LMFDB - Embedded newform 546.2.u.a.425.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(185,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1, 2]))

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

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

chi := DirichletCharacter("546.185");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.u (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$76$
Relative dimension:	$38$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			425.16
Character	$\chi$	$=$	546.425
Dual form			546.2.u.a.185.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(1.30626 - 1.13741i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.604752 + 1.04746i) q^{5} +(-0.562548 + 1.63815i) q^{6} +(-2.45540 - 0.985399i) q^{7} +1.00000i q^{8} +(0.412611 - 2.97149i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(1.30626 - 1.13741i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.604752 + 1.04746i) q^{5} +(-0.562548 + 1.63815i) q^{6} +(-2.45540 - 0.985399i) q^{7} +1.00000i q^{8} +(0.412611 - 2.97149i) q^{9} -1.20950i q^{10} +1.19922i q^{11} +(-0.331895 - 1.69995i) q^{12} +(-1.92468 - 3.04887i) q^{13} +(2.61914 - 0.374319i) q^{14} +(0.401428 + 2.05610i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.61925 - 4.53667i) q^{17} +(1.12841 + 2.77969i) q^{18} -7.35805i q^{19} +(0.604752 + 1.04746i) q^{20} +(-4.32818 + 1.50561i) q^{21} +(-0.599608 - 1.03855i) q^{22} +(3.13524 - 1.81013i) q^{23} +(1.13741 + 1.30626i) q^{24} +(1.76855 + 3.06322i) q^{25} +(3.19125 + 1.67806i) q^{26} +(-2.84082 - 4.35083i) q^{27} +(-2.08108 + 1.63374i) q^{28} +(-1.43268 - 0.827158i) q^{29} +(-1.37570 - 1.57992i) q^{30} +(-3.45662 + 1.99568i) q^{31} +(0.866025 + 0.500000i) q^{32} +(1.36400 + 1.56648i) q^{33} +5.23850i q^{34} +(2.51707 - 1.97601i) q^{35} +(-2.36708 - 1.84308i) q^{36} +(-4.50203 - 7.79774i) q^{37} +(3.67902 + 6.37226i) q^{38} +(-5.98193 - 1.79347i) q^{39} +(-1.04746 - 0.604752i) q^{40} +(0.0914442 - 0.158386i) q^{41} +(2.99551 - 3.46798i) q^{42} +(0.527263 + 0.913245i) q^{43} +(1.03855 + 0.599608i) q^{44} +(2.86299 + 2.22921i) q^{45} +(-1.81013 + 3.13524i) q^{46} +(-3.56307 + 6.17142i) q^{47} +(-1.63815 - 0.562548i) q^{48} +(5.05798 + 4.83910i) q^{49} +(-3.06322 - 1.76855i) q^{50} +(-1.73863 - 8.90520i) q^{51} +(-3.60274 + 0.142382i) q^{52} +(1.91564 - 1.10599i) q^{53} +(4.63564 + 2.34752i) q^{54} +(-1.25613 - 0.725228i) q^{55} +(0.985399 - 2.45540i) q^{56} +(-8.36910 - 9.61150i) q^{57} +1.65432 q^{58} +(-5.63264 + 9.75602i) q^{59} +(1.98135 + 0.680403i) q^{60} -6.61123i q^{61} +(1.99568 - 3.45662i) q^{62} +(-3.94123 + 6.88961i) q^{63} -1.00000 q^{64} +(4.35752 - 0.172212i) q^{65} +(-1.96450 - 0.674616i) q^{66} +10.7447 q^{67} +(-2.61925 - 4.53667i) q^{68} +(2.03657 - 5.93053i) q^{69} +(-1.19184 + 2.96981i) q^{70} +(-6.08827 + 3.51507i) q^{71} +(2.97149 + 0.412611i) q^{72} +(5.40931 - 3.12307i) q^{73} +(7.79774 + 4.50203i) q^{74} +(5.79431 + 1.98979i) q^{75} +(-6.37226 - 3.67902i) q^{76} +(1.18171 - 2.94455i) q^{77} +(6.07724 - 1.43778i) q^{78} +(2.23131 - 3.86475i) q^{79} +1.20950 q^{80} +(-8.65951 - 2.45214i) q^{81} +0.182888i q^{82} +16.6675 q^{83} +(-0.860198 + 4.50112i) q^{84} +(3.16799 + 5.48712i) q^{85} +(-0.913245 - 0.527263i) q^{86} +(-2.81226 + 0.549060i) q^{87} -1.19922 q^{88} +(-3.59604 - 6.22852i) q^{89} +(-3.59403 - 0.499054i) q^{90} +(1.72149 + 9.38277i) q^{91} -3.62026i q^{92} +(-2.24533 + 6.53845i) q^{93} -7.12615i q^{94} +(7.70727 + 4.44979i) q^{95} +(1.69995 - 0.331895i) q^{96} +(11.8894 - 6.86436i) q^{97} +(-6.79989 - 1.66179i) q^{98} +(3.56346 + 0.494809i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q + 38 q^{4} + 10 q^{7} - 8 q^{9}+O(q^{10}) $ 76 * q + 38 * q^4 + 10 * q^7 - 8 * q^9	$ 76 q + 38 q^{4} + 10 q^{7} - 8 q^{9} + 2 q^{13} + 12 q^{15} - 38 q^{16} - 8 q^{21} - 42 q^{25} + 20 q^{28} + 20 q^{30} + 12 q^{31} - 4 q^{36} - 6 q^{37} + 12 q^{39} + 8 q^{42} - 2 q^{43} - 4 q^{46} + 2 q^{49} + 10 q^{51} - 14 q^{52} + 18 q^{54} + 24 q^{55} + 8 q^{57} + 16 q^{58} - 12 q^{60} + 32 q^{63} - 76 q^{64} - 24 q^{66} + 96 q^{67} - 30 q^{69} - 54 q^{73} - 12 q^{75} + 18 q^{76} - 12 q^{78} - 60 q^{79} + 8 q^{81} + 8 q^{84} + 8 q^{85} - 24 q^{87} + 48 q^{91} + 16 q^{93} - 66 q^{97}+O(q^{100}) $ 76 * q + 38 * q^4 + 10 * q^7 - 8 * q^9 + 2 * q^13 + 12 * q^15 - 38 * q^16 - 8 * q^21 - 42 * q^25 + 20 * q^28 + 20 * q^30 + 12 * q^31 - 4 * q^36 - 6 * q^37 + 12 * q^39 + 8 * q^42 - 2 * q^43 - 4 * q^46 + 2 * q^49 + 10 * q^51 - 14 * q^52 + 18 * q^54 + 24 * q^55 + 8 * q^57 + 16 * q^58 - 12 * q^60 + 32 * q^63 - 76 * q^64 - 24 * q^66 + 96 * q^67 - 30 * q^69 - 54 * q^73 - 12 * q^75 + 18 * q^76 - 12 * q^78 - 60 * q^79 + 8 * q^81 + 8 * q^84 + 8 * q^85 - 24 * q^87 + 48 * q^91 + 16 * q^93 - 66 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	1.30626	−	1.13741i	0.754167	−	0.656682i
$3$	1.30626	−	1.13741i	0.754167	−	0.656682i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−0.604752	+	1.04746i	−0.270453	+	0.468439i	−0.968978	−	0.247147i	$-0.920507\pi$
$5$	−0.604752	+	1.04746i	−0.270453	+	0.468439i	0.698525	+	0.715586i	$0.253840\pi$
$6$	−0.562548	+	1.63815i	−0.229659	+	0.668773i
$7$	−2.45540	−	0.985399i	−0.928054	−	0.372446i
$7$	−2.45540	−	0.985399i	−0.928054	−	0.372446i
$8$			1.00000i			0.353553i
$9$	0.412611	−	2.97149i	0.137537	−	0.990497i
$10$		−	1.20950i		−	0.382478i
$11$			1.19922i			0.361577i	0.983522	+	0.180789i	$0.0578650\pi$
$11$			1.19922i			0.361577i	−0.983522	+	0.180789i	$0.942135\pi$
$12$	−0.331895	−	1.69995i	−0.0958099	−	0.490735i
$13$	−1.92468	−	3.04887i	−0.533809	−	0.845605i
$13$	−1.92468	−	3.04887i	−0.533809	−	0.845605i
$14$	2.61914	−	0.374319i	0.699994	−	0.100041i
$15$	0.401428	+	2.05610i	0.103648	+	0.530883i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	2.61925	−	4.53667i	0.635261	−	1.10030i	−0.351199	−	0.936301i	$-0.614226\pi$
$17$	2.61925	−	4.53667i	0.635261	−	1.10030i	0.986460	−	0.164003i	$-0.0524407\pi$
$18$	1.12841	+	2.77969i	0.265970	+	0.655179i
$19$		−	7.35805i		−	1.68805i	−0.536302	−	0.844026i	$-0.680179\pi$
$19$		−	7.35805i		−	1.68805i	0.536302	−	0.844026i	$-0.319821\pi$
$20$	0.604752	+	1.04746i	0.135227	+	0.234219i
$21$	−4.32818	+	1.50561i	−0.944487	+	0.328550i
$22$	−0.599608	−	1.03855i	−0.127837	−	0.221420i
$23$	3.13524	−	1.81013i	0.653742	−	0.377438i	−0.136146	−	0.990689i	$-0.543472\pi$
$23$	3.13524	−	1.81013i	0.653742	−	0.377438i	0.789888	+	0.613251i	$0.210138\pi$
$24$	1.13741	+	1.30626i	0.232172	+	0.266638i
$25$	1.76855	+	3.06322i	0.353710	+	0.612644i
$26$	3.19125	+	1.67806i	0.625856	+	0.329095i
$27$	−2.84082	−	4.35083i	−0.546716	−	0.837318i
$28$	−2.08108	+	1.63374i	−0.393287	+	0.308748i
$29$	−1.43268	−	0.827158i	−0.266042	−	0.153599i	0.361046	−	0.932548i	$-0.382420\pi$
$29$	−1.43268	−	0.827158i	−0.266042	−	0.153599i	−0.627088	+	0.778949i	$0.715753\pi$
$30$	−1.37570	−	1.57992i	−0.251167	−	0.288453i
$31$	−3.45662	+	1.99568i	−0.620827	+	0.358435i	−0.777191	−	0.629265i	$-0.783356\pi$
$31$	−3.45662	+	1.99568i	−0.620827	+	0.358435i	0.156364	+	0.987700i	$0.450023\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	1.36400	+	1.56648i	0.237441	+	0.272690i
$34$			5.23850i			0.898395i
$35$	2.51707	−	1.97601i	0.425463	−	0.334007i
$36$	−2.36708	−	1.84308i	−0.394513	−	0.307179i
$37$	−4.50203	−	7.79774i	−0.740128	−	1.28194i	−0.952436	−	0.304737i	$-0.901431\pi$
$37$	−4.50203	−	7.79774i	−0.740128	−	1.28194i	0.212308	−	0.977203i	$-0.431902\pi$
$38$	3.67902	+	6.37226i	0.596817	+	1.03372i
$39$	−5.98193	−	1.79347i	−0.957875	−	0.287185i
$40$	−1.04746	−	0.604752i	−0.165618	−	0.0956196i
$41$	0.0914442	−	0.158386i	0.0142812	−	0.0247357i	−0.858796	−	0.512317i	$-0.828787\pi$
$41$	0.0914442	−	0.158386i	0.0142812	−	0.0247357i	0.873078	+	0.487581i	$0.162121\pi$
$42$	2.99551	−	3.46798i	0.462218	−	0.535121i
$43$	0.527263	+	0.913245i	0.0804068	+	0.139269i	0.903425	−	0.428747i	$-0.141045\pi$
$43$	0.527263	+	0.913245i	0.0804068	+	0.139269i	−0.823018	+	0.568015i	$0.807711\pi$
$44$	1.03855	+	0.599608i	0.156567	+	0.0903943i
$45$	2.86299	+	2.22921i	0.426790	+	0.332310i
$46$	−1.81013	+	3.13524i	−0.266889	+	0.462265i
$47$	−3.56307	+	6.17142i	−0.519728	+	0.900195i	0.480009	+	0.877263i	$0.340633\pi$
$47$	−3.56307	+	6.17142i	−0.519728	+	0.900195i	−0.999737	+	0.0229314i	$0.992700\pi$
$48$	−1.63815	−	0.562548i	−0.236447	−	0.0811967i
$49$	5.05798	+	4.83910i	0.722568	+	0.691300i
$50$	−3.06322	−	1.76855i	−0.433205	−	0.250111i
$51$	−1.73863	−	8.90520i	−0.243457	−	1.24698i
$52$	−3.60274	+	0.142382i	−0.499610	+	0.0197449i
$53$	1.91564	−	1.10599i	0.263133	−	0.151920i	−0.362630	−	0.931933i	$-0.618121\pi$
$53$	1.91564	−	1.10599i	0.263133	−	0.151920i	0.625763	+	0.780013i	$0.284788\pi$
$54$	4.63564	+	2.34752i	0.630830	+	0.319457i
$55$	−1.25613	−	0.725228i	−0.169377	−	0.0977897i
$56$	0.985399	−	2.45540i	0.131680	−	0.328117i
$57$	−8.36910	−	9.61150i	−1.10851	−	1.27307i
$58$	1.65432			0.217222
$59$	−5.63264	+	9.75602i	−0.733308	+	1.27013i	0.222154	+	0.975012i	$0.428691\pi$
$59$	−5.63264	+	9.75602i	−0.733308	+	1.27013i	−0.955462	+	0.295115i	$0.904642\pi$
$60$	1.98135	+	0.680403i	0.255791	+	0.0878397i
$61$		−	6.61123i		−	0.846481i	−0.906017	−	0.423241i	$-0.860893\pi$
