LMFDB - Embedded newform 570.2.x.b.103.10

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			103.10
Character	$\chi$	$=$	570.103
Dual form			570.2.x.b.487.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.965926 - 0.258819i) q^{2} +(0.258819 + 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} +(2.10507 - 0.754119i) q^{5} +(0.500000 + 0.866025i) q^{6} +(-0.506739 + 0.506739i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 + 0.500000i) q^{9} +O(q^{10})$	\(q+(0.965926 - 0.258819i) q^{2} +(0.258819 + 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} +(2.10507 - 0.754119i) q^{5} +(0.500000 + 0.866025i) q^{6} +(-0.506739 + 0.506739i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 + 0.500000i) q^{9} +(1.83816 - 1.27325i) q^{10} -1.16303 q^{11} +(0.707107 + 0.707107i) q^{12} +(6.66537 + 1.78598i) q^{13} +(-0.358318 + 0.620626i) q^{14} +(1.27325 + 1.83816i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-0.465536 - 1.73740i) q^{17} +(-0.707107 + 0.707107i) q^{18} +(-4.14953 - 1.33469i) q^{19} +(1.44598 - 1.70562i) q^{20} +(-0.620626 - 0.358318i) q^{21} +(-1.12340 + 0.301014i) q^{22} +(-0.517533 + 1.93146i) q^{23} +(0.866025 + 0.500000i) q^{24} +(3.86261 - 3.17494i) q^{25} +6.90050 q^{26} +(-0.707107 - 0.707107i) q^{27} +(-0.185479 + 0.692218i) q^{28} +(2.32693 + 4.03036i) q^{29} +(1.70562 + 1.44598i) q^{30} -0.506614i q^{31} +(0.258819 - 0.965926i) q^{32} +(-0.301014 - 1.12340i) q^{33} +(-0.899346 - 1.55771i) q^{34} +(-0.684577 + 1.44886i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-3.08717 - 3.08717i) q^{37} +(-4.35358 - 0.215233i) q^{38} +6.90050i q^{39} +(0.955264 - 2.02175i) q^{40} +(-2.46012 - 1.42035i) q^{41} +(-0.692218 - 0.185479i) q^{42} +(-4.03864 + 1.08215i) q^{43} +(-1.00721 + 0.581514i) q^{44} +(-1.44598 + 1.70562i) q^{45} +1.99959i q^{46} +(-1.65457 - 0.443341i) q^{47} +(0.965926 + 0.258819i) q^{48} +6.48643i q^{49} +(2.90926 - 4.06647i) q^{50} +(1.55771 - 0.899346i) q^{51} +(6.66537 - 1.78598i) q^{52} +(-9.62256 - 2.57836i) q^{53} +(-0.866025 - 0.500000i) q^{54} +(-2.44825 + 0.877061i) q^{55} +0.716637i q^{56} +(0.215233 - 4.35358i) q^{57} +(3.29077 + 3.29077i) q^{58} +(6.04573 - 10.4715i) q^{59} +(2.02175 + 0.955264i) q^{60} +(7.75737 + 13.4362i) q^{61} +(-0.131121 - 0.489351i) q^{62} +(0.185479 - 0.692218i) q^{63} -1.00000i q^{64} +(15.3779 - 1.26687i) q^{65} +(-0.581514 - 1.00721i) q^{66} +(1.91246 - 7.13741i) q^{67} +(-1.27187 - 1.27187i) q^{68} -1.99959 q^{69} +(-0.286258 + 1.57667i) q^{70} +(-6.60544 - 3.81365i) q^{71} +(-0.258819 + 0.965926i) q^{72} +(-2.63928 + 0.707194i) q^{73} +(-3.78100 - 2.18296i) q^{74} +(4.06647 + 2.90926i) q^{75} +(-4.26094 + 0.918891i) q^{76} +(0.589351 - 0.589351i) q^{77} +(1.78598 + 6.66537i) q^{78} +(-7.23536 + 12.5320i) q^{79} +(0.399447 - 2.20010i) q^{80} +(0.500000 - 0.866025i) q^{81} +(-2.74391 - 0.735227i) q^{82} +(-9.66217 - 9.66217i) q^{83} -0.716637 q^{84} +(-2.29019 - 3.30628i) q^{85} +(-3.62094 + 2.09055i) q^{86} +(-3.29077 + 3.29077i) q^{87} +(-0.822385 + 0.822385i) q^{88} +(-2.91613 - 5.05089i) q^{89} +(-0.955264 + 2.02175i) q^{90} +(-4.28263 + 2.47258i) q^{91} +(0.517533 + 1.93146i) q^{92} +(0.489351 - 0.131121i) q^{93} -1.71294 q^{94} +(-9.74155 + 0.319632i) q^{95} +1.00000 q^{96} +(3.21549 - 0.861589i) q^{97} +(1.67881 + 6.26541i) q^{98} +(1.00721 - 0.581514i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 20 q^{6} - 8 q^{7}+O(q^{10}) $ 40 * q + 20 * q^6 - 8 * q^7	$ 40 q + 20 q^{6} - 8 q^{7} + 12 q^{10} + 8 q^{11} + 24 q^{13} + 20 q^{16} + 36 q^{21} - 8 q^{23} + 16 q^{25} + 4 q^{28} - 4 q^{35} - 20 q^{36} + 24 q^{38} + 12 q^{41} - 4 q^{42} - 12 q^{43} - 16 q^{47} + 24 q^{52} + 72 q^{53} + 8 q^{55} - 24 q^{57} - 16 q^{58} + 12 q^{60} + 24 q^{61} - 4 q^{63} + 4 q^{66} - 36 q^{67} - 24 q^{70} - 72 q^{71} - 32 q^{73} + 8 q^{76} - 88 q^{77} + 24 q^{78} + 20 q^{81} + 8 q^{82} - 88 q^{83} - 24 q^{85} - 48 q^{86} + 16 q^{87} - 24 q^{91} + 8 q^{92} - 96 q^{95} + 40 q^{96} - 60 q^{97} - 48 q^{98}+O(q^{100}) $ 40 * q + 20 * q^6 - 8 * q^7 + 12 * q^10 + 8 * q^11 + 24 * q^13 + 20 * q^16 + 36 * q^21 - 8 * q^23 + 16 * q^25 + 4 * q^28 - 4 * q^35 - 20 * q^36 + 24 * q^38 + 12 * q^41 - 4 * q^42 - 12 * q^43 - 16 * q^47 + 24 * q^52 + 72 * q^53 + 8 * q^55 - 24 * q^57 - 16 * q^58 + 12 * q^60 + 24 * q^61 - 4 * q^63 + 4 * q^66 - 36 * q^67 - 24 * q^70 - 72 * q^71 - 32 * q^73 + 8 * q^76 - 88 * q^77 + 24 * q^78 + 20 * q^81 + 8 * q^82 - 88 * q^83 - 24 * q^85 - 48 * q^86 + 16 * q^87 - 24 * q^91 + 8 * q^92 - 96 * q^95 + 40 * q^96 - 60 * q^97 - 48 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$3$	0.258819	+	0.965926i	0.149429	+	0.557678i
$3$	0.258819	+	0.965926i	0.149429	+	0.557678i
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$	2.10507	−	0.754119i	0.941414	−	0.337252i
$5$	2.10507	−	0.754119i	0.941414	−	0.337252i
$6$	0.500000	+	0.866025i	0.204124	+	0.353553i
$7$	−0.506739	+	0.506739i	−0.191529	+	0.191529i	−0.796357	−	0.604827i	$-0.793242\pi$
$7$	−0.506739	+	0.506739i	−0.191529	+	0.191529i	0.604827	+	0.796357i	$0.293242\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	−0.866025	+	0.500000i	−0.288675	+	0.166667i
$10$	1.83816	−	1.27325i	0.581276	−	0.402638i
$11$	−1.16303			−0.350666			−0.175333	−	0.984509i	$-0.556100\pi$
$11$	−1.16303			−0.350666			−0.175333	+	0.984509i	$0.556100\pi$
$12$	0.707107	+	0.707107i	0.204124	+	0.204124i
$13$	6.66537	+	1.78598i	1.84864	+	0.495342i	0.999463	−	0.0327634i	$-0.0104308\pi$
$13$	6.66537	+	1.78598i	1.84864	+	0.495342i	0.849179	+	0.528106i	$0.177097\pi$
$14$	−0.358318	+	0.620626i	−0.0957646	+	0.165869i
$15$	1.27325	+	1.83816i	0.328753	+	0.474610i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−0.465536	−	1.73740i	−0.112909	−	0.421382i	0.886213	−	0.463278i	$-0.153327\pi$
$17$	−0.465536	−	1.73740i	−0.112909	−	0.421382i	−0.999122	+	0.0418959i	$0.986660\pi$
$18$	−0.707107	+	0.707107i	−0.166667	+	0.166667i
$19$	−4.14953	−	1.33469i	−0.951968	−	0.306199i
$19$	−4.14953	−	1.33469i	−0.951968	−	0.306199i
$20$	1.44598	−	1.70562i	0.323331	−	0.381388i
$21$	−0.620626	−	0.358318i	−0.135432	−	0.0781915i
$22$	−1.12340	+	0.301014i	−0.239509	+	0.0641763i
$23$	−0.517533	+	1.93146i	−0.107913	+	0.402737i	−0.998659	−	0.0517639i	$-0.983516\pi$
$23$	−0.517533	+	1.93146i	−0.107913	+	0.402737i	0.890746	+	0.454501i	$0.150182\pi$
$24$	0.866025	+	0.500000i	0.176777	+	0.102062i
$25$	3.86261	−	3.17494i	0.772522	−	0.634988i
$26$	6.90050			1.35330
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$	−0.185479	+	0.692218i	−0.0350523	+	0.130817i
$29$	2.32693	+	4.03036i	0.432100	+	0.748419i	0.997054	−	0.0767037i	$-0.0244395\pi$
$29$	2.32693	+	4.03036i	0.432100	+	0.748419i	−0.564954	+	0.825122i	$0.691106\pi$
$30$	1.70562	+	1.44598i	0.311402	+	0.263999i
$31$		−	0.506614i		−	0.0909905i	−0.998965	−	0.0454952i	$-0.985513\pi$
$31$		−	0.506614i		−	0.0909905i	0.998965	−	0.0454952i	$-0.0144866\pi$
$32$	0.258819	−	0.965926i	0.0457532	−	0.170753i
$33$	−0.301014	−	1.12340i	−0.0523997	−	0.195559i
$34$	−0.899346	−	1.55771i	−0.154237	−	0.267146i
$35$	−0.684577	+	1.44886i	−0.115715	+	0.244902i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	−3.08717	−	3.08717i	−0.507528	−	0.507528i	0.406239	−	0.913767i	$-0.366840\pi$
$37$	−3.08717	−	3.08717i	−0.507528	−	0.507528i	−0.913767	+	0.406239i	$0.866840\pi$
$38$	−4.35358	−	0.215233i	−0.706244	−	0.0349153i
$39$			6.90050i			1.10496i
$40$	0.955264	−	2.02175i	0.151041	−	0.319667i
$41$	−2.46012	−	1.42035i	−0.384206	−	0.221821i	0.295441	−	0.955361i	$-0.404534\pi$
$41$	−2.46012	−	1.42035i	−0.384206	−	0.221821i	−0.679647	+	0.733540i	$0.737867\pi$
$42$	−0.692218	−	0.185479i	−0.106812	−	0.0286201i
$43$	−4.03864	+	1.08215i	−0.615886	+	0.165026i	−0.553257	−	0.833011i	$-0.686615\pi$
$43$	−4.03864	+	1.08215i	−0.615886	+	0.165026i	−0.0626293	+	0.998037i	$0.519949\pi$
$44$	−1.00721	+	0.581514i	−0.151843	+	0.0876665i
$45$	−1.44598	+	1.70562i	−0.215554	+	0.254259i
$46$			1.99959i			0.294824i
$47$	−1.65457	−	0.443341i	−0.241344	−	0.0646679i	0.136119	−	0.990692i	$-0.456537\pi$
$47$	−1.65457	−	0.443341i	−0.241344	−	0.0646679i	−0.377463	+	0.926025i	$0.623204\pi$
$48$	0.965926	+	0.258819i	0.139419	+	0.0373573i
$49$			6.48643i			0.926633i
$50$	2.90926	−	4.06647i	0.411431	−	0.575086i
$51$	1.55771	−	0.899346i	0.218123	−	0.125934i
$52$	6.66537	−	1.78598i	0.924321	−	0.247671i
$53$	−9.62256	−	2.57836i	−1.32176	−	0.354165i	−0.472124	−	0.881532i	$-0.656512\pi$
$53$	−9.62256	−	2.57836i	−1.32176	−	0.354165i	−0.849637	+	0.527368i	$0.823179\pi$
$54$	−0.866025	−	0.500000i	−0.117851	−	0.0680414i
$55$	−2.44825	+	0.877061i	−0.330122	+	0.118263i
$56$			0.716637i			0.0957646i
$57$	0.215233	−	4.35358i	0.0285082	−	0.576646i
$58$	3.29077	+	3.29077i	0.432100	+	0.432100i
$59$	6.04573	−	10.4715i	0.787086	−	1.36327i	−0.140658	−	0.990058i	$-0.544922\pi$
$59$	6.04573	−	10.4715i	0.787086	−	1.36327i	0.927745	−	0.373215i	$-0.121745\pi$
$60$	2.02175	+	0.955264i	0.261007	+	0.123324i
$61$	7.75737	+	13.4362i	0.993230	+	1.72032i	0.597220	+	0.802078i	$0.296272\pi$
$61$	7.75737	+	13.4362i	0.993230	+	1.72032i	0.396010	+	0.918246i	$0.370395\pi$
$62$	−0.131121	−	0.489351i	−0.0166524	−	0.0621477i
$63$	0.185479	−	0.692218i	0.0233682	−	0.0872113i
$64$		−	1.00000i		−	0.125000i
$65$	15.3779	−	1.26687i	1.90739	−	0.157136i
$66$	−0.581514	−	1.00721i	−0.0715794	−	0.123979i
