LMFDB - Embedded newform 230.2.l.a.53.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [230,2,Mod(7,230)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("230.7"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(230, base_ring=CyclotomicField(44)) chi = DirichletCharacter(H, H._module([11, 38])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	230.l (of order $44$, degree $20$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.83655924649$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			53.7
Character	$\chi$	$=$	230.53
Dual form			230.2.l.a.217.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0713392 + 0.997452i) q^{2} +(-3.06400 - 0.666533i) q^{3} +(-0.989821 + 0.142315i) q^{4} +(-1.99070 - 1.01838i) q^{5} +(0.446251 - 3.10375i) q^{6} +(2.74884 + 1.50098i) q^{7} +(-0.212565 - 0.977147i) q^{8} +(6.21495 + 2.83827i) q^{9} +(0.873771 - 2.05828i) q^{10} +(3.61103 - 3.12898i) q^{11} +(3.12767 + 0.223696i) q^{12} +(1.90500 + 3.48874i) q^{13} +(-1.30106 + 2.84892i) q^{14} +(5.42074 + 4.44719i) q^{15} +(0.959493 - 0.281733i) q^{16} +(-1.03605 + 0.775576i) q^{17} +(-2.38767 + 6.40160i) q^{18} +(-0.898012 - 6.24581i) q^{19} +(2.11537 + 0.724708i) q^{20} +(-7.42201 - 6.43121i) q^{21} +(3.37861 + 3.37861i) q^{22} +(0.105632 - 4.79467i) q^{23} +3.13566i q^{24} +(2.92580 + 4.05459i) q^{25} +(-3.34395 + 2.14903i) q^{26} +(-9.62015 - 7.20156i) q^{27} +(-2.93448 - 1.09450i) q^{28} +(6.15162 + 0.884470i) q^{29} +(-4.04915 + 5.72419i) q^{30} +(5.07661 + 3.26254i) q^{31} +(0.349464 + 0.936950i) q^{32} +(-13.1498 + 7.18032i) q^{33} +(-0.847511 - 0.978080i) q^{34} +(-3.94356 - 5.78738i) q^{35} +(-6.55562 - 1.92490i) q^{36} +(2.17939 - 0.812871i) q^{37} +(6.16584 - 1.34130i) q^{38} +(-3.51156 - 11.9593i) q^{39} +(-0.571953 + 2.16168i) q^{40} +(1.61534 + 3.53711i) q^{41} +(5.88534 - 7.86190i) q^{42} +(-1.38557 + 6.36935i) q^{43} +(-3.12898 + 3.61103i) q^{44} +(-9.48169 - 11.9794i) q^{45} +(4.78999 - 0.236685i) q^{46} +(3.13655 - 3.13655i) q^{47} +(-3.12767 + 0.223696i) q^{48} +(1.51870 + 2.36315i) q^{49} +(-3.83553 + 3.20760i) q^{50} +(3.69140 - 1.68581i) q^{51} +(-2.38211 - 3.18212i) q^{52} +(2.37346 - 4.34666i) q^{53} +(6.49691 - 10.1094i) q^{54} +(-10.3750 + 2.55146i) q^{55} +(0.882371 - 3.00508i) q^{56} +(-1.41153 + 19.7357i) q^{57} +(-0.443365 + 6.19905i) q^{58} +(0.731919 - 2.49269i) q^{59} +(-5.99846 - 3.63047i) q^{60} +(-1.44682 + 2.25130i) q^{61} +(-2.89207 + 5.29642i) q^{62} +(12.8237 + 17.1305i) q^{63} +(-0.909632 + 0.415415i) q^{64} +(-0.239419 - 8.88506i) q^{65} +(-8.10012 - 12.6040i) q^{66} +(-0.563079 + 0.0402722i) q^{67} +(0.915127 - 0.915127i) q^{68} +(-3.51946 + 14.6205i) q^{69} +(5.49130 - 4.34638i) q^{70} +(3.48160 - 4.01798i) q^{71} +(1.45233 - 6.67624i) q^{72} +(3.19870 - 4.27296i) q^{73} +(0.966276 + 2.11585i) q^{74} +(-6.26215 - 14.3734i) q^{75} +(1.77774 + 6.05444i) q^{76} +(14.6227 - 3.18097i) q^{77} +(11.6783 - 4.35577i) q^{78} +(-2.54941 - 0.748575i) q^{79} +(-2.19698 - 0.416283i) q^{80} +(11.2533 + 12.9870i) q^{81} +(-3.41286 + 1.86356i) q^{82} +(-2.59627 - 6.96086i) q^{83} +(8.26172 + 5.30949i) q^{84} +(2.85230 - 0.488851i) q^{85} +(-6.45196 - 0.927652i) q^{86} +(-18.2591 - 6.81028i) q^{87} +(-3.82505 - 2.86340i) q^{88} +(-3.18420 + 2.04636i) q^{89} +(11.2724 - 10.3121i) q^{90} +12.4494i q^{91} +(0.577796 + 4.76090i) q^{92} +(-13.3802 - 13.3802i) q^{93} +(3.35232 + 2.90480i) q^{94} +(-4.57294 + 13.3481i) q^{95} +(-0.446251 - 3.10375i) q^{96} +(0.929246 - 2.49141i) q^{97} +(-2.24879 + 1.68342i) q^{98} +(31.3233 - 9.19735i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 8 q^{3} - 8 q^{6} - 8 q^{12} + 16 q^{13} + 24 q^{16} - 72 q^{18} - 80 q^{23} - 8 q^{26} + 16 q^{27} - 44 q^{28} + 24 q^{31} - 44 q^{33} - 8 q^{35} - 32 q^{36} - 88 q^{37} - 24 q^{41} - 8 q^{46}+ \cdots + 24 q^{98}+O(q^{100}) $ 240 * q - 8 * q^3 - 8 * q^6 - 8 * q^12 + 16 * q^13 + 24 * q^16 - 72 * q^18 - 80 * q^23 - 8 * q^26 + 16 * q^27 - 44 * q^28 + 24 * q^31 - 44 * q^33 - 8 * q^35 - 32 * q^36 - 88 * q^37 - 24 * q^41 - 8 * q^46 - 80 * q^47 + 8 * q^48 + 8 * q^50 + 16 * q^52 - 44 * q^56 - 88 * q^57 - 176 * q^61 - 32 * q^62 - 176 * q^66 + 24 * q^70 - 336 * q^71 + 16 * q^72 - 88 * q^73 - 36 * q^75 - 24 * q^77 + 40 * q^78 - 136 * q^81 + 40 * q^82 - 100 * q^85 - 44 * q^86 + 40 * q^87 + 8 * q^92 + 56 * q^93 + 52 * q^95 + 8 * q^96 + 132 * q^97 + 24 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{19}{22}\right)$

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 $

$2$	0.0713392	+	0.997452i	0.0504444	+	0.705305i
$2$	0.0713392	+	0.997452i	0.0504444	+	0.705305i
$3$	−3.06400	−	0.666533i	−1.76900	−	0.384823i	−0.794159	−	0.607710i	$-0.792088\pi$
$3$	−3.06400	−	0.666533i	−1.76900	−	0.384823i	−0.974844	+	0.222887i	$0.928452\pi$
$4$	−0.989821	+	0.142315i	−0.494911	+	0.0711574i
$5$	−1.99070	−	1.01838i	−0.890270	−	0.455434i
$5$	−1.99070	−	1.01838i	−0.890270	−	0.455434i
$6$	0.446251	−	3.10375i	0.182181	−	1.26710i
$7$	2.74884	+	1.50098i	1.03896	+	0.567318i	0.905769	−	0.423772i	$-0.139294\pi$
$7$	2.74884	+	1.50098i	1.03896	+	0.567318i	0.133196	+	0.991090i	$0.457476\pi$
$8$	−0.212565	−	0.977147i	−0.0751532	−	0.345474i
$9$	6.21495	+	2.83827i	2.07165	+	0.946091i
$10$	0.873771	−	2.05828i	0.276311	−	0.650886i
$11$	3.61103	−	3.12898i	1.08877	−	0.943422i	0.0901464	−	0.995929i	$-0.471266\pi$
$11$	3.61103	−	3.12898i	1.08877	−	0.943422i	0.998621	+	0.0525065i	$0.0167210\pi$
$12$	3.12767	+	0.223696i	0.902882	+	0.0645754i
$13$	1.90500	+	3.48874i	0.528351	+	0.967603i	0.996471	+	0.0839380i	$0.0267498\pi$
$13$	1.90500	+	3.48874i	0.528351	+	0.967603i	−0.468120	+	0.883665i	$0.655068\pi$
$14$	−1.30106	+	2.84892i	−0.347722	+	0.761405i
$15$	5.42074	+	4.44719i	1.39963	+	1.14826i
$16$	0.959493	−	0.281733i	0.239873	−	0.0704331i
$17$	−1.03605	+	0.775576i	−0.251279	+	0.188105i	−0.717491	−	0.696568i	$-0.754709\pi$
$17$	−1.03605	+	0.775576i	−0.251279	+	0.188105i	0.466212	+	0.884673i	$0.345618\pi$
$18$	−2.38767	+	6.40160i	−0.562780	+	1.50887i
$19$	−0.898012	−	6.24581i	−0.206018	−	1.43289i	−0.785984	−	0.618247i	$-0.787843\pi$
$19$	−0.898012	−	6.24581i	−0.206018	−	1.43289i	0.579966	−	0.814641i	$-0.303066\pi$
$20$	2.11537	+	0.724708i	0.473012	+	0.162050i
$21$	−7.42201	−	6.43121i	−1.61962	−	1.40340i
$22$	3.37861	+	3.37861i	0.720323	+	0.720323i
$23$	0.105632	−	4.79467i	0.0220258	−	0.999757i
$23$	0.105632	−	4.79467i	0.0220258	−	0.999757i
$24$			3.13566i			0.640065i
$25$	2.92580	+	4.05459i	0.585161	+	0.810917i
$26$	−3.34395	+	2.14903i	−0.655803	+	0.421459i
$27$	−9.62015	−	7.20156i	−1.85140	−	1.38594i
$28$	−2.93448	−	1.09450i	−0.554564	−	0.206842i
$29$	6.15162	+	0.884470i	1.14233	+	0.164242i	0.687395	−	0.726284i	$-0.258754\pi$
$29$	6.15162	+	0.884470i	1.14233	+	0.164242i	0.454933	+	0.890526i	$0.349663\pi$
$30$	−4.04915	+	5.72419i	−0.739270	+	1.04509i
$31$	5.07661	+	3.26254i	0.911786	+	0.585970i	0.910264	−	0.414029i	$-0.135879\pi$
$31$	5.07661	+	3.26254i	0.911786	+	0.585970i	0.00152290	+	0.999999i	$0.499515\pi$
$32$	0.349464	+	0.936950i	0.0617771	+	0.165631i
$33$	−13.1498	+	7.18032i	−2.28908	+	1.24993i
$34$	−0.847511	−	0.978080i	−0.145347	−	0.167739i
$35$	−3.94356	−	5.78738i	−0.666583	−	0.978245i
$36$	−6.55562	−	1.92490i	−1.09260	−	0.320817i
$37$	2.17939	−	0.812871i	0.358290	−	0.133635i	−0.163872	−	0.986482i	$-0.552398\pi$
$37$	2.17939	−	0.812871i	0.358290	−	0.133635i	0.522162	+	0.852846i	$0.325126\pi$
$38$	6.16584	−	1.34130i	1.00023	−	0.217587i
$39$	−3.51156	−	11.9593i	−0.562299	−	1.91501i
$40$	−0.571953	+	2.16168i	−0.0904337	+	0.341792i
$41$	1.61534	+	3.53711i	0.252274	+	0.552404i	0.992822	−	0.119600i	$-0.0381612\pi$
$41$	1.61534	+	3.53711i	0.252274	+	0.552404i	−0.740548	+	0.672004i	$0.765434\pi$
$42$	5.88534	−	7.86190i	0.908128	−	1.21312i
$43$	−1.38557	+	6.36935i	−0.211297	+	0.971316i	0.742262	+	0.670110i	$0.233753\pi$
$43$	−1.38557	+	6.36935i	−0.211297	+	0.971316i	−0.953559	+	0.301207i	$0.902611\pi$
$44$	−3.12898	+	3.61103i	−0.471711	+	0.544384i
$45$	−9.48169	−	11.9794i	−1.41345	−	1.78578i
$46$	4.78999	−	0.236685i	0.706245	−	0.0348973i
$47$	3.13655	−	3.13655i	0.457513	−	0.457513i	−0.440325	−	0.897838i	$-0.645137\pi$
$47$	3.13655	−	3.13655i	0.457513	−	0.457513i	0.897838	+	0.440325i	$0.145137\pi$
$48$	−3.12767	+	0.223696i	−0.451441	+	0.0322877i
$49$	1.51870	+	2.36315i	0.216958	+	0.337593i
$50$	−3.83553	+	3.20760i	−0.542426	+	0.453623i
$51$	3.69140	−	1.68581i	0.516900	−	0.236060i
$52$	−2.38211	−	3.18212i	−0.330339	−	0.441281i
$53$	2.37346	−	4.34666i	0.326019	−	0.597060i	−0.662339	−	0.749204i	$-0.730436\pi$
$53$	2.37346	−	4.34666i	0.326019	−	0.597060i	0.988358	+	0.152144i	$0.0486179\pi$
$54$	6.49691	−	10.1094i	0.884118	−	1.37571i
$55$	−10.3750	+	2.55146i	−1.39896	+	0.344039i
$56$	0.882371	−	3.00508i	0.117912	−	0.401571i
$57$	−1.41153	+	19.7357i	−0.186962	+	2.61406i
$58$	−0.443365	+	6.19905i	−0.0582166	+	0.813975i
$59$	0.731919	−	2.49269i	0.0952878	−	0.324520i	−0.898030	−	0.439935i	$-0.855001\pi$
$59$	0.731919	−	2.49269i	0.0952878	−	0.324520i	0.993317	+	0.115415i	$0.0368197\pi$
$60$	−5.99846	−	3.63047i	−0.774398	−	0.468692i
$61$	−1.44682	+	2.25130i	−0.185247	+	0.288250i	−0.921439	−	0.388523i	$-0.872986\pi$
$61$	−1.44682	+	2.25130i	−0.185247	+	0.288250i	0.736192	+	0.676772i	$0.236622\pi$
$62$	−2.89207	+	5.29642i	−0.367293	+	0.672647i
$63$	12.8237	+	17.1305i	1.61564	+	2.15824i
$64$	−0.909632	+	0.415415i	−0.113704	+	0.0519269i
$65$	−0.239419	−	8.88506i	−0.0296962	−	1.10206i
$66$	−8.10012	−	12.6040i	−0.997056	−	1.55145i
