q^{22} +(2.74170 + 4.74876i) q^{23} +(1.54441 + 0.784098i) 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} +(-5.68520 - 1.19982i) q^{30} +(1.65420 - 0.443241i) q^{31} +(0.258819 + 0.965926i) q^{32} +(9.18355 - 5.98280i) 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} +(-1.98231 - 5.92203i) q^{39} +(-1.67733 - 2.90521i) q^{40} +(-7.12298 + 7.12298i) q^{41} +(-2.38656 - 3.91208i) q^{42} +2.56093i q^{43} +(6.11240 + 1.63781i) q^{44} +(-9.38502 + 3.63381i) 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} +(-1.45513 + 6.89496i) q^{51} +(1.77961 - 3.13576i) q^{52} +(-2.68874 - 1.55235i) q^{53} +(4.02392 - 3.28757i) q^{54} -21.2283 q^{55} +(0.760185 - 2.53419i) q^{56} +(-0.216005 - 4.01043i) q^{57} +(0.0330492 - 0.123341i) q^{58} +(6.18587 - 1.65750i) q^{59} +(-5.18095 - 2.63038i) q^{60} +(1.79532 + 3.10959i) q^{61} +1.71255 q^{62} +(-7.16216 - 3.42104i) q^{63} +1.00000i q^{64} +(-3.04394 + 11.7061i) q^{65} +(10.4191 - 3.40207i) 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} +(2.96441 + 0.460715i) q^{72} +(1.09357 + 4.08124i) q^{73} +(-6.79858 - 3.92516i) q^{74} +(10.5983 + 2.23669i) q^{75} +(1.63962 - 1.63962i) q^{76} +(-11.4827 - 12.1842i) q^{77} +(-0.382026 - 6.23330i) q^{78} +(3.01834 + 5.22792i) q^{79} +(-0.868248 - 3.24035i) q^{80} +(2.73150 - 8.57548i) q^{81} +(-8.72383 + 5.03671i) q^{82} +(0.395201 - 0.395201i) q^{83} +(-1.29272 - 4.39646i) q^{84} +(9.65087 - 9.65087i) q^{85} +(-0.662816 + 2.47366i) q^{86} +(-0.0686499 - 0.210246i) 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} +(2.48534 - 1.61912i) q^{93} +(-4.90911 + 8.50283i) q^{94} +(-3.88935 + 6.73655i) q^{95} +(0.945446 + 1.45125i) q^{96} +(2.43118 + 2.43118i) q^{97} +(-5.23422 + 4.64789i) q^{98} +(11.9043 - 14.7879i) 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
$3$	1.64650	−	0.537619i	0.950608	−	0.310395i
$3$	1.64650	−	0.537619i	0.950608	−	0.310395i
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$	−3.24035	−	0.868248i	−1.44913	−	0.388292i	−0.553407	−	0.832911i	$-0.686673\pi$
$5$	−3.24035	−	0.868248i	−1.44913	−	0.388292i	−0.895720	+	0.444619i	$0.853339\pi$
$6$	1.72954	−	0.0931546i	0.706083	−	0.0380302i
$7$	−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
$9$	2.42193	−	1.77038i	0.807310	−	0.590127i
$10$	−2.90521	−	1.67733i	−0.918710	−	0.530417i
$11$	6.11240	−	1.63781i	1.84296	−	0.493819i	0.843871	−	0.536546i	$-0.180271\pi$
$11$	6.11240	−	1.63781i	1.84296	−	0.493819i	0.999087	+	0.0427270i	$0.0136046\pi$
$12$	1.69472	+	0.357658i	0.489224	+	0.103247i
$13$	−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
$15$	−5.80202	+	0.312501i	−1.49808	+	0.0806875i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−2.03425	+	3.52342i	−0.493377	+	0.854555i	−0.999971	−	0.00763036i	$-0.997571\pi$
$17$	−2.03425	+	3.52342i	−0.493377	+	0.854555i	0.506594	+	0.862185i	$0.330904\pi$
$18$	2.79761	−	1.08322i	0.659404	−	0.255316i
$19$	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
$21$	−3.31776	−	3.16109i	−0.723994	−	0.689806i
$22$	6.32802			1.34914
$23$	2.74170	+	4.74876i	0.571684	+	0.990185i	0.996393	+	0.0848557i	$0.0270429\pi$
$23$	2.74170	+	4.74876i	0.571684	+	0.990185i	−0.424709	+	0.905330i	$0.639624\pi$
$24$	1.54441	+	0.784098i	0.315251	+	0.160053i
$25$	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	$-0.996226\pi$
$29$		−	0.127692i		−	0.0237119i	0.999930	−	0.0118559i	$-0.00377395\pi$
$30$	−5.68520	−	1.19982i	−1.03797	−	0.219056i
$31$	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
$33$	9.18355	−	5.98280i	1.59865	−	1.04147i
$34$	−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
$39$	−1.98231	−	5.92203i	−0.317423	−	0.948284i
$40$	−1.67733	−	2.90521i	−0.265209	−	0.459355i
$41$	−7.12298	+	7.12298i	−1.11242	+	1.11242i	−0.119600	+	0.992822i	$0.538161\pi$
$41$	−7.12298	+	7.12298i	−1.11242	+	1.11242i	−0.992822	+	0.119600i	$0.961839\pi$
$42$	−2.38656	−	3.91208i	−0.368254	−	0.603646i
$43$			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
$45$	−9.38502	+	3.63381i	−1.39904	+	0.541697i
$46$	1.41921	+	5.29656i	0.209251	+	0.780935i
$47$	−2.54114	+	9.48367i	−0.370664	+	1.38334i	0.488914	+	0.872332i	$0.337393\pi$
$47$	−2.54114	+	9.48367i	−0.370664	+	1.38334i	−0.859578	+	0.511004i	$0.829274\pi$
$48$	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
$51$	−1.45513	+	6.89496i	−0.203759	+	0.965488i
$52$	1.77961	−	3.13576i	0.246788	−	0.434851i
$53$	−2.68874	−	1.55235i	−0.369327	−	0.213231i	0.303837	−	0.952724i	$-0.401732\pi$
$53$	−2.68874	−	1.55235i	−0.369327	−	0.213231i	−0.673165	+	0.739493i	$0.735065\pi$
$54$	4.02392	−	3.28757i	0.547586	−	0.447381i
$55$	−21.2283			−2.86243
$56$	0.760185	−	2.53419i	0.101584	−	0.338645i
$57$	−0.216005	−	4.01043i	−0.0286106	−	0.531195i
$58$	0.0330492	−	0.123341i	0.00433957	−	0.0161955i
$59$	6.18587	−	1.65750i	0.805332	−	0.215788i	0.167408	−	0.985888i	$-0.446460\pi$
$59$	6.18587	−	1.65750i	0.805332	−	0.215788i	0.637924	+	0.770100i	$0.279793\pi$
$60$	−5.18095	−	2.63038i	−0.668857	−	0.339580i
$61$	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
$63$	−7.16216	−	3.42104i	−0.902347	−	0.431011i
$64$			1.00000i			0.125000i
$65$	−3.04394	+	11.7061i	−0.377555	+	1.45196i
$66$	10.4191	−	3.40207i	1.28250	−	0.418766i
$67$	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	$-0.489042\pi$
$71$	8.71117	−	8.71117i	1.03383	−	1.03383i	0.999408	−	0.0344187i	$-0.0109580\pi$
$72$	2.96441	+	0.460715i	0.349359	+	0.0542958i
$73$	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
$75$	10.5983	+	2.23669i	1.22378	+	0.258270i
$76$	1.63962	−	1.63962i	0.188078	−	0.188078i
$77$	−11.4827	−	12.1842i	−1.30858	−	1.38852i
$78$	−0.382026	−	6.23330i	−0.0432560	−	0.705782i
$79$	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
$81$	2.73150	−	8.57548i	0.303500	−	0.952832i
$82$	−8.72383	+	5.03671i	−0.963386	+	0.556211i
$83$	0.395201	−	0.395201i	0.0433790	−	0.0433790i	−0.685085	−	0.728464i	$-0.740235\pi$
$83$	0.395201	−	0.395201i	0.0433790	−	0.0433790i	0.728464	+	0.685085i	$0.240235\pi$
$84$	−1.29272	−	4.39646i	−0.141047	−	0.479693i
$85$	9.65087	−	9.65087i	1.04678	−	1.04678i
$86$	−0.662816	+	2.47366i	−0.0714733	+	0.266742i
$87$	−0.0686499	−	0.210246i	−0.00736004	−	0.0225407i
$88$	5.48023	+	3.16401i	0.584194	+	0.337285i
$89$	0.836494	−	3.12184i	0.0886682	−	0.330914i	−0.907315	−	0.420451i	$-0.861872\pi$
$89$	0.836494	−	3.12184i	0.0886682	−	0.330914i	0.995984	+	0.0895366i	$0.0285386\pi$
$90$	−10.0057	+	1.08097i	−1.05470	+	0.113944i
$91$	−8.36533	+	4.58489i	−0.876925	+	0.480627i
$92$			5.48340i			0.571684i
$93$	2.48534	−	1.61912i	0.257718	−	0.167895i
