LMFDB - Embedded newform 81.11.f.a.71.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [81,11,Mod(8,81)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(81, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 11, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("81.8"); S:= CuspForms(chi, 11); N := Newforms(S);

Level:	$ N $	$=$	$ 81 = 3^{4} $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	81.f (of order $18$, degree $6$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$51.4639374666$
Analytic rank:	$0$
Dimension:	$174$
Relative dimension:	$29$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			71.13
Character	$\chi$	$=$	81.71
Dual form			81.11.f.a.8.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-9.99045 + 1.76159i) q^{2} +(-865.539 + 315.031i) q^{4} +(-2619.44 + 3121.73i) q^{5} +(-15129.3 - 5506.60i) q^{7} +(17088.5 - 9866.04i) q^{8} +(20670.2 - 35801.9i) q^{10} +(-45611.2 - 54357.3i) q^{11} +(121958. - 691659. i) q^{13} +(160849. + 28361.9i) q^{14} +(569186. - 477604. i) q^{16} +(-109192. - 63041.9i) q^{17} +(-1.20002e6 - 2.07849e6i) q^{19} +(1.28379e6 - 3.52719e6i) q^{20} +(551431. + 462706. i) q^{22} +(2.26289e6 + 6.21725e6i) q^{23} +(-1.18794e6 - 6.73715e6i) q^{25} +7.12483e6i q^{26} +1.48297e7 q^{28} +(-2.11083e7 + 3.72196e6i) q^{29} +(-4.32758e7 + 1.57511e7i) q^{31} +(-1.78330e7 + 2.12526e7i) q^{32} +(1.20193e6 + 437466. i) q^{34} +(5.68204e7 - 3.28053e7i) q^{35} +(3.39317e7 - 5.87714e7i) q^{37} +(1.56501e7 + 1.86511e7i) q^{38} +(-1.39632e7 + 7.91892e7i) q^{40} +(8.50271e7 + 1.49926e7i) q^{41} +(-8.62677e7 + 7.23872e7i) q^{43} +(5.66025e7 + 3.26795e7i) q^{44} +(-3.35595e7 - 5.81268e7i) q^{46} +(8.10430e7 - 2.22664e8i) q^{47} +(-1.78166e7 - 1.49499e7i) q^{49} +(2.37361e7 + 6.52145e7i) q^{50} +(1.12334e8 + 6.37078e8i) q^{52} -5.12143e8i q^{53} +2.89165e8 q^{55} +(-3.12865e8 + 5.51665e7i) q^{56} +(2.04325e8 - 7.43681e7i) q^{58} +(-7.08786e8 + 8.44699e8i) q^{59} +(-6.03944e8 - 2.19817e8i) q^{61} +(4.04598e8 - 2.33595e8i) q^{62} +(-2.39704e8 + 4.15180e8i) q^{64} +(1.83971e9 + 2.19248e9i) q^{65} +(-3.30698e8 + 1.87548e9i) q^{67} +(1.14370e8 + 2.01665e7i) q^{68} +(-5.09872e8 + 4.27834e8i) q^{70} +(1.80207e9 + 1.04043e9i) q^{71} +(-1.61956e7 - 2.80516e7i) q^{73} +(-2.35462e8 + 6.46927e8i) q^{74} +(1.69345e9 + 1.42097e9i) q^{76} +(3.90740e8 + 1.07355e9i) q^{77} +(-5.52812e7 - 3.13515e8i) q^{79} +3.02791e9i q^{80} -8.75870e8 q^{82} +(5.26514e9 - 9.28386e8i) q^{83} +(4.82822e8 - 1.75733e8i) q^{85} +(7.34337e8 - 8.75149e8i) q^{86} +(-1.31572e9 - 4.78882e8i) q^{88} +(-5.25641e9 + 3.03479e9i) q^{89} +(-5.65383e9 + 9.79271e9i) q^{91} +(-3.91724e9 - 4.66839e9i) q^{92} +(-4.17415e8 + 2.36728e9i) q^{94} +(9.63186e9 + 1.69836e9i) q^{95} +(4.82972e9 - 4.05261e9i) q^{97} +(2.04332e8 + 1.17971e8i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 174 q + 6 q^{2} - 6 q^{4} + 4965 q^{5} - 6 q^{7} + 9 q^{8} - 3 q^{10} + 978 q^{11} - 6 q^{13} - 2134569 q^{14} - 3078 q^{16} + 9 q^{17} - 3 q^{19} - 15925353 q^{20} + 10420410 q^{22} - 8437692 q^{23} - 14881965 q^{25}+ \cdots + 103117506282 q^{98}+O(q^{100}) $ 174 * q + 6 * q^2 - 6 * q^4 + 4965 * q^5 - 6 * q^7 + 9 * q^8 - 3 * q^10 + 978 * q^11 - 6 * q^13 - 2134569 * q^14 - 3078 * q^16 + 9 * q^17 - 3 * q^19 - 15925353 * q^20 + 10420410 * q^22 - 8437692 * q^23 - 14881965 * q^25 - 12 * q^28 - 7820868 * q^29 - 51711531 * q^31 - 76244832 * q^32 + 92236410 * q^34 + 260153622 * q^35 - 3 * q^37 - 250645020 * q^38 - 26151153 * q^40 + 837714012 * q^41 - 213300456 * q^43 - 2245906431 * q^44 - 3 * q^46 + 1685998563 * q^47 - 183168366 * q^49 - 2548576023 * q^50 - 912655665 * q^52 - 12 * q^55 + 4260806997 * q^56 - 496853331 * q^58 - 1806342150 * q^59 - 1784159286 * q^61 - 2786630112 * q^62 + 8858370045 * q^64 + 2961878001 * q^65 - 915608058 * q^67 - 11412166995 * q^68 + 1945422669 * q^70 + 5512912173 * q^71 + 2110132140 * q^73 - 22008588729 * q^74 + 11875694586 * q^76 + 2702962221 * q^77 + 6660721974 * q^79 - 12 * q^82 - 7670489421 * q^83 - 6965484381 * q^85 + 33241766118 * q^86 + 28790289402 * q^88 - 34430237370 * q^89 - 991980102 * q^91 - 40280154009 * q^92 - 62587945905 * q^94 + 12104972679 * q^95 + 48297833958 * q^97 + 103117506282 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/81\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{17}{18}\right)$

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 $

$2$	−9.99045	+	1.76159i	−0.312202	+	0.0550496i	−0.327554	−	0.944833i	$-0.606224\pi$
$2$	−9.99045	+	1.76159i	−0.312202	+	0.0550496i	0.0153520	+	0.999882i	$0.495113\pi$
$3$		0			0
$3$		0			0
$4$	−865.539	+	315.031i	−0.845253	+	0.307647i
$5$	−2619.44	+	3121.73i	−0.838222	+	0.998954i	0.161704	+	0.986839i	$0.448301\pi$
$5$	−2619.44	+	3121.73i	−0.838222	+	0.998954i	−0.999927	+	0.0121151i	$0.996144\pi$
$6$		0			0
$7$	−15129.3	−	5506.60i	−0.900176	−	0.327637i	−0.149853	−	0.988708i	$-0.547880\pi$
$7$	−15129.3	−	5506.60i	−0.900176	−	0.327637i	−0.750323	+	0.661071i	$0.770102\pi$
$8$	17088.5	−	9866.04i	0.521499	−	0.301088i
$9$		0			0
$10$	20670.2	−	35801.9i	0.206702	−	0.358019i
$11$	−45611.2	−	54357.3i	−0.283210	−	0.337516i	0.605620	−	0.795754i	$-0.292925\pi$
$11$	−45611.2	−	54357.3i	−0.283210	−	0.337516i	−0.888830	+	0.458238i	$0.848481\pi$
$12$		0			0
$13$	121958.	−	691659.i	0.328469	−	1.86284i	−0.155616	−	0.987818i	$-0.549736\pi$
$13$	121958.	−	691659.i	0.328469	−	1.86284i	0.484085	−	0.875021i	$-0.339153\pi$
$14$	160849.	+	28361.9i	0.299073	+	0.0527346i
$15$		0			0
$16$	569186.	−	477604.i	0.542819	−	0.455479i
$17$	−109192.	−	63041.9i	−0.0769033	−	0.0444002i	0.461055	−	0.887371i	$-0.347471\pi$
$17$	−109192.	−	63041.9i	−0.0769033	−	0.0444002i	−0.537959	+	0.842971i	$0.680804\pi$
$18$		0			0
$19$	−1.20002e6	−	2.07849e6i	−0.484640	−	0.839420i	0.515205	−	0.857067i	$-0.327716\pi$
$19$	−1.20002e6	−	2.07849e6i	−0.484640	−	0.839420i	−0.999844	+	0.0176468i	$0.994383\pi$
$20$	1.28379e6	−	3.52719e6i	0.401185	−	1.10225i
$21$		0			0
$22$	551431.	+	462706.i	0.106999	+	0.0897825i
$23$	2.26289e6	+	6.21725e6i	0.351580	+	0.965959i	0.981863	+	0.189593i	$0.0607169\pi$
$23$	2.26289e6	+	6.21725e6i	0.351580	+	0.965959i	−0.630282	+	0.776366i	$0.717061\pi$
$24$		0			0
$25$	−1.18794e6	−	6.73715e6i	−0.121645	−	0.689884i
$26$			7.12483e6i			0.599663i
$27$		0			0
$28$	1.48297e7			0.861674
$29$	−2.11083e7	+	3.72196e6i	−1.02911	+	0.181460i	−0.662616	−	0.748959i	$-0.730554\pi$
$29$	−2.11083e7	+	3.72196e6i	−1.02911	+	0.181460i	−0.366497	+	0.930419i	$0.619443\pi$
$30$		0			0
$31$	−4.32758e7	+	1.57511e7i	−1.51160	+	0.550177i	−0.959034	−	0.283292i	$-0.908574\pi$
$31$	−4.32758e7	+	1.57511e7i	−1.51160	+	0.550177i	−0.552566	+	0.833469i	$0.686351\pi$
$32$	−1.78330e7	+	2.12526e7i	−0.531466	+	0.633376i
$33$		0			0
$34$	1.20193e6	+	437466.i	0.0264536	+	0.00962831i
$35$	5.68204e7	−	3.28053e7i	1.08184	−	0.624602i
$36$		0			0
$37$	3.39317e7	−	5.87714e7i	0.489325	−	0.847535i	−0.510600	−	0.859818i	$-0.670577\pi$
$37$	3.39317e7	−	5.87714e7i	0.489325	−	0.847535i	0.999925	+	0.0122834i	$0.00391003\pi$
$38$	1.56501e7	+	1.86511e7i	0.197515	+	0.235389i
$39$		0			0
$40$	−1.39632e7	+	7.91892e7i	−0.136359	+	0.773332i
$41$	8.50271e7	+	1.49926e7i	0.733902	+	0.129407i	0.528094	−	0.849186i	$-0.322907\pi$
$41$	8.50271e7	+	1.49926e7i	0.733902	+	0.129407i	0.205808	+	0.978592i	$0.434018\pi$
$42$		0			0
$43$	−8.62677e7	+	7.23872e7i	−0.586821	+	0.492402i	−0.887179	−	0.461425i	$-0.847338\pi$
$43$	−8.62677e7	+	7.23872e7i	−0.586821	+	0.492402i	0.300358	+	0.953827i	$0.402894\pi$
$44$	5.66025e7	+	3.26795e7i	0.343220	+	0.198158i
$45$		0			0
$46$	−3.35595e7	−	5.81268e7i	−0.162940	−	0.282220i
$47$	8.10430e7	−	2.22664e8i	0.353367	−	0.970868i	−0.627913	−	0.778283i	$-0.716091\pi$
$47$	8.10430e7	−	2.22664e8i	0.353367	−	0.970868i	0.981280	−	0.192585i	$-0.0616870\pi$
$48$		0			0
$49$	−1.78166e7	−	1.49499e7i	−0.0630733	−	0.0529248i
$50$	2.37361e7	+	6.52145e7i	0.0759556	+	0.208686i
$51$		0			0
$52$	1.12334e8	+	6.37078e8i	0.295457	+	1.67562i
$53$		−	5.12143e8i		−	1.22465i	−0.790606	−	0.612325i	$-0.790235\pi$
$53$		−	5.12143e8i		−	1.22465i	0.790606	−	0.612325i	$-0.209765\pi$
$54$		0			0
$55$	2.89165e8			0.574556
$56$	−3.12865e8	+	5.51665e7i	−0.568089	+	0.100169i
$57$		0			0
$58$	2.04325e8	−	7.43681e7i	0.311301	−	0.113304i
$59$	−7.08786e8	+	8.44699e8i	−0.991415	+	1.18152i	−0.00803363	+	0.999968i	$0.502557\pi$
$59$	−7.08786e8	+	8.44699e8i	−0.991415	+	1.18152i	−0.983381	+	0.181554i	$0.941887\pi$
$60$		0			0
