LMFDB - Embedded newform 162.3.f.a.143.1

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			143.1
Character	$\chi$	$=$	162.143
Dual form			162.3.f.a.17.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.483690 - 1.32893i) q^{2} +(-1.53209 + 1.28558i) q^{4} +(-5.90332 + 1.04091i) q^{5} +(5.59840 + 4.69762i) q^{7} +(2.44949 + 1.41421i) q^{8} +O(q^{10})$	\(q+(-0.483690 - 1.32893i) q^{2} +(-1.53209 + 1.28558i) q^{4} +(-5.90332 + 1.04091i) q^{5} +(5.59840 + 4.69762i) q^{7} +(2.44949 + 1.41421i) q^{8} +(4.23867 + 7.34160i) q^{10} +(20.3832 + 3.59412i) q^{11} +(6.40830 + 2.33243i) q^{13} +(3.53490 - 9.71205i) q^{14} +(0.694593 - 3.93923i) q^{16} +(-1.96510 + 1.13455i) q^{17} +(-12.1634 + 21.0675i) q^{19} +(7.70624 - 9.18394i) q^{20} +(-5.08285 - 28.8263i) q^{22} +(15.5320 + 18.5103i) q^{23} +(10.2734 - 3.73921i) q^{25} -9.64433i q^{26} -14.6164 q^{28} +(-6.32777 - 17.3854i) q^{29} +(16.6469 - 13.9684i) q^{31} +(-5.57091 + 0.982302i) q^{32} +(2.45823 + 2.06270i) q^{34} +(-37.9390 - 21.9041i) q^{35} +(22.3832 + 38.7688i) q^{37} +(33.8805 + 5.97405i) q^{38} +(-15.9322 - 5.79885i) q^{40} +(-17.5398 + 48.1902i) q^{41} +(6.41470 - 36.3796i) q^{43} +(-35.8494 + 20.6977i) q^{44} +(17.0861 - 29.5941i) q^{46} +(-8.15595 + 9.71989i) q^{47} +(0.765740 + 4.34273i) q^{49} +(-9.93826 - 11.8440i) q^{50} +(-12.8166 + 4.66486i) q^{52} -17.7730i q^{53} -124.070 q^{55} +(7.06980 + 19.4241i) q^{56} +(-20.0432 + 16.8183i) q^{58} +(-64.9049 + 11.4445i) q^{59} +(32.3438 + 27.1396i) q^{61} +(-26.6150 - 15.3662i) q^{62} +(4.00000 + 6.92820i) q^{64} +(-40.2581 - 7.09859i) q^{65} +(-111.190 - 40.4700i) q^{67} +(1.55216 - 4.26451i) q^{68} +(-10.7582 + 61.0129i) q^{70} +(46.1702 - 26.6564i) q^{71} +(33.8569 - 58.6419i) q^{73} +(40.6944 - 48.4976i) q^{74} +(-8.44858 - 47.9143i) q^{76} +(97.2298 + 115.874i) q^{77} +(104.610 - 38.0750i) q^{79} +23.9776i q^{80} +72.5250 q^{82} +(-8.63542 - 23.7256i) q^{83} +(10.4196 - 8.74311i) q^{85} +(-51.4485 + 9.07175i) q^{86} +(44.8457 + 37.6300i) q^{88} +(35.4447 + 20.4640i) q^{89} +(24.9194 + 43.1616i) q^{91} +(-47.5927 - 8.39188i) q^{92} +(16.8620 + 6.13725i) q^{94} +(49.8747 - 137.030i) q^{95} +(7.02010 - 39.8130i) q^{97} +(5.40078 - 3.11814i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{7}{18}\right)$

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 $

$2$	−0.483690	−	1.32893i	−0.241845	−	0.664463i
$2$	−0.483690	−	1.32893i	−0.241845	−	0.664463i
$3$		0			0
$3$		0			0
$4$	−1.53209	+	1.28558i	−0.383022	+	0.321394i
$5$	−5.90332	+	1.04091i	−1.18066	+	0.208183i	−0.729324	−	0.684169i	$-0.760165\pi$
$5$	−5.90332	+	1.04091i	−1.18066	+	0.208183i	−0.451341	+	0.892352i	$0.649054\pi$
$6$		0			0
$7$	5.59840	+	4.69762i	0.799772	+	0.671088i	0.948143	−	0.317844i	$-0.102959\pi$
$7$	5.59840	+	4.69762i	0.799772	+	0.671088i	−0.148371	+	0.988932i	$0.547403\pi$
$8$	2.44949	+	1.41421i	0.306186	+	0.176777i
$9$		0			0
$10$	4.23867	+	7.34160i	0.423867	+	0.734160i
$11$	20.3832	+	3.59412i	1.85302	+	0.326738i	0.985369	−	0.170433i	$-0.0545165\pi$
$11$	20.3832	+	3.59412i	1.85302	+	0.326738i	0.867653	+	0.497170i	$0.165628\pi$
$12$		0			0
$13$	6.40830	+	2.33243i	0.492946	+	0.179418i	0.576519	−	0.817084i	$-0.304411\pi$
$13$	6.40830	+	2.33243i	0.492946	+	0.179418i	−0.0835725	+	0.996502i	$0.526633\pi$
$14$	3.53490	−	9.71205i	0.252493	−	0.693718i
$15$		0			0
$16$	0.694593	−	3.93923i	0.0434120	−	0.246202i
$17$	−1.96510	+	1.13455i	−0.115594	+	0.0667382i	−0.556682	−	0.830725i	$-0.687926\pi$
$17$	−1.96510	+	1.13455i	−0.115594	+	0.0667382i	0.441088	+	0.897464i	$0.354593\pi$
$18$		0			0
$19$	−12.1634	+	21.0675i	−0.640176	+	1.10882i	0.345217	+	0.938523i	$0.387805\pi$
$19$	−12.1634	+	21.0675i	−0.640176	+	1.10882i	−0.985393	+	0.170295i	$0.945528\pi$
$20$	7.70624	−	9.18394i	0.385312	−	0.459197i
$21$		0			0
$22$	−5.08285	−	28.8263i	−0.231039	−	1.31028i
$23$	15.5320	+	18.5103i	0.675303	+	0.804795i	0.989495	−	0.144564i	$-0.0461781\pi$
$23$	15.5320	+	18.5103i	0.675303	+	0.804795i	−0.314192	+	0.949359i	$0.601734\pi$
$24$		0			0
$25$	10.2734	−	3.73921i	0.410935	−	0.149568i
$26$		−	9.64433i		−	0.370936i
$27$		0			0
$28$	−14.6164			−0.522014
$29$	−6.32777	−	17.3854i	−0.218199	−	0.599497i	0.781503	−	0.623901i	$-0.214453\pi$
$29$	−6.32777	−	17.3854i	−0.218199	−	0.599497i	−0.999702	+	0.0244045i	$0.992231\pi$
$30$		0			0
$31$	16.6469	−	13.9684i	0.536998	−	0.450595i	−0.333512	−	0.942746i	$-0.608234\pi$
$31$	16.6469	−	13.9684i	0.536998	−	0.450595i	0.870510	+	0.492151i	$0.163789\pi$
$32$	−5.57091	+	0.982302i	−0.174091	+	0.0306970i
$33$		0			0
$34$	2.45823	+	2.06270i	0.0723009	+	0.0606677i
$35$	−37.9390	−	21.9041i	−1.08397	−	0.625831i
$36$		0			0
$37$	22.3832	+	38.7688i	0.604951	+	1.04781i	0.992059	+	0.125771i	$0.0401405\pi$
$37$	22.3832	+	38.7688i	0.604951	+	1.04781i	−0.387109	+	0.922034i	$0.626526\pi$
$38$	33.8805	+	5.97405i	0.891592	+	0.157212i
$39$		0			0
$40$	−15.9322	−	5.79885i	−0.398305	−	0.144971i
$41$	−17.5398	+	48.1902i	−0.427800	+	1.17537i	0.519345	+	0.854565i	$0.326176\pi$
$41$	−17.5398	+	48.1902i	−0.427800	+	1.17537i	−0.947145	+	0.320806i	$0.896046\pi$
$42$		0			0
$43$	6.41470	−	36.3796i	0.149179	−	0.846036i	−0.814737	−	0.579830i	$-0.803119\pi$
$43$	6.41470	−	36.3796i	0.149179	−	0.846036i	0.963916	−	0.266206i	$-0.0857701\pi$
$44$	−35.8494	+	20.6977i	−0.814760	+	0.470402i
$45$		0			0
$46$	17.0861	−	29.5941i	0.371438	−	0.643350i
$47$	−8.15595	+	9.71989i	−0.173531	+	0.206806i	−0.845799	−	0.533502i	$-0.820876\pi$
$47$	−8.15595	+	9.71989i	−0.173531	+	0.206806i	0.672268	+	0.740308i	$0.265320\pi$
$48$		0			0
$49$	0.765740	+	4.34273i	0.0156273	+	0.0886271i
$50$	−9.93826	−	11.8440i	−0.198765	−	0.236879i
$51$		0			0
$52$	−12.8166	+	4.66486i	−0.246473	+	0.0897089i
$53$		−	17.7730i		−	0.335339i	−0.985843	−	0.167670i	$-0.946376\pi$
$53$		−	17.7730i		−	0.335339i	0.985843	−	0.167670i	$-0.0536242\pi$
$54$		0			0
$55$	−124.070			−2.25582
$56$	7.06980	+	19.4241i	0.126246	+	0.346859i
$57$		0			0
$58$	−20.0432	+	16.8183i	−0.345573	+	0.289970i
$59$	−64.9049	+	11.4445i	−1.10008	+	0.193974i	−0.694080	−	0.719897i	$-0.744189\pi$
$59$	−64.9049	+	11.4445i	−1.10008	+	0.193974i	−0.406003	+	0.913872i	$0.633078\pi$
$60$		0			0
$61$	32.3438	+	27.1396i	0.530226	+	0.444912i	0.868179	−	0.496251i	$-0.165290\pi$
$61$	32.3438	+	27.1396i	0.530226	+	0.444912i	−0.337954	+	0.941163i	$0.609735\pi$
$62$	−26.6150	−	15.3662i	−0.429274	−	0.247841i
$63$		0			0
$64$	4.00000	+	6.92820i	0.0625000	+	0.108253i
$65$	−40.2581	−	7.09859i	−0.619356	−	0.109209i
$66$		0			0
$67$	−111.190	−	40.4700i	−1.65956	−	0.604030i	−0.669266	−	0.743023i	$-0.733391\pi$
$67$	−111.190	−	40.4700i	−1.65956	−	0.604030i	−0.990293	+	0.138993i	$0.955613\pi$
$68$	1.55216	−	4.26451i	0.0228258	−	0.0627134i
$69$		0			0
$70$	−10.7582	+	61.0129i	−0.153689	+	0.871613i
$71$	46.1702	−	26.6564i	0.650284	−	0.375442i	−0.138281	−	0.990393i	$-0.544158\pi$
$71$	46.1702	−	26.6564i	0.650284	−	0.375442i	0.788565	+	0.614951i	$0.210824\pi$
$72$		0			0
$73$	33.8569	−	58.6419i	0.463793	−	0.803314i	−0.535353	−	0.844629i	$-0.679821\pi$
$73$	33.8569	−	58.6419i	0.463793	−	0.803314i	0.999146	+	0.0413148i	$0.0131546\pi$
$74$	40.6944	−	48.4976i	0.549924	−	0.655374i
$75$		0			0
$76$	−8.44858	−	47.9143i	−0.111165	−	0.630451i
$77$	97.2298	+	115.874i	1.26273	+	1.50486i
$78$		0			0
$79$	104.610	−	38.0750i	1.32418	−	0.481962i	0.419385	−	0.907809i	$-0.362246\pi$
$79$	104.610	−	38.0750i	1.32418	−	0.481962i	0.904795	+	0.425846i	$0.140024\pi$
