LMFDB - Embedded newform 270.2.r.a.257.18

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			257.18
Character	$\chi$	$=$	270.257
Dual form			270.2.r.a.83.18

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.819152 + 0.573576i) q^{2} +(1.70429 + 0.308872i) q^{3} +(0.342020 + 0.939693i) q^{4} +(-0.463117 + 2.18758i) q^{5} +(1.21891 + 1.23055i) q^{6} +(-1.78738 - 3.83305i) q^{7} +(-0.258819 + 0.965926i) q^{8} +(2.80920 + 1.05281i) q^{9} +(-1.63411 + 1.52633i) q^{10} +(3.34414 + 3.98539i) q^{11} +(0.292656 + 1.70715i) q^{12} +(-0.215597 - 0.307904i) q^{13} +(0.734411 - 4.16505i) q^{14} +(-1.46497 + 3.58523i) q^{15} +(-0.766044 + 0.642788i) q^{16} +(-1.58114 - 5.90088i) q^{17} +(1.69729 + 2.47370i) q^{18} +(-2.93211 + 1.69286i) q^{19} +(-2.21405 + 0.313010i) q^{20} +(-1.86229 - 7.08470i) q^{21} +(0.453432 + 5.18276i) q^{22} +(-1.01274 - 0.472247i) q^{23} +(-0.739450 + 1.56627i) q^{24} +(-4.57105 - 2.02621i) q^{25} -0.375881i q^{26} +(4.46249 + 2.66198i) q^{27} +(2.99057 - 2.99057i) q^{28} +(-1.75816 - 9.97103i) q^{29} +(-3.25643 + 2.09658i) q^{30} +(-3.35678 + 1.22177i) q^{31} +(-0.996195 + 0.0871557i) q^{32} +(4.46840 + 7.82516i) q^{33} +(2.08941 - 5.74062i) q^{34} +(9.21289 - 2.13490i) q^{35} +(-0.0285197 + 2.99986i) q^{36} +(5.63980 - 1.51118i) q^{37} +(-3.37283 - 0.295084i) q^{38} +(-0.272336 - 0.591349i) q^{39} +(-1.99318 - 1.01353i) q^{40} +(4.77146 + 0.841337i) q^{41} +(2.53812 - 6.87161i) q^{42} +(0.570435 - 6.52010i) q^{43} +(-2.60128 + 4.50554i) q^{44} +(-3.60410 + 5.65778i) q^{45} +(-0.558716 - 0.967725i) q^{46} +(-6.65173 + 3.10175i) q^{47} +(-1.50410 + 0.858886i) q^{48} +(-6.99804 + 8.33994i) q^{49} +(-2.58219 - 4.28162i) q^{50} +(-0.872094 - 10.5452i) q^{51} +(0.215597 - 0.307904i) 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} +(-5.52004 + 1.97947i) q^{57} +(4.27895 - 9.17623i) q^{58} +(2.30891 + 1.93741i) q^{59} +(-3.87006 - 0.150399i) q^{60} +(-7.18421 - 2.61484i) q^{61} +(-3.45049 - 0.924557i) q^{62} +(-0.985615 - 12.6496i) q^{63} +(-0.866025 - 0.500000i) q^{64} +(0.773412 - 0.329040i) q^{65} +(-0.828029 + 8.97296i) q^{66} +(0.199873 - 0.139953i) q^{67} +(5.00423 - 3.50400i) q^{68} +(-1.58013 - 1.11765i) q^{69} +(8.77128 + 3.53549i) q^{70} +(0.0530319 + 0.0306180i) q^{71} +(-1.74401 + 2.44099i) q^{72} +(6.38669 + 1.71131i) q^{73} +(5.48663 + 1.99697i) q^{74} +(-7.16454 - 4.86512i) q^{75} +(-2.59360 - 2.17629i) q^{76} +(9.29895 - 19.9417i) q^{77} +(0.116099 - 0.640610i) 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} +(-2.73944 + 3.91233i) q^{83} +(6.02050 - 4.17309i) q^{84} +(13.6409 - 0.726069i) q^{85} +(4.20705 - 5.01377i) q^{86} +(0.0833582 - 17.5366i) q^{87} +(-4.71511 + 2.19869i) q^{88} +(4.63875 + 8.03454i) q^{89} +(-6.19748 + 2.56735i) q^{90} +(-0.794859 + 1.37674i) q^{91} +(0.0973907 - 1.11318i) q^{92} +(-6.09830 + 1.04543i) q^{93} +(-7.22787 - 1.27447i) q^{94} +(-2.34535 - 7.19823i) q^{95} +(-1.72472 - 0.159158i) q^{96} +(-15.6011 - 1.36492i) q^{97} +(-10.5161 + 2.81777i) 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 $\left(\mathbb{Z}/270\mathbb{Z}\right)^\times$ .