$94$	−4.90911	+	8.50283i	−0.506336	+	0.877000i
$95$	−3.88935	+	6.73655i	−0.399039	+	0.691156i
$96$	0.945446	+	1.45125i	0.0964942	+	0.148118i
$97$	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
$99$	11.9043	−	14.7879i	1.19642	−	1.48624i
$100$	3.12685	+	5.41586i	0.312685	+	0.541586i
$101$	−0.867612	+	1.50275i	−0.0863306	+	0.149529i	−0.905957	−	0.423369i	$-0.860847\pi$
$101$	−0.867612	+	1.50275i	−0.0863306	+	0.149529i	0.819627	+	0.572898i	$0.194181\pi$
$102$	−3.19010	+	6.28341i	−0.315867	+	0.622150i
$103$	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
$105$	8.00608	+	13.1237i	0.781313	+	1.28074i
$106$	−2.19535	−	2.19535i	−0.213231	−	0.213231i
$107$	−15.1052	+	8.72097i	−1.46027	+	0.843088i	−0.999023	−	0.0441826i	$-0.985932\pi$
$107$	−15.1052	+	8.72097i	−1.46027	+	0.843088i	−0.461248	+	0.887271i	$0.652598\pi$
$108$	4.73769	−	2.13408i	0.455884	−	0.205352i
$109$	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
$111$	−13.5775	+	0.731294i	−1.28872	+	0.0694114i
$112$	1.39018	−	2.25109i	0.131360	−	0.212708i
$113$			0.606621i			0.0570661i	0.999593	+	0.0285331i	$0.00908359\pi$
$113$			0.606621i			0.0570661i	−0.999593	+	0.0285331i	$0.990916\pi$
$114$	0.829331	−	3.92968i	0.0776740	−	0.368049i
$115$	−4.76095	−	17.7681i	−0.443961	−	1.65688i
$116$	0.0638462	−	0.110585i	0.00592797	−	0.0102675i
$117$	−6.44767	−	8.68490i	−0.596087	−	0.802920i
$118$	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
$123$	−7.89854	+	15.5574i	−0.712187	+	1.40277i
$124$	1.65420	+	0.443241i	0.148551	+	0.0398042i
$125$	−2.97389	−	2.97389i	−0.265993	−	0.265993i
$126$	−6.03268	−	5.15818i	−0.537434	−	0.459527i
$127$			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
$129$	1.37680	+	4.21657i	0.121221	+	0.371248i
$130$	−5.96998	+	10.5194i	−0.523602	+	0.922611i
$131$	3.33860	−	1.92754i	0.291695	−	0.168410i	−0.347011	−	0.937861i	$-0.612803\pi$
$131$	3.33860	−	1.92754i	0.291695	−	0.168410i	0.638706	+	0.769451i	$0.279470\pi$
$132$	10.9446	−	0.589485i	0.952604	−	0.0513080i
$133$	−5.97031	+	1.41157i	−0.517692	+	0.122399i
$134$	3.26786			0.282300
$135$	−13.4988	+	11.0286i	−1.16180	+	0.949195i
$136$	−3.92986	+	1.05300i	−0.336983	+	0.0902943i
$137$	2.36895	−	0.634758i	0.202393	−	0.0542311i	−0.156198	−	0.987726i	$-0.549924\pi$
$137$	2.36895	−	0.634758i	0.202393	−	0.0542311i	0.358591	+	0.933495i	$0.383257\pi$
$138$	5.18426	+	7.95779i	0.441313	+	0.677412i
$139$	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
$141$	0.914613	+	16.9810i	0.0770243	+	1.43006i
$142$	10.6690	−	6.15973i	0.895320	−	0.516913i
$143$	−6.06820	−	21.9943i	−0.507448	−	1.83925i
$144$	2.74416	+	1.21226i	0.228680	+	0.101022i
$145$	−0.110869	+	0.413767i	−0.00920714	+	0.0343615i
$146$			4.22521i			0.349681i
$147$	−3.20184	+	11.6939i	−0.264083	+	0.964500i
$148$	−5.55102	−	5.55102i	−0.456291	−	0.456291i
$149$	−5.67339	−	1.52018i	−0.464783	−	0.124538i	0.0188255	−	0.999823i	$-0.494007\pi$
$149$	−5.67339	−	1.52018i	−0.464783	−	0.124538i	−0.483608	+	0.875285i	$0.660674\pi$
$150$	9.65825	+	4.90351i	0.788593	+	0.400370i
$151$	−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
$156$	1.24429	−	6.11978i	0.0996228	−	0.489975i
$157$	−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
$159$	−5.26159	−	1.11042i	−0.417271	−	0.0880620i
$160$		−	3.35465i		−	0.265209i
$161$	7.62291	−	12.3436i	0.600769	−	0.972813i
$162$	4.85792	−	7.57632i	0.381674	−	0.595252i
$163$	−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
$165$	−34.9524	+	11.4128i	−2.72104	+	0.888482i
$166$	0.484021	−	0.279450i	0.0375673	−	0.0216895i
$167$	−7.85626	−	7.85626i	−0.607935	−	0.607935i	0.334471	−	0.942406i	$-0.391442\pi$
$167$	−7.85626	−	7.85626i	−0.607935	−	0.607935i	−0.942406	+	0.334471i	$0.891442\pi$
$168$	−0.110784	−	4.58124i	−0.00854714	−	0.353450i
$169$	−12.9986	+	0.192461i	−0.999890	+	0.0148047i
$170$	11.8198	−	6.82419i	0.906541	−	0.523392i
$171$	−2.51174	−	6.48705i	−0.192077	−	0.496077i
$172$	−1.28046	+	2.21783i	−0.0976344	+	0.169108i
$173$	7.45262	+	12.9083i	0.566612	+	0.981401i	0.996898	+	0.0787079i	$0.0250794\pi$
$173$	7.45262	+	12.9083i	0.566612	+	0.981401i	−0.430286	+	0.902693i	$0.641587\pi$
$174$	−0.0118951	−	0.220850i	−0.000901768	−	0.0167426i
$175$	0.490203	−	16.5385i	0.0370559	−	1.25019i
$176$	4.47459	+	4.47459i	0.337285	+	0.337285i
$177$	9.29394	−	6.05472i	0.698576	−	0.455101i
$178$	1.61598	−	2.79896i	0.121123	−	0.209791i
$179$	−4.86804	+	8.43169i	−0.363854	+	0.630214i	−0.988592	−	0.150621i	$-0.951873\pi$
$179$	−4.86804	+	8.43169i	−0.363854	+	0.630214i	0.624737	+	0.780835i	$0.285206\pi$
$180$	−9.94458	−	1.54554i	−0.741225	−	0.115198i
$181$		−	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
$186$	2.81972	−	0.920700i	0.206752	−	0.0675090i
$187$	−6.66343	+	24.8683i	−0.487278	+	1.81855i
$188$	−6.94253	+	6.94253i	−0.506336	+	0.506336i
$189$	−13.6317	−	1.78224i	−0.991561	−	0.129639i
$190$	−5.50037	+	5.50037i	−0.399039	+	0.399039i
$191$	−21.0580	+	12.1578i	−1.52370	+	0.879711i	−0.524098	+	0.851658i	$0.675597\pi$
$191$	−21.0580	+	12.1578i	−1.52370	+	0.879711i	−0.999606	+	0.0280531i	$0.991069\pi$
$192$	0.537619	+	1.64650i	0.0387993	+	0.118826i
$193$	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
$195$	1.28157	+	20.9106i	0.0917749	+	1.49744i
$196$	−6.25883	+	3.13480i	−0.447060	+	0.223915i
$197$	3.35030	−	3.35030i	0.238699	−	0.238699i	−0.577612	−	0.816311i	$-0.696015\pi$
$197$	3.35030	−	3.35030i	0.238699	−	0.238699i	0.816311	+	0.577612i	$0.196015\pi$
$198$	15.3260	−	11.2030i	1.08917	−	0.796163i
$199$	−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
$201$	4.74249	−	3.08959i	0.334509	−	0.217923i
$202$	−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
$207$	15.0473	+	6.64732i	1.04586	+	0.462021i
$208$	3.10907	−	1.82584i	0.215575	−	0.126599i
$209$		−	14.6733i		−	1.01497i
$210$	4.33663	+	14.7486i	0.299256	+	1.01775i
$211$	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
$213$	9.65966	−	19.0263i	0.661869	−	1.30366i
$214$	−16.8476	+	4.51431i	−1.15168	+	0.308592i
$215$	2.22352	−	8.29829i	0.151643	−	0.565938i
$216$	5.12860	−	0.835158i	0.348957	−	0.0568253i
$217$	−3.10756	−	3.29740i	−0.210955	−	0.223842i
$218$	5.28096			0.357672
$219$	3.99471	+	6.13185i	0.269938	+	0.414352i
$220$	−18.3843	−	10.6142i	−1.23947	−	0.715606i
$221$	12.7578	+	7.24034i	0.858183	+	0.487038i
$222$	−13.3041	−	2.80773i	−0.892913	−	0.188443i
$223$	−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	$-0.891865\pi$
$227$	−4.41341	−	16.4711i	−0.292928	−	1.09322i	0.649921	−	0.760002i	$-0.274802\pi$
$228$	1.81815	−	3.58114i	0.120410	−	0.237167i
$229$	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
