LMFDB - Embedded newform 360.2.bo.a.43.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,2,Mod(43,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 6, 8, 9]))

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

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

chi := DirichletCharacter("360.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	360.bo (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:	$2.87461447277$
Analytic rank:	$0$
Dimension:	$272$
Relative dimension:	$68$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			43.10
Character	$\chi$	$=$	360.43
Dual form			360.2.bo.a.67.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.27550 + 0.610814i) q^{2} +(1.53896 - 0.794731i) q^{3} +(1.25381 - 1.55819i) q^{4} +(0.533101 + 2.17159i) q^{5} +(-1.47752 + 1.95370i) q^{6} +(4.60452 - 1.23378i) q^{7} +(-0.647478 + 2.75332i) q^{8} +(1.73680 - 2.44612i) q^{9} +O(q^{10})$	\(q+(-1.27550 + 0.610814i) q^{2} +(1.53896 - 0.794731i) q^{3} +(1.25381 - 1.55819i) q^{4} +(0.533101 + 2.17159i) q^{5} +(-1.47752 + 1.95370i) q^{6} +(4.60452 - 1.23378i) q^{7} +(-0.647478 + 2.75332i) q^{8} +(1.73680 - 2.44612i) q^{9} +(-2.00641 - 2.44424i) q^{10} +(-0.264986 + 0.458969i) q^{11} +(0.691229 - 3.39444i) q^{12} +(-4.29389 - 1.15054i) q^{13} +(-5.11947 + 4.38619i) q^{14} +(2.54625 + 2.91832i) q^{15} +(-0.855905 - 3.90736i) q^{16} +(-0.100984 + 0.100984i) q^{17} +(-0.721174 + 4.18090i) q^{18} +5.41595i q^{19} +(4.05216 + 1.89210i) q^{20} +(6.10566 - 5.55810i) q^{21} +(0.0576455 - 0.747273i) q^{22} +(-2.57362 - 0.689600i) q^{23} +(1.19171 + 4.75182i) q^{24} +(-4.43161 + 2.31535i) q^{25} +(6.17963 - 1.15524i) q^{26} +(0.728866 - 5.14478i) q^{27} +(3.85075 - 8.72165i) q^{28} +(3.58092 - 6.20233i) q^{29} +(-5.03030 - 2.16704i) q^{30} +(4.51145 - 2.60469i) q^{31} +(3.47838 + 4.46104i) q^{32} +(-0.0430460 + 0.916927i) q^{33} +(0.0671229 - 0.190488i) q^{34} +(5.13394 + 9.34141i) q^{35} +(-1.63389 - 5.77325i) q^{36} +(4.12775 + 4.12775i) q^{37} +(-3.30814 - 6.90806i) q^{38} +(-7.52250 + 1.64184i) q^{39} +(-6.32425 + 0.0617390i) q^{40} +(0.791137 + 1.37029i) q^{41} +(-4.39283 + 10.8188i) q^{42} +(-6.77375 + 1.81502i) q^{43} +(0.382917 + 0.988359i) q^{44} +(6.23786 + 2.46760i) q^{45} +(3.70388 - 0.692418i) q^{46} +(-4.02857 + 1.07945i) q^{47} +(-4.42250 - 5.33305i) q^{48} +(13.6173 - 7.86193i) q^{49} +(4.23828 - 5.66012i) q^{50} +(-0.0751553 + 0.235666i) q^{51} +(-7.17650 + 5.24812i) q^{52} +(-5.44677 + 5.44677i) q^{53} +(2.21283 + 7.00738i) q^{54} +(-1.13796 - 0.330764i) q^{55} +(0.415657 + 13.4766i) q^{56} +(4.30423 + 8.33494i) q^{57} +(-0.779000 + 10.0984i) q^{58} +(3.56981 - 2.06103i) q^{59} +(7.73982 - 0.308511i) q^{60} +(2.28966 + 1.32193i) q^{61} +(-4.16339 + 6.07794i) q^{62} +(4.97919 - 13.4061i) q^{63} +(-7.16154 - 3.56543i) q^{64} +(0.209435 - 9.93792i) q^{65} +(-0.505167 - 1.19584i) q^{66} +(-5.04934 - 1.35297i) q^{67} +(0.0307371 + 0.283967i) q^{68} +(-4.50875 + 0.984070i) q^{69} +(-12.2542 - 8.77911i) q^{70} +0.813528i q^{71} +(5.61041 + 6.36579i) q^{72} +(-7.72899 - 7.72899i) q^{73} +(-7.78624 - 2.74367i) q^{74} +(-4.97999 + 7.08517i) q^{75} +(8.43908 + 6.79059i) q^{76} +(-0.653867 + 2.44027i) q^{77} +(8.59211 - 6.68902i) q^{78} +(-2.48192 + 4.29882i) q^{79} +(8.02889 - 3.94169i) q^{80} +(-2.96702 - 8.49687i) q^{81} +(-1.84609 - 1.26457i) q^{82} +(-10.9906 + 2.94492i) q^{83} +(-1.00520 - 16.4826i) q^{84} +(-0.273130 - 0.165461i) q^{85} +(7.53129 - 6.45256i) q^{86} +(0.581708 - 12.3910i) q^{87} +(-1.09212 - 1.02676i) q^{88} +3.78973i q^{89} +(-9.46366 + 0.662745i) q^{90} -21.1908 q^{91} +(-4.30137 + 3.14556i) q^{92} +(4.87292 - 7.59391i) q^{93} +(4.47910 - 3.83755i) q^{94} +(-11.7612 + 2.88725i) q^{95} +(8.89842 + 4.10100i) q^{96} +(-1.21447 - 4.53246i) q^{97} +(-12.5667 + 18.3455i) q^{98} +(0.662465 + 1.44533i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 272 q - 2 q^{2} - 8 q^{3} - 8 q^{6} - 8 q^{8}+O(q^{10}) $ 272 * q - 2 * q^2 - 8 * q^3 - 8 * q^6 - 8 * q^8	$ 272 q - 2 q^{2} - 8 q^{3} - 8 q^{6} - 8 q^{8} - 8 q^{10} - 8 q^{11} - 10 q^{12} - 4 q^{16} - 16 q^{17} + 20 q^{18} + 14 q^{20} + 6 q^{22} - 4 q^{25} - 48 q^{26} - 8 q^{27} + 8 q^{28} - 34 q^{30} - 22 q^{32} + 4 q^{33} - 16 q^{35} - 8 q^{36} - 26 q^{38} - 2 q^{40} - 8 q^{41} - 66 q^{42} - 4 q^{43} - 40 q^{46} - 38 q^{48} - 42 q^{50} - 16 q^{51} + 14 q^{52} + 24 q^{56} + 16 q^{57} + 6 q^{58} + 14 q^{60} - 76 q^{62} - 4 q^{65} - 44 q^{66} - 4 q^{67} - 46 q^{68} + 18 q^{70} + 38 q^{72} - 16 q^{73} - 120 q^{75} - 38 q^{78} + 92 q^{80} - 32 q^{81} - 4 q^{83} - 40 q^{86} - 42 q^{88} - 14 q^{90} - 32 q^{91} + 52 q^{92} + 108 q^{96} - 4 q^{97} - 140 q^{98}+O(q^{100}) $ 272 * q - 2 * q^2 - 8 * q^3 - 8 * q^6 - 8 * q^8 - 8 * q^10 - 8 * q^11 - 10 * q^12 - 4 * q^16 - 16 * q^17 + 20 * q^18 + 14 * q^20 + 6 * q^22 - 4 * q^25 - 48 * q^26 - 8 * q^27 + 8 * q^28 - 34 * q^30 - 22 * q^32 + 4 * q^33 - 16 * q^35 - 8 * q^36 - 26 * q^38 - 2 * q^40 - 8 * q^41 - 66 * q^42 - 4 * q^43 - 40 * q^46 - 38 * q^48 - 42 * q^50 - 16 * q^51 + 14 * q^52 + 24 * q^56 + 16 * q^57 + 6 * q^58 + 14 * q^60 - 76 * q^62 - 4 * q^65 - 44 * q^66 - 4 * q^67 - 46 * q^68 + 18 * q^70 + 38 * q^72 - 16 * q^73 - 120 * q^75 - 38 * q^78 + 92 * q^80 - 32 * q^81 - 4 * q^83 - 40 * q^86 - 42 * q^88 - 14 * q^90 - 32 * q^91 + 52 * q^92 + 108 * q^96 - 4 * q^97 - 140 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.27550	+	0.610814i	−0.901916	+	0.431911i
$2$	−1.27550	+	0.610814i	−0.901916	+	0.431911i
$3$	1.53896	−	0.794731i	0.888520	−	0.458838i
$3$	1.53896	−	0.794731i	0.888520	−	0.458838i
$4$	1.25381	−	1.55819i	0.626907	−	0.779094i
$5$	0.533101	+	2.17159i	0.238410	+	0.971165i
$5$	0.533101	+	2.17159i	0.238410	+	0.971165i
$6$	−1.47752	+	1.95370i	−0.603194	+	0.797595i
$7$	4.60452	−	1.23378i	1.74035	−	0.466324i	0.757823	−	0.652461i	$-0.226263\pi$
$7$	4.60452	−	1.23378i	1.74035	−	0.466324i	0.982524	+	0.186136i	$0.0595965\pi$
$8$	−0.647478	+	2.75332i	−0.228918	+	0.973446i
$9$	1.73680	−	2.44612i	0.578935	−	0.815374i
$10$	−2.00641	−	2.44424i	−0.634482	−	0.772938i
$11$	−0.264986	+	0.458969i	−0.0798962	+	0.138384i	−0.903205	−	0.429209i	$-0.858792\pi$
$11$	−0.264986	+	0.458969i	−0.0798962	+	0.138384i	0.823309	+	0.567594i	$0.192126\pi$
$12$	0.691229	−	3.39444i	0.199541	−	0.979890i
$13$	−4.29389	−	1.15054i	−1.19091	−	0.319103i	−0.391665	−	0.920108i	$-0.628101\pi$
$13$	−4.29389	−	1.15054i	−1.19091	−	0.319103i	−0.799246	+	0.601005i	$0.794767\pi$
$14$	−5.11947	+	4.38619i	−1.36824	+	1.17226i
$15$	2.54625	+	2.91832i	0.657439	+	0.753507i
$16$	−0.855905	−	3.90736i	−0.213976	−	0.976839i
$17$	−0.100984	+	0.100984i	−0.0244922	+	0.0244922i	−0.719247	−	0.694755i	$-0.755513\pi$
$17$	−0.100984	+	0.100984i	−0.0244922	+	0.0244922i	0.694755	+	0.719247i	$0.255513\pi$
$18$	−0.721174	+	4.18090i	−0.169982	+	0.985447i
$19$			5.41595i			1.24250i	0.783611	+	0.621252i	$0.213376\pi$
$19$			5.41595i			1.24250i	−0.783611	+	0.621252i	$0.786624\pi$
$20$	4.05216	+	1.89210i	0.906090	+	0.423086i
$21$	6.10566	−	5.55810i	1.33236	−	1.21288i
$22$	0.0576455	−	0.747273i	0.0122901	−	0.159319i
$23$	−2.57362	−	0.689600i	−0.536638	−	0.143792i	−0.0196859	−	0.999806i	$-0.506267\pi$
$23$	−2.57362	−	0.689600i	−0.536638	−	0.143792i	−0.516952	+	0.856015i	$0.672933\pi$
$24$	1.19171	+	4.75182i	0.243256	+	0.969962i
$25$	−4.43161	+	2.31535i	−0.886321	+	0.463070i
$26$	6.17963	−	1.15524i	1.21193	−	0.226562i
$27$	0.728866	−	5.14478i	0.140270	−	0.990113i
$28$	3.85075	−	8.72165i	0.727724	−	1.64824i
$29$	3.58092	−	6.20233i	0.664960	−	1.15174i	−0.314337	−	0.949312i	$-0.601782\pi$
$29$	3.58092	−	6.20233i	0.664960	−	1.15174i	0.979296	−	0.202432i	$-0.0648846\pi$
$30$	−5.03030	−	2.16704i	−0.918403	−	0.395646i
$31$	4.51145	−	2.60469i	0.810281	−	0.467816i	−0.0367727	−	0.999324i	$-0.511708\pi$
$31$	4.51145	−	2.60469i	0.810281	−	0.467816i	0.847053	+	0.531508i	$0.178374\pi$
$32$	3.47838	+	4.46104i	0.614896	+	0.788608i
$33$	−0.0430460	+	0.916927i	−0.00749335	+	0.159617i
$34$	0.0671229	−	0.190488i	0.0115115	−	0.0326684i
$35$	5.13394	+	9.34141i	0.867794	+	1.57899i
$36$	−1.63389	−	5.77325i	−0.272315	−	0.962208i
$37$	4.12775	+	4.12775i	0.678597	+	0.678597i	0.959683	−	0.281085i	$-0.0906944\pi$
$37$	4.12775	+	4.12775i	0.678597	+	0.678597i	−0.281085	+	0.959683i	$0.590694\pi$
$38$	−3.30814	−	6.90806i	−0.536651	−	1.12064i
$39$	−7.52250	+	1.64184i	−1.20456	+	0.262905i
$40$	−6.32425	+	0.0617390i	−0.999952	+	0.00976179i
$41$	0.791137	+	1.37029i	0.123555	+	0.214003i	0.921167	−	0.389167i	$-0.127237\pi$
$41$	0.791137	+	1.37029i	0.123555	+	0.214003i	−0.797612	+	0.603170i	$0.793904\pi$
$42$	−4.39283	+	10.8188i	−0.677828	+	1.66938i
$43$	−6.77375	+	1.81502i	−1.03299	+	0.276788i	−0.735204	−	0.677846i	$-0.762914\pi$
$43$	−6.77375	+	1.81502i	−1.03299	+	0.276788i	−0.297783	+	0.954634i	$0.596247\pi$
$44$	0.382917	+	0.988359i	0.0577270	+	0.149001i
$45$	6.23786	+	2.46760i	0.929886	+	0.367848i
$46$	3.70388	−	0.692418i	0.546107	−	0.102091i
$47$	−4.02857	+	1.07945i	−0.587627	+	0.157454i	−0.540368	−	0.841429i	$-0.681715\pi$
$47$	−4.02857	+	1.07945i	−0.587627	+	0.157454i	−0.0472584	+	0.998883i	$0.515048\pi$
$48$	−4.42250	−	5.33305i	−0.638333	−	0.769760i
$49$	13.6173	−	7.86193i	1.94532	−	1.12313i
$50$	4.23828	−	5.66012i	0.599383	−	0.800462i
$51$	−0.0751553	+	0.235666i	−0.0105239	+	0.0329998i
$52$	−7.17650	+	5.24812i	−0.995201	+	0.727784i
$53$	−5.44677	+	5.44677i	−0.748171	+	0.748171i	−0.974136	−	0.225964i	$-0.927447\pi$
$53$	−5.44677	+	5.44677i	−0.748171	+	0.748171i	0.225964	+	0.974136i	$0.427447\pi$
$54$	2.21283	+	7.00738i	0.301128	+	0.953584i
$55$	−1.13796	−	0.330764i	−0.153442	−	0.0446002i
$56$	0.415657	+	13.4766i	0.0555445	+	1.80088i
$57$	4.30423	+	8.33494i	0.570109	+	1.10399i
