LMFDB - Embedded newform 270.2.r.a.203.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [270,2,Mod(23,270)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(270, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([22, 27]))

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

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

chi := DirichletCharacter("270.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 270 = 2 \cdot 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	270.r (of order $36$, degree $12$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.15596085457$
Analytic rank:	$0$
Dimension:	$216$
Relative dimension:	$18$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			203.13
Character	$\chi$	$=$	270.203
Dual form			270.2.r.a.137.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.573576 - 0.819152i) q^{2} +(-0.308872 + 1.70429i) q^{3} +(-0.342020 - 0.939693i) q^{4} +(-2.07393 + 0.835951i) q^{5} +(1.21891 + 1.23055i) q^{6} +(-3.83305 + 1.78738i) q^{7} +(-0.965926 - 0.258819i) q^{8} +(-2.80920 - 1.05281i) q^{9} +(-0.504786 + 2.17835i) q^{10} +(3.34414 + 3.98539i) q^{11} +(1.70715 - 0.292656i) q^{12} +(0.307904 - 0.215597i) q^{13} +(-0.734411 + 4.16505i) q^{14} +(-0.784123 - 3.79278i) q^{15} +(-0.766044 + 0.642788i) q^{16} +(-5.90088 + 1.58114i) q^{17} +(-2.47370 + 1.69729i) q^{18} +(2.93211 - 1.69286i) q^{19} +(1.49486 + 1.66294i) q^{20} +(-1.86229 - 7.08470i) q^{21} +(5.18276 - 0.453432i) q^{22} +(0.472247 - 1.01274i) q^{23} +(0.739450 - 1.56627i) q^{24} +(3.60237 - 3.46741i) q^{25} -0.375881i q^{26} +(2.66198 - 4.46249i) q^{27} +(2.99057 + 2.99057i) q^{28} +(1.75816 + 9.97103i) q^{29} +(-3.55661 - 1.53313i) q^{30} +(-3.35678 + 1.22177i) q^{31} +(0.0871557 + 0.996195i) q^{32} +(-7.82516 + 4.46840i) q^{33} +(-2.08941 + 5.74062i) q^{34} +(6.45532 - 6.91115i) q^{35} +(-0.0285197 + 2.99986i) q^{36} +(-1.51118 - 5.63980i) q^{37} +(0.295084 - 3.37283i) q^{38} +(0.272336 + 0.591349i) q^{39} +(2.21962 - 0.270694i) q^{40} +(4.77146 + 0.841337i) q^{41} +(-6.87161 - 2.53812i) q^{42} +(6.52010 + 0.570435i) q^{43} +(2.60128 - 4.50554i) q^{44} +(6.70618 - 0.164889i) q^{45} +(-0.558716 - 0.967725i) q^{46} +(3.10175 + 6.65173i) q^{47} +(-0.858886 - 1.50410i) q^{48} +(6.99804 - 8.33994i) q^{49} +(-0.774099 - 4.93971i) q^{50} +(-0.872094 - 10.5452i) q^{51} +(-0.307904 - 0.215597i) q^{52} +(-6.39299 + 6.39299i) q^{53} +(-2.12861 - 4.74015i) q^{54} +(-10.2671 - 5.46988i) q^{55} +(4.16505 - 0.734411i) q^{56} +(1.97947 + 5.52004i) q^{57} +(9.17623 + 4.27895i) q^{58} +(-2.30891 - 1.93741i) q^{59} +(-3.29586 + 2.03404i) q^{60} +(-7.18421 - 2.61484i) q^{61} +(-0.924557 + 3.45049i) q^{62} +(12.6496 - 0.985615i) q^{63} +(0.866025 + 0.500000i) q^{64} +(-0.458343 + 0.704525i) q^{65} +(-0.828029 + 8.97296i) q^{66} +(-0.139953 - 0.199873i) q^{67} +(3.50400 + 5.00423i) q^{68} +(1.58013 + 1.11765i) q^{69} +(-1.95866 - 9.25196i) q^{70} +(0.0530319 + 0.0306180i) q^{71} +(2.44099 + 1.74401i) q^{72} +(-1.71131 + 6.38669i) q^{73} +(-5.48663 - 1.99697i) q^{74} +(4.79679 + 7.21046i) q^{75} +(-2.59360 - 2.17629i) q^{76} +(-19.9417 - 9.29895i) q^{77} +(0.640610 + 0.116099i) q^{78} +(5.15835 - 0.909556i) q^{79} +(1.05138 - 1.97347i) q^{80} +(6.78317 + 5.91512i) q^{81} +(3.42598 - 3.42598i) q^{82} +(-3.91233 - 2.73944i) q^{83} +(-6.02050 + 4.17309i) q^{84} +(10.9163 - 8.21201i) q^{85} +(4.20705 - 5.01377i) q^{86} +(-17.5366 - 0.0833582i) q^{87} +(-2.19869 - 4.71511i) q^{88} +(-4.63875 - 8.03454i) q^{89} +(3.71144 - 5.58795i) q^{90} +(-0.794859 + 1.37674i) q^{91} +(-1.11318 - 0.0973907i) q^{92} +(-1.04543 - 6.09830i) q^{93} +(7.22787 + 1.27447i) q^{94} +(-4.66585 + 5.96196i) q^{95} +(-1.72472 - 0.159158i) q^{96} +(-1.36492 + 15.6011i) q^{97} +(-2.81777 - 10.5161i) q^{98} +(-5.19847 - 14.7165i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q + 12 q^{6} + 24 q^{11} - 24 q^{20} + 24 q^{23} + 36 q^{25} + 12 q^{27} - 72 q^{30} - 12 q^{33} - 108 q^{35} - 12 q^{36} - 36 q^{38} - 72 q^{41} - 48 q^{42} - 60 q^{45} - 48 q^{47} - 12 q^{48} - 48 q^{50}+ \cdots - 72 q^{97}+O(q^{100}) $ 216 * q + 12 * q^6 + 24 * q^11 - 24 * q^20 + 24 * q^23 + 36 * q^25 + 12 * q^27 - 72 * q^30 - 12 * q^33 - 108 * q^35 - 12 * q^36 - 36 * q^38 - 72 * q^41 - 48 * q^42 - 60 * q^45 - 48 * q^47 - 12 * q^48 - 48 * q^50 - 192 * q^51 - 12 * q^56 - 36 * q^57 + 36 * q^61 + 84 * q^63 + 24 * q^65 - 72 * q^67 + 36 * q^68 - 48 * q^72 - 36 * q^75 - 240 * q^77 + 24 * q^78 - 24 * q^81 - 60 * q^83 + 72 * q^86 - 252 * q^87 - 48 * q^92 - 96 * q^93 - 60 * q^95 - 72 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/270\mathbb{Z}\right)^\times$.

$n$	$191$	$217$
$\chi(n)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.573576	−	0.819152i	0.405580	−	0.579228i
$2$	0.573576	−	0.819152i	0.405580	−	0.579228i
$3$	−0.308872	+	1.70429i	−0.178327	+	0.983971i
$3$	−0.308872	+	1.70429i	−0.178327	+	0.983971i
$4$	−0.342020	−	0.939693i	−0.171010	−	0.469846i
$5$	−2.07393	+	0.835951i	−0.927490	+	0.373849i
$5$	−2.07393	+	0.835951i	−0.927490	+	0.373849i
$6$	1.21891	+	1.23055i	0.497618	+	0.502371i
$7$	−3.83305	+	1.78738i	−1.44876	+	0.675567i	−0.978364	−	0.206890i	$-0.933666\pi$
$7$	−3.83305	+	1.78738i	−1.44876	+	0.675567i	−0.470393	+	0.882457i	$0.655888\pi$
$8$	−0.965926	−	0.258819i	−0.341506	−	0.0915064i
$9$	−2.80920	−	1.05281i	−0.936399	−	0.350938i
$10$	−0.504786	+	2.17835i	−0.159627	+	0.688853i
$11$	3.34414	+	3.98539i	1.00830	+	1.20164i	0.979374	+	0.202058i	$0.0647629\pi$
$11$	3.34414	+	3.98539i	1.00830	+	1.20164i	0.0289216	+	0.999582i	$0.490793\pi$
$12$	1.70715	−	0.292656i	0.492811	−	0.0844825i
$13$	0.307904	−	0.215597i	0.0853972	−	0.0597958i	−0.530098	−	0.847936i	$-0.677845\pi$
$13$	0.307904	−	0.215597i	0.0853972	−	0.0597958i	0.615495	+	0.788141i	$0.288956\pi$
$14$	−0.734411	+	4.16505i	−0.196280	+	1.11316i
$15$	−0.784123	−	3.79278i	−0.202460	−	0.979291i
$16$	−0.766044	+	0.642788i	−0.191511	+	0.160697i
$17$	−5.90088	+	1.58114i	−1.43117	+	0.383482i	−0.889433	−	0.457065i	$-0.848901\pi$
$17$	−5.90088	+	1.58114i	−1.43117	+	0.383482i	−0.541739	+	0.840546i	$0.682234\pi$
$18$	−2.47370	+	1.69729i	−0.583057	+	0.400055i
$19$	2.93211	−	1.69286i	0.672672	−	0.388368i	−0.124416	−	0.992230i	$-0.539706\pi$
$19$	2.93211	−	1.69286i	0.672672	−	0.388368i	0.797088	+	0.603863i	$0.206372\pi$
$20$	1.49486	+	1.66294i	0.334262	+	0.371846i
$21$	−1.86229	−	7.08470i	−0.406385	−	1.54601i
$22$	5.18276	−	0.453432i	1.10497	−	0.0966721i
$23$	0.472247	−	1.01274i	0.0984704	−	0.211170i	−0.850901	−	0.525326i	$-0.823943\pi$
$23$	0.472247	−	1.01274i	0.0984704	−	0.211170i	0.949372	+	0.314155i	$0.101721\pi$
$24$	0.739450	−	1.56627i	0.150940	−	0.319714i
$25$	3.60237	−	3.46741i	0.720474	−	0.693482i
$26$		−	0.375881i		−	0.0737164i
$27$	2.66198	−	4.46249i	0.512298	−	0.858808i
$28$	2.99057	+	2.99057i	0.565165	+	0.565165i
$29$	1.75816	+	9.97103i	0.326483	+	1.85157i	0.499045	+	0.866576i	$0.333684\pi$
$29$	1.75816	+	9.97103i	0.326483	+	1.85157i	−0.172563	+	0.984999i	$0.555205\pi$
$30$	−3.55661	−	1.53313i	−0.649346	−	0.279910i
$31$	−3.35678	+	1.22177i	−0.602896	+	0.219436i	−0.625392	−	0.780311i	$-0.715061\pi$
$31$	−3.35678	+	1.22177i	−0.602896	+	0.219436i	0.0224959	+	0.999747i	$0.492839\pi$
$32$	0.0871557	+	0.996195i	0.0154071	+	0.176104i
$33$	−7.82516	+	4.46840i	−1.36219	+	0.777848i
$34$	−2.08941	+	5.74062i	−0.358331	+	0.984508i
$35$	6.45532	−	6.91115i	1.09115	−	1.16820i
$36$	−0.0285197	+	2.99986i	−0.00475329	+	0.499977i
$37$	−1.51118	−	5.63980i	−0.248436	−	0.927178i	−0.971625	−	0.236527i	$-0.923991\pi$
$37$	−1.51118	−	5.63980i	−0.248436	−	0.927178i	0.723188	−	0.690651i	$-0.242676\pi$
$38$	0.295084	−	3.37283i	0.0478690	−	0.547145i
$39$	0.272336	+	0.591349i	0.0436087	+	0.0946916i
$40$	2.21962	−	0.270694i	0.350953	−	0.0428005i
$41$	4.77146	+	0.841337i	0.745177	+	0.131395i	0.533329	−	0.845908i	$-0.320941\pi$
$41$	4.77146	+	0.841337i	0.745177	+	0.131395i	0.211848	+	0.977303i	$0.432052\pi$
$42$	−6.87161	−	2.53812i	−1.06031	−	0.391640i
$43$	6.52010	+	0.570435i	0.994306	+	0.0869905i	0.572680	−	0.819779i	$-0.305904\pi$
$43$	6.52010	+	0.570435i	0.994306	+	0.0869905i	0.421626	+	0.906770i	$0.361459\pi$
$44$	2.60128	−	4.50554i	0.392157	−	0.679236i
$45$	6.70618	−	0.164889i	0.999698	−	0.0245801i
$46$	−0.558716	−	0.967725i	−0.0823782	−	0.142683i
$47$	3.10175	+	6.65173i	0.452437	+	0.970254i	0.991755	+	0.128152i	$0.0409044\pi$
$47$	3.10175	+	6.65173i	0.452437	+	0.970254i	−0.539318	+	0.842102i	$0.681318\pi$
$48$	−0.858886	−	1.50410i	−0.123969	−	0.217098i
$49$	6.99804	−	8.33994i	0.999721	−	1.19142i
$50$	−0.774099	−	4.93971i	−0.109474	−	0.698581i
$51$	−0.872094	−	10.5452i	−0.122118	−	1.47662i
$52$	−0.307904	−	0.215597i	−0.0426986	−	0.0298979i
$53$	−6.39299	+	6.39299i	−0.878144	+	0.878144i	−0.993343	−	0.115198i	$-0.963250\pi$
$53$	−6.39299	+	6.39299i	−0.878144	+	0.878144i	0.115198	+	0.993343i	$0.463250\pi$
$54$	−2.12861	−	4.74015i	−0.289668	−	0.645053i
$55$	−10.2671	−	5.46988i	−1.38441	−	0.737558i
$56$	4.16505	−	0.734411i	0.556579	−	0.0981398i
$57$	1.97947	+	5.52004i	0.262187	+	0.731147i
$58$	9.17623	+	4.27895i	1.20490	+	0.561853i
$59$	−2.30891	−	1.93741i	−0.300595	−	0.252229i	0.479997	−	0.877270i	$-0.340638\pi$
$59$	−2.30891	−	1.93741i	−0.300595	−	0.252229i	−0.780592	+	0.625041i	$0.785082\pi$
$60$	−3.29586	+	2.03404i	−0.425493	+	0.262593i
$61$	−7.18421	−	2.61484i	−0.919844	−	0.334796i	−0.161668	−	0.986845i	$-0.551687\pi$
$61$	−7.18421	−	2.61484i	−0.919844	−	0.334796i	−0.758176	+	0.652049i	$0.773909\pi$
$62$	−0.924557	+	3.45049i	−0.117419	+	0.438213i
$63$	12.6496	−	0.985615i	1.59370	−	0.124176i
$64$	0.866025	+	0.500000i	0.108253	+	0.0625000i
