LMFDB - Embedded newform 378.2.z.a.293.7

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			293.7
Character	$\chi$	$=$	378.293
Dual form			378.2.z.a.209.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.342020 + 0.939693i) q^{2} +(0.0584270 - 1.73107i) q^{3} +(-0.766044 - 0.642788i) q^{4} +(-0.439464 + 2.49233i) q^{5} +(1.60669 + 0.646963i) q^{6} +(0.411710 - 2.61352i) q^{7} +(0.866025 - 0.500000i) q^{8} +(-2.99317 - 0.202282i) q^{9} +O(q^{10})$	\(q+(-0.342020 + 0.939693i) q^{2} +(0.0584270 - 1.73107i) q^{3} +(-0.766044 - 0.642788i) q^{4} +(-0.439464 + 2.49233i) q^{5} +(1.60669 + 0.646963i) q^{6} +(0.411710 - 2.61352i) q^{7} +(0.866025 - 0.500000i) q^{8} +(-2.99317 - 0.202282i) q^{9} +(-2.19171 - 1.26539i) q^{10} +(5.67484 - 1.00063i) q^{11} +(-1.15746 + 1.28852i) q^{12} +(-0.939285 - 2.58066i) q^{13} +(2.31509 + 1.28076i) q^{14} +(4.28870 + 0.906360i) q^{15} +(0.173648 + 0.984808i) q^{16} +(1.32323 - 2.29190i) q^{17} +(1.21381 - 2.74348i) q^{18} +(-0.0684419 + 0.0395149i) q^{19} +(1.93869 - 1.62675i) q^{20} +(-4.50012 - 0.865397i) q^{21} +(-1.00063 + 5.67484i) q^{22} +(0.0439715 - 0.0524032i) q^{23} +(-0.814933 - 1.52836i) q^{24} +(-1.32009 - 0.480475i) q^{25} +2.74628 q^{26} +(-0.525045 + 5.16956i) q^{27} +(-1.99533 + 1.73743i) q^{28} +(3.25621 - 8.94637i) q^{29} +(-2.31852 + 3.72007i) q^{30} +(6.33874 - 7.55421i) q^{31} +(-0.984808 - 0.173648i) q^{32} +(-1.40059 - 9.88198i) q^{33} +(1.70111 + 2.02730i) q^{34} +(6.33281 + 2.17466i) q^{35} +(2.16288 + 2.07893i) q^{36} +(-2.36082 + 4.08905i) q^{37} +(-0.0137234 - 0.0778292i) q^{38} +(-4.52218 + 1.47518i) q^{39} +(0.865576 + 2.37815i) q^{40} +(2.92039 - 1.06294i) q^{41} +(2.35234 - 3.93275i) q^{42} +(0.166535 + 0.944466i) q^{43} +(-4.99037 - 2.88119i) q^{44} +(1.81954 - 7.37106i) q^{45} +(0.0342038 + 0.0592427i) q^{46} +(-5.94050 + 4.98467i) q^{47} +(1.71491 - 0.243057i) q^{48} +(-6.66099 - 2.15203i) q^{49} +(0.902998 - 1.07615i) q^{50} +(-3.89011 - 2.42450i) q^{51} +(-0.939285 + 2.58066i) q^{52} +11.8856i q^{53} +(-4.67822 - 2.26147i) q^{54} +14.5833i q^{55} +(-0.950210 - 2.46923i) q^{56} +(0.0644041 + 0.120786i) q^{57} +(7.29314 + 6.11967i) q^{58} +(-1.48510 + 8.42242i) q^{59} +(-2.70274 - 3.45104i) q^{60} +(-1.31788 - 1.57059i) q^{61} +(4.93066 + 8.54016i) q^{62} +(-1.76099 + 7.73944i) q^{63} +(0.500000 - 0.866025i) q^{64} +(6.84464 - 1.20689i) q^{65} +(9.76505 + 2.06371i) q^{66} +(-0.412498 + 0.150137i) q^{67} +(-2.48686 + 0.905142i) q^{68} +(-0.0881442 - 0.0791793i) q^{69} +(-4.20947 + 5.20712i) q^{70} +(-6.39570 - 3.69256i) q^{71} +(-2.69330 + 1.32141i) q^{72} +(-7.57975 + 4.37617i) q^{73} +(-3.03501 - 3.61698i) q^{74} +(-0.908863 + 2.25710i) q^{75} +(0.0778292 + 0.0137234i) q^{76} +(-0.278774 - 15.2433i) q^{77} +(0.160457 - 4.75400i) q^{78} +(-1.93834 - 0.705499i) q^{79} -2.53077 q^{80} +(8.91816 + 1.21093i) q^{81} +3.10782i q^{82} +(4.09628 + 1.49092i) q^{83} +(2.89103 + 3.55555i) q^{84} +(5.13065 + 4.30512i) q^{85} +(-0.944466 - 0.166535i) q^{86} +(-15.2965 - 6.15942i) q^{87} +(4.41424 - 3.70399i) q^{88} +(8.31838 + 14.4079i) q^{89} +(6.30421 + 4.23087i) q^{90} +(-7.13133 + 1.39236i) q^{91} +(-0.0673683 + 0.0118788i) q^{92} +(-12.7065 - 11.4141i) q^{93} +(-2.65229 - 7.28710i) q^{94} +(-0.0684063 - 0.187945i) q^{95} +(-0.358136 + 1.69462i) q^{96} +(-5.68626 + 1.00264i) q^{97} +(4.30043 - 5.52325i) q^{98} +(-17.1882 + 1.84713i) 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
$3$	0.0584270	−	1.73107i	0.0337328	−	0.999431i
$3$	0.0584270	−	1.73107i	0.0337328	−	0.999431i
$4$	−0.766044	−	0.642788i	−0.383022	−	0.321394i
$5$	−0.439464	+	2.49233i	−0.196534	+	1.11460i	0.713682	+	0.700470i	$0.247026\pi$
$5$	−0.439464	+	2.49233i	−0.196534	+	1.11460i	−0.910217	+	0.414132i	$0.864085\pi$
$6$	1.60669	+	0.646963i	0.655927	+	0.264121i
$7$	0.411710	−	2.61352i	0.155612	−	0.987818i
$7$	0.411710	−	2.61352i	0.155612	−	0.987818i
$8$	0.866025	−	0.500000i	0.306186	−	0.176777i
$9$	−2.99317	−	0.202282i	−0.997724	−	0.0674273i
$10$	−2.19171	−	1.26539i	−0.693081	−	0.400150i
$11$	5.67484	−	1.00063i	1.71103	−	0.301701i	0.769503	−	0.638643i	$-0.220504\pi$
$11$	5.67484	−	1.00063i	1.71103	−	0.301701i	0.941525	+	0.336942i	$0.109393\pi$
$12$	−1.15746	+	1.28852i	−0.334131	+	0.371963i
$13$	−0.939285	−	2.58066i	−0.260511	−	0.715747i	−0.999133	−	0.0416280i	$-0.986746\pi$
$13$	−0.939285	−	2.58066i	−0.260511	−	0.715747i	0.738622	−	0.674119i	$-0.235477\pi$
$14$	2.31509	+	1.28076i	0.618735	+	0.342297i
$15$	4.28870	+	0.906360i	1.10734	+	0.234021i
$16$	0.173648	+	0.984808i	0.0434120	+	0.246202i
$17$	1.32323	−	2.29190i	0.320930	−	0.555867i	−0.659750	−	0.751485i	$-0.729338\pi$
$17$	1.32323	−	2.29190i	0.320930	−	0.555867i	0.980680	+	0.195618i	$0.0626712\pi$
$18$	1.21381	−	2.74348i	0.286097	−	0.646644i
$19$	−0.0684419	+	0.0395149i	−0.0157016	+	0.00906535i	−0.507830	−	0.861457i	$-0.669552\pi$
$19$	−0.0684419	+	0.0395149i	−0.0157016	+	0.00906535i	0.492129	+	0.870522i	$0.336219\pi$
$20$	1.93869	−	1.62675i	0.433503	−	0.363752i
$21$	−4.50012	−	0.865397i	−0.982007	−	0.188845i
$22$	−1.00063	+	5.67484i	−0.213334	+	1.20988i
$23$	0.0439715	−	0.0524032i	0.00916869	−	0.0109268i	−0.761441	−	0.648235i	$-0.775508\pi$
$23$	0.0439715	−	0.0524032i	0.00916869	−	0.0109268i	0.770609	+	0.637308i	$0.219952\pi$
$24$	−0.814933	−	1.52836i	−0.166348	−	0.311975i
$25$	−1.32009	−	0.480475i	−0.264019	−	0.0960950i
$26$	2.74628			0.538591
$27$	−0.525045	+	5.16956i	−0.101045	+	0.994882i
$28$	−1.99533	+	1.73743i	−0.377081	+	0.328344i
$29$	3.25621	−	8.94637i	0.604663	−	1.66130i	−0.137036	−	0.990566i	$-0.543758\pi$
$29$	3.25621	−	8.94637i	0.604663	−	1.66130i	0.741699	−	0.670732i	$-0.234020\pi$
$30$	−2.31852	+	3.72007i	−0.423302	+	0.679188i
$31$	6.33874	−	7.55421i	1.13847	−	1.35678i	0.213407	−	0.976963i	$-0.431544\pi$
$31$	6.33874	−	7.55421i	1.13847	−	1.35678i	0.925063	−	0.379813i	$-0.124012\pi$
$32$	−0.984808	−	0.173648i	−0.174091	−	0.0306970i
$33$	−1.40059	−	9.88198i	−0.243811	−	1.72023i
$34$	1.70111	+	2.02730i	0.291738	+	0.347680i
$35$	6.33281	+	2.17466i	1.07044	+	0.367585i
$36$	2.16288	+	2.07893i	0.360480	+	0.346489i
$37$	−2.36082	+	4.08905i	−0.388116	+	0.672236i	−0.992196	−	0.124687i	$-0.960207\pi$
$37$	−2.36082	+	4.08905i	−0.388116	+	0.672236i	0.604080	+	0.796923i	$0.293541\pi$
$38$	−0.0137234	−	0.0778292i	−0.00222623	−	0.0126256i
$39$	−4.52218	+	1.47518i	−0.724128	+	0.236218i
$40$	0.865576	+	2.37815i	0.136860	+	0.376018i
$41$	2.92039	−	1.06294i	0.456089	−	0.166003i	−0.103752	−	0.994603i	$-0.533085\pi$
$41$	2.92039	−	1.06294i	0.456089	−	0.166003i	0.559840	+	0.828601i	$0.310862\pi$
$42$	2.35234	−	3.93275i	0.362974	−	0.606836i
$43$	0.166535	+	0.944466i	0.0253963	+	0.144030i	0.994869	−	0.101168i	$-0.0322581\pi$
$43$	0.166535	+	0.944466i	0.0253963	+	0.144030i	−0.969473	+	0.245198i	$0.921147\pi$
$44$	−4.99037	−	2.88119i	−0.752327	−	0.434356i
$45$	1.81954	−	7.37106i	0.271242	−	1.09881i
$46$	0.0342038	+	0.0592427i	0.00504307	+	0.00873485i
$47$	−5.94050	+	4.98467i	−0.866511	+	0.727089i	−0.963360	−	0.268210i	$-0.913568\pi$
$47$	−5.94050	+	4.98467i	−0.866511	+	0.727089i	0.0968495	+	0.995299i	$0.469123\pi$
$48$	1.71491	−	0.243057i	0.247526	−	0.0350823i
$49$	−6.66099	−	2.15203i	−0.951570	−	0.307432i
$50$	0.902998	−	1.07615i	0.127703	−	0.152191i
$51$	−3.89011	−	2.42450i	−0.544725	−	0.339498i
$52$	−0.939285	+	2.58066i	−0.130255	+	0.357874i
$53$			11.8856i			1.63262i	0.577614	+	0.816310i	$0.303984\pi$
$53$			11.8856i			1.63262i	−0.577614	+	0.816310i	$0.696016\pi$
$54$	−4.67822	−	2.26147i	−0.636625	−	0.307748i
$55$			14.5833i			1.96641i
$56$	−0.950210	−	2.46923i	−0.126977	−	0.329965i
$57$	0.0644041	+	0.120786i	0.00853053	+	0.0159985i
$58$	7.29314	+	6.11967i	0.957637	+	0.803553i
$59$	−1.48510	+	8.42242i	−0.193344	+	1.09651i	0.721414	+	0.692504i	$0.243492\pi$
$59$	−1.48510	+	8.42242i	−0.193344	+	1.09651i	−0.914758	+	0.404002i	$0.867619\pi$
$60$	−2.70274	−	3.45104i	−0.348922	−	0.445527i
$61$	−1.31788	−	1.57059i	−0.168738	−	0.201094i	0.675048	−	0.737774i	$-0.264123\pi$
$61$	−1.31788	−	1.57059i	−0.168738	−	0.201094i	−0.843786	+	0.536680i	$0.819678\pi$
$62$	4.93066	+	8.54016i	0.626195	+	1.08460i
$63$	−1.76099	+	7.73944i	−0.221863	+	0.975078i
$64$	0.500000	−	0.866025i	0.0625000	−	0.108253i
$65$	6.84464	−	1.20689i	0.848973	−	0.149697i
$66$	9.76505	+	2.06371i	1.20199	+	0.254026i
$67$	−0.412498	+	0.150137i	−0.0503946	+	0.0183421i	−0.367094	−	0.930184i	$-0.619647\pi$
$67$	−0.412498	+	0.150137i	−0.0503946	+	0.0183421i	0.316700	+	0.948526i	$0.397425\pi$
$68$	−2.48686	+	0.905142i	−0.301576	+	0.109765i
$69$	−0.0881442	−	0.0791793i	−0.0106113	−	0.00953207i
$70$	−4.20947	+	5.20712i	−0.503127	+	0.622370i
$71$	−6.39570	−	3.69256i	−0.759030	−	0.438226i	0.0699172	−	0.997553i	$-0.477726\pi$
$71$	−6.39570	−	3.69256i	−0.759030	−	0.438226i	−0.828947	+	0.559326i	$0.811060\pi$
$72$	−2.69330	+	1.32141i	−0.317409	+	0.155729i
$73$	−7.57975	+	4.37617i	−0.887143	+	0.512192i	−0.873007	−	0.487708i	$-0.837833\pi$
$73$	−7.57975	+	4.37617i	−0.887143	+	0.512192i	−0.0141362	+	0.999900i	$0.504500\pi$
$74$	−3.03501	−	3.61698i	−0.352812	−	0.420465i
$75$	−0.908863	+	2.25710i	−0.104946	+	0.260627i
$76$	0.0778292	+	0.0137234i	0.00892763	+	0.00157418i
$77$	−0.278774	−	15.2433i	−0.0317692	−	1.73713i
$78$	0.160457	−	4.75400i	0.0181682	−	0.538284i
