LMFDB - Embedded newform 384.2.v.a.229.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [384,2,Mod(13,384)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(384, base_ring=CyclotomicField(32))

chi = DirichletCharacter(H, H._module([0, 15, 0]))

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

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

chi := DirichletCharacter("384.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 384 = 2^{7} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	384.v (of order $32$, degree $16$, 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:	$3.06625543762$
Analytic rank:	$0$
Dimension:	$512$
Relative dimension:	$32$ over $\Q(\zeta_{32})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			229.2
Character	$\chi$	$=$	384.229
Dual form			384.2.v.a.109.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36711 + 0.361948i) q^{2} +(0.881921 - 0.471397i) q^{3} +(1.73799 - 0.989646i) q^{4} +(-2.41932 - 2.94794i) q^{5} +(-1.03506 + 0.963661i) q^{6} +(-0.0684071 + 0.0457082i) q^{7} +(-2.01782 + 1.98202i) q^{8} +(0.555570 - 0.831470i) q^{9} +O(q^{10})$	\(q+(-1.36711 + 0.361948i) q^{2} +(0.881921 - 0.471397i) q^{3} +(1.73799 - 0.989646i) q^{4} +(-2.41932 - 2.94794i) q^{5} +(-1.03506 + 0.963661i) q^{6} +(-0.0684071 + 0.0457082i) q^{7} +(-2.01782 + 1.98202i) q^{8} +(0.555570 - 0.831470i) q^{9} +(4.37448 + 3.15450i) q^{10} +(0.433093 - 0.131377i) q^{11} +(1.06625 - 1.69207i) q^{12} +(-2.71297 - 2.22648i) q^{13} +(0.0769762 - 0.0872480i) q^{14} +(-3.52330 - 1.45940i) q^{15} +(2.04120 - 3.43999i) q^{16} +(-6.00920 + 2.48909i) q^{17} +(-0.458578 + 1.33780i) q^{18} +(0.162863 + 1.65357i) q^{19} +(-7.12216 - 2.72922i) q^{20} +(-0.0387830 + 0.0725579i) q^{21} +(-0.544534 + 0.336364i) q^{22} +(-1.77580 + 0.353229i) q^{23} +(-0.845244 + 2.69918i) q^{24} +(-1.86184 + 9.36009i) q^{25} +(4.51481 + 2.06189i) q^{26} +(0.0980171 - 0.995185i) q^{27} +(-0.0736558 + 0.147139i) q^{28} +(1.51723 - 5.00165i) q^{29} +(5.34497 + 0.719909i) q^{30} +(-3.65231 - 3.65231i) q^{31} +(-1.54545 + 5.44165i) q^{32} +(0.320023 - 0.320023i) q^{33} +(7.31433 - 5.57788i) q^{34} +(0.300244 + 0.0910779i) q^{35} +(0.142713 - 1.99490i) q^{36} +(4.62773 + 0.455791i) q^{37} +(-0.821159 - 2.20167i) q^{38} +(-3.44218 - 0.684693i) q^{39} +(10.7246 + 1.15330i) q^{40} +(-1.27095 - 6.38951i) q^{41} +(0.0267585 - 0.113232i) q^{42} +(-3.58417 - 1.91578i) q^{43} +(0.622693 - 0.656941i) q^{44} +(-3.79523 + 0.373797i) q^{45} +(2.29987 - 1.12565i) q^{46} +(-3.11894 - 7.52978i) q^{47} +(0.178581 - 3.99601i) q^{48} +(-2.67619 + 6.46090i) q^{49} +(-0.842525 - 13.4702i) q^{50} +(-4.12629 + 5.02790i) q^{51} +(-6.91854 - 1.18471i) q^{52} +(1.05605 + 3.48132i) q^{53} +(0.226205 + 1.39601i) q^{54} +(-1.43508 - 0.958890i) q^{55} +(0.0474390 - 0.227815i) q^{56} +(0.923122 + 1.38155i) q^{57} +(-0.263891 + 7.38698i) q^{58} +(10.5654 - 8.67080i) q^{59} +(-7.56773 + 0.950403i) q^{60} +(-3.48644 - 6.52266i) q^{61} +(6.31506 + 3.67117i) q^{62} +0.0822726i q^{63} +(0.143213 - 7.99872i) q^{64} +13.3842i q^{65} +(-0.321675 + 0.553339i) q^{66} +(-7.45946 - 13.9557i) q^{67} +(-7.98060 + 10.2730i) q^{68} +(-1.39961 + 1.14863i) q^{69} +(-0.443432 - 0.0158411i) q^{70} +(4.59326 + 6.87430i) q^{71} +(0.526945 + 2.77891i) q^{72} +(12.1245 + 8.10136i) q^{73} +(-6.49159 + 1.05188i) q^{74} +(2.77032 + 9.13252i) q^{75} +(1.91951 + 2.71271i) q^{76} +(-0.0236216 + 0.0287830i) q^{77} +(4.95367 - 0.309840i) q^{78} +(2.30496 - 5.56468i) q^{79} +(-15.0792 + 2.30506i) q^{80} +(-0.382683 - 0.923880i) q^{81} +(4.05021 + 8.27516i) q^{82} +(13.3481 - 1.31467i) q^{83} +(0.00440227 + 0.164486i) q^{84} +(21.8759 + 11.6929i) q^{85} +(5.59337 + 1.32180i) q^{86} +(-1.01968 - 5.12628i) q^{87} +(-0.613512 + 1.12349i) q^{88} +(5.29652 + 1.05354i) q^{89} +(5.05320 - 1.88470i) q^{90} +(0.287355 + 0.0283020i) q^{91} +(-2.73675 + 2.37133i) q^{92} +(-4.94273 - 1.49936i) q^{93} +(6.98932 + 9.16515i) q^{94} +(4.48063 - 4.48063i) q^{95} +(1.20221 + 5.52763i) q^{96} +(-4.02690 - 4.02690i) q^{97} +(1.32014 - 9.80142i) q^{98} +(0.131377 - 0.433093i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 512 q+O(q^{10}) $ 512 * q	$ 512 q - 96 q^{50} - 96 q^{52} - 32 q^{54} - 224 q^{56} - 192 q^{60} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 192 q^{70} - 224 q^{74} - 32 q^{76} - 96 q^{78} - 96 q^{80}+O(q^{100}) $ 512 * q - 96 * q^50 - 96 * q^52 - 32 * q^54 - 224 * q^56 - 192 * q^60 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 192 * q^70 - 224 * q^74 - 32 * q^76 - 96 * q^78 - 96 * q^80

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$1$	$e\left(\frac{9}{32}\right)$	$1$

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 $

$2$	−1.36711	+	0.361948i	−0.966694	+	0.255936i
$2$	−1.36711	+	0.361948i	−0.966694	+	0.255936i
$3$	0.881921	−	0.471397i	0.509177	−	0.272161i
$3$	0.881921	−	0.471397i	0.509177	−	0.272161i
$4$	1.73799	−	0.989646i	0.868994	−	0.494823i
$5$	−2.41932	−	2.94794i	−1.08195	−	1.31836i	−0.944741	−	0.327819i	$-0.893686\pi$
$5$	−2.41932	−	2.94794i	−1.08195	−	1.31836i	−0.137210	−	0.990542i	$-0.543814\pi$
$6$	−1.03506	+	0.963661i	−0.422563	+	0.393413i
$7$	−0.0684071	+	0.0457082i	−0.0258555	+	0.0172761i	−0.568431	−	0.822731i	$-0.692449\pi$
$7$	−0.0684071	+	0.0457082i	−0.0258555	+	0.0172761i	0.542575	+	0.840007i	$0.317449\pi$
$8$	−2.01782	+	1.98202i	−0.713408	+	0.700749i
$9$	0.555570	−	0.831470i	0.185190	−	0.277157i
$10$	4.37448	+	3.15450i	1.38333	+	0.997541i
$11$	0.433093	−	0.131377i	0.130582	−	0.0396117i	−0.224317	−	0.974516i	$-0.572015\pi$
$11$	0.433093	−	0.131377i	0.130582	−	0.0396117i	0.354899	+	0.934904i	$0.384515\pi$
$12$	1.06625	−	1.69207i	0.307800	−	0.488459i
$13$	−2.71297	−	2.22648i	−0.752443	−	0.617514i	0.177966	−	0.984037i	$-0.443048\pi$
$13$	−2.71297	−	2.22648i	−0.752443	−	0.617514i	−0.930409	+	0.366522i	$0.880548\pi$
$14$	0.0769762	−	0.0872480i	0.0205728	−	0.0233180i
$15$	−3.52330	−	1.45940i	−0.909711	−	0.376815i
$16$	2.04120	−	3.43999i	0.510300	−	0.859996i
$17$	−6.00920	+	2.48909i	−1.45745	+	0.603694i	−0.963957	−	0.266059i	$-0.914279\pi$
$17$	−6.00920	+	2.48909i	−1.45745	+	0.603694i	−0.493489	+	0.869752i	$0.664279\pi$
$18$	−0.458578	+	1.33780i	−0.108088	+	0.315322i
$19$	0.162863	+	1.65357i	0.0373633	+	0.379356i	0.995623	+	0.0934576i	$0.0297919\pi$
$19$	0.162863	+	1.65357i	0.0373633	+	0.379356i	−0.958260	+	0.285898i	$0.907708\pi$
$20$	−7.12216	−	2.72922i	−1.59256	−	0.610273i
$21$	−0.0387830	+	0.0725579i	−0.00846315	+	0.0158334i
$22$	−0.544534	+	0.336364i	−0.116095	+	0.0717131i
$23$	−1.77580	+	0.353229i	−0.370281	+	0.0736534i	−0.376723	−	0.926326i	$-0.622949\pi$
$23$	−1.77580	+	0.353229i	−0.370281	+	0.0736534i	0.00644264	+	0.999979i	$0.497949\pi$
$24$	−0.845244	+	2.69918i	−0.172535	+	0.550967i
$25$	−1.86184	+	9.36009i	−0.372367	+	1.87202i
$26$	4.51481	+	2.06189i	0.885426	+	0.404370i
$27$	0.0980171	−	0.995185i	0.0188634	−	0.191523i
$28$	−0.0736558	+	0.147139i	−0.0139196	+	0.0278067i
$29$	1.51723	−	5.00165i	0.281743	−	0.928784i	−0.695833	−	0.718203i	$-0.744965\pi$
$29$	1.51723	−	5.00165i	0.281743	−	0.928784i	0.977577	−	0.210580i	$-0.0675353\pi$
$30$	5.34497	+	0.719909i	0.975853	+	0.131437i
$31$	−3.65231	−	3.65231i	−0.655974	−	0.655974i	0.298451	−	0.954425i	$-0.403530\pi$
$31$	−3.65231	−	3.65231i	−0.655974	−	0.655974i	−0.954425	+	0.298451i	$0.903530\pi$
$32$	−1.54545	+	5.44165i	−0.273200	+	0.961957i
$33$	0.320023	−	0.320023i	0.0557088	−	0.0557088i
$34$	7.31433	−	5.57788i	1.25440	−	0.956599i
$35$	0.300244	+	0.0910779i	0.0507504	+	0.0153950i
$36$	0.142713	−	1.99490i	0.0237856	−	0.332484i
$37$	4.62773	+	0.455791i	0.760794	+	0.0749316i	0.470971	−	0.882149i	$-0.343904\pi$
$37$	4.62773	+	0.455791i	0.760794	+	0.0749316i	0.289823	+	0.957080i	$0.406404\pi$
$38$	−0.821159	−	2.20167i	−0.133210	−	0.357158i
$39$	−3.44218	−	0.684693i	−0.551190	−	0.109639i
$40$	10.7246	+	1.15330i	1.69571	+	0.182353i
$41$	−1.27095	−	6.38951i	−0.198490	−	0.997874i	−0.943639	−	0.330977i	$-0.892622\pi$
$41$	−1.27095	−	6.38951i	−0.198490	−	0.997874i	0.745149	−	0.666898i	$-0.232378\pi$
$42$	0.0267585	−	0.113232i	0.00412893	−	0.0174721i
$43$	−3.58417	−	1.91578i	−0.546580	−	0.292153i	0.174902	−	0.984586i	$-0.444039\pi$
$43$	−3.58417	−	1.91578i	−0.546580	−	0.292153i	−0.721483	+	0.692432i	$0.756539\pi$
$44$	0.622693	−	0.656941i	0.0938745	−	0.0990375i
$45$	−3.79523	+	0.373797i	−0.565759	+	0.0557224i
$46$	2.29987	−	1.12565i	0.339097	−	0.165968i
$47$	−3.11894	−	7.52978i	−0.454944	−	1.09833i	−0.970419	−	0.241427i	$-0.922385\pi$
$47$	−3.11894	−	7.52978i	−0.454944	−	1.09833i	0.515475	−	0.856904i	$-0.327615\pi$
$48$	0.178581	−	3.99601i	0.0257759	−	0.576775i
$49$	−2.67619	+	6.46090i	−0.382313	+	0.922986i
$50$	−0.842525	−	13.4702i	−0.119151	−	1.90497i
$51$	−4.12629	+	5.02790i	−0.577797	+	0.704047i
$52$	−6.91854	−	1.18471i	−0.959429	−	0.164290i
$53$	1.05605	+	3.48132i	0.145059	+	0.478195i	0.999118	−	0.0419800i	$-0.0133666\pi$
$53$	1.05605	+	3.48132i	0.145059	+	0.478195i	−0.854059	+	0.520175i	$0.825867\pi$
$54$	0.226205	+	1.39601i	0.0307826	+	0.189972i
$55$	−1.43508	−	0.958890i	−0.193506	−	0.129297i
$56$	0.0474390	−	0.227815i	0.00633931	−	0.0304431i
$57$	0.923122	+	1.38155i	0.122270	+	0.182991i
$58$	−0.263891	+	7.38698i	−0.0346506	+	0.969958i
$59$	10.5654	−	8.67080i	1.37550	−	1.12884i	0.398122	−	0.917332i	$-0.369662\pi$
$59$	10.5654	−	8.67080i	1.37550	−	1.12884i	0.977376	−	0.211510i	$-0.0678381\pi$
$60$	−7.56773	+	0.950403i	−0.976990	+	0.122696i
$61$	−3.48644	−	6.52266i	−0.446392	−	0.835141i	−0.999997	−	0.00236184i	$-0.999248\pi$
$61$	−3.48644	−	6.52266i	−0.446392	−	0.835141i	0.553605	−	0.832779i	$-0.313252\pi$