$65$	−0.458343	+	0.704525i	−0.0568505	+	0.0873856i
$66$	−0.828029	+	8.97296i	−0.101923	+	1.10450i
$67$	−0.139953	−	0.199873i	−0.0170979	−	0.0244184i	0.810512	−	0.585722i	$-0.199189\pi$
$67$	−0.139953	−	0.199873i	−0.0170979	−	0.0244184i	−0.827610	+	0.561304i	$0.810300\pi$
$68$	3.50400	+	5.00423i	0.424922	+	0.606852i
$69$	1.58013	+	1.11765i	0.190226	+	0.134549i
$70$	−1.95866	−	9.25196i	−0.234105	−	1.10582i
$71$	0.0530319	+	0.0306180i	0.00629373	+	0.00363369i	0.503144	−	0.864203i	$-0.332177\pi$
$71$	0.0530319	+	0.0306180i	0.00629373	+	0.00363369i	−0.496850	+	0.867837i	$0.665510\pi$
$72$	2.44099	+	1.74401i	0.287673	+	0.205534i
$73$	−1.71131	+	6.38669i	−0.200294	+	0.747506i	0.790539	+	0.612412i	$0.209800\pi$
$73$	−1.71131	+	6.38669i	−0.200294	+	0.747506i	−0.990833	+	0.135094i	$0.956866\pi$
$74$	−5.48663	−	1.99697i	−0.637808	−	0.232143i
$75$	4.79679	+	7.21046i	0.553886	+	0.832593i
$76$	−2.59360	−	2.17629i	−0.297507	−	0.249638i
$77$	−19.9417	−	9.29895i	−2.27256	−	1.05971i
$78$	0.640610	+	0.116099i	0.0725348	+	0.0131457i
$79$	5.15835	−	0.909556i	0.580360	−	0.102333i	0.124241	−	0.992252i	$-0.460350\pi$
$79$	5.15835	−	0.909556i	0.580360	−	0.102333i	0.456119	+	0.889919i	$0.349239\pi$
$80$	1.05138	−	1.97347i	0.117548	−	0.220641i
$81$	6.78317	+	5.91512i	0.753685	+	0.657236i
$82$	3.42598	−	3.42598i	0.378336	−	0.378336i
$83$	−3.91233	−	2.73944i	−0.429434	−	0.300693i	0.338804	−	0.940857i	$-0.389978\pi$
$83$	−3.91233	−	2.73944i	−0.429434	−	0.300693i	−0.768238	+	0.640164i	$0.778866\pi$
$84$	−6.02050	+	4.17309i	−0.656890	+	0.455321i
$85$	10.9163	−	8.21201i	1.18403	−	0.890717i
$86$	4.20705	−	5.01377i	0.453658	−	0.540648i
$87$	−17.5366	−	0.0833582i	−1.88012	−	0.00893694i
$88$	−2.19869	−	4.71511i	−0.234382	−	0.502633i
$89$	−4.63875	−	8.03454i	−0.491706	−	0.851660i	0.508248	−	0.861211i	$-0.330293\pi$
$89$	−4.63875	−	8.03454i	−0.491706	−	0.851660i	−0.999954	+	0.00955058i	$0.996960\pi$
$90$	3.71144	−	5.58795i	0.391220	−	0.589022i
$91$	−0.794859	+	1.37674i	−0.0833238	+	0.144321i
$92$	−1.11318	−	0.0973907i	−0.116057	−	0.0101537i
$93$	−1.04543	−	6.09830i	−0.108406	−	0.632364i
$94$	7.22787	+	1.27447i	0.745497	+	0.131451i
$95$	−4.66585	+	5.96196i	−0.478706	+	0.611685i
$96$	−1.72472	−	0.159158i	−0.176029	−	0.0162440i
$97$	−1.36492	+	15.6011i	−0.138587	+	1.58405i	0.534940	+	0.844890i	$0.320334\pi$
$97$	−1.36492	+	15.6011i	−0.138587	+	1.58405i	−0.673527	+	0.739163i	$0.735221\pi$
$98$	−2.81777	−	10.5161i	−0.284638	−	1.06228i
$99$	−5.19847	−	14.7165i	−0.522465	−	1.47906i
$100$	−4.49038	−	2.19920i	−0.449038	−	0.219920i
$101$	−3.00976	+	8.26924i	−0.299482	+	0.822820i	0.695104	+	0.718909i	$0.255358\pi$
$101$	−3.00976	+	8.26924i	−0.299482	+	0.822820i	−0.994587	+	0.103912i	$0.966864\pi$
$102$	−9.13830	−	5.33408i	−0.904827	−	0.528152i
$103$	−0.000152761	−	0.00174607i	−1.50520e−5	−	0.000172045i	0.996187	−	0.0872418i	$-0.0278053\pi$
$103$	−0.000152761	−	0.00174607i	−1.50520e−5	−	0.000172045i	−0.996202	+	0.0870697i	$0.972250\pi$
$104$	−0.353213	+	0.128559i	−0.0346354	+	0.0126062i
$105$	9.78472	+	13.1364i	0.954891	+	1.28198i
$106$	1.56996	+	8.90369i	0.152488	+	0.864803i
$107$	7.92458	+	7.92458i	0.766098	+	0.766098i	0.977417	−	0.211319i	$-0.0677759\pi$
$107$	7.92458	+	7.92458i	0.766098	+	0.766098i	−0.211319	+	0.977417i	$0.567776\pi$
$108$	−5.10382	−	0.975180i	−0.491116	−	0.0938367i
$109$		−	2.21477i		−	0.212137i	−0.994359	−	0.106068i	$-0.966174\pi$
$109$		−	2.21477i		−	0.212137i	0.994359	−	0.106068i	$-0.0338262\pi$
$110$	−10.3696	+	5.27292i	−0.988705	+	0.502753i
$111$	10.0786	−	0.833510i	0.956619	−	0.0791132i
$112$	1.78738	−	3.83305i	0.168892	−	0.362189i
$113$	1.25379	−	0.109693i	0.117947	−	0.0103190i	−0.0280294	−	0.999607i	$-0.508923\pi$
$113$	1.25379	−	0.109693i	0.117947	−	0.0103190i	0.145976	+	0.989288i	$0.453368\pi$
$114$	5.65713	+	1.54468i	0.529838	+	0.144673i
$115$	−0.132809	+	2.49512i	−0.0123845	+	0.232671i
$116$	8.76838	−	5.06243i	0.814124	−	0.470034i
$117$	−1.09195	+	0.281488i	−0.100950	+	0.0260236i
$118$	−2.91137	+	0.780099i	−0.268013	+	0.0718139i
$119$	19.7923	−	16.6077i	1.81435	−	1.52242i
$120$	−0.224238	+	3.86649i	−0.0204701	+	0.352960i
$121$	−2.78993	+	15.8225i	−0.253630	+	1.43841i
$122$	−6.26265	+	4.38515i	−0.566993	+	0.397013i
$123$	−2.90765	+	7.87208i	−0.262174	+	0.709801i
$124$	2.29618	+	2.73648i	0.206203	+	0.245743i
$125$	−4.57248	+	10.2026i	−0.408975	+	0.912545i
$126$	6.44813	−	10.9273i	0.574445	−	0.973477i
$127$	7.23174	+	1.93774i	0.641713	+	0.171947i	0.564979	−	0.825105i	$-0.308884\pi$
$127$	7.23174	+	1.93774i	0.641713	+	0.171947i	0.0767340	+	0.997052i	$0.475551\pi$
$128$	0.906308	−	0.422618i	0.0801070	−	0.0373545i
$129$	−2.98606	+	10.9359i	−0.262908	+	0.962856i
$130$	0.314218	+	0.779552i	0.0275588	+	0.0683712i
$131$	4.22294	+	11.6024i	0.368960	+	1.01371i	0.975758	+	0.218853i	$0.0702317\pi$
$131$	4.22294	+	11.6024i	0.368960	+	1.01371i	−0.606797	+	0.794856i	$0.707546\pi$
$132$	6.87528	+	5.82496i	0.598417	+	0.506998i
$133$	−8.21316	+	11.7296i	−0.712171	+	1.01709i
$134$	−0.244000			−0.0210784
$135$	−1.79033	+	11.4802i	−0.154087	+	0.988057i
$136$	6.10904			0.523846
$137$	7.28471	−	10.4036i	0.622374	−	0.888843i	−0.376926	−	0.926243i	$-0.623019\pi$
$137$	7.28471	−	10.4036i	0.622374	−	0.888843i	0.999300	+	0.0374006i	$0.0119078\pi$
$138$	1.82185	−	0.653310i	0.155087	−	0.0556135i
$139$	−1.49351	−	4.10338i	−0.126678	−	0.348045i	0.860099	−	0.510126i	$-0.170401\pi$
$139$	−1.49351	−	4.10338i	−0.126678	−	0.348045i	−0.986777	+	0.162082i	$0.948179\pi$
$140$	−8.70220	−	3.70226i	−0.735471	−	0.312898i
$141$	−12.2945	+	3.23175i	−1.03538	+	0.272162i
$142$	0.0554986	−	0.0258794i	0.00465734	−	0.00217175i
$143$	1.88891	+	0.506132i	0.157959	+	0.0423249i
$144$	2.82870	−	0.999214i	0.235725	−	0.0832679i
$145$	−11.9816	−	19.2095i	−0.995018	−	1.59526i
$146$	4.25011	+	5.06508i	0.351741	+	0.419189i
$147$	12.0522	+	14.5027i	0.994046	+	1.19616i
$148$	−4.78283	+	3.34897i	−0.393146	+	0.275284i
$149$	−0.130359	+	0.739301i	−0.0106794	+	0.0605659i	−0.989682	−	0.143283i	$-0.954234\pi$
$149$	−0.130359	+	0.739301i	−0.0106794	+	0.0605659i	0.979002	+	0.203849i	$0.0653452\pi$
$150$	8.65779	+	0.206451i	0.706906	+	0.0168567i
$151$	1.91410	−	1.60612i	0.155767	−	0.130704i	−0.561573	−	0.827427i	$-0.689804\pi$
$151$	1.91410	−	1.60612i	0.155767	−	0.130704i	0.717340	+	0.696723i	$0.245359\pi$
$152$	−3.27034	+	0.876286i	−0.265260	+	0.0710762i
$153$	18.2414	+	1.77081i	1.47473	+	0.143161i
$154$	−19.0553	+	11.0016i	−1.53552	+	0.886534i
$155$	5.94040	−	5.33997i	0.477144	−	0.428917i
$156$	0.462542	−	0.458165i	0.0370330	−	0.0366826i
$157$	−6.79890	+	0.594827i	−0.542611	+	0.0474723i	−0.355167	−	0.934803i	$-0.615576\pi$
$157$	−6.79890	+	0.594827i	−0.542611	+	0.0474723i	−0.187444	+	0.982275i	$0.560020\pi$
$158$	2.21364	−	4.74717i	0.176108	−	0.377665i
$159$	−8.92088	−	12.8701i	−0.707471	−	1.02067i
$160$	−1.01353	−	1.99318i	−0.0801262	−	0.157575i
$161$			4.72596i			0.372458i
$162$	8.73605	−	2.16367i	0.686369	−	0.169994i
$163$	−0.670477	−	0.670477i	−0.0525158	−	0.0525158i	0.680361	−	0.732877i	$-0.261823\pi$
$163$	−0.670477	−	0.670477i	−0.0525158	−	0.0525158i	−0.732877	+	0.680361i	$0.761823\pi$
$164$	−0.841337	−	4.77146i	−0.0656974	−	0.372588i
$165$	12.4935	−	15.8086i	0.972615	−	1.23070i
$166$	−4.48804	+	1.63351i	−0.348340	+	0.126785i
$167$	0.437147	+	4.99662i	0.0338275	+	0.386650i	0.994170	+	0.107826i	$0.0343890\pi$
$167$	0.437147	+	4.99662i	0.0338275	+	0.386650i	−0.960342	+	0.278824i	$0.910055\pi$
$168$	−0.0348200	+	7.32529i	−0.00268642	+	0.565158i
$169$	−4.39794	+	12.0832i	−0.338303	+	0.929480i
$170$	−0.465578	−	13.6523i	−0.0357082	−	1.04708i
$171$	−10.0191	+	1.66859i	−0.766183	+	0.127601i
$172$	−1.69397	−	6.32199i	−0.129164	−	0.482047i
$173$	−0.494717	+	5.65464i	−0.0376127	+	0.429915i	0.953920	+	0.300060i	$0.0970067\pi$
$173$	−0.494717	+	5.65464i	−0.0376127	+	0.429915i	−0.991533	+	0.129855i	$0.958549\pi$
$174$	−10.1268	+	14.3173i	−0.767714	+	1.08539i
$175$	−7.61050	+	19.7296i	−0.575299	+	1.49142i
$176$	−5.12351	−	0.903414i	−0.386199	−	0.0680974i
$177$	4.01506	−	3.33664i	0.301790	−	0.250797i
$178$	−9.24219	−	0.808587i	−0.692731	−	0.0606061i
$179$	7.12420	−	12.3395i	0.532488	−	0.922296i	−0.466793	−	0.884367i	$-0.654591\pi$
$179$	7.12420	−	12.3395i	0.532488	−	0.922296i	0.999280	−	0.0379289i	$-0.0120760\pi$
$180$	−2.44859	−	6.24535i	−0.182507	−	0.465501i
$181$	−6.55430	−	11.3524i	−0.487177	−	0.843816i	0.512714	−	0.858559i	$-0.328640\pi$
$181$	−6.55430	−	11.3524i	−0.487177	−	0.843816i	−0.999891	+	0.0147438i	$0.995307\pi$
$182$	0.671843	+	1.44077i	0.0498004	+	0.106797i
$183$	6.67544	−	11.4363i	0.493463	−	0.845397i
$184$	−0.718272	+	0.856003i	−0.0529517	+	0.0631054i
$185$	7.84868	+	10.4333i	0.577046	+	0.767070i
$186$	−5.59507	−	2.64147i	−0.410250	−	0.193682i
$187$	−26.0348	−	18.2297i	−1.90385	−	1.33309i
$188$	5.18972	−	5.18972i	0.378499	−	0.378499i
$189$	−2.22733	+	21.8630i	−0.162014	+	1.59030i
$190$	2.20753	+	7.24168i	0.160151	+	0.525367i
$191$	1.41468	−	0.249446i	0.102363	−	0.0180493i	−0.122232	−	0.992502i	$-0.539005\pi$
$191$	1.41468	−	0.249446i	0.102363	−	0.0180493i	0.224595	+	0.974452i	$0.427894\pi$
$192$	−1.11964	+	1.32152i	−0.0808027	+	0.0953725i
$193$	17.8178	+	8.30860i	1.28256	+	0.598066i	0.939918	−	0.341401i	$-0.110902\pi$
$193$	17.8178	+	8.30860i	1.28256	+	0.598066i	0.342639	+	0.939467i	$0.388679\pi$
$194$	11.9968	+	10.0665i	0.861320	+	0.722733i
$195$	−1.05914	−	0.998757i	−0.0758469	−	0.0715225i
$196$	−10.2305	−	3.72358i	−0.730747	−	0.265970i
$197$	5.11551	−	19.0913i	0.364465	−	1.36020i	−0.503680	−	0.863890i	$-0.668021\pi$
$197$	5.11551	−	19.0913i	0.364465	−	1.36020i	0.868145	−	0.496311i	$-0.165312\pi$
