LMFDB - Embedded newform 230.2.l.a.33.1

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			33.1
Character	$\chi$	$=$	230.33
Dual form			230.2.l.a.7.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.997452 - 0.0713392i) q^{2} +(-0.666533 - 3.06400i) q^{3} +(0.989821 + 0.142315i) q^{4} +(-0.533993 - 2.17137i) q^{5} +(0.446251 + 3.10375i) q^{6} +(-1.50098 - 2.74884i) q^{7} +(-0.977147 - 0.212565i) q^{8} +(-6.21495 + 2.83827i) q^{9} +(0.377729 + 2.20393i) q^{10} +(3.61103 + 3.12898i) q^{11} +(-0.223696 - 3.12767i) q^{12} +(3.48874 + 1.90500i) q^{13} +(1.30106 + 2.84892i) q^{14} +(-6.29716 + 3.08345i) q^{15} +(0.959493 + 0.281733i) q^{16} +(-0.775576 + 1.03605i) q^{17} +(6.40160 - 2.38767i) q^{18} +(0.898012 - 6.24581i) q^{19} +(-0.219540 - 2.22526i) q^{20} +(-7.42201 + 6.43121i) q^{21} +(-3.37861 - 3.37861i) q^{22} +(-4.79467 + 0.105632i) q^{23} +3.13566i q^{24} +(-4.42970 + 2.31899i) q^{25} +(-3.34395 - 2.14903i) q^{26} +(7.20156 + 9.62015i) q^{27} +(-1.09450 - 2.93448i) q^{28} +(-6.15162 + 0.884470i) q^{29} +(6.50109 - 2.62636i) q^{30} +(5.07661 - 3.26254i) q^{31} +(-0.936950 - 0.349464i) q^{32} +(7.18032 - 13.1498i) q^{33} +(0.847511 - 0.978080i) q^{34} +(-5.16724 + 4.72705i) q^{35} +(-6.55562 + 1.92490i) q^{36} +(0.812871 - 2.17939i) q^{37} +(-1.34130 + 6.16584i) q^{38} +(3.51156 - 11.9593i) q^{39} +(0.0602316 + 2.23526i) q^{40} +(1.61534 - 3.53711i) q^{41} +(7.86190 - 5.88534i) q^{42} +(6.36935 - 1.38557i) 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} +(0.223696 - 3.12767i) q^{48} +(-1.51870 + 2.36315i) q^{49} +(4.58385 - 1.99707i) q^{50} +(3.69140 + 1.68581i) q^{51} +(3.18212 + 2.38211i) q^{52} +(-4.34666 + 2.37346i) q^{53} +(-6.49691 - 10.1094i) q^{54} +(4.86590 - 9.51174i) q^{55} +(0.882371 + 3.00508i) q^{56} +(-19.7357 + 1.41153i) q^{57} +(6.19905 - 0.443365i) q^{58} +(-0.731919 - 2.49269i) q^{59} +(-6.67189 + 2.15588i) q^{60} +(-1.44682 - 2.25130i) q^{61} +(-5.29642 + 2.89207i) q^{62} +(17.1305 + 12.8237i) q^{63} +(0.909632 + 0.415415i) q^{64} +(2.27349 - 8.59261i) q^{65} +(-8.10012 + 12.6040i) q^{66} +(-0.0402722 + 0.563079i) 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} +(6.67624 - 1.45233i) q^{72} +(-4.27296 + 3.19870i) q^{73} +(-0.966276 + 2.11585i) q^{74} +(10.0579 + 12.0269i) q^{75} +(1.77774 - 6.05444i) q^{76} +(3.18097 - 14.6227i) q^{77} +(-4.35577 + 11.6783i) q^{78} +(2.54941 - 0.748575i) q^{79} +(0.0993832 - 2.23386i) q^{80} +(11.2533 - 12.9870i) q^{81} +(-1.86356 + 3.41286i) q^{82} +(-6.96086 - 2.59627i) q^{83} +(-8.26172 + 5.30949i) q^{84} +(2.66380 + 1.13082i) q^{85} +(-6.45196 + 0.927652i) q^{86} +(6.81028 + 18.2591i) q^{87} +(-2.86340 - 3.82505i) q^{88} +(3.18420 + 2.04636i) q^{89} +(-8.60293 - 12.6252i) q^{90} -12.4494i q^{91} +(-4.76090 - 0.577796i) q^{92} +(-13.3802 - 13.3802i) q^{93} +(-3.35232 + 2.90480i) q^{94} +(-14.0415 + 1.38530i) q^{95} +(-0.446251 + 3.10375i) q^{96} +(2.49141 - 0.929246i) q^{97} +(1.68342 - 2.24879i) 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 $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.997452	−	0.0713392i	−0.705305	−	0.0504444i
$2$	−0.997452	−	0.0713392i	−0.705305	−	0.0504444i
$3$	−0.666533	−	3.06400i	−0.384823	−	1.76900i	−0.607710	−	0.794159i	$-0.707912\pi$
$3$	−0.666533	−	3.06400i	−0.384823	−	1.76900i	0.222887	−	0.974844i	$-0.428452\pi$
$4$	0.989821	+	0.142315i	0.494911	+	0.0711574i
$5$	−0.533993	−	2.17137i	−0.238809	−	0.971067i
$5$	−0.533993	−	2.17137i	−0.238809	−	0.971067i
$6$	0.446251	+	3.10375i	0.182181	+	1.26710i
$7$	−1.50098	−	2.74884i	−0.567318	−	1.03896i	−0.991090	−	0.133196i	$-0.957476\pi$
$7$	−1.50098	−	2.74884i	−0.567318	−	1.03896i	0.423772	−	0.905769i	$-0.360706\pi$
$8$	−0.977147	−	0.212565i	−0.345474	−	0.0751532i
$9$	−6.21495	+	2.83827i	−2.07165	+	0.946091i
$10$	0.377729	+	2.20393i	0.119448	+	0.696945i
$11$	3.61103	+	3.12898i	1.08877	+	0.943422i	0.998621	−	0.0525065i	$-0.0167210\pi$
$11$	3.61103	+	3.12898i	1.08877	+	0.943422i	0.0901464	+	0.995929i	$0.471266\pi$
$12$	−0.223696	−	3.12767i	−0.0645754	−	0.902882i
$13$	3.48874	+	1.90500i	0.967603	+	0.528351i	0.883665	−	0.468120i	$-0.155068\pi$
$13$	3.48874	+	1.90500i	0.967603	+	0.528351i	0.0839380	+	0.996471i	$0.473250\pi$
$14$	1.30106	+	2.84892i	0.347722	+	0.761405i
$15$	−6.29716	+	3.08345i	−1.62592	+	0.796143i
$16$	0.959493	+	0.281733i	0.239873	+	0.0704331i
$17$	−0.775576	+	1.03605i	−0.188105	+	0.251279i	−0.884673	−	0.466212i	$-0.845618\pi$
$17$	−0.775576	+	1.03605i	−0.188105	+	0.251279i	0.696568	+	0.717491i	$0.254709\pi$
$18$	6.40160	−	2.38767i	1.50887	−	0.562780i
$19$	0.898012	−	6.24581i	0.206018	−	1.43289i	−0.579966	−	0.814641i	$-0.696934\pi$
$19$	0.898012	−	6.24581i	0.206018	−	1.43289i	0.785984	−	0.618247i	$-0.212157\pi$
$20$	−0.219540	−	2.22526i	−0.0490905	−	0.497584i
$21$	−7.42201	+	6.43121i	−1.61962	+	1.40340i
$22$	−3.37861	−	3.37861i	−0.720323	−	0.720323i
$23$	−4.79467	+	0.105632i	−0.999757	+	0.0220258i
$23$	−4.79467	+	0.105632i	−0.999757	+	0.0220258i
$24$			3.13566i			0.640065i
$25$	−4.42970	+	2.31899i	−0.885941	+	0.463799i
$26$	−3.34395	−	2.14903i	−0.655803	−	0.421459i
$27$	7.20156	+	9.62015i	1.38594	+	1.85140i
$28$	−1.09450	−	2.93448i	−0.206842	−	0.554564i
$29$	−6.15162	+	0.884470i	−1.14233	+	0.164242i	−0.687395	−	0.726284i	$-0.741246\pi$
$29$	−6.15162	+	0.884470i	−1.14233	+	0.164242i	−0.454933	+	0.890526i	$0.650337\pi$
$30$	6.50109	−	2.62636i	1.18693	−	0.479505i
$31$	5.07661	−	3.26254i	0.911786	−	0.585970i	0.00152290	−	0.999999i	$-0.499515\pi$
$31$	5.07661	−	3.26254i	0.911786	−	0.585970i	0.910264	+	0.414029i	$0.135879\pi$
$32$	−0.936950	−	0.349464i	−0.165631	−	0.0617771i
$33$	7.18032	−	13.1498i	1.24993	−	2.28908i
$34$	0.847511	−	0.978080i	0.145347	−	0.167739i
$35$	−5.16724	+	4.72705i	−0.873423	+	0.799017i
$36$	−6.55562	+	1.92490i	−1.09260	+	0.320817i
$37$	0.812871	−	2.17939i	0.133635	−	0.358290i	−0.852846	−	0.522162i	$-0.825126\pi$
$37$	0.812871	−	2.17939i	0.133635	−	0.358290i	0.986482	+	0.163872i	$0.0523984\pi$
$38$	−1.34130	+	6.16584i	−0.217587	+	1.00023i
$39$	3.51156	−	11.9593i	0.562299	−	1.91501i
$40$	0.0602316	+	2.23526i	0.00952346	+	0.353425i
$41$	1.61534	−	3.53711i	0.252274	−	0.552404i	−0.740548	−	0.672004i	$-0.765434\pi$
$41$	1.61534	−	3.53711i	0.252274	−	0.552404i	0.992822	+	0.119600i	$0.0381612\pi$
$42$	7.86190	−	5.88534i	1.21312	−	0.908128i
$43$	6.36935	−	1.38557i	0.971316	−	0.211297i	0.301207	−	0.953559i	$-0.402611\pi$
$43$	6.36935	−	1.38557i	0.971316	−	0.211297i	0.670110	+	0.742262i	$0.266247\pi$
$44$	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	$0.145137\pi$
$48$	0.223696	−	3.12767i	0.0322877	−	0.451441i
$49$	−1.51870	+	2.36315i	−0.216958	+	0.337593i
$50$	4.58385	−	1.99707i	0.648254	−	0.282429i
$51$	3.69140	+	1.68581i	0.516900	+	0.236060i
$52$	3.18212	+	2.38211i	0.441281	+	0.330339i
$53$	−4.34666	+	2.37346i	−0.597060	+	0.326019i	−0.749204	−	0.662339i	$-0.769564\pi$
$53$	−4.34666	+	2.37346i	−0.597060	+	0.326019i	0.152144	+	0.988358i	$0.451382\pi$
$54$	−6.49691	−	10.1094i	−0.884118	−	1.37571i
$55$	4.86590	−	9.51174i	0.656118	−	1.28256i
$56$	0.882371	+	3.00508i	0.117912	+	0.401571i
$57$	−19.7357	+	1.41153i	−2.61406	+	0.186962i
$58$	6.19905	−	0.443365i	0.813975	−	0.0582166i
$59$	−0.731919	−	2.49269i	−0.0952878	−	0.324520i	0.898030	−	0.439935i	$-0.144999\pi$
$59$	−0.731919	−	2.49269i	−0.0952878	−	0.324520i	−0.993317	+	0.115415i	$0.963180\pi$
$60$	−6.67189	+	2.15588i	−0.861337	+	0.278323i
$61$	−1.44682	−	2.25130i	−0.185247	−	0.288250i	0.736192	−	0.676772i	$-0.236622\pi$
$61$	−1.44682	−	2.25130i	−0.185247	−	0.288250i	−0.921439	+	0.388523i	$0.872986\pi$
$62$	−5.29642	+	2.89207i	−0.672647	+	0.367293i
$63$	17.1305	+	12.8237i	2.15824	+	1.61564i
$64$	0.909632	+	0.415415i	0.113704	+	0.0519269i
$65$	2.27349	−	8.59261i	0.281992	−	1.06578i
$66$	−8.10012	+	12.6040i	−0.997056	+	1.55145i
$67$	−0.0402722	+	0.563079i	−0.00492004	+	0.0687911i	−0.999319	−	0.0369012i	$-0.988251\pi$
$67$	−0.0402722	+	0.563079i	−0.00492004	+	0.0687911i	0.994399	+	0.105692i	$0.0337059\pi$
$68$	−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	0.923750	−	0.382995i	$-0.125107\pi$
$71$	3.48160	+	4.01798i	0.413190	+	0.476847i	−0.510560	+	0.859842i	$0.670562\pi$
$72$	6.67624	−	1.45233i	0.786803	−	0.171158i
$73$	−4.27296	+	3.19870i	−0.500113	+	0.374380i	−0.819349	−	0.573296i	$-0.805665\pi$
$73$	−4.27296	+	3.19870i	−0.500113	+	0.374380i	0.319236	+	0.947675i	$0.396574\pi$
$74$	−0.966276	+	2.11585i	−0.112327	+	0.245962i
$75$	10.0579	+	12.0269i	1.16139	+	1.38875i
$76$	1.77774	−	6.05444i	0.203921	−	0.694492i
$77$	3.18097	−	14.6227i	0.362505	−	1.66641i
$78$	−4.35577	+	11.6783i	−0.493194	+	1.32230i
$79$	2.54941	−	0.748575i	0.286831	−	0.0842213i	−0.135152	−	0.990825i	$-0.543152\pi$
$79$	2.54941	−	0.748575i	0.286831	−	0.0842213i	0.421983	+	0.906604i	$0.361334\pi$
$80$	0.0993832	−	2.23386i	0.0111114	−	0.249753i
