LMFDB - Embedded newform 570.2.x.b.103.3

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			103.3
Character	$\chi$	$=$	570.103
Dual form			570.2.x.b.487.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 + 0.258819i) q^{2} +(-0.258819 - 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} +(0.0149760 + 2.23602i) q^{5} +(0.500000 + 0.866025i) q^{6} +(1.36100 - 1.36100i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.866025 + 0.500000i) q^{9} +O(q^{10})$	\(q+(-0.965926 + 0.258819i) q^{2} +(-0.258819 - 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} +(0.0149760 + 2.23602i) q^{5} +(0.500000 + 0.866025i) q^{6} +(1.36100 - 1.36100i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.866025 + 0.500000i) q^{9} +(-0.593190 - 2.15595i) q^{10} -2.04820 q^{11} +(-0.707107 - 0.707107i) q^{12} +(4.35290 + 1.16636i) q^{13} +(-0.962371 + 1.66688i) q^{14} +(2.15595 - 0.593190i) q^{15} +(0.500000 - 0.866025i) q^{16} +(0.419369 + 1.56511i) q^{17} +(0.707107 - 0.707107i) q^{18} +(1.91571 + 3.91536i) q^{19} +(1.13098 + 1.92896i) q^{20} +(-1.66688 - 0.962371i) q^{21} +(1.97841 - 0.530114i) q^{22} +(0.422267 - 1.57592i) q^{23} +(0.866025 + 0.500000i) q^{24} +(-4.99955 + 0.0669730i) q^{25} -4.50646 q^{26} +(0.707107 + 0.707107i) q^{27} +(0.498160 - 1.85916i) q^{28} +(2.53592 + 4.39234i) q^{29} +(-1.92896 + 1.13098i) q^{30} -5.82030i q^{31} +(-0.258819 + 0.965926i) q^{32} +(0.530114 + 1.97841i) q^{33} +(-0.810159 - 1.40324i) q^{34} +(3.06360 + 3.02283i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(5.98171 + 5.98171i) q^{37} +(-2.86380 - 3.28613i) q^{38} -4.50646i q^{39} +(-1.59169 - 1.57051i) q^{40} +(-1.54887 - 0.894242i) q^{41} +(1.85916 + 0.498160i) q^{42} +(5.44964 - 1.46023i) q^{43} +(-1.77379 + 1.02410i) q^{44} +(-1.13098 - 1.92896i) q^{45} +1.63151i q^{46} +(11.1336 + 2.98324i) q^{47} +(-0.965926 - 0.258819i) q^{48} +3.29537i q^{49} +(4.81186 - 1.35867i) q^{50} +(1.40324 - 0.810159i) q^{51} +(4.35290 - 1.16636i) q^{52} +(13.4533 + 3.60480i) q^{53} +(-0.866025 - 0.500000i) q^{54} +(-0.0306738 - 4.57982i) q^{55} +1.92474i q^{56} +(3.28613 - 2.86380i) q^{57} +(-3.58633 - 3.58633i) q^{58} +(-3.15626 + 5.46681i) q^{59} +(1.57051 - 1.59169i) q^{60} +(-1.71953 - 2.97831i) q^{61} +(1.50640 + 5.62197i) q^{62} +(-0.498160 + 1.85916i) q^{63} -1.00000i q^{64} +(-2.54281 + 9.75064i) q^{65} +(-1.02410 - 1.77379i) q^{66} +(2.29730 - 8.57363i) q^{67} +(1.14574 + 1.14574i) q^{68} -1.63151 q^{69} +(-3.74158 - 2.12692i) q^{70} +(-3.15265 - 1.82018i) q^{71} +(0.258819 - 0.965926i) q^{72} +(-3.18493 + 0.853400i) q^{73} +(-7.32607 - 4.22971i) q^{74} +(1.35867 + 4.81186i) q^{75} +(3.61673 + 2.43295i) q^{76} +(-2.78760 + 2.78760i) q^{77} +(1.16636 + 4.35290i) q^{78} +(-1.26556 + 2.19201i) q^{79} +(1.94394 + 1.10504i) q^{80} +(0.500000 - 0.866025i) q^{81} +(1.72754 + 0.462894i) q^{82} +(-8.18953 - 8.18953i) q^{83} -1.92474 q^{84} +(-3.49333 + 0.961156i) q^{85} +(-4.88602 + 2.82094i) q^{86} +(3.58633 - 3.58633i) q^{87} +(1.44830 - 1.44830i) q^{88} +(3.55068 + 6.14996i) q^{89} +(1.59169 + 1.57051i) q^{90} +(7.51171 - 4.33689i) q^{91} +(-0.422267 - 1.57592i) q^{92} +(-5.62197 + 1.50640i) q^{93} -11.5264 q^{94} +(-8.72613 + 4.34219i) q^{95} +1.00000 q^{96} +(0.767038 - 0.205527i) q^{97} +(-0.852903 - 3.18308i) q^{98} +(1.77379 - 1.02410i) 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
$5$	0.0149760	+	2.23602i	0.00669745	+	0.999978i
$5$	0.0149760	+	2.23602i	0.00669745	+	0.999978i
$6$	0.500000	+	0.866025i	0.204124	+	0.353553i
$7$	1.36100	−	1.36100i	0.514409	−	0.514409i	−0.401465	−	0.915874i	$-0.631499\pi$
$7$	1.36100	−	1.36100i	0.514409	−	0.514409i	0.915874	+	0.401465i	$0.131499\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	−0.866025	+	0.500000i	−0.288675	+	0.166667i
$10$	−0.593190	−	2.15595i	−0.187583	−	0.681772i
$11$	−2.04820			−0.617556			−0.308778	−	0.951134i	$-0.599920\pi$
$11$	−2.04820			−0.617556			−0.308778	+	0.951134i	$0.599920\pi$
$12$	−0.707107	−	0.707107i	−0.204124	−	0.204124i
$13$	4.35290	+	1.16636i	1.20728	+	0.323489i	0.805693	−	0.592333i	$-0.201793\pi$
$13$	4.35290	+	1.16636i	1.20728	+	0.323489i	0.401585	+	0.915822i	$0.368460\pi$
$14$	−0.962371	+	1.66688i	−0.257205	+	0.445491i
$15$	2.15595	−	0.593190i	0.556664	−	0.153161i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	0.419369	+	1.56511i	0.101712	+	0.379594i	0.997951	−	0.0639763i	$-0.0203782\pi$
$17$	0.419369	+	1.56511i	0.101712	+	0.379594i	−0.896239	+	0.443571i	$0.853712\pi$
$18$	0.707107	−	0.707107i	0.166667	−	0.166667i
$19$	1.91571	+	3.91536i	0.439494	+	0.898246i
$19$	1.91571	+	3.91536i	0.439494	+	0.898246i
$20$	1.13098	+	1.92896i	0.252894	+	0.431329i
$21$	−1.66688	−	0.962371i	−0.363742	−	0.210007i
$22$	1.97841	−	0.530114i	0.421799	−	0.113021i
$23$	0.422267	−	1.57592i	0.0880487	−	0.328602i	−0.907825	−	0.419348i	$-0.862259\pi$
$23$	0.422267	−	1.57592i	0.0880487	−	0.328602i	0.995874	+	0.0907462i	$0.0289252\pi$
$24$	0.866025	+	0.500000i	0.176777	+	0.102062i
$25$	−4.99955	+	0.0669730i	−0.999910	+	0.0133946i
$26$	−4.50646			−0.883789
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$	0.498160	−	1.85916i	0.0941434	−	0.351348i
$29$	2.53592	+	4.39234i	0.470908	+	0.815637i	0.999446	−	0.0332726i	$-0.0105929\pi$
$29$	2.53592	+	4.39234i	0.470908	+	0.815637i	−0.528538	+	0.848910i	$0.677260\pi$
$30$	−1.92896	+	1.13098i	−0.352178	+	0.206487i
$31$		−	5.82030i		−	1.04536i	−0.852530	−	0.522678i	$-0.824933\pi$
$31$		−	5.82030i		−	1.04536i	0.852530	−	0.522678i	$-0.175067\pi$
$32$	−0.258819	+	0.965926i	−0.0457532	+	0.170753i
$33$	0.530114	+	1.97841i	0.0922809	+	0.344397i
$34$	−0.810159	−	1.40324i	−0.138941	−	0.240653i
$35$	3.06360	+	3.02283i	0.517843	+	0.510952i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	5.98171	+	5.98171i	0.983388	+	0.983388i	0.999864	−	0.0164765i	$-0.00524488\pi$
$37$	5.98171	+	5.98171i	0.983388	+	0.983388i	−0.0164765	+	0.999864i	$0.505245\pi$
$38$	−2.86380	−	3.28613i	−0.464570	−	0.533080i
$39$		−	4.50646i		−	0.721611i
$40$	−1.59169	−	1.57051i	−0.251669	−	0.248320i
$41$	−1.54887	−	0.894242i	−0.241893	−	0.139657i	0.374153	−	0.927367i	$-0.377933\pi$
$41$	−1.54887	−	0.894242i	−0.241893	−	0.139657i	−0.616047	+	0.787710i	$0.711267\pi$
$42$	1.85916	+	0.498160i	0.286874	+	0.0768678i
$43$	5.44964	−	1.46023i	0.831063	−	0.222683i	0.181886	−	0.983320i	$-0.441780\pi$
$43$	5.44964	−	1.46023i	0.831063	−	0.222683i	0.649177	+	0.760637i	$0.275113\pi$
$44$	−1.77379	+	1.02410i	−0.267410	+	0.154389i
$45$	−1.13098	−	1.92896i	−0.168596	−	0.287552i
$46$			1.63151i			0.240554i
$47$	11.1336	+	2.98324i	1.62400	+	0.435151i	0.952174	−	0.305555i	$-0.0988421\pi$
$47$	11.1336	+	2.98324i	1.62400	+	0.435151i	0.671830	+	0.740706i	$0.265509\pi$
$48$	−0.965926	−	0.258819i	−0.139419	−	0.0373573i
$49$			3.29537i			0.470767i
$50$	4.81186	−	1.35867i	0.680500	−	0.192145i
$51$	1.40324	−	0.810159i	0.196492	−	0.113445i
$52$	4.35290	−	1.16636i	0.603639	−	0.161745i
$53$	13.4533	+	3.60480i	1.84795	+	0.495158i	0.999422	−	0.0339852i	$-0.0108199\pi$
$53$	13.4533	+	3.60480i	1.84795	+	0.495158i	0.848533	+	0.529143i	$0.177487\pi$
$54$	−0.866025	−	0.500000i	−0.117851	−	0.0680414i
$55$	−0.0306738	−	4.57982i	−0.00413605	−	0.617542i
$56$			1.92474i			0.257205i
$57$	3.28613	−	2.86380i	0.435258	−	0.379320i
$58$	−3.58633	−	3.58633i	−0.470908	−	0.470908i
$59$	−3.15626	+	5.46681i	−0.410910	+	0.711718i	−0.994990	−	0.0999791i	$-0.968122\pi$
$59$	−3.15626	+	5.46681i	−0.410910	+	0.711718i	0.584079	+	0.811697i	$0.301456\pi$
$60$	1.57051	−	1.59169i	0.202752	−	0.205487i
$61$	−1.71953	−	2.97831i	−0.220163	−	0.381334i	0.734694	−	0.678398i	$-0.237326\pi$
$61$	−1.71953	−	2.97831i	−0.220163	−	0.381334i	−0.954857	+	0.297065i	$0.903992\pi$
$62$	1.50640	+	5.62197i	0.191313	+	0.713991i
$63$	−0.498160	+	1.85916i	−0.0627623	+	0.234232i
$64$		−	1.00000i		−	0.125000i
$65$	−2.54281	+	9.75064i	−0.315396	+	1.20942i
$66$	−1.02410	−	1.77379i	−0.126058	−	0.218339i
$67$	2.29730	−	8.57363i	0.280660	−	1.04744i	−0.671293	−	0.741192i	$-0.734261\pi$
$67$	2.29730	−	8.57363i	0.280660	−	1.04744i	0.951953	−	0.306244i	$-0.0990724\pi$
$68$	1.14574	+	1.14574i	0.138941	+	0.138941i
$69$	−1.63151			−0.196411
$70$	−3.74158	−	2.12692i	−0.447204	−	0.254215i
$71$	−3.15265	−	1.82018i	−0.374151	−	0.216016i	0.301120	−	0.953586i	$-0.402640\pi$
$71$	−3.15265	−	1.82018i	−0.374151	−	0.216016i	−0.675270	+	0.737570i	$0.735973\pi$
$72$	0.258819	−	0.965926i	0.0305021	−	0.113835i
$73$	−3.18493	+	0.853400i	−0.372768	+	0.0998829i	−0.440339	−	0.897832i	$-0.645142\pi$
$73$	−3.18493	+	0.853400i	−0.372768	+	0.0998829i	0.0675711	+	0.997714i	$0.478475\pi$
$74$	−7.32607	−	4.22971i	−0.851639	−	0.491694i
$75$	1.35867	+	4.81186i	0.156886	+	0.555626i
$76$	3.61673	+	2.43295i	0.414868	+	0.279078i
$77$	−2.78760	+	2.78760i	−0.317676	+	0.317676i
$78$	1.16636	+	4.35290i	0.132064	+	0.492869i
$79$	−1.26556	+	2.19201i	−0.142387	+	0.246621i	−0.928395	−	0.371595i	$-0.878811\pi$
$79$	−1.26556	+	2.19201i	−0.142387	+	0.246621i	0.786008	+	0.618216i	$0.212144\pi$
