LMFDB - Embedded newform 231.2.s.a.8.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(8,231)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 0, 3]))

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

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

chi := DirichletCharacter("231.8");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.s (of order $10$, degree $4$, 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:	$1.84454428669$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$24$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			8.17
Character	$\chi$	$=$	231.8
Dual form			231.2.s.a.29.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.723708 - 0.525805i) q^{2} +(1.01468 - 1.40372i) q^{3} +(-0.370751 + 1.14105i) q^{4} +(0.915619 - 1.26024i) q^{5} +(-0.00375218 - 1.54941i) q^{6} +(0.951057 + 0.309017i) q^{7} +(0.884520 + 2.72227i) q^{8} +(-0.940859 - 2.84865i) q^{9} +O(q^{10})$	\(q+(0.723708 - 0.525805i) q^{2} +(1.01468 - 1.40372i) q^{3} +(-0.370751 + 1.14105i) q^{4} +(0.915619 - 1.26024i) q^{5} +(-0.00375218 - 1.54941i) q^{6} +(0.951057 + 0.309017i) q^{7} +(0.884520 + 2.72227i) q^{8} +(-0.940859 - 2.84865i) q^{9} -1.39348i q^{10} +(2.61790 + 2.03631i) q^{11} +(1.22553 + 1.67823i) q^{12} +(-3.74899 - 5.16004i) q^{13} +(0.850770 - 0.276432i) q^{14} +(-0.839968 - 2.56401i) q^{15} +(0.130240 + 0.0946248i) q^{16} +(0.286176 + 0.207919i) q^{17} +(-2.17874 - 1.56688i) q^{18} +(-5.06803 + 1.64670i) q^{19} +(1.09854 + 1.51201i) q^{20} +(1.39879 - 1.02146i) q^{21} +(2.96530 + 0.0971906i) q^{22} +5.86029i q^{23} +(4.71881 + 1.52061i) q^{24} +(0.795235 + 2.44748i) q^{25} +(-5.42634 - 1.76313i) q^{26} +(-4.95337 - 1.56975i) q^{27} +(-0.705211 + 0.970639i) q^{28} +(0.585320 - 1.80143i) q^{29} +(-1.95606 - 1.41394i) q^{30} +(2.16406 - 1.57228i) q^{31} -5.58072 q^{32} +(5.51474 - 1.60860i) q^{33} +0.316433 q^{34} +(1.26024 - 0.915619i) q^{35} +(3.59929 - 0.0174328i) q^{36} +(-2.08217 + 6.40825i) q^{37} +(-2.80193 + 3.85653i) q^{38} +(-11.0473 + 0.0267531i) q^{39} +(4.24061 + 1.37786i) q^{40} +(2.18147 + 6.71389i) q^{41} +(0.475224 - 1.47473i) q^{42} -4.45367i q^{43} +(-3.29414 + 2.23221i) q^{44} +(-4.45145 - 1.42257i) q^{45} +(3.08137 + 4.24114i) q^{46} +(4.76608 - 1.54859i) q^{47} +(0.264978 - 0.0868066i) q^{48} +(0.809017 + 0.587785i) q^{49} +(1.86241 + 1.35312i) q^{50} +(0.582237 - 0.190740i) q^{51} +(7.27783 - 2.36471i) q^{52} +(-5.28174 - 7.26970i) q^{53} +(-4.41018 + 1.46846i) q^{54} +(4.96325 - 1.43470i) q^{55} +2.86237i q^{56} +(-2.83091 + 8.78497i) q^{57} +(-0.523600 - 1.61147i) q^{58} +(9.50501 + 3.08836i) q^{59} +(3.23710 - 0.00783925i) q^{60} +(-8.22276 + 11.3177i) q^{61} +(0.739434 - 2.27574i) q^{62} +(-0.0145301 - 2.99996i) q^{63} +(-4.29930 + 3.12362i) q^{64} -9.93554 q^{65} +(3.14525 - 4.06384i) q^{66} -5.39282 q^{67} +(-0.343347 + 0.249456i) q^{68} +(8.22621 + 5.94631i) q^{69} +(0.430610 - 1.32528i) q^{70} +(6.27540 - 8.63734i) q^{71} +(6.92258 - 5.08096i) q^{72} +(-8.13270 - 2.64247i) q^{73} +(1.86261 + 5.73252i) q^{74} +(4.24248 + 1.36712i) q^{75} -6.39342i q^{76} +(1.86052 + 2.74563i) q^{77} +(-7.98093 + 5.82806i) q^{78} +(-2.43034 - 3.34507i) q^{79} +(0.238500 - 0.0774934i) q^{80} +(-7.22957 + 5.36035i) q^{81} +(5.10894 + 3.71186i) q^{82} +(-5.74526 - 4.17418i) q^{83} +(0.646944 + 1.97480i) q^{84} +(0.524057 - 0.170276i) q^{85} +(-2.34176 - 3.22316i) q^{86} +(-1.93479 - 2.64950i) q^{87} +(-3.22781 + 8.92781i) q^{88} -7.49250i q^{89} +(-3.96954 + 1.31107i) q^{90} +(-1.97096 - 6.06599i) q^{91} +(-6.68692 - 2.17271i) q^{92} +(-0.0112199 - 4.63309i) q^{93} +(2.63499 - 3.62675i) q^{94} +(-2.56514 + 7.89470i) q^{95} +(-5.66264 + 7.83377i) q^{96} +(9.11241 - 6.62056i) q^{97} +0.894552 q^{98} +(3.33766 - 9.37337i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 6 q^{3} - 24 q^{4} - 10 q^{6} - 20 q^{9}+O(q^{10}) $ 96 * q + 6 * q^3 - 24 * q^4 - 10 * q^6 - 20 * q^9	$ 96 q + 6 q^{3} - 24 q^{4} - 10 q^{6} - 20 q^{9} - 20 q^{12} - 32 q^{16} - 10 q^{18} - 60 q^{19} + 30 q^{24} + 12 q^{25} - 40 q^{28} + 60 q^{30} + 40 q^{31} - 44 q^{33} + 8 q^{34} + 2 q^{36} + 16 q^{37} - 10 q^{39} - 96 q^{45} - 40 q^{46} + 48 q^{48} + 24 q^{49} - 30 q^{51} - 40 q^{52} + 28 q^{55} - 30 q^{57} + 36 q^{58} - 32 q^{60} + 40 q^{61} - 28 q^{64} + 118 q^{66} - 56 q^{67} + 26 q^{69} + 20 q^{70} + 150 q^{72} + 40 q^{73} + 2 q^{75} - 20 q^{78} - 40 q^{79} + 8 q^{81} - 16 q^{82} + 40 q^{84} - 60 q^{85} - 156 q^{88} + 100 q^{90} + 36 q^{91} - 36 q^{93} + 160 q^{96} - 88 q^{97} - 94 q^{99}+O(q^{100}) $ 96 * q + 6 * q^3 - 24 * q^4 - 10 * q^6 - 20 * q^9 - 20 * q^12 - 32 * q^16 - 10 * q^18 - 60 * q^19 + 30 * q^24 + 12 * q^25 - 40 * q^28 + 60 * q^30 + 40 * q^31 - 44 * q^33 + 8 * q^34 + 2 * q^36 + 16 * q^37 - 10 * q^39 - 96 * q^45 - 40 * q^46 + 48 * q^48 + 24 * q^49 - 30 * q^51 - 40 * q^52 + 28 * q^55 - 30 * q^57 + 36 * q^58 - 32 * q^60 + 40 * q^61 - 28 * q^64 + 118 * q^66 - 56 * q^67 + 26 * q^69 + 20 * q^70 + 150 * q^72 + 40 * q^73 + 2 * q^75 - 20 * q^78 - 40 * q^79 + 8 * q^81 - 16 * q^82 + 40 * q^84 - 60 * q^85 - 156 * q^88 + 100 * q^90 + 36 * q^91 - 36 * q^93 + 160 * q^96 - 88 * q^97 - 94 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/231\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{10}\right)$

Coefficient data

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

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

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

$2$	0.723708	−	0.525805i	0.511739	−	0.371800i	−0.301744	−	0.953389i	$-0.597569\pi$
$2$	0.723708	−	0.525805i	0.511739	−	0.371800i	0.813483	+	0.581589i	$0.197569\pi$
$3$	1.01468	−	1.40372i	0.585824	−	0.810438i
$3$	1.01468	−	1.40372i	0.585824	−	0.810438i
$4$	−0.370751	+	1.14105i	−0.185376	+	0.570527i
$5$	0.915619	−	1.26024i	0.409477	−	0.563597i	−0.553614	−	0.832774i	$-0.686752\pi$
$5$	0.915619	−	1.26024i	0.409477	−	0.563597i	0.963091	+	0.269177i	$0.0867515\pi$
$6$	−0.00375218	−	1.54941i	−0.00153182	−	0.632542i
$7$	0.951057	+	0.309017i	0.359466	+	0.116797i
$7$	0.951057	+	0.309017i	0.359466	+	0.116797i
$8$	0.884520	+	2.72227i	0.312725	+	0.962469i
$9$	−0.940859	−	2.84865i	−0.313620	−	0.949549i
$10$		−	1.39348i		−	0.440658i
$11$	2.61790	+	2.03631i	0.789328	+	0.613972i
$11$	2.61790	+	2.03631i	0.789328	+	0.613972i
$12$	1.22553	+	1.67823i	0.353780	+	0.484464i
$13$	−3.74899	−	5.16004i	−1.03978	−	1.43114i	−0.897343	−	0.441334i	$-0.854506\pi$
$13$	−3.74899	−	5.16004i	−1.03978	−	1.43114i	−0.142439	−	0.989804i	$-0.545494\pi$
$14$	0.850770	−	0.276432i	0.227378	−	0.0738795i
$15$	−0.839968	−	2.56401i	−0.216879	−	0.662025i
$16$	0.130240	+	0.0946248i	0.0325600	+	0.0236562i
$17$	0.286176	+	0.207919i	0.0694079	+	0.0504278i	0.621948	−	0.783058i	$-0.286341\pi$
$17$	0.286176	+	0.207919i	0.0694079	+	0.0504278i	−0.552540	+	0.833486i	$0.686341\pi$
$18$	−2.17874	−	1.56688i	−0.513534	−	0.369317i
$19$	−5.06803	+	1.64670i	−1.16269	+	0.377780i	−0.825908	−	0.563804i	$-0.809337\pi$
$19$	−5.06803	+	1.64670i	−1.16269	+	0.377780i	−0.336778	+	0.941584i	$0.609337\pi$
$20$	1.09854	+	1.51201i	0.245641	+	0.338095i
$21$	1.39879	−	1.02146i	0.305241	−	0.222902i
$22$	2.96530	+	0.0971906i	0.632205	+	0.0207211i
$23$			5.86029i			1.22196i	0.791648	+	0.610978i	$0.209224\pi$
$23$			5.86029i			1.22196i	−0.791648	+	0.610978i	$0.790776\pi$
$24$	4.71881	+	1.52061i	0.963223	+	0.310393i
$25$	0.795235	+	2.44748i	0.159047	+	0.489496i
$26$	−5.42634	−	1.76313i	−1.06419	−	0.345778i
$27$	−4.95337	−	1.56975i	−0.953276	−	0.302099i
$28$	−0.705211	+	0.970639i	−0.133272	+	0.183434i
$29$	0.585320	−	1.80143i	0.108691	−	0.334517i	−0.881888	−	0.471459i	$-0.843727\pi$
$29$	0.585320	−	1.80143i	0.108691	−	0.334517i	0.990579	+	0.136942i	$0.0437274\pi$
$30$	−1.95606	−	1.41394i	−0.357126	−	0.258148i
$31$	2.16406	−	1.57228i	0.388676	−	0.282390i	−0.376237	−	0.926524i	$-0.622782\pi$
$31$	2.16406	−	1.57228i	0.388676	−	0.282390i	0.764913	+	0.644134i	$0.222782\pi$
$32$	−5.58072			−0.986542
$33$	5.51474	−	1.60860i	0.959994	−	0.280022i
$34$	0.316433			0.0542678
$35$	1.26024	−	0.915619i	0.213020	−	0.154768i
$36$	3.59929	−	0.0174328i	0.599881	−	0.00290547i
$37$	−2.08217	+	6.40825i	−0.342306	+	1.05351i	0.620704	+	0.784045i	$0.286847\pi$
$37$	−2.08217	+	6.40825i	−0.342306	+	1.05351i	−0.963010	+	0.269465i	$0.913153\pi$
$38$	−2.80193	+	3.85653i	−0.454533	+	0.625611i
$39$	−11.0473	+	0.0267531i	−1.76898	+	0.00428392i
$40$	4.24061	+	1.37786i	0.670499	+	0.217858i
$41$	2.18147	+	6.71389i	0.340689	+	1.04853i	0.963851	+	0.266440i	$0.0858475\pi$
$41$	2.18147	+	6.71389i	0.340689	+	1.04853i	−0.623162	+	0.782092i	$0.714152\pi$
$42$	0.475224	−	1.47473i	0.0733287	−	0.227556i
$43$		−	4.45367i		−	0.679179i	−0.940574	−	0.339589i	$-0.889712\pi$
$43$		−	4.45367i		−	0.679179i	0.940574	−	0.339589i	$-0.110288\pi$
$44$	−3.29414	+	2.23221i	−0.496610	+	0.336518i
$45$	−4.45145	−	1.42257i	−0.663583	−	0.212063i
$46$	3.08137	+	4.24114i	0.454323	+	0.625322i
$47$	4.76608	−	1.54859i	0.695204	−	0.225885i	0.0599641	−	0.998201i	$-0.480901\pi$
$47$	4.76608	−	1.54859i	0.695204	−	0.225885i	0.635240	+	0.772315i	$0.280901\pi$
$48$	0.264978	−	0.0868066i	0.0382463	−	0.0125295i
$49$	0.809017	+	0.587785i	0.115574	+	0.0839693i
$50$	1.86241	+	1.35312i	0.263385	+	0.191361i
$51$	0.582237	−	0.190740i	0.0815295	−	0.0267090i
$52$	7.27783	−	2.36471i	1.00925	−	0.327926i
$53$	−5.28174	−	7.26970i	−0.725503	−	0.998569i	−0.999323	−	0.0367885i	$-0.988287\pi$
$53$	−5.28174	−	7.26970i	−0.725503	−	0.998569i	0.273820	−	0.961781i	$-0.411713\pi$