$81$	11.2533	−	12.9870i	1.25037	−	1.44300i
$82$	−1.86356	+	3.41286i	−0.205796	+	0.376887i
$83$	−6.96086	−	2.59627i	−0.764053	−	0.284977i	−0.0629307	−	0.998018i	$-0.520045\pi$
$83$	−6.96086	−	2.59627i	−0.764053	−	0.284977i	−0.701123	+	0.713041i	$0.747317\pi$
$84$	−8.26172	+	5.30949i	−0.901428	+	0.579312i
$85$	2.66380	+	1.13082i	0.288929	+	0.122655i
$86$	−6.45196	+	0.927652i	−0.695733	+	0.100031i
$87$	6.81028	+	18.2591i	0.730139	+	1.95758i
$88$	−2.86340	−	3.82505i	−0.305239	−	0.407752i
$89$	3.18420	+	2.04636i	0.337524	+	0.216914i	0.698413	−	0.715695i	$-0.253890\pi$
$89$	3.18420	+	2.04636i	0.337524	+	0.216914i	−0.360888	+	0.932609i	$0.617526\pi$
$90$	−8.60293	−	12.6252i	−0.906829	−	1.33082i
$91$		−	12.4494i		−	1.30505i
$92$	−4.76090	−	0.577796i	−0.496358	−	0.0602393i
$93$	−13.3802	−	13.3802i	−1.38746	−	1.38746i
$94$	−3.35232	+	2.90480i	−0.345765	+	0.299607i
$95$	−14.0415	+	1.38530i	−1.44063	+	0.142129i
$96$	−0.446251	+	3.10375i	−0.0455453	+	0.316775i
$97$	2.49141	−	0.929246i	0.252964	−	0.0943507i	−0.219783	−	0.975549i	$-0.570535\pi$
$97$	2.49141	−	0.929246i	0.252964	−	0.0943507i	0.472747	+	0.881198i	$0.343262\pi$
$98$	1.68342	−	2.24879i	0.170051	−	0.227162i
$99$	−31.3233	−	9.19735i	−3.14811	−	0.924368i
$100$	−4.71464	+	1.66498i	−0.471464	+	0.166498i
$101$	−4.80527	−	10.5221i	−0.478142	−	1.04699i	−0.982970	−	0.183766i	$-0.941171\pi$
$101$	−4.80527	−	10.5221i	−0.478142	−	1.04699i	0.504828	−	0.863220i	$-0.331556\pi$
$102$	−3.56173	−	1.94485i	−0.352664	−	0.192569i
$103$	−0.439677	−	6.14749i	−0.0433227	−	0.605730i	−0.972021	−	0.234894i	$-0.924526\pi$
$103$	−0.439677	−	6.14749i	−0.0433227	−	0.605730i	0.928698	−	0.370836i	$-0.120929\pi$
$104$	−3.00408	−	2.60305i	−0.294574	−	0.255250i
$105$	17.9278	+	12.6817i	1.74958	+	1.23761i
$106$	4.50491	−	2.05732i	0.437555	−	0.199825i
$107$	3.20305	+	0.696782i	0.309651	+	0.0673604i	0.364706	−	0.931123i	$-0.381170\pi$
$107$	3.20305	+	0.696782i	0.309651	+	0.0673604i	−0.0550546	+	0.998483i	$0.517533\pi$
$108$	5.75916	+	10.5471i	0.554176	+	1.01490i
$109$	1.06176	+	7.38469i	0.101698	+	0.707325i	0.975332	+	0.220742i	$0.0708478\pi$
$109$	1.06176	+	7.38469i	0.101698	+	0.707325i	−0.873634	+	0.486583i	$0.838243\pi$
$110$	−5.53206	+	9.14038i	−0.527462	+	0.871501i
$111$	−7.21947	−	1.03800i	−0.685242	−	0.0985229i
$112$	−0.665743	−	3.06037i	−0.0629068	−	0.289178i
$113$	15.1502	+	1.08357i	1.42521	+	0.101933i	0.762524	−	0.646960i	$-0.223960\pi$
$113$	15.1502	+	1.08357i	1.42521	+	0.101933i	0.662690	+	0.748894i	$0.269415\pi$
$114$	19.7862			1.85314
$115$	2.78969	+	10.3546i	0.260140	+	0.965571i
$116$	−6.21488			−0.577037
$117$	−27.0893	−	1.93746i	−2.50440	−	0.179119i
$118$	0.552228	+	2.53855i	0.0508367	+	0.233693i
$119$	4.01206	+	0.576847i	0.367785	+	0.0528795i
$120$	6.80869	−	1.67442i	0.621545	−	0.152853i
$121$	1.68359	+	11.7096i	0.153054	+	1.06451i
$122$	1.28253	+	2.34878i	0.116115	+	0.212649i
$123$	−11.9144	−	2.59182i	−1.07428	−	0.233696i
$124$	5.48925	−	2.50686i	0.492949	−	0.225122i
$125$	7.40083	+	8.38020i	0.661950	+	0.749548i
$126$	−16.1720	−	14.0131i	−1.44072	−	1.24839i
$127$	−1.25956	−	17.6109i	−0.111768	−	1.56272i	−0.675874	−	0.737017i	$-0.736234\pi$
$127$	−1.25956	−	17.6109i	−0.111768	−	1.56272i	0.564107	−	0.825702i	$-0.309221\pi$
$128$	−0.877679	−	0.479249i	−0.0775766	−	0.0423600i
$129$	−8.49076	−	18.5922i	−0.747570	−	1.63695i
$130$	−2.88069	+	8.40853i	−0.252653	+	0.737477i
$131$	−2.62943	−	0.772071i	−0.229735	−	0.0674561i	0.164839	−	0.986320i	$-0.447290\pi$
$131$	−2.62943	−	0.772071i	−0.229735	−	0.0674561i	−0.394574	+	0.918864i	$0.629108\pi$
$132$	8.97865	−	11.9941i	0.781491	−	1.04395i
$133$	−18.5167	+	6.90636i	−1.60560	+	0.598857i
$134$	0.0803392	−	0.558772i	0.00694025	−	0.0482705i
$135$	17.0433	−	20.7743i	1.46686	−	1.78797i
$136$	0.978080	−	0.847511i	0.0838697	−	0.0726735i
$137$	11.2484	+	11.2484i	0.961018	+	0.961018i	0.999268	−	0.0382498i	$-0.0121782\pi$
$137$	11.2484	+	11.2484i	0.961018	+	0.961018i	−0.0382498	+	0.999268i	$0.512178\pi$
$138$	−2.46748	−	14.8343i	−0.210046	−	1.26278i
$139$			15.0290i			1.27474i	0.770558	+	0.637370i	$0.219978\pi$
$139$			15.0290i			1.27474i	−0.770558	+	0.637370i	$0.780022\pi$
$140$	−5.78738	+	3.94356i	−0.489123	+	0.333292i
$141$	−11.7010	−	7.51979i	−0.985404	−	0.633281i
$142$	−3.18609	−	4.25612i	−0.267371	−	0.357166i
$143$	6.63727	+	17.7952i	0.555036	+	1.48811i
$144$	−6.76284	+	0.972349i	−0.563570	+	0.0810291i
$145$	5.20544	+	12.8852i	0.432288	+	1.07005i
$146$	4.49027	−	2.88572i	0.371617	−	0.238824i
$147$	8.25297	+	3.07820i	0.680693	+	0.253885i
$148$	1.11476	−	2.04152i	0.0916325	−	0.167812i
$149$	9.92413	−	11.4531i	0.813016	−	0.938271i	−0.186003	−	0.982549i	$-0.559553\pi$
$149$	9.92413	−	11.4531i	0.813016	−	0.938271i	0.999019	+	0.0442783i	$0.0140988\pi$
$150$	−9.17433	−	12.7138i	−0.749081	−	1.03808i
$151$	2.19293	−	0.643902i	0.178458	−	0.0524000i	−0.191283	−	0.981535i	$-0.561265\pi$
$151$	2.19293	−	0.643902i	0.178458	−	0.0524000i	0.369741	+	0.929135i	$0.379447\pi$
$152$	−2.20513	+	5.91219i	−0.178860	+	0.479542i
$153$	1.87958	−	8.64029i	0.151955	−	0.698526i
$154$	−4.21604	+	14.3585i	−0.339738	+	1.15704i
$155$	−9.79506	−	9.28103i	−0.786758	−	0.745471i
$156$	5.17779	−	11.3378i	0.414555	−	0.907749i
$157$	10.5797	−	7.91986i	0.844352	−	0.632074i	−0.0869946	−	0.996209i	$-0.527726\pi$
$157$	10.5797	−	7.91986i	0.844352	−	0.632074i	0.931346	+	0.364135i	$0.118635\pi$
$158$	−2.59632	+	0.564795i	−0.206552	+	0.0449327i
$159$	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
$163$	−1.05025	+	14.6844i	−0.0822617	+	1.15017i	0.773847	+	0.633373i	$0.218330\pi$
$163$	−1.05025	+	14.6844i	−0.0822617	+	1.15017i	−0.856108	+	0.516796i	$0.827124\pi$
$164$	2.10228	−	3.27122i	0.164161	−	0.255439i
$165$	−32.3873	−	8.56925i	−2.52135	−	0.667115i
$166$	6.75791	+	3.08623i	0.524515	+	0.239538i
$167$	−10.4816	−	7.84639i	−0.811087	−	0.607172i	0.111147	−	0.993804i	$-0.464547\pi$
$167$	−10.4816	−	7.84639i	−0.811087	−	0.607172i	−0.922234	+	0.386632i	$0.873638\pi$
$168$	8.61944	−	4.70657i	0.665005	−	0.363120i
$169$	1.51398	+	2.35579i	0.116460	+	0.181215i
$170$	−2.57634	−	1.31797i	−0.197596	−	0.101084i
$171$	12.1462	+	41.3662i	0.928845	+	3.16336i
$172$	6.50170	−	0.465011i	0.495750	−	0.0354568i
$173$	−10.7418	+	0.768272i	−0.816688	+	0.0584107i	−0.473431	−	0.880831i	$-0.656985\pi$
$173$	−10.7418	+	0.768272i	−0.816688	+	0.0584107i	−0.343257	+	0.939242i	$0.611530\pi$
$174$	−5.49034	−	18.6984i	−0.416222	−	1.41752i
$175$	13.0235	+	8.69579i	0.984481	+	0.657340i
$176$	2.58322	+	4.01958i	0.194718	+	0.302987i
$177$	−7.14976	+	3.90406i	−0.537409	+	0.293447i
$178$	−3.03010	−	2.26830i	−0.227115	−	0.170016i
$179$	14.3971	+	6.57496i	1.07609	+	0.491435i	0.872998	−	0.487724i	$-0.162173\pi$
$179$	14.3971	+	6.57496i	1.07609	+	0.491435i	0.203095	+	0.979159i	$0.434900\pi$
$180$	7.68034	+	13.2068i	0.572459	+	0.984377i
$181$	0.828503	−	1.28918i	0.0615821	−	0.0958237i	−0.809097	−	0.587675i	$-0.800043\pi$
$181$	0.828503	−	1.28918i	0.0615821	−	0.0958237i	0.870679	+	0.491851i	$0.163680\pi$
$182$	−0.888128	+	12.4177i	−0.0658324	+	0.920457i
$183$	−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
$187$	−6.04240	+	1.31444i	−0.441864	+	0.0961217i
$188$	3.55101	−	2.65825i	0.258984	−	0.193873i
$189$	15.6349	−	34.2356i	1.13727	−	2.49028i
$190$	14.1046	−	0.380064i	1.02325	−	0.0275728i
$191$	2.21085	−	7.52946i	0.159971	−	0.544812i	−0.840026	−	0.542546i	$-0.817460\pi$
$191$	2.21085	−	7.52946i	0.159971	−	0.544812i	0.999997	−	0.00226633i	$-0.000721397\pi$
$192$	0.666533	−	3.06400i	0.0481029	−	0.221125i
$193$	−0.166470	+	0.446324i	−0.0119828	+	0.0321271i	−0.942803	−	0.333349i	$-0.891821\pi$
$193$	−0.166470	+	0.446324i	−0.0119828	+	0.0321271i	0.930821	+	0.365476i	$0.119094\pi$
$194$	−2.55135	+	0.749144i	−0.183176	+	0.0537854i
$195$	−27.8431	−	1.23873i	−1.99389	−	0.0887071i
$196$	−1.83956	+	2.12296i	−0.131397	+	0.151640i
$197$	−10.1627	+	18.6117i	−0.724065	+	1.32603i	0.213062	+	0.977039i	$0.431656\pi$
$197$	−10.1627	+	18.6117i	−0.724065	+	1.32603i	−0.937127	+	0.348988i	$0.886525\pi$
$198$	30.5874	+	11.4085i	2.17375	+	0.810766i
$199$	6.83690	−	4.39381i	0.484655	−	0.311469i	−0.275398	−	0.961330i	$-0.588809\pi$
$199$	6.83690	−	4.39381i	0.484655	−	0.311469i	0.760053	+	0.649862i	$0.225173\pi$
$200$	4.82141	−	1.32440i	0.340925	−	0.0936490i
$201$	1.75212	−	0.251917i	0.123585	−	0.0177688i
$202$	4.04239	+	10.8381i	0.284422	+	0.762564i
$203$	11.6647	+	15.5823i	0.818705	+	1.09366i
$204$	3.41391	+	2.19399i	0.239022	+	0.153610i
$205$	−8.54296	−	1.61872i	−0.596666	−	0.113056i
$206$			6.16319i			0.429410i
$207$	29.4988	−	14.2651i	2.05031	−	0.991492i
$208$	2.81072	+	2.81072i	0.194889	+	0.194889i
$209$	22.7858	−	19.7440i	1.57612	−	1.36572i
$210$	−16.9775	−	13.9284i	−1.17156	−	0.961148i
$211$	1.13926	−	7.92374i	0.0784300	−	0.545493i	−0.912287	−	0.409552i	$-0.865685\pi$
$211$	1.13926	−	7.92374i	0.0784300	−	0.545493i	0.990717	−	0.135941i	$-0.0434058\pi$
