LMFDB - Embedded newform 378.2.z.a.293.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(41,378)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(378, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([17, 9]))

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

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

chi := DirichletCharacter("378.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.z (of order $18$, degree $6$, 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:	$3.01834519640$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$24$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			293.14
Character	$\chi$	$=$	378.293
Dual form			378.2.z.a.209.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.342020 - 0.939693i) q^{2} +(-1.71772 - 0.222380i) q^{3} +(-0.766044 - 0.642788i) q^{4} +(0.673387 - 3.81897i) q^{5} +(-0.796462 + 1.53807i) q^{6} +(-2.61421 + 0.407338i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(2.90109 + 0.763972i) q^{9} +O(q^{10})$	\(q+(0.342020 - 0.939693i) q^{2} +(-1.71772 - 0.222380i) q^{3} +(-0.766044 - 0.642788i) q^{4} +(0.673387 - 3.81897i) q^{5} +(-0.796462 + 1.53807i) q^{6} +(-2.61421 + 0.407338i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(2.90109 + 0.763972i) q^{9} +(-3.35834 - 1.93894i) q^{10} +(-1.75486 + 0.309429i) q^{11} +(1.17290 + 1.27448i) q^{12} +(0.186600 + 0.512680i) q^{13} +(-0.511339 + 2.59587i) q^{14} +(-2.00595 + 6.41015i) q^{15} +(0.173648 + 0.984808i) q^{16} +(0.365471 - 0.633014i) q^{17} +(1.71013 - 2.46484i) q^{18} +(-4.82869 + 2.78784i) q^{19} +(-2.97063 + 2.49265i) q^{20} +(4.58105 - 0.118342i) q^{21} +(-0.309429 + 1.75486i) q^{22} +(1.91324 - 2.28011i) q^{23} +(1.59878 - 0.666271i) q^{24} +(-9.43258 - 3.43318i) q^{25} +0.545583 q^{26} +(-4.81336 - 1.95743i) q^{27} +(2.26443 + 1.36834i) q^{28} +(-0.179723 + 0.493784i) q^{29} +(5.33749 + 4.07738i) q^{30} +(-2.55787 + 3.04836i) q^{31} +(0.984808 + 0.173648i) q^{32} +(3.08316 - 0.141265i) q^{33} +(-0.469840 - 0.559934i) q^{34} +(-0.204763 + 10.2579i) q^{35} +(-1.73130 - 2.45002i) q^{36} +(2.56696 - 4.44610i) q^{37} +(0.968208 + 5.49098i) q^{38} +(-0.206516 - 0.922135i) q^{39} +(1.32631 + 3.64401i) q^{40} +(-8.29798 + 3.02022i) q^{41} +(1.45561 - 4.34525i) q^{42} +(-2.17178 - 12.3168i) q^{43} +(1.54320 + 0.890967i) q^{44} +(4.87114 - 10.5647i) q^{45} +(-1.48824 - 2.57770i) q^{46} +(3.84942 - 3.23005i) q^{47} +(-0.0792764 - 1.73024i) q^{48} +(6.66815 - 2.12973i) q^{49} +(-6.45227 + 7.68951i) q^{50} +(-0.768545 + 1.00606i) q^{51} +(0.186600 - 0.512680i) q^{52} +6.08851i q^{53} +(-3.48565 + 3.85360i) q^{54} +6.91012i q^{55} +(2.06030 - 1.65987i) q^{56} +(8.91427 - 3.71492i) q^{57} +(0.402536 + 0.337768i) q^{58} +(2.16758 - 12.2930i) q^{59} +(5.65701 - 3.62106i) q^{60} +(-5.59146 - 6.66364i) q^{61} +(1.98967 + 3.44621i) q^{62} +(-7.89525 - 0.815456i) q^{63} +(0.500000 - 0.866025i) q^{64} +(2.08356 - 0.367388i) q^{65} +(0.921758 - 2.94554i) q^{66} +(9.60642 - 3.49645i) q^{67} +(-0.686860 + 0.249997i) q^{68} +(-3.79346 + 3.49112i) q^{69} +(9.56920 + 3.70081i) q^{70} +(8.89149 + 5.13351i) q^{71} +(-2.89441 + 0.788928i) q^{72} +(3.00231 - 1.73338i) q^{73} +(-3.30002 - 3.93281i) q^{74} +(15.4390 + 7.99485i) q^{75} +(5.49098 + 0.968208i) q^{76} +(4.46153 - 1.52373i) q^{77} +(-0.937156 - 0.121327i) q^{78} +(-9.95144 - 3.62203i) q^{79} +3.87788 q^{80} +(7.83269 + 4.43271i) q^{81} +8.83052i q^{82} +(6.14522 + 2.23668i) q^{83} +(-3.58535 - 2.85399i) q^{84} +(-2.17136 - 1.82198i) q^{85} +(-12.3168 - 2.17178i) q^{86} +(0.418520 - 0.808214i) q^{87} +(1.36504 - 1.14540i) q^{88} +(0.0632320 + 0.109521i) q^{89} +(-8.26157 - 8.19073i) q^{90} +(-0.696646 - 1.26424i) q^{91} +(-2.93126 + 0.516860i) q^{92} +(5.07159 - 4.66739i) q^{93} +(-1.71867 - 4.72201i) q^{94} +(7.39510 + 20.3179i) q^{95} +(-1.65300 - 0.517280i) q^{96} +(6.93239 - 1.22237i) q^{97} +(0.279351 - 6.99442i) q^{98} +(-5.32741 - 0.442981i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 12 q^{9}+O(q^{10}) $ 144 * q - 12 * q^9	$ 144 q - 12 q^{9} + 12 q^{11} + 6 q^{14} + 12 q^{15} + 24 q^{21} - 60 q^{23} + 12 q^{29} - 72 q^{30} + 54 q^{35} - 12 q^{36} + 48 q^{39} + 24 q^{42} + 18 q^{49} - 60 q^{50} - 36 q^{51} + 6 q^{56} - 60 q^{57} - 36 q^{60} - 78 q^{63} + 72 q^{64} - 120 q^{65} + 36 q^{70} - 72 q^{71} - 24 q^{72} - 36 q^{74} + 66 q^{77} - 60 q^{78} - 72 q^{79} + 12 q^{84} - 72 q^{85} - 48 q^{86} - 18 q^{91} + 12 q^{92} + 24 q^{93} - 120 q^{95} + 36 q^{98} + 144 q^{99}+O(q^{100}) $ 144 * q - 12 * q^9 + 12 * q^11 + 6 * q^14 + 12 * q^15 + 24 * q^21 - 60 * q^23 + 12 * q^29 - 72 * q^30 + 54 * q^35 - 12 * q^36 + 48 * q^39 + 24 * q^42 + 18 * q^49 - 60 * q^50 - 36 * q^51 + 6 * q^56 - 60 * q^57 - 36 * q^60 - 78 * q^63 + 72 * q^64 - 120 * q^65 + 36 * q^70 - 72 * q^71 - 24 * q^72 - 36 * q^74 + 66 * q^77 - 60 * q^78 - 72 * q^79 + 12 * q^84 - 72 * q^85 - 48 * q^86 - 18 * q^91 + 12 * q^92 + 24 * q^93 - 120 * q^95 + 36 * q^98 + 144 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{11}{18}\right)$	$-1$

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 $

$2$	0.342020	−	0.939693i	0.241845	−	0.664463i
$2$	0.342020	−	0.939693i	0.241845	−	0.664463i
$3$	−1.71772	−	0.222380i	−0.991724	−	0.128391i
$3$	−1.71772	−	0.222380i	−0.991724	−	0.128391i
$4$	−0.766044	−	0.642788i	−0.383022	−	0.321394i
$5$	0.673387	−	3.81897i	0.301148	−	1.70789i	−0.339958	−	0.940441i	$-0.610413\pi$
$5$	0.673387	−	3.81897i	0.301148	−	1.70789i	0.641106	−	0.767453i	$-0.278476\pi$
$6$	−0.796462	+	1.53807i	−0.325154	+	0.627913i
$7$	−2.61421	+	0.407338i	−0.988077	+	0.153959i
$7$	−2.61421	+	0.407338i	−0.988077	+	0.153959i
$8$	−0.866025	+	0.500000i	−0.306186	+	0.176777i
$9$	2.90109	+	0.763972i	0.967031	+	0.254657i
$10$	−3.35834	−	1.93894i	−1.06200	−	0.613147i
$11$	−1.75486	+	0.309429i	−0.529111	+	0.0932965i	−0.431821	−	0.901960i	$-0.642129\pi$
$11$	−1.75486	+	0.309429i	−0.529111	+	0.0932965i	−0.0972902	+	0.995256i	$0.531018\pi$
$12$	1.17290	+	1.27448i	0.338588	+	0.367911i
$13$	0.186600	+	0.512680i	0.0517536	+	0.142192i	0.962876	−	0.269944i	$-0.0870052\pi$
$13$	0.186600	+	0.512680i	0.0517536	+	0.142192i	−0.911122	+	0.412136i	$0.864783\pi$
$14$	−0.511339	+	2.59587i	−0.136661	+	0.693775i
$15$	−2.00595	+	6.41015i	−0.517934	+	1.65509i
$16$	0.173648	+	0.984808i	0.0434120	+	0.246202i
$17$	0.365471	−	0.633014i	0.0886397	−	0.153528i	−0.818297	−	0.574796i	$-0.805081\pi$
$17$	0.365471	−	0.633014i	0.0886397	−	0.153528i	0.906936	+	0.421268i	$0.138415\pi$
$18$	1.71013	−	2.46484i	0.403082	−	0.580969i
$19$	−4.82869	+	2.78784i	−1.10778	+	0.639575i	−0.938253	−	0.345951i	$-0.887556\pi$
$19$	−4.82869	+	2.78784i	−1.10778	+	0.639575i	−0.169524	+	0.985526i	$0.554223\pi$
$20$	−2.97063	+	2.49265i	−0.664253	+	0.557374i
$21$	4.58105	−	0.118342i	0.999666	−	0.0258244i
$22$	−0.309429	+	1.75486i	−0.0659706	+	0.374138i
$23$	1.91324	−	2.28011i	0.398939	−	0.475437i	−0.528757	−	0.848773i	$-0.677342\pi$
$23$	1.91324	−	2.28011i	0.398939	−	0.475437i	0.927696	+	0.373336i	$0.121786\pi$
$24$	1.59878	−	0.666271i	0.326349	−	0.136002i
$25$	−9.43258	−	3.43318i	−1.88652	−	0.686636i
$26$	0.545583			0.106998
$27$	−4.81336	−	1.95743i	−0.926332	−	0.376708i
$28$	2.26443	+	1.36834i	0.427937	+	0.258592i
$29$	−0.179723	+	0.493784i	−0.0333737	+	0.0916934i	−0.955260	−	0.295766i	$-0.904425\pi$
$29$	−0.179723	+	0.493784i	−0.0333737	+	0.0916934i	0.921887	+	0.387460i	$0.126647\pi$
$30$	5.33749	+	4.07738i	0.974489	+	0.744424i
$31$	−2.55787	+	3.04836i	−0.459408	+	0.547501i	−0.945165	−	0.326593i	$-0.894099\pi$
$31$	−2.55787	+	3.04836i	−0.459408	+	0.547501i	0.485757	+	0.874094i	$0.338544\pi$
$32$	0.984808	+	0.173648i	0.174091	+	0.0306970i
$33$	3.08316	−	0.141265i	0.536710	−	0.0245911i
$34$	−0.469840	−	0.559934i	−0.0805769	−	0.0960278i
$35$	−0.204763	+	10.2579i	−0.0346113	+	1.73389i
$36$	−1.73130	−	2.45002i	−0.288549	−	0.408337i
$37$	2.56696	−	4.44610i	0.422005	−	0.730934i	−0.574130	−	0.818764i	$-0.694660\pi$
$37$	2.56696	−	4.44610i	0.422005	−	0.730934i	0.996136	+	0.0878296i	$0.0279931\pi$
$38$	0.968208	+	5.49098i	0.157064	+	0.890754i
$39$	−0.206516	−	0.922135i	−0.0330691	−	0.147660i
$40$	1.32631	+	3.64401i	0.209708	+	0.576169i
$41$	−8.29798	+	3.02022i	−1.29593	+	0.471679i	−0.895668	−	0.444724i	$-0.853302\pi$
$41$	−8.29798	+	3.02022i	−1.29593	+	0.471679i	−0.400258	+	0.916402i	$0.631080\pi$
$42$	1.45561	−	4.34525i	0.224605	−	0.670487i
$43$	−2.17178	−	12.3168i	−0.331193	−	1.87829i	−0.461997	−	0.886881i	$-0.652867\pi$
$43$	−2.17178	−	12.3168i	−0.331193	−	1.87829i	0.130804	−	0.991408i	$-0.458244\pi$
$44$	1.54320	+	0.890967i	0.232646	+	0.134318i
$45$	4.87114	−	10.5647i	0.726147	−	1.57490i
$46$	−1.48824	−	2.57770i	−0.219429	−	0.380062i
$47$	3.84942	−	3.23005i	0.561496	−	0.471151i	−0.317316	−	0.948320i	$-0.602781\pi$
$47$	3.84942	−	3.23005i	0.561496	−	0.471151i	0.878812	+	0.477169i	$0.158337\pi$
$48$	−0.0792764	−	1.73024i	−0.0114426	−	0.249738i
$49$	6.66815	−	2.12973i	0.952593	−	0.304247i
$50$	−6.45227	+	7.68951i	−0.912488	+	1.08746i
$51$	−0.768545	+	1.00606i	−0.107618	+	0.140877i
$52$	0.186600	−	0.512680i	0.0258768	−	0.0710960i
$53$			6.08851i			0.836322i	0.908373	+	0.418161i	$0.137325\pi$
$53$			6.08851i			0.836322i	−0.908373	+	0.418161i	$0.862675\pi$
$54$	−3.48565	+	3.85360i	−0.474337	+	0.524408i
$55$			6.91012i			0.931761i
$56$	2.06030	−	1.65987i	0.275319	−	0.221809i
$57$	8.91427	−	3.71492i	1.18072	−	0.492053i
$58$	0.402536	+	0.337768i	0.0528556	+	0.0443511i
$59$	2.16758	−	12.2930i	0.282195	−	1.60041i	−0.432941	−	0.901422i	$-0.642524\pi$
$59$	2.16758	−	12.2930i	0.282195	−	1.60041i	0.715136	−	0.698985i	$-0.246365\pi$