$231$	−25.4567	−	13.8880i	−1.67493	−	0.913761i
$232$	0.0902921	−	0.0902921i	0.00592797	−	0.00592797i
$233$	9.19291	+	15.9226i	0.602248	+	1.04312i	0.992480	+	0.122407i	$0.0390613\pi$
$233$	9.19291	+	15.9226i	0.602248	+	1.04312i	−0.390232	+	0.920716i	$0.627605\pi$
$234$	−3.98015	−	10.0578i	−0.260191	−	0.657496i
$235$	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	−0.799629	−	0.600495i	$-0.794970\pi$
$239$	−3.07854	+	3.07854i	−0.199134	+	0.199134i	0.600495	+	0.799629i	$0.294970\pi$
$240$	−3.17164	−	4.86845i	−0.204729	−	0.314257i
$241$	−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
$243$	−0.112933	−	15.5880i	−0.00724462	−	0.999974i
$244$			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
$249$	0.438232	−	0.863167i	0.0277718	−	0.0547010i
$250$	−2.10286	−	3.64226i	−0.132997	−	0.230357i
$251$	−25.3659			−1.60108			−0.800542	−	0.599276i	$-0.795455\pi$
$251$	−25.3659			−1.60108			−0.800542	+	0.599276i	$0.795455\pi$
$252$	−4.49209	−	6.54379i	−0.282975	−	0.412220i
$253$	24.5359	+	24.5359i	1.54256	+	1.54256i
$254$	−5.30864	+	19.8121i	−0.333094	+	1.24312i
$255$	10.7017	−	21.0787i	0.670164	−	1.32000i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−11.3035	−	19.5783i	−0.705096	−	1.22126i	−0.966657	−	0.256075i	$-0.917571\pi$
$257$	−11.3035	−	19.5783i	−0.705096	−	1.22126i	0.261561	−	0.965187i	$-0.415763\pi$
$258$	0.238562	+	4.42923i	0.0148522	+	0.275752i
$259$	4.77892	+	20.2127i	0.296948	+	1.25596i
$260$	−8.48917	+	8.61580i	−0.526476	+	0.534329i
$261$	−0.226064	−	0.309262i	−0.0139930	−	0.0191428i
$262$	3.72373	−	0.997770i	0.230053	−	0.0616424i
$263$	−16.2993	−	9.41043i	−1.00506	−	0.580272i	−0.0953187	−	0.995447i	$-0.530387\pi$
$263$	−16.2993	−	9.41043i	−1.00506	−	0.580272i	−0.909742	+	0.415175i	$0.863720\pi$
$264$	10.7242	+	2.26327i	0.660031	+	0.139295i
$265$	7.36464	+	7.36464i	0.452406	+	0.452406i
$266$	−6.13222	−	0.181760i	−0.375991	−	0.0111444i
$267$	−0.301072	−	5.58982i	−0.0184253	−	0.342092i
$268$	3.15651	+	0.845785i	0.192815	+	0.0516645i
$269$	4.49802	+	2.59693i	0.274249	+	0.158338i	0.630817	−	0.775932i	$-0.282720\pi$
$269$	4.49802	+	2.59693i	0.274249	+	0.158338i	−0.356568	+	0.934269i	$0.616053\pi$
$270$	−15.8933	+	7.15910i	−0.967236	+	0.435689i
$271$	−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
$273$	−11.3086	+	12.0464i	−0.684428	+	0.729081i
$274$	2.45252			0.148162
$275$	38.2251	+	10.2424i	2.30506	+	0.617639i
$276$	2.94798	+	9.02842i	0.177448	+	0.543447i
$277$	−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
$279$	3.22165	−	4.00206i	0.192875	−	0.239597i
$280$	−4.66357	+	7.55162i	−0.278702	+	0.451296i
$281$	−7.47121	−	7.47121i	−0.445695	−	0.445695i	0.448226	−	0.893920i	$-0.352056\pi$
$281$	−7.47121	−	7.47121i	−0.445695	−	0.445695i	−0.893920	+	0.448226i	$0.852056\pi$
$282$	−3.51157	+	16.6392i	−0.209111	+	0.990847i
$283$	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
$285$	−2.78212	+	13.1827i	−0.164798	+	0.780878i
$286$	−0.168896	−	22.8154i	−0.00998704	−	1.34910i
$287$	25.5279	+	7.65766i	1.50687	+	0.452017i
$288$	2.33690	+	1.88120i	0.137703	+	0.110851i
$289$	0.223679	+	0.387423i	0.0131576	+	0.0227896i
$290$	−0.214182	+	0.370974i	−0.0125772	+	0.0217843i
$291$	5.30999	+	2.69589i	0.311277	+	0.158036i
$292$	−1.09357	+	4.08124i	−0.0639961	+	0.238837i
$293$	11.5897	+	11.5897i	0.677076	+	0.677076i	0.959338	−	0.282261i	$-0.0910845\pi$
$293$	11.5897	+	11.5897i	0.677076	+	0.677076i	−0.282261	+	0.959338i	$0.591084\pi$
$294$	−6.11936	+	10.4668i	−0.356888	+	0.610435i
$295$	−21.4835			−1.25082
$296$	−3.92516	−	6.79858i	−0.228145	−	0.395159i
$297$	11.6501	−	30.7483i	0.676006	−	1.78420i
$298$	−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
$303$	−0.620618	+	2.94072i	−0.0356536	+	0.168940i
$304$	2.23977	−	0.600144i	0.128460	−	0.0344206i
$305$	−3.11757	−	11.6349i	−0.178512	−	0.666214i
$306$	−1.87442	+	12.0607i	−0.107153	+	0.689464i
$307$	−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	−0.988447	−	0.151569i	$-0.951568\pi$
$311$	−6.40089	+	11.0867i	−0.362961	+	0.628667i	0.625486	+	0.780236i	$0.284901\pi$
$312$	2.78581	−	5.58921i	0.157715	−	0.316427i
$313$	−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
$315$	20.2375	+	17.3039i	1.14026	+	0.974964i
$316$			6.03668i			0.339590i
$317$	−0.351074	−	0.0940699i	−0.0197183	−	0.00528349i	0.248946	−	0.968517i	$-0.419916\pi$
$317$	−0.351074	−	0.0940699i	−0.0197183	−	0.00528349i	−0.268665	+	0.963234i	$0.586582\pi$
$318$	−4.79491	−	2.43438i	−0.268885	−	0.136513i
$319$	−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
$324$	6.65329	−	6.06084i	0.369627	−	0.336713i
$325$	11.1292	−	19.6101i	0.617334	−	1.08777i
$326$	−8.03428	−	4.63859i	−0.444977	−	0.256908i
$327$	7.66401	−	4.99287i	0.423821	−	0.276106i
$328$	−10.0734			−0.556211
$329$	25.2796	−	5.97689i	1.39371	−	0.329517i
$330$	−36.7153	+	1.97752i	−2.02111	+	0.108859i
$331$	−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
$333$	−21.9622	+	8.50359i	−1.20352	+	0.465994i
$334$	−5.55521	−	9.62191i	−0.303968	−	0.526487i
$335$	−10.9625			−0.598948
$336$	1.07870	−	4.45381i	0.0588480	−	0.242975i
$337$		−	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
$339$	0.326131	+	0.998803i	0.0177130	+	0.0542475i
$340$	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
$345$	−17.3914	−	26.6956i	−0.936321	−	1.43724i
$346$	3.85776	+	14.3973i	0.207394	+	0.774006i
$347$	−18.0884	−	10.4434i	−0.971038	−	0.560629i	−0.0714856	−	0.997442i	$-0.522774\pi$
$347$	−18.0884	−	10.4434i	−0.971038	−	0.560629i	−0.899553	+	0.436812i	$0.856107\pi$
$348$	0.0456702	−	0.216403i	0.00244818	−	0.0116004i
$349$	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
$351$	−15.2853	−	10.8333i	−0.815867	−	0.578239i
$352$	3.16401	+	5.48023i	0.168642	+	0.292097i
$353$	4.76936	+	17.7995i	0.253848	+	0.947372i	0.968728	+	0.248125i	$0.0798145\pi$
$353$	4.76936	+	17.7995i	0.253848	+	0.947372i	−0.714880	+	0.699247i	$0.753519\pi$
$354$	10.5443	−	3.44296i	0.560425	−	0.182991i
$355$	−35.7907	+	20.6638i	−1.89957	+	1.09672i
$356$	2.28534	−	2.28534i	0.121123	−	0.121123i
$357$	17.8870	−	5.25942i	0.946679	−	0.278358i
$358$	−6.88445	+	6.88445i	−0.363854	+	0.363854i
$359$	−2.23711	+	8.34901i	−0.118070	+	0.440644i	−0.999498	−	0.0316744i	$-0.989916\pi$
$359$	−2.23711	+	8.34901i	−0.118070	+	0.440644i	0.881428	+	0.472318i	$0.156583\pi$
$360$	−9.20571	−	4.06672i	−0.485183	−	0.214335i
$361$	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
$366$	3.39476	+	5.21093i	0.177447	+	0.272380i
$367$	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
$369$	−4.64097	+	29.8617i	−0.241599	+	1.55454i
