LMFDB - Embedded newform 180.2.n.d.119.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [180,2,Mod(59,180)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(180, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 5, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("180.59"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 180 = 2^{2} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	180.n (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.43730723638$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			119.6
Character	$\chi$	$=$	180.119
Dual form			180.2.n.d.59.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.00727 + 0.992675i) q^{2} +(1.30213 + 1.14213i) q^{3} +(0.0291929 - 1.99979i) q^{4} +(1.64183 + 1.51803i) q^{5} +(-2.44536 + 0.142161i) q^{6} +(1.65751 - 2.87089i) q^{7} +(1.95573 + 2.04331i) q^{8} +(0.391092 + 2.97440i) q^{9} +(-3.16067 + 0.100737i) q^{10} +(1.17952 - 2.04298i) q^{11} +(2.32202 - 2.57064i) q^{12} +(-3.81058 + 2.20004i) q^{13} +(1.18030 + 4.53714i) q^{14} +(0.404097 + 3.85184i) q^{15} +(-3.99830 - 0.116759i) q^{16} -0.889368 q^{17} +(-3.34655 - 2.60780i) q^{18} -3.03537i q^{19} +(3.08366 - 3.23899i) q^{20} +(5.43722 - 1.84519i) q^{21} +(0.839925 + 3.22872i) q^{22} +(-6.29952 + 3.63703i) q^{23} +(0.212904 + 4.89435i) q^{24} +(0.391197 + 4.98467i) q^{25} +(1.65437 - 5.99870i) q^{26} +(-2.88789 + 4.31973i) q^{27} +(-5.69278 - 3.39848i) q^{28} +(1.03714 + 0.598791i) q^{29} +(-4.23067 - 3.47872i) q^{30} +(0.205172 - 0.118456i) q^{31} +(4.14327 - 3.85140i) q^{32} +(3.86923 - 1.31308i) q^{33} +(0.895835 - 0.882853i) q^{34} +(7.07943 - 2.19737i) q^{35} +(5.95958 - 0.695270i) q^{36} -11.4975i q^{37} +(3.01314 + 3.05745i) q^{38} +(-7.47460 - 1.48743i) q^{39} +(0.109183 + 6.32361i) q^{40} +(2.45213 - 1.41574i) q^{41} +(-3.64508 + 7.25600i) q^{42} +(4.17637 - 7.23369i) q^{43} +(-4.05110 - 2.41842i) q^{44} +(-3.87311 + 5.47714i) q^{45} +(2.73494 - 9.91686i) q^{46} +(-6.55796 - 3.78624i) q^{47} +(-5.07295 - 4.71860i) q^{48} +(-1.99467 - 3.45488i) q^{49} +(-5.34220 - 4.63259i) q^{50} +(-1.15807 - 1.01577i) q^{51} +(4.28837 + 7.68457i) q^{52} +0.772055 q^{53} +(-1.37920 - 7.21788i) q^{54} +(5.03787 - 1.56369i) q^{55} +(9.10776 - 2.22789i) q^{56} +(3.46678 - 3.95246i) q^{57} +(-1.63908 + 0.426394i) q^{58} +(1.06446 + 1.84370i) q^{59} +(7.71466 - 0.695662i) q^{60} +(1.91303 - 3.31346i) q^{61} +(-0.0890754 + 0.322986i) q^{62} +(9.18741 + 3.80731i) q^{63} +(-0.350216 + 7.99233i) q^{64} +(-9.59603 - 2.17247i) q^{65} +(-2.59391 + 5.16352i) q^{66} +(3.17238 + 5.49472i) q^{67} +(-0.0259632 + 1.77855i) q^{68} +(-12.3568 - 2.45896i) q^{69} +(-4.94964 + 9.24092i) q^{70} -11.7244 q^{71} +(-5.31274 + 6.61625i) q^{72} +6.10889i q^{73} +(11.4133 + 11.5811i) q^{74} +(-5.18374 + 6.93750i) q^{75} +(-6.07010 - 0.0886114i) q^{76} +(-3.91012 - 6.77253i) q^{77} +(9.00548 - 5.92160i) q^{78} +(8.94873 + 5.16655i) q^{79} +(-6.38727 - 6.26121i) q^{80} +(-8.69409 + 2.32653i) q^{81} +(-1.06459 + 3.86020i) q^{82} +(-2.25103 - 1.29963i) q^{83} +(-3.53126 - 10.9271i) q^{84} +(-1.46019 - 1.35008i) q^{85} +(2.97396 + 11.4321i) q^{86} +(0.666593 + 1.96425i) q^{87} +(6.48127 - 1.58541i) q^{88} +4.68130i q^{89} +(-1.53575 - 9.36170i) q^{90} +14.5863i q^{91} +(7.08939 + 12.7039i) q^{92} +(0.402452 + 0.0800869i) q^{93} +(10.3642 - 2.69615i) q^{94} +(4.60778 - 4.98356i) q^{95} +(9.79387 - 0.282883i) q^{96} +(5.34684 + 3.08700i) q^{97} +(5.43875 + 1.49994i) q^{98} +(6.53795 + 2.70936i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 2 q^{4} - 18 q^{5} - 12 q^{9} - 16 q^{10} - 42 q^{14} + 30 q^{16} - 12 q^{21} - 6 q^{24} - 26 q^{25} - 12 q^{30} - 4 q^{34} + 96 q^{36} + 10 q^{40} + 96 q^{41} - 66 q^{45} + 4 q^{46} + 32 q^{49}+ \cdots + 54 q^{96}+O(q^{100}) $ 48 * q - 2 * q^4 - 18 * q^5 - 12 * q^9 - 16 * q^10 - 42 * q^14 + 30 * q^16 - 12 * q^21 - 6 * q^24 - 26 * q^25 - 12 * q^30 - 4 * q^34 + 96 * q^36 + 10 * q^40 + 96 * q^41 - 66 * q^45 + 4 * q^46 + 32 * q^49 - 90 * q^50 - 30 * q^54 + 6 * q^56 - 42 * q^60 + 8 * q^61 - 20 * q^64 - 6 * q^65 + 36 * q^66 - 96 * q^69 + 4 * q^70 + 72 * q^74 + 36 * q^81 - 6 * q^84 - 4 * q^85 + 108 * q^86 - 6 * q^90 - 62 * q^94 + 54 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/180\mathbb{Z}\right)^\times$.

$n$	$37$	$91$	$101$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−1.00727	+	0.992675i	−0.712249	+	0.701927i
$2$	−1.00727	+	0.992675i	−0.712249	+	0.701927i
$3$	1.30213	+	1.14213i	0.751786	+	0.659407i
$3$	1.30213	+	1.14213i	0.751786	+	0.659407i
$4$	0.0291929	−	1.99979i	0.0145965	−	0.999893i
$5$	1.64183	+	1.51803i	0.734248	+	0.678882i
$5$	1.64183	+	1.51803i	0.734248	+	0.678882i
$6$	−2.44536	+	0.142161i	−0.998314	+	0.0580370i
$7$	1.65751	−	2.87089i	0.626480	−	1.08509i	−0.361773	−	0.932266i	$-0.617828\pi$
$7$	1.65751	−	2.87089i	0.626480	−	1.08509i	0.988253	−	0.152828i	$-0.0488382\pi$
$8$	1.95573	+	2.04331i	0.691456	+	0.722418i
$9$	0.391092	+	2.97440i	0.130364	+	0.991466i
$10$	−3.16067	+	0.100737i	−0.999492	+	0.0318558i
$11$	1.17952	−	2.04298i	0.355638	−	0.615983i	−0.631589	−	0.775303i	$-0.717597\pi$
$11$	1.17952	−	2.04298i	0.355638	−	0.615983i	0.987227	+	0.159320i	$0.0509303\pi$
$12$	2.32202	−	2.57064i	0.670310	−	0.742081i
$13$	−3.81058	+	2.20004i	−1.05686	+	0.610181i	−0.924563	−	0.381029i	$-0.875570\pi$
$13$	−3.81058	+	2.20004i	−1.05686	+	0.610181i	−0.132301	+	0.991210i	$0.542237\pi$
$14$	1.18030	+	4.53714i	0.315448	+	1.21260i
$15$	0.404097	+	3.85184i	0.104338	+	0.994542i
$16$	−3.99830	−	0.116759i	−0.999574	−	0.0291898i
$17$	−0.889368			−0.215703			−0.107852	−	0.994167i	$-0.534397\pi$
$17$	−0.889368			−0.215703			−0.107852	+	0.994167i	$0.534397\pi$
$18$	−3.34655	−	2.60780i	−0.788789	−	0.614664i
$19$		−	3.03537i		−	0.696363i	−0.937427	−	0.348181i	$-0.886799\pi$
$19$		−	3.03537i		−	0.696363i	0.937427	−	0.348181i	$-0.113201\pi$
$20$	3.08366	−	3.23899i	0.689527	−	0.724260i
$21$	5.43722	−	1.84519i	1.18650	−	0.402654i
$22$	0.839925	+	3.22872i	0.179073	+	0.688365i
$23$	−6.29952	+	3.63703i	−1.31354	+	0.758374i	−0.982681	−	0.185306i	$-0.940672\pi$
$23$	−6.29952	+	3.63703i	−1.31354	+	0.758374i	−0.330861	+	0.943680i	$0.607339\pi$
$24$	0.212904	+	4.89435i	0.0434589	+	0.999055i
$25$	0.391197	+	4.98467i	0.0782393	+	0.996935i
$26$	1.65437	−	5.99870i	0.324448	−	1.17644i
$27$	−2.88789	+	4.31973i	−0.555774	+	0.831333i
$28$	−5.69278	−	3.39848i	−1.07583	−	0.642251i
$29$	1.03714	+	0.598791i	0.192592	+	0.111193i	0.593195	−	0.805059i	$-0.297866\pi$
$29$	1.03714	+	0.598791i	0.192592	+	0.111193i	−0.400604	+	0.916251i	$0.631200\pi$
$30$	−4.23067	−	3.47872i	−0.772410	−	0.635124i
$31$	0.205172	−	0.118456i	0.0368499	−	0.0212753i	−0.481462	−	0.876467i	$-0.659894\pi$
$31$	0.205172	−	0.118456i	0.0368499	−	0.0212753i	0.518312	+	0.855192i	$0.326561\pi$
$32$	4.14327	−	3.85140i	0.732434	−	0.680838i
$33$	3.86923	−	1.31308i	0.673547	−	0.228577i
$34$	0.895835	−	0.882853i	0.153634	−	0.151408i
$35$	7.07943	−	2.19737i	1.19664	−	0.371423i
$36$	5.95958	−	0.695270i	0.993263	−	0.115878i
$37$		−	11.4975i		−	1.89018i	−0.326807	−	0.945091i	$-0.605973\pi$
$37$		−	11.4975i		−	1.89018i	0.326807	−	0.945091i	$-0.394027\pi$
$38$	3.01314	+	3.05745i	0.488796	+	0.495983i
$39$	−7.47460	−	1.48743i	−1.19689	−	0.238179i
$40$	0.109183	+	6.32361i	0.0172633	+	0.999851i
$41$	2.45213	−	1.41574i	0.382958	−	0.221101i	−0.296146	−	0.955143i	$-0.595702\pi$
$41$	2.45213	−	1.41574i	0.382958	−	0.221101i	0.679105	+	0.734042i	$0.262368\pi$
$42$	−3.64508	+	7.25600i	−0.562448	+	1.11962i
$43$	4.17637	−	7.23369i	0.636891	−	1.10313i	−0.349220	−	0.937041i	$-0.613553\pi$
$43$	4.17637	−	7.23369i	0.636891	−	1.10313i	0.986111	−	0.166087i	$-0.0531132\pi$
$44$	−4.05110	−	2.41842i	−0.610726	−	0.364591i
$45$	−3.87311	+	5.47714i	−0.577369	+	0.816484i
$46$	2.73494	−	9.91686i	0.403245	−	1.46216i
$47$	−6.55796	−	3.78624i	−0.956577	−	0.552280i	−0.0614594	−	0.998110i	$-0.519575\pi$
$47$	−6.55796	−	3.78624i	−0.956577	−	0.552280i	−0.895118	+	0.445829i	$0.852909\pi$
$48$	−5.07295	−	4.71860i	−0.732218	−	0.681071i
$49$	−1.99467	−	3.45488i	−0.284954	−	0.493554i
$50$	−5.34220	−	4.63259i	−0.755501	−	0.655147i
$51$	−1.15807	−	1.01577i	−0.162163	−	0.142236i
$52$	4.28837	+	7.68457i	0.594689	+	1.06566i
$53$	0.772055			0.106050			0.0530249	−	0.998593i	$-0.483114\pi$
$53$	0.772055			0.106050			0.0530249	+	0.998593i	$0.483114\pi$
$54$	−1.37920	−	7.21788i	−0.187686	−	0.982229i
$55$	5.03787	−	1.56369i	0.679306	−	0.210848i
$56$	9.10776	−	2.22789i	1.21708	−	0.297715i
$57$	3.46678	−	3.95246i	0.459187	−	0.523516i
$58$	−1.63908	+	0.426394i	−0.215222	+	0.0559883i
$59$	1.06446	+	1.84370i	0.138581	+	0.240029i	0.926960	−	0.375161i	$-0.122413\pi$
$59$	1.06446	+	1.84370i	0.138581	+	0.240029i	−0.788379	+	0.615190i	$0.789079\pi$
$60$	7.71466	−	0.695662i	0.995959	−	0.0898096i
$61$	1.91303	−	3.31346i	0.244938	−	0.424245i	−0.717176	−	0.696892i	$-0.754566\pi$
$61$	1.91303	−	3.31346i	0.244938	−	0.424245i	0.962114	+	0.272647i	$0.0878990\pi$
$62$	−0.0890754	+	0.322986i	−0.0113126	+	0.0410193i
$63$	9.18741	+	3.80731i	1.15751	+	0.479676i
$64$	−0.350216	+	7.99233i	−0.0437769	+	0.999041i
$65$	−9.59603	−	2.17247i	−1.19024	−	0.269462i
$66$	−2.59391	+	5.16352i	−0.319289	+	0.635585i
$67$	3.17238	+	5.49472i	0.387567	+	0.671287i	0.992122	−	0.125277i	$-0.0399821\pi$
$67$	3.17238	+	5.49472i	0.387567	+	0.671287i	−0.604554	+	0.796564i	$0.706649\pi$
$68$	−0.0259632	+	1.77855i	−0.00314851	+	0.215680i