$212$	−4.64020	+	1.73070i	−0.318690	+	0.118865i
$213$	9.99051	−	13.3458i	0.684538	−	0.914436i
$214$	−3.14519	−	0.923510i	−0.215000	−	0.0631298i
$215$	−6.40977	−	13.0903i	−0.437143	−	0.892753i
$216$	−4.99207	−	10.9311i	−0.339667	−	0.743767i
$217$	−16.5881	−	9.05779i	−1.12607	−	0.614883i
$218$	−0.532235	−	7.44162i	−0.0360475	−	0.504010i
$219$	12.6489	+	10.9603i	0.854733	+	0.740631i
$220$	6.17004	−	8.72244i	0.415984	−	0.588066i
$221$	−4.67946	+	2.13704i	−0.314774	+	0.143753i
$222$	7.12702	+	1.55039i	0.478335	+	0.104055i
$223$	−11.5611	−	21.1726i	−0.774188	−	1.41782i	−0.904557	−	0.426354i	$-0.859798\pi$
$223$	−11.5611	−	21.1726i	−0.774188	−	1.41782i	0.130369	−	0.991466i	$-0.458384\pi$
$224$	0.445722	+	3.10007i	0.0297811	+	0.207132i
$225$	20.9485	−	26.9852i	1.39656	−	1.79901i
$226$	−15.0343	−	2.16161i	−1.00007	−	0.143788i
$227$	4.81479	+	22.1332i	0.319569	+	1.46903i	0.804223	+	0.594328i	$0.202582\pi$
$227$	4.81479	+	22.1332i	0.319569	+	1.46903i	−0.484654	+	0.874706i	$0.661054\pi$
$228$	−19.7357	−	1.41153i	−1.30703	−	0.0934808i
$229$	3.88570			0.256775			0.128387	−	0.991724i	$-0.459020\pi$
$229$	3.88570			0.256775			0.128387	+	0.991724i	$0.459020\pi$
$230$	−2.04389	−	10.5272i	−0.134770	−	0.694145i
$231$	−46.9242			−3.08739
$232$	6.19905	+	0.443365i	0.406987	+	0.0291083i
$233$	0.154733	+	0.711294i	0.0101369	+	0.0465984i	0.981937	−	0.189206i	$-0.0605913\pi$
$233$	0.154733	+	0.711294i	0.0101369	+	0.0465984i	−0.971801	+	0.235804i	$0.924228\pi$
$234$	26.8820	+	3.86505i	1.75733	+	0.252666i
$235$	−8.48552	−	5.13572i	−0.553534	−	0.335018i
$236$	−0.369723	−	2.57148i	−0.0240669	−	0.167389i
$237$	−3.99290	−	7.31246i	−0.259367	−	0.474995i
$238$	−3.96069	−	0.861595i	−0.256733	−	0.0558489i
$239$	11.5582	−	5.27843i	0.747635	−	0.341433i	−0.00489810	−	0.999988i	$-0.501559\pi$
$239$	11.5582	−	5.27843i	0.747635	−	0.341433i	0.752533	+	0.658555i	$0.228832\pi$
$240$	−6.91079	+	1.18443i	−0.446090	+	0.0764546i
$241$	18.3119	+	15.8674i	1.17958	+	1.02211i	0.999259	+	0.0384993i	$0.0122577\pi$
$241$	18.3119	+	15.8674i	1.17958	+	1.02211i	0.180317	+	0.983609i	$0.442288\pi$
$242$	−0.843946	−	11.7999i	−0.0542509	−	0.758527i
$243$	−15.6517	−	8.54646i	−1.00405	−	0.548255i
$244$	−1.11170	−	2.43429i	−0.0711696	−	0.155840i
$245$	5.94225	+	2.03576i	0.379637	+	0.130060i
$246$	11.6991	+	3.43518i	0.745910	+	0.219019i
$247$	15.0312	−	20.0793i	0.956412	−	1.27762i
$248$	−5.65410	+	2.10887i	−0.359036	+	0.133913i
$249$	−3.31532	+	23.0586i	−0.210100	+	1.46128i
$250$	−6.78413	−	8.88682i	−0.429066	−	0.562052i
$251$	11.6834	−	10.1237i	0.737448	−	0.639002i	−0.202907	−	0.979198i	$-0.565039\pi$
$251$	11.6834	−	10.1237i	0.737448	−	0.639002i	0.940355	+	0.340196i	$0.110493\pi$
$252$	15.1311	+	15.1311i	0.953172	+	0.953172i
$253$	−17.6442	−	14.6210i	−1.10928	−	0.919212i
$254$			17.6559i			1.10783i
$255$	1.68933	−	8.91562i	0.105790	−	0.558317i
$256$	0.841254	+	0.540641i	0.0525783	+	0.0337901i
$257$	0.632061	+	0.844335i	0.0394269	+	0.0526682i	0.819821	−	0.572619i	$-0.194073\pi$
$257$	0.632061	+	0.844335i	0.0394269	+	0.0526682i	−0.780395	+	0.625287i	$0.784982\pi$
$258$	7.14278	+	19.1505i	0.444690	+	1.19226i
$259$	−7.21091	+	1.03677i	−0.448064	+	0.0644219i
$260$	3.47321	−	8.18160i	0.215399	−	0.507401i
$261$	35.7217	−	22.9569i	2.21112	−	1.42100i
$262$	2.56765	+	0.957685i	0.158630	+	0.0591660i
$263$	11.4511	−	20.9711i	0.706105	−	1.29313i	−0.240472	−	0.970656i	$-0.577302\pi$
$263$	11.4511	−	20.9711i	0.706105	−	1.29313i	0.946577	−	0.322479i	$-0.104516\pi$
$264$	−9.81142	+	11.3230i	−0.603851	+	0.696881i
$265$	7.47474	+	8.17081i	0.459170	+	0.501929i
$266$	18.9622	−	5.56780i	1.16265	−	0.341384i
$267$	4.14768	−	11.1204i	0.253834	−	0.680555i
$268$	−0.119997	+	0.551617i	−0.00732998	+	0.0336954i
$269$	−6.90680	+	23.5224i	−0.421115	+	1.43419i	0.426940	+	0.904280i	$0.359591\pi$
$269$	−6.90680	+	23.5224i	−0.421115	+	1.43419i	−0.848056	+	0.529907i	$0.822227\pi$
$270$	−18.4819	+	19.5056i	−1.12478	+	1.18707i
$271$	−8.22947	+	18.0200i	−0.499905	+	1.09464i	0.476596	+	0.879123i	$0.341871\pi$
$271$	−8.22947	+	18.0200i	−0.499905	+	1.09464i	−0.976500	+	0.215516i	$0.930857\pi$
$272$	−1.03605	+	0.775576i	−0.0628197	+	0.0470262i
$273$	−38.1449	+	8.29792i	−2.30863	+	0.502213i
$274$	−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	$0.204887\pi$
$278$	1.07215	−	14.9907i	0.0643035	−	0.899081i
$279$	−22.2909	+	34.6854i	−1.33452	+	2.07656i
$280$	6.05396	−	3.52065i	0.361793	−	0.210399i
$281$	5.20349	+	2.37635i	0.310414	+	0.141761i	0.564530	−	0.825412i	$-0.309057\pi$
$281$	5.20349	+	2.37635i	0.310414	+	0.141761i	−0.254116	+	0.967174i	$0.581785\pi$
$282$	11.1348	+	8.33537i	0.663065	+	0.496364i
$283$	−3.61099	+	1.97175i	−0.214651	+	0.117208i	−0.582978	−	0.812488i	$-0.698113\pi$
$283$	−3.61099	+	1.97175i	−0.214651	+	0.117208i	0.368327	+	0.929696i	$0.379931\pi$
$284$	2.87435	+	4.47257i	0.170561	+	0.265398i
$285$	13.6037	+	42.0999i	0.805814	+	2.49378i
$286$	−5.35086	−	18.2234i	−0.316403	−	1.07757i
$287$	−12.1476	+	0.868810i	−0.717048	+	0.0512843i
$288$	6.81497	−	0.487417i	0.401576	−	0.0287213i
$289$	4.31758	+	14.7043i	0.253975	+	0.864959i
$290$	−4.27296	−	13.2237i	−0.250917	−	0.776521i
$291$	−4.50782	−	7.01430i	−0.264253	−	0.411186i
$292$	−4.68469	+	2.55804i	−0.274151	+	0.149698i
$293$	21.1737	+	15.8504i	1.23698	+	0.925991i	0.998975	−	0.0452731i	$-0.0144158\pi$
$293$	21.1737	+	15.8504i	1.23698	+	0.925991i	0.238004	+	0.971264i	$0.423507\pi$
$294$	−8.01234	−	3.65911i	−0.467289	−	0.213404i
$295$	−5.02171	+	2.92035i	−0.292375	+	0.170029i
$296$	−1.25756	+	1.95680i	−0.0730940	+	0.113737i
$297$	−4.09619	+	57.2722i	−0.237685	+	3.32327i
$298$	−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
$302$	−2.23328	+	0.485820i	−0.128511	+	0.0279558i
$303$	−29.0368	+	21.7367i	−1.66812	+	1.24874i
$304$	2.62129	−	5.73981i	0.150341	−	0.329201i
$305$	−4.11582	+	4.34377i	−0.235671	+	0.248724i
$306$	−2.49118	+	8.48419i	−0.142411	+	0.485009i
$307$	−6.50974	+	29.9248i	−0.371530	+	1.70790i	0.289196	+	0.957270i	$0.406612\pi$
$307$	−6.50974	+	29.9248i	−0.371530	+	1.70790i	−0.660726	+	0.750627i	$0.729752\pi$
$308$	5.22962	−	14.0212i	0.297985	−	0.798930i
$309$	−18.5429	+	5.44468i	−1.05487	+	0.309737i
$310$	9.10800	+	9.95616i	0.517300	+	0.565472i
$311$	5.15631	−	5.95070i	0.292387	−	0.337433i	−0.590483	−	0.807050i	$-0.701063\pi$
$311$	5.15631	−	5.95070i	0.292387	−	0.337433i	0.882870	+	0.469617i	$0.155608\pi$
$312$	−5.97343	+	10.9395i	−0.338179	+	0.619328i
$313$	16.1656	+	6.02945i	0.913733	+	0.340805i	0.761970	−	0.647612i	$-0.224232\pi$
$313$	16.1656	+	6.02945i	0.913733	+	0.340805i	0.151763	+	0.988417i	$0.451505\pi$
$314$	−11.1177	+	7.14493i	−0.627410	+	0.403212i
$315$	18.6975	−	44.0445i	1.05349	−	2.48162i
$316$	2.63000	−	0.378136i	0.147949	−	0.0212718i
$317$	−5.95988	−	15.9791i	−0.334740	−	0.897474i	−0.989872	−	0.141960i	$-0.954660\pi$
$317$	−5.95988	−	15.9791i	−0.334740	−	0.897474i	0.655132	−	0.755514i	$-0.272613\pi$
$318$	−9.30631	−	12.4318i	−0.521872	−	0.697140i
$319$	−24.9812	−	16.0544i	−1.39868	−	0.898876i
$320$	0.416283	−	2.19698i	0.0232709	−	0.122815i
$321$		−	10.2786i		−	0.573695i
$322$	−6.53907	−	13.5222i	−0.364408	−	0.753562i
$323$	5.77449	+	5.77449i	0.321301	+	0.321301i
$324$	12.9870	−	11.2533i	0.721502	−	0.625185i
$325$	−19.8718	−	0.348199i	−1.10229	−	0.0193146i
$326$	2.09514	−	14.5720i	0.116039	−	0.807071i
$327$	21.9190	−	8.17537i	1.21212	−	0.452099i
$328$	−2.33029	+	3.11291i	−0.128669	+	0.171882i
$329$	−13.3298	−	3.91398i	−0.734896	−	0.215785i
$330$	31.6934	+	10.8579i	1.74467	+	0.597708i
$331$	−14.6042	−	31.9788i	−0.802721	−	1.75771i	−0.635967	−	0.771716i	$-0.719399\pi$
$331$	−14.6042	−	31.9788i	−0.802721	−	1.75771i	−0.166754	−	0.985999i	$-0.553329\pi$
$332$	−6.52052	−	3.56047i	−0.357860	−	0.195406i
$333$	1.13376	+	15.8520i	0.0621294	+	0.868683i
$334$	9.89509	+	8.57414i	0.541435	+	0.469156i
$335$	1.24416	−	0.213235i	0.0679757	−	0.0116502i
$336$	−8.93325	+	4.07968i	−0.487349	+	0.222565i
$337$	22.8583	+	4.97251i	1.24517	+	0.270870i	0.786418	−	0.617695i	$-0.211933\pi$
$337$	22.8583	+	4.97251i	1.24517	+	0.270870i	0.458751	+	0.888565i	$0.348297\pi$
$338$	−1.34206	−	2.45780i	−0.0729984	−	0.133687i
$339$	−6.77808	−	47.1426i	−0.368135	−	2.56043i
$340$	2.47575	+	1.49841i	0.134266	+	0.0812626i
$341$	28.5402	+	4.10346i	1.54554	+	0.222215i
$342$	−9.16425	−	42.1274i	−0.495546	−	2.27799i
$343$	−13.0923	−	0.936379i	−0.706917	−	0.0505597i
$344$	−6.51831			−0.351444
$345$	29.8671	−	15.4493i	1.60799	−	0.831762i
$346$	10.7693			0.578960
$347$	13.8438	+	0.990128i	0.743174	+	0.0531528i	0.437791	−	0.899077i	$-0.355761\pi$
$347$	13.8438	+	0.990128i	0.743174	+	0.0531528i	0.305383	+	0.952230i	$0.401216\pi$
$348$	4.14243	+	19.0424i	0.222057	+	1.02078i
$349$	14.6921	+	2.11241i	0.786452	+	0.113075i	0.523828	−	0.851824i	$-0.324503\pi$
