LMFDB - Embedded newform 726.2.h.f.161.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [726,2,Mod(161,726)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(726, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 7])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("726.161"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 726 = 2 \cdot 3 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	726.h (of order $10$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,2,-3,-2,5,-2,5,2,7] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.79713918674$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	8.0.185640625.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + x^{6} + x^{5} + 4x^{4} + 3x^{3} + 9x^{2} - 81x + 81 $ x^8 - 3x^7 + x^6 + x^5 + 4x^4 + 3x^3 + 9x^2 - 81*x + 81
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 66)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			161.1
Root			$1.55470 - 0.763481i$ of defining polynomial
Character	$\chi$	$=$	726.161
Dual form			726.2.h.f.239.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.809017 + 0.587785i) q^{2} +(-1.55470 - 0.763481i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-0.554701 - 0.763481i) q^{5} +(-0.809017 - 1.53150i) q^{6} +(-1.45223 + 0.471857i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(1.83419 + 2.37397i) q^{9} -0.943715i q^{10} +(0.245684 - 1.71454i) q^{12} +(2.49137 - 3.42908i) q^{13} +(-1.45223 - 0.471857i) q^{14} +(0.279492 + 1.61049i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(2.37235 - 1.72361i) q^{17} +(0.0885088 + 2.99869i) q^{18} +(6.74300 + 2.19093i) q^{19} +(0.554701 - 0.763481i) q^{20} +(2.61803 + 0.375151i) q^{21} +1.18465i q^{23} +(1.20654 - 1.24268i) q^{24} +(1.26988 - 3.90827i) q^{25} +(4.03112 - 1.30979i) q^{26} +(-1.03914 - 5.09119i) q^{27} +(-0.897526 - 1.23534i) q^{28} +(-1.97581 - 6.08092i) q^{29} +(-0.720508 + 1.46719i) q^{30} +(7.03805 + 5.11344i) q^{31} -1.00000 q^{32} +2.93239 q^{34} +(1.16581 + 0.847008i) q^{35} +(-1.69098 + 2.47802i) q^{36} +(0.873335 + 2.68785i) q^{37} +(4.16740 + 5.73594i) q^{38} +(-6.49137 + 3.42908i) q^{39} +(0.897526 - 0.291624i) q^{40} +(2.26124 - 6.95939i) q^{41} +(1.89753 + 1.84235i) q^{42} -5.34587i q^{43} +(0.795052 - 2.71722i) q^{45} +(-0.696317 + 0.958399i) q^{46} +(9.03112 + 2.93439i) q^{47} +(1.70654 - 0.296161i) q^{48} +(-3.77680 + 2.74401i) q^{49} +(3.32458 - 2.41545i) q^{50} +(-5.00424 + 0.868459i) q^{51} +(4.03112 + 1.30979i) q^{52} +(2.86103 - 3.93787i) q^{53} +(2.15184 - 4.72965i) q^{54} -1.52696i q^{56} +(-8.81061 - 8.55440i) q^{57} +(1.97581 - 6.08092i) q^{58} +(-4.43667 + 1.44156i) q^{59} +(-1.44530 + 0.763481i) q^{60} +(-0.423754 - 0.583248i) q^{61} +(2.68830 + 8.27372i) q^{62} +(-3.78384 - 2.58207i) q^{63} +(-0.809017 - 0.587785i) q^{64} -4.00000 q^{65} +3.89379 q^{67} +(2.37235 + 1.72361i) q^{68} +(0.904455 - 1.84177i) q^{69} +(0.445299 + 1.37049i) q^{70} +(5.85410 + 8.05748i) q^{71} +(-2.82458 + 1.01082i) q^{72} +(-1.66740 + 0.541771i) q^{73} +(-0.873335 + 2.68785i) q^{74} +(-4.95817 + 5.10667i) q^{75} +7.09001i q^{76} +(-7.26719 - 1.04135i) q^{78} +(-0.967787 + 1.33204i) q^{79} +(0.897526 + 0.291624i) q^{80} +(-2.27147 + 8.70864i) q^{81} +(5.92001 - 4.30114i) q^{82} +(-4.98335 + 3.62061i) q^{83} +(0.452227 + 2.60583i) q^{84} +(-2.63189 - 0.855153i) q^{85} +(3.14222 - 4.32490i) q^{86} +(-1.57087 + 10.9625i) q^{87} +17.3406i q^{89} +(2.24035 - 1.73095i) q^{90} +(-2.00000 + 6.15537i) q^{91} +(-1.12667 + 0.366076i) q^{92} +(-7.03805 - 13.3233i) q^{93} +(5.58154 + 7.68233i) q^{94} +(-2.06761 - 6.36346i) q^{95} +(1.55470 + 0.763481i) q^{96} +(-9.26977 - 6.73488i) q^{97} -4.66839 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} - 3 q^{3} - 2 q^{4} + 5 q^{5} - 2 q^{6} + 5 q^{7} + 2 q^{8} + 7 q^{9} - 3 q^{12} + 10 q^{13} + 5 q^{14} + 4 q^{15} - 2 q^{16} + 15 q^{17} - 2 q^{18} + 10 q^{19} - 5 q^{20} + 12 q^{21} - 2 q^{24}+ \cdots - 22 q^{98}+O(q^{100}) $ 8 * q + 2 * q^2 - 3 * q^3 - 2 * q^4 + 5 * q^5 - 2 * q^6 + 5 * q^7 + 2 * q^8 + 7 * q^9 - 3 * q^12 + 10 * q^13 + 5 * q^14 + 4 * q^15 - 2 * q^16 + 15 * q^17 - 2 * q^18 + 10 * q^19 - 5 * q^20 + 12 * q^21 - 2 * q^24 - q^25 - 15 * q^27 - 22 * q^29 - 4 * q^30 - 2 * q^31 - 8 * q^32 + 10 * q^34 + 17 * q^35 - 18 * q^36 + 6 * q^37 + 15 * q^38 - 42 * q^39 - 3 * q^41 + 8 * q^42 - 8 * q^45 - 10 * q^46 + 40 * q^47 + 2 * q^48 + 7 * q^49 + 6 * q^50 + 25 * q^51 - 30 * q^53 + 15 * q^54 - 40 * q^57 + 22 * q^58 - 35 * q^59 - 21 * q^60 + 20 * q^61 - 13 * q^62 - 29 * q^63 - 2 * q^64 - 32 * q^65 - 2 * q^67 + 15 * q^68 - 26 * q^69 + 13 * q^70 + 20 * q^71 - 2 * q^72 + 5 * q^73 - 6 * q^74 + 6 * q^75 - 8 * q^78 + 25 * q^79 + 19 * q^81 - 2 * q^82 + 9 * q^83 - 13 * q^84 + 40 * q^85 + 10 * q^86 + 42 * q^87 + 13 * q^90 - 16 * q^91 - 10 * q^92 + 2 * q^93 - 10 * q^94 - 30 * q^95 + 3 * q^96 - q^97 - 22 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/726\mathbb{Z}\right)^\times$.

$n$	$485$	$607$
$\chi(n)$	$-1$	$e\left(\frac{7}{10}\right)$

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 $

$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$3$	−1.55470	−	0.763481i	−0.897607	−	0.440796i
$3$	−1.55470	−	0.763481i	−0.897607	−	0.440796i
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	−0.554701	−	0.763481i	−0.248070	−	0.341439i	0.666764	−	0.745269i	$-0.267679\pi$
$5$	−0.554701	−	0.763481i	−0.248070	−	0.341439i	−0.914834	+	0.403830i	$0.867679\pi$
$6$	−0.809017	−	1.53150i	−0.330280	−	0.625232i
$7$	−1.45223	+	0.471857i	−0.548890	+	0.178345i	−0.570316	−	0.821425i	$-0.693179\pi$
$7$	−1.45223	+	0.471857i	−0.548890	+	0.178345i	0.0214260	+	0.999770i	$0.493179\pi$
$8$	−0.309017	+	0.951057i	−0.109254	+	0.336249i
$9$	1.83419	+	2.37397i	0.611398	+	0.791323i
$10$		−	0.943715i		−	0.298429i
$11$		0			0
$11$		0			0
$12$	0.245684	−	1.71454i	0.0709230	−	0.494944i
$13$	2.49137	−	3.42908i	0.690981	−	0.951054i	−0.309019	−	0.951056i	$-0.600001\pi$
$13$	2.49137	−	3.42908i	0.690981	−	0.951054i	1.00000		1.66535e-6i	$5.30097e-7\pi$
$14$	−1.45223	−	0.471857i	−0.388124	−	0.126109i
$15$	0.279492	+	1.61049i	0.0721645	+	0.415827i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	2.37235	−	1.72361i	0.575379	−	0.418038i	−0.261676	−	0.965156i	$-0.584275\pi$
$17$	2.37235	−	1.72361i	0.575379	−	0.418038i	0.837055	+	0.547118i	$0.184275\pi$
$18$	0.0885088	+	2.99869i	0.0208617	+	0.706799i
$19$	6.74300	+	2.19093i	1.54695	+	0.502634i	0.953283	−	0.302077i	$-0.0976800\pi$
$19$	6.74300	+	2.19093i	1.54695	+	0.502634i	0.593666	+	0.804712i	$0.297680\pi$
$20$	0.554701	−	0.763481i	0.124035	−	0.170720i
$21$	2.61803	+	0.375151i	0.571302	+	0.0818646i
$22$		0			0
$23$			1.18465i			0.247016i	0.992344	+	0.123508i	$0.0394144\pi$
$23$			1.18465i			0.247016i	−0.992344	+	0.123508i	$0.960586\pi$
$24$	1.20654	−	1.24268i	0.246285	−	0.253661i
$25$	1.26988	−	3.90827i	0.253975	−	0.781655i
$26$	4.03112	−	1.30979i	0.790568	−	0.256871i
$27$	−1.03914	−	5.09119i	−0.199983	−	0.979799i
$28$	−0.897526	−	1.23534i	−0.169616	−	0.233457i
$29$	−1.97581	−	6.08092i	−0.366899	−	1.12920i	−0.948784	−	0.315927i	$-0.897685\pi$
$29$	−1.97581	−	6.08092i	−0.366899	−	1.12920i	0.581885	−	0.813271i	$-0.302315\pi$
$30$	−0.720508	+	1.46719i	−0.131546	+	0.267872i
$31$	7.03805	+	5.11344i	1.26407	+	0.918401i	0.998950	−	0.0458140i	$-0.0145882\pi$
$31$	7.03805	+	5.11344i	1.26407	+	0.918401i	0.265121	+	0.964215i	$0.414588\pi$
$32$	−1.00000			−0.176777
$33$		0			0
$34$	2.93239			0.502900
$35$	1.16581	+	0.847008i	0.197057	+	0.143171i
$36$	−1.69098	+	2.47802i	−0.281831	+	0.413003i
$37$	0.873335	+	2.68785i	0.143575	+	0.441880i	0.996825	−	0.0796231i	$-0.0253717\pi$
$37$	0.873335	+	2.68785i	0.143575	+	0.441880i	−0.853250	+	0.521503i	$0.825372\pi$
$38$	4.16740	+	5.73594i	0.676042	+	0.930492i
$39$	−6.49137	+	3.42908i	−1.03945	+	0.549091i
$40$	0.897526	−	0.291624i	0.141911	−	0.0461098i
$41$	2.26124	−	6.95939i	0.353147	−	1.08687i	−0.603929	−	0.797038i	$-0.706399\pi$
$41$	2.26124	−	6.95939i	0.353147	−	1.08687i	0.957076	−	0.289837i	$-0.0936010\pi$
$42$	1.89753	+	1.84235i	0.292795	+	0.284280i
$43$		−	5.34587i		−	0.815238i	−0.913152	−	0.407619i	$-0.866359\pi$
$43$		−	5.34587i		−	0.815238i	0.913152	−	0.407619i	$-0.133641\pi$
$44$		0			0
$45$	0.795052	−	2.71722i	0.118519	−	0.405059i
$46$	−0.696317	+	0.958399i	−0.102666	+	0.141308i
$47$	9.03112	+	2.93439i	1.31732	+	0.428025i	0.881575	−	0.472044i	$-0.156484\pi$
$47$	9.03112	+	2.93439i	1.31732	+	0.428025i	0.435749	+	0.900068i	$0.356484\pi$
$48$	1.70654	−	0.296161i	0.246318	−	0.0427472i
$49$	−3.77680	+	2.74401i	−0.539543	+	0.392001i
$50$	3.32458	−	2.41545i	0.470166	−	0.341596i
$51$	−5.00424	+	0.868459i	−0.700734	+	0.121609i
$52$	4.03112	+	1.30979i	0.559016	+	0.181635i
$53$	2.86103	−	3.93787i	0.392993	−	0.540908i	−0.565975	−	0.824422i	$-0.691500\pi$
$53$	2.86103	−	3.93787i	0.392993	−	0.540908i	0.958968	+	0.283514i	$0.0915003\pi$
$54$	2.15184	−	4.72965i	0.292829	−	0.643624i
$55$		0			0
$56$		−	1.52696i		−	0.204049i
$57$	−8.81061	−	8.55440i	−1.16699	−	1.13306i
$58$	1.97581	−	6.08092i	0.259436	−	0.798463i
$59$	−4.43667	+	1.44156i	−0.577605	+	0.187675i	−0.583227	−	0.812309i	$-0.698210\pi$