$198$	−15.0368	−	4.18270i	−1.06862	−	0.297251i
$199$	6.74271	+	3.89290i	0.477978	+	0.275961i	0.719573	−	0.694416i	$-0.244337\pi$
$199$	6.74271	+	3.89290i	0.477978	+	0.275961i	−0.241596	+	0.970377i	$0.577671\pi$
$200$	−4.37705	+	2.41690i	−0.309505	+	0.170900i
$201$	0.383868	−	0.176784i	0.0270760	−	0.0124694i
$202$	5.04744	+	7.20849i	0.355137	+	0.507188i
$203$	−24.5612	−	35.0770i	−1.72386	−	2.46192i
$204$	−9.61094	+	4.42616i	−0.672900	+	0.309893i
$205$	−10.5990	+	2.24383i	−0.740265	+	0.156716i
$206$	−0.00151792		0.000876370i	−0.000105758		6.10596e-5i
$207$	−2.39286	+	2.34779i	−0.166315	+	0.163183i
$208$	−0.0972853	+	0.363074i	−0.00674552	+	0.0251746i
$209$	16.5521	+	6.02446i	1.14493	+	0.416721i
$210$	16.3730	−	0.480455i	1.12984	−	0.0331546i
$211$	0.399400	+	0.335137i	0.0274959	+	0.0230718i	0.656432	−	0.754385i	$-0.272065\pi$
$211$	0.399400	+	0.335137i	0.0274959	+	0.0230718i	−0.628936	+	0.777457i	$0.716509\pi$
$212$	8.19397	+	3.82091i	0.562764	+	0.262421i
$213$	−0.0685619	+	0.0809246i	−0.00469779	+	0.00554486i
$214$	11.0368	−	1.94608i	0.754459	−	0.133032i
$215$	−13.9991	+	4.26745i	−0.954730	+	0.291037i
$216$	−3.72625	+	3.62147i	−0.253539	+	0.246410i
$217$	10.6830	−	10.6830i	0.725207	−	0.725207i
$218$	−1.81424	−	1.27034i	−0.122876	−	0.0860384i
$219$	−10.3562	−	4.88924i	−0.699807	−	0.330384i
$220$	−1.62845	+	11.5187i	−0.109790	+	0.776592i
$221$	−1.47602	+	1.75905i	−0.0992876	+	0.118326i
$222$	5.09808	−	8.73399i	0.342161	−	0.586187i
$223$	3.66422	+	7.85795i	0.245375	+	0.526208i	0.989965	−	0.141314i	$-0.0451328\pi$
$223$	3.66422	+	7.85795i	0.245375	+	0.526208i	−0.744590	+	0.667522i	$0.767355\pi$
$224$	−2.11465	−	3.66269i	−0.141291	−	0.244723i
$225$	−13.7703	+	5.94800i	−0.918020	+	0.396534i
$226$	0.629291	−	1.08996i	0.0418598	−	0.0725033i
$227$	−6.18305	−	0.540947i	−0.410383	−	0.0359039i	−0.119905	−	0.992785i	$-0.538259\pi$
$227$	−6.18305	−	0.540947i	−0.410383	−	0.0359039i	−0.290479	+	0.956882i	$0.593814\pi$
$228$	4.51012	−	3.74805i	0.298690	−	0.248221i
$229$	−23.6091	−	4.16292i	−1.56013	−	0.275093i	−0.674073	−	0.738665i	$-0.735457\pi$
$229$	−23.6091	−	4.16292i	−1.56013	−	0.275093i	−0.886060	+	0.463571i	$0.846568\pi$
$230$	1.96771	+	1.53993i	0.129747	+	0.101540i
$231$	22.0075	−	31.1141i	1.44799	−	2.04716i
$232$	0.882439	−	10.0863i	0.0579350	−	0.662200i
$233$	−3.02370	−	11.2846i	−0.198089	−	0.739278i	−0.991446	−	0.130521i	$-0.958335\pi$
$233$	−3.02370	−	11.2846i	−0.198089	−	0.739278i	0.793357	−	0.608757i	$-0.208332\pi$
$234$	−0.395733	+	1.05592i	−0.0258699	+	0.0690279i
$235$	−11.9933	−	11.2023i	−0.782359	−	0.730758i
$236$	−1.03087	+	2.83230i	−0.0671041	+	0.184367i
$237$	−0.0431240	+	9.07225i	−0.00280120	+	0.589306i
$238$	−2.25184	−	25.7387i	−0.145965	−	1.66839i
$239$	−17.3288	+	6.30716i	−1.12091	+	0.407976i	−0.834983	−	0.550276i	$-0.814522\pi$
$239$	−17.3288	+	6.30716i	−1.12091	+	0.407976i	−0.285923	+	0.958253i	$0.592300\pi$
$240$	3.03862	+	2.40141i	0.196142	+	0.155010i
$241$	0.864030	+	4.90016i	0.0556571	+	0.315647i	0.999908	−	0.0135803i	$-0.00432289\pi$
$241$	0.864030	+	4.90016i	0.0556571	+	0.315647i	−0.944251	+	0.329227i	$0.893212\pi$
$242$	11.3608	+	11.3608i	0.730298	+	0.730298i
$243$	−12.1762	+	9.73345i	−0.781104	+	0.624401i
$244$			7.64528i			0.489439i
$245$	−7.54167	+	23.1465i	−0.481819	+	1.47877i
$246$	4.78067	+	6.89704i	0.304804	+	0.439740i
$247$	0.537835	−	1.15339i	0.0342216	−	0.0733885i
$248$	3.55862	−	0.311339i	0.225973	−	0.0197700i
$249$	5.87721	−	5.82160i	0.372453	−	0.368929i
$250$	5.73479	+	9.59751i	0.362700	+	0.607000i
$251$	11.3319	−	6.54248i	0.715264	−	0.412958i	−0.0977433	−	0.995212i	$-0.531162\pi$
$251$	11.3319	−	6.54248i	0.715264	−	0.412958i	0.813007	+	0.582254i	$0.197829\pi$
$252$	−5.25259	−	11.5496i	−0.330882	−	0.727557i
$253$	5.61541	−	1.50465i	0.353038	−	0.0945962i
$254$	5.73526	−	4.81246i	0.359862	−	0.301960i
$255$	10.6239	+	21.1409i	0.665295	+	1.32389i
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	1.65673	−	1.16005i	0.103344	−	0.0723622i	−0.520762	−	0.853702i	$-0.674352\pi$
$257$	1.65673	−	1.16005i	0.103344	−	0.0723622i	0.624106	+	0.781340i	$0.285463\pi$
$258$	7.24546	+	8.71864i	0.451083	+	0.542799i
$259$	15.8729	+	18.9166i	0.986295	+	1.17542i
$260$	0.818800	+	0.189740i	0.0507798	+	0.0117672i
$261$	5.55862	−	29.8616i	0.344070	−	1.84839i
$262$	11.9263	+	3.19565i	0.736812	+	0.197428i
$263$	10.1370	−	4.72696i	0.625074	−	0.291477i	−0.0841574	−	0.996452i	$-0.526820\pi$
$263$	10.1370	−	4.72696i	0.625074	−	0.291477i	0.709232	+	0.704976i	$0.249042\pi$
$264$	8.71503	−	2.29084i	0.536373	−	0.140992i
$265$	7.91438	−	18.6028i	0.486177	−	1.14276i
$266$	4.89746	+	13.4556i	0.300282	+	0.825019i
$267$	15.1260	−	5.42411i	0.925694	−	0.331950i
$268$	−0.139953	+	0.199873i	−0.00854896	+	0.0122092i
$269$	9.40361			0.573348			0.286674	−	0.958028i	$-0.407450\pi$
$269$	9.40361			0.573348			0.286674	+	0.958028i	$0.407450\pi$
$270$	8.37713	+	8.05132i	0.509816	+	0.489988i
$271$	−1.37745			−0.0836741			−0.0418370	−	0.999124i	$-0.513321\pi$
$271$	−1.37745			−0.0836741			−0.0418370	+	0.999124i	$0.513321\pi$
$272$	3.50400	−	5.00423i	0.212461	−	0.303426i
$273$	−2.10084	−	1.77990i	−0.127149	−	0.107725i
$274$	−4.34383	−	11.9346i	−0.262420	−	0.720993i
$275$	25.8658	+	2.76136i	1.55977	+	0.166516i
$276$	0.509812	−	1.86710i	0.0306871	−	0.112386i
$277$	26.2073	−	12.2207i	1.57465	−	0.734269i	0.577994	−	0.816041i	$-0.303836\pi$
$277$	26.2073	−	12.2207i	1.57465	−	0.734269i	0.996651	+	0.0817715i	$0.0260578\pi$
$278$	−4.21794	−	1.13019i	−0.252975	−	0.0677845i
$279$	10.7162	+	0.101879i	0.641560	+	0.00609931i
$280$	−8.02410	+	5.00490i	−0.479531	+	0.299100i
$281$	−20.9375	−	24.9523i	−1.24903	−	1.48853i	−0.805875	−	0.592085i	$-0.798305\pi$
$281$	−20.9375	−	24.9523i	−1.24903	−	1.48853i	−0.443151	−	0.896447i	$-0.646140\pi$
$282$	−4.40455	+	11.9247i	−0.262287	+	0.710107i
$283$	21.4778	−	15.0389i	1.27672	−	0.893970i	0.278924	−	0.960313i	$-0.410022\pi$
$283$	21.4778	−	15.0389i	1.27672	−	0.893970i	0.997797	+	0.0663434i	$0.0211333\pi$
$284$	0.0106335	−	0.0603057i	0.000630983	−	0.00357848i
$285$	−8.71976	−	9.79344i	−0.516514	−	0.580113i
$286$	1.49803	−	1.25700i	0.0885805	−	0.0743279i
$287$	−19.7930	+	5.30353i	−1.16835	+	0.313057i
$288$	0.803970	−	2.89027i	0.0473744	−	0.170311i
$289$	17.5979	−	10.1602i	1.03517	−	0.597657i
$290$	−22.6079	−	1.20336i	−1.32758	−	0.0706635i
$291$	−26.1672	−	7.14497i	−1.53395	−	0.418845i
$292$	6.58683	−	0.576273i	0.385465	−	0.0337238i
$293$	9.83988	−	21.1017i	0.574852	−	1.23277i	−0.376999	−	0.926214i	$-0.623044\pi$
$293$	9.83988	−	21.1017i	0.574852	−	1.23277i	0.951851	−	0.306561i	$-0.0991782\pi$
$294$	18.7927	−	1.55417i	1.09601	−	0.0906413i
$295$	6.40810	+	2.08791i	0.373094	+	0.121563i
$296$			5.83875i			0.339371i
$297$	26.6868	−	4.31417i	1.54852	−	0.250334i
$298$	0.530829	+	0.530829i	0.0307501	+	0.0307501i
$299$	−0.0729361	−	0.413641i	−0.00421800	−	0.0239215i
$300$	5.13502	−	6.97363i	0.296471	−	0.402623i
$301$	−26.0115	+	9.46740i	−1.49928	+	0.545692i
$302$	−0.217774	−	2.48917i	−0.0125315	−	0.143235i
$303$	−13.1635	−	7.68363i	−0.756226	−	0.441413i
$304$	−1.15798	+	3.18153i	−0.0664148	+	0.182473i
$305$	17.0854	−	0.582657i	0.978309	−	0.0333628i
$306$	11.9134	−	13.9268i	0.681042	−	0.796140i
$307$	3.78873	+	14.1397i	0.216234	+	0.806997i	0.985728	+	0.168343i	$0.0538416\pi$
$307$	3.78873	+	14.1397i	0.216234	+	0.806997i	−0.769494	+	0.638654i	$0.779492\pi$
$308$	−1.91770	+	21.9195i	−0.109271	+	1.24898i
$309$	0.00302299		0.000278963i	0.000171972		1.58696e-5i
$310$	−0.966978	−	7.92897i	−0.0549207	−	0.450335i
$311$	13.9613	+	2.46175i	0.791672	+	0.139593i	0.554840	−	0.831957i	$-0.312780\pi$
$311$	13.9613	+	2.46175i	0.791672	+	0.139593i	0.236833	+	0.971550i	$0.423891\pi$
$312$	−0.110004	−	0.641685i	−0.00622775	−	0.0363283i
$313$	6.64066	+	0.580982i	0.375352	+	0.0328391i	0.273271	−	0.961937i	$-0.411894\pi$
$313$	6.64066	+	0.580982i	0.375352	+	0.0328391i	0.102081	+	0.994776i	$0.467450\pi$
$314$	−3.41244	+	5.91051i	−0.192575	+	0.333550i
$315$	−25.4104	+	12.6185i	−1.43171	+	0.710973i
$316$	−2.61896	−	4.53618i	−0.147328	−	0.255180i
$317$	−2.79105	−	5.98543i	−0.156761	−	0.336175i	0.812204	−	0.583374i	$-0.198268\pi$
$317$	−2.79105	−	5.98543i	−0.156761	−	0.336175i	−0.968965	+	0.247199i	$0.920490\pi$
$318$	−15.6594	−	0.0744352i	−0.878134	−	0.00417412i
$319$	−33.8589	+	40.3515i	−1.89573	+	2.25925i
$320$	−2.21405	−	0.313010i	−0.123769	−	0.0174978i
$321$	−15.9534	+	11.0581i	−0.890435	+	0.617202i
$322$	3.87128	+	2.71070i	0.215738	+	0.151061i
$323$	−14.6254	+	14.6254i	−0.813779	+	0.813779i
$324$	3.23842	−	8.39718i	0.179912	−	0.466510i
$325$	0.361623	−	1.84429i	0.0200592	−	0.102303i
$326$	−0.933793	+	0.164653i	−0.0517180	+	0.00911928i
$327$	3.77461	+	0.684081i	0.208736	+	0.0378298i
$328$	−4.39112	−	2.04761i	−0.242459	−	0.113061i
$329$	−23.7783	−	19.9524i	−1.31094	−	1.10001i
$330$	−5.78368	−	19.3015i	−0.318381	−	1.06251i
$331$	8.71424	+	3.17172i	0.478978	+	0.174334i	0.570215	−	0.821495i	$-0.306860\pi$
$331$	8.71424	+	3.17172i	0.478978	+	0.174334i	−0.0912370	+	0.995829i	$0.529082\pi$
$332$	−1.23614	+	4.61333i	−0.0678419	+	0.253190i
$333$	−1.69246	+	17.4343i	−0.0927462	+	0.955394i
$334$	4.34373	+	2.50785i	0.237678	+	0.137224i
$335$	0.457336	+	0.297529i	0.0249869	+	0.0162557i
$336$	5.98055	+	4.23014i	0.326266	+	0.230773i
$337$	−20.1713	−	28.8075i	−1.09880	−	1.56925i	−0.784721	−	0.619849i	$-0.787194\pi$
$337$	−20.1713	−	28.8075i	−1.09880	−	1.56925i	−0.314078	−	0.949397i	$-0.601695\pi$
$338$	7.37545	+	10.5332i	0.401172	+	0.572933i
$339$	−0.200314	+	2.17071i	−0.0108795	+	0.117897i
$340$	−11.4503	−	7.44925i	−0.620982	−	0.403992i
$341$	−16.0948	−	9.29232i	−0.871581	−	0.503207i