$79$	−1.93834	−	0.705499i	−0.218081	−	0.0793749i	0.230669	−	0.973032i	$-0.425908\pi$
$79$	−1.93834	−	0.705499i	−0.218081	−	0.0793749i	−0.448750	+	0.893657i	$0.648131\pi$
$80$	−2.53077			−0.282949
$81$	8.91816	+	1.21093i	0.990907	+	0.134548i
$82$			3.10782i			0.343201i
$83$	4.09628	+	1.49092i	0.449625	+	0.163650i	0.556901	−	0.830579i	$-0.311990\pi$
$83$	4.09628	+	1.49092i	0.449625	+	0.163650i	−0.107275	+	0.994229i	$0.534213\pi$
$84$	2.89103	+	3.55555i	0.315437	+	0.387943i
$85$	5.13065	+	4.30512i	0.556497	+	0.466956i
$86$	−0.944466	−	0.166535i	−0.101844	−	0.0179579i
$87$	−15.2965	−	6.15942i	−1.63996	−	0.660359i
$88$	4.41424	−	3.70399i	0.470560	−	0.394847i
$89$	8.31838	+	14.4079i	0.881747	+	1.52723i	0.849397	+	0.527754i	$0.176966\pi$
$89$	8.31838	+	14.4079i	0.881747	+	1.52723i	0.0323494	+	0.999477i	$0.489701\pi$
$90$	6.30421	+	4.23087i	0.664523	+	0.445972i
$91$	−7.13133	+	1.39236i	−0.747567	+	0.145959i
$92$	−0.0673683	+	0.0118788i	−0.00702363	+	0.00123845i
$93$	−12.7065	−	11.4141i	−1.31760	−	1.18359i
$94$	−2.65229	−	7.28710i	−0.273563	−	0.751607i
$95$	−0.0684063	−	0.187945i	−0.00701834	−	0.0192827i
$96$	−0.358136	+	1.69462i	−0.0365521	+	0.172956i
$97$	−5.68626	+	1.00264i	−0.577352	+	0.101803i	−0.454696	−	0.890647i	$-0.650252\pi$
$97$	−5.68626	+	1.00264i	−0.577352	+	0.101803i	−0.122656	+	0.992449i	$0.539141\pi$
$98$	4.30043	−	5.52325i	0.434410	−	0.557932i
$99$	−17.1882	+	1.84713i	−1.72748	+	0.185644i
$100$	0.702408	+	1.21661i	0.0702408	+	0.121661i
$101$	11.6019	−	9.73518i	1.15444	−	0.968687i	0.154622	−	0.987974i	$-0.450584\pi$
$101$	11.6019	−	9.73518i	1.15444	−	0.968687i	0.999814	+	0.0192866i	$0.00613951\pi$
$102$	3.60878	−	2.82628i	0.357323	−	0.279844i
$103$	6.96549	+	1.22820i	0.686330	+	0.121019i	0.505930	−	0.862575i	$-0.331150\pi$
$103$	6.96549	+	1.22820i	0.686330	+	0.121019i	0.180400	+	0.983593i	$0.442261\pi$
$104$	−2.10378	−	1.76528i	−0.206292	−	0.173100i
$105$	4.13449	−	10.8355i	0.403485	−	1.05743i
$106$	−11.1689	−	4.06513i	−1.08482	−	0.394840i
$107$			1.46967i			0.142079i	0.997474	+	0.0710393i	$0.0226316\pi$
$107$			1.46967i			0.142079i	−0.997474	+	0.0710393i	$0.977368\pi$
$108$	3.72514	−	3.62262i	0.358451	−	0.348587i
$109$	−20.3221			−1.94650			−0.973252	−	0.229738i	$-0.926213\pi$
$109$	−20.3221			−1.94650			−0.973252	+	0.229738i	$0.926213\pi$
$110$	−13.7038	−	4.98778i	−1.30661	−	0.475566i
$111$	6.94048	+	4.32564i	0.658762	+	0.410571i
$112$	2.64531	−	0.0483782i	0.249958	−	0.00457131i
$113$	−5.70623	−	1.00616i	−0.536797	−	0.0946518i	−0.101324	−	0.994853i	$-0.532308\pi$
$113$	−5.70623	−	1.00616i	−0.536797	−	0.0946518i	−0.435473	+	0.900202i	$0.643419\pi$
$114$	−0.135529	+	0.0192088i	−0.0126935	+	0.00179907i
$115$	0.111282	+	0.132621i	0.0103771	+	0.0123669i
$116$	−8.24502	+	4.76026i	−0.765530	+	0.441979i
$117$	2.28942	+	7.91437i	0.211657	+	0.731684i
$118$	−7.40655	−	4.27618i	−0.681828	−	0.393654i
$119$	−5.44514	−	4.40188i	−0.499155	−	0.403520i
$120$	4.16730	−	1.35942i	0.380421	−	0.124097i
$121$	20.8659	−	7.59458i	1.89690	−	0.690416i
$122$	1.92662	−	0.701231i	0.174428	−	0.0634865i
$123$	−1.66938	−	5.11749i	−0.150523	−	0.461429i
$124$	−9.71151	+	1.71240i	−0.872119	+	0.153778i
$125$	−4.54930	+	7.87962i	−0.406902	+	0.704774i
$126$	−6.67040	−	4.30183i	−0.594247	−	0.383238i
$127$	−7.70758	−	13.3499i	−0.683937	−	1.18461i	−0.973769	−	0.227537i	$-0.926933\pi$
$127$	−7.70758	−	13.3499i	−0.683937	−	1.18461i	0.289832	−	0.957078i	$-0.406401\pi$
$128$	0.642788	+	0.766044i	0.0568149	+	0.0677094i
$129$	1.64466	−	0.233100i	0.144804	−	0.0205233i
$130$	−1.20689	+	6.84464i	−0.105852	+	0.600314i
$131$	8.28940	+	6.95564i	0.724249	+	0.607717i	0.928557	−	0.371190i	$-0.121050\pi$
$131$	8.28940	+	6.95564i	0.724249	+	0.607717i	−0.204308	+	0.978907i	$0.565495\pi$
$132$	−5.27910	+	8.47032i	−0.459487	+	0.737246i
$133$	0.0750950	+	0.195143i	0.00651156	+	0.0169210i
$134$		−	0.438971i		−	0.0379213i
$135$	−12.6535	−	3.58042i	−1.08904	−	0.308153i
$136$		−	2.64646i		−	0.226932i
$137$	−6.38887	+	17.5533i	−0.545838	+	1.49968i	0.293441	+	0.955977i	$0.405200\pi$
$137$	−6.38887	+	17.5533i	−0.545838	+	1.49968i	−0.839279	+	0.543701i	$0.817022\pi$
$138$	0.104551	−	0.0557476i	0.00890000	−	0.00474555i
$139$	2.27325	−	2.70915i	0.192814	−	0.229787i	−0.660972	−	0.750410i	$-0.729856\pi$
$139$	2.27325	−	2.70915i	0.192814	−	0.229787i	0.853787	+	0.520623i	$0.174300\pi$
$140$	−3.45337	−	5.73654i	−0.291863	−	0.484826i
$141$	8.28171	+	10.5746i	0.697445	+	0.890545i
$142$	5.65733	−	4.74706i	0.474753	−	0.398365i
$143$	−7.91257	−	13.7050i	−0.661683	−	1.14607i
$144$	−0.320550	−	2.98283i	−0.0267125	−	0.248569i
$145$	20.8663	+	12.0471i	1.73285	+	1.00046i
$146$	−1.51983	−	8.61938i	−0.125782	−	0.713345i
$147$	−4.11448	+	11.4049i	−0.339356	+	0.940658i
$148$	4.43688	−	1.61489i	0.364710	−	0.132743i
$149$	−1.46161	−	4.01575i	−0.119740	−	0.328983i	0.865314	−	0.501231i	$-0.167119\pi$
$149$	−1.46161	−	4.01575i	−0.119740	−	0.328983i	−0.985054	+	0.172248i	$0.944897\pi$
$150$	−1.81013	−	1.62602i	−0.147796	−	0.132764i
$151$	−0.653239	−	3.70470i	−0.0531598	−	0.301484i	0.946623	−	0.322344i	$-0.104471\pi$
$151$	−0.653239	−	3.70470i	−0.0531598	−	0.301484i	−0.999782	+	0.0208597i	$0.993360\pi$
$152$	−0.0395149	+	0.0684419i	−0.00320509	+	0.00555137i
$153$	−4.42426	+	6.59238i	−0.357680	+	0.532963i
$154$	14.4193	+	4.95155i	1.16194	+	0.399007i
$155$	16.0419	+	19.1180i	1.28852	+	1.53559i
$156$	4.41242	+	1.77674i	0.353276	+	0.142253i
$157$	13.6837	+	2.41281i	1.09208	+	0.192563i	0.690552	−	0.723283i	$-0.257368\pi$
$157$	13.6837	+	2.41281i	1.09208	+	0.192563i	0.401529	+	0.915846i	$0.368479\pi$
$158$	1.32590	−	1.58015i	0.105483	−	0.125710i
$159$	20.5748	+	0.694443i	1.63169	+	0.0550729i
$160$	0.865576	−	2.37815i	0.0684298	−	0.188009i
$161$	−0.118853	−	0.136495i	−0.00936696	−	0.0107573i
$162$	−4.18809	+	7.96617i	−0.329048	+	0.625882i
$163$	19.8404			1.55402			0.777008	−	0.629490i	$-0.216736\pi$
$163$	19.8404			1.55402			0.777008	+	0.629490i	$0.216736\pi$
$164$	−2.92039	−	1.06294i	−0.228044	−	0.0830013i
$165$	25.2446	+	0.852057i	1.96529	+	0.0663326i
$166$	−2.80202	+	3.33932i	−0.217479	+	0.259181i
$167$	−2.04551	+	11.6007i	−0.158286	+	0.897686i	0.797433	+	0.603407i	$0.206191\pi$
$167$	−2.04551	+	11.6007i	−0.158286	+	0.897686i	−0.955720	+	0.294279i	$0.904920\pi$
$168$	−4.32992	+	1.50060i	−0.334060	+	0.115774i
$169$	4.18101	−	3.50828i	0.321616	−	0.269868i
$170$	−5.80028	+	3.34879i	−0.444861	+	0.256841i
$171$	0.212852	−	0.104430i	0.0162772	−	0.00798600i
$172$	0.479518	−	0.830550i	0.0365629	−	0.0633288i
$173$	−2.93691	−	16.6560i	−0.223289	−	1.26633i	−0.865929	−	0.500167i	$-0.833272\pi$
$173$	−2.93691	−	16.6560i	−0.223289	−	1.26633i	0.642640	−	0.766168i	$-0.277839\pi$
$174$	11.0197	−	12.2674i	0.835399	−	0.929986i
$175$	−1.79923	+	3.25228i	−0.136009	+	0.245849i
$176$	1.97085	+	5.41487i	0.148558	+	0.408161i
$177$	14.4930	+	3.06290i	1.08936	+	0.230222i
$178$	−16.3840	+	2.88894i	−1.22803	+	0.216536i
$179$	9.01685	+	5.20588i	0.673951	+	0.389106i	0.797572	−	0.603224i	$-0.206117\pi$
$179$	9.01685	+	5.20588i	0.673951	+	0.389106i	−0.123621	+	0.992329i	$0.539451\pi$
$180$	−6.13188	+	4.47698i	−0.457043	+	0.333695i
$181$	5.74686	−	3.31795i	0.427161	−	0.246621i	−0.270976	−	0.962586i	$-0.587346\pi$
$181$	5.74686	−	3.31795i	0.427161	−	0.246621i	0.698136	+	0.715965i	$0.254013\pi$
$182$	1.13067	−	7.17747i	0.0838110	−	0.532030i
$183$	−2.79580	+	2.18958i	−0.206671	+	0.161858i
$184$	0.0118788	−	0.0673683i	0.000875720	−	0.00496645i
$185$	−9.15376	−	7.68092i	−0.672998	−	0.564712i
$186$	15.0716	−	8.03632i	1.10511	−	0.589252i
$187$	5.21577	−	14.3302i	0.381415	−	1.04793i
$188$	7.75477			0.565575
$189$	13.2946	+	3.50057i	0.967039	+	0.254629i
$190$	0.200007			0.0145100
$191$	−2.88001	+	7.91277i	−0.208390	+	0.572548i	−0.999220	−	0.0394885i	$-0.987427\pi$
$191$	−2.88001	+	7.91277i	−0.208390	+	0.572548i	0.790830	+	0.612036i	$0.209649\pi$
$192$	−1.46993	−	0.916132i	−0.106083	−	0.0661161i
$193$	−7.44722	−	6.24896i	−0.536063	−	0.449810i	0.334126	−	0.942528i	$-0.391559\pi$
$193$	−7.44722	−	6.24896i	−0.536063	−	0.449810i	−0.870189	+	0.492718i	$0.836003\pi$
$194$	1.00264	−	5.68626i	0.0719854	−	0.408249i
$195$	−1.68930	−	11.9190i	−0.120973	−	0.853539i
$196$	3.71932	+	5.93015i	0.265666	+	0.423582i
$197$	−4.51790	+	2.60841i	−0.321887	+	0.185842i	−0.652233	−	0.758018i	$-0.726168\pi$
$197$	−4.51790	+	2.60841i	−0.321887	+	0.185842i	0.330346	+	0.943860i	$0.392834\pi$
$198$	4.14297	−	16.7834i	0.294428	−	1.19274i
$199$	6.08386	+	3.51252i	0.431274	+	0.248996i	0.699889	−	0.714252i	$-0.253233\pi$
$199$	6.08386	+	3.51252i	0.431274	+	0.248996i	−0.268615	+	0.963247i	$0.586566\pi$
$200$	−1.38347	+	0.243944i	−0.0978263	+	0.0172494i
$201$	0.235796	+	0.722833i	0.0166318	+	0.0509847i
$202$	5.17998	+	14.2319i	0.364462	+	1.00135i
$203$	−22.0409	−	12.1935i	−1.54697	−	0.855815i
$204$	1.42156	+	4.35779i	0.0995291	+	0.305107i
$205$	1.36577	+	7.74569i	0.0953898	+	0.540982i
$206$	−3.53647	+	6.12535i	−0.246398	+	0.426773i
$207$	−0.142215	+	0.147957i	−0.00988459	+	0.0102837i
$208$	2.37835	−	1.37314i	0.164909	−	0.0952103i
$209$	−0.348857	+	0.292726i	−0.0241309	+	0.0202483i
$210$	8.76792	+	7.59110i	0.605044	+	0.523835i
$211$	−2.65848	+	15.0770i	−0.183017	+	1.03794i	0.745459	+	0.666551i	$0.232230\pi$
