LMFDB - Embedded newform 570.2.x.a.217.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(103,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 9, 2]))

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

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

chi := DirichletCharacter("570.103");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.x (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:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			217.2
Character	$\chi$	$=$	570.217
Dual form			570.2.x.a.373.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 - 0.965926i) q^{2} +(0.965926 - 0.258819i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-1.23980 + 1.86088i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(1.93610 + 1.93610i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(-0.258819 - 0.965926i) q^{2} +(0.965926 - 0.258819i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-1.23980 + 1.86088i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(1.93610 + 1.93610i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.866025 - 0.500000i) q^{9} +(2.11836 + 0.715924i) q^{10} -6.13624 q^{11} +(-0.707107 + 0.707107i) q^{12} +(-1.66245 + 6.20436i) q^{13} +(1.36903 - 2.37123i) q^{14} +(-0.715924 + 2.11836i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-3.56853 + 0.956186i) q^{17} +(-0.707107 - 0.707107i) q^{18} +(-3.01126 - 3.15156i) q^{19} +(0.143258 - 2.23147i) q^{20} +(2.37123 + 1.36903i) q^{21} +(1.58818 + 5.92715i) q^{22} +(-0.234151 - 0.0627405i) q^{23} +(0.866025 + 0.500000i) q^{24} +(-1.92578 - 4.61426i) q^{25} +6.42322 q^{26} +(0.707107 - 0.707107i) q^{27} +(-2.64476 - 0.708662i) q^{28} +(3.45840 + 5.99013i) q^{29} +(2.23147 + 0.143258i) q^{30} +7.31215i q^{31} +(-0.965926 - 0.258819i) q^{32} +(-5.92715 + 1.58818i) q^{33} +(1.84721 + 3.19946i) q^{34} +(-6.00324 + 1.20248i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(7.48634 - 7.48634i) q^{37} +(-2.26480 + 3.72434i) q^{38} +6.42322i q^{39} +(-2.19252 + 0.439172i) q^{40} +(4.33183 + 2.50098i) q^{41} +(0.708662 - 2.64476i) q^{42} +(1.46909 + 5.48270i) q^{43} +(5.31414 - 3.06812i) q^{44} +(-0.143258 + 2.23147i) q^{45} +0.242411i q^{46} +(2.04807 - 7.64349i) q^{47} +(0.258819 - 0.965926i) q^{48} +0.496968i q^{49} +(-3.95860 + 3.05442i) q^{50} +(-3.19946 + 1.84721i) q^{51} +(-1.66245 - 6.20436i) q^{52} +(0.398130 - 1.48584i) q^{53} +(-0.866025 - 0.500000i) q^{54} +(7.60772 - 11.4188i) q^{55} +2.73806i q^{56} +(-3.72434 - 2.26480i) q^{57} +(4.89092 - 4.89092i) q^{58} +(0.890408 - 1.54223i) q^{59} +(-0.439172 - 2.19252i) q^{60} +(5.98482 + 10.3660i) q^{61} +(7.06300 - 1.89252i) q^{62} +(2.64476 + 0.708662i) q^{63} +1.00000i q^{64} +(-9.48448 - 10.7858i) q^{65} +(3.06812 + 5.31414i) q^{66} +(7.33274 + 1.96480i) q^{67} +(2.61235 - 2.61235i) q^{68} -0.242411 q^{69} +(2.71526 + 5.48746i) q^{70} +(-2.59944 - 1.50079i) q^{71} +(0.965926 + 0.258819i) q^{72} +(0.428415 + 1.59887i) q^{73} +(-9.16885 - 5.29364i) q^{74} +(-3.05442 - 3.95860i) q^{75} +(4.18361 + 1.22370i) q^{76} +(-11.8804 - 11.8804i) q^{77} +(6.20436 - 1.66245i) q^{78} +(2.06110 - 3.56993i) q^{79} +(0.991672 + 2.00414i) q^{80} +(0.500000 - 0.866025i) q^{81} +(1.29460 - 4.83153i) q^{82} +(-4.54261 + 4.54261i) q^{83} -2.73806 q^{84} +(2.64492 - 7.82611i) q^{85} +(4.91566 - 2.83806i) q^{86} +(4.89092 + 4.89092i) q^{87} +(-4.33898 - 4.33898i) q^{88} +(-3.75665 - 6.50671i) q^{89} +(2.19252 - 0.439172i) q^{90} +(-15.2309 + 8.79358i) q^{91} +(0.234151 - 0.0627405i) q^{92} +(1.89252 + 7.06300i) q^{93} -7.91312 q^{94} +(9.59805 - 1.69631i) q^{95} -1.00000 q^{96} +(0.640895 + 2.39185i) q^{97} +(0.480034 - 0.128625i) q^{98} +(-5.31414 + 3.06812i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 8 q^{5} - 20 q^{6} - 8 q^{7}+O(q^{10}) $ 40 * q - 8 * q^5 - 20 * q^6 - 8 * q^7	$ 40 q - 8 q^{5} - 20 q^{6} - 8 q^{7} - 12 q^{10} + 8 q^{11} - 24 q^{13} + 20 q^{16} + 8 q^{17} + 12 q^{21} + 24 q^{22} + 16 q^{23} - 16 q^{25} + 32 q^{26} + 4 q^{28} + 16 q^{30} - 24 q^{33} - 4 q^{35} - 20 q^{36} - 8 q^{38} - 36 q^{41} + 4 q^{42} - 4 q^{43} + 8 q^{47} - 24 q^{52} - 16 q^{55} - 8 q^{57} + 16 q^{58} + 12 q^{60} - 8 q^{61} - 16 q^{62} - 4 q^{63} - 4 q^{66} - 36 q^{67} - 16 q^{68} + 48 q^{70} + 72 q^{71} - 16 q^{73} - 8 q^{76} + 24 q^{77} + 24 q^{78} + 8 q^{80} + 20 q^{81} - 24 q^{82} - 40 q^{83} - 48 q^{85} + 16 q^{87} - 72 q^{91} - 16 q^{92} + 16 q^{93} - 16 q^{95} - 40 q^{96} + 36 q^{97} - 48 q^{98}+O(q^{100}) $ 40 * q - 8 * q^5 - 20 * q^6 - 8 * q^7 - 12 * q^10 + 8 * q^11 - 24 * q^13 + 20 * q^16 + 8 * q^17 + 12 * q^21 + 24 * q^22 + 16 * q^23 - 16 * q^25 + 32 * q^26 + 4 * q^28 + 16 * q^30 - 24 * q^33 - 4 * q^35 - 20 * q^36 - 8 * q^38 - 36 * q^41 + 4 * q^42 - 4 * q^43 + 8 * q^47 - 24 * q^52 - 16 * q^55 - 8 * q^57 + 16 * q^58 + 12 * q^60 - 8 * q^61 - 16 * q^62 - 4 * q^63 - 4 * q^66 - 36 * q^67 - 16 * q^68 + 48 * q^70 + 72 * q^71 - 16 * q^73 - 8 * q^76 + 24 * q^77 + 24 * q^78 + 8 * q^80 + 20 * q^81 - 24 * q^82 - 40 * q^83 - 48 * q^85 + 16 * q^87 - 72 * q^91 - 16 * q^92 + 16 * q^93 - 16 * q^95 - 40 * q^96 + 36 * q^97 - 48 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−0.258819	−	0.965926i	−0.183013	−	0.683013i
$2$	−0.258819	−	0.965926i	−0.183013	−	0.683013i
$3$	0.965926	−	0.258819i	0.557678	−	0.149429i
$3$	0.965926	−	0.258819i	0.557678	−	0.149429i
$4$	−0.866025	+	0.500000i	−0.433013	+	0.250000i
$5$	−1.23980	+	1.86088i	−0.554456	+	0.832213i
$5$	−1.23980	+	1.86088i	−0.554456	+	0.832213i
$6$	−0.500000	−	0.866025i	−0.204124	−	0.353553i
$7$	1.93610	+	1.93610i	0.731777	+	0.731777i	0.970972	−	0.239195i	$-0.0768834\pi$
$7$	1.93610	+	1.93610i	0.731777	+	0.731777i	−0.239195	+	0.970972i	$0.576883\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	0.866025	−	0.500000i	0.288675	−	0.166667i
$10$	2.11836	+	0.715924i	0.669884	+	0.226395i
$11$	−6.13624			−1.85015			−0.925073	−	0.379789i	$-0.875997\pi$
$11$	−6.13624			−1.85015			−0.925073	+	0.379789i	$0.875997\pi$
$12$	−0.707107	+	0.707107i	−0.204124	+	0.204124i
$13$	−1.66245	+	6.20436i	−0.461081	+	1.72078i	0.208484	+	0.978026i	$0.433147\pi$
$13$	−1.66245	+	6.20436i	−0.461081	+	1.72078i	−0.669566	+	0.742753i	$0.733520\pi$
$14$	1.36903	−	2.37123i	0.365889	−	0.633738i
$15$	−0.715924	+	2.11836i	−0.184851	+	0.546958i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−3.56853	+	0.956186i	−0.865497	+	0.231909i	−0.664139	−	0.747609i	$-0.731202\pi$
$17$	−3.56853	+	0.956186i	−0.865497	+	0.231909i	−0.201357	+	0.979518i	$0.564535\pi$
$18$	−0.707107	−	0.707107i	−0.166667	−	0.166667i
$19$	−3.01126	−	3.15156i	−0.690831	−	0.723016i
$19$	−3.01126	−	3.15156i	−0.690831	−	0.723016i
$20$	0.143258	−	2.23147i	0.0320334	−	0.498973i
$21$	2.37123	+	1.36903i	0.517445	+	0.298747i
$22$	1.58818	+	5.92715i	0.338600	+	1.26367i
$23$	−0.234151	−	0.0627405i	−0.0488238	−	0.0130823i	0.234324	−	0.972158i	$-0.424712\pi$
$23$	−0.234151	−	0.0627405i	−0.0488238	−	0.0130823i	−0.283148	+	0.959076i	$0.591379\pi$
$24$	0.866025	+	0.500000i	0.176777	+	0.102062i
$25$	−1.92578	−	4.61426i	−0.385156	−	0.922851i
$26$	6.42322			1.25970
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$	−2.64476	−	0.708662i	−0.499813	−	0.133925i
$29$	3.45840	+	5.99013i	0.642209	+	1.11234i	0.984939	+	0.172905i	$0.0553153\pi$
$29$	3.45840	+	5.99013i	0.642209	+	1.11234i	−0.342729	+	0.939434i	$0.611351\pi$
$30$	2.23147	+	0.143258i	0.407410	+	0.0261552i
$31$			7.31215i			1.31330i	0.754195	+	0.656651i	$0.228027\pi$
$31$			7.31215i			1.31330i	−0.754195	+	0.656651i	$0.771973\pi$
$32$	−0.965926	−	0.258819i	−0.170753	−	0.0457532i
$33$	−5.92715	+	1.58818i	−1.03178	+	0.276466i
$34$	1.84721	+	3.19946i	0.316794	+	0.548703i
$35$	−6.00324	+	1.20248i	−1.01473	+	0.203256i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	7.48634	−	7.48634i	1.23075	−	1.23075i	0.267068	−	0.963678i	$-0.413945\pi$
$37$	7.48634	−	7.48634i	1.23075	−	1.23075i	0.963678	−	0.267068i	$-0.0860549\pi$
$38$	−2.26480	+	3.72434i	−0.367399	+	0.604167i
$39$			6.42322i			1.02854i
$40$	−2.19252	+	0.439172i	−0.346667	+	0.0694391i
$41$	4.33183	+	2.50098i	0.676518	+	0.390588i	0.798542	−	0.601939i	$-0.205605\pi$
$41$	4.33183	+	2.50098i	0.676518	+	0.390588i	−0.122024	+	0.992527i	$0.538938\pi$
$42$	0.708662	−	2.64476i	0.109349	−	0.408096i
$43$	1.46909	+	5.48270i	0.224034	+	0.836105i	0.982789	+	0.184729i	$0.0591409\pi$
$43$	1.46909	+	5.48270i	0.224034	+	0.836105i	−0.758756	+	0.651375i	$0.774192\pi$
$44$	5.31414	−	3.06812i	0.801137	−	0.462537i
$45$	−0.143258	+	2.23147i	−0.0213556	+	0.332649i
$46$			0.242411i			0.0357415i
$47$	2.04807	−	7.64349i	0.298741	−	1.11492i	−0.639459	−	0.768825i	$-0.720842\pi$
$47$	2.04807	−	7.64349i	0.298741	−	1.11492i	0.938201	−	0.346092i	$-0.112492\pi$
$48$	0.258819	−	0.965926i	0.0373573	−	0.139419i
$49$			0.496968i			0.0709954i
$50$	−3.95860	+	3.05442i	−0.559831	+	0.431960i
$51$	−3.19946	+	1.84721i	−0.448014	+	0.258661i
$52$	−1.66245	−	6.20436i	−0.230541	−	0.860389i
$53$	0.398130	−	1.48584i	0.0546873	−	0.204096i	−0.933176	−	0.359419i	$-0.882975\pi$
$53$	0.398130	−	1.48584i	0.0546873	−	0.204096i	0.987864	+	0.155323i	$0.0496417\pi$
$54$	−0.866025	−	0.500000i	−0.117851	−	0.0680414i
$55$	7.60772	−	11.4188i	1.02583	−	1.53972i
$56$			2.73806i			0.365889i
$57$	−3.72434	−	2.26480i	−0.493301	−	0.299980i
$58$	4.89092	−	4.89092i	0.642209	−	0.642209i
$59$	0.890408	−	1.54223i	0.115921	−	0.200782i	−0.802226	−	0.597020i	$-0.796351\pi$
$59$	0.890408	−	1.54223i	0.115921	−	0.200782i	0.918148	+	0.396238i	$0.129685\pi$
