LMFDB - Embedded newform 819.2.ew.a.470.76

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(176,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 0, 11]))

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

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

chi := DirichletCharacter("819.176");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.ew (of order $12$, 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:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$336$
Relative dimension:	$84$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			470.76
Character	$\chi$	$=$	819.470
Dual form			819.2.ew.a.176.76

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.70967 + 1.70967i) q^{2} +(1.58556 - 0.697137i) q^{3} +3.84596i q^{4} +(-0.668510 + 2.49492i) q^{5} +(3.90266 + 1.51891i) q^{6} +(0.258819 - 0.965926i) q^{7} +(-3.15599 + 3.15599i) q^{8} +(2.02800 - 2.21070i) q^{9} +O(q^{10})$	\(q+(1.70967 + 1.70967i) q^{2} +(1.58556 - 0.697137i) q^{3} +3.84596i q^{4} +(-0.668510 + 2.49492i) q^{5} +(3.90266 + 1.51891i) q^{6} +(0.258819 - 0.965926i) q^{7} +(-3.15599 + 3.15599i) q^{8} +(2.02800 - 2.21070i) q^{9} +(-5.40842 + 3.12255i) q^{10} +(-3.92271 + 3.92271i) q^{11} +(2.68116 + 6.09800i) q^{12} +(-2.50393 + 2.59428i) q^{13} +(2.09391 - 1.20892i) q^{14} +(0.679334 + 4.42188i) q^{15} -3.09951 q^{16} +(2.36103 - 4.08942i) q^{17} +(7.24680 - 0.312364i) q^{18} +(0.461934 + 1.72396i) q^{19} +(-9.59535 - 2.57107i) q^{20} +(-0.263009 - 1.71197i) q^{21} -13.4131 q^{22} +(3.54343 - 6.13740i) q^{23} +(-2.80386 + 7.20418i) q^{24} +(-1.44757 - 0.835754i) q^{25} +(-8.71629 + 0.154470i) q^{26} +(1.67435 - 4.91900i) q^{27} +(3.71492 + 0.995408i) q^{28} -2.71145i q^{29} +(-6.39853 + 8.72141i) q^{30} +(7.98361 + 2.13920i) q^{31} +(1.01285 + 1.01285i) q^{32} +(-3.48503 + 8.95436i) q^{33} +(11.0282 - 2.95499i) q^{34} +(2.23688 + 1.29146i) q^{35} +(8.50229 + 7.79961i) q^{36} +(-0.852036 + 3.17984i) q^{37} +(-2.15765 + 3.73717i) q^{38} +(-2.16157 + 5.85898i) q^{39} +(-5.76412 - 9.98375i) q^{40} +(8.21444 - 2.20105i) q^{41} +(2.47724 - 3.37656i) q^{42} +(-8.80842 + 5.08554i) q^{43} +(-15.0866 - 15.0866i) q^{44} +(4.15978 + 6.53757i) q^{45} +(16.5511 - 4.43484i) q^{46} +(-2.94989 - 11.0091i) q^{47} +(-4.91445 + 2.16078i) q^{48} +(-0.866025 - 0.500000i) q^{49} +(-1.04600 - 3.90373i) q^{50} +(0.892666 - 8.12998i) q^{51} +(-9.97752 - 9.63004i) q^{52} -0.0631920i q^{53} +(11.2725 - 5.54728i) q^{54} +(-7.16446 - 12.4092i) q^{55} +(2.23162 + 3.86529i) q^{56} +(1.93426 + 2.41141i) q^{57} +(4.63570 - 4.63570i) q^{58} +(5.08824 - 5.08824i) q^{59} +(-17.0064 + 2.61269i) q^{60} +(-4.38239 - 7.59052i) q^{61} +(9.99203 + 17.3067i) q^{62} +(-1.61049 - 2.53107i) q^{63} +9.66228i q^{64} +(-4.79861 - 7.98141i) q^{65} +(-21.2673 + 9.35077i) q^{66} +(-0.439759 - 1.64120i) q^{67} +(15.7278 + 9.08043i) q^{68} +(1.33971 - 12.2015i) q^{69} +(1.61635 + 6.03231i) q^{70} +(0.771888 - 0.206827i) q^{71} +(0.576612 + 13.3773i) q^{72} +(-3.25414 - 3.25414i) q^{73} +(-6.89319 + 3.97979i) q^{74} +(-2.87784 - 0.315985i) q^{75} +(-6.63029 + 1.77658i) q^{76} +(2.77378 + 4.80432i) q^{77} +(-13.7125 + 6.32137i) q^{78} +(-6.50648 + 11.2696i) q^{79} +(2.07205 - 7.73300i) q^{80} +(-0.774428 - 8.96662i) q^{81} +(17.8071 + 10.2809i) q^{82} +(4.57034 - 1.22462i) q^{83} +(6.58416 - 1.01152i) q^{84} +(8.62438 + 8.62438i) q^{85} +(-23.7541 - 6.36490i) q^{86} +(-1.89025 - 4.29917i) q^{87} -24.7601i q^{88} +(4.86179 + 1.30271i) q^{89} +(-4.06524 + 18.2890i) q^{90} +(1.85782 + 3.09007i) q^{91} +(23.6042 + 13.6279i) q^{92} +(14.1498 - 2.17384i) q^{93} +(13.7787 - 23.8653i) q^{94} -4.60995 q^{95} +(2.31202 + 0.899835i) q^{96} +(-15.0373 - 4.02923i) q^{97} +(-0.625784 - 2.33546i) q^{98} +(0.716695 + 16.6272i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 336 q + 24 q^{6} - 36 q^{8}+O(q^{10}) $ 336 * q + 24 * q^6 - 36 * q^8	$ 336 q + 24 q^{6} - 36 q^{8} + 16 q^{15} - 336 q^{16} + 20 q^{18} + 8 q^{21} + 8 q^{24} + 96 q^{26} + 24 q^{27} - 96 q^{30} - 72 q^{32} - 36 q^{33} - 12 q^{36} - 72 q^{38} - 16 q^{39} - 48 q^{41} - 28 q^{45} + 60 q^{47} - 48 q^{48} + 132 q^{50} - 36 q^{52} - 108 q^{54} + 68 q^{57} - 72 q^{58} - 44 q^{60} - 36 q^{62} - 8 q^{63} - 72 q^{65} - 20 q^{66} - 72 q^{69} + 48 q^{71} - 104 q^{72} + 12 q^{74} + 104 q^{78} - 12 q^{79} + 96 q^{80} - 68 q^{81} - 120 q^{83} - 12 q^{84} + 36 q^{85} + 48 q^{86} - 24 q^{87} - 60 q^{89} - 72 q^{92} - 172 q^{93} - 48 q^{94} - 152 q^{96} + 48 q^{97}+O(q^{100}) $ 336 * q + 24 * q^6 - 36 * q^8 + 16 * q^15 - 336 * q^16 + 20 * q^18 + 8 * q^21 + 8 * q^24 + 96 * q^26 + 24 * q^27 - 96 * q^30 - 72 * q^32 - 36 * q^33 - 12 * q^36 - 72 * q^38 - 16 * q^39 - 48 * q^41 - 28 * q^45 + 60 * q^47 - 48 * q^48 + 132 * q^50 - 36 * q^52 - 108 * q^54 + 68 * q^57 - 72 * q^58 - 44 * q^60 - 36 * q^62 - 8 * q^63 - 72 * q^65 - 20 * q^66 - 72 * q^69 + 48 * q^71 - 104 * q^72 + 12 * q^74 + 104 * q^78 - 12 * q^79 + 96 * q^80 - 68 * q^81 - 120 * q^83 - 12 * q^84 + 36 * q^85 + 48 * q^86 - 24 * q^87 - 60 * q^89 - 72 * q^92 - 172 * q^93 - 48 * q^94 - 152 * q^96 + 48 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{12}\right)$	$1$

Coefficient data

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

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

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

$2$	1.70967	+	1.70967i	1.20892	+	1.20892i	0.971377	+	0.237545i	$0.0763426\pi$
$2$	1.70967	+	1.70967i	1.20892	+	1.20892i	0.237545	+	0.971377i	$0.423657\pi$
$3$	1.58556	−	0.697137i	0.915423	−	0.402492i
$3$	1.58556	−	0.697137i	0.915423	−	0.402492i
$4$			3.84596i			1.92298i
$5$	−0.668510	+	2.49492i	−0.298967	+	1.11576i	0.639048	+	0.769166i	$0.279328\pi$
$5$	−0.668510	+	2.49492i	−0.298967	+	1.11576i	−0.938015	+	0.346593i	$0.887338\pi$
$6$	3.90266	+	1.51891i	1.59326	+	0.620094i
$7$	0.258819	−	0.965926i	0.0978244	−	0.365086i
$7$	0.258819	−	0.965926i	0.0978244	−	0.365086i
$8$	−3.15599	+	3.15599i	−1.11581	+	1.11581i
$9$	2.02800	−	2.21070i	0.676000	−	0.736901i
$10$	−5.40842	+	3.12255i	−1.71029	+	0.987438i
$11$	−3.92271	+	3.92271i	−1.18274	+	1.18274i	−0.203711	+	0.979031i	$0.565300\pi$
$11$	−3.92271	+	3.92271i	−1.18274	+	1.18274i	−0.979031	+	0.203711i	$0.934700\pi$
$12$	2.68116	+	6.09800i	0.773985	+	1.76034i
$13$	−2.50393	+	2.59428i	−0.694466	+	0.719525i
$13$	−2.50393	+	2.59428i	−0.694466	+	0.719525i
$14$	2.09391	−	1.20892i	0.559622	−	0.323098i
$15$	0.679334	+	4.42188i	0.175403	+	1.14172i
$16$	−3.09951			−0.774876
$17$	2.36103	−	4.08942i	0.572633	−	0.991830i	−0.423661	−	0.905821i	$-0.639255\pi$
$17$	2.36103	−	4.08942i	0.572633	−	0.991830i	0.996294	−	0.0860093i	$-0.0274115\pi$
$18$	7.24680	−	0.312364i	1.70809	−	0.0736249i
$19$	0.461934	+	1.72396i	0.105975	+	0.395504i	0.998454	−	0.0555850i	$-0.0177024\pi$
$19$	0.461934	+	1.72396i	0.105975	+	0.395504i	−0.892479	+	0.451089i	$0.851036\pi$
$20$	−9.59535	−	2.57107i	−2.14559	−	0.574908i
$21$	−0.263009	−	1.71197i	−0.0573933	−	0.373582i
$22$	−13.4131			−2.85968
$23$	3.54343	−	6.13740i	0.738856	−	1.27974i	−0.214155	−	0.976800i	$-0.568700\pi$
$23$	3.54343	−	6.13740i	0.738856	−	1.27974i	0.953011	−	0.302937i	$-0.0979670\pi$
$24$	−2.80386	+	7.20418i	−0.572335	+	1.47055i
$25$	−1.44757	−	0.835754i	−0.289514	−	0.167151i
$26$	−8.71629	+	0.154470i	−1.70940	+	0.0302941i
$27$	1.67435	−	4.91900i	0.322229	−	0.946662i
$28$	3.71492	+	0.995408i	0.702053	+	0.188115i
$29$		−	2.71145i		−	0.503504i	−0.967792	−	0.251752i	$-0.918993\pi$
$29$		−	2.71145i		−	0.503504i	0.967792	−	0.251752i	$-0.0810067\pi$
$30$	−6.39853	+	8.72141i	−1.16821	+	1.59230i
$31$	7.98361	+	2.13920i	1.43390	+	0.384212i	0.890393	−	0.455193i	$-0.150430\pi$
$31$	7.98361	+	2.13920i	1.43390	+	0.384212i	0.543506	+	0.839405i	$0.317096\pi$
$32$	1.01285	+	1.01285i	0.179047	+	0.179047i
$33$	−3.48503	+	8.95436i	−0.606665	+	1.55875i
$34$	11.0282	−	2.95499i	1.89131	−	0.506776i
$35$	2.23688	+	1.29146i	0.378102	+	0.218297i
$36$	8.50229	+	7.79961i	1.41705	+	1.29994i
$37$	−0.852036	+	3.17984i	−0.140074	+	0.522763i	0.859852	+	0.510544i	$0.170556\pi$
$37$	−0.852036	+	3.17984i	−0.140074	+	0.522763i	−0.999925	+	0.0122185i	$0.996111\pi$
$38$	−2.15765	+	3.73717i	−0.350018	+	0.606249i
$39$	−2.16157	+	5.85898i	−0.346128	+	0.938187i
$40$	−5.76412	−	9.98375i	−0.911387	−	1.57857i
$41$	8.21444	−	2.20105i	1.28288	−	0.343747i	0.447928	−	0.894069i	$-0.352162\pi$
$41$	8.21444	−	2.20105i	1.28288	−	0.343747i	0.834952	+	0.550323i	$0.185495\pi$
$42$	2.47724	−	3.37656i	0.382247	−	0.521015i
$43$	−8.80842	+	5.08554i	−1.34327	+	0.775538i	−0.987286	−	0.158953i	$-0.949188\pi$
$43$	−8.80842	+	5.08554i	−1.34327	+	0.775538i	−0.355986	+	0.934491i	$0.615855\pi$
$44$	−15.0866	−	15.0866i	−2.27439	−	2.27439i
$45$	4.15978	+	6.53757i	0.620103	+	0.974563i
$46$	16.5511	−	4.43484i	2.44032	−	0.653882i
$47$	−2.94989	−	11.0091i	−0.430285	−	1.60585i	−0.752104	−	0.659045i	$-0.770961\pi$
$47$	−2.94989	−	11.0091i	−0.430285	−	1.60585i	0.321818	−	0.946801i	$-0.395706\pi$
$48$	−4.91445	+	2.16078i	−0.709340	+	0.311882i
$49$	−0.866025	−	0.500000i	−0.123718	−	0.0714286i
$50$	−1.04600	−	3.90373i	−0.147927	−	0.552071i
$51$	0.892666	−	8.12998i	0.124998	−	1.13843i
$52$	−9.97752	−	9.63004i	−1.38363	−	1.33545i
$53$		−	0.0631920i		−	0.00868009i	−0.999991	−	0.00434004i	$-0.998619\pi$
$53$		−	0.0631920i		−	0.00868009i	0.999991	−	0.00434004i	$-0.00138148\pi$
$54$	11.2725	−	5.54728i	1.53399	−	0.754889i
$55$	−7.16446	−	12.4092i	−0.966055	−	1.67326i