$61$	−6.03944e8	−	2.19817e8i	−0.715068	−	0.260263i	−0.0412373	−	0.999149i	$-0.513130\pi$
$61$	−6.03944e8	−	2.19817e8i	−0.715068	−	0.260263i	−0.673830	+	0.738886i	$0.735352\pi$
$62$	4.04598e8	−	2.33595e8i	0.441637	−	0.254979i
$63$		0			0
$64$	−2.39704e8	+	4.15180e8i	−0.223242	+	0.386667i
$65$	1.83971e9	+	2.19248e9i	1.58556	+	1.88960i
$66$		0			0
$67$	−3.30698e8	+	1.87548e9i	−0.244939	+	1.38912i	0.575697	+	0.817663i	$0.304731\pi$
$67$	−3.30698e8	+	1.87548e9i	−0.244939	+	1.38912i	−0.820635	+	0.571452i	$0.806380\pi$
$68$	1.14370e8	+	2.01665e7i	0.0786624	+	0.0138703i
$69$		0			0
$70$	−5.09872e8	+	4.27834e8i	−0.303369	+	0.254557i
$71$	1.80207e9	+	1.04043e9i	0.998805	+	0.576660i	0.907894	−	0.419199i	$-0.137689\pi$
$71$	1.80207e9	+	1.04043e9i	0.998805	+	0.576660i	0.0909103	+	0.995859i	$0.471022\pi$
$72$		0			0
$73$	−1.61956e7	−	2.80516e7i	−0.00781237	−	0.0135314i	0.862093	−	0.506750i	$-0.169153\pi$
$73$	−1.61956e7	−	2.80516e7i	−0.00781237	−	0.0135314i	−0.869905	+	0.493219i	$0.835820\pi$
$74$	−2.35462e8	+	6.46927e8i	−0.106111	+	0.291539i
$75$		0			0
$76$	1.69345e9	+	1.42097e9i	0.667888	+	0.560425i
$77$	3.90740e8	+	1.07355e9i	0.144356	+	0.396614i
$78$		0			0
$79$	−5.52812e7	−	3.13515e8i	−0.0179656	−	0.101888i	0.974506	−	0.224360i	$-0.0720291\pi$
$79$	−5.52812e7	−	3.13515e8i	−0.0179656	−	0.101888i	−0.992472	+	0.122472i	$0.960918\pi$
$80$			3.02791e9i			0.924043i
$81$		0			0
$82$	−8.75870e8			−0.236249
$83$	5.26514e9	−	9.28386e8i	1.33665	−	0.235688i	0.540788	−	0.841159i	$-0.318126\pi$
$83$	5.26514e9	−	9.28386e8i	1.33665	−	0.235688i	0.795867	+	0.605471i	$0.207015\pi$
$84$		0			0
$85$	4.82822e8	−	1.75733e8i	0.108816	−	0.0396057i
$86$	7.34337e8	−	8.75149e8i	0.156100	−	0.186033i
$87$		0			0
$88$	−1.31572e9	−	4.78882e8i	−0.249315	−	0.0907434i
$89$	−5.25641e9	+	3.03479e9i	−0.941324	+	0.543473i	−0.890375	−	0.455228i	$-0.849558\pi$
$89$	−5.25641e9	+	3.03479e9i	−0.941324	+	0.543473i	−0.0509486	+	0.998701i	$0.516224\pi$
$90$		0			0
$91$	−5.65383e9	+	9.79271e9i	−0.906015	+	1.56926i
$92$	−3.91724e9	−	4.66839e9i	−0.594349	−	0.708318i
$93$		0			0
$94$	−4.17415e8	+	2.36728e9i	−0.0568759	+	0.322559i
$95$	9.63186e9	+	1.69836e9i	1.24478	+	0.219488i
$96$		0			0
$97$	4.82972e9	−	4.05261e9i	0.562423	−	0.471929i	−0.316699	−	0.948526i	$-0.602574\pi$
$97$	4.82972e9	−	4.05261e9i	0.562423	−	0.471929i	0.879122	+	0.476597i	$0.158130\pi$
$98$	2.04332e8	+	1.17971e8i	0.0226051	+	0.0130510i
$99$		0			0
$100$	3.15062e9	+	5.45703e9i	0.315062	+	0.545703i
$101$	1.32022e9	−	3.62727e9i	0.125614	−	0.345122i	−0.860906	−	0.508765i	$-0.830102\pi$
$101$	1.32022e9	−	3.62727e9i	0.125614	−	0.345122i	0.986520	+	0.163643i	$0.0523245\pi$
$102$		0			0
$103$	4.64727e9	+	3.89952e9i	0.400877	+	0.336376i	0.820833	−	0.571169i	$-0.193510\pi$
$103$	4.64727e9	+	3.89952e9i	0.400877	+	0.336376i	−0.419955	+	0.907545i	$0.637954\pi$
$104$	−4.73986e9	−	1.30226e10i	−0.389582	−	1.07037i
$105$		0			0
$106$	9.02184e8	+	5.11654e9i	0.0674164	+	0.382338i
$107$			7.88025e9i			0.561851i	0.959730	+	0.280926i	$0.0906414\pi$
$107$			7.88025e9i			0.561851i	−0.959730	+	0.280926i	$0.909359\pi$
$108$		0			0
$109$	4.24804e9			0.276093			0.138047	−	0.990426i	$-0.455918\pi$
$109$	4.24804e9			0.276093			0.138047	+	0.990426i	$0.455918\pi$
$110$	−2.88889e9	+	5.09389e8i	−0.179377	+	0.0316290i
$111$		0			0
$112$	−1.12413e10	+	4.09152e9i	−0.637864	+	0.232164i
$113$	−9.97564e9	+	1.18885e10i	−0.541438	+	0.645261i	−0.965509	−	0.260368i	$-0.916156\pi$
$113$	−9.97564e9	+	1.18885e10i	−0.541438	+	0.645261i	0.424072	+	0.905629i	$0.360601\pi$
$114$		0			0
$115$	−2.53361e10	−	9.22159e9i	−1.25965	−	0.458476i
$116$	1.70975e10	−	9.87126e9i	0.814035	−	0.469983i
$117$		0			0
$118$	5.59309e9	−	9.68751e9i	0.244479	−	0.423450i
$119$	1.30484e9	+	1.55505e9i	0.0546794	+	0.0651644i
$120$		0			0
$121$	3.62965e9	−	2.05848e10i	0.139939	−	0.793632i
$122$	6.42090e9	+	1.13218e9i	0.237573	+	0.0418905i
$123$		0			0
$124$	3.24948e10	−	2.72664e10i	1.10842	−	0.930078i
$125$	−1.03212e10	−	5.95896e9i	−0.338206	−	0.195263i
$126$		0			0
$127$	−1.29148e10	−	2.23692e10i	−0.390904	−	0.677066i	0.601665	−	0.798749i	$-0.294504\pi$
$127$	−1.29148e10	−	2.23692e10i	−0.390904	−	0.677066i	−0.992569	+	0.121683i	$0.961171\pi$
$128$	1.13799e10	−	3.12659e10i	0.331198	−	0.909958i
$129$		0			0
$130$	−2.22418e10	−	1.86631e10i	−0.599036	−	0.502651i
$131$	9.89610e9	+	2.71893e10i	0.256512	+	0.704761i	0.999376	+	0.0353185i	$0.0112446\pi$
$131$	9.89610e9	+	2.71893e10i	0.256512	+	0.704761i	−0.742864	+	0.669442i	$0.766533\pi$
$132$		0			0
$133$	6.70995e9	+	3.80540e10i	0.161236	+	0.914412i
$134$		−	1.93194e10i		−	0.447168i
$135$		0			0
$136$	−2.48790e9			−0.0534734
$137$	−4.59637e10	+	8.10465e9i	−0.952385	+	0.167931i	−0.628191	−	0.778059i	$-0.716204\pi$
$137$	−4.59637e10	+	8.10465e9i	−0.952385	+	0.167931i	−0.324194	+	0.945991i	$0.605093\pi$
$138$		0			0
$139$	2.81258e10	−	1.02369e10i	0.542039	−	0.197286i	−0.0564669	−	0.998404i	$-0.517984\pi$
$139$	2.81258e10	−	1.02369e10i	0.542039	−	0.197286i	0.598506	+	0.801118i	$0.295761\pi$
$140$	−3.88456e10	+	4.62944e10i	−0.722274	+	0.860773i
$141$		0			0
$142$	−1.98363e10	−	7.21983e9i	−0.343573	−	0.125050i
$143$	−4.31594e10	+	2.49181e10i	−0.721763	+	0.416710i
$144$		0			0
$145$	4.36730e10	−	7.56439e10i	0.681355	−	1.18014i
$146$	2.11217e8	+	2.51718e8i	0.00318393	+	0.00379446i
$147$		0			0
$148$	−1.08544e10	+	6.15585e10i	−0.152862	+	0.866921i
$149$	−6.94305e10	−	1.22425e10i	−0.945407	−	0.166701i	−0.320367	−	0.947293i	$-0.603806\pi$
$149$	−6.94305e10	−	1.22425e10i	−0.945407	−	0.166701i	−0.625040	+	0.780593i	$0.714917\pi$
$150$		0			0
$151$	2.46243e10	−	2.06622e10i	0.313674	−	0.263204i	−0.472335	−	0.881419i	$-0.656589\pi$
$151$	2.46243e10	−	2.06622e10i	0.313674	−	0.263204i	0.786009	+	0.618216i	$0.212144\pi$
$152$	−4.10129e10	−	2.36788e10i	−0.505478	−	0.291838i
$153$		0			0
$154$	−5.79481e9	−	1.00369e10i	−0.0669015	−	0.115877i
$155$	6.41879e10	−	1.76355e11i	0.717455	−	1.97119i
$156$		0			0
$157$	8.44811e10	+	7.08880e10i	0.885648	+	0.743147i	0.967332	−	0.253511i	$-0.0815855\pi$
$157$	8.44811e10	+	7.08880e10i	0.885648	+	0.743147i	−0.0816845	+	0.996658i	$0.526030\pi$
$158$	1.10457e9	+	3.03478e9i	0.0112178	+	0.0308206i
$159$		0			0
$160$	−1.96322e10	−	1.11340e11i	−0.187228	−	1.06182i
$161$		−	1.06523e11i		−	0.984725i
$162$		0			0
$163$	1.22297e11			1.06286			0.531430	−	0.847102i	$-0.321655\pi$
$163$	1.22297e11			1.06286			0.531430	+	0.847102i	$0.321655\pi$
$164$	−7.83174e10	+	1.38095e10i	−0.660145	+	0.116401i
$165$		0			0
$166$	−5.09657e10	+	1.85500e10i	−0.404331	+	0.147165i
$167$	7.41669e10	−	8.83886e10i	0.570989	−	0.680478i	−0.400845	−	0.916146i	$-0.631283\pi$
$167$	7.41669e10	−	8.83886e10i	0.570989	−	0.680478i	0.971834	+	0.235668i	$0.0757278\pi$
$168$		0			0
$169$	−3.33974e11	−	1.21556e11i	−2.42258	−	0.881748i
$170$	−4.51404e9	+	2.60618e9i	−0.0317922	+	0.0183552i
$171$		0			0
$172$	5.18639e10	−	8.98309e10i	0.344527	−	0.596738i
$173$	1.95267e11	+	2.32710e11i	1.26008	+	1.50170i	0.781845	+	0.623472i	$0.214279\pi$
$173$	1.95267e11	+	2.32710e11i	1.26008	+	1.50170i	0.478234	+	0.878232i	$0.341277\pi$
$174$		0			0
$175$	−1.91261e10	+	1.08470e11i	−0.116530	+	0.660873i
$176$	−5.19225e10	−	9.15534e9i	−0.307463	−	0.0542140i
$177$		0			0
$178$	4.71678e10	−	3.95785e10i	0.263965	−	0.221493i
$179$	−2.29281e11	−	1.32375e11i	−1.24768	−	0.720348i	−0.277033	−	0.960860i	$-0.589351\pi$
$179$	−2.29281e11	−	1.32375e11i	−1.24768	−	0.720348i	−0.970646	+	0.240512i	$0.922685\pi$
$180$		0			0
$181$	1.37071e11	+	2.37413e11i	0.705588	+	1.22211i	0.966479	+	0.256746i	$0.0826505\pi$
$181$	1.37071e11	+	2.37413e11i	0.705588	+	1.22211i	−0.260891	+	0.965368i	$0.584016\pi$
$182$	3.92336e10	−	1.07793e11i	0.196472	−	0.539803i
$183$		0			0
$184$	1.00009e11	+	8.39175e10i	0.474187	+	0.397890i
$185$	9.45865e10	+	2.59874e11i	0.436486	+	1.19924i
$186$		0			0
$187$	1.55358e9	+	8.81078e9i	0.00679399	+	0.0385307i
$188$			2.18255e11i			0.929342i
$189$		0			0
$190$	−9.92184e10			−0.400705
$191$	4.42635e11	−	7.80484e10i	1.74132	−	0.307042i	0.789512	−	0.613736i	$-0.210334\pi$
$191$	4.42635e11	−	7.80484e10i	1.74132	−	0.307042i	0.951808	+	0.306694i	$0.0992228\pi$
$192$		0			0
$193$	−7.92276e10	+	2.88365e10i	−0.295863	+	0.107685i	−0.485687	−	0.874133i	$-0.661430\pi$
$193$	−7.92276e10	+	2.88365e10i	−0.295863	+	0.107685i	0.189824	+	0.981818i	$0.439208\pi$
$194$	−4.11120e10	+	4.89954e10i	−0.149610	+	0.178298i
$195$		0			0
$196$	2.01307e10	+	7.32697e9i	0.0695951	+	0.0253305i