$n$	$191$	$217$
$\chi(n)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	0.819152	+	0.573576i	0.579228	+	0.405580i
$2$	0.819152	+	0.573576i	0.579228	+	0.405580i
$3$	1.70429	+	0.308872i	0.983971	+	0.178327i
$3$	1.70429	+	0.308872i	0.983971	+	0.178327i
$4$	0.342020	+	0.939693i	0.171010	+	0.469846i
$5$	−0.463117	+	2.18758i	−0.207112	+	0.978317i
$5$	−0.463117	+	2.18758i	−0.207112	+	0.978317i
$6$	1.21891	+	1.23055i	0.497618	+	0.502371i
$7$	−1.78738	−	3.83305i	−0.675567	−	1.44876i	−0.882457	−	0.470393i	$-0.844112\pi$
$7$	−1.78738	−	3.83305i	−0.675567	−	1.44876i	0.206890	−	0.978364i	$-0.433666\pi$
$8$	−0.258819	+	0.965926i	−0.0915064	+	0.341506i
$9$	2.80920	+	1.05281i	0.936399	+	0.350938i
$10$	−1.63411	+	1.52633i	−0.516751	+	0.482668i
$11$	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	$0.490793\pi$
$12$	0.292656	+	1.70715i	0.0844825	+	0.492811i
$13$	−0.215597	−	0.307904i	−0.0597958	−	0.0853972i	0.788141	−	0.615495i	$-0.211044\pi$
$13$	−0.215597	−	0.307904i	−0.0597958	−	0.0853972i	−0.847936	+	0.530098i	$0.822155\pi$
$14$	0.734411	−	4.16505i	0.196280	−	1.11316i
$15$	−1.46497	+	3.58523i	−0.378253	+	0.925702i
$16$	−0.766044	+	0.642788i	−0.191511	+	0.160697i
$17$	−1.58114	−	5.90088i	−0.383482	−	1.43117i	−0.840546	−	0.541739i	$-0.817766\pi$
$17$	−1.58114	−	5.90088i	−0.383482	−	1.43117i	0.457065	−	0.889433i	$-0.348901\pi$
$18$	1.69729	+	2.47370i	0.400055	+	0.583057i
$19$	−2.93211	+	1.69286i	−0.672672	+	0.388368i	−0.797088	−	0.603863i	$-0.793628\pi$
$19$	−2.93211	+	1.69286i	−0.672672	+	0.388368i	0.124416	+	0.992230i	$0.460294\pi$
$20$	−2.21405	+	0.313010i	−0.495077	+	0.0699912i
$21$	−1.86229	−	7.08470i	−0.406385	−	1.54601i
$22$	0.453432	+	5.18276i	0.0966721	+	1.10497i
$23$	−1.01274	−	0.472247i	−0.211170	−	0.0984704i	0.314155	−	0.949372i	$-0.398279\pi$
$23$	−1.01274	−	0.472247i	−0.211170	−	0.0984704i	−0.525326	+	0.850901i	$0.676057\pi$
$24$	−0.739450	+	1.56627i	−0.150940	+	0.319714i
$25$	−4.57105	−	2.02621i	−0.914209	−	0.405243i
$26$		−	0.375881i		−	0.0737164i
$27$	4.46249	+	2.66198i	0.858808	+	0.512298i
$28$	2.99057	−	2.99057i	0.565165	−	0.565165i
$29$	−1.75816	−	9.97103i	−0.326483	−	1.85157i	−0.499045	−	0.866576i	$-0.666316\pi$
$29$	−1.75816	−	9.97103i	−0.326483	−	1.85157i	0.172563	−	0.984999i	$-0.444795\pi$
$30$	−3.25643	+	2.09658i	−0.594541	+	0.382781i
$31$	−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	$0.492839\pi$
$32$	−0.996195	+	0.0871557i	−0.176104	+	0.0154071i
$33$	4.46840	+	7.82516i	0.777848	+	1.36219i
$34$	2.08941	−	5.74062i	0.358331	−	0.984508i
$35$	9.21289	−	2.13490i	1.55726	−	0.360863i
$36$	−0.0285197	+	2.99986i	−0.00475329	+	0.499977i
$37$	5.63980	−	1.51118i	0.927178	−	0.248436i	0.236527	−	0.971625i	$-0.423991\pi$
$37$	5.63980	−	1.51118i	0.927178	−	0.248436i	0.690651	+	0.723188i	$0.257324\pi$
$38$	−3.37283	−	0.295084i	−0.547145	−	0.0478690i
$39$	−0.272336	−	0.591349i	−0.0436087	−	0.0946916i
$40$	−1.99318	−	1.01353i	−0.315149	−	0.160252i
$41$	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	$0.432052\pi$
$42$	2.53812	−	6.87161i	0.391640	−	1.06031i
$43$	0.570435	−	6.52010i	0.0869905	−	0.994306i	−0.819779	−	0.572680i	$-0.805904\pi$
$43$	0.570435	−	6.52010i	0.0869905	−	0.994306i	0.906770	−	0.421626i	$-0.138541\pi$
$44$	−2.60128	+	4.50554i	−0.392157	+	0.679236i
$45$	−3.60410	+	5.65778i	−0.537268	+	0.843411i
$46$	−0.558716	−	0.967725i	−0.0823782	−	0.142683i
$47$	−6.65173	+	3.10175i	−0.970254	+	0.452437i	−0.842102	−	0.539318i	$-0.818682\pi$
$47$	−6.65173	+	3.10175i	−0.970254	+	0.452437i	−0.128152	+	0.991755i	$0.540904\pi$
$48$	−1.50410	+	0.858886i	−0.217098	+	0.123969i
$49$	−6.99804	+	8.33994i	−0.999721	+	1.19142i
$50$	−2.58219	−	4.28162i	−0.365177	−	0.605513i
$51$	−0.872094	−	10.5452i	−0.122118	−	1.47662i
$52$	0.215597	−	0.307904i	0.0298979	−	0.0426986i
$53$	6.39299	+	6.39299i	0.878144	+	0.878144i	0.993343	−	0.115198i	$-0.0367504\pi$
$53$	6.39299	+	6.39299i	0.878144	+	0.878144i	−0.115198	+	0.993343i	$0.536750\pi$
$54$	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
$57$	−5.52004	+	1.97947i	−0.731147	+	0.262187i
$58$	4.27895	−	9.17623i	0.561853	−	1.20490i
$59$	2.30891	+	1.93741i	0.300595	+	0.252229i	0.780592	−	0.625041i	$-0.214918\pi$
$59$	2.30891	+	1.93741i	0.300595	+	0.252229i	−0.479997	+	0.877270i	$0.659362\pi$
$60$	−3.87006	−	0.150399i	−0.499623	−	0.0194165i
$61$	−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	$0.773909\pi$
$62$	−3.45049	−	0.924557i	−0.438213	−	0.117419i
$63$	−0.985615	−	12.6496i	−0.124176	−	1.59370i
$64$	−0.866025	−	0.500000i	−0.108253	−	0.0625000i
$65$	0.773412	−	0.329040i	0.0959300	−	0.0408124i
$66$	−0.828029	+	8.97296i	−0.101923	+	1.10450i
$67$	0.199873	−	0.139953i	0.0244184	−	0.0170979i	−0.561304	−	0.827610i	$-0.689700\pi$
$67$	0.199873	−	0.139953i	0.0244184	−	0.0170979i	0.585722	+	0.810512i	$0.300811\pi$
$68$	5.00423	−	3.50400i	0.606852	−	0.424922i
$69$	−1.58013	−	1.11765i	−0.190226	−	0.134549i
$70$	8.77128	+	3.53549i	1.04837	+	0.422572i
$71$	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	$0.665510\pi$
$72$	−1.74401	+	2.44099i	−0.205534	+	0.287673i
$73$	6.38669	+	1.71131i	0.747506	+	0.200294i	0.612412	−	0.790539i	$-0.290200\pi$
$73$	6.38669	+	1.71131i	0.747506	+	0.200294i	0.135094	+	0.990833i	$0.456866\pi$
$74$	5.48663	+	1.99697i	0.637808	+	0.232143i
$75$	−7.16454	−	4.86512i	−0.827290	−	0.561776i
$76$	−2.59360	−	2.17629i	−0.297507	−	0.249638i
$77$	9.29895	−	19.9417i	1.05971	−	2.27256i
$78$	0.116099	−	0.640610i	0.0131457	−	0.0725348i
$79$	−5.15835	+	0.909556i	−0.580360	+	0.102333i	−0.456119	−	0.889919i	$-0.650761\pi$
$79$	−5.15835	+	0.909556i	−0.580360	+	0.102333i	−0.124241	+	0.992252i	$0.539650\pi$
$80$	−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
$83$	−2.73944	+	3.91233i	−0.300693	+	0.429434i	−0.940857	−	0.338804i	$-0.889978\pi$
$83$	−2.73944	+	3.91233i	−0.300693	+	0.429434i	0.640164	+	0.768238i	$0.278866\pi$
$84$	6.02050	−	4.17309i	0.656890	−	0.455321i
$85$	13.6409	−	0.726069i	1.47956	−	0.0787533i
$86$	4.20705	−	5.01377i	0.453658	−	0.540648i
$87$	0.0833582	−	17.5366i	0.00893694	−	1.88012i
$88$	−4.71511	+	2.19869i	−0.502633	+	0.234382i
$89$	4.63875	+	8.03454i	0.491706	+	0.851660i	0.999954	−	0.00955058i	$-0.00304009\pi$
$89$	4.63875	+	8.03454i	0.491706	+	0.851660i	−0.508248	+	0.861211i	$0.669707\pi$
$90$	−6.19748	+	2.56735i	−0.653271	+	0.270622i
$91$	−0.794859	+	1.37674i	−0.0833238	+	0.144321i
$92$	0.0973907	−	1.11318i	0.0101537	−	0.116057i
$93$	−6.09830	+	1.04543i	−0.632364	+	0.108406i
$94$	−7.22787	−	1.27447i	−0.745497	−	0.131451i
$95$	−2.34535	−	7.19823i	−0.240628	−	0.738523i
$96$	−1.72472	−	0.159158i	−0.176029	−	0.0162440i
$97$	−15.6011	−	1.36492i	−1.58405	−	0.138587i	−0.739163	−	0.673527i	$-0.764779\pi$
$97$	−15.6011	−	1.36492i	−1.58405	−	0.138587i	−0.844890	+	0.534940i	$0.820334\pi$
$98$	−10.5161	+	2.81777i	−1.06228	+	0.284638i
$99$	5.19847	+	14.7165i	0.522465	+	1.47906i
$100$	0.340629	−	4.98838i	0.0340629	−	0.498838i
$101$	−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	$0.966864\pi$
$102$	5.33408	−	9.13830i	0.528152	−	0.904827i
$103$	−0.00174607		0.000152761i	−0.000172045		1.50520e-5i	−0.0872418	−	0.996187i	$-0.527805\pi$
$103$	−0.00174607		0.000152761i	−0.000172045		1.50520e-5i	0.0870697	+	0.996202i	$0.472250\pi$
$104$	0.353213	−	0.128559i	0.0346354	−	0.0126062i
$105$	16.3608	−	0.792873i	1.59665	−	0.0773765i
$106$	1.56996	+	8.90369i	0.152488	+	0.864803i
$107$	−7.92458	+	7.92458i	−0.766098	+	0.766098i	−0.977417	−	0.211319i	$-0.932224\pi$
$107$	−7.92458	+	7.92458i	−0.766098	+	0.766098i	0.211319	+	0.977417i	$0.432224\pi$
$108$	−0.975180	+	5.10382i	−0.0938367	+	0.491116i
$109$			2.21477i			0.212137i	0.994359	+	0.106068i	$0.0338262\pi$
$109$			2.21477i			0.212137i	−0.994359	+	0.106068i	$0.966174\pi$
$110$	−11.5477	−	1.40830i	−1.10103	−	0.134276i
$111$	10.0786	−	0.833510i	0.956619	−	0.0791132i
$112$	3.83305	+	1.78738i	0.362189	+	0.168892i
$113$	−0.109693	−	1.25379i	−0.0103190	−	0.117947i	0.989288	−	0.145976i	$-0.0466323\pi$
$113$	−0.109693	−	1.25379i	−0.0103190	−	0.117947i	−0.999607	+	0.0280294i	$0.991077\pi$
$114$	−5.65713	−	1.54468i	−0.529838	−	0.144673i
$115$	1.50210	−	1.99674i	0.140071	−	0.186197i
$116$	8.76838	−	5.06243i	0.814124	−	0.470034i
$117$	−0.281488	−	1.09195i	−0.0260236	−	0.100950i
$118$	0.780099	+	2.91137i	0.0718139	+	0.268013i
$119$	−19.7923	+	16.6077i	−1.81435	+	1.52242i
$120$	−3.08390	−	2.34298i	−0.281521	−	0.213883i
$121$	−2.78993	+	15.8225i	−0.253630	+	1.43841i
$122$	−4.38515	−	6.26265i	−0.397013	−	0.566993i
$123$	7.87208	+	2.90765i	0.709801	+	0.262174i
$124$	−2.29618	−	2.73648i	−0.206203	−	0.245743i
$125$	6.54944	−	9.06117i	0.585800	−	0.810456i
$126$	6.44813	−	10.9273i	0.574445	−	0.973477i
$127$	−1.93774	+	7.23174i	−0.171947	+	0.641713i	0.825105	+	0.564979i	$0.191116\pi$
$127$	−1.93774	+	7.23174i	−0.171947	+	0.641713i	−0.997052	+	0.0767340i	$0.975551\pi$
$128$	−0.422618	−	0.906308i	−0.0373545	−	0.0801070i
$129$	2.98606	−	10.9359i	0.262908	−	0.962856i
$130$	0.822272	+	0.174077i	0.0721180	+	0.0152676i
$131$	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	$0.707546\pi$
$132$	−5.82496	+	6.87528i	−0.506998	+	0.598417i