$59$	−4.43667	+	1.44156i	−0.577605	+	0.187675i	0.00562242	+	0.999984i	$0.498210\pi$
$60$	−1.44530	+	0.763481i	−0.186587	+	0.0985650i
$61$	−0.423754	−	0.583248i	−0.0542562	−	0.0746772i	0.781027	−	0.624498i	$-0.214696\pi$
$61$	−0.423754	−	0.583248i	−0.0542562	−	0.0746772i	−0.835283	+	0.549820i	$0.814696\pi$
$62$	2.68830	+	8.27372i	0.341414	+	1.05076i
$63$	−3.78384	−	2.58207i	−0.476719	−	0.325310i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	−4.00000			−0.496139
$66$		0			0
$67$	3.89379			0.475702			0.237851	−	0.971302i	$-0.423557\pi$
$67$	3.89379			0.475702			0.237851	+	0.971302i	$0.423557\pi$
$68$	2.37235	+	1.72361i	0.287690	+	0.209019i
$69$	0.904455	−	1.84177i	0.108884	−	0.221723i
$70$	0.445299	+	1.37049i	0.0532234	+	0.163805i
$71$	5.85410	+	8.05748i	0.694754	+	0.956247i	0.999992	+	0.00397087i	$0.00126397\pi$
$71$	5.85410	+	8.05748i	0.694754	+	0.956247i	−0.305238	+	0.952276i	$0.598736\pi$
$72$	−2.82458	+	1.01082i	−0.332880	+	0.119127i
$73$	−1.66740	+	0.541771i	−0.195155	+	0.0634096i	−0.404964	−	0.914333i	$-0.632716\pi$
$73$	−1.66740	+	0.541771i	−0.195155	+	0.0634096i	0.209809	+	0.977742i	$0.432716\pi$
$74$	−0.873335	+	2.68785i	−0.101523	+	0.312456i
$75$	−4.95817	+	5.10667i	−0.572520	+	0.589668i
$76$			7.09001i			0.813280i
$77$		0			0
$78$	−7.26719	−	1.04135i	−0.822847	−	0.117910i
$79$	−0.967787	+	1.33204i	−0.108885	+	0.149867i	−0.859982	−	0.510325i	$-0.829525\pi$
$79$	−0.967787	+	1.33204i	−0.108885	+	0.149867i	0.751097	+	0.660192i	$0.229525\pi$
$80$	0.897526	+	0.291624i	0.100346	+	0.0326045i
$81$	−2.27147	+	8.70864i	−0.252386	+	0.967627i
$82$	5.92001	−	4.30114i	0.653756	−	0.474982i
$83$	−4.98335	+	3.62061i	−0.546993	+	0.397414i	−0.826676	−	0.562679i	$-0.809771\pi$
$83$	−4.98335	+	3.62061i	−0.546993	+	0.397414i	0.279682	+	0.960093i	$0.409771\pi$
$84$	0.452227	+	2.60583i	0.0493420	+	0.284319i
$85$	−2.63189	−	0.855153i	−0.285469	−	0.0927544i
$86$	3.14222	−	4.32490i	0.338835	−	0.466366i
$87$	−1.57087	+	10.9625i	−0.168415	+	1.17530i
$88$		0			0
$89$			17.3406i			1.83811i	0.394135	+	0.919053i	$0.371044\pi$
$89$			17.3406i			1.83811i	−0.394135	+	0.919053i	$0.628956\pi$
$90$	2.24035	−	1.73095i	0.236154	−	0.182459i
$91$	−2.00000	+	6.15537i	−0.209657	+	0.645258i
$92$	−1.12667	+	0.366076i	−0.117463	+	0.0381660i
$93$	−7.03805	−	13.3233i	−0.729812	−	1.38156i
$94$	5.58154	+	7.68233i	0.575692	+	0.792372i
$95$	−2.06761	−	6.36346i	−0.212133	−	0.652878i
$96$	1.55470	+	0.763481i	0.158676	+	0.0779225i
$97$	−9.26977	−	6.73488i	−0.941202	−	0.683823i	0.00750748	−	0.999972i	$-0.497610\pi$
$97$	−9.26977	−	6.73488i	−0.941202	−	0.683823i	−0.948710	+	0.316148i	$0.897610\pi$
$98$	−4.66839			−0.471578
$99$		0			0
$100$	4.10940			0.410940
$101$	3.79077	+	2.75416i	0.377196	+	0.274049i	0.760188	−	0.649703i	$-0.225107\pi$
$101$	3.79077	+	2.75416i	0.377196	+	0.274049i	−0.382993	+	0.923751i	$0.625107\pi$
$102$	−4.55898	−	2.23882i	−0.451407	−	0.221676i
$103$	−3.91248	−	12.0414i	−0.385508	−	1.18647i	−0.936111	−	0.351704i	$-0.885602\pi$
$103$	−3.91248	−	12.0414i	−0.385508	−	1.18647i	0.550603	−	0.834767i	$-0.314398\pi$
$104$	2.49137	+	3.42908i	0.244299	+	0.336248i
$105$	−1.16581	−	2.20692i	−0.113771	−	0.215373i
$106$	4.62924	−	1.50413i	0.449632	−	0.146094i
$107$	−0.222103	+	0.683562i	−0.0214715	+	0.0660824i	−0.961218	−	0.275789i	$-0.911061\pi$
$107$	−0.222103	+	0.683562i	−0.0214715	+	0.0660824i	0.939747	+	0.341872i	$0.111061\pi$
$108$	4.52089	−	2.56155i	0.435023	−	0.246485i
$109$		−	9.20929i		−	0.882090i	−0.897485	−	0.441045i	$-0.854608\pi$
$109$		−	9.20929i		−	0.882090i	0.897485	−	0.441045i	$-0.145392\pi$
$110$		0			0
$111$	0.694346	−	4.84558i	0.0659044	−	0.459922i
$112$	0.897526	−	1.23534i	0.0848082	−	0.116728i
$113$	−4.66471	−	1.51566i	−0.438819	−	0.142581i	0.0812715	−	0.996692i	$-0.474102\pi$
$113$	−4.66471	−	1.51566i	−0.438819	−	0.142581i	−0.520091	+	0.854111i	$0.674102\pi$
$114$	−2.09979	−	12.0994i	−0.196663	−	1.13321i
$115$	0.904455	−	0.657125i	0.0843408	−	0.0612772i
$116$	5.17274	−	3.75821i	0.480276	−	0.348941i
$117$	12.7102	−	0.375151i	1.17506	−	0.0346827i
$118$	−4.43667	−	1.44156i	−0.408428	−	0.132706i
$119$	−2.63189	+	3.62249i	−0.241265	+	0.332073i
$120$	−1.61803	−	0.231856i	−0.147706	−	0.0211655i
$121$		0			0
$122$		−	0.720934i		−	0.0652703i
$123$	−8.82893	+	9.09336i	−0.796077	+	0.819921i
$124$	−2.68830	+	8.27372i	−0.241416	+	0.743002i
$125$	−8.17592	+	2.65652i	−0.731277	+	0.237606i
$126$	−1.54349	−	4.31302i	−0.137505	−	0.384235i
$127$	−3.10743	−	4.27701i	−0.275740	−	0.379524i	0.648577	−	0.761149i	$-0.275364\pi$
$127$	−3.10743	−	4.27701i	−0.275740	−	0.379524i	−0.924317	+	0.381625i	$0.875364\pi$
$128$	−0.309017	−	0.951057i	−0.0273135	−	0.0840623i
$129$	−4.08147	+	8.31124i	−0.359354	+	0.731763i
$130$	−3.23607	−	2.35114i	−0.283822	−	0.206209i
$131$	−10.6492			−0.930421			−0.465210	−	0.885200i	$-0.654021\pi$
$131$	−10.6492			−0.930421			−0.465210	+	0.885200i	$0.654021\pi$
$132$		0			0
$133$	−10.8262			−0.938748
$134$	3.15014	+	2.28871i	0.272131	+	0.197714i
$135$	−3.31061	+	3.61745i	−0.284932	+	0.311341i
$136$	0.906157	+	2.78886i	0.0777023	+	0.239143i
$137$	−0.350362	−	0.482232i	−0.0299335	−	0.0411999i	0.793788	−	0.608195i	$-0.208106\pi$
$137$	−0.350362	−	0.482232i	−0.0299335	−	0.0411999i	−0.823721	+	0.566995i	$0.808106\pi$
$138$	1.81428	−	0.958399i	0.154442	−	0.0815843i
$139$	4.88522	−	1.58730i	0.414359	−	0.134633i	−0.0944162	−	0.995533i	$-0.530098\pi$
$139$	4.88522	−	1.58730i	0.414359	−	0.134633i	0.508775	+	0.860899i	$0.330098\pi$
$140$	−0.445299	+	1.37049i	−0.0376346	+	0.115827i
$141$	−11.8003	−	11.4572i	−0.993768	−	0.964869i
$142$			9.95959i			0.835790i
$143$		0			0
$144$	−2.87928	−	0.842471i	−0.239940	−	0.0702059i
$145$	−3.54668	+	4.88159i	−0.294536	+	0.405394i
$146$	−1.66740	−	0.541771i	−0.137995	−	0.0448373i
$147$	7.96680	−	1.38260i	0.657091	−	0.114035i
$148$	−2.28642	+	1.66118i	−0.187943	+	0.136548i
$149$	14.0519	−	10.2093i	1.15118	−	0.836379i	0.162540	−	0.986702i	$-0.448031\pi$
$149$	14.0519	−	10.2093i	1.15118	−	0.836379i	0.988637	+	0.150323i	$0.0480313\pi$
$150$	−7.01287	+	1.21705i	−0.572599	+	0.0993714i
$151$	−14.3729	−	4.67002i	−1.16965	−	0.380041i	−0.341135	−	0.940014i	$-0.610811\pi$
$151$	−14.3729	−	4.67002i	−1.16965	−	0.380041i	−0.828511	+	0.559973i	$0.810811\pi$
$152$	−4.16740	+	5.73594i	−0.338021	+	0.465246i
$153$	8.44315	+	2.47045i	0.682588	+	0.199724i
$154$		0			0
$155$		−	8.20985i		−	0.659431i
$156$	−5.26719	−	5.11402i	−0.421713	−	0.409449i
$157$	−1.14590	+	3.52671i	−0.0914526	+	0.281462i	−0.986313	−	0.164884i	$-0.947275\pi$
$157$	−1.14590	+	3.52671i	−0.0914526	+	0.281462i	0.894860	+	0.446346i	$0.147275\pi$
$158$	−1.56591	+	0.508796i	−0.124577	+	0.0404776i
$159$	−7.45454	+	3.93787i	−0.591183	+	0.312293i
$160$	0.554701	+	0.763481i	0.0438530	+	0.0603585i
$161$	−0.558984	−	1.72037i	−0.0440541	−	0.135585i
$162$	−6.95647	+	5.71030i	−0.546552	+	0.448644i
$163$	−8.71782	−	6.33387i	−0.682832	−	0.496107i	0.191464	−	0.981500i	$-0.438677\pi$
$163$	−8.71782	−	6.33387i	−0.682832	−	0.496107i	−0.874296	+	0.485393i	$0.838677\pi$
$164$	7.31754			0.571404
$165$		0			0
$166$	−6.15976			−0.478090
$167$	10.7586	+	7.81655i	0.832522	+	0.604863i	0.920272	−	0.391280i	$-0.127968\pi$
$167$	10.7586	+	7.81655i	0.832522	+	0.604863i	−0.0877496	+	0.996143i	$0.527968\pi$
$168$	−1.16581	+	2.37397i	−0.0899439	+	0.183156i
$169$	−1.53442	−	4.72245i	−0.118032	−	0.363265i
$170$	−1.62660	−	2.23882i	−0.124754	−	0.171710i
$171$	7.16675	+	20.0263i	0.548055	+	1.53145i
$172$	5.08423	−	1.65197i	0.387669	−	0.125961i
$173$	2.19693	−	6.76144i	0.167029	−	0.514063i	−0.832151	−	0.554549i	$-0.812891\pi$
$173$	2.19693	−	6.76144i	0.167029	−	0.514063i	0.999180	+	0.0404862i	$0.0128907\pi$
$174$	−7.71446	+	7.94551i	−0.584831	+	0.602348i
$175$			6.27490i			0.474338i
$176$		0			0
$177$	7.99830	+	1.14612i	0.601189	+	0.0861473i
$178$	−10.1926	+	14.0289i	−0.763966	+	1.05151i
$179$	4.00523	+	1.30138i	0.299365	+	0.0972695i	0.454848	−	0.890569i	$-0.349694\pi$
$179$	4.00523	+	1.30138i	0.299365	+	0.0972695i	−0.155483	+	0.987838i	$0.549694\pi$
$180$	2.82991	−	0.0835271i	0.210929	−	0.00622574i
$181$	−7.01386	+	5.09587i	−0.521336	+	0.378773i	−0.817107	−	0.576486i	$-0.804423\pi$
$181$	−7.01386	+	5.09587i	−0.521336	+	0.378773i	0.295771	+	0.955259i	$0.404423\pi$
$182$	−5.23607	+	3.80423i	−0.388123	+	0.281988i
$183$	0.213513	+	1.23030i	0.0157833	+	0.0909467i
$184$	−1.12667	−	0.366076i	−0.0830588	−	0.0269875i
$185$	1.56768	−	2.15773i	0.115258	−	0.158639i
$186$	2.13733	−	14.9156i	0.156717	−	1.09367i
$187$		0			0
$188$			9.49588i			0.692558i
$189$	3.91138	+	6.90323i	0.284511	+	0.502136i
$190$	2.06761	−	6.36346i	0.150001	−	0.461654i
$191$	12.7897	−	4.15562i	0.925428	−	0.300690i	0.192737	−	0.981251i	$-0.438264\pi$
$191$	12.7897	−	4.15562i	0.925428	−	0.300690i	0.732692	+	0.680561i	$0.238264\pi$
$192$	0.809017	+	1.53150i	0.0583858	+	0.110526i
$193$	4.11314	+	5.66126i	0.296070	+	0.407506i	0.930974	−	0.365085i	$-0.118960\pi$
$193$	4.11314	+	5.66126i	0.296070	+	0.407506i	−0.634904	+	0.772591i	$0.718960\pi$
$194$	−3.54074	−	10.8973i	−0.254210	−	0.782378i