$211$	−2.65848	+	15.0770i	−0.183017	+	1.03794i	−0.928477	+	0.371391i	$0.878881\pi$
$212$	7.63995	−	9.10494i	0.524714	−	0.625330i
$213$	−6.76574	+	10.8556i	−0.463581	+	0.743816i
$214$	−1.38104	−	0.502657i	−0.0944059	−	0.0343609i
$215$	−2.42710			−0.165527
$216$	2.13008	+	4.73949i	0.144933	+	0.322482i
$217$	−17.1334	−	19.6766i	−1.16309	−	1.33573i
$218$	6.95057	−	19.0965i	0.470752	−	1.29338i
$219$	7.13258	+	13.3767i	0.481975	+	0.903916i
$220$	9.37396	−	11.1714i	0.631992	−	0.753179i
$221$	−7.15751	−	1.26206i	−0.481466	−	0.0848955i
$222$	−6.43856	+	5.04247i	−0.432128	+	0.338428i
$223$	11.0017	+	13.1113i	0.736729	+	0.878000i	0.996141	−	0.0877670i	$-0.0279731\pi$
$223$	11.0017	+	13.1113i	0.736729	+	0.878000i	−0.259412	+	0.965767i	$0.583529\pi$
$224$	−0.859288	+	2.50232i	−0.0574136	+	0.167194i
$225$	3.85408	+	1.70518i	0.256939	+	0.113678i
$226$	2.89713	−	5.01798i	0.192714	−	0.333791i
$227$	0.324118	+	1.83816i	0.0215125	+	0.122003i	0.993673	−	0.112313i	$-0.0358260\pi$
$227$	0.324118	+	1.83816i	0.0215125	+	0.122003i	−0.972160	+	0.234316i	$0.924715\pi$
$228$	0.0283034	−	0.133926i	0.00187444	−	0.00886944i
$229$	−7.12438	−	19.5741i	−0.470793	−	1.29349i	−0.917116	−	0.398620i	$-0.869489\pi$
$229$	−7.12438	−	19.5741i	−0.470793	−	1.29349i	0.446323	−	0.894872i	$-0.352733\pi$
$230$	−0.162683	+	0.0592119i	−0.0107270	+	0.00390432i
$231$	−26.4034	−	0.408044i	−1.73722	−	0.0268473i
$232$	−1.65322	−	9.37589i	−0.108539	−	0.615557i
$233$	0.212113	+	0.122464i	0.0138960	+	0.00802287i	0.506932	−	0.861986i	$-0.330780\pi$
$233$	0.212113	+	0.122464i	0.0138960	+	0.00802287i	−0.493036	+	0.870009i	$0.664113\pi$
$234$	−8.22010	−	0.555523i	−0.537365	−	0.0363157i
$235$	−9.81279	−	16.9962i	−0.640116	−	1.10871i
$236$	6.55148	−	5.49735i	0.426465	−	0.357847i
$237$	−1.33452	+	3.31418i	−0.0866862	+	0.215279i
$238$	5.99877	−	3.61123i	0.388842	−	0.234081i
$239$	−14.5657	+	17.3588i	−0.942180	+	1.12285i	0.0500896	+	0.998745i	$0.484049\pi$
$239$	−14.5657	+	17.3588i	−0.942180	+	1.12285i	−0.992270	+	0.124102i	$0.960395\pi$
$240$	−0.147865	+	4.38093i	−0.00954467	+	0.282788i
$241$	4.50703	−	12.3830i	0.290324	−	0.797658i	−0.705695	−	0.708515i	$-0.749365\pi$
$241$	4.50703	−	12.3830i	0.290324	−	0.797658i	0.996019	−	0.0891422i	$-0.0284125\pi$
$242$			22.2051i			1.42740i
$243$	2.61726	−	15.3672i	0.167897	−	0.985805i
$244$			2.05026i			0.131255i
$245$	8.29081	−	15.6556i	0.529681	−	1.00020i
$246$	5.37983	+	0.181580i	0.343006	+	0.0115771i
$247$	0.166261	+	0.139510i	0.0105789	+	0.00887679i
$248$	1.71240	−	9.71151i	0.108738	−	0.616681i
$249$	2.82022	−	7.00382i	0.178724	−	0.443849i
$250$	−5.84847	−	6.96993i	−0.369890	−	0.440817i
$251$	1.43551	+	2.48637i	0.0906084	+	0.156938i	0.907767	−	0.419474i	$-0.137786\pi$
$251$	1.43551	+	2.48637i	0.0906084	+	0.156938i	−0.817159	+	0.576412i	$0.804452\pi$
$252$	6.32381	−	4.79681i	0.398363	−	0.302171i
$253$	0.197095	−	0.341379i	0.0123913	−	0.0214623i
$254$	15.1810	−	2.67682i	0.952539	−	0.167958i
$255$	7.75222	−	8.62995i	0.485463	−	0.540428i
$256$	−0.939693	+	0.342020i	−0.0587308	+	0.0213763i
$257$	1.98634	−	0.722970i	0.123905	−	0.0450976i	−0.279324	−	0.960197i	$-0.590110\pi$
$257$	1.98634	−	0.722970i	0.123905	−	0.0450976i	0.403228	+	0.915099i	$0.367888\pi$
$258$	−0.343465	+	1.62520i	−0.0213832	+	0.101181i
$259$	9.71486	+	7.85355i	0.603652	+	0.487996i
$260$	−6.01907	−	3.47511i	−0.373287	−	0.215517i
$261$	−11.5561	+	26.1193i	−0.715304	+	1.61675i
$262$	−9.37130	+	5.41052i	−0.578961	+	0.334263i
$263$	2.09424	+	2.49582i	0.129137	+	0.153899i	0.826738	−	0.562587i	$-0.190194\pi$
$263$	2.09424	+	2.49582i	0.129137	+	0.153899i	−0.697602	+	0.716486i	$0.745749\pi$
$264$	−6.15393	−	7.85775i	−0.378748	−	0.483611i
$265$	−29.6229	−	5.22332i	−1.81972	−	0.320866i
$266$	−0.209058	+	0.00382332i	−0.0128182	+	0.000234423i
$267$	25.4270	−	13.5579i	1.55611	−	0.829727i
$268$	0.412498	+	0.150137i	0.0251973	+	0.00917107i
$269$	9.84781			0.600431			0.300216	−	0.953871i	$-0.402941\pi$
$269$	9.84781			0.600431			0.300216	+	0.953871i	$0.402941\pi$
$270$	7.69224	−	10.6658i	0.468135	−	0.649100i
$271$			15.5902i			0.947039i	0.880783	+	0.473520i	$0.157017\pi$
$271$			15.5902i			0.947039i	−0.880783	+	0.473520i	$0.842983\pi$
$272$	2.48686	+	0.905142i	0.150788	+	0.0548823i
$273$	1.99360	+	12.4262i	0.120658	+	0.752065i
$274$	−14.3096	−	12.0072i	−0.864473	−	0.725379i
$275$	−7.97210	−	1.40570i	−0.480736	−	0.0847667i
$276$	0.0166269	+	0.117313i	0.00100082	+	0.00706141i
$277$	13.8273	−	11.6025i	0.830801	−	0.697125i	−0.124674	−	0.992198i	$-0.539788\pi$
$277$	13.8273	−	11.6025i	0.830801	−	0.697125i	0.955475	+	0.295073i	$0.0953440\pi$
$278$	1.76827	+	3.06274i	0.106054	+	0.183691i
$279$	−20.5010	+	21.3288i	−1.22736	+	1.27692i
$280$	6.57171	−	1.28309i	0.392735	−	0.0766795i
$281$	−2.31856	+	0.408825i	−0.138314	+	0.0243885i	−0.242376	−	0.970182i	$-0.577927\pi$
$281$	−2.31856	+	0.408825i	−0.138314	+	0.0243885i	0.104063	+	0.994571i	$0.466816\pi$
$282$	−12.7694	+	4.16552i	−0.760407	+	0.248053i
$283$	2.12368	+	5.83477i	0.126240	+	0.346841i	0.986672	−	0.162725i	$-0.0520282\pi$
$283$	2.12368	+	5.83477i	0.126240	+	0.346841i	−0.860432	+	0.509566i	$0.829806\pi$
$284$	2.52586	+	6.93974i	0.149882	+	0.411798i
$285$	−0.329342	+	0.107435i	−0.0195085	+	0.00636389i
$286$	15.5847	−	2.74801i	0.921544	−	0.162493i
$287$	−1.57565	−	8.07013i	−0.0930078	−	0.476365i
$288$	2.91257	+	0.718968i	0.171625	+	0.0423656i
$289$	4.99813	+	8.65702i	0.294008	+	0.509237i
$290$	−18.4573	+	15.4875i	−1.08385	+	0.909458i
$291$	1.40341	+	9.90186i	0.0822691	+	0.580457i
$292$	8.61938	+	1.51983i	0.504411	+	0.0889413i
$293$	−9.75529	−	8.18566i	−0.569910	−	0.478211i	0.311706	−	0.950179i	$-0.399100\pi$
$293$	−9.75529	−	8.18566i	−0.569910	−	0.478211i	−0.881616	+	0.471967i	$0.843544\pi$
$294$	−9.30984	−	7.76704i	−0.542961	−	0.452983i
$295$	−20.3388	−	7.40271i	−1.18417	−	0.431002i
$296$			4.72163i			0.274439i
$297$	2.19325	+	29.8618i	0.127266	+	1.73276i
$298$	4.27347			0.247555
$299$	−0.176537	−	0.0642541i	−0.0102094	−	0.00371591i
$300$	2.14706	−	1.14483i	0.123961	−	0.0660968i
$301$	2.53695	−	0.0463964i	0.146227	−	0.00267425i
$302$	3.70470	+	0.653239i	0.213182	+	0.0375897i
$303$	−16.1744	−	20.6525i	−0.929193	−	1.18646i
$304$	−0.0507994	−	0.0605404i	−0.00291355	−	0.00347223i
$305$	4.49359	−	2.59438i	0.257302	−	0.148554i
$306$	−4.68163	−	6.41217i	−0.267631	−	0.366560i
$307$	20.2524	+	11.6928i	1.15587	+	0.667341i	0.950310	−	0.311304i	$-0.100766\pi$
$307$	20.2524	+	11.6928i	1.15587	+	0.667341i	0.205558	+	0.978645i	$0.434099\pi$
$308$	−9.58464	+	11.8562i	−0.546136	+	0.675571i
$309$	2.53307	−	11.9860i	0.144102	−	0.681857i
$310$	−23.4517	+	8.53572i	−1.33197	+	0.484796i
$311$	−21.9617	+	7.99341i	−1.24534	+	0.453265i	−0.878823	−	0.477148i	$-0.841670\pi$
$311$	−21.9617	+	7.99341i	−1.24534	+	0.453265i	−0.366512	+	0.930413i	$0.619448\pi$
$312$	−3.17873	+	3.53863i	−0.179960	+	0.200336i
$313$	−24.4565	+	4.31234i	−1.38236	+	0.243748i	−0.814877	−	0.579634i	$-0.803195\pi$
$313$	−24.4565	+	4.31234i	−1.38236	+	0.243748i	−0.567487	+	0.823382i	$0.692084\pi$
$314$	−6.94742	+	12.0333i	−0.392065	+	0.679077i
$315$	−18.5153	−	7.79016i	−1.04322	−	0.438926i
$316$	1.03137	+	1.78639i	0.0580191	+	0.100492i
$317$	−19.1306	−	22.7990i	−1.07448	−	1.28052i	−0.957827	−	0.287344i	$-0.907228\pi$
$317$	−19.1306	−	22.7990i	−1.07448	−	1.28052i	−0.116654	−	0.993173i	$-0.537217\pi$
$318$	−7.68957	+	19.0965i	−0.431210	+	1.07088i
$319$	9.52650	−	54.0274i	0.533381	−	3.02496i
$320$	1.93869	+	1.62675i	0.108376	+	0.0909381i
$321$	2.54410	+	0.0858685i	0.141998	+	0.00479271i
$322$	0.168914	−	0.0650015i	0.00941321	−	0.00362239i
$323$			0.209149i			0.0116374i
$324$	−6.05334	−	6.66011i	−0.336297	−	0.370006i
$325$			3.85802i			0.214005i
$326$	−6.78580	+	18.6438i	−0.375831	+	1.03259i
$327$	−1.18736	+	35.1789i	−0.0656611	+	1.94540i
$328$	1.99767	−	2.38073i	0.110303	−	0.131454i
$329$	10.5818	+	17.5779i	0.583393	+	0.969099i
$330$	−9.43484	+	23.4308i	−0.519371	+	1.28982i
$331$	20.0485	−	16.8227i	1.10197	−	0.924659i	0.104410	−	0.994534i	$-0.466704\pi$
$331$	20.0485	−	16.8227i	1.10197	−	0.924659i	0.997556	+	0.0698749i	$0.0222600\pi$
$332$	−2.17959	−	3.77515i	−0.119620	−	0.207188i
$333$	7.89347	−	11.7617i	0.432560	−	0.644537i
$334$	−10.2015	−	5.88981i	−0.558199	−	0.322276i
$335$	−0.192912	−	1.09406i	−0.0105399	−	0.0597748i
$336$	0.0708116	−	4.58203i	0.00386309	−	0.249970i
$337$	0.547537	−	0.199287i	0.0298262	−	0.0108559i	−0.327064	−	0.945002i	$-0.606059\pi$
$337$	0.547537	−	0.199287i	0.0298262	−	0.0108559i	0.356890	+	0.934146i	$0.383837\pi$
$338$	1.86672	+	5.12877i	0.101536	+	0.278968i
$339$	−2.07513	+	9.81907i	−0.112706	+	0.533299i
$340$	−1.16302	−	6.59583i	−0.0630738	−	0.357709i
$341$	28.4124	−	49.2117i	1.53862	−	2.66496i
$342$	0.0253331	+	0.235732i	0.00136985	+	0.0127469i
$343$	−8.36676	+	16.5226i	−0.451763	+	0.892138i
$344$	0.616457	+	0.734664i	0.0332371	+	0.0396104i
$345$	0.236077	−	0.184888i	0.0127100	−	0.00995402i
$346$	16.6560	+	2.93691i	0.895434	+	0.157889i
$347$	−4.86182	+	5.79410i	−0.260996	+	0.311043i	−0.880590	−	0.473880i	$-0.842853\pi$
$347$	−4.86182	+	5.79410i	−0.260996	+	0.311043i	0.619593	+	0.784923i	$0.287298\pi$
$348$	7.75859	+	14.5508i	0.415904	+	0.780004i
$349$	12.1137	−	33.2822i	0.648433	−	1.78156i	0.0249882	−	0.999688i	$-0.492045\pi$