$67$	−0.563079	+	0.0402722i	−0.0687911	+	0.00492004i	−0.105692	−	0.994399i	$-0.533706\pi$
$67$	−0.563079	+	0.0402722i	−0.0687911	+	0.00492004i	0.0369012	+	0.999319i	$0.488251\pi$
$68$	0.915127	−	0.915127i	0.110975	−	0.110975i
$69$	−3.51946	+	14.6205i	−0.423693	+	1.76010i
$70$	5.49130	−	4.34638i	0.656336	−	0.519492i
$71$	3.48160	−	4.01798i	0.413190	−	0.476847i	−0.510560	−	0.859842i	$-0.670562\pi$
$71$	3.48160	−	4.01798i	0.413190	−	0.476847i	0.923750	+	0.382995i	$0.125107\pi$
$72$	1.45233	−	6.67624i	0.171158	−	0.786803i
$73$	3.19870	−	4.27296i	0.374380	−	0.500113i	−0.573296	−	0.819349i	$-0.694335\pi$
$73$	3.19870	−	4.27296i	0.374380	−	0.500113i	0.947675	+	0.319236i	$0.103426\pi$
$74$	0.966276	+	2.11585i	0.112327	+	0.245962i
$75$	−6.26215	−	14.3734i	−0.723091	−	1.65970i
$76$	1.77774	+	6.05444i	0.203921	+	0.694492i
$77$	14.6227	−	3.18097i	1.66641	−	0.362505i
$78$	11.6783	−	4.35577i	1.32230	−	0.493194i
$79$	−2.54941	−	0.748575i	−0.286831	−	0.0842213i	0.135152	−	0.990825i	$-0.456848\pi$
$79$	−2.54941	−	0.748575i	−0.286831	−	0.0842213i	−0.421983	+	0.906604i	$0.638666\pi$
$80$	−2.19698	−	0.416283i	−0.245630	−	0.0465418i
$81$	11.2533	+	12.9870i	1.25037	+	1.44300i
$82$	−3.41286	+	1.86356i	−0.376887	+	0.205796i
$83$	−2.59627	−	6.96086i	−0.284977	−	0.764053i	−0.998018	−	0.0629307i	$-0.979955\pi$
$83$	−2.59627	−	6.96086i	−0.284977	−	0.764053i	0.713041	−	0.701123i	$-0.247317\pi$
$84$	8.26172	+	5.30949i	0.901428	+	0.579312i
$85$	2.85230	−	0.488851i	0.309375	−	0.0530233i
$86$	−6.45196	−	0.927652i	−0.695733	−	0.100031i
$87$	−18.2591	−	6.81028i	−1.95758	−	0.730139i
$88$	−3.82505	−	2.86340i	−0.407752	−	0.305239i
$89$	−3.18420	+	2.04636i	−0.337524	+	0.216914i	−0.698413	−	0.715695i	$-0.746110\pi$
$89$	−3.18420	+	2.04636i	−0.337524	+	0.216914i	0.360888	+	0.932609i	$0.382474\pi$
$90$	11.2724	−	10.3121i	1.18822	−	1.08699i
$91$			12.4494i			1.30505i
$92$	0.577796	+	4.76090i	0.0602393	+	0.496358i
$93$	−13.3802	−	13.3802i	−1.38746	−	1.38746i
$94$	3.35232	+	2.90480i	0.345765	+	0.299607i
$95$	−4.57294	+	13.3481i	−0.469173	+	1.36948i
$96$	−0.446251	−	3.10375i	−0.0455453	−	0.316775i
$97$	0.929246	−	2.49141i	0.0943507	−	0.252964i	−0.881198	−	0.472747i	$-0.843262\pi$
$97$	0.929246	−	2.49141i	0.0943507	−	0.252964i	0.975549	+	0.219783i	$0.0705351\pi$
$98$	−2.24879	+	1.68342i	−0.227162	+	0.170051i
$99$	31.3233	−	9.19735i	3.14811	−	0.924368i
$100$	−3.47305	−	3.59693i	−0.347305	−	0.359693i
$101$	−4.80527	+	10.5221i	−0.478142	+	1.04699i	0.504828	+	0.863220i	$0.331556\pi$
$101$	−4.80527	+	10.5221i	−0.478142	+	1.04699i	−0.982970	+	0.183766i	$0.941171\pi$
$102$	1.94485	+	3.56173i	0.192569	+	0.352664i
$103$	−6.14749	−	0.439677i	−0.605730	−	0.0433227i	−0.234894	−	0.972021i	$-0.575474\pi$
$103$	−6.14749	−	0.439677i	−0.605730	−	0.0433227i	−0.370836	+	0.928698i	$0.620929\pi$
$104$	3.00408	−	2.60305i	0.294574	−	0.255250i
$105$	8.22561	+	20.3611i	0.802737	+	1.98704i
$106$	4.50491	+	2.05732i	0.437555	+	0.199825i
$107$	−0.696782	−	3.20305i	−0.0673604	−	0.309651i	0.931123	−	0.364706i	$-0.118830\pi$
$107$	−0.696782	−	3.20305i	−0.0673604	−	0.309651i	−0.998483	+	0.0550546i	$0.982467\pi$
$108$	10.5471	+	5.75916i	1.01490	+	0.554176i
$109$	−1.06176	+	7.38469i	−0.101698	+	0.707325i	0.873634	+	0.486583i	$0.161757\pi$
$109$	−1.06176	+	7.38469i	−0.101698	+	0.707325i	−0.975332	+	0.220742i	$0.929152\pi$
$110$	−3.28510	−	10.1665i	−0.313222	−	0.969341i
$111$	−7.21947	+	1.03800i	−0.685242	+	0.0985229i
$112$	3.06037	+	0.665743i	0.289178	+	0.0629068i
$113$	1.08357	+	15.1502i	0.101933	+	1.42521i	0.748894	+	0.662690i	$0.230585\pi$
$113$	1.08357	+	15.1502i	0.101933	+	1.42521i	−0.646960	+	0.762524i	$0.723960\pi$
$114$	−19.7862			−1.85314
$115$	−5.09308	+	9.43719i	−0.474932	+	0.880023i
$116$	−6.21488			−0.577037
$117$	1.93746	+	27.0893i	0.179119	+	2.50440i
$118$	2.53855	+	0.552228i	0.233693	+	0.0508367i
$119$	−4.01206	+	0.576847i	−0.367785	+	0.0528795i
$120$	3.19330	−	6.24218i	0.291507	−	0.569830i
$121$	1.68359	−	11.7096i	0.153054	−	1.06451i
$122$	−2.34878	−	1.28253i	−0.212649	−	0.116115i
$123$	−2.59182	−	11.9144i	−0.233696	−	1.07428i
$124$	−5.48925	−	2.50686i	−0.492949	−	0.225122i
$125$	−1.69529	−	11.0511i	−0.151632	−	0.988437i
$126$	−16.1720	+	14.0131i	−1.44072	+	1.24839i
$127$	17.6109	+	1.25956i	1.56272	+	0.111768i	0.825702	−	0.564107i	$-0.190779\pi$
$127$	17.6109	+	1.25956i	1.56272	+	0.111768i	0.737017	+	0.675874i	$0.236234\pi$
$128$	−0.479249	−	0.877679i	−0.0423600	−	0.0775766i
$129$	8.49076	−	18.5922i	0.747570	−	1.63695i
$130$	8.84535	−	0.872662i	0.775788	−	0.0765375i
$131$	−2.62943	+	0.772071i	−0.229735	+	0.0674561i	−0.394574	−	0.918864i	$-0.629108\pi$
$131$	−2.62943	+	0.772071i	−0.229735	+	0.0674561i	0.164839	+	0.986320i	$0.447290\pi$
$132$	11.9941	−	8.97865i	1.04395	−	0.781491i
$133$	6.90636	−	18.5167i	0.598857	−	1.60560i
$134$	−0.0803392	−	0.558772i	−0.00694025	−	0.0482705i
$135$	11.8170	+	24.1331i	1.01704	+	2.07705i
$136$	0.978080	+	0.847511i	0.0838697	+	0.0726735i
$137$	−11.2484	−	11.2484i	−0.961018	−	0.961018i	0.0382498	−	0.999268i	$-0.487822\pi$
$137$	−11.2484	−	11.2484i	−0.961018	−	0.961018i	−0.999268	+	0.0382498i	$0.987822\pi$
$138$	−14.8343	−	2.46748i	−1.26278	−	0.210046i
$139$			15.0290i			1.27474i	0.770558	+	0.637370i	$0.219978\pi$
$139$			15.0290i			1.27474i	−0.770558	+	0.637370i	$0.780022\pi$
$140$	4.72705	+	5.16724i	0.399509	+	0.436712i
$141$	−11.7010	+	7.51979i	−0.985404	+	0.633281i
$142$	4.25612	+	3.18609i	0.357166	+	0.267371i
$143$	17.7952	+	6.63727i	1.48811	+	0.555036i
$144$	6.76284	+	0.972349i	0.563570	+	0.0810291i
$145$	−11.3453	−	8.02541i	−0.942179	−	0.666474i
$146$	4.49027	+	2.88572i	0.371617	+	0.238824i
$147$	−3.07820	−	8.25297i	−0.253885	−	0.680693i
$148$	−2.04152	+	1.11476i	−0.167812	+	0.0916325i
$149$	−9.92413	−	11.4531i	−0.813016	−	0.938271i	0.186003	−	0.982549i	$-0.440447\pi$
$149$	−9.92413	−	11.4531i	−0.813016	−	0.938271i	−0.999019	+	0.0442783i	$0.985901\pi$
$150$	13.8901	−	7.27158i	1.13412	−	0.593722i
$151$	2.19293	+	0.643902i	0.178458	+	0.0524000i	0.369741	−	0.929135i	$-0.379447\pi$
$151$	2.19293	+	0.643902i	0.178458	+	0.0524000i	−0.191283	+	0.981535i	$0.561265\pi$
$152$	−5.91219	+	2.20513i	−0.479542	+	0.178860i
$153$	−8.64029	+	1.87958i	−0.698526	+	0.151955i
$154$	4.21604	+	14.3585i	0.339738	+	1.15704i
$155$	−6.78352	−	11.6647i	−0.544866	−	0.936929i
$156$	5.17779	+	11.3378i	0.414555	+	0.907749i
$157$	7.91986	−	10.5797i	0.632074	−	0.844352i	−0.364135	−	0.931346i	$-0.618635\pi$
$157$	7.91986	−	10.5797i	0.632074	−	0.844352i	0.996209	+	0.0869946i	$0.0277263\pi$
$158$	0.564795	−	2.59632i	0.0449327	−	0.206552i
$159$	−10.1695	+	11.7362i	−0.806492	+	0.930741i
$160$	0.258492	−	2.22108i	0.0204356	−	0.175592i
$161$	7.48707	−	13.0212i	0.590064	−	1.02622i
$162$	−12.1511	+	12.1511i	−0.954684	+	0.954684i
$163$	14.6844	−	1.05025i	1.15017	−	0.0822617i	0.516796	−	0.856108i	$-0.327124\pi$
$163$	14.6844	−	1.05025i	1.15017	−	0.0822617i	0.633373	+	0.773847i	$0.281670\pi$
$164$	−2.10228	−	3.27122i	−0.164161	−	0.255439i
$165$	33.4896	−	0.902418i	2.60716	−	0.0702531i
$166$	6.75791	−	3.08623i	0.524515	−	0.239538i
$167$	7.84639	+	10.4816i	0.607172	+	0.811087i	0.993804	−	0.111147i	$-0.0354526\pi$
$167$	7.84639	+	10.4816i	0.607172	+	0.811087i	−0.386632	+	0.922234i	$0.626362\pi$
$168$	−4.70657	+	8.61944i	−0.363120	+	0.665005i
$169$	−1.51398	+	2.35579i	−0.116460	+	0.181215i
$170$	0.691086	+	2.81016i	0.0530039	+	0.215529i
$171$	12.1462	−	41.3662i	0.928845	−	3.16336i
$172$	0.465011	−	6.50170i	0.0354568	−	0.495750i
$173$	0.768272	−	10.7418i	0.0584107	−	0.816688i	−0.880831	−	0.473431i	$-0.843015\pi$
$173$	0.768272	−	10.7418i	0.0584107	−	0.816688i	0.939242	−	0.343257i	$-0.111530\pi$
$174$	5.49034	−	18.6984i	0.416222	−	1.41752i
$175$	1.95671	+	15.5370i	0.147913	+	1.17449i
$176$	2.58322	−	4.01958i	0.194718	−	0.302987i
$177$	−3.90406	+	7.14976i	−0.293447	+	0.537409i
$178$	−2.26830	−	3.03010i	−0.170016	−	0.227115i
$179$	−14.3971	+	6.57496i	−1.07609	+	0.491435i	−0.872998	−	0.487724i	$-0.837827\pi$
$179$	−14.3971	+	6.57496i	−1.07609	+	0.491435i	−0.203095	+	0.979159i	$0.565100\pi$
$180$	11.0900	+	10.5080i	0.826601	+	0.783223i
$181$	0.828503	+	1.28918i	0.0615821	+	0.0958237i	0.870679	−	0.491851i	$-0.163680\pi$
$181$	0.828503	+	1.28918i	0.0615821	+	0.0958237i	−0.809097	+	0.587675i	$0.800043\pi$
$182$	−12.4177	+	0.888128i	−0.920457	+	0.0658324i
$183$	5.93364	−	5.93364i	0.438628	−	0.438628i
$184$	−4.70755	+	0.915962i	−0.347045	+	0.0675256i
$185$	−5.16633	−	0.601264i	−0.379837	−	0.0442058i
$186$	12.3915	−	14.3006i	0.908592	−	1.04857i
$187$	−1.31444	+	6.04240i	−0.0961217	+	0.441864i
$188$	−2.65825	+	3.55101i	−0.193873	+	0.258984i
$189$	−15.6349	−	34.2356i	−1.13727	−	2.49028i
$190$	−13.6403	−	3.60904i	−0.989572	−	0.261828i
$191$	2.21085	+	7.52946i	0.159971	+	0.544812i	0.999997	+	0.00226633i	$0.000721397\pi$
$191$	2.21085	+	7.52946i	0.159971	+	0.544812i	−0.840026	+	0.542546i	$0.817460\pi$
$192$	3.06400	−	0.666533i	0.221125	−	0.0481029i
$193$	0.446324	−	0.166470i	0.0321271	−	0.0119828i	−0.333349	−	0.942803i	$-0.608179\pi$
$193$	0.446324	−	0.166470i	0.0321271	−	0.0119828i	0.365476	+	0.930821i	$0.380906\pi$
$194$	2.55135	+	0.749144i	0.183176	+	0.0537854i
$195$	−5.18861	+	27.3834i	−0.371564	+	1.96097i
$196$	−1.83956	−	2.12296i	−0.131397	−	0.151640i
$197$	−18.6117	+	10.1627i	−1.32603	+	0.724065i	−0.977039	−	0.213062i	$-0.931656\pi$
$197$	−18.6117	+	10.1627i	−1.32603	+	0.724065i	−0.348988	+	0.937127i	$0.613475\pi$
$198$	11.4085	+	30.5874i	0.810766	+	2.17375i