$342$	−4.37991	+	9.16426i	−0.236838	+	0.495547i
$343$	−4.25483	+	15.8792i	−0.229739	+	0.857399i
$344$	−6.15030	−	2.23852i	−0.331602	−	0.120693i
$345$	−4.21139	−	0.997018i	−0.226733	−	0.0536776i
$346$	4.34826	+	3.64862i	0.233764	+	0.196151i
$347$	16.8242	+	7.84524i	0.903169	+	0.421155i	0.818004	−	0.575212i	$-0.195081\pi$
$347$	16.8242	+	7.84524i	0.903169	+	0.421155i	0.0851649	+	0.996367i	$0.472858\pi$
$348$	5.91953	+	16.5075i	0.317320	+	0.884894i
$349$	9.68283	−	1.70734i	0.518310	−	0.0913920i	0.0916271	−	0.995793i	$-0.470793\pi$
$349$	9.68283	−	1.70734i	0.518310	−	0.0913920i	0.426683	+	0.904401i	$0.359682\pi$
$350$	11.7963	+	17.5506i	0.630540	+	0.938117i
$351$	−0.142465	−	1.94793i	−0.00760421	−	0.103973i
$352$	−3.67876	+	3.67876i	−0.196079	+	0.196079i
$353$	2.68228	+	1.87815i	0.142763	+	0.0999639i	0.642776	−	0.766054i	$-0.277783\pi$
$353$	2.68228	+	1.87815i	0.142763	+	0.0999639i	−0.500013	+	0.866018i	$0.666671\pi$
$354$	−0.430273	−	5.20276i	−0.0228687	−	0.276524i
$355$	−0.135580	−	0.0191675i	−0.00719582	−	0.00101730i
$356$	−5.96346	+	7.10697i	−0.316063	+	0.376669i
$357$	22.1910	+	38.8614i	1.17447	+	2.05676i
$358$	−6.02163	−	12.9134i	−0.318253	−	0.682496i
$359$	8.24511	+	14.2809i	0.435160	+	0.753719i	0.997309	−	0.0733169i	$-0.0233584\pi$
$359$	8.24511	+	14.2809i	0.435160	+	0.753719i	−0.562149	+	0.827036i	$0.690025\pi$
$360$	−6.52035	−	1.57642i	−0.343652	−	0.0830844i
$361$	−3.76848	+	6.52720i	−0.198341	+	0.343537i
$362$	−13.0587	−	1.14249i	−0.686351	−	0.0600479i
$363$	−26.1043	−	9.64196i	−1.37012	−	0.506072i
$364$	1.56557	+	0.276051i	0.0820579	+	0.0144690i
$365$	−1.78983	−	14.6761i	−0.0936839	−	0.768184i
$366$	−5.53921	−	12.0278i	−0.289539	−	0.628703i
$367$	−2.85258	+	32.6051i	−0.148903	+	1.70197i	0.443455	+	0.896297i	$0.353753\pi$
$367$	−2.85258	+	32.6051i	−0.148903	+	1.70197i	−0.592358	+	0.805675i	$0.701803\pi$
$368$	0.289213	+	1.07936i	0.0150763	+	0.0562654i
$369$	−12.5182	−	7.38694i	−0.651671	−	0.384549i
$370$	13.0483	−	0.444979i	0.678347	−	0.0231333i
$371$	13.0779	−	35.9314i	0.678973	−	1.86546i
$372$	−5.37297	+	3.06812i	−0.278575	+	0.159075i
$373$	−0.540647	−	6.17963i	−0.0279937	−	0.319969i	−0.997261	−	0.0739600i	$-0.976436\pi$
$373$	−0.540647	−	6.17963i	−0.0279937	−	0.319969i	0.969268	−	0.246009i	$-0.0791193\pi$
$374$	−29.8659	+	10.8703i	−1.54433	+	0.562089i
$375$	−15.9758	−	10.9441i	−0.824987	−	0.565152i
$376$	−1.27447	−	7.22787i	−0.0657257	−	0.372749i
$377$	2.69107	+	2.69107i	0.138597	+	0.138597i
$378$	16.6315	+	14.3646i	0.855434	+	0.738835i
$379$		−	6.82213i		−	0.350429i	−0.984530	−	0.175215i	$-0.943938\pi$
$379$		−	6.82213i		−	0.350429i	0.984530	−	0.175215i	$-0.0560620\pi$
$380$	7.19823	+	2.34535i	0.369261	+	0.120314i
$381$	−5.53615	+	11.7265i	−0.283626	+	0.600765i
$382$	0.607093	−	1.30191i	0.0310616	−	0.0666117i
$383$	−3.44055	+	0.301009i	−0.175804	+	0.0153808i	−0.174718	−	0.984619i	$-0.555901\pi$
$383$	−3.44055	+	0.301009i	−0.175804	+	0.0153808i	−0.00108604	+	0.999999i	$0.500346\pi$
$384$	0.440330	+	1.67514i	0.0224705	+	0.0854844i
$385$	49.1311	+	2.61512i	2.50395	+	0.133279i
$386$	17.0259	−	9.82991i	0.866596	−	0.500329i
$387$	−17.7157	−	8.46692i	−0.900539	−	0.430398i
$388$	15.1271	−	4.05329i	0.767961	−	0.205775i
$389$	−9.14718	+	7.67539i	−0.463780	+	0.389158i	−0.844520	−	0.535525i	$-0.820114\pi$
$389$	−9.14718	+	7.67539i	−0.463780	+	0.389158i	0.380739	+	0.924682i	$0.375669\pi$
$390$	−1.42563	+	0.294737i	−0.0721898	+	0.0149246i
$391$	−1.18540	+	6.72273i	−0.0599482	+	0.339983i
$392$	−8.91813	+	6.24454i	−0.450433	+	0.315397i
$393$	−21.0783	+	3.61344i	−1.06326	+	0.182274i
$394$	−12.7046	−	15.1407i	−0.640047	−	0.762778i
$395$	−9.93771	+	6.19848i	−0.500020	+	0.311880i
$396$	−12.0510	+	9.91830i	−0.605585	+	0.498413i
$397$	−2.51612	−	0.674193i	−0.126280	−	0.0338368i	0.195125	−	0.980778i	$-0.437489\pi$
$397$	−2.51612	−	0.674193i	−0.126280	−	0.0338368i	−0.321406	+	0.946942i	$0.604155\pi$
$398$	7.05634	−	3.29042i	0.353702	−	0.164934i
$399$	−17.4538	−	17.6205i	−0.873783	−	0.882130i
$400$	−0.530769	+	4.97175i	−0.0265385	+	0.248587i
$401$	2.31034	+	6.34761i	0.115373	+	0.316984i	0.983917	−	0.178628i	$-0.0571659\pi$
$401$	2.31034	+	6.34761i	0.115373	+	0.316984i	−0.868544	+	0.495612i	$0.834944\pi$
$402$	0.0753647	−	0.415846i	0.00375885	−	0.0207405i
$403$	−0.770158	+	1.09990i	−0.0383643	+	0.0547899i
$404$	8.79994			0.437814
$405$	−19.0126	−	6.59715i	−0.944742	−	0.327815i
$406$	−42.8211			−2.12518
$407$	17.4232	−	24.8829i	0.863636	−	1.23340i
$408$	−1.88691	+	10.4116i	−0.0934160	+	0.515449i
$409$	−1.32960	−	3.65304i	−0.0657444	−	0.180631i	0.902470	−	0.430752i	$-0.141752\pi$
$409$	−1.32960	−	3.65304i	−0.0657444	−	0.180631i	−0.968215	+	0.250121i	$0.919530\pi$
$410$	−4.24129	+	9.96919i	−0.209462	+	0.492343i
$411$	15.4808	+	15.6286i	0.763609	+	0.770904i
$412$	−0.00158852		0.000740740i	−7.82609e−5		3.64936e-5i
$413$	12.3131	+	3.29928i	0.605886	+	0.162347i
$414$	0.550709	+	3.30675i	0.0270659	+	0.162518i
$415$	10.4039	+	2.41090i	0.510709	+	0.118346i
$416$	0.241612	+	0.287942i	0.0118460	+	0.0141175i
$417$	7.45465	−	1.27795i	0.365056	−	0.0625815i
$418$	14.4288	−	10.1032i	0.705737	−	0.494162i
$419$	−2.47543	+	14.0389i	−0.120933	+	0.685844i	0.862708	+	0.505703i	$0.168767\pi$
$419$	−2.47543	+	14.0389i	−0.120933	+	0.685844i	−0.983641	+	0.180141i	$0.942344\pi$
$420$	8.99759	−	13.6875i	0.439037	−	0.667884i
$421$	21.8367	−	18.3232i	1.06426	−	0.893018i	0.0697379	−	0.997565i	$-0.477784\pi$
$421$	21.8367	−	18.3232i	1.06426	−	0.893018i	0.994520	+	0.104547i	$0.0333392\pi$
$422$	0.503615	−	0.134943i	0.0245156	−	0.00656893i
$423$	−1.71040	−	21.9516i	−0.0831624	−	1.06732i
$424$	7.82978	−	4.52052i	0.380248	−	0.219536i
$425$	−15.7747	+	26.1566i	−0.765186	+	1.26878i
$426$	0.0269640	+	0.102579i	0.00130641	+	0.00496997i
$427$	32.2112	−	2.81811i	1.55881	−	0.136378i
$428$	4.73630	−	10.1570i	0.228938	−	0.490959i
$429$	−1.44603	+	3.06292i	−0.0698148	+	0.147879i
$430$	−4.53386	+	13.9151i	−0.218642	+	0.671045i
$431$			38.9178i			1.87461i	0.348515	+	0.937303i	$0.386686\pi$
$431$			38.9178i			1.87461i	−0.348515	+	0.937303i	$0.613314\pi$
$432$	0.829241	+	5.12956i	0.0398969	+	0.246796i
$433$	8.50667	+	8.50667i	0.408804	+	0.408804i	0.881321	−	0.472517i	$-0.156655\pi$
$433$	8.50667	+	8.50667i	0.408804	+	0.408804i	−0.472517	+	0.881321i	$0.656655\pi$
$434$	−2.62347	−	14.8785i	−0.125931	−	0.714189i
$435$	36.4393	−	14.4868i	1.74713	−	0.694590i
$436$	−2.08121	+	0.757497i	−0.0996717	+	0.0362775i
$437$	−0.329737	−	3.76891i	−0.0157734	−	0.180291i
$438$	−9.94509	+	5.67894i	−0.475195	+	0.271350i
$439$	12.9045	−	35.4547i	0.615896	−	1.69216i	−0.100917	−	0.994895i	$-0.532178\pi$
$439$	12.9045	−	35.4547i	0.615896	−	1.69216i	0.716813	−	0.697266i	$-0.245600\pi$
$440$	8.50154	+	7.94082i	0.405295	+	0.378564i
$441$	−28.4393	+	16.0609i	−1.35425	+	0.764805i
$442$	0.594319	+	2.21803i	0.0282689	+	0.105501i
$443$	−3.23888	+	37.0206i	−0.153884	+	1.75890i	0.390999	+	0.920391i	$0.372129\pi$
$443$	−3.23888	+	37.0206i	−0.153884	+	1.75890i	−0.544883	+	0.838512i	$0.683426\pi$
$444$	−4.23033	−	9.18572i	−0.200763	−	0.435935i
$445$	16.3369	+	12.7853i	0.774444	+	0.606082i
$446$	8.53857	+	1.50558i	0.404313	+	0.0712913i
$447$	−1.21972	−	0.450518i	−0.0576906	−	0.0213088i
$448$	−4.21321	−	0.368608i	−0.199056	−	0.0174151i
$449$	−19.5467	+	33.8559i	−0.922466	+	1.59776i	−0.126878	+	0.991918i	$0.540496\pi$
$449$	−19.5467	+	33.8559i	−0.922466	+	1.59776i	−0.795587	+	0.605839i	$0.792838\pi$
$450$	−3.02600	+	14.6916i	−0.142647	+	0.692569i
$451$	12.6034	+	21.8297i	0.593469	+	1.02792i
$452$	−0.531900	−	1.14066i	−0.0250185	−	0.0536523i
$453$	2.14608	+	3.75826i	0.100831	+	0.176578i
$454$	−3.98957	+	4.75458i	−0.187240	+	0.223144i
$455$	0.497597	−	3.51972i	0.0233277	−	0.165007i
$456$	−0.483326	−	5.84427i	−0.0226338	−	0.273683i
$457$	−7.27339	−	5.09288i	−0.340235	−	0.238235i	0.390954	−	0.920410i	$-0.372145\pi$
$457$	−7.27339	−	5.09288i	−0.340235	−	0.238235i	−0.731189	+	0.682175i	$0.761034\pi$
$458$	−16.9517	+	16.9517i	−0.792100	+	0.792100i
$459$	−8.65221	+	30.5416i	−0.403851	+	1.42556i
$460$	2.39007	−	0.728583i	0.111438	−	0.0339704i
$461$	−33.1532	+	5.84580i	−1.54410	+	0.272266i	−0.879851	−	0.475249i	$-0.842358\pi$
$461$	−33.1532	+	5.84580i	−1.54410	+	0.272266i	−0.664245	+	0.747515i	$0.731247\pi$
$462$	−12.8642	−	35.8738i	−0.598498	−	1.66900i
$463$	8.97141	+	4.18344i	0.416937	+	0.194421i	0.619755	−	0.784796i	$-0.287232\pi$
$463$	8.97141	+	4.18344i	0.416937	+	0.194421i	−0.202818	+	0.979216i	$0.565010\pi$
$464$	−7.75609	−	6.50813i	−0.360067	−	0.302132i
$465$	7.26603	+	11.7735i	0.336954	+	0.545984i
$466$	−10.9781	−	3.99571i	−0.508551	−	0.185098i
$467$	−2.05693	+	7.67657i	−0.0951834	+	0.355229i	−0.997047	−	0.0767911i	$-0.975533\pi$
$467$	−2.05693	+	7.67657i	−0.0951834	+	0.355229i	0.901864	+	0.432021i	$0.142199\pi$
$468$	0.637980	+	0.929819i	0.0294906	+	0.0429809i
$469$	0.893695	+	0.515975i	0.0412670	+	0.0238255i
$470$	−16.0555	+	3.39899i	−0.740584	+	0.156784i
$471$	1.08623	−	11.7710i	0.0500510	−	0.542380i
$472$	1.72880	+	2.46898i	0.0795745	+	0.113644i
$473$	19.5307	+	27.8927i	0.898023	+	1.28251i
$474$	7.40682	+	5.23895i	0.340206	+	0.240633i
$475$	4.69273	−	16.2651i	0.215317	−	0.746295i
$476$	−22.3755	−	12.9185i	−1.02558	−	0.592118i
$477$	24.6898	−	11.2285i	1.13047	−	0.514119i
$478$	−4.77286	+	17.8125i	−0.218305	+	0.814727i
$479$	−14.8140	−	5.39184i	−0.676867	−	0.246359i	−0.0193652	−	0.999812i	$-0.506165\pi$
$479$	−14.8140	−	5.39184i	−0.676867	−	0.246359i	−0.657502	+	0.753453i	$0.728387\pi$
$480$	3.71000	−	1.11170i	0.169338	−	0.0507420i
$481$	−1.68122	−	1.41071i	−0.0766571	−	0.0643229i
$482$	4.50956	+	2.10284i	0.205405	+	0.0957819i