$349$	12.1137	−	33.2822i	0.648433	−	1.78156i	0.623445	−	0.781867i	$-0.285733\pi$
$350$	−2.44077	−	2.80307i	−0.130465	−	0.149830i
$351$	13.8341	−	3.50072i	0.738407	−	0.186855i
$352$	−5.76238			−0.307136
$353$	21.8064	+	7.93690i	1.16064	+	0.422438i	0.849326	−	0.527869i	$-0.177009\pi$
$353$	21.8064	+	7.93690i	1.16064	+	0.422438i	0.311314	+	0.950307i	$0.399231\pi$
$354$	−7.83508	+	12.5714i	−0.416430	+	0.668161i
$355$	12.0137	−	14.3174i	0.637623	−	0.759890i
$356$	2.88894	−	16.3840i	0.153114	−	0.868351i
$357$	−7.93809	+	9.16870i	−0.420128	+	0.485259i
$358$	−7.97587	+	6.69255i	−0.421538	+	0.353712i
$359$	16.5273	−	9.54204i	0.872277	−	0.503610i	0.00417293	−	0.999991i	$-0.498672\pi$
$359$	16.5273	−	9.54204i	0.872277	−	0.503610i	0.868104	+	0.496382i	$0.165338\pi$
$360$	−2.10976	−	7.29330i	−0.111194	−	0.384391i
$361$	−9.49688	+	16.4491i	−0.499836	+	0.865741i
$362$	1.15231	+	6.53509i	0.0605642	+	0.343477i
$363$	−11.9276	−	36.5640i	−0.626035	−	1.91911i
$364$	6.35791	+	3.51733i	0.333245	+	0.184358i
$365$	−7.57582	−	20.8144i	−0.396536	−	1.08947i
$366$	−1.10131	−	3.37607i	−0.0575664	−	0.176470i
$367$	−26.2793	+	4.63374i	−1.37177	+	0.241879i	−0.810492	−	0.585750i	$-0.800800\pi$
$367$	−26.2793	+	4.63374i	−1.37177	+	0.241879i	−0.561275	+	0.827630i	$0.689689\pi$
$368$	0.0592427	+	0.0342038i	0.00308824	+	0.00178299i
$369$	−8.95625	+	2.59081i	−0.466244	+	0.134872i
$370$	10.3485	−	5.97469i	0.537991	−	0.310609i
$371$	31.0634	+	4.89344i	1.61273	+	0.254055i
$372$	2.39686	+	16.9113i	0.124272	+	0.876810i
$373$	−5.13978	+	29.1491i	−0.266128	+	1.50929i	0.499677	+	0.866212i	$0.333452\pi$
$373$	−5.13978	+	29.1491i	−0.266128	+	1.50929i	−0.765805	+	0.643073i	$0.777659\pi$
$374$	11.6821	+	9.80245i	0.604067	+	0.506872i
$375$	13.3743	+	8.33552i	0.690647	+	0.430444i
$376$	−2.65229	+	7.28710i	−0.136781	+	0.375804i
$377$	−26.1461			−1.34659
$378$	−7.83648	+	11.2956i	−0.403065	+	0.580981i
$379$	−9.39104			−0.482386			−0.241193	−	0.970477i	$-0.577539\pi$
$379$	−9.39104			−0.482386			−0.241193	+	0.970477i	$0.577539\pi$
$380$	−0.0684063	+	0.187945i	−0.00350917	+	0.00964137i
$381$	−23.5599	+	12.5623i	−1.20701	+	0.643588i
$382$	−6.45055	−	5.41265i	−0.330039	−	0.276935i
$383$	−3.50869	+	19.8987i	−0.179285	+	1.01678i	0.753795	+	0.657110i	$0.228221\pi$
$383$	−3.50869	+	19.8987i	−0.179285	+	1.01678i	−0.933080	+	0.359668i	$0.882890\pi$
$384$	1.36363	−	1.06795i	0.0695874	−	0.0544986i
$385$	38.1137	+	6.00408i	1.94246	+	0.305996i
$386$	8.41920	−	4.86083i	0.428526	−	0.247410i
$387$	−0.307419	−	2.86064i	−0.0156270	−	0.145414i
$388$	5.00041	+	2.88699i	0.253857	+	0.146565i
$389$	−3.87304	+	0.682922i	−0.196371	+	0.0346255i	−0.270969	−	0.962588i	$-0.587344\pi$
$389$	−3.87304	+	0.682922i	−0.196371	+	0.0346255i	0.0745974	+	0.997214i	$0.476233\pi$
$390$	11.7780	+	2.48912i	0.596402	+	0.126042i
$391$	−0.0619185	−	0.170120i	−0.00313135	−	0.00860332i
$392$	−6.84460	+	1.46679i	−0.345704	+	0.0740839i
$393$	12.5250	−	13.9431i	0.631802	−	0.703336i
$394$	−0.905891	−	5.13756i	−0.0456381	−	0.258827i
$395$	2.61017	−	4.52094i	0.131332	−	0.227473i
$396$	14.3542	+	9.63336i	0.721327	+	0.484095i
$397$	−18.2605	+	10.5427i	−0.916467	+	0.529122i	−0.882506	−	0.470301i	$-0.844145\pi$
$397$	−18.2605	+	10.5427i	−0.916467	+	0.529122i	−0.0339605	+	0.999423i	$0.510812\pi$
$398$	−5.38149	+	4.51561i	−0.269750	+	0.226347i
$399$	0.342193	−	0.118593i	0.0171311	−	0.00593706i
$400$	0.243944	−	1.38347i	0.0121972	−	0.0691736i
$401$	−18.6356	+	22.2091i	−0.930620	+	1.10907i	0.0631930	+	0.998001i	$0.479872\pi$
$401$	−18.6356	+	22.2091i	−0.930620	+	1.10907i	−0.993813	+	0.111068i	$0.964573\pi$
$402$	−0.759887	−	0.0256477i	−0.0378997	−	0.00127919i
$403$	−25.4488	−	9.26259i	−1.26769	−	0.461402i
$404$	−15.1453			−0.753505
$405$	−6.93724	+	21.6948i	−0.344714	+	1.07802i
$406$	18.9966	−	16.5413i	0.942784	−	0.820929i
$407$	−9.30564	+	25.5670i	−0.461263	+	1.26731i
$408$	−4.58119	−	0.154624i	−0.226803	−	0.00765505i
$409$	−21.1366	+	25.1896i	−1.04514	+	1.24555i	−0.0765013	+	0.997069i	$0.524375\pi$
$409$	−21.1366	+	25.1896i	−1.04514	+	1.24555i	−0.968637	+	0.248478i	$0.920070\pi$
$410$	−7.74569	−	1.36577i	−0.382532	−	0.0674508i
$411$	30.0126	+	12.0851i	1.48041	+	0.596116i
$412$	−4.54640	−	5.41819i	−0.223985	−	0.266935i
$413$	21.4007	+	7.34894i	1.05306	+	0.361617i
$414$	−0.0903941	−	0.184242i	−0.00444263	−	0.00905502i
$415$	−5.51604	+	9.55406i	−0.270772	+	0.468990i
$416$	0.476887	+	2.70456i	0.0233813	+	0.132602i
$417$	−4.55690	−	4.09343i	−0.223152	−	0.200456i
$418$	−0.155756	−	0.427936i	−0.00761828	−	0.0209311i
$419$	8.73797	−	3.18036i	0.426878	−	0.155371i	−0.119642	−	0.992817i	$-0.538175\pi$
$419$	8.73797	−	3.18036i	0.426878	−	0.155371i	0.546520	+	0.837446i	$0.315952\pi$
$420$	−10.1321	+	5.64284i	−0.494396	+	0.275342i
$421$	3.39696	+	19.2651i	0.165558	+	0.938923i	0.948488	+	0.316814i	$0.102613\pi$
$421$	3.39696	+	19.2651i	0.165558	+	0.938923i	−0.782930	+	0.622110i	$0.786276\pi$
$422$	−13.2585	−	7.65478i	−0.645412	−	0.372629i
$423$	18.7893	−	13.7183i	0.913565	−	0.667008i
$424$	5.94282	+	10.2933i	0.288609	+	0.499886i
$425$	−2.84799	+	2.38974i	−0.138148	+	0.115920i
$426$	−7.88694	−	10.0706i	−0.382123	−	0.487920i
$427$	−4.64736	+	2.79769i	−0.224902	+	0.135390i
$428$	0.944687	−	1.12583i	0.0456632	−	0.0544192i
$429$	−24.1865	+	12.8964i	−1.16774	+	0.622646i
$430$	0.830118	−	2.28073i	0.0400319	−	0.109987i
$431$			4.60755i			0.221938i	0.993824	+	0.110969i	$0.0353954\pi$
$431$			4.60755i			0.221938i	−0.993824	+	0.110969i	$0.964605\pi$
$432$	−5.18219	+	0.380616i	−0.249328	+	0.0183124i
$433$		−	14.1232i		−	0.678717i	−0.940657	−	0.339359i	$-0.889790\pi$
$433$		−	14.1232i		−	0.678717i	0.940657	−	0.339359i	$-0.110210\pi$
$434$	24.3499	−	9.37032i	1.16883	−	0.449790i
$435$	22.0735	−	35.4170i	1.05835	−	1.69811i
$436$	15.5676	+	13.0628i	0.745555	+	0.625595i
$437$	−0.000938784		0.00532411i	−4.49081e−5		0.000254687i
$438$	−15.0095	+	2.12732i	−0.717182	+	0.101647i
$439$	8.86378	+	10.5634i	0.423045	+	0.504165i	0.934902	−	0.354905i	$-0.115487\pi$
$439$	8.86378	+	10.5634i	0.423045	+	0.504165i	−0.511857	+	0.859070i	$0.671042\pi$
$440$	7.29164	+	12.6295i	0.347615	+	0.602088i
$441$	19.5022	+	7.78878i	0.928675	+	0.370894i
$442$	3.63396	−	6.29421i	0.172850	−	0.299385i
$443$	−2.68386	+	0.473236i	−0.127514	+	0.0224841i	−0.237041	−	0.971500i	$-0.576178\pi$
$443$	−2.68386	+	0.473236i	−0.127514	+	0.0224841i	0.109527	+	0.993984i	$0.465066\pi$
$444$	−2.53625	−	7.77489i	−0.120365	−	0.368980i
$445$	−39.5647	+	14.4004i	−1.87555	+	0.682643i
$446$	−16.0834	+	5.85389i	−0.761573	+	0.277190i
$447$	−7.03691	+	2.29552i	−0.332835	+	0.108574i
$448$	−2.05752	−	1.66331i	−0.0972087	−	0.0785841i
$449$	−16.1414	−	9.31926i	−0.761761	−	0.439803i	0.0681666	−	0.997674i	$-0.478285\pi$
$449$	−16.1414	−	9.31926i	−0.761761	−	0.439803i	−0.829928	+	0.557871i	$0.811618\pi$
$450$	−2.92051	+	3.03845i	−0.137674	+	0.143234i
$451$	15.5092	−	8.95421i	0.730298	−	0.421637i
$452$	3.72448	+	4.43866i	0.175185	+	0.208777i
$453$	−6.45124	+	0.914344i	−0.303106	+	0.0429596i
$454$	−1.83816	−	0.324118i	−0.0862693	−	0.0152116i
$455$	−0.336239	−	18.3855i	−0.0157631	−	0.861925i
$456$	0.116169	+	0.0724018i	0.00544009	+	0.00339052i
$457$	3.14218	+	1.14366i	0.146985	+	0.0534981i	0.414465	−	0.910065i	$-0.363969\pi$
$457$	3.14218	+	1.14366i	0.146985	+	0.0534981i	−0.267480	+	0.963563i	$0.586191\pi$
$458$	20.8303			0.973336
$459$	11.1533	+	8.04386i	0.520594	+	0.375455i
$460$		−	0.173124i		−	0.00807195i
$461$	−15.3779	−	5.59708i	−0.716218	−	0.260682i	−0.0418989	−	0.999122i	$-0.513341\pi$
$461$	−15.3779	−	5.59708i	−0.716218	−	0.260682i	−0.674320	+	0.738440i	$0.735563\pi$
$462$	9.41393	−	24.6715i	0.437976	−	1.14782i
$463$	7.02738	+	5.89667i	0.326590	+	0.274042i	0.791309	−	0.611417i	$-0.209400\pi$
$463$	7.02738	+	5.89667i	0.326590	+	0.274042i	−0.464719	+	0.885458i	$0.653845\pi$
$464$	9.37589	+	1.65322i	0.435265	+	0.0767489i
$465$	34.0318	−	26.6526i	1.57819	−	1.23598i
$466$	−0.187625	+	0.157436i	−0.00869158	+	0.00729310i
$467$	−15.2488	−	26.4118i	−0.705632	−	1.22219i	−0.966463	−	0.256806i	$-0.917330\pi$
$467$	−15.2488	−	26.4118i	−0.705632	−	1.22219i	0.260831	−	0.965384i	$-0.416003\pi$
$468$	3.33346	−	7.53437i	0.154089	−	0.348276i
$469$	0.222557	+	1.13988i	0.0102767	+	0.0526350i
$470$	19.3274	−	3.40795i	0.891507	−	0.157197i
$471$	4.97624	−	23.5465i	0.229293	−	1.08496i
$472$	2.92508	+	8.03658i	0.134638	+	0.369914i
$473$	1.89012	+	5.19306i	0.0869077	+	0.238777i
$474$	−2.65788	−	2.38755i	−0.122080	−	0.109664i
$475$	0.109336	−	0.0192788i	0.00501667	−	0.000884574i
$476$	1.34174	+	6.87211i	0.0614987	+	0.314983i
$477$	2.40425	−	35.5758i	0.110083	−	1.62890i
$478$	−11.3301	−	19.6244i	−0.518229	−	0.897598i
$479$	−11.8919	+	9.97851i	−0.543356	+	0.455930i	−0.872684	−	0.488286i	$-0.837622\pi$
$479$	−11.8919	+	9.97851i	−0.543356	+	0.455930i	0.329328	+	0.944216i	$0.393178\pi$
$480$	−4.06616	−	1.63732i	−0.185594	−	0.0747329i
$481$	12.7700	+	2.25169i	0.582260	+	0.102668i
$482$	10.0947	+	8.47045i	0.459801	+	0.385819i
$483$	−0.243227	+	0.197768i	−0.0110672	+	0.00899875i
$484$	−20.8659	−	7.59458i	−0.948451	−	0.345208i
$485$		−	14.6126i		−	0.663525i
$486$	13.5453	+	7.71530i	0.614426	+	0.349973i
$487$	3.78825			0.171662			0.0858309	−	0.996310i	$-0.472646\pi$
$487$	3.78825			0.171662			0.0858309	+	0.996310i	$0.472646\pi$