$80$	1.94394	+	1.10504i	0.217339	+	0.123547i
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$	1.72754	+	0.462894i	0.190775	+	0.0511181i
$83$	−8.18953	−	8.18953i	−0.898918	−	0.898918i	0.0964227	−	0.995340i	$-0.469260\pi$
$83$	−8.18953	−	8.18953i	−0.898918	−	0.898918i	−0.995340	+	0.0964227i	$0.969260\pi$
$84$	−1.92474			−0.210007
$85$	−3.49333	+	0.961156i	−0.378905	+	0.104252i
$86$	−4.88602	+	2.82094i	−0.526873	+	0.304190i
$87$	3.58633	−	3.58633i	0.384495	−	0.384495i
$88$	1.44830	−	1.44830i	0.154389	−	0.154389i
$89$	3.55068	+	6.14996i	0.376371	+	0.651894i	0.990531	−	0.137287i	$-0.0438384\pi$
$89$	3.55068	+	6.14996i	0.376371	+	0.651894i	−0.614160	+	0.789182i	$0.710505\pi$
$90$	1.59169	+	1.57051i	0.167779	+	0.165547i
$91$	7.51171	−	4.33689i	0.787441	−	0.454629i
$92$	−0.422267	−	1.57592i	−0.0440244	−	0.164301i
$93$	−5.62197	+	1.50640i	−0.582972	+	0.156207i
$94$	−11.5264			−1.18885
$95$	−8.72613	+	4.34219i	−0.895282	+	0.445500i
$96$	1.00000			0.102062
$97$	0.767038	−	0.205527i	0.0778809	−	0.0208681i	−0.219668	−	0.975575i	$-0.570497\pi$
$97$	0.767038	−	0.205527i	0.0778809	−	0.0208681i	0.297549	+	0.954707i	$0.403831\pi$
$98$	−0.852903	−	3.18308i	−0.0861563	−	0.321540i
$99$	1.77379	−	1.02410i	0.178273	−	0.102926i
$100$	−4.29625	+	2.55778i	−0.429625	+	0.255778i
$101$	−8.85942	−	15.3450i	−0.881545	−	1.52688i	−0.849623	−	0.527391i	$-0.823170\pi$
$101$	−8.85942	−	15.3450i	−0.881545	−	1.52688i	−0.0319226	−	0.999490i	$-0.510163\pi$
$102$	−1.14574	+	1.14574i	−0.113445	+	0.113445i
$103$	−9.55639	+	9.55639i	−0.941619	+	0.941619i	−0.998387	−	0.0567679i	$-0.981920\pi$
$103$	−9.55639	+	9.55639i	−0.941619	+	0.941619i	0.0567679	+	0.998387i	$0.481920\pi$
$104$	−3.90271	+	2.25323i	−0.382692	+	0.220947i
$105$	2.12692	−	3.74158i	0.207566	−	0.365141i
$106$	−13.9279			−1.35280
$107$	4.85331	+	4.85331i	0.469187	+	0.469187i	0.901651	−	0.432464i	$-0.142356\pi$
$107$	4.85331	+	4.85331i	0.469187	+	0.469187i	−0.432464	+	0.901651i	$0.642356\pi$
$108$	0.965926	+	0.258819i	0.0929463	+	0.0249049i
$109$	0.225208	−	0.390071i	0.0215710	−	0.0373620i	−0.855038	−	0.518565i	$-0.826467\pi$
$109$	0.225208	−	0.390071i	0.0215710	−	0.0373620i	0.876609	+	0.481203i	$0.159800\pi$
$110$	1.21497	+	4.41582i	0.115843	+	0.421032i
$111$	4.22971	−	7.32607i	0.401466	−	0.695360i
$112$	−0.498160	−	1.85916i	−0.0470717	−	0.175674i
$113$	−3.00110	+	3.00110i	−0.282320	+	0.282320i	−0.834034	−	0.551714i	$-0.813974\pi$
$113$	−3.00110	+	3.00110i	−0.282320	+	0.282320i	0.551714	+	0.834034i	$0.313974\pi$
$114$	−2.43295	+	3.61673i	−0.227867	+	0.338738i
$115$	3.53011	+	0.920595i	0.329185	+	0.0858459i
$116$	4.39234	+	2.53592i	0.407819	+	0.235454i
$117$	−4.35290	+	1.16636i	−0.402426	+	0.107830i
$118$	1.63380	−	6.09743i	0.150404	−	0.561314i
$119$	2.70087	+	1.55935i	0.247588	+	0.142945i
$120$	−1.10504	+	1.94394i	−0.100876	+	0.177456i
$121$	−6.80487			−0.618624
$122$	2.43178	+	2.43178i	0.220163	+	0.220163i
$123$	−0.462894	+	1.72754i	−0.0417377	+	0.155767i
$124$	−2.91015	−	5.04052i	−0.261339	−	0.452652i
$125$	−0.224626	−	11.1781i	−0.0200911	−	0.999798i
$126$		−	1.92474i		−	0.171470i
$127$	−0.100921	+	0.376641i	−0.00895526	+	0.0334215i	−0.970259	−	0.242070i	$-0.922174\pi$
$127$	−0.100921	+	0.376641i	−0.00895526	+	0.0334215i	0.961304	+	0.275491i	$0.0888404\pi$
$128$	0.258819	+	0.965926i	0.0228766	+	0.0853766i
$129$	−2.82094	−	4.88602i	−0.248370	−	0.430190i
$130$	−0.0674885	−	10.0765i	−0.00591913	−	0.883769i
$131$	2.36842	−	4.10222i	0.206930	−	0.358413i	−0.743816	−	0.668384i	$-0.766986\pi$
$131$	2.36842	−	4.10222i	0.206930	−	0.358413i	0.950746	+	0.309971i	$0.100319\pi$
$132$	1.44830	+	1.44830i	0.126058	+	0.126058i
$133$	7.93608	+	2.72153i	0.688145	+	0.235986i
$134$			8.87608i			0.766776i
$135$	−1.57051	+	1.59169i	−0.135168	+	0.136991i
$136$	−1.40324	−	0.810159i	−0.120327	−	0.0694706i
$137$	−15.9034	−	4.26130i	−1.35872	−	0.364067i	−0.495372	−	0.868681i	$-0.664968\pi$
$137$	−15.9034	−	4.26130i	−1.35872	−	0.364067i	−0.863345	+	0.504614i	$0.831635\pi$
$138$	1.57592	−	0.422267i	0.134151	−	0.0359457i
$139$	3.01067	−	1.73821i	0.255362	−	0.147433i	−0.366855	−	0.930278i	$-0.619566\pi$
$139$	3.01067	−	1.73821i	0.255362	−	0.147433i	0.622217	+	0.782845i	$0.286232\pi$
$140$	4.16457	+	1.08605i	0.351971	+	0.0917882i
$141$		−	11.5264i		−	0.970695i
$142$	3.51632	+	0.942196i	0.295083	+	0.0790673i
$143$	−8.91563	−	2.38893i	−0.745562	−	0.199773i
$144$			1.00000i			0.0833333i
$145$	−9.78337	+	5.73614i	−0.812465	+	0.476360i
$146$	2.85553	−	1.64864i	0.236325	−	0.136443i
$147$	3.18308	−	0.852903i	0.262536	−	0.0703463i
$148$	8.17117	+	2.18946i	0.671666	+	0.179972i
$149$	−14.4256	−	8.32864i	−1.18179	−	0.682308i	−0.225364	−	0.974275i	$-0.572357\pi$
$149$	−14.4256	−	8.32864i	−1.18179	−	0.682308i	−0.956429	+	0.291966i	$0.905691\pi$
$150$	−2.55778	−	4.29625i	−0.208842	−	0.350788i
$151$			12.9018i			1.04994i	0.851122	+	0.524968i	$0.175923\pi$
$151$			12.9018i			1.04994i	−0.851122	+	0.524968i	$0.824077\pi$
$152$	−4.12319	−	1.41397i	−0.334435	−	0.114688i
$153$	−1.14574	−	1.14574i	−0.0926274	−	0.0926274i
$154$	1.97113	−	3.41410i	0.158838	−	0.275116i
$155$	13.0143	−	0.0871645i	1.04533	−	0.00700122i
$156$	−2.25323	−	3.90271i	−0.180403	−	0.312467i
$157$	−2.88238	−	10.7572i	−0.230039	−	0.858516i	−0.980323	−	0.197401i	$-0.936750\pi$
$157$	−2.88238	−	10.7572i	−0.230039	−	0.858516i	0.750284	−	0.661115i	$-0.229917\pi$
$158$	0.655102	−	2.44487i	0.0521171	−	0.194504i
$159$		−	13.9279i		−	1.10455i
$160$	−2.16370	−	0.564258i	−0.171056	−	0.0446085i
$161$	−1.57012	−	2.71953i	−0.123743	−	0.214329i
$162$	−0.258819	+	0.965926i	−0.0203347	+	0.0758903i
$163$	−11.5631	−	11.5631i	−0.905690	−	0.905690i	0.0902309	−	0.995921i	$-0.471240\pi$
$163$	−11.5631	−	11.5631i	−0.905690	−	0.905690i	−0.995921	+	0.0902309i	$0.971240\pi$
$164$	−1.78848			−0.139657
$165$	−4.41582	+	1.21497i	−0.343771	+	0.0945855i
$166$	10.0301	+	5.79087i	0.778486	+	0.449459i
$167$	3.13041	−	11.6829i	0.242239	−	0.904047i	−0.732513	−	0.680753i	$-0.761652\pi$
$167$	3.13041	−	11.6829i	0.242239	−	0.904047i	0.974751	−	0.223294i	$-0.0716808\pi$
$168$	1.85916	−	0.498160i	0.143437	−	0.0384339i
$169$	6.32905	+	3.65408i	0.486850	+	0.281083i
$170$	3.12553	−	1.83254i	0.239717	−	0.140550i
$171$	−3.61673	−	2.43295i	−0.276578	−	0.186052i
$172$	3.98942	−	3.98942i	0.304190	−	0.304190i
$173$	−4.75962	−	17.7631i	−0.361867	−	1.35051i	−0.871619	−	0.490185i	$-0.836929\pi$
$173$	−4.75962	−	17.7631i	−0.361867	−	1.35051i	0.509752	−	0.860322i	$-0.329737\pi$
$174$	−2.53592	+	4.39234i	−0.192247	+	0.332982i
$175$	−6.71323	+	6.89553i	−0.507473	+	0.521253i
$176$	−1.02410	+	1.77379i	−0.0771945	+	0.133705i
$177$	6.09743	+	1.63380i	0.458311	+	0.122804i
$178$	−5.02142	−	5.02142i	−0.376371	−	0.376371i
$179$	−4.92720			−0.368277			−0.184138	−	0.982900i	$-0.558949\pi$
$179$	−4.92720			−0.368277			−0.184138	+	0.982900i	$0.558949\pi$
$180$	−1.94394	−	1.10504i	−0.144892	−	0.0823648i
$181$	−12.7463	+	7.35910i	−0.947428	+	0.546998i	−0.892281	−	0.451481i	$-0.850896\pi$
$181$	−12.7463	+	7.35910i	−0.947428	+	0.546998i	−0.0551469	+	0.998478i	$0.517563\pi$
$182$	−6.13328	+	6.13328i	−0.454629	+	0.454629i
$183$	−2.43178	+	2.43178i	−0.179762	+	0.179762i
$184$	0.815757	+	1.41293i	0.0601384	+	0.104163i
$185$	−13.2856	+	13.4648i	−0.976779	+	0.989952i
$186$	5.04052	−	2.91015i	0.369589	−	0.213382i
$187$	−0.858953	−	3.20566i	−0.0628129	−	0.234421i
$188$	11.1336	−	2.98324i	0.812002	−	0.217575i
$189$	1.92474			0.140004
$190$	7.30495	−	6.45273i	0.529957	−	0.468130i
$191$	8.35971			0.604888			0.302444	−	0.953167i	$-0.402198\pi$
$191$	8.35971			0.604888			0.302444	+	0.953167i	$0.402198\pi$
$192$	−0.965926	+	0.258819i	−0.0697097	+	0.0186787i
$193$	2.28281	+	8.51957i	0.164320	+	0.613252i	0.998126	+	0.0611937i	$0.0194907\pi$
$193$	2.28281	+	8.51957i	0.164320	+	0.613252i	−0.833806	+	0.552058i	$0.813843\pi$
$194$	−0.687707	+	0.397048i	−0.0493745	+	0.0285064i
$195$	10.0765	−	0.0674885i	0.721594	−	0.00483295i
$196$	1.64768	+	2.85387i	0.117692	+	0.203848i
$197$	−10.6545	+	10.6545i	−0.759102	+	0.759102i	−0.976159	−	0.217057i	$-0.930354\pi$
$197$	−10.6545	+	10.6545i	−0.759102	+	0.759102i	0.217057	+	0.976159i	$0.430354\pi$
$198$	−1.44830	+	1.44830i	−0.102926	+	0.102926i
$199$	15.9209	−	9.19196i	1.12861	−	0.651600i	0.185021	−	0.982735i	$-0.440765\pi$
$199$	15.9209	−	9.19196i	1.12861	−	0.651600i	0.943584	+	0.331134i	$0.107431\pi$
$200$	3.48786	−	3.58257i	0.246629	−	0.253326i
$201$	−8.87608			−0.626070
$202$	12.5291	+	12.5291i	0.881545	+	0.881545i
$203$	9.42935	+	2.52659i	0.661811	+	0.177332i
$204$	0.810159	−	1.40324i	0.0567225	−	0.0982462i
$205$	1.97635	−	3.47670i	0.138034	−	0.242823i
$206$	6.75739	−	11.7041i	0.470810	−	0.815466i
$207$	0.422267	+	1.57592i	0.0293496	+	0.109534i
$208$	3.18655	−	3.18655i	0.220947	−	0.220947i
$209$	−3.92376	−	8.01945i	−0.271412	−	0.554717i
$210$	−1.08605	+	4.16457i	−0.0749447	+	0.287383i
$211$	10.3326	+	5.96551i	0.711323	+	0.410682i	0.811551	−	0.584282i	$-0.198624\pi$
$211$	10.3326	+	5.96551i	0.711323	+	0.410682i	−0.100228	+	0.994965i	$0.531957\pi$