$483$	−8.05440	−	1.45972i	−0.366488	−	0.0664195i
$484$	15.8225	−	2.78993i	0.719203	−	0.126815i
$485$	−10.2110	−	33.4966i	−0.463659	−	1.52100i
$486$	0.989197	+	15.5570i	0.0448709	+	0.705682i
$487$	−6.08544	+	6.08544i	−0.275758	+	0.275758i	−0.831413	−	0.555655i	$-0.812467\pi$
$487$	−6.08544	+	6.08544i	−0.275758	+	0.275758i	0.555655	+	0.831413i	$0.312467\pi$
$488$	6.26265	+	4.38515i	0.283497	+	0.198506i
$489$	1.34978	−	0.935595i	0.0610391	−	0.0423091i
$490$	14.6348	+	19.4540i	0.661131	+	0.878844i
$491$	−19.9695	+	23.7987i	−0.901209	+	1.07402i	0.0956967	+	0.995411i	$0.469492\pi$
$491$	−19.9695	+	23.7987i	−0.901209	+	1.07402i	−0.996906	+	0.0786084i	$0.974952\pi$
$492$	8.39181	+	0.0398896i	0.378332	+	0.00179836i
$493$	−26.1402	−	56.0579i	−1.17730	−	2.52472i
$494$	−0.636313	−	1.10213i	−0.0286291	−	0.0495870i
$495$	23.0835	+	26.1753i	1.03753	+	1.17649i
$496$	1.78611	−	3.09363i	0.0801986	−	0.138908i
$497$	−0.258000	−	0.0225721i	−0.0115729	−	0.00101250i
$498$	−1.39775	−	8.15346i	−0.0626346	−	0.365365i
$499$	12.8962	+	2.27395i	0.577313	+	0.101796i	0.454678	−	0.890656i	$-0.349754\pi$
$499$	12.8962	+	2.27395i	0.577313	+	0.101796i	0.122635	+	0.992452i	$0.460866\pi$
$500$	11.1512	+	0.807244i	0.498695	+	0.0361010i
$501$	−8.65070	−	0.798290i	−0.386485	−	0.0356650i
$502$	1.14043	−	13.0352i	0.0508999	−	0.581788i
$503$	−1.81455	−	6.77201i	−0.0809070	−	0.301949i	0.913601	−	0.406613i	$-0.133290\pi$
$503$	−1.81455	−	6.77201i	−0.0809070	−	0.301949i	−0.994508	+	0.104664i	$0.966623\pi$
$504$	−12.4736	−	2.32192i	−0.555620	−	0.103427i
$505$	−0.670655	−	19.6658i	−0.0298438	−	0.875118i
$506$	1.98833	−	5.46291i	0.0883923	−	0.242856i
$507$	−19.2349	−	11.2275i	−0.854253	−	0.498632i
$508$	−0.652522	−	7.45836i	−0.0289510	−	0.330911i
$509$	15.4656	−	5.62900i	0.685499	−	0.249501i	0.0242921	−	0.999705i	$-0.492267\pi$
$509$	15.4656	−	5.62900i	0.685499	−	0.249501i	0.661207	+	0.750204i	$0.270045\pi$
$510$	23.4112	+	3.42333i	1.03667	+	0.151588i
$511$	−4.85592	−	27.5393i	−0.214813	−	1.21827i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	0.250864	−	17.5909i	0.0110759	−	0.776656i
$514$		−	2.02249i		−	0.0892083i
$515$	0.00177645	+	0.00349353i	7.82796e−5	+	0.000153943i
$516$	11.2977	−	0.934331i	0.497354	−	0.0411316i
$517$	−16.1370	+	34.6060i	−0.709706	+	1.52197i
$518$	24.5999	−	2.15221i	1.08086	−	0.0945628i
$519$	−9.48434	−	2.58970i	−0.416316	−	0.113675i
$520$	0.625070	−	0.561891i	0.0274111	−	0.0246406i
$521$	0.953086	−	0.550265i	0.0417555	−	0.0241075i	−0.478977	−	0.877827i	$-0.658992\pi$
$521$	0.953086	−	0.550265i	0.0417555	−	0.0241075i	0.520732	+	0.853720i	$0.325659\pi$
$522$	−21.2729	−	21.6813i	−0.931090	−	0.948963i
$523$	3.11458	−	0.834549i	0.136191	−	0.0364923i	−0.190080	−	0.981769i	$-0.560875\pi$
$523$	3.11458	−	0.834549i	0.136191	−	0.0364923i	0.326271	+	0.945276i	$0.394208\pi$
$524$	9.45840	−	7.93654i	0.413192	−	0.346709i
$525$	−31.2742	−	19.0644i	−1.36492	−	0.832038i
$526$	1.94224	−	11.0150i	0.0846859	−	0.480278i
$527$	17.8762	−	12.5170i	0.778699	−	0.545251i
$528$	3.12219	−	8.45291i	0.135876	−	0.367866i
$529$	13.9815	+	16.6625i	0.607891	+	0.724456i
$530$	−10.6990	−	17.1532i	−0.464737	−	0.745088i
$531$	4.44646	+	7.87341i	0.192960	+	0.341677i
$532$	13.8313	+	3.70608i	0.599662	+	0.160679i
$533$	1.65054	−	0.769660i	0.0714929	−	0.0333377i
$534$	4.23272	−	15.5016i	0.183168	−	0.670820i
$535$	−23.0596	−	9.81046i	−0.996953	−	0.424143i
$536$	0.0834528	+	0.229285i	0.00360461	+	0.00990359i
$537$	18.8296	+	15.9530i	0.812555	+	0.688423i
$538$	5.39369	−	7.70299i	0.232538	−	0.332099i
$539$	56.6403			2.43967
$540$	11.4002	−	2.24409i	0.490586	−	0.0965704i
$541$	45.1758			1.94226			0.971129	−	0.238553i	$-0.0766732\pi$
$541$	45.1758			1.94226			0.971129	+	0.238553i	$0.0766732\pi$
$542$	−0.790072	+	1.12834i	−0.0339365	+	0.0484664i
$543$	21.3722	−	7.66398i	0.917167	−	0.328893i
$544$	−2.08941	−	5.74062i	−0.0895829	−	0.246127i
$545$	1.85144	+	4.59328i	0.0793070	+	0.196755i
$546$	−2.66301	+	0.700000i	−0.113966	+	0.0299573i
$547$	−38.8206	+	18.1023i	−1.65985	+	0.774000i	−0.660110	+	0.751169i	$0.729490\pi$
$547$	−38.8206	+	18.1023i	−1.65985	+	0.774000i	−0.999739	+	0.0228315i	$0.992732\pi$
$548$	−12.2677	−	3.28713i	−0.524052	−	0.140419i
$549$	17.4289	+	14.9092i	0.743848	+	0.636311i
$550$	17.0980	−	19.6042i	0.729060	−	0.835924i
$551$	22.0346	+	26.2599i	0.938707	+	1.11871i
$552$	−1.23702	−	1.48854i	−0.0526511	−	0.0633564i
$553$	−18.1465	+	12.7063i	−0.771668	+	0.540327i
$554$	5.02131	−	28.4773i	0.213335	−	1.20988i
$555$	−20.2056	+	10.1539i	−0.857678	+	0.431008i
$556$	−3.34511	+	2.80688i	−0.141864	+	0.119038i
$557$	−20.2153	+	5.41667i	−0.856549	+	0.229512i	−0.660262	−	0.751035i	$-0.729555\pi$
$557$	−20.2153	+	5.41667i	−0.856549	+	0.229512i	−0.196286	+	0.980547i	$0.562888\pi$
$558$	6.22999	−	8.71973i	0.263737	−	0.369136i
$559$	2.13055	−	1.23007i	0.0901127	−	0.0520266i
$560$	−0.502660	+	9.44365i	−0.0212413	+	0.399067i
$561$	39.1102	−	38.7401i	1.65123	−	1.63561i
$562$	−32.4490	+	2.83892i	−1.36878	+	0.119753i
$563$	15.7802	−	33.8407i	0.665055	−	1.42621i	−0.226822	−	0.973936i	$-0.572833\pi$
$563$	15.7802	−	33.8407i	0.665055	−	1.42621i	0.891877	−	0.452279i	$-0.149389\pi$
$564$	7.24181	+	10.4477i	0.304935	+	0.439929i
$565$	−2.50858	+	1.27560i	−0.105537	+	0.0536651i
$566$		−	26.2195i		−	1.10209i
$567$	−36.5728	−	10.5489i	−1.53591	−	0.443011i
$568$	−0.0433004	−	0.0433004i	−0.00181684	−	0.00181684i
$569$	−4.38237	−	24.8537i	−0.183719	−	1.04192i	−0.927591	−	0.373598i	$-0.878124\pi$
$569$	−4.38237	−	24.8537i	−0.183719	−	1.04192i	0.743872	−	0.668322i	$-0.232987\pi$
$570$	−13.0238	+	1.52552i	−0.545505	+	0.0638971i
$571$	32.0935	−	11.6811i	1.34307	−	0.488837i	0.432292	−	0.901734i	$-0.357705\pi$
$571$	32.0935	−	11.6811i	1.34307	−	0.488837i	0.910778	+	0.412897i	$0.135483\pi$
$572$	−0.170437	−	1.94810i	−0.00712632	−	0.0814542i
$573$	−0.0118268	+	2.48807i	−0.000494071	+	0.103941i
$574$	−7.00843	+	19.2555i	−0.292526	+	0.803709i
$575$	−1.81036	−	5.28573i	−0.0754974	−	0.220430i
$576$	−1.90643	−	2.31636i	−0.0794345	−	0.0965151i
$577$	6.06339	+	22.6289i	0.252422	+	0.942052i	0.969506	+	0.245066i	$0.0788096\pi$
$577$	6.06339	+	22.6289i	0.252422	+	0.942052i	−0.717084	+	0.696986i	$0.754524\pi$
$578$	1.77103	−	20.2430i	0.0736653	−	0.841998i
$579$	−19.6637	+	27.8004i	−0.817195	+	1.15535i
$580$	−13.9531	+	17.8291i	−0.579369	+	0.740311i
$581$	19.8926	+	3.50760i	0.825284	+	0.145520i
$582$	−20.8617	+	17.3367i	−0.864746	+	0.718631i
$583$	−46.8575	−	4.09950i	−1.94064	−	0.169784i
$584$	3.30600	−	5.72615i	0.136803	−	0.236950i
$585$	2.02931	−	1.49660i	0.0839016	−	0.0618768i
$586$	−11.6416	−	20.1638i	−0.480909	−	0.832959i
$587$	−8.93875	−	19.1692i	−0.368942	−	0.791198i	−0.999882	−	0.0153665i	$-0.995109\pi$
$587$	−8.93875	−	19.1692i	−0.368942	−	0.791198i	0.630940	−	0.775831i	$-0.282669\pi$
$588$	9.50596	−	16.2855i	0.392019	−	0.671604i
$589$	−7.77418	+	9.26491i	−0.320330	+	0.381754i
$590$	5.38585	−	4.05163i	0.221732	−	0.166803i
$591$	30.9571	+	14.6151i	1.27340	+	0.601184i
$592$	4.78283	+	3.34897i	0.196573	+	0.137642i
$593$	1.68491	−	1.68491i	0.0691910	−	0.0691910i	−0.671664	−	0.740855i	$-0.734420\pi$
$593$	1.68491	−	1.68491i	0.0691910	−	0.0691910i	0.740855	+	0.671664i	$0.234420\pi$
$594$	11.7730	−	24.3351i	0.483050	−	0.998479i
$595$	−27.1646	+	50.9886i	−1.11364	+	2.09033i
$596$	0.739301	−	0.130359i	0.0302829	−	0.00533970i
$597$	−8.71726	+	10.2891i	−0.356774	+	0.421105i
$598$	−0.380669	−	0.177509i	−0.0155667	−	0.00725888i
$599$	−11.6914	−	9.81029i	−0.477700	−	0.400838i	0.371894	−	0.928275i	$-0.378708\pi$
$599$	−11.6914	−	9.81029i	−0.477700	−	0.400838i	−0.849594	+	0.527438i	$0.823153\pi$
$600$	−2.76714	−	8.20627i	−0.112968	−	0.335020i
$601$	43.3179	+	15.7664i	1.76697	+	0.643126i	0.999999	+	0.00144762i	$0.000460792\pi$
$601$	43.3179	+	15.7664i	1.76697	+	0.643126i	0.766974	+	0.641678i	$0.221761\pi$
$602$	−7.16433	+	26.7376i	−0.291996	+	1.08974i
$603$	0.182725	+	0.708826i	0.00744114	+	0.0288656i
$604$	−2.16392	−	1.24934i	−0.0880485	−	0.0508348i
$605$	−7.44070	−	35.1469i	−0.302507	−	1.42893i
$606$	−13.8444	+	6.37579i	−0.562389	+	0.258999i
$607$	−16.5602	−	23.6505i	−0.672159	−	0.959942i	−0.999885	−	0.0151695i	$-0.995171\pi$
$607$	−16.5602	−	23.6505i	−0.672159	−	0.959942i	0.327726	−	0.944773i	$-0.393718\pi$
$608$	1.94196	+	2.77341i	0.0787570	+	0.112477i
$609$	67.3675	−	31.0250i	2.72987	−	1.25720i
$610$	9.32252	−	14.3298i	0.377458	−	0.580195i
$611$	2.38913	+	1.37937i	0.0966539	+	0.0558032i
$612$	−4.57490	−	17.7469i	−0.184929	−	0.717377i
$613$	7.09621	−	26.4834i	0.286613	−	1.06966i	−0.661039	−	0.750351i	$-0.729884\pi$
$613$	7.09621	−	26.4834i	0.286613	−	1.06966i	0.947652	−	0.319304i	$-0.103449\pi$
$614$	13.7557	+	5.00667i	0.555135	+	0.202053i
$615$	−0.550406	−	18.7568i	−0.0221945	−	0.756347i
$616$	16.8554	+	14.1434i	0.679124	+	0.569853i
$617$	1.03346	+	0.481909i	0.0416054	+	0.0194009i	0.443310	−	0.896369i	$-0.353804\pi$
$617$	1.03346	+	0.481909i	0.0416054	+	0.0194009i	−0.401704	+	0.915769i	$0.631582\pi$
$618$	0.00196243	−	0.00231628i	7.89405e−5	−	9.31746e-5i
$619$	−36.3650	+	6.41213i	−1.46163	+	0.257725i	−0.847213	−	0.531254i	$-0.821721\pi$
$619$	−36.3650	+	6.41213i	−1.46163	+	0.257725i	−0.614420	+	0.788979i	$0.710610\pi$
$620$	−7.04967	−	3.75577i	−0.283121	−	0.150835i
$621$	−3.26222	−	4.80329i	−0.130909	−	0.192749i
$622$	10.0244	−	10.0244i	0.401943	−	0.401943i
$623$	32.1414	+	22.5056i	1.28772	+	0.901669i
$624$	−0.588733	−	0.277945i	−0.0235682	−	0.0111267i
$625$	0.954158	−	24.9818i	0.0381663	−	0.999271i
$626$	4.28484	−	5.10647i	0.171257	−	0.204096i
$627$	−15.3799	+	26.3487i	−0.614213	+	1.05227i
