LMFDB - Embedded newform 162.3.f.a.71.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,3,Mod(17,162)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(162, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([11]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("162.17");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	162.f (of order $18$, degree $6$, not 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:	$4.41418028264$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 54)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			71.4
Character	$\chi$	$=$	162.71
Dual form			162.3.f.a.89.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.39273 - 0.245576i) q^{2} +(1.87939 - 0.684040i) q^{4} +(-5.54906 + 6.61311i) q^{5} +(7.83131 + 2.85036i) q^{7} +(2.44949 - 1.41421i) q^{8} +O(q^{10})$	\(q+(1.39273 - 0.245576i) q^{2} +(1.87939 - 0.684040i) q^{4} +(-5.54906 + 6.61311i) q^{5} +(7.83131 + 2.85036i) q^{7} +(2.44949 - 1.41421i) q^{8} +(-6.10431 + 10.5730i) q^{10} +(10.8191 + 12.8937i) q^{11} +(0.524960 - 2.97720i) q^{13} +(11.6069 + 2.04660i) q^{14} +(3.06418 - 2.57115i) q^{16} +(-8.43596 - 4.87051i) q^{17} +(3.84677 + 6.66281i) q^{19} +(-5.90519 + 16.2244i) q^{20} +(18.2344 + 15.3005i) q^{22} +(-10.1434 - 27.8689i) q^{23} +(-8.59998 - 48.7729i) q^{25} -4.27534i q^{26} +16.6678 q^{28} +(10.5809 - 1.86569i) q^{29} +(-10.8017 + 3.93149i) q^{31} +(3.63616 - 4.33340i) q^{32} +(-12.9451 - 4.71163i) q^{34} +(-62.3062 + 35.9725i) q^{35} +(-11.5925 + 20.0787i) q^{37} +(6.99373 + 8.33481i) q^{38} +(-4.24001 + 24.0463i) q^{40} +(16.7264 + 2.94931i) q^{41} +(18.0881 - 15.1778i) q^{43} +(29.1530 + 16.8315i) q^{44} +(-20.9710 - 36.3228i) q^{46} +(5.67901 - 15.6029i) q^{47} +(15.6687 + 13.1476i) q^{49} +(-23.9549 - 65.8155i) q^{50} +(-1.04992 - 5.95439i) q^{52} -75.3383i q^{53} -145.303 q^{55} +(23.2137 - 4.09321i) q^{56} +(14.2781 - 5.19681i) q^{58} +(38.6968 - 46.1170i) q^{59} +(32.1023 + 11.6843i) q^{61} +(-14.0783 + 8.12813i) q^{62} +(4.00000 - 6.92820i) q^{64} +(16.7755 + 19.9923i) q^{65} +(6.53483 - 37.0609i) q^{67} +(-19.1860 - 3.38302i) q^{68} +(-77.9416 + 65.4008i) q^{70} +(-44.0325 - 25.4222i) q^{71} +(49.2453 + 85.2954i) q^{73} +(-11.2143 + 30.8110i) q^{74} +(11.7872 + 9.89063i) q^{76} +(47.9758 + 131.813i) q^{77} +(-14.0913 - 79.9158i) q^{79} +34.5312i q^{80} +24.0196 q^{82} +(15.8868 - 2.80127i) q^{83} +(79.0209 - 28.7612i) q^{85} +(21.4646 - 25.5805i) q^{86} +(44.7356 + 16.2824i) q^{88} +(-14.0161 + 8.09222i) q^{89} +(12.5972 - 21.8190i) q^{91} +(-38.1269 - 45.4378i) q^{92} +(4.07761 - 23.1253i) q^{94} +(-65.4078 - 11.5332i) q^{95} +(-101.648 + 85.2929i) q^{97} +(25.0509 + 14.4632i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 18 q^{5}+O(q^{10}) $ 36 * q - 18 * q^5	$ 36 q - 18 q^{5} + 18 q^{11} + 36 q^{14} + 72 q^{20} + 36 q^{22} + 180 q^{23} + 18 q^{25} - 144 q^{29} - 90 q^{31} - 72 q^{34} - 486 q^{35} - 180 q^{38} + 90 q^{41} + 90 q^{43} + 378 q^{47} + 72 q^{49} + 72 q^{56} - 252 q^{59} - 144 q^{61} + 144 q^{64} - 18 q^{65} - 594 q^{67} + 180 q^{68} - 360 q^{70} + 648 q^{71} + 126 q^{73} + 504 q^{74} - 72 q^{76} + 342 q^{77} - 72 q^{79} - 594 q^{83} + 360 q^{85} - 540 q^{86} + 144 q^{88} - 648 q^{89} - 198 q^{91} - 396 q^{92} + 504 q^{94} - 252 q^{95} + 702 q^{97} - 648 q^{98}+O(q^{100}) $ 36 * q - 18 * q^5 + 18 * q^11 + 36 * q^14 + 72 * q^20 + 36 * q^22 + 180 * q^23 + 18 * q^25 - 144 * q^29 - 90 * q^31 - 72 * q^34 - 486 * q^35 - 180 * q^38 + 90 * q^41 + 90 * q^43 + 378 * q^47 + 72 * q^49 + 72 * q^56 - 252 * q^59 - 144 * q^61 + 144 * q^64 - 18 * q^65 - 594 * q^67 + 180 * q^68 - 360 * q^70 + 648 * q^71 + 126 * q^73 + 504 * q^74 - 72 * q^76 + 342 * q^77 - 72 * q^79 - 594 * q^83 + 360 * q^85 - 540 * q^86 + 144 * q^88 - 648 * q^89 - 198 * q^91 - 396 * q^92 + 504 * q^94 - 252 * q^95 + 702 * q^97 - 648 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{17}{18}\right)$

Coefficient data

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

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

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

$2$	1.39273	−	0.245576i	0.696364	−	0.122788i
$2$	1.39273	−	0.245576i	0.696364	−	0.122788i
$3$		0			0
$3$		0			0
$4$	1.87939	−	0.684040i	0.469846	−	0.171010i
$5$	−5.54906	+	6.61311i	−1.10981	+	1.32262i	−0.168264	+	0.985742i	$0.553816\pi$
$5$	−5.54906	+	6.61311i	−1.10981	+	1.32262i	−0.941547	+	0.336880i	$0.890628\pi$
$6$		0			0
$7$	7.83131	+	2.85036i	1.11876	+	0.407195i	0.834199	−	0.551463i	$-0.185930\pi$
$7$	7.83131	+	2.85036i	1.11876	+	0.407195i	0.284560	+	0.958658i	$0.408153\pi$
$8$	2.44949	−	1.41421i	0.306186	−	0.176777i
$9$		0			0
$10$	−6.10431	+	10.5730i	−0.610431	+	1.05730i
$11$	10.8191	+	12.8937i	0.983551	+	1.17215i	0.985070	+	0.172152i	$0.0550719\pi$
$11$	10.8191	+	12.8937i	0.983551	+	1.17215i	−0.00151930	+	0.999999i	$0.500484\pi$
$12$		0			0
$13$	0.524960	−	2.97720i	0.0403815	−	0.229015i	−0.957937	−	0.286978i	$-0.907349\pi$
$13$	0.524960	−	2.97720i	0.0403815	−	0.229015i	0.998319	+	0.0579628i	$0.0184605\pi$
$14$	11.6069	+	2.04660i	0.829062	+	0.146186i
$15$		0			0
$16$	3.06418	−	2.57115i	0.191511	−	0.160697i
$17$	−8.43596	−	4.87051i	−0.496233	−	0.286500i	0.230924	−	0.972972i	$-0.425825\pi$
$17$	−8.43596	−	4.87051i	−0.496233	−	0.286500i	−0.727157	+	0.686472i	$0.759159\pi$
$18$		0			0
$19$	3.84677	+	6.66281i	0.202462	+	0.350674i	0.949321	−	0.314308i	$-0.101772\pi$
$19$	3.84677	+	6.66281i	0.202462	+	0.350674i	−0.746859	+	0.664982i	$0.768439\pi$
$20$	−5.90519	+	16.2244i	−0.295259	+	0.811218i
$21$		0			0
$22$	18.2344	+	15.3005i	0.828836	+	0.695476i
$23$	−10.1434	−	27.8689i	−0.441019	−	1.21169i	−0.938823	−	0.344400i	$-0.888082\pi$
$23$	−10.1434	−	27.8689i	−0.441019	−	1.21169i	0.497804	−	0.867290i	$-0.334140\pi$
$24$		0			0
$25$	−8.59998	−	48.7729i	−0.343999	−	1.95092i
$26$		−	4.27534i		−	0.164436i
$27$		0			0
$28$	16.6678			0.595279
$29$	10.5809	−	1.86569i	0.364858	−	0.0643342i	0.0117860	−	0.999931i	$-0.496248\pi$
$29$	10.5809	−	1.86569i	0.364858	−	0.0643342i	0.353072	+	0.935596i	$0.385137\pi$
$30$		0			0
$31$	−10.8017	+	3.93149i	−0.348441	+	0.126822i	−0.510311	−	0.859990i	$-0.670470\pi$
$31$	−10.8017	+	3.93149i	−0.348441	+	0.126822i	0.161870	+	0.986812i	$0.448248\pi$
$32$	3.63616	−	4.33340i	0.113630	−	0.135419i
$33$		0			0
$34$	−12.9451	−	4.71163i	−0.380738	−	0.138577i
$35$	−62.3062	+	35.9725i	−1.78018	+	1.02779i
$36$		0			0
$37$	−11.5925	+	20.0787i	−0.313309	+	0.542668i	−0.979077	−	0.203492i	$-0.934771\pi$
$37$	−11.5925	+	20.0787i	−0.313309	+	0.542668i	0.665767	+	0.746160i	$0.268104\pi$
$38$	6.99373	+	8.33481i	0.184046	+	0.219337i
$39$		0			0
$40$	−4.24001	+	24.0463i	−0.106000	+	0.601158i
$41$	16.7264	+	2.94931i	0.407960	+	0.0719344i	0.373863	−	0.927484i	$-0.378033\pi$
$41$	16.7264	+	2.94931i	0.407960	+	0.0719344i	0.0340976	+	0.999419i	$0.489144\pi$
$42$		0			0
$43$	18.0881	−	15.1778i	0.420655	−	0.352971i	−0.407757	−	0.913090i	$-0.633689\pi$
$43$	18.0881	−	15.1778i	0.420655	−	0.352971i	0.828412	+	0.560119i	$0.189245\pi$
$44$	29.1530	+	16.8315i	0.662567	+	0.382533i
$45$		0			0
$46$	−20.9710	−	36.3228i	−0.455891	−	0.789626i
$47$	5.67901	−	15.6029i	0.120830	−	0.331977i	−0.864501	−	0.502631i	$-0.832366\pi$
$47$	5.67901	−	15.6029i	0.120830	−	0.331977i	0.985331	+	0.170653i	$0.0545878\pi$
$48$		0			0
$49$	15.6687	+	13.1476i	0.319769	+	0.268318i
$50$	−23.9549	−	65.8155i	−0.479097	−	1.31631i
$51$		0			0
$52$	−1.04992	−	5.95439i	−0.0201908	−	0.114508i
$53$		−	75.3383i		−	1.42148i	−0.703456	−	0.710739i	$-0.748361\pi$
$53$		−	75.3383i		−	1.42148i	0.703456	−	0.710739i	$-0.251639\pi$
$54$		0			0
$55$	−145.303			−2.64187
$56$	23.2137	−	4.09321i	0.414531	−	0.0730930i
$57$		0			0
$58$	14.2781	−	5.19681i	0.246174	−	0.0896001i
$59$	38.6968	−	46.1170i	0.655878	−	0.781645i	−0.330910	−	0.943662i	$-0.607356\pi$