$56$	2.23162	+	3.86529i	0.298213	+	0.516521i
$57$	1.93426	+	2.41141i	0.256199	+	0.319399i
$58$	4.63570	−	4.63570i	0.608697	−	0.608697i
$59$	5.08824	−	5.08824i	0.662432	−	0.662432i	−0.293520	−	0.955953i	$-0.594827\pi$
$59$	5.08824	−	5.08824i	0.662432	−	0.662432i	0.955953	+	0.293520i	$0.0948269\pi$
$60$	−17.0064	+	2.61269i	−2.19552	+	0.337297i
$61$	−4.38239	−	7.59052i	−0.561107	−	0.971866i	−0.997400	−	0.0720617i	$-0.977042\pi$
$61$	−4.38239	−	7.59052i	−0.561107	−	0.971866i	0.436293	−	0.899805i	$-0.356291\pi$
$62$	9.99203	+	17.3067i	1.26899	+	2.19795i
$63$	−1.61049	−	2.53107i	−0.202903	−	0.318885i
$64$			9.66228i			1.20778i
$65$	−4.79861	−	7.98141i	−0.595195	−	0.989972i
$66$	−21.2673	+	9.35077i	−2.61782	+	1.15100i
$67$	−0.439759	−	1.64120i	−0.0537251	−	0.200505i	0.933847	−	0.357674i	$-0.116430\pi$
$67$	−0.439759	−	1.64120i	−0.0537251	−	0.200505i	−0.987572	+	0.157169i	$0.949763\pi$
$68$	15.7278	+	9.08043i	1.90727	+	1.10116i
$69$	1.33971	−	12.2015i	0.161282	−	1.46888i
$70$	1.61635	+	6.03231i	0.193191	+	0.720999i
$71$	0.771888	−	0.206827i	0.0916062	−	0.0245458i	−0.212725	−	0.977112i	$-0.568234\pi$
$71$	0.771888	−	0.206827i	0.0916062	−	0.0245458i	0.304331	+	0.952566i	$0.401567\pi$
$72$	0.576612	+	13.3773i	0.0679544	+	1.57653i
$73$	−3.25414	−	3.25414i	−0.380869	−	0.380869i	0.490546	−	0.871415i	$-0.336797\pi$
$73$	−3.25414	−	3.25414i	−0.380869	−	0.380869i	−0.871415	+	0.490546i	$0.836797\pi$
$74$	−6.89319	+	3.97979i	−0.801317	+	0.462641i
$75$	−2.87784	−	0.315985i	−0.332304	−	0.0364868i
$76$	−6.63029	+	1.77658i	−0.760547	+	0.203788i
$77$	2.77378	+	4.80432i	0.316101	+	0.547503i
$78$	−13.7125	+	6.32137i	−1.55264	+	0.715754i
$79$	−6.50648	+	11.2696i	−0.732036	+	1.26792i	0.223975	+	0.974595i	$0.428096\pi$
$79$	−6.50648	+	11.2696i	−0.732036	+	1.26792i	−0.956012	+	0.293329i	$0.905237\pi$
$80$	2.07205	−	7.73300i	0.231662	−	0.864576i
$81$	−0.774428	−	8.96662i	−0.0860475	−	0.996291i
$82$	17.8071	+	10.2809i	1.96646	+	1.13534i
$83$	4.57034	−	1.22462i	0.501660	−	0.134419i	0.000889686	−	1.00000i	$-0.499717\pi$
$83$	4.57034	−	1.22462i	0.501660	−	0.134419i	0.500770	+	0.865580i	$0.333050\pi$
$84$	6.58416	−	1.01152i	0.718390	−	0.110366i
$85$	8.62438	+	8.62438i	0.935446	+	0.935446i
$86$	−23.7541	−	6.36490i	−2.56147	−	0.686345i
$87$	−1.89025	−	4.29917i	−0.202656	−	0.460919i
$88$		−	24.7601i		−	2.63944i
$89$	4.86179	+	1.30271i	0.515348	+	0.138087i	0.507114	−	0.861879i	$-0.330712\pi$
$89$	4.86179	+	1.30271i	0.515348	+	0.138087i	0.00823419	+	0.999966i	$0.497379\pi$
$90$	−4.06524	+	18.2890i	−0.428514	+	1.92783i
$91$	1.85782	+	3.09007i	0.194753	+	0.323927i
$92$	23.6042	+	13.6279i	2.46091	+	1.42081i
$93$	14.1498	−	2.17384i	1.46727	−	0.225416i
$94$	13.7787	−	23.8653i	1.42116	−	2.46152i
$95$	−4.60995			−0.472970
$96$	2.31202	+	0.899835i	0.235969	+	0.0918390i
$97$	−15.0373	−	4.02923i	−1.52681	−	0.409107i	−0.604831	−	0.796354i	$-0.706759\pi$
$97$	−15.0373	−	4.02923i	−1.52681	−	0.409107i	−0.921976	+	0.387248i	$0.873426\pi$
$98$	−0.625784	−	2.33546i	−0.0632137	−	0.235917i
$99$	0.716695	+	16.6272i	0.0720305	+	1.67110i
$100$	3.21428	−	5.56729i	0.321428	−	0.556729i
$101$	6.70262			0.666935			0.333468	−	0.942762i	$-0.391781\pi$
$101$	6.70262			0.666935			0.333468	+	0.942762i	$0.391781\pi$
$102$	15.4258	−	12.3734i	1.52738	−	1.22515i
$103$	1.40114	−	0.808947i	0.138058	−	0.0797080i	−0.429380	−	0.903124i	$-0.641268\pi$
$103$	1.40114	−	0.808947i	0.138058	−	0.0797080i	0.567438	+	0.823416i	$0.307935\pi$
$104$	−0.285146	−	16.0899i	−0.0279609	−	1.57775i
$105$	4.44703	+	0.488281i	0.433986	+	0.0476513i
$106$	0.108038	−	0.108038i	0.0104935	−	0.0104935i
$107$	−8.15420	+	4.70783i	−0.788297	+	0.455123i	−0.839363	−	0.543572i	$-0.817071\pi$
$107$	−8.15420	+	4.70783i	−0.788297	+	0.455123i	0.0510658	+	0.998695i	$0.483738\pi$
$108$	18.9183	+	6.43950i	1.82041	+	0.619641i
$109$	−8.81832	+	8.81832i	−0.844642	+	0.844642i	−0.989459	−	0.144817i	$-0.953741\pi$
$109$	−8.81832	+	8.81832i	−0.844642	+	0.844642i	0.144817	+	0.989459i	$0.453741\pi$
$110$	8.96680	−	33.4646i	0.854951	−	3.19072i
$111$	0.865830	+	5.63581i	0.0821810	+	0.534928i
$112$	−0.802211	+	2.99389i	−0.0758018	+	0.282896i
$113$		−	12.2936i		−	1.15649i	−0.815865	−	0.578243i	$-0.803739\pi$
$113$		−	12.2936i		−	1.15649i	0.815865	−	0.578243i	$-0.196261\pi$
$114$	−0.815774	+	7.42968i	−0.0764042	+	0.695854i
$115$	12.9435	+	12.9435i	1.20698	+	1.20698i
$116$	10.4281			0.968229
$117$	0.657217	+	10.7967i	0.0607597	+	0.998152i
$118$	17.3985			1.60166
$119$	−3.33900	−	3.33900i	−0.306085	−	0.306085i
$120$	−16.0994	−	11.8115i	−1.46967	−	1.07823i
$121$		−	19.7753i		−	1.79776i
$122$	5.48485	−	20.4698i	0.496575	−	1.85324i
$123$	11.4901	−	9.21649i	1.03602	−	0.831023i
$124$	−8.22729	+	30.7047i	−0.738833	+	2.75736i
$125$	−6.07917	+	6.07917i	−0.543738	+	0.543738i
$126$	1.57389	−	7.08072i	0.140213	−	0.630800i
$127$	−9.39196	+	5.42245i	−0.833402	+	0.481165i	−0.855016	−	0.518602i	$-0.826453\pi$
$127$	−9.39196	+	5.42245i	−0.833402	+	0.481165i	0.0216141	+	0.999766i	$0.493119\pi$
$128$	−14.4936	+	14.4936i	−1.28107	+	1.28107i
$129$	−10.4210	+	14.2041i	−0.917514	+	1.25060i
$130$	5.44154	−	21.8497i	0.477255	−	1.91634i
$131$	8.41117	−	4.85619i	0.734888	−	0.424288i	−0.0853199	−	0.996354i	$-0.527191\pi$
$131$	8.41117	−	4.85619i	0.734888	−	0.424288i	0.820208	+	0.572066i	$0.193858\pi$
$132$	−34.4381	−	13.4033i	−2.99746	−	1.16661i
$133$	1.78478			0.154760
$134$	2.05407	−	3.55776i	0.177445	−	0.307344i
$135$	11.1532	+	7.46577i	0.959911	+	0.642551i
$136$	5.45479	+	20.3576i	0.467745	+	1.74565i
$137$	−2.57876	−	0.690978i	−0.220319	−	0.0590342i	0.146971	−	0.989141i	$-0.453048\pi$
$137$	−2.57876	−	0.690978i	−0.220319	−	0.0590342i	−0.367290	+	0.930107i	$0.619714\pi$
$138$	23.1510	−	18.5701i	1.97074	−	1.58079i
$139$	−0.439319			−0.0372626			−0.0186313	−	0.999826i	$-0.505931\pi$
$139$	−0.439319			−0.0372626			−0.0186313	+	0.999826i	$0.505931\pi$
$140$	−4.96692	+	8.60296i	−0.419781	+	0.727083i
$141$	−12.3521	−	15.3992i	−1.04023	−	1.29684i
$142$	1.67328	+	0.966070i	0.140419	+	0.0810708i
$143$	−0.354419	−	19.9988i	−0.0296380	−	1.67239i
$144$	−6.28580	+	6.85209i	−0.523817	+	0.571008i
$145$	6.76484	+	1.81263i	0.561790	+	0.150531i
$146$		−	11.1270i		−	0.920881i
$147$	−1.72170	−	0.189042i	−0.142004	−	0.0155919i
$148$	−12.2296	−	3.27690i	−1.00526	−	0.269359i
$149$	−6.58548	−	6.58548i	−0.539504	−	0.539504i	0.383880	−	0.923383i	$-0.374588\pi$
$149$	−6.58548	−	6.58548i	−0.539504	−	0.539504i	−0.923383	+	0.383880i	$0.874588\pi$
$150$	−4.37993	−	5.46040i	−0.357620	−	0.445839i
$151$	13.1089	−	3.51253i	1.06679	−	0.285845i	0.317616	−	0.948219i	$-0.397118\pi$
$151$	13.1089	−	3.51253i	1.06679	−	0.285845i	0.749173	+	0.662374i	$0.230451\pi$
$152$	−6.89867	−	3.98295i	−0.559556	−	0.323060i
$153$	−4.25233	−	13.5129i	−0.343781	−	1.09245i
$154$	−3.47157	+	12.9561i	−0.279747	+	1.04403i
$155$	−10.6743	+	18.4884i	−0.857377	+	1.48502i
$156$	−22.5334	−	8.31330i	−1.80412	−	0.665597i
$157$	8.02382	+	13.8977i	0.640370	+	1.10915i	0.985350	+	0.170544i	$0.0545524\pi$
$157$	8.02382	+	13.8977i	0.640370	+	1.10915i	−0.344980	+	0.938610i	$0.612114\pi$
$158$	−30.3912	+	8.14330i	−2.41779	+	0.647846i
$159$	−0.0440535	−	0.100195i	−0.00349367	−	0.00794596i
$160$	−3.20406	+	1.84987i	−0.253303	+	0.146245i
$161$	−5.01117	−	5.01117i	−0.394935	−	0.394935i
$162$	14.0060	−	16.6540i	1.10041	−	1.30846i
$163$	12.6010	−	3.37642i	0.986983	−	0.264461i	0.271000	−	0.962579i	$-0.412646\pi$
$163$	12.6010	−	3.37642i	0.986983	−	0.264461i	0.715983	+	0.698118i	$0.245979\pi$
$164$	8.46517	+	31.5924i	0.661019	+	2.46696i
$165$	−20.0106	−	14.6809i	−1.55782	−	1.14291i
$166$	9.90748	+	5.72009i	0.768970	+	0.443965i
$167$	5.53831	+	20.6693i	0.428568	+	1.59944i	0.756007	+	0.654564i	$0.227148\pi$
$167$	5.53831	+	20.6693i	0.428568	+	1.59944i	−0.327439	+	0.944872i	$0.606186\pi$
$168$	6.23301	+	4.57290i	0.480887	+	0.352807i
$169$	−0.460627	−	12.9918i	−0.0354329	−	0.999372i
$170$			29.4898i			2.26176i
$171$	4.74797	+	2.47500i	0.363087	+	0.189268i
$172$	−19.5588	−	33.8769i	−1.49135	−	2.58309i
$173$	−0.119541	−	0.207051i	−0.00908852	−	0.0157418i	0.861445	−	0.507850i	$-0.169560\pi$
$173$	−0.119541	−	0.207051i	−0.00908852	−	0.0157418i	−0.870534	+	0.492108i	$0.836226\pi$
$174$	4.11846	−	10.5819i	0.312220	−	0.802211i
$175$	−1.18193	+	1.18193i	−0.0893458	+	0.0893458i
$176$	12.1585	−	12.1585i	0.916479	−	0.916479i
$177$	4.52051	−	11.6149i	0.339782	−	0.873030i
$178$	6.08485	+	10.5393i	0.456079	+	0.789952i
$179$	−5.76615	−	9.98727i	−0.430983	−	0.746484i	0.565976	−	0.824422i	$-0.308500\pi$
$179$	−5.76615	−	9.98727i	−0.430983	−	0.746484i	−0.996958	+	0.0779383i	$0.975166\pi$
$180$	−25.1432	+	15.9984i	−1.87407	+	1.19245i
$181$		−	8.60343i		−	0.639488i	−0.947504	−	0.319744i	$-0.896403\pi$
$181$		−	8.60343i		−	0.639488i	0.947504	−	0.319744i	$-0.103597\pi$
$182$	−2.10673	+	8.45927i	−0.156162	+	0.627043i
$183$	−12.2402	−	8.98010i	−0.904819	−	0.663828i
$184$	8.18655	+	30.5526i	0.603521	+	2.25237i
$185$	−7.36384	−	4.25151i	−0.541400	−	0.312578i
$186$	27.9081	+	20.4750i	2.04632	+	1.50130i
$187$	6.77998	+	25.3032i	0.495802	+	1.85036i
$188$	42.3407	−	11.3452i	3.08801	−	0.827430i
$189$	−4.31803	−	2.89043i	−0.314091	−	0.210248i
$190$	−7.88150	−	7.88150i	−0.571784	−	0.571784i
$191$	11.2666	−	6.50478i	0.815223	−	0.470669i	−0.0335436	−	0.999437i	$-0.510679\pi$
$191$	11.2666	−	6.50478i	0.815223	−	0.470669i	0.848766	+	0.528768i	$0.177346\pi$
$192$	6.73593	+	15.3201i	0.486124	+	1.10563i