$628$	2.88432	+	6.18543i	0.115097	+	0.246826i
$629$	17.8346	+	30.8904i	0.711111	+	1.23168i
$630$	−4.23832	+	28.0527i	−0.168859	+	1.11765i
$631$	−23.0047	+	39.8453i	−0.915802	+	1.58622i	−0.110078	+	0.993923i	$0.535110\pi$
$631$	−23.0047	+	39.8453i	−0.915802	+	1.58622i	−0.805723	+	0.592292i	$0.798223\pi$
$632$	−5.21799	−	0.456515i	−0.207561	−	0.0181592i
$633$	−0.694533	+	0.577179i	−0.0276052	+	0.0229408i
$634$	−6.50386	−	1.14681i	−0.258301	−	0.0455455i
$635$	−16.6180	+	2.02665i	−0.659465	+	0.0804250i
$636$	−9.04282	+	12.7847i	−0.358571	+	0.506947i
$637$	0.356661	−	4.07666i	0.0141314	−	0.161523i
$638$	13.6333	+	50.8802i	0.539748	+	2.01437i
$639$	−0.116742	−	0.141845i	−0.00461824	−	0.00561129i
$640$	−1.52633	+	1.63411i	−0.0603335	+	0.0645939i
$641$	−2.49833	+	6.86411i	−0.0986782	+	0.271116i	−0.979203	−	0.202885i	$-0.934968\pi$
$641$	−2.49833	+	6.86411i	−0.0986782	+	0.271116i	0.880524	+	0.474001i	$0.157191\pi$
$642$	−0.0922679	+	19.4110i	−0.00364153	+	0.766089i
$643$	3.42538	+	39.1523i	0.135084	+	1.54402i	0.697150	+	0.716925i	$0.254451\pi$
$643$	3.42538	+	39.1523i	0.135084	+	1.54402i	−0.562066	+	0.827092i	$0.689993\pi$
$644$	4.44095	−	1.61637i	0.174998	−	0.0636941i
$645$	−2.94903	−	25.1766i	−0.116118	−	0.991327i
$646$	3.59164	+	20.3692i	0.141311	+	0.801415i
$647$	24.0132	+	24.0132i	0.944058	+	0.944058i	0.998516	−	0.0544579i	$-0.0173431\pi$
$647$	24.0132	+	24.0132i	0.944058	+	0.944058i	−0.0544579	+	0.998516i	$0.517343\pi$
$648$	−5.02109	−	7.46918i	−0.197247	−	0.293417i
$649$		−	15.6809i		−	0.615528i
$650$	−1.30333	−	1.35406i	−0.0511210	−	0.0531108i
$651$	14.9072	+	21.5065i	0.584258	+	0.842907i
$652$	−0.400726	+	0.859359i	−0.0156936	+	0.0336551i
$653$	1.84923	−	0.161787i	0.0723659	−	0.00633120i	−0.0509153	−	0.998703i	$-0.516214\pi$
$653$	1.84923	−	0.161787i	0.0723659	−	0.00633120i	0.123281	+	0.992372i	$0.460658\pi$
$654$	2.72539	−	2.69961i	0.106571	−	0.105563i
$655$	−18.4572	−	20.5325i	−0.721181	−	0.802270i
$656$	−4.19595	+	2.42253i	−0.163824	+	0.0945840i
$657$	11.5314	−	16.1398i	0.449883	−	0.629673i
$658$	−29.9828	+	8.03385i	−1.16885	+	0.313192i
$659$	−7.92888	+	6.65312i	−0.308865	+	0.259169i	−0.784023	−	0.620732i	$-0.786835\pi$
$659$	−7.92888	+	6.65312i	−0.308865	+	0.259169i	0.475158	+	0.879901i	$0.342391\pi$
$660$	−19.1282	−	6.33316i	−0.744566	−	0.246518i
$661$	4.12789	−	23.4104i	0.160556	−	0.910561i	−0.792972	−	0.609258i	$-0.791467\pi$
$661$	4.12789	−	23.4104i	0.160556	−	0.910561i	0.953529	−	0.301303i	$-0.0974215\pi$
$662$	7.59641	−	5.31906i	0.295243	−	0.206731i
$663$	−2.54202	−	3.05888i	−0.0987240	−	0.118797i
$664$	3.07000	+	3.65868i	0.119139	+	0.141985i
$665$	7.22814	−	31.1922i	0.280295	−	1.20958i
$666$	13.3106	+	11.3863i	0.515775	+	0.441210i
$667$	10.9283	+	2.92824i	0.423147	+	0.113382i
$668$	4.54577	−	2.11973i	0.175881	−	0.0820147i
$669$	−14.5240	+	3.81779i	−0.561530	+	0.147604i
$670$	0.506038	−	0.203972i	0.0195500	−	0.00788012i
$671$	−13.6038	−	37.3762i	−0.525170	−	1.44289i
$672$	6.89543	−	2.47268i	0.265997	−	0.0953856i
$673$	−4.06091	+	5.79958i	−0.156537	+	0.223558i	−0.889758	−	0.456432i	$-0.849127\pi$
$673$	−4.06091	+	5.79958i	−0.156537	+	0.223558i	0.733221	+	0.679990i	$0.238016\pi$
$674$	−35.1675			−1.35460
$675$	−5.88385	−	25.3057i	−0.226470	−	0.974018i
$676$	12.8587			0.494566
$677$	13.5327	−	19.3267i	0.520105	−	0.742787i	−0.470068	−	0.882630i	$-0.655771\pi$
$677$	13.5327	−	19.3267i	0.520105	−	0.742787i	0.990174	+	0.139843i	$0.0446597\pi$
$678$	1.66324	+	1.40915i	0.0638764	+	0.0541182i
$679$	−22.6533	−	62.2395i	−0.869355	−	2.38853i
$680$	−12.6697	+	5.10686i	−0.485861	+	0.195839i
$681$	2.83170	−	10.3706i	0.108511	−	0.397403i
$682$	−16.8434	+	7.85421i	−0.644967	+	0.300753i
$683$	−45.4832	−	12.1872i	−1.74037	−	0.466330i	−0.757839	−	0.652442i	$-0.773745\pi$
$683$	−45.4832	−	12.1872i	−1.74037	−	0.466330i	−0.982529	+	0.186112i	$0.940411\pi$
$684$	4.99471	+	8.84422i	0.190978	+	0.338167i
$685$	−6.41104	+	27.6661i	−0.244953	+	1.05707i
$686$	10.5670	+	12.5933i	0.403452	+	0.480815i
$687$	14.3870	−	38.9509i	0.548898	−	1.48607i
$688$	−5.36136	+	3.75406i	−0.204400	+	0.143122i
$689$	−0.590119	+	3.34673i	−0.0224818	+	0.127500i
$690$	−3.23226	+	2.87790i	−0.123050	+	0.109560i
$691$	12.4777	−	10.4701i	0.474675	−	0.398300i	−0.373821	−	0.927501i	$-0.621953\pi$
$691$	12.4777	−	10.4701i	0.474675	−	0.398300i	0.848497	+	0.529201i	$0.177508\pi$
$692$	5.48283	−	1.46912i	0.208426	−	0.0558476i
$693$	46.2300	+	47.1174i	1.75613	+	1.78984i
$694$	16.0764	−	9.28171i	0.610252	−	0.352329i
$695$	6.52766	+	7.26163i	0.247608	+	0.275449i
$696$	16.9174	+	4.61931i	0.641254	+	0.175095i
$697$	−29.4861	+	2.57970i	−1.11686	+	0.0977129i
$698$	4.15527	−	8.91100i	0.157279	−	0.337286i
$699$	20.1661	−	1.66776i	0.762753	−	0.0630803i
$700$	21.1427	+	0.403616i	0.799118	+	0.0152553i
$701$			20.7744i			0.784637i	0.919829	+	0.392319i	$0.128327\pi$
$701$			20.7744i			0.784637i	−0.919829	+	0.392319i	$0.871673\pi$
$702$	−1.67737	−	1.00059i	−0.0633082	−	0.0377648i
$703$	−13.9783	−	13.9783i	−0.527202	−	0.527202i
$704$	0.903414	+	5.12351i	0.0340487	+	0.193100i
$705$	22.7964	−	16.9800i	0.858560	−	0.639504i
$706$	3.07698	−	1.11993i	0.115804	−	0.0421491i
$707$	−3.24373	−	37.0760i	−0.121993	−	1.39439i
$708$	−4.50865	−	2.63172i	−0.169445	−	0.0989062i
$709$	−13.3009	+	36.5440i	−0.499527	+	1.37244i	0.392207	+	0.919877i	$0.371712\pi$
$709$	−13.3009	+	36.5440i	−0.499527	+	1.37244i	−0.891733	+	0.452561i	$0.850510\pi$
$710$	−0.0934664	+	0.100066i	−0.00350773	+	0.00375542i
$711$	−15.4484	−	2.87566i	−0.579361	−	0.107846i
$712$	2.40119	+	8.96137i	0.0899885	+	0.335842i
$713$	−0.347900	+	3.97652i	−0.0130290	+	0.148922i
$714$	44.5616	+	4.11217i	1.66768	+	0.153894i
$715$	−4.34057	+	0.529354i	−0.162328	+	0.0197967i
$716$	−14.0319	−	2.47421i	−0.524398	−	0.0924655i
$717$	−5.39684	−	31.4813i	−0.201549	−	1.17569i
$718$	16.4275	+	1.43722i	0.613067	+	0.0536365i
$719$	−6.20709	+	10.7510i	−0.231485	+	0.400945i	−0.958245	−	0.285947i	$-0.907692\pi$
$719$	−6.20709	+	10.7510i	−0.231485	+	0.400945i	0.726760	+	0.686891i	$0.241025\pi$
$720$	−5.03124	+	4.43696i	−0.187503	+	0.165356i
$721$	0.00370644	+	0.00641974i	0.000138035	+	0.000239083i
$722$	3.18526	+	6.83081i	0.118543	+	0.254216i
$723$	−8.61816	−	0.0409655i	−0.320513	−	0.00152352i
$724$	−8.42604	+	10.0418i	−0.313151	+	0.373199i
$725$	40.9072	+	29.8231i	1.51926	+	1.10760i
$726$	−22.8711	+	15.8530i	−0.848825	+	0.588360i
$727$	11.1593	+	7.81380i	0.413874	+	0.289798i	0.761909	−	0.647684i	$-0.224262\pi$
$727$	11.1593	+	7.81380i	0.413874	+	0.289798i	−0.348035	+	0.937481i	$0.613151\pi$
$728$	1.12410	−	1.12410i	0.0416619	−	0.0416619i
$729$	−12.8277	−	23.7581i	−0.475101	−	0.879931i
$730$	−13.0486	−	6.95174i	−0.482950	−	0.257295i
$731$	−39.3763	+	6.94310i	−1.45638	+	0.256800i
$732$	−13.0298	−	2.36141i	−0.481594	−	0.0872803i
$733$	15.6829	+	7.31307i	0.579263	+	0.270115i	0.690088	−	0.723725i	$-0.257572\pi$
$733$	15.6829	+	7.31307i	0.579263	+	0.270115i	−0.110826	+	0.993840i	$0.535349\pi$
$734$	25.0724	+	21.0382i	0.925437	+	0.776534i
$735$	−37.1189	−	20.0025i	−1.36915	−	0.737802i
$736$	1.05004	+	0.382184i	0.0387051	+	0.0140875i
$737$	0.328551	−	1.22617i	0.0121023	−	0.0451665i
$738$	−13.2312	+	6.01733i	−0.487046	+	0.221501i
$739$	28.8265	+	16.6430i	1.06040	+	0.612223i	0.925543	−	0.378642i	$-0.123609\pi$
$739$	28.8265	+	16.6430i	1.06040	+	0.612223i	0.134858	+	0.990865i	$0.456942\pi$
$740$	7.11967	−	10.9437i	0.261724	−	0.402300i
$741$	1.79959	+	1.27288i	0.0661095	+	0.0467602i
$742$	−21.9320	−	31.3222i	−0.805151	−	1.14987i
$743$	−10.3182	−	14.7359i	−0.378537	−	0.540607i	0.584001	−	0.811753i	$-0.301486\pi$
$743$	−10.3182	−	14.7359i	−0.378537	−	0.540607i	−0.962538	+	0.271146i	$0.912598\pi$
$744$	−0.568547	+	6.16108i	−0.0208440	+	0.225876i
$745$	−0.347665	−	1.64223i	−0.0127374	−	0.0601667i
$746$	−5.37216	−	3.10162i	−0.196689	−	0.113558i
$747$	8.10638	+	11.8146i	0.296597	+	0.432273i
$748$	−8.22594	+	30.6996i	−0.300770	+	1.12249i
$749$	−44.5396	−	16.2111i	−1.62744	−	0.592340i
$750$	−18.1282	+	6.80933i	−0.661950	+	0.248641i
$751$	15.4184	+	12.9376i	0.562627	+	0.472100i	0.879190	−	0.476471i	$-0.158084\pi$
$751$	15.4184	+	12.9376i	0.562627	+	0.472100i	−0.316563	+	0.948571i	$0.602529\pi$
$752$	−6.65173	−	3.10175i	−0.242563	−	0.113109i
$753$	7.65016	+	21.3336i	0.278787	+	0.777441i
$754$	3.74793	−	0.660860i	0.136491	−	0.0240671i
$755$	−2.62707	+	4.93106i	−0.0956087	+	0.179460i
$756$	21.3062	−	5.38457i	0.774901	−	0.195835i
$757$	−18.5041	+	18.5041i	−0.672541	+	0.672541i	−0.958301	−	0.285760i	$-0.907754\pi$
$757$	−18.5041	+	18.5041i	−0.672541	+	0.672541i	0.285760	+	0.958301i	$0.407754\pi$
$758$	−5.58836	−	3.91301i	−0.202979	−	0.142127i
$759$	0.829905	+	10.0350i	0.0301236	+	0.364248i
$760$	6.04993	−	4.55121i	0.219454	−	0.165090i
$761$	13.7056	−	16.3338i	0.496829	−	0.592098i	−0.458111	−	0.888895i	$-0.651474\pi$
$761$	13.7056	−	16.3338i	0.496829	−	0.592098i	0.954941	+	0.296797i	$0.0959184\pi$
$762$	6.43035	+	11.2610i	0.232947	+	0.407942i
$763$	3.95864	+	8.48934i	0.143313	+	0.307335i
$764$	−0.718252	−	1.24405i	−0.0259854	−	0.0450081i
$765$	−39.3116	+	11.5764i	−1.42131	+	0.418544i
$766$	−1.72684	+	2.99098i	−0.0623934	+	0.108069i
$767$	−1.12862	−	0.0987416i	−0.0407522	−	0.00356535i
$768$	1.62476	+	0.600126i	0.0586285	+	0.0216552i
$769$	13.6805	+	2.41225i	0.493332	+	0.0869878i	0.414779	−	0.909922i	$-0.363859\pi$
$769$	13.6805	+	2.41225i	0.493332	+	0.0869878i	0.0785532	+	0.996910i	$0.474970\pi$
$770$	30.3226	−	38.7459i	1.09275	−	1.39630i
$771$	1.46535	+	3.18185i	0.0527733	+	0.114592i
$772$	1.71347	−	19.5850i	0.0616690	−	0.704880i
$773$	−7.16421	−	26.7372i	−0.257679	−	0.961671i	−0.966580	−	0.256363i	$-0.917476\pi$