$58$	−0.779000	+	10.0984i	−0.102288	+	1.32598i
$59$	3.56981	−	2.06103i	0.464749	−	0.268323i	−0.249290	−	0.968429i	$-0.580197\pi$
$59$	3.56981	−	2.06103i	0.464749	−	0.268323i	0.714039	+	0.700106i	$0.246864\pi$
$60$	7.73982	−	0.308511i	0.999207	−	0.0398286i
$61$	2.28966	+	1.32193i	0.293160	+	0.169256i	0.639366	−	0.768902i	$-0.279197\pi$
$61$	2.28966	+	1.32193i	0.293160	+	0.169256i	−0.346206	+	0.938159i	$0.612530\pi$
$62$	−4.16339	+	6.07794i	−0.528751	+	0.771900i
$63$	4.97919	−	13.4061i	0.627319	−	1.68900i
$64$	−7.16154	−	3.56543i	−0.895193	−	0.445679i
$65$	0.209435	−	9.93792i	0.0259772	−	1.23265i
$66$	−0.505167	−	1.19584i	−0.0621817	−	0.147197i
$67$	−5.04934	−	1.35297i	−0.616875	−	0.165291i	−0.0631684	−	0.998003i	$-0.520121\pi$
$67$	−5.04934	−	1.35297i	−0.616875	−	0.165291i	−0.553707	+	0.832712i	$0.686787\pi$
$68$	0.0307371	+	0.283967i	0.00372742	+	0.0344361i
$69$	−4.50875	+	0.984070i	−0.542790	+	0.118468i
$70$	−12.2542	−	8.77911i	−1.46466	−	1.04930i
$71$			0.813528i			0.0965480i	0.998834	+	0.0482740i	$0.0153721\pi$
$71$			0.813528i			0.0965480i	−0.998834	+	0.0482740i	$0.984628\pi$
$72$	5.61041	+	6.36579i	0.661193	+	0.750216i
$73$	−7.72899	−	7.72899i	−0.904610	−	0.904610i	0.0912211	−	0.995831i	$-0.470923\pi$
$73$	−7.72899	−	7.72899i	−0.904610	−	0.904610i	−0.995831	+	0.0912211i	$0.970923\pi$
$74$	−7.78624	−	2.74367i	−0.905132	−	0.318945i
$75$	−4.97999	+	7.08517i	−0.575040	+	0.818125i
$76$	8.43908	+	6.79059i	0.968028	+	0.778934i
$77$	−0.653867	+	2.44027i	−0.0745151	+	0.278094i
$78$	8.59211	−	6.68902i	0.972865	−	0.757383i
$79$	−2.48192	+	4.29882i	−0.279238	+	0.483655i	−0.971196	−	0.238284i	$-0.923415\pi$
$79$	−2.48192	+	4.29882i	−0.279238	+	0.483655i	0.691957	+	0.721938i	$0.256749\pi$
$80$	8.02889	−	3.94169i	0.897657	−	0.440694i
$81$	−2.96702	−	8.49687i	−0.329669	−	0.944097i
$82$	−1.84609	−	1.26457i	−0.203866	−	0.139648i
$83$	−10.9906	+	2.94492i	−1.20637	+	0.323247i	−0.805338	−	0.592816i	$-0.798016\pi$
$83$	−10.9906	+	2.94492i	−1.20637	+	0.323247i	−0.401035	+	0.916063i	$0.631350\pi$
$84$	−1.00520	−	16.4826i	−0.109677	−	1.79840i
$85$	−0.273130	−	0.165461i	−0.0296252	−	0.0179468i
$86$	7.53129	−	6.45256i	0.812120	−	0.695798i
$87$	0.581708	−	12.3910i	0.0623656	−	1.32846i
$88$	−1.09212	−	1.02676i	−0.116420	−	0.109453i
$89$			3.78973i			0.401710i	0.979621	+	0.200855i	$0.0643720\pi$
$89$			3.78973i			0.401710i	−0.979621	+	0.200855i	$0.935628\pi$
$90$	−9.46366	+	0.662745i	−0.997557	+	0.0698595i
$91$	−21.1908			−2.22140
$92$	−4.30137	+	3.14556i	−0.448449	+	0.327947i
$93$	4.87292	−	7.59391i	0.505299	−	0.787451i
$94$	4.47910	−	3.83755i	0.461984	−	0.395813i
$95$	−11.7612	+	2.88725i	−1.20668	+	0.296225i
$96$	8.89842	+	4.10100i	0.908191	+	0.418556i
$97$	−1.21447	−	4.53246i	−0.123311	−	0.460202i	0.876463	−	0.481469i	$-0.159897\pi$
$97$	−1.21447	−	4.53246i	−0.123311	−	0.460202i	−0.999774	+	0.0212673i	$0.993230\pi$
$98$	−12.5667	+	18.3455i	−1.26943	+	1.85318i
$99$	0.662465	+	1.44533i	0.0665802	+	0.145261i
$100$	−1.94865	+	9.80830i	−0.194865	+	0.980830i
$101$	−16.3514	−	9.44051i	−1.62703	−	0.939366i	−0.984973	−	0.172708i	$-0.944748\pi$
$101$	−16.3514	−	9.44051i	−1.62703	−	0.939366i	−0.642056	−	0.766658i	$-0.721918\pi$
$102$	−0.0480870	−	0.346498i	−0.00476132	−	0.0343084i
$103$	−5.05842	−	1.35540i	−0.498421	−	0.133552i	0.000845934	−	1.00000i	$-0.499731\pi$
$103$	−5.05842	−	1.35540i	−0.498421	−	0.133552i	−0.499267	+	0.866448i	$0.666397\pi$
$104$	5.94802	−	11.0775i	0.583251	−	1.08624i
$105$	15.3248	+	10.2960i	1.49555	+	1.00478i
$106$	3.62041	−	10.2743i	0.351645	−	0.997931i
$107$	−4.11512	+	4.11512i	−0.397824	+	0.397824i	−0.877465	−	0.479641i	$-0.840767\pi$
$107$	−4.11512	+	4.11512i	−0.397824	+	0.397824i	0.479641	+	0.877465i	$0.340767\pi$
$108$	−7.10268	−	7.58630i	−0.683455	−	0.729992i
$109$	10.6423			1.01934			0.509671	−	0.860369i	$-0.329767\pi$
$109$	10.6423			1.01934			0.509671	+	0.860369i	$0.329767\pi$
$110$	1.65350	−	0.273189i	0.157655	−	0.0260476i
$111$	9.63289	+	3.07199i	0.914314	+	0.291581i
$112$	−8.76185	−	16.9355i	−0.827917	−	1.60026i
$113$	3.15566	−	11.7771i	0.296859	−	1.10789i	−0.642870	−	0.765975i	$-0.722256\pi$
$113$	3.15566	−	11.7771i	0.296859	−	1.10789i	0.939729	−	0.341919i	$-0.111077\pi$
$114$	−10.5811	−	8.00216i	−0.991015	−	0.749471i
$115$	0.125529	−	5.95648i	0.0117056	−	0.555445i
$116$	−5.17460	−	13.3563i	−0.480450	−	1.24010i
$117$	−10.2720	+	8.50510i	−0.949648	+	0.786297i
$118$	−3.29439	+	4.80933i	−0.303273	+	0.442735i
$119$	−0.340391	+	0.589575i	−0.0312036	+	0.0540463i
$120$	−9.68372	+	5.12110i	−0.883998	+	0.467490i
$121$	5.35957	+	9.28304i	0.487233	+	0.843913i
$122$	−3.72792	−	0.287576i	−0.337510	−	0.0260359i
$123$	2.30654	+	1.48008i	0.207974	+	0.133454i
$124$	1.59792	−	10.2955i	0.143498	−	0.924562i
$125$	−7.39049	−	8.38932i	−0.661025	−	0.750363i
$126$	1.83764	+	20.1408i	0.163710	+	1.79429i
$127$	8.82741	+	8.82741i	0.783306	+	0.783306i	0.980387	−	0.197082i	$-0.0631464\pi$
$127$	8.82741	+	8.82741i	0.783306	+	0.783306i	−0.197082	+	0.980387i	$0.563146\pi$
$128$	11.3124	+	0.173347i	0.999883	+	0.0153218i
$129$	−8.98208	+	8.17656i	−0.790828	+	0.719906i
$130$	5.80308	+	12.8038i	0.508964	+	1.12296i
$131$	4.81770	+	8.34449i	0.420924	+	0.729062i	0.996030	−	0.0890170i	$-0.0283726\pi$
$131$	4.81770	+	8.34449i	0.420924	+	0.729062i	−0.575106	+	0.818079i	$0.695039\pi$
$132$	1.37477	+	1.21673i	0.119659	+	0.105903i
$133$	6.68209	+	24.9379i	0.579410	+	2.16239i
$134$	7.26686	−	1.35849i	0.627761	−	0.117356i
$135$	11.5609	−	1.15989i	0.995005	−	0.0998271i
$136$	−0.212656	−	0.343426i	−0.0182351	−	0.0294486i
$137$	−6.03054	−	22.5063i	−0.515224	−	1.92284i	−0.350786	−	0.936456i	$-0.614086\pi$
$137$	−6.03054	−	22.5063i	−0.515224	−	1.92284i	−0.164438	−	0.986387i	$-0.552581\pi$
$138$	5.14984	−	4.00919i	0.438384	−	0.341285i
$139$	−12.9765	+	7.49199i	−1.10065	+	0.635462i	−0.936392	−	0.350955i	$-0.885857\pi$
$139$	−12.9765	+	7.49199i	−1.10065	+	0.635462i	−0.164260	+	0.986417i	$0.552524\pi$
$140$	20.9927	+	3.71274i	1.77421	+	0.313784i
$141$	−5.34193	+	4.86286i	−0.449872	+	0.409527i
$142$	−0.496914	−	1.03766i	−0.0417001	−	0.0870782i
$143$	1.66588	−	1.66588i	0.139308	−	0.139308i
$144$	−11.0444	−	4.69266i	−0.920367	−	0.391055i
$145$	15.3779	+	4.46982i	1.27707	+	0.371198i
$146$	14.5793	+	5.13737i	1.20659	+	0.425172i
$147$	14.7083	−	22.9213i	1.21312	−	1.89051i
$148$	11.6072	−	1.25639i	0.954109	−	0.103274i
$149$	3.50787	+	6.07580i	0.287376	+	0.497749i	0.973182	−	0.230034i	$-0.0738839\pi$
$149$	3.50787	+	6.07580i	0.287376	+	0.497749i	−0.685807	+	0.727784i	$0.740551\pi$
$150$	2.02427	−	12.0790i	0.165281	−	0.986247i
$151$	−1.08291	−	0.625218i	−0.0881259	−	0.0508795i	0.455289	−	0.890343i	$-0.349536\pi$
$151$	−1.08291	−	0.625218i	−0.0881259	−	0.0508795i	−0.543415	+	0.839464i	$0.682869\pi$
$152$	−14.9118	−	3.50671i	−1.20951	−	0.284432i
$153$	0.0716296	+	0.422409i	0.00579091	+	0.0341497i
$154$	−0.656539	−	3.51196i	−0.0529054	−	0.283002i
$155$	8.06137	+	8.40846i	0.647505	+	0.675384i
$156$	−6.87351	+	13.7800i	−0.550321	+	1.10329i
$157$	0.153102	−	0.571384i	0.0122189	−	0.0456014i	−0.959547	−	0.281548i	$-0.909152\pi$
$157$	0.153102	−	0.571384i	0.0122189	−	0.0456014i	0.971766	+	0.235946i	$0.0758189\pi$
$158$	0.539922	−	6.99914i	0.0429539	−	0.556822i
$159$	−4.05365	+	12.7111i	−0.321475	+	1.00805i
$160$	−7.83323	+	9.93179i	−0.619271	+	0.785177i
$161$	−12.7011			−1.00099
$162$	8.97445	+	9.02548i	0.705099	+	0.709109i
$163$	17.5218	+	17.5218i	1.37242	+	1.37242i	0.856850	+	0.515565i	$0.172418\pi$
$163$	17.5218	+	17.5218i	1.37242	+	1.37242i	0.515565	+	0.856850i	$0.327582\pi$
$164$	3.12711	+	0.485346i	0.244186	+	0.0378992i
$165$	−2.01414	+	0.395336i	−0.156800	+	0.0307769i
$166$	12.2197	−	10.4695i	0.948434	−	0.812587i
$167$	−1.88426	+	7.03217i	−0.145809	+	0.544165i	0.853909	+	0.520422i	$0.174225\pi$
$167$	−1.88426	+	7.03217i	−0.145809	+	0.544165i	−0.999718	+	0.0237437i	$0.992441\pi$
$168$	11.3499	+	20.4096i	0.875666	+	1.57463i
$169$	5.85539	+	3.38061i	0.450415	+	0.260047i
$170$	0.449445	+	0.0442143i	0.0344708	+	0.00339108i
$171$	13.2481	+	9.40645i	1.01311	+	0.719329i
$172$	−5.66487	+	12.8305i	−0.431942	+	0.978315i
$173$	−0.485684	−	1.81260i	−0.0369258	−	0.137809i	0.945002	−	0.327064i	$-0.106059\pi$
$173$	−0.485684	−	1.81260i	−0.0369258	−	0.137809i	−0.981928	+	0.189255i	$0.939393\pi$
$174$	6.82663	+	16.1601i	0.517526	+	1.22509i
$175$	−17.5488	+	16.1287i	−1.32657	+	1.21922i
$176$	2.02016	+	0.642559i	0.152275	+	0.0484347i
$177$	3.85583	−	6.00888i	0.289822	−	0.451655i
$178$	−2.31482	−	4.83380i	−0.173503	−	0.362309i
$179$		−	13.8942i		−	1.03850i	−0.854622	−	0.519250i	$-0.826211\pi$
$179$		−	13.8942i		−	1.03850i	0.854622	−	0.519250i	$-0.173789\pi$
$180$	11.6661	−	6.62586i	0.869540	−	0.493863i
$181$		−	5.92332i		−	0.440277i	−0.975469	−	0.220139i	$-0.929349\pi$
$181$		−	5.92332i		−	0.440277i	0.975469	−	0.220139i	$-0.0706510\pi$
$182$	27.0290	−	12.9436i	2.00352	−	0.959447i
$183$	4.57427	+	0.214744i	0.338140	+	0.0158743i
$184$	3.56506	−	6.63951i	0.262819	−	0.489471i
$185$	−6.76327	+	11.1643i	−0.497246	+	0.820814i
$186$	−1.57696	+	12.6625i	−0.115629	+	0.928459i
$187$	−0.0195892	−	0.0731078i	−0.00143250	−	0.00534617i
$188$	−3.36908	+	7.63070i	−0.245715	+	0.556526i
$189$	−2.99144	−	24.5885i	−0.217595	−	1.78855i
$190$	13.2379	−	10.8666i	0.960378	−	0.788347i
$191$	−2.05395	−	1.18585i	−0.148619	−	0.0858052i	0.423846	−	0.905734i	$-0.360680\pi$
$191$	−2.05395	−	1.18585i	−0.148619	−	0.0858052i	−0.572465	+	0.819929i	$0.694013\pi$
$192$	−13.8549	+	0.204441i	−0.999891	+	0.0147543i
$193$	−1.47811	+	5.51640i	−0.106397	+	0.397079i	−0.998500	−	0.0547533i	$-0.982563\pi$
$193$	−1.47811	+	5.51640i	−0.106397	+	0.397079i	0.892103	+	0.451832i	$0.149229\pi$
$194$	4.31755	+	5.03935i	0.309982	+	0.361804i