$61$		−	6.61123i		−	0.846481i	0.906017	−	0.423241i	$-0.139107\pi$
$62$	1.99568	−	3.45662i	0.253452	−	0.438991i
$63$	−3.94123	+	6.88961i	−0.496548	+	0.868009i
$64$	−1.00000			−0.125000
$65$	4.35752	−	0.172212i	0.540484	−	0.0213602i
$66$	−1.96450	−	0.674616i	−0.241813	−	0.0830395i
$67$	10.7447			1.31268			0.656338	−	0.754467i	$-0.272105\pi$
$67$	10.7447			1.31268			0.656338	+	0.754467i	$0.272105\pi$
$68$	−2.61925	−	4.53667i	−0.317630	−	0.550152i
$69$	2.03657	−	5.93053i	0.245174	−	0.713952i
$70$	−1.19184	+	2.96981i	−0.142453	+	0.354961i
$71$	−6.08827	+	3.51507i	−0.722545	+	0.417162i	−0.815689	−	0.578491i	$-0.803642\pi$
$71$	−6.08827	+	3.51507i	−0.722545	+	0.417162i	0.0931436	+	0.995653i	$0.470308\pi$
$72$	2.97149	+	0.412611i	0.350193	+	0.0486266i
$73$	5.40931	−	3.12307i	0.633112	−	0.365527i	−0.148845	−	0.988861i	$-0.547555\pi$
$73$	5.40931	−	3.12307i	0.633112	−	0.365527i	0.781956	+	0.623333i	$0.214222\pi$
$74$	7.79774	+	4.50203i	0.906468	+	0.523350i
$75$	5.79431	+	1.98979i	0.669069	+	0.229761i
$76$	−6.37226	−	3.67902i	−0.730948	−	0.422013i
$77$	1.18171	−	2.94455i	0.134668	−	0.335563i
$78$	6.07724	−	1.43778i	0.688112	−	0.162796i
$79$	2.23131	−	3.86475i	0.251042	−	0.434818i	−0.712771	−	0.701397i	$-0.752560\pi$
$79$	2.23131	−	3.86475i	0.251042	−	0.434818i	0.963813	+	0.266579i	$0.0858934\pi$
$80$	1.20950			0.135227
$81$	−8.65951	−	2.45214i	−0.962167	−	0.272460i
$82$			0.182888i			0.0201966i
$83$	16.6675			1.82949			0.914747	−	0.404027i	$-0.132390\pi$
$83$	16.6675			1.82949			0.914747	+	0.404027i	$0.132390\pi$
$84$	−0.860198	+	4.50112i	−0.0938553	+	0.491112i
$85$	3.16799	+	5.48712i	0.343617	+	0.595161i
$86$	−0.913245	−	0.527263i	−0.0984778	−	0.0568562i
$87$	−2.81226	+	0.549060i	−0.301506	+	0.0588654i
$88$	−1.19922			−0.127837
$89$	−3.59604	−	6.22852i	−0.381179	−	0.660222i	0.610052	−	0.792362i	$-0.291149\pi$
$89$	−3.59604	−	6.22852i	−0.381179	−	0.660222i	−0.991231	+	0.132139i	$0.957815\pi$
$90$	−3.59403	−	0.499054i	−0.378844	−	0.0526049i
$91$	1.72149	+	9.38277i	0.180461	+	0.983582i
$92$		−	3.62026i		−	0.377438i
$93$	−2.24533	+	6.53845i	−0.232830	+	0.678006i
$94$		−	7.12615i		−	0.735006i
$95$	7.70727	+	4.44979i	0.790749	+	0.456539i
$96$	1.69995	−	0.331895i	0.173501	−	0.0338739i
$97$	11.8894	−	6.86436i	1.20719	−	0.696970i	0.245044	−	0.969512i	$-0.421198\pi$
$97$	11.8894	−	6.86436i	1.20719	−	0.696970i	0.962144	+	0.272541i	$0.0878642\pi$
$98$	−6.79989	−	1.66179i	−0.686892	−	0.167867i
$99$	3.56346	+	0.494809i	0.358141	+	0.0497302i
$100$	3.53710			0.353710
$101$	3.25021			0.323408			0.161704	−	0.986839i	$-0.448301\pi$
$101$	3.25021			0.323408			0.161704	+	0.986839i	$0.448301\pi$
$102$	5.95830	+	6.84282i	0.589960	+	0.677540i
$103$	−0.504870	−	0.291487i	−0.0497463	−	0.0287210i	0.474921	−	0.880029i	$-0.342477\pi$
$103$	−0.504870	−	0.291487i	−0.0497463	−	0.0287210i	−0.524667	+	0.851308i	$0.675810\pi$
$104$	3.04887	−	1.92468i	0.298967	−	0.188730i
$105$	1.04041	−	5.44412i	0.101534	−	0.531291i
$106$	−1.10599	+	1.91564i	−0.107424	+	0.186063i
$107$	−8.21634	+	4.74371i	−0.794304	+	0.458592i	−0.841476	−	0.540295i	$-0.818313\pi$
$107$	−8.21634	+	4.74371i	−0.794304	+	0.458592i	0.0471717	+	0.998887i	$0.484979\pi$
$108$	−5.18834	+	0.284804i	−0.499248	+	0.0274053i
$109$	6.23249	+	10.7950i	0.596964	+	1.03397i	0.993266	+	0.115852i	$0.0369599\pi$
$109$	6.23249	+	10.7950i	0.596964	+	1.03397i	−0.396302	+	0.918120i	$0.629707\pi$
$110$	1.45046			0.138295
$111$	−14.7500	−	5.06521i	−1.40001	−	0.480768i
$112$	0.374319	+	2.61914i	0.0353698	+	0.247485i
$113$	−9.73622	+	5.62121i	−0.915907	+	0.528799i	−0.882327	−	0.470637i	$-0.844024\pi$
$113$	−9.73622	+	5.62121i	−0.915907	+	0.528799i	−0.0335797	+	0.999436i	$0.510691\pi$
$114$	12.0536	+	4.13925i	1.12892	+	0.387677i
$115$			4.37872i			0.408317i
$116$	−1.43268	+	0.827158i	−0.133021	+	0.0767997i
$117$	−9.85383	+	4.46116i	−0.910987	+	0.412434i
$118$		−	11.2653i		−	1.03705i
$119$	−10.9017	+	8.55833i	−0.999360	+	0.784541i
$120$	−2.05610	+	0.401428i	−0.187695	+	0.0366452i
$121$	9.56188			0.869262
$122$	3.30561	+	5.72549i	0.299276	+	0.518362i
$123$	−0.0606998	−	0.310902i	−0.00547311	−	0.0280331i
$124$			3.99136i			0.358435i
$125$	−10.3257			−0.923554
$126$	−0.0316014	−	7.93719i	−0.00281527	−	0.707101i
$127$	−5.39553	+	9.34534i	−0.478776	+	0.829265i	−0.999704	−	0.0243362i	$-0.992253\pi$
$127$	−5.39553	+	9.34534i	−0.478776	+	0.829265i	0.520928	+	0.853601i	$0.325586\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	1.72747	+	0.593220i	0.152095	+	0.0522301i
$130$	−3.68762	+	2.32790i	−0.323426	+	0.204170i
$131$	−9.42418	+	16.3232i	−0.823394	+	1.42616i	0.0797457	+	0.996815i	$0.474589\pi$
$131$	−9.42418	+	16.3232i	−0.823394	+	1.42616i	−0.903140	+	0.429346i	$0.858744\pi$
$132$	2.03861	−	0.398014i	0.177438	−	0.0346427i
$133$	−7.25062	+	18.0670i	−0.628708	+	1.56660i
$134$	−9.30520	+	5.37236i	−0.803846	+	0.464101i
$135$	6.27532	−	0.344472i	0.540093	−	0.0296474i
$136$	4.53667	+	2.61925i	0.389016	+	0.224599i
$137$	9.25524	+	5.34351i	0.790728	+	0.456527i	0.840219	−	0.542247i	$-0.182426\pi$
$137$	9.25524	+	5.34351i	0.790728	+	0.456527i	−0.0494906	+	0.998775i	$0.515760\pi$
$138$	1.20155	+	6.15428i	0.102282	+	0.523887i
$139$	−2.36204	+	1.36372i	−0.200345	+	0.115669i	−0.596817	−	0.802378i	$-0.703568\pi$
$139$	−2.36204	+	1.36372i	−0.200345	+	0.115669i	0.396471	+	0.918047i	$0.370235\pi$
$140$	−0.452740	−	3.16786i	−0.0382635	−	0.267733i
$141$	2.36513	+	12.1141i	0.199180	+	1.02019i
$142$	3.51507	−	6.08827i	0.294978	−	0.510917i
$143$	3.65626	−	2.30810i	0.305751	−	0.193013i
$144$	−2.77969	+	1.12841i	−0.231641	+	0.0940345i
$145$	1.73283	−	1.00045i	0.143904	−	0.0830829i
$146$	−3.12307	+	5.40931i	−0.258467	+	0.447678i
$147$	12.1110	+	0.568124i	0.998902	+	0.0468581i
$148$	−9.00405			−0.740128
$149$			1.51291i			0.123943i	0.998078	+	0.0619714i	$0.0197387\pi$
$149$			1.51291i			0.123943i	−0.998078	+	0.0619714i	$0.980261\pi$
$150$	−6.01291	+	1.17395i	−0.490952	+	0.0958524i
$151$	1.52530	+	2.64189i	0.124127	+	0.214994i	0.921391	−	0.388636i	$-0.127054\pi$
$151$	1.52530	+	2.64189i	0.124127	+	0.214994i	−0.797264	+	0.603630i	$0.793720\pi$
$152$	7.35805			0.596817
$153$	−12.3999	−	9.65495i	−1.00248	−	0.780556i
$154$	0.448889	+	3.14091i	0.0361725	+	0.253102i
$155$		−	4.82756i		−	0.387759i
$156$	−4.54415	+	4.28377i	−0.363823	+	0.342976i
$157$	2.30973	−	1.33352i	0.184336	−	0.106427i	−0.404992	−	0.914320i	$-0.632726\pi$
$157$	2.30973	−	1.33352i	0.184336	−	0.106427i	0.589328	+	0.807894i	$0.299392\pi$
$158$			4.46262i			0.355027i
$159$	1.24435	−	3.62357i	0.0986833	−	0.287368i
$160$	−1.04746	+	0.604752i	−0.0828090	+	0.0478098i
$161$	−9.48196	+	1.35513i	−0.747283	+	0.106799i
$162$	8.72542	−	2.20614i	0.685534	−	0.173331i
$163$	−17.9191			−1.40353			−0.701766	−	0.712408i	$-0.747605\pi$
$163$	−17.9191			−1.40353			−0.701766	+	0.712408i	$0.747605\pi$
$164$	−0.0914442	−	0.158386i	−0.00714059	−	0.0123679i
$165$	−2.46571	+	0.481399i	−0.191955	+	0.0374769i
$166$	−14.4345	+	8.33374i	−1.12033	+	0.646824i
$167$	9.94539	−	17.2259i	0.769597	−	1.33298i	−0.168184	−	0.985756i	$-0.553790\pi$
$167$	9.94539	−	17.2259i	0.769597	−	1.33298i	0.937782	−	0.347226i	$-0.112876\pi$
$168$	−1.50561	−	4.32818i	−0.116160	−	0.333926i
$169$	−5.59124	+	11.7362i	−0.430096	+	0.902783i
$170$	−5.48712	−	3.16799i	−0.420843	−	0.242974i
$171$	−21.8644	−	3.03601i	−1.67201	−	0.232169i
$172$	1.05453			0.0804068
$173$	17.5486			1.33419			0.667096	−	0.744971i	$-0.267537\pi$
$173$	17.5486			1.33419			0.667096	+	0.744971i	$0.267537\pi$
$174$	2.16096	−	1.88163i	0.163822	−	0.142646i
$175$	−1.32400	−	9.26416i	−0.100085	−	0.700305i
$176$	1.03855	−	0.599608i	0.0782837	−	0.0451971i
$177$	3.73890	+	19.1505i	0.281033	+	1.43944i
$178$	6.22852	+	3.59604i	0.466848	+	0.269535i
$179$		−	22.9984i		−	1.71898i	−0.511152	−	0.859490i	$-0.670781\pi$
$179$		−	22.9984i		−	1.71898i	0.511152	−	0.859490i	$-0.329219\pi$
$180$	3.36205	−	1.36482i	0.250592	−	0.101728i
$181$		−	7.49251i		−	0.556914i	−0.960449	−	0.278457i	$-0.910177\pi$
$181$		−	7.49251i		−	0.556914i	0.960449	−	0.278457i	$-0.0898230\pi$
$182$	−6.18224	−	7.26498i	−0.458258	−	0.538516i
$183$	−7.51966	−	8.63596i	−0.555869	−	0.638388i
$184$	1.81013	+	3.13524i	0.133445	+	0.231133i
$185$	10.8904			0.800680
$186$	−1.32471	−	6.78513i	−0.0971327	−	0.497510i
$187$	5.44045	+	3.14104i	0.397845	+	0.229696i
$188$	3.56307	+	6.17142i	0.259864	+	0.450097i
$189$	2.68804	+	13.4824i	0.195526	+	0.980699i
$190$	−8.89958			−0.645644
$191$			20.6038i			1.49084i	0.666596	+	0.745419i	$0.267751\pi$
$191$			20.6038i			1.49084i	−0.666596	+	0.745419i	$0.732249\pi$
$192$	−1.30626	+	1.13741i	−0.0942709	+	0.0820853i
$193$	7.99346			0.575382			0.287691	−	0.957723i	$-0.407112\pi$
$193$	7.99346			0.575382			0.287691	+	0.957723i	$0.407112\pi$
$194$	−6.86436	+	11.8894i	−0.492833	+	0.853611i
$195$	5.49617	−	5.18123i	0.393589	−	0.371036i
$196$	6.71977	−	1.96079i	0.479984	−	0.140056i
$197$	12.3941	+	7.15573i	0.883042	+	0.509825i	0.871660	−	0.490111i	$-0.163044\pi$
$197$	12.3941	+	7.15573i	0.883042	+	0.509825i	0.0113819	+	0.999935i	$0.496377\pi$
$198$	−3.33345	+	1.35321i	−0.236898	+	0.0961686i