$69$	−12.3568	−	2.45896i	−1.48758	−	0.296024i
$70$	−4.94964	+	9.24092i	−0.591595	+	1.10450i
$71$	−11.7244			−1.39143			−0.695717	−	0.718316i	$-0.744913\pi$
$71$	−11.7244			−1.39143			−0.695717	+	0.718316i	$0.744913\pi$
$72$	−5.31274	+	6.61625i	−0.626112	+	0.779733i
$73$			6.10889i			0.714992i	0.933915	+	0.357496i	$0.116369\pi$
$73$			6.10889i			0.714992i	−0.933915	+	0.357496i	$0.883631\pi$
$74$	11.4133	+	11.5811i	1.32677	+	1.34628i
$75$	−5.18374	+	6.93750i	−0.598567	+	0.801073i
$76$	−6.07010	−	0.0886114i	−0.696288	−	0.0101644i
$77$	−3.91012	−	6.77253i	−0.445600	−	0.771802i
$78$	9.00548	−	5.92160i	1.01967	−	0.670490i
$79$	8.94873	+	5.16655i	1.00681	+	0.581283i	0.910256	−	0.414045i	$-0.135884\pi$
$79$	8.94873	+	5.16655i	1.00681	+	0.581283i	0.0965546	+	0.995328i	$0.469218\pi$
$80$	−6.38727	−	6.26121i	−0.714118	−	0.700025i
$81$	−8.69409	+	2.32653i	−0.966010	+	0.258503i
$82$	−1.06459	+	3.86020i	−0.117565	+	0.426288i
$83$	−2.25103	−	1.29963i	−0.247083	−	0.142653i	0.371345	−	0.928495i	$-0.378897\pi$
$83$	−2.25103	−	1.29963i	−0.247083	−	0.142653i	−0.618428	+	0.785842i	$0.712230\pi$
$84$	−3.53126	−	10.9271i	−0.385292	−	1.19225i
$85$	−1.46019	−	1.35008i	−0.158380	−	0.146437i
$86$	2.97396	+	11.4321i	0.320690	+	1.23275i
$87$	0.666593	+	1.96425i	0.0714663	+	0.210589i
$88$	6.48127	−	1.58541i	0.690906	−	0.169006i
$89$			4.68130i			0.496217i	0.968732	+	0.248108i	$0.0798089\pi$
$89$			4.68130i			0.496217i	−0.968732	+	0.248108i	$0.920191\pi$
$90$	−1.53575	−	9.36170i	−0.161882	−	0.986810i
$91$			14.5863i			1.52906i
$92$	7.08939	+	12.7039i	0.739120	+	1.32447i
$93$	0.402452	+	0.0800869i	0.0417324	+	0.00830463i
$94$	10.3642	−	2.69615i	1.06898	−	0.278087i
$95$	4.60778	−	4.98356i	0.472748	−	0.511303i
$96$	9.79387	−	0.282883i	0.999583	−	0.0288716i
$97$	5.34684	+	3.08700i	0.542890	+	0.313438i	0.746249	−	0.665667i	$-0.231853\pi$
$97$	5.34684	+	3.08700i	0.542890	+	0.313438i	−0.203360	+	0.979104i	$0.565186\pi$
$98$	5.43875	+	1.49994i	0.549397	+	0.151517i
$99$	6.53795	+	2.70936i	0.657089	+	0.272301i
$100$	9.97970	−	0.636793i	0.997970	−	0.0636793i
$101$	−6.72336	−	3.88174i	−0.669000	−	0.386247i	0.126698	−	0.991941i	$-0.459562\pi$
$101$	−6.72336	−	3.88174i	−0.669000	−	0.386247i	−0.795697	+	0.605694i	$0.792895\pi$
$102$	2.17482	−	0.126433i	0.215340	−	0.0125188i
$103$	−6.58033	−	11.3975i	−0.648379	−	1.12302i	−0.983510	−	0.180853i	$-0.942114\pi$
$103$	−6.58033	−	11.3975i	−0.648379	−	1.12302i	0.335131	−	0.942171i	$-0.391219\pi$
$104$	−11.9478	−	3.48350i	−1.17158	−	0.341585i
$105$	11.7280	+	5.22435i	1.14454	+	0.509844i
$106$	−0.777669	+	0.766400i	−0.0755339	+	0.0744393i
$107$			0.252175i			0.0243786i	0.999926	+	0.0121893i	$0.00388008\pi$
$107$			0.252175i			0.0243786i	−0.999926	+	0.0121893i	$0.996120\pi$
$108$	8.55424	+	5.90127i	0.823132	+	0.567850i
$109$	0.459068			0.0439708			0.0219854	−	0.999758i	$-0.493001\pi$
$109$	0.459068			0.0439708			0.0219854	+	0.999758i	$0.493001\pi$
$110$	−3.52227	+	6.57603i	−0.335835	+	0.627000i
$111$	13.1316	−	14.9713i	1.24640	−	1.42101i
$112$	−6.96242	+	11.2851i	−0.657886	+	1.06635i
$113$	8.71557	+	15.0958i	0.819892	+	1.42009i	0.905761	+	0.423788i	$0.139300\pi$
$113$	8.71557	+	15.0958i	0.819892	+	1.42009i	−0.0858696	+	0.996306i	$0.527367\pi$
$114$	0.431512	+	7.42259i	0.0404148	+	0.695189i
$115$	−15.8638	−	3.59146i	−1.47931	−	0.334905i
$116$	1.22773	−	2.05657i	0.113992	−	0.190948i
$117$	−8.03408	−	10.4738i	−0.742751	−	0.968300i
$118$	−2.90240	−	0.800444i	−0.267187	−	0.0736868i
$119$	−1.47414	+	2.55328i	−0.135134	+	0.234059i
$120$	−7.08020	+	8.35888i	−0.646331	+	0.763057i
$121$	2.71748	+	4.70681i	0.247043	+	0.427891i
$122$	1.36225	+	5.23657i	0.123332	+	0.474097i
$123$	4.80995	+	0.957167i	0.433698	+	0.0863048i
$124$	−0.230897	−	0.413758i	−0.0207352	−	0.0371565i
$125$	−6.92458	+	8.77782i	−0.619354	+	0.785112i
$126$	−13.0336	+	5.28512i	−1.16113	+	0.470836i
$127$	−10.5666			−0.937635			−0.468817	−	0.883295i	$-0.655320\pi$
$127$	−10.5666			−0.937635			−0.468817	+	0.883295i	$0.655320\pi$
$128$	−7.58102	−	8.39810i	−0.670074	−	0.742294i
$129$	13.7000	−	4.64927i	1.20622	−	0.409345i
$130$	11.8224	−	7.33747i	1.03689	−	0.643538i
$131$	−8.12900	−	14.0798i	−0.710234	−	1.23016i	−0.964769	−	0.263098i	$-0.915256\pi$
$131$	−8.12900	−	14.0798i	−0.710234	−	1.23016i	0.254535	−	0.967064i	$-0.418078\pi$
$132$	−2.51292	−	7.77598i	−0.218721	−	0.676812i
$133$	−8.71423	−	5.03116i	−0.755619	−	0.436257i
$134$	−8.64991	−	2.38554i	−0.747239	−	0.206079i
$135$	−11.2989	+	2.70837i	−0.972453	+	0.233100i
$136$	−1.73937	−	1.81725i	−0.149149	−	0.155828i
$137$	6.59587	−	11.4244i	0.563523	−	0.976051i	−0.433662	−	0.901076i	$-0.642779\pi$
$137$	6.59587	−	11.4244i	0.563523	−	0.976051i	0.997185	−	0.0749753i	$-0.0238878\pi$
$138$	14.8876	−	9.78940i	1.26731	−	0.833329i
$139$	−5.61535	+	3.24202i	−0.476288	+	0.274985i	−0.718868	−	0.695146i	$-0.755340\pi$
$139$	−5.61535	+	3.24202i	−0.476288	+	0.274985i	0.242580	+	0.970131i	$0.422006\pi$
$140$	−4.18759	−	14.2215i	−0.353916	−	1.20194i
$141$	−4.21496	−	12.4202i	−0.354964	−	1.04597i
$142$	11.8097	−	11.6385i	0.991047	−	0.976685i
$143$			10.3799i			0.868014i
$144$	−1.21641	−	11.9382i	−0.101368	−	0.994849i
$145$	0.793820	+	2.55751i	0.0659232	+	0.212390i
$146$	−6.06415	−	6.15332i	−0.501872	−	0.509252i
$147$	1.34858	−	6.77688i	0.111229	−	0.558947i
$148$	−22.9926	−	0.335646i	−1.88998	−	0.0275900i
$149$	7.25009	−	4.18584i	0.593950	−	0.342917i	−0.172708	−	0.984973i	$-0.555252\pi$
$149$	7.25009	−	4.18584i	0.593950	−	0.342917i	0.766658	+	0.642056i	$0.221918\pi$
$150$	−1.66524	−	12.1337i	−0.135966	−	0.990713i
$151$	14.2008	+	8.19886i	1.15565	+	0.667214i	0.950257	−	0.311466i	$-0.100820\pi$
$151$	14.2008	+	8.19886i	1.15565	+	0.667214i	0.205391	+	0.978680i	$0.434153\pi$
$152$	6.20220	−	5.93638i	0.503065	−	0.481504i
$153$	−0.347825	−	2.64533i	−0.0281200	−	0.213863i
$154$	10.6615	+	2.94030i	0.859127	+	0.236936i
$155$	0.516676	+	0.116972i	0.0415004	+	0.00939539i
$156$	−3.19274	+	14.9042i	−0.255624	+	1.19329i
$157$	−9.27700	+	5.35608i	−0.740386	+	0.427462i	−0.822209	−	0.569185i	$-0.807259\pi$
$157$	−9.27700	+	5.35608i	−0.740386	+	0.427462i	0.0818239	+	0.996647i	$0.473925\pi$
$158$	−14.1425	+	3.67906i	−1.12512	+	0.292690i
$159$	1.00532	+	0.881785i	0.0797268	+	0.0699301i
$160$	12.6491	−	0.0337379i	0.999996	−	0.00266722i
$161$			24.1137i			1.90042i
$162$	6.44783	−	10.9739i	0.506589	−	0.862187i
$163$	−1.33584			−0.104631			−0.0523153	−	0.998631i	$-0.516660\pi$
$163$	−1.33584			−0.104631			−0.0523153	+	0.998631i	$0.516660\pi$
$164$	−2.75959	−	4.94507i	−0.215488	−	0.386145i
$165$	8.34590	+	3.71775i	0.649727	+	0.289427i
$166$	3.55752	−	0.925458i	0.276117	−	0.0718295i
$167$	6.20942	−	3.58501i	0.480500	−	0.277417i	−0.240125	−	0.970742i	$-0.577188\pi$
$167$	6.20942	−	3.58501i	0.480500	−	0.277417i	0.720625	+	0.693325i	$0.243855\pi$
$168$	14.4040	+	7.50121i	1.11130	+	0.578731i
$169$	3.18034	−	5.50851i	0.244641	−	0.423731i
$170$	2.81100	−	0.0895921i	0.215594	−	0.00687140i
$171$	9.02841	−	1.18711i	0.690420	−	0.0907806i
$172$	−14.3439	−	8.56303i	−1.09371	−	0.652925i
$173$	−1.28765	+	2.23027i	−0.0978979	+	0.169564i	−0.910814	−	0.412816i	$-0.864545\pi$
$173$	−1.28765	+	2.23027i	−0.0978979	+	0.169564i	0.812916	+	0.582380i	$0.197879\pi$
$174$	−2.62130	−	1.31682i	−0.198720	−	0.0998279i
$175$	14.9589	+	7.13906i	1.13078	+	0.539662i
$176$	−4.95460	+	8.03074i	−0.373467	+	0.605340i
$177$	−0.719672	+	3.61649i	−0.0540939	+	0.271832i
$178$	−4.64701	−	4.71534i	−0.348308	−	0.353430i
$179$	10.1847			0.761243			0.380622	−	0.924731i	$-0.375710\pi$
$179$	10.1847			0.761243			0.380622	+	0.924731i	$0.375710\pi$
$180$	10.8400	+	7.90528i	0.807969	+	0.589225i
$181$	4.17537			0.310353			0.155176	−	0.987887i	$-0.450405\pi$
$181$	4.17537			0.310353			0.155176	+	0.987887i	$0.450405\pi$
$182$	−14.4795	−	14.6924i	−1.07329	−	1.08907i
$183$	6.27541	−	2.12964i	0.463891	−	0.157428i
$184$	−19.7518	−	5.75880i	−1.45612	−	0.424545i
$185$	17.4535	−	18.8770i	1.28321	−	1.38786i
$186$	−0.484879	+	0.318835i	−0.0355531	+	0.0233781i
$187$	−1.04902	+	1.81696i	−0.0767123	+	0.132870i
$188$	−7.76312	+	13.0040i	−0.566184	+	0.948414i
$189$	7.61478	+	15.4508i	0.553894	+	1.12388i
$190$	0.305774	+	9.59382i	0.0221832	+	0.696009i
$191$	−12.5152	+	21.6770i	−0.905570	+	1.56849i	−0.0854186	+	0.996345i	$0.527223\pi$
$191$	−12.5152	+	21.6770i	−0.905570	+	1.56849i	−0.820151	+	0.572147i	$0.806111\pi$
$192$	−9.58428	+	10.0071i	−0.691686	+	0.722198i
$193$	16.3830	−	9.45871i	1.17927	−	0.680853i	0.223426	−	0.974721i	$-0.428276\pi$
$193$	16.3830	−	9.45871i	1.17927	−	0.680853i	0.955846	+	0.293868i	$0.0949425\pi$
$194$	−8.45011	+	2.19823i	−0.606683	+	0.157824i
$195$	−10.0141	−	13.7887i	−0.717121	−	0.987431i
$196$	−6.96725	+	3.88807i	−0.497661	+	0.277719i
$197$	−5.25418			−0.374345			−0.187172	−	0.982327i	$-0.559932\pi$
$197$	−5.25418			−0.374345			−0.187172	+	0.982327i	$0.559932\pi$
$198$	−9.27501	+	3.76100i	−0.659146	+	0.267282i
$199$		−	18.8487i		−	1.33615i	−0.744095	−	0.668074i	$-0.767119\pi$
$199$		−	18.8487i		−	1.33615i	0.744095	−	0.668074i	$-0.232881\pi$
$200$	−9.42015	+	10.5480i	−0.666105	+	0.745858i
$201$	−2.14481	+	10.7781i	−0.151284	+	0.760229i
$202$	10.6256	−	2.76415i	0.747612	−	0.194485i
$203$	3.43813	−	1.98500i	0.241309	−	0.139320i
$204$	−2.06513	+	2.28625i	−0.144588	+	0.160069i
$205$	6.17510	+	1.39800i	0.431288	+	0.0976404i
$206$	17.9421	+	4.94821i	1.25009	+	0.344758i