$133$	11.7296	+	8.21316i	1.01709	+	0.712171i
$134$	0.244000			0.0210784
$135$	−7.88996	+	8.52927i	−0.679060	+	0.734083i
$136$	6.10904			0.523846
$137$	10.4036	+	7.28471i	0.888843	+	0.622374i	0.926243	−	0.376926i	$-0.123019\pi$
$137$	10.4036	+	7.28471i	0.888843	+	0.622374i	−0.0374006	+	0.999300i	$0.511908\pi$
$138$	−0.653310	−	1.82185i	−0.0556135	−	0.155087i
$139$	1.49351	+	4.10338i	0.126678	+	0.348045i	0.986777	−	0.162082i	$-0.0518209\pi$
$139$	1.49351	+	4.10338i	0.126678	+	0.348045i	−0.860099	+	0.510126i	$0.829599\pi$
$140$	5.15714	+	7.92711i	0.435858	+	0.669963i
$141$	−12.2945	+	3.23175i	−1.03538	+	0.272162i
$142$	0.0258794	+	0.0554986i	0.00217175	+	0.00465734i
$143$	0.506132	−	1.88891i	0.0423249	−	0.157959i
$144$	−2.82870	+	0.999214i	−0.235725	+	0.0832679i
$145$	22.6267	+	0.771628i	1.87905	+	0.0640802i
$146$	4.25011	+	5.06508i	0.351741	+	0.419189i
$147$	−14.5027	+	12.0522i	−1.19616	+	0.994046i
$148$	3.34897	+	4.78283i	0.275284	+	0.393146i
$149$	0.130359	−	0.739301i	0.0106794	−	0.0605659i	−0.979002	−	0.203849i	$-0.934655\pi$
$149$	0.130359	−	0.739301i	0.0106794	−	0.0605659i	0.989682	+	0.143283i	$0.0457660\pi$
$150$	−3.07833	−	8.09468i	−0.251344	−	0.660928i
$151$	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	$0.245359\pi$
$152$	−0.876286	−	3.27034i	−0.0710762	−	0.265260i
$153$	1.77081	−	18.2414i	0.143161	−	1.47473i
$154$	19.0553	−	11.0016i	1.53552	−	0.886534i
$155$	−1.11814	−	7.90907i	−0.0898111	−	0.635272i
$156$	0.462542	−	0.458165i	0.0370330	−	0.0366826i
$157$	−0.594827	−	6.79890i	−0.0474723	−	0.542611i	−0.982275	−	0.187444i	$-0.939980\pi$
$157$	−0.594827	−	6.79890i	−0.0474723	−	0.542611i	0.934803	−	0.355167i	$-0.115576\pi$
$158$	−4.74717	−	2.21364i	−0.377665	−	0.176108i
$159$	8.92088	+	12.8701i	0.707471	+	1.02067i
$160$	0.270694	−	2.21962i	0.0214003	−	0.175477i
$161$			4.72596i			0.372458i
$162$	2.16367	+	8.73605i	0.169994	+	0.686369i
$163$	−0.670477	+	0.670477i	−0.0525158	+	0.0525158i	−0.732877	−	0.680361i	$-0.761823\pi$
$163$	−0.670477	+	0.670477i	−0.0525158	+	0.0525158i	0.680361	+	0.732877i	$0.261823\pi$
$164$	0.841337	+	4.77146i	0.0656974	+	0.372588i
$165$	−19.1876	+	6.15103i	−1.49375	+	0.478857i
$166$	−4.48804	+	1.63351i	−0.348340	+	0.126785i
$167$	−4.99662	+	0.437147i	−0.386650	+	0.0338275i	−0.278824	−	0.960342i	$-0.589945\pi$
$167$	−4.99662	+	0.437147i	−0.386650	+	0.0338275i	−0.107826	+	0.994170i	$0.534389\pi$
$168$	7.32529	+	0.0348200i	0.565158	+	0.00268642i
$169$	4.39794	−	12.0832i	0.338303	−	0.929480i
$170$	11.5904	+	7.22934i	0.888946	+	0.554465i
$171$	−10.0191	+	1.66859i	−0.766183	+	0.127601i
$172$	6.32199	−	1.69397i	0.482047	−	0.129164i
$173$	5.65464	+	0.494717i	0.429915	+	0.0376127i	0.300060	−	0.953920i	$-0.402993\pi$
$173$	5.65464	+	0.494717i	0.429915	+	0.0376127i	0.129855	+	0.991533i	$0.458549\pi$
$174$	10.1268	−	14.3173i	0.767714	−	1.08539i
$175$	0.403616	+	21.1427i	0.0305105	+	1.59824i
$176$	−5.12351	−	0.903414i	−0.386199	−	0.0680974i
$177$	3.33664	+	4.01506i	0.250797	+	0.301790i
$178$	−0.808587	+	9.24219i	−0.0606061	+	0.692731i
$179$	−7.12420	+	12.3395i	−0.532488	+	0.922296i	0.466793	+	0.884367i	$0.345409\pi$
$179$	−7.12420	+	12.3395i	−0.532488	+	0.922296i	−0.999280	+	0.0379289i	$0.987924\pi$
$180$	−6.54925	−	1.45168i	−0.488152	−	0.108202i
$181$	−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	$0.995307\pi$
$182$	−1.44077	+	0.671843i	−0.106797	+	0.0498004i
$183$	−11.4363	−	6.67544i	−0.845397	−	0.493463i
$184$	0.718272	−	0.856003i	0.0529517	−	0.0631054i
$185$	0.693945	+	13.0374i	0.0510199	+	0.958528i
$186$	−5.59507	−	2.64147i	−0.410250	−	0.193682i
$187$	18.2297	−	26.0348i	1.33309	−	1.90385i
$188$	−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	$0.427894\pi$
$192$	−1.32152	−	1.11964i	−0.0953725	−	0.0808027i
$193$	8.30860	−	17.8178i	0.598066	−	1.28256i	−0.341401	−	0.939918i	$-0.610902\pi$
$193$	8.30860	−	17.8178i	0.598066	−	1.28256i	0.939467	−	0.342639i	$-0.111321\pi$
$194$	−11.9968	−	10.0665i	−0.861320	−	0.722733i
$195$	1.41975	−	0.321894i	0.101670	−	0.0230513i
$196$	−10.2305	−	3.72358i	−0.730747	−	0.265970i
$197$	19.0913	+	5.11551i	1.36020	+	0.364465i	0.863890	−	0.503680i	$-0.168021\pi$
$197$	19.0913	+	5.11551i	1.36020	+	0.364465i	0.496311	+	0.868145i	$0.334688\pi$
$198$	−4.18270	+	15.0368i	−0.297251	+	1.06862i
$199$	−6.74271	−	3.89290i	−0.477978	−	0.275961i	0.241596	−	0.970377i	$-0.422329\pi$
$199$	−6.74271	−	3.89290i	−0.477978	−	0.275961i	−0.719573	+	0.694416i	$0.755663\pi$
$200$	3.14025	−	3.89087i	0.222049	−	0.275126i
$201$	0.383868	−	0.176784i	0.0270760	−	0.0124694i
$202$	−7.20849	+	5.04744i	−0.507188	+	0.355137i
$203$	−35.0770	+	24.5612i	−2.46192	+	1.72386i
$204$	9.61094	−	4.42616i	0.672900	−	0.309893i
$205$	−4.05024	+	10.0483i	−0.282881	+	0.701806i
$206$	−0.00151792		0.000876370i	−0.000105758		6.10596e-5i
$207$	−2.34779	−	2.39286i	−0.163183	−	0.166315i
$208$	0.363074	+	0.0972853i	0.0251746	+	0.00674552i
$209$	−16.5521	−	6.02446i	−1.14493	−	0.416721i
$210$	13.8568	+	8.73470i	0.956209	+	0.602752i
$211$	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	$0.716509\pi$
$212$	−3.82091	+	8.19397i	−0.262421	+	0.562764i
$213$	0.0809246	+	0.0685619i	0.00554486	+	0.00469779i
$214$	−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
$218$	−1.27034	+	1.81424i	−0.0860384	+	0.122876i
$219$	10.3562	+	4.88924i	0.699807	+	0.330384i
$220$	−8.65156	−	7.77710i	−0.583288	−	0.524332i
$221$	−1.47602	+	1.75905i	−0.0992876	+	0.118326i
$222$	8.73399	+	5.09808i	0.586187	+	0.342161i
$223$	7.85795	−	3.66422i	0.526208	−	0.245375i	−0.141314	−	0.989965i	$-0.545133\pi$
$223$	7.85795	−	3.66422i	0.526208	−	0.245375i	0.667522	+	0.744590i	$0.267355\pi$
$224$	2.11465	+	3.66269i	0.141291	+	0.244723i
$225$	−10.7077	−	10.5045i	−0.713849	−	0.700300i
$226$	0.629291	−	1.08996i	0.0418598	−	0.0725033i
$227$	0.540947	−	6.18305i	0.0359039	−	0.410383i	−0.956882	−	0.290479i	$-0.906186\pi$
$227$	0.540947	−	6.18305i	0.0359039	−	0.410383i	0.992785	−	0.119905i	$-0.0382589\pi$
$228$	−3.74805	−	4.51012i	−0.248221	−	0.298690i
$229$	23.6091	+	4.16292i	1.56013	+	0.275093i	0.886060	−	0.463571i	$-0.153432\pi$
$229$	23.6091	+	4.16292i	1.56013	+	0.275093i	0.674073	+	0.738665i	$0.264543\pi$
$230$	2.37573	−	0.774069i	0.156651	−	0.0510406i
$231$	22.0075	−	31.1141i	1.44799	−	2.04716i
$232$	10.0863	+	0.882439i	0.662200	+	0.0579350i
$233$	−11.2846	+	3.02370i	−0.739278	+	0.198089i	−0.608757	−	0.793357i	$-0.708332\pi$
$233$	−11.2846	+	3.02370i	−0.739278	+	0.198089i	−0.130521	+	0.991446i	$0.541665\pi$
$234$	0.395733	−	1.05592i	0.0258699	−	0.0690279i
$235$	−3.70481	−	15.9877i	−0.241675	−	1.04292i
$236$	−1.03087	+	2.83230i	−0.0671041	+	0.184367i
$237$	−9.07225	−	0.0431240i	−0.589306	−	0.00280120i
$238$	−25.7387	+	2.25184i	−1.66839	+	0.145965i
$239$	17.3288	−	6.30716i	1.12091	−	0.407976i	0.285923	−	0.958253i	$-0.407700\pi$
$239$	17.3288	−	6.30716i	1.12091	−	0.407976i	0.834983	+	0.550276i	$0.185478\pi$
$240$	−1.18231	−	3.68811i	−0.0763178	−	0.238066i
$241$	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
$243$	9.73345	+	12.1762i	0.624401	+	0.781104i
$244$		−	7.64528i		−	0.489439i
$245$	−15.0034	−	19.1712i	−0.958533	−	1.22480i
$246$	4.78067	+	6.89704i	0.304804	+	0.439740i
$247$	1.15339	+	0.537835i	0.0733885	+	0.0342216i
$248$	−0.311339	−	3.55862i	−0.0197700	−	0.225973i
$249$	−5.87721	+	5.82160i	−0.372453	+	0.368929i
$250$	10.5623	−	3.66587i	0.668016	−	0.231850i
$251$	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	$0.197829\pi$
$252$	11.5496	−	5.25259i	0.727557	−	0.330882i
$253$	−1.50465	−	5.61541i	−0.0945962	−	0.353038i
$254$	−5.73526	+	4.81246i	−0.359862	+	0.301960i
$255$	23.4723	+	2.97586i	1.46989	+	0.186356i
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	1.16005	+	1.65673i	0.0723622	+	0.103344i	0.853702	−	0.520762i	$-0.174352\pi$
$257$	1.16005	+	1.65673i	0.0723622	+	0.103344i	−0.781340	+	0.624106i	$0.785463\pi$
$258$	8.71864	−	7.24546i	0.542799	−	0.451083i
$259$	−15.8729	−	18.9166i	−0.986295	−	1.17542i
$260$	0.573719	+	0.614231i	0.0355806	+	0.0380930i
$261$	5.55862	−	29.8616i	0.344070	−	1.84839i
$262$	−3.19565	+	11.9263i	−0.197428	+	0.736812i
$263$	−4.72696	−	10.1370i	−0.291477	−	0.625074i	0.704976	−	0.709232i	$-0.250958\pi$
$263$	−4.72696	−	10.1370i	−0.291477	−	0.625074i	−0.996452	+	0.0841574i	$0.973180\pi$
$264$	−8.71503	+	2.29084i	−0.536373	+	0.140992i
$265$	−16.9459	+	11.0245i	−1.04098	+	0.677229i
$266$	4.89746	+	13.4556i	0.300282	+	0.825019i
$267$	5.42411	+	15.1260i	0.331950	+	0.925694i
$268$	0.199873	+	0.139953i	0.0122092	+	0.00854896i
$269$	−9.40361			−0.573348			−0.286674	−	0.958028i	$-0.592550\pi$
$269$	−9.40361			−0.573348			−0.286674	+	0.958028i	$0.592550\pi$
$270$	−11.3553	+	2.46128i	−0.691060	+	0.149788i
$271$	−1.37745			−0.0836741			−0.0418370	−	0.999124i	$-0.513321\pi$
$271$	−1.37745			−0.0836741			−0.0418370	+	0.999124i	$0.513321\pi$
$272$	5.00423	+	3.50400i	0.303426	+	0.212461i
$273$	−1.77990	+	2.10084i	−0.107725	+	0.127149i
$274$	4.34383	+	11.9346i	0.262420	+	0.720993i
$275$	−7.21095	−	24.9933i	−0.434837	−	1.50715i
$276$	0.509812	−	1.86710i	0.0306871	−	0.112386i