$212$	13.4533	−	3.60480i	0.923977	−	0.247579i
$213$	−0.942196	+	3.51632i	−0.0645582	+	0.240935i
$214$	−5.94406	−	3.43181i	−0.406328	−	0.234593i
$215$	3.34671	+	12.1636i	0.228244	+	0.829553i
$216$	−1.00000			−0.0680414
$217$	−7.92141	−	7.92141i	−0.537741	−	0.537741i
$218$	−0.116576	+	0.435068i	−0.00789553	+	0.0294665i
$219$	1.64864	+	2.85553i	0.111405	+	0.192959i
$220$	−2.31647	−	3.95090i	−0.156177	−	0.266370i
$221$			7.30189i			0.491179i
$222$	−2.18946	+	8.17117i	−0.146947	+	0.548413i
$223$	−4.95427	−	18.4896i	−0.331762	−	1.23815i	−0.907337	−	0.420404i	$-0.861888\pi$
$223$	−4.95427	−	18.4896i	−0.331762	−	1.23815i	0.575575	−	0.817749i	$-0.304778\pi$
$224$	0.962371	+	1.66688i	0.0643011	+	0.111373i
$225$	4.29625	−	2.55778i	0.286417	−	0.170518i
$226$	2.12210	−	3.67559i	0.141160	−	0.244496i
$227$	14.9067	+	14.9067i	0.989393	+	0.989393i	0.999944	−	0.0105513i	$-0.00335866\pi$
$227$	14.9067	+	14.9067i	0.989393	+	0.989393i	−0.0105513	+	0.999944i	$0.503359\pi$
$228$	1.41397	−	4.12319i	0.0936424	−	0.273065i
$229$			25.9919i			1.71759i	0.512316	+	0.858797i	$0.328788\pi$
$229$			25.9919i			1.71759i	−0.512316	+	0.858797i	$0.671212\pi$
$230$	−3.64809	+	0.0244335i	−0.240548	+	0.00161110i
$231$	3.41410	+	1.97113i	0.224631	+	0.129691i
$232$	−4.89902	−	1.31269i	−0.321636	−	0.0861822i
$233$	20.2560	−	5.42759i	1.32702	−	0.355573i	0.475415	−	0.879762i	$-0.342298\pi$
$233$	20.2560	−	5.42759i	1.32702	−	0.355573i	0.851602	+	0.524188i	$0.175631\pi$
$234$	3.90271	−	2.25323i	0.255128	−	0.147298i
$235$	−6.50385	+	24.9396i	−0.424264	+	1.62688i
$236$			6.31252i			0.410910i
$237$	2.44487	+	0.655102i	0.158812	+	0.0425534i
$238$	−3.01243	−	0.807178i	−0.195267	−	0.0523216i
$239$		−	11.5530i		−	0.747303i	−0.927569	−	0.373651i	$-0.878106\pi$
$239$		−	11.5530i		−	0.747303i	0.927569	−	0.373651i	$-0.121894\pi$
$240$	0.564258	−	2.16370i	0.0364227	−	0.139666i
$241$	−10.3168	+	5.95641i	−0.664563	+	0.383686i	−0.794014	−	0.607900i	$-0.792012\pi$
$241$	−10.3168	+	5.95641i	−0.664563	+	0.383686i	0.129450	+	0.991586i	$0.458679\pi$
$242$	6.57300	−	1.76123i	0.422528	−	0.113216i
$243$	−0.965926	−	0.258819i	−0.0619642	−	0.0166032i
$244$	−2.97831	−	1.71953i	−0.190667	−	0.110082i
$245$	−7.36850	+	0.0493512i	−0.470756	+	0.00315294i
$246$		−	1.78848i		−	0.114030i
$247$	3.77218	+	19.2776i	0.240018	+	1.22660i
$248$	4.11557	+	4.11557i	0.261339	+	0.261339i
$249$	−5.79087	+	10.0301i	−0.366982	+	0.635631i
$250$	3.11007	+	10.7391i	0.196698	+	0.679198i
$251$	−1.67883	−	2.90782i	−0.105967	−	0.183540i	0.808166	−	0.588955i	$-0.200460\pi$
$251$	−1.67883	−	2.90782i	−0.105967	−	0.183540i	−0.914133	+	0.405415i	$0.867127\pi$
$252$	0.498160	+	1.85916i	0.0313811	+	0.117116i
$253$	−0.864888	+	3.22780i	−0.0543750	+	0.202930i
$254$		−	0.389928i		−	0.0244662i
$255$	1.83254	+	3.12553i	0.114758	+	0.195728i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−1.62548	+	6.06639i	−0.101395	+	0.378411i	−0.997911	−	0.0645998i	$-0.979423\pi$
$257$	−1.62548	+	6.06639i	−0.101395	+	0.378411i	0.896516	+	0.443011i	$0.146090\pi$
$258$	3.98942	+	3.98942i	0.248370	+	0.248370i
$259$	16.2822			1.01173
$260$	2.67318	+	9.71570i	0.165784	+	0.602542i
$261$	−4.39234	−	2.53592i	−0.271879	−	0.156969i
$262$	−1.22598	+	4.57544i	−0.0757416	+	0.282671i
$263$	−24.2239	+	6.49078i	−1.49371	+	0.400239i	−0.910988	−	0.412432i	$-0.864679\pi$
$263$	−24.2239	+	6.49078i	−1.49371	+	0.400239i	−0.582723	+	0.812671i	$0.698013\pi$
$264$	−1.77379	−	1.02410i	−0.109170	−	0.0630291i
$265$	−7.85893	+	30.1358i	−0.482770	+	1.85123i
$266$	−8.37005	−	0.574785i	−0.513200	−	0.0352423i
$267$	5.02142	−	5.02142i	0.307306	−	0.307306i
$268$	−2.29730	−	8.57363i	−0.140330	−	0.523718i
$269$	2.11330	−	3.66034i	0.128850	−	0.223175i	−0.794381	−	0.607419i	$-0.792205\pi$
$269$	2.11330	−	3.66034i	0.128850	−	0.223175i	0.923231	+	0.384245i	$0.125538\pi$
$270$	1.10504	−	1.94394i	0.0672506	−	0.118304i
$271$	−13.8521	+	23.9925i	−0.841455	+	1.45744i	0.0472095	+	0.998885i	$0.484967\pi$
$271$	−13.8521	+	23.9925i	−0.841455	+	1.45744i	−0.888665	+	0.458558i	$0.848366\pi$
$272$	1.56511	+	0.419369i	0.0948986	+	0.0254280i
$273$	−6.13328	−	6.13328i	−0.371203	−	0.371203i
$274$	16.4644			0.994650
$275$	10.2401	−	0.137174i	0.617501	−	0.00827192i
$276$	−1.41293	+	0.815757i	−0.0850485	+	0.0491028i
$277$	−4.63550	+	4.63550i	−0.278520	+	0.278520i	−0.832518	−	0.553998i	$-0.813102\pi$
$277$	−4.63550	+	4.63550i	−0.278520	+	0.278520i	0.553998	+	0.832518i	$0.313102\pi$
$278$	−2.45820	+	2.45820i	−0.147433	+	0.147433i
$279$	2.91015	+	5.04052i	0.174226	+	0.301768i
$280$	−4.30376	+	0.0288249i	−0.257199	+	0.00172261i
$281$	23.0848	−	13.3280i	1.37713	−	0.795084i	0.385314	−	0.922786i	$-0.374093\pi$
$281$	23.0848	−	13.3280i	1.37713	−	0.795084i	0.991813	+	0.127701i	$0.0407599\pi$
$282$	2.98324	+	11.1336i	0.177649	+	0.662997i
$283$	29.9557	−	8.02661i	1.78068	−	0.477132i	0.789974	−	0.613140i	$-0.210094\pi$
$283$	29.9557	−	8.02661i	1.78068	−	0.477132i	0.990708	+	0.136008i	$0.0434274\pi$
$284$	−3.64037			−0.216016
$285$	6.45273	+	7.30495i	0.382226	+	0.432708i
$286$	9.23013			0.545789
$287$	−3.32508	+	0.890952i	−0.196273	+	0.0525912i
$288$	−0.258819	−	0.965926i	−0.0152511	−	0.0569177i
$289$	12.4487	−	7.18728i	0.732279	−	0.422781i
$290$	7.96539	−	8.07281i	0.467744	−	0.474052i
$291$	−0.397048	−	0.687707i	−0.0232754	−	0.0403141i
$292$	−2.33153	+	2.33153i	−0.136443	+	0.136443i
$293$	7.74130	−	7.74130i	0.452252	−	0.452252i	−0.443850	−	0.896101i	$-0.646388\pi$
$293$	7.74130	−	7.74130i	0.452252	−	0.452252i	0.896101	+	0.443850i	$0.146388\pi$
$294$	−2.85387	+	1.64768i	−0.166441	+	0.0960948i
$295$	−12.2711	−	6.97559i	−0.714454	−	0.406134i
$296$	−8.45942			−0.491694
$297$	−1.44830	−	1.44830i	−0.0840387	−	0.0840387i
$298$	16.0897	+	4.31122i	0.932051	+	0.249742i
$299$	3.67617	−	6.36732i	0.212599	−	0.368232i
$300$	3.58257	+	3.48786i	0.206840	+	0.201372i
$301$	5.42959	−	9.40432i	0.312956	−	0.542056i
$302$	−3.33924	−	12.4622i	−0.192152	−	0.717120i
$303$	−12.5291	+	12.5291i	−0.719779	+	0.719779i
$304$	4.34866	+	0.298629i	0.249413	+	0.0171276i
$305$	6.63380	−	3.88950i	0.379850	−	0.222712i
$306$	1.40324	+	0.810159i	0.0802177	+	0.0463137i
$307$	−22.5075	+	6.03086i	−1.28457	+	0.344200i	−0.835596	−	0.549345i	$-0.814877\pi$
$307$	−22.5075	+	6.03086i	−1.28457	+	0.344200i	−0.448975	+	0.893544i	$0.648211\pi$
$308$	−1.02033	+	3.80793i	−0.0581388	+	0.216977i
$309$	11.7041	+	6.75739i	0.665826	+	0.384415i
$310$	−12.5483	+	3.45254i	−0.712694	+	0.196091i
$311$	−6.43841			−0.365089			−0.182544	−	0.983198i	$-0.558433\pi$
$311$	−6.43841			−0.365089			−0.182544	+	0.983198i	$0.558433\pi$
$312$	3.18655	+	3.18655i	0.180403	+	0.180403i
$313$	6.02457	−	22.4840i	0.340529	−	1.27087i	−0.557221	−	0.830364i	$-0.688132\pi$
$313$	6.02457	−	22.4840i	0.340529	−	1.27087i	0.897750	−	0.440506i	$-0.145201\pi$
$314$	5.56832	+	9.64462i	0.314239	+	0.544277i
$315$	−4.16457	−	1.08605i	−0.234647	−	0.0611921i
$316$			2.53112i			0.142387i
$317$	7.39416	−	27.5954i	0.415297	−	1.54991i	−0.368942	−	0.929452i	$-0.620280\pi$
$317$	7.39416	−	27.5954i	0.415297	−	1.54991i	0.784240	−	0.620458i	$-0.213053\pi$
$318$	3.60480	+	13.4533i	0.202147	+	0.754424i
$319$	−5.19407	−	8.99640i	−0.290812	−	0.503702i
$320$	2.23602	−	0.0149760i	0.124997	−	0.000837181i
$321$	3.43181	−	5.94406i	0.191545	−	0.331765i
$322$	2.22049	+	2.22049i	0.123743	+	0.123743i
$323$	−5.32457	+	4.64027i	−0.296267	+	0.258192i
$324$		−	1.00000i		−	0.0555556i
$325$	−21.8407	−	5.53973i	−1.21150	−	0.307289i
$326$	14.1618	+	8.17633i	0.784351	+	0.452845i
$327$	−0.435068	−	0.116576i	−0.0240593	−	0.00644667i
$328$	1.72754	−	0.462894i	0.0953876	−	0.0255590i
$329$	19.2130	−	11.0926i	1.05925	−	0.611557i
$330$	3.95090	−	2.31647i	0.217490	−	0.127518i
$331$		−	26.7902i		−	1.47252i	−0.676698	−	0.736261i	$-0.736590\pi$
$331$		−	26.7902i		−	1.47252i	0.676698	−	0.736261i	$-0.263410\pi$
$332$	−11.1871	−	2.99758i	−0.613972	−	0.164513i
$333$	−8.17117	−	2.18946i	−0.447778	−	0.119982i
$334$			12.0950i			0.661808i
$335$	19.2052	+	5.00840i	1.04929	+	0.273638i
$336$	−1.66688	+	0.962371i	−0.0909355	+	0.0525017i
$337$	23.0518	−	6.17671i	1.25571	−	0.336467i	0.431171	−	0.902270i	$-0.358100\pi$
$337$	23.0518	−	6.17671i	1.25571	−	0.336467i	0.824540	+	0.565803i	$0.191434\pi$
$338$	−7.05914	−	1.89149i	−0.383966	−	0.102883i
$339$	3.67559	+	2.12210i	0.199630	+	0.115257i
$340$	−2.54473	+	2.57905i	−0.138007	+	0.139869i
$341$			11.9211i			0.645566i
$342$	4.12319	+	1.41397i	0.222957	+	0.0764587i
$343$	14.0120	+	14.0120i	0.756576	+	0.756576i
$344$	−2.82094	+	4.88602i	−0.152095	+	0.263436i
$345$	−0.0244335	−	3.64809i	−0.00131545	−	0.196407i
$346$	9.19488	+	15.9260i	0.494320	+	0.856187i
$347$	−2.87455	−	10.7280i	−0.154314	−	0.575907i	−0.999163	−	0.0409029i	$-0.986977\pi$
$347$	−2.87455	−	10.7280i	−0.154314	−	0.575907i	0.844849	−	0.535004i	$-0.179690\pi$
$348$	1.31269	−	4.89902i	0.0703675	−	0.262615i
$349$		−	0.526695i		−	0.0281933i	−0.999901	−	0.0140967i	$-0.995513\pi$
$349$		−	0.526695i		−	0.0281933i	0.999901	−	0.0140967i	$-0.00448725\pi$
$350$	4.69979	−	8.39809i	0.251214	−	0.448897i