$199$	2.84181	+	1.64072i	0.201451	+	0.116308i	0.597332	−	0.801994i	$-0.296227\pi$
$199$	2.84181	+	1.64072i	0.201451	+	0.116308i	−0.395881	+	0.918302i	$0.629561\pi$
$200$	−3.06322	+	1.76855i	−0.216602	+	0.125055i
$201$	14.0353	−	12.2211i	0.989977	−	0.862011i
$202$	−2.81477	+	1.62511i	−0.198046	+	0.114342i
$203$	2.70272	+	3.44277i	0.189694	+	0.241635i
$204$	−8.58145	−	2.94690i	−0.600822	−	0.206324i
$205$	0.110602	+	0.191568i	0.00772478	+	0.0133797i
$206$	0.582974			0.0406177
$207$	−4.08515	−	10.0632i	−0.283938	−	0.699441i
$208$	−1.67806	+	3.19125i	−0.116353	+	0.221274i
$209$	8.82389			0.610361
$210$	1.82103	+	5.23495i	0.125663	+	0.361246i
$211$	5.52912	−	9.57673i	0.380641	−	0.659289i	−0.610513	−	0.792006i	$-0.709037\pi$
$211$	5.52912	−	9.57673i	0.380641	−	0.659289i	0.991154	+	0.132717i	$0.0423702\pi$
$212$		−	2.21199i		−	0.151920i
$213$	−3.95478	+	11.5164i	−0.270977	+	0.789092i
$214$	4.74371	−	8.21634i	0.324273	−	0.561658i
$215$	−1.27545			−0.0869851
$216$	4.35083	−	2.84082i	0.296037	−	0.193293i
$217$	10.4539	−	1.49404i	0.709658	−	0.101422i
$218$	−10.7950	−	6.23249i	−0.731129	−	0.422117i
$219$	3.51375	−	10.2321i	0.237437	−	0.691422i
$220$	−1.25613	+	0.725228i	−0.0846883	+	0.0488948i
$221$	−18.8729	+	0.745868i	−1.26953	+	0.0501725i
$222$	15.3065	−	2.98840i	1.02730	−	0.200568i
$223$	−10.5899	−	6.11409i	−0.709153	−	0.409429i	0.101595	−	0.994826i	$-0.467606\pi$
$223$	−10.5899	−	6.11409i	−0.709153	−	0.409429i	−0.810747	+	0.585396i	$0.800939\pi$
$224$	−1.63374	−	2.08108i	−0.109159	−	0.139048i
$225$	9.83205	−	3.99131i	0.655470	−	0.266088i
$226$	5.62121	−	9.73622i	0.373917	−	0.647644i
$227$	14.5055	−	25.1243i	0.962766	−	1.66756i	0.247266	−	0.968948i	$-0.420468\pi$
$227$	14.5055	−	25.1243i	0.962766	−	1.66756i	0.715500	−	0.698613i	$-0.246199\pi$
$228$	−12.5083	+	2.44210i	−0.828386	+	0.161732i
$229$	24.0075	+	13.8607i	1.58646	+	0.915943i	0.993884	+	0.110428i	$0.0352222\pi$
$229$	24.0075	+	13.8607i	1.58646	+	0.915943i	0.592576	+	0.805515i	$0.298111\pi$
$230$	−2.18936	−	3.79208i	−0.144362	−	0.250042i
$231$	−1.80555	−	5.19042i	−0.118796	−	0.341505i
$232$	0.827158	−	1.43268i	0.0543056	−	0.0940601i
$233$	3.05589	+	1.76432i	0.200198	+	0.115584i	0.596748	−	0.802429i	$-0.296459\pi$
$233$	3.05589	+	1.76432i	0.200198	+	0.115584i	−0.396550	+	0.918013i	$0.629793\pi$
$234$	6.30309	−	8.79039i	0.412046	−	0.574646i
$235$	−4.30955	−	7.46436i	−0.281124	−	0.486921i
$236$	5.63264	+	9.75602i	0.366654	+	0.635063i
$237$	−1.48112	−	7.58626i	−0.0962093	−	0.492780i
$238$	5.16201	−	12.8626i	0.334603	−	0.833759i
$239$		−	7.54413i		−	0.487989i	−0.969777	−	0.243994i	$-0.921542\pi$
$239$		−	7.54413i		−	0.487989i	0.969777	−	0.243994i	$-0.0784579\pi$
$240$	1.57992	−	1.37570i	0.101983	−	0.0888009i
$241$	−10.6818	−	6.16717i	−0.688078	−	0.397262i	0.114814	−	0.993387i	$-0.463373\pi$
$241$	−10.6818	−	6.16717i	−0.688078	−	0.397262i	−0.802892	+	0.596125i	$0.796706\pi$
$242$	−8.28083	+	4.78094i	−0.532312	+	0.307331i
$243$	−14.1006	+	6.64626i	−0.904554	+	0.426358i
$244$	−5.72549	−	3.30561i	−0.366537	−	0.211620i
$245$	−8.12758	+	2.37158i	−0.519252	+	0.151515i
$246$	0.208018	+	0.238899i	0.0132628	+	0.0152316i
$247$	−22.4338	+	14.1619i	−1.42743	+	0.901098i
$248$	−1.99568	−	3.45662i	−0.126726	−	0.219495i
$249$	21.7720	−	18.9577i	1.37974	−	1.20140i
$250$	8.94228	−	5.16283i	0.565559	−	0.326526i
$251$	5.07909	+	8.79724i	0.320589	+	0.555277i	0.980610	−	0.195971i	$-0.0627858\pi$
$251$	5.07909	+	8.79724i	0.320589	+	0.555277i	−0.660020	+	0.751248i	$0.729452\pi$
$252$	3.99596	+	6.85801i	0.251722	+	0.432014i
$253$	2.17074	+	3.75983i	0.136473	+	0.236378i
$254$		−	10.7911i		−	0.677092i
$255$	10.3793	+	3.56429i	0.649976	+	0.223204i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−6.83862	−	11.8448i	−0.426581	−	0.738860i	0.569985	−	0.821655i	$-0.306949\pi$
$257$	−6.83862	−	11.8448i	−0.426581	−	0.738860i	−0.996567	+	0.0827945i	$0.973615\pi$
$258$	−1.79264	+	0.349992i	−0.111605	+	0.0217895i
$259$	3.37039	+	23.5829i	0.209426	+	1.46537i
$260$	2.02962	−	3.85983i	0.125872	−	0.239377i
$261$	−3.04903	+	3.91590i	−0.188730	+	0.242388i
$262$		−	18.8484i		−	1.16446i
$263$			21.5058i			1.32610i	0.748574	+	0.663051i	$0.230739\pi$
$263$			21.5058i			1.32610i	−0.748574	+	0.663051i	$0.769261\pi$
$264$	−1.56648	+	1.36400i	−0.0964104	+	0.0839482i
$265$			2.67541i			0.164349i
$266$	−2.75426	−	19.2717i	−0.168874	−	1.18163i
$267$	−11.7817	−	4.04589i	−0.721029	−	0.247604i
$268$	5.37236	−	9.30520i	0.328169	−	0.568405i
$269$	14.0784	−	24.3845i	0.858373	−	1.48675i	−0.0151065	−	0.999886i	$-0.504809\pi$
$269$	14.0784	−	24.3845i	0.858373	−	1.48675i	0.873480	−	0.486860i	$-0.161858\pi$
$270$	−5.26235	+	3.43598i	−0.320256	+	0.209107i
$271$	2.61384	−	1.50910i	0.158779	−	0.0916712i	−0.418505	−	0.908214i	$-0.637446\pi$
$271$	2.61384	−	1.50910i	0.158779	−	0.0916712i	0.577284	+	0.816543i	$0.304112\pi$
$272$	−5.23850			−0.317630
$273$	12.9207	+	10.2983i	0.781999	+	0.623280i
$274$	−10.6870			−0.645627
$275$	−3.67346	+	2.12087i	−0.221518	+	0.127894i
$276$	−4.11771	−	4.72899i	−0.247857	−	0.284652i
$277$	5.66656	−	9.81478i	0.340471	−	0.589713i	−0.644049	−	0.764984i	$-0.722747\pi$
$277$	5.66656	−	9.81478i	0.340471	−	0.589713i	0.984520	+	0.175271i	$0.0560802\pi$
$278$	1.36372	−	2.36204i	0.0817906	−	0.141665i
$279$	4.50390	+	11.0947i	0.269642	+	0.664225i
$280$	1.97601	+	2.51707i	0.118089	+	0.150424i
$281$		−	8.18525i		−	0.488291i	−0.969739	−	0.244146i	$-0.921493\pi$
$281$		−	8.18525i		−	0.488291i	0.969739	−	0.244146i	$-0.0785075\pi$
$282$	−8.10533	−	9.30857i	−0.482665	−	0.554317i
$283$		−	13.0035i		−	0.772980i	−0.922294	−	0.386490i	$-0.873687\pi$
$283$		−	13.0035i		−	0.772980i	0.922294	−	0.386490i	$-0.126313\pi$
$284$			7.03013i			0.417162i
$285$	15.1289	−	2.95373i	0.896158	−	0.174964i
$286$	−2.01236	+	3.82700i	−0.118993	+	0.226295i
$287$	−0.380605	+	0.298792i	−0.0224664	+	0.0176371i
$288$	1.84308	−	2.36708i	0.108604	−	0.139482i
$289$	−5.22092	−	9.04289i	−0.307113	−	0.531935i
$290$	−1.00045	+	1.73283i	−0.0587485	+	0.101755i
$291$	7.72306	−	22.4897i	0.452734	−	1.31837i
$292$		−	6.24613i		−	0.365527i
$293$	−9.77684	−	16.9340i	−0.571169	−	0.989294i	−0.996446	−	0.0842309i	$-0.973157\pi$
$293$	−9.77684	−	16.9340i	−0.571169	−	0.989294i	0.425277	−	0.905063i	$-0.360177\pi$
$294$	−10.7725	+	5.56351i	−0.628267	+	0.324470i
$295$	−6.81270	−	11.7999i	−0.396651	−	0.687019i
$296$	7.79774	−	4.50203i	0.453234	−	0.261675i
$297$	5.21759	−	3.40675i	0.302755	−	0.197680i
$298$	−0.756457	−	1.31022i	−0.0438204	−	0.0758991i
$299$	−11.5532	−	6.07502i	−0.668137	−	0.351328i
$300$	4.62036	−	4.02312i	0.266757	−	0.232275i
$301$	−0.394729	−	2.76195i	−0.0227518	−	0.159196i
$302$	−2.64189	−	1.52530i	−0.152024	−	0.0877710i
$303$	4.24561	−	3.69682i	0.243904	−	0.212377i
$304$	−6.37226	+	3.67902i	−0.365474	+	0.211007i
$305$	6.92500	+	3.99815i	0.396524	+	0.228933i
$306$	15.5661	+	2.16146i	0.889857	+	0.123562i
$307$			27.7274i			1.58248i	0.611503	+	0.791242i	$0.290565\pi$
$307$			27.7274i			1.58248i	−0.611503	+	0.791242i	$0.709435\pi$
$308$	−1.95921	−	2.49566i	−0.111636	−	0.142204i
$309$	−0.991029	+	0.193486i	−0.0563776	+	0.0110070i
$310$	2.41378	+	4.18079i	0.137094	+	0.237453i
$311$	−3.82623	−	6.62722i	−0.216965	−	0.375795i	0.736913	−	0.675987i	$-0.236283\pi$
$311$	−3.82623	−	6.62722i	−0.216965	−	0.375795i	−0.953879	+	0.300192i	$0.902949\pi$
$312$	1.79347	−	5.98193i	0.101535	−	0.338660i
$313$	3.76450	+	2.17344i	0.212782	+	0.122850i	0.602604	−	0.798041i	$-0.294130\pi$
$313$	3.76450	+	2.17344i	0.212782	+	0.122850i	−0.389821	+	0.920890i	$0.627463\pi$
$314$	−1.33352	+	2.30973i	−0.0752550	+	0.130345i
$315$	−4.83313	−	8.29478i	−0.272316	−	0.467358i
$316$	−2.23131	−	3.86475i	−0.125521	−	0.217409i
$317$	13.4867	+	7.78654i	0.757488	+	0.437336i	0.828393	−	0.560147i	$-0.189255\pi$
$317$	13.4867	+	7.78654i	0.757488	+	0.437336i	−0.0709052	+	0.997483i	$0.522589\pi$
$318$	0.734148	+	3.76028i	0.0411690	+	0.210866i
$319$	0.991941	−	1.71809i	0.0555380	−	0.0961947i
$320$	0.604752	−	1.04746i	0.0338066	−	0.0585548i
$321$	−5.33712	+	15.5418i	−0.297889	+	0.867460i
$322$	7.53405	−	5.91456i	0.419856	−	0.329605i
$323$	−33.3810	−	19.2726i	−1.85737	−	1.07235i
$324$	−6.45336	+	6.27328i	−0.358520	+	0.348516i
$325$	5.93548	−	11.2878i	0.329241	−	0.626134i
$326$	15.5184	−	8.95954i	0.859484	−	0.496223i
$327$	20.4195	+	7.01214i	1.12920	+	0.387772i
$328$	0.158386	+	0.0914442i	0.00874540	+	0.00504916i
$329$	14.8301	−	11.6423i	0.817609	−	0.641859i
$330$	1.89467	−	1.64976i	0.104298	−	0.0908162i
$331$	−15.6922			−0.862520			−0.431260	−	0.902228i	$-0.641931\pi$
$331$	−15.6922			−0.862520			−0.431260	+	0.902228i	$0.641931\pi$
$332$	8.33374	−	14.4345i	0.457374	−	0.792194i
$333$	−25.0285	+	10.1603i	−1.37155	+	0.556781i
$334$			19.8908i			1.08837i
$335$	−6.49788	+	11.2547i	−0.355017	+	0.614908i
$336$	3.46798	+	2.99551i	0.189194	+	0.163419i
$337$	0.251195			0.0136835			0.00684174	−	0.999977i	$-0.497822\pi$
$337$	0.251195			0.0136835			0.00684174	+	0.999977i	$0.497822\pi$
$338$	−1.02593	−	12.9595i	−0.0558033	−	0.704901i
$339$	−6.32440	+	18.4168i	−0.343494	+	1.00026i
$340$	6.33598			0.343617
$341$	−2.39325	−	4.14523i	−0.129602	−	0.224477i
$342$	20.4531	−	8.30292i	1.10598	−	0.448971i