$488$	−1.92662	−	0.701231i	−0.0872139	−	0.0317432i
$489$	1.15921	−	34.3450i	0.0524214	−	1.55313i
$490$	11.8758	+	13.1454i	0.536496	+	0.593847i
$491$	21.9460	+	3.86967i	0.990409	+	0.174636i	0.645302	−	0.763927i	$-0.276731\pi$
$491$	21.9460	+	3.86967i	0.990409	+	0.174636i	0.345107	+	0.938563i	$0.387843\pi$
$492$	−2.01064	+	4.99328i	−0.0906467	+	0.225115i
$493$	−16.1955	−	19.3010i	−0.729407	−	0.869273i
$494$	−0.187961	+	0.108519i	−0.00845676	+	0.00488251i
$495$	2.94993	−	43.6503i	0.132590	−	1.96193i
$496$	8.54016	+	4.93066i	0.383464	+	0.221393i
$497$	−12.2838	+	15.1950i	−0.551002	+	0.681591i
$498$	5.61686	+	5.04559i	0.251698	+	0.226098i
$499$	14.3356	−	5.21773i	0.641750	−	0.233578i	−0.000587503	−	1.00000i	$-0.500187\pi$
$499$	14.3356	−	5.21773i	0.641750	−	0.233578i	0.642337	+	0.766422i	$0.277965\pi$
$500$	8.54989	−	3.11190i	0.382363	−	0.139169i
$501$	19.9620	+	4.21870i	0.891836	+	0.188478i
$502$	−2.82740	+	0.498546i	−0.126193	+	0.0222512i
$503$	−8.55797	+	14.8228i	−0.381581	+	0.660917i	−0.991288	−	0.131709i	$-0.957954\pi$
$503$	−8.55797	+	14.8228i	−0.381581	+	0.660917i	0.609708	+	0.792626i	$0.291287\pi$
$504$	2.34466	+	7.58304i	0.104439	+	0.337776i
$505$	19.1646	+	33.1941i	0.852814	+	1.47712i
$506$	0.253381	+	0.301967i	0.0112641	+	0.0134241i
$507$	−5.82878	−	7.44258i	−0.258865	−	0.330537i
$508$	−2.67682	+	15.1810i	−0.118764	+	0.673547i
$509$	24.6782	+	20.7074i	1.09384	+	0.917841i	0.996996	−	0.0774586i	$-0.0246806\pi$
$509$	24.6782	+	20.7074i	1.09384	+	0.917841i	0.0968446	+	0.995300i	$0.469125\pi$
$510$	5.45808	+	10.2363i	0.241688	+	0.453272i
$511$	8.31656	+	21.6116i	0.367903	+	0.956039i
$512$		−	1.00000i		−	0.0441942i
$513$	−0.168340	−	0.374561i	−0.00743238	−	0.0165373i
$514$			2.11382i			0.0932368i
$515$	−6.12217	+	16.8205i	−0.269775	+	0.741201i
$516$	−1.40972	−	0.878604i	−0.0620594	−	0.0386784i
$517$	−28.7236	+	34.2314i	−1.26326	+	1.50550i
$518$	−10.7026	+	6.44291i	−0.470245	+	0.283085i
$519$	−29.0043	+	4.11082i	−1.27315	+	0.180445i
$520$	5.32418	−	4.46752i	0.233481	−	0.195914i
$521$	−12.5855	−	21.7987i	−0.551381	−	0.955020i	−0.998175	−	0.0603834i	$-0.980768\pi$
$521$	−12.5855	−	21.7987i	−0.551381	−	0.955020i	0.446794	−	0.894637i	$-0.352566\pi$
$522$	−20.5917	−	19.7925i	−0.901276	−	0.866295i
$523$	−30.8478	−	17.8100i	−1.34888	−	0.778777i	−0.360791	−	0.932647i	$-0.617493\pi$
$523$	−30.8478	−	17.8100i	−1.34888	−	0.778777i	−0.988091	+	0.153870i	$0.950826\pi$
$524$	−1.87906	−	10.6567i	−0.0820869	−	0.465538i
$525$	5.52478	+	3.30460i	0.241121	+	0.144225i
$526$	−3.06158	+	1.11432i	−0.133491	+	0.0485868i
$527$	−8.92589	−	24.5237i	−0.388818	−	1.06827i
$528$	9.48864	−	3.09530i	0.412940	−	0.134706i
$529$	3.99310	+	22.6460i	0.173613	+	0.984607i
$530$	15.0399	−	26.0499i	0.653293	−	1.13154i
$531$	6.14886	−	24.9094i	0.266838	−	1.08097i
$532$	0.0679095	−	0.197758i	0.00294425	−	0.00857391i
$533$	−5.48616	−	6.53815i	−0.237632	−	0.283199i
$534$	4.04368	+	28.5306i	0.174987	+	1.23464i
$535$	−3.66290	−	0.645868i	−0.158361	−	0.0279233i
$536$	−0.282165	+	0.336271i	−0.0121877	+	0.0145247i
$537$	9.53854	−	15.3046i	0.411619	−	0.660442i
$538$	−3.36815	+	9.25391i	−0.145211	+	0.398964i
$539$	−39.9534	−	5.54723i	−1.72092	−	0.238936i
$540$	7.39168	+	10.8763i	0.318087	+	0.468040i
$541$	13.1222			0.564167			0.282083	−	0.959390i	$-0.408975\pi$
$541$	13.1222			0.564167			0.282083	+	0.959390i	$0.408975\pi$
$542$	−14.6500	−	5.33217i	−0.629273	−	0.229036i
$543$	−5.40782	−	10.1420i	−0.232072	−	0.435237i
$544$	−1.70111	+	2.02730i	−0.0729345	+	0.0869199i
$545$	8.93084	−	50.6493i	0.382555	−	2.16958i
$546$	−12.3586	−	2.37663i	−0.528900	−	0.101710i
$547$	18.5836	−	15.5935i	0.794577	−	0.666729i	−0.152297	−	0.988335i	$-0.548667\pi$
$547$	18.5836	−	15.5935i	0.794577	−	0.666729i	0.946874	+	0.321606i	$0.104223\pi$
$548$	16.1772	−	9.33991i	0.691056	−	0.398981i
$549$	3.62695	+	4.96764i	0.154795	+	0.212014i
$550$	4.04754	−	7.01055i	0.172588	−	0.298931i
$551$	0.130654	+	0.740975i	0.00556604	+	0.0315666i
$552$	−0.115925	−	0.0244992i	−0.00493409	−	0.00104275i
$553$	−2.64187	+	4.77544i	−0.112344	+	0.203072i
$554$	6.17354	+	16.9617i	0.262289	+	0.720633i
$555$	−13.8310	+	15.3970i	−0.587093	+	0.653565i
$556$	−3.48282	+	0.614114i	−0.147704	+	0.0260443i
$557$	−3.66622	−	2.11669i	−0.155343	−	0.0896870i	0.420314	−	0.907379i	$-0.361920\pi$
$557$	−3.66622	−	2.11669i	−0.155343	−	0.0896870i	−0.575656	+	0.817692i	$0.695253\pi$
$558$	−13.0308	−	26.5595i	−0.551638	−	1.12436i
$559$	2.28093	−	1.31689i	0.0964729	−	0.0556986i
$560$	−1.04194	+	6.61423i	−0.0440302	+	0.279502i
$561$	−24.5018	−	9.86611i	−1.03447	−	0.416548i
$562$	0.408825	−	2.31856i	0.0172453	−	0.0978027i
$563$	11.5964	+	9.73057i	0.488732	+	0.410095i	0.853572	−	0.520976i	$-0.174432\pi$
$563$	11.5964	+	9.73057i	0.488732	+	0.410095i	−0.364840	+	0.931070i	$0.618876\pi$
$564$	0.453088	−	13.4240i	0.0190784	−	0.565253i
$565$	5.01537	−	13.7796i	0.210998	−	0.579713i
$566$	−6.20924			−0.260994
$567$	6.83648	−	22.8093i	0.287105	−	0.957899i
$568$	−7.38512			−0.309873
$569$	5.90112	−	16.2132i	0.247388	−	0.679693i	−0.752392	−	0.658716i	$-0.771100\pi$
$569$	5.90112	−	16.2132i	0.247388	−	0.679693i	0.999780	−	0.0209771i	$-0.00667771\pi$
$570$	0.0116858	−	0.346225i	0.000489464	−	0.0145018i
$571$	13.3937	+	11.2387i	0.560510	+	0.470324i	0.878482	−	0.477776i	$-0.158557\pi$
$571$	13.3937	+	11.2387i	0.560510	+	0.470324i	−0.317971	+	0.948100i	$0.603002\pi$
$572$	−2.74801	+	15.5847i	−0.114900	+	0.651630i
$573$	13.5292	+	5.44781i	0.565192	+	0.227585i
$574$	8.12234	+	1.27952i	0.339020	+	0.0534061i
$575$	−0.0832250	+	0.0480500i	−0.00347072	+	0.00200382i
$576$	−1.67177	+	2.49102i	−0.0696570	+	0.103793i
$577$	−1.05208	−	0.607421i	−0.0437989	−	0.0252873i	0.477941	−	0.878392i	$-0.341383\pi$
$577$	−1.05208	−	0.607421i	−0.0437989	−	0.0252873i	−0.521740	+	0.853105i	$0.674717\pi$
$578$	−9.84440	+	1.73583i	−0.409473	+	0.0722012i
$579$	−11.2525	+	12.5265i	−0.467637	+	0.520584i
$580$	−8.24073	−	22.6412i	−0.342178	−	0.940126i
$581$	5.58304	−	10.0919i	0.231624	−	0.418682i
$582$	−9.78470	−	2.06787i	−0.405589	−	0.0857158i
$583$	11.8931	+	67.4492i	0.492562	+	2.79346i
$584$	−4.37617	+	7.57975i	−0.181087	+	0.313652i
$585$	−20.7313	+	2.22790i	−0.857134	+	0.0921122i
$586$	11.0285	−	6.36731i	0.455583	−	0.263031i
$587$	29.9943	−	25.1682i	1.23800	−	1.03880i	0.240319	−	0.970694i	$-0.422748\pi$
$587$	29.9943	−	25.1682i	1.23800	−	1.03880i	0.997678	−	0.0681090i	$-0.0216966\pi$
$588$	10.4828	−	6.09190i	0.432303	−	0.251226i
$589$	−0.135331	+	0.767499i	−0.00557621	+	0.0316243i
$590$	13.9125	−	16.5803i	0.572770	−	0.682601i
$591$	4.25136	+	7.97318i	0.174878	+	0.327973i
$592$	−4.43688	−	1.61489i	−0.182355	−	0.0663717i
$593$	−1.63386			−0.0670946			−0.0335473	−	0.999437i	$-0.510680\pi$
$593$	−1.63386			−0.0670946			−0.0335473	+	0.999437i	$0.510680\pi$
$594$	−28.8110	−	8.15235i	−1.18213	−	0.334495i
$595$	13.3639	−	11.6366i	0.547865	−	0.477054i
$596$	−1.46161	+	4.01575i	−0.0598700	+	0.164491i
$597$	6.43586	−	10.3263i	0.263402	−	0.422629i
$598$	0.120758	−	0.143914i	0.00493817	−	0.00588509i
$599$	27.9141	+	4.92202i	1.14054	+	0.201108i	0.711842	−	0.702339i	$-0.247861\pi$
$599$	27.9141	+	4.92202i	1.14054	+	0.201108i	0.428699	+	0.903448i	$0.358972\pi$
$600$	0.341450	+	2.40913i	0.0139396	+	0.0983525i
$601$	0.326842	+	0.389515i	0.0133322	+	0.0158887i	0.772669	−	0.634809i	$-0.218921\pi$
$601$	0.326842	+	0.389515i	0.0133322	+	0.0158887i	−0.759337	+	0.650697i	$0.774477\pi$
$602$	−0.824089	+	2.39982i	−0.0335873	+	0.0978093i
$603$	1.26505	−	0.365945i	0.0515167	−	0.0149024i
$604$	−1.88093	+	3.25786i	−0.0765338	+	0.132560i
$605$	9.75833	+	55.3422i	0.396733	+	2.24998i
$606$	24.9390	−	8.13536i	1.01308	−	0.330476i
$607$	−3.01757	−	8.29070i	−0.122479	−	0.336509i	0.863267	−	0.504747i	$-0.168414\pi$
$607$	−3.01757	−	8.29070i	−0.122479	−	0.336509i	−0.985746	+	0.168238i	$0.946192\pi$
$608$	0.0742638	−	0.0270298i	0.00301179	−	0.00109620i
$609$	−22.3955	+	37.4418i	−0.907511	+	1.51722i
$610$	0.901017	+	5.10992i	0.0364811	+	0.206895i
$611$	18.4436	+	10.6484i	0.746147	+	0.430788i
$612$	7.62668	−	2.20620i	0.308290	−	0.0891803i
$613$	−0.107140	−	0.185572i	−0.00432734	−	0.00749517i	0.863854	−	0.503743i	$-0.168044\pi$
$613$	−0.107140	−	0.185572i	−0.00432734	−	0.00749517i	−0.868181	+	0.496248i	$0.834711\pi$
$614$	−17.9143	+	15.0319i	−0.722964	+	0.606639i
$615$	13.4881	−	1.91169i	0.543892	−	0.0770866i
$616$	−7.86307	−	13.0617i	−0.316812	−	0.526270i
$617$	−2.96780	+	3.53689i	−0.119479	+	0.142390i	−0.822469	−	0.568811i	$-0.807404\pi$
$617$	−2.96780	+	3.53689i	−0.119479	+	0.142390i	0.702989	+	0.711200i	$0.251848\pi$
$618$	10.3968	+	6.47975i	0.418219	+	0.260654i
$619$	−2.14642	+	5.89725i	−0.0862720	+	0.237030i	−0.975325	−	0.220774i	$-0.929142\pi$
$619$	−2.14642	+	5.89725i	−0.0862720	+	0.237030i	0.889053	+	0.457804i	$0.151364\pi$
$620$		−	24.9568i		−	1.00229i
$621$	0.247814	+	0.254827i	0.00994445	+	0.0102259i
$622$		−	23.3712i		−	0.937099i
$623$	41.0800	−	15.8084i	1.64584	−	0.633351i
$624$	−2.23804	−	4.19731i	−0.0895933	−	0.168027i
$625$	−23.0201	−	19.3161i	−0.920803	−	0.772645i
$626$	4.31234	−	24.4565i	0.172356	−	0.977479i
$627$	0.486345	+	0.620997i	0.0194227	+	0.0248002i
$628$	−8.93143	−	10.6441i	−0.356403	−	0.424744i