$80$			23.9776i			0.299719i
$81$		0			0
$82$	72.5250			0.884452
$83$	−8.63542	−	23.7256i	−0.104041	−	0.285851i	0.876739	−	0.480966i	$-0.159714\pi$
$83$	−8.63542	−	23.7256i	−0.104041	−	0.285851i	−0.980780	+	0.195115i	$0.937492\pi$
$84$		0			0
$85$	10.4196	−	8.74311i	0.122584	−	0.102860i
$86$	−51.4485	+	9.07175i	−0.598238	+	0.105486i
$87$		0			0
$88$	44.8457	+	37.6300i	0.509610	+	0.427614i
$89$	35.4447	+	20.4640i	0.398254	+	0.229932i	0.685731	−	0.727855i	$-0.259483\pi$
$89$	35.4447	+	20.4640i	0.398254	+	0.229932i	−0.287476	+	0.957788i	$0.592816\pi$
$90$		0			0
$91$	24.9194	+	43.1616i	0.273839	+	0.474304i
$92$	−47.5927	−	8.39188i	−0.517312	−	0.0912161i
$93$		0			0
$94$	16.8620	+	6.13725i	0.179383	+	0.0652899i
$95$	49.8747	−	137.030i	0.524996	−	1.44242i
$96$		0			0
$97$	7.02010	−	39.8130i	0.0723722	−	0.410443i	−0.927002	−	0.375057i	$-0.877623\pi$
$97$	7.02010	−	39.8130i	0.0723722	−	0.410443i	0.999374	−	0.0353855i	$-0.0112659\pi$
$98$	5.40078	−	3.11814i	0.0551100	−	0.0318178i
$99$		0			0
$100$	−10.9327	+	18.9360i	−0.109327	+	0.189360i
$101$	−7.45688	+	8.88677i	−0.0738305	+	0.0879878i	−0.801695	−	0.597733i	$-0.796068\pi$
$101$	−7.45688	+	8.88677i	−0.0738305	+	0.0879878i	0.727865	+	0.685721i	$0.240513\pi$
$102$		0			0
$103$	21.6451	+	122.756i	0.210147	+	1.19180i	0.889132	+	0.457650i	$0.151309\pi$
$103$	21.6451	+	122.756i	0.210147	+	1.19180i	−0.678985	+	0.734152i	$0.737580\pi$
$104$	12.3985	+	14.7760i	0.119216	+	0.142077i
$105$		0			0
$106$	−23.6190	+	8.59660i	−0.222820	+	0.0811000i
$107$		−	142.548i		−	1.33223i	−0.745850	−	0.666113i	$-0.767957\pi$
$107$		−	142.548i		−	1.33223i	0.745850	−	0.666113i	$-0.232043\pi$
$108$		0			0
$109$	−119.276			−1.09427			−0.547137	−	0.837043i	$-0.684282\pi$
$109$	−119.276			−1.09427			−0.547137	+	0.837043i	$0.684282\pi$
$110$	60.0114	+	164.880i	0.545558	+	1.49891i
$111$		0			0
$112$	22.3936	−	18.7905i	0.199943	−	0.167772i
$113$	102.092	−	18.0016i	0.903471	−	0.159306i	0.297434	−	0.954743i	$-0.403869\pi$
$113$	102.092	−	18.0016i	0.903471	−	0.159306i	0.606037	+	0.795436i	$0.292758\pi$
$114$		0			0
$115$	−110.958	−	93.1047i	−0.964851	−	0.809606i
$116$	32.0450	+	18.5012i	0.276250	+	0.159493i
$117$		0			0
$118$	46.6027	+	80.7183i	0.394938	+	0.684053i
$119$	−16.3311	−	2.87961i	−0.137236	−	0.0241984i
$120$		0			0
$121$	288.856	+	105.135i	2.38724	+	0.868885i
$122$	20.4222	−	56.1096i	0.167395	−	0.459915i
$123$		0			0
$124$	−7.54711	+	42.8018i	−0.0608638	+	0.345176i
$125$	73.0275	−	42.1624i	0.584220	−	0.337299i
$126$		0			0
$127$	109.770	−	190.127i	0.864329	−	1.49706i	−0.00338367	−	0.999994i	$-0.501077\pi$
$127$	109.770	−	190.127i	0.864329	−	1.49706i	0.867712	−	0.497067i	$-0.165590\pi$
$128$	7.27231	−	8.66680i	0.0568149	−	0.0677094i
$129$		0			0
$130$	10.0389	+	56.9336i	0.0772225	+	0.437951i
$131$	−83.9745	−	100.077i	−0.641027	−	0.763946i	0.343505	−	0.939151i	$-0.388386\pi$
$131$	−83.9745	−	100.077i	−0.641027	−	0.763946i	−0.984532	+	0.175205i	$0.943941\pi$
$132$		0			0
$133$	−167.063	+	60.8058i	−1.25611	+	0.457187i
$134$			167.339i			1.24880i
$135$		0			0
$136$	−6.41798			−0.0471911
$137$	−26.4097	−	72.5602i	−0.192772	−	0.529636i	0.805220	−	0.592976i	$-0.202047\pi$
$137$	−26.4097	−	72.5602i	−0.192772	−	0.529636i	−0.997992	+	0.0633396i	$0.979825\pi$
$138$		0			0
$139$	−81.8517	+	68.6818i	−0.588861	+	0.494113i	−0.887844	−	0.460145i	$-0.847797\pi$
$139$	−81.8517	+	68.6818i	−0.588861	+	0.494113i	0.298982	+	0.954259i	$0.403353\pi$
$140$	86.2852	−	15.2144i	0.616323	−	0.108674i
$141$		0			0
$142$	−57.7564	−	48.4633i	−0.406735	−	0.341291i
$143$	122.239	+	70.5747i	0.854818	+	0.493529i
$144$		0			0
$145$	55.4516	+	96.0450i	0.382425	+	0.662379i
$146$	−94.3070	−	16.6289i	−0.645938	−	0.113896i
$147$		0			0
$148$	−84.1332	−	30.6220i	−0.568468	−	0.206905i
$149$	−53.0524	+	145.760i	−0.356056	+	0.978257i	0.624328	+	0.781162i	$0.285373\pi$
$149$	−53.0524	+	145.760i	−0.356056	+	0.978257i	−0.980384	+	0.197095i	$0.936849\pi$
$150$		0			0
$151$	−26.9250	+	152.699i	−0.178311	+	1.01125i	0.755940	+	0.654641i	$0.227180\pi$
$151$	−26.9250	+	152.699i	−0.178311	+	1.01125i	−0.934252	+	0.356614i	$0.883931\pi$
$152$	−59.5880	+	34.4032i	−0.392026	+	0.226337i
$153$		0			0
$154$	106.959	−	185.258i	0.694538	−	1.20298i
$155$	−83.7323	+	99.7883i	−0.540208	+	0.643795i
$156$		0			0
$157$	−21.0948	−	119.634i	−0.134362	−	0.762003i	−0.975302	−	0.220875i	$-0.929109\pi$
$157$	−21.0948	−	119.634i	−0.134362	−	0.762003i	0.840941	−	0.541128i	$-0.182002\pi$
$158$	−101.198	−	120.603i	−0.640492	−	0.763309i
$159$		0			0
$160$	31.8644	−	11.5977i	0.199153	−	0.0724856i
$161$			176.591i			1.09684i
$162$		0			0
$163$	−66.9033			−0.410450			−0.205225	−	0.978715i	$-0.565793\pi$
$163$	−66.9033			−0.410450			−0.205225	+	0.978715i	$0.565793\pi$
$164$	−35.0796	−	96.3804i	−0.213900	−	0.587685i
$165$		0			0
$166$	−27.3527	+	22.9517i	−0.164776	+	0.138263i
$167$	7.14238	−	1.25939i	0.0427687	−	0.00754128i	−0.152223	−	0.988346i	$-0.548643\pi$
$167$	7.14238	−	1.25939i	0.0427687	−	0.00754128i	0.194992	+	0.980805i	$0.437532\pi$
$168$		0			0
$169$	−93.8354	−	78.7373i	−0.555239	−	0.465901i
$170$	−16.6588	−	9.61798i	−0.0979931	−	0.0565763i
$171$		0			0
$172$	36.9408	+	63.9833i	0.214772	+	0.371996i
$173$	71.4004	+	12.5898i	0.412719	+	0.0727735i	0.376153	−	0.926558i	$-0.377247\pi$
$173$	71.4004	+	12.5898i	0.412719	+	0.0727735i	0.0365665	+	0.999331i	$0.488358\pi$
$174$		0			0
$175$	75.0799	+	27.3268i	0.429028	+	0.156153i
$176$	28.3161	−	77.7979i	0.160887	−	0.442033i
$177$		0			0
$178$	10.0509	−	57.0015i	0.0564658	−	0.320233i
$179$	−219.366	+	126.651i	−1.22551	+	0.707547i	−0.966087	−	0.258218i	$-0.916865\pi$
$179$	−219.366	+	126.651i	−1.22551	+	0.707547i	−0.259420	+	0.965765i	$0.583531\pi$
$180$		0			0
$181$	19.4150	−	33.6278i	0.107265	−	0.185789i	−0.807396	−	0.590010i	$-0.799124\pi$
$181$	19.4150	−	33.6278i	0.107265	−	0.185789i	0.914662	+	0.404221i	$0.132457\pi$
$182$	45.3054	−	53.9928i	0.248931	−	0.296664i
$183$		0			0
$184$	11.8679	+	67.3063i	0.0644995	+	0.365795i
$185$	−172.490	−	205.566i	−0.932379	−	1.11117i
$186$		0			0
$187$	−44.1328	+	16.0630i	−0.236004	+	0.0858985i
$188$		−	25.3768i		−	0.134983i
$189$		0			0
$190$	−206.226			−1.08540
$191$	−67.8767	−	186.490i	−0.355375	−	0.976385i	−0.980614	−	0.195951i	$-0.937220\pi$
$191$	−67.8767	−	186.490i	−0.355375	−	0.976385i	0.625238	−	0.780434i	$-0.285002\pi$
$192$		0			0
$193$	43.6611	−	36.6360i	0.226223	−	0.189824i	−0.522630	−	0.852560i	$-0.675049\pi$
$193$	43.6611	−	36.6360i	0.226223	−	0.189824i	0.748853	+	0.662736i	$0.230605\pi$
$194$	−56.3040	+	9.92792i	−0.290227	+	0.0511748i
$195$		0			0
$196$	−6.75608	−	5.66903i	−0.0344698	−	0.0289236i
$197$	64.8251	+	37.4268i	0.329061	+	0.189984i	0.655424	−	0.755261i	$-0.272490\pi$
$197$	64.8251	+	37.4268i	0.329061	+	0.189984i	−0.326363	+	0.945245i	$0.605823\pi$
$198$		0			0
$199$	−65.2158	−	112.957i	−0.327717	−	0.567623i	0.654341	−	0.756200i	$-0.272946\pi$
$199$	−65.2158	−	112.957i	−0.327717	−	0.567623i	−0.982059	+	0.188576i	$0.939613\pi$
$200$	30.4526	+	5.36961i	0.152263	+	0.0268481i
$201$		0			0
$202$	15.4167	+	5.61121i	0.0763201	+	0.0277783i
$203$	46.2446	−	127.056i	0.227806	−	0.625891i
$204$		0			0
$205$	53.3812	−	302.740i	0.260396	−	1.47678i
$206$	152.664	−	88.1404i	0.741085	−	0.427866i
$207$		0			0
$208$	13.6391	−	23.6237i	0.0655728	−	0.113575i
$209$	−323.648	+	385.708i	−1.54855	+	1.84549i
$210$		0			0
$211$	5.49032	+	31.1372i	0.0260205	+	0.147570i	0.995050	−	0.0993753i	$-0.0316844\pi$