$195$	6.21881	+	3.05392i	0.445338	+	0.218696i
$196$	−3.77680	−	2.74401i	−0.269772	−	0.196001i
$197$	22.8937			1.63111			0.815554	−	0.578680i	$-0.196432\pi$
$197$	22.8937			1.63111			0.815554	+	0.578680i	$0.196432\pi$
$198$		0			0
$199$	−20.8937			−1.48112			−0.740558	−	0.671993i	$-0.765439\pi$
$199$	−20.8937			−1.48112			−0.740558	+	0.671993i	$0.765439\pi$
$200$	3.32458	+	2.41545i	0.235083	+	0.170798i
$201$	−6.05367	−	2.97283i	−0.426993	−	0.209687i
$202$	1.44795	+	4.45632i	0.101877	+	0.313545i
$203$	5.73865	+	7.89857i	0.402774	+	0.554371i
$204$	−2.37235	−	4.49095i	−0.166098	−	0.314429i
$205$	−6.56768	+	2.13397i	−0.458707	+	0.149043i
$206$	3.91248	−	12.0414i	0.272595	−	0.838962i
$207$	−2.81231	+	2.17287i	−0.195469	+	0.151025i
$208$			4.23857i			0.293892i
$209$		0			0
$210$	0.354035	−	2.47068i	0.0244308	−	0.170493i
$211$	2.33113	−	3.20852i	0.160482	−	0.220884i	−0.721202	−	0.692724i	$-0.756410\pi$
$211$	2.33113	−	3.20852i	0.160482	−	0.220884i	0.881684	+	0.471841i	$0.156410\pi$
$212$	4.62924	+	1.50413i	0.317938	+	0.103304i
$213$	−2.94965	−	16.9965i	−0.202107	−	1.16458i
$214$	−0.581472	+	0.422464i	−0.0397486	+	0.0288791i
$215$	−4.08147	+	2.96536i	−0.278354	+	0.202236i
$216$	5.16312	+	0.584981i	0.351306	+	0.0398029i
$217$	−12.6337	−	4.10493i	−0.857629	−	0.278660i
$218$	5.41309	−	7.45047i	0.366620	−	0.504610i
$219$	3.00594	+	0.430736i	0.203123	+	0.0291065i
$220$		0			0
$221$		−	12.4291i		−	0.836073i
$222$	3.40990	−	3.51203i	0.228857	−	0.235712i
$223$	−2.89753	+	8.91767i	−0.194033	+	0.597171i	0.805954	+	0.591978i	$0.201653\pi$
$223$	−2.89753	+	8.91767i	−0.194033	+	0.597171i	−0.999987	+	0.00519280i	$0.998347\pi$
$224$	1.45223	−	0.471857i	0.0970310	−	0.0315273i
$225$	11.6073	−	4.15388i	0.773822	−	0.276926i
$226$	−2.88295	−	3.96804i	−0.191771	−	0.263950i
$227$	0.561021	+	1.72665i	0.0372363	+	0.114601i	0.967947	−	0.251155i	$-0.0808103\pi$
$227$	0.561021	+	1.72665i	0.0372363	+	0.114601i	−0.930711	+	0.365756i	$0.880810\pi$
$228$	5.41309	−	11.0228i	0.358490	−	0.730006i
$229$	15.0398	+	10.9271i	0.993859	+	0.722081i	0.960763	−	0.277371i	$-0.0894632\pi$
$229$	15.0398	+	10.9271i	0.993859	+	0.722081i	0.0330963	+	0.999452i	$0.489463\pi$
$230$	1.11797			0.0737166
$231$		0			0
$232$	6.39385			0.419777
$233$	−14.6282	−	10.6280i	−0.958326	−	0.696265i	−0.00556498	−	0.999985i	$-0.501771\pi$
$233$	−14.6282	−	10.6280i	−0.958326	−	0.696265i	−0.952761	+	0.303720i	$0.901771\pi$
$234$	10.5033	+	7.16735i	0.686619	+	0.468544i
$235$	−2.76923	−	8.52280i	−0.180644	−	0.555966i
$236$	−2.74201	−	3.77405i	−0.178490	−	0.245670i
$237$	2.52161	−	1.33204i	0.163796	−	0.0865256i
$238$	−4.25849	+	1.38367i	−0.276037	+	0.0896898i
$239$	−6.17702	+	19.0109i	−0.399558	+	1.22971i	0.525796	+	0.850610i	$0.323767\pi$
$239$	−6.17702	+	19.0109i	−0.399558	+	1.22971i	−0.925355	+	0.379103i	$0.876233\pi$
$240$	−1.17274	−	1.13863i	−0.0756997	−	0.0734984i
$241$		−	1.79512i		−	0.115634i	−0.998327	−	0.0578169i	$-0.981586\pi$
$241$		−	1.79512i		−	0.115634i	0.998327	−	0.0578169i	$-0.0184140\pi$
$242$		0			0
$243$	10.1803	−	11.8051i	0.653069	−	0.757298i
$244$	0.423754	−	0.583248i	0.0271281	−	0.0373386i
$245$	4.19000	+	1.36141i	0.267689	+	0.0869775i
$246$	−12.4877	+	2.16717i	−0.796186	+	0.138174i
$247$	24.3122	−	17.6638i	1.54695	−	1.12392i
$248$	−7.03805	+	5.11344i	−0.446917	+	0.324704i
$249$	10.5119	−	1.82428i	0.666164	−	0.115609i
$250$	−8.17592	−	2.65652i	−0.517091	−	0.168013i
$251$	−7.46453	+	10.2740i	−0.471157	+	0.648492i	−0.976776	−	0.214265i	$-0.931264\pi$
$251$	−7.46453	+	10.2740i	−0.471157	+	0.648492i	0.505618	+	0.862757i	$0.331264\pi$
$252$	1.28642	−	4.39655i	0.0810369	−	0.276957i
$253$		0			0
$254$		−	5.28668i		−	0.331716i
$255$	3.43891	+	3.33891i	0.215353	+	0.209091i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	5.03903	−	1.63728i	0.314326	−	0.102131i	−0.147605	−	0.989046i	$-0.547157\pi$
$257$	5.03903	−	1.63728i	0.314326	−	0.102131i	0.461932	+	0.886916i	$0.347157\pi$
$258$	−8.18720	+	4.32490i	−0.509713	+	0.269257i
$259$	−2.53656	−	3.49128i	−0.157614	−	0.216937i
$260$	−1.23607	−	3.80423i	−0.0766577	−	0.235928i
$261$	10.8119	−	15.8441i	0.669240	−	0.980724i
$262$	−8.61535	−	6.25942i	−0.532258	−	0.386708i
$263$	−9.51711			−0.586850			−0.293425	−	0.955982i	$-0.594795\pi$
$263$	−9.51711			−0.586850			−0.293425	+	0.955982i	$0.594795\pi$
$264$		0			0
$265$	−4.59351			−0.282177
$266$	−8.75856	−	6.36346i	−0.537022	−	0.390169i
$267$	13.2393	−	26.9595i	0.810229	−	1.64990i
$268$	1.20325	+	3.70321i	0.0735000	+	0.226210i
$269$	0.0430063	+	0.0591931i	0.00262214	+	0.00360906i	0.810326	−	0.585979i	$-0.199290\pi$
$269$	0.0430063	+	0.0591931i	0.00262214	+	0.00360906i	−0.807704	+	0.589588i	$0.799290\pi$
$270$	−4.80463	+	0.980653i	−0.292400	+	0.0596806i
$271$	−0.0106686	+	0.00346643i	−0.000648069	+	0.000210571i	−0.309341	−	0.950951i	$-0.600108\pi$
$271$	−0.0106686	+	0.00346643i	−0.000648069	+	0.000210571i	0.308693	+	0.951162i	$0.400108\pi$
$272$	−0.906157	+	2.78886i	−0.0549438	+	0.169100i
$273$	7.80891	−	8.04280i	0.472617	−	0.486772i
$274$		−	0.596072i		−	0.0360100i
$275$		0			0
$276$	2.03112	+	0.291049i	0.122259	+	0.0175191i
$277$	8.15976	−	11.2309i	0.490272	−	0.674802i	−0.490166	−	0.871629i	$-0.663064\pi$
$277$	8.15976	−	11.2309i	0.490272	−	0.674802i	0.980438	+	0.196827i	$0.0630638\pi$
$278$	4.88522	+	1.58730i	0.292996	+	0.0952002i
$279$	0.769983	+	26.0872i	0.0460977	+	1.56180i
$280$	−1.16581	+	0.847008i	−0.0696703	+	0.0506184i
$281$	13.7462	−	9.98719i	0.820029	−	0.595786i	−0.0966920	−	0.995314i	$-0.530826\pi$
$281$	13.7462	−	9.98719i	0.820029	−	0.595786i	0.916721	+	0.399529i	$0.130826\pi$
$282$	−2.81231	−	16.2051i	−0.167471	−	0.965001i
$283$	22.0309	+	7.15827i	1.30960	+	0.425515i	0.878912	−	0.476985i	$-0.158270\pi$
$283$	22.0309	+	7.15827i	1.30960	+	0.425515i	0.430690	+	0.902500i	$0.358270\pi$
$284$	−5.85410	+	8.05748i	−0.347377	+	0.478123i
$285$	−1.64386	+	11.4719i	−0.0973739	+	0.679535i
$286$		0			0
$287$			11.1736i			0.659557i
$288$	−1.83419	−	2.37397i	−0.108081	−	0.139888i
$289$	−2.59609	+	7.98994i	−0.152711	+	0.469996i
$290$	−5.73865	+	1.86460i	−0.336985	+	0.109493i
$291$	9.26977	+	17.5480i	0.543403	+	1.02868i
$292$	−1.03051	−	1.41838i	−0.0603061	−	0.0830042i
$293$	7.23661	+	22.2720i	0.422767	+	1.30114i	0.905116	+	0.425165i	$0.139784\pi$
$293$	7.23661	+	22.2720i	0.422767	+	1.30114i	−0.482349	+	0.875979i	$0.660216\pi$
$294$	7.25795	+	3.56422i	0.423292	+	0.207870i
$295$	3.56163	+	2.58768i	0.207366	+	0.150660i
$296$	−2.82617			−0.164268
$297$		0			0
$298$	17.3691			1.00617
$299$	4.06224	+	2.95139i	0.234925	+	0.170683i
$300$	−6.38889	−	3.13745i	−0.368863	−	0.181141i
$301$	2.52249	+	7.76342i	0.145394	+	0.447476i
$302$	−8.88291	−	12.2263i	−0.511154	−	0.703543i
$303$	−3.79077	−	7.17607i	−0.217774	−	0.412254i
$304$	−6.74300	+	2.19093i	−0.386737	+	0.125659i
$305$	−0.210241	+	0.647057i	−0.0120384	+	0.0370504i
$306$	5.37856	+	6.96140i	0.307472	+	0.397956i
$307$		−	4.98612i		−	0.284573i	−0.989826	−	0.142286i	$-0.954555\pi$
$307$		−	4.98612i		−	0.284573i	0.989826	−	0.142286i	$-0.0454454\pi$
$308$		0			0
$309$	−3.11062	+	21.7078i	−0.176957	+	1.23492i
$310$	4.82563	−	6.64191i	0.274077	−	0.377235i
$311$	−13.3003	−	4.32152i	−0.754190	−	0.245051i	−0.0934066	−	0.995628i	$-0.529776\pi$
$311$	−13.3003	−	4.32152i	−0.754190	−	0.245051i	−0.660783	+	0.750577i	$0.729776\pi$
$312$	−1.25530	−	7.23330i	−0.0710674	−	0.409505i
$313$	−12.6718	+	9.20657i	−0.716250	+	0.520386i	−0.885184	−	0.465242i	$-0.845967\pi$
$313$	−12.6718	+	9.20657i	−0.716250	+	0.520386i	0.168934	+	0.985627i	$0.445967\pi$
$314$	−3.00000	+	2.17963i	−0.169300	+	0.123004i
$315$	0.127543	+	4.32117i	0.00718622	+	0.243470i
$316$	−1.56591	−	0.508796i	−0.0880895	−	0.0286220i
$317$	18.8109	−	25.8910i	1.05652	−	1.45418i	0.173512	−	0.984832i	$-0.444489\pi$
$317$	18.8109	−	25.8910i	1.05652	−	1.45418i	0.883013	−	0.469349i	$-0.155511\pi$
$318$	−8.34547	−	1.19586i	−0.467991	−	0.0670607i
$319$		0			0
$320$			0.943715i			0.0527552i
$321$	0.867190	−	0.893163i	0.0484018	−	0.0498515i
$322$	0.558984	−	1.72037i	0.0311509	−	0.0958727i
$323$	19.7731	−	6.42466i	1.10020	−	0.357478i
$324$	−8.98433	+	0.530822i	−0.499130	+	0.0294901i
$325$	−10.2380	−	14.0915i	−0.567904	−	0.781653i
$326$	−3.32991	−	10.2484i	−0.184427	−	0.567607i
$327$	−7.03112	+	14.3177i	−0.388822	+	0.791771i
$328$	5.92001	+	4.30114i	0.326878	+	0.237491i
$329$	−14.4999			−0.799403
$330$		0			0
$331$	5.76590			0.316923			0.158461	−	0.987365i	$-0.449347\pi$
$331$	5.76590			0.316923			0.158461	+	0.987365i	$0.449347\pi$
$332$	−4.98335	−	3.62061i	−0.273497	−	0.198707i
$333$	−4.77901	+	7.00331i	−0.261888	+	0.383779i
$334$	4.10940	+	12.6474i	0.224857	+	0.692037i
$335$	−2.15989	−	2.97283i	−0.118007	−	0.162423i
$336$	−2.33854	+	1.23534i	−0.127578	+	0.0673932i
$337$	−29.9803	+	9.74118i	−1.63313	+	0.530636i	−0.974988	−	0.222258i	$-0.928657\pi$
$337$	−29.9803	+	9.74118i	−1.63313	+	0.530636i	−0.658142	+	0.752894i	$0.728657\pi$
$338$	1.53442	−	4.72245i	0.0834612	−	0.256867i
$339$	6.09506	+	5.91782i	0.331038	+	0.321412i
$340$		−	2.76733i		−	0.150080i
$341$		0			0
$342$	−5.97312	+	20.4141i	−0.322989	+	1.10387i