$67$	1.91246	−	7.13741i	0.233645	−	0.871973i	−0.745111	−	0.666941i	$-0.767603\pi$
$67$	1.91246	−	7.13741i	0.233645	−	0.871973i	0.978755	−	0.205033i	$-0.0657300\pi$
$68$	−1.27187	−	1.27187i	−0.154237	−	0.154237i
$69$	−1.99959			−0.240723
$70$	−0.286258	+	1.57667i	−0.0342144	+	0.188448i
$71$	−6.60544	−	3.81365i	−0.783921	−	0.452597i	0.0538971	−	0.998546i	$-0.482836\pi$
$71$	−6.60544	−	3.81365i	−0.783921	−	0.452597i	−0.837818	+	0.545949i	$0.816169\pi$
$72$	−0.258819	+	0.965926i	−0.0305021	+	0.113835i
$73$	−2.63928	+	0.707194i	−0.308905	+	0.0827708i	−0.409941	−	0.912112i	$-0.634451\pi$
$73$	−2.63928	+	0.707194i	−0.308905	+	0.0827708i	0.101036	+	0.994883i	$0.467784\pi$
$74$	−3.78100	−	2.18296i	−0.439532	−	0.253764i
$75$	4.06647	+	2.90926i	0.469556	+	0.335932i
$76$	−4.26094	+	0.918891i	−0.488764	+	0.105404i
$77$	0.589351	−	0.589351i	0.0671628	−	0.0671628i
$78$	1.78598	+	6.66537i	0.202223	+	0.754705i
$79$	−7.23536	+	12.5320i	−0.814042	+	1.40996i	0.0959721	+	0.995384i	$0.469404\pi$
$79$	−7.23536	+	12.5320i	−0.814042	+	1.40996i	−0.910014	+	0.414578i	$0.863929\pi$
$80$	0.399447	−	2.20010i	0.0446595	−	0.245979i
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$	−2.74391	−	0.735227i	−0.303014	−	0.0811923i
$83$	−9.66217	−	9.66217i	−1.06056	−	1.06056i	−0.998044	−	0.0625173i	$-0.980087\pi$
$83$	−9.66217	−	9.66217i	−1.06056	−	1.06056i	−0.0625173	−	0.998044i	$-0.519913\pi$
$84$	−0.716637			−0.0781915
$85$	−2.29019	−	3.30628i	−0.248406	−	0.358616i
$86$	−3.62094	+	2.09055i	−0.390456	+	0.225430i
$87$	−3.29077	+	3.29077i	−0.352808	+	0.352808i
$88$	−0.822385	+	0.822385i	−0.0876665	+	0.0876665i
$89$	−2.91613	−	5.05089i	−0.309109	−	0.535393i	0.669059	−	0.743210i	$-0.266698\pi$
$89$	−2.91613	−	5.05089i	−0.309109	−	0.535393i	−0.978168	+	0.207817i	$0.933364\pi$
$90$	−0.955264	+	2.02175i	−0.100694	+	0.213111i
$91$	−4.28263	+	2.47258i	−0.448941	+	0.259196i
$92$	0.517533	+	1.93146i	0.0539565	+	0.201368i
$93$	0.489351	−	0.131121i	0.0507434	−	0.0135966i
$94$	−1.71294			−0.176676
$95$	−9.74155	+	0.319632i	−0.999462	+	0.0327935i
$96$	1.00000			0.102062
$97$	3.21549	−	0.861589i	0.326484	−	0.0874811i	−0.0918542	−	0.995772i	$-0.529279\pi$
$97$	3.21549	−	0.861589i	0.326484	−	0.0874811i	0.418338	+	0.908291i	$0.362613\pi$
$98$	1.67881	+	6.26541i	0.169586	+	0.632902i
$99$	1.00721	−	0.581514i	0.101229	−	0.0584443i
$100$	1.75765	−	4.68088i	0.175765	−	0.468088i
$101$	−6.35996	−	11.0158i	−0.632840	−	1.09611i	−0.986968	−	0.160914i	$-0.948556\pi$
$101$	−6.35996	−	11.0158i	−0.632840	−	1.09611i	0.354128	−	0.935197i	$-0.384778\pi$
$102$	1.27187	−	1.27187i	0.125934	−	0.125934i
$103$	−3.39294	+	3.39294i	−0.334316	+	0.334316i	−0.854223	−	0.519907i	$-0.825967\pi$
$103$	−3.39294	+	3.39294i	−0.334316	+	0.334316i	0.519907	+	0.854223i	$0.325967\pi$
$104$	5.97601	−	3.45025i	0.585996	−	0.338325i
$105$	−1.57667	−	0.286258i	−0.153868	−	0.0279360i
$106$	−9.96201			−0.967596
$107$	−1.75329	−	1.75329i	−0.169497	−	0.169497i	0.617261	−	0.786758i	$-0.288242\pi$
$107$	−1.75329	−	1.75329i	−0.169497	−	0.169497i	−0.786758	+	0.617261i	$0.788242\pi$
$108$	−0.965926	−	0.258819i	−0.0929463	−	0.0249049i
$109$	2.48478	−	4.30377i	0.237999	−	0.412227i	−0.722141	−	0.691746i	$-0.756842\pi$
$109$	2.48478	−	4.30377i	0.237999	−	0.412227i	0.960140	+	0.279519i	$0.0901751\pi$
$110$	−2.13783	+	1.48083i	−0.203834	+	0.141192i
$111$	2.18296	−	3.78100i	0.207197	−	0.358876i
$112$	0.185479	+	0.692218i	0.0175261	+	0.0654084i
$113$	−8.25488	+	8.25488i	−0.776554	+	0.776554i	−0.979243	−	0.202689i	$-0.935032\pi$
$113$	−8.25488	+	8.25488i	−0.776554	+	0.776554i	0.202689	+	0.979243i	$0.435032\pi$
$114$	−0.918891	−	4.26094i	−0.0860621	−	0.399074i
$115$	0.367109	+	4.45613i	0.0342330	+	0.415536i
$116$	4.03036	+	2.32693i	0.374209	+	0.216050i
$117$	−6.66537	+	1.78598i	−0.616214	+	0.165114i
$118$	3.12950	−	11.6794i	0.288094	−	1.07518i
$119$	1.11631	+	0.644505i	0.102332	+	0.0590816i
$120$	2.20010	+	0.399447i	0.200841	+	0.0364644i
$121$	−9.64737			−0.877033
$122$	10.9706	+	10.9706i	0.993230	+	0.993230i
$123$	0.735227	−	2.74391i	0.0662932	−	0.247410i
$124$	−0.253307	−	0.438740i	−0.0227476	−	0.0394000i
$125$	5.73677	−	9.59633i	0.513112	−	0.858322i
$126$		−	0.716637i		−	0.0638431i
$127$	1.84462	−	6.88422i	0.163684	−	0.610876i	−0.834521	−	0.550976i	$-0.814255\pi$
$127$	1.84462	−	6.88422i	0.163684	−	0.610876i	0.998204	−	0.0598992i	$-0.0190779\pi$
$128$	−0.258819	−	0.965926i	−0.0228766	−	0.0853766i
$129$	−2.09055	−	3.62094i	−0.184063	−	0.318806i
$130$	14.5260	−	5.20380i	1.27402	−	0.456403i
$131$	−3.25534	+	5.63841i	−0.284420	+	0.492630i	−0.972468	−	0.233035i	$-0.925134\pi$
$131$	−3.25534	+	5.63841i	−0.284420	+	0.492630i	0.688048	+	0.725665i	$0.258468\pi$
$132$	−0.822385	−	0.822385i	−0.0715794	−	0.0715794i
$133$	2.77907	−	1.42639i	0.240976	−	0.123684i
$134$		−	7.38919i		−	0.638329i
$135$	−2.02175	−	0.955264i	−0.174004	−	0.0822160i
$136$	−1.55771	−	0.899346i	−0.133573	−	0.0771183i
$137$	−12.4364	−	3.33231i	−1.06251	−	0.284699i	−0.315098	−	0.949059i	$-0.602037\pi$
$137$	−12.4364	−	3.33231i	−1.06251	−	0.284699i	−0.747412	+	0.664361i	$0.768704\pi$
$138$	−1.93146	+	0.517533i	−0.164417	+	0.0440553i
$139$	−7.93847	+	4.58328i	−0.673333	+	0.388749i	−0.797338	−	0.603533i	$-0.793759\pi$
$139$	−7.93847	+	4.58328i	−0.673333	+	0.388749i	0.124006	+	0.992282i	$0.460426\pi$
$140$	0.131569	+	1.59704i	0.0111196	+	0.134974i
$141$		−	1.71294i		−	0.144255i
$142$	−7.36741	−	1.97409i	−0.618259	−	0.165662i
$143$	−7.75201	−	2.07715i	−0.648256	−	0.173700i
$144$			1.00000i			0.0833333i
$145$	7.93771	+	6.72939i	0.659191	+	0.558845i
$146$	−2.36632	+	1.36619i	−0.195838	+	0.113067i
$147$	−6.26541	+	1.67881i	−0.516762	+	0.138466i
$148$	−4.21716	−	1.12998i	−0.346648	−	0.0928841i
$149$	18.3115	+	10.5721i	1.50014	+	0.866103i	1.00000		0.000156177i	$4.97126e-5\pi$
$149$	18.3115	+	10.5721i	1.50014	+	0.866103i	0.500135	+	0.865947i	$0.333284\pi$
$150$	4.68088	+	1.75765i	0.382193	+	0.143511i
$151$			9.48739i			0.772073i	0.922484	+	0.386036i	$0.126156\pi$
$151$			9.48739i			0.772073i	−0.922484	+	0.386036i	$0.873844\pi$
$152$	−3.87793	+	1.99039i	−0.314542	+	0.161442i
$153$	1.27187	+	1.27187i	0.102824	+	0.102824i
$154$	0.416734	−	0.721805i	0.0335814	−	0.0581647i
$155$	−0.382047	−	1.06646i	−0.0306867	−	0.0856598i
$156$	3.45025	+	5.97601i	0.276241	+	0.478464i
$157$	−2.09270	−	7.81006i	−0.167016	−	0.623310i	−0.997775	−	0.0666782i	$-0.978760\pi$
$157$	−2.09270	−	7.81006i	−0.167016	−	0.623310i	0.830759	−	0.556632i	$-0.187907\pi$
$158$	−3.74530	+	13.9776i	−0.297960	+	1.11200i
$159$		−	9.96201i		−	0.790039i
$160$	−0.183592	−	2.22852i	−0.0145142	−	0.176180i
$161$	−0.716491	−	1.24100i	−0.0564674	−	0.0978044i
$162$	0.258819	−	0.965926i	0.0203347	−	0.0758903i
$163$	10.1573	+	10.1573i	0.795583	+	0.795583i	0.982396	−	0.186812i	$-0.0598157\pi$
$163$	10.1573	+	10.1573i	0.795583	+	0.795583i	−0.186812	+	0.982396i	$0.559816\pi$
$164$	−2.84070			−0.221821
$165$	−1.48083	−	2.13783i	−0.115282	−	0.166430i
$166$	−11.8337	−	6.83219i	−0.918473	−	0.530281i
$167$	1.51700	−	5.66153i	0.117389	−	0.438102i	−0.882065	−	0.471127i	$-0.843847\pi$
$167$	1.51700	−	5.66153i	0.117389	−	0.438102i	0.999455	+	0.0330247i	$0.0105140\pi$
$168$	−0.692218	+	0.185479i	−0.0534058	+	0.0143100i
$169$	29.9791	+	17.3085i	2.30609	+	1.33142i
$170$	−3.06788	−	2.60088i	−0.235296	−	0.199478i
$171$	4.26094	−	0.918891i	0.325842	−	0.0702694i
$172$	−2.95649	+	2.95649i	−0.225430	+	0.225430i
$173$	−0.0830357	−	0.309893i	−0.00631309	−	0.0235608i	0.962697	−	0.270580i	$-0.0872155\pi$
$173$	−0.0830357	−	0.309893i	−0.00631309	−	0.0235608i	−0.969011	+	0.247019i	$0.920549\pi$
$174$	−2.32693	+	4.03036i	−0.176404	+	0.305541i
$175$	−0.348468	+	3.56620i	−0.0263417	+	0.269579i
$176$	−0.581514	+	1.00721i	−0.0438332	+	0.0759214i
$177$	11.6794	+	3.12950i	0.877881	+	0.235227i
$178$	−4.12403	−	4.12403i	−0.309109	−	0.309109i
$179$	3.62283			0.270783			0.135392	−	0.990792i	$-0.456771\pi$
$179$	3.62283			0.270783			0.135392	+	0.990792i	$0.456771\pi$
$180$	−0.399447	+	2.20010i	−0.0297730	+	0.163986i
$181$	−17.1565	+	9.90530i	−1.27523	+	0.736255i	−0.975968	−	0.217916i	$-0.930074\pi$
$181$	−17.1565	+	9.90530i	−1.27523	+	0.736255i	−0.299263	+	0.954171i	$0.596741\pi$
$182$	−3.49675	+	3.49675i	−0.259196	+	0.259196i
$183$	−10.9706	+	10.9706i	−0.810969	+	0.810969i
$184$	0.999796	+	1.73170i	0.0737060	+	0.127662i
$185$	−8.82680	−	4.17061i	−0.648959	−	0.306629i
$186$	0.438740	−	0.253307i	0.0321700	−	0.0185734i
$187$	0.541431	+	2.02065i	0.0395933	+	0.147764i
$188$	−1.65457	+	0.443341i	−0.120672	+	0.0323340i
$189$	0.716637			0.0521277
$190$	−9.32689	+	2.83004i	−0.676644	+	0.205313i
$191$	15.4162			1.11547			0.557737	−	0.830018i	$-0.311670\pi$
$191$	15.4162			1.11547			0.557737	+	0.830018i	$0.311670\pi$
$192$	0.965926	−	0.258819i	0.0697097	−	0.0186787i
$193$	−0.951461	−	3.55090i	−0.0684877	−	0.255599i	0.923190	−	0.384343i	$-0.125572\pi$
$193$	−0.951461	−	3.55090i	−0.0684877	−	0.255599i	−0.991678	+	0.128744i	$0.958905\pi$
$194$	2.88293	−	1.66446i	0.206982	−	0.119501i
$195$	5.20380	+	14.5260i	0.372652	+	1.04023i
$196$	3.24322	+	5.61741i	0.231658	+	0.401244i
$197$	18.7320	−	18.7320i	1.33460	−	1.33460i	0.433397	−	0.901203i	$-0.357315\pi$
$197$	18.7320	−	18.7320i	1.33460	−	1.33460i	0.901203	−	0.433397i	$-0.142685\pi$
$198$	0.822385	−	0.822385i	0.0584443	−	0.0584443i
$199$	14.0676	−	8.12191i	0.997223	−	0.575747i	0.0897976	−	0.995960i	$-0.471378\pi$