$60$	5.65701	−	3.62106i	0.730317	−	0.467477i
$61$	−5.59146	−	6.66364i	−0.715913	−	0.853192i	0.278314	−	0.960490i	$-0.410224\pi$
$61$	−5.59146	−	6.66364i	−0.715913	−	0.853192i	−0.994227	+	0.107298i	$0.965780\pi$
$62$	1.98967	+	3.44621i	0.252689	+	0.437670i
$63$	−7.89525	−	0.815456i	−0.994708	−	0.102738i
$64$	0.500000	−	0.866025i	0.0625000	−	0.108253i
$65$	2.08356	−	0.367388i	0.258434	−	0.0455689i
$66$	0.921758	−	2.94554i	0.113461	−	0.362571i
$67$	9.60642	−	3.49645i	1.17361	−	0.427160i	0.319670	−	0.947529i	$-0.396428\pi$
$67$	9.60642	−	3.49645i	1.17361	−	0.427160i	0.853941	+	0.520369i	$0.174206\pi$
$68$	−0.686860	+	0.249997i	−0.0832941	+	0.0303166i
$69$	−3.79346	+	3.49112i	−0.456679	+	0.420281i
$70$	9.56920	+	3.70081i	1.14374	+	0.442331i
$71$	8.89149	+	5.13351i	1.05523	+	0.609235i	0.924108	−	0.382132i	$-0.124810\pi$
$71$	8.89149	+	5.13351i	1.05523	+	0.609235i	0.131118	+	0.991367i	$0.458143\pi$
$72$	−2.89441	+	0.788928i	−0.341109	+	0.0929760i
$73$	3.00231	−	1.73338i	0.351393	−	0.202877i	−0.313905	−	0.949454i	$-0.601637\pi$
$73$	3.00231	−	1.73338i	0.351393	−	0.202877i	0.665299	+	0.746577i	$0.268304\pi$
$74$	−3.30002	−	3.93281i	−0.383619	−	0.457179i
$75$	15.4390	+	7.99485i	1.78275	+	0.923165i
$76$	5.49098	+	0.968208i	0.629858	+	0.111061i
$77$	4.46153	−	1.52373i	0.508438	−	0.173646i
$78$	−0.937156	−	0.121327i	−0.106112	−	0.0137376i
$79$	−9.95144	−	3.62203i	−1.11962	−	0.407510i	−0.285109	−	0.958495i	$-0.592030\pi$
$79$	−9.95144	−	3.62203i	−1.11962	−	0.407510i	−0.834515	+	0.550985i	$0.814252\pi$
$80$	3.87788			0.433560
$81$	7.83269	+	4.43271i	0.870299	+	0.492523i
$82$			8.83052i			0.975168i
$83$	6.14522	+	2.23668i	0.674526	+	0.245507i	0.656495	−	0.754330i	$-0.272038\pi$
$83$	6.14522	+	2.23668i	0.674526	+	0.245507i	0.0180304	+	0.999837i	$0.494260\pi$
$84$	−3.58535	−	2.85399i	−0.391194	−	0.311395i
$85$	−2.17136	−	1.82198i	−0.235517	−	0.197622i
$86$	−12.3168	−	2.17178i	−1.32815	−	0.234189i
$87$	0.418520	−	0.808214i	0.0448701	−	0.0866496i
$88$	1.36504	−	1.14540i	0.145514	−	0.122101i
$89$	0.0632320	+	0.109521i	0.00670258	+	0.0116092i	0.869357	−	0.494184i	$-0.164533\pi$
$89$	0.0632320	+	0.109521i	0.00670258	+	0.0116092i	−0.862655	+	0.505793i	$0.831200\pi$
$90$	−8.26157	−	8.19073i	−0.870846	−	0.863378i
$91$	−0.696646	−	1.26424i	−0.0730283	−	0.132529i
$92$	−2.93126	+	0.516860i	−0.305605	+	0.0538864i
$93$	5.07159	−	4.66739i	0.525900	−	0.483986i
$94$	−1.71867	−	4.72201i	−0.177268	−	0.487039i
$95$	7.39510	+	20.3179i	0.758722	+	2.08457i
$96$	−1.65300	−	0.517280i	−0.168709	−	0.0527947i
$97$	6.93239	−	1.22237i	0.703878	−	0.124113i	0.189758	−	0.981831i	$-0.439230\pi$
$97$	6.93239	−	1.22237i	0.703878	−	0.124113i	0.514120	+	0.857718i	$0.328119\pi$
$98$	0.279351	−	6.99442i	0.0282187	−	0.706543i
$99$	−5.32741	−	0.442981i	−0.535425	−	0.0445213i
$100$	5.01897	+	8.69312i	0.501897	+	0.869312i
$101$	8.41665	−	7.06241i	0.837488	−	0.702736i	−0.119509	−	0.992833i	$-0.538132\pi$
$101$	8.41665	−	7.06241i	0.837488	−	0.702736i	0.956997	+	0.290097i	$0.0936877\pi$
$102$	0.682534	+	1.06629i	0.0675809	+	0.105578i
$103$	−17.0363	−	3.00396i	−1.67864	−	0.295989i	−0.748482	−	0.663155i	$-0.769217\pi$
$103$	−17.0363	−	3.00396i	−1.67864	−	0.295989i	−0.930155	+	0.367166i	$0.880328\pi$
$104$	−0.417941	−	0.350694i	−0.0409825	−	0.0343884i
$105$	2.63287	−	17.5746i	0.256942	−	1.71510i
$106$	5.72133	+	2.08239i	0.555705	+	0.202260i
$107$		−	19.1256i		−	1.84894i	−0.381258	−	0.924469i	$-0.624509\pi$
$107$		−	19.1256i		−	1.84894i	0.381258	−	0.924469i	$-0.375491\pi$
$108$	2.42904	+	4.59345i	0.233734	+	0.442005i
$109$	−15.9982			−1.53235			−0.766174	−	0.642633i	$-0.777842\pi$
$109$	−15.9982			−1.53235			−0.766174	+	0.642633i	$0.777842\pi$
$110$	6.49339	+	2.36340i	0.619121	+	0.225341i
$111$	−5.39803	+	7.06629i	−0.512358	+	0.670703i
$112$	−0.855102	−	2.50376i	−0.0807995	−	0.236583i
$113$	−19.8991	−	3.50876i	−1.87195	−	0.330076i	−0.881976	−	0.471294i	$-0.843787\pi$
$113$	−19.8991	−	3.50876i	−1.87195	−	0.330076i	−0.989978	+	0.141218i	$0.954898\pi$
$114$	−0.442020	−	9.64725i	−0.0413990	−	0.903548i
$115$	−7.41932	−	8.84200i	−0.691855	−	0.824521i
$116$	0.455074	−	0.262737i	0.0422525	−	0.0243945i
$117$	0.149672	+	1.62989i	0.0138372	+	0.150683i
$118$	−10.8102	−	6.24130i	−0.995164	−	0.574558i
$119$	−0.697566	+	1.80370i	−0.0639457	+	0.165345i
$120$	−1.46787	−	6.55433i	−0.133998	−	0.598325i
$121$	−7.35283	+	2.67621i	−0.668439	+	0.243292i
$122$	−8.17416	+	2.97515i	−0.740054	+	0.269358i
$123$	14.9252	−	3.34257i	1.34576	−	0.301389i
$124$	3.91889	−	0.691006i	0.351927	−	0.0620542i
$125$	−9.76827	+	16.9191i	−0.873701	+	1.51329i
$126$	−3.46661	+	7.14021i	−0.308831	+	0.636100i
$127$	7.40886	+	12.8325i	0.657430	+	1.13870i	0.981279	+	0.192593i	$0.0616899\pi$
$127$	7.40886	+	12.8325i	0.657430	+	1.13870i	−0.323848	+	0.946109i	$0.604977\pi$
$128$	−0.642788	−	0.766044i	−0.0568149	−	0.0677094i
$129$	0.991492	+	21.6397i	0.0872960	+	1.90527i
$130$	0.367388	−	2.08356i	0.0322221	−	0.182740i
$131$	2.73331	+	2.29352i	0.238810	+	0.200386i	0.754336	−	0.656488i	$-0.227959\pi$
$131$	2.73331	+	2.29352i	0.238810	+	0.200386i	−0.515526	+	0.856874i	$0.672403\pi$
$132$	−2.45264	−	1.87360i	−0.213475	−	0.163076i
$133$	11.4876	−	9.25490i	0.996100	−	0.802502i
$134$		−	10.2229i		−	0.883128i
$135$	−10.7166	+	17.0640i	−0.922340	+	1.46863i
$136$			0.730942i			0.0626777i
$137$	0.129951	−	0.357037i	0.0111024	−	0.0305037i	−0.934018	−	0.357227i	$-0.883722\pi$
$137$	0.129951	−	0.357037i	0.0111024	−	0.0305037i	0.945120	+	0.326723i	$0.105944\pi$
$138$	1.98314	+	4.75872i	0.168816	+	0.405089i
$139$	−6.87948	+	8.19864i	−0.583510	+	0.695400i	−0.974345	−	0.225061i	$-0.927742\pi$
$139$	−6.87948	+	8.19864i	−0.583510	+	0.695400i	0.390835	+	0.920461i	$0.372186\pi$
$140$	6.75048	−	7.72636i	0.570520	−	0.652996i
$141$	−7.33051	+	4.69227i	−0.617340	+	0.395160i
$142$	7.86499	−	6.59951i	0.660015	−	0.553818i
$143$	−0.486096	−	0.841943i	−0.0406494	−	0.0704068i
$144$	−0.248596	+	2.98968i	−0.0207163	+	0.249140i
$145$	1.76472	+	1.01886i	0.146552	+	0.0846119i
$146$	−0.601997	−	3.41410i	−0.0498217	−	0.282553i
$147$	−11.9276	+	2.17540i	−0.983772	+	0.179424i
$148$	−4.82430	+	1.75590i	−0.396555	+	0.144334i
$149$	−4.16632	−	11.4469i	−0.341318	−	0.937764i	−0.985013	−	0.172482i	$-0.944821\pi$
$149$	−4.16632	−	11.4469i	−0.341318	−	0.937764i	0.643694	−	0.765283i	$-0.277401\pi$
$150$	12.7932	−	11.7735i	1.04456	−	0.961305i
$151$	2.21521	+	12.5631i	0.180271	+	1.02237i	0.931882	+	0.362762i	$0.118166\pi$
$151$	2.21521	+	12.5631i	0.180271	+	1.02237i	−0.751611	+	0.659607i	$0.770723\pi$
$152$	2.78784	−	4.82869i	0.226124	−	0.391658i
$153$	1.54387	−	1.55722i	0.124815	−	0.125894i
$154$	0.0940913	−	4.71361i	0.00758209	−	0.379834i
$155$	9.91913	+	11.8212i	0.796723	+	0.949498i
$156$	−0.434536	+	0.839143i	−0.0347907	+	0.0671852i
$157$	15.7623	+	2.77932i	1.25797	+	0.221814i	0.762600	−	0.646870i	$-0.223922\pi$
$157$	15.7623	+	2.77932i	1.25797	+	0.221814i	0.495367	+	0.868684i	$0.335033\pi$
$158$	−6.80718	+	8.11248i	−0.541550	+	0.645395i
$159$	1.35397	−	10.4583i	0.107376	−	0.829400i
$160$	1.32631	−	3.64401i	0.104854	−	0.288085i
$161$	−4.07283	+	6.74002i	−0.320984	+	0.531188i
$162$	6.84432	−	5.84425i	0.537741	−	0.459167i
$163$	5.89439			0.461684			0.230842	−	0.972991i	$-0.425852\pi$
$163$	5.89439			0.461684			0.230842	+	0.972991i	$0.425852\pi$
$164$	8.29798	+	3.02022i	0.647963	+	0.235839i
$165$	1.53667	−	11.8696i	0.119630	−	0.924049i
$166$	4.20358	−	5.00963i	0.326261	−	0.388823i
$167$	−0.603695	+	3.42372i	−0.0467153	+	0.264936i	−0.999216	−	0.0396023i	$-0.987391\pi$
$167$	−0.603695	+	3.42372i	−0.0467153	+	0.264936i	0.952500	+	0.304538i	$0.0985020\pi$
$168$	−3.90813	+	2.39301i	−0.301519	+	0.184625i
$169$	9.73056	−	8.16491i	0.748504	−	0.628070i
$170$	−2.45475	+	1.41725i	−0.188271	+	0.108698i
$171$	−16.1383	+	4.39881i	−1.23413	+	0.336386i
$172$	−6.25339	+	10.8312i	−0.476816	+	0.825870i
$173$	0.810496	+	4.59655i	0.0616209	+	0.349470i	0.999993	+	0.00384179i	$0.00122288\pi$
$173$	0.810496	+	4.59655i	0.0616209	+	0.349470i	−0.938372	+	0.345628i	$0.887666\pi$
$174$	−0.616330	−	0.669706i	−0.0467239	−	0.0507703i
$175$	26.0572	+	5.13279i	1.96974	+	0.388003i
$176$	−0.609457	−	1.67447i	−0.0459396	−	0.126218i
$177$	−6.45700	+	20.6338i	−0.485338	+	1.55093i
$178$	0.124543	−	0.0219602i	0.00933487	−	0.00164599i
$179$	13.5903	+	7.84634i	1.01578	+	0.586463i	0.912880	−	0.408229i	$-0.133853\pi$
$179$	13.5903	+	7.84634i	1.01578	+	0.586463i	0.102904	+	0.994691i	$0.467187\pi$
$180$	−10.5224	+	4.96194i	−0.784292	+	0.369841i
$181$	−18.7112	+	10.8029i	−1.39079	+	0.802973i	−0.993403	−	0.114678i	$-0.963416\pi$
$181$	−18.7112	+	10.8029i	−1.39079	+	0.802973i	−0.397387	+	0.917651i	$0.630083\pi$
$182$	−1.42627	+	0.222236i	−0.105722	+	0.0164733i
$183$	8.12267	+	12.6897i	0.600445	+	0.938047i
$184$	−0.516860	+	2.93126i	−0.0381034	+	0.216095i
$185$	−15.2509	−	12.7971i	−1.12127	−	0.940859i
$186$	−2.65132	−	6.36208i	−0.194404	−	0.466490i
$187$	−0.445478	+	1.22394i	−0.0325765	+	0.0895033i
$188$	−5.02506			−0.366490
$189$	13.3805	+	3.15647i	0.973285	+	0.229599i
$190$	21.6218			1.56861
$191$	2.33111	−	6.40466i	0.168673	−	0.463425i	−0.826340	−	0.563172i	$-0.809581\pi$
$191$	2.33111	−	6.40466i	0.168673	−	0.463425i	0.995013	+	0.0997466i	$0.0318032\pi$
$192$	−1.05144	+	1.37640i	−0.0758815	+	0.0993328i
$193$	−6.17183	−	5.17878i	−0.444258	−	0.372777i	0.393042	−	0.919521i	$-0.371423\pi$
$193$	−6.17183	−	5.17878i	−0.444258	−	0.372777i	−0.837300	+	0.546744i	$0.815867\pi$
$194$	1.22237	−	6.93239i	0.0877609	−	0.497717i
$195$	−3.66067	+	0.167725i	−0.262146	+	0.0120111i