$343$	10.4727	−	14.4144i	0.565471	−	0.778305i
$344$	5.08423	+	1.65197i	0.274123	+	0.0890680i
$345$	−1.90786	+	0.331099i	−0.102716	+	0.0178258i
$346$	5.75163	−	4.17880i	0.309209	−	0.224654i
$347$	−24.4381	+	17.7553i	−1.31191	+	0.953156i	−0.311911	+	0.950111i	$0.600969\pi$
$347$	−24.4381	+	17.7553i	−1.31191	+	0.953156i	−0.999995	+	0.00304473i	$0.999031\pi$
$348$	−10.9114	+	1.89361i	−0.584912	+	0.101508i
$349$	9.17824	+	2.98219i	0.491300	+	0.159633i	0.544181	−	0.838968i	$-0.316840\pi$
$349$	9.17824	+	2.98219i	0.491300	+	0.159633i	−0.0528813	+	0.998601i	$0.516840\pi$
$350$	−3.68830	+	5.07650i	−0.197148	+	0.271350i
$351$	−20.0469	−	9.12073i	−1.07003	−	0.486829i
$352$		0			0
$353$		−	13.7385i		−	0.731224i	−0.930767	−	0.365612i	$-0.880860\pi$
$353$		−	13.7385i		−	0.731224i	0.930767	−	0.365612i	$-0.119140\pi$
$354$	5.79709	+	5.62851i	0.308112	+	0.299152i
$355$	2.90445	−	8.93899i	0.154152	−	0.474432i
$356$	−16.4919	+	5.35856i	−0.874071	+	0.284003i
$357$	6.85751	−	3.62249i	0.362938	−	0.191722i
$358$	2.47537	+	3.40705i	0.130827	+	0.180068i
$359$	9.03771	+	27.8152i	0.476992	+	1.46803i	0.843252	+	0.537519i	$0.180638\pi$
$359$	9.03771	+	27.8152i	0.476992	+	1.46803i	−0.366260	+	0.930513i	$0.619362\pi$
$360$	2.33854	+	1.59581i	0.123252	+	0.0841063i
$361$	25.2965	+	18.3790i	1.33139	+	0.967315i
$362$	−8.66960			−0.455664
$363$		0			0
$364$	−6.47214			−0.339232
$365$	1.33854	+	0.972508i	0.0700625	+	0.0509034i
$366$	−0.550419	+	1.12084i	−0.0287709	+	0.0585871i
$367$	3.48566	+	10.7278i	0.181950	+	0.559984i	0.999882	−	0.0153299i	$-0.00487985\pi$
$367$	3.48566	+	10.7278i	0.181950	+	0.559984i	−0.817933	+	0.575314i	$0.804880\pi$
$368$	−0.696317	−	0.958399i	−0.0362980	−	0.0499600i
$369$	20.6690	−	7.39675i	1.07598	−	0.385059i
$370$	2.53656	−	0.824179i	0.131870	−	0.0428470i
$371$	−2.29675	+	7.06868i	−0.119242	+	0.366988i
$372$	10.4963	−	10.8107i	0.544209	−	0.560509i
$373$		−	5.73545i		−	0.296971i	−0.988915	−	0.148485i	$-0.952560\pi$
$373$		−	5.73545i		−	0.296971i	0.988915	−	0.148485i	$-0.0474398\pi$
$374$		0			0
$375$	14.7393	+	2.11207i	0.761135	+	0.109067i
$376$	−5.58154	+	7.68233i	−0.287846	+	0.396186i
$377$	−25.7744	−	8.37461i	−1.32745	−	0.431314i
$378$	−0.893244	+	7.88389i	−0.0459435	+	0.405503i
$379$	−21.8364	+	15.8650i	−1.12166	+	0.814932i	−0.984460	−	0.175611i	$-0.943810\pi$
$379$	−21.8364	+	15.8650i	−1.12166	+	0.814932i	−0.137199	+	0.990544i	$0.543810\pi$
$380$	5.41309	−	3.93284i	0.277685	−	0.201750i
$381$	1.56571	+	9.02194i	0.0802138	+	0.462208i
$382$	12.7897	+	4.15562i	0.654377	+	0.212620i
$383$	−0.371431	+	0.511231i	−0.0189792	+	0.0261227i	−0.818401	−	0.574647i	$-0.805139\pi$
$383$	−0.371431	+	0.511231i	−0.0189792	+	0.0261227i	0.799422	+	0.600770i	$0.205139\pi$
$384$	−0.245684	+	1.71454i	−0.0125375	+	0.0874946i
$385$		0			0
$386$			6.99770i			0.356173i
$387$	12.6909	−	9.80536i	0.645117	−	0.498435i
$388$	3.54074	−	10.8973i	0.179754	−	0.553225i
$389$	−25.4322	+	8.26343i	−1.28947	+	0.418973i	−0.871904	−	0.489676i	$-0.837115\pi$
$389$	−25.4322	+	8.26343i	−1.28947	+	0.418973i	−0.417561	+	0.908649i	$0.637115\pi$
$390$	3.23607	+	6.12600i	0.163865	+	0.310202i
$391$	2.04187	+	2.81039i	0.103262	+	0.142128i
$392$	−1.44261	−	4.43990i	−0.0728628	−	0.224249i
$393$	16.5563	+	8.13043i	0.835153	+	0.410126i
$394$	18.5214	+	13.4566i	0.933094	+	0.677933i
$395$	1.55382			0.0781814
$396$		0			0
$397$	36.0170			1.80764			0.903820	−	0.427913i	$-0.140751\pi$
$397$	36.0170			1.80764			0.903820	+	0.427913i	$0.140751\pi$
$398$	−16.9034	−	12.2810i	−0.847289	−	0.615591i
$399$	16.8315	+	8.26558i	0.842627	+	0.413796i
$400$	1.26988	+	3.90827i	0.0634938	+	0.195414i
$401$	−12.1840	−	16.7699i	−0.608441	−	0.837447i	0.388007	−	0.921656i	$-0.373163\pi$
$401$	−12.1840	−	16.7699i	−0.608441	−	0.837447i	−0.996448	+	0.0842096i	$0.973163\pi$
$402$	−3.15014	−	5.96333i	−0.157115	−	0.297424i
$403$	35.0688	−	11.3945i	1.74690	−	0.567602i
$404$	−1.44795	+	4.45632i	−0.0720380	+	0.221710i
$405$	7.90887	−	3.09647i	0.392995	−	0.153865i
$406$			9.76317i			0.484538i
$407$		0			0
$408$	0.720442	−	5.02768i	0.0356672	−	0.248907i
$409$	−9.70908	+	13.3634i	−0.480083	+	0.660778i	−0.978521	−	0.206148i	$-0.933907\pi$
$409$	−9.70908	+	13.3634i	−0.480083	+	0.660778i	0.498438	+	0.866926i	$0.333907\pi$
$410$	−6.56768	−	2.13397i	−0.324355	−	0.105389i
$411$	0.176533	+	1.01722i	0.00870775	+	0.0501759i
$412$	10.2430	−	7.44197i	0.504636	−	0.366640i
$413$	5.76284	−	4.18695i	0.283571	−	0.206026i
$414$	−3.55239	+	0.104852i	−0.174590	+	0.00515318i
$415$	5.52854	+	1.79633i	0.271385	+	0.0881784i
$416$	−2.49137	+	3.42908i	−0.122149	+	0.168124i
$417$	−8.80694	−	1.26199i	−0.431278	−	0.0617999i
$418$		0			0
$419$		−	16.0213i		−	0.782693i	−0.920243	−	0.391347i	$-0.872009\pi$
$419$		−	16.0213i		−	0.782693i	0.920243	−	0.391347i	$-0.127991\pi$
$420$	1.73865	−	1.79072i	0.0848373	−	0.0873783i
$421$	4.04838	−	12.4596i	0.197306	−	0.607246i	−0.802636	−	0.596469i	$-0.796570\pi$
$421$	4.04838	−	12.4596i	0.197306	−	0.607246i	0.999942	−	0.0107763i	$-0.00343026\pi$
$422$	3.77185	−	1.22555i	0.183611	−	0.0596587i
$423$	9.59867	+	26.8218i	0.466703	+	1.30412i
$424$	2.86103	+	3.93787i	0.138944	+	0.191240i
$425$	−3.72376	−	11.4606i	−0.180629	−	0.555919i
$426$	7.60396	−	15.4842i	0.368413	−	0.750212i
$427$	0.890597	+	0.647057i	0.0430990	+	0.0313133i
$428$	−0.718739			−0.0347416
$429$		0			0
$430$	−5.04498			−0.243290
$431$	−9.55912	−	6.94510i	−0.460446	−	0.334534i	0.333260	−	0.942835i	$-0.391851\pi$
$431$	−9.55912	−	6.94510i	−0.460446	−	0.334534i	−0.793706	+	0.608301i	$0.791851\pi$
$432$	3.83321	+	3.50806i	0.184425	+	0.168782i
$433$	3.52562	+	10.8507i	0.169430	+	0.521453i	0.999335	−	0.0364515i	$-0.0116054\pi$
$433$	3.52562	+	10.8507i	0.169430	+	0.521453i	−0.829905	+	0.557905i	$0.811605\pi$
$434$	−7.80803	−	10.7468i	−0.374798	−	0.515865i
$435$	9.24103	−	4.88159i	0.443073	−	0.234054i
$436$	8.75856	−	2.84583i	0.419459	−	0.136290i
$437$	−2.59548	+	7.98806i	−0.124159	+	0.382121i
$438$	2.17868	+	2.11532i	0.104101	+	0.101074i
$439$		−	16.0229i		−	0.764733i	−0.924011	−	0.382366i	$-0.875109\pi$
$439$		−	16.0229i		−	0.764733i	0.924011	−	0.382366i	$-0.124891\pi$
$440$		0			0
$441$	−13.4416	−	3.93298i	−0.640075	−	0.187285i
$442$	7.30565	−	10.0554i	0.347495	−	0.478285i
$443$	−4.50336	−	1.46323i	−0.213961	−	0.0695202i	0.200075	−	0.979781i	$-0.435881\pi$
$443$	−4.50336	−	1.46323i	−0.213961	−	0.0695202i	−0.414036	+	0.910260i	$0.635881\pi$
$444$	4.82298	−	0.837003i	0.228889	−	0.0397224i
$445$	13.2393	−	9.61888i	0.627601	−	0.455979i
$446$	−7.58582	+	5.51142i	−0.359199	+	0.260973i
$447$	−29.6411	+	5.14406i	−1.40198	+	0.243306i
$448$	1.45223	+	0.471857i	0.0686113	+	0.0222932i
$449$	−15.2006	+	20.9219i	−0.717362	+	0.987364i	0.282245	+	0.959342i	$0.408921\pi$
$449$	−15.2006	+	20.9219i	−0.717362	+	0.987364i	−0.999607	+	0.0280217i	$0.991079\pi$
$450$	11.8321	+	3.46205i	0.557771	+	0.163203i
$451$		0			0
$452$		−	4.90477i		−	0.230701i
$453$	18.7800	+	18.2339i	0.882362	+	0.856703i
$454$	−0.561021	+	1.72665i	−0.0263300	+	0.0810355i
$455$	5.80891	−	1.88743i	0.272326	−	0.0884840i
$456$	10.8583	−	5.73594i	0.508488	−	0.268610i
$457$	−13.4553	−	18.5197i	−0.629415	−	0.866315i	0.368581	−	0.929596i	$-0.379844\pi$
$457$	−13.4553	−	18.5197i	−0.629415	−	0.866315i	−0.997996	+	0.0632806i	$0.979844\pi$
$458$	5.74470	+	17.6804i	0.268432	+	0.826149i
$459$	−11.2404	−	10.2870i	−0.524659	−	0.480156i
$460$	0.904455	+	0.657125i	0.0421704	+	0.0306386i
$461$	21.2809			0.991151			0.495575	−	0.868565i	$-0.334957\pi$
$461$	21.2809			0.991151			0.495575	+	0.868565i	$0.334957\pi$
$462$		0			0
$463$	−20.7617			−0.964880			−0.482440	−	0.875929i	$-0.660249\pi$
$463$	−20.7617			−0.964880			−0.482440	+	0.875929i	$0.660249\pi$
$464$	5.17274	+	3.75821i	0.240138	+	0.174471i
$465$	−6.26807	+	12.7639i	−0.290675	+	0.591910i
$466$	−5.58748	−	17.1965i	−0.258835	−	0.796613i
$467$	2.29151	+	3.15400i	0.106039	+	0.145949i	0.858738	−	0.512414i	$-0.171249\pi$
$467$	2.29151	+	3.15400i	0.106039	+	0.145949i	−0.752700	+	0.658364i	$0.771249\pi$
$468$	4.28445	+	11.9722i	0.198049	+	0.553414i
$469$	−5.65466	+	1.83731i	−0.261108	+	0.0848391i
$470$	2.76923	−	8.52280i	0.127735	−	0.393127i
$471$	4.47411	−	4.60811i	0.206156	−	0.212331i
$472$		−	4.66499i		−	0.214723i
$473$		0			0
$474$	2.82298	+	0.404519i	0.129664	+	0.0185802i
$475$	17.1255	−	23.5713i	0.785773	−	1.08152i
$476$	−4.25849	−	1.38367i	−0.195188	−	0.0634203i
$477$	14.5961	−	0.430815i	0.668308	−	0.0197256i
$478$	−16.1716	+	11.7494i	−0.739674	+	0.537404i
$479$	−28.1803	+	20.4742i	−1.28759	+	0.935491i	−0.999754	−	0.0221881i	$-0.992937\pi$
$479$	−28.1803	+	20.4742i	−1.28759	+	0.935491i	−0.287839	+	0.957679i	$0.592937\pi$
$480$	−0.279492	−	1.61049i	−0.0127570	−	0.0735084i
$481$	11.3926	+	3.70169i	0.519459	+	0.168783i
$482$	1.05514	−	1.45228i	0.0480605	−	0.0661496i
$483$	−0.444421	+	3.10144i	−0.0202219	+	0.141121i
$484$		0			0
$485$			10.8131i			0.490999i
$486$	15.1749	−	3.56668i	0.688349	−	0.161788i
$487$	1.55634	−	4.78991i	0.0705244	−	0.217052i	−0.909582	−	0.415524i	$-0.863598\pi$
$487$	1.55634	−	4.78991i	0.0705244	−	0.217052i	0.980106	+	0.198473i	$0.0635981\pi$