$199$	−6.83690	−	4.39381i	−0.484655	−	0.311469i	0.275398	−	0.961330i	$-0.411191\pi$
$199$	−6.83690	−	4.39381i	−0.484655	−	0.311469i	−0.760053	+	0.649862i	$0.774827\pi$
$200$	3.34000	−	3.72080i	0.236174	−	0.263101i
$201$	1.75212	+	0.251917i	0.123585	+	0.0177688i
$202$	−10.8381	−	4.04239i	−0.762564	−	0.284422i
$203$	15.5823	+	11.6647i	1.09366	+	0.818705i
$204$	−3.41391	+	2.19399i	−0.239022	+	0.153610i
$205$	0.386452	−	8.68637i	0.0269910	−	0.606682i
$206$		−	6.16319i		−	0.429410i
$207$	14.2651	−	29.4988i	0.991492	−	2.05031i
$208$	2.81072	+	2.81072i	0.194889	+	0.194889i
$209$	−22.7858	−	19.7440i	−1.57612	−	1.36572i
$210$	−19.7224	+	9.65719i	−1.36097	+	0.666409i
$211$	1.13926	+	7.92374i	0.0784300	+	0.545493i	0.990717	+	0.135941i	$0.0434058\pi$
$211$	1.13926	+	7.92374i	0.0784300	+	0.545493i	−0.912287	+	0.409552i	$0.865685\pi$
$212$	−1.73070	+	4.64020i	−0.118865	+	0.318690i
$213$	−13.3458	+	9.99051i	−0.914436	+	0.684538i
$214$	3.14519	−	0.923510i	0.215000	−	0.0631298i
$215$	9.24467	−	11.2685i	0.630481	−	0.768502i
$216$	−4.99207	+	10.9311i	−0.339667	+	0.743767i
$217$	9.05779	+	16.5881i	0.614883	+	1.12607i
$218$	−7.44162	−	0.532235i	−0.504010	−	0.0360475i
$219$	−12.6489	+	10.9603i	−0.854733	+	0.740631i
$220$	9.90627	−	4.00201i	0.667881	−	0.269815i
$221$	−4.67946	−	2.13704i	−0.314774	−	0.143753i
$222$	−1.55039	−	7.12702i	−0.104055	−	0.478335i
$223$	−21.1726	−	11.5611i	−1.41782	−	0.774188i	−0.426354	−	0.904557i	$-0.640202\pi$
$223$	−21.1726	−	11.5611i	−1.41782	−	0.774188i	−0.991466	+	0.130369i	$0.958384\pi$
$224$	−0.445722	+	3.10007i	−0.0297811	+	0.207132i
$225$	6.67570	+	33.5033i	0.445047	+	2.23355i
$226$	−15.0343	+	2.16161i	−1.00007	+	0.143788i
$227$	−22.1332	−	4.81479i	−1.46903	−	0.319569i	−0.594328	−	0.804223i	$-0.702582\pi$
$227$	−22.1332	−	4.81479i	−1.46903	−	0.319569i	−0.874706	+	0.484654i	$0.838946\pi$
$228$	−1.41153	−	19.7357i	−0.0934808	−	1.30703i
$229$	−3.88570			−0.256775			−0.128387	−	0.991724i	$-0.540980\pi$
$229$	−3.88570			−0.256775			−0.128387	+	0.991724i	$0.540980\pi$
$230$	−9.77648	−	4.40686i	−0.644642	−	0.290580i
$231$	−46.9242			−3.08739
$232$	−0.443365	−	6.19905i	−0.0291083	−	0.406987i
$233$	0.711294	+	0.154733i	0.0465984	+	0.0101369i	0.235804	−	0.971801i	$-0.424228\pi$
$233$	0.711294	+	0.154733i	0.0465984	+	0.0101369i	−0.189206	+	0.981937i	$0.560591\pi$
$234$	−26.8820	+	3.86505i	−1.75733	+	0.252666i
$235$	−9.43815	+	3.04974i	−0.615677	+	0.198943i
$236$	−0.369723	+	2.57148i	−0.0240669	+	0.167389i
$237$	7.31246	+	3.99290i	0.474995	+	0.259367i
$238$	−0.861595	−	3.96069i	−0.0558489	−	0.256733i
$239$	−11.5582	−	5.27843i	−0.747635	−	0.341433i	0.00489810	−	0.999988i	$-0.498441\pi$
$239$	−11.5582	−	5.27843i	−0.747635	−	0.341433i	−0.752533	+	0.658555i	$0.771168\pi$
$240$	6.45408	+	2.73985i	0.416609	+	0.176857i
$241$	18.3119	−	15.8674i	1.17958	−	1.02211i	0.180317	−	0.983609i	$-0.442288\pi$
$241$	18.3119	−	15.8674i	1.17958	−	1.02211i	0.999259	−	0.0384993i	$-0.0122577\pi$
$242$	11.7999	+	0.843946i	0.758527	+	0.0542509i
$243$	−8.54646	−	15.6517i	−0.548255	−	1.00405i
$244$	1.11170	−	2.43429i	0.0711696	−	0.155840i
$245$	−0.616705	−	6.25095i	−0.0393998	−	0.399359i
$246$	11.6991	−	3.43518i	0.745910	−	0.219019i
$247$	20.0793	−	15.0312i	1.27762	−	0.956412i
$248$	2.10887	−	5.65410i	0.133913	−	0.359036i
$249$	3.31532	+	23.0586i	0.210100	+	1.46128i
$250$	10.9020	−	2.47935i	0.689501	−	0.156808i
$251$	11.6834	+	10.1237i	0.737448	+	0.639002i	0.940355	−	0.340196i	$-0.110493\pi$
$251$	11.6834	+	10.1237i	0.737448	+	0.639002i	−0.202907	+	0.979198i	$0.565039\pi$
$252$	−15.1311	−	15.1311i	−0.953172	−	0.953172i
$253$	−14.6210	−	17.6442i	−0.919212	−	1.10928i
$254$			17.6559i			1.10783i
$255$	−9.06528	−	0.403310i	−0.567690	−	0.0252562i
$256$	0.841254	−	0.540641i	0.0525783	−	0.0337901i
$257$	−0.844335	−	0.632061i	−0.0526682	−	0.0394269i	0.572619	−	0.819821i	$-0.305927\pi$
$257$	−0.844335	−	0.632061i	−0.0526682	−	0.0394269i	−0.625287	+	0.780395i	$0.715018\pi$
$258$	19.1505	+	7.14278i	1.19226	+	0.444690i
$259$	7.21091	+	1.03677i	0.448064	+	0.0644219i
$260$	1.50146	+	8.76055i	0.0931165	+	0.543306i
$261$	35.7217	+	22.9569i	2.21112	+	1.42100i
$262$	−0.957685	−	2.56765i	−0.0591660	−	0.158630i
$263$	−20.9711	+	11.4511i	−1.29313	+	0.706105i	−0.970656	−	0.240472i	$-0.922698\pi$
$263$	−20.9711	+	11.4511i	−1.29313	+	0.706105i	−0.322479	+	0.946577i	$0.604516\pi$
$264$	9.81142	+	11.3230i	0.603851	+	0.696881i
$265$	−9.15140	+	6.23583i	−0.562166	+	0.383064i
$266$	18.9622	+	5.56780i	1.16265	+	0.341384i
$267$	11.1204	−	4.14768i	0.680555	−	0.253834i
$268$	0.551617	−	0.119997i	0.0336954	−	0.00732998i
$269$	6.90680	+	23.5224i	0.421115	+	1.43419i	0.848056	+	0.529907i	$0.177773\pi$
$269$	6.90680	+	23.5224i	0.421115	+	1.43419i	−0.426940	+	0.904280i	$0.640409\pi$
$270$	−23.2286	+	13.5085i	−1.41365	+	0.822100i
$271$	−8.22947	−	18.0200i	−0.499905	−	1.09464i	−0.976500	−	0.215516i	$-0.930857\pi$
$271$	−8.22947	−	18.0200i	−0.499905	−	1.09464i	0.476596	−	0.879123i	$-0.341871\pi$
$272$	−0.775576	+	1.03605i	−0.0470262	+	0.0628197i
$273$	8.29792	−	38.1449i	0.502213	−	2.30863i
$274$	10.4173	−	12.0222i	0.629333	−	0.726289i
$275$	23.2519	+	5.48647i	1.40214	+	0.330847i
$276$	1.40293	−	14.9725i	0.0844464	−	0.901240i
$277$	3.32466	−	3.32466i	0.199759	−	0.199759i	−0.600137	−	0.799897i	$-0.704887\pi$
$277$	3.32466	−	3.32466i	0.199759	−	0.199759i	0.799897	+	0.600137i	$0.204887\pi$
$278$	−14.9907	+	1.07215i	−0.899081	+	0.0643035i
$279$	22.2909	+	34.6854i	1.33452	+	2.07656i
$280$	−4.81685	+	5.08363i	−0.287862	+	0.303805i
$281$	5.20349	−	2.37635i	0.310414	−	0.141761i	−0.254116	−	0.967174i	$-0.581785\pi$
$281$	5.20349	−	2.37635i	0.310414	−	0.141761i	0.564530	+	0.825412i	$0.309057\pi$
$282$	−8.33537	−	11.1348i	−0.496364	−	0.663065i
$283$	1.97175	−	3.61099i	0.117208	−	0.214651i	−0.812488	−	0.582978i	$-0.801887\pi$
$283$	1.97175	−	3.61099i	0.117208	−	0.214651i	0.929696	+	0.368327i	$0.120069\pi$
$284$	−2.87435	+	4.47257i	−0.170561	+	0.265398i
$285$	22.9084	−	37.8506i	1.35698	−	2.24207i
$286$	−5.35086	+	18.2234i	−0.316403	+	1.07757i
$287$	−0.868810	+	12.1476i	−0.0512843	+	0.717048i
$288$	−0.487417	+	6.81497i	−0.0287213	+	0.401576i
$289$	−4.31758	+	14.7043i	−0.253975	+	0.864959i
$290$	7.19560	−	11.8890i	0.422540	−	0.698143i
$291$	−4.50782	+	7.01430i	−0.264253	+	0.411186i
$292$	−2.55804	+	4.68469i	−0.149698	+	0.274151i
$293$	15.8504	+	21.1737i	0.925991	+	1.23698i	0.971264	+	0.238004i	$0.0764933\pi$
$293$	15.8504	+	21.1737i	0.925991	+	1.23698i	−0.0452731	+	0.998975i	$0.514416\pi$
$294$	8.01234	−	3.65911i	0.467289	−	0.213404i
$295$	−3.99554	+	4.21683i	−0.232629	+	0.245513i
$296$	−1.25756	−	1.95680i	−0.0730940	−	0.113737i
$297$	−57.2722	+	4.09619i	−3.32327	+	0.237685i
$298$	10.7159	−	10.7159i	0.620755	−	0.620755i
$299$	16.9286	−	8.76531i	0.979006	−	0.506911i
$300$	8.24396	+	13.3359i	0.475965	+	0.769949i
$301$	−13.3690	+	15.4286i	−0.770575	+	0.889291i
$302$	−0.485820	+	2.23328i	−0.0279558	+	0.128511i
$303$	21.7367	−	29.0368i	1.24874	−	1.66812i
$304$	−2.62129	−	5.73981i	−0.150341	−	0.329201i
$305$	5.17288	−	3.00826i	0.296198	−	0.172252i
$306$	−2.49118	−	8.48419i	−0.142411	−	0.485009i
$307$	−29.9248	+	6.50974i	−1.70790	+	0.371530i	−0.957270	−	0.289196i	$-0.906612\pi$
$307$	−29.9248	+	6.50974i	−1.70790	+	0.371530i	−0.750627	+	0.660726i	$0.770248\pi$
$308$	−14.0212	+	5.22962i	−0.798930	+	0.297985i
$309$	18.5429	+	5.44468i	1.05487	+	0.309737i
$310$	11.1510	−	7.59839i	0.633336	−	0.431559i
$311$	5.15631	+	5.95070i	0.292387	+	0.337433i	0.882870	−	0.469617i	$-0.155608\pi$
$311$	5.15631	+	5.95070i	0.292387	+	0.337433i	−0.590483	+	0.807050i	$0.701063\pi$
$312$	−10.9395	+	5.97343i	−0.619328	+	0.338179i
$313$	6.02945	+	16.1656i	0.340805	+	0.913733i	0.988417	+	0.151763i	$0.0484950\pi$
$313$	6.02945	+	16.1656i	0.340805	+	0.913733i	−0.647612	+	0.761970i	$0.724232\pi$
$314$	11.1177	+	7.14493i	0.627410	+	0.403212i
$315$	−8.08289	−	47.1612i	−0.455419	−	2.65723i
$316$	2.63000	+	0.378136i	0.147949	+	0.0212718i
$317$	15.9791	+	5.95988i	0.897474	+	0.334740i	0.755514	−	0.655132i	$-0.227387\pi$
$317$	15.9791	+	5.95988i	0.897474	+	0.334740i	0.141960	+	0.989872i	$0.454660\pi$
$318$	−12.4318	−	9.30631i	−0.697140	−	0.521872i
$319$	24.9812	−	16.0544i	1.39868	−	0.898876i
$320$	2.23386	+	0.0993832i	0.124876	+	0.00555569i
$321$			10.2786i			0.573695i
$322$	13.5222	+	6.53907i	0.753562	+	0.364408i
$323$	5.77449	+	5.77449i	0.321301	+	0.321301i
$324$	−12.9870	−	11.2533i	−0.721502	−	0.625185i
$325$	−8.57176	+	17.9313i	−0.475476	+	0.994652i
$326$	2.09514	+	14.5720i	0.116039	+	0.807071i
$327$	8.17537	−	21.9190i	0.452099	−	1.21212i
$328$	3.11291	−	2.33029i	0.171882	−	0.128669i
$329$	13.3298	−	3.91398i	0.734896	−	0.215785i
$330$	3.28924	+	33.3399i	0.181067	+	1.83530i
$331$	−14.6042	+	31.9788i	−0.802721	+	1.75771i	−0.166754	+	0.985999i	$0.553329\pi$
$331$	−14.6042	+	31.9788i	−0.802721	+	1.75771i	−0.635967	+	0.771716i	$0.719399\pi$
$332$	3.56047	+	6.52052i	0.195406	+	0.357860i
$333$	15.8520	+	1.13376i	0.868683	+	0.0621294i
$334$	−9.89509	+	8.57414i	−0.541435	+	0.469156i
$335$	1.16194	+	0.493259i	0.0634834	+	0.0269496i
$336$	−8.93325	−	4.07968i	−0.487349	−	0.222565i
$337$	−4.97251	−	22.8583i	−0.270870	−	1.24517i	−0.888565	−	0.458751i	$-0.848297\pi$
$337$	−4.97251	−	22.8583i	−0.270870	−	1.24517i	0.617695	−	0.786418i	$-0.288067\pi$
$338$	−2.45780	−	1.34206i	−0.133687	−	0.0729984i
$339$	6.77808	−	47.1426i	0.368135	−	2.56043i
$340$	−2.75369	+	0.889799i	−0.149340	+	0.0482561i
$341$	28.5402	−	4.10346i	1.54554	−	0.222215i