$54$	−4.41018	+	1.46846i	−0.600149	+	0.199832i
$55$	4.96325	−	1.43470i	0.669245	−	0.193455i
$56$			2.86237i			0.382500i
$57$	−2.83091	+	8.78497i	−0.374963	+	1.16360i
$58$	−0.523600	−	1.61147i	−0.0687520	−	0.211597i
$59$	9.50501	+	3.08836i	1.23745	+	0.402071i	0.853407	−	0.521246i	$-0.174532\pi$
$59$	9.50501	+	3.08836i	1.23745	+	0.402071i	0.384040	+	0.923316i	$0.374532\pi$
$60$	3.23710	−	0.00783925i	0.417907	−	0.00101204i
$61$	−8.22276	+	11.3177i	−1.05282	+	1.44908i	−0.166476	+	0.986046i	$0.553239\pi$
$61$	−8.22276	+	11.3177i	−1.05282	+	1.44908i	−0.886341	+	0.463033i	$0.846761\pi$
$62$	0.739434	−	2.27574i	0.0939082	−	0.289020i
$63$	−0.0145301	−	2.99996i	−0.00183062	−	0.377960i
$64$	−4.29930	+	3.12362i	−0.537412	+	0.390453i
$65$	−9.93554			−1.23235
$66$	3.14525	−	4.06384i	0.387154	−	0.500224i
$67$	−5.39282			−0.658838			−0.329419	−	0.944184i	$-0.606853\pi$
$67$	−5.39282			−0.658838			−0.329419	+	0.944184i	$0.606853\pi$
$68$	−0.343347	+	0.249456i	−0.0416370	+	0.0302510i
$69$	8.22621	+	5.94631i	0.990319	+	0.715851i
$70$	0.430610	−	1.32528i	0.0514678	−	0.158401i
$71$	6.27540	−	8.63734i	0.744753	−	1.02506i	−0.253579	−	0.967315i	$-0.581608\pi$
$71$	6.27540	−	8.63734i	0.744753	−	1.02506i	0.998331	−	0.0577491i	$-0.0183923\pi$
$72$	6.92258	−	5.08096i	0.815834	−	0.598797i
$73$	−8.13270	−	2.64247i	−0.951860	−	0.309278i	−0.208389	−	0.978046i	$-0.566822\pi$
$73$	−8.13270	−	2.64247i	−0.951860	−	0.309278i	−0.743471	+	0.668768i	$0.766822\pi$
$74$	1.86261	+	5.73252i	0.216524	+	0.666392i
$75$	4.24248	+	1.36712i	0.489880	+	0.157861i
$76$		−	6.39342i		−	0.733376i
$77$	1.86052	+	2.74563i	0.212026	+	0.312893i
$78$	−7.98093	+	5.82806i	−0.903662	+	0.659898i
$79$	−2.43034	−	3.34507i	−0.273434	−	0.376350i	0.650111	−	0.759839i	$-0.274722\pi$
$79$	−2.43034	−	3.34507i	−0.273434	−	0.376350i	−0.923545	+	0.383489i	$0.874722\pi$
$80$	0.238500	−	0.0774934i	0.0266651	−	0.00866402i
$81$	−7.22957	+	5.36035i	−0.803285	+	0.595594i
$82$	5.10894	+	3.71186i	0.564188	+	0.409907i
$83$	−5.74526	−	4.17418i	−0.630624	−	0.458175i	0.225992	−	0.974129i	$-0.427438\pi$
$83$	−5.74526	−	4.17418i	−0.630624	−	0.458175i	−0.856616	+	0.515954i	$0.827438\pi$
$84$	0.646944	+	1.97480i	0.0705874	+	0.215469i
$85$	0.524057	−	0.170276i	0.0568419	−	0.0184691i
$86$	−2.34176	−	3.22316i	−0.252519	−	0.347562i
$87$	−1.93479	−	2.64950i	−0.207432	−	0.284056i
$88$	−3.22781	+	8.92781i	−0.344086	+	0.951708i
$89$		−	7.49250i		−	0.794203i	−0.917775	−	0.397102i	$-0.870016\pi$
$89$		−	7.49250i		−	0.794203i	0.917775	−	0.397102i	$-0.129984\pi$
$90$	−3.96954	+	1.31107i	−0.418426	+	0.138199i
$91$	−1.97096	−	6.06599i	−0.206613	−	0.635888i
$92$	−6.68692	−	2.17271i	−0.697159	−	0.226521i
$93$	−0.0112199	−	4.63309i	−0.00116345	−	0.480429i
$94$	2.63499	−	3.62675i	0.271779	−	0.374071i
$95$	−2.56514	+	7.89470i	−0.263178	+	0.809979i
$96$	−5.66264	+	7.83377i	−0.577940	+	0.799531i
$97$	9.11241	−	6.62056i	0.925225	−	0.672216i	−0.0195937	−	0.999808i	$-0.506237\pi$
$97$	9.11241	−	6.62056i	0.925225	−	0.672216i	0.944819	+	0.327592i	$0.106237\pi$
$98$	0.894552			0.0903634
$99$	3.33766	−	9.37337i	0.335447	−	0.942059i
$100$	−3.08754			−0.308754
$101$	−3.01559	+	2.19096i	−0.300063	+	0.218008i	−0.727621	−	0.685980i	$-0.759374\pi$
$101$	−3.01559	+	2.19096i	−0.300063	+	0.218008i	0.427558	+	0.903988i	$0.359374\pi$
$102$	0.321077	−	0.444183i	0.0317914	−	0.0439807i
$103$	3.67741	−	11.3179i	0.362346	−	1.11518i	−0.589281	−	0.807928i	$-0.700589\pi$
$103$	3.67741	−	11.3179i	0.362346	−	1.11518i	0.951627	−	0.307257i	$-0.0994111\pi$
$104$	10.7310	−	14.7699i	1.05226	−	1.44831i
$105$	−0.00653393	−	2.69808i	−0.000637646	−	0.263306i
$106$	−7.64488	−	2.48397i	−0.742536	−	0.241265i
$107$	1.58817	+	4.88790i	0.153535	+	0.472531i	0.998009	−	0.0630644i	$-0.0200874\pi$
$107$	1.58817	+	4.88790i	0.153535	+	0.472531i	−0.844475	+	0.535595i	$0.820087\pi$
$108$	3.62764	−	5.07008i	0.349070	−	0.487868i
$109$		−	8.57254i		−	0.821101i	−0.911838	−	0.410550i	$-0.865337\pi$
$109$		−	8.57254i		−	0.821101i	0.911838	−	0.410550i	$-0.134663\pi$
$110$	2.83757	−	3.64801i	0.270552	−	0.347824i
$111$	6.88267	+	9.42509i	0.653274	+	0.894590i
$112$	0.0946248	+	0.130240i	0.00894120	+	0.0123065i
$113$	7.20442	−	2.34086i	0.677735	−	0.220209i	0.0501314	−	0.998743i	$-0.484036\pi$
$113$	7.20442	−	2.34086i	0.677735	−	0.220209i	0.627603	+	0.778533i	$0.284036\pi$
$114$	2.57043	+	7.84626i	0.240743	+	0.734870i
$115$	7.38539	+	5.36580i	0.688691	+	0.500363i
$116$	1.83852	+	1.33577i	0.170703	+	0.124023i
$117$	−11.1719	+	15.5344i	−1.03284	+	1.43616i
$118$	8.50273	−	2.76270i	0.782740	−	0.254327i
$119$	0.207919	+	0.286176i	0.0190599	+	0.0262337i
$120$	6.23697	−	4.55454i	0.569355	−	0.415771i
$121$	2.70685	+	10.6618i	0.246077	+	0.969250i
$122$			12.5143i			1.13299i
$123$	11.6379	+	3.75025i	1.04935	+	0.338149i
$124$	0.991731	+	3.05223i	0.0890601	+	0.274099i
$125$	11.2201	+	3.64562i	1.00355	+	0.326074i
$126$	−1.58791	−	2.16346i	−0.141462	−	0.192736i
$127$	11.5302	−	15.8700i	1.02314	−	1.40823i	0.113163	−	0.993576i	$-0.463902\pi$
$127$	11.5302	−	15.8700i	1.02314	−	1.40823i	0.909978	−	0.414656i	$-0.136098\pi$
$128$	1.98006	−	6.09399i	0.175014	−	0.538638i
$129$	−6.25171	−	4.51904i	−0.550432	−	0.397880i
$130$	−7.19043	+	5.22415i	−0.630642	+	0.458189i
$131$	−6.92885			−0.605376			−0.302688	−	0.953090i	$-0.597884\pi$
$131$	−6.92885			−0.605376			−0.302688	+	0.953090i	$0.597884\pi$
$132$	−0.209094	+	6.88902i	−0.0181993	+	0.599612i
$133$	−5.32885			−0.462069
$134$	−3.90283	+	2.83557i	−0.337153	+	0.244956i
$135$	−6.51367	+	4.80514i	−0.560607	+	0.413561i
$136$	−0.312884	+	0.962958i	−0.0268296	+	0.0825730i
$137$	3.39574	−	4.67383i	0.290118	−	0.399313i	−0.638935	−	0.769261i	$-0.720625\pi$
$137$	3.39574	−	4.67383i	0.290118	−	0.399313i	0.929052	+	0.369948i	$0.120625\pi$
$138$	9.07997	−	0.0219889i	0.772938	−	0.00187182i
$139$	2.18435	+	0.709737i	0.185274	+	0.0601991i	0.400184	−	0.916435i	$-0.368946\pi$
$139$	2.18435	+	0.709737i	0.185274	+	0.0601991i	−0.214911	+	0.976634i	$0.568946\pi$
$140$	0.577536	+	1.77747i	0.0488107	+	0.150224i
$141$	2.66224	−	8.26156i	0.224201	−	0.695749i
$142$		−	9.55055i		−	0.801464i
$143$	0.692969	−	21.1426i	0.0579490	−	1.76803i
$144$	0.147015	−	0.460036i	0.0122513	−	0.0383363i
$145$	−1.73431	−	2.38707i	−0.144026	−	0.198235i
$146$	−7.27513	+	2.36383i	−0.602094	+	0.195632i
$147$	1.64598	−	0.539221i	0.135758	−	0.0444742i
$148$	−6.54020	−	4.75174i	−0.537601	−	0.390590i
$149$	5.04706	+	3.66690i	0.413471	+	0.300404i	0.775006	−	0.631954i	$-0.217747\pi$
$149$	5.04706	+	3.66690i	0.413471	+	0.300404i	−0.361534	+	0.932359i	$0.617747\pi$
$150$	3.78916	−	1.24132i	0.309383	−	0.101354i
$151$	8.99574	−	2.92289i	0.732063	−	0.237862i	0.0808174	−	0.996729i	$-0.474247\pi$
$151$	8.99574	−	2.92289i	0.732063	−	0.237862i	0.651245	+	0.758867i	$0.274247\pi$
$152$	−8.96555	−	12.3400i	−0.727202	−	1.00091i
$153$	0.323037	−	1.01084i	0.0261160	−	0.0817214i
$154$	2.79014	+	1.00876i	0.224836	+	0.0812884i
$155$		−	4.16685i		−	0.334689i
$156$	4.06526	−	12.6155i	0.325481	−	1.01004i
$157$	−2.58026	−	7.94121i	−0.205927	−	0.633778i	−0.999674	−	0.0255300i	$-0.991873\pi$
$157$	−2.58026	−	7.94121i	−0.205927	−	0.633778i	0.793747	−	0.608248i	$-0.208127\pi$
$158$	−3.51771	−	1.14297i	−0.279854	−	0.0909300i
$159$	−15.5639	+	0.0376909i	−1.23430	+	0.00298908i
$160$	−5.10982	+	7.03306i	−0.403967	+	0.556012i
$161$	−1.81093	+	5.57347i	−0.142721	+	0.439251i
$162$	−2.41360	+	7.68067i	−0.189630	+	0.603450i
$163$	−6.55670	+	4.76372i	−0.513560	+	0.373123i	−0.814173	−	0.580623i	$-0.802809\pi$
$163$	−6.55670	+	4.76372i	−0.513560	+	0.373123i	0.300612	+	0.953746i	$0.402809\pi$
$164$	−8.46970			−0.661372
$165$	3.02218	−	8.42278i	0.235276	−	0.655712i
$166$	−6.35269			−0.493065
$167$	4.53132	−	3.29220i	0.350644	−	0.254758i	−0.398495	−	0.917170i	$-0.630467\pi$
$167$	4.53132	−	3.29220i	0.350644	−	0.254758i	0.749139	+	0.662413i	$0.230467\pi$
$168$	4.01796	+	2.90438i	0.309992	+	0.224078i
$169$	−8.55387	+	26.3261i	−0.657990	+	2.02508i
$170$	0.289732	−	0.398782i	0.0222214	−	0.0305852i
$171$	9.45918	+	12.8877i	0.723362	+	0.985548i
$172$	5.08189	+	1.65120i	0.387490	+	0.125903i
$173$	−4.45718	−	13.7178i	−0.338873	−	1.04294i	−0.964783	−	0.263049i	$-0.915272\pi$
$173$	−4.45718	−	13.7178i	−0.338873	−	1.04294i	0.625909	−	0.779896i	$-0.284728\pi$
$174$	−2.79334	−	0.900139i	−0.211763	−	0.0682394i
$175$			2.57343i			0.194533i
$176$	0.148270	+	0.512928i	0.0111762	+	0.0386634i
$177$	13.9797	−	10.2087i	1.05078	−	0.767331i
$178$	−3.93959	−	5.42238i	−0.295285	−	0.406425i
$179$	−16.0249	+	5.20682i	−1.19776	+	0.389176i	−0.838936	−	0.544229i	$-0.816822\pi$
$179$	−16.0249	+	5.20682i	−1.19776	+	0.389176i	−0.358824	+	0.933405i	$0.616822\pi$
$180$	3.27361	−	4.55193i	0.244000	−	0.339281i
$181$	9.51749	+	6.91486i	0.707430	+	0.513978i	0.882344	−	0.470606i	$-0.155965\pi$
$181$	9.51749	+	6.91486i	0.707430	+	0.513978i	−0.174914	+	0.984584i	$0.555965\pi$
$182$	−4.61592	−	3.35367i	−0.342155	−	0.248590i
$183$	7.54338	+	23.0262i	0.557622	+	1.70215i
$184$	−15.9533	+	5.18355i	−1.17609	+	0.382136i
$185$	6.16948	+	8.49156i	0.453589	+	0.624312i
$186$	−2.44422	−	3.34710i	−0.179219	−	0.245422i
$187$	0.325793	+	1.12706i	0.0238244	+	0.0824186i
$188$			6.01250i			0.438506i
$189$	−4.22585	−	3.02360i	−0.307386	−	0.219935i
$190$	2.29465	+	7.06222i	0.166472	+	0.512347i
$191$	25.8874	+	8.41132i	1.87315	+	0.608622i	0.990297	+	0.138965i	$0.0443775\pi$
$191$	25.8874	+	8.41132i	1.87315	+	0.608622i	0.882849	+	0.469657i	$0.155622\pi$
