LMFDB - Embedded newform 804.2.l.a.431.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(431,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 4]))

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

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

chi := DirichletCharacter("804.431");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.l (of order $6$, degree $2$, 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:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$264$
Relative dimension:	$132$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			431.6
Character	$\chi$	$=$	804.431
Dual form			804.2.l.a.707.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40119 - 0.191474i) q^{2} +(-0.473255 - 1.66614i) q^{3} +(1.92668 + 0.536583i) q^{4} -0.531500i q^{5} +(0.344098 + 2.42520i) q^{6} +(0.910512 - 0.525684i) q^{7} +(-2.59690 - 1.12076i) q^{8} +(-2.55206 + 1.57702i) q^{9} +O(q^{10})$	\(q+(-1.40119 - 0.191474i) q^{2} +(-0.473255 - 1.66614i) q^{3} +(1.92668 + 0.536583i) q^{4} -0.531500i q^{5} +(0.344098 + 2.42520i) q^{6} +(0.910512 - 0.525684i) q^{7} +(-2.59690 - 1.12076i) q^{8} +(-2.55206 + 1.57702i) q^{9} +(-0.101768 + 0.744733i) q^{10} +(2.86965 + 4.97037i) q^{11} +(-0.0177859 - 3.46406i) q^{12} +(0.517455 - 0.896257i) q^{13} +(-1.37646 + 0.562245i) q^{14} +(-0.885554 + 0.251535i) q^{15} +(3.42416 + 2.06764i) q^{16} +(0.480115 + 0.277195i) q^{17} +(3.87788 - 1.72105i) q^{18} +(5.41874 + 3.12851i) q^{19} +(0.285193 - 1.02403i) q^{20} +(-1.30677 - 1.26826i) q^{21} +(-3.06923 - 7.51391i) q^{22} +(-2.18538 + 3.78520i) q^{23} +(-0.638354 + 4.85721i) q^{24} +4.71751 q^{25} +(-0.896663 + 1.15675i) q^{26} +(3.83531 + 3.50576i) q^{27} +(2.03633 - 0.524258i) q^{28} +(0.383122 - 0.221196i) q^{29} +(1.28899 - 0.182888i) q^{30} +(-3.07570 + 1.77576i) q^{31} +(-4.40200 - 3.55280i) q^{32} +(6.92328 - 7.13349i) q^{33} +(-0.619658 - 0.480332i) q^{34} +(-0.279401 - 0.483937i) q^{35} +(-5.76319 + 1.66902i) q^{36} +(-0.686263 + 1.18864i) q^{37} +(-6.99366 - 5.42118i) q^{38} +(-1.73818 - 0.437994i) q^{39} +(-0.595685 + 1.38025i) q^{40} +(3.45373 - 1.99401i) q^{41} +(1.58819 + 2.02729i) q^{42} +6.20627i q^{43} +(2.86186 + 11.1161i) q^{44} +(0.838186 + 1.35642i) q^{45} +(3.78691 - 4.88534i) q^{46} +(-1.62370 - 2.81233i) q^{47} +(1.82448 - 6.68366i) q^{48} +(-2.94731 + 5.10489i) q^{49} +(-6.61013 - 0.903279i) q^{50} +(0.234629 - 0.931124i) q^{51} +(1.47788 - 1.44914i) q^{52} -12.0440i q^{53} +(-4.70275 - 5.64661i) q^{54} +(2.64175 - 1.52522i) q^{55} +(-2.95367 + 0.344682i) q^{56} +(2.64810 - 10.5090i) q^{57} +(-0.579180 + 0.236580i) q^{58} +6.55143 q^{59} +(-1.84114 + 0.00945319i) q^{60} +(1.68526 - 2.91895i) q^{61} +(4.64966 - 1.89926i) q^{62} +(-1.49467 + 2.77747i) q^{63} +(5.48778 + 5.82102i) q^{64} +(-0.476361 - 0.275027i) q^{65} +(-11.0667 + 8.66977i) q^{66} +(-7.83059 - 2.38366i) q^{67} +(0.776289 + 0.791686i) q^{68} +(7.34092 + 1.84980i) q^{69} +(0.298833 + 0.731586i) q^{70} +(6.44628 + 11.1653i) q^{71} +(8.39491 - 1.23511i) q^{72} +(2.95490 - 5.11805i) q^{73} +(1.18918 - 1.53411i) q^{74} +(-2.23258 - 7.86004i) q^{75} +(8.76144 + 8.93522i) q^{76} +(5.22569 + 3.01706i) q^{77} +(2.35166 + 0.946530i) q^{78} +(10.0472 - 5.80073i) q^{79} +(1.09895 - 1.81994i) q^{80} +(4.02602 - 8.04930i) q^{81} +(-5.22114 + 2.13270i) q^{82} +(2.50168 - 4.33304i) q^{83} +(-1.83719 - 3.14471i) q^{84} +(0.147329 - 0.255181i) q^{85} +(1.18834 - 8.69618i) q^{86} +(-0.549858 - 0.533654i) q^{87} +(-1.88158 - 16.1238i) q^{88} -11.4126i q^{89} +(-0.914740 - 2.06109i) q^{90} -1.08807i q^{91} +(-6.24160 + 6.12021i) q^{92} +(4.41426 + 4.28417i) q^{93} +(1.73662 + 4.25150i) q^{94} +(1.66280 - 2.88006i) q^{95} +(-3.83620 + 9.01574i) q^{96} +(-2.86039 + 4.95434i) q^{97} +(5.10720 - 6.58860i) q^{98} +(-15.1619 - 8.15920i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 264 q - 2 q^{4} - 3 q^{6} - 12 q^{9}+O(q^{10}) $ 264 * q - 2 * q^4 - 3 * q^6 - 12 * q^9	$ 264 q - 2 q^{4} - 3 q^{6} - 12 q^{9} + 2 q^{10} + 2 q^{12} - 18 q^{16} + q^{18} - 4 q^{22} - 248 q^{25} + 7 q^{30} - 38 q^{34} + 13 q^{36} + 4 q^{37} + 48 q^{40} - 12 q^{42} + 48 q^{45} - 2 q^{46} - 11 q^{48} + 128 q^{49} + 32 q^{52} - 8 q^{54} - 2 q^{57} - 32 q^{58} + 68 q^{60} - 8 q^{61} + 4 q^{64} + 30 q^{66} - 40 q^{69} - 140 q^{70} + 108 q^{72} - 4 q^{73} - 120 q^{76} + 44 q^{78} - 28 q^{81} - 64 q^{82} + 33 q^{84} + 16 q^{85} - 14 q^{88} + 42 q^{90} + 16 q^{93} - 12 q^{94} - 4 q^{96} + 20 q^{97}+O(q^{100}) $ 264 * q - 2 * q^4 - 3 * q^6 - 12 * q^9 + 2 * q^10 + 2 * q^12 - 18 * q^16 + q^18 - 4 * q^22 - 248 * q^25 + 7 * q^30 - 38 * q^34 + 13 * q^36 + 4 * q^37 + 48 * q^40 - 12 * q^42 + 48 * q^45 - 2 * q^46 - 11 * q^48 + 128 * q^49 + 32 * q^52 - 8 * q^54 - 2 * q^57 - 32 * q^58 + 68 * q^60 - 8 * q^61 + 4 * q^64 + 30 * q^66 - 40 * q^69 - 140 * q^70 + 108 * q^72 - 4 * q^73 - 120 * q^76 + 44 * q^78 - 28 * q^81 - 64 * q^82 + 33 * q^84 + 16 * q^85 - 14 * q^88 + 42 * q^90 + 16 * q^93 - 12 * q^94 - 4 * q^96 + 20 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$-1$

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 $

$2$	−1.40119	−	0.191474i	−0.990792	−	0.135392i
$2$	−1.40119	−	0.191474i	−0.990792	−	0.135392i
$3$	−0.473255	−	1.66614i	−0.273234	−	0.961948i
$3$	−0.473255	−	1.66614i	−0.273234	−	0.961948i
$4$	1.92668	+	0.536583i	0.963338	+	0.268291i
$5$		−	0.531500i		−	0.237694i	−0.992913	−	0.118847i	$-0.962080\pi$
$5$		−	0.531500i		−	0.237694i	0.992913	−	0.118847i	$-0.0379198\pi$
$6$	0.344098	+	2.42520i	0.140478	+	0.990084i
$7$	0.910512	−	0.525684i	0.344141	−	0.198690i	−0.317961	−	0.948104i	$-0.602998\pi$
$7$	0.910512	−	0.525684i	0.344141	−	0.198690i	0.662102	+	0.749414i	$0.269665\pi$
$8$	−2.59690	−	1.12076i	−0.918143	−	0.396249i
$9$	−2.55206	+	1.57702i	−0.850687	+	0.525673i
$10$	−0.101768	+	0.744733i	−0.0321819	+	0.235505i
$11$	2.86965	+	4.97037i	0.865231	+	1.49862i	0.866818	+	0.498625i	$0.166162\pi$
$11$	2.86965	+	4.97037i	0.865231	+	1.49862i	−0.00158652	+	0.999999i	$0.500505\pi$
$12$	−0.0177859	−	3.46406i	−0.00513434	−	0.999987i
$13$	0.517455	−	0.896257i	0.143516	−	0.248577i	−0.785302	−	0.619113i	$-0.787492\pi$
$13$	0.517455	−	0.896257i	0.143516	−	0.248577i	0.928818	+	0.370535i	$0.120826\pi$
$14$	−1.37646	+	0.562245i	−0.367873	+	0.150266i
$15$	−0.885554	+	0.251535i	−0.228649	+	0.0649460i
$16$	3.42416	+	2.06764i	0.856040	+	0.516910i
$17$	0.480115	+	0.277195i	0.116445	+	0.0672296i	0.557091	−	0.830451i	$-0.311917\pi$
$17$	0.480115	+	0.277195i	0.116445	+	0.0672296i	−0.440646	+	0.897681i	$0.645251\pi$
$18$	3.87788	−	1.72105i	0.914026	−	0.405657i
$19$	5.41874	+	3.12851i	1.24314	+	0.717729i	0.969733	−	0.244168i	$-0.0785150\pi$
$19$	5.41874	+	3.12851i	1.24314	+	0.717729i	0.273410	+	0.961898i	$0.411848\pi$
$20$	0.285193	−	1.02403i	0.0637712	−	0.228979i
$21$	−1.30677	−	1.26826i	−0.285160	−	0.276757i
$22$	−3.06923	−	7.51391i	−0.654362	−	1.60197i
$23$	−2.18538	+	3.78520i	−0.455684	+	0.789268i	−0.998727	−	0.0504369i	$-0.983939\pi$
$23$	−2.18538	+	3.78520i	−0.455684	+	0.789268i	0.543043	+	0.839705i	$0.317272\pi$
$24$	−0.638354	+	4.85721i	−0.130303	+	0.991474i
$25$	4.71751			0.943502
$26$	−0.896663	+	1.15675i	−0.175850	+	0.226857i
$27$	3.83531	+	3.50576i	0.738107	+	0.674684i
$28$	2.03633	−	0.524258i	0.384831	−	0.0990755i
$29$	0.383122	−	0.221196i	0.0711440	−	0.0410750i	−0.464006	−	0.885832i	$-0.653588\pi$
$29$	0.383122	−	0.221196i	0.0711440	−	0.0410750i	0.535150	+	0.844757i	$0.320255\pi$
$30$	1.28899	−	0.182888i	0.235337	−	0.0333907i
$31$	−3.07570	+	1.77576i	−0.552413	+	0.318936i	−0.750095	−	0.661331i	$-0.769992\pi$
$31$	−3.07570	+	1.77576i	−0.552413	+	0.318936i	0.197682	+	0.980266i	$0.436659\pi$
$32$	−4.40200	−	3.55280i	−0.778172	−	0.628052i
$33$	6.92328	−	7.13349i	1.20519	−	1.24178i
$34$	−0.619658	−	0.480332i	−0.106270	−	0.0823763i
$35$	−0.279401	−	0.483937i	−0.0472274	−	0.0818002i
$36$	−5.76319	+	1.66902i	−0.960532	+	0.278169i
$37$	−0.686263	+	1.18864i	−0.112821	+	0.195411i	−0.916907	−	0.399102i	$-0.869322\pi$
$37$	−0.686263	+	1.18864i	−0.112821	+	0.195411i	0.804086	+	0.594513i	$0.202655\pi$
$38$	−6.99366	−	5.42118i	−1.13452	−	0.879432i
$39$	−1.73818	−	0.437994i	−0.278332	−	0.0701352i
$40$	−0.595685	+	1.38025i	−0.0941861	+	0.218237i
$41$	3.45373	−	1.99401i	0.539383	−	0.311413i	−0.205446	−	0.978668i	$-0.565865\pi$
$41$	3.45373	−	1.99401i	0.539383	−	0.311413i	0.744829	+	0.667256i	$0.232531\pi$
$42$	1.58819	+	2.02729i	0.245064	+	0.312817i
$43$			6.20627i			0.946448i	0.880942	+	0.473224i	$0.156910\pi$
$43$			6.20627i			0.946448i	−0.880942	+	0.473224i	$0.843090\pi$
$44$	2.86186	+	11.1161i	0.431442	+	1.67582i
$45$	0.838186	+	1.35642i	0.124949	+	0.202203i
$46$	3.78691	−	4.88534i	0.558349	−	0.720304i
$47$	−1.62370	−	2.81233i	−0.236841	−	0.410220i	0.722965	−	0.690884i	$-0.242779\pi$
$47$	−1.62370	−	2.81233i	−0.236841	−	0.410220i	−0.959806	+	0.280664i	$0.909445\pi$
$48$	1.82448	−	6.68366i	0.263342	−	0.964703i
$49$	−2.94731	+	5.10489i	−0.421045	+	0.729271i
$50$	−6.61013	−	0.903279i	−0.934814	−	0.127743i
$51$	0.234629	−	0.931124i	0.0328546	−	0.130383i
$52$	1.47788	−	1.44914i	0.204946	−	0.200960i
$53$		−	12.0440i		−	1.65437i	−0.561927	−	0.827187i	$-0.689940\pi$
$53$		−	12.0440i		−	1.65437i	0.561927	−	0.827187i	$-0.310060\pi$
$54$	−4.70275	−	5.64661i	−0.639963	−	0.768406i
$55$	2.64175	−	1.52522i	0.356214	−	0.205660i
$56$	−2.95367	+	0.344682i	−0.394701	+	0.0460600i
$57$	2.64810	−	10.5090i	0.350749	−	1.39195i