$342$	42.1274	+	9.16425i	2.27799	+	0.495546i
$343$	−0.936379	−	13.0923i	−0.0505597	−	0.706917i
$344$	6.51831			0.351444
$345$	21.8954	−	25.5209i	1.17881	−	1.37400i
$346$	10.7693			0.578960
$347$	−0.990128	−	13.8438i	−0.0531528	−	0.743174i	−0.952230	−	0.305383i	$-0.901216\pi$
$347$	−0.990128	−	13.8438i	−0.0531528	−	0.743174i	0.899077	−	0.437791i	$-0.144239\pi$
$348$	19.0424	+	4.14243i	1.02078	+	0.222057i
$349$	−14.6921	+	2.11241i	−0.786452	+	0.113075i	−0.523828	−	0.851824i	$-0.675497\pi$
$349$	−14.6921	+	2.11241i	−0.786452	+	0.113075i	−0.262623	+	0.964898i	$0.584588\pi$
$350$	−15.3578	+	3.06012i	−0.820910	+	0.163570i
$351$	6.79801	−	47.2812i	0.362851	−	2.52368i
$352$	4.19362	+	2.28989i	0.223521	+	0.122052i
$353$	0.265955	+	1.22258i	0.0141554	+	0.0650712i	0.983683	−	0.179912i	$-0.0575813\pi$
$353$	0.265955	+	1.22258i	0.0141554	+	0.0650712i	−0.969527	+	0.244983i	$0.921218\pi$
$354$	−7.41005	−	3.38406i	−0.393840	−	0.179861i
$355$	−11.0227	+	4.45302i	−0.585023	+	0.236342i
$356$	2.86056	−	2.47869i	0.151609	−	0.131370i
$357$	12.6775	+	0.906709i	0.670962	+	0.0479881i
$358$	−7.58529	−	13.8914i	−0.400895	−	0.734184i
$359$	9.19096	−	20.1254i	0.485080	−	1.06218i	−0.495955	−	0.868348i	$-0.665182\pi$
$359$	9.19096	−	20.1254i	0.485080	−	1.06218i	0.981035	−	0.193829i	$-0.0620908\pi$
$360$	−9.69011	+	11.8114i	−0.510714	+	0.622515i
$361$	−19.9734	+	5.86472i	−1.05123	+	0.308669i
$362$	−1.22679	+	0.918361i	−0.0644784	+	0.0482680i
$363$	−12.9634	+	34.7562i	−0.680401	+	1.82423i
$364$	−1.77173	−	12.3227i	−0.0928639	−	0.645883i
$365$	−10.7192	+	5.24871i	−0.561067	+	0.274730i
$366$	6.34183	+	5.49522i	0.331493	+	0.287240i
$367$	−12.5625	−	12.5625i	−0.655755	−	0.655755i	0.298617	−	0.954373i	$-0.403475\pi$
$367$	−12.5625	−	12.5625i	−0.655755	−	0.655755i	−0.954373	+	0.298617i	$0.903475\pi$
$368$	−1.24946	−	4.63021i	−0.0651327	−	0.241366i
$369$			26.5678i			1.38306i
$370$	0.231170	−	5.19607i	0.0120180	−	0.270131i
$371$	13.0485	−	8.38577i	0.677445	−	0.435368i
$372$	15.1482	+	11.3398i	0.785396	+	0.587940i
$373$	13.9396	+	5.19920i	0.721765	+	0.269204i	0.683384	−	0.730059i	$-0.260507\pi$
$373$	13.9396	+	5.19920i	0.721765	+	0.269204i	0.0383805	+	0.999263i	$0.487780\pi$
$374$	−6.12078	−	0.880035i	−0.316498	−	0.0455055i
$375$	−2.17151	+	34.9905i	−0.112136	+	1.80690i
$376$	−3.73159	−	2.39815i	−0.192442	−	0.123675i
$377$	8.63314	+	23.1463i	0.444629	+	1.19210i
$378$	33.0330	−	18.0374i	1.69903	−	0.927743i
$379$	13.3948	+	15.4584i	0.688043	+	0.794044i	0.987085	−	0.160196i	$-0.0512127\pi$
$379$	13.3948	+	15.4584i	0.688043	+	0.794044i	−0.299043	+	0.954240i	$0.596667\pi$
$380$	2.62676	−	13.8630i	0.134750	−	0.711158i
$381$	−53.1205	−	15.5976i	−2.72144	−	0.799088i
$382$	−7.35255	+	2.74236i	−0.376189	+	0.140311i
$383$	−3.93849	+	0.856766i	−0.201248	+	0.0437787i	−0.312059	−	0.950063i	$-0.601019\pi$
$383$	−3.93849	+	0.856766i	−0.201248	+	0.0437787i	0.110811	+	0.993841i	$0.464655\pi$
$384$	0.883418	+	3.00865i	0.0450818	+	0.153534i
$385$	−32.3489	−	8.55909i	−1.64865	−	0.436212i
$386$	0.197886	+	0.433311i	0.0100722	+	0.0220549i
$387$	−26.6892	+	35.6526i	−1.35669	+	1.81232i
$388$	−0.565224	+	2.59829i	−0.0286949	+	0.131908i
$389$	−1.45694	+	1.68140i	−0.0738698	+	0.0852503i	−0.791481	−	0.611193i	$-0.790690\pi$
$389$	−1.45694	+	1.68140i	−0.0738698	+	0.0852503i	0.717612	+	0.696443i	$0.245235\pi$
$390$	−27.6838	−	3.22188i	−1.40183	−	0.163146i
$391$	3.60919	+	5.04943i	0.182525	+	0.255361i
$392$	1.98632	−	1.98632i	0.100324	−	0.100324i
$393$	8.57120	−	0.613024i	0.432360	−	0.0309230i
$394$	−11.4646	−	17.8393i	−0.577578	−	0.898729i
$395$	4.31279	+	4.08646i	0.217000	+	0.205612i
$396$	−29.6955	+	13.5615i	−1.49226	+	0.681491i
$397$	−9.21507	−	12.3099i	−0.462491	−	0.617816i	0.507295	−	0.861772i	$-0.330645\pi$
$397$	−9.21507	−	12.3099i	−0.462491	−	0.617816i	−0.969786	+	0.243957i	$0.921555\pi$
$398$	3.89488	−	7.13293i	0.195232	−	0.357542i
$399$	−33.5031	+	52.1318i	−1.67725	+	2.60985i
$400$	3.94960	+	3.06605i	0.197480	+	0.153303i
$401$	−8.38008	+	28.5399i	−0.418481	+	1.42522i	0.433267	+	0.901266i	$0.357361\pi$
$401$	−8.38008	+	28.5399i	−0.418481	+	1.42522i	−0.851748	+	0.523951i	$0.824457\pi$
$402$	−0.126280	+	1.76563i	−0.00629828	+	0.0880615i
$403$	−1.71123	+	23.9261i	−0.0852424	+	1.19185i
$404$	3.25891	−	11.0988i	0.162137	−	0.552188i
$405$	−9.17630	−	37.3135i	−0.455974	−	1.85412i
$406$	−10.5234	+	16.3747i	−0.522267	+	0.812664i
$407$	5.32640	−	9.75457i	0.264020	−	0.483516i
$408$	−2.43195	−	3.24870i	−0.120399	−	0.160835i
$409$	30.2505	−	13.8150i	1.49579	−	0.683106i	0.511441	−	0.859318i	$-0.329112\pi$
$409$	30.2505	−	13.8150i	1.49579	−	0.683106i	0.984352	+	0.176212i	$0.0563845\pi$
$410$	8.69181	−	0.234211i	0.429258	−	0.0115669i
$411$	26.9678	+	41.9627i	1.33022	+	2.06987i
$412$	6.14749	−	0.439677i	0.302865	−	0.0216613i
$413$	5.75341	−	5.75341i	0.283107	−	0.283107i
$414$	30.4413	+	12.1243i	1.49611	+	0.595878i
$415$	−1.92041	+	16.5010i	−0.0942690	+	0.810002i
$416$	−2.60305	+	3.00408i	−0.127625	+	0.147287i
$417$	10.0173	−	46.0488i	0.490549	−	2.25502i
$418$	18.0681	−	24.1362i	0.883742	−	1.18054i
$419$	−6.01416	−	13.1692i	−0.293811	−	0.643356i	0.703949	−	0.710250i	$-0.251418\pi$
$419$	−6.01416	−	13.1692i	−0.293811	−	0.643356i	−0.997760	+	0.0668942i	$0.978691\pi$
$420$	−11.0396	−	18.9832i	−0.538675	−	0.926285i
$421$	−6.88343	−	23.4428i	−0.335478	−	1.14253i	−0.938636	−	0.344911i	$-0.887909\pi$
$421$	−6.88343	−	23.4428i	−0.335478	−	1.14253i	0.603158	−	0.797622i	$-0.293909\pi$
$422$	−7.82228	+	1.70163i	−0.380783	+	0.0828342i
$423$	28.3959	−	10.5911i	1.38066	−	0.514959i
$424$	−4.75184	−	1.39527i	−0.230770	−	0.0677601i
$425$	−6.17592	−	1.93157i	−0.299576	−	0.0936947i
$426$	−10.9171	−	12.5990i	−0.528937	−	0.610425i
$427$	−7.35626	+	4.01682i	−0.355994	+	0.194388i
$428$	1.14553	+	3.07129i	0.0553714	+	0.148456i
$429$	−50.1006	−	32.1977i	−2.41888	−	1.55452i
$430$	11.8992	+	8.41724i	0.573833	+	0.405915i
$431$	−21.8114	−	3.13601i	−1.05062	−	0.151056i	−0.404690	−	0.914454i	$-0.632621\pi$
$431$	−21.8114	−	3.13601i	−1.05062	−	0.151056i	−0.645929	+	0.763398i	$0.723530\pi$
$432$	−11.2594	−	4.19953i	−0.541717	−	0.202050i
$433$	25.1921	+	18.8586i	1.21065	+	0.906284i	0.997495	−	0.0707335i	$-0.0225340\pi$
$433$	25.1921	+	18.8586i	1.21065	+	0.906284i	0.213159	+	0.977018i	$0.431625\pi$
$434$	−15.8997	+	10.2181i	−0.763209	+	0.490484i
$435$	29.4129	+	32.1519i	1.41024	+	1.54157i
$436$		−	7.46063i		−	0.357299i
$437$	−30.0415	+	3.64591i	−1.43708	+	0.174408i
$438$	−11.8348	−	11.8348i	−0.565487	−	0.565487i
$439$	26.7358	+	23.1667i	1.27603	+	1.10569i	0.989024	+	0.147756i	$0.0472050\pi$
$439$	26.7358	+	23.1667i	1.27603	+	1.10569i	0.287005	+	0.957929i	$0.407340\pi$
$440$	4.69851	+	9.59553i	0.223993	+	0.457449i
$441$	2.73141	+	18.9974i	0.130067	+	0.904637i
$442$	1.79776	−	4.81999i	0.0855108	−	0.229263i
$443$	−28.8502	+	21.5970i	−1.37071	+	1.02610i	−0.375660	+	0.926758i	$0.622584\pi$
$443$	−28.8502	+	21.5970i	−1.37071	+	1.02610i	−0.995053	+	0.0993451i	$0.968325\pi$
$444$	6.99826	−	2.05488i	0.332123	−	0.0975201i
$445$	8.42276	−	0.830971i	0.399277	−	0.0393918i
$446$	10.0212	−	21.9434i	0.474518	−	1.03905i
$447$	22.7737	+	41.7070i	1.07716	+	1.97267i
$448$	−3.12397	−	0.223430i	−0.147594	−	0.0105561i
$449$	−0.121112	+	0.104944i	−0.00571564	+	0.00495263i	−0.657714	−	0.753268i	$-0.728476\pi$
$449$	−0.121112	+	0.104944i	−0.00571564	+	0.00495263i	0.651998	+	0.758220i	$0.273931\pi$
$450$	−32.9417	+	9.04879i	−1.55289	+	0.426564i
$451$	16.9006	+	7.71824i	0.795817	+	0.363438i
$452$	−3.22864	−	14.8418i	−0.151862	−	0.698100i
$453$	−6.28996	−	3.43458i	−0.295528	−	0.161371i
$454$	3.22356	−	22.4203i	0.151289	−	1.05224i
$455$	12.6782	−	24.7830i	0.594363	−	1.16185i
$456$	19.5848	−	2.81586i	0.917141	−	0.131865i
$457$	13.3595	+	2.90618i	0.624931	+	0.135945i	0.513870	−	0.857868i	$-0.328211\pi$
$457$	13.3595	+	2.90618i	0.624931	+	0.135945i	0.111061	+	0.993814i	$0.464575\pi$
$458$	−0.277203	−	3.87580i	−0.0129528	−	0.181104i
$459$	15.5523			0.725919
$460$	3.69819	−	10.0660i	0.172429	−	0.469328i
$461$	37.2335			1.73414			0.867068	−	0.498190i	$-0.166002\pi$
$461$	37.2335			1.73414			0.867068	+	0.498190i	$0.166002\pi$
$462$	−3.34753	−	46.8047i	−0.155741	−	2.17755i
$463$	−29.2442	−	6.36168i	−1.35909	−	0.295652i	−0.526799	−	0.849990i	$-0.676608\pi$
$463$	−29.2442	−	6.36168i	−1.35909	−	0.295652i	−0.832292	+	0.554338i	$0.812972\pi$
$464$	6.15162	−	0.884470i	0.285582	−	0.0410605i
$465$	13.0098	+	40.2620i	0.603317	+	1.86711i
$466$	−0.103595	+	0.720520i	−0.00479895	+	0.0333775i
$467$	22.6685	+	12.3779i	1.04897	+	0.572782i	0.908751	−	0.417338i	$-0.137037\pi$
$467$	22.6685	+	12.3779i	1.04897	+	0.572782i	0.140221	+	0.990120i	$0.455219\pi$
$468$	−5.77295	−	26.5378i	−0.266855	−	1.22671i
$469$	−1.60826	−	0.734470i	−0.0742628	−	0.0339147i
$470$	−3.71528	−	9.19654i	−0.171373	−	0.424205i
$471$	−31.3182	+	27.1374i	−1.44307	+	1.25042i
$472$	−2.59130	−	0.185334i	−0.119274	−	0.00853067i
$473$	14.9262	+	27.3353i	0.686308	+	1.25688i
$474$	−3.46107	+	7.57868i	−0.158972	+	0.348100i
$475$	22.6968	−	21.9151i	1.04140	−	1.00553i
$476$	3.88913	−	1.14195i	0.178258	−	0.0523413i
$477$	27.0879	−	20.2778i	1.24027	−	0.928456i
$478$	4.44043	−	11.9053i	0.203101	−	0.544534i
$479$	−3.26031	−	22.6760i	−0.148968	−	1.03609i	−0.917914	−	0.396779i	$-0.870128\pi$
$479$	−3.26031	−	22.6760i	−0.148968	−	1.03609i	0.768947	−	0.639313i	$-0.220781\pi$
$480$	−2.27244	+	6.63309i	−0.103722	+	0.302758i
$481$	6.98763	+	6.05482i	0.318609	+	0.276076i