$195$	−7.57566	−	15.4605i	−0.542504	−	1.10715i
$196$	4.82313	−	31.0756i	0.344509	−	2.21969i
$197$	4.62328	+	4.62328i	0.329395	+	0.329395i	0.852356	−	0.522961i	$-0.175173\pi$
$197$	4.62328	+	4.62328i	0.329395	+	0.329395i	−0.522961	+	0.852356i	$0.675173\pi$
$198$	−1.72780	−	1.43887i	−0.122789	−	0.102256i
$199$	−18.4717			−1.30943			−0.654713	−	0.755877i	$-0.727211\pi$
$199$	−18.4717			−1.30943			−0.654713	+	0.755877i	$0.727211\pi$
$200$	−3.50554	−	13.7008i	−0.247879	−	0.968791i
$201$	−8.84599	+	1.93071i	−0.623948	+	0.136181i
$202$	26.6227	+	2.05371i	1.87317	+	0.144498i
$203$	8.83612	−	32.9768i	0.620174	−	2.31452i
$204$	0.272981	+	0.412587i	0.0191125	+	0.0288869i
$205$	−2.55395	+	2.44853i	−0.178376	+	0.171013i
$206$	7.27993	−	1.36094i	0.507217	−	0.0948210i
$207$	−6.15673	+	5.09769i	−0.427922	+	0.354314i
$208$	−0.820421	+	17.7625i	−0.0568860	+	1.23161i
$209$	−2.48575	−	1.43515i	−0.171943	−	0.0992714i
$210$	−25.8358	−	3.77191i	−1.78284	−	0.260287i
$211$	−7.54498	−	13.0683i	−0.519418	−	0.899658i	−0.999745	−	0.0225685i	$-0.992816\pi$
$211$	−7.54498	−	13.0683i	−0.519418	−	0.899658i	0.480328	−	0.877089i	$-0.340518\pi$
$212$	1.65786	+	15.3163i	0.113863	+	1.05193i
$213$	0.646536	+	1.25199i	0.0442999	+	0.0857848i
$214$	2.73527	−	7.76242i	0.186979	−	0.530628i
$215$	−7.55257	−	13.7422i	−0.515081	−	0.937211i
$216$	13.6933	+	5.33794i	0.931711	+	0.363201i
$217$	17.5595	−	17.5595i	1.19202	−	1.19202i
$218$	−13.5742	+	6.50043i	−0.919362	+	0.440265i
$219$	−18.0371	−	5.75215i	−1.21883	−	0.388694i
$220$	−1.94218	+	1.35843i	−0.130942	+	0.0915856i
$221$	0.549800	−	0.317427i	0.0369836	−	0.0213525i
$222$	−14.1632	+	1.96557i	−0.950571	+	0.131920i
$223$	3.00012	+	11.1966i	0.200903	+	0.749781i	0.990659	+	0.136360i	$0.0435404\pi$
$223$	3.00012	+	11.1966i	0.200903	+	0.749781i	−0.789756	+	0.613421i	$0.789793\pi$
$224$	21.5202	+	16.2494i	1.43788	+	1.08571i
$225$	−2.03320	+	14.8616i	−0.135547	+	0.990771i
$226$	3.16855	+	16.9492i	0.210769	+	1.12745i
$227$	4.44592	+	16.5924i	0.295086	+	1.10128i	0.941149	+	0.337993i	$0.109748\pi$
$227$	4.44592	+	16.5924i	0.295086	+	1.10128i	−0.646062	+	0.763285i	$0.723585\pi$
$228$	18.3841	+	3.74366i	1.21752	+	0.247930i
$229$	−8.13337	−	14.0874i	−0.537468	−	0.930922i	−0.999039	−	0.0438189i	$-0.986048\pi$
$229$	−8.13337	−	14.0874i	−0.537468	−	0.930922i	0.461572	−	0.887103i	$-0.347286\pi$
$230$	3.47819	+	7.67418i	0.229345	+	0.506020i
$231$	0.933079	+	4.27512i	0.0613921	+	0.281283i
$232$	14.7584	+	13.8753i	0.968939	+	0.910957i
$233$	−3.13438	−	3.13438i	−0.205340	−	0.205340i	0.596943	−	0.802284i	$-0.296382\pi$
$233$	−3.13438	−	3.13438i	−0.205340	−	0.205340i	−0.802284	+	0.596943i	$0.796382\pi$
$234$	7.90695	−	17.1226i	0.516893	−	1.11934i
$235$	−4.49176	−	8.17294i	−0.293010	−	0.533144i
$236$	1.26440	−	8.14658i	0.0823053	−	0.530297i
$237$	−0.403180	+	8.58817i	−0.0261894	+	0.557862i
$238$	0.0740494	−	0.959920i	0.00479991	−	0.0622224i
$239$	10.1521	+	17.5839i	0.656683	+	1.13741i	0.981469	+	0.191620i	$0.0613742\pi$
$239$	10.1521	+	17.5839i	0.656683	+	1.13741i	−0.324786	+	0.945787i	$0.605292\pi$
$240$	9.22357	−	12.4469i	0.595379	−	0.803445i
$241$	−5.21124	+	9.02614i	−0.335686	+	0.581425i	−0.983616	−	0.180275i	$-0.942301\pi$
$241$	−5.21124	+	9.02614i	−0.335686	+	0.581425i	0.647931	+	0.761699i	$0.275635\pi$
$242$	−12.5063	−	8.56684i	−0.803938	−	0.550698i
$243$	−11.3189	−	10.7184i	−0.726105	−	0.687584i
$244$	4.93062	−	1.91026i	0.315651	−	0.122292i
$245$	24.3323	+	25.3799i	1.55453	+	1.62146i
$246$	−3.84605	−	0.478980i	−0.245215	−	0.0305387i
$247$	6.23129	−	23.2555i	0.396487	−	1.47971i
$248$	4.25047	+	14.1080i	0.269905	+	0.895856i
$249$	−14.5737	+	13.2667i	−0.923569	+	0.840742i
$250$	14.5509	+	6.18638i	0.920280	+	0.391261i
$251$	26.2633			1.65773			0.828863	−	0.559451i	$-0.188988\pi$
$251$	26.2633			1.65773			0.828863	+	0.559451i	$0.188988\pi$
$252$	−14.6462	−	24.5672i	−0.922624	−	1.54759i
$253$	0.998478	−	0.998478i	0.0627738	−	0.0627738i
$254$	−16.6513	−	5.86748i	−1.04479	−	0.368158i
$255$	−0.551834	−	0.0375731i	−0.0345572	−	0.00235292i
$256$	−14.5349	+	6.68865i	−0.908428	+	0.418041i
$257$	−7.82875	−	2.09771i	−0.488344	−	0.130851i	0.00624113	−	0.999981i	$-0.498013\pi$
$257$	−7.82875	−	2.09771i	−0.488344	−	0.130851i	−0.494585	+	0.869129i	$0.664680\pi$
$258$	6.46232	−	15.9156i	0.402326	−	0.990862i
$259$	24.0990	+	13.9136i	1.49744	+	0.864548i
$260$	−15.2226	−	12.7866i	−0.944063	−	0.792993i
$261$	−8.95230	−	19.5316i	−0.554133	−	1.20898i
$262$	−11.2419	−	7.70071i	−0.694528	−	0.475751i
$263$	−2.33166	−	8.70186i	−0.143776	−	0.536580i	−0.999807	−	0.0196547i	$-0.993743\pi$
$263$	−2.33166	−	8.70186i	−0.143776	−	0.536580i	0.856031	−	0.516925i	$-0.172923\pi$
$264$	−2.49672	−	0.712210i	−0.153663	−	0.0438335i
$265$	−14.7318	−	8.92447i	−0.904969	−	0.548226i
$266$	−23.7554	−	27.7268i	−1.45654	−	1.70004i
$267$	3.01181	+	5.83224i	0.184320	+	0.356927i
$268$	−8.43911	+	6.17146i	−0.515501	+	0.376982i
$269$	9.73938			0.593820			0.296910	−	0.954905i	$-0.404044\pi$
$269$	9.73938			0.593820			0.296910	+	0.954905i	$0.404044\pi$
$270$	−14.0375	+	8.54100i	−0.854295	+	0.519789i
$271$		−	5.13221i		−	0.311759i	−0.987776	−	0.155880i	$-0.950179\pi$
$271$		−	5.13221i		−	0.311759i	0.987776	−	0.155880i	$-0.0498212\pi$
$272$	0.481013	+	0.308148i	0.0291657	+	0.0186842i
$273$	−32.6119	+	16.8410i	−1.97376	+	1.01926i
$274$	21.4391	+	25.0233i	1.29519	+	1.51171i
$275$	0.111638	−	2.64750i	0.00673204	−	0.159650i
$276$	−4.11977	+	8.25933i	−0.247981	+	0.497153i
$277$	−8.32621	+	2.23100i	−0.500273	+	0.134048i	−0.500127	−	0.865952i	$-0.666713\pi$
$277$	−8.32621	+	2.23100i	−0.500273	+	0.134048i	−0.000146399		1.00000i	$0.500047\pi$
$278$	11.9754	−	17.4823i	0.718234	−	1.04852i
$279$	1.46413	−	15.5594i	0.0876550	−	0.931516i
$280$	−29.0440	+	8.08701i	−1.73571	+	0.483291i
$281$	6.17843	−	10.7014i	0.368575	−	0.638390i	−0.620768	−	0.783994i	$-0.713179\pi$
$281$	6.17843	−	10.7014i	0.368575	−	0.638390i	0.989343	+	0.145604i	$0.0465126\pi$
$282$	3.84335	−	9.46552i	0.228868	−	0.563663i
$283$	4.60650	−	17.1917i	0.273828	−	1.02194i	−0.682794	−	0.730611i	$-0.739236\pi$
$283$	4.60650	−	17.1917i	0.273828	−	1.02194i	0.956623	−	0.291330i	$-0.0940978\pi$
$284$	1.26763	+	1.02001i	0.0752200	+	0.0605266i
$285$	−15.8055	+	13.7904i	−0.936236	+	0.816871i
$286$	−1.10729	+	3.14238i	−0.0654756	+	0.185813i
$287$	5.33344	+	5.33344i	0.314823	+	0.314823i
$288$	16.9535	−	0.760570i	0.998995	−	0.0448170i
$289$			16.9796i			0.998800i
$290$	−22.3448	+	3.69177i	−1.31213	+	0.216788i
$291$	−5.47111	−	6.01011i	−0.320722	−	0.352319i
$292$	−21.7339	+	2.35252i	−1.27188	+	0.137671i
$293$	−16.1058	−	4.31554i	−0.940911	−	0.252116i	−0.244410	−	0.969672i	$-0.578594\pi$
$293$	−16.1058	−	4.31554i	−0.940911	−	0.252116i	−0.696501	+	0.717556i	$0.745261\pi$
$294$	−4.75987	+	38.2202i	−0.277601	+	2.22905i
$295$	6.37878	+	6.65342i	0.371387	+	0.387377i
$296$	−14.0376	+	8.69238i	−0.815921	+	0.505234i
$297$	2.16815	+	1.69782i	0.125809	+	0.0985175i
$298$	−8.18548	−	5.60705i	−0.474172	−	0.324808i
$299$	10.2574	+	5.92213i	0.593203	+	0.342486i
$300$	4.79606	+	16.6433i	0.276901	+	0.960898i
$301$	−28.9506	+	16.7146i	−1.66868	+	0.963414i
$302$	1.76315	+	0.136011i	0.101458	+	0.00782657i
$303$	−32.6669	−	1.53358i	−1.87666	−	0.0881018i
$304$	21.1620	−	4.63554i	1.21373	−	0.265867i
$305$	−1.65008	+	5.67692i	−0.0944833	+	0.325059i
$306$	−0.349377	−	0.495031i	−0.0199725	−	0.0282990i
$307$	3.63737	−	3.63737i	0.207596	−	0.207596i	−0.595649	−	0.803245i	$-0.703105\pi$
$307$	3.63737	−	3.63737i	0.207596	−	0.207596i	0.803245	+	0.595649i	$0.203105\pi$
$308$	2.98257	+	4.07849i	0.169948	+	0.232393i
$309$	−8.86190	+	1.93418i	−0.504136	+	0.110032i
$310$	−15.4183	−	5.80102i	−0.875701	−	0.329476i
$311$	26.0518	−	15.0410i	1.47726	−	0.852899i	0.477595	−	0.878580i	$-0.341509\pi$
$311$	26.0518	−	15.0410i	1.47726	−	0.852899i	0.999670	+	0.0256812i	$0.00817547\pi$
$312$	0.350135	−	21.7749i	0.0198225	−	1.23276i
$313$	9.16363	−	2.45539i	0.517959	−	0.138787i	0.00963652	−	0.999954i	$-0.496933\pi$
$313$	9.16363	−	2.45539i	0.517959	−	0.138787i	0.508322	+	0.861167i	$0.330266\pi$
$314$	0.153727	+	0.822319i	0.00867534	+	0.0464061i
$315$	31.7669	+	3.66598i	1.78986	+	0.206554i
$316$	3.58650	+	9.25722i	0.201756	+	0.520759i
$317$	8.45452	−	2.26538i	0.474853	−	0.127237i	−0.0134519	−	0.999910i	$-0.504282\pi$
$317$	8.45452	−	2.26538i	0.474853	−	0.127237i	0.488305	+	0.872673i	$0.337615\pi$
$318$	−2.59366	−	18.6890i	−0.145445	−	1.04803i
$319$	1.89778	+	3.28706i	0.106255	+	0.184040i
$320$	3.92483	−	17.4527i	0.219405	−	0.975634i
$321$	−3.06260	+	9.60342i	−0.170937	+	0.536011i
$322$	16.2003	−	7.75802i	0.902808	−	0.432338i
$323$	−0.546924	−	0.546924i	−0.0304317	−	0.0304317i
$324$	−16.9598	−	6.03031i	−0.942212	−	0.335017i
$325$	21.6927	−	4.84310i	1.20330	−	0.268647i
$326$	−33.0517	−	11.6466i	−1.83056	−	0.645043i
$327$	16.3780	−	8.45773i	0.905706	−	0.467713i
$328$	−4.28509	+	1.29102i	−0.236604	+	0.0712847i
$329$	−17.2178	+	9.94072i	−0.949249	+	0.548049i
$330$	2.32756	−	1.73452i	0.128128	−	0.0954820i
$331$	−2.56793	+	4.44778i	−0.141146	+	0.244472i	−0.927928	−	0.372758i	$-0.878412\pi$
$331$	−2.56793	+	4.44778i	−0.141146	+	0.244472i	0.786782	+	0.617230i	$0.211745\pi$
$332$	−9.19140	+	20.8178i	−0.504444	+	1.14252i
$333$	17.2661	−	2.92788i	0.946174	−	0.160447i
$334$	−1.89196	−	10.1205i	−0.103524	−	0.553768i
$335$	0.246282	−	11.6864i	0.0134558	−	0.638494i
$336$	−26.9433	−	19.0998i	−1.46988	−	1.04198i
$337$	22.3878	+	5.99879i	1.21954	+	0.326775i	0.810499	−	0.585740i	$-0.199196\pi$
$337$	22.3878	+	5.99879i	1.21954	+	0.326775i	0.409042	+	0.912515i	$0.365863\pi$
$338$	−9.53349	−	0.735425i	−0.518553	−	0.0400018i
$339$	−4.50318	−	20.6324i	−0.244579	−	1.12060i
$340$	−0.600274	+	0.218131i	−0.0325544	+	0.0118298i