$197$	−3.58667e11	+	2.07077e11i	−1.20882	+	0.697911i	−0.962501	−	0.271278i	$-0.912554\pi$
$197$	−3.58667e11	+	2.07077e11i	−1.20882	+	0.697911i	−0.246317	+	0.969189i	$0.579220\pi$
$198$		0			0
$199$	−2.60376e9	+	4.50985e9i	−0.00834326	+	0.0144510i	−0.870167	−	0.492757i	$-0.835989\pi$
$199$	−2.60376e9	+	4.50985e9i	−0.00834326	+	0.0144510i	0.861824	+	0.507208i	$0.169322\pi$
$200$	−8.67691e10	−	1.03407e11i	−0.271153	−	0.323148i
$201$		0			0
$202$	−6.79982e9	+	3.85637e10i	−0.0202181	+	0.114663i
$203$	3.39848e11	+	5.99244e10i	0.985836	+	0.173830i
$204$		0			0
$205$	−2.69527e11	+	2.26160e11i	−0.744445	+	0.624663i
$206$	−5.32977e10	−	3.07714e10i	−0.143672	−	0.0829491i
$207$		0			0
$208$	−2.60922e11	−	4.51931e11i	−0.670185	−	1.16079i
$209$	−5.82468e10	+	1.60032e11i	−0.146063	+	0.401305i
$210$		0			0
$211$	−5.56689e10	−	4.67117e10i	−0.133107	−	0.111690i	0.573804	−	0.818993i	$-0.305467\pi$
$211$	−5.56689e10	−	4.67117e10i	−0.133107	−	0.111690i	−0.706911	+	0.707303i	$0.749912\pi$
$212$	1.61341e11	+	4.43280e11i	0.376760	+	1.03514i
$213$		0			0
$214$	−1.38818e10	−	7.87273e10i	−0.0309297	−	0.175411i
$215$		−	4.58919e11i		−	0.998950i
$216$		0			0
$217$	7.41466e11			1.54097
$218$	−4.24399e10	+	7.48329e9i	−0.0861969	+	0.0151988i
$219$		0			0
$220$	−2.50284e11	+	9.10958e10i	−0.485645	+	0.176760i
$221$	−5.69203e10	+	6.78350e10i	−0.107971	+	0.128674i
$222$		0			0
$223$	2.56481e11	+	9.33515e10i	0.465084	+	0.169277i	0.563924	−	0.825827i	$-0.309291\pi$
$223$	2.56481e11	+	9.33515e10i	0.465084	+	0.169277i	−0.0988402	+	0.995103i	$0.531513\pi$
$224$	3.86830e11	−	2.23337e11i	0.685931	−	0.396022i
$225$		0			0
$226$	7.87186e10	−	1.36345e11i	0.133517	−	0.231257i
$227$	−5.97259e10	−	7.11786e10i	−0.0990909	−	0.118092i	0.714220	−	0.699921i	$-0.246782\pi$
$227$	−5.97259e10	−	7.11786e10i	−0.0990909	−	0.118092i	−0.813311	+	0.581829i	$0.802337\pi$
$228$		0			0
$229$	−1.86324e11	+	1.05670e12i	−0.295864	+	1.67793i	0.367807	+	0.929902i	$0.380109\pi$
$229$	−1.86324e11	+	1.05670e12i	−0.295864	+	1.67793i	−0.663671	+	0.748025i	$0.731002\pi$
$230$	2.69364e11	+	4.74961e10i	0.418504	+	0.0737936i
$231$		0			0
$232$	−3.23988e11	+	2.71858e11i	−0.482046	+	0.404485i
$233$	3.90677e11	+	2.25557e11i	0.568903	+	0.328456i	0.756711	−	0.653750i	$-0.226805\pi$
$233$	3.90677e11	+	2.25557e11i	0.568903	+	0.328456i	−0.187808	+	0.982206i	$0.560138\pi$
$234$		0			0
$235$	4.82809e11	+	8.36250e11i	0.673653	+	1.16680i
$236$	3.47377e11	−	9.54409e11i	0.474505	−	1.30369i
$237$		0			0
$238$	−1.57753e10	−	1.32371e10i	−0.0206583	−	0.0173344i
$239$	3.40143e11	+	9.34536e11i	0.436187	+	1.19841i	0.941954	+	0.335743i	$0.108987\pi$
$239$	3.40143e11	+	9.34536e11i	0.436187	+	1.19841i	−0.505767	+	0.862670i	$0.668790\pi$
$240$		0			0
$241$	−4.66091e10	−	2.64333e11i	−0.0573305	−	0.325137i	0.942632	−	0.333834i	$-0.108343\pi$
$241$	−4.66091e10	−	2.64333e11i	−0.0573305	−	0.325137i	−0.999962	+	0.00869729i	$0.997232\pi$
$242$			2.12045e11i			0.255477i
$243$		0			0
$244$	5.91986e11			0.684483
$245$	9.33394e10	−	1.64583e10i	0.105739	−	0.0186446i
$246$		0			0
$247$	−1.58396e12	+	5.76513e11i	−1.72289	+	0.627082i
$248$	−5.84117e11	+	6.96124e11i	−0.622646	+	0.742041i
$249$		0			0
$250$	1.13611e11	+	4.13510e10i	0.116338	+	0.0423434i
$251$	−9.74308e11	+	5.62517e11i	−0.977975	+	0.564634i	−0.901658	−	0.432449i	$-0.857649\pi$
$251$	−9.74308e11	+	5.62517e11i	−0.977975	+	0.564634i	−0.0763169	+	0.997084i	$0.524316\pi$
$252$		0			0
$253$	2.34739e11	−	4.06581e11i	0.226456	−	0.392233i
$254$	1.68430e11	+	2.00728e11i	0.159313	+	0.189862i
$255$		0			0
$256$	2.66340e10	−	1.51049e11i	0.0242235	−	0.137378i
$257$	1.61231e12	+	2.84294e11i	1.43808	+	0.253572i	0.837695	−	0.546139i	$-0.183903\pi$
$257$	1.61231e12	+	2.84294e11i	1.43808	+	0.253572i	0.600385	+	0.799711i	$0.295014\pi$
$258$		0			0
$259$	−8.36992e11	+	7.02320e11i	−0.718162	+	0.602610i
$260$	−2.28304e12	−	1.31811e12i	−1.92153	−	1.10940i
$261$		0			0
$262$	−1.46763e11	−	2.54201e11i	−0.118880	−	0.205907i
$263$	3.83886e11	−	1.05472e12i	0.305087	−	0.838220i	−0.688509	−	0.725228i	$-0.741734\pi$
$263$	3.83886e11	−	1.05472e12i	0.305087	−	0.838220i	0.993596	−	0.112992i	$-0.0360434\pi$
$264$		0			0
$265$	1.59877e12	+	1.34153e12i	1.22337	+	1.02653i
$266$	−1.34071e11	−	3.68357e11i	−0.100676	−	0.276605i
$267$		0			0
$268$	−3.04602e11	−	1.72748e12i	−0.220322	−	1.24951i
$269$			4.74835e11i			0.337118i	0.985692	+	0.168559i	$0.0539113\pi$
$269$			4.74835e11i			0.337118i	−0.985692	+	0.168559i	$0.946089\pi$
$270$		0			0
$271$	9.85383e11			0.674154			0.337077	−	0.941477i	$-0.390562\pi$
$271$	9.85383e11			0.674154			0.337077	+	0.941477i	$0.390562\pi$
$272$	−9.22595e10	+	1.62678e10i	−0.0619679	+	0.0109266i
$273$		0			0
$274$	4.44922e11	−	1.61938e11i	0.288092	−	0.104857i
$275$	−3.12030e11	+	3.71862e11i	−0.198396	+	0.236439i
$276$		0			0
$277$	−1.23505e12	−	4.49522e11i	−0.757332	−	0.275646i	−0.0656445	−	0.997843i	$-0.520910\pi$
$277$	−1.23505e12	−	4.49522e11i	−0.757332	−	0.275646i	−0.691688	+	0.722197i	$0.743133\pi$
$278$	−2.62956e11	+	1.51818e11i	−0.158365	+	0.0914321i
$279$		0			0
$280$	6.47316e11	−	1.12118e12i	0.376120	−	0.651459i
$281$	2.98197e11	+	3.55378e11i	0.170205	+	0.202842i	0.844403	−	0.535708i	$-0.179955\pi$
$281$	2.98197e11	+	3.55378e11i	0.170205	+	0.202842i	−0.674198	+	0.738550i	$0.735511\pi$
$282$		0			0
$283$	2.26890e11	−	1.28676e12i	0.124993	−	0.708868i	−0.856320	−	0.516446i	$-0.827255\pi$
$283$	2.26890e11	−	1.28676e12i	0.124993	−	0.708868i	0.981312	−	0.192422i	$-0.0616342\pi$
$284$	−1.88753e12	−	3.32823e11i	−1.02165	−	0.180145i
$285$		0			0
$286$	3.87286e11	−	3.24972e11i	0.202396	−	0.169830i
$287$	−1.20384e12	−	6.95037e11i	−0.618243	−	0.356943i
$288$		0			0
$289$	−1.00005e12	−	1.73213e12i	−0.496057	−	0.859196i
$290$	−3.03060e11	+	8.32651e11i	−0.147754	+	0.405950i
$291$		0			0
$292$	2.28550e10	+	1.91776e10i	0.0107663	+	0.00903402i
$293$	−3.98373e11	−	1.09452e12i	−0.184481	−	0.506858i	0.812633	−	0.582776i	$-0.198033\pi$
$293$	−3.98373e11	−	1.09452e12i	−0.184481	−	0.506858i	−0.997114	+	0.0759181i	$0.975811\pi$
$294$		0			0
$295$	−7.80297e11	−	4.42528e12i	−0.349261	−	1.98076i
$296$		−	1.33909e12i		−	0.589318i
$297$		0			0
$298$	7.15208e11			0.304334
$299$	4.57619e12	−	8.06906e11i	1.91491	−	0.337650i
$300$		0			0
$301$	1.70377e12	−	6.20123e11i	0.689572	−	0.250984i
$302$	−2.09609e11	+	2.49803e11i	−0.0834403	+	0.0994403i
$303$		0			0
$304$	−1.67573e12	−	6.09915e11i	−0.645410	−	0.234910i
$305$	2.26821e12	−	1.30955e12i	0.859377	−	0.496161i
$306$		0			0
$307$	4.75877e11	−	8.24244e11i	0.174503	−	0.302248i	−0.765486	−	0.643452i	$-0.777501\pi$
$307$	4.75877e11	−	8.24244e11i	0.174503	−	0.302248i	0.939989	+	0.341204i	$0.110835\pi$
$308$	−6.76401e11	−	8.06103e11i	−0.244034	−	0.290829i
$309$		0			0
$310$	−3.30602e11	+	1.87494e12i	−0.115477	+	0.654904i
$311$	−2.37003e12	−	4.17900e11i	−0.814614	−	0.143638i	−0.249207	−	0.968450i	$-0.580170\pi$
$311$	−2.37003e12	−	4.17900e11i	−0.814614	−	0.143638i	−0.565407	+	0.824812i	$0.691281\pi$
$312$		0			0
$313$	−1.53320e11	+	1.28651e11i	−0.0510361	+	0.0428243i	−0.667949	−	0.744207i	$-0.732828\pi$
$313$	−1.53320e11	+	1.28651e11i	−0.0510361	+	0.0428243i	0.616913	+	0.787031i	$0.288383\pi$
$314$	−9.68880e11	−	5.59383e11i	−0.317411	−	0.183257i
$315$		0			0
$316$	1.46615e11	+	2.53945e11i	0.0465311	+	0.0805941i
$317$	−1.58311e11	+	4.34957e11i	−0.0494556	+	0.135878i	−0.961961	−	0.273186i	$-0.911923\pi$
$317$	−1.58311e11	+	4.34957e11i	−0.0494556	+	0.135878i	0.912506	+	0.409064i	$0.134145\pi$
$318$		0			0
$319$	1.16509e12	+	9.77626e11i	0.352700	+	0.295951i
$320$	−6.68189e11	−	1.83584e12i	−0.199136	−	0.547122i
$321$		0			0
$322$	1.87650e11	+	1.06422e12i	0.0542087	+	0.307433i
$323$			3.02605e11i			0.0860723i
$324$		0			0
$325$	−4.80469e12			−1.32510
$326$	−1.22180e12	+	2.15436e11i	−0.331827	+	0.0585100i
$327$		0			0
$328$	1.60090e12	−	5.82681e11i	0.421692	−	0.153483i
$329$	−2.45224e12	+	2.92247e12i	−0.636185	+	0.758176i
$330$		0			0
$331$	2.52288e12	+	9.18253e11i	0.634975	+	0.231112i	0.639395	−	0.768878i	$-0.279185\pi$
$331$	2.52288e12	+	9.18253e11i	0.634975	+	0.231112i	−0.00442042	+	0.999990i	$0.501407\pi$
$332$	−4.26471e12	+	2.46223e12i	−1.05730	+	0.610434i
$333$		0			0
$334$	−5.85257e11	+	1.01369e12i	−0.140804	+	0.243879i
$335$	−4.98850e12	−	5.94506e12i	−1.18235	−	1.40907i
$336$		0			0
$337$	−1.82497e11	+	1.03499e12i	−0.0419863	+	0.238116i	−0.998578	−	0.0533166i	$-0.983021\pi$