$349$	14.6921	+	2.11241i	0.786452	+	0.113075i	0.262623	+	0.964898i	$0.415412\pi$
$350$	−12.3699	−	9.60271i	−0.661200	−	0.513287i
$351$	6.79801	+	47.2812i	0.362851	+	2.52368i
$352$	−2.28989	−	4.19362i	−0.122052	−	0.223521i
$353$	1.22258	+	0.265955i	0.0650712	+	0.0141554i	0.244983	−	0.969527i	$-0.421218\pi$
$353$	1.22258	+	0.265955i	0.0650712	+	0.0141554i	−0.179912	+	0.983683i	$0.557581\pi$
$354$	7.41005	−	3.38406i	0.393840	−	0.179861i
$355$	6.86538	−	9.70542i	0.364376	−	0.515110i
$356$	2.86056	+	2.47869i	0.151609	+	0.131370i
$357$	−0.906709	−	12.6775i	−0.0479881	−	0.670962i
$358$	−13.8914	−	7.58529i	−0.734184	−	0.400895i
$359$	−9.19096	−	20.1254i	−0.485080	−	1.06218i	−0.981035	−	0.193829i	$-0.937909\pi$
$359$	−9.19096	−	20.1254i	−0.485080	−	1.06218i	0.495955	−	0.868348i	$-0.334818\pi$
$360$	−6.71861	−	13.7211i	−0.354102	−	0.723164i
$361$	−19.9734	−	5.86472i	−1.05123	−	0.308669i
$362$	−0.918361	+	1.22679i	−0.0482680	+	0.0644784i
$363$	34.7562	−	12.9634i	1.82423	−	0.680401i
$364$	1.77173	−	12.3227i	0.0928639	−	0.645883i
$365$	9.22730	+	7.57010i	0.482979	+	0.396237i
$366$	6.34183	−	5.49522i	0.331493	−	0.287240i
$367$	12.5625	+	12.5625i	0.655755	+	0.655755i	0.954373	−	0.298617i	$-0.0965255\pi$
$367$	12.5625	+	12.5625i	0.655755	+	0.655755i	−0.298617	+	0.954373i	$0.596525\pi$
$368$	−4.63021	−	1.24946i	−0.241366	−	0.0651327i
$369$			26.5678i			1.38306i
$370$	5.11028	+	0.968294i	0.265671	+	0.0503392i
$371$	13.0485	+	8.38577i	0.677445	+	0.435368i
$372$	−11.3398	−	15.1482i	−0.587940	−	0.785396i
$373$	5.19920	+	13.9396i	0.269204	+	0.721765i	0.999263	+	0.0383805i	$0.0122199\pi$
$373$	5.19920	+	13.9396i	0.269204	+	0.721765i	−0.730059	+	0.683384i	$0.760507\pi$
$374$	6.12078	−	0.880035i	0.316498	−	0.0455055i
$375$	20.7441	−	28.2618i	1.07122	−	1.45944i
$376$	−3.73159	+	2.39815i	−0.192442	+	0.123675i
$377$	−23.1463	−	8.63314i	−1.19210	−	0.444629i
$378$	−18.0374	+	33.0330i	−0.927743	+	1.69903i
$379$	−13.3948	+	15.4584i	−0.688043	+	0.794044i	−0.987085	−	0.160196i	$-0.948787\pi$
$379$	−13.3948	+	15.4584i	−0.688043	+	0.794044i	0.299043	+	0.954240i	$0.403333\pi$
$380$	−14.0957	−	0.627112i	−0.723096	−	0.0321702i
$381$	−53.1205	+	15.5976i	−2.72144	+	0.799088i
$382$	−2.74236	+	7.35255i	−0.140311	+	0.376189i
$383$	0.856766	−	3.93849i	0.0437787	−	0.201248i	−0.950063	−	0.312059i	$-0.898981\pi$
$383$	0.856766	−	3.93849i	0.0437787	−	0.201248i	0.993841	+	0.110811i	$0.0353450\pi$
$384$	−0.883418	+	3.00865i	−0.0450818	+	0.153534i
$385$	−33.4499	+	0.901348i	−1.70477	+	0.0459369i
$386$	0.197886	−	0.433311i	0.0100722	−	0.0220549i
$387$	−35.6526	+	26.6892i	−1.81232	+	1.35669i
$388$	2.59829	−	0.565224i	0.131908	−	0.0286949i
$389$	1.45694	+	1.68140i	0.0738698	+	0.0852503i	0.791481	−	0.611193i	$-0.209310\pi$
$389$	1.45694	+	1.68140i	0.0738698	+	0.0852503i	−0.717612	+	0.696443i	$0.754765\pi$
$390$	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
$393$	−0.613024	+	8.57120i	−0.0309230	+	0.432360i
$394$	11.4646	−	17.8393i	0.577578	−	0.898729i
$395$	−2.98680	−	5.13599i	−0.150282	−	0.258419i
$396$	−29.6955	−	13.5615i	−1.49226	−	0.681491i
$397$	12.3099	+	9.21507i	0.617816	+	0.462491i	0.861772	−	0.507295i	$-0.169355\pi$
$397$	12.3099	+	9.21507i	0.617816	+	0.462491i	−0.243957	+	0.969786i	$0.578445\pi$
$398$	−7.13293	+	3.89488i	−0.357542	+	0.195232i
$399$	33.5031	+	52.1318i	1.67725	+	2.60985i
$400$	−4.90360	+	0.977067i	−0.245180	+	0.0488534i
$401$	−8.38008	−	28.5399i	−0.418481	−	1.42522i	−0.851748	−	0.523951i	$-0.824457\pi$
$401$	−8.38008	−	28.5399i	−0.418481	−	1.42522i	0.433267	−	0.901266i	$-0.357361\pi$
$402$	−1.76563	+	0.126280i	−0.0880615	+	0.00629828i
$403$	23.9261	−	1.71123i	1.19185	−	0.0852424i
$404$	−3.25891	−	11.0988i	−0.162137	−	0.552188i
$405$	−34.2089	−	17.5002i	−1.69985	−	0.869590i
$406$	−10.5234	−	16.3747i	−0.522267	−	0.812664i
$407$	9.75457	−	5.32640i	0.483516	−	0.264020i
$408$	−3.24870	−	2.43195i	−0.160835	−	0.120399i
$409$	−30.2505	−	13.8150i	−1.49579	−	0.683106i	−0.511441	−	0.859318i	$-0.670888\pi$
$409$	−30.2505	−	13.8150i	−1.49579	−	0.683106i	−0.984352	+	0.176212i	$0.943615\pi$
$410$	8.40571	+	2.22404i	0.415129	+	0.109838i
$411$	26.9678	−	41.9627i	1.33022	−	2.06987i
$412$	0.439677	−	6.14749i	0.0216613	−	0.302865i
$413$	−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
$417$	46.0488	−	10.0173i	2.25502	−	0.490549i
$418$	−24.1362	+	18.0681i	−1.18054	+	0.883742i
$419$	6.01416	−	13.1692i	0.293811	−	0.643356i	−0.703949	−	0.710250i	$-0.748582\pi$
$419$	6.01416	−	13.1692i	0.293811	−	0.643356i	0.997760	+	0.0668942i	$0.0213090\pi$
$420$	15.9406	+	15.1040i	0.777820	+	0.737001i
$421$	−6.88343	+	23.4428i	−0.335478	+	1.14253i	0.603158	+	0.797622i	$0.293909\pi$
$421$	−6.88343	+	23.4428i	−0.335478	+	1.14253i	−0.938636	+	0.344911i	$0.887909\pi$
$422$	−1.70163	+	7.82228i	−0.0828342	+	0.380783i
$423$	−10.5911	+	28.3959i	−0.514959	+	1.38066i
$424$	4.75184	−	1.39527i	0.230770	−	0.0677601i
$425$	1.03298	−	6.38794i	0.0501070	−	0.309861i
$426$	−10.9171	+	12.5990i	−0.528937	+	0.610425i
$427$	−4.01682	+	7.35626i	−0.194388	+	0.355994i
$428$	3.07129	+	1.14553i	0.148456	+	0.0553714i
$429$	50.1006	−	32.1977i	2.41888	−	1.55452i
$430$	5.45958	+	13.5142i	0.263284	+	0.651715i
$431$	−21.8114	+	3.13601i	−1.05062	+	0.151056i	−0.645929	−	0.763398i	$-0.723530\pi$
$431$	−21.8114	+	3.13601i	−1.05062	+	0.151056i	−0.404690	+	0.914454i	$0.632621\pi$
$432$	4.19953	+	11.2594i	0.202050	+	0.541717i
$433$	18.8586	+	25.1921i	0.906284	+	1.21065i	0.977018	+	0.213159i	$0.0683751\pi$
$433$	18.8586	+	25.1921i	0.906284	+	1.21065i	−0.0707335	+	0.997495i	$0.522534\pi$
$434$	15.8997	+	10.2181i	0.763209	+	0.490484i
$435$	36.0106	−	24.5379i	1.72657	−	1.17650i
$436$			7.46063i			0.357299i
$437$	−3.64591	+	30.0415i	−0.174408	+	1.43708i
$438$	−11.8348	−	11.8348i	−0.565487	−	0.565487i
$439$	−26.7358	+	23.1667i	−1.27603	+	1.10569i	−0.287005	+	0.957929i	$0.592660\pi$
$439$	−26.7358	+	23.1667i	−1.27603	+	1.10569i	−0.989024	+	0.147756i	$0.952795\pi$
$440$	−6.77657	+	8.26005i	−0.323060	+	0.393782i
$441$	2.73141	−	18.9974i	0.130067	−	0.904637i
$442$	4.81999	−	1.79776i	0.229263	−	0.0855108i
$443$	21.5970	−	28.8502i	1.02610	−	1.37071i	0.0993451	−	0.995053i	$-0.468325\pi$
$443$	21.5970	−	28.8502i	1.02610	−	1.37071i	0.926758	−	0.375660i	$-0.122584\pi$
$444$	−6.99826	−	2.05488i	−0.332123	−	0.0975201i
$445$	2.74306	−	8.00681i	0.130034	−	0.379559i
$446$	10.0212	+	21.9434i	0.474518	+	1.03905i
$447$	−41.7070	−	22.7737i	−1.97267	−	1.07716i
$448$	−0.223430	−	3.12397i	−0.0105561	−	0.147594i
$449$	0.121112	+	0.104944i	0.00571564	+	0.00495263i	0.657714	−	0.753268i	$-0.271524\pi$
$449$	0.121112	+	0.104944i	0.00571564	+	0.00495263i	−0.651998	+	0.758220i	$0.726069\pi$
$450$	−22.8202	+	25.4220i	−1.07575	+	1.19840i
$451$	16.9006	−	7.71824i	0.795817	−	0.363438i
$452$	14.8418	+	3.22864i	0.698100	+	0.151862i
$453$	−3.43458	−	6.28996i	−0.161371	−	0.295528i
$454$	−3.22356	−	22.4203i	−0.151289	−	1.05224i
$455$	−27.0322	+	6.64788i	−1.26729	+	0.311657i
$456$	19.5848	+	2.81586i	0.917141	+	0.131865i
$457$	−2.90618	−	13.3595i	−0.135945	−	0.624931i	−0.993814	−	0.111061i	$-0.964575\pi$
$457$	−2.90618	−	13.3595i	−0.135945	−	0.624931i	0.857868	−	0.513870i	$-0.171789\pi$
$458$	−3.87580	−	0.277203i	−0.181104	−	0.0129528i
$459$	−15.5523			−0.725919
$460$	1.28768	+	10.6462i	0.0600383	+	0.496382i
$461$	37.2335			1.73414			0.867068	−	0.498190i	$-0.166002\pi$
$461$	37.2335			1.73414			0.867068	+	0.498190i	$0.166002\pi$
$462$	46.8047	+	3.34753i	2.17755	+	0.155741i
$463$	−6.36168	−	29.2442i	−0.295652	−	1.35909i	−0.849990	−	0.526799i	$-0.823392\pi$
$463$	−6.36168	−	29.2442i	−0.295652	−	1.35909i	0.554338	−	0.832292i	$-0.312972\pi$
$464$	−6.15162	−	0.884470i	−0.285582	−	0.0410605i
$465$	−21.9084	+	36.1982i	−1.01598	+	1.67865i
$466$	−0.103595	−	0.720520i	−0.00479895	−	0.0333775i
$467$	−12.3779	−	22.6685i	−0.572782	−	1.04897i	−0.990120	−	0.140221i	$-0.955219\pi$
$467$	−12.3779	−	22.6685i	−0.572782	−	1.04897i	0.417338	−	0.908751i	$-0.362963\pi$
$468$	−26.5378	−	5.77295i	−1.22671	−	0.266855i
$469$	1.60826	−	0.734470i	0.0742628	−	0.0339147i
$470$	8.09752	+	5.72799i	0.373511	+	0.264212i
$471$	−31.3182	−	27.1374i	−1.44307	−	1.25042i
$472$	0.185334	+	2.59130i	0.00853067	+	0.119274i
$473$	27.3353	+	14.9262i	1.25688	+	0.686308i
$474$	3.46107	+	7.57868i	0.158972	+	0.348100i
$475$	10.5061	+	29.7496i	0.482052	+	1.36500i
$476$	3.88913	+	1.14195i	0.178258	+	0.0523413i
$477$	20.2778	−	27.0879i	0.928456	−	1.24027i
$478$	−11.9053	+	4.44043i	−0.544534	+	0.203101i
$479$	3.26031	−	22.6760i	0.148968	−	1.03609i	−0.768947	−	0.639313i	$-0.779219\pi$
$479$	3.26031	−	22.6760i	0.148968	−	1.03609i	0.917914	−	0.396779i	$-0.129872\pi$
$480$	6.97768	−	0.688402i	0.318486	−	0.0314211i
$481$	6.98763	−	6.05482i	0.318609	−	0.276076i
$482$	−17.1333	−	17.1333i	−0.780401	−	0.780401i
$483$	34.9067	−	31.6195i	1.58831	−	1.43874i
$484$			11.8300i			0.537729i