$773$	−7.16421	−	26.7372i	−0.257679	−	0.961671i	0.708902	−	0.705307i	$-0.249191\pi$
$774$	−17.0970	+	9.65542i	−0.614539	+	0.347057i
$775$	−7.85601	+	16.0406i	−0.282196	+	0.576196i
$776$	5.35628	−	14.7163i	0.192279	−	0.528283i
$777$	−37.1420	+	21.2092i	−1.33246	+	0.760876i
$778$	1.04071	+	11.8954i	0.0373112	+	0.426469i
$779$	15.4147	−	5.61050i	0.552289	−	0.201017i
$780$	−0.576276	+	1.33687i	−0.0206340	+	0.0478675i
$781$	0.0553214	+	0.313743i	0.00197956	+	0.0112266i
$782$	4.82702	+	4.82702i	0.172614	+	0.172614i
$783$	49.1759	+	18.6969i	1.75740	+	0.668173i
$784$			10.8870i			0.388822i
$785$	13.6032	−	6.91718i	0.485519	−	0.246885i
$786$	−9.13003	+	19.3389i	−0.325657	+	0.689795i
$787$	1.63245	−	3.50081i	0.0581906	−	0.124790i	−0.875062	−	0.484011i	$-0.839180\pi$
$787$	1.63245	−	3.50081i	0.0581906	−	0.124790i	0.933253	+	0.359220i	$0.116957\pi$
$788$	−19.6896	+	1.72262i	−0.701413	+	0.0613657i
$789$	4.92507	+	18.7364i	0.175337	+	0.667033i
$790$	−0.622536	+	11.6958i	−0.0221488	+	0.416118i
$791$	−4.60979	+	2.66146i	−0.163905	+	0.0946308i
$792$	1.21242	+	15.5605i	0.0430816	+	0.552918i
$793$	−2.77580	+	0.743773i	−0.0985715	+	0.0264122i
$794$	−1.99545	+	1.67438i	−0.0708160	+	0.0594217i
$795$	29.2600	+	19.2343i	1.03775	+	0.682170i
$796$	1.35199	−	7.66752i	0.0479201	−	0.271768i
$797$	10.3397	−	7.23990i	0.366249	−	0.256451i	−0.375935	−	0.926646i	$-0.622679\pi$
$797$	10.3397	−	7.23990i	0.366249	−	0.256451i	0.742185	+	0.670195i	$0.233790\pi$
$798$	−24.4450	+	4.19060i	−0.865343	+	0.148346i
$799$	−28.8203	−	34.3467i	−1.01959	−	1.21510i
$800$	3.76818	+	3.28646i	0.133225	+	0.116194i
$801$	4.57227	+	27.4543i	0.161553	+	0.970052i
$802$	6.52481	+	1.74832i	0.230399	+	0.0617353i
$803$	−31.1763	+	14.5377i	−1.10019	+	0.513026i
$804$	−0.297414	−	0.300255i	−0.0104890	−	0.0105892i
$805$	−3.95067	−	9.80132i	−0.139243	−	0.345451i
$806$	0.459240	+	1.26175i	0.0161761	+	0.0444433i
$807$	−2.90451	+	16.0265i	−0.102244	+	0.564158i
$808$	5.04744	−	7.20849i	0.177568	−	0.253594i
$809$	−9.03399			−0.317618			−0.158809	−	0.987309i	$-0.550765\pi$
$809$	−9.03399			−0.317618			−0.158809	+	0.987309i	$0.550765\pi$
$810$	−16.3092	+	11.7902i	−0.573048	+	0.414266i
$811$	−18.4143			−0.646613			−0.323307	−	0.946294i	$-0.604795\pi$
$811$	−18.4143			−0.646613			−0.323307	+	0.946294i	$0.604795\pi$
$812$	−24.5612	+	35.0770i	−0.861928	+	1.23096i
$813$	0.425455	−	2.34757i	0.0149214	−	0.0823329i
$814$	−10.3893	−	28.5445i	−0.364146	−	1.00048i
$815$	1.95101	+	0.830037i	0.0683409	+	0.0290749i
$816$	7.44636	+	7.51749i	0.260675	+	0.263165i
$817$	20.0833	−	9.36501i	0.702627	−	0.327640i
$818$	−3.75502	−	1.00616i	−0.131291	−	0.0351794i
$819$	3.68236	−	3.03068i	0.128672	−	0.105901i
$820$	5.73358	+	9.19235i	0.200225	+	0.321011i
$821$	−2.83979	−	3.38433i	−0.0991094	−	0.118114i	0.714210	−	0.699932i	$-0.246786\pi$
$821$	−2.83979	−	3.38433i	−0.0991094	−	0.118114i	−0.813319	+	0.581818i	$0.802342\pi$
$822$	21.6816	−	3.71688i	0.756233	−	0.129641i
$823$	33.4072	−	23.3920i	1.16450	−	0.815394i	0.178800	−	0.983885i	$-0.442779\pi$
$823$	33.4072	−	23.3920i	1.16450	−	0.815394i	0.985703	+	0.168492i	$0.0538896\pi$
$824$	−0.000304360		0.00172611i	−1.06029e−5		6.01320e-5i
$825$	−12.6954	+	43.2298i	−0.441996	+	1.50507i
$826$	9.76509	−	8.19389i	0.339771	−	0.285102i
$827$	−1.19491	+	0.320175i	−0.0415511	+	0.0111336i	−0.279535	−	0.960136i	$-0.590180\pi$
$827$	−1.19491	+	0.320175i	−0.0415511	+	0.0111336i	0.237984	+	0.971269i	$0.423514\pi$
$828$	3.02461	+	1.44556i	0.105112	+	0.0502367i
$829$	−16.1883	+	9.34633i	−0.562243	+	0.324611i	−0.754045	−	0.656822i	$-0.771900\pi$
$829$	−16.1883	+	9.34633i	−0.562243	+	0.324611i	0.191802	+	0.981434i	$0.438567\pi$
$830$	7.94235	−	7.13958i	0.275683	−	0.247818i
$831$	12.7328	+	48.4395i	0.441697	+	1.68035i
$832$	0.374451	−	0.0327602i	0.0129818	−	0.00113576i
$833$	−28.1080	+	60.2778i	−0.973885	+	2.08850i
$834$	3.22898	−	6.83950i	0.111810	−	0.236832i
$835$	−5.08354	−	9.99720i	−0.175923	−	0.345967i
$836$		−	17.6143i		−	0.609205i
$837$	−3.48355	+	18.2320i	−0.120409	+	0.630189i
$838$	10.0801	+	10.0801i	0.348212	+	0.348212i
$839$	−0.681446	−	3.86467i	−0.0235261	−	0.133423i	0.970783	−	0.239961i	$-0.0771346\pi$
$839$	−0.681446	−	3.86467i	−0.0235261	−	0.133423i	−0.994309	+	0.106538i	$0.966024\pi$
$840$	−6.05137	−	15.2212i	−0.208792	−	0.525183i
$841$	−69.0793	+	25.1428i	−2.38204	+	0.866993i
$842$	−2.48445	−	28.3974i	−0.0856197	−	0.978638i
$843$	48.9930	−	27.9765i	1.68741	−	0.963560i
$844$	0.178323	−	0.489937i	0.00613811	−	0.0168643i
$845$	−0.979979	−	28.7363i	−0.0337123	−	0.988557i
$846$	−18.9627	−	11.1898i	−0.651952	−	0.384714i
$847$	−17.5869	−	65.6350i	−0.604292	−	2.25525i
$848$	0.787979	−	9.00664i	0.0270593	−	0.309289i
$849$	18.9967	+	41.2494i	0.651966	+	1.41568i
$850$	12.3782	+	27.9247i	0.424569	+	0.957809i
$851$	−6.42529	−	1.13295i	−0.220256	−	0.0388371i
$852$	0.0994938	+	0.0367493i	0.00340860	+	0.00125901i
$853$	−48.3346	−	4.22873i	−1.65494	−	0.144789i	−0.778942	−	0.627096i	$-0.784243\pi$
$853$	−48.3346	−	4.22873i	−1.65494	−	0.144789i	−0.876002	+	0.482307i	$0.839799\pi$
$854$	16.1671	−	28.0023i	0.553227	−	0.958217i
$855$	19.3841	−	11.8361i	0.662923	−	0.404785i
$856$	−5.60352	−	9.70559i	−0.191524	−	0.331730i
$857$	22.3284	+	47.8835i	0.762725	+	1.63567i	0.771927	+	0.635712i	$0.219293\pi$
$857$	22.3284	+	47.8835i	0.762725	+	1.63567i	−0.00920138	+	0.999958i	$0.502929\pi$
$858$	1.67959	+	2.94133i	0.0573402	+	0.100415i
$859$	15.5714	−	18.5573i	0.531291	−	0.633168i	−0.431921	−	0.901912i	$-0.642164\pi$
$859$	15.5714	−	18.5573i	0.531291	−	0.633168i	0.963212	+	0.268744i	$0.0866084\pi$
$860$	8.79806	+	11.6953i	0.300011	+	0.398806i
$861$	−2.92523	−	35.3712i	−0.0996914	−	1.20545i
$862$	31.8796	+	22.3224i	1.08582	+	0.760302i
$863$	−13.3492	+	13.3492i	−0.454411	+	0.454411i	−0.896816	−	0.442405i	$-0.854126\pi$
$863$	−13.3492	+	13.3492i	−0.454411	+	0.454411i	0.442405	+	0.896816i	$0.354126\pi$
$864$	4.67752	+	2.26292i	0.159132	+	0.0769861i
$865$	−3.70100	−	12.1409i	−0.125838	−	0.412803i
$866$	11.8475	−	2.08903i	0.402594	−	0.0709881i
$867$	11.8803	+	33.1301i	0.403478	+	1.12516i
$868$	−13.6925	−	6.38491i	−0.464753	−	0.216718i
$869$	20.8752	+	17.5163i	0.708141	+	0.594201i
$870$	9.03380	−	38.1586i	0.306274	−	1.29370i
$871$	−0.0861839	−	0.0313684i	−0.00292023	−	0.00106288i
$872$	−0.573225	+	2.13931i	−0.0194119	+	0.0724460i
$873$	20.2594	−	42.3896i	0.685677	−	1.43467i
$874$	−3.27644	−	1.89165i	−0.110827	−	0.0639861i
$875$	−0.709321	−	47.2798i	−0.0239794	−	1.59835i
$876$	−1.05235	+	11.4039i	−0.0355557	+	0.385301i
$877$	−2.48312	−	3.54626i	−0.0838489	−	0.119749i	0.775036	−	0.631917i	$-0.217731\pi$
$877$	−2.48312	−	3.54626i	−0.0838489	−	0.119749i	−0.858885	+	0.512168i	$0.828843\pi$
$878$	−21.6411	−	30.9067i	−0.730352	−	1.04305i
$879$	32.9241	+	23.2877i	1.11050	+	0.785475i
$880$	11.3810	−	2.40939i	0.383654	−	0.0812206i
$881$	−15.2989	−	8.83285i	−0.515434	−	0.297586i	0.219630	−	0.975583i	$-0.429515\pi$
$881$	−15.2989	−	8.83285i	−0.515434	−	0.297586i	−0.735065	+	0.677997i	$0.762848\pi$
$882$	−3.15578	+	32.5083i	−0.106261	+	1.09461i
$883$	−14.0502	+	52.4360i	−0.472826	+	1.76461i	0.156716	+	0.987644i	$0.449909\pi$
$883$	−14.0502	+	52.4360i	−0.472826	+	1.76461i	−0.629542	+	0.776967i	$0.716757\pi$
$884$	2.15779	+	0.785372i	0.0725744	+	0.0264149i
$885$	−5.53768	+	10.2764i	−0.186147	+	0.345436i
$886$	28.4678	+	23.8873i	0.956393	+	0.802509i
$887$	−24.2523	−	11.3090i	−0.814313	−	0.379721i	−0.0295865	−	0.999562i	$-0.509419\pi$
$887$	−24.2523	−	11.3090i	−0.814313	−	0.379721i	−0.784727	+	0.619842i	$0.787197\pi$
$888$	−9.95092	−	1.80343i	−0.333931	−	0.0605190i
$889$	−31.1831	+	5.49843i	−1.04585	+	0.184411i
$890$	19.8436	−	6.04907i	0.665159	−	0.202765i
$891$	−0.890212	+	46.8145i	−0.0298232	+	1.56835i
$892$	6.13082	−	6.13082i	0.205275	−	0.205275i
$893$	20.3551	+	14.2528i	0.681157	+	0.476951i
$894$	−1.06864	+	0.740727i	−0.0357408	+	0.0247736i
$895$	−4.45989	+	31.5467i	−0.149078	+	1.05449i
$896$	−2.71855	+	3.23984i	−0.0908202	+	0.108235i
$897$	0.727491	+	0.00345805i	0.0242902	+	0.000115461i
$898$	16.5216	+	35.4306i	0.551332	+	1.18234i
$899$	−18.0841	−	31.3225i	−0.603138	−	1.04467i
$900$	10.2990	+	10.9055i	0.343301	+	0.363517i
$901$	27.6160	−	47.8324i	0.920024	−	1.59353i
$902$	25.1108	+	2.19691i	0.836098	+	0.0731491i
$903$	−8.10097	−	47.2553i	−0.269583	−	1.57256i
$904$	−1.23946	−	0.218550i	−0.0412239	−	0.00726888i
$905$	23.0832	+	18.0650i	0.767311	+	0.600500i
$906$	4.30952	+	0.397684i	0.143174	+	0.0132122i
$907$	0.342126	−	3.91052i	0.0113601	−	0.129847i	−0.988397	−	0.151894i	$-0.951463\pi$
$907$	0.342126	−	3.91052i	0.0113601	−	0.129847i	0.999757	+	0.0220472i	$0.00701840\pi$
$908$	1.60640	+	5.99518i	0.0533104	+	0.198957i
$909$	17.1610	−	20.0612i	0.569193	−	0.665388i
$910$	−2.59777	−	2.42643i	−0.0861153	−	0.0804355i
$911$	10.6171	−	29.1702i	0.351760	−	0.966452i	−0.630045	−	0.776559i	$-0.716964\pi$
$911$	10.6171	−	29.1702i	0.351760	−	0.966452i	0.981805	−	0.189893i	$-0.0608143\pi$
$912$	−5.06457	−	2.95622i	−0.167705	−	0.0978902i
$913$	−2.16563	−	24.7532i	−0.0716718	−	0.819212i
$914$	−8.34368	+	3.03685i	−0.275985	+	0.100450i
$915$	−4.28420	+	29.2985i	−0.141631	+	0.968577i
$916$	4.16292	+	23.6091i	0.137547	+	0.780066i
$917$	−36.9248	−	36.9248i	−1.21936	−	1.21936i
$918$	20.0555	+	24.6054i	0.661930	+	0.812099i
$919$		−	36.3601i		−	1.19941i	−0.800222	−	0.599705i	$-0.795285\pi$
$919$		−	36.3601i		−	1.19941i	0.800222	−	0.599705i	$-0.204715\pi$
$920$	0.774069	−	2.37573i	0.0255203	−	0.0783255i
$921$	−25.2684	+	2.08972i	−0.832622	+	0.0688586i
$922$	−14.2273	+	30.5105i	−0.468550	+	1.00481i
$923$	0.0229299	−	0.00200610i	0.000754746	−	6.60317e-5i
