LMFDB - Embedded newform 702.2.bs.a.5.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [702,2,Mod(5,702)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(702, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([10, 27]))

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

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

chi := DirichletCharacter("702.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 702 = 2 \cdot 3^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	702.bs (of order $36$, degree $12$, 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:	$5.60549822189$
Analytic rank:	$0$
Dimension:	$504$
Relative dimension:	$42$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			5.9
Character	$\chi$	$=$	702.5
Dual form			702.2.bs.a.281.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.996195 - 0.0871557i) q^{2} +(-0.624455 + 1.61557i) q^{3} +(0.984808 + 0.173648i) q^{4} +(-3.34201 - 1.55841i) q^{5} +(0.762885 - 1.55499i) q^{6} +(-0.371998 + 0.531269i) q^{7} +(-0.965926 - 0.258819i) q^{8} +(-2.22011 - 2.01770i) q^{9} +(3.19347 + 1.84375i) q^{10} +(2.16932 - 1.01157i) q^{11} +(-0.895509 + 1.48259i) q^{12} +(-3.44065 - 1.07794i) q^{13} +(0.416886 - 0.496825i) q^{14} +(4.60465 - 4.42609i) q^{15} +(0.939693 + 0.342020i) q^{16} +(0.586965 - 1.01665i) q^{17} +(2.03581 + 2.20352i) q^{18} +(6.50411 + 1.74277i) q^{19} +(-3.02063 - 2.11507i) q^{20} +(-0.626004 - 0.932742i) q^{21} +(-2.24923 + 0.818653i) q^{22} +(-0.948289 + 5.37801i) q^{23} +(1.02132 - 1.39890i) q^{24} +(5.52648 + 6.58621i) q^{25} +(3.33360 + 1.37371i) q^{26} +(4.64609 - 2.32678i) q^{27} +(-0.458601 + 0.458601i) q^{28} +(-4.08659 - 4.87021i) q^{29} +(-4.97288 + 4.00793i) q^{30} +(3.22653 + 4.60797i) q^{31} +(-0.906308 - 0.422618i) q^{32} +(0.279617 + 4.13636i) q^{33} +(-0.673339 + 0.961628i) q^{34} +(2.07116 - 1.19578i) q^{35} +(-1.83601 - 2.37256i) q^{36} +(6.33950 - 1.69867i) q^{37} +(-6.32747 - 2.30301i) q^{38} +(3.89002 - 4.88546i) q^{39} +(2.82479 + 2.37028i) q^{40} +(-0.647875 - 7.40524i) q^{41} +(0.542328 + 0.983752i) q^{42} +(-1.74919 + 4.80587i) q^{43} +(2.31202 - 0.619504i) q^{44} +(4.27525 + 10.2030i) q^{45} +(1.41340 - 5.27490i) q^{46} +(5.84259 + 4.09102i) q^{47} +(-1.13935 + 1.30456i) q^{48} +(2.25028 + 6.18259i) q^{49} +(-4.93143 - 7.04281i) q^{50} +(1.27594 + 1.58314i) q^{51} +(-3.20119 - 1.65903i) q^{52} +8.02983i q^{53} +(-4.83120 + 1.91299i) q^{54} -8.82634 q^{55} +(0.496825 - 0.416886i) q^{56} +(-6.87709 + 9.41955i) q^{57} +(3.64657 + 5.20785i) q^{58} +(1.15461 - 2.47606i) q^{59} +(5.30327 - 3.55926i) q^{60} +(0.846233 + 4.79922i) q^{61} +(-2.81265 - 4.87164i) q^{62} +(1.89782 - 0.428895i) q^{63} +(0.866025 + 0.500000i) q^{64} +(9.81881 + 8.96442i) q^{65} +(0.0819554 - 4.14499i) q^{66} +(-3.63401 + 0.317935i) q^{67} +(0.754588 - 0.899283i) q^{68} +(-8.09637 - 4.89035i) q^{69} +(-2.16749 + 1.01072i) q^{70} +(-1.36940 + 0.366929i) q^{71} +(1.62224 + 2.52355i) q^{72} +(2.20581 - 8.23218i) q^{73} +(-6.46343 + 1.13968i) q^{74} +(-14.0915 + 4.81561i) q^{75} +(6.10267 + 2.84572i) q^{76} +(-0.269568 + 1.52880i) q^{77} +(-4.30101 + 4.52784i) q^{78} +(9.84516 - 8.26107i) q^{79} +(-2.60746 - 2.60746i) q^{80} +(0.857788 + 8.95903i) q^{81} +7.43353i q^{82} +(17.5076 + 1.53172i) q^{83} +(-0.454524 - 1.02728i) q^{84} +(-3.54601 + 2.48294i) q^{85} +(2.16139 - 4.63513i) q^{86} +(10.4200 - 3.56093i) q^{87} +(-2.35722 + 0.415641i) q^{88} +(16.7680 + 4.49298i) q^{89} +(-3.36973 - 10.5368i) q^{90} +(1.85259 - 1.42691i) q^{91} +(-1.86776 + 5.13164i) q^{92} +(-9.45931 + 2.33521i) q^{93} +(-5.46380 - 4.58467i) q^{94} +(-19.0209 - 15.9604i) q^{95} +(1.24872 - 1.20029i) q^{96} +(-0.0772885 + 0.0360402i) q^{97} +(-1.70287 - 6.35518i) q^{98} +(-6.85718 - 2.13124i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 504 q - 24 q^{11} + 24 q^{15} + 24 q^{21} - 144 q^{27} + 24 q^{39} + 48 q^{41} + 12 q^{45} + 132 q^{47} + 24 q^{50} + 72 q^{54} - 72 q^{57} + 12 q^{63} - 156 q^{65} + 96 q^{66} - 48 q^{72} + 36 q^{73} - 96 q^{74}+ \cdots - 144 q^{99}+O(q^{100}) $ 504 * q - 24 * q^11 + 24 * q^15 + 24 * q^21 - 144 * q^27 + 24 * q^39 + 48 * q^41 + 12 * q^45 + 132 * q^47 + 24 * q^50 + 72 * q^54 - 72 * q^57 + 12 * q^63 - 156 * q^65 + 96 * q^66 - 48 * q^72 + 36 * q^73 - 96 * q^74 - 24 * q^78 + 288 * q^79 + 24 * q^83 + 24 * q^84 - 144 * q^85 - 96 * q^86 - 192 * q^87 + 96 * q^92 - 60 * q^93 - 72 * q^98 - 144 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/702\mathbb{Z}\right)^\times$.

$n$	$379$	$677$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{18}\right)$

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 $

$2$	−0.996195	−	0.0871557i	−0.704416	−	0.0616284i
$2$	−0.996195	−	0.0871557i	−0.704416	−	0.0616284i
$3$	−0.624455	+	1.61557i	−0.360529	+	0.932748i
$3$	−0.624455	+	1.61557i	−0.360529	+	0.932748i
$4$	0.984808	+	0.173648i	0.492404	+	0.0868241i
$5$	−3.34201	−	1.55841i	−1.49459	−	0.696941i	−0.508185	−	0.861248i	$-0.669683\pi$
$5$	−3.34201	−	1.55841i	−1.49459	−	0.696941i	−0.986409	+	0.164308i	$0.947461\pi$
$6$	0.762885	−	1.55499i	0.311446	−	0.634824i
$7$	−0.371998	+	0.531269i	−0.140602	+	0.200801i	−0.883277	−	0.468852i	$-0.844668\pi$
$7$	−0.371998	+	0.531269i	−0.140602	+	0.200801i	0.742675	+	0.669652i	$0.233557\pi$
$8$	−0.965926	−	0.258819i	−0.341506	−	0.0915064i
$9$	−2.22011	−	2.01770i	−0.740037	−	0.672566i
$10$	3.19347	+	1.84375i	1.00986	+	0.583046i
$11$	2.16932	−	1.01157i	0.654075	−	0.305000i	−0.0671070	−	0.997746i	$-0.521377\pi$
$11$	2.16932	−	1.01157i	0.654075	−	0.305000i	0.721182	+	0.692746i	$0.243599\pi$
$12$	−0.895509	+	1.48259i	−0.258511	+	0.427986i
$13$	−3.44065	−	1.07794i	−0.954263	−	0.298968i
$13$	−3.44065	−	1.07794i	−0.954263	−	0.298968i
$14$	0.416886	−	0.496825i	0.111417	−	0.132782i
$15$	4.60465	−	4.42609i	1.18891	−	1.14281i
$16$	0.939693	+	0.342020i	0.234923	+	0.0855050i
$17$	0.586965	−	1.01665i	0.142360	−	0.246575i	−0.786025	−	0.618195i	$-0.787864\pi$
$17$	0.586965	−	1.01665i	0.142360	−	0.246575i	0.928385	+	0.371620i	$0.121198\pi$
$18$	2.03581	+	2.20352i	0.479845	+	0.519374i
$19$	6.50411	+	1.74277i	1.49215	+	0.399819i	0.910461	−	0.413595i	$-0.135727\pi$
$19$	6.50411	+	1.74277i	1.49215	+	0.399819i	0.581685	+	0.813414i	$0.302394\pi$
$20$	−3.02063	−	2.11507i	−0.675433	−	0.472943i
$21$	−0.626004	−	0.932742i	−0.136605	−	0.203541i
$22$	−2.24923	+	0.818653i	−0.479538	+	0.174537i
$23$	−0.948289	+	5.37801i	−0.197732	+	1.12139i	0.710742	+	0.703452i	$0.248359\pi$
$23$	−0.948289	+	5.37801i	−0.197732	+	1.12139i	−0.908474	+	0.417941i	$0.862752\pi$
$24$	1.02132	−	1.39890i	0.208475	−	0.285549i
$25$	5.52648	+	6.58621i	1.10530	+	1.31724i
$26$	3.33360	+	1.37371i	0.653773	+	0.269407i
$27$	4.64609	−	2.32678i	0.894140	−	0.447788i
$28$	−0.458601	+	0.458601i	−0.0866674	+	0.0866674i
$29$	−4.08659	−	4.87021i	−0.758861	−	0.904375i	0.238914	−	0.971041i	$-0.423208\pi$
$29$	−4.08659	−	4.87021i	−0.758861	−	0.904375i	−0.997775	+	0.0666653i	$0.978764\pi$
$30$	−4.97288	+	4.00793i	−0.907920	+	0.731744i
$31$	3.22653	+	4.60797i	0.579503	+	0.827616i	0.996698	−	0.0812014i	$-0.0258757\pi$
$31$	3.22653	+	4.60797i	0.579503	+	0.827616i	−0.417195	+	0.908817i	$0.636987\pi$
$32$	−0.906308	−	0.422618i	−0.160214	−	0.0747091i
$33$	0.279617	+	4.13636i	0.0486750	+	0.720049i
$34$	−0.673339	+	0.961628i	−0.115477	+	0.164918i
$35$	2.07116	−	1.19578i	0.350089	−	0.202124i
$36$	−1.83601	−	2.37256i	−0.306002	−	0.395427i
$37$	6.33950	−	1.69867i	1.04221	−	0.279259i	0.303180	−	0.952933i	$-0.401952\pi$
$37$	6.33950	−	1.69867i	1.04221	−	0.279259i	0.739028	+	0.673675i	$0.235285\pi$
$38$	−6.32747	−	2.30301i	−1.02645	−	0.373598i
$39$	3.89002	−	4.88546i	0.622901	−	0.782300i
$40$	2.82479	+	2.37028i	0.446639	+	0.374774i
$41$	−0.647875	−	7.40524i	−0.101181	−	1.15650i	−0.861780	−	0.507282i	$-0.830650\pi$
$41$	−0.647875	−	7.40524i	−0.101181	−	1.15650i	0.760599	−	0.649222i	$-0.224905\pi$
$42$	0.542328	+	0.983752i	0.0836830	+	0.151796i
$43$	−1.74919	+	4.80587i	−0.266749	+	0.732888i	0.731924	+	0.681387i	$0.238623\pi$
$43$	−1.74919	+	4.80587i	−0.266749	+	0.732888i	−0.998673	+	0.0515010i	$0.983599\pi$
$44$	2.31202	−	0.619504i	0.348550	−	0.0933938i
$45$	4.27525	+	10.2030i	0.637316	+	1.52097i
$46$	1.41340	−	5.27490i	0.208395	−	0.777741i
$47$	5.84259	+	4.09102i	0.852229	+	0.596737i	0.915978	−	0.401229i	$-0.131417\pi$
$47$	5.84259	+	4.09102i	0.852229	+	0.596737i	−0.0637490	+	0.997966i	$0.520306\pi$
$48$	−1.13935	+	1.30456i	−0.164451	+	0.188297i
$49$	2.25028	+	6.18259i	0.321468	+	0.883227i
$50$	−4.93143	−	7.04281i	−0.697409	−	0.996004i
$51$	1.27594	+	1.58314i	0.178667	+	0.221683i
$52$	−3.20119	−	1.65903i	−0.443925	−	0.230066i
$53$			8.02983i			1.10298i	0.834181	+	0.551491i	$0.185941\pi$
$53$			8.02983i			1.10298i	−0.834181	+	0.551491i	$0.814059\pi$
$54$	−4.83120	+	1.91299i	−0.657443	+	0.260325i
$55$	−8.82634			−1.19014
$56$	0.496825	−	0.416886i	0.0663911	−	0.0557087i
$57$	−6.87709	+	9.41955i	−0.910893	+	1.24765i
$58$	3.64657	+	5.20785i	0.478819	+	0.683824i
$59$	1.15461	−	2.47606i	0.150317	−	0.322356i	−0.816702	−	0.577059i	$-0.804200\pi$
$59$	1.15461	−	2.47606i	0.150317	−	0.322356i	0.967019	+	0.254703i	$0.0819779\pi$
$60$	5.30327	−	3.55926i	0.684650	−	0.459498i
$61$	0.846233	+	4.79922i	0.108349	+	0.614478i	0.989830	+	0.142258i	$0.0454361\pi$
$61$	0.846233	+	4.79922i	0.108349	+	0.614478i	−0.881481	+	0.472220i	$0.843453\pi$
$62$	−2.81265	−	4.87164i	−0.357206	−	0.618700i
$63$	1.89782	−	0.428895i	0.239103	−	0.0540357i
$64$	0.866025	+	0.500000i	0.108253	+	0.0625000i
$65$	9.81881	+	8.96442i	1.21787	+	1.11190i