$58$	−0.579180	+	0.236580i	−0.0760501	+	0.0310644i
$59$	6.55143			0.852923			0.426462	−	0.904506i	$-0.359760\pi$
$59$	6.55143			0.852923			0.426462	+	0.904506i	$0.359760\pi$
$60$	−1.84114	+	0.00945319i	−0.237691	+	0.00122040i
$61$	1.68526	−	2.91895i	0.215775	−	0.373734i	−0.737737	−	0.675088i	$-0.764106\pi$
$61$	1.68526	−	2.91895i	0.215775	−	0.373734i	0.953512	+	0.301355i	$0.0974388\pi$
$62$	4.64966	−	1.89926i	0.590508	−	0.241206i
$63$	−1.49467	+	2.77747i	−0.188310	+	0.349929i
$64$	5.48778	+	5.82102i	0.685973	+	0.727627i
$65$	−0.476361	−	0.275027i	−0.0590853	−	0.0341129i
$66$	−11.0667	+	8.66977i	−1.36222	+	1.06717i
$67$	−7.83059	−	2.38366i	−0.956659	−	0.291210i
$67$	−7.83059	−	2.38366i	−0.956659	−	0.291210i
$68$	0.776289	+	0.791686i	0.0941388	+	0.0960060i
$69$	7.34092	+	1.84980i	0.883743	+	0.222689i
$70$	0.298833	+	0.731586i	0.0357174	+	0.0874412i
$71$	6.44628	+	11.1653i	0.765032	+	1.32507i	0.940230	+	0.340541i	$0.110610\pi$
$71$	6.44628	+	11.1653i	0.765032	+	1.32507i	−0.175197	+	0.984533i	$0.556056\pi$
$72$	8.39491	−	1.23511i	0.989350	−	0.145559i
$73$	2.95490	−	5.11805i	0.345845	−	0.599022i	−0.639662	−	0.768657i	$-0.720925\pi$
$73$	2.95490	−	5.11805i	0.345845	−	0.599022i	0.985507	+	0.169635i	$0.0542588\pi$
$74$	1.18918	−	1.53411i	0.138239	−	0.178337i
$75$	−2.23258	−	7.86004i	−0.257797	−	0.907599i
$76$	8.76144	+	8.93522i	1.00501	+	1.02494i
$77$	5.22569	+	3.01706i	0.595523	+	0.343825i
$78$	2.35166	+	0.946530i	0.266273	+	0.107173i
$79$	10.0472	−	5.80073i	1.13039	−	0.652634i	0.186361	−	0.982481i	$-0.440331\pi$
$79$	10.0472	−	5.80073i	1.13039	−	0.652634i	0.944034	+	0.329848i	$0.106997\pi$
$80$	1.09895	−	1.81994i	0.122866	−	0.203475i
$81$	4.02602	−	8.04930i	0.447335	−	0.894366i
$82$	−5.22114	+	2.13270i	−0.576579	+	0.235517i
$83$	2.50168	−	4.33304i	0.274595	−	0.475612i	−0.695438	−	0.718586i	$-0.744790\pi$
$83$	2.50168	−	4.33304i	0.274595	−	0.475612i	0.970033	+	0.242974i	$0.0781229\pi$
$84$	−1.83719	−	3.14471i	−0.200454	−	0.343116i
$85$	0.147329	−	0.255181i	0.0159801	−	0.0276783i
$86$	1.18834	−	8.69618i	0.128142	−	0.937733i
$87$	−0.549858	−	0.533654i	−0.0589509	−	0.0572137i
$88$	−1.88158	−	16.1238i	−0.200577	−	1.71880i
$89$		−	11.4126i		−	1.20973i	−0.796328	−	0.604865i	$-0.793227\pi$
$89$		−	11.4126i		−	1.20973i	0.796328	−	0.604865i	$-0.206773\pi$
$90$	−0.914740	−	2.06109i	−0.0964221	−	0.217258i
$91$		−	1.08807i		−	0.114061i
$92$	−6.24160	+	6.12021i	−0.650731	+	0.638075i
$93$	4.41426	+	4.28417i	0.457737	+	0.444248i
$94$	1.73662	+	4.25150i	0.179119	+	0.438509i
$95$	1.66280	−	2.88006i	0.170600	−	0.295487i
$96$	−3.83620	+	9.01574i	−0.391530	+	0.920165i
$97$	−2.86039	+	4.95434i	−0.290429	+	0.503037i	−0.973911	−	0.226930i	$-0.927131\pi$
$97$	−2.86039	+	4.95434i	−0.290429	+	0.503037i	0.683483	+	0.729967i	$0.260465\pi$
$98$	5.10720	−	6.58860i	0.515905	−	0.665549i
$99$	−15.1619	−	8.15920i	−1.52383	−	0.820030i
$100$	9.08911	+	2.53133i	0.908911	+	0.253133i
$101$	−2.85816	+	1.65016i	−0.284398	+	0.164197i	−0.635413	−	0.772173i	$-0.719170\pi$
$101$	−2.85816	+	1.65016i	−0.284398	+	0.164197i	0.351015	+	0.936370i	$0.385837\pi$
$102$	−0.507046	+	1.25976i	−0.0502050	+	0.124735i
$103$	16.4527	−	9.49896i	1.62113	−	0.935960i	0.634512	−	0.772913i	$-0.281201\pi$
$103$	16.4527	−	9.49896i	1.62113	−	0.935960i	0.986618	−	0.163047i	$-0.0521321\pi$
$104$	−2.34827	+	1.74755i	−0.230267	+	0.171361i
$105$	−0.674079	+	0.694547i	−0.0657834	+	0.0677808i
$106$	−2.30611	+	16.8760i	−0.223989	+	1.63914i
$107$	6.75990			0.653504			0.326752	−	0.945110i	$-0.394046\pi$
$107$	6.75990			0.653504			0.326752	+	0.945110i	$0.394046\pi$
$108$	5.50828	+	8.81243i	0.530034	+	0.847976i
$109$	−9.73792			−0.932724			−0.466362	−	0.884594i	$-0.654436\pi$
$109$	−9.73792			−0.932724			−0.466362	+	0.884594i	$0.654436\pi$
$110$	−3.99364	+	1.63129i	−0.380779	+	0.155538i
$111$	2.30522	+	0.580880i	0.218802	+	0.0551347i
$112$	4.20466	+	0.0825857i	0.397303	+	0.00780362i
$113$	6.44838	−	3.72297i	0.606612	−	0.350228i	−0.165026	−	0.986289i	$-0.552771\pi$
$113$	6.44838	−	3.72297i	0.606612	−	0.350228i	0.771638	+	0.636061i	$0.219438\pi$
$114$	−5.72268	+	14.2180i	−0.535978	+	1.33164i
$115$	2.01183	+	1.16153i	0.187604	+	0.108313i
$116$	0.856841	−	0.220596i	0.0795557	−	0.0204818i
$117$	0.0928413	+	3.10334i	0.00858318	+	0.286904i
$118$	−9.17981	−	1.25443i	−0.845070	−	0.115479i
$119$	0.582867			0.0534314
$120$	2.58161	+	0.339285i	0.235667	+	0.0309723i
$121$	−10.9697	+	19.0002i	−0.997250	+	1.72729i
$122$	−2.92027	+	3.76733i	−0.264389	+	0.341078i
$123$	−4.95681	−	4.81073i	−0.446940	−	0.433769i
$124$	−6.87872	+	1.77094i	−0.617728	+	0.159035i
$125$		−	5.16485i		−	0.461958i
$126$	2.62613	−	3.60558i	0.233954	−	0.321211i
$127$	−9.45619	+	5.45953i	−0.839101	+	0.484455i	−0.856958	−	0.515385i	$-0.827649\pi$
$127$	−9.45619	+	5.45953i	−0.839101	+	0.484455i	0.0178577	+	0.999841i	$0.494315\pi$
$128$	−6.57486	−	9.20713i	−0.581141	−	0.813803i
$129$	10.3405	−	2.93715i	0.910433	−	0.258602i
$130$	0.614812	+	0.476576i	0.0539226	+	0.0417985i
$131$	−1.05983			−0.0925979			−0.0462989	−	0.998928i	$-0.514743\pi$
$131$	−1.05983			−0.0925979			−0.0462989	+	0.998928i	$0.514743\pi$
$132$	17.1666	−	10.0290i	1.49416	−	0.872914i
$133$	6.57843			0.570422
$134$	10.5158	+	4.83931i	0.908423	+	0.418053i
$135$	1.86331	−	2.03847i	0.160368	−	0.175443i
$136$	−0.936142	−	1.25794i	−0.0802735	−	0.107868i
$137$			6.80773i			0.581624i	0.956780	+	0.290812i	$0.0939254\pi$
$137$			6.80773i			0.581624i	−0.956780	+	0.290812i	$0.906075\pi$
$138$	−9.93184	−	3.99751i	−0.845455	−	0.340291i
$139$			5.41165i			0.459010i	0.973307	+	0.229505i	$0.0737108\pi$
$139$			5.41165i			0.459010i	−0.973307	+	0.229505i	$0.926289\pi$
$140$	−0.278643	−	1.08231i	−0.0235496	−	0.0914719i
$141$	−3.91731	+	4.03626i	−0.329897	+	0.339914i
$142$	−6.89461	−	16.8790i	−0.578583	−	1.41645i
$143$	5.93965			0.496698
$144$	−11.9994	+	0.123223i	−0.999947	+	0.0102685i
$145$	−0.117565	−	0.203629i	−0.00976327	−	0.0169105i
$146$	−5.12036	+	6.60558i	−0.423764	+	0.546681i
$147$	9.90031	+	2.49472i	0.816564	+	0.205761i
$148$	−1.96001	+	1.92189i	−0.161112	+	0.157978i
$149$			4.51715i			0.370059i	0.982733	+	0.185030i	$0.0592381\pi$
$149$			4.51715i			0.370059i	−0.982733	+	0.185030i	$0.940762\pi$
$150$	1.62329	+	11.4409i	0.132541	+	0.934146i
$151$	1.37628	+	0.794594i	0.112000	+	0.0646632i	0.554954	−	0.831881i	$-0.312736\pi$
$151$	1.37628	+	0.794594i	0.112000	+	0.0646632i	−0.442954	+	0.896545i	$0.646069\pi$
$152$	−10.5656	−	14.1975i	−0.856983	−	1.15157i
$153$	−1.66242	+	0.0497341i	−0.134399	+	0.00402076i
$154$	−6.74451	−	5.22806i	−0.543488	−	0.421289i
$155$	0.943815	+	1.63474i	0.0758090	+	0.131305i
$156$	−3.11389	−	1.77655i	−0.249311	−	0.142238i
$157$	−6.33861	+	10.9788i	−0.505876	+	0.876203i	0.494101	+	0.869405i	$0.335497\pi$
$157$	−6.33861	+	10.9788i	−0.505876	+	0.876203i	−0.999977	+	0.00679829i	$0.997836\pi$
$158$	−15.1887	+	6.20417i	−1.20835	+	0.493577i
$159$	−20.0670	+	5.69989i	−1.59142	+	0.452031i
$160$	−1.88831	+	2.33966i	−0.149284	+	0.184967i
$161$			4.59529i			0.362159i
$162$	−7.18245	+	10.5077i	−0.564306	+	0.825565i
$163$	−7.09886	+	4.09853i	−0.556025	+	0.321021i	−0.751549	−	0.659678i	$-0.770693\pi$
$163$	−7.09886	+	4.09853i	−0.556025	+	0.321021i	0.195523	+	0.980699i	$0.437359\pi$
$164$	7.72418	−	1.98860i	0.603157	−	0.155284i
$165$	−3.79145	−	3.67972i	−0.295164	−	0.286466i
$166$	−4.33499	+	5.59241i	−0.336461	+	0.434055i
$167$	9.88553	+	17.1222i	0.764965	+	1.32496i	0.940265	+	0.340444i	$0.110577\pi$
$167$	9.88553	+	17.1222i	0.764965	+	1.32496i	−0.175299	+	0.984515i	$0.556089\pi$
$168$	1.97213	+	4.75812i	0.152153	+	0.367097i
$169$	5.96448	+	10.3308i	0.458806	+	0.794676i
$170$	−0.255296	+	0.329348i	−0.0195803	+	0.0252598i
$171$	−18.7627	+	0.561315i	−1.43482	+	0.0429248i
$172$	−3.33018	+	11.9575i	−0.253924	+	0.911749i
$173$	−19.7293	−	11.3907i	−1.49999	−	0.866019i	−0.499989	−	0.866032i	$-0.666662\pi$
$173$	−19.7293	−	11.3907i	−1.49999	−	0.866019i	−1.00000		1.32618e-5i	$0.999996\pi$
$174$	0.668275	+	0.853034i	0.0506618	+	0.0646684i
$175$	4.29535	−	2.47992i	0.324698	−	0.187464i
$176$	−0.450826	+	22.9527i	−0.0339823	+	1.73013i
$177$	−3.10050	−	10.9156i	−0.233048	−	0.820468i
$178$	−2.18521	+	15.9912i	−0.163788	+	1.19859i
$179$	−22.1591			−1.65625			−0.828124	−	0.560544i	$-0.810592\pi$
$179$	−22.1591			−1.65625			−0.828124	+	0.560544i	$0.810592\pi$
$180$	0.887081	+	3.06313i	0.0661191	+	0.228313i
$181$	0.649640	+	1.12521i	0.0482874	+	0.0836362i	0.889159	−	0.457599i	$-0.151290\pi$
$181$	0.649640	+	1.12521i	0.0482874	+	0.0836362i	−0.840871	+	0.541235i	$0.817957\pi$
$182$	−0.208337	+	1.52460i	−0.0154430	+	0.113011i
$183$	−5.66095	−	1.42647i	−0.418469	−	0.105448i
$184$	9.91753	−	7.38048i	0.731130	−	0.544096i
$185$	0.631763	+	0.364748i	0.0464481	+	0.0268168i
$186$	−5.36491	−	6.84816i	−0.393375	−	0.502132i
$187$			3.18180i			0.232676i
$188$	−1.61929	−	6.28969i	−0.118099	−	0.458723i
$189$	5.33502	+	1.17587i	0.388066	+	0.0855321i
$190$	−2.88136	+	3.71713i	−0.209036	+	0.269669i
$191$	1.49757	−	2.59387i	0.108360	−	0.187686i	−0.806746	−	0.590899i	$-0.798773\pi$
$191$	1.49757	−	2.59387i	0.108360	−	0.187686i	0.915106	+	0.403213i	$0.132107\pi$
$192$	7.10152	−	11.8983i	0.512508	−	0.858682i
$193$	21.7830			1.56798			0.783989	−	0.620775i	$-0.213182\pi$
$193$	21.7830			1.56798			0.783989	+	0.620775i	$0.213182\pi$
$194$	4.95658	−	6.39429i	0.355862	−	0.459083i
$195$	−0.232794	+	0.923842i	−0.0166707	+	0.0661577i