$277$	12.2207	+	26.2073i	0.734269	+	1.57465i	0.816041	+	0.577994i	$0.196164\pi$
$277$	12.2207	+	26.2073i	0.734269	+	1.57465i	−0.0817715	+	0.996651i	$0.526058\pi$
$278$	−1.13019	+	4.21794i	−0.0677845	+	0.252975i
$279$	−10.7162	−	0.101879i	−0.641560	−	0.00609931i
$280$	−0.322321	+	9.45152i	−0.0192624	+	0.564836i
$281$	−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	$-0.646140\pi$
$282$	−11.9247	−	4.40455i	−0.710107	−	0.262287i
$283$	−15.0389	−	21.4778i	−0.893970	−	1.27672i	−0.960313	−	0.278924i	$-0.910022\pi$
$283$	−15.0389	−	21.4778i	−0.893970	−	1.27672i	0.0663434	−	0.997797i	$-0.478867\pi$
$284$	−0.0106335	+	0.0603057i	−0.000630983	+	0.00357848i
$285$	−1.77382	−	12.9923i	−0.105072	−	0.769596i
$286$	1.49803	−	1.25700i	0.0885805	−	0.0743279i
$287$	−5.30353	−	19.7930i	−0.313057	−	1.16835i
$288$	−2.89027	−	0.803970i	−0.170311	−	0.0473744i
$289$	−17.5979	+	10.1602i	−1.03517	+	0.597657i
$290$	18.0921	+	13.6102i	1.06241	+	0.799220i
$291$	−26.1672	−	7.14497i	−1.53395	−	0.418845i
$292$	0.576273	+	6.58683i	0.0337238	+	0.385465i
$293$	−21.1017	−	9.83988i	−1.23277	−	0.574852i	−0.306561	−	0.951851i	$-0.599178\pi$
$293$	−21.1017	−	9.83988i	−1.23277	−	0.574852i	−0.926214	+	0.376999i	$0.876956\pi$
$294$	−18.7927	+	1.55417i	−1.09601	+	0.0906413i
$295$	−5.30754	+	4.15369i	−0.309017	+	0.241837i
$296$			5.83875i			0.339371i
$297$	4.31417	+	26.6868i	0.250334	+	1.54852i
$298$	0.530829	−	0.530829i	0.0307501	−	0.0307501i
$299$	0.0729361	+	0.413641i	0.00421800	+	0.0239215i
$300$	2.12130	−	8.39643i	0.122473	−	0.484768i
$301$	−26.0115	+	9.46740i	−1.49928	+	0.545692i
$302$	2.48917	−	0.217774i	0.143235	−	0.0125315i
$303$	−7.68363	+	13.1635i	−0.441413	+	0.756226i
$304$	1.15798	−	3.18153i	0.0664148	−	0.182473i
$305$	9.04731	−	14.5051i	0.518047	−	0.830559i
$306$	11.9134	−	13.9268i	0.681042	−	0.796140i
$307$	−14.1397	+	3.78873i	−0.806997	+	0.216234i	−0.638654	−	0.769494i	$-0.720508\pi$
$307$	−14.1397	+	3.78873i	−0.806997	+	0.216234i	−0.168343	+	0.985728i	$0.553842\pi$
$308$	21.9195	+	1.91770i	1.24898	+	0.109271i
$309$	−0.00302299		0.000278963i	−0.000171972		1.58696e-5i
$310$	3.62053	−	7.12007i	0.205632	−	0.404393i
$311$	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	$0.423891\pi$
$312$	0.641685	−	0.110004i	0.0363283	−	0.00622775i
$313$	0.580982	−	6.64066i	0.0328391	−	0.375352i	−0.961937	−	0.273271i	$-0.911894\pi$
$313$	0.580982	−	6.64066i	0.0328391	−	0.375352i	0.994776	−	0.102081i	$-0.0325501\pi$
$314$	3.41244	−	5.91051i	0.192575	−	0.333550i
$315$	28.1285	+	3.70212i	1.58486	+	0.208591i
$316$	−2.61896	−	4.53618i	−0.147328	−	0.255180i
$317$	5.98543	−	2.79105i	0.336175	−	0.156761i	−0.247199	−	0.968965i	$-0.579510\pi$
$317$	5.98543	−	2.79105i	0.336175	−	0.156761i	0.583374	+	0.812204i	$0.301732\pi$
$318$	−0.0744352	+	15.6594i	−0.00417412	+	0.878134i
$319$	33.8589	−	40.3515i	1.89573	−	2.25925i
$320$	1.49486	−	1.66294i	0.0835654	−	0.0929614i
$321$	−15.9534	+	11.0581i	−0.890435	+	0.617202i
$322$	−2.71070	+	3.87128i	−0.151061	+	0.215738i
$323$	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
$327$	−0.684081	+	3.77461i	−0.0378298	+	0.208736i
$328$	−2.04761	+	4.39112i	−0.113061	+	0.242459i
$329$	23.7783	+	19.9524i	1.31094	+	1.10001i
$330$	−19.2456	−	5.96691i	−1.05944	−	0.328468i
$331$	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	$0.529082\pi$
$332$	−4.61333	−	1.23614i	−0.253190	−	0.0678419i
$333$	17.4343	+	1.69246i	0.955394	+	0.0927462i
$334$	−4.34373	−	2.50785i	−0.237678	−	0.137224i
$335$	0.213593	+	0.502053i	0.0116698	+	0.0274301i
$336$	5.98055	+	4.23014i	0.326266	+	0.230773i
$337$	28.8075	−	20.1713i	1.56925	−	1.09880i	0.619849	−	0.784721i	$-0.287194\pi$
$337$	28.8075	−	20.1713i	1.56925	−	1.09880i	0.949397	−	0.314078i	$-0.101695\pi$
$338$	10.5332	−	7.37545i	0.572933	−	0.401172i
$339$	0.200314	−	2.17071i	0.0108795	−	0.117897i
$340$	5.34775	+	12.5699i	0.290022	+	0.681700i
$341$	−16.0948	−	9.29232i	−0.871581	−	0.503207i
$342$	−9.16426	−	4.37991i	−0.495547	−	0.236838i
$343$	15.8792	+	4.25483i	0.857399	+	0.229739i
$344$	6.15030	+	2.23852i	0.331602	+	0.120693i
$345$	3.17674	−	2.93907i	0.171030	−	0.158234i
$346$	4.34826	+	3.64862i	0.233764	+	0.196151i
$347$	−7.84524	+	16.8242i	−0.421155	+	0.903169i	0.575212	+	0.818004i	$0.304919\pi$
$347$	−7.84524	+	16.8242i	−0.421155	+	0.903169i	−0.996367	+	0.0851649i	$0.972858\pi$
$348$	16.5075	−	5.91953i	0.884894	−	0.317320i
$349$	−9.68283	+	1.70734i	−0.518310	+	0.0913920i	−0.426683	−	0.904401i	$-0.640318\pi$
$349$	−9.68283	+	1.70734i	−0.518310	+	0.0913920i	−0.0916271	+	0.995793i	$0.529207\pi$
$350$	−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
$353$	1.87815	−	2.68228i	0.0999639	−	0.142763i	−0.766054	−	0.642776i	$-0.777783\pi$
$353$	1.87815	−	2.68228i	0.0999639	−	0.142763i	0.866018	+	0.500013i	$0.166671\pi$
$354$	0.430273	+	5.20276i	0.0228687	+	0.276524i
$355$	−0.0915394	+	0.101832i	−0.00485841	+	0.00540468i
$356$	−5.96346	+	7.10697i	−0.316063	+	0.376669i
$357$	−38.8614	+	22.1910i	−2.05676	+	1.17447i
$358$	−12.9134	+	6.02163i	−0.682496	+	0.318253i
$359$	−8.24511	−	14.2809i	−0.435160	−	0.753719i	0.562149	−	0.827036i	$-0.309975\pi$
$359$	−8.24511	−	14.2809i	−0.435160	−	0.753719i	−0.997309	+	0.0733169i	$0.976642\pi$
$360$	−4.53218	−	4.94564i	−0.238867	−	0.260658i
$361$	−3.76848	+	6.52720i	−0.198341	+	0.343537i
$362$	1.14249	−	13.0587i	0.0600479	−	0.686351i
$363$	−9.64196	+	26.1043i	−0.506072	+	1.37012i
$364$	−1.56557	−	0.276051i	−0.0820579	−	0.0144690i
$365$	−6.70142	+	13.1789i	−0.350768	+	0.689815i
$366$	−5.53921	−	12.0278i	−0.289539	−	0.628703i
$367$	−32.6051	−	2.85258i	−1.70197	−	0.148903i	−0.805675	−	0.592358i	$-0.798197\pi$
$367$	−32.6051	−	2.85258i	−1.70197	−	0.148903i	−0.896297	+	0.443455i	$0.853753\pi$
$368$	1.07936	−	0.289213i	0.0562654	−	0.0150763i
$369$	12.5182	+	7.38694i	0.651671	+	0.384549i
$370$	−6.90949	+	11.0776i	−0.359207	+	0.575899i
$371$	13.0779	−	35.9314i	0.678973	−	1.86546i
$372$	−3.06812	−	5.37297i	−0.159075	−	0.278575i
$373$	−6.17963	+	0.540647i	−0.319969	+	0.0279937i	−0.246009	−	0.969268i	$-0.579119\pi$
$373$	−6.17963	+	0.540647i	−0.319969	+	0.0279937i	−0.0739600	+	0.997261i	$0.523564\pi$
$374$	29.8659	−	10.8703i	1.54433	−	0.562089i
$375$	13.9609	−	13.4199i	0.720937	−	0.693001i
$376$	−1.27447	−	7.22787i	−0.0657257	−	0.372749i
$377$	−2.69107	+	2.69107i	−0.138597	+	0.138597i
$378$	14.3646	−	16.6315i	0.738835	−	0.855434i
$379$			6.82213i			0.350429i	0.984530	+	0.175215i	$0.0560620\pi$
$379$			6.82213i			0.350429i	−0.984530	+	0.175215i	$0.943938\pi$
$380$	5.96196	−	4.66585i	0.305842	−	0.239353i
$381$	−5.53615	+	11.7265i	−0.283626	+	0.600765i
$382$	1.30191	+	0.607093i	0.0666117	+	0.0310616i
$383$	0.301009	+	3.44055i	0.0153808	+	0.175804i	0.999999	+	0.00108604i	$0.000345697\pi$
$383$	0.301009	+	3.44055i	0.0153808	+	0.175804i	−0.984619	+	0.174718i	$0.944099\pi$
$384$	−0.440330	−	1.67514i	−0.0224705	−	0.0854844i
$385$	39.3175	+	29.5776i	2.00381	+	1.50741i
$386$	17.0259	−	9.82991i	0.866596	−	0.500329i
$387$	8.46692	−	17.7157i	0.430398	−	0.900539i
$388$	−4.05329	−	15.1271i	−0.205775	−	0.767961i
$389$	9.14718	−	7.67539i	0.463780	−	0.389158i	−0.380739	−	0.924682i	$-0.624331\pi$
$389$	9.14718	−	7.67539i	0.463780	−	0.389158i	0.844520	+	0.535525i	$0.179886\pi$
$390$	1.34762	+	0.550654i	0.0682394	+	0.0278835i
$391$	−1.18540	+	6.72273i	−0.0599482	+	0.339983i
$392$	−6.24454	−	8.91813i	−0.315397	−	0.450433i
$393$	3.61344	+	21.0783i	0.182274	+	1.06326i
$394$	12.7046	+	15.1407i	0.640047	+	0.762778i
$395$	0.399189	−	11.7056i	0.0200854	−	0.588970i
$396$	−12.0510	+	9.91830i	−0.605585	+	0.498413i
$397$	0.674193	−	2.51612i	0.0338368	−	0.126280i	−0.946942	−	0.321406i	$-0.895845\pi$
$397$	0.674193	−	2.51612i	0.0338368	−	0.126280i	0.980778	+	0.195125i	$0.0625113\pi$
$398$	−3.29042	−	7.05634i	−0.164934	−	0.353702i
$399$	17.4538	+	17.6205i	0.873783	+	0.882130i
$400$	4.80405	−	1.38604i	0.240202	−	0.0693020i
$401$	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	$0.834944\pi$
$402$	0.415846	+	0.0753647i	0.0207405	+	0.00375885i
$403$	1.09990	+	0.770158i	0.0547899	+	0.0383643i
$404$	−8.79994			−0.437814
$405$	−16.0812	+	12.0994i	−0.799082	+	0.601222i
$406$	−42.8211			−2.12518
$407$	24.8829	+	17.4232i	1.23340	+	0.863636i
$408$	10.4116	+	1.88691i	0.515449	+	0.0934160i
$409$	1.32960	+	3.65304i	0.0657444	+	0.180631i	0.968215	−	0.250121i	$-0.0804704\pi$
$409$	1.32960	+	3.65304i	0.0657444	+	0.180631i	−0.902470	+	0.430752i	$0.858248\pi$
$410$	−9.08125	+	5.90799i	−0.448491	+	0.291775i
$411$	15.4808	+	15.6286i	0.763609	+	0.770904i
$412$	−0.000740740	−	0.00158852i	−3.64936e−5	−	7.82609e-5i
$413$	3.29928	−	12.3131i	0.162347	−	0.605886i
$414$	−0.550709	−	3.30675i	−0.0270659	−	0.162518i
$415$	−7.28987	−	7.80463i	−0.357846	−	0.383114i
$416$	0.241612	+	0.287942i	0.0118460	+	0.0141175i
$417$	1.27795	+	7.45465i	0.0625815	+	0.365056i
$418$	−10.1032	−	14.4288i	−0.494162	−	0.705737i
$419$	2.47543	−	14.0389i	0.120933	−	0.685844i	−0.862708	−	0.505703i	$-0.831233\pi$
$419$	2.47543	−	14.0389i	0.120933	−	0.685844i	0.983641	−	0.180141i	$-0.0576556\pi$
$420$	6.34079	+	15.1030i	0.309399	+	0.736950i
$421$	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	$0.0333392\pi$