$60$	−0.439172	−	2.19252i	−0.0566968	−	0.283053i
$61$	5.98482	+	10.3660i	0.766277	+	1.32723i	0.939569	+	0.342361i	$0.111226\pi$
$61$	5.98482	+	10.3660i	0.766277	+	1.32723i	−0.173291	+	0.984871i	$0.555440\pi$
$62$	7.06300	−	1.89252i	0.897002	−	0.240351i
$63$	2.64476	+	0.708662i	0.333209	+	0.0892830i
$64$			1.00000i			0.125000i
$65$	−9.48448	−	10.7858i	−1.17640	−	1.33781i
$66$	3.06812	+	5.31414i	0.377660	+	0.654125i
$67$	7.33274	+	1.96480i	0.895837	+	0.240039i	0.677227	−	0.735774i	$-0.263181\pi$
$67$	7.33274	+	1.96480i	0.895837	+	0.240039i	0.218609	+	0.975812i	$0.429848\pi$
$68$	2.61235	−	2.61235i	0.316794	−	0.316794i
$69$	−0.242411			−0.0291828
$70$	2.71526	+	5.48746i	0.324535	+	0.655877i
$71$	−2.59944	−	1.50079i	−0.308497	−	0.178111i	0.337757	−	0.941233i	$-0.390332\pi$
$71$	−2.59944	−	1.50079i	−0.308497	−	0.178111i	−0.646254	+	0.763123i	$0.723665\pi$
$72$	0.965926	+	0.258819i	0.113835	+	0.0305021i
$73$	0.428415	+	1.59887i	0.0501422	+	0.187133i	0.986454	−	0.164035i	$-0.0524511\pi$
$73$	0.428415	+	1.59887i	0.0501422	+	0.187133i	−0.936312	+	0.351168i	$0.885784\pi$
$74$	−9.16885	−	5.29364i	−1.06586	−	0.615373i
$75$	−3.05442	−	3.95860i	−0.352694	−	0.457100i
$76$	4.18361	+	1.22370i	0.479893	+	0.140368i
$77$	−11.8804	−	11.8804i	−1.35389	−	1.35389i
$78$	6.20436	−	1.66245i	0.702505	−	0.188236i
$79$	2.06110	−	3.56993i	0.231892	−	0.401649i	−0.726473	−	0.687195i	$-0.758842\pi$
$79$	2.06110	−	3.56993i	0.231892	−	0.401649i	0.958365	+	0.285546i	$0.0921751\pi$
$80$	0.991672	+	2.00414i	0.110872	+	0.224070i
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$	1.29460	−	4.83153i	0.142965	−	0.533553i
$83$	−4.54261	+	4.54261i	−0.498616	+	0.498616i	−0.911007	−	0.412391i	$-0.864694\pi$
$83$	−4.54261	+	4.54261i	−0.498616	+	0.498616i	0.412391	+	0.911007i	$0.364694\pi$
$84$	−2.73806			−0.298747
$85$	2.64492	−	7.82611i	0.286882	−	0.848861i
$86$	4.91566	−	2.83806i	0.530069	−	0.306036i
$87$	4.89092	+	4.89092i	0.524362	+	0.524362i
$88$	−4.33898	−	4.33898i	−0.462537	−	0.462537i
$89$	−3.75665	−	6.50671i	−0.398204	−	0.689710i	0.595300	−	0.803503i	$-0.297033\pi$
$89$	−3.75665	−	6.50671i	−0.398204	−	0.689710i	−0.993504	+	0.113793i	$0.963700\pi$
$90$	2.19252	−	0.439172i	0.231112	−	0.0462928i
$91$	−15.2309	+	8.79358i	−1.59664	+	0.921818i
$92$	0.234151	−	0.0627405i	0.0244119	−	0.00654115i
$93$	1.89252	+	7.06300i	0.196246	+	0.732399i
$94$	−7.91312			−0.816176
$95$	9.59805	−	1.69631i	0.984739	−	0.174037i
$96$	−1.00000			−0.102062
$97$	0.640895	+	2.39185i	0.0650730	+	0.242856i	0.990799	−	0.135338i	$-0.0432120\pi$
$97$	0.640895	+	2.39185i	0.0650730	+	0.242856i	−0.925727	+	0.378194i	$0.876545\pi$
$98$	0.480034	−	0.128625i	0.0484908	−	0.0129931i
$99$	−5.31414	+	3.06812i	−0.534091	+	0.308358i
$100$	3.97490	+	3.03317i	0.397490	+	0.303317i
$101$	5.87701	+	10.1793i	0.584785	+	1.01288i	0.994902	+	0.100844i	$0.0321543\pi$
$101$	5.87701	+	10.1793i	0.584785	+	1.01288i	−0.410118	+	0.912033i	$0.634512\pi$
$102$	2.61235	+	2.61235i	0.258661	+	0.258661i
$103$	−0.830421	−	0.830421i	−0.0818238	−	0.0818238i	0.665010	−	0.746834i	$-0.268427\pi$
$103$	−0.830421	−	0.830421i	−0.0818238	−	0.0818238i	−0.746834	+	0.665010i	$0.768427\pi$
$104$	−5.56267	+	3.21161i	−0.545465	+	0.314924i
$105$	−5.48746	+	2.71526i	−0.535521	+	0.264982i
$106$	−1.53826			−0.149409
$107$	0.468814	−	0.468814i	0.0453220	−	0.0453220i	−0.684083	−	0.729405i	$-0.739797\pi$
$107$	0.468814	−	0.468814i	0.0453220	−	0.0453220i	0.729405	+	0.684083i	$0.239797\pi$
$108$	−0.258819	+	0.965926i	−0.0249049	+	0.0929463i
$109$	−8.22240	+	14.2416i	−0.787563	+	1.36410i	0.139893	+	0.990167i	$0.455324\pi$
$109$	−8.22240	+	14.2416i	−0.787563	+	1.36410i	−0.927456	+	0.373933i	$0.878009\pi$
$110$	−12.9988	−	4.39308i	−1.23938	−	0.418864i
$111$	5.29364	−	9.16885i	0.502450	−	0.870269i
$112$	2.64476	−	0.708662i	0.249907	−	0.0669623i
$113$	−1.01524	−	1.01524i	−0.0955058	−	0.0955058i	0.657740	−	0.753245i	$-0.271513\pi$
$113$	−1.01524	−	1.01524i	−0.0955058	−	0.0955058i	−0.753245	+	0.657740i	$0.771513\pi$
$114$	−1.22370	+	4.18361i	−0.114610	+	0.391831i
$115$	0.407053	−	0.357942i	0.0379579	−	0.0333782i
$116$	−5.99013	−	3.45840i	−0.556170	−	0.321105i
$117$	1.66245	+	6.20436i	0.153694	+	0.573593i
$118$	−1.72014	−	0.460909i	−0.158351	−	0.0424301i
$119$	−8.76031	−	5.05777i	−0.803056	−	0.463645i
$120$	−2.00414	+	0.991672i	−0.182952	+	0.0905269i
$121$	26.6534			2.42304
$122$	8.46381	−	8.46381i	0.766277	−	0.766277i
$123$	4.83153	+	1.29460i	0.435644	+	0.116731i
$124$	−3.65608	−	6.33251i	−0.328325	−	0.568676i
$125$	10.9742	+	2.13711i	0.981561	+	0.191149i
$126$		−	2.73806i		−	0.243926i
$127$	−14.6064	−	3.91378i	−1.29611	−	0.347292i	−0.456133	−	0.889911i	$-0.650766\pi$
$127$	−14.6064	−	3.91378i	−1.29611	−	0.347292i	−0.839979	+	0.542619i	$0.817433\pi$
$128$	0.965926	−	0.258819i	0.0853766	−	0.0228766i
$129$	2.83806	+	4.91566i	0.249877	+	0.432800i
$130$	−7.96352	+	11.9529i	−0.698447	+	1.04834i
$131$	−8.81098	+	15.2611i	−0.769819	+	1.33336i	0.167843	+	0.985814i	$0.446320\pi$
$131$	−8.81098	+	15.2611i	−0.769819	+	1.33336i	−0.937661	+	0.347551i	$0.887013\pi$
$132$	4.33898	−	4.33898i	0.377660	−	0.377660i
$133$	0.271622	−	11.9318i	0.0235526	−	1.03462i
$134$		−	7.59141i		−	0.655798i
$135$	0.439172	+	2.19252i	0.0377979	+	0.188702i
$136$	−3.19946	−	1.84721i	−0.274351	−	0.158397i
$137$	−0.0279276	+	0.104227i	−0.00238602	+	0.00890473i	−0.967109	−	0.254364i	$-0.918134\pi$
$137$	−0.0279276	+	0.104227i	−0.00238602	+	0.00890473i	0.964723	+	0.263269i	$0.0848006\pi$
$138$	0.0627405	+	0.234151i	0.00534083	+	0.0199322i
$139$	7.26574	−	4.19488i	0.616272	−	0.355805i	−0.159144	−	0.987255i	$-0.550873\pi$
$139$	7.26574	−	4.19488i	0.616272	−	0.355805i	0.775416	+	0.631450i	$0.217540\pi$
$140$	4.59772	−	4.04300i	0.388578	−	0.341696i
$141$		−	7.91312i		−	0.666405i
$142$	−0.776864	+	2.89930i	−0.0651930	+	0.243304i
$143$	10.2012	−	38.0714i	0.853068	−	3.18369i
$144$		−	1.00000i		−	0.0833333i
$145$	−15.4347	−	0.990886i	−1.28178	−	0.0822886i
$146$	1.43350	−	0.827634i	0.118638	−	0.0684955i
$147$	0.128625	+	0.480034i	0.0106088	+	0.0395926i
$148$	−2.74019	+	10.2265i	−0.225242	+	0.840615i
$149$	2.70904	+	1.56407i	0.221933	+	0.128133i	0.606845	−	0.794820i	$-0.292435\pi$
$149$	2.70904	+	1.56407i	0.221933	+	0.128133i	−0.384912	+	0.922953i	$0.625768\pi$
$150$	−3.03317	+	3.97490i	−0.247657	+	0.324550i
$151$		−	11.4137i		−	0.928838i	−0.885616	−	0.464419i	$-0.846263\pi$
$151$		−	11.4137i		−	0.928838i	0.885616	−	0.464419i	$-0.153737\pi$
$152$	0.0992023	−	4.35777i	0.00804637	−	0.353462i
$153$	−2.61235	+	2.61235i	−0.211196	+	0.211196i
$154$	−8.40069	+	14.5504i	−0.676947	+	1.17251i
$155$	−13.6071	−	9.06562i	−1.09295	−	0.728168i
$156$	−3.21161	−	5.56267i	−0.257135	−	0.445370i
$157$	−20.6527	+	5.53388i	−1.64827	+	0.441652i	−0.959127	−	0.282976i	$-0.908678\pi$
$157$	−20.6527	+	5.53388i	−1.64827	+	0.441652i	−0.689140	+	0.724628i	$0.742012\pi$
$158$	−3.98174	−	1.06690i	−0.316770	−	0.0848784i
$159$		−	1.53826i		−	0.121992i
$160$	1.67919	−	1.47659i	0.132752	−	0.116735i
$161$	−0.331867	−	0.574811i	−0.0261548	−	0.0453015i
$162$	−0.965926	−	0.258819i	−0.0758903	−	0.0203347i
$163$	16.6635	−	16.6635i	1.30518	−	1.30518i	0.380337	−	0.924848i	$-0.375808\pi$
$163$	16.6635	−	16.6635i	1.30518	−	1.30518i	0.924848	−	0.380337i	$-0.124192\pi$
$164$	−5.00197			−0.390588
$165$	4.39308	−	12.9988i	0.342001	−	1.01195i
$166$	5.56354	+	3.21211i	0.431815	+	0.249308i
$167$	0.0648198	+	0.0173684i	0.00501591	+	0.00134401i	0.261326	−	0.965251i	$-0.415840\pi$
$167$	0.0648198	+	0.0173684i	0.00501591	+	0.00134401i	−0.256310	+	0.966595i	$0.582507\pi$
$168$	0.708662	+	2.64476i	0.0546744	+	0.204048i
$169$	−24.4720	−	14.1289i	−1.88246	−	1.08684i
$170$	−8.24400	−	0.529254i	−0.632286	−	0.0405919i
$171$	−4.18361	−	1.22370i	−0.319928	−	0.0935784i
$172$	−4.01362	−	4.01362i	−0.306036	−	0.306036i
$173$	−5.41422	+	1.45073i	−0.411635	+	0.110297i	−0.458693	−	0.888595i	$-0.651682\pi$
$173$	−5.41422	+	1.45073i	−0.411635	+	0.110297i	0.0470577	+	0.998892i	$0.485016\pi$
$174$	3.45840	−	5.99013i	0.262181	−	0.454111i
$175$	5.20516	−	12.6622i	0.393473	−	0.957170i
$176$	−3.06812	+	5.31414i	−0.231268	+	0.400568i
$177$	0.460909	−	1.72014i	0.0346441	−	0.129293i
$178$	−5.31271	+	5.31271i	−0.398204	+	0.398204i
$179$	12.1046			0.904738			0.452369	−	0.891831i	$-0.350579\pi$
$179$	12.1046			0.904738			0.452369	+	0.891831i	$0.350579\pi$
$180$	−0.991672	−	2.00414i	−0.0739149	−	0.149380i
$181$	−18.8419	+	10.8784i	−1.40050	+	0.808582i	−0.994444	−	0.105265i	$-0.966431\pi$
$181$	−18.8419	+	10.8784i	−1.40050	+	0.808582i	−0.406060	+	0.913846i	$0.633098\pi$
$182$	12.4360	+	12.4360i	0.921818	+	0.921818i
$183$	8.46381	+	8.46381i	0.625663	+	0.625663i
$184$	−0.121205	−	0.209934i	−0.00893538	−	0.0154765i
$185$	4.64963	+	23.2128i	0.341848	+	1.70664i
$186$	6.33251	−	3.65608i	0.464322	−	0.268077i
$187$	21.8974	−	5.86739i	1.60130	−	0.429066i
$188$	2.04807	+	7.64349i	0.149371	+	0.557459i
$189$	2.73806			0.199164
$190$	−4.12266	−	8.83197i	−0.299089	−	0.640738i
$191$	3.65250			0.264286			0.132143	−	0.991231i	$-0.457814\pi$
$191$	3.65250			0.264286			0.132143	+	0.991231i	$0.457814\pi$
$192$	0.258819	+	0.965926i	0.0186787	+	0.0697097i
$193$	16.1558	−	4.32893i	1.16292	−	0.311603i	0.374788	−	0.927111i	$-0.377716\pi$
$193$	16.1558	−	4.32893i	1.16292	−	0.311603i	0.788131	+	0.615507i	$0.211049\pi$
$194$	2.14448	−	1.23811i	0.153964	−	0.0888914i
$195$	−11.9529	−	7.96352i	−0.855963	−	0.570280i