$629$	6.24780	+	10.8215i	0.249116	+	0.431482i
$630$	13.6530	−	14.7343i	0.543947	−	0.587029i
$631$	13.0751	−	22.6468i	0.520513	−	0.901555i	−0.479202	−	0.877704i	$-0.659074\pi$
$631$	13.0751	−	22.6468i	0.520513	−	0.901555i	0.999716	−	0.0238507i	$-0.00759264\pi$
$632$	−2.03140	+	0.358191i	−0.0808049	+	0.0142481i
$633$	25.9439	+	5.48290i	1.03118	+	0.217926i
$634$	27.9671	−	10.1792i	1.11071	−	0.404267i
$635$	36.6596	−	13.3430i	1.45479	−	0.529500i
$636$	−15.3149	−	13.7572i	−0.607274	−	0.545509i
$637$	0.702913	+	19.2111i	0.0278504	+	0.761173i
$638$	47.5109	+	27.4305i	1.88098	+	1.08598i
$639$	18.3965	+	12.3462i	0.727754	+	0.488408i
$640$	−2.19171	+	1.26539i	−0.0866351	+	0.0500188i
$641$	−23.5568	−	28.0739i	−0.930438	−	1.10885i	−0.993835	−	0.110865i	$-0.964638\pi$
$641$	−23.5568	−	28.0739i	−0.930438	−	1.10885i	0.0633971	−	0.997988i	$-0.479807\pi$
$642$	−0.950823	+	2.36130i	−0.0375260	+	0.0931931i
$643$	−38.1296	−	6.72327i	−1.50368	−	0.265140i	−0.639686	−	0.768636i	$-0.720936\pi$
$643$	−38.1296	−	6.72327i	−1.50368	−	0.265140i	−0.863998	+	0.503496i	$0.832047\pi$
$644$	0.00330943	+	0.180959i	0.000130410	+	0.00713079i
$645$	−0.141808	+	4.20147i	−0.00558370	+	0.165433i
$646$	−0.196536	−	0.0715332i	−0.00773260	−	0.00281444i
$647$	30.6855			1.20637			0.603187	−	0.797600i	$-0.293897\pi$
$647$	30.6855			1.20637			0.603187	+	0.797600i	$0.293897\pi$
$648$	8.32882	−	3.41039i	0.327187	−	0.133973i
$649$			49.2819i			1.93448i
$650$	−3.62536	−	1.31952i	−0.142198	−	0.0517559i
$651$	−35.0625	+	28.5093i	−1.37421	+	1.11737i
$652$	−15.1986	−	12.7531i	−0.595223	−	0.499451i
$653$	22.2092	+	3.91608i	0.869114	+	0.153248i	0.590385	−	0.807122i	$-0.298976\pi$
$653$	22.2092	+	3.91608i	0.869114	+	0.153248i	0.278729	+	0.960370i	$0.410087\pi$
$654$	−32.6512	−	13.1476i	−1.27676	−	0.514113i
$655$	−20.9786	+	17.6031i	−0.819702	+	0.687812i
$656$	1.55391	+	2.69145i	0.0606699	+	0.105083i
$657$	23.5727	−	11.5654i	0.919660	−	0.451209i
$658$	−20.1370	+	3.93164i	−0.785021	+	0.153271i
$659$	−23.7251	+	4.18337i	−0.924197	+	0.162961i	−0.615443	−	0.788181i	$-0.711023\pi$
$659$	−23.7251	+	4.18337i	−0.924197	+	0.162961i	−0.308754	+	0.951142i	$0.599912\pi$
$660$	−18.7908	−	16.8796i	−0.731431	−	0.657039i
$661$	8.55853	+	23.5144i	0.332888	+	0.914603i	0.987357	+	0.158514i	$0.0506702\pi$
$661$	8.55853	+	23.5144i	0.332888	+	0.914603i	−0.654469	+	0.756089i	$0.727108\pi$
$662$	8.95117	+	24.5931i	0.347897	+	0.955840i
$663$	−2.60290	+	12.3164i	−0.101088	+	0.478328i
$664$	4.29295	−	0.756962i	0.166599	−	0.0293758i
$665$	−0.519362	+	0.101403i	−0.0201400	+	0.00393223i
$666$	8.35265	+	11.4402i	0.323659	+	0.443298i
$667$	−0.325638	−	0.564021i	−0.0126087	−	0.0218390i
$668$	9.02372	−	7.57180i	0.349138	−	0.292962i
$669$	23.3394	−	18.2786i	0.902352	−	0.706693i
$670$	1.09406	+	0.192912i	0.0422672	+	0.00745284i
$671$	−9.05036	−	7.59415i	−0.349385	−	0.293169i
$672$	4.28148	+	1.63369i	0.165162	+	0.0630209i
$673$	32.3425	+	11.7717i	1.24671	+	0.453766i	0.879289	−	0.476288i	$-0.158018\pi$
$673$	32.3425	+	11.7717i	1.24671	+	0.453766i	0.367422	+	0.930054i	$0.380240\pi$
$674$			0.582676i			0.0224438i
$675$	3.17695	−	6.57203i	0.122281	−	0.252958i
$676$	−5.45792			−0.209920
$677$	−44.9413	−	16.3573i	−1.72723	−	0.628662i	−0.728807	−	0.684719i	$-0.759925\pi$
$677$	−44.9413	−	16.3573i	−1.72723	−	0.628662i	−0.998428	+	0.0560571i	$0.982147\pi$
$678$	−8.51717	−	5.30831i	−0.327100	−	0.203864i
$679$	0.279334	+	15.2740i	0.0107199	+	0.586160i
$680$	6.59583	+	1.16302i	0.252939	+	0.0445999i
$681$	3.20092	−	0.453671i	0.122659	−	0.0173847i
$682$	36.5262	+	43.5303i	1.39866	+	1.66686i
$683$	16.1037	−	9.29746i	0.616190	−	0.355757i	−0.159194	−	0.987247i	$-0.550890\pi$
$683$	16.1037	−	9.29746i	0.616190	−	0.355757i	0.775384	+	0.631490i	$0.217556\pi$
$684$	−0.230180	−	0.0568199i	−0.00880117	−	0.00217256i
$685$	−40.9408	−	23.6372i	−1.56427	−	0.903131i
$686$	−12.6646	−	13.5133i	−0.483536	−	0.515938i
$687$	−34.3003	+	11.1891i	−1.30864	+	0.426892i
$688$	−0.901199	+	0.328010i	−0.0343579	+	0.0125053i
$689$	30.6729	−	11.1640i	1.16854	−	0.425315i
$690$	0.0929945	+	0.285075i	0.00354024	+	0.0108526i
$691$	13.7850	−	2.43067i	0.524407	−	0.0924671i	0.0948232	−	0.995494i	$-0.469771\pi$
$691$	13.7850	−	2.43067i	0.524407	−	0.0924671i	0.429584	+	0.903027i	$0.358660\pi$
$692$	−8.45649	+	14.6471i	−0.321468	+	0.556798i
$693$	−2.24902	+	45.6822i	−0.0854333	+	1.73532i
$694$	−3.78183	−	6.55032i	−0.143556	−	0.248647i
$695$	5.75307	+	6.85624i	0.218226	+	0.260072i
$696$	−16.3269	+	2.31403i	−0.618868	+	0.0877131i
$697$	1.42820	−	8.09975i	0.0540971	−	0.306800i
$698$	27.1319	+	22.7664i	1.02696	+	0.861720i
$699$	0.224386	−	0.360027i	0.00848705	−	0.0136175i
$700$	3.46881	−	1.33487i	0.131109	−	0.0504533i
$701$			30.6999i			1.15952i	0.814788	+	0.579760i	$0.196854\pi$
$701$			30.6999i			1.15952i	−0.814788	+	0.579760i	$0.803146\pi$
$702$	−1.44192	+	14.1971i	−0.0544219	+	0.535834i
$703$		−	0.373150i		−	0.0140736i
$704$	1.97085	−	5.41487i	0.0742792	−	0.204081i
$705$	−29.9949	+	15.9935i	−1.12967	+	0.602351i
$706$	−14.9165	+	17.7768i	−0.561389	+	0.669038i
$707$	−20.6665	−	34.3300i	−0.777243	−	1.29111i
$708$	−9.13348	−	11.6622i	−0.343257	−	0.438294i
$709$	−32.3242	+	27.1233i	−1.21396	+	1.01864i	−0.214844	+	0.976648i	$0.568924\pi$
$709$	−32.3242	+	27.1233i	−1.21396	+	1.01864i	−0.999118	+	0.0419868i	$0.986631\pi$
$710$	9.34504	+	16.1861i	0.350713	+	0.607453i
$711$	5.65909	+	2.50377i	0.212232	+	0.0938988i
$712$	14.4079	+	8.31838i	0.539957	+	0.311745i
$713$	−0.117141	−	0.664340i	−0.00438697	−	0.0248797i
$714$	−5.90078	−	10.5952i	−0.220831	−	0.396517i
$715$	37.6346	−	13.6979i	1.40745	−	0.512271i
$716$	−3.56103	−	9.78385i	−0.133082	−	0.365640i
$717$	29.1981	+	26.2285i	1.09042	+	0.979520i
$718$	3.31392	+	18.7941i	0.123674	+	0.701391i
$719$	−16.2045	+	28.0670i	−0.604326	+	1.04672i	0.387831	+	0.921730i	$0.373224\pi$
$719$	−16.2045	+	28.0670i	−0.604326	+	1.04672i	−0.992158	+	0.124993i	$0.960109\pi$
$720$	7.57504	+	0.511929i	0.282305	+	0.0190785i
$721$	6.07770	−	17.6988i	0.226345	−	0.659138i
$722$	−12.2089	−	14.5501i	−0.454370	−	0.541497i
$723$	−21.1724	−	8.52547i	−0.787410	−	0.317066i
$724$	−6.53509	−	1.15231i	−0.242875	−	0.0428254i
$725$	−8.59701	+	10.2455i	−0.319285	+	0.380509i
$726$	38.4384	+	1.29737i	1.42658	+	0.0481501i
$727$	12.3903	−	34.0422i	0.459532	−	1.26255i	−0.466302	−	0.884625i	$-0.654414\pi$
$727$	12.3903	−	34.0422i	0.459532	−	1.26255i	0.925835	−	0.377929i	$-0.123364\pi$
$728$	−5.47974	+	4.77148i	−0.203093	+	0.176843i
$729$	−26.4487	−	5.42850i	−0.979580	−	0.201056i
$730$	22.1502			0.819816
$731$	2.38498	+	0.868063i	0.0882118	+	0.0321065i
$732$	3.54914	+	0.119791i	0.131180	+	0.00442759i
$733$	−2.86119	+	3.40984i	−0.105681	+	0.125945i	−0.816292	−	0.577639i	$-0.803974\pi$
$733$	−2.86119	+	3.40984i	−0.105681	+	0.125945i	0.710611	+	0.703585i	$0.248418\pi$
$734$	4.63374	−	26.2793i	0.171035	−	0.969985i
$735$	−26.6165	−	15.2666i	−0.981764	−	0.563119i
$736$	−0.0524032	+	0.0439715i	−0.00193161	+	0.00162081i
$737$	−2.19063	+	1.26476i	−0.0806928	+	0.0465880i
$738$	0.628655	−	9.30223i	0.0231411	−	0.342420i
$739$	8.18059	−	14.1692i	0.300928	−	0.521223i	−0.675418	−	0.737435i	$-0.736037\pi$
$739$	8.18059	−	14.1692i	0.300928	−	0.521223i	0.976346	+	0.216212i	$0.0693703\pi$
$740$	2.07499	+	11.7678i	0.0762781	+	0.432595i
$741$	0.251215	−	0.279658i	0.00922860	−	0.0102735i
$742$	−15.2226	+	27.5164i	−0.558841	+	1.01016i
$743$	5.41213	+	14.8697i	0.198552	+	0.545517i	0.998512	−	0.0545367i	$-0.0173682\pi$
$743$	5.41213	+	14.8697i	0.198552	+	0.545517i	−0.799960	+	0.600053i	$0.795146\pi$
$744$	−16.7112	−	3.53169i	−0.612662	−	0.129478i
$745$	10.6509	−	1.87804i	0.390218	−	0.0688059i
$746$	−25.6333	−	14.7994i	−0.938503	−	0.541845i
$747$	−11.9593	−	5.29120i	−0.437567	−	0.193595i
$748$	−13.2068	+	7.62495i	−0.482888	+	0.278796i
$749$	3.84102	+	0.605078i	0.140348	+	0.0221091i
$750$	−12.4071	+	9.71684i	−0.453044	+	0.354809i
$751$	5.47824	−	31.0687i	0.199904	−	1.13371i	−0.705356	−	0.708853i	$-0.749213\pi$
$751$	5.47824	−	31.0687i	0.199904	−	1.13371i	0.905260	−	0.424858i	$-0.139676\pi$
$752$	−5.94050	−	4.98467i	−0.216628	−	0.181772i
$753$	4.38794	−	2.33968i	0.159905	−	0.0852628i
$754$	8.94248	−	24.5693i	0.325666	−	0.894760i
$755$	9.52039			0.346483
$756$	−7.93412	−	11.2272i	−0.288561	−	0.408329i
$757$	−4.80352			−0.174587			−0.0872934	−	0.996183i	$-0.527822\pi$
$757$	−4.80352			−0.174587			−0.0872934	+	0.996183i	$0.527822\pi$
$758$	3.21193	−	8.82469i	0.116662	−	0.320527i
$759$	−0.579433	−	0.361130i	−0.0210321	−	0.0131082i
$760$	−0.153214	−	0.128562i	−0.00555766	−	0.00466343i
$761$	−2.37023	+	13.4423i	−0.0859208	+	0.487281i	0.911233	+	0.411891i	$0.135131\pi$
$761$	−2.37023	+	13.4423i	−0.0859208	+	0.487281i	−0.997154	+	0.0753906i	$0.975980\pi$
$762$	−3.74676	−	26.4357i	−0.135731	−	0.957663i
$763$	−8.36681	+	53.1123i	−0.302899	+	1.92279i
$764$	7.29245	−	4.21030i	0.263831	−	0.152323i
$765$	−14.4861	−	13.9238i	−0.523745	−	0.503417i
$766$	−17.4987	−	10.1029i	−0.632252	−	0.365031i
$767$	23.1304	−	4.07851i	0.835189	−	0.147266i
$768$	0.537156	+	1.64665i	0.0193829	+	0.0594184i
$769$	0.908873	+	2.49711i	0.0327748	+	0.0900480i	0.955001	−	0.296603i	$-0.0958539\pi$
$769$	0.908873	+	2.49711i	0.0327748	+	0.0900480i	−0.922226	+	0.386651i	$0.873632\pi$