$343$	−7.65091	−	16.8660i	−0.413110	−	0.910681i
$344$	−0.913245	+	0.527263i	−0.0492389	+	0.0284281i
$345$	4.98038	+	5.71972i	0.268135	+	0.307940i
$346$	−15.1975	+	8.77428i	−0.817023	+	0.471708i
$347$	18.4144	+	10.6315i	0.988535	+	0.570731i	0.904836	−	0.425760i	$-0.139993\pi$
$347$	18.4144	+	10.6315i	0.988535	+	0.570731i	0.0836992	+	0.996491i	$0.473326\pi$
$348$	−0.930632	+	2.71002i	−0.0498871	+	0.145272i
$349$	−3.33934	−	1.92797i	−0.178751	−	0.103202i	0.407955	−	0.913002i	$-0.366242\pi$
$349$	−3.33934	−	1.92797i	−0.178751	−	0.103202i	−0.586706	+	0.809800i	$0.699575\pi$
$350$	5.77870	+	7.36099i	0.308885	+	0.393462i
$351$	−7.79748	+	17.0352i	−0.416199	+	0.909274i
$352$	−0.599608	+	1.03855i	−0.0319592	+	0.0553550i
$353$	8.71387			0.463792			0.231896	−	0.972741i	$-0.425507\pi$
$353$	8.71387			0.463792			0.231896	+	0.972741i	$0.425507\pi$
$354$	−12.8132	−	14.7154i	−0.681015	−	0.782112i
$355$		−	8.50297i		−	0.451291i
$356$	−7.19208			−0.381179
$357$	−4.50615	+	23.5791i	−0.238491	+	1.24794i
$358$	11.4992	+	19.9172i	0.607751	+	1.05266i
$359$	−17.7662	−	10.2573i	−0.937663	−	0.541360i	−0.0484360	−	0.998826i	$-0.515424\pi$
$359$	−17.7662	−	10.2573i	−0.937663	−	0.541360i	−0.889227	+	0.457466i	$0.848757\pi$
$360$	−2.22921	+	2.86299i	−0.117489	+	0.150893i
$361$	−35.1409			−1.84952
$362$	3.74626	+	6.48871i	0.196899	+	0.341039i
$363$	12.4903	−	10.8758i	0.655569	−	0.570829i
$364$	8.98647	+	3.20053i	0.471019	+	0.167753i
$365$			7.55472i			0.395432i
$366$	10.8302	+	3.71913i	0.566103	+	0.194402i
$367$			23.8743i			1.24623i	0.782131	+	0.623114i	$0.214133\pi$
$367$			23.8743i			1.24623i	−0.782131	+	0.623114i	$0.785867\pi$
$368$	−3.13524	−	1.81013i	−0.163436	−	0.0943595i
$369$	−0.432911	−	0.337077i	−0.0225365	−	0.0175475i
$370$	−9.43139	+	5.44521i	−0.490314	+	0.283083i
$371$	−5.79350	+	0.827989i	−0.300784	+	0.0429871i
$372$	4.53980	+	5.21374i	0.235378	+	0.270320i
$373$	3.06102			0.158493			0.0792467	−	0.996855i	$-0.474749\pi$
$373$	3.06102			0.158493			0.0792467	+	0.996855i	$0.474749\pi$
$374$	−6.28209			−0.324839
$375$	−13.4879	+	11.7445i	−0.696515	+	0.606482i
$376$	−6.17142	−	3.56307i	−0.318267	−	0.183751i
$377$	0.235545	+	5.96007i	0.0121312	+	0.306959i
$378$	−9.06910	−	10.3321i	−0.466464	−	0.531424i
$379$	8.74613	−	15.1487i	0.449259	−	0.778139i	−0.549079	−	0.835770i	$-0.685021\pi$
$379$	8.74613	−	15.1487i	0.449259	−	0.778139i	0.998338	+	0.0576314i	$0.0183548\pi$
$380$	7.70727	−	4.44979i	0.395374	−	0.228270i
$381$	3.58150	+	18.3443i	0.183486	+	0.939808i
$382$	−10.3019	−	17.8434i	−0.527091	−	0.912948i
$383$	−28.4752			−1.45501			−0.727506	−	0.686101i	$-0.759321\pi$
$383$	−28.4752			−1.45501			−0.727506	+	0.686101i	$0.759321\pi$
$384$	0.562548	−	1.63815i	0.0287074	−	0.0835966i
$385$	2.36967	+	3.01851i	0.120769	+	0.153838i
$386$	−6.92254	+	3.99673i	−0.352348	+	0.203428i
$387$	2.93125	−	1.18994i	0.149004	−	0.0604881i
$388$		−	13.7287i		−	0.696970i
$389$	−31.0564	+	17.9304i	−1.57462	+	0.909107i	−0.579029	+	0.815307i	$0.696568\pi$
$389$	−31.0564	+	17.9304i	−1.57462	+	0.909107i	−0.995591	+	0.0938003i	$0.970098\pi$
$390$	−2.16921	+	7.23516i	−0.109842	+	0.366367i
$391$		−	18.9647i		−	0.959087i
$392$	−4.83910	+	5.05798i	−0.244411	+	0.255466i
$393$	6.25568	+	32.0414i	0.315557	+	1.61627i
$394$	−14.3115			−0.721001
$395$	2.69878	+	4.67442i	0.135790	+	0.235196i
$396$	2.21025	−	2.83864i	0.111069	−	0.142647i
$397$		−	33.2599i		−	1.66927i	−0.550806	−	0.834633i	$-0.685680\pi$
$397$		−	33.2599i		−	1.66927i	0.550806	−	0.834633i	$-0.314320\pi$
$398$	−3.28144			−0.164484
$399$	11.0783	+	31.8470i	0.554610	+	1.59434i
$400$	1.76855	−	3.06322i	0.0884276	−	0.153161i
$401$	−5.40499	+	3.12057i	−0.269912	+	0.155834i	−0.628848	−	0.777528i	$-0.716473\pi$
$401$	−5.40499	+	3.12057i	−0.269912	+	0.155834i	0.358936	+	0.933362i	$0.383140\pi$
$402$	−6.04441	+	17.6015i	−0.301468	+	0.877881i
$403$	12.7374	+	6.69775i	0.634497	+	0.333639i
$404$	1.62511	−	2.81477i	0.0808521	−	0.140040i
$405$	7.80537	−	7.58756i	0.387852	−	0.377029i
$406$	−4.06201	−	1.63016i	−0.201594	−	0.0809036i
$407$	9.35117	−	5.39890i	0.463520	−	0.267614i
$408$	8.90520	−	1.73863i	0.440873	−	0.0860751i
$409$	26.8373	+	15.4945i	1.32702	+	0.766154i	0.984837	−	0.173481i	$-0.0555014\pi$
$409$	26.8373	+	15.4945i	1.32702	+	0.766154i	0.342180	+	0.939634i	$0.388835\pi$
$410$	−0.191568	−	0.110602i	−0.00946088	−	0.00546224i
$411$	18.1675	−	3.54697i	0.896135	−	0.174959i
$412$	−0.504870	+	0.291487i	−0.0248732	+	0.0143605i
$413$	23.4440	−	18.4045i	1.15360	−	0.905628i
$414$	8.56945	+	6.67241i	0.421165	+	0.327931i
$415$	−10.0797	+	17.4585i	−0.494792	+	0.857006i
$416$	−0.142382	−	3.60274i	−0.00698086	−	0.176639i
$417$	−1.53432	+	4.46797i	−0.0751358	+	0.218797i
$418$	−7.64171	+	4.41194i	−0.373768	+	0.215795i
$419$	12.6145	−	21.8489i	0.616258	−	1.06739i	−0.373904	−	0.927467i	$-0.621981\pi$
$419$	12.6145	−	21.8489i	0.616258	−	1.06739i	0.990162	−	0.139923i	$-0.0446856\pi$
$420$	−4.19454	−	3.62308i	−0.204672	−	0.176788i
$421$	−8.22465			−0.400845			−0.200422	−	0.979710i	$-0.564231\pi$
$421$	−8.22465			−0.400845			−0.200422	+	0.979710i	$0.564231\pi$
$422$			11.0582i			0.538307i
$423$	16.8682	+	13.1340i	0.820158	+	0.638598i
$424$	1.10599	+	1.91564i	0.0537118	+	0.0930316i
$425$	18.5291			0.898793
$426$	−2.33327	−	11.9509i	−0.113047	−	0.579023i
$427$	−6.51470	+	16.2332i	−0.315268	+	0.785580i
$428$			9.48742i			0.458592i
$429$	2.15076	−	7.17362i	0.103839	−	0.346346i
$430$	1.10457	−	0.637726i	0.0532673	−	0.0307539i
$431$			19.9545i			0.961177i	0.876946	+	0.480588i	$0.159577\pi$
$431$			19.9545i			0.961177i	−0.876946	+	0.480588i	$0.840423\pi$
$432$	−2.34752	+	4.63564i	−0.112945	+	0.223032i
$433$	19.2106	−	11.0912i	0.923202	−	0.533011i	0.0385467	−	0.999257i	$-0.487727\pi$
$433$	19.2106	−	11.0912i	0.923202	−	0.533011i	0.884655	+	0.466246i	$0.154394\pi$
$434$	−8.30634	+	6.52084i	−0.398717	+	0.313010i
$435$	1.12560	−	3.27778i	0.0539685	−	0.157157i
$436$	12.4650			0.596964
$437$	−13.3190	−	23.0692i	−0.637135	−	1.10355i
$438$	2.07306	+	10.6181i	0.0990547	+	0.507354i
$439$	−23.6668	+	13.6641i	−1.12956	+	0.652150i	−0.943823	−	0.330451i	$-0.892799\pi$
$439$	−23.6668	+	13.6641i	−1.12956	+	0.652150i	−0.185733	+	0.982600i	$0.559466\pi$
$440$	0.725228	−	1.25613i	0.0345739	−	0.0598837i
$441$	16.4663	−	13.0331i	0.784110	−	0.620622i
$442$	15.9715	−	10.0824i	0.759687	−	0.479571i
$443$	−19.5551	−	11.2902i	−0.929093	−	0.536412i	−0.0425684	−	0.999094i	$-0.513554\pi$
$443$	−19.5551	−	11.2902i	−0.929093	−	0.536412i	−0.886525	+	0.462681i	$0.846887\pi$
$444$	−11.7616	+	10.2413i	−0.558181	+	0.486029i
$445$	8.69884			0.412365
$446$	12.2282			0.579021
$447$	1.72080	+	1.97625i	0.0813910	+	0.0934736i
$448$	2.45540	+	0.985399i	0.116007	+	0.0465557i
$449$	−7.97653	+	4.60525i	−0.376436	+	0.217335i	−0.676266	−	0.736657i	$-0.736403\pi$
$449$	−7.97653	+	4.60525i	−0.376436	+	0.217335i	0.299831	+	0.953992i	$0.403070\pi$
$450$	−6.51915	+	8.37261i	−0.307316	+	0.394688i
$451$	0.189939	+	0.109661i	0.00894387	+	0.00516375i
$452$			11.2424i			0.528799i
$453$	4.99734	+	1.71610i	0.234795	+	0.0806296i
$454$			29.0111i			1.36156i
$455$	−10.8692	−	3.87105i	−0.509554	−	0.181478i
$456$	9.61150	−	8.36910i	0.450100	−	0.391919i
$457$	3.32459	+	5.75837i	0.155518	+	0.269365i	0.933248	−	0.359234i	$-0.116962\pi$
$457$	3.32459	+	5.75837i	0.155518	+	0.269365i	−0.777730	+	0.628599i	$0.783629\pi$
$458$	−27.7215			−1.29534
$459$	−27.1791	+	1.49195i	−1.26861	+	0.0696381i
$460$	3.79208	+	2.18936i	0.176807	+	0.102079i
$461$	11.8184	+	20.4701i	0.550439	+	0.953388i	0.998243	+	0.0592563i	$0.0188729\pi$
$461$	11.8184	+	20.4701i	0.550439	+	0.953388i	−0.447804	+	0.894132i	$0.647794\pi$
$462$	4.15886	+	3.59227i	0.193488	+	0.167127i
$463$	8.09426			0.376172			0.188086	−	0.982153i	$-0.439772\pi$
$463$	8.09426			0.376172			0.188086	+	0.982153i	$0.439772\pi$
$464$			1.65432i			0.0767997i
$465$	−5.49090	−	6.30603i	−0.254634	−	0.292435i
$466$	−3.52864			−0.163461
$467$	−1.92869	+	3.34059i	−0.0892492	+	0.154584i	−0.907194	−	0.420713i	$-0.861780\pi$
$467$	−1.92869	+	3.34059i	−0.0892492	+	0.154584i	0.817945	+	0.575297i	$0.195113\pi$
$468$	−1.06344	+	10.7643i	−0.0491576	+	0.497578i
$469$	−26.3826	−	10.5878i	−1.21823	−	0.488901i
$470$	7.46436	+	4.30955i	0.344305	+	0.198785i
$471$	1.50034	−	4.36902i	0.0691320	−	0.201314i
$472$	−9.75602	−	5.63264i	−0.449057	−	0.259263i
$473$	−1.09518	+	0.632301i	−0.0503564	+	0.0290733i
$474$	5.07582	+	5.82933i	0.233140	+	0.267750i
$475$	22.5393	−	13.0131i	1.03418	−	0.597081i
$476$	1.96087	+	13.7203i	0.0898763	+	0.628871i
$477$	−2.49604	−	6.14864i	−0.114286	−	0.281527i
$478$	3.77206	+	6.53341i	0.172530	+	0.298831i
$479$	8.22973			0.376026			0.188013	−	0.982167i	$-0.439795\pi$
$479$	8.22973			0.376026			0.188013	+	0.982167i	$0.439795\pi$
$480$	−0.680403	+	1.98135i	−0.0310560	+	0.0904358i
$481$	−15.1094	+	28.7342i	−0.688928	+	1.31017i
$482$	12.3343			0.561813
$483$	−10.8445	+	12.5550i	−0.493443	+	0.571272i
$484$	4.78094	−	8.28083i	0.217315	−	0.376401i
$485$			16.6049i			0.753991i
$486$	8.88835	−	12.8061i	0.403184	−	0.580898i
$487$	11.5091	−	19.9343i	0.521525	−	0.903308i	−0.478162	−	0.878272i	$-0.658697\pi$
