LMFDB - Embedded newform 81.11.f.a.71.11

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)

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);

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")

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			71.11
Character	$\chi$	$=$	81.71
Dual form			81.11.f.a.8.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-12.8751 + 2.27023i) q^{2} +(-801.631 + 291.770i) q^{4} +(2001.83 - 2385.69i) q^{5} +(-5414.20 - 1970.61i) q^{7} +(21252.6 - 12270.2i) q^{8} +(-20357.7 + 35260.6i) q^{10} +(-5862.12 - 6986.20i) q^{11} +(50114.5 - 284213. i) q^{13} +(74182.1 + 13080.3i) q^{14} +(423406. - 355280. i) q^{16} +(483672. + 279248. i) q^{17} +(461520. + 799376. i) q^{19} +(-908659. + 2.49652e6i) q^{20} +(91335.7 + 76639.7i) q^{22} +(547430. + 1.50405e6i) q^{23} +(11593.0 + 65747.1i) q^{25} +3.77305e6i q^{26} +4.91516e6 q^{28} +(-1.05674e7 + 1.86331e6i) q^{29} +(3.50314e7 - 1.27504e7i) q^{31} +(-2.07977e7 + 2.47857e7i) q^{32} +(-6.86129e6 - 2.49731e6i) q^{34} +(-1.55396e7 + 8.97179e6i) q^{35} +(8.95940e6 - 1.55181e7i) q^{37} +(-7.75688e6 - 9.24429e6i) q^{38} +(1.32713e7 - 7.52651e7i) q^{40} +(-1.02384e7 - 1.80531e6i) q^{41} +(-9.64927e7 + 8.09670e7i) q^{43} +(6.73762e6 + 3.88997e6i) q^{44} +(-1.04628e7 - 1.81220e7i) q^{46} +(1.34535e8 - 3.69632e8i) q^{47} +(-1.90958e8 - 1.60233e8i) q^{49} +(-298522. - 820182. i) q^{50} +(4.27516e7 + 2.42456e8i) q^{52} +2.30982e8i q^{53} -2.84019e7 q^{55} +(-1.39246e8 + 2.45528e7i) q^{56} +(1.31826e8 - 4.79807e7i) q^{58} +(-4.14069e8 + 4.93469e8i) q^{59} +(-1.44479e8 - 5.25861e7i) q^{61} +(-4.22086e8 + 2.43692e8i) q^{62} +(-7.14884e7 + 1.23821e8i) q^{64} +(-5.77725e8 - 6.88506e8i) q^{65} +(3.88344e8 - 2.20241e9i) q^{67} +(-4.69203e8 - 8.27332e7i) q^{68} +(1.79706e8 - 1.50791e8i) q^{70} +(-2.85073e9 - 1.64587e9i) q^{71} +(-1.88036e9 - 3.25688e9i) q^{73} +(-8.01235e7 + 2.20137e8i) q^{74} +(-6.03202e8 - 5.06147e8i) q^{76} +(1.79716e7 + 4.93766e7i) q^{77} +(-8.39932e8 - 4.76349e9i) q^{79} -1.72133e9i q^{80} +1.35919e8 q^{82} +(-6.01546e9 + 1.06069e9i) q^{83} +(1.63443e9 - 5.94885e8i) q^{85} +(1.05854e9 - 1.26152e9i) q^{86} +(-2.10307e8 - 7.65456e7i) q^{88} +(5.85736e7 - 3.38175e7i) q^{89} +(-8.31403e8 + 1.44003e9i) q^{91} +(-8.77673e8 - 1.04597e9i) q^{92} +(-8.93003e8 + 5.06447e9i) q^{94} +(2.83095e9 + 4.99173e8i) q^{95} +(-4.70128e9 + 3.94484e9i) q^{97} +(2.82237e9 + 1.62950e9i) 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 $

$2$	−12.8751	+	2.27023i	−0.402347	+	0.0709446i	−0.371160	−	0.928569i	$-0.621040\pi$
$2$	−12.8751	+	2.27023i	−0.402347	+	0.0709446i	−0.0311870	+	0.999514i	$0.509929\pi$
$3$		0			0
$3$		0			0
$4$	−801.631	+	291.770i	−0.782843	+	0.284931i
$5$	2001.83	−	2385.69i	0.640587	−	0.763421i	−0.343876	−	0.939015i	$-0.611740\pi$
$5$	2001.83	−	2385.69i	0.640587	−	0.763421i	0.984463	+	0.175594i	$0.0561845\pi$
$6$		0			0
$7$	−5414.20	−	1970.61i	−0.322140	−	0.117249i	0.175889	−	0.984410i	$-0.443720\pi$
$7$	−5414.20	−	1970.61i	−0.322140	−	0.117249i	−0.498028	+	0.867161i	$0.665942\pi$
$8$	21252.6	−	12270.2i	0.648578	−	0.374457i
$9$		0			0
$10$	−20357.7	+	35260.6i	−0.203577	+	0.352606i
$11$	−5862.12	−	6986.20i	−0.0363992	−	0.0433788i	0.747538	−	0.664219i	$-0.231236\pi$
$11$	−5862.12	−	6986.20i	−0.0363992	−	0.0433788i	−0.783937	+	0.620841i	$0.786791\pi$
$12$		0			0
$13$	50114.5	−	284213.i	0.134973	−	0.765470i	−0.839906	−	0.542732i	$-0.817390\pi$
$13$	50114.5	−	284213.i	0.134973	−	0.765470i	0.974879	−	0.222737i	$-0.0714991\pi$
$14$	74182.1	+	13080.3i	0.137930	+	0.0243208i
$15$		0			0
$16$	423406.	−	355280.i	0.403792	−	0.338821i
$17$	483672.	+	279248.i	0.340649	+	0.196674i	0.660559	−	0.750774i	$-0.270319\pi$
$17$	483672.	+	279248.i	0.340649	+	0.196674i	−0.319910	+	0.947448i	$0.603653\pi$
$18$		0			0
$19$	461520.	+	799376.i	0.186390	+	0.322837i	0.944044	−	0.329820i	$-0.106988\pi$
$19$	461520.	+	799376.i	0.186390	+	0.322837i	−0.757654	+	0.652656i	$0.773655\pi$
$20$	−908659.	+	2.49652e6i	−0.283956	+	0.780162i
$21$		0			0
$22$	91335.7	+	76639.7i	0.0177226	+	0.0148710i
$23$	547430.	+	1.50405e6i	0.0850529	+	0.233681i	0.974927	−	0.222526i	$-0.0714301\pi$
$23$	547430.	+	1.50405e6i	0.0850529	+	0.233681i	−0.889874	+	0.456206i	$0.849208\pi$
$24$		0			0
$25$	11593.0	+	65747.1i	0.00118712	+	0.00673251i
$26$			3.77305e6i			0.317560i
$27$		0			0
$28$	4.91516e6			0.285593
$29$	−1.05674e7	+	1.86331e6i	−0.515201	+	0.0908438i	−0.425203	−	0.905098i	$-0.639797\pi$
$29$	−1.05674e7	+	1.86331e6i	−0.515201	+	0.0908438i	−0.0899982	+	0.995942i	$0.528686\pi$
$30$		0			0
$31$	3.50314e7	−	1.27504e7i	1.22363	−	0.445364i	0.352216	−	0.935919i	$-0.385428\pi$
$31$	3.50314e7	−	1.27504e7i	1.22363	−	0.445364i	0.871410	+	0.490555i	$0.163206\pi$
$32$	−2.07977e7	+	2.47857e7i	−0.619819	+	0.738671i
$33$		0			0
$34$	−6.86129e6	−	2.49731e6i	−0.151012	−	0.0549638i
$35$	−1.55396e7	+	8.97179e6i	−0.295869	+	0.170820i
$36$		0			0
$37$	8.95940e6	−	1.55181e7i	0.129202	−	0.223785i	−0.794165	−	0.607702i	$-0.792092\pi$
$37$	8.95940e6	−	1.55181e7i	0.129202	−	0.223785i	0.923368	+	0.383917i	$0.125425\pi$
$38$	−7.75688e6	−	9.24429e6i	−0.0978969	−	0.116669i
$39$		0			0
$40$	1.32713e7	−	7.52651e7i	0.129602	−	0.735010i
$41$	−1.02384e7	−	1.80531e6i	−0.0883718	−	0.0155823i	0.129287	−	0.991607i	$-0.458731\pi$
$41$	−1.02384e7	−	1.80531e6i	−0.0883718	−	0.0155823i	−0.217659	+	0.976025i	$0.569842\pi$
$42$		0			0
$43$	−9.64927e7	+	8.09670e7i	−0.656375	+	0.550764i	−0.908998	−	0.416801i	$-0.863151\pi$
$43$	−9.64927e7	+	8.09670e7i	−0.656375	+	0.550764i	0.252623	+	0.967565i	$0.418707\pi$
$44$	6.73762e6	+	3.88997e6i	0.0408548	+	0.0235875i
$45$		0			0
$46$	−1.04628e7	−	1.81220e7i	−0.0507992	−	0.0879868i
$47$	1.34535e8	−	3.69632e8i	0.586605	−	1.61168i	−0.190062	−	0.981772i	$-0.560869\pi$
$47$	1.34535e8	−	3.69632e8i	0.586605	−	1.61168i	0.776667	−	0.629912i	$-0.216909\pi$
$48$		0			0
$49$	−1.90958e8	−	1.60233e8i	−0.676018	−	0.567246i
$50$	−298522.	−	820182.i	−0.000955270	−	0.00262458i
$51$		0			0
$52$	4.27516e7	+	2.42456e8i	0.112444	+	0.637700i
$53$			2.30982e8i			0.552331i	0.961110	+	0.276166i	$0.0890638\pi$
$53$			2.30982e8i			0.552331i	−0.961110	+	0.276166i	$0.910936\pi$
$54$		0			0
$55$	−2.84019e7			−0.0564331
$56$	−1.39246e8	+	2.45528e7i	−0.252837	+	0.0445821i
$57$		0			0
$58$	1.31826e8	−	4.79807e7i	0.200845	−	0.0731015i
$59$	−4.14069e8	+	4.93469e8i	−0.579179	+	0.690239i	−0.973488	−	0.228739i	$-0.926540\pi$