$422$	0.134943	+	0.503615i	0.00656893	+	0.0245156i
$423$	−21.9516	+	1.71040i	−1.06732	+	0.0831624i
$424$	−7.82978	+	4.52052i	−0.380248	+	0.219536i
$425$	−4.72900	+	30.1769i	−0.229390	+	1.46379i
$426$	0.0269640	+	0.102579i	0.00130641	+	0.00496997i
$427$	2.81811	+	32.2112i	0.136378	+	1.55881i
$428$	−10.1570	−	4.73630i	−0.490959	−	0.228938i
$429$	1.44603	−	3.06292i	0.0698148	−	0.147879i
$430$	9.01968	+	11.5252i	0.434968	+	0.555796i
$431$			38.9178i			1.87461i	0.348515	+	0.937303i	$0.386686\pi$
$431$			38.9178i			1.87461i	−0.348515	+	0.937303i	$0.613314\pi$
$432$	−5.12956	+	0.829241i	−0.246796	+	0.0398969i
$433$	8.50667	−	8.50667i	0.408804	−	0.408804i	−0.472517	−	0.881321i	$-0.656655\pi$
$433$	8.50667	−	8.50667i	0.408804	−	0.408804i	0.881321	+	0.472517i	$0.156655\pi$
$434$	2.62347	+	14.8785i	0.125931	+	0.714189i
$435$	38.3241	+	8.30383i	1.83750	+	0.398138i
$436$	−2.08121	+	0.757497i	−0.0996717	+	0.0362775i
$437$	3.76891	−	0.329737i	0.180291	−	0.0157734i
$438$	5.67894	+	9.94509i	0.271350	+	0.475195i
$439$	−12.9045	+	35.4547i	−0.615896	+	1.69216i	0.100917	+	0.994895i	$0.467822\pi$
$439$	−12.9045	+	35.4547i	−0.615896	+	1.69216i	−0.716813	+	0.697266i	$0.754400\pi$
$440$	−2.62618	−	11.3330i	−0.125198	−	0.540278i
$441$	−28.4393	+	16.0609i	−1.35425	+	0.764805i
$442$	−2.21803	+	0.594319i	−0.105501	+	0.0282689i
$443$	37.0206	+	3.23888i	1.75890	+	0.153884i	0.920391	−	0.390999i	$-0.127871\pi$
$443$	37.0206	+	3.23888i	1.75890	+	0.153884i	0.838512	+	0.544883i	$0.183426\pi$
$444$	4.23033	+	9.18572i	0.200763	+	0.435935i
$445$	−19.7245	+	6.42671i	−0.935032	+	0.304655i
$446$	8.53857	+	1.50558i	0.404313	+	0.0712913i
$447$	0.450518	−	1.21972i	0.0213088	−	0.0576906i
$448$	−0.368608	+	4.21321i	−0.0174151	+	0.199056i
$449$	19.5467	−	33.8559i	0.922466	−	1.59776i	0.126878	−	0.991918i	$-0.459504\pi$
$449$	19.5467	−	33.8559i	0.922466	−	1.59776i	0.795587	−	0.605839i	$-0.207162\pi$
$450$	−2.74613	−	14.7465i	−0.129454	−	0.695156i
$451$	12.6034	+	21.8297i	0.593469	+	1.02792i
$452$	1.14066	−	0.531900i	0.0536523	−	0.0250185i
$453$	3.75826	−	2.14608i	0.176578	−	0.100831i
$454$	3.98957	−	4.75458i	0.187240	−	0.223144i
$455$	−2.64361	−	2.37641i	−0.123934	−	0.111408i
$456$	−0.483326	−	5.84427i	−0.0226338	−	0.273683i
$457$	5.09288	−	7.27339i	0.238235	−	0.340235i	−0.682175	−	0.731189i	$-0.738966\pi$
$457$	5.09288	−	7.27339i	0.238235	−	0.340235i	0.920410	+	0.390954i	$0.127855\pi$
$458$	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	$0.731247\pi$
$462$	35.8738	−	12.8642i	1.66900	−	0.598498i
$463$	4.18344	−	8.97141i	0.194421	−	0.416937i	−0.784796	−	0.619755i	$-0.787232\pi$
$463$	4.18344	−	8.97141i	0.194421	−	0.416937i	0.979216	+	0.202818i	$0.0650099\pi$
$464$	7.75609	+	6.50813i	0.360067	+	0.302132i
$465$	0.537258	−	13.8247i	0.0249148	−	0.641105i
$466$	−10.9781	−	3.99571i	−0.508551	−	0.185098i
$467$	−7.67657	−	2.05693i	−0.355229	−	0.0951834i	0.0767911	−	0.997047i	$-0.475533\pi$
$467$	−7.67657	−	2.05693i	−0.355229	−	0.0951834i	−0.432021	+	0.901864i	$0.642199\pi$
$468$	0.929819	−	0.637980i	0.0429809	−	0.0294906i
$469$	−0.893695	−	0.515975i	−0.0412670	−	0.0238255i
$470$	6.13535	−	15.2213i	0.283003	−	0.702108i
$471$	1.08623	−	11.7710i	0.0500510	−	0.542380i
$472$	−2.46898	+	1.72880i	−0.113644	+	0.0795745i
$473$	27.8927	−	19.5307i	1.28251	−	0.898023i
$474$	−7.40682	−	5.23895i	−0.340206	−	0.240633i
$475$	16.8329	−	1.79703i	0.772346	−	0.0824535i
$476$	−22.3755	−	12.9185i	−1.02558	−	0.592118i
$477$	11.2285	+	24.6898i	0.514119	+	1.13047i
$478$	17.8125	+	4.77286i	0.814727	+	0.218305i
$479$	14.8140	+	5.39184i	0.676867	+	0.246359i	0.657502	−	0.753453i	$-0.271613\pi$
$479$	14.8140	+	5.39184i	0.676867	+	0.246359i	0.0193652	+	0.999812i	$0.493835\pi$
$480$	1.14692	−	3.69927i	0.0523495	−	0.168848i
$481$	−1.68122	−	1.41071i	−0.0766571	−	0.0643229i
$482$	−2.10284	+	4.50956i	−0.0957819	+	0.205405i
$483$	−1.45972	+	8.05440i	−0.0664195	+	0.366488i
$484$	−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	0.555655	−	0.831413i	$-0.312467\pi$
$487$	−6.08544	−	6.08544i	−0.275758	−	0.275758i	−0.831413	+	0.555655i	$0.812467\pi$
$488$	4.38515	−	6.26265i	0.198506	−	0.283497i
$489$	−1.34978	+	0.935595i	−0.0610391	+	0.0423091i
$490$	−1.29394	−	24.3097i	−0.0584543	−	1.09820i
$491$	−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	$0.974952\pi$
$492$	−0.0398896	+	8.39181i	−0.00179836	+	0.378332i
$493$	−56.0579	+	26.1402i	−2.52472	+	1.17730i
$494$	0.636313	+	1.10213i	0.0286291	+	0.0495870i
$495$	−34.6010	+	4.55662i	−1.55520	+	0.204805i
$496$	1.78611	−	3.09363i	0.0801986	−	0.138908i
$497$	0.0225721	−	0.258000i	0.00101250	−	0.0115729i
$498$	−8.15346	+	1.39775i	−0.365365	+	0.0626346i
$499$	−12.8962	−	2.27395i	−0.577313	−	0.101796i	−0.122635	−	0.992452i	$-0.539134\pi$
$499$	−12.8962	−	2.27395i	−0.577313	−	0.101796i	−0.454678	+	0.890656i	$0.650246\pi$
$500$	10.7548	+	3.05536i	0.480967	+	0.136640i
$501$	−8.65070	−	0.798290i	−0.386485	−	0.0356650i
$502$	13.0352	+	1.14043i	0.581788	+	0.0508999i
$503$	−6.77201	+	1.81455i	−0.301949	+	0.0809070i	−0.406613	−	0.913601i	$-0.633290\pi$
$503$	−6.77201	+	1.81455i	−0.301949	+	0.0809070i	0.104664	+	0.994508i	$0.466623\pi$
$504$	12.4736	+	2.32192i	0.555620	+	0.103427i
$505$	−16.6958	−	10.4137i	−0.742953	−	0.463405i
$506$	1.98833	−	5.46291i	0.0883923	−	0.242856i
$507$	11.2275	−	19.2349i	0.498632	−	0.854253i
$508$	−7.45836	+	0.652522i	−0.330911	+	0.0289510i
$509$	−15.4656	+	5.62900i	−0.685499	+	0.249501i	−0.661207	−	0.750204i	$-0.729955\pi$
$509$	−15.4656	+	5.62900i	−0.685499	+	0.249501i	−0.0242921	+	0.999705i	$0.507733\pi$
$510$	17.5205	+	15.9008i	0.775821	+	0.704101i
$511$	−4.85592	−	27.5393i	−0.214813	−	1.21827i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−17.5909	−	0.250864i	−0.776656	−	0.0110759i
$514$			2.02249i			0.0892083i
$515$	0.000474457	−	0.00389042i	2.09071e−5	−	0.000171432i
$516$	11.2977	−	0.934331i	0.497354	−	0.0411316i
$517$	−34.6060	−	16.1370i	−1.52197	−	0.709706i
$518$	−2.15221	−	24.5999i	−0.0945628	−	1.08086i
$519$	9.48434	+	2.58970i	0.416316	+	0.113675i
$520$	0.117655	+	0.832221i	0.00515950	+	0.0364953i
$521$	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	$0.325659\pi$
$522$	21.6813	−	21.2729i	0.948963	−	0.931090i
$523$	−0.834549	−	3.11458i	−0.0364923	−	0.136191i	0.945276	−	0.326271i	$-0.105792\pi$
$523$	−0.834549	−	3.11458i	−0.0364923	−	0.136191i	−0.981769	+	0.190080i	$0.939125\pi$
$524$	−9.45840	+	7.93654i	−0.413192	+	0.346709i
$525$	−5.84250	+	36.1579i	−0.254988	+	1.57806i
$526$	1.94224	−	11.0150i	0.0846859	−	0.480278i
$527$	12.5170	+	17.8762i	0.545251	+	0.778699i
$528$	−8.45291	−	3.12219i	−0.367866	−	0.135876i
$529$	−13.9815	−	16.6625i	−0.607891	−	0.724456i
$530$	−20.2047	−	0.689030i	−0.877634	−	0.0299295i
$531$	4.44646	+	7.87341i	0.192960	+	0.341677i
$532$	−3.70608	+	13.8313i	−0.160679	+	0.599662i
$533$	−0.769660	−	1.65054i	−0.0333377	−	0.0714929i
$534$	−4.23272	+	15.5016i	−0.183168	+	0.670820i
$535$	−13.6657	−	21.0057i	−0.590819	−	0.908155i
$536$	0.0834528	+	0.229285i	0.00360461	+	0.00990359i
$537$	−15.9530	+	18.8296i	−0.688423	+	0.812555i
$538$	−7.70299	−	5.39369i	−0.332099	−	0.232538i
$539$	−56.6403			−2.43967
$540$	−10.7134	−	4.49696i	−0.461032	−	0.193518i
$541$	45.1758			1.94226			0.971129	−	0.238553i	$-0.0766732\pi$
$541$	45.1758			1.94226			0.971129	+	0.238553i	$0.0766732\pi$
$542$	−1.12834	−	0.790072i	−0.0484664	−	0.0339365i
$543$	−7.66398	−	21.3722i	−0.328893	−	0.917167i
$544$	2.08941	+	5.74062i	0.0895829	+	0.246127i
$545$	−4.84500	−	1.02570i	−0.207537	−	0.0439361i
$546$	−2.66301	+	0.700000i	−0.113966	+	0.0299573i
$547$	−18.1023	−	38.8206i	−0.774000	−	1.65985i	−0.751169	−	0.660110i	$-0.770510\pi$
$547$	−18.1023	−	38.8206i	−0.774000	−	1.65985i	−0.0228315	−	0.999739i	$-0.507268\pi$
$548$	−3.28713	+	12.2677i	−0.140419	+	0.524052i
$549$	−17.4289	−	14.9092i	−0.743848	−	0.636311i
$550$	8.42872	−	24.6094i	0.359402	−	1.04935i
$551$	22.0346	+	26.2599i	0.938707	+	1.11871i
$552$	1.48854	−	1.23702i	0.0633564	−	0.0526511i
$553$	12.7063	+	18.1465i	0.540327	+	0.771668i
$554$	−5.02131	+	28.4773i	−0.213335	+	1.20988i
$555$	−2.84420	+	22.4338i	−0.120730	+	0.952262i
$556$	−3.34511	+	2.80688i	−0.141864	+	0.119038i
$557$	−5.41667	−	20.2153i	−0.229512	−	0.856549i	−0.980547	−	0.196286i	$-0.937112\pi$
$557$	−5.41667	−	20.2153i	−0.229512	−	0.856549i	0.751035	−	0.660262i	$-0.229555\pi$
$558$	−8.71973	−	6.22999i	−0.369136	−	0.263737i
$559$	−2.13055	+	1.23007i	−0.0901127	+	0.0520266i
$560$	−5.68520	+	7.55736i	−0.240243	+	0.319357i
$561$	39.1102	−	38.7401i	1.65123	−	1.63561i
$562$	−2.83892	−	32.4490i	−0.119753	−	1.36878i
$563$	−33.8407	−	15.7802i	−1.42621	−	0.665055i	−0.452279	−	0.891877i	$-0.649389\pi$
$563$	−33.8407	−	15.7802i	−1.42621	−	0.665055i	−0.973936	+	0.226822i	$0.927167\pi$
$564$	−7.24181	−	10.4477i	−0.304935	−	0.439929i
$565$	2.79358	+	0.340691i	0.117527	+	0.0143330i
$566$		−	26.2195i		−	1.10209i
$567$	10.5489	−	36.5728i	0.443011	−	1.53591i
$568$	−0.0433004	+	0.0433004i	−0.00181684	+	0.00181684i
$569$	4.38237	+	24.8537i	0.183719	+	1.04192i	0.927591	+	0.373598i	$0.121876\pi$
$569$	4.38237	+	24.8537i	0.183719	+	1.04192i	−0.743872	+	0.668322i	$0.767013\pi$