$207$	−13.2817	−	17.3149i	−0.923140	−	1.20347i
$208$	15.4927	−	8.35148i	1.07423	−	0.579071i
$209$	−6.20122	−	3.58028i	−0.428948	−	0.247653i
$210$	−16.9994	+	6.37977i	−1.17307	+	0.440246i
$211$	−3.96081	+	2.28678i	−0.272674	+	0.157428i	−0.630102	−	0.776512i	$-0.716987\pi$
$211$	−3.96081	+	2.28678i	−0.272674	+	0.157428i	0.357428	+	0.933941i	$0.383654\pi$
$212$	0.0225385	−	1.54395i	0.00154795	−	0.106039i
$213$	−15.2667	−	13.3908i	−1.04606	−	0.917521i
$214$	−0.250327	−	0.254008i	−0.0171120	−	0.0173636i
$215$	17.8378	−	5.53663i	1.21653	−	0.377595i
$216$	−14.4745	+	2.54740i	−0.984864	+	0.173329i
$217$		−	0.785367i		−	0.0533142i
$218$	−0.462407	+	0.455706i	−0.0313181	+	0.0308643i
$219$	−6.97713	+	7.95458i	−0.471471	+	0.537521i
$220$	−2.97998	−	10.1203i	−0.200910	−	0.682311i
$221$	3.38900	−	1.95664i	0.227969	−	0.131618i
$222$	1.63450	+	28.1156i	0.109700	+	1.88700i
$223$	−11.8767	+	20.5711i	−0.795323	+	1.37754i	0.127310	+	0.991863i	$0.459366\pi$
$223$	−11.8767	+	20.5711i	−0.795323	+	1.37754i	−0.922634	+	0.385677i	$0.873968\pi$
$224$	−4.18943	−	18.2786i	−0.279918	−	1.22129i
$225$	−14.6734	+	3.11304i	−0.978227	+	0.207536i
$226$	−23.7642	−	6.55386i	−1.58077	−	0.435956i
$227$	24.1252	+	13.9287i	1.60124	+	0.924478i	0.991239	+	0.132081i	$0.0421658\pi$
$227$	24.1252	+	13.9287i	1.60124	+	0.924478i	0.610005	+	0.792398i	$0.291168\pi$
$228$	−7.80286	−	7.04821i	−0.516757	−	0.466779i
$229$	8.35991	+	14.4798i	0.552439	+	0.956852i	0.998098	+	0.0616492i	$0.0196360\pi$
$229$	8.35991	+	14.4798i	0.552439	+	0.956852i	−0.445659	+	0.895203i	$0.647031\pi$
$230$	19.5444	−	12.1301i	1.28872	−	0.799833i
$231$	2.64360	−	13.2846i	0.173936	−	0.874061i
$232$	0.804848	+	3.29027i	0.0528409	+	0.216017i
$233$	1.67938			0.110020			0.0550101	−	0.998486i	$-0.482481\pi$
$233$	1.67938			0.110020			0.0550101	+	0.998486i	$0.482481\pi$
$234$	18.4895	+	2.57470i	1.20870	+	0.168313i
$235$	−5.01943	−	16.1715i	−0.327432	−	1.05491i
$236$	3.71808	−	2.07487i	0.242027	−	0.135063i
$237$	5.75157	+	16.9481i	0.373604	+	1.10090i
$238$	−1.04972	−	4.03518i	−0.0680432	−	0.261562i
$239$	5.41085	+	9.37186i	0.349999	+	0.606215i	0.986249	−	0.165267i	$-0.0528487\pi$
$239$	5.41085	+	9.37186i	0.349999	+	0.606215i	−0.636250	+	0.771483i	$0.719515\pi$
$240$	−1.16596	−	15.4480i	−0.0752626	−	0.997164i
$241$	−5.45657	+	9.45105i	−0.351488	+	0.608796i	−0.986510	−	0.163698i	$-0.947658\pi$
$241$	−5.45657	+	9.45105i	−0.351488	+	0.608796i	0.635022	+	0.772494i	$0.280991\pi$
$242$	−7.40957	−	2.04346i	−0.476305	−	0.131359i
$243$	−13.9780	−	6.90031i	−0.896692	−	0.442655i
$244$	−6.57037	−	3.92238i	−0.420625	−	0.251104i
$245$	1.96968	−	8.70028i	0.125838	−	0.555841i
$246$	−5.79508	+	3.81059i	−0.369481	+	0.242954i
$247$	6.67794	+	11.5665i	0.424907	+	0.735961i
$248$	0.643303	+	0.187561i	0.0408498	+	0.0119101i
$249$	−1.44679	−	4.26326i	−0.0916867	−	0.270173i
$250$	−1.73858	−	15.7155i	−0.109958	−	0.993936i
$251$	−5.05766			−0.319237			−0.159618	−	0.987179i	$-0.551026\pi$
$251$	−5.05766			−0.319237			−0.159618	+	0.987179i	$0.551026\pi$
$252$	7.88202	−	18.2617i	0.496520	−	1.15038i
$253$			17.1598i			1.07883i
$254$	10.6434	−	10.4892i	0.667829	−	0.658151i
$255$	−0.359391	−	3.42571i	−0.0225059	−	0.214526i
$256$	15.9727	+	0.933676i	0.998296	+	0.0583548i
$257$	6.69541	+	11.5968i	0.417649	+	0.723388i	0.995702	−	0.0926101i	$-0.0295210\pi$
$257$	6.69541	+	11.5968i	0.417649	+	0.723388i	−0.578054	+	0.815999i	$0.696188\pi$
$258$	−9.18439	+	18.2827i	−0.571795	+	1.13823i
$259$	−33.0081	−	19.0573i	−2.05103	−	1.18416i
$260$	−4.62462	+	19.1266i	−0.286807	+	1.18618i
$261$	−1.37543	+	3.31904i	−0.0851369	+	0.205444i
$262$	22.1648	+	6.11278i	1.36935	+	0.377649i
$263$	9.43213	+	5.44564i	0.581610	+	0.335793i	0.761773	−	0.647844i	$-0.224329\pi$
$263$	9.43213	+	5.44564i	0.581610	+	0.335793i	−0.180163	+	0.983637i	$0.557663\pi$
$264$	10.2502	+	5.33801i	0.630857	+	0.328532i
$265$	1.26758	+	1.17200i	0.0778669	+	0.0719953i
$266$	13.7719	−	3.58265i	0.844410	−	0.219666i
$267$	−5.34664	+	6.09567i	−0.327209	+	0.373049i
$268$	11.0809	−	6.18367i	0.676872	−	0.377728i
$269$		−	21.5020i		−	1.31100i	−0.755195	−	0.655500i	$-0.772458\pi$
$269$		−	21.5020i		−	1.31100i	0.755195	−	0.655500i	$-0.227542\pi$
$270$	8.69251	−	13.9442i	0.529009	−	0.848616i
$271$			18.9445i			1.15080i	0.817873	+	0.575399i	$0.195153\pi$
$271$			18.9445i			1.15080i	−0.817873	+	0.575399i	$0.804847\pi$
$272$	3.55595	+	0.103842i	0.215611	+	0.00629634i
$273$	−16.6594	+	18.9933i	−1.00828	+	1.14953i
$274$	4.69686	+	18.0550i	0.283748	+	1.09074i
$275$	10.6450	+	5.08030i	0.641920	+	0.306354i
$276$	−5.27813	+	24.6391i	−0.317706	+	1.48310i
$277$	16.1616	+	9.33092i	0.971058	+	0.560641i	0.899559	−	0.436800i	$-0.143888\pi$
$277$	16.1616	+	9.33092i	0.971058	+	0.560641i	0.0714994	+	0.997441i	$0.477222\pi$
$278$	2.43791	−	8.83982i	0.146216	−	0.530177i
$279$	0.432576	+	0.563935i	0.0258977	+	0.0337619i
$280$	18.3354	+	10.1680i	1.09575	+	0.607654i
$281$	−5.84683	−	3.37567i	−0.348792	−	0.201375i	0.315361	−	0.948972i	$-0.397874\pi$
$281$	−5.84683	−	3.37567i	−0.348792	−	0.201375i	−0.664153	+	0.747596i	$0.731208\pi$
$282$	16.5748	+	8.32644i	0.987018	+	0.495832i
$283$	−2.63488	−	4.56374i	−0.156627	−	0.271286i	0.777023	−	0.629472i	$-0.216729\pi$
$283$	−2.63488	−	4.56374i	−0.156627	−	0.271286i	−0.933650	+	0.358186i	$0.883395\pi$
$284$	−0.342270	+	23.4464i	−0.0203100	+	1.39129i
$285$	11.6918	−	1.22659i	0.692562	−	0.0726567i
$286$	−10.3039	−	10.4554i	−0.609283	−	0.618242i
$287$		−	9.38639i		−	0.554061i
$288$	13.0760	+	10.8175i	0.770511	+	0.637427i
$289$	−16.2090			−0.953472
$290$	−3.33837	−	1.78811i	−0.196036	−	0.105001i
$291$	3.43655	+	10.1265i	0.201454	+	0.593623i
$292$	12.2165	+	0.178336i	0.714916	+	0.0104364i
$293$	−11.1453	−	19.3041i	−0.651113	−	1.12776i	−0.982853	−	0.184390i	$-0.940969\pi$
$293$	−11.1453	−	19.3041i	−0.651113	−	1.12776i	0.331741	−	0.943371i	$-0.392364\pi$
$294$	5.36885	+	8.16486i	0.313118	+	0.476184i
$295$	−1.05112	+	4.64292i	−0.0611988	+	0.270321i
$296$	23.4930	−	22.4861i	1.36550	−	1.30698i
$297$	5.41884	+	10.9951i	0.314433	+	0.638001i
$298$	−3.14763	+	11.4133i	−0.182337	+	0.661153i
$299$	16.0032	−	27.7184i	0.925490	−	1.60300i
$300$	13.7222	+	10.5689i	0.792251	+	0.610196i
$301$	−13.8448	−	23.9798i	−0.797999	−	1.38217i
$302$	−22.4429	+	5.83834i	−1.29144	+	0.335959i
$303$	−4.32127	−	12.7335i	−0.248250	−	0.731518i
$304$	−0.354408	+	12.1363i	−0.0203267	+	0.696066i
$305$	8.17078	−	2.53611i	0.467857	−	0.145217i
$306$	2.97631	+	2.31929i	0.170144	+	0.132585i
$307$	0.415414			0.0237089			0.0118545	−	0.999930i	$-0.496227\pi$
$307$	0.415414			0.0237089			0.0118545	+	0.999930i	$0.496227\pi$
$308$	−13.6578	+	7.62170i	−0.778224	+	0.434287i
$309$	4.44890	−	22.3566i	0.253089	−	1.27182i
$310$	−0.636548	+	0.395069i	−0.0361535	+	0.0224384i
$311$	−0.284562	−	0.492876i	−0.0161360	−	0.0279484i	0.857845	−	0.513909i	$-0.171803\pi$
$311$	−0.284562	−	0.492876i	−0.0161360	−	0.0279484i	−0.873981	+	0.485961i	$0.838470\pi$
$312$	−11.5790	−	18.1819i	−0.655535	−	1.02935i
$313$	−24.3028	−	14.0312i	−1.37367	−	0.793091i	−0.382285	−	0.924044i	$-0.624863\pi$
$313$	−24.3028	−	14.0312i	−1.37367	−	0.793091i	−0.991388	+	0.130954i	$0.958196\pi$
$314$	4.02762	−	14.6041i	0.227292	−	0.824156i
$315$	9.30455	+	20.1977i	0.524252	+	1.13801i
$316$	10.5932	−	17.7447i	0.595917	−	0.998219i
$317$	−6.63676	+	11.4952i	−0.372758	+	0.645635i	−0.989989	−	0.141147i	$-0.954921\pi$
$317$	−6.63676	+	11.4952i	−0.372758	+	0.645635i	0.617231	+	0.786782i	$0.288254\pi$
$318$	−1.88795	+	0.109756i	−0.105871	+	0.00615481i
$319$	2.44664	−	1.41257i	0.136986	−	0.0790887i
$320$	−12.7076	+	12.5904i	−0.710374	+	0.703824i
$321$	−0.288015	+	0.328364i	−0.0160754	+	0.0183275i
$322$	−23.9370	−	24.2890i	−1.33396	−	1.35357i
$323$			2.69956i			0.150208i
$324$	4.39875	+	17.4543i	0.244375	+	0.969681i
$325$	−12.4572	−	18.1338i	−0.690999	−	1.00588i
$326$	1.34555	−	1.32605i	0.0745231	−	0.0734431i
$327$	0.597767	+	0.524314i	0.0330566	+	0.0289947i
$328$	7.68850	+	2.24165i	0.424526	+	0.123774i
$329$	−21.7398	+	12.5515i	−1.19855	+	0.691985i
$330$	−12.0971	+	4.53998i	−0.665924	+	0.249917i
$331$	7.43989	+	4.29542i	0.408933	+	0.236098i	0.690331	−	0.723493i	$-0.257465\pi$
$331$	7.43989	+	4.29542i	0.408933	+	0.236098i	−0.281398	+	0.959591i	$0.590798\pi$
$332$	−2.66471	+	4.46364i	−0.146245	+	0.244974i
$333$	34.1982	−	4.49659i	1.87405	−	0.246412i
$334$	−2.69583	+	9.77502i	−0.147509	+	0.534865i
$335$	−3.13263	+	13.8371i	−0.171154	+	0.756003i
$336$	−21.9550	+	6.74277i	−1.19775	+	0.367848i
$337$	0.914017	−	0.527708i	0.0497897	−	0.0287461i	−0.474899	−	0.880041i	$-0.657515\pi$
$337$	0.914017	−	0.527708i	0.0497897	−	0.0287461i	0.524688	+	0.851294i	$0.324182\pi$
$338$	2.26469	+	8.70561i	0.123183	+	0.473523i
$339$	−5.89251	+	29.6110i	−0.320037	+	1.60825i
$340$	−2.74250	+	2.88065i	−0.148733	+	0.156225i
$341$		−	0.558884i		−	0.0302652i
$342$	−7.91565	+	10.1580i	−0.428029	+	0.549283i
$343$	9.98036			0.538889
$344$	22.9485	−	5.61355i	1.23730	−	0.302662i
$345$	−16.5549	−	22.7951i	−0.891286	−	1.22725i
$346$	−0.916922	−	3.52470i	−0.0492940	−	0.189489i
$347$	−5.97844	+	3.45165i	−0.320939	+	0.185294i	−0.651811	−	0.758381i	$-0.725991\pi$
$347$	−5.97844	+	3.45165i	−0.320939	+	0.185294i	0.330872	+	0.943676i	$0.392657\pi$
$348$	3.94754	−	1.27570i	0.211610	−	0.0683848i
$349$	−15.5145	+	26.8719i	−0.830473	+	1.43842i	0.0671899	+	0.997740i	$0.478597\pi$