$196$	−6.47706	−	2.65474i	−0.462647	−	0.189624i
$197$	18.2513	−	10.5374i	1.30035	−	0.750757i	0.319885	−	0.947456i	$-0.396356\pi$
$197$	18.2513	−	10.5374i	1.30035	−	0.750757i	0.980464	+	0.196700i	$0.0630224\pi$
$198$	−2.23835	+	4.85462i	−0.159073	+	0.345003i
$199$	20.5111	+	11.8421i	1.45399	+	0.839463i	0.998705	−	0.0508813i	$-0.0162030\pi$
$199$	20.5111	+	11.8421i	1.45399	+	0.839463i	0.455288	+	0.890344i	$0.349536\pi$
$200$	9.88545	−	1.74307i	0.699007	−	0.123254i
$201$	−17.2786	+	3.86963i	−1.21874	+	0.272943i
$202$	−3.75783	−	10.3245i	−0.264400	−	0.726433i
$203$	0.268695	−	1.36406i	0.0188587	−	0.0957383i
$204$	1.23543	−	0.276679i	0.0864971	−	0.0193714i
$205$	5.94636	+	33.7235i	0.415311	+	2.35535i
$206$	−8.64956	+	14.9815i	−0.602644	+	1.04381i
$207$	7.29244	−	5.15316i	0.506860	−	0.358169i
$208$	−0.472489	+	0.272791i	−0.0327612	+	0.0189147i
$209$	7.61103	−	6.38642i	0.526466	−	0.441758i
$210$	−15.6142	−	8.48494i	−1.07748	−	0.585516i
$211$	0.486461	−	2.75886i	0.0334894	−	0.189928i	−0.963474	−	0.267803i	$-0.913702\pi$
$211$	0.486461	−	2.75886i	0.0334894	−	0.189928i	0.996963	+	0.0778752i	$0.0248136\pi$
$212$	3.91362	−	4.66407i	0.268789	−	0.320330i
$213$	−14.1315	−	10.7952i	−0.968272	−	0.739675i
$214$	−17.9721	−	6.54133i	−1.22855	−	0.447156i
$215$	−48.4998			−3.30766
$216$	5.14721	−	0.711494i	0.350223	−	0.0484111i
$217$	5.44510	−	9.01095i	0.369638	−	0.611703i
$218$	−5.47170	+	15.0334i	−0.370590	+	1.01819i
$219$	−5.54258	+	2.30980i	−0.374533	+	0.156082i
$220$	4.44174	−	5.29346i	0.299462	−	0.356885i
$221$	0.392731	+	0.0692490i	0.0264179	+	0.00465819i
$222$	4.79391	+	7.48930i	0.321746	+	0.502649i
$223$	−5.12591	−	6.10882i	−0.343256	−	0.409077i	0.566605	−	0.823989i	$-0.308257\pi$
$223$	−5.12591	−	6.10882i	−0.343256	−	0.409077i	−0.909861	+	0.414913i	$0.863812\pi$
$224$	−2.64522	−	0.0528029i	−0.176741	−	0.00352804i
$225$	−24.7420	−	17.1662i	−1.64946	−	1.14441i
$226$	−10.1031	+	17.4990i	−0.672046	+	1.16402i
$227$	−0.100183	−	0.568168i	−0.00664940	−	0.0377106i	0.981303	−	0.192472i	$-0.0616504\pi$
$227$	−0.100183	−	0.568168i	−0.00664940	−	0.0377106i	−0.987952	+	0.154761i	$0.950539\pi$
$228$	−9.21663	−	2.88419i	−0.610386	−	0.191010i
$229$	4.71625	+	12.9578i	0.311658	+	0.856274i	0.992322	+	0.123679i	$0.0394692\pi$
$229$	4.71625	+	12.9578i	0.311658	+	0.856274i	−0.680664	+	0.732596i	$0.738309\pi$
$230$	−10.8463	+	3.94774i	−0.715185	+	0.260306i
$231$	−8.00249	+	1.62519i	−0.526525	+	0.106929i
$232$	−0.0912476	−	0.517491i	−0.00599070	−	0.0339749i
$233$	2.26835	+	1.30963i	0.148605	+	0.0857969i	0.572459	−	0.819934i	$-0.305990\pi$
$233$	2.26835	+	1.30963i	0.148605	+	0.0857969i	−0.423854	+	0.905730i	$0.639323\pi$
$234$	1.58279	+	0.416810i	0.103470	+	0.0272477i
$235$	−9.74329	−	16.8759i	−0.635582	−	1.10086i
$236$	−9.56222	+	8.02366i	−0.622448	+	0.522296i
$237$	16.2883	+	8.43461i	1.05804	+	0.547887i
$238$	1.45634	+	1.27240i	0.0944006	+	0.0824774i
$239$	0.582414	−	0.694094i	0.0376732	−	0.0448972i	−0.746879	−	0.664960i	$-0.768449\pi$
$239$	0.582414	−	0.694094i	0.0376732	−	0.0448972i	0.784552	+	0.620063i	$0.212893\pi$
$240$	−6.66109	−	0.862364i	−0.429972	−	0.0556653i
$241$	0.906556	−	2.49074i	0.0583964	−	0.160443i	−0.907064	−	0.420993i	$-0.861682\pi$
$241$	0.906556	−	2.49074i	0.0583964	−	0.160443i	0.965460	+	0.260550i	$0.0839039\pi$
$242$			7.82471i			0.502992i
$243$	−12.4686	−	9.35597i	−0.799861	−	0.600186i
$244$			8.69876i			0.556881i
$245$	−3.64312	−	26.8996i	−0.232750	−	1.71855i
$246$	1.96373	−	15.1683i	0.125203	−	0.967097i
$247$	−2.33031	−	1.95536i	−0.148274	−	0.124417i
$248$	0.691006	−	3.91889i	0.0438789	−	0.248850i
$249$	−10.0583	−	5.20855i	−0.637422	−	0.330079i
$250$	12.5578	+	14.9659i	0.794228	+	0.946524i
$251$	−0.194771	−	0.337354i	−0.0122939	−	0.0212936i	0.859813	−	0.510609i	$-0.170580\pi$
$251$	−0.194771	−	0.337354i	−0.0122939	−	0.0212936i	−0.872107	+	0.489315i	$0.837247\pi$
$252$	5.52395	+	5.69965i	0.347976	+	0.359044i
$253$	−2.65194	+	4.59330i	−0.166726	+	0.288778i
$254$	14.5926	−	2.57307i	0.915622	−	0.161449i
$255$	3.32460	+	3.61252i	0.208194	+	0.226225i
$256$	−0.939693	+	0.342020i	−0.0587308	+	0.0213763i
$257$	18.7506	−	6.82465i	1.16963	−	0.425710i	0.317101	−	0.948392i	$-0.397291\pi$
$257$	18.7506	−	6.82465i	1.16963	−	0.425710i	0.852528	+	0.522682i	$0.175068\pi$
$258$	20.6737	+	6.46950i	1.28709	+	0.402774i
$259$	−4.89949	+	12.6686i	−0.304440	+	0.787191i
$260$	−1.83225	−	1.05785i	−0.113632	−	0.0656052i
$261$	−0.898630	+	1.29521i	−0.0556238	+	0.0801715i
$262$	3.09005	−	1.78404i	0.190904	−	0.110218i
$263$	−15.2818	−	18.2121i	−0.942314	−	1.12301i	−0.992250	−	0.124254i	$-0.960346\pi$
$263$	−15.2818	−	18.2121i	−0.942314	−	1.12301i	0.0499366	−	0.998752i	$-0.484098\pi$
$264$	−2.59947	+	1.66392i	−0.159986	+	0.102407i
$265$	23.2518	+	4.09992i	1.42835	+	0.251856i
$266$	−4.76778	−	13.9602i	−0.292331	−	0.855953i
$267$	−0.0842593	−	0.202188i	−0.00515659	−	0.0123737i
$268$	−9.60642	−	3.49645i	−0.586806	−	0.213580i
$269$	20.7719			1.26648			0.633242	−	0.773954i	$-0.281724\pi$
$269$	20.7719			1.26648			0.633242	+	0.773954i	$0.281724\pi$
$270$	12.3696	+	15.9065i	0.752788	+	0.968042i
$271$		−	22.2512i		−	1.35167i	−0.737055	−	0.675833i	$-0.763784\pi$
$271$		−	22.2512i		−	1.35167i	0.737055	−	0.675833i	$-0.236216\pi$
$272$	0.686860	+	0.249997i	0.0416470	+	0.0151583i
$273$	0.915497	+	2.32653i	0.0554084	+	0.140808i
$274$	−0.291059	−	0.244228i	−0.0175835	−	0.0147543i
$275$	17.6152	+	3.10604i	1.06224	+	0.187301i
$276$	5.15001	−	0.235964i	0.309994	−	0.0142034i
$277$	−4.48779	+	3.76571i	−0.269645	+	0.226259i	−0.767577	−	0.640957i	$-0.778538\pi$
$277$	−4.48779	+	3.76571i	−0.269645	+	0.226259i	0.497931	+	0.867216i	$0.334093\pi$
$278$	5.35128	+	9.26869i	0.320949	+	0.555899i
$279$	−9.74949	+	6.88942i	−0.583687	+	0.412459i
$280$	−4.95160	−	8.98595i	−0.295915	−	0.537013i
$281$	5.10565	−	0.900263i	0.304577	−	0.0537052i	−0.0192707	−	0.999814i	$-0.506134\pi$
$281$	5.10565	−	0.900263i	0.304577	−	0.0537052i	0.323848	+	0.946109i	$0.395023\pi$
$282$	1.90211	+	8.49328i	0.113269	+	0.505767i
$283$	1.44109	+	3.95937i	0.0856642	+	0.235360i	0.975127	−	0.221647i	$-0.0711434\pi$
$283$	1.44109	+	3.95937i	0.0856642	+	0.235360i	−0.889463	+	0.457008i	$0.848921\pi$
$284$	−3.51152	−	9.64783i	−0.208371	−	0.572494i
$285$	−8.18439	−	36.5449i	−0.484801	−	2.16473i
$286$	−0.957423	+	0.168819i	−0.0566136	+	0.00998250i
$287$	20.4624	−	11.2755i	1.20786	−	0.665575i
$288$	2.72436	+	1.25614i	0.160534	+	0.0740185i
$289$	8.23286	+	14.2597i	0.484286	+	0.838808i
$290$	1.56099	−	1.30982i	0.0916643	−	0.0769155i
$291$	−12.1797	+	0.558053i	−0.713987	+	0.0327136i
$292$	−3.41410	−	0.601997i	−0.199795	−	0.0352292i
$293$	3.87253	+	3.24944i	0.226236	+	0.189834i	0.748859	−	0.662729i	$-0.230602\pi$
$293$	3.87253	+	3.24944i	0.226236	+	0.189834i	−0.522623	+	0.852564i	$0.675047\pi$
$294$	−2.03527	+	11.9523i	−0.118699	+	0.697073i
$295$	−45.4868	−	16.5558i	−2.64834	−	0.963918i
$296$			5.13391i			0.298403i
$297$	9.05247	+	1.94563i	0.525278	+	0.112897i
$298$	−12.1815			−0.705656
$299$	1.52598	+	0.555412i	0.0882497	+	0.0321203i
$300$	−6.68799	−	16.0484i	−0.386131	−	0.926556i
$301$	10.6946	+	31.3139i	0.616424	+	1.80491i
$302$	12.5631	+	2.21521i	0.722924	+	0.127471i
$303$	−16.0279	+	10.2595i	−0.920782	+	0.589393i
$304$	−3.58398	−	4.27122i	−0.205555	−	0.244971i
$305$	−29.2134	+	16.8664i	−1.67276	+	0.965766i
$306$	−0.935277	−	1.98337i	−0.0534662	−	0.113381i
$307$	−6.98759	−	4.03428i	−0.398803	−	0.230249i	0.287165	−	0.957881i	$-0.407287\pi$
$307$	−6.98759	−	4.03428i	−0.398803	−	0.230249i	−0.685967	+	0.727632i	$0.740621\pi$
$308$	−4.39717	−	1.70057i	−0.250552	−	0.0968988i
$309$	28.5955	+	8.94849i	1.62674	+	0.509062i
$310$	14.5008	−	5.27786i	0.823590	−	0.299762i
$311$	9.74091	−	3.54540i	0.552356	−	0.201041i	−0.0507368	−	0.998712i	$-0.516157\pi$
$311$	9.74091	−	3.54540i	0.552356	−	0.201041i	0.603093	+	0.797671i	$0.293935\pi$
$312$	0.639916	+	0.695334i	0.0362281	+	0.0393655i
$313$	6.29544	−	1.11006i	0.355839	−	0.0627441i	0.00712893	−	0.999975i	$-0.497731\pi$
$313$	6.29544	−	1.11006i	0.355839	−	0.0627441i	0.348710	+	0.937231i	$0.386620\pi$
$314$	8.00273	−	13.8611i	0.451620	−	0.782229i
$315$	−8.43076	+	29.6026i	−0.475019	+	1.66792i
$316$	5.29505	+	9.17129i	0.297870	+	0.515926i
$317$	−14.5819	−	17.3780i	−0.819000	−	0.976047i	0.180972	−	0.983488i	$-0.442076\pi$
$317$	−14.5819	−	17.3780i	−0.819000	−	0.976047i	−0.999972	+	0.00744159i	$0.997631\pi$
$318$	−9.36454	−	4.84927i	−0.525137	−	0.271934i
$319$	0.162597	−	0.922134i	0.00910369	−	0.0516296i
$320$	−2.97063	−	2.49265i	−0.166063	−	0.139344i
$321$	−4.25315	+	32.8523i	−0.237388	+	1.83364i
$322$	4.94056	+	6.13244i	0.275327	+	0.341747i
$323$			4.07550i			0.226767i
$324$	−3.15090	−	8.43041i	−0.175050	−	0.468356i
$325$		−	5.47653i		−	0.303783i
$326$	2.01600	−	5.53892i	0.111656	−	0.306772i
$327$	27.4803	+	3.55768i	1.51967	+	0.196740i
$328$	5.67615	−	6.76457i	0.313413	−	0.373511i
$329$	−8.74746	+	10.0120i	−0.482263	+	0.551981i
$330$	−10.6282	−	5.50365i	−0.585065	−	0.302966i
$331$	9.12742	−	7.65881i	0.501688	−	0.420966i	−0.356505	−	0.934293i	$-0.616032\pi$
$331$	9.12742	−	7.65881i	0.501688	−	0.420966i	0.858193	+	0.513327i	$0.171587\pi$
$332$	−3.26980	−	5.66347i	−0.179454	−	0.310823i
$333$	10.8437	−	10.9375i	0.594230	−	0.599370i
$334$	3.01077	+	1.73827i	0.164742	+	0.0951139i
$335$	−6.88399	−	39.0411i	−0.376113	−	2.13304i
$336$	0.912035	+	4.49090i	0.0497556	+	0.244999i
$337$	−24.0185	+	8.74202i	−1.30837	+	0.476208i	−0.899714	−	0.436479i	$-0.856225\pi$
$337$	−24.0185	+	8.74202i	−1.30837	+	0.476208i	−0.408658	+	0.912688i	$0.634003\pi$