$341$			2.76082i			0.149507i
$342$	−22.6435	−	3.90584i	−1.22442	−	0.211204i
$343$	29.4059	−	29.4059i	1.58777	−	1.58777i
$344$	−0.611476	−	19.8255i	−0.0329686	−	1.06892i
$345$	−4.54062	−	9.26656i	−0.244459	−	0.498895i
$346$	1.72665	+	2.01531i	0.0928252	+	0.108344i
$347$	7.06396	+	1.89278i	0.379213	+	0.101610i	0.443390	−	0.896329i	$-0.353776\pi$
$347$	7.06396	+	1.89278i	0.379213	+	0.101610i	−0.0641769	+	0.997939i	$0.520442\pi$
$348$	−18.5782	−	16.4424i	−0.995895	−	0.881407i
$349$	13.9106	−	24.0939i	0.744618	−	1.28972i	−0.205755	−	0.978604i	$-0.565965\pi$
$349$	13.9106	−	24.0939i	0.744618	−	1.28972i	0.950373	−	0.311113i	$-0.100702\pi$
$350$	12.5319	−	31.2913i	0.669859	−	1.67259i
$351$	−9.04896	+	21.2525i	−0.482998	+	1.13438i
$352$	−2.96920	+	0.414353i	−0.158259	+	0.0220851i
$353$	−1.69546	+	0.454296i	−0.0902400	+	0.0241797i	−0.303657	−	0.952782i	$-0.598208\pi$
$353$	−1.69546	+	0.454296i	−0.0902400	+	0.0241797i	0.213416	+	0.976961i	$0.431541\pi$
$354$	−1.24781	+	10.0195i	−0.0663206	+	0.532532i
$355$	−1.76665	+	0.433692i	−0.0937640	+	0.0230180i
$356$	5.90511	+	4.75161i	0.312970	+	0.251835i
$357$	−0.0552954	+	1.17785i	−0.00292654	+	0.0623386i
$358$	8.48676	+	17.7221i	0.448539	+	0.936640i
$359$	0.264432			0.0139562			0.00697810	−	0.999976i	$-0.497779\pi$
$359$	0.264432			0.0139562			0.00697810	+	0.999976i	$0.497779\pi$
$360$	−10.8330	+	15.5771i	−0.570948	+	0.820986i
$361$	−10.3325			−0.543818
$362$	3.61805	+	7.55521i	0.190160	+	0.397093i
$363$	15.6257	+	10.0268i	0.820136	+	0.526272i
$364$	−26.5693	+	33.0193i	−1.39261	+	1.73068i
$365$	12.6639	−	20.9045i	0.662857	−	1.09419i
$366$	−5.96567	+	2.52012i	−0.311830	+	0.131729i
$367$	30.9260	−	8.28660i	1.61432	−	0.432557i	0.664997	−	0.746846i	$-0.268433\pi$
$367$	30.9260	−	8.28660i	1.61432	−	0.432557i	0.949327	+	0.314289i	$0.101766\pi$
$368$	−0.491735	+	10.6463i	−0.0256335	+	0.554976i
$369$	4.72594	+	0.444708i	0.246023	+	0.0231506i
$370$	1.80727	−	18.3712i	0.0939556	−	0.955071i
$371$	−18.3597	+	31.7999i	−0.953187	+	1.65097i
$372$	−5.72300	−	17.1143i	−0.296724	−	0.887334i
$373$	16.6512	+	4.46167i	0.862166	+	0.231017i	0.662697	−	0.748888i	$-0.269412\pi$
$373$	16.6512	+	4.46167i	0.862166	+	0.231017i	0.199469	+	0.979904i	$0.436078\pi$
$374$	0.0696413	+	0.0812838i	0.00360107	+	0.00420309i
$375$	−18.0409	−	7.03739i	−0.931630	−	0.363409i
$376$	−0.363664	−	11.7909i	−0.0187546	−	0.608067i
$377$	−22.5121	+	22.5121i	−1.15943	+	1.15943i
$378$	18.8346	+	29.5355i	0.968747	+	1.51914i
$379$		−	3.40417i		−	0.174860i	−0.996171	−	0.0874302i	$-0.972135\pi$
$379$		−	3.40417i		−	0.174860i	0.996171	−	0.0874302i	$-0.0278655\pi$
$380$	−10.2475	+	21.9463i	−0.525686	+	1.12582i
$381$	20.6005	+	6.56962i	1.05539	+	0.336572i
$382$	3.34416	+	0.257972i	0.171102	+	0.0131990i
$383$	19.6320	+	5.26038i	1.00315	+	0.268793i	0.722764	−	0.691095i	$-0.242872\pi$
$383$	19.6320	+	5.26038i	1.00315	+	0.268793i	0.280384	+	0.959888i	$0.409538\pi$
$384$	17.5471	−	8.72353i	0.895446	−	0.445171i
$385$	−5.64783	−	0.119024i	−0.287840	−	0.00606604i
$386$	−1.48415	−	7.93903i	−0.0755414	−	0.404086i
$387$	−7.32492	+	19.7217i	−0.372346	+	1.00251i
$388$	−8.58515	−	3.79049i	−0.435845	−	0.192433i
$389$	−1.52927	+	2.64877i	−0.0775368	+	0.134298i	−0.902187	−	0.431346i	$-0.858039\pi$
$389$	−1.52927	+	2.64877i	−0.0775368	+	0.134298i	0.824650	+	0.565644i	$0.191372\pi$
$390$	19.1063	+	15.0926i	0.967484	+	0.764244i
$391$	0.329533	−	0.190256i	0.0166652	−	0.00962167i
$392$	12.8295	+	42.5831i	0.647989	+	2.15077i
$393$	14.0459	+	9.01308i	0.708521	+	0.454650i
$394$	−8.72097	−	3.07304i	−0.439356	−	0.154818i
$395$	−10.6584	−	3.09802i	−0.536281	−	0.155878i
$396$	3.08270	+	0.779924i	0.154911	+	0.0391926i
$397$	−26.4772	−	26.4772i	−1.32885	−	1.32885i	−0.906373	−	0.422478i	$-0.861160\pi$
$397$	−26.4772	−	26.4772i	−1.32885	−	1.32885i	−0.422478	−	0.906373i	$-0.638840\pi$
$398$	23.5607	−	11.2828i	1.18099	−	0.565555i
$399$	30.1024	+	33.0680i	1.50700	+	1.65547i
$400$	12.8399	+	15.3341i	0.641997	+	0.766707i
$401$	12.6429	+	21.8981i	0.631354	+	1.09354i	0.987275	+	0.159022i	$0.0508339\pi$
$401$	12.6429	+	21.8981i	0.631354	+	1.09354i	−0.355921	+	0.934516i	$0.615833\pi$
$402$	10.1038	−	7.86587i	0.503931	−	0.392314i
$403$	−22.3685	+	5.99361i	−1.11425	+	0.298563i
$404$	−35.2117	+	13.6420i	−1.75185	+	0.678715i
$405$	16.8700	−	10.9728i	0.838277	−	0.545245i
$406$	8.87222	+	47.4593i	0.440321	+	2.35536i
$407$	−2.98830	+	0.800713i	−0.148125	+	0.0396899i
$408$	−0.600201	−	0.359515i	−0.0297144	−	0.0177986i
$409$	−2.29952	+	1.32763i	−0.113704	+	0.0656470i	−0.555773	−	0.831334i	$-0.687578\pi$
$409$	−2.29952	+	1.32763i	−0.113704	+	0.0656470i	0.442069	+	0.896981i	$0.354244\pi$
$410$	1.76198	−	4.68309i	0.0870178	−	0.231281i
$411$	−27.1672	−	29.8437i	−1.34006	−	1.47208i
$412$	−8.45429	+	6.18256i	−0.416513	+	0.304593i
$413$	13.8944	−	13.8944i	0.683699	−	0.683699i
$414$	4.73918	−	10.2627i	0.232918	−	0.504386i
$415$	−12.2542	−	22.2971i	−0.601537	−	1.09452i
$416$	−9.80313	−	23.1572i	−0.480638	−	1.13538i
$417$	−14.0162	+	21.8427i	−0.686377	+	1.06964i
$418$	4.04719	+	0.312205i	0.197955	+	0.0152705i
$419$	−7.69654	+	4.44360i	−0.376000	+	0.217084i	−0.676077	−	0.736831i	$-0.736321\pi$
$419$	−7.69654	+	4.44360i	−0.376000	+	0.217084i	0.300076	+	0.953915i	$0.402988\pi$
$420$	35.2576	−	10.9698i	1.72039	−	0.535270i
$421$	−5.48153	−	3.16476i	−0.267153	−	0.154241i	0.360440	−	0.932782i	$-0.382627\pi$
$421$	−5.48153	−	3.16476i	−0.267153	−	0.154241i	−0.627593	+	0.778541i	$0.715960\pi$
$422$	17.6059	+	12.0600i	0.857043	+	0.587074i
$423$	−4.35636	+	11.7292i	−0.211814	+	0.570291i
$424$	−11.4700	−	18.5234i	−0.557034	−	0.899574i
$425$	0.213708	−	0.681335i	0.0103664	−	0.0330496i
$426$	−1.58939	−	1.20200i	−0.0770062	−	0.0582371i
$427$	12.1737	+	3.26195i	0.589129	+	0.157857i
$428$	1.25254	+	11.5717i	0.0605439	+	0.559340i
$429$	1.23980	−	3.88766i	0.0598581	−	0.187698i
$430$	18.0273	+	12.9150i	0.869351	+	0.622817i
$431$			34.6621i			1.66962i	0.550541	+	0.834808i	$0.314421\pi$
$431$			34.6621i			1.66962i	−0.550541	+	0.834808i	$0.685579\pi$
$432$	−20.7263	+	1.55550i	−0.997196	+	0.0748392i
$433$	16.8070	+	16.8070i	0.807695	+	0.807695i	0.984285	−	0.176590i	$-0.0565065\pi$
$433$	16.8070	+	16.8070i	0.807695	+	0.807695i	−0.176590	+	0.984285i	$0.556507\pi$
$434$	−11.6716	+	33.1227i	−0.560254	+	1.58994i
$435$	27.2183	−	5.34243i	1.30502	−	0.256150i
$436$	13.3434	−	16.5826i	0.639033	−	0.794164i
$437$	3.73484	−	13.9386i	0.178662	−	0.666775i
$438$	26.5198	−	3.68042i	1.26717	−	0.175857i
$439$	−14.3538	+	24.8616i	−0.685071	+	1.18658i	0.288343	+	0.957527i	$0.406896\pi$
$439$	−14.3538	+	24.8616i	−0.685071	+	1.18658i	−0.973414	+	0.229051i	$0.926438\pi$
$440$	1.64750	−	2.91899i	0.0785415	−	0.139158i
$441$	4.41929	−	46.9641i	0.210442	−	2.23639i
$442$	−0.507383	+	0.740705i	−0.0241337	+	0.0352317i
$443$	−17.9570	+	4.81157i	−0.853164	+	0.228605i	−0.658794	−	0.752324i	$-0.728933\pi$
$443$	−17.9570	+	4.81157i	−0.853164	+	0.228605i	−0.194370	+	0.980928i	$0.562266\pi$
$444$	16.8646	−	11.1582i	0.800358	−	0.529543i
$445$	−8.22973	+	2.02031i	−0.390127	+	0.0957717i
$446$	−10.6657	−	12.4488i	−0.505036	−	0.589467i
$447$	10.2271	+	6.56261i	0.483725	+	0.310401i
$448$	−37.3745	−	7.58136i	−1.76578	−	0.358185i
$449$		−	29.4385i		−	1.38929i	−0.719354	−	0.694644i	$-0.755562\pi$
$449$		−	29.4385i		−	1.38929i	0.719354	−	0.694644i	$-0.244438\pi$
$450$	−6.48429	−	20.1979i	−0.305672	−	0.952137i
$451$	−0.838560			−0.0394862
$452$	−14.3943	−	19.6834i	−0.677051	−	0.925828i
$453$	−2.16344	−	0.101565i	−0.101647	−	0.00477192i
$454$	−15.8057	−	18.4480i	−0.741796	−	0.865809i
$455$	−11.2968	−	46.0178i	−0.529604	−	2.15735i
$456$	−25.7357	+	6.45422i	−1.20518	+	0.302246i
$457$	−3.23423	−	12.0703i	−0.151291	−	0.564626i	−0.999394	−	0.0347952i	$-0.988922\pi$
$457$	−3.23423	−	12.0703i	−0.151291	−	0.564626i	0.848103	−	0.529831i	$-0.177745\pi$
$458$	18.9789	+	13.0005i	0.886826	+	0.607476i
$459$	0.445936	+	0.593144i	0.0208145	+	0.0276856i
$460$	−9.12393	−	7.66391i	−0.425406	−	0.357332i
$461$	12.7574	+	7.36547i	0.594170	+	0.343044i	0.766745	−	0.641952i	$-0.221875\pi$
$461$	12.7574	+	7.36547i	0.594170	+	0.343044i	−0.172575	+	0.984996i	$0.555209\pi$
$462$	−3.80145	−	4.88299i	−0.176859	−	0.227177i
$463$	−5.07743	−	1.36049i	−0.235968	−	0.0632275i	0.138897	−	0.990307i	$-0.455644\pi$
$463$	−5.07743	−	1.36049i	−0.235968	−	0.0632275i	−0.374865	+	0.927079i	$0.622311\pi$
$464$	−27.2996	−	8.68331i	−1.26735	−	0.403112i
$465$	19.0886	+	6.53368i	0.885213	+	0.302992i
$466$	5.91244	+	2.08339i	0.273888	+	0.0965112i
$467$	16.1054	−	16.1054i	0.745270	−	0.745270i	−0.228317	−	0.973587i	$-0.573322\pi$
$467$	16.1054	−	16.1054i	0.745270	−	0.745270i	0.973587	+	0.228317i	$0.0733223\pi$
$468$	0.373368	+	26.6695i	0.0172590	+	1.23280i
$469$	−24.9191			−1.15066
$470$	10.7214	+	7.68098i	0.494541	+	0.354297i
$471$	−0.218479	−	1.00101i	−0.0100670	−	0.0461243i
$472$	3.36330	+	11.1633i	0.154808	+	0.513832i
$473$	0.961909	−	3.58989i	0.0442286	−	0.165063i
$474$	−4.73152	−	11.2005i	−0.217326	−	0.514456i
$475$	−12.5398	−	24.0014i	−0.575367	−	1.10126i
$476$	0.491882	+	1.26961i	0.0225454	+	0.0581925i
$477$	3.86348	+	22.7834i	0.176897	+	1.04318i
$478$	−23.6895	−	16.2273i	−1.08353	−	0.742219i
$479$	−4.01907	+	6.96123i	−0.183636	+	0.318067i	−0.943116	−	0.332464i	$-0.892120\pi$
$479$	−4.01907	+	6.96123i	−0.183636	+	0.318067i	0.759480	+	0.650531i	$0.225453\pi$
$480$	−4.16194	+	21.5100i	−0.189966	+	0.981791i
$481$	−12.9749	−	22.4732i	−0.591606	−	1.02469i
$482$	1.13366	−	14.6960i	0.0516370	−	0.669383i
$483$	−19.5465	+	10.0940i	−0.889398	+	0.459292i
$484$	21.1846	+	3.28798i	0.962937	+	0.149454i
$485$	9.19521	−	5.05359i	0.417533	−	0.229472i
$486$	20.9842	+	6.75760i	0.951861	+	0.306531i