$349$	−15.5145	+	26.8719i	−0.830473	+	1.43842i	−0.897663	+	0.440682i	$0.854737\pi$
$350$	−22.1544	+	7.65831i	−1.18420	+	0.409354i
$351$	1.50094	−	22.8142i	0.0801142	−	1.21773i
$352$	−2.98128	−	13.0074i	−0.158903	−	0.693299i
$353$	7.67847	−	13.2995i	0.408684	−	0.707861i	−0.586059	−	0.810269i	$-0.699321\pi$
$353$	7.67847	−	13.2995i	0.408684	−	0.707861i	0.994743	+	0.102408i	$0.0326546\pi$
$354$	−2.86509	−	4.35719i	−0.152278	−	0.231582i
$355$	−19.2495	−	17.7980i	−1.02166	−	0.944619i
$356$	9.36161	+	0.136661i	0.496164	+	0.00724301i
$357$	−4.83568	+	1.64105i	−0.255932	+	0.0868537i
$358$	−10.2588	+	10.1101i	−0.542194	+	0.534337i
$359$	−8.51196			−0.449244			−0.224622	−	0.974446i	$-0.572115\pi$
$359$	−8.51196			−0.449244			−0.224622	+	0.974446i	$0.572115\pi$
$360$	−18.7662	+	2.79787i	−0.989068	+	0.147461i
$361$	9.78650			0.515079
$362$	−4.20573	+	4.14478i	−0.221048	+	0.217845i
$363$	−1.83726	+	9.23258i	−0.0964311	+	0.484585i
$364$	29.1696	+	0.425818i	1.52890	+	0.0223189i
$365$	−9.27346	+	10.0298i	−0.485395	+	0.524981i
$366$	−4.20700	+	8.37456i	−0.219903	+	0.437746i
$367$	0.646542	−	1.11984i	0.0337492	−	0.0584553i	−0.848657	−	0.528943i	$-0.822589\pi$
$367$	0.646542	−	1.11984i	0.0337492	−	0.0584553i	0.882407	+	0.470488i	$0.155922\pi$
$368$	25.6120	−	13.8064i	1.33512	−	0.719708i
$369$	5.16998	+	6.73993i	0.269138	+	0.350867i
$370$	1.15823	+	36.3399i	0.0602133	+	1.88922i
$371$	1.27969	−	2.21648i	0.0664381	−	0.115074i
$372$	0.171906	−	0.802481i	0.00891289	−	0.0416067i
$373$	14.1837	−	8.18898i	0.734406	−	0.424010i	−0.0856259	−	0.996327i	$-0.527289\pi$
$373$	14.1837	−	8.18898i	0.734406	−	0.424010i	0.820032	+	0.572318i	$0.193956\pi$
$374$	−0.747002	−	2.87152i	−0.0386265	−	0.148483i
$375$	−19.0421	+	3.52112i	−0.983330	+	0.181830i
$376$	−5.08917	−	20.8048i	−0.262454	−	1.07293i
$377$	−5.26946			−0.271391
$378$	−23.0078	−	8.00416i	−1.18339	−	0.411689i
$379$			11.7940i			0.605818i	0.953020	+	0.302909i	$0.0979578\pi$
$379$			11.7940i			0.605818i	−0.953020	+	0.302909i	$0.902042\pi$
$380$	−9.83155	−	9.36005i	−0.504348	−	0.480161i
$381$	−13.7591	−	12.0684i	−0.704901	−	0.618283i
$382$	−8.91198	−	34.2582i	−0.455977	−	1.75280i
$383$	9.75933	−	5.63455i	0.498678	−	0.287912i	−0.229489	−	0.973311i	$-0.573706\pi$
$383$	9.75933	−	5.63455i	0.498678	−	0.287912i	0.728168	+	0.685399i	$0.240372\pi$
$384$	−0.279794	−	19.5939i	−0.0142782	−	0.999898i
$385$	3.86113	−	17.0550i	0.196781	−	0.869203i
$386$	−7.11268	+	25.7905i	−0.362026	+	1.31270i
$387$	23.1492	+	9.59316i	1.17674	+	0.487648i
$388$	6.32944	−	10.6024i	0.321328	−	0.538257i
$389$	17.4583	+	10.0796i	0.885172	+	0.511054i	0.872360	−	0.488864i	$-0.162589\pi$
$389$	17.4583	+	10.0796i	0.885172	+	0.511054i	0.0128115	+	0.999918i	$0.495922\pi$
$390$	23.7746	+	3.94830i	1.20387	+	0.199930i
$391$	5.60259	−	3.23466i	0.283335	−	0.163584i
$392$	3.15833	−	10.8326i	0.159520	−	0.547127i
$393$	5.49594	−	27.6182i	0.277234	−	1.39315i
$394$	5.29239	−	5.21569i	0.266627	−	0.262763i
$395$	6.84932	+	22.0670i	0.344627	+	1.11031i
$396$	5.60901	−	12.9954i	0.281863	−	0.653044i
$397$			5.11859i			0.256895i	0.991716	+	0.128447i	$0.0409993\pi$
$397$			5.11859i			0.256895i	−0.991716	+	0.128447i	$0.959001\pi$
$398$	18.7106	+	18.9858i	0.937879	+	0.951670i
$399$	−5.60084	−	16.5040i	−0.280393	−	0.826233i
$400$	−0.982113	−	19.9759i	−0.0491056	−	0.998794i
$401$	9.58291	−	5.53269i	0.478548	−	0.276290i	−0.241263	−	0.970460i	$-0.577562\pi$
$401$	9.58291	−	5.53269i	0.478548	−	0.276290i	0.719811	+	0.694170i	$0.244228\pi$
$402$	−8.53874	−	12.9856i	−0.425874	−	0.647662i
$403$	−0.521215	+	0.902771i	−0.0259636	+	0.0449702i
$404$	−7.95892	+	13.3320i	−0.395971	+	0.663291i
$405$	−17.8059	−	9.37810i	−0.884784	−	0.466001i
$406$	−1.49267	+	5.41238i	−0.0740798	+	0.268612i
$407$	−23.4893	−	13.5615i	−1.16432	−	0.672221i
$408$	−0.189350	−	4.35288i	−0.00937423	−	0.215500i
$409$	−8.08315	−	14.0004i	−0.399686	−	0.692276i	0.594001	−	0.804464i	$-0.297548\pi$
$409$	−8.08315	−	14.0004i	−0.399686	−	0.692276i	−0.993687	+	0.112188i	$0.964214\pi$
$410$	−7.60776	+	4.72170i	−0.375721	+	0.233188i
$411$	21.6368	−	7.34273i	1.06726	−	0.362190i
$412$	−22.9846	+	12.8265i	−1.13237	+	0.631917i
$413$	7.05742			0.347273
$414$	30.5663	+	4.25640i	1.50225	+	0.209191i
$415$	−1.72293	−	5.55090i	−0.0845753	−	0.272483i
$416$	−7.31504	+	23.7914i	−0.358650	+	1.16647i
$417$	−11.0147	−	2.19190i	−0.539394	−	0.107338i
$418$	9.80037	−	2.54949i	0.479352	−	0.124699i
$419$	3.65564	+	6.33176i	0.178590	+	0.309327i	0.941398	−	0.337298i	$-0.109513\pi$
$419$	3.65564	+	6.33176i	0.178590	+	0.309327i	−0.762808	+	0.646625i	$0.776180\pi$
$420$	10.7900	−	23.3010i	0.526496	−	1.13697i
$421$	14.9731	−	25.9341i	0.729742	−	1.26395i	−0.227250	−	0.973836i	$-0.572973\pi$
$421$	14.9731	−	25.9341i	0.729742	−	1.26395i	0.956992	−	0.290114i	$-0.0936932\pi$
$422$	1.71959	−	6.23521i	0.0837083	−	0.303525i
$423$	8.69702	−	20.9868i	0.422864	−	1.02041i
$424$	1.50993	+	1.57755i	0.0733288	+	0.0766124i
$425$	−0.347917	−	4.43321i	−0.0168765	−	0.215042i
$426$	28.6705	−	1.66676i	1.38909	−	0.0807546i
$427$	−6.34172	−	10.9842i	−0.306897	−	0.531562i
$428$	0.504295	+	0.00736171i	0.0243760	+	0.000355842i
$429$	−11.8552	+	13.5160i	−0.572375	+	0.652561i
$430$	−12.4715	+	23.2840i	−0.601427	+	1.12286i
$431$	−30.7505			−1.48120			−0.740599	−	0.671947i	$-0.765458\pi$
$431$	−30.7505			−1.48120			−0.740599	+	0.671947i	$0.765458\pi$
$432$	12.0510	−	16.9344i	0.579804	−	0.814756i
$433$			29.3734i			1.41160i	0.708413	+	0.705798i	$0.249411\pi$
$433$			29.3734i			1.41160i	−0.708413	+	0.705798i	$0.750589\pi$
$434$	0.779614	+	0.791078i	0.0374227	+	0.0379730i
$435$	−1.88735	+	4.23686i	−0.0904914	+	0.203142i
$436$	0.0134016	−	0.918039i	0.000641818	−	0.0439661i
$437$	11.0398	+	19.1214i	0.528103	+	0.914701i
$438$	−0.868446	−	14.9384i	−0.0414960	−	0.713787i
$439$	6.77418	+	3.91108i	0.323314	+	0.186665i	0.652869	−	0.757471i	$-0.273565\pi$
$439$	6.77418	+	3.91108i	0.323314	+	0.186665i	−0.329555	+	0.944136i	$0.606899\pi$
$440$	13.0478	+	7.23575i	0.622031	+	0.344951i
$441$	9.49608	−	7.28413i	0.452194	−	0.346863i
$442$	−1.47134	+	5.33505i	−0.0699844	+	0.253763i
$443$	−23.1263	−	13.3520i	−1.09876	−	0.634371i	−0.162867	−	0.986648i	$-0.552074\pi$
$443$	−23.1263	−	13.3520i	−1.09876	−	0.634371i	−0.935896	+	0.352277i	$0.885408\pi$
$444$	−29.5560	−	26.6975i	−1.40267	−	1.26701i
$445$	−7.10634	+	7.68589i	−0.336873	+	0.364346i
$446$	−8.45731	−	32.5104i	−0.400465	−	1.53941i
$447$	14.2213	+	2.83001i	0.672646	+	0.133855i
$448$	22.3646	+	14.2528i	1.05663	+	0.673381i
$449$		−	23.8441i		−	1.12527i	−0.826704	−	0.562637i	$-0.809787\pi$
$449$		−	23.8441i		−	1.12527i	0.826704	−	0.562637i	$-0.190213\pi$
$450$	11.6899	−	17.7016i	0.551066	−	0.834462i
$451$		−	6.67955i		−	0.314528i
$452$	30.4428	−	16.9886i	1.43191	−	0.799076i
$453$	9.12722	+	26.8952i	0.428834	+	1.26364i
$454$	−38.1272	+	9.91849i	−1.78940	+	0.465498i
$455$	−22.1424	+	23.9483i	−1.03805	+	1.12271i
$456$	14.8562	−	0.646244i	0.695705	−	0.0302632i
$457$	−13.6451	−	7.87798i	−0.638289	−	0.368516i	0.145666	−	0.989334i	$-0.453468\pi$
$457$	−13.6451	−	7.87798i	−0.638289	−	0.368516i	−0.783955	+	0.620817i	$0.786801\pi$
$458$	−22.7944	−	6.28641i	−1.06511	−	0.293745i
$459$	2.56839	−	3.84183i	0.119882	−	0.179321i
$460$	−7.64526	+	31.6195i	−0.356462	+	1.47426i
$461$	9.24515	+	5.33769i	0.430590	+	0.248601i	0.699598	−	0.714537i	$-0.253363\pi$
$461$	9.24515	+	5.33769i	0.430590	+	0.248601i	−0.269008	+	0.963138i	$0.586696\pi$
$462$	10.5245	+	16.0054i	0.489642	+	0.744640i
$463$	3.17644	+	5.50175i	0.147622	+	0.255688i	0.930348	−	0.366678i	$-0.119505\pi$
$463$	3.17644	+	5.50175i	0.147622	+	0.255688i	−0.782726	+	0.622366i	$0.786172\pi$
$464$	−4.07687	−	2.51524i	−0.189264	−	0.116767i
$465$	0.539183	+	0.742422i	0.0250040	+	0.0344290i
$466$	−1.69160	+	1.66708i	−0.0783617	+	0.0772261i
$467$			7.76191i			0.359179i	0.983742	+	0.179589i	$0.0574769\pi$
$467$			7.76191i			0.359179i	−0.983742	+	0.179589i	$0.942523\pi$
$468$	−21.1798	+	15.7607i	−0.979038	+	0.728538i
$469$	21.0330			0.971213
$470$	21.1090	+	11.3064i	0.973685	+	0.521527i
$471$	−18.1972	−	3.62120i	−0.838483	−	0.166856i
$472$	−1.68545	+	5.78081i	−0.0775790	+	0.266083i
$473$	−9.85221	−	17.0645i	−0.453005	−	0.784628i
$474$	−22.6174	−	11.3619i	−1.03885	−	0.521871i
$475$	15.1303	−	1.18743i	0.694228	−	0.0544829i
$476$	5.06298	+	3.02249i	0.232061	+	0.138536i
$477$	0.301945	+	2.29640i	0.0138251	+	0.105145i
$478$	−14.7534	−	4.06880i	−0.674805	−	0.186103i
$479$	−3.56565	+	6.17588i	−0.162919	+	0.282183i	−0.935914	−	0.352228i	$-0.885424\pi$
$479$	−3.56565	+	6.17588i	−0.162919	+	0.282183i	0.772996	+	0.634411i	$0.218757\pi$
$480$	16.5093	+	14.4029i	0.753542	+	0.657400i
$481$	25.2950	+	43.8122i	1.15335	+	1.99767i
$482$	−3.88558	−	14.9364i	−0.176983	−	0.680333i
$483$	−27.5409	+	31.3992i	−1.25315	+	1.42871i
$484$	9.49194	−	5.29697i	0.431452	−	0.240771i
$485$	4.09245	+	13.1850i	0.185829	+	0.598699i
$486$	20.9295	−	6.92516i	0.949379	−	0.314132i
$487$	15.1089			0.684649			0.342325	−	0.939582i	$-0.388786\pi$
$487$	15.1089			0.684649			0.342325	+	0.939582i	$0.388786\pi$
$488$	10.5118	−	2.57134i	0.475846	−	0.116399i
$489$	−1.73943	−	1.52569i	−0.0786599	−	0.0689942i
$490$	6.65255	+	10.7188i	0.300531	+	0.484226i
$491$	−14.7215	−	25.4984i	−0.664372	−	1.15073i	−0.979455	−	0.201662i	$-0.935366\pi$
$491$	−14.7215	−	25.4984i	−0.664372	−	1.15073i	0.315083	−	0.949064i	$-0.397968\pi$
$492$	2.05455	−	9.59093i	0.0926261	−	0.432392i