$193$	−17.6426	+	4.72733i	−1.26994	+	0.340280i	−0.830009	−	0.557749i	$-0.811665\pi$
$193$	−17.6426	+	4.72733i	−1.26994	+	0.340280i	−0.439935	+	0.898030i	$0.644998\pi$
$194$	−18.8202	−	32.5975i	−1.35121	−	2.34037i
$195$	−13.1726	−	9.30971i	−0.943311	−	0.666682i
$196$	1.92298	−	3.33070i	0.137356	−	0.237907i
$197$	−0.215919	+	0.805820i	−0.0153836	+	0.0574123i	−0.973191	−	0.229999i	$-0.926128\pi$
$197$	−0.215919	+	0.805820i	−0.0153836	+	0.0574123i	0.957807	+	0.287411i	$0.0927945\pi$
$198$	−27.2018	+	29.6524i	−1.93315	+	2.10731i
$199$	10.5188	+	6.07304i	0.745659	+	0.430507i	0.824123	−	0.566410i	$-0.191668\pi$
$199$	10.5188	+	6.07304i	0.745659	+	0.430507i	−0.0784640	+	0.996917i	$0.525002\pi$
$200$	7.20615	−	1.93088i	0.509552	−	0.136534i
$201$	−1.84141	−	2.29565i	−0.129883	−	0.161923i
$202$	11.4593	+	11.4593i	0.806272	+	0.806272i
$203$	−2.61906	−	0.701776i	−0.183822	−	0.0492550i
$204$	31.2676	+	3.43316i	2.18917	+	0.240369i
$205$			21.9658i			1.53416i
$206$	3.77852	+	1.01245i	0.263262	+	0.0705409i
$207$	−6.38190	−	20.2801i	−0.443573	−	1.40957i
$208$	7.76096	−	8.04100i	0.538126	−	0.557543i
$209$	−8.57464	−	4.95057i	−0.593120	−	0.342438i
$210$	6.76817	+	8.43777i	0.467048	+	0.582262i
$211$	1.18384	−	2.05048i	0.0814991	−	0.141161i	−0.822395	−	0.568917i	$-0.807363\pi$
$211$	1.18384	−	2.05048i	0.0814991	−	0.141161i	0.903894	+	0.427756i	$0.140696\pi$
$212$	0.243034			0.0166916
$213$	1.07969	−	0.866048i	0.0739790	−	0.0593406i
$214$	−21.9899	−	5.89217i	−1.50320	−	0.402780i
$215$	−6.79948	−	25.3760i	−0.463721	−	1.73063i
$216$	10.2401	+	20.8086i	0.696749	+	1.41584i
$217$	4.13262	−	7.15791i	0.280541	−	0.485911i
$218$	−30.1529			−2.04221
$219$	−7.42822	−	2.89106i	−0.501953	−	0.195360i
$220$	47.7253	−	27.5542i	3.21764	−	1.85771i
$221$	4.69726	+	16.3648i	0.315972	+	1.10082i
$222$	−8.15511	+	11.1157i	−0.547335	+	0.746036i
$223$	−19.4269	+	19.4269i	−1.30092	+	1.30092i	−0.373155	+	0.927769i	$0.621724\pi$
$223$	−19.4269	+	19.4269i	−1.30092	+	1.30092i	−0.927769	+	0.373155i	$0.878276\pi$
$224$	1.24048	−	0.716190i	0.0828829	−	0.0478524i
$225$	−4.78327	+	1.50524i	−0.318885	+	0.100349i
$226$	21.0181	−	21.0181i	1.39810	−	1.39810i
$227$	0.991462	−	3.70019i	0.0658056	−	0.245590i	−0.925186	−	0.379514i	$-0.876091\pi$
$227$	0.991462	−	3.70019i	0.0658056	−	0.245590i	0.990992	+	0.133924i	$0.0427578\pi$
$228$	−9.27421	+	7.43910i	−0.614199	+	0.492666i
$229$	1.06394	−	3.97069i	0.0703073	−	0.262391i	−0.921821	−	0.387616i	$-0.873299\pi$
$229$	1.06394	−	3.97069i	0.0703073	−	0.262391i	0.992128	+	0.125225i	$0.0399654\pi$
$230$			44.2582i			2.91830i
$231$	7.74726	+	5.68384i	0.509732	+	0.373969i
$232$	8.55733	+	8.55733i	0.561816	+	0.561816i
$233$	−13.6212			−0.892353			−0.446177	−	0.894945i	$-0.647215\pi$
$233$	−13.6212			−0.892353			−0.446177	+	0.894945i	$0.647215\pi$
$234$	−17.3351	+	19.5824i	−1.13323	+	1.28014i
$235$	29.4389			1.92038
$236$	19.5692	+	19.5692i	1.27385	+	1.27385i
$237$	−2.45999	+	22.4045i	−0.159794	+	1.45533i
$238$		−	11.4172i		−	0.740066i
$239$	−6.56826	+	24.5131i	−0.424865	+	1.58562i	0.339351	+	0.940660i	$0.389793\pi$
$239$	−6.56826	+	24.5131i	−0.424865	+	1.58562i	−0.764217	+	0.644960i	$0.776874\pi$
$240$	−2.10560	−	13.7056i	−0.135916	−	0.884695i
$241$	5.27081	−	19.6709i	0.339523	−	1.26712i	−0.559359	−	0.828926i	$-0.688953\pi$
$241$	5.27081	−	19.6709i	0.339523	−	1.26712i	0.898882	−	0.438191i	$-0.144381\pi$
$242$	33.8093	−	33.8093i	2.17335	−	2.17335i
$243$	−7.47886	−	13.6772i	−0.479769	−	0.877395i
$244$	29.1929	−	16.8545i	1.86888	−	1.07900i
$245$	1.82640	−	1.82640i	0.116685	−	0.116685i
$246$	35.4014	+	3.88705i	2.25711	+	0.247829i
$247$	−5.62910	−	3.11830i	−0.358171	−	0.198413i
$248$	−31.9475	+	18.4449i	−2.02867	+	1.17125i
$249$	6.39282	−	5.12786i	0.405129	−	0.324965i
$250$	−20.7868			−1.31467
$251$	0.241681	−	0.418603i	0.0152547	−	0.0264220i	−0.858297	−	0.513153i	$-0.828477\pi$
$251$	0.241681	−	0.418603i	0.0152547	−	0.0264220i	0.873552	+	0.486731i	$0.161811\pi$
$252$	9.73440	−	6.19389i	0.613210	−	0.390178i
$253$	10.1754	+	37.9751i	0.639722	+	2.38747i
$254$	−25.3278	−	6.78656i	−1.58921	−	0.425827i
$255$	19.6869	+	7.66210i	1.23284	+	0.479819i
$256$	−30.2342			−1.88964
$257$	−1.12823	+	1.95416i	−0.0703774	+	0.121897i	−0.899067	−	0.437812i	$-0.855754\pi$
$257$	−1.12823	+	1.95416i	−0.0703774	+	0.121897i	0.828689	+	0.559709i	$0.189087\pi$
$258$	−42.1008	+	6.46795i	−2.62108	+	0.402677i
$259$	2.85097	+	1.64601i	0.177150	+	0.102278i
$260$	30.6962	−	18.4553i	1.90370	−	1.14455i
$261$	−5.99422	−	5.49883i	−0.371033	−	0.340369i
$262$	22.6829	+	6.07785i	1.40135	+	0.375491i
$263$			7.63398i			0.470732i	0.971907	+	0.235366i	$0.0756288\pi$
$263$			7.63398i			0.470732i	−0.971907	+	0.235366i	$0.924371\pi$
$264$	−17.2612	−	39.2586i	−1.06235	−	2.41620i
$265$	0.157659	+	0.0422445i	0.00968489	+	0.00259506i
$266$	3.05138	+	3.05138i	0.187092	+	0.187092i
$267$	8.61682	−	1.32380i	0.527341	−	0.0810154i
$268$	6.31200	−	1.69130i	0.385567	−	0.103312i
$269$	−9.04085	−	5.21974i	−0.551230	−	0.318253i	0.198388	−	0.980124i	$-0.436429\pi$
$269$	−9.04085	−	5.21974i	−0.551230	−	0.318253i	−0.749618	+	0.661871i	$0.769763\pi$
$270$	6.30423	+	31.8323i	0.383663	+	1.93725i
$271$	7.97389	−	29.7590i	0.484379	−	1.80773i	−0.0984599	−	0.995141i	$-0.531392\pi$
$271$	7.97389	−	29.7590i	0.484379	−	1.80773i	0.582839	−	0.812587i	$-0.301942\pi$
$272$	−7.31802	+	12.6752i	−0.443720	+	0.768546i
$273$	5.09988	+	3.60433i	0.308659	+	0.218144i
$274$	−3.22750	−	5.59019i	−0.194980	−	0.337716i
$275$	8.95681	−	2.39997i	0.540116	−	0.144724i
$276$	46.9264	+	5.15248i	2.82464	+	0.310143i
$277$	−6.09850	+	3.52097i	−0.366423	+	0.211555i	−0.671895	−	0.740647i	$-0.734519\pi$
$277$	−6.09850	+	3.52097i	−0.366423	+	0.211555i	0.305471	+	0.952201i	$0.401186\pi$
$278$	−0.751092	−	0.751092i	−0.0450475	−	0.0450475i
$279$	20.9199	−	13.3111i	1.25244	−	0.796915i
$280$	−11.1354	+	2.98373i	−0.665469	+	0.178312i
$281$	−0.777723	−	2.90250i	−0.0463951	−	0.173149i	0.938841	−	0.344352i	$-0.111901\pi$
$281$	−0.777723	−	2.90250i	−0.0463951	−	0.173149i	−0.985236	+	0.171203i	$0.945235\pi$
$282$	5.20949	−	47.4456i	0.310220	−	2.82534i
$283$	−10.3335	−	5.96603i	−0.614261	−	0.354644i	0.160370	−	0.987057i	$-0.448731\pi$
$283$	−10.3335	−	5.96603i	−0.614261	−	0.354644i	−0.774631	+	0.632413i	$0.782064\pi$
$284$	0.795448	+	2.96865i	0.0472012	+	0.176157i
$285$	−7.30935	+	3.21376i	−0.432968	+	0.190367i
$286$	33.5855	−	34.7974i	1.98595	−	2.05761i
$287$		−	8.50422i		−	0.501988i
$288$	4.29315	−	0.185051i	0.252976	−	0.0109042i
$289$	−2.64891	−	4.58804i	−0.155818	−	0.269885i
$290$	8.46666	+	14.6647i	0.497179	+	0.861140i
$291$	−26.6515	+	4.09447i	−1.56234	+	0.240022i
$292$	12.5153	−	12.5153i	0.732404	−	0.732404i
$293$	−10.1104	+	10.1104i	−0.590653	+	0.590653i	−0.937808	−	0.347155i	$-0.887148\pi$
$293$	−10.1104	+	10.1104i	−0.590653	+	0.590653i	0.347155	+	0.937808i	$0.387148\pi$
$294$	−2.62035	−	3.26675i	−0.152822	−	0.190521i
$295$	9.29318	+	16.0963i	0.541070	+	0.937161i
$296$	−7.34654	−	12.7246i	−0.427009	−	0.739601i
$297$	12.7278	+	25.8638i	0.738542	+	1.50077i
$298$		−	22.5180i		−	1.30443i
$299$	7.04965	+	24.5603i	0.407692	+	1.42036i
$300$	1.21527	−	11.0681i	0.0701634	−	0.639015i
$301$	2.63247	+	9.82452i	0.151733	+	0.566276i
$302$	28.4172	+	16.4067i	1.63523	+	0.944100i
$303$	10.6274	−	4.67264i	0.610528	−	0.268436i
$304$	−1.43177	−	5.34343i	−0.0821175	−	0.306467i
$305$	21.8674	−	5.85935i	1.25212	−	0.335505i
$306$	15.8325	−	30.3727i	0.905084	−	1.73629i
$307$	4.85761	+	4.85761i	0.277238	+	0.277238i	0.832006	−	0.554767i	$-0.187193\pi$
$307$	4.85761	+	4.85761i	0.277238	+	0.277238i	−0.554767	+	0.832006i	$0.687193\pi$
$308$	−18.4772	+	10.6678i	−1.05284	+	0.607857i
$309$	1.65764	−	2.25942i	0.0942999	−	0.128534i
$310$	−49.8585	+	13.3596i	−2.83177	+	0.758772i
$311$	8.53063	+	14.7755i	0.483728	+	0.837841i	0.999825	−	0.0186886i	$-0.00594911\pi$
$311$	8.53063	+	14.7755i	0.483728	+	0.837841i	−0.516097	+	0.856530i	$0.672616\pi$
$312$	−11.6690	−	25.3128i	−0.660627	−	1.43305i
$313$	−5.87481	+	10.1755i	−0.332064	+	0.575151i	−0.982916	−	0.184053i	$-0.941078\pi$
$313$	−5.87481	+	10.1755i	−0.332064	+	0.575151i	0.650853	+	0.759204i	$0.274412\pi$
$314$	−10.0423	+	37.4785i	−0.566722	+	2.11504i
$315$	7.39144	−	2.32599i	0.416460	−	0.131055i
$316$	−43.3423	−	25.0237i	−2.43819	−	1.40769i
$317$	−23.1311	+	6.19796i	−1.29917	+	0.348112i	−0.841137	−	0.540822i	$-0.818113\pi$
$317$	−23.1311	+	6.19796i	−1.29917	+	0.348112i	−0.458035	+	0.888934i	$0.651447\pi$
$318$	0.0959831	−	0.246617i	0.00538247	−	0.0138296i
$319$	10.6362	+	10.6362i	0.595515	+	0.595515i
$320$	−24.1066	−	6.45933i	−1.34760	−	0.361088i
$321$	−9.64698	+	13.1491i	−0.538442	+	0.733914i
$322$		−	17.1349i		−	0.954891i
$323$	8.14064	+	2.18128i	0.452958	+	0.121370i
$324$	34.4853	−	2.97842i	1.91585	−	0.165468i
$325$	5.79280	−	1.66273i	0.321327	−	0.0922317i
$326$	27.3161	+	15.7709i	1.51290	+	0.873472i
$327$	−7.83440	+	20.1296i	−0.433243	+	1.11317i
$328$	−18.9782	+	32.8712i	−1.04790	+	1.81501i
$329$	−11.3975			−0.628364
$330$	−9.11198	−	59.3112i	−0.501598	−	3.26497i
$331$	−2.87850	−	0.771292i	−0.158217	−	0.0423940i	0.178841	−	0.983878i	$-0.442765\pi$
$331$	−2.87850	−	0.771292i	−0.158217	−	0.0423940i	−0.337058	+	0.941484i	$0.609432\pi$
$332$	4.70984	+	17.5774i	0.258486	+	0.964683i
$333$	5.30176	+	8.33232i	0.290535	+	0.456608i
$334$	−25.8690	+	44.8064i	−1.41549	+	2.45170i
$335$	4.38864			0.239777
$336$	0.815199	+	5.30625i	0.0444728	+	0.289479i