$66$	0.0819554	−	4.14499i	0.0100880	−	0.510214i
$67$	−3.63401	+	0.317935i	−0.443965	+	0.0388419i	−0.306947	−	0.951727i	$-0.599307\pi$
$67$	−3.63401	+	0.317935i	−0.443965	+	0.0388419i	−0.137018	+	0.990569i	$0.543752\pi$
$68$	0.754588	−	0.899283i	0.0915073	−	0.109054i
$69$	−8.09637	−	4.89035i	−0.974689	−	0.588729i
$70$	−2.16749	+	1.01072i	−0.259065	+	0.120804i
$71$	−1.36940	+	0.366929i	−0.162518	+	0.0435465i	−0.339160	−	0.940729i	$-0.610143\pi$
$71$	−1.36940	+	0.366929i	−0.162518	+	0.0435465i	0.176643	+	0.984275i	$0.443476\pi$
$72$	1.62224	+	2.52355i	0.191183	+	0.297404i
$73$	2.20581	−	8.23218i	0.258170	−	0.963504i	−0.708129	−	0.706083i	$-0.750461\pi$
$73$	2.20581	−	8.23218i	0.258170	−	0.963504i	0.966299	−	0.257421i	$-0.0828728\pi$
$74$	−6.46343	+	1.13968i	−0.751358	+	0.132485i
$75$	−14.0915	+	4.81561i	−1.62715	+	0.556059i
$76$	6.10267	+	2.84572i	0.700025	+	0.326427i
$77$	−0.269568	+	1.52880i	−0.0307201	+	0.174222i
$78$	−4.30101	+	4.52784i	−0.486994	+	0.512676i
$79$	9.84516	−	8.26107i	1.10767	−	0.929443i	0.109751	−	0.993959i	$-0.464995\pi$
$79$	9.84516	−	8.26107i	1.10767	−	0.929443i	0.997917	+	0.0645158i	$0.0205503\pi$
$80$	−2.60746	−	2.60746i	−0.291523	−	0.291523i
$81$	0.857788	+	8.95903i	0.0953098	+	0.995448i
$82$			7.43353i			0.820896i
$83$	17.5076	+	1.53172i	1.92171	+	0.168128i	0.983864	−	0.178921i	$-0.0572605\pi$
$83$	17.5076	+	1.53172i	1.92171	+	0.168128i	0.937847	+	0.347048i	$0.112816\pi$
$84$	−0.454524	−	1.02728i	−0.0495927	−	0.112085i
$85$	−3.54601	+	2.48294i	−0.384618	+	0.269313i
$86$	2.16139	−	4.63513i	0.233069	−	0.499818i
$87$	10.4200	−	3.56093i	1.11715	−	0.381772i
$88$	−2.35722	+	0.415641i	−0.251280	+	0.0443075i
$89$	16.7680	+	4.49298i	1.77741	+	0.476254i	0.990107	−	0.140317i	$-0.0448121\pi$
$89$	16.7680	+	4.49298i	1.77741	+	0.476254i	0.787299	+	0.616571i	$0.211479\pi$
$90$	−3.36973	−	10.5368i	−0.355201	−	1.11068i
$91$	1.85259	−	1.42691i	0.194204	−	0.149581i
$92$	−1.86776	+	5.13164i	−0.194728	+	0.535010i
$93$	−9.45931	+	2.33521i	−0.980884	+	0.242150i
$94$	−5.46380	−	4.58467i	−0.563548	−	0.472873i
$95$	−19.0209	−	15.9604i	−1.95150	−	1.63750i
$96$	1.24872	−	1.20029i	0.127447	−	0.122505i
$97$	−0.0772885	+	0.0360402i	−0.00784746	+	0.00365933i	−0.426538	−	0.904470i	$-0.640267\pi$
$97$	−0.0772885	+	0.0360402i	−0.00784746	+	0.00365933i	0.418691	+	0.908129i	$0.362489\pi$
$98$	−1.70287	−	6.35518i	−0.172015	−	0.641971i
$99$	−6.85718	−	2.13124i	−0.689173	−	0.214197i
$100$	4.29884	+	7.44581i	0.429884	+	0.744581i
$101$	−0.946954	−	5.37044i	−0.0942254	−	0.534379i	−0.994982	−	0.100054i	$-0.968098\pi$
$101$	−0.946954	−	5.37044i	−0.0942254	−	0.534379i	0.900757	−	0.434324i	$-0.143013\pi$
$102$	−1.13310	−	1.68832i	−0.112194	−	0.167168i
$103$	−4.99045	−	13.7111i	−0.491723	−	1.35100i	−0.899102	−	0.437739i	$-0.855779\pi$
$103$	−4.99045	−	13.7111i	−0.491723	−	1.35100i	0.407379	−	0.913259i	$-0.366443\pi$
$104$	3.04442	+	1.93172i	0.298530	+	0.189421i
$105$	0.638522	+	4.09280i	0.0623134	+	0.399417i
$106$	0.699846	−	7.99928i	0.0679750	−	0.776958i
$107$			2.10477i			0.203476i	0.994811	+	0.101738i	$0.0324403\pi$
$107$			2.10477i			0.203476i	−0.994811	+	0.101738i	$0.967560\pi$
$108$	4.97954	−	1.48464i	0.479157	−	0.142860i
$109$	7.46061	−	7.46061i	0.714597	−	0.714597i	−0.252896	−	0.967493i	$-0.581383\pi$
$109$	7.46061	−	7.46061i	0.714597	−	0.714597i	0.967493	+	0.252896i	$0.0813831\pi$
$110$	8.79275	+	0.769266i	0.838356	+	0.0733467i
$111$	−1.21443	+	11.3026i	−0.115269	+	1.07280i
$112$	−0.531269	+	0.371998i	−0.0502002	+	0.0351505i
$113$	4.72596	+	12.9845i	0.444581	+	1.22148i	0.936448	+	0.350807i	$0.114093\pi$
$113$	4.72596	+	12.9845i	0.444581	+	1.22148i	−0.491867	+	0.870671i	$0.663685\pi$
$114$	7.67189	−	8.78433i	0.718539	−	0.822727i
$115$	11.5503	−	16.4956i	1.07707	−	1.53822i
$116$	−3.17880	−	5.50585i	−0.295145	−	0.511205i
$117$	5.46365	+	9.33534i	0.505115	+	0.863052i
$118$	−1.36602	+	2.36601i	−0.125752	+	0.217809i
$119$	0.321766	+	0.690030i	0.0294963	+	0.0632549i
$120$	−5.59330	+	3.08350i	−0.510596	+	0.281484i
$121$	−3.38798	+	4.03764i	−0.307999	+	0.367058i
$122$	−0.424733	−	4.85472i	−0.0384535	−	0.439525i
$123$	12.3682	+	3.57756i	1.11521	+	0.322577i
$124$	2.37735	+	5.09824i	0.213492	+	0.457836i
$125$	−3.43361	−	12.8144i	−0.307112	−	1.14616i
$126$	−1.92798	+	0.261857i	−0.171758	+	0.0233281i
$127$	−7.81914	+	4.51438i	−0.693836	+	0.400587i	−0.805048	−	0.593210i	$-0.797860\pi$
$127$	−7.81914	+	4.51438i	−0.693836	+	0.400587i	0.111211	+	0.993797i	$0.464527\pi$
$128$	−0.819152	−	0.573576i	−0.0724035	−	0.0506975i
$129$	−6.67190	−	5.82698i	−0.587428	−	0.513037i
$130$	−9.00014	−	9.78608i	−0.789365	−	0.858296i
$131$	2.20386	+	0.388599i	0.192552	+	0.0339521i	0.269092	−	0.963114i	$-0.413276\pi$
$131$	2.20386	+	0.388599i	0.192552	+	0.0339521i	−0.0765405	+	0.997066i	$0.524387\pi$
$132$	−0.442904	+	4.12208i	−0.0385498	+	0.358781i
$133$	−3.34540	+	2.80712i	−0.290083	+	0.243409i
$134$	3.64789			0.315130
$135$	−19.1533	+	0.535625i	−1.64846	+	0.0460992i
$136$	−0.830094	+	0.830094i	−0.0711800	+	0.0711800i
$137$	1.02497	−	11.7154i	0.0875687	−	1.00091i	−0.817579	−	0.575817i	$-0.804684\pi$
$137$	1.02497	−	11.7154i	0.0875687	−	1.00091i	0.905147	−	0.425098i	$-0.139760\pi$
$138$	7.63934	+	5.57739i	0.650304	+	0.474779i
$139$	2.40720	−	13.6519i	0.204176	−	1.15794i	−0.694556	−	0.719439i	$-0.744399\pi$
$139$	2.40720	−	13.6519i	0.204176	−	1.15794i	0.898732	−	0.438499i	$-0.144490\pi$
$140$	2.24734	−	0.817963i	0.189935	−	0.0691305i
$141$	−10.2578	+	6.88443i	−0.863859	+	0.579773i
$142$	1.39617	−	0.246182i	0.117164	−	0.0206591i
$143$	−8.55428	+	1.14205i	−0.715345	+	0.0955032i
$144$	−1.39613	−	2.65534i	−0.116344	−	0.221278i
$145$	6.06768	+	22.6449i	0.503893	+	1.88055i
$146$	−2.91490	+	8.00861i	−0.241238	+	0.662797i
$147$	−11.3936	−	0.225275i	−0.939726	−	0.0185804i
$148$	6.53816	−	0.572015i	0.537434	−	0.0470194i
$149$	−1.55014	−	17.7182i	−0.126993	−	1.45153i	−0.745894	−	0.666065i	$-0.767977\pi$
$149$	−1.55014	−	17.7182i	−0.126993	−	1.45153i	0.618901	−	0.785469i	$-0.287578\pi$
$150$	14.4576	−	3.56913i	1.18046	−	0.291418i
$151$	2.72839	+	5.85105i	0.222033	+	0.476152i	0.985496	−	0.169700i	$-0.0542800\pi$
$151$	2.72839	+	5.85105i	0.222033	+	0.476152i	−0.763462	+	0.645852i	$0.776502\pi$
$152$	−5.83143	−	3.36678i	−0.472991	−	0.273082i
$153$	−3.35443	+	1.07277i	−0.271190	+	0.0867280i
$154$	0.401785	−	1.49948i	0.0323768	−	0.120832i
$155$	−3.60203	−	20.4281i	−0.289322	−	1.64083i
$156$	4.67927	−	4.13575i	0.374642	−	0.331125i
$157$	7.30961	−	2.66048i	0.583370	−	0.212329i	−0.0334409	−	0.999441i	$-0.510647\pi$
$157$	7.30961	−	2.66048i	0.583370	−	0.212329i	0.616811	+	0.787111i	$0.288424\pi$
$158$	−10.5277	+	7.37157i	−0.837539	+	0.586451i
$159$	−12.9727	−	5.01427i	−1.02880	−	0.397658i
$160$	2.37028	+	2.82479i	0.187387	+	0.223319i
$161$	−2.50441	−	2.50441i	−0.197375	−	0.197375i
$162$	−0.0736932	−	8.99970i	−0.00578989	−	0.707083i
$163$	−15.0189	−	15.0189i	−1.17637	−	1.17637i	−0.980661	−	0.195713i	$-0.937298\pi$
$163$	−15.0189	−	15.0189i	−1.17637	−	1.17637i	−0.195713	−	0.980661i	$-0.562702\pi$
$164$	0.647875	−	7.40524i	0.0505905	−	0.578252i
$165$	5.51165	−	14.2595i	0.429082	−	1.11010i
$166$	−17.3075	−	3.05178i	−1.34332	−	0.236864i
$167$	−8.88564	+	19.0553i	−0.687591	+	1.47454i	0.183294	+	0.983058i	$0.441324\pi$
$167$	−8.88564	+	19.0553i	−0.687591	+	1.47454i	−0.870886	+	0.491486i	$0.836454\pi$
$168$	0.363262	+	1.06298i	0.0280263	+	0.0820108i
$169$	10.6761	+	7.41764i	0.821237	+	0.570588i
$170$	3.74891	−	2.16444i	0.287529	−	0.166005i
$171$	−10.9235	−	16.9925i	−0.835339	−	1.29945i
$172$	−2.55715	+	4.42911i	−0.194981	+	0.337716i
$173$	−10.6052	−	3.85999i	−0.806301	−	0.293469i	−0.0942058	−	0.995553i	$-0.530031\pi$
$173$	−10.6052	−	3.85999i	−0.806301	−	0.293469i	−0.712095	+	0.702083i	$0.752253\pi$
$174$	−10.6907	+	2.63922i	−0.810463	+	0.200078i
$175$	−5.55489	+	0.485990i	−0.419910	+	0.0367374i
$176$	2.38447	−	0.208614i	0.179736	−	0.0157249i
$177$	3.27924	+	3.41154i	0.246483	+	0.256427i
$178$	−16.3126	−	5.93731i	−1.22268	−	0.445020i
$179$	−4.31467	+	7.47322i	−0.322493	+	0.558575i	−0.981002	−	0.193998i	$-0.937854\pi$
$179$	−4.31467	+	7.47322i	−0.322493	+	0.558575i	0.658508	+	0.752573i	$0.271188\pi$
$180$	2.43856	+	10.7904i	0.181760	+	0.804268i
$181$	12.1424	−	7.01044i	0.902541	−	0.521082i	0.0245170	−	0.999699i	$-0.492195\pi$
$181$	12.1424	−	7.01044i	0.902541	−	0.521082i	0.878024	+	0.478617i	$0.158862\pi$
$182$	−1.96991	+	1.26002i	−0.146019	+	0.0933989i
$183$	−8.28190	−	1.62976i	−0.612216	−	0.120475i
$184$	2.30791	−	4.94933i	0.170141	−	0.364869i
$185$	−23.8339	−	4.20256i	−1.75230	−	0.308979i
$186$	9.62684	−	1.50189i	0.705874	−	0.110124i
$187$	0.244899	−	2.79921i	0.0179088	−	0.204698i
$188$	5.04343	+	5.04343i	0.367830	+	0.367830i
$189$	−0.492193	+	3.33388i	−0.0358018	+	0.242504i
$190$	17.5575	+	17.5575i	1.27375	+	1.27375i
$191$	11.8266	+	14.0944i	0.855743	+	1.01984i	0.999543	+	0.0302285i	$0.00962350\pi$
$191$	11.8266	+	14.0944i	0.855743	+	1.01984i	−0.143800	+	0.989607i	$0.545932\pi$
$192$	−1.34858	+	1.08689i	−0.0973252	+	0.0784398i
$193$	−3.73944	+	2.61839i	−0.269171	+	0.188476i	−0.700367	−	0.713783i	$-0.746980\pi$
$193$	−3.73944	+	2.61839i	−0.269171	+	0.188476i	0.431196	+	0.902258i	$0.358092\pi$
$194$	0.0801355	−	0.0291670i	0.00575340	−	0.00209407i
$195$	−20.6140	+	10.2651i	−1.47620	+	0.735096i
$196$	1.14250	+	6.47942i	0.0816068	+	0.462815i
$197$	2.02700	−	7.56488i	0.144418	−	0.538976i	−0.855363	−	0.518030i	$-0.826666\pi$
$197$	2.02700	−	7.56488i	0.144418	−	0.538976i	0.999781	−	0.0209457i	$-0.00666773\pi$