$351$	2.25323	+	3.90271i	0.120268	+	0.208311i
$352$	0.530114	−	1.97841i	0.0282552	−	0.105450i
$353$	−8.11069	−	8.11069i	−0.431689	−	0.431689i	0.457514	−	0.889203i	$-0.348740\pi$
$353$	−8.11069	−	8.11069i	−0.431689	−	0.431689i	−0.889203	+	0.457514i	$0.848740\pi$
$354$	−6.31252			−0.335507
$355$	4.02275	−	7.07664i	0.213505	−	0.375589i
$356$	6.14996	+	3.55068i	0.325947	+	0.188186i
$357$	0.807178	−	3.01243i	0.0427204	−	0.159435i
$358$	4.75931	−	1.27525i	0.251538	−	0.0673993i
$359$	−5.97509	−	3.44972i	−0.315353	−	0.182069i	0.333966	−	0.942585i	$-0.391613\pi$
$359$	−5.97509	−	3.44972i	−0.315353	−	0.182069i	−0.649319	+	0.760516i	$0.724946\pi$
$360$	2.16370	+	0.564258i	0.114037	+	0.0297390i
$361$	−11.6601	+	15.0014i	−0.613691	+	0.789546i
$362$	10.4073	−	10.4073i	0.546998	−	0.546998i
$363$	1.76123	+	6.57300i	0.0924406	+	0.344993i
$364$	4.33689	−	7.51171i	0.227315	−	0.393720i
$365$	−1.95591	−	7.10878i	−0.102377	−	0.372091i
$366$	1.71953	−	2.97831i	0.0898812	−	0.155679i
$367$	−26.6770	−	7.14808i	−1.39253	−	0.373127i	−0.516873	−	0.856062i	$-0.672904\pi$
$367$	−26.6770	−	7.14808i	−1.39253	−	0.373127i	−0.875656	+	0.482936i	$0.839571\pi$
$368$	−1.15365	−	1.15365i	−0.0601384	−	0.0601384i
$369$	1.78848			0.0931048
$370$	9.34799	−	16.4446i	0.485979	−	0.854913i
$371$	23.2161	−	13.4038i	1.20532	−	0.695891i
$372$	−4.11557	+	4.11557i	−0.213382	+	0.213382i
$373$	−19.1977	+	19.1977i	−0.994018	+	0.994018i	−0.999982	−	0.00596450i	$-0.998101\pi$
$373$	−19.1977	+	19.1977i	−0.994018	+	0.994018i	0.00596450	+	0.999982i	$0.498101\pi$
$374$	1.65937	+	2.87411i	0.0858040	+	0.148617i
$375$	−10.7391	+	3.11007i	−0.554563	+	0.160603i
$376$	−9.98212	+	5.76318i	−0.514789	+	0.297213i
$377$	5.91557	+	22.0772i	0.304667	+	1.13703i
$378$	−1.85916	+	0.498160i	−0.0956248	+	0.0256226i
$379$	0.812664			0.0417437			0.0208719	−	0.999782i	$-0.493356\pi$
$379$	0.812664			0.0417437			0.0208719	+	0.999782i	$0.493356\pi$
$380$	−5.38595	+	8.12352i	−0.276294	+	0.416728i
$381$	0.389928			0.0199766
$382$	−8.07486	+	2.16365i	−0.413146	+	0.110702i
$383$	4.58881	+	17.1257i	0.234477	+	0.875082i	0.978384	+	0.206798i	$0.0663042\pi$
$383$	4.58881	+	17.1257i	0.234477	+	0.875082i	−0.743906	+	0.668284i	$0.767029\pi$
$384$	0.866025	−	0.500000i	0.0441942	−	0.0255155i
$385$	−6.27487	−	6.19138i	−0.319797	−	0.315542i
$386$	−4.41005	−	7.63844i	−0.224466	−	0.388786i
$387$	−3.98942	+	3.98942i	−0.202793	+	0.202793i
$388$	0.561511	−	0.561511i	0.0285064	−	0.0285064i
$389$	2.44773	−	1.41319i	0.124105	−	0.0716518i	−0.436663	−	0.899625i	$-0.643840\pi$
$389$	2.44773	−	1.41319i	0.124105	−	0.0716518i	0.560767	+	0.827974i	$0.310506\pi$
$390$	−9.71570	+	2.67318i	−0.491974	+	0.135362i
$391$	2.64357			0.133691
$392$	−2.33018	−	2.33018i	−0.117692	−	0.117692i
$393$	−4.57544	−	1.22598i	−0.230800	−	0.0618427i
$394$	7.53388	−	13.0491i	0.379551	−	0.657402i
$395$	−4.92033	−	2.79699i	−0.247569	−	0.140732i
$396$	1.02410	−	1.77379i	0.0514630	−	0.0891366i
$397$	−1.26071	−	4.70504i	−0.0632733	−	0.236139i	0.927046	−	0.374948i	$-0.122339\pi$
$397$	−1.26071	−	4.70504i	−0.0632733	−	0.236139i	−0.990319	+	0.138809i	$0.955673\pi$
$398$	−12.9994	+	12.9994i	−0.651600	+	0.651600i
$399$	0.574785	−	8.37005i	0.0287752	−	0.419026i
$400$	−2.44178	+	4.36323i	−0.122089	+	0.218161i
$401$	−22.7530	−	13.1364i	−1.13623	−	0.656002i	−0.190735	−	0.981641i	$-0.561087\pi$
$401$	−22.7530	−	13.1364i	−1.13623	−	0.656002i	−0.945494	+	0.325639i	$0.894421\pi$
$402$	8.57363	−	2.29730i	0.427614	−	0.114579i
$403$	6.78854	−	25.3352i	0.338161	−	1.26204i
$404$	−15.3450	−	8.85942i	−0.763441	−	0.440773i
$405$	1.94394	+	1.10504i	0.0965950	+	0.0549098i
$406$	−9.76198			−0.484479
$407$	−12.2518	−	12.2518i	−0.607297	−	0.607297i
$408$	−0.419369	+	1.56511i	−0.0207619	+	0.0774844i
$409$	10.2391	+	17.7347i	0.506292	+	0.876923i	0.999973	+	0.00728043i	$0.00231745\pi$
$409$	10.2391	+	17.7347i	0.506292	+	0.876923i	−0.493682	+	0.869643i	$0.664349\pi$
$410$	−1.00917	+	3.86975i	−0.0498392	+	0.191113i
$411$			16.4644i			0.812128i
$412$	−3.49788	+	13.0543i	−0.172328	+	0.643138i
$413$	3.14465	+	11.7360i	0.154738	+	0.577490i
$414$	−0.815757	−	1.41293i	−0.0400923	−	0.0694418i
$415$	18.1893	−	18.4346i	0.892877	−	0.904918i
$416$	−2.25323	+	3.90271i	−0.110474	+	0.191346i
$417$	−2.45820	−	2.45820i	−0.120379	−	0.120379i
$418$	5.86565	+	6.73065i	0.286898	+	0.329207i
$419$			8.83317i			0.431529i	0.976445	+	0.215764i	$0.0692243\pi$
$419$			8.83317i			0.431529i	−0.976445	+	0.215764i	$0.930776\pi$
$420$	−0.0288249	−	4.30376i	−0.00140651	−	0.210002i
$421$	20.2760	+	11.7064i	0.988193	+	0.570534i	0.904734	−	0.425978i	$-0.140070\pi$
$421$	20.2760	+	11.7064i	0.988193	+	0.570534i	0.0834594	+	0.996511i	$0.473403\pi$
$422$	−11.5245	−	3.08797i	−0.561003	−	0.150320i
$423$	−11.1336	+	2.98324i	−0.541335	+	0.145050i
$424$	−12.0619	+	6.96395i	−0.585778	+	0.338199i
$425$	−2.20148	−	7.79675i	−0.106787	−	0.378198i
$426$		−	3.64037i		−	0.176376i
$427$	−6.39375	−	1.71320i	−0.309415	−	0.0829076i
$428$	6.62974	+	1.77643i	0.320461	+	0.0858671i
$429$			9.23013i			0.445635i
$430$	−6.38085	−	10.8830i	−0.307712	−	0.524824i
$431$	26.8655	−	15.5108i	1.29406	−	0.747128i	0.314692	−	0.949194i	$-0.398099\pi$
$431$	26.8655	−	15.5108i	1.29406	−	0.747128i	0.979372	+	0.202065i	$0.0647653\pi$
$432$	0.965926	−	0.258819i	0.0464731	−	0.0124524i
$433$	26.1796	+	7.01482i	1.25811	+	0.337110i	0.825466	−	0.564452i	$-0.190913\pi$
$433$	26.1796	+	7.01482i	1.25811	+	0.337110i	0.432648	+	0.901563i	$0.357579\pi$
$434$	9.70171	+	5.60129i	0.465697	+	0.268870i
$435$	8.07281	+	7.96539i	0.387061	+	0.381911i
$436$		−	0.450415i		−	0.0215710i
$437$	6.97924	−	1.36568i	0.333862	−	0.0653292i
$438$	−2.33153	−	2.33153i	−0.111405	−	0.111405i
$439$	4.29636	−	7.44152i	0.205054	−	0.355164i	−0.745096	−	0.666957i	$-0.767596\pi$
$439$	4.29636	−	7.44152i	0.205054	−	0.355164i	0.950150	+	0.311793i	$0.100930\pi$
$440$	3.26011	+	3.21673i	0.155420	+	0.153352i
$441$	−1.64768	−	2.85387i	−0.0784611	−	0.135899i
$442$	−1.88987	−	7.05309i	−0.0898919	−	0.335481i
$443$	3.65295	−	13.6330i	0.173557	−	0.647723i	−0.823236	−	0.567699i	$-0.807834\pi$
$443$	3.65295	−	13.6330i	0.173557	−	0.647723i	0.996793	−	0.0800239i	$-0.0254997\pi$
$444$		−	8.45942i		−	0.401466i
$445$	−13.6982	+	8.03148i	−0.649359	+	0.380729i
$446$	9.57091	+	16.5773i	0.453196	+	0.784958i
$447$	−4.31122	+	16.0897i	−0.203914	+	0.761016i
$448$	−1.36100	−	1.36100i	−0.0643011	−	0.0643011i
$449$	−26.0451			−1.22915			−0.614573	−	0.788860i	$-0.710672\pi$
$449$	−26.0451			−1.22915			−0.614573	+	0.788860i	$0.710672\pi$
$450$	−3.48786	+	3.58257i	−0.164419	+	0.168884i
$451$	3.17241	+	1.83159i	0.149383	+	0.0862462i
$452$	−1.09848	+	4.09958i	−0.0516682	+	0.192828i
$453$	12.4622	−	3.33924i	0.585526	−	0.156891i
$454$	−18.2569	−	10.5406i	−0.856839	−	0.494696i
$455$	9.80985	+	16.7314i	0.459893	+	0.784378i
$456$	−0.298629	+	4.34866i	−0.0139846	+	0.203645i
$457$	0.703715	−	0.703715i	0.0329184	−	0.0329184i	−0.690456	−	0.723374i	$-0.742590\pi$
$457$	0.703715	−	0.703715i	0.0329184	−	0.0329184i	0.723374	+	0.690456i	$0.242590\pi$
$458$	−6.72720	−	25.1063i	−0.314342	−	1.17314i
$459$	−0.810159	+	1.40324i	−0.0378150	+	0.0654975i
$460$	3.51746	−	0.967797i	0.164003	−	0.0451238i
$461$	3.26972	−	5.66332i	0.152286	−	0.263767i	−0.779781	−	0.626052i	$-0.784670\pi$
$461$	3.26972	−	5.66332i	0.152286	−	0.263767i	0.932068	+	0.362285i	$0.118003\pi$
$462$	−3.80793	−	1.02033i	−0.177161	−	0.0474702i
$463$	7.39117	+	7.39117i	0.343497	+	0.343497i	0.857680	−	0.514184i	$-0.171905\pi$
$463$	7.39117	+	7.39117i	0.343497	+	0.343497i	−0.514184	+	0.857680i	$0.671905\pi$
$464$	5.07184			0.235454
$465$	−3.45254	−	12.5483i	−0.160108	−	0.581912i
$466$	−18.1611	+	10.4853i	−0.841295	+	0.485722i
$467$	−3.09651	+	3.09651i	−0.143289	+	0.143289i	−0.775113	−	0.631823i	$-0.782307\pi$
$467$	−3.09651	+	3.09651i	−0.143289	+	0.143289i	0.631823	+	0.775113i	$0.282307\pi$
$468$	−3.18655	+	3.18655i	−0.147298	+	0.147298i
$469$	−8.54208	−	14.7953i	−0.394437	−	0.683184i
$470$	−0.172618	−	25.7731i	−0.00796229	−	1.18883i
$471$	−9.64462	+	5.56832i	−0.444401	+	0.256575i
$472$	−1.63380	−	6.09743i	−0.0752018	−	0.280657i
$473$	−11.1620	+	2.99084i	−0.513228	+	0.137519i
$474$	−2.53112			−0.116258
$475$	−9.83990	−	19.4468i	−0.451486	−	0.892278i
$476$	3.11870			0.142945
$477$	−13.4533	+	3.60480i	−0.615985	+	0.165053i
$478$	2.99014	+	11.1594i	0.136766	+	0.510417i
$479$	−18.9541	+	10.9432i	−0.866036	+	0.500006i	−0.866029	−	0.499994i	$-0.833336\pi$
$479$	−18.9541	+	10.9432i	−0.866036	+	0.500006i	−7.32171e−6		1.00000i	$0.500002\pi$
$480$	0.0149760	+	2.23602i	0.000683556	+	0.102060i
$481$	19.0610	+	33.0146i	0.869107	+	1.50534i
$482$	8.42363	−	8.42363i	0.383686	−	0.383686i
$483$	−2.22049	+	2.22049i	−0.101036	+	0.101036i
$484$	−5.89319	+	3.40243i	−0.267872	+	0.154656i
$485$	0.471050	+	1.71203i	0.0213893	+	0.0777394i
$486$	1.00000			0.0453609
$487$	−18.2152	−	18.2152i	−0.825407	−	0.825407i	0.161470	−	0.986878i	$-0.448376\pi$
$487$	−18.2152	−	18.2152i	−0.825407	−	0.825407i	−0.986878	+	0.161470i	$0.948376\pi$