$196$	−0.248484	−	0.430387i	−0.0177489	−	0.0307419i
$197$	−3.51981	−	3.51981i	−0.250776	−	0.250776i	0.570513	−	0.821289i	$-0.306744\pi$
$197$	−3.51981	−	3.51981i	−0.250776	−	0.250776i	−0.821289	+	0.570513i	$0.806744\pi$
$198$	4.33898	+	4.33898i	0.308358	+	0.308358i
$199$	9.80328	−	5.65993i	0.694936	−	0.401222i	−0.110522	−	0.993874i	$-0.535252\pi$
$199$	9.80328	−	5.65993i	0.694936	−	0.401222i	0.805459	+	0.592652i	$0.201919\pi$
$200$	1.90104	−	4.62451i	0.134424	−	0.327002i
$201$	7.59141			0.535457
$202$	8.31135	−	8.31135i	0.584785	−	0.584785i
$203$	−4.90168	+	18.2933i	−0.344030	+	1.28394i
$204$	1.84721	−	3.19946i	0.129331	−	0.224007i
$205$	−10.0247	+	4.96031i	−0.700152	+	0.346443i
$206$	−0.587196	+	1.01705i	−0.0409119	+	0.0708615i
$207$	−0.234151	+	0.0627405i	−0.0162746	+	0.00436077i
$208$	4.54190	+	4.54190i	0.314924	+	0.314924i
$209$	18.4778	+	19.3387i	1.27814	+	1.33769i
$210$	4.04300	+	4.59772i	0.278993	+	0.317273i
$211$	0.110519	+	0.0638079i	0.00760841	+	0.00439272i	0.503799	−	0.863821i	$-0.331935\pi$
$211$	0.110519	+	0.0638079i	0.00760841	+	0.00439272i	−0.496191	+	0.868213i	$0.665268\pi$
$212$	0.398130	+	1.48584i	0.0273437	+	0.102048i
$213$	−2.89930	−	0.776864i	−0.198657	−	0.0532299i
$214$	−0.574178	−	0.331502i	−0.0392500	−	0.0226610i
$215$	−12.0241	−	4.06367i	−0.820034	−	0.277140i
$216$	1.00000			0.0680414
$217$	−14.1571	+	14.1571i	−0.961044	+	0.961044i
$218$	15.8845	+	4.25623i	1.07583	+	0.288268i
$219$	0.827634	+	1.43350i	0.0559263	+	0.0968673i
$220$	−0.879064	+	13.6929i	−0.0592665	+	0.923173i
$221$		−	23.7301i		−	1.59626i
$222$	−10.2265	−	2.74019i	−0.686359	−	0.183909i
$223$	−3.29986	+	0.884194i	−0.220975	+	0.0592100i	−0.367608	−	0.929981i	$-0.619823\pi$
$223$	−3.29986	+	0.884194i	−0.220975	+	0.0592100i	0.146633	+	0.989191i	$0.453156\pi$
$224$	−1.36903	−	2.37123i	−0.0914721	−	0.158434i
$225$	−3.97490	−	3.03317i	−0.264994	−	0.202211i
$226$	−0.717883	+	1.24341i	−0.0477529	+	0.0827104i
$227$	6.42221	−	6.42221i	0.426257	−	0.426257i	−0.461094	−	0.887351i	$-0.652543\pi$
$227$	6.42221	−	6.42221i	0.426257	−	0.426257i	0.887351	+	0.461094i	$0.152543\pi$
$228$	4.35777	+	0.0992023i	0.288600	+	0.00656983i
$229$			14.7195i			0.972695i	0.873766	+	0.486347i	$0.161671\pi$
$229$			14.7195i			0.972695i	−0.873766	+	0.486347i	$0.838329\pi$
$230$	−0.451098	−	0.300541i	−0.0297445	−	0.0198171i
$231$	−14.5504	−	8.40069i	−0.957348	−	0.552725i
$232$	−1.79020	+	6.68112i	−0.117532	+	0.438637i
$233$	1.36300	+	5.08680i	0.0892933	+	0.333247i	0.996093	−	0.0883155i	$-0.0281484\pi$
$233$	1.36300	+	5.08680i	0.0892933	+	0.333247i	−0.906799	+	0.421563i	$0.861482\pi$
$234$	5.56267	−	3.21161i	0.363643	−	0.209950i
$235$	11.6844	+	13.2876i	0.762209	+	0.866789i
$236$			1.78082i			0.115921i
$237$	1.06690	−	3.98174i	0.0693029	−	0.258642i
$238$	−2.61809	+	9.77086i	−0.169706	+	0.633351i
$239$		−	7.02273i		−	0.454263i	−0.973864	−	0.227131i	$-0.927065\pi$
$239$		−	7.02273i		−	0.454263i	0.973864	−	0.227131i	$-0.0729347\pi$
$240$	1.47659	+	1.67919i	0.0953136	+	0.108391i
$241$	−11.1471	+	6.43580i	−0.718050	+	0.414567i	−0.814035	−	0.580816i	$-0.802733\pi$
$241$	−11.1471	+	6.43580i	−0.718050	+	0.414567i	0.0959843	+	0.995383i	$0.469400\pi$
$242$	−6.89842	−	25.7453i	−0.443447	−	1.65497i
$243$	0.258819	−	0.965926i	0.0166032	−	0.0619642i
$244$	−10.3660	−	5.98482i	−0.663616	−	0.383139i
$245$	−0.924800	−	0.616142i	−0.0590833	−	0.0393639i
$246$		−	5.00197i		−	0.318914i
$247$	24.5594	−	13.4436i	1.56268	−	0.855398i
$248$	−5.17047	+	5.17047i	−0.328325	+	0.328325i
$249$	−3.21211	+	5.56354i	−0.203559	+	0.352575i
$250$	−0.776042	−	11.1534i	−0.0490812	−	0.705401i
$251$	6.45268	+	11.1764i	0.407289	+	0.705446i	0.994585	−	0.103927i	$-0.0331407\pi$
$251$	6.45268	+	11.1764i	0.407289	+	0.705446i	−0.587296	+	0.809373i	$0.699807\pi$
$252$	−2.64476	+	0.708662i	−0.166604	+	0.0446415i
$253$	1.43681	+	0.384991i	0.0903312	+	0.0242042i
$254$			15.1217i			0.948820i
$255$	0.529254	−	8.24400i	0.0331432	−	0.516259i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	13.2438	+	3.54866i	0.826125	+	0.221360i	0.647022	−	0.762471i	$-0.276014\pi$
$257$	13.2438	+	3.54866i	0.826125	+	0.221360i	0.179102	+	0.983830i	$0.442681\pi$
$258$	4.01362	−	4.01362i	0.249877	−	0.249877i
$259$	28.9886			1.80126
$260$	13.6067	+	4.59854i	0.843852	+	0.285189i
$261$	5.99013	+	3.45840i	0.370780	+	0.214070i
$262$	17.0215	+	4.56090i	1.05159	+	0.281773i
$263$	1.89551	+	7.07416i	0.116882	+	0.436211i	0.999421	−	0.0340292i	$-0.0108339\pi$
$263$	1.89551	+	7.07416i	0.116882	+	0.436211i	−0.882538	+	0.470240i	$0.844167\pi$
$264$	−5.31414	−	3.06812i	−0.327063	−	0.188830i
$265$	2.27138	+	2.58302i	0.139529	+	0.158674i
$266$	−11.5956	+	2.82582i	−0.710970	+	0.173262i
$267$	−5.31271	−	5.31271i	−0.325132	−	0.325132i
$268$	−7.33274	+	1.96480i	−0.447918	+	0.120019i
$269$	−11.5461	+	19.9985i	−0.703979	+	1.21933i	0.263080	+	0.964774i	$0.415262\pi$
$269$	−11.5461	+	19.9985i	−0.703979	+	1.21933i	−0.967059	+	0.254553i	$0.918072\pi$
$270$	2.00414	−	0.991672i	0.121968	−	0.0603513i
$271$	−4.81169	+	8.33409i	−0.292289	+	0.506260i	−0.974351	−	0.225035i	$-0.927750\pi$
$271$	−4.81169	+	8.33409i	−0.292289	+	0.506260i	0.682061	+	0.731295i	$0.261084\pi$
$272$	−0.956186	+	3.56853i	−0.0579773	+	0.216374i
$273$	−12.4360	+	12.4360i	−0.752661	+	0.752661i
$274$	0.107904			0.00651872
$275$	11.8171	+	28.3142i	0.712596	+	1.70741i
$276$	0.209934	−	0.121205i	0.0126365	−	0.00729570i
$277$	11.1301	+	11.1301i	0.668743	+	0.668743i	0.957425	−	0.288682i	$-0.0932171\pi$
$277$	11.1301	+	11.1301i	0.668743	+	0.668743i	−0.288682	+	0.957425i	$0.593217\pi$
$278$	−5.93245	−	5.93245i	−0.355805	−	0.355805i
$279$	3.65608	+	6.33251i	0.218884	+	0.379117i
$280$	−5.09521	−	3.39465i	−0.304497	−	0.202869i
$281$	1.68319	−	0.971790i	0.100411	−	0.0579721i	−0.448954	−	0.893555i	$-0.648203\pi$
$281$	1.68319	−	0.971790i	0.100411	−	0.0579721i	0.549364	+	0.835583i	$0.314870\pi$
$282$	−7.64349	+	2.04807i	−0.455163	+	0.121961i
$283$	1.12636	+	4.20362i	0.0669549	+	0.249879i	0.991289	−	0.131705i	$-0.0420453\pi$
$283$	1.12636	+	4.20362i	0.0669549	+	0.249879i	−0.924334	+	0.381584i	$0.875379\pi$
$284$	3.00157			0.178111
$285$	8.83197	−	4.12266i	0.523161	−	0.244206i
$286$	−39.4144			−2.33062
$287$	3.54470	+	13.2290i	0.209237	+	0.780884i
$288$	−0.965926	+	0.258819i	−0.0569177	+	0.0152511i
$289$	−2.90229	+	1.67564i	−0.170723	+	0.0985669i
$290$	3.03766	+	15.1652i	0.178378	+	0.890532i
$291$	1.23811	+	2.14448i	0.0725795	+	0.125711i
$292$	−1.17045	−	1.17045i	−0.0684955	−	0.0684955i
$293$	3.20703	+	3.20703i	0.187357	+	0.187357i	0.794552	−	0.607196i	$-0.207706\pi$
$293$	3.20703	+	3.20703i	0.187357	+	0.187357i	−0.607196	+	0.794552i	$0.707706\pi$
$294$	0.430387	−	0.248484i	0.0251007	−	0.0144919i
$295$	1.76599	+	3.56901i	0.102820	+	0.207796i
$296$	10.5873			0.615373
$297$	−4.33898	+	4.33898i	−0.251773	+	0.251773i
$298$	0.809620	−	3.02154i	0.0469000	−	0.175033i
$299$	0.778529	−	1.34845i	0.0450235	−	0.0779830i
$300$	4.62451	+	1.90104i	0.266996	+	0.109757i
$301$	−7.77077	+	13.4594i	−0.447900	+	0.775785i
$302$	−11.0248	+	2.95410i	−0.634408	+	0.169989i
$303$	8.31135	+	8.31135i	0.477475	+	0.477475i
$304$	−4.23496	+	1.03205i	−0.242891	+	0.0591922i
$305$	−26.7099	−	1.71474i	−1.52941	−	0.0981859i
$306$	3.19946	+	1.84721i	0.182901	+	0.105598i
$307$	−8.98929	−	33.5485i	−0.513046	−	1.91471i	−0.384899	−	0.922959i	$-0.625764\pi$
$307$	−8.98929	−	33.5485i	−0.513046	−	1.91471i	−0.128147	−	0.991755i	$-0.540903\pi$
$308$	16.2289	+	4.34852i	0.924727	+	0.247780i
$309$	−1.01705	−	0.587196i	−0.0578582	−	0.0334044i
$310$	−5.23495	+	15.4898i	−0.297325	+	0.879760i
$311$	27.5134			1.56014			0.780070	−	0.625692i	$-0.215183\pi$
$311$	27.5134			1.56014			0.780070	+	0.625692i	$0.215183\pi$
$312$	−4.54190	+	4.54190i	−0.257135	+	0.257135i
$313$	−8.78727	−	2.35454i	−0.496686	−	0.133087i	0.00177559	−	0.999998i	$-0.499435\pi$
$313$	−8.78727	−	2.35454i	−0.496686	−	0.133087i	−0.498462	+	0.866912i	$0.666101\pi$
$314$	10.6906	+	18.5167i	0.603308	+	1.04496i
$315$	−4.59772	+	4.04300i	−0.259052	+	0.227797i
$316$			4.12220i			0.231892i
$317$	23.2766	+	6.23695i	1.30734	+	0.350302i	0.844223	−	0.535993i	$-0.180063\pi$
$317$	23.2766	+	6.23695i	1.30734	+	0.350302i	0.463122	+	0.886295i	$0.346729\pi$
$318$	−1.48584	+	0.398130i	−0.0833218	+	0.0223260i
$319$	−21.2216	−	36.7569i	−1.18818	−	2.05799i
$320$	−1.86088	−	1.23980i	−0.104027	−	0.0693070i
$321$	0.331502	−	0.574178i	0.0185026	−	0.0320475i
$322$	−0.469331	+	0.469331i	−0.0261548	+	0.0261548i
$323$	13.7593	+	8.36711i	0.765586	+	0.465558i
$324$			1.00000i			0.0555556i
$325$	31.8300	−	4.27726i	1.76561	−	0.237260i
$326$	−20.4085	−	11.7829i	−1.13032	−	0.652592i
$327$	−4.25623	+	15.8845i	−0.235370	+	0.878413i
$328$	1.29460	+	4.83153i	0.0714826	+	0.266777i
$329$	18.7638	−	10.8333i	1.03448	−	0.597259i
$330$	−13.6929	−	0.879064i	−0.753767	−	0.0483909i
$331$			7.35497i			0.404266i	0.979358	+	0.202133i	$0.0647873\pi$
$331$			7.35497i			0.404266i	−0.979358	+	0.202133i	$0.935213\pi$
$332$	1.66271	−	6.20532i	0.0912531	−	0.340561i
$333$	2.74019	−	10.2265i	0.150161	−	0.560410i
$334$		−	0.0671064i		−	0.00367190i
$335$	−12.7474	+	11.2094i	−0.696466	+	0.612436i
$336$	2.37123	−	1.36903i	0.129361	−	0.0746867i
$337$	1.29954	+	4.84996i	0.0707906	+	0.264194i	0.992246	−	0.124290i	$-0.0396654\pi$
$337$	1.29954	+	4.84996i	0.0707906	+	0.264194i	−0.921455	+	0.388484i	$0.872999\pi$
$338$	−7.31365	+	27.2949i	−0.397810	+	1.48465i
$339$	−1.24341	−	0.717883i	−0.0675328	−	0.0389901i