$196$	−8.41771	+	8.25400i	−0.601265	+	0.589571i
$197$	7.31851	−	4.22534i	0.521422	−	0.301043i	−0.216094	−	0.976372i	$-0.569332\pi$
$197$	7.31851	−	4.22534i	0.521422	−	0.301043i	0.737516	+	0.675329i	$0.235999\pi$
$198$	19.6824	+	14.3357i	1.39877	+	1.01879i
$199$	−8.52176	−	4.92004i	−0.604092	−	0.348772i	0.166558	−	0.986032i	$-0.446735\pi$
$199$	−8.52176	−	4.92004i	−0.604092	−	0.348772i	−0.770650	+	0.637259i	$0.780068\pi$
$200$	−12.2509	−	5.28721i	−0.866269	−	0.373862i
$201$	−0.265646	+	14.1750i	−0.0187372	+	0.999824i
$202$	4.32079	−	1.76493i	0.304010	−	0.124180i
$203$	0.232558	−	0.402802i	0.0163224	−	0.0282712i
$204$	0.951679	−	1.66808i	0.0666308	−	0.116789i
$205$	−1.05982	−	1.83566i	−0.0740209	−	0.128208i
$206$	−24.8721	+	10.1596i	−1.73292	+	0.707853i
$207$	−0.392100	−	13.1064i	−0.0272528	−	0.910960i
$208$	3.62499	−	1.99902i	0.251347	−	0.138607i
$209$			35.9109i			2.48401i
$210$	1.07750	−	0.844125i	0.0743547	−	0.0582502i
$211$	−16.3395	−	9.43364i	−1.12486	−	0.649438i	−0.182223	−	0.983257i	$-0.558329\pi$
$211$	−16.3395	−	9.43364i	−1.12486	−	0.649438i	−0.942637	+	0.333819i	$0.891663\pi$
$212$	6.46261	−	23.2049i	0.443854	−	1.59372i
$213$	15.5522	−	16.0244i	1.06562	−	1.09798i
$214$	−9.47191	−	1.29434i	−0.647487	−	0.0884794i
$215$	3.29863			0.224965
$216$	−6.03080	−	13.4026i	−0.410344	−	0.911931i
$217$	−1.86698	+	3.23370i	−0.126739	+	0.219518i
$218$	13.6447	+	1.86456i	0.924135	+	0.126284i
$219$	−9.92581	−	2.50115i	−0.670724	−	0.169012i
$220$	5.90820	−	1.52108i	0.398331	−	0.102551i
$221$	0.496876	−	0.286871i	0.0334235	−	0.0192970i
$222$	−3.11884	−	1.25531i	−0.209323	−	0.0842512i
$223$			7.31394i			0.489777i	0.969551	+	0.244889i	$0.0787514\pi$
$223$			7.31394i			0.489777i	−0.969551	+	0.244889i	$0.921249\pi$
$224$	−5.87572	−	0.920800i	−0.392588	−	0.0615236i
$225$	−12.0394	+	7.43960i	−0.802624	+	0.495974i
$226$	−9.74826	+	3.98190i	−0.648445	+	0.264872i
$227$	−5.10103	−	8.83524i	−0.338567	−	0.586415i	0.645596	−	0.763679i	$-0.276609\pi$
$227$	−5.10103	−	8.83524i	−0.338567	−	0.586415i	−0.984163	+	0.177264i	$0.943276\pi$
$228$	10.7410	−	18.8264i	0.711337	−	1.24681i
$229$	12.9850	−	22.4906i	0.858070	−	1.48622i	−0.0156973	−	0.999877i	$-0.504997\pi$
$229$	12.9850	−	22.4906i	0.858070	−	1.48622i	0.873767	−	0.486344i	$-0.161670\pi$
$230$	−2.59656	−	2.01274i	−0.171212	−	0.132716i
$231$	2.55376	−	10.1346i	0.168025	−	0.666807i
$232$	−1.24284	+	0.145034i	−0.0815963	+	0.00952195i
$233$	−18.6133	+	10.7464i	−1.21940	+	0.704021i	−0.964790	−	0.263023i	$-0.915280\pi$
$233$	−18.6133	+	10.7464i	−1.21940	+	0.704021i	−0.254610	+	0.967044i	$0.581947\pi$
$234$	0.464119	−	4.36615i	0.0303404	−	0.285424i
$235$	−1.49475	+	0.862994i	−0.0975067	+	0.0562955i
$236$	12.6225	+	3.51538i	0.821653	+	0.228832i
$237$	−14.4197	−	13.9948i	−0.936661	−	0.909059i
$238$	−0.816709	−	0.111604i	−0.0529394	−	0.00723420i
$239$	−3.62441	−	6.27766i	−0.234444	−	0.406068i	0.724667	−	0.689099i	$-0.241993\pi$
$239$	−3.62441	−	6.27766i	−0.234444	−	0.406068i	−0.959111	+	0.283031i	$0.908660\pi$
$240$	−3.55236	−	0.969713i	−0.229304	−	0.0625947i
$241$	19.9082			1.28240			0.641199	−	0.767374i	$-0.278437\pi$
$241$	19.9082			1.28240			0.641199	+	0.767374i	$0.278437\pi$
$242$	19.0087	−	24.5224i	1.22193	−	1.57636i
$243$	−15.3166	−	2.89854i	−0.982561	−	0.185942i
$244$	4.81320	−	4.71959i	0.308134	−	0.302141i
$245$	2.71325	+	1.56650i	0.173343	+	0.100080i
$246$	6.02431	+	7.68986i	0.384096	+	0.490287i
$247$	5.60790	−	3.23772i	0.356822	−	0.206011i
$248$	9.97750	−	1.16433i	0.633572	−	0.0739352i
$249$	−8.40338	−	2.11752i	−0.532543	−	0.134193i
$250$	−0.988933	+	7.23695i	−0.0625456	+	0.457705i
$251$	−0.913787	+	1.58273i	−0.0576777	+	0.0999008i	−0.893423	−	0.449217i	$-0.851703\pi$
$251$	−0.913787	+	1.58273i	−0.0576777	+	0.0999008i	0.835745	+	0.549118i	$0.185036\pi$
$252$	−4.37008	+	4.54928i	−0.275289	+	0.286577i
$253$	−25.0851			−1.57709
$254$	14.2953	−	5.83924i	0.896966	−	0.366386i
$255$	−0.494892	−	0.124705i	−0.0309913	−	0.00780934i
$256$	7.44972	+	14.1599i	0.465607	+	0.884991i
$257$	−17.1125	+	9.87993i	−1.06745	+	0.616293i	−0.927484	−	0.373863i	$-0.878033\pi$
$257$	−17.1125	+	9.87993i	−1.06745	+	0.616293i	−0.139967	+	0.990156i	$0.544700\pi$
$258$	−15.0515	+	2.13557i	−0.937063	+	0.132955i
$259$			1.44303i			0.0896655i
$260$	−0.770218	−	0.785494i	−0.0477669	−	0.0487143i
$261$	−0.628920	+	1.16870i	−0.0389292	+	0.0723404i
$262$	1.48503	+	0.202930i	0.0917452	+	0.0125370i
$263$	23.5345			1.45120			0.725601	−	0.688115i	$-0.241562\pi$
$263$	23.5345			1.45120			0.725601	+	0.688115i	$0.241562\pi$
$264$	−25.9740	+	10.7656i	−1.59859	+	0.662578i
$265$	−6.40139			−0.393234
$266$	−9.21764	−	1.25960i	−0.565170	−	0.0772308i
$267$	−19.0150	+	5.40105i	−1.16370	+	0.330539i
$268$	−13.8080	−	8.79429i	−0.843457	−	0.537197i
$269$			11.7168i			0.714384i	0.934031	+	0.357192i	$0.116266\pi$
$269$			11.7168i			0.714384i	−0.934031	+	0.357192i	$0.883734\pi$
$270$	−3.00117	+	2.49951i	−0.182645	+	0.152115i
$271$		−	18.0385i		−	1.09576i	−0.836556	−	0.547882i	$-0.815434\pi$
$271$		−	18.0385i		−	1.09576i	0.836556	−	0.547882i	$-0.184566\pi$
$272$	1.07085	+	1.94186i	0.0649299	+	0.117743i
$273$	−1.81288	+	0.514935i	−0.109720	+	0.0311653i
$274$	1.30350	−	9.53894i	0.0787474	−	0.576268i
$275$	13.5376	+	23.4478i	0.816347	+	1.41395i
$276$	13.1510	+	7.50297i	0.791597	+	0.451626i
$277$	−33.1132			−1.98958			−0.994789	−	0.101955i	$-0.967490\pi$
$277$	−33.1132			−1.98958			−0.994789	+	0.101955i	$0.967490\pi$
$278$	1.03619	−	7.58276i	0.0621465	−	0.454784i
$279$	5.04897	−	9.38229i	0.302274	−	0.561703i
$280$	0.183198	+	1.56988i	0.0109482	+	0.0938181i
$281$	8.10125	+	4.67726i	0.483280	+	0.279022i	0.721782	−	0.692120i	$-0.243323\pi$
$281$	8.10125	+	4.67726i	0.483280	+	0.279022i	−0.238502	+	0.971142i	$0.576656\pi$
$282$	6.26174	−	4.90551i	0.372881	−	0.292119i
$283$			23.4844i			1.39600i	0.716097	+	0.698001i	$0.245927\pi$
$283$			23.4844i			1.39600i	−0.716097	+	0.698001i	$0.754073\pi$
$284$	6.42879	+	24.9708i	0.381478	+	1.48175i
$285$	−5.58551	−	1.40746i	−0.330857	−	0.0833709i
$286$	−8.32258	−	1.13729i	−0.492125	−	0.0672491i
$287$	2.09644	−	3.63115i	0.123749	−	0.214340i
$288$	16.8370	+	2.12490i	0.992130	+	0.125211i
$289$	−8.34633	−	14.4563i	−0.490960	−	0.850368i
$290$	0.125742	+	0.307834i	0.00738382	+	0.0180766i
$291$	9.60833	+	2.42115i	0.563250	+	0.141930i
$292$	8.43940	−	8.27526i	0.493878	−	0.484273i
$293$			24.1024i			1.40808i	0.710161	+	0.704039i	$0.248622\pi$
$293$			24.1024i			1.40808i	−0.710161	+	0.704039i	$0.751378\pi$
$294$	−13.3946	−	5.39124i	−0.781186	−	0.314423i
$295$		−	3.48208i		−	0.202735i
$296$	3.11434	−	2.31765i	0.181017	−	0.134710i
$297$	−6.41895	+	29.1232i	−0.372465	+	1.68990i
$298$	0.864915	−	6.32939i	0.0501032	−	0.366652i
$299$	2.26167	+	3.91733i	0.130796	+	0.226545i
$300$	−0.0839050	−	16.3417i	−0.00484426	−	0.943489i
$301$	3.26254	+	5.65088i	0.188050	+	0.325712i
$302$	−1.77628	−	1.37690i	−0.102214	−	0.0792317i
$303$	4.10204	+	3.98115i	0.235656	+	0.228711i
$304$	12.0860	+	21.9165i	0.693178	+	1.25700i
$305$	−1.55142	−	0.895714i	−0.0888342	−	0.0512884i
$306$	2.33890	+	0.248624i	0.133706	+	0.0142129i
$307$	4.50509	+	2.60102i	0.257119	+	0.148448i	0.623020	−	0.782206i	$-0.285906\pi$
$307$	4.50509	+	2.60102i	0.257119	+	0.148448i	−0.365900	+	0.930654i	$0.619239\pi$
$308$	8.44932	+	8.61690i	0.481444	+	0.490994i
$309$	−23.6129	−	22.9171i	−1.34329	−	1.30371i
$310$	−1.00946	−	2.47129i	−0.0573333	−	0.140360i
$311$	16.1844			0.917734			0.458867	−	0.888505i	$-0.348255\pi$
$311$	16.1844			0.917734			0.458867	+	0.888505i	$0.348255\pi$
$312$	4.02299	+	3.08552i	0.227757	+	0.174683i
$313$	27.1782			1.53620			0.768100	−	0.640330i	$-0.221202\pi$
$313$	27.1782			1.53620			0.768100	+	0.640330i	$0.221202\pi$
$314$	10.9838	−	14.1697i	0.619849	−	0.799643i
$315$	1.47623	+	0.794414i	0.0831759	+	0.0447602i
$316$	22.4702	−	5.78500i	1.26405	−	0.325432i
$317$	11.4674	+	6.62070i	0.644073	+	0.371856i	0.786182	−	0.617995i	$-0.212055\pi$
$317$	11.4674	+	6.62070i	0.644073	+	0.371856i	−0.142109	+	0.989851i	$0.545388\pi$
$318$	29.2092	−	4.14433i	1.63797	−	0.232402i
$319$	2.19885	+	1.26951i	0.123112	+	0.0710787i
$320$	3.09387	−	2.91675i	0.172953	−	0.163052i
$321$	−3.19916	−	11.2630i	−0.178559	−	0.628637i
$322$	0.879876	−	6.43888i	0.0490336	−	0.358825i
$323$	1.73441	+	3.00409i	0.0965052	+	0.167152i
$324$	12.0759	−	13.3481i	0.670886	−	0.741561i
$325$	2.44110	−	4.22810i	0.135408	−	0.234533i
$326$	10.7316	−	4.38358i	0.594369	−	0.242784i
$327$	4.60852	+	16.2248i	0.254852	+	0.897231i
$328$	−11.2038	+	1.30744i	−0.618627	+	0.0721913i
$329$	−2.95679	−	1.70710i	−0.163013	−	0.0941157i
$330$	4.60798	+	5.88195i	0.253661	+	0.323791i
$331$	9.46144	−	5.46256i	0.520048	−	0.300250i	−0.216907	−	0.976192i	$-0.569597\pi$
$331$	9.46144	−	5.46256i	0.520048	−	0.300250i	0.736954	+	0.675943i	$0.236263\pi$
$332$	7.14496	−	7.00600i	0.392130	−	0.384504i
$333$	−0.123129	−	4.11573i	−0.00674741	−	0.225541i
$334$	−10.5731	−	25.8844i	−0.578532	−	1.41633i
$335$	−1.26691	+	4.16196i	−0.0692189	+	0.227392i
$336$	−1.85228	−	7.04465i	−0.101050	−	0.384317i
$337$	8.72362	−	15.1098i	0.475206	−	0.823081i	−0.524391	−	0.851478i	$-0.675707\pi$
$337$	8.72362	−	15.1098i	0.475206	−	0.823081i	0.999597	+	0.0283970i	$0.00904027\pi$
$338$	−6.37931	−	15.6175i	−0.346989	−	0.849477i
$339$	−9.25473	−	8.98200i	−0.502648	−	0.487835i
$340$	0.420781	−	0.412597i	0.0228200	−	0.0223762i
$341$	−17.6524	−	10.1916i	−0.955929	−	0.551906i