$199$	14.0676	−	8.12191i	0.997223	−	0.575747i	0.907425	+	0.420213i	$0.138045\pi$
$200$	0.486255	−	4.97630i	0.0343834	−	0.351878i
$201$	7.38919			0.521193
$202$	−8.99435	−	8.99435i	−0.632840	−	0.632840i
$203$	−3.22148	−	0.863194i	−0.226104	−	0.0605843i
$204$	0.899346	−	1.55771i	0.0629668	−	0.109062i
$205$	−6.24982	−	1.13471i	−0.436507	−	0.0792515i
$206$	−2.39917	+	4.15548i	−0.167158	+	0.289526i
$207$	−0.517533	−	1.93146i	−0.0359710	−	0.134246i
$208$	4.87939	−	4.87939i	0.338325	−	0.338325i
$209$	4.82602	+	1.55228i	0.333823	+	0.107373i
$210$	−1.59704	+	0.131569i	−0.110206	+	0.00907909i
$211$	14.1676	+	8.17968i	0.975339	+	0.563112i	0.900860	−	0.434110i	$-0.142937\pi$
$211$	14.1676	+	8.17968i	0.975339	+	0.563112i	0.0744792	+	0.997223i	$0.476271\pi$
$212$	−9.62256	+	2.57836i	−0.660880	+	0.177082i
$213$	1.97409	−	7.36741i	0.135262	−	0.504806i
$214$	−2.14733	−	1.23976i	−0.146788	−	0.0847483i
$215$	−7.68553	+	5.32361i	−0.524149	+	0.363067i
$216$	−1.00000			−0.0680414
$217$	0.256721	+	0.256721i	0.0174273	+	0.0174273i
$218$	1.28622	−	4.80023i	0.0871137	−	0.325113i
$219$	−1.36619	−	2.36632i	−0.0923189	−	0.159901i
$220$	−1.68172	+	1.98368i	−0.113381	+	0.133740i
$221$		−	12.4119i		−	0.834913i
$222$	1.12998	−	4.21716i	0.0758395	−	0.283037i
$223$	6.56480	+	24.5002i	0.439611	+	1.64065i	0.729784	+	0.683678i	$0.239621\pi$
$223$	6.56480	+	24.5002i	0.439611	+	1.64065i	−0.290172	+	0.956974i	$0.593713\pi$
$224$	0.358318	+	0.620626i	0.0239412	+	0.0414673i
$225$	−1.75765	+	4.68088i	−0.117176	+	0.312059i
$226$	−5.83708	+	10.1101i	−0.388277	+	0.672515i
$227$	1.49339	+	1.49339i	0.0991197	+	0.0991197i	0.754928	−	0.655808i	$-0.227672\pi$
$227$	1.49339	+	1.49339i	0.0991197	+	0.0991197i	−0.655808	+	0.754928i	$0.727672\pi$
$228$	−1.99039	−	3.87793i	−0.131817	−	0.256822i
$229$		−	1.75069i		−	0.115689i	−0.998326	−	0.0578443i	$-0.981577\pi$
$229$		−	1.75069i		−	0.115689i	0.998326	−	0.0578443i	$-0.0184227\pi$
$230$	1.50793	+	4.20928i	0.0994300	+	0.277551i
$231$	0.721805	+	0.416734i	0.0474913	+	0.0274191i
$232$	4.49528	+	1.20451i	0.295130	+	0.0790797i
$233$	11.5245	−	3.08798i	0.754995	−	0.202300i	0.139263	−	0.990255i	$-0.455527\pi$
$233$	11.5245	−	3.08798i	0.754995	−	0.202300i	0.615733	+	0.787955i	$0.288860\pi$
$234$	−5.97601	+	3.45025i	−0.390664	+	0.225550i
$235$	−3.81731	+	0.314481i	−0.249014	+	0.0205145i
$236$		−	12.0915i		−	0.787086i
$237$	−13.9776	−	3.74530i	−0.907946	−	0.243283i
$238$	1.24509	+	0.333620i	0.0807070	+	0.0216254i
$239$		−	2.51341i		−	0.162579i	−0.996691	−	0.0812895i	$-0.974096\pi$
$239$		−	2.51341i		−	0.162579i	0.996691	−	0.0812895i	$-0.0259038\pi$
$240$	2.22852	−	0.183592i	0.143850	−	0.0118508i
$241$	−0.816926	+	0.471653i	−0.0526229	+	0.0303818i	−0.526081	−	0.850435i	$-0.676339\pi$
$241$	−0.816926	+	0.471653i	−0.0526229	+	0.0303818i	0.473458	+	0.880817i	$0.343006\pi$
$242$	−9.31864	+	2.49692i	−0.599025	+	0.160508i
$243$	0.965926	+	0.258819i	0.0619642	+	0.0166032i
$244$	13.4362	+	7.75737i	0.860162	+	0.496615i
$245$	4.89154	+	13.6544i	0.312509	+	0.872346i
$246$		−	2.84070i		−	0.181116i
$247$	−25.2744	−	16.3072i	−1.60817	−	1.03760i
$248$	−0.358230	−	0.358230i	−0.0227476	−	0.0227476i
$249$	6.83219	−	11.8337i	0.432972	−	0.749930i
$250$	3.05758	−	10.7541i	0.193378	−	0.680151i
$251$	12.8135	+	22.1936i	0.808780	+	1.40085i	0.913710	+	0.406368i	$0.133205\pi$
$251$	12.8135	+	22.1936i	0.808780	+	1.40085i	−0.104930	+	0.994480i	$0.533462\pi$
$252$	−0.185479	−	0.692218i	−0.0116841	−	0.0436056i
$253$	0.601905	−	2.24634i	0.0378414	−	0.141226i
$254$		−	7.12707i		−	0.447192i
$255$	2.60088	−	3.06788i	0.162873	−	0.192118i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	2.56201	−	9.56155i	0.159814	−	0.596433i	−0.838831	−	0.544392i	$-0.816761\pi$
$257$	2.56201	−	9.56155i	0.159814	−	0.596433i	0.998645	−	0.0520413i	$-0.0165727\pi$
$258$	−2.95649	−	2.95649i	−0.184063	−	0.184063i
$259$	3.12878			0.194413
$260$	12.6842	−	8.78609i	0.786641	−	0.544890i
$261$	−4.03036	−	2.32693i	−0.249473	−	0.144033i
$262$	−1.68509	+	6.28883i	−0.104105	+	0.388525i
$263$	−7.45643	+	1.99794i	−0.459783	+	0.123199i	−0.481273	−	0.876570i	$-0.659826\pi$
$263$	−7.45643	+	1.99794i	−0.459783	+	0.123199i	0.0214902	+	0.999769i	$0.493159\pi$
$264$	−1.00721	−	0.581514i	−0.0619896	−	0.0357897i
$265$	−22.2005	+	1.82894i	−1.36377	+	0.112351i
$266$	2.31520	−	2.09706i	0.141954	−	0.128579i
$267$	4.12403	−	4.12403i	0.252387	−	0.252387i
$268$	−1.91246	−	7.13741i	−0.116822	−	0.435987i
$269$	−5.39137	+	9.33812i	−0.328717	+	0.569355i	−0.982258	−	0.187537i	$-0.939950\pi$
$269$	−5.39137	+	9.33812i	−0.328717	+	0.569355i	0.653540	+	0.756892i	$0.273283\pi$
$270$	−2.20010	−	0.399447i	−0.133894	−	0.0243096i
$271$	7.72789	−	13.3851i	0.469436	−	0.813087i	−0.529953	−	0.848027i	$-0.677791\pi$
$271$	7.72789	−	13.3851i	0.469436	−	0.813087i	0.999389	+	0.0349398i	$0.0111240\pi$
$272$	−1.73740	−	0.465536i	−0.105346	−	0.0282273i
$273$	−3.49675	−	3.49675i	−0.211633	−	0.211633i
$274$	−12.8751			−0.777811
$275$	−4.49232	+	3.69254i	−0.270897	+	0.222669i
$276$	−1.73170	+	0.999796i	−0.104236	+	0.0601807i
$277$	14.6153	−	14.6153i	0.878151	−	0.878151i	−0.115192	−	0.993343i	$-0.536748\pi$
$277$	14.6153	−	14.6153i	0.878151	−	0.878151i	0.993343	+	0.115192i	$0.0367485\pi$
$278$	−6.48174	+	6.48174i	−0.388749	+	0.388749i
$279$	0.253307	+	0.438740i	0.0151651	+	0.0262667i
$280$	0.540429	+	1.50857i	0.0322968	+	0.0901542i
$281$	9.73336	−	5.61956i	0.580643	−	0.335235i	−0.180746	−	0.983530i	$-0.557851\pi$
$281$	9.73336	−	5.61956i	0.580643	−	0.335235i	0.761389	+	0.648295i	$0.224518\pi$
$282$	−0.443341	−	1.65457i	−0.0264006	−	0.0985282i
$283$	11.5031	−	3.08225i	0.683789	−	0.183221i	0.0998307	−	0.995004i	$-0.468170\pi$
$283$	11.5031	−	3.08225i	0.683789	−	0.183221i	0.583958	+	0.811784i	$0.301503\pi$
$284$	−7.62730			−0.452597
$285$	−2.83004	−	9.32689i	−0.167637	−	0.552477i
$286$	−8.02547			−0.474556
$287$	1.96638	−	0.526891i	0.116072	−	0.0311014i
$288$	0.258819	+	0.965926i	0.0152511	+	0.0569177i
$289$	11.9206	−	6.88235i	0.701211	−	0.404844i
$290$	9.40893	+	4.44566i	0.552511	+	0.261058i
$291$	1.66446	+	2.88293i	0.0975725	+	0.169000i
$292$	−1.93209	+	1.93209i	−0.113067	+	0.113067i
$293$	−10.0456	+	10.0456i	−0.586870	+	0.586870i	−0.936782	−	0.349912i	$-0.886211\pi$
$293$	−10.0456	+	10.0456i	−0.586870	+	0.586870i	0.349912	+	0.936782i	$0.386211\pi$
$294$	−5.61741	+	3.24322i	−0.327614	+	0.189148i
$295$	4.82989	−	26.6024i	0.281207	−	1.54885i
$296$	−4.36592			−0.253764
$297$	0.822385	+	0.822385i	0.0477196	+	0.0477196i
$298$	20.4238	+	5.47254i	1.18312	+	0.317016i
$299$	−6.89910	+	11.9496i	−0.398985	+	0.691062i
$300$	4.97630	+	0.486255i	0.287307	+	0.0280739i
$301$	1.49817	−	2.59490i	0.0863529	−	0.149568i
$302$	2.45552	+	9.16412i	0.141299	+	0.527336i
$303$	8.99435	−	8.99435i	0.516712	−	0.516712i
$304$	−3.23064	+	2.92625i	−0.185290	+	0.167832i
$305$	26.4622	+	22.4340i	1.51522	+	1.28457i
$306$	1.55771	+	0.899346i	0.0890485	+	0.0514122i
$307$	−6.76518	+	1.81272i	−0.386109	+	0.103458i	−0.446652	−	0.894708i	$-0.647384\pi$
$307$	−6.76518	+	1.81272i	−0.386109	+	0.103458i	0.0605424	+	0.998166i	$0.480717\pi$
$308$	0.215717	−	0.805068i	0.0122916	−	0.0458730i
$309$	−4.15548	−	2.39917i	−0.236397	−	0.136484i
$310$	−0.645048	−	0.931236i	−0.0366363	−	0.0528906i
$311$	27.2346			1.54433			0.772166	−	0.635421i	$-0.219173\pi$
$311$	27.2346			1.54433			0.772166	+	0.635421i	$0.219173\pi$
$312$	4.87939	+	4.87939i	0.276241	+	0.276241i
$313$	−0.701275	+	2.61719i	−0.0396384	+	0.147932i	−0.982909	−	0.184093i	$-0.941065\pi$
$313$	−0.701275	+	2.61719i	−0.0396384	+	0.147932i	0.943270	+	0.332025i	$0.107732\pi$
$314$	−4.04278	−	7.00231i	−0.228147	−	0.395163i
$315$	−0.131569	−	1.59704i	−0.00741305	−	0.0899829i
$316$			14.4707i			0.814042i
$317$	2.33615	−	8.71862i	0.131211	−	0.489686i	−0.868774	−	0.495209i	$-0.835091\pi$
$317$	2.33615	−	8.71862i	0.131211	−	0.489686i	0.999985	+	0.00552303i	$0.00175804\pi$
$318$	−2.57836	−	9.62256i	−0.144587	−	0.539607i
$319$	−2.70628	−	4.68742i	−0.151523	−	0.262445i
$320$	−0.754119	−	2.10507i	−0.0421565	−	0.117677i
$321$	1.23976	−	2.14733i	0.0691967	−	0.119852i
$322$	−1.01327	−	1.01327i	−0.0564674	−	0.0564674i
$323$	−0.387137	+	7.83075i	−0.0215409	+	0.435715i
$324$		−	1.00000i		−	0.0555556i
$325$	31.4161	−	14.2636i	1.74265	−	0.791203i
$326$	12.4401	+	7.18231i	0.688995	+	0.397792i
$327$	4.80023	+	1.28622i	0.265454	+	0.0711281i
$328$	−2.74391	+	0.735227i	−0.151507	+	0.0405961i
$329$	1.06309	−	0.613777i	0.0586102	−	0.0338386i
$330$	−1.98368	−	1.68172i	−0.109198	−	0.0925754i
$331$			27.2790i			1.49939i	0.661785	+	0.749693i	$0.269799\pi$
$331$			27.2790i			1.49939i	−0.661785	+	0.749693i	$0.730201\pi$
$332$	−13.1988	−	3.53660i	−0.724377	−	0.194096i
$333$	4.21716	+	1.12998i	0.231099	+	0.0619227i
$334$		−	5.86125i		−	0.320713i
$335$	−1.35659	−	16.4669i	−0.0741186	−	0.899685i
$336$	−0.620626	+	0.358318i	−0.0338579	+	0.0195479i
$337$	3.52294	−	0.943968i	0.191907	−	0.0514212i	−0.161586	−	0.986859i	$-0.551661\pi$
$337$	3.52294	−	0.943968i	0.191907	−	0.0514212i	0.353492	+	0.935437i	$0.384994\pi$
$338$	33.4374	+	8.95952i	1.81875	+	0.487334i
$339$	−10.1101	−	5.83708i	−0.549106	−	0.317027i
$340$	−3.63651	−	1.71823i	−0.197217	−	0.0931839i
$341$			0.589205i			0.0319073i
$342$	3.87793	−	1.99039i	0.209694	−	0.107628i
$343$	−6.83410	−	6.83410i	−0.369007	−	0.369007i
$344$	−2.09055	+	3.62094i	−0.112715	+	0.195228i