$570$	5.99903	−	11.6601i	0.251272	−	0.488386i
$571$	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	$0.135483\pi$
$572$	1.94810	−	0.170437i	0.0814542	−	0.00712632i
$573$	2.48807	+	0.0118268i	0.103941	+	0.000494071i
$574$	7.00843	−	19.2555i	0.292526	−	0.803709i
$575$	3.67240	+	4.21069i	0.153149	+	0.175598i
$576$	−1.90643	−	2.31636i	−0.0794345	−	0.0965151i
$577$	−22.6289	+	6.06339i	−0.942052	+	0.252422i	−0.696986	−	0.717084i	$-0.745476\pi$
$577$	−22.6289	+	6.06339i	−0.942052	+	0.252422i	−0.245066	+	0.969506i	$0.578810\pi$
$578$	−20.2430	−	1.77103i	−0.841998	−	0.0736653i
$579$	19.6637	−	27.8004i	0.817195	−	1.15535i
$580$	7.01370	+	21.5261i	0.291228	+	0.893821i
$581$	19.8926	+	3.50760i	0.825284	+	0.145520i
$582$	−17.3367	−	20.8617i	−0.718631	−	0.864746i
$583$	−4.09950	+	46.8575i	−0.169784	+	1.94064i
$584$	−3.30600	+	5.72615i	−0.136803	+	0.236950i
$585$	2.51909	−	0.110079i	0.104151	−	0.00455123i
$586$	−11.6416	−	20.1638i	−0.480909	−	0.832959i
$587$	19.1692	−	8.93875i	0.791198	−	0.368942i	0.0153665	−	0.999882i	$-0.495109\pi$
$587$	19.1692	−	8.93875i	0.791198	−	0.368942i	0.775831	+	0.630940i	$0.217331\pi$
$588$	−16.2855	−	9.50596i	−0.671604	−	0.392019i
$589$	7.77418	−	9.26491i	0.320330	−	0.381754i
$590$	−6.73014	+	0.358227i	−0.277075	+	0.0147480i
$591$	30.9571	+	14.6151i	1.27340	+	0.601184i
$592$	−3.34897	+	4.78283i	−0.137642	+	0.196573i
$593$	−1.68491	−	1.68491i	−0.0691910	−	0.0691910i	0.671664	−	0.740855i	$-0.265580\pi$
$593$	−1.68491	−	1.68491i	−0.0691910	−	0.0691910i	−0.740855	+	0.671664i	$0.765580\pi$
$594$	−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
$597$	−10.2891	−	8.71726i	−0.421105	−	0.356774i
$598$	−0.177509	+	0.380669i	−0.00725888	+	0.0155667i
$599$	11.6914	+	9.81029i	0.477700	+	0.400838i	0.849594	−	0.527438i	$-0.176847\pi$
$599$	11.6914	+	9.81029i	0.477700	+	0.400838i	−0.371894	+	0.928275i	$0.621292\pi$
$600$	6.55367	−	5.66123i	0.267552	−	0.231119i
$601$	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	$0.221761\pi$
$602$	−26.7376	−	7.16433i	−1.08974	−	0.291996i
$603$	0.708826	−	0.182725i	0.0288656	−	0.00744114i
$604$	2.16392	+	1.24934i	0.0880485	+	0.0508348i
$605$	−33.3209	−	13.4309i	−1.35469	−	0.546042i
$606$	−13.8444	+	6.37579i	−0.562389	+	0.258999i
$607$	23.6505	−	16.5602i	0.959942	−	0.672159i	0.0151695	−	0.999885i	$-0.495171\pi$
$607$	23.6505	−	16.5602i	0.959942	−	0.672159i	0.944773	+	0.327726i	$0.106282\pi$
$608$	2.77341	−	1.94196i	0.112477	−	0.0787570i
$609$	−67.3675	+	31.0250i	−2.72987	+	1.25720i
$610$	15.7309	−	6.69255i	0.636926	−	0.270973i
$611$	2.38913	+	1.37937i	0.0966539	+	0.0558032i
$612$	17.7469	−	4.57490i	0.717377	−	0.184929i
$613$	−26.4834	−	7.09621i	−1.06966	−	0.286613i	−0.319304	−	0.947652i	$-0.603449\pi$
$613$	−26.4834	−	7.09621i	−1.06966	−	0.286613i	−0.750351	+	0.661039i	$0.770116\pi$
$614$	−13.7557	−	5.00667i	−0.555135	−	0.202053i
$615$	−10.0064	+	15.8742i	−0.403498	+	0.640111i
$616$	16.8554	+	14.1434i	0.679124	+	0.569853i
$617$	−0.481909	+	1.03346i	−0.0194009	+	0.0416054i	−0.915769	−	0.401704i	$-0.868418\pi$
$617$	−0.481909	+	1.03346i	−0.0194009	+	0.0416054i	0.896369	+	0.443310i	$0.146196\pi$
$618$	−0.00231628	−	0.00196243i	−9.31746e−5	−	7.89405e-5i
$619$	36.3650	−	6.41213i	1.46163	−	0.257725i	0.614420	−	0.788979i	$-0.289390\pi$
$619$	36.3650	−	6.41213i	1.46163	−	0.257725i	0.847213	+	0.531254i	$0.178279\pi$
$620$	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
$623$	22.5056	−	32.1414i	0.901669	−	1.28772i
$624$	0.588733	+	0.277945i	0.0235682	+	0.0111267i
$625$	16.7889	+	18.5238i	0.671556	+	0.740953i
$626$	4.28484	−	5.10647i	0.171257	−	0.204096i
$627$	−26.3487	−	15.3799i	−1.05227	−	0.614213i
$628$	6.18543	−	2.88432i	0.246826	−	0.115097i
$629$	−17.8346	−	30.8904i	−0.711111	−	1.23168i
$630$	20.9180	+	19.1664i	0.833395	+	0.763608i
$631$	−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	$0.798223\pi$
$632$	0.456515	−	5.21799i	0.0181592	−	0.207561i
$633$	0.577179	+	0.694533i	0.0229408	+	0.0276052i
$634$	6.50386	+	1.14681i	0.258301	+	0.0455455i
$635$	−14.9226	−	7.58811i	−0.592187	−	0.301125i
$636$	−9.04282	+	12.7847i	−0.358571	+	0.506947i
$637$	4.07666	+	0.356661i	0.161523	+	0.0141314i
$638$	50.8802	−	13.6333i	2.01437	−	0.539748i
$639$	0.116742	+	0.141845i	0.00461824	+	0.00561129i
$640$	2.17835	−	0.504786i	0.0861067	−	0.0199534i
$641$	−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	$0.157191\pi$
$642$	−19.4110	−	0.0922679i	−0.766089	−	0.00364153i
$643$	39.1523	−	3.42538i	1.54402	−	0.135084i	0.716925	−	0.697150i	$-0.245549\pi$
$643$	39.1523	−	3.42538i	1.54402	−	0.135084i	0.827092	+	0.562066i	$0.189993\pi$
$644$	−4.44095	+	1.61637i	−0.174998	+	0.0636941i
$645$	22.5404	+	11.5969i	0.887527	+	0.456627i
$646$	3.59164	+	20.3692i	0.141311	+	0.801415i
$647$	−24.0132	+	24.0132i	−0.944058	+	0.944058i	−0.998516	−	0.0544579i	$-0.982657\pi$
$647$	−24.0132	+	24.0132i	−0.944058	+	0.944058i	0.0544579	+	0.998516i	$0.482657\pi$
$648$	−7.46918	+	5.02109i	−0.293417	+	0.197247i
$649$			15.6809i			0.615528i
$650$	−0.761616	+	1.71817i	−0.0298730	+	0.0673922i
$651$	14.9072	+	21.5065i	0.584258	+	0.842907i
$652$	−0.859359	−	0.400726i	−0.0336551	−	0.0156936i
$653$	−0.161787	−	1.84923i	−0.00633120	−	0.0723659i	0.992372	−	0.123281i	$-0.0393417\pi$
$653$	−0.161787	−	1.84923i	−0.00633120	−	0.0723659i	−0.998703	+	0.0509153i	$0.983786\pi$
$654$	−2.72539	+	2.69961i	−0.106571	+	0.105563i
$655$	−27.3370	+	3.86475i	−1.06815	+	0.151008i
$656$	−4.19595	+	2.42253i	−0.163824	+	0.0945840i
$657$	16.1398	+	11.5314i	0.629673	+	0.449883i
$658$	8.03385	+	29.9828i	0.313192	+	1.16885i
$659$	7.92888	−	6.65312i	0.308865	−	0.259169i	−0.475158	−	0.879901i	$-0.657609\pi$
$659$	7.92888	−	6.65312i	0.308865	−	0.259169i	0.784023	+	0.620732i	$0.213165\pi$
$660$	−12.3426	−	15.9267i	−0.480436	−	0.619944i
$661$	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	$-0.0974215\pi$
$662$	5.31906	+	7.59641i	0.206731	+	0.295243i
$663$	−3.05888	+	2.54202i	−0.118797	+	0.0987240i
$664$	−3.07000	−	3.65868i	−0.119139	−	0.141985i
$665$	−23.3991	+	21.8558i	−0.907380	+	0.847533i
$666$	13.3106	+	11.3863i	0.515775	+	0.441210i
$667$	−2.92824	+	10.9283i	−0.113382	+	0.423147i
$668$	−2.11973	−	4.54577i	−0.0820147	−	0.175881i
$669$	14.5240	−	3.81779i	0.561530	−	0.147604i
$670$	−0.113000	+	0.533770i	−0.00436559	+	0.0206213i
$671$	−13.6038	−	37.3762i	−0.525170	−	1.44289i
$672$	2.47268	+	6.89543i	0.0953856	+	0.265997i
$673$	5.79958	+	4.06091i	0.223558	+	0.156537i	0.679990	−	0.733221i	$-0.261984\pi$
$673$	5.79958	+	4.06091i	0.223558	+	0.156537i	−0.456432	+	0.889758i	$0.650873\pi$
$674$	35.1675			1.35460
$675$	−15.0045	−	21.2100i	−0.577524	−	0.816373i
$676$	12.8587			0.494566
$677$	19.3267	+	13.5327i	0.742787	+	0.520105i	0.882630	−	0.470068i	$-0.155771\pi$
$677$	19.3267	+	13.5327i	0.742787	+	0.520105i	−0.139843	+	0.990174i	$0.544660\pi$
$678$	1.40915	−	1.66324i	0.0541182	−	0.0638764i
$679$	22.6533	+	62.2395i	0.869355	+	2.38853i
$680$	−2.82920	+	13.3640i	−0.108495	+	0.512487i
$681$	2.83170	−	10.3706i	0.108511	−	0.397403i
$682$	−7.85421	−	16.8434i	−0.300753	−	0.644967i
$683$	−12.1872	+	45.4832i	−0.466330	+	1.74037i	0.186112	+	0.982529i	$0.440411\pi$
$683$	−12.1872	+	45.4832i	−0.466330	+	1.74037i	−0.652442	+	0.757839i	$0.726255\pi$
$684$	−4.99471	−	8.84422i	−0.190978	−	0.338167i
$685$	−20.7540	+	19.3852i	−0.792970	+	0.740669i
$686$	10.5670	+	12.5933i	0.403452	+	0.480815i
$687$	38.9509	+	14.3870i	1.48607	+	0.548898i
$688$	3.75406	+	5.36136i	0.143122	+	0.204400i
$689$	0.590119	−	3.34673i	0.0224818	−	0.127500i
$690$	4.28802	−	0.585439i	0.163242	−	0.0222873i
$691$	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	$0.177508\pi$
$692$	1.46912	+	5.48283i	0.0558476	+	0.208426i
$693$	47.1174	−	46.2300i	1.78984	−	1.75613i
$694$	−16.0764	+	9.28171i	−0.610252	+	0.352329i
$695$	−9.66817	+	1.36683i	−0.366734	+	0.0518468i
$696$	16.9174	+	4.61931i	0.641254	+	0.175095i
$697$	−2.57970	−	29.4861i	−0.0977129	−	1.11686i
$698$	−8.91100	−	4.15527i	−0.337286	−	0.157279i
$699$	−20.1661	+	1.66776i	−0.762753	+	0.0630803i
$700$	−19.7296	+	7.61050i	−0.745708	+	0.287650i
$701$			20.7744i			0.784637i	0.919829	+	0.392319i	$0.128327\pi$
$701$			20.7744i			0.784637i	−0.919829	+	0.392319i	$0.871673\pi$
$702$	1.00059	−	1.67737i	0.0377648	−	0.0633082i
$703$	−13.9783	+	13.9783i	−0.527202	+	0.527202i
$704$	−0.903414	−	5.12351i	−0.0340487	−	0.193100i
$705$	−1.37592	−	28.3919i	−0.0518201	−	1.06930i
$706$	3.07698	−	1.11993i	0.115804	−	0.0421491i
$707$	37.0760	−	3.24373i	1.39439	−	0.121993i
$708$	−2.63172	+	4.50865i	−0.0989062	+	0.169445i
$709$	13.3009	−	36.5440i	0.499527	−	1.37244i	−0.392207	−	0.919877i	$-0.628288\pi$
$709$	13.3009	−	36.5440i	0.499527	−	1.37244i	0.891733	−	0.452561i	$-0.149490\pi$
$710$	−0.133393	+	0.0309111i	−0.00500616	+	0.00116007i
$711$	−15.4484	−	2.87566i	−0.579361	−	0.107846i
$712$	−8.96137	+	2.40119i	−0.335842	+	0.0899885i
$713$	3.97652	+	0.347900i	0.148922	+	0.0130290i
$714$	−44.5616	−	4.11217i	−1.66768	−	0.153894i
$715$	3.89775	+	1.98199i	0.145768	+	0.0741223i
$716$	−14.0319	−	2.47421i	−0.524398	−	0.0924655i