$59$	−4.14069e8	+	4.93469e8i	−0.579179	+	0.690239i	0.394308	+	0.918978i	$0.370984\pi$
$60$		0			0
$61$	−1.44479e8	−	5.25861e7i	−0.171063	−	0.0622618i	0.255069	−	0.966923i	$-0.417902\pi$
$61$	−1.44479e8	−	5.25861e7i	−0.171063	−	0.0622618i	−0.426132	+	0.904661i	$0.640124\pi$
$62$	−4.22086e8	+	2.43692e8i	−0.460726	+	0.266000i
$63$		0			0
$64$	−7.14884e7	+	1.23821e8i	−0.0665787	+	0.115318i
$65$	−5.77725e8	−	6.88506e8i	−0.497914	−	0.593391i
$66$		0			0
$67$	3.88344e8	−	2.20241e9i	0.287636	−	1.63126i	−0.408079	−	0.912947i	$-0.633801\pi$
$67$	3.88344e8	−	2.20241e9i	0.287636	−	1.63126i	0.695715	−	0.718318i	$-0.255088\pi$
$68$	−4.69203e8	−	8.27332e7i	−0.322713	−	0.0569030i
$69$		0			0
$70$	1.79706e8	−	1.50791e8i	0.106923	−	0.0897192i
$71$	−2.85073e9	−	1.64587e9i	−1.58002	−	0.912228i	−0.994854	−	0.101318i	$-0.967694\pi$
$71$	−2.85073e9	−	1.64587e9i	−1.58002	−	0.912228i	−0.585171	−	0.810910i	$-0.698973\pi$
$72$		0			0
$73$	−1.88036e9	−	3.25688e9i	−0.907040	−	1.57104i	−0.818156	−	0.574997i	$-0.805003\pi$
$73$	−1.88036e9	−	3.25688e9i	−0.907040	−	1.57104i	−0.0888837	−	0.996042i	$-0.528330\pi$
$74$	−8.01235e7	+	2.20137e8i	−0.0361078	+	0.0992054i
$75$		0			0
$76$	−6.03202e8	−	5.06147e8i	−0.237900	−	0.199622i
$77$	1.79716e7	+	4.93766e7i	0.00663948	+	0.0182418i
$78$		0			0
$79$	−8.39932e8	−	4.76349e9i	−0.272966	−	1.54807i	−0.745349	−	0.666675i	$-0.767717\pi$
$79$	−8.39932e8	−	4.76349e9i	−0.272966	−	1.54807i	0.472383	−	0.881393i	$-0.343394\pi$
$80$		−	1.72133e9i		−	0.525308i
$81$		0			0
$82$	1.35919e8			0.0366616
$83$	−6.01546e9	+	1.06069e9i	−1.52714	+	0.269276i	−0.873234	−	0.487302i	$-0.837981\pi$
$83$	−6.01546e9	+	1.06069e9i	−1.52714	+	0.269276i	−0.653904	+	0.756578i	$0.726870\pi$
$84$		0			0
$85$	1.63443e9	−	5.94885e8i	0.368360	−	0.134072i
$86$	1.05854e9	−	1.26152e9i	0.225017	−	0.268165i
$87$		0			0
$88$	−2.10307e8	−	7.65456e7i	−0.0398512	−	0.0145046i
$89$	5.85736e7	−	3.38175e7i	0.0104894	−	0.00605607i	−0.494746	−	0.869038i	$-0.664739\pi$
$89$	5.85736e7	−	3.38175e7i	0.0104894	−	0.00605607i	0.505236	+	0.862981i	$0.331406\pi$
$90$		0			0
$91$	−8.31403e8	+	1.44003e9i	−0.133231	+	0.230763i
$92$	−8.77673e8	−	1.04597e9i	−0.133166	−	0.158701i
$93$		0			0
$94$	−8.93003e8	+	5.06447e9i	−0.121678	+	0.690072i
$95$	2.83095e9	+	4.99173e8i	0.365859	+	0.0645109i
$96$		0			0
$97$	−4.70128e9	+	3.94484e9i	−0.547466	+	0.459379i	−0.874082	−	0.485779i	$-0.838536\pi$
$97$	−4.70128e9	+	3.94484e9i	−0.547466	+	0.459379i	0.326616	+	0.945157i	$0.394092\pi$
$98$	2.82237e9	+	1.62950e9i	0.312237	+	0.180270i
$99$		0			0
$100$	−2.84763e7	−	4.93225e7i	−0.00284763	−	0.00493225i
$101$	−2.83333e9	+	7.78451e9i	−0.269582	+	0.740670i	0.728849	+	0.684674i	$0.240055\pi$
$101$	−2.83333e9	+	7.78451e9i	−0.269582	+	0.740670i	−0.998431	+	0.0559955i	$0.982167\pi$
$102$		0			0
$103$	−1.26630e9	−	1.06255e9i	−0.109232	−	0.0916568i	0.586536	−	0.809923i	$-0.300491\pi$
$103$	−1.26630e9	−	1.06255e9i	−0.109232	−	0.0916568i	−0.695768	+	0.718267i	$0.744936\pi$
$104$	−2.42229e9	−	6.65519e9i	−0.199095	−	0.547008i
$105$		0			0
$106$	−5.24383e8	−	2.97392e9i	−0.0391849	−	0.222229i
$107$		−	2.10630e9i		−	0.150177i	−0.997177	−	0.0750883i	$-0.976076\pi$
$107$		−	2.10630e9i		−	0.150177i	0.997177	−	0.0750883i	$-0.0239239\pi$
$108$		0			0
$109$	1.14750e10			0.745797			0.372899	−	0.927872i	$-0.378364\pi$
$109$	1.14750e10			0.745797			0.372899	+	0.927872i	$0.378364\pi$
$110$	3.65678e8	−	6.44788e7i	0.0227057	−	0.00400363i
$111$		0			0
$112$	−2.99252e9	+	1.08919e9i	−0.169804	+	0.0618035i
$113$	−6.10448e9	+	7.27503e9i	−0.331327	+	0.394860i	−0.905829	−	0.423643i	$-0.860751\pi$
$113$	−6.10448e9	+	7.27503e9i	−0.331327	+	0.394860i	0.574503	+	0.818503i	$0.305196\pi$
$114$		0			0
$115$	4.68406e9	+	1.70486e9i	0.232881	+	0.0847617i
$116$	7.92747e9	−	4.57693e9i	0.377437	−	0.217913i
$117$		0			0
$118$	4.21090e9	−	7.29349e9i	0.184062	−	0.318805i
$119$	−2.06841e9	−	2.46504e9i	−0.0866766	−	0.103297i
$120$		0			0
$121$	4.48954e9	−	2.54615e10i	0.173091	−	0.981650i
$122$	1.97957e9	+	3.49051e8i	0.0732438	+	0.0129149i
$123$		0			0
$124$	−2.43621e10	+	2.04422e10i	−0.831009	+	0.697299i
$125$	2.65186e10	+	1.53105e10i	0.868960	+	0.501694i
$126$		0			0
$127$	1.30512e10	+	2.26054e10i	0.395033	+	0.684217i	0.993105	−	0.117225i	$-0.0373999\pi$
$127$	1.30512e10	+	2.26054e10i	0.395033	+	0.684217i	−0.598073	+	0.801442i	$0.704067\pi$
$128$	1.19711e10	−	3.28904e10i	0.348405	−	0.957236i
$129$		0			0
$130$	9.00133e9	+	7.55301e9i	0.242432	+	0.203425i
$131$	5.98262e9	+	1.64371e10i	0.155072	+	0.426058i	0.992763	−	0.120086i	$-0.0383172\pi$
$131$	5.98262e9	+	1.64371e10i	0.155072	+	0.426058i	−0.837691	+	0.546144i	$0.816095\pi$
$132$		0			0
$133$	−9.23505e8	−	5.23746e9i	−0.0221912	−	0.125853i
$134$			2.92379e10i			0.676740i
$135$		0			0
$136$	1.37057e10			0.294583
$137$	−6.32409e10	+	1.11511e10i	−1.31037	+	0.231054i	−0.784829	−	0.619712i	$-0.787249\pi$
$137$	−6.32409e10	+	1.11511e10i	−1.31037	+	0.231054i	−0.525544	+	0.850766i	$0.676138\pi$
$138$		0			0
$139$	3.42328e10	−	1.24597e10i	0.659734	−	0.240123i	0.00961236	−	0.999954i	$-0.496940\pi$
$139$	3.42328e10	−	1.24597e10i	0.659734	−	0.240123i	0.650121	+	0.759830i	$0.274718\pi$
$140$	9.83932e9	−	1.17260e10i	0.182947	−	0.218028i
$141$		0			0
$142$	4.04399e10	+	1.47189e10i	0.700436	+	0.254938i
$143$	−2.27935e9	+	1.31598e9i	−0.0381181	+	0.0220075i
$144$		0			0
$145$	−1.67088e10	+	2.89405e10i	−0.260679	+	0.451509i
$146$	3.16036e10	+	3.76638e10i	0.476401	+	0.567753i
$147$		0			0
$148$	−2.65441e9	+	1.50539e10i	−0.0373817	+	0.212002i
$149$	1.14907e11	+	2.02612e10i	1.56465	+	0.275889i	0.887798	−	0.460234i	$-0.152234\pi$
$149$	1.14907e11	+	2.02612e10i	1.56465	+	0.275889i	0.676848	+	0.736123i	$0.263345\pi$
$150$		0			0
$151$	−1.14129e11	+	9.57657e10i	−1.45382	+	1.21990i	−0.524093	+	0.851661i	$0.675596\pi$
$151$	−1.14129e11	+	9.57657e10i	−1.45382	+	1.21990i	−0.929730	+	0.368242i	$0.879960\pi$
$152$	1.96170e10	+	1.13259e10i	0.241777	+	0.139590i
$153$		0			0
$154$	−3.43483e8	−	5.94930e8i	−0.00396553	−	0.00686850i
$155$	3.97085e10	−	1.09098e11i	0.443839	−	1.21944i
$156$		0			0
$157$	7.27878e10	+	6.10762e10i	0.763063	+	0.640285i	0.938922	−	0.344130i	$-0.111826\pi$
$157$	7.27878e10	+	6.10762e10i	0.763063	+	0.640285i	−0.175860	+	0.984415i	$0.556270\pi$
$158$	2.16284e10	+	5.94236e10i	0.219654	+	0.603495i
$159$		0			0
$160$	1.74976e10	+	9.92337e10i	0.166870	+	0.946366i
$161$		−	9.22200e9i		−	0.0852503i
$162$		0			0