$192$	0.0222904	+	9.20447i	0.00160867	+	0.664276i
$193$	−2.29286	+	3.15585i	−0.165044	+	0.227163i	−0.883526	−	0.468382i	$-0.844837\pi$
$193$	−2.29286	+	3.15585i	−0.165044	+	0.227163i	0.718482	+	0.695545i	$0.244837\pi$
$194$	3.11361	−	9.58270i	0.223544	−	0.687998i
$195$	−10.0814	+	13.9467i	−0.721942	+	0.998745i
$196$	−0.970639	+	0.705211i	−0.0693314	+	0.0503722i
$197$	−3.90792			−0.278428			−0.139214	−	0.990262i	$-0.544458\pi$
$197$	−3.90792			−0.278428			−0.139214	+	0.990262i	$0.544458\pi$
$198$	−2.51307	−	8.53854i	−0.178596	−	0.606808i
$199$	−11.1253			−0.788648			−0.394324	−	0.918971i	$-0.629021\pi$
$199$	−11.1253			−0.788648			−0.394324	+	0.918971i	$0.629021\pi$
$200$	−5.95931	+	4.32969i	−0.421387	+	0.306155i
$201$	−5.47197	+	7.57001i	−0.385963	+	0.533947i
$202$	−1.03039	+	3.17122i	−0.0724982	+	0.223127i
$203$	1.11335	−	1.53239i	0.0781415	−	0.107553i
$204$	0.00178014	+	0.735081i	0.000124635	+	0.0514660i
$205$	10.4585	+	3.39818i	0.730454	+	0.237339i
$206$	−3.28963	−	10.1244i	−0.229200	−	0.705404i
$207$	16.6939	−	5.51371i	1.16031	−	0.383229i
$208$		−	1.02679i		−	0.0711950i
$209$	−16.6208	−	6.00919i	−1.14969	−	0.415665i
$210$	−1.42339	−	1.94919i	−0.0982235	−	0.134507i
$211$	5.10317	+	7.02391i	0.351316	+	0.483546i	0.947704	−	0.319151i	$-0.103398\pi$
$211$	5.10317	+	7.02391i	0.351316	+	0.483546i	−0.596387	+	0.802697i	$0.703398\pi$
$212$	10.2533	−	3.33151i	0.704202	−	0.228809i
$213$	−5.75690	−	17.5730i	−0.394457	−	1.20408i
$214$	3.71945	+	2.70234i	0.254257	+	0.184728i
$215$	−5.61270	−	4.07787i	−0.382783	−	0.278108i
$216$	−0.108054	−	14.8729i	−0.00735217	−	1.01197i
$217$	2.54400	−	0.826597i	0.172698	−	0.0561130i
$218$	−4.50748	−	6.20402i	−0.305285	−	0.420189i
$219$	−11.9614	+	8.73477i	−0.808274	+	0.590241i
$220$	−0.203056	+	6.19526i	−0.0136900	+	0.417684i
$221$		−	2.25617i		−	0.151766i
$222$	9.93680	+	3.20208i	0.666914	+	0.214909i
$223$	2.57887	+	7.93695i	0.172694	+	0.531498i	0.999521	−	0.0309592i	$-0.00985619\pi$
$223$	2.57887	+	7.93695i	0.172694	+	0.531498i	−0.826827	+	0.562457i	$0.809856\pi$
$224$	−5.30758	−	1.72454i	−0.354628	−	0.115226i
$225$	6.22380	−	4.56808i	0.414920	−	0.304538i
$226$	3.98306	−	5.48222i	0.264949	−	0.364672i
$227$	−3.29598	+	10.1440i	−0.218762	+	0.673280i	0.780103	+	0.625651i	$0.215166\pi$
$227$	−3.29598	+	10.1440i	−0.218762	+	0.673280i	−0.998865	+	0.0476288i	$0.984834\pi$
$228$	−8.97457	−	6.48726i	−0.594356	−	0.429629i
$229$	1.59210	−	1.15673i	0.105209	−	0.0764388i	−0.533937	−	0.845524i	$-0.679288\pi$
$229$	1.59210	−	1.15673i	0.105209	−	0.0764388i	0.639146	+	0.769086i	$0.279288\pi$
$230$	8.16622			0.538465
$231$	5.74192	+	0.174278i	0.377790	+	0.0114666i
$232$	5.42171			0.355953
$233$	−16.9446	+	12.3110i	−1.11008	+	0.806518i	−0.982676	−	0.185333i	$-0.940663\pi$
$233$	−16.9446	+	12.3110i	−1.11008	+	0.806518i	−0.127401	+	0.991851i	$0.540663\pi$
$234$	0.0829027	+	17.1166i	0.00541952	+	1.11895i
$235$	2.41231	−	7.42433i	0.157362	−	0.484310i
$236$	−7.04799	+	9.70072i	−0.458785	+	0.631463i
$237$	−7.16155	+	0.0173431i	−0.465193	+	0.00112655i
$238$	0.300946	+	0.0977831i	0.0195074	+	0.00633834i
$239$	2.22247	+	6.84007i	0.143760	+	0.442448i	0.996849	−	0.0793170i	$-0.0252739\pi$
$239$	2.22247	+	6.84007i	0.143760	+	0.442448i	−0.853090	+	0.521765i	$0.825274\pi$
$240$	0.133222	−	0.413418i	0.00859942	−	0.0266860i
$241$			15.4062i			0.992402i	0.868208	+	0.496201i	$0.165272\pi$
$241$			15.4062i			0.992402i	−0.868208	+	0.496201i	$0.834728\pi$
$242$	7.56497	+	6.29272i	0.486295	+	0.404512i
$243$	0.188747	+	15.5873i	0.0121081	+	0.999927i
$244$	−9.86548	−	13.5787i	−0.631572	−	0.869285i
$245$	1.48150	−	0.481369i	0.0946497	−	0.0307536i
$246$	10.3943	−	3.40518i	0.662719	−	0.217106i
$247$	27.4970	+	19.9778i	1.74960	+	1.27116i
$248$	6.19433	+	4.50044i	0.393340	+	0.285779i
$249$	−11.6890	+	3.82929i	−0.740758	+	0.242672i
$250$	10.0369	−	3.26120i	0.634791	−	0.206256i
$251$	−13.0122	−	17.9097i	−0.821322	−	1.13045i	−0.989477	−	0.144692i	$-0.953781\pi$
$251$	−13.0122	−	17.9097i	−0.821322	−	1.13045i	0.168155	−	0.985761i	$-0.446219\pi$
$252$	3.42851	+	1.09566i	0.215976	+	0.0690202i
$253$	−11.9334	+	15.3417i	−0.750246	+	0.964524i
$254$		−	17.5479i		−	1.10105i
$255$	0.292728	−	0.908405i	0.0183314	−	0.0568865i
$256$	−5.05563	−	15.5596i	−0.315977	−	0.972478i
$257$	18.0750	+	5.87291i	1.12748	+	0.366342i	0.812620	−	0.582795i	$-0.198041\pi$
$257$	18.0750	+	5.87291i	1.12748	+	0.366342i	0.314865	+	0.949136i	$0.398041\pi$
$258$	−6.90055	+	0.0167110i	−0.429609	+	0.00104038i
$259$	−3.96052	+	5.45119i	−0.246095	+	0.338720i
$260$	3.68361	−	11.3370i	0.228448	−	0.703091i
$261$	−5.68234	+	0.0275219i	−0.351728	+	0.00170356i
$262$	−5.01446	+	3.64322i	−0.309795	+	0.225079i
$263$	20.1894			1.24493			0.622467	−	0.782646i	$-0.286131\pi$
$263$	20.1894			1.24493			0.622467	+	0.782646i	$0.286131\pi$
$264$	9.25696	+	13.5898i	0.569726	+	0.836394i
$265$	−13.9976			−0.859868
$266$	−3.85653	+	2.80193i	−0.236459	+	0.171797i
$267$	−10.5174	−	7.60247i	−0.643652	−	0.465264i
$268$	1.99939	−	6.15350i	0.122132	−	0.375885i
$269$	−15.1488	+	20.8506i	−0.923641	+	1.27128i	0.0386474	+	0.999253i	$0.487695\pi$
$269$	−15.1488	+	20.8506i	−0.923641	+	1.27128i	−0.962289	+	0.272030i	$0.912305\pi$
$270$	−2.18743	+	6.90244i	−0.133123	+	0.420069i
$271$	−11.8482	−	3.84972i	−0.719729	−	0.233854i	−0.0738231	−	0.997271i	$-0.523520\pi$
$271$	−11.8482	−	3.84972i	−0.719729	−	0.233854i	−0.645906	+	0.763417i	$0.723520\pi$
$272$	0.0175972	+	0.0541587i	0.00106699	+	0.00328385i
$273$	−10.5148	−	3.38835i	−0.636387	−	0.205072i
$274$		−	5.16799i		−	0.312210i
$275$	−2.90199	+	8.02662i	−0.174997	+	0.484023i
$276$	−9.83494	+	7.18196i	−0.591994	+	0.432303i
$277$	−11.0006	−	15.1411i	−0.660964	−	0.909738i	0.338549	−	0.940949i	$-0.390064\pi$
$277$	−11.0006	−	15.1411i	−0.660964	−	0.909738i	−0.999513	+	0.0312103i	$0.990064\pi$
$278$	1.95401	−	0.634897i	0.117194	−	0.0380786i
$279$	−6.51494	−	4.68534i	−0.390040	−	0.280504i
$280$	3.60727	+	2.62084i	0.215576	+	0.156625i
$281$	−14.9766	−	10.8812i	−0.893431	−	0.649116i	0.0433394	−	0.999060i	$-0.486200\pi$
$281$	−14.9766	−	10.8812i	−0.893431	−	0.649116i	−0.936770	+	0.349945i	$0.886200\pi$
$282$	−2.41728	−	7.37877i	−0.143947	−	0.439400i
$283$	5.21111	−	1.69319i	0.309768	−	0.100650i	−0.150007	−	0.988685i	$-0.547930\pi$
$283$	5.21111	−	1.69319i	0.309768	−	0.100650i	0.459776	+	0.888035i	$0.347930\pi$
$284$	7.52907	+	10.3629i	0.446768	+	0.614924i
$285$	8.47915	+	11.6113i	0.502262	+	0.687795i
$286$	−10.6154	−	15.6654i	−0.627700	−	0.926317i
$287$			7.05940i			0.416703i
$288$	5.25068	+	15.8975i	0.309399	+	0.936770i
$289$	−5.21462	−	16.0490i	−0.306742	−	0.944056i
$290$	−2.51026	−	0.815634i	−0.147408	−	0.0478957i
$291$	−0.0472448	−	19.5090i	−0.00276954	−	1.14364i
$292$	6.03042	−	8.30016i	0.352903	−	0.485730i
$293$	−4.91449	+	15.1252i	−0.287108	+	0.883626i	0.698651	+	0.715462i	$0.253784\pi$
$293$	−4.91449	+	15.1252i	−0.287108	+	0.883626i	−0.985759	+	0.168164i	$0.946216\pi$
$294$	0.907682	−	1.25570i	0.0529371	−	0.0732340i
$295$	12.5951	−	9.15084i	0.733312	−	0.532783i
$296$	−19.2867			−1.12102
$297$	−9.77093	−	14.1961i	−0.566967	−	0.823740i
$298$	5.58067			0.323280
$299$	30.2393	−	21.9702i	1.74879	−	1.27057i
$300$	−3.13286	+	4.33405i	−0.180876	+	0.250226i
$301$	1.37626	−	4.23570i	0.0793264	−	0.244141i
$302$	4.97342	−	6.84532i	0.286188	−	0.393904i
$303$	0.0156348	+	6.45616i	0.000898198	+	0.370897i
$304$	−0.815879	−	0.265095i	−0.0467938	−	0.0152042i
$305$	6.73407	+	20.7253i	0.385592	+	1.18673i
$306$	−0.297719	−	0.901405i	−0.0170194	−	0.0515299i
$307$			5.28463i			0.301610i	0.988564	+	0.150805i	$0.0481865\pi$
$307$			5.28463i			0.301610i	−0.988564	+	0.150805i	$0.951814\pi$
$308$	−3.82270	+	1.10501i	−0.217819	+	0.0629638i
$309$	−12.1558	−	16.6461i	−0.691517	−	0.946961i
$310$	−2.19095	−	3.01558i	−0.124437	−	0.171273i
$311$	12.2872	−	3.99236i	0.696744	−	0.226386i	0.0608328	−	0.998148i	$-0.480624\pi$
$311$	12.2872	−	3.99236i	0.696744	−	0.226386i	0.635911	+	0.771762i	$0.280624\pi$
$312$	−9.84435	−	30.0500i	−0.557327	−	1.70125i
$313$	3.65950	+	2.65878i	0.206847	+	0.150283i	0.686386	−	0.727237i	$-0.259196\pi$
$313$	3.65950	+	2.65878i	0.206847	+	0.150283i	−0.479539	+	0.877521i	$0.659196\pi$
$314$	−6.04288	−	4.39041i	−0.341019	−	0.247765i
$315$	−3.79398	−	2.72851i	−0.213767	−	0.153734i
$316$	4.71796	−	1.53296i	0.265406	−	0.0862356i
$317$	13.6164	+	18.7414i	0.764775	+	1.05262i	0.996802	+	0.0799132i	$0.0254643\pi$
$317$	13.6164	+	18.7414i	0.764775	+	1.05262i	−0.232027	+	0.972709i	$0.574536\pi$
$318$	−11.2439	+	8.21084i	−0.630526	+	0.460441i
$319$	5.20059	−	3.52408i	0.291177	−	0.197310i
$320$			8.27820i			0.462765i
$321$	8.47272	+	2.73029i	0.472901	+	0.152390i
$322$	1.61997	+	4.98576i	0.0902775	+	0.277846i
$323$	−1.79273	−	0.582494i	−0.0997503	−	0.0324108i
$324$	−3.43608	−	10.2367i	−0.190893	−	0.568705i
$325$	9.64777	−	13.2790i	0.535162	−	0.736587i
$326$	−2.24035	+	6.89509i	−0.124081	+	0.381884i
$327$	−12.0335	−	8.69837i	−0.665451	−	0.481021i
$328$	−16.3475	+	11.8771i	−0.902638	+	0.655805i
$329$	5.01135			0.276285
$330$	−2.24156	−	7.68471i	−0.123394	−	0.423029i
$331$	20.5487			1.12946			0.564730	−	0.825276i	$-0.308980\pi$
$331$	20.5487			1.12946			0.564730	+	0.825276i	$0.308980\pi$
$332$	6.89303	−	5.00808i	0.378304	−	0.274854i
$333$	20.2139	−	0.0979041i	1.10771	−	0.00536511i
$334$	1.54830	−	4.76518i	0.0847192	−	0.260739i
$335$	−4.93777	+	6.79626i	−0.269779	+	0.371319i
$336$	0.278834		0.000675250i	0.0152116		3.68379e-5i