$62$	6.31506	+	3.67117i	0.802013	+	0.466239i
$63$			0.0822726i			0.0103654i
$64$	0.143213	−	7.99872i	0.0179017	−	0.999840i
$65$			13.3842i			1.66011i
$66$	−0.321675	+	0.553339i	−0.0395955	+	0.0681113i
$67$	−7.45946	−	13.9557i	−0.911318	−	1.70496i	−0.681637	−	0.731691i	$-0.738732\pi$
$67$	−7.45946	−	13.9557i	−0.911318	−	1.70496i	−0.229682	−	0.973266i	$-0.573768\pi$
$68$	−7.98060	+	10.2730i	−0.967789	+	1.24578i
$69$	−1.39961	+	1.14863i	−0.168493	+	0.138279i
$70$	−0.443432	−	0.0158411i	−0.0530003	−	0.00189337i
$71$	4.59326	+	6.87430i	0.545120	+	0.815829i	0.997092	−	0.0762026i	$-0.0242796\pi$
$71$	4.59326	+	6.87430i	0.545120	+	0.815829i	−0.451973	+	0.892032i	$0.649280\pi$
$72$	0.526945	+	2.77891i	0.0621011	+	0.327497i
$73$	12.1245	+	8.10136i	1.41907	+	0.948193i	0.999175	+	0.0406209i	$0.0129336\pi$
$73$	12.1245	+	8.10136i	1.41907	+	0.948193i	0.419896	+	0.907572i	$0.362066\pi$
$74$	−6.49159	+	1.05188i	−0.754632	+	0.122278i
$75$	2.77032	+	9.13252i	0.319889	+	1.05453i
$76$	1.91951	+	2.71271i	0.220183	+	0.311170i
$77$	−0.0236216	+	0.0287830i	−0.00269193	+	0.00328013i
$78$	4.95367	−	0.309840i	0.560893	−	0.0350824i
$79$	2.30496	−	5.56468i	0.259329	−	0.626075i	−0.739566	−	0.673084i	$-0.764969\pi$
$79$	2.30496	−	5.56468i	0.259329	−	0.626075i	0.998894	+	0.0470093i	$0.0149690\pi$
$80$	−15.0792	+	2.30506i	−1.68591	+	0.257714i
$81$	−0.382683	−	0.923880i	−0.0425204	−	0.102653i
$82$	4.05021	+	8.27516i	0.447270	+	0.913838i
$83$	13.3481	−	1.31467i	1.46514	−	0.144304i	0.666227	−	0.745749i	$-0.267908\pi$
$83$	13.3481	−	1.31467i	1.46514	−	0.144304i	0.798914	+	0.601445i	$0.205408\pi$
$84$	0.00440227	+	0.164486i	0.000480327	+	0.0179469i
$85$	21.8759	+	11.6929i	2.37277	+	1.26827i
$86$	5.59337	+	1.32180i	0.603148	+	0.142533i
$87$	−1.01968	−	5.12628i	−0.109321	−	0.549595i
$88$	−0.613512	+	1.12349i	−0.0654006	+	0.119765i
$89$	5.29652	+	1.05354i	0.561429	+	0.111675i	0.467644	−	0.883917i	$-0.345103\pi$
$89$	5.29652	+	1.05354i	0.561429	+	0.111675i	0.0937859	+	0.995592i	$0.470103\pi$
$90$	5.05320	−	1.88470i	0.532654	−	0.198664i
$91$	0.287355	+	0.0283020i	0.0301230	+	0.00296686i
$92$	−2.73675	+	2.37133i	−0.285326	+	0.247228i
$93$	−4.94273	−	1.49936i	−0.512538	−	0.155477i
$94$	6.98932	+	9.16515i	0.720893	+	0.945313i
$95$	4.48063	−	4.48063i	0.459703	−	0.459703i
$96$	1.20221	+	5.52763i	0.122700	+	0.564161i
$97$	−4.02690	−	4.02690i	−0.408869	−	0.408869i	0.472475	−	0.881344i	$-0.343361\pi$
$97$	−4.02690	−	4.02690i	−0.408869	−	0.408869i	−0.881344	+	0.472475i	$0.843361\pi$
$98$	1.32014	−	9.80142i	0.133355	−	0.990093i
$99$	0.131377	−	0.433093i	0.0132039	−	0.0435275i
$100$	6.02732	+	18.1103i	0.602732	+	1.81103i
$101$	−1.70578	+	17.3191i	−0.169732	+	1.72331i	0.413070	+	0.910699i	$0.364456\pi$
$101$	−1.70578	+	17.3191i	−0.169732	+	1.72331i	−0.582802	+	0.812614i	$0.698044\pi$
$102$	3.82126	−	8.36720i	0.378361	−	0.828477i
$103$	1.85522	−	9.32682i	0.182800	−	0.918999i	−0.775087	−	0.631855i	$-0.782294\pi$
$103$	1.85522	−	9.32682i	0.182800	−	0.918999i	0.957887	−	0.287145i	$-0.0927061\pi$
$104$	9.88722	−	0.884520i	0.969521	−	0.0867343i
$105$	0.307725	−	0.0612103i	0.0300309	−	0.00597352i
$106$	−2.70379	−	4.37711i	−0.262615	−	0.425143i
$107$	−8.63104	+	16.1475i	−0.834394	+	1.56104i	−0.00662167	+	0.999978i	$0.502108\pi$
$107$	−8.63104	+	16.1475i	−0.834394	+	1.56104i	−0.827773	+	0.561064i	$0.810392\pi$
$108$	−0.814528	−	1.82662i	−0.0783780	−	0.175767i
$109$	−0.149201	−	1.51487i	−0.0142909	−	0.145098i	0.985391	−	0.170305i	$-0.0544754\pi$
$109$	−0.149201	−	1.51487i	−0.0142909	−	0.145098i	−0.999682	+	0.0252074i	$0.991975\pi$
$110$	2.30898	+	0.791486i	0.220153	+	0.0754652i
$111$	4.29615	−	1.77952i	0.407772	−	0.168905i
$112$	0.0176028	+	0.328619i	0.00166331	+	0.0310516i
$113$	−1.96007	−	0.811886i	−0.184387	−	0.0763758i	0.288580	−	0.957456i	$-0.406817\pi$
$113$	−1.96007	−	0.811886i	−0.184387	−	0.0763758i	−0.472967	+	0.881080i	$0.656817\pi$
$114$	−1.76206	−	1.55461i	−0.165032	−	0.145603i
$115$	5.33753	+	4.38040i	0.497727	+	0.408474i
$116$	−2.31293	−	10.1943i	−0.214750	−	0.946520i
$117$	−3.35850	+	1.01879i	−0.310493	+	0.0941871i
$118$	−11.3057	+	15.6781i	−1.04077	+	1.44328i
$119$	0.297300	−	0.444941i	0.0272535	−	0.0407877i
$120$	10.0019	−	4.03843i	0.913048	−	0.368657i
$121$	−8.97586	+	5.99748i	−0.815987	+	0.545225i
$122$	7.12721	+	7.65530i	0.645267	+	0.693078i
$123$	−4.13288	−	5.03593i	−0.372649	−	0.454074i
$124$	−9.96216	−	2.73317i	−0.894628	−	0.245446i
$125$	15.2810	−	8.16784i	1.36677	−	0.730554i
$126$	−0.0297784	−	0.112476i	−0.00265287	−	0.0100201i
$127$	5.63302			0.499850			0.249925	−	0.968265i	$-0.419594\pi$
$127$	5.63302			0.499850			0.249925	+	0.968265i	$0.419594\pi$
$128$	2.69933	+	10.9870i	0.238589	+	0.971121i
$129$	−4.06405			−0.357819
$130$	−4.84440	−	18.2978i	−0.424882	−	1.60482i
$131$	5.08556	−	2.71829i	0.444328	−	0.237498i	−0.234031	−	0.972229i	$-0.575192\pi$
$131$	5.08556	−	2.71829i	0.444328	−	0.237498i	0.678359	+	0.734731i	$0.262692\pi$
$132$	0.239486	−	0.872905i	0.0208446	−	0.0759767i
$133$	−0.0867229	−	0.105672i	−0.00751983	−	0.00916293i
$134$	15.2491	+	16.3790i	1.31733	+	1.41493i
$135$	−3.17088	+	2.11872i	−0.272906	+	0.182350i
$136$	7.19208	−	16.9329i	0.616715	−	1.45198i
$137$	5.00484	−	7.49028i	0.427593	−	0.639938i	−0.553642	−	0.832755i	$-0.686762\pi$
$137$	5.00484	−	7.49028i	0.427593	−	0.639938i	0.981235	+	0.192817i	$0.0617624\pi$
$138$	1.49768	−	2.07689i	0.127491	−	0.176796i
$139$	15.2480	−	4.62542i	1.29332	−	0.392323i	0.432682	−	0.901547i	$-0.357567\pi$
$139$	15.2480	−	4.62542i	1.29332	−	0.392323i	0.860634	+	0.509223i	$0.170067\pi$
$140$	0.611955	−	0.138843i	0.0517196	−	0.0117344i
$141$	−6.30017	−	5.17041i	−0.530570	−	0.435427i
$142$	−8.76764	−	7.73541i	−0.735764	−	0.649141i
$143$	−1.46748	−	0.607849i	−0.122717	−	0.0508309i
$144$	−1.72621	−	3.60835i	−0.143851	−	0.300696i
$145$	−18.4153	+	7.62785i	−1.52930	+	0.633459i
$146$	−19.5079	−	6.68701i	−1.61448	−	0.553421i
$147$	0.685457	+	6.95956i	0.0565355	+	0.574015i
$148$	8.49400	−	3.78765i	0.698203	−	0.311343i
$149$	2.23196	−	4.17570i	0.182849	−	0.342087i	−0.773751	−	0.633489i	$-0.781622\pi$
$149$	2.23196	−	4.17570i	0.182849	−	0.342087i	0.956600	+	0.291403i	$0.0941220\pi$
$150$	−7.09283	−	11.4825i	−0.579128	−	0.937539i
$151$	−5.35237	+	1.06465i	−0.435570	+	0.0866403i	−0.408005	−	0.912980i	$-0.633775\pi$
$151$	−5.35237	+	1.06465i	−0.435570	+	0.0866403i	−0.0275652	+	0.999620i	$0.508775\pi$
$152$	−3.60604	−	3.01382i	−0.292489	−	0.244453i
$153$	−1.26893	+	6.37933i	−0.102587	+	0.515739i
$154$	0.0218754	−	0.0478994i	0.00176277	−	0.00385985i
$155$	−1.93072	+	19.6029i	−0.155079	+	1.57454i
$156$	−6.66008	+	2.21656i	−0.533233	+	0.177467i
$157$	−0.379323	+	1.25046i	−0.0302733	+	0.0997976i	−0.970775	−	0.239991i	$-0.922856\pi$
$157$	−0.379323	+	1.25046i	−0.0302733	+	0.0997976i	0.940502	+	0.339789i	$0.110356\pi$
$158$	−1.13702	+	8.44181i	−0.0904565	+	0.671594i
$159$	2.57243	+	2.57243i	0.204007	+	0.204007i
$160$	19.7806	−	8.60916i	1.56380	−	0.680614i
$161$	0.105332	−	0.105332i	0.00830134	−	0.00830134i
$162$	0.857567	+	1.12453i	0.0673768	+	0.0883518i
$163$	−15.8692	−	4.81388i	−1.24297	−	0.377052i	−0.400753	−	0.916186i	$-0.631252\pi$
$163$	−15.8692	−	4.81388i	−1.24297	−	0.377052i	−0.842220	+	0.539134i	$0.818752\pi$
$164$	−8.53226	−	9.84710i	−0.666258	−	0.768929i
$165$	−1.71765	−	0.169173i	−0.133719	−	0.0131701i
$166$	−17.7725	+	6.62860i	−1.37941	+	0.514479i
$167$	−6.64738	−	1.32225i	−0.514390	−	0.102318i	−0.0689318	−	0.997621i	$-0.521959\pi$
$167$	−6.64738	−	1.32225i	−0.514390	−	0.102318i	−0.445458	+	0.895303i	$0.646959\pi$
$168$	−0.0655538	−	0.223278i	−0.00505759	−	0.0172262i
$169$	−0.133163	−	0.669454i	−0.0102433	−	0.0514965i
$170$	−34.1390	−	8.06756i	−2.61834	−	0.618754i
$171$	1.46538	+	0.783261i	0.112060	+	0.0598975i
$172$	−8.12518	+	0.217461i	−0.619539	+	0.0165812i
$173$	−1.97220	+	0.194244i	−0.149943	+	0.0147681i	−0.172710	−	0.984973i	$-0.555252\pi$
$173$	−1.97220	+	0.194244i	−0.149943	+	0.0147681i	0.0227670	+	0.999741i	$0.492752\pi$
$174$	3.24947	+	6.63913i	0.246341	+	0.503311i
$175$	−0.300470	−	0.725398i	−0.0227134	−	0.0548349i
$176$	0.432094	−	1.75800i	0.0325703	−	0.132514i
$177$	5.23047	−	12.6275i	0.393146	−	0.949138i
$178$	−7.62225	+	0.476753i	−0.571312	+	0.0357341i
$179$	11.9073	−	14.5091i	0.889995	−	1.08446i	−0.105939	−	0.994373i	$-0.533785\pi$
$179$	11.9073	−	14.5091i	0.889995	−	1.08446i	0.995934	−	0.0900894i	$-0.0287153\pi$
$180$	−6.22613	+	4.40559i	−0.464068	+	0.328373i
$181$	−3.93927	−	12.9860i	−0.292804	−	0.965245i	−0.972725	−	0.231960i	$-0.925486\pi$
$181$	−3.93927	−	12.9860i	−0.292804	−	0.965245i	0.679922	−	0.733285i	$-0.262014\pi$
$182$	−0.403090	+	0.0653156i	−0.0298790	+	0.00484151i
$183$	−6.14952	−	4.10898i	−0.454586	−	0.303745i
$184$	2.88315	−	4.23243i	0.212549	−	0.312019i
$185$	−9.85228	−	14.7450i	−0.724354	−	1.08407i
$186$	7.29996	+	0.260783i	0.535259	+	0.0191215i
$187$	−2.27553	+	1.86748i	−0.166403	+	0.136564i
$188$	−12.8725	−	10.0000i	−0.938823	−	0.729326i
$189$	0.0387830	+	0.0725579i	0.00282105	+	0.00527781i
$190$	−4.50376	+	7.74727i	−0.326737	+	0.562046i
$191$			3.82167i			0.276526i	0.990396	+	0.138263i	$0.0441520\pi$
$191$			3.82167i			0.276526i	−0.990396	+	0.138263i	$0.955848\pi$
$192$	−3.64427	−	7.12175i	−0.263002	−	0.513968i
$193$			4.77663i			0.343829i	0.985112	+	0.171915i	$0.0549954\pi$
$193$			4.77663i			0.343829i	−0.985112	+	0.171915i	$0.945005\pi$
$194$	6.96274	+	4.04769i	0.499896	+	0.290607i
$195$	6.30929	+	11.8039i	0.451818	+	0.845291i
$196$	1.74282	+	13.8775i	0.124487	+	0.991247i
$197$	19.5421	−	16.0378i	1.39232	−	1.14265i	0.420396	−	0.907341i	$-0.361891\pi$