$163$	−2.01365e11			−1.75003			−0.875017	−	0.484093i	$-0.839150\pi$
$163$	−2.01365e11			−1.75003			−0.875017	+	0.484093i	$0.839150\pi$
$164$	8.73417e9	−	1.54007e9i	0.0736211	−	0.0129814i
$165$		0			0
$166$	7.50416e10	−	2.73129e10i	0.595335	−	0.216684i
$167$	1.28130e11	−	1.52699e11i	0.986435	−	1.17559i	0.00197178	−	0.999998i	$-0.499372\pi$
$167$	1.28130e11	−	1.52699e11i	0.986435	−	1.17559i	0.984463	−	0.175590i	$-0.0561832\pi$
$168$		0			0
$169$	5.12788e10	+	1.86639e10i	0.371967	+	0.135385i
$170$	−1.96930e10	+	1.13697e10i	−0.138697	+	0.0800766i
$171$		0			0
$172$	5.37278e10	−	9.30593e10i	0.356908	−	0.618184i
$173$	−3.38764e10	−	4.03723e10i	−0.218608	−	0.260527i	0.645583	−	0.763690i	$-0.276614\pi$
$173$	−3.38764e10	−	4.03723e10i	−0.218608	−	0.260527i	−0.864192	+	0.503162i	$0.832170\pi$
$174$		0			0
$175$	6.67950e7	−	3.78814e8i	0.000406962	−	0.00230800i
$176$	−4.96411e9	−	8.75307e8i	−0.0293953	−	0.00518319i
$177$		0			0
$178$	−6.77367e8	+	5.68379e8i	−0.00379074	+	0.00318081i
$179$	−3.79620e10	−	2.19174e10i	−0.206578	−	0.119268i	0.393142	−	0.919478i	$-0.371388\pi$
$179$	−3.79620e10	−	2.19174e10i	−0.206578	−	0.119268i	−0.599720	+	0.800210i	$0.704721\pi$
$180$		0			0
$181$	−1.42121e11	−	2.46160e11i	−0.731585	−	1.26714i	−0.956206	−	0.292696i	$-0.905448\pi$
$181$	−1.42121e11	−	2.46160e11i	−0.731585	−	1.26714i	0.224621	−	0.974446i	$-0.427886\pi$
$182$	7.43520e9	−	2.04280e10i	0.0372337	−	0.102299i
$183$		0			0
$184$	3.00893e10	+	2.52479e10i	0.142667	+	0.119712i
$185$	−1.90863e10	−	5.24391e10i	−0.0880770	−	0.241989i
$186$		0			0
$187$	−8.84460e8	−	5.01602e9i	−0.00386785	−	0.0219357i
$188$			3.35561e11i			1.42884i
$189$		0			0
$190$	−3.75820e10			−0.151779
$191$	−4.24220e11	+	7.48015e10i	−1.66888	+	0.294268i	−0.926663	−	0.375894i	$-0.877336\pi$
$191$	−4.24220e11	+	7.48015e10i	−1.66888	+	0.294268i	−0.742215	+	0.670162i	$0.766225\pi$
$192$		0			0
$193$	1.38420e11	−	5.03809e10i	0.516908	−	0.188139i	−0.0703754	−	0.997521i	$-0.522420\pi$
$193$	1.38420e11	−	5.03809e10i	0.516908	−	0.188139i	0.587283	+	0.809382i	$0.300197\pi$
$194$	5.15737e10	−	6.14632e10i	0.187681	−	0.223669i
$195$		0			0
$196$	1.99829e11	+	7.27319e10i	0.690842	+	0.251446i
$197$	−3.50254e11	+	2.02219e11i	−1.18046	+	0.681540i	−0.956121	−	0.292971i	$-0.905356\pi$
$197$	−3.50254e11	+	2.02219e11i	−1.18046	+	0.681540i	−0.224340	+	0.974511i	$0.572023\pi$
$198$		0			0
$199$	1.06945e11	−	1.85235e11i	0.342686	−	0.593549i	−0.642245	−	0.766500i	$-0.721997\pi$
$199$	1.06945e11	−	1.85235e11i	0.342686	−	0.593549i	0.984931	+	0.172950i	$0.0553300\pi$
$200$	1.05311e9	+	1.25505e9i	0.00329097	+	0.00392203i
$201$		0			0
$202$	1.88068e10	−	1.06659e11i	0.0559188	−	0.317132i
$203$	6.08857e10	+	1.07358e10i	0.176618	+	0.0311425i
$204$		0			0
$205$	−2.48025e10	+	2.08118e10i	−0.0685057	+	0.0574831i
$206$	1.87160e10	+	1.08057e10i	0.0504518	+	0.0291284i
$207$		0			0
$208$	−7.97566e10	−	1.38142e11i	−0.204856	−	0.354822i
$209$	2.87912e9	−	7.91031e9i	0.00721984	−	0.0198364i
$210$		0			0
$211$	2.74310e11	+	2.30173e11i	0.655887	+	0.550354i	0.908851	−	0.417122i	$-0.136961\pi$
$211$	2.74310e11	+	2.30173e11i	0.655887	+	0.550354i	−0.252964	+	0.967476i	$0.581405\pi$
$212$	−6.73937e10	−	1.85163e11i	−0.157377	−	0.432389i
$213$		0			0
$214$	4.78179e9	+	2.71189e10i	0.0106542	+	0.0604231i
$215$			3.92284e11i			0.853903i
$216$		0			0
$217$	−2.14793e11			−0.446397
$218$	−1.47742e11	+	2.60509e10i	−0.300069	+	0.0529103i
$219$		0			0
$220$	2.27679e10	−	8.28682e9i	0.0441783	−	0.0160796i
$221$	1.03605e11	−	1.23472e11i	0.196526	−	0.234211i
$222$		0			0
$223$	−8.54608e11	−	3.11052e11i	−1.54968	−	0.564038i	−0.581339	−	0.813661i	$-0.697471\pi$
$223$	−8.54608e11	−	3.11052e11i	−1.54968	−	0.564038i	−0.968343	+	0.249623i	$0.919693\pi$
$224$	1.61446e11	−	9.32107e10i	0.286277	−	0.165282i
$225$		0			0
$226$	6.20798e10	−	1.07525e11i	0.105295	−	0.182376i
$227$	−5.38250e11	−	6.41461e11i	−0.893007	−	1.06424i	−0.997566	−	0.0697255i	$-0.977788\pi$
$227$	−5.38250e11	−	6.41461e11i	−0.893007	−	1.06424i	0.104559	−	0.994519i	$-0.466657\pi$
$228$		0			0
$229$	1.07722e11	−	6.10920e11i	0.171051	−	0.970078i	−0.771553	−	0.636165i	$-0.780520\pi$
$229$	1.07722e11	−	6.10920e11i	0.171051	−	0.970078i	0.942604	−	0.333913i	$-0.108369\pi$
$230$	−6.41782e10	−	1.13164e10i	−0.0997123	−	0.0175820i
$231$		0			0
$232$	−2.01721e11	+	1.69264e11i	−0.300131	+	0.251840i
$233$	1.50960e11	+	8.71569e10i	0.219828	+	0.126918i	0.605871	−	0.795563i	$-0.292825\pi$
$233$	1.50960e11	+	8.71569e10i	0.219828	+	0.126918i	−0.386043	+	0.922481i	$0.626158\pi$
$234$		0			0
$235$	−6.12511e11	−	1.06090e12i	−0.854623	−	1.48025i
$236$	1.87952e11	−	5.16393e11i	0.256736	−	0.705375i
$237$		0			0
$238$	3.22272e10	+	2.70418e10i	0.0422025	+	0.0354121i
$239$	−2.63210e11	−	7.23163e11i	−0.337530	−	0.927356i	−0.986093	−	0.166195i	$-0.946852\pi$
$239$	−2.63210e11	−	7.23163e11i	−0.337530	−	0.927356i	0.648563	−	0.761161i	$-0.275370\pi$
$240$		0			0
$241$	1.27734e11	+	7.24418e11i	0.157117	+	0.891054i	0.956825	+	0.290665i	$0.0938764\pi$
$241$	1.27734e11	+	7.24418e11i	0.157117	+	0.891054i	−0.799708	+	0.600389i	$0.795012\pi$
$242$			3.38011e11i			0.407244i
$243$		0			0
$244$	1.31162e11			0.151656
$245$	−7.64533e11	+	1.34808e11i	−0.866096	+	0.152716i
$246$		0			0
$247$	2.50322e11	−	9.11098e10i	0.272279	−	0.0991015i
$248$	5.88058e11	−	7.00821e11i	0.626848	−	0.747048i
$249$		0			0
$250$	−3.76188e11	−	1.36921e11i	−0.385216	−	0.140207i
$251$	−5.01926e11	+	2.89787e11i	−0.503815	+	0.290878i	−0.730288	−	0.683140i	$-0.760614\pi$
$251$	−5.01926e11	+	2.89787e11i	−0.503815	+	0.290878i	0.226472	+	0.974018i	$0.427281\pi$
$252$		0			0
$253$	7.29850e9	−	1.26414e10i	0.00704095	−	0.0121953i
$254$	−2.19355e11	−	2.61418e11i	−0.207482	−	0.247267i
$255$		0			0
$256$	−5.40372e10	+	3.06460e11i	−0.0491465	+	0.278724i
$257$	2.29445e11	+	4.04573e10i	0.204650	+	0.0360854i	0.275034	−	0.961435i	$-0.411311\pi$
$257$	2.29445e11	+	4.04573e10i	0.204650	+	0.0360854i	−0.0703830	+	0.997520i	$0.522422\pi$
$258$		0			0
$259$	−7.90881e10	+	6.63628e10i	−0.0678598	+	0.0569411i
$260$	6.64007e11	+	3.83365e11i	0.558864	+	0.322660i
$261$		0			0
$262$	−1.14343e11	−	1.98047e11i	−0.0926194	−	0.160422i
$263$	−6.73609e10	+	1.85073e11i	−0.0535339	+	0.147083i	−0.963577	−	0.267429i	$-0.913826\pi$
$263$	−6.73609e10	+	1.85073e11i	−0.0535339	+	0.147083i	0.910043	+	0.414513i	$0.136048\pi$
$264$		0			0
$265$	5.51053e11	+	4.62388e11i	0.421662	+	0.353816i