$342$	26.3976	+	2.80605i	1.42742	+	0.151734i
$343$			13.5570i			0.732009i
$344$	6.95576	−	16.1171i	0.375029	−	0.868974i
$345$	0.983167	−	3.90169i	0.0529319	−	0.210060i
$346$	25.4635	+	19.7382i	1.36892	+	1.06113i
$347$	14.2612	+	24.7012i	0.765584	+	1.32603i	0.939937	+	0.341347i	$0.110883\pi$
$347$	14.2612	+	24.7012i	0.765584	+	1.32603i	−0.174354	+	0.984683i	$0.555784\pi$
$348$	−0.773048	−	1.32322i	−0.0414397	−	0.0709321i
$349$	−22.3280			−1.19519			−0.597595	−	0.801798i	$-0.703877\pi$
$349$	−22.3280			−1.19519			−0.597595	+	0.801798i	$0.703877\pi$
$350$	−6.49344	+	2.65240i	−0.347089	+	0.141777i
$351$	5.12667	−	1.62336i	0.273641	−	0.0866484i
$352$	5.02654	−	32.0749i	0.267915	−	1.70960i
$353$	12.3913	+	7.15413i	0.659523	+	0.380776i	0.792095	−	0.610398i	$-0.208990\pi$
$353$	12.3913	+	7.15413i	0.659523	+	0.380776i	−0.132572	+	0.991173i	$0.542324\pi$
$354$	2.25434	+	15.8885i	0.119817	+	0.844466i
$355$	5.93434	−	3.42619i	0.314962	−	0.181843i
$356$	6.12378	−	21.9883i	0.324560	−	1.16538i
$357$	−0.275845	−	0.971140i	−0.0145993	−	0.0513982i
$358$	31.0491	+	4.24288i	1.64100	+	0.224243i
$359$	−13.6437			−0.720090			−0.360045	−	0.932935i	$-0.617239\pi$
$359$	−13.6437			−0.720090			−0.360045	+	0.932935i	$0.617239\pi$
$360$	−0.656461	−	4.46189i	−0.0345985	−	0.235162i
$361$	10.0751	+	17.4506i	0.530270	+	0.918454i
$362$	−0.694822	−	1.70102i	−0.0365190	−	0.0894038i
$363$	36.8484	+	9.28524i	1.93404	+	0.487349i
$364$	0.583840	−	2.09636i	0.0306015	−	0.109879i
$365$	−2.72024	−	1.57053i	−0.142384	−	0.0822053i
$366$	7.65894	+	3.08268i	0.400339	+	0.161134i
$367$	13.0749	−	7.54880i	0.682504	−	0.394044i	−0.118294	−	0.992979i	$-0.537742\pi$
$367$	13.0749	−	7.54880i	0.682504	−	0.394044i	0.800798	+	0.598935i	$0.204409\pi$
$368$	−15.3095	+	8.44252i	−0.798064	+	0.440097i
$369$	−5.66953	+	10.5354i	−0.295144	+	0.548454i
$370$	−0.815381	−	0.632048i	−0.0423896	−	0.0328586i
$371$	−6.33135	−	10.9662i	−0.328707	−	0.569338i
$372$	6.20603	+	10.6228i	0.321768	+	0.550768i
$373$	−13.9658	−	24.1895i	−0.723122	−	1.25248i	−0.959742	−	0.280882i	$-0.909373\pi$
$373$	−13.9658	−	24.1895i	−0.723122	−	1.25248i	0.236620	−	0.971602i	$-0.423960\pi$
$374$	0.609232	−	4.45832i	0.0315026	−	0.230534i
$375$	−8.60538	+	2.44429i	−0.444380	+	0.126223i
$376$	1.06463	+	9.12311i	0.0549041	+	0.470488i
$377$		−	0.457834i		−	0.0235797i
$378$	−7.25024	−	2.66914i	−0.372912	−	0.137286i
$379$	−12.6006	−	7.27498i	−0.647251	−	0.373690i	0.140151	−	0.990130i	$-0.455241\pi$
$379$	−12.6006	−	7.27498i	−0.647251	−	0.373690i	−0.787402	+	0.616440i	$0.788574\pi$
$380$	4.74907	−	4.65670i	0.243622	−	0.238884i
$381$	13.5715	+	13.1716i	0.695291	+	0.674801i
$382$	−2.59504	+	3.34776i	−0.132774	+	0.171286i
$383$	7.29345	−	12.6326i	0.372678	−	0.645497i	−0.617299	−	0.786729i	$-0.711773\pi$
$383$	7.29345	−	12.6326i	0.372678	−	0.645497i	0.989977	+	0.141232i	$0.0451063\pi$
$384$	−12.2288	+	15.3120i	−0.624048	+	0.781386i
$385$	1.60356	−	2.77745i	0.0817252	−	0.141552i
$386$	−30.5222	−	4.17088i	−1.55354	−	0.212292i
$387$	−9.78742	−	15.8388i	−0.497522	−	0.805131i
$388$	−8.16946	+	8.01057i	−0.414741	+	0.406675i
$389$	8.36905	+	4.83187i	0.424328	+	0.244986i	0.696927	−	0.717142i	$-0.254550\pi$
$389$	8.36905	+	4.83187i	0.424328	+	0.244986i	−0.272600	+	0.962128i	$0.587883\pi$
$390$	0.503080	−	1.24991i	0.0254745	−	0.0632915i
$391$	−2.09847	+	1.21155i	−0.106124	+	0.0612709i
$392$	13.3753	−	9.95367i	0.675552	−	0.502736i
$393$	0.501570	+	1.76583i	0.0253009	+	0.0890743i
$394$	−11.0637	+	4.51921i	−0.557380	+	0.227675i
$395$	−3.08309	−	5.34007i	−0.155127	−	0.268688i
$396$	−24.8340	−	23.8557i	−1.24795	−	1.19880i
$397$	15.5148			0.778663			0.389332	−	0.921098i	$-0.372706\pi$
$397$	15.5148			0.778663			0.389332	+	0.921098i	$0.372706\pi$
$398$	10.9986	+	8.52561i	0.551308	+	0.427350i
$399$	−3.11327	−	10.9606i	−0.155859	−	0.548716i
$400$	16.1535	+	9.75411i	0.807675	+	0.487706i
$401$			2.47454i			0.123573i	0.998089	+	0.0617864i	$0.0196797\pi$
$401$			2.47454i			0.123573i	−0.998089	+	0.0617864i	$0.980320\pi$
$402$	3.08635	−	19.8110i	0.153933	−	0.988081i
$403$			3.67550i			0.183090i
$404$	−6.39219	+	1.64568i	−0.318024	+	0.0818758i
$405$	−4.27820	−	2.13983i	−0.212585	−	0.106329i
$406$	−0.402984	+	0.519874i	−0.0199998	+	0.0258009i
$407$	−7.87732			−0.390464
$408$	−1.65288	+	2.15507i	−0.0818296	+	0.106692i
$409$	6.94356	+	12.0266i	0.343337	+	0.594677i	0.985050	−	0.172267i	$-0.0551093\pi$
$409$	6.94356	+	12.0266i	0.343337	+	0.594677i	−0.641713	+	0.766945i	$0.721776\pi$
$410$	1.13353	+	2.77504i	0.0559809	+	0.137049i
$411$	11.3427	−	3.22179i	0.559492	−	0.158919i
$412$	36.7959	−	9.47319i	1.81281	−	0.466710i
$413$	5.96515	−	3.44398i	0.293526	−	0.169467i
$414$	−1.96013	+	18.4397i	−0.0963352	+	0.906262i
$415$	−2.30301	−	1.32964i	−0.113050	−	0.0652695i
$416$	−5.46206	+	2.10692i	−0.267799	+	0.103300i
$417$	9.01658	−	2.56109i	0.441544	−	0.125417i
$418$	6.87598	−	50.3180i	0.336315	−	2.46113i
$419$	10.5508	−	18.2745i	0.515439	−	0.892766i	−0.484401	−	0.874846i	$-0.660962\pi$
$419$	10.5508	−	18.2745i	0.515439	−	0.892766i	0.999839	−	0.0179199i	$-0.00570440\pi$
$420$	−1.67141	+	0.976468i	−0.0815567	+	0.0476467i
$421$	1.70017	−	2.94478i	0.0828612	−	0.143520i	−0.821617	−	0.570040i	$-0.806928\pi$
$421$	1.70017	−	2.94478i	0.0828612	−	0.143520i	0.904478	+	0.426521i	$0.140261\pi$
$422$	21.0885	+	16.3469i	1.02657	+	0.795756i
$423$	8.57886	+	4.61662i	0.417119	+	0.224468i
$424$	−13.4985	+	31.2771i	−0.655544	+	1.51895i
$425$	2.26495	+	1.30767i	0.109866	+	0.0634312i
$426$	−24.8599	+	19.4755i	−1.20447	+	0.943589i
$427$		−	3.54365i		−	0.171489i
$428$	13.0241	+	3.62724i	0.629545	+	0.175329i
$429$	−2.81097	−	9.89630i	−0.135715	−	0.477798i
$430$	−4.62202	−	0.631601i	−0.222893	−	0.0304585i
$431$	−8.17798	−	14.1647i	−0.393920	−	0.682289i	0.599043	−	0.800717i	$-0.295548\pi$
$431$	−8.17798	−	14.1647i	−0.393920	−	0.682289i	−0.992963	+	0.118428i	$0.962215\pi$
$432$	5.88407	+	19.9343i	0.283097	+	0.959091i
$433$	−5.17376	−	8.96121i	−0.248635	−	0.430648i	0.714512	−	0.699623i	$-0.246649\pi$
$433$	−5.17376	−	8.96121i	−0.248635	−	0.430648i	−0.963147	+	0.268974i	$0.913315\pi$
$434$	3.23516	−	4.17355i	0.155293	−	0.200337i
$435$	−0.283637	+	0.292249i	−0.0135993	+	0.0140123i
$436$	−18.7618	−	5.22520i	−0.898528	−	0.250242i
$437$	−23.6840	+	13.6740i	−1.13296	+	0.654115i
$438$	13.4291	+	5.40512i	0.641665	+	0.258267i
$439$	7.44373	+	4.29764i	0.355270	+	0.205115i	0.667004	−	0.745054i	$-0.267576\pi$
$439$	7.44373	+	4.29764i	0.355270	+	0.205115i	−0.311734	+	0.950169i	$0.600910\pi$
$440$	−8.56977	+	1.00006i	−0.408548	+	0.0476759i
$441$	−0.528805	−	17.6760i	−0.0251812	−	0.841713i
$442$	−0.751146	+	0.306823i	−0.0357284	+	0.0145941i
$443$	0.787530	+	1.36404i	0.0374167	+	0.0648076i	0.884127	−	0.467246i	$-0.154754\pi$
$443$	0.787530	+	1.36404i	0.0374167	+	0.0648076i	−0.846711	+	0.532054i	$0.821420\pi$
$444$	4.12973	+	2.35611i	0.195988	+	0.111816i
$445$	−6.06577			−0.287545
$446$	1.40043	−	10.2482i	0.0663121	−	0.485268i
$447$	7.52621	−	2.13776i	0.355977	−	0.101113i
$448$	8.05671	+	2.41526i	0.380644	+	0.114111i
$449$	−8.87074	+	5.12152i	−0.418636	+	0.241700i	−0.694494	−	0.719499i	$-0.744372\pi$
$449$	−8.87074	+	5.12152i	−0.418636	+	0.241700i	0.275857	+	0.961199i	$0.411038\pi$
$450$	18.2939	−	8.11909i	0.862385	−	0.382738i
$451$	19.8220	+	11.4442i	0.933381	+	0.538888i
$452$	14.4216	−	3.71287i	0.678336	−	0.174639i
$453$	0.672577	−	2.66912i	0.0316004	−	0.125406i
$454$	5.45580	+	13.3566i	0.256053	+	0.626855i
$455$	−0.578309			−0.0271115
$456$	−18.6549	+	24.3228i	−0.873596	+	1.13902i
$457$	−10.2315	−	17.7215i	−0.478611	−	0.828979i	0.521088	−	0.853503i	$-0.325526\pi$
$457$	−10.2315	−	17.7215i	−0.478611	−	0.828979i	−0.999699	+	0.0245239i	$0.992193\pi$
$458$	−22.5008	+	29.0274i	−1.05139	+	1.35636i
$459$	0.869615	+	2.74630i	0.0405901	+	0.128186i
$460$	3.25289	+	3.31741i	0.151667	+	0.154675i
$461$		−	25.2058i		−	1.17395i	−0.809605	−	0.586975i	$-0.800319\pi$
$461$		−	25.2058i		−	1.17395i	0.809605	−	0.586975i	$-0.199681\pi$
$462$	−5.51881	+	13.7115i	−0.256758	+	0.637917i
$463$	−28.3766	−	16.3832i	−1.31877	−	0.761393i	−0.335240	−	0.942133i	$-0.608817\pi$
$463$	−28.3766	−	16.3832i	−1.31877	−	0.761393i	−0.983531	+	0.180740i	$0.942151\pi$
$464$	1.76922	+	0.0347501i	0.0821341	+	0.00161323i
$465$	2.27704	−	2.34618i	0.105595	−	0.108801i
$466$	28.1385	−	11.4938i	1.30349	−	0.532441i
$467$	3.90198	−	6.75843i	0.180562	−	0.312743i	−0.761510	−	0.648153i	$-0.775542\pi$
$467$	3.90198	−	6.75843i	0.180562	−	0.312743i	0.942072	+	0.335410i	$0.108875\pi$
$468$	−1.48632	+	6.02894i	−0.0687053	+	0.278688i
$469$	−8.38290	+	1.94607i	−0.387086	+	0.0898612i
$470$	2.25967	−	0.923015i	0.104231	−	0.0425755i
$471$	21.2920	+	5.36525i	0.981084	+	0.247218i
$472$	−17.0134	−	7.34260i	−0.783106	−	0.337970i
$473$	−30.8475	+	17.8098i	−1.41837	+	0.818896i
$474$	17.5252	+	22.3704i	0.804957	+	1.02751i
$475$	25.5629	+	14.7588i	1.17291	+	0.677178i
$476$	1.12300	+	0.312756i	0.0514725	+	0.0143352i
$477$	18.9937	+	30.7371i	0.869660	+	1.40735i
$478$	3.87649	+	9.49019i	0.177306	+	0.434071i
$479$	−20.9819	+	36.3418i	−0.958689	+	1.66050i	−0.233000	+	0.972477i	$0.574854\pi$
$479$	−20.9819	+	36.3418i	−0.958689	+	1.66050i	−0.725690	+	0.688022i	$0.758479\pi$
$480$	4.79186	+	2.03894i	0.218718	+	0.0930643i
$481$	0.710219	+	1.23014i	0.0323832	+	0.0560894i
$482$	−27.8952	−	3.81189i	−1.27059	−	0.173627i
$483$	7.65640	−	2.17474i	0.348378	−	0.0989542i
$484$	−31.3303	+	30.7210i	−1.42410	+	1.39641i