$59$	38.6968	−	46.1170i	0.655878	−	0.781645i	0.986788	+	0.162017i	$0.0518001\pi$
$60$		0			0
$61$	32.1023	+	11.6843i	0.526267	+	0.191546i	0.591471	−	0.806326i	$-0.298547\pi$
$61$	32.1023	+	11.6843i	0.526267	+	0.191546i	−0.0652037	+	0.997872i	$0.520770\pi$
$62$	−14.0783	+	8.12813i	−0.227070	+	0.131099i
$63$		0			0
$64$	4.00000	−	6.92820i	0.0625000	−	0.108253i
$65$	16.7755	+	19.9923i	0.258085	+	0.307573i
$66$		0			0
$67$	6.53483	−	37.0609i	0.0975348	−	0.553147i	−0.896406	−	0.443233i	$-0.853831\pi$
$67$	6.53483	−	37.0609i	0.0975348	−	0.553147i	0.993941	−	0.109914i	$-0.0350575\pi$
$68$	−19.1860	−	3.38302i	−0.282148	−	0.0497503i
$69$		0			0
$70$	−77.9416	+	65.4008i	−1.11345	+	0.934297i
$71$	−44.0325	−	25.4222i	−0.620175	−	0.358058i	0.156762	−	0.987636i	$-0.449894\pi$
$71$	−44.0325	−	25.4222i	−0.620175	−	0.358058i	−0.776937	+	0.629578i	$0.783228\pi$
$72$		0			0
$73$	49.2453	+	85.2954i	0.674593	+	1.16843i	0.976588	+	0.215120i	$0.0690144\pi$
$73$	49.2453	+	85.2954i	0.674593	+	1.16843i	−0.301994	+	0.953310i	$0.597652\pi$
$74$	−11.2143	+	30.8110i	−0.151545	+	0.416365i
$75$		0			0
$76$	11.7872	+	9.89063i	0.155095	+	0.130140i
$77$	47.9758	+	131.813i	0.623063	+	1.71185i
$78$		0			0
$79$	−14.0913	−	79.9158i	−0.178371	−	1.01159i	−0.934180	−	0.356801i	$-0.883867\pi$
$79$	−14.0913	−	79.9158i	−0.178371	−	1.01159i	0.755809	−	0.654792i	$-0.227244\pi$
$80$			34.5312i			0.431640i
$81$		0			0
$82$	24.0196			0.292921
$83$	15.8868	−	2.80127i	0.191407	−	0.0337503i	−0.0771226	−	0.997022i	$-0.524573\pi$
$83$	15.8868	−	2.80127i	0.191407	−	0.0337503i	0.268530	+	0.963271i	$0.413462\pi$
$84$		0			0
$85$	79.0209	−	28.7612i	0.929657	−	0.338368i
$86$	21.4646	−	25.5805i	0.249588	−	0.297448i
$87$		0			0
$88$	44.7356	+	16.2824i	0.508359	+	0.185027i
$89$	−14.0161	+	8.09222i	−0.157485	+	0.0909238i	−0.576671	−	0.816976i	$-0.695649\pi$
$89$	−14.0161	+	8.09222i	−0.157485	+	0.0909238i	0.419187	+	0.907900i	$0.362315\pi$
$90$		0			0
$91$	12.5972	−	21.8190i	0.138431	−	0.239769i
$92$	−38.1269	−	45.4378i	−0.414422	−	0.493889i
$93$		0			0
$94$	4.07761	−	23.1253i	0.0433788	−	0.246014i
$95$	−65.4078	−	11.5332i	−0.688504	−	0.121402i
$96$		0			0
$97$	−101.648	+	85.2929i	−1.04792	+	0.879308i	−0.992873	−	0.119176i	$-0.961975\pi$
$97$	−101.648	+	85.2929i	−1.04792	+	0.879308i	−0.0550452	+	0.998484i	$0.517530\pi$
$98$	25.0509	+	14.4632i	0.255622	+	0.147583i
$99$		0			0
$100$	−49.5253	−	85.7803i	−0.495253	−	0.857803i
$101$	5.20626	−	14.3041i	0.0515471	−	0.141625i	−0.911247	−	0.411860i	$-0.864879\pi$
$101$	5.20626	−	14.3041i	0.0515471	−	0.141625i	0.962794	+	0.270235i	$0.0871015\pi$
$102$		0			0
$103$	−28.9968	−	24.3312i	−0.281522	−	0.236225i	0.491082	−	0.871113i	$-0.336602\pi$
$103$	−28.9968	−	24.3312i	−0.281522	−	0.236225i	−0.772604	+	0.634889i	$0.781046\pi$
$104$	−2.92451	−	8.03502i	−0.0281203	−	0.0772598i
$105$		0			0
$106$	−18.5013	−	104.926i	−0.174540	−	0.989866i
$107$			118.659i			1.10897i	0.832195	+	0.554483i	$0.187084\pi$
$107$			118.659i			1.10897i	−0.832195	+	0.554483i	$0.812916\pi$
$108$		0			0
$109$	206.055			1.89042			0.945208	−	0.326468i	$-0.105859\pi$
$109$	206.055			1.89042			0.945208	+	0.326468i	$0.105859\pi$
$110$	−202.367	+	35.6828i	−1.83970	+	0.324389i
$111$		0			0
$112$	31.3252	−	11.4015i	0.279690	−	0.101799i
$113$	45.6567	−	54.4116i	0.404042	−	0.481519i	−0.525206	−	0.850975i	$-0.676012\pi$
$113$	45.6567	−	54.4116i	0.404042	−	0.481519i	0.929248	+	0.369457i	$0.120456\pi$
$114$		0			0
$115$	240.586	+	87.5663i	2.09206	+	0.761446i
$116$	18.6093	−	10.7441i	0.160425	−	0.0926215i
$117$		0			0
$118$	42.5689	−	73.7315i	0.360753	−	0.624843i
$119$	−52.1819	−	62.1880i	−0.438504	−	0.522588i
$120$		0			0
$121$	−28.1828	+	159.833i	−0.232916	+	1.32093i
$122$	47.5792	+	8.38949i	0.389993	+	0.0687663i
$123$		0			0
$124$	−17.6112	+	14.7776i	−0.142026	+	0.119174i
$125$	183.357	+	105.861i	1.46685	+	0.846888i
$126$		0			0
$127$	−19.1347	−	33.1422i	−0.150667	−	0.260963i	0.780806	−	0.624774i	$-0.214809\pi$
$127$	−19.1347	−	33.1422i	−0.150667	−	0.260963i	−0.931473	+	0.363811i	$0.881475\pi$
$128$	3.86952	−	10.6314i	0.0302306	−	0.0830579i
$129$		0			0
$130$	28.2733	+	23.7241i	0.217487	+	0.182493i
$131$	74.5355	+	204.785i	0.568973	+	1.56324i	0.806110	+	0.591765i	$0.201569\pi$
$131$	74.5355	+	204.785i	0.568973	+	1.56324i	−0.237137	+	0.971476i	$0.576209\pi$
$132$		0			0
$133$	11.1339	+	63.1432i	0.0837132	+	0.474761i
$134$		−	53.2205i		−	0.397168i
$135$		0			0
$136$	−27.5517			−0.202586
$137$	181.295	−	31.9672i	1.32332	−	0.233337i	0.533045	−	0.846087i	$-0.321048\pi$
$137$	181.295	−	31.9672i	1.32332	−	0.233337i	0.790277	+	0.612749i	$0.209936\pi$
$138$		0			0
$139$	−228.486	+	83.1623i	−1.64379	+	0.598290i	−0.987695	−	0.156391i	$-0.950014\pi$
$139$	−228.486	+	83.1623i	−1.64379	+	0.598290i	−0.656092	+	0.754681i	$0.727792\pi$
$140$	−92.4907	+	110.226i	−0.660648	+	0.787329i
$141$		0			0
$142$	−67.5683	−	24.5929i	−0.475833	−	0.173189i
$143$	44.0665	−	25.4418i	0.308157	−	0.177915i
$144$		0			0
$145$	−46.3758	+	80.3253i	−0.319833	+	0.553968i
$146$	89.5318	+	106.700i	0.613232	+	0.730821i
$147$		0			0
$148$	−8.05203	+	45.6653i	−0.0544056	+	0.308550i
$149$	−141.886	−	25.0183i	−0.952255	−	0.167908i	−0.324123	−	0.946015i	$-0.605069\pi$
$149$	−141.886	−	25.0183i	−0.952255	−	0.167908i	−0.628132	+	0.778107i	$0.716180\pi$
$150$		0			0
$151$	−77.8368	+	65.3129i	−0.515476	+	0.432535i	−0.863051	−	0.505117i	$-0.831449\pi$
$151$	−77.8368	+	65.3129i	−0.515476	+	0.432535i	0.347575	+	0.937652i	$0.387005\pi$
$152$	18.8453	+	10.8803i	0.123982	+	0.0715810i
$153$		0			0
$154$	99.1872	+	171.797i	0.644073	+	1.11557i
$155$	33.9398	−	93.2488i	0.218966	−	0.601605i
$156$		0			0
$157$	−237.118	−	198.965i	−1.51030	−	1.26730i	−0.863162	−	0.504927i	$-0.831519\pi$
$157$	−237.118	−	198.965i	−1.51030	−	1.26730i	−0.647143	−	0.762369i	$-0.724036\pi$
$158$	−39.2508	−	107.841i	−0.248423	−	0.682535i
$159$		0			0
$160$	8.48002	+	48.0926i	0.0530001	+	0.300579i
$161$		−	247.162i		−	1.53517i
$162$		0			0
$163$	160.056			0.981937			0.490969	−	0.871177i	$-0.336643\pi$
$163$	160.056			0.981937			0.490969	+	0.871177i	$0.336643\pi$
$164$	33.4527	−	5.89862i	0.203980	−	0.0359672i
$165$		0			0
$166$	21.4381	−	7.80282i	0.129145	−	0.0470050i
$167$	−160.019	+	190.703i	−0.958197	+	1.14193i	0.0316076	+	0.999500i	$0.489937\pi$
$167$	−160.019	+	190.703i	−0.958197	+	1.14193i	−0.989804	+	0.142434i	$0.954507\pi$
$168$		0			0
$169$	150.220	+	54.6756i	0.888875	+	0.323524i
$170$	102.992	−	59.4622i	0.605833	−	0.349778i
$171$		0			0
$172$	23.6124	−	40.8979i	0.137281	−	0.237778i
$173$	−43.4383	−	51.7678i	−0.251088	−	0.299236i	0.625747	−	0.780026i	$-0.284794\pi$
$173$	−43.4383	−	51.7678i	−0.251088	−	0.299236i	−0.876836	+	0.480790i	$0.840350\pi$
$174$		0			0
$175$	71.6714	−	406.469i	0.409551	−	2.32268i
$176$	66.3031	+	11.6910i	0.376722	+	0.0664262i
$177$		0			0
$178$	−17.5334	+	14.7123i	−0.0985024	+	0.0826533i
$179$	−203.717	−	117.616i	−1.13808	−	0.657073i	−0.192128	−	0.981370i	$-0.561539\pi$
$179$	−203.717	−	117.616i	−1.13808	−	0.657073i	−0.945955	+	0.324297i	$0.894872\pi$
$180$		0			0
$181$	−108.916	−	188.647i	−0.601744	−	1.04225i	−0.992557	−	0.121781i	$-0.961140\pi$
$181$	−108.916	−	188.647i	−0.601744	−	1.04225i	0.390813	−	0.920470i	$-0.372194\pi$
$182$	12.1863	−	33.4815i	0.0669576	−	0.183965i
$183$		0			0
$184$	−64.2588	−	53.9195i	−0.349233	−	0.293041i
$185$	−68.4556	−	188.080i	−0.370030	−	1.01665i
$186$		0			0
$187$	−28.4706	−	161.465i	−0.152249	−	0.863448i
$188$		−	33.2086i		−	0.176642i
$189$		0			0
$190$	−93.9276			−0.494356
$191$	−253.418	+	44.6844i	−1.32679	+	0.233950i	−0.791735	−	0.610864i	$-0.790822\pi$
$191$	−253.418	+	44.6844i	−1.32679	+	0.233950i	−0.535060	+	0.844814i	$0.679711\pi$
$192$		0			0
$193$	72.0472	−	26.2230i	0.373302	−	0.135871i	−0.148554	−	0.988904i	$-0.547462\pi$
$193$	72.0472	−	26.2230i	0.373302	−	0.135871i	0.521856	+	0.853034i	$0.325240\pi$