$197$	19.5421	−	16.0378i	1.39232	−	1.14265i	0.971922	−	0.235304i	$-0.0756087\pi$
$198$	−0.0228503	+	0.639638i	−0.00162390	+	0.0454571i
$199$	−3.77082	−	5.64343i	−0.267306	−	0.400052i	0.673398	−	0.739280i	$-0.264834\pi$
$199$	−3.77082	−	5.64343i	−0.267306	−	0.400052i	−0.940704	+	0.339228i	$0.889834\pi$
$200$	−14.7950	−	22.5772i	−1.04616	−	1.59645i
$201$	−13.1573	−	8.79144i	−0.928046	−	0.620100i
$202$	−3.93661	−	24.2945i	−0.276979	−	1.70936i
$203$	0.124827	+	0.411499i	0.00876113	+	0.0288816i
$204$	−2.19560	+	12.8220i	−0.153723	+	0.897720i
$205$	−15.7611	+	19.2049i	−1.10080	+	1.34133i
$206$	0.839531	+	13.4223i	0.0584929	+	0.935176i
$207$	−0.692884	+	1.67277i	−0.0481588	+	0.116266i
$208$	−13.1968	+	4.78790i	−0.915032	+	0.331981i
$209$	0.287777	+	0.694755i	0.0199059	+	0.0480572i
$210$	−0.398540	+	0.195062i	−0.0275018	+	0.0134605i
$211$	13.8943	−	1.36847i	0.956526	−	0.0942095i	0.392306	−	0.919835i	$-0.371677\pi$
$211$	13.8943	−	1.36847i	0.956526	−	0.0942095i	0.564219	+	0.825625i	$0.309177\pi$
$212$	5.28066	+	5.00537i	0.362678	+	0.343770i
$213$	7.29141	+	3.89734i	0.499600	+	0.267042i
$214$	5.95503	−	25.1995i	0.407077	−	1.72260i
$215$	3.02363	+	15.2008i	0.206210	+	1.03669i
$216$	1.77469	+	2.20238i	0.120753	+	0.149853i
$217$	0.416784	+	0.0829035i	0.0282932	+	0.00562786i
$218$	0.752277	+	2.01699i	0.0509506	+	0.136608i
$219$	14.5119	+	1.42929i	0.980620	+	0.0965827i
$220$	−3.44312	−	0.246317i	−0.232135	−	0.0166067i
$221$	21.8447	+	6.62652i	1.46943	+	0.445748i
$222$	−5.22922	+	3.98779i	−0.350962	+	0.267643i
$223$	−6.02079	+	6.02079i	−0.403182	+	0.403182i	−0.879353	−	0.476171i	$-0.842024\pi$
$223$	−6.02079	+	6.02079i	−0.403182	+	0.403182i	0.476171	+	0.879353i	$0.342024\pi$
$224$	−0.143008	−	0.442888i	−0.00955512	−	0.0295917i
$225$	6.74825	+	6.74825i	0.449883	+	0.449883i
$226$	2.97349	+	0.400497i	0.197794	+	0.0266406i
$227$	4.71448	−	15.5416i	0.312911	−	1.03153i	−0.649598	−	0.760278i	$-0.725063\pi$
$227$	4.71448	−	15.5416i	0.312911	−	1.03153i	0.962509	−	0.271251i	$-0.0874373\pi$
$228$	2.97162	+	1.48755i	0.196800	+	0.0985155i
$229$	1.22875	−	12.4757i	0.0811981	−	0.824418i	−0.865203	−	0.501423i	$-0.832810\pi$
$229$	1.22875	−	12.4757i	0.0811981	−	0.824418i	0.946401	−	0.322995i	$-0.104690\pi$
$230$	−8.88247	−	4.05658i	−0.585693	−	0.267483i
$231$	−0.00726419	+	0.0365195i	−0.000477948	+	0.00240281i
$232$	6.85185	+	13.0996i	0.449846	+	0.860033i
$233$	−9.07993	+	1.80611i	−0.594846	+	0.118322i	−0.483327	−	0.875440i	$-0.660572\pi$
$233$	−9.07993	+	1.80611i	−0.594846	+	0.118322i	−0.111519	+	0.993762i	$0.535572\pi$
$234$	4.22269	−	2.60840i	0.276046	−	0.170516i
$235$	−14.6517	+	27.4114i	−0.955770	+	1.78812i
$236$	9.78151	−	25.5258i	0.636722	−	1.66159i
$237$	−0.590373	−	5.99416i	−0.0383489	−	0.389363i
$238$	−0.245397	+	0.715892i	−0.0159067	+	0.0464044i
$239$	13.7619	−	5.70037i	0.890184	−	0.368726i	0.109746	−	0.993960i	$-0.464996\pi$
$239$	13.7619	−	5.70037i	0.890184	−	0.368726i	0.780438	+	0.625233i	$0.214996\pi$
$240$	−12.2121	+	9.14117i	−0.788285	+	0.590060i
$241$	8.80105	+	3.64552i	0.566926	+	0.234828i	0.647689	−	0.761905i	$-0.275736\pi$
$241$	8.80105	+	3.64552i	0.566926	+	0.234828i	−0.0807631	+	0.996733i	$0.525736\pi$
$242$	10.1002	−	11.4480i	0.649267	−	0.735906i
$243$	−0.773010	−	0.634393i	−0.0495886	−	0.0406963i
$244$	−12.5145	−	7.88597i	−0.801159	−	0.504847i
$245$	25.5209	−	7.74169i	1.63047	−	0.494599i
$246$	7.47285	+	5.38878i	0.476451	+	0.343576i
$247$	3.23981	−	4.84871i	0.206144	−	0.308516i
$248$	14.6086	+	0.130770i	0.927650	+	0.00830390i
$249$	11.1522	−	7.45167i	0.706743	−	0.472230i
$250$	−17.9344	+	16.6973i	−1.13427	+	1.05603i
$251$	−11.3854	−	13.8732i	−0.718640	−	0.875665i	0.277742	−	0.960656i	$-0.410414\pi$
$251$	−11.3854	−	13.8732i	−0.718640	−	0.875665i	−0.996382	+	0.0849903i	$0.972914\pi$
$252$	0.0814207	+	0.142989i	0.00512902	+	0.00900744i
$253$	−0.722681	+	0.386281i	−0.0454346	+	0.0242853i
$254$	−7.70096	+	2.03886i	−0.483201	+	0.127929i
$255$	24.8048			1.55334
$256$	−7.66700	−	14.0434i	−0.479187	−	0.877713i
$257$	7.72126			0.481639			0.240820	−	0.970570i	$-0.422584\pi$
$257$	7.72126			0.481639			0.240820	+	0.970570i	$0.422584\pi$
$258$	5.55600	−	1.47097i	0.345902	−	0.0915788i
$259$	−0.337403	+	0.180346i	−0.0209652	+	0.0112061i
$260$	13.2457	+	23.2617i	0.821462	+	1.44263i
$261$	−3.31579	−	4.04030i	−0.205242	−	0.250089i
$262$	−5.96865	+	5.55692i	−0.368745	+	0.343307i
$263$	−22.9299	+	15.3213i	−1.41392	+	0.944752i	−0.414524	+	0.910038i	$0.636052\pi$
$263$	−22.9299	+	15.3213i	−1.41392	+	0.944752i	−0.999397	+	0.0347135i	$0.988948\pi$
$264$	−0.0114583	+	1.28004i	−0.000705212	+	0.0787811i
$265$	7.70782	−	11.5356i	0.473487	−	0.708624i
$266$	0.156808	+	0.113076i	0.00961449	+	0.00693316i
$267$	5.16775	−	1.56762i	0.316261	−	0.0959367i
$268$	−26.7756	−	16.8726i	−1.63558	−	1.03066i
$269$	−10.0920	−	8.28229i	−0.615320	−	0.504980i	0.274322	−	0.961638i	$-0.411546\pi$
$269$	−10.0920	−	8.28229i	−0.615320	−	0.504980i	−0.889642	+	0.456658i	$0.849046\pi$
$270$	3.56809	−	4.04422i	0.217147	−	0.246123i
$271$	−6.65227	−	2.75546i	−0.404096	−	0.167382i	0.171372	−	0.985206i	$-0.445180\pi$
$271$	−6.65227	−	2.75546i	−0.404096	−	0.167382i	−0.575468	+	0.817824i	$0.695180\pi$
$272$	−3.70354	+	25.7523i	−0.224560	+	1.56146i
$273$	0.266766	−	0.110498i	0.0161454	−	0.00668765i
$274$	−4.13109	+	12.0515i	−0.249568	+	0.728060i
$275$	0.423354	+	4.29839i	0.0255292	+	0.259203i
$276$	−1.29577	+	3.38142i	−0.0779959	+	0.203537i
$277$	−13.2391	+	24.7686i	−0.795461	+	1.48820i	0.0756595	+	0.997134i	$0.475894\pi$
$277$	−13.2391	+	24.7686i	−0.795461	+	1.48820i	−0.871121	+	0.491069i	$0.836606\pi$
$278$	−19.1715	+	11.8424i	−1.14983	+	0.710262i
$279$	−5.06590	+	1.00767i	−0.303287	+	0.0603276i
$280$	−0.786356	+	0.411309i	−0.0469938	+	0.0245804i
$281$	0.120530	−	0.605946i	0.00719023	−	0.0361477i	−0.977024	−	0.213131i	$-0.931634\pi$
$281$	0.120530	−	0.605946i	0.00719023	−	0.0361477i	0.984214	+	0.176983i	$0.0566339\pi$
$282$	10.4845	+	4.78820i	0.624340	+	0.285133i
$283$	−2.13461	+	21.6730i	−0.126889	+	1.28833i	0.695136	+	0.718878i	$0.255344\pi$
$283$	−2.13461	+	21.6730i	−0.126889	+	1.28833i	−0.822026	+	0.569450i	$0.807156\pi$
$284$	14.7862	+	7.40174i	0.877397	+	0.439213i
$285$	1.83941	−	6.06371i	0.108957	−	0.359183i
$286$	2.22622	+	0.299847i	0.131639	+	0.0177303i
$287$	0.378995	+	0.378995i	0.0223714	+	0.0223714i
$288$	3.66596	+	4.30822i	0.216019	+	0.253864i
$289$	17.8941	−	17.8941i	1.05259	−	1.05259i
$290$	22.4148	−	17.0935i	1.31624	−	1.00376i
$291$	−5.44967	−	1.65314i	−0.319465	−	0.0969088i
$292$	29.0898	+	2.08106i	1.70235	+	0.121785i
$293$	−26.0090	−	2.56166i	−1.51946	−	0.149654i	−0.696419	−	0.717636i	$-0.745224\pi$
$293$	−26.0090	−	2.56166i	−1.51946	−	0.149654i	−0.823041	+	0.567982i	$0.807724\pi$
$294$	−3.45609	−	9.26639i	−0.201563	−	0.540427i
$295$	−51.1221	−	10.1688i	−2.97644	−	0.592051i
$296$	−10.2413	+	8.25253i	−0.595264	+	0.479669i
$297$	−0.0882941	−	0.443885i	−0.00512335	−	0.0257568i
$298$	−1.53995	+	6.51650i	−0.0892069	+	0.377491i
$299$	5.60416	+	2.99549i	0.324097	+	0.173234i
$300$	13.8527	+	13.1306i	0.799789	+	0.758094i
$301$	0.332749	−	0.0327730i	0.0191794	−	0.00188900i
$302$	6.93194	−	3.39278i	0.398889	−	0.195233i
$303$	6.65980	+	16.0782i	0.382595	+	0.923667i
$304$	6.02071	+	2.81503i	0.345311	+	0.161453i
$305$	−10.7937	+	26.0582i	−0.618043	+	1.49209i
$306$	−0.574220	−	9.18055i	−0.0328260	−	0.524817i
$307$	8.06219	−	9.82380i	0.460133	−	0.560674i	−0.490320	−	0.871543i	$-0.663120\pi$
$307$	8.06219	−	9.82380i	0.460133	−	0.560674i	0.950453	+	0.310869i	$0.100620\pi$
$308$	−0.0125691	+	0.0734016i	−0.000716189	+	0.00418244i
$309$	−2.76048	−	9.10007i	−0.157038	−	0.517685i
$310$	−4.45572	−	27.4981i	−0.253068	−	1.56179i
$311$	−15.7327	−	10.5123i	−0.892122	−	0.596097i	0.0227944	−	0.999740i	$-0.492744\pi$
$311$	−15.7327	−	10.5123i	−0.892122	−	0.596097i	−0.914916	+	0.403643i	$0.867744\pi$
$312$	8.30279	−	5.44088i	0.470053	−	0.308029i
$313$	9.20923	+	13.7826i	0.520537	+	0.779038i	0.994854	−	0.101316i	$-0.0323052\pi$
$313$	9.20923	+	13.7826i	0.520537	+	0.779038i	−0.474318	+	0.880354i	$0.657305\pi$
$314$	0.0659754	−	1.84681i	0.00372321	−	0.104222i
$315$	0.242535	−	0.199043i	0.0136653	−	0.0112148i
$316$	−1.50106	−	11.9524i	−0.0844413	−	0.672377i
$317$	11.9466	+	22.3505i	0.670986	+	1.25533i	0.955028	+	0.296515i	$0.0958245\pi$
$317$	11.9466	+	22.3505i	0.670986	+	1.25533i	−0.284042	+	0.958812i	$0.591675\pi$
$318$	−4.44788	−	2.58571i	−0.249425	−	0.145000i
$319$		−	2.36551i		−	0.132443i
$320$	−23.9263	+	18.9292i	−1.33752	+	1.05818i
$321$			18.3095i			1.02194i
$322$	−0.105876	+	0.182126i	−0.00590024	+	0.0101495i
$323$	−5.09457	−	9.53128i	−0.283470	−	0.530335i
$324$	−1.57941	−	1.22697i	−0.0877452	−	0.0681650i
$325$	25.8912	−	21.2483i	1.43618	−	1.17864i
$326$	23.4374	+	0.837274i	1.29808	+	0.0463723i
$327$	−0.845686	−	1.26566i	−0.0467666	−	0.0699911i
$328$	15.2287	+	10.3739i	0.840864	+	0.572800i
$329$	0.557530	+	0.372530i	0.0307376	+	0.0205382i
$330$	2.40945	−	0.390420i	0.132636	−	0.0214919i
$331$	4.35101	+	14.3433i	0.239153	+	0.788382i	0.991556	+	0.129679i	$0.0413946\pi$
$331$	4.35101	+	14.3433i	0.239153	+	0.788382i	−0.752403	+	0.658703i	$0.771105\pi$
$332$	21.8977	−	15.4947i	1.20179	−	0.850384i
$333$	2.95000	−	3.59459i	0.161659	−	0.196982i
$334$	9.56629	−	0.598347i	0.523444	−	0.0327401i
$335$	−23.0938	+	55.7532i	−1.26175	+	3.04613i
$336$	0.170434	+	0.281518i	0.00929795	+	0.0153581i
$337$	6.96802	+	16.8223i	0.379572	+	0.916368i	0.992046	+	0.125877i	$0.0401745\pi$
$337$	6.96802	+	16.8223i	0.379572	+	0.916368i	−0.612474	+	0.790491i	$0.709826\pi$