$488$	0.685649	−	0.222781i	0.0310379	−	0.0100848i
$489$	8.71782	+	16.5032i	0.394233	+	0.746299i
$490$	2.58956	+	3.56422i	0.116984	+	0.161015i
$491$	−4.33218	−	13.3331i	−0.195509	−	0.601714i	−0.999970	−	0.00770906i	$-0.997546\pi$
$491$	−4.33218	−	13.3331i	−0.195509	−	0.601714i	0.804462	−	0.594005i	$-0.202454\pi$
$492$	−11.3766	−	5.58680i	−0.512896	−	0.251873i
$493$	−15.1685	−	11.0205i	−0.683153	−	0.496340i
$494$	30.0515			1.35208
$495$		0			0
$496$	−8.69951			−0.390619
$497$	−12.3035	−	8.93899i	−0.551886	−	0.400969i
$498$	9.57658	+	4.70286i	0.429137	+	0.210740i
$499$	−4.27851	−	13.1679i	−0.191532	−	0.589476i	−1.00000		0.000934574i	$-0.999703\pi$
$499$	−4.27851	−	13.1679i	−0.191532	−	0.589476i	0.808467	−	0.588541i	$-0.200297\pi$
$500$	−5.05300	−	6.95486i	−0.225977	−	0.311031i
$501$	−10.7586	−	20.3664i	−0.480657	−	0.909902i
$502$	−12.0779	+	3.92434i	−0.539062	+	0.175152i
$503$	6.97942	−	21.4804i	0.311197	−	0.957765i	−0.666095	−	0.745867i	$-0.732035\pi$
$503$	6.97942	−	21.4804i	0.311197	−	0.957765i	0.977292	−	0.211898i	$-0.0679645\pi$
$504$	3.62496	−	2.80074i	0.161469	−	0.124755i
$505$		−	4.42191i		−	0.196773i
$506$		0			0
$507$	−1.21994	+	8.51349i	−0.0541795	+	0.378098i
$508$	3.10743	−	4.27701i	0.137870	−	0.189762i
$509$	24.5753	+	7.98499i	1.08928	+	0.353928i	0.797968	−	0.602700i	$-0.205908\pi$
$509$	24.5753	+	7.98499i	1.08928	+	0.353928i	0.291312	+	0.956628i	$0.405908\pi$
$510$	0.819578	+	4.72257i	0.0362915	+	0.209119i
$511$	2.16581	−	1.57355i	0.0958096	−	0.0696098i
$512$	0.809017	−	0.587785i	0.0357538	−	0.0259767i
$513$	4.14752	−	36.6065i	0.183117	−	1.61622i
$514$	5.03903	+	1.63728i	0.222262	+	0.0722174i
$515$	−7.02310	+	9.66646i	−0.309475	+	0.425955i
$516$	−9.16570	−	1.31340i	−0.403497	−	0.0578191i
$517$		0			0
$518$		−	4.31546i		−	0.189610i
$519$	−8.57780	+	8.83472i	−0.376524	+	0.387801i
$520$	1.23607	−	3.80423i	0.0542052	−	0.166826i
$521$	27.3245	−	8.87828i	1.19711	−	0.388965i	0.358413	−	0.933563i	$-0.383318\pi$
$521$	27.3245	−	8.87828i	1.19711	−	0.388965i	0.838697	+	0.544599i	$0.183318\pi$
$522$	18.0599	−	6.46306i	0.790462	−	0.282881i
$523$	−2.13431	−	2.93763i	−0.0933269	−	0.128453i	0.759800	−	0.650157i	$-0.225297\pi$
$523$	−2.13431	−	2.93763i	−0.0933269	−	0.128453i	−0.853127	+	0.521703i	$0.825297\pi$
$524$	−3.29077	−	10.1279i	−0.143758	−	0.442441i
$525$	4.79077	−	9.75560i	0.209086	−	0.425769i
$526$	−7.69951	−	5.59402i	−0.335714	−	0.243911i
$527$	25.5103			1.11125
$528$		0			0
$529$	21.5966			0.938983
$530$	−3.71623	−	2.70000i	−0.161423	−	0.117280i
$531$	−11.5599	−	7.88842i	−0.501658	−	0.342328i
$532$	−3.34547	−	10.2963i	−0.145045	−	0.446401i
$533$	−18.2307	−	25.0924i	−0.789659	−	1.08687i
$534$	26.5572	−	14.0289i	1.14924	−	0.607089i
$535$	0.645087	−	0.209601i	0.0278895	−	0.00906186i
$536$	−1.20325	+	3.70321i	−0.0519723	+	0.159954i
$537$	−5.23335	−	5.08117i	−0.225836	−	0.219269i
$538$			0.0731666i			0.00315444i
$539$		0			0
$540$	−4.46344	−	2.03072i	−0.192076	−	0.0873884i
$541$	−24.0045	+	33.0394i	−1.03204	+	1.42048i	−0.128628	+	0.991693i	$0.541057\pi$
$541$	−24.0045	+	33.0394i	−1.03204	+	1.42048i	−0.903408	+	0.428783i	$0.858943\pi$
$542$	−0.0106686	−	0.00346643i	−0.000458254	−	0.000148896i
$543$	14.7951	−	2.56760i	0.634916	−	0.110186i
$544$	−2.37235	+	1.72361i	−0.101714	+	0.0738993i
$545$	−7.03112	+	5.10841i	−0.301180	+	0.218820i
$546$	11.0450	−	1.91680i	0.472681	−	0.0820313i
$547$	−6.84711	−	2.22476i	−0.292761	−	0.0951239i	0.158954	−	0.987286i	$-0.449188\pi$
$547$	−6.84711	−	2.22476i	−0.292761	−	0.0951239i	−0.451715	+	0.892162i	$0.649188\pi$
$548$	0.350362	−	0.482232i	0.0149667	−	0.0205999i
$549$	0.607365	−	2.07577i	0.0259217	−	0.0885917i
$550$		0			0
$551$		−	45.3325i		−	1.93123i
$552$	1.47214	+	1.42933i	0.0626583	+	0.0608361i
$553$	0.776912	−	2.39109i	0.0330377	−	0.101679i
$554$	13.2028	−	4.28984i	0.560932	−	0.182258i
$555$	−4.08466	+	2.15773i	−0.173384	+	0.0915905i
$556$	3.01923	+	4.15562i	0.128044	+	0.176237i
$557$	10.4252	+	32.0854i	0.441729	+	1.35950i	0.886031	+	0.463626i	$0.153452\pi$
$557$	10.4252	+	32.0854i	0.441729	+	1.35950i	−0.444302	+	0.895877i	$0.646548\pi$
$558$	−14.7107	+	21.5575i	−0.622754	+	0.912603i
$559$	−18.3314	−	13.3185i	−0.775336	−	0.563314i
$560$	−1.44102			−0.0608941
$561$		0			0
$562$	16.9912			0.716731
$563$	−3.85580	−	2.80141i	−0.162503	−	0.118065i	0.503562	−	0.863959i	$-0.332023\pi$
$563$	−3.85580	−	2.80141i	−0.162503	−	0.118065i	−0.666065	+	0.745894i	$0.732023\pi$
$564$	7.24993	−	14.7633i	0.305277	−	0.621645i
$565$	1.43035	+	4.40216i	0.0601752	+	0.185200i
$566$	13.6158	+	18.7406i	0.572317	+	0.787726i
$567$	−0.810545	−	13.7187i	−0.0340397	−	0.576133i
$568$	−9.47214	+	3.07768i	−0.397442	+	0.129137i
$569$	−4.59915	+	14.1547i	−0.192806	+	0.593397i	0.807189	+	0.590293i	$0.200988\pi$
$569$	−4.59915	+	14.1547i	−0.192806	+	0.593397i	−0.999995	+	0.00310384i	$0.999012\pi$
$570$	−8.07291	+	8.31470i	−0.338137	+	0.348265i
$571$			8.91378i			0.373030i	0.982452	+	0.186515i	$0.0597193\pi$
$571$			8.91378i			0.373030i	−0.982452	+	0.186515i	$0.940281\pi$
$572$		0			0
$573$	−23.0569	−	3.30393i	−0.963214	−	0.138024i
$574$	−6.56768	+	9.03964i	−0.274130	+	0.377307i
$575$	4.62992	+	1.50435i	0.193081	+	0.0627358i
$576$	−0.0885088	−	2.99869i	−0.00368787	−	0.124946i
$577$	8.64844	−	6.28346i	0.360039	−	0.261584i	−0.393029	−	0.919526i	$-0.628573\pi$
$577$	8.64844	−	6.28346i	0.360039	−	0.261584i	0.753068	+	0.657942i	$0.228573\pi$
$578$	−6.79665	+	4.93805i	−0.282703	+	0.205396i
$579$	−2.07245	−	11.9419i	−0.0861280	−	0.496287i
$580$	−5.73865	−	1.86460i	−0.238284	−	0.0774233i
$581$	5.52854	−	7.60938i	0.229362	−	0.315690i
$582$	−2.81507	+	19.6453i	−0.116688	+	0.814323i
$583$		0			0
$584$		−	1.75321i		−	0.0725483i
$585$	−7.33677	−	9.49588i	−0.303338	−	0.392606i
$586$	−7.23661	+	22.2720i	−0.298942	+	0.920048i
$587$	−26.9765	+	8.76521i	−1.11344	+	0.361779i	−0.807261	−	0.590195i	$-0.799051\pi$
$587$	−26.9765	+	8.76521i	−1.11344	+	0.361779i	−0.306180	+	0.951974i	$0.599051\pi$
$588$	3.77680	+	7.14963i	0.155753	+	0.294846i
$589$	36.2543	+	49.8998i	1.49383	+	2.05609i
$590$	1.36042	+	4.18695i	0.0560077	+	0.172374i
$591$	−35.5929	−	17.4789i	−1.46410	−	0.718986i
$592$	−2.28642	−	1.66118i	−0.0939713	−	0.0682742i
$593$	26.8555			1.10282			0.551411	−	0.834234i	$-0.314090\pi$
$593$	26.8555			1.10282			0.551411	+	0.834234i	$0.314090\pi$
$594$		0			0
$595$	4.22562			0.173233
$596$	14.0519	+	10.2093i	0.575588	+	0.418190i
$597$	32.4835	+	15.9519i	1.32946	+	0.652870i
$598$	1.55164	+	4.77545i	0.0634512	+	0.195283i
$599$	−9.81156	−	13.5045i	−0.400890	−	0.551777i	0.560077	−	0.828440i	$-0.310771\pi$
$599$	−9.81156	−	13.5045i	−0.400890	−	0.551777i	−0.960967	+	0.276663i	$0.910771\pi$
$600$	−3.32458	−	6.29355i	−0.135725	−	0.256933i
$601$	−7.70259	+	2.50272i	−0.314195	+	0.102088i	−0.461870	−	0.886948i	$-0.652821\pi$
$601$	−7.70259	+	2.50272i	−0.314195	+	0.102088i	0.147675	+	0.989036i	$0.452821\pi$
$602$	−2.52249	+	7.76342i	−0.102809	+	0.316413i
$603$	7.14196	+	9.24373i	0.290843	+	0.376434i
$604$		−	15.1125i		−	0.614919i
$605$		0			0
$606$	1.15119	−	8.03372i	0.0467639	−	0.326348i
$607$	2.96880	−	4.08620i	0.120500	−	0.165854i	−0.744506	−	0.667616i	$-0.767315\pi$
$607$	2.96880	−	4.08620i	0.120500	−	0.165854i	0.865006	+	0.501762i	$0.167315\pi$
$608$	−6.74300	−	2.19093i	−0.273465	−	0.0888540i
$609$	−2.89147	−	16.6613i	−0.117168	−	0.675149i
$610$	−0.550419	+	0.399903i	−0.0222858	+	0.0161916i
$611$	32.5621	−	23.6577i	1.31732	−	0.957090i
$612$	0.259542	+	8.79333i	0.0104914	+	0.355449i
$613$	−28.5879	−	9.28878i	−1.15466	−	0.375170i	−0.331760	−	0.943364i	$-0.607642\pi$
$613$	−28.5879	−	9.28878i	−1.15466	−	0.375170i	−0.822895	+	0.568194i	$0.807642\pi$
$614$	2.93077	−	4.03385i	0.118276	−	0.162793i
$615$	11.8400	+	1.69662i	0.477436	+	0.0684141i
$616$		0			0
$617$			1.33268i			0.0536518i	0.999640	+	0.0268259i	$0.00853997\pi$
$617$			1.33268i			0.0536518i	−0.999640	+	0.0268259i	$0.991460\pi$
$618$	−15.2761	+	15.7336i	−0.614494	+	0.632899i
$619$	−0.426675	+	1.31317i	−0.0171495	+	0.0527807i	−0.959265	−	0.282508i	$-0.908834\pi$
$619$	−0.426675	+	1.31317i	−0.0171495	+	0.0527807i	0.942116	+	0.335288i	$0.108834\pi$
$620$	7.80803	−	2.53698i	0.313578	−	0.101888i
$621$	6.03125	−	1.23101i	0.242026	−	0.0493989i
$622$	−8.22002	−	11.3139i	−0.329593	−	0.453646i
$623$	−8.18231	−	25.1826i	−0.327817	−	1.00892i
$624$	3.23607	−	6.58971i	0.129546	−	0.263800i
$625$	−10.0595	−	7.30864i	−0.402379	−	0.292346i
$626$	−15.6631			−0.626025
$627$		0			0
$628$	−3.70820			−0.147973
$629$	6.70467	+	4.87123i	0.267333	+	0.194228i
$630$	−2.43673	+	3.57087i	−0.0970818	+	0.142267i
$631$	−5.64222	−	17.3650i	−0.224613	−	0.691289i	−0.998331	−	0.0577579i	$-0.981605\pi$
$631$	−5.64222	−	17.3650i	−0.224613	−	0.691289i	0.773717	−	0.633531i	$-0.218395\pi$
$632$	−0.967787	−	1.33204i	−0.0384965	−	0.0529859i
$633$	−6.07386	+	3.20852i	−0.241414	+	0.127527i
$634$	30.4366	−	9.88946i	1.20879	−	0.392761i
$635$	−1.54172	+	4.74493i	−0.0611814	+	0.188297i
$636$	−6.04872	−	5.87282i	−0.239847	−	0.232872i
$637$			19.7873i			0.784001i
$638$		0			0
$639$	−8.39066	+	28.6764i	−0.331930	+	1.13442i