$266$	2.37804e10	+	6.53362e10i	0.0178571	+	0.0490621i
$267$		0			0
$268$	3.31288e11	+	1.87883e12i	0.239625	+	1.35898i
$269$			1.49158e12i			1.05897i	0.848318	+	0.529487i	$0.177616\pi$
$269$			1.49158e12i			1.05897i	−0.848318	+	0.529487i	$0.822384\pi$
$270$		0			0
$271$	−3.91112e11			−0.267581			−0.133790	−	0.991010i	$-0.542715\pi$
$271$	−3.91112e11			−0.267581			−0.133790	+	0.991010i	$0.542715\pi$
$272$	3.04001e11	−	5.36036e10i	0.204188	−	0.0360039i
$273$		0			0
$274$	7.88917e11	−	2.87142e11i	0.510833	−	0.185928i
$275$	3.91363e8	−	4.66409e8i	0.000248838	−	0.000296554i
$276$		0			0
$277$	6.11171e11	+	2.22448e11i	0.374769	+	0.136405i	0.522536	−	0.852617i	$-0.324986\pi$
$277$	6.11171e11	+	2.22448e11i	0.374769	+	0.136405i	−0.147766	+	0.989022i	$0.547208\pi$
$278$	−4.12465e11	+	2.38137e11i	−0.248406	+	0.143417i
$279$		0			0
$280$	−2.20171e11	+	3.81348e11i	−0.127929	+	0.221580i
$281$	−1.93872e11	−	2.31048e11i	−0.110658	−	0.131878i	0.707872	−	0.706341i	$-0.249655\pi$
$281$	−1.93872e11	−	2.31048e11i	−0.110658	−	0.131878i	−0.818530	+	0.574463i	$0.805211\pi$
$282$		0			0
$283$	2.19715e11	−	1.24606e12i	0.121040	−	0.686449i	−0.862542	−	0.505985i	$-0.831129\pi$
$283$	2.19715e11	−	1.24606e12i	0.121040	−	0.686449i	0.983582	−	0.180464i	$-0.0577599\pi$
$284$	2.76545e12	+	4.87623e11i	1.49683	+	0.263932i
$285$		0			0
$286$	2.63593e10	−	2.21181e10i	0.0137754	−	0.0115589i
$287$	5.18753e10	+	2.99502e10i	0.0266411	+	0.0153812i
$288$		0			0
$289$	−8.52038e11	−	1.47577e12i	−0.422639	−	0.732032i
$290$	1.49426e11	−	4.10545e11i	0.0728512	−	0.200157i
$291$		0			0
$292$	2.45761e12	+	2.06218e12i	1.15771	+	0.971432i
$293$	9.02468e11	+	2.47951e12i	0.417920	+	1.14823i	0.952880	+	0.303349i	$0.0981048\pi$
$293$	9.02468e11	+	2.47951e12i	0.417920	+	1.14823i	−0.534959	+	0.844878i	$0.679673\pi$
$294$		0			0
$295$	3.48366e11	+	1.97568e12i	0.155929	+	0.884316i
$296$		−	4.39734e11i		−	0.193523i
$297$		0			0
$298$	−1.52544e12			−0.649103
$299$	4.54906e11	−	8.02121e10i	0.190355	−	0.0335648i
$300$		0			0
$301$	6.81985e11	−	2.48222e11i	0.276021	−	0.100463i
$302$	1.25201e12	−	1.49209e12i	0.498396	−	0.593965i
$303$		0			0
$304$	4.79412e11	+	1.74492e11i	0.184647	+	0.0672059i
$305$	−4.14678e11	+	2.39414e11i	−0.157113	+	0.0907091i
$306$		0			0
$307$	4.65939e11	−	8.07030e11i	0.170859	−	0.295936i	−0.767862	−	0.640616i	$-0.778679\pi$
$307$	4.65939e11	−	8.07030e11i	0.170859	−	0.295936i	0.938720	+	0.344680i	$0.112013\pi$
$308$	−2.88132e10	−	3.43383e10i	−0.0103953	−	0.0123887i
$309$		0			0
$310$	−2.63573e11	+	1.49480e12i	−0.0920646	+	0.522124i
$311$	2.64487e12	+	4.66363e11i	0.909082	+	0.160296i	0.608587	−	0.793487i	$-0.291737\pi$
$311$	2.64487e12	+	4.66363e11i	0.909082	+	0.160296i	0.300496	+	0.953783i	$0.402848\pi$
$312$		0			0
$313$	−7.51264e11	+	6.30385e11i	−0.250075	+	0.209838i	−0.759205	−	0.650852i	$-0.774412\pi$
$313$	−7.51264e11	+	6.30385e11i	−0.250075	+	0.209838i	0.509129	+	0.860690i	$0.329967\pi$
$314$	−1.07581e12	−	6.21117e11i	−0.352441	−	0.203482i
$315$		0			0
$316$	2.06316e12	+	3.57350e12i	0.654783	+	1.13412i
$317$	−9.83978e11	+	2.70346e12i	−0.307390	+	0.844546i	0.685774	+	0.727815i	$0.259464\pi$
$317$	−9.83978e11	+	2.70346e12i	−0.307390	+	0.844546i	−0.993164	+	0.116731i	$0.962758\pi$
$318$		0			0
$319$	7.49646e10	+	6.29028e10i	0.0226936	+	0.0190422i
$320$	1.52292e11	+	4.18419e11i	0.0453866	+	0.124699i
$321$		0			0
$322$	2.09360e10	+	1.18734e11i	0.00604805	+	0.0343002i
$323$			5.15515e11i			0.146632i
$324$		0			0
$325$	1.92672e10			0.00531376
$326$	2.59260e12	−	4.57145e11i	0.704121	−	0.124155i
$327$		0			0
$328$	−2.39745e11	+	8.72599e10i	−0.0631509	+	0.0229851i
$329$	−1.45680e12	+	1.73614e12i	−0.377937	+	0.450408i
$330$		0			0
$331$	−1.46270e12	−	5.32380e11i	−0.368142	−	0.133993i	0.151323	−	0.988484i	$-0.451647\pi$
$331$	−1.46270e12	−	5.32380e11i	−0.368142	−	0.133993i	−0.519465	+	0.854492i	$0.673869\pi$
$332$	4.51270e12	−	2.60541e12i	1.11878	−	0.645930i
$333$		0			0
$334$	−1.30302e12	+	2.25690e12i	−0.313488	+	0.542976i
$335$	−4.47687e12	−	5.33533e12i	−1.06109	−	1.26455i
$336$		0			0
$337$	9.10879e11	−	5.16585e12i	0.209561	−	1.18848i	−0.680537	−	0.732714i	$-0.738254\pi$
$337$	9.10879e11	−	5.16585e12i	0.209561	−	1.18848i	0.890099	−	0.455768i	$-0.150635\pi$
$338$	−7.02591e11	−	1.23886e11i	−0.159265	−	0.0280826i
$339$		0			0
$340$	−1.13664e12	+	9.53756e11i	−0.250167	+	0.209915i
$341$	−2.94435e11	−	1.69992e11i	−0.0638583	−	0.0368686i
$342$		0			0
$343$	1.53190e12	+	2.65332e12i	0.322670	+	0.558881i
$344$	−1.05724e12	+	2.90474e12i	−0.219473	+	0.602997i
$345$		0			0
$346$	5.27817e11	+	4.42891e11i	0.106439	+	0.0893133i
$347$	−1.30766e12	−	3.59276e12i	−0.259924	−	0.714135i	−0.999171	−	0.0407013i	$-0.987041\pi$
$347$	−1.30766e12	−	3.59276e12i	−0.259924	−	0.714135i	0.739247	−	0.673434i	$-0.235181\pi$
$348$		0			0
$349$	−7.01546e11	−	3.97867e12i	−0.135497	−	0.768441i	−0.974512	−	0.224333i	$-0.927980\pi$
$349$	−7.01546e11	−	3.97867e12i	−0.135497	−	0.768441i	0.839016	−	0.544107i	$-0.183132\pi$
$350$			5.02890e9i			0.000957487i
$351$		0			0
$352$	2.95076e11			0.0546036
$353$	1.94975e12	−	3.43793e11i	0.355717	−	0.0627225i	0.00706577	−	0.999975i	$-0.497751\pi$
$353$	1.94975e12	−	3.43793e11i	0.355717	−	0.0627225i	0.348651	+	0.937253i	$0.386640\pi$
$354$		0			0
$355$	−9.63322e12	+	3.50620e12i	−1.70856	+	0.621864i
$356$	−3.70875e10	+	4.41991e10i	−0.00648600	+	0.00772972i
$357$		0			0
$358$	5.38522e11	+	1.96006e11i	0.0915773	+	0.0333314i
$359$	4.24855e12	−	2.45290e12i	0.712473	−	0.411347i	−0.0995028	−	0.995037i	$-0.531725\pi$
$359$	4.24855e12	−	2.45290e12i	0.712473	−	0.411347i	0.811976	+	0.583691i	$0.198392\pi$
$360$		0			0
$361$	2.63953e12	−	4.57180e12i	0.430518	−	0.745678i
$362$	2.38866e12	+	2.84669e12i	0.384248	+	0.457929i
$363$		0			0
$364$	2.46321e11	−	1.39695e12i	0.0385473	−	0.218612i
$365$	−1.15341e13	−	2.03377e12i	−1.78040	−	0.313933i
$366$		0			0
$367$	−2.24222e12	+	1.88144e12i	−0.336781	+	0.282593i	−0.795456	−	0.606011i	$-0.792769\pi$
$367$	−2.24222e12	+	1.88144e12i	−0.336781	+	0.282593i	0.458675	+	0.888604i	$0.348324\pi$
$368$	7.66144e11	+	4.42333e11i	0.113520	+	0.0655406i
$369$		0			0
$370$	3.64786e11	+	6.31828e11i	0.0526053	+	0.0911151i
$371$	4.55176e11	−	1.25059e12i	0.0647604	−	0.177928i
$372$		0			0
$373$	−6.53194e12	−	5.48095e12i	−0.904686	−	0.759122i	0.0664144	−	0.997792i	$-0.478844\pi$
$373$	−6.53194e12	−	5.48095e12i	−0.904686	−	0.759122i	−0.971101	+	0.238670i	$0.923289\pi$