$338$	0.424356	+	0.867020i	0.0230819	+	0.0471597i
$339$	−2.11134	+	0.207949i	−0.114672	+	0.0112943i
$340$	49.5918	−	1.32726i	2.68949	−	0.0719810i
$341$	−2.06162	−	1.10196i	−0.111643	−	0.0596744i
$342$	−2.28683	−	0.540415i	−0.123658	−	0.0292223i
$343$	−0.224600	−	1.12914i	−0.0121272	−	0.0609677i
$344$	11.0293	−	3.23818i	0.594661	−	0.174591i
$345$	6.77218	+	1.34707i	0.364602	+	0.0725239i
$346$	2.62591	−	0.979386i	0.141170	−	0.0526521i
$347$	10.0223	+	0.987115i	0.538028	+	0.0529911i	0.363382	−	0.931640i	$-0.381622\pi$
$347$	10.0223	+	0.987115i	0.538028	+	0.0529911i	0.174646	+	0.984631i	$0.444122\pi$
$348$	−6.84540	−	7.90029i	−0.366952	−	0.423500i
$349$	−23.1524	−	7.02320i	−1.23932	−	0.375943i	−0.398454	−	0.917188i	$-0.630453\pi$
$349$	−23.1524	−	7.02320i	−1.23932	−	0.375943i	−0.840865	+	0.541245i	$0.817953\pi$
$350$	0.673332	+	0.882946i	0.0359911	+	0.0471954i
$351$	−2.48168	+	2.48168i	−0.132462	+	0.132462i
$352$	0.0455844	+	2.55978i	0.00242966	+	0.136437i
$353$	−21.2471	−	21.2471i	−1.13087	−	1.13087i	−0.990033	−	0.140834i	$-0.955021\pi$
$353$	−21.2471	−	21.2471i	−1.13087	−	1.13087i	−0.140834	−	0.990033i	$-0.544979\pi$
$354$	−2.58015	+	19.1563i	−0.137133	+	1.01815i
$355$	9.15251	−	30.1718i	0.485765	−	1.60135i
$356$	10.2479	−	3.41063i	0.543138	−	0.180763i
$357$	0.0524516	−	0.532550i	0.00277603	−	0.0281855i
$358$	−11.0271	+	24.1454i	−0.582800	+	1.27612i
$359$	−3.94015	+	19.8085i	−0.207953	+	1.04545i	0.725902	+	0.687798i	$0.241423\pi$
$359$	−3.94015	+	19.8085i	−0.207953	+	1.04545i	−0.933855	+	0.357652i	$0.883577\pi$
$360$	6.91722	−	8.27646i	0.364569	−	0.436208i
$361$	15.9271	−	3.16810i	0.838270	−	0.166742i
$362$	10.0857	+	16.3276i	0.530092	+	0.858157i
$363$	−5.08881	+	9.52049i	−0.267093	+	0.499696i
$364$	0.527428	−	0.235191i	0.0276448	−	0.0123274i
$365$	−5.45074	−	55.3422i	−0.285305	−	2.89675i
$366$	9.89432	+	3.39163i	0.517184	+	0.177283i
$367$	25.3571	−	10.5033i	1.32363	−	0.548266i	0.394800	−	0.918767i	$-0.370814\pi$
$367$	25.3571	−	10.5033i	1.32363	−	0.548266i	0.928832	+	0.370501i	$0.120814\pi$
$368$	−2.40967	+	6.82975i	−0.125613	+	0.356025i
$369$	−6.01879	−	2.49306i	−0.313326	−	0.129784i
$370$	18.8061	+	16.5920i	0.977682	+	0.862578i
$371$	−0.231366	−	0.189877i	−0.0120119	−	0.00985792i
$372$	−10.0742	+	2.28568i	−0.522325	+	0.118507i
$373$	−35.4024	+	10.7392i	−1.83307	+	0.556054i	−0.833069	+	0.553169i	$0.813419\pi$
$373$	−35.4024	+	10.7392i	−1.83307	+	0.556054i	−0.999996	+	0.00288563i	$0.999081\pi$
$374$	2.43498	−	3.37668i	0.125910	−	0.174604i
$375$	9.62631	−	14.4068i	0.497100	−	0.743963i
$376$	21.2176	+	9.01197i	1.09421	+	0.464757i
$377$	−15.2523	+	10.1913i	−0.785533	+	0.524876i
$378$	−0.0792829	−	0.0851574i	−0.00407787	−	0.00438002i
$379$	6.70511	+	8.17020i	0.344418	+	0.419675i	0.916194	−	0.400735i	$-0.131245\pi$
$379$	6.70511	+	8.17020i	0.344418	+	0.419675i	−0.571776	+	0.820410i	$0.693745\pi$
$380$	3.35304	−	12.2215i	0.172007	−	0.626950i
$381$	4.96788	−	2.65539i	0.254512	−	0.136040i
$382$	−1.38325	−	5.22465i	−0.0707730	−	0.267316i
$383$	16.2985			0.832812			0.416406	−	0.909179i	$-0.363289\pi$
$383$	16.2985			0.832812			0.416406	+	0.909179i	$0.363289\pi$
$384$	7.55982	+	8.41719i	0.385786	+	0.429538i
$385$	0.141999			0.00723694
$386$	−1.72889	−	6.53019i	−0.0879983	−	0.332378i
$387$	−3.58417	+	1.91578i	−0.182193	+	0.0973845i
$388$	−10.9839	−	3.01349i	−0.557623	−	0.152987i
$389$	−0.0969579	−	0.118144i	−0.00491596	−	0.00599012i	0.770547	−	0.637384i	$-0.219983\pi$
$389$	−0.0969579	−	0.118144i	−0.00491596	−	0.00599012i	−0.775463	+	0.631393i	$0.782483\pi$
$390$	−12.8979	−	13.8535i	−0.653110	−	0.701502i
$391$	9.79194	−	6.54277i	0.495200	−	0.330882i
$392$	−7.40554	−	18.3412i	−0.374036	−	0.926371i
$393$	3.20367	−	4.79464i	0.161604	−	0.241857i
$394$	−20.9114	+	28.9987i	−1.05350	+	1.46093i
$395$	−21.9808	+	6.66780i	−1.10597	+	0.335493i
$396$	−0.200277	−	0.882727i	−0.0100643	−	0.0443587i
$397$	−9.60390	−	7.88171i	−0.482006	−	0.395572i	0.361770	−	0.932267i	$-0.382172\pi$
$397$	−9.60390	−	7.88171i	−0.482006	−	0.395572i	−0.843776	+	0.536695i	$0.819672\pi$
$398$	7.19775	+	6.35035i	0.360791	+	0.318314i
$399$	−0.126296	−	0.0523136i	−0.00632272	−	0.00261896i
$400$	28.3982	+	25.5105i	1.41991	+	1.27553i
$401$	−34.7746	+	14.4041i	−1.73656	+	0.719308i	−0.737530	+	0.675314i	$0.764008\pi$
$401$	−34.7746	+	14.4041i	−1.73656	+	0.719308i	−0.999032	+	0.0439935i	$0.985992\pi$
$402$	21.1696	+	7.25661i	1.05584	+	0.361927i
$403$	1.77682	+	18.0404i	0.0885099	+	0.898656i
$404$	14.1751	+	31.7885i	0.705240	+	1.58154i
$405$	−1.79771	+	3.36329i	−0.0893291	+	0.167123i
$406$	−0.319593	−	0.517384i	−0.0158612	−	0.0256773i
$407$	2.06412	−	0.410578i	0.102314	−	0.0203516i
$408$	−1.63926	−	18.3238i	−0.0811557	−	0.907163i
$409$	−0.459058	+	2.30784i	−0.0226990	+	0.114115i	−0.990474	−	0.137702i	$-0.956028\pi$
$409$	−0.459058	+	2.30784i	−0.0226990	+	0.114115i	0.967775	+	0.251818i	$0.0810283\pi$
$410$	14.5960	−	31.9600i	0.720844	−	1.57839i
$411$	0.882985	−	8.96510i	0.0435545	−	0.442216i
$412$	−6.00591	−	18.0459i	−0.295890	−	0.889059i
$413$	−0.326422	+	1.07607i	−0.0160622	+	0.0529500i
$414$	0.341794	−	2.53765i	0.0167983	−	0.124719i
$415$	−36.1688	−	36.1688i	−1.77545	−	1.77545i
$416$	16.3085	−	11.3221i	0.799590	−	0.555113i
$417$	11.2671	−	11.2671i	0.551753	−	0.551753i
$418$	−0.644888	−	0.845647i	−0.0315425	−	0.0413619i
$419$	−4.09547	−	1.24235i	−0.200077	−	0.0606926i	0.188656	−	0.982043i	$-0.439587\pi$
$419$	−4.09547	−	1.24235i	−0.200077	−	0.0606926i	−0.388732	+	0.921351i	$0.627087\pi$
$420$	0.474246	−	0.410922i	0.0231408	−	0.0200509i
$421$	34.3695	+	3.38510i	1.67507	+	0.164980i	0.890476	−	0.455031i	$-0.150372\pi$
$421$	34.3695	+	3.38510i	1.67507	+	0.164980i	0.784593	+	0.620011i	$0.212872\pi$
$422$	−18.4998	+	6.89988i	−0.900556	+	0.335881i
$423$	−7.99357	−	1.59002i	−0.388661	−	0.0773094i
$424$	−9.03094	−	4.93158i	−0.438581	−	0.239498i
$425$	−12.1100	−	60.8809i	−0.587420	−	2.95316i
$426$	−11.3788	−	2.68899i	−0.551305	−	0.130282i
$427$	0.536636	+	0.286838i	0.0259696	+	0.0138811i
$428$	0.979712	+	36.6059i	0.0473562	+	1.76941i
$429$	−1.58074	+	0.155689i	−0.0763188	+	0.00751674i
$430$	−9.63553	−	19.6868i	−0.464667	−	0.949381i
$431$	12.3098	+	29.7186i	0.592944	+	1.43149i	0.880646	+	0.473775i	$0.157109\pi$
$431$	12.3098	+	29.7186i	0.592944	+	1.43149i	−0.287702	+	0.957720i	$0.592891\pi$
$432$	−3.22335	−	2.36855i	−0.155083	−	0.113957i
$433$	10.2346	−	24.7085i	0.491843	−	1.18741i	−0.461938	−	0.886912i	$-0.652846\pi$
$433$	10.2346	−	24.7085i	0.491843	−	1.18741i	0.953781	−	0.300502i	$-0.0971541\pi$
$434$	−0.599797	+	0.0375158i	−0.0287912	+	0.00180082i
$435$	−12.6451	+	15.4081i	−0.606285	+	0.738760i
$436$	−1.75849	−	2.48516i	−0.0842164	−	0.119018i
$437$	−0.873303	−	2.87889i	−0.0417758	−	0.137716i
$438$	−20.3567	+	3.29853i	−0.972678	+	0.157610i
$439$	24.6291	+	16.4566i	1.17548	+	0.785432i	0.980720	−	0.195419i	$-0.0626066\pi$
$439$	24.6291	+	16.4566i	1.17548	+	0.785432i	0.194762	+	0.980851i	$0.437607\pi$
$440$	4.79628	−	0.909485i	0.228653	−	0.0433580i
$441$	3.88523	+	5.81466i	0.185011	+	0.276889i
$442$	−32.2626	−	1.15255i	−1.53458	−	0.0548210i
$443$	28.8113	−	23.6448i	1.36887	−	1.12340i	0.389563	−	0.921000i	$-0.372626\pi$
$443$	28.8113	−	23.6448i	1.36887	−	1.12340i	0.979303	−	0.202399i	$-0.0648739\pi$
$444$	5.70556	−	7.34446i	0.270774	−	0.348553i
$445$	−9.70816	−	18.1627i	−0.460211	−	0.860994i
$446$	6.05188	−	10.4103i	0.286565	−	0.492942i
$447$		−	4.73478i		−	0.223947i
$448$	0.355810	+	0.553716i	0.0168104	+	0.0261606i
$449$		−	4.49527i		−	0.212145i	−0.994358	−	0.106072i	$-0.966172\pi$
$449$		−	4.49527i		−	0.212145i	0.994358	−	0.106072i	$-0.0338275\pi$
$450$	−11.6681	−	6.78309i	−0.550040	−	0.319758i
$451$	−1.38988	−	2.60028i	−0.0654468	−	0.122442i
$452$	−4.21005	+	0.528724i	−0.198024	+	0.0248691i
$453$	−4.21850	+	3.46203i	−0.198202	+	0.162660i
$454$	−0.819986	+	22.9534i	−0.0384838	+	1.07726i
$455$	−0.611770	−	0.915578i	−0.0286802	−	0.0429230i
$456$	−4.60095	−	0.958077i	−0.215459	−	0.0448661i
$457$	−6.65625	−	4.44756i	−0.311366	−	0.208048i	0.390062	−	0.920789i	$-0.372454\pi$
$457$	−6.65625	−	4.44756i	−0.311366	−	0.208048i	−0.701428	+	0.712740i	$0.747454\pi$
$458$	2.83572	+	17.5004i	0.132504	+	0.817741i
$459$	1.88810	+	6.22424i	0.0881291	+	0.290523i
$460$	13.6116	+	2.33081i	0.634644	+	0.108675i
$461$	1.82176	−	2.21983i	0.0848480	−	0.103388i	−0.728856	−	0.684667i	$-0.759948\pi$
$461$	1.82176	−	2.21983i	0.0848480	−	0.103388i	0.813704	+	0.581279i	$0.197448\pi$
$462$	−0.00328721	−	0.0525555i	−0.000152935	−	0.00244510i
$463$	−3.17151	+	7.65669i	−0.147392	+	0.355837i	−0.980282	−	0.197602i	$-0.936685\pi$
$463$	−3.17151	+	7.65669i	−0.147392	+	0.355837i	0.832890	+	0.553439i	$0.186685\pi$
$464$	−14.1086	−	15.4286i	−0.654977	−	0.716257i
$465$	7.53799	+	18.1983i	0.349566	+	0.843927i
$466$	11.7596	−	5.75562i	0.544751	−	0.266624i
$467$	−39.9006	+	3.92986i	−1.84638	+	0.181852i	−0.959792	−	0.280711i	$-0.909430\pi$
$467$	−39.9006	+	3.92986i	−1.84638	+	0.181852i	−0.886586	+	0.462563i	$0.846930\pi$
$468$	−4.82878	+	5.09437i	−0.223211	+	0.235487i
$469$	1.14817	+	0.613709i	0.0530175	+	0.0283385i
$470$	10.1090	−	42.7775i	0.466293	−	1.97318i
$471$	0.254930	+	1.28162i	0.0117466	+	0.0590539i
$472$	−4.13342	+	38.4370i	−0.190256	+	1.76920i
$473$	−1.80397	−	0.358831i	−0.0829465	−	0.0164991i
$474$	2.97668	+	7.98100i	0.136723	+	0.366580i
$475$	−15.7808	−	1.55427i	−0.724074	−	0.0713150i
$476$	0.0763697	−	1.06752i	0.00350040	−	0.0489299i
$477$	3.48132	+	1.05605i	0.159398	+	0.0483530i
$478$	−16.7508	+	12.7741i	−0.766166	+	0.584276i
$479$	21.3176	−	21.3176i	0.974024	−	0.974024i	−0.0256467	−	0.999671i	$-0.508165\pi$