$488$	3.32187	+	0.890093i	0.150374	+	0.0402926i
$489$	−8.17633	+	14.1618i	−0.369746	+	0.640420i
$490$	7.10465	−	1.95478i	0.320955	−	0.0883078i
$491$	14.6937	−	25.4503i	0.663119	−	1.14856i	−0.316673	−	0.948535i	$-0.602566\pi$
$491$	14.6937	−	25.4503i	0.663119	−	1.14856i	0.979792	−	0.200021i	$-0.0641010\pi$
$492$	0.462894	+	1.72754i	0.0208689	+	0.0778837i
$493$	−5.81100	+	5.81100i	−0.261714	+	0.261714i
$494$	−8.63306	−	17.6444i	−0.388420	−	0.793860i
$495$	2.31647	+	3.95090i	0.104118	+	0.177580i
$496$	−5.04052	−	2.91015i	−0.226326	−	0.130669i
$497$	−6.76802	+	1.81348i	−0.303587	+	0.0813459i
$498$	2.99758	−	11.1871i	0.134325	−	0.501306i
$499$	−5.35742	−	3.09311i	−0.239831	−	0.138466i	0.375268	−	0.926916i	$-0.377551\pi$
$499$	−5.35742	−	3.09311i	−0.239831	−	0.138466i	−0.615099	+	0.788450i	$0.710884\pi$
$500$	−5.78357	−	9.56819i	−0.258649	−	0.427903i
$501$	−12.0950			−0.540364
$502$	2.37423	+	2.37423i	0.105967	+	0.105967i
$503$	−4.16411	+	15.5407i	−0.185668	+	0.692924i	0.808818	+	0.588059i	$0.200108\pi$
$503$	−4.16411	+	15.5407i	−0.185668	+	0.692924i	−0.994486	+	0.104865i	$0.966559\pi$
$504$	−0.962371	−	1.66688i	−0.0428674	−	0.0742486i
$505$	34.1789	−	20.0396i	1.52094	−	0.891752i
$506$		−	3.34167i		−	0.148555i
$507$	1.89149	−	7.05914i	0.0840040	−	0.313507i
$508$	0.100921	+	0.376641i	0.00447763	+	0.0167108i
$509$	−8.00792	−	13.8701i	−0.354945	−	0.614782i	0.632164	−	0.774835i	$-0.282167\pi$
$509$	−8.00792	−	13.8701i	−0.354945	−	0.614782i	−0.987108	+	0.160053i	$0.948834\pi$
$510$	−2.57905	−	2.54473i	−0.114202	−	0.112683i
$511$	−3.17321	+	5.49616i	−0.140375	+	0.243136i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−1.41397	+	4.12319i	−0.0624283	+	0.182043i
$514$		−	6.28039i		−	0.277016i
$515$	−21.5114	−	21.2252i	−0.947905	−	0.935292i
$516$	−4.88602	−	2.82094i	−0.215095	−	0.124185i
$517$	−22.8039	−	6.11028i	−1.00291	−	0.268730i
$518$	−15.7274	+	4.21415i	−0.691023	+	0.185159i
$519$	−15.9260	+	9.19488i	−0.699073	+	0.403610i
$520$	−5.09671	−	8.69278i	−0.223505	−	0.381203i
$521$		−	12.0125i		−	0.526275i	−0.964758	−	0.263138i	$-0.915243\pi$
$521$		−	12.0125i		−	0.526275i	0.964758	−	0.263138i	$-0.0847573\pi$
$522$	4.89902	+	1.31269i	0.214424	+	0.0574548i
$523$	−43.0759	−	11.5421i	−1.88358	−	0.504703i	−0.999287	−	0.0377658i	$-0.987976\pi$
$523$	−43.0759	−	11.5421i	−1.88358	−	0.504703i	−0.884291	−	0.466937i	$-0.845357\pi$
$524$		−	4.73684i		−	0.206930i
$525$	8.39809	+	4.69979i	0.366522	+	0.205116i
$526$	21.7186	−	12.5392i	0.946975	−	0.546736i
$527$	9.10939	−	2.44085i	0.396811	−	0.106325i
$528$	1.97841	+	0.530114i	0.0860993	+	0.0230702i
$529$	17.6134	+	10.1691i	0.765799	+	0.442134i
$530$	−0.208584	−	31.1430i	−0.00906029	−	1.35277i
$531$		−	6.31252i		−	0.273940i
$532$	8.23361	−	1.61113i	0.356972	−	0.0698512i
$533$	−5.69909	−	5.69909i	−0.246855	−	0.246855i
$534$	−3.55068	+	6.14996i	−0.153653	+	0.266135i
$535$	−10.7794	+	10.9248i	−0.466034	+	0.472319i
$536$	4.43804	+	7.68691i	0.191694	+	0.332024i
$537$	1.27525	+	4.75931i	0.0550313	+	0.205380i
$538$	−1.09392	+	4.08258i	−0.0471624	+	0.176012i
$539$		−	6.74958i		−	0.290725i
$540$	−0.564258	+	2.16370i	−0.0242818	+	0.0931110i
$541$	12.9275	+	22.3910i	0.555795	+	0.962665i	0.997841	+	0.0656726i	$0.0209193\pi$
$541$	12.9275	+	22.3910i	0.555795	+	0.962665i	−0.442046	+	0.896992i	$0.645747\pi$
$542$	7.17037	−	26.7602i	0.307994	−	1.14945i
$543$	10.4073	+	10.4073i	0.446622	+	0.446622i
$544$	−1.62032			−0.0694706
$545$	0.875579	+	0.497727i	0.0375057	+	0.0213203i
$546$	7.51171	+	4.33689i	0.321471	+	0.185602i
$547$	8.49556	−	31.7059i	0.363244	−	1.35565i	−0.506541	−	0.862216i	$-0.669076\pi$
$547$	8.49556	−	31.7059i	0.363244	−	1.35565i	0.869786	−	0.493430i	$-0.164257\pi$
$548$	−15.9034	+	4.26130i	−0.679358	+	0.182034i
$549$	2.97831	+	1.71953i	0.127111	+	0.0733877i
$550$	−9.85567	+	2.78283i	−0.420247	+	0.118660i
$551$	−12.3395	+	18.3435i	−0.525681	+	0.781459i
$552$	1.15365	−	1.15365i	0.0491028	−	0.0491028i
$553$	1.26090	+	4.70575i	0.0536190	+	0.200109i
$554$	3.27780	−	5.67731i	0.139260	−	0.241206i
$555$	16.4446	+	9.34799i	0.698033	+	0.396800i
$556$	1.73821	−	3.01067i	0.0737166	−	0.127681i
$557$	20.2232	+	5.41879i	0.856885	+	0.229602i	0.660408	−	0.750907i	$-0.270383\pi$
$557$	20.2232	+	5.41879i	0.856885	+	0.229602i	0.196477	+	0.980508i	$0.437050\pi$
$558$	−4.11557	−	4.11557i	−0.174226	−	0.174226i
$559$	25.4249			1.07536
$560$	4.14965	−	1.14174i	0.175355	−	0.0482472i
$561$	−2.87411	+	1.65937i	−0.121345	+	0.0700586i
$562$	−18.8487	+	18.8487i	−0.795084	+	0.795084i
$563$	8.88120	−	8.88120i	0.374298	−	0.374298i	−0.494742	−	0.869040i	$-0.664737\pi$
$563$	8.88120	−	8.88120i	0.374298	−	0.374298i	0.869040	+	0.494742i	$0.164737\pi$
$564$	−5.76318	−	9.98212i	−0.242674	−	0.420323i
$565$	−6.75546	−	6.66558i	−0.284205	−	0.280423i
$566$	−26.8575	+	15.5062i	−1.12891	+	0.651775i
$567$	−0.498160	−	1.85916i	−0.0209208	−	0.0780773i
$568$	3.51632	−	0.942196i	0.147542	−	0.0395337i
$569$	−39.8863			−1.67212			−0.836060	−	0.548638i	$-0.815147\pi$
$569$	−39.8863			−1.67212			−0.836060	+	0.548638i	$0.815147\pi$
$570$	−8.12352	−	5.38595i	−0.340257	−	0.225593i
$571$	19.3476			0.809673			0.404837	−	0.914389i	$-0.367328\pi$
$571$	19.3476			0.809673			0.404837	+	0.914389i	$0.367328\pi$
$572$	−8.91563	+	2.38893i	−0.372781	+	0.0998864i
$573$	−2.16365	−	8.07486i	−0.0903879	−	0.337332i
$574$	2.98118	−	1.72119i	0.124432	−	0.0718409i
$575$	−2.00560	+	7.90718i	−0.0836393	+	0.329752i
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$	−3.81365	+	3.81365i	−0.158764	+	0.158764i	−0.782019	−	0.623255i	$-0.785810\pi$
$577$	−3.81365	+	3.81365i	−0.158764	+	0.158764i	0.623255	+	0.782019i	$0.285810\pi$
$578$	−10.1644	+	10.1644i	−0.422781	+	0.422781i
$579$	7.63844	−	4.41005i	0.317443	−	0.183276i
$580$	−5.60458	+	9.85933i	−0.232718	+	0.409386i
$581$	−22.2919			−0.924823
$582$	0.561511	+	0.561511i	0.0232754	+	0.0232754i
$583$	−27.5551	−	7.38337i	−1.14122	−	0.305788i
$584$	1.64864	−	2.85553i	0.0682213	−	0.118163i
$585$	−2.67318	−	9.71570i	−0.110523	−	0.401695i
$586$	−5.47393	+	9.48112i	−0.226126	+	0.391661i
$587$	2.42487	+	9.04974i	0.100085	+	0.373523i	0.997741	−	0.0671738i	$-0.0213982\pi$
$587$	2.42487	+	9.04974i	0.100085	+	0.373523i	−0.897656	+	0.440696i	$0.854732\pi$
$588$	2.33018	−	2.33018i	0.0960948	−	0.0960948i
$589$	22.7886	−	11.1500i	0.938987	−	0.459427i
$590$	13.6584	+	3.56189i	0.562309	+	0.146641i
$591$	13.0491	+	7.53388i	0.536766	+	0.309902i
$592$	8.17117	−	2.18946i	0.335833	−	0.0899862i
$593$	−8.88921	+	33.1750i	−0.365036	+	1.36233i	0.502336	+	0.864673i	$0.332474\pi$
$593$	−8.88921	+	33.1750i	−0.365036	+	1.36233i	−0.867372	+	0.497661i	$0.834193\pi$
$594$	1.77379	+	1.02410i	0.0727797	+	0.0420194i
$595$	−3.44628	+	6.06254i	−0.141284	+	0.248540i
$596$	−16.6573			−0.682308
$597$	−12.9994	−	12.9994i	−0.532030	−	0.532030i
$598$	−1.90293	+	7.10182i	−0.0778165	+	0.290415i
$599$	7.80914	+	13.5258i	0.319073	+	0.552650i	0.980295	−	0.197540i	$-0.0632952\pi$
$599$	7.80914	+	13.5258i	0.319073	+	0.552650i	−0.661222	+	0.750190i	$0.729962\pi$
$600$	−4.36323	−	2.44178i	−0.178128	−	0.0996851i
$601$			10.7032i			0.436593i	0.975883	+	0.218296i	$0.0700499\pi$
$601$			10.7032i			0.436593i	−0.975883	+	0.218296i	$0.929950\pi$
$602$	−2.81056	+	10.4892i	−0.114550	+	0.427506i
$603$	2.29730	+	8.57363i	0.0935532	+	0.349145i
$604$	6.45092	+	11.1733i	0.262484	+	0.454636i
$605$	−0.101909	−	15.2158i	−0.00414321	−	0.618611i
$606$	8.85942	−	15.3450i	0.359889	−	0.623347i
$607$	−1.76036	−	1.76036i	−0.0714508	−	0.0714508i	0.670478	−	0.741929i	$-0.266089\pi$
$607$	−1.76036	−	1.76036i	−0.0714508	−	0.0714508i	−0.741929	+	0.670478i	$0.766089\pi$
$608$	−4.27777	+	0.837061i	−0.173487	+	0.0339473i
$609$		−	9.76198i		−	0.395575i
$610$	−5.40109	+	5.47392i	−0.218684	+	0.221633i
$611$	44.9840	+	25.9715i	1.81986	+	1.05070i
$612$	−1.56511	−	0.419369i	−0.0632657	−	0.0169520i
$613$	−6.40821	+	1.71707i	−0.258825	+	0.0693520i	−0.385898	−	0.922541i	$-0.626108\pi$
$613$	−6.40821	+	1.71707i	−0.258825	+	0.0693520i	0.127073	+	0.991893i	$0.459442\pi$
$614$	20.1797	−	11.6507i	0.814385	−	0.470185i
$615$	−3.86975	−	1.00917i	−0.156043	−	0.0406936i
$616$		−	3.94226i		−	0.158838i
$617$	−27.1544	−	7.27601i	−1.09320	−	0.292921i	−0.333205	−	0.942854i	$-0.608130\pi$
$617$	−27.1544	−	7.27601i	−1.09320	−	0.292921i	−0.759991	+	0.649933i	$0.774797\pi$
$618$	−13.0543	−	3.49788i	−0.525120	−	0.140705i
$619$		−	15.3191i		−	0.615726i	−0.951431	−	0.307863i	$-0.900386\pi$
$619$		−	15.3191i		−	0.615726i	0.951431	−	0.307863i	$-0.0996138\pi$
$620$	11.2271	−	6.58263i	0.450892	−	0.264365i
$621$	1.41293	−	0.815757i	0.0566990	−	0.0327352i
$622$	6.21903	−	1.66638i	0.249360	−	0.0668159i
$623$	13.2026	+	3.53761i	0.528949	+	0.141731i
$624$	−3.90271	−	2.25323i	−0.156233	−	0.0902013i
$625$	24.9910	−	0.669670i	0.999641	−	0.0267868i
$626$			23.2771i			0.930341i
$627$	−6.73065	+	5.86565i	−0.268796	+	0.234251i
$628$	−7.87480	−	7.87480i	−0.314239	−	0.314239i
$629$	−6.85348	+	11.8706i	−0.273266	+	0.473311i