$485$	−3.34813	−	4.91355i	−0.152031	−	0.223113i
$486$	15.0021	+	9.64126i	0.680509	+	0.437336i
$487$	17.7646	+	23.7307i	0.804990	+	1.07534i	0.995603	+	0.0936755i	$0.0298616\pi$
$487$	17.7646	+	23.7307i	0.804990	+	1.07534i	−0.190613	+	0.981665i	$0.561047\pi$
$488$	0.935211	+	2.50740i	0.0423350	+	0.113505i
$489$	45.6930	−	6.56966i	2.06631	−	0.297090i
$490$	−5.78188	−	2.45449i	−0.261199	−	0.110883i
$491$	−29.3771	+	18.8795i	−1.32577	+	0.852020i	−0.995763	−	0.0919594i	$-0.970687\pi$
$491$	−29.3771	+	18.8795i	−1.32577	+	0.852020i	−0.330006	+	0.943979i	$0.607051\pi$
$492$	−11.4243	−	4.26103i	−0.515046	−	0.192102i
$493$	3.85470	−	7.05936i	0.173607	−	0.317937i
$494$	−16.4253	+	18.9558i	−0.739011	+	0.852864i
$495$	−3.24443	+	72.9258i	−0.145826	+	3.27777i
$496$	5.79014	−	1.70014i	0.259985	−	0.0763384i
$497$	5.81898	−	15.6013i	0.261017	−	0.699814i
$498$	4.95186	−	22.7633i	0.221898	−	1.02005i
$499$	−8.46321	+	28.8230i	−0.378865	+	1.29030i	0.520786	+	0.853687i	$0.325639\pi$
$499$	−8.46321	+	28.8230i	−0.378865	+	1.29030i	−0.899651	+	0.436609i	$0.856179\pi$
$500$	6.13287	+	9.34815i	0.274270	+	0.418062i
$501$	−17.0551	+	37.3454i	−0.761964	+	1.66847i
$502$	−12.3758	+	9.26442i	−0.552360	+	0.413491i
$503$	−5.73537	+	1.24765i	−0.255728	+	0.0556301i	−0.338601	−	0.940930i	$-0.609954\pi$
$503$	−5.73537	+	1.24765i	−0.255728	+	0.0556301i	0.0828737	+	0.996560i	$0.473590\pi$
$504$	−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
$508$	1.25956	−	17.6109i	0.0558839	−	0.781359i
$509$	9.46167	−	14.7226i	0.419381	−	0.652570i	−0.565710	−	0.824604i	$-0.691398\pi$
$509$	9.46167	−	14.7226i	0.419381	−	0.652570i	0.985091	+	0.172035i	$0.0550341\pi$
$510$	−2.32106	+	8.77238i	−0.102778	+	0.388448i
$511$	15.2064	+	6.94451i	0.672690	+	0.307207i
$512$	−0.800541	−	0.599278i	−0.0353793	−	0.0264846i
$513$	66.5528	−	36.3406i	2.93838	−	1.60448i
$514$	−0.570217	−	0.887275i	−0.0251512	−	0.0391360i
$515$	−13.1137	+	4.23742i	−0.577858	+	0.186723i
$516$	−5.75840	−	19.6113i	−0.253499	−	0.863339i
$517$	21.1404	−	1.51199i	0.929753	−	0.0664973i
$518$	7.26650	−	0.519710i	0.319272	−	0.0228348i
$519$	9.51379	+	32.4010i	0.417609	+	1.42225i
$520$	−4.04803	+	7.91298i	−0.177518	+	0.347007i
$521$	−16.4222	−	25.5535i	−0.719471	−	1.11952i	−0.987730	−	0.156172i	$-0.950085\pi$
$521$	−16.4222	−	25.5535i	−0.719471	−	1.11952i	0.268259	−	0.963347i	$-0.413552\pi$
$522$	−37.2684	+	20.3501i	−1.63119	+	0.890699i
$523$	−14.2077	−	10.6357i	−0.621259	−	0.465069i	0.241694	−	0.970352i	$-0.422297\pi$
$523$	−14.2077	−	10.6357i	−0.621259	−	0.465069i	−0.862953	+	0.505284i	$0.831388\pi$
$524$	−2.49279	−	1.13842i	−0.108898	−	0.0497321i
$525$	17.9634	−	45.6999i	0.783985	−	1.99451i
$526$	−12.9180	+	20.1008i	−0.563251	+	0.876436i
$527$	−0.557149	+	7.78997i	−0.0242698	+	0.339336i
$528$	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
$532$	−19.3111	+	4.20086i	−0.837241	+	0.182131i
$533$	12.3737	−	9.26283i	0.535964	−	0.401218i
$534$	−4.93043	+	10.7961i	−0.213360	+	0.467194i
$535$	−0.197437	−	7.32709i	−0.00853596	−	0.316778i
$536$	0.159043	−	0.541651i	0.00686961	−	0.0233957i
$537$	10.5495	−	48.4953i	0.455245	−	2.09273i
$538$	8.56728	−	22.9698i	0.369362	−	0.990297i
$539$	−12.8783	+	3.78142i	−0.554709	+	0.162877i
$540$	19.8264	−	18.1374i	0.853191	−	0.780508i
$541$	−19.4380	+	22.4327i	−0.835707	+	0.964457i	−0.999758	−	0.0219949i	$-0.992998\pi$
$541$	−19.4380	+	22.4327i	−0.835707	+	0.964457i	0.164051	+	0.986452i	$0.447544\pi$
$542$	9.49403	−	17.3870i	0.407804	−	0.746837i
$543$	−4.50226	−	1.67926i	−0.193211	−	0.0720638i
$544$	1.08874	−	0.699689i	0.0466792	−	0.0299989i
$545$	15.4679	−	6.24884i	0.662573	−	0.267671i
$546$	38.6397	−	5.55555i	1.65363	−	0.237756i
$547$	7.47468	+	20.0404i	0.319594	+	0.856865i	0.993056	+	0.117643i	$0.0375339\pi$
$547$	7.47468	+	20.0404i	0.319594	+	0.856865i	−0.673462	+	0.739222i	$0.735193\pi$
$548$	9.53312	+	12.7348i	0.407235	+	0.544002i
$549$	15.3818	+	9.88526i	0.656478	+	0.421893i
$550$	22.8012	+	7.13127i	0.972248	+	0.304078i
$551$			39.2162i			1.67066i
$552$	−0.331227	−	15.0345i	−0.0140979	−	0.639909i
$553$	−5.88434	−	5.88434i	−0.250227	−	0.250227i
$554$	−3.55337	+	3.07901i	−0.150968	+	0.130815i
$555$	1.60126	+	16.2304i	0.0679696	+	0.688943i
$556$	−2.13884	+	14.8760i	−0.0907072	+	0.630882i
$557$	−5.24604	+	1.95667i	−0.222282	+	0.0829068i	−0.458138	−	0.888881i	$-0.651483\pi$
$557$	−5.24604	+	1.95667i	−0.222282	+	0.0829068i	0.235856	+	0.971788i	$0.424211\pi$
$558$	24.7086	−	33.0068i	1.04600	−	1.39729i
$559$	24.8605	+	7.29971i	1.05149	+	0.308745i
$560$	−6.28970	+	3.07979i	−0.265788	+	0.130145i
$561$	8.05492	+	17.6378i	0.340079	+	0.744669i
$562$	−5.02071	−	2.74151i	−0.211786	−	0.115644i
$563$	2.27398	+	31.7943i	0.0958366	+	1.33997i	0.786857	+	0.617136i	$0.211707\pi$
$563$	2.27398	+	31.7943i	0.0958366	+	1.33997i	−0.691020	+	0.722836i	$0.742838\pi$
$564$	−10.5117	−	9.10848i	−0.442624	−	0.383536i
$565$	−5.73730	−	33.4754i	−0.241370	−	1.40832i
$566$	3.74245	−	1.70912i	0.157307	−	0.0718396i
$567$	−52.5904	−	11.4403i	−2.20859	−	0.480449i
$568$	−2.54795	−	4.66623i	−0.106910	−	0.195791i
$569$	1.28670	+	8.94923i	0.0539415	+	0.375171i	0.998855	+	0.0478498i	$0.0152369\pi$
$569$	1.28670	+	8.94923i	0.0539415	+	0.375171i	−0.944913	+	0.327321i	$0.893854\pi$
$570$	−10.5657	−	42.9631i	−0.442547	−	1.79953i
$571$	−41.6936	−	5.99463i	−1.74482	−	0.250868i	−0.805181	−	0.593029i	$-0.797932\pi$
$571$	−41.6936	−	5.99463i	−1.74482	−	0.250868i	−0.939641	+	0.342161i	$0.888841\pi$
$572$	4.03719	+	18.5587i	0.168803	+	0.775976i
$573$	−24.5439	−	1.75541i	−1.02534	−	0.0733334i
$574$	12.1786			0.508324
$575$	20.9940	−	11.5867i	0.875510	−	0.483200i
$576$	−6.83238			−0.284683
$577$	−14.6341	−	1.04665i	−0.609227	−	0.0435728i	−0.236682	−	0.971587i	$-0.576060\pi$
$577$	−14.6341	−	1.04665i	−0.609227	−	0.0435728i	−0.372545	+	0.928014i	$0.621515\pi$
$578$	−3.25758	−	14.9749i	−0.135498	−	0.622872i
$579$	1.47850	+	0.212576i	0.0614442	+	0.00883434i
$580$	3.31870	+	13.4948i	0.137802	+	0.560342i
$581$	3.31139	+	23.0312i	0.137380	+	0.955497i
$582$	3.99594	+	7.31802i	0.165637	+	0.303341i
$583$	−23.1224	−	5.02998i	−0.957633	−	0.208320i
$584$	4.85525	−	2.21732i	0.200911	−	0.0917532i
$585$	10.2585	+	59.8555i	0.424138	+	2.47472i
$586$	−19.9890	−	17.3205i	−0.825737	−	0.715505i
$587$	2.09474	+	29.2882i	0.0864590	+	1.20886i	0.836689	+	0.547678i	$0.184488\pi$
$587$	2.09474	+	29.2882i	0.0864590	+	1.20886i	−0.750230	+	0.661177i	$0.770057\pi$
$588$	7.73089	+	4.22139i	0.318817	+	0.174087i
$589$	−15.8184	−	34.6374i	−0.651784	−	1.42721i
$590$	5.21725	−	2.55466i	0.214791	−	0.105174i
$591$	63.8000	+	18.7334i	2.62438	+	0.770588i
$592$	1.39395	−	1.86210i	0.0572910	−	0.0765318i
$593$	−18.7364	+	6.98833i	−0.769414	+	0.286976i	−0.703355	−	0.710839i	$-0.748315\pi$
$593$	−18.7364	+	6.98833i	−0.769414	+	0.286976i	−0.0660592	+	0.997816i	$0.521043\pi$
$594$	8.17150	−	56.8340i	0.335281	−	2.33193i
$595$	−0.889863	−	9.01970i	−0.0364808	−	0.369772i
$596$	11.4531	−	9.92413i	0.469135	−	0.406508i
$597$	−18.0197	−	18.0197i	−0.737496	−	0.737496i
$598$	16.2601	+	9.95065i	0.664927	+	0.406912i
$599$		−	23.6198i		−	0.965077i	−0.875875	−	0.482539i	$-0.839715\pi$
$599$		−	23.6198i		−	0.965077i	0.875875	−	0.482539i	$-0.160285\pi$
$600$	−7.27158	−	13.8901i	−0.296861	−	0.567059i
$601$	−1.75001	−	1.12466i	−0.0713843	−	0.0458759i	0.504462	−	0.863434i	$-0.331691\pi$
$601$	−1.75001	−	1.12466i	−0.0713843	−	0.0458759i	−0.575846	+	0.817558i	$0.695327\pi$
$602$	12.2343	+	16.3430i	0.498631	+	0.666093i
$603$	−1.34788	−	3.61382i	−0.0548901	−	0.147166i
$604$	2.26224	−	0.325262i	0.0920494	−	0.0132347i
$605$	24.5269	−	9.90856i	0.997161	−	0.402840i
$606$	30.5135	−	19.6098i	1.23953	−	0.796595i
$607$	−4.96923	−	1.85343i	−0.201695	−	0.0752283i	0.246587	−	0.969121i	$-0.420691\pi$
$607$	−4.96923	−	1.85343i	−0.201695	−	0.0752283i	−0.448281	+	0.893892i	$0.647964\pi$
$608$	−3.02408	+	5.53819i	−0.122643	+	0.224603i
$609$	39.9692	−	46.1269i	1.61963	−	1.86916i
$610$	4.41521	−	4.03909i	0.178767	−	0.163538i
$611$	16.9177	−	4.96750i	0.684419	−	0.200964i
$612$	3.09009	−	8.28485i	0.124910	−	0.334895i
$613$	−3.10559	+	14.2762i	−0.125434	+	0.576609i	0.870930	+	0.491407i	$0.163517\pi$
$613$	−3.10559	+	14.2762i	−0.125434	+	0.576609i	−0.996364	+	0.0852018i	$0.972846\pi$
$614$	8.62796	−	29.3841i	0.348196	−	1.18585i
$615$	0.734407	+	27.2546i	0.0296141	+	1.09901i
$616$	−6.21655	+	13.6124i	−0.250472	+	0.548457i
$617$	−23.8235	+	17.8340i	−0.959097	+	0.717971i	−0.959406	−	0.282029i	$-0.908992\pi$
$617$	−23.8235	+	17.8340i	−0.959097	+	0.717971i	0.000309194		1.00000i	$0.499902\pi$
$618$	18.8840	−	4.10797i	0.759627	−	0.165247i
$619$	−13.5424	−	15.6287i	−0.544314	−	0.628172i	0.415235	−	0.909714i	$-0.363699\pi$
$619$	−13.5424	−	15.6287i	−0.544314	−	0.628172i	−0.959549	+	0.281542i	$0.909154\pi$
$620$	−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
$623$	0.845698	−	11.8244i	0.0338822	−	0.473735i