$338$	−4.34446	−	11.9363i	−0.236307	−	0.649249i
$339$	33.4008	+	10.4522i	1.81408	+	0.567687i
$340$	0.492206	+	2.79144i	0.0266936	+	0.151387i
$341$	3.54546	−	6.14092i	0.191998	−	0.332550i
$342$	−1.38609	+	16.6695i	−0.0749513	+	0.901385i
$343$	−16.5644	+	8.28374i	−0.894394	+	0.447280i
$344$	8.03920	+	9.58075i	0.433445	+	0.516559i
$345$	10.7780	+	16.8380i	0.580268	+	0.906525i
$346$	4.59655	+	0.810496i	0.247112	+	0.0435726i
$347$	8.22432	−	9.80137i	0.441505	−	0.526165i	−0.498700	−	0.866775i	$-0.666189\pi$
$347$	8.22432	−	9.80137i	0.441505	−	0.526165i	0.940205	+	0.340610i	$0.110633\pi$
$348$	−0.840115	+	0.350108i	−0.0450349	+	0.0187678i
$349$	−4.23079	+	11.6240i	−0.226469	+	0.622219i	−0.999932	−	0.0116222i	$-0.996300\pi$
$349$	−4.23079	+	11.6240i	−0.226469	+	0.622219i	0.773463	+	0.633841i	$0.218523\pi$
$350$	13.7353	−	22.7302i	0.734184	−	1.21498i
$351$	0.105362	−	2.83297i	0.00562381	−	0.151213i
$352$	−1.78193			−0.0949774
$353$	5.98309	+	2.17767i	0.318448	+	0.115906i	0.496299	−	0.868152i	$-0.334692\pi$
$353$	5.98309	+	2.17767i	0.318448	+	0.115906i	−0.177851	+	0.984058i	$0.556914\pi$
$354$	17.1810	+	13.1248i	0.913159	+	0.697573i
$355$	25.5921	−	30.4995i	1.35829	−	1.61874i
$356$	0.0219602	−	0.124543i	0.00116389	−	0.00660075i
$357$	1.59933	−	2.94312i	0.0846453	−	0.155766i
$358$	12.0213	−	10.0871i	0.635345	−	0.533117i
$359$	17.2588	−	9.96437i	0.910884	−	0.525899i	0.0301688	−	0.999545i	$-0.490396\pi$
$359$	17.2588	−	9.96437i	0.910884	−	0.525899i	0.880716	+	0.473645i	$0.157062\pi$
$360$	1.06383	+	11.5849i	0.0560689	+	0.610578i
$361$	6.04413	−	10.4687i	0.318112	−	0.550987i
$362$	3.75181	+	21.2775i	0.197191	+	1.11832i
$363$	13.2252	−	2.96184i	0.694143	−	0.155456i
$364$	−0.278978	+	1.41626i	−0.0146224	+	0.0742323i
$365$	−4.59801	−	12.6329i	−0.240671	−	0.661238i
$366$	14.7025	−	3.29269i	0.768512	−	0.172112i
$367$	−6.81801	+	1.20220i	−0.355897	+	0.0627542i	−0.348738	−	0.937220i	$-0.613390\pi$
$367$	−6.81801	+	1.20220i	−0.355897	+	0.0627542i	−0.00715867	+	0.999974i	$0.502279\pi$
$368$	2.57770	+	1.48824i	0.134372	+	0.0775798i
$369$	−26.3806	+	2.42251i	−1.37332	+	0.126111i
$370$	−17.2414	+	9.95435i	−0.896340	+	0.517502i
$371$	−2.48008	−	15.9166i	−0.128759	−	0.826351i
$372$	−6.88521	+	0.315468i	−0.356981	+	0.0163563i
$373$	−0.882215	+	5.00329i	−0.0456794	+	0.259061i	−0.999092	−	0.0426093i	$-0.986433\pi$
$373$	−0.882215	+	5.00329i	−0.0456794	+	0.259061i	0.953412	+	0.301670i	$0.0975440\pi$
$374$	0.997765	+	0.837224i	0.0515932	+	0.0432918i
$375$	20.5416	−	26.8900i	1.06076	−	1.38859i
$376$	−1.71867	+	4.72201i	−0.0886338	+	0.243519i
$377$	−0.286690			−0.0147653
$378$	7.54250	−	11.4939i	0.387944	−	0.591185i
$379$	0.204444			0.0105016			0.00525078	−	0.999986i	$-0.498329\pi$
$379$	0.204444			0.0105016			0.00525078	+	0.999986i	$0.498329\pi$
$380$	7.39510	−	20.3179i	0.379361	−	1.04229i
$381$	−9.87262	−	23.6902i	−0.505789	−	1.21369i
$382$	−5.22113	−	4.38105i	−0.267136	−	0.224154i
$383$	−2.53398	+	14.3709i	−0.129480	+	0.734320i	0.849065	+	0.528288i	$0.177166\pi$
$383$	−2.53398	+	14.3709i	−0.129480	+	0.734320i	−0.978545	+	0.206031i	$0.933945\pi$
$384$	0.933773	+	1.45879i	0.0476514	+	0.0744436i
$385$	−2.81475	−	18.0645i	−0.143453	−	0.920651i
$386$	−6.97735	+	4.02837i	−0.355138	+	0.205039i
$387$	3.10913	−	37.3913i	0.158046	−	1.90071i
$388$	−6.09624	−	3.51967i	−0.309490	−	0.178684i
$389$	−0.967705	+	0.170633i	−0.0490646	+	0.00865142i	−0.198127	−	0.980176i	$-0.563486\pi$
$389$	−0.967705	+	0.170633i	−0.0490646	+	0.00865142i	0.149062	+	0.988828i	$0.452375\pi$
$390$	−1.09441	+	3.49727i	−0.0554177	+	0.177091i
$391$	−0.744110	−	2.04442i	−0.0376312	−	0.103391i
$392$	−4.70992	+	5.17848i	−0.237887	+	0.261553i
$393$	−4.18502	−	4.54745i	−0.211106	−	0.229388i
$394$	−3.65959	−	20.7546i	−0.184368	−	1.04560i
$395$	−20.5336	+	35.5652i	−1.03316	+	1.78948i
$396$	3.79629	+	3.76374i	0.190771	+	0.189135i
$397$	27.0671	−	15.6272i	1.35846	−	0.784306i	0.369042	−	0.929413i	$-0.379686\pi$
$397$	27.0671	−	15.6272i	1.35846	−	0.784306i	0.989416	+	0.145107i	$0.0463526\pi$
$398$	18.1431	−	15.2239i	0.909433	−	0.763105i
$399$	−21.7905	+	13.3427i	−1.09089	+	0.667969i
$400$	1.74307	−	9.88545i	0.0871536	−	0.494272i
$401$	4.17979	−	4.98128i	0.208729	−	0.248753i	−0.651516	−	0.758635i	$-0.725866\pi$
$401$	4.17979	−	4.98128i	0.208729	−	0.248753i	0.860244	+	0.509882i	$0.170311\pi$
$402$	−2.27338	+	17.5601i	−0.113386	+	0.875819i
$403$	−2.04013	−	0.742547i	−0.101626	−	0.0369889i
$404$	−10.9872			−0.546631
$405$	22.2028	−	26.9279i	1.10327	−	1.33806i
$406$	−1.18990	−	0.719027i	−0.0590537	−	0.0356847i
$407$	−3.12890	+	8.59658i	−0.155094	+	0.426117i
$408$	0.162547	−	1.25555i	0.00804728	−	0.0621590i
$409$	−4.05279	+	4.82993i	−0.200398	+	0.238825i	−0.856879	−	0.515518i	$-0.827600\pi$
$409$	−4.05279	+	4.82993i	−0.200398	+	0.238825i	0.656481	+	0.754342i	$0.272044\pi$
$410$	33.7235	+	5.94636i	1.66548	+	0.293670i
$411$	−0.302617	+	0.584390i	−0.0149270	+	0.0288258i
$412$	11.1197	+	13.2519i	0.547826	+	0.652874i
$413$	−0.659118	+	33.0193i	−0.0324331	+	1.62477i
$414$	−2.34823	−	8.61514i	−0.115409	−	0.423411i
$415$	12.6799	−	21.9622i	0.622432	−	1.07808i
$416$	0.0947395	+	0.537294i	0.00464498	+	0.0263430i
$417$	13.6402	−	12.5531i	0.667963	−	0.614727i
$418$	−3.39814	−	9.33632i	−0.166209	−	0.456654i
$419$	28.6661	−	10.4336i	1.40043	−	0.509715i	0.472124	−	0.881532i	$-0.343488\pi$
$419$	28.6661	−	10.4336i	1.40043	−	0.509715i	0.928306	+	0.371818i	$0.121265\pi$
$420$	−13.3136	+	11.7705i	−0.649637	+	0.574342i
$421$	3.64141	+	20.6514i	0.177471	+	1.00649i	0.935253	+	0.353981i	$0.115172\pi$
$421$	3.64141	+	20.6514i	0.177471	+	1.00649i	−0.757781	+	0.652509i	$0.773717\pi$
$422$	−2.42610	−	1.40071i	−0.118101	−	0.0681854i
$423$	13.6352	−	6.42982i	0.662966	−	0.312629i
$424$	−3.04426	−	5.27281i	−0.147842	−	0.256070i
$425$	−5.62059	+	4.71623i	−0.272638	+	0.228771i
$426$	−14.9774	+	9.58706i	−0.725658	+	0.464495i
$427$	17.3316	+	15.1425i	0.838734	+	0.732798i
$428$	−12.2937	+	14.6510i	−0.594237	+	0.708184i
$429$	0.647743	+	1.55432i	0.0312733	+	0.0750431i
$430$	−16.5879	+	45.5749i	−0.799939	+	2.19782i
$431$			19.5907i			0.943652i	0.881692	+	0.471826i	$0.156405\pi$
$431$			19.5907i			0.943652i	−0.881692	+	0.471826i	$0.843595\pi$
$432$	1.09186	−	5.08014i	0.0525323	−	0.244418i
$433$		−	15.0708i		−	0.724257i	−0.932128	−	0.362128i	$-0.882050\pi$
$433$		−	15.0708i		−	0.724257i	0.932128	−	0.362128i	$-0.117950\pi$
$434$	−6.60519	−	8.19865i	−0.317059	−	0.393548i
$435$	−2.80471	−	2.14255i	−0.134476	−	0.102728i
$436$	12.2553	+	10.2834i	0.586923	+	0.492487i
$437$	−2.88185	+	16.3438i	−0.137857	+	0.781829i
$438$	0.274833	+	5.99832i	0.0131320	+	0.286611i
$439$	−9.10927	−	10.8560i	−0.434762	−	0.518129i	0.503528	−	0.863979i	$-0.332035\pi$
$439$	−9.10927	−	10.8560i	−0.434762	−	0.518129i	−0.938290	+	0.345850i	$0.887591\pi$
$440$	−3.45506	−	5.98434i	−0.164714	−	0.285292i
$441$	20.9720	−	1.08426i	0.998666	−	0.0516316i
$442$	0.199395	−	0.345362i	0.00948423	−	0.0164272i
$443$	−32.6357	+	5.75456i	−1.55057	+	0.273407i	−0.882364	−	0.470568i	$-0.844049\pi$
$443$	−32.6357	+	5.75456i	−1.55057	+	0.273407i	−0.668207	+	0.743976i	$0.732938\pi$
$444$	8.67725	−	1.94331i	0.411804	−	0.0922254i
$445$	0.460837	−	0.167731i	0.0218458	−	0.00795121i
$446$	−7.49357	+	2.72744i	−0.354831	+	0.129148i
$447$	4.61100	+	20.5890i	0.218093	+	0.973825i
$448$	−0.954339	+	2.46764i	−0.0450883	+	0.116585i
$449$	13.1710	+	7.60427i	0.621577	+	0.358867i	0.777483	−	0.628904i	$-0.216496\pi$
$449$	13.1710	+	7.60427i	0.621577	+	0.358867i	−0.155906	+	0.987772i	$0.549830\pi$
$450$	−24.5932	+	17.3786i	−1.15933	+	0.819237i
$451$	13.6273	−	7.86770i	0.641682	−	0.370476i
$452$	12.9882	+	15.4788i	0.610916	+	0.728061i
$453$	−1.01132	−	22.0724i	−0.0475159	−	1.03705i
$454$	−0.568168	−	0.100183i	−0.0266654	−	0.00470184i
$455$	−5.29721	+	1.80914i	−0.248337	+	0.0848139i
$456$	−5.86253	+	7.67435i	−0.274538	+	0.359384i
$457$	20.8039	+	7.57199i	0.973164	+	0.354203i	0.779179	−	0.626802i	$-0.215636\pi$
$457$	20.8039	+	7.57199i	0.973164	+	0.354203i	0.193985	+	0.981004i	$0.437859\pi$
$458$	13.7894			0.644336
$459$	−2.99823	+	2.33154i	−0.139945	+	0.108827i
$460$			11.5424i			0.538168i
$461$	−9.53482	−	3.47039i	−0.444081	−	0.161632i	0.110295	−	0.993899i	$-0.464821\pi$
$461$	−9.53482	−	3.47039i	−0.444081	−	0.161632i	−0.554375	+	0.832267i	$0.687043\pi$
$462$	−1.20984	+	8.07572i	−0.0562867	+	0.375717i
$463$	11.7696	+	9.87586i	0.546979	+	0.458970i	0.873917	−	0.486076i	$-0.161572\pi$
$463$	11.7696	+	9.87586i	0.546979	+	0.458970i	−0.326937	+	0.945046i	$0.606017\pi$
$464$	−0.517491	−	0.0912476i	−0.0240239	−	0.00423606i
$465$	−14.4094	−	22.5112i	−0.668222	−	1.04393i
$466$	2.00647	−	1.68363i	0.0929481	−	0.0779927i
$467$	3.92716	+	6.80203i	0.181727	+	0.314761i	0.942469	−	0.334294i	$-0.108498\pi$
$467$	3.92716	+	6.80203i	0.181727	+	0.314761i	−0.760742	+	0.649055i	$0.775165\pi$
$468$	0.933019	−	1.34478i	0.0431288	−	0.0621623i
$469$	−23.6889	+	13.0535i	−1.09385	+	0.602755i
$470$	−19.1905	+	3.38381i	−0.885194	+	0.156084i
$471$	−26.4571	−	8.27930i	−1.21908	−	0.381490i
$472$	4.26930	+	11.7298i	0.196510	+	0.539908i
$473$	7.62234	+	20.9422i	0.350476	+	0.962924i
$474$	13.4969	−	12.4212i	0.619931	−	0.570523i
$475$	55.1181	−	9.71882i	2.52899	−	0.445930i
$476$	1.69376	−	0.933327i	0.0776335	−	0.0427790i
$477$	−4.65146	+	17.6634i	−0.212976	+	0.808749i
$478$	−0.453037	−	0.784684i	−0.0207215	−	0.0358906i
$479$	−31.9871	+	26.8403i	−1.46153	+	1.22637i	−0.537935	+	0.842986i	$0.680795\pi$
$479$	−31.9871	+	26.8403i	−1.46153	+	1.22637i	−0.923591	+	0.383379i	$0.874760\pi$
$480$	−3.08859	+	5.96443i	−0.140974	+	0.272238i