$211$	5.49032	+	31.1372i	0.0260205	+	0.147570i	−0.969030	+	0.246945i	$0.920573\pi$
$212$	22.8485	+	27.2298i	0.107776	+	0.128442i
$213$		0			0
$214$	−189.436	+	68.9491i	−0.885215	+	0.322192i
$215$			221.437i			1.02994i
$216$		0			0
$217$	158.815			0.731865
$218$	57.6925	+	158.509i	0.264644	+	0.727105i
$219$		0			0
$220$	190.086	−	159.501i	0.864029	−	0.725006i
$221$	−15.2392	+	2.68708i	−0.0689557	+	0.0121587i
$222$		0			0
$223$	78.1769	+	65.5982i	0.350569	+	0.294162i	0.801019	−	0.598639i	$-0.204292\pi$
$223$	78.1769	+	65.5982i	0.350569	+	0.294162i	−0.450449	+	0.892802i	$0.648736\pi$
$224$	−35.8027	−	20.6707i	−0.159833	−	0.0922799i
$225$		0			0
$226$	−73.3037	−	126.966i	−0.324353	−	0.561796i
$227$	253.309	+	44.6652i	1.11590	+	0.196763i	0.701039	−	0.713123i	$-0.252720\pi$
$227$	253.309	+	44.6652i	1.11590	+	0.196763i	0.414859	+	0.909886i	$0.363831\pi$
$228$		0			0
$229$	−258.391	−	94.0468i	−1.12835	−	0.410685i	−0.290655	−	0.956828i	$-0.593873\pi$
$229$	−258.391	−	94.0468i	−1.12835	−	0.410685i	−0.837692	+	0.546143i	$0.816095\pi$
$230$	−70.0601	+	192.489i	−0.304609	+	0.836907i
$231$		0			0
$232$	9.08687	−	51.5342i	0.0391675	−	0.222130i
$233$	223.311	−	128.928i	0.958414	−	0.553341i	0.0627296	−	0.998031i	$-0.480019\pi$
$233$	223.311	−	128.928i	0.958414	−	0.553341i	0.895685	+	0.444690i	$0.146686\pi$
$234$		0			0
$235$	38.0296	−	65.8693i	0.161828	−	0.280295i
$236$	84.7273	−	100.974i	0.359014	−	0.427856i
$237$		0			0
$238$	4.07239	+	23.0957i	0.0171109	+	0.0970406i
$239$	80.0566	+	95.4078i	0.334965	+	0.399196i	0.907067	−	0.420987i	$-0.138316\pi$
$239$	80.0566	+	95.4078i	0.334965	+	0.399196i	−0.572102	+	0.820183i	$0.693872\pi$
$240$		0			0
$241$	−61.5004	+	22.3843i	−0.255188	+	0.0928809i	−0.466447	−	0.884549i	$-0.654466\pi$
$241$	−61.5004	+	22.3843i	−0.255188	+	0.0928809i	0.211258	+	0.977430i	$0.432244\pi$
$242$		−	434.721i		−	1.79637i
$243$		0			0
$244$	−84.4436			−0.346080
$245$	−9.04081	−	24.8394i	−0.0369013	−	0.101385i
$246$		0			0
$247$	−127.085	+	106.637i	−0.514514	+	0.431729i
$248$	60.5309	−	10.6732i	0.244076	−	0.0430372i
$249$		0			0
$250$	−91.3534	−	76.6546i	−0.365413	−	0.306618i
$251$	−202.528	−	116.930i	−0.806884	−	0.465855i	0.0389884	−	0.999240i	$-0.487586\pi$
$251$	−202.528	−	116.930i	−0.806884	−	0.465855i	−0.845873	+	0.533385i	$0.820920\pi$
$252$		0			0
$253$	250.064	+	433.123i	0.988395	+	1.71195i
$254$	−305.759	−	53.9135i	−1.20378	−	0.212258i
$255$		0			0
$256$	−15.0351	−	5.47232i	−0.0587308	−	0.0213763i
$257$	−25.7075	+	70.6309i	−0.100029	+	0.274828i	−0.979606	−	0.200929i	$-0.935604\pi$
$257$	−25.7075	+	70.6309i	−0.100029	+	0.274828i	0.879576	+	0.475758i	$0.157826\pi$
$258$		0			0
$259$	−56.8110	+	322.191i	−0.219347	+	1.24398i
$260$	70.8048	−	40.8792i	0.272326	−	0.157228i
$261$		0			0
$262$	−92.3773	+	160.002i	−0.352585	+	0.610695i
$263$	97.3609	−	116.030i	0.370194	−	0.441180i	−0.548500	−	0.836151i	$-0.684801\pi$
$263$	97.3609	−	116.030i	0.370194	−	0.441180i	0.918694	+	0.394971i	$0.129245\pi$
$264$		0			0
$265$	18.5001	+	104.920i	0.0698119	+	0.395923i
$266$	161.613	+	192.603i	0.607567	+	0.724070i
$267$		0			0
$268$	222.381	−	80.9400i	0.829780	−	0.302015i
$269$		−	170.868i		−	0.635198i	−0.948225	−	0.317599i	$-0.897123\pi$
$269$		−	170.868i		−	0.635198i	0.948225	−	0.317599i	$-0.102877\pi$
$270$		0			0
$271$	−8.46530			−0.0312373			−0.0156186	−	0.999878i	$-0.504972\pi$
$271$	−8.46530			−0.0312373			−0.0156186	+	0.999878i	$0.504972\pi$
$272$	3.10431	+	8.52903i	0.0114129	+	0.0313567i
$273$		0			0
$274$	−83.6530	+	70.1932i	−0.305303	+	0.256180i
$275$	222.844	−	39.2934i	0.810342	−	0.142885i
$276$		0			0
$277$	382.880	+	321.274i	1.38224	+	1.15984i	0.968376	+	0.249496i	$0.0802649\pi$
$277$	382.880	+	321.274i	1.38224	+	1.15984i	0.413862	+	0.910340i	$0.364180\pi$
$278$	130.864	+	75.5542i	0.470733	+	0.271778i
$279$		0			0
$280$	−61.9541	−	107.308i	−0.221265	−	0.383242i
$281$	68.9552	+	12.1587i	0.245392	+	0.0432693i	0.294991	−	0.955500i	$-0.404683\pi$
$281$	68.9552	+	12.1587i	0.245392	+	0.0432693i	−0.0495990	+	0.998769i	$0.515794\pi$
$282$		0			0
$283$	33.6840	+	12.2600i	0.119025	+	0.0433214i	0.400846	−	0.916145i	$-0.368716\pi$
$283$	33.6840	+	12.2600i	0.119025	+	0.0433214i	−0.281821	+	0.959467i	$0.590939\pi$
$284$	−36.4680	+	100.195i	−0.128409	+	0.352800i
$285$		0			0
$286$	34.6628	−	196.583i	0.121199	−	0.687352i
$287$	−324.574	+	187.393i	−1.13092	+	0.652937i
$288$		0			0
$289$	−141.926	+	245.822i	−0.491092	+	0.850596i
$290$	100.815	−	120.147i	0.347639	−	0.414300i
$291$		0			0
$292$	23.5168	+	133.370i	0.0805369	+	0.456747i
$293$	21.9392	+	26.1461i	0.0748779	+	0.0892360i	0.802183	−	0.597078i	$-0.203672\pi$
$293$	21.9392	+	26.1461i	0.0748779	+	0.0892360i	−0.727305	+	0.686314i	$0.759227\pi$
$294$		0			0
$295$	371.242	−	135.121i	1.25845	−	0.458037i
$296$			126.618i			0.427765i
$297$		0			0
$298$	219.366			0.736126
$299$	56.3596	+	154.847i	0.188494	+	0.517882i
$300$		0			0
$301$	206.809	−	173.534i	0.687074	−	0.576524i
$302$	215.950	−	38.0777i	0.715065	−	0.126085i
$303$		0			0
$304$	74.5414	+	62.5476i	0.245202	+	0.205749i
$305$	−219.186	−	126.547i	−0.718642	−	0.414908i
$306$		0			0
$307$	−165.305	−	286.316i	−0.538452	−	0.932627i	−0.998988	−	0.0449854i	$-0.985676\pi$
$307$	−165.305	−	286.316i	−0.538452	−	0.932627i	0.460535	−	0.887641i	$-0.347657\pi$
$308$	−297.929	−	52.5330i	−0.967303	−	0.170562i
$309$		0			0
$310$	173.112	+	63.0075i	0.558425	+	0.203250i
$311$	−82.6437	+	227.062i	−0.265735	+	0.730102i	0.733019	+	0.680208i	$0.238111\pi$
$311$	−82.6437	+	227.062i	−0.265735	+	0.730102i	−0.998755	+	0.0498938i	$0.984112\pi$
$312$		0			0
$313$	−54.4006	+	308.521i	−0.173804	+	0.985691i	0.765712	+	0.643184i	$0.222387\pi$
$313$	−54.4006	+	308.521i	−0.173804	+	0.985691i	−0.939515	+	0.342507i	$0.888724\pi$
$314$	−148.782	+	85.8993i	−0.473828	+	0.273565i
$315$		0			0
$316$	−111.324	+	192.819i	−0.352291	+	0.610186i
$317$	317.348	−	378.201i	1.00110	−	1.19306i	0.0199518	−	0.999801i	$-0.493649\pi$
$317$	317.348	−	378.201i	1.00110	−	1.19306i	0.981147	−	0.193262i	$-0.0619068\pi$
$318$		0			0
$319$	−66.4953	−	377.114i	−0.208449	−	1.18217i
$320$	−30.8250	−	36.7358i	−0.0963280	−	0.114799i
$321$		0			0
$322$	234.677	−	85.4154i	0.728810	−	0.265265i
$323$		−	55.1997i		−	0.170897i
$324$		0			0
$325$	74.5564			0.229404
$326$	32.3604	+	88.9096i	0.0992651	+	0.272729i
$327$		0			0
$328$	−111.115	+	93.2364i	−0.338765	+	0.284257i
$329$	−91.3206	+	16.1023i	−0.277570	+	0.0489431i
$330$		0			0
$331$	198.545	+	166.599i	0.599833	+	0.503320i	0.891392	−	0.453233i	$-0.149730\pi$
$331$	198.545	+	166.599i	0.599833	+	0.503320i	−0.291559	+	0.956553i	$0.594174\pi$
$332$	43.7313	+	25.2483i	0.131721	+	0.0760491i
$333$		0			0
$334$	−5.12833	−	8.88254i	−0.0153543	−	0.0265944i
$335$	698.519	+	123.168i	2.08513	+	0.367665i
$336$		0			0
$337$	−431.168	−	156.932i	−1.27943	−	0.465675i	−0.389187	−	0.921159i	$-0.627244\pi$
$337$	−431.168	−	156.932i	−1.27943	−	0.465675i	−0.890244	+	0.455484i	$0.849466\pi$
$338$	−59.2488	+	162.785i	−0.175292	+	0.481612i
$339$		0			0
$340$	−4.72388	+	26.7905i	−0.0138938	+	0.0787955i
$341$	389.523	−	224.891i	1.14230	−	0.659505i
$342$		0			0
$343$	162.937	−	282.216i	0.475036	−	0.822786i
$344$	67.1612	−	80.0396i	0.195236	−	0.232673i
$345$		0			0
$346$	−17.8047	−	100.975i	−0.0514587	−	0.291837i
$347$	−173.848	−	207.184i	−0.501002	−	0.597071i	0.454978	−	0.890503i	$-0.349647\pi$
$347$	−173.848	−	207.184i	−0.501002	−	0.597071i	−0.955980	+	0.293432i	$0.905203\pi$