$624$	6.73863	−	10.4855i	0.269761	−	0.419756i
$625$	14.2445	−	20.5449i	0.569781	−	0.821796i
$626$	−15.6943	−	7.16733i	−0.627269	−	0.286464i
$627$	−75.6831	−	56.6556i	−3.02249	−	2.26261i
$628$	11.5991	−	6.33360i	0.462855	−	0.252738i
$629$	1.62751	+	2.53246i	0.0648932	+	0.100976i
$630$	−21.7920	+	42.5984i	−0.868213	+	1.69716i
$631$	7.01663	+	23.8964i	0.279327	+	0.951302i	0.972960	+	0.230973i	$0.0741909\pi$
$631$	7.01663	+	23.8964i	0.279327	+	0.951302i	−0.693633	+	0.720329i	$0.743991\pi$
$632$	−2.65027	+	0.189551i	−0.105422	+	0.00753994i
$633$	−25.0377	+	1.79073i	−0.995160	+	0.0711753i
$634$	4.80477	+	16.3635i	0.190822	+	0.649879i
$635$	−37.5673	+	12.1391i	−1.49081	+	0.481725i
$636$	8.39573	+	13.0640i	0.332912	+	0.518022i
$637$	−9.80016	+	5.35129i	−0.388297	+	0.212026i
$638$	23.7722	+	17.7957i	0.941152	+	0.704537i
$639$	−33.0421	−	15.0898i	−1.30713	−	0.596945i
$640$	−0.571953	+	2.16168i	−0.0226084	+	0.0854480i
$641$	−16.4885	+	25.6565i	−0.651255	+	1.01337i	0.345921	+	0.938264i	$0.387567\pi$
$641$	−16.4885	+	25.6565i	−0.651255	+	1.01337i	−0.997175	+	0.0751083i	$0.976070\pi$
$642$	−0.733267	+	10.2524i	−0.0289397	+	0.404630i
$643$	31.8011	−	31.8011i	1.25411	−	1.25411i	0.300256	−	0.953859i	$-0.402928\pi$
$643$	31.8011	−	31.8011i	1.25411	−	1.25411i	0.953859	−	0.300256i	$-0.0970720\pi$
$644$	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
$647$	−31.0025	+	6.74417i	−1.21883	+	0.265141i	−0.775576	−	0.631254i	$-0.782540\pi$
$647$	−31.0025	+	6.74417i	−1.21883	+	0.265141i	−0.443256	+	0.896395i	$0.646177\pi$
$648$	−13.7567	+	10.2982i	−0.540416	+	0.404550i
$649$	5.15658	−	11.2913i	0.202413	−	0.443224i
$650$	19.7963	+	1.76495i	0.776475	+	0.0692269i
$651$	−16.6966	+	56.8634i	−0.654391	+	2.22865i
$652$	−3.12936	+	14.3854i	−0.122555	+	0.563378i
$653$	6.60490	−	17.7084i	0.258470	−	0.692984i	−0.741293	−	0.671182i	$-0.765787\pi$
$653$	6.60490	−	17.7084i	0.258470	−	0.692984i	0.999762	−	0.0218018i	$-0.00694029\pi$
$654$	−22.4464	+	6.59086i	−0.877723	+	0.257723i
$655$	−0.272354	+	6.12175i	−0.0106417	+	0.239197i
$656$	2.54643	−	2.93874i	0.0994214	−	0.114738i
$657$	17.4775	−	32.0076i	0.681861	−	1.24874i
$658$	13.0166	+	4.85495i	0.507440	+	0.189266i
$659$	−24.8232	+	15.9529i	−0.966975	+	0.621437i	−0.925920	−	0.377719i	$-0.876708\pi$
$659$	−24.8232	+	15.9529i	−0.966975	+	0.621437i	−0.0410554	+	0.999157i	$0.513072\pi$
$660$	−30.8381	−	13.0912i	−1.20037	−	0.509575i
$661$	−35.0666	+	5.04181i	−1.36393	+	0.196104i	−0.785113	−	0.619353i	$-0.787395\pi$
$661$	−35.0666	+	5.04181i	−1.36393	+	0.196104i	−0.578818	+	0.815456i	$0.696486\pi$
$662$	12.2857	+	32.9392i	0.477497	+	1.28022i
$663$	9.66690	+	12.9135i	0.375431	+	0.501517i
$664$	6.24990	+	4.01657i	0.242543	+	0.155873i
$665$	24.8840	+	36.5186i	0.964961	+	1.41613i
$666$		−	15.8925i		−	0.615820i
$667$	29.4016	−	4.89055i	1.13843	−	0.189363i
$668$	−9.25821	−	9.25821i	−0.358211	−	0.358211i
$669$	−57.1669	+	49.5354i	−2.21020	+	1.91515i
$670$	−1.25620	+	0.123934i	−0.0485313	+	0.00478799i
$671$	1.81975	−	12.6566i	0.0702505	−	0.488603i
$672$	9.20153	−	3.43199i	0.354957	−	0.132392i
$673$	−15.0988	+	20.1697i	−0.582017	+	0.777483i	−0.990827	−	0.135136i	$-0.956853\pi$
$673$	−15.0988	+	20.1697i	−0.582017	+	0.777483i	0.408810	+	0.912619i	$0.365944\pi$
$674$	−22.4453	−	6.59053i	−0.864560	−	0.253858i
$675$	−54.2098	−	25.9141i	−2.08654	−	0.997432i
$676$	1.16330	+	2.54728i	0.0447424	+	0.0979721i
$677$	19.0852	+	10.4213i	0.733503	+	0.400523i	0.802154	−	0.597118i	$-0.203687\pi$
$677$	19.0852	+	10.4213i	0.733503	+	0.400523i	−0.0686504	+	0.997641i	$0.521869\pi$
$678$	3.39770	+	47.5060i	0.130488	+	1.82446i
$679$	−6.29391	−	5.45370i	−0.241538	−	0.209294i
$680$	−2.36255	−	1.67121i	−0.0905996	−	0.0640879i
$681$	64.6071	−	29.5051i	2.47575	−	1.13064i
$682$	−28.1748	−	6.12905i	−1.07887	−	0.234693i
$683$	19.3265	+	35.3938i	0.739506	+	1.35431i	0.928130	+	0.372256i	$0.121416\pi$
$683$	19.3265	+	35.3938i	0.739506	+	1.35431i	−0.188624	+	0.982049i	$0.560403\pi$
$684$	6.13556	+	42.6738i	0.234599	+	1.63167i
$685$	18.4179	−	30.4311i	0.703713	−	1.16271i
$686$	12.9921	+	1.86799i	0.496042	+	0.0713200i
$687$	−2.58995	−	11.9058i	−0.0988128	−	0.454235i
$688$	6.50170	+	0.465011i	0.247875	+	0.0177284i
$689$	−19.6858			−0.749970
$690$	−30.8931	+	13.2792i	−1.17608	+	0.505532i
$691$	49.2336			1.87293			0.936467	−	0.350755i	$-0.114075\pi$
$691$	49.2336			1.87293			0.936467	+	0.350755i	$0.114075\pi$
$692$	−10.7418	−	0.768272i	−0.408344	−	0.0292053i
$693$	21.7336	+	99.9079i	0.825592	+	3.79519i
$694$	−13.7379	−	1.97521i	−0.521483	−	0.0749780i
$695$	32.6334	−	8.02536i	1.23786	−	0.304419i
$696$	−2.77340	−	19.2894i	−0.105125	−	0.731164i
$697$	2.41179	+	4.41687i	0.0913532	+	0.167301i
$698$	−14.5040	−	3.15515i	−0.548984	−	0.119424i
$699$	2.07627	−	0.948202i	0.0785319	−	0.0358643i
$700$	11.6534	+	10.4607i	0.440455	+	0.395378i
$701$	1.44090	+	1.24855i	0.0544221	+	0.0471570i	0.681647	−	0.731681i	$-0.261264\pi$
$701$	1.44090	+	1.24855i	0.0544221	+	0.0471570i	−0.627225	+	0.778838i	$0.715809\pi$
$702$	−3.40769	−	47.6457i	−0.128615	−	1.79827i
$703$	−12.8821	−	7.03416i	−0.485858	−	0.265298i
$704$	1.98489	+	4.34629i	0.0748082	+	0.163807i
$705$	−10.0800	+	29.4228i	−0.379634	+	1.10813i
$706$	−1.20049	−	0.352495i	−0.0451810	−	0.0132663i
$707$	−21.7109	+	29.0024i	−0.816523	+	1.09075i
$708$	−7.63259	+	2.84681i	−0.286850	+	0.106990i
$709$	−1.40020	+	9.73862i	−0.0525857	+	0.365742i	0.946489	+	0.322736i	$0.104603\pi$
$709$	−1.40020	+	9.73862i	−0.0525857	+	0.365742i	−0.999075	+	0.0430059i	$0.986307\pi$
$710$	−7.54026	+	9.19092i	−0.282981	+	0.344929i
$711$	−13.7198	+	11.8883i	−0.514533	+	0.445846i
$712$	−2.67644	−	2.67644i	−0.100304	−	0.100304i
$713$	−23.9960	+	16.1791i	−0.898659	+	0.605910i
$714$			12.7098i			0.475654i
$715$	35.0957	−	23.9145i	1.31251	−	0.894351i
$716$	13.3149	+	8.55696i	0.497601	+	0.319789i
$717$	−23.8770	−	31.8960i	−0.891704	−	1.19118i
$718$	7.73181	+	20.7298i	0.288549	+	0.773629i
$719$	−22.9216	+	3.29563i	−0.854833	+	0.122906i	−0.555779	−	0.831330i	$-0.687580\pi$
$719$	−22.9216	+	3.29563i	−0.854833	+	0.122906i	−0.299054	+	0.954236i	$0.596671\pi$
$720$	5.72264	+	14.1654i	0.213270	+	0.527913i
$721$	−16.2385	+	10.4359i	−0.604754	+	0.388652i
$722$	19.5041	+	7.27466i	0.725868	+	0.270735i
$723$	36.4122	−	66.6840i	1.35418	−	2.48000i
$724$	1.00354	−	1.15815i	0.0372962	−	0.0430421i
$725$	25.1988	−	18.1835i	0.935859	−	0.675319i
$726$	−35.5924	+	10.4509i	−1.32096	+	0.387869i
$727$	3.81349	−	10.2244i	0.141434	−	0.379200i	−0.846848	−	0.531834i	$-0.821503\pi$
$727$	3.81349	−	10.2244i	0.141434	−	0.379200i	0.988283	+	0.152634i	$0.0487756\pi$
$728$	−2.64630	+	12.1649i	−0.0980785	+	0.450860i
$729$	−1.22988	+	4.18858i	−0.0455510	+	0.155132i
$730$	−8.66374	−	8.20908i	−0.320659	−	0.303832i
$731$	−3.50440	+	7.67357i	−0.129615	+	0.283817i
$732$	−6.71769	+	5.02880i	−0.248293	+	0.185870i
$733$	−18.5591	+	4.03728i	−0.685495	+	0.149120i	−0.541807	−	0.840503i	$-0.682260\pi$
$733$	−18.5591	+	4.03728i	−0.685495	+	0.149120i	−0.143688	+	0.989623i	$0.545896\pi$
$734$	−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
$738$	1.89532	−	26.5001i	0.0697678	−	0.975481i
$739$	15.7194	−	24.4599i	0.578249	−	0.899773i	−0.421727	−	0.906723i	$-0.638576\pi$
$739$	15.7194	−	24.4599i	0.578249	−	0.899773i	0.999976	+	0.00694976i	$0.00221220\pi$
$740$	−5.02818	−	1.33039i	−0.184840	−	0.0489061i
$741$	−71.5419	−	32.6721i	−2.62816	−	1.20024i
$742$	−12.4170	−	9.29528i	−0.455844	−	0.341240i
$743$	8.71392	−	4.75816i	0.319683	−	0.174560i	−0.311393	−	0.950281i	$-0.600796\pi$
$743$	8.71392	−	4.75816i	0.319683	−	0.174560i	0.631076	+	0.775721i	$0.282614\pi$
$744$	10.2302	+	15.9185i	0.375058	+	0.583602i
$745$	−30.1682	−	15.4331i	−1.10528	−	0.565425i
$746$	−4.19151	−	14.2750i	−0.153462	−	0.522644i
$747$	50.6303	−	3.62115i	1.85247	−	0.132491i
$748$	−6.16796	+	0.441141i	−0.225523	+	0.0161297i
$749$	−2.89238	−	9.85055i	−0.105685	−	0.359931i
$750$	−22.7074	+	26.7100i	−0.829157	+	0.975310i
$751$	14.4018	+	22.4096i	0.525528	+	0.817738i	0.997974	−	0.0636220i	$-0.0202652\pi$
$751$	14.4018	+	22.4096i	0.525528	+	0.817738i	−0.472446	+	0.881360i	$0.656629\pi$
$752$	3.89317	−	2.12583i	0.141969	−	0.0775211i
$753$	−38.8064	−	29.0501i	−1.41418	−	1.05864i
$754$	22.4715	+	10.2624i	0.818363	+	0.373734i
$755$	−2.56916	−	4.41782i	−0.0935013	−	0.160781i
$756$	20.3480	−	31.6621i	0.740049	−	1.15154i
$757$	1.14700	−	16.0371i	0.0416883	−	0.582878i	−0.933081	−	0.359665i	$-0.882891\pi$
$757$	1.14700	−	16.0371i	0.0416883	−	0.582878i	0.974770	−	0.223213i	$-0.0716545\pi$
$758$	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	0.403745	−	0.914872i	$-0.367708\pi$
$761$	−15.4283	−	17.8052i	−0.559274	−	0.645436i	−0.963018	+	0.269435i	$0.913163\pi$
$762$	54.0978	−	11.7683i	1.95976	−	0.426319i
$763$	18.7057	−	14.0029i	0.677191	−	0.506939i
$764$	3.25990	−	7.13818i	0.117939	−	0.258250i