$198$	6.64534	+	2.72077i	0.472264	+	0.193357i
$199$	1.25549	+	0.724857i	0.0889993	+	0.0513838i	0.543839	−	0.839189i	$-0.316970\pi$
$199$	1.25549	+	0.724857i	0.0889993	+	0.0513838i	−0.454840	+	0.890573i	$0.650303\pi$
$200$	−3.63354	−	7.79215i	−0.256930	−	0.550988i
$201$	1.75563	−	6.06952i	0.123833	−	0.428111i
$202$	0.475285	+	5.43254i	0.0334410	+	0.382232i
$203$	4.10759	−	0.359368i	0.288297	−	0.0252227i
$204$	0.981645	+	1.78065i	0.0687289	+	0.124670i
$205$	−9.37517	+	25.7581i	−0.654790	+	1.79902i
$206$	3.77645	+	14.0939i	0.263118	+	0.981969i
$207$	12.9565	−	10.0264i	0.900540	−	0.696885i
$208$	−2.86447	−	2.18971i	−0.198615	−	0.151829i
$209$	15.8725	−	2.79874i	1.09792	−	0.193593i
$210$	−0.279381	−	4.13288i	−0.0192791	−	0.285196i
$211$	−0.646992	+	0.235486i	−0.0445408	+	0.0162115i	−0.364194	−	0.931323i	$-0.618656\pi$
$211$	−0.646992	+	0.235486i	−0.0445408	+	0.0162115i	0.319654	+	0.947534i	$0.396433\pi$
$212$	−1.39437	+	7.90784i	−0.0957654	+	0.543113i
$213$	0.262329	−	2.44149i	0.0179745	−	0.167288i
$214$	0.183443	−	2.09676i	0.0125399	−	0.143331i
$215$	13.3353	−	13.3353i	0.909461	−	0.909461i
$216$	−5.08999	+	1.04500i	−0.346330	+	0.0711030i
$217$	−3.64833			−0.247665
$218$	−8.08246	+	6.78199i	−0.547413	+	0.459334i
$219$	11.9222	+	8.70426i	0.805629	+	0.588179i
$220$	−8.69225	−	1.53268i	−0.586031	−	0.103333i
$221$	−3.11543	+	2.86523i	−0.209567	+	0.192736i
$222$	2.19490	−	11.1538i	0.147312	−	0.748593i
$223$	6.29386	+	4.40701i	0.421468	+	0.295115i	0.765005	−	0.644024i	$-0.222736\pi$
$223$	6.29386	+	4.40701i	0.421468	+	0.295115i	−0.343537	+	0.939139i	$0.611625\pi$
$224$	0.561669	−	0.324280i	0.0375281	−	0.0216668i
$225$	1.01957	−	25.7729i	0.0679712	−	1.71819i
$226$	−3.57631	−	13.3470i	−0.237893	−	0.887827i
$227$	1.64218	+	3.52166i	0.108995	+	0.233741i	0.953238	−	0.302219i	$-0.0977275\pi$
$227$	1.64218	+	3.52166i	0.108995	+	0.233741i	−0.844243	+	0.535960i	$0.819950\pi$
$228$	−8.40830	+	8.08225i	−0.556853	+	0.535260i
$229$	−1.42611	−	16.3006i	−0.0942403	−	1.07717i	−0.885171	−	0.465266i	$-0.845959\pi$
$229$	−1.42611	−	16.3006i	−0.0942403	−	1.07717i	0.790931	−	0.611906i	$-0.209597\pi$
$230$	−12.9441	+	15.4261i	−0.853506	+	1.01717i
$231$	−2.30154	−	1.39017i	−0.151430	−	0.0914664i
$232$	2.68684	+	5.76195i	0.176400	+	0.378291i
$233$	−13.7121	+	23.7500i	−0.898308	+	1.55592i	−0.0686516	+	0.997641i	$0.521870\pi$
$233$	−13.7121	+	23.7500i	−0.898308	+	1.55592i	−0.829656	+	0.558274i	$0.811464\pi$
$234$	−4.62923	−	9.77600i	−0.302622	−	0.639077i
$235$	−13.1505	−	22.7774i	−0.857846	−	1.48583i
$236$	1.56703	−	2.23795i	0.102005	−	0.145678i
$237$	7.19845	+	21.0642i	0.467590	+	1.36827i
$238$	−0.260402	−	0.715448i	−0.0168793	−	0.0463756i
$239$	−20.4469	+	14.3171i	−1.32260	+	0.926093i	−0.999792	−	0.0203723i	$-0.993515\pi$
$239$	−20.4469	+	14.3171i	−1.32260	+	0.926093i	−0.322805	+	0.946465i	$0.604626\pi$
$240$	5.84076	−	2.58428i	0.377020	−	0.166815i
$241$	−2.14265	−	0.187457i	−0.138020	−	0.0120752i	0.0179364	−	0.999839i	$-0.494290\pi$
$241$	−2.14265	−	0.187457i	−0.138020	−	0.0120752i	−0.155956	+	0.987764i	$0.549846\pi$
$242$	3.72700	−	3.72700i	0.239580	−	0.239580i
$243$	−15.0096	−	4.20870i	−0.962864	−	0.269988i
$244$			4.87326i			0.311979i
$245$	2.11452	−	24.1691i	0.135092	−	1.54411i
$246$	−12.0094	−	4.64190i	−0.765689	−	0.295957i
$247$	−20.4997	−	13.0073i	−1.30437	−	0.827636i
$248$	−1.92396	−	5.28604i	−0.122172	−	0.335664i
$249$	−13.4073	+	27.3282i	−0.849654	+	1.73186i
$250$	2.30370	+	13.0649i	0.145699	+	0.826298i
$251$	3.00416	+	5.20337i	0.189621	+	0.328434i	0.945124	−	0.326712i	$-0.105941\pi$
$251$	3.00416	+	5.20337i	0.189621	+	0.328434i	−0.755503	+	0.655145i	$0.772607\pi$
$252$	1.94346	−	0.0928268i	0.122427	−	0.00584754i
$253$	3.38310	+	12.6259i	0.212694	+	0.793784i
$254$	8.18284	−	3.81572i	0.513437	−	0.239420i
$255$	−1.79703	−	7.27929i	−0.112535	−	0.455847i
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	1.72075	+	1.44388i	0.107337	+	0.0900668i	0.694877	−	0.719129i	$-0.255459\pi$
$257$	1.72075	+	1.44388i	0.107337	+	0.0900668i	−0.587539	+	0.809196i	$0.699903\pi$
$258$	6.13866	+	6.38631i	0.382176	+	0.397594i
$259$	−1.45584	+	3.99988i	−0.0904613	+	0.248540i
$260$	8.11298	+	10.5333i	0.503146	+	0.653245i
$261$	−0.753926	+	19.0579i	−0.0466669	+	1.17966i
$262$	−2.16160	−	0.579199i	−0.133544	−	0.0357830i
$263$	−1.75638	+	0.309697i	−0.108303	+	0.0190968i	−0.227537	−	0.973769i	$-0.573067\pi$
$263$	−1.75638	+	0.309697i	−0.108303	+	0.0190968i	0.119234	+	0.992866i	$0.461956\pi$
$264$	0.800481	−	4.06779i	0.0492662	−	0.250355i
$265$	12.5137	−	26.8358i	0.768713	−	1.64851i
$266$	3.57733	−	2.50487i	0.219340	−	0.153584i
$267$	−17.7296	+	24.2842i	−1.08503	+	1.48617i
$268$	−3.63401	−	0.317935i	−0.221982	−	0.0194209i
$269$		−	7.43709i		−	0.453447i	−0.973959	−	0.226724i	$-0.927199\pi$
$269$		−	7.43709i		−	0.453447i	0.973959	−	0.226724i	$-0.0728014\pi$
$270$	19.1271	+	1.13574i	1.16404	+	0.0691188i
$271$	−0.881439	−	0.881439i	−0.0535436	−	0.0535436i	0.679828	−	0.733372i	$-0.262054\pi$
$271$	−0.881439	−	0.881439i	−0.0535436	−	0.0535436i	−0.733372	+	0.679828i	$0.762054\pi$
$272$	0.899283	−	0.754588i	0.0545271	−	0.0457536i
$273$	1.14841	+	3.88403i	0.0695052	+	0.235072i
$274$	−2.04213	+	11.5815i	−0.123370	+	0.699664i
$275$	18.6511	+	8.69717i	1.12471	+	0.524459i
$276$	−7.12417	−	6.22198i	−0.428825	−	0.374519i
$277$	13.6992	−	2.41553i	0.823103	−	0.145135i	0.253794	−	0.967258i	$-0.418322\pi$
$277$	13.6992	−	2.41553i	0.823103	−	0.145135i	0.569310	+	0.822123i	$0.307210\pi$
$278$	−3.58788	+	13.3901i	−0.215186	+	0.803087i
$279$	2.13422	−	16.7404i	0.127773	−	1.00222i
$280$	−2.31007	+	0.618982i	−0.138053	+	0.0369913i
$281$	20.2800	−	9.45670i	1.20980	−	0.564139i	0.290189	−	0.956969i	$-0.406282\pi$
$281$	20.2800	−	9.45670i	1.20980	−	0.564139i	0.919611	+	0.392830i	$0.128504\pi$
$282$	10.8187	−	5.96421i	0.644246	−	0.355163i
$283$	11.5982	−	13.8222i	0.689443	−	0.821646i	−0.301845	−	0.953357i	$-0.597603\pi$
$283$	11.5982	−	13.8222i	0.689443	−	0.821646i	0.991288	+	0.131711i	$0.0420470\pi$
$284$	−1.41231	+	0.123561i	−0.0838052	+	0.00733201i
$285$	37.6628	−	20.7629i	2.23095	−	1.22989i
$286$	8.62127	−	0.392152i	0.509786	−	0.0231884i
$287$	4.17518	+	2.41054i	0.246453	+	0.142290i
$288$	1.15939	+	2.76692i	0.0683176	+	0.163042i
$289$	7.81094	+	13.5290i	0.459467	+	0.795821i
$290$	−4.07096	−	23.0875i	−0.239055	−	1.35575i
$291$	−0.00996217	−	0.147370i	−0.000583993	−	0.00863900i
$292$	3.60180	−	7.72408i	0.210779	−	0.452018i
$293$	11.1223	+	15.8843i	0.649770	+	0.927968i	0.999962	−	0.00871006i	$-0.00277253\pi$
$293$	11.1223	+	15.8843i	0.649770	+	0.927968i	−0.350192	+	0.936678i	$0.613884\pi$
$294$	11.3306	+	1.21743i	0.660813	+	0.0710022i
$295$	−7.71743	+	6.47569i	−0.449326	+	0.377029i
$296$	−6.56314			−0.381475
$297$	7.72515	−	9.74737i	0.448259	−	0.565600i
$298$			17.7859i			1.03031i
$299$	9.05992	−	17.4816i	0.523949	−	1.01099i
$300$	−14.7136	+	2.29549i	−0.849492	+	0.132530i
$301$	−1.90251	−	2.71706i	−0.109659	−	0.156609i
$302$	−2.20806	−	6.06658i	−0.127059	−	0.349093i
$303$	9.26764	+	1.82373i	0.532412	+	0.104771i
$304$	5.51581	+	3.86221i	0.316353	+	0.221513i
$305$	4.65102	−	17.3578i	0.266317	−	0.993907i
$306$	3.43516	−	0.776326i	0.196375	−	0.0443796i
$307$	27.0263	−	7.24166i	1.54247	−	0.413304i	0.615407	−	0.788209i	$-0.288992\pi$
$307$	27.0263	−	7.24166i	1.54247	−	0.413304i	0.927063	+	0.374906i	$0.122325\pi$
$308$	−0.530945	+	1.45876i	−0.0302534	+	0.0831205i
$309$	25.2676	+	0.499594i	1.43742	+	0.0284209i
$310$	1.80790	+	20.6643i	0.102682	+	1.17366i
$311$	18.1722	+	15.2483i	1.03045	+	0.864653i	0.990905	−	0.134565i	$-0.0429637\pi$
$311$	18.1722	+	15.2483i	1.03045	+	0.864653i	0.0395483	+	0.999218i	$0.487408\pi$
$312$	−5.02192	+	3.71219i	−0.284310	+	0.210161i
$313$	24.0181	+	8.74187i	1.35758	+	0.494120i	0.915306	−	0.402759i	$-0.131949\pi$
$313$	24.0181	+	8.74187i	1.35758	+	0.494120i	0.442277	+	0.896879i	$0.354171\pi$
$314$	−7.51367	+	2.01328i	−0.424021	+	0.113616i
$315$	−7.01092	−	1.52420i	−0.395021	−	0.0858788i
$316$	11.1301	−	6.42597i	0.626118	−	0.361489i
$317$	−9.49537	+	13.5608i	−0.533313	+	0.761650i	−0.991903	−	0.126998i	$-0.959466\pi$
$317$	−9.49537	+	13.5608i	−0.533313	+	0.761650i	0.458590	+	0.888648i	$0.348355\pi$
$318$	12.4863	+	6.12584i	0.700199	+	0.343520i
$319$	−13.7917	−	6.43117i	−0.772187	−	0.360077i
$320$	−2.11507	−	3.02063i	−0.118236	−	0.168858i
$321$	−3.40039	−	1.31433i	−0.189791	−	0.0733589i
$322$	2.27660	+	2.71315i	0.126870	+	0.151198i
$323$	5.58949	−	5.58949i	0.311007	−	0.311007i
$324$	−0.710963	+	8.97187i	−0.0394979	+	0.498437i
$325$	−11.9151	−	28.6180i	−0.660931	−	1.58744i
$326$	13.6528	+	16.2708i	0.756159	+	0.901155i
$327$	7.39430	+	16.7119i	0.408906	+	0.924172i
$328$	−1.29082	+	7.32059i	−0.0712735	+	0.404212i
$329$	−4.34686	+	1.58213i	−0.239650	+	0.0872256i
$330$	−6.73348	+	13.7249i	−0.370666	+	0.755531i
$331$	−3.31360	−	2.32021i	−0.182132	−	0.127530i	0.478955	−	0.877839i	$-0.341016\pi$
$331$	−3.31360	−	2.32021i	−0.182132	−	0.127530i	−0.661087	+	0.750309i	$0.729905\pi$
$332$	16.9757	+	4.54861i	0.931660	+	0.249638i
$333$	−17.5018	−	9.01998i	−0.959093	−	0.494292i
$334$	10.5126	−	18.2084i	0.575224	−	0.996317i
$335$	12.6404	+	4.60072i	0.690618	+	0.251364i
$336$	−0.269235	−	1.09060i	−0.0146880	−	0.0594969i
$337$	1.59292	−	1.89837i	0.0867720	−	0.103411i	−0.720911	−	0.693027i	$-0.756277\pi$
$337$	1.59292	−	1.89837i	0.0867720	−	0.103411i	0.807683	+	0.589616i	$0.200721\pi$
$338$	−9.98896	−	8.31990i	−0.543328	−	0.452543i
$339$	−23.9284	−	0.473117i	−1.29962	−	0.0256962i
$340$	−3.92329	+	1.82946i	−0.212770	+	0.0992165i