$485$	2.63323	+	1.52030i	0.119569	+	0.0690331i
$486$	20.9065	+	6.99414i	0.948338	+	0.317261i
$487$	−18.8947	−	10.9088i	−0.856199	−	0.494327i	0.00653838	−	0.999979i	$-0.497919\pi$
$487$	−18.8947	−	10.9088i	−0.856199	−	0.494327i	−0.862738	+	0.505652i	$0.831252\pi$
$488$	−7.64790	+	5.69145i	−0.346204	+	0.257640i
$489$	10.1883	+	9.88806i	0.460731	+	0.447153i
$490$	−3.50184	−	2.71448i	−0.158197	−	0.122628i
$491$	−22.5439			−1.01739			−0.508696	−	0.860946i	$-0.669872\pi$
$491$	−22.5439			−1.01739			−0.508696	+	0.860946i	$0.669872\pi$
$492$	−6.96880	−	11.9285i	−0.314178	−	0.537777i
$493$	0.245257			0.0110458
$494$	−8.47768	+	3.46290i	−0.381429	+	0.155803i
$495$	−4.33661	+	8.05854i	−0.194916	+	0.362204i
$496$	−14.2033	−	0.278974i	−0.637748	−	0.0125263i
$497$	11.7388	+	6.77741i	0.526558	+	0.304008i
$498$	11.3693	+	4.57608i	0.509471	+	0.205059i
$499$	−23.2686	−	13.4341i	−1.04165	−	0.601395i	−0.121347	−	0.992610i	$-0.538721\pi$
$499$	−23.2686	−	13.4341i	−1.04165	−	0.601395i	−0.920299	+	0.391216i	$0.872055\pi$
$500$	2.77137	−	9.95099i	0.123939	−	0.445022i
$501$	23.8497	−	24.5739i	1.06553	−	1.09788i
$502$	1.58344	−	2.04274i	0.0706724	−	0.0911718i
$503$	−13.6814	−	23.6969i	−0.610024	−	1.05659i	−0.991236	−	0.132105i	$-0.957826\pi$
$503$	−13.6814	−	23.6969i	−0.610024	−	1.05659i	0.381211	−	0.924488i	$-0.375507\pi$
$504$	6.99438	−	5.53765i	0.311555	−	0.246667i
$505$	0.877059	+	1.51911i	0.0390286	+	0.0675995i
$506$	35.1491	+	4.80314i	1.56257	+	0.213526i
$507$	14.3898	−	14.8268i	0.639075	−	0.658480i
$508$	−21.1485	+	5.44472i	−0.938313	+	0.241570i
$509$		−	16.2685i		−	0.721090i	−0.932742	−	0.360545i	$-0.882591\pi$
$509$		−	16.2685i		−	0.721090i	0.932742	−	0.360545i	$-0.117409\pi$
$510$	0.669561	+	0.269495i	0.0296487	+	0.0119334i
$511$		−	6.21339i		−	0.274864i
$512$	−7.72724	−	21.2671i	−0.341499	−	0.939882i
$513$	9.81475	+	30.9956i	0.433332	+	1.36849i
$514$	25.8697	−	10.5671i	1.14106	−	0.466094i
$515$	−5.04869	−	8.74459i	−0.222472	−	0.385333i
$516$	21.4989	−	0.110384i	0.946435	−	0.00485939i
$517$	9.31887	−	16.1408i	0.409844	−	0.709870i
$518$	0.276302	−	2.02196i	0.0121400	−	0.0888398i
$519$	−9.64155	+	38.2625i	−0.423217	+	1.67954i
$520$	0.928821	+	1.24810i	0.0407315	+	0.0547330i
$521$		−	11.4439i		−	0.501365i	−0.968069	−	0.250683i	$-0.919345\pi$
$521$		−	11.4439i		−	0.501365i	0.968069	−	0.250683i	$-0.0806551\pi$
$522$	1.10501	−	1.51714i	0.0483651	−	0.0664036i
$523$	1.72375	+	0.995207i	0.0753743	+	0.0435174i	0.537213	−	0.843446i	$-0.319477\pi$
$523$	1.72375	+	0.995207i	0.0753743	+	0.0435174i	−0.461839	+	0.886964i	$0.652810\pi$
$524$	−2.04195	−	0.568687i	−0.0892030	−	0.0248432i
$525$	−6.16469	−	5.98302i	−0.269049	−	0.261121i
$526$	−32.9764	−	4.50625i	−1.43784	−	0.196482i
$527$	−1.96892			−0.0857676
$528$	38.4559	−	10.1114i	1.67358	−	0.440041i
$529$	1.94820	+	3.37438i	0.0847042	+	0.146712i
$530$	8.96958	+	1.22570i	0.389613	+	0.0532409i
$531$	−16.7196	+	10.3317i	−0.725570	+	0.448359i
$532$	12.6745	+	3.52987i	0.549509	+	0.153039i
$533$		−	4.12725i		−	0.178771i
$534$	27.6778	−	3.92705i	1.19773	−	0.169940i
$535$		−	3.59288i		−	0.155334i
$536$	17.6638	+	14.9664i	0.762958	+	0.646448i
$537$	10.4869	+	36.9202i	0.452543	+	1.59322i
$538$	2.24345	−	16.4174i	0.0967221	−	0.707806i
$539$	−33.8310			−1.45720
$540$	4.68380	−	2.92765i	0.201559	−	0.125986i
$541$	−12.0523			−0.518169			−0.259084	−	0.965855i	$-0.583421\pi$
$541$	−12.0523			−0.518169			−0.259084	+	0.965855i	$0.583421\pi$
$542$	−3.45390	+	25.2754i	−0.148358	+	1.08567i
$543$	1.56731	−	1.61490i	0.0672599	−	0.0693021i
$544$	−1.12865	−	2.92596i	−0.0483906	−	0.125450i
$545$			5.17570i			0.221703i
$546$	2.63879	−	0.374403i	0.112930	−	0.0160230i
$547$	−24.5204	+	14.1568i	−1.04841	+	0.605303i	−0.922205	−	0.386701i	$-0.873615\pi$
$547$	−24.5204	+	14.1568i	−1.04841	+	0.605303i	−0.126210	+	0.992004i	$0.540281\pi$
$548$	−3.65291	+	13.1163i	−0.156045	+	0.560300i
$549$	0.302368	+	10.1070i	0.0129047	+	0.431357i
$550$	−14.4791	−	35.4469i	−0.617391	−	1.51146i
$551$	2.76805			0.117923
$552$	−16.9904	−	13.0312i	−0.723161	−	0.554643i
$553$	6.09871	−	10.5633i	0.259343	−	0.449196i
$554$	46.3979	+	6.34030i	1.97126	+	0.269374i
$555$	0.308738	−	1.22523i	0.0131052	−	0.0520079i
$556$	−2.90380	+	10.4265i	−0.123149	+	0.442182i
$557$	3.51921	−	2.03181i	0.149114	−	0.0860907i	−0.423587	−	0.905855i	$-0.639229\pi$
$557$	3.51921	−	2.03181i	0.149114	−	0.0860907i	0.572700	+	0.819765i	$0.305896\pi$
$558$	−8.87104	+	12.1796i	−0.375541	+	0.515605i
$559$	5.56242	+	3.21146i	0.235265	+	0.135830i
$560$	0.0438943	−	2.23478i	0.00185487	−	0.0944365i
$561$	5.30134	−	1.50580i	0.223823	−	0.0635751i
$562$	−10.4558	−	8.10492i	−0.441053	−	0.341885i
$563$	35.1746			1.48243			0.741216	−	0.671267i	$-0.234249\pi$
$563$	35.1746			1.48243			0.741216	+	0.671267i	$0.234249\pi$
$564$	−9.71317	+	5.67460i	−0.408998	+	0.238944i
$565$	−1.97876	−	3.42731i	−0.0832470	−	0.144188i
$566$	4.49664	−	32.9061i	0.189008	−	1.38315i
$567$	−0.565654	−	9.44539i	−0.0237552	−	0.396669i
$568$	−4.22671	−	36.2199i	−0.177349	−	1.51975i
$569$	−2.15636	+	1.24498i	−0.0903994	+	0.0521921i	−0.544518	−	0.838749i	$-0.683287\pi$
$569$	−2.15636	+	1.24498i	−0.0903994	+	0.0521921i	0.454119	+	0.890941i	$0.349954\pi$
$570$	7.55688	+	3.04160i	0.316523	+	0.127399i
$571$	−18.5458	+	10.7074i	−0.776117	+	0.448091i	−0.835052	−	0.550170i	$-0.814563\pi$
$571$	−18.5458	+	10.7074i	−0.776117	+	0.448091i	0.0589353	+	0.998262i	$0.481229\pi$
$572$	11.4438	+	3.18711i	0.478488	+	0.133260i
$573$	−5.03049	−	1.26760i	−0.210152	−	0.0529549i
$574$	−3.63279	+	4.68652i	−0.151630	+	0.195611i
$575$	−10.3096	+	17.8567i	−0.429939	+	0.744675i
$576$	−23.1850	−	6.20124i	−0.966042	−	0.258385i
$577$	−22.3997	−	38.7973i	−0.932510	−	1.61515i	−0.779015	−	0.627005i	$-0.784280\pi$
$577$	−22.3997	−	38.7973i	−0.932510	−	1.61515i	−0.153495	−	0.988149i	$-0.549053\pi$
$578$	8.92681	+	21.8541i	0.371306	+	0.909010i
$579$	−10.3089	−	36.2936i	−0.428424	−	1.50831i
$580$	−0.117246	−	0.455411i	−0.00486839	−	0.0189099i
$581$		−	5.26037i		−	0.218237i
$582$	−12.9995	−	5.23224i	−0.538848	−	0.216883i
$583$	59.8633	−	34.5621i	2.47928	−	1.43142i
$584$	−13.4097	+	9.97931i	−0.554898	+	0.412947i
$585$	1.64942	−	0.0493451i	0.0681953	−	0.00204017i
$586$	4.61498	−	33.7721i	0.190643	−	1.39511i
$587$	1.92855	−	3.34034i	0.0795997	−	0.137871i	−0.823478	−	0.567349i	$-0.807969\pi$
$587$	1.92855	−	3.34034i	0.0795997	−	0.137871i	0.903077	+	0.429478i	$0.141302\pi$
$588$	17.7361	+	10.1189i	0.731423	+	0.417295i
$589$	−22.2219			−0.915637
$590$	−0.666727	+	4.87906i	−0.0274487	+	0.200868i
$591$	−10.5035	−	10.1940i	−0.432058	−	0.419325i
$592$	−4.80756	+	2.65115i	−0.197589	+	0.108962i
$593$	−3.11527	−	1.79860i	−0.127929	−	0.0738597i	0.434670	−	0.900590i	$-0.356865\pi$
$593$	−3.11527	−	1.79860i	−0.127929	−	0.0738597i	−0.562599	+	0.826730i	$0.690198\pi$
$594$	14.5705	−	39.5782i	0.597835	−	1.62391i
$595$		−	0.309794i		−	0.0127003i
$596$	−2.42382	+	8.70308i	−0.0992836	+	0.356492i
$597$	−4.16452	+	16.5269i	−0.170443	+	0.676401i
$598$	−2.41897	−	5.92198i	−0.0989191	−	0.242168i
$599$	−7.26951	−	12.5912i	−0.297024	−	0.514461i	0.678430	−	0.734665i	$-0.262661\pi$
$599$	−7.26951	−	12.5912i	−0.297024	−	0.514461i	−0.975454	+	0.220205i	$0.929328\pi$
$600$	−3.01144	+	22.9139i	−0.122942	+	0.935457i
$601$	−19.6300	+	34.0001i	−0.800723	+	1.38689i	0.118418	+	0.992964i	$0.462218\pi$
$601$	−19.6300	+	34.0001i	−0.800723	+	1.38689i	−0.919141	+	0.393929i	$0.871116\pi$
$602$	−3.48945	−	8.54266i	−0.142219	−	0.348173i
$603$	23.7432	−	6.26576i	0.966898	−	0.255162i
$604$	2.22527	+	2.26941i	0.0905451	+	0.0923411i
$605$	10.0986	+	5.83042i	0.410566	+	0.237040i
$606$	−4.98546	−	6.36379i	−0.202520	−	0.258511i
$607$	−29.0704	+	16.7838i	−1.17993	+	0.681233i	−0.955999	−	0.293371i	$-0.905223\pi$
$607$	−29.0704	+	16.7838i	−1.17993	+	0.681233i	−0.223932	+	0.974605i	$0.571889\pi$
$608$	−12.7383	−	33.0234i	−0.516608	−	1.33927i
$609$	−0.781185	−	0.196846i	−0.0316552	−	0.00797662i
$610$	2.00233	+	1.55212i	0.0810721	+	0.0628436i
$611$	−3.36076			−0.135962
$612$	−3.22964	−	0.796207i	−0.130550	−	0.0321847i
$613$	23.8603	−	41.3273i	0.963710	−	1.66919i	0.250669	−	0.968073i	$-0.419349\pi$
$613$	23.8603	−	41.3273i	0.963710	−	1.66919i	0.713041	−	0.701122i	$-0.247317\pi$
$614$	−5.81447	−	4.50713i	−0.234653	−	0.181893i
$615$	−2.55690	+	2.63454i	−0.103104	+	0.106235i
$616$	−10.1892	−	13.6918i	−0.410535	−	0.551656i
$617$		−	44.8531i		−	1.80572i	−0.429938	−	0.902858i	$-0.641465\pi$
$617$		−	44.8531i		−	1.80572i	0.429938	−	0.902858i	$-0.358535\pi$
$618$	28.6982	+	36.6325i	1.15441	+	1.47357i
$619$	−9.97112	−	5.75683i	−0.400773	−	0.231387i	0.286044	−	0.958216i	$-0.407660\pi$
$619$	−9.97112	−	5.75683i	−0.400773	−	0.231387i	−0.686818	+	0.726830i	$0.740993\pi$
$620$	0.941255	+	3.65604i	0.0378017	+	0.146830i
$621$	−21.6516	+	6.85598i	−0.868850	+	0.275121i
$622$	−22.6775	−	3.09889i	−0.909283	−	0.124254i
$623$	−5.99940	−	10.3913i	−0.240361	−	0.416318i
$624$	−5.04619	−	5.09370i	−0.202009	−	0.203911i
$625$	20.8424			0.833697
$626$	−38.0818	−	5.20390i	−1.52205	−	0.207990i
$627$	59.8326	−	16.9950i	2.38948	−	0.678714i
$628$	−18.1035	+	17.7514i	−0.722407	+	0.708357i
$629$	−0.658970	+	0.380457i	−0.0262749	+	0.0151698i
$630$	−1.91637	−	1.39578i	−0.0763498	−	0.0556094i
$631$	16.0820	+	9.28493i	0.640213	+	0.369627i	0.784697	−	0.619880i	$-0.212819\pi$
$631$	16.0820	+	9.28493i	0.640213	+	0.369627i	−0.144483	+	0.989507i	$0.546152\pi$