$481$	2.75842	+	0.486384i	0.125773	+	0.0221772i
$482$	−2.03047	−	1.70377i	−0.0924855	−	0.0776045i
$483$	8.49482	−	10.6717i	0.386528	−	0.485580i
$484$	7.35283	+	2.67621i	0.334219	+	0.121646i
$485$		−	27.2977i		−	1.23952i
$486$	−13.0562	+	8.51671i	−0.592243	+	0.386326i
$487$	9.64119			0.436884			0.218442	−	0.975850i	$-0.429903\pi$
$487$	9.64119			0.436884			0.218442	+	0.975850i	$0.429903\pi$
$488$	8.17416	+	2.97515i	0.370027	+	0.134679i
$489$	−10.1249	−	1.31080i	−0.457863	−	0.0592763i
$490$	−26.5234	−	5.77678i	−1.19820	−	0.260968i
$491$	13.8925	+	2.44963i	0.626961	+	0.110550i	0.478096	−	0.878307i	$-0.341327\pi$
$491$	13.8925	+	2.44963i	0.626961	+	0.110550i	0.148865	+	0.988858i	$0.452438\pi$
$492$	−13.5819	−	7.03318i	−0.612321	−	0.317080i
$493$	0.246889	+	0.294231i	0.0111193	+	0.0132515i
$494$	−2.63445	+	1.52100i	−0.118529	+	0.0684330i
$495$	−5.27914	+	20.0469i	−0.237280	+	0.901042i
$496$	−3.44621	−	1.98967i	−0.154740	−	0.0893389i
$497$	−25.3353	−	9.79820i	−1.13644	−	0.439510i
$498$	−8.33459	+	7.67033i	−0.373482	+	0.343716i
$499$	−8.91416	+	3.24449i	−0.399052	+	0.145243i	−0.533747	−	0.845644i	$-0.679217\pi$
$499$	−8.91416	+	3.24449i	−0.399052	+	0.145243i	0.134695	+	0.990887i	$0.456994\pi$
$500$	18.3583	−	6.68189i	0.821010	−	0.298823i
$501$	1.79834	−	5.74673i	0.0803441	−	0.256745i
$502$	−0.383625	+	0.0676434i	−0.0171220	+	0.00301907i
$503$	2.22153	−	3.84780i	0.0990531	−	0.171565i	−0.812240	−	0.583324i	$-0.801752\pi$
$503$	2.22153	−	3.84780i	0.0990531	−	0.171565i	0.911293	+	0.411759i	$0.135085\pi$
$504$	7.24522	−	3.24142i	0.322728	−	0.144384i
$505$	−21.3034	−	36.8986i	−0.947990	−	1.64197i
$506$	3.40927	+	4.06301i	0.151561	+	0.180623i
$507$	−18.5300	+	11.8611i	−0.822948	+	0.526770i
$508$	2.57307	−	14.5926i	0.114162	−	0.647442i
$509$	4.04886	+	3.39739i	0.179462	+	0.150587i	0.728094	−	0.685478i	$-0.240407\pi$
$509$	4.04886	+	3.39739i	0.179462	+	0.150587i	−0.548631	+	0.836064i	$0.684851\pi$
$510$	4.53173	−	1.88855i	0.200669	−	0.0836263i
$511$	−7.14258	+	5.75437i	−0.315969	+	0.254558i
$512$			1.00000i			0.0441942i
$513$	28.6992	−	3.96707i	1.26710	−	0.175150i
$514$		−	19.9539i		−	0.880131i
$515$	−22.9440	+	63.0383i	−1.01104	+	2.77780i
$516$	13.1502	−	17.2143i	0.578905	−	0.757816i
$517$	−5.75573	+	6.85941i	−0.253137	+	0.301677i
$518$	10.2289	+	8.93695i	0.449432	+	0.392667i
$519$	−0.370020	−	8.07581i	−0.0162421	−	0.354489i
$520$	−1.62072	+	1.35995i	−0.0710734	+	0.0596377i
$521$	−17.0581	−	29.5454i	−0.747328	−	1.29441i	−0.949099	−	0.314977i	$-0.898003\pi$
$521$	−17.0581	−	29.5454i	−0.747328	−	1.29441i	0.201772	−	0.979433i	$-0.435330\pi$
$522$	0.909750	+	1.28742i	0.0398187	+	0.0563490i
$523$	14.8751	+	8.58813i	0.650442	+	0.375533i	0.788626	−	0.614874i	$-0.210793\pi$
$523$	14.8751	+	8.58813i	0.650442	+	0.375533i	−0.138184	+	0.990407i	$0.544126\pi$
$524$	−0.619591	−	3.51388i	−0.0270670	−	0.153504i
$525$	−43.6174	−	14.6113i	−1.90362	−	0.637689i
$526$	−22.3404	+	8.13126i	−0.974090	+	0.354540i
$527$	0.994824	+	2.73326i	0.0433352	+	0.119062i
$528$	0.674505	+	3.01179i	0.0293541	+	0.131072i
$529$	2.45549	+	13.9258i	0.106760	+	0.605468i
$530$	11.8053	−	20.4473i	0.512788	−	0.888175i
$531$	15.6798	−	34.0071i	0.680447	−	1.47578i
$532$	−14.7489	−	0.294412i	−0.639448	−	0.0127644i
$533$	−3.09681	−	3.69063i	−0.134138	−	0.159859i
$534$	−0.218813	+	0.0100256i	−0.00946895	+	0.000433851i
$535$	−73.0399	−	12.8789i	−3.15779	−	0.556803i
$536$	−6.57118	+	7.83123i	−0.283832	+	0.338258i
$537$	−21.5993	−	16.5000i	−0.932080	−	0.712027i
$538$	7.10440	−	19.5192i	0.306293	−	0.841532i
$539$	−11.0427	+	5.80070i	−0.475642	+	0.249854i
$540$	19.1779	−	6.18324i	0.825286	−	0.266084i
$541$	−12.3242			−0.529857			−0.264928	−	0.964268i	$-0.585348\pi$
$541$	−12.3242			−0.529857			−0.264928	+	0.964268i	$0.585348\pi$
$542$	−20.9093	−	7.61037i	−0.898132	−	0.326893i
$543$	34.5428	−	14.3953i	1.48237	−	0.617762i
$544$	0.469840	−	0.559934i	0.0201442	−	0.0240070i
$545$	−10.7730	+	61.0965i	−0.461463	+	2.61709i
$546$	2.49934	−	0.0645656i	0.106962	−	0.00276315i
$547$	18.6762	−	15.6712i	0.798538	−	0.670053i	−0.149305	−	0.988791i	$-0.547704\pi$
$547$	18.6762	−	15.6712i	0.798538	−	0.670053i	0.947843	+	0.318738i	$0.103259\pi$
$548$	−0.329047	+	0.189975i	−0.0140562	+	0.00811535i
$549$	−11.1305	−	23.6036i	−0.475039	−	1.00738i
$550$	8.94348	−	15.4906i	0.381351	−	0.660519i
$551$	−0.508768	−	2.88537i	−0.0216742	−	0.122921i
$552$	1.53967	−	4.92013i	0.0655328	−	0.209415i
$553$	27.4905	+	5.41513i	1.16901	+	0.230275i
$554$	2.00369	+	5.50509i	0.0851286	+	0.233889i
$555$	23.3510	+	25.3732i	0.991194	+	1.07703i
$556$	10.5400	−	1.85848i	0.446994	−	0.0788172i
$557$	−18.7683	−	10.8359i	−0.795240	−	0.459132i	0.0465642	−	0.998915i	$-0.485173\pi$
$557$	−18.7683	−	10.8359i	−0.795240	−	0.459132i	−0.841804	+	0.539783i	$0.818506\pi$
$558$	3.13942	+	11.5178i	0.132902	+	0.487589i
$559$	5.90931	−	3.41174i	0.249937	−	0.144301i
$560$	−10.1376	+	1.57961i	−0.428391	+	0.0667505i
$561$	1.03738	−	2.00331i	0.0437984	−	0.0845800i
$562$	0.900263	−	5.10565i	0.0379753	−	0.215369i
$563$	4.63725	+	3.89111i	0.195437	+	0.163991i	0.735255	−	0.677791i	$-0.237063\pi$
$563$	4.63725	+	3.89111i	0.195437	+	0.163991i	−0.539818	+	0.841782i	$0.681507\pi$
$564$	8.63163	+	1.11747i	0.363457	+	0.0470542i
$565$	−26.7996	+	73.6314i	−1.12747	+	3.09770i
$566$	4.21348			0.177106
$567$	−22.2819	−	8.39747i	−0.935751	−	0.352661i
$568$	−10.2670			−0.430794
$569$	−6.28299	+	17.2624i	−0.263397	+	0.723677i	0.735536	+	0.677486i	$0.236930\pi$
$569$	−6.28299	+	17.2624i	−0.263397	+	0.723677i	−0.998933	+	0.0461909i	$0.985292\pi$
$570$	−37.1402	−	4.80827i	−1.55563	−	0.201396i
$571$	−23.3990	−	19.6341i	−0.979219	−	0.821662i	0.00475275	−	0.999989i	$-0.498487\pi$
$571$	−23.3990	−	19.6341i	−0.979219	−	0.821662i	−0.983971	+	0.178327i	$0.942932\pi$
$572$	−0.168819	+	0.957423i	−0.00705869	+	0.0400318i
$573$	−5.42845	+	10.4830i	−0.226777	+	0.437933i
$574$	−3.59700	−	23.0848i	−0.150136	−	0.963541i
$575$	−25.8749	+	14.9389i	−1.07906	+	0.622993i
$576$	2.11217	−	2.13044i	0.0880069	−	0.0887681i
$577$	6.87338	+	3.96835i	0.286143	+	0.165205i	0.636201	−	0.771523i	$-0.280505\pi$
$577$	6.87338	+	3.96835i	0.286143	+	0.165205i	−0.350058	+	0.936728i	$0.613838\pi$
$578$	16.2156	−	2.85924i	0.674479	−	0.118929i
$579$	9.44979	+	10.2682i	0.392720	+	0.426730i
$580$	−0.696943	−	1.91483i	−0.0289390	−	0.0795092i
$581$	−16.9760	−	3.34396i	−0.704281	−	0.138731i
$582$	−3.64131	+	11.6360i	−0.150937	+	0.482330i
$583$	−1.88397	−	10.6845i	−0.0780259	−	0.442507i
$584$	−1.73338	+	3.00231i	−0.0717279	+	0.124236i
$585$	6.32528	+	0.525956i	0.261518	+	0.0217456i
$586$	4.37796	−	2.52762i	0.180852	−	0.104415i
$587$	30.1882	−	25.3309i	1.24600	−	1.04552i	0.248969	−	0.968511i	$-0.419908\pi$
$587$	30.1882	−	25.3309i	1.24600	−	1.04552i	0.997031	−	0.0770067i	$-0.0245363\pi$
$588$	10.5354	+	6.00046i	0.434472	+	0.247455i
$589$	3.85283	−	21.8505i	0.158753	−	0.900334i
$590$	−31.1148	+	37.0812i	−1.28098	+	1.52661i
$591$	−33.6938	+	14.0415i	−1.38598	+	0.577590i
$592$	4.82430	+	1.75590i	0.198278	+	0.0721671i
$593$	−16.8271			−0.691004			−0.345502	−	0.938418i	$-0.612291\pi$
$593$	−16.8271			−0.691004			−0.345502	+	0.938418i	$0.612291\pi$
$594$	4.92442	−	7.84110i	0.202051	−	0.321724i
$595$	6.41853	+	3.87857i	0.263134	+	0.159006i
$596$	−4.16632	+	11.4469i	−0.170659	+	0.468882i
$597$	−32.5988	−	24.9026i	−1.33418	−	1.01920i
$598$	1.04383	−	1.24399i	0.0426855	−	0.0508706i
$599$	−36.3040	−	6.40138i	−1.48334	−	0.261553i	−0.627430	−	0.778673i	$-0.715893\pi$
$599$	−36.3040	−	6.40138i	−1.48334	−	0.261553i	−0.855913	+	0.517120i	$0.827004\pi$
$600$	−17.3680	+	0.795772i	−0.709046	+	0.0324873i
$601$	−24.0662	−	28.6810i	−0.981682	−	1.16992i	−0.985456	−	0.169931i	$-0.945646\pi$
$601$	−24.0662	−	28.6810i	−0.981682	−	1.16992i	0.00377369	−	0.999993i	$-0.498799\pi$
$602$	33.0832	+	0.660394i	1.34837	+	0.0269157i
$603$	30.5403	−	2.80450i	1.24370	−	0.114208i
$604$	6.37844	−	11.0478i	0.259535	−	0.449528i
$605$	5.26906	+	29.8823i	0.214218	+	1.21489i
$606$	4.15890	+	18.5703i	0.168944	+	0.754367i
$607$	−9.61092	−	26.4058i	−0.390095	−	1.07178i	−0.966958	−	0.254936i	$-0.917945\pi$
$607$	−9.61092	−	26.4058i	−0.390095	−	1.07178i	0.576863	−	0.816841i	$-0.304277\pi$
$608$	−5.23943	+	1.90700i	−0.212487	+	0.0773389i
$609$	−0.764883	+	2.28332i	−0.0309946	+	0.0925247i
$610$	5.85763	+	33.2203i	0.237169	+	1.34505i
$611$	2.37429	+	1.37079i	0.0960533	+	0.0554564i
$612$	−2.18364	+	0.200522i	−0.0882683	+	0.00810562i
$613$	5.06048	+	8.76500i	0.204391	+	0.354015i	0.949938	−	0.312437i	$-0.101145\pi$
$613$	5.06048	+	8.76500i	0.204391	+	0.354015i	−0.745548	+	0.666452i	$0.767812\pi$
$614$	−6.18088	+	5.18638i	−0.249440	+	0.209305i
$615$	−2.71472	−	59.2497i	−0.109468	−	2.38918i
$616$	−3.10193	+	3.55036i	−0.124980	+	0.143048i
$617$	0.788434	−	0.939619i	0.0317411	−	0.0378276i	−0.749940	−	0.661505i	$-0.769918\pi$
$617$	0.788434	−	0.939619i	0.0317411	−	0.0378276i	0.781681	+	0.623678i	$0.214362\pi$
$618$	18.1891	−	23.8104i	0.731672	−	0.957796i
$619$	4.10220	−	11.2707i	0.164881	−	0.453008i	−0.829545	−	0.558440i	$-0.811400\pi$
$619$	4.10220	−	11.2707i	0.164881	−	0.453008i	0.994427	+	0.105432i	$0.0336224\pi$
$620$		−	15.4314i		−	0.619741i
$621$	−13.6723	+	7.22997i	−0.548650	+	0.290129i
$622$		−	10.3661i		−	0.415641i
$623$	−0.209914	−	0.260554i	−0.00841001	−	0.0104389i
$624$	0.872265	−	0.363506i	0.0349185	−	0.0145519i
$625$	19.5882	+	16.4365i	0.783530	+	0.657459i
$626$	1.11006	−	6.29544i	0.0443668	−	0.251616i
$627$	−14.4938	+	9.27750i	−0.578827	+	0.370508i
$628$	−10.2881	−	12.2609i	−0.410540	−	0.489263i