$337$	0.363979	+	0.118264i	0.0198272	+	0.00644224i	0.318914	−	0.947784i	$-0.396682\pi$
$337$	0.363979	+	0.118264i	0.0198272	+	0.00644224i	−0.299087	+	0.954226i	$0.596682\pi$
$338$	7.65188	+	23.5501i	0.416208	+	1.28096i
$339$	4.02425	−	12.4882i	0.218567	−	0.678266i
$340$			0.661108i			0.0358536i
$341$	8.86696	+	0.290623i	0.480173	+	0.0157381i
$342$	13.6221	+	4.35326i	0.736599	+	0.235397i
$343$	0.587785	+	0.809017i	0.0317374	+	0.0436828i
$344$	12.1241	−	3.93936i	0.653689	−	0.212396i
$345$	15.0259	−	4.92246i	0.808965	−	0.265016i
$346$	−10.4386	−	7.58407i	−0.561181	−	0.407722i
$347$	20.2829	+	14.7364i	1.08884	+	0.791090i	0.979203	−	0.202882i	$-0.0650307\pi$
$347$	20.2829	+	14.7364i	1.08884	+	0.791090i	0.109638	+	0.993972i	$0.465031\pi$
$348$	3.74055	−	1.22540i	0.200514	−	0.0656884i
$349$	−1.36705	+	0.444182i	−0.0731766	+	0.0237765i	−0.345377	−	0.938464i	$-0.612249\pi$
$349$	−1.36705	+	0.444182i	−0.0731766	+	0.0237765i	0.272200	+	0.962241i	$0.412249\pi$
$350$	1.35312	+	1.86241i	0.0723275	+	0.0995502i
$351$	10.4701	+	31.4446i	0.558854	+	1.67839i
$352$	−14.6098	−	11.3641i	−0.778705	−	0.605709i
$353$		−	13.6058i		−	0.724163i	−0.932146	−	0.362081i	$-0.882066\pi$
$353$		−	13.6058i		−	0.724163i	0.932146	−	0.362081i	$-0.117934\pi$
$354$	4.74946	−	14.7387i	0.252431	−	0.783353i
$355$	−5.13926	−	15.8170i	−0.272764	−	0.839481i
$356$	8.54935	+	2.77785i	0.453115	+	0.147226i
$357$	0.612682	−	0.00148373i	0.0324266	−	7.85272e-5i
$358$	−8.85961	+	12.1942i	−0.468245	+	0.644484i
$359$	10.0034	−	30.7872i	0.527958	−	1.62489i	−0.230433	−	0.973088i	$-0.574014\pi$
$359$	10.0034	−	30.7872i	0.527958	−	1.62489i	0.758391	−	0.651800i	$-0.225986\pi$
$360$	−0.0647872	−	13.3764i	−0.00341458	−	0.704996i
$361$	7.60200	−	5.52318i	0.400105	−	0.290694i
$362$	10.5238			0.553116
$363$	17.7127	+	7.01858i	0.929675	+	0.368380i
$364$	7.65236			0.401093
$365$	−10.7766	+	7.82967i	−0.564074	+	0.409823i
$366$	17.5665	+	12.6979i	0.918216	+	0.663732i
$367$	−2.78605	+	8.57458i	−0.145431	+	0.447589i	−0.997066	−	0.0765451i	$-0.975611\pi$
$367$	−2.78605	+	8.57458i	−0.145431	+	0.447589i	0.851636	+	0.524134i	$0.175611\pi$
$368$	−0.554529	+	0.763243i	−0.0289068	+	0.0397868i
$369$	17.0730	−	12.5311i	0.888786	−	0.652341i
$370$	8.92980	+	2.90147i	0.464238	+	0.150840i
$371$	−2.77678	−	8.54604i	−0.144163	−	0.443688i
$372$	5.29077	+	1.70492i	0.274314	+	0.0883960i
$373$		−	24.2546i		−	1.25586i	−0.778271	−	0.627929i	$-0.783903\pi$
$373$		−	24.2546i		−	1.25586i	0.778271	−	0.627929i	$-0.216097\pi$
$374$	0.828391	+	0.644357i	0.0428351	+	0.0333189i
$375$	16.5022	−	12.0507i	0.852169	−	0.622295i
$376$	8.43138	+	11.6048i	0.434815	+	0.598472i
$377$	−11.4898	+	3.73327i	−0.591755	+	0.192273i
$378$	−4.64811	+	0.0337694i	−0.239073	+	0.00173691i
$379$	−9.38954	−	6.82190i	−0.482308	−	0.350417i	0.319911	−	0.947448i	$-0.396347\pi$
$379$	−9.38954	−	6.82190i	−0.482308	−	0.350417i	−0.802219	+	0.597030i	$0.796347\pi$
$380$	−8.05725	−	5.85394i	−0.413328	−	0.300301i
$381$	−10.5776	−	32.2881i	−0.541904	−	1.65417i
$382$	23.1576	−	7.52437i	1.18485	−	0.384980i
$383$	−2.16211	−	2.97589i	−0.110479	−	0.152061i	0.750197	−	0.661214i	$-0.229959\pi$
$383$	−2.16211	−	2.97589i	−0.110479	−	0.152061i	−0.860676	+	0.509153i	$0.829959\pi$
$384$	−6.54514	−	8.96288i	−0.334005	−	0.457385i
$385$	5.16368	+	0.169245i	0.263166	+	0.00862550i
$386$			3.48951i			0.177612i
$387$	−12.6869	+	4.19028i	−0.644913	+	0.213004i
$388$	4.17598	+	12.8523i	0.212003	+	0.652479i
$389$	−19.5842	−	6.36328i	−0.992956	−	0.322631i	−0.232909	−	0.972499i	$-0.574824\pi$
$389$	−19.5842	−	6.36328i	−0.992956	−	0.322631i	−0.760047	+	0.649868i	$0.774824\pi$
$390$	0.0372800	+	15.3942i	0.00188774	+	0.779515i
$391$	−1.21847	+	1.67708i	−0.0616205	+	0.0848134i
$392$	−0.884520	+	2.72227i	−0.0446750	+	0.137496i
$393$	−7.03055	+	9.72616i	−0.354644	+	0.490620i
$394$	−2.82819	+	2.05480i	−0.142482	+	0.103519i
$395$	−6.44086			−0.324075
$396$	9.45809	+	7.28364i	0.475287	+	0.366017i
$397$	13.7826			0.691731			0.345865	−	0.938284i	$-0.387585\pi$
$397$	13.7826			0.691731			0.345865	+	0.938284i	$0.387585\pi$
$398$	−8.05144	+	5.84971i	−0.403582	+	0.293220i
$399$	−5.40706	+	7.48021i	−0.270692	+	0.374479i
$400$	−0.128021	+	0.394008i	−0.00640105	+	0.0197004i
$401$	−19.1180	+	26.3136i	−0.954706	+	1.31404i	−0.00530135	+	0.999986i	$0.501687\pi$
$401$	−19.1180	+	26.3136i	−0.954706	+	1.31404i	−0.949405	+	0.314055i	$0.898313\pi$
$402$	0.0202348	+	8.35567i	0.00100922	+	0.416743i
$403$	−16.2261	−	5.27217i	−0.808277	−	0.262625i
$404$	−1.38197	−	4.25326i	−0.0687554	−	0.211607i
$405$	0.135803	+	14.0190i	0.00674811	+	0.696612i
$406$		−	1.69440i		−	0.0840919i
$407$	−18.5001	+	12.5363i	−0.917018	+	0.621399i
$408$	1.03425	+	1.41629i	0.0512029	+	0.0701170i
$409$	10.2447	+	14.1006i	0.506566	+	0.697228i	0.983336	−	0.181800i	$-0.0581923\pi$
$409$	10.2447	+	14.1006i	0.506566	+	0.697228i	−0.476769	+	0.879028i	$0.658192\pi$
$410$	9.35569	−	3.03985i	0.462045	−	0.150127i
$411$	−3.11517	−	9.50910i	−0.153660	−	0.469049i
$412$	11.5509	+	8.39224i	0.569074	+	0.413456i
$413$	8.08544	+	5.87442i	0.397859	+	0.289061i
$414$	9.18238	−	12.7680i	0.451289	−	0.627515i
$415$	−10.5209	+	3.41846i	−0.516453	+	0.167806i
$416$	20.9221	+	28.7968i	1.02579	+	1.41188i
$417$	3.21268	−	2.34606i	0.157326	−	0.114887i
$418$	−15.1883	+	4.39041i	−0.742884	+	0.214742i
$419$		−	23.5512i		−	1.15055i	−0.817960	−	0.575275i	$-0.804895\pi$
$419$		−	23.5512i		−	1.15055i	0.817960	−	0.575275i	$-0.195105\pi$
$420$	3.08108	+	0.992862i	0.150342	+	0.0484467i
$421$	−9.00496	−	27.7144i	−0.438875	−	1.35072i	−0.889063	−	0.457785i	$-0.848643\pi$
$421$	−9.00496	−	27.7144i	−0.438875	−	1.35072i	0.450188	−	0.892934i	$-0.351357\pi$
$422$	7.38641	+	2.39999i	0.359565	+	0.116830i
$423$	−8.89560	−	12.1199i	−0.432519	−	0.589288i
$424$	15.1183	−	20.8085i	0.734209	−	1.01055i
$425$	−0.281301	+	0.865755i	−0.0136451	+	0.0419953i
$426$	−13.4063	−	9.69073i	−0.649537	−	0.469517i
$427$	−11.3177	+	8.22276i	−0.547700	+	0.397927i
$428$	−6.16617			−0.298053
$429$	−28.9752	−	22.4257i	−1.39893	−	1.08272i
$430$	−6.20612			−0.299286
$431$	−1.44628	+	1.05078i	−0.0696649	+	0.0506145i	−0.622073	−	0.782960i	$-0.713709\pi$
$431$	−1.44628	+	1.05078i	−0.0696649	+	0.0506145i	0.552408	+	0.833574i	$0.313709\pi$
$432$	−0.496588	−	0.673156i	−0.0238921	−	0.0323872i
$433$	−10.3131	+	31.7405i	−0.495616	+	1.52535i	0.320378	+	0.947290i	$0.396190\pi$
$433$	−10.3131	+	31.7405i	−0.495616	+	1.52535i	−0.815994	+	0.578060i	$0.803810\pi$
$434$	1.40649	−	1.93586i	0.0675136	−	0.0929244i
$435$	−5.11054	+	0.0123762i	−0.245032	+	0.000593391i
$436$	9.78174	+	3.17828i	0.468461	+	0.152212i
$437$	−9.65017	−	29.7002i	−0.461630	−	1.42075i
$438$	−4.06375	+	12.6108i	−0.194173	+	0.602566i
$439$		−	9.30872i		−	0.444281i	−0.975015	−	0.222141i	$-0.928696\pi$
$439$		−	9.30872i		−	0.444281i	0.975015	−	0.222141i	$-0.0713044\pi$
$440$	8.29575	+	12.2423i	0.395484	+	0.583629i
$441$	0.913221	−	2.85763i	0.0434867	−	0.136077i
$442$	−1.18630	−	1.63281i	−0.0564267	−	0.0776647i
$443$	−14.7608	+	4.79608i	−0.701307	+	0.227868i	−0.637900	−	0.770119i	$-0.720197\pi$
$443$	−14.7608	+	4.79608i	−0.701307	+	0.227868i	−0.0634071	+	0.997988i	$0.520197\pi$
$444$	−13.3063	+	4.35913i	−0.631489	+	0.206875i
$445$	−9.44236	−	6.86027i	−0.447611	−	0.325208i
$446$	6.03964	+	4.38805i	0.285985	+	0.207780i
$447$	10.2684	−	3.36393i	0.485681	−	0.159109i
$448$	−5.05412	+	1.64218i	−0.238785	+	0.0775859i
$449$	17.5357	+	24.1358i	0.827559	+	1.13904i	0.988373	+	0.152052i	$0.0485881\pi$
$449$	17.5357	+	24.1358i	0.827559	+	1.13904i	−0.160814	+	0.986985i	$0.551412\pi$
$450$	2.10230	−	6.57846i	0.0991034	−	0.310111i
$451$	−7.96069	+	22.0185i	−0.374854	+	1.03681i
$452$			9.08851i			0.427488i
$453$	5.02485	−	15.5933i	0.236088	−	0.732636i
$454$	2.94843	+	9.07432i	0.138376	+	0.425879i
$455$	−9.44926	−	3.07025i	−0.442988	−	0.143936i
$456$	−26.4191	+	0.0639789i	−1.23719	+	0.00299609i
$457$	−3.82515	+	5.26487i	−0.178933	+	0.246280i	−0.889057	−	0.457796i	$-0.848639\pi$
$457$	−3.82515	+	5.26487i	−0.178933	+	0.246280i	0.710124	+	0.704077i	$0.248639\pi$
$458$	0.544003	−	1.67427i	0.0254196	−	0.0782334i
$459$	−1.09115	−	1.47913i	−0.0509307	−	0.0690397i
$460$	−8.86081	+	6.43775i	−0.413137	+	0.300162i
$461$	−4.60414			−0.214436			−0.107218	−	0.994236i	$-0.534194\pi$
$461$	−4.60414			−0.214436			−0.107218	+	0.994236i	$0.534194\pi$
$462$	4.24711	−	2.89300i	0.197593	−	0.134595i
$463$	−7.10049			−0.329988			−0.164994	−	0.986295i	$-0.552760\pi$
$463$	−7.10049			−0.329988			−0.164994	+	0.986295i	$0.552760\pi$
$464$	0.246692	−	0.179232i	0.0114524	−	0.00832065i
$465$	−5.84909	−	4.22801i	−0.271245	−	0.196069i
$466$	−5.78977	+	17.8191i	−0.268206	+	0.825453i
$467$	−3.26147	+	4.48903i	−0.150923	+	0.207727i	−0.877784	−	0.479057i	$-0.840979\pi$
$467$	−3.26147	+	4.48903i	−0.150923	+	0.207727i	0.726861	+	0.686785i	$0.240979\pi$
$468$	−13.5836	−	18.5071i	−0.627904	−	0.855491i
$469$	−5.12888	−	1.66647i	−0.236830	−	0.0769506i
$470$	−2.15794	−	6.64145i	−0.0995383	−	0.306347i
$471$	−13.7654	−	4.43581i	−0.634275	−	0.204392i
$472$			28.6069i			1.31674i
$473$	9.06908	−	11.6593i	0.416997	−	0.536095i
$474$	−5.17375	+	3.77813i	−0.237638	+	0.173535i
$475$	−8.06055	−	11.0944i	−0.369843	−	0.509046i
$476$	−0.403629	+	0.131147i	−0.0185003	+	0.00601111i
$477$	−15.7394	+	21.8856i	−0.720658	+	1.00207i
$478$	5.20497	+	3.78163i	0.238070	+	0.172968i
$479$	12.5279	+	9.10203i	0.572413	+	0.415882i	0.835981	−	0.548758i	$-0.184899\pi$
$479$	12.5279	+	9.10203i	0.572413	+	0.415882i	−0.263568	+	0.964641i	$0.584899\pi$