$924$	−36.7647	−	10.0386i	−1.20947	−	0.330247i
$925$	−24.9993	−	15.0768i	−0.821973	−	0.495721i
$926$	8.57266	−	4.94943i	0.281715	−	0.162648i
$927$	−0.00140915	+	0.00506588i	−4.62826e−5	+	0.000166385i
$928$	−9.77986	+	2.62050i	−0.321040	+	0.0860223i
$929$	−23.1288	+	19.4073i	−0.758830	+	0.636734i	−0.937822	−	0.347117i	$-0.887161\pi$
$929$	−23.1288	+	19.4073i	−0.758830	+	0.636734i	0.178992	+	0.983850i	$0.442716\pi$
$930$	13.8119	+	0.801028i	0.452911	+	0.0262667i
$931$	6.40073	−	36.3003i	0.209775	−	1.18969i
$932$	−9.56988	+	6.70090i	−0.313472	+	0.219495i
$933$	−8.50779	+	23.0337i	−0.278533	+	0.754090i
$934$	5.10847	+	6.08804i	0.167154	+	0.199207i
$935$	69.2335	+	16.0434i	2.26418	+	0.524676i
$936$	1.12759	+	0.0107200i	0.0368565	+	0.000350395i
$937$	−5.91649	−	1.58532i	−0.193283	−	0.0517901i	0.160879	−	0.986974i	$-0.448567\pi$
$937$	−5.91649	−	1.58532i	−0.193283	−	0.0517901i	−0.354162	+	0.935184i	$0.615234\pi$
$938$	0.935264	−	0.436121i	0.0305375	−	0.0142398i
$939$	−3.04127	+	11.1381i	−0.0992482	+	0.363480i
$940$	−6.42476	+	15.1015i	−0.209553	+	0.492555i
$941$	10.4752	+	28.7803i	0.341481	+	0.938212i	0.984965	+	0.172753i	$0.0552661\pi$
$941$	10.4752	+	28.7803i	0.341481	+	0.938212i	−0.643484	+	0.765460i	$0.722512\pi$
$942$	−9.01921	−	7.64137i	−0.293862	−	0.248969i
$943$	3.10536	−	4.43492i	0.101125	−	0.144421i
$944$	3.01407			0.0980996
$945$	−13.6570	−	47.2042i	−0.444263	−	1.53555i
$946$	34.0508			1.10709
$947$	4.41542	−	6.30587i	0.143482	−	0.204913i	−0.740978	−	0.671529i	$-0.765638\pi$
$947$	4.41542	−	6.30587i	0.143482	−	0.204913i	0.884460	+	0.466616i	$0.154527\pi$
$948$	8.53988	−	3.06237i	0.277362	−	0.0994611i
$949$	0.850031	+	2.33544i	0.0275932	+	0.0758116i
$950$	−10.6320	−	13.1734i	−0.344946	−	0.427400i
$951$	11.0630	−	2.90802i	0.358742	−	0.0942992i
$952$	−23.4163	+	10.9192i	−0.758925	+	0.353893i
$953$	25.3300	+	6.78716i	0.820520	+	0.219858i	0.644574	−	0.764542i	$-0.277035\pi$
$953$	25.3300	+	6.78716i	0.820520	+	0.219858i	0.175946	+	0.984400i	$0.443701\pi$
$954$	4.96360	−	26.6651i	0.160703	−	0.863314i
$955$	−2.72542	+	1.69994i	−0.0881926	+	0.0550087i
$956$	11.8536	+	14.1265i	0.383372	+	0.456885i
$957$	−58.3124	−	70.1687i	−1.88497	−	2.26823i
$958$	−12.9137	+	9.04225i	−0.417222	+	0.292142i
$959$	−9.32739	+	52.8982i	−0.301197	+	1.70817i
$960$	1.21732	−	3.67670i	0.0392888	−	0.118665i
$961$	−13.9721	+	11.7240i	−0.450713	+	0.378193i
$962$	−2.11990	+	0.568024i	−0.0683482	+	0.0183138i
$963$	−13.9186	−	30.6048i	−0.448520	−	0.986226i
$964$	4.30913	−	2.48788i	0.138788	−	0.0801291i
$965$	−43.8985	−	2.33660i	−1.41314	−	0.0752179i
$966$	−5.81555	+	5.76052i	−0.187112	+	0.185342i
$967$	46.8539	−	4.09918i	1.50672	−	0.131821i	0.696333	−	0.717718i	$-0.254813\pi$
$967$	46.8539	−	4.09918i	1.50672	−	0.131821i	0.810385	+	0.585898i	$0.199258\pi$
$968$	6.79002	−	14.5613i	0.218240	−	0.468016i
$969$	−20.4085	−	29.4433i	−0.655616	−	0.945854i
$970$	−33.2956	−	10.8485i	−1.06906	−	0.348324i
$971$		−	52.7240i		−	1.69199i	−0.533188	−	0.845997i	$-0.679006\pi$
$971$		−	52.7240i		−	1.69199i	0.533188	−	0.845997i	$-0.320994\pi$
$972$	13.3110	+	8.11285i	0.426949	+	0.260220i
$973$	13.0590	+	13.0590i	0.418653	+	0.418653i
$974$	1.49444	+	8.47537i	0.0478848	+	0.271568i
$975$	3.03150	+	1.18596i	0.0970858	+	0.0379811i
$976$	7.18421	−	2.61484i	0.229961	−	0.0836990i
$977$	3.68487	+	42.1182i	0.117889	+	1.34748i	0.792755	+	0.609541i	$0.208646\pi$
$977$	3.68487	+	42.1182i	0.117889	+	1.34748i	−0.674866	+	0.737941i	$0.735798\pi$
$978$	0.00780654	−	1.64231i	0.000249626	−	0.0525152i
$979$	16.5082	−	45.3558i	0.527603	−	1.44958i
$980$	24.3300	−	0.829714i	0.777193	−	0.0265042i
$981$	−2.33174	+	6.22173i	−0.0744468	+	0.198645i
$982$	8.04072	+	30.0084i	0.256590	+	0.957606i
$983$	−2.31573	+	26.4689i	−0.0738602	+	0.844226i	0.865414	+	0.501058i	$0.167056\pi$
$983$	−2.31573	+	26.4689i	−0.0738602	+	0.844226i	−0.939274	+	0.343168i	$0.888500\pi$
$984$	4.84602	−	6.85129i	0.154485	−	0.218411i
$985$	5.35022	+	43.8704i	0.170472	+	1.39783i
$986$	−60.9134	−	10.7407i	−1.93988	−	0.342053i
$987$	41.3491	−	34.3624i	1.31616	−	1.09377i
$988$	−1.26778	−	0.110917i	−0.0403335	−	0.00352873i
$989$	3.65680	−	6.33377i	0.116280	−	0.201402i
$990$	34.6817	−	3.89538i	1.10226	−	0.123803i
$991$	−1.05011	−	1.81884i	−0.0333578	−	0.0577774i	0.848865	−	0.528610i	$-0.177287\pi$
$991$	−1.05011	−	1.81884i	−0.0333578	−	0.0577774i	−0.882222	+	0.470833i	$0.843953\pi$
$992$	−1.50968	−	3.23753i	−0.0479325	−	0.102792i
$993$	−8.09712	+	13.8719i	−0.256954	+	0.440212i
$994$	−0.166473	+	0.198395i	−0.00528020	+	0.00629269i
$995$	−17.2382	−	2.43704i	−0.546487	−	0.0772592i
$996$	−7.48064	−	3.53167i	−0.237033	−	0.111905i
$997$	40.6738	+	28.4801i	1.28815	+	0.901975i	0.998478	−	0.0551503i	$-0.0175638\pi$
$997$	40.6738	+	28.4801i	1.28815	+	0.901975i	0.289675	+	0.957125i	$0.406453\pi$
$998$	9.25966	−	9.25966i	0.293109	−	0.293109i
$999$	−29.1903	−	8.26941i	−0.923541	−	0.261632i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	270.2.r.a.203.13	yes	216
3.2	odd	2		810.2.s.a.233.8		216
5.2	odd	4	inner	270.2.r.a.257.18	yes	216
15.2	even	4		810.2.s.a.557.6		216
27.2	odd	18	inner	270.2.r.a.83.18	✓	216
27.25	even	9		810.2.s.a.413.6		216
135.2	even	36	inner	270.2.r.a.137.13	yes	216
135.52	odd	36		810.2.s.a.737.8		216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
270.2.r.a.83.18	✓	216	27.2	odd	18	inner
270.2.r.a.137.13	yes	216	135.2	even	36	inner
270.2.r.a.203.13	yes	216	1.1	even	1	trivial
270.2.r.a.257.18	yes	216	5.2	odd	4	inner
810.2.s.a.233.8		216	3.2	odd	2
810.2.s.a.413.6		216	27.25	even	9
810.2.s.a.557.6		216	15.2	even	4
810.2.s.a.737.8		216	135.52	odd	36

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 270 = 2 \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	270.r (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.573576 - 0.819152i) q^{2} +(-0.308872 + 1.70429i) q^{3} +(-0.342020 - 0.939693i) q^{4} +(-2.07393 + 0.835951i) q^{5} +(1.21891 + 1.23055i) q^{6} +(-3.83305 + 1.78738i) q^{7} +(-0.965926 - 0.258819i) q^{8} +(-2.80920 - 1.05281i) q^{9} +(-0.504786 + 2.17835i) q^{10} +(3.34414 + 3.98539i) q^{11} +(1.70715 - 0.292656i) q^{12} +(0.307904 - 0.215597i) q^{13} +(-0.734411 + 4.16505i) q^{14} +(-0.784123 - 3.79278i) q^{15} +(-0.766044 + 0.642788i) q^{16} +(-5.90088 + 1.58114i) q^{17} +(-2.47370 + 1.69729i) q^{18} +(2.93211 - 1.69286i) q^{19} +(1.49486 + 1.66294i) q^{20} +(-1.86229 - 7.08470i) q^{21} +(5.18276 - 0.453432i) q^{22} +(0.472247 - 1.01274i) q^{23} +(0.739450 - 1.56627i) q^{24} +(3.60237 - 3.46741i) q^{25} -0.375881i q^{26} +(2.66198 - 4.46249i) q^{27} +(2.99057 + 2.99057i) q^{28} +(1.75816 + 9.97103i) q^{29} +(-3.55661 - 1.53313i) q^{30} +(-3.35678 + 1.22177i) q^{31} +(0.0871557 + 0.996195i) q^{32} +(-7.82516 + 4.46840i) q^{33} +(-2.08941 + 5.74062i) q^{34} +(6.45532 - 6.91115i) q^{35} +(-0.0285197 + 2.99986i) q^{36} +(-1.51118 - 5.63980i) q^{37} +(0.295084 - 3.37283i) q^{38} +(0.272336 + 0.591349i) q^{39} +(2.21962 - 0.270694i) q^{40} +(4.77146 + 0.841337i) q^{41} +(-6.87161 - 2.53812i) q^{42} +(6.52010 + 0.570435i) q^{43} +(2.60128 - 4.50554i) q^{44} +(6.70618 - 0.164889i) q^{45} +(-0.558716 - 0.967725i) q^{46} +(3.10175 + 6.65173i) q^{47} +(-0.858886 - 1.50410i) q^{48} +(6.99804 - 8.33994i) q^{49} +(-0.774099 - 4.93971i) q^{50} +(-0.872094 - 10.5452i) q^{51} +(-0.307904 - 0.215597i) q^{52} +(-6.39299 + 6.39299i) q^{53} +(-2.12861 - 4.74015i) q^{54} +(-10.2671 - 5.46988i) q^{55} +(4.16505 - 0.734411i) q^{56} +(1.97947 + 5.52004i) q^{57} +(9.17623 + 4.27895i) q^{58} +(-2.30891 - 1.93741i) q^{59} +(-3.29586 + 2.03404i) q^{60} +(-7.18421 - 2.61484i) q^{61} +(-0.924557 + 3.45049i) q^{62} +(12.6496 - 0.985615i) q^{63} +(0.866025 + 0.500000i) q^{64} +(-0.458343 + 0.704525i) q^{65} +(-0.828029 + 8.97296i) q^{66} +(-0.139953 - 0.199873i) q^{67} +(3.50400 + 5.00423i) q^{68} +(1.58013 + 1.11765i) q^{69} +(-1.95866 - 9.25196i) q^{70} +(0.0530319 + 0.0306180i) q^{71} +(2.44099 + 1.74401i) q^{72} +(-1.71131 + 6.38669i) q^{73} +(-5.48663 - 1.99697i) q^{74} +(4.79679 + 7.21046i) q^{75} +(-2.59360 - 2.17629i) q^{76} +(-19.9417 - 9.29895i) q^{77} +(0.640610 + 0.116099i) q^{78} +(5.15835 - 0.909556i) q^{79} +(1.05138 - 1.97347i) q^{80} +(6.78317 + 5.91512i) q^{81} +(3.42598 - 3.42598i) q^{82} +(-3.91233 - 2.73944i) q^{83} +(-6.02050 + 4.17309i) q^{84} +(10.9163 - 8.21201i) q^{85} +(4.20705 - 5.01377i) q^{86} +(-17.5366 - 0.0833582i) q^{87} +(-2.19869 - 4.71511i) q^{88} +(-4.63875 - 8.03454i) q^{89} +(3.71144 - 5.58795i) q^{90} +(-0.794859 + 1.37674i) q^{91} +(-1.11318 - 0.0973907i) q^{92} +(-1.04543 - 6.09830i) q^{93} +(7.22787 + 1.27447i) q^{94} +(-4.66585 + 5.96196i) q^{95} +(-1.72472 - 0.159158i) q^{96} +(-1.36492 + 15.6011i) q^{97} +(-2.81777 - 10.5161i) q^{98} +(-5.19847 - 14.7165i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q + 12 q^{6} + 24 q^{11} - 24 q^{20} + 24 q^{23} + 36 q^{25} + 12 q^{27} - 72 q^{30} - 12 q^{33} - 108 q^{35} - 12 q^{36} - 36 q^{38} - 72 q^{41} - 48 q^{42} - 60 q^{45} - 48 q^{47} - 12 q^{48} - 48 q^{50}+ \cdots - 72 q^{97}+O(q^{100}) \) 216 * q + 12 * q^6 + 24 * q^11 - 24 * q^20 + 24 * q^23 + 36 * q^25 + 12 * q^27 - 72 * q^30 - 12 * q^33 - 108 * q^35 - 12 * q^36 - 36 * q^38 - 72 * q^41 - 48 * q^42 - 60 * q^45 - 48 * q^47 - 12 * q^48 - 48 * q^50 - 192 * q^51 - 12 * q^56 - 36 * q^57 + 36 * q^61 + 84 * q^63 + 24 * q^65 - 72 * q^67 + 36 * q^68 - 48 * q^72 - 36 * q^75 - 240 * q^77 + 24 * q^78 - 24 * q^81 - 60 * q^83 + 72 * q^86 - 252 * q^87 - 48 * q^92 - 96 * q^93 - 60 * q^95 - 72 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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