$632$	−32.5927	+	3.80344i	−1.29647	+	0.151293i
$633$	−7.98501	+	31.6885i	−0.317376	+	1.25951i
$634$	−14.8003	−	11.4726i	−0.587796	−	0.455634i
$635$	2.90174	+	5.02596i	0.115152	+	0.199449i
$636$	−41.7212	+	0.214213i	−1.65435	+	0.00849412i
$637$	3.05020	+	5.28310i	0.120853	+	0.209324i
$638$	−2.83793	−	2.19984i	−0.112355	−	0.0870926i
$639$	−34.0591	−	18.3285i	−1.34736	−	0.725066i
$640$	−4.89358	+	3.49454i	−0.193436	+	0.138134i
$641$	34.5312	−	19.9366i	1.36390	−	0.787448i	0.373760	−	0.927526i	$-0.378069\pi$
$641$	34.5312	−	19.9366i	1.36390	−	0.787448i	0.990141	+	0.140078i	$0.0447352\pi$
$642$	2.32607	+	16.3941i	0.0918027	+	0.647024i
$643$		−	12.5098i		−	0.493337i	−0.969100	−	0.246668i	$-0.920664\pi$
$643$		−	12.5098i		−	0.493337i	0.969100	−	0.246668i	$-0.0793359\pi$
$644$	−2.46575	+	8.85363i	−0.0971642	+	0.348882i
$645$	−1.56109	−	5.49599i	−0.0614680	−	0.216404i
$646$	−1.85504	−	4.54140i	−0.0729855	−	0.178679i
$647$	−20.0747	+	34.7705i	−0.789220	+	1.36697i	0.137226	+	0.990540i	$0.456181\pi$
$647$	−20.0747	+	34.7705i	−0.789220	+	1.36697i	−0.926446	+	0.376429i	$0.877152\pi$
$648$	−19.4765	+	16.3910i	−0.765110	+	0.643900i
$649$	18.8003	+	32.5631i	0.737976	+	1.27821i
$650$	−4.23001	+	5.45698i	−0.165915	+	0.214040i
$651$	6.27135	+	1.58028i	0.245794	+	0.0619362i
$652$	−15.8764	+	4.08741i	−0.621767	+	0.160075i
$653$	22.1055	+	12.7626i	0.865057	+	0.499441i	0.865702	−	0.500559i	$-0.166872\pi$
$653$	22.1055	+	12.7626i	0.865057	+	0.499441i	−0.000645569		1.00000i	$0.500205\pi$
$654$	−3.35080	−	23.6164i	−0.131027	−	0.923475i
$655$			0.563300i			0.0220099i
$656$	15.9490	+	0.313263i	0.622705	+	0.0122308i
$657$	0.530167	+	17.7215i	0.0206838	+	0.691382i
$658$	3.81616	+	2.95813i	0.148770	+	0.115320i
$659$	4.27902	+	7.41147i	0.166687	+	0.288710i	0.937253	−	0.348650i	$-0.113360\pi$
$659$	4.27902	+	7.41147i	0.166687	+	0.288710i	−0.770566	+	0.637360i	$0.780026\pi$
$660$	−5.33042	−	9.12405i	−0.207486	−	0.355153i
$661$	16.1072			0.626499			0.313249	−	0.949671i	$-0.398582\pi$
$661$	16.1072			0.626499			0.313249	+	0.949671i	$0.398582\pi$
$662$	−14.3032	+	5.84248i	−0.555910	+	0.227074i
$663$	−0.713117	−	0.692102i	−0.0276952	−	0.0268790i
$664$	−11.3529	+	8.44867i	−0.440579	+	0.327872i
$665$		−	3.49643i		−	0.135586i
$666$	−0.615528	+	5.79051i	−0.0238512	+	0.224378i
$667$			1.93359i			0.0748688i
$668$	9.85872	+	38.2934i	0.381445	+	1.48162i
$669$	12.1861	−	3.46136i	0.471140	−	0.133824i
$670$	2.57209	−	5.58912i	0.0993686	−	0.215926i
$671$	19.3444			0.746781
$672$	1.24653	+	10.2256i	0.0480860	+	0.394460i
$673$	33.8074			1.30318			0.651590	−	0.758571i	$-0.274102\pi$
$673$	33.8074			1.30318			0.651590	+	0.758571i	$0.274102\pi$
$674$	−15.1166	+	19.5013i	−0.582269	+	0.751163i
$675$	18.0931	+	16.5385i	0.696405	+	0.636566i
$676$	5.94830	+	23.1045i	0.228781	+	0.888635i
$677$	−14.9805	+	8.64902i	−0.575749	+	0.332409i	−0.759442	−	0.650575i	$-0.774528\pi$
$677$	−14.9805	+	8.64902i	−0.575749	+	0.332409i	0.183693	+	0.982984i	$0.441195\pi$
$678$	11.2478	+	14.3575i	0.431970	+	0.551398i
$679$			6.01465i			0.230821i
$680$	−0.668596	+	0.497559i	−0.0256395	+	0.0190805i
$681$	−12.3067	+	12.6804i	−0.471593	+	0.485912i
$682$	22.7829	+	17.6603i	0.872403	+	0.676250i
$683$	11.8212	−	20.4750i	0.452326	−	0.783452i	−0.546204	−	0.837652i	$-0.683928\pi$
$683$	11.8212	−	20.4750i	0.452326	−	0.783452i	0.998530	+	0.0542000i	$0.0172609\pi$
$684$	−36.4507	−	8.98624i	−1.39373	−	0.343598i
$685$	3.61831			0.138248
$686$	2.59581	−	18.9960i	0.0991084	−	0.725269i
$687$	−43.6177	−	10.9910i	−1.66412	−	0.419333i
$688$	−12.8323	+	21.2513i	−0.489229	+	0.810197i
$689$	−10.7945	−	6.23223i	−0.411239	−	0.237429i
$690$	−2.12468	+	5.27877i	−0.0808851	+	0.200959i
$691$	−41.8610	+	24.1685i	−1.59247	+	0.919412i	−0.599586	+	0.800310i	$0.704668\pi$
$691$	−41.8610	+	24.1685i	−1.59247	+	0.919412i	−0.992882	+	0.119101i	$0.961999\pi$
$692$	−31.8999	−	32.5326i	−1.21265	−	1.23670i
$693$	−18.0942	+	0.541318i	−0.687343	+	0.0205630i
$694$	−15.2531	−	37.3418i	−0.579000	−	1.41747i
$695$	2.87629			0.109104
$696$	0.829826	+	2.00211i	0.0314545	+	0.0758896i
$697$	2.21092			0.0837446
$698$	31.2858	+	4.27522i	1.18419	+	0.161820i
$699$	26.7139	+	25.9267i	1.01041	+	0.980636i
$700$	9.60642	−	2.47319i	0.363089	−	0.0934779i
$701$	27.1422	−	15.6706i	1.02515	−	0.591870i	0.109557	−	0.993980i	$-0.465057\pi$
$701$	27.1422	−	15.6706i	1.02515	−	0.591870i	0.915591	+	0.402111i	$0.131723\pi$
$702$	−7.49427	+	1.29301i	−0.282853	+	0.0488016i
$703$	−7.43735	+	4.29396i	−0.280505	+	0.161950i
$704$	−13.1846	+	43.9806i	−0.496915	+	1.65758i
$705$	2.14527	+	2.08205i	0.0807955	+	0.0784145i
$706$	−15.9928	−	12.3969i	−0.601896	−	0.466564i
$707$	−1.73493	+	3.00498i	−0.0652486	+	0.113014i
$708$	−0.116523	−	22.6945i	−0.00437920	−	0.852912i
$709$	−3.01746	+	5.22639i	−0.113323	+	0.196281i	−0.917108	−	0.398638i	$-0.869483\pi$
$709$	−3.01746	+	5.22639i	−0.113323	+	0.196281i	0.803785	+	0.594920i	$0.202816\pi$
$710$	−8.97117	+	3.66448i	−0.336682	+	0.137526i
$711$	−16.4931	+	30.6484i	−0.618539	+	1.14940i
$712$	−12.7908	+	29.6373i	−0.479355	+	1.11070i
$713$		−	15.5229i		−	0.581335i
$714$	0.200564	+	1.41357i	0.00750591	+	0.0529015i
$715$		−	3.15692i		−	0.118062i
$716$	−42.6934	−	11.8902i	−1.59553	−	0.444357i
$717$	−8.74421	+	9.00972i	−0.326558	+	0.336474i
$718$	19.1175	+	2.61242i	0.713459	+	0.0974946i
$719$	11.6544	−	20.1860i	0.434636	−	0.752812i	−0.562629	−	0.826709i	$-0.690210\pi$
$719$	11.6544	−	20.1860i	0.434636	−	0.752812i	0.997266	+	0.0738968i	$0.0235435\pi$
$720$	0.0654927	+	6.37766i	0.00244077	+	0.237681i
$721$	9.98690	−	17.2978i	0.371932	−	0.644204i
$722$	−10.7758	−	26.3808i	−0.401035	−	0.981792i
$723$	−9.42165	−	33.1699i	−0.350395	−	1.23360i
$724$	0.647878	+	2.51650i	0.0240782	+	0.0935250i
$725$	1.80738	−	1.04349i	0.0671244	−	0.0387543i
$726$	−49.8539	−	20.0659i	−1.85025	−	0.744716i
$727$	−14.0207	−	8.09485i	−0.519999	−	0.300221i	0.216935	−	0.976186i	$-0.430394\pi$
$727$	−14.0207	−	8.09485i	−0.519999	−	0.300221i	−0.736934	+	0.675965i	$0.763727\pi$
$728$	−1.21947	+	2.82561i	−0.0451965	+	0.104724i
$729$	2.41927	+	26.8914i	0.0896027	+	0.995978i
$730$	3.51086	+	2.72147i	0.129943	+	0.100726i
$731$	−1.72035	+	2.97973i	−0.0636293	+	0.110209i
$732$	−10.1414	−	5.78591i	−0.374836	−	0.213853i
$733$	−15.1542	−	26.2478i	−0.559733	−	0.969485i	−0.997518	−	0.0704060i	$-0.977571\pi$
$733$	−15.1542	−	26.2478i	−0.559733	−	0.969485i	0.437786	−	0.899079i	$-0.355763\pi$
$734$	−19.7658	+	8.07381i	−0.729570	+	0.298010i
$735$	1.32595	−	5.26201i	0.0489082	−	0.194092i
$736$	23.0681	−	8.89822i	0.850301	−	0.327993i
$737$	−10.6234	−	45.7612i	−0.391317	−	1.68564i
$738$	9.96136	−	13.6766i	0.366683	−	0.503443i
$739$	−28.5146	−	16.4629i	−1.04892	−	0.605597i	−0.126577	−	0.991957i	$-0.540399\pi$
$739$	−28.5146	−	16.4629i	−1.04892	−	0.605597i	−0.922348	+	0.386360i	$0.873732\pi$
$740$	1.02148	+	1.04174i	0.0375505	+	0.0382953i
$741$	−8.04847	−	7.81129i	−0.295668	−	0.286955i
$742$	6.77169	+	16.5781i	0.248597	+	0.608600i
$743$	−24.7007	+	42.7829i	−0.906181	+	1.56955i	−0.0868578	+	0.996221i	$0.527683\pi$
$743$	−24.7007	+	42.7829i	−0.906181	+	1.56955i	−0.819324	+	0.573331i	$0.805651\pi$
$744$	−6.66185	−	16.0729i	−0.244235	−	0.589261i
$745$	2.40086			0.0879608
$746$	14.9371	+	36.5682i	0.546887	+	1.33886i
$747$	0.448849	+	15.0034i	0.0164225	+	0.548944i
$748$	−1.70730	+	6.13030i	−0.0624251	+	0.224146i
$749$	6.15497	−	3.55357i	0.224898	−	0.129845i
$750$	12.5258	−	1.77722i	0.457378	−	0.0648948i
$751$		−	19.1273i		−	0.697965i	−0.937129	−	0.348982i	$-0.886527\pi$
$751$		−	19.1273i		−	0.697965i	0.937129	−	0.348982i	$-0.113473\pi$
$752$	0.255085	−	12.9871i	0.00930200	−	0.473590i
$753$	3.06950	+	0.773467i	0.111859	+	0.0281867i
$754$	−0.0876633	+	0.641514i	−0.00319251	+	0.0233626i
$755$	0.422327	−	0.731491i	0.0153700	−	0.0266217i
$756$	9.64790	+	5.12820i	0.350891	+	0.186511i
$757$	8.43704	+	14.6134i	0.306649	+	0.531132i	0.977627	−	0.210345i	$-0.0674587\pi$
$757$	8.43704	+	14.6134i	0.306649	+	0.531132i	−0.670978	+	0.741478i	$0.734125\pi$
$758$	16.2629	+	12.6063i	0.590696	+	0.457882i
$759$	11.8717	+	41.7954i	0.430914	+	1.51708i
$760$	−7.54599	+	5.61561i	−0.273722	+	0.203700i
$761$		−	20.7023i		−	0.750458i	−0.926932	−	0.375229i	$-0.877564\pi$
$761$		−	20.7023i		−	0.750458i	0.926932	−	0.375229i	$-0.122436\pi$
$762$	−16.4943	−	21.0545i	−0.597526	−	0.762725i
$763$	−8.86649	+	5.11907i	−0.320988	+	0.185323i
$764$	4.27716	−	4.19397i	0.154742	−	0.151733i
$765$	0.0264336	+	0.883578i	0.000955710	+	0.0319458i
$766$	−12.6383	+	16.3042i	−0.456642	+	0.589096i
$767$	3.39007	−	5.87177i	0.122408	−	0.212017i
$768$	20.0667	−	19.1135i	0.724096	−	0.689700i
$769$	5.85946	+	10.1489i	0.211297	+	0.365978i	0.952121	−	0.305722i	$-0.0988978\pi$
$769$	5.85946	+	10.1489i	0.211297	+	0.365978i	−0.740823	+	0.671700i	$0.765564\pi$
$770$	−2.77871	+	3.58470i	−0.100138	+	0.129184i
$771$	24.5600	+	23.8362i	0.884506	+	0.858440i
$772$	41.9688	+	11.6884i	1.51049	+	0.420675i
$773$	26.3140	−	15.1924i	0.946448	−	0.546432i	0.0544725	−	0.998515i	$-0.482652\pi$
$773$	26.3140	−	15.1924i	0.946448	−	0.546432i	0.891976	+	0.452083i	$0.149319\pi$
$774$	10.6813	+	24.0672i	0.383933	+	0.865078i
$775$	−14.5097	+	8.37715i	−0.521202	+	0.300916i
$776$	12.9808	−	9.66011i	0.465983	−	0.346778i
$777$	2.40429	−	0.682921i	0.0862535	−	0.0244996i
$778$	−10.8015	−	8.37283i	−0.387251	−	0.300181i
$779$	24.9532			0.894040
$780$	−0.944236	+	1.65503i	−0.0338091	+	0.0592596i