$480$	4.68763	+	14.3090i	0.213960	+	0.653115i
$481$	40.8729	−	13.2804i	1.86364	−	0.605534i
$482$	8.10066	+	11.1496i	0.368975	+	0.507851i
$483$	5.98608	+	8.19731i	0.272376	+	0.372991i
$484$	−13.1692	−	0.864195i	−0.598601	−	0.0392816i
$485$		−	17.5457i		−	0.796711i
$486$	8.33248	+	11.1814i	0.377969	+	0.507200i
$487$	−0.711461	−	2.18965i	−0.0322394	−	0.0992226i	0.933642	−	0.358208i	$-0.116612\pi$
$487$	−0.711461	−	2.18965i	−0.0322394	−	0.0992226i	−0.965881	+	0.258985i	$0.916612\pi$
$488$	−38.0830	−	12.3739i	−1.72394	−	0.560140i
$489$	0.0339943	+	14.0374i	0.00153727	+	0.634794i
$490$	0.819069	−	1.12735i	0.0370018	−	0.0509286i
$491$	−1.66328	+	5.11903i	−0.0750626	+	0.231019i	−0.981547	−	0.191220i	$-0.938756\pi$
$491$	−1.66328	+	5.11903i	−0.0750626	+	0.231019i	0.906485	+	0.422239i	$0.138756\pi$
$492$	−8.59401	+	11.8891i	−0.387448	+	0.536001i
$493$	0.542057	−	0.393827i	0.0244130	−	0.0177371i
$494$	30.4042			1.36795
$495$	−8.75668	−	12.7887i	−0.393584	−	0.574809i
$496$	0.430623			0.0193356
$497$	8.63734	−	6.27540i	0.387438	−	0.281490i
$498$	−6.44593	+	8.91740i	−0.288849	+	0.399598i
$499$	−7.44000	+	22.8980i	−0.333060	+	1.02505i	0.634610	+	0.772833i	$0.281161\pi$
$499$	−7.44000	+	22.8980i	−0.333060	+	1.02505i	−0.967670	+	0.252221i	$0.918839\pi$
$500$	−8.31970	+	11.4511i	−0.372068	+	0.512108i
$501$	−0.0234934	−	9.70122i	−0.00104961	−	0.433418i
$502$	−18.8340	−	6.11955i	−0.840605	−	0.273129i
$503$	−1.90363	−	5.85876i	−0.0848785	−	0.261229i	0.899606	−	0.436703i	$-0.143854\pi$
$503$	−1.90363	−	5.85876i	−0.0848785	−	0.261229i	−0.984484	+	0.175474i	$0.943854\pi$
$504$	8.15387	−	2.69308i	0.363202	−	0.119959i
$505$			5.80646i			0.258384i
$506$	−0.569565	+	17.3775i	−0.0253203	+	0.772526i
$507$	28.2751	+	38.7197i	1.25574	+	1.71960i
$508$	13.8337	+	19.0404i	0.613770	+	0.844782i
$509$	−10.6177	+	3.44992i	−0.470623	+	0.152915i	−0.534721	−	0.845029i	$-0.679583\pi$
$509$	−10.6177	+	3.44992i	−0.470623	+	0.152915i	0.0640974	+	0.997944i	$0.479583\pi$
$510$	−0.265794	−	0.811338i	−0.0117695	−	0.0359266i
$511$	−6.91809	−	5.02628i	−0.306038	−	0.222350i
$512$	−1.47242	−	1.06978i	−0.0650724	−	0.0472779i
$513$	27.6888	−	0.201164i	1.22249	−	0.00888161i
$514$	16.1690	−	5.25362i	0.713184	−	0.231727i
$515$	−10.8962	−	14.9973i	−0.480143	−	0.660860i
$516$	7.47430	−	5.45810i	0.329038	−	0.240280i
$517$	15.6306	+	5.65116i	0.687431	+	0.248538i
$518$			6.02753i			0.264834i
$519$	−23.7785	−	7.66250i	−1.04376	−	0.336347i
$520$	−8.78818	−	27.0473i	−0.385387	−	1.18610i
$521$	−36.3185	−	11.8006i	−1.59114	−	0.516994i	−0.626247	−	0.779625i	$-0.715410\pi$
$521$	−36.3185	−	11.8006i	−1.59114	−	0.516994i	−0.964896	+	0.262631i	$0.915410\pi$
$522$	−4.09789	+	3.00772i	−0.179360	+	0.131644i
$523$	−18.8092	+	25.8886i	−0.822468	+	1.13203i	0.166810	+	0.985989i	$0.446653\pi$
$523$	−18.8092	+	25.8886i	−0.822468	+	1.13203i	−0.989278	+	0.146041i	$0.953347\pi$
$524$	2.56888	−	7.90620i	0.112222	−	0.345384i
$525$	3.61238	+	2.61120i	0.157657	+	0.113962i
$526$	14.6113	−	10.6157i	0.637081	−	0.462866i
$527$	0.946209			0.0412175
$528$	0.870453	+	0.312327i	0.0378816	+	0.0135923i
$529$	−11.3430			−0.493176
$530$	−10.1302	+	7.36002i	−0.440028	+	0.319699i
$531$	−0.145216	−	29.9821i	−0.00630183	−	1.30111i
$532$	1.97568	−	6.08050i	0.0856564	−	0.263623i
$533$	26.4656	−	36.4268i	1.14635	−	1.57782i
$534$	−11.6089	+	0.0281132i	−0.502367	+	0.00121658i
$535$	7.61409	+	2.47397i	0.329186	+	0.106959i
$536$	−4.77006	−	14.6807i	−0.206035	−	0.634111i
$537$	−8.95123	+	27.7778i	−0.386274	+	1.19870i
$538$			23.0551i			0.993975i
$539$	0.921014	+	3.18618i	0.0396709	+	0.137238i
$540$	−3.06798	−	9.21397i	−0.132025	−	0.396506i
$541$	−2.69394	−	3.70789i	−0.115821	−	0.159414i	0.747170	−	0.664633i	$-0.231412\pi$
$541$	−2.69394	−	3.70789i	−0.115821	−	0.159414i	−0.862992	+	0.505218i	$0.831412\pi$
$542$	−10.5989	+	3.44378i	−0.455260	+	0.147923i
$543$	19.3637	−	6.34354i	0.830977	−	0.272227i
$544$	−1.59707	−	1.16034i	−0.0684738	−	0.0497492i
$545$	−10.8035	−	7.84919i	−0.462770	−	0.336222i
$546$	−9.39128	+	3.07658i	−0.401910	+	0.131665i
$547$	32.7000	−	10.6249i	1.39815	−	0.454286i	0.489557	−	0.871971i	$-0.337158\pi$
$547$	32.7000	−	10.6249i	1.39815	−	0.454286i	0.908592	+	0.417685i	$0.137158\pi$
$548$	4.07413	+	5.60756i	0.174038	+	0.239543i
$549$	39.9765	+	12.7754i	1.70615	+	0.545242i
$550$	2.12024	+	7.33481i	0.0904073	+	0.312757i
$551$			10.0936i			0.430000i
$552$	−8.91123	+	27.6536i	−0.379287	+	1.17702i
$553$	−1.27770	−	3.93237i	−0.0543335	−	0.167221i
$554$	−15.9225	−	5.17353i	−0.676482	−	0.219802i
$555$	18.1798	−	0.0440259i	0.771689	−	0.00186879i
$556$	−1.61970	+	2.22932i	−0.0686905	+	0.0945443i
$557$	3.44881	−	10.6143i	0.146131	−	0.449744i	−0.851024	−	0.525127i	$-0.824018\pi$
$557$	3.44881	−	10.6143i	0.146131	−	0.449744i	0.997155	+	0.0753829i	$0.0240179\pi$
$558$	−7.17849	+	0.0347684i	−0.303890	+	0.00147186i
$559$	−22.9811	+	16.6968i	−0.971998	+	0.706198i
$560$	0.250774			0.0105971
$561$	1.91265	+	0.686277i	0.0807520	+	0.0289747i
$562$	−16.5601			−0.698545
$563$	11.6340	−	8.45261i	0.490315	−	0.356235i	−0.314990	−	0.949095i	$-0.602001\pi$
$563$	11.6340	−	8.45261i	0.490315	−	0.356235i	0.805306	+	0.592860i	$0.202001\pi$
$564$	8.43986	+	6.10075i	0.355382	+	0.256888i
$565$	3.64646	−	11.2226i	0.153408	−	0.472140i
$566$	2.88103	−	3.96540i	0.121099	−	0.166678i
$567$	−8.53217	+	2.86393i	−0.358317	+	0.120274i
$568$	29.0639	+	9.44344i	1.21949	+	0.396238i
$569$	2.99009	+	9.20254i	0.125351	+	0.385791i	0.993965	−	0.109699i	$-0.0349887\pi$
$569$	2.99009	+	9.20254i	0.125351	+	0.385791i	−0.868614	+	0.495490i	$0.834989\pi$
$570$	12.2417	+	3.94482i	0.512749	+	0.165231i
$571$			33.0036i			1.38116i	0.723257	+	0.690579i	$0.242644\pi$
$571$			33.0036i			1.38116i	−0.723257	+	0.690579i	$0.757356\pi$
$572$	23.8680	+	8.62936i	0.997969	+	0.360812i
$573$	38.0745	−	27.8039i	1.59059	−	1.16152i
$574$	3.71186	+	5.10894i	0.154930	+	0.213243i
$575$	−14.3430	+	4.66031i	−0.598142	+	0.194348i
$576$	12.9431	+	9.30828i	0.539297	+	0.387845i
$577$	−8.53894	−	6.20390i	−0.355481	−	0.258272i	0.395684	−	0.918387i	$-0.370508\pi$
$577$	−8.53894	−	6.20390i	−0.355481	−	0.258272i	−0.751165	+	0.660115i	$0.770508\pi$
$578$	−12.2125	−	8.87289i	−0.507972	−	0.369063i
$579$	2.10342	+	6.42071i	0.0874151	+	0.266836i
$580$	3.36677	−	1.09393i	0.139798	−	0.0454230i
$581$	−4.17418	−	5.74526i	−0.173174	−	0.238354i
$582$	−10.2921	−	14.0940i	−0.426622	−	0.584214i
$583$	0.976286	−	29.7867i	0.0404336	−	1.23364i
$584$		−	24.4767i		−	1.01286i
$585$	9.34794	+	28.3028i	0.386490	+	1.17018i
$586$	4.39627	+	13.5303i	0.181608	+	0.558932i
$587$	13.5103	+	4.38977i	0.557631	+	0.181185i	0.574255	−	0.818677i	$-0.305292\pi$
$587$	13.5103	+	4.38977i	0.557631	+	0.181185i	−0.0166240	+	0.999862i	$0.505292\pi$
$588$	0.00503244	+	2.07807i	0.000207534	+	0.0856980i
$589$	−8.37844	+	11.5319i	−0.345228	+	0.475165i
$590$	4.30359	−	13.2451i	0.177176	−	0.545291i
$591$	−3.96528	+	5.48563i	−0.163110	+	0.225648i
$592$	−0.877561	+	0.637585i	−0.0360675	+	0.0262046i
$593$	5.30627			0.217902			0.108951	−	0.994047i	$-0.465251\pi$
$593$	5.30627			0.217902			0.108951	+	0.994047i	$0.465251\pi$
$594$	−14.5357	−	5.13622i	−0.596406	−	0.210742i
$595$	0.551026			0.0225899
$596$	−6.05534	+	4.39946i	−0.248036	+	0.180209i
$597$	−11.2885	+	15.6167i	−0.462009	+	0.639151i
$598$	10.3324	−	31.8000i	0.422525	−	1.30040i
$599$	−2.38974	+	3.28920i	−0.0976423	+	0.134393i	−0.855043	−	0.518558i	$-0.826469\pi$
$599$	−2.38974	+	3.28920i	−0.0976423	+	0.134393i	0.757400	+	0.652951i	$0.226469\pi$
$600$	0.0308970	+	12.7584i	0.00126137	+	0.520861i
$601$	8.05543	+	2.61737i	0.328588	+	0.106765i	0.468665	−	0.883376i	$-0.344735\pi$
$601$	8.05543	+	2.61737i	0.328588	+	0.106765i	−0.140077	+	0.990141i	$0.544735\pi$
$602$	−1.23114	−	3.78905i	−0.0501774	−	0.154430i
$603$	5.07388	+	15.3622i	0.206625	+	0.625599i
$604$			11.3483i			0.461755i
$605$	15.9148	+	6.35082i	0.647030	+	0.258198i
$606$	3.40599	+	4.66415i	0.138359	+	0.189468i
$607$	−21.5373	−	29.6435i	−0.874171	−	1.20319i	−0.978001	−	0.208598i	$-0.933110\pi$
$607$	−21.5373	−	29.6435i	−0.874171	−	1.20319i	0.103830	−	0.994595i	$-0.466890\pi$
$608$	28.2833	−	9.18980i	1.14704	−	0.372696i
$609$	−1.02136	−	3.11771i	−0.0413875	−	0.126336i
$610$	15.7710	+	11.4583i	0.638548	+	0.463933i
$611$	−25.8588	−	18.7875i	−1.04613	−	0.760060i
$612$	1.03365	+	0.743372i	0.0417830	+	0.0300490i
$613$	−19.2160	+	6.24366i	−0.776127	+	0.252179i	−0.670186	−	0.742194i	$-0.733786\pi$
$613$	−19.2160	+	6.24366i	−0.776127	+	0.252179i	−0.105941	+	0.994372i	$0.533786\pi$
$614$	2.77868	+	3.82453i	0.112138	+	0.154345i
$615$	15.3821	−	11.2328i	0.620267	−	0.452949i
$616$	−5.82868	+	7.49340i	−0.234844	+	0.301918i
$617$		−	11.0076i		−	0.443150i	−0.975143	−	0.221575i	$-0.928880\pi$
$617$		−	11.0076i		−	0.443150i	0.975143	−	0.221575i	$-0.0711197\pi$
$618$	−17.5498	−	5.65533i	−0.705957	−	0.227491i
$619$	−8.92459	−	27.4671i	−0.358709	−	1.10399i	−0.953827	−	0.300356i	$-0.902895\pi$
$619$	−8.92459	−	27.4671i	−0.358709	−	1.10399i	0.595118	−	0.803638i	$-0.297105\pi$
$620$	4.75460	+	1.54486i	0.190949	+	0.0620432i
$621$	9.19922	−	29.0282i	0.369152	−	1.16486i
$622$	6.79316	−	9.34998i	0.272381	−	0.374900i
$623$	2.31531	−	7.12579i	0.0927609	−	0.285489i
$624$	−1.44132	−	1.04186i	−0.0576992	−	0.0417078i
$625$	4.45791	−	3.23886i	0.178316	−	0.129554i
$626$	4.04641			0.161727
$627$	−25.3000	+	17.2336i	−1.01039	+	0.688244i
$628$	10.0180			0.399762
$629$	−1.92827	+	1.40097i	−0.0768850	+	0.0558602i