$629$	−1.87630	−	3.24984i	−0.0748128	−	0.129580i
$630$	24.9338	+	18.0470i	0.993388	+	0.719010i
$631$	−18.9416	+	32.8078i	−0.754053	+	1.30606i	0.191791	+	0.981436i	$0.438571\pi$
$631$	−18.9416	+	32.8078i	−0.754053	+	1.30606i	−0.945844	+	0.324622i	$0.894763\pi$
$632$	10.4292	−	1.83895i	0.414852	−	0.0731495i
$633$	−1.44912	+	4.63075i	−0.0575972	+	0.184056i
$634$	−21.3173	+	7.75886i	−0.846618	+	0.308144i
$635$	53.9960	−	19.6529i	2.14277	−	0.779903i
$636$	−7.75969	+	7.14124i	−0.307692	+	0.283169i
$637$	2.33615	+	3.02122i	0.0925616	+	0.119705i
$638$	−0.810911	−	0.468180i	−0.0321043	−	0.0185354i
$639$	21.8732	+	21.6856i	0.865290	+	0.857870i
$640$	−3.35834	+	1.93894i	−0.132750	+	0.0766433i
$641$	24.6513	+	29.3782i	0.973667	+	1.16037i	0.987042	+	0.160460i	$0.0512978\pi$
$641$	24.6513	+	29.3782i	0.973667	+	1.16037i	−0.0133756	+	0.999911i	$0.504258\pi$
$642$	29.4164	+	15.2328i	1.16097	+	0.601190i
$643$	−21.3067	−	3.75694i	−0.840253	−	0.148159i	−0.263072	−	0.964776i	$-0.584736\pi$
$643$	−21.3067	−	3.75694i	−0.840253	−	0.148159i	−0.577180	+	0.816617i	$0.695847\pi$
$644$	7.45238	−	2.54519i	0.293665	−	0.100295i
$645$	83.3088	+	10.7854i	3.28028	+	0.424674i
$646$	3.82972	+	1.39390i	0.150678	+	0.0548424i
$647$	30.2060			1.18752			0.593760	−	0.804642i	$-0.297643\pi$
$647$	30.2060			1.18752			0.593760	+	0.804642i	$0.297643\pi$
$648$	−8.99967	+	0.0775072i	−0.353540	+	0.00304477i
$649$			22.2432i			0.873120i
$650$	−5.14626	−	1.87308i	−0.201853	−	0.0734684i
$651$	−11.3570	+	14.2674i	−0.445116	+	0.559182i
$652$	−4.51537	−	3.78884i	−0.176835	−	0.148382i
$653$	−21.3769	−	3.76932i	−0.836542	−	0.147505i	−0.261063	−	0.965322i	$-0.584073\pi$
$653$	−21.3769	−	3.76932i	−0.836542	−	0.147505i	−0.575479	+	0.817817i	$0.695184\pi$
$654$	12.7419	−	24.6063i	0.498250	−	0.962181i
$655$	10.5994	−	8.89399i	0.414155	−	0.347517i
$656$	−4.41526	−	7.64746i	−0.172387	−	0.298583i
$657$	10.0342	−	2.73503i	0.391473	−	0.106704i
$658$	6.41642	+	11.6442i	0.250138	+	0.453940i
$659$	34.9951	−	6.17058i	1.36321	−	0.240372i	0.556272	−	0.831001i	$-0.312231\pi$
$659$	34.9951	−	6.17058i	1.36321	−	0.240372i	0.806943	+	0.590629i	$0.201120\pi$
$660$	−8.80681	+	8.10490i	−0.342805	+	0.315483i
$661$	−5.16931	−	14.2026i	−0.201063	−	0.552416i	0.797651	−	0.603119i	$-0.206076\pi$
$661$	−5.16931	−	14.2026i	−0.201063	−	0.552416i	−0.998714	+	0.0507038i	$0.983854\pi$
$662$	−4.07517	−	11.1964i	−0.158386	−	0.435162i
$663$	−0.659200	−	0.206286i	−0.0256012	−	0.00801147i
$664$	−6.44026	+	1.13559i	−0.249930	+	0.0440695i
$665$	−27.6086	−	50.1028i	−1.07061	−	1.94290i
$666$	−6.56910	−	13.9306i	−0.254548	−	0.539798i
$667$	0.782030	+	1.35452i	0.0302803	+	0.0524471i
$668$	2.66318	−	2.23468i	0.103042	−	0.0864622i
$669$	7.44637	+	11.6331i	0.287893	+	0.449762i
$670$	−39.0411	−	6.88399i	−1.50829	−	0.265952i
$671$	11.8742	+	9.96361i	0.458397	+	0.384641i
$672$	4.53200	+	0.678946i	0.174826	+	0.0261909i
$673$	−9.26336	−	3.37159i	−0.357076	−	0.129965i	0.157252	−	0.987559i	$-0.449736\pi$
$673$	−9.26336	−	3.37159i	−0.357076	−	0.129965i	−0.514328	+	0.857593i	$0.671959\pi$
$674$			25.5600i			0.984533i
$675$	38.6822	+	34.9888i	1.48888	+	1.34672i
$676$	−12.7023			−0.488552
$677$	18.8651	+	6.86633i	0.725044	+	0.263895i	0.678066	−	0.735001i	$-0.262818\pi$
$677$	18.8651	+	6.86633i	0.725044	+	0.263895i	0.0469787	+	0.998896i	$0.485041\pi$
$678$	21.2456	−	27.8116i	0.815933	−	1.06810i
$679$	−17.6248	+	6.01935i	−0.676377	+	0.231001i
$680$	2.79144	+	0.492206i	0.107047	+	0.0188753i
$681$	0.0457372	+	0.998230i	0.00175265	+	0.0382523i
$682$	−4.55796	−	5.43197i	−0.174533	−	0.208001i
$683$	−3.48437	+	2.01170i	−0.133326	+	0.0769756i	−0.565179	−	0.824968i	$-0.691193\pi$
$683$	−3.48437	+	2.01170i	−0.133326	+	0.0769756i	0.431854	+	0.901944i	$0.357860\pi$
$684$	15.1902	+	7.00382i	0.580810	+	0.267798i
$685$	−1.27600	−	0.736702i	−0.0487536	−	0.0281479i
$686$	2.11881	+	18.3987i	0.0808966	+	0.702464i
$687$	−5.21962	−	23.3066i	−0.199141	−	0.889202i
$688$	11.7525	−	4.27757i	0.448061	−	0.163081i
$689$	−3.12146	+	1.13612i	−0.118918	+	0.0432827i
$690$	19.5088	−	4.36908i	0.742687	−	0.166328i
$691$	−19.6070	+	3.45725i	−0.745887	+	0.131520i	−0.533658	−	0.845700i	$-0.679183\pi$
$691$	−19.6070	+	3.45725i	−0.745887	+	0.131520i	−0.212228	+	0.977220i	$0.568072\pi$
$692$	2.33373	−	4.04214i	0.0887152	−	0.153659i
$693$	14.1074	−	1.01201i	0.535896	−	0.0384431i
$694$	−6.39739	−	11.0806i	−0.242842	−	0.420614i
$695$	26.6778	+	31.7933i	1.01195	+	1.20599i
$696$	0.0416577	+	0.909194i	0.00157903	+	0.0344629i
$697$	−1.12083	+	6.35654i	−0.0424544	+	0.240771i
$698$	9.47598	+	7.95129i	0.358671	+	0.300961i
$699$	−3.60514	−	2.75401i	−0.136359	−	0.104166i
$700$	−16.6617	−	20.6812i	−0.629752	−	0.781675i
$701$			6.61122i			0.249702i	0.992175	+	0.124851i	$0.0398453\pi$
$701$			6.61122i			0.249702i	−0.992175	+	0.124851i	$0.960155\pi$
$702$	−2.62609	−	1.06794i	−0.0991153	−	0.0403069i
$703$			28.6251i			1.07962i
$704$	−0.609457	+	1.67447i	−0.0229698	+	0.0631089i
$705$	12.9833	+	31.1547i	0.488981	+	1.17335i
$706$	4.09268	−	4.87746i	0.154030	−	0.183566i
$707$	−19.1261	+	21.8910i	−0.719310	+	0.823296i
$708$	18.2095	−	11.6559i	0.684354	−	0.438056i
$709$	3.82507	−	3.20962i	0.143654	−	0.120540i	−0.568129	−	0.822940i	$-0.692333\pi$
$709$	3.82507	−	3.20962i	0.143654	−	0.120540i	0.711783	+	0.702400i	$0.247888\pi$
$710$	−19.9071	−	34.4801i	−0.747101	−	1.29402i
$711$	−26.1029	−	18.1105i	−0.978936	−	0.679195i
$712$	−0.109521	−	0.0632320i	−0.00410448	−	0.00236972i
$713$	2.05676	+	11.6645i	0.0770264	+	0.436838i
$714$	−2.21862	−	2.50948i	−0.0830299	−	0.0939150i
$715$	−3.54268	+	1.28943i	−0.132489	+	0.0482220i
$716$	−5.36721	−	14.7463i	−0.200582	−	0.551095i
$717$	−1.15477	+	1.06274i	−0.0431258	+	0.0396887i
$718$	−3.46059	−	19.6260i	−0.129148	−	0.732435i
$719$	7.99621	−	13.8498i	0.298208	−	0.516512i	−0.677518	−	0.735506i	$-0.736944\pi$
$719$	7.99621	−	13.8498i	0.298208	−	0.516512i	0.975726	+	0.218994i	$0.0702776\pi$
$720$	11.2501	+	2.96259i	0.419266	+	0.110409i
$721$	45.7601	+	0.913444i	1.70419	+	0.0340184i
$722$	−7.77019	−	9.26015i	−0.289176	−	0.344627i
$723$	−2.11110	+	4.07679i	−0.0785126	+	0.151617i
$724$	21.2775	+	3.75181i	0.790774	+	0.139435i
$725$	3.39050	−	4.04064i	0.125920	−	0.150066i
$726$	1.74006	−	13.4406i	0.0645798	−	0.498829i
$727$	1.09242	−	3.00140i	0.0405156	−	0.111316i	−0.917785	−	0.397077i	$-0.870024\pi$
$727$	1.09242	−	3.00140i	0.0405156	−	0.111316i	0.958301	+	0.285762i	$0.0922466\pi$
$728$	1.23543	+	0.746543i	0.0457882	+	0.0276687i
$729$	19.3369	+	18.8437i	0.716182	+	0.697914i
$730$	−13.4437			−0.497573
$731$	−8.59041	−	3.12665i	−0.317728	−	0.115643i
$732$	1.93443	−	14.9420i	0.0714987	−	0.552272i
$733$	−12.6991	+	15.1342i	−0.469051	+	0.558993i	−0.947762	−	0.318980i	$-0.896660\pi$
$733$	−12.6991	+	15.1342i	−0.469051	+	0.558993i	0.478711	+	0.877973i	$0.341104\pi$
$734$	−1.20220	+	6.81801i	−0.0443740	+	0.251657i
$735$	0.275909	+	47.0160i	0.0101770	+	1.73421i
$736$	2.28011	−	1.91324i	0.0840461	−	0.0705231i
$737$	−15.7760	+	9.10830i	−0.581118	+	0.335509i
$738$	−6.74627	+	25.6182i	−0.248334	+	0.943018i
$739$	9.89424	−	17.1373i	0.363966	−	0.630407i	−0.624644	−	0.780910i	$-0.714756\pi$
$739$	9.89424	−	17.1373i	0.363966	−	0.630407i	0.988610	+	0.150503i	$0.0480893\pi$
$740$	3.45711	+	19.6062i	0.127086	+	0.720740i
$741$	3.56797	+	3.87696i	0.131073	+	0.142424i
$742$	−15.8050	−	3.11330i	−0.580219	−	0.114293i
$743$	−2.72261	−	7.48032i	−0.0998830	−	0.274426i	0.879679	−	0.475567i	$-0.157757\pi$
$743$	−2.72261	−	7.48032i	−0.0998830	−	0.274426i	−0.979562	+	0.201141i	$0.935535\pi$
$744$	−2.05844	+	6.57787i	−0.0754659	+	0.241157i
$745$	−46.5208	+	8.20286i	−1.70439	+	0.300530i
$746$	4.39982	+	2.54024i	0.161089	+	0.0930047i
$747$	16.1191	+	11.1836i	0.589767	+	0.409186i
$748$	1.12799	−	0.651245i	0.0412434	−	0.0238119i
$749$	7.79056	+	49.9982i	0.284661	+	1.82689i
$750$	−18.2427	−	28.4997i	−0.666129	−	1.04066i
$751$	2.70656	−	15.3496i	0.0987636	−	0.560116i	−0.894765	−	0.446537i	$-0.852657\pi$
$751$	2.70656	−	15.3496i	0.0987636	−	0.560116i	0.993529	−	0.113580i	$-0.0362317\pi$
$752$	3.84942	+	3.23005i	0.140374	+	0.117788i
$753$	0.259541	+	0.622791i	0.00945820	+	0.0226958i
$754$	−0.0980536	+	0.269400i	−0.00357090	+	0.00981097i
$755$	49.4697			1.80038
$756$	−8.22109	−	11.0188i	−0.298998	−	0.400750i
$757$	−32.5349			−1.18250			−0.591251	−	0.806487i	$-0.701366\pi$
$757$	−32.5349			−1.18250			−0.591251	+	0.806487i	$0.701366\pi$
$758$	0.0699238	−	0.192114i	0.00253975	−	0.00697790i
$759$	5.57674	−	7.30024i	0.202423	−	0.264982i
$760$	−16.5633	−	13.8982i	−0.600814	−	0.504142i
$761$	7.68715	−	43.5960i	0.278659	−	1.58035i	−0.448435	−	0.893815i	$-0.648019\pi$
$761$	7.68715	−	43.5960i	0.278659	−	1.58035i	0.727094	−	0.686538i	$-0.240870\pi$
$762$	−25.6382	+	1.17470i	−0.928772	+	0.0425547i
$763$	41.8225	−	6.51666i	1.51408	−	0.235919i
$764$	−5.90257	+	3.40785i	−0.213547	+	0.123292i
$765$	−4.90736	−	6.94460i	−0.177426	−	0.251083i
$766$	12.6376	+	7.29631i	0.456614	+	0.263626i
$767$	6.70683	−	1.18259i	0.242170	−	0.0427010i
$768$	1.69018	−	0.378524i	0.0609892	−	0.0136588i
$769$	−5.52512	−	15.1801i	−0.199241	−	0.547410i	0.799328	−	0.600895i	$-0.205189\pi$
$769$	−5.52512	−	15.1801i	−0.199241	−	0.547410i	−0.998569	+	0.0534856i	$0.982967\pi$
$770$	−17.9378	−	3.53342i	−0.646432	−	0.127335i
$771$	−33.7258	+	7.55305i	−1.21461	+	0.272017i
$772$	1.39904	+	7.93435i	0.0503525	+	0.285563i
$773$	−3.09347	+	5.35804i	−0.111264	+	0.192715i	−0.916280	−	0.400538i	$-0.868823\pi$
$773$	−3.09347	+	5.35804i	−0.111264	+	0.192715i	0.805016	+	0.593253i	$0.202157\pi$
$774$	−34.0729	−	15.7102i	−1.22473	−	0.564692i