$493$	−0.922396	−	0.532546i	−0.0415426	−	0.0239847i
$494$	−18.2083	−	5.02162i	−0.819230	−	0.225933i
$495$	6.62131	+	14.3731i	0.297606	+	0.646022i
$496$	−0.834168	+	0.449666i	−0.0374552	+	0.0201906i
$497$	−19.4333	+	33.6595i	−0.871705	+	1.50984i
$498$	5.68934	+	2.85807i	0.254946	+	0.128073i
$499$	18.0795	−	10.4382i	0.809351	−	0.467279i	−0.0373795	−	0.999301i	$-0.511901\pi$
$499$	18.0795	−	10.4382i	0.809351	−	0.467279i	0.846730	+	0.532022i	$0.178568\pi$
$500$	17.3516	+	14.1039i	0.775988	+	0.630748i
$501$	12.1800	+	2.42379i	0.544163	+	0.108287i
$502$	5.09444	−	5.02061i	0.227376	−	0.224081i
$503$		−	22.6713i		−	1.01086i	−0.862867	−	0.505431i	$-0.831333\pi$
$503$		−	22.6713i		−	1.01086i	0.862867	−	0.505431i	$-0.168667\pi$
$504$	10.1886	+	26.2188i	0.453837	+	1.16788i
$505$	−5.14603	−	16.5794i	−0.228995	−	0.737773i
$506$	−17.0341	−	17.2846i	−0.757257	−	0.768392i
$507$	10.4326	−	3.54045i	0.463330	−	0.157237i
$508$	−0.308470	+	21.1310i	−0.0136862	+	0.937535i
$509$	−23.5593	+	13.6020i	−1.04425	+	0.602896i	−0.921033	−	0.389484i	$-0.872653\pi$
$509$	−23.5593	+	13.6020i	−1.04425	+	0.602896i	−0.123213	+	0.992380i	$0.539320\pi$
$510$	3.76262	+	3.09386i	0.166611	+	0.136998i
$511$	17.5380	+	10.1255i	0.775834	+	0.447928i
$512$	−17.0157	+	14.9153i	−0.751996	+	0.659168i
$513$	13.1120	+	8.76582i	0.578909	+	0.387020i
$514$	−18.2560	−	5.03476i	−0.805236	−	0.222074i
$515$	6.49787	−	28.7018i	0.286330	−	1.26475i
$516$	−8.89760	−	27.5328i	−0.391695	−	1.21206i
$517$	−15.4705	+	8.93188i	−0.680390	+	0.392824i
$518$	52.1658	−	13.5705i	2.29204	−	0.596254i
$519$	−4.22393	+	1.43345i	−0.185410	+	0.0629213i
$520$	−14.3282	−	23.8564i	−0.628335	−	1.04617i
$521$			2.18176i			0.0955847i	0.998857	+	0.0477924i	$0.0152186\pi$
$521$			2.18176i			0.0955847i	−0.998857	+	0.0477924i	$0.984781\pi$
$522$	−1.90930	−	4.70853i	−0.0835678	−	0.206087i
$523$	28.8185			1.26014			0.630071	−	0.776537i	$-0.283026\pi$
$523$	28.8185			1.26014			0.630071	+	0.776537i	$0.283026\pi$
$524$	−28.3940	+	15.8452i	−1.24040	+	0.692203i
$525$	11.3247	+	26.3809i	0.494250	+	1.15136i
$526$	−14.9065	+	3.87779i	−0.649953	+	0.169080i
$527$	−0.182473	+	0.105351i	−0.00794865	+	0.00458916i
$528$	−15.6237	+	4.79829i	−0.679932	+	0.208819i
$529$	14.9560	−	25.9046i	0.650261	−	1.12629i
$530$	−2.44021	+	0.0777744i	−0.105996	+	0.00337830i
$531$	−5.06760	+	3.88719i	−0.219915	+	0.168690i
$532$	−10.3156	+	17.2797i	−0.447240	+	0.749171i
$533$	−6.22935	+	10.7896i	−0.269823	+	0.467348i
$534$	−0.665498	−	11.4475i	−0.0287989	−	0.495381i
$535$	−0.382807	+	0.414027i	−0.0165502	+	0.0179000i
$536$	−5.02308	+	17.2283i	−0.216964	+	0.744151i
$537$	13.2619	+	11.6323i	0.572292	+	0.501969i
$538$	21.3445	+	21.6584i	0.920227	+	0.933759i
$539$	−9.41102			−0.405361
$540$	5.08632	+	22.6744i	0.218880	+	0.975752i
$541$	3.32257			0.142848			0.0714242	−	0.997446i	$-0.477246\pi$
$541$	3.32257			0.142848			0.0714242	+	0.997446i	$0.477246\pi$
$542$	−18.8058	−	19.0823i	−0.807777	−	0.819655i
$543$	5.43688	+	4.76880i	0.233319	+	0.204649i
$544$	−3.68489	+	3.42531i	−0.157989	+	0.146859i
$545$	0.753711	+	0.696878i	0.0322854	+	0.0298510i
$546$	−2.07361	−	35.6689i	−0.0887422	−	1.52649i
$547$	13.8697	−	24.0231i	0.593027	−	1.02715i	−0.400795	−	0.916168i	$-0.631266\pi$
$547$	13.8697	−	24.0231i	0.593027	−	1.02715i	0.993822	−	0.110986i	$-0.0354008\pi$
$548$	−22.6538	−	13.5238i	−0.967721	−	0.577710i
$549$	10.6037	+	4.39424i	0.452556	+	0.187541i
$550$	−15.7655	+	5.44981i	−0.672244	+	0.232381i
$551$	1.81756	−	3.14810i	0.0774305	−	0.134114i
$552$	−19.1421	−	30.0577i	−0.814742	−	1.27934i
$553$	29.6652	−	17.1272i	1.26149	−	0.728323i
$554$	−25.5417	+	6.64447i	−1.08516	+	0.282296i
$555$	44.2867	−	4.64612i	1.87987	−	0.197217i
$556$	6.31943	+	11.3241i	0.268003	+	0.480251i
$557$	30.0401			1.27284			0.636419	−	0.771344i	$-0.280415\pi$
$557$	30.0401			1.27284			0.636419	+	0.771344i	$0.280415\pi$
$558$	−0.995526	−	0.138628i	−0.0421440	−	0.00586861i
$559$			36.7527i			1.55447i
$560$	−28.5622	+	7.95913i	−1.20697	+	0.336335i
$561$	−3.44117	+	1.16781i	−0.145286	+	0.0493048i
$562$	9.24028	−	2.40378i	0.389778	−	0.101398i
$563$	1.52959	−	0.883109i	0.0644645	−	0.0372186i	−0.467421	−	0.884035i	$-0.654817\pi$
$563$	1.52959	−	0.883109i	0.0644645	−	0.0372186i	0.531886	+	0.846816i	$0.321484\pi$
$564$	−24.9608	+	8.06644i	−1.05104	+	0.339658i
$565$	−8.60636	+	38.0152i	−0.362072	+	1.59931i
$566$	7.18435	+	1.98135i	0.301981	+	0.0832824i
$567$	−7.73134	+	28.8160i	−0.324686	+	1.21016i
$568$	−22.9298	−	23.9566i	−0.962115	−	1.00520i
$569$	31.9951	+	18.4724i	1.34131	+	0.774403i	0.986999	−	0.160726i	$-0.0513837\pi$
$569$	31.9951	+	18.4724i	1.34131	+	0.774403i	0.354306	+	0.935129i	$0.384717\pi$
$570$	−10.5592	+	12.8417i	−0.442277	+	0.537878i
$571$	−26.5164	+	15.3092i	−1.10968	+	0.640672i	−0.938745	−	0.344612i	$-0.888011\pi$
$571$	−26.5164	+	15.3092i	−1.10968	+	0.640672i	−0.170930	+	0.985283i	$0.554677\pi$
$572$	20.7577	+	0.303021i	0.867922	+	0.0126699i
$573$	−41.0543	+	13.9323i	−1.71507	+	0.582031i
$574$	9.31764	+	9.45465i	0.388911	+	0.394629i
$575$	−20.5938	−	29.9783i	−0.858819	−	1.25018i
$576$	−23.9093	+	2.08406i	−0.996223	+	0.0868357i
$577$			23.6405i			0.984168i	0.870548	+	0.492084i	$0.163765\pi$
$577$			23.6405i			0.984168i	−0.870548	+	0.492084i	$0.836235\pi$
$578$	16.3269	−	16.0903i	0.679109	−	0.669268i
$579$	32.1358	+	6.39495i	1.33552	+	0.265765i
$580$	5.13766	−	1.51281i	0.213330	−	0.0628160i
$581$	−7.46221	+	4.30831i	−0.309585	+	0.178739i
$582$	−13.5138	−	6.78872i	−0.560166	−	0.281402i
$583$	0.910652	−	1.57730i	0.0377154	−	0.0653249i
$584$	−12.4824	+	11.9474i	−0.516523	+	0.494385i
$585$	2.70886	−	29.3920i	0.111998	−	1.21521i
$586$	30.3890	+	8.38091i	1.25536	+	0.346212i
$587$	0.0513568	+	0.0296509i	0.00211972	+	0.00122382i	0.501059	−	0.865413i	$-0.332944\pi$
$587$	0.0513568	+	0.0296509i	0.00211972	+	0.00122382i	−0.498940	+	0.866637i	$0.666277\pi$
$588$	−13.5129	−	2.89471i	−0.557264	−	0.119376i
$589$	−0.359558	−	0.622773i	−0.0148153	−	0.0256609i
$590$	−3.55014	−	5.72010i	−0.146157	−	0.235493i
$591$	−6.84163	−	6.00094i	−0.281427	−	0.246846i
$592$	−1.34244	+	45.9705i	−0.0551741	+	1.88938i
$593$	−44.6245			−1.83251			−0.916255	−	0.400596i	$-0.868803\pi$
$593$	−44.6245			−1.83251			−0.916255	+	0.400596i	$0.868803\pi$
$594$	−16.3728	−	5.69592i	−0.671785	−	0.233707i
$595$	−6.29622	+	1.95427i	−0.258120	+	0.0801171i
$596$	−8.15914	−	14.6208i	−0.334211	−	0.598893i
$597$	21.5276	−	24.5435i	0.881066	−	1.00450i
$598$	11.3958	+	43.8059i	0.466007	+	1.79136i
$599$	11.5001	+	19.9187i	0.469881	+	0.813857i	0.999407	−	0.0344362i	$-0.0109636\pi$
$599$	11.5001	+	19.9187i	0.469881	+	0.813857i	−0.529526	+	0.848294i	$0.677630\pi$
$600$	−24.3135	+	2.97591i	−0.992593	+	0.121491i
$601$	0.981232	−	1.69954i	0.0400253	−	0.0693259i	−0.845319	−	0.534262i	$-0.820589\pi$
$601$	0.981232	−	1.69954i	0.0400253	−	0.0693259i	0.885344	+	0.464936i	$0.153923\pi$
$602$	37.7496	+	10.4109i	1.53856	+	0.424315i
$603$	−15.1028	+	11.5849i	−0.615033	+	0.471772i
$604$	16.8105	−	28.1593i	0.684011	−	1.14579i
$605$	−2.68343	+	11.8530i	−0.109097	+	0.481891i
$606$	16.9929	+	8.53645i	0.690289	+	0.346769i
$607$	−10.1049	−	17.5023i	−0.410146	−	0.710394i	0.584759	−	0.811207i	$-0.301189\pi$
$607$	−10.1049	−	17.5023i	−0.410146	−	0.710394i	−0.994905	+	0.100813i	$0.967856\pi$
$608$	−11.6904	−	12.5764i	−0.474110	−	0.510040i
$609$	6.74402	+	1.34204i	0.273282	+	0.0543823i
$610$	−5.71267	+	10.6655i	−0.231299	+	0.431833i
$611$	33.3195			1.34796
$612$	−5.30026	+	0.618350i	−0.214250	+	0.0249953i
$613$		−	24.8672i		−	1.00438i	−0.864758	−	0.502189i	$-0.832528\pi$
$613$		−	24.8672i		−	1.00438i	0.864758	−	0.502189i	$-0.167472\pi$
$614$	−0.418434	+	0.412371i	−0.0168866	+	0.0166419i
$615$	6.44410	+	8.87312i	0.259851	+	0.357799i
$616$	6.19121	−	21.2349i	0.249451	−	0.855577i
$617$	−16.3707	−	28.3549i	−0.659059	−	1.14152i	−0.980860	−	0.194717i	$-0.937621\pi$
$617$	−16.3707	−	28.3549i	−0.659059	−	1.14152i	0.321800	−	0.946808i	$-0.395712\pi$
$618$	17.7115	+	26.9354i	0.712463	+	1.08350i
$619$	11.9754	+	6.91400i	0.481332	+	0.277897i	0.720971	−	0.692965i	$-0.243696\pi$
$619$	11.9754	+	6.91400i	0.481332	+	0.277897i	−0.239640	+	0.970862i	$0.577029\pi$
$620$	0.249002	−	1.02983i	0.0100001	−	0.0413588i
$621$	2.48130	−	37.7156i	0.0995713	−	1.51348i
$622$	0.775897	+	0.213982i	0.0311106	+	0.00857991i
$623$	13.4395	+	7.75930i	0.538442	+	0.310870i
$624$	29.7120	+	6.81989i	1.18943	+	0.273014i
$625$	−24.6939	+	3.89997i	−0.987757	+	0.155999i
$626$	38.4079	−	9.99151i	1.53509	−	0.399341i
$627$	−3.98568	−	11.7446i	−0.159173	−	0.469033i
$628$	10.4402	+	18.7084i	0.416609	+	0.746546i
$629$			10.2255i			0.407719i
$630$	−29.4219	−	11.1082i	−1.17220	−	0.442559i
$631$		−	0.298908i		−	0.0118994i	−0.999982	−	0.00594968i	$-0.998106\pi$
$631$		−	0.298908i		−	0.0118994i	0.999982	−	0.00594968i	$-0.00189385\pi$
$632$	6.94447	+	28.3894i	0.276236	+	1.12927i
$633$	−7.76929	−	1.54607i	−0.308802	−	0.0614507i
$634$	−4.72598	−	18.1669i	−0.187693	−	0.721501i
$635$	−17.3485	−	16.0404i	−0.688456	−	0.636543i
$636$	1.79273	−	1.98468i	0.0710864	−	0.0786976i
$637$	15.2017	+	8.77672i	0.602314	+	0.347746i
$638$	−1.06221	+	3.85156i	−0.0420534	+	0.152485i
$639$	−4.58533	−	34.8731i	−0.181393	−	1.37956i
$640$	0.301795	−	25.2964i	0.0119295	−	0.999929i
$641$	12.2453	+	7.06982i	0.483660	+	0.279241i	0.721940	−	0.691955i	$-0.243250\pi$
$641$	12.2453	+	7.06982i	0.483660	+	0.279241i	−0.238281	+	0.971196i	$0.576584\pi$