$770$	−18.6777	+	33.7617i	−0.673096	+	1.21669i
$771$	−1.13545	−	3.48073i	−0.0408923	−	0.125356i
$772$	1.68815	+	9.57396i	0.0607578	+	0.344574i
$773$	−9.31601	+	16.1358i	−0.335074	+	0.580365i	−0.983499	−	0.180914i	$-0.942095\pi$
$773$	−9.31601	+	16.1358i	−0.335074	+	0.580365i	0.648425	+	0.761278i	$0.275428\pi$
$774$	2.79326	+	0.689516i	0.100402	+	0.0247841i
$775$	−11.9973	+	6.92667i	−0.430957	+	0.248813i
$776$	−4.42312	+	3.71144i	−0.158781	+	0.133233i
$777$	14.1626	−	16.3582i	0.508081	−	0.586847i
$778$	0.682922	−	3.87304i	0.0244839	−	0.138855i
$779$	−0.157875	+	0.188148i	−0.00565647	+	0.00674112i
$780$	−6.36732	+	10.2164i	−0.227987	+	0.365804i
$781$	−39.9895	−	14.5550i	−1.43094	−	0.520818i
$782$	0.181038			0.00647389
$783$	44.5391	+	21.5304i	1.59170	+	0.769434i
$784$	0.962662	−	6.93349i	0.0343808	−	0.247625i
$785$	−12.0270	+	33.0440i	−0.429263	+	1.17939i
$786$	8.81843	+	16.5385i	0.314543	+	0.589907i
$787$	21.7415	−	25.9106i	0.775002	−	0.923612i	−0.223694	−	0.974659i	$-0.571812\pi$
$787$	21.7415	−	25.9106i	0.775002	−	0.923612i	0.998696	+	0.0510477i	$0.0162561\pi$
$788$	5.13756	+	0.905891i	0.183018	+	0.0322710i
$789$	4.44279	−	3.47945i	0.158168	−	0.123872i
$790$	3.35557	+	3.99901i	0.119386	+	0.142278i
$791$	−4.97894	+	14.4991i	−0.177031	+	0.515529i
$792$	−13.9618	+	10.1938i	−0.496112	+	0.362219i
$793$	−2.81530	+	4.87625i	−0.0999743	+	0.173161i
$794$	−3.66144	−	20.7650i	−0.129940	−	0.736924i
$795$	−10.7727	+	50.9740i	−0.382068	+	1.80786i
$796$	−2.40271	−	6.60138i	−0.0851616	−	0.233980i
$797$	8.26255	−	3.00732i	0.292675	−	0.106525i	−0.191510	−	0.981491i	$-0.561339\pi$
$797$	8.26255	−	3.00732i	0.292675	−	0.106525i	0.484185	+	0.874966i	$0.339116\pi$
$798$	−0.00559623	+	0.362117i	−0.000198105	+	0.0128188i
$799$	3.56372	+	20.2109i	0.126075	+	0.715010i
$800$	1.21661	+	0.702408i	0.0430135	+	0.0248339i
$801$	−21.9839	−	44.8079i	−0.776763	−	1.58321i
$802$	−14.4960	−	25.1077i	−0.511870	−	0.886585i
$803$	−38.6350	+	32.4186i	−1.36340	+	1.14403i
$804$	0.283998	−	0.705289i	0.0100158	−	0.0248736i
$805$	0.392423	−	0.236237i	0.0138311	−	0.00832624i
$806$	17.4080	−	20.7460i	0.613170	−	0.730747i
$807$	0.575377	−	17.0472i	0.0202542	−	0.600090i
$808$	5.17998	−	14.2319i	0.182231	−	0.500676i
$809$		−	33.1632i		−	1.16595i	−0.812488	−	0.582977i	$-0.801888\pi$
$809$		−	33.1632i		−	1.16595i	0.812488	−	0.582977i	$-0.198112\pi$
$810$	−18.0138	−	13.9389i	−0.632940	−	0.489764i
$811$		−	24.7600i		−	0.869442i	−0.900565	−	0.434721i	$-0.856847\pi$
$811$		−	24.7600i		−	0.869442i	0.900565	−	0.434721i	$-0.143153\pi$
$812$	9.04649	+	23.5084i	0.317470	+	0.824982i
$813$	26.9877	+	0.910890i	0.946500	+	0.0319463i
$814$	−20.8424	−	17.4889i	−0.730527	−	0.612985i
$815$	−8.71913	+	49.4486i	−0.305418	+	1.73211i
$816$	1.71216	−	4.25202i	0.0599375	−	0.148851i
$817$	−0.0487185	−	0.0580604i	−0.00170444	−	0.00203128i
$818$	−16.4414	−	28.4773i	−0.574859	−	0.995685i
$819$	21.6270	−	2.72502i	0.755707	−	0.0952200i
$820$	3.93259	−	6.81144i	0.137332	−	0.237866i
$821$	2.44218	−	0.430622i	0.0852326	−	0.0150288i	−0.130869	−	0.991400i	$-0.541777\pi$
$821$	2.44218	−	0.430622i	0.0852326	−	0.0150288i	0.216102	+	0.976371i	$0.430666\pi$
$822$	−21.6212	+	24.0693i	−0.754127	+	0.839512i
$823$	−44.1356	+	16.0640i	−1.53847	+	0.559957i	−0.965677	−	0.259744i	$-0.916362\pi$
$823$	−44.1356	+	16.0640i	−1.53847	+	0.559957i	−0.572792	+	0.819701i	$0.694140\pi$
$824$	6.64639	−	2.41909i	0.231538	−	0.0842730i
$825$	−2.89914	+	13.7181i	−0.100935	+	0.477603i
$826$	−14.2252	+	17.5966i	−0.494959	+	0.612265i
$827$	−2.28320	−	1.31821i	−0.0793948	−	0.0458386i	0.459777	−	0.888034i	$-0.347929\pi$
$827$	−2.28320	−	1.31821i	−0.0793948	−	0.0458386i	−0.539172	+	0.842196i	$0.681263\pi$
$828$	0.204048	−	0.0219281i	0.00709115	−	0.000762053i
$829$	23.3009	−	13.4528i	0.809275	−	0.467235i	−0.0374291	−	0.999299i	$-0.511917\pi$
$829$	23.3009	−	13.4528i	0.809275	−	0.467235i	0.846704	+	0.532064i	$0.178583\pi$
$830$	−7.09128	−	8.45106i	−0.246142	−	0.293341i
$831$	−19.2767	−	24.6138i	−0.668703	−	0.853844i
$832$	−2.70456	−	0.476887i	−0.0937638	−	0.0165331i
$833$	−13.7462	+	12.4187i	−0.476279	+	0.430282i
$834$	5.40511	−	2.88205i	0.187164	−	0.0997971i
$835$	−28.0137	−	10.1962i	−0.969454	−	0.352852i
$836$	0.455401			0.0157504
$837$	35.7238	+	36.7348i	1.23480	+	1.26974i
$838$			9.29875i			0.321220i
$839$	26.6557	+	9.70187i	0.920256	+	0.334946i	0.758340	−	0.651859i	$-0.226011\pi$
$839$	26.6557	+	9.70187i	0.920256	+	0.334946i	0.161916	+	0.986805i	$0.448233\pi$
$840$	−1.83715	−	11.4510i	−0.0633878	−	0.395098i
$841$	−47.2193	−	39.6217i	−1.62825	−	1.36626i
$842$	−19.2651	−	3.39696i	−0.663919	−	0.117067i
$843$	0.572236	+	4.03747i	0.0197089	+	0.139058i
$844$	11.7278	−	9.84080i	0.403688	−	0.338734i
$845$	6.90638	+	11.9622i	0.237587	+	0.411512i
$846$	6.46471	+	22.3481i	0.222261	+	0.768342i
$847$	−11.2579	−	57.6603i	−0.386825	−	1.98123i
$848$	−11.7051	+	2.06392i	−0.401954	+	0.0708753i
$849$	10.2245	−	3.33533i	0.350902	−	0.114468i
$850$	−1.27156	−	3.49357i	−0.0436140	−	0.119829i
$851$	0.110471	+	0.303516i	0.00378689	+	0.0104044i
$852$	12.1607	−	3.96696i	0.416620	−	0.135906i
$853$	10.2721	−	1.81124i	0.351709	−	0.0620158i	0.00499717	−	0.999988i	$-0.498409\pi$
$853$	10.2721	−	1.81124i	0.351709	−	0.0620158i	0.346712	+	0.937972i	$0.387298\pi$
$854$	−1.03948	−	5.32396i	−0.0355701	−	0.182182i
$855$	0.166734	+	0.576389i	0.00570219	+	0.0197121i
$856$	0.734836	+	1.27277i	0.0251162	+	0.0435025i
$857$	−20.7347	+	17.3985i	−0.708285	+	0.594321i	−0.924117	−	0.382109i	$-0.875198\pi$
$857$	−20.7347	+	17.3985i	−0.708285	+	0.594321i	0.215833	+	0.976430i	$0.430753\pi$
$858$	−3.84641	−	27.1387i	−0.131314	−	0.926501i
$859$	26.5092	+	4.67429i	0.904483	+	0.159485i	0.606497	−	0.795086i	$-0.292574\pi$
$859$	26.5092	+	4.67429i	0.904483	+	0.159485i	0.297986	+	0.954570i	$0.403685\pi$
$860$	1.85927	+	1.56011i	0.0634005	+	0.0531994i
$861$	−14.0620	+	2.25604i	−0.479231	+	0.0768857i
$862$	−4.32968	−	1.57587i	−0.147469	−	0.0536745i
$863$		−	43.4031i		−	1.47746i	−0.674002	−	0.738729i	$-0.735426\pi$
$863$		−	43.4031i		−	1.47746i	0.674002	−	0.738729i	$-0.264574\pi$
$864$	1.41475	−	4.99985i	0.0481309	−	0.170098i
$865$	42.8029			1.45534
$866$	13.2715	+	4.83041i	0.450982	+	0.164144i
$867$	15.2779	−	8.14629i	0.518864	−	0.276663i
$868$	0.477073	+	26.0862i	0.0161929	+	0.885425i
$869$	−11.7057	−	2.06404i	−0.397090	−	0.0700176i
$870$	25.7315	+	32.8557i	0.872379	+	1.11391i
$871$	0.774906	+	0.923497i	0.0262567	+	0.0312915i
$872$	−17.5995	+	10.1611i	−0.595993	+	0.344097i
$873$	17.2228	−	1.85085i	0.582902	−	0.0626418i
$874$	−0.00468194	−	0.00270312i	−0.000158369	−	9.14344e-5i
$875$	18.7206	+	15.1338i	0.632870	+	0.511616i
$876$	3.13453	−	14.8319i	0.105906	−	0.501124i
$877$	−9.88882	+	3.59924i	−0.333922	+	0.121538i	−0.503539	−	0.863972i	$-0.667969\pi$
$877$	−9.88882	+	3.59924i	−0.333922	+	0.121538i	0.169617	+	0.985510i	$0.445747\pi$
$878$	−12.9580	+	4.71632i	−0.437310	+	0.159168i
$879$	−14.7399	+	16.4088i	−0.497164	+	0.553454i
$880$	−14.3617	+	2.53236i	−0.484134	+	0.0853659i
$881$	−25.0935	+	43.4633i	−0.845423	+	1.46432i	0.0398306	+	0.999206i	$0.487318\pi$
$881$	−25.0935	+	43.4633i	−0.845423	+	1.46432i	−0.885253	+	0.465109i	$0.846015\pi$
$882$	−13.9892	+	15.6621i	−0.471041	+	0.527371i
$883$	8.46950	+	14.6696i	0.285021	+	0.493671i	0.972614	−	0.232425i	$-0.0746660\pi$
$883$	8.46950	+	14.6696i	0.285021	+	0.493671i	−0.687593	+	0.726096i	$0.741333\pi$
$884$	4.67173	+	5.56755i	0.157127	+	0.187257i
$885$	−14.0029	+	34.7752i	−0.470702	+	1.16896i
$886$	0.473236	−	2.68386i	0.0158987	−	0.0901659i
$887$	−22.4411	−	18.8303i	−0.753499	−	0.632260i	0.182927	−	0.983127i	$-0.441443\pi$
$887$	−22.4411	−	18.8303i	−0.753499	−	0.632260i	−0.936426	+	0.350866i	$0.885887\pi$
$888$	8.17345	+	0.275871i	0.274283	+	0.00925762i
$889$	−38.0636	+	14.6476i	−1.27661	+	0.491266i
$890$		−	42.1039i		−	1.41133i
$891$	51.8208	−	2.05193i	1.73606	−	0.0687423i
$892$		−	17.1156i		−	0.573074i
$893$	0.209610	−	0.575899i	0.00701433	−	0.0192717i
$894$	0.249686	−	7.39765i	0.00835074	−	0.247414i
$895$	−16.9373	+	20.1851i	−0.566153	+	0.674714i
$896$	2.26672	−	1.36455i	0.0757257	−	0.0455865i
$897$	−0.121543	+	0.301843i	−0.00405819	+	0.0100782i
$898$	14.2779	−	11.9806i	0.476461	−	0.399798i
$899$	−46.9425	−	81.3068i	−1.56562	−	2.71173i
$900$	−1.85633	−	3.78359i	−0.0618777	−	0.126120i
$901$	27.2407	+	15.7274i	0.907519	+	0.523957i
$902$	3.10977	+	17.6364i	0.103544	+	0.587227i
$903$	0.0679109	−	4.39433i	0.00225993	−	0.146234i
$904$	−5.44482	+	1.98175i	−0.181092	+	0.0659121i
$905$	5.74388	+	15.7812i	0.190933	+	0.524584i
$906$	1.34725	−	6.37491i	0.0447595	−	0.211792i
$907$	−5.08849	−	28.8583i	−0.168960	−	0.958223i	−0.944886	−	0.327398i	$-0.893828\pi$
$907$	−5.08849	−	28.8583i	−0.168960	−	0.958223i	0.775926	−	0.630824i	$-0.217283\pi$
$908$	0.933260	−	1.61645i	0.0309713	−	0.0536439i
$909$	−36.6959	+	26.7922i	−1.21712	+	0.888642i
$910$	17.3917	+	5.97225i	0.576530	+	0.197978i
$911$	−27.6312	−	32.9296i	−0.915464	−	1.09101i	−0.995551	−	0.0942197i	$-0.969964\pi$
$911$	−27.6312	−	32.9296i	−0.915464	−	1.09101i	0.0800874	−	0.996788i	$-0.474480\pi$
$912$	−0.107767	+	0.0843999i	−0.00356854	+	0.00279476i
$913$	24.7376	+	4.36191i	0.818695	+	0.144358i
$914$	−2.14938	+	2.56153i	−0.0710951	+	0.0847278i
$915$	−4.22849	−	7.93028i	−0.139789	−	0.262167i