$337$	16.8733	−	9.74181i	0.919148	−	0.530670i	0.0357848	−	0.999360i	$-0.488607\pi$
$337$	16.8733	−	9.74181i	0.919148	−	0.530670i	0.883363	+	0.468689i	$0.155274\pi$
$338$	21.4243	−	22.9993i	1.16533	−	1.25100i
$339$	−8.57033	−	19.4923i	−0.465476	−	1.05867i
$340$	−33.1691	+	33.1691i	−1.79885	+	1.79885i
$341$	−39.7089	+	22.9259i	−2.15036	+	1.24151i
$342$	3.88605	+	12.3489i	0.210133	+	0.667753i
$343$	−0.707107	+	0.707107i	−0.0381802	+	0.0381802i
$344$	11.7494	−	43.8493i	0.633484	−	2.36419i
$345$	29.5460	+	11.4993i	1.59070	+	0.619100i
$346$	0.149613	−	0.558365i	0.00804327	−	0.0300179i
$347$			16.8386i			0.903944i	0.892032	+	0.451972i	$0.149279\pi$
$347$			16.8386i			0.903944i	−0.892032	+	0.451972i	$0.850721\pi$
$348$	16.5345	−	7.26985i	0.886340	−	0.389705i
$349$	−11.3048	−	11.3048i	−0.605133	−	0.605133i	0.336537	−	0.941670i	$-0.390744\pi$
$349$	−11.3048	−	11.3048i	−0.605133	−	0.605133i	−0.941670	+	0.336537i	$0.890744\pi$
$350$	−4.04144			−0.216024
$351$	8.56881	+	16.6606i	0.457369	+	0.889277i
$352$	−7.94620			−0.423534
$353$	−18.7895	−	18.7895i	−1.00006	−	1.00006i	−1.00000		6.15844e-5i	$-0.999980\pi$
$353$	−18.7895	−	18.7895i	−1.00006	−	1.00006i	−6.15844e−5	−	1.00000i	$-0.500020\pi$
$354$	27.5863	−	12.1291i	1.46619	−	0.644654i
$355$			2.06406i			0.109549i
$356$	−5.01018	+	18.6982i	−0.265539	+	0.991005i
$357$	−7.62192	−	2.96644i	−0.403395	−	0.157001i
$358$	7.21673	−	26.9332i	0.381416	−	1.42346i
$359$	−7.80400	+	7.80400i	−0.411879	+	0.411879i	−0.882393	−	0.470513i	$-0.844069\pi$
$359$	−7.80400	+	7.80400i	−0.411879	+	0.411879i	0.470513	+	0.882393i	$0.344069\pi$
$360$	−33.7608	−	7.50428i	−1.77935	−	0.395510i
$361$	13.6958	−	7.90729i	0.720833	−	0.416173i
$362$	14.7090	−	14.7090i	0.773090	−	0.773090i
$363$	−13.7861	−	31.3550i	−0.723583	−	1.64571i
$364$	−11.8843	+	7.14511i	−0.622905	+	0.374506i
$365$	10.2942	−	5.94338i	0.538825	−	0.311091i
$366$	−5.57366	−	36.2797i	−0.291340	−	1.89637i
$367$	−15.0520			−0.785707			−0.392854	−	0.919601i	$-0.628512\pi$
$367$	−15.0520			−0.785707			−0.392854	+	0.919601i	$0.628512\pi$
$368$	−10.9829	+	19.0229i	−0.572522	+	0.991638i
$369$	11.7930	−	22.6234i	0.613920	−	1.17773i
$370$	−5.32106	−	19.8585i	−0.276629	−	1.03239i
$371$	−0.0610388	−	0.0163553i	−0.00316898	−	0.000849124i
$372$	8.36049	+	54.4197i	0.433471	+	2.82153i
$373$	28.2309			1.46174			0.730871	−	0.682516i	$-0.239114\pi$
$373$	28.2309			1.46174			0.730871	+	0.682516i	$0.239114\pi$
$374$	−31.6687	+	54.8518i	−1.63755	+	2.83632i
$375$	−5.40088	+	13.8769i	−0.278900	+	0.716601i
$376$	44.0545	+	25.4349i	2.27194	+	1.31171i
$377$	7.03428	+	6.78930i	0.362284	+	0.349667i
$378$	−2.44073	−	12.3241i	−0.125538	−	0.633884i
$379$	−20.6867	−	5.54297i	−1.06260	−	0.284723i	−0.315152	−	0.949041i	$-0.602055\pi$
$379$	−20.6867	−	5.54297i	−1.06260	−	0.284723i	−0.747450	+	0.664318i	$0.768722\pi$
$380$		−	17.7297i		−	0.909513i
$381$	−11.1113	+	15.1451i	−0.569251	+	0.775907i
$382$	30.3832	+	8.14117i	1.55454	+	0.416538i
$383$	3.13534	+	3.13534i	0.160208	+	0.160208i	0.782659	−	0.622451i	$-0.213863\pi$
$383$	3.13534	+	3.13534i	0.160208	+	0.160208i	−0.622451	+	0.782659i	$0.713863\pi$
$384$	−12.8765	+	33.0846i	−0.657101	+	1.68834i
$385$	−13.8407	+	3.70860i	−0.705386	+	0.189008i
$386$	−38.2453	−	22.0809i	−1.94663	−	1.12389i
$387$	−6.62085	+	29.7863i	−0.336557	+	1.51412i
$388$	15.4963	−	57.8329i	0.786704	−	2.93602i
$389$	−1.29031	+	2.23488i	−0.0654212	+	0.113313i	−0.896881	−	0.442272i	$-0.854172\pi$
$389$	−1.29031	+	2.23488i	−0.0654212	+	0.113313i	0.831460	+	0.555585i	$0.187506\pi$
$390$	−6.60432	−	38.4374i	−0.334423	−	1.94636i
$391$	−16.7323	−	28.9811i	−0.846187	−	1.46564i
$392$	4.31117	−	1.15517i	0.217747	−	0.0583451i
$393$	9.95099	−	13.5635i	0.501961	−	0.684189i
$394$	−1.74684	+	1.00854i	−0.0880045	+	0.0508094i
$395$	−23.7669	−	23.7669i	−1.19584	−	1.19584i
$396$	−63.9477	+	2.75638i	−3.21349	+	0.138513i
$397$	18.3262	−	4.91049i	0.919765	−	0.246450i	0.232280	−	0.972649i	$-0.425381\pi$
$397$	18.3262	−	4.91049i	0.919765	−	0.246450i	0.687485	+	0.726199i	$0.258715\pi$
$398$	7.60082	+	28.3667i	0.380995	+	1.42189i
$399$	2.82987	−	1.24423i	0.141671	−	0.0622896i
$400$	4.48674	+	2.59042i	0.224337	+	0.129521i
$401$	−8.84160	−	32.9973i	−0.441529	−	1.64781i	−0.724943	−	0.688809i	$-0.758134\pi$
$401$	−8.84160	−	32.9973i	−0.441529	−	1.64781i	0.283414	−	0.958998i	$-0.408533\pi$
$402$	0.776612	−	7.07302i	0.0387339	−	0.352770i
$403$	−25.5401	+	15.3553i	−1.27225	+	0.764904i
$404$			25.7780i			1.28250i
$405$	22.8887	+	4.06215i	1.13735	+	0.201850i
$406$	−3.27793	−	5.67755i	−0.162681	−	0.281772i
$407$	−9.13131	−	15.8159i	−0.452622	−	0.783964i
$408$	22.8409	+	28.4754i	1.13079	+	1.40974i
$409$	−11.5112	+	11.5112i	−0.569191	+	0.569191i	−0.931902	−	0.362711i	$-0.881851\pi$
$409$	−11.5112	+	11.5112i	−0.569191	+	0.569191i	0.362711	+	0.931902i	$0.381851\pi$
$410$	−37.5543	+	37.5543i	−1.85467	+	1.85467i
$411$	−4.57049	+	0.702165i	−0.225446	+	0.0346352i
$412$	3.11118	+	5.38873i	0.153277	+	0.265483i
$413$	−3.59793	−	6.23180i	−0.177043	−	0.306647i
$414$	23.7614	−	45.5833i	1.16781	−	2.24030i
$415$			12.2213i			0.599919i
$416$	−5.16371	+	0.0915112i	−0.253172	+	0.00448670i
$417$	−0.696567	+	0.306266i	−0.0341110	+	0.0149979i
$418$	−6.19597	−	23.1237i	−0.303055	−	1.13102i
$419$	−6.38361	−	3.68558i	−0.311860	−	0.180052i	0.335899	−	0.941898i	$-0.390960\pi$
$419$	−6.38361	−	3.68558i	−0.311860	−	0.180052i	−0.647758	+	0.761846i	$0.724293\pi$
$420$	−1.87791	+	17.1031i	−0.0916326	+	0.834547i
$421$	−2.26400	−	8.44937i	−0.110341	−	0.411797i	0.888555	−	0.458769i	$-0.151710\pi$
$421$	−2.26400	−	8.44937i	−0.110341	−	0.411797i	−0.998896	+	0.0469720i	$0.985043\pi$
$422$	5.52963	−	1.48166i	0.269178	−	0.0721260i
$423$	−30.3203	−	15.8052i	−1.47422	−	0.768475i
$424$	0.199433	+	0.199433i	0.00968535	+	0.00968535i
$425$	−6.83550	+	3.94648i	−0.331570	+	0.191432i
$426$	3.32657	+	0.365255i	0.161173	+	0.0176967i
$427$	−8.46612	+	2.26849i	−0.409704	+	0.109780i
$428$	−18.1061	−	31.3608i	−0.875194	−	1.51588i
$429$	−14.5039	−	31.4623i	−0.700254	−	1.51901i
$430$	31.7598	−	55.0096i	1.53159	−	2.65280i
$431$	−8.65037	+	32.2836i	−0.416674	+	1.55505i	0.364786	+	0.931091i	$0.381142\pi$
$431$	−8.65037	+	32.2836i	−0.416674	+	1.55505i	−0.781460	+	0.623956i	$0.785524\pi$
$432$	−5.18967	+	15.2465i	−0.249688	+	0.733546i
$433$	−0.614512	−	0.354789i	−0.0295316	−	0.0170501i	0.485162	−	0.874425i	$-0.338761\pi$
$433$	−0.614512	−	0.354789i	−0.0295316	−	0.0170501i	−0.514693	+	0.857374i	$0.672094\pi$
$434$	19.3031	−	5.17225i	0.926579	−	0.248276i
$435$	11.9897	−	1.84198i	0.574863	−	0.0883162i
$436$	−33.9149	−	33.9149i	−1.62423	−	1.62423i
$437$	12.2175	+	3.27366i	0.584441	+	0.156600i
$438$	−7.75707	−	17.6426i	−0.370647	−	0.842996i
$439$			13.9606i			0.666304i	0.942873	+	0.333152i	$0.108112\pi$
$439$			13.9606i			0.666304i	−0.942873	+	0.333152i	$0.891888\pi$
$440$	61.7743	+	16.5524i	2.94498	+	0.789104i
$441$	−2.86165	+	0.900526i	−0.136269	+	0.0428822i
$442$	−19.9477	+	36.0093i	−0.948816	+	1.71279i
$443$	6.18228	+	3.56934i	0.293729	+	0.169585i	0.639622	−	0.768689i	$-0.279091\pi$
$443$	6.18228	+	3.56934i	0.293729	+	0.169585i	−0.345893	+	0.938274i	$0.612424\pi$
$444$	−21.6751	+	3.32995i	−1.02866	+	0.158033i
$445$	−6.50031	+	11.2589i	−0.308144	+	0.533721i
$446$	−66.4274			−3.14543
$447$	−15.0327	−	5.85069i	−0.711020	−	0.276728i
$448$	9.33305	+	2.50078i	0.440945	+	0.118151i
$449$	−4.24038	−	15.8253i	−0.200116	−	0.746843i	−0.990883	−	0.134726i	$-0.956985\pi$
$449$	−4.24038	−	15.8253i	−0.200116	−	0.746843i	0.790767	−	0.612117i	$-0.209682\pi$
$450$	−10.7513	−	5.60437i	−0.506821	−	0.264193i
$451$	−23.5888	+	40.8570i	−1.11075	+	1.92388i
$452$	47.2808			2.22390
$453$	18.3363	−	14.7080i	0.861513	−	0.691044i
$454$	8.02118	−	4.63103i	0.376453	−	0.217345i
$455$	−8.95142	+	2.56936i	−0.419649	+	0.120454i
$456$	−13.7149	−	1.50589i	−0.642260	−	0.0705197i
$457$	−10.9660	+	10.9660i	−0.512968	+	0.512968i	−0.915435	−	0.402466i	$-0.868153\pi$
$457$	−10.9660	+	10.9660i	−0.512968	+	0.512968i	0.402466	+	0.915435i	$0.368153\pi$
$458$	8.60757	−	4.96959i	0.402206	−	0.232213i
$459$	−16.1627	−	18.4610i	−0.754408	−	0.861687i
$460$	−49.7801	+	49.7801i	−2.32101	+	2.32101i
$461$	0.887905	−	3.31371i	0.0413539	−	0.154335i	−0.942162	−	0.335159i	$-0.891210\pi$
$461$	0.887905	−	3.31371i	0.0413539	−	0.154335i	0.983515	+	0.180824i	$0.0578766\pi$
$462$	3.52777	+	22.9628i	0.164127	+	1.06833i
$463$	−8.31948	+	31.0487i	−0.386639	+	1.44296i	0.448928	+	0.893568i	$0.351806\pi$
$463$	−8.31948	+	31.0487i	−0.386639	+	1.44296i	−0.835567	+	0.549388i	$0.814861\pi$
$464$			8.40416i			0.390153i
$465$	−4.03576	+	36.7558i	−0.187154	+	1.70451i
$466$	−23.2878	−	23.2878i	−1.07878	−	1.07878i
$467$	2.77083			0.128219			0.0641094	−	0.997943i	$-0.479579\pi$
$467$	2.77083			0.128219			0.0641094	+	0.997943i	$0.479579\pi$
$468$	−41.5236	+	2.52763i	−1.91943	+	0.116840i
$469$	−1.69910			−0.0784570
$470$	50.3308	+	50.3308i	2.32159	+	2.32159i
$471$	22.4108	+	16.4419i	1.03264	+	0.757601i
$472$			32.1169i			1.47830i
$473$	14.6038	−	54.5020i	0.671482	−	2.50601i
$474$	−42.5101	+	34.0985i	−1.95255	+	1.56620i
$475$	0.772126	−	2.88161i	0.0354276	−	0.132218i
$476$	12.8417	−	12.8417i	0.588597	−	0.588597i
$477$	−0.139699	−	0.128153i	−0.00639637	−	0.00586774i
$478$	−53.1389	+	30.6798i	−2.43052	+	1.40326i
$479$	8.67019	−	8.67019i	0.396151	−	0.396151i	−0.480722	−	0.876873i	$-0.659625\pi$
$479$	8.67019	−	8.67019i	0.396151	−	0.396151i	0.876873	+	0.480722i	$0.159625\pi$