$781$	−36.9971	+	64.0808i	−1.32386	+	2.29299i
$782$	3.17234	−	1.29582i	0.113443	−	0.0463383i
$783$	2.24485	+	0.494780i	0.0802245	+	0.0176820i
$784$	−20.6472	+	11.3860i	−0.737398	+	0.406642i
$785$	5.83522	+	3.36897i	0.208268	+	0.120244i
$786$	−0.364686	−	2.57030i	−0.0130079	−	0.0916796i
$787$	16.1281	+	9.31155i	0.574904	+	0.331921i	0.759106	−	0.650968i	$-0.225637\pi$
$787$	16.1281	+	9.31155i	0.574904	+	0.331921i	−0.184202	+	0.982888i	$0.558970\pi$
$788$	16.3676	−	4.21388i	0.583073	−	0.150113i
$789$	−11.1378	−	39.2119i	−0.396518	−	1.39598i
$790$	3.29752	+	8.07279i	0.117320	+	0.287217i
$791$	3.91421	−	6.77962i	0.139173	−	0.241055i
$792$	30.2294	+	38.1815i	1.07415	+	1.35672i
$793$	−1.74409	−	3.02085i	−0.0619344	−	0.107274i
$794$	−21.7391	−	2.97067i	−0.771493	−	0.105425i
$795$	3.02949	+	10.6656i	0.107445	+	0.378271i
$796$	−13.7787	−	14.0520i	−0.488372	−	0.498058i
$797$	−41.0739	+	23.7140i	−1.45491	+	0.839994i	−0.998754	−	0.0499043i	$-0.984108\pi$
$797$	−41.0739	+	23.7140i	−1.45491	+	0.839994i	−0.456159	+	0.889898i	$0.650775\pi$
$798$	2.26363	+	15.9540i	0.0801315	+	0.564766i
$799$		−	1.80032i		−	0.0636908i
$800$	−20.7665	−	16.7604i	−0.734206	−	0.592568i
$801$	17.9978	+	29.1255i	0.635923	+	1.02910i
$802$	0.473810	−	3.46731i	0.0167308	−	0.122435i
$803$	33.9181			1.19694
$804$	−8.11785	+	27.1680i	−0.286294	+	0.958142i
$805$	2.44239			0.0860830
$806$	0.703761	−	5.15007i	0.0247889	−	0.181404i
$807$	19.5218	−	5.54502i	0.687200	−	0.195194i
$808$	9.27179	−	1.08198i	0.326181	−	0.0380639i
$809$		−	20.7631i		−	0.729991i	−0.931009	−	0.364996i	$-0.881071\pi$
$809$		−	20.7631i		−	0.729991i	0.931009	−	0.364996i	$-0.118929\pi$
$810$	5.58486	+	3.81747i	0.196232	+	0.134132i
$811$	−19.0628	+	11.0059i	−0.669384	+	0.386469i	−0.795843	−	0.605503i	$-0.792972\pi$
$811$	−19.0628	+	11.0059i	−0.669384	+	0.386469i	0.126459	+	0.991972i	$0.459639\pi$
$812$	0.664200	−	0.651283i	0.0233089	−	0.0228555i
$813$	−30.0548	+	8.53683i	−1.05407	+	0.299400i
$814$	11.0376	+	1.50830i	0.386869	+	0.0528659i
$815$	2.17837	+	3.77304i	0.0763048	+	0.132164i
$816$	2.72864	−	2.70319i	0.0955214	−	0.0946305i
$817$	−19.4164	+	33.6302i	−0.679293	+	1.17657i
$818$	−7.42649	−	18.1811i	−0.259661	−	0.635687i
$819$	1.71591	+	2.77682i	0.0599587	+	0.0970300i
$820$	−1.05694	−	4.10540i	−0.0369100	−	0.143367i
$821$	0.588774	+	0.339929i	0.0205484	+	0.0118636i	0.510239	−	0.860033i	$-0.329557\pi$
$821$	0.588774	+	0.339929i	0.0205484	+	0.0118636i	−0.489691	+	0.871896i	$0.662890\pi$
$822$	−16.5101	+	2.34253i	−0.575857	+	0.0817052i
$823$	26.6050	+	15.3604i	0.927394	+	0.535431i	0.885986	−	0.463711i	$-0.153483\pi$
$823$	26.6050	+	15.3604i	0.927394	+	0.535431i	0.0414074	+	0.999142i	$0.486816\pi$
$824$	−53.3720	+	6.22830i	−1.85930	+	0.216973i
$825$	32.6606	−	33.6523i	1.13710	−	1.17162i
$826$	−9.01775	+	3.68351i	−0.313768	+	0.128166i
$827$	−9.51423	+	16.4791i	−0.330842	+	0.573035i	−0.982677	−	0.185325i	$-0.940666\pi$
$827$	−9.51423	+	16.4791i	−0.330842	+	0.573035i	0.651835	+	0.758361i	$0.273999\pi$
$828$	6.27724	−	25.4622i	0.218149	−	0.884874i
$829$	16.7316			0.581114			0.290557	−	0.956858i	$-0.406159\pi$
$829$	16.7316			0.581114			0.290557	+	0.956858i	$0.406159\pi$
$830$	2.97236	+	2.30405i	0.103172	+	0.0799747i
$831$	15.6710	+	55.1713i	0.543620	+	1.91387i
$832$	8.05681	−	1.90635i	0.279320	−	0.0660909i
$833$	−2.83010	+	1.63396i	−0.0980571	+	0.0566133i
$834$	−13.1243	+	1.86214i	−0.454459	+	0.0644807i
$835$	9.10047	−	5.25416i	0.314935	−	0.181828i
$836$	−19.2691	+	69.1886i	−0.666437	+	2.39294i
$837$	−18.0217	−	3.97209i	−0.622920	−	0.137296i
$838$	−18.2827	+	23.5858i	−0.631566	+	0.814759i
$839$	−21.5212	−	37.2757i	−0.742993	−	1.28690i	−0.951127	−	0.308801i	$-0.900072\pi$
$839$	−21.5212	−	37.2757i	−0.742993	−	1.28690i	0.208134	−	0.978100i	$-0.433261\pi$
$840$	2.52894	−	1.04819i	0.0872567	−	0.0361659i
$841$	−14.4021	+	24.9452i	−0.496626	+	0.860181i
$842$	−2.94611	+	3.80067i	−0.101530	+	0.130980i
$843$	3.95902	−	15.7114i	0.136356	−	0.541129i
$844$	−26.4191	−	26.9431i	−0.909382	−	0.927419i
$845$	5.49081	−	3.17012i	0.188890	−	0.109055i
$846$	−11.1367	−	8.11140i	−0.382887	−	0.278876i
$847$			23.0665i			0.792574i
$848$	24.9027	−	41.2406i	0.855163	−	1.41621i
$849$	39.1283	−	11.1141i	1.34288	−	0.381435i
$850$	−2.92324	−	2.26597i	−0.100266	−	0.0777222i
$851$	−2.99949	−	5.19528i	−0.102821	−	0.178092i
$852$	38.5625	−	22.5288i	1.32113	−	0.771826i
$853$	−10.9018	+	18.8824i	−0.373270	+	0.646523i	−0.990066	−	0.140600i	$-0.955097\pi$
$853$	−10.9018	+	18.8824i	−0.373270	+	0.646523i	0.616796	+	0.787123i	$0.288430\pi$
$854$	−0.678516	+	4.96534i	−0.0232183	+	0.169910i
$855$	0.298339	+	9.97234i	0.0102030	+	0.341047i
$856$	−17.5548	−	7.57624i	−0.600010	−	0.258951i
$857$			34.0173i			1.16201i	0.813901	+	0.581004i	$0.197340\pi$
$857$			34.0173i			1.16201i	−0.813901	+	0.581004i	$0.802660\pi$
$858$	2.04382	+	14.4048i	0.0697750	+	0.491773i
$859$	25.0534	−	14.4646i	0.854812	−	0.493526i	−0.00745926	−	0.999972i	$-0.502374\pi$
$859$	25.0534	−	14.4646i	0.854812	−	0.493526i	0.862272	+	0.506446i	$0.169041\pi$
$860$	6.35540	+	1.76999i	0.216717	+	0.0603561i
$861$	−7.04216	−	1.77451i	−0.239996	−	0.0604753i
$862$	8.74676	+	21.4133i	0.297916	+	0.729340i
$863$	−41.8217			−1.42363			−0.711813	−	0.702369i	$-0.752126\pi$
$863$	−41.8217			−1.42363			−0.711813	+	0.702369i	$0.752126\pi$
$864$	−4.42780	−	29.0585i	−0.150637	−	0.988589i
$865$	−6.05415	+	10.4861i	−0.205847	+	0.356538i
$866$	5.53359	+	13.5470i	0.188039	+	0.460346i
$867$	−20.1362	+	20.7477i	−0.683863	+	0.704628i
$868$	−5.33220	+	5.22850i	−0.180987	+	0.177467i
$869$	57.6636	+	33.2921i	1.95611	+	1.12936i
$870$	0.453387	−	0.355188i	0.0153713	−	0.0120420i
$871$	−6.18835	+	5.78479i	−0.209684	+	0.196010i
$872$	25.2884	+	10.9139i	0.856374	+	0.369591i
$873$	−0.513209	−	17.1547i	−0.0173695	−	0.580597i
$874$	35.8041	−	14.6250i	1.21109	−	0.494698i
$875$	−2.71508	−	4.70266i	−0.0917865	−	0.158979i
$876$	−17.7818	−	10.1449i	−0.600790	−	0.342765i
$877$	15.0456	−	26.0598i	0.508054	−	0.879976i	−0.491902	−	0.870650i	$-0.663698\pi$
$877$	15.0456	−	26.0598i	0.508054	−	0.879976i	0.999957	−	0.00932549i	$-0.00296844\pi$
$878$	−9.60721	−	7.44710i	−0.324228	−	0.251327i
$879$	40.1581	−	11.4066i	1.35450	−	0.384735i
$880$	12.1994	+	0.239614i	0.411241	+	0.00807738i
$881$	−45.5953	−	26.3245i	−1.53614	−	0.886894i	−0.999059	−	0.0433658i	$-0.986192\pi$
$881$	−45.5953	−	26.3245i	−1.53614	−	0.886894i	−0.537086	−	0.843528i	$-0.680475\pi$
$882$	−2.64353	+	24.8687i	−0.0890121	+	0.837372i
$883$	9.16361	−	5.29061i	0.308380	−	0.178043i	−0.337821	−	0.941210i	$-0.609690\pi$
$883$	9.16361	−	5.29061i	0.308380	−	0.178043i	0.646201	+	0.763167i	$0.276357\pi$
$884$	1.11125	−	0.286093i	0.0373753	−	0.00962235i
$885$	−5.80164	+	1.64791i	−0.195020	+	0.0553940i
$886$	−0.842302	−	2.06208i	−0.0282977	−	0.0692768i
$887$	18.1402	−	31.4198i	0.609089	−	1.05497i	−0.382302	−	0.924038i	$-0.624868\pi$
$887$	18.1402	−	31.4198i	0.609089	−	1.05497i	0.991391	−	0.130936i	$-0.0417982\pi$
$888$	−5.33541	−	4.09210i	−0.179044	−	0.137322i
$889$	−5.73998	+	9.94193i	−0.192513	+	0.333442i
$890$	8.49931	+	1.16144i	0.284898	+	0.0389314i
$891$	51.5613	−	3.08784i	1.72737	−	0.103446i
$892$	−3.92453	+	14.0916i	−0.131403	+	0.471821i
$893$		−	20.3190i		−	0.679949i
$894$	−10.9550	+	1.55434i	−0.366389	+	0.0519850i
$895$			11.7776i			0.393680i
$896$	−10.8265	−	4.92689i	−0.361689	−	0.164596i
$897$	5.45649	−	5.62217i	0.182187	−	0.187719i
$898$	13.4102	−	5.47772i	0.447506	−	0.182794i
$899$	−0.785580	+	1.36066i	−0.0262005	+	0.0453807i
$900$	−27.1879	+	7.87359i	−0.906264	+	0.262453i
$901$	3.33854	−	5.78252i	0.111223	−	0.192644i
$902$	−25.5831	−	19.8309i	−0.851825	−	0.660298i
$903$	7.87116	−	8.11016i	0.261936	−	0.269889i
$904$	−20.9184	+	2.44109i	−0.695734	+	0.0811894i
$905$	0.598048	−	0.345283i	0.0198798	−	0.0114776i
$906$	−1.45347	+	3.61117i	−0.0482885	+	0.119973i
$907$	6.64651	−	3.83736i	0.220694	−	0.127418i	−0.385578	−	0.922675i	$-0.625998\pi$
$907$	6.64651	−	3.83736i	0.220694	−	0.127418i	0.606271	+	0.795258i	$0.292664\pi$
$908$	−5.08719	−	19.7598i	−0.168824	−	0.655751i
$909$	4.69186	−	8.71868i	0.155619	−	0.289180i
$910$	0.810322	+	0.110731i	0.0268619	+	0.00367070i
$911$	50.8780			1.68566			0.842832	−	0.538177i	$-0.180887\pi$
$911$	50.8780			1.68566			0.842832	+	0.538177i	$0.180887\pi$
$912$	30.7963	−	30.5090i	1.01977	−	1.01026i
$913$	28.7157			0.950352
$914$	10.9431	+	26.7904i	0.361967	+	0.886146i
$915$	−0.758169	+	3.00879i	−0.0250643	+	0.0994676i
$916$	37.0859	−	36.3646i	1.22535	−	1.20152i
$917$	−0.964988	+	0.557136i	−0.0318667	+	0.0183983i
$918$	−0.692653	−	4.01460i	−0.0228609	−	0.132501i
$919$	3.31155	+	1.91193i	0.109238	+	0.0630686i	0.553624	−	0.832767i	$-0.313245\pi$
$919$	3.31155	+	1.91193i	0.109238	+	0.0630686i	−0.444386	+	0.895836i	$0.646578\pi$
$920$	−3.92272	−	5.27116i	−0.129328	−	0.173785i
$921$	2.20161	−	8.73707i	0.0725454	−	0.287896i
$922$	−4.82624	+	35.3181i	−0.158944	+	1.16314i
$923$	13.3426			0.439178
$924$	10.3583	−	18.1558i	0.340763	−	0.597280i
$925$	−3.23745	+	5.60743i	−0.106447	+	0.184371i
$926$	36.6240	+	28.3894i	1.20354	+	0.932933i
$927$	−27.0082	+	50.1881i	−0.887064	+	1.64839i
$928$	−2.47237	−	0.387451i	−0.0811594	−	0.0127187i
$929$			33.9266i			1.11310i	0.830815	+	0.556548i	$0.187874\pi$
$929$			33.9266i			1.11310i	−0.830815	+	0.556548i	$0.812126\pi$
$930$	−3.63980	+	2.85145i	−0.119354	+	0.0935027i
$931$	−31.9414	+	18.4414i	−1.04684	+	0.604392i