$479$	21.3176	−	21.3176i	0.974024	−	0.974024i	0.999671	+	0.0256467i	$0.00816451\pi$
$480$	13.3866	−	16.9171i	0.611013	−	0.772157i
$481$	−11.5401	−	11.5401i	−0.526183	−	0.526183i
$482$	−13.3515	−	1.79830i	−0.608145	−	0.0819105i
$483$	0.0432414	−	0.142548i	0.00196755	−	0.00648616i
$484$	−9.66455	+	19.3065i	−0.439298	+	0.877566i
$485$	−2.12873	+	21.6134i	−0.0966608	+	0.981414i
$486$	1.28641	+	0.587497i	0.0583527	+	0.0266494i
$487$	−2.58285	+	12.9849i	−0.117040	+	0.588400i	0.877101	+	0.480307i	$0.159475\pi$
$487$	−2.58285	+	12.9849i	−0.117040	+	0.588400i	−0.994141	+	0.108093i	$0.965525\pi$
$488$	19.9630	+	6.25140i	0.903684	+	0.282987i
$489$	−16.2647	+	3.23524i	−0.735513	+	0.146303i
$490$	−32.0879	+	19.8210i	−1.44958	+	0.895422i
$491$	6.72443	−	12.5805i	0.303469	−	0.567751i	−0.683250	−	0.730184i	$-0.739434\pi$
$491$	6.72443	−	12.5805i	0.303469	−	0.567751i	0.986720	+	0.162433i	$0.0519341\pi$
$492$	−12.1667	−	4.66229i	−0.548516	−	0.210192i
$493$	3.33221	+	33.8325i	0.150075	+	1.52374i
$494$	−2.67419	+	7.80137i	−0.120318	+	0.351000i
$495$	−1.59458	+	0.660495i	−0.0716709	+	0.0296871i
$496$	−20.0190	+	5.10879i	−0.898878	+	0.229391i
$497$	−0.628424	−	0.260302i	−0.0281886	−	0.0116761i
$498$	−12.5492	+	14.2238i	−0.562343	+	0.637383i
$499$	−4.39671	−	3.60829i	−0.196824	−	0.161529i	0.530819	−	0.847485i	$-0.321884\pi$
$499$	−4.39671	−	3.60829i	−0.196824	−	0.161529i	−0.727643	+	0.685956i	$0.759384\pi$
$500$	18.4748	−	29.3183i	0.826220	−	1.31116i
$501$	−6.48577	+	1.96744i	−0.289763	+	0.0878986i
$502$	20.5865	+	14.8452i	0.918819	+	0.662575i
$503$	10.0108	−	14.9822i	0.446357	−	0.668021i	−0.538253	−	0.842783i	$-0.680916\pi$
$503$	10.0108	−	14.9822i	0.446357	−	0.668021i	0.984611	+	0.174762i	$0.0559156\pi$
$504$	−0.163066	−	0.166011i	−0.00726352	−	0.00739474i
$505$	55.1825	−	36.8718i	2.45559	−	1.64077i
$506$	0.848172	−	0.789663i	0.0377059	−	0.0351048i
$507$	−0.433017	−	0.527633i	−0.0192310	−	0.0234330i
$508$	9.79012	−	5.57470i	0.434366	−	0.247337i
$509$	−22.9504	+	12.2673i	−1.01726	+	0.543737i	−0.893731	−	0.448604i	$-0.851921\pi$
$509$	−22.9504	+	12.2673i	−1.01726	+	0.543737i	−0.123530	+	0.992341i	$0.539421\pi$
$510$	−33.9109	+	8.97804i	−1.50160	+	0.397554i
$511$	−1.19970			−0.0530718
$512$	15.5646	+	16.4238i	0.687866	+	0.725838i
$513$	1.66157			0.0733603
$514$	−10.5558	+	2.79470i	−0.465598	+	0.123269i
$515$	−31.9833	+	17.0954i	−1.40935	+	0.753315i
$516$	−7.06326	+	4.02197i	−0.310943	+	0.177057i
$517$	−2.34003	−	2.85134i	−0.102914	−	0.125402i
$518$	0.395992	−	0.368675i	0.0173989	−	0.0161986i
$519$	−1.64776	+	1.10100i	−0.0723284	+	0.0483283i
$520$	−26.5278	−	27.0070i	−1.16332	−	1.18434i
$521$	−20.3202	+	30.4114i	−0.890246	+	1.33235i	0.0524258	+	0.998625i	$0.483305\pi$
$521$	−20.3202	+	30.4114i	−0.890246	+	1.33235i	−0.942672	+	0.333722i	$0.891695\pi$
$522$	5.99544	+	4.32340i	0.262413	+	0.189230i
$523$	8.87262	−	2.69148i	0.387973	−	0.117690i	−0.0902714	−	0.995917i	$-0.528773\pi$
$523$	8.87262	−	2.69148i	0.387973	−	0.117690i	0.478244	+	0.878227i	$0.341273\pi$
$524$	6.14850	−	9.75727i	0.268599	−	0.426248i
$525$	−0.606941	−	0.498104i	−0.0264891	−	0.0217390i
$526$	25.8023	−	29.2454i	1.12503	−	1.27516i
$527$	31.0384	+	12.8565i	1.35205	+	0.560039i
$528$	−0.447643	−	1.75411i	−0.0194812	−	0.0763376i
$529$	−18.2205	+	7.54719i	−0.792197	+	0.328139i
$530$	−6.36217	+	18.5602i	−0.276355	+	0.806205i
$531$	−1.33969	−	13.6021i	−0.0581374	−	0.590279i
$532$	−0.255301	−	0.0978319i	−0.0110687	−	0.00424155i
$533$	−10.7781	+	20.1643i	−0.466850	+	0.873414i
$534$	−6.49749	+	4.01356i	−0.281174	+	0.173684i
$535$	68.4833	−	13.6222i	2.96079	−	0.588938i
$536$	42.7123	+	13.3753i	1.84489	+	0.577724i
$537$	3.66177	−	18.4090i	0.158017	−	0.794406i
$538$	16.7946	+	7.67003i	0.724069	+	0.330679i
$539$	−0.310224	+	3.14976i	−0.0133623	+	0.135670i
$540$	−3.41418	+	6.82036i	−0.146923	+	0.293501i
$541$	−10.7253	+	35.3565i	−0.461116	+	1.52010i	0.350872	+	0.936423i	$0.385885\pi$
$541$	−10.7253	+	35.3565i	−0.461116	+	1.52010i	−0.811989	+	0.583673i	$0.801615\pi$
$542$	10.0917	+	1.35925i	0.433477	+	0.0583846i
$543$	−9.59570	−	9.59570i	−0.411791	−	0.411791i
$544$	−4.25783	−	36.5468i	−0.182553	−	1.56693i
$545$	−4.10477	+	4.10477i	−0.175829	+	0.175829i
$546$	−0.324704	+	0.247619i	−0.0138961	+	0.0105971i
$547$	−1.96322	−	0.595537i	−0.0839413	−	0.0254633i	0.248035	−	0.968751i	$-0.420215\pi$
$547$	−1.96322	−	0.595537i	−0.0839413	−	0.0254633i	−0.331976	+	0.943288i	$0.607715\pi$
$548$	1.28563	−	17.9710i	0.0549194	−	0.767684i
$549$	−7.36036	−	0.724932i	−0.314132	−	0.0309393i
$550$	−2.13457	−	5.72315i	−0.0910182	−	0.244036i
$551$	8.51770	+	1.69428i	0.362866	+	0.0721786i
$552$	0.547558	−	5.09177i	0.0233056	−	0.216720i
$553$	0.0966753	+	0.486019i	0.00411105	+	0.0206677i
$554$	9.13439	−	38.6533i	0.388083	−	1.64222i
$555$	−15.6397	−	8.35958i	−0.663867	−	0.354844i
$556$	21.9233	−	23.1290i	0.929753	−	0.980889i
$557$	−17.0035	+	1.67470i	−0.720460	+	0.0709592i	−0.451601	−	0.892220i	$-0.649147\pi$
$557$	−17.0035	+	1.67470i	−0.720460	+	0.0709592i	−0.268860	+	0.963179i	$0.586647\pi$
$558$	6.56092	−	3.21119i	0.277746	−	0.135940i
$559$	5.45831	+	13.1775i	0.230862	+	0.557350i
$560$	0.926164	−	0.846925i	0.0391376	−	0.0357891i
$561$	−1.12652	+	2.71965i	−0.0475615	+	0.114824i
$562$	0.0545428	+	0.872022i	0.00230075	+	0.0367840i
$563$	0.0310414	−	0.0378241i	0.00130824	−	0.00159410i	−0.772356	−	0.635190i	$-0.780922\pi$
$563$	0.0310414	−	0.0378241i	0.00130824	−	0.00159410i	0.773664	+	0.633596i	$0.218422\pi$
$564$	−16.0665	−	2.75118i	−0.676522	−	0.115846i
$565$	2.34862	+	7.74237i	0.0988073	+	0.325724i
$566$	−4.92626	−	30.4021i	−0.207066	−	1.27789i
$567$	0.0684071	+	0.0457082i	0.00287283	+	0.00191956i
$568$	−22.8934	−	4.76719i	−0.960584	−	0.200027i
$569$	−1.47604	−	2.20904i	−0.0618787	−	0.0926080i	0.799240	−	0.601012i	$-0.205236\pi$
$569$	−1.47604	−	2.20904i	−0.0618787	−	0.0926080i	−0.861119	+	0.508404i	$0.830236\pi$
$570$	−0.319927	+	8.95554i	−0.0134003	+	0.375106i
$571$	−11.3641	+	9.32631i	−0.475575	+	0.390294i	−0.841420	−	0.540382i	$-0.818280\pi$
$571$	−11.3641	+	9.32631i	−0.475575	+	0.390294i	0.365845	+	0.930676i	$0.380780\pi$
$572$	−3.15201	+	0.395850i	−0.131792	+	0.0165513i
$573$	1.80152	+	3.37041i	0.0752597	+	0.140801i
$574$	−0.655306	−	0.380952i	−0.0273519	−	0.0159006i
$575$		−	17.2793i		−	0.720598i
$576$	−6.57113	−	4.56293i	−0.273797	−	0.190122i
$577$		−	29.1517i		−	1.21360i	−0.794854	−	0.606801i	$-0.792452\pi$
$577$		−	29.1517i		−	1.21360i	0.794854	−	0.606801i	$-0.207548\pi$
$578$	−17.9865	+	30.9400i	−0.748140	+	1.28693i
$579$	2.25169	+	4.21261i	0.0935770	+	0.175070i
$580$	−24.4566	+	31.4817i	−1.01551	+	1.30721i
$581$	−0.853012	+	0.700049i	−0.0353889	+	0.0290429i
$582$	8.04866	+	0.287529i	0.333628	+	0.0119185i
$583$	0.914731	+	1.36899i	0.0378843	+	0.0566979i
$584$	−40.5222	+	7.68395i	−1.67682	+	0.317964i
$585$	11.1286	+	7.43589i	0.460111	+	0.307436i
$586$	36.4843	−	5.91182i	1.50715	−	0.244215i
$587$	−11.1677	−	36.8150i	−0.460940	−	1.51952i	−0.812279	−	0.583269i	$-0.801773\pi$
$587$	−11.1677	−	36.8150i	−0.460940	−	1.51952i	0.351339	−	0.936248i	$-0.385727\pi$
$588$	8.07881	+	11.4173i	0.333165	+	0.470840i
$589$	5.44453	−	6.63418i	0.224338	−	0.273357i
$590$	73.5702	−	4.60163i	3.02884	−	0.189446i
$591$	9.67444	−	23.3562i	0.397953	−	0.960744i
$592$	11.0140	−	14.9890i	0.452674	−	0.616042i
$593$	6.27703	+	15.1541i	0.257767	+	0.622304i	0.998790	−	0.0491752i	$-0.0156593\pi$
$593$	6.27703	+	15.1541i	0.257767	+	0.622304i	−0.741023	+	0.671479i	$0.765659\pi$
$594$	0.281371	+	0.574882i	0.0115448	+	0.0235877i
$595$	−2.03093	+	0.200029i	−0.0832599	+	0.00820038i
$596$	−0.253350	−	9.46616i	−0.0103776	−	0.387749i
$597$	−5.98586	−	3.19951i	−0.244985	−	0.130947i
$598$	−8.74573	−	2.06675i	−0.357639	−	0.0845157i
$599$	8.07184	+	40.5799i	0.329807	+	1.65805i	0.688981	+	0.724779i	$0.258058\pi$
$599$	8.07184	+	40.5799i	0.329807	+	1.65805i	−0.359175	+	0.933270i	$0.616942\pi$
$600$	−23.6908	−	12.9370i	−0.967174	−	0.528150i
$601$	22.9927	+	4.57353i	0.937892	+	0.186558i	0.640291	−	0.768132i	$-0.278814\pi$
$601$	22.9927	+	4.57353i	0.937892	+	0.186558i	0.297601	+	0.954690i	$0.403814\pi$
$602$	−0.443043	+	0.165242i	−0.0180571	+	0.00673477i
$603$	−15.7480	−	1.55104i	−0.641307	−	0.0631632i
$604$	−8.24873	+	7.14731i	−0.335636	+	0.290820i
$605$	39.3956	+	11.9505i	1.60166	+	0.485859i
$606$	−14.9241	−	19.5702i	−0.606252	−	0.794983i
$607$	1.72803	−	1.72803i	0.0701384	−	0.0701384i	−0.671167	−	0.741306i	$-0.734207\pi$
$607$	1.72803	−	1.72803i	0.0701384	−	0.0701384i	0.741306	+	0.671167i	$0.234207\pi$
$608$	−9.24987	−	1.66928i	−0.375132	−	0.0676982i
$609$	0.304067	+	0.304067i	0.0123214	+	0.0123214i
$610$	5.32442	−	39.5312i	0.215580	−	1.60057i
$611$	−8.30331	+	27.3723i	−0.335916	+	1.10737i
$612$	4.10790	+	12.3430i	0.166052	+	0.498936i
$613$	−0.288436	+	2.92854i	−0.0116498	+	0.118283i	−0.999251	−	0.0387026i	$-0.987678\pi$
$613$	−0.288436	+	2.92854i	−0.0116498	+	0.118283i	0.987601	+	0.156985i	$0.0501775\pi$
$614$	−7.46620	+	16.3483i	−0.301311	+	0.659765i
$615$	−4.84689	+	24.3670i	−0.195446	+	0.982572i
$616$	−0.00938424	−	0.104898i	−0.000378102	−	0.00422644i
$617$	18.0954	−	3.59941i	0.728495	−	0.144907i	0.183110	−	0.983092i	$-0.441384\pi$
$617$	18.0954	−	3.59941i	0.728495	−	0.144907i	0.545385	+	0.838186i	$0.316384\pi$
$618$	7.06763	+	11.4417i	0.284302	+	0.460251i
$619$	1.25595	−	2.34972i	0.0504810	−	0.0944432i	−0.855416	−	0.517942i	$-0.826698\pi$
$619$	1.25595	−	2.34972i	0.0504810	−	0.0944432i	0.905897	+	0.423499i	$0.139198\pi$
$620$	16.0444	+	35.9803i	0.644357	+	1.44500i
$621$	0.177469	+	1.80188i	0.00712159	+	0.0723068i
$622$	25.3133	+	8.67703i	1.01497	+	0.347917i