$370$	18.6217	+	18.6217i	0.968098	+	0.968098i
$371$	−0.243365	+	8.21064i	−0.0126349	+	0.426275i
$372$	2.96193	−	0.159532i	0.153569	−	0.00827135i
$373$	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
$375$	−6.49534	−	3.29770i	−0.335418	−	0.170292i
$376$	−8.50283	+	4.90911i	−0.438500	+	0.253168i
$377$	−0.460389	+	0.00340814i	−0.0237112	+	0.000175528i
$378$	−12.7059	−	5.24965i	−0.653523	−	0.270013i
$379$	−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
$381$	11.0271	+	33.7714i	0.564937	+	1.73016i
$382$	−23.4872	+	6.29337i	−1.20171	+	0.321997i
$383$	8.85758	+	2.37338i	0.452601	+	0.121274i	0.477916	−	0.878405i	$-0.341392\pi$
$383$	8.85758	+	2.37338i	0.452601	+	0.121274i	−0.0253151	+	0.999680i	$0.508059\pi$
$384$	0.0931546	+	1.72954i	0.00475378	+	0.0882604i
$385$	26.6290	+	49.4508i	1.35714	+	2.52025i
$386$			0.871878i			0.0443774i
$387$	4.53382	+	6.20238i	0.230467	+	0.315285i
$388$	0.889874	+	3.32105i	0.0451765	+	0.168601i
$389$	17.7461	−	30.7371i	0.899761	−	1.55843i	0.0719626	−	0.997407i	$-0.477074\pi$
$389$	17.7461	−	30.7371i	0.899761	−	1.55843i	0.827799	−	0.561025i	$-0.189593\pi$
$390$	−4.17415	+	20.5298i	−0.211367	+	1.03956i
$391$	−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
$396$	17.7034	−	6.85461i	0.889627	−	0.344457i
$397$	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
$399$	−9.07124	+	5.53391i	−0.454130	+	0.277042i
$400$			6.25370i			0.312685i
$401$	3.88669	−	14.5053i	0.194092	−	0.724362i	−0.798408	−	0.602117i	$-0.794324\pi$
$401$	3.88669	−	14.5053i	0.194092	−	0.724362i	0.992500	−	0.122245i	$-0.0390093\pi$
$402$	5.38054	−	1.75687i	0.268357	−	0.0876245i
$403$	−1.64223	−	5.95230i	−0.0818055	−	0.296505i
$404$	−1.50275	+	0.867612i	−0.0747645	+	0.0431653i
$405$	−16.2966	+	25.4159i	−0.809787	+	1.26293i
$406$	−0.328778	+	0.0777334i	−0.0163170	+	0.00385784i
$407$	−49.6770			−2.46240
$408$	−5.90441	+	3.84654i	−0.292312	+	0.190432i
$409$	−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
$411$	3.55922	−	2.31872i	0.175563	−	0.114374i
$412$	12.7916			0.630196
$413$	−11.6207	−	12.3307i	−0.571819	−	0.606752i
$414$	12.8141	+	10.3154i	0.629781	+	0.506972i
$415$	−1.62372	+	0.937456i	−0.0797054	+	0.0460179i
$416$	3.47569	−	0.958941i	0.170410	−	0.0470159i
$417$	28.4646	−	9.29432i	1.39392	−	0.455145i
$418$	3.79773	−	14.1733i	0.185753	−	0.693239i
$419$		−	22.9443i		−	1.12090i	−0.828187	−	0.560451i	$-0.810628\pi$
$419$		−	22.9443i		−	1.12090i	0.828187	−	0.560451i	$-0.189372\pi$
$420$	0.371641	+	15.3685i	0.0181342	+	0.749904i
$421$	−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
$423$	10.6353	+	27.4676i	0.517104	+	1.33552i
$424$	−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
$429$	−21.8158	−	32.9512i	−1.05328	−	1.59090i
$430$	4.29551	−	7.44004i	0.207148	−	0.358791i
$431$	2.78931	+	10.4099i	0.134356	+	0.501425i	1.00000		0.000763751i	$0.000243109\pi$
$431$	2.78931	+	10.4099i	0.134356	+	0.501425i	−0.865643	+	0.500661i	$0.833090\pi$
$432$	5.17000	+	0.520678i	0.248742	+	0.0250511i
$433$		−	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
$435$	0.0399040	+	0.740874i	0.00191325	+	0.0355222i
$436$	5.10102	+	1.36681i	0.244294	+	0.0654585i
$437$	12.2815	−	3.29083i	0.587506	−	0.157422i
$438$	2.27156	+	6.95682i	0.108539	+	0.332410i
$439$	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
$441$	1.01505	+	20.9755i	0.0483358	+	0.998831i
$442$	10.4492	+	10.2956i	0.497016	+	0.489712i
$443$	12.2531	−	7.07436i	0.582165	−	0.336113i	−0.179828	−	0.983698i	$-0.557554\pi$
$443$	12.2531	−	7.07436i	0.582165	−	0.336113i	0.761993	+	0.647585i	$0.224221\pi$
$444$	−12.1241	−	6.15542i	−0.575384	−	0.292123i
$445$	−5.42106	+	9.38955i	−0.256983	+	0.445107i
$446$	−2.88200	−	4.99176i	−0.136466	−	0.236367i
$447$	−10.1585	+	0.547147i	−0.480482	+	0.0258791i
$448$	2.32948	−	1.25441i	0.110057	−	0.0592653i
$449$	−16.7895	−	16.7895i	−0.792348	−	0.792348i	0.189528	−	0.981875i	$-0.439304\pi$
$449$	−16.7895	−	16.7895i	−0.792348	−	0.792348i	−0.981875	+	0.189528i	$0.939304\pi$
$450$	18.5385	+	2.88117i	0.873915	+	0.135820i
$451$	−31.8724	+	55.2046i	−1.50081	+	2.59948i
$452$	−0.303311	+	0.525349i	−0.0142665	+	0.0247104i
$453$	−10.2983	−	15.8078i	−0.483856	−	0.742715i
$454$		−	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
$459$	8.68249	+	19.2753i	0.405264	+	0.899692i
$460$	4.76095	−	17.7681i	0.221980	−	0.828442i
$461$	2.27891	−	2.27891i	0.106140	−	0.106140i	−0.652043	−	0.758182i	$-0.726088\pi$
$461$	2.27891	−	2.27891i	0.106140	−	0.106140i	0.758182	+	0.652043i	$0.226088\pi$
$462$	−20.9949	−	20.0034i	−0.976769	−	0.930644i
$463$	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
$465$	−9.45917	+	3.08863i	−0.438659	+	0.143232i
$466$	4.75860	+	17.7593i	0.220438	+	0.822685i
$467$	0.964739	+	1.67098i	0.0446428	+	0.0773236i	0.887483	−	0.460840i	$-0.152452\pi$
$467$	0.964739	+	1.67098i	0.0446428	+	0.0773236i	−0.842841	+	0.538163i	$0.819118\pi$
$468$	−1.24139	−	10.7452i	−0.0573834	−	0.496696i
$469$	−5.92980	−	6.29206i	−0.273813	−	0.290540i
$470$	23.2898	−	23.2898i	1.07428	−	1.07428i
$471$	−2.66734	+	12.6389i	−0.122905	+	0.582369i
$472$	5.54610	+	3.20204i	0.255280	+	0.147386i
$473$	4.19432	+	15.6534i	0.192855	+	0.719744i
$474$	5.70736	+	8.76074i	0.262148	+	0.402394i
$475$	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	−0.361425	−	0.932401i	$-0.617710\pi$
$479$	−4.55727	+	1.22112i	−0.208227	+	0.0557942i	0.153198	+	0.988196i	$0.451043\pi$
$480$	−1.80353	−	5.52344i	−0.0823193	−	0.252109i
$481$	−7.12322	+	27.3938i	−0.324791	+	1.24905i
$482$		−	17.8381i		−	0.812505i
$483$	5.91496	−	24.4220i	0.269140	−	1.11124i
$484$	29.0439			1.32018
$485$	−5.76700	−	9.98873i	−0.261866	−	0.453565i
$486$	3.92540	−	15.0861i	0.178060	−	0.684321i
$487$	−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
$489$	−16.0453	+	0.864212i	−0.725593	+	0.0390810i
$490$	20.9962	−	10.5162i	0.948512	−	0.475072i
$491$	24.8371			1.12088			0.560442	−	0.828194i	$-0.310631\pi$
$491$	24.8371			1.12088			0.560442	+	0.828194i	$0.310631\pi$
$492$	−14.6191	+	9.52387i	−0.659078	+	0.429369i
$493$	0.449914	+	0.259758i	0.0202631	+	0.0116989i
$494$	−7.27113	−	4.12653i	−0.327144	−	0.185661i
$495$	−51.4135	+	37.5822i	−2.31087	+	1.68920i
$496$	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
$501$	−17.1590	−	8.71166i	−0.766608	−	0.389208i
$502$	−24.5016	−	6.56519i	−1.09356	−	0.293019i
$503$			27.6359i			1.23222i	0.787658	+	0.616112i	$0.211293\pi$
$503$			27.6359i			1.23222i	−0.787658	+	0.616112i	$0.788707\pi$
$504$	−2.64537	−	7.48345i	−0.117834	−	0.333339i
$505$	4.11612	−	4.11612i	0.183165	−	0.183165i