$482$	17.1333	+	17.1333i	0.780401	+	0.780401i
$483$	−31.6195	+	34.9067i	−1.43874	+	1.58831i
$484$			11.8300i			0.537729i
$485$	−4.38705	+	4.01332i	−0.199206	+	0.182236i
$486$	15.0021	−	9.64126i	0.680509	−	0.437336i
$487$	−23.7307	−	17.7646i	−1.07534	−	0.804990i	−0.0936755	−	0.995603i	$-0.529862\pi$
$487$	−23.7307	−	17.7646i	−1.07534	−	0.804990i	−0.981665	+	0.190613i	$0.938953\pi$
$488$	2.50740	+	0.935211i	0.113505	+	0.0423350i
$489$	−45.6930	−	6.56966i	−2.06631	−	0.297090i
$490$	6.19103	−	1.06107i	0.279682	−	0.0479343i
$491$	−29.3771	−	18.8795i	−1.32577	−	0.852020i	−0.330006	−	0.943979i	$-0.607051\pi$
$491$	−29.3771	−	18.8795i	−1.32577	−	0.852020i	−0.995763	+	0.0919594i	$0.970687\pi$
$492$	4.26103	+	11.4243i	0.192102	+	0.515046i
$493$	−7.05936	+	3.85470i	−0.317937	+	0.173607i
$494$	16.4253	+	18.9558i	0.739011	+	0.852864i
$495$	−71.7218	−	13.5898i	−3.22365	−	0.610817i
$496$	5.79014	+	1.70014i	0.259985	+	0.0763384i
$497$	15.6013	−	5.81898i	0.699814	−	0.261017i
$498$	−22.7633	+	4.95186i	−1.02005	+	0.221898i
$499$	8.46321	+	28.8230i	0.378865	+	1.29030i	0.899651	+	0.436609i	$0.143821\pi$
$499$	8.46321	+	28.8230i	0.378865	+	1.29030i	−0.520786	+	0.853687i	$0.674361\pi$
$500$	3.25077	+	10.6973i	0.145379	+	0.478398i
$501$	−17.0551	−	37.3454i	−0.761964	−	1.66847i
$502$	−9.26442	+	12.3758i	−0.413491	+	0.552360i
$503$	1.24765	−	5.73537i	0.0556301	−	0.255728i	−0.940930	−	0.338601i	$-0.890046\pi$
$503$	1.24765	−	5.73537i	0.0556301	−	0.255728i	0.996560	+	0.0828737i	$0.0264098\pi$
$504$	14.0131	−	16.1720i	0.624195	−	0.720359i
$505$	20.2813	−	16.0527i	0.902508	−	0.714338i
$506$	16.5562	−	15.8424i	0.736014	−	0.704282i
$507$	6.20904	−	6.20904i	0.275753	−	0.275753i
$508$	−17.6109	+	1.25956i	−0.781359	+	0.0558839i
$509$	−9.46167	−	14.7226i	−0.419381	−	0.652570i	0.565710	−	0.824604i	$-0.308602\pi$
$509$	−9.46167	−	14.7226i	−0.419381	−	0.652570i	−0.985091	+	0.172035i	$0.944966\pi$
$510$	−0.244428	−	9.07096i	−0.0108234	−	0.401669i
$511$	15.2064	−	6.94451i	0.672690	−	0.307207i
$512$	0.599278	+	0.800541i	0.0264846	+	0.0353793i
$513$	−36.3406	+	66.5528i	−1.60448	+	2.93838i
$514$	0.570217	−	0.887275i	0.0251512	−	0.0391360i
$515$	11.7901	+	7.13575i	0.519532	+	0.314439i
$516$	−5.75840	+	19.6113i	−0.253499	+	0.863339i
$517$	1.51199	−	21.1404i	0.0664973	−	0.929753i
$518$	−0.519710	+	7.26650i	−0.0228348	+	0.319272i
$519$	−9.51379	+	32.4010i	−0.417609	+	1.42225i
$520$	−8.63112	+	2.12260i	−0.378500	+	0.0930823i
$521$	−16.4222	+	25.5535i	−0.719471	+	1.11952i	0.268259	+	0.963347i	$0.413552\pi$
$521$	−16.4222	+	25.5535i	−0.719471	+	1.11952i	−0.987730	+	0.156172i	$0.950085\pi$
$522$	−20.3501	+	37.2684i	−0.890699	+	1.63119i
$523$	−10.6357	−	14.2077i	−0.465069	−	0.621259i	0.505284	−	0.862953i	$-0.331388\pi$
$523$	−10.6357	−	14.2077i	−0.465069	−	0.621259i	−0.970352	+	0.241694i	$0.922297\pi$
$524$	2.49279	−	1.13842i	0.108898	−	0.0497321i
$525$	4.36056	−	48.9096i	0.190310	−	2.13459i
$526$	−12.9180	−	20.1008i	−0.563251	−	0.876436i
$527$	−7.78997	+	0.557149i	−0.339336	+	0.0242698i
$528$	−10.5942	+	10.5942i	−0.461053	+	0.461053i
$529$	−22.9777	−	1.01294i	−0.999030	−	0.0440409i
$530$	−6.87280	−	8.68323i	−0.298535	−	0.377175i
$531$	11.6238	−	13.4146i	0.504429	−	0.582142i
$532$	−4.20086	+	19.3111i	−0.182131	+	0.837241i
$533$	−9.26283	+	12.3737i	−0.401218	+	0.535964i
$534$	4.93043	+	10.7961i	0.213360	+	0.467194i
$535$	−1.87484	+	7.08592i	−0.0810565	+	0.306351i
$536$	0.159043	+	0.541651i	0.00686961	+	0.0233957i
$537$	48.4953	−	10.5495i	2.09273	−	0.455245i
$538$	−22.9698	+	8.56728i	−0.990297	+	0.369362i
$539$	12.8783	+	3.78142i	0.554709	+	0.162877i
$540$	−15.1312	−	22.2058i	−0.651142	−	0.955584i
$541$	−19.4380	−	22.4327i	−0.835707	−	0.964457i	0.164051	−	0.986452i	$-0.447544\pi$
$541$	−19.4380	−	22.4327i	−0.835707	−	0.964457i	−0.999758	+	0.0219949i	$0.992998\pi$
$542$	17.3870	−	9.49403i	0.746837	−	0.407804i
$543$	−1.67926	−	4.50226i	−0.0720638	−	0.193211i
$544$	−1.08874	−	0.699689i	−0.0466792	−	0.0299989i
$545$	9.63407	−	13.6195i	0.412678	−	0.583393i
$546$	38.6397	+	5.55555i	1.65363	+	0.237756i
$547$	−20.0404	−	7.47468i	−0.856865	−	0.319594i	−0.117643	−	0.993056i	$-0.537534\pi$
$547$	−20.0404	−	7.47468i	−0.856865	−	0.319594i	−0.739222	+	0.673462i	$0.764807\pi$
$548$	12.7348	+	9.53312i	0.544002	+	0.407235i
$549$	−15.3818	+	9.88526i	−0.656478	+	0.421893i
$550$	−3.81373	+	23.5840i	−0.162618	+	1.00563i
$551$		−	39.2162i		−	1.67066i
$552$	15.0345	+	0.331227i	0.639909	+	0.0140979i
$553$	−5.88434	−	5.88434i	−0.250227	−	0.250227i
$554$	3.55337	+	3.07901i	0.150968	+	0.130815i
$555$	15.4289	+	5.28581i	0.654921	+	0.224370i
$556$	−2.13884	−	14.8760i	−0.0907072	−	0.630882i
$557$	−1.95667	+	5.24604i	−0.0829068	+	0.222282i	−0.971788	−	0.235856i	$-0.924211\pi$
$557$	−1.95667	+	5.24604i	−0.0829068	+	0.222282i	0.888881	+	0.458138i	$0.151483\pi$
$558$	−33.0068	+	24.7086i	−1.39729	+	1.04600i
$559$	−24.8605	+	7.29971i	−1.05149	+	0.308745i
$560$	−5.41431	−	4.44192i	−0.228796	−	0.187705i
$561$	8.05492	−	17.6378i	0.340079	−	0.744669i
$562$	2.74151	+	5.02071i	0.115644	+	0.211786i
$563$	31.7943	+	2.27398i	1.33997	+	0.0958366i	0.722836	−	0.691020i	$-0.242838\pi$
$563$	31.7943	+	2.27398i	1.33997	+	0.0958366i	0.617136	+	0.786857i	$0.288293\pi$
$564$	10.5117	−	9.10848i	0.442624	−	0.383536i
$565$	13.2716	−	31.2631i	0.558342	−	1.31525i
$566$	3.74245	+	1.70912i	0.157307	+	0.0718396i
$567$	11.4403	+	52.5904i	0.480449	+	2.20859i
$568$	−4.66623	−	2.54795i	−0.195791	−	0.106910i
$569$	−1.28670	+	8.94923i	−0.0539415	+	0.375171i	0.944913	+	0.327321i	$0.106146\pi$
$569$	−1.28670	+	8.94923i	−0.0539415	+	0.375171i	−0.998855	+	0.0478498i	$0.984763\pi$
$570$	39.3884	+	20.1498i	1.64980	+	0.843984i
$571$	−41.6936	+	5.99463i	−1.74482	+	0.250868i	−0.939641	−	0.342161i	$-0.888841\pi$
$571$	−41.6936	+	5.99463i	−1.74482	+	0.250868i	−0.805181	+	0.593029i	$0.797932\pi$
$572$	−18.5587	−	4.03719i	−0.775976	−	0.168803i
$573$	−1.75541	−	24.5439i	−0.0733334	−	1.02534i
$574$	−12.1786			−0.508324
$575$	19.7495	−	13.6000i	0.823609	−	0.567157i
$576$	−6.83238			−0.284683
$577$	1.04665	+	14.6341i	0.0435728	+	0.609227i	0.971587	+	0.236682i	$0.0760601\pi$
$577$	1.04665	+	14.6341i	0.0435728	+	0.609227i	−0.928014	+	0.372545i	$0.878485\pi$
$578$	−14.9749	−	3.25758i	−0.622872	−	0.135498i
$579$	−1.47850	+	0.212576i	−0.0614442	+	0.00883434i
$580$	12.3720	+	6.32911i	0.513719	+	0.262802i
$581$	3.31139	−	23.0312i	0.137380	−	0.955497i
$582$	−7.31802	−	3.99594i	−0.303341	−	0.165637i
$583$	−5.02998	−	23.1224i	−0.208320	−	0.957633i
$584$	−4.85525	−	2.21732i	−0.200911	−	0.0917532i
$585$	23.7303	−	55.8998i	0.981126	−	2.31117i
$586$	−19.9890	+	17.3205i	−0.825737	+	0.715505i
$587$	−29.2882	−	2.09474i	−1.20886	−	0.0864590i	−0.547678	−	0.836689i	$-0.684488\pi$
$587$	−29.2882	−	2.09474i	−1.20886	−	0.0864590i	−0.661177	+	0.750230i	$0.729943\pi$
$588$	4.22139	+	7.73089i	0.174087	+	0.318817i
$589$	15.8184	−	34.6374i	0.651784	−	1.42721i
$590$	−4.49113	−	3.68453i	−0.184897	−	0.151690i
$591$	63.8000	−	18.7334i	2.62438	−	0.770588i
$592$	1.86210	−	1.39395i	0.0765318	−	0.0572910i
$593$	6.98833	−	18.7364i	0.286976	−	0.769414i	−0.710839	−	0.703355i	$-0.751685\pi$
$593$	6.98833	−	18.7364i	0.286976	−	0.769414i	0.997816	−	0.0660592i	$-0.0210426\pi$
$594$	−8.17150	−	56.8340i	−0.335281	−	2.33193i
$595$	8.57427	+	2.93747i	0.351511	+	0.120425i
$596$	11.4531	+	9.92413i	0.469135	+	0.406508i
$597$	18.0197	+	18.0197i	0.737496	+	0.737496i
$598$	9.95065	+	16.2601i	0.406912	+	0.664927i
$599$		−	23.6198i		−	0.965077i	−0.875875	−	0.482539i	$-0.839715\pi$
$599$		−	23.6198i		−	0.965077i	0.875875	−	0.482539i	$-0.160285\pi$
$600$	−12.7138	+	9.17433i	−0.519040	+	0.374541i
$601$	−1.75001	+	1.12466i	−0.0713843	+	0.0458759i	−0.575846	−	0.817558i	$-0.695327\pi$
$601$	−1.75001	+	1.12466i	−0.0713843	+	0.0458759i	0.504462	+	0.863434i	$0.331691\pi$
$602$	−16.3430	−	12.2343i	−0.666093	−	0.498631i
$603$	−3.61382	−	1.34788i	−0.147166	−	0.0548901i
$604$	−2.26224	−	0.325262i	−0.0920494	−	0.0132347i
$605$	−15.2764	+	21.5959i	−0.621074	+	0.877997i
$606$	30.5135	+	19.6098i	1.23953	+	0.796595i
$607$	1.85343	+	4.96923i	0.0752283	+	0.201695i	0.969121	−	0.246587i	$-0.0793090\pi$
$607$	1.85343	+	4.96923i	0.0752283	+	0.201695i	−0.893892	+	0.448281i	$0.852036\pi$
$608$	5.53819	−	3.02408i	0.224603	−	0.122643i
$609$	−39.9692	−	46.1269i	−1.61963	−	1.86916i
$610$	3.36962	+	4.94509i	0.136432	+	0.200221i
$611$	16.9177	+	4.96750i	0.684419	+	0.200964i
$612$	8.28485	−	3.09009i	0.334895	−	0.124910i
$613$	14.2762	−	3.10559i	0.576609	−	0.125434i	0.0852018	−	0.996364i	$-0.472846\pi$
$613$	14.2762	−	3.10559i	0.576609	−	0.125434i	0.491407	+	0.870930i	$0.336483\pi$
$614$	−8.62796	−	29.3841i	−0.348196	−	1.18585i
$615$	−6.97384	+	26.3575i	−0.281212	+	1.06284i
$616$	−6.21655	−	13.6124i	−0.250472	−	0.548457i
$617$	−17.8340	+	23.8235i	−0.717971	+	0.959097i	−1.00000		0.000309194i	$-0.999902\pi$
$617$	−17.8340	+	23.8235i	−0.717971	+	0.959097i	0.282029	+	0.959406i	$0.408992\pi$
$618$	−4.10797	+	18.8840i	−0.165247	+	0.759627i
$619$	13.5424	−	15.6287i	0.544314	−	0.628172i	−0.415235	−	0.909714i	$-0.636301\pi$
$619$	13.5424	−	15.6287i	0.544314	−	0.628172i	0.959549	+	0.281542i	$0.0908460\pi$
$620$	8.37453	+	10.5805i	0.336329	+	0.424925i
$621$	−35.5453	+	45.3647i	−1.42638	+	1.82042i
$622$	−5.56769	+	5.56769i	−0.223244	+	0.223244i
$623$	−11.8244	+	0.845698i	−0.473735	+	0.0338822i
$624$	−6.73863	−	10.4855i	−0.269761	−	0.419756i
$625$	−7.87936	+	23.7258i	−0.315174	+	0.949034i
$626$	−15.6943	+	7.16733i	−0.627269	+	0.286464i