$623$	−0.410475	+	0.170024i	−0.0164453	+	0.00681188i
$624$	−9.38152	+	10.4435i	−0.375561	+	0.418073i
$625$	−16.9627	−	7.02620i	−0.678510	−	0.281048i
$626$	−17.5786	−	15.5091i	−0.702583	−	0.619867i
$627$	0.581301	+	0.477062i	0.0232149	+	0.0190520i
$628$	0.578255	+	2.54868i	0.0230749	+	0.101703i
$629$	−28.9435	+	8.77990i	−1.15405	+	0.350078i
$630$	−0.259529	+	0.359899i	−0.0103399	+	0.0143387i
$631$	−2.28938	+	3.42630i	−0.0911387	+	0.136399i	−0.874237	−	0.485499i	$-0.838638\pi$
$631$	−2.28938	+	3.42630i	−0.0911387	+	0.136399i	0.783099	+	0.621898i	$0.213638\pi$
$632$	6.37828	+	15.7970i	0.253714	+	0.628371i
$633$	11.6086	−	7.75663i	0.461401	−	0.308298i
$634$	−24.4220	−	26.2315i	−0.969921	−	1.04179i
$635$	−13.6280	−	16.6058i	−0.540813	−	0.658982i
$636$	7.01665	+	1.92506i	0.278228	+	0.0763334i
$637$	21.6455	−	11.5698i	0.857626	−	0.458411i
$638$	0.856191	+	3.23392i	0.0338969	+	0.128032i
$639$	8.26765			0.327063
$640$	25.8585	−	34.5384i	1.02215	−	1.36525i
$641$	20.2964			0.801661			0.400830	−	0.916152i	$-0.368722\pi$
$641$	20.2964			0.801661			0.400830	+	0.916152i	$0.368722\pi$
$642$	−6.62709	−	25.0311i	−0.261550	−	0.987900i
$643$	−14.7492	+	7.88360i	−0.581651	+	0.310899i	−0.735854	−	0.677140i	$-0.763219\pi$
$643$	−14.7492	+	7.88360i	−0.581651	+	0.310899i	0.154203	+	0.988039i	$0.450719\pi$
$644$	0.0788244	−	0.287308i	0.00310612	−	0.0113215i
$645$	9.83221	+	11.9806i	0.387143	+	0.471735i
$646$	10.4147	+	11.1863i	0.409760	+	0.440121i
$647$	−1.82902	+	1.22211i	−0.0719062	+	0.0480462i	−0.591004	−	0.806669i	$-0.701268\pi$
$647$	−1.82902	+	1.22211i	−0.0719062	+	0.0480462i	0.519097	+	0.854715i	$0.326268\pi$
$648$	2.60333	+	1.10574i	0.102269	+	0.0434375i
$649$	3.43665	−	5.14332i	0.134900	−	0.201893i
$650$	−27.7053	+	38.4201i	−1.08669	+	1.50696i
$651$	0.406651	−	0.123356i	0.0159379	−	0.00483472i
$652$	−32.3445	+	7.33846i	−1.26671	+	0.287396i
$653$	12.3962	+	10.1733i	0.485102	+	0.398113i	0.844906	−	0.534915i	$-0.179656\pi$
$653$	12.3962	+	10.1733i	0.485102	+	0.398113i	−0.359804	+	0.933028i	$0.617156\pi$
$654$	1.61425	+	1.42420i	0.0631222	+	0.0556907i
$655$	−20.3170	−	8.41556i	−0.793849	−	0.328823i
$656$	−24.5741	−	8.67022i	−0.959458	−	0.338515i
$657$	13.4721	−	5.58032i	0.525596	−	0.217709i
$658$	−0.897042	−	0.307493i	−0.0349703	−	0.0119873i
$659$	−3.52467	−	35.7866i	−0.137302	−	1.39405i	−0.778968	−	0.627063i	$-0.784257\pi$
$659$	−3.52467	−	35.7866i	−0.137302	−	1.39405i	0.641667	−	0.766984i	$-0.278243\pi$
$660$	−3.15267	+	1.40584i	−0.122717	+	0.0547223i
$661$	−14.9982	+	28.0597i	−0.583364	+	1.09140i	0.401137	+	0.916018i	$0.368615\pi$
$661$	−14.9982	+	28.0597i	−0.583364	+	1.09140i	−0.984501	+	0.175379i	$0.943885\pi$
$662$	−11.1399	−	18.0341i	−0.432963	−	0.700916i
$663$	22.3890	−	4.45346i	0.869518	−	0.172958i
$664$	−24.3283	+	29.1089i	−0.944122	+	1.12964i
$665$	−0.101706	+	0.511308i	−0.00394397	+	0.0198277i
$666$	−2.73193	+	5.98195i	−0.105860	+	0.231796i
$667$	−0.927581	+	9.41789i	−0.0359161	+	0.364662i
$668$	−12.8616	+	4.28051i	−0.497631	+	0.165618i
$669$	−2.47168	+	8.14804i	−0.0955607	+	0.315022i
$670$	11.3920	−	84.5796i	0.440110	−	3.26760i
$671$	−2.36688	−	2.36688i	−0.0913724	−	0.0913724i
$672$	−0.334898	−	0.323179i	−0.0129190	−	0.0124669i
$673$	−17.1049	+	17.1049i	−0.659347	+	0.659347i	−0.955226	−	0.295879i	$-0.904388\pi$
$673$	−17.1049	+	17.1049i	−0.659347	+	0.659347i	0.295879	+	0.955226i	$0.404388\pi$
$674$	−15.6148	−	20.4759i	−0.601461	−	0.788701i
$675$	9.13252	+	2.77032i	0.351511	+	0.106630i
$676$	−0.893957	−	1.03172i	−0.0343830	−	0.0396815i
$677$	0.532383	+	0.0524352i	0.0204611	+	0.00201525i	0.108243	−	0.994125i	$-0.465478\pi$
$677$	0.532383	+	0.0524352i	0.0204611	+	0.00201525i	−0.0877814	+	0.996140i	$0.527978\pi$
$678$	2.81118	−	1.04849i	0.107963	−	0.0402669i
$679$	0.459531	+	0.0914063i	0.0176352	+	0.00350785i
$680$	−67.3171	+	19.7642i	−2.58149	+	0.757921i
$681$	−3.16844	−	15.9288i	−0.121415	−	0.610394i
$682$	3.21731	+	0.760301i	0.123197	+	0.0291134i
$683$	−23.5966	−	12.6126i	−0.902899	−	0.482609i	−0.0464963	−	0.998918i	$-0.514806\pi$
$683$	−23.5966	−	12.6126i	−0.902899	−	0.482609i	−0.856402	+	0.516309i	$0.827306\pi$
$684$	3.32196	−	0.0889082i	0.127018	−	0.00339949i
$685$	−34.1892	+	3.36734i	−1.30630	+	0.128660i
$686$	0.715742	+	1.46236i	0.0273271	+	0.0558333i
$687$	−4.79735	−	11.5818i	−0.183030	−	0.441874i
$688$	−13.9063	+	8.41900i	−0.530171	+	0.320971i
$689$	4.88605	−	11.7960i	0.186144	−	0.449391i
$690$	−9.74590	+	0.609581i	−0.371020	+	0.0232064i
$691$	−11.7781	+	14.3517i	−0.448061	+	0.545964i	−0.947236	−	0.320537i	$-0.896137\pi$
$691$	−11.7781	+	14.3517i	−0.448061	+	0.545964i	0.499175	+	0.866501i	$0.333637\pi$
$692$	−3.23542	+	2.28937i	−0.122992	+	0.0870288i
$693$	0.0108087	+	0.0356317i	0.000410590	+	0.00135353i
$694$	−14.0589	+	2.27807i	−0.533670	+	0.0864744i
$695$	−50.5252	−	33.7598i	−1.91653	−	1.28058i
$696$	12.2179	+	8.32290i	0.463119	+	0.315479i
$697$	23.5415	+	35.2324i	0.891698	+	1.33452i
$698$	34.1939	+	1.22154i	1.29426	+	0.0462360i
$699$	−7.15639	+	5.87310i	−0.270680	+	0.222141i
$700$	−1.24010	−	0.963374i	−0.0468714	−	0.0364121i
$701$	−11.0503	−	20.6736i	−0.417363	−	0.780830i	0.582116	−	0.813105i	$-0.302225\pi$
$701$	−11.0503	−	20.6736i	−0.417363	−	0.780830i	−0.999479	+	0.0322750i	$0.989725\pi$
$702$	2.49449	−	4.29096i	0.0941485	−	0.161952i
$703$			7.72652i			0.291411i
$704$	−0.988825	−	3.48300i	−0.0372678	−	0.131271i
$705$			31.0814i			1.17059i
$706$	36.7374	+	21.3568i	1.38263	+	0.803773i
$707$	−0.674937	−	1.26272i	−0.0253836	−	0.0474894i
$708$	−3.40623	−	27.1227i	−0.128014	−	1.01933i
$709$	10.5032	−	8.61976i	0.394456	−	0.323722i	−0.416169	−	0.909287i	$-0.636627\pi$
$709$	10.5032	−	8.61976i	0.394456	−	0.323722i	0.810625	+	0.585565i	$0.199127\pi$
$710$	−1.59189	+	44.5609i	−0.0597425	+	1.67234i
$711$	−3.34629	−	5.00808i	−0.125496	−	0.187818i
$712$	−12.7756	+	8.37192i	−0.478785	+	0.313751i
$713$	7.77588	+	5.19568i	0.291209	+	0.194580i
$714$	0.121048	+	0.747040i	0.00453011	+	0.0279573i
$715$	1.75839	+	5.79662i	0.0657599	+	0.216781i
$716$	6.33589	−	37.0007i	0.236783	−	1.38278i
$717$	9.44979	−	11.5146i	0.352909	−	0.430021i
$718$	−1.78301	−	28.5065i	−0.0665413	−	1.06385i
$719$	−1.43846	+	3.47275i	−0.0536454	+	0.129512i	−0.948430	−	0.316986i	$-0.897329\pi$
$719$	−1.43846	+	3.47275i	−0.0536454	+	0.129512i	0.894785	+	0.446498i	$0.147329\pi$
$720$	−6.46096	+	13.8185i	−0.240786	+	0.514986i
$721$	0.299402	+	0.722820i	0.0111503	+	0.0269192i
$722$	−20.6275	+	10.0959i	−0.767675	+	0.375732i
$723$	9.48032	−	0.933730i	0.352577	−	0.0347258i
$724$	−19.6980	−	18.6711i	−0.732070	−	0.693905i
$725$	43.9911	+	23.5137i	1.63379	+	0.873277i
$726$	3.51105	−	14.8575i	0.130307	−	0.551412i
$727$	1.42057	+	7.14170i	0.0526861	+	0.264871i	0.998146	−	0.0608682i	$-0.0193869\pi$
$727$	1.42057	+	7.14170i	0.0526861	+	0.264871i	−0.945460	+	0.325739i	$0.894387\pi$
$728$	−0.635927	+	0.512434i	−0.0235690	+	0.0189921i
$729$	−0.980785	−	0.195090i	−0.0363254	−	0.00722557i
$730$	27.4828	+	73.6861i	1.01718	+	2.72725i
$731$	26.3065	+	2.59097i	0.972982	+	0.0958304i
$732$	−14.7542	−	1.05550i	−0.545332	−	0.0390125i
$733$	2.46699	+	0.748352i	0.0911202	+	0.0276410i	0.335516	−	0.942035i	$-0.391089\pi$
$733$	2.46699	+	0.748352i	0.0911202	+	0.0276410i	−0.244395	+	0.969676i	$0.578589\pi$
$734$	−30.8644	+	23.5371i	−1.13923	+	0.868770i
$735$	18.8580	−	18.8580i	0.695590	−	0.695590i
$736$	0.822271	−	10.2092i	0.0303093	−	0.376316i
$737$	−5.06410	−	5.06410i	−0.186538	−	0.186538i
$738$	9.13072	+	1.22981i	0.336106	+	0.0452699i
$739$	13.4743	−	44.4187i	0.495659	−	1.63397i	−0.250438	−	0.968133i	$-0.580575\pi$
$739$	13.4743	−	44.4187i	0.495659	−	1.63397i	0.746098	−	0.665837i	$-0.231925\pi$
$740$	−31.7155	−	15.8763i	−1.16588	−	0.583625i
$741$	0.571587	−	5.80342i	0.0209978	−	0.213194i
$742$	0.385028	+	0.175841i	0.0141348	+	0.00645531i
$743$	9.43705	−	47.4433i	0.346212	−	1.74052i	−0.279203	−	0.960232i	$-0.590070\pi$
$743$	9.43705	−	47.4433i	0.346212	−	1.74052i	0.625415	−	0.780292i	$-0.284930\pi$
$744$	12.9453	−	6.77114i	0.474598	−	0.248242i
$745$	−17.7095	+	3.52265i	−0.648827	+	0.129060i
$746$	44.5120	−	27.4955i	1.62970	−	1.00668i
$747$	6.32268	−	11.8289i	0.231335	−	0.432797i
$748$	−2.10670	+	5.49763i	−0.0770286	+	0.201013i
$749$	−0.147650	−	1.49912i	−0.00539502	−	0.0547765i
$750$	−7.94573	+	23.1799i	−0.290137	+	0.846410i
$751$	18.0446	−	7.47431i	0.658456	−	0.272741i	−0.0283327	−	0.999599i	$-0.509020\pi$
$751$	18.0446	−	7.47431i	0.658456	−	0.272741i	0.686789	+	0.726857i	$0.259020\pi$
$752$	−32.2687	−	4.64069i	−1.17672	−	0.169229i
$753$	−16.5808	−	6.86799i	−0.604237	−	0.250283i
$754$	17.1629	−	19.4531i	0.625035	−	0.708441i
$755$	16.0876	+	13.2028i	0.585488	+	0.480498i
$756$	0.139211	+	0.0877233i	0.00506306	+	0.00319047i
$757$	33.2132	−	10.0751i	1.20715	−	0.366186i	0.378316	−	0.925676i	$-0.376503\pi$
$757$	33.2132	−	10.0751i	1.20715	−	0.366186i	0.828837	+	0.559490i	$0.189003\pi$
$758$	−12.1238	−	8.74267i	−0.440357	−	0.317548i
$759$	−0.455256	+	0.681339i	−0.0165248	+	0.0247311i
$760$	−0.160428	+	17.9218i	−0.00581932	+	0.650092i
$761$	10.2681	−	6.86092i	0.372218	−	0.248708i	−0.355365	−	0.934728i	$-0.615643\pi$
$761$	10.2681	−	6.86092i	0.372218	−	0.248708i	0.727583	+	0.686019i	$0.240643\pi$
$762$	−5.83053	+	5.42832i	−0.211218	+	0.196647i
$763$	0.0794482	+	0.0968079i	0.00287622	+	0.00350468i
$764$	3.78210	+	6.64202i	0.136832	+	0.240300i
$765$	21.8759	−	11.6929i	0.790923	−	0.422757i
$766$	−22.2818	+	5.89919i	−0.805074	+	0.213146i
$767$	−47.9690			−1.73206
$768$	−13.3817	−	8.77098i	−0.482871	−	0.316495i
$769$	34.2663			1.23568			0.617838	−	0.786306i	$-0.288009\pi$