$642$	−0.0358494	−	0.616658i	−0.00141486	−	0.0243375i
$643$	18.2808	+	31.6633i	0.720925	+	1.24868i	0.960629	+	0.277833i	$0.0896162\pi$
$643$	18.2808	+	31.6633i	0.720925	+	1.24868i	−0.239704	+	0.970846i	$0.577050\pi$
$644$	48.2222	+	0.703948i	1.90022	+	0.0277394i
$645$	29.5507	+	13.1636i	1.16356	+	0.518317i
$646$	−2.67979	−	2.71919i	−0.105435	−	0.106985i
$647$			25.4645i			1.00111i	0.865704	+	0.500556i	$0.166871\pi$
$647$			25.4645i			1.00111i	−0.865704	+	0.500556i	$0.833129\pi$
$648$	−21.7571	−	13.2146i	−0.854701	−	0.519120i
$649$	5.02220			0.197139
$650$	30.5488	+	5.89980i	1.19822	+	0.231409i
$651$	0.896989	−	1.02265i	0.0351558	−	0.0400809i
$652$	−0.0389969	+	2.67139i	−0.00152724	+	0.104620i
$653$	11.2123	+	19.4203i	0.438772	+	0.759976i	0.997595	−	0.0693112i	$-0.0220801\pi$
$653$	11.2123	+	19.4203i	0.438772	+	0.759976i	−0.558823	+	0.829287i	$0.688747\pi$
$654$	−1.12259	+	0.0652616i	−0.0438967	+	0.00255193i
$655$	8.02715	−	35.4567i	0.313647	−	1.38541i
$656$	−9.96964	+	5.37423i	−0.389249	+	0.209828i
$657$	−18.1703	+	2.38914i	−0.708890	+	0.0932092i
$658$	9.43834	−	34.2233i	0.367945	−	1.33416i
$659$	3.28193	−	5.68446i	0.127846	−	0.221435i	−0.794996	−	0.606615i	$-0.792527\pi$
$659$	3.28193	−	5.68446i	0.127846	−	0.221435i	0.922842	+	0.385179i	$0.125860\pi$
$660$	7.67836	−	16.5815i	0.298880	−	0.645434i
$661$	−9.44856	−	16.3654i	−0.367506	−	0.636540i	0.621669	−	0.783280i	$-0.286455\pi$
$661$	−9.44856	−	16.3654i	−0.367506	−	0.636540i	−0.989175	+	0.146741i	$0.953122\pi$
$662$	−11.7579	+	3.05873i	−0.456986	+	0.118881i
$663$	6.64766	+	1.32287i	0.258174	+	0.0513759i
$664$	−1.74687	−	7.14129i	−0.0677915	−	0.277136i
$665$	−6.66983	−	21.4887i	−0.258645	−	0.833297i
$666$	−29.9833	+	38.4770i	−1.16183	+	1.49095i
$667$	−8.71129			−0.337303
$668$	−6.98799	−	12.5222i	−0.270373	−	0.484498i
$669$	−38.9598	+	13.2215i	−1.50627	+	0.511173i
$670$	−10.5804	−	17.0474i	−0.408755	−	0.658600i
$671$	−4.51290	−	7.81657i	−0.174219	−	0.301755i
$672$	15.4213	−	28.5860i	0.594890	−	1.10273i
$673$	−27.1258	−	15.6611i	−1.04562	−	0.603690i	−0.124201	−	0.992257i	$-0.539637\pi$
$673$	−27.1258	−	15.6611i	−1.04562	−	0.603690i	−0.921420	+	0.388567i	$0.872970\pi$
$674$	−0.396821	+	1.43887i	−0.0152850	+	0.0554231i
$675$	−22.6622	−	12.7053i	−0.872268	−	0.489028i
$676$	−10.9230	−	6.52081i	−0.420115	−	0.250800i
$677$	20.4922	−	35.4936i	0.787580	−	1.36413i	−0.139866	−	0.990171i	$-0.544667\pi$
$677$	20.4922	−	35.4936i	0.787580	−	1.36413i	0.927446	−	0.373958i	$-0.122000\pi$
$678$	−23.4587	−	35.6757i	−0.900928	−	1.37012i
$679$	17.7249	−	10.2335i	0.680219	−	0.392724i
$680$	−0.0971038	−	5.62402i	−0.00372376	−	0.215671i
$681$	15.5058	+	45.6910i	0.594185	+	1.75088i
$682$	0.554790	+	0.562948i	0.0212440	+	0.0215564i
$683$		−	42.0703i		−	1.60978i	−0.593427	−	0.804888i	$-0.702225\pi$
$683$		−	42.0703i		−	1.60978i	0.593427	−	0.804888i	$-0.297775\pi$
$684$	−2.11040	−	18.0896i	−0.0806933	−	0.691671i
$685$	28.1718	−	8.74417i	1.07639	−	0.334097i
$686$	−10.0529	+	9.90726i	−0.383823	+	0.378261i
$687$	−5.65206	+	28.4027i	−0.215639	+	1.08363i
$688$	−17.5430	+	28.4348i	−0.668820	+	1.08407i
$689$	−2.94198	+	1.69855i	−0.112080	+	0.0647096i
$690$	39.3034	+	6.52720i	1.49625	+	0.248486i
$691$	−30.3277	−	17.5097i	−1.15372	−	0.666101i	−0.203930	−	0.978986i	$-0.565371\pi$
$691$	−30.3277	−	17.5097i	−1.15372	−	0.666101i	−0.949791	+	0.312885i	$0.898705\pi$
$692$	4.42247	+	2.64012i	0.168117	+	0.100362i
$693$	18.6150	−	14.2789i	0.707125	−	0.542412i
$694$	2.59554	−	9.41140i	0.0985255	−	0.357252i
$695$	−14.1409	−	3.20140i	−0.536395	−	0.121436i
$696$	−2.70988	+	5.20360i	−0.102718	+	0.197242i
$697$	−2.18084	+	1.25911i	−0.0826054	+	0.0476922i
$698$	−11.0478	−	42.4682i	−0.418164	−	1.60745i
$699$	2.18678	+	1.91807i	0.0827116	+	0.0725481i
$700$	14.7133	−	29.7061i	0.556110	−	1.12279i
$701$		−	41.5315i		−	1.56862i	−0.620366	−	0.784312i	$-0.713016\pi$
$701$		−	41.5315i		−	1.56862i	0.620366	−	0.784312i	$-0.286984\pi$
$702$	21.1352	+	24.4700i	0.797696	+	0.923560i
$703$	−34.8993			−1.31625
$704$	15.9151	+	10.1426i	0.599824	+	0.382263i
$705$	11.9340	−	26.7903i	0.449459	−	1.00898i
$706$	5.46777	+	21.0184i	0.205782	+	0.791039i
$707$	−22.2881	+	12.8680i	−0.838229	+	0.483952i
$708$	7.21120	+	1.54477i	0.271013	+	0.0580559i
$709$	5.69139	−	9.85778i	0.213745	−	0.370217i	−0.739139	−	0.673553i	$-0.764767\pi$
$709$	5.69139	−	9.85778i	0.213745	−	0.370217i	0.952883	+	0.303337i	$0.0981006\pi$
$710$	37.0571	−	1.18108i	1.39073	−	0.0443252i
$711$	−11.8676	+	28.6377i	−0.445070	+	1.07400i
$712$	−9.56534	+	9.15538i	−0.358476	+	0.343112i
$713$	−0.861656	+	1.49243i	−0.0322693	+	0.0558920i
$714$	3.24182	−	6.45325i	0.121322	−	0.241507i
$715$	−15.7570	+	17.0421i	−0.589279	+	0.637337i
$716$	0.297322	−	20.3673i	0.0111115	−	0.761162i
$717$	−3.65822	+	18.3833i	−0.136619	+	0.686536i
$718$	8.57386	−	8.44961i	0.319974	−	0.315337i
$719$	−24.0599			−0.897282			−0.448641	−	0.893712i	$-0.648092\pi$
$719$	−24.0599			−0.897282			−0.448641	+	0.893712i	$0.648092\pi$
$720$	16.1253	−	21.4470i	0.600956	−	0.799282i
$721$	−43.6278			−1.62478
$722$	−9.85767	+	9.71482i	−0.366864	+	0.361548i
$723$	−17.8995	+	6.07442i	−0.665689	+	0.225910i
$724$	0.121891	−	8.34985i	0.00453005	−	0.310320i
$725$	−2.57906	+	5.40403i	−0.0957837	+	0.200701i
$726$	−7.31433	−	11.1235i	−0.271460	−	0.412833i
$727$	−2.85756	+	4.94944i	−0.105981	+	0.183565i	−0.914139	−	0.405402i	$-0.867132\pi$
$727$	−2.85756	+	4.94944i	−0.105981	+	0.183565i	0.808158	+	0.588966i	$0.200465\pi$
$728$	−29.8044	+	28.5270i	−1.10462	+	1.05728i
$729$	−10.3202	−	24.9498i	−0.382230	−	0.924067i
$730$	−0.615391	−	19.3082i	−0.0227766	−	0.714629i
$731$	−3.71433	+	6.43341i	−0.137380	+	0.237948i
$732$	−4.07563	−	12.6116i	−0.150640	−	0.466140i
$733$	22.3900	−	12.9269i	0.826994	−	0.477465i	−0.0258286	−	0.999666i	$-0.508222\pi$
$733$	22.3900	−	12.9269i	0.826994	−	0.477465i	0.852822	+	0.522201i	$0.174889\pi$
$734$	0.460397	+	1.76979i	0.0169936	+	0.0653242i
$735$	12.5016	−	9.07928i	0.461129	−	0.334894i
$736$	−12.0930	+	39.3312i	−0.445754	+	1.44977i
$737$	14.9675			0.551335
$738$	−11.8981	−	1.65683i	−0.437976	−	0.0609888i
$739$		−	18.0774i		−	0.664989i	−0.943105	−	0.332495i	$-0.892110\pi$
$739$		−	18.0774i		−	0.664989i	0.943105	−	0.332495i	$-0.107890\pi$
$740$	−37.2404	−	35.4544i	−1.36898	−	1.30333i
$741$	−4.51489	+	22.6882i	−0.165859	+	0.833472i
$742$	0.911255	+	3.50292i	0.0334532	+	0.128596i
$743$	−15.5973	+	9.00512i	−0.572210	+	0.330366i	−0.758032	−	0.652218i	$-0.773839\pi$
$743$	−15.5973	+	9.00512i	−0.572210	+	0.330366i	0.185821	+	0.982584i	$0.440505\pi$
$744$	0.623447	+	0.978963i	0.0228567	+	0.0358905i
$745$	18.2576	+	4.13339i	0.668907	+	0.151436i
$746$	−6.15788	+	22.3284i	−0.225456	+	0.817500i
$747$	2.98527	−	7.20374i	0.109225	−	0.263571i
$748$	3.60292	+	2.15087i	0.131736	+	0.0786435i
$749$	0.723965	+	0.417982i	0.0264531	+	0.0152727i
$750$	15.6852	−	22.4493i	0.572744	−	0.819734i
$751$	35.2487	−	20.3509i	1.28624	−	0.742613i	0.308262	−	0.951302i	$-0.400253\pi$
$751$	35.2487	−	20.3509i	1.28624	−	0.742613i	0.977982	+	0.208689i	$0.0669195\pi$
$752$	25.7786	+	15.9042i	0.940049	+	0.579967i
$753$	−6.58574	−	5.77649i	−0.239998	−	0.210507i
$754$	5.30778	−	5.23086i	0.193298	−	0.190497i
$755$	10.8693	+	35.0184i	0.395573	+	1.27445i
$756$	31.1206	−	14.7769i	1.13185	−	0.537430i
$757$		−	35.4823i		−	1.28963i	−0.764340	−	0.644813i	$-0.776935\pi$
$757$		−	35.4823i		−	1.28963i	0.764340	−	0.644813i	$-0.223065\pi$
$758$	−11.7076	−	11.8798i	−0.425240	−	0.431493i
$759$	−19.5986	+	22.3443i	−0.711386	+	0.811046i
$760$	19.1945	−	0.331411i	0.696259	−	0.0120215i
$761$	−34.0009	+	19.6304i	−1.23253	+	0.711602i	−0.967557	−	0.252654i	$-0.918697\pi$
$761$	−34.0009	+	19.6304i	−1.23253	+	0.711602i	−0.264974	+	0.964256i	$0.585363\pi$
$762$	25.8392	−	1.50216i	0.936054	−	0.0544175i
$763$	0.760910	−	1.31794i	0.0275468	−	0.0477125i
$764$	42.9840	+	25.6606i	1.55511	+	0.928367i
$765$	3.44462	−	4.87119i	0.124540	−	0.176118i
$766$	−4.23702	+	15.3634i	−0.153090	+	0.555101i
$767$	−8.11242	−	4.68371i	−0.292923	−	0.169119i
$768$	19.7322	+	19.4587i	0.712025	+	0.702154i
$769$	−3.27941	−	5.68011i	−0.118259	−	0.204830i	0.800819	−	0.598906i	$-0.204398\pi$
$769$	−3.27941	−	5.68011i	−0.118259	−	0.204830i	−0.919078	+	0.394076i	$0.871065\pi$
$770$	13.0409	+	21.0119i	0.469960	+	0.757215i
$771$	−4.52671	+	22.7476i	−0.163025	+	0.819234i
$772$	−18.4371	−	33.0386i	−0.663567	−	1.18908i
$773$	34.2118			1.23051			0.615256	−	0.788327i	$-0.289053\pi$
$773$	34.2118			1.23051			0.615256	+	0.788327i	$0.289053\pi$
$774$	−32.8405	+	13.3167i	−1.18043	+	0.478660i
$775$	0.670727	+	0.976374i	0.0240932	+	0.0350724i
$776$	4.14930	+	16.9626i	0.148951	+	0.608922i
$777$	−21.2151	−	62.5146i	−0.761089	−	2.24270i
$778$	−27.5910	+	7.17757i	−0.989185	+	0.257328i
$779$	−4.29729	−	7.44313i	−0.153967	−	0.266678i
$780$	−27.8669	+	19.6234i	−0.997793	+	0.702632i
$781$	−13.8292	+	23.9528i	−0.494847	+	0.857099i
$782$	−2.43237	+	8.81973i	−0.0869813	+	0.315393i
$783$	−5.58176	+	2.75092i	−0.199476	+	0.0983097i
$784$	7.57191	+	14.0465i	0.270425	+	0.501661i
$785$	−23.3619	−	5.28897i	−0.833822	−	0.188771i
$786$	21.8800	+	33.2747i	0.780432	+	1.18687i
$787$	−8.68943	−	15.0505i	−0.309745	−	0.536494i	0.668562	−	0.743657i	$-0.266910\pi$
$787$	−8.68943	−	15.0505i	−0.309745	−	0.536494i	−0.978306	+	0.207163i	$0.933577\pi$
$788$	−0.153385	+	10.5072i	−0.00546411	+	0.374305i