$337$	−1.82497e11	+	1.03499e12i	−0.0419863	+	0.238116i	0.956591	+	0.291432i	$0.0941319\pi$
$338$	3.55068e12	+	6.26081e11i	0.804874	+	0.141921i
$339$		0			0
$340$	−3.62540e11	+	3.04207e11i	−0.0797923	+	0.0669537i
$341$	2.83005e12	+	1.63393e12i	0.613793	+	0.354374i
$342$		0			0
$343$	2.46119e12	+	4.26290e12i	0.518411	+	0.897914i
$344$	−7.60009e11	+	2.08811e12i	−0.157771	+	0.433472i
$345$		0			0
$346$	−2.36074e12	−	1.98090e12i	−0.476067	−	0.399468i
$347$	1.44397e12	+	3.96727e12i	0.287019	+	0.788578i	0.996480	+	0.0838331i	$0.0267163\pi$
$347$	1.44397e12	+	3.96727e12i	0.287019	+	0.788578i	−0.709461	+	0.704745i	$0.751062\pi$
$348$		0			0
$349$	1.56302e12	+	8.86431e12i	0.301881	+	1.71205i	0.637832	+	0.770175i	$0.279831\pi$
$349$	1.56302e12	+	8.86431e12i	0.301881	+	1.71205i	−0.335951	+	0.941879i	$0.609058\pi$
$350$		−	1.11735e12i		−	0.212740i
$351$		0			0
$352$	1.96862e12			0.364291
$353$	4.68733e12	−	8.26502e11i	0.855169	−	0.150789i	0.271158	−	0.962535i	$-0.412594\pi$
$353$	4.68733e12	−	8.26502e11i	0.855169	−	0.150789i	0.584011	+	0.811746i	$0.301482\pi$
$354$		0			0
$355$	−7.96836e12	+	2.90025e12i	−1.41328	+	0.514391i
$356$	3.59358e12	−	4.28266e12i	0.628459	−	0.748968i
$357$		0			0
$358$	2.52381e12	+	9.18593e11i	0.429183	+	0.156210i
$359$	6.94809e12	−	4.01148e12i	1.16518	−	0.672718i	0.212641	−	0.977130i	$-0.431794\pi$
$359$	6.94809e12	−	4.01148e12i	1.16518	−	0.672718i	0.952540	+	0.304413i	$0.0984602\pi$
$360$		0			0
$361$	1.85458e11	−	3.21224e11i	0.0302490	−	0.0523928i
$362$	−1.78762e12	−	2.13040e12i	−0.287563	−	0.342704i
$363$		0			0
$364$	1.80860e12	−	1.02571e13i	0.283033	−	1.60516i
$365$	1.29993e11	+	2.29213e10i	0.0200658	+	0.00353814i
$366$		0			0
$367$	6.31275e12	−	5.29702e12i	0.948174	−	0.795613i	−0.0308149	−	0.999525i	$-0.509810\pi$
$367$	6.31275e12	−	5.29702e12i	0.948174	−	0.795613i	0.978989	+	0.203912i	$0.0653658\pi$
$368$	4.25739e12	+	2.45801e12i	0.630818	+	0.364203i
$369$		0			0
$370$	−1.40275e12	−	2.42964e12i	−0.202289	−	0.350375i
$371$	−2.82017e12	+	7.74835e12i	−0.401241	+	1.10240i
$372$		0			0
$373$	2.38443e12	+	2.00077e12i	0.330248	+	0.277111i	0.792801	−	0.609481i	$-0.208622\pi$
$373$	2.38443e12	+	2.00077e12i	0.330248	+	0.277111i	−0.462553	+	0.886592i	$0.653066\pi$
$374$	−3.10419e10	−	8.52869e10i	−0.00424219	−	0.0116553i
$375$		0			0
$376$	−8.11908e11	−	4.60456e12i	−0.108036	−	0.612701i
$377$			1.50537e13i			1.97667i
$378$		0			0
$379$	−1.54124e12			−0.197094			−0.0985471	−	0.995132i	$-0.531419\pi$
$379$	−1.54124e12			−0.197094			−0.0985471	+	0.995132i	$0.531419\pi$
$380$	−8.87178e12	+	1.56434e12i	−1.11968	+	0.197429i
$381$		0			0
$382$	−4.28463e12	+	1.55948e12i	−0.526740	+	0.191718i
$383$	4.62166e12	−	5.50788e12i	0.560795	−	0.668330i	−0.408919	−	0.912571i	$-0.634094\pi$
$383$	4.62166e12	−	5.50788e12i	0.560795	−	0.668330i	0.969715	+	0.244241i	$0.0785387\pi$
$384$		0			0
$385$	−4.37485e12	−	1.59232e12i	−0.517201	−	0.188246i
$386$	7.40722e11	−	4.27656e11i	0.0864408	−	0.0499066i
$387$		0			0
$388$	−2.90361e12	+	5.02920e12i	−0.330202	+	0.571927i
$389$	2.57745e12	+	3.07168e12i	0.289362	+	0.344849i	0.891068	−	0.453869i	$-0.149957\pi$
$389$	2.57745e12	+	3.07168e12i	0.289362	+	0.344849i	−0.601706	+	0.798718i	$0.705512\pi$
$390$		0			0
$391$	1.44858e11	−	8.21529e11i	0.0158510	−	0.0898957i
$392$	−4.51956e11	−	7.96921e10i	−0.0488277	−	0.00860964i
$393$		0			0
$394$	3.21847e12	−	2.70061e12i	0.338975	−	0.284434i
$395$	1.12352e12	+	6.48663e11i	0.116841	+	0.0674580i
$396$		0			0
$397$	3.02106e12	+	5.23262e12i	0.306342	+	0.530600i	0.977559	−	0.210661i	$-0.0675616\pi$
$397$	3.02106e12	+	5.23262e12i	0.306342	+	0.530600i	−0.671217	+	0.741261i	$0.734228\pi$
$398$	1.80683e10	−	4.96422e10i	0.00180926	−	0.00497090i
$399$		0			0
$400$	−3.89385e12	−	3.26733e12i	−0.380259	−	0.319075i
$401$	1.63980e12	+	4.50531e12i	0.158150	+	0.434513i	0.993308	−	0.115497i	$-0.0368460\pi$
$401$	1.63980e12	+	4.50531e12i	0.158150	+	0.434513i	−0.835158	+	0.550010i	$0.814624\pi$
$402$		0			0
$403$	5.61656e12	+	3.18531e13i	0.528378	+	2.99658i
$404$			3.55545e12i			0.330360i
$405$		0			0
$406$	−3.50080e12			−0.317349
$407$	−4.74232e12	+	8.36199e11i	−0.424638	+	0.0748751i
$408$		0			0
$409$	1.15109e13	−	4.18961e12i	1.00575	−	0.366064i	0.213952	−	0.976844i	$-0.431366\pi$
$409$	1.15109e13	−	4.18961e12i	1.00575	−	0.366064i	0.791800	+	0.610780i	$0.209144\pi$
$410$	2.29429e12	−	2.73423e12i	0.198029	−	0.236002i
$411$		0			0
$412$	−5.25086e12	−	1.91116e12i	−0.442328	−	0.160994i
$413$	1.53748e13	−	8.87667e12i	1.27956	−	0.738754i
$414$		0			0
$415$	−1.08936e13	+	1.88682e13i	−0.884972	+	1.53282i
$416$	1.25247e13	+	1.49263e13i	1.00531	+	1.19808i
$417$		0			0
$418$	3.00002e11	−	1.70140e12i	0.0235095	−	0.133329i
$419$	−1.37363e13	−	2.42209e12i	−1.06366	−	0.187551i	−0.385678	−	0.922633i	$-0.626032\pi$
$419$	−1.37363e13	−	2.42209e12i	−1.06366	−	0.187551i	−0.677978	+	0.735082i	$0.737144\pi$
$420$		0			0
$421$	−3.46784e12	+	2.90986e12i	−0.262210	+	0.220020i	−0.764409	−	0.644732i	$-0.776969\pi$
$421$	−3.46784e12	+	2.90986e12i	−0.262210	+	0.220020i	0.502199	+	0.864752i	$0.332525\pi$
$422$	6.38444e11	+	3.68606e11i	0.0477046	+	0.0275423i
$423$		0			0
$424$	−5.05282e12	−	8.75175e12i	−0.368727	−	0.638654i
$425$	−2.95009e11	+	8.10531e11i	−0.0212760	+	0.0584554i
$426$		0			0
$427$	7.92677e12	+	6.65135e12i	0.558415	+	0.468566i
$428$	−2.48252e12	−	6.82067e12i	−0.172852	−	0.474907i
$429$		0			0
$430$	8.08425e11	+	4.58481e12i	0.0549918	+	0.311874i
$431$			3.63360e12i			0.244316i	0.992511	+	0.122158i	$0.0389814\pi$
$431$			3.63360e12i			0.244316i	−0.992511	+	0.122158i	$0.961019\pi$
$432$		0			0
$433$	−2.75243e13			−1.80832			−0.904162	−	0.427189i	$-0.859504\pi$
$433$	−2.75243e13			−1.80832			−0.904162	+	0.427189i	$0.859504\pi$
$434$	−7.40759e12	+	1.30616e12i	−0.481092	+	0.0848295i
$435$		0			0
$436$	−3.67685e12	+	1.33826e12i	−0.233369	+	0.0849393i
$437$	1.02070e13	−	1.21642e13i	0.640456	−	0.763266i
$438$		0			0
$439$	2.19176e13	+	7.97734e12i	1.34422	+	0.489255i	0.911138	−	0.412101i	$-0.135205\pi$
$439$	2.19176e13	+	7.97734e12i	1.34422	+	0.489255i	0.433079	+	0.901356i	$0.357427\pi$
$440$	4.94139e12	−	2.85291e12i	0.299630	−	0.172992i
$441$		0			0
$442$	4.49162e11	−	7.77972e11i	0.0266252	−	0.0461161i
$443$	1.17695e13	+	1.40264e13i	0.689828	+	0.822105i	0.991335	−	0.131359i	$-0.0419340\pi$
$443$	1.17695e13	+	1.40264e13i	0.689828	+	0.822105i	−0.301507	+	0.953464i	$0.597490\pi$
$444$		0			0
$445$	4.29507e12	−	2.43586e13i	0.246133	−	1.39589i
$446$	−2.72681e12	−	4.80810e11i	−0.154519	−	0.0272458i
$447$		0			0
$448$	5.91279e12	−	4.96142e12i	0.327644	−	0.274926i
$449$	−1.63500e13	−	9.43966e12i	−0.895953	−	0.517279i	−0.0200679	−	0.999799i	$-0.506388\pi$
$449$	−1.63500e13	−	9.43966e12i	−0.895953	−	0.517279i	−0.875885	+	0.482520i	$0.839722\pi$
$450$		0			0
$451$	−3.06323e12	−	5.30567e12i	−0.164171	−	0.284353i
$452$	4.88907e12	−	1.34326e13i	0.259140	−	0.711980i
$453$		0			0
$454$	7.22076e11	+	6.05894e11i	0.0374372	+	0.0314136i
$455$	−1.57604e13	−	4.33012e13i	−0.808181	−	2.22046i
$456$		0			0
$457$	−6.34401e12	−	3.59786e13i	−0.318260	−	1.80494i	−0.553326	−	0.832965i	$-0.686642\pi$
$457$	−6.34401e12	−	3.59786e13i	−0.318260	−	1.80494i	0.235066	−	0.971980i	$-0.424470\pi$
$458$		−	1.08851e13i		−	0.540139i
$459$		0			0
$460$	2.48345e13			1.20577
$461$	−1.35602e13	+	2.39103e12i	−0.651270	+	0.114836i	−0.489516	−	0.871995i	$-0.662826\pi$
$461$	−1.35602e13	+	2.39103e12i	−0.651270	+	0.114836i	−0.161754	+	0.986831i	$0.551715\pi$
$462$		0			0
$463$	1.64814e13	−	5.99872e12i	0.774619	−	0.281938i	0.0756918	−	0.997131i	$-0.475883\pi$
$463$	1.64814e13	−	5.99872e12i	0.774619	−	0.281938i	0.698927	+	0.715193i	$0.253661\pi$
$464$	−1.02369e13	+	1.21999e13i	−0.475970	+	0.567239i
$465$		0			0
$466$	−4.30038e12	−	1.56521e12i	−0.195694	−	0.0712267i
$467$	1.20289e13	−	6.94489e12i	0.541554	−	0.312666i	−0.204155	−	0.978939i	$-0.565445\pi$
$467$	1.20289e13	−	6.94489e12i	0.541554	−	0.312666i	0.745708	+	0.666272i	$0.232111\pi$
$468$		0			0
$469$	1.53307e13	−	2.65536e13i	0.675614	−	1.17020i
$470$	−6.29661e12	−	7.50400e12i	−0.274547	−	0.327193i
$471$		0			0
$472$	−3.77825e12	+	2.14275e13i	−0.161280	+	0.914665i
$473$	7.86954e12	+	1.38761e12i	0.332387	+	0.0586088i
$474$		0			0
$475$	−1.25775e13	+	1.05538e13i	−0.520148	+	0.436456i
$476$	−1.61928e12	−	9.34893e11i	−0.0662656	−	0.0382584i
$477$		0			0
$478$	−5.04445e12	−	8.73725e12i	−0.202150	−	0.350135i
$479$	−1.49020e13	+	4.09429e13i	−0.590972	+	1.62368i	0.177734	+	0.984079i	$0.443123\pi$