$194$	−120.622	+	143.752i	−0.621765	+	0.740990i
$195$		0			0
$196$	38.4410	+	13.9914i	0.196127	+	0.0713845i
$197$	211.300	−	121.994i	1.07259	−	0.619260i	0.143702	−	0.989621i	$-0.454099\pi$
$197$	211.300	−	121.994i	1.07259	−	0.619260i	0.928888	+	0.370361i	$0.120766\pi$
$198$		0			0
$199$	−41.0539	+	71.1075i	−0.206301	+	0.357324i	−0.950547	−	0.310582i	$-0.899476\pi$
$199$	−41.0539	+	71.1075i	−0.206301	+	0.357324i	0.744245	+	0.667906i	$0.232809\pi$
$200$	−90.0408	−	107.307i	−0.450204	−	0.536533i
$201$		0			0
$202$	3.73817	−	21.2002i	0.0185058	−	0.104952i
$203$	88.1800	+	15.5485i	0.434384	+	0.0765936i
$204$		0			0
$205$	−112.320	+	94.2474i	−0.547901	+	0.459743i
$206$	−46.3597	−	26.7658i	−0.225047	−	0.129931i
$207$		0			0
$208$	−6.04625	−	10.4724i	−0.0290685	−	0.0503481i
$209$	−44.2895	+	121.684i	−0.211911	+	0.582221i
$210$		0			0
$211$	44.0427	+	36.9562i	0.208733	+	0.175148i	0.741161	−	0.671328i	$-0.234276\pi$
$211$	44.0427	+	36.9562i	0.208733	+	0.175148i	−0.532427	+	0.846476i	$0.678720\pi$
$212$	−51.5344	−	141.590i	−0.243087	−	0.667876i
$213$		0			0
$214$	29.1399	+	165.260i	0.136168	+	0.772245i
$215$			203.841i			0.948098i
$216$		0			0
$217$	−95.7975			−0.441463
$218$	286.979	−	50.6022i	1.31642	−	0.232120i
$219$		0			0
$220$	−273.080	+	99.3930i	−1.24127	+	0.451786i
$221$	−18.9290	+	22.5587i	−0.0856516	+	0.102076i
$222$		0			0
$223$	−217.997	−	79.3444i	−0.977565	−	0.355805i	−0.196672	−	0.980469i	$-0.563013\pi$
$223$	−217.997	−	79.3444i	−0.977565	−	0.355805i	−0.780893	+	0.624665i	$0.785236\pi$
$224$	40.8276	−	23.5718i	0.182266	−	0.105231i
$225$		0			0
$226$	50.2253	−	86.9928i	0.222236	−	0.384924i
$227$	−137.899	−	164.342i	−0.607485	−	0.723973i	0.371379	−	0.928481i	$-0.378885\pi$
$227$	−137.899	−	164.342i	−0.607485	−	0.723973i	−0.978865	+	0.204508i	$0.934440\pi$
$228$		0			0
$229$	−68.6623	+	389.403i	−0.299835	+	1.70045i	0.347036	+	0.937852i	$0.387188\pi$
$229$	−68.6623	+	389.403i	−0.299835	+	1.70045i	−0.646871	+	0.762599i	$0.723923\pi$
$230$	356.576	+	62.8739i	1.55033	+	0.273365i
$231$		0			0
$232$	23.2792	−	19.5336i	0.100342	−	0.0841966i
$233$	−82.9298	−	47.8796i	−0.355922	−	0.205492i	0.311368	−	0.950289i	$-0.399213\pi$
$233$	−82.9298	−	47.8796i	−0.355922	−	0.205492i	−0.667290	+	0.744798i	$0.732546\pi$
$234$		0			0
$235$	71.6708	+	124.138i	0.304982	+	0.528245i
$236$	41.1803	−	113.142i	0.174493	−	0.479415i
$237$		0			0
$238$	−87.9471	−	73.7964i	−0.369526	−	0.310069i
$239$	30.1617	+	82.8687i	0.126200	+	0.346731i	0.986662	−	0.162784i	$-0.0520473\pi$
$239$	30.1617	+	82.8687i	0.126200	+	0.346731i	−0.860462	+	0.509514i	$0.829825\pi$
$240$		0			0
$241$	−66.8780	−	379.284i	−0.277502	−	1.57379i	−0.730901	−	0.682484i	$-0.760900\pi$
$241$	−66.8780	−	379.284i	−0.277502	−	1.57379i	0.453399	−	0.891308i	$-0.350211\pi$
$242$			229.525i			0.948449i
$243$		0			0
$244$	68.3251			0.280021
$245$	−173.893	+	30.6620i	−0.709767	+	0.125151i
$246$		0			0
$247$	21.8559	−	7.95489i	0.0884854	−	0.0322060i
$248$	−20.8986	+	24.9060i	−0.0842687	+	0.100428i
$249$		0			0
$250$	281.363	+	102.408i	1.12545	+	0.409631i
$251$	126.850	−	73.2368i	0.505378	−	0.291780i	−0.225554	−	0.974231i	$-0.572419\pi$
$251$	126.850	−	73.2368i	0.505378	−	0.291780i	0.730932	+	0.682451i	$0.239086\pi$
$252$		0			0
$253$	249.589	−	432.301i	0.986518	−	1.70870i
$254$	−34.7883	−	41.4591i	−0.136962	−	0.163225i
$255$		0			0
$256$	2.77837	−	15.7569i	0.0108530	−	0.0615505i
$257$	−204.456	−	36.0511i	−0.795548	−	0.140277i	−0.238921	−	0.971039i	$-0.576794\pi$
$257$	−204.456	−	36.0511i	−0.795548	−	0.140277i	−0.556627	+	0.830762i	$0.687905\pi$
$258$		0			0
$259$	−148.016	+	124.200i	−0.571489	+	0.479536i
$260$	45.2031	+	26.0980i	0.173858	+	0.100377i
$261$		0			0
$262$	154.098	+	266.905i	0.588160	+	1.01872i
$263$	11.3833	−	31.2753i	0.0432825	−	0.118918i	−0.916168	−	0.400794i	$-0.868734\pi$
$263$	11.3833	−	31.2753i	0.0432825	−	0.118918i	0.959451	+	0.281876i	$0.0909567\pi$
$264$		0			0
$265$	498.221	+	418.057i	1.88008	+	1.57757i
$266$	31.0129	+	85.2071i	0.116590	+	0.320328i
$267$		0			0
$268$	−13.0697	−	74.1217i	−0.0487674	−	0.276574i
$269$			399.099i			1.48364i	0.670599	+	0.741820i	$0.266037\pi$
$269$			399.099i			1.48364i	−0.670599	+	0.741820i	$0.733963\pi$
$270$		0			0
$271$	−83.9974			−0.309954			−0.154977	−	0.987918i	$-0.549530\pi$
$271$	−83.9974			−0.309954			−0.154977	+	0.987918i	$0.549530\pi$
$272$	−38.3721	+	6.76604i	−0.141074	+	0.0248751i
$273$		0			0
$274$	244.645	−	89.0434i	0.892864	−	0.324976i
$275$	535.817	−	638.562i	1.94843	−	2.32204i
$276$		0			0
$277$	−168.403	−	61.2936i	−0.607953	−	0.221277i	0.0196546	−	0.999807i	$-0.493743\pi$
$277$	−168.403	−	61.2936i	−0.607953	−	0.221277i	−0.627607	+	0.778530i	$0.715966\pi$
$278$	−297.797	+	171.933i	−1.07121	+	0.618465i
$279$		0			0
$280$	−101.746	+	176.228i	−0.363377	+	0.629387i
$281$	298.873	+	356.183i	1.06361	+	1.26756i	0.962093	+	0.272722i	$0.0879239\pi$
$281$	298.873	+	356.183i	1.06361	+	1.26756i	0.101513	+	0.994834i	$0.467632\pi$
$282$		0			0
$283$	45.4847	−	257.956i	0.160723	−	0.911507i	−0.792642	−	0.609687i	$-0.791295\pi$
$283$	45.4847	−	257.956i	0.160723	−	0.911507i	0.953365	−	0.301819i	$-0.0975939\pi$
$284$	−100.144	−	17.6580i	−0.352619	−	0.0621762i
$285$		0			0
$286$	55.1248	−	46.2552i	0.192744	−	0.161731i
$287$	122.583	+	70.7732i	0.427118	+	0.246596i
$288$		0			0
$289$	−97.0563	−	168.107i	−0.335835	−	0.581683i
$290$	−44.8630	+	123.260i	−0.154700	+	0.425035i
$291$		0			0
$292$	150.896	+	126.617i	0.516769	+	0.433620i
$293$	33.5970	+	92.3071i	0.114666	+	0.315041i	0.983729	−	0.179660i	$-0.0574997\pi$
$293$	33.5970	+	92.3071i	0.114666	+	0.315041i	−0.869063	+	0.494701i	$0.835278\pi$
$294$		0			0
$295$	90.2463	+	511.812i	0.305920	+	1.73496i
$296$			65.5768i			0.221543i
$297$		0			0
$298$	−203.753			−0.683733
$299$	−88.2960	+	15.5690i	−0.295304	+	0.0520701i
$300$		0			0
$301$	184.916	−	67.3039i	0.614339	−	0.223601i
$302$	−92.3663	+	110.078i	−0.305849	+	0.364496i
$303$		0			0
$304$	28.9183	+	10.5254i	0.0951259	+	0.0346230i
$305$	−255.407	+	147.459i	−0.837400	+	0.483473i
$306$		0			0
$307$	−246.426	+	426.822i	−0.802690	+	1.39030i	0.115150	+	0.993348i	$0.463265\pi$
$307$	−246.426	+	426.822i	−0.802690	+	1.39030i	−0.917840	+	0.396952i	$0.870068\pi$
$308$	180.330	+	214.909i	0.585487	+	0.697757i
$309$		0			0
$310$	24.3693	−	138.205i	0.0786106	−	0.445823i
$311$	16.6486	+	2.93559i	0.0535324	+	0.00943921i	0.200350	−	0.979724i	$-0.435792\pi$
$311$	16.6486	+	2.93559i	0.0535324	+	0.00943921i	−0.146818	+	0.989164i	$0.546903\pi$
$312$		0			0
$313$	319.525	−	268.113i	1.02085	−	0.856591i	0.0311120	−	0.999516i	$-0.490095\pi$
$313$	319.525	−	268.113i	1.02085	−	0.856591i	0.989734	+	0.142925i	$0.0456507\pi$
$314$	−379.102	−	218.875i	−1.20733	−	0.697053i
$315$		0			0
$316$	−81.1487	−	140.554i	−0.256800	−	0.444790i
$317$	−155.193	+	426.388i	−0.489567	+	1.34507i	0.411507	+	0.911407i	$0.365003\pi$
$317$	−155.193	+	426.388i	−0.489567	+	1.34507i	−0.901074	+	0.433666i	$0.857220\pi$
$318$		0			0
$319$	138.531	+	116.241i	0.434265	+	0.364392i
$320$	23.6207	+	64.8975i	0.0738148	+	0.202805i
$321$		0			0
$322$	−60.6970	−	344.230i	−0.188500	−	1.06904i
$323$		−	74.9429i		−	0.232021i
$324$		0			0
$325$	−149.721			−0.460680
$326$	222.914	−	39.3058i	0.683786	−	0.120570i
$327$		0			0
$328$	45.1420	−	16.4303i	0.137628	−	0.0500925i
$329$	88.9481	−	106.004i	0.270359	−	0.322201i
$330$		0			0
$331$	220.616	+	80.2978i	0.666515	+	0.242591i	0.653046	−	0.757318i	$-0.273491\pi$
$331$	220.616	+	80.2978i	0.666515	+	0.242591i	0.0134681	+	0.999909i	$0.495713\pi$
$332$	27.9412	−	16.1319i	0.0841604	−	0.0485900i
$333$		0			0
$334$	−176.031	+	304.894i	−0.527038	+	0.912857i
$335$	208.825	+	248.868i	0.623360	+	0.742891i
$336$		0			0
$337$	−55.0894	+	312.428i	−0.163470	+	0.927085i	0.787158	+	0.616752i	$0.211552\pi$