$340$	1.62248	+	8.10007i	0.0879915	+	0.439288i
$341$		−	44.8691i		−	2.42980i
$342$	−0.0992023	+	4.35777i	−0.00536424	+	0.235641i
$343$	12.5905	−	12.5905i	0.679824	−	0.679824i
$344$	−2.83806	+	4.91566i	−0.153018	+	0.265035i
$345$	0.300541	−	0.451098i	0.0161806	−	0.0242863i
$346$	2.80260	+	4.85425i	0.150669	+	0.260966i
$347$	7.55426	−	2.02416i	0.405534	−	0.108662i	−0.0502853	−	0.998735i	$-0.516013\pi$
$347$	7.55426	−	2.02416i	0.405534	−	0.108662i	0.455819	+	0.890072i	$0.349346\pi$
$348$	−6.68112	−	1.79020i	−0.358146	−	0.0959648i
$349$		−	12.4726i		−	0.667642i	−0.942636	−	0.333821i	$-0.891662\pi$
$349$		−	12.4726i		−	0.667642i	0.942636	−	0.333821i	$-0.108338\pi$
$350$	−13.5779	−	1.75058i	−0.725770	−	0.0935726i
$351$	3.21161	+	5.56267i	0.171423	+	0.296914i
$352$	5.92715	+	1.58818i	0.315918	+	0.0846501i
$353$	−2.83675	+	2.83675i	−0.150985	+	0.150985i	−0.778558	−	0.627573i	$-0.784048\pi$
$353$	−2.83675	+	2.83675i	−0.150985	+	0.150985i	0.627573	+	0.778558i	$0.284048\pi$
$354$	−1.78082			−0.0946493
$355$	6.01558	−	2.97658i	0.319274	−	0.157980i
$356$	6.50671	+	3.75665i	0.344855	+	0.199102i
$357$	−9.77086	−	2.61809i	−0.517129	−	0.138564i
$358$	−3.13289	−	11.6921i	−0.165579	−	0.617948i
$359$	30.5322	+	17.6278i	1.61143	+	0.930359i	0.989040	+	0.147651i	$0.0471711\pi$
$359$	30.5322	+	17.6278i	1.61143	+	0.930359i	0.622389	+	0.782708i	$0.286162\pi$
$360$	−1.67919	+	1.47659i	−0.0885010	+	0.0778232i
$361$	−0.864601	+	18.9803i	−0.0455053	+	0.998964i
$362$	15.3843	+	15.3843i	0.808582	+	0.808582i
$363$	25.7453	−	6.89842i	1.35128	−	0.362073i
$364$	8.79358	−	15.2309i	0.460909	−	0.798318i
$365$	−3.50646	−	1.18505i	−0.183536	−	0.0620282i
$366$	5.98482	−	10.3660i	0.312831	−	0.541840i
$367$	5.83611	−	21.7806i	0.304642	−	1.13694i	−0.628611	−	0.777720i	$-0.716376\pi$
$367$	5.83611	−	21.7806i	0.304642	−	1.13694i	0.933253	−	0.359220i	$-0.116957\pi$
$368$	−0.171410	+	0.171410i	−0.00893538	+	0.00893538i
$369$	5.00197			0.260392
$370$	21.2184	−	10.4991i	1.10309	−	0.545823i
$371$	3.64756	−	2.10592i	0.189372	−	0.109334i
$372$	−5.17047	−	5.17047i	−0.268077	−	0.268077i
$373$	−13.5296	−	13.5296i	−0.700538	−	0.700538i	0.263988	−	0.964526i	$-0.414962\pi$
$373$	−13.5296	−	13.5296i	−0.700538	−	0.700538i	−0.964526	+	0.263988i	$0.914962\pi$
$374$	−11.3349	−	19.6327i	−0.586115	−	1.01518i
$375$	11.1534	−	0.776042i	0.575958	−	0.0400747i
$376$	6.85296	−	3.95656i	0.353415	−	0.204044i
$377$	−42.9143	+	11.4989i	−2.21020	+	0.592221i
$378$	−0.708662	−	2.64476i	−0.0364496	−	0.136032i
$379$	8.28035			0.425333			0.212666	−	0.977125i	$-0.431785\pi$
$379$	8.28035			0.425333			0.212666	+	0.977125i	$0.431785\pi$
$380$	−7.46400	+	6.26807i	−0.382895	+	0.321545i
$381$	−15.1217			−0.774708
$382$	−0.945337	−	3.52805i	−0.0483677	−	0.180511i
$383$	−31.4763	+	8.43405i	−1.60836	+	0.430960i	−0.947555	−	0.319594i	$-0.896454\pi$
$383$	−31.4763	+	8.43405i	−1.60836	+	0.430960i	−0.660809	+	0.750554i	$0.729787\pi$
$384$	0.866025	−	0.500000i	0.0441942	−	0.0255155i
$385$	36.8373	−	7.37869i	1.87740	−	0.376053i
$386$	−8.36285	−	14.4849i	−0.425658	−	0.737261i
$387$	4.01362	+	4.01362i	0.204024	+	0.204024i
$388$	−1.75096	−	1.75096i	−0.0888914	−	0.0888914i
$389$	−16.8053	+	9.70253i	−0.852061	+	0.491938i	−0.861346	−	0.508019i	$-0.830378\pi$
$389$	−16.8053	+	9.70253i	−0.852061	+	0.491938i	0.00928483	+	0.999957i	$0.497045\pi$
$390$	−4.59854	+	13.6067i	−0.232856	+	0.689002i
$391$	0.895566			0.0452907
$392$	−0.351409	+	0.351409i	−0.0177489	+	0.0177489i
$393$	−4.56090	+	17.0215i	−0.230067	+	0.858621i
$394$	−2.48888	+	4.31087i	−0.125388	+	0.217178i
$395$	4.08787	+	8.26148i	0.205683	+	0.415680i
$396$	3.06812	−	5.31414i	0.154179	−	0.267046i
$397$	12.5790	−	3.37053i	0.631322	−	0.169162i	0.0710522	−	0.997473i	$-0.477364\pi$
$397$	12.5790	−	3.37053i	0.631322	−	0.169162i	0.560269	+	0.828310i	$0.310698\pi$
$398$	−8.00434	−	8.00434i	−0.401222	−	0.401222i
$399$	−2.82582	−	11.5956i	−0.141468	−	0.580504i
$400$	−4.95895	−	0.639352i	−0.247948	−	0.0319676i
$401$	−7.54284	−	4.35486i	−0.376672	−	0.217471i	0.299698	−	0.954034i	$-0.403114\pi$
$401$	−7.54284	−	4.35486i	−0.376672	−	0.217471i	−0.676369	+	0.736563i	$0.736448\pi$
$402$	−1.96480	−	7.33274i	−0.0979954	−	0.365724i
$403$	−45.3672	−	12.1561i	−2.25990	−	0.605539i
$404$	−10.1793	−	5.87701i	−0.506438	−	0.292392i
$405$	0.991672	+	2.00414i	0.0492766	+	0.0995866i
$406$	18.9386			0.939908
$407$	−45.9380	+	45.9380i	−2.27706	+	2.27706i
$408$	−3.56853	−	0.956186i	−0.176669	−	0.0473382i
$409$	8.44755	+	14.6316i	0.417704	+	0.723485i	0.995708	−	0.0925488i	$-0.0295014\pi$
$409$	8.44755	+	14.6316i	0.417704	+	0.723485i	−0.578004	+	0.816034i	$0.696168\pi$
$410$	7.38586	+	8.39925i	0.364762	+	0.414809i
$411$			0.107904i			0.00532251i
$412$	1.13438	+	0.303955i	0.0558867	+	0.0149748i
$413$	4.70984	−	1.26200i	0.231756	−	0.0620988i
$414$	0.121205	+	0.209934i	0.00595692	+	0.0103177i
$415$	−2.82134	−	14.0852i	−0.138494	−	0.691416i
$416$	3.21161	−	5.56267i	0.157462	−	0.272732i
$417$	5.93245	−	5.93245i	0.290514	−	0.290514i
$418$	13.8973	−	22.8534i	0.679741	−	1.11780i
$419$		−	0.522609i		−	0.0255311i	−0.999919	−	0.0127656i	$-0.995936\pi$
$419$		−	0.522609i		−	0.0255311i	0.999919	−	0.0127656i	$-0.00406351\pi$
$420$	3.39465	−	5.09521i	0.165642	−	0.248621i
$421$	−9.12036	−	5.26564i	−0.444499	−	0.256632i	0.261005	−	0.965337i	$-0.415946\pi$
$421$	−9.12036	−	5.26564i	−0.444499	−	0.256632i	−0.705504	+	0.708706i	$0.749279\pi$
$422$	0.0330294	−	0.123267i	0.00160785	−	0.00600057i
$423$	−2.04807	−	7.64349i	−0.0995804	−	0.371639i
$424$	1.33217	−	0.769128i	0.0646958	−	0.0373521i
$425$	11.2843	+	14.6247i	0.547369	+	0.709403i
$426$			3.00157i			0.145427i
$427$	−8.48242	+	31.6568i	−0.410493	+	1.53198i
$428$	−0.171598	+	0.640412i	−0.00829450	+	0.0309555i
$429$		−	39.4144i		−	1.90295i
$430$	−0.813147	+	12.6661i	−0.0392134	+	0.610814i
$431$	3.89690	−	2.24988i	0.187707	−	0.108373i	−0.403202	−	0.915111i	$-0.632103\pi$
$431$	3.89690	−	2.24988i	0.187707	−	0.108373i	0.590909	+	0.806738i	$0.298769\pi$
$432$	−0.258819	−	0.965926i	−0.0124524	−	0.0464731i
$433$	−3.24440	+	12.1082i	−0.155916	+	0.581885i	0.843110	+	0.537742i	$0.180723\pi$
$433$	−3.24440	+	12.1082i	−0.155916	+	0.581885i	−0.999025	+	0.0441434i	$0.985944\pi$
$434$	17.3388	+	10.0106i	0.832288	+	0.480522i
$435$	−15.1652	+	3.03766i	−0.727116	+	0.145645i
$436$		−	16.4448i		−	0.787563i
$437$	0.507359	+	0.926867i	0.0242703	+	0.0443381i
$438$	1.17045	−	1.17045i	0.0559263	−	0.0559263i
$439$	−12.7640	+	22.1079i	−0.609193	+	1.05515i	0.382181	+	0.924088i	$0.375173\pi$
$439$	−12.7640	+	22.1079i	−0.609193	+	1.05515i	−0.991374	+	0.131065i	$0.958160\pi$
$440$	13.4538	−	2.69486i	0.641385	−	0.128473i
$441$	0.248484	+	0.430387i	0.0118326	+	0.0204946i
$442$	−22.9215	+	6.14179i	−1.09026	+	0.292135i
$443$	−21.5720	−	5.78021i	−1.02492	−	0.274626i	−0.293068	−	0.956092i	$-0.594676\pi$
$443$	−21.5720	−	5.78021i	−1.02492	−	0.274626i	−0.731850	+	0.681466i	$0.761343\pi$
$444$			10.5873i			0.502450i
$445$	16.7657	+	1.07634i	0.794772	+	0.0510234i
$446$	1.70813	+	2.95857i	0.0808824	+	0.140092i
$447$	3.02154	+	0.809620i	0.142914	+	0.0382937i
$448$	−1.93610	+	1.93610i	−0.0914721	+	0.0914721i
$449$	27.2350			1.28530			0.642648	−	0.766161i	$-0.277836\pi$
$449$	27.2350			1.28530			0.642648	+	0.766161i	$0.277836\pi$
$450$	−1.90104	+	4.62451i	−0.0896158	+	0.218001i
$451$	−26.5812	−	15.3466i	−1.25166	−	0.722645i
$452$	1.38684	+	0.371604i	0.0652316	+	0.0174788i
$453$	−2.95410	−	11.0248i	−0.138795	−	0.517992i
$454$	−7.86557	−	4.54119i	−0.369150	−	0.213129i
$455$	2.51950	−	39.2453i	0.118116	−	1.83985i
$456$	−1.03205	−	4.23496i	−0.0483303	−	0.198320i
$457$	−12.8404	−	12.8404i	−0.600648	−	0.600648i	0.339837	−	0.940484i	$-0.389628\pi$
$457$	−12.8404	−	12.8404i	−0.600648	−	0.600648i	−0.940484	+	0.339837i	$0.889628\pi$
$458$	14.2180	−	3.80970i	0.664363	−	0.178015i
$459$	−1.84721	+	3.19946i	−0.0862203	+	0.149338i
$460$	−0.173548	+	0.513513i	−0.00809170	+	0.0239427i
$461$	19.0985	−	33.0796i	0.889507	−	1.54067i	0.0490476	−	0.998796i	$-0.484381\pi$
$461$	19.0985	−	33.0796i	0.889507	−	1.54067i	0.840459	−	0.541875i	$-0.182285\pi$
$462$	−4.34852	+	16.2289i	−0.202311	+	0.755037i
$463$	9.17369	−	9.17369i	0.426338	−	0.426338i	−0.461041	−	0.887379i	$-0.652524\pi$
$463$	9.17369	−	9.17369i	0.426338	−	0.426338i	0.887379	+	0.461041i	$0.152524\pi$
$464$	6.91681			0.321105
$465$	−15.4898	−	5.23495i	−0.718321	−	0.242765i
$466$	4.56070	−	2.63312i	0.211270	−	0.121977i
$467$	−4.93046	−	4.93046i	−0.228154	−	0.228154i	0.583767	−	0.811921i	$-0.301578\pi$
$467$	−4.93046	−	4.93046i	−0.228154	−	0.228154i	−0.811921	+	0.583767i	$0.801578\pi$
$468$	−4.54190	−	4.54190i	−0.209950	−	0.209950i
$469$	10.3929	+	18.0010i	0.479898	+	0.831208i
$470$	9.81070	−	14.7254i	0.452534	−	0.679232i
$471$	−18.5167	+	10.6906i	−0.853206	+	0.492599i
$472$	1.72014	−	0.460909i	0.0791757	−	0.0212151i
$473$	−9.01467	−	33.6432i	−0.414495	−	1.54692i
$474$	−4.12220			−0.189339
$475$	−8.74305	+	19.9639i	−0.401159	+	0.916009i
$476$	10.1155			0.463645
$477$	−0.398130	−	1.48584i	−0.0182291	−	0.0680320i
$478$	−6.78344	+	1.81762i	−0.310267	+	0.0831358i
$479$	15.7607	−	9.09946i	0.720126	−	0.415765i	−0.0946732	−	0.995508i	$-0.530181\pi$
$479$	15.7607	−	9.09946i	0.720126	−	0.415765i	0.814799	+	0.579744i	$0.196847\pi$
$480$	1.23980	−	1.86088i	0.0565890	−	0.0849374i
$481$	34.0022	+	58.8936i	1.55037	+	2.68532i
$482$	9.10160	+	9.10160i	0.414567	+	0.414567i
$483$	−0.469331	−	0.469331i	−0.0213553	−	0.0213553i