$374$	2.27750e10	+	6.25739e10i	0.00311244	+	0.00855136i
$375$		0			0
$376$	−1.67624e12	−	9.50640e12i	−0.223047	−	1.26496i
$377$			3.09677e12i			0.406632i
$378$		0			0
$379$	9.94813e12			1.27217			0.636086	−	0.771619i	$-0.280553\pi$
$379$	9.94813e12			1.27217			0.636086	+	0.771619i	$0.280553\pi$
$380$	−2.41502e12	+	4.25833e11i	−0.304792	+	0.0537430i
$381$		0			0
$382$	5.29206e12	−	1.92615e12i	0.650591	−	0.236796i
$383$	−5.36395e12	+	6.39250e12i	−0.650865	+	0.775670i	−0.986044	−	0.166484i	$-0.946759\pi$
$383$	−5.36395e12	+	6.39250e12i	−0.650865	+	0.775670i	0.335179	+	0.942154i	$0.391203\pi$
$384$		0			0
$385$	1.53774e11	+	5.59690e10i	0.0181794	+	0.00661674i
$386$	−1.66780e12	+	9.62904e11i	−0.194629	+	0.112369i
$387$		0			0
$388$	2.61770e12	−	4.53400e12i	0.297688	−	0.515611i
$389$	8.74661e11	+	1.04238e12i	0.0981955	+	0.117025i	0.812904	−	0.582397i	$-0.197885\pi$
$389$	8.74661e11	+	1.04238e12i	0.0981955	+	0.117025i	−0.714709	+	0.699422i	$0.753441\pi$
$390$		0			0
$391$	−1.55227e11	+	8.80337e11i	−0.0169857	+	0.0963308i
$392$	−6.02445e12	−	1.06227e12i	−0.650859	−	0.114764i
$393$		0			0
$394$	4.05047e12	−	3.39875e12i	0.426603	−	0.357963i
$395$	−1.30456e13	−	7.53190e12i	−1.35669	−	0.783284i
$396$		0			0
$397$	−1.97136e12	−	3.41449e12i	−0.199900	−	0.346237i	0.748596	−	0.663026i	$-0.230728\pi$
$397$	−1.97136e12	−	3.41449e12i	−0.199900	−	0.346237i	−0.948496	+	0.316790i	$0.897395\pi$
$398$	−9.56406e11	+	2.62770e12i	−0.0957695	+	0.263124i
$399$		0			0
$400$	2.82672e10	+	2.37190e10i	0.00276047	+	0.00231631i
$401$	6.86161e11	+	1.88521e12i	0.0661765	+	0.181819i	0.968373	−	0.249507i	$-0.0802684\pi$
$401$	6.86161e11	+	1.88521e12i	0.0661765	+	0.181819i	−0.902197	+	0.431325i	$0.858046\pi$
$402$		0			0
$403$	−1.86825e12	−	1.05954e13i	−0.175756	−	0.996761i
$404$		−	7.06699e12i		−	0.656640i
$405$		0			0
$406$	−8.08282e11			−0.0732711
$407$	−1.60934e11	+	2.83770e10i	−0.0144104	+	0.00254094i
$408$		0			0
$409$	−1.39696e13	+	5.08453e12i	−1.22059	+	0.444257i	−0.870363	−	0.492410i	$-0.836116\pi$
$409$	−1.39696e13	+	5.08453e12i	−1.22059	+	0.444257i	−0.350222	+	0.936667i	$0.613894\pi$
$410$	2.72088e11	−	3.24261e11i	0.0234849	−	0.0279883i
$411$		0			0
$412$	1.32513e12	+	4.82307e11i	0.111628	+	0.0406291i
$413$	3.21429e12	−	1.85577e12i	0.267507	−	0.154445i
$414$		0			0
$415$	−9.51147e12	+	1.64743e13i	−0.772693	+	1.33834i
$416$	6.00217e12	+	7.15310e12i	0.481772	+	0.574153i
$417$		0			0
$418$	−1.91107e10	+	1.08382e11i	−0.00149760	+	0.00849331i
$419$	−6.19419e12	−	1.09220e12i	−0.479639	−	0.0845733i	−0.0713990	−	0.997448i	$-0.522746\pi$
$419$	−6.19419e12	−	1.09220e12i	−0.479639	−	0.0845733i	−0.408240	+	0.912874i	$0.633857\pi$
$420$		0			0
$421$	1.21559e13	−	1.02000e13i	0.919130	−	0.771241i	−0.0547041	−	0.998503i	$-0.517422\pi$
$421$	1.21559e13	−	1.02000e13i	0.919130	−	0.771241i	0.973834	+	0.227261i	$0.0729771\pi$
$422$	−4.05431e12	−	2.34076e12i	−0.302939	−	0.174902i
$423$		0			0
$424$	2.83420e12	+	4.90898e12i	0.206824	+	0.358230i
$425$	−1.27526e10	+	3.50374e10i	−0.000919715	+	0.00252690i
$426$		0			0
$427$	6.78613e11	+	5.69424e11i	0.0478060	+	0.0401140i
$428$	6.14556e11	+	1.68848e12i	0.0427900	+	0.117565i
$429$		0			0
$430$	−8.90575e11	−	5.05070e12i	−0.0605798	−	0.343565i
$431$		−	9.69546e12i		−	0.651902i	−0.945387	−	0.325951i	$-0.894316\pi$
$431$		−	9.69546e12i		−	0.651902i	0.945387	−	0.325951i	$-0.105684\pi$
$432$		0			0
$433$	−4.86634e12			−0.319715			−0.159858	−	0.987140i	$-0.551103\pi$
$433$	−4.86634e12			−0.319715			−0.159858	+	0.987140i	$0.551103\pi$
$434$	2.76548e12	−	4.87629e11i	0.179606	−	0.0316695i
$435$		0			0
$436$	−9.19873e12	+	3.34806e12i	−0.583842	+	0.212501i
$437$	−9.49652e11	+	1.13175e12i	−0.0595878	+	0.0710140i
$438$		0			0
$439$	2.07869e13	+	7.56583e12i	1.27488	+	0.464017i	0.888734	−	0.458423i	$-0.151585\pi$
$439$	2.07869e13	+	7.56583e12i	1.27488	+	0.464017i	0.386142	+	0.922440i	$0.373808\pi$
$440$	−6.03615e11	+	3.48497e11i	−0.0366013	+	0.0211318i
$441$		0			0
$442$	−1.05362e12	+	1.82492e12i	−0.0624557	+	0.108176i
$443$	1.42070e13	+	1.69312e13i	0.832690	+	0.992362i	0.999979	+	0.00645366i	$0.00205428\pi$
$443$	1.42070e13	+	1.69312e13i	0.832690	+	0.992362i	−0.167289	+	0.985908i	$0.553501\pi$
$444$		0			0
$445$	3.65765e10	−	2.07435e11i	0.00209605	−	0.0118873i
$446$	1.17093e13	+	2.06467e12i	0.663525	+	0.116997i
$447$		0			0
$448$	6.31056e11	−	5.29519e11i	0.0349686	−	0.0293421i
$449$	−1.84551e13	−	1.06551e13i	−1.01131	−	0.583881i	−0.0997359	−	0.995014i	$-0.531800\pi$
$449$	−1.84551e13	−	1.06551e13i	−1.01131	−	0.583881i	−0.911575	+	0.411133i	$0.865133\pi$
$450$		0			0
$451$	4.74066e10	+	8.21106e10i	0.00254072	+	0.00440065i
$452$	2.77090e12	−	7.61299e12i	0.146869	−	0.403518i
$453$		0			0
$454$	8.38629e12	+	7.03693e12i	0.434801	+	0.364841i
$455$	1.77114e12	+	4.86618e12i	0.0908232	+	0.249535i
$456$		0			0
$457$	−1.11818e12	−	6.34153e12i	−0.0560960	−	0.318136i	0.943828	−	0.330436i	$-0.107196\pi$
$457$	−1.11818e12	−	6.34153e12i	−0.0560960	−	0.318136i	−0.999924	+	0.0123000i	$0.996085\pi$
$458$			8.11021e12i			0.402443i
$459$		0			0
$460$	−4.25232e12			−0.206460
$461$	2.41288e13	−	4.25455e12i	1.15886	−	0.204338i	0.439019	−	0.898478i	$-0.355326\pi$
$461$	2.41288e13	−	4.25455e12i	1.15886	−	0.204338i	0.719840	+	0.694140i	$0.244215\pi$
$462$		0			0
$463$	−1.35103e13	+	4.91736e12i	−0.634981	+	0.231114i	−0.639398	−	0.768876i	$-0.720816\pi$
$463$	−1.35103e13	+	4.91736e12i	−0.634981	+	0.231114i	0.00441674	+	0.999990i	$0.498594\pi$
$464$	−3.81229e12	+	4.54331e12i	−0.177254	+	0.211243i
$465$		0			0
$466$	−2.14149e12	−	7.79440e11i	−0.0974512	−	0.0354693i
$467$	2.90321e13	−	1.67617e13i	1.30706	−	0.754630i	0.325453	−	0.945558i	$-0.394483\pi$
$467$	2.90321e13	−	1.67617e13i	1.30706	−	0.754630i	0.981604	+	0.190929i	$0.0611499\pi$
$468$		0			0
$469$	−6.44266e12	+	1.11590e13i	−0.283923	+	0.491770i
$470$	1.02946e13	+	1.22687e13i	0.448871	+	0.534943i
$471$		0			0
$472$	−2.74510e12	+	1.55682e13i	−0.117178	+	0.664552i
$473$	1.13130e12	+	1.99479e11i	0.0477830	+	0.00842543i
$474$		0			0
$475$	−4.72063e10	+	3.96108e10i	−0.00195223	+	0.00163812i
$476$	2.37733e12	+	1.37255e12i	0.0972868	+	0.0561685i
$477$		0			0
$478$	5.03060e12	+	8.71325e12i	0.201595	+	0.349173i
$479$	6.26922e12	−	1.72245e13i	0.248620	−	0.683077i	−0.751118	−	0.660168i	$-0.770485\pi$
$479$	6.26922e12	−	1.72245e13i	0.248620	−	0.683077i	0.999738	−	0.0229090i	$-0.00729281\pi$
$480$		0			0
$481$	−3.96147e12	−	3.32407e12i	−0.153862	−	0.129105i