$348$		0			0
$349$	−314.152	+	114.342i	−0.900148	+	0.327627i	−0.750312	−	0.661084i	$-0.770097\pi$
$349$	−314.152	+	114.342i	−0.900148	+	0.327627i	−0.149836	+	0.988711i	$0.547875\pi$
$350$		−	112.993i		−	0.322838i
$351$		0			0
$352$	−117.084			−0.332624
$353$	−179.081	−	492.021i	−0.507312	−	1.39383i	−0.884000	−	0.467487i	$-0.845159\pi$
$353$	−179.081	−	492.021i	−0.507312	−	1.39383i	0.376688	−	0.926340i	$-0.377063\pi$
$354$		0			0
$355$	−244.810	+	205.420i	−0.689607	+	0.578649i
$356$	−80.6123	+	14.2141i	−0.226439	+	0.0399273i
$357$		0			0
$358$	274.415	+	230.261i	0.766521	+	0.643188i
$359$	46.0527	+	26.5885i	0.128280	+	0.0740627i	0.562767	−	0.826616i	$-0.309737\pi$
$359$	46.0527	+	26.5885i	0.128280	+	0.0740627i	−0.434487	+	0.900678i	$0.643070\pi$
$360$		0			0
$361$	−115.394	−	199.869i	−0.319652	−	0.553653i
$362$	−54.0798	−	9.53572i	−0.149392	−	0.0263418i
$363$		0			0
$364$	−93.6662	−	34.0917i	−0.257325	−	0.0936586i
$365$	−138.827	+	381.424i	−0.380348	+	1.04500i
$366$		0			0
$367$	76.2686	−	432.541i	0.207816	−	1.17859i	−0.685129	−	0.728421i	$-0.740254\pi$
$367$	76.2686	−	432.541i	0.207816	−	1.17859i	0.892946	−	0.450164i	$-0.148635\pi$
$368$	83.7047	−	48.3269i	0.227458	−	0.131323i
$369$		0			0
$370$	−189.750	+	328.657i	−0.512838	+	0.888261i
$371$	83.4906	−	99.5002i	0.225042	−	0.268195i
$372$		0			0
$373$	−102.738	−	582.657i	−0.275438	−	1.56208i	−0.737568	−	0.675272i	$-0.764026\pi$
$373$	−102.738	−	582.657i	−0.275438	−	1.56208i	0.462131	−	0.886812i	$-0.347085\pi$
$374$	42.6931	+	50.8797i	0.114153	+	0.136042i
$375$		0			0
$376$	−33.7239	+	12.2745i	−0.0896913	+	0.0326450i
$377$		−	126.170i		−	0.334668i
$378$		0			0
$379$	198.665			0.524183			0.262092	−	0.965043i	$-0.415588\pi$
$379$	198.665			0.524183			0.262092	+	0.965043i	$0.415588\pi$
$380$	99.7493	+	274.059i	0.262498	+	0.721208i
$381$		0			0
$382$	−215.000	+	180.406i	−0.562826	+	0.472267i
$383$	−31.8457	+	5.61525i	−0.0831479	+	0.0146612i	−0.215067	−	0.976599i	$-0.568997\pi$
$383$	−31.8457	+	5.61525i	−0.0831479	+	0.0146612i	0.131919	+	0.991260i	$0.457886\pi$
$384$		0			0
$385$	−694.594	−	582.833i	−1.80414	−	1.51385i
$386$	−69.8050	−	40.3019i	−0.180842	−	0.104409i
$387$		0			0
$388$	40.4271	+	70.0219i	0.104194	+	0.180469i
$389$	−215.378	−	37.9769i	−0.553671	−	0.0976271i	−0.110189	−	0.993911i	$-0.535146\pi$
$389$	−215.378	−	37.9769i	−0.553671	−	0.0976271i	−0.443482	+	0.896284i	$0.646257\pi$
$390$		0			0
$391$	−51.5227	−	18.7527i	−0.131772	−	0.0479610i
$392$	−4.26587	+	11.7204i	−0.0108823	+	0.0298989i
$393$		0			0
$394$	18.3822	−	104.251i	0.0466553	−	0.264596i
$395$	−577.915	+	333.659i	−1.46308	+	0.844707i
$396$		0			0
$397$	−264.698	+	458.471i	−0.666746	+	1.15484i	0.312062	+	0.950062i	$0.398980\pi$
$397$	−264.698	+	458.471i	−0.666746	+	1.15484i	−0.978809	+	0.204777i	$0.934353\pi$
$398$	−118.567	+	141.303i	−0.297908	+	0.355033i
$399$		0			0
$400$	−7.59378	−	43.0665i	−0.0189844	−	0.107666i
$401$	167.829	+	200.011i	0.418526	+	0.498780i	0.933576	−	0.358380i	$-0.116671\pi$
$401$	167.829	+	200.011i	0.418526	+	0.498780i	−0.515049	+	0.857161i	$0.672226\pi$
$402$		0			0
$403$	139.259	−	50.6862i	0.345556	−	0.125772i
$404$		−	23.2017i		−	0.0574299i
$405$		0			0
$406$	−191.216			−0.470975
$407$	316.902	+	870.682i	0.778629	+	2.13927i
$408$		0			0
$409$	489.930	−	411.100i	1.19787	−	1.00513i	0.198184	−	0.980165i	$-0.436496\pi$
$409$	489.930	−	411.100i	1.19787	−	1.00513i	0.999688	−	0.0249695i	$-0.00794888\pi$
$410$	−428.139	+	75.4924i	−1.04424	+	0.184128i
$411$		0			0
$412$	−190.974	−	160.246i	−0.463529	−	0.388947i
$413$	−417.126	−	240.828i	−1.00999	−	0.583118i
$414$		0			0
$415$	75.6740	+	131.071i	0.182347	+	0.315834i
$416$	−37.9912	−	6.69888i	−0.0913251	−	0.0161031i
$417$		0			0
$418$	669.123	+	243.541i	1.60077	+	0.582634i
$419$	244.237	−	671.034i	0.582904	−	1.60151i	−0.200290	−	0.979737i	$-0.564189\pi$
$419$	244.237	−	671.034i	0.582904	−	1.60151i	0.783194	−	0.621778i	$-0.213589\pi$
$420$		0			0
$421$	−12.1583	+	68.9530i	−0.0288795	+	0.163784i	−0.995837	−	0.0911549i	$-0.970944\pi$
$421$	−12.1583	+	68.9530i	−0.0288795	+	0.163784i	0.966957	+	0.254939i	$0.0820553\pi$
$422$	38.7234	−	22.3570i	0.0917616	−	0.0529786i
$423$		0			0
$424$	25.1348	−	43.5347i	0.0592801	−	0.102676i
$425$	−15.9459	+	19.0036i	−0.0375197	+	0.0447143i
$426$		0			0
$427$	53.5818	+	303.877i	0.125484	+	0.711656i
$428$	183.257	+	218.397i	0.428169	+	0.510272i
$429$		0			0
$430$	294.274	−	107.107i	0.684358	−	0.249086i
$431$			76.1177i			0.176607i	0.996094	+	0.0883036i	$0.0281446\pi$
$431$			76.1177i			0.176607i	−0.996094	+	0.0883036i	$0.971855\pi$
$432$		0			0
$433$	109.713			0.253380			0.126690	−	0.991942i	$-0.459565\pi$
$433$	109.713			0.253380			0.126690	+	0.991942i	$0.459565\pi$
$434$	−76.8170	−	211.053i	−0.176998	−	0.486297i
$435$		0			0
$436$	182.741	−	153.338i	0.419131	−	0.351693i
$437$	−578.887	+	102.073i	−1.32468	+	0.233578i
$438$		0			0
$439$	87.3258	+	73.2751i	0.198920	+	0.166914i	0.736807	−	0.676103i	$-0.236333\pi$
$439$	87.3258	+	73.2751i	0.198920	+	0.166914i	−0.537887	+	0.843017i	$0.680777\pi$
$440$	−303.908	−	175.461i	−0.690701	−	0.398776i
$441$		0			0
$442$	10.9420	+	18.9521i	0.0247556	+	0.0428780i
$443$	−170.087	−	29.9909i	−0.383944	−	0.0676996i	−0.0216549	−	0.999766i	$-0.506893\pi$
$443$	−170.087	−	29.9909i	−0.383944	−	0.0676996i	−0.362289	+	0.932066i	$0.618005\pi$
$444$		0			0
$445$	−230.542	−	83.9106i	−0.518073	−	0.188563i
$446$	49.3618	−	135.621i	0.110677	−	0.304082i
$447$		0			0
$448$	−10.1524	+	57.5773i	−0.0226617	+	0.128521i
$449$	−164.941	+	95.2288i	−0.367352	+	0.212091i	−0.672301	−	0.740278i	$-0.734694\pi$
$449$	−164.941	+	95.2288i	−0.367352	+	0.212091i	0.304949	+	0.952369i	$0.401361\pi$
$450$		0			0
$451$	−530.719	+	919.233i	−1.17676	+	2.03821i
$452$	−133.272	+	158.827i	−0.294849	+	0.351388i
$453$		0			0
$454$	−63.1661	−	358.233i	−0.139132	−	0.789059i
$455$	−192.035	−	228.858i	−0.422054	−	0.502985i
$456$		0			0
$457$	−135.071	+	49.1618i	−0.295560	+	0.107575i	−0.485544	−	0.874212i	$-0.661379\pi$
$457$	−135.071	+	49.1618i	−0.295560	+	0.107575i	0.189984	+	0.981787i	$0.439156\pi$
$458$			388.872i			0.849066i
$459$		0			0
$460$	289.690			0.629762
$461$	−223.385	−	613.745i	−0.484566	−	1.33133i	−0.905540	−	0.424261i	$-0.860534\pi$
$461$	−223.385	−	613.745i	−0.484566	−	1.33133i	0.420974	−	0.907073i	$-0.361688\pi$
$462$		0			0
$463$	17.1769	−	14.4132i	0.0370992	−	0.0311299i	−0.624050	−	0.781385i	$-0.714514\pi$
$463$	17.1769	−	14.4132i	0.0370992	−	0.0311299i	0.661149	+	0.750255i	$0.270069\pi$
$464$	−72.8804	+	12.8508i	−0.157070	+	0.0276956i
$465$		0			0
$466$	−279.349	−	234.402i	−0.599462	−	0.503008i
$467$	413.326	+	238.634i	0.885065	+	0.510993i	0.872325	−	0.488926i	$-0.162611\pi$
$467$	413.326	+	238.634i	0.885065	+	0.510993i	0.0127402	+	0.999919i	$0.495945\pi$
$468$		0			0
$469$	−432.376	−	748.898i	−0.921911	−	1.59680i
$470$	−105.930	−	18.6783i	−0.225383	−	0.0397411i
$471$		0			0
$472$	−175.169	−	63.7563i	−0.371120	−	0.135077i
$473$	261.505	−	718.478i	0.552864	−	1.51898i
$474$		0			0
$475$	−46.1829	+	261.916i	−0.0972272	+	0.551403i
$476$	28.7226	−	16.5830i	0.0603417	−	0.0348383i
$477$		0			0
$478$	88.0673	−	152.537i	0.184241	−	0.319115i
$479$	−383.849	+	457.454i	−0.801356	+	0.955019i	−0.999685	−	0.0251168i	$-0.992004\pi$
$479$	−383.849	+	457.454i	−0.801356	+	0.955019i	0.198329	+	0.980136i	$0.436449\pi$
$480$		0			0
$481$	53.0126	+	300.649i	0.110213	+	0.625051i
$482$	59.4942	+	70.9024i	0.123432	+	0.147100i