$627$	56.6556	+	75.6831i	2.26261	+	3.02249i
$628$	−6.33360	+	11.5991i	−0.252738	+	0.462855i
$629$	−1.62751	+	2.53246i	−0.0648932	+	0.100976i
$630$	46.4644	−	11.4267i	1.85119	−	0.455252i
$631$	7.01663	−	23.8964i	0.279327	−	0.951302i	−0.693633	−	0.720329i	$-0.743991\pi$
$631$	7.01663	−	23.8964i	0.279327	−	0.951302i	0.972960	−	0.230973i	$-0.0741909\pi$
$632$	−0.189551	+	2.65027i	−0.00753994	+	0.105422i
$633$	1.79073	−	25.0377i	0.0711753	−	0.995160i
$634$	−4.80477	+	16.3635i	−0.190822	+	0.649879i
$635$	−33.7755	−	20.4421i	−1.34034	−	0.811218i
$636$	8.39573	−	13.0640i	0.332912	−	0.518022i
$637$	−5.35129	+	9.80016i	−0.212026	+	0.388297i
$638$	17.7957	+	23.7722i	0.704537	+	0.941152i
$639$	33.0421	−	15.0898i	1.30713	−	0.596945i
$640$	0.0602316	+	2.23526i	0.00238086	+	0.0883563i
$641$	−16.4885	−	25.6565i	−0.651255	−	1.01337i	−0.997175	−	0.0751083i	$-0.976070\pi$
$641$	−16.4885	−	25.6565i	−0.651255	−	1.01337i	0.345921	−	0.938264i	$-0.387567\pi$
$642$	−10.2524	+	0.733267i	−0.404630	+	0.0289397i
$643$	−31.8011	+	31.8011i	−1.25411	+	1.25411i	−0.300256	+	0.953859i	$0.597072\pi$
$643$	−31.8011	+	31.8011i	−1.25411	+	1.25411i	−0.953859	+	0.300256i	$0.902928\pi$
$644$	−5.55775	+	13.9542i	−0.219006	+	0.549873i
$645$	−35.8365	+	28.3647i	−1.41106	+	1.11686i
$646$	−5.34783	+	6.17172i	−0.210408	+	0.242823i
$647$	−6.74417	+	31.0025i	−0.265141	+	1.21883i	0.631254	+	0.775576i	$0.282540\pi$
$647$	−6.74417	+	31.0025i	−0.265141	+	1.21883i	−0.896395	+	0.443256i	$0.853823\pi$
$648$	10.2982	−	13.7567i	0.404550	−	0.540416i
$649$	−5.15658	−	11.2913i	−0.202413	−	0.443224i
$650$	−18.4972	−	7.27072i	−0.725518	−	0.285181i
$651$	−16.6966	−	56.8634i	−0.654391	−	2.22865i
$652$	−14.3854	+	3.12936i	−0.563378	+	0.122555i
$653$	−17.7084	+	6.60490i	−0.692984	+	0.258470i	−0.671182	−	0.741293i	$-0.734213\pi$
$653$	−17.7084	+	6.60490i	−0.692984	+	0.258470i	−0.0218018	+	0.999762i	$0.506940\pi$
$654$	22.4464	+	6.59086i	0.877723	+	0.257723i
$655$	6.02068	+	1.14080i	0.235248	+	0.0445747i
$656$	2.54643	+	2.93874i	0.0994214	+	0.114738i
$657$	32.0076	−	17.4775i	1.24874	−	0.681861i
$658$	4.85495	+	13.0166i	0.189266	+	0.507440i
$659$	24.8232	+	15.9529i	0.966975	+	0.621437i	0.925920	−	0.377719i	$-0.123292\pi$
$659$	24.8232	+	15.9529i	0.966975	+	0.621437i	0.0410554	+	0.999157i	$0.486928\pi$
$660$	−33.0203	+	5.65930i	−1.28531	+	0.220288i
$661$	−35.0666	−	5.04181i	−1.36393	−	0.196104i	−0.578818	−	0.815456i	$-0.696486\pi$
$661$	−35.0666	−	5.04181i	−1.36393	−	0.196104i	−0.785113	+	0.619353i	$0.787395\pi$
$662$	−32.9392	−	12.2857i	−1.28022	−	0.477497i
$663$	12.9135	+	9.66690i	0.501517	+	0.375431i
$664$	−6.24990	+	4.01657i	−0.242543	+	0.155873i
$665$	−32.6055	+	29.8279i	−1.26439	+	1.15668i
$666$			15.8925i			0.615820i
$667$	4.89055	−	29.4016i	0.189363	−	1.13843i
$668$	−9.25821	−	9.25821i	−0.358211	−	0.358211i
$669$	57.1669	+	49.5354i	2.21020	+	1.91515i
$670$	−0.409111	+	1.19416i	−0.0158053	+	0.0461346i
$671$	1.81975	+	12.6566i	0.0702505	+	0.488603i
$672$	3.43199	−	9.20153i	0.132392	−	0.354957i
$673$	20.1697	−	15.0988i	0.777483	−	0.582017i	−0.135136	−	0.990827i	$-0.543147\pi$
$673$	20.1697	−	15.0988i	0.777483	−	0.582017i	0.912619	+	0.408810i	$0.134056\pi$
$674$	22.4453	−	6.59053i	0.864560	−	0.253858i
$675$	1.05267	−	60.0761i	0.0405173	−	2.31233i
$676$	1.16330	−	2.54728i	0.0447424	−	0.0979721i
$677$	−10.4213	−	19.0852i	−0.400523	−	0.733503i	0.597118	−	0.802154i	$-0.296313\pi$
$677$	−10.4213	−	19.0852i	−0.400523	−	0.733503i	−0.997641	+	0.0686504i	$0.978131\pi$
$678$	47.5060	+	3.39770i	1.82446	+	0.130488i
$679$	6.29391	−	5.45370i	0.241538	−	0.209294i
$680$	−1.08398	−	2.68320i	−0.0415687	−	0.102896i
$681$	64.6071	+	29.5051i	2.47575	+	1.13064i
$682$	6.12905	+	28.1748i	0.234693	+	1.07887i
$683$	35.3938	+	19.3265i	1.35431	+	0.739506i	0.982049	−	0.188624i	$-0.0604027\pi$
$683$	35.3938	+	19.3265i	1.35431	+	0.739506i	0.372256	+	0.928130i	$0.378584\pi$
$684$	−6.13556	+	42.6738i	−0.234599	+	1.63167i
$685$	10.9371	+	33.8475i	0.417886	+	1.29325i
$686$	12.9921	−	1.86799i	0.496042	−	0.0713200i
$687$	11.9058	+	2.58995i	0.454235	+	0.0988128i
$688$	0.465011	+	6.50170i	0.0177284	+	0.247875i
$689$	19.6858			0.749970
$690$	27.0179	+	20.0190i	1.02855	+	0.762110i
$691$	49.2336			1.87293			0.936467	−	0.350755i	$-0.114075\pi$
$691$	49.2336			1.87293			0.936467	+	0.350755i	$0.114075\pi$
$692$	0.768272	+	10.7418i	0.0292053	+	0.408344i
$693$	99.9079	+	21.7336i	3.79519	+	0.825592i
$694$	13.7379	−	1.97521i	0.521483	−	0.0749780i
$695$	15.3052	−	29.9182i	0.580559	−	1.13486i
$696$	−2.77340	+	19.2894i	−0.105125	+	0.731164i
$697$	−4.41687	−	2.41179i	−0.167301	−	0.0913532i
$698$	−3.15515	−	14.5040i	−0.119424	−	0.548984i
$699$	−2.07627	−	0.948202i	−0.0785319	−	0.0358643i
$700$	−4.14794	−	15.1004i	−0.156777	−	0.570741i
$701$	1.44090	−	1.24855i	0.0544221	−	0.0471570i	−0.627225	−	0.778838i	$-0.715809\pi$
$701$	1.44090	−	1.24855i	0.0544221	−	0.0471570i	0.681647	+	0.731681i	$0.261264\pi$
$702$	47.6457	+	3.40769i	1.79827	+	0.128615i
$703$	−7.03416	−	12.8821i	−0.265298	−	0.485858i
$704$	−1.98489	+	4.34629i	−0.0748082	+	0.163807i
$705$	30.9513	−	3.05358i	1.16569	−	0.115005i
$706$	−1.20049	+	0.352495i	−0.0451810	+	0.0132663i
$707$	−29.0024	+	21.7109i	−1.09075	+	0.816523i
$708$	2.84681	−	7.63259i	0.106990	−	0.286850i
$709$	1.40020	+	9.73862i	0.0525857	+	0.365742i	0.999075	+	0.0430059i	$0.0136934\pi$
$709$	1.40020	+	9.73862i	0.0525857	+	0.365742i	−0.946489	+	0.322736i	$0.895397\pi$
$710$	−5.22802	−	10.6769i	−0.196204	−	0.400697i
$711$	−13.7198	−	11.8883i	−0.514533	−	0.445846i
$712$	2.67644	+	2.67644i	0.100304	+	0.100304i
$713$	16.1791	−	23.9960i	0.605910	−	0.898659i
$714$			12.7098i			0.475654i
$715$	−28.6657	−	31.3351i	−1.07204	−	1.17187i
$716$	13.3149	−	8.55696i	0.497601	−	0.319789i
$717$	31.8960	+	23.8770i	1.19118	+	0.891704i
$718$	20.7298	+	7.73181i	0.773629	+	0.288549i
$719$	22.9216	+	3.29563i	0.854833	+	0.122906i	0.555779	−	0.831330i	$-0.312420\pi$
$719$	22.9216	+	3.29563i	0.854833	+	0.122906i	0.299054	+	0.954236i	$0.403329\pi$
$720$	−12.4726	−	8.82280i	−0.464826	−	0.328806i
$721$	−16.2385	−	10.4359i	−0.604754	−	0.388652i
$722$	−7.27466	−	19.5041i	−0.270735	−	0.725868i
$723$	−66.6840	+	36.4122i	−2.48000	+	1.35418i
$724$	−1.00354	−	1.15815i	−0.0372962	−	0.0430421i
$725$	14.4123	+	27.5301i	0.535259	+	1.02244i
$726$	−35.5924	−	10.4509i	−1.32096	−	0.387869i
$727$	10.2244	−	3.81349i	0.379200	−	0.141434i	−0.152634	−	0.988283i	$-0.548776\pi$
$727$	10.2244	−	3.81349i	0.379200	−	0.141434i	0.531834	+	0.846848i	$0.321503\pi$
$728$	12.1649	−	2.64630i	0.450860	−	0.0980785i
$729$	1.22988	+	4.18858i	0.0455510	+	0.155132i
$730$	−6.00003	−	10.3174i	−0.222071	−	0.381865i
$731$	−3.50440	−	7.67357i	−0.129615	−	0.283817i
$732$	−5.02880	+	6.71769i	−0.185870	+	0.248293i
$733$	4.03728	−	18.5591i	0.149120	−	0.685495i	−0.840503	−	0.541807i	$-0.817740\pi$
$733$	4.03728	−	18.5591i	0.149120	−	0.685495i	0.989623	−	0.143688i	$-0.0458960\pi$
$734$	11.6343	−	13.4267i	0.429428	−	0.495587i
$735$	−2.27688	+	19.5640i	−0.0839840	+	0.721629i
$736$	4.52928	−	1.57659i	0.166951	−	0.0581140i
$737$	−1.90729	+	1.90729i	−0.0702558	+	0.0702558i
$738$	−26.5001	+	1.89532i	−0.975481	+	0.0697678i
$739$	−15.7194	−	24.4599i	−0.578249	−	0.899773i	0.421727	−	0.906723i	$-0.361424\pi$
$739$	−15.7194	−	24.4599i	−0.578249	−	0.899773i	−0.999976	+	0.00694976i	$0.997788\pi$
$740$	5.19932	−	0.140102i	0.191131	−	0.00515024i
$741$	−71.5419	+	32.6721i	−2.62816	+	1.20024i
$742$	9.29528	+	12.4170i	0.341240	+	0.455844i
$743$	−4.75816	+	8.71392i	−0.174560	+	0.319683i	−0.950281	−	0.311393i	$-0.899204\pi$
$743$	−4.75816	+	8.71392i	−0.174560	+	0.319683i	0.775721	+	0.631076i	$0.217386\pi$
$744$	−10.2302	+	15.9185i	−0.375058	+	0.583602i
$745$	8.09243	+	32.9062i	0.296484	+	1.20559i
$746$	−4.19151	+	14.2750i	−0.153462	+	0.522644i
$747$	3.62115	−	50.6303i	0.132491	−	1.85247i
$748$	0.441141	−	6.16796i	0.0161297	−	0.225523i
$749$	2.89238	−	9.85055i	0.105685	−	0.359931i
$750$	−35.0562	+	0.330211i	−1.28007	+	0.0120576i
$751$	14.4018	−	22.4096i	0.525528	−	0.817738i	−0.472446	−	0.881360i	$-0.656629\pi$
$751$	14.4018	−	22.4096i	0.525528	−	0.817738i	0.997974	+	0.0636220i	$0.0202652\pi$
$752$	2.12583	−	3.89317i	0.0775211	−	0.141969i
$753$	−29.0501	−	38.8064i	−1.05864	−	1.41418i
$754$	−22.4715	+	10.2624i	−0.818363	+	0.373734i
$755$	−3.70973	−	3.51505i	−0.135011	−	0.127926i
$756$	20.3480	+	31.6621i	0.740049	+	1.15154i
$757$	16.0371	−	1.14700i	0.582878	−	0.0416883i	0.223213	−	0.974770i	$-0.428345\pi$
$757$	16.0371	−	1.14700i	0.582878	−	0.0416883i	0.359665	+	0.933081i	$0.382891\pi$
$758$	−14.4634	+	14.4634i	−0.525335	+	0.525335i
$759$	33.0382	+	63.8073i	1.19921	+	2.31606i
$760$	14.0151	+	1.63109i	0.508381	+	0.0591659i
$761$	−15.4283	+	17.8052i	−0.559274	+	0.645436i	−0.963018	−	0.269435i	$-0.913163\pi$
$761$	−15.4283	+	17.8052i	−0.559274	+	0.645436i	0.403745	+	0.914872i	$0.367708\pi$
$762$	11.7683	−	54.0978i	0.426319	−	1.95976i
$763$	−14.0029	+	18.7057i	−0.506939	+	0.677191i
$764$	−3.25990	−	7.13818i	−0.117939	−	0.258250i
$765$	19.1144	+	5.05742i	0.691082	+	0.182851i
$766$	−1.13555	−	3.86734i	−0.0410292	−	0.139733i
$767$	10.0907	−	2.19509i	0.364352	−	0.0792600i
$768$	−2.93796	+	1.09580i	−0.106014	+	0.0395413i
$769$	−31.9547	−	9.38273i	−1.15231	−	0.338350i	−0.350873	−	0.936423i	$-0.614115\pi$
$769$	−31.9547	−	9.38273i	−1.15231	−	0.338350i	−0.801441	+	0.598073i	$0.795933\pi$
$770$	6.22954	−	32.8771i	0.224497	−	1.18481i
$771$	2.16576	+	2.49942i	0.0779978	+	0.0900143i