$484$	−23.0826	+	13.3267i	−1.04921	+	0.605760i
$485$	−5.24554	−	1.77279i	−0.238188	−	0.0804983i
$486$	−1.00000			−0.0453609
$487$	7.53058	−	7.53058i	0.341243	−	0.341243i	−0.515591	−	0.856835i	$-0.672428\pi$
$487$	7.53058	−	7.53058i	0.341243	−	0.341243i	0.856835	+	0.515591i	$0.172428\pi$
$488$	−3.09797	+	11.5618i	−0.140238	+	0.523377i
$489$	11.7829	−	20.4085i	0.532839	−	0.922905i
$490$	−0.355791	+	1.05276i	−0.0160730	+	0.0475587i
$491$	−15.7093	+	27.2092i	−0.708949	+	1.22793i	0.256299	+	0.966598i	$0.417497\pi$
$491$	−15.7093	+	27.2092i	−0.708949	+	1.22793i	−0.965248	+	0.261337i	$0.915836\pi$
$492$	−4.83153	+	1.29460i	−0.217822	+	0.0583653i
$493$	−18.0691	−	18.0691i	−0.813792	−	0.813792i
$494$	−19.3420	−	20.2431i	−0.870238	−	0.910782i
$495$	0.879064	−	13.6929i	0.0395110	−	0.615448i
$496$	6.33251	+	3.65608i	0.284338	+	0.164163i
$497$	−2.12710	−	7.93845i	−0.0954135	−	0.356088i
$498$	6.20532	+	1.66271i	0.278067	+	0.0745079i
$499$	−9.26891	−	5.35141i	−0.414933	−	0.239562i	0.277974	−	0.960589i	$-0.410337\pi$
$499$	−9.26891	−	5.35141i	−0.414933	−	0.239562i	−0.692907	+	0.721027i	$0.743670\pi$
$500$	−10.5725	+	3.63631i	−0.472816	+	0.162621i
$501$	0.0671064			0.00299809
$502$	9.12546	−	9.12546i	0.407289	−	0.407289i
$503$	19.5676	+	5.24313i	0.872477	+	0.233780i	0.667159	−	0.744916i	$-0.267510\pi$
$503$	19.5676	+	5.24313i	0.872477	+	0.233780i	0.205319	+	0.978695i	$0.434177\pi$
$504$	1.36903	+	2.37123i	0.0609814	+	0.105623i
$505$	−26.2288	−	1.68386i	−1.16717	−	0.0749306i
$506$		−	1.48749i		−	0.0661270i
$507$	−27.2949	−	7.31365i	−1.21221	−	0.324811i
$508$	14.6064	−	3.91378i	0.648056	−	0.173646i
$509$	−6.64123	−	11.5029i	−0.294367	−	0.509859i	0.680470	−	0.732776i	$-0.261776\pi$
$509$	−6.64123	−	11.5029i	−0.294367	−	0.509859i	−0.974837	+	0.222917i	$0.928442\pi$
$510$	−8.10007	+	1.62248i	−0.358677	+	0.0718448i
$511$	−2.26611	+	3.92502i	−0.100247	+	0.173633i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−4.35777	−	0.0992023i	−0.192400	−	0.00437989i
$514$		−	13.7110i		−	0.604765i
$515$	2.57487	−	0.515760i	0.113463	−	0.0227271i
$516$	−4.91566	−	2.83806i	−0.216400	−	0.124938i
$517$	−12.5674	+	46.9023i	−0.552715	+	2.06276i
$518$	−7.50280	−	28.0008i	−0.329654	−	1.23029i
$519$	−4.85425	+	2.80260i	−0.213078	+	0.123021i
$520$	0.920176	−	14.3333i	0.0403524	−	0.628555i
$521$			36.3035i			1.59049i	0.606290	+	0.795244i	$0.292657\pi$
$521$			36.3035i			1.59049i	−0.606290	+	0.795244i	$0.707343\pi$
$522$	1.79020	−	6.68112i	0.0783550	−	0.292425i
$523$	8.24453	−	30.7690i	0.360508	−	1.34543i	−0.512901	−	0.858448i	$-0.671429\pi$
$523$	8.24453	−	30.7690i	0.360508	−	1.34543i	0.873409	−	0.486987i	$-0.161904\pi$
$524$		−	17.6220i		−	0.769819i
$525$	1.75058	−	13.5779i	0.0764017	−	0.592589i
$526$	6.34251	−	3.66185i	0.276547	−	0.159664i
$527$	−6.99178	−	26.0937i	−0.304567	−	1.13666i
$528$	−1.58818	+	5.92715i	−0.0691165	+	0.257946i
$529$	−19.8677	−	11.4706i	−0.863813	−	0.498723i
$530$	1.90713	−	2.86252i	0.0828405	−	0.124340i
$531$		−	1.78082i		−	0.0772809i
$532$	5.73068	+	10.4691i	0.248457	+	0.453892i
$533$	−22.7185	+	22.7185i	−0.984045	+	0.984045i
$534$	−3.75665	+	6.50671i	−0.162566	+	0.281573i
$535$	0.291172	+	1.45365i	0.0125885	+	0.0628466i
$536$	3.79571	+	6.57435i	0.163949	+	0.283969i
$537$	11.6921	−	3.13289i	0.504552	−	0.135194i
$538$	22.3054	+	5.97671i	0.961653	+	0.257674i
$539$		−	3.04952i		−	0.131352i
$540$	−1.47659	−	1.67919i	−0.0635424	−	0.0722608i
$541$	−12.6162	−	21.8519i	−0.542414	−	0.939488i	−0.998765	−	0.0496881i	$-0.984177\pi$
$541$	−12.6162	−	21.8519i	−0.542414	−	0.939488i	0.456351	−	0.889800i	$-0.349156\pi$
$542$	9.29547	+	2.49071i	0.399274	+	0.106985i
$543$	−15.3843	+	15.3843i	−0.660204	+	0.660204i
$544$	3.69442			0.158397
$545$	−16.3079	−	32.9577i	−0.698552	−	1.41175i
$546$	15.2309	+	8.79358i	0.651824	+	0.376331i
$547$	−19.2227	−	5.15070i	−0.821902	−	0.220228i	−0.176724	−	0.984260i	$-0.556550\pi$
$547$	−19.2227	−	5.15070i	−0.821902	−	0.220228i	−0.645178	+	0.764033i	$0.723217\pi$
$548$	−0.0279276	−	0.104227i	−0.00119301	−	0.00445237i
$549$	10.3660	+	5.98482i	0.442410	+	0.255426i
$550$	24.2909	−	18.7427i	1.03577	−	0.799190i
$551$	8.46407	−	28.9372i	0.360581	−	1.23277i
$552$	−0.171410	−	0.171410i	−0.00729570	−	0.00729570i
$553$	10.9022	−	2.92125i	0.463611	−	0.124224i
$554$	7.87017	−	13.6315i	0.334371	−	0.579148i
$555$	10.4991	+	21.2184i	0.445662	+	0.900671i
$556$	−4.19488	+	7.26574i	−0.177902	+	0.308136i
$557$	−1.40405	+	5.23999i	−0.0594916	+	0.222026i	−0.989271	−	0.146091i	$-0.953331\pi$
$557$	−1.40405	+	5.23999i	−0.0594916	+	0.222026i	0.929780	+	0.368117i	$0.119997\pi$
$558$	5.17047	−	5.17047i	0.218884	−	0.218884i
$559$	−36.4589			−1.54205
$560$	−1.96024	+	5.80020i	−0.0828354	+	0.245103i
$561$	19.6327	−	11.3349i	0.828891	−	0.478561i
$562$	−1.37432	−	1.37432i	−0.0579721	−	0.0579721i
$563$	−1.61575	−	1.61575i	−0.0680957	−	0.0680957i	0.672239	−	0.740334i	$-0.265333\pi$
$563$	−1.61575	−	1.61575i	−0.0680957	−	0.0680957i	−0.740334	+	0.672239i	$0.765333\pi$
$564$	3.95656	+	6.85296i	0.166601	+	0.288562i
$565$	3.14794	−	0.630548i	0.132435	−	0.0265274i
$566$	3.76886	−	2.17595i	0.158417	−	0.0914621i
$567$	2.64476	−	0.708662i	0.111070	−	0.0297610i
$568$	−0.776864	−	2.89930i	−0.0325965	−	0.121652i
$569$	39.9821			1.67614			0.838068	−	0.545565i	$-0.183685\pi$
$569$	39.9821			1.67614			0.838068	+	0.545565i	$0.183685\pi$
$570$	−6.26807	−	7.46400i	−0.262541	−	0.312633i
$571$	−4.25230			−0.177953			−0.0889765	−	0.996034i	$-0.528360\pi$
$571$	−4.25230			−0.177953			−0.0889765	+	0.996034i	$0.528360\pi$
$572$	10.2012	+	38.0714i	0.426534	+	1.59185i
$573$	3.52805	−	0.945337i	0.147386	−	0.0394920i
$574$	11.8608	−	6.84784i	0.495061	−	0.285823i
$575$	0.161423	+	1.20126i	0.00673179	+	0.0500958i
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$	19.2762	+	19.2762i	0.802481	+	0.802481i	0.983483	−	0.181002i	$-0.0579340\pi$
$577$	19.2762	+	19.2762i	0.802481	+	0.802481i	−0.181002	+	0.983483i	$0.557934\pi$
$578$	2.36971	+	2.36971i	0.0985669	+	0.0985669i
$579$	14.4849	−	8.36285i	0.601971	−	0.347548i
$580$	13.8623	−	6.85920i	0.575599	−	0.284813i
$581$	−17.5899			−0.729752
$582$	1.75096	−	1.75096i	0.0725795	−	0.0725795i
$583$	−2.44302	+	9.11747i	−0.101180	+	0.377607i
$584$	−0.827634	+	1.43350i	−0.0342477	+	0.0593188i
$585$	−13.6067	−	4.59854i	−0.562568	−	0.190126i
$586$	2.26771	−	3.92779i	0.0936783	−	0.162256i
$587$	−4.82045	+	1.29164i	−0.198961	+	0.0533115i	−0.356923	−	0.934134i	$-0.616174\pi$
$587$	−4.82045	+	1.29164i	−0.198961	+	0.0533115i	0.157962	+	0.987445i	$0.449508\pi$
$588$	−0.351409	−	0.351409i	−0.0144919	−	0.0144919i
$589$	23.0447	−	22.0188i	0.949538	−	0.907269i
$590$	2.99033	−	2.62954i	0.123110	−	0.108256i
$591$	−4.31087	−	2.48888i	−0.177325	−	0.102379i
$592$	−2.74019	−	10.2265i	−0.112621	−	0.420308i
$593$	17.7127	+	4.74611i	0.727375	+	0.194899i	0.603460	−	0.797393i	$-0.293788\pi$
$593$	17.7127	+	4.74611i	0.727375	+	0.194899i	0.123915	+	0.992293i	$0.460455\pi$
$594$	5.31414	+	3.06812i	0.218042	+	0.125887i
$595$	20.2730	−	10.0313i	0.831111	−	0.411243i
$596$	−3.12813			−0.128133
$597$	8.00434	−	8.00434i	0.327596	−	0.327596i
$598$	−1.50400	−	0.402996i	−0.0615032	−	0.0164797i
$599$	13.9449	+	24.1533i	0.569774	+	0.986878i	0.996588	+	0.0825384i	$0.0263027\pi$
$599$	13.9449	+	24.1533i	0.569774	+	0.986878i	−0.426814	+	0.904340i	$0.640364\pi$
$600$	0.639352	−	4.95895i	0.0261014	−	0.202448i
$601$		−	41.8538i		−	1.70725i	−0.520886	−	0.853626i	$-0.674398\pi$
$601$		−	41.8538i		−	1.70725i	0.520886	−	0.853626i	$-0.325602\pi$
$602$	15.0120	+	4.02245i	0.611842	+	0.163943i
$603$	7.33274	−	1.96480i	0.298612	−	0.0800129i
$604$	5.70687	+	9.88459i	0.232209	+	0.402198i
$605$	−33.0450	+	49.5990i	−1.34347	+	2.01649i
$606$	5.87701	−	10.1793i	0.238737	−	0.413505i
$607$	−2.94800	+	2.94800i	−0.119656	+	0.119656i	−0.764399	−	0.644743i	$-0.776964\pi$
$607$	−2.94800	+	2.94800i	−0.119656	+	0.119656i	0.644743	+	0.764399i	$0.276964\pi$
$608$	2.09297	+	3.82354i	0.0848813	+	0.155065i
$609$			18.9386i			0.767432i
$610$	5.25672	+	26.2436i	0.212839	+	1.06257i
$611$	44.0181	+	25.4139i	1.78078	+	1.02813i
$612$	0.956186	−	3.56853i	0.0386515	−	0.144249i
$613$	12.3603	+	46.1294i	0.499230	+	1.86315i	0.504919	+	0.863167i	$0.331522\pi$
$613$	12.3603	+	46.1294i	0.499230	+	1.86315i	−0.00568936	+	0.999984i	$0.501811\pi$
$614$	−30.0788	+	17.3660i	−1.21388	+	0.700834i
$615$	−8.39925	+	7.38586i	−0.338690	+	0.297827i
$616$		−	16.8014i		−	0.676947i
$617$	0.125072	−	0.466776i	0.00503522	−	0.0187917i	−0.963363	−	0.268203i	$-0.913570\pi$
$617$	0.125072	−	0.466776i	0.00503522	−	0.0187917i	0.968398	+	0.249411i	$0.0802370\pi$
$618$	−0.303955	+	1.13438i	−0.0122269	+	0.0456313i
$619$		−	2.80843i		−	0.112880i	−0.998406	−	0.0564402i	$-0.982025\pi$
$619$		−	2.80843i		−	0.112880i	0.998406	−	0.0564402i	$-0.0179750\pi$
$620$	16.3169	+	1.04752i	0.655302	+	0.0420695i
$621$	−0.209934	+	0.121205i	−0.00842435	+	0.00486380i
$622$	−7.12098	−	26.5759i	−0.285525	−	1.06560i
$623$	5.32439	−	19.8709i	0.213317	−	0.796111i
$624$	5.56267	+	3.21161i	0.222685	+	0.128567i
$625$	−17.5827	+	17.7721i	−0.703309	+	0.710884i
$626$			9.09725i			0.363599i
$627$	22.8534	+	13.8973i	0.912678	+	0.555006i
$628$	15.1188	−	15.1188i	0.603308	−	0.603308i
$629$	−19.5569	+	33.8736i	−0.779785	+	1.35063i
$630$	5.09521	+	3.39465i	0.202998	+	0.135246i
$631$	−11.5684	−	20.0371i	−0.460533	−	0.797666i	0.538455	−	0.842654i	$-0.319008\pi$
$631$	−11.5684	−	20.0371i	−0.460533	−	0.797666i	−0.998988	+	0.0449886i	$0.985675\pi$