$480$	−3.79062	+	5.16674i	−0.173017	+	0.235828i
$481$	−6.11597	−	10.1725i	−0.278864	−	0.463828i
$482$	42.6423	−	24.6195i	1.94230	−	1.12139i
$483$	−11.4390	−	4.45204i	−0.520491	−	0.202575i
$484$	76.0552			3.45705
$485$	20.1052	−	34.8232i	0.912929	−	1.58124i
$486$	10.5972	−	36.1700i	0.480698	−	1.64070i
$487$	−2.42476	−	9.04932i	−0.109876	−	0.410064i	0.888976	−	0.457953i	$-0.151417\pi$
$487$	−2.42476	−	9.04932i	−0.109876	−	0.410064i	−0.998853	+	0.0478891i	$0.984751\pi$
$488$	37.7864	+	10.1248i	1.71051	+	0.458330i
$489$	17.6257	−	14.1381i	0.797064	−	0.639347i
$490$	6.24511			0.282125
$491$	−7.83620	+	13.5727i	−0.353643	+	0.612527i	−0.986885	−	0.161427i	$-0.948390\pi$
$491$	−7.83620	+	13.5727i	−0.353643	+	0.612527i	0.633242	+	0.773954i	$0.281724\pi$
$492$	35.4463	+	44.1903i	1.59804	+	1.99225i
$493$	−11.0883	−	6.40182i	−0.499391	−	0.288323i
$494$	−4.29265	−	14.9552i	−0.193135	−	0.672866i
$495$	−41.9626	−	9.32738i	−1.88608	−	0.419234i
$496$	−24.7453	−	6.63047i	−1.11109	−	0.297717i
$497$		−	0.799117i		−	0.0358453i
$498$	19.6966	+	2.16267i	0.882625	+	0.0969116i
$499$	−4.47880	−	1.20009i	−0.200499	−	0.0537235i	0.157172	−	0.987571i	$-0.449762\pi$
$499$	−4.47880	−	1.20009i	−0.200499	−	0.0537235i	−0.357671	+	0.933848i	$0.616429\pi$
$500$	−23.3803	−	23.3803i	−1.04560	−	1.04560i
$501$	23.1906	+	28.9114i	1.03608	+	1.29167i
$502$	1.12887	−	0.302479i	0.0503839	−	0.0135003i
$503$	11.0430	+	6.37567i	0.492382	+	0.284277i	0.725562	−	0.688157i	$-0.241580\pi$
$503$	11.0430	+	6.37567i	0.492382	+	0.284277i	−0.233180	+	0.972434i	$0.574913\pi$
$504$	13.0707	+	2.90534i	0.582217	+	0.129414i
$505$	−4.48077	+	16.7225i	−0.199392	+	0.744140i
$506$	−47.5284	+	82.3216i	−2.11289	+	3.65964i
$507$	−9.78744	−	20.2782i	−0.434675	−	0.900587i
$508$	−20.8546	−	36.1211i	−0.925271	−	1.60262i
$509$	35.4288	−	9.49312i	1.57035	−	0.420775i	0.634431	−	0.772980i	$-0.281235\pi$
$509$	35.4288	−	9.49312i	1.57035	−	0.420775i	0.935923	+	0.352205i	$0.114568\pi$
$510$	20.5584	+	46.7578i	0.910341	+	2.07047i
$511$	−3.98550	+	2.30103i	−0.176308	+	0.101791i
$512$	−22.7034	−	22.7034i	−1.00336	−	1.00336i
$513$	9.25361	+	0.614267i	0.408557	+	0.0271206i
$514$	−5.26989	+	1.41206i	−0.232445	+	0.0622834i
$515$	1.08158	+	4.03651i	0.0476601	+	0.177870i
$516$	−54.6285	−	40.0786i	−2.40489	−	1.76436i
$517$	54.7572	+	31.6141i	2.40822	+	1.39039i
$518$	2.06009	+	7.68836i	0.0905151	+	0.337807i
$519$	−0.333882	−	0.244955i	−0.0146558	−	0.0107523i
$520$	40.3337	+	10.0449i	1.76875	+	0.440497i
$521$		−	10.4319i		−	0.457032i	−0.973540	−	0.228516i	$-0.926613\pi$
$521$		−	10.4319i		−	0.457032i	0.973540	−	0.228516i	$-0.0733872\pi$
$522$	−0.846960	−	19.6494i	−0.0370704	−	0.860029i
$523$	−4.65259	−	8.05852i	−0.203443	−	0.352374i	0.746192	−	0.665730i	$-0.231880\pi$
$523$	−4.65259	−	8.05852i	−0.203443	−	0.352374i	−0.949636	+	0.313356i	$0.898547\pi$
$524$	18.6767	+	32.3491i	0.815897	+	1.41318i
$525$	−1.05006	+	2.69800i	−0.0458283	+	0.117750i
$526$	−13.0516	+	13.0516i	−0.569078	+	0.569078i
$527$	27.5976	−	27.5976i	1.20217	−	1.20217i
$528$	10.8019	−	27.7541i	0.470091	−	1.20784i
$529$	−13.6118	−	23.5763i	−0.591817	−	1.02506i
$530$	0.197320	+	0.341769i	0.00857105	+	0.0148455i
$531$	−0.929641	−	21.5675i	−0.0403430	−	0.935952i
$532$			6.86418i			0.297600i
$533$	−14.8583	+	26.8219i	−0.643583	+	1.16179i
$534$	16.9952	+	12.4687i	0.735455	+	0.539572i
$535$	−6.29447	−	23.4913i	−0.272134	−	1.01562i
$536$	6.56750	+	3.79175i	0.283673	+	0.163778i
$537$	−16.1051	−	11.8156i	−0.694985	−	0.509882i
$538$	−6.53285	−	24.3809i	−0.281651	−	1.05114i
$539$	5.35852	−	1.43581i	0.230808	−	0.0618448i
$540$	−28.7131	+	42.8946i	−1.23561	+	1.84589i
$541$	12.3954	+	12.3954i	0.532922	+	0.532922i	0.921441	−	0.388519i	$-0.127013\pi$
$541$	12.3954	+	12.3954i	0.532922	+	0.532922i	−0.388519	+	0.921441i	$0.627013\pi$
$542$	64.5108	−	37.2454i	2.77098	−	1.59982i
$543$	−5.99776	−	13.6412i	−0.257389	−	0.585402i
$544$	6.53331	−	1.75059i	0.280113	−	0.0750561i
$545$	−16.1058	−	27.8961i	−0.689898	−	1.19494i
$546$	2.55691	+	14.8814i	0.109426	+	0.636863i
$547$	0.582040	−	1.00812i	0.0248862	−	0.0431042i	−0.853314	−	0.521397i	$-0.825411\pi$
$547$	0.582040	−	1.00812i	0.0248862	−	0.0431042i	0.878200	+	0.478293i	$0.158744\pi$
$548$	2.65748	−	9.91783i	0.113522	−	0.423669i
$549$	−25.6679	−	5.70541i	−1.09548	−	0.243501i
$550$	19.4164	+	11.2101i	0.827917	+	0.477998i
$551$	4.67444	−	1.25251i	0.199138	−	0.0533588i
$552$	34.2796	+	42.7359i	1.45904	+	1.81896i
$553$	9.20155	+	9.20155i	0.391290	+	0.391290i
$554$	−16.4461	−	4.40673i	−0.698730	−	0.187224i
$555$	−14.6397	−	1.60743i	−0.621420	−	0.0682315i
$556$		−	1.68961i		−	0.0716552i
$557$	21.7747	+	5.83450i	0.922622	+	0.247216i	0.688706	−	0.725041i	$-0.258179\pi$
$557$	21.7747	+	5.83450i	0.922622	+	0.247216i	0.233916	+	0.972257i	$0.424846\pi$
$558$	58.5238	+	13.0086i	2.47751	+	0.550697i
$559$	8.86236	−	35.5854i	0.374838	−	1.50510i
$560$	−6.93322	−	4.00290i	−0.292982	−	0.169153i
$561$	28.3899	+	35.3932i	1.19862	+	1.49430i
$562$	3.63268	−	6.29198i	0.153235	−	0.265411i
$563$	−3.13247			−0.132018			−0.0660090	−	0.997819i	$-0.521027\pi$
$563$	−3.13247			−0.132018			−0.0660090	+	0.997819i	$0.521027\pi$
$564$	59.2246	−	47.5057i	2.49380	−	2.00035i
$565$	30.6715	+	8.21841i	1.29036	+	0.345751i
$566$	−7.46689	−	27.8668i	−0.313857	−	1.17133i
$567$	−8.86153	−	1.57269i	−0.372149	−	0.0660469i
$568$	−1.78333	+	3.08882i	−0.0748268	+	0.129604i
$569$	36.5350			1.53163			0.765813	−	0.643064i	$-0.222337\pi$
$569$	36.5350			1.53163			0.765813	+	0.643064i	$0.222337\pi$
$570$	−17.9911	−	7.00211i	−0.753563	−	0.293286i
$571$	15.1667	−	8.75651i	0.634707	−	0.366448i	−0.147866	−	0.989007i	$-0.547240\pi$
$571$	15.1667	−	8.75651i	0.634707	−	0.366448i	0.782573	+	0.622559i	$0.213907\pi$
$572$	76.9148	−	1.36308i	3.21597	−	0.0569934i
$573$	13.3292	−	18.1681i	0.556833	−	0.758982i
$574$	14.5394	−	14.5394i	0.606864	−	0.606864i
$575$	−10.2587	+	5.92287i	−0.427818	+	0.247001i
$576$	21.3604	+	19.5951i	0.890018	+	0.816463i
$577$	−28.0526	+	28.0526i	−1.16784	+	1.16784i	−0.185131	+	0.982714i	$0.559271\pi$
$577$	−28.0526	+	28.0526i	−1.16784	+	1.16784i	−0.982714	+	0.185131i	$0.940729\pi$
$578$	3.31529	−	12.3728i	0.137898	−	0.514641i
$579$	−24.6778	+	19.7948i	−1.02558	+	0.822643i
$580$	−6.97133	+	26.0173i	−0.289469	+	1.08031i
$581$		−	4.73156i		−	0.196298i
$582$	−52.5655	−	38.5651i	−2.17891	−	1.59857i
$583$	0.247884	+	0.247884i	0.0102663	+	0.0102663i
$584$	20.5401			0.849956
$585$	−27.3761	−	5.57799i	−1.13186	−	0.230621i
$586$	−34.5708			−1.42811
$587$	−28.3669	−	28.3669i	−1.17083	−	1.17083i	−0.982013	−	0.188816i	$-0.939535\pi$
$587$	−28.3669	−	28.3669i	−1.17083	−	1.17083i	−0.188816	−	0.982013i	$-0.560465\pi$
$588$	0.727048	−	6.62161i	0.0299829	−	0.273071i
$589$			14.7516i			0.607830i
$590$	−11.6310	+	43.4077i	−0.478843	+	1.78707i
$591$	0.219415	+	1.42820i	0.00902551	+	0.0587483i
$592$	2.64089	−	9.85594i	0.108540	−	0.405076i
$593$	13.0152	−	13.0152i	0.534470	−	0.534470i	−0.387429	−	0.921899i	$-0.626637\pi$
$593$	13.0152	−	13.0152i	0.534470	−	0.534470i	0.921899	+	0.387429i	$0.126637\pi$
$594$	−22.4583	+	65.9790i	−0.921474	+	2.70715i
$595$	10.5627	−	6.09836i	0.433027	−	0.250008i
$596$	25.3275	−	25.3275i	1.03746	−	1.03746i
$597$	20.9120	+	2.29612i	0.855870	+	0.0939738i
$598$	−29.9375	+	54.0427i	−1.22424	+	2.20997i
$599$	−27.7356	+	16.0132i	−1.13325	+	0.654281i	−0.944750	−	0.327793i	$-0.893695\pi$
$599$	−27.7356	+	16.0132i	−1.13325	+	0.654281i	−0.188498	+	0.982074i	$0.560362\pi$
$600$	10.0797	−	8.08520i	0.411502	−	0.330077i
$601$	34.1246			1.39197			0.695986	−	0.718056i	$-0.254968\pi$
$601$	34.1246			1.39197			0.695986	+	0.718056i	$0.254968\pi$
$602$	−12.2960	+	21.2974i	−0.501149	+	0.868016i
$603$	−4.52004	−	2.35618i	−0.184070	−	0.0959511i
$604$	13.5090	+	50.4164i	0.549675	+	2.05142i
$605$	49.3378	+	13.2200i	2.00587	+	0.537470i
$606$	26.1581	+	10.1807i	1.06260	+	0.413562i
$607$	−25.1829			−1.02214			−0.511071	−	0.859538i	$-0.670751\pi$
$607$	−25.1829			−1.02214			−0.511071	+	0.859538i	$0.670751\pi$
$608$	−1.27824	+	2.21397i	−0.0518394	+	0.0897885i
$609$	−4.64191	+	0.713137i	−0.188100	+	0.0288978i
$610$	47.4036	+	27.3685i	1.91932	+	1.10812i
$611$	35.9471	+	19.9133i	1.45427	+	0.805605i
$612$	51.9700	−	16.3543i	2.10076	−	0.661084i
$613$	17.6471	+	4.72852i	0.712758	+	0.190983i	0.596938	−	0.802287i	$-0.296384\pi$
$613$	17.6471	+	4.72852i	0.712758	+	0.190983i	0.115820	+	0.993270i	$0.463050\pi$
$614$			16.6098i			0.670319i
$615$	15.3131	+	34.8280i	0.617485	+	1.40440i
$616$	−23.9164	−	6.40838i	−0.963620	−	0.258201i
$617$	29.4460	+	29.4460i	1.18545	+	1.18545i	0.978311	+	0.207141i	$0.0664160\pi$
$617$	29.4460	+	29.4460i	1.18545	+	1.18545i	0.207141	+	0.978311i	$0.433584\pi$
$618$	6.69689	−	1.02884i	0.269389	−	0.0413862i
$619$	−14.7715	+	3.95802i	−0.593718	+	0.159086i	−0.543152	−	0.839635i	$-0.682769\pi$
$619$	−14.7715	+	3.95802i	−0.593718	+	0.159086i	−0.0505660	+	0.998721i	$0.516103\pi$
$620$	−71.1055	−	41.0528i	−2.85567	−	1.64872i
$621$	−24.2569	−	27.7063i	−0.973396	−	1.11182i
$622$	−10.6767	+	39.8459i	−0.428095	+	1.59767i
$623$	2.51665	−	4.35896i	0.100827	−	0.174638i
$624$	6.69979	−	18.1599i	0.268206	−	0.726979i
$625$	−15.2818	−	26.4689i	−0.611272	−	1.05875i
$626$	−27.4407	+	7.35272i	−1.09675	+	0.293874i
$627$	−17.0468	−	1.87173i	−0.680785	−	0.0747496i
$628$	−53.4499	+	30.8593i	−2.13288	+	1.23142i
$629$	10.9920	+	10.9920i	0.438281	+	0.438281i
$630$	16.6136	+	8.66025i	0.661903	+	0.345033i