$479$	−1.49020e13	+	4.09429e13i	−0.590972	+	1.62368i	−0.768706	+	0.639603i	$0.779099\pi$
$480$		0			0
$481$	−3.65115e13	−	3.06368e13i	−1.41809	−	1.18992i
$482$	9.31292e11	+	2.55870e12i	0.0357973	+	0.0983523i
$483$		0			0
$484$	3.34323e12	+	1.89604e13i	0.125875	+	0.713872i
$485$			2.56927e13i			0.957416i
$486$		0			0
$487$	1.25305e13			0.457429			0.228714	−	0.973494i	$-0.426548\pi$
$487$	1.25305e13			0.457429			0.228714	+	0.973494i	$0.426548\pi$
$488$	−1.24892e13	+	2.20218e12i	−0.451269	+	0.0795710i
$489$		0			0
$490$	−9.03511e11	+	3.28851e11i	−0.0319855	+	0.0116418i
$491$	−9.59230e12	+	1.14317e13i	−0.336136	+	0.400592i	−0.907464	−	0.420131i	$-0.861984\pi$
$491$	−9.59230e12	+	1.14317e13i	−0.336136	+	0.400592i	0.571327	+	0.820722i	$0.306429\pi$
$492$		0			0
$493$	2.53949e12	+	9.24299e11i	0.0871991	+	0.0317379i
$494$	1.48089e13	−	8.54990e12i	0.503370	−	0.290621i
$495$		0			0
$496$	−1.71092e13	+	2.96340e13i	−0.569930	+	0.987148i
$497$	−2.15348e13	−	2.56642e13i	−0.710165	−	0.846342i
$498$		0			0
$499$	9.25634e12	−	5.24953e13i	0.299183	−	1.69675i	−0.350515	−	0.936557i	$-0.613994\pi$
$499$	9.25634e12	−	5.24953e13i	0.299183	−	1.69675i	0.649698	−	0.760192i	$-0.274895\pi$
$500$	1.08107e13	+	1.90621e12i	0.345942	+	0.0609988i
$501$		0			0
$502$	8.74286e12	−	7.33613e12i	0.274243	−	0.230117i
$503$	−6.45379e12	−	3.72610e12i	−0.200436	−	0.115722i	0.396423	−	0.918068i	$-0.370251\pi$
$503$	−6.45379e12	−	3.72610e12i	−0.200436	−	0.115722i	−0.596859	+	0.802346i	$0.703585\pi$
$504$		0			0
$505$	7.86512e12	+	1.36228e13i	0.239469	+	0.414772i
$506$	−1.62893e12	+	4.47544e12i	−0.0491076	+	0.134922i
$507$		0			0
$508$	1.82253e13	+	1.52928e13i	0.538711	+	0.452032i
$509$	−3.42725e12	−	9.41630e12i	−0.100313	−	0.275608i	0.879377	−	0.476126i	$-0.157959\pi$
$509$	−3.42725e12	−	9.41630e12i	−0.100313	−	0.275608i	−0.979690	+	0.200519i	$0.935737\pi$
$510$		0			0
$511$	9.05585e10	+	5.13583e11i	0.00259911	+	0.0147403i
$512$			3.56270e13i			1.01258i
$513$		0			0
$514$	−1.66085e13			−0.462930
$515$	−2.43465e13	+	4.29295e12i	−0.672049	+	0.118500i
$516$		0			0
$517$	−1.57999e13	+	5.75068e12i	−0.427760	+	0.155692i
$518$	7.12474e12	−	8.49093e12i	0.191038	−	0.227670i
$519$		0			0
$520$	5.30690e13	+	1.93155e13i	1.39580	+	0.508031i
$521$	8.26731e12	−	4.77314e12i	0.215365	−	0.124341i	−0.388437	−	0.921475i	$-0.626985\pi$
$521$	8.26731e12	−	4.77314e12i	0.215365	−	0.124341i	0.603802	+	0.797134i	$0.293652\pi$
$522$		0			0
$523$	1.87328e13	−	3.24462e13i	0.478734	−	0.829192i	−0.520969	−	0.853576i	$-0.674429\pi$
$523$	1.87328e13	−	3.24462e13i	0.478734	−	0.829192i	0.999703	+	0.0243840i	$0.00776244\pi$
$524$	−1.71309e13	−	2.04158e13i	−0.433635	−	0.516786i
$525$		0			0
$526$	−1.97722e12	+	1.12134e13i	−0.0491050	+	0.278489i
$527$	5.71834e12	+	1.00830e12i	0.140675	+	0.0248048i
$528$		0			0
$529$	−1.79891e12	+	1.50947e12i	−0.0434242	+	0.0364372i
$530$	−1.83357e13	−	1.05861e13i	−0.438448	−	0.253138i
$531$		0			0
$532$	−1.77959e13	−	3.08234e13i	−0.417601	−	0.723306i
$533$	2.07395e13	−	5.69813e13i	0.482128	−	1.32464i
$534$		0			0
$535$	−2.46000e13	−	2.06419e13i	−0.561264	−	0.470956i
$536$	1.28524e13	+	3.53118e13i	0.290510	+	0.798171i
$537$		0			0
$538$	−8.36464e11	−	4.74382e12i	−0.0185582	−	0.105249i
$539$			1.65035e12i			0.0362771i
$540$		0			0
$541$	−5.58959e13			−1.20613			−0.603064	−	0.797692i	$-0.706054\pi$
$541$	−5.58959e13			−1.20613			−0.603064	+	0.797692i	$0.706054\pi$
$542$	−9.84443e12	+	1.73584e12i	−0.210472	+	0.0371119i
$543$		0			0
$544$	3.28702e12	−	1.19638e12i	0.0689935	−	0.0251116i
$545$	−1.11275e13	+	1.32612e13i	−0.231428	+	0.275805i
$546$		0			0
$547$	1.27180e13	+	4.62899e12i	0.259707	+	0.0945255i	0.468592	−	0.883415i	$-0.344761\pi$
$547$	1.27180e13	+	4.62899e12i	0.259707	+	0.0945255i	−0.208885	+	0.977940i	$0.566984\pi$
$548$	3.72302e13	−	2.14949e13i	0.753343	−	0.434943i
$549$		0			0
$550$	2.46225e12	−	4.26474e12i	0.0489236	−	0.0847382i
$551$	3.30663e13	+	3.94069e13i	0.651070	+	0.775915i
$552$		0			0
$553$	−8.90040e11	+	5.04767e12i	−0.0172101	+	0.0976034i
$554$	1.31306e13	+	2.31528e12i	0.251615	+	0.0443665i
$555$		0			0
$556$	−2.11190e13	+	1.77210e13i	−0.397466	+	0.333513i
$557$	−3.34073e13	−	1.92877e13i	−0.623111	−	0.359753i	0.154968	−	0.987919i	$-0.450472\pi$
$557$	−3.34073e13	−	1.92877e13i	−0.623111	−	0.359753i	−0.778079	+	0.628166i	$0.783806\pi$
$558$		0			0
$559$	3.95462e13	+	6.84960e13i	0.724512	+	1.25489i
$560$	1.66735e13	−	4.58100e13i	0.302751	−	0.831802i
$561$		0			0
$562$	−3.60515e12	−	3.02508e12i	−0.0643046	−	0.0539580i
$563$	−1.41182e13	−	3.87895e13i	−0.249596	−	0.685760i	−0.999701	−	0.0244411i	$-0.992219\pi$
$563$	−1.41182e13	−	3.87895e13i	−0.249596	−	0.685760i	0.750105	−	0.661319i	$-0.230003\pi$
$564$		0			0
$565$	−1.09821e13	−	6.22826e13i	−0.190741	−	1.08174i
$566$			1.32550e13i			0.228191i
$567$		0			0
$568$	4.10596e13			0.694501
$569$	2.30034e13	−	4.05612e12i	0.385684	−	0.0680064i	0.0225554	−	0.999746i	$-0.492820\pi$
$569$	2.30034e13	−	4.05612e12i	0.385684	−	0.0680064i	0.363128	+	0.931739i	$0.381709\pi$
$570$		0			0
$571$	2.48593e13	−	9.04806e12i	0.409552	−	0.149065i	−0.129024	−	0.991641i	$-0.541185\pi$
$571$	2.48593e13	−	9.04806e12i	0.409552	−	0.149065i	0.538576	+	0.842577i	$0.318962\pi$
$572$	2.95062e13	−	3.51641e13i	0.481873	−	0.574274i
$573$		0			0
$574$	1.32513e13	+	4.82307e12i	0.212666	+	0.0774041i
$575$	3.91983e13	−	2.26312e13i	0.623632	−	0.360054i
$576$		0			0
$577$	−2.73120e13	+	4.73057e13i	−0.427046	+	0.739665i	−0.996609	−	0.0822828i	$-0.973779\pi$
$577$	−2.73120e13	+	4.73057e13i	−0.427046	+	0.739665i	0.569563	+	0.821947i	$0.307112\pi$
$578$	1.30422e13	+	1.55431e13i	0.202168	+	0.240935i
$579$		0			0
$580$	−1.39706e13	+	7.92311e13i	−0.212850	+	1.20713i
$581$	−8.47699e13	−	1.49472e13i	−1.28045	−	0.225777i
$582$		0			0
$583$	−2.78387e13	+	2.33594e13i	−0.413339	+	0.346832i
$584$	−5.53516e11	−	3.19573e11i	−0.00814829	−	0.00470442i
$585$		0			0
$586$	5.90802e12	+	1.02330e13i	0.0854976	+	0.148086i
$587$	−9.49394e12	+	2.60844e13i	−0.136225	+	0.374274i	−0.988983	−	0.148032i	$-0.952706\pi$
$587$	−9.49394e12	+	2.60844e13i	−0.136225	+	0.374274i	0.852758	+	0.522306i	$0.174928\pi$
$588$		0			0
$589$	8.46701e13	+	7.10467e13i	1.19441	+	1.00223i
$590$	1.55910e13	+	4.28360e13i	0.218080	+	0.599169i
$591$		0			0
$592$	−8.75601e12	−	4.96578e13i	−0.120420	−	0.682935i
$593$			9.96408e13i			1.35883i	0.733756	+	0.679413i	$0.237765\pi$
$593$			9.96408e13i			1.35883i	−0.733756	+	0.679413i	$0.762235\pi$
$594$		0			0
$595$	−8.27243e12			−0.110930
$596$	6.39516e13	−	1.12764e13i	0.850393	−	0.149947i
$597$		0			0
$598$	−4.42968e13	+	1.61227e13i	−0.579250	+	0.210830i
$599$	−2.81867e13	+	3.35916e13i	−0.365520	+	0.435609i	−0.917188	−	0.398454i	$-0.869547\pi$
$599$	−2.81867e13	+	3.35916e13i	−0.365520	+	0.435609i	0.551669	+	0.834063i	$0.313991\pi$
$600$		0			0
$601$	−8.80659e13	−	3.20534e13i	−1.12314	−	0.408791i	−0.287345	−	0.957827i	$-0.592773\pi$
$601$	−8.80659e13	−	3.20534e13i	−1.12314	−	0.408791i	−0.835798	+	0.549036i	$0.814995\pi$
$602$	−1.59291e13	+	9.19666e12i	−0.201469	+	0.116318i
$603$		0			0
$604$	−1.48040e13	+	2.56413e13i	−0.184160	+	0.318975i
$605$	5.47525e13	+	6.52515e13i	0.675503	+	0.805033i
$606$		0			0
$607$	−1.38808e13	+	7.87220e13i	−0.168450	+	0.955328i	0.776985	+	0.629519i	$0.216748\pi$
$607$	−1.38808e13	+	7.87220e13i	−0.168450	+	0.955328i	−0.945435	+	0.325809i	$0.894363\pi$
$608$	6.55732e13	+	1.15623e13i	0.789238	+	0.139164i
$609$		0			0
$610$	−2.03535e13	+	1.70786e13i	−0.240985	+	0.202211i
$611$	−1.44124e14	−	8.32097e13i	−1.69250	−	0.977165i
$612$		0			0
$613$	−3.09829e13	−	5.36639e13i	−0.357947	−	0.619983i	0.629670	−	0.776862i	$-0.283190\pi$
$613$	−3.09829e13	−	5.36639e13i	−0.357947	−	0.619983i	−0.987618	+	0.156879i	$0.949857\pi$
$614$	−3.30225e12	+	9.07287e12i	−0.0378415	+	0.103969i
$615$		0			0
$616$	1.72688e13	+	1.44903e13i	0.194697	+	0.163370i
$617$	4.20061e13	+	1.15411e14i	0.469771	+	1.29069i	0.917934	+	0.396734i	$0.129856\pi$
$617$	4.20061e13	+	1.15411e14i	0.469771	+	1.29069i	−0.448163	+	0.893952i	$0.647921\pi$
$618$		0			0
$619$	−3.00636e11	−	1.70499e12i	−0.00330817	−	0.0187616i	0.983109	−	0.183021i	$-0.0585877\pi$
$619$	−3.00636e11	−	1.70499e12i	−0.00330817	−	0.0187616i	−0.986417	+	0.164260i	$0.947477\pi$
$620$			1.72863e14i			1.88688i
$621$		0			0
$622$	2.44138e13			0.262231
$623$	9.62369e13	−	1.69692e13i	1.02542	−	0.180809i
$624$		0			0
$625$	1.08417e14	−	3.94604e13i	1.13683	−	0.413772i