$506$	17.3495	+	30.0503i	0.771281	+	1.33590i
$507$	−21.2987	+	7.30517i	−0.945908	+	0.324434i
$508$	−10.2555	+	17.7631i	−0.455015	+	0.788109i
$509$	−3.42423	−	0.917520i	−0.151776	−	0.0406684i	0.182131	−	0.983274i	$-0.441701\pi$
$509$	−3.42423	−	0.917520i	−0.151776	−	0.0406684i	−0.333907	+	0.942606i	$0.608367\pi$
$510$	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
$513$	−7.62314	−	9.33057i	−0.336570	−	0.411955i
$514$	−5.85115	−	21.8368i	−0.258083	−	0.963179i
$515$	−41.4492	+	11.1063i	−1.82647	+	0.489401i
$516$	−0.915937	+	4.34006i	−0.0403219	+	0.191060i
$517$			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	0.402564	−	0.915392i	$-0.368119\pi$
$521$	−4.31187	−	2.48946i	−0.188906	−	0.109065i	−0.591471	+	0.806327i	$0.701452\pi$
$522$	−0.138318	−	0.357234i	−0.00605403	−	0.0156357i
$523$	−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
$525$	−8.08428	−	27.4941i	−0.352827	−	1.19994i
$526$	−13.3084	−	13.3084i	−0.580272	−	0.580272i
$527$	−1.80332	+	6.73009i	−0.0785540	+	0.293167i
$528$	9.77304	+	4.96179i	0.425317	+	0.215934i
$529$	−3.53383	+	6.12077i	−0.153645	+	0.266121i
$530$	5.20758	+	9.01980i	0.226203	+	0.391795i
$531$	12.0474	−	14.9657i	0.522810	−	0.649456i
$532$	−5.87623	−	1.76270i	−0.254767	−	0.0764228i
$533$	25.8717	+	25.4914i	1.12063	+	1.10416i
$534$	1.15594	−	5.47728i	0.0500224	−	0.237025i
$535$	56.5179	−	15.1439i	2.44348	−	0.654730i
$536$	2.83005	+	1.63393i	0.122240	+	0.0705751i
$537$	−3.48219	+	16.4999i	−0.150268	+	0.712025i
$538$	3.67262	+	3.67262i	0.158338	+	0.158338i
$539$	−13.9787	+	42.0326i	−0.602107	+	1.81047i
$540$	−17.2047	+	2.80167i	−0.740371	+	0.120565i
$541$	−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
$543$	−0.222090	−	0.680166i	−0.00953077	−	0.0291887i
$544$	−3.92986	−	1.05300i	−0.168492	−	0.0451472i
$545$	−17.7158			−0.758862
$546$	−14.0411	+	8.70904i	−0.600904	+	0.372713i
$547$	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
$549$	9.85330	+	4.35280i	0.420529	+	0.185773i
$550$	34.2717	+	19.7868i	1.46135	+	0.843711i
$551$	−0.286001	−	0.0766338i	−0.0121841	−	0.00326471i
$552$	0.510804	+	9.48378i	0.0217413	+	0.403656i
$553$	8.39207	−	13.5891i	0.356867	−	0.577867i
$554$	−5.01150	−	5.01150i	−0.212918	−	0.212918i
$555$	44.6307	+	9.41897i	1.89447	+	0.399813i
$556$	14.9718	+	8.64396i	0.634945	+	0.366586i
$557$	−10.5106	+	2.81630i	−0.445347	+	0.119330i	−0.474521	−	0.880244i	$-0.657379\pi$
$557$	−10.5106	+	2.81630i	−0.445347	+	0.119330i	0.0291745	+	0.999574i	$0.490712\pi$
$558$	4.14768	−	3.03187i	0.175585	−	0.128349i
$559$	9.23330	−	0.0683516i	0.390527	−	0.00289097i
$560$	−6.45917	+	6.08729i	−0.272950	+	0.257235i
$561$	2.39831	+	44.5280i	0.101257	+	1.87997i
$562$	−5.28294	−	9.15032i	−0.222847	−	0.385983i
$563$	10.7017	−	18.5359i	0.451024	−	0.781196i	−0.547426	−	0.836854i	$-0.684392\pi$
$563$	10.7017	−	18.5359i	0.451024	−	0.781196i	0.998450	+	0.0556577i	$0.0177256\pi$
$564$	−7.69845	+	15.1633i	−0.324163	+	0.638491i
$565$	0.526698	−	1.96566i	0.0221583	−	0.0826961i
$566$	8.25554	+	8.25554i	0.347006	+	0.347006i
$567$	−23.4028	+	4.39422i	−0.982825	+	0.184540i
$568$	12.3195			0.516913
$569$	6.50476	+	11.2666i	0.272694	+	0.472319i	0.969551	−	0.244891i	$-0.0787521\pi$
$569$	6.50476	+	11.2666i	0.272694	+	0.472319i	−0.696857	+	0.717210i	$0.745419\pi$
$570$	−6.09926	+	12.0135i	−0.255470	+	0.503189i
$571$	−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
$576$	1.77038	+	2.42193i	0.0737659	+	0.100914i
$577$	−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
$579$	0.824314	+	1.26531i	0.0342573	+	0.0525847i
$580$	−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
$585$	13.3520	+	33.7403i	0.552038	+	1.39499i
$586$	8.19514	+	14.1944i	0.338538	+	0.586365i
$587$	−11.6106	+	11.6106i	−0.479223	+	0.479223i	−0.904883	−	0.425660i	$-0.860042\pi$
$587$	−11.6106	+	11.6106i	−0.479223	+	0.479223i	0.425660	+	0.904883i	$0.360042\pi$
$588$	−8.61985	+	8.52633i	−0.355476	+	0.351620i
$589$		−	3.97103i		−	0.163623i
$590$	−20.7515	−	5.56034i	−0.854324	−	0.228915i
$591$	3.71509	−	7.31746i	0.152818	−	0.301000i
$592$	−2.03181	−	7.58283i	−0.0835070	−	0.311652i
$593$	−9.64729	+	36.0042i	−0.396167	+	1.47851i	0.423617	+	0.905841i	$0.360760\pi$
$593$	−9.64729	+	36.0042i	−0.396167	+	1.47851i	−0.819784	+	0.572673i	$0.805906\pi$
$594$	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
$597$	−38.6231	−	8.15111i	−1.58074	−	0.333603i
$598$	19.0586	−	5.25825i	0.779364	−	0.215026i
$599$	36.8375	+	21.2681i	1.50514	+	0.868993i	0.999982	+	0.00596522i	$0.00189880\pi$
$599$	36.8375	+	21.2681i	1.50514	+	0.868993i	0.505157	+	0.863027i	$0.331435\pi$
$600$	5.91254	+	9.07569i	0.241378	+	0.370513i
$601$	−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
$603$	6.14749	−	7.63666i	0.250345	−	0.310989i
$604$	2.81919	−	10.5214i	0.114711	−	0.428108i
$605$	−94.1122	+	25.2173i	−3.82620	+	1.02523i
$606$	−1.36059	+	2.67989i	−0.0552700	+	0.108863i
$607$	−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
$609$	−0.403647	+	0.423652i	−0.0163566	+	0.0171673i
$610$		−	12.0454i		−	0.487703i
$611$	34.2608	+	8.90885i	1.38604	+	0.360413i
$612$	−4.93208	+	11.1646i	−0.199368	+	0.451302i
$613$	−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	−1.00000		0.000106988i	$-0.999966\pi$
$617$	−24.8368	+	24.8368i	−0.999893	+	0.999893i	0.000106988		1.00000i	$0.499966\pi$
$618$	18.5638	−	12.0938i	0.746746	−	0.486482i
$619$	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
$621$	28.3492	+	2.85508i	1.13761	+	0.114571i
$622$	−9.05222	+	9.05222i	−0.362961	+	0.362961i
$623$	−8.32155	+	1.96747i	−0.333396	+	0.0788252i
$624$	4.13748	−	4.67774i	0.165632	−	0.187260i
$625$	−8.57988	−	14.8608i	−0.343195	−	0.594431i
$626$	−4.22379	−	15.7634i	−0.168817	−	0.630033i
$627$	−7.88864	−	24.1596i	−0.315042	−	0.964841i
$628$	−6.45864	+	3.72889i	−0.257728	+	0.148799i
$629$	22.5843	−	22.5843i	0.900494	−	0.900494i
$630$	15.0694	+	21.9521i	0.600379	+	0.874594i
$631$	−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
$633$	22.5887	−	7.37572i	0.897821	−	0.293159i
$634$	−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
$639$	5.67576	−	36.5200i	0.224530	−	1.44471i
$640$	1.67733	−	2.90521i	0.0663022	−	0.114839i
$641$	12.8018	−	22.1734i	0.505641	−	0.875795i	−0.494338	−	0.869270i	$-0.664589\pi$
$641$	12.8018	−	22.1734i	0.505641	−	0.875795i	0.999979	−	0.00652568i	$-0.00207720\pi$
$642$	−25.3127	+	16.4904i	−0.999011	+	0.650825i
$643$	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
$645$	−0.800293	−	14.8585i	−0.0315115	−	0.585055i
$646$	4.71697	+	8.17003i	0.185587	+	0.321446i
$647$	−0.186170	+	0.322457i	−0.00731911	+	0.0126771i	−0.869662	−	0.493648i	$-0.835663\pi$