$631$	12.6489	−	3.38925i	0.503544	−	0.134924i	0.00189945	−	0.999998i	$-0.499395\pi$
$631$	12.6489	−	3.38925i	0.503544	−	0.134924i	0.501644	+	0.865074i	$0.332729\pi$
$632$	−15.0322	−	56.1010i	−0.597950	−	2.23158i
$633$	0.447591	−	4.07645i	0.0177902	−	0.162024i
$634$	−50.1431	−	28.9501i	−1.99144	−	1.14976i
$635$	−7.24993	−	27.0571i	−0.287705	−	1.07373i
$636$	0.385345	−	0.169428i	0.0152799	−	0.00671826i
$637$	3.46561	−	0.994749i	0.137313	−	0.0394134i
$638$			36.3690i			1.43986i
$639$	1.10816	−	2.12586i	0.0438380	−	0.0840978i
$640$	−26.4713	−	45.8496i	−1.04637	−	1.81236i
$641$	−9.80546	−	16.9836i	−0.387292	−	0.670810i	0.604792	−	0.796384i	$-0.293256\pi$
$641$	−9.80546	−	16.9836i	−0.387292	−	0.670810i	−0.992084	+	0.125573i	$0.959923\pi$
$642$	−38.9739	+	5.98756i	−1.53818	+	0.236310i
$643$	6.20860	−	6.20860i	0.244843	−	0.244843i	−0.574007	−	0.818850i	$-0.694612\pi$
$643$	6.20860	−	6.20860i	0.244843	−	0.244843i	0.818850	+	0.574007i	$0.194612\pi$
$644$	19.2728	−	19.2728i	0.759453	−	0.759453i
$645$	−28.4715	−	35.4950i	−1.12107	−	1.39761i
$646$	10.1886	+	17.6471i	0.400864	+	0.694316i
$647$	12.8484	+	22.2541i	0.505123	+	0.874899i	0.999982	+	0.00592561i	$0.00188619\pi$
$647$	12.8484	+	22.2541i	0.505123	+	0.874899i	−0.494859	+	0.868973i	$0.664780\pi$
$648$	30.7427	+	25.8545i	1.20769	+	1.01566i
$649$			39.9194i			1.56697i
$650$	12.7465	+	7.06106i	0.499959	+	0.276958i
$651$	1.56248	−	14.2303i	0.0612383	−	0.557729i
$652$	12.9856	+	48.4628i	0.508554	+	1.89795i
$653$	−16.7745	−	9.68474i	−0.656435	−	0.378993i	0.134482	−	0.990916i	$-0.457063\pi$
$653$	−16.7745	−	9.68474i	−0.656435	−	0.378993i	−0.790917	+	0.611923i	$0.790396\pi$
$654$	−47.8092	+	21.0207i	−1.86949	+	0.821974i
$655$	6.49283	+	24.2316i	0.253696	+	0.946806i
$656$	−25.4607	+	6.82218i	−0.994074	+	0.266361i
$657$	−13.7934	+	0.594545i	−0.538130	+	0.0231954i
$658$	−19.4860	−	19.4860i	−0.759642	−	0.759642i
$659$	20.4591	−	11.8120i	0.796972	−	0.460132i	−0.0454391	−	0.998967i	$-0.514469\pi$
$659$	20.4591	−	11.8120i	0.796972	−	0.460132i	0.842411	+	0.538835i	$0.181135\pi$
$660$	56.4623	−	76.9600i	2.19779	−	2.99566i
$661$	−40.0128	+	10.7214i	−1.55632	+	0.417014i	−0.931495	−	0.363753i	$-0.881495\pi$
$661$	−40.0128	+	10.7214i	−1.55632	+	0.417014i	−0.624822	+	0.780767i	$0.714829\pi$
$662$	−3.60264	−	6.23995i	−0.140021	−	0.242523i
$663$	18.8563	+	22.6728i	0.732318	+	0.880537i
$664$	−10.5591	+	18.2888i	−0.409771	+	0.709745i
$665$	−1.19314	+	4.45287i	−0.0462681	+	0.172675i
$666$	−5.18126	+	23.3098i	−0.200770	+	0.903237i
$667$	−16.6413	−	9.60784i	−0.644353	−	0.372017i
$668$	−79.4933	+	21.3002i	−3.07569	+	0.824128i
$669$	−17.2593	+	44.3458i	−0.667285	+	1.71451i
$670$	7.50314	+	7.50314i	0.289872	+	0.289872i
$671$	46.9663	+	12.5846i	1.81311	+	0.485822i
$672$	1.46757	−	2.00034i	0.0566127	−	0.0771649i
$673$			25.3187i			0.975964i	0.872854	+	0.487982i	$0.162267\pi$
$673$			25.3187i			0.975964i	−0.872854	+	0.487982i	$0.837733\pi$
$674$	45.5032	+	12.1925i	1.75272	+	0.469639i
$675$	−6.53481	+	5.72124i	−0.251525	+	0.220210i
$676$	49.9661	−	1.77156i	1.92177	−	0.0681367i
$677$	−12.5429	−	7.24164i	−0.482063	−	0.278319i	0.239213	−	0.970967i	$-0.423111\pi$
$677$	−12.5429	−	7.24164i	−0.482063	−	0.278319i	−0.721276	+	0.692648i	$0.756444\pi$
$678$	18.6729	−	47.9778i	0.717129	−	1.84258i
$679$	−7.78388	+	13.4821i	−0.298718	+	0.517394i
$680$	−54.4370			−2.08756
$681$	−1.00751	−	6.55805i	−0.0386080	−	0.251305i
$682$	−107.085	−	28.6933i	−4.10050	−	1.09873i
$683$	6.29594	+	23.4968i	0.240908	+	0.899079i	0.975396	+	0.220459i	$0.0707554\pi$
$683$	6.29594	+	23.4968i	0.240908	+	0.899079i	−0.734489	+	0.678621i	$0.762578\pi$
$684$	−9.51874	+	18.2605i	−0.363958	+	0.698209i
$685$	3.44786	−	5.97187i	0.131736	−	0.228174i
$686$	−2.41784			−0.0923137
$687$	−1.08117	−	7.03748i	−0.0412491	−	0.268497i
$688$	27.3018	−	15.7627i	1.04087	−	0.600946i
$689$	0.163938	+	0.158229i	0.00624554	+	0.00602803i
$690$	30.8540	+	70.1740i	1.17459	+	2.67148i
$691$	−0.236076	+	0.236076i	−0.00898077	+	0.00898077i	−0.711583	−	0.702602i	$-0.752021\pi$
$691$	−0.236076	+	0.236076i	−0.00898077	+	0.00898077i	0.702602	+	0.711583i	$0.252021\pi$
$692$	0.796310	−	0.459750i	0.0302712	−	0.0174771i
$693$	16.2462	+	3.61117i	0.617140	+	0.137177i
$694$	−28.7885	+	28.7885i	−1.09280	+	1.09280i
$695$	0.293690	−	1.09606i	0.0111403	−	0.0415761i
$696$	19.5338	+	7.60253i	0.740426	+	0.288173i
$697$	10.3935	−	38.7891i	0.393682	−	1.46924i
$698$		−	38.6551i		−	1.46312i
$699$	−21.5972	+	9.49583i	−0.816881	+	0.359165i
$700$	−4.54567	−	4.54567i	−0.171810	−	0.171810i
$701$	−28.5113			−1.07686			−0.538428	−	0.842672i	$-0.680981\pi$
$701$	−28.5113			−1.07686			−0.538428	+	0.842672i	$0.680981\pi$
$702$	−13.8343	+	43.1340i	−0.522142	+	1.62799i
$703$	−5.87551			−0.221599
$704$	−37.9023	−	37.9023i	−1.42850	−	1.42850i
$705$	46.6771	−	20.5229i	1.75796	−	0.772938i
$706$		−	64.2476i		−	2.41799i
$707$	1.73477	−	6.47423i	0.0652426	−	0.243489i
$708$	44.6705	+	17.3857i	1.67882	+	0.653395i
$709$	13.5244	−	50.4739i	0.507921	−	1.89559i	0.0676780	−	0.997707i	$-0.478441\pi$
$709$	13.5244	−	50.4739i	0.507921	−	1.89559i	0.440243	−	0.897879i	$-0.354892\pi$
$710$	−3.52887	+	3.52887i	−0.132436	+	0.132436i
$711$	11.7185	+	37.2386i	0.439478	+	1.39656i
$712$	−19.4551	+	11.2324i	−0.729111	+	0.420952i
$713$	41.4185	−	41.4185i	1.55114	−	1.55114i
$714$	−7.95934	−	18.1026i	−0.297871	−	0.677474i
$715$	50.1323	+	12.4852i	1.87484	+	0.466920i
$716$	38.4107	−	22.1764i	1.43547	−	0.828771i
$717$	6.67460	+	43.4459i	0.249268	+	1.62252i
$718$	−26.6846			−0.995860
$719$	22.7041	−	39.3247i	0.846720	−	1.46656i	−0.0373987	−	0.999300i	$-0.511907\pi$
$719$	22.7041	−	39.3247i	0.846720	−	1.46656i	0.884119	−	0.467262i	$-0.154759\pi$
$720$	−12.8933	−	20.2632i	−0.480503	−	0.755166i
$721$	−0.418742	−	1.56277i	−0.0155948	−	0.0582005i
$722$	36.9342	+	9.89650i	1.37455	+	0.368310i
$723$	−5.35615	−	34.8639i	−0.199197	−	1.29660i
$724$	33.0885			1.22972
$725$	−2.26611	+	3.92501i	−0.0841611	+	0.145771i
$726$	30.0370	−	77.1765i	1.11478	−	2.86429i
$727$	29.7712	+	17.1884i	1.10415	+	0.637484i	0.937309	−	0.348499i	$-0.113309\pi$
$727$	29.7712	+	17.1884i	1.10415	+	0.637484i	0.166845	+	0.985983i	$0.446642\pi$
$728$	−15.6155	−	3.88895i	−0.578749	−	0.144134i
$729$	−21.3931	−	16.4723i	−0.792336	−	0.610084i
$730$	27.7610	+	7.43855i	1.02748	+	0.275313i
$731$			48.0285i			1.77640i
$732$	34.5371	−	47.0752i	1.27653	−	1.73995i
$733$	11.8216	+	3.16759i	0.436641	+	0.116998i	0.470442	−	0.882431i	$-0.344095\pi$
$733$	11.8216	+	3.16759i	0.436641	+	0.116998i	−0.0338009	+	0.999429i	$0.510761\pi$
$734$	−25.7340	−	25.7340i	−0.949858	−	0.949858i
$735$	1.62262	−	4.16913i	0.0598512	−	0.153781i
$736$	9.80518	−	2.62729i	0.361424	−	0.0968432i
$737$	8.16301	+	4.71291i	0.300688	+	0.173602i
$738$	58.8409	−	18.5165i	2.16596	−	0.681601i
$739$	−8.44151	+	31.5041i	−0.310526	+	1.15890i	0.617557	+	0.786526i	$0.288122\pi$
$739$	−8.44151	+	31.5041i	−0.310526	+	1.15890i	−0.928083	+	0.372373i	$0.878544\pi$
$740$	16.3512	−	28.3210i	0.601081	−	1.04110i
$741$	−11.0992	−	1.02000i	−0.407738	−	0.0374705i
$742$	−0.0763941	−	0.132319i	−0.00280452	−	0.00485757i
$743$	10.5994	−	2.84010i	0.388855	−	0.104193i	−0.0590943	−	0.998252i	$-0.518821\pi$
$743$	10.5994	−	2.84010i	0.388855	−	0.104193i	0.447949	+	0.894059i	$0.352155\pi$
$744$	−37.7961	+	51.5173i	−1.38567	+	1.88872i
$745$	20.8327	−	12.0277i	0.763250	−	0.440663i
$746$	48.2656	+	48.2656i	1.76713	+	1.76713i
$747$	6.56138	−	12.5872i	0.240068	−	0.460542i
$748$	−97.3154	+	26.0756i	−3.55820	+	0.953417i
$749$	2.43695	+	9.09483i	0.0890443	+	0.332318i
$750$	−32.9587	+	14.4912i	−1.20348	+	0.529145i
$751$	−11.4633	−	6.61832i	−0.418300	−	0.241506i	0.276050	−	0.961143i	$-0.410975\pi$
$751$	−11.4633	−	6.61832i	−0.418300	−	0.241506i	−0.694350	+	0.719638i	$0.744308\pi$
$752$	9.14319	+	34.1229i	0.333418	+	1.24433i
$753$	0.0913754	−	0.832204i	0.00332991	−	0.0303272i
$754$	0.418838	+	23.6338i	0.0152532	+	0.860692i
$755$			35.0538i			1.27574i
$756$	11.1165	−	16.6070i	0.404303	−	0.603991i
$757$	−1.25819	−	2.17925i	−0.0457298	−	0.0792063i	0.842255	−	0.539080i	$-0.181228\pi$
$757$	−1.25819	−	2.17925i	−0.0457298	−	0.0792063i	−0.887984	+	0.459874i	$0.847895\pi$
$758$	−25.8907	−	44.8441i	−0.940394	−	1.62881i
$759$	42.6075	+	53.1181i	1.54656	+	1.92807i
$760$	14.5490	−	14.5490i	0.527746	−	0.527746i
$761$	1.38501	−	1.38501i	0.0502067	−	0.0502067i	−0.681558	−	0.731764i	$-0.738697\pi$
$761$	1.38501	−	1.38501i	0.0502067	−	0.0502067i	0.731764	+	0.681558i	$0.238697\pi$
$762$	−44.8899	+	6.89644i	−1.62619	+	0.249832i
$763$	6.23549	+	10.8002i	0.225740	+	0.390993i
$764$	25.0171	+	43.3309i	0.905088	+	1.56766i
$765$	36.5562	−	1.57571i	1.32169	−	0.0569699i
$766$			10.7208i			0.387359i
$767$	0.459726	+	25.9410i	0.0165997	+	0.936674i
$768$	−47.9382	+	21.0774i	−1.72982	+	0.760565i
$769$	7.30688	+	27.2697i	0.263493	+	0.983369i	0.963166	+	0.268906i	$0.0866621\pi$
$769$	7.30688	+	27.2697i	0.263493	+	0.983369i	−0.699674	+	0.714463i	$0.746671\pi$
$770$	−30.0035	−	17.3225i	−1.08125	−	0.624261i
$771$	−0.426567	+	3.88497i	−0.0153624	+	0.139914i
$772$	−18.1811	−	67.8529i	−0.654353	−	2.44208i
$773$	−15.3394	+	4.11018i	−0.551721	+	0.147833i	−0.523900	−	0.851780i	$-0.675523\pi$
$773$	−15.3394	+	4.11018i	−0.551721	+	0.147833i	−0.0278207	+	0.999613i	$0.508857\pi$
$774$	−62.2443	+	39.6054i	−2.23733	+	1.42359i
$775$	−9.76897	−	9.76897i	−0.350912	−	0.350912i
$776$	60.1738	−	34.7414i	2.16011	−	1.24714i