$626$	1.30511e12	−	1.55537e12i	0.0135761	−	0.0161793i
$627$		0			0
$628$	−9.54536e13	−	3.47423e13i	−0.977224	−	0.355680i
$629$	−7.41012e12	+	4.27824e12i	−0.0752614	+	0.0434522i
$630$		0			0
$631$	4.82379e13	−	8.35504e13i	0.482215	−	0.835222i	−0.517576	−	0.855637i	$-0.673166\pi$
$631$	4.82379e13	−	8.35504e13i	0.482215	−	0.835222i	0.999792	+	0.0204154i	$0.00649889\pi$
$632$	−4.03783e12	−	4.81210e12i	−0.0400463	−	0.0477253i
$633$		0			0
$634$	8.15388e11	−	4.62429e12i	0.00796009	−	0.0451439i
$635$	1.03660e14	+	1.82781e13i	1.00402	+	0.177036i
$636$		0			0
$637$	−1.25131e13	+	1.04998e13i	−0.119308	+	0.100111i
$638$	−1.33619e13	−	7.71452e12i	−0.126406	−	0.0729803i
$639$		0			0
$640$	6.77949e13	+	1.17424e14i	0.631390	+	1.09360i
$641$	4.13375e13	−	1.13574e14i	0.381992	−	1.04952i	−0.588524	−	0.808480i	$-0.700291\pi$
$641$	4.13375e13	−	1.13574e14i	0.381992	−	1.04952i	0.970516	−	0.241035i	$-0.0774870\pi$
$642$		0			0
$643$	−3.76309e13	−	3.15761e13i	−0.342365	−	0.287279i	0.455350	−	0.890312i	$-0.349514\pi$
$643$	−3.76309e13	−	3.15761e13i	−0.342365	−	0.287279i	−0.797716	+	0.603034i	$0.793958\pi$
$644$	3.35581e13	+	9.22000e13i	0.302948	+	0.832342i
$645$		0			0
$646$	−5.33065e11	−	3.02316e12i	−0.00473824	−	0.0268719i
$647$		−	1.09289e14i		−	0.963953i	−0.876184	−	0.481976i	$-0.839919\pi$
$647$		−	1.09289e14i		−	0.963953i	0.876184	−	0.481976i	$-0.160081\pi$
$648$		0			0
$649$	7.82441e13			0.679561
$650$	4.80010e13	−	8.46387e12i	0.413698	−	0.0729461i
$651$		0			0
$652$	−1.05852e14	+	3.85272e13i	−0.898386	+	0.326986i
$653$	−5.36919e13	+	6.39876e13i	−0.452213	+	0.538927i	−0.943193	−	0.332244i	$-0.892194\pi$
$653$	−5.36919e13	+	6.39876e13i	−0.452213	+	0.538927i	0.490980	+	0.871171i	$0.336639\pi$
$654$		0			0
$655$	−1.10800e14	−	4.03279e13i	−0.919038	−	0.334502i
$656$	5.55568e13	−	3.20757e13i	0.457318	−	0.264033i
$657$		0			0
$658$	1.93508e13	−	3.35166e13i	0.156881	−	0.271726i
$659$	−1.10487e14	−	1.31673e14i	−0.888965	−	1.05943i	−0.997861	−	0.0653744i	$-0.979176\pi$
$659$	−1.10487e14	−	1.31673e14i	−0.888965	−	1.05943i	0.108896	−	0.994053i	$-0.465269\pi$
$660$		0			0
$661$	−3.34541e13	+	1.89728e14i	−0.265120	+	1.50357i	0.503575	+	0.863952i	$0.332018\pi$
$661$	−3.34541e13	+	1.89728e14i	−0.265120	+	1.50357i	−0.768694	+	0.639616i	$0.779093\pi$
$662$	−2.68223e13	−	4.72949e12i	−0.210963	−	0.0371984i
$663$		0			0
$664$	8.08137e13	−	6.78108e13i	0.626102	−	0.525362i
$665$	−1.36371e14	−	7.87337e13i	−1.04861	−	0.605414i
$666$		0			0
$667$	−7.09061e13	−	1.22813e14i	−0.537099	−	0.930283i
$668$	−3.63492e13	+	9.98687e13i	−0.273283	+	0.750839i
$669$		0			0
$670$	6.03101e13	+	5.06062e13i	0.446700	+	0.374826i
$671$	1.55979e13	+	4.28549e13i	0.114671	+	0.315056i
$672$		0			0
$673$	2.30414e13	+	1.30674e14i	0.166891	+	0.946485i	0.947093	+	0.320958i	$0.104005\pi$
$673$	2.30414e13	+	1.30674e14i	0.166891	+	0.946485i	−0.780202	+	0.625527i	$0.784884\pi$
$674$		−	1.06615e13i		−	0.0766515i
$675$		0			0
$676$	3.27361e14			2.31896
$677$	1.21705e14	−	2.14599e13i	0.855788	−	0.150899i	0.271494	−	0.962440i	$-0.412482\pi$
$677$	1.21705e14	−	2.14599e13i	0.855788	−	0.150899i	0.584295	+	0.811542i	$0.301371\pi$
$678$		0			0
$679$	−9.53862e13	+	3.47177e13i	−0.660901	+	0.240548i
$680$	6.51690e12	−	7.76654e12i	0.0448226	−	0.0534175i
$681$		0			0
$682$	−3.11518e13	−	1.13383e13i	−0.211135	−	0.0768470i
$683$	2.13529e14	−	1.23281e14i	1.43666	−	0.829453i	0.439040	−	0.898468i	$-0.355319\pi$
$683$	2.13529e14	−	1.23281e14i	1.43666	−	0.829453i	0.997616	+	0.0690143i	$0.0219854\pi$
$684$		0			0
$685$	9.50989e13	−	1.64716e14i	0.630555	−	1.09215i
$686$	−3.20978e13	−	3.82527e13i	−0.211278	−	0.251792i
$687$		0			0
$688$	−1.45300e13	+	8.24036e13i	−0.0942590	+	0.534569i
$689$	−3.54228e14	−	6.24600e13i	−2.28132	−	0.402259i
$690$		0			0
$691$	5.25801e13	−	4.41199e13i	0.333757	−	0.280056i	−0.460471	−	0.887675i	$-0.652320\pi$
$691$	5.25801e13	−	4.41199e13i	0.333757	−	0.280056i	0.794229	+	0.607619i	$0.207875\pi$
$692$	−2.42322e14	−	1.39905e14i	−1.52708	−	0.881661i
$693$		0			0
$694$	−2.14146e13	−	3.70912e13i	−0.133019	−	0.230395i
$695$	−4.17169e13	+	1.14616e14i	−0.257269	+	0.706842i
$696$		0			0
$697$	−8.33910e12	−	6.99734e12i	−0.0506938	−	0.0425372i
$698$	−3.12305e13	−	8.58051e13i	−0.188496	−	0.517888i
$699$		0			0
$700$	−1.76168e13	−	9.99100e13i	−0.104818	−	0.594455i
$701$			8.47626e13i			0.500742i	0.968150	+	0.250371i	$0.0805526\pi$
$701$			8.47626e13i			0.500742i	−0.968150	+	0.250371i	$0.919447\pi$
$702$		0			0
$703$	−1.62874e14			−0.948584
$704$	3.35013e13	−	5.90718e12i	0.193731	−	0.0341599i
$705$		0			0
$706$	−4.53726e13	+	1.65143e13i	−0.258684	+	0.0941534i
$707$	−3.99478e13	+	4.76080e13i	−0.226150	+	0.269515i
$708$		0			0
$709$	8.27516e13	+	3.01191e13i	0.461897	+	0.168117i	0.562478	−	0.826812i	$-0.309848\pi$
$709$	8.27516e13	+	3.01191e13i	0.461897	+	0.168117i	−0.100581	+	0.994929i	$0.532070\pi$
$710$	7.44985e13	−	4.30118e13i	0.412911	−	0.238394i
$711$		0			0
$712$	−5.98827e13	+	1.03720e14i	−0.327266	+	0.566842i
$713$	−1.95857e14	−	2.33413e14i	−1.06290	−	1.26671i
$714$		0			0
$715$	3.52660e13	−	2.00003e14i	0.188724	−	1.07030i
$716$	2.40154e14	+	4.23456e13i	1.27622	+	0.225032i
$717$		0			0
$718$	−6.23480e13	+	5.23162e13i	−0.326739	+	0.274166i
$719$	−2.12924e14	−	1.22931e14i	−1.10810	−	0.639762i	−0.169764	−	0.985485i	$-0.554300\pi$
$719$	−2.12924e14	−	1.22931e14i	−1.10810	−	0.639762i	−0.938337	+	0.345723i	$0.887634\pi$
$720$		0			0
$721$	−4.88366e13	−	8.45875e13i	−0.250651	−	0.434140i
$722$	−1.28695e12	+	3.53587e12i	−0.00655958	+	0.0180223i
$723$		0			0
$724$	−1.93432e14	−	1.62309e14i	−0.972381	−	0.815924i
$725$	5.01508e13	+	1.37788e14i	0.250373	+	0.687894i
$726$		0			0
$727$	3.98357e13	+	2.25919e14i	0.196155	+	1.11245i	0.910764	+	0.412928i	$0.135494\pi$
$727$	3.98357e13	+	2.25919e14i	0.196155	+	1.11245i	−0.714608	+	0.699525i	$0.753395\pi$
$728$			2.23124e14i			1.09116i
$729$		0			0
$730$	−1.33907e12			−0.00645934
$731$	1.39831e13	−	2.46561e12i	0.0669912	−	0.0118124i
$732$		0			0
$733$	2.87961e14	−	1.04809e14i	1.36086	−	0.495313i	0.444540	−	0.895759i	$-0.353367\pi$
$733$	2.87961e14	−	1.04809e14i	1.36086	−	0.495313i	0.916320	+	0.400446i	$0.131145\pi$
$734$	−5.37361e13	+	6.40401e13i	−0.252223	+	0.300588i
$735$		0			0
$736$	−1.72487e14	−	6.27800e13i	−0.798669	−	0.290692i
$737$	1.17030e14	−	6.75670e13i	0.538218	−	0.310740i
$738$		0			0
$739$	1.09594e14	−	1.89823e14i	0.497241	−	0.861246i	−0.502754	−	0.864429i	$-0.667680\pi$
$739$	1.09594e14	−	1.89823e14i	0.497241	−	0.861246i	0.999995	+	0.00318340i	$0.00101331\pi$
$740$	−1.63737e14	−	1.95134e14i	−0.737882	−	0.879374i
$741$		0			0
$742$	1.45254e13	−	8.23775e13i	0.0645814	−	0.366259i
$743$	3.56907e14	+	6.29324e13i	1.57620	+	0.277927i	0.892229	−	0.451583i	$-0.149140\pi$
$743$	3.56907e14	+	6.29324e13i	1.57620	+	0.277927i	0.683971	+	0.729509i	$0.260251\pi$
$744$		0			0
$745$	2.20087e14	−	1.84675e14i	0.958988	−	0.804686i
$746$	−2.73461e13	−	1.57883e13i	−0.118359	−	0.0683345i
$747$		0			0
$748$	−4.12035e12	−	7.13665e12i	−0.0175965	−	0.0304780i
$749$	4.33934e13	−	1.19222e14i	0.184083	−	0.505765i
$750$		0			0
$751$	−1.46418e14	−	1.22859e14i	−0.612905	−	0.514289i	0.282659	−	0.959220i	$-0.408783\pi$
$751$	−1.46418e14	−	1.22859e14i	−0.612905	−	0.514289i	−0.895564	+	0.444932i	$0.853228\pi$
$752$	−6.02166e13	−	1.65444e14i	−0.250396	−	0.687956i
$753$		0			0
$754$	−2.65183e13	−	1.50393e14i	−0.108815	−	0.617121i
$755$			1.30994e14i			0.533969i
$756$		0			0
$757$	−1.12893e14			−0.454139			−0.227070	−	0.973879i	$-0.572914\pi$
$757$	−1.12893e14			−0.454139			−0.227070	+	0.973879i	$0.572914\pi$
$758$	1.53977e13	−	2.71502e12i	0.0615331	−	0.0108499i
$759$		0			0
$760$	1.81350e14	−	6.60060e13i	0.715236	−	0.260325i
$761$	1.09973e14	−	1.31061e14i	0.430886	−	0.513510i	−0.506292	−	0.862362i	$-0.668984\pi$
$761$	1.09973e14	−	1.31061e14i	0.430886	−	0.513510i	0.937178	+	0.348852i	$0.113429\pi$
$762$		0			0
$763$	−6.42697e13	−	2.33923e13i	−0.248533	−	0.0904585i
$764$	−3.58530e14	+	2.06997e14i	−1.37740	+	0.795240i
$765$		0			0
$766$	−3.64699e13	+	6.31677e13i	−0.138290	+	0.239525i
$767$	4.97801e14	+	5.93256e14i	1.87534	+	2.23494i
$768$		0			0
$769$	−5.45862e12	+	3.09574e13i	−0.0202979	+	0.115115i	−0.993273	−	0.115794i	$-0.963059\pi$
$769$	−5.45862e12	+	3.09574e13i	−0.0202979	+	0.115115i	0.972975	+	0.230909i	$0.0741699\pi$
$770$	4.65118e13	+	8.20128e12i	0.171834	+	0.0302990i
$771$		0			0
$772$	5.94902e13	−	4.99182e13i	0.216950	−	0.182042i