$717$	31.4813	−	5.39684i	1.17569	−	0.201549i
$718$	1.43722	−	16.4275i	0.0536365	−	0.613067i
$719$	6.20709	−	10.7510i	0.231485	−	0.400945i	−0.726760	−	0.686891i	$-0.758975\pi$
$719$	6.20709	−	10.7510i	0.231485	−	0.400945i	0.958245	+	0.285947i	$0.0923081\pi$
$720$	−0.875844	−	6.65078i	−0.0326408	−	0.247860i
$721$	0.00370644	+	0.00641974i	0.000138035	+	0.000239083i
$722$	−6.83081	+	3.18526i	−0.254216	+	0.118543i
$723$	−0.0409655	+	8.61816i	−0.00152352	+	0.320513i
$724$	8.42604	−	10.0418i	0.313151	−	0.373199i
$725$	−12.1668	+	49.1405i	−0.451864	+	1.82503i
$726$	−22.8711	+	15.8530i	−0.848825	+	0.588360i
$727$	−7.81380	+	11.1593i	−0.289798	+	0.413874i	−0.937481	−	0.348035i	$-0.886849\pi$
$727$	−7.81380	+	11.1593i	−0.289798	+	0.413874i	0.647684	+	0.761909i	$0.275738\pi$
$728$	−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
$732$	2.36141	−	13.0298i	0.0872803	−	0.481594i
$733$	7.31307	−	15.6829i	0.270115	−	0.579263i	−0.723725	−	0.690088i	$-0.757572\pi$
$733$	7.31307	−	15.6829i	0.270115	−	0.579263i	0.993840	+	0.110826i	$0.0353495\pi$
$734$	−25.0724	−	21.0382i	−0.925437	−	0.776534i
$735$	−19.6487	−	37.3073i	−0.724753	−	1.37610i
$736$	1.05004	+	0.382184i	0.0387051	+	0.0140875i
$737$	1.22617	+	0.328551i	0.0451665	+	0.0121023i
$738$	6.01733	+	13.2312i	0.221501	+	0.487046i
$739$	−28.8265	−	16.6430i	−1.06040	−	0.612223i	−0.134858	−	0.990865i	$-0.543058\pi$
$739$	−28.8265	−	16.6430i	−1.06040	−	0.612223i	−0.925543	+	0.378642i	$0.876391\pi$
$740$	−12.0138	+	5.11115i	−0.441636	+	0.187889i
$741$	1.79959	+	1.27288i	0.0661095	+	0.0467602i
$742$	31.3222	−	21.9320i	1.14987	−	0.805151i
$743$	−14.7359	+	10.3182i	−0.540607	+	0.378537i	−0.811753	−	0.584001i	$-0.801486\pi$
$743$	−14.7359	+	10.3182i	−0.540607	+	0.378537i	0.271146	+	0.962538i	$0.412598\pi$
$744$	0.568547	−	6.16108i	0.0208440	−	0.225876i
$745$	1.55691	+	0.627553i	0.0570408	+	0.0229918i
$746$	−5.37216	−	3.10162i	−0.196689	−	0.113558i
$747$	−11.8146	+	8.10638i	−0.432273	+	0.296597i
$748$	30.6996	+	8.22594i	1.12249	+	0.300770i
$749$	44.5396	+	16.2111i	1.62744	+	0.592340i
$750$	19.1334	−	2.98531i	0.698654	−	0.109008i
$751$	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	$0.602529\pi$
$752$	3.10175	−	6.65173i	0.113109	−	0.242563i
$753$	21.3336	−	7.65016i	0.777441	−	0.278787i
$754$	−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	0.285760	−	0.958301i	$-0.407754\pi$
$757$	−18.5041	−	18.5041i	−0.672541	−	0.672541i	−0.958301	+	0.285760i	$0.907754\pi$
$758$	−3.91301	+	5.58836i	−0.142127	+	0.202979i
$759$	−0.829905	−	10.0350i	−0.0301236	−	0.364248i
$760$	7.55998	−	0.402397i	0.274229	−	0.0145965i
$761$	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	$0.0959184\pi$
$762$	−11.2610	+	6.43035i	−0.407942	+	0.232947i
$763$	8.48934	−	3.95864i	0.307335	−	0.143313i
$764$	0.718252	+	1.24405i	0.0259854	+	0.0450081i
$765$	39.0844	+	12.3217i	1.41310	+	0.445491i
$766$	−1.72684	+	2.99098i	−0.0623934	+	0.108069i
$767$	0.0987416	−	1.12862i	0.00356535	−	0.0407522i
$768$	0.600126	−	1.62476i	0.0216552	−	0.0586285i
$769$	−13.6805	−	2.41225i	−0.493332	−	0.0869878i	−0.0785532	−	0.996910i	$-0.525030\pi$
$769$	−13.6805	−	2.41225i	−0.493332	−	0.0869878i	−0.414779	+	0.909922i	$0.636141\pi$
$770$	15.2421	+	46.7801i	0.549286	+	1.68584i
$771$	1.46535	+	3.18185i	0.0527733	+	0.114592i
$772$	19.5850	+	1.71347i	0.704880	+	0.0616690i
$773$	−26.7372	+	7.16421i	−0.961671	+	0.257679i	−0.705307	−	0.708902i	$-0.749191\pi$
$773$	−26.7372	+	7.16421i	−0.961671	+	0.257679i	−0.256363	+	0.966580i	$0.582524\pi$
$774$	17.0970	−	9.65542i	0.614539	−	0.347057i
$775$	17.8196	+	1.21680i	0.640098	+	0.0437088i
$776$	5.35628	−	14.7163i	0.192279	−	0.528283i
$777$	−21.2092	−	37.1420i	−0.760876	−	1.33246i
$778$	11.8954	−	1.04071i	0.426469	−	0.0373112i
$779$	−15.4147	+	5.61050i	−0.552289	+	0.201017i
$780$	0.788064	+	1.22403i	0.0282172	+	0.0438274i
$781$	0.0553214	+	0.313743i	0.00197956	+	0.0112266i
$782$	−4.82702	+	4.82702i	−0.172614	+	0.172614i
$783$	18.6969	−	49.1759i	0.668173	−	1.75740i
$784$		−	10.8870i		−	0.388822i
$785$	15.1486	+	1.84745i	0.540678	+	0.0659384i
$786$	−9.13003	+	19.3389i	−0.325657	+	0.689795i
$787$	3.50081	+	1.63245i	0.124790	+	0.0581906i	0.484011	−	0.875062i	$-0.339180\pi$
$787$	3.50081	+	1.63245i	0.124790	+	0.0581906i	−0.359220	+	0.933253i	$0.616957\pi$
$788$	1.72262	+	19.6896i	0.0613657	+	0.701413i
$789$	−4.92507	−	18.7364i	−0.175337	−	0.667033i
$790$	7.04103	−	9.35966i	0.250508	−	0.333002i
$791$	−4.60979	+	2.66146i	−0.163905	+	0.0946308i
$792$	−15.5605	+	1.21242i	−0.552918	+	0.0430816i
$793$	0.743773	+	2.77580i	0.0264122	+	0.0985715i
$794$	1.99545	−	1.67438i	0.0708160	−	0.0594217i
$795$	−32.2858	+	13.5548i	−1.14506	+	0.480739i
$796$	1.35199	−	7.66752i	0.0479201	−	0.271768i
$797$	7.23990	+	10.3397i	0.256451	+	0.366249i	0.926646	−	0.375935i	$-0.122679\pi$
$797$	7.23990	+	10.3397i	0.256451	+	0.366249i	−0.670195	+	0.742185i	$0.733790\pi$
$798$	4.19060	+	24.4450i	0.148346	+	0.865343i
$799$	28.8203	+	34.3467i	1.01959	+	1.21510i
$800$	4.73025	+	1.62011i	0.167239	+	0.0572796i
$801$	4.57227	+	27.4543i	0.161553	+	0.970052i
$802$	−1.74832	+	6.52481i	−0.0617353	+	0.230399i
$803$	14.5377	+	31.1763i	0.513026	+	1.10019i
$804$	0.297414	+	0.300255i	0.0104890	+	0.0105892i
$805$	−10.3384	−	2.18867i	−0.364382	−	0.0771406i
$806$	0.459240	+	1.26175i	0.0161761	+	0.0444433i
$807$	−16.0265	−	2.90451i	−0.564158	−	0.102244i
$808$	−7.20849	−	5.04744i	−0.253594	−	0.177568i
$809$	9.03399			0.317618			0.158809	−	0.987309i	$-0.449235\pi$
$809$	9.03399			0.317618			0.158809	+	0.987309i	$0.449235\pi$
$810$	−20.1129	+	0.687397i	−0.706694	+	0.0241527i
$811$	−18.4143			−0.646613			−0.323307	−	0.946294i	$-0.604795\pi$
$811$	−18.4143			−0.646613			−0.323307	+	0.946294i	$0.604795\pi$
$812$	−35.0770	−	24.5612i	−1.23096	−	0.861928i
$813$	−2.34757	−	0.425455i	−0.0823329	−	0.0149214i
$814$	10.3893	+	28.5445i	0.364146	+	1.00048i
$815$	−1.15622	−	1.77723i	−0.0405005	−	0.0622538i
$816$	7.44636	+	7.51749i	0.260675	+	0.263165i
$817$	9.36501	+	20.0833i	0.327640	+	0.702627i
$818$	−1.00616	+	3.75502i	−0.0351794	+	0.131291i
$819$	−3.68236	+	3.03068i	−0.128672	+	0.105901i
$820$	−10.8276	−	0.369249i	−0.378116	−	0.0128947i
$821$	−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	$0.802342\pi$
$822$	3.71688	+	21.6816i	0.129641	+	0.756233i
$823$	−23.3920	−	33.4072i	−0.815394	−	1.16450i	−0.983885	−	0.178800i	$-0.942779\pi$
$823$	−23.3920	−	33.4072i	−0.815394	−	1.16450i	0.168492	−	0.985703i	$-0.446110\pi$
$824$	0.000304360	−	0.00172611i	1.06029e−5	−	6.01320e-5i
$825$	−4.56980	−	44.8231i	−0.159100	−	1.56054i
$826$	9.76509	−	8.19389i	0.339771	−	0.285102i
$827$	−0.320175	−	1.19491i	−0.0111336	−	0.0415511i	0.960136	−	0.279535i	$-0.0901802\pi$
$827$	−0.320175	−	1.19491i	−0.0111336	−	0.0415511i	−0.971269	+	0.237984i	$0.923514\pi$
$828$	1.44556	−	3.02461i	0.0502367	−	0.105112i
$829$	16.1883	−	9.34633i	0.562243	−	0.324611i	−0.191802	−	0.981434i	$-0.561433\pi$
$829$	16.1883	−	9.34633i	0.562243	−	0.324611i	0.754045	+	0.656822i	$0.228100\pi$
$830$	−1.49496	−	10.5745i	−0.0518908	−	0.367045i
$831$	12.7328	+	48.4395i	0.441697	+	1.68035i
$832$	0.0327602	+	0.374451i	0.00113576	+	0.0129818i
$833$	60.2778	+	28.1080i	2.08850	+	0.973885i
$834$	−3.22898	+	6.83950i	−0.111810	+	0.236832i
$835$	1.35772	−	11.1330i	0.0469859	−	0.385272i
$836$		−	17.6143i		−	0.609205i
$837$	−18.2320	−	3.48355i	−0.630189	−	0.120409i
$838$	10.0801	−	10.0801i	0.348212	−	0.348212i
$839$	0.681446	+	3.86467i	0.0235261	+	0.133423i	0.994309	−	0.106538i	$-0.0339765\pi$
$839$	0.681446	+	3.86467i	0.0235261	+	0.133423i	−0.970783	+	0.239961i	$0.922865\pi$
$840$	−3.46864	+	16.0086i	−0.119679	+	0.552348i
$841$	−69.0793	+	25.1428i	−2.38204	+	0.866993i
$842$	28.3974	−	2.48445i	0.978638	−	0.0856197i
$843$	−27.9765	−	48.9930i	−0.963560	−	1.68741i
$844$	−0.178323	+	0.489937i	−0.00613811	+	0.0168643i
$845$	24.3963	+	15.2168i	0.839259	+	0.523474i
$846$	−18.9627	−	11.1898i	−0.651952	−	0.384714i
$847$	65.6350	−	17.5869i	2.25525	−	0.604292i
$848$	−9.00664	−	0.787979i	−0.309289	−	0.0270593i
$849$	−18.9967	−	41.2494i	−0.651966	−	1.41568i
$850$	−21.1825	+	22.0070i	−0.726555	+	0.754835i
$851$	−6.42529	−	1.13295i	−0.220256	−	0.0388371i
$852$	−0.0367493	+	0.0994938i	−0.00125901	+	0.00340860i
$853$	−4.22873	+	48.3346i	−0.144789	+	1.65494i	0.482307	+	0.876002i	$0.339799\pi$
$853$	−4.22873	+	48.3346i	−0.144789	+	1.65494i	−0.627096	+	0.778942i	$0.715757\pi$
$854$	−16.1671	+	28.0023i	−0.553227	+	0.958217i
$855$	0.989841	−	22.6905i	0.0338519	−	0.775997i
$856$	−5.60352	−	9.70559i	−0.191524	−	0.331730i
$857$	−47.8835	+	22.3284i	−1.63567	+	0.762725i	−0.999958	−	0.00920138i	$-0.997071\pi$
$857$	−47.8835	+	22.3284i	−1.63567	+	0.762725i	−0.635712	+	0.771927i	$0.719293\pi$
$858$	2.94133	−	1.67959i	0.100415	−	0.0573402i
$859$	−15.5714	+	18.5573i	−0.531291	+	0.633168i	−0.963212	−	0.268744i	$-0.913392\pi$
$859$	−15.5714	+	18.5573i	−0.531291	+	0.633168i	0.431921	+	0.901912i	$0.357836\pi$
$860$	0.777885	+	14.6144i	0.0265257	+	0.498347i
$861$	−2.92523	−	35.3712i	−0.0996914	−	1.20545i
$862$	−22.3224	+	31.8796i	−0.760302	+	1.08582i