$487$	11.5091	−	19.9343i	0.521525	−	0.903308i	0.999687	−	0.0250358i	$-0.00796999\pi$
$488$	6.61123			0.299276
$489$	−23.4069	+	20.3813i	−1.05850	+	0.921674i
$490$	5.85290	−	6.11764i	0.264407	−	0.276367i
$491$	−25.3393	−	14.6297i	−1.14355	−	0.660228i	−0.196241	−	0.980556i	$-0.562873\pi$
$491$	−25.3393	−	14.6297i	−1.14355	−	0.660228i	−0.947307	+	0.320328i	$0.896207\pi$
$492$	−0.299599	−	0.102883i	−0.0135070	−	0.00463834i
$493$	−7.50509	+	4.33306i	−0.338012	+	0.195151i
$494$	12.3473	−	23.4814i	0.555530	−	1.05648i
$495$	−2.67330	+	3.43334i	−0.120156	+	0.154317i
$496$	3.45662	+	1.99568i	0.155207	+	0.0896086i
$497$	18.4129	−	2.63151i	0.825931	−	0.118039i
$498$	−9.37625	+	27.3039i	−0.420160	+	1.22352i
$499$	15.3836	−	26.6451i	0.688663	−	1.19280i	−0.283607	−	0.958941i	$-0.591531\pi$
$499$	15.3836	−	26.6451i	0.688663	−	1.19280i	0.972270	−	0.233859i	$-0.0751355\pi$
$500$	−5.16283	+	8.94228i	−0.230889	+	0.399911i
$501$	−6.60165	−	33.8134i	−0.294940	−	1.51067i
$502$	−8.79724	−	5.07909i	−0.392640	−	0.226691i
$503$	−10.0612	−	17.4265i	−0.448606	−	0.777008i	0.549690	−	0.835369i	$-0.314746\pi$
$503$	−10.0612	−	17.4265i	−0.448606	−	0.777008i	−0.998296	+	0.0583607i	$0.981413\pi$
$504$	−6.88961	−	3.94123i	−0.306888	−	0.175556i
$505$	−1.96557	+	3.40447i	−0.0874668	+	0.151497i
$506$	−3.75983	−	2.17074i	−0.167145	−	0.0965010i
$507$	6.04522	+	21.6900i	0.268478	+	0.963286i
$508$	5.39553	+	9.34534i	0.239388	+	0.414632i
$509$	−5.34216	−	9.25288i	−0.236787	−	0.410127i	0.723004	−	0.690844i	$-0.242761\pi$
$509$	−5.34216	−	9.25288i	−0.236787	−	0.410127i	−0.959790	+	0.280717i	$0.909428\pi$
$510$	−10.7709	+	2.10288i	−0.476942	+	0.0931171i
$511$	−16.3595	+	2.33805i	−0.723701	+	0.103429i
$512$		−	1.00000i		−	0.0441942i
$513$	−32.0136	+	20.9029i	−1.41344	+	0.922885i
$514$	11.8448	+	6.83862i	0.522453	+	0.301638i
$515$	0.610642	−	0.352554i	0.0269081	−	0.0155354i
$516$	1.37748	−	1.19942i	0.0606402	−	0.0528017i
$517$	−7.40087	−	4.27289i	−0.325490	−	0.187922i
$518$	−14.7103	−	18.7382i	−0.646332	−	0.823307i
$519$	22.9229	−	19.9599i	1.00620	−	0.876141i
$520$	0.172212	+	4.35752i	0.00755198	+	0.191090i
$521$	9.16008	+	15.8657i	0.401310	+	0.695090i	0.993884	−	0.110426i	$-0.0352215\pi$
$521$	9.16008	+	15.8657i	0.401310	+	0.695090i	−0.592574	+	0.805516i	$0.701888\pi$
$522$	0.682588	−	4.91579i	0.0298761	−	0.215158i
$523$	−1.26376	+	0.729631i	−0.0552603	+	0.0319045i	−0.527376	−	0.849632i	$-0.676824\pi$
$523$	−1.26376	+	0.729631i	−0.0552603	+	0.0319045i	0.472115	+	0.881537i	$0.343491\pi$
$524$	9.42418	+	16.3232i	0.411697	+	0.713081i
$525$	−12.2666	−	10.5954i	−0.535359	−	0.462423i
$526$	−10.7529	−	18.6245i	−0.468848	−	0.812069i
$527$			20.9087i			0.910798i
$528$	0.674616	−	1.96450i	0.0293589	−	0.0854938i
$529$	−4.94686	+	8.56821i	−0.215081	+	0.372531i
$530$	−1.33770	−	2.31697i	−0.0581061	−	0.100643i
$531$	26.6658	+	20.7628i	1.15720	+	0.901028i
$532$	12.0211	+	15.3127i	0.521182	+	0.663890i
$533$	−0.658899	+	0.0260400i	−0.0285401	+	0.00112792i
$534$	12.2262	−	2.38702i	0.529080	−	0.103296i
$535$		−	11.4751i		−	0.496110i
$536$			10.7447i			0.464101i
$537$	−26.1585	−	30.0418i	−1.12882	−	1.29640i
$538$			28.1567i			1.21392i
$539$	−5.80312	+	6.06560i	−0.249958	+	0.261264i
$540$	2.83934	−	5.60682i	0.122186	−	0.241279i
$541$	16.5670	−	28.6949i	0.712270	−	1.23369i	−0.251733	−	0.967797i	$-0.581000\pi$
$541$	16.5670	−	28.6949i	0.712270	−	1.23369i	0.964003	−	0.265892i	$-0.0856663\pi$
$542$	−1.50910	+	2.61384i	−0.0648213	+	0.112274i
$543$	−8.52204	−	9.78714i	−0.365716	−	0.420007i
$544$	4.53667	−	2.61925i	0.194508	−	0.112299i
$545$	−15.0764			−0.645803
$546$	−16.3388	−	2.45819i	−0.699237	−	0.105201i
$547$	29.1612			1.24684			0.623421	−	0.781886i	$-0.285742\pi$
$547$	29.1612			1.24684			0.623421	+	0.781886i	$0.285742\pi$
$548$	9.25524	−	5.34351i	0.395364	−	0.228264i
$549$	−19.6452	−	2.72786i	−0.838437	−	0.116422i
$550$	2.12087	−	3.67346i	0.0904344	−	0.156637i
$551$	−6.08627	+	10.5417i	−0.259284	+	0.449093i
$552$	5.93053	+	2.03657i	0.252420	+	0.0866821i
$553$	−9.28708	+	7.29076i	−0.394927	+	0.310035i
$554$			11.3331i			0.481499i
$555$	14.2257	−	12.3868i	0.603847	−	0.525792i
$556$			2.72744i			0.115669i
$557$		−	7.16241i		−	0.303481i	−0.988420	−	0.151741i	$-0.951512\pi$
$557$		−	7.16241i		−	0.303481i	0.988420	−	0.151741i	$-0.0484878\pi$
$558$	−9.44787	−	7.35638i	−0.399960	−	0.311420i
$559$	1.76956	−	3.36526i	0.0748444	−	0.142335i
$560$	−2.96981	−	1.19184i	−0.125498	−	0.0503646i
$561$	10.6793	−	2.08499i	0.450879	−	0.0880285i
$562$	4.09263	+	7.08863i	0.172637	+	0.299016i
$563$	19.6837	−	34.0933i	0.829571	−	1.43686i	−0.0688039	−	0.997630i	$-0.521918\pi$
$563$	19.6837	−	34.0933i	0.829571	−	1.43686i	0.898375	−	0.439229i	$-0.144748\pi$
$564$	11.6737	+	4.00880i	0.491552	+	0.168801i
$565$		−	13.5977i		−	0.572061i
$566$	6.50177	+	11.2614i	0.273290	+	0.473351i
$567$	18.8462	+	14.5540i	0.791467	+	0.611212i
$568$	−3.51507	−	6.08827i	−0.147489	−	0.255458i
$569$	−28.5546	+	16.4860i	−1.19707	+	0.691129i	−0.959901	−	0.280339i	$-0.909553\pi$
$569$	−28.5546	+	16.4860i	−1.19707	+	0.691129i	−0.237170	+	0.971468i	$0.576220\pi$
$570$	−11.6251	+	10.1224i	−0.486923	+	0.423983i
$571$	17.1019	+	29.6214i	0.715693	+	1.23962i	0.962692	+	0.270600i	$0.0872222\pi$
$571$	17.1019	+	29.6214i	0.715693	+	1.23962i	−0.246999	+	0.969016i	$0.579444\pi$
$572$	−0.170747	−	4.32046i	−0.00713929	−	0.180648i
$573$	23.4349	+	26.9138i	0.979007	+	1.12434i
$574$	0.180218	−	0.449064i	0.00752216	−	0.0187436i
$575$	11.0897	+	6.40261i	0.462470	+	0.267007i
$576$	−0.412611	+	2.97149i	−0.0171921	+	0.123812i
$577$	30.4639	−	17.5883i	1.26823	−	0.732212i	0.293576	−	0.955936i	$-0.405155\pi$
$577$	30.4639	−	17.5883i	1.26823	−	0.732212i	0.974653	+	0.223723i	$0.0718212\pi$
$578$	9.04289	+	5.22092i	0.376135	+	0.217161i
$579$	10.4415	−	9.09182i	0.433934	−	0.377843i
$580$		−	2.00090i		−	0.0830829i
$581$	−40.9253	−	16.4241i	−1.69787	−	0.681388i
$582$	4.55650	+	23.3382i	0.188873	+	0.967400i
$583$	1.32633	+	2.29726i	0.0549308	+	0.0951429i
$584$	3.12307	+	5.40931i	0.129233	+	0.223839i
$585$	1.28623	−	13.0194i	0.0531793	−	0.538286i
$586$	16.9340	+	9.77684i	0.699537	+	0.403878i
$587$	−14.3923	+	24.9281i	−0.594032	+	1.02889i	0.399650	+	0.916668i	$0.369132\pi$
$587$	−14.3923	+	24.9281i	−0.594032	+	1.02889i	−0.993683	+	0.112226i	$0.964202\pi$
$588$	6.54753	−	10.2044i	0.270016	−	0.420823i
$589$	14.6843	+	25.4340i	0.605056	+	1.04799i
$590$	11.7999	+	6.81270i	0.485796	+	0.280474i
$591$	24.3288	−	4.74991i	1.00075	−	0.195385i
$592$	−4.50203	+	7.79774i	−0.185032	+	0.320485i
$593$	12.0411	−	20.8558i	0.494469	−	0.856445i	−0.505511	−	0.862820i	$-0.668696\pi$
$593$	12.0411	−	20.8558i	0.494469	−	0.856445i	0.999980	+	0.00637535i	$0.00202935\pi$
$594$	−2.81519	+	5.55913i	−0.115508	+	0.228094i
$595$	−2.37168	−	16.5948i	−0.0972293	−	0.680320i
$596$	1.31022	+	0.756457i	0.0536688	+	0.0309857i
$597$	5.57830	−	1.08910i	0.228305	−	0.0445737i
$598$	13.0428	−	0.515460i	0.533362	−	0.0210787i
$599$	−0.694359	+	0.400888i	−0.0283707	+	0.0163798i	−0.514118	−	0.857719i	$-0.671881\pi$
$599$	−0.694359	+	0.400888i	−0.0283707	+	0.0163798i	0.485748	+	0.874099i	$0.338547\pi$
$600$	−1.98979	+	5.79431i	−0.0812328	+	0.236552i
$601$	−12.0618	−	6.96387i	−0.492010	−	0.284062i	0.233398	−	0.972381i	$-0.425016\pi$
$601$	−12.0618	−	6.96387i	−0.492010	−	0.284062i	−0.725408	+	0.688319i	$0.758349\pi$
$602$	1.72282	+	2.19455i	0.0702168	+	0.0894433i
$603$	4.43338	−	31.9278i	0.180541	−	1.30020i
$604$	3.05059			0.124127
$605$	−5.78256	+	10.0157i	−0.235095	+	0.407196i
$606$	−1.82840	+	5.32434i	−0.0742737	+	0.216287i
$607$		−	5.64804i		−	0.229247i	−0.993409	−	0.114623i	$-0.963434\pi$
$607$		−	5.64804i		−	0.229247i	0.993409	−	0.114623i	$-0.0365661\pi$
$608$	3.67902	−	6.37226i	0.149204	−	0.258429i
$609$	7.44627	+	1.42304i	0.301738	+	0.0576645i
$610$	−7.99630			−0.323761
$611$	25.6736	−	1.01464i	1.03864	−	0.0410478i
$612$	−14.5614	+	5.91119i	−0.588610	+	0.238946i
$613$	15.8467			0.640043			0.320022	−	0.947410i	$-0.396310\pi$
$613$	15.8467			0.640043			0.320022	+	0.947410i	$0.396310\pi$
$614$	−13.8637	−	24.0126i	−0.559493	−	0.969070i
$615$	0.362366	+	0.124438i	0.0146120	+	0.00501782i
$616$	2.94455	+	1.18171i	0.118639	+	0.0476123i
$617$	−8.95185	+	5.16835i	−0.360388	+	0.208070i	−0.669251	−	0.743036i	$-0.733385\pi$
$617$	−8.95185	+	5.16835i	−0.360388	+	0.208070i	0.308863	+	0.951107i	$0.400052\pi$
$618$	0.761513	−	0.663078i	0.0306325	−	0.0266729i
$619$	−5.47367	+	3.16022i	−0.220005	+	0.127020i	−0.605953	−	0.795501i	$-0.707208\pi$
$619$	−5.47367	+	3.16022i	−0.220005	+	0.127020i	0.385947	+	0.922521i	$0.373875\pi$
$620$	−4.18079	−	2.41378i	−0.167905	−	0.0969398i
$621$	−16.7822	−	8.49864i	−0.673447	−	0.341039i
$622$	6.62722	+	3.82623i	0.265727	+	0.153418i
$623$	2.69213	+	18.8371i	0.107858	+	0.754691i
$624$	1.43778	+	6.07724i	0.0575571	+	0.243284i
$625$	−2.59830	+	4.50039i	−0.103932	+	0.180016i
$626$	−4.34687			−0.173736
$627$	11.5263	−	10.0364i	0.460314	−	0.400813i
$628$		−	2.66704i		−	0.106427i
$629$	−47.1677			−1.88070
$630$	8.33300	+	4.76693i	0.331995	+	0.189919i
$631$	3.51416	+	6.08670i	0.139897	+	0.242308i	0.927457	−	0.373929i	$-0.121990\pi$
$631$	3.51416	+	6.08670i	0.139897	+	0.242308i	−0.787561	+	0.616237i	$0.788656\pi$