$337$	−55.0894	+	312.428i	−0.163470	+	0.927085i	−0.950628	+	0.310333i	$0.899559\pi$
$338$	222.643	+	39.2579i	0.658706	+	0.116148i
$339$		0			0
$340$	128.837	−	108.107i	0.378932	−	0.317961i
$341$	−167.555	−	96.7381i	−0.491365	−	0.283689i
$342$		0			0
$343$	−118.950	−	206.027i	−0.346793	−	0.600662i
$344$	22.8421	−	62.7583i	0.0664016	−	0.182437i
$345$		0			0
$346$	−73.2107	−	61.4310i	−0.211592	−	0.177546i
$347$	15.0965	+	41.4774i	0.0435059	+	0.119531i	0.959543	−	0.281562i	$-0.0908525\pi$
$347$	15.0965	+	41.4774i	0.0435059	+	0.119531i	−0.916037	+	0.401093i	$0.868630\pi$
$348$		0			0
$349$	57.3986	+	325.523i	0.164466	+	0.932732i	0.949614	+	0.313423i	$0.101476\pi$
$349$	57.3986	+	325.523i	0.164466	+	0.932732i	−0.785148	+	0.619309i	$0.787413\pi$
$350$		−	583.701i		−	1.66772i
$351$		0			0
$352$	95.2132			0.270492
$353$	466.298	−	82.2209i	1.32096	−	0.232920i	0.531673	−	0.846949i	$-0.321563\pi$
$353$	466.298	−	82.2209i	1.32096	−	0.232920i	0.789283	+	0.614029i	$0.210452\pi$
$354$		0			0
$355$	412.458	−	150.123i	1.16185	−	0.422880i
$356$	−20.8063	+	24.7960i	−0.0584447	+	0.0696517i
$357$		0			0
$358$	−312.606	−	113.779i	−0.873201	−	0.317819i
$359$	−378.055	+	218.270i	−1.05308	+	0.607994i	−0.923509	−	0.383576i	$-0.874692\pi$
$359$	−378.055	+	218.270i	−1.05308	+	0.607994i	−0.129568	+	0.991571i	$0.541359\pi$
$360$		0			0
$361$	150.905	−	261.375i	0.418018	−	0.724029i
$362$	−198.017	−	235.988i	−0.547009	−	0.651899i
$363$		0			0
$364$	8.74994	−	49.6234i	0.0240383	−	0.136328i
$365$	−837.333	−	147.644i	−2.29406	−	0.404505i
$366$		0			0
$367$	365.154	−	306.401i	0.994970	−	0.834879i	0.00869048	−	0.999962i	$-0.497234\pi$
$367$	365.154	−	306.401i	0.994970	−	0.834879i	0.986280	+	0.165083i	$0.0527893\pi$
$368$	−102.736	−	59.3149i	−0.279175	−	0.161182i
$369$		0			0
$370$	−141.528	−	245.134i	−0.382508	−	0.662523i
$371$	214.742	−	589.998i	0.578818	−	1.59029i
$372$		0			0
$373$	−282.763	−	237.266i	−0.758077	−	0.636102i	0.179549	−	0.983749i	$-0.442536\pi$
$373$	−282.763	−	237.266i	−0.758077	−	0.636102i	−0.937625	+	0.347647i	$0.886981\pi$
$374$	−79.3036	−	217.885i	−0.212042	−	0.582580i
$375$		0			0
$376$	−8.15522	−	46.2506i	−0.0216894	−	0.123007i
$377$		−	32.4807i		−	0.0861558i
$378$		0			0
$379$	−216.903			−0.572304			−0.286152	−	0.958184i	$-0.592376\pi$
$379$	−216.903			−0.572304			−0.286152	+	0.958184i	$0.592376\pi$
$380$	−130.816	+	23.0663i	−0.344252	+	0.0607009i
$381$		0			0
$382$	−341.969	+	124.466i	−0.895206	+	0.325828i
$383$	346.686	−	413.164i	0.905185	−	1.07876i	−0.0913699	−	0.995817i	$-0.529125\pi$
$383$	346.686	−	413.164i	0.905185	−	1.07876i	0.996555	−	0.0829400i	$-0.0264310\pi$
$384$		0			0
$385$	−1137.91	−	414.166i	−2.95561	−	1.07576i
$386$	93.9025	−	54.2146i	0.243271	−	0.140452i
$387$		0			0
$388$	−132.692	+	229.830i	−0.341990	+	0.592344i
$389$	−94.9161	−	113.117i	−0.244000	−	0.290788i	0.630120	−	0.776498i	$-0.283006\pi$
$389$	−94.9161	−	113.117i	−0.244000	−	0.290788i	−0.874120	+	0.485710i	$0.838561\pi$
$390$		0			0
$391$	−50.1658	+	284.504i	−0.128301	+	0.727633i
$392$	56.9738	+	10.0460i	0.145341	+	0.0256276i
$393$		0			0
$394$	264.325	−	221.795i	0.670875	−	0.562931i
$395$	606.686	+	350.270i	1.53591	+	0.886760i
$396$		0			0
$397$	251.308	+	435.278i	0.633017	+	1.09642i	0.986932	+	0.161139i	$0.0515169\pi$
$397$	251.308	+	435.278i	0.633017	+	1.09642i	−0.353915	+	0.935278i	$0.615150\pi$
$398$	−39.7147	+	109.115i	−0.0997857	+	0.274159i
$399$		0			0
$400$	−151.754	−	127.337i	−0.379386	−	0.318342i
$401$	−79.1589	−	217.487i	−0.197404	−	0.542362i	0.801011	−	0.598650i	$-0.204296\pi$
$401$	−79.1589	−	217.487i	−0.197404	−	0.542362i	−0.998415	+	0.0562876i	$0.982074\pi$
$402$		0			0
$403$	6.03437	+	34.2226i	0.0149736	+	0.0849196i
$404$		−	30.4442i		−	0.0753569i
$405$		0			0
$406$	126.629			0.311894
$407$	−384.307	+	67.7638i	−0.944244	+	0.166496i
$408$		0			0
$409$	−423.279	+	154.061i	−1.03491	+	0.376677i	−0.802949	−	0.596048i	$-0.796737\pi$
$409$	−423.279	+	154.061i	−1.03491	+	0.376677i	−0.231963	+	0.972725i	$0.574515\pi$
$410$	−133.286	+	158.844i	−0.325088	+	0.387424i
$411$		0			0
$412$	−71.1396	−	25.8927i	−0.172669	−	0.0628463i
$413$	434.497	−	250.857i	1.05205	−	0.607402i
$414$		0			0
$415$	−69.6317	+	120.606i	−0.167787	+	0.290616i
$416$	−10.9926	−	13.1004i	−0.0264244	−	0.0314914i
$417$		0			0
$418$	−31.8005	+	180.350i	−0.0760777	+	0.431458i
$419$	324.142	+	57.1549i	0.773608	+	0.136408i	0.546497	−	0.837461i	$-0.315961\pi$
$419$	324.142	+	57.1549i	0.773608	+	0.136408i	0.227111	+	0.973869i	$0.427072\pi$
$420$		0			0
$421$	−156.740	+	131.520i	−0.372303	+	0.312399i	−0.809672	−	0.586883i	$-0.800355\pi$
$421$	−156.740	+	131.520i	−0.372303	+	0.312399i	0.437369	+	0.899282i	$0.355910\pi$
$422$	70.4151	+	40.6542i	0.166860	+	0.0963369i
$423$		0			0
$424$	−106.544	−	184.540i	−0.251284	−	0.435237i
$425$	−165.000	+	453.333i	−0.388234	+	1.06666i
$426$		0			0
$427$	218.099	+	183.006i	0.510770	+	0.428587i
$428$	81.1678	+	223.007i	0.189645	+	0.521044i
$429$		0			0
$430$	50.0584	+	283.895i	0.116415	+	0.660222i
$431$		−	5.85402i		−	0.0135824i	−0.999977	−	0.00679120i	$-0.997838\pi$
$431$		−	5.85402i		−	0.0135824i	0.999977	−	0.00679120i	$-0.00216172\pi$
$432$		0			0
$433$	233.310			0.538821			0.269411	−	0.963025i	$-0.413171\pi$
$433$	233.310			0.538821			0.269411	+	0.963025i	$0.413171\pi$
$434$	−133.420	+	23.5255i	−0.307419	+	0.0542063i
$435$		0			0
$436$	387.257	−	140.950i	0.888205	−	0.323280i
$437$	146.665	−	174.789i	0.335619	−	0.399975i
$438$		0			0
$439$	126.662	+	46.1012i	0.288524	+	0.105014i	0.482227	−	0.876046i	$-0.339828\pi$
$439$	126.662	+	46.1012i	0.288524	+	0.105014i	−0.193704	+	0.981060i	$0.562050\pi$
$440$	−355.918	+	205.489i	−0.808904	+	0.467021i
$441$		0			0
$442$	−20.8231	+	36.0666i	−0.0471110	+	0.0815987i
$443$	−18.4121	−	21.9426i	−0.0415622	−	0.0495319i	0.744863	−	0.667218i	$-0.232515\pi$
$443$	−18.4121	−	21.9426i	−0.0415622	−	0.0495319i	−0.786425	+	0.617686i	$0.788070\pi$
$444$		0			0
$445$	24.2616	−	137.594i	0.0545205	−	0.309201i
$446$	−323.096	−	56.9705i	−0.724430	−	0.127737i
$447$		0			0
$448$	51.0731	−	42.8555i	0.114003	−	0.0956595i
$449$	−430.226	−	248.391i	−0.958188	−	0.553210i	−0.0625728	−	0.998040i	$-0.519931\pi$
$449$	−430.226	−	248.391i	−0.958188	−	0.553210i	−0.895615	+	0.444831i	$0.853264\pi$
$450$		0			0
$451$	142.936	+	247.573i	0.316932	+	0.548942i
$452$	48.5869	−	133.491i	0.107493	−	0.295335i
$453$		0			0
$454$	−232.414	−	195.019i	−0.511926	−	0.429557i
$455$	74.3889	+	204.382i	0.163492	+	0.449191i
$456$		0			0
$457$	−80.5387	−	456.758i	−0.176234	−	0.999470i	−0.936710	−	0.350105i	$-0.886146\pi$
$457$	−80.5387	−	456.758i	−0.176234	−	0.999470i	0.760477	−	0.649365i	$-0.224965\pi$
$458$			559.195i			1.22095i
$459$		0			0
$460$	512.054			1.11316
$461$	262.335	−	46.2568i	0.569057	−	0.100340i	0.118286	−	0.992980i	$-0.462260\pi$
$461$	262.335	−	46.2568i	0.569057	−	0.100340i	0.450771	+	0.892640i	$0.351149\pi$
$462$		0			0
$463$	−224.935	+	81.8697i	−0.485821	+	0.176824i	−0.573306	−	0.819341i	$-0.694339\pi$
$463$	−224.935	+	81.8697i	−0.485821	+	0.176824i	0.0874848	+	0.996166i	$0.472117\pi$
$464$	27.6247	−	32.9218i	0.0595360	−	0.0709522i
$465$		0			0
$466$	−127.257	−	46.3177i	−0.273083	−	0.0993942i
$467$	184.565	−	106.559i	0.395215	−	0.228177i	−0.289202	−	0.957268i	$-0.593390\pi$
$467$	184.565	−	106.559i	0.395215	−	0.228177i	0.684417	+	0.729091i	$0.260057\pi$
$468$		0			0
$469$	156.813	−	271.609i	0.334357	−	0.579123i
$470$	130.303	+	155.289i	0.277241	+	0.330403i
$471$		0			0
$472$	29.5681	−	167.689i	0.0626442	−	0.355273i
$473$	391.394	+	69.0132i	0.827470	+	0.145905i
$474$		0			0
$475$	291.882	−	244.918i	0.614489	−	0.515617i
$476$	−140.609	−	81.1807i	−0.295397	−	0.170548i
$477$		0			0
$478$	62.3576	+	108.007i	0.130455	+	0.225955i
$479$	−136.882	+	376.079i	−0.285765	+	0.785134i	0.710882	+	0.703312i	$0.248296\pi$