$630$	4.30376	−	0.0288249i	0.171466	−	0.00114841i
$631$	−13.2145	−	22.8882i	−0.526061	−	0.911165i	−0.999539	−	0.0303589i	$-0.990335\pi$
$631$	−13.2145	−	22.8882i	−0.526061	−	0.911165i	0.473478	−	0.880806i	$-0.342998\pi$
$632$	−0.655102	−	2.44487i	−0.0260585	−	0.0972518i
$633$	3.08797	−	11.5245i	0.122736	−	0.458057i
$634$			28.5688i			1.13461i
$635$	−0.843688	−	0.220020i	−0.0334807	−	0.00873122i
$636$	−6.96395	−	12.0619i	−0.276139	−	0.478286i
$637$	−3.84357	+	14.3444i	−0.152288	+	0.568346i
$638$	7.34553	+	7.34553i	0.290812	+	0.290812i
$639$	3.64037			0.144011
$640$	−2.15595	+	0.593190i	−0.0852215	+	0.0234479i
$641$	4.52140	+	2.61043i	0.178584	+	0.103106i	0.586627	−	0.809857i	$-0.300455\pi$
$641$	4.52140	+	2.61043i	0.178584	+	0.103106i	−0.408043	+	0.912963i	$0.633789\pi$
$642$	−1.77643	+	6.62974i	−0.0701102	+	0.261655i
$643$	11.2739	−	3.02084i	0.444600	−	0.119130i	−0.0295718	−	0.999563i	$-0.509414\pi$
$643$	11.2739	−	3.02084i	0.444600	−	0.119130i	0.474171	+	0.880433i	$0.342748\pi$
$644$	−2.71953	−	1.57012i	−0.107165	−	0.0618715i
$645$	10.8830	−	6.38085i	0.428517	−	0.251246i
$646$	3.94215	−	5.86026i	0.155102	−	0.230569i
$647$	−0.741137	+	0.741137i	−0.0291371	+	0.0291371i	−0.721525	−	0.692388i	$-0.756559\pi$
$647$	−0.741137	+	0.741137i	−0.0291371	+	0.0291371i	0.692388	+	0.721525i	$0.256559\pi$
$648$	0.258819	+	0.965926i	0.0101674	+	0.0379452i
$649$	6.46466	−	11.1971i	0.253760	−	0.439526i
$650$	22.5303	−	0.301811i	0.883710	−	0.0118380i
$651$	−5.60129	+	9.70171i	−0.219532	+	0.380240i
$652$	−15.7955	−	4.23238i	−0.618598	−	0.165753i
$653$	20.5653	+	20.5653i	0.804781	+	0.804781i	0.983839	−	0.179057i	$-0.0573048\pi$
$653$	20.5653	+	20.5653i	0.804781	+	0.804781i	−0.179057	+	0.983839i	$0.557305\pi$
$654$	0.450415			0.0176126
$655$	9.20811	+	5.23439i	0.359791	+	0.204525i
$656$	−1.54887	+	0.894242i	−0.0604733	+	0.0349143i
$657$	2.33153	−	2.33153i	0.0909617	−	0.0909617i
$658$	−15.6874	+	15.6874i	−0.611557	+	0.611557i
$659$	11.3729	+	19.6985i	0.443026	+	0.767343i	0.997912	−	0.0645828i	$-0.0205717\pi$
$659$	11.3729	+	19.6985i	0.443026	+	0.767343i	−0.554887	+	0.831926i	$0.687238\pi$
$660$	−3.21673	+	3.26011i	−0.125211	+	0.126900i
$661$	−16.4998	+	9.52616i	−0.641768	+	0.370525i	−0.785295	−	0.619122i	$-0.787489\pi$
$661$	−16.4998	+	9.52616i	−0.641768	+	0.370525i	0.143528	+	0.989646i	$0.454155\pi$
$662$	6.93381	+	25.8773i	0.269490	+	1.00575i
$663$	7.05309	−	1.88987i	0.273919	−	0.0733964i
$664$	11.5817			0.449459
$665$	−5.96653	+	17.7860i	−0.231372	+	0.689710i
$666$	8.45942			0.327796
$667$	7.99282	−	2.14167i	0.309483	−	0.0829257i
$668$	−3.13041	−	11.6829i	−0.121119	−	0.452024i
$669$	−16.5773	+	9.57091i	−0.640915	+	0.370033i
$670$	−19.8471	+	0.132928i	−0.766759	+	0.00513545i
$671$	3.52194	+	6.10018i	0.135963	+	0.235495i
$672$	1.36100	−	1.36100i	0.0525017	−	0.0525017i
$673$	21.0061	−	21.0061i	0.809725	−	0.809725i	−0.174867	−	0.984592i	$-0.555950\pi$
$673$	21.0061	−	21.0061i	0.809725	−	0.809725i	0.984592	+	0.174867i	$0.0559495\pi$
$674$	−20.6677	+	11.9325i	−0.796089	+	0.459622i
$675$	−3.58257	−	3.48786i	−0.137893	−	0.134248i
$676$	7.30816			0.281083
$677$	4.74311	+	4.74311i	0.182293	+	0.182293i	0.792354	−	0.610061i	$-0.208855\pi$
$677$	4.74311	+	4.74311i	0.182293	+	0.182293i	−0.610061	+	0.792354i	$0.708855\pi$
$678$	−4.09958	−	1.09848i	−0.157444	−	0.0421869i
$679$	0.764215	−	1.32366i	0.0293279	−	0.0507974i
$680$	1.79052	−	3.14980i	0.0686631	−	0.120789i
$681$	10.5406	−	18.2569i	0.403918	−	0.699606i
$682$	−3.08542	−	11.5149i	−0.118147	−	0.440930i
$683$	2.05505	−	2.05505i	0.0786343	−	0.0786343i	−0.666696	−	0.745330i	$-0.732292\pi$
$683$	2.05505	−	2.05505i	0.0786343	−	0.0786343i	0.745330	+	0.666696i	$0.232292\pi$
$684$	−4.34866	−	0.298629i	−0.166275	−	0.0114184i
$685$	9.29016	−	35.6240i	0.354959	−	1.36112i
$686$	−17.1611	−	9.90796i	−0.655214	−	0.378288i
$687$	25.1063	−	6.72720i	0.957864	−	0.256659i
$688$	1.46023	−	5.44964i	0.0556707	−	0.207766i
$689$	54.3565	+	31.3827i	2.07082	+	1.19559i
$690$	0.967797	+	3.51746i	0.0368434	+	0.133908i
$691$	−45.8469			−1.74410			−0.872049	−	0.489419i	$-0.837209\pi$
$691$	−45.8469			−1.74410			−0.872049	+	0.489419i	$0.837209\pi$
$692$	−13.0035	−	13.0035i	−0.494320	−	0.494320i
$693$	1.02033	−	3.80793i	0.0387592	−	0.144651i
$694$	5.55320	+	9.61843i	0.210797	+	0.365111i
$695$	3.93176	+	6.70588i	0.149140	+	0.254369i
$696$			5.07184i			0.192247i
$697$	0.750035	−	2.79917i	0.0284096	−	0.106026i
$698$	0.136319	+	0.508748i	0.00515974	+	0.0192564i
$699$	−10.4853	−	18.1611i	−0.396590	−	0.686915i
$700$	−2.36606	+	9.32832i	−0.0894288	+	0.352577i
$701$	−0.998176	+	1.72889i	−0.0377006	+	0.0652994i	−0.884260	−	0.466995i	$-0.845337\pi$
$701$	−0.998176	+	1.72889i	−0.0377006	+	0.0652994i	0.846559	+	0.532294i	$0.178670\pi$
$702$	−3.18655	−	3.18655i	−0.120268	−	0.120268i
$703$	−11.9614	+	34.8798i	−0.451131	+	1.31552i
$704$			2.04820i			0.0771945i
$705$	25.7731	−	0.172618i	0.970673	−	0.00650118i
$706$	9.93353	+	5.73513i	0.373853	+	0.215844i
$707$	−32.9421	−	8.82682i	−1.23892	−	0.331967i
$708$	6.09743	−	1.63380i	0.229155	−	0.0614020i
$709$	29.6093	−	17.0949i	1.11200	−	0.642013i	0.172653	−	0.984983i	$-0.444766\pi$
$709$	29.6093	−	17.0949i	1.11200	−	0.642013i	0.939346	+	0.342970i	$0.111433\pi$
$710$	−2.05411	+	7.87667i	−0.0770893	+	0.295606i
$711$		−	2.53112i		−	0.0949244i
$712$	−6.85939	−	1.83797i	−0.257066	−	0.0688807i
$713$	−9.17233	−	2.45772i	−0.343506	−	0.0920422i
$714$			3.11870i			0.116714i
$715$	5.20818	−	19.9713i	0.194775	−	0.746883i
$716$	−4.26708	+	2.46360i	−0.159468	+	0.0920691i
$717$	−11.1594	+	2.99014i	−0.416754	+	0.111669i
$718$	6.66435	+	1.78571i	0.248711	+	0.0666420i
$719$	−9.01298	−	5.20365i	−0.336127	−	0.194063i	0.322431	−	0.946593i	$-0.395500\pi$
$719$	−9.01298	−	5.20365i	−0.336127	−	0.194063i	−0.658558	+	0.752530i	$0.728833\pi$
$720$	−2.23602	+	0.0149760i	−0.0833315	+	0.000558121i
$721$			26.0125i			0.968755i
$722$	7.38017	−	17.5081i	0.274662	−	0.651583i
$723$	8.42363	+	8.42363i	0.313278	+	0.313278i
$724$	−7.35910	+	12.7463i	−0.273499	+	0.473714i
$725$	−12.9726	−	21.7899i	−0.481791	−	0.809256i
$726$	−3.40243	−	5.89319i	−0.126276	−	0.218717i
$727$	−9.30106	−	34.7120i	−0.344957	−	1.28740i	−0.892662	−	0.450726i	$-0.851165\pi$
$727$	−9.30106	−	34.7120i	−0.344957	−	1.28740i	0.547705	−	0.836671i	$-0.315502\pi$
$728$	−2.24494	+	8.37822i	−0.0832029	+	0.310517i
$729$			1.00000i			0.0370370i
$730$	3.72916	+	6.36033i	0.138022	+	0.235406i
$731$	4.57083	+	7.91690i	0.169058	+	0.292817i
$732$	−0.890093	+	3.32187i	−0.0328988	+	0.122780i
$733$	16.2151	+	16.2151i	0.598919	+	0.598919i	0.940025	−	0.341106i	$-0.110802\pi$
$733$	16.2151	+	16.2151i	0.598919	+	0.598919i	−0.341106	+	0.940025i	$0.610802\pi$
$734$	27.6181			1.01940
$735$	1.95478	+	7.10465i	0.0721030	+	0.262059i
$736$	1.41293	+	0.815757i	0.0520814	+	0.0300692i
$737$	−4.70533	+	17.5605i	−0.173323	+	0.646850i
$738$	−1.72754	+	0.462894i	−0.0635918	+	0.0170394i
$739$	5.34234	+	3.08440i	0.196521	+	0.113461i	0.595032	−	0.803702i	$-0.297139\pi$
$739$	5.34234	+	3.08440i	0.196521	+	0.113461i	−0.398511	+	0.917164i	$0.630473\pi$
$740$	−4.77330	+	18.3037i	−0.175470	+	0.672857i
$741$	17.6444	−	8.63306i	0.648184	−	0.317143i
$742$	−18.9558	+	18.9558i	−0.695891	+	0.695891i
$743$	−7.04958	−	26.3094i	−0.258624	−	0.965198i	−0.966038	−	0.258399i	$-0.916805\pi$
$743$	−7.04958	−	26.3094i	−0.258624	−	0.965198i	0.707414	−	0.706799i	$-0.249862\pi$
$744$	2.91015	−	5.04052i	0.106691	−	0.184795i
$745$	18.4069	−	32.3807i	0.674378	−	1.18634i
$746$	13.5748	−	23.5122i	0.497009	−	0.860845i
$747$	11.1871	+	2.99758i	0.409315	+	0.109676i
$748$	−2.34670	−	2.34670i	−0.0858040	−	0.0858040i
$749$	13.2107			0.482708
$750$	9.56819	−	5.78357i	0.349381	−	0.211186i
$751$	−14.9432	+	8.62746i	−0.545285	+	0.314821i	−0.747218	−	0.664579i	$-0.768611\pi$
$751$	−14.9432	+	8.62746i	−0.545285	+	0.314821i	0.201933	+	0.979399i	$0.435278\pi$
$752$	8.15037	−	8.15037i	0.297213	−	0.297213i
$753$	−2.37423	+	2.37423i	−0.0865216	+	0.0865216i
$754$	−11.4280	−	19.7939i	−0.416184	−	0.720851i
$755$	−28.8487	+	0.193217i	−1.04991	+	0.00703190i
$756$	1.66688	−	0.962371i	0.0606237	−	0.0350011i
$757$	−11.4374	−	42.6849i	−0.415699	−	1.55141i	−0.783432	−	0.621478i	$-0.786533\pi$
$757$	−11.4374	−	42.6849i	−0.415699	−	1.55141i	0.367733	−	0.929931i	$-0.380134\pi$
$758$	−0.784973	+	0.210333i	−0.0285115	+	0.00763963i
$759$	3.34167			0.121295
$760$	3.09991	−	9.24070i	0.112446	−	0.335195i
$761$	−23.7823			−0.862109			−0.431055	−	0.902326i	$-0.641858\pi$
$761$	−23.7823			−0.862109			−0.431055	+	0.902326i	$0.641858\pi$
$762$	−0.376641	+	0.100921i	−0.0136443	+	0.00365597i
$763$	−0.224379	−	0.837393i	−0.00812306	−	0.0303157i
$764$	7.23972	−	4.17986i	0.261924	−	0.151222i
$765$	2.54473	−	2.57905i	0.0920050	−	0.0932457i
$766$	−8.86491	−	15.3545i	−0.320302	−	0.554780i
$767$	−20.1152	+	20.1152i	−0.726316	+	0.726316i
$768$	−0.707107	+	0.707107i	−0.0255155	+	0.0255155i
$769$	−38.3294	+	22.1295i	−1.38219	+	0.798010i	−0.992419	−	0.122901i	$-0.960780\pi$