$483$		0			0
$484$	−577.712	+	210.270i	−1.19362	+	0.434442i
$485$			242.336i			0.499662i
$486$		0			0
$487$	758.948			1.55842			0.779208	−	0.626766i	$-0.215622\pi$
$487$	758.948			1.55842			0.779208	+	0.626766i	$0.215622\pi$
$488$	40.8445	+	112.219i	0.0836977	+	0.229957i
$489$		0			0
$490$	−28.6368	+	24.0291i	−0.0584425	+	0.0490391i
$491$	−258.651	+	45.6071i	−0.526783	+	0.0928861i	−0.430714	−	0.902489i	$-0.641738\pi$
$491$	−258.651	+	45.6071i	−0.526783	+	0.0928861i	−0.0960694	+	0.995375i	$0.530627\pi$
$492$		0			0
$493$	32.1593	+	26.9849i	0.0652319	+	0.0547360i
$494$	203.182	+	117.307i	0.411300	+	0.237464i
$495$		0			0
$496$	−43.4621	−	75.2785i	−0.0876252	−	0.151771i
$497$	383.701	+	67.6568i	0.772033	+	0.136130i
$498$		0			0
$499$	85.4398	+	31.0975i	0.171222	+	0.0623197i	0.426209	−	0.904625i	$-0.359849\pi$
$499$	85.4398	+	31.0975i	0.171222	+	0.0623197i	−0.254987	+	0.966945i	$0.582071\pi$
$500$	−57.6816	+	158.479i	−0.115363	+	0.316958i
$501$		0			0
$502$	−57.4301	+	325.702i	−0.114403	+	0.648809i
$503$	368.263	−	212.617i	0.732134	−	0.422698i	−0.0870685	−	0.996202i	$-0.527750\pi$
$503$	368.263	−	212.617i	0.732134	−	0.422698i	0.819202	+	0.573505i	$0.194417\pi$
$504$		0			0
$505$	34.7700	−	60.2234i	0.0688515	−	0.119254i
$506$	454.636	−	541.814i	0.898490	−	1.07078i
$507$		0			0
$508$	76.2453	+	432.408i	0.150089	+	0.851198i
$509$	434.422	+	517.724i	0.853481	+	1.01714i	0.999611	+	0.0278737i	$0.00887363\pi$
$509$	434.422	+	517.724i	0.853481	+	1.01714i	−0.146130	+	0.989265i	$0.546682\pi$
$510$		0			0
$511$	465.022	−	169.254i	0.910023	−	0.331221i
$512$			22.6274i			0.0441942i
$513$		0			0
$514$	106.298			0.206805
$515$	−255.556	−	702.135i	−0.496226	−	1.36337i
$516$		0			0
$517$	−201.179	+	168.809i	−0.389128	+	0.326517i
$518$	455.647	−	80.3428i	0.879627	−	0.155102i
$519$		0			0
$520$	−88.5729	−	74.3215i	−0.170333	−	0.142926i
$521$	677.597	+	391.211i	1.30057	+	0.750885i	0.980502	−	0.196509i	$-0.0629606\pi$
$521$	677.597	+	391.211i	1.30057	+	0.750885i	0.320069	+	0.947394i	$0.396294\pi$
$522$		0			0
$523$	−342.909	−	593.936i	−0.655658	−	1.13563i	−0.981729	−	0.190287i	$-0.939058\pi$
$523$	−342.909	−	593.936i	−0.655658	−	1.13563i	0.326071	−	0.945345i	$-0.394275\pi$
$524$	257.313	+	45.3712i	0.491055	+	0.0865863i
$525$		0			0
$526$	−201.288	−	73.2629i	−0.382677	−	0.139283i
$527$	−16.8650	+	46.3362i	−0.0320019	+	0.0879244i
$528$		0			0
$529$	−9.52859	+	54.0393i	−0.0180124	+	0.102154i
$530$	130.482	−	75.3338i	0.246192	−	0.142139i
$531$		0			0
$532$	177.784	−	307.931i	0.334181	−	0.578819i
$533$	−224.801	+	267.907i	−0.421765	+	0.502640i
$534$		0			0
$535$	148.381	+	841.508i	0.277347	+	1.57291i
$536$	−215.127	−	256.378i	−0.401356	−	0.478317i
$537$		0			0
$538$	−227.071	+	82.6472i	−0.422066	+	0.153619i
$539$			91.2710i			0.169334i
$540$		0			0
$541$	884.789			1.63547			0.817735	−	0.575595i	$-0.195229\pi$
$541$	884.789			1.63547			0.817735	+	0.575595i	$0.195229\pi$
$542$	4.09458	+	11.2498i	0.00755457	+	0.0207560i
$543$		0			0
$544$	9.83292	−	8.25080i	0.0180752	−	0.0151669i
$545$	704.124	−	124.156i	1.29197	−	0.227809i
$546$		0			0
$547$	263.600	+	221.186i	0.481901	+	0.404363i	0.851113	−	0.524982i	$-0.175928\pi$
$547$	263.600	+	221.186i	0.481901	+	0.404363i	−0.369212	+	0.929345i	$0.620373\pi$
$548$	133.744	+	77.2169i	0.244058	+	0.140907i
$549$		0			0
$550$	−160.005	−	277.137i	−0.290919	−	0.503886i
$551$	443.235	+	78.1542i	0.804419	+	0.141841i
$552$		0			0
$553$	764.512	+	278.260i	1.38248	+	0.503182i
$554$	241.755	−	664.216i	0.436381	−	1.19895i
$555$		0			0
$556$	37.1086	−	210.453i	0.0667420	−	0.378513i
$557$	274.575	−	158.526i	0.492953	−	0.284606i	−0.232846	−	0.972514i	$-0.574804\pi$
$557$	274.575	−	158.526i	0.492953	−	0.284606i	0.725799	+	0.687907i	$0.241470\pi$
$558$		0			0
$559$	125.960	−	218.169i	0.225331	−	0.390285i
$560$	−112.637	+	134.236i	−0.201138	+	0.239707i
$561$		0			0
$562$	−17.1950	−	97.5174i	−0.0305960	−	0.173519i
$563$	−130.488	−	155.510i	−0.231773	−	0.276216i	0.637605	−	0.770363i	$-0.279925\pi$
$563$	−130.488	−	155.510i	−0.231773	−	0.276216i	−0.869379	+	0.494147i	$0.835481\pi$
$564$		0			0
$565$	−583.945	+	212.539i	−1.03353	+	0.376174i
$566$		−	50.6935i		−	0.0895646i
$567$		0			0
$568$	150.791			0.265477
$569$	80.4994	+	221.170i	0.141475	+	0.388700i	0.990113	−	0.140275i	$-0.0447987\pi$
$569$	80.4994	+	221.170i	0.141475	+	0.388700i	−0.848637	+	0.528975i	$0.822576\pi$
$570$		0			0
$571$	50.2848	−	42.1940i	0.0880645	−	0.0738949i	−0.597693	−	0.801725i	$-0.703916\pi$
$571$	50.2848	−	42.1940i	0.0880645	−	0.0738949i	0.685757	+	0.727830i	$0.259471\pi$
$572$	−278.010	+	49.0207i	−0.486031	+	0.0857005i
$573$		0			0
$574$	406.024	+	340.695i	0.707359	+	0.593545i
$575$	228.780	+	132.086i	0.397878	+	0.229715i
$576$		0			0
$577$	72.1281	+	124.930i	0.125005	+	0.216516i	0.921735	−	0.387820i	$-0.126772\pi$
$577$	72.1281	+	124.930i	0.125005	+	0.216516i	−0.796730	+	0.604336i	$0.793439\pi$
$578$	395.328	+	69.7069i	0.683958	+	0.120600i
$579$		0			0
$580$	−208.430	−	75.8622i	−0.359362	−	0.130797i
$581$	63.1094	−	173.392i	0.108622	−	0.298436i
$582$		0			0
$583$	63.8781	−	362.271i	0.109568	−	0.621391i
$584$	165.864	−	95.7618i	0.284014	−	0.163976i
$585$		0			0
$586$	24.1345	−	41.8022i	0.0411852	−	0.0713348i
$587$	−364.747	+	434.688i	−0.621375	+	0.740526i	−0.981306	−	0.192453i	$-0.938356\pi$
$587$	−364.747	+	434.688i	−0.621375	+	0.740526i	0.359931	+	0.932979i	$0.382800\pi$
$588$		0			0
$589$	91.7982	+	520.613i	0.155854	+	0.883894i
$590$	−359.132	−	427.996i	−0.608698	−	0.725418i
$591$		0			0
$592$	168.266	−	61.2440i	0.284234	−	0.103453i
$593$			174.635i			0.294494i	0.989100	+	0.147247i	$0.0470412\pi$
$593$			174.635i			0.294494i	−0.989100	+	0.147247i	$0.952959\pi$
$594$		0			0
$595$	99.4051			0.167067
$596$	−106.105	−	291.521i	−0.178028	−	0.489128i
$597$		0			0
$598$	178.519	−	149.796i	0.298527	−	0.250494i
$599$	424.905	−	74.9222i	0.709357	−	0.125079i	0.192683	−	0.981261i	$-0.438281\pi$
$599$	424.905	−	74.9222i	0.709357	−	0.125079i	0.516674	+	0.856182i	$0.327170\pi$
$600$		0			0
$601$	−636.447	−	534.042i	−1.05898	−	0.888589i	−0.0649703	−	0.997887i	$-0.520695\pi$
$601$	−636.447	−	534.042i	−1.05898	−	0.888589i	−0.994009	+	0.109298i	$0.965140\pi$
$602$	−330.645	−	190.898i	−0.549244	−	0.317106i
$603$		0			0
$604$	−155.055	−	268.563i	−0.256714	−	0.444641i
$605$	−1814.65	−	319.971i	−2.99942	−	0.528878i
$606$		0			0
$607$	352.792	+	128.406i	0.581205	+	0.211541i	0.615857	−	0.787858i	$-0.288810\pi$
$607$	352.792	+	128.406i	0.581205	+	0.211541i	−0.0346516	+	0.999399i	$0.511032\pi$
$608$	47.0663	−	129.314i	0.0774117	−	0.212687i
$609$		0			0
$610$	−62.1537	+	352.491i	−0.101891	+	0.577854i
$611$	−74.9368	+	43.2648i	−0.122646	+	0.0708098i
$612$		0			0
$613$	192.466	−	333.361i	0.313974	−	0.543820i	−0.665245	−	0.746626i	$-0.731673\pi$
$613$	192.466	−	333.361i	0.313974	−	0.543820i	0.979219	+	0.202806i	$0.0650060\pi$
$614$	−300.537	+	358.166i	−0.489474	+	0.583333i
$615$		0			0
$616$	74.2929	+	421.336i	0.120605	+	0.683987i
$617$	106.165	+	126.523i	0.172066	+	0.205061i	0.845185	−	0.534474i	$-0.179490\pi$
$617$	106.165	+	126.523i	0.172066	+	0.205061i	−0.673119	+	0.739534i	$0.735046\pi$
$618$		0			0
$619$	−449.740	+	163.692i	−0.726560	+	0.264446i	−0.678708	−	0.734408i	$-0.737460\pi$
$619$	−449.740	+	163.692i	−0.726560	+	0.264446i	−0.0478519	+	0.998854i	$0.515238\pi$
$620$		−	260.529i		−	0.420208i
$621$		0			0
$622$	341.722			0.549392
$623$	102.301	+	281.071i	0.164208	+	0.451157i