$777$	5.66787	+	0.622328i	0.203334	+	0.0223259i
$778$	−6.02692	+	1.61491i	−0.216076	+	0.0578973i
$779$	7.58906	+	13.1446i	0.271906	+	0.470956i
$780$	35.8048	−	50.6614i	1.28202	−	1.81397i
$781$	−2.21657	+	3.83921i	−0.0793152	+	0.137378i
$782$	20.9416	−	78.1550i	0.748869	−	2.79482i
$783$	−13.3376	−	4.53993i	−0.476648	−	0.162244i
$784$	2.68425	+	1.54975i	0.0958661	+	0.0553483i
$785$	−40.0375	+	10.7280i	−1.42900	+	0.382899i
$786$	40.2021	−	6.17625i	1.43396	−	0.220300i
$787$	−4.63177	−	4.63177i	−0.165105	−	0.165105i	0.619719	−	0.784824i	$-0.287247\pi$
$787$	−4.63177	−	4.63177i	−0.165105	−	0.165105i	−0.784824	+	0.619719i	$0.787247\pi$
$788$	−3.09915	−	0.830416i	−0.110403	−	0.0295823i
$789$	5.32193	+	12.1041i	0.189466	+	0.430919i
$790$		−	81.2673i		−	2.89136i
$791$	−11.8747	−	3.18182i	−0.422216	−	0.113133i
$792$	−54.7373	−	50.2135i	−1.94500	−	1.78426i
$793$	30.6652	+	7.63700i	1.08895	+	0.271198i
$794$	39.7271	+	22.9365i	1.40986	+	0.813984i
$795$	0.279427	−	0.0429285i	0.00991027	−	0.00152252i
$796$	−23.3567	+	40.4550i	−0.827856	+	1.43389i
$797$	−10.5674			−0.374317			−0.187159	−	0.982330i	$-0.559928\pi$
$797$	−10.5674			−0.374317			−0.187159	+	0.982330i	$0.559928\pi$
$798$	6.96538	+	2.71092i	0.246572	+	0.0959655i
$799$	−51.9857	−	13.9295i	−1.83912	−	0.492791i
$800$	−0.619673	−	2.31265i	−0.0219087	−	0.0817646i
$801$	12.7396	−	8.10607i	0.450132	−	0.286414i
$802$	41.2984	−	71.5309i	1.45830	−	2.52584i
$803$	25.5301			0.900939
$804$	8.82899	−	7.08198i	0.311375	−	0.249762i
$805$	15.8525	−	9.15242i	0.558725	−	0.322580i
$806$	−69.9179	−	17.4127i	−2.46275	−	0.613335i
$807$	−17.9737	−	1.97350i	−0.632704	−	0.0694704i
$808$	−21.1534	+	21.1534i	−0.744175	+	0.744175i
$809$	−15.1397	+	8.74094i	−0.532285	+	0.307315i	−0.741947	−	0.670459i	$-0.766097\pi$
$809$	−15.1397	+	8.74094i	−0.532285	+	0.307315i	0.209661	+	0.977774i	$0.432764\pi$
$810$	32.1872	+	46.0771i	1.13094	+	1.61898i
$811$	5.64391	−	5.64391i	0.198185	−	0.198185i	−0.601037	−	0.799221i	$-0.705245\pi$
$811$	5.64391	−	5.64391i	0.198185	−	0.198185i	0.799221	+	0.601037i	$0.205245\pi$
$812$	2.69900	−	10.0728i	0.0947164	−	0.353487i
$813$	−8.10299	−	52.7435i	−0.284184	−	1.84980i
$814$	11.4284	−	42.6515i	0.400567	−	1.49494i
$815$			33.6955i			1.18030i
$816$	−2.76682	+	25.1989i	−0.0968582	+	0.882139i
$817$	−12.8362	−	12.8362i	−0.449082	−	0.449082i
$818$	−39.3607			−1.37621
$819$	10.5989	+	2.15956i	0.370355	+	0.0754612i
$820$	−84.4795			−2.95015
$821$	−5.97609	−	5.97609i	−0.208567	−	0.208567i	0.595091	−	0.803658i	$-0.297116\pi$
$821$	−5.97609	−	5.97609i	−0.208567	−	0.208567i	−0.803658	+	0.595091i	$0.797116\pi$
$822$	−9.01452	−	6.61357i	−0.314417	−	0.230675i
$823$		−	18.9281i		−	0.659792i	−0.944017	−	0.329896i	$-0.892986\pi$
$823$		−	18.9281i		−	0.659792i	0.944017	−	0.329896i	$-0.107014\pi$
$824$	−1.86895	+	6.97501i	−0.0651079	+	0.242986i
$825$	12.5285	−	10.0494i	0.436185	−	0.349876i
$826$	4.50305	−	16.8056i	0.156681	−	0.584742i
$827$	8.86787	−	8.86787i	0.308366	−	0.308366i	−0.535909	−	0.844275i	$-0.680031\pi$
$827$	8.86787	−	8.86787i	0.308366	−	0.308366i	0.844275	+	0.535909i	$0.180031\pi$
$828$	77.9966	−	24.5446i	2.71057	−	0.852982i
$829$	14.0597	−	8.11734i	0.488312	−	0.281927i	−0.235562	−	0.971859i	$-0.575693\pi$
$829$	14.0597	−	8.11734i	0.488312	−	0.281927i	0.723874	+	0.689932i	$0.242360\pi$
$830$	−20.8944	+	20.8944i	−0.725255	+	0.725255i
$831$	−7.21494	+	9.83420i	−0.250283	+	0.341145i
$832$	−25.0667	−	24.1937i	−0.869032	−	0.838766i
$833$	−4.08942	+	2.36103i	−0.141690	+	0.0818048i
$834$	−1.71452	−	0.667288i	−0.0593688	−	0.0231063i
$835$	−55.2705			−1.91271
$836$	19.0397	−	32.9777i	0.658502	−	1.14056i
$837$	23.8901	−	35.6896i	0.825763	−	1.23361i
$838$	−4.61275	−	17.2150i	−0.159345	−	0.594683i
$839$	17.2811	+	4.63045i	0.596609	+	0.159861i	0.544472	−	0.838779i	$-0.316730\pi$
$839$	17.2811	+	4.63045i	0.596609	+	0.159861i	0.0521372	+	0.998640i	$0.483397\pi$
$840$	−15.5758	+	12.4938i	−0.537417	+	0.431077i
$841$	21.6480			0.746484
$842$	10.5750	−	18.3164i	0.364437	−	0.631224i
$843$	−3.25657	−	4.05991i	−0.112162	−	0.139831i
$844$	7.88605	+	4.55302i	0.271449	+	0.156721i
$845$	32.7215	+	7.53595i	1.12565	+	0.259245i
$846$	−24.8161	−	78.8595i	−0.853195	−	2.71125i
$847$	−19.1015	−	5.11823i	−0.656335	−	0.175864i
$848$			0.195864i			0.00672600i
$849$	−20.5435	−	2.25566i	−0.705050	−	0.0774140i
$850$	−18.4336	−	4.93928i	−0.632269	−	0.169416i
$851$	16.4968	+	16.4968i	0.565504	+	0.565504i
$852$	3.33079	+	4.15244i	0.114111	+	0.142260i
$853$	28.0221	−	7.50850i	0.959459	−	0.257086i	0.255088	−	0.966918i	$-0.417896\pi$
$853$	28.0221	−	7.50850i	0.959459	−	0.257086i	0.704371	+	0.709832i	$0.251229\pi$
$854$	−18.3527	−	10.5959i	−0.628016	−	0.362585i
$855$	−9.34897	+	10.1912i	−0.319728	+	0.348533i
$856$	10.8767	−	40.5925i	0.371759	−	1.38742i
$857$	22.1035	−	38.2844i	0.755042	−	1.30777i	−0.190311	−	0.981724i	$-0.560950\pi$
$857$	22.1035	−	38.2844i	0.755042	−	1.30777i	0.945353	−	0.326048i	$-0.105717\pi$
$858$	28.9933	−	78.5871i	0.989816	−	2.68292i
$859$	−19.7209	−	34.1576i	−0.672869	−	1.16544i	−0.977087	−	0.212841i	$-0.931728\pi$
$859$	−19.7209	−	34.1576i	−0.672869	−	1.16544i	0.304218	−	0.952603i	$-0.401605\pi$
$860$	97.5952	−	26.1505i	3.32797	−	0.891726i
$861$	−5.92860	−	13.4839i	−0.202046	−	0.459532i
$862$	−69.9837	+	40.4051i	−2.38366	+	1.37620i
$863$	40.1222	+	40.1222i	1.36577	+	1.36577i	0.866368	+	0.499406i	$0.166449\pi$
$863$	40.1222	+	40.1222i	1.36577	+	1.36577i	0.499406	+	0.866368i	$0.333551\pi$
$864$	6.67804	−	3.28632i	0.227192	−	0.111803i
$865$	0.596489	−	0.159829i	0.0202812	−	0.00543434i
$866$	−0.444042	−	1.65719i	−0.0150892	−	0.0563135i
$867$	−7.39849	−	5.42796i	−0.251266	−	0.184343i
$868$	27.5291	+	15.8939i	0.934397	+	0.539474i
$869$	−18.6842	−	69.7302i	−0.633817	−	2.36544i
$870$	23.6477	+	17.3493i	0.801732	+	0.588197i
$871$	5.35887	+	2.96860i	0.181578	+	0.100587i
$872$		−	55.6611i		−	1.88492i
$873$	−39.4031	+	25.0717i	−1.33359	+	0.848550i
$874$	15.2910	+	26.4848i	0.517226	+	0.895861i
$875$	4.29863	+	7.44544i	0.145320	+	0.251702i
$876$	11.1189	−	28.5687i	0.375673	−	0.965246i
$877$	18.7927	−	18.7927i	0.634585	−	0.634585i	−0.314629	−	0.949215i	$-0.601880\pi$
$877$	18.7927	−	18.7927i	0.634585	−	0.634585i	0.949215	+	0.314629i	$0.101880\pi$
$878$	−23.8681	+	23.8681i	−0.805509	+	0.805509i
$879$	−8.98227	+	23.0789i	−0.302965	+	0.778431i
$880$	22.2063	+	38.4624i	0.748573	+	1.29657i
$881$	6.51120	+	11.2777i	0.219368	+	0.379956i	0.954615	−	0.297843i	$-0.0962672\pi$
$881$	6.51120	+	11.2777i	0.219368	+	0.379956i	−0.735247	+	0.677799i	$0.762934\pi$
$882$	−6.43209	−	3.35288i	−0.216580	−	0.112897i
$883$		−	39.8204i		−	1.34006i	−0.742333	−	0.670031i	$-0.766281\pi$
$883$		−	39.8204i		−	1.34006i	0.742333	−	0.670031i	$-0.233719\pi$
$884$	−62.9385	+	18.0655i	−2.11685	+	0.607608i
$885$	25.9562	+	19.0430i	0.872508	+	0.640123i
$886$	4.46727	+	16.6721i	0.150081	+	0.560110i
$887$	−15.2183	−	8.78631i	−0.510982	−	0.295015i	0.222255	−	0.974988i	$-0.428658\pi$
$887$	−15.2183	−	8.78631i	−0.510982	−	0.295015i	−0.733237	+	0.679973i	$0.761991\pi$
$888$	−20.5191	−	15.0540i	−0.688577	−	0.505180i
$889$	2.80687	+	10.4754i	0.0941393	+	0.351333i
$890$	−30.3624	+	8.13558i	−1.01775	+	0.272705i
$891$	38.2113	+	32.1356i	1.28013	+	1.07658i
$892$	−74.7153	−	74.7153i	−2.50165	−	2.50165i
$893$	17.6167	−	10.1710i	0.589519	−	0.340359i
$894$	−15.6981	−	35.7037i	−0.525025	−	1.19411i
$895$	28.7721	−	7.70947i	0.961746	−	0.257699i
$896$	10.2486	+	17.7510i	0.342380	+	0.593020i
$897$	28.2995	+	34.0273i	0.944894	+	1.13614i
$898$	19.8065	−	34.3058i	0.660950	−	1.14480i
$899$	5.80035	−	21.6472i	0.193452	−	0.721974i
$900$	−5.78908	−	18.3963i	−0.192969	−	0.613210i
$901$	−0.258419	−	0.149198i	−0.00860917	−	0.00497051i
$902$	−110.181	+	29.5230i	−3.66863	+	0.983007i
$903$	11.0230	+	13.7422i	0.366822	+	0.457311i
$904$	38.7985	+	38.7985i	1.29042	+	1.29042i
$905$	21.4648	+	5.75148i	0.713515	+	0.191186i
$906$	56.4950	+	6.20311i	1.87692	+	0.206084i
$907$			17.3117i			0.574827i	0.957807	+	0.287414i	$0.0927954\pi$
$907$			17.3117i			0.574827i	−0.957807	+	0.287414i	$0.907205\pi$
$908$	14.2308	+	3.81313i	0.472265	+	0.126543i
$909$	13.5929	−	14.8175i	0.450848	−	0.491466i
$910$	−19.6968	−	10.9112i	−0.652942	−	0.361704i
$911$	−7.00974	−	4.04708i	−0.232243	−	0.134086i	0.379363	−	0.925248i	$-0.376143\pi$
$911$	−7.00974	−	4.04708i	−0.232243	−	0.134086i	−0.611606	+	0.791162i	$0.709476\pi$
$912$	−5.99525	−	7.47419i	−0.198523	−	0.247495i
$913$	−13.1243	+	22.7319i	−0.434351	+	0.752318i
$914$	−37.4966			−1.24028
$915$	30.5873	−	24.5349i	1.01118	−	0.811099i
$916$	15.2711	+	4.09189i	0.504572	+	0.135200i
$917$	−2.51375	−	9.38144i	−0.0830114	−	0.309803i
$918$	3.92946	−	59.1952i	0.129691	−	1.95373i
$919$	8.61501	−	14.9216i	0.284183	−	0.492219i	−0.688228	−	0.725495i	$-0.741611\pi$
$919$	8.61501	−	14.9216i	0.284183	−	0.492219i	0.972411	+	0.233275i	$0.0749444\pi$
$920$	−81.6990			−2.69354
$921$	11.0884	+	4.31561i	0.365377	+	0.142204i
$922$	7.18338	−	4.14733i	0.236572	−	0.136585i
$923$	−1.39619	+	2.52038i	−0.0459561	+	0.0829592i
$924$	−21.8598	+	29.7957i	−0.719135	+	0.980205i
$925$	3.89094	−	3.89094i	0.127933	−	0.127933i
$926$	−67.3067	+	38.8596i	−2.21184	+	1.27700i
$927$	1.05317	−	4.73805i	0.0345905	−	0.155618i
$928$	2.74628	−	2.74628i	0.0901511	−	0.0901511i
$929$	−4.26590	+	15.9206i	−0.139960	+	0.522337i	0.859968	+	0.510347i	$0.170483\pi$
$929$	−4.26590	+	15.9206i	−0.139960	+	0.522337i	−0.999928	+	0.0119895i	$0.996184\pi$