$632$	3.98174	−	1.06690i	0.158385	−	0.0424392i
$633$	0.123267	+	0.0330294i	0.00489944	+	0.00131280i
$634$		−	24.0977i		−	0.957043i
$635$	25.3922	−	22.3286i	1.00766	−	0.886083i
$636$	0.769128	+	1.33217i	0.0304979	+	0.0528239i
$637$	−3.08337	−	0.826185i	−0.122167	−	0.0327347i
$638$	−30.0119	+	30.0119i	−1.18818	+	1.18818i
$639$	−3.00157			−0.118740
$640$	−0.715924	+	2.11836i	−0.0282994	+	0.0837356i
$641$	−7.18143	−	4.14620i	−0.283649	−	0.163765i	0.351425	−	0.936216i	$-0.385697\pi$
$641$	−7.18143	−	4.14620i	−0.283649	−	0.163765i	−0.635074	+	0.772451i	$0.719031\pi$
$642$	−0.640412	−	0.171598i	−0.0252751	−	0.00677243i
$643$	7.40862	+	27.6493i	0.292167	+	1.09038i	0.943441	+	0.331541i	$0.107568\pi$
$643$	7.40862	+	27.6493i	0.292167	+	1.09038i	−0.651274	+	0.758843i	$0.725765\pi$
$644$	0.574811	+	0.331867i	0.0226507	+	0.0130774i
$645$	−12.6661	−	0.813147i	−0.498727	−	0.0320176i
$646$	4.52084	−	15.4560i	0.177870	−	0.608108i
$647$	6.15374	+	6.15374i	0.241928	+	0.241928i	0.817648	−	0.575719i	$-0.195278\pi$
$647$	6.15374	+	6.15374i	0.241928	+	0.241928i	−0.575719	+	0.817648i	$0.695278\pi$
$648$	0.965926	−	0.258819i	0.0379452	−	0.0101674i
$649$	−5.46376	+	9.46351i	−0.214471	+	0.371475i
$650$	−12.3697	−	29.6384i	−0.485181	−	1.16251i
$651$	−10.0106	+	17.3388i	−0.392345	+	0.679561i
$652$	−6.09926	+	22.7627i	−0.238865	+	0.891458i
$653$	22.6506	−	22.6506i	0.886387	−	0.886387i	−0.107787	−	0.994174i	$-0.534376\pi$
$653$	22.6506	−	22.6506i	0.886387	−	0.886387i	0.994174	+	0.107787i	$0.0343763\pi$
$654$	16.4448			0.643043
$655$	−17.4752	−	35.3169i	−0.682813	−	1.37995i
$656$	4.33183	−	2.50098i	0.169130	−	0.0976470i
$657$	1.17045	+	1.17045i	0.0456637	+	0.0456637i
$658$	−15.3206	−	15.3206i	−0.597259	−	0.597259i
$659$	−19.0994	−	33.0811i	−0.744006	−	1.28866i	−0.950658	−	0.310242i	$-0.899590\pi$
$659$	−19.0994	−	33.0811i	−0.744006	−	1.28866i	0.206652	−	0.978415i	$-0.433743\pi$
$660$	2.69486	+	13.4538i	0.104897	+	0.523689i
$661$	16.5198	−	9.53773i	0.642547	−	0.370975i	−0.143048	−	0.989716i	$-0.545690\pi$
$661$	16.5198	−	9.53773i	0.642547	−	0.370975i	0.785595	+	0.618741i	$0.212357\pi$
$662$	7.10436	−	1.90361i	0.276119	−	0.0739858i
$663$	−6.14179	−	22.9215i	−0.238527	−	0.890197i
$664$	−6.42422			−0.249308
$665$	21.8670	+	15.2986i	0.847966	+	0.593253i
$666$	−10.5873			−0.410249
$667$	−0.433964	−	1.61958i	−0.0168031	−	0.0627102i
$668$	−0.0648198	+	0.0173684i	−0.00250795	+	0.000672004i
$669$	−2.95857	+	1.70813i	−0.114385	+	0.0660402i
$670$	14.1267	+	9.41185i	0.545763	+	0.363611i
$671$	−36.7243	−	63.6083i	−1.41773	−	2.45557i
$672$	−1.93610	−	1.93610i	−0.0746867	−	0.0746867i
$673$	−20.7956	−	20.7956i	−0.801612	−	0.801612i	0.181735	−	0.983347i	$-0.441829\pi$
$673$	−20.7956	−	20.7956i	−0.801612	−	0.801612i	−0.983347	+	0.181735i	$0.941829\pi$
$674$	4.34835	−	2.51052i	0.167492	−	0.0967017i
$675$	−4.62451	−	1.90104i	−0.177997	−	0.0731710i
$676$	28.2578			1.08684
$677$	−11.0987	+	11.0987i	−0.426558	+	0.426558i	−0.887454	−	0.460896i	$-0.847528\pi$
$677$	−11.0987	+	11.0987i	−0.426558	+	0.426558i	0.460896	+	0.887454i	$0.347528\pi$
$678$	−0.371604	+	1.38684i	−0.0142714	+	0.0532614i
$679$	−3.39003	+	5.87170i	−0.130097	+	0.225335i
$680$	7.40414	−	3.66365i	0.283936	−	0.140495i
$681$	4.54119	−	7.86557i	0.174019	−	0.301409i
$682$	−43.3403	+	11.6130i	−1.65958	+	0.444684i
$683$	17.9184	+	17.9184i	0.685627	+	0.685627i	0.961262	−	0.275635i	$-0.0888881\pi$
$683$	17.9184	+	17.9184i	0.685627	+	0.685627i	−0.275635	+	0.961262i	$0.588888\pi$
$684$	4.23496	−	1.03205i	0.161928	−	0.0394615i
$685$	−0.159330	−	0.181191i	−0.00608769	−	0.00692296i
$686$	−15.4202	−	8.90284i	−0.588745	−	0.339912i
$687$	3.80970	+	14.2180i	0.145349	+	0.542450i
$688$	5.48270	+	1.46909i	0.209026	+	0.0560084i
$689$	8.55681	+	4.94028i	0.325989	+	0.188210i
$690$	−0.513513	−	0.173548i	−0.0195491	−	0.00660685i
$691$	−18.7495			−0.713265			−0.356633	−	0.934245i	$-0.616075\pi$
$691$	−18.7495			−0.713265			−0.356633	+	0.934245i	$0.616075\pi$
$692$	3.96348	−	3.96348i	0.150669	−	0.150669i
$693$	−16.2289	−	4.34852i	−0.616485	−	0.165187i
$694$	−3.91037	−	6.77296i	−0.148436	−	0.257098i
$695$	−1.20190	+	18.7215i	−0.0455906	+	0.710148i
$696$			6.91681i			0.262181i
$697$	−17.8497	−	4.78281i	−0.676105	−	0.181162i
$698$	−12.0476	+	3.22814i	−0.456008	+	0.122187i
$699$	2.63312	+	4.56070i	0.0995938	+	0.172501i
$700$	1.82329	+	13.5683i	0.0689138	+	0.512835i
$701$	−11.1848	+	19.3726i	−0.422442	+	0.731692i	−0.996178	−	0.0873491i	$-0.972160\pi$
$701$	−11.1848	+	19.3726i	−0.422442	+	0.731692i	0.573735	+	0.819041i	$0.305494\pi$
$702$	4.54190	−	4.54190i	0.171423	−	0.171423i
$703$	−46.1369	−	1.05028i	−1.74009	−	0.0396121i
$704$		−	6.13624i		−	0.231268i
$705$	14.7254	+	9.81070i	0.554591	+	0.369492i
$706$	3.47429	+	2.00588i	0.130757	+	0.0754924i
$707$	−8.32963	+	31.0866i	−0.313268	+	1.16913i
$708$	0.460909	+	1.72014i	0.0173220	+	0.0646467i
$709$	−4.40418	+	2.54275i	−0.165402	+	0.0954952i	−0.580416	−	0.814320i	$-0.697110\pi$
$709$	−4.40418	+	2.54275i	−0.165402	+	0.0954952i	0.415014	+	0.909815i	$0.363777\pi$
$710$	−4.43210	−	5.04021i	−0.166334	−	0.189156i
$711$		−	4.12220i		−	0.154595i
$712$	1.94459	−	7.25729i	0.0728764	−	0.271979i
$713$	0.458768	−	1.71215i	0.0171810	−	0.0641204i
$714$			10.1155i			0.378564i
$715$	58.1990	+	66.1843i	2.17652	+	2.47515i
$716$	−10.4829	+	6.05228i	−0.391763	+	0.226184i
$717$	−1.81762	−	6.78344i	−0.0678801	−	0.253332i
$718$	9.12481	−	34.0543i	0.340535	−	1.27089i
$719$	−12.3993	−	7.15876i	−0.462417	−	0.266977i	0.250643	−	0.968080i	$-0.419358\pi$
$719$	−12.3993	−	7.15876i	−0.462417	−	0.266977i	−0.713060	+	0.701103i	$0.752691\pi$
$720$	1.86088	+	1.23980i	0.0693511	+	0.0462047i
$721$		−	3.21556i		−	0.119754i
$722$	18.5574	−	4.07733i	0.690633	−	0.151742i
$723$	−9.10160	+	9.10160i	−0.338492	+	0.338492i
$724$	10.8784	−	18.8419i	0.404291	−	0.700252i
$725$	20.9799	−	27.4936i	0.779173	−	1.02109i
$726$	−13.3267	−	23.0826i	−0.494601	−	0.856674i
$727$	16.4847	−	4.41707i	0.611385	−	0.163820i	0.0601764	−	0.998188i	$-0.480834\pi$
$727$	16.4847	−	4.41707i	0.611385	−	0.163820i	0.551208	+	0.834368i	$0.314167\pi$
$728$	−16.9879	−	4.55189i	−0.629613	−	0.168704i
$729$		−	1.00000i		−	0.0370370i
$730$	−0.237130	+	3.69369i	−0.00877658	+	0.136710i
$731$	−10.4850	−	18.1605i	−0.387801	−	0.671690i
$732$	−11.5618	−	3.09797i	−0.427336	−	0.114504i
$733$	14.0769	−	14.0769i	0.519943	−	0.519943i	−0.397611	−	0.917554i	$-0.630161\pi$
$733$	14.0769	−	14.0769i	0.519943	−	0.519943i	0.917554	+	0.397611i	$0.130161\pi$
$734$	−22.5490			−0.832298
$735$	−1.05276	−	0.355791i	−0.0388315	−	0.0131236i
$736$	0.209934	+	0.121205i	0.00773826	+	0.00446769i
$737$	−44.9955	−	12.0565i	−1.65743	−	0.444107i
$738$	−1.29460	−	4.83153i	−0.0476550	−	0.177851i
$739$	12.6613	+	7.31001i	0.465754	+	0.268903i	0.714461	−	0.699676i	$-0.246672\pi$
$739$	12.6613	+	7.31001i	0.465754	+	0.268903i	−0.248707	+	0.968579i	$0.580006\pi$
$740$	−15.6331	−	17.7780i	−0.574684	−	0.653534i
$741$	20.2431	−	19.3420i	0.743650	−	0.710546i
$742$	−2.97822	−	2.97822i	−0.109334	−	0.109334i
$743$	−3.06464	+	0.821168i	−0.112431	+	0.0301257i	−0.314596	−	0.949226i	$-0.601869\pi$
$743$	−3.06464	+	0.821168i	−0.112431	+	0.0301257i	0.202165	+	0.979351i	$0.435202\pi$
$744$	−3.65608	+	6.33251i	−0.134038	+	0.232161i
$745$	−6.26922	+	3.10208i	−0.229686	+	0.113651i
$746$	−9.56689	+	16.5703i	−0.350269	+	0.606684i
$747$	−1.66271	+	6.20532i	−0.0608354	+	0.227041i
$748$	−16.0300	+	16.0300i	−0.586115	+	0.586115i
$749$	1.81534			0.0663312
$750$	−3.63631	−	10.5725i	−0.132779	−	0.386052i
$751$	−7.18396	+	4.14766i	−0.262146	+	0.151350i	−0.625313	−	0.780374i	$-0.715029\pi$
$751$	−7.18396	+	4.14766i	−0.262146	+	0.151350i	0.363167	+	0.931724i	$0.381695\pi$
$752$	−5.59542	−	5.59542i	−0.204044	−	0.204044i
$753$	9.12546	+	9.12546i	0.332550	+	0.332550i
$754$	22.2141	+	38.4759i	0.808989	+	1.40121i
$755$	21.2397	+	14.1508i	0.772991	+	0.515000i
$756$	−2.37123	+	1.36903i	−0.0862408	+	0.0497911i
$757$	11.3983	−	3.05416i	0.414277	−	0.111005i	−0.0456592	−	0.998957i	$-0.514539\pi$
$757$	11.3983	−	3.05416i	0.414277	−	0.111005i	0.459937	+	0.887952i	$0.347872\pi$
$758$	−2.14311	−	7.99820i	−0.0778413	−	0.290508i
$759$	1.48749			0.0539925
$760$	7.98632	+	5.58738i	0.289694	+	0.202675i
$761$	23.0915			0.837065			0.418532	−	0.908202i	$-0.362545\pi$
$761$	23.0915			0.837065			0.418532	+	0.908202i	$0.362545\pi$
$762$	3.91378	+	14.6064i	0.141781	+	0.529136i
$763$	−43.4926	+	11.6538i	−1.57454	+	0.421896i
$764$	−3.16316	+	1.82625i	−0.114439	+	0.0660715i
$765$	−1.62248	−	8.10007i	−0.0586610	−	0.292859i
$766$	16.2933	+	28.2209i	0.588702	+	1.01966i
$767$	8.08830	+	8.08830i	0.292051	+	0.292051i
$768$	−0.707107	−	0.707107i	−0.0255155	−	0.0255155i
$769$	−6.23842	+	3.60175i	−0.224963	+	0.129882i	−0.608246	−	0.793748i	$-0.708127\pi$
$769$	−6.23842	+	3.60175i	−0.224963	+	0.129882i	0.383283	+	0.923631i	$0.374793\pi$
$770$	−16.6615	−	33.6724i	−0.600438	−	1.21347i
$771$	13.7110			0.493789
$772$	−11.8269	+	11.8269i	−0.425658	+	0.425658i
$773$	10.0292	−	37.4296i	0.360726	−	1.34625i	−0.512397	−	0.858749i	$-0.671242\pi$
$773$	10.0292	−	37.4296i	0.360726	−	1.34625i	0.873123	−	0.487500i	$-0.162091\pi$
$774$	2.83806	−	4.91566i	0.102012	−	0.176690i
$775$	33.7402	−	14.0816i	1.21198	−	0.505827i
$776$	−1.23811	+	2.14448i	−0.0444457	+	0.0769822i
$777$	28.0008	−	7.50280i	1.00452	−	0.269161i
$778$	13.7214	+	13.7214i	0.491938	+	0.491938i
$779$	−5.16229	−	21.1831i	−0.184958	−	0.758964i