$630$	−4.18040	+	0.0202474i	−0.166551	+	0.000806676i
$631$	0.864189	−	2.65970i	0.0344028	−	0.105881i	−0.932380	−	0.361478i	$-0.882272\pi$
$631$	0.864189	−	2.65970i	0.0344028	−	0.105881i	0.966783	+	0.255597i	$0.0822721\pi$
$632$	6.95652	−	9.57482i	0.276715	−	0.380866i
$633$	15.0377	−	0.0364166i	0.597694	−	0.00144743i
$634$	19.7086	+	6.40373i	0.782730	+	0.254324i
$635$	−9.44272	−	29.0617i	−0.374723	−	1.15328i
$636$	5.72732	−	17.7732i	0.227103	−	0.704754i
$637$		−	6.37816i		−	0.252712i
$638$	1.91073	−	5.28490i	0.0756467	−	0.209231i
$639$	−30.5090	−	9.74986i	−1.20692	−	0.385699i
$640$	−5.86692	−	8.07512i	−0.231910	−	0.319197i
$641$	−32.3302	+	10.5047i	−1.27697	+	0.414912i	−0.867511	−	0.497418i	$-0.834281\pi$
$641$	−32.3302	+	10.5047i	−1.27697	+	0.414912i	−0.409456	+	0.912330i	$0.634281\pi$
$642$	7.56737	−	2.47907i	0.298660	−	0.0978409i
$643$	−1.72062	−	1.25011i	−0.0678547	−	0.0492994i	0.553341	−	0.832955i	$-0.313353\pi$
$643$	−1.72062	−	1.25011i	−0.0678547	−	0.0492994i	−0.621196	+	0.783656i	$0.713353\pi$
$644$	−5.68823	−	4.13274i	−0.224148	−	0.162853i
$645$	−11.4193	+	3.74094i	−0.449633	+	0.147300i
$646$	−1.60369	+	0.521071i	−0.0630964	+	0.0205013i
$647$	−18.1438	−	24.9729i	−0.713308	−	0.981784i	−0.999720	−	0.0236777i	$-0.992462\pi$
$647$	−18.1438	−	24.9729i	−0.713308	−	0.981784i	0.286412	−	0.958107i	$-0.407538\pi$
$648$	−20.9870	−	14.9395i	−0.824448	−	0.586880i
$649$	18.5943	+	27.4402i	0.729891	+	1.07712i
$650$		−	14.6830i		−	0.575913i
$651$	1.42103	−	4.40980i	0.0556947	−	0.172834i
$652$	−3.00476	−	9.24771i	−0.117676	−	0.362168i
$653$	43.1798	+	14.0300i	1.68976	+	0.549035i	0.986764	−	0.162162i	$-0.0518466\pi$
$653$	43.1798	+	14.0300i	1.68976	+	0.549035i	0.702993	+	0.711197i	$0.251847\pi$
$654$	−13.2823	+	0.0321658i	−0.519381	+	0.00125778i
$655$	−6.34419	+	8.73203i	−0.247888	+	0.341188i
$656$	−0.351185	+	1.08084i	−0.0137115	+	0.0421996i
$657$	0.124250	+	25.6534i	0.00484745	+	1.00083i
$658$	3.62675	−	2.63499i	0.141386	−	0.102723i
$659$	36.9820			1.44061			0.720307	−	0.693656i	$-0.244001\pi$
$659$	36.9820			1.44061			0.720307	+	0.693656i	$0.244001\pi$
$660$	8.49037	+	6.57122i	0.330487	+	0.255785i
$661$	−8.93223			−0.347423			−0.173712	−	0.984797i	$-0.555576\pi$
$661$	−8.93223			−0.347423			−0.173712	+	0.984797i	$0.555576\pi$
$662$	14.8713	−	10.8046i	0.577989	−	0.419933i
$663$	−3.16703	−	2.28928i	−0.122997	−	0.0889083i
$664$	6.28145	−	19.3323i	0.243767	−	0.750239i
$665$	−4.87919	+	6.71563i	−0.189207	+	0.260421i
$666$	14.5775	−	10.6994i	0.564865	−	0.414594i
$667$	10.5569	+	3.43015i	0.408765	+	0.132816i
$668$	2.07658	+	6.39107i	0.0803454	+	0.247278i
$669$	13.7580	+	4.43343i	0.531914	+	0.171406i
$670$			7.51481i			0.290322i
$671$	−44.5727	+	12.8844i	−1.72071	+	0.497398i
$672$	−7.80626	+	5.70051i	−0.301133	+	0.219902i
$673$	2.72594	+	3.75193i	0.105077	+	0.144626i	0.858317	−	0.513119i	$-0.171510\pi$
$673$	2.72594	+	3.75193i	0.105077	+	0.144626i	−0.753240	+	0.657746i	$0.771510\pi$
$674$	0.325598	−	0.105793i	0.0125416	−	0.00407500i
$675$	−0.0971472	−	13.3716i	−0.00373920	−	0.514673i
$676$	−26.8682	−	19.5209i	−1.03339	−	0.750803i
$677$	15.3410	+	11.1459i	0.589603	+	0.428372i	0.842173	−	0.539207i	$-0.181276\pi$
$677$	15.3410	+	11.1459i	0.589603	+	0.428372i	−0.252570	+	0.967579i	$0.581276\pi$
$678$	−3.65397	−	11.1538i	−0.140330	−	0.428359i
$679$	10.7123	−	3.48063i	0.411100	−	0.133574i
$680$	0.927078	+	1.27601i	0.0355518	+	0.0489329i
$681$	10.8950	+	14.9195i	0.417495	+	0.571716i
$682$	6.56990	−	4.45196i	0.251574	−	0.170474i
$683$			20.6849i			0.791487i	0.918361	+	0.395743i	$0.129513\pi$
$683$			20.6849i			0.791487i	−0.918361	+	0.395743i	$0.870487\pi$
$684$	−18.2126	+	6.01531i	−0.696376	+	0.230001i
$685$	−2.78096	−	8.55890i	−0.106255	−	0.327019i
$686$	0.850770	+	0.276432i	0.0324825	+	0.0105542i
$687$	−0.00825451	−	3.40857i	−0.000314929	−	0.130045i
$688$	0.421428	−	0.580046i	0.0160668	−	0.0221140i
$689$	−17.7107	+	54.5080i	−0.674725	+	2.07659i
$690$	8.28608	−	11.4631i	0.315446	−	0.436392i
$691$	−12.2509	+	8.90078i	−0.466045	+	0.338602i	−0.795898	−	0.605431i	$-0.793001\pi$
$691$	−12.2509	+	8.90078i	−0.466045	+	0.338602i	0.329853	+	0.944032i	$0.393001\pi$
$692$	17.3053			0.657847
$693$	6.07083	−	7.88321i	0.230612	−	0.299458i
$694$	22.4273			0.851330
$695$	2.89447	−	2.10295i	0.109793	−	0.0797696i
$696$	5.50129	−	7.61057i	0.208526	−	0.288478i
$697$	−0.771660	+	2.37492i	−0.0292287	+	0.0899567i
$698$	−0.755793	+	1.04026i	−0.0286072	+	0.0393744i
$699$	0.0878520	+	36.2771i	0.00332287	+	1.37213i
$700$	−2.93643	−	0.954103i	−0.110987	−	0.0360617i
$701$	7.71635	+	23.7485i	0.291443	+	0.896968i	0.984393	+	0.175983i	$0.0563104\pi$
$701$	7.71635	+	23.7485i	0.291443	+	0.896968i	−0.692951	+	0.720985i	$0.743690\pi$
$702$	24.1110	+	17.2514i	0.910012	+	0.651114i
$703$		−	35.9060i		−	1.35422i
$704$	−17.6158	−	0.577375i	−0.663921	−	0.0217606i
$705$	−7.97396	−	10.9195i	−0.300317	−	0.411252i
$706$	−7.15398	−	9.84661i	−0.269244	−	0.370582i
$707$	−3.54504	+	1.15185i	−0.133325	+	0.0433199i
$708$	6.46566	+	19.7365i	0.242994	+	0.741743i
$709$	−15.7726	−	11.4595i	−0.592352	−	0.430369i	0.250804	−	0.968038i	$-0.419305\pi$
$709$	−15.7726	−	11.4595i	−0.592352	−	0.430369i	−0.843156	+	0.537669i	$0.819305\pi$
$710$	−12.0360	−	8.74466i	−0.451703	−	0.328181i
$711$	−7.24232	+	10.0704i	−0.271608	+	0.377670i
$712$	20.3966	−	6.62726i	0.764396	−	0.248367i
$713$	9.21403	+	12.6820i	0.345068	+	0.474945i
$714$	0.442623	−	0.323225i	0.0165647	−	0.0120964i
$715$	−26.0103	−	20.2319i	−0.972730	−	0.756629i
$716$		−	20.2158i		−	0.755499i
$717$	11.8566	+	3.82074i	0.442794	+	0.142688i
$718$	−8.94855	−	27.5408i	−0.333957	−	1.02781i
$719$	−19.4933	−	6.33377i	−0.726979	−	0.236210i	−0.0779325	−	0.996959i	$-0.524832\pi$
$719$	−19.4933	−	6.33377i	−0.726979	−	0.236210i	−0.649046	+	0.760749i	$0.724832\pi$
$720$	−0.445146	−	0.606492i	−0.0165896	−	0.0226026i
$721$	6.99484	−	9.62757i	0.260501	−	0.358550i
$722$	2.59752	−	7.99434i	0.0966696	−	0.297518i
$723$	21.6260	+	15.6323i	0.804280	+	0.581373i
$724$	−11.4189	+	8.29629i	−0.424379	+	0.308329i
$725$	4.87443			0.181032
$726$	16.5092	−	4.23401i	0.612715	−	0.157139i
$727$	−29.1404			−1.08076			−0.540380	−	0.841421i	$-0.681719\pi$
$727$	−29.1404			−1.08076			−0.540380	+	0.841421i	$0.681719\pi$
$728$	14.7699	−	10.7310i	0.547410	−	0.397717i
$729$	22.0717	+	15.5511i	0.817472	+	0.575969i
$730$	−3.68224	+	11.3328i	−0.136286	+	0.419445i
$731$	0.926004	−	1.27454i	0.0342495	−	0.0471404i
$732$	−29.0709	+	0.0704008i	−1.07449	+	0.00260209i
$733$	−17.3909	−	5.65064i	−0.642347	−	0.208711i	−0.0303104	−	0.999541i	$-0.509650\pi$
$733$	−17.3909	−	5.65064i	−0.642347	−	0.208711i	−0.612037	+	0.790829i	$0.709650\pi$
$734$	2.49227	+	7.67041i	0.0919913	+	0.283120i
$735$	0.827540	−	2.56805i	0.0305243	−	0.0947239i
$736$		−	32.7047i		−	1.20551i
$737$	−14.1179	−	10.9815i	−0.520039	−	0.404508i
$738$	5.76699	−	18.0459i	0.212286	−	0.664279i
$739$	6.89870	+	9.49525i	0.253773	+	0.349288i	0.916828	−	0.399282i	$-0.130741\pi$
$739$	6.89870	+	9.49525i	0.253773	+	0.349288i	−0.663055	+	0.748570i	$0.730741\pi$
$740$	−11.9767	+	3.89146i	−0.440271	+	0.143053i
$741$	55.9438	−	18.3272i	2.05515	−	0.673265i
$742$	−6.50312	−	4.72480i	−0.238737	−	0.173453i
$743$	37.3018	+	27.1013i	1.36847	+	0.994251i	0.997855	+	0.0654641i	$0.0208528\pi$
$743$	37.3018	+	27.1013i	1.36847	+	0.994251i	0.370614	+	0.928787i	$0.379147\pi$
$744$	12.6026	−	4.12860i	0.462034	−	0.151362i
$745$	9.24237	−	3.00303i	0.338614	−	0.110022i
$746$	−12.7532	−	17.5533i	−0.466928	−	0.642671i
$747$	−6.48527	+	20.2935i	−0.237284	+	0.742501i
$748$	−1.40682	−	0.0461099i	−0.0514385	−	0.00168595i
$749$			5.13944i			0.187791i
$750$	5.60644	−	17.3981i	0.204718	−	0.635289i
$751$	12.0283	+	37.0194i	0.438920	+	1.35086i	0.889016	+	0.457876i	$0.151390\pi$
$751$	12.0283	+	37.0194i	0.438920	+	1.35086i	−0.450097	+	0.892980i	$0.648610\pi$
$752$	0.767268	+	0.249300i	0.0279794	+	0.00909105i
$753$	−38.3434	+	0.0928560i	−1.39731	+	0.00338386i
$754$	−6.35230	+	8.74319i	−0.231337	+	0.318408i
$755$	4.55312	−	14.0131i	0.165705	−	0.509987i
$756$	5.01683	−	3.70093i	0.182461	−	0.134601i
$757$	−8.50034	+	6.17586i	−0.308950	+	0.224465i	−0.731446	−	0.681900i	$-0.761154\pi$
$757$	−8.50034	+	6.17586i	−0.308950	+	0.224465i	0.422496	+	0.906365i	$0.361154\pi$
$758$	−10.3823			−0.377101
$759$	9.42688	+	32.3180i	0.342174	+	1.17307i
$760$	−23.7604			−0.861882
$761$	−19.6150	+	14.2511i	−0.711043	+	0.516603i	−0.883510	−	0.468412i	$-0.844826\pi$
$761$	−19.6150	+	14.2511i	−0.711043	+	0.516603i	0.172467	+	0.985015i	$0.444826\pi$
$762$	−24.6323	−	17.8054i	−0.892334	−	0.645023i
$763$	2.64906	−	8.15297i	0.0959025	−	0.295158i
$764$	−19.1956	+	26.4204i	−0.694471	+	0.955858i
$765$	−0.978121	−	1.33265i	−0.0353640	−	0.0481819i
$766$	−3.12948	−	1.01683i	−0.113073	−	0.0367395i
$767$	−19.6981	−	60.6244i	−0.711256	−	2.18902i
$768$	−26.9712	−	8.69133i	−0.973240	−	0.313621i
$769$		−	32.1151i		−	1.15810i	−0.815292	−	0.579050i	$-0.803424\pi$
$769$		−	32.1151i		−	1.15810i	0.815292	−	0.579050i	$-0.196576\pi$
$770$	3.82599	−	2.59260i	0.137879	−	0.0934310i
$771$	26.5842	−	19.4131i	0.957405	−	0.699144i
$772$	−2.75092	−	3.78632i	−0.0990078	−	0.136273i
$773$	−3.53484	+	1.14854i	−0.127139	+	0.0413101i	−0.371896	−	0.928275i	$-0.621292\pi$
$773$	−3.53484	+	1.14854i	−0.127139	+	0.0413101i	0.244756	+	0.969585i	$0.421292\pi$
$774$	−6.97837	+	9.70339i	−0.250832	+	0.348781i
$775$	5.56906	+	4.04616i	0.200047	+	0.145342i
$776$	26.0831	+	18.9505i	0.936328	+	0.680282i
$777$	3.63329	+	11.0907i	0.130344	+	0.397875i