$772$	−0.418090	+	0.228294i	−0.0150474	+	0.00821649i
$773$	1.96767	+	5.27553i	0.0707722	+	0.189748i	0.967520	−	0.252794i	$-0.0813496\pi$
$773$	1.96767	+	5.27553i	0.0707722	+	0.189748i	−0.896748	+	0.442542i	$0.854077\pi$
$774$	−37.4657	−	24.0778i	−1.34668	−	0.865457i
$775$	1.62491	+	30.1291i	0.0583685	+	1.08227i
$776$	−2.63199	−	0.378424i	−0.0944831	−	0.0135846i
$777$	−21.4032	−	7.98298i	−0.767836	−	0.286388i
$778$	−1.78105	−	1.33328i	−0.0638538	−	0.0478003i
$779$	20.6415	−	13.2655i	0.739559	−	0.475286i
$780$	1.23873	−	27.8431i	0.0443535	−	0.996944i
$781$		−	25.4029i		−	0.908988i
$782$	−4.77909	+	3.96022i	−0.170900	+	0.141617i
$783$	−52.8100	−	52.8100i	−1.88728	−	1.88728i
$784$	2.12296	+	1.83956i	0.0758201	+	0.0656985i
$785$	−26.5402	+	12.9956i	−0.947262	+	0.463833i
$786$	1.22292	+	8.50563i	0.0436203	+	0.303386i
$787$	−1.92071	+	5.14963i	−0.0684660	+	0.183565i	−0.966676	−	0.256001i	$-0.917595\pi$
$787$	−1.92071	+	5.14963i	−0.0684660	+	0.183565i	0.898210	+	0.439566i	$0.144868\pi$
$788$	16.9759	−	12.7080i	0.604742	−	0.452704i
$789$	71.8881	−	21.1083i	2.55929	−	0.751474i
$790$	−3.76838	+	4.59333i	−0.134073	+	0.163423i
$791$	−19.7617	+	43.2720i	−0.702644	+	1.53858i
$792$	−15.6454	−	28.6524i	−0.555935	−	1.01812i
$793$	−10.6104	−	0.758872i	−0.376787	−	0.0269483i
$794$	11.6211	−	10.0698i	0.412418	−	0.357363i
$795$	32.1963	−	13.0069i	1.14189	−	0.461307i
$796$	7.39262	+	3.37609i	0.262024	+	0.119662i
$797$	0.714613	+	3.28502i	0.0253129	+	0.116361i	0.988070	−	0.154007i	$-0.0492180\pi$
$797$	0.714613	+	3.28502i	0.0253129	+	0.116361i	−0.962757	+	0.270369i	$0.912854\pi$
$798$	−54.3890	−	29.6987i	−1.92535	−	1.05132i
$799$	−0.816985	+	5.68226i	−0.0289029	+	0.201024i
$800$	−2.77648	+	4.15826i	−0.0981634	+	0.147017i
$801$	−25.5978	+	3.68040i	−0.904452	+	0.130041i
$802$	−29.0651	−	6.32272i	−1.02632	−	0.223263i
$803$	−1.81939	−	25.4385i	−0.0642051	−	0.897704i
$804$	−1.77014			−0.0624279
$805$	−28.1651	+	18.2967i	−0.992690	+	0.644875i
$806$	−23.9872			−0.844914
$807$	−5.48400	−	76.6764i	−0.193046	−	2.69914i
$808$	11.3030	+	2.45883i	0.397640	+	0.0865013i
$809$	−30.1990	+	4.34197i	−1.06174	+	0.152655i	−0.650986	−	0.759090i	$-0.725644\pi$
$809$	−30.1990	+	4.34197i	−1.06174	+	0.152655i	−0.410756	+	0.911745i	$0.634735\pi$
$810$	36.5638	−	11.8148i	1.28472	−	0.415131i
$811$	−3.16655	+	22.0239i	−0.111193	+	0.773362i	0.855570	+	0.517687i	$0.173207\pi$
$811$	−3.16655	+	22.0239i	−0.111193	+	0.773362i	−0.966763	+	0.255675i	$0.917702\pi$
$812$	−17.0837	−	9.32843i	−0.599522	−	0.327364i
$813$	13.2042	+	60.6986i	0.463091	+	2.12879i
$814$	10.1097	+	4.61694i	0.354345	+	0.161824i
$815$	−30.3018	−	12.8636i	−1.06143	−	0.450591i
$816$	3.06693	−	2.65751i	0.107364	−	0.0930314i
$817$	41.0260	+	2.93424i	1.43532	+	0.102656i
$818$	15.9378	+	29.1879i	0.557253	+	1.02053i
$819$	−35.3347	+	77.3723i	−1.23470	+	2.70361i
$820$	0.853681	+	8.65295i	0.0298118	+	0.302174i
$821$	−28.5404	+	8.38022i	−0.996067	+	0.292472i	−0.738841	−	0.673880i	$-0.764627\pi$
$821$	−28.5404	+	8.38022i	−0.996067	+	0.292472i	−0.257226	+	0.966351i	$0.582808\pi$
$822$	−39.9319	+	29.8927i	−1.39279	+	1.04263i
$823$	−17.1220	+	45.9058i	−0.596835	+	1.60018i	0.189162	+	0.981946i	$0.439423\pi$
$823$	−17.1220	+	45.9058i	−0.596835	+	1.60018i	−0.785997	+	0.618231i	$0.787850\pi$
$824$	0.877113	+	6.10046i	0.0305557	+	0.212520i
$825$	−67.5869	−	32.3087i	−2.35307	−	1.12485i
$826$	6.14920	+	5.32831i	0.213958	+	0.185396i
$827$	−14.8810	−	14.8810i	−0.517462	−	0.517462i	0.399341	−	0.916803i	$-0.369239\pi$
$827$	−14.8810	−	14.8810i	−0.517462	−	0.517462i	−0.916803	+	0.399341i	$0.869239\pi$
$828$	−9.92176	+	31.2287i	−0.344805	+	1.08527i
$829$		−	21.0848i		−	0.732307i	−0.930555	−	0.366153i	$-0.880675\pi$
$829$		−	21.0848i		−	0.732307i	0.930555	−	0.366153i	$-0.119325\pi$
$830$	−16.5959	−	0.738345i	−0.576054	−	0.0256283i
$831$	−12.4028	+	7.97077i	−0.430247	+	0.276503i
$832$	−3.18212	−	2.38211i	−0.110320	−	0.0825847i
$833$	−3.40625	−	1.27047i	−0.118020	−	0.0440191i
$834$	46.6461	+	6.70670i	1.61522	+	0.232234i
$835$	−4.94563	−	28.8563i	−0.171151	−	0.998612i
$836$	25.3637	+	16.3003i	0.877222	+	0.563756i
$837$	−25.3424	−	67.9457i	−0.875962	−	2.34855i
$838$	12.7066	−	6.93831i	0.438941	−	0.239680i
$839$	16.0961	+	18.5759i	0.555700	+	0.641312i	0.962202	−	0.272338i	$-0.0877970\pi$
$839$	16.0961	+	18.5759i	0.555700	+	0.641312i	−0.406502	+	0.913650i	$0.633252\pi$
$840$	18.1473	−	12.3657i	0.626140	−	0.426656i
$841$	9.23490	+	2.71161i	0.318445	+	0.0935038i
$842$	22.8920	−	8.53828i	0.788911	−	0.294249i
$843$	−17.5274	+	3.81286i	−0.603677	+	0.131322i
$844$	−2.25533	−	7.68096i	−0.0776317	−	0.264389i
$845$	5.41297	−	3.14788i	0.186212	−	0.108290i
$846$	12.5899	+	27.5680i	0.432849	+	0.947808i
$847$	22.2039	−	29.6609i	0.762934	−	1.01916i
$848$	1.05272	−	4.83927i	0.0361505	−	0.166181i
$849$	−8.44828	+	9.74984i	−0.289944	+	0.334614i
$850$	1.48606	−	6.29798i	0.0509714	−	0.216019i
$851$	−3.66723	−	10.5353i	−0.125711	−	0.361146i
$852$	11.7881	−	11.7881i	0.403854	−	0.403854i
$853$	40.3571	−	2.88639i	1.38180	−	0.0988283i	0.639446	−	0.768836i	$-0.279164\pi$
$853$	40.3571	−	2.88639i	1.38180	−	0.0988283i	0.742354	+	0.670008i	$0.233709\pi$
$854$	−4.53138	−	7.05096i	−0.155060	−	0.241279i
$855$	−66.3061	+	69.9785i	−2.26762	+	2.39321i
$856$	−2.98174	+	1.36172i	−0.101914	+	0.0465425i
$857$	25.7348	+	34.3777i	0.879084	+	1.17432i	0.983702	+	0.179807i	$0.0575473\pi$
$857$	25.7348	+	34.3777i	0.879084	+	1.17432i	−0.104617	+	0.994513i	$0.533362\pi$
$858$	28.5415	−	52.2699i	0.974392	−	1.78446i
$859$	−8.68467	+	13.5136i	−0.296317	+	0.461078i	−0.957207	−	0.289405i	$-0.906543\pi$
$859$	−8.68467	+	13.5136i	−0.296317	+	0.461078i	0.660890	+	0.750483i	$0.270179\pi$
$860$	−7.54691	+	12.4694i	−0.257347	+	0.425203i
$861$	10.7588	−	36.6411i	0.366658	−	1.24872i
$862$	1.57201	−	21.9796i	0.0535429	−	0.748627i
$863$	2.27102	−	31.7531i	0.0773066	−	1.08089i	−0.799697	−	0.600404i	$-0.795007\pi$
$863$	2.27102	−	31.7531i	0.0773066	−	1.08089i	0.877004	−	0.480484i	$-0.159539\pi$
$864$	3.38560	−	11.5303i	0.115180	−	0.392268i
$865$	−12.4687	+	20.6014i	−0.423948	+	0.700470i
$866$	−17.0133	+	26.4732i	−0.578136	+	0.899597i
$867$	23.0300	−	42.1763i	0.782139	−	1.43238i
$868$	−11.3263	−	15.1302i	−0.384441	−	0.513553i
$869$	−11.5483	+	5.27392i	−0.391749	+	0.178906i
$870$	−29.9717	+	31.6317i	−1.01614	+	1.07241i
$871$	−1.21316	−	1.88772i	−0.0411065	−	0.0639630i
$872$	7.44162	−	0.532235i	0.252005	−	0.0180238i
$873$	12.8465	−	12.8465i	0.434789	−	0.434789i
$874$	−5.77976	−	29.7048i	−0.195503	−	1.00478i
$875$	11.9273	−	32.9222i	0.403218	−	1.11297i
$876$	10.9603	−	12.6489i	0.370315	−	0.427367i
$877$	−5.59604	+	25.7246i	−0.188965	+	0.868658i	0.780831	+	0.624742i	$0.214796\pi$
$877$	−5.59604	+	25.7246i	−0.188965	+	0.868658i	−0.969796	+	0.243916i	$0.921568\pi$
$878$	−21.2003	+	28.3203i	−0.715477	+	0.955765i
$879$	−34.4528	−	75.4410i	−1.16206	−	2.54456i
$880$	−9.23589	+	5.37108i	−0.311342	+	0.181059i
$881$	2.54069	+	8.65279i	0.0855980	+	0.291520i	0.991156	−	0.132703i	$-0.0423656\pi$
$881$	2.54069	+	8.65279i	0.0855980	+	0.291520i	−0.905558	+	0.424223i	$0.860547\pi$
$882$	−18.7541	+	4.07971i	−0.631484	+	0.137371i
$883$	48.5666	−	18.1144i	1.63439	−	0.609598i	0.646250	−	0.763125i	$-0.276336\pi$
$883$	48.5666	−	18.1144i	1.63439	−	0.609598i	0.988144	+	0.153528i	$0.0490634\pi$
$884$	4.93596	+	1.44933i	0.166014	+	0.0487462i
$885$	15.0530	−	10.2572i	0.506001	−	0.344793i
$886$	−23.6001	−	27.2360i	−0.792860	−	0.915010i
$887$	−10.6306	+	5.80476i	−0.356941	+	0.194905i	−0.647707	−	0.761890i	$-0.724272\pi$
$887$	−10.6306	+	5.80476i	−0.356941	+	0.194905i	0.290766	+	0.956794i	$0.406090\pi$
$888$	2.54889	+	6.83384i	0.0855351	+	0.229329i
$889$	46.5191	+	29.8960i	1.56020	+	1.00268i
$890$	1.42973	+	8.34202i	0.0479245	+	0.279625i
$891$	81.2723	+	11.6852i	2.72272	+	0.391468i
$892$	22.6024	+	8.43025i	0.756783	+	0.282266i
$893$	−22.4070	−	16.7737i	−0.749821	−	0.561309i
$894$	−39.9760	+	25.6910i	−1.33700	+	0.859237i
$895$	35.3563	+	1.57298i	1.18183	+	0.0525790i
$896$		−	3.13195i		−	0.104631i
$897$	−57.7116	+	15.5735i	−1.92693	+	0.519983i
$898$	−0.113317	−	0.113317i	−0.00378144	−	0.00378144i
$899$	28.3438	+	24.5600i	0.945318	+	0.819123i
$900$	−11.3758	−	32.2122i	−0.379192	−	1.07374i
$901$	0.912151	+	6.34415i	0.0303882	+	0.211354i
$902$	−6.49290	+	17.4081i	−0.216190	+	0.579628i
$903$	51.2463	−	38.3625i	1.70537	−	1.27662i
$904$	14.5737	−	4.27922i	0.484713	−	0.142325i
$905$	−0.336433	−	3.41010i	−0.0111834	−	0.113355i
$906$	2.97711	−	6.51895i	0.0989077	−	0.216578i
$907$	−6.43009	−	11.7758i	−0.213508	−	0.391010i	0.748874	−	0.662713i	$-0.230595\pi$
$907$	−6.43009	−	11.7758i	−0.213508	−	0.391010i	−0.962381	+	0.271703i	$0.912413\pi$
$908$	22.5932	+	1.61589i	0.749780	+	0.0536253i
$909$	−59.7291	+	51.7555i	−1.98109	+	1.71662i
$910$	25.6243	+	10.8779i	0.849438	+	0.360599i
$911$	−5.81560	−	2.65590i	−0.192679	−	0.0879938i	0.316739	−	0.948513i	$-0.397412\pi$
$911$	−5.81560	−	2.65590i	−0.192679	−	0.0879938i	−0.509418	+	0.860519i	$0.670139\pi$
$912$	4.20585	+	19.3340i	0.139270	+	0.640212i
$913$	−31.1556	−	17.0122i	−1.03110	−	0.563022i
$914$	−1.94572	+	13.5328i	−0.0643587	+	0.447624i
$915$	−17.8548	+	5.76942i	−0.590263	+	0.190731i
$916$	3.84615	−	0.552993i	0.127080	−	0.0182714i
$917$	−8.38676	−	1.82443i	−0.276955	−	0.0602479i
$918$	1.10949	+	15.5127i	0.0366186	+	0.511995i
$919$	17.2296			0.568353			0.284177	−	0.958772i	$-0.408280\pi$
$919$	17.2296			0.568353			0.284177	+	0.958772i	$0.408280\pi$