$632$	3.86475	+	2.23131i	0.153731	+	0.0887568i
$633$	−3.67018	−	18.7985i	−0.145877	−	0.747174i
$634$	−15.5731			−0.618486
$635$	−6.52591	−	11.3032i	−0.258973	−	0.448554i
$636$	−2.51593	−	2.88942i	−0.0997631	−	0.114573i
$637$	5.01883	−	24.7348i	0.198853	−	0.980029i
$638$			1.98388i			0.0785427i
$639$	7.93290	+	19.5416i	0.313821	+	0.773054i
$640$			1.20950i			0.0478098i
$641$	41.0657	+	23.7093i	1.62200	+	0.936461i	0.986385	+	0.164453i	$0.0525859\pi$
$641$	41.0657	+	23.7093i	1.62200	+	0.936461i	0.635613	+	0.772008i	$0.280747\pi$
$642$	−3.14883	−	16.1282i	−0.124274	−	0.636528i
$643$	16.3622	−	9.44671i	0.645261	−	0.372542i	−0.141377	−	0.989956i	$-0.545153\pi$
$643$	16.3622	−	9.44671i	0.645261	−	0.372542i	0.786638	+	0.617414i	$0.211820\pi$
$644$	−3.56740	+	8.88918i	−0.140575	+	0.350283i
$645$	−1.66607	+	1.45071i	−0.0656013	+	0.0571215i
$646$	38.5451			1.51654
$647$	21.4469			0.843165			0.421582	−	0.906790i	$-0.361475\pi$
$647$	21.4469			0.843165			0.421582	+	0.906790i	$0.361475\pi$
$648$	2.45214	−	8.65951i	0.0963290	−	0.340177i
$649$	−11.6996	−	6.75475i	−0.459249	−	0.265147i
$650$	0.503620	+	12.7433i	0.0197536	+	0.499832i
$651$	11.9562	−	13.8420i	0.468599	−	0.542509i
$652$	−8.95954	+	15.5184i	−0.350883	+	0.607747i
$653$	1.35464	−	0.782101i	0.0530111	−	0.0306060i	−0.473260	−	0.880923i	$-0.656923\pi$
$653$	1.35464	−	0.782101i	0.0530111	−	0.0306060i	0.526271	+	0.850317i	$0.323590\pi$
$654$	−21.1899	+	4.13707i	−0.828591	+	0.161772i
$655$	−11.3986	−	19.7429i	−0.445379	−	0.771419i
$656$	−0.182888			−0.00714059
$657$	−7.04822	−	17.3623i	−0.274977	−	0.677368i
$658$	−7.02210	+	17.4975i	−0.273750	+	0.682125i
$659$	5.73747	−	3.31253i	0.223500	−	0.129038i	−0.384070	−	0.923304i	$-0.625478\pi$
$659$	5.73747	−	3.31253i	0.223500	−	0.129038i	0.607570	+	0.794266i	$0.292144\pi$
$660$	−0.815950	+	2.37607i	−0.0317608	+	0.0924882i
$661$			23.7415i			0.923439i	0.887026	+	0.461719i	$0.152767\pi$
$661$			23.7415i			0.923439i	−0.887026	+	0.461719i	$0.847233\pi$
$662$	13.5898	−	7.84608i	0.528183	−	0.304947i
$663$	−23.8045	+	22.4405i	−0.924491	+	0.871517i
$664$			16.6675i			0.646824i
$665$	−14.5396	−	18.5208i	−0.563821	−	0.718204i
$666$	16.5952	−	21.3133i	0.643049	−	0.825874i
$667$	−5.98906			−0.231897
$668$	−9.94539	−	17.2259i	−0.384799	−	0.666491i
$669$	−20.7873	+	4.05847i	−0.803685	+	0.156910i
$670$		−	12.9958i		−	0.502070i
$671$	7.92829			0.306068
$672$	−4.50112	−	0.860198i	−0.173634	−	0.0331829i
$673$	9.99916	−	17.3191i	0.385439	−	0.667601i	−0.606391	−	0.795167i	$-0.707383\pi$
$673$	9.99916	−	17.3191i	0.385439	−	0.667601i	0.991830	+	0.127566i	$0.0407166\pi$
$674$	−0.217541	+	0.125598i	−0.00837938	+	0.00483784i
$675$	8.30343	−	16.3967i	0.319599	−	0.631110i
$676$	7.36821	+	10.7103i	0.283393	+	0.411933i
$677$	8.62455	−	14.9382i	0.331469	−	0.574120i	−0.651332	−	0.758793i	$-0.725789\pi$
$677$	8.62455	−	14.9382i	0.331469	−	0.574120i	0.982800	+	0.184673i	$0.0591226\pi$
$678$	−3.73131	−	19.1116i	−0.143300	−	0.733977i
$679$	−35.9574	+	5.13892i	−1.37992	+	0.197214i
$680$	−5.48712	+	3.16799i	−0.210421	+	0.121487i
$681$	−9.62864	−	49.3175i	−0.368970	−	1.88985i
$682$	4.14523	+	2.39325i	0.158729	+	0.0916423i
$683$	−8.54591	−	4.93398i	−0.327000	−	0.188794i	0.327508	−	0.944848i	$-0.393791\pi$
$683$	−8.54591	−	4.93398i	−0.327000	−	0.188794i	−0.654508	+	0.756055i	$0.727124\pi$
$684$	−13.5614	+	17.4171i	−0.518535	+	0.665959i
$685$	−11.1942	+	6.46300i	−0.427710	+	0.246938i
$686$	15.0589	+	10.7810i	0.574952	+	0.411619i
$687$	47.1252	−	9.20062i	1.79794	−	0.351026i
$688$	0.527263	−	0.913245i	0.0201017	−	0.0348172i
$689$	−7.05902	−	3.71186i	−0.268927	−	0.141410i
$690$	−7.17300	−	2.46324i	−0.273071	−	0.0937738i
$691$	−41.3606	+	23.8795i	−1.57343	+	0.908420i	−0.577686	+	0.816259i	$0.696044\pi$
$691$	−41.3606	+	23.8795i	−1.57343	+	0.908420i	−0.995744	+	0.0921613i	$0.970622\pi$
$692$	8.77428	−	15.1975i	0.333548	−	0.577722i
$693$	−8.26213	−	4.72638i	−0.313852	−	0.179540i
$694$	−21.2631			−0.807136
$695$		−	3.29885i		−	0.125133i
$696$	−0.549060	−	2.81226i	−0.0208121	−	0.106599i
$697$	−0.479030	−	0.829704i	−0.0181445	−	0.0314273i
$698$	3.85594			0.145949
$699$	5.99853	−	1.17114i	0.226885	−	0.0442966i
$700$	−8.68500	−	3.48546i	−0.328262	−	0.131738i
$701$			27.3612i			1.03342i	0.856161	+	0.516709i	$0.172843\pi$
$701$			27.3612i			1.03342i	−0.856161	+	0.516709i	$0.827157\pi$
$702$	−1.76480	−	18.6517i	−0.0666082	−	0.703963i
$703$	−57.3761	+	33.1261i	−2.16398	+	1.24938i
$704$		−	1.19922i		−	0.0451971i
$705$	−14.1194	−	4.84865i	−0.531767	−	0.182611i
$706$	−7.54643	+	4.35693i	−0.284014	+	0.163975i
$707$	−7.98058	−	3.20276i	−0.300140	−	0.120452i
$708$	18.4542	+	6.33726i	0.693553	+	0.238169i
$709$	11.6657			0.438116			0.219058	−	0.975712i	$-0.429702\pi$
$709$	11.6657			0.438116			0.219058	+	0.975712i	$0.429702\pi$
$710$	4.25148	+	7.36379i	0.159555	+	0.276358i
$711$	−10.5634	−	8.22496i	−0.396158	−	0.308460i
$712$	6.22852	−	3.59604i	0.233424	−	0.134767i
$713$	−7.22488	+	12.5139i	−0.270574	+	0.468647i
$714$	−7.88710	−	22.6732i	−0.295167	−	0.848522i
$715$	0.206519	+	5.22561i	0.00772337	+	0.195427i
$716$	−19.9172	−	11.4992i	−0.744340	−	0.429745i
$717$	−8.58074	−	9.85456i	−0.320454	−	0.368025i
$718$	20.5146			0.765599
$719$	13.5634			0.505829			0.252914	−	0.967489i	$-0.418611\pi$
$719$	13.5634			0.505829			0.252914	+	0.967489i	$0.418611\pi$
$720$	0.499054	−	3.59403i	0.0185986	−	0.133941i
$721$	0.952427	+	1.21322i	0.0354702	+	0.0451825i
$722$	30.4329	−	17.5704i	1.13260	−	0.653904i
$723$	−20.9678	+	4.09371i	−0.779801	+	0.152247i
$724$	−6.48871	−	3.74626i	−0.241151	−	0.139229i
$725$		−	5.85149i		−	0.217319i
$726$	−5.37901	+	15.6638i	−0.199634	+	0.581339i
$727$			22.4921i			0.834186i	0.908864	+	0.417093i	$0.136951\pi$
$727$			22.4921i			0.834186i	−0.908864	+	0.417093i	$0.863049\pi$
$728$	−9.38277	+	1.72149i	−0.347749	+	0.0638028i
$729$	−10.8595	+	24.7199i	−0.402204	+	0.915550i
$730$	−3.77736	−	6.54258i	−0.139806	−	0.242152i
$731$	5.52412			0.204317
$732$	−11.2388	+	2.19424i	−0.415398	+	0.0811013i
$733$	−5.25647	−	3.03483i	−0.194152	−	0.112094i	0.399773	−	0.916614i	$-0.369089\pi$
$733$	−5.25647	−	3.03483i	−0.194152	−	0.112094i	−0.593925	+	0.804520i	$0.702422\pi$
$734$	−11.9372	−	20.6758i	−0.440608	−	0.763156i
$735$	−7.91926	+	12.3423i	−0.292106	+	0.455251i
$736$	3.62026			0.133445
$737$			12.8852i			0.474634i
$738$	0.543451	+	0.0754617i	0.0200047	+	0.00277778i
$739$	−41.5994			−1.53026			−0.765129	−	0.643877i	$-0.777325\pi$
$739$	−41.5994			−1.53026			−0.765129	+	0.643877i	$0.777325\pi$
$740$	5.44521	−	9.43139i	0.200170	−	0.346705i
$741$	−13.1964	+	44.0153i	−0.484783	+	1.61694i
$742$	4.60333	−	3.61381i	0.168993	−	0.132667i
$743$	47.1331	+	27.2123i	1.72914	+	0.998322i	0.893523	+	0.449017i	$0.148226\pi$
$743$	47.1331	+	27.2123i	1.72914	+	0.998322i	0.835622	+	0.549305i	$0.185107\pi$
$744$	−6.53845	−	2.24533i	−0.239711	−	0.0823178i
$745$	−1.58472	−	0.914937i	−0.0580596	−	0.0335207i
$746$	−2.65092	+	1.53051i	−0.0970570	+	0.0560359i
$747$	6.87718	−	49.5273i	0.251623	−	1.81211i
$748$	5.44045	−	3.14104i	0.198922	−	0.114848i
$749$	24.8489	−	3.55132i	0.907957	−	0.129762i
$750$	5.80867	−	16.9150i	0.212103	−	0.617648i
$751$	2.92540	+	5.06695i	0.106749	+	0.184896i	0.914452	−	0.404695i	$-0.132622\pi$
$751$	2.92540	+	5.06695i	0.106749	+	0.184896i	−0.807702	+	0.589591i	$0.799289\pi$
$752$	7.12615			0.259864
$753$	16.6406	+	5.71446i	0.606418	+	0.208246i
$754$	−3.18402	−	5.04380i	−0.115955	−	0.183684i
$755$	−3.68970			−0.134282
$756$	13.0201	+	4.41328i	0.473536	+	0.160509i
$757$	1.38330	−	2.39594i	0.0502768	−	0.0870820i	−0.839792	−	0.542909i	$-0.817323\pi$
$757$	1.38330	−	2.39594i	0.0502768	−	0.0870820i	0.890069	+	0.455827i	$0.150656\pi$
$758$			17.4923i			0.635348i
$759$	7.11199	+	2.44228i	0.258149	+	0.0886493i
$760$	−4.44979	+	7.70727i	−0.161411	+	0.279572i
$761$	−50.7252			−1.83879			−0.919393	−	0.393341i	$-0.871319\pi$
$761$	−50.7252			−1.83879			−0.919393	+	0.393341i	$0.871319\pi$
$762$	−12.2738	−	14.0959i	−0.444634	−	0.510641i
$763$	−4.66588	−	32.6475i	−0.168916	−	1.18192i
$764$	17.8434	+	10.3019i	0.645552	+	0.372710i
$765$	17.6121	−	7.14960i	0.636765	−	0.258494i
$766$	24.6602	−	14.2376i	0.891009	−	0.514425i
$767$	40.5859	−	1.60398i	1.46547	−	0.0579162i
$768$	0.331895	+	1.69995i	0.0119762	+	0.0613418i
$769$	−6.29042	−	3.63178i	−0.226838	−	0.130965i	0.382274	−	0.924049i	$-0.375141\pi$
$769$	−6.29042	−	3.63178i	−0.226838	−	0.130965i	−0.609113	+	0.793084i	$0.708474\pi$
$770$	−3.56145	−	1.42928i	−0.128346	−	0.0515076i
$771$	−22.4054	−	7.69409i	−0.806910	−	0.277096i
$772$	3.99673	−	6.92254i	0.143845	−	0.249148i
$773$	−20.0043	+	34.6484i	−0.719504	+	1.24622i	0.241693	+	0.970353i	$0.422297\pi$
$773$	−20.0043	+	34.6484i	−0.719504	+	1.24622i	−0.961197	+	0.275864i	$0.911036\pi$
$774$	−1.94357	+	2.49615i	−0.0698602	+	0.0897221i
$775$	−12.2264	−	7.05892i	−0.439186	−	0.253564i
$776$	6.86436	+	11.8894i	0.246416	+	0.426806i
$777$	31.2259	+	26.9717i	1.12022	+	0.967606i
$778$	17.9304	−	31.0564i	0.642836	−	1.11342i
$779$	−1.16541	−	0.672851i	−0.0417552	−	0.0241074i
$780$	−1.73899	−	7.35044i	−0.0622660	−	0.263188i