$789$	6.06225	+	17.8636i	0.215822	+	0.635962i
$790$	−28.8045	−	15.4283i	−1.02482	−	0.548915i
$791$	57.7846			2.05458
$792$	7.25043	+	18.6578i	0.257633	+	0.662977i
$793$			16.8349i			0.597826i
$794$	−5.08109	−	5.15581i	−0.180321	−	0.182973i
$795$	0.311985	+	2.97384i	0.0110650	+	0.105471i
$796$	−37.6934	−	0.550249i	−1.33601	−	0.0195030i
$797$	3.50633	+	6.07314i	0.124201	+	0.215122i	0.921420	−	0.388568i	$-0.127030\pi$
$797$	3.50633	+	6.07314i	0.124201	+	0.215122i	−0.797220	+	0.603689i	$0.793697\pi$
$798$	22.0247	+	11.0642i	0.779665	+	0.391668i
$799$	5.83244	+	3.36736i	0.206337	+	0.119129i
$800$	20.8188	+	19.1462i	0.736056	+	0.676921i
$801$	−13.9241	+	1.83082i	−0.491982	+	0.0646889i
$802$	−4.16042	+	15.0856i	−0.146910	+	0.532692i
$803$	12.4804	+	7.20555i	0.440423	+	0.254278i
$804$	21.4913	+	4.60381i	0.757939	+	0.162364i
$805$	−36.6052	+	39.5905i	−1.29016	+	1.39538i
$806$	−0.371153	−	1.42673i	−0.0130733	−	0.0502545i
$807$	24.5580	−	27.9984i	0.864483	−	0.985592i
$808$	−5.21752	−	21.3295i	−0.183552	−	0.750371i
$809$		−	38.9234i		−	1.36847i	−0.729261	−	0.684236i	$-0.760136\pi$
$809$		−	38.9234i		−	1.36847i	0.729261	−	0.684236i	$-0.239864\pi$
$810$	27.2448	−	8.22921i	0.957285	−	0.289145i
$811$		−	35.7891i		−	1.25673i	−0.777920	−	0.628363i	$-0.783725\pi$
$811$		−	35.7891i		−	1.25673i	0.777920	−	0.628363i	$-0.216275\pi$
$812$	−3.86922	−	6.93347i	−0.135783	−	0.243317i
$813$	−21.6371	+	24.6683i	−0.758845	+	0.865154i
$814$	37.1223	−	9.65706i	1.30114	−	0.338480i
$815$	−2.19321	−	2.02783i	−0.0768248	−	0.0710319i
$816$	4.51172	+	4.19657i	0.157942	+	0.146909i
$817$	−21.9570	−	12.6769i	−0.768177	−	0.443507i
$818$	22.0398	+	6.07829i	0.770604	+	0.212523i
$819$	−43.3856	+	5.70460i	−1.51601	+	0.199335i
$820$	2.97597	−	12.3081i	0.103925	−	0.429817i
$821$	−27.8765	−	16.0945i	−0.972895	−	0.561701i	−0.0727775	−	0.997348i	$-0.523186\pi$
$821$	−27.8765	−	16.0945i	−0.972895	−	0.561701i	−0.900118	+	0.435647i	$0.856520\pi$
$822$	−14.5052	+	28.8744i	−0.505926	+	1.00711i
$823$	−8.65813	−	14.9963i	−0.301804	−	0.522739i	0.674741	−	0.738055i	$-0.264255\pi$
$823$	−8.65813	−	14.9963i	−0.301804	−	0.522739i	−0.976545	+	0.215315i	$0.930922\pi$
$824$	10.4192	−	35.7360i	0.362969	−	1.24492i
$825$	8.05888	+	18.7732i	0.280574	+	0.653599i
$826$	−7.10874	+	7.00572i	−0.247345	+	0.243760i
$827$		−	15.5363i		−	0.540249i	−0.962825	−	0.270124i	$-0.912935\pi$
$827$		−	15.5363i		−	0.540249i	0.962825	−	0.270124i	$-0.0870648\pi$
$828$	−35.0138	+	26.0551i	−1.21681	+	0.905476i
$829$	−27.4645			−0.953882			−0.476941	−	0.878935i	$-0.658254\pi$
$829$	−27.4645			−0.953882			−0.476941	+	0.878935i	$0.658254\pi$
$830$	7.24570	+	3.88096i	0.251502	+	0.134710i
$831$	10.3875	+	30.6087i	0.360337	+	1.06180i
$832$	−16.2489	−	31.2259i	−0.563330	−	1.08256i
$833$	1.77400	+	3.07266i	0.0614654	+	0.106461i
$834$	13.2707	−	8.72620i	0.459526	−	0.302164i
$835$	15.6369	+	3.54009i	0.541139	+	0.122510i
$836$	−7.34082	+	12.2966i	−0.253888	+	0.425287i
$837$	−0.0808146	+	1.22837i	−0.00279336	+	0.0424588i
$838$	−9.96761	−	2.74894i	−0.344325	−	0.0949605i
$839$	−6.91476	+	11.9767i	−0.238724	+	0.413482i	−0.960348	−	0.278803i	$-0.910062\pi$
$839$	−6.91476	+	11.9767i	−0.238724	+	0.413482i	0.721624	+	0.692285i	$0.243396\pi$
$840$	12.2619	+	34.1814i	0.423076	+	1.17937i
$841$	−13.7829	−	23.8727i	−0.475272	−	0.823196i
$842$	10.6622	+	40.9861i	0.367443	+	1.41247i
$843$	−3.75790	−	11.0734i	−0.129429	−	0.381387i
$844$	4.45744	+	7.98754i	0.153431	+	0.274943i
$845$	13.5836	−	4.21619i	0.467291	−	0.145041i
$846$	12.0728	+	29.7727i	0.415070	+	1.02361i
$847$	18.0170			0.619070
$848$	−3.08690	−	0.0901446i	−0.106005	−	0.00309558i
$849$	1.78142	−	8.95196i	0.0611380	−	0.307230i
$850$	4.75118	+	4.12007i	0.162964	+	0.141317i
$851$	41.8169	+	72.4290i	1.43346	+	2.48283i
$852$	−27.2244	+	30.1393i	−0.932692	+	1.03256i
$853$	31.2866	+	18.0633i	1.07123	+	0.618476i	0.928518	−	0.371288i	$-0.121084\pi$
$853$	31.2866	+	18.0633i	1.07123	+	0.618476i	0.142714	+	0.989764i	$0.454417\pi$
$854$	17.2916	+	4.76879i	0.591705	+	0.163185i
$855$	16.6252	+	11.7563i	0.568569	+	0.402058i
$856$	−0.515270	+	0.493186i	−0.0176116	+	0.0168568i
$857$	3.70493	−	6.41713i	0.126558	−	0.219205i	−0.795783	−	0.605582i	$-0.792940\pi$
$857$	3.70493	−	6.41713i	0.126558	−	0.219205i	0.922341	+	0.386377i	$0.126274\pi$
$858$	−1.47562	−	25.3827i	−0.0503769	−	0.866551i
$859$	−35.7586	+	20.6452i	−1.22007	+	0.704407i	−0.964932	−	0.262499i	$-0.915453\pi$
$859$	−35.7586	+	20.6452i	−1.22007	+	0.704407i	−0.255136	+	0.966905i	$0.582120\pi$
$860$	−10.5513	−	35.8335i	−0.359798	−	1.22191i
$861$	10.7205	−	12.2223i	0.365352	−	0.416535i
$862$	30.9741	−	30.5252i	1.05498	−	1.03969i
$863$			46.7922i			1.59282i	0.604754	+	0.796412i	$0.293271\pi$
$863$			46.7922i			1.59282i	−0.604754	+	0.796412i	$0.706729\pi$
$864$	4.67171	+	29.0203i	0.158935	+	0.987289i
$865$	−5.49970	+	1.70704i	−0.186995	+	0.0580410i
$866$	−29.1583	−	29.5870i	−0.990838	−	1.00541i
$867$	−21.1063	−	18.5128i	−0.716807	−	0.628726i
$868$	−1.57057	−	0.0229272i	−0.0533085	−	0.000778199i
$869$	21.1104	−	12.1881i	0.716120	−	0.413452i
$870$	−2.30475	−	6.14119i	−0.0781385	−	0.208206i
$871$	−24.1772	−	13.9587i	−0.819213	−	0.472973i
$872$	0.897815	+	0.938018i	0.0304039	+	0.0317653i
$873$	−7.09086	+	17.1109i	−0.239989	+	0.579118i
$874$	−30.1014	−	8.30157i	−1.01819	−	0.280805i
$875$	13.7226	+	34.4290i	0.463909	+	1.16391i
$876$	15.7038	+	14.1850i	0.530582	+	0.479267i
$877$	−12.2576	+	7.07692i	−0.413909	+	0.238970i	−0.692468	−	0.721449i	$-0.743477\pi$
$877$	−12.2576	+	7.07692i	−0.413909	+	0.238970i	0.278559	+	0.960419i	$0.410143\pi$
$878$	−10.7059	+	2.78504i	−0.361306	+	0.0939907i
$879$	7.53520	−	37.8658i	0.254156	−	1.27718i
$880$	−20.3255	+	5.66388i	−0.685171	+	0.190929i
$881$			13.5705i			0.457200i	0.973520	+	0.228600i	$0.0734148\pi$
$881$			13.5705i			0.457200i	−0.973520	+	0.228600i	$0.926585\pi$
$882$	−2.33436	+	16.7636i	−0.0786020	+	0.564461i
$883$	46.0353			1.54921			0.774606	−	0.632444i	$-0.217948\pi$
$883$	46.0353			1.54921			0.774606	+	0.632444i	$0.217948\pi$
$884$	−3.81393	−	6.83441i	−0.128276	−	0.229866i
$885$	−6.67150	+	4.84517i	−0.224260	+	0.162869i
$886$	36.5486	−	9.50783i	1.22788	−	0.319422i
$887$	17.1621	−	9.90855i	0.576247	−	0.332696i	−0.183393	−	0.983040i	$-0.558708\pi$
$887$	17.1621	−	9.90855i	0.576247	−	0.332696i	0.759641	+	0.650343i	$0.225375\pi$
$888$	56.2729	−	2.44787i	1.88840	−	0.0821453i
$889$	−17.5143	+	30.3356i	−0.587409	+	1.01742i
$890$	−0.471580	−	14.7961i	−0.0158074	−	0.495965i
$891$	−5.50178	+	20.5061i	−0.184316	+	0.686980i
$892$	40.7910	+	24.3514i	1.36578	+	0.815346i
$893$	−11.4927	+	19.9059i	−0.384587	+	0.666125i
$894$	−17.1340	+	11.2666i	−0.573047	+	0.376811i
$895$	16.7216	+	15.4607i	0.558941	+	0.516794i
$896$	−36.6756	+	7.84436i	−1.22525	+	0.262062i
$897$	52.4962	−	17.8153i	1.75280	−	0.594835i
$898$	23.6695	+	24.0175i	0.789860	+	0.801475i
$899$	0.283722			0.00946265
$900$	5.79706	+	29.4346i	0.193235	+	0.981152i
$901$	−0.686641			−0.0228753
$902$	6.63062	+	6.72812i	0.220776	+	0.224022i
$903$	9.36031	−	47.0374i	0.311492	−	1.56531i
$904$	−13.8001	+	47.3320i	−0.458983	+	1.57424i
$905$	6.85524	+	6.33832i	0.227876	+	0.210693i
$906$	−35.8917	−	18.0304i	−1.19242	−	0.599019i
$907$	−24.4653	+	42.3752i	−0.812358	+	1.40705i	0.0988513	+	0.995102i	$0.468483\pi$
$907$	−24.4653	+	42.3752i	−0.812358	+	1.40705i	−0.911209	+	0.411943i	$0.864850\pi$
$908$	28.5587	−	47.8386i	0.947752	−	1.58758i
$909$	8.91637	−	21.5161i	0.295737	−	0.713643i
$910$	−1.46938	−	46.1026i	−0.0487095	−	1.52829i
$911$	16.0978	−	27.8822i	0.533343	−	0.923778i	−0.465898	−	0.884838i	$-0.654269\pi$
$911$	16.0978	−	27.8822i	0.533343	−	0.923778i	0.999242	−	0.0389396i	$-0.0123980\pi$
$912$	−14.3227	+	15.3983i	−0.474272	+	0.509889i
$913$	−5.31026	+	3.06588i	−0.175744	+	0.101466i
$914$	21.5646	−	5.60985i	0.713292	−	0.185557i
$915$	13.5360	+	6.02972i	0.447486	+	0.199336i
$916$	29.2006	−	16.2953i	0.964814	−	0.538413i
$917$	−53.8956			−1.77979
$918$	1.22662	+	6.41935i	0.0404845	+	0.211870i
$919$		−	37.8553i		−	1.24873i	−0.781133	−	0.624365i	$-0.785358\pi$
$919$		−	37.8553i		−	1.24873i	0.781133	−	0.624365i	$-0.214642\pi$
$920$	−23.6870	−	39.4386i	−0.780937	−	1.30025i
$921$	0.540923	+	0.474455i	0.0178240	+	0.0156338i
$922$	−14.6110	+	3.80093i	−0.481187	+	0.125177i
$923$	44.6768	−	25.7942i	1.47056	−	0.849026i
$924$	−26.4892	−	5.67445i	−0.871429	−	0.186676i
$925$	57.3114	−	4.49779i	1.88439	−	0.147887i
$926$	−8.66098	−	2.38859i	−0.284618	−	0.0784939i
$927$	31.3271	−	24.0300i	1.02892	−	0.789248i
$928$	6.60333	−	1.51347i	0.216765	−	0.0496822i
$929$	14.4535	+	8.34474i	0.474205	+	0.273782i	0.717998	−	0.696045i	$-0.245059\pi$
$929$	14.4535	+	8.34474i	0.474205	+	0.273782i	−0.243794	+	0.969827i	$0.578392\pi$
$930$	−1.28009	−	0.212587i	−0.0419757	−	0.00697100i
$931$	−10.4868	+	6.05458i	−0.343693	+	0.198431i
$932$	0.0490261	−	3.35841i	0.00160590	−	0.110008i
$933$	0.192390	−	0.966795i	0.00629855	−	0.0316514i
$934$	−7.70506	−	7.81836i	−0.252117	−	0.255824i
$935$	−4.48052	+	1.39070i	−0.146529	+	0.0454806i
$936$	5.68861	−	36.9000i	0.185938	−	1.20611i
$937$		−	41.7514i		−	1.36396i	−0.731372	−	0.681979i	$-0.761120\pi$
$937$		−	41.7514i		−	1.36396i	0.731372	−	0.681979i	$-0.238880\pi$
$938$	−21.1859	+	20.8789i	−0.691745	+	0.681721i
$939$	−15.6200	−	46.0273i	−0.509739	−	1.50204i
$940$	−32.4861	+	9.56570i	−1.05958	+	0.311999i