$487$	4.69703	+	4.69703i	0.212843	+	0.212843i	0.805474	−	0.592631i	$-0.201911\pi$
$487$	4.69703	+	4.69703i	0.212843	+	0.212843i	−0.592631	+	0.805474i	$0.701911\pi$
$488$	−5.12221	+	5.44823i	−0.231871	+	0.246630i
$489$	40.8906	+	13.0403i	1.84914	+	0.589702i
$490$	−46.5382	−	17.5097i	−2.10238	−	0.791006i
$491$	−1.43069	−	2.47803i	−0.0645663	−	0.111832i	0.831935	−	0.554873i	$-0.187233\pi$
$491$	−1.43069	−	2.47803i	−0.0645663	−	0.111832i	−0.896502	+	0.443041i	$0.853900\pi$
$492$	5.19822	−	1.73828i	0.234354	−	0.0783678i
$493$	0.264721	+	0.987951i	0.0119224	+	0.0444951i
$494$	6.25675	+	33.4686i	0.281504	+	1.50582i
$495$	−2.78550	+	2.20911i	−0.125199	+	0.0992919i
$496$	−14.0388	−	15.3985i	−0.630362	−	0.691412i
$497$	1.00371	+	3.74591i	0.0450227	+	0.168027i
$498$	10.4853	−	25.8235i	0.469857	−	1.15718i
$499$	0.233169	−	0.134620i	0.0104381	−	0.00602643i	−0.494772	−	0.869023i	$-0.664748\pi$
$499$	0.233169	−	0.134620i	0.0104381	−	0.00602643i	0.505210	+	0.862996i	$0.331415\pi$
$500$	−22.3384	+	0.997141i	−0.999005	+	0.0445935i
$501$	2.68887	+	12.3197i	0.120130	+	0.550404i
$502$	−33.4989	+	16.0420i	−1.49513	+	0.715990i
$503$	−26.1571	+	26.1571i	−1.16629	+	1.16629i	−0.183216	+	0.983073i	$0.558651\pi$
$503$	−26.1571	+	26.1571i	−1.16629	+	1.16629i	−0.983073	+	0.183216i	$0.941349\pi$
$504$	33.6873	+	22.3894i	1.50055	+	0.997304i
$505$	11.7840	−	40.5414i	0.524379	−	1.80407i
$506$	−0.663677	+	1.88345i	−0.0295040	+	0.0837294i
$507$	11.6979	+	0.549169i	0.519522	+	0.0243894i
$508$	24.8227	−	2.68685i	1.10133	−	0.119210i
$509$	−2.74477	−	4.75409i	−0.121660	−	0.210721i	0.798762	−	0.601647i	$-0.205488\pi$
$509$	−2.74477	−	4.75409i	−0.121660	−	0.210721i	−0.920422	+	0.390925i	$0.872155\pi$
$510$	0.726816	−	0.289143i	0.0321840	−	0.0128035i
$511$	−45.1242	−	26.0525i	−1.99618	−	1.15249i
$512$	14.4537	−	17.4095i	0.638770	−	0.769398i
$513$	27.8639	+	3.94751i	1.23022	+	0.174287i
$514$	11.2669	−	2.10628i	0.496962	−	0.0929039i
$515$	0.246725	−	11.7074i	0.0108720	−	0.515889i
$516$	1.47876	+	24.2477i	0.0650989	+	1.06744i
$517$	0.572078	−	2.13502i	0.0251600	−	0.0938983i
$518$	−39.2370	−	3.02679i	−1.72397	−	0.132990i
$519$	−2.18797	−	2.40353i	−0.0960414	−	0.105503i
$520$	27.2267	+	7.01123i	1.19397	+	0.307463i
$521$	35.2890			1.54604			0.773019	−	0.634383i	$-0.218746\pi$
$521$	35.2890			1.54604			0.773019	+	0.634383i	$0.218746\pi$
$522$	23.3488	+	19.4444i	1.02195	+	0.851059i
$523$	15.5217	+	15.5217i	0.678714	+	0.678714i	0.959709	−	0.280995i	$-0.0906644\pi$
$523$	15.5217	+	15.5217i	0.678714	+	0.678714i	−0.280995	+	0.959709i	$0.590664\pi$
$524$	19.0428	+	2.95556i	0.831888	+	0.129114i
$525$	−14.1889	+	38.7681i	−0.619257	+	1.69198i
$526$	8.28925	+	9.67503i	0.361428	+	0.421851i
$527$	−0.192553	+	0.718616i	−0.00838772	+	0.0313034i
$528$	3.61960	−	0.616607i	0.157523	−	0.0268344i
$529$	−13.7706	−	7.95046i	−0.598722	−	0.345672i
$530$	24.2417	+	2.38479i	1.05299	+	0.103588i
$531$	1.15853	−	12.3118i	0.0502759	−	0.534286i
$532$	47.2360	+	20.8555i	2.04794	+	0.904200i
$533$	−1.82048	−	6.79411i	−0.0788535	−	0.294285i
$534$	−7.40399	−	5.59938i	−0.320402	−	0.242309i
$535$	−11.1301	−	6.74258i	−0.481197	−	0.291507i
$536$	6.99449	−	13.0264i	0.302116	−	0.562656i
$537$	−11.0421	−	21.3826i	−0.476504	−	0.922728i
$538$	−12.4226	+	5.94894i	−0.535576	+	0.256477i
$539$			8.33319i			0.358936i
$540$	12.6879	−	19.4684i	0.546000	−	0.837785i
$541$			10.2366i			0.440104i	0.975488	+	0.220052i	$0.0706228\pi$
$541$			10.2366i			0.440104i	−0.975488	+	0.220052i	$0.929377\pi$
$542$	3.13482	+	6.54614i	0.134652	+	0.281181i
$543$	−4.70745	−	9.11577i	−0.202016	−	0.391195i
$544$	−0.801754	−	0.0992336i	−0.0343749	−	0.00425461i
$545$	5.67339	+	23.1106i	0.243021	+	0.989950i
$546$	31.3098	−	41.4005i	1.33994	−	1.77178i
$547$	−2.27468	−	8.48922i	−0.0972583	−	0.362973i	0.900094	−	0.435696i	$-0.143498\pi$
$547$	−2.27468	−	8.48922i	−0.0972583	−	0.362973i	−0.997352	+	0.0727231i	$0.976831\pi$
$548$	−42.6302	−	18.8220i	−1.82107	−	0.804035i
$549$	7.21029	−	3.30484i	0.307728	−	0.141047i
$550$	1.47474	+	3.44509i	0.0628830	+	0.146899i
$551$	33.5915	+	19.3941i	1.43105	+	0.826215i
$552$	0.209860	−	13.0512i	0.00893223	−	0.555496i
$553$	−6.12429	+	22.8561i	−0.260431	+	0.971942i
$554$	9.25737	−	7.93141i	0.393308	−	0.336973i
$555$	−1.53581	+	22.5564i	−0.0651915	+	0.957465i
$556$	−4.59618	+	29.6134i	−0.194921	+	1.25589i
$557$	−23.7528	−	23.7528i	−1.00644	−	1.00644i	−0.999979	−	0.00646096i	$-0.997943\pi$
$557$	−23.7528	−	23.7528i	−1.00644	−	1.00644i	−0.00646096	−	0.999979i	$-0.502057\pi$
$558$	7.63639	+	20.7404i	0.323274	+	0.878009i
$559$	31.1740			1.31852
$560$	32.1061	−	28.0555i	1.35673	−	1.18556i
$561$	−0.0882480	−	0.0969419i	−0.00372583	−	0.00409289i
$562$	−1.34407	+	17.4235i	−0.0566961	+	0.734965i
$563$	0.281302	−	1.04983i	0.0118555	−	0.0442452i	−0.959745	−	0.280874i	$-0.909376\pi$
$563$	0.281302	−	1.04983i	0.0118555	−	0.0442452i	0.971600	+	0.236629i	$0.0760424\pi$
$564$	0.879468	+	14.4209i	0.0370323	+	0.607228i
$565$	27.2573	+	0.574429i	1.14672	+	0.0241664i
$566$	4.62532	+	24.7418i	0.194417	+	1.03997i
$567$	−24.1450	−	35.4634i	−1.01399	−	1.48932i
$568$	−2.23990	−	0.526742i	−0.0939842	−	0.0221016i
$569$	23.3653	+	13.4900i	0.979526	+	0.565529i	0.902127	−	0.431471i	$-0.142005\pi$
$569$	23.3653	+	13.4900i	0.979526	+	0.565529i	0.0773988	+	0.997000i	$0.475339\pi$
$570$	11.7366	−	27.2439i	0.491592	−	1.14112i
$571$	12.3255	+	21.3484i	0.515805	+	0.893401i	0.999832	+	0.0183477i	$0.00584058\pi$
$571$	12.3255	+	21.3484i	0.515805	+	0.893401i	−0.484026	+	0.875053i	$0.660826\pi$
$572$	−0.507054	−	4.68446i	−0.0212010	−	0.195867i
$573$	−4.10339	−	0.192638i	−0.171422	−	0.00804755i
$574$	−10.0606	−	3.54508i	−0.419920	−	0.147969i
$575$	13.0020	−	2.90281i	0.542219	−	0.121055i
$576$	−21.1597	+	11.3255i	−0.881653	+	0.471898i
$577$	−27.8028	+	27.8028i	−1.15744	+	1.15744i	−0.172421	+	0.985023i	$0.555159\pi$
$577$	−27.8028	+	27.8028i	−1.15744	+	1.15744i	−0.985023	+	0.172421i	$0.944841\pi$
$578$	−10.3714	−	21.6575i	−0.431392	−	0.900834i
$579$	2.10929	+	9.66423i	0.0876592	+	0.401632i
$580$	26.2458	−	18.3574i	1.08980	−	0.762248i
$581$	−46.9730	+	27.1199i	−1.94877	+	1.12512i
$582$	10.6495	+	4.32408i	0.441435	+	0.179239i
$583$	−1.05658	−	3.94321i	−0.0437591	−	0.163311i
$584$	26.2847	−	16.2760i	1.08767	−	0.673507i
$585$	−23.9456	−	17.7725i	−0.990029	−	0.734804i
$586$	23.1790	−	4.33317i	0.957515	−	0.179001i
$587$	−3.64940	−	13.6197i	−0.150627	−	0.562147i	−0.999440	−	0.0334544i	$-0.989349\pi$
$587$	−3.64940	−	13.6197i	−0.150627	−	0.562147i	0.848813	−	0.528692i	$-0.177318\pi$
$588$	−17.2742	−	51.6573i	−0.712375	−	2.13031i
$589$	14.1069	+	24.4338i	0.581263	+	1.00678i
$590$	−12.2001	−	4.59021i	−0.502272	−	0.188976i
$591$	10.7893	+	3.44078i	0.443813	+	0.141535i
$592$	12.5956	−	19.6615i	0.517677	−	0.808084i
$593$	−8.56767	−	8.56767i	−0.351832	−	0.351832i	0.508959	−	0.860791i	$-0.330031\pi$
$593$	−8.56767	−	8.56767i	−0.351832	−	0.351832i	−0.860791	+	0.508959i	$0.830031\pi$
$594$	−3.80254	−	0.841235i	−0.156020	−	0.0345163i
$595$	−1.46178	−	0.424888i	−0.0599271	−	0.0174187i
$596$	13.8655	+	2.15200i	0.567951	+	0.0881495i
$597$	−28.4273	+	14.6801i	−1.16345	+	0.600815i
$598$	−16.7007	−	1.28831i	−0.682942	−	0.0526830i
$599$	0.336125	+	0.582186i	0.0137337	+	0.0237875i	0.872811	−	0.488059i	$-0.162295\pi$
$599$	0.336125	+	0.582186i	0.0137337	+	0.0237875i	−0.859077	+	0.511847i	$0.828962\pi$
$600$	−16.2833	−	18.2990i	−0.664764	−	0.747054i
$601$	−10.7603	+	18.6375i	−0.438924	+	0.760238i	−0.997607	−	0.0691432i	$-0.977973\pi$
$601$	−10.7603	+	18.6375i	−0.438924	+	0.760238i	0.558683	+	0.829381i	$0.311307\pi$
$602$	26.7170	−	39.0029i	1.08890	−	1.58964i
$603$	−12.0792	+	10.0015i	−0.491905	+	0.407291i
$604$	−2.33197	+	0.903471i	−0.0948867	+	0.0367617i
$605$	−17.3018	+	16.5876i	−0.703417	+	0.674381i
$606$	42.6034	−	17.9973i	1.73065	−	0.731091i
$607$	−8.98552	+	33.5344i	−0.364711	+	1.36112i	0.503101	+	0.864228i	$0.332192\pi$
$607$	−8.98552	+	33.5344i	−0.364711	+	1.36112i	−0.867812	+	0.496893i	$0.834474\pi$
$608$	−24.1608	+	18.8387i	−0.979849	+	0.764011i
$609$	−12.6093	−	57.7724i	−0.510954	−	2.34106i
$610$	−1.36286	−	8.24881i	−0.0551805	−	0.333985i
$611$	18.5402			0.750055
$612$	0.748002	+	0.418009i	0.0302362	+	0.0168970i
$613$	−3.63661	+	3.63661i	−0.146881	+	0.146881i	−0.776723	−	0.629842i	$-0.783120\pi$
$613$	−3.63661	+	3.63661i	−0.146881	+	0.146881i	0.629842	+	0.776723i	$0.283120\pi$
$614$	−2.41772	+	6.86124i	−0.0975713	+	0.276897i
$615$	−1.98451	+	5.79789i	−0.0800232	+	0.233794i
$616$	−6.29547	−	3.38033i	−0.253652	−	0.136197i
$617$	30.5988	+	8.19893i	1.23186	+	0.330076i	0.815304	−	0.579033i	$-0.196570\pi$
$617$	30.5988	+	8.19893i	1.23186	+	0.330076i	0.416558	+	0.909109i	$0.363236\pi$
$618$	10.1220	−	7.88002i	0.407165	−	0.316981i
$619$	−10.9008	−	6.29357i	−0.438140	−	0.252960i	0.264668	−	0.964339i	$-0.414737\pi$
$619$	−10.9008	−	6.29357i	−0.438140	−	0.252960i	−0.702808	+	0.711379i	$0.748071\pi$
$620$	23.2094	−	2.01850i	0.932113	−	0.0810649i
$621$	−5.42367	+	12.7381i	−0.217644	+	0.511162i
$622$	−24.0419	+	35.0977i	−0.963993	+	1.40729i
$623$	4.67568	+	17.4499i	0.187327	+	0.699115i
$624$	12.8538	+	27.9878i	0.514565	+	1.12041i
$625$	14.2783	−	20.5215i	0.571131	−	0.820859i
$626$	−10.1884	+	8.72912i	−0.407212	+	0.348886i
$627$	−4.96603	−	0.233135i	−0.198324	−	0.00931052i
$628$	−0.698363	−	0.954971i	−0.0278677	−	0.0381075i
$629$	−0.833673			−0.0332407
$630$	−42.7580	+	14.7277i	−1.70352	+	0.586765i
$631$		−	34.4295i		−	1.37062i	−0.728252	−	0.685309i	$-0.759667\pi$
$631$		−	34.4295i		−	1.37062i	0.728252	−	0.685309i	$-0.240333\pi$
$632$	−10.2290	−	9.61692i	−0.406889	−	0.382541i
$633$	−21.9972	−	14.1154i	−0.874310	−	0.561035i
$634$	−9.40004	+	8.05364i	−0.373323	+	0.319851i