$769$	34.2663			1.23568			0.617838	+	0.786306i	$0.288009\pi$
$770$	−0.194128	+	0.0513962i	−0.00699590	+	0.00185219i
$771$	6.80955	−	3.63978i	0.245240	−	0.131083i
$772$	4.72718	+	8.30173i	0.170135	+	0.298786i
$773$	6.74169	+	8.21478i	0.242482	+	0.295465i	0.880003	−	0.474968i	$-0.157540\pi$
$773$	6.74169	+	8.21478i	0.242482	+	0.295465i	−0.637521	+	0.770433i	$0.720040\pi$
$774$	4.20655	−	3.91636i	0.151201	−	0.140771i
$775$	40.9859	−	27.3859i	1.47226	−	0.983731i
$776$	16.1069	+	0.144182i	0.578206	+	0.00517583i
$777$	−0.212549	+	0.318101i	−0.00762514	+	0.0114118i
$778$	0.175314	+	0.126422i	0.00628531	+	0.00453244i
$779$	10.3585	−	3.14223i	0.371133	−	0.112582i
$780$	22.6471	+	14.2710i	0.810896	+	0.510983i
$781$	2.89243	+	2.37376i	0.103499	+	0.0849398i
$782$	−11.0185	+	12.4889i	−0.394022	+	0.446601i
$783$	−4.82885	−	2.00018i	−0.172569	−	0.0714805i
$784$	16.7628	+	22.3941i	0.598670	+	0.799788i
$785$	4.60399	−	1.90704i	0.164324	−	0.0680650i
$786$	−2.64437	+	7.71437i	−0.0943216	+	0.275162i
$787$	−4.00836	−	40.6976i	−0.142883	−	1.45071i	−0.752801	−	0.658248i	$-0.771298\pi$
$787$	−4.00836	−	40.6976i	−0.142883	−	1.45071i	0.609919	−	0.792464i	$-0.291202\pi$
$788$	18.0922	−	47.2132i	0.644508	−	1.68190i
$789$	−13.0000	+	24.3213i	−0.462812	+	0.865861i
$790$	27.6368	−	17.0715i	0.983273	−	0.607378i
$791$	0.171192	−	0.0340523i	0.00608690	−	0.00121076i
$792$	0.593302	+	1.13430i	0.0210821	+	0.0403055i
$793$	−5.06397	+	25.4583i	−0.179827	+	0.904050i
$794$	15.9824	+	7.29907i	0.567193	+	0.259034i
$795$	1.35986	−	13.8069i	0.0482293	−	0.489680i
$796$	−12.1386	−	6.07643i	−0.430242	−	0.215373i
$797$	−11.1255	+	36.6759i	−0.394086	+	1.29913i	0.505667	+	0.862729i	$0.331247\pi$
$797$	−11.1255	+	36.6759i	−0.394086	+	1.29913i	−0.899753	+	0.436399i	$0.856253\pi$
$798$	0.191596	+	0.0258059i	0.00678242	+	0.000913518i
$799$	37.4846	+	37.4846i	1.32611	+	1.32611i
$800$	−48.0569	−	24.5970i	−1.69907	−	0.869637i
$801$	3.81857	−	3.81857i	0.134923	−	0.134923i
$802$	42.3273	−	32.2786i	1.49463	−	1.13980i
$803$	6.31539	+	1.91575i	0.222865	+	0.0676054i
$804$	−31.5677	−	2.25832i	−1.11331	−	0.0796448i
$805$	−0.565345	−	0.0556816i	−0.0199258	−	0.00196252i
$806$	−8.95880	−	24.0201i	−0.315560	−	0.846072i
$807$	−12.8046	−	2.54699i	−0.450743	−	0.0896584i
$808$	−30.8848	−	38.3277i	−1.08652	−	1.34836i
$809$	−3.01263	−	15.1455i	−0.105918	−	0.532487i	−0.996916	−	0.0784790i	$-0.974994\pi$
$809$	−3.01263	−	15.1455i	−0.105918	−	0.532487i	0.890997	−	0.454008i	$-0.150006\pi$
$810$	1.24034	−	5.24866i	0.0435811	−	0.184419i
$811$	−2.95339	−	1.57862i	−0.103708	−	0.0554329i	0.418727	−	0.908112i	$-0.362476\pi$
$811$	−2.95339	−	1.57862i	−0.103708	−	0.0554329i	−0.522435	+	0.852679i	$0.674976\pi$
$812$	0.624186	+	0.591646i	0.0219046	+	0.0207627i
$813$	−7.16569	+	0.705759i	−0.251312	+	0.0247520i
$814$	−2.67327	+	1.30841i	−0.0936980	+	0.0458597i
$815$	24.2016	+	58.4279i	0.847746	+	2.04664i
$816$	8.87332	+	24.4573i	0.310628	+	0.856178i
$817$	2.58415	−	6.23870i	0.0904080	−	0.218264i
$818$	−0.207735	−	3.32123i	−0.00726327	−	0.116124i
$819$	0.183178	−	0.223203i	0.00640076	−	0.00779935i
$820$	−8.38648	+	48.9759i	−0.292869	+	1.71031i
$821$	12.8196	+	42.2605i	0.447406	+	1.47490i	0.833540	+	0.552458i	$0.186310\pi$
$821$	12.8196	+	42.2605i	0.447406	+	1.47490i	−0.386134	+	0.922443i	$0.626190\pi$
$822$	2.03776	+	12.5759i	0.0710750	+	0.438634i
$823$	45.5122	+	30.4103i	1.58645	+	1.06004i	0.959780	+	0.280755i	$0.0905847\pi$
$823$	45.5122	+	30.4103i	1.58645	+	1.06004i	0.626675	+	0.779281i	$0.284415\pi$
$824$	14.7424	+	22.4970i	0.513577	+	0.783719i
$825$	2.39961	+	3.59127i	0.0835438	+	0.125032i
$826$	0.0567744	−	1.58926i	0.00197543	−	0.0552973i
$827$	21.8720	−	17.9499i	0.760566	−	0.624180i	−0.172035	−	0.985091i	$-0.555034\pi$
$827$	21.8720	−	17.9499i	0.760566	−	0.624180i	0.932600	+	0.360911i	$0.117534\pi$
$828$	0.451227	+	3.59296i	0.0156812	+	0.124864i
$829$	−5.78922	−	10.8309i	−0.201068	−	0.376171i	0.761098	−	0.648637i	$-0.224661\pi$
$829$	−5.78922	−	10.8309i	−0.201068	−	0.376171i	−0.962165	+	0.272466i	$0.912161\pi$
$830$	62.5379	+	36.3555i	2.17072	+	1.26192i
$831$			28.0849i			0.974253i
$832$	−18.1975	+	21.3814i	−0.630885	+	0.741268i
$833$		−	45.4862i		−	1.57600i
$834$	−11.3253	+	19.4815i	−0.392163	+	0.674589i
$835$	12.1842	+	22.7950i	0.421652	+	0.788855i
$836$	1.18771	+	0.922678i	0.0410779	+	0.0319115i
$837$	−3.99271	+	3.27673i	−0.138008	+	0.113260i
$838$	6.04862	+	0.216080i	0.208946	+	0.00746437i
$839$	−1.73661	−	2.59902i	−0.0599544	−	0.0897282i	0.800281	−	0.599625i	$-0.204684\pi$
$839$	−1.73661	−	2.59902i	−0.0599544	−	0.0897282i	−0.860236	+	0.509897i	$0.829684\pi$
$840$	−0.499615	+	0.733428i	−0.0172383	+	0.0253057i
$841$	1.39808	+	0.934170i	0.0482098	+	0.0322128i
$842$	−48.2122	+	7.81217i	−1.66150	+	0.269225i
$843$	−0.179343	−	0.591215i	−0.00617690	−	0.0203625i
$844$	22.7939	−	16.1289i	0.784598	−	0.555178i
$845$	−1.65135	+	2.01218i	−0.0568082	+	0.0692210i
$846$	11.5036	−	0.719521i	0.395502	−	0.0247376i
$847$	0.339879	−	0.820540i	0.0116784	−	0.0281941i
$848$	14.1313	+	3.47328i	0.485270	+	0.119273i
$849$	8.33404	+	20.1202i	0.286024	+	0.690522i
$850$	38.5914	+	78.8478i	1.32367	+	2.70446i
$851$	−8.37893	+	0.825253i	−0.287226	+	0.0282893i
$852$	16.5294	−	0.442389i	0.566287	−	0.0151560i
$853$	−15.1743	−	8.11081i	−0.519557	−	0.277709i	0.190704	−	0.981648i	$-0.438923\pi$
$853$	−15.1743	−	8.11081i	−0.519557	−	0.277709i	−0.710261	+	0.703939i	$0.751423\pi$
$854$	−0.837462	−	0.197905i	−0.0286574	−	0.00677218i
$855$	−1.23620	−	6.21481i	−0.0422772	−	0.212542i
$856$	−14.5888	−	49.6897i	−0.498635	−	1.69836i
$857$	29.6934	+	5.90638i	1.01431	+	0.201758i	0.674137	−	0.738606i	$-0.264516\pi$
$857$	29.6934	+	5.90638i	1.01431	+	0.201758i	0.340169	+	0.940364i	$0.389516\pi$
$858$	2.10469	−	0.784989i	0.0718531	−	0.0267991i
$859$	4.44818	+	0.438108i	0.151770	+	0.0149480i	0.173617	−	0.984813i	$-0.444455\pi$
$859$	4.44818	+	0.438108i	0.151770	+	0.0149480i	−0.0218468	+	0.999761i	$0.506955\pi$
$860$	20.2984	+	23.4265i	0.692171	+	0.798836i
$861$	0.512901	+	0.155587i	0.0174796	+	0.00530239i
$862$	−27.5855	−	36.1731i	−0.939566	−	1.23206i
$863$	26.7998	−	26.7998i	0.912274	−	0.912274i	−0.0841764	−	0.996451i	$-0.526826\pi$
$863$	26.7998	−	26.7998i	0.912274	−	0.912274i	0.996451	+	0.0841764i	$0.0268259\pi$
$864$	5.26397	+	2.07139i	0.179084	+	0.0704700i
$865$	5.34399	+	5.34399i	0.181701	+	0.181701i
$866$	−5.04864	+	37.4836i	−0.171560	+	1.27375i
$867$	7.34597	−	24.2164i	0.249482	−	0.822433i
$868$	0.806411	−	0.268384i	0.0273714	−	0.00910953i
$869$	0.267192	−	2.71284i	0.00906385	−	0.0920269i
$870$	11.7103	−	25.6414i	0.397016	−	0.869325i
$871$	−10.8347	+	54.4697i	−0.367120	+	1.84564i
$872$	3.30355	+	2.76101i	0.111872	+	0.0934996i
$873$	−5.58547	+	1.11102i	−0.189039	+	0.0376023i
$874$	2.23591	+	3.61968i	0.0756309	+	0.122437i
$875$	−0.671989	+	1.25720i	−0.0227174	+	0.0425012i
$876$	26.6359	−	11.8775i	0.899944	−	0.401304i
$877$	−3.15855	−	32.0693i	−0.106657	−	1.08290i	−0.888327	−	0.459211i	$-0.848132\pi$
$877$	−3.15855	−	32.0693i	−0.106657	−	1.08290i	0.781671	−	0.623691i	$-0.214368\pi$
$878$	−39.6271	−	13.5836i	−1.33735	−	0.458424i
$879$	−24.1454	+	10.0014i	−0.814405	+	0.337337i
$880$	−6.22786	+	2.97937i	−0.209941	+	0.100435i
$881$	15.7567	+	6.52663i	0.530856	+	0.219888i	0.631978	−	0.774986i	$-0.282243\pi$
$881$	15.7567	+	6.52663i	0.530856	+	0.219888i	−0.101122	+	0.994874i	$0.532243\pi$
$882$	−7.41615	−	6.54304i	−0.249715	−	0.220315i
$883$	24.3246	+	19.9626i	0.818586	+	0.671796i	0.947463	−	0.319864i	$-0.103637\pi$
$883$	24.3246	+	19.9626i	0.818586	+	0.671796i	−0.128877	+	0.991661i	$0.541137\pi$
$884$	44.5237	−	10.1017i	1.49750	−	0.339758i
$885$	−49.8792	+	15.1307i	−1.67667	+	0.508613i
$886$	−30.8301	+	42.7533i	−1.03576	+	1.43632i
$887$	−18.1372	+	27.1443i	−0.608989	+	0.911416i	−0.999960	−	0.00898705i	$-0.997139\pi$
$887$	−18.1372	+	27.1443i	−0.608989	+	0.911416i	0.390971	+	0.920403i	$0.372139\pi$
$888$	−5.14182	+	12.1058i	−0.172548	+	0.406244i
$889$	−0.385339	+	0.257475i	−0.0129238	+	0.00863544i
$890$	19.8461	+	21.3166i	0.665242	+	0.714533i
$891$	−0.287114	−	0.349850i	−0.00961869	−	0.0117204i
$892$	−4.50561	+	16.4225i	−0.150859	+	0.549866i
$893$	11.9431	−	6.38371i	0.399660	−	0.213623i
$894$	1.71374	+	6.47297i	0.0573161	+	0.216488i
$895$	−71.5796			−2.39264
$896$	−0.686848	−	0.628206i	−0.0229460	−	0.0209869i
$897$	6.35449			0.212170
$898$	1.62705	+	6.14553i	0.0542954	+	0.205079i
$899$	−23.8090	+	12.7262i	−0.794074	+	0.424441i
$900$	18.4067	+	5.04999i	0.613558	+	0.168333i
$901$	−15.0113	−	18.2913i	−0.500099	−	0.609373i
$902$	2.84128	+	3.05181i	0.0946044	+	0.101614i
$903$	0.278010	−	0.185760i	0.00925158	−	0.00618171i
$904$	5.56424	−	2.24664i	0.185064	−	0.0747222i
$905$	−28.7518	+	43.0301i	−0.955741	+	1.43037i
$906$	4.51408	−	6.25986i	0.149970	−	0.207970i
$907$	10.5504	−	3.20041i	0.350319	−	0.106268i	−0.110221	−	0.993907i	$-0.535156\pi$
$907$	10.5504	−	3.20041i	0.350319	−	0.106268i	0.460540	+	0.887639i	$0.347656\pi$
$908$	−7.18693	−	31.6767i	−0.238507	−	1.05123i
$909$	13.4526	+	11.0403i	0.446195	+	0.366183i
$910$	1.16775	+	1.03027i	0.0387105	+	0.0341531i
$911$	−18.4770	−	7.65341i	−0.612169	−	0.253569i	0.0549865	−	0.998487i	$-0.482488\pi$
$911$	−18.4770	−	7.65341i	−0.612169	−	0.253569i	−0.667156	+	0.744918i	$0.732488\pi$
$912$	6.63678	−	0.355505i	0.219766	−	0.0117720i
$913$	5.60823	−	2.32301i	0.185605	−	0.0768803i
$914$	10.7096	+	3.67110i	0.354243	+	0.121429i
$915$	2.76459	+	28.0694i	0.0913946	+	0.927945i
$916$	−10.2110	−	22.8986i	−0.337380	−	0.756593i
$917$	−0.223641	+	0.418403i	−0.00738527	+	0.0138169i
$918$	−4.83410	−	7.82583i	−0.159549	−	0.258291i