$482$	−3.28919e12	−	9.03696e12i	−0.126431	−	0.347366i
$483$		0			0
$484$	3.82993e12	+	2.17206e13i	0.144200	+	0.817797i
$485$			1.91127e13i			0.712219i
$486$		0			0
$487$	3.15810e13			1.15287			0.576436	−	0.817142i	$-0.304443\pi$
$487$	3.15810e13			1.15287			0.576436	+	0.817142i	$0.304443\pi$
$488$	−3.71580e12	+	6.55196e11i	−0.134262	+	0.0236740i
$489$		0			0
$490$	9.53740e12	−	3.47133e12i	0.337637	−	0.122890i
$491$	−1.90991e13	+	2.27614e13i	−0.669275	+	0.797611i	−0.988685	−	0.150006i	$-0.952071\pi$
$491$	−1.90991e13	+	2.27614e13i	−0.669275	+	0.797611i	0.319410	+	0.947617i	$0.396515\pi$
$492$		0			0
$493$	−5.63147e12	−	2.04969e12i	−0.193369	−	0.0703806i
$494$	−3.01608e12	+	1.74134e12i	−0.102520	+	0.0591900i
$495$		0			0
$496$	1.03025e13	−	1.78445e13i	0.343191	−	0.594425i
$497$	1.21910e13	+	1.45287e13i	0.402031	+	0.479121i
$498$		0			0
$499$	−5.16349e11	+	2.92836e12i	−0.0166894	+	0.0946503i	−0.992015	−	0.126122i	$-0.959747\pi$
$499$	−5.16349e11	+	2.92836e12i	−0.0166894	+	0.0946503i	0.975325	+	0.220773i	$0.0708579\pi$
$500$	−2.57252e13	−	4.53605e12i	−0.823208	−	0.145154i
$501$		0			0
$502$	5.80447e12	−	4.87053e12i	0.182072	−	0.152777i
$503$	−6.97565e12	−	4.02739e12i	−0.216643	−	0.125079i	0.387752	−	0.921764i	$-0.373252\pi$
$503$	−6.97565e12	−	4.02739e12i	−0.216643	−	0.125079i	−0.604395	+	0.796685i	$0.706585\pi$
$504$		0			0
$505$	1.28996e13	+	2.23428e13i	0.392753	+	0.680268i
$506$	−6.52702e10	+	1.79328e11i	−0.00196771	+	0.00540625i
$507$		0			0
$508$	−1.70579e13	−	1.43132e13i	−0.504203	−	0.423077i
$509$	2.86140e12	+	7.86164e12i	0.0837510	+	0.230104i	0.974498	−	0.224395i	$-0.0720405\pi$
$509$	2.86140e12	+	7.86164e12i	0.0837510	+	0.230104i	−0.890747	+	0.454499i	$0.849818\pi$
$510$		0			0
$511$	3.76261e12	+	2.13388e13i	0.107990	+	0.612444i
$512$			3.17729e13i			0.903039i
$513$		0			0
$514$	−3.04597e12			−0.0849006
$515$	−5.06985e12	+	8.93951e11i	−0.139946	+	0.0246762i
$516$		0			0
$517$	−3.37098e12	+	1.22694e12i	−0.0912649	+	0.0332177i
$518$	8.67609e11	−	1.03398e12i	0.0232635	−	0.0277244i
$519$		0			0
$520$	−2.07263e13	−	7.54374e12i	−0.545135	−	0.198413i
$521$	5.10994e13	−	2.95023e13i	1.33115	−	0.768540i	0.345675	−	0.938354i	$-0.387650\pi$
$521$	5.10994e13	−	2.95023e13i	1.33115	−	0.768540i	0.985476	+	0.169814i	$0.0543167\pi$
$522$		0			0
$523$	−7.53885e12	+	1.30577e13i	−0.192662	+	0.333701i	−0.946132	−	0.323782i	$-0.895045\pi$
$523$	−7.53885e12	+	1.30577e13i	−0.192662	+	0.333701i	0.753469	+	0.657483i	$0.228379\pi$
$524$	−9.59170e12	−	1.14309e13i	−0.242795	−	0.289351i
$525$		0			0
$526$	4.47122e11	−	2.53575e12i	0.0111044	−	0.0629765i
$527$	2.05042e13	+	3.61545e12i	0.504418	+	0.0889425i
$528$		0			0
$529$	2.97721e13	−	2.49817e13i	0.718672	−	0.603037i
$530$	−8.14459e12	−	4.70228e12i	−0.194756	−	0.112442i
$531$		0			0
$532$	2.26844e12	+	3.92906e12i	0.0532316	+	0.0921998i
$533$	−1.02619e12	+	2.81943e12i	−0.0238556	+	0.0655427i
$534$		0			0
$535$	−5.02499e12	−	4.21647e12i	−0.114648	−	0.0962011i
$536$	−1.87707e13	−	5.15720e13i	−0.424283	−	1.16571i
$537$		0			0
$538$	−3.38623e12	−	1.92043e13i	−0.0751286	−	0.426075i
$539$			2.27338e12i			0.0499721i
$540$		0			0
$541$	2.98697e13			0.644533			0.322267	−	0.946649i	$-0.395555\pi$
$541$	2.98697e13			0.644533			0.322267	+	0.946649i	$0.395555\pi$
$542$	5.03561e12	−	8.87914e11i	0.107660	−	0.0189834i
$543$		0			0
$544$	−1.69806e13	+	6.18044e12i	−0.356418	+	0.129725i
$545$	2.29711e13	−	2.73759e13i	0.477748	−	0.569358i
$546$		0			0
$547$	−5.24289e13	−	1.90826e13i	−1.07062	−	0.389673i	−0.254209	−	0.967149i	$-0.581815\pi$
$547$	−5.24289e13	−	1.90826e13i	−1.07062	−	0.389673i	−0.816407	+	0.577477i	$0.804037\pi$
$548$	4.74423e13	−	2.73908e13i	0.959982	−	0.554246i
$549$		0			0
$550$	−3.97999e9	+	6.89354e9i	−7.90803e−5	+	0.000136971i
$551$	−6.36653e12	−	7.58734e12i	−0.125356	−	0.149393i
$552$		0			0
$553$	−4.83941e12	+	2.74457e13i	−0.0935766	+	0.530699i
$554$	−8.37390e12	−	1.47654e12i	−0.160464	−	0.0282942i
$555$		0			0
$556$	−2.38067e13	+	1.99762e13i	−0.448049	+	0.375958i
$557$	−1.63464e13	−	9.43761e12i	−0.304893	−	0.176030i	0.339746	−	0.940517i	$-0.389659\pi$
$557$	−1.63464e13	−	9.43761e12i	−0.304893	−	0.176030i	−0.644639	+	0.764487i	$0.722992\pi$
$558$		0			0
$559$	1.81762e13	+	3.14821e13i	0.333000	+	0.576773i
$560$	−3.39206e12	+	9.31962e12i	−0.0615919	+	0.169222i
$561$		0			0
$562$	3.02066e12	+	2.53463e12i	0.0538791	+	0.0452099i
$563$	3.17116e13	+	8.71268e13i	0.560629	+	1.54032i	0.818719	+	0.574195i	$0.194685\pi$
$563$	3.17116e13	+	8.71268e13i	0.560629	+	1.54032i	−0.258090	+	0.966121i	$0.583093\pi$
$564$		0			0
$565$	5.13584e12	+	2.91268e13i	0.0892009	+	0.505884i
$566$			1.65420e13i			0.284778i
$567$		0			0
$568$	−8.07805e13			−1.36636
$569$	−5.70413e13	+	1.00579e13i	−0.956375	+	0.168635i	−0.629991	−	0.776603i	$-0.716941\pi$
$569$	−5.70413e13	+	1.00579e13i	−0.956375	+	0.168635i	−0.326384	+	0.945237i	$0.605830\pi$
$570$		0			0
$571$	6.76791e13	−	2.46332e13i	1.11500	−	0.405826i	0.282173	−	0.959364i	$-0.408945\pi$
$571$	6.76791e13	−	2.46332e13i	1.11500	−	0.405826i	0.832824	+	0.553538i	$0.186723\pi$
$572$	1.44323e12	−	1.71998e12i	0.0235698	−	0.0280894i
$573$		0			0
$574$	−7.35894e11	−	2.67844e11i	−0.0118102	−	0.00429855i
$575$	−9.25407e10	+	5.34284e10i	−0.00147229	+	0.000850027i
$576$		0			0
$577$	4.92174e12	−	8.52471e12i	0.0769556	−	0.133291i	−0.824979	−	0.565163i	$-0.808813\pi$
$577$	4.92174e12	−	8.52471e12i	0.0769556	−	0.133291i	0.901935	+	0.431872i	$0.142147\pi$
$578$	1.43204e13	+	1.70664e13i	0.221981	+	0.264547i
$579$		0			0
$580$	4.95033e12	−	2.80747e13i	0.0754214	−	0.427736i
$581$	3.46591e13	+	6.11133e12i	0.523524	+	0.0923114i
$582$		0			0
$583$	1.61369e12	−	1.35405e12i	0.0239595	−	0.0201044i
$584$	−7.99250e13	−	4.61447e13i	−1.17657	−	0.679294i
$585$		0			0
$586$	−1.72484e13	−	2.98751e13i	−0.249610	−	0.432336i
$587$	−3.72007e12	+	1.02208e13i	−0.0533779	+	0.146654i	−0.963516	−	0.267650i	$-0.913753\pi$
$587$	−3.72007e12	+	1.02208e13i	−0.0533779	+	0.146654i	0.910138	+	0.414304i	$0.135975\pi$
$588$		0			0
$589$	2.63600e13	+	2.21187e13i	0.371851	+	0.312020i
$590$	−8.97051e12	−	2.46463e13i	−0.125475	−	0.344740i
$591$		0			0
$592$	−1.71982e12	−	9.75357e12i	−0.0236523	−	0.134139i
$593$			1.02116e14i			1.39259i	0.717758	+	0.696293i	$0.245169\pi$
$593$			1.02116e14i			1.39259i	−0.717758	+	0.696293i	$0.754831\pi$
$594$		0			0
$595$	−1.00214e13			−0.134383
$596$	−9.80248e13	+	1.72844e13i	−1.30348	+	0.229839i