$775$	34.5929	−	19.9722i	1.24261	−	0.717424i
$776$	−5.39244	+	4.52480i	−0.193577	+	0.162431i
$777$	11.2332	−	20.6716i	0.402988	−	0.741588i
$778$	−0.170633	+	0.967705i	−0.00611747	+	0.0346939i
$779$	31.6484	−	37.7171i	1.13392	−	1.35136i
$780$	2.91205	+	2.22455i	0.104268	+	0.0796515i
$781$	−17.1918	−	6.25730i	−0.615171	−	0.223904i
$782$	−2.17563			−0.0778004
$783$	1.83162	−	2.02497i	0.0654567	−	0.0723664i
$784$	3.25529	+	6.19702i	0.116260	+	0.221322i
$785$	21.2282	−	58.3241i	0.757668	−	2.08168i
$786$	−5.70456	+	2.37731i	−0.203475	+	0.0847958i
$787$	−4.09486	+	4.88006i	−0.145966	+	0.173955i	−0.834074	−	0.551653i	$-0.813997\pi$
$787$	−4.09486	+	4.88006i	−0.145966	+	0.173955i	0.688108	+	0.725609i	$0.258442\pi$
$788$	−20.7546	−	3.65959i	−0.739351	−	0.130368i
$789$	22.1997	+	34.6816i	0.790331	+	1.23470i
$790$	26.3974	+	31.4592i	0.939178	+	1.11927i
$791$	53.4497	+	1.06694i	1.90045	+	0.0379361i
$792$	4.83517	−	2.28007i	0.171810	−	0.0810189i
$793$	2.37295	−	4.11007i	0.0842659	−	0.145953i
$794$	−5.42726	−	30.7795i	−0.192606	−	1.09233i
$795$	−39.0283	−	12.2133i	−1.38419	−	0.433159i
$796$	−8.10046	−	22.2558i	−0.287113	−	0.788837i
$797$	−43.0164	+	15.6567i	−1.52372	+	0.554589i	−0.962074	−	0.272789i	$-0.912054\pi$
$797$	−43.0164	+	15.6567i	−1.52372	+	0.554589i	−0.561646	+	0.827378i	$0.689832\pi$
$798$	5.08522	+	25.0399i	0.180015	+	0.886401i
$799$	−0.637815	−	3.61723i	−0.0225643	−	0.127968i
$800$	−8.69312	−	5.01897i	−0.307348	−	0.177447i
$801$	0.0997710	+	0.366038i	0.00352523	+	0.0129333i
$802$	−3.25130	−	5.63142i	−0.114807	−	0.198852i
$803$	−4.73227	+	3.97085i	−0.166998	+	0.140128i
$804$	15.7236	+	8.14219i	0.554527	+	0.287153i
$805$	22.9973	+	20.0927i	0.810549	+	0.708173i
$806$	−1.39553	+	1.66313i	−0.0491555	+	0.0585813i
$807$	−35.6802	−	4.61926i	−1.25600	−	0.162606i
$808$	−3.75783	+	10.3245i	−0.132200	+	0.363216i
$809$		−	13.4572i		−	0.473129i	−0.971616	−	0.236564i	$-0.923979\pi$
$809$		−	13.4572i		−	0.473129i	0.971616	−	0.236564i	$-0.0760214\pi$
$810$	−17.7101	−	30.0737i	−0.622270	−	1.05668i
$811$			53.6909i			1.88534i	0.333725	+	0.942671i	$0.391694\pi$
$811$			53.6909i			1.88534i	−0.333725	+	0.942671i	$0.608306\pi$
$812$	−1.08263	+	0.872217i	−0.0379930	+	0.0306088i
$813$	−4.94823	+	38.2213i	−0.173542	+	1.34048i
$814$	7.00800	+	5.88041i	0.245630	+	0.206108i
$815$	3.96920	−	22.5105i	0.139035	−	0.788508i
$816$	−1.12424	−	0.582168i	−0.0393562	−	0.0203799i
$817$	44.8241	+	53.4192i	1.56820	+	1.86890i
$818$	3.15251	+	5.46031i	0.110225	+	0.190915i
$819$	−1.05519	−	4.19990i	−0.0368713	−	0.146757i
$820$	17.1218	−	29.6559i	0.597921	−	1.03563i
$821$	−11.8208	+	2.08433i	−0.412550	+	0.0727437i	−0.376071	−	0.926591i	$-0.622725\pi$
$821$	−11.8208	+	2.08433i	−0.412550	+	0.0727437i	−0.0364787	+	0.999334i	$0.511614\pi$
$822$	0.445646	+	0.484240i	0.0155437	+	0.0168898i
$823$	−0.455621	+	0.165833i	−0.0158820	+	0.00578056i	−0.349949	−	0.936769i	$-0.613801\pi$
$823$	−0.455621	+	0.165833i	−0.0158820	+	0.00578056i	0.334067	+	0.942549i	$0.391579\pi$
$824$	16.2559	−	5.91665i	0.566300	−	0.206116i
$825$	−29.5672	−	9.25256i	−1.02940	−	0.322133i
$826$	30.8025	+	11.9126i	1.07176	+	0.414493i
$827$	−35.7704	−	20.6521i	−1.24386	−	0.718143i	−0.273982	−	0.961735i	$-0.588341\pi$
$827$	−35.7704	−	20.6521i	−1.24386	−	0.718143i	−0.969878	+	0.243592i	$0.921674\pi$
$828$	−8.89872	−	0.739940i	−0.309252	−	0.0257147i
$829$	28.6577	−	16.5455i	0.995323	−	0.574650i	0.0884619	−	0.996080i	$-0.471805\pi$
$829$	28.6577	−	16.5455i	0.995323	−	0.574650i	0.906861	+	0.421430i	$0.138472\pi$
$830$	−16.3010	−	19.4267i	−0.565815	−	0.674312i
$831$	8.54617	−	5.47041i	0.296463	−	0.189767i
$832$	0.537294	+	0.0947395i	0.0186273	+	0.00328450i
$833$	1.08887	−	4.99939i	0.0377270	−	0.173219i
$834$	−7.13081	−	17.1110i	−0.246920	−	0.592505i
$835$	12.6686	+	4.61098i	0.438413	+	0.159569i
$836$	−9.93550			−0.343626
$837$	18.2789	−	9.66597i	0.631812	−	0.334105i
$838$		−	30.5058i		−	1.05381i
$839$	−27.7512	−	10.1006i	−0.958077	−	0.348711i	−0.184797	−	0.982777i	$-0.559163\pi$
$839$	−27.7512	−	10.1006i	−0.958077	−	0.348711i	−0.773280	+	0.634065i	$0.781385\pi$
$840$	6.50714	+	16.5364i	0.224518	+	0.570562i
$841$	22.0038	+	18.4634i	0.758751	+	0.636667i
$842$	20.6514	+	3.64141i	0.711696	+	0.125491i
$843$	−8.97025	+	0.411001i	−0.308952	+	0.0141556i
$844$	−2.14601	+	1.80072i	−0.0738687	+	0.0619832i
$845$	−24.6291	−	42.6588i	−0.847266	−	1.46751i
$846$	−1.37854	−	15.0120i	−0.0473953	−	0.516124i
$847$	18.1317	−	9.99125i	0.623012	−	0.343303i
$848$	−5.99602	+	1.05726i	−0.205904	+	0.0363064i
$849$	−1.59490	−	7.12155i	−0.0547369	−	0.244411i
$850$	2.50945	+	6.89467i	0.0860736	+	0.236485i
$851$	−5.22640	−	14.3594i	−0.179159	−	0.492235i
$852$	3.88631	+	17.3531i	0.133143	+	0.594508i
$853$	33.9485	−	5.98603i	1.16237	−	0.204958i	0.441002	−	0.897506i	$-0.354623\pi$
$853$	33.9485	−	5.98603i	1.16237	−	0.204958i	0.721372	+	0.692548i	$0.243512\pi$
$854$	20.1571	−	11.1073i	0.689761	−	0.380084i
$855$	5.93160	+	64.5937i	0.202856	+	2.20906i
$856$	9.56278	+	16.5632i	0.326849	+	0.566119i
$857$	−28.0343	+	23.5236i	−0.957634	+	0.803550i	−0.980567	−	0.196187i	$-0.937144\pi$
$857$	−28.0343	+	23.5236i	−0.957634	+	0.803550i	0.0229327	+	0.999737i	$0.492700\pi$
$858$	1.68212	−	0.0770719i	0.0574267	−	0.00263119i
$859$	−34.5911	−	6.09935i	−1.18023	−	0.208107i	−0.451097	−	0.892475i	$-0.648967\pi$
$859$	−34.5911	−	6.09935i	−1.18023	−	0.208107i	−0.729137	+	0.684367i	$0.760078\pi$
$860$	37.1530	+	31.1750i	1.26691	+	1.06306i
$861$	−37.6560	+	14.8178i	−1.28331	+	0.504988i
$862$	18.4093	+	6.70042i	0.627022	+	0.228217i
$863$			22.4647i			0.764707i	0.924016	+	0.382353i	$0.124886\pi$
$863$			22.4647i			0.764707i	−0.924016	+	0.382353i	$0.875114\pi$
$864$	−4.40033	−	2.76353i	−0.149702	−	0.0940171i
$865$	18.0999			0.615414
$866$	−14.1619	−	5.15452i	−0.481242	−	0.175158i
$867$	−10.9706	−	26.3250i	−0.372582	−	0.894044i
$868$	−9.96332	+	3.40274i	−0.338177	+	0.115497i
$869$	18.5842	+	3.27689i	0.630424	+	0.111161i
$870$	−2.97261	+	1.90277i	−0.100781	+	0.0645100i
$871$	3.58512	+	4.27258i	0.121477	+	0.144771i
$872$	13.8548	−	7.99909i	0.469184	−	0.270883i
$873$	21.0454	+	1.74995i	0.712278	+	0.0592269i
$874$	14.3725	+	8.29795i	0.486156	+	0.280682i
$875$	18.6445	−	48.2091i	0.630298	−	1.62977i
$876$	5.73057	+	1.79329i	0.193618	+	0.0605896i
$877$	−13.4829	+	4.90738i	−0.455285	+	0.165710i	−0.559475	−	0.828847i	$-0.688997\pi$
$877$	−13.4829	+	4.90738i	−0.455285	+	0.165710i	0.104190	+	0.994557i	$0.466775\pi$
$878$	−13.3169	+	4.84694i	−0.449422	+	0.163576i
$879$	−5.92930	−	6.44279i	−0.199990	−	0.217310i
$880$	−6.80514	+	1.19993i	−0.229401	+	0.0404496i
$881$	−0.157050	+	0.272018i	−0.00529113	+	0.00916451i	−0.868659	−	0.495411i	$-0.835018\pi$
$881$	−0.157050	+	0.272018i	−0.00529113	+	0.00916451i	0.863368	+	0.504575i	$0.168351\pi$
$882$	6.15397	−	20.0781i	0.207215	−	0.676064i
$883$	−19.4538	−	33.6951i	−0.654674	−	1.13393i	−0.981975	−	0.189009i	$-0.939473\pi$
$883$	−19.4538	−	33.6951i	−0.654674	−	1.13393i	0.327301	−	0.944920i	$-0.393861\pi$
$884$	−0.256337	−	0.305490i	−0.00862154	−	0.0102747i
$885$	74.4516	+	38.5536i	2.50266	+	1.29596i
$886$	−5.75456	+	32.6357i	−0.193328	+	1.09642i
$887$	16.7327	+	14.0404i	0.561830	+	0.471432i	0.878923	−	0.476963i	$-0.158262\pi$
$887$	16.7327	+	14.0404i	0.561830	+	0.471432i	−0.317093	+	0.948394i	$0.602707\pi$
$888$	1.14168	−	8.81860i	0.0383123	−	0.295933i
$889$	−24.5955	−	30.5290i	−0.824905	−	1.02391i
$890$		−	0.490412i		−	0.0164387i
$891$	−15.1169	−	5.35513i	−0.506435	−	0.179404i
$892$			7.97449i			0.267006i
$893$	−9.58278	+	26.3285i	−0.320675	+	0.881049i
$894$	20.9244	+	2.70893i	0.699815	+	0.0906001i
$895$	39.1164	−	46.6171i	1.30752	−	1.55824i
$896$	1.99242	+	1.74077i	0.0665620	+	0.0581549i
$897$	−2.49769	−	1.29339i	−0.0833954	−	0.0431849i
$898$	11.6504	−	9.77586i	0.388779	−	0.326225i
$899$	−1.04552	−	1.81090i	−0.0348701	−	0.0603968i
$900$	7.91921	+	29.0539i	0.263974	+	0.968463i
$901$	3.85412	+	2.22517i	0.128399	+	0.0741313i
$902$	−2.73242	−	15.4963i	−0.0909798	−	0.515972i
$903$	−11.4066	−	56.1667i	−0.379588	−	1.86911i
$904$	18.9875	−	6.91090i	0.631516	−	0.229853i
$905$	28.6560	+	78.7318i	0.952559	+	2.61713i
$906$	−21.0872	−	6.59888i	−0.700575	−	0.219233i
$907$	1.13503	+	6.43708i	0.0376881	+	0.213740i	0.997836	−	0.0657528i	$-0.0209449\pi$
$907$	1.13503	+	6.43708i	0.0376881	+	0.213740i	−0.960148	+	0.279493i	$0.909834\pi$
$908$	−0.288466	+	0.499639i	−0.00957310	+	0.0165811i
$909$	29.8130	−	14.0586i	0.988834	−	0.466295i
$910$	−0.111715	+	5.59651i	−0.00370333	+	0.185523i
$911$	−27.0476	−	32.2341i	−0.896126	−	1.06796i	−0.997325	−	0.0730956i	$-0.976712\pi$
$911$	−27.0476	−	32.2341i	−0.896126	−	1.06796i	0.101199	−	0.994866i	$-0.467732\pi$
$912$	5.20643	+	8.13375i	0.172402	+	0.269335i
$913$	−11.4761	−	2.02355i	−0.379804	−	0.0669696i
$914$	14.2307	−	16.9595i	0.470709	−	0.560969i
$915$	53.9311	−	22.4752i	1.78291	−	0.743006i
$916$	4.71625	−	12.9578i	0.155829	−	0.428137i
$917$	−8.07967	−	4.88235i	−0.266814	−	0.161230i
$918$	1.16548	+	3.61484i	0.0384665	+	0.119308i
$919$	4.95945			0.163597			0.0817986	−	0.996649i	$-0.473934\pi$
$919$	4.95945			0.163597			0.0817986	+	0.996649i	$0.473934\pi$
$920$	10.8463	+	3.94774i	0.357593	+	0.130153i
$921$	11.1055	+	8.48365i	0.365940	+	0.279546i
$922$	−6.52220	+	7.77285i	−0.214797	+	0.255985i
$923$	−0.972691	+	5.51641i	−0.0320165	+	0.181575i
$924$	7.17491	+	3.89893i	0.236037	+	0.128266i
$925$	−39.4773	+	33.1254i	−1.29801	+	1.08916i
$926$	13.3057	−	7.68205i	0.437253	−	0.252448i
$927$	−47.1290	−	21.7300i	−1.54792	−	0.713708i
$928$	−0.262737	+	0.455074i	−0.00862476	+	0.0149385i