$920$	10.3041	+	2.97067i	0.339717	+	0.0979400i
$921$	96.0286			3.16425
$922$	2.65620	+	37.1386i	0.0874775	+	1.22309i
$923$	20.6501	+	4.49216i	0.679708	+	0.147861i
$924$	46.4466	−	6.67801i	1.52798	−	0.219690i
$925$	9.67233	+	6.45823i	0.318024	+	0.212345i
$926$	4.25921	−	29.6235i	0.139966	−	0.973488i
$927$	−36.9584	−	20.1808i	−1.21387	−	0.662825i
$928$	1.32107	+	6.07285i	0.0433662	+	0.199351i
$929$	−49.7975	−	22.7417i	−1.63380	−	0.746132i	−0.634168	−	0.773195i	$-0.718657\pi$
$929$	−49.7975	−	22.7417i	−1.63380	−	0.746132i	−0.999634	+	0.0270626i	$0.991385\pi$
$930$	−39.2313	+	15.8490i	−1.28645	+	0.519708i
$931$	13.3960	−	11.6077i	0.439036	−	0.380426i
$932$	−0.726075	−	0.0519299i	−0.0237834	−	0.00170102i
$933$	−11.8326	−	21.6698i	−0.387382	−	0.709438i
$934$	−10.7292	+	23.4938i	−0.351071	+	0.768739i
$935$	8.77013	−	10.6900i	0.286814	−	0.349601i
$936$	26.0584	−	7.65143i	0.851744	−	0.250095i
$937$	25.6276	−	19.1846i	0.837218	−	0.626734i	−0.0922087	−	0.995740i	$-0.529393\pi$
$937$	25.6276	−	19.1846i	0.837218	−	0.626734i	0.929427	+	0.369006i	$0.120302\pi$
$938$	0.617866	−	1.65656i	0.0201740	−	0.0540887i
$939$	−7.69936	−	53.5502i	−0.251259	−	1.74755i
$940$	8.90806	−	4.36189i	0.290549	−	0.142269i
$941$	30.8788	+	26.7566i	1.00662	+	0.872241i	0.991819	−	0.127649i	$-0.0407431\pi$
$941$	30.8788	+	26.7566i	1.00662	+	0.872241i	0.0148009	+	0.999890i	$0.495289\pi$
$942$	−29.3024	−	29.3024i	−0.954725	−	0.954725i
$943$	17.1299	−	7.37140i	0.557826	−	0.240046i
$944$		−	2.59792i		−	0.0845552i
$945$	−3.74046	+	84.0752i	−0.121677	+	2.73497i
$946$	−26.2009	+	16.8383i	−0.851863	+	0.547459i
$947$	17.1440	+	12.8338i	0.557105	+	0.417044i	0.840382	−	0.541994i	$-0.182331\pi$
$947$	17.1440	+	12.8338i	0.557105	+	0.417044i	−0.283277	+	0.959038i	$0.591421\pi$
$948$	−7.80628	−	2.91159i	−0.253536	−	0.0945641i
$949$	21.0008	+	3.01946i	0.681714	+	0.0980157i
$950$	23.4784	+	21.0756i	0.761741	+	0.683781i
$951$	−44.9875	−	28.9117i	−1.45882	−	0.937526i
$952$	1.41649	+	3.79775i	0.0459087	+	0.123086i
$953$	−7.94949	+	4.34075i	−0.257509	+	0.140611i	−0.602819	−	0.797878i	$-0.705956\pi$
$953$	−7.94949	+	4.34075i	−0.257509	+	0.140611i	0.345309	+	0.938489i	$0.387774\pi$
$954$	22.1585	+	25.5723i	0.717410	+	0.827935i
$955$	3.26671	−	17.2404i	0.105708	−	0.557886i
$956$	12.1917	+	3.57981i	0.394308	+	0.115779i
$957$	−87.2433	+	32.5401i	−2.82017	+	1.05187i
$958$	22.3856	−	4.86969i	0.723246	−	0.157333i
$959$	−14.0365	−	47.8039i	−0.453262	−	1.54367i
$960$	−6.77831	−	1.79345i	−0.218769	−	0.0578834i
$961$	2.24996	+	4.92671i	0.0725792	+	0.158926i
$962$	−5.54090	+	7.40177i	−0.178646	+	0.238643i
$963$	4.76068	−	21.8845i	0.153411	−	0.705218i
$964$	−15.8674	+	18.3119i	−0.511054	+	0.589788i
$965$	−1.05803	−	0.123135i	−0.0340592	−	0.00396385i
$966$	−37.0735	−	29.0487i	−1.19282	−	0.934627i
$967$	−9.11189	+	9.11189i	−0.293019	+	0.293019i	−0.838272	−	0.545253i	$-0.816434\pi$
$967$	−9.11189	+	9.11189i	−0.293019	+	0.293019i	0.545253	+	0.838272i	$0.316434\pi$
$968$	−11.7999	+	0.843946i	−0.379263	+	0.0271254i
$969$	−13.8442	−	21.5419i	−0.444739	−	0.692027i
$970$	−4.31607	−	4.08957i	−0.138581	−	0.131308i
$971$	−29.0352	+	13.2599i	−0.931783	+	0.425531i	−0.822683	−	0.568500i	$-0.807524\pi$
$971$	−29.0352	+	13.2599i	−0.931783	+	0.425531i	−0.109099	+	0.994031i	$0.534797\pi$
$972$	10.6869	+	14.2761i	0.342783	+	0.457905i
$973$	−22.5582	+	41.3123i	−0.723183	+	1.32441i
$974$	16.0264	−	24.9376i	0.513519	−	0.799051i
$975$	38.2158	−	49.2283i	1.22388	−	1.57657i
$976$	−0.753953	+	2.56773i	−0.0241334	+	0.0821909i
$977$	−0.339558	+	4.74764i	−0.0108634	+	0.151890i	0.989125	+	0.147077i	$0.0469866\pi$
$977$	−0.339558	+	4.74764i	−0.0108634	+	0.151890i	−0.999988	+	0.00481314i	$0.998468\pi$
$978$	3.29322	−	46.0453i	0.105306	−	1.47237i
$979$	−5.09522	+	17.3527i	−0.162844	+	0.554596i
$980$	1.50003	+	6.09956i	0.0479167	+	0.194843i
$981$	−27.5586	+	42.8819i	−0.879877	+	1.36912i
$982$	16.7357	−	30.6491i	0.534056	−	0.978051i
$983$	34.3376	+	45.8696i	1.09520	+	1.46301i	0.872813	+	0.488055i	$0.162294\pi$
$983$	34.3376	+	45.8696i	1.09520	+	1.46301i	0.222386	+	0.974959i	$0.428616\pi$
$984$	−11.0912	+	5.06517i	−0.353574	+	0.161472i
$985$	47.3999	−	1.27725i	1.51029	−	0.0406964i
$986$	−4.34849	−	6.76638i	−0.138484	−	0.215485i
$987$	−43.4513	+	3.10770i	−1.38307	+	0.0989192i
$988$	−17.7358	+	17.7358i	−0.564250	+	0.564250i
$989$	30.3925	+	7.31614i	0.966427	+	0.232640i
$990$	8.43863	−	72.5085i	0.268197	−	2.30447i
$991$	24.7738	−	28.5904i	0.786965	−	0.908206i	−0.210627	−	0.977566i	$-0.567551\pi$
$991$	24.7738	−	28.5904i	0.786965	−	0.908206i	0.997592	+	0.0693609i	$0.0220960\pi$
$992$	−1.28274	+	5.89667i	−0.0407271	+	0.187220i
$993$	66.0624	−	88.2490i	2.09643	−	2.80050i
$994$	6.91714	+	15.1464i	0.219398	+	0.480415i
$995$	9.13567	+	15.7093i	0.289620	+	0.498020i
$996$	−6.56316	−	22.3521i	−0.207962	−	0.708252i
$997$	34.3105	−	7.46380i	1.08662	−	0.236381i	0.366635	−	0.930365i	$-0.380510\pi$
$997$	34.3105	−	7.46380i	1.08662	−	0.236381i	0.719990	+	0.693984i	$0.244146\pi$
$998$	−28.1458	+	10.4979i	−0.890941	+	0.332304i
$999$	−26.8200	−	7.87507i	−0.848548	−	0.249156i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.2.l.a.53.7	yes	240
5.2	odd	4	inner	230.2.l.a.7.1	✓	240
23.10	odd	22	inner	230.2.l.a.33.1	yes	240
115.102	even	44	inner	230.2.l.a.217.7	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.l.a.7.1	✓	240	5.2	odd	4	inner
230.2.l.a.33.1	yes	240	23.10	odd	22	inner
230.2.l.a.53.7	yes	240	1.1	even	1	trivial
230.2.l.a.217.7	yes	240	115.102	even	44	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	230.l (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0713392 + 0.997452i) q^{2} +(-3.06400 - 0.666533i) q^{3} +(-0.989821 + 0.142315i) q^{4} +(-1.99070 - 1.01838i) q^{5} +(0.446251 - 3.10375i) q^{6} +(2.74884 + 1.50098i) q^{7} +(-0.212565 - 0.977147i) q^{8} +(6.21495 + 2.83827i) q^{9} +(0.873771 - 2.05828i) q^{10} +(3.61103 - 3.12898i) q^{11} +(3.12767 + 0.223696i) q^{12} +(1.90500 + 3.48874i) q^{13} +(-1.30106 + 2.84892i) q^{14} +(5.42074 + 4.44719i) q^{15} +(0.959493 - 0.281733i) q^{16} +(-1.03605 + 0.775576i) q^{17} +(-2.38767 + 6.40160i) q^{18} +(-0.898012 - 6.24581i) q^{19} +(2.11537 + 0.724708i) q^{20} +(-7.42201 - 6.43121i) q^{21} +(3.37861 + 3.37861i) q^{22} +(0.105632 - 4.79467i) q^{23} +3.13566i q^{24} +(2.92580 + 4.05459i) q^{25} +(-3.34395 + 2.14903i) q^{26} +(-9.62015 - 7.20156i) q^{27} +(-2.93448 - 1.09450i) q^{28} +(6.15162 + 0.884470i) q^{29} +(-4.04915 + 5.72419i) q^{30} +(5.07661 + 3.26254i) q^{31} +(0.349464 + 0.936950i) q^{32} +(-13.1498 + 7.18032i) q^{33} +(-0.847511 - 0.978080i) q^{34} +(-3.94356 - 5.78738i) q^{35} +(-6.55562 - 1.92490i) q^{36} +(2.17939 - 0.812871i) q^{37} +(6.16584 - 1.34130i) q^{38} +(-3.51156 - 11.9593i) q^{39} +(-0.571953 + 2.16168i) q^{40} +(1.61534 + 3.53711i) q^{41} +(5.88534 - 7.86190i) q^{42} +(-1.38557 + 6.36935i) q^{43} +(-3.12898 + 3.61103i) q^{44} +(-9.48169 - 11.9794i) q^{45} +(4.78999 - 0.236685i) q^{46} +(3.13655 - 3.13655i) q^{47} +(-3.12767 + 0.223696i) q^{48} +(1.51870 + 2.36315i) q^{49} +(-3.83553 + 3.20760i) q^{50} +(3.69140 - 1.68581i) q^{51} +(-2.38211 - 3.18212i) q^{52} +(2.37346 - 4.34666i) q^{53} +(6.49691 - 10.1094i) q^{54} +(-10.3750 + 2.55146i) q^{55} +(0.882371 - 3.00508i) q^{56} +(-1.41153 + 19.7357i) q^{57} +(-0.443365 + 6.19905i) q^{58} +(0.731919 - 2.49269i) q^{59} +(-5.99846 - 3.63047i) q^{60} +(-1.44682 + 2.25130i) q^{61} +(-2.89207 + 5.29642i) q^{62} +(12.8237 + 17.1305i) q^{63} +(-0.909632 + 0.415415i) q^{64} +(-0.239419 - 8.88506i) q^{65} +(-8.10012 - 12.6040i) q^{66} +(-0.563079 + 0.0402722i) q^{67} +(0.915127 - 0.915127i) q^{68} +(-3.51946 + 14.6205i) q^{69} +(5.49130 - 4.34638i) q^{70} +(3.48160 - 4.01798i) q^{71} +(1.45233 - 6.67624i) q^{72} +(3.19870 - 4.27296i) q^{73} +(0.966276 + 2.11585i) q^{74} +(-6.26215 - 14.3734i) q^{75} +(1.77774 + 6.05444i) q^{76} +(14.6227 - 3.18097i) q^{77} +(11.6783 - 4.35577i) q^{78} +(-2.54941 - 0.748575i) q^{79} +(-2.19698 - 0.416283i) q^{80} +(11.2533 + 12.9870i) q^{81} +(-3.41286 + 1.86356i) q^{82} +(-2.59627 - 6.96086i) q^{83} +(8.26172 + 5.30949i) q^{84} +(2.85230 - 0.488851i) q^{85} +(-6.45196 - 0.927652i) q^{86} +(-18.2591 - 6.81028i) q^{87} +(-3.82505 - 2.86340i) q^{88} +(-3.18420 + 2.04636i) q^{89} +(11.2724 - 10.3121i) q^{90} +12.4494i q^{91} +(0.577796 + 4.76090i) q^{92} +(-13.3802 - 13.3802i) q^{93} +(3.35232 + 2.90480i) q^{94} +(-4.57294 + 13.3481i) q^{95} +(-0.446251 - 3.10375i) q^{96} +(0.929246 - 2.49141i) q^{97} +(-2.24879 + 1.68342i) q^{98} +(31.3233 - 9.19735i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 8 q^{3} - 8 q^{6} - 8 q^{12} + 16 q^{13} + 24 q^{16} - 72 q^{18} - 80 q^{23} - 8 q^{26} + 16 q^{27} - 44 q^{28} + 24 q^{31} - 44 q^{33} - 8 q^{35} - 32 q^{36} - 88 q^{37} - 24 q^{41} - 8 q^{46}+ \cdots + 24 q^{98}+O(q^{100}) \) 240 * q - 8 * q^3 - 8 * q^6 - 8 * q^12 + 16 * q^13 + 24 * q^16 - 72 * q^18 - 80 * q^23 - 8 * q^26 + 16 * q^27 - 44 * q^28 + 24 * q^31 - 44 * q^33 - 8 * q^35 - 32 * q^36 - 88 * q^37 - 24 * q^41 - 8 * q^46 - 80 * q^47 + 8 * q^48 + 8 * q^50 + 16 * q^52 - 44 * q^56 - 88 * q^57 - 176 * q^61 - 32 * q^62 - 176 * q^66 + 24 * q^70 - 336 * q^71 + 16 * q^72 - 88 * q^73 - 36 * q^75 - 24 * q^77 + 40 * q^78 - 136 * q^81 + 40 * q^82 - 100 * q^85 - 44 * q^86 + 40 * q^87 + 8 * q^92 + 56 * q^93 + 52 * q^95 + 8 * q^96 + 132 * q^97 + 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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