$624$		0			0
$625$	−596.591	+	500.599i	−0.954545	+	0.800958i
$626$	436.315	−	76.9341i	0.696989	−	0.122898i
$627$		0			0
$628$	186.118	+	156.172i	0.296366	+	0.248681i
$629$	−87.9703	−	50.7897i	−0.139857	−	0.0807467i
$630$		0			0
$631$	124.618	+	215.844i	0.197493	+	0.342067i	0.947715	−	0.319119i	$-0.103387\pi$
$631$	124.618	+	215.844i	0.197493	+	0.342067i	−0.750222	+	0.661186i	$0.770053\pi$
$632$	310.088	+	54.6769i	0.490645	+	0.0865140i
$633$		0			0
$634$	−656.099	−	238.801i	−1.03486	−	0.376657i
$635$	−450.100	+	1236.64i	−0.708819	+	1.94746i
$636$		0			0
$637$	−5.22202	+	29.6155i	−0.00819783	+	0.0464922i
$638$	−468.993	+	270.773i	−0.735099	+	0.424410i
$639$		0			0
$640$	−33.9094	+	58.7328i	−0.0529834	+	0.0917700i
$641$	−144.405	+	172.096i	−0.225282	+	0.268480i	−0.866832	−	0.498601i	$-0.833847\pi$
$641$	−144.405	+	172.096i	−0.225282	+	0.268480i	0.641550	+	0.767081i	$0.278292\pi$
$642$		0			0
$643$	−63.2329	−	358.612i	−0.0983404	−	0.557716i	−0.993672	−	0.112317i	$-0.964173\pi$
$643$	−63.2329	−	358.612i	−0.0983404	−	0.557716i	0.895332	−	0.445399i	$-0.146938\pi$
$644$	−227.021	−	270.554i	−0.352518	−	0.420114i
$645$		0			0
$646$	−73.3564	+	26.6995i	−0.113555	+	0.0413305i
$647$		−	1200.78i		−	1.85593i	−0.372671	−	0.927964i	$-0.621558\pi$
$647$		−	1200.78i		−	1.85593i	0.372671	−	0.927964i	$-0.378442\pi$
$648$		0			0
$649$	−1364.11			−2.10186
$650$	−36.0621	−	99.0799i	−0.0554802	−	0.152431i
$651$		0			0
$652$	102.502	−	86.0092i	0.157211	−	0.131916i
$653$	−626.194	+	110.415i	−0.958949	+	0.169089i	−0.631152	−	0.775659i	$-0.717417\pi$
$653$	−626.194	+	110.415i	−0.958949	+	0.169089i	−0.327797	+	0.944748i	$0.606306\pi$
$654$		0			0
$655$	599.900	+	503.376i	0.915878	+	0.768513i
$656$	177.649	+	102.566i	0.270807	+	0.156350i
$657$		0			0
$658$	65.5696	+	113.570i	0.0996498	+	0.172599i
$659$	−1147.84	−	202.395i	−1.74179	−	0.307125i	−0.789825	−	0.613332i	$-0.789829\pi$
$659$	−1147.84	−	202.395i	−1.74179	−	0.307125i	−0.951965	+	0.306207i	$0.900940\pi$
$660$		0			0
$661$	904.893	+	329.354i	1.36898	+	0.498266i	0.918818	−	0.394683i	$-0.129145\pi$
$661$	904.893	+	329.354i	1.36898	+	0.498266i	0.450158	+	0.892949i	$0.351368\pi$
$662$	125.363	−	344.433i	0.189371	−	0.520292i
$663$		0			0
$664$	12.4007	−	70.3280i	0.0186758	−	0.105916i
$665$	922.931	−	532.854i	1.38787	−	0.801285i
$666$		0			0
$667$	223.526	−	387.159i	0.335122	−	0.580448i
$668$	−9.32371	+	11.1116i	−0.0139577	+	0.0166341i
$669$		0			0
$670$	−174.185	−	987.855i	−0.259978	−	1.47441i
$671$	561.728	+	669.441i	0.837150	+	0.997677i
$672$		0			0
$673$	612.694	−	223.002i	0.910392	−	0.331355i	0.155982	−	0.987760i	$-0.450146\pi$
$673$	612.694	−	223.002i	0.910392	−	0.331355i	0.754409	+	0.656404i	$0.227923\pi$
$674$			648.897i			0.962755i
$675$		0			0
$676$	244.987			0.362407
$677$	258.040	+	708.958i	0.381152	+	1.04721i	0.970872	+	0.239598i	$0.0770158\pi$
$677$	258.040	+	708.958i	0.381152	+	1.04721i	−0.589720	+	0.807608i	$0.700762\pi$
$678$		0			0
$679$	226.327	−	189.911i	0.333325	−	0.279693i
$680$	37.8874	−	6.68058i	0.0557168	−	0.00982438i
$681$		0			0
$682$	−487.272	−	408.870i	−0.714475	−	0.599516i
$683$	405.766	+	234.269i	0.594094	+	0.343000i	0.766715	−	0.641988i	$-0.221890\pi$
$683$	405.766	+	234.269i	0.594094	+	0.343000i	−0.172621	+	0.984988i	$0.555224\pi$
$684$		0			0
$685$	231.434	+	400.856i	0.337860	+	0.585191i
$686$	−453.855	−	80.0268i	−0.661596	−	0.116657i
$687$		0			0
$688$	−138.852	−	50.5380i	−0.201820	−	0.0734563i
$689$	41.4542	−	113.895i	0.0601658	−	0.165304i
$690$		0			0
$691$	37.3428	−	211.781i	0.0540416	−	0.306485i	−0.945791	−	0.324776i	$-0.894711\pi$
$691$	37.3428	−	211.781i	0.0540416	−	0.306485i	0.999833	+	0.0182903i	$0.00582232\pi$
$692$	−125.577	+	72.5019i	−0.181470	+	0.104772i
$693$		0			0
$694$	−191.243	+	331.243i	−0.275567	+	0.477296i
$695$	411.705	−	490.651i	0.592382	−	0.705973i
$696$		0			0
$697$	−20.2068	−	114.598i	−0.0289911	−	0.164416i
$698$	303.904	+	362.178i	0.435392	+	0.518880i
$699$		0			0
$700$	−150.160	+	54.6537i	−0.214514	+	0.0780767i
$701$			848.227i			1.21002i	0.796216	+	0.605012i	$0.206832\pi$
$701$			848.227i			1.21002i	−0.796216	+	0.605012i	$0.793168\pi$
$702$		0			0
$703$	−1089.02			−1.54910
$704$	56.6322	+	155.596i	0.0804435	+	0.221017i
$705$		0			0
$706$	−567.240	+	475.971i	−0.803456	+	0.674180i
$707$	−83.4932	+	14.7221i	−0.118095	+	0.0208234i
$708$		0			0
$709$	−63.9344	−	53.6473i	−0.0901754	−	0.0756662i	0.596586	−	0.802549i	$-0.296524\pi$
$709$	−63.9344	−	53.6473i	−0.0901754	−	0.0756662i	−0.686761	+	0.726883i	$0.740968\pi$
$710$	391.401	+	225.975i	0.551268	+	0.318275i
$711$		0			0
$712$	57.8809	+	100.253i	0.0812934	+	0.140804i
$713$	517.120	+	91.1822i	0.725273	+	0.127885i
$714$		0			0
$715$	−795.078	−	289.385i	−1.11200	−	0.404734i
$716$	173.269	−	476.052i	0.241995	−	0.664876i
$717$		0			0
$718$	13.0590	−	74.0612i	0.0181880	−	0.103149i
$719$	−1032.07	+	595.867i	−1.43543	+	0.828744i	−0.997527	−	0.0702802i	$-0.977611\pi$
$719$	−1032.07	+	595.867i	−1.43543	+	0.828744i	−0.437899	+	0.899024i	$0.644277\pi$
$720$		0			0
$721$	−455.481	+	788.916i	−0.631735	+	1.09420i
$722$	−209.796	+	250.025i	−0.290576	+	0.346295i
$723$		0			0
$724$	13.4855	+	76.4803i	0.0186264	+	0.105636i
$725$	−130.015	−	154.946i	−0.179331	−	0.213719i
$726$		0			0
$727$	−633.829	+	230.695i	−0.871842	+	0.317325i	−0.738913	−	0.673801i	$-0.764661\pi$
$727$	−633.829	+	230.695i	−0.871842	+	0.317325i	−0.132929	+	0.991126i	$0.542438\pi$
$728$			140.965i			0.193634i
$729$		0			0
$730$	574.034			0.786348
$731$	28.6689	+	78.7672i	0.0392188	+	0.107753i
$732$		0			0
$733$	−149.604	+	125.532i	−0.204098	+	0.171259i	−0.739107	−	0.673588i	$-0.764752\pi$
$733$	−149.604	+	125.532i	−0.204098	+	0.171259i	0.535010	+	0.844846i	$0.320308\pi$
$734$	−611.705	+	107.860i	−0.833386	+	0.146948i
$735$		0			0
$736$	−104.710	−	87.8621i	−0.142269	−	0.119378i
$737$	−2120.97	−	1224.54i	−2.87784	−	1.66152i
$738$		0			0
$739$	−718.905	−	1245.18i	−0.972807	−	1.68495i	−0.686989	−	0.726668i	$-0.741068\pi$
$739$	−718.905	−	1245.18i	−0.972807	−	1.68495i	−0.285818	−	0.958284i	$-0.592265\pi$
$740$	528.540	+	93.1959i	0.714244	+	0.125940i
$741$		0			0
$742$	−172.612	−	62.8256i	−0.232631	−	0.0846707i
$743$	342.663	−	941.458i	0.461188	−	1.26710i	−0.463405	−	0.886147i	$-0.653372\pi$
$743$	342.663	−	941.458i	0.461188	−	1.26710i	0.924593	−	0.380957i	$-0.124405\pi$
$744$		0			0
$745$	161.461	−	915.693i	0.216727	−	1.22912i
$746$	−724.615	+	418.357i	−0.971334	+	0.560800i
$747$		0			0
$748$	46.9651	−	81.3460i	0.0627876	−	0.108751i
$749$	669.637	−	798.043i	0.894042	−	1.06548i
$750$		0			0
$751$	−129.904	−	736.724i	−0.172975	−	0.980990i	−0.940455	−	0.339918i	$-0.889601\pi$
$751$	−129.904	−	736.724i	−0.172975	−	0.980990i	0.767480	−	0.641073i	$-0.221510\pi$
$752$	32.6238	+	38.8795i	0.0433827	+	0.0517015i
$753$		0			0
$754$	−167.671	+	61.0271i	−0.222375	+	0.0809378i
$755$		−	929.460i		−	1.23107i
$756$		0			0
$757$	788.946			1.04220			0.521100	−	0.853496i	$-0.325522\pi$
$757$	788.946			1.04220			0.521100	+	0.853496i	$0.325522\pi$
$758$	−96.0924	−	264.012i	−0.126771	−	0.348300i
$759$		0			0
$760$	315.956	−	265.119i	0.415732	−	0.348841i
$761$	−512.126	+	90.3016i	−0.672965	+	0.118662i	−0.499680	−	0.866210i	$-0.666549\pi$
$761$	−512.126	+	90.3016i	−0.672965	+	0.118662i	−0.173284	+	0.984872i	$0.555438\pi$
$762$		0			0
$763$	−667.754	−	560.312i	−0.875170	−	0.734354i
$764$	343.739	+	198.458i	0.449921	+	0.259762i
$765$		0			0