$479$	−136.882	+	376.079i	−0.285765	+	0.785134i	−0.996647	+	0.0818220i	$0.973926\pi$
$480$		0			0
$481$	53.6927	+	45.0535i	0.111627	+	0.0936664i
$482$	−186.286	−	511.816i	−0.386485	−	1.06186i
$483$		0			0
$484$	56.3657	+	319.666i	0.116458	+	0.660466i
$485$		−	1145.51i		−	2.36187i
$486$		0			0
$487$	−323.676			−0.664632			−0.332316	−	0.943168i	$-0.607830\pi$
$487$	−323.676			−0.664632			−0.332316	+	0.943168i	$0.607830\pi$
$488$	95.1583	−	16.7790i	0.194997	−	0.0343832i
$489$		0			0
$490$	−234.656	+	85.4077i	−0.478889	+	0.174301i
$491$	−589.862	+	702.970i	−1.20135	+	1.43171i	−0.327956	+	0.944693i	$0.606360\pi$
$491$	−589.862	+	702.970i	−1.20135	+	1.43171i	−0.873392	+	0.487018i	$0.838085\pi$
$492$		0			0
$493$	−98.3467	−	35.7953i	−0.199486	−	0.0726070i
$494$	28.4858	−	16.4463i	0.0576635	−	0.0332921i
$495$		0			0
$496$	−22.9898	+	39.8195i	−0.0463504	+	0.0802813i
$497$	−272.369	−	324.597i	−0.548027	−	0.653113i
$498$		0			0
$499$	−37.5201	+	212.787i	−0.0751906	+	0.426427i	0.923855	+	0.382743i	$0.125021\pi$
$499$	−37.5201	+	212.787i	−0.0751906	+	0.426427i	−0.999045	+	0.0436840i	$0.986091\pi$
$500$	417.011	+	73.5303i	0.834022	+	0.147061i
$501$		0			0
$502$	158.682	−	133.150i	0.316100	−	0.265240i
$503$	−31.3557	−	18.1032i	−0.0623373	−	0.0359905i	0.468507	−	0.883460i	$-0.344792\pi$
$503$	−31.3557	−	18.1032i	−0.0623373	−	0.0359905i	−0.530845	+	0.847469i	$0.678125\pi$
$504$		0			0
$505$	65.7046	+	113.804i	0.130108	+	0.225354i
$506$	241.447	−	663.371i	0.477169	−	1.31101i
$507$		0			0
$508$	−58.6321	−	49.1982i	−0.115417	−	0.0968468i
$509$	79.8138	+	219.287i	0.156805	+	0.430818i	0.993072	−	0.117503i	$-0.0374891\pi$
$509$	79.8138	+	219.287i	0.156805	+	0.430818i	−0.836267	+	0.548322i	$0.815267\pi$
$510$		0			0
$511$	142.532	+	808.342i	0.278929	+	1.58188i
$512$		−	22.6274i		−	0.0441942i
$513$		0			0
$514$	−293.605			−0.571216
$515$	321.809	−	56.7437i	0.624873	−	0.110182i
$516$		0			0
$517$	262.620	−	95.5860i	0.507970	−	0.184886i
$518$	−175.645	+	209.326i	−0.339083	+	0.404104i
$519$		0			0
$520$	69.3647	+	25.2467i	0.133394	+	0.0485513i
$521$	119.806	−	69.1700i	0.229954	−	0.132764i	−0.380597	−	0.924741i	$-0.624281\pi$
$521$	119.806	−	69.1700i	0.229954	−	0.132764i	0.610551	+	0.791977i	$0.290948\pi$
$522$		0			0
$523$	98.4346	−	170.494i	0.188212	−	0.325992i	−0.756442	−	0.654060i	$-0.773064\pi$
$523$	98.4346	−	170.494i	0.188212	−	0.325992i	0.944654	+	0.328068i	$0.106398\pi$
$524$	280.162	+	333.884i	0.534660	+	0.637183i
$525$		0			0
$526$	8.17338	−	46.3535i	0.0155387	−	0.0881246i
$527$	110.271	+	19.4437i	0.209243	+	0.0368951i
$528$		0			0
$529$	−268.547	+	225.338i	−0.507651	+	0.425969i
$530$	796.551	+	459.889i	1.50293	+	0.867715i
$531$		0			0
$532$	64.1173	+	111.054i	0.120521	+	0.208749i
$533$	17.5613	−	48.2494i	0.0329481	−	0.0905242i
$534$		0			0
$535$	−784.708	−	658.448i	−1.46674	−	1.23074i
$536$	−36.4050	−	100.022i	−0.0679197	−	0.186608i
$537$		0			0
$538$	98.0090	+	555.837i	0.182173	+	1.03315i
$539$			344.271i			0.638722i
$540$		0			0
$541$	−136.735			−0.252745			−0.126373	−	0.991983i	$-0.540334\pi$
$541$	−136.735			−0.252745			−0.126373	+	0.991983i	$0.540334\pi$
$542$	−116.986	+	20.6277i	−0.215841	+	0.0380585i
$543$		0			0
$544$	−51.7803	+	18.8465i	−0.0951844	+	0.0346443i
$545$	−1143.41	+	1362.67i	−2.09801	+	2.50031i
$546$		0			0
$547$	625.697	+	227.735i	1.14387	+	0.416335i	0.843310	−	0.537428i	$-0.180604\pi$
$547$	625.697	+	227.735i	1.14387	+	0.416335i	0.300561	+	0.953763i	$0.402826\pi$
$548$	318.857	−	184.092i	0.581855	−	0.335934i
$549$		0			0
$550$	589.433	−	1020.93i	1.07170	−	1.85623i
$551$	53.1330	+	63.3214i	0.0964300	+	0.114921i
$552$		0			0
$553$	117.436	−	666.011i	0.212361	−	1.20436i
$554$	−249.592	−	44.0098i	−0.450527	−	0.0794400i
$555$		0			0
$556$	−372.528	+	312.588i	−0.670014	+	0.562208i
$557$	943.861	+	544.939i	1.69454	+	0.978346i	0.950761	+	0.309926i	$0.100304\pi$
$557$	943.861	+	544.939i	1.69454	+	0.978346i	0.743784	+	0.668420i	$0.233029\pi$
$558$		0			0
$559$	−35.6916	−	61.8197i	−0.0638490	−	0.110590i
$560$	−98.4265	+	270.425i	−0.175762	+	0.482901i
$561$		0			0
$562$	503.719	+	422.671i	0.896298	+	0.752083i
$563$	−209.400	−	575.323i	−0.371937	−	1.02189i	−0.974612	−	0.223901i	$-0.928121\pi$
$563$	−209.400	−	575.323i	−0.371937	−	1.02189i	0.602675	−	0.797987i	$-0.294102\pi$
$564$		0			0
$565$	106.478	+	603.866i	0.188457	+	1.06879i
$566$		−	370.433i		−	0.654475i
$567$		0			0
$568$	−143.809			−0.253186
$569$	−491.784	+	86.7148i	−0.864295	+	0.152399i	−0.588184	−	0.808727i	$-0.700157\pi$
$569$	−491.784	+	86.7148i	−0.864295	+	0.152399i	−0.276111	+	0.961126i	$0.589046\pi$
$570$		0			0
$571$	284.552	−	103.569i	0.498341	−	0.181381i	−0.0806069	−	0.996746i	$-0.525686\pi$
$571$	284.552	−	103.569i	0.498341	−	0.181381i	0.578947	+	0.815365i	$0.303464\pi$
$572$	65.4147	−	77.9582i	0.114361	−	0.136291i
$573$		0			0
$574$	188.105	+	68.4645i	0.327708	+	0.119276i
$575$	−1272.01	+	734.397i	−2.21220	+	1.27721i
$576$		0			0
$577$	−18.5614	+	32.1493i	−0.0321688	+	0.0557181i	−0.881662	−	0.471882i	$-0.843575\pi$
$577$	−18.5614	+	32.1493i	−0.0321688	+	0.0557181i	0.849493	+	0.527600i	$0.176908\pi$
$578$	−176.456	−	210.292i	−0.305287	−	0.363827i
$579$		0			0
$580$	−32.2123	+	182.685i	−0.0555385	+	0.314974i
$581$	132.399	+	23.3455i	0.227881	+	0.0401817i
$582$		0			0
$583$	971.386	−	815.090i	1.66619	−	1.39810i
$584$	241.252	+	139.287i	0.413102	+	0.238505i
$585$		0			0
$586$	69.4599	+	120.308i	0.118532	+	0.205304i
$587$	299.988	−	824.210i	0.511053	−	1.40411i	−0.369088	−	0.929394i	$-0.620330\pi$
$587$	299.988	−	824.210i	0.511053	−	1.40411i	0.880141	−	0.474712i	$-0.157448\pi$
$588$		0			0
$589$	−67.7464	−	56.8459i	−0.115019	−	0.0965126i
$590$	251.377	+	690.653i	0.426063	+	1.17060i
$591$		0			0
$592$	16.1041	+	91.3307i	0.0272028	+	0.154275i
$593$			284.591i			0.479917i	0.970783	+	0.239958i	$0.0771338\pi$
$593$			284.591i			0.479917i	−0.970783	+	0.239958i	$0.922866\pi$
$594$		0			0
$595$	700.817			1.17784
$596$	−283.772	+	50.0367i	−0.476127	+	0.0839541i
$597$		0			0
$598$	−119.149	+	43.3667i	−0.199246	+	0.0725195i
$599$	211.516	−	252.075i	0.353115	−	0.420827i	−0.560022	−	0.828477i	$-0.689207\pi$
$599$	211.516	−	252.075i	0.353115	−	0.420827i	0.913138	+	0.407651i	$0.133652\pi$
$600$		0			0
$601$	−6.64685	−	2.41926i	−0.0110597	−	0.00402538i	0.336484	−	0.941689i	$-0.390762\pi$
$601$	−6.64685	−	2.41926i	−0.0110597	−	0.00402538i	−0.347544	+	0.937664i	$0.612984\pi$
$602$	241.010	−	139.147i	0.400348	−	0.231141i
$603$		0			0
$604$	−101.609	+	175.992i	−0.168226	+	0.291377i
$605$	−900.604	−	1073.30i	−1.48860	−	1.77405i
$606$		0			0
$607$	83.8924	−	475.778i	0.138208	−	0.783818i	−0.834363	−	0.551215i	$-0.814165\pi$
$607$	83.8924	−	475.778i	0.138208	−	0.783818i	0.972572	−	0.232603i	$-0.0747244\pi$
$608$	42.8601	+	7.55739i	0.0704936	+	0.0124299i
$609$		0			0
$610$	−319.500	+	268.092i	−0.523771	+	0.439496i
$611$	−43.4718	−	25.0984i	−0.0711485	−	0.0410776i
$612$		0			0
$613$	−287.932	−	498.713i	−0.469710	−	0.813562i	0.529690	−	0.848191i	$-0.322308\pi$
$613$	−287.932	−	498.713i	−0.469710	−	0.813562i	−0.999400	+	0.0346296i	$0.988975\pi$
$614$	−238.387	+	654.963i	−0.388253	+	1.06672i
$615$		0			0
$616$	303.927	+	255.025i	0.493389	+	0.414002i
$617$	239.991	+	659.369i	0.388964	+	1.06867i	0.967469	+	0.252991i	$0.0814143\pi$
$617$	239.991	+	659.369i	0.388964	+	1.06867i	−0.578505	+	0.815679i	$0.696364\pi$
$618$		0			0
$619$	78.3389	+	444.282i	0.126557	+	0.717741i	0.980371	+	0.197162i	$0.0631726\pi$
$619$	78.3389	+	444.282i	0.126557	+	0.717741i	−0.853814	+	0.520579i	$0.825716\pi$
$620$		−	198.467i		−	0.320107i
$621$		0			0
$622$	23.9079			0.0384371
$623$	−132.830	+	23.4216i	−0.213211	+	0.0375949i
$624$		0			0
$625$	−554.064	+	201.663i	−0.886502	+	0.322660i
$626$	379.169	−	451.876i	0.605701	−	0.721847i
$627$		0			0
$628$	−581.736	−	211.735i	−0.926331	−	0.337157i