$765$	−19.7650	+	0.532590i	−0.714604	+	0.0192558i
$766$	−1.13555	+	3.86734i	−0.0410292	+	0.139733i
$767$	2.19509	−	10.0907i	0.0792600	−	0.364352i
$768$	1.09580	−	2.93796i	0.0395413	−	0.106014i
$769$	31.9547	−	9.38273i	1.15231	−	0.338350i	0.350873	−	0.936423i	$-0.385885\pi$
$769$	31.9547	−	9.38273i	1.15231	−	0.338350i	0.801441	+	0.598073i	$0.204067\pi$
$770$	33.4290	+	1.48724i	1.20470	+	0.0535963i
$771$	2.16576	−	2.49942i	0.0779978	−	0.0900143i
$772$	−0.228294	+	0.418090i	−0.00821649	+	0.0150474i
$773$	5.27553	+	1.96767i	0.189748	+	0.0707722i	0.442542	−	0.896748i	$-0.354077\pi$
$773$	5.27553	+	1.96767i	0.189748	+	0.0707722i	−0.252794	+	0.967520i	$0.581350\pi$
$774$	37.4657	−	24.0778i	1.34668	−	0.865457i
$775$	−14.9221	+	26.2247i	−0.536017	+	0.942020i
$776$	−2.63199	+	0.378424i	−0.0944831	+	0.0135846i
$777$	7.98298	+	21.4032i	0.286388	+	0.767836i
$778$	−1.33328	−	1.78105i	−0.0478003	−	0.0638538i
$779$	−20.6415	−	13.2655i	−0.739559	−	0.475286i
$780$	−27.3834	−	5.18861i	−0.980485	−	0.185782i
$781$			25.4029i			0.908988i
$782$	−3.96022	+	4.77909i	−0.141617	+	0.170900i
$783$	−52.8100	−	52.8100i	−1.88728	−	1.88728i
$784$	−2.12296	+	1.83956i	−0.0758201	+	0.0656985i
$785$	−22.8464	−	18.7433i	−0.815424	−	0.668977i
$786$	1.22292	−	8.50563i	0.0436203	−	0.303386i
$787$	−5.14963	+	1.92071i	−0.183565	+	0.0684660i	−0.439566	−	0.898210i	$-0.644868\pi$
$787$	−5.14963	+	1.92071i	−0.183565	+	0.0684660i	0.256001	+	0.966676i	$0.417595\pi$
$788$	−12.7080	+	16.9759i	−0.452704	+	0.604742i
$789$	−71.8881	−	21.1083i	−2.55929	−	0.751474i
$790$	2.61280	+	5.33598i	0.0929591	+	0.189845i
$791$	−19.7617	−	43.2720i	−0.702644	−	1.53858i
$792$	28.6524	+	15.6454i	1.01812	+	0.555935i
$793$	−0.758872	−	10.6104i	−0.0269483	−	0.376787i
$794$	−11.6211	−	10.0698i	−0.412418	−	0.357363i
$795$	20.0532	−	28.3487i	0.711214	−	1.00543i
$796$	7.39262	−	3.37609i	0.262024	−	0.119662i
$797$	−3.28502	−	0.714613i	−0.116361	−	0.0253129i	0.154007	−	0.988070i	$-0.450782\pi$
$797$	−3.28502	−	0.714613i	−0.116361	−	0.0253129i	−0.270369	+	0.962757i	$0.587146\pi$
$798$	−29.6987	−	54.3890i	−1.05132	−	1.92535i
$799$	0.816985	+	5.68226i	0.0289029	+	0.201024i
$800$	4.96081	−	0.624759i	0.175391	−	0.0220886i
$801$	−25.5978	−	3.68040i	−0.904452	−	0.130041i
$802$	6.32272	+	29.0651i	0.223263	+	1.02632i
$803$	−25.4385	−	1.81939i	−0.897704	−	0.0642051i
$804$	1.77014			0.0624279
$805$	24.2759	−	23.2105i	0.855613	−	0.818061i
$806$	−23.9872			−0.844914
$807$	76.6764	+	5.48400i	2.69914	+	0.193046i
$808$	2.45883	+	11.3030i	0.0865013	+	0.397640i
$809$	30.1990	+	4.34197i	1.06174	+	0.152655i	0.650986	−	0.759090i	$-0.274356\pi$
$809$	30.1990	+	4.34197i	1.06174	+	0.152655i	0.410756	+	0.911745i	$0.365265\pi$
$810$	32.8733	+	19.8960i	1.15505	+	0.699074i
$811$	−3.16655	−	22.0239i	−0.111193	−	0.773362i	−0.966763	−	0.255675i	$-0.917702\pi$
$811$	−3.16655	−	22.0239i	−0.111193	−	0.773362i	0.855570	−	0.517687i	$-0.173207\pi$
$812$	9.32843	+	17.0837i	0.327364	+	0.599522i
$813$	60.6986	+	13.2042i	2.12879	+	0.463091i
$814$	−10.1097	+	4.61694i	−0.354345	+	0.161824i
$815$	32.4461	−	5.56088i	1.13654	−	0.194789i
$816$	3.06693	+	2.65751i	0.107364	+	0.0930314i
$817$	−2.93424	−	41.0260i	−0.102656	−	1.43532i
$818$	29.1879	+	15.9378i	1.02053	+	0.557253i
$819$	35.3347	+	77.3723i	1.23470	+	2.70361i
$820$	−8.22563	−	2.81803i	−0.287252	−	0.0984099i
$821$	−28.5404	−	8.38022i	−0.996067	−	0.292472i	−0.257226	−	0.966351i	$-0.582808\pi$
$821$	−28.5404	−	8.38022i	−0.996067	−	0.292472i	−0.738841	+	0.673880i	$0.764627\pi$
$822$	−29.8927	+	39.9319i	−1.04263	+	1.39279i
$823$	45.9058	−	17.1220i	1.60018	−	0.596835i	0.618231	−	0.785997i	$-0.287850\pi$
$823$	45.9058	−	17.1220i	1.60018	−	0.596835i	0.981946	+	0.189162i	$0.0605770\pi$
$824$	−0.877113	+	6.10046i	−0.0305557	+	0.212520i
$825$	−1.31243	+	74.9007i	−0.0456930	+	2.60771i
$826$	6.14920	−	5.32831i	0.213958	−	0.185396i
$827$	14.8810	+	14.8810i	0.517462	+	0.517462i	0.916803	−	0.399341i	$-0.130761\pi$
$827$	14.8810	+	14.8810i	0.517462	+	0.517462i	−0.399341	+	0.916803i	$0.630761\pi$
$828$	31.2287	−	9.92176i	1.08527	−	0.344805i
$829$		−	21.0848i		−	0.732307i	−0.930555	−	0.366153i	$-0.880675\pi$
$829$		−	21.0848i		−	0.732307i	0.930555	−	0.366153i	$-0.119325\pi$
$830$	3.09268	−	16.3219i	0.107348	−	0.566543i
$831$	−12.4028	−	7.97077i	−0.430247	−	0.276503i
$832$	2.38211	+	3.18212i	0.0825847	+	0.110320i
$833$	−1.27047	−	3.40625i	−0.0440191	−	0.118020i
$834$	−46.6461	+	6.70670i	−1.61522	+	0.232234i
$835$	−11.4403	+	26.9493i	−0.395910	+	0.932617i
$836$	25.3637	−	16.3003i	0.877222	−	0.563756i
$837$	67.9457	+	25.3424i	2.34855	+	0.875962i
$838$	−6.93831	+	12.7066i	−0.239680	+	0.438941i
$839$	−16.0961	+	18.5759i	−0.555700	+	0.641312i	−0.962202	−	0.272338i	$-0.912203\pi$
$839$	−16.0961	+	18.5759i	−0.555700	+	0.641312i	0.406502	+	0.913650i	$0.366748\pi$
$840$	−14.8224	−	16.2027i	−0.511423	−	0.559047i
$841$	9.23490	−	2.71161i	0.318445	−	0.0935038i
$842$	8.53828	−	22.8920i	0.294249	−	0.788911i
$843$	3.81286	−	17.5274i	0.131322	−	0.603677i
$844$	2.25533	−	7.68096i	0.0776317	−	0.264389i
$845$	4.30685	−	4.54538i	0.148160	−	0.156366i
$846$	12.5899	−	27.5680i	0.432849	−	0.947808i
$847$	29.6609	−	22.2039i	1.01916	−	0.762934i
$848$	−4.83927	+	1.05272i	−0.166181	+	0.0361505i
$849$	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
$853$	−2.88639	+	40.3571i	−0.0988283	+	1.38180i	0.670008	+	0.742354i	$0.266291\pi$
$853$	−2.88639	+	40.3571i	−0.0988283	+	1.38180i	−0.768836	+	0.639446i	$0.779164\pi$
$854$	4.53138	−	7.05096i	0.155060	−	0.241279i
$855$	83.3355	−	48.4633i	2.85001	−	1.65741i
$856$	−2.98174	−	1.36172i	−0.101914	−	0.0465425i
$857$	−34.3777	−	25.7348i	−1.17432	−	0.879084i	−0.179807	−	0.983702i	$-0.557547\pi$
$857$	−34.3777	−	25.7348i	−1.17432	−	0.879084i	−0.994513	+	0.104617i	$0.966638\pi$
$858$	−52.2699	+	28.5415i	−1.78446	+	0.974392i
$859$	8.68467	+	13.5136i	0.296317	+	0.461078i	0.957207	−	0.289405i	$-0.0934573\pi$
$859$	8.68467	+	13.5136i	0.296317	+	0.461078i	−0.660890	+	0.750483i	$0.729821\pi$
$860$	−4.48158	−	13.8693i	−0.152820	−	0.472939i
$861$	10.7588	+	36.6411i	0.366658	+	1.24872i
$862$	21.9796	−	1.57201i	0.748627	−	0.0535429i
$863$	−31.7531	+	2.27102i	−1.08089	+	0.0773066i	−0.600404	−	0.799697i	$-0.704993\pi$
$863$	−31.7531	+	2.27102i	−1.08089	+	0.0773066i	−0.480484	+	0.877004i	$0.659539\pi$
$864$	−3.38560	−	11.5303i	−0.115180	−	0.392268i
$865$	7.40428	+	22.9143i	0.251753	+	0.779109i
$866$	−17.0133	−	26.4732i	−0.578136	−	0.899597i
$867$	42.1763	−	23.0300i	1.43238	−	0.782139i
$868$	−15.1302	−	11.3263i	−0.513553	−	0.384441i
$869$	11.5483	+	5.27392i	0.391749	+	0.178906i
$870$	−37.6693	+	21.9064i	−1.27711	+	0.742696i
$871$	−1.21316	+	1.88772i	−0.0411065	+	0.0639630i
$872$	0.532235	−	7.44162i	0.0180238	−	0.252005i
$873$	−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
$877$	−25.7246	+	5.59604i	−0.868658	+	0.188965i	−0.624742	−	0.780831i	$-0.714796\pi$
$877$	−25.7246	+	5.59604i	−0.868658	+	0.188965i	−0.243916	+	0.969796i	$0.578432\pi$
$878$	28.3203	−	21.2003i	0.955765	−	0.715477i
$879$	34.4528	−	75.4410i	1.16206	−	2.54456i
$880$	7.34857	−	7.75557i	0.247720	−	0.261440i
$881$	2.54069	−	8.65279i	0.0855980	−	0.291520i	−0.905558	−	0.424223i	$-0.860547\pi$
$881$	2.54069	−	8.65279i	0.0855980	−	0.291520i	0.991156	+	0.132703i	$0.0423656\pi$
$882$	−4.07971	+	18.7541i	−0.137371	+	0.631484i
$883$	−18.1144	+	48.5666i	−0.609598	+	1.63439i	0.153528	+	0.988144i	$0.450937\pi$
$883$	−18.1144	+	48.5666i	−0.609598	+	1.63439i	−0.763125	+	0.646250i	$0.776336\pi$
$884$	−4.93596	+	1.44933i	−0.166014	+	0.0487462i
$885$	12.2951	+	13.4400i	0.413295	+	0.451782i
$886$	−23.6001	+	27.2360i	−0.792860	+	0.915010i
$887$	−5.80476	+	10.6306i	−0.194905	+	0.356941i	−0.956794	−	0.290766i	$-0.906090\pi$
$887$	−5.80476	+	10.6306i	−0.194905	+	0.356941i	0.761890	+	0.647707i	$0.224272\pi$
$888$	6.83384	+	2.54889i	0.229329	+	0.0855351i
$889$	−46.5191	+	29.8960i	−1.56020	+	1.00268i
$890$	−3.30728	+	7.79072i	−0.110860	+	0.261146i
$891$	81.2723	−	11.6852i	2.72272	−	0.391468i
$892$	−8.43025	−	22.6024i	−0.282266	−	0.756783i
$893$	−16.7737	−	22.4070i	−0.561309	−	0.749821i
$894$	39.9760	+	25.6910i	1.33700	+	0.859237i
$895$	6.58869	−	34.7725i	0.220236	−	1.16232i
$896$			3.13195i			0.104631i
$897$	−15.5735	+	57.7116i	−0.519983	+	1.92693i
$898$	−0.113317	−	0.113317i	−0.00378144	−	0.00378144i
$899$	−28.3438	+	24.5600i	−0.945318	+	0.819123i
$900$	24.5756	−	23.7292i	0.819187	−	0.790974i
$901$	0.912151	−	6.34415i	0.0303882	−	0.211354i
$902$	−17.4081	+	6.49290i	−0.579628	+	0.216190i
$903$	−38.3625	+	51.2463i	−1.27662	+	1.70537i
$904$	−14.5737	−	4.27922i	−0.484713	−	0.142325i
$905$	−3.24169	−	1.11058i	−0.107758	−	0.0369168i
$906$	2.97711	+	6.51895i	0.0989077	+	0.216578i
$907$	11.7758	+	6.43009i	0.391010	+	0.213508i	0.662713	−	0.748874i	$-0.269405\pi$