$778$	−17.5191	+	5.69229i	−0.628089	+	0.204078i
$779$	−22.1116	−	30.4340i	−0.792229	−	1.09041i
$780$	−12.1763	−	16.6742i	−0.435981	−	0.597031i
$781$	34.0167	−	9.83306i	1.21721	−	0.351854i
$782$			1.85439i			0.0663128i
$783$	−5.72711	+	8.00434i	−0.204670	+	0.286052i
$784$	0.0497472	+	0.153106i	0.00177668	+	0.00546807i
$785$	−12.3704	−	4.01938i	−0.441518	−	0.143458i
$786$	0.0259983	+	10.7356i	0.000927329	+	0.382926i
$787$	−7.45655	+	10.2631i	−0.265797	+	0.365839i	−0.920965	−	0.389645i	$-0.872598\pi$
$787$	−7.45655	+	10.2631i	−0.265797	+	0.365839i	0.655168	+	0.755483i	$0.272598\pi$
$788$	1.44887	−	4.45915i	0.0516137	−	0.158851i
$789$	20.4858	−	28.3403i	0.729312	−	1.00894i
$790$	−4.66130	+	3.38663i	−0.165842	+	0.120491i
$791$	7.57518			0.269342
$792$	28.4691	+	0.795088i	1.01161	+	0.0282522i
$793$	89.2266			3.16853
$794$	9.97461	−	7.24698i	0.353986	−	0.257186i
$795$	−14.2031	+	19.6488i	−0.503732	+	0.696870i
$796$	4.12470	−	12.6945i	0.146196	−	0.449946i
$797$	21.4150	−	29.4752i	0.758557	−	1.04406i	−0.238776	−	0.971075i	$-0.576746\pi$
$797$	21.4150	−	29.4752i	0.758557	−	1.04406i	0.997333	−	0.0729895i	$-0.0232540\pi$
$798$	0.0199948	+	8.25654i	0.000707808	+	0.292278i
$799$	1.68592	+	0.547788i	0.0596435	+	0.0193794i
$800$	−4.43798	−	13.6587i	−0.156906	−	0.482908i
$801$	−21.3435	+	7.04938i	−0.754135	+	0.249078i
$802$			29.0957i			1.02741i
$803$	−15.9097	−	23.4785i	−0.561442	−	0.828537i
$804$	−6.60906	−	9.05041i	−0.233083	−	0.319183i
$805$	5.36580	+	7.38539i	0.189119	+	0.260301i
$806$	−14.5151	+	4.71623i	−0.511271	+	0.166122i
$807$	13.8972	+	42.4214i	0.489205	+	1.49330i
$808$	−8.63173	−	6.27132i	−0.303663	−	0.220624i
$809$	18.7112	+	13.5945i	0.657851	+	0.477957i	0.865937	−	0.500154i	$-0.166723\pi$
$809$	18.7112	+	13.5945i	0.657851	+	0.477957i	−0.208085	+	0.978111i	$0.566723\pi$
$810$	7.46956	+	10.0743i	0.262454	+	0.353974i
$811$	11.2947	−	3.66986i	0.396610	−	0.128866i	−0.103920	−	0.994586i	$-0.533139\pi$
$811$	11.2947	−	3.66986i	0.396610	−	0.128866i	0.500530	+	0.865719i	$0.333139\pi$
$812$	1.33577	+	1.83852i	0.0468762	+	0.0645195i
$813$	−17.4261	+	12.7254i	−0.611159	+	0.446298i
$814$	−6.79708	+	18.8000i	−0.238238	+	0.658941i
$815$			12.6248i			0.442227i
$816$	0.0938792	+	0.0302520i	0.00328643	+	0.00105903i
$817$	7.33388	+	22.5714i	0.256580	+	0.789672i
$818$	14.8283	+	4.81800i	0.518459	+	0.168458i
$819$	−15.4255	+	11.3218i	−0.539009	+	0.395616i
$820$	−7.75501	+	10.6739i	−0.270817	+	0.372747i
$821$	3.19173	−	9.82313i	0.111392	−	0.342830i	−0.879785	−	0.475371i	$-0.842314\pi$
$821$	3.19173	−	9.82313i	0.111392	−	0.342830i	0.991177	+	0.132542i	$0.0423138\pi$
$822$	−7.25441	−	5.24384i	−0.253027	−	0.182900i
$823$	−17.6078	+	12.7928i	−0.613768	+	0.445929i	−0.850739	−	0.525588i	$-0.823845\pi$
$823$	−17.6078	+	12.7928i	−0.613768	+	0.445929i	0.236971	+	0.971517i	$0.423845\pi$
$824$	34.0631			1.18665
$825$	8.32254	+	12.2180i	0.289754	+	0.425377i
$826$	8.94030			0.311073
$827$	15.3670	−	11.1648i	0.534364	−	0.388238i	−0.287623	−	0.957744i	$-0.592865\pi$
$827$	15.3670	−	11.1648i	0.534364	−	0.388238i	0.821988	+	0.569505i	$0.192865\pi$
$828$	0.102161	+	21.0929i	0.00355036	+	0.733028i
$829$	−0.727625	+	2.23940i	−0.0252715	+	0.0777776i	−0.962897	−	0.269870i	$-0.913019\pi$
$829$	−0.727625	+	2.23940i	−0.0252715	+	0.0777776i	0.937625	+	0.347647i	$0.113019\pi$
$830$	−5.81665	+	8.00593i	−0.201899	+	0.277890i
$831$	−32.4159	+	0.0785013i	−1.12450	+	0.00272318i
$832$	32.2360	+	10.4741i	1.11758	+	0.363125i
$833$	0.109310	+	0.336420i	0.00378735	+	0.0116563i
$834$	1.09147	−	3.38710i	0.0377947	−	0.117286i
$835$		−	8.72495i		−	0.301939i
$836$	13.0190	−	16.7374i	0.450272	−	0.578874i
$837$	−13.1875	+	4.39105i	−0.455826	+	0.151777i
$838$	−12.3833	−	17.0442i	−0.427774	−	0.588781i
$839$	−21.6088	+	7.02113i	−0.746019	+	0.242396i	−0.657267	−	0.753657i	$-0.728288\pi$
$839$	−21.6088	+	7.02113i	−0.746019	+	0.242396i	−0.0887518	+	0.996054i	$0.528288\pi$
$840$	7.33914	−	2.40430i	0.253224	−	0.0829561i
$841$	20.5589	+	14.9369i	0.708929	+	0.515067i
$842$	−21.0893	−	15.3223i	−0.726787	−	0.528041i
$843$	−30.4706	+	9.98213i	−1.04946	+	0.343803i
$844$	−9.90667	+	3.21887i	−0.341002	+	0.110798i
$845$	25.3452	+	34.8846i	0.871900	+	1.20007i
$846$	−12.8105	−	4.09389i	−0.440434	−	0.140751i
$847$	−0.720297	+	10.9764i	−0.0247497	+	0.377153i
$848$		−	1.44659i		−	0.0496760i
$849$	2.91083	−	9.03298i	0.0998994	−	0.310011i
$850$	0.251638	+	0.774463i	0.00863112	+	0.0265639i
$851$	−37.5543	−	12.2021i	−1.28734	−	0.418283i
$852$	22.1862	−	0.0537280i	0.760085	−	0.00184069i
$853$	31.0784	−	42.7758i	1.06411	−	1.46462i	0.188202	−	0.982130i	$-0.439734\pi$
$853$	31.0784	−	42.7758i	1.06411	−	1.46462i	0.875904	−	0.482485i	$-0.160266\pi$
$854$	−3.86712	+	11.9018i	−0.132330	+	0.407270i
$855$	24.9026	−	0.120614i	0.851652	−	0.00412490i
$856$	−11.9014	+	8.64688i	−0.406782	+	0.295544i
$857$	55.8722			1.90856			0.954280	−	0.298916i	$-0.0966249\pi$
$857$	55.8722			1.90856			0.954280	+	0.298916i	$0.0966249\pi$
$858$	−32.7611	−	0.994359i	−1.11844	−	0.0339469i
$859$	27.2777			0.930702			0.465351	−	0.885126i	$-0.345928\pi$
$859$	27.2777			0.930702			0.465351	+	0.885126i	$0.345928\pi$
$860$	6.73399	−	4.89253i	0.229627	−	0.166834i
$861$	9.90942	+	7.16301i	0.337712	+	0.244115i
$862$	−0.494178	+	1.52092i	−0.0168318	+	0.0518028i
$863$	19.1554	−	26.3651i	0.652056	−	0.897478i	−0.347130	−	0.937817i	$-0.612844\pi$
$863$	19.1554	−	26.3651i	0.652056	−	0.897478i	0.999186	+	0.0403388i	$0.0128437\pi$
$864$	27.6434	+	8.76037i	0.940447	+	0.298034i
$865$	−21.3688	−	6.94315i	−0.726561	−	0.236074i
$866$	9.22562	+	28.3935i	0.313499	+	0.964851i
$867$	−27.8194	−	8.96465i	−0.944796	−	0.304455i
$868$			3.20931i			0.108931i
$869$	0.449227	−	13.7060i	0.0152390	−	0.464944i
$870$	−3.69203	+	2.69610i	−0.125172	+	0.0914064i
$871$	20.2176	+	27.8272i	0.685048	+	0.942887i
$872$	23.3368	−	7.58259i	0.790284	−	0.256779i
$873$	−27.4331	−	19.7290i	−0.928470	−	0.667727i
$874$	−22.6004	−	16.4201i	−0.764469	−	0.555420i
$875$	9.54435	+	6.93438i	0.322658	+	0.234425i
$876$	−5.53217	−	16.8870i	−0.186915	−	0.570559i
$877$	−46.1160	+	14.9840i	−1.55723	+	0.505974i	−0.956065	−	0.293153i	$-0.905295\pi$
$877$	−46.1160	+	14.9840i	−1.55723	+	0.505974i	−0.601162	+	0.799127i	$0.705295\pi$
$878$	−4.89457	−	6.73680i	−0.165184	−	0.227356i
$879$	16.2450	+	22.2458i	0.547930	+	0.750333i
$880$	0.782171	+	0.282791i	0.0263670	+	0.00953288i
$881$			30.2066i			1.01769i	0.860859	+	0.508843i	$0.169927\pi$
$881$			30.2066i			1.01769i	−0.860859	+	0.508843i	$0.830073\pi$
$882$	−0.841648	−	2.54826i	−0.0283398	−	0.0858045i
$883$	3.12724	+	9.62467i	0.105240	+	0.323896i	0.989787	−	0.142556i	$-0.0455321\pi$
$883$	3.12724	+	9.62467i	0.105240	+	0.323896i	−0.884547	+	0.466452i	$0.845532\pi$
$884$	2.57441	+	0.836476i	0.0865868	+	0.0281337i
$885$	−0.0653011	−	26.9651i	−0.00219507	−	0.906421i
$886$	−8.16071	+	11.2323i	−0.274165	+	0.377355i
$887$	−15.2524	+	46.9420i	−0.512125	+	1.57616i	0.276329	+	0.961063i	$0.410882\pi$
$887$	−15.2524	+	46.9420i	−0.512125	+	1.57616i	−0.788453	+	0.615094i	$0.789118\pi$
$888$	−19.5698	+	27.0732i	−0.656720	+	0.908516i
$889$	15.8700	−	11.5302i	0.532262	−	0.386711i
$890$	−10.4407			−0.349972
$891$	−29.8417	−	0.688793i	−0.999734	−	0.0230754i
$892$	−10.0126			−0.335247
$893$	−21.6046	+	15.6966i	−0.722969	+	0.525268i
$894$	5.66258	−	7.83370i	0.189385	−	0.261998i
$895$	−8.11089	+	24.9628i	−0.271117	+	0.834413i
$896$	3.76629	−	5.18386i	0.125823	−	0.173181i
$897$	−0.156781	−	64.7402i	−0.00523476	−	2.16161i
$898$	25.3814	+	8.24691i	0.846988	+	0.275203i
$899$	−1.56569	−	4.81869i	−0.0522186	−	0.160712i
$900$	2.90494	+	8.79532i	0.0968314	+	0.293177i
$901$		−	3.17859i		−	0.105894i
$902$	5.81620	+	20.1207i	0.193658	+	0.669947i
$903$	−4.54927	−	6.22975i	−0.151390	−	0.207313i
$904$	12.7449	+	17.5419i	0.423889	+	0.583434i
$905$	17.4288	−	5.66296i	0.579353	−	0.188243i
$906$	−4.56250	−	13.9271i	−0.151579	−	0.462696i
$907$	44.4981	+	32.3298i	1.47754	+	1.07349i	0.978340	+	0.207004i	$0.0663713\pi$
$907$	44.4981	+	32.3298i	1.47754	+	1.07349i	0.499196	+	0.866489i	$0.333629\pi$
$908$	−10.3528	−	7.52179i	−0.343571	−	0.249619i
$909$	9.07850	+	6.52897i	0.301115	+	0.216552i
$910$	−8.45286	+	2.74650i	−0.280209	+	0.0910456i
$911$	0.541598	+	0.745445i	0.0179439	+	0.0246977i	0.817895	−	0.575368i	$-0.195141\pi$
$911$	0.541598	+	0.745445i	0.0179439	+	0.0246977i	−0.799951	+	0.600066i	$0.795141\pi$
$912$	−1.19997	+	0.876279i	−0.0397351	+	0.0290165i
$913$	−6.54061	−	22.6267i	−0.216463	−	0.748836i
$914$			5.82152i			0.192559i
$915$	35.9255	+	11.5768i	1.18766	+	0.382717i
$916$	0.729618	+	2.24553i	0.0241073	+	0.0741945i
$917$	−6.58973	−	2.14113i	−0.217612	−	0.0707064i
$918$	−1.56741	−	0.496722i	−0.0517322	−	0.0163943i
$919$	5.86938	−	8.07850i	0.193613	−	0.266485i	−0.701163	−	0.713001i	$-0.747335\pi$
$919$	5.86938	−	8.07850i	0.193613	−	0.266485i	0.894776	+	0.446516i	$0.147335\pi$
$920$	−8.07464	+	24.8512i	−0.266213	+	0.819319i
$921$	7.41814	+	5.36219i	0.244436	+	0.176690i
$922$	−3.33206	+	2.42088i	−0.109735	+	0.0797274i
$923$	−68.0954			−2.24139
$924$	−2.32768	+	6.48723i	−0.0765752	+	0.213414i
$925$	−17.3399			−0.570132
$926$	−5.13868	+	3.73347i	−0.168867	+	0.122689i
$927$	−35.7006	+	0.172913i	−1.17256	+	0.00567920i
$928$	−3.26651	+	10.0533i	−0.107229	+	0.330015i
$929$	−33.4675	+	46.0640i	−1.09803	+	1.51131i	−0.260065	+	0.965591i	$0.583744\pi$
$929$	−33.4675	+	46.0640i	−1.09803	+	1.51131i	−0.837967	+	0.545720i	$0.816256\pi$