$766$	22.8657	+	39.6045i	0.0298507	+	0.0517030i
$767$	−442.624	−	78.0465i	−0.577084	−	0.101756i
$768$		0			0
$769$	683.962	+	248.942i	0.889417	+	0.323721i	0.746004	−	0.665942i	$-0.231970\pi$
$769$	683.962	+	248.942i	0.889417	+	0.323721i	0.143413	+	0.989663i	$0.454192\pi$
$770$	−438.575	+	1204.97i	−0.569578	+	1.56490i
$771$		0			0
$772$	−19.7943	+	112.259i	−0.0256403	+	0.145414i
$773$	980.568	−	566.131i	1.26852	−	0.732382i	0.293814	−	0.955862i	$-0.405075\pi$
$773$	980.568	−	566.131i	1.26852	−	0.732382i	0.974708	+	0.223480i	$0.0717419\pi$
$774$		0			0
$775$	118.790	−	205.750i	0.153277	−	0.265483i
$776$	73.4997	−	87.5935i	0.0947161	−	0.112878i
$777$		0			0
$778$	53.7075	+	304.590i	0.0690328	+	0.391504i
$779$	−801.907	−	955.675i	−1.02941	−	1.22680i
$780$		0			0
$781$	1036.90	−	377.402i	1.32766	−	0.483229i
$782$			77.5404i			0.0991565i
$783$		0			0
$784$	17.6389			0.0224986
$785$	249.058	+	684.282i	0.317272	+	0.871697i
$786$		0			0
$787$	−591.843	+	496.615i	−0.752024	+	0.631023i	−0.936037	−	0.351901i	$-0.885536\pi$
$787$	−591.843	+	496.615i	−0.752024	+	0.631023i	0.184013	+	0.982924i	$0.441091\pi$
$788$	−147.433	+	25.9964i	−0.187097	+	0.0329903i
$789$		0			0
$790$	722.940	+	606.619i	0.915114	+	0.767872i
$791$	656.118	+	378.810i	0.829479	+	0.478900i
$792$		0			0
$793$	143.967	+	249.359i	0.181548	+	0.314450i
$794$	737.306	+	130.007i	0.928597	+	0.163737i
$795$		0			0
$796$	245.131	+	89.2204i	0.307954	+	0.112086i
$797$	−383.656	+	1054.09i	−0.481375	+	1.32257i	0.426940	+	0.904280i	$0.359592\pi$
$797$	−383.656	+	1054.09i	−0.481375	+	1.32257i	−0.908315	+	0.418287i	$0.862631\pi$
$798$		0			0
$799$	4.99955	−	28.3539i	0.00625726	−	0.0354867i
$800$	−53.5591	+	30.9224i	−0.0669489	+	0.0386530i
$801$		0			0
$802$	184.623	−	319.776i	0.230203	−	0.398723i
$803$	900.880	−	1073.63i	1.12189	−	1.33702i
$804$		0			0
$805$	−183.817	−	1042.48i	−0.228343	−	1.29500i
$806$	−134.716	−	160.549i	−0.167142	−	0.199192i
$807$		0			0
$808$	−30.8333	+	11.2224i	−0.0381601	+	0.0138891i
$809$			1053.93i			1.30275i	0.758754	+	0.651377i	$0.225808\pi$
$809$			1053.93i			1.30275i	−0.758754	+	0.651377i	$0.774192\pi$
$810$		0			0
$811$	−440.011			−0.542554			−0.271277	−	0.962501i	$-0.587446\pi$
$811$	−440.011			−0.542554			−0.271277	+	0.962501i	$0.587446\pi$
$812$	92.4892	+	254.112i	0.113903	+	0.312946i
$813$		0			0
$814$	1003.79	−	842.279i	1.23316	−	1.03474i
$815$	394.952	−	69.6407i	0.484603	−	0.0854487i
$816$		0			0
$817$	688.404	+	577.639i	0.842600	+	0.707025i
$818$	−783.295	−	452.236i	−0.957574	−	0.552855i
$819$		0			0
$820$	307.410	+	532.450i	0.374890	+	0.649329i
$821$	293.175	+	51.6946i	0.357095	+	0.0629654i	0.349318	−	0.937004i	$-0.386413\pi$
$821$	293.175	+	51.6946i	0.357095	+	0.0629654i	0.00777691	+	0.999970i	$0.497525\pi$
$822$		0			0
$823$	−452.037	−	164.528i	−0.549255	−	0.199912i	0.0524604	−	0.998623i	$-0.483294\pi$
$823$	−452.037	−	164.528i	−0.549255	−	0.199912i	−0.601715	+	0.798711i	$0.705516\pi$
$824$	−120.583	+	331.299i	−0.146339	+	0.402062i
$825$		0			0
$826$	−118.283	+	670.815i	−0.143199	+	0.812125i
$827$	271.357	−	156.668i	0.328122	−	0.189441i	−0.326885	−	0.945064i	$-0.605999\pi$
$827$	271.357	−	156.668i	0.328122	−	0.189441i	0.655007	+	0.755623i	$0.272666\pi$
$828$		0			0
$829$	320.622	−	555.333i	0.386757	−	0.669883i	−0.605254	−	0.796032i	$-0.706928\pi$
$829$	320.622	−	555.333i	0.386757	−	0.669883i	0.992011	+	0.126149i	$0.0402618\pi$
$830$	137.581	−	163.963i	0.165761	−	0.197546i
$831$		0			0
$832$	9.47365	+	53.7277i	0.0113866	+	0.0645766i
$833$	−6.43179	−	7.66511i	−0.00772124	−	0.00920182i
$834$		0			0
$835$	−40.8528	+	14.8692i	−0.0489255	+	0.0178074i
$836$		−	1007.01i		−	1.20456i
$837$		0			0
$838$	−1009.89			−1.20512
$839$	−301.891	−	829.438i	−0.359822	−	0.988603i	−0.979091	−	0.203424i	$-0.934793\pi$
$839$	−301.891	−	829.438i	−0.359822	−	0.988603i	0.619269	−	0.785179i	$-0.287429\pi$
$840$		0			0
$841$	382.032	−	320.563i	0.454259	−	0.381168i
$842$	97.5142	−	17.1944i	0.115813	−	0.0204209i
$843$		0			0
$844$	−48.4408	−	40.6467i	−0.0573944	−	0.0481596i
$845$	635.899	+	367.137i	0.752544	+	0.434481i
$846$		0			0
$847$	1123.25	+	1945.52i	1.32615	+	2.29696i
$848$	−70.0118	−	12.3450i	−0.0825611	−	0.0145578i
$849$		0			0
$850$	32.9672	+	11.9991i	0.0387850	+	0.0141166i
$851$	−369.967	+	1016.47i	−0.434743	+	1.19445i
$852$		0			0
$853$	−241.895	+	1371.85i	−0.283581	+	1.60827i	0.426730	+	0.904379i	$0.359666\pi$
$853$	−241.895	+	1371.85i	−0.283581	+	1.60827i	−0.710311	+	0.703888i	$0.751446\pi$
$854$	377.913	−	218.188i	0.442522	−	0.255490i
$855$		0			0
$856$	201.594	−	349.171i	0.235507	−	0.407910i
$857$	81.1695	−	96.7341i	0.0947135	−	0.112875i	−0.716606	−	0.697478i	$-0.754305\pi$
$857$	81.1695	−	96.7341i	0.0947135	−	0.112875i	0.811319	+	0.584603i	$0.198750\pi$
$858$		0			0
$859$	197.472	+	1119.92i	0.229886	+	1.30375i	0.853120	+	0.521714i	$0.174707\pi$
$859$	197.472	+	1119.92i	0.229886	+	1.30375i	−0.623234	+	0.782035i	$0.714182\pi$
$860$	−284.674	−	339.262i	−0.331017	−	0.394490i
$861$		0			0
$862$	101.155	−	36.8173i	0.117349	−	0.0427115i
$863$			458.427i			0.531202i	0.964083	+	0.265601i	$0.0855703\pi$
$863$			458.427i			0.531202i	−0.964083	+	0.265601i	$0.914430\pi$
$864$		0			0
$865$	−434.605			−0.502433
$866$	−53.0672	−	145.801i	−0.0612786	−	0.168362i
$867$		0			0
$868$	−243.318	+	204.168i	−0.280321	+	0.235217i
$869$	2269.14	−	400.111i	2.61121	−	0.460427i
$870$		0			0
$871$	−618.148	−	518.688i	−0.709700	−	0.595509i
$872$	−292.165	−	168.682i	−0.335052	−	0.193442i
$873$		0			0
$874$	415.650	+	719.926i	0.475572	+	0.823714i
$875$	606.900	+	107.013i	0.693600	+	0.122300i
$876$		0			0
$877$	−1234.89	−	449.462i	−1.40808	−	0.512500i	−0.477515	−	0.878623i	$-0.658462\pi$
$877$	−1234.89	−	449.462i	−1.40808	−	0.512500i	−0.930566	+	0.366124i	$0.880685\pi$
$878$	55.1386	−	151.492i	0.0628002	−	0.172542i
$879$		0			0
$880$	−86.1781	+	488.740i	−0.0979297	+	0.555387i
$881$	−1313.98	+	758.626i	−1.49146	+	0.861096i	−0.999952	−	0.00977549i	$-0.996888\pi$
$881$	−1313.98	+	758.626i	−1.49146	+	0.861096i	−0.491510	+	0.870872i	$0.663555\pi$
$882$		0			0
$883$	−761.692	+	1319.29i	−0.862619	+	1.49410i	0.00677344	+	0.999977i	$0.497844\pi$
$883$	−761.692	+	1319.29i	−0.862619	+	1.49410i	−0.869392	+	0.494123i	$0.835489\pi$
$884$	19.8934	−	23.7080i	0.0225038	−	0.0268190i
$885$		0			0
$886$	42.4136	+	240.539i	0.0478709	+	0.271489i
$887$	506.405	+	603.510i	0.570919	+	0.680394i	0.971819	−	0.235727i	$-0.0757472\pi$
$887$	506.405	+	603.510i	0.570919	+	0.680394i	−0.400901	+	0.916122i	$0.631303\pi$
$888$		0			0
$889$	1507.68	−	548.750i	1.69593	−	0.617266i
$890$			346.960i			0.389843i
$891$		0			0
$892$	−204.105			−0.228818
$893$	−105.570	−	290.052i	−0.118220	−	0.324807i
$894$		0			0
$895$	1163.15	−	976.002i	1.29961	−	1.09050i
$896$	81.4267	−	14.3577i	0.0908780	−	0.0160242i
$897$		0			0
$898$	206.332	+	173.133i	0.229769	+	0.192799i
$899$	−348.185	−	201.025i	−0.387303	−	0.223609i
$900$		0			0
$901$	20.1643	+	34.9256i	0.0223799	+	0.0387632i
$902$	1478.30	+	260.663i	1.63891	+	0.288984i
$903$		0			0
$904$	275.532	+	100.285i	0.304792	+	0.110935i
$905$	−79.6095	+	218.725i	−0.0879663	+	0.241685i
$906$		0			0
$907$	295.268	−	1674.55i	0.325544	−	1.84625i	−0.180281	−	0.983615i	$-0.557701\pi$
$907$	295.268	−	1674.55i	0.325544	−	1.84625i	0.505825	−	0.862636i	$-0.331188\pi$
$908$	−445.512	+	257.217i	−0.490652	+	0.283278i
$909$		0			0
$910$	−211.250	+	365.896i	−0.232143	+	0.402084i
$911$	195.203	−	232.634i	0.214273	−	0.255361i	−0.648192	−	0.761477i	$-0.724475\pi$