$640$	−0.554701	+	0.763481i	−0.0219265	+	0.0301792i
$641$	−20.0886	−	6.52719i	−0.793453	−	0.257809i	−0.115879	−	0.993263i	$-0.536969\pi$
$641$	−20.0886	−	6.52719i	−0.793453	−	0.257809i	−0.677574	+	0.735455i	$0.736969\pi$
$642$	1.22656	−	0.212863i	0.0484084	−	0.00840103i
$643$	0.597314	−	0.433974i	0.0235558	−	0.0171143i	−0.575945	−	0.817488i	$-0.695366\pi$
$643$	0.597314	−	0.433974i	0.0235558	−	0.0171143i	0.599501	+	0.800374i	$0.295366\pi$
$644$	1.46344	−	1.06325i	0.0576675	−	0.0418979i
$645$	8.60947	−	1.49413i	0.338998	−	0.0588312i
$646$	19.7731	+	6.42466i	0.777961	+	0.252775i
$647$	−21.0793	+	29.0131i	−0.828712	+	1.14062i	0.159449	+	0.987206i	$0.449028\pi$
$647$	−21.0793	+	29.0131i	−0.828712	+	1.14062i	−0.988161	+	0.153418i	$0.950972\pi$
$648$	−7.58049	−	4.85141i	−0.297790	−	0.190582i
$649$		0			0
$650$		−	17.4180i		−	0.683190i
$651$	16.5075	+	16.0275i	0.646981	+	0.628167i
$652$	3.32991	−	10.2484i	0.130409	−	0.401359i
$653$	−15.9233	+	5.17378i	−0.623126	+	0.202466i	−0.603528	−	0.797342i	$-0.706239\pi$
$653$	−15.9233	+	5.17378i	−0.623126	+	0.202466i	−0.0195981	+	0.999808i	$0.506239\pi$
$654$	−14.1040	+	7.45047i	−0.551511	+	0.291337i
$655$	5.90710	+	8.13043i	0.230810	+	0.317682i
$656$	2.26124	+	6.95939i	0.0882868	+	0.271719i
$657$	−4.34449	−	2.96465i	−0.169495	−	0.115662i
$658$	−11.7306	−	8.52280i	−0.457307	−	0.332253i
$659$	−36.3989			−1.41790			−0.708951	−	0.705258i	$-0.750831\pi$
$659$	−36.3989			−1.41790			−0.708951	+	0.705258i	$0.750831\pi$
$660$		0			0
$661$	−16.8578			−0.655694			−0.327847	−	0.944731i	$-0.606323\pi$
$661$	−16.8578			−0.655694			−0.327847	+	0.944731i	$0.606323\pi$
$662$	4.66471	+	3.38911i	0.181299	+	0.131722i
$663$	−9.48940	+	19.3236i	−0.368538	+	0.750465i
$664$	−1.90347	−	5.85828i	−0.0738689	−	0.227345i
$665$	6.00529	+	8.26558i	0.232875	+	0.320525i
$666$	−7.98274	+	2.85676i	−0.309325	+	0.110697i
$667$	7.20373	−	2.34063i	0.278930	−	0.0906297i
$668$	−4.10940	+	12.6474i	−0.158998	+	0.489344i
$669$	11.3133	−	11.6521i	0.437396	−	0.450496i
$670$		−	3.67462i		−	0.141963i
$671$		0			0
$672$	−2.61803	−	0.375151i	−0.100993	−	0.0144718i
$673$	−5.99777	+	8.25523i	−0.231197	+	0.318216i	−0.908816	−	0.417198i	$-0.863012\pi$
$673$	−5.99777	+	8.25523i	−0.231197	+	0.318216i	0.677618	+	0.735414i	$0.263012\pi$
$674$	−29.9803	−	9.74118i	−1.15480	−	0.375216i
$675$	−21.2173	−	2.40392i	−0.816656	−	0.0925270i
$676$	4.01715	−	2.91863i	0.154506	−	0.112255i
$677$	−25.3675	+	18.4305i	−0.974951	+	0.708344i	−0.956575	−	0.291488i	$-0.905850\pi$
$677$	−25.3675	+	18.4305i	−0.974951	+	0.708344i	−0.0183767	+	0.999831i	$0.505850\pi$
$678$	1.45260	+	8.37020i	0.0557869	+	0.321456i
$679$	16.6397	+	5.40657i	0.638574	+	0.207485i
$680$	1.62660	−	2.23882i	0.0623772	−	0.0858549i
$681$	0.446041	−	3.11275i	0.0170923	−	0.119281i
$682$		0			0
$683$			46.5132i			1.77978i	0.456178	+	0.889889i	$0.349218\pi$
$683$			46.5132i			1.77978i	−0.456178	+	0.889889i	$0.650782\pi$
$684$	−16.8315	+	13.0044i	−0.643567	+	0.497237i
$685$	−0.173829	+	0.534990i	−0.00664165	+	0.0204409i
$686$	16.9451	−	5.50581i	0.646969	−	0.210213i
$687$	−15.0398	−	28.4709i	−0.573805	−	1.08623i
$688$	3.14222	+	4.32490i	0.119796	+	0.164885i
$689$	−6.37537	−	19.6214i	−0.242882	−	0.747515i
$690$	−1.73811	−	0.853547i	−0.0661685	−	0.0324940i
$691$	−23.7888	−	17.2835i	−0.904967	−	0.657497i	0.0347700	−	0.999395i	$-0.488930\pi$
$691$	−23.7888	−	17.2835i	−0.904967	−	0.657497i	−0.939737	+	0.341898i	$0.888930\pi$
$692$	7.10940			0.270259
$693$		0			0
$694$	−30.2072			−1.14665
$695$	−3.92172	−	2.84929i	−0.148759	−	0.108080i
$696$	−9.94053	−	4.88159i	−0.376795	−	0.185036i
$697$	−6.63084	−	20.4076i	−0.251161	−	0.772994i
$698$	5.67246	+	7.80747i	0.214706	+	0.295517i
$699$	14.6282	+	27.6918i	0.553290	+	1.04740i
$700$	−5.96779	+	1.93905i	−0.225561	+	0.0732893i
$701$	8.45693	−	26.0277i	0.319414	−	0.983054i	−0.654486	−	0.756074i	$-0.727115\pi$
$701$	8.45693	−	26.0277i	0.319414	−	0.983054i	0.973899	−	0.226980i	$-0.0728852\pi$
$702$	−10.8573	−	19.1621i	−0.409782	−	0.723228i
$703$			20.0376i			0.755731i
$704$		0			0
$705$	−2.20168	+	15.3647i	−0.0829200	+	0.578667i
$706$	8.07526	−	11.1146i	0.303916	−	0.418305i
$707$	−6.80463	−	2.21096i	−0.255914	−	0.0831516i
$708$	1.38159	+	7.96100i	0.0519233	+	0.299193i
$709$	−34.4634	+	25.0391i	−1.29430	+	0.940363i	−0.999883	−	0.0153145i	$-0.995125\pi$
$709$	−34.4634	+	25.0391i	−1.29430	+	0.940363i	−0.294416	+	0.955677i	$0.595125\pi$
$710$	7.60396	−	5.52460i	0.285372	−	0.207335i
$711$	−4.93734	+	0.145730i	−0.185165	+	0.00546529i
$712$	−16.4919	−	5.35856i	−0.618061	−	0.200820i
$713$	−6.05762	+	8.33759i	−0.226860	+	0.312245i
$714$	7.67708	+	1.10009i	0.287308	+	0.0411697i
$715$		0			0
$716$			4.21134i			0.157385i
$717$	24.1179	−	24.8402i	0.900699	−	0.927676i
$718$	−9.03771	+	27.8152i	−0.337284	+	1.03805i
$719$	−15.5448	+	5.05082i	−0.579724	+	0.188364i	−0.584177	−	0.811626i	$-0.698583\pi$
$719$	−15.5448	+	5.05082i	−0.579724	+	0.188364i	0.00445278	+	0.999990i	$0.498583\pi$
$720$	0.953930	+	2.66559i	0.0355509	+	0.0993408i
$721$	11.3636	+	15.6407i	0.423203	+	0.582489i
$722$	9.66240	+	29.7378i	0.359597	+	1.10673i
$723$	−1.37054	+	2.79087i	−0.0509709	+	0.103794i
$724$	−7.01386	−	5.09587i	−0.260668	−	0.189386i
$725$	−26.2749			−0.975826
$726$		0			0
$727$	−21.6566			−0.803197			−0.401599	−	0.915816i	$-0.631545\pi$
$727$	−21.6566			−0.803197			−0.401599	+	0.915816i	$0.631545\pi$
$728$	−5.23607	−	3.80423i	−0.194062	−	0.140994i
$729$	−24.8404	+	10.5809i	−0.920014	+	0.391886i
$730$	0.511278	+	1.57355i	0.0189232	+	0.0582397i
$731$	−9.21421	−	12.6823i	−0.340800	−	0.469071i
$732$	−1.10411	+	0.583248i	−0.0408091	+	0.0215575i
$733$	26.0234	−	8.45552i	0.961197	−	0.312312i	0.213940	−	0.976847i	$-0.431370\pi$
$733$	26.0234	−	8.45552i	0.961197	−	0.312312i	0.747257	+	0.664535i	$0.231370\pi$
$734$	−3.48566	+	10.7278i	−0.128658	+	0.395969i
$735$	−5.47478	−	5.31557i	−0.201940	−	0.196068i
$736$		−	1.18465i		−	0.0436666i
$737$		0			0
$738$	21.0692	+	6.16481i	0.775569	+	0.226930i
$739$	−29.2885	+	40.3121i	−1.07739	+	1.48291i	−0.215036	+	0.976606i	$0.568987\pi$
$739$	−29.2885	+	40.3121i	−1.07739	+	1.48291i	−0.862358	+	0.506300i	$0.831013\pi$
$740$	2.53656	+	0.824179i	0.0932459	+	0.0302974i
$741$	−51.2842	+	8.90009i	−1.88397	+	0.326953i
$742$	−6.01298	+	4.36869i	−0.220743	+	0.160379i
$743$	16.4912	−	11.9815i	0.605002	−	0.439559i	−0.242649	−	0.970114i	$-0.578016\pi$
$743$	16.4912	−	11.9815i	0.605002	−	0.439559i	0.847651	+	0.530555i	$0.178016\pi$
$744$	14.8461	−	2.57646i	0.544284	−	0.0944575i
$745$	−15.5892	−	5.06525i	−0.571145	−	0.185576i
$746$	3.37122	−	4.64008i	0.123429	−	0.169885i
$747$	−17.7357	−	5.18941i	−0.648914	−	0.189871i
$748$		0			0
$749$		−	1.09749i		−	0.0401013i
$750$	10.6829	+	10.3723i	0.390085	+	0.378741i
$751$	−5.90778	+	18.1823i	−0.215578	+	0.663480i	0.783534	+	0.621349i	$0.213415\pi$
$751$	−5.90778	+	18.1823i	−0.215578	+	0.663480i	−0.999112	+	0.0421317i	$0.986585\pi$
$752$	−9.03112	+	2.93439i	−0.329331	+	0.107006i
$753$	19.4492	−	10.2740i	0.708767	−	0.374407i
$754$	−15.9294	−	21.9250i	−0.580116	−	0.798461i
$755$	4.40717	+	13.5639i	0.160393	+	0.493640i
$756$	−5.35668	+	5.85316i	−0.194821	+	0.212877i
$757$	−15.2166	−	11.0555i	−0.553057	−	0.401820i	0.275854	−	0.961200i	$-0.411039\pi$
$757$	−15.2166	−	11.0555i	−0.553057	−	0.401820i	−0.828911	+	0.559380i	$0.811039\pi$
$758$	−26.9912			−0.980365
$759$		0			0
$760$	6.69094			0.242706
$761$	−19.0042	−	13.8074i	−0.688903	−	0.500517i	0.187396	−	0.982284i	$-0.439995\pi$
$761$	−19.0042	−	13.8074i	−0.688903	−	0.500517i	−0.876299	+	0.481767i	$0.839995\pi$
$762$	−4.03628	+	8.21921i	−0.146219	+	0.297750i
$763$	4.34547	+	13.3740i	0.157317	+	0.484171i
$764$	7.90445	+	10.8795i	0.285973	+	0.393608i
$765$	−2.79729	−	7.81655i	−0.101136	−	0.282608i
$766$	−0.600988	+	0.195273i	−0.0217146	+	0.00705549i
$767$	−6.11016	+	18.8051i	−0.220625	+	0.679014i
$768$	−1.20654	+	1.24268i	−0.0435374	+	0.0448414i
$769$			38.7115i			1.39597i	0.716111	+	0.697987i	$0.245920\pi$
$769$			38.7115i			1.39597i	−0.716111	+	0.697987i	$0.754080\pi$
$770$		0			0
$771$	−9.08423	−	1.30172i	−0.327160	−	0.0468804i
$772$	−4.11314	+	5.66126i	−0.148035	+	0.203753i
$773$	21.9006	+	7.11595i	0.787711	+	0.255943i	0.675129	−	0.737700i	$-0.264088\pi$
$773$	21.9006	+	7.11595i	0.787711	+	0.255943i	0.112582	+	0.993642i	$0.464088\pi$
$774$	16.0306	−	0.473157i	0.576209	−	0.0170073i
$775$	28.9222	−	21.0132i	1.03892	−	0.754816i
$776$	9.26977	−	6.73488i	0.332765	−	0.241768i
$777$	1.27807	+	7.36451i	0.0458506	+	0.264200i
$778$	−25.4322	−	8.26343i	−0.911790	−	0.296258i
$779$	30.4951	−	41.9729i	1.09260	−	1.50384i
$780$	−0.982738	+	6.85815i	−0.0351877	+	0.245561i
$781$		0			0
$782$			3.47384i			0.124224i
$783$	−28.9059	+	16.3781i	−1.03301	+	0.585307i
$784$	1.44261	−	4.43990i	0.0515218	−	0.158568i
$785$	3.32821	−	1.08140i	0.118789	−	0.0385968i
$786$	8.61535	+	16.3092i	0.307299	+	0.581729i
$787$	−11.8379	−	16.2935i	−0.421975	−	0.580799i	0.544113	−	0.839012i	$-0.316866\pi$
$787$	−11.8379	−	16.2935i	−0.421975	−	0.580799i	−0.966088	+	0.258213i	$0.916866\pi$
$788$	7.07454	+	21.7732i	0.252020	+	0.775638i