$941$	9.78882	−	5.65158i	0.319106	−	0.184236i	−0.331888	−	0.943319i	$-0.607686\pi$
$941$	9.78882	−	5.65158i	0.319106	−	0.184236i	0.650994	+	0.759083i	$0.274352\pi$
$942$	21.9242	−	14.4164i	0.714329	−	0.469711i
$943$	−10.2982	+	17.8369i	−0.335354	+	0.580851i
$944$	−4.04076	−	7.49595i	−0.131516	−	0.243972i
$945$	−10.9526	+	36.9270i	−0.356287	+	1.20124i
$946$	26.8634	+	7.40858i	0.873404	+	0.240874i
$947$	4.45025	+	2.56935i	0.144614	+	0.0834928i	0.570561	−	0.821255i	$-0.306726\pi$
$947$	4.45025	+	2.56935i	0.144614	+	0.0834928i	−0.425947	+	0.904748i	$0.640059\pi$
$948$	34.0605	−	11.0071i	1.10623	−	0.357495i
$949$	−13.4398	−	23.2784i	−0.436274	−	0.755649i
$950$	−14.0616	+	16.2156i	−0.456220	+	0.526103i
$951$	−21.7709	+	7.38824i	−0.705970	+	0.239580i
$952$	−8.10015	+	1.98142i	−0.262527	+	0.0642181i
$953$	22.9718			0.744131			0.372066	−	0.928206i	$-0.378650\pi$
$953$	22.9718			0.744131			0.372066	+	0.928206i	$0.378650\pi$
$954$	−2.58372	−	2.01336i	−0.0836510	−	0.0651851i
$955$	−53.4541	+	16.5915i	−1.72973	+	0.536887i
$956$	18.8997	−	10.5470i	0.611260	−	0.341113i
$957$	4.79919	+	0.955025i	0.155136	+	0.0308716i
$958$	−2.53907	−	9.76032i	−0.0820336	−	0.315342i
$959$	−21.8654	−	37.8720i	−0.706072	−	1.22295i
$960$	−30.9267	+	1.88070i	−0.998156	+	0.0606995i
$961$	−15.4719	+	26.7982i	−0.499095	+	0.864457i
$962$	−68.9703	−	19.0211i	−2.22369	−	0.613265i
$963$	−0.750067	+	0.0986235i	−0.0241706	+	0.00317810i
$964$	18.7408	+	11.1879i	0.603601	+	0.360337i
$965$	41.2566	+	9.34019i	1.32810	+	0.300671i
$966$	−3.42802	−	58.9666i	−0.110295	−	1.89722i
$967$	21.0871	+	36.5239i	0.678115	+	1.17453i	0.975548	+	0.219787i	$0.0705361\pi$
$967$	21.0871	+	36.5239i	0.678115	+	1.17453i	−0.297433	+	0.954743i	$0.596131\pi$
$968$	−4.30280	+	14.7579i	−0.138297	+	0.474337i
$969$	−3.08324	+	3.51519i	−0.0990481	+	0.112924i
$970$	−17.2106	−	9.21838i	−0.552599	−	0.295984i
$971$	−29.9678			−0.961712			−0.480856	−	0.876799i	$-0.659674\pi$
$971$	−29.9678			−0.961712			−0.480856	+	0.876799i	$0.659674\pi$
$972$	−14.2072	+	27.7517i	−0.455697	+	0.890135i
$973$			21.4947i			0.689090i
$974$	−15.2188	+	14.9982i	−0.487641	+	0.480574i
$975$	4.49029	−	37.8403i	0.143804	−	1.21186i
$976$	−8.03573	+	13.0248i	−0.257217	+	0.416915i
$977$	−18.5590	−	32.1452i	−0.593756	−	1.02842i	−0.993721	−	0.111885i	$-0.964311\pi$
$977$	−18.5590	−	32.1452i	−0.593756	−	1.02842i	0.399965	−	0.916530i	$-0.369022\pi$
$978$	3.26660	−	0.189904i	0.104454	−	0.00607245i
$979$	9.56383	+	5.52168i	0.305661	+	0.176474i
$980$	−17.3412	−	4.19293i	−0.553945	−	0.133938i
$981$	0.179538	+	1.36545i	0.00573221	+	0.0435955i
$982$	40.1402	+	11.0701i	1.28092	+	0.353262i
$983$	24.8903	+	14.3704i	0.793876	+	0.458345i	0.841325	−	0.540529i	$-0.181776\pi$
$983$	24.8903	+	14.3704i	0.793876	+	0.458345i	−0.0474493	+	0.998874i	$0.515109\pi$
$984$	7.45119	+	11.7002i	0.237535	+	0.372988i
$985$	−8.62646	−	7.97598i	−0.274862	−	0.254136i
$986$	1.45775	−	0.379221i	0.0464242	−	0.0120769i
$987$	−42.6434	−	8.48593i	−1.35735	−	0.270110i
$988$	23.3255	−	13.0168i	0.742084	−	0.414119i
$989$			60.7584i			1.93201i
$990$	−20.9373	−	7.90479i	−0.665430	−	0.251231i
$991$		−	5.20653i		−	0.165391i	−0.996575	−	0.0826954i	$-0.973647\pi$
$991$		−	5.20653i		−	0.165391i	0.996575	−	0.0826954i	$-0.0263529\pi$
$992$	0.393862	−	1.28099i	0.0125051	−	0.0406716i
$993$	4.78180	+	14.0905i	0.151746	+	0.447149i
$994$	−13.8383	−	53.1953i	−0.438925	−	1.68725i
$995$	28.6128	−	30.9463i	0.907087	−	0.981064i
$996$	−8.56784	+	2.76882i	−0.271483	+	0.0877334i
$997$	18.1724	+	10.4918i	0.575525	+	0.332279i	0.759353	−	0.650679i	$-0.225516\pi$
$997$	18.1724	+	10.4918i	0.575525	+	0.332279i	−0.183828	+	0.982958i	$0.558849\pi$
$998$	−7.84924	+	28.4612i	−0.248463	+	0.900924i
$999$	49.6663	+	33.2036i	1.57137	+	1.05051i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	180.2.n.d.119.6	yes	48
3.2	odd	2		540.2.n.d.359.19		48
4.3	odd	2	inner	180.2.n.d.119.10	yes	48
5.2	odd	4		900.2.r.g.551.7		48
5.3	odd	4		900.2.r.g.551.18		48
5.4	even	2	inner	180.2.n.d.119.19	yes	48
9.4	even	3		540.2.n.d.179.10		48
9.5	odd	6	inner	180.2.n.d.59.15	yes	48
12.11	even	2		540.2.n.d.359.15		48
15.14	odd	2		540.2.n.d.359.6		48
20.3	even	4		900.2.r.g.551.22		48
20.7	even	4		900.2.r.g.551.3		48
20.19	odd	2	inner	180.2.n.d.119.15	yes	48
36.23	even	6	inner	180.2.n.d.59.19	yes	48
36.31	odd	6		540.2.n.d.179.6		48
45.4	even	6		540.2.n.d.179.15		48
45.14	odd	6	inner	180.2.n.d.59.10	yes	48
45.23	even	12		900.2.r.g.851.22		48
45.32	even	12		900.2.r.g.851.3		48
60.59	even	2		540.2.n.d.359.10		48
180.23	odd	12		900.2.r.g.851.18		48
180.59	even	6	inner	180.2.n.d.59.6	✓	48
180.139	odd	6		540.2.n.d.179.19		48
180.167	odd	12		900.2.r.g.851.7		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.2.n.d.59.6	✓	48	180.59	even	6	inner
180.2.n.d.59.10	yes	48	45.14	odd	6	inner
180.2.n.d.59.15	yes	48	9.5	odd	6	inner
180.2.n.d.59.19	yes	48	36.23	even	6	inner
180.2.n.d.119.6	yes	48	1.1	even	1	trivial
180.2.n.d.119.10	yes	48	4.3	odd	2	inner
180.2.n.d.119.15	yes	48	20.19	odd	2	inner
180.2.n.d.119.19	yes	48	5.4	even	2	inner
540.2.n.d.179.6		48	36.31	odd	6
540.2.n.d.179.10		48	9.4	even	3
540.2.n.d.179.15		48	45.4	even	6
540.2.n.d.179.19		48	180.139	odd	6
540.2.n.d.359.6		48	15.14	odd	2
540.2.n.d.359.10		48	60.59	even	2
540.2.n.d.359.15		48	12.11	even	2
540.2.n.d.359.19		48	3.2	odd	2
900.2.r.g.551.3		48	20.7	even	4
900.2.r.g.551.7		48	5.2	odd	4
900.2.r.g.551.18		48	5.3	odd	4
900.2.r.g.551.22		48	20.3	even	4
900.2.r.g.851.3		48	45.32	even	12
900.2.r.g.851.7		48	180.167	odd	12
900.2.r.g.851.18		48	180.23	odd	12
900.2.r.g.851.22		48	45.23	even	12

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 180 = 2^{2} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	180.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00727 + 0.992675i) q^{2} +(1.30213 + 1.14213i) q^{3} +(0.0291929 - 1.99979i) q^{4} +(1.64183 + 1.51803i) q^{5} +(-2.44536 + 0.142161i) q^{6} +(1.65751 - 2.87089i) q^{7} +(1.95573 + 2.04331i) q^{8} +(0.391092 + 2.97440i) q^{9} +(-3.16067 + 0.100737i) q^{10} +(1.17952 - 2.04298i) q^{11} +(2.32202 - 2.57064i) q^{12} +(-3.81058 + 2.20004i) q^{13} +(1.18030 + 4.53714i) q^{14} +(0.404097 + 3.85184i) q^{15} +(-3.99830 - 0.116759i) q^{16} -0.889368 q^{17} +(-3.34655 - 2.60780i) q^{18} -3.03537i q^{19} +(3.08366 - 3.23899i) q^{20} +(5.43722 - 1.84519i) q^{21} +(0.839925 + 3.22872i) q^{22} +(-6.29952 + 3.63703i) q^{23} +(0.212904 + 4.89435i) q^{24} +(0.391197 + 4.98467i) q^{25} +(1.65437 - 5.99870i) q^{26} +(-2.88789 + 4.31973i) q^{27} +(-5.69278 - 3.39848i) q^{28} +(1.03714 + 0.598791i) q^{29} +(-4.23067 - 3.47872i) q^{30} +(0.205172 - 0.118456i) q^{31} +(4.14327 - 3.85140i) q^{32} +(3.86923 - 1.31308i) q^{33} +(0.895835 - 0.882853i) q^{34} +(7.07943 - 2.19737i) q^{35} +(5.95958 - 0.695270i) q^{36} -11.4975i q^{37} +(3.01314 + 3.05745i) q^{38} +(-7.47460 - 1.48743i) q^{39} +(0.109183 + 6.32361i) q^{40} +(2.45213 - 1.41574i) q^{41} +(-3.64508 + 7.25600i) q^{42} +(4.17637 - 7.23369i) q^{43} +(-4.05110 - 2.41842i) q^{44} +(-3.87311 + 5.47714i) q^{45} +(2.73494 - 9.91686i) q^{46} +(-6.55796 - 3.78624i) q^{47} +(-5.07295 - 4.71860i) q^{48} +(-1.99467 - 3.45488i) q^{49} +(-5.34220 - 4.63259i) q^{50} +(-1.15807 - 1.01577i) q^{51} +(4.28837 + 7.68457i) q^{52} +0.772055 q^{53} +(-1.37920 - 7.21788i) q^{54} +(5.03787 - 1.56369i) q^{55} +(9.10776 - 2.22789i) q^{56} +(3.46678 - 3.95246i) q^{57} +(-1.63908 + 0.426394i) q^{58} +(1.06446 + 1.84370i) q^{59} +(7.71466 - 0.695662i) q^{60} +(1.91303 - 3.31346i) q^{61} +(-0.0890754 + 0.322986i) q^{62} +(9.18741 + 3.80731i) q^{63} +(-0.350216 + 7.99233i) q^{64} +(-9.59603 - 2.17247i) q^{65} +(-2.59391 + 5.16352i) q^{66} +(3.17238 + 5.49472i) q^{67} +(-0.0259632 + 1.77855i) q^{68} +(-12.3568 - 2.45896i) q^{69} +(-4.94964 + 9.24092i) q^{70} -11.7244 q^{71} +(-5.31274 + 6.61625i) q^{72} +6.10889i q^{73} +(11.4133 + 11.5811i) q^{74} +(-5.18374 + 6.93750i) q^{75} +(-6.07010 - 0.0886114i) q^{76} +(-3.91012 - 6.77253i) q^{77} +(9.00548 - 5.92160i) q^{78} +(8.94873 + 5.16655i) q^{79} +(-6.38727 - 6.26121i) q^{80} +(-8.69409 + 2.32653i) q^{81} +(-1.06459 + 3.86020i) q^{82} +(-2.25103 - 1.29963i) q^{83} +(-3.53126 - 10.9271i) q^{84} +(-1.46019 - 1.35008i) q^{85} +(2.97396 + 11.4321i) q^{86} +(0.666593 + 1.96425i) q^{87} +(6.48127 - 1.58541i) q^{88} +4.68130i q^{89} +(-1.53575 - 9.36170i) q^{90} +14.5863i q^{91} +(7.08939 + 12.7039i) q^{92} +(0.402452 + 0.0800869i) q^{93} +(10.3642 - 2.69615i) q^{94} +(4.60778 - 4.98356i) q^{95} +(9.79387 - 0.282883i) q^{96} +(5.34684 + 3.08700i) q^{97} +(5.43875 + 1.49994i) q^{98} +(6.53795 + 2.70936i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 2 q^{4} - 18 q^{5} - 12 q^{9} - 16 q^{10} - 42 q^{14} + 30 q^{16} - 12 q^{21} - 6 q^{24} - 26 q^{25} - 12 q^{30} - 4 q^{34} + 96 q^{36} + 10 q^{40} + 96 q^{41} - 66 q^{45} + 4 q^{46} + 32 q^{49}+ \cdots + 54 q^{96}+O(q^{100}) \) 48 * q - 2 * q^4 - 18 * q^5 - 12 * q^9 - 16 * q^10 - 42 * q^14 + 30 * q^16 - 12 * q^21 - 6 * q^24 - 26 * q^25 - 12 * q^30 - 4 * q^34 + 96 * q^36 + 10 * q^40 + 96 * q^41 - 66 * q^45 + 4 * q^46 + 32 * q^49 - 90 * q^50 - 30 * q^54 + 6 * q^56 - 42 * q^60 + 8 * q^61 - 20 * q^64 - 6 * q^65 + 36 * q^66 - 96 * q^69 + 4 * q^70 + 72 * q^74 + 36 * q^81 - 6 * q^84 - 4 * q^85 + 108 * q^86 - 6 * q^90 - 62 * q^94 + 54 * q^96

Introduction

L-functions

Modular forms

Varieties

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