$780$	14.3333	+	0.920176i	0.513213	+	0.0329476i
$781$	15.9508	+	9.20919i	0.570764	+	0.329531i
$782$	−0.231790	−	0.865051i	−0.00828878	−	0.0309342i
$783$	6.68112	+	1.79020i	0.238764	+	0.0639766i
$784$	0.430387	+	0.248484i	0.0153710	+	0.00887443i
$785$	15.3074	−	45.2933i	0.546344	−	1.61659i
$786$	17.6220			0.628554
$787$	0.472710	−	0.472710i	0.0168503	−	0.0168503i	−0.698631	−	0.715482i	$-0.746207\pi$
$787$	0.472710	−	0.472710i	0.0168503	−	0.0168503i	0.715482	+	0.698631i	$0.246207\pi$
$788$	4.80815	+	1.28834i	0.171283	+	0.0458952i
$789$	3.66185	+	6.34251i	0.130365	+	0.225799i
$790$	6.92196	−	6.08681i	0.246272	−	0.216559i
$791$		−	3.93121i		−	0.139778i
$792$	−5.92715	−	1.58818i	−0.210612	−	0.0564334i
$793$	−74.2639	+	19.8989i	−2.63719	+	0.706632i
$794$	−6.51137	−	11.2780i	−0.231080	−	0.400242i
$795$	2.86252	+	1.90713i	0.101523	+	0.0676390i
$796$	−5.65993	+	9.80328i	−0.200611	+	0.347468i
$797$	−5.34637	+	5.34637i	−0.189378	+	0.189378i	−0.795427	−	0.606049i	$-0.792754\pi$
$797$	−5.34637	+	5.34637i	−0.189378	+	0.189378i	0.606049	+	0.795427i	$0.292754\pi$
$798$	−10.4691	+	5.73068i	−0.370601	+	0.202864i
$799$			29.2344i			1.03424i
$800$	0.665905	+	4.95546i	0.0235433	+	0.175202i
$801$	−6.50671	−	3.75665i	−0.229903	−	0.132735i
$802$	−2.25424	+	8.41295i	−0.0796001	+	0.297071i
$803$	−2.62886	−	9.81103i	−0.0927704	−	0.346224i
$804$	−6.57435	+	3.79571i	−0.231860	+	0.133864i
$805$	1.48111	+	0.0950852i	0.0522022	+	0.00335131i
$806$			46.9676i			1.65436i
$807$	−5.97671	+	22.3054i	−0.210390	+	0.785187i
$808$	−3.04217	+	11.3535i	−0.107023	+	0.399415i
$809$			34.7296i			1.22103i	0.792005	+	0.610514i	$0.209037\pi$
$809$			34.7296i			1.22103i	−0.792005	+	0.610514i	$0.790963\pi$
$810$	1.67919	−	1.47659i	0.0590007	−	0.0518822i
$811$	−17.9872	+	10.3849i	−0.631617	+	0.364664i	−0.781378	−	0.624058i	$-0.785483\pi$
$811$	−17.9872	+	10.3849i	−0.631617	+	0.364664i	0.149761	+	0.988722i	$0.452150\pi$
$812$	−4.90168	−	18.2933i	−0.172015	−	0.641969i
$813$	−2.49071	+	9.29547i	−0.0873531	+	0.326006i
$814$	56.2623	+	32.4830i	1.97199	+	1.13853i
$815$	10.3494	+	51.6682i	0.362524	+	1.80986i
$816$			3.69442i			0.129331i
$817$	12.8552	−	21.1398i	0.449748	−	0.739587i
$818$	11.9466	−	11.9466i	0.417704	−	0.417704i
$819$	−8.79358	+	15.2309i	−0.307273	+	0.532212i
$820$	6.20145	−	9.30808i	0.216564	−	0.325052i
$821$	−8.04804	−	13.9396i	−0.280879	−	0.486496i	0.690723	−	0.723120i	$-0.257292\pi$
$821$	−8.04804	−	13.9396i	−0.280879	−	0.486496i	−0.971601	+	0.236624i	$0.923959\pi$
$822$	0.104227	−	0.0279276i	0.00363534	−	0.000974087i
$823$	1.18468	+	0.317435i	0.0412955	+	0.0110651i	0.279408	−	0.960173i	$-0.409862\pi$
$823$	1.18468	+	0.317435i	0.0412955	+	0.0110651i	−0.238112	+	0.971238i	$0.576529\pi$
$824$		−	1.17439i		−	0.0409119i
$825$	18.7427	+	24.2909i	0.652536	+	0.845701i
$826$	−2.43799	−	4.22272i	−0.0848285	−	0.146927i
$827$	−36.6620	−	9.82356i	−1.27486	−	0.341599i	−0.442971	−	0.896536i	$-0.646076\pi$
$827$	−36.6620	−	9.82356i	−1.27486	−	0.341599i	−0.831892	+	0.554937i	$0.812742\pi$
$828$	0.171410	−	0.171410i	0.00595692	−	0.00595692i
$829$	5.91550			0.205454			0.102727	−	0.994710i	$-0.467243\pi$
$829$	5.91550			0.205454			0.102727	+	0.994710i	$0.467243\pi$
$830$	−12.8751	+	6.37072i	−0.446900	+	0.221131i
$831$	13.6315	+	7.87017i	0.472873	+	0.273013i
$832$	−6.20436	−	1.66245i	−0.215097	−	0.0576352i
$833$	−0.475194	−	1.77345i	−0.0164645	−	0.0614463i
$834$	−7.26574	−	4.19488i	−0.251592	−	0.145257i
$835$	−0.112684	+	0.0990887i	−0.00389960	+	0.00342911i
$836$	−25.6716	−	7.50889i	−0.887872	−	0.259700i
$837$	5.17047	+	5.17047i	0.178718	+	0.178718i
$838$	−0.504801	+	0.135261i	−0.0174381	+	0.00467252i
$839$	20.9233	−	36.2401i	0.722351	−	1.25115i	−0.237704	−	0.971338i	$-0.576395\pi$
$839$	20.9233	−	36.2401i	0.722351	−	1.25115i	0.960055	−	0.279811i	$-0.0902718\pi$
$840$	−5.80020	−	1.96024i	−0.200126	−	0.0676348i
$841$	−9.42110	+	16.3178i	−0.324866	+	0.562684i
$842$	−2.72570	+	10.1724i	−0.0939337	+	0.350565i
$843$	1.37432	−	1.37432i	0.0473341	−	0.0473341i
$844$	−0.127616			−0.00439272
$845$	56.6326	−	28.0225i	1.94822	−	0.964002i
$846$	−6.85296	+	3.95656i	−0.235610	+	0.136029i
$847$	51.6037	+	51.6037i	1.77313	+	1.77313i
$848$	−1.08771	−	1.08771i	−0.0373521	−	0.0373521i
$849$	2.17595	+	3.76886i	0.0746785	+	0.129347i
$850$	11.2058	−	14.6850i	0.384356	−	0.503690i
$851$	−2.22263	+	1.28323i	−0.0761907	+	0.0439887i
$852$	2.89930	−	0.776864i	0.0993283	−	0.0266149i
$853$	13.8636	+	51.7398i	0.474682	+	1.77154i	0.622602	+	0.782539i	$0.286076\pi$
$853$	13.8636	+	51.7398i	0.474682	+	1.77154i	−0.147920	+	0.988999i	$0.547258\pi$
$854$	32.7736			1.12149
$855$	7.46400	−	6.26807i	0.255263	−	0.214363i
$856$	0.663004			0.0226610
$857$	−11.5110	−	42.9595i	−0.393207	−	1.46747i	−0.824812	−	0.565407i	$-0.808719\pi$
$857$	−11.5110	−	42.9595i	−0.393207	−	1.46747i	0.431605	−	0.902063i	$-0.357947\pi$
$858$	−38.0714	+	10.2012i	−1.29974	+	0.348263i
$859$	−25.3602	+	14.6417i	−0.865279	+	0.499569i	−0.865776	−	0.500431i	$-0.833175\pi$
$859$	−25.3602	+	14.6417i	−0.865279	+	0.499569i	0.000497653		1.00000i	$0.499842\pi$
$860$	12.4450	−	2.49279i	0.424370	−	0.0850034i
$861$	6.84784	+	11.8608i	0.233374	+	0.404215i
$862$	−3.18181	−	3.18181i	−0.108373	−	0.108373i
$863$	−11.8264	−	11.8264i	−0.402575	−	0.402575i	0.476565	−	0.879139i	$-0.341882\pi$
$863$	−11.8264	−	11.8264i	−0.402575	−	0.402575i	−0.879139	+	0.476565i	$0.841882\pi$
$864$	−0.866025	+	0.500000i	−0.0294628	+	0.0170103i
$865$	4.01291	−	11.8739i	0.136443	−	0.403723i
$866$	12.5354			0.425970
$867$	−2.36971	+	2.36971i	−0.0804796	+	0.0804796i
$868$	5.18184	−	19.3389i	0.175883	−	0.656405i
$869$	−12.6474	+	21.9060i	−0.429034	+	0.743109i
$870$	6.85920	+	13.8623i	0.232549	+	0.469975i
$871$	−24.3807	+	42.2285i	−0.826107	+	1.43086i
$872$	−15.8845	+	4.25623i	−0.537916	+	0.144134i
$873$	1.75096	+	1.75096i	0.0592609	+	0.0592609i
$874$	0.763971	−	0.729962i	0.0258417	−	0.0246913i
$875$	17.1095	+	25.3848i	0.578406	+	0.858162i
$876$	−1.43350	−	0.827634i	−0.0484336	−	0.0279632i
$877$	−9.54654	−	35.6282i	−0.322364	−	1.20308i	−0.916936	−	0.399035i	$-0.869345\pi$
$877$	−9.54654	−	35.6282i	−0.322364	−	1.20308i	0.594572	−	0.804042i	$-0.297321\pi$
$878$	24.6582	+	6.60714i	0.832173	+	0.222980i
$879$	3.92779	+	2.26771i	0.132481	+	0.0764880i
$880$	−6.08514	−	12.2979i	−0.205130	−	0.414562i
$881$	2.19108			0.0738193			0.0369097	−	0.999319i	$-0.488249\pi$
$881$	2.19108			0.0738193			0.0369097	+	0.999319i	$0.488249\pi$
$882$	0.351409	−	0.351409i	0.0118326	−	0.0118326i
$883$	33.9962	+	9.10927i	1.14406	+	0.306551i	0.780584	−	0.625051i	$-0.214922\pi$
$883$	33.9962	+	9.10927i	1.14406	+	0.306551i	0.363481	+	0.931602i	$0.381588\pi$
$884$	11.8650	+	20.5508i	0.399064	+	0.691200i
$885$	2.62954	+	2.99033i	0.0883910	+	0.100519i
$886$			22.3330i			0.750292i
$887$	34.3813	+	9.21245i	1.15441	+	0.309324i	0.784732	−	0.619835i	$-0.212801\pi$
$887$	34.3813	+	9.21245i	1.15441	+	0.309324i	0.369680	+	0.929159i	$0.379467\pi$
$888$	10.2265	−	2.74019i	0.343180	−	0.0919547i
$889$	−20.7021	−	35.8570i	−0.694325	−	1.20261i
$890$	−3.29963	−	16.4730i	−0.110604	−	0.552178i
$891$	−3.06812	+	5.31414i	−0.102786	+	0.178030i
$892$	2.41566	−	2.41566i	0.0808824	−	0.0808824i
$893$	−30.2561	+	16.5619i	−1.01248	+	0.554224i
$894$		−	3.12813i		−	0.104620i
$895$	−15.0073	+	22.5252i	−0.501638	+	0.752935i
$896$	2.37123	+	1.36903i	0.0792172	+	0.0457361i
$897$	0.402996	−	1.50400i	0.0134556	−	0.0502172i
$898$	−7.04892	−	26.3069i	−0.235226	−	0.877874i
$899$	−43.8007	+	25.2884i	−1.46084	+	0.843414i
$900$	4.95895	+	0.639352i	0.165298	+	0.0213117i
$901$			5.68296i			0.189327i
$902$	−7.94400	+	29.6474i	−0.264506	+	0.987151i
$903$	−4.02245	+	15.0120i	−0.133859	+	0.499567i
$904$		−	1.43577i		−	0.0477529i
$905$	3.11682	−	48.5495i	0.103607	−	1.61384i
$906$	−9.88459	+	5.70687i	−0.328394	+	0.189598i
$907$	5.83651	+	21.7821i	0.193798	+	0.723264i	0.992575	+	0.121637i	$0.0388142\pi$
$907$	5.83651	+	21.7821i	0.193798	+	0.723264i	−0.798777	+	0.601628i	$0.794519\pi$
$908$	−2.35069	+	8.77291i	−0.0780105	+	0.291139i
$909$	10.1793	+	5.87701i	0.337626	+	0.194928i
$910$	−38.5601	+	7.72378i	−1.27826	+	0.256041i
$911$			25.6684i			0.850432i	0.905092	+	0.425216i	$0.139802\pi$
$911$			25.6684i			0.850432i	−0.905092	+	0.425216i	$0.860198\pi$
$912$	−3.82354	+	2.09297i	−0.126610	+	0.0693053i
$913$	27.8746	−	27.8746i	0.922513	−	0.922513i
$914$	−9.07952	+	15.7262i	−0.300324	+	0.520176i
$915$	−26.2436	+	5.25672i	−0.867587	+	0.173782i
$916$	−7.35977	−	12.7475i	−0.243174	−	0.421189i
$917$	−46.6059	+	12.4880i	−1.53906	+	0.412390i
$918$	3.56853	+	0.956186i	0.117779	+	0.0315588i
$919$		−	39.3716i		−	1.29875i	−0.760468	−	0.649375i	$-0.775031\pi$
$919$		−	39.3716i		−	1.29875i	0.760468	−	0.649375i	$-0.224969\pi$
$920$	0.540933	+	0.0347272i	0.0178340	+	0.00114492i
$921$	−17.3660	−	30.0788i	−0.572229	−	0.991129i
$922$	−36.8955	−	9.88612i	−1.21509	−	0.325582i
$923$	13.6329	−	13.6329i	0.448731	−	0.448731i
$924$	16.8014			0.552725
$925$	−48.9609	−	20.1268i	−1.60983	−	0.661766i
$926$	−11.2354	−	6.48678i	−0.369219	−	0.213169i
$927$	−1.13438	−	0.303955i	−0.0372578	−	0.00998320i
$928$	−1.79020	−	6.68112i	−0.0587662	−	0.219319i
$929$	−29.6336	−	17.1090i	−0.972247	−	0.561327i	−0.0723262	−	0.997381i	$-0.523042\pi$
$929$	−29.6336	−	17.1090i	−0.972247	−	0.561327i	−0.899920	+	0.436054i	$0.856376\pi$
$930$	−1.04752	+	16.3169i	−0.0343496	+	0.535052i
$931$	1.56622	−	1.49650i	0.0513309	−	0.0490458i
$932$	−3.72380	−	3.72380i	−0.121977	−	0.121977i