$789$	14.7963	+	7.26614i	0.526761	+	0.258681i
$790$	1.25707	+	0.913315i	0.0447245	+	0.0324943i
$791$	7.48940			0.266292
$792$		0			0
$793$	−3.05573			−0.108512
$794$	29.1383	+	21.1702i	1.03408	+	0.751304i
$795$	7.14153	+	3.50706i	0.253284	+	0.124382i
$796$	−6.45651	−	19.8711i	−0.228845	−	0.704312i
$797$	−5.02805	−	6.92052i	−0.178103	−	0.245137i	0.710627	−	0.703569i	$-0.248411\pi$
$797$	−5.02805	−	6.92052i	−0.178103	−	0.245137i	−0.888730	+	0.458432i	$0.848411\pi$
$798$	8.75856	+	16.5803i	0.310050	+	0.586936i
$799$	26.4827	−	8.60476i	0.936891	−	0.304414i
$800$	−1.26988	+	3.90827i	−0.0448969	+	0.138178i
$801$	−41.1662	+	31.8061i	−1.45454	+	1.12381i
$802$		−	20.7287i		−	0.731955i
$803$		0			0
$804$	0.956643	−	6.67604i	0.0337382	−	0.235446i
$805$	−1.00340	+	1.38107i	−0.0353654	+	0.0486762i
$806$	35.0688	+	11.3945i	1.23524	+	0.401355i
$807$	−0.0216691	−	0.124862i	−0.000762790	−	0.00439535i
$808$	−3.79077	+	2.75416i	−0.133359	+	0.0968908i
$809$	−21.5020	+	15.6221i	−0.755970	+	0.549244i	−0.897671	−	0.440665i	$-0.854743\pi$
$809$	−21.5020	+	15.6221i	−0.755970	+	0.549244i	0.141702	+	0.989909i	$0.454743\pi$
$810$	8.21847	+	2.14362i	0.288768	+	0.0753191i
$811$	16.8527	+	5.47577i	0.591778	+	0.192280i	0.589570	−	0.807717i	$-0.299297\pi$
$811$	16.8527	+	5.47577i	0.591778	+	0.192280i	0.00220809	+	0.999998i	$0.499297\pi$
$812$	−5.73865	+	7.89857i	−0.201387	+	0.277186i
$813$	0.0192330	+	0.00275599i	0.000674530	+	9.66568e-5i
$814$		0			0
$815$			10.1693i			0.356215i
$816$	3.53805	−	3.64402i	0.123856	−	0.127566i
$817$	11.7124	−	36.0472i	0.409767	−	1.26113i
$818$	−15.7096	+	5.10437i	−0.549274	+	0.178470i
$819$	−18.2810	+	6.54219i	−0.638791	+	0.228603i
$820$	−4.05905	−	5.58680i	−0.141748	−	0.195100i
$821$	−11.9694	−	36.8381i	−0.417736	−	1.28566i	−0.909781	−	0.415089i	$-0.863751\pi$
$821$	−11.9694	−	36.8381i	−0.417736	−	1.28566i	0.492045	−	0.870570i	$-0.336249\pi$
$822$	−0.455089	+	0.926714i	−0.0158731	+	0.0323228i
$823$	27.1029	+	19.6914i	0.944749	+	0.686400i	0.949559	−	0.313588i	$-0.101531\pi$
$823$	27.1029	+	19.6914i	0.944749	+	0.686400i	−0.00481019	+	0.999988i	$0.501531\pi$
$824$	12.6610			0.441068
$825$		0			0
$826$	7.12326			0.247850
$827$	−27.9531	−	20.3091i	−0.972025	−	0.706218i	−0.0161130	−	0.999870i	$-0.505129\pi$
$827$	−27.9531	−	20.3091i	−0.972025	−	0.706218i	−0.955912	+	0.293652i	$0.905129\pi$
$828$	−2.93557	−	2.00322i	−0.102018	−	0.0696166i
$829$	9.30158	+	28.6273i	0.323057	+	0.994268i	0.972310	+	0.233695i	$0.0750817\pi$
$829$	9.30158	+	28.6273i	0.323057	+	0.994268i	−0.649253	+	0.760573i	$0.724918\pi$
$830$	3.41683	+	4.70286i	0.118600	+	0.163239i
$831$	−21.2606	+	11.2309i	−0.737522	+	0.389597i
$832$	−4.03112	+	1.30979i	−0.139754	+	0.0454088i
$833$	−4.23029	+	13.0195i	−0.146571	+	0.451099i
$834$	−6.38318	−	6.19756i	−0.221032	−	0.214604i
$835$		−	12.5498i		−	0.434304i
$836$		0			0
$837$	18.7200	−	41.1456i	0.647056	−	1.42220i
$838$	9.41710	−	12.9615i	0.325308	−	0.447748i
$839$	10.4999	+	3.41164i	0.362498	+	0.117783i	0.484602	−	0.874735i	$-0.338964\pi$
$839$	10.4999	+	3.41164i	0.362498	+	0.117783i	−0.122104	+	0.992517i	$0.538964\pi$
$840$	2.45916	−	0.426773i	0.0848489	−	0.0147251i
$841$	−9.61222	+	6.98368i	−0.331456	+	0.240817i
$842$	10.5988	−	7.70048i	0.365259	−	0.265376i
$843$	−28.9962	+	5.03214i	−0.998684	+	0.173316i
$844$	3.77185	+	1.22555i	0.129832	+	0.0421851i
$845$	−2.75436	+	3.79105i	−0.0947528	+	0.130416i
$846$	−8.00000	+	27.3413i	−0.275046	+	0.940013i
$847$		0			0
$848$			4.86748i			0.167150i
$849$	−28.7863	−	27.9492i	−0.987942	−	0.959213i
$850$	3.72376	−	11.4606i	0.127724	−	0.393094i
$851$	−3.18415	+	1.03459i	−0.109151	+	0.0354654i
$852$	15.2531	−	8.05748i	0.522563	−	0.276045i
$853$	9.31352	+	12.8190i	0.318889	+	0.438913i	0.938127	−	0.346290i	$-0.112559\pi$
$853$	9.31352	+	12.8190i	0.318889	+	0.438913i	−0.619239	+	0.785203i	$0.712559\pi$
$854$	0.340178	+	1.04696i	0.0116406	+	0.0358262i
$855$	11.3143	−	16.5803i	0.386940	−	0.567034i
$856$	−0.581472	−	0.422464i	−0.0198743	−	0.0144395i
$857$	−37.7235			−1.28861			−0.644305	−	0.764769i	$-0.722853\pi$
$857$	−37.7235			−1.28861			−0.644305	+	0.764769i	$0.722853\pi$
$858$		0			0
$859$	22.4943			0.767497			0.383749	−	0.923438i	$-0.374633\pi$
$859$	22.4943			0.767497			0.383749	+	0.923438i	$0.374633\pi$
$860$	−4.08147	−	2.96536i	−0.139177	−	0.101118i
$861$	8.53084	−	17.3716i	0.290730	−	0.592023i
$862$	−3.65126	−	11.2374i	−0.124362	−	0.382748i
$863$	−2.75191	−	3.78768i	−0.0936762	−	0.128934i	0.759606	−	0.650383i	$-0.225392\pi$
$863$	−2.75191	−	3.78768i	−0.0936762	−	0.128934i	−0.853282	+	0.521449i	$0.825392\pi$
$864$	1.03914	+	5.09119i	0.0353523	+	0.173206i
$865$	−6.38087	+	2.07327i	−0.216956	+	0.0704933i
$866$	−3.52562	+	10.8507i	−0.119805	+	0.368723i
$867$	10.1363	−	10.4399i	0.344247	−	0.354558i
$868$		−	13.2838i		−	0.450882i
$869$		0			0
$870$	10.3455	+	1.48245i	0.350744	+	0.0502599i
$871$	9.70086	−	13.3521i	0.328701	−	0.452418i
$872$	8.75856	+	2.84583i	0.296602	+	0.0963719i
$873$	−1.01414	−	34.3592i	−0.0343234	−	1.16288i
$874$	−6.79505	+	4.93689i	−0.229846	+	0.166993i
$875$	10.6198	−	7.71574i	0.359015	−	0.260840i
$876$	0.519233	+	2.99193i	0.0175433	+	0.101088i
$877$	−38.9333	−	12.6502i	−1.31468	−	0.427167i	−0.434018	−	0.900904i	$-0.642905\pi$
$877$	−38.9333	−	12.6502i	−1.31468	−	0.427167i	−0.880666	+	0.473737i	$0.842905\pi$
$878$	9.41804	−	12.9628i	0.317844	−	0.437474i
$879$	5.75348	−	40.1513i	0.194060	−	1.35427i
$880$		0			0
$881$			53.8892i			1.81557i	0.419431	+	0.907787i	$0.362230\pi$
$881$			53.8892i			1.81557i	−0.419431	+	0.907787i	$0.637770\pi$
$882$	−8.56272	−	11.0826i	−0.288322	−	0.373171i
$883$	−3.39517	+	10.4493i	−0.114257	+	0.351646i	−0.991791	−	0.127867i	$-0.959187\pi$
$883$	−3.39517	+	10.4493i	−0.114257	+	0.351646i	0.877535	+	0.479513i	$0.159187\pi$
$884$	11.8208	−	3.84081i	0.397576	−	0.129180i
$885$	−3.56163	−	6.74230i	−0.119723	−	0.226640i
$886$	−2.78323	−	3.83079i	−0.0935045	−	0.128698i
$887$	−8.51841	−	26.2170i	−0.286020	−	0.880280i	−0.986091	−	0.166206i	$-0.946848\pi$
$887$	−8.51841	−	26.2170i	−0.286020	−	0.880280i	0.700071	−	0.714074i	$-0.253152\pi$
$888$	4.39385	+	2.15773i	0.147448	+	0.0724086i
$889$	6.53084	+	4.74493i	0.219037	+	0.159140i
$890$	16.3646			0.548543
$891$		0			0
$892$	−9.37659			−0.313951
$893$	54.4678	+	39.5731i	1.82269	+	1.32426i
$894$	−27.0038	−	13.2610i	−0.903142	−	0.443514i
$895$	−1.22813	−	3.77979i	−0.0410518	−	0.126344i
$896$	0.897526	+	1.23534i	0.0299842	+	0.0412698i
$897$	−4.06224	−	7.68997i	−0.135634	−	0.256761i
$898$	−24.5951	+	7.99144i	−0.820750	+	0.266678i
$899$	17.1886	−	52.9010i	0.573271	−	1.76435i
$900$	7.53744	+	9.75560i	0.251248	+	0.325187i
$901$		−	14.2733i		−	0.475513i
$902$		0			0
$903$	2.00551	−	13.9957i	0.0667392	−	0.465747i
$904$	2.88295	−	3.96804i	0.0958855	−	0.131975i
$905$	7.78119	+	2.52826i	0.258656	+	0.0840423i
$906$	4.47574	+	25.7901i	0.148697	+	0.856820i
$907$	42.0054	−	30.5187i	1.39477	−	1.01336i	0.399442	−	0.916758i	$-0.369204\pi$
$907$	42.0054	−	30.5187i	1.39477	−	1.01336i	0.995323	−	0.0965982i	$-0.0307962\pi$
$908$	−1.46877	+	1.06713i	−0.0487429	+	0.0354138i
$909$	0.414721	+	14.0508i	0.0137554	+	0.466037i
$910$	5.80891	+	1.88743i	0.192563	+	0.0625677i
$911$	20.3799	−	28.0505i	0.675217	−	0.929356i	−0.324648	−	0.945835i	$-0.605246\pi$
$911$	20.3799	−	28.0505i	0.675217	−	0.929356i	0.999864	+	0.0164791i	$0.00524569\pi$
$912$	12.1561	+	1.74190i	0.402528	+	0.0576802i
$913$		0			0
$914$		−	22.8916i		−	0.757187i
$915$	0.820878	−	0.845465i	0.0271374	−	0.0279502i
$916$	−5.74470	+	17.6804i	−0.189810	+	0.584176i
$917$	15.4650	−	5.02488i	0.510699	−	0.165936i
$918$	−3.04716	−	14.9293i	−0.100571	−	0.492741i
$919$	1.75041	+	2.40924i	0.0577409	+	0.0794735i	0.836911	−	0.547339i	$-0.184359\pi$
$919$	1.75041	+	2.40924i	0.0577409	+	0.0794735i	−0.779170	+	0.626813i	$0.784359\pi$
$920$	0.345471	+	1.06325i	0.0113898	+	0.0350543i
$921$	−3.80681	+	7.75192i	−0.125438	+	0.255435i
$922$	17.2166	+	12.5086i	0.566999	+	0.411949i
$923$	42.2144			1.38950
$924$		0			0
$925$	11.6139			0.381862
$926$	−16.7966	−	12.2034i	−0.551971	−	0.401030i
$927$	21.4096	−	31.3743i	0.703184	−	1.03047i
$928$	1.97581	+	6.08092i	0.0648591	+	0.199616i
$929$	27.1242	+	37.3332i	0.889915	+	1.22486i	0.973575	+	0.228369i	$0.0733393\pi$
$929$	27.1242	+	37.3332i	0.889915	+	1.22486i	−0.0836592	+	0.996494i	$0.526661\pi$
$930$	−12.5734	+	6.64191i	−0.412297	+	0.217797i
$931$	−31.4789	+	10.2281i	−1.03168	+	0.335213i
$932$	5.58748	−	17.1965i	0.183024	−	0.563290i
$933$	17.3786	+	16.8732i	0.568949	+	0.552403i
$934$			3.89855i			0.127565i
$935$		0			0
$936$	−3.57087	+	12.2040i	−0.116718	+	0.398901i
$937$	21.1283	−	29.0806i	0.690232	−	0.950022i	−0.309768	−	0.950812i	$-0.600251\pi$
$937$	21.1283	−	29.0806i	0.690232	−	0.950022i	1.00000		0.000789912i	$0.000251437\pi$
$938$	−5.65466	−	1.83731i	−0.184631	−	0.0599903i
$939$	26.7298	−	4.63882i	0.872295	−	0.151382i
$940$	7.24993	−	5.26738i	0.236466	−	0.171803i
$941$	−11.6091	+	8.43452i	−0.378447	+	0.274957i	−0.760705	−	0.649098i	$-0.775146\pi$
$941$	−11.6091	+	8.43452i	−0.378447	+	0.274957i	0.382258	+	0.924056i	$0.375146\pi$