$769$	−38.3294	+	22.1295i	−1.38219	+	0.798010i	−0.389774	+	0.920910i	$0.627447\pi$
$770$	7.66351	+	4.35635i	0.276174	+	0.156992i
$771$	6.28039			0.226183
$772$	6.23676	+	6.23676i	0.224466	+	0.224466i
$773$	51.6680	+	13.8444i	1.85837	+	0.497949i	0.999889	−	0.0148965i	$-0.00474189\pi$
$773$	51.6680	+	13.8444i	1.85837	+	0.497949i	0.858481	+	0.512845i	$0.171409\pi$
$774$	2.82094	−	4.88602i	0.101397	−	0.175624i
$775$	0.389803	+	29.0989i	0.0140021	+	1.04526i
$776$	−0.397048	+	0.687707i	−0.0142532	+	0.0246873i
$777$	−4.21415	−	15.7274i	−0.151182	−	0.564218i
$778$	−1.99856	+	1.99856i	−0.0716518	+	0.0716518i
$779$	0.534094	−	7.77751i	0.0191359	−	0.278658i
$780$	8.69278	−	5.09671i	0.311251	−	0.182491i
$781$	6.45726	+	3.72810i	0.231059	+	0.133402i
$782$	−2.55349	+	0.684207i	−0.0913127	+	0.0244672i
$783$	−1.31269	+	4.89902i	−0.0469116	+	0.175077i
$784$	2.85387	+	1.64768i	0.101924	+	0.0588458i
$785$	24.0101	−	6.60614i	0.856956	−	0.235783i
$786$	4.73684			0.168957
$787$	3.50066	+	3.50066i	0.124785	+	0.124785i	0.766741	−	0.641956i	$-0.221877\pi$
$787$	3.50066	+	3.50066i	0.124785	+	0.124785i	−0.641956	+	0.766741i	$0.721877\pi$
$788$	−3.89982	+	14.5543i	−0.138925	+	0.518477i
$789$	12.5392	+	21.7186i	0.446408	+	0.773202i
$790$	5.47659	+	1.42820i	0.194848	+	0.0508132i
$791$			8.16899i			0.290456i
$792$	−0.530114	+	1.97841i	−0.0188368	+	0.0702998i
$793$	−4.01117	−	14.9699i	−0.142441	−	0.531596i
$794$	2.43551	+	4.21843i	0.0864330	+	0.149706i
$795$	31.1430	−	0.208584i	1.10453	−	0.00739770i
$796$	9.19196	−	15.9209i	0.325800	−	0.564303i
$797$	25.4541	+	25.4541i	0.901630	+	0.901630i	0.995577	−	0.0939470i	$-0.0299484\pi$
$797$	25.4541	+	25.4541i	0.901630	+	0.901630i	−0.0939470	+	0.995577i	$0.529948\pi$
$798$	1.61113	+	8.23361i	0.0570333	+	0.291467i
$799$			18.6764i			0.660723i
$800$	1.22929	−	4.84653i	0.0434619	−	0.171351i
$801$	−6.14996	−	3.55068i	−0.217298	−	0.125457i
$802$	25.3777	+	6.79992i	0.896116	+	0.240114i
$803$	6.52338	−	1.74793i	0.230205	−	0.0616833i
$804$	−7.68691	+	4.43804i	−0.271096	+	0.156518i
$805$	6.05741	−	3.55155i	0.213495	−	0.125176i
$806$			26.2289i			0.923874i
$807$	−4.08258	−	1.09392i	−0.143714	−	0.0385079i
$808$	17.1151	+	4.58597i	0.602107	+	0.161334i
$809$		−	23.3652i		−	0.821477i	−0.911753	−	0.410739i	$-0.865271\pi$
$809$		−	23.3652i		−	0.821477i	0.911753	−	0.410739i	$-0.134729\pi$
$810$	−2.16370	−	0.564258i	−0.0760248	−	0.0198260i
$811$	−0.724160	+	0.418094i	−0.0254287	+	0.0146813i	−0.512660	−	0.858591i	$-0.671340\pi$
$811$	−0.724160	+	0.418094i	−0.0254287	+	0.0146813i	0.487232	+	0.873273i	$0.338007\pi$
$812$	9.42935	−	2.52659i	0.330905	−	0.0886658i
$813$	26.7602	+	7.17037i	0.938521	+	0.251476i
$814$	15.0053	+	8.66330i	0.525935	+	0.303649i
$815$	25.6821	−	26.0284i	0.899604	−	0.911736i
$816$		−	1.62032i		−	0.0567225i
$817$	16.1572	+	18.5400i	0.565270	+	0.648631i
$818$	−14.4803	−	14.4803i	−0.506292	−	0.506292i
$819$	−4.33689	+	7.51171i	−0.151543	+	0.262480i
$820$	−0.0267843	−	3.99908i	−0.000935347	−	0.139654i
$821$	−16.1814	−	28.0269i	−0.564733	−	0.978147i	−0.997074	−	0.0764367i	$-0.975646\pi$
$821$	−16.1814	−	28.0269i	−0.564733	−	0.978147i	0.432341	−	0.901710i	$-0.357688\pi$
$822$	−4.26130	−	15.9034i	−0.148630	−	0.554694i
$823$	−11.2016	+	41.8051i	−0.390465	+	1.45723i	0.438905	+	0.898533i	$0.355366\pi$
$823$	−11.2016	+	41.8051i	−0.390465	+	1.45723i	−0.829370	+	0.558700i	$0.811300\pi$
$824$		−	13.5148i		−	0.470810i
$825$	−2.78283	−	9.85567i	−0.0968857	−	0.343130i
$826$	−6.07499	−	10.5222i	−0.211376	−	0.366114i
$827$	−9.80128	+	36.5789i	−0.340824	+	1.27197i	0.556592	+	0.830786i	$0.312109\pi$
$827$	−9.80128	+	36.5789i	−0.340824	+	1.27197i	−0.897416	+	0.441186i	$0.854558\pi$
$828$	1.15365	+	1.15365i	0.0400923	+	0.0400923i
$829$	−2.40244			−0.0834403			−0.0417201	−	0.999129i	$-0.513284\pi$
$829$	−2.40244			−0.0834403			−0.0417201	+	0.999129i	$0.513284\pi$
$830$	−12.7983	+	22.5142i	−0.444235	+	0.781478i
$831$	5.67731	+	3.27780i	0.196944	+	0.113706i
$832$	1.16636	−	4.35290i	0.0404362	−	0.150910i
$833$	−5.15760	+	1.38197i	−0.178700	+	0.0478826i
$834$	3.01067	+	1.73821i	0.104251	+	0.0601893i
$835$	26.1700	+	6.82470i	0.905649	+	0.236178i
$836$	−7.40780	−	4.98317i	−0.256204	−	0.172347i
$837$	4.11557	−	4.11557i	0.142255	−	0.142255i
$838$	−2.28619	−	8.53219i	−0.0789752	−	0.294740i
$839$	−8.99056	+	15.5721i	−0.310389	+	0.537609i	−0.978447	−	0.206500i	$-0.933793\pi$
$839$	−8.99056	+	15.5721i	−0.310389	+	0.537609i	0.668058	+	0.744109i	$0.267126\pi$
$840$	1.14174	+	4.14965i	0.0393937	+	0.143177i
$841$	1.63823	−	2.83750i	0.0564908	−	0.0978450i
$842$	−22.6150	−	6.05966i	−0.779363	−	0.208830i
$843$	−18.8487	−	18.8487i	−0.649184	−	0.649184i
$844$	11.9310			0.410682
$845$	−8.07580	+	14.2066i	−0.277816	+	0.488722i
$846$	9.98212	−	5.76318i	0.343192	−	0.198142i
$847$	−9.26142	+	9.26142i	−0.318226	+	0.318226i
$848$	9.84851	−	9.84851i	0.338199	−	0.338199i
$849$	−15.5062	−	26.8575i	−0.532172	−	0.921749i
$850$	4.14441	+	6.96130i	0.142152	+	0.238770i
$851$	11.9526	−	6.90083i	0.409729	−	0.236557i
$852$	0.942196	+	3.51632i	0.0322791	+	0.120467i
$853$	−31.4321	+	8.42219i	−1.07621	+	0.288370i	−0.753044	−	0.657971i	$-0.771415\pi$
$853$	−31.4321	+	8.42219i	−1.07621	+	0.288370i	−0.323170	+	0.946341i	$0.604748\pi$
$854$	6.61930			0.226508
$855$	5.38595	−	8.12352i	0.184196	−	0.277818i
$856$	−6.86361			−0.234593
$857$	37.7624	−	10.1184i	1.28994	−	0.345638i	0.452301	−	0.891865i	$-0.350603\pi$
$857$	37.7624	−	10.1184i	1.28994	−	0.345638i	0.837637	+	0.546227i	$0.183936\pi$
$858$	−2.38893	−	8.91563i	−0.0815569	−	0.304374i
$859$	−44.5020	+	25.6932i	−1.51839	+	0.876641i	−0.518621	+	0.855004i	$0.673555\pi$
$859$	−44.5020	+	25.6932i	−1.51839	+	0.876641i	−0.999766	+	0.0216373i	$0.993112\pi$
$860$	8.98015	+	8.86066i	0.306221	+	0.302146i
$861$	1.72119	+	2.98118i	0.0586579	+	0.101598i
$862$	−21.9356	+	21.9356i	−0.747128	+	0.747128i
$863$	−24.7993	+	24.7993i	−0.844178	+	0.844178i	−0.989399	−	0.145221i	$-0.953611\pi$
$863$	−24.7993	+	24.7993i	−0.844178	+	0.844178i	0.145221	+	0.989399i	$0.453611\pi$
$864$	−0.866025	+	0.500000i	−0.0294628	+	0.0170103i
$865$	39.6474	−	10.9086i	1.34805	−	0.370904i
$866$	−27.1032			−0.921003
$867$	−10.1644	−	10.1644i	−0.345200	−	0.345200i
$868$	−10.8209	−	2.89944i	−0.367284	−	0.0984134i
$869$	2.59212	−	4.48969i	0.0879317	−	0.152302i
$870$	−9.85933	−	5.60458i	−0.334263	−	0.190013i
$871$	19.9998	−	34.6407i	0.677668	−	1.17376i
$872$	0.116576	+	0.435068i	0.00394776	+	0.0147333i
$873$	−0.561511	+	0.561511i	−0.0190043	+	0.0190043i
$874$	−6.38797	+	3.12550i	−0.216076	+	0.105722i
$875$	−15.5191	−	14.9076i	−0.524640	−	0.503970i
$876$	2.85553	+	1.64864i	0.0964794	+	0.0557024i
$877$	1.15148	−	0.308538i	0.0388827	−	0.0104186i	−0.239325	−	0.970939i	$-0.576926\pi$
$877$	1.15148	−	0.308538i	0.0388827	−	0.0104186i	0.278208	+	0.960521i	$0.410260\pi$
$878$	−2.22396	+	8.29993i	−0.0750550	+	0.280109i
$879$	−9.48112	−	5.47393i	−0.319790	−	0.184631i
$880$	−3.98157	−	2.26334i	−0.134219	−	0.0762973i
$881$	−30.0756			−1.01327			−0.506637	−	0.862160i	$-0.669111\pi$
$881$	−30.0756			−1.01327			−0.506637	+	0.862160i	$0.669111\pi$
$882$	2.33018	+	2.33018i	0.0784611	+	0.0784611i
$883$	15.1799	−	56.6520i	0.510843	−	1.90649i	0.0994252	−	0.995045i	$-0.468300\pi$
$883$	15.1799	−	56.6520i	0.510843	−	1.90649i	0.411418	−	0.911447i	$-0.365034\pi$
$884$	3.65095	+	6.32363i	0.122795	+	0.212687i
$885$	−3.56189	+	13.6584i	−0.119732	+	0.459123i
$886$			14.1139i			0.474166i
$887$	−7.07054	+	26.3876i	−0.237406	+	0.886010i	0.739644	+	0.672998i	$0.234994\pi$
$887$	−7.07054	+	26.3876i	−0.237406	+	0.886010i	−0.977050	+	0.213011i	$0.931673\pi$
$888$	2.18946	+	8.17117i	0.0734734	+	0.274207i
$889$	0.375255	+	0.649961i	0.0125857	+	0.0217990i
$890$	11.1528	−	11.3032i	0.373842	−	0.378884i
$891$	−1.02410	+	1.77379i	−0.0343087	+	0.0594244i
$892$	−13.5353	−	13.5353i	−0.453196	−	0.453196i
$893$	9.64827	+	49.3071i	0.322867	+	1.65000i
$894$		−	16.6573i		−	0.557102i
$895$	−0.0737896	−	11.0173i	−0.00246651	−	0.368268i
$896$	1.66688	+	0.962371i	0.0556864	+	0.0321506i
$897$	−7.10182	−	1.90293i	−0.237123	−	0.0635369i
$898$	25.1577	−	6.74098i	0.839523	−	0.224949i
$899$	25.5647	−	14.7598i	0.852631	−	0.492267i
$900$	2.44178	−	4.36323i	0.0813925	−	0.145441i
$901$			22.5676i			0.751837i
$902$	−3.53836	−	0.948100i	−0.117814	−	0.0315683i
$903$	−10.4892	−	2.81056i	−0.349057	−	0.0935297i
$904$		−	4.24420i		−	0.141160i
$905$	−16.6460	−	28.3908i	−0.553331	−	0.943743i
$906$	−11.1733	+	6.45092i	−0.371209	+	0.214317i
$907$	−4.20549	+	1.12686i	−0.139641	+	0.0374167i	−0.327962	−	0.944691i	$-0.606362\pi$
$907$	−4.20549	+	1.12686i	−0.139641	+	0.0374167i	0.188322	+	0.982107i	$0.439695\pi$
$908$	20.3629	+	5.45623i	0.675768	+	0.181071i
$909$	15.3450	+	8.85942i	0.508960	+	0.293848i
$910$	−13.8060	−	13.6223i	−0.457664	−	0.451574i
$911$		−	58.7244i		−	1.94562i	−0.231595	−	0.972812i	$-0.574394\pi$
$911$		−	58.7244i		−	1.94562i	0.231595	−	0.972812i	$-0.425606\pi$
$912$	−0.837061	−	4.27777i	−0.0277179	−	0.141651i
$913$	16.7738	+	16.7738i	0.555132	+	0.555132i