$629$	195.587	−	112.922i	0.310949	−	0.179527i
$630$		0			0
$631$	283.716	−	491.411i	0.449630	−	0.778782i	−0.548732	−	0.835998i	$-0.684889\pi$
$631$	283.716	−	491.411i	0.449630	−	0.778782i	0.998362	+	0.0572166i	$0.0182226\pi$
$632$	−147.535	−	175.825i	−0.233441	−	0.278204i
$633$		0			0
$634$	−111.431	+	631.954i	−0.175758	+	0.996773i
$635$	325.353	+	57.3685i	0.512367	+	0.0903441i
$636$		0			0
$637$	47.3684	−	39.7468i	0.0743616	−	0.0623968i
$638$	221.482	+	127.872i	0.347150	+	0.200427i
$639$		0			0
$640$	48.8345	+	84.5839i	0.0763039	+	0.132162i
$641$	−50.9735	+	140.049i	−0.0795219	+	0.218485i	−0.973082	−	0.230459i	$-0.925977\pi$
$641$	−50.9735	+	140.049i	−0.0795219	+	0.218485i	0.893560	+	0.448943i	$0.148200\pi$
$642$		0			0
$643$	−20.8996	−	17.5368i	−0.0325032	−	0.0272734i	0.626391	−	0.779509i	$-0.284531\pi$
$643$	−20.8996	−	17.5368i	−0.0325032	−	0.0272734i	−0.658895	+	0.752235i	$0.728976\pi$
$644$	−169.069	−	464.513i	−0.262529	−	0.721294i
$645$		0			0
$646$	−18.4042	−	104.375i	−0.0284894	−	0.161571i
$647$		−	263.970i		−	0.407991i	−0.978972	−	0.203996i	$-0.934607\pi$
$647$		−	263.970i		−	0.407991i	0.978972	−	0.203996i	$-0.0653929\pi$
$648$		0			0
$649$	1013.28			1.56129
$650$	−208.521	+	36.7679i	−0.320801	+	0.0565659i
$651$		0			0
$652$	300.806	−	109.485i	0.461360	−	0.167921i
$653$	538.345	−	641.575i	0.824418	−	0.982503i	−0.175580	−	0.984465i	$-0.556180\pi$
$653$	538.345	−	641.575i	0.824418	−	0.982503i	0.999998	+	0.00196193i	$0.000624502\pi$
$654$		0			0
$655$	−1767.87	−	643.450i	−2.69903	−	0.982367i
$656$	58.8357	−	33.9688i	0.0896885	−	0.0517817i
$657$		0			0
$658$	97.8485	−	169.479i	0.148706	−	0.257566i
$659$	477.726	+	569.332i	0.724926	+	0.863933i	0.995100	−	0.0988784i	$-0.0315255\pi$
$659$	477.726	+	569.332i	0.724926	+	0.863933i	−0.270173	+	0.962812i	$0.587081\pi$
$660$		0			0
$661$	46.6386	−	264.501i	0.0705577	−	0.400152i	−0.928991	−	0.370103i	$-0.879322\pi$
$661$	46.6386	−	264.501i	0.0705577	−	0.400152i	0.999548	−	0.0300495i	$-0.00956649\pi$
$662$	326.978	+	57.6550i	0.493924	+	0.0870922i
$663$		0			0
$664$	34.9530	−	29.3290i	0.0526400	−	0.0441702i
$665$	−479.355	−	276.756i	−0.720835	−	0.416174i
$666$		0			0
$667$	−159.321	−	275.952i	−0.238862	−	0.413722i
$668$	−170.289	+	467.864i	−0.254923	+	0.700395i
$669$		0			0
$670$	351.953	+	295.324i	0.525303	+	0.440782i
$671$	196.664	+	540.329i	0.293090	+	0.805259i
$672$		0			0
$673$	114.573	+	649.776i	0.170242	+	0.965492i	0.943493	+	0.331392i	$0.107518\pi$
$673$	114.573	+	649.776i	0.170242	+	0.965492i	−0.773251	+	0.634100i	$0.781371\pi$
$674$			448.656i			0.665661i
$675$		0			0
$676$	319.721			0.472961
$677$	−251.116	+	44.2786i	−0.370925	+	0.0654041i	−0.356004	−	0.934485i	$-0.615861\pi$
$677$	−251.116	+	44.2786i	−0.370925	+	0.0654041i	−0.0149216	+	0.999889i	$0.504750\pi$
$678$		0			0
$679$	−1039.15	+	378.221i	−1.53042	+	0.557026i
$680$	152.886	−	182.203i	0.224833	−	0.267945i
$681$		0			0
$682$	−257.116	−	93.5824i	−0.377002	−	0.137218i
$683$	376.413	−	217.322i	0.551117	−	0.318187i	−0.198456	−	0.980110i	$-0.563593\pi$
$683$	376.413	−	217.322i	0.551117	−	0.318187i	0.749572	+	0.661923i	$0.230259\pi$
$684$		0			0
$685$	−794.615	+	1376.31i	−1.16002	+	2.00922i
$686$	−216.260	−	257.729i	−0.315248	−	0.375698i
$687$		0			0
$688$	16.4010	−	93.0147i	0.0238387	−	0.135196i
$689$	−224.297	−	39.5496i	−0.325540	−	0.0574015i
$690$		0			0
$691$	−1022.63	+	858.086i	−1.47992	+	1.24180i	−0.573657	+	0.819096i	$0.694476\pi$
$691$	−1022.63	+	858.086i	−1.47992	+	1.24180i	−0.906266	+	0.422707i	$0.861080\pi$
$692$	−117.049	−	67.5780i	−0.169145	−	0.0976561i
$693$		0			0
$694$	31.2112	+	54.0594i	0.0449729	+	0.0778954i
$695$	717.924	−	1972.48i	1.03298	−	2.83810i
$696$		0			0
$697$	−126.738	−	106.346i	−0.181834	−	0.152577i
$698$	159.881	+	439.270i	0.229056	+	0.629327i
$699$		0			0
$700$	−143.343	−	812.938i	−0.204775	−	1.16134i
$701$			1001.61i			1.42883i	0.699722	+	0.714415i	$0.253307\pi$
$701$			1001.61i			1.42883i	−0.699722	+	0.714415i	$0.746693\pi$
$702$		0			0
$703$	−178.374			−0.253733
$704$	132.606	−	23.3820i	0.188361	−	0.0332131i
$705$		0			0
$706$	629.235	−	229.023i	0.891267	−	0.324395i
$707$	81.5437	−	97.1800i	0.115338	−	0.137454i
$708$		0			0
$709$	720.055	+	262.078i	1.01559	+	0.369645i	0.795578	−	0.605852i	$-0.207167\pi$
$709$	720.055	+	262.078i	1.01559	+	0.369645i	0.220014	+	0.975497i	$0.429390\pi$
$710$	537.576	−	310.370i	0.757149	−	0.437140i
$711$		0			0
$712$	−22.8883	+	39.6436i	−0.0321464	+	0.0556792i
$713$	219.132	+	261.152i	0.307339	+	0.366272i
$714$		0			0
$715$	−76.2782	+	432.595i	−0.106683	+	0.605028i
$716$	−463.317	−	81.6953i	−0.647090	−	0.114100i
$717$		0			0
$718$	−472.926	+	396.832i	−0.658671	+	0.552691i
$719$	−544.595	−	314.422i	−0.757434	−	0.437305i	0.0709399	−	0.997481i	$-0.477400\pi$
$719$	−544.595	−	314.422i	−0.757434	−	0.437305i	−0.828374	+	0.560176i	$0.810733\pi$
$720$		0			0
$721$	−157.730	−	273.196i	−0.218765	−	0.378913i
$722$	145.982	−	401.082i	0.202191	−	0.555516i
$723$		0			0
$724$	−333.737	−	280.038i	−0.460962	−	0.386793i
$725$	−181.990	−	500.015i	−0.251021	−	0.689675i
$726$		0			0
$727$	−116.145	−	658.690i	−0.159759	−	0.906039i	−0.954305	−	0.298835i	$-0.903402\pi$
$727$	−116.145	−	658.690i	−0.159759	−	0.906039i	0.794546	−	0.607204i	$-0.207709\pi$
$728$		−	71.2606i		−	0.0978855i
$729$		0			0
$730$	−1202.44			−1.64717
$731$	−226.514	+	39.9406i	−0.309869	+	0.0546383i
$732$		0			0
$733$	−104.288	+	37.9578i	−0.142276	+	0.0517842i	−0.412177	−	0.911104i	$-0.635231\pi$
$733$	−104.288	+	37.9578i	−0.142276	+	0.0517842i	0.269901	+	0.962888i	$0.413009\pi$
$734$	433.316	−	516.406i	0.590349	−	0.703550i
$735$		0			0
$736$	−157.650	−	57.3800i	−0.214199	−	0.0779619i
$737$	548.551	−	316.706i	0.744302	−	0.429723i
$738$		0			0
$739$	−231.298	+	400.619i	−0.312987	+	0.542110i	−0.979008	−	0.203824i	$-0.934663\pi$
$739$	−231.298	+	400.619i	−0.312987	+	0.542110i	0.666020	+	0.745934i	$0.267996\pi$
$740$	−257.309	−	306.649i	−0.347715	−	0.414390i
$741$		0			0
$742$	154.188	−	874.442i	0.207800	−	1.17849i
$743$	−952.218	−	167.902i	−1.28159	−	0.225978i	−0.508932	−	0.860807i	$-0.669960\pi$
$743$	−952.218	−	167.902i	−1.28159	−	0.225978i	−0.772653	+	0.634829i	$0.781071\pi$
$744$		0			0
$745$	952.783	−	799.480i	1.27890	−	1.07313i
$746$	−452.078	−	261.007i	−0.606003	−	0.349876i
$747$		0			0
$748$	−163.956	−	283.979i	−0.219192	−	0.379652i
$749$	−338.223	+	929.259i	−0.451566	+	1.24067i
$750$		0			0
$751$	−805.112	−	675.569i	−1.07205	−	0.899560i	−0.0768166	−	0.997045i	$-0.524476\pi$
$751$	−805.112	−	675.569i	−1.07205	−	0.899560i	−0.995237	+	0.0974855i	$0.968920\pi$
$752$	−22.7160	−	62.4118i	−0.0302075	−	0.0829944i
$753$		0			0
$754$	−7.97648	−	45.2368i	−0.0105789	−	0.0599958i
$755$		−	877.168i		−	1.16181i
$756$		0			0
$757$	−266.724			−0.352343			−0.176172	−	0.984359i	$-0.556371\pi$
$757$	−266.724			−0.352343			−0.176172	+	0.984359i	$0.556371\pi$
$758$	−302.087	+	53.2662i	−0.398532	+	0.0702720i
$759$		0			0
$760$	−176.526	+	64.2503i	−0.232271	+	0.0845399i
$761$	0.229396	−	0.273383i	0.000301440	−	0.000359242i	−0.765894	−	0.642967i	$-0.777703\pi$
$761$	0.229396	−	0.273383i	0.000301440	−	0.000359242i	0.766195	+	0.642608i	$0.222148\pi$
$762$		0			0
$763$	1613.68	+	587.333i	2.11492	+	0.769768i
$764$	−445.704	+	257.327i	−0.583382	+	0.336816i
$765$		0			0
$766$	381.376	−	660.563i	0.497880	−	0.862353i
$767$	−116.985	−	139.418i	−0.152523	−	0.181770i
$768$		0			0
$769$	77.8630	−	441.583i	0.101252	−	0.574230i	−0.891399	−	0.453220i	$-0.850275\pi$
$769$	77.8630	−	441.583i	0.101252	−	0.574230i	0.992651	−	0.121011i	$-0.0386136\pi$
$770$	−1686.51	−	297.377i	−2.19027	−	0.386204i
$771$		0			0
$772$	117.467	−	98.5664i	0.152159	−	0.127677i
$773$	−580.814	−	335.333i	−0.751376	−	0.433807i	0.0748149	−	0.997197i	$-0.476163\pi$
$773$	−580.814	−	335.333i	−0.751376	−	0.433807i	−0.826191	+	0.563390i	$0.809497\pi$