$781$	−4.21532	−	7.30115i	−0.150836	−	0.261256i
$782$	9.48236	+	16.4239i	0.339088	+	0.587318i
$783$	0.471157	+	8.58316i	0.0168378	+	0.306737i
$784$	1.66179	−	6.79989i	0.0593498	−	0.242853i
$785$			3.22580i			0.115134i
$786$	−21.4383	−	24.6208i	−0.764677	−	0.878194i
$787$	3.70522	+	2.13921i	0.132077	+	0.0762545i	0.564583	−	0.825377i	$-0.309037\pi$
$787$	3.70522	+	2.13921i	0.132077	+	0.0762545i	−0.432506	+	0.901631i	$0.642371\pi$
$788$	12.3941	−	7.15573i	0.441521	−	0.254912i
$789$	24.4608	+	28.0921i	0.870828	+	1.00010i
$790$	−4.67442	−	2.69878i	−0.166308	−	0.0960182i
$791$	29.4454	−	4.20825i	1.04696	−	0.149628i
$792$	−0.494809	+	3.56346i	−0.0175823	+	0.126622i
$793$	−20.1568	+	12.7245i	−0.715789	+	0.451859i
$794$	16.6300	+	28.8039i	0.590175	+	1.02221i
$795$	3.04303	+	3.49477i	0.107925	+	0.123947i
$796$	2.84181	−	1.64072i	0.100725	−	0.0581538i
$797$	20.0925	+	34.8013i	0.711714	+	1.23273i	0.964213	+	0.265128i	$0.0854142\pi$
$797$	20.0925	+	34.8013i	0.711714	+	1.23273i	−0.252499	+	0.967597i	$0.581252\pi$
$798$	−25.5176	−	22.0411i	−0.903313	−	0.780247i
$799$	18.6651	+	32.3290i	0.660325	+	1.14372i
$800$			3.53710i			0.125055i
$801$	−19.9918	+	8.11564i	−0.706374	+	0.286752i
$802$	3.12057	−	5.40499i	0.110191	−	0.190857i
$803$	3.74523	+	6.48693i	0.132166	+	0.228919i
$804$	−3.56612	−	18.2655i	−0.125767	−	0.644175i
$805$	4.31478	−	10.7515i	0.152076	−	0.378940i
$806$	−14.3798	+	0.568298i	−0.506508	+	0.0200175i
$807$	−9.34509	−	47.8652i	−0.328963	−	1.68493i
$808$			3.25021i			0.114342i
$809$		−	9.75337i		−	0.342910i	−0.985192	−	0.171455i	$-0.945153\pi$
$809$		−	9.75337i		−	0.342910i	0.985192	−	0.171455i	$-0.0548469\pi$
$810$	−2.96587	+	10.4737i	−0.104210	+	0.368008i
$811$			31.7759i			1.11580i	0.829907	+	0.557902i	$0.188393\pi$
$811$			31.7759i			1.11580i	−0.829907	+	0.557902i	$0.811607\pi$
$812$	4.33288	−	0.619242i	0.152054	−	0.0217311i
$813$	1.69788	−	4.94426i	0.0595472	−	0.173403i
$814$	−5.39890	+	9.35117i	−0.189231	+	0.327758i
$815$	10.8366	−	18.7695i	0.379589	−	0.657468i
$816$	−6.84282	+	5.95830i	−0.239547	+	0.208582i
$817$	6.71971	−	3.87962i	0.235093	−	0.135731i
$818$	−30.9890			−1.08350
$819$	28.5911	−	1.24397i	0.999055	−	0.0434677i
$820$	0.221204			0.00772478
$821$	18.7324	−	10.8151i	0.653764	−	0.377451i	−0.136133	−	0.990691i	$-0.543467\pi$
$821$	18.7324	−	10.8151i	0.653764	−	0.377451i	0.789897	+	0.613240i	$0.210134\pi$
$822$	−13.9600	+	12.1555i	−0.486911	+	0.423972i
$823$	−24.3797	+	42.2269i	−0.849822	+	1.47194i	0.0315441	+	0.999502i	$0.489958\pi$
$823$	−24.3797	+	42.2269i	−0.849822	+	1.47194i	−0.881366	+	0.472433i	$0.843376\pi$
$824$	0.291487	−	0.504870i	0.0101544	−	0.0175880i
$825$	−2.38619	+	6.94863i	−0.0830763	+	0.241920i
$826$	−11.1008	+	27.6608i	−0.386246	+	0.962442i
$827$		−	12.1112i		−	0.421149i	−0.977578	−	0.210575i	$-0.932467\pi$
$827$		−	12.1112i		−	0.421149i	0.977578	−	0.210575i	$-0.0675335\pi$
$828$	−10.7576	−	1.49376i	−0.373851	−	0.0519117i
$829$		−	23.5007i		−	0.816214i	−0.912934	−	0.408107i	$-0.866189\pi$
$829$		−	23.5007i		−	0.816214i	0.912934	−	0.408107i	$-0.133811\pi$
$830$		−	20.1594i		−	0.699742i
$831$	−3.76141	−	19.2658i	−0.130482	−	0.668323i
$832$	1.92468	+	3.04887i	0.0667261	+	0.105701i
$833$	35.2015	−	10.2716i	1.21966	−	0.355889i
$834$	−0.905226	−	4.63653i	−0.0313454	−	0.160550i
$835$	12.0290	+	20.8348i	0.416280	+	0.721018i
$836$	4.41194	−	7.64171i	0.152590	−	0.264294i
$837$	18.5025	+	9.36981i	0.639540	+	0.323868i
$838$			25.2290i			0.871521i
$839$	−8.86105	−	15.3478i	−0.305917	−	0.529864i	0.671548	−	0.740961i	$-0.265630\pi$
$839$	−8.86105	−	15.3478i	−0.305917	−	0.529864i	−0.977465	+	0.211097i	$0.932296\pi$
$840$	5.44412	+	1.04041i	0.187840	+	0.0358976i
$841$	−13.1316	−	22.7446i	−0.452814	−	0.784298i
$842$	7.12276	−	4.11232i	0.245466	−	0.141720i
$843$	−9.30996	−	10.6920i	−0.320652	−	0.368253i
$844$	−5.52912	−	9.57673i	−0.190320	−	0.329644i
$845$	−8.91187	−	12.9541i	−0.306578	−	0.445634i
$846$	−21.1753	−	2.94032i	−0.728021	−	0.101090i
$847$	−23.4782	−	9.42227i	−0.806722	−	0.323753i
$848$	−1.91564	−	1.10599i	−0.0657833	−	0.0379800i
$849$	−14.7903	−	16.9859i	−0.507602	−	0.582956i
$850$	−16.0467	+	9.26455i	−0.550396	+	0.317771i
$851$	−28.2298	−	16.2985i	−0.967706	−	0.558705i
$852$	7.99612	+	9.18315i	0.273943	+	0.314610i
$853$		−	31.2313i		−	1.06934i	−0.845061	−	0.534669i	$-0.820436\pi$
$853$		−	31.2313i		−	1.06934i	0.845061	−	0.534669i	$-0.179564\pi$
$854$	−2.47471	−	17.3157i	−0.0846828	−	0.592532i
$855$	16.4026	−	21.0660i	0.560957	−	0.720443i
$856$	−4.74371	−	8.21634i	−0.162137	−	0.280829i
$857$	−8.47281	−	14.6753i	−0.289426	−	0.501300i	0.684247	−	0.729250i	$-0.260131\pi$
$857$	−8.47281	−	14.6753i	−0.289426	−	0.501300i	−0.973673	+	0.227950i	$0.926798\pi$
$858$	1.72420	+	7.28792i	0.0588633	+	0.248805i
$859$	18.2086	+	10.5127i	0.621269	+	0.358690i	0.777363	−	0.629052i	$-0.216557\pi$
$859$	18.2086	+	10.5127i	0.621269	+	0.358690i	−0.156094	+	0.987742i	$0.549890\pi$
$860$	−0.637726	+	1.10457i	−0.0217463	+	0.0376656i
$861$	−0.157320	+	0.823202i	−0.00536146	+	0.0280546i
$862$	−9.97727	−	17.2811i	−0.339827	−	0.588598i
$863$	17.7086	+	10.2241i	0.602809	+	0.348032i	0.770146	−	0.637868i	$-0.220183\pi$
$863$	17.7086	+	10.2241i	0.602809	+	0.348032i	−0.167337	+	0.985900i	$0.553517\pi$
$864$	−0.284804	−	5.18834i	−0.00968924	−	0.176511i
$865$	−10.6125	+	18.3814i	−0.360837	+	0.624987i
$866$	−11.0912	+	19.2106i	−0.376896	+	0.652802i
$867$	−17.1053	−	5.87403i	−0.580927	−	0.199492i
$868$	3.93308	−	9.80038i	0.133497	−	0.332647i
$869$	4.63466	+	2.67582i	0.157220	+	0.0907711i
$870$	0.664090	+	3.40144i	0.0225147	+	0.115320i
$871$	−20.6801	−	32.7593i	−0.700718	−	1.11001i
$872$	−10.7950	+	6.23249i	−0.365564	+	0.211059i
$873$	−15.4917	−	38.1616i	−0.524314	−	1.29158i
$874$	23.0692	+	13.3190i	0.780328	+	0.450523i
$875$	25.3536	+	10.1749i	0.857108	+	0.343974i
$876$	−7.10439	−	8.15905i	−0.240035	−	0.275669i
$877$	−41.2083			−1.39150			−0.695752	−	0.718282i	$-0.744929\pi$
$877$	−41.2083			−1.39150			−0.695752	+	0.718282i	$0.744929\pi$
$878$	13.6641	−	23.6668i	0.461139	−	0.798717i
$879$	−32.0319	−	10.9999i	−1.08041	−	0.371017i
$880$			1.45046i			0.0488948i
$881$	−9.30917	+	16.1240i	−0.313634	+	0.543230i	−0.979146	−	0.203157i	$-0.934880\pi$
$881$	−9.30917	+	16.1240i	−0.313634	+	0.543230i	0.665512	+	0.746387i	$0.268213\pi$
$882$	−7.74371	+	19.5201i	−0.260744	+	0.657277i
$883$	28.5626			0.961209			0.480604	−	0.876938i	$-0.340417\pi$
$883$	28.5626			0.961209			0.480604	+	0.876938i	$0.340417\pi$
$884$	−8.79052	+	16.7174i	−0.295657	+	0.562266i
$885$	−22.3205	−	7.66494i	−0.750294	−	0.257654i
$886$	22.5803			0.758601
$887$	22.2089	+	38.4669i	0.745701	+	1.29159i	0.949867	+	0.312655i	$0.101218\pi$
$887$	22.2089	+	38.4669i	0.745701	+	1.29159i	−0.204166	+	0.978936i	$0.565448\pi$
$888$	5.06521	−	14.7500i	0.169977	−	0.494978i
$889$	22.4571	−	17.6298i	0.753186	−	0.591284i
$890$	−7.53342	+	4.34942i	−0.252521	+	0.145793i
$891$	2.94064	−	10.3846i	0.0985152	−	0.347898i
$892$	−10.5899	+	6.11409i	−0.354576	+	0.204715i
$893$	45.4096	+	26.2173i	1.51958	+	0.877328i
$894$	−2.47838	−	0.851086i	−0.0828895	−	0.0284646i
$895$	24.0899	+	13.9083i	0.805237	+	0.464904i
$896$	−2.61914	+	0.374319i	−0.0874993	+	0.0125051i
$897$	−22.0012	+	5.20512i	−0.734598	+	0.173794i
$898$	4.60525	−	7.97653i	0.153679	−	0.266180i
$899$	6.60297			0.220221
$900$	1.45945	−	10.5105i	0.0486482	−	0.350349i
$901$		−	11.5875i		−	0.386035i
$902$	−0.219323			−0.00730264
$903$	−3.65707	−	3.15884i	−0.121700	−	0.105120i
$904$	−5.62121	−	9.73622i	−0.186959	−	0.323822i
$905$	7.84811	+	4.53111i	0.260880	+	0.150619i
$906$	−5.18587	+	1.01248i	−0.172289	+	0.0336373i
$907$	15.9877			0.530863			0.265431	−	0.964130i	$-0.414486\pi$
$907$	15.9877			0.530863			0.265431	+	0.964130i	$0.414486\pi$
$908$	−14.5055	−	25.1243i	−0.481383	−	0.833780i
$909$	1.34107	−	9.65798i	0.0444806	−	0.320335i
$910$	11.3485	−	2.08215i	0.376199	−	0.0690226i
$911$			23.0432i			0.763457i	0.924275	+	0.381728i	$0.124671\pi$
$911$			23.0432i			0.763457i	−0.924275	+	0.381728i	$0.875329\pi$
$912$	−4.13925	+	12.0536i	−0.137064	+	0.399135i
$913$			19.9879i			0.661503i
$914$	−5.75837	−	3.32459i	−0.190470	−	0.109968i
$915$	13.5933	−	2.65393i	0.449382	−	0.0877364i
$916$	24.0075	−	13.8607i	0.793230	−	0.457971i
$917$	39.2250	−	30.7933i	1.29532	−	1.01688i
$918$	22.7918	−	14.8816i	0.752242	−	0.491166i
$919$	15.2023			0.501477			0.250738	−	0.968055i	$-0.419327\pi$
$919$	15.2023			0.501477			0.250738	+	0.968055i	$0.419327\pi$
$920$	−4.37872			−0.144362
$921$	31.5373	+	36.2190i	1.03919	+	1.19346i
$922$	−20.4701	−	11.8184i	−0.674147	−	0.389219i
$923$	22.4349	+	11.7970i	0.738455	+	0.388303i
$924$	−5.39781	−	1.03156i	−0.177575	−	0.0339359i
$925$	15.9241	−	27.5814i	0.523582	−	0.906871i
$926$	−7.00983	+	4.04713i	−0.230357	+	0.132997i
$927$	−1.07446	+	1.37995i	−0.0352900	+	0.0453234i
$928$	−0.827158	−	1.43268i	−0.0271528	−	0.0470300i
$929$	−14.5804			−0.478366			−0.239183	−	0.970975i	$-0.576880\pi$
$929$	−14.5804			−0.478366			−0.239183	+	0.970975i	$0.576880\pi$
$930$	7.90828	+	2.71573i	0.259323	+	0.0890524i
$931$	35.6063	−	37.2168i	1.16695	−	1.21973i
$932$	3.05589	−	1.76432i	0.100099	−	0.0577922i