$647$	−0.186170	+	0.322457i	−0.00731911	+	0.0126771i	0.862343	+	0.506325i	$0.168996\pi$
$648$	7.99524	−	4.13232i	0.314083	−	0.162333i
$649$	35.0959	−	20.2626i	1.37763	−	0.795377i
$650$	15.8254	−	16.0615i	0.620723	−	0.629982i
$651$	−6.88935	−	3.75850i	−0.270015	−	0.147307i
$652$	−6.55996	−	6.55996i	−0.256908	−	0.256908i
$653$	6.47137	−	3.73625i	0.253244	−	0.146211i	−0.368005	−	0.929824i	$-0.619959\pi$
$653$	6.47137	−	3.73625i	0.253244	−	0.146211i	0.621249	+	0.783613i	$0.286626\pi$
$654$	8.69511	−	2.83915i	0.340006	−	0.111019i
$655$	−12.4918	+	3.34717i	−0.488096	+	0.130785i
$656$	−9.73017	−	2.60719i	−0.379899	−	0.101794i
$657$	9.87389	+	7.94846i	0.385217	+	0.310099i
$658$	25.9652	+	0.769612i	1.01223	+	0.0300026i
$659$		−	32.4190i		−	1.26286i	−0.775431	−	0.631432i	$-0.782468\pi$
$659$		−	32.4190i		−	1.26286i	0.775431	−	0.631432i	$-0.217532\pi$
$660$	−35.9761	−	7.59249i	−1.40037	−	0.295537i
$661$	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
$663$	24.8983	+	5.06238i	0.966970	+	0.196606i
$664$	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
$669$	−8.90194	−	4.51953i	−0.344169	−	0.174735i
$670$	−10.5890	−	2.83732i	−0.409089	−	0.109615i
$671$	16.0666	+	16.0666i	0.620246	+	0.620246i
$672$	2.19468	−	4.02286i	0.0846615	−	0.155185i
$673$		−	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
$675$	29.6281	−	13.3459i	1.14039	−	0.513683i
$676$	−11.3533	−	6.33261i	−0.436666	−	0.243562i
$677$	21.2839	−	12.2883i	0.818006	−	0.472276i	−0.0317225	−	0.999497i	$-0.510099\pi$
$677$	21.2839	−	12.2883i	0.818006	−	0.472276i	0.849728	+	0.527221i	$0.176766\pi$
$678$	0.0565096	+	1.04918i	0.00217024	+	0.0402934i
$679$	2.61368	−	8.71307i	0.100304	−	0.334377i
$680$	13.6484			0.523392
$681$	−16.1218	−	24.7469i	−0.617790	−	0.948303i
$682$	10.4678	−	2.80484i	0.400833	−	0.107403i
$683$	30.6088	−	8.20161i	1.17121	−	0.313826i	0.379778	−	0.925078i	$-0.376000\pi$
$683$	30.6088	−	8.20161i	1.17121	−	0.313826i	0.791436	+	0.611252i	$0.209334\pi$
$684$	1.06830	−	6.87382i	0.0408473	−	0.262827i
$685$	−8.22735			−0.314351
$686$	17.3930	+	6.36263i	0.664068	+	0.242926i
$687$	17.1864	−	0.925671i	0.655700	−	0.0353165i
$688$	−2.21783	+	1.28046i	−0.0845539	+	0.0488172i
$689$	−5.52515	+	9.73557i	−0.210491	+	0.370896i
$690$	−9.88945	−	30.2872i	−0.376485	−	1.15301i
$691$	−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
$693$	−49.3810	−	9.18051i	−1.87583	−	0.348739i
$694$	−14.7691	−	14.7691i	−0.560629	−	0.560629i
$695$	−56.0189	−	15.0102i	−2.12492	−	0.569370i
$696$	0.100123	−	0.197209i	0.00379516	−	0.00747518i
$697$	−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	$-0.561205\pi$
$701$	−10.1192			−0.382196			−0.191098	+	0.981571i	$0.561205\pi$
$702$	−11.9606	−	14.4203i	−0.451422	−	0.544259i
$703$	−9.10158	+	15.7644i	−0.343273	+	0.594566i
$704$	1.63781	+	6.11240i	0.0617274	+	0.230370i
$705$	11.7801	−	55.8186i	0.443664	−	2.10225i
$706$			18.4274i			0.693525i
$707$	4.58896	+	0.136017i	0.172585	+	0.00511546i
$708$	11.0762	−	0.596570i	0.416267	−	0.0224205i
$709$	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
$711$	16.5656	+	7.31804i	0.621259	+	0.274448i
$712$	2.79896	−	1.61598i	0.104896	−	0.0605615i
$713$	6.64016	+	6.64016i	0.248676	+	0.248676i
$714$	18.6387	−	0.450723i	0.697537	−	0.0168679i
$715$	0.566588	+	76.5377i	0.0211892	+	2.86235i
$716$	−8.43169	+	4.86804i	−0.315107	+	0.181927i
$717$	−3.41374	+	6.72391i	−0.127488	+	0.251109i
$718$	−4.32177	+	7.48552i	−0.161287	+	0.279357i
$719$	−20.6861	−	35.8293i	−0.771460	−	1.33621i	−0.936763	−	0.349966i	$-0.886193\pi$
$719$	−20.6861	−	35.8293i	−0.771460	−	1.33621i	0.165302	−	0.986243i	$-0.447140\pi$
$720$	−7.83949	−	6.31076i	−0.292160	−	0.235188i
$721$	−28.7950	−	17.7826i	−1.07238	−	0.662259i
$722$	9.63310	+	9.63310i	0.358507	+	0.358507i
$723$	−16.8650	−	25.8876i	−0.627216	−	0.962771i
$724$	0.206549	−	0.357753i	0.00767633	−	0.0132958i
$725$	0.399275	−	0.691564i	0.0148287	−	0.0256840i
$726$	42.1499	−	27.4594i	1.56433	−	1.01911i
$727$			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
$732$	1.93040	+	5.91200i	0.0713496	+	0.218514i
$733$	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
$735$	20.5283	−	35.1124i	0.757198	−	1.29514i
$736$	−3.87735	+	3.87735i	−0.142921	+	0.142921i
$737$	17.9086	−	10.3396i	0.659673	−	0.380862i
$738$	−12.2116	+	27.6431i	−0.449516	+	1.01756i
$739$	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
$741$	−14.4537	+	0.885835i	−0.530968	+	0.0325420i
$742$	−2.36014	+	7.86788i	−0.0866435	+	0.288839i
$743$	−1.93223	+	1.93223i	−0.0708866	+	0.0708866i	−0.741661	−	0.670775i	$-0.765962\pi$
$743$	−1.93223	+	1.93223i	−0.0708866	+	0.0708866i	0.670775	+	0.741661i	$0.265962\pi$
$744$	2.90230	+	0.612508i	0.106403	+	0.0224556i
$745$	17.0639	+	9.85183i	0.625172	+	0.360943i
$746$	0.335393	+	1.25170i	0.0122796	+	0.0458282i
$747$	0.257493	−	1.65681i	0.00942118	−	0.0606194i
$748$	−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
$753$	−41.7651	+	13.6372i	−1.52200	+	0.496968i
$754$	−0.445583	−	0.115865i	−0.0162272	−	0.00421957i
$755$			36.5406i			1.32985i
$756$	−10.9143	−	8.35932i	−0.396949	−	0.304025i
$757$	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
$759$	53.5895	+	27.2075i	1.94517	+	0.987568i
$760$	−7.51365	+	2.01328i	−0.272549	+	0.0730292i
$761$	−8.27536	+	30.8841i	−0.299981	+	1.11955i	0.637198	+	0.770700i	$0.280093\pi$
$761$	−8.27536	+	30.8841i	−0.299981	+	1.11955i	−0.937180	+	0.348846i	$0.886573\pi$
$762$	1.91070	+	35.4747i	0.0692173	+	1.28511i
$763$	−9.58273	−	10.1682i	−0.346918	−	0.368112i
$764$	−24.3157			−0.879711
$765$	6.28801	−	40.4594i	0.227344	−	1.46281i
$766$	7.94149	+	4.58502i	0.286938	+	0.165664i
$767$	−6.14114	−	22.2586i	−0.221744	−	0.803713i
$768$	−0.357658	+	1.69472i	−0.0129059	+	0.0611530i
$769$	−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	$0.0318632\pi$
$773$	5.09546	+	19.0165i	0.183271	+	0.683977i	−0.811723	+	0.584043i	$0.801470\pi$
$774$	2.77403	+	7.16448i	0.0997106	+	0.257522i
$775$	10.3448	+	2.77189i	0.371598	+	0.0995694i
$776$			3.43821i			0.123424i
$777$	18.7353	+	30.7111i	0.672124	+	1.10175i
$778$	25.0967	−	25.0967i	0.899761	−	0.899761i
$779$	11.6790	+	20.2286i	0.418444	+	0.724766i
$780$	−9.34541	+	18.7499i	−0.334620	+	0.671353i
$781$	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
$786$	5.59470	−	3.64478i	0.199556	−	0.130005i
$787$	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
$789$	−31.8961	−	6.73144i	−1.13553	−	0.239646i
$790$		−	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
$795$	16.0853	+	8.16651i	0.570485	+	0.289636i