$635$	−14.4636	+	23.8754i	−0.573971	+	0.947466i
$636$	14.7238	+	22.2537i	0.583835	+	0.882416i
$637$	−67.5165	+	18.0910i	−2.67510	+	0.716791i
$638$	−4.42841	−	3.03346i	−0.175322	−	0.120096i
$639$	1.98999	+	1.41294i	0.0787227	+	0.0558950i
$640$	5.65420	+	24.6583i	0.223502	+	0.974704i
$641$	20.6895	−	35.8353i	0.817186	−	1.41541i	−0.0905615	−	0.995891i	$-0.528866\pi$
$641$	20.6895	−	35.8353i	0.817186	−	1.41541i	0.907748	−	0.419517i	$-0.137801\pi$
$642$	−1.95955	−	14.1199i	−0.0773374	−	0.557267i
$643$	4.77327	−	17.8141i	0.188239	−	0.702519i	−0.805674	−	0.592359i	$-0.798197\pi$
$643$	4.77327	−	17.8141i	0.188239	−	0.702519i	0.993914	−	0.110160i	$-0.0351364\pi$
$644$	−15.9248	+	19.7908i	−0.627526	+	0.779865i
$645$	−22.5445	−	15.1465i	−0.887688	−	0.596392i
$646$	1.03167	+	0.363534i	0.0405906	+	0.0143031i
$647$	5.63466	+	5.63466i	0.221521	+	0.221521i	0.809139	−	0.587617i	$-0.199934\pi$
$647$	5.63466	+	5.63466i	0.221521	+	0.221521i	−0.587617	+	0.809139i	$0.699934\pi$
$648$	25.3157	−	2.66761i	0.994494	−	0.104794i
$649$			2.18457i			0.0857520i
$650$	−24.7109	+	19.4276i	−0.969241	+	0.762014i
$651$	13.0683	−	40.9784i	0.512187	−	1.60607i
$652$	49.2714	−	5.33322i	1.92962	−	0.208865i
$653$	33.8007	+	9.05687i	1.32272	+	0.354423i	0.849998	−	0.526787i	$-0.176603\pi$
$653$	33.8007	+	9.05687i	1.32272	+	0.354423i	0.472726	+	0.881209i	$0.343270\pi$
$654$	−15.7241	+	20.7918i	−0.614861	+	0.813023i
$655$	−15.5525	+	14.9105i	−0.607687	+	0.582602i
$656$	4.67707	−	4.26409i	0.182609	−	0.166485i
$657$	−32.3298	+	5.48230i	−1.26130	+	0.213885i
$658$	15.8895	−	23.1963i	0.619435	−	0.904286i
$659$	25.4838	+	14.7131i	0.992706	+	0.573139i	0.906082	−	0.423102i	$-0.139059\pi$
$659$	25.4838	+	14.7131i	0.992706	+	0.573139i	0.0866242	+	0.996241i	$0.472392\pi$
$660$	−1.90934	+	3.63409i	−0.0743211	+	0.141457i
$661$	37.6660	−	21.7465i	1.46504	−	0.845840i	0.465801	−	0.884889i	$-0.345766\pi$
$661$	37.6660	−	21.7465i	1.46504	−	0.845840i	0.999237	+	0.0390491i	$0.0124329\pi$
$662$	0.558632	−	7.24168i	0.0217118	−	0.281456i
$663$	0.593852	−	0.925452i	0.0230633	−	0.0359416i
$664$	−0.992136	−	32.1674i	−0.0385023	−	1.24834i
$665$	−50.5926	+	27.8052i	−1.96190	+	1.07824i
$666$	−20.2345	+	14.2809i	−0.784072	+	0.553372i
$667$	−13.4931	+	13.4931i	−0.522453	+	0.522453i
$668$	8.59493	+	11.7531i	0.332548	+	0.454740i
$669$	13.5154	+	14.8469i	0.522535	+	0.574013i
$670$	6.82406	+	15.0564i	0.263636	+	0.581680i
$671$	−1.21345	+	0.700587i	−0.0468448	+	0.0270459i
$672$	46.0327	+	7.90447i	1.77575	+	0.304922i
$673$	18.4528	−	4.94442i	0.711304	−	0.190593i	0.115016	−	0.993364i	$-0.463308\pi$
$673$	18.4528	−	4.94442i	0.711304	−	0.190593i	0.596288	+	0.802770i	$0.296642\pi$
$674$	−32.2198	+	6.02330i	−1.24106	+	0.232009i
$675$	8.68193	+	24.4872i	0.334168	+	0.942514i
$676$	12.6092	−	4.88515i	0.484969	−	0.187890i
$677$	30.0686	−	8.05686i	1.15563	−	0.309650i	0.370411	−	0.928868i	$-0.379217\pi$
$677$	30.0686	−	8.05686i	1.15563	−	0.309650i	0.785220	+	0.619218i	$0.212550\pi$
$678$	18.3463	+	23.5660i	0.704587	+	0.905048i
$679$	−11.1841	−	19.3714i	−0.429207	−	0.743408i
$680$	0.632414	−	0.644883i	0.0242520	−	0.0247301i
$681$	20.0286	+	22.0018i	0.767498	+	0.843110i
$682$	−1.68635	−	3.52143i	−0.0645736	−	0.134843i
$683$	23.2119	+	23.2119i	0.888180	+	0.888180i	0.994348	−	0.106168i	$-0.0338582\pi$
$683$	23.2119	+	23.2119i	0.888180	+	0.888180i	−0.106168	+	0.994348i	$0.533858\pi$
$684$	31.2676	−	8.84907i	1.19555	−	0.338353i
$685$	45.6596	−	25.0940i	1.74456	−	0.958792i
$686$	−19.5458	+	55.4688i	−0.746261	+	2.11781i
$687$	−23.7126	−	15.2161i	−0.904694	−	0.580532i
$688$	12.8896	+	24.9140i	0.491412	+	0.949836i
$689$	29.6546	−	17.1211i	1.12975	−	0.652261i
$690$	11.4517	+	9.04604i	0.435959	+	0.344377i
$691$	−7.87987	+	13.6483i	−0.299764	+	0.519207i	−0.976082	−	0.217403i	$-0.930241\pi$
$691$	−7.87987	+	13.6483i	−0.299764	+	0.519207i	0.676317	+	0.736610i	$0.263575\pi$
$692$	−3.43332	−	1.51587i	−0.130515	−	0.0576247i
$693$	4.83355	+	5.83770i	0.183611	+	0.221756i
$694$	−10.1662	+	1.90052i	−0.385905	+	0.0721426i
$695$	−23.1873	−	24.1857i	−0.879545	−	0.917414i
$696$	33.7398	+	9.62454i	1.27890	+	0.364817i
$697$	−0.218269	−	0.0584851i	−0.00826755	−	0.00221528i
$698$	−3.02614	+	39.2286i	−0.114541	+	1.48482i
$699$	−7.31469	−	2.33270i	−0.276667	−	0.0882309i
$700$	3.12866	+	47.5668i	0.118252	+	1.79785i
$701$		−	4.46813i		−	0.168759i	−0.996434	−	0.0843796i	$-0.973109\pi$
$701$		−	4.46813i		−	0.168759i	0.996434	−	0.0843796i	$-0.0268908\pi$
$702$	−1.43935	−	32.6349i	−0.0543248	−	1.23172i
$703$	−22.3557	+	22.3557i	−0.843160	+	0.843160i
$704$	3.53413	−	2.34214i	0.133197	−	0.0882726i
$705$	−13.4079	−	9.00810i	−0.504972	−	0.339265i
$706$	1.88507	−	1.61506i	0.0709455	−	0.0607837i
$707$	−86.9381	−	23.2950i	−3.26964	−	0.876098i
$708$	−4.52848	−	13.5421i	−0.170191	−	0.508944i
$709$	22.0704	−	38.2271i	0.828872	−	1.43565i	−0.0700510	−	0.997543i	$-0.522316\pi$
$709$	22.0704	−	38.2271i	0.828872	−	1.43565i	0.898923	−	0.438106i	$-0.144350\pi$
$710$	1.98846	−	1.63227i	0.0746256	−	0.0612580i
$711$	6.20481	+	13.5373i	0.232699	+	0.507688i
$712$	−10.4343	−	2.45377i	−0.391043	−	0.0919588i
$713$	−13.4070	+	3.59239i	−0.502095	+	0.134536i
$714$	−0.648919	−	1.53613i	−0.0242852	−	0.0574882i
$715$	4.50570	+	2.72953i	0.168503	+	0.102079i
$716$	−21.6498	−	17.4207i	−0.809090	−	0.651042i
$717$	29.5981	+	18.9928i	1.10536	+	0.709298i
$718$	−0.337284	+	0.161519i	−0.0125873	+	0.00602783i
$719$	5.57079			0.207755			0.103878	−	0.994590i	$-0.466875\pi$
$719$	5.57079			0.207755			0.103878	+	0.994590i	$0.466875\pi$
$720$	4.30276	−	26.4856i	0.160355	−	0.987059i
$721$	−24.9639			−0.929704
$722$	13.1792	−	6.31125i	0.490478	−	0.234881i
$723$	−0.846549	+	18.0324i	−0.0314835	+	0.670633i
$724$	−9.22966	−	7.42674i	−0.343017	−	0.276013i
$725$	−1.50864	+	35.7774i	−0.0560294	+	1.32874i
$726$	−26.0551	−	3.24486i	−0.966996	−	0.120428i
$727$	−4.17429	+	1.11850i	−0.154816	+	0.0414828i	−0.335395	−	0.942078i	$-0.608870\pi$
$727$	−4.17429	+	1.11850i	−0.154816	+	0.0414828i	0.180579	+	0.983561i	$0.442203\pi$
$728$	13.7206	−	58.3451i	0.508519	−	2.16241i
$729$	−25.9375	−	7.49971i	−0.960648	−	0.277767i
$730$	−3.38402	+	34.3990i	−0.125248	+	1.27317i
$731$	0.500752	−	0.867328i	0.0185210	−	0.0320793i
$732$	6.06990	−	6.85833i	0.224350	−	0.253491i
$733$	−17.0336	−	4.56415i	−0.629152	−	0.168581i	−0.0698672	−	0.997556i	$-0.522258\pi$
$733$	−17.0336	−	4.56415i	−0.629152	−	0.168581i	−0.559285	+	0.828975i	$0.688924\pi$
$734$	−34.3846	+	29.4596i	−1.26916	+	1.08737i
$735$	57.6166	+	19.7211i	2.12522	+	0.727423i
$736$	−5.87569	−	13.8797i	−0.216581	−	0.511614i
$737$	1.95897	−	1.95897i	0.0721597	−	0.0721597i
$738$	−6.29959	+	2.31945i	−0.231891	+	0.0853800i
$739$		−	37.4450i		−	1.37744i	−0.725029	−	0.688718i	$-0.758174\pi$
$739$		−	37.4450i		−	1.37744i	0.725029	−	0.688718i	$-0.241826\pi$
$740$	8.91618	+	24.5364i	0.327765	+	0.901975i
$741$	−8.89215	−	40.7415i	−0.326661	−	1.49668i
$742$	3.99400	−	51.7752i	0.146624	−	1.90073i
$743$	14.0596	+	3.76726i	0.515797	+	0.138207i	0.507322	−	0.861757i	$-0.330636\pi$
$743$	14.0596	+	3.76726i	0.515797	+	0.138207i	0.00847530	+	0.999964i	$0.497302\pi$
$744$	17.7533	+	18.3336i	0.650869	+	0.672143i
$745$	−11.3241	+	10.8567i	−0.414883	+	0.397757i
$746$	−23.9639	+	4.47990i	−0.877380	+	0.164021i
$747$	−11.8849	+	31.9991i	−0.434845	+	1.17078i
$748$	−0.138477	−	0.0611399i	−0.00506322	−	0.00223550i
$749$	−13.8710	+	24.0253i	−0.506836	+	0.877866i
$750$	27.3098	−	2.04345i	0.997212	−	0.0746161i
$751$	19.1484	−	11.0553i	0.698734	−	0.403414i	−0.108142	−	0.994135i	$-0.534490\pi$
$751$	19.1484	−	11.0553i	0.698734	−	0.403414i	0.806876	+	0.590721i	$0.201157\pi$
$752$	7.66587	+	14.8171i	0.279545	+	0.540325i
$753$	40.4182	−	20.8723i	1.47292	−	0.760628i
$754$	14.9635	−	42.4650i	0.544940	−	1.54648i
$755$	0.780418	−	2.68494i	0.0284023	−	0.0977150i
$756$	−42.0643	−	26.1682i	−1.52986	−	0.951728i
$757$	10.2233	+	10.2233i	0.371572	+	0.371572i	0.868050	−	0.496478i	$-0.165373\pi$
$757$	10.2233	+	10.2233i	0.371572	+	0.371572i	−0.496478	+	0.868050i	$0.665373\pi$
$758$	2.07931	+	4.34203i	0.0755241	+	0.157710i
$759$	0.743098	−	2.33014i	0.0269727	−	0.0845788i
$760$	−0.334375	−	34.2519i	−0.0121291	−	1.24245i
$761$	20.2572	+	35.0864i	0.734322	+	1.27188i	0.955020	+	0.296540i	$0.0958329\pi$
$761$	20.2572	+	35.0864i	0.734322	+	1.27188i	−0.220699	+	0.975342i	$0.570834\pi$
$762$	−30.2887	+	4.20347i	−1.09725	+	0.152276i
$763$	49.0025	−	13.1302i	1.77401	−	0.475345i
$764$	−4.42306	+	1.71361i	−0.160021	+	0.0619964i
$765$	−0.879112	+	0.380736i	−0.0317844	+	0.0137656i
$766$	−28.2538	+	5.28187i	−1.02085	+	0.190842i
$767$	−17.6997	+	4.74261i	−0.639097	+	0.171246i
$768$	−17.0529	+	21.8449i	−0.615343	+	0.788259i
$769$	−19.2990	+	11.1423i	−0.695939	+	0.401801i	−0.805833	−	0.592143i	$-0.798282\pi$
$769$	−19.2990	+	11.1423i	−0.695939	+	0.401801i	0.109894	+	0.993943i	$0.464949\pi$
$770$	7.27653	−	3.29796i	0.262228	−	0.118850i
$771$	−13.7153	+	2.99346i	−0.493943	+	0.107807i
$772$	6.74231	+	9.21971i	0.242661	+	0.331825i
$773$	−15.8513	+	15.8513i	−0.570132	+	0.570132i	−0.932165	−	0.362033i	$-0.882083\pi$
$773$	−15.8513	+	15.8513i	−0.570132	+	0.570132i	0.362033	+	0.932165i	$0.382083\pi$
$774$	−2.70336	−	29.6293i	−0.0971704	−	1.06500i
$775$	−13.9622	+	21.9886i	−0.501537	+	0.789852i
$776$	13.2657	−	0.409152i	0.476209	−	0.0146877i
$777$	48.1451	+	2.26022i	1.72719	+	0.0810848i
$778$	0.332679	−	4.31260i	0.0119271	−	0.154614i
$779$	−7.42142	+	4.28476i	−0.265900	+	0.153517i
$780$	−33.5889	−	7.58029i	−1.20267	−	0.271418i
$781$	−0.373384	−	0.215573i	−0.0133607	−	0.00771382i
$782$	−0.304109	+	0.443956i	−0.0108749	+	0.0158758i
$783$	−29.2996	−	22.9437i	−1.04708	−	0.819941i