$773$	−1.41721e14	−	8.18225e13i	−0.513495	−	0.296466i	0.220774	−	0.975325i	$-0.429142\pi$
$773$	−1.41721e14	−	8.18225e13i	−0.513495	−	0.296466i	−0.734269	+	0.678859i	$0.762475\pi$
$774$		0			0
$775$	1.57527e14	+	2.72844e14i	0.563437	+	0.975902i
$776$	4.25493e13	−	1.16903e14i	0.151211	−	0.415449i
$777$		0			0
$778$	−3.11609e13	−	2.61471e13i	−0.109323	−	0.0917330i
$779$	−7.08720e13	−	1.94719e14i	−0.247051	−	0.678768i
$780$		0			0
$781$	−2.56399e13	−	1.45411e14i	−0.0882390	−	0.500428i
$782$			8.46263e12i			0.0289382i
$783$		0			0
$784$	−1.72811e13			−0.0583435
$785$	−4.42587e14	+	7.80400e13i	−1.48474	+	0.261800i
$786$		0			0
$787$	−3.50294e14	+	1.27496e14i	−1.16027	+	0.422303i	−0.849193	−	0.528082i	$-0.822911\pi$
$787$	−3.50294e14	+	1.27496e14i	−1.16027	+	0.422303i	−0.311075	+	0.950385i	$0.600689\pi$
$788$	2.45205e14	−	2.92224e14i	0.807047	−	0.961801i
$789$		0			0
$790$	−1.23671e13	−	4.50126e12i	−0.0401914	−	0.0146285i
$791$	2.16389e14	−	1.24932e14i	0.698801	−	0.403453i
$792$		0			0
$793$	−2.25695e14	+	3.90914e14i	−0.719706	+	1.24657i
$794$	−3.93994e13	−	4.69544e13i	−0.124850	−	0.148790i
$795$		0			0
$796$	8.32918e11	−	4.72371e12i	0.00260638	−	0.0147815i
$797$	−4.22217e14	−	7.44482e13i	−1.31294	−	0.231506i	−0.527028	−	0.849848i	$-0.676694\pi$
$797$	−4.22217e14	−	7.44482e13i	−1.31294	−	0.231506i	−0.785909	+	0.618342i	$0.787805\pi$
$798$		0			0
$799$	−2.28864e13	+	1.92039e13i	−0.0702818	+	0.0589734i
$800$	1.64366e14	+	9.48970e13i	0.501606	+	0.289603i
$801$		0			0
$802$	−2.43188e13	−	4.21215e13i	−0.0732945	−	0.126950i
$803$	−7.86108e11	+	2.15981e12i	−0.00235453	+	0.00646902i
$804$		0			0
$805$	3.32537e14	+	2.79032e14i	0.983695	+	0.825418i
$806$	−1.12224e14	−	3.08333e14i	−0.329921	−	0.906451i
$807$		0			0
$808$	−1.32263e13	−	7.50098e13i	−0.0384043	−	0.217802i
$809$			3.70981e14i			1.07055i	0.844676	+	0.535277i	$0.179793\pi$
$809$			3.70981e14i			1.07055i	−0.844676	+	0.535277i	$0.820207\pi$
$810$		0			0
$811$	4.10883e13			0.117115			0.0585577	−	0.998284i	$-0.481350\pi$
$811$	4.10883e13			0.117115			0.0585577	+	0.998284i	$0.481350\pi$
$812$	−3.13030e14	+	5.51956e13i	−0.886759	+	0.156360i
$813$		0			0
$814$	4.59049e13	−	1.67080e13i	0.128451	−	0.0467523i
$815$	−3.20349e14	+	3.81777e14i	−0.890913	+	1.06175i
$816$		0			0
$817$	2.53978e14	+	9.24406e13i	0.697729	+	0.253952i
$818$	−1.07618e14	+	6.21335e13i	−0.293846	+	0.169652i
$819$		0			0
$820$	1.62039e14	−	2.80659e14i	0.437068	−	0.757025i
$821$	3.61207e14	+	4.30470e14i	0.968368	+	1.15406i	0.988032	+	0.154249i	$0.0492959\pi$
$821$	3.61207e14	+	4.30470e14i	0.968368	+	1.15406i	−0.0196641	+	0.999807i	$0.506260\pi$
$822$		0			0
$823$	−1.15181e13	+	6.53224e13i	−0.0305057	+	0.173007i	−0.996254	−	0.0864737i	$-0.972440\pi$
$823$	−1.15181e13	+	6.53224e13i	−0.0305057	+	0.173007i	0.965748	+	0.259480i	$0.0835513\pi$
$824$	1.17888e14	+	2.07868e13i	0.310336	+	0.0547206i
$825$		0			0
$826$	−1.37965e14	+	1.15766e14i	−0.358812	+	0.301079i
$827$	−7.15261e13	−	4.12956e13i	−0.184900	−	0.106752i	0.404693	−	0.914453i	$-0.367378\pi$
$827$	−7.15261e13	−	4.12956e13i	−0.184900	−	0.106752i	−0.589593	+	0.807701i	$0.700712\pi$
$828$		0			0
$829$	7.85456e13	+	1.36045e14i	0.200608	+	0.347464i	0.948725	−	0.316104i	$-0.102375\pi$
$829$	7.85456e13	+	1.36045e14i	0.200608	+	0.347464i	−0.748116	+	0.663568i	$0.769041\pi$
$830$	7.55937e13	−	2.07692e14i	0.191909	−	0.527265i
$831$		0			0
$832$	2.57929e14	+	2.16428e14i	0.646970	+	0.542872i
$833$	1.00296e12	+	2.75561e12i	0.00250068	+	0.00687056i
$834$		0			0
$835$	8.16497e13	+	4.63058e14i	0.201151	+	1.14078i
$836$		−	1.56863e14i		−	0.384141i
$837$		0			0
$838$	1.41499e14			0.342400
$839$	2.60896e14	−	4.60029e13i	0.627562	−	0.110656i	0.149183	−	0.988810i	$-0.452336\pi$
$839$	2.60896e14	−	4.60029e13i	0.627562	−	0.110656i	0.478379	+	0.878153i	$0.341224\pi$
$840$		0			0
$841$	3.63712e13	−	1.32380e13i	0.0864526	−	0.0314662i
$842$	2.95193e13	−	3.51798e13i	0.0697503	−	0.0831252i
$843$		0			0
$844$	6.28992e13	+	2.28934e13i	0.146870	+	0.0534563i
$845$	1.25429e15	−	7.24166e14i	2.91149	−	1.68095i
$846$		0			0
$847$	−1.68266e14	+	2.91445e14i	−0.385993	+	0.668560i
$848$	−2.44602e14	−	2.91505e14i	−0.557802	−	0.664762i
$849$		0			0
$850$	1.51945e12	−	8.61726e12i	0.00342447	−	0.0194211i
$851$	4.42180e14	+	7.79683e13i	0.990721	+	0.174691i
$852$		0			0
$853$	−6.72605e14	+	5.64382e14i	−1.48941	+	1.24976i	−0.594048	+	0.804430i	$0.702471\pi$
$853$	−6.72605e14	+	5.64382e14i	−1.48941	+	1.24976i	−0.895364	+	0.445335i	$0.853085\pi$
$854$	−9.09090e13	−	5.24863e13i	−0.200132	−	0.115547i
$855$		0			0
$856$	7.77469e13	+	1.34662e14i	0.169167	+	0.293005i
$857$	−2.31946e14	+	6.37267e14i	−0.501745	+	1.37853i	0.387824	+	0.921733i	$0.373227\pi$
$857$	−2.31946e14	+	6.37267e14i	−0.501745	+	1.37853i	−0.889569	+	0.456800i	$0.848995\pi$
$858$		0			0
$859$	−7.04258e13	−	5.90943e13i	−0.150580	−	0.126351i	0.564386	−	0.825511i	$-0.309113\pi$
$859$	−7.04258e13	−	5.90943e13i	−0.150580	−	0.126351i	−0.714965	+	0.699160i	$0.753558\pi$
$860$	1.44573e14	+	3.97212e14i	0.307324	+	0.844365i
$861$		0			0
$862$	−6.40091e12	−	3.63014e13i	−0.0134495	−	0.0762758i
$863$			7.91444e14i			1.65336i	0.562675	+	0.826678i	$0.309772\pi$
$863$			7.91444e14i			1.65336i	−0.562675	+	0.826678i	$0.690228\pi$
$864$		0			0
$865$	−1.23795e15			−2.55636
$866$	2.74980e14	−	4.84864e13i	0.564562	−	0.0995475i
$867$		0			0
$868$	−6.41768e14	+	2.33585e14i	−1.30251	+	0.474073i
$869$	−1.45204e13	+	1.73047e13i	−0.0293008	+	0.0349194i
$870$		0			0
$871$	1.25686e15	+	4.57460e14i	2.50724	+	0.912562i
$872$	7.25926e13	−	4.19113e13i	0.143983	−	0.0831283i
$873$		0			0
$874$	−8.05439e13	+	1.39506e14i	−0.157934	+	0.273550i
$875$	1.23339e14	+	1.46989e14i	0.240469	+	0.286580i
$876$		0			0
$877$	1.40488e14	−	7.96747e14i	0.270796	−	1.53576i	−0.481213	−	0.876604i	$-0.659803\pi$
$877$	1.40488e14	−	7.96747e14i	0.270796	−	1.53576i	0.752008	−	0.659154i	$-0.229085\pi$
$878$	−2.33019e14	−	4.10876e13i	−0.446600	−	0.0787477i
$879$		0			0
$880$	1.64589e14	−	1.38106e14i	0.311879	−	0.261698i
$881$	4.36217e14	+	2.51850e14i	0.821908	+	0.474529i	0.851074	−	0.525046i	$-0.175952\pi$
$881$	4.36217e14	+	2.51850e14i	0.821908	+	0.474529i	−0.0291662	+	0.999575i	$0.509285\pi$
$882$		0			0
$883$	−3.75469e14	−	6.50331e14i	−0.699472	−	1.21152i	−0.968650	−	0.248431i	$-0.920085\pi$
$883$	−3.75469e14	−	6.50331e14i	−0.699472	−	1.21152i	0.269177	−	0.963091i	$-0.413248\pi$
$884$	2.78967e13	−	7.66455e13i	0.0516763	−	0.141979i
$885$		0			0
$886$	−1.42292e14	−	1.19397e14i	−0.260622	−	0.218688i
$887$	−4.36674e13	−	1.19975e14i	−0.0795315	−	0.218511i	0.893554	−	0.448956i	$-0.148204\pi$
$887$	−4.36674e13	−	1.19975e14i	−0.0795315	−	0.218511i	−0.973085	+	0.230445i	$0.925982\pi$
$888$		0			0
$889$	7.22140e13	+	4.09546e14i	0.130051	+	0.737554i
$890$			2.50919e14i			0.449349i
$891$		0			0
$892$	−2.51403e14			−0.445191
$893$	−5.60057e14	+	9.87531e13i	−0.986222	+	0.173898i
$894$		0			0
$895$	1.01383e15	−	3.69004e14i	1.76543	−	0.642563i
$896$	−3.44338e14	+	4.10366e14i	−0.596273	+	0.710610i
$897$		0			0
$898$	1.79972e14	+	6.55046e13i	0.308194	+	0.112173i
$899$	8.54853e14	−	4.93550e14i	1.45577	−	0.840490i
$900$		0			0
$901$	−3.22865e13	+	5.59218e13i	−0.0543746	+	0.0941796i
$902$	3.99495e13	+	4.76099e13i	0.0669080	+	0.0797379i
$903$		0			0
$904$	−5.31761e13	+	3.01577e14i	−0.0880794	+	0.499523i
$905$	−1.10019e15	−	1.93993e14i	−1.81228	−	0.319553i
$906$		0			0
$907$	−3.17141e14	+	2.66113e14i	−0.516673	+	0.433540i	−0.863470	−	0.504400i	$-0.831714\pi$
$907$	−3.17141e14	+	2.66113e14i	−0.516673	+	0.433540i	0.346797	+	0.937940i	$0.387269\pi$
$908$	7.41186e13	+	4.27924e13i	0.120087	+	0.0693325i
$909$		0			0
$910$	2.33732e14	+	4.04836e14i	0.374551	+	0.648741i
$911$	−1.02063e14	+	2.80417e14i	−0.162659	+	0.446902i	−0.994068	−	0.108759i	$-0.965312\pi$
$911$	−1.02063e14	+	2.80417e14i	−0.162659	+	0.446902i	0.831409	+	0.555661i	$0.187535\pi$
$912$		0			0
$913$	−2.90614e14	−	2.43854e14i	−0.458102	−	0.384393i
$914$	1.26759e14	+	3.48267e14i	0.198723	+	0.545987i
$915$		0			0
$916$	−1.71621e14	−	9.73310e14i	−0.266129	−	1.50929i
$917$		−	4.65848e14i		−	0.718452i
$918$		0			0
$919$	9.70745e14			1.48091			0.740453	−	0.672108i	$-0.234611\pi$
$919$	9.70745e14			1.48091			0.740453	+	0.672108i	$0.234611\pi$
$920$	−5.23936e14	+	9.23841e13i	−0.794949	+	0.140171i
$921$		0			0
$922$	1.31260e14	−	4.77749e13i	0.197006	−	0.0717043i
$923$	9.39398e14	−	1.11953e15i	1.40230	−	1.67120i
$924$		0			0
$925$	−4.36261e14	−	1.58786e14i	−0.644225	−	0.234479i