$341$	11.6607	+	6.73230i	0.631461	+	0.364574i
$342$	9.40091	+	17.8799i	0.508343	+	0.966833i
$343$	−8.50693	−	2.27943i	−0.459331	−	0.123077i
$344$	2.93344	−	4.18939i	0.158160	−	0.225877i
$345$	19.4370	+	28.9611i	1.04645	+	1.55921i
$346$	10.2285	+	4.76961i	0.549885	+	0.256416i
$347$	15.6963	+	2.76769i	0.842623	+	0.148577i	0.578267	−	0.815848i	$-0.303729\pi$
$347$	15.6963	+	2.76769i	0.842623	+	0.148577i	0.264357	+	0.964425i	$0.414840\pi$
$348$	10.8801	−	1.69741i	0.583234	−	0.0909909i
$349$	−23.7283	−	2.07596i	−1.27015	−	0.111124i	−0.567926	−	0.823080i	$-0.692254\pi$
$349$	−23.7283	−	2.07596i	−1.27015	−	0.111124i	−0.702224	+	0.711956i	$0.747809\pi$
$350$	5.57611			0.298055
$351$	−18.4937	+	2.99739i	−0.987119	+	0.159989i
$352$	−2.39358			−0.127578
$353$	2.19729	+	0.192238i	0.116950	+	0.0102318i	0.145481	−	0.989361i	$-0.453527\pi$
$353$	2.19729	+	0.192238i	0.116950	+	0.0102318i	−0.0285304	+	0.999593i	$0.509083\pi$
$354$	−2.96943	−	3.68436i	−0.157823	−	0.195821i
$355$	5.14837	+	0.907797i	0.273247	+	0.0481809i
$356$	15.7331	+	7.33645i	0.833851	+	0.388831i
$357$	−1.31572	+	0.0889420i	−0.0696352	+	0.00470731i
$358$	4.94958	−	7.06874i	0.261594	−	0.373594i
$359$	−6.84783	−	1.83487i	−0.361414	−	0.0968407i	0.0735422	−	0.997292i	$-0.476570\pi$
$359$	−6.84783	−	1.83487i	−0.361414	−	0.0968407i	−0.434957	+	0.900451i	$0.643236\pi$
$360$	−1.48884	−	10.9619i	−0.0784687	−	0.577741i
$361$	22.8118	+	13.1704i	1.20062	+	0.693178i
$362$	−12.7072	+	5.92548i	−0.667878	+	0.311436i
$363$	−4.40744	−	7.99484i	−0.231330	−	0.419620i
$364$	2.07223	−	1.08354i	0.108614	−	0.0567927i
$365$	−20.2009	+	24.0745i	−1.05736	+	1.26012i
$366$	8.10834	+	2.34537i	0.423830	+	0.122594i
$367$	5.89737	+	2.14647i	0.307840	+	0.112045i	0.491321	−	0.870979i	$-0.336514\pi$
$367$	5.89737	+	2.14647i	0.307840	+	0.112045i	−0.183481	+	0.983023i	$0.558736\pi$
$368$	−2.73049	+	4.72935i	−0.142337	+	0.246534i
$369$	−13.5032	+	17.7477i	−0.702948	+	0.923907i
$370$	23.3769	+	6.26383i	1.21531	+	0.325641i
$371$	−4.26600	−	2.98708i	−0.221480	−	0.155082i
$372$	−9.72110	+	0.657143i	−0.504016	+	0.0340713i
$373$	0.859570	−	0.312858i	0.0445068	−	0.0161992i	−0.319671	−	0.947529i	$-0.603572\pi$
$373$	0.859570	−	0.312858i	0.0445068	−	0.0161992i	0.364178	+	0.931330i	$0.381350\pi$
$374$	−0.487934	+	2.76721i	−0.0252305	+	0.143089i
$375$	22.8467	+	2.45480i	1.17980	+	0.126765i
$376$	−4.58467	−	5.46380i	−0.236436	−	0.281774i
$377$	8.81070	+	21.1618i	0.453774	+	1.08989i
$378$	0.780887	−	3.27829i	0.0401645	−	0.168617i
$379$	−2.71814	+	2.71814i	−0.139621	+	0.139621i	−0.773463	−	0.633842i	$-0.781477\pi$
$379$	−2.71814	+	2.71814i	−0.139621	+	0.139621i	0.633842	+	0.773463i	$0.281477\pi$
$380$	−15.9604	−	19.0209i	−0.818752	−	0.975751i
$381$	−2.41058	−	15.4514i	−0.123498	−	0.791598i
$382$	−10.5532	−	15.0715i	−0.539949	−	0.771126i
$383$	−0.249517	−	0.116352i	−0.0127497	−	0.00594530i	0.416233	−	0.909258i	$-0.363350\pi$
$383$	−0.249517	−	0.116352i	−0.0127497	−	0.00594530i	−0.428983	+	0.903313i	$0.641128\pi$
$384$	1.43817	−	0.965222i	0.0733915	−	0.0492563i
$385$	3.28338	−	4.68916i	0.167337	−	0.238982i
$386$	3.95342	−	2.28251i	0.201224	−	0.116177i
$387$	13.5802	−	7.14022i	0.690320	−	0.362958i
$388$	−0.0823727	+	0.0220717i	−0.00418184	+	0.00112052i
$389$	0.159346	+	0.0579970i	0.00807914	+	0.00294057i	0.346057	−	0.938214i	$-0.387521\pi$
$389$	0.159346	+	0.0579970i	0.00807914	+	0.00294057i	−0.337977	+	0.941154i	$0.609743\pi$
$390$	21.4302	−	8.42936i	1.08516	−	0.426837i
$391$	4.91097	+	4.12079i	0.248358	+	0.208397i
$392$	−0.573430	−	6.55433i	−0.0289626	−	0.331044i
$393$	−2.00402	+	3.31781i	−0.101089	+	0.167362i
$394$	−2.67861	+	7.35943i	−0.134947	+	0.370763i
$395$	−45.7768	+	12.2658i	−2.30328	+	0.617162i
$396$	−6.38292	−	3.28959i	−0.320754	−	0.165308i
$397$	−9.48784	+	35.4091i	−0.476181	+	1.77713i	0.140674	+	0.990056i	$0.455073\pi$
$397$	−9.48784	+	35.4091i	−0.476181	+	1.77713i	−0.616855	+	0.787077i	$0.711594\pi$
$398$	−1.18754	−	0.831522i	−0.0595258	−	0.0416804i
$399$	−2.44604	−	7.15764i	−0.122455	−	0.358330i
$400$	2.94058	+	8.07918i	0.147029	+	0.403959i
$401$	6.46208	+	9.22881i	0.322701	+	0.460865i	0.947424	−	0.319982i	$-0.103677\pi$
$401$	6.46208	+	9.22881i	0.322701	+	0.460865i	−0.624723	+	0.780847i	$0.714788\pi$
$402$	−2.27794	+	5.89341i	−0.113614	+	0.293937i
$403$	−6.13423	−	19.3324i	−0.305568	−	0.963016i
$404$		−	5.45329i		−	0.271311i
$405$	11.0951	−	31.2780i	0.551318	−	1.55422i
$406$	−4.12329			−0.204635
$407$	12.0341	−	10.0978i	0.596508	−	0.500530i
$408$	−0.822716	−	1.85943i	−0.0407305	−	0.0920555i
$409$	−17.1930	−	24.5541i	−0.850137	−	1.21412i	−0.975057	−	0.221954i	$-0.928756\pi$
$409$	−17.1930	−	24.5541i	−0.850137	−	1.21412i	0.124920	−	0.992167i	$-0.460133\pi$
$410$	11.5845	−	24.8429i	0.572115	−	1.22691i
$411$	18.2870	+	8.97165i	0.902030	+	0.442539i
$412$	−2.53372	−	14.3694i	−0.124827	−	0.707930i
$413$	0.885943	+	1.53450i	0.0435944	+	0.0755077i
$414$	−13.7811	+	8.85904i	−0.677303	+	0.435398i
$415$	−56.1237	−	32.4030i	−2.75500	−	1.59060i
$416$	2.66272	+	2.43103i	0.130551	+	0.119191i
$417$	20.5523	+	12.4140i	1.00645	+	0.607915i
$418$	−16.0560	+	1.40472i	−0.785324	+	0.0687069i
$419$	11.4091	−	13.5968i	0.557370	−	0.664247i	−0.411618	−	0.911357i	$-0.635036\pi$
$419$	11.4091	−	13.5968i	0.557370	−	0.664247i	0.968988	+	0.247109i	$0.0794806\pi$
$420$	−0.0818863	+	4.14150i	−0.00399564	+	0.202085i
$421$	−30.1693	+	14.0682i	−1.47036	+	0.685641i	−0.982325	−	0.187183i	$-0.940064\pi$
$421$	−30.1693	+	14.0682i	−1.47036	+	0.685641i	−0.488036	+	0.872823i	$0.662287\pi$
$422$	0.665054	−	0.178201i	0.0323743	−	0.00867468i
$423$	−4.71674	−	20.8711i	−0.229336	−	1.01479i
$424$	2.07827	−	7.75622i	0.100930	−	0.376675i
$425$	9.93975	−	1.75265i	0.482149	−	0.0850158i
$426$	−0.474121	+	2.40933i	−0.0229712	+	0.116732i
$427$	−2.86447	−	1.33573i	−0.138622	−	0.0646403i
$428$	−0.365489	+	2.07279i	−0.0176666	+	0.100192i
$429$	3.49670	−	14.5332i	0.168822	−	0.701668i
$430$	−14.4468	+	12.1223i	−0.696687	+	0.584590i
$431$	22.1701	+	22.1701i	1.06790	+	1.06790i	0.997520	+	0.0703766i	$0.0224201\pi$
$431$	22.1701	+	22.1701i	1.06790	+	1.06790i	0.0703766	+	0.997520i	$0.477580\pi$
$432$	5.16170	−	0.597399i	0.248342	−	0.0287424i
$433$			0.471379i			0.0226530i	0.999936	+	0.0113265i	$0.00360542\pi$
$433$			0.471379i			0.0226530i	−0.999936	+	0.0113265i	$0.996395\pi$
$434$	3.63445	+	0.317973i	0.174459	+	0.0152632i
$435$	−40.3733	−	4.33798i	−1.93575	−	0.207990i
$436$	8.64279	−	6.05175i	0.413915	−	0.289826i
$437$	−15.5404	+	33.3266i	−0.743400	+	1.59423i
$438$	−11.1182	−	9.71023i	−0.531249	−	0.463973i
$439$	−32.3024	+	5.69579i	−1.54171	+	0.271845i	−0.878923	−	0.476963i	$-0.841737\pi$
$439$	−32.3024	+	5.69579i	−1.54171	+	0.271845i	−0.662787	+	0.748808i	$0.730626\pi$
$440$	8.52559	+	2.28442i	0.406442	+	0.108906i
$441$	7.47873	−	18.2664i	0.356130	−	0.869829i
$442$	3.35330	−	2.58280i	0.159500	−	0.122851i
$443$	4.50747	−	12.3842i	0.214156	−	0.588390i	−0.785374	−	0.619021i	$-0.787529\pi$
$443$	4.50747	−	12.3842i	0.214156	−	0.588390i	0.999531	+	0.0306311i	$0.00975170\pi$
$444$	−3.15866	+	10.9200i	−0.149903	+	0.518242i
$445$	−49.0370	−	41.1470i	−2.32458	−	1.95055i
$446$	−5.88581	−	4.93878i	−0.278701	−	0.233858i
$447$	29.5930	+	8.55988i	1.39970	+	0.404869i
$448$	−0.587794	+	0.274093i	−0.0277707	+	0.0129497i
$449$	0.0448224	+	0.167279i	0.00211530	+	0.00789441i	0.966975	−	0.254870i	$-0.0820326\pi$
$449$	0.0448224	+	0.167279i	0.00211530	+	0.00789441i	−0.964860	+	0.262764i	$0.915366\pi$
$450$	−3.26194	+	25.5860i	−0.153770	+	1.20613i
$451$	−8.89638	−	15.4090i	−0.418914	−	0.725580i
$452$	2.39944	+	13.6079i	0.112860	+	0.640061i
$453$	−11.1565	+	0.754177i	−0.524179	+	0.0354343i
$454$	−1.32900	−	3.65139i	−0.0623729	−	0.171368i
$455$	−8.41510	+	1.88167i	−0.394506	+	0.0882142i
$456$	9.08072	−	7.31866i	0.425244	−	0.342728i
$457$	−2.77778	+	31.7501i	−0.129939	+	1.48521i	0.599065	+	0.800700i	$0.295539\pi$
$457$	−2.77778	+	31.7501i	−0.129939	+	1.48521i	−0.729004	+	0.684509i	$0.760017\pi$
$458$			16.3628i			0.764585i
$459$	0.361566	−	6.08920i	0.0168765	−	0.284219i
$460$	14.2393	−	14.2393i	0.663910	−	0.663910i
$461$	−32.6050	−	2.85257i	−1.51857	−	0.132857i	−0.702863	−	0.711325i	$-0.748095\pi$
$461$	−32.6050	−	2.85257i	−1.51857	−	0.132857i	−0.815705	+	0.578468i	$0.803651\pi$
$462$	2.17162	+	1.58547i	0.101033	+	0.0737628i
$463$	−23.3760	+	16.3680i	−1.08637	+	0.760687i	−0.972522	−	0.232810i	$-0.925208\pi$
$463$	−23.3760	+	16.3680i	−1.08637	+	0.760687i	−0.113852	+	0.993498i	$0.536319\pi$
$464$	−2.17443	−	5.97420i	−0.100945	−	0.277345i
$465$	35.2523	+	6.93714i	1.63479	+	0.321702i
$466$	15.7298	−	22.4646i	0.728671	−	1.04065i
$467$	8.32518	+	14.4196i	0.385244	+	0.667262i	0.991803	−	0.127777i	$-0.0407841\pi$
$467$	8.32518	+	14.4196i	0.385244	+	0.667262i	−0.606559	+	0.795038i	$0.707451\pi$
$468$	3.75958	+	10.1423i	0.173787	+	0.468826i
$469$	1.18294	−	2.04891i	0.0546229	−	0.0946097i
$470$	11.1153	+	23.8368i	0.512711	+	1.09951i
$471$	−0.266341	+	13.4705i	−0.0122723	+	0.620688i
$472$	−1.75612	+	2.09286i	−0.0808318	+	0.0963316i
$473$	1.06692	+	12.1949i	0.0490568	+	0.560722i
$474$	−5.33519	−	21.6114i	−0.245054	−	0.992645i
$475$	24.4666	+	52.4688i	1.12261	+	2.40744i
$476$	0.197055	+	0.735421i	0.00903202	+	0.0337080i
$477$	16.2018	−	17.8271i	0.741828	−	0.816248i
$478$	21.6169	−	12.4805i	0.988733	−	0.570845i
$479$	13.4827	+	9.44072i	0.616042	+	0.431357i	0.839503	−	0.543356i	$-0.182846\pi$
$479$	13.4827	+	9.44072i	0.616042	+	0.431357i	−0.223460	+	0.974713i	$0.571735\pi$
$480$	−6.04377	+	2.06539i	−0.275859	+	0.0942718i