$796$	−11.3951	−	19.7369i	−0.403889	−	0.699556i
$797$	−21.8139			−0.772687			−0.386344	−	0.922355i	$-0.626262\pi$
$797$	−21.8139			−0.772687			−0.386344	+	0.922355i	$0.626262\pi$
$798$	−10.1944	+	2.99753i	−0.360879	+	0.106111i
$799$	−28.2456	−	28.2456i	−0.999259	−	0.999259i
$800$	−1.61858	+	6.04061i	−0.0572253	+	0.213568i
$801$	−3.50091	−	9.04179i	−0.123699	−	0.319476i
$802$	7.50852	−	13.0051i	0.265135	−	0.459227i
$803$	13.3686	+	23.1551i	0.471768	+	0.817127i
$804$	5.65191	−	0.304416i	0.199328	−	0.0107359i
$805$	−35.4182	+	33.3790i	−1.24833	+	1.17646i
$806$	−0.0457083	−	6.17452i	−0.00161001	−	0.217488i
$807$	8.80215	+	1.85763i	0.309850	+	0.0653916i
$808$	−1.67610	+	0.449109i	−0.0589649	+	0.0157996i
$809$	8.41983	+	4.86119i	0.296026	+	0.170910i	0.640656	−	0.767828i	$-0.278662\pi$
$809$	8.41983	+	4.86119i	0.296026	+	0.170910i	−0.344631	+	0.938738i	$0.611996\pi$
$810$	−22.3195	+	20.3320i	−0.784226	+	0.714394i
$811$	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
$813$	−7.52390	+	0.405243i	−0.263875	+	0.0142125i
$814$	−47.9843	−	12.8574i	−1.68185	−	0.450650i
$815$	26.9522	+	15.5609i	0.944095	+	0.545073i
$816$	−6.69878	+	2.18730i	−0.234504	+	0.0765709i
$817$	5.73588	+	1.53692i	0.200673	+	0.0537702i
$818$	−28.2076			−0.986256
$819$	−12.1432	+	25.9141i	−0.424319	+	0.905513i
$820$	33.7928			1.18010
$821$	−47.1195	−	12.6256i	−1.64448	−	0.440638i	−0.686421	−	0.727204i	$-0.740819\pi$
$821$	−47.1195	−	12.6256i	−1.64448	−	0.440638i	−0.958060	+	0.286566i	$0.907486\pi$
$822$	4.03807	−	1.31852i	0.140844	−	0.0459887i
$823$	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
$825$	68.4442	−	3.68646i	2.38292	−	0.128346i
$826$	−8.03336	−	14.9182i	−0.279516	−	0.519069i
$827$	−22.1257	−	22.1257i	−0.769387	−	0.769387i	0.208612	−	0.977999i	$-0.433105\pi$
$827$	−22.1257	−	22.1257i	−0.769387	−	0.769387i	−0.977999	+	0.208612i	$0.933105\pi$
$828$	9.70771	+	13.2804i	0.337366	+	0.461526i
$829$	−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
$831$	−12.0110	−	2.53484i	−0.416658	−	0.0879327i
$832$	3.60545	−	0.0266902i	0.124997	−	0.000925316i
$833$	−12.7539	−	25.4640i	−0.441897	−	0.882276i
$834$	29.9002	−	1.61045i	1.03536	−	0.0557653i
$835$	18.6358	+	32.2782i	0.644919	+	1.11703i
$836$	7.33664	−	12.7074i	0.253743	−	0.439496i
$837$	3.15286	−	8.32141i	0.108979	−	0.287630i
$838$	5.93842	−	22.1625i	0.205139	−	0.765591i
$839$	35.7272	+	35.7272i	1.23344	+	1.23344i	0.962634	+	0.270806i	$0.0872901\pi$
$839$	35.7272	+	35.7272i	1.23344	+	1.23344i	0.270806	+	0.962634i	$0.412710\pi$
$840$	−3.61867	+	14.9410i	−0.124856	+	0.515513i
$841$	28.9837			0.999438
$842$	−12.6568	−	21.9222i	−0.436181	−	0.755488i
$843$	−16.3180	−	8.28469i	−0.562022	−	0.285340i
$844$	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
$849$	19.7860	+	4.17570i	0.679055	+	0.143310i
$850$	−24.5762	+	6.58517i	−0.842956	+	0.225869i
$851$	−11.1412	−	41.5797i	−0.381917	−	1.42533i
$852$	17.8786	−	11.6474i	0.612512	−	0.399033i
$853$	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	−0.982518	−	0.186166i	$-0.940394\pi$
$857$	−9.66161	+	16.7344i	−0.330034	+	0.571636i	0.652484	+	0.757803i	$0.273727\pi$
$858$	−12.5441	−	37.4747i	−0.428248	−	1.27937i
$859$	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
$861$	46.1487	−	1.11597i	1.57274	−	0.0380321i
$862$			10.7771i			0.367069i
$863$	−7.73101	−	2.07152i	−0.263167	−	0.0705153i	0.124823	−	0.992179i	$-0.460164\pi$
$863$	−7.73101	−	2.07152i	−0.263167	−	0.0705153i	−0.387990	+	0.921664i	$0.626830\pi$
$864$	4.85907	+	1.84103i	0.165309	+	0.0626331i
$865$	−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
$870$	−0.153208	+	0.725957i	−0.00519423	+	0.0246122i
$871$	−3.13369	−	11.3581i	−0.106181	−	0.384854i
$872$	4.57345	+	2.64048i	0.154877	+	0.0894180i
$873$	10.1923	+	1.58403i	0.344956	+	0.0536114i
$874$	12.7148			0.430084
$875$	−3.19713	+	10.6581i	−0.108083	+	0.360309i
$876$	0.393598	+	7.30769i	0.0132984	+	0.246904i
$877$	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
$879$	25.3133	+	12.8516i	0.853795	+	0.433473i
$880$	−10.6142	−	18.3843i	−0.357803	−	0.619733i
$881$	17.8123			0.600111			0.300056	−	0.953922i	$-0.402995\pi$
$881$	17.8123			0.600111			0.300056	+	0.953922i	$0.402995\pi$
$882$	−4.44838	+	20.5234i	−0.149785	+	0.691060i
$883$			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
$885$	−35.3726	+	11.5499i	−1.18904	+	0.388247i
$886$	13.6666	−	3.66196i	0.459139	−	0.123026i
$887$	−13.0811	+	7.55237i	−0.439220	+	0.253584i	−0.703267	−	0.710926i	$-0.748276\pi$
$887$	−13.0811	+	7.55237i	−0.439220	+	0.253584i	0.264047	+	0.964510i	$0.414943\pi$
$888$	−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
$891$	2.65097	−	56.8905i	0.0888109	−	1.90590i
$892$	−1.49183	−	5.56759i	−0.0499502	−	0.186417i
$893$	19.7162	+	11.3831i	0.659777	+	0.380922i
$894$	−9.95400	−	2.10072i	−0.332911	−	0.0702585i
$895$	23.0949	−	23.0949i	0.771979	−	0.771979i
$896$	2.57477	−	0.608755i	0.0860169	−	0.0203371i
$897$	22.6874	−	25.6499i	0.757511	−	0.856426i
$898$	−11.8720	−	20.5629i	−0.396174	−	0.686193i
$899$	−0.0565985	−	0.211228i	−0.00188766	−	0.00704486i
$900$	17.1612	+	7.58113i	0.572038	+	0.252704i
$901$	10.9391	−	6.31571i	0.364435	−	0.210407i
$902$	−45.0744	+	45.0744i	−1.50081	+	1.50081i
$903$	8.09531	−	8.49653i	0.269395	−	0.282747i
$904$	−0.428946	+	0.428946i	−0.0142665	+	0.0142665i
$905$	−0.358672	+	1.33858i	−0.0119226	+	0.0444959i
$906$	−5.85603	−	17.9345i	−0.194554	−	0.595835i
$907$	−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	$-0.742153\pi$
$911$		−	43.7241i		−	1.44864i	0.689462	−	0.724322i	$-0.257847\pi$
$912$	3.36513	−	2.19228i	0.111431	−	0.0725937i
$913$	1.76836	−	3.06289i	0.0585243	−	0.101367i
$914$	−19.2768	+	33.3885i	−0.637621	+	1.10439i
$915$	−11.3882	−	17.4809i	−0.376484	−	0.577899i
$916$	7.02647	+	7.02647i	0.232161	+	0.232161i
$917$	−8.67814	−	5.35926i	−0.286578	−	0.176978i
$918$	3.39784	+	20.8657i	0.112145	+	0.688670i
$919$	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
$921$	−20.6861	+	40.7447i	−0.681631	+	1.34258i
$922$	2.79109	−	1.61144i	0.0919196	−	0.0530698i
$923$	−31.6402	−	31.1752i	−1.04145	−	1.02614i
$924$	−15.1022	−	24.7557i	−0.496826	−	0.814403i
$925$	−34.7144	−	34.7144i	−1.14140	−	1.14140i
$926$	12.7418	−	7.35647i	0.418721	−	0.241749i
$927$	15.5068	−	35.1022i	0.509309	−	1.15291i
$928$	0.123341	−	0.0330492i	0.00404888	−	0.00108489i
$929$	−20.3377	−	5.44946i	−0.667257	−	0.178791i	−0.0907383	−	0.995875i	$-0.528923\pi$
$929$	−20.3377	−	5.44946i	−0.667257	−	0.178791i	−0.576519	+	0.817084i	$0.695589\pi$
$930$	−9.93625	+	0.535175i	−0.325823	+	0.0175491i
$931$	10.7774	+	12.1370i	0.353216	+	0.397774i