$926$	−1.54089e14	+	8.89633e13i	−0.226317	+	0.130664i
$927$		0			0
$928$	2.97323e14	−	5.14979e14i	0.432006	−	0.748256i
$929$	1.90340e14	+	2.26839e14i	0.275075	+	0.327822i	0.885841	−	0.463990i	$-0.153583\pi$
$929$	1.90340e14	+	2.26839e14i	0.275075	+	0.327822i	−0.610765	+	0.791812i	$0.709138\pi$
$930$		0			0
$931$	−9.69302e12	+	5.49718e13i	−0.0138583	+	0.0785945i
$932$	−4.09203e14	−	7.21536e13i	−0.581915	−	0.102607i
$933$		0			0
$934$	−1.07940e14	+	9.05726e13i	−0.151862	+	0.127427i
$935$	−3.15744e13	−	1.82295e13i	−0.0441852	−	0.0255104i
$936$		0			0
$937$	−3.20169e14	−	5.54550e14i	−0.443284	−	0.767790i	0.554647	−	0.832086i	$-0.312853\pi$
$937$	−3.20169e14	−	5.54550e14i	−0.443284	−	0.767790i	−0.997931	+	0.0642955i	$0.979520\pi$
$938$	−1.06384e14	+	2.92289e14i	−0.146509	+	0.402530i
$939$		0			0
$940$	−6.81334e14	−	5.71707e14i	−0.928370	−	0.778995i
$941$	−3.05110e14	−	8.38283e14i	−0.413531	−	1.13617i	−0.955299	−	0.295640i	$-0.904467\pi$
$941$	−3.05110e14	−	8.38283e14i	−0.413531	−	1.13617i	0.541768	−	0.840528i	$-0.317755\pi$
$942$		0			0
$943$	9.91947e13	+	5.62561e14i	0.133024	+	0.754416i
$944$			8.19310e14i			1.09292i
$945$		0			0
$946$	−8.10647e13			−0.106998
$947$	−2.93964e14	+	5.18339e13i	−0.385962	+	0.0680556i	−0.363263	−	0.931687i	$-0.618337\pi$
$947$	−2.93964e14	+	5.18339e13i	−0.385962	+	0.0680556i	−0.0226997	+	0.999742i	$0.507226\pi$
$948$		0			0
$949$	−2.13773e13	+	7.78071e12i	−0.0277730	+	0.0101085i
$950$	1.07064e14	−	1.27594e14i	0.138364	−	0.164896i
$951$		0			0
$952$	3.76400e13	+	1.36998e13i	0.0481355	+	0.0175199i
$953$	−6.87575e14	+	3.96972e14i	−0.874693	+	0.505004i	−0.868905	−	0.494979i	$-0.835176\pi$
$953$	−6.87575e14	+	3.96972e14i	−0.874693	+	0.505004i	−0.00578794	+	0.999983i	$0.501842\pi$
$954$		0			0
$955$	−9.15810e14	+	1.58623e15i	−1.15289	+	1.99687i
$956$	−5.88815e14	−	7.01722e14i	−0.737376	−	0.878771i
$957$		0			0
$958$	7.67532e13	−	4.35289e14i	0.0951194	−	0.539449i
$959$	7.40027e14	+	1.30487e14i	0.912335	+	0.160869i
$960$		0			0
$961$	9.96827e14	−	8.36438e14i	1.21619	−	1.02051i
$962$	4.18736e14	+	2.41757e14i	0.508236	+	0.293430i
$963$		0			0
$964$	1.23615e14	+	2.14108e14i	0.148486	+	0.257186i
$965$	1.17513e14	−	3.22863e14i	0.140426	−	0.385817i
$966$		0			0
$967$	5.72046e14	+	4.80004e14i	0.676548	+	0.567691i	0.914995	−	0.403464i	$-0.132194\pi$
$967$	5.72046e14	+	4.80004e14i	0.676548	+	0.567691i	−0.238447	+	0.971155i	$0.576638\pi$
$968$	−1.41065e14	−	3.87573e14i	−0.165975	−	0.456012i
$969$		0			0
$970$	−4.52599e13	−	2.56681e14i	−0.0527053	−	0.298907i
$971$		−	7.09172e14i		−	0.821591i	−0.911728	−	0.410795i	$-0.865251\pi$
$971$		−	7.09172e14i		−	0.821591i	0.911728	−	0.410795i	$-0.134749\pi$
$972$		0			0
$973$	−4.81893e14			−0.552569
$974$	−1.25185e14	+	2.20736e13i	−0.142810	+	0.0251813i
$975$		0			0
$976$	−4.48742e14	+	1.63329e14i	−0.506696	+	0.184422i
$977$	4.26967e14	−	5.08839e14i	0.479646	−	0.571620i	−0.470906	−	0.882183i	$-0.656073\pi$
$977$	4.26967e14	−	5.08839e14i	0.479646	−	0.571620i	0.950553	+	0.310563i	$0.100518\pi$
$978$		0			0
$979$	4.04714e14	+	1.47304e14i	0.450023	+	0.163795i
$980$	−7.56041e13	+	4.36500e13i	−0.0836402	+	0.0482897i
$981$		0			0
$982$	7.56936e13	−	1.31105e14i	0.0828899	−	0.143570i
$983$	−7.15276e13	−	8.52433e13i	−0.0779303	−	0.0928737i	0.725671	−	0.688042i	$-0.241530\pi$
$983$	−7.15276e13	−	8.52433e13i	−0.0779303	−	0.0928737i	−0.803601	+	0.595169i	$0.797085\pi$
$984$		0			0
$985$	2.93071e14	−	1.66209e15i	0.316076	−	1.79256i
$986$	−2.69989e13	−	4.76063e12i	−0.0289709	−	0.00510834i
$987$		0			0
$988$	1.18936e15	−	9.97989e14i	1.26336	−	1.06009i
$989$	−6.45263e14	−	3.72543e14i	−0.681955	−	0.393727i
$990$		0			0
$991$	2.19628e13	+	3.80407e13i	0.0229784	+	0.0397997i	0.877286	−	0.479968i	$-0.159352\pi$
$991$	2.19628e13	+	3.80407e13i	0.0229784	+	0.0397997i	−0.854308	+	0.519768i	$0.826018\pi$
$992$	4.36987e14	−	1.20061e15i	0.454894	−	1.24981i
$993$		0			0
$994$	2.60352e14	+	2.18461e14i	0.268305	+	0.225135i
$995$	−7.25813e12	−	1.99415e13i	−0.00744233	−	0.0204476i
$996$		0			0
$997$	−7.08333e13	−	4.01715e14i	−0.0719054	−	0.407796i	−0.999421	−	0.0340123i	$-0.989171\pi$
$997$	−7.08333e13	−	4.01715e14i	−0.0719054	−	0.407796i	0.927516	−	0.373783i	$-0.121940\pi$
$998$			5.40758e14i			0.546198i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.11.f.a.71.13		174
3.2	odd	2		27.11.f.a.14.17	yes	174
27.2	odd	18	inner	81.11.f.a.8.13		174
27.25	even	9		27.11.f.a.2.17	✓	174

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.11.f.a.2.17	✓	174	27.25	even	9
27.11.f.a.14.17	yes	174	3.2	odd	2
81.11.f.a.8.13		174	27.2	odd	18	inner
81.11.f.a.71.13		174	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 81 = 3^{4} \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	81.f (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-9.99045 + 1.76159i) q^{2} +(-865.539 + 315.031i) q^{4} +(-2619.44 + 3121.73i) q^{5} +(-15129.3 - 5506.60i) q^{7} +(17088.5 - 9866.04i) q^{8} +(20670.2 - 35801.9i) q^{10} +(-45611.2 - 54357.3i) q^{11} +(121958. - 691659. i) q^{13} +(160849. + 28361.9i) q^{14} +(569186. - 477604. i) q^{16} +(-109192. - 63041.9i) q^{17} +(-1.20002e6 - 2.07849e6i) q^{19} +(1.28379e6 - 3.52719e6i) q^{20} +(551431. + 462706. i) q^{22} +(2.26289e6 + 6.21725e6i) q^{23} +(-1.18794e6 - 6.73715e6i) q^{25} +7.12483e6i q^{26} +1.48297e7 q^{28} +(-2.11083e7 + 3.72196e6i) q^{29} +(-4.32758e7 + 1.57511e7i) q^{31} +(-1.78330e7 + 2.12526e7i) q^{32} +(1.20193e6 + 437466. i) q^{34} +(5.68204e7 - 3.28053e7i) q^{35} +(3.39317e7 - 5.87714e7i) q^{37} +(1.56501e7 + 1.86511e7i) q^{38} +(-1.39632e7 + 7.91892e7i) q^{40} +(8.50271e7 + 1.49926e7i) q^{41} +(-8.62677e7 + 7.23872e7i) q^{43} +(5.66025e7 + 3.26795e7i) q^{44} +(-3.35595e7 - 5.81268e7i) q^{46} +(8.10430e7 - 2.22664e8i) q^{47} +(-1.78166e7 - 1.49499e7i) q^{49} +(2.37361e7 + 6.52145e7i) q^{50} +(1.12334e8 + 6.37078e8i) q^{52} -5.12143e8i q^{53} +2.89165e8 q^{55} +(-3.12865e8 + 5.51665e7i) q^{56} +(2.04325e8 - 7.43681e7i) q^{58} +(-7.08786e8 + 8.44699e8i) q^{59} +(-6.03944e8 - 2.19817e8i) q^{61} +(4.04598e8 - 2.33595e8i) q^{62} +(-2.39704e8 + 4.15180e8i) q^{64} +(1.83971e9 + 2.19248e9i) q^{65} +(-3.30698e8 + 1.87548e9i) q^{67} +(1.14370e8 + 2.01665e7i) q^{68} +(-5.09872e8 + 4.27834e8i) q^{70} +(1.80207e9 + 1.04043e9i) q^{71} +(-1.61956e7 - 2.80516e7i) q^{73} +(-2.35462e8 + 6.46927e8i) q^{74} +(1.69345e9 + 1.42097e9i) q^{76} +(3.90740e8 + 1.07355e9i) q^{77} +(-5.52812e7 - 3.13515e8i) q^{79} +3.02791e9i q^{80} -8.75870e8 q^{82} +(5.26514e9 - 9.28386e8i) q^{83} +(4.82822e8 - 1.75733e8i) q^{85} +(7.34337e8 - 8.75149e8i) q^{86} +(-1.31572e9 - 4.78882e8i) q^{88} +(-5.25641e9 + 3.03479e9i) q^{89} +(-5.65383e9 + 9.79271e9i) q^{91} +(-3.91724e9 - 4.66839e9i) q^{92} +(-4.17415e8 + 2.36728e9i) q^{94} +(9.63186e9 + 1.69836e9i) q^{95} +(4.82972e9 - 4.05261e9i) q^{97} +(2.04332e8 + 1.17971e8i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 174 q + 6 q^{2} - 6 q^{4} + 4965 q^{5} - 6 q^{7} + 9 q^{8} - 3 q^{10} + 978 q^{11} - 6 q^{13} - 2134569 q^{14} - 3078 q^{16} + 9 q^{17} - 3 q^{19} - 15925353 q^{20} + 10420410 q^{22} - 8437692 q^{23} - 14881965 q^{25}+ \cdots + 103117506282 q^{98}+O(q^{100}) \) 174 * q + 6 * q^2 - 6 * q^4 + 4965 * q^5 - 6 * q^7 + 9 * q^8 - 3 * q^10 + 978 * q^11 - 6 * q^13 - 2134569 * q^14 - 3078 * q^16 + 9 * q^17 - 3 * q^19 - 15925353 * q^20 + 10420410 * q^22 - 8437692 * q^23 - 14881965 * q^25 - 12 * q^28 - 7820868 * q^29 - 51711531 * q^31 - 76244832 * q^32 + 92236410 * q^34 + 260153622 * q^35 - 3 * q^37 - 250645020 * q^38 - 26151153 * q^40 + 837714012 * q^41 - 213300456 * q^43 - 2245906431 * q^44 - 3 * q^46 + 1685998563 * q^47 - 183168366 * q^49 - 2548576023 * q^50 - 912655665 * q^52 - 12 * q^55 + 4260806997 * q^56 - 496853331 * q^58 - 1806342150 * q^59 - 1784159286 * q^61 - 2786630112 * q^62 + 8858370045 * q^64 + 2961878001 * q^65 - 915608058 * q^67 - 11412166995 * q^68 + 1945422669 * q^70 + 5512912173 * q^71 + 2110132140 * q^73 - 22008588729 * q^74 + 11875694586 * q^76 + 2702962221 * q^77 + 6660721974 * q^79 - 12 * q^82 - 7670489421 * q^83 - 6965484381 * q^85 + 33241766118 * q^86 + 28790289402 * q^88 - 34430237370 * q^89 - 991980102 * q^91 - 40280154009 * q^92 - 62587945905 * q^94 + 12104972679 * q^95 + 48297833958 * q^97 + 103117506282 * q^98

Introduction

L-functions

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Database

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