$481$	−23.6430	−	0.989122i	−1.07803	−	0.0451001i
$482$	2.11816	+	0.373488i	0.0964793	+	0.0170119i
$483$	5.60993	−	2.48215i	0.255261	−	0.112942i
$484$	−4.03764	+	3.38798i	−0.183529	+	0.153999i
$485$	0.314465			0.0142791
$486$	14.5856	+	5.50085i	0.661618	+	0.249524i
$487$	6.64928	−	6.64928i	0.301308	−	0.301308i	−0.540218	−	0.841525i	$-0.681658\pi$
$487$	6.64928	−	6.64928i	0.301308	−	0.301308i	0.841525	+	0.540218i	$0.181658\pi$
$488$	0.424733	−	4.85472i	0.0192267	−	0.219763i
$489$	33.6428	−	14.8854i	1.52138	−	0.673143i
$490$	−4.21296	+	23.8929i	−0.190322	+	1.07937i
$491$	−26.3391	+	9.58666i	−1.18867	+	0.432640i	−0.859256	−	0.511546i	$-0.829073\pi$
$491$	−26.3391	+	9.58666i	−1.18867	+	0.432640i	−0.329412	+	0.944186i	$0.606851\pi$
$492$	11.5591	+	5.67093i	0.521124	+	0.255665i
$493$	−7.35001	+	1.29600i	−0.331028	+	0.0583691i
$494$	19.2881	+	14.7445i	0.867811	+	0.663386i
$495$	19.5955	+	17.8089i	0.880750	+	0.800450i
$496$	1.45593	+	5.43361i	0.0653733	+	0.243976i
$497$	0.314476	−	0.864015i	0.0141062	−	0.0387564i
$498$	15.7381	−	26.0557i	0.705242	−	1.16758i
$499$	32.2381	−	2.82047i	1.44317	−	0.126261i	0.661499	−	0.749946i	$-0.269921\pi$
$499$	32.2381	−	2.82047i	1.44317	−	0.126261i	0.781676	+	0.623685i	$0.214365\pi$
$500$	−1.15625	−	13.2160i	−0.0517090	−	0.591037i
$501$	−25.2364	−	26.2545i	−1.12748	−	1.17297i
$502$	−2.53923	−	5.44540i	−0.113331	−	0.243040i
$503$	0.578491	+	0.333992i	0.0257936	+	0.0148920i	0.512841	−	0.858483i	$-0.328593\pi$
$503$	0.578491	+	0.333992i	0.0257936	+	0.0148920i	−0.487048	+	0.873375i	$0.661926\pi$
$504$	−1.94416	−	0.0769103i	−0.0865996	−	0.00342586i
$505$	−5.20460	+	19.4238i	−0.231602	+	0.864349i
$506$	−2.26981	−	12.8727i	−0.100905	−	0.572262i
$507$	−18.6504	+	12.6159i	−0.828294	+	0.560293i
$508$	−8.48426	+	3.08802i	−0.376428	+	0.137009i
$509$	18.5820	−	13.0113i	0.823634	−	0.576715i	−0.0840054	−	0.996465i	$-0.526771\pi$
$509$	18.5820	−	13.0113i	0.823634	−	0.576715i	0.907640	+	0.419750i	$0.137882\pi$
$510$	1.15576	+	7.40822i	0.0511780	+	0.328041i
$511$	3.55294	+	4.23423i	0.157173	+	0.187312i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	34.2737	−	7.03655i	1.51322	−	0.310671i
$514$	−1.58836	−	1.58836i	−0.0700595	−	0.0700595i
$515$	−4.68939	+	53.5999i	−0.206639	+	2.36190i
$516$	−5.55870	−	6.89702i	−0.244708	−	0.303625i
$517$	16.8128	+	2.96455i	0.739427	+	0.130381i
$518$	1.79891	−	3.85778i	0.0790396	−	0.169501i
$519$	12.8586	−	14.7231i	0.564428	−	0.646271i
$520$	−7.16408	−	11.2003i	−0.314166	−	0.491164i
$521$	9.04220	−	5.22052i	0.396146	−	0.228715i	−0.288674	−	0.957428i	$-0.593214\pi$
$521$	9.04220	−	5.22052i	0.396146	−	0.228715i	0.684820	+	0.728713i	$0.259881\pi$
$522$	2.41206	−	18.9197i	0.105573	−	0.828092i
$523$	−11.7165	+	20.2936i	−0.512329	+	0.887379i	0.487569	+	0.873084i	$0.337884\pi$
$523$	−11.7165	+	20.2936i	−0.512329	+	0.887379i	−0.999898	+	0.0142949i	$0.995450\pi$
$524$	2.10289	+	0.765391i	0.0918654	+	0.0334363i
$525$	2.68363	−	9.27777i	0.117123	−	0.404915i
$526$	1.77669	−	0.155440i	0.0774673	−	0.00677751i
$527$	6.57857	−	0.575551i	0.286567	−	0.0250714i
$528$	−1.15197	+	3.98255i	−0.0501329	+	0.173318i
$529$	−6.41084	−	2.33335i	−0.278732	−	0.101450i
$530$	−14.8050	+	25.6430i	−0.643089	+	1.11386i
$531$	−7.55930	+	3.16749i	−0.328046	+	0.137457i
$532$	−3.78203	+	2.18355i	−0.163972	+	0.0946691i
$533$	−5.75332	+	26.1772i	−0.249204	+	1.13386i
$534$	19.7786	−	22.6465i	0.855904	−	0.980011i
$535$	3.28008	−	7.03416i	0.141810	−	0.304113i
$536$	3.59247	+	0.633450i	0.155171	+	0.0273609i
$537$	−9.37917	−	11.6373i	−0.404741	−	0.502188i
$538$	−0.648185	+	7.40879i	−0.0279452	+	0.319416i
$539$	11.1357	+	11.1357i	0.479649	+	0.479649i
$540$	−18.9554	−	2.79846i	−0.815709	−	0.120426i
$541$	4.92435	+	4.92435i	0.211714	+	0.211714i	0.804995	−	0.593281i	$-0.202168\pi$
$541$	4.92435	+	4.92435i	0.211714	+	0.211714i	−0.593281	+	0.804995i	$0.702168\pi$
$542$	0.801262	+	0.954907i	0.0344172	+	0.0410168i
$543$	3.74343	+	23.9946i	0.160646	+	1.02971i
$544$	−0.961628	+	0.673339i	−0.0412295	+	0.0288692i
$545$	−36.5601	+	13.3068i	−1.56606	+	0.570001i
$546$	−0.805528	−	3.96934i	−0.0344734	−	0.169872i
$547$	0.179283	+	1.01676i	0.00766558	+	0.0434737i	0.988401	−	0.151869i	$-0.0485292\pi$
$547$	0.179283	+	1.01676i	0.00766558	+	0.0434737i	−0.980735	+	0.195343i	$0.937418\pi$
$548$	3.04375	−	11.3594i	0.130023	−	0.485251i
$549$	7.80466	−	12.3623i	0.333095	−	0.527608i
$550$	−17.8222	−	10.2896i	−0.759939	−	0.438751i
$551$	−18.0920	−	38.7984i	−0.770745	−	1.65287i
$552$	6.55478	+	6.81921i	0.278990	+	0.290245i
$553$	0.726465	+	8.30353i	0.0308924	+	0.353102i
$554$	−13.8576	+	1.21238i	−0.588752	+	0.0515091i
$555$	21.6727	−	35.8810i	0.919956	−	1.52306i
$556$	4.74125	−	13.0265i	0.201074	−	0.552446i
$557$	−5.19926	−	19.4039i	−0.220300	−	0.822169i	−0.984233	−	0.176874i	$-0.943401\pi$
$557$	−5.19926	−	19.4039i	−0.220300	−	0.822169i	0.763934	−	0.645294i	$-0.223265\pi$
$558$	−3.58512	+	16.4907i	−0.151770	+	0.698105i
$559$	11.1988	−	14.6497i	0.473659	−	0.619618i
$560$	2.35523	−	0.415291i	0.0995267	−	0.0175492i
$561$	4.36938	+	2.14363i	0.184475	+	0.0905041i
$562$	−21.0270	+	7.65320i	−0.886970	+	0.322831i
$563$	3.82863	−	21.7132i	0.161357	−	0.915103i	−0.791384	−	0.611320i	$-0.790639\pi$
$563$	3.82863	−	21.7132i	0.161357	−	0.915103i	0.952741	−	0.303784i	$-0.0982500\pi$
$564$	−11.2974	+	4.99860i	−0.475706	+	0.210479i
$565$	4.44086	−	50.7593i	0.186828	−	2.13546i
$566$	−12.7588	+	12.7588i	−0.536292	+	0.536292i
$567$	−5.07875	−	2.87703i	−0.213287	−	0.120824i
$568$	1.41771			0.0594856
$569$	−20.8598	+	17.5035i	−0.874489	+	0.733784i	−0.965038	−	0.262108i	$-0.915582\pi$
$569$	−20.8598	+	17.5035i	−0.874489	+	0.733784i	0.0905492	+	0.995892i	$0.471138\pi$
$570$	−39.3291	+	17.4014i	−1.64732	+	0.728865i
$571$	41.4634	+	7.31111i	1.73519	+	0.305960i	0.949757	−	0.312989i	$-0.101330\pi$
$571$	41.4634	+	7.31111i	1.73519	+	0.305960i	0.785431	+	0.618950i	$0.212441\pi$
$572$	−8.62264	−	0.360734i	−0.360531	−	0.0150830i
$573$	−30.1556	+	10.3054i	−1.25977	+	0.430512i
$574$	−3.94920	−	2.76526i	−0.164836	−	0.115420i
$575$	−40.6614	+	23.4759i	−1.69570	+	0.979012i
$576$	−0.913824	−	2.85743i	−0.0380760	−	0.119060i
$577$	1.37177	+	5.11952i	0.0571076	+	0.213128i	0.988583	−	0.150675i	$-0.0481447\pi$
$577$	1.37177	+	5.11952i	0.0571076	+	0.213128i	−0.931476	+	0.363803i	$0.881478\pi$
$578$	−6.60209	−	14.1582i	−0.274611	−	0.588905i
$579$	−1.89506	−	7.67638i	−0.0787561	−	0.319020i
$580$	2.04325	+	23.3545i	0.0848415	+	0.969742i
$581$	−7.32656	+	8.73145i	−0.303957	+	0.362242i
$582$	−0.00291990	+	0.147678i	−0.000121034	+	0.00612144i
$583$	8.12275	+	17.4193i	0.336410	+	0.721433i
$584$	−4.26129	+	7.38077i	−0.176334	+	0.305419i
$585$	−3.71134	−	39.7134i	−0.153445	−	1.64195i
$586$	−9.69555	−	16.7932i	−0.400519	−	0.693720i
$587$	6.94157	−	9.91359i	0.286509	−	0.409178i	−0.649937	−	0.759988i	$-0.725205\pi$
$587$	6.94157	−	9.91359i	0.286509	−	0.409178i	0.936447	+	0.350810i	$0.114094\pi$
$588$	−11.1814	−	2.20033i	−0.461112	−	0.0907400i
$589$	12.9551	+	35.5939i	0.533806	+	1.46662i
$590$	8.25245	−	5.77843i	0.339748	−	0.237894i
$591$	10.9558	+	7.99869i	0.450661	+	0.329022i
$592$	6.53816	+	0.572015i	0.268717	+	0.0235097i
$593$	18.7387	−	18.7387i	0.769504	−	0.769504i	−0.208515	−	0.978019i	$-0.566863\pi$
$593$	18.7387	−	18.7387i	0.769504	−	0.769504i	0.978019	+	0.208515i	$0.0668629\pi$
$594$	−8.54530	+	9.03699i	−0.350618	+	0.370792i
$595$		−	2.80753i		−	0.115098i
$596$	1.55014	−	17.7182i	0.0634964	−	0.725767i
$597$	−1.95505	+	1.57569i	−0.0800150	+	0.0644885i
$598$	−10.5491	+	16.6255i	−0.431383	+	0.679867i
$599$	−9.02121	−	24.7856i	−0.368597	−	1.01271i	−0.975896	−	0.218237i	$-0.929969\pi$
$599$	−9.02121	−	24.7856i	−0.368597	−	1.01271i	0.607299	−	0.794473i	$-0.292253\pi$
$600$	14.8577	−	1.00438i	0.606564	−	0.0410035i
$601$	−2.98026	−	16.9019i	−0.121568	−	0.689444i	−0.983288	−	0.182060i	$-0.941724\pi$
$601$	−2.98026	−	16.9019i	−0.121568	−	0.689444i	0.861720	−	0.507384i	$-0.169387\pi$
$602$	1.65846	+	2.87254i	0.0675939	+	0.117076i
$603$	8.70940	+	6.62648i	0.354674	+	0.269851i
$604$	1.67092	+	6.23594i	0.0679886	+	0.253737i
$605$	17.6150	−	8.21400i	0.716151	−	0.333947i
$606$	−9.07342	−	2.62452i	−0.368583	−	0.106614i
$607$	35.8619	+	30.0917i	1.45559	+	1.22138i	0.928372	+	0.371653i	$0.121209\pi$
$607$	35.8619	+	30.0917i	1.45559	+	1.22138i	0.527217	+	0.849731i	$0.323235\pi$
$608$	−5.15820	−	4.32825i	−0.209193	−	0.175534i
$609$	−1.98443	+	6.86050i	−0.0804130	+	0.278002i
$610$	−6.14616	+	16.8864i	−0.248851	+	0.683712i
$611$	−15.6924	−	20.3737i	−0.634846	−	0.824233i
$612$	−3.48975	+	0.473978i	−0.141065	+	0.0191594i
$613$	8.50560	+	2.27907i	0.343538	+	0.0920508i	0.426463	−	0.904505i	$-0.359759\pi$
$613$	8.50560	+	2.27907i	0.343538	+	0.0920508i	−0.0829248	+	0.996556i	$0.526426\pi$
$614$	−27.5546	+	4.85861i	−1.11201	+	0.196078i
$615$	−35.7595	−	31.2310i	−1.44196	−	1.25935i
$616$	0.656064	−	1.40693i	0.0264336	−	0.0566870i
$617$	−1.14814	+	0.803936i	−0.0462223	+	0.0323652i	−0.596459	−	0.802643i	$-0.703426\pi$
$617$	−1.14814	+	0.803936i	−0.0462223	+	0.0323652i	0.550237	+	0.835009i	$0.314537\pi$
$618$	−25.1279	−	2.69991i	−1.01079	−	0.108606i
$619$	−25.1063	−	2.19651i	−1.00911	−	0.0882853i	−0.429403	−	0.903113i	$-0.641276\pi$
$619$	−25.1063	−	2.19651i	−1.00911	−	0.0882853i	−0.579703	+	0.814828i	$0.696831\pi$
$620$		−	20.7433i		−	0.833070i
$621$	8.10760	+	27.1932i	0.325347	+	1.09122i
$622$	−16.7741	−	16.7741i	−0.672580	−	0.672580i
$623$	−8.62465	+	7.23694i	−0.345539	+	0.289942i
$624$	5.32635	−	3.26037i	0.213225	−	0.130519i