$774$		0			0
$775$	284.644	+	493.018i	0.367283	+	0.636153i
$776$	−128.364	+	352.676i	−0.165417	+	0.454479i
$777$		0			0
$778$	−159.971	−	134.232i	−0.205618	−	0.172534i
$779$	44.6918	+	122.790i	0.0573708	+	0.157625i
$780$		0			0
$781$	−148.605	−	842.783i	−0.190276	−	1.07911i
$782$			408.557i			0.522451i
$783$		0			0
$784$	81.8160			0.104357
$785$	2631.56	−	464.015i	3.35231	−	0.591102i
$786$		0			0
$787$	1152.23	−	419.377i	1.46408	−	0.532881i	0.517592	−	0.855627i	$-0.326828\pi$
$787$	1152.23	−	419.377i	1.46408	−	0.532881i	0.946485	+	0.322747i	$0.104606\pi$
$788$	313.665	−	373.812i	0.398053	−	0.474381i
$789$		0			0
$790$	930.967	+	338.844i	1.17844	+	0.428917i
$791$	512.645	−	295.976i	0.648097	−	0.374179i
$792$		0			0
$793$	51.6388	−	89.4411i	0.0651183	−	0.112788i
$794$	456.897	+	544.508i	0.575437	+	0.685779i
$795$		0			0
$796$	−28.5158	+	161.721i	−0.0358238	+	0.203167i
$797$	391.758	+	69.0776i	0.491541	+	0.0866720i	0.413924	−	0.910311i	$-0.364158\pi$
$797$	391.758	+	69.0776i	0.491541	+	0.0866720i	0.0776168	+	0.996983i	$0.475269\pi$
$798$		0			0
$799$	−123.902	+	103.966i	−0.155071	+	0.130120i
$800$	−242.623	−	140.079i	−0.303279	−	0.175098i
$801$		0			0
$802$	−163.656	−	283.461i	−0.204060	−	0.353443i
$803$	−566.981	+	1557.77i	−0.706079	+	1.93994i
$804$		0			0
$805$	1634.51	+	1371.52i	2.03045	+	1.70375i
$806$	16.8085	+	46.1809i	0.0208542	+	0.0572964i
$807$		0			0
$808$	−7.47635	−	42.4005i	−0.00925290	−	0.0524758i
$809$		−	438.654i		−	0.542218i	−0.962549	−	0.271109i	$-0.912610\pi$
$809$		−	438.654i		−	0.542218i	0.962549	−	0.271109i	$-0.0873903\pi$
$810$		0			0
$811$	−1037.62			−1.27943			−0.639716	−	0.768611i	$-0.720948\pi$
$811$	−1037.62			−1.27943			−0.639716	+	0.768611i	$0.720948\pi$
$812$	176.360	−	31.0970i	0.217192	−	0.0382968i
$813$		0			0
$814$	−518.595	+	188.753i	−0.637094	+	0.231883i
$815$	−888.159	+	1058.47i	−1.08977	+	1.29873i
$816$		0			0
$817$	170.707	+	62.1324i	0.208944	+	0.0760495i
$818$	−551.679	+	318.512i	−0.674424	+	0.389379i
$819$		0			0
$820$	−146.623	+	253.958i	−0.178808	+	0.309705i
$821$	919.156	+	1095.41i	1.11956	+	1.33424i	0.936312	+	0.351168i	$0.114216\pi$
$821$	919.156	+	1095.41i	1.11956	+	1.33424i	0.183245	+	0.983067i	$0.441340\pi$
$822$		0			0
$823$	−245.722	+	1393.56i	−0.298568	+	1.69327i	0.353765	+	0.935334i	$0.384901\pi$
$823$	−245.722	+	1393.56i	−0.298568	+	1.69327i	−0.652334	+	0.757932i	$0.726210\pi$
$824$	−105.437	−	18.5913i	−0.127957	−	0.0225623i
$825$		0			0
$826$	543.532	−	456.078i	0.658029	−	0.552152i
$827$	−609.863	−	352.105i	−0.737440	−	0.425761i	0.0836977	−	0.996491i	$-0.473327\pi$
$827$	−609.863	−	352.105i	−0.737440	−	0.425761i	−0.821138	+	0.570730i	$0.806660\pi$
$828$		0			0
$829$	−145.579	−	252.151i	−0.175608	−	0.304162i	0.764763	−	0.644311i	$-0.222856\pi$
$829$	−145.579	−	252.151i	−0.175608	−	0.304162i	−0.940372	+	0.340149i	$0.889523\pi$
$830$	−67.3602	+	185.071i	−0.0811569	+	0.222977i
$831$		0			0
$832$	−18.5268	−	15.5458i	−0.0222678	−	0.0186849i
$833$	−68.1450	−	187.227i	−0.0818067	−	0.224762i
$834$		0			0
$835$	−373.186	−	2116.44i	−0.446930	−	2.53466i
$836$			258.987i			0.309794i
$837$		0			0
$838$	465.477			0.555462
$839$	−852.208	+	150.267i	−1.01574	+	0.179103i	−0.656647	−	0.754198i	$-0.728026\pi$
$839$	−852.208	+	150.267i	−1.01574	+	0.179103i	−0.359096	+	0.933301i	$0.616915\pi$
$840$		0			0
$841$	−681.808	+	248.158i	−0.810710	+	0.295074i
$842$	−185.997	+	221.663i	−0.220900	+	0.263258i
$843$		0			0
$844$	108.053	+	39.3280i	0.128025	+	0.0465971i
$845$	−1195.16	+	690.023i	−1.41438	+	0.816595i
$846$		0			0
$847$	−676.290	+	1171.37i	−0.798454	+	1.38296i
$848$	−193.706	−	230.850i	−0.228427	−	0.272229i
$849$		0			0
$850$	−118.472	+	671.889i	−0.139379	+	0.790458i
$851$	677.158	+	119.401i	0.795721	+	0.140307i
$852$		0			0
$853$	−83.2215	+	69.8311i	−0.0975633	+	0.0818653i	−0.690265	−	0.723557i	$-0.742506\pi$
$853$	−83.2215	+	69.8311i	−0.0975633	+	0.0818653i	0.592701	+	0.805422i	$0.298061\pi$
$854$	348.694	+	201.319i	0.408307	+	0.235736i
$855$		0			0
$856$	167.810	+	290.655i	0.196039	+	0.339550i
$857$	364.690	−	1001.98i	0.425543	−	1.16917i	−0.522948	−	0.852364i	$-0.675168\pi$
$857$	364.690	−	1001.98i	0.425543	−	1.16917i	0.948491	−	0.316804i	$-0.102610\pi$
$858$		0			0
$859$	−42.4891	−	35.6526i	−0.0494635	−	0.0415048i	0.617721	−	0.786398i	$-0.288056\pi$
$859$	−42.4891	−	35.6526i	−0.0494635	−	0.0415048i	−0.667184	+	0.744893i	$0.732501\pi$
$860$	139.436	+	383.096i	0.162134	+	0.445461i
$861$		0			0
$862$	−1.43760	−	8.15306i	−0.00166775	−	0.00945830i
$863$			75.8244i			0.0878614i	0.999035	+	0.0439307i	$0.0139881\pi$
$863$			75.8244i			0.0878614i	−0.999035	+	0.0439307i	$0.986012\pi$
$864$		0			0
$865$	583.388			0.674437
$866$	324.937	−	57.2952i	0.375216	−	0.0661607i
$867$		0			0
$868$	−180.040	+	65.5293i	−0.207420	+	0.0754946i
$869$	877.953	−	1046.30i	1.01030	−	1.20403i
$870$		0			0
$871$	−106.907	−	38.9109i	−0.122740	−	0.0446739i
$872$	504.731	−	291.406i	0.578820	−	0.334182i
$873$		0			0
$874$	161.341	−	279.451i	0.184601	−	0.319738i
$875$	1134.18	+	1351.66i	1.29621	+	1.54476i
$876$		0			0
$877$	100.329	−	568.994i	0.114400	−	0.648796i	−0.872645	−	0.488355i	$-0.837597\pi$
$877$	100.329	−	568.994i	0.114400	−	0.648796i	0.987045	−	0.160441i	$-0.0512918\pi$
$878$	187.727	+	33.1013i	0.213812	+	0.0377008i
$879$		0			0
$880$	−445.234	+	373.595i	−0.505947	+	0.424540i
$881$	−118.578	−	68.4609i	−0.134594	−	0.0777082i	0.431191	−	0.902261i	$-0.358094\pi$
$881$	−118.578	−	68.4609i	−0.134594	−	0.0777082i	−0.565785	+	0.824553i	$0.691427\pi$
$882$		0			0
$883$	634.745	+	1099.41i	0.718851	+	1.24509i	0.961455	+	0.274961i	$0.0886648\pi$
$883$	634.745	+	1099.41i	0.718851	+	1.24509i	−0.242605	+	0.970125i	$0.578002\pi$
$884$	−20.1438	+	55.3447i	−0.0227871	+	0.0626071i
$885$		0			0
$886$	−31.0316	−	26.0386i	−0.0350244	−	0.0293889i
$887$	−220.369	−	605.458i	−0.248443	−	0.682591i	−0.999744	−	0.0226314i	$-0.992796\pi$
$887$	−220.369	−	605.458i	−0.248443	−	0.682591i	0.751301	−	0.659960i	$-0.229427\pi$
$888$		0			0
$889$	−55.3822	−	314.088i	−0.0622972	−	0.353305i
$890$		−	197.590i		−	0.222011i
$891$		0			0
$892$	−463.975			−0.520152
$893$	125.805	−	22.1829i	0.140879	−	0.0248408i
$894$		0			0
$895$	1908.25	−	694.545i	2.13212	−	0.776027i
$896$	60.6068	−	72.2283i	0.0676415	−	0.0806120i
$897$		0			0
$898$	−660.187	−	240.288i	−0.735175	−	0.267582i
$899$	−106.956	+	61.7512i	−0.118972	+	0.0686888i
$900$		0			0
$901$	−366.936	+	635.551i	−0.407254	+	0.705384i
$902$	259.869	+	309.700i	0.288103	+	0.343348i
$903$		0			0
$904$	34.8861	−	197.849i	0.0385908	−	0.218860i
$905$	1851.93	+	326.544i	2.04633	+	0.360823i
$906$		0			0
$907$	−468.430	+	393.059i	−0.516461	+	0.433362i	−0.863396	−	0.504527i	$-0.831667\pi$
$907$	−468.430	+	393.059i	−0.516461	+	0.433362i	0.346935	+	0.937889i	$0.387222\pi$
$908$	−371.582	−	214.533i	−0.409231	−	0.236270i
$909$		0			0
$910$	153.795	+	266.380i	0.169005	+	0.292726i
$911$	−359.212	+	986.926i	−0.394305	+	1.08334i	0.570711	+	0.821151i	$0.306668\pi$
$911$	−359.212	+	986.926i	−0.394305	+	1.08334i	−0.965016	+	0.262193i	$0.915554\pi$
$912$		0			0
$913$	207.999	+	174.532i	0.227819	+	0.191163i
$914$	−224.337	−	616.361i	−0.245445	−	0.674356i
$915$		0			0
$916$	137.325	+	778.806i	0.149918	+	0.850225i
$917$			1816.19i			1.98057i
$918$		0			0
$919$	133.483			0.145248			0.0726238	−	0.997359i	$-0.476863\pi$
$919$	133.483			0.145248			0.0726238	+	0.997359i	$0.476863\pi$
$920$	713.152	−	125.748i	0.775165	−	0.136682i
$921$		0			0
$922$	354.002	−	128.846i	0.383950	−	0.139747i
$923$	−98.8020	+	117.748i	−0.107044	+	0.127571i
$924$		0			0
$925$	1078.99	+	392.721i	1.16648	+	0.424563i
$926$	−293.168	+	169.261i	−0.316597	+	0.182787i
$927$		0			0
$928$	30.3889	−	52.6351i	0.0327467	−	0.0567189i
$929$	−714.192	−	851.141i	−0.768775	−	0.916190i	0.229594	−	0.973287i	$-0.426260\pi$