$345$	−4.20928	+	1.50793i	−0.226620	+	0.0811843i
$346$	−0.160413	−	0.277843i	−0.00862383	−	0.0149369i
$347$	0.199724	+	0.745380i	0.0107217	+	0.0400141i	0.971079	−	0.238756i	$-0.0767398\pi$
$347$	0.199724	+	0.745380i	0.0107217	+	0.0400141i	−0.960358	+	0.278771i	$0.910073\pi$
$348$	−1.20451	+	4.49528i	−0.0645683	+	0.240972i
$349$			4.58648i			0.245509i	0.992437	+	0.122754i	$0.0391727\pi$
$349$			4.58648i			0.245509i	−0.992437	+	0.122754i	$0.960827\pi$
$350$	0.586406	+	3.53487i	0.0313447	+	0.188947i
$351$	−3.45025	−	5.97601i	−0.184161	−	0.318976i
$352$	−0.301014	+	1.12340i	−0.0160441	+	0.0598773i
$353$	−20.5803	−	20.5803i	−1.09538	−	1.09538i	−0.994944	−	0.100434i	$-0.967977\pi$
$353$	−20.5803	−	20.5803i	−1.09538	−	1.09538i	−0.100434	−	0.994944i	$-0.532023\pi$
$354$	12.0915			0.642653
$355$	−16.7808	−	3.04670i	−0.890634	−	0.161702i
$356$	−5.05089	−	2.91613i	−0.267696	−	0.154555i
$357$	−0.333620	+	1.24509i	−0.0176570	+	0.0658970i
$358$	3.49939	−	0.937659i	0.184948	−	0.0495568i
$359$	21.2739	+	12.2825i	1.12280	+	0.648247i	0.942113	−	0.335295i	$-0.108836\pi$
$359$	21.2739	+	12.2825i	1.12280	+	0.648247i	0.180683	+	0.983541i	$0.442169\pi$
$360$	0.183592	+	2.22852i	0.00967613	+	0.117453i
$361$	15.4372	+	11.0767i	0.812485	+	0.582982i
$362$	−14.0082	+	14.0082i	−0.736255	+	0.736255i
$363$	−2.49692	−	9.31864i	−0.131054	−	0.489102i
$364$	−2.47258	+	4.28263i	−0.129598	+	0.224471i
$365$	−5.02256	+	3.47903i	−0.262893	+	0.182101i
$366$	−7.75737	+	13.4362i	−0.405484	+	0.702319i
$367$	3.28723	+	0.880812i	0.171592	+	0.0459780i	0.343592	−	0.939119i	$-0.388356\pi$
$367$	3.28723	+	0.880812i	0.171592	+	0.0459780i	−0.172000	+	0.985097i	$0.555023\pi$
$368$	1.41393	+	1.41393i	0.0737060	+	0.0737060i
$369$	2.84070			0.147881
$370$	−9.60546	−	1.74395i	−0.499364	−	0.0906639i
$371$	6.18268	−	3.56957i	0.320989	−	0.185323i
$372$	0.358230	−	0.358230i	0.0185734	−	0.0185734i
$373$	22.3523	−	22.3523i	1.15736	−	1.15736i	0.172314	−	0.985042i	$-0.444876\pi$
$373$	22.3523	−	22.3523i	1.15736	−	1.15736i	0.985042	−	0.172314i	$-0.0551245\pi$
$374$	1.04596	+	1.81166i	0.0540855	+	0.0936789i
$375$	10.7541	+	3.05758i	0.555341	+	0.157893i
$376$	−1.48345	+	0.856469i	−0.0765030	+	0.0441690i
$377$	8.31170	+	31.0197i	0.428074	+	1.59759i
$378$	0.692218	−	0.185479i	0.0356038	−	0.00954002i
$379$	−23.2523			−1.19439			−0.597196	−	0.802095i	$-0.703719\pi$
$379$	−23.2523			−1.19439			−0.597196	+	0.802095i	$0.703719\pi$
$380$	−8.27662	+	5.14759i	−0.424581	+	0.264066i
$381$	7.12707			0.365131
$382$	14.8909	−	3.99000i	0.761883	−	0.204146i
$383$	4.26174	+	15.9050i	0.217765	+	0.812709i	0.985175	+	0.171553i	$0.0548784\pi$
$383$	4.26174	+	15.9050i	0.217765	+	0.812709i	−0.767410	+	0.641156i	$0.778455\pi$
$384$	0.866025	−	0.500000i	0.0441942	−	0.0255155i
$385$	0.796182	−	1.68506i	0.0405772	−	0.0858788i
$386$	−1.83808	−	3.18365i	−0.0935559	−	0.162044i
$387$	2.95649	−	2.95649i	0.150287	−	0.150287i
$388$	2.35390	−	2.35390i	0.119501	−	0.119501i
$389$	−29.8179	+	17.2154i	−1.51183	+	0.872854i	−0.511923	+	0.859031i	$0.671067\pi$
$389$	−29.8179	+	17.2154i	−1.51183	+	0.872854i	−0.999904	+	0.0138227i	$0.995600\pi$
$390$	8.78609	+	12.6842i	0.444901	+	0.642290i
$391$	3.59665			0.181891
$392$	4.58660	+	4.58660i	0.231658	+	0.231658i
$393$	−6.28883	−	1.68509i	−0.317229	−	0.0850013i
$394$	13.2455	−	22.9419i	0.667300	−	1.15580i
$395$	−5.78029	+	31.8370i	−0.290838	+	1.60190i
$396$	0.581514	−	1.00721i	0.0292222	−	0.0506143i
$397$	8.56444	+	31.9629i	0.429837	+	1.60417i	0.753128	+	0.657874i	$0.228544\pi$
$397$	8.56444	+	31.9629i	0.429837	+	1.60417i	−0.323291	+	0.946300i	$0.604789\pi$
$398$	11.4861	−	11.4861i	0.575747	−	0.575747i
$399$	2.09706	+	2.31520i	0.104984	+	0.115905i
$400$	−0.818275	−	4.93259i	−0.0409137	−	0.246629i
$401$	−29.8364	−	17.2260i	−1.48996	−	0.860227i	−0.490024	−	0.871709i	$-0.663012\pi$
$401$	−29.8364	−	17.2260i	−1.48996	−	0.860227i	−0.999934	+	0.0114818i	$0.996345\pi$
$402$	7.13741	−	1.91246i	0.355982	−	0.0953850i
$403$	0.904802	−	3.37677i	0.0450714	−	0.168209i
$404$	−11.0158	−	6.35996i	−0.548056	−	0.316420i
$405$	0.399447	−	2.20010i	0.0198487	−	0.109324i
$406$	−3.33512			−0.165519
$407$	3.59047	+	3.59047i	0.177973	+	0.177973i
$408$	0.465536	−	1.73740i	0.0230475	−	0.0860143i
$409$	11.5996	+	20.0910i	0.573561	+	0.993437i	0.996196	+	0.0871373i	$0.0277719\pi$
$409$	11.5996	+	20.0910i	0.573561	+	0.993437i	−0.422635	+	0.906300i	$0.638895\pi$
$410$	−6.33055	+	0.521529i	−0.312644	+	0.0257565i
$411$		−	12.8751i		−	0.635080i
$412$	−1.24190	+	4.63484i	−0.0611841	+	0.228342i
$413$	2.24271	+	8.36992i	0.110357	+	0.411857i
$414$	−0.999796	−	1.73170i	−0.0491373	−	0.0851083i
$415$	−27.6259	−	13.0531i	−1.35610	−	0.640751i
$416$	3.45025	−	5.97601i	0.169162	−	0.292998i
$417$	−6.48174	−	6.48174i	−0.317412	−	0.317412i
$418$	5.06333	+	0.250321i	0.247656	+	0.0122436i
$419$			29.8216i			1.45688i	0.685110	+	0.728440i	$0.259754\pi$
$419$			29.8216i			1.45688i	−0.685110	+	0.728440i	$0.740246\pi$
$420$	−1.50857	+	0.540429i	−0.0736106	+	0.0263703i
$421$	−21.9937	−	12.6981i	−1.07191	−	0.618866i	−0.143205	−	0.989693i	$-0.545741\pi$
$421$	−21.9937	−	12.6981i	−1.07191	−	0.618866i	−0.928702	+	0.370827i	$0.879074\pi$
$422$	15.8019	+	4.23411i	0.769226	+	0.206113i
$423$	1.65457	−	0.443341i	0.0804480	−	0.0215560i
$424$	−8.62736	+	4.98101i	−0.418981	+	0.241899i
$425$	−7.31434	−	5.23286i	−0.354797	−	0.253831i
$426$		−	7.62730i		−	0.369544i
$427$	−10.7396	−	2.87766i	−0.519725	−	0.139260i
$428$	−2.39503	−	0.641748i	−0.115768	−	0.0310200i
$429$		−	8.02547i		−	0.387473i
$430$	−6.04580	+	7.13137i	−0.291554	+	0.343905i
$431$	11.8940	−	6.86700i	0.572913	−	0.330772i	−0.185399	−	0.982663i	$-0.559358\pi$
$431$	11.8940	−	6.86700i	0.572913	−	0.330772i	0.758312	+	0.651892i	$0.226024\pi$
$432$	−0.965926	+	0.258819i	−0.0464731	+	0.0124524i
$433$	32.4368	+	8.69142i	1.55881	+	0.417683i	0.932288	−	0.361717i	$-0.117810\pi$
$433$	32.4368	+	8.69142i	1.55881	+	0.417683i	0.626526	+	0.779400i	$0.284476\pi$
$434$	0.314417	+	0.181529i	0.0150925	+	0.00871367i
$435$	−4.44566	+	9.40893i	−0.213153	+	0.451124i
$436$		−	4.96957i		−	0.237999i
$437$	4.72541	−	7.32390i	0.226047	−	0.350350i
$438$	−1.93209	−	1.93209i	−0.0923189	−	0.0923189i
$439$	15.1805	−	26.2934i	0.724525	−	1.25491i	−0.234645	−	0.972081i	$-0.575393\pi$
$439$	15.1805	−	26.2934i	0.724525	−	1.25491i	0.959169	−	0.282832i	$-0.0912740\pi$
$440$	−1.11100	+	2.35135i	−0.0529648	+	0.112096i
$441$	−3.24322	−	5.61741i	−0.154439	−	0.267496i
$442$	−3.21243	−	11.9890i	−0.152800	−	0.570256i
$443$	4.06678	−	15.1774i	0.193219	−	0.721102i	−0.799502	−	0.600663i	$-0.794903\pi$
$443$	4.06678	−	15.1774i	0.193219	−	0.721102i	0.992721	−	0.120439i	$-0.0384301\pi$
$444$		−	4.36592i		−	0.207197i
$445$	−9.94762	−	8.43334i	−0.471562	−	0.399779i
$446$	12.6822	+	21.9662i	0.600520	+	1.04013i
$447$	−5.47254	+	20.4238i	−0.258842	+	0.966013i
$448$	0.506739	+	0.506739i	0.0239412	+	0.0239412i
$449$	2.51757			0.118811			0.0594057	−	0.998234i	$-0.481079\pi$
$449$	2.51757			0.118811			0.0594057	+	0.998234i	$0.481079\pi$
$450$	−0.486255	+	4.97630i	−0.0229223	+	0.234585i
$451$	2.86118	+	1.65191i	0.134728	+	0.0777852i
$452$	−3.02150	+	11.2764i	−0.142119	+	0.530396i
$453$	−9.16412	+	2.45552i	−0.430568	+	0.115370i
$454$	1.82902	+	1.05599i	0.0858402	+	0.0495598i
$455$	−7.15060	+	8.43455i	−0.335225	+	0.395418i
$456$	−2.92625	−	3.23064i	−0.137034	−	0.151289i
$457$	10.8302	−	10.8302i	0.506617	−	0.506617i	−0.406869	−	0.913486i	$-0.633380\pi$
$457$	10.8302	−	10.8302i	0.506617	−	0.506617i	0.913486	+	0.406869i	$0.133380\pi$
$458$	−0.453111	−	1.69103i	−0.0211725	−	0.0790168i
$459$	−0.899346	+	1.55771i	−0.0419779	+	0.0727078i
$460$	2.54599	+	3.67557i	0.118707	+	0.171374i
$461$	−2.89224	+	5.00951i	−0.134705	+	0.233316i	−0.925485	−	0.378785i	$-0.876342\pi$
$461$	−2.89224	+	5.00951i	−0.134705	+	0.233316i	0.790780	+	0.612101i	$0.209675\pi$
$462$	0.805068	+	0.215717i	0.0374552	+	0.0100361i
$463$	−22.3482	−	22.3482i	−1.03861	−	1.03861i	−0.999224	−	0.0393865i	$-0.987460\pi$
$463$	−22.3482	−	22.3482i	−1.03861	−	1.03861i	−0.0393865	−	0.999224i	$-0.512540\pi$
$464$	4.65386			0.216050
$465$	0.931236	−	0.645048i	0.0431850	−	0.0299134i
$466$	10.3326	−	5.96552i	0.478648	−	0.276347i
$467$	−14.0839	+	14.0839i	−0.651724	+	0.651724i	−0.953408	−	0.301684i	$-0.902451\pi$
$467$	−14.0839	+	14.0839i	−0.651724	+	0.651724i	0.301684	+	0.953408i	$0.402451\pi$
$468$	−4.87939	+	4.87939i	−0.225550	+	0.225550i
$469$	2.64768	+	4.58592i	0.122259	+	0.211758i
$470$	−3.60585	+	1.29176i	−0.166325	+	0.0595844i
$471$	7.00231	−	4.04278i	0.322649	−	0.186282i
$472$	−3.12950	−	11.6794i	−0.144047	−	0.537590i
$473$	4.69705	−	1.25857i	0.215970	−	0.0578691i
$474$	−14.4707			−0.664662
$475$	−20.2656	+	8.01913i	−0.929848	+	0.367943i
$476$	1.28901			0.0590816
$477$	9.62256	−	2.57836i	0.440587	−	0.118055i
$478$	−0.650519	−	2.42777i	−0.0297540	−	0.111044i
$479$	14.8156	−	8.55377i	0.676941	−	0.390832i	−0.121761	−	0.992559i	$-0.538854\pi$
$479$	14.8156	−	8.55377i	0.676941	−	0.390832i	0.798701	+	0.601728i	$0.205521\pi$
$480$	2.10507	−	0.754119i	0.0960827	−	0.0344207i
$481$	−15.0635	−	26.0908i	−0.686837	−	1.18964i
$482$	−0.667018	+	0.667018i	−0.0303818	+	0.0303818i
$483$	1.01327	−	1.01327i	0.0461054	−	0.0461054i
$484$	−8.35487	+	4.82368i	−0.379767	+	0.219258i
$485$	6.11909	−	4.23857i	0.277853	−	0.192463i
$486$	1.00000			0.0453609