$625$	−1.03003	+	5.84161i	−0.0412014	+	0.233665i
$626$	−23.1648	−	10.8019i	−0.925851	−	0.431732i
$627$	−5.39008	+	27.3907i	−0.215259	+	1.09388i
$628$	7.66054	−	1.35076i	0.305689	−	0.0539012i
$629$	1.99412	−	7.44214i	0.0795106	−	0.296738i
$630$	6.85140	+	2.12944i	0.272966	+	0.0848389i
$631$	2.58063	−	0.691477i	0.102733	−	0.0275273i	−0.207086	−	0.978323i	$-0.566398\pi$
$631$	2.58063	−	0.691477i	0.102733	−	0.0275273i	0.309819	+	0.950795i	$0.399731\pi$
$632$	−11.6478	+	5.43147i	−0.463325	+	0.216052i
$633$	0.0235745	−	1.19231i	0.000937003	−	0.0473901i
$634$	10.6411	−	12.6816i	0.422614	−	0.503651i
$635$	33.1669	−	2.90173i	1.31619	−	0.115152i
$636$	−11.9049	−	7.19078i	−0.472061	−	0.285133i
$637$	−1.07793	−	23.6978i	−0.0427091	−	0.938939i
$638$	13.1787	+	7.60873i	0.521750	+	0.301232i
$639$	3.78057	+	1.94841i	0.149557	+	0.0770779i
$640$	1.84375	+	3.19347i	0.0728807	+	0.126233i
$641$	−0.397493	−	2.25429i	−0.0157000	−	0.0890393i	0.975951	−	0.217990i	$-0.0699501\pi$
$641$	−0.397493	−	2.25429i	−0.0157000	−	0.0890393i	−0.991651	+	0.128951i	$0.958839\pi$
$642$	3.27290	+	1.60570i	0.129171	+	0.0633718i
$643$	−4.55145	+	9.76061i	−0.179492	+	0.384921i	−0.975383	−	0.220519i	$-0.929225\pi$
$643$	−4.55145	+	9.76061i	−0.179492	+	0.384921i	0.795891	+	0.605440i	$0.207003\pi$
$644$	−2.03147	−	2.90125i	−0.0800513	−	0.114325i
$645$	13.2168	+	29.8714i	0.520410	+	1.17619i
$646$	−6.05537	+	5.08106i	−0.238245	+	0.199912i
$647$	−19.4860			−0.766072			−0.383036	−	0.923733i	$-0.625121\pi$
$647$	−19.4860			−0.766072			−0.383036	+	0.923733i	$0.625121\pi$
$648$	1.49021	−	8.87577i	0.0585409	−	0.348673i
$649$		−	6.53934i		−	0.256692i
$650$	9.37555	+	29.5476i	0.367739	+	1.15895i
$651$	2.27822	−	5.89413i	0.0892905	−	0.231009i
$652$	−12.1828	−	17.3988i	−0.477114	−	0.681389i
$653$	−16.4777	−	45.2720i	−0.644821	−	1.77163i	−0.636023	−	0.771670i	$-0.719422\pi$
$653$	−16.4777	−	45.2720i	−0.644821	−	1.77163i	−0.00879842	−	0.999961i	$-0.502801\pi$
$654$	−5.90962	−	17.2928i	−0.231084	−	0.676202i
$655$	−6.75972	−	4.73321i	−0.264124	−	0.184942i
$656$	1.92394	−	7.18024i	0.0751172	−	0.280341i
$657$	−21.5072	+	13.8257i	−0.839076	+	0.539392i
$658$	4.46822	−	1.19725i	0.174189	−	0.0466738i
$659$	−2.62679	+	7.21706i	−0.102325	+	0.281137i	−0.980282	−	0.197603i	$-0.936684\pi$
$659$	−2.62679	+	7.21706i	−0.102325	+	0.281137i	0.877957	+	0.478740i	$0.158906\pi$
$660$	7.90406	−	13.0858i	0.307665	−	0.509365i
$661$	−1.34434	−	15.3659i	−0.0522887	−	0.597663i	−0.976462	−	0.215689i	$-0.930800\pi$
$661$	−1.34434	−	15.3659i	−0.0522887	−	0.597663i	0.924173	−	0.381973i	$-0.124755\pi$
$662$	3.09877	+	2.60018i	0.120437	+	0.101059i
$663$	−2.68352	−	6.82240i	−0.104219	−	0.264960i
$664$	−16.5146	−	6.01083i	−0.640892	−	0.233265i
$665$	15.5550	−	4.16795i	0.603197	−	0.161626i
$666$	16.6491	+	10.5110i	0.645138	+	0.407295i
$667$	30.0673	−	17.3594i	1.16421	−	0.672158i
$668$	−12.0596	+	17.2228i	−0.466598	+	0.666372i
$669$	−11.0501	+	7.41617i	−0.427220	+	0.286726i
$670$	−12.1913	−	5.68490i	−0.470991	−	0.219627i
$671$	6.69051	+	9.55504i	0.258284	+	0.368868i
$672$	0.173158	+	1.10991i	0.00667973	+	0.0428158i
$673$	−6.23737	−	7.43340i	−0.240433	−	0.286537i	0.632311	−	0.774714i	$-0.282106\pi$
$673$	−6.23737	−	7.43340i	−0.240433	−	0.286537i	−0.872744	+	0.488178i	$0.837662\pi$
$674$	−1.75231	+	1.75231i	−0.0674966	+	0.0674966i
$675$	41.0011	+	17.7412i	1.57813	+	0.682859i
$676$	9.22582	+	9.15883i	0.354839	+	0.352263i
$677$	−15.7510	−	18.7713i	−0.605360	−	0.721440i	0.373120	−	0.927783i	$-0.378288\pi$
$677$	−15.7510	−	18.7713i	−0.605360	−	0.721440i	−0.978480	+	0.206343i	$0.933844\pi$
$678$	23.7962	+	2.55682i	0.913886	+	0.0981940i
$679$	0.00960416	−	0.0544679i	0.000368574	−	0.00209029i
$680$	4.06781	−	1.48056i	0.155993	−	0.0567770i
$681$	−6.71495	+	0.453928i	−0.257317	+	0.0173946i
$682$	−11.0295	−	7.72297i	−0.422343	−	0.295728i
$683$	−5.88769	−	1.57760i	−0.225286	−	0.0603653i	0.144410	−	0.989518i	$-0.453872\pi$
$683$	−5.88769	−	1.57760i	−0.225286	−	0.0603653i	−0.369696	+	0.929153i	$0.620538\pi$
$684$	−7.80680	−	18.6312i	−0.298501	−	0.712381i
$685$	−21.6828	+	37.5557i	−0.828458	+	1.43493i
$686$	8.27590	+	3.01218i	0.315975	+	0.115006i
$687$	27.2252	+	7.87499i	1.03871	+	0.300450i
$688$	−3.28741	+	3.91778i	−0.125331	+	0.149364i
$689$	8.65570	−	27.6278i	0.329756	−	1.05254i
$690$	−16.8389	−	30.5449i	−0.641048	−	1.16282i
$691$	−38.9412	+	18.1586i	−1.48139	+	0.690785i	−0.984234	−	0.176874i	$-0.943402\pi$
$691$	−38.9412	+	18.1586i	−1.48139	+	0.690785i	−0.497160	+	0.867659i	$0.665624\pi$
$692$	−9.77383	−	5.64292i	−0.371545	−	0.214512i
$693$	3.68312	−	2.85019i	0.139910	−	0.108270i
$694$	−15.3954	−	4.12518i	−0.584401	−	0.156590i
$695$	−29.3201	+	41.8734i	−1.11217	+	1.58835i
$696$	−10.9866	+	0.742691i	−0.416447	+	0.0281516i
$697$	−7.90885	−	3.68796i	−0.299569	−	0.139691i
$698$	23.4571	+	4.13612i	0.887865	+	0.156555i
$699$	−29.8072	−	36.9836i	−1.12741	−	1.39885i
$700$	−5.55489	−	0.485990i	−0.209955	−	0.0183687i
$701$	−1.34074			−0.0506390			−0.0253195	−	0.999679i	$-0.508060\pi$
$701$	−1.34074			−0.0506390			−0.0253195	+	0.999679i	$0.508060\pi$
$702$	18.6845	−	1.37416i	0.705202	−	0.0518642i
$703$	44.1933			1.66678
$704$	2.38447	+	0.208614i	0.0898682	+	0.00786245i
$705$	45.0103	−	7.02210i	1.69519	−	0.264467i
$706$	−2.17218	−	0.383014i	−0.0817510	−	0.0144149i
$707$	3.20541	+	1.49471i	0.120552	+	0.0562143i
$708$	2.63702	+	3.92914i	0.0991052	+	0.147666i
$709$	8.43882	−	12.0519i	0.316927	−	0.452618i	−0.628807	−	0.777561i	$-0.716456\pi$
$709$	8.43882	−	12.0519i	0.316927	−	0.452618i	0.945733	+	0.324944i	$0.105345\pi$
$710$	−5.04966	−	1.35305i	−0.189510	−	0.0507792i
$711$	−38.5257	−	1.52407i	−1.44483	−	0.0571570i
$712$	−15.0338	−	8.67976i	−0.563415	−	0.325288i
$713$	−27.8414	+	12.9827i	−1.04267	+	0.486204i
$714$	1.31846	+	0.0260688i	0.0493422	+	0.000975601i
$715$	30.3683	+	9.51429i	1.13571	+	0.355814i
$716$	−5.54683	+	6.61045i	−0.207295	+	0.247044i
$717$	−10.3620	−	41.9736i	−0.386976	−	1.56753i
$718$	6.66185	+	2.42471i	0.248618	+	0.0904896i
$719$	8.53653	−	14.7857i	0.318359	−	0.551414i	−0.661787	−	0.749692i	$-0.730202\pi$
$719$	8.53653	−	14.7857i	0.318359	−	0.551414i	0.980146	+	0.198278i	$0.0635350\pi$
$720$	0.527784	+	11.0499i	0.0196693	+	0.411806i
$721$	9.14073	+	2.44925i	0.340419	+	0.0912149i
$722$	−21.5771	−	15.1084i	−0.803016	−	0.562278i
$723$	1.64084	−	3.34453i	0.0610234	−	0.124384i
$724$	13.1753	−	4.79542i	0.489657	−	0.178221i
$725$	9.49173	−	53.8303i	0.352514	−	1.99921i
$726$	3.69387	+	8.34855i	0.137092	+	0.309844i
$727$	−27.9707	−	33.3342i	−1.03738	−	1.23630i	−0.971144	−	0.238493i	$-0.923347\pi$
$727$	−27.9707	−	33.3342i	−1.03738	−	1.23630i	−0.0662319	−	0.997804i	$-0.521098\pi$
$728$	−2.15878	+	0.898807i	−0.0800097	+	0.0333120i
$729$	16.1722	−	21.6208i	0.598972	−	0.800770i
$730$	22.2223	−	22.2223i	0.822484	−	0.822484i
$731$	3.85919	+	4.59920i	0.142737	+	0.170108i
$732$	−7.87308	−	3.04313i	−0.290997	−	0.112477i
$733$	25.4025	+	36.2785i	0.938261	+	1.33998i	0.940433	+	0.339978i	$0.110420\pi$
$733$	25.4025	+	36.2785i	0.938261	+	1.33998i	−0.00217231	+	0.999998i	$0.500691\pi$
$734$	−5.68785	−	2.65229i	−0.209942	−	0.0978977i
$735$	37.7264	+	18.5087i	1.39156	+	0.682704i
$736$	3.13229	−	4.47337i	0.115458	−	0.164891i
$737$	−7.56172	+	4.36576i	−0.278540	+	0.160815i
$738$	14.9986	−	16.5033i	0.552107	−	0.607493i
$739$	11.2927	−	3.02588i	0.415410	−	0.111309i	−0.0450595	−	0.998984i	$-0.514348\pi$
$739$	11.2927	−	3.02588i	0.415410	−	0.111309i	0.460470	+	0.887676i	$0.347681\pi$
$740$	−22.7421	−	8.27743i	−0.836015	−	0.304284i
$741$	33.8154	−	24.9962i	1.24224	−	0.918259i
$742$	3.98942	+	3.34752i	0.146456	+	0.122891i
$743$	−2.18522	−	24.9772i	−0.0801679	−	0.916323i	−0.924670	−	0.380770i	$-0.875659\pi$
$743$	−2.18522	−	24.9772i	−0.0801679	−	0.916323i	0.844502	−	0.535553i	$-0.179897\pi$
$744$	9.74139	+	0.192608i	0.357137	+	0.00706135i
$745$	−22.4316	+	61.6303i	−0.821830	+	2.25796i
$746$	−0.883566	+	0.236751i	−0.0323497	+	0.00866807i
$747$	−35.7783	−	38.7257i	−1.30906	−	1.41690i
$748$	0.727255	−	2.71415i	0.0265911	−	0.0992393i
$749$	−1.11820	−	0.782970i	−0.0408580	−	0.0286091i
$750$	−22.5458	−	4.43668i	−0.823256	−	0.162005i
$751$	−1.87673	−	5.15626i	−0.0684827	−	0.188155i	0.900730	−	0.434379i	$-0.143032\pi$
$751$	−1.87673	−	5.15626i	−0.0684827	−	0.188155i	−0.969213	+	0.246224i	$0.920810\pi$
$752$	4.09102	+	5.84259i	0.149184	+	0.213057i
$753$	−10.2824	+	1.60416i	−0.374710	+	0.0584588i
$754$	−6.93280	−	21.8492i	−0.252478	−	0.795699i
$755$		−	23.8062i		−	0.866398i
$756$	−1.06364	+	3.19776i	−0.0386841	+	0.116301i
$757$	−28.3322			−1.02975			−0.514876	−	0.857265i	$-0.672162\pi$
$757$	−28.3322			−1.02975			−0.514876	+	0.857265i	$0.672162\pi$
$758$	2.94470	−	2.47089i	0.106956	−	0.0897469i
$759$	−22.5106	−	2.41869i	−0.817082	−	0.0877928i
$760$	14.2419	+	20.3396i	0.516608	+	0.737793i
$761$	−16.5666	+	35.5272i	−0.600538	+	1.28786i	0.337500	+	0.941326i	$0.390419\pi$
$761$	−16.5666	+	35.5272i	−0.600538	+	1.28786i	−0.938038	+	0.346533i	$0.887359\pi$
$762$	1.05473	+	15.6027i	0.0382090	+	0.565225i
$763$	1.18825	+	6.73893i	0.0430177	+	0.243965i
$764$	9.19947	+	15.9339i	0.332825	+	0.576470i
$765$	12.8824	+	1.64237i	0.465762	+	0.0593799i
$766$	0.238427	+	0.137656i	0.00861472	+	0.00497371i
$767$	−6.64165	+	7.27465i	−0.239816	+	0.262673i
$768$	−1.51683	+	0.836204i	−0.0547338	+	0.0301739i
$769$	−42.9839	+	3.76061i	−1.55004	+	0.135611i	−0.829779	−	0.558092i	$-0.811534\pi$
$769$	−42.9839	+	3.76061i	−1.55004	+	0.135611i	−0.720261	+	0.693703i	$0.755978\pi$