$930$	−6.45614	+	0.0156348i	−0.211705	+	0.000512684i
$931$	−5.06803	−	1.64670i	−0.166098	−	0.0539685i
$932$	−7.76526	−	23.8990i	−0.254359	−	0.782838i
$933$	6.86341	−	21.2988i	0.224698	−	0.697290i
$934$			4.96364i			0.162415i
$935$	1.71867	+	0.621377i	0.0562064	+	0.0203212i
$936$	−52.1706	−	16.6723i	−1.70525	−	0.544953i
$937$	−25.0685	−	34.5038i	−0.818952	−	1.12719i	−0.989880	−	0.141908i	$-0.954676\pi$
$937$	−25.0685	−	34.5038i	−0.818952	−	1.12719i	0.170928	−	0.985284i	$-0.445324\pi$
$938$	−4.58805	+	1.49075i	−0.149805	+	0.0486746i
$939$	7.44540	−	2.43911i	0.242971	−	0.0795972i
$940$	7.57720	+	5.50516i	0.247141	+	0.179558i
$941$	−29.1326	−	21.1661i	−0.949696	−	0.689995i	0.00103859	−	0.999999i	$-0.499669\pi$
$941$	−29.1326	−	21.1661i	−0.949696	−	0.689995i	−0.950735	+	0.310005i	$0.899669\pi$
$942$	−12.2945	+	4.02766i	−0.400576	+	0.131228i
$943$	−39.3453	+	12.7841i	−1.28126	+	0.416307i
$944$	0.945695	+	1.30164i	0.0307797	+	0.0423647i
$945$	−7.67974	+	2.55713i	−0.249822	+	0.0831834i
$946$	0.432855	−	13.2065i	0.0140733	−	0.429380i
$947$		−	9.38290i		−	0.304903i	−0.988311	−	0.152452i	$-0.951283\pi$
$947$		−	9.38290i		−	0.304903i	0.988311	−	0.152452i	$-0.0487168\pi$
$948$	2.63536	−	8.17815i	0.0855927	−	0.265614i
$949$	16.8541	+	51.8716i	0.547108	+	1.68382i
$950$	−11.6670	−	3.79083i	−0.378526	−	0.122991i
$951$	40.1240	−	0.0971679i	1.30111	−	0.00315089i
$952$	−0.595141	+	0.819141i	−0.0192886	+	0.0265485i
$953$	−3.36999	+	10.3718i	−0.109165	+	0.335975i	−0.990685	−	0.136171i	$-0.956520\pi$
$953$	−3.36999	+	10.3718i	−0.109165	+	0.335975i	0.881521	+	0.472146i	$0.156520\pi$
$954$	0.116797	+	24.1146i	0.00378144	+	0.780740i
$955$	34.3033	−	24.9228i	1.11003	−	0.806483i
$956$	−8.62888			−0.279078
$957$	0.330106	−	10.8760i	0.0106708	−	0.351570i
$958$	13.8524			0.447551
$959$	4.67383	−	3.39574i	0.150926	−	0.109654i
$960$	11.6203	+	8.39970i	0.375043	+	0.271099i
$961$	−7.36844	+	22.6777i	−0.237692	+	0.731540i
$962$	22.5971	−	31.1023i	0.728561	−	1.00278i
$963$	12.4296	−	9.12296i	0.400539	−	0.293983i
$964$	−17.5793	−	5.71187i	−0.566193	−	0.183967i
$965$	1.87775	+	5.77912i	0.0604469	+	0.186036i
$966$	8.64236	+	2.78495i	0.278063	+	0.0896044i
$967$		−	30.5515i		−	0.982470i	−0.871027	−	0.491235i	$-0.836546\pi$
$967$		−	30.5515i		−	0.982470i	0.871027	−	0.491235i	$-0.163454\pi$
$968$	−26.6299	+	16.7993i	−0.855919	+	0.539950i
$969$	−2.63670	+	1.92545i	−0.0847031	+	0.0618544i
$970$	−9.22564	−	12.6980i	−0.296217	−	0.407708i
$971$	−2.15779	+	0.701110i	−0.0692469	+	0.0224997i	−0.343436	−	0.939176i	$-0.611591\pi$
$971$	−2.15779	+	0.701110i	−0.0692469	+	0.0224997i	0.274189	+	0.961676i	$0.411591\pi$
$972$	−17.8560	−	5.56364i	−0.572730	−	0.178454i
$973$	1.85812	+	1.35000i	0.0595684	+	0.0432790i
$974$	−1.66622	−	1.21058i	−0.0533891	−	0.0387895i
$975$	−8.85064	−	27.0167i	−0.283447	−	0.865226i
$976$	−2.14186	+	0.695933i	−0.0685593	+	0.0222763i
$977$	−20.4196	−	28.1052i	−0.653281	−	0.899164i	0.345955	−	0.938251i	$-0.387555\pi$
$977$	−20.4196	−	28.1052i	−0.653281	−	0.899164i	−0.999236	+	0.0390871i	$0.987555\pi$
$978$	7.40554	+	10.1411i	0.236803	+	0.324277i
$979$	15.2571	−	19.6146i	0.487618	−	0.626887i
$980$			1.86894i			0.0597012i
$981$	−24.4201	+	8.06556i	−0.779675	+	0.257513i
$982$	1.48789	+	4.57924i	0.0474804	+	0.146130i
$983$	−1.89291	−	0.615045i	−0.0603745	−	0.0196169i	0.278674	−	0.960386i	$-0.410105\pi$
$983$	−1.89291	−	0.615045i	−0.0603745	−	0.0196169i	−0.339049	+	0.940769i	$0.610105\pi$
$984$	0.0847561	+	34.9987i	0.00270193	+	1.11572i
$985$	−3.57817	+	4.92492i	−0.114010	+	0.156921i
$986$	0.185215	−	0.570032i	0.00589844	−	0.0181535i
$987$	5.08490	−	7.03453i	0.161854	−	0.223912i
$988$	−32.9903	+	23.9689i	−1.04956	+	0.762551i
$989$	26.0998			0.829926
$990$	−13.0616	−	4.65097i	−0.415126	−	0.147818i
$991$	−48.1017			−1.52800			−0.764001	−	0.645215i	$-0.776768\pi$
$991$	−48.1017			−1.52800			−0.764001	+	0.645215i	$0.776768\pi$
$992$	−12.0770	+	8.77447i	−0.383446	+	0.278590i
$993$	20.8503	−	28.8446i	0.661665	−	0.915357i
$994$	2.95128	−	9.08311i	0.0936090	−	0.288099i
$995$	−10.1865	+	14.0205i	−0.322934	+	0.444480i
$996$	−0.0357380	−	14.7575i	−0.00113240	−	0.467608i
$997$	−16.7610	−	5.44598i	−0.530826	−	0.172476i	0.0313269	−	0.999509i	$-0.490027\pi$
$997$	−16.7610	−	5.44598i	−0.530826	−	0.172476i	−0.562153	+	0.827033i	$0.690027\pi$
$998$	6.65547	+	20.4834i	0.210675	+	0.648392i
$999$	20.3731	−	28.4740i	0.644577	−	0.900876i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.s.a.8.17	yes	96
3.2	odd	2	inner	231.2.s.a.8.8	✓	96
11.7	odd	10	inner	231.2.s.a.29.8	yes	96
33.29	even	10	inner	231.2.s.a.29.17	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.s.a.8.8	✓	96	3.2	odd	2	inner
231.2.s.a.8.17	yes	96	1.1	even	1	trivial
231.2.s.a.29.8	yes	96	11.7	odd	10	inner
231.2.s.a.29.17	yes	96	33.29	even	10	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:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.s (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.723708 - 0.525805i) q^{2} +(1.01468 - 1.40372i) q^{3} +(-0.370751 + 1.14105i) q^{4} +(0.915619 - 1.26024i) q^{5} +(-0.00375218 - 1.54941i) q^{6} +(0.951057 + 0.309017i) q^{7} +(0.884520 + 2.72227i) q^{8} +(-0.940859 - 2.84865i) q^{9} +O(q^{10})\)	\(q+(0.723708 - 0.525805i) q^{2} +(1.01468 - 1.40372i) q^{3} +(-0.370751 + 1.14105i) q^{4} +(0.915619 - 1.26024i) q^{5} +(-0.00375218 - 1.54941i) q^{6} +(0.951057 + 0.309017i) q^{7} +(0.884520 + 2.72227i) q^{8} +(-0.940859 - 2.84865i) q^{9} -1.39348i q^{10} +(2.61790 + 2.03631i) q^{11} +(1.22553 + 1.67823i) q^{12} +(-3.74899 - 5.16004i) q^{13} +(0.850770 - 0.276432i) q^{14} +(-0.839968 - 2.56401i) q^{15} +(0.130240 + 0.0946248i) q^{16} +(0.286176 + 0.207919i) q^{17} +(-2.17874 - 1.56688i) q^{18} +(-5.06803 + 1.64670i) q^{19} +(1.09854 + 1.51201i) q^{20} +(1.39879 - 1.02146i) q^{21} +(2.96530 + 0.0971906i) q^{22} +5.86029i q^{23} +(4.71881 + 1.52061i) q^{24} +(0.795235 + 2.44748i) q^{25} +(-5.42634 - 1.76313i) q^{26} +(-4.95337 - 1.56975i) q^{27} +(-0.705211 + 0.970639i) q^{28} +(0.585320 - 1.80143i) q^{29} +(-1.95606 - 1.41394i) q^{30} +(2.16406 - 1.57228i) q^{31} -5.58072 q^{32} +(5.51474 - 1.60860i) q^{33} +0.316433 q^{34} +(1.26024 - 0.915619i) q^{35} +(3.59929 - 0.0174328i) q^{36} +(-2.08217 + 6.40825i) q^{37} +(-2.80193 + 3.85653i) q^{38} +(-11.0473 + 0.0267531i) q^{39} +(4.24061 + 1.37786i) q^{40} +(2.18147 + 6.71389i) q^{41} +(0.475224 - 1.47473i) q^{42} -4.45367i q^{43} +(-3.29414 + 2.23221i) q^{44} +(-4.45145 - 1.42257i) q^{45} +(3.08137 + 4.24114i) q^{46} +(4.76608 - 1.54859i) q^{47} +(0.264978 - 0.0868066i) q^{48} +(0.809017 + 0.587785i) q^{49} +(1.86241 + 1.35312i) q^{50} +(0.582237 - 0.190740i) q^{51} +(7.27783 - 2.36471i) q^{52} +(-5.28174 - 7.26970i) q^{53} +(-4.41018 + 1.46846i) q^{54} +(4.96325 - 1.43470i) q^{55} +2.86237i q^{56} +(-2.83091 + 8.78497i) q^{57} +(-0.523600 - 1.61147i) q^{58} +(9.50501 + 3.08836i) q^{59} +(3.23710 - 0.00783925i) q^{60} +(-8.22276 + 11.3177i) q^{61} +(0.739434 - 2.27574i) q^{62} +(-0.0145301 - 2.99996i) q^{63} +(-4.29930 + 3.12362i) q^{64} -9.93554 q^{65} +(3.14525 - 4.06384i) q^{66} -5.39282 q^{67} +(-0.343347 + 0.249456i) q^{68} +(8.22621 + 5.94631i) q^{69} +(0.430610 - 1.32528i) q^{70} +(6.27540 - 8.63734i) q^{71} +(6.92258 - 5.08096i) q^{72} +(-8.13270 - 2.64247i) q^{73} +(1.86261 + 5.73252i) q^{74} +(4.24248 + 1.36712i) q^{75} -6.39342i q^{76} +(1.86052 + 2.74563i) q^{77} +(-7.98093 + 5.82806i) q^{78} +(-2.43034 - 3.34507i) q^{79} +(0.238500 - 0.0774934i) q^{80} +(-7.22957 + 5.36035i) q^{81} +(5.10894 + 3.71186i) q^{82} +(-5.74526 - 4.17418i) q^{83} +(0.646944 + 1.97480i) q^{84} +(0.524057 - 0.170276i) q^{85} +(-2.34176 - 3.22316i) q^{86} +(-1.93479 - 2.64950i) q^{87} +(-3.22781 + 8.92781i) q^{88} -7.49250i q^{89} +(-3.96954 + 1.31107i) q^{90} +(-1.97096 - 6.06599i) q^{91} +(-6.68692 - 2.17271i) q^{92} +(-0.0112199 - 4.63309i) q^{93} +(2.63499 - 3.62675i) q^{94} +(-2.56514 + 7.89470i) q^{95} +(-5.66264 + 7.83377i) q^{96} +(9.11241 - 6.62056i) q^{97} +0.894552 q^{98} +(3.33766 - 9.37337i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 6 q^{3} - 24 q^{4} - 10 q^{6} - 20 q^{9}+O(q^{10}) \) 96 * q + 6 * q^3 - 24 * q^4 - 10 * q^6 - 20 * q^9	\( 96 q + 6 q^{3} - 24 q^{4} - 10 q^{6} - 20 q^{9} - 20 q^{12} - 32 q^{16} - 10 q^{18} - 60 q^{19} + 30 q^{24} + 12 q^{25} - 40 q^{28} + 60 q^{30} + 40 q^{31} - 44 q^{33} + 8 q^{34} + 2 q^{36} + 16 q^{37} - 10 q^{39} - 96 q^{45} - 40 q^{46} + 48 q^{48} + 24 q^{49} - 30 q^{51} - 40 q^{52} + 28 q^{55} - 30 q^{57} + 36 q^{58} - 32 q^{60} + 40 q^{61} - 28 q^{64} + 118 q^{66} - 56 q^{67} + 26 q^{69} + 20 q^{70} + 150 q^{72} + 40 q^{73} + 2 q^{75} - 20 q^{78} - 40 q^{79} + 8 q^{81} - 16 q^{82} + 40 q^{84} - 60 q^{85} - 156 q^{88} + 100 q^{90} + 36 q^{91} - 36 q^{93} + 160 q^{96} - 88 q^{97} - 94 q^{99}+O(q^{100}) \) 96 * q + 6 * q^3 - 24 * q^4 - 10 * q^6 - 20 * q^9 - 20 * q^12 - 32 * q^16 - 10 * q^18 - 60 * q^19 + 30 * q^24 + 12 * q^25 - 40 * q^28 + 60 * q^30 + 40 * q^31 - 44 * q^33 + 8 * q^34 + 2 * q^36 + 16 * q^37 - 10 * q^39 - 96 * q^45 - 40 * q^46 + 48 * q^48 + 24 * q^49 - 30 * q^51 - 40 * q^52 + 28 * q^55 - 30 * q^57 + 36 * q^58 - 32 * q^60 + 40 * q^61 - 28 * q^64 + 118 * q^66 - 56 * q^67 + 26 * q^69 + 20 * q^70 + 150 * q^72 + 40 * q^73 + 2 * q^75 - 20 * q^78 - 40 * q^79 + 8 * q^81 - 16 * q^82 + 40 * q^84 - 60 * q^85 - 156 * q^88 + 100 * q^90 + 36 * q^91 - 36 * q^93 + 160 * q^96 - 88 * q^97 - 94 * q^99

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