$487$	−1.05807	−	1.05807i	−0.0479455	−	0.0479455i	0.682728	−	0.730673i	$-0.260794\pi$
$487$	−1.05807	−	1.05807i	−0.0479455	−	0.0479455i	−0.730673	+	0.682728i	$0.760794\pi$
$488$	14.9861	+	4.01551i	0.678388	+	0.181774i
$489$	−7.18231	+	12.4401i	−0.324795	+	0.562562i
$490$	8.25888	+	11.9231i	0.373098	+	0.538630i
$491$	−8.42097	+	14.5855i	−0.380033	+	0.658237i	−0.991067	−	0.133368i	$-0.957421\pi$
$491$	−8.42097	+	14.5855i	−0.380033	+	0.658237i	0.611033	+	0.791605i	$0.290754\pi$
$492$	−0.735227	−	2.74391i	−0.0331466	−	0.123705i
$493$	5.91909	−	5.91909i	0.266582	−	0.266582i
$494$	−28.6338	−	9.21002i	−1.28830	−	0.414378i
$495$	1.68172	−	1.98368i	0.0755875	−	0.0891599i
$496$	−0.438740	−	0.253307i	−0.0197000	−	0.0113738i
$497$	5.27975	−	1.41471i	0.236829	−	0.0634582i
$498$	3.53660	−	13.1988i	0.158479	−	0.591451i
$499$	10.5304	+	6.07974i	0.471406	+	0.272166i	0.716828	−	0.697250i	$-0.245593\pi$
$499$	10.5304	+	6.07974i	0.471406	+	0.272166i	−0.245422	+	0.969416i	$0.578927\pi$
$500$	0.170021	−	11.1790i	0.00760358	−	0.499942i
$501$	5.86125			0.261861
$502$	18.1210	+	18.1210i	0.808780	+	0.808780i
$503$	−4.92766	+	18.3903i	−0.219714	+	0.819983i	0.764740	+	0.644339i	$0.222867\pi$
$503$	−4.92766	+	18.3903i	−0.219714	+	0.819983i	−0.984454	+	0.175644i	$0.943799\pi$
$504$	−0.358318	−	0.620626i	−0.0159608	−	0.0276449i
$505$	−21.6954	−	18.3928i	−0.965431	−	0.818468i
$506$		−	2.32558i		−	0.103385i
$507$	−8.95952	+	33.4374i	−0.397906	+	1.48501i
$508$	−1.84462	−	6.88422i	−0.0818418	−	0.305438i
$509$	2.68395	+	4.64874i	0.118964	+	0.206052i	0.919357	−	0.393423i	$-0.128709\pi$
$509$	2.68395	+	4.64874i	0.118964	+	0.206052i	−0.800393	+	0.599475i	$0.795376\pi$
$510$	1.71823	−	3.63651i	0.0760843	−	0.161027i
$511$	0.979065	−	1.69579i	0.0433113	−	0.0750174i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	1.99039	+	3.87793i	0.0878780	+	0.171215i
$514$		−	9.89884i		−	0.436619i
$515$	−4.58368	+	9.70104i	−0.201981	+	0.427479i
$516$	−3.62094	−	2.09055i	−0.159403	−	0.0920314i
$517$	1.92431	+	0.515617i	0.0846311	+	0.0226768i
$518$	3.02217	−	0.809788i	0.132786	−	0.0355800i
$519$	0.277843	−	0.160413i	0.0121959	−	0.00704133i
$520$	9.97800	−	11.7696i	0.437564	−	0.516132i
$521$			10.8275i			0.474360i	0.971466	+	0.237180i	$0.0762231\pi$
$521$			10.8275i			0.474360i	−0.971466	+	0.237180i	$0.923777\pi$
$522$	−4.49528	−	1.20451i	−0.196753	−	0.0527198i
$523$	−40.9650	−	10.9765i	−1.79128	−	0.479971i	−0.798714	−	0.601711i	$-0.794486\pi$
$523$	−40.9650	−	10.9765i	−1.79128	−	0.479971i	−0.992562	+	0.121740i	$0.961153\pi$
$524$			6.51067i			0.284420i
$525$	−3.53487	+	0.586406i	−0.154275	+	0.0255928i
$526$	−6.68525	+	3.85973i	−0.291491	+	0.168292i
$527$	−0.880192	+	0.235847i	−0.0383418	+	0.0102736i
$528$	−1.12340	−	0.301014i	−0.0488896	−	0.0130999i
$529$	16.4559	+	9.50081i	0.715474	+	0.413079i
$530$	−20.9707	+	7.51254i	−0.910909	+	0.326324i
$531$			12.0915i			0.524724i
$532$	1.69355	−	2.62482i	0.0734246	−	0.113800i
$533$	−13.8609	−	13.8609i	−0.600382	−	0.600382i
$534$	2.91613	−	5.05089i	0.126193	−	0.218573i
$535$	−5.01297	−	2.36860i	−0.216730	−	0.102403i
$536$	−3.69460	−	6.39923i	−0.159582	−	0.276405i
$537$	0.937659	+	3.49939i	0.0404630	+	0.151010i
$538$	−2.79078	+	10.4153i	−0.120319	+	0.449036i
$539$		−	7.54390i		−	0.324939i
$540$	−2.22852	+	0.183592i	−0.0959002	+	0.00790053i
$541$	−14.1458	−	24.5013i	−0.608177	−	1.05339i	−0.991541	−	0.129795i	$-0.958568\pi$
$541$	−14.1458	−	24.5013i	−0.608177	−	1.05339i	0.383364	−	0.923597i	$-0.374765\pi$
$542$	4.00025	−	14.9291i	0.171825	−	0.641261i
$543$	−14.0082	−	14.0082i	−0.601150	−	0.601150i
$544$	−1.79869			−0.0771183
$545$	1.98508	−	10.9335i	0.0850315	−	0.468342i
$546$	−4.28263	−	2.47258i	−0.183280	−	0.105817i
$547$	0.334874	−	1.24977i	0.0143182	−	0.0534361i	−0.958397	−	0.285438i	$-0.907861\pi$
$547$	0.334874	−	1.24977i	0.0143182	−	0.0534361i	0.972715	+	0.232002i	$0.0745276\pi$
$548$	−12.4364	+	3.33231i	−0.531255	+	0.142349i
$549$	−13.4362	−	7.75737i	−0.573441	−	0.331077i
$550$	−3.38355	+	4.72942i	−0.144275	+	0.201663i
$551$	−4.27639	−	19.8298i	−0.182180	−	0.844779i
$552$	−1.41393	+	1.41393i	−0.0601807	+	0.0601807i
$553$	−2.68402	−	10.0169i	−0.114136	−	0.425962i
$554$	10.3346	−	17.9001i	0.439075	−	0.760501i
$555$	1.74395	−	9.60546i	0.0740267	−	0.407729i
$556$	−4.58328	+	7.93847i	−0.194374	+	0.336666i
$557$	14.2400	+	3.81561i	0.603370	+	0.161673i	0.547557	−	0.836769i	$-0.315558\pi$
$557$	14.2400	+	3.81561i	0.603370	+	0.161673i	0.0558135	+	0.998441i	$0.482225\pi$
$558$	0.358230	+	0.358230i	0.0151651	+	0.0151651i
$559$	−28.8517			−1.22030
$560$	0.912461	+	1.31729i	0.0385585	+	0.0556657i
$561$	−1.81166	+	1.04596i	−0.0764885	+	0.0441606i
$562$	7.94725	−	7.94725i	0.335235	−	0.335235i
$563$	−6.77882	+	6.77882i	−0.285693	+	0.285693i	−0.835374	−	0.549681i	$-0.814749\pi$
$563$	−6.77882	+	6.77882i	−0.285693	+	0.285693i	0.549681	+	0.835374i	$0.314749\pi$
$564$	−0.856469	−	1.48345i	−0.0360638	−	0.0624644i
$565$	−11.1519	+	23.6022i	−0.469164	+	0.992953i
$566$	10.3134	−	5.95445i	0.433505	−	0.250284i
$567$	0.185479	+	0.692218i	0.00778940	+	0.0290704i
$568$	−7.36741	+	1.97409i	−0.309130	+	0.0828310i
$569$	−24.8789			−1.04298			−0.521489	−	0.853258i	$-0.674623\pi$
$569$	−24.8789			−1.04298			−0.521489	+	0.853258i	$0.674623\pi$
$570$	−5.14759	−	8.27662i	−0.215609	−	0.346669i
$571$	−18.7712			−0.785549			−0.392775	−	0.919635i	$-0.628485\pi$
$571$	−18.7712			−0.785549			−0.392775	+	0.919635i	$0.628485\pi$
$572$	−7.75201	+	2.07715i	−0.324128	+	0.0868498i
$573$	3.99000	+	14.8909i	0.166685	+	0.622075i
$574$	1.76301	−	1.01787i	0.0735867	−	0.0424853i
$575$	4.13324	+	9.10360i	0.172368	+	0.379647i
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$	13.3497	−	13.3497i	0.555756	−	0.555756i	−0.372341	−	0.928096i	$-0.621445\pi$
$577$	13.3497	−	13.3497i	0.555756	−	0.555756i	0.928096	+	0.372341i	$0.121445\pi$
$578$	9.73312	−	9.73312i	0.404844	−	0.404844i
$579$	3.18365	−	1.83808i	0.132308	−	0.0763881i
$580$	10.2389	+	1.85897i	0.425149	+	0.0771895i
$581$	9.79239			0.406257
$582$	2.35390	+	2.35390i	0.0975725	+	0.0975725i
$583$	11.1913	+	2.99870i	0.463497	+	0.124194i
$584$	−1.36619	+	2.36632i	−0.0565335	+	0.0979189i
$585$	−12.6842	+	8.78609i	−0.524428	+	0.363260i
$586$	−7.10331	+	12.3033i	−0.293435	+	0.508244i
$587$	9.64425	+	35.9928i	0.398061	+	1.48558i	0.816504	+	0.577340i	$0.195909\pi$
$587$	9.64425	+	35.9928i	0.398061	+	1.48558i	−0.418443	+	0.908243i	$0.637424\pi$
$588$	−4.58660	+	4.58660i	−0.189148	+	0.189148i
$589$	−0.676171	+	2.10221i	−0.0278612	+	0.0866200i
$590$	−2.21989	−	26.9460i	−0.0913914	−	1.10935i
$591$	22.9419	+	13.2455i	0.943705	+	0.544848i
$592$	−4.21716	+	1.12998i	−0.173324	+	0.0464420i
$593$	0.517306	−	1.93061i	0.0212432	−	0.0792808i	−0.954490	−	0.298241i	$-0.903600\pi$
$593$	0.517306	−	1.93061i	0.0212432	−	0.0792808i	0.975734	+	0.218961i	$0.0702666\pi$
$594$	1.00721	+	0.581514i	0.0413264	+	0.0238598i
$595$	2.83595	+	0.514891i	0.116263	+	0.0211085i
$596$	21.1443			0.866103
$597$	11.4861	+	11.4861i	0.470095	+	0.470095i
$598$	−3.57124	+	13.3280i	−0.146039	+	0.545024i
$599$	−22.4206	−	38.8337i	−0.916083	−	1.58670i	−0.805308	−	0.592856i	$-0.798000\pi$
$599$	−22.4206	−	38.8337i	−0.916083	−	1.58670i	−0.110774	−	0.993846i	$-0.535333\pi$
$600$	4.93259	−	0.818275i	0.201372	−	0.0334059i
$601$			27.0157i			1.10199i	0.834507	+	0.550997i	$0.185752\pi$
$601$			27.0157i			1.10199i	−0.834507	+	0.550997i	$0.814248\pi$
$602$	0.775508	−	2.89424i	0.0316074	−	0.117960i
$603$	1.91246	+	7.13741i	0.0778815	+	0.290658i
$604$	4.74370	+	8.21632i	0.193018	+	0.334317i
$605$	−20.3083	+	7.27526i	−0.825652	+	0.295781i
$606$	6.35996	−	11.0158i	0.258356	−	0.447486i
$607$	−19.8415	−	19.8415i	−0.805342	−	0.805342i	0.178583	−	0.983925i	$-0.442849\pi$
$607$	−19.8415	−	19.8415i	−0.805342	−	0.805342i	−0.983925	+	0.178583i	$0.942849\pi$
$608$	−2.36319	+	3.66270i	−0.0958399	+	0.148542i
$609$		−	3.33512i		−	0.135146i
$610$	31.3669	+	14.8207i	1.27001	+	0.600072i
$611$	−10.2365	−	5.91006i	−0.414126	−	0.239096i
$612$	1.73740	+	0.465536i	0.0702304	+	0.0188182i
$613$	5.05085	−	1.35337i	0.204002	−	0.0546622i	−0.155371	−	0.987856i	$-0.549657\pi$
$613$	5.05085	−	1.35337i	0.204002	−	0.0546622i	0.359373	+	0.933194i	$0.382991\pi$
$614$	−6.06549	+	3.50191i	−0.244783	+	0.141326i
$615$	−0.521529	−	6.33055i	−0.0210301	−	0.255272i
$616$		−	0.833468i		−	0.0335814i
$617$	−3.79737	−	1.01750i	−0.152877	−	0.0409631i	0.181569	−	0.983378i	$-0.441882\pi$
$617$	−3.79737	−	1.01750i	−0.152877	−	0.0409631i	−0.334446	+	0.942415i	$0.608549\pi$
$618$	−4.63484	−	1.24190i	−0.186441	−	0.0499566i
$619$		−	29.8832i		−	1.20111i	−0.799584	−	0.600554i	$-0.794947\pi$
$619$		−	29.8832i		−	1.20111i	0.799584	−	0.600554i	$-0.205053\pi$
$620$	−0.864090	−	0.732554i	−0.0347027	−	0.0294201i
$621$	1.73170	−	0.999796i	0.0694906	−	0.0401204i
$622$	26.3066	−	7.04883i	1.05480	−	0.282632i
$623$	4.03720	+	1.08176i	0.161747	+	0.0433399i
$624$	5.97601	+	3.45025i	0.239232	+	0.138121i
$625$	4.83950	−	24.5271i	0.193580	−	0.981084i
$626$			2.70952i			0.108294i
$627$	−0.250321	+	5.06333i	−0.00999687	+	0.202210i
$628$	−5.71736	−	5.71736i	−0.228147	−	0.228147i
$629$	−3.92647	+	6.80085i	−0.156559	+	0.271168i
$630$	−0.540429	−	1.50857i	−0.0215312	−	0.0601028i
$631$	−16.1782	−	28.0214i	−0.644043	−	1.11551i	−0.984522	−	0.175263i	$-0.943923\pi$
$631$	−16.1782	−	28.0214i	−0.644043	−	1.11551i	0.340479	−	0.940252i	$-0.389411\pi$