$770$	−3.67958	+	4.38515i	−0.132603	+	0.158030i
$771$	−3.40722	+	1.87835i	−0.122708	+	0.0676470i
$772$	−4.13731	+	1.92926i	−0.148905	+	0.0694356i
$773$	30.0621	−	8.05512i	1.08126	−	0.289722i	0.326147	−	0.945319i	$-0.394249\pi$
$773$	30.0621	−	8.05512i	1.08126	−	0.289722i	0.755111	+	0.655596i	$0.227583\pi$
$774$	−14.1508	+	5.92945i	−0.508641	+	0.213130i
$775$	−12.5176	+	46.7165i	−0.449647	+	1.67811i
$776$	0.0839829	−	0.0148084i	0.00301481	−	0.000531592i
$777$	−5.55297	−	4.84975i	−0.199212	−	0.173984i
$778$	−0.153684	−	0.0716642i	−0.00550985	−	0.00256929i
$779$	8.69180	−	49.2936i	0.311416	−	1.76613i
$780$	−22.0834	+	6.52952i	−0.790711	+	0.233794i
$781$	−2.59949	+	2.18123i	−0.0930171	+	0.0780506i
$782$	−4.53313	−	4.53313i	−0.162104	−	0.162104i
$783$	−30.3185	−	13.1188i	−1.08350	−	0.468829i
$784$			6.57937i			0.234978i
$785$	−28.5749	−	2.49998i	−1.01988	−	0.0892281i
$786$	2.28556	−	3.13053i	0.0815231	−	0.111662i
$787$	36.1433	−	25.3078i	1.28837	−	0.902125i	0.289878	−	0.957064i	$-0.406385\pi$
$787$	36.1433	−	25.3078i	1.28837	−	0.902125i	0.998490	+	0.0549387i	$0.0174963\pi$
$788$	3.30984	−	7.09797i	0.117908	−	0.252855i
$789$	0.596444	−	3.03094i	0.0212340	−	0.107904i
$790$	46.6716	−	8.22947i	1.66050	−	0.292791i
$791$	−8.65630	−	2.31945i	−0.307783	−	0.0824701i
$792$	6.07192	+	3.83338i	0.215756	+	0.136213i
$793$	2.26170	−	17.4246i	0.0803155	−	0.618766i
$794$	12.5378	−	34.4475i	0.444952	−	1.22249i
$795$	35.5408	+	36.9745i	1.26050	+	1.31135i
$796$	1.11055	+	0.931859i	0.0393623	+	0.0330288i
$797$	22.8847	+	19.2026i	0.810619	+	0.680190i	0.950755	−	0.309942i	$-0.100310\pi$
$797$	22.8847	+	19.2026i	0.810619	+	0.680190i	−0.140136	+	0.990132i	$0.544754\pi$
$798$	1.81291	+	7.34359i	0.0641762	+	0.259960i
$799$	7.58855	−	3.53860i	0.268464	−	0.125187i
$800$	−2.22524	−	8.30472i	−0.0786743	−	0.293616i
$801$	−28.1614	−	43.8077i	−0.995034	−	1.54787i
$802$	−5.63315	−	9.75689i	−0.198913	−	0.344528i
$803$	−3.54234	−	20.0896i	−0.125006	−	0.708946i
$804$	2.78292	−	5.67245i	0.0981460	−	0.200052i
$805$	4.46688	+	12.2726i	0.157437	+	0.432554i
$806$	4.42596	+	19.7935i	0.155898	+	0.697195i
$807$	12.0151	+	4.64413i	0.422952	+	0.163481i
$808$	−0.475285	+	5.43254i	−0.0167205	+	0.191116i
$809$			43.7963i			1.53980i	0.638167	+	0.769898i	$0.279693\pi$
$809$			43.7963i			1.53980i	−0.638167	+	0.769898i	$0.720307\pi$
$810$	−13.7789	+	30.1920i	−0.484141	+	1.06084i
$811$	38.4196	−	38.4196i	1.34909	−	1.34909i	0.462448	−	0.886646i	$-0.346971\pi$
$811$	38.4196	−	38.4196i	1.34909	−	1.34909i	0.886646	−	0.462448i	$-0.153029\pi$
$812$	4.10759	+	0.359368i	0.144148	+	0.0126113i
$813$	1.97444	−	0.873604i	0.0692467	−	0.0306386i
$814$	−12.8684	+	9.01054i	−0.451037	+	0.315819i
$815$	26.7879	+	73.5991i	0.938339	+	2.57806i
$816$	0.657525	+	1.92406i	0.0230180	+	0.0673555i
$817$	−19.7525	+	28.2095i	−0.691052	+	0.986924i
$818$	14.9875	+	25.9591i	0.524026	+	0.907639i
$819$	−6.99204	−	0.570063i	−0.244322	−	0.0199196i
$820$	−13.7056	+	23.7388i	−0.478620	+	0.828993i
$821$	15.2147	+	32.6281i	0.530998	+	1.13873i	0.970636	+	0.240553i	$0.0773289\pi$
$821$	15.2147	+	32.6281i	0.530998	+	1.13873i	−0.439638	+	0.898175i	$0.644893\pi$
$822$	−17.4355	−	10.5313i	−0.608131	−	0.367322i
$823$	2.85413	−	3.40142i	0.0994886	−	0.118566i	−0.714003	−	0.700143i	$-0.753120\pi$
$823$	2.85413	−	3.40142i	0.0994886	−	0.118566i	0.813491	+	0.581577i	$0.197564\pi$
$824$	1.27170	+	14.5356i	0.0443017	+	0.506370i
$825$	−25.6977	+	24.7012i	−0.894677	+	0.859984i
$826$	−0.748831	−	1.60587i	−0.0260552	−	0.0558755i
$827$	−8.14421	−	30.3946i	−0.283202	−	1.05692i	−0.950143	−	0.311814i	$-0.899063\pi$
$827$	−8.14421	−	30.3946i	−0.283202	−	1.05692i	0.666941	−	0.745111i	$-0.267603\pi$
$828$	14.5007	−	7.62423i	0.503936	−	0.264960i
$829$	4.15492	−	2.39885i	0.144306	−	0.0833154i	−0.426108	−	0.904672i	$-0.640116\pi$
$829$	4.15492	−	2.39885i	0.144306	−	0.0833154i	0.570415	+	0.821357i	$0.306782\pi$
$830$	53.0860	+	37.1712i	1.84264	+	1.29023i
$831$	−4.65206	+	23.6403i	−0.161378	+	0.820073i
$832$	−2.44071	−	2.65385i	−0.0846165	−	0.0920057i
$833$	7.60639	+	1.34121i	0.263546	+	0.0464702i
$834$	−19.3922	−	14.1580i	−0.671497	−	0.490251i
$835$	59.3918	−	49.8357i	2.05534	−	1.72463i
$836$	16.1173			0.557429
$837$	25.7125	+	13.9016i	0.888753	+	0.480509i
$838$	−12.5507	+	12.5507i	−0.433557	+	0.433557i
$839$	3.96670	−	45.3396i	0.136946	−	1.56530i	−0.547860	−	0.836570i	$-0.684557\pi$
$839$	3.96670	−	45.3396i	0.136946	−	1.56530i	0.684806	−	0.728726i	$-0.259887\pi$
$840$	0.442530	−	4.11861i	0.0152687	−	0.142105i
$841$	−1.98292	+	11.2457i	−0.0683765	+	0.387782i
$842$	31.2806	−	11.3852i	1.07800	−	0.392360i
$843$	2.61400	+	38.6689i	0.0900310	+	1.33183i
$844$	−0.678055	+	0.119559i	−0.0233396	+	0.00411540i
$845$	−24.1199	−	41.4275i	−0.829750	−	1.42515i
$846$	2.87976	+	21.2028i	0.0990081	+	0.728966i
$847$	−0.884748	−	3.30193i	−0.0304003	−	0.113456i
$848$	−2.74636	+	7.54557i	−0.0943105	+	0.259116i
$849$	15.0882	+	27.3691i	0.517824	+	0.939304i
$850$	−10.0547	+	0.879670i	−0.344873	+	0.0301724i
$851$	3.12376	+	35.7048i	0.107081	+	1.22394i
$852$	0.682304	−	2.35884i	0.0233753	−	0.0808125i
$853$	−10.4569	−	22.4248i	−0.358037	−	0.767812i	−0.999999	−	0.00107611i	$-0.999657\pi$
$853$	−10.4569	−	22.4248i	−0.358037	−	0.767812i	0.641963	−	0.766736i	$-0.278120\pi$
$854$	2.73716	+	1.58030i	0.0936636	+	0.0540767i
$855$	10.0252	+	73.8123i	0.342854	+	2.52433i
$856$	0.544754	−	2.03305i	0.0186193	−	0.0694882i
$857$	−8.22760	−	46.6610i	−0.281049	−	1.59391i	−0.719065	−	0.694943i	$-0.755430\pi$
$857$	−8.22760	−	46.6610i	−0.281049	−	1.59391i	0.438016	−	0.898967i	$-0.355681\pi$
$858$	−4.75005	+	14.1731i	−0.162164	+	0.483862i
$859$	−27.8653	+	10.1421i	−0.950752	+	0.346046i	−0.770403	−	0.637557i	$-0.779945\pi$
$859$	−27.8653	+	10.1421i	−0.950752	+	0.346046i	−0.180349	+	0.983603i	$0.557723\pi$
$860$	15.4484	−	10.8171i	0.526785	−	0.368859i
$861$	−6.50160	+	5.24001i	−0.221574	+	0.178579i
$862$	−20.1535	−	24.0180i	−0.686431	−	0.818057i
$863$	14.6193	+	14.6193i	0.497645	+	0.497645i	0.910704	−	0.413059i	$-0.135540\pi$
$863$	14.6193	+	14.6193i	0.497645	+	0.497645i	−0.413059	+	0.910704i	$0.635540\pi$
$864$	−5.19412	+	0.145254i	−0.176708	+	0.00494164i
$865$	29.4274	+	29.4274i	1.00056	+	1.00056i
$866$	0.0410834	−	0.469585i	0.00139607	−	0.0159571i
$867$	−26.7345	+	4.17088i	−0.907951	+	0.141650i
$868$	−3.59291	−	0.633527i	−0.121951	−	0.0215033i
$869$	13.0007	−	27.8800i	0.441017	−	0.945764i
$870$	39.8416	+	7.84023i	1.35076	+	0.265809i
$871$	12.8461	+	2.82336i	0.435272	+	0.0956657i
$872$	−9.13735	+	5.27545i	−0.309430	+	0.178649i
$873$	0.244307	+	0.0759316i	0.00826855	+	0.00256990i
$874$	18.3859	−	31.8453i	0.621912	−	1.07718i
$875$	8.08520	+	2.94277i	0.273330	+	0.0994839i
$876$	10.2296	+	10.6423i	0.345627	+	0.359570i
$877$	−17.8744	+	1.56381i	−0.603577	+	0.0528061i	−0.384849	−	0.922980i	$-0.625746\pi$
$877$	−17.8744	+	1.56381i	−0.603577	+	0.0528061i	−0.218728	+	0.975786i	$0.570191\pi$
$878$	32.6759	−	2.85877i	1.10276	−	0.0964789i
$879$	−32.6074	+	8.04977i	−1.09982	+	0.271512i
$880$	−8.29405	−	3.01879i	−0.279592	−	0.101763i
$881$	−16.1326	+	27.9425i	−0.543522	+	0.941408i	0.455176	+	0.890401i	$0.349576\pi$
$881$	−16.1326	+	27.9425i	−0.543522	+	0.941408i	−0.998698	+	0.0510064i	$0.983757\pi$
$882$	−9.04229	+	17.5451i	−0.304470	+	0.590774i
$883$	−10.4625	+	6.04054i	−0.352092	+	0.203280i	−0.665606	−	0.746303i	$-0.731827\pi$
$883$	−10.4625	+	6.04054i	−0.352092	+	0.203280i	0.313514	+	0.949583i	$0.398494\pi$
$884$	−3.56565	+	2.28071i	−0.119926	+	0.0767086i
$885$	−5.64272	−	16.5118i	−0.189678	−	0.555038i
$886$	−5.56967	+	11.9442i	−0.187117	+	0.401273i
$887$	4.32232	+	0.762142i	0.145129	+	0.0255902i	0.245741	−	0.969336i	$-0.420969\pi$
$887$	4.32232	+	0.762142i	0.145129	+	0.0255902i	−0.100611	+	0.994926i	$0.532080\pi$
$888$	4.09839	−	10.6032i	0.137533	−	0.355820i
$889$	0.510357	−	5.83341i	0.0171168	−	0.195646i
$890$	45.2642	+	45.2642i	1.51726	+	1.51726i
$891$	10.9235	+	18.5673i	0.365951	+	0.622028i
$892$	5.43297	+	5.43297i	0.181909	+	0.181909i
$893$	30.8711	+	36.7908i	1.03306	+	1.23116i
$894$	−28.7343	−	11.1065i	−0.961020	−	0.371457i
$895$	26.0660	−	18.2516i	0.871290	−	0.610084i
$896$	0.609446	−	0.221820i	0.0203602	−	0.00741050i
$897$	22.5852	+	25.5534i	0.754099	+	0.853203i
$898$	−0.0300725	−	0.170549i	−0.00100353	−	0.00569131i
$899$	9.25625	−	34.5448i	0.308713	−	1.15213i
$900$	5.47949	−	25.2043i	0.182650	−	0.840143i
$901$	8.16356	+	4.71323i	0.271968	+	0.157021i
$902$	7.51954	+	16.1257i	0.250373	+	0.536927i
$903$	5.57763	−	1.37695i	0.185612	−	0.0458219i
$904$	−1.20430	−	13.7652i	−0.0400544	−	0.457824i
$905$	−51.5053	+	4.50613i	−1.71209	+	0.149789i
$906$	11.1798	+	0.221049i	0.371424	+	0.00734385i
$907$	−7.72720	+	21.2303i	−0.256578	+	0.704941i	0.742795	+	0.669519i	$0.233500\pi$
$907$	−7.72720	+	21.2303i	−0.256578	+	0.704941i	−0.999372	+	0.0354221i	$0.988722\pi$
$908$	1.00570	+	3.75332i	0.0333753	+	0.124558i
$909$	−8.73359	+	13.8336i	−0.289675	+	0.458833i
$910$	8.54707	−	1.14109i	0.283333	−	0.0378268i
$911$	50.7167	−	8.94272i	1.68032	−	0.296286i	0.749565	−	0.661931i	$-0.230263\pi$
$911$	50.7167	−	8.94272i	1.68032	−	0.296286i	0.930754	+	0.365646i	$0.119152\pi$
$912$	−9.68403	+	6.49938i	−0.320670	+	0.215216i
$913$	39.5291	−	14.3874i	1.30822	−	0.476154i
$914$	5.53441	−	31.3872i	0.183062	−	1.03820i
$915$	25.1384	+	18.3532i	0.831050	+	0.606739i
$916$	1.42611	−	16.3006i	0.0471202	−	0.538586i
$917$	−1.02628	+	1.02628i	−0.0338908	+	0.0338908i
$918$	−0.890899	+	6.03451i	−0.0294041	+	0.199169i
$919$	−40.7821			−1.34528			−0.672638	−	0.739971i	$-0.734839\pi$