$784$	−42.3744	−	46.4784i	−1.51337	−	1.65994i
$785$	1.32243	+	0.0278693i	0.0471996	+	0.000994699i
$786$	−23.4209	−	2.91679i	−0.835395	−	0.104039i
$787$	−25.2541	−	6.76683i	−0.900213	−	0.241211i	−0.221105	−	0.975250i	$-0.570966\pi$
$787$	−25.2541	−	6.76683i	−0.900213	−	0.241211i	−0.679108	+	0.734039i	$0.737633\pi$
$788$	13.0007	−	1.40721i	0.463130	−	0.0501299i
$789$	−10.5040	−	11.5388i	−0.373951	−	0.410792i
$790$	15.4871	−	2.55876i	0.551006	−	0.0910365i
$791$		−	58.1212i		−	2.06655i
$792$	−4.40838	+	0.888160i	−0.156645	+	0.0315594i
$793$	−8.31058	−	8.31058i	−0.295117	−	0.295117i
$794$	49.9443	+	17.5991i	1.77246	+	0.624568i
$795$	−29.7643	−	2.02658i	−1.05563	−	0.0718753i
$796$	−23.1601	+	28.7824i	−0.820888	+	1.02017i
$797$	7.78189	−	29.0424i	0.275649	−	1.02874i	−0.679757	−	0.733438i	$-0.737915\pi$
$797$	7.78189	−	29.0424i	0.275649	−	1.02874i	0.955405	−	0.295298i	$-0.0954188\pi$
$798$	−58.5940	−	23.7913i	−2.07421	−	0.842204i
$799$	0.297813	−	0.515828i	0.0105359	−	0.0182487i
$800$	−25.7437	−	11.7159i	−0.910177	−	0.414220i
$801$	9.27013	+	6.58201i	0.327544	+	0.232564i
$802$	−29.5016	−	20.2086i	−1.04174	−	0.713591i
$803$	5.59543	−	1.49929i	0.197459	−	0.0529089i
$804$	−8.08281	+	16.2045i	−0.285059	+	0.571487i
$805$	−6.77098	−	27.5816i	−0.238646	−	0.972125i
$806$	24.8701	−	21.3078i	0.876011	−	0.750537i
$807$	14.9885	−	7.74019i	0.527621	−	0.272467i
$808$	36.5799	−	38.9082i	1.28688	−	1.36879i
$809$		−	31.4281i		−	1.10495i	−0.833528	−	0.552477i	$-0.813683\pi$
$809$		−	31.4281i		−	1.10495i	0.833528	−	0.552477i	$-0.186317\pi$
$810$	−14.8154	+	24.3003i	−0.520559	+	0.853826i
$811$	38.6170			1.35603			0.678014	−	0.735049i	$-0.262841\pi$
$811$	38.6170			1.35603			0.678014	+	0.735049i	$0.262841\pi$
$812$	−40.3053	−	55.1151i	−1.41444	−	1.93416i
$813$	−4.07873	−	7.89827i	−0.143047	−	0.277004i
$814$	3.32250	−	2.84661i	0.116454	−	0.0997735i
$815$	−28.7093	+	47.3911i	−1.00564	+	1.66004i
$816$	0.985155	+	0.0919512i	0.0344873	+	0.00321893i
$817$	−9.83006	−	36.6863i	−0.343910	−	1.28349i
$818$	2.12211	−	3.09797i	0.0741978	−	0.108318i
$819$	−36.8043	+	51.8353i	−1.28605	+	1.81127i
$820$	0.613091	+	7.04953i	0.0214101	+	0.246180i
$821$	−13.9656	−	8.06304i	−0.487403	−	0.281402i	0.236094	−	0.971730i	$-0.424133\pi$
$821$	−13.9656	−	8.06304i	−0.487403	−	0.281402i	−0.723496	+	0.690328i	$0.757466\pi$
$822$	52.8808	+	21.4715i	1.84443	+	0.748906i
$823$	−34.2915	−	9.18837i	−1.19533	−	0.320287i	−0.394337	−	0.918966i	$-0.629026\pi$
$823$	−34.2915	−	9.18837i	−1.19533	−	0.320287i	−0.800989	+	0.598679i	$0.795692\pi$
$824$	7.00707	−	13.0499i	0.244103	−	0.454614i
$825$	−1.93225	−	4.16313i	−0.0672722	−	0.144942i
$826$	−9.23546	+	26.2092i	−0.321343	+	0.911936i
$827$	−7.59260	+	7.59260i	−0.264021	+	0.264021i	−0.826685	−	0.562665i	$-0.809776\pi$
$827$	−7.59260	+	7.59260i	−0.264021	+	0.264021i	0.562665	+	0.826685i	$0.309776\pi$
$828$	0.223785	+	15.9849i	0.00777708	+	0.555514i
$829$	−21.8191			−0.757808			−0.378904	−	0.925436i	$-0.623699\pi$
$829$	−21.8191			−0.757808			−0.378904	+	0.925436i	$0.623699\pi$
$830$	29.2497	+	20.9550i	1.01527	+	0.727357i
$831$	−11.0407	+	10.0505i	−0.382996	+	0.348649i
$832$	26.6487	+	23.5492i	0.923877	+	0.816423i
$833$	−0.581196	+	2.16905i	−0.0201373	+	0.0751533i
$834$	4.53590	−	36.4217i	0.157065	−	1.26118i
$835$	−16.2755	−	0.342995i	−0.563236	−	0.0118698i
$836$	−5.35290	+	2.07386i	−0.185134	+	0.0717260i
$837$	−10.1123	−	25.1089i	−0.349532	−	0.867890i
$838$	7.10274	−	10.3690i	0.245360	−	0.358190i
$839$	3.58311	−	6.20614i	0.123703	−	0.214260i	−0.797522	−	0.603289i	$-0.793856\pi$
$839$	3.58311	−	6.20614i	0.123703	−	0.214260i	0.921225	+	0.389030i	$0.127190\pi$
$840$	−38.2706	+	35.5278i	−1.32046	+	1.22582i
$841$	−11.1459	−	19.3053i	−0.384343	−	0.665701i
$842$	8.92478	+	0.688469i	0.307568	+	0.0237262i
$843$	1.00367	−	21.3792i	0.0345681	−	0.736338i
$844$	−29.8228	−	4.62868i	−1.02654	−	0.159326i
$845$	−4.21979	+	14.5177i	−0.145165	+	0.499425i
$846$	−1.60778	−	17.6215i	−0.0552765	−	0.605839i
$847$	36.1315	+	36.1315i	1.24149	+	1.24149i
$848$	25.9444	+	16.6205i	0.890934	+	0.570752i
$849$	−6.57355	−	30.1183i	−0.225604	−	1.03366i
$850$	0.143584	+	0.999580i	0.00492488	+	0.0342853i
$851$	−7.77677	−	13.4698i	−0.266584	−	0.461737i
$852$	2.76147	+	0.562334i	0.0946064	+	0.0192652i
$853$	4.22828	+	15.7801i	0.144773	+	0.540302i	0.999765	+	0.0216606i	$0.00689534\pi$
$853$	4.22828	+	15.7801i	0.144773	+	0.540302i	−0.854992	+	0.518641i	$0.826438\pi$
$854$	−17.5201	+	3.27527i	−0.599525	+	0.112078i
$855$	−13.3644	+	33.7840i	−0.457053	+	1.15539i
$856$	−8.66579	−	13.9947i	−0.296191	−	0.478329i
$857$	13.6949	+	51.1102i	0.467810	+	1.74589i	0.647402	+	0.762149i	$0.275856\pi$
$857$	13.6949	+	51.1102i	0.467810	+	1.74589i	−0.179592	+	0.983741i	$0.557478\pi$
$858$	0.793267	+	5.71600i	0.0270817	+	0.195141i
$859$	−3.13332	+	1.80902i	−0.106908	+	0.0617231i	−0.552500	−	0.833513i	$-0.686326\pi$
$859$	−3.13332	+	1.80902i	−0.106908	+	0.0617231i	0.445593	+	0.895236i	$0.352993\pi$
$860$	−30.8825	−	5.46184i	−1.05308	−	0.186247i
$861$	12.4466	+	3.96931i	0.424180	+	0.135274i
$862$	−21.1721	−	44.2116i	−0.721125	−	1.50585i
$863$	33.5777	−	33.5777i	1.14300	−	1.14300i	0.155099	−	0.987899i	$-0.450430\pi$
$863$	33.5777	−	33.5777i	1.14300	−	1.14300i	0.987899	−	0.155099i	$-0.0495698\pi$
$864$	25.4864	−	14.6440i	0.867063	−	0.498198i
$865$	3.67730	−	2.02100i	0.125032	−	0.0687161i
$866$	−31.7034	−	11.1715i	−1.07733	−	0.379621i
$867$	13.4942	+	26.1310i	0.458288	+	0.887454i
$868$	−5.34468	−	49.3773i	−0.181410	−	1.67597i
$869$	−1.31535	−	2.27825i	−0.0446201	−	0.0772843i
$870$	−31.4538	+	23.4396i	−1.06638	+	0.794677i
$871$	20.1247	+	11.6190i	0.681898	+	0.393694i
$872$	−6.89063	+	29.3015i	−0.233346	+	0.992275i
$873$	−13.1962	−	4.90126i	−0.446625	−	0.165882i
$874$	3.75010	+	20.0600i	0.126849	+	0.678541i
$875$	−44.3803	−	29.5106i	−1.50033	−	0.997640i
$876$	−31.5781	+	20.8931i	−1.06692	+	0.705911i
$877$	3.47037	−	12.9516i	0.117186	−	0.437345i	−0.882255	−	0.470772i	$-0.843975\pi$
$877$	3.47037	−	12.9516i	0.117186	−	0.437345i	0.999441	+	0.0334271i	$0.0106422\pi$
$878$	3.12256	−	40.4785i	0.105381	−	1.36608i
$879$	−28.2159	+	6.15834i	−0.951699	+	0.207716i
$880$	−0.318429	+	4.72950i	−0.0107342	+	0.159431i
$881$	−31.6488			−1.06627			−0.533137	−	0.846029i	$-0.678987\pi$
$881$	−31.6488			−1.06627			−0.533137	+	0.846029i	$0.678987\pi$
$882$	23.0495	+	62.6022i	0.776117	+	2.10793i
$883$	−8.10242	−	8.10242i	−0.272668	−	0.272668i	0.557505	−	0.830173i	$-0.311759\pi$
$883$	−8.10242	−	8.10242i	−0.272668	−	0.272668i	−0.830173	+	0.557505i	$0.811759\pi$
$884$	0.194735	−	1.25469i	0.00654965	−	0.0421997i
$885$	15.1044	+	5.16995i	0.507728	+	0.173786i
$886$	19.9653	−	17.1056i	0.670746	−	0.574673i
$887$	−2.32261	+	8.66809i	−0.0779856	+	0.291046i	−0.993894	−	0.110342i	$-0.964805\pi$
$887$	−2.32261	+	8.66809i	−0.0779856	+	0.291046i	0.915908	+	0.401388i	$0.131472\pi$
$888$	−14.6953	+	24.5334i	−0.493141	+	0.823287i
$889$	51.5371	+	29.7549i	1.72850	+	0.997949i
$890$	9.26301	−	7.60374i	0.310497	−	0.254878i
$891$	4.68601	+	0.889780i	0.156987	+	0.0298087i
$892$	21.2080	+	9.36370i	0.710098	+	0.313520i
$893$	−5.84625	−	21.8185i	−0.195637	−	0.730129i
$894$	−17.0532	−	2.12378i	−0.570345	−	0.0710298i
$895$	30.1725	−	7.40700i	1.00855	−	0.247589i
$896$	52.3020	−	13.1588i	1.74729	−	0.439604i
$897$	20.4923	+	0.962030i	0.684218	+	0.0321213i
$898$	17.9814	+	37.5489i	0.600048	+	1.25302i
$899$		−	37.3087i		−	1.24431i
$900$	20.6079	+	21.8017i	0.686929	+	0.726725i
$901$		−	1.10007i		−	0.0366487i
$902$	1.06959	−	0.512204i	0.0356133	−	0.0170545i
$903$	−31.2702	+	48.7311i	−1.04061	+	1.62167i
$904$	30.3829	+	16.3139i	1.01052	+	0.542594i
$905$	12.8630	−	3.15773i	0.427582	−	0.104966i
$906$	2.82151	−	1.19191i	0.0937383	−	0.0395986i
$907$	12.9340	+	48.2703i	0.429466	+	1.60279i	0.753973	+	0.656905i	$0.228135\pi$
$907$	12.9340	+	48.2703i	0.429466	+	1.60279i	−0.324508	+	0.945883i	$0.605199\pi$
$908$	31.4285	+	13.8762i	1.04299	+	0.460498i
$909$	−51.4919	+	23.6013i	−1.70788	+	0.782805i
$910$	42.5175	+	51.7955i	1.40944	+	1.71701i
$911$	2.39054	+	1.38018i	0.0792021	+	0.0457273i	0.539078	−	0.842256i	$-0.318773\pi$
$911$	2.39054	+	1.38018i	0.0792021	+	0.0457273i	−0.459876	+	0.887983i	$0.652106\pi$
$912$	28.8836	−	23.9521i	0.956430	−	0.793132i
$913$	1.56072	−	5.82470i	0.0516524	−	0.192769i
$914$	11.4980	+	13.4202i	0.380320	+	0.443901i
$915$	1.97221	+	10.0479i	0.0651994	+	0.332174i
$916$	−32.1486	−	4.98965i	−1.06222	−	0.164863i
$917$	32.4785	+	32.4785i	1.07253	+	1.07253i
$918$	−0.931094	−	0.484173i	−0.0307307	−	0.0159801i
$919$	−24.8157			−0.818595			−0.409298	−	0.912401i	$-0.634226\pi$
$919$	−24.8157			−0.818595			−0.409298	+	0.912401i	$0.634226\pi$
$920$	16.3188	+	4.20231i	0.538016	+	0.138546i
$921$	2.70704	−	8.48851i	0.0892001	−	0.279706i
$922$	−20.7710	−	1.60230i	−0.684056	−	0.0527689i
$923$	0.935999	−	3.49320i	0.0308088	−	0.114980i
$924$	7.83136	+	3.90629i	0.257633	+	0.128508i
$925$	−27.8497	−	8.73537i	−0.915694	−	0.287217i
$926$	7.30729	−	1.36605i	0.240132	−	0.0448913i
$927$	−12.1010	+	10.0195i	−0.397448	+	0.329082i
$928$	40.1246	−	5.59941i	1.31716	−	0.183810i
$929$	4.79543	+	2.76864i	0.157333	+	0.0908362i	0.576599	−	0.817027i	$-0.304379\pi$
$929$	4.79543	+	2.76864i	0.157333	+	0.0908362i	−0.419266	+	0.907863i	$0.637713\pi$
$930$	−28.3384	+	3.32587i	−0.929254	+	0.109059i
$931$	42.5798	+	73.7504i	1.39550	+	2.41707i
$932$	−8.81389	+	0.954031i	−0.288709	+	0.0312503i
$933$	28.1392	−	43.8518i	0.921236	−	1.43564i
$934$	−10.7051	+	30.3799i	−0.350281	+	0.994061i
$935$	0.148317	−	0.0815135i	0.00485049	−	0.00266578i
$936$	−16.7664	−	33.7890i	−0.548026	−	1.10443i
$937$	−18.5811	+	18.5811i	−0.607017	+	0.607017i	−0.942165	−	0.335149i	$-0.891213\pi$