$597$		0			0
$598$	−5.67486e12	+	2.06548e12i	−0.0742077	+	0.0270094i
$599$	1.29030e13	−	1.53772e13i	0.167324	−	0.199409i	−0.675866	−	0.737024i	$-0.736230\pi$
$599$	1.29030e13	−	1.53772e13i	0.167324	−	0.199409i	0.843190	+	0.537615i	$0.180675\pi$
$600$		0			0
$601$	5.47511e13	+	1.99278e13i	0.698265	+	0.254148i	0.666670	−	0.745353i	$-0.267719\pi$
$601$	5.47511e13	+	1.99278e13i	0.698265	+	0.254148i	0.0315953	+	0.999501i	$0.489941\pi$
$602$	−8.21710e12	+	4.74415e12i	−0.103929	+	0.0600034i
$603$		0			0
$604$	6.35479e13	−	1.10068e14i	0.790526	−	1.36923i
$605$	−5.17559e13	−	6.16803e13i	−0.638533	−	0.760973i
$606$		0			0
$607$	9.96951e12	−	5.65399e13i	0.120985	−	0.686138i	−0.862627	−	0.505840i	$-0.831183\pi$
$607$	9.96951e12	−	5.65399e13i	0.120985	−	0.686138i	0.983612	−	0.180298i	$-0.0577062\pi$
$608$	−2.94116e13	−	5.18606e12i	−0.353998	−	0.0624194i
$609$		0			0
$610$	4.79549e12	−	4.02389e12i	0.0567785	−	0.0476428i
$611$	−9.83121e13	−	5.67605e13i	−1.15452	−	0.666562i
$612$		0			0
$613$	−7.06986e13	−	1.22454e14i	−0.816786	−	1.41471i	−0.908038	−	0.418887i	$-0.862420\pi$
$613$	−7.06986e13	−	1.22454e14i	−0.816786	−	1.41471i	0.0912525	−	0.995828i	$-0.470913\pi$
$614$	−4.16687e12	+	1.14484e13i	−0.0477494	+	0.131190i
$615$		0			0
$616$	9.87805e11	+	8.28867e11i	0.0111370	+	0.00934504i
$617$	−9.19988e12	−	2.52765e13i	−0.102886	−	0.282677i	0.877559	−	0.479468i	$-0.159170\pi$
$617$	−9.19988e12	−	2.52765e13i	−0.102886	−	0.282677i	−0.980446	+	0.196791i	$0.936948\pi$
$618$		0			0
$619$	5.65772e12	+	3.20865e13i	0.0622570	+	0.353077i	0.999984	+	0.00570323i	$0.00181541\pi$
$619$	5.65772e12	+	3.20865e13i	0.0622570	+	0.353077i	−0.937727	+	0.347374i	$0.887073\pi$
$620$			9.90423e13i			1.08109i
$621$		0			0
$622$	−3.51118e13			−0.377139
$623$	−3.83770e11	+	6.76690e10i	−0.00408913	+	0.000721024i
$624$		0			0
$625$	8.89992e13	−	3.23931e13i	0.933225	−	0.339666i
$626$	8.24148e12	−	9.82182e12i	0.0857302	−	0.102169i
$627$		0			0
$628$	−7.61691e13	−	2.77233e13i	−0.779795	−	0.283822i
$629$	8.66683e12	−	5.00380e12i	0.0880252	−	0.0508214i
$630$		0			0
$631$	−2.60764e13	+	4.51656e13i	−0.260676	+	0.451504i	−0.966422	−	0.256961i	$-0.917279\pi$
$631$	−2.60764e13	+	4.51656e13i	−0.260676	+	0.451504i	0.705746	+	0.708465i	$0.250612\pi$
$632$	−7.62997e13	−	9.09305e13i	−0.756724	−	0.901829i
$633$		0			0
$634$	6.53135e12	−	3.70411e13i	0.0637613	−	0.361608i
$635$	8.00560e13	+	1.41160e13i	0.775399	+	0.136724i
$636$		0			0
$637$	−5.51102e13	+	4.62429e13i	−0.525454	+	0.440908i
$638$	−1.10798e12	−	6.39693e11i	−0.0104816	−	0.00605157i
$639$		0			0
$640$	−5.45021e13	−	9.44004e13i	−0.507591	−	0.879173i
$641$	3.03698e13	−	8.34403e13i	0.280641	−	0.771056i	−0.716645	−	0.697438i	$-0.754323\pi$
$641$	3.03698e13	−	8.34403e13i	0.280641	−	0.771056i	0.997287	−	0.0736179i	$-0.0234545\pi$
$642$		0			0
$643$	−9.16496e13	−	7.69031e13i	−0.833826	−	0.699663i	0.122340	−	0.992488i	$-0.460960\pi$
$643$	−9.16496e13	−	7.69031e13i	−0.833826	−	0.699663i	−0.956166	+	0.292825i	$0.905405\pi$
$644$	2.69070e12	+	7.39264e12i	0.0242905	+	0.0667376i
$645$		0			0
$646$	−1.17034e12	−	6.63730e12i	−0.0104027	−	0.0589969i
$647$			1.01695e14i			0.896974i	0.893789	+	0.448487i	$0.148037\pi$
$647$			1.01695e14i			0.896974i	−0.893789	+	0.448487i	$0.851963\pi$
$648$		0			0
$649$	5.87480e12			0.0510234
$650$	−2.48067e11	+	4.37409e10i	−0.00213797	+	0.000376983i
$651$		0			0
$652$	1.61421e14	−	5.87523e13i	1.37000	−	0.498640i
$653$	5.56385e13	−	6.63073e13i	0.468608	−	0.558465i	−0.479036	−	0.877795i	$-0.659014\pi$
$653$	5.56385e13	−	6.63073e13i	0.468608	−	0.558465i	0.947643	+	0.319331i	$0.103458\pi$
$654$		0			0
$655$	5.11901e13	+	1.86317e13i	0.424599	+	0.154541i
$656$	−4.97640e12	+	2.87313e12i	−0.0409634	+	0.0236502i
$657$		0			0
$658$	1.48150e13	−	2.56603e13i	0.120108	−	0.208033i
$659$	−1.09446e14	−	1.30433e14i	−0.880590	−	1.04945i	−0.998408	−	0.0564110i	$-0.982034\pi$
$659$	−1.09446e14	−	1.30433e14i	−0.880590	−	1.04945i	0.117818	−	0.993035i	$-0.462410\pi$
$660$		0			0
$661$	−1.35548e13	+	7.68732e13i	−0.107420	+	0.609211i	0.882806	+	0.469738i	$0.155652\pi$
$661$	−1.35548e13	+	7.68732e13i	−0.107420	+	0.609211i	−0.990226	+	0.139472i	$0.955459\pi$
$662$	2.00410e13	+	3.53378e12i	0.157627	+	0.0277939i
$663$		0			0
$664$	−1.14829e14	+	9.63532e13i	−0.889636	+	0.746493i
$665$	−1.43437e13	−	8.28132e12i	−0.110294	−	0.0636782i
$666$		0			0
$667$	−8.58740e12	−	1.48738e13i	−0.0650478	−	0.112666i
$668$	−5.81599e13	+	1.59793e14i	−0.437262	+	1.20137i
$669$		0			0
$670$	6.97526e13	+	5.85294e13i	0.516638	+	0.433511i
$671$	4.79577e11	+	1.31763e12i	0.00352570	+	0.00968679i
$672$		0			0
$673$	2.46024e13	+	1.39527e14i	0.178198	+	1.01061i	0.934387	+	0.356258i	$0.115948\pi$
$673$	2.46024e13	+	1.39527e14i	0.178198	+	1.01061i	−0.756189	+	0.654353i	$0.772941\pi$
$674$			6.85788e13i			0.493049i
$675$		0			0
$676$	−4.65522e13			−0.329767
$677$	2.46472e14	−	4.34596e13i	1.73310	−	0.305592i	0.784046	−	0.620703i	$-0.213153\pi$
$677$	2.46472e14	−	4.34596e13i	1.73310	−	0.305592i	0.949055	+	0.315111i	$0.102042\pi$
$678$		0			0
$679$	3.32274e13	−	1.20938e13i	0.230222	−	0.0837941i
$680$	2.74366e13	−	3.26977e13i	0.188706	−	0.224891i
$681$		0			0
$682$	4.17680e12	+	1.52023e12i	0.0283088	+	0.0103036i
$683$	1.66554e14	−	9.61598e13i	1.12060	−	0.646979i	0.179046	−	0.983841i	$-0.442699\pi$
$683$	1.66554e14	−	9.61598e13i	1.12060	−	0.646979i	0.941554	+	0.336862i	$0.109366\pi$
$684$		0			0
$685$	−9.99947e13	+	1.73196e14i	−0.663016	+	1.14838i
$686$	−2.57469e13	−	3.06840e13i	−0.169475	−	0.201972i
$687$		0			0
$688$	−1.20897e13	+	6.85638e13i	−0.0784281	+	0.444788i
$689$	6.56483e13	+	1.15756e13i	0.422793	+	0.0745498i
$690$		0			0
$691$	−1.62990e14	+	1.36765e14i	−1.03459	+	0.868127i	−0.991390	−	0.130939i	$-0.958201\pi$
$691$	−1.62990e14	+	1.36765e14i	−1.03459	+	0.868127i	−0.0432034	+	0.999066i	$0.513756\pi$
$692$	3.89358e13	+	2.24796e13i	0.245368	+	0.141664i
$693$		0			0
$694$	2.49926e13	+	4.32884e13i	0.155244	+	0.268890i
$695$	3.88033e13	−	1.06611e14i	0.239301	−	0.657475i
$696$		0			0
$697$	−4.44791e12	−	3.73224e12i	−0.0270391	−	0.0226885i
$698$	1.80650e13	+	4.96331e13i	0.109033	+	0.299567i
$699$		0			0
$700$	5.69814e10	+	3.23157e11i	0.000339034	+	0.00192275i
$701$			2.95802e14i			1.74748i	0.486397	+	0.873738i	$0.338311\pi$
$701$			2.95802e14i			1.74748i	−0.486397	+	0.873738i	$0.661689\pi$
$702$		0			0
$703$	1.65398e13			0.0963280
$704$	1.28412e12	−	2.26424e11i	0.00742576	−	0.00130936i