$929$	−714.192	−	851.141i	−0.768775	−	0.916190i	−0.998369	+	0.0570965i	$0.981816\pi$
$930$		0			0
$931$	−27.3259	+	154.973i	−0.0293512	+	0.166459i
$932$	−188.609	−	33.2568i	−0.202370	−	0.0356833i
$933$		0			0
$934$	230.881	−	193.732i	0.247196	−	0.207422i
$935$	1225.77	+	707.698i	1.31098	+	0.756896i
$936$		0			0
$937$	862.772	+	1494.36i	0.920781	+	1.59484i	0.798209	+	0.602380i	$0.205781\pi$
$937$	862.772	+	1494.36i	0.920781	+	1.59484i	0.122572	+	0.992460i	$0.460886\pi$
$938$	151.698	−	416.786i	0.161725	−	0.444335i
$939$		0			0
$940$	219.612	+	184.277i	0.233630	+	0.196039i
$941$	−465.200	−	1278.13i	−0.494368	−	1.35827i	−0.896646	−	0.442748i	$-0.854004\pi$
$941$	−465.200	−	1278.13i	−0.494368	−	1.35827i	0.402278	−	0.915517i	$-0.368218\pi$
$942$		0			0
$943$	−87.4689	−	496.061i	−0.0927560	−	0.526046i
$944$		−	240.806i		−	0.255091i
$945$		0			0
$946$	562.053			0.594136
$947$	−1590.14	+	280.385i	−1.67914	+	0.296077i	−0.930334	−	0.366714i	$-0.880483\pi$
$947$	−1590.14	+	280.385i	−1.67914	+	0.296077i	−0.748804	+	0.662792i	$0.769372\pi$
$948$		0			0
$949$	279.793	−	101.836i	0.294829	−	0.107309i
$950$	346.367	−	412.784i	0.364597	−	0.434509i
$951$		0			0
$952$	−215.766	−	78.5325i	−0.226645	−	0.0824921i
$953$	181.146	−	104.585i	0.190080	−	0.109743i	−0.401940	−	0.915666i	$-0.631664\pi$
$953$	181.146	−	104.585i	0.190080	−	0.109743i	0.592020	+	0.805923i	$0.298331\pi$
$954$		0			0
$955$	1110.73	−	1923.84i	1.16307	−	2.01449i
$956$	113.371	+	135.110i	0.118589	+	0.141329i
$957$		0			0
$958$	−98.2830	+	557.391i	−0.102592	+	0.581827i
$959$	1510.90	+	266.412i	1.57549	+	0.277802i
$960$		0			0
$961$	−634.949	+	532.786i	−0.660717	+	0.554407i
$962$	85.8434	+	49.5617i	0.0892343	+	0.0515194i
$963$		0			0
$964$	−385.135	−	667.073i	−0.399518	−	0.691985i
$965$	−226.378	+	621.969i	−0.234589	+	0.644528i
$966$		0			0
$967$	672.104	+	563.962i	0.695041	+	0.583208i	0.920358	−	0.391077i	$-0.127897\pi$
$967$	672.104	+	563.962i	0.695041	+	0.583208i	−0.225317	+	0.974285i	$0.572342\pi$
$968$	157.004	+	431.365i	0.162194	+	0.445625i
$969$		0			0
$970$	−281.308	−	1595.38i	−0.290008	−	1.64472i
$971$			686.372i			0.706871i	0.935459	+	0.353435i	$0.114987\pi$
$971$			686.372i			0.706871i	−0.935459	+	0.353435i	$0.885013\pi$
$972$		0			0
$973$	−2026.39			−2.08262
$974$	−450.793	+	79.4869i	−0.462826	+	0.0816087i
$975$		0			0
$976$	128.409	−	46.7371i	0.131567	−	0.0478864i
$977$	−905.640	+	1079.30i	−0.926960	+	1.10471i	0.0673015	+	0.997733i	$0.478561\pi$
$977$	−905.640	+	1079.30i	−0.926960	+	1.10471i	−0.994262	+	0.106975i	$0.965883\pi$
$978$		0			0
$979$	−255.980	−	93.1690i	−0.261471	−	0.0951675i
$980$	−305.838	+	176.575i	−0.312079	+	0.180179i
$981$		0			0
$982$	−648.885	+	1123.90i	−0.660779	+	1.14450i
$983$	−606.673	−	723.005i	−0.617165	−	0.735508i	0.363415	−	0.931627i	$-0.381611\pi$
$983$	−606.673	−	723.005i	−0.617165	−	0.735508i	−0.980580	+	0.196119i	$0.937166\pi$
$984$		0			0
$985$	−365.756	+	2074.30i	−0.371326	+	2.10589i
$986$	−145.761	−	25.7015i	−0.147830	−	0.0260665i
$987$		0			0
$988$	35.6342	−	29.9006i	0.0360670	−	0.0302638i
$989$	−606.463	−	350.142i	−0.613208	−	0.354036i
$990$		0			0
$991$	−424.153	−	734.654i	−0.428005	−	0.741326i	0.568691	−	0.822551i	$-0.307450\pi$
$991$	−424.153	−	734.654i	−0.428005	−	0.741326i	−0.996696	+	0.0812254i	$0.974117\pi$
$992$	−22.2399	+	61.1035i	−0.0224192	+	0.0615963i
$993$		0			0
$994$	−459.050	−	385.189i	−0.461821	−	0.387514i
$995$	−242.431	−	666.074i	−0.243649	−	0.669421i
$996$		0			0
$997$	−29.2963	−	166.148i	−0.0293845	−	0.166648i	0.966584	−	0.256349i	$-0.0825198\pi$
$997$	−29.2963	−	166.148i	−0.0293845	−	0.166648i	−0.995969	+	0.0897017i	$0.971409\pi$
$998$			305.569i			0.306181i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.3.f.a.71.4		36
3.2	odd	2		54.3.f.a.41.1	yes	36
12.11	even	2		432.3.bc.c.257.6		36
27.2	odd	18	inner	162.3.f.a.89.4		36
27.5	odd	18		1458.3.b.c.1457.19		36
27.22	even	9		1458.3.b.c.1457.18		36
27.25	even	9		54.3.f.a.29.1	✓	36
108.79	odd	18		432.3.bc.c.353.6		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.3.f.a.29.1	✓	36	27.25	even	9
54.3.f.a.41.1	yes	36	3.2	odd	2
162.3.f.a.71.4		36	1.1	even	1	trivial
162.3.f.a.89.4		36	27.2	odd	18	inner
432.3.bc.c.257.6		36	12.11	even	2
432.3.bc.c.353.6		36	108.79	odd	18
1458.3.b.c.1457.18		36	27.22	even	9
1458.3.b.c.1457.19		36	27.5	odd	18

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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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	162.f (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.39273 - 0.245576i) q^{2} +(1.87939 - 0.684040i) q^{4} +(-5.54906 + 6.61311i) q^{5} +(7.83131 + 2.85036i) q^{7} +(2.44949 - 1.41421i) q^{8} +O(q^{10})\)	\(q+(1.39273 - 0.245576i) q^{2} +(1.87939 - 0.684040i) q^{4} +(-5.54906 + 6.61311i) q^{5} +(7.83131 + 2.85036i) q^{7} +(2.44949 - 1.41421i) q^{8} +(-6.10431 + 10.5730i) q^{10} +(10.8191 + 12.8937i) q^{11} +(0.524960 - 2.97720i) q^{13} +(11.6069 + 2.04660i) q^{14} +(3.06418 - 2.57115i) q^{16} +(-8.43596 - 4.87051i) q^{17} +(3.84677 + 6.66281i) q^{19} +(-5.90519 + 16.2244i) q^{20} +(18.2344 + 15.3005i) q^{22} +(-10.1434 - 27.8689i) q^{23} +(-8.59998 - 48.7729i) q^{25} -4.27534i q^{26} +16.6678 q^{28} +(10.5809 - 1.86569i) q^{29} +(-10.8017 + 3.93149i) q^{31} +(3.63616 - 4.33340i) q^{32} +(-12.9451 - 4.71163i) q^{34} +(-62.3062 + 35.9725i) q^{35} +(-11.5925 + 20.0787i) q^{37} +(6.99373 + 8.33481i) q^{38} +(-4.24001 + 24.0463i) q^{40} +(16.7264 + 2.94931i) q^{41} +(18.0881 - 15.1778i) q^{43} +(29.1530 + 16.8315i) q^{44} +(-20.9710 - 36.3228i) q^{46} +(5.67901 - 15.6029i) q^{47} +(15.6687 + 13.1476i) q^{49} +(-23.9549 - 65.8155i) q^{50} +(-1.04992 - 5.95439i) q^{52} -75.3383i q^{53} -145.303 q^{55} +(23.2137 - 4.09321i) q^{56} +(14.2781 - 5.19681i) q^{58} +(38.6968 - 46.1170i) q^{59} +(32.1023 + 11.6843i) q^{61} +(-14.0783 + 8.12813i) q^{62} +(4.00000 - 6.92820i) q^{64} +(16.7755 + 19.9923i) q^{65} +(6.53483 - 37.0609i) q^{67} +(-19.1860 - 3.38302i) q^{68} +(-77.9416 + 65.4008i) q^{70} +(-44.0325 - 25.4222i) q^{71} +(49.2453 + 85.2954i) q^{73} +(-11.2143 + 30.8110i) q^{74} +(11.7872 + 9.89063i) q^{76} +(47.9758 + 131.813i) q^{77} +(-14.0913 - 79.9158i) q^{79} +34.5312i q^{80} +24.0196 q^{82} +(15.8868 - 2.80127i) q^{83} +(79.0209 - 28.7612i) q^{85} +(21.4646 - 25.5805i) q^{86} +(44.7356 + 16.2824i) q^{88} +(-14.0161 + 8.09222i) q^{89} +(12.5972 - 21.8190i) q^{91} +(-38.1269 - 45.4378i) q^{92} +(4.07761 - 23.1253i) q^{94} +(-65.4078 - 11.5332i) q^{95} +(-101.648 + 85.2929i) q^{97} +(25.0509 + 14.4632i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 18 q^{5}+O(q^{10}) \) 36 * q - 18 * q^5	\( 36 q - 18 q^{5} + 18 q^{11} + 36 q^{14} + 72 q^{20} + 36 q^{22} + 180 q^{23} + 18 q^{25} - 144 q^{29} - 90 q^{31} - 72 q^{34} - 486 q^{35} - 180 q^{38} + 90 q^{41} + 90 q^{43} + 378 q^{47} + 72 q^{49} + 72 q^{56} - 252 q^{59} - 144 q^{61} + 144 q^{64} - 18 q^{65} - 594 q^{67} + 180 q^{68} - 360 q^{70} + 648 q^{71} + 126 q^{73} + 504 q^{74} - 72 q^{76} + 342 q^{77} - 72 q^{79} - 594 q^{83} + 360 q^{85} - 540 q^{86} + 144 q^{88} - 648 q^{89} - 198 q^{91} - 396 q^{92} + 504 q^{94} - 252 q^{95} + 702 q^{97} - 648 q^{98}+O(q^{100}) \) 36 * q - 18 * q^5 + 18 * q^11 + 36 * q^14 + 72 * q^20 + 36 * q^22 + 180 * q^23 + 18 * q^25 - 144 * q^29 - 90 * q^31 - 72 * q^34 - 486 * q^35 - 180 * q^38 + 90 * q^41 + 90 * q^43 + 378 * q^47 + 72 * q^49 + 72 * q^56 - 252 * q^59 - 144 * q^61 + 144 * q^64 - 18 * q^65 - 594 * q^67 + 180 * q^68 - 360 * q^70 + 648 * q^71 + 126 * q^73 + 504 * q^74 - 72 * q^76 + 342 * q^77 - 72 * q^79 - 594 * q^83 + 360 * q^85 - 540 * q^86 + 144 * q^88 - 648 * q^89 - 198 * q^91 - 396 * q^92 + 504 * q^94 - 252 * q^95 + 702 * q^97 - 648 * q^98

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