$916$	−7.12438	+	19.5741i	−0.235396	+	0.646746i
$917$	21.5915	−	18.8008i	0.713015	−	0.620858i
$918$	−11.3734	+	7.72956i	−0.375379	+	0.255113i
$919$	−21.1752			−0.698507			−0.349253	−	0.937028i	$-0.613565\pi$
$919$	−21.1752			−0.698507			−0.349253	+	0.937028i	$0.613565\pi$
$920$	0.162683	+	0.0592119i	0.00536351	+	0.00195216i
$921$	21.4242	−	34.3751i	0.705952	−	1.13270i
$922$	10.5191	−	12.5361i	0.346427	−	0.412856i
$923$	−3.52187	+	19.9735i	−0.115924	+	0.657436i
$924$	19.9639	+	17.2844i	0.656764	+	0.568614i
$925$	5.08119	−	4.26362i	0.167068	−	0.140187i
$926$	−7.94457	+	4.58680i	−0.261075	+	0.150732i
$927$	−20.6005	−	5.08522i	−0.676608	−	0.167020i
$928$	−4.76026	+	8.24502i	−0.156263	+	0.270656i
$929$	2.18056	+	12.3666i	0.0715418	+	0.405734i	0.999457	+	0.0329430i	$0.0104880\pi$
$929$	2.18056	+	12.3666i	0.0715418	+	0.405734i	−0.927915	+	0.372791i	$0.878401\pi$
$930$	13.4057	+	41.0951i	0.439589	+	1.34756i
$931$	0.540928	−	0.115920i	0.0177282	−	0.00379912i
$932$	−0.0837701	−	0.230157i	−0.00274398	−	0.00753903i
$933$	12.5540	+	38.4842i	0.410998	+	1.25992i
$934$	30.0343	−	5.29586i	0.982753	−	0.173286i
$935$	33.4234	+	19.2970i	1.09306	+	0.631080i
$936$	5.93988	+	5.70934i	0.194151	+	0.186615i
$937$	27.7307	−	16.0103i	0.905923	−	0.523035i	0.0268059	−	0.999641i	$-0.491466\pi$
$937$	27.7307	−	16.0103i	0.905923	−	0.523035i	0.879117	+	0.476606i	$0.158133\pi$
$938$	−1.14726	−	0.180729i	−0.0374594	−	0.00590100i
$939$	6.03602	+	42.5878i	0.196978	+	1.38980i
$940$	−3.40795	+	19.3274i	−0.111155	+	0.630391i
$941$	−3.91410	−	3.28432i	−0.127596	−	0.107066i	0.576757	−	0.816916i	$-0.304318\pi$
$941$	−3.91410	−	3.28432i	−0.127596	−	0.107066i	−0.704353	+	0.709850i	$0.748763\pi$
$942$	20.4245	+	12.7295i	0.665465	+	0.414750i
$943$	0.0727128	−	0.199777i	0.00236785	−	0.00650563i
$944$	−8.55235			−0.278355
$945$	−14.5671	+	31.5961i	−0.473867	+	1.02782i
$946$	−5.52633			−0.179677
$947$	14.3067	−	39.3075i	0.464907	−	1.27732i	−0.456847	−	0.889545i	$-0.651021\pi$
$947$	14.3067	−	39.3075i	0.464907	−	1.27732i	0.921754	−	0.387776i	$-0.126757\pi$
$948$	3.15261	−	1.68100i	0.102392	−	0.0545962i
$949$	18.4130	+	15.4503i	0.597711	+	0.501539i
$950$	−0.0192788	+	0.109336i	−0.000625488	+	0.00354732i
$951$	−40.5842	+	31.7842i	−1.31603	+	1.03067i
$952$	−6.91657	−	1.08957i	−0.224167	−	0.0353132i
$953$	−33.2624	+	19.2041i	−1.07748	+	0.622081i	−0.930214	−	0.367016i	$-0.880379\pi$
$953$	−33.2624	+	19.2041i	−1.07748	+	0.622081i	−0.147262	+	0.989098i	$0.547046\pi$
$954$	32.6080	+	14.4269i	1.05572	+	0.467088i
$955$	−18.4555	−	10.6553i	−0.597207	−	0.344798i
$956$	22.3160	−	3.93492i	0.721752	−	0.127264i
$957$	−92.9684	−	19.6476i	−3.00524	−	0.635118i
$958$	−5.30946	−	14.5876i	−0.171541	−	0.471304i
$959$	43.2455	+	23.9243i	1.39647	+	0.772557i
$960$	2.92928	−	3.26094i	0.0945422	−	0.105247i
$961$	−11.5034	−	65.2393i	−0.371079	−	2.10449i
$962$	−6.48347	+	11.2297i	−0.209036	+	0.362060i
$963$	0.297288	−	4.39898i	0.00957997	−	0.141755i
$964$	−11.4122	+	6.58884i	−0.367563	+	0.212212i
$965$	18.8472	−	15.8147i	0.606714	−	0.509093i
$966$	−0.102653	−	0.296199i	−0.00330280	−	0.00953005i
$967$	−5.72408	+	32.4629i	−0.184074	+	1.04394i	0.743065	+	0.669219i	$0.233371\pi$
$967$	−5.72408	+	32.4629i	−0.184074	+	1.04394i	−0.927139	+	0.374717i	$0.877740\pi$
$968$	14.2731	−	17.0101i	0.458756	−	0.546724i
$969$	0.362051	+	0.0122200i	0.0116307	+	0.000392561i
$970$	13.7314	+	4.99781i	0.440888	+	0.160470i
$971$	−13.4179			−0.430601			−0.215301	−	0.976548i	$-0.569073\pi$
$971$	−13.4179			−0.430601			−0.215301	+	0.976548i	$0.569073\pi$
$972$	−11.8828	+	10.0896i	−0.381140	+	0.323624i
$973$	−6.14450	−	7.05656i	−0.196984	−	0.226223i
$974$	−1.29566	+	3.55979i	−0.0415155	+	0.114063i
$975$	6.67849	+	0.225413i	0.213883	+	0.00721898i
$976$	1.31788	−	1.57059i	0.0421844	−	0.0502734i
$977$	28.8089	+	5.07979i	0.921680	+	0.162517i	0.614302	−	0.789071i	$-0.289438\pi$
$977$	28.8089	+	5.07979i	0.921680	+	0.162517i	0.307377	+	0.951588i	$0.400549\pi$
$978$	31.8772	+	12.8360i	1.01932	+	0.410449i
$979$	61.6224	+	73.4387i	1.96946	+	2.34711i
$980$	−16.4144	+	6.66367i	−0.524338	+	0.212863i
$981$	60.8276	+	4.11079i	1.94207	+	0.131247i
$982$	−11.1423	+	19.2990i	−0.355564	+	0.615856i
$983$	−5.28946	−	29.9980i	−0.168708	−	0.956789i	−0.945159	−	0.326611i	$-0.894093\pi$
$983$	−5.28946	−	29.9980i	−0.168708	−	0.956789i	0.776451	−	0.630178i	$-0.217018\pi$
$984$	−4.00447	−	3.59719i	−0.127658	−	0.114674i
$985$	−4.51555	−	12.4064i	−0.143877	−	0.395300i
$986$	23.6762	−	8.61742i	0.754003	−	0.274435i
$987$	31.0467	−	17.2907i	0.988227	−	0.550370i
$988$	−0.0376884	−	0.213741i	−0.00119903	−	0.00680002i
$989$	0.0568159	+	0.0328026i	0.00180664	+	0.00104306i
$990$	40.0089	+	17.7013i	1.27157	+	0.562585i
$991$	−10.8718	−	18.8306i	−0.345355	−	0.598172i	0.640063	−	0.768322i	$-0.278908\pi$
$991$	−10.8718	−	18.8306i	−0.345355	−	0.598172i	−0.985418	+	0.170150i	$0.945575\pi$
$992$	−7.55421	+	6.33874i	−0.239846	+	0.201255i
$993$	−27.9498	−	35.6882i	−0.886961	−	1.13253i
$994$	−10.0774	−	16.7400i	−0.319635	−	0.530960i
$995$	−11.4280	+	13.6193i	−0.362291	+	0.431762i
$996$	−6.66238	+	3.55243i	−0.211106	+	0.112563i
$997$	−9.05432	+	24.8765i	−0.286753	+	0.787848i	0.709762	+	0.704441i	$0.248802\pi$
$997$	−9.05432	+	24.8765i	−0.286753	+	0.787848i	−0.996516	+	0.0834069i	$0.973420\pi$
$998$			15.2556i			0.482909i
$999$	−19.8991	−	14.3513i	−0.629579	−	0.454056i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.z.a.293.7	yes	144
7.6	odd	2	inner	378.2.z.a.293.6	yes	144
27.20	odd	18	inner	378.2.z.a.209.6	✓	144
189.20	even	18	inner	378.2.z.a.209.7	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.z.a.209.6	✓	144	27.20	odd	18	inner
378.2.z.a.209.7	yes	144	189.20	even	18	inner
378.2.z.a.293.6	yes	144	7.6	odd	2	inner
378.2.z.a.293.7	yes	144	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:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	378.z (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.342020 + 0.939693i) q^{2} +(0.0584270 - 1.73107i) q^{3} +(-0.766044 - 0.642788i) q^{4} +(-0.439464 + 2.49233i) q^{5} +(1.60669 + 0.646963i) q^{6} +(0.411710 - 2.61352i) q^{7} +(0.866025 - 0.500000i) q^{8} +(-2.99317 - 0.202282i) q^{9} +O(q^{10})\)	\(q+(-0.342020 + 0.939693i) q^{2} +(0.0584270 - 1.73107i) q^{3} +(-0.766044 - 0.642788i) q^{4} +(-0.439464 + 2.49233i) q^{5} +(1.60669 + 0.646963i) q^{6} +(0.411710 - 2.61352i) q^{7} +(0.866025 - 0.500000i) q^{8} +(-2.99317 - 0.202282i) q^{9} +(-2.19171 - 1.26539i) q^{10} +(5.67484 - 1.00063i) q^{11} +(-1.15746 + 1.28852i) q^{12} +(-0.939285 - 2.58066i) q^{13} +(2.31509 + 1.28076i) q^{14} +(4.28870 + 0.906360i) q^{15} +(0.173648 + 0.984808i) q^{16} +(1.32323 - 2.29190i) q^{17} +(1.21381 - 2.74348i) q^{18} +(-0.0684419 + 0.0395149i) q^{19} +(1.93869 - 1.62675i) q^{20} +(-4.50012 - 0.865397i) q^{21} +(-1.00063 + 5.67484i) q^{22} +(0.0439715 - 0.0524032i) q^{23} +(-0.814933 - 1.52836i) q^{24} +(-1.32009 - 0.480475i) q^{25} +2.74628 q^{26} +(-0.525045 + 5.16956i) q^{27} +(-1.99533 + 1.73743i) q^{28} +(3.25621 - 8.94637i) q^{29} +(-2.31852 + 3.72007i) q^{30} +(6.33874 - 7.55421i) q^{31} +(-0.984808 - 0.173648i) q^{32} +(-1.40059 - 9.88198i) q^{33} +(1.70111 + 2.02730i) q^{34} +(6.33281 + 2.17466i) q^{35} +(2.16288 + 2.07893i) q^{36} +(-2.36082 + 4.08905i) q^{37} +(-0.0137234 - 0.0778292i) q^{38} +(-4.52218 + 1.47518i) q^{39} +(0.865576 + 2.37815i) q^{40} +(2.92039 - 1.06294i) q^{41} +(2.35234 - 3.93275i) q^{42} +(0.166535 + 0.944466i) q^{43} +(-4.99037 - 2.88119i) q^{44} +(1.81954 - 7.37106i) q^{45} +(0.0342038 + 0.0592427i) q^{46} +(-5.94050 + 4.98467i) q^{47} +(1.71491 - 0.243057i) q^{48} +(-6.66099 - 2.15203i) q^{49} +(0.902998 - 1.07615i) q^{50} +(-3.89011 - 2.42450i) q^{51} +(-0.939285 + 2.58066i) q^{52} +11.8856i q^{53} +(-4.67822 - 2.26147i) q^{54} +14.5833i q^{55} +(-0.950210 - 2.46923i) q^{56} +(0.0644041 + 0.120786i) q^{57} +(7.29314 + 6.11967i) q^{58} +(-1.48510 + 8.42242i) q^{59} +(-2.70274 - 3.45104i) q^{60} +(-1.31788 - 1.57059i) q^{61} +(4.93066 + 8.54016i) q^{62} +(-1.76099 + 7.73944i) q^{63} +(0.500000 - 0.866025i) q^{64} +(6.84464 - 1.20689i) q^{65} +(9.76505 + 2.06371i) q^{66} +(-0.412498 + 0.150137i) q^{67} +(-2.48686 + 0.905142i) q^{68} +(-0.0881442 - 0.0791793i) q^{69} +(-4.20947 + 5.20712i) q^{70} +(-6.39570 - 3.69256i) q^{71} +(-2.69330 + 1.32141i) q^{72} +(-7.57975 + 4.37617i) q^{73} +(-3.03501 - 3.61698i) q^{74} +(-0.908863 + 2.25710i) q^{75} +(0.0778292 + 0.0137234i) q^{76} +(-0.278774 - 15.2433i) q^{77} +(0.160457 - 4.75400i) q^{78} +(-1.93834 - 0.705499i) q^{79} -2.53077 q^{80} +(8.91816 + 1.21093i) q^{81} +3.10782i q^{82} +(4.09628 + 1.49092i) q^{83} +(2.89103 + 3.55555i) q^{84} +(5.13065 + 4.30512i) q^{85} +(-0.944466 - 0.166535i) q^{86} +(-15.2965 - 6.15942i) q^{87} +(4.41424 - 3.70399i) q^{88} +(8.31838 + 14.4079i) q^{89} +(6.30421 + 4.23087i) q^{90} +(-7.13133 + 1.39236i) q^{91} +(-0.0673683 + 0.0118788i) q^{92} +(-12.7065 - 11.4141i) q^{93} +(-2.65229 - 7.28710i) q^{94} +(-0.0684063 - 0.187945i) q^{95} +(-0.358136 + 1.69462i) q^{96} +(-5.68626 + 1.00264i) q^{97} +(4.30043 - 5.52325i) q^{98} +(-17.1882 + 1.84713i) 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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