$911$	195.203	−	232.634i	0.214273	−	0.255361i	0.862466	+	0.506116i	$0.168919\pi$
$912$		0			0
$913$	−90.7453	−	514.642i	−0.0993924	−	0.563682i
$914$	130.665	+	155.720i	0.142959	+	0.170372i
$915$		0			0
$916$	516.783	−	188.094i	0.564173	−	0.205342i
$917$		−	954.751i		−	1.04117i
$918$		0			0
$919$	−682.579			−0.742741			−0.371370	−	0.928485i	$-0.621112\pi$
$919$	−682.579			−0.742741			−0.371370	+	0.928485i	$0.621112\pi$
$920$	−140.120	−	384.977i	−0.152305	−	0.418453i
$921$		0			0
$922$	−707.573	+	593.724i	−0.767432	+	0.643952i
$923$	358.046	−	63.1332i	0.387916	−	0.0684001i
$924$		0			0
$925$	374.915	+	314.591i	0.405314	+	0.340099i
$926$	−27.4623	−	15.8554i	−0.0296570	−	0.0171224i
$927$		0			0
$928$	52.3292	+	90.6368i	0.0563892	+	0.0976690i
$929$	786.356	+	138.656i	0.846454	+	0.149253i	0.580022	−	0.814601i	$-0.303044\pi$
$929$	786.356	+	138.656i	0.846454	+	0.149253i	0.266432	+	0.963854i	$0.414155\pi$
$930$		0			0
$931$	−100.805	−	36.6898i	−0.108276	−	0.0394091i
$932$	−176.384	+	484.612i	−0.189254	+	0.519970i
$933$		0			0
$934$	117.205	−	664.704i	0.125487	−	0.711674i
$935$	243.810	−	140.764i	0.260759	−	0.150549i
$936$		0			0
$937$	−386.927	+	670.176i	−0.412942	+	0.715236i	−0.995210	−	0.0977605i	$-0.968832\pi$
$937$	−386.927	+	670.176i	−0.412942	+	0.715236i	0.582268	+	0.812997i	$0.302165\pi$
$938$	−786.094	+	936.830i	−0.838053	+	0.998753i
$939$		0			0
$940$	26.4151	+	149.808i	0.0281012	+	0.159370i
$941$	−838.349	−	999.106i	−0.890913	−	1.06175i	−0.997721	−	0.0674693i	$-0.978508\pi$
$941$	−838.349	−	999.106i	−0.890913	−	1.06175i	0.106808	−	0.994280i	$-0.465937\pi$
$942$		0			0
$943$	−1164.44	+	423.822i	−1.23483	+	0.449440i
$944$			263.625i			0.279263i
$945$		0			0
$946$	−1081.29			−1.14301
$947$	282.223	+	775.402i	0.298018	+	0.818799i	0.994831	+	0.101545i	$0.0323787\pi$
$947$	282.223	+	775.402i	0.298018	+	0.818799i	−0.696813	+	0.717253i	$0.745399\pi$
$948$		0			0
$949$	353.744	−	296.826i	0.372754	−	0.312778i
$950$	370.405	−	65.3125i	0.389901	−	0.0687500i
$951$		0			0
$952$	−35.9305	−	30.1492i	−0.0377421	−	0.0316694i
$953$	−1058.27	−	610.995i	−1.11047	−	0.641128i	−0.171516	−	0.985181i	$-0.554866\pi$
$953$	−1058.27	−	610.995i	−1.11047	−	0.641128i	−0.938950	+	0.344054i	$0.888200\pi$
$954$		0			0
$955$	594.817	+	1030.25i	0.622846	+	1.07880i
$956$	−245.308	−	43.2544i	−0.256598	−	0.0452452i
$957$		0			0
$958$	793.586	+	288.842i	0.828378	+	0.301505i
$959$	193.008	−	530.284i	0.201259	−	0.552955i
$960$		0			0
$961$	−84.8726	+	481.336i	−0.0883169	+	0.500870i
$962$	373.899	−	215.871i	0.388669	−	0.224398i
$963$		0			0
$964$	65.4473	−	113.358i	0.0678914	−	0.117591i
$965$	−219.611	+	261.722i	−0.227576	+	0.271214i
$966$		0			0
$967$	−46.9384	−	266.201i	−0.0485403	−	0.275286i	0.950871	−	0.309587i	$-0.100191\pi$
$967$	−46.9384	−	266.201i	−0.0485403	−	0.275286i	−0.999412	+	0.0343010i	$0.989080\pi$
$968$	558.867	+	666.032i	0.577342	+	0.688049i
$969$		0			0
$970$	322.047	−	117.215i	0.332007	−	0.120841i
$971$		−	1817.80i		−	1.87209i	−0.351883	−	0.936044i	$-0.614458\pi$
$971$		−	1817.80i		−	1.87209i	0.351883	−	0.936044i	$-0.385542\pi$
$972$		0			0
$973$	−780.879			−0.802548
$974$	−367.095	−	1008.59i	−0.376895	−	1.03551i
$975$		0			0
$976$	129.375	−	108.559i	0.132556	−	0.111228i
$977$	−1295.60	+	228.448i	−1.32610	+	0.233826i	−0.791442	−	0.611245i	$-0.790669\pi$
$977$	−1295.60	+	228.448i	−1.32610	+	0.233826i	−0.534654	+	0.845071i	$0.679558\pi$
$978$		0			0
$979$	648.927	+	544.514i	0.662847	+	0.556195i
$980$	45.7843	+	26.4336i	0.0467187	+	0.0269730i
$981$		0			0
$982$	185.715	+	321.668i	0.189119	+	0.327564i
$983$	−623.860	−	110.003i	−0.634649	−	0.111906i	−0.152938	−	0.988236i	$-0.548873\pi$
$983$	−623.860	−	110.003i	−0.634649	−	0.111906i	−0.481711	+	0.876330i	$0.659984\pi$
$984$		0			0
$985$	−421.641	−	153.465i	−0.428062	−	0.155802i
$986$	20.3058	−	55.7896i	0.0205941	−	0.0565818i
$987$		0			0
$988$	57.6157	−	326.755i	0.0583155	−	0.330723i
$989$	773.029	−	446.309i	0.781627	−	0.451273i
$990$		0			0
$991$	817.383	−	1415.75i	0.824806	−	1.42861i	−0.0772613	−	0.997011i	$-0.524618\pi$
$991$	817.383	−	1415.75i	0.824806	−	1.42861i	0.902067	−	0.431595i	$-0.142049\pi$
$992$	−79.0175	+	94.1693i	−0.0796547	+	0.0949288i
$993$		0			0
$994$	−95.6811	−	542.635i	−0.0962587	−	0.545910i
$995$	502.568	+	598.938i	0.505094	+	0.601947i
$996$		0			0
$997$	412.548	−	150.155i	0.413789	−	0.150607i	−0.126733	−	0.991937i	$-0.540449\pi$
$997$	412.548	−	150.155i	0.413789	−	0.150607i	0.540522	+	0.841330i	$0.318227\pi$
$998$		−	128.585i		−	0.128842i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.3.f.a.143.1		36
3.2	odd	2		54.3.f.a.47.5	yes	36
12.11	even	2		432.3.bc.c.209.2		36
27.2	odd	18		1458.3.b.c.1457.4		36
27.4	even	9		54.3.f.a.23.5	✓	36
27.23	odd	18	inner	162.3.f.a.17.1		36
27.25	even	9		1458.3.b.c.1457.33		36
108.31	odd	18		432.3.bc.c.401.2		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.3.f.a.23.5	✓	36	27.4	even	9
54.3.f.a.47.5	yes	36	3.2	odd	2
162.3.f.a.17.1		36	27.23	odd	18	inner
162.3.f.a.143.1		36	1.1	even	1	trivial
432.3.bc.c.209.2		36	12.11	even	2
432.3.bc.c.401.2		36	108.31	odd	18
1458.3.b.c.1457.4		36	27.2	odd	18
1458.3.b.c.1457.33		36	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.483690 - 1.32893i) q^{2} +(-1.53209 + 1.28558i) q^{4} +(-5.90332 + 1.04091i) q^{5} +(5.59840 + 4.69762i) q^{7} +(2.44949 + 1.41421i) q^{8} +O(q^{10})\)	\(q+(-0.483690 - 1.32893i) q^{2} +(-1.53209 + 1.28558i) q^{4} +(-5.90332 + 1.04091i) q^{5} +(5.59840 + 4.69762i) q^{7} +(2.44949 + 1.41421i) q^{8} +(4.23867 + 7.34160i) q^{10} +(20.3832 + 3.59412i) q^{11} +(6.40830 + 2.33243i) q^{13} +(3.53490 - 9.71205i) q^{14} +(0.694593 - 3.93923i) q^{16} +(-1.96510 + 1.13455i) q^{17} +(-12.1634 + 21.0675i) q^{19} +(7.70624 - 9.18394i) q^{20} +(-5.08285 - 28.8263i) q^{22} +(15.5320 + 18.5103i) q^{23} +(10.2734 - 3.73921i) q^{25} -9.64433i q^{26} -14.6164 q^{28} +(-6.32777 - 17.3854i) q^{29} +(16.6469 - 13.9684i) q^{31} +(-5.57091 + 0.982302i) q^{32} +(2.45823 + 2.06270i) q^{34} +(-37.9390 - 21.9041i) q^{35} +(22.3832 + 38.7688i) q^{37} +(33.8805 + 5.97405i) q^{38} +(-15.9322 - 5.79885i) q^{40} +(-17.5398 + 48.1902i) q^{41} +(6.41470 - 36.3796i) q^{43} +(-35.8494 + 20.6977i) q^{44} +(17.0861 - 29.5941i) q^{46} +(-8.15595 + 9.71989i) q^{47} +(0.765740 + 4.34273i) q^{49} +(-9.93826 - 11.8440i) q^{50} +(-12.8166 + 4.66486i) q^{52} -17.7730i q^{53} -124.070 q^{55} +(7.06980 + 19.4241i) q^{56} +(-20.0432 + 16.8183i) q^{58} +(-64.9049 + 11.4445i) q^{59} +(32.3438 + 27.1396i) q^{61} +(-26.6150 - 15.3662i) q^{62} +(4.00000 + 6.92820i) q^{64} +(-40.2581 - 7.09859i) q^{65} +(-111.190 - 40.4700i) q^{67} +(1.55216 - 4.26451i) q^{68} +(-10.7582 + 61.0129i) q^{70} +(46.1702 - 26.6564i) q^{71} +(33.8569 - 58.6419i) q^{73} +(40.6944 - 48.4976i) q^{74} +(-8.44858 - 47.9143i) q^{76} +(97.2298 + 115.874i) q^{77} +(104.610 - 38.0750i) q^{79} +23.9776i q^{80} +72.5250 q^{82} +(-8.63542 - 23.7256i) q^{83} +(10.4196 - 8.74311i) q^{85} +(-51.4485 + 9.07175i) q^{86} +(44.8457 + 37.6300i) q^{88} +(35.4447 + 20.4640i) q^{89} +(24.9194 + 43.1616i) q^{91} +(-47.5927 - 8.39188i) q^{92} +(16.8620 + 6.13725i) q^{94} +(49.8747 - 137.030i) q^{95} +(7.02010 - 39.8130i) q^{97} +(5.40078 - 3.11814i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 18 q^{5}+O(q^{10}) \) 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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