$932$	−41.6282	+	10.7173i	−1.36358	+	0.351055i
$933$	−7.65935	−	26.9655i	−0.250756	−	0.882812i
$934$	−6.76149	+	8.72273i	−0.221243	+	0.285416i
$935$	1.69113			0.0553058
$936$	3.23701	−	8.16311i	0.105805	−	0.266820i
$937$	10.2654			0.335357			0.167678	−	0.985842i	$-0.446373\pi$
$937$	10.2654			0.335357			0.167678	+	0.985842i	$0.446373\pi$
$938$	12.1187	−	1.12171i	0.395688	−	0.0366252i
$939$	−12.8622	−	45.2827i	−0.419742	−	1.47774i
$940$	−3.34297	+	0.860653i	−0.109036	+	0.0280714i
$941$		−	15.6336i		−	0.509642i	−0.966988	−	0.254821i	$-0.917983\pi$
$941$		−	15.6336i		−	0.509642i	0.966988	−	0.254821i	$-0.0820166\pi$
$942$	−28.8069	−	11.5946i	−0.938579	−	0.377773i
$943$			17.4307i			0.567623i
$944$	22.4331	+	13.5460i	0.730136	+	0.440885i
$945$	0.624976	−	2.83556i	0.0203305	−	0.0922408i
$946$	46.6334	−	19.0485i	1.51618	−	0.619319i
$947$	−20.3377			−0.660886			−0.330443	−	0.943826i	$-0.607198\pi$
$947$	−20.3377			−0.660886			−0.330443	+	0.943826i	$0.607198\pi$
$948$	−20.2728	−	34.7008i	−0.658429	−	1.12703i
$949$	−3.05806	−	5.29671i	−0.0992688	−	0.171939i
$950$	−32.9926	−	25.5745i	−1.07042	−	0.829746i
$951$	5.60403	−	22.2396i	0.181723	−	0.721168i
$952$	−1.51365	−	0.653256i	−0.0490576	−	0.0211721i
$953$		−	32.5154i		−	1.05328i	−0.850089	−	0.526638i	$-0.823452\pi$
$953$		−	32.5154i		−	1.05328i	0.850089	−	0.526638i	$-0.176548\pi$
$954$	−20.7284	−	46.7053i	−0.671107	−	1.51214i
$955$	−1.37864	−	0.795958i	−0.0446117	−	0.0257566i
$956$	−3.61458	−	14.0398i	−0.116904	−	0.454080i
$957$	1.07456	−	4.26440i	0.0347356	−	0.137848i
$958$	36.3582	−	46.9043i	1.17468	−	1.51541i
$959$	3.57872	+	6.19852i	0.115563	+	0.200161i
$960$	−6.32392	−	3.77446i	−0.204104	−	0.121820i
$961$	−9.19337	+	15.9234i	−0.296560	+	0.513657i
$962$	−0.759615	−	1.85964i	−0.0244910	−	0.0599573i
$963$	−17.2517	+	10.6605i	−0.555927	+	0.343530i
$964$	38.3566	+	10.6824i	1.23538	+	0.344056i
$965$		−	11.5777i		−	0.372699i
$966$	−11.1445	+	1.58123i	−0.358568	+	0.0508753i
$967$	−35.4535	+	20.4691i	−1.14011	+	0.658241i	−0.946457	−	0.322829i	$-0.895366\pi$
$967$	−35.4535	+	20.4691i	−1.14011	+	0.658241i	−0.193650	+	0.981071i	$0.562033\pi$
$968$	49.7820	−	37.0470i	1.60005	−	1.19074i
$969$	4.18442	−	4.31148i	0.134423	−	0.138505i
$970$	−3.39856	−	2.63442i	−0.109121	−	0.0845862i
$971$	0.0659380	+	0.114208i	0.00211605	+	0.00366511i	0.867081	−	0.498166i	$-0.165993\pi$
$971$	0.0659380	+	0.114208i	0.00211605	+	0.00366511i	−0.864965	+	0.501831i	$0.832660\pi$
$972$	−27.9548	−	13.8032i	−0.896651	−	0.442737i
$973$	2.84482	+	4.92737i	0.0912007	+	0.157964i
$974$	24.3863	+	18.9032i	0.781387	+	0.605698i
$975$	−8.19988	−	2.06624i	−0.262606	−	0.0661727i
$976$	11.8059	−	6.51045i	0.377899	−	0.208394i
$977$	−6.77330	−	3.91057i	−0.216697	−	0.125110i	0.387723	−	0.921776i	$-0.373262\pi$
$977$	−6.77330	−	3.91057i	−0.216697	−	0.125110i	−0.604420	+	0.796666i	$0.706595\pi$
$978$	−12.3825	−	15.8059i	−0.395947	−	0.505415i
$979$	56.7247	−	32.7500i	1.81293	−	1.04670i
$980$	4.38700	+	4.47401i	0.140138	+	0.142917i
$981$	24.8518	−	15.3569i	0.793455	−	0.490308i
$982$	31.5883	+	4.31656i	1.00802	+	0.137747i
$983$	−46.4596			−1.48183			−0.740915	−	0.671599i	$-0.765608\pi$
$983$	−46.4596			−1.48183			−0.740915	+	0.671599i	$0.765608\pi$
$984$	7.48064	+	18.0484i	0.238474	+	0.575362i
$985$	−2.24577	−	3.88978i	−0.0715561	−	0.123939i
$986$	−0.343652	−	0.0469602i	−0.0109441	−	0.00149552i
$987$	−1.44496	+	5.73433i	−0.0459936	+	0.182526i
$988$	12.5419	−	3.22894i	0.399011	−	0.102726i
$989$	−23.4920	−	13.5631i	−0.747001	−	0.431281i
$990$	7.61942	−	10.4612i	0.242161	−	0.332479i
$991$		−	23.8069i		−	0.756250i	−0.925755	−	0.378125i	$-0.876569\pi$
$991$		−	23.8069i		−	0.756250i	0.925755	−	0.378125i	$-0.123431\pi$
$992$	19.8482	+	3.11046i	0.630180	+	0.0987572i
$993$	−13.5791	−	13.1789i	−0.430919	−	0.418220i
$994$	−15.1506	−	11.7441i	−0.480549	−	0.372501i
$995$	−2.61500	+	4.52931i	−0.0829011	+	0.143589i
$996$	−15.0544	−	8.58889i	−0.477016	−	0.272149i
$997$	−30.5143			−0.966397			−0.483199	−	0.875511i	$-0.660525\pi$
$997$	−30.5143			−0.966397			−0.483199	+	0.875511i	$0.660525\pi$
$998$	30.0315	+	23.2791i	0.950630	+	0.736888i
$999$	−6.79913	+	2.15294i	−0.215115	+	0.0681160i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.l.a.431.6	✓	264
3.2	odd	2	inner	804.2.l.a.431.127	yes	264
4.3	odd	2	inner	804.2.l.a.431.39	yes	264
12.11	even	2	inner	804.2.l.a.431.94	yes	264
67.37	even	3	inner	804.2.l.a.707.94	yes	264
201.104	odd	6	inner	804.2.l.a.707.39	yes	264
268.171	odd	6	inner	804.2.l.a.707.127	yes	264
804.707	even	6	inner	804.2.l.a.707.6	yes	264

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.l.a.431.6	✓	264	1.1	even	1	trivial
804.2.l.a.431.39	yes	264	4.3	odd	2	inner
804.2.l.a.431.94	yes	264	12.11	even	2	inner
804.2.l.a.431.127	yes	264	3.2	odd	2	inner
804.2.l.a.707.6	yes	264	804.707	even	6	inner
804.2.l.a.707.39	yes	264	201.104	odd	6	inner
804.2.l.a.707.94	yes	264	67.37	even	3	inner
804.2.l.a.707.127	yes	264	268.171	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.l (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40119 - 0.191474i) q^{2} +(-0.473255 - 1.66614i) q^{3} +(1.92668 + 0.536583i) q^{4} -0.531500i q^{5} +(0.344098 + 2.42520i) q^{6} +(0.910512 - 0.525684i) q^{7} +(-2.59690 - 1.12076i) q^{8} +(-2.55206 + 1.57702i) q^{9} +O(q^{10})\)	\(q+(-1.40119 - 0.191474i) q^{2} +(-0.473255 - 1.66614i) q^{3} +(1.92668 + 0.536583i) q^{4} -0.531500i q^{5} +(0.344098 + 2.42520i) q^{6} +(0.910512 - 0.525684i) q^{7} +(-2.59690 - 1.12076i) q^{8} +(-2.55206 + 1.57702i) q^{9} +(-0.101768 + 0.744733i) q^{10} +(2.86965 + 4.97037i) q^{11} +(-0.0177859 - 3.46406i) q^{12} +(0.517455 - 0.896257i) q^{13} +(-1.37646 + 0.562245i) q^{14} +(-0.885554 + 0.251535i) q^{15} +(3.42416 + 2.06764i) q^{16} +(0.480115 + 0.277195i) q^{17} +(3.87788 - 1.72105i) q^{18} +(5.41874 + 3.12851i) q^{19} +(0.285193 - 1.02403i) q^{20} +(-1.30677 - 1.26826i) q^{21} +(-3.06923 - 7.51391i) q^{22} +(-2.18538 + 3.78520i) q^{23} +(-0.638354 + 4.85721i) q^{24} +4.71751 q^{25} +(-0.896663 + 1.15675i) q^{26} +(3.83531 + 3.50576i) q^{27} +(2.03633 - 0.524258i) q^{28} +(0.383122 - 0.221196i) q^{29} +(1.28899 - 0.182888i) q^{30} +(-3.07570 + 1.77576i) q^{31} +(-4.40200 - 3.55280i) q^{32} +(6.92328 - 7.13349i) q^{33} +(-0.619658 - 0.480332i) q^{34} +(-0.279401 - 0.483937i) q^{35} +(-5.76319 + 1.66902i) q^{36} +(-0.686263 + 1.18864i) q^{37} +(-6.99366 - 5.42118i) q^{38} +(-1.73818 - 0.437994i) q^{39} +(-0.595685 + 1.38025i) q^{40} +(3.45373 - 1.99401i) q^{41} +(1.58819 + 2.02729i) q^{42} +6.20627i q^{43} +(2.86186 + 11.1161i) q^{44} +(0.838186 + 1.35642i) q^{45} +(3.78691 - 4.88534i) q^{46} +(-1.62370 - 2.81233i) q^{47} +(1.82448 - 6.68366i) q^{48} +(-2.94731 + 5.10489i) q^{49} +(-6.61013 - 0.903279i) q^{50} +(0.234629 - 0.931124i) q^{51} +(1.47788 - 1.44914i) q^{52} -12.0440i q^{53} +(-4.70275 - 5.64661i) q^{54} +(2.64175 - 1.52522i) q^{55} +(-2.95367 + 0.344682i) q^{56} +(2.64810 - 10.5090i) q^{57} +(-0.579180 + 0.236580i) q^{58} +6.55143 q^{59} +(-1.84114 + 0.00945319i) q^{60} +(1.68526 - 2.91895i) q^{61} +(4.64966 - 1.89926i) q^{62} +(-1.49467 + 2.77747i) q^{63} +(5.48778 + 5.82102i) q^{64} +(-0.476361 - 0.275027i) q^{65} +(-11.0667 + 8.66977i) q^{66} +(-7.83059 - 2.38366i) q^{67} +(0.776289 + 0.791686i) q^{68} +(7.34092 + 1.84980i) q^{69} +(0.298833 + 0.731586i) q^{70} +(6.44628 + 11.1653i) q^{71} +(8.39491 - 1.23511i) q^{72} +(2.95490 - 5.11805i) q^{73} +(1.18918 - 1.53411i) q^{74} +(-2.23258 - 7.86004i) q^{75} +(8.76144 + 8.93522i) q^{76} +(5.22569 + 3.01706i) q^{77} +(2.35166 + 0.946530i) q^{78} +(10.0472 - 5.80073i) q^{79} +(1.09895 - 1.81994i) q^{80} +(4.02602 - 8.04930i) q^{81} +(-5.22114 + 2.13270i) q^{82} +(2.50168 - 4.33304i) q^{83} +(-1.83719 - 3.14471i) q^{84} +(0.147329 - 0.255181i) q^{85} +(1.18834 - 8.69618i) q^{86} +(-0.549858 - 0.533654i) q^{87} +(-1.88158 - 16.1238i) q^{88} -11.4126i q^{89} +(-0.914740 - 2.06109i) q^{90} -1.08807i q^{91} +(-6.24160 + 6.12021i) q^{92} +(4.41426 + 4.28417i) q^{93} +(1.73662 + 4.25150i) q^{94} +(1.66280 - 2.88006i) q^{95} +(-3.83620 + 9.01574i) q^{96} +(-2.86039 + 4.95434i) q^{97} +(5.10720 - 6.58860i) q^{98} +(-15.1619 - 8.15920i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 264 q - 2 q^{4} - 3 q^{6} - 12 q^{9}+O(q^{10}) \) 264 * q - 2 * q^4 - 3 * q^6 - 12 * q^9	\( 264 q - 2 q^{4} - 3 q^{6} - 12 q^{9} + 2 q^{10} + 2 q^{12} - 18 q^{16} + q^{18} - 4 q^{22} - 248 q^{25} + 7 q^{30} - 38 q^{34} + 13 q^{36} + 4 q^{37} + 48 q^{40} - 12 q^{42} + 48 q^{45} - 2 q^{46} - 11 q^{48} + 128 q^{49} + 32 q^{52} - 8 q^{54} - 2 q^{57} - 32 q^{58} + 68 q^{60} - 8 q^{61} + 4 q^{64} + 30 q^{66} - 40 q^{69} - 140 q^{70} + 108 q^{72} - 4 q^{73} - 120 q^{76} + 44 q^{78} - 28 q^{81} - 64 q^{82} + 33 q^{84} + 16 q^{85} - 14 q^{88} + 42 q^{90} + 16 q^{93} - 12 q^{94} - 4 q^{96} + 20 q^{97}+O(q^{100}) \) 264 * q - 2 * q^4 - 3 * q^6 - 12 * q^9 + 2 * q^10 + 2 * q^12 - 18 * q^16 + q^18 - 4 * q^22 - 248 * q^25 + 7 * q^30 - 38 * q^34 + 13 * q^36 + 4 * q^37 + 48 * q^40 - 12 * q^42 + 48 * q^45 - 2 * q^46 - 11 * q^48 + 128 * q^49 + 32 * q^52 - 8 * q^54 - 2 * q^57 - 32 * q^58 + 68 * q^60 - 8 * q^61 + 4 * q^64 + 30 * q^66 - 40 * q^69 - 140 * q^70 + 108 * q^72 - 4 * q^73 - 120 * q^76 + 44 * q^78 - 28 * q^81 - 64 * q^82 + 33 * q^84 + 16 * q^85 - 14 * q^88 + 42 * q^90 + 16 * q^93 - 12 * q^94 - 4 * q^96 + 20 * q^97

Introduction

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