$632$	3.74530	+	13.9776i	0.148980	+	0.556001i
$633$	−4.23411	+	15.8019i	−0.168291	+	0.628070i
$634$		−	9.02618i		−	0.358475i
$635$	−1.30847	−	15.8828i	−0.0519251	−	0.630290i
$636$	−4.98101	−	8.62736i	−0.197510	−	0.342097i
$637$	−11.5846	+	43.2345i	−0.459000	+	1.71301i
$638$	−3.82726	−	3.82726i	−0.151523	−	0.151523i
$639$	7.62730			0.301731
$640$	−1.27325	−	1.83816i	−0.0503298	−	0.0726596i
$641$	−23.6061	−	13.6290i	−0.932385	−	0.538313i	−0.0448198	−	0.998995i	$-0.514271\pi$
$641$	−23.6061	−	13.6290i	−0.932385	−	0.538313i	−0.887565	+	0.460682i	$0.847605\pi$
$642$	0.641748	−	2.39503i	0.0253278	−	0.0945245i
$643$	30.7109	−	8.22895i	1.21112	−	0.324518i	0.403918	−	0.914795i	$-0.367648\pi$
$643$	30.7109	−	8.22895i	1.21112	−	0.324518i	0.807201	+	0.590277i	$0.200982\pi$
$644$	−1.24100	−	0.716491i	−0.0489022	−	0.0282337i
$645$	−7.13137	−	6.04580i	−0.280798	−	0.238053i
$646$	1.65280	+	7.66413i	0.0650287	+	0.301541i
$647$	−20.6263	+	20.6263i	−0.810902	+	0.810902i	−0.984769	−	0.173867i	$-0.944374\pi$
$647$	−20.6263	+	20.6263i	−0.810902	+	0.810902i	0.173867	+	0.984769i	$0.444374\pi$
$648$	−0.258819	−	0.965926i	−0.0101674	−	0.0379452i
$649$	−7.03134	+	12.1786i	−0.276004	+	0.478054i
$650$	26.6539	−	21.9087i	1.04545	−	0.859329i
$651$	−0.181529	+	0.314417i	−0.00711468	+	0.0123230i
$652$	13.8752	+	3.71784i	0.543393	+	0.145602i
$653$	12.2710	+	12.2710i	0.480202	+	0.480202i	0.905196	−	0.424994i	$-0.139724\pi$
$653$	12.2710	+	12.2710i	0.480202	+	0.480202i	−0.424994	+	0.905196i	$0.639724\pi$
$654$	4.96957			0.194325
$655$	−2.60067	+	14.3241i	−0.101617	+	0.559690i
$656$	−2.46012	+	1.42035i	−0.0960515	+	0.0554553i
$657$	1.93209	−	1.93209i	0.0753780	−	0.0753780i
$658$	0.868012	−	0.868012i	0.0338386	−	0.0338386i
$659$	−17.8909	−	30.9879i	−0.696929	−	1.20712i	−0.969526	−	0.244988i	$-0.921216\pi$
$659$	−17.8909	−	30.9879i	−0.696929	−	1.20712i	0.272597	−	0.962128i	$-0.412117\pi$
$660$	−2.35135	−	1.11100i	−0.0915262	−	0.0432455i
$661$	−37.5816	+	21.6978i	−1.46176	+	0.843945i	−0.999093	−	0.0425892i	$-0.986439\pi$
$661$	−37.5816	+	21.6978i	−1.46176	+	0.843945i	−0.462663	+	0.886534i	$0.653106\pi$
$662$	7.06031	+	26.3494i	0.274407	+	1.02410i
$663$	11.9890	−	3.21243i	0.465612	−	0.124760i
$664$	−13.6644			−0.530281
$665$	4.77445	−	5.09839i	0.185145	−	0.197707i
$666$	4.36592			0.169176
$667$	−8.98873	+	2.40852i	−0.348045	+	0.0932584i
$668$	−1.51700	−	5.66153i	−0.0586946	−	0.219051i
$669$	−21.9662	+	12.6822i	−0.849264	+	0.490323i
$670$	−5.57233	−	15.5547i	−0.215278	−	0.600932i
$671$	−9.02203	−	15.6266i	−0.348292	−	0.603259i
$672$	−0.506739	+	0.506739i	−0.0195479	+	0.0195479i
$673$	1.23703	−	1.23703i	0.0476841	−	0.0476841i	−0.682863	−	0.730547i	$-0.739265\pi$
$673$	1.23703	−	1.23703i	0.0476841	−	0.0476841i	0.730547	+	0.682863i	$0.239265\pi$
$674$	3.15858	−	1.82361i	0.121664	−	0.0702427i
$675$	−4.97630	−	0.486255i	−0.191538	−	0.0187160i
$676$	34.6169			1.33142
$677$	−20.7047	−	20.7047i	−0.795745	−	0.795745i	0.186676	−	0.982421i	$-0.440228\pi$
$677$	−20.7047	−	20.7047i	−0.795745	−	0.795745i	−0.982421	+	0.186676i	$0.940228\pi$
$678$	−11.2764	−	3.02150i	−0.433067	−	0.116040i
$679$	−1.19281	+	2.06602i	−0.0457760	+	0.0792864i
$680$	−3.95730	−	0.718482i	−0.151756	−	0.0275525i
$681$	−1.05599	+	1.82902i	−0.0404654	+	0.0700882i
$682$	0.152498	+	0.569129i	0.00583943	+	0.0217931i
$683$	32.9417	−	32.9417i	1.26048	−	1.26048i	0.309617	−	0.950861i	$-0.399799\pi$
$683$	32.9417	−	32.9417i	1.26048	−	1.26048i	0.950861	−	0.309617i	$-0.100201\pi$
$684$	3.23064	−	2.92625i	0.123527	−	0.111888i
$685$	−28.6923	+	2.36375i	−1.09628	+	0.0903144i
$686$	−8.37003	−	4.83244i	−0.319569	−	0.184503i
$687$	1.69103	−	0.453111i	0.0645169	−	0.0172873i
$688$	−1.08215	+	4.03864i	−0.0412566	+	0.153972i
$689$	−59.5331	−	34.3714i	−2.26803	−	1.30945i
$690$	−3.67557	+	2.54599i	−0.139926	+	0.0969242i
$691$	−26.6999			−1.01571			−0.507855	−	0.861442i	$-0.669562\pi$
$691$	−26.6999			−1.01571			−0.507855	+	0.861442i	$0.669562\pi$
$692$	−0.226858	−	0.226858i	−0.00862383	−	0.00862383i
$693$	−0.215717	+	0.805068i	−0.00819443	+	0.0305820i
$694$	0.385837	+	0.668289i	0.0146462	+	0.0253679i
$695$	−13.2547	+	15.6347i	−0.502779	+	0.593057i
$696$			4.65386i			0.176404i
$697$	−1.32245	+	4.93544i	−0.0500913	+	0.186943i
$698$	1.18707	+	4.43020i	0.0449312	+	0.167686i
$699$	5.96552	+	10.3326i	0.225637	+	0.390814i
$700$	1.48132	+	3.26265i	0.0559885	+	0.123317i
$701$	10.5536	−	18.2794i	0.398604	−	0.690402i	−0.594950	−	0.803763i	$-0.702828\pi$
$701$	10.5536	−	18.2794i	0.398604	−	0.690402i	0.993554	+	0.113360i	$0.0361615\pi$
$702$	−4.87939	−	4.87939i	−0.184161	−	0.184161i
$703$	8.68990	+	16.9307i	0.327746	+	0.638555i
$704$			1.16303i			0.0438332i
$705$	−1.29176	−	3.60585i	−0.0486504	−	0.135804i
$706$	−25.2056	−	14.5525i	−0.948625	−	0.547689i
$707$	8.80496	+	2.35928i	0.331145	+	0.0887300i
$708$	11.6794	−	3.12950i	0.438940	−	0.117614i
$709$	−6.22551	+	3.59430i	−0.233804	+	0.134987i	−0.612326	−	0.790606i	$-0.709766\pi$
$709$	−6.22551	+	3.59430i	−0.233804	+	0.134987i	0.378522	+	0.925592i	$0.376433\pi$
$710$	−16.9976	+	1.40031i	−0.637908	+	0.0525527i
$711$		−	14.4707i		−	0.542695i
$712$	−5.63353	−	1.50950i	−0.211126	−	0.0565709i
$713$	0.978503	+	0.262189i	0.0366452	+	0.00981906i
$714$			1.28901i			0.0482400i
$715$	−17.8849	+	1.47341i	−0.668858	+	0.0551024i
$716$	3.13747	−	1.81142i	0.117253	−	0.0676958i
$717$	2.42777	−	0.650519i	0.0906667	−	0.0242941i
$718$	23.7280	+	6.35790i	0.885521	+	0.237275i
$719$	40.7995	+	23.5556i	1.52156	+	0.878475i	0.999676	+	0.0254607i	$0.00810525\pi$
$719$	40.7995	+	23.5556i	1.52156	+	0.878475i	0.521887	+	0.853014i	$0.325228\pi$
$720$	0.754119	+	2.10507i	0.0281044	+	0.0784512i
$721$		−	3.43867i		−	0.128063i
$722$	17.7781	+	6.70379i	0.661631	+	0.249489i
$723$	−0.667018	−	0.667018i	−0.0248066	−	0.0248066i
$724$	−9.90530	+	17.1565i	−0.368127	+	0.637615i
$725$	21.7842	+	8.17984i	0.809043	+	0.303792i
$726$	−4.82368	−	8.35487i	−0.179024	−	0.310078i
$727$	11.4834	+	42.8565i	0.425894	+	1.58946i	0.761962	+	0.647622i	$0.224236\pi$
$727$	11.4834	+	42.8565i	0.425894	+	1.58946i	−0.336068	+	0.941838i	$0.609097\pi$
$728$	−1.27990	+	4.77665i	−0.0474362	+	0.177034i
$729$			1.00000i			0.0370370i
$730$	−3.95098	+	4.66042i	−0.146232	+	0.172490i
$731$	3.76026	+	6.51296i	0.139078	+	0.240891i
$732$	−4.01551	+	14.9861i	−0.148418	+	0.553902i
$733$	3.88988	+	3.88988i	0.143676	+	0.143676i	0.775286	−	0.631610i	$-0.217606\pi$
$733$	3.88988	+	3.88988i	0.143676	+	0.143676i	−0.631610	+	0.775286i	$0.717606\pi$
$734$	3.40319			0.125614
$735$	−11.9231	+	8.25888i	−0.439790	+	0.304633i
$736$	1.73170	+	0.999796i	0.0638312	+	0.0368530i
$737$	−2.22425	+	8.30100i	−0.0819312	+	0.305771i
$738$	2.74391	−	0.735227i	0.101005	−	0.0270641i
$739$	24.3534	+	14.0604i	0.895853	+	0.517221i	0.875852	−	0.482579i	$-0.160300\pi$
$739$	24.3534	+	14.0604i	0.895853	+	0.517221i	0.0200005	+	0.999800i	$0.493633\pi$
$740$	−9.72953	+	0.801547i	−0.357665	+	0.0294654i
$741$	9.21002	−	28.6338i	0.338339	−	1.05189i
$742$	5.04814	−	5.04814i	0.185323	−	0.185323i
$743$	−1.87374	−	6.99289i	−0.0687409	−	0.256544i	0.923000	−	0.384799i	$-0.125729\pi$
$743$	−1.87374	−	6.99289i	−0.0687409	−	0.256544i	−0.991741	+	0.128255i	$0.959063\pi$
$744$	0.253307	−	0.438740i	0.00928668	−	0.0160850i
$745$	46.5195	+	8.44602i	1.70434	+	0.309438i
$746$	15.8054	−	27.3758i	0.578678	−	1.00230i
$747$	13.1988	+	3.53660i	0.482918	+	0.129397i
$748$	1.47922	+	1.47922i	0.0540855	+	0.0540855i
$749$	1.77692			0.0649271
$750$	11.1790	+	0.170021i	0.408201	+	0.00620829i
$751$	41.9205	−	24.2028i	1.52970	−	0.883173i	0.530327	−	0.847793i	$-0.322069\pi$
$751$	41.9205	−	24.2028i	1.52970	−	0.883173i	0.999374	−	0.0353797i	$-0.0112641\pi$
$752$	−1.21123	+	1.21123i	−0.0441690	+	0.0441690i
$753$	−18.1210	+	18.1210i	−0.660366	+	0.660366i
$754$	16.0570	+	27.8115i	0.584760	+	1.01283i
$755$	7.15462	+	19.9716i	0.260383	+	0.726841i
$756$	0.620626	−	0.358318i	0.0225719	−	0.0130319i
$757$	5.09127	+	19.0009i	0.185045	+	0.690598i	0.994621	+	0.103583i	$0.0330307\pi$
$757$	5.09127	+	19.0009i	0.185045	+	0.690598i	−0.809576	+	0.587016i	$0.800303\pi$
$758$	−22.4600	+	6.01815i	−0.815785	+	0.218589i
$759$	2.32558			0.0844132
$760$	−6.66230	+	7.11433i	−0.241667	+	0.258064i
$761$	−4.80951			−0.174344			−0.0871722	−	0.996193i	$-0.527783\pi$
$761$	−4.80951			−0.174344			−0.0871722	+	0.996193i	$0.527783\pi$
$762$	6.88422	−	1.84462i	0.249389	−	0.0668236i
$763$	0.921752	+	3.44002i	0.0333697	+	0.124537i
$764$	13.3508	−	7.70808i	0.483015	−	0.278869i
$765$	3.63651	+	1.71823i	0.131478	+	0.0621226i
$766$	8.23305	+	14.2601i	0.297472	+	0.515237i
$767$	58.9989	−	58.9989i	2.13033	−	2.13033i
$768$	0.707107	−	0.707107i	0.0255155	−	0.0255155i
$769$	4.14947	−	2.39570i	0.149634	−	0.0863912i	−0.423314	−	0.905983i	$-0.639133\pi$
$769$	4.14947	−	2.39570i	0.149634	−	0.0863912i	0.572948	+	0.819592i	$0.305800\pi$
$770$	0.332926	−	1.83371i	0.0119978	−	0.0660824i
$771$	9.89884			0.356498
$772$	−2.59944	−	2.59944i	−0.0935559	−	0.0935559i
$773$	−25.1686	−	6.74391i	−0.905253	−	0.242562i	−0.223982	−	0.974593i	$-0.571906\pi$
$773$	−25.1686	−	6.74391i	−0.905253	−	0.242562i	−0.681271	+	0.732032i	$0.738572\pi$
$774$	2.09055	−	3.62094i	0.0751434	−	0.130152i
$775$	−1.60847	−	1.95685i	−0.0577779	−	0.0702921i
$776$	1.66446	−	2.88293i	0.0597507	−	0.103491i
$777$	0.809788	+	3.02217i	0.0290510	+	0.108420i