$932$			18.3858i			0.602248i
$933$	−4.57866	+	21.6954i	−0.149899	+	0.710277i
$934$	0.499386	+	1.86373i	0.0163404	+	0.0609832i
$935$	43.1836	−	74.7963i	1.41226	−	2.44610i
$936$	1.58196	−	10.7003i	0.0517081	−	0.349752i
$937$	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	0.999988	−	0.00485964i	$-0.00154688\pi$
$941$	4.03518	+	15.0595i	0.131543	+	0.490926i	−0.868445	+	0.495786i	$0.834880\pi$
$942$	−5.84764	+	11.5179i	−0.190526	+	0.375272i
$943$	−53.3544	−	14.2963i	−1.73746	−	0.465551i
$944$	4.52837	+	4.52837i	0.147386	+	0.147386i
$945$	42.6241	+	17.6108i	1.38656	+	0.572878i
$946$			16.2056i			0.526889i
$947$	−11.0500	+	41.2392i	−0.359077	+	1.34009i	0.516198	+	0.856469i	$0.327347\pi$
$947$	−11.0500	+	41.2392i	−0.359077	+	1.34009i	−0.875275	+	0.483625i	$0.839320\pi$
$948$	3.24544	+	9.93940i	0.105407	+	0.322817i
$949$	14.6855	−	4.05173i	0.476713	−	0.131525i
$950$	12.5582	−	7.25047i	0.407441	−	0.235236i
$951$	−0.628617	+	0.0338578i	−0.0203843	+	0.00109791i
$952$	7.38261	+	7.83362i	0.239272	+	0.253889i
$953$	−24.5509			−0.795283			−0.397641	−	0.917541i	$-0.630171\pi$
$953$	−24.5509			−0.795283			−0.397641	+	0.917541i	$0.630171\pi$
$954$	−9.20359	−	1.43038i	−0.297977	−	0.0463102i
$955$	78.7913	−	21.1121i	2.54963	−	0.683170i
$956$	−4.20537	+	1.12682i	−0.136011	+	0.0364441i
$957$	−0.763958	−	1.17267i	−0.0246953	−	0.0379070i
$958$	−4.71803			−0.152433
$959$	−4.45029	−	4.72216i	−0.143707	−	0.152487i
$960$	−0.312501	−	5.80202i	−0.0100859	−	0.187259i
$961$	−24.3069	+	14.0336i	−0.784093	+	0.452696i
$962$	−13.9705	+	24.6167i	−0.450428	+	0.793675i
$963$	−21.1442	+	47.8635i	−0.681363	+	1.54238i
$964$	4.61685	−	17.2303i	0.148699	−	0.554951i
$965$		−	2.92485i		−	0.0941542i
$966$	12.0343	−	22.0589i	0.387197	−	0.709735i
$967$	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
$969$	14.5698	+	7.39713i	0.468051	+	0.237630i
$970$	−2.98522	−	11.1410i	−0.0958496	−	0.357715i
$971$	17.9367	−	10.3557i	0.575615	−	0.332332i	−0.183774	−	0.982969i	$-0.558831\pi$
$971$	17.9367	−	10.3557i	0.575615	−	0.332332i	0.759389	+	0.650637i	$0.225498\pi$
$972$	7.69622	−	13.5561i	0.246856	−	0.434812i
$973$	−21.6862	−	40.2718i	−0.695226	−	1.29105i
$974$	−17.0911			−0.547633
$975$	7.78140	−	38.2713i	0.249204	−	1.22566i
$976$	−1.79532	+	3.10959i	−0.0574669	+	0.0995355i
$977$	4.50162	+	16.8003i	0.144020	+	0.537489i	0.999797	+	0.0201445i	$0.00641264\pi$
$977$	4.50162	+	16.8003i	0.144020	+	0.537489i	−0.855777	+	0.517344i	$0.826921\pi$
$978$	−15.7222	−	3.31806i	−0.502742	−	0.106100i
$979$		−	20.4519i		−	0.653647i
$980$	23.0026	−	4.72363i	0.734790	−	0.150891i
$981$	9.93453	−	12.3411i	0.317185	−	0.394020i
$982$	23.9908	+	6.42832i	0.765578	+	0.205136i
$983$	−13.4884	+	3.61420i	−0.430212	+	0.115275i	−0.467426	−	0.884032i	$-0.654819\pi$
$983$	−13.4884	+	3.61420i	−0.430212	+	0.115275i	0.0372135	+	0.999307i	$0.488152\pi$
$984$	−16.5859	+	5.41566i	−0.528739	+	0.172645i
$985$	−13.7650	+	7.94724i	−0.438590	+	0.253220i
$986$	0.367353	+	0.367353i	0.0116989	+	0.0116989i
$987$	38.4096	−	23.4318i	1.22259	−	0.745842i
$988$	−5.95535	−	5.86783i	−0.189465	−	0.186680i
$989$	−12.1612	+	7.02129i	−0.386705	+	0.223264i
$990$	−59.3886	+	22.9948i	−1.88749	+	0.730824i
$991$	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
$993$	1.27468	+	23.6662i	0.0404507	+	0.751023i
$994$	−27.7322	−	17.1263i	−0.879612	−	0.543212i
$995$	54.0606	+	54.0606i	1.71384	+	1.71384i
$996$	0.811103	−	0.528409i	0.0257008	−	0.0167433i
$997$	−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
$999$	−31.5890	+	25.8085i	−0.999433	+	0.816544i

Twists

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

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

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)

\(f(q)\)	\(=\)	\(q+(0.965926 + 0.258819i) q^{2} +(1.64650 - 0.537619i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-3.24035 - 0.868248i) q^{5} +(1.72954 - 0.0931546i) q^{6} +(-1.25441 - 2.32948i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.42193 - 1.77038i) q^{9} +O(q^{10})\)	\(q+(0.965926 + 0.258819i) q^{2} +(1.64650 - 0.537619i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-3.24035 - 0.868248i) q^{5} +(1.72954 - 0.0931546i) q^{6} +(-1.25441 - 2.32948i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.42193 - 1.77038i) q^{9} +(-2.90521 - 1.67733i) q^{10} +(6.11240 - 1.63781i) q^{11} +(1.69472 + 0.357658i) q^{12} +(-0.0266902 - 3.60545i) q^{13} +(-0.608755 - 2.57477i) q^{14} +(-5.80202 + 0.312501i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-2.03425 + 3.52342i) q^{17} +(2.79761 - 1.08322i) q^{18} +(0.600144 - 2.23977i) q^{19} +(-2.37210 - 2.37210i) q^{20} +(-3.31776 - 3.16109i) q^{21} +6.32802 q^{22} +(2.74170 + 4.74876i) q^{23} +(1.54441 + 0.784098i) 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} +(-5.68520 - 1.19982i) q^{30} +(1.65420 - 0.443241i) q^{31} +(0.258819 + 0.965926i) q^{32} +(9.18355 - 5.98280i) 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} +(-1.98231 - 5.92203i) q^{39} +(-1.67733 - 2.90521i) q^{40} +(-7.12298 + 7.12298i) q^{41} +(-2.38656 - 3.91208i) q^{42} +2.56093i q^{43} +(6.11240 + 1.63781i) q^{44} +(-9.38502 + 3.63381i) 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} +(-1.45513 + 6.89496i) q^{51} +(1.77961 - 3.13576i) q^{52} +(-2.68874 - 1.55235i) q^{53} +(4.02392 - 3.28757i) q^{54} -21.2283 q^{55} +(0.760185 - 2.53419i) q^{56} +(-0.216005 - 4.01043i) q^{57} +(0.0330492 - 0.123341i) q^{58} +(6.18587 - 1.65750i) q^{59} +(-5.18095 - 2.63038i) q^{60} +(1.79532 + 3.10959i) q^{61} +1.71255 q^{62} +(-7.16216 - 3.42104i) q^{63} +1.00000i q^{64} +(-3.04394 + 11.7061i) q^{65} +(10.4191 - 3.40207i) 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} +(2.96441 + 0.460715i) q^{72} +(1.09357 + 4.08124i) q^{73} +(-6.79858 - 3.92516i) q^{74} +(10.5983 + 2.23669i) q^{75} +(1.63962 - 1.63962i) q^{76} +(-11.4827 - 12.1842i) q^{77} +(-0.382026 - 6.23330i) q^{78} +(3.01834 + 5.22792i) q^{79} +(-0.868248 - 3.24035i) q^{80} +(2.73150 - 8.57548i) q^{81} +(-8.72383 + 5.03671i) q^{82} +(0.395201 - 0.395201i) q^{83} +(-1.29272 - 4.39646i) q^{84} +(9.65087 - 9.65087i) q^{85} +(-0.662816 + 2.47366i) q^{86} +(-0.0686499 - 0.210246i) 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} +(2.48534 - 1.61912i) q^{93} +(-4.90911 + 8.50283i) q^{94} +(-3.88935 + 6.73655i) q^{95} +(0.945446 + 1.45125i) q^{96} +(2.43118 + 2.43118i) q^{97} +(-5.23422 + 4.64789i) q^{98} +(11.9043 - 14.7879i) 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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