$907$	11.7758	+	6.43009i	0.391010	+	0.213508i	−0.271703	+	0.962381i	$0.587587\pi$
$908$	1.61589	+	22.5932i	0.0536253	+	0.749780i
$909$	59.7291	+	51.7555i	1.98109	+	1.71662i
$910$	27.4376	−	4.70248i	0.909547	−	0.155886i
$911$	−5.81560	+	2.65590i	−0.192679	+	0.0879938i	−0.509418	−	0.860519i	$-0.670139\pi$
$911$	−5.81560	+	2.65590i	−0.192679	+	0.0879938i	0.316739	+	0.948513i	$0.397412\pi$
$912$	−19.3340	−	4.20585i	−0.640212	−	0.139270i
$913$	−17.0122	−	31.1556i	−0.563022	−	1.03110i
$914$	1.94572	+	13.5328i	0.0643587	+	0.447624i
$915$	16.0527	+	9.71561i	0.530685	+	0.321188i
$916$	3.84615	+	0.552993i	0.127080	+	0.0182714i
$917$	1.82443	+	8.38676i	0.0602479	+	0.276955i
$918$	15.5127	+	1.10949i	0.511995	+	0.0366186i
$919$	−17.2296			−0.568353			−0.284177	−	0.958772i	$-0.591720\pi$
$919$	−17.2296			−0.568353			−0.284177	+	0.958772i	$0.591720\pi$
$920$	−0.524906	−	10.7110i	−0.0173056	−	0.353130i
$921$	96.0286			3.16425
$922$	−37.1386	−	2.65620i	−1.22309	−	0.0874775i
$923$	4.49216	+	20.6501i	0.147861	+	0.679708i
$924$	−46.4466	−	6.67801i	−1.52798	−	0.219690i
$925$	1.45322	+	11.5391i	0.0477816	+	0.379403i
$926$	4.25921	+	29.6235i	0.139966	+	0.973488i
$927$	20.1808	+	36.9584i	0.662825	+	1.21387i
$928$	6.07285	+	1.32107i	0.199351	+	0.0433662i
$929$	49.7975	−	22.7417i	1.63380	−	0.746132i	0.634168	−	0.773195i	$-0.281343\pi$
$929$	49.7975	−	22.7417i	1.63380	−	0.746132i	0.999634	+	0.0270626i	$0.00861534\pi$
$930$	24.4349	−	34.5431i	0.801252	−	1.13271i
$931$	13.3960	+	11.6077i	0.439036	+	0.380426i
$932$	0.0519299	+	0.726075i	0.00170102	+	0.0237834i
$933$	−21.6698	−	11.8326i	−0.709438	−	0.387382i
$934$	10.7292	+	23.4938i	0.351071	+	0.768739i
$935$	6.08075	+	12.4184i	0.198862	+	0.406125i
$936$	26.0584	+	7.65143i	0.851744	+	0.250095i
$937$	19.1846	−	25.6276i	0.626734	−	0.837218i	−0.369006	−	0.929427i	$-0.620302\pi$
$937$	19.1846	−	25.6276i	0.626734	−	0.837218i	0.995740	+	0.0922087i	$0.0293927\pi$
$938$	−1.65656	+	0.617866i	−0.0540887	+	0.0201740i
$939$	7.69936	−	53.5502i	0.251259	−	1.74755i
$940$	−7.66826	−	6.29106i	−0.250111	−	0.205192i
$941$	30.8788	−	26.7566i	1.00662	−	0.872241i	0.0148009	−	0.999890i	$-0.495289\pi$
$941$	30.8788	−	26.7566i	1.00662	−	0.872241i	0.991819	+	0.127649i	$0.0407431\pi$
$942$	29.3024	+	29.3024i	0.954725	+	0.954725i
$943$	−7.37140	+	17.1299i	−0.240046	+	0.557826i
$944$		−	2.59792i		−	0.0845552i
$945$	−82.6872	−	15.6675i	−2.68981	−	0.509665i
$946$	−26.2009	−	16.8383i	−0.851863	−	0.547459i
$947$	−12.8338	−	17.1440i	−0.417044	−	0.557105i	0.541994	−	0.840382i	$-0.317669\pi$
$947$	−12.8338	−	17.1440i	−0.417044	−	0.557105i	−0.959038	+	0.283277i	$0.908579\pi$
$948$	−2.91159	−	7.80628i	−0.0945641	−	0.253536i
$949$	−21.0008	+	3.01946i	−0.681714	+	0.0980157i
$950$	−8.35700	−	30.4233i	−0.271137	−	0.987061i
$951$	−44.9875	+	28.9117i	−1.45882	+	0.937526i
$952$	−3.79775	−	1.41649i	−0.123086	−	0.0459087i
$953$	4.34075	−	7.94949i	0.140611	−	0.257509i	−0.797878	−	0.602819i	$-0.794044\pi$
$953$	4.34075	−	7.94949i	0.140611	−	0.257509i	0.938489	+	0.345309i	$0.112226\pi$
$954$	−22.1585	+	25.5723i	−0.717410	+	0.827935i
$955$	−17.5298	−	0.779893i	−0.567252	−	0.0252367i
$956$	12.1917	−	3.57981i	0.394308	−	0.115779i
$957$	−32.5401	+	87.2433i	−1.05187	+	2.82017i
$958$	−4.86969	+	22.3856i	−0.157333	+	0.723246i
$959$	14.0365	−	47.8039i	0.453262	−	1.54367i
$960$	−7.00901	+	0.188866i	−0.226215	+	0.00609563i
$961$	2.24996	−	4.92671i	0.0725792	−	0.158926i
$962$	−7.40177	+	5.54090i	−0.238643	+	0.178646i
$963$	−21.8845	+	4.76068i	−0.705218	+	0.153411i
$964$	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	$0.316434\pi$
$968$	0.843946	−	11.7999i	0.0271254	−	0.379263i
$969$	13.8442	−	21.5419i	0.444739	−	0.692027i
$970$	2.98907	+	5.13989i	0.0959733	+	0.165032i
$971$	−29.0352	−	13.2599i	−0.931783	−	0.425531i	−0.109099	−	0.994031i	$-0.534797\pi$
$971$	−29.0352	−	13.2599i	−0.931783	−	0.425531i	−0.822683	+	0.568500i	$0.807524\pi$
$972$	−14.2761	−	10.6869i	−0.457905	−	0.342783i
$973$	41.3123	−	22.5582i	1.32441	−	0.723183i
$974$	−16.0264	−	24.9376i	−0.513519	−	0.799051i
$975$	12.1783	+	61.1193i	0.390018	+	1.95738i
$976$	−0.753953	−	2.56773i	−0.0241334	−	0.0821909i
$977$	−4.74764	+	0.339558i	−0.151890	+	0.0108634i	−0.147077	−	0.989125i	$-0.546987\pi$
$977$	−4.74764	+	0.339558i	−0.151890	+	0.0108634i	−0.00481314	+	0.999988i	$0.501532\pi$
$978$	−46.0453	+	3.29322i	−1.47237	+	0.105306i
$979$	5.09522	+	17.3527i	0.162844	+	0.554596i
$980$	5.59205	+	2.86071i	0.178632	+	0.0913822i
$981$	−27.5586	−	42.8819i	−0.879877	−	1.36912i
$982$	30.6491	−	16.7357i	0.978051	−	0.534056i
$983$	45.8696	+	34.3376i	1.46301	+	1.09520i	0.974959	+	0.222386i	$0.0713844\pi$
$983$	45.8696	+	34.3376i	1.46301	+	1.09520i	0.488055	+	0.872813i	$0.337706\pi$
$984$	11.0912	+	5.06517i	0.353574	+	0.161472i
$985$	45.8397	+	12.1286i	1.46057	+	0.386449i
$986$	−4.34849	+	6.76638i	−0.138484	+	0.215485i
$987$	−3.10770	+	43.4513i	−0.0989192	+	1.38307i
$988$	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	0.997592	−	0.0693609i	$-0.0220960\pi$
$991$	24.7738	+	28.5904i	0.786965	+	0.908206i	−0.210627	+	0.977566i	$0.567551\pi$
$992$	−5.89667	+	1.28274i	−0.187220	+	0.0407271i
$993$	−88.2490	+	66.0624i	−2.80050	+	2.09643i
$994$	−6.91714	+	15.1464i	−0.219398	+	0.480415i
$995$	−13.1914	−	12.4992i	−0.418197	−	0.396251i
$996$	−6.56316	+	22.3521i	−0.207962	+	0.708252i
$997$	7.46380	−	34.3105i	0.236381	−	1.08662i	−0.693984	−	0.719990i	$-0.744146\pi$
$997$	7.46380	−	34.3105i	0.236381	−	1.08662i	0.930365	−	0.366635i	$-0.119490\pi$
$998$	10.4979	−	28.1458i	0.332304	−	0.890941i
$999$	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.33.1	yes	240
5.2	odd	4	inner	230.2.l.a.217.7	yes	240
23.7	odd	22	inner	230.2.l.a.53.7	yes	240
115.7	even	44	inner	230.2.l.a.7.1	✓	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.l.a.7.1	✓	240	115.7	even	44	inner
230.2.l.a.33.1	yes	240	1.1	even	1	trivial
230.2.l.a.53.7	yes	240	23.7	odd	22	inner
230.2.l.a.217.7	yes	240	5.2	odd	4	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+(-0.997452 - 0.0713392i) q^{2} +(-0.666533 - 3.06400i) q^{3} +(0.989821 + 0.142315i) q^{4} +(-0.533993 - 2.17137i) q^{5} +(0.446251 + 3.10375i) q^{6} +(-1.50098 - 2.74884i) q^{7} +(-0.977147 - 0.212565i) q^{8} +(-6.21495 + 2.83827i) q^{9} +(0.377729 + 2.20393i) q^{10} +(3.61103 + 3.12898i) q^{11} +(-0.223696 - 3.12767i) q^{12} +(3.48874 + 1.90500i) q^{13} +(1.30106 + 2.84892i) q^{14} +(-6.29716 + 3.08345i) q^{15} +(0.959493 + 0.281733i) q^{16} +(-0.775576 + 1.03605i) q^{17} +(6.40160 - 2.38767i) q^{18} +(0.898012 - 6.24581i) q^{19} +(-0.219540 - 2.22526i) q^{20} +(-7.42201 + 6.43121i) q^{21} +(-3.37861 - 3.37861i) q^{22} +(-4.79467 + 0.105632i) q^{23} +3.13566i q^{24} +(-4.42970 + 2.31899i) q^{25} +(-3.34395 - 2.14903i) q^{26} +(7.20156 + 9.62015i) q^{27} +(-1.09450 - 2.93448i) q^{28} +(-6.15162 + 0.884470i) q^{29} +(6.50109 - 2.62636i) q^{30} +(5.07661 - 3.26254i) q^{31} +(-0.936950 - 0.349464i) q^{32} +(7.18032 - 13.1498i) q^{33} +(0.847511 - 0.978080i) q^{34} +(-5.16724 + 4.72705i) q^{35} +(-6.55562 + 1.92490i) q^{36} +(0.812871 - 2.17939i) q^{37} +(-1.34130 + 6.16584i) q^{38} +(3.51156 - 11.9593i) q^{39} +(0.0602316 + 2.23526i) q^{40} +(1.61534 - 3.53711i) q^{41} +(7.86190 - 5.88534i) q^{42} +(6.36935 - 1.38557i) 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} +(0.223696 - 3.12767i) q^{48} +(-1.51870 + 2.36315i) q^{49} +(4.58385 - 1.99707i) q^{50} +(3.69140 + 1.68581i) q^{51} +(3.18212 + 2.38211i) q^{52} +(-4.34666 + 2.37346i) q^{53} +(-6.49691 - 10.1094i) q^{54} +(4.86590 - 9.51174i) q^{55} +(0.882371 + 3.00508i) q^{56} +(-19.7357 + 1.41153i) q^{57} +(6.19905 - 0.443365i) q^{58} +(-0.731919 - 2.49269i) q^{59} +(-6.67189 + 2.15588i) q^{60} +(-1.44682 - 2.25130i) q^{61} +(-5.29642 + 2.89207i) q^{62} +(17.1305 + 12.8237i) q^{63} +(0.909632 + 0.415415i) q^{64} +(2.27349 - 8.59261i) q^{65} +(-8.10012 + 12.6040i) q^{66} +(-0.0402722 + 0.563079i) 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} +(6.67624 - 1.45233i) q^{72} +(-4.27296 + 3.19870i) q^{73} +(-0.966276 + 2.11585i) q^{74} +(10.0579 + 12.0269i) q^{75} +(1.77774 - 6.05444i) q^{76} +(3.18097 - 14.6227i) q^{77} +(-4.35577 + 11.6783i) q^{78} +(2.54941 - 0.748575i) q^{79} +(0.0993832 - 2.23386i) q^{80} +(11.2533 - 12.9870i) q^{81} +(-1.86356 + 3.41286i) q^{82} +(-6.96086 - 2.59627i) q^{83} +(-8.26172 + 5.30949i) q^{84} +(2.66380 + 1.13082i) q^{85} +(-6.45196 + 0.927652i) q^{86} +(6.81028 + 18.2591i) q^{87} +(-2.86340 - 3.82505i) q^{88} +(3.18420 + 2.04636i) q^{89} +(-8.60293 - 12.6252i) q^{90} -12.4494i q^{91} +(-4.76090 - 0.577796i) q^{92} +(-13.3802 - 13.3802i) q^{93} +(-3.35232 + 2.90480i) q^{94} +(-14.0415 + 1.38530i) q^{95} +(-0.446251 + 3.10375i) q^{96} +(2.49141 - 0.929246i) q^{97} +(1.68342 - 2.24879i) 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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