$933$	−12.5359	−	4.30487i	−0.410406	−	0.140935i
$934$		−	3.85738i		−	0.126217i
$935$	−6.58024	+	3.79910i	−0.215197	+	0.124244i
$936$	−4.46116	−	9.85383i	−0.145818	−	0.322083i
$937$		−	32.9784i		−	1.07736i	−0.842511	−	0.538678i	$-0.818924\pi$
$937$		−	32.9784i		−	1.07736i	0.842511	−	0.538678i	$-0.181076\pi$
$938$	28.1419	−	4.02195i	0.918865	−	0.131321i
$939$	7.38949	−	1.44271i	0.241147	−	0.0470810i
$940$	−8.61910			−0.281124
$941$	6.25946	+	10.8417i	0.204053	+	0.353430i	0.949830	−	0.312765i	$-0.101255\pi$
$941$	6.25946	+	10.8417i	0.204053	+	0.353430i	−0.745778	+	0.666195i	$0.767922\pi$
$942$	0.885179	+	4.53385i	0.0288407	+	0.147721i
$943$		−	0.662103i		−	0.0215610i
$944$	11.2653			0.366654
$945$	−15.7479	−	5.33788i	−0.512278	−	0.173641i
$946$	0.632301	−	1.09518i	0.0205579	−	0.0356073i
$947$	−4.69511	+	2.71072i	−0.152571	+	0.0880866i	−0.574342	−	0.818616i	$-0.694742\pi$
$947$	−4.69511	+	2.71072i	−0.152571	+	0.0880866i	0.421771	+	0.906702i	$0.361409\pi$
$948$	−7.31045	−	2.51044i	−0.237433	−	0.0815352i
$949$	−19.9330	−	10.4814i	−0.647052	−	0.340241i
$950$	−13.0131	+	22.5393i	−0.422200	+	0.731272i
$951$	26.4735	−	5.16863i	0.858463	−	0.167604i
$952$	−8.55833	−	10.9017i	−0.277377	−	0.353327i
$953$	−40.2976	+	23.2658i	−1.30537	+	0.753654i	−0.981319	−	0.192386i	$-0.938377\pi$
$953$	−40.2976	+	23.2658i	−1.30537	+	0.753654i	−0.324048	+	0.946040i	$0.605044\pi$
$954$	5.23595	+	4.07686i	0.169520	+	0.131993i
$955$	−21.5817	−	12.4602i	−0.698366	−	0.403202i
$956$	−6.53341	−	3.77206i	−0.211305	−	0.121997i
$957$	−0.658441	−	3.37251i	−0.0212844	−	0.109018i
$958$	−7.12716	+	4.11487i	−0.230268	+	0.132945i
$959$	−17.4598	−	22.2406i	−0.563807	−	0.718185i
$960$	−0.401428	−	2.05610i	−0.0129560	−	0.0663604i
$961$	−7.53453	+	13.0502i	−0.243049	+	0.420974i
$962$	−1.28202	−	32.4392i	−0.0413339	−	1.04588i
$963$	10.7057	+	26.3721i	0.344987	+	0.849829i
$964$	−10.6818	+	6.16717i	−0.344039	+	0.198631i
$965$	−4.83406	+	8.37283i	−0.155614	+	0.269531i
$966$	3.11414	−	16.2952i	0.100196	−	0.524290i
$967$	−27.2924			−0.877664			−0.438832	−	0.898569i	$-0.644608\pi$
$967$	−27.2924			−0.877664			−0.438832	+	0.898569i	$0.644608\pi$
$968$			9.56188i			0.307331i
$969$	−65.5249	+	12.7929i	−2.10496	+	0.410968i
$970$	−8.30247	−	14.3803i	−0.266576	−	0.461724i
$971$	−31.3639			−1.00651			−0.503257	−	0.864137i	$-0.667865\pi$
$971$	−31.3639			−1.00651			−0.503257	+	0.864137i	$0.667865\pi$
$972$	−1.29447	+	15.5346i	−0.0415202	+	0.498273i
$973$	7.14355	−	1.02093i	0.229012	−	0.0327297i
$974$			23.0181i			0.737548i
$975$	−5.08556	−	21.4958i	−0.162868	−	0.688417i
$976$	−5.72549	+	3.30561i	−0.183269	+	0.105810i
$977$		−	50.2411i		−	1.60735i	−0.595066	−	0.803677i	$-0.702874\pi$
$977$		−	50.2411i		−	1.60735i	0.595066	−	0.803677i	$-0.297126\pi$
$978$	10.0803	−	29.3542i	0.322334	−	0.938643i
$979$	7.46934	−	4.31243i	0.238721	−	0.137826i
$980$	−2.00995	+	8.22448i	−0.0642053	+	0.262721i
$981$	34.6488	−	14.0657i	1.10625	−	0.449082i
$982$	29.2593			0.933703
$983$	18.7346	+	32.4492i	0.597540	+	1.03497i	0.993183	+	0.116565i	$0.0371884\pi$
$983$	18.7346	+	32.4492i	0.597540	+	1.03497i	−0.395643	+	0.918404i	$0.629478\pi$
$984$	0.310902	−	0.0606998i	0.00991119	−	0.00193504i
$985$	−14.9907	+	8.65488i	−0.477643	+	0.275767i
$986$	4.33306	−	7.50509i	0.137993	−	0.239011i
$987$	6.12990	−	32.0756i	0.195117	−	1.02098i
$988$	1.04766	+	26.5091i	0.0333304	+	0.843368i
$989$	3.30619	+	1.90883i	0.105131	+	0.0606972i
$990$	0.598473	−	4.31001i	0.0190207	−	0.136981i
$991$	24.4638			0.777117			0.388559	−	0.921424i	$-0.372973\pi$
$991$	24.4638			0.777117			0.388559	+	0.921424i	$0.372973\pi$
$992$	−3.99136			−0.126726
$993$	−20.4980	+	17.8484i	−0.650484	+	0.566401i
$994$	−14.6303	+	11.4854i	−0.464044	+	0.364295i
$995$	−3.43718	+	1.98446i	−0.108966	+	0.0629115i
$996$	−5.53186	−	28.3340i	−0.175284	−	0.897796i
$997$	6.93927	+	4.00639i	0.219769	+	0.126884i	0.605843	−	0.795584i	$-0.292836\pi$
$997$	6.93927	+	4.00639i	0.219769	+	0.126884i	−0.386074	+	0.922468i	$0.626169\pi$
$998$			30.7671i			0.973917i
$999$	−21.1372	+	41.7395i	−0.668752	+	1.32058i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.u.a.425.16	yes	76
3.2	odd	2	inner	546.2.u.a.425.23	yes	76
7.3	odd	6		546.2.bb.a.269.18	yes	76
13.3	even	3		546.2.bb.a.341.12	yes	76
21.17	even	6		546.2.bb.a.269.31	yes	76
39.29	odd	6		546.2.bb.a.341.37	yes	76
91.3	odd	6	inner	546.2.u.a.185.23	yes	76
273.185	even	6	inner	546.2.u.a.185.16	✓	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.u.a.185.16	✓	76	273.185	even	6	inner
546.2.u.a.185.23	yes	76	91.3	odd	6	inner
546.2.u.a.425.16	yes	76	1.1	even	1	trivial
546.2.u.a.425.23	yes	76	3.2	odd	2	inner
546.2.bb.a.269.18	yes	76	7.3	odd	6
546.2.bb.a.269.31	yes	76	21.17	even	6
546.2.bb.a.341.12	yes	76	13.3	even	3
546.2.bb.a.341.37	yes	76	39.29	odd	6

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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.u (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(1.30626 - 1.13741i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.604752 + 1.04746i) q^{5} +(-0.562548 + 1.63815i) q^{6} +(-2.45540 - 0.985399i) q^{7} +1.00000i q^{8} +(0.412611 - 2.97149i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(1.30626 - 1.13741i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.604752 + 1.04746i) q^{5} +(-0.562548 + 1.63815i) q^{6} +(-2.45540 - 0.985399i) q^{7} +1.00000i q^{8} +(0.412611 - 2.97149i) q^{9} -1.20950i q^{10} +1.19922i q^{11} +(-0.331895 - 1.69995i) q^{12} +(-1.92468 - 3.04887i) q^{13} +(2.61914 - 0.374319i) q^{14} +(0.401428 + 2.05610i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.61925 - 4.53667i) q^{17} +(1.12841 + 2.77969i) q^{18} -7.35805i q^{19} +(0.604752 + 1.04746i) q^{20} +(-4.32818 + 1.50561i) q^{21} +(-0.599608 - 1.03855i) q^{22} +(3.13524 - 1.81013i) q^{23} +(1.13741 + 1.30626i) q^{24} +(1.76855 + 3.06322i) q^{25} +(3.19125 + 1.67806i) q^{26} +(-2.84082 - 4.35083i) q^{27} +(-2.08108 + 1.63374i) q^{28} +(-1.43268 - 0.827158i) q^{29} +(-1.37570 - 1.57992i) q^{30} +(-3.45662 + 1.99568i) q^{31} +(0.866025 + 0.500000i) q^{32} +(1.36400 + 1.56648i) q^{33} +5.23850i q^{34} +(2.51707 - 1.97601i) q^{35} +(-2.36708 - 1.84308i) q^{36} +(-4.50203 - 7.79774i) q^{37} +(3.67902 + 6.37226i) q^{38} +(-5.98193 - 1.79347i) q^{39} +(-1.04746 - 0.604752i) q^{40} +(0.0914442 - 0.158386i) q^{41} +(2.99551 - 3.46798i) q^{42} +(0.527263 + 0.913245i) q^{43} +(1.03855 + 0.599608i) q^{44} +(2.86299 + 2.22921i) q^{45} +(-1.81013 + 3.13524i) q^{46} +(-3.56307 + 6.17142i) q^{47} +(-1.63815 - 0.562548i) q^{48} +(5.05798 + 4.83910i) q^{49} +(-3.06322 - 1.76855i) q^{50} +(-1.73863 - 8.90520i) q^{51} +(-3.60274 + 0.142382i) q^{52} +(1.91564 - 1.10599i) q^{53} +(4.63564 + 2.34752i) q^{54} +(-1.25613 - 0.725228i) q^{55} +(0.985399 - 2.45540i) q^{56} +(-8.36910 - 9.61150i) q^{57} +1.65432 q^{58} +(-5.63264 + 9.75602i) q^{59} +(1.98135 + 0.680403i) q^{60} -6.61123i q^{61} +(1.99568 - 3.45662i) q^{62} +(-3.94123 + 6.88961i) q^{63} -1.00000 q^{64} +(4.35752 - 0.172212i) q^{65} +(-1.96450 - 0.674616i) q^{66} +10.7447 q^{67} +(-2.61925 - 4.53667i) q^{68} +(2.03657 - 5.93053i) q^{69} +(-1.19184 + 2.96981i) q^{70} +(-6.08827 + 3.51507i) q^{71} +(2.97149 + 0.412611i) q^{72} +(5.40931 - 3.12307i) q^{73} +(7.79774 + 4.50203i) q^{74} +(5.79431 + 1.98979i) q^{75} +(-6.37226 - 3.67902i) q^{76} +(1.18171 - 2.94455i) q^{77} +(6.07724 - 1.43778i) q^{78} +(2.23131 - 3.86475i) q^{79} +1.20950 q^{80} +(-8.65951 - 2.45214i) q^{81} +0.182888i q^{82} +16.6675 q^{83} +(-0.860198 + 4.50112i) q^{84} +(3.16799 + 5.48712i) q^{85} +(-0.913245 - 0.527263i) q^{86} +(-2.81226 + 0.549060i) q^{87} -1.19922 q^{88} +(-3.59604 - 6.22852i) q^{89} +(-3.59403 - 0.499054i) q^{90} +(1.72149 + 9.38277i) q^{91} -3.62026i q^{92} +(-2.24533 + 6.53845i) q^{93} -7.12615i q^{94} +(7.70727 + 4.44979i) q^{95} +(1.69995 - 0.331895i) q^{96} +(11.8894 - 6.86436i) q^{97} +(-6.79989 - 1.66179i) q^{98} +(3.56346 + 0.494809i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q + 38 q^{4} + 10 q^{7} - 8 q^{9}+O(q^{10}) \) 76 * q + 38 * q^4 + 10 * q^7 - 8 * q^9	\( 76 q + 38 q^{4} + 10 q^{7} - 8 q^{9} + 2 q^{13} + 12 q^{15} - 38 q^{16} - 8 q^{21} - 42 q^{25} + 20 q^{28} + 20 q^{30} + 12 q^{31} - 4 q^{36} - 6 q^{37} + 12 q^{39} + 8 q^{42} - 2 q^{43} - 4 q^{46} + 2 q^{49} + 10 q^{51} - 14 q^{52} + 18 q^{54} + 24 q^{55} + 8 q^{57} + 16 q^{58} - 12 q^{60} + 32 q^{63} - 76 q^{64} - 24 q^{66} + 96 q^{67} - 30 q^{69} - 54 q^{73} - 12 q^{75} + 18 q^{76} - 12 q^{78} - 60 q^{79} + 8 q^{81} + 8 q^{84} + 8 q^{85} - 24 q^{87} + 48 q^{91} + 16 q^{93} - 66 q^{97}+O(q^{100}) \) 76 * q + 38 * q^4 + 10 * q^7 - 8 * q^9 + 2 * q^13 + 12 * q^15 - 38 * q^16 - 8 * q^21 - 42 * q^25 + 20 * q^28 + 20 * q^30 + 12 * q^31 - 4 * q^36 - 6 * q^37 + 12 * q^39 + 8 * q^42 - 2 * q^43 - 4 * q^46 + 2 * q^49 + 10 * q^51 - 14 * q^52 + 18 * q^54 + 24 * q^55 + 8 * q^57 + 16 * q^58 - 12 * q^60 + 32 * q^63 - 76 * q^64 - 24 * q^66 + 96 * q^67 - 30 * q^69 - 54 * q^73 - 12 * q^75 + 18 * q^76 - 12 * q^78 - 60 * q^79 + 8 * q^81 + 8 * q^84 + 8 * q^85 - 24 * q^87 + 48 * q^91 + 16 * q^93 - 66 * q^97

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