$930$	−69.7402	+	55.9406i	−2.28687	+	1.83436i
$931$	0.461934	−	1.72396i	0.0151393	−	0.0565006i
$932$		−	52.3866i		−	1.71598i
$933$	23.8264	+	17.4804i	0.780040	+	0.572283i
$934$	4.73722	+	4.73722i	0.155006	+	0.155006i
$935$	−67.6619			−2.21278
$936$	−36.1484	−	32.0000i	−1.18155	−	1.04595i
$937$	15.0582			0.491932			0.245966	−	0.969279i	$-0.420895\pi$
$937$	15.0582			0.491932			0.245966	+	0.969279i	$0.420895\pi$
$938$	−2.90490	−	2.90490i	−0.0948484	−	0.0948484i
$939$	−2.22117	+	20.2294i	−0.0724851	+	0.660160i
$940$			113.221i			3.69286i
$941$	−2.71116	+	10.1182i	−0.0883812	+	0.329843i	−0.995933	−	0.0900970i	$-0.971282\pi$
$941$	−2.71116	+	10.1182i	−0.0883812	+	0.329843i	0.907552	+	0.419940i	$0.137949\pi$
$942$	10.2049	+	66.4254i	0.332495	+	2.16426i
$943$	15.5986	−	58.2146i	0.507959	−	1.89573i
$944$	−15.7710	+	15.7710i	−0.513303	+	0.513303i
$945$	10.0980	−	8.84084i	0.328489	−	0.287593i
$946$	118.148	−	68.2130i	3.84133	−	2.21779i
$947$	−30.9789	+	30.9789i	−1.00668	+	1.00668i	−0.00669996	+	0.999978i	$0.502133\pi$
$947$	−30.9789	+	30.9789i	−1.00668	+	1.00668i	−0.999978	+	0.00669996i	$0.997867\pi$
$948$	−86.1667	−	9.46104i	−2.79856	−	0.307280i
$949$	16.5903	−	0.294014i	0.538545	−	0.00954410i
$950$	6.24670	−	3.60653i	0.202670	−	0.117011i
$951$	−32.3549	+	25.9528i	−1.04918	+	0.841577i
$952$	21.0757			0.683068
$953$	5.27756	−	9.14100i	0.170957	−	0.296106i	−0.767798	−	0.640692i	$-0.778647\pi$
$953$	5.27756	−	9.14100i	0.170957	−	0.296106i	0.938755	+	0.344586i	$0.111981\pi$
$954$	−0.0197389	−	0.457940i	−0.000639070	−	0.0148263i
$955$	8.69702	+	32.4577i	0.281429	+	1.05031i
$956$	−94.2764	−	25.2613i	−3.04912	−	0.817008i
$957$	24.2793	+	9.44949i	0.784839	+	0.305459i
$958$	29.6464			0.957831
$959$	−1.33487	+	2.31206i	−0.0431051	+	0.0746602i
$960$	−42.7254	+	6.56391i	−1.37896	+	0.211849i
$961$	32.3151	+	18.6571i	1.04242	+	0.601843i
$962$	6.93540	−	27.8480i	0.223606	−	0.897856i
$963$	−6.12911	+	27.5740i	−0.197508	+	0.888560i
$964$	75.6537	+	20.2714i	2.43664	+	0.652896i
$965$		−	47.1771i		−	1.51869i
$966$	−11.9454	−	27.1684i	−0.384336	−	0.874130i
$967$	6.52692	+	1.74888i	0.209892	+	0.0562403i	0.362233	−	0.932088i	$-0.382015\pi$
$967$	6.52692	+	1.74888i	0.209892	+	0.0562403i	−0.152341	+	0.988328i	$0.548681\pi$
$968$	62.4108	+	62.4108i	2.00596	+	2.00596i
$969$	14.4281	−	2.21659i	0.463498	−	0.0712073i
$970$	93.9096	−	25.1630i	3.01525	−	0.807935i
$971$	−0.228527	−	0.131940i	−0.00733379	−	0.00423416i	0.496329	−	0.868135i	$-0.334681\pi$
$971$	−0.228527	−	0.131940i	−0.00733379	−	0.00423416i	−0.503662	+	0.863901i	$0.668014\pi$
$972$	52.6021	−	28.7634i	1.68721	−	0.922587i
$973$	−0.113704	+	0.424350i	−0.00364519	+	0.0136040i
$974$	11.3258	−	19.6169i	0.362903	−	0.628567i
$975$	8.02568	−	6.67473i	0.257027	−	0.213762i
$976$	13.5832	+	23.5269i	0.434789	+	0.753076i
$977$	−7.38994	+	1.98013i	−0.236425	+	0.0633499i	−0.375086	−	0.926990i	$-0.622387\pi$
$977$	−7.38994	+	1.98013i	−0.236425	+	0.0633499i	0.138661	+	0.990340i	$0.455720\pi$
$978$	54.3058	+	5.96274i	1.73651	+	0.190667i
$979$	−24.1815	+	13.9612i	−0.772845	+	0.446203i
$980$	7.02428	+	7.02428i	0.224383	+	0.224383i
$981$	1.61114	+	37.3783i	0.0514398	+	1.19340i
$982$	−36.6022	+	9.80753i	−1.16802	+	0.312971i
$983$	8.20565	+	30.6239i	0.261719	+	0.976750i	0.964228	+	0.265075i	$0.0853967\pi$
$983$	8.20565	+	30.6239i	0.261719	+	0.976750i	−0.702508	+	0.711675i	$0.747937\pi$
$984$	−7.17535	+	65.3497i	−0.228742	+	2.08327i
$985$	−1.86611	−	1.07740i	−0.0594591	−	0.0343288i
$986$	−8.01230	−	29.9023i	−0.255164	−	0.952284i
$987$	−18.0714	+	7.94561i	−0.575219	+	0.252911i
$988$	11.9929	−	21.6493i	0.381544	−	0.688756i
$989$			72.0811i			2.29204i
$990$	−55.7956	−	87.6891i	−1.77330	−	2.78694i
$991$	−9.45166	−	16.3707i	−0.300242	−	0.520034i	0.675949	−	0.736949i	$-0.263734\pi$
$991$	−9.45166	−	16.3707i	−0.300242	−	0.520034i	−0.976191	+	0.216915i	$0.930401\pi$
$992$	5.91948	+	10.2528i	0.187944	+	0.325528i
$993$	−5.10173	+	0.783779i	−0.161899	+	0.0248725i
$994$	1.36623	−	1.36623i	0.0433342	−	0.0433342i
$995$	−22.1837	+	22.1837i	−0.703270	+	0.703270i
$996$	19.7216	+	24.5866i	0.624901	+	0.779055i
$997$	−14.5437	−	25.1904i	−0.460604	−	0.797789i	0.538387	−	0.842698i	$-0.319034\pi$
$997$	−14.5437	−	25.1904i	−0.460604	−	0.797789i	−0.998991	+	0.0449081i	$0.985700\pi$
$998$	−5.60553	−	9.70905i	−0.177440	−	0.307335i
$999$	14.2150	+	9.51534i	0.449743	+	0.301052i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.ew.a.470.76	yes	336
9.5	odd	6		819.2.fy.a.743.76	yes	336
13.7	odd	12		819.2.fy.a.722.76	yes	336
117.59	even	12	inner	819.2.ew.a.176.76	✓	336

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
819.2.ew.a.176.76	✓	336	117.59	even	12	inner
819.2.ew.a.470.76	yes	336	1.1	even	1	trivial
819.2.fy.a.722.76	yes	336	13.7	odd	12
819.2.fy.a.743.76	yes	336	9.5	odd	6

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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.ew (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.70967 + 1.70967i) q^{2} +(1.58556 - 0.697137i) q^{3} +3.84596i q^{4} +(-0.668510 + 2.49492i) q^{5} +(3.90266 + 1.51891i) q^{6} +(0.258819 - 0.965926i) q^{7} +(-3.15599 + 3.15599i) q^{8} +(2.02800 - 2.21070i) q^{9} +O(q^{10})\)	\(q+(1.70967 + 1.70967i) q^{2} +(1.58556 - 0.697137i) q^{3} +3.84596i q^{4} +(-0.668510 + 2.49492i) q^{5} +(3.90266 + 1.51891i) q^{6} +(0.258819 - 0.965926i) q^{7} +(-3.15599 + 3.15599i) q^{8} +(2.02800 - 2.21070i) q^{9} +(-5.40842 + 3.12255i) q^{10} +(-3.92271 + 3.92271i) q^{11} +(2.68116 + 6.09800i) q^{12} +(-2.50393 + 2.59428i) q^{13} +(2.09391 - 1.20892i) q^{14} +(0.679334 + 4.42188i) q^{15} -3.09951 q^{16} +(2.36103 - 4.08942i) q^{17} +(7.24680 - 0.312364i) q^{18} +(0.461934 + 1.72396i) q^{19} +(-9.59535 - 2.57107i) q^{20} +(-0.263009 - 1.71197i) q^{21} -13.4131 q^{22} +(3.54343 - 6.13740i) q^{23} +(-2.80386 + 7.20418i) q^{24} +(-1.44757 - 0.835754i) q^{25} +(-8.71629 + 0.154470i) q^{26} +(1.67435 - 4.91900i) q^{27} +(3.71492 + 0.995408i) q^{28} -2.71145i q^{29} +(-6.39853 + 8.72141i) q^{30} +(7.98361 + 2.13920i) q^{31} +(1.01285 + 1.01285i) q^{32} +(-3.48503 + 8.95436i) q^{33} +(11.0282 - 2.95499i) q^{34} +(2.23688 + 1.29146i) q^{35} +(8.50229 + 7.79961i) q^{36} +(-0.852036 + 3.17984i) q^{37} +(-2.15765 + 3.73717i) q^{38} +(-2.16157 + 5.85898i) q^{39} +(-5.76412 - 9.98375i) q^{40} +(8.21444 - 2.20105i) q^{41} +(2.47724 - 3.37656i) q^{42} +(-8.80842 + 5.08554i) q^{43} +(-15.0866 - 15.0866i) q^{44} +(4.15978 + 6.53757i) q^{45} +(16.5511 - 4.43484i) q^{46} +(-2.94989 - 11.0091i) q^{47} +(-4.91445 + 2.16078i) q^{48} +(-0.866025 - 0.500000i) q^{49} +(-1.04600 - 3.90373i) q^{50} +(0.892666 - 8.12998i) q^{51} +(-9.97752 - 9.63004i) q^{52} -0.0631920i q^{53} +(11.2725 - 5.54728i) q^{54} +(-7.16446 - 12.4092i) q^{55} +(2.23162 + 3.86529i) q^{56} +(1.93426 + 2.41141i) q^{57} +(4.63570 - 4.63570i) q^{58} +(5.08824 - 5.08824i) q^{59} +(-17.0064 + 2.61269i) q^{60} +(-4.38239 - 7.59052i) q^{61} +(9.99203 + 17.3067i) q^{62} +(-1.61049 - 2.53107i) q^{63} +9.66228i q^{64} +(-4.79861 - 7.98141i) q^{65} +(-21.2673 + 9.35077i) q^{66} +(-0.439759 - 1.64120i) q^{67} +(15.7278 + 9.08043i) q^{68} +(1.33971 - 12.2015i) q^{69} +(1.61635 + 6.03231i) q^{70} +(0.771888 - 0.206827i) q^{71} +(0.576612 + 13.3773i) q^{72} +(-3.25414 - 3.25414i) q^{73} +(-6.89319 + 3.97979i) q^{74} +(-2.87784 - 0.315985i) q^{75} +(-6.63029 + 1.77658i) q^{76} +(2.77378 + 4.80432i) q^{77} +(-13.7125 + 6.32137i) q^{78} +(-6.50648 + 11.2696i) q^{79} +(2.07205 - 7.73300i) q^{80} +(-0.774428 - 8.96662i) q^{81} +(17.8071 + 10.2809i) q^{82} +(4.57034 - 1.22462i) q^{83} +(6.58416 - 1.01152i) q^{84} +(8.62438 + 8.62438i) q^{85} +(-23.7541 - 6.36490i) q^{86} +(-1.89025 - 4.29917i) q^{87} -24.7601i q^{88} +(4.86179 + 1.30271i) q^{89} +(-4.06524 + 18.2890i) q^{90} +(1.85782 + 3.09007i) q^{91} +(23.6042 + 13.6279i) q^{92} +(14.1498 - 2.17384i) q^{93} +(13.7787 - 23.8653i) q^{94} -4.60995 q^{95} +(2.31202 + 0.899835i) q^{96} +(-15.0373 - 4.02923i) q^{97} +(-0.625784 - 2.33546i) q^{98} +(0.716695 + 16.6272i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 336 q + 24 q^{6} - 36 q^{8}+O(q^{10}) \) 336 * q + 24 * q^6 - 36 * q^8	\( 336 q + 24 q^{6} - 36 q^{8} + 16 q^{15} - 336 q^{16} + 20 q^{18} + 8 q^{21} + 8 q^{24} + 96 q^{26} + 24 q^{27} - 96 q^{30} - 72 q^{32} - 36 q^{33} - 12 q^{36} - 72 q^{38} - 16 q^{39} - 48 q^{41} - 28 q^{45} + 60 q^{47} - 48 q^{48} + 132 q^{50} - 36 q^{52} - 108 q^{54} + 68 q^{57} - 72 q^{58} - 44 q^{60} - 36 q^{62} - 8 q^{63} - 72 q^{65} - 20 q^{66} - 72 q^{69} + 48 q^{71} - 104 q^{72} + 12 q^{74} + 104 q^{78} - 12 q^{79} + 96 q^{80} - 68 q^{81} - 120 q^{83} - 12 q^{84} + 36 q^{85} + 48 q^{86} - 24 q^{87} - 60 q^{89} - 72 q^{92} - 172 q^{93} - 48 q^{94} - 152 q^{96} + 48 q^{97}+O(q^{100}) \) 336 * q + 24 * q^6 - 36 * q^8 + 16 * q^15 - 336 * q^16 + 20 * q^18 + 8 * q^21 + 8 * q^24 + 96 * q^26 + 24 * q^27 - 96 * q^30 - 72 * q^32 - 36 * q^33 - 12 * q^36 - 72 * q^38 - 16 * q^39 - 48 * q^41 - 28 * q^45 + 60 * q^47 - 48 * q^48 + 132 * q^50 - 36 * q^52 - 108 * q^54 + 68 * q^57 - 72 * q^58 - 44 * q^60 - 36 * q^62 - 8 * q^63 - 72 * q^65 - 20 * q^66 - 72 * q^69 + 48 * q^71 - 104 * q^72 + 12 * q^74 + 104 * q^78 - 12 * q^79 + 96 * q^80 - 68 * q^81 - 120 * q^83 - 12 * q^84 + 36 * q^85 + 48 * q^86 - 24 * q^87 - 60 * q^89 - 72 * q^92 - 172 * q^93 - 48 * q^94 - 152 * q^96 + 48 * q^97

Introduction

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