$929$	8.29232	+	47.0281i	0.272062	+	1.54294i	0.748142	+	0.663539i	$0.230946\pi$
$929$	8.29232	+	47.0281i	0.272062	+	1.54294i	−0.476079	+	0.879402i	$0.657943\pi$
$930$	−26.0819	+	5.84117i	−0.855260	+	0.191539i
$931$	−26.2611	+	28.8736i	−0.860671	+	0.946292i
$932$	−0.895841	−	2.46130i	−0.0293443	−	0.0806227i
$933$	−17.5205	+	3.92381i	−0.573597	+	0.128460i
$934$	7.73499	−	1.36389i	0.253096	−	0.0446277i
$935$	4.37420	+	2.52545i	0.143052	+	0.0825910i
$936$	−0.944565	−	1.33669i	−0.0308741	−	0.0436911i
$937$	−8.40936	+	4.85515i	−0.274722	+	0.158611i	−0.631031	−	0.775757i	$-0.717368\pi$
$937$	−8.40936	+	4.85515i	−0.274722	+	0.158611i	0.356310	+	0.934368i	$0.384035\pi$
$938$	4.16419	+	26.7249i	0.135966	+	0.872598i
$939$	−11.0606	+	0.506779i	−0.360950	+	0.0165381i
$940$	−3.38381	+	19.1905i	−0.110368	+	0.625926i
$941$	−42.0583	−	35.2911i	−1.37106	−	1.15046i	−0.972390	−	0.233361i	$-0.925028\pi$
$941$	−42.0583	−	35.2911i	−1.37106	−	1.15046i	−0.398670	−	0.917095i	$-0.630528\pi$
$942$	−16.8288	+	22.0298i	−0.548313	+	0.717771i
$943$	−8.98960	+	24.6987i	−0.292742	+	0.804301i
$944$	12.4826			0.406274
$945$	21.0647	−	48.9740i	0.685234	−	1.59312i
$946$	22.2862			0.724588
$947$	7.60485	−	20.8941i	0.247124	−	0.678969i	−0.752664	−	0.658405i	$-0.771232\pi$
$947$	7.60485	−	20.8941i	0.247124	−	0.678969i	0.999789	−	0.0205640i	$-0.00654619\pi$
$948$	−7.05587	−	16.9312i	−0.229164	−	0.549899i
$949$	1.44890	+	1.21577i	0.0470334	+	0.0394657i
$950$	9.71882	−	55.1181i	0.315320	−	1.78827i
$951$	21.1830	+	33.0932i	0.686906	+	1.07312i
$952$	−0.297740	−	1.91083i	−0.00964981	−	0.0619304i
$953$	16.1303	−	9.31282i	0.522511	−	0.301672i	−0.215450	−	0.976515i	$-0.569122\pi$
$953$	16.1303	−	9.31282i	0.522511	−	0.301672i	0.737961	+	0.674843i	$0.235789\pi$
$954$	15.0072	+	10.4122i	0.485877	+	0.337106i
$955$	−22.8894	−	13.2152i	−0.740685	−	0.427635i
$956$	−0.892310	+	0.157338i	−0.0288594	+	0.00508868i
$957$	−0.484360	+	1.54781i	−0.0156571	+	0.0500335i
$958$	14.2814	+	39.2379i	0.461412	+	1.26772i
$959$	−0.194284	+	0.986302i	−0.00627375	+	0.0318494i
$960$	4.54838	+	4.94228i	0.146798	+	0.159511i
$961$	2.63334	+	14.9344i	0.0849465	+	0.481755i
$962$	1.40049	−	2.42572i	0.0451535	−	0.0782082i
$963$	14.6114	−	55.4850i	0.470846	−	1.78798i
$964$	−2.29548	+	1.32530i	−0.0739325	+	0.0426849i
$965$	−23.9336	+	20.0827i	−0.770450	+	0.646484i
$966$	−7.12274	−	11.6325i	−0.229170	−	0.374268i
$967$	2.81054	−	15.9394i	0.0903810	−	0.512576i	−0.905684	−	0.423953i	$-0.860642\pi$
$967$	2.81054	−	15.9394i	0.0903810	−	0.512576i	0.996065	−	0.0886232i	$-0.0282467\pi$
$968$	5.02963	−	5.99408i	0.161658	−	0.192657i
$969$	0.906311	−	7.00055i	0.0291149	−	0.224890i
$970$	−25.6514	−	9.33636i	−0.823618	−	0.299772i
$971$	−49.3484			−1.58367			−0.791833	−	0.610738i	$-0.790873\pi$
$971$	−49.3484			−1.58367			−0.791833	+	0.610738i	$0.790873\pi$
$972$	3.53759	+	15.1817i	0.113468	+	0.486955i
$973$	14.6448	−	24.2352i	0.469489	−	0.776945i
$974$	3.29748	−	9.05975i	0.105658	−	0.290293i
$975$	−1.21787	+	9.40712i	−0.0390031	+	0.301269i
$976$	5.59146	−	6.66364i	0.178978	−	0.213298i
$977$	33.6973	+	5.94175i	1.07807	+	0.190093i	0.684363	−	0.729141i	$-0.260080\pi$
$977$	33.6973	+	5.94175i	1.07807	+	0.190093i	0.393710	+	0.919235i	$0.371191\pi$
$978$	−4.69466	+	9.06596i	−0.150119	+	0.289898i
$979$	−0.144852	−	0.172628i	−0.00462951	−	0.00551723i
$980$	−14.4999	+	22.9480i	−0.463183	+	0.733048i
$981$	−46.4122	−	12.2222i	−1.48183	−	0.390224i
$982$	7.05342	−	12.2169i	0.225084	−	0.389856i
$983$	5.12805	+	29.0826i	0.163559	+	0.927591i	0.950537	+	0.310610i	$0.100533\pi$
$983$	5.12805	+	29.0826i	0.163559	+	0.927591i	−0.786978	+	0.616981i	$0.788356\pi$
$984$	−11.2543	+	10.3573i	−0.358775	+	0.330180i
$985$	−27.9517	−	76.7967i	−0.890615	−	2.44695i
$986$	0.360927	−	0.131367i	0.0114943	−	0.00418357i
$987$	17.2521	−	15.2526i	0.549141	−	0.485494i
$988$	0.528237	+	2.99578i	0.0168055	+	0.0953086i
$989$	−32.2388	−	18.6131i	−1.02513	−	0.591861i
$990$	17.0324	+	11.8172i	0.541324	+	0.375576i
$991$	15.1296	+	26.2053i	0.480609	+	0.832439i	0.999752	−	0.0222483i	$-0.00708245\pi$
$991$	15.1296	+	26.2053i	0.480609	+	0.832439i	−0.519144	+	0.854687i	$0.673749\pi$
$992$	−3.04836	+	2.55787i	−0.0967854	+	0.0812126i
$993$	−17.3815	+	11.1259i	−0.551584	+	0.353070i
$994$	−17.8725	+	20.4562i	−0.566880	+	0.648831i
$995$	59.0364	−	70.3568i	1.87158	−	2.23046i
$996$	4.35715	+	10.4554i	0.138062	+	0.331291i
$997$	1.43966	−	3.95542i	0.0455944	−	0.125270i	−0.914806	−	0.403894i	$-0.867656\pi$
$997$	1.43966	−	3.95542i	0.0455944	−	0.125270i	0.960400	+	0.278625i	$0.0898786\pi$
$998$			9.48625i			0.300282i
$999$	−21.0586	+	16.3760i	−0.666266	+	0.518115i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.z.a.293.14	yes	144
7.6	odd	2	inner	378.2.z.a.293.23	yes	144
27.20	odd	18	inner	378.2.z.a.209.23	yes	144
189.20	even	18	inner	378.2.z.a.209.14	✓	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.z.a.209.14	✓	144	189.20	even	18	inner
378.2.z.a.209.23	yes	144	27.20	odd	18	inner
378.2.z.a.293.14	yes	144	1.1	even	1	trivial
378.2.z.a.293.23	yes	144	7.6	odd	2	inner

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:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	378.z (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.342020 - 0.939693i) q^{2} +(-1.71772 - 0.222380i) q^{3} +(-0.766044 - 0.642788i) q^{4} +(0.673387 - 3.81897i) q^{5} +(-0.796462 + 1.53807i) q^{6} +(-2.61421 + 0.407338i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(2.90109 + 0.763972i) q^{9} +O(q^{10})\)	\(q+(0.342020 - 0.939693i) q^{2} +(-1.71772 - 0.222380i) q^{3} +(-0.766044 - 0.642788i) q^{4} +(0.673387 - 3.81897i) q^{5} +(-0.796462 + 1.53807i) q^{6} +(-2.61421 + 0.407338i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(2.90109 + 0.763972i) q^{9} +(-3.35834 - 1.93894i) q^{10} +(-1.75486 + 0.309429i) q^{11} +(1.17290 + 1.27448i) q^{12} +(0.186600 + 0.512680i) q^{13} +(-0.511339 + 2.59587i) q^{14} +(-2.00595 + 6.41015i) q^{15} +(0.173648 + 0.984808i) q^{16} +(0.365471 - 0.633014i) q^{17} +(1.71013 - 2.46484i) q^{18} +(-4.82869 + 2.78784i) q^{19} +(-2.97063 + 2.49265i) q^{20} +(4.58105 - 0.118342i) q^{21} +(-0.309429 + 1.75486i) q^{22} +(1.91324 - 2.28011i) q^{23} +(1.59878 - 0.666271i) q^{24} +(-9.43258 - 3.43318i) q^{25} +0.545583 q^{26} +(-4.81336 - 1.95743i) q^{27} +(2.26443 + 1.36834i) q^{28} +(-0.179723 + 0.493784i) q^{29} +(5.33749 + 4.07738i) q^{30} +(-2.55787 + 3.04836i) q^{31} +(0.984808 + 0.173648i) q^{32} +(3.08316 - 0.141265i) q^{33} +(-0.469840 - 0.559934i) q^{34} +(-0.204763 + 10.2579i) q^{35} +(-1.73130 - 2.45002i) q^{36} +(2.56696 - 4.44610i) q^{37} +(0.968208 + 5.49098i) q^{38} +(-0.206516 - 0.922135i) q^{39} +(1.32631 + 3.64401i) q^{40} +(-8.29798 + 3.02022i) q^{41} +(1.45561 - 4.34525i) q^{42} +(-2.17178 - 12.3168i) q^{43} +(1.54320 + 0.890967i) q^{44} +(4.87114 - 10.5647i) q^{45} +(-1.48824 - 2.57770i) q^{46} +(3.84942 - 3.23005i) q^{47} +(-0.0792764 - 1.73024i) q^{48} +(6.66815 - 2.12973i) q^{49} +(-6.45227 + 7.68951i) q^{50} +(-0.768545 + 1.00606i) q^{51} +(0.186600 - 0.512680i) q^{52} +6.08851i q^{53} +(-3.48565 + 3.85360i) q^{54} +6.91012i q^{55} +(2.06030 - 1.65987i) q^{56} +(8.91427 - 3.71492i) q^{57} +(0.402536 + 0.337768i) q^{58} +(2.16758 - 12.2930i) q^{59} +(5.65701 - 3.62106i) q^{60} +(-5.59146 - 6.66364i) q^{61} +(1.98967 + 3.44621i) q^{62} +(-7.89525 - 0.815456i) q^{63} +(0.500000 - 0.866025i) q^{64} +(2.08356 - 0.367388i) q^{65} +(0.921758 - 2.94554i) q^{66} +(9.60642 - 3.49645i) q^{67} +(-0.686860 + 0.249997i) q^{68} +(-3.79346 + 3.49112i) q^{69} +(9.56920 + 3.70081i) q^{70} +(8.89149 + 5.13351i) q^{71} +(-2.89441 + 0.788928i) q^{72} +(3.00231 - 1.73338i) q^{73} +(-3.30002 - 3.93281i) q^{74} +(15.4390 + 7.99485i) q^{75} +(5.49098 + 0.968208i) q^{76} +(4.46153 - 1.52373i) q^{77} +(-0.937156 - 0.121327i) q^{78} +(-9.95144 - 3.62203i) q^{79} +3.87788 q^{80} +(7.83269 + 4.43271i) q^{81} +8.83052i q^{82} +(6.14522 + 2.23668i) q^{83} +(-3.58535 - 2.85399i) q^{84} +(-2.17136 - 1.82198i) q^{85} +(-12.3168 - 2.17178i) q^{86} +(0.418520 - 0.808214i) q^{87} +(1.36504 - 1.14540i) q^{88} +(0.0632320 + 0.109521i) q^{89} +(-8.26157 - 8.19073i) q^{90} +(-0.696646 - 1.26424i) q^{91} +(-2.93126 + 0.516860i) q^{92} +(5.07159 - 4.66739i) q^{93} +(-1.71867 - 4.72201i) q^{94} +(7.39510 + 20.3179i) q^{95} +(-1.65300 - 0.517280i) q^{96} +(6.93239 - 1.22237i) q^{97} +(0.279351 - 6.99442i) q^{98} +(-5.32741 - 0.442981i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 12 q^{9}+O(q^{10}) \) 144 * q - 12 * q^9	\( 144 q - 12 q^{9} + 12 q^{11} + 6 q^{14} + 12 q^{15} + 24 q^{21} - 60 q^{23} + 12 q^{29} - 72 q^{30} + 54 q^{35} - 12 q^{36} + 48 q^{39} + 24 q^{42} + 18 q^{49} - 60 q^{50} - 36 q^{51} + 6 q^{56} - 60 q^{57} - 36 q^{60} - 78 q^{63} + 72 q^{64} - 120 q^{65} + 36 q^{70} - 72 q^{71} - 24 q^{72} - 36 q^{74} + 66 q^{77} - 60 q^{78} - 72 q^{79} + 12 q^{84} - 72 q^{85} - 48 q^{86} - 18 q^{91} + 12 q^{92} + 24 q^{93} - 120 q^{95} + 36 q^{98} + 144 q^{99}+O(q^{100}) \) 144 * q - 12 * q^9 + 12 * q^11 + 6 * q^14 + 12 * q^15 + 24 * q^21 - 60 * q^23 + 12 * q^29 - 72 * q^30 + 54 * q^35 - 12 * q^36 + 48 * q^39 + 24 * q^42 + 18 * q^49 - 60 * q^50 - 36 * q^51 + 6 * q^56 - 60 * q^57 - 36 * q^60 - 78 * q^63 + 72 * q^64 - 120 * q^65 + 36 * q^70 - 72 * q^71 - 24 * q^72 - 36 * q^74 + 66 * q^77 - 60 * q^78 - 72 * q^79 + 12 * q^84 - 72 * q^85 - 48 * q^86 - 18 * q^91 + 12 * q^92 + 24 * q^93 - 120 * q^95 + 36 * q^98 + 144 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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