$937$	−18.5811	+	18.5811i	−0.607017	+	0.607017i	0.335149	+	0.942165i	$0.391213\pi$
$938$	31.7843	−	15.2209i	1.03780	−	0.496980i
$939$	12.1511	−	11.0614i	0.396536	−	0.360974i
$940$	−18.3668	−	3.24833i	−0.599059	−	0.105949i
$941$	6.98507	−	4.03283i	0.227707	−	0.131467i	−0.381807	−	0.924242i	$-0.624698\pi$
$941$	6.98507	−	4.03283i	0.227707	−	0.131467i	0.609514	+	0.792776i	$0.291365\pi$
$942$	0.890103	+	1.14334i	0.0290011	+	0.0372522i
$943$	−1.09114	−	4.07218i	−0.0355323	−	0.132608i
$944$	−11.1086	−	12.1845i	−0.361554	−	0.396570i
$945$	51.8015	−	19.6043i	1.68510	−	0.637729i
$946$	0.965839	+	5.16646i	0.0314021	+	0.167976i
$947$	3.13459	+	11.6984i	0.101860	+	0.380148i	0.997970	−	0.0636844i	$-0.0202851\pi$
$947$	3.13459	+	11.6984i	0.101860	+	0.380148i	−0.896110	+	0.443833i	$0.853618\pi$
$948$	12.8765	+	11.3962i	0.418209	+	0.370131i
$949$	24.2949	+	42.0799i	0.788645	+	1.36597i
$950$	30.6550	+	22.9543i	0.994578	+	0.744736i
$951$	11.2108	−	10.2054i	0.363536	−	0.330933i
$952$	−1.40289	−	1.31894i	−0.0454680	−	0.0427472i
$953$	−22.9473	−	22.9473i	−0.743335	−	0.743335i	0.229884	−	0.973218i	$-0.426165\pi$
$953$	−22.9473	−	22.9473i	−0.743335	−	0.743335i	−0.973218	+	0.229884i	$0.926165\pi$
$954$	−18.8443	−	26.7005i	−0.610107	−	0.864459i
$955$	1.48022	−	5.09253i	0.0478987	−	0.164790i
$956$	40.1278	+	6.22808i	1.29783	+	0.201431i
$957$	5.53294	+	3.55043i	0.178855	+	0.114769i
$958$	0.874316	−	11.3340i	0.0282479	−	0.366184i
$959$	−55.5356	−	96.1905i	−1.79334	−	3.10615i
$960$	−7.83002	−	29.9782i	−0.252713	−	0.967541i
$961$	−1.93120	+	3.34494i	−0.0622968	+	0.107901i
$962$	30.2765	+	20.7394i	0.976154	+	0.668665i
$963$	2.91892	+	17.2132i	0.0940610	+	0.554689i
$964$	7.53050	+	19.4372i	0.242541	+	0.626030i
$965$	−12.7673	−	0.269063i	−0.410995	−	0.00866145i
$966$	18.7661	−	24.8142i	0.603790	−	0.798384i
$967$	3.10093	−	11.5728i	0.0997190	−	0.372156i	−0.897974	−	0.440049i	$-0.854961\pi$
$967$	3.10093	−	11.5728i	0.0997190	−	0.372156i	0.997693	+	0.0678929i	$0.0216276\pi$
$968$	−29.0294	+	8.74603i	−0.933040	+	0.281108i
$969$	−1.27635	−	0.407038i	−0.0410024	−	0.0130759i
$970$	−8.64171	+	12.0624i	−0.277469	+	0.387301i
$971$	−9.74293			−0.312665			−0.156333	−	0.987704i	$-0.549967\pi$
$971$	−9.74293			−0.312665			−0.156333	+	0.987704i	$0.549967\pi$
$972$	−30.8930	+	4.19808i	−0.990893	+	0.134653i
$973$	−50.5072	+	50.5072i	−1.61919	+	1.61919i
$974$	−8.86009	−	3.12207i	−0.283896	−	0.100037i
$975$	29.5353	−	24.6932i	0.945887	−	0.790817i
$976$	3.20553	−	10.0779i	0.102607	−	0.322587i
$977$	−10.4265	−	2.79377i	−0.333573	−	0.0893805i	0.0881452	−	0.996108i	$-0.471906\pi$
$977$	−10.4265	−	2.79377i	−0.333573	−	0.0893805i	−0.421718	+	0.906727i	$0.638573\pi$
$978$	−60.1212	+	8.34362i	−1.92246	+	0.266799i
$979$	−1.73937	−	1.00422i	−0.0555904	−	0.0320951i
$980$	70.0548	−	6.09259i	2.23782	−	0.194621i
$981$	18.4835	−	26.0322i	0.590133	−	0.831145i
$982$	3.33847	+	2.28685i	0.106535	+	0.0729764i
$983$	3.83891	+	14.3270i	0.122442	+	0.456960i	0.999736	−	0.0229942i	$-0.00731993\pi$
$983$	3.83891	+	14.3270i	0.122442	+	0.456960i	−0.877294	+	0.479954i	$0.840653\pi$
$984$	−5.56857	+	5.39232i	−0.177520	+	0.171901i
$985$	−7.57520	+	12.5045i	−0.241366	+	0.398428i
$986$	−0.941106	−	1.09844i	−0.0299709	−	0.0349814i
$987$	−18.5974	+	28.9819i	−0.591961	+	0.922505i
$988$	−28.4236	−	38.8676i	−0.904274	−	1.23654i
$989$	18.6847			0.594139
$990$	2.20355	−	4.51914i	0.0700335	−	0.143628i
$991$			56.5896i			1.79763i	0.438330	+	0.898814i	$0.355570\pi$
$991$			56.5896i			1.79763i	−0.438330	+	0.898814i	$0.644430\pi$
$992$	27.3121	+	11.0657i	0.867162	+	0.351336i
$993$	−0.417151	+	8.88577i	−0.0132379	+	0.281981i
$994$	−3.56829	−	4.16483i	−0.113179	−	0.132101i
$995$	−9.84729	−	40.1130i	−0.312180	−	1.27167i
$996$	2.39933	+	39.3425i	0.0760258	+	1.24661i
$997$	4.96912	−	1.33147i	0.157374	−	0.0421681i	−0.179272	−	0.983800i	$-0.557374\pi$
$997$	4.96912	−	1.33147i	0.157374	−	0.0421681i	0.336646	+	0.941631i	$0.390708\pi$
$998$	−0.215180	+	0.314131i	−0.00681140	+	0.00994366i
$999$	24.2449	−	18.2278i	0.767076	−	0.576701i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.2.bo.a.43.10	✓	272
5.2	odd	4	inner	360.2.bo.a.187.27	yes	272
8.3	odd	2	inner	360.2.bo.a.43.67	yes	272
9.4	even	3	inner	360.2.bo.a.283.37	yes	272
40.27	even	4	inner	360.2.bo.a.187.37	yes	272
45.22	odd	12	inner	360.2.bo.a.67.67	yes	272
72.67	odd	6	inner	360.2.bo.a.283.27	yes	272
360.67	even	12	inner	360.2.bo.a.67.10	yes	272

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.bo.a.43.10	✓	272	1.1	even	1	trivial
360.2.bo.a.43.67	yes	272	8.3	odd	2	inner
360.2.bo.a.67.10	yes	272	360.67	even	12	inner
360.2.bo.a.67.67	yes	272	45.22	odd	12	inner
360.2.bo.a.187.27	yes	272	5.2	odd	4	inner
360.2.bo.a.187.37	yes	272	40.27	even	4	inner
360.2.bo.a.283.27	yes	272	72.67	odd	6	inner
360.2.bo.a.283.37	yes	272	9.4	even	3	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:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	360.bo (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.27550 + 0.610814i) q^{2} +(1.53896 - 0.794731i) q^{3} +(1.25381 - 1.55819i) q^{4} +(0.533101 + 2.17159i) q^{5} +(-1.47752 + 1.95370i) q^{6} +(4.60452 - 1.23378i) q^{7} +(-0.647478 + 2.75332i) q^{8} +(1.73680 - 2.44612i) q^{9} +O(q^{10})\)	\(q+(-1.27550 + 0.610814i) q^{2} +(1.53896 - 0.794731i) q^{3} +(1.25381 - 1.55819i) q^{4} +(0.533101 + 2.17159i) q^{5} +(-1.47752 + 1.95370i) q^{6} +(4.60452 - 1.23378i) q^{7} +(-0.647478 + 2.75332i) q^{8} +(1.73680 - 2.44612i) q^{9} +(-2.00641 - 2.44424i) q^{10} +(-0.264986 + 0.458969i) q^{11} +(0.691229 - 3.39444i) q^{12} +(-4.29389 - 1.15054i) q^{13} +(-5.11947 + 4.38619i) q^{14} +(2.54625 + 2.91832i) q^{15} +(-0.855905 - 3.90736i) q^{16} +(-0.100984 + 0.100984i) q^{17} +(-0.721174 + 4.18090i) q^{18} +5.41595i q^{19} +(4.05216 + 1.89210i) q^{20} +(6.10566 - 5.55810i) q^{21} +(0.0576455 - 0.747273i) q^{22} +(-2.57362 - 0.689600i) q^{23} +(1.19171 + 4.75182i) q^{24} +(-4.43161 + 2.31535i) q^{25} +(6.17963 - 1.15524i) q^{26} +(0.728866 - 5.14478i) q^{27} +(3.85075 - 8.72165i) q^{28} +(3.58092 - 6.20233i) q^{29} +(-5.03030 - 2.16704i) q^{30} +(4.51145 - 2.60469i) q^{31} +(3.47838 + 4.46104i) q^{32} +(-0.0430460 + 0.916927i) q^{33} +(0.0671229 - 0.190488i) q^{34} +(5.13394 + 9.34141i) q^{35} +(-1.63389 - 5.77325i) q^{36} +(4.12775 + 4.12775i) q^{37} +(-3.30814 - 6.90806i) q^{38} +(-7.52250 + 1.64184i) q^{39} +(-6.32425 + 0.0617390i) q^{40} +(0.791137 + 1.37029i) q^{41} +(-4.39283 + 10.8188i) q^{42} +(-6.77375 + 1.81502i) q^{43} +(0.382917 + 0.988359i) q^{44} +(6.23786 + 2.46760i) q^{45} +(3.70388 - 0.692418i) q^{46} +(-4.02857 + 1.07945i) q^{47} +(-4.42250 - 5.33305i) q^{48} +(13.6173 - 7.86193i) q^{49} +(4.23828 - 5.66012i) q^{50} +(-0.0751553 + 0.235666i) q^{51} +(-7.17650 + 5.24812i) q^{52} +(-5.44677 + 5.44677i) q^{53} +(2.21283 + 7.00738i) q^{54} +(-1.13796 - 0.330764i) q^{55} +(0.415657 + 13.4766i) q^{56} +(4.30423 + 8.33494i) q^{57} +(-0.779000 + 10.0984i) q^{58} +(3.56981 - 2.06103i) q^{59} +(7.73982 - 0.308511i) q^{60} +(2.28966 + 1.32193i) q^{61} +(-4.16339 + 6.07794i) q^{62} +(4.97919 - 13.4061i) q^{63} +(-7.16154 - 3.56543i) q^{64} +(0.209435 - 9.93792i) q^{65} +(-0.505167 - 1.19584i) q^{66} +(-5.04934 - 1.35297i) q^{67} +(0.0307371 + 0.283967i) q^{68} +(-4.50875 + 0.984070i) q^{69} +(-12.2542 - 8.77911i) q^{70} +0.813528i q^{71} +(5.61041 + 6.36579i) q^{72} +(-7.72899 - 7.72899i) q^{73} +(-7.78624 - 2.74367i) q^{74} +(-4.97999 + 7.08517i) q^{75} +(8.43908 + 6.79059i) q^{76} +(-0.653867 + 2.44027i) q^{77} +(8.59211 - 6.68902i) q^{78} +(-2.48192 + 4.29882i) q^{79} +(8.02889 - 3.94169i) q^{80} +(-2.96702 - 8.49687i) q^{81} +(-1.84609 - 1.26457i) q^{82} +(-10.9906 + 2.94492i) q^{83} +(-1.00520 - 16.4826i) q^{84} +(-0.273130 - 0.165461i) q^{85} +(7.53129 - 6.45256i) q^{86} +(0.581708 - 12.3910i) q^{87} +(-1.09212 - 1.02676i) q^{88} +3.78973i q^{89} +(-9.46366 + 0.662745i) q^{90} -21.1908 q^{91} +(-4.30137 + 3.14556i) q^{92} +(4.87292 - 7.59391i) q^{93} +(4.47910 - 3.83755i) q^{94} +(-11.7612 + 2.88725i) q^{95} +(8.89842 + 4.10100i) q^{96} +(-1.21447 - 4.53246i) q^{97} +(-12.5667 + 18.3455i) q^{98} +(0.662465 + 1.44533i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 272 q - 2 q^{2} - 8 q^{3} - 8 q^{6} - 8 q^{8}+O(q^{10}) \) 272 * q - 2 * q^2 - 8 * q^3 - 8 * q^6 - 8 * q^8	\( 272 q - 2 q^{2} - 8 q^{3} - 8 q^{6} - 8 q^{8} - 8 q^{10} - 8 q^{11} - 10 q^{12} - 4 q^{16} - 16 q^{17} + 20 q^{18} + 14 q^{20} + 6 q^{22} - 4 q^{25} - 48 q^{26} - 8 q^{27} + 8 q^{28} - 34 q^{30} - 22 q^{32} + 4 q^{33} - 16 q^{35} - 8 q^{36} - 26 q^{38} - 2 q^{40} - 8 q^{41} - 66 q^{42} - 4 q^{43} - 40 q^{46} - 38 q^{48} - 42 q^{50} - 16 q^{51} + 14 q^{52} + 24 q^{56} + 16 q^{57} + 6 q^{58} + 14 q^{60} - 76 q^{62} - 4 q^{65} - 44 q^{66} - 4 q^{67} - 46 q^{68} + 18 q^{70} + 38 q^{72} - 16 q^{73} - 120 q^{75} - 38 q^{78} + 92 q^{80} - 32 q^{81} - 4 q^{83} - 40 q^{86} - 42 q^{88} - 14 q^{90} - 32 q^{91} + 52 q^{92} + 108 q^{96} - 4 q^{97} - 140 q^{98}+O(q^{100}) \) 272 * q - 2 * q^2 - 8 * q^3 - 8 * q^6 - 8 * q^8 - 8 * q^10 - 8 * q^11 - 10 * q^12 - 4 * q^16 - 16 * q^17 + 20 * q^18 + 14 * q^20 + 6 * q^22 - 4 * q^25 - 48 * q^26 - 8 * q^27 + 8 * q^28 - 34 * q^30 - 22 * q^32 + 4 * q^33 - 16 * q^35 - 8 * q^36 - 26 * q^38 - 2 * q^40 - 8 * q^41 - 66 * q^42 - 4 * q^43 - 40 * q^46 - 38 * q^48 - 42 * q^50 - 16 * q^51 + 14 * q^52 + 24 * q^56 + 16 * q^57 + 6 * q^58 + 14 * q^60 - 76 * q^62 - 4 * q^65 - 44 * q^66 - 4 * q^67 - 46 * q^68 + 18 * q^70 + 38 * q^72 - 16 * q^73 - 120 * q^75 - 38 * q^78 + 92 * q^80 - 32 * q^81 - 4 * q^83 - 40 * q^86 - 42 * q^88 - 14 * q^90 - 32 * q^91 + 52 * q^92 + 108 * q^96 - 4 * q^97 - 140 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more