$942$	6.32821	−	1.09823i	0.206184	−	0.0357822i
$943$	8.24442	+	2.67877i	0.268475	+	0.0872329i
$944$	2.74201	−	3.77405i	0.0892449	−	0.122835i
$945$	3.10084	−	6.81550i	0.100870	−	0.221708i
$946$		0			0
$947$		−	12.3625i		−	0.401726i	−0.979619	−	0.200863i	$-0.935625\pi$
$947$		−	12.3625i		−	0.401726i	0.979619	−	0.200863i	$-0.0643746\pi$
$948$	2.04607	+	1.98657i	0.0664533	+	0.0645208i
$949$	−2.29634	+	7.06740i	−0.0745422	+	0.229417i
$950$	27.7097	−	9.00342i	0.899021	−	0.292110i
$951$	−49.0126	+	25.8910i	−1.58934	+	0.839572i
$952$	−2.63189	−	3.62249i	−0.0853001	−	0.117406i
$953$	−7.10543	−	21.8683i	−0.230167	−	0.708383i	−0.997726	−	0.0674035i	$-0.978529\pi$
$953$	−7.10543	−	21.8683i	−0.230167	−	0.708383i	0.767558	−	0.640979i	$-0.221471\pi$
$954$	12.0617	+	8.23082i	0.390512	+	0.266483i
$955$	−10.2672	−	7.45955i	−0.332238	−	0.241385i
$956$	−19.9892			−0.646499
$957$		0			0
$958$	−34.8328			−1.12540
$959$	0.736350	+	0.534990i	0.0237780	+	0.0172757i
$960$	0.720508	−	1.46719i	0.0232543	−	0.0473535i
$961$	13.8073	+	42.4945i	0.445397	+	1.37079i
$962$	7.04104	+	9.69115i	0.227012	+	0.312455i
$963$	−2.03013	+	0.726519i	−0.0654202	+	0.0234118i
$964$	1.70726	−	0.554722i	0.0549871	−	0.0178664i
$965$	2.04069	−	6.28061i	0.0656923	−	0.202180i
$966$	−2.18253	+	2.24790i	−0.0702216	+	0.0723249i
$967$			58.6116i			1.88482i	0.334455	+	0.942412i	$0.391448\pi$
$967$			58.6116i			1.88482i	−0.334455	+	0.942412i	$0.608552\pi$
$968$		0			0
$969$	−35.6463	−	5.10794i	−1.14512	−	0.164091i
$970$	−6.35580	+	8.74801i	−0.204073	+	0.280882i
$971$	33.1975	+	10.7865i	1.06536	+	0.346156i	0.788679	−	0.614806i	$-0.210766\pi$
$971$	33.1975	+	10.7865i	1.06536	+	0.346156i	0.276681	+	0.960962i	$0.410766\pi$
$972$	14.3732	+	6.03410i	0.461021	+	0.193544i
$973$	−6.34547	+	4.61025i	−0.203426	+	0.147798i
$974$	4.07454	−	2.96033i	0.130557	−	0.0948551i
$975$	5.15854	+	29.7245i	0.165205	+	0.951947i
$976$	0.685649	+	0.222781i	0.0219471	+	0.00713104i
$977$	−28.2696	+	38.9098i	−0.904425	+	1.24483i	0.0646094	+	0.997911i	$0.479420\pi$
$977$	−28.2696	+	38.9098i	−0.904425	+	1.24483i	−0.969035	+	0.246924i	$0.920580\pi$
$978$	−2.64745	+	18.4755i	−0.0846562	+	0.590783i
$979$		0			0
$980$			4.40562i			0.140733i
$981$	21.8626	−	16.8916i	0.698019	−	0.539308i
$982$	4.33218	−	13.3331i	0.138245	−	0.425476i
$983$	−5.71577	+	1.85716i	−0.182305	+	0.0592344i	−0.398747	−	0.917061i	$-0.630555\pi$
$983$	−5.71577	+	1.85716i	−0.182305	+	0.0592344i	0.216442	+	0.976295i	$0.430555\pi$
$984$	−5.92001	−	11.2068i	−0.188723	−	0.357260i
$985$	−12.6992	−	17.4789i	−0.404629	−	0.556924i
$986$	−5.79383	−	17.8316i	−0.184513	−	0.567873i
$987$	22.5429	+	11.0704i	0.717550	+	0.352373i
$988$	24.3122	+	17.6638i	0.773473	+	0.561961i
$989$	6.33296			0.201377
$990$		0			0
$991$	51.4597			1.63467			0.817336	−	0.576161i	$-0.195450\pi$
$991$	51.4597			1.63467			0.817336	+	0.576161i	$0.195450\pi$
$992$	−7.03805	−	5.11344i	−0.223458	−	0.162352i
$993$	−8.96426	−	4.40216i	−0.284472	−	0.139698i
$994$	−4.69951	−	14.4636i	−0.149059	−	0.458757i
$995$	11.5898	+	15.9519i	0.367420	+	0.505711i
$996$	4.98335	+	9.43366i	0.157903	+	0.298917i
$997$	−35.1597	+	11.4241i	−1.11352	+	0.361804i	−0.807290	−	0.590154i	$-0.799067\pi$
$997$	−35.1597	+	11.4241i	−1.11352	+	0.361804i	−0.306228	+	0.951958i	$0.599067\pi$
$998$	4.27851	−	13.1679i	0.135434	−	0.416822i
$999$	12.7768	−	7.23937i	0.404241	−	0.229043i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	726.2.h.f.161.1		8
3.2	odd	2		726.2.h.c.161.2		8
11.2	odd	10		66.2.h.a.17.1	✓	8
11.3	even	5		726.2.h.h.239.2		8
11.4	even	5		66.2.h.b.35.2	yes	8
11.5	even	5		726.2.b.c.725.5		8
11.6	odd	10		726.2.b.e.725.5		8
11.7	odd	10		726.2.h.d.233.2		8
11.8	odd	10		726.2.h.c.239.2		8
11.9	even	5		726.2.h.j.215.1		8
11.10	odd	2		726.2.h.a.161.1		8
33.2	even	10		66.2.h.b.17.1	yes	8
33.5	odd	10		726.2.b.e.725.6		8
33.8	even	10	inner	726.2.h.f.239.1		8
33.14	odd	10		726.2.h.a.239.1		8
33.17	even	10		726.2.b.c.725.6		8
33.20	odd	10		726.2.h.d.215.1		8
33.26	odd	10		66.2.h.a.35.1	yes	8
33.29	even	10		726.2.h.j.233.1		8
33.32	even	2		726.2.h.h.161.2		8
44.15	odd	10		528.2.bn.a.497.1		8
44.35	even	10		528.2.bn.b.17.2		8
132.35	odd	10		528.2.bn.a.17.2		8
132.59	even	10		528.2.bn.b.497.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
66.2.h.a.17.1	✓	8	11.2	odd	10
66.2.h.a.35.1	yes	8	33.26	odd	10
66.2.h.b.17.1	yes	8	33.2	even	10
66.2.h.b.35.2	yes	8	11.4	even	5
528.2.bn.a.17.2		8	132.35	odd	10
528.2.bn.a.497.1		8	44.15	odd	10
528.2.bn.b.17.2		8	44.35	even	10
528.2.bn.b.497.2		8	132.59	even	10
726.2.b.c.725.5		8	11.5	even	5
726.2.b.c.725.6		8	33.17	even	10
726.2.b.e.725.5		8	11.6	odd	10
726.2.b.e.725.6		8	33.5	odd	10
726.2.h.a.161.1		8	11.10	odd	2
726.2.h.a.239.1		8	33.14	odd	10
726.2.h.c.161.2		8	3.2	odd	2
726.2.h.c.239.2		8	11.8	odd	10
726.2.h.d.215.1		8	33.20	odd	10
726.2.h.d.233.2		8	11.7	odd	10
726.2.h.f.161.1		8	1.1	even	1	trivial
726.2.h.f.239.1		8	33.8	even	10	inner
726.2.h.h.161.2		8	33.32	even	2
726.2.h.h.239.2		8	11.3	even	5
726.2.h.j.215.1		8	11.9	even	5
726.2.h.j.233.1		8	33.29	even	10

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 726 = 2 \cdot 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	726.h (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 + 0.587785i) q^{2} +(-1.55470 - 0.763481i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-0.554701 - 0.763481i) q^{5} +(-0.809017 - 1.53150i) q^{6} +(-1.45223 + 0.471857i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(1.83419 + 2.37397i) q^{9} -0.943715i q^{10} +(0.245684 - 1.71454i) q^{12} +(2.49137 - 3.42908i) q^{13} +(-1.45223 - 0.471857i) q^{14} +(0.279492 + 1.61049i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(2.37235 - 1.72361i) q^{17} +(0.0885088 + 2.99869i) q^{18} +(6.74300 + 2.19093i) q^{19} +(0.554701 - 0.763481i) q^{20} +(2.61803 + 0.375151i) q^{21} +1.18465i q^{23} +(1.20654 - 1.24268i) q^{24} +(1.26988 - 3.90827i) q^{25} +(4.03112 - 1.30979i) q^{26} +(-1.03914 - 5.09119i) q^{27} +(-0.897526 - 1.23534i) q^{28} +(-1.97581 - 6.08092i) q^{29} +(-0.720508 + 1.46719i) q^{30} +(7.03805 + 5.11344i) q^{31} -1.00000 q^{32} +2.93239 q^{34} +(1.16581 + 0.847008i) q^{35} +(-1.69098 + 2.47802i) q^{36} +(0.873335 + 2.68785i) q^{37} +(4.16740 + 5.73594i) q^{38} +(-6.49137 + 3.42908i) q^{39} +(0.897526 - 0.291624i) q^{40} +(2.26124 - 6.95939i) q^{41} +(1.89753 + 1.84235i) q^{42} -5.34587i q^{43} +(0.795052 - 2.71722i) q^{45} +(-0.696317 + 0.958399i) q^{46} +(9.03112 + 2.93439i) q^{47} +(1.70654 - 0.296161i) q^{48} +(-3.77680 + 2.74401i) q^{49} +(3.32458 - 2.41545i) q^{50} +(-5.00424 + 0.868459i) q^{51} +(4.03112 + 1.30979i) q^{52} +(2.86103 - 3.93787i) q^{53} +(2.15184 - 4.72965i) q^{54} -1.52696i q^{56} +(-8.81061 - 8.55440i) q^{57} +(1.97581 - 6.08092i) q^{58} +(-4.43667 + 1.44156i) q^{59} +(-1.44530 + 0.763481i) q^{60} +(-0.423754 - 0.583248i) q^{61} +(2.68830 + 8.27372i) q^{62} +(-3.78384 - 2.58207i) q^{63} +(-0.809017 - 0.587785i) q^{64} -4.00000 q^{65} +3.89379 q^{67} +(2.37235 + 1.72361i) q^{68} +(0.904455 - 1.84177i) q^{69} +(0.445299 + 1.37049i) q^{70} +(5.85410 + 8.05748i) q^{71} +(-2.82458 + 1.01082i) q^{72} +(-1.66740 + 0.541771i) q^{73} +(-0.873335 + 2.68785i) q^{74} +(-4.95817 + 5.10667i) q^{75} +7.09001i q^{76} +(-7.26719 - 1.04135i) q^{78} +(-0.967787 + 1.33204i) q^{79} +(0.897526 + 0.291624i) q^{80} +(-2.27147 + 8.70864i) q^{81} +(5.92001 - 4.30114i) q^{82} +(-4.98335 + 3.62061i) q^{83} +(0.452227 + 2.60583i) q^{84} +(-2.63189 - 0.855153i) q^{85} +(3.14222 - 4.32490i) q^{86} +(-1.57087 + 10.9625i) q^{87} +17.3406i q^{89} +(2.24035 - 1.73095i) q^{90} +(-2.00000 + 6.15537i) q^{91} +(-1.12667 + 0.366076i) q^{92} +(-7.03805 - 13.3233i) q^{93} +(5.58154 + 7.68233i) q^{94} +(-2.06761 - 6.36346i) q^{95} +(1.55470 + 0.763481i) q^{96} +(-9.26977 - 6.73488i) q^{97} -4.66839 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} - 3 q^{3} - 2 q^{4} + 5 q^{5} - 2 q^{6} + 5 q^{7} + 2 q^{8} + 7 q^{9} - 3 q^{12} + 10 q^{13} + 5 q^{14} + 4 q^{15} - 2 q^{16} + 15 q^{17} - 2 q^{18} + 10 q^{19} - 5 q^{20} + 12 q^{21} - 2 q^{24}+ \cdots - 22 q^{98}+O(q^{100}) \) 8 * q + 2 * q^2 - 3 * q^3 - 2 * q^4 + 5 * q^5 - 2 * q^6 + 5 * q^7 + 2 * q^8 + 7 * q^9 - 3 * q^12 + 10 * q^13 + 5 * q^14 + 4 * q^15 - 2 * q^16 + 15 * q^17 - 2 * q^18 + 10 * q^19 - 5 * q^20 + 12 * q^21 - 2 * q^24 - q^25 - 15 * q^27 - 22 * q^29 - 4 * q^30 - 2 * q^31 - 8 * q^32 + 10 * q^34 + 17 * q^35 - 18 * q^36 + 6 * q^37 + 15 * q^38 - 42 * q^39 - 3 * q^41 + 8 * q^42 - 8 * q^45 - 10 * q^46 + 40 * q^47 + 2 * q^48 + 7 * q^49 + 6 * q^50 + 25 * q^51 - 30 * q^53 + 15 * q^54 - 40 * q^57 + 22 * q^58 - 35 * q^59 - 21 * q^60 + 20 * q^61 - 13 * q^62 - 29 * q^63 - 2 * q^64 - 32 * q^65 - 2 * q^67 + 15 * q^68 - 26 * q^69 + 13 * q^70 + 20 * q^71 - 2 * q^72 + 5 * q^73 - 6 * q^74 + 6 * q^75 - 8 * q^78 + 25 * q^79 + 19 * q^81 - 2 * q^82 + 9 * q^83 - 13 * q^84 + 40 * q^85 + 10 * q^86 + 42 * q^87 + 13 * q^90 - 16 * q^91 - 10 * q^92 + 2 * q^93 - 10 * q^94 - 30 * q^95 + 3 * q^96 - q^97 - 22 * q^98

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