$778$	−24.3462	+	24.3462i	−0.872854	+	0.872854i
$779$	8.31261	+	9.17728i	0.297830	+	0.328810i
$780$	11.7696	+	9.97800i	0.421420	+	0.357270i
$781$	7.68230	+	4.43538i	0.274894	+	0.158710i
$782$	3.47410	−	0.930882i	0.124234	−	0.0332883i
$783$	1.20451	−	4.49528i	0.0430455	−	0.160648i
$784$	5.61741	+	3.24322i	0.200622	+	0.115829i
$785$	−10.2950	−	14.8625i	−0.367444	−	0.530467i
$786$	−6.51067			−0.232228
$787$	8.93591	+	8.93591i	0.318531	+	0.318531i	0.848203	−	0.529672i	$-0.177685\pi$
$787$	8.93591	+	8.93591i	0.318531	+	0.318531i	−0.529672	+	0.848203i	$0.677685\pi$
$788$	6.85639	−	25.5884i	0.244249	−	0.911549i
$789$	−3.85973	−	6.68525i	−0.137410	−	0.238001i
$790$	2.65670	+	32.2483i	0.0945213	+	1.14734i
$791$		−	8.36613i		−	0.297465i
$792$	0.301014	−	1.12340i	0.0106961	−	0.0399182i
$793$	27.7090	+	103.412i	0.983977	+	3.67225i
$794$	16.5452	+	28.6572i	0.587168	+	1.01701i
$795$	−7.51254	−	20.9707i	−0.266442	−	0.743754i
$796$	8.12191	−	14.0676i	0.287874	−	0.498612i
$797$	−8.71627	−	8.71627i	−0.308746	−	0.308746i	0.535677	−	0.844423i	$-0.320056\pi$
$797$	−8.71627	−	8.71627i	−0.308746	−	0.308746i	−0.844423	+	0.535677i	$0.820056\pi$
$798$	2.62482	+	1.69355i	0.0929177	+	0.0599509i
$799$			3.08105i			0.109000i
$800$	−2.06704	−	4.55273i	−0.0730809	−	0.160963i
$801$	5.05089	+	2.91613i	0.178464	+	0.103036i
$802$	−33.2782	−	8.91685i	−1.17509	−	0.314865i
$803$	3.06956	−	0.822486i	0.108322	−	0.0290249i
$804$	6.39923	−	3.69460i	0.225683	−	0.130298i
$805$	−2.44412	−	2.07206i	−0.0861439	−	0.0730307i
$806$		−	3.49589i		−	0.123137i
$807$	−10.4153	−	2.79078i	−0.366637	−	0.0982400i
$808$	−12.2865	−	3.29216i	−0.432238	−	0.115818i
$809$		−	19.7214i		−	0.693368i	−0.937982	−	0.346684i	$-0.887308\pi$
$809$		−	19.7214i		−	0.693368i	0.937982	−	0.346684i	$-0.112692\pi$
$810$	−0.183592	−	2.22852i	−0.00645075	−	0.0783022i
$811$	23.9733	−	13.8410i	0.841815	−	0.486022i	−0.0160656	−	0.999871i	$-0.505114\pi$
$811$	23.9733	−	13.8410i	0.841815	−	0.486022i	0.857881	+	0.513849i	$0.171781\pi$
$812$	−3.22148	+	0.863194i	−0.113052	+	0.0302922i
$813$	14.9291	+	4.00025i	0.523588	+	0.140295i
$814$	4.39740	+	2.53884i	0.154129	+	0.0889864i
$815$	29.0417	+	13.7220i	1.01729	+	0.480661i
$816$		−	1.79869i		−	0.0629668i
$817$	18.2028	+	0.899910i	0.636835	+	0.0314839i
$818$	16.4043	+	16.4043i	0.573561	+	0.573561i
$819$	2.47258	−	4.28263i	0.0863988	−	0.149647i
$820$	−5.97986	+	2.14223i	−0.208826	+	0.0748098i
$821$	26.0446	+	45.1106i	0.908963	+	1.57437i	0.815507	+	0.578747i	$0.196458\pi$
$821$	26.0446	+	45.1106i	0.908963	+	1.57437i	0.0934564	+	0.995623i	$0.470208\pi$
$822$	−3.33231	−	12.4364i	−0.116228	−	0.433768i
$823$	10.4632	−	39.0493i	0.364725	−	1.36117i	−0.503068	−	0.864247i	$-0.667795\pi$
$823$	10.4632	−	39.0493i	0.364725	−	1.36117i	0.867793	−	0.496926i	$-0.165538\pi$
$824$			4.79834i			0.167158i
$825$	−4.72942	−	3.38355i	−0.164657	−	0.117800i
$826$	4.33259	+	7.50426i	0.150750	+	0.261107i
$827$	1.72163	−	6.42519i	0.0598668	−	0.223426i	−0.929511	−	0.368795i	$-0.879770\pi$
$827$	1.72163	−	6.42519i	0.0598668	−	0.223426i	0.989377	+	0.145369i	$0.0464370\pi$
$828$	−1.41393	−	1.41393i	−0.0491373	−	0.0491373i
$829$	−21.4966			−0.746607			−0.373303	−	0.927709i	$-0.621775\pi$
$829$	−21.4966			−0.746607			−0.373303	+	0.927709i	$0.621775\pi$
$830$	−30.0630	−	5.45819i	−1.04350	−	0.189457i
$831$	17.9001	+	10.3346i	0.620946	+	0.358504i
$832$	1.78598	−	6.66537i	0.0619178	−	0.231080i
$833$	11.2695	−	3.01967i	0.390467	−	0.104625i
$834$	−7.93847	−	4.58328i	−0.274887	−	0.158706i
$835$	−1.07608	−	13.0619i	−0.0372392	−	0.452026i
$836$	4.95559	−	1.06870i	0.171393	−	0.0369616i
$837$	−0.358230	+	0.358230i	−0.0123822	+	0.0123822i
$838$	7.71839	+	28.8054i	0.266627	+	0.995067i
$839$	−2.02015	+	3.49901i	−0.0697434	+	0.120799i	−0.898788	−	0.438383i	$-0.855551\pi$
$839$	−2.02015	+	3.49901i	−0.0697434	+	0.120799i	0.829045	+	0.559182i	$0.188885\pi$
$840$	−1.31729	+	0.912461i	−0.0454509	+	0.0314829i
$841$	3.67081	−	6.35804i	0.126580	−	0.219243i
$842$	−24.5308	−	6.57300i	−0.845387	−	0.226521i
$843$	7.94725	+	7.94725i	0.273718	+	0.273718i
$844$	16.3594			0.563112
$845$	76.1607	+	13.8276i	2.62001	+	0.475685i
$846$	1.48345	−	0.856469i	0.0510020	−	0.0294460i
$847$	4.88869	−	4.88869i	0.167978	−	0.167978i
$848$	−7.04421	+	7.04421i	−0.241899	+	0.241899i
$849$	5.95445	+	10.3134i	0.204356	+	0.353955i
$850$	−8.41947	−	3.16147i	−0.288785	−	0.108437i
$851$	7.56046	−	4.36503i	0.259169	−	0.149631i
$852$	−1.97409	−	7.36741i	−0.0676312	−	0.252403i
$853$	−24.0710	+	6.44980i	−0.824175	+	0.220837i	−0.646171	−	0.763193i	$-0.723631\pi$
$853$	−24.0710	+	6.44980i	−0.824175	+	0.220837i	−0.178004	+	0.984030i	$0.556964\pi$
$854$	−11.1184			−0.380465
$855$	8.27662	−	5.14759i	0.283054	−	0.176044i
$856$	−2.47952			−0.0847483
$857$	−7.38206	+	1.97802i	−0.252166	+	0.0675678i	−0.382688	−	0.923878i	$-0.625002\pi$
$857$	−7.38206	+	1.97802i	−0.252166	+	0.0675678i	0.130521	+	0.991445i	$0.458335\pi$
$858$	−2.07715	−	7.75201i	−0.0709126	−	0.264649i
$859$	−18.1131	+	10.4576i	−0.618013	+	0.356810i	−0.776095	−	0.630616i	$-0.782802\pi$
$859$	−18.1131	+	10.4576i	−0.618013	+	0.356810i	0.158082	+	0.987426i	$0.449469\pi$
$860$	−3.99406	+	8.45315i	−0.136196	+	0.288250i
$861$	1.01787	+	1.76301i	0.0346891	+	0.0600833i
$862$	9.71140	−	9.71140i	0.330772	−	0.330772i
$863$	23.0061	−	23.0061i	0.783136	−	0.783136i	−0.197223	−	0.980359i	$-0.563192\pi$
$863$	23.0061	−	23.0061i	0.783136	−	0.783136i	0.980359	+	0.197223i	$0.0631922\pi$
$864$	−0.866025	+	0.500000i	−0.0294628	+	0.0170103i
$865$	−0.408492	−	0.589727i	−0.0138891	−	0.0200513i
$866$	33.5811			1.14113
$867$	9.73312	+	9.73312i	0.330554	+	0.330554i
$868$	0.350687	+	0.0939663i	0.0119031	+	0.00318942i
$869$	8.41492	−	14.5751i	0.285457	−	0.494426i
$870$	−1.85897	+	10.2389i	−0.0630249	+	0.347133i
$871$	25.4946	−	44.1579i	0.863850	−	1.49623i
$872$	−1.28622	−	4.80023i	−0.0435569	−	0.162556i
$873$	−2.35390	+	2.35390i	−0.0796676	+	0.0796676i
$874$	2.66883	−	8.29737i	0.0902746	−	0.280663i
$875$	1.95579	+	7.76987i	0.0661177	+	0.262670i
$876$	−2.36632	−	1.36619i	−0.0799505	−	0.0461594i
$877$	−46.0825	+	12.3478i	−1.55610	+	0.416955i	−0.931425	−	0.363934i	$-0.881433\pi$
$877$	−46.0825	+	12.3478i	−1.55610	+	0.416955i	−0.624671	+	0.780888i	$0.714767\pi$
$878$	7.85799	−	29.3264i	0.265194	−	0.989719i
$879$	−12.3033	−	7.10331i	−0.414980	−	0.239589i
$880$	−0.464568	+	2.55878i	−0.0156606	+	0.0862564i
$881$	−47.8080			−1.61069			−0.805346	−	0.592805i	$-0.798020\pi$
$881$	−47.8080			−1.61069			−0.805346	+	0.592805i	$0.798020\pi$
$882$	−4.58660	−	4.58660i	−0.154439	−	0.154439i
$883$	7.62303	−	28.4495i	0.256535	−	0.957403i	−0.710695	−	0.703501i	$-0.751619\pi$
$883$	7.62303	−	28.4495i	0.256535	−	0.957403i	0.967230	−	0.253902i	$-0.0817141\pi$
$884$	−6.20594	−	10.7490i	−0.208728	−	0.361528i
$885$	26.9460	−	2.21989i	0.905781	−	0.0746208i
$886$		−	15.7128i		−	0.527883i
$887$	10.0628	−	37.5550i	0.337877	−	1.26097i	−0.562839	−	0.826566i	$-0.690291\pi$
$887$	10.0628	−	37.5550i	0.337877	−	1.26097i	0.900716	−	0.434408i	$-0.143042\pi$
$888$	−1.12998	−	4.21716i	−0.0379198	−	0.141518i
$889$	2.55376	+	4.42324i	0.0856503	+	0.148351i
$890$	−11.7914	−	5.57135i	−0.395248	−	0.186752i
$891$	−0.581514	+	1.00721i	−0.0194814	+	0.0337428i
$892$	17.9354	+	17.9354i	0.600520	+	0.600520i
$893$	6.27397	+	4.04799i	0.209950	+	0.135461i
$894$			21.1443i			0.707171i
$895$	7.62631	−	2.73205i	0.254919	−	0.0913223i
$896$	0.620626	+	0.358318i	0.0207336	+	0.0119706i
$897$	−13.3280	−	3.57124i	−0.445010	−	0.119240i
$898$	2.43178	−	0.651595i	0.0811497	−	0.0217440i
$899$	2.04183	−	1.17885i	0.0680990	−	0.0393170i
$900$	0.818275	+	4.93259i	0.0272758	+	0.164420i
$901$			17.9186i			0.596955i
$902$	3.19124	+	0.855089i	0.106257	+	0.0284714i
$903$	2.89424	+	0.775508i	0.0963141	+	0.0258073i
$904$			11.6742i			0.388277i
$905$	−28.6458	+	33.7893i	−0.952217	+	1.12320i
$906$	−8.21632	+	4.74370i	−0.272969	+	0.157599i
$907$	19.6807	−	5.27343i	0.653487	−	0.175101i	0.0831821	−	0.996534i	$-0.473492\pi$
$907$	19.6807	−	5.27343i	0.653487	−	0.175101i	0.570305	+	0.821433i	$0.306825\pi$
$908$	2.04001	+	0.546618i	0.0677000	+	0.0181402i
$909$	11.0158	+	6.35996i	0.365370	+	0.210947i
$910$	−4.72393	+	9.99786i	−0.156597	+	0.331426i
$911$		−	17.4306i		−	0.577502i	−0.957404	−	0.288751i	$-0.906760\pi$
$911$		−	17.4306i		−	0.577502i	0.957404	−	0.288751i	$-0.0932400\pi$
$912$	−3.66270	−	2.36319i	−0.121284	−	0.0782530i
$913$	11.2374	+	11.2374i	0.371903	+	0.371903i
$914$	7.65813	−	13.2643i	0.253308	−	0.438743i
$915$	−14.8207	+	31.3669i	−0.489956	+	1.03696i
$916$	−0.875343	−	1.51614i	−0.0289221	−	0.0500946i
$917$	−1.20759	−	4.50680i	−0.0398783	−	0.148828i
$918$	−0.465536	+	1.73740i	−0.0153650	+	0.0573429i
$919$			31.3011i			1.03253i	0.856429	+	0.516264i	$0.172678\pi$
$919$			31.3011i			1.03253i	−0.856429	+	0.516264i	$0.827322\pi$
$920$	3.41054	+	2.89137i	0.112442	+	0.0953258i
$921$	−3.50191	−	6.06549i	−0.115392	−	0.199865i
$922$	−1.49713	+	5.58738i	−0.0493055	+	0.184011i
$923$	−37.2166	−	37.2166i	−1.22500	−	1.22500i
$924$	0.833468			0.0274191
$925$	−21.7261	−	2.12295i	−0.714351	−	0.0698022i
$926$	−27.3709	−	15.8026i	−0.899463	−	0.519305i
$927$	1.24190	−	4.63484i	0.0407894	−	0.152228i
$928$	4.49528	−	1.20451i	0.147565	−	0.0395399i
$929$	18.6631	+	10.7752i	0.612317	+	0.353521i	0.773872	−	0.633342i	$-0.218317\pi$