$933$	26.5759	−	7.12098i	0.870055	−	0.233131i
$934$	−3.48636	+	6.03856i	−0.114077	+	0.197588i
$935$	−16.2299	+	48.0229i	−0.530774	+	1.57052i
$936$	−3.21161	+	5.56267i	−0.104975	+	0.181822i
$937$	0.0477311	−	0.178135i	0.00155931	−	0.00581941i	−0.965142	−	0.261728i	$-0.915708\pi$
$937$	0.0477311	−	0.178135i	0.00155931	−	0.00581941i	0.966701	+	0.255908i	$0.0823745\pi$
$938$	14.6977	−	14.6977i	0.479898	−	0.479898i
$939$	−9.09725			−0.296878
$940$	−16.7628	−	5.66520i	−0.546744	−	0.184778i
$941$	10.6960	−	6.17535i	0.348680	−	0.201310i	−0.315424	−	0.948951i	$-0.602147\pi$
$941$	10.6960	−	6.17535i	0.348680	−	0.201310i	0.664104	+	0.747640i	$0.268813\pi$
$942$	15.1188	+	15.1188i	0.492599	+	0.492599i
$943$	−0.857388	−	0.857388i	−0.0279204	−	0.0279204i
$944$	−0.890408	−	1.54223i	−0.0289803	−	0.0501954i
$945$	−3.39465	+	5.09521i	−0.110428	+	0.165747i
$946$	−30.1637	+	17.4150i	−0.980705	+	0.566210i
$947$	−1.91779	+	0.513870i	−0.0623197	+	0.0166985i	−0.289844	−	0.957074i	$-0.593603\pi$
$947$	−1.91779	+	0.513870i	−0.0623197	+	0.0166985i	0.227524	+	0.973772i	$0.426937\pi$
$948$	1.06690	+	3.98174i	0.0346515	+	0.129321i
$949$	−10.6322			−0.345134
$950$	21.5466	+	3.27809i	0.699063	+	0.106355i
$951$	24.0977			0.781422
$952$	−2.61809	−	9.77086i	−0.0848529	−	0.316675i
$953$	27.8195	−	7.45422i	0.901163	−	0.241466i	0.221648	−	0.975127i	$-0.428857\pi$
$953$	27.8195	−	7.45422i	0.901163	−	0.241466i	0.679516	+	0.733661i	$0.262190\pi$
$954$	−1.33217	+	0.769128i	−0.0431305	+	0.0249014i
$955$	−4.52838	+	6.79689i	−0.146535	+	0.219942i
$956$	3.51136	+	6.08186i	0.113566	+	0.196701i
$957$	−30.0119	−	30.0119i	−0.970146	−	0.970146i
$958$	−12.8686	−	12.8686i	−0.415765	−	0.415765i
$959$	−0.255865	+	0.147724i	−0.00826231	+	0.00477025i
$960$	−2.11836	−	0.715924i	−0.0683698	−	0.0231064i
$961$	−22.4676			−0.724761
$962$	48.0864	−	48.0864i	1.55037	−	1.55037i
$963$	0.171598	−	0.640412i	0.00552967	−	0.0206370i
$964$	6.43580	−	11.1471i	0.207283	−	0.359025i
$965$	−11.9743	+	35.4311i	−0.385468	+	1.14057i
$966$	−0.331867	+	0.574811i	−0.0106777	+	0.0184942i
$967$	13.1617	−	3.52668i	0.423253	−	0.113410i	−0.0409043	−	0.999163i	$-0.513024\pi$
$967$	13.1617	−	3.52668i	0.423253	−	0.113410i	0.464157	+	0.885753i	$0.346357\pi$
$968$	18.8468	+	18.8468i	0.605760	+	0.605760i
$969$	15.4560	+	4.52084i	0.496518	+	0.145230i
$970$	−0.354739	+	5.52564i	−0.0113900	+	0.177417i
$971$	−11.1333	−	6.42780i	−0.357284	−	0.206278i	0.310605	−	0.950539i	$-0.399468\pi$
$971$	−11.1333	−	6.42780i	−0.357284	−	0.206278i	−0.667889	+	0.744261i	$0.732802\pi$
$972$	0.258819	+	0.965926i	0.00830162	+	0.0309821i
$973$	22.1889	+	5.94550i	0.711344	+	0.190604i
$974$	−9.22305	−	5.32493i	−0.295525	−	0.170622i
$975$	29.6384	−	12.3697i	0.949188	−	0.396148i
$976$	11.9696			0.383139
$977$	26.7372	−	26.7372i	0.855399	−	0.855399i	−0.135393	−	0.990792i	$-0.543230\pi$
$977$	26.7372	−	26.7372i	0.855399	−	0.855399i	0.990792	+	0.135393i	$0.0432296\pi$
$978$	−22.7627	−	6.09926i	−0.727872	−	0.195033i
$979$	23.0517	+	39.9267i	0.736736	+	1.27606i
$980$	1.10897	+	0.0711945i	0.0354248	+	0.00227423i
$981$			16.4448i			0.525042i
$982$	30.3479	+	8.13171i	0.968442	+	0.259493i
$983$	−44.5015	+	11.9242i	−1.41938	+	0.380321i	−0.885263	−	0.465090i	$-0.846022\pi$
$983$	−44.5015	+	11.9242i	−1.41938	+	0.380321i	−0.534115	+	0.845412i	$0.679355\pi$
$984$	2.50098	+	4.33183i	0.0797284	+	0.138094i
$985$	10.9138	−	2.18609i	0.347743	−	0.0696546i
$986$	−12.7768	+	22.1300i	−0.406896	+	0.704764i
$987$	15.3206	−	15.3206i	0.487660	−	0.487660i
$988$	−14.5473	+	23.9223i	−0.462811	+	0.761068i
$989$		−	1.37595i		−	0.0437527i
$990$	−13.4538	+	2.69486i	−0.427590	+	0.0856484i
$991$	21.4421	+	12.3796i	0.681130	+	0.393250i	0.800280	−	0.599626i	$-0.204684\pi$
$991$	21.4421	+	12.3796i	0.681130	+	0.393250i	−0.119151	+	0.992876i	$0.538017\pi$
$992$	1.89252	−	7.06300i	0.0600877	−	0.224250i
$993$	1.90361	+	7.10436i	0.0604091	+	0.225450i
$994$	−7.11742	+	4.10924i	−0.225751	+	0.130337i
$995$	−1.62166	+	25.2600i	−0.0514100	+	0.800795i
$996$		−	6.42422i		−	0.203559i
$997$	−1.93727	+	7.22999i	−0.0613540	+	0.228976i	−0.989794	−	0.142507i	$-0.954484\pi$
$997$	−1.93727	+	7.22999i	−0.0613540	+	0.228976i	0.928440	+	0.371483i	$0.121150\pi$
$998$	−2.77009	+	10.3381i	−0.0876857	+	0.327248i
$999$		−	10.5873i		−	0.334967i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.x.a.217.2	yes	40
5.3	odd	4	inner	570.2.x.a.103.2	✓	40
19.12	odd	6	inner	570.2.x.a.487.2	yes	40
95.88	even	12	inner	570.2.x.a.373.2	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.x.a.103.2	✓	40	5.3	odd	4	inner
570.2.x.a.217.2	yes	40	1.1	even	1	trivial
570.2.x.a.373.2	yes	40	95.88	even	12	inner
570.2.x.a.487.2	yes	40	19.12	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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.x (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.258819 - 0.965926i) q^{2} +(0.965926 - 0.258819i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-1.23980 + 1.86088i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(1.93610 + 1.93610i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(-0.258819 - 0.965926i) q^{2} +(0.965926 - 0.258819i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-1.23980 + 1.86088i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(1.93610 + 1.93610i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.866025 - 0.500000i) q^{9} +(2.11836 + 0.715924i) q^{10} -6.13624 q^{11} +(-0.707107 + 0.707107i) q^{12} +(-1.66245 + 6.20436i) q^{13} +(1.36903 - 2.37123i) q^{14} +(-0.715924 + 2.11836i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-3.56853 + 0.956186i) q^{17} +(-0.707107 - 0.707107i) q^{18} +(-3.01126 - 3.15156i) q^{19} +(0.143258 - 2.23147i) q^{20} +(2.37123 + 1.36903i) q^{21} +(1.58818 + 5.92715i) q^{22} +(-0.234151 - 0.0627405i) q^{23} +(0.866025 + 0.500000i) q^{24} +(-1.92578 - 4.61426i) q^{25} +6.42322 q^{26} +(0.707107 - 0.707107i) q^{27} +(-2.64476 - 0.708662i) q^{28} +(3.45840 + 5.99013i) q^{29} +(2.23147 + 0.143258i) q^{30} +7.31215i q^{31} +(-0.965926 - 0.258819i) q^{32} +(-5.92715 + 1.58818i) q^{33} +(1.84721 + 3.19946i) q^{34} +(-6.00324 + 1.20248i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(7.48634 - 7.48634i) q^{37} +(-2.26480 + 3.72434i) q^{38} +6.42322i q^{39} +(-2.19252 + 0.439172i) q^{40} +(4.33183 + 2.50098i) q^{41} +(0.708662 - 2.64476i) q^{42} +(1.46909 + 5.48270i) q^{43} +(5.31414 - 3.06812i) q^{44} +(-0.143258 + 2.23147i) q^{45} +0.242411i q^{46} +(2.04807 - 7.64349i) q^{47} +(0.258819 - 0.965926i) q^{48} +0.496968i q^{49} +(-3.95860 + 3.05442i) q^{50} +(-3.19946 + 1.84721i) q^{51} +(-1.66245 - 6.20436i) q^{52} +(0.398130 - 1.48584i) q^{53} +(-0.866025 - 0.500000i) q^{54} +(7.60772 - 11.4188i) q^{55} +2.73806i q^{56} +(-3.72434 - 2.26480i) q^{57} +(4.89092 - 4.89092i) q^{58} +(0.890408 - 1.54223i) q^{59} +(-0.439172 - 2.19252i) q^{60} +(5.98482 + 10.3660i) q^{61} +(7.06300 - 1.89252i) q^{62} +(2.64476 + 0.708662i) q^{63} +1.00000i q^{64} +(-9.48448 - 10.7858i) q^{65} +(3.06812 + 5.31414i) q^{66} +(7.33274 + 1.96480i) q^{67} +(2.61235 - 2.61235i) q^{68} -0.242411 q^{69} +(2.71526 + 5.48746i) q^{70} +(-2.59944 - 1.50079i) q^{71} +(0.965926 + 0.258819i) q^{72} +(0.428415 + 1.59887i) q^{73} +(-9.16885 - 5.29364i) q^{74} +(-3.05442 - 3.95860i) q^{75} +(4.18361 + 1.22370i) q^{76} +(-11.8804 - 11.8804i) q^{77} +(6.20436 - 1.66245i) q^{78} +(2.06110 - 3.56993i) q^{79} +(0.991672 + 2.00414i) q^{80} +(0.500000 - 0.866025i) q^{81} +(1.29460 - 4.83153i) q^{82} +(-4.54261 + 4.54261i) q^{83} -2.73806 q^{84} +(2.64492 - 7.82611i) q^{85} +(4.91566 - 2.83806i) q^{86} +(4.89092 + 4.89092i) q^{87} +(-4.33898 - 4.33898i) q^{88} +(-3.75665 - 6.50671i) q^{89} +(2.19252 - 0.439172i) q^{90} +(-15.2309 + 8.79358i) q^{91} +(0.234151 - 0.0627405i) q^{92} +(1.89252 + 7.06300i) q^{93} -7.91312 q^{94} +(9.59805 - 1.69631i) q^{95} -1.00000 q^{96} +(0.640895 + 2.39185i) q^{97} +(0.480034 - 0.128625i) q^{98} +(-5.31414 + 3.06812i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 8 q^{5} - 20 q^{6} - 8 q^{7}+O(q^{10}) \) 40 * q - 8 * q^5 - 20 * q^6 - 8 * q^7	\( 40 q - 8 q^{5} - 20 q^{6} - 8 q^{7} - 12 q^{10} + 8 q^{11} - 24 q^{13} + 20 q^{16} + 8 q^{17} + 12 q^{21} + 24 q^{22} + 16 q^{23} - 16 q^{25} + 32 q^{26} + 4 q^{28} + 16 q^{30} - 24 q^{33} - 4 q^{35} - 20 q^{36} - 8 q^{38} - 36 q^{41} + 4 q^{42} - 4 q^{43} + 8 q^{47} - 24 q^{52} - 16 q^{55} - 8 q^{57} + 16 q^{58} + 12 q^{60} - 8 q^{61} - 16 q^{62} - 4 q^{63} - 4 q^{66} - 36 q^{67} - 16 q^{68} + 48 q^{70} + 72 q^{71} - 16 q^{73} - 8 q^{76} + 24 q^{77} + 24 q^{78} + 8 q^{80} + 20 q^{81} - 24 q^{82} - 40 q^{83} - 48 q^{85} + 16 q^{87} - 72 q^{91} - 16 q^{92} + 16 q^{93} - 16 q^{95} - 40 q^{96} + 36 q^{97} - 48 q^{98}+O(q^{100}) \) 40 * q - 8 * q^5 - 20 * q^6 - 8 * q^7 - 12 * q^10 + 8 * q^11 - 24 * q^13 + 20 * q^16 + 8 * q^17 + 12 * q^21 + 24 * q^22 + 16 * q^23 - 16 * q^25 + 32 * q^26 + 4 * q^28 + 16 * q^30 - 24 * q^33 - 4 * q^35 - 20 * q^36 - 8 * q^38 - 36 * q^41 + 4 * q^42 - 4 * q^43 + 8 * q^47 - 24 * q^52 - 16 * q^55 - 8 * q^57 + 16 * q^58 + 12 * q^60 - 8 * q^61 - 16 * q^62 - 4 * q^63 - 4 * q^66 - 36 * q^67 - 16 * q^68 + 48 * q^70 + 72 * q^71 - 16 * q^73 - 8 * q^76 + 24 * q^77 + 24 * q^78 + 8 * q^80 + 20 * q^81 - 24 * q^82 - 40 * q^83 - 48 * q^85 + 16 * q^87 - 72 * q^91 - 16 * q^92 + 16 * q^93 - 16 * q^95 - 40 * q^96 + 36 * q^97 - 48 * q^98

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