$919$	8.26088	−	1.64319i	0.272501	−	0.0542039i	−0.0569480	−	0.998377i	$-0.518137\pi$
$919$	8.26088	−	1.64319i	0.272501	−	0.0542039i	0.329449	+	0.944173i	$0.393137\pi$
$920$	−19.4522	+	1.74021i	−0.641320	+	0.0573731i
$921$	2.47930	−	12.4643i	0.0816959	−	0.410713i
$922$	−1.68709	+	3.69413i	−0.0555614	+	0.121660i
$923$	2.84409	−	28.8766i	0.0936145	−	0.950484i
$924$	0.0235163	+	0.0706595i	0.000773631	+	0.00232453i
$925$	−12.8823	+	42.4673i	−0.423568	+	1.39632i
$926$	1.56448	−	11.6155i	0.0514119	−	0.381708i
$927$	−6.72427	−	6.72427i	−0.220854	−	0.220854i
$928$	24.8724	+	15.9861i	0.816478	+	0.524769i
$929$	−2.19868	+	2.19868i	−0.0721362	+	0.0721362i	−0.742254	−	0.670118i	$-0.766243\pi$
$929$	−2.19868	+	2.19868i	−0.0721362	+	0.0721362i	0.670118	+	0.742254i	$0.266243\pi$
$930$	−16.8921	−	22.1508i	−0.553915	−	0.726353i
$931$	−11.1194	−	3.37304i	−0.364425	−	0.110547i
$932$	−13.9934	+	12.1249i	−0.458369	+	0.397165i
$933$	−18.8305	−	1.85464i	−0.616483	−	0.0607183i
$934$	53.1261	−	19.8145i	1.73834	−	0.648350i
$935$	11.0105	+	2.19012i	0.360080	+	0.0716245i
$936$	4.75759	−	8.71233i	0.155507	−	0.284772i
$937$	0.615038	+	3.09201i	0.0200924	+	0.101011i	0.989530	−	0.144326i	$-0.0461013\pi$
$937$	0.615038	+	3.09201i	0.0200924	+	0.101011i	−0.969438	+	0.245337i	$0.921101\pi$
$938$	−1.79181	−	0.423431i	−0.0585045	−	0.0138255i
$939$	14.6189	+	7.81396i	0.477069	+	0.254999i
$940$	1.66312	+	62.1406i	0.0542449	+	2.02680i
$941$	−51.4570	+	5.06807i	−1.67745	+	0.165214i	−0.891483	−	0.453055i	$-0.850334\pi$
$941$	−51.4570	+	5.06807i	−1.67745	+	0.165214i	−0.785966	+	0.618269i	$0.787834\pi$
$942$	−0.812397	−	1.65985i	−0.0264693	−	0.0540807i
$943$	4.51393	+	10.8976i	0.146994	+	0.354874i
$944$	−8.26132	−	54.0437i	−0.268883	−	1.75897i
$945$	0.120068	−	0.289871i	0.00390582	−	0.00942949i
$946$	2.59610	−	0.162380i	0.0844066	−	0.00527942i
$947$	25.1557	−	30.6523i	0.817450	−	0.996066i	−0.182467	−	0.983212i	$-0.558408\pi$
$947$	25.1557	−	30.6523i	0.817450	−	0.996066i	0.999917	−	0.0128539i	$-0.00409165\pi$
$948$	−6.95816	−	9.83351i	−0.225991	−	0.319378i
$949$	−14.8561	−	48.9738i	−0.482248	−	1.58976i
$950$	22.1367	−	3.58697i	0.718210	−	0.116377i
$951$	21.0719	+	14.0798i	0.683302	+	0.456568i
$952$	0.281982	+	1.48707i	0.00913910	+	0.0481961i
$953$	−3.31165	−	4.95624i	−0.107275	−	0.160548i	0.773948	−	0.633249i	$-0.218279\pi$
$953$	−3.31165	−	4.95624i	−0.107275	−	0.160548i	−0.881223	+	0.472701i	$0.843279\pi$
$954$	−5.14158	−	0.183677i	−0.166465	−	0.00594677i
$955$	11.2661	−	9.24583i	0.364562	−	0.299188i
$956$	18.2767	−	23.5266i	0.591110	−	0.760905i
$957$	−1.11509	−	2.08619i	−0.0360459	−	0.0674371i
$958$	−21.4276	+	36.8593i	−0.692296	+	1.19087i
$959$			0.741151i			0.0239330i
$960$	−12.1779	+	27.9729i	−0.393040	+	0.902820i
$961$		−	4.32131i		−	0.139397i
$962$	19.9535	+	11.5997i	0.643327	+	0.373989i
$963$	8.63104	+	16.1475i	0.278131	+	0.520347i
$964$	18.9039	−	2.37407i	0.608853	−	0.0764636i
$965$	14.0812	−	11.5562i	0.453291	−	0.372007i
$966$	−0.00752095	+	0.210530i	−0.000241983	+	0.00677369i
$967$	7.66562	+	11.4724i	0.246510	+	0.368928i	0.934004	−	0.357262i	$-0.116290\pi$
$967$	7.66562	+	11.4724i	0.246510	+	0.368928i	−0.687495	+	0.726189i	$0.741290\pi$
$968$	6.22458	−	29.8921i	0.200066	−	0.960770i
$969$	−8.98603	−	6.00427i	−0.288673	−	0.192885i
$970$	−4.91271	−	30.3184i	−0.157738	−	0.973466i
$971$	−7.83960	−	25.8437i	−0.251585	−	0.829364i	−0.988216	−	0.153069i	$-0.951084\pi$
$971$	−7.83960	−	25.8437i	−0.251585	−	0.829364i	0.736631	−	0.676295i	$-0.236416\pi$
$972$	−1.97131	−	0.337561i	−0.0632297	−	0.0108273i
$973$	−0.831651	+	1.01337i	−0.0266615	+	0.0324871i
$974$	−1.16880	−	18.6866i	−0.0374507	−	0.598757i
$975$	12.8176	−	30.9443i	0.410491	−	0.991012i
$976$	−29.5544	−	1.32078i	−0.946013	−	0.0422770i
$977$	1.38271	+	3.33815i	0.0442367	+	0.106797i	0.944453	−	0.328645i	$-0.106592\pi$
$977$	1.38271	+	3.33815i	0.0442367	+	0.106797i	−0.900217	+	0.435442i	$0.856592\pi$
$978$	21.0646	−	10.3099i	0.673572	−	0.329674i
$979$	2.43229	−	0.239560i	0.0777365	−	0.00765637i
$980$	36.6935	−	38.7117i	1.17213	−	1.23660i
$981$	−1.34246	−	0.717558i	−0.0428613	−	0.0229099i
$982$	−4.63955	+	19.6329i	−0.148054	+	0.626510i
$983$	1.07441	+	5.40141i	0.0342683	+	0.172278i	0.994129	−	0.108197i	$-0.0345078\pi$
$983$	1.07441	+	5.40141i	0.0342683	+	0.172278i	−0.959861	+	0.280476i	$0.909508\pi$
$984$	18.3207	+	1.97017i	0.584043	+	0.0628066i
$985$	−94.5570	−	18.8086i	−3.01284	−	0.599291i
$986$	−16.8011	−	45.0467i	−0.535056	−	1.43458i
$987$	0.667307	+	0.0657240i	0.0212406	+	0.00209202i
$988$	0.832232	−	11.6333i	0.0264768	−	0.370103i
$989$	7.04149	+	2.13601i	0.223906	+	0.0679212i
$990$	1.94090	−	1.48012i	0.0616858	−	0.0470414i
$991$	23.1016	−	23.1016i	0.733845	−	0.733845i	−0.237534	−	0.971379i	$-0.576339\pi$
$991$	23.1016	−	23.1016i	0.733845	−	0.733845i	0.971379	+	0.237534i	$0.0763391\pi$
$992$	25.5191	−	14.2301i	0.810231	−	0.451806i
$993$	10.5987	+	10.5987i	0.336338	+	0.336338i
$994$	0.953341	+	0.128405i	0.0302381	+	0.00407275i
$995$	−7.51371	+	24.7694i	−0.238201	+	0.785242i
$996$	12.0079	−	23.9877i	0.380485	−	0.760078i
$997$	4.58393	−	46.5414i	0.145175	−	1.47398i	−0.596170	−	0.802858i	$-0.703312\pi$
$997$	4.58393	−	46.5414i	0.145175	−	1.47398i	0.741345	−	0.671124i	$-0.234188\pi$
$998$	7.31680	+	3.34155i	0.231609	+	0.105775i
$999$	0.907193	−	4.56077i	0.0287023	−	0.144296i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.2.v.a.229.2	yes	512
128.109	even	32	inner	384.2.v.a.109.2	✓	512

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
384.2.v.a.109.2	✓	512	128.109	even	32	inner
384.2.v.a.229.2	yes	512	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 384 = 2^{7} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	384.v (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.36711 + 0.361948i) q^{2} +(0.881921 - 0.471397i) q^{3} +(1.73799 - 0.989646i) q^{4} +(-2.41932 - 2.94794i) q^{5} +(-1.03506 + 0.963661i) q^{6} +(-0.0684071 + 0.0457082i) q^{7} +(-2.01782 + 1.98202i) q^{8} +(0.555570 - 0.831470i) q^{9} +O(q^{10})\)	\(q+(-1.36711 + 0.361948i) q^{2} +(0.881921 - 0.471397i) q^{3} +(1.73799 - 0.989646i) q^{4} +(-2.41932 - 2.94794i) q^{5} +(-1.03506 + 0.963661i) q^{6} +(-0.0684071 + 0.0457082i) q^{7} +(-2.01782 + 1.98202i) q^{8} +(0.555570 - 0.831470i) q^{9} +(4.37448 + 3.15450i) q^{10} +(0.433093 - 0.131377i) q^{11} +(1.06625 - 1.69207i) q^{12} +(-2.71297 - 2.22648i) q^{13} +(0.0769762 - 0.0872480i) q^{14} +(-3.52330 - 1.45940i) q^{15} +(2.04120 - 3.43999i) q^{16} +(-6.00920 + 2.48909i) q^{17} +(-0.458578 + 1.33780i) q^{18} +(0.162863 + 1.65357i) q^{19} +(-7.12216 - 2.72922i) q^{20} +(-0.0387830 + 0.0725579i) q^{21} +(-0.544534 + 0.336364i) q^{22} +(-1.77580 + 0.353229i) q^{23} +(-0.845244 + 2.69918i) q^{24} +(-1.86184 + 9.36009i) q^{25} +(4.51481 + 2.06189i) q^{26} +(0.0980171 - 0.995185i) q^{27} +(-0.0736558 + 0.147139i) q^{28} +(1.51723 - 5.00165i) q^{29} +(5.34497 + 0.719909i) q^{30} +(-3.65231 - 3.65231i) q^{31} +(-1.54545 + 5.44165i) q^{32} +(0.320023 - 0.320023i) q^{33} +(7.31433 - 5.57788i) q^{34} +(0.300244 + 0.0910779i) q^{35} +(0.142713 - 1.99490i) q^{36} +(4.62773 + 0.455791i) q^{37} +(-0.821159 - 2.20167i) q^{38} +(-3.44218 - 0.684693i) q^{39} +(10.7246 + 1.15330i) q^{40} +(-1.27095 - 6.38951i) q^{41} +(0.0267585 - 0.113232i) q^{42} +(-3.58417 - 1.91578i) q^{43} +(0.622693 - 0.656941i) q^{44} +(-3.79523 + 0.373797i) q^{45} +(2.29987 - 1.12565i) q^{46} +(-3.11894 - 7.52978i) q^{47} +(0.178581 - 3.99601i) q^{48} +(-2.67619 + 6.46090i) q^{49} +(-0.842525 - 13.4702i) q^{50} +(-4.12629 + 5.02790i) q^{51} +(-6.91854 - 1.18471i) q^{52} +(1.05605 + 3.48132i) q^{53} +(0.226205 + 1.39601i) q^{54} +(-1.43508 - 0.958890i) q^{55} +(0.0474390 - 0.227815i) q^{56} +(0.923122 + 1.38155i) q^{57} +(-0.263891 + 7.38698i) q^{58} +(10.5654 - 8.67080i) q^{59} +(-7.56773 + 0.950403i) q^{60} +(-3.48644 - 6.52266i) q^{61} +(6.31506 + 3.67117i) q^{62} +0.0822726i q^{63} +(0.143213 - 7.99872i) q^{64} +13.3842i q^{65} +(-0.321675 + 0.553339i) q^{66} +(-7.45946 - 13.9557i) q^{67} +(-7.98060 + 10.2730i) q^{68} +(-1.39961 + 1.14863i) q^{69} +(-0.443432 - 0.0158411i) q^{70} +(4.59326 + 6.87430i) q^{71} +(0.526945 + 2.77891i) q^{72} +(12.1245 + 8.10136i) q^{73} +(-6.49159 + 1.05188i) q^{74} +(2.77032 + 9.13252i) q^{75} +(1.91951 + 2.71271i) q^{76} +(-0.0236216 + 0.0287830i) q^{77} +(4.95367 - 0.309840i) q^{78} +(2.30496 - 5.56468i) q^{79} +(-15.0792 + 2.30506i) q^{80} +(-0.382683 - 0.923880i) q^{81} +(4.05021 + 8.27516i) q^{82} +(13.3481 - 1.31467i) q^{83} +(0.00440227 + 0.164486i) q^{84} +(21.8759 + 11.6929i) q^{85} +(5.59337 + 1.32180i) q^{86} +(-1.01968 - 5.12628i) q^{87} +(-0.613512 + 1.12349i) q^{88} +(5.29652 + 1.05354i) q^{89} +(5.05320 - 1.88470i) q^{90} +(0.287355 + 0.0283020i) q^{91} +(-2.73675 + 2.37133i) q^{92} +(-4.94273 - 1.49936i) q^{93} +(6.98932 + 9.16515i) q^{94} +(4.48063 - 4.48063i) q^{95} +(1.20221 + 5.52763i) q^{96} +(-4.02690 - 4.02690i) q^{97} +(1.32014 - 9.80142i) q^{98} +(0.131377 - 0.433093i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 512 q+O(q^{10}) \) 512 * q	\( 512 q - 96 q^{50} - 96 q^{52} - 32 q^{54} - 224 q^{56} - 192 q^{60} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 192 q^{70} - 224 q^{74} - 32 q^{76} - 96 q^{78} - 96 q^{80}+O(q^{100}) \) 512 * q - 96 * q^50 - 96 * q^52 - 32 * q^54 - 224 * q^56 - 192 * q^60 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 192 * q^70 - 224 * q^74 - 32 * q^76 - 96 * q^78 - 96 * q^80

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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