$929$	18.6631	+	10.7752i	0.612317	+	0.353521i	−0.161555	+	0.986864i	$0.551651\pi$
$930$	0.732554	−	0.864090i	0.0240214	−	0.0283346i
$931$	8.65737	−	26.9156i	0.283734	−	0.882125i
$932$	8.43652	−	8.43652i	0.276347	−	0.276347i
$933$	7.04883	+	26.3066i	0.230768	+	0.861240i
$934$	−9.95880	+	17.2491i	−0.325862	+	0.564409i
$935$	2.66356	+	3.84529i	0.0871076	+	0.125755i
$936$	−3.45025	+	5.97601i	−0.112775	+	0.195332i
$937$	21.6343	+	5.79690i	0.706763	+	0.189377i	0.594258	−	0.804275i	$-0.297446\pi$
$937$	21.6343	+	5.79690i	0.706763	+	0.189377i	0.112505	+	0.993651i	$0.464113\pi$
$938$	3.74439	+	3.74439i	0.122259	+	0.122259i
$939$	−2.70952			−0.0884218
$940$	−3.14865	+	2.18100i	−0.102698	+	0.0711365i
$941$	30.0105	−	17.3266i	0.978316	−	0.564831i	0.0765544	−	0.997065i	$-0.475608\pi$
$941$	30.0105	−	17.3266i	0.978316	−	0.564831i	0.901761	+	0.432235i	$0.142275\pi$
$942$	5.71736	−	5.71736i	0.186282	−	0.186282i
$943$	4.01654	−	4.01654i	0.130796	−	0.130796i
$944$	−6.04573	−	10.4715i	−0.196772	−	0.340818i
$945$	1.50857	−	0.540429i	0.0490737	−	0.0175802i
$946$	4.21126	−	2.43137i	0.136920	−	0.0790506i
$947$	6.85378	+	25.5786i	0.222718	+	0.831194i	0.983306	+	0.181960i	$0.0582440\pi$
$947$	6.85378	+	25.5786i	0.222718	+	0.831194i	−0.760588	+	0.649235i	$0.775089\pi$
$948$	−13.9776	+	3.74530i	−0.453973	+	0.121642i
$949$	−18.8549			−0.612054
$950$	−17.4995	+	12.9910i	−0.567760	+	0.421484i
$951$	9.02618			0.292694
$952$	1.24509	−	0.333620i	0.0403535	−	0.0108127i
$953$	11.4323	+	42.6660i	0.370329	+	1.38209i	0.860051	+	0.510208i	$0.170431\pi$
$953$	11.4323	+	42.6660i	0.370329	+	1.38209i	−0.489722	+	0.871878i	$0.662902\pi$
$954$	8.62736	−	4.98101i	0.279321	−	0.161266i
$955$	32.4521	−	11.6256i	1.05012	−	0.376196i
$956$	−1.25671	−	2.17668i	−0.0406448	−	0.0703988i
$957$	3.82726	−	3.82726i	0.123718	−	0.123718i
$958$	12.0969	−	12.0969i	0.390832	−	0.390832i
$959$	7.99060	−	4.61337i	0.258030	−	0.148974i
$960$	1.83816	−	1.27325i	0.0593263	−	0.0410941i
$961$	30.7433			0.991721
$962$	−21.3030	−	21.3030i	−0.686837	−	0.686837i
$963$	2.39503	+	0.641748i	0.0771789	+	0.0206800i
$964$	−0.471653	+	0.816926i	−0.0151909	+	0.0263114i
$965$	−4.68069	−	6.75737i	−0.150677	−	0.217527i
$966$	0.716491	−	1.24100i	0.0230527	−	0.0399285i
$967$	−9.27827	−	34.6270i	−0.298369	−	1.11353i	−0.938505	−	0.345266i	$-0.887789\pi$
$967$	−9.27827	−	34.6270i	−0.298369	−	1.11353i	0.640136	−	0.768262i	$-0.278878\pi$
$968$	−6.82172	+	6.82172i	−0.219258	+	0.219258i
$969$	−7.66413	+	1.65280i	−0.246207	+	0.0530957i
$970$	4.81356	−	5.67788i	0.154554	−	0.182306i
$971$	−37.1967	−	21.4755i	−1.19370	−	0.689183i	−0.234557	−	0.972102i	$-0.575364\pi$
$971$	−37.1967	−	21.4755i	−1.19370	−	0.689183i	−0.959144	+	0.282919i	$0.908697\pi$
$972$	0.965926	−	0.258819i	0.0309821	−	0.00830162i
$973$	1.70021	−	6.34526i	0.0545061	−	0.203420i
$974$	−1.29586	−	0.748166i	−0.0415221	−	0.0239728i
$975$	21.9087	+	26.6539i	0.701639	+	0.853609i
$976$	15.5147			0.496615
$977$	−9.84823	−	9.84823i	−0.315073	−	0.315073i	0.531798	−	0.846871i	$-0.321516\pi$
$977$	−9.84823	−	9.84823i	−0.315073	−	0.315073i	−0.846871	+	0.531798i	$0.821516\pi$
$978$	−3.71784	+	13.8752i	−0.118883	+	0.443679i
$979$	3.39154	+	5.87432i	0.108394	+	0.187744i
$980$	11.0634	+	9.37926i	0.353407	+	0.299609i
$981$			4.96957i			0.158666i
$982$	−4.35902	+	16.2681i	−0.139102	+	0.519135i
$983$	0.890692	+	3.32411i	0.0284087	+	0.106023i	0.978674	−	0.205418i	$-0.0658553\pi$
$983$	0.890692	+	3.32411i	0.0284087	+	0.106023i	−0.950266	+	0.311440i	$0.899189\pi$
$984$	−1.42035	−	2.46012i	−0.0452791	−	0.0784257i
$985$	25.3060	−	53.5583i	0.806315	−	1.70651i
$986$	4.18543	−	7.24937i	0.133291	−	0.230867i
$987$	0.868012	+	0.868012i	0.0276291	+	0.0276291i
$988$	−30.0419	−	1.48521i	−0.955760	−	0.0472509i
$989$		−	8.36051i		−	0.265849i
$990$	1.11100	−	2.35135i	0.0353098	−	0.0747308i
$991$	30.1871	+	17.4285i	0.958925	+	0.553636i	0.895842	−	0.444373i	$-0.146573\pi$
$991$	30.1871	+	17.4285i	0.958925	+	0.553636i	0.0630831	+	0.998008i	$0.479907\pi$
$992$	−0.489351	−	0.131121i	−0.0155369	−	0.00416310i
$993$	−26.3494	+	7.06031i	−0.836174	+	0.224052i
$994$	4.73370	−	2.73300i	0.150144	−	0.0866856i
$995$	23.4883	−	27.7058i	0.744628	−	0.878332i
$996$		−	13.6644i		−	0.432972i
$997$	12.5103	+	3.35212i	0.396205	+	0.106163i	0.451420	−	0.892312i	$-0.350918\pi$
$997$	12.5103	+	3.35212i	0.396205	+	0.106163i	−0.0552150	+	0.998474i	$0.517584\pi$
$998$	11.7451	+	3.14710i	0.371786	+	0.0996198i
$999$			4.36592i			0.138132i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.x.b.103.10	✓	40
5.2	odd	4	inner	570.2.x.b.217.8	yes	40
19.12	odd	6	inner	570.2.x.b.373.8	yes	40
95.12	even	12	inner	570.2.x.b.487.10	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.x.b.103.10	✓	40	1.1	even	1	trivial
570.2.x.b.217.8	yes	40	5.2	odd	4	inner
570.2.x.b.373.8	yes	40	19.12	odd	6	inner
570.2.x.b.487.10	yes	40	95.12	even	12	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)

\(f(q)\)	\(=\)	\(q+(0.965926 - 0.258819i) q^{2} +(0.258819 + 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} +(2.10507 - 0.754119i) q^{5} +(0.500000 + 0.866025i) q^{6} +(-0.506739 + 0.506739i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 + 0.500000i) q^{9} +O(q^{10})\)	\(q+(0.965926 - 0.258819i) q^{2} +(0.258819 + 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} +(2.10507 - 0.754119i) q^{5} +(0.500000 + 0.866025i) q^{6} +(-0.506739 + 0.506739i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 + 0.500000i) q^{9} +(1.83816 - 1.27325i) q^{10} -1.16303 q^{11} +(0.707107 + 0.707107i) q^{12} +(6.66537 + 1.78598i) q^{13} +(-0.358318 + 0.620626i) q^{14} +(1.27325 + 1.83816i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-0.465536 - 1.73740i) q^{17} +(-0.707107 + 0.707107i) q^{18} +(-4.14953 - 1.33469i) q^{19} +(1.44598 - 1.70562i) q^{20} +(-0.620626 - 0.358318i) q^{21} +(-1.12340 + 0.301014i) q^{22} +(-0.517533 + 1.93146i) q^{23} +(0.866025 + 0.500000i) q^{24} +(3.86261 - 3.17494i) q^{25} +6.90050 q^{26} +(-0.707107 - 0.707107i) q^{27} +(-0.185479 + 0.692218i) q^{28} +(2.32693 + 4.03036i) q^{29} +(1.70562 + 1.44598i) q^{30} -0.506614i q^{31} +(0.258819 - 0.965926i) q^{32} +(-0.301014 - 1.12340i) q^{33} +(-0.899346 - 1.55771i) q^{34} +(-0.684577 + 1.44886i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-3.08717 - 3.08717i) q^{37} +(-4.35358 - 0.215233i) q^{38} +6.90050i q^{39} +(0.955264 - 2.02175i) q^{40} +(-2.46012 - 1.42035i) q^{41} +(-0.692218 - 0.185479i) q^{42} +(-4.03864 + 1.08215i) q^{43} +(-1.00721 + 0.581514i) q^{44} +(-1.44598 + 1.70562i) q^{45} +1.99959i q^{46} +(-1.65457 - 0.443341i) q^{47} +(0.965926 + 0.258819i) q^{48} +6.48643i q^{49} +(2.90926 - 4.06647i) q^{50} +(1.55771 - 0.899346i) q^{51} +(6.66537 - 1.78598i) q^{52} +(-9.62256 - 2.57836i) q^{53} +(-0.866025 - 0.500000i) q^{54} +(-2.44825 + 0.877061i) q^{55} +0.716637i q^{56} +(0.215233 - 4.35358i) q^{57} +(3.29077 + 3.29077i) q^{58} +(6.04573 - 10.4715i) q^{59} +(2.02175 + 0.955264i) q^{60} +(7.75737 + 13.4362i) q^{61} +(-0.131121 - 0.489351i) q^{62} +(0.185479 - 0.692218i) q^{63} -1.00000i q^{64} +(15.3779 - 1.26687i) q^{65} +(-0.581514 - 1.00721i) q^{66} +(1.91246 - 7.13741i) q^{67} +(-1.27187 - 1.27187i) q^{68} -1.99959 q^{69} +(-0.286258 + 1.57667i) q^{70} +(-6.60544 - 3.81365i) q^{71} +(-0.258819 + 0.965926i) q^{72} +(-2.63928 + 0.707194i) q^{73} +(-3.78100 - 2.18296i) q^{74} +(4.06647 + 2.90926i) q^{75} +(-4.26094 + 0.918891i) q^{76} +(0.589351 - 0.589351i) q^{77} +(1.78598 + 6.66537i) q^{78} +(-7.23536 + 12.5320i) q^{79} +(0.399447 - 2.20010i) q^{80} +(0.500000 - 0.866025i) q^{81} +(-2.74391 - 0.735227i) q^{82} +(-9.66217 - 9.66217i) q^{83} -0.716637 q^{84} +(-2.29019 - 3.30628i) q^{85} +(-3.62094 + 2.09055i) q^{86} +(-3.29077 + 3.29077i) q^{87} +(-0.822385 + 0.822385i) q^{88} +(-2.91613 - 5.05089i) q^{89} +(-0.955264 + 2.02175i) q^{90} +(-4.28263 + 2.47258i) q^{91} +(0.517533 + 1.93146i) q^{92} +(0.489351 - 0.131121i) q^{93} -1.71294 q^{94} +(-9.74155 + 0.319632i) q^{95} +1.00000 q^{96} +(3.21549 - 0.861589i) q^{97} +(1.67881 + 6.26541i) q^{98} +(1.00721 - 0.581514i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 20 q^{6} - 8 q^{7}+O(q^{10}) \) 40 * q + 20 * q^6 - 8 * q^7	\( 40 q + 20 q^{6} - 8 q^{7} + 12 q^{10} + 8 q^{11} + 24 q^{13} + 20 q^{16} + 36 q^{21} - 8 q^{23} + 16 q^{25} + 4 q^{28} - 4 q^{35} - 20 q^{36} + 24 q^{38} + 12 q^{41} - 4 q^{42} - 12 q^{43} - 16 q^{47} + 24 q^{52} + 72 q^{53} + 8 q^{55} - 24 q^{57} - 16 q^{58} + 12 q^{60} + 24 q^{61} - 4 q^{63} + 4 q^{66} - 36 q^{67} - 24 q^{70} - 72 q^{71} - 32 q^{73} + 8 q^{76} - 88 q^{77} + 24 q^{78} + 20 q^{81} + 8 q^{82} - 88 q^{83} - 24 q^{85} - 48 q^{86} + 16 q^{87} - 24 q^{91} + 8 q^{92} - 96 q^{95} + 40 q^{96} - 60 q^{97} - 48 q^{98}+O(q^{100}) \) 40 * q + 20 * q^6 - 8 * q^7 + 12 * q^10 + 8 * q^11 + 24 * q^13 + 20 * q^16 + 36 * q^21 - 8 * q^23 + 16 * q^25 + 4 * q^28 - 4 * q^35 - 20 * q^36 + 24 * q^38 + 12 * q^41 - 4 * q^42 - 12 * q^43 - 16 * q^47 + 24 * q^52 + 72 * q^53 + 8 * q^55 - 24 * q^57 - 16 * q^58 + 12 * q^60 + 24 * q^61 - 4 * q^63 + 4 * q^66 - 36 * q^67 - 24 * q^70 - 72 * q^71 - 32 * q^73 + 8 * q^76 - 88 * q^77 + 24 * q^78 + 20 * q^81 + 8 * q^82 - 88 * q^83 - 24 * q^85 - 48 * q^86 + 16 * q^87 - 24 * q^91 + 8 * q^92 - 96 * q^95 + 40 * q^96 - 60 * q^97 - 48 * q^98

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