$863$	13.3492	+	13.3492i	0.454411	+	0.454411i	0.896816	−	0.442405i	$-0.145874\pi$
$863$	13.3492	+	13.3492i	0.454411	+	0.454411i	−0.442405	+	0.896816i	$0.645874\pi$
$864$	−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
$867$	−33.1301	+	11.8803i	−1.12516	+	0.403478i
$868$	−6.38491	+	13.6925i	−0.216718	+	0.464753i
$869$	−20.8752	−	17.5163i	−0.708141	−	0.594201i
$870$	26.6304	+	28.7839i	0.902854	+	0.975866i
$871$	−0.0861839	−	0.0313684i	−0.00292023	−	0.00106288i
$872$	−2.13931	−	0.573225i	−0.0724460	−	0.0194119i
$873$	−42.3896	−	20.2594i	−1.43467	−	0.685677i
$874$	3.27644	+	1.89165i	0.110827	+	0.0639861i
$875$	−46.4383	−	8.90859i	−1.56990	−	0.301165i
$876$	−1.05235	+	11.4039i	−0.0355557	+	0.385301i
$877$	3.54626	−	2.48312i	0.119749	−	0.0838489i	−0.512168	−	0.858885i	$-0.671157\pi$
$877$	3.54626	−	2.48312i	0.119749	−	0.0838489i	0.631917	+	0.775036i	$0.282269\pi$
$878$	−30.9067	+	21.6411i	−1.04305	+	0.730352i
$879$	−32.9241	−	23.2877i	−1.11050	−	0.785475i
$880$	4.34908	−	10.7897i	0.146607	−	0.363722i
$881$	−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	$0.762848\pi$
$882$	−32.5083	−	3.15578i	−1.09461	−	0.106261i
$883$	52.4360	+	14.0502i	1.76461	+	0.472826i	0.987644	−	0.156716i	$-0.0500906\pi$
$883$	52.4360	+	14.0502i	1.76461	+	0.472826i	0.776967	+	0.629542i	$0.216757\pi$
$884$	−2.15779	−	0.785372i	−0.0725744	−	0.0264149i
$885$	−10.3285	+	5.43974i	−0.347190	+	0.182855i
$886$	28.4678	+	23.8873i	0.956393	+	0.802509i
$887$	11.3090	−	24.2523i	0.379721	−	0.814313i	−0.619842	−	0.784727i	$-0.712803\pi$
$887$	11.3090	−	24.2523i	0.379721	−	0.814313i	0.999562	−	0.0295865i	$-0.00941905\pi$
$888$	−1.80343	+	9.95092i	−0.0605190	+	0.333931i
$889$	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
$893$	14.2528	−	20.3551i	0.476951	−	0.681157i
$894$	1.06864	−	0.740727i	0.0357408	−	0.0247736i
$895$	−23.6943	−	21.2994i	−0.792013	−	0.711961i
$896$	−2.71855	+	3.23984i	−0.0908202	+	0.108235i
$897$	−0.00345805	+	0.727491i	−0.000115461	+	0.0242902i
$898$	35.4306	−	16.5216i	1.18234	−	0.551332i
$899$	18.0841	+	31.3225i	0.603138	+	1.04467i
$900$	6.20873	−	13.6547i	0.206958	−	0.455158i
$901$	27.6160	−	47.8324i	0.920024	−	1.59353i
$902$	−2.19691	+	25.1108i	−0.0731491	+	0.836098i
$903$	−47.2553	+	8.10097i	−1.57256	+	0.269583i
$904$	1.23946	+	0.218550i	0.0412239	+	0.00726888i
$905$	27.8697	−	9.08060i	0.926420	−	0.301849i
$906$	4.30952	+	0.397684i	0.143174	+	0.0132122i
$907$	3.91052	+	0.342126i	0.129847	+	0.0113601i	0.151894	−	0.988397i	$-0.451463\pi$
$907$	3.91052	+	0.342126i	0.129847	+	0.0113601i	−0.0220472	+	0.999757i	$0.507018\pi$
$908$	5.99518	−	1.60640i	0.198957	−	0.0533104i
$909$	−17.1610	+	20.0612i	−0.569193	+	0.665388i
$910$	−0.802467	−	3.46295i	−0.0266015	−	0.114796i
$911$	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	$-0.0608143\pi$
$912$	2.95622	−	5.06457i	0.0978902	−	0.167705i
$913$	−24.7532	+	2.16563i	−0.819212	+	0.0716718i
$914$	8.34368	−	3.03685i	0.275985	−	0.100450i
$915$	19.8994	−	21.9264i	0.657855	−	0.724864i
$916$	4.16292	+	23.6091i	0.137547	+	0.780066i
$917$	36.9248	−	36.9248i	1.21936	−	1.21936i
$918$	24.6054	−	20.0555i	0.812099	−	0.661930i
$919$			36.3601i			1.19941i	0.800222	+	0.599705i	$0.204715\pi$
$919$			36.3601i			1.19941i	−0.800222	+	0.599705i	$0.795285\pi$
$920$	1.53993	+	1.96771i	0.0507701	+	0.0648734i
$921$	−25.2684	+	2.08972i	−0.832622	+	0.0688586i
$922$	−30.5105	−	14.2273i	−1.00481	−	0.468550i
$923$	−0.00200610	−	0.0229299i	−6.60317e−5	−	0.000754746i
$924$	36.7647	+	10.0386i	1.20947	+	0.330247i
$925$	−28.8418	−	4.51977i	−0.948311	−	0.148609i
$926$	8.57266	−	4.94943i	0.281715	−	0.162648i
$927$	−0.00506588	−	0.00140915i	−0.000166385	−	4.62826e-5i
$928$	2.62050	+	9.77986i	0.0860223	+	0.321040i
$929$	23.1288	−	19.4073i	0.758830	−	0.636734i	−0.178992	−	0.983850i	$-0.557284\pi$
$929$	23.1288	−	19.4073i	0.758830	−	0.636734i	0.937822	+	0.347117i	$0.112839\pi$
$930$	8.36961	−	11.0164i	0.274450	−	0.361241i
$931$	6.40073	−	36.3003i	0.209775	−	1.18969i
$932$	−6.70090	−	9.56988i	−0.219495	−	0.313472i
$933$	23.0337	+	8.50779i	0.754090	+	0.278533i
$934$	−5.10847	−	6.08804i	−0.167154	−	0.199207i
$935$	48.5107	+	51.9362i	1.58647	+	1.69850i
$936$	1.12759	+	0.0107200i	0.0368565	+	0.000350395i
$937$	1.58532	−	5.91649i	0.0517901	−	0.193283i	−0.935184	−	0.354162i	$-0.884766\pi$
$937$	1.58532	−	5.91649i	0.0517901	−	0.193283i	0.986974	+	0.160879i	$0.0514328\pi$
$938$	−0.436121	−	0.935264i	−0.0142398	−	0.0305375i
$939$	3.04127	−	11.1381i	0.0992482	−	0.363480i
$940$	13.7564	−	8.94949i	0.448684	−	0.291900i
$941$	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	$0.722512\pi$
$942$	7.64137	−	9.01921i	0.248969	−	0.293862i
$943$	−4.43492	−	3.10536i	−0.144421	−	0.101125i
$944$	−3.01407			−0.0980996
$945$	46.7955	+	14.9976i	1.52226	+	0.487871i
$946$	34.0508			1.10709
$947$	6.30587	+	4.41542i	0.204913	+	0.143482i	0.671529	−	0.740978i	$-0.265638\pi$
$947$	6.30587	+	4.41542i	0.204913	+	0.143482i	−0.466616	+	0.884460i	$0.654527\pi$
$948$	−3.06237	−	8.53988i	−0.0994611	−	0.277362i
$949$	−0.850031	−	2.33544i	−0.0275932	−	0.0758116i
$950$	14.8194	+	8.18291i	0.480806	+	0.265489i
$951$	11.0630	−	2.90802i	0.358742	−	0.0942992i
$952$	−10.9192	−	23.4163i	−0.353893	−	0.758925i
$953$	6.78716	−	25.3300i	0.219858	−	0.820520i	−0.764542	−	0.644574i	$-0.777035\pi$
$953$	6.78716	−	25.3300i	0.219858	−	0.820520i	0.984400	−	0.175946i	$-0.0562985\pi$
$954$	−4.96360	+	26.6651i	−0.160703	+	0.863314i
$955$	−0.109478	+	3.21025i	−0.00354262	+	0.103881i
$956$	11.8536	+	14.1265i	0.383372	+	0.456885i
$957$	70.1687	−	58.3124i	2.26823	−	1.88497i
$958$	9.04225	+	12.9137i	0.292142	+	0.417222i
$959$	9.32739	−	52.8982i	0.301197	−	1.70817i
$960$	3.06131	−	2.37242i	0.0988035	−	0.0765694i
$961$	−13.9721	+	11.7240i	−0.450713	+	0.378193i
$962$	−0.568024	−	2.11990i	−0.0183138	−	0.0683482i
$963$	−30.6048	+	13.9186i	−0.986226	+	0.448520i
$964$	−4.30913	+	2.48788i	−0.138788	+	0.0801291i
$965$	35.1302	+	26.4275i	1.13088	+	0.850731i
$966$	−5.81555	+	5.76052i	−0.187112	+	0.185342i
$967$	4.09918	+	46.8539i	0.131821	+	1.50672i	0.717718	+	0.696333i	$0.245187\pi$
$967$	4.09918	+	46.8539i	0.131821	+	1.50672i	−0.585898	+	0.810385i	$0.699258\pi$
$968$	−14.5613	−	6.79002i	−0.468016	−	0.218240i
$969$	20.4085	+	29.4433i	0.655616	+	0.945854i
$970$	27.5773	−	21.5820i	0.885452	−	0.692957i
$971$		−	52.7240i		−	1.69199i	−0.533188	−	0.845997i	$-0.679006\pi$
$971$		−	52.7240i		−	1.69199i	0.533188	−	0.845997i	$-0.320994\pi$
$972$	−8.11285	+	13.3110i	−0.260220	+	0.426949i
$973$	13.0590	−	13.0590i	0.418653	−	0.418653i
$974$	−1.49444	−	8.47537i	−0.0478848	−	0.271568i
$975$	0.0466603	+	3.25489i	0.00149433	+	0.104240i
$976$	7.18421	−	2.61484i	0.229961	−	0.0836990i
$977$	−42.1182	+	3.68487i	−1.34748	+	0.117889i	−0.737941	−	0.674866i	$-0.764202\pi$
$977$	−42.1182	+	3.68487i	−1.34748	+	0.117889i	−0.609541	+	0.792755i	$0.708646\pi$
$978$	−1.64231	−	0.00780654i	−0.0525152	−	0.000249626i
$979$	−16.5082	+	45.3558i	−0.527603	+	1.44958i
$980$	12.8835	−	20.6555i	0.411550	−	0.659817i
$981$	−2.33174	+	6.22173i	−0.0744468	+	0.198645i
$982$	−30.0084	+	8.04072i	−0.957606	+	0.256590i
$983$	26.4689	+	2.31573i	0.844226	+	0.0738602i	0.501058	−	0.865414i	$-0.332944\pi$
$983$	26.4689	+	2.31573i	0.844226	+	0.0738602i	0.343168	+	0.939274i	$0.388500\pi$
$984$	−4.84602	+	6.85129i	−0.154485	+	0.218411i
$985$	−20.0321	+	39.3948i	−0.638277	+	1.25522i
$986$	−60.9134	−	10.7407i	−1.93988	−	0.342053i
$987$	34.3624	+	41.3491i	1.09377	+	1.31616i
$988$	−0.110917	+	1.26778i	−0.00352873	+	0.0403335i
$989$	−3.65680	+	6.33377i	−0.116280	+	0.201402i
$990$	−30.9571	−	16.1138i	−0.983881	−	0.512129i
$991$	−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	$0.843953\pi$
$992$	3.23753	−	1.50968i	0.102792	−	0.0479325i
$993$	13.8719	+	8.09712i	0.440212	+	0.256954i
$994$	0.166473	−	0.198395i	0.00528020	−	0.00629269i
$995$	11.6387	−	12.9474i	0.368972	−	0.410459i
$996$	−7.48064	−	3.53167i	−0.237033	−	0.111905i
$997$	−28.4801	+	40.6738i	−0.901975	+	1.28815i	0.0551503	+	0.998478i	$0.482436\pi$
$997$	−28.4801	+	40.6738i	−0.901975	+	1.28815i	−0.957125	+	0.289675i	$0.906453\pi$
$998$	−9.25966	−	9.25966i	−0.293109	−	0.293109i
$999$	29.1903	+	8.26941i	0.923541	+	0.261632i

Display

a_p

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p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

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n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
270.2.r.a.83.18	✓	216	135.83	even	36	inner
270.2.r.a.137.13	yes	216	27.2	odd	18	inner
270.2.r.a.203.13	yes	216	5.3	odd	4	inner
270.2.r.a.257.18	yes	216	1.1	even	1	trivial
810.2.s.a.233.8		216	15.8	even	4
810.2.s.a.413.6		216	135.133	odd	36
810.2.s.a.557.6		216	3.2	odd	2
810.2.s.a.737.8		216	27.25	even	9

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Classical	Maass
Hilbert	Bianchi

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

Introduction

L-functions

Modular forms

Varieties

Fields

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	270.2.r.a.257.18

Level	$270$
Weight	$2$
Character	270.257
Analytic conductor	$2.156$
Analytic rank	$0$
Dimension	$216$
Inner twists	$4$