$919$	−40.7821			−1.34528			−0.672638	+	0.739971i	$0.734839\pi$
$920$	−15.4261	+	12.9441i	−0.508584	+	0.426753i
$921$	−5.17730	+	48.1848i	−0.170598	+	1.58774i
$922$	32.2323	+	5.68343i	1.06152	+	0.187174i
$923$	5.10714	+	0.213661i	0.168104	+	0.00703272i
$924$	−2.02517	−	1.76871i	−0.0666233	−	0.0581862i
$925$	46.2229	+	32.3656i	1.51980	+	1.06418i
$926$	24.7136	−	14.2684i	0.812139	−	0.468889i
$927$	−16.5856	+	40.5095i	−0.544742	+	1.33051i
$928$	1.64547	+	6.14098i	0.0540152	+	0.201587i
$929$	−20.1272	−	43.1629i	−0.660352	−	1.41613i	−0.895895	−	0.444265i	$-0.853465\pi$
$929$	−20.1272	−	43.1629i	−0.660352	−	1.41613i	0.235544	−	0.971864i	$-0.424313\pi$
$930$	−34.5136	−	9.98318i	−1.13174	−	0.327361i
$931$	3.86122	+	44.1340i	0.126546	+	1.44643i
$932$	−17.6279	+	21.0081i	−0.577421	+	0.688144i
$933$	−35.9824	+	19.8366i	−1.17801	+	0.649420i
$934$	−7.03675	−	15.0904i	−0.230250	−	0.493772i
$935$	−5.18076	+	8.97333i	−0.169429	+	0.293459i
$936$	−2.86132	−	10.4313i	−0.0935251	−	0.340959i
$937$	−28.0129	−	48.5197i	−0.915141	−	1.58507i	−0.806695	−	0.590968i	$-0.798746\pi$
$937$	−28.0129	−	48.5197i	−0.915141	−	1.58507i	−0.108446	−	0.994102i	$-0.534588\pi$
$938$	−1.35701	+	1.93801i	−0.0443079	+	0.0632783i
$939$	−29.1213	+	33.3439i	−0.950338	+	1.08814i
$940$	−8.99549	−	24.7149i	−0.293400	−	0.806111i
$941$	−30.0252	+	21.0239i	−0.978794	+	0.685359i	−0.949354	−	0.314208i	$-0.898261\pi$
$941$	−30.0252	+	21.0239i	−0.978794	+	0.685359i	−0.0294395	+	0.999567i	$0.509372\pi$
$942$	1.43936	−	13.3960i	0.0468969	−	0.436466i
$943$	40.4398	+	3.53803i	1.31690	+	0.115214i
$944$	1.93184	−	1.93184i	0.0628760	−	0.0628760i
$945$	6.84045	−	10.3748i	0.222520	−	0.337493i
$946$		−	12.2415i		−	0.398005i
$947$	2.60800	−	29.8095i	0.0847485	−	0.968680i	−0.828154	−	0.560501i	$-0.810609\pi$
$947$	2.60800	−	29.8095i	0.0847485	−	0.968680i	0.912902	−	0.408179i	$-0.133836\pi$
$948$	3.43133	+	21.9942i	0.111444	+	0.714338i
$949$	−16.4632	+	25.9463i	−0.534419	+	0.842252i
$950$	−19.8006	−	54.4016i	−0.642415	−	1.76502i
$951$	−15.9789	−	23.8085i	−0.518152	−	0.772044i
$952$	−0.132209	−	0.749797i	−0.00428493	−	0.0243011i
$953$	−0.784962	−	1.35959i	−0.0254274	−	0.0440416i	0.853032	−	0.521859i	$-0.174761\pi$
$953$	−0.784962	−	1.35959i	−0.0254274	−	0.0440416i	−0.878459	+	0.477818i	$0.841428\pi$
$954$	−17.6939	+	16.3472i	−0.572860	+	0.529260i
$955$	−17.5599	−	65.5344i	−0.568224	−	2.12064i
$956$	−22.6224	+	10.5490i	−0.731660	+	0.341178i
$957$	19.0023	−	18.2654i	0.614257	−	0.590437i
$958$	−12.6086	−	10.5799i	−0.407366	−	0.341821i
$959$	5.84274	+	4.90264i	0.188672	+	0.158315i
$960$	6.20079	−	1.53078i	0.200130	−	0.0494058i
$961$	−0.220226	+	0.605066i	−0.00710407	+	0.0195183i
$962$	23.4669	+	3.04599i	0.756602	+	0.0982065i
$963$	4.24679	−	4.67282i	0.136851	−	0.150579i
$964$	−2.07754	−	0.556676i	−0.0669132	−	0.0179293i
$965$	16.5778	−	2.92311i	0.533658	−	0.0940982i
$966$	−5.80491	+	1.98376i	−0.186770	+	0.0638266i
$967$	2.85042	−	6.11274i	0.0916633	−	0.196573i	−0.855131	−	0.518412i	$-0.826523\pi$
$967$	2.85042	−	6.11274i	0.0916633	−	0.196573i	0.946794	+	0.321839i	$0.104301\pi$
$968$	4.31756	−	3.02319i	0.138772	−	0.0971690i
$969$	5.53980	+	12.5206i	0.177964	+	0.402219i
$970$	−0.313268	−	0.0274074i	−0.0100584	−	0.000879999i
$971$			54.9466i			1.76332i	0.471884	+	0.881661i	$0.343574\pi$
$971$			54.9466i			1.76332i	−0.471884	+	0.881661i	$0.656426\pi$
$972$	−14.0507	−	6.75114i	−0.450676	−	0.216543i
$973$	6.35735	+	6.35735i	0.203807	+	0.203807i
$974$	−7.20350	+	6.04445i	−0.230815	+	0.193677i
$975$	53.6748	−	1.37898i	1.71897	−	0.0441625i
$976$	−0.846233	+	4.79922i	−0.0270873	+	0.153619i
$977$	−24.5349	−	11.4408i	−0.784940	−	0.366024i	−0.0115331	−	0.999933i	$-0.503671\pi$
$977$	−24.5349	−	11.4408i	−0.784940	−	0.366024i	−0.773407	+	0.633910i	$0.781449\pi$
$978$	−34.8121	+	11.8966i	−1.11317	+	0.380413i
$979$	40.9202	−	7.21533i	1.30781	−	0.230603i
$980$	6.27933	−	23.4348i	0.200586	−	0.748596i
$981$	−31.6167	+	1.51013i	−1.00944	+	0.0482146i
$982$	27.0744	−	7.25457i	0.863980	−	0.231503i
$983$	28.2829	−	13.1885i	0.902085	−	0.420649i	0.0844779	−	0.996425i	$-0.473078\pi$
$983$	28.2829	−	13.1885i	0.902085	−	0.420649i	0.817607	+	0.575776i	$0.195300\pi$
$984$	−11.0209	−	6.65679i	−0.351332	−	0.212211i
$985$	−18.5634	+	22.1230i	−0.591480	+	0.704899i
$986$	7.43499	−	0.650477i	0.236778	−	0.0207154i
$987$	0.158387	−	8.01062i	0.00504151	−	0.254981i
$988$	−17.9296	−	16.3695i	−0.570417	−	0.520782i
$989$	−24.1873	−	13.9645i	−0.769110	−	0.444046i
$990$	−17.9687	−	19.4490i	−0.571084	−	0.618129i
$991$	14.8877	+	25.7863i	0.472925	+	0.819130i	0.999520	−	0.0309864i	$-0.00986484\pi$
$991$	14.8877	+	25.7863i	0.472925	+	0.819130i	−0.526595	+	0.850116i	$0.676532\pi$
$992$	−0.976822	−	5.53983i	−0.0310141	−	0.175890i
$993$	5.81764	−	3.90447i	0.184617	−	0.123905i
$994$	−0.388583	+	0.833319i	−0.0123251	+	0.0264313i
$995$	−3.06624	−	4.37905i	−0.0972064	−	0.138825i
$996$	−17.9491	+	24.5849i	−0.568740	+	0.779002i
$997$	−13.0220	+	10.9268i	−0.412412	+	0.346055i	−0.825268	−	0.564741i	$-0.808976\pi$
$997$	−13.0220	+	10.9268i	−0.412412	+	0.346055i	0.412856	+	0.910797i	$0.364531\pi$
$998$	−32.3612			−1.02438
$999$	25.5015	−	22.6427i	0.806831	−	0.716385i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	702.2.bs.a.5.9	✓	504
13.8	odd	4	inner	702.2.bs.a.437.30	yes	504
27.11	odd	18	inner	702.2.bs.a.551.30	yes	504
351.281	even	36	inner	702.2.bs.a.281.9	yes	504

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
702.2.bs.a.5.9	✓	504	1.1	even	1	trivial
702.2.bs.a.281.9	yes	504	351.281	even	36	inner
702.2.bs.a.437.30	yes	504	13.8	odd	4	inner
702.2.bs.a.551.30	yes	504	27.11	odd	18	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:	\( N \)	\(=\)	\( 702 = 2 \cdot 3^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	702.bs (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.996195 - 0.0871557i) q^{2} +(-0.624455 + 1.61557i) q^{3} +(0.984808 + 0.173648i) q^{4} +(-3.34201 - 1.55841i) q^{5} +(0.762885 - 1.55499i) q^{6} +(-0.371998 + 0.531269i) q^{7} +(-0.965926 - 0.258819i) q^{8} +(-2.22011 - 2.01770i) q^{9} +(3.19347 + 1.84375i) q^{10} +(2.16932 - 1.01157i) q^{11} +(-0.895509 + 1.48259i) q^{12} +(-3.44065 - 1.07794i) q^{13} +(0.416886 - 0.496825i) q^{14} +(4.60465 - 4.42609i) q^{15} +(0.939693 + 0.342020i) q^{16} +(0.586965 - 1.01665i) q^{17} +(2.03581 + 2.20352i) q^{18} +(6.50411 + 1.74277i) q^{19} +(-3.02063 - 2.11507i) q^{20} +(-0.626004 - 0.932742i) q^{21} +(-2.24923 + 0.818653i) q^{22} +(-0.948289 + 5.37801i) q^{23} +(1.02132 - 1.39890i) q^{24} +(5.52648 + 6.58621i) q^{25} +(3.33360 + 1.37371i) q^{26} +(4.64609 - 2.32678i) q^{27} +(-0.458601 + 0.458601i) q^{28} +(-4.08659 - 4.87021i) q^{29} +(-4.97288 + 4.00793i) q^{30} +(3.22653 + 4.60797i) q^{31} +(-0.906308 - 0.422618i) q^{32} +(0.279617 + 4.13636i) q^{33} +(-0.673339 + 0.961628i) q^{34} +(2.07116 - 1.19578i) q^{35} +(-1.83601 - 2.37256i) q^{36} +(6.33950 - 1.69867i) q^{37} +(-6.32747 - 2.30301i) q^{38} +(3.89002 - 4.88546i) q^{39} +(2.82479 + 2.37028i) q^{40} +(-0.647875 - 7.40524i) q^{41} +(0.542328 + 0.983752i) q^{42} +(-1.74919 + 4.80587i) q^{43} +(2.31202 - 0.619504i) q^{44} +(4.27525 + 10.2030i) q^{45} +(1.41340 - 5.27490i) q^{46} +(5.84259 + 4.09102i) q^{47} +(-1.13935 + 1.30456i) q^{48} +(2.25028 + 6.18259i) q^{49} +(-4.93143 - 7.04281i) q^{50} +(1.27594 + 1.58314i) q^{51} +(-3.20119 - 1.65903i) q^{52} +8.02983i q^{53} +(-4.83120 + 1.91299i) q^{54} -8.82634 q^{55} +(0.496825 - 0.416886i) q^{56} +(-6.87709 + 9.41955i) q^{57} +(3.64657 + 5.20785i) q^{58} +(1.15461 - 2.47606i) q^{59} +(5.30327 - 3.55926i) q^{60} +(0.846233 + 4.79922i) q^{61} +(-2.81265 - 4.87164i) q^{62} +(1.89782 - 0.428895i) q^{63} +(0.866025 + 0.500000i) q^{64} +(9.81881 + 8.96442i) q^{65} +(0.0819554 - 4.14499i) q^{66} +(-3.63401 + 0.317935i) q^{67} +(0.754588 - 0.899283i) q^{68} +(-8.09637 - 4.89035i) q^{69} +(-2.16749 + 1.01072i) q^{70} +(-1.36940 + 0.366929i) q^{71} +(1.62224 + 2.52355i) q^{72} +(2.20581 - 8.23218i) q^{73} +(-6.46343 + 1.13968i) q^{74} +(-14.0915 + 4.81561i) q^{75} +(6.10267 + 2.84572i) q^{76} +(-0.269568 + 1.52880i) q^{77} +(-4.30101 + 4.52784i) q^{78} +(9.84516 - 8.26107i) q^{79} +(-2.60746 - 2.60746i) q^{80} +(0.857788 + 8.95903i) q^{81} +7.43353i q^{82} +(17.5076 + 1.53172i) q^{83} +(-0.454524 - 1.02728i) q^{84} +(-3.54601 + 2.48294i) q^{85} +(2.16139 - 4.63513i) q^{86} +(10.4200 - 3.56093i) q^{87} +(-2.35722 + 0.415641i) q^{88} +(16.7680 + 4.49298i) q^{89} +(-3.36973 - 10.5368i) q^{90} +(1.85259 - 1.42691i) q^{91} +(-1.86776 + 5.13164i) q^{92} +(-9.45931 + 2.33521i) q^{93} +(-5.46380 - 4.58467i) q^{94} +(-19.0209 - 15.9604i) q^{95} +(1.24872 - 1.20029i) q^{96} +(-0.0772885 + 0.0360402i) q^{97} +(-1.70287 - 6.35518i) q^{98} +(-6.85718 - 2.13124i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 504 q - 24 q^{11} + 24 q^{15} + 24 q^{21} - 144 q^{27} + 24 q^{39} + 48 q^{41} + 12 q^{45} + 132 q^{47} + 24 q^{50} + 72 q^{54} - 72 q^{57} + 12 q^{63} - 156 q^{65} + 96 q^{66} - 48 q^{72} + 36 q^{73} - 96 q^{74}+ \cdots - 144 q^{99}+O(q^{100}) \) 504 * q - 24 * q^11 + 24 * q^15 + 24 * q^21 - 144 * q^27 + 24 * q^39 + 48 * q^41 + 12 * q^45 + 132 * q^47 + 24 * q^50 + 72 * q^54 - 72 * q^57 + 12 * q^63 - 156 * q^65 + 96 * q^66 - 48 * q^72 + 36 * q^73 - 96 * q^74 - 24 * q^78 + 288 * q^79 + 24 * q^83 + 24 * q^84 - 144 * q^85 - 96 * q^86 - 192 * q^87 + 96 * q^92 - 60 * q^93 - 72 * q^98 - 144 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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