$914$	−0.497601	+	0.861871i	−0.0164592	+	0.0285082i
$915$	−5.47392	−	5.40109i	−0.180962	−	0.178554i
$916$	12.9960	+	22.5097i	0.429399	+	0.743740i
$917$	−2.35970	−	8.80654i	−0.0779243	−	0.290817i
$918$	0.419369	−	1.56511i	0.0138412	−	0.0516562i
$919$		−	40.7914i		−	1.34558i	−0.739832	−	0.672792i	$-0.765095\pi$
$919$		−	40.7914i		−	1.34558i	0.739832	−	0.672792i	$-0.234905\pi$
$920$	−3.14712	+	1.84521i	−0.103758	+	0.0608347i
$921$	11.6507	+	20.1797i	0.383905	+	0.664943i
$922$	−1.69253	+	6.31662i	−0.0557406	+	0.208027i
$923$	−11.6002	−	11.6002i	−0.381825	−	0.381825i
$924$	3.94226			0.129691
$925$	−30.3065	−	29.5053i	−0.996472	−	0.970127i
$926$	−9.05229	−	5.22634i	−0.297477	−	0.171748i
$927$	3.49788	−	13.0543i	0.114886	−	0.428759i
$928$	−4.89902	+	1.31269i	−0.160818	+	0.0430911i
$929$	49.9216	+	28.8222i	1.63787	+	0.945627i	0.981564	+	0.191135i	$0.0612168\pi$
$929$	49.9216	+	28.8222i	1.63787	+	0.945627i	0.656310	+	0.754492i	$0.272117\pi$
$930$	6.58263	+	11.2271i	0.215853	+	0.368152i
$931$	−12.9026	+	6.31296i	−0.422864	+	0.206899i
$932$	14.8285	−	14.8285i	0.485722	−	0.485722i
$933$	1.66638	+	6.21903i	0.0545549	+	0.203602i
$934$	2.18956	−	3.79243i	0.0716447	−	0.124092i
$935$	7.15504	−	1.96864i	0.233995	−	0.0643815i
$936$	2.25323	−	3.90271i	0.0736491	−	0.127564i
$937$	31.2366	+	8.36983i	1.02046	+	0.273430i	0.729992	−	0.683455i	$-0.239524\pi$
$937$	31.2366	+	8.36983i	1.02046	+	0.273430i	0.290464	+	0.956886i	$0.406190\pi$
$938$	12.0803	+	12.0803i	0.394437	+	0.394437i
$939$	−23.2771			−0.759621
$940$	6.83732	+	24.8503i	0.223009	+	0.810527i
$941$	35.1845	−	20.3138i	1.14698	−	0.662210i	0.198832	−	0.980034i	$-0.436285\pi$
$941$	35.1845	−	20.3138i	1.14698	−	0.662210i	0.948150	+	0.317823i	$0.102952\pi$
$942$	7.87480	−	7.87480i	0.256575	−	0.256575i
$943$	−2.06329	+	2.06329i	−0.0671901	+	0.0671901i
$944$	3.15626	+	5.46681i	0.102728	+	0.177929i
$945$	0.0288249	+	4.30376i	0.000937673	+	0.140001i
$946$	10.0075	−	5.77786i	0.325373	−	0.187854i
$947$	9.80262	+	36.5839i	0.318542	+	1.18882i	0.920646	+	0.390398i	$0.127663\pi$
$947$	9.80262	+	36.5839i	0.318542	+	1.18882i	−0.602104	+	0.798418i	$0.705671\pi$
$948$	2.44487	−	0.655102i	0.0794058	−	0.0212767i
$949$	−14.8591			−0.482346
$950$	14.5378	+	16.2374i	0.471669	+	0.526810i
$951$	−28.5688			−0.926408
$952$	−3.01243	+	0.807178i	−0.0976334	+	0.0261608i
$953$	6.83890	+	25.5231i	0.221534	+	0.826775i	0.983764	+	0.179469i	$0.0574378\pi$
$953$	6.83890	+	25.5231i	0.221534	+	0.826775i	−0.762230	+	0.647306i	$0.775896\pi$
$954$	12.0619	−	6.96395i	0.390519	−	0.225466i
$955$	0.125195	+	18.6925i	0.00405120	+	0.604874i
$956$	−5.77651	−	10.0052i	−0.186826	−	0.323592i
$957$	−7.34553	+	7.34553i	−0.237447	+	0.237447i
$958$	15.4760	−	15.4760i	0.500006	−	0.500006i
$959$	−27.4441	+	15.8448i	−0.886216	+	0.511657i
$960$	−0.593190	−	2.15595i	−0.0191451	−	0.0695830i
$961$	−2.87584			−0.0927691
$962$	−26.9563	−	26.9563i	−0.869107	−	0.869107i
$963$	−6.62974	−	1.77643i	−0.213640	−	0.0572448i
$964$	−5.95641	+	10.3168i	−0.191843	+	0.332282i
$965$	−19.0157	+	5.23200i	−0.612138	+	0.168424i
$966$	1.57012	−	2.71953i	0.0505178	−	0.0874995i
$967$	6.37968	+	23.8093i	0.205157	+	0.765655i	0.989402	+	0.145204i	$0.0463837\pi$
$967$	6.37968	+	23.8093i	0.205157	+	0.765655i	−0.784245	+	0.620451i	$0.786950\pi$
$968$	4.81177	−	4.81177i	0.154656	−	0.154656i
$969$	5.86026	+	3.94215i	0.188259	+	0.126640i
$970$	−0.898106	−	1.53178i	−0.0288364	−	0.0491825i
$971$	−20.3548	−	11.7519i	−0.653218	−	0.377135i	0.136470	−	0.990644i	$-0.456424\pi$
$971$	−20.3548	−	11.7519i	−0.653218	−	0.377135i	−0.789688	+	0.613509i	$0.789757\pi$
$972$	−0.965926	+	0.258819i	−0.0309821	+	0.00830162i
$973$	1.73181	−	6.46322i	0.0555194	−	0.207201i
$974$	22.3089	+	12.8801i	0.714824	+	0.412704i
$975$	0.301811	+	22.5303i	0.00966569	+	0.721546i
$976$	−3.43906			−0.110082
$977$	−22.4317	−	22.4317i	−0.717652	−	0.717652i	0.250472	−	0.968124i	$-0.419414\pi$
$977$	−22.4317	−	22.4317i	−0.717652	−	0.717652i	−0.968124	+	0.250472i	$0.919414\pi$
$978$	4.23238	−	15.7955i	0.135337	−	0.505083i
$979$	−7.27251	−	12.5964i	−0.232430	−	0.402581i
$980$	−6.35663	+	3.72699i	−0.203055	+	0.119054i
$981$			0.450415i			0.0143807i
$982$	−7.60604	+	28.3861i	−0.242718	+	0.905837i
$983$	8.21139	+	30.6453i	0.261903	+	0.977435i	0.964119	+	0.265471i	$0.0855274\pi$
$983$	8.21139	+	30.6453i	0.261903	+	0.977435i	−0.702216	+	0.711964i	$0.747806\pi$
$984$	−0.894242	−	1.54887i	−0.0285074	−	0.0493763i
$985$	−23.9832	−	23.6641i	−0.764169	−	0.754001i
$986$	4.10899	−	7.11699i	0.130857	−	0.226651i
$987$	−15.6874	−	15.6874i	−0.499334	−	0.499334i
$988$	12.9056	+	14.8088i	0.410582	+	0.471131i
$989$		−	9.20481i		−	0.292696i
$990$	−3.26011	−	3.21673i	−0.103613	−	0.102234i
$991$	3.63811	+	2.10046i	0.115568	+	0.0667234i	0.556670	−	0.830734i	$-0.312079\pi$
$991$	3.63811	+	2.10046i	0.115568	+	0.0667234i	−0.441102	+	0.897457i	$0.645412\pi$
$992$	5.62197	+	1.50640i	0.178498	+	0.0478284i
$993$	−25.8773	+	6.93381i	−0.821192	+	0.220038i
$994$	6.06804	−	3.50338i	0.192467	−	0.111121i
$995$	20.7918	+	35.4618i	0.659145	+	1.12422i
$996$			11.5817i			0.366982i
$997$	32.1266	+	8.60831i	1.01746	+	0.272628i	0.728744	−	0.684787i	$-0.240105\pi$
$997$	32.1266	+	8.60831i	1.01746	+	0.272628i	0.288717	+	0.957414i	$0.406771\pi$
$998$	5.97542	+	1.60111i	0.189149	+	0.0506822i
$999$			8.45942i			0.267644i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.x.b.103.3	✓	40
5.2	odd	4	inner	570.2.x.b.217.2	yes	40
19.12	odd	6	inner	570.2.x.b.373.2	yes	40
95.12	even	12	inner	570.2.x.b.487.3	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.x.b.103.3	✓	40	1.1	even	1	trivial
570.2.x.b.217.2	yes	40	5.2	odd	4	inner
570.2.x.b.373.2	yes	40	19.12	odd	6	inner
570.2.x.b.487.3	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)

\(f(q)\)	\(=\)	\(q+(-0.965926 + 0.258819i) q^{2} +(-0.258819 - 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} +(0.0149760 + 2.23602i) q^{5} +(0.500000 + 0.866025i) q^{6} +(1.36100 - 1.36100i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.866025 + 0.500000i) q^{9} +O(q^{10})\)	\(q+(-0.965926 + 0.258819i) q^{2} +(-0.258819 - 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} +(0.0149760 + 2.23602i) q^{5} +(0.500000 + 0.866025i) q^{6} +(1.36100 - 1.36100i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.866025 + 0.500000i) q^{9} +(-0.593190 - 2.15595i) q^{10} -2.04820 q^{11} +(-0.707107 - 0.707107i) q^{12} +(4.35290 + 1.16636i) q^{13} +(-0.962371 + 1.66688i) q^{14} +(2.15595 - 0.593190i) q^{15} +(0.500000 - 0.866025i) q^{16} +(0.419369 + 1.56511i) q^{17} +(0.707107 - 0.707107i) q^{18} +(1.91571 + 3.91536i) q^{19} +(1.13098 + 1.92896i) q^{20} +(-1.66688 - 0.962371i) q^{21} +(1.97841 - 0.530114i) q^{22} +(0.422267 - 1.57592i) q^{23} +(0.866025 + 0.500000i) q^{24} +(-4.99955 + 0.0669730i) q^{25} -4.50646 q^{26} +(0.707107 + 0.707107i) q^{27} +(0.498160 - 1.85916i) q^{28} +(2.53592 + 4.39234i) q^{29} +(-1.92896 + 1.13098i) q^{30} -5.82030i q^{31} +(-0.258819 + 0.965926i) q^{32} +(0.530114 + 1.97841i) q^{33} +(-0.810159 - 1.40324i) q^{34} +(3.06360 + 3.02283i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(5.98171 + 5.98171i) q^{37} +(-2.86380 - 3.28613i) q^{38} -4.50646i q^{39} +(-1.59169 - 1.57051i) q^{40} +(-1.54887 - 0.894242i) q^{41} +(1.85916 + 0.498160i) q^{42} +(5.44964 - 1.46023i) q^{43} +(-1.77379 + 1.02410i) q^{44} +(-1.13098 - 1.92896i) q^{45} +1.63151i q^{46} +(11.1336 + 2.98324i) q^{47} +(-0.965926 - 0.258819i) q^{48} +3.29537i q^{49} +(4.81186 - 1.35867i) q^{50} +(1.40324 - 0.810159i) q^{51} +(4.35290 - 1.16636i) q^{52} +(13.4533 + 3.60480i) q^{53} +(-0.866025 - 0.500000i) q^{54} +(-0.0306738 - 4.57982i) q^{55} +1.92474i q^{56} +(3.28613 - 2.86380i) q^{57} +(-3.58633 - 3.58633i) q^{58} +(-3.15626 + 5.46681i) q^{59} +(1.57051 - 1.59169i) q^{60} +(-1.71953 - 2.97831i) q^{61} +(1.50640 + 5.62197i) q^{62} +(-0.498160 + 1.85916i) q^{63} -1.00000i q^{64} +(-2.54281 + 9.75064i) q^{65} +(-1.02410 - 1.77379i) q^{66} +(2.29730 - 8.57363i) q^{67} +(1.14574 + 1.14574i) q^{68} -1.63151 q^{69} +(-3.74158 - 2.12692i) q^{70} +(-3.15265 - 1.82018i) q^{71} +(0.258819 - 0.965926i) q^{72} +(-3.18493 + 0.853400i) q^{73} +(-7.32607 - 4.22971i) q^{74} +(1.35867 + 4.81186i) q^{75} +(3.61673 + 2.43295i) q^{76} +(-2.78760 + 2.78760i) q^{77} +(1.16636 + 4.35290i) q^{78} +(-1.26556 + 2.19201i) q^{79} +(1.94394 + 1.10504i) q^{80} +(0.500000 - 0.866025i) q^{81} +(1.72754 + 0.462894i) q^{82} +(-8.18953 - 8.18953i) q^{83} -1.92474 q^{84} +(-3.49333 + 0.961156i) q^{85} +(-4.88602 + 2.82094i) q^{86} +(3.58633 - 3.58633i) q^{87} +(1.44830 - 1.44830i) q^{88} +(3.55068 + 6.14996i) q^{89} +(1.59169 + 1.57051i) q^{90} +(7.51171 - 4.33689i) q^{91} +(-0.422267 - 1.57592i) q^{92} +(-5.62197 + 1.50640i) q^{93} -11.5264 q^{94} +(-8.72613 + 4.34219i) q^{95} +1.00000 q^{96} +(0.767038 - 0.205527i) q^{97} +(-0.852903 - 3.18308i) q^{98} +(1.77379 - 1.02410i) 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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