$705$		0			0
$706$	−2.43227e13	+	8.85274e12i	−0.138672	+	0.0504724i
$707$	3.06804e13	−	3.65635e13i	0.173686	−	0.206991i
$708$		0			0
$709$	2.58665e14	+	9.41462e13i	1.44380	+	0.525499i	0.940851	−	0.338820i	$-0.110028\pi$
$709$	2.58665e14	+	9.41462e13i	1.44380	+	0.525499i	0.502944	+	0.864319i	$0.332250\pi$
$710$	1.16069e14	−	6.70123e13i	0.643315	−	0.371418i
$711$		0			0
$712$	8.29894e11	−	1.43742e12i	0.00453547	−	0.00785567i
$713$	3.83544e13	+	4.57090e13i	0.208146	+	0.248059i
$714$		0			0
$715$	−1.42335e12	+	8.07221e12i	−0.00761695	+	0.0431978i
$716$	3.68263e13	+	6.49347e12i	0.195701	+	0.0345074i
$717$		0			0
$718$	−4.91319e13	+	4.12265e13i	−0.257479	+	0.216050i
$719$	−1.35697e14	−	7.83447e13i	−0.706197	−	0.407723i	0.103454	−	0.994634i	$-0.467010\pi$
$719$	−1.35697e14	−	7.83447e13i	−0.706197	−	0.407723i	−0.809651	+	0.586911i	$0.800344\pi$
$720$		0			0
$721$	4.76214e12	+	8.24826e12i	0.0244414	+	0.0423337i
$722$	−2.36052e13	+	6.48548e13i	−0.120316	+	0.330564i
$723$		0			0
$724$	1.85751e14	+	1.55863e14i	0.933764	+	0.783521i
$725$	−2.45015e11	−	6.73173e11i	−0.00122321	−	0.00336075i
$726$		0			0
$727$	−2.47932e13	−	1.40609e14i	−0.122084	−	0.692374i	−0.982997	−	0.183622i	$-0.941218\pi$
$727$	−2.47932e13	−	1.40609e14i	−0.122084	−	0.692374i	0.860913	−	0.508753i	$-0.169893\pi$
$728$			4.08059e13i			0.199557i
$729$		0			0
$730$	1.53119e14			0.738611
$731$	−6.92808e13	+	1.22161e13i	−0.331914	+	0.0585254i
$732$		0			0
$733$	−4.89041e13	+	1.77996e13i	−0.231113	+	0.0841184i	−0.454981	−	0.890501i	$-0.650354\pi$
$733$	−4.89041e13	+	1.77996e13i	−0.231113	+	0.0841184i	0.223868	+	0.974620i	$0.428132\pi$
$734$	2.45975e13	−	2.93141e13i	0.115454	−	0.137593i
$735$		0			0
$736$	−4.86642e13	−	1.77123e13i	−0.225331	−	0.0820137i
$737$	−1.76630e13	+	1.01977e13i	−0.0812320	+	0.0468993i
$738$		0			0
$739$	8.12019e13	−	1.40646e14i	0.368421	−	0.638123i	−0.620898	−	0.783891i	$-0.713232\pi$
$739$	8.12019e13	−	1.40646e14i	0.368421	−	0.638123i	0.989319	+	0.145768i	$0.0465653\pi$
$740$	3.06003e13	+	3.64680e13i	0.137901	+	0.164344i
$741$		0			0
$742$	−3.02132e12	+	1.71348e13i	−0.0134331	+	0.0761831i
$743$	6.03736e12	+	1.06455e12i	0.0266626	+	0.00470134i	0.186964	−	0.982367i	$-0.440135\pi$
$743$	6.03736e12	+	1.06455e12i	0.0266626	+	0.00470134i	−0.160301	+	0.987068i	$0.551246\pi$
$744$		0			0
$745$	2.78362e14	−	2.33574e14i	1.21291	−	1.01775i
$746$	9.65424e13	+	5.57388e13i	0.417853	+	0.241248i
$747$		0			0
$748$	2.17253e12	+	3.76294e12i	0.00927809	+	0.0160701i
$749$	−4.15070e12	+	1.14040e13i	−0.0176081	+	0.0483778i
$750$		0			0
$751$	−8.16514e13	−	6.85137e13i	−0.341794	−	0.286799i	0.455691	−	0.890138i	$-0.349392\pi$
$751$	−8.16514e13	−	6.85137e13i	−0.341794	−	0.286799i	−0.797485	+	0.603339i	$0.793837\pi$
$752$	−7.43598e13	−	2.04302e14i	−0.309207	−	0.849538i
$753$		0			0
$754$	−7.03037e12	−	3.98712e13i	−0.0288484	−	0.163607i
$755$			4.63984e14i			1.89133i
$756$		0			0
$757$	−2.30843e13			−0.0928619			−0.0464309	−	0.998922i	$-0.514785\pi$
$757$	−2.30843e13			−0.0928619			−0.0464309	+	0.998922i	$0.514785\pi$
$758$	−1.28083e14	+	2.25845e13i	−0.511854	+	0.0902537i
$759$		0			0
$760$	6.62900e13	−	2.41276e13i	0.261445	−	0.0951581i
$761$	−4.75616e13	+	5.66818e13i	−0.186352	+	0.222085i	−0.851129	−	0.524956i	$-0.824082\pi$
$761$	−4.75616e13	+	5.66818e13i	−0.186352	+	0.222085i	0.664778	+	0.747041i	$0.268526\pi$
$762$		0			0
$763$	−6.21281e13	−	2.26128e13i	−0.240251	−	0.0874442i
$764$	3.18243e14	−	1.83738e14i	1.22262	−	0.705881i
$765$		0			0
$766$	5.45489e13	−	9.44815e13i	0.206844	−	0.358264i
$767$	1.19500e14	+	1.42414e14i	0.450184	+	0.536508i
$768$		0			0
$769$	−5.23121e13	+	2.96677e14i	−0.194523	+	1.10319i	0.718574	+	0.695451i	$0.244795\pi$
$769$	−5.23121e13	+	2.96677e14i	−0.194523	+	1.10319i	−0.913097	+	0.407743i	$0.866316\pi$
$770$	−2.10691e12	−	3.71506e11i	−0.00778383	−	0.00137250i
$771$		0			0
$772$	−9.62623e13	+	8.07737e13i	−0.351051	+	0.294567i
$773$	−4.33167e14	−	2.50089e14i	−1.56949	−	0.906144i	−0.996228	−	0.0867690i	$-0.972346\pi$
$773$	−4.33167e14	−	2.50089e14i	−1.56949	−	0.906144i	−0.573258	−	0.819375i	$-0.694321\pi$
$774$		0			0
$775$	1.24442e12	+	2.15540e12i	0.00445101	+	0.00770937i
$776$	−5.15104e13	+	1.41524e14i	−0.183057	+	0.502945i
$777$		0			0
$778$	−1.36278e13	−	1.14351e13i	−0.0478109	−	0.0401181i
$779$	−3.28211e12	−	9.01753e12i	−0.0114411	−	0.0314341i
$780$		0			0
$781$	5.21294e12	+	2.95640e13i	0.0179402	+	0.101744i
$782$		−	1.16868e13i		−	0.0399634i
$783$		0			0
$784$	−1.37781e14			−0.465165
$785$	2.91418e14	−	5.13848e13i	0.977615	−	0.172380i
$786$		0			0
$787$	−1.93246e14	+	7.03358e13i	−0.640084	+	0.232971i	−0.641614	−	0.767027i	$-0.721735\pi$
$787$	−1.93246e14	+	7.03358e13i	−0.640084	+	0.232971i	0.00153054	+	0.999999i	$0.499513\pi$
$788$	2.21773e14	−	2.64299e14i	0.729923	−	0.869889i
$789$		0			0
$790$	1.85063e14	+	6.73574e13i	0.601429	+	0.218902i
$791$	4.73871e13	−	2.73590e13i	0.153030	−	0.0883522i
$792$		0			0
$793$	−2.21862e13	+	3.84276e13i	−0.0707484	+	0.122540i
$794$	3.31331e13	+	3.94865e13i	0.104993	+	0.125125i
$795$		0			0
$796$	−3.16848e13	+	1.79693e14i	−0.0991483	+	0.562298i
$797$	−1.17657e14	−	2.07462e13i	−0.365871	−	0.0645129i	−0.0123095	−	0.999924i	$-0.503918\pi$
$797$	−1.17657e14	−	2.07462e13i	−0.365871	−	0.0645129i	−0.353561	+	0.935411i	$0.615029\pi$
$798$		0			0
$799$	1.68290e14	−	1.41212e14i	0.516802	−	0.433648i
$800$	−1.87070e12	−	1.08005e12i	−0.00570891	−	0.00329604i
$801$		0			0
$802$	−1.31143e13	−	2.27145e13i	−0.0395250	−	0.0684593i
$803$	−1.17303e13	+	3.22288e13i	−0.0351343	+	0.0965308i
$804$		0			0
$805$	−2.20009e13	−	1.84609e13i	−0.0650819	−	0.0546102i
$806$	4.81078e13	+	1.32175e14i	0.141430	+	0.388575i
$807$		0			0
$808$	3.53018e13	+	2.00207e14i	0.102504	+	0.581329i
$809$		−	2.13433e14i		−	0.615911i	−0.951401	−	0.307956i	$-0.900355\pi$
$809$		−	2.13433e14i		−	0.615911i	0.951401	−	0.307956i	$-0.0996448\pi$
$810$		0			0
$811$	−2.61791e14			−0.746192			−0.373096	−	0.927793i	$-0.621704\pi$
$811$	−2.61791e14			−0.746192			−0.373096	+	0.927793i	$0.621704\pi$
$812$	−5.19402e13	+	9.15847e12i	−0.147138	+	0.0259443i
$813$		0			0
$814$	2.00762e12	−	7.30713e11i	0.00561771	−	0.00204468i
$815$	−4.03100e14	+	4.80395e14i	−1.12105	+	1.33601i
$816$		0			0
$817$	−1.09256e14	−	3.97660e13i	−0.300149	−	0.109245i
$818$	1.68317e14	−	9.71780e13i	0.459581	−	0.265339i
$819$		0			0
$820$	1.38102e13	−	2.39200e13i	0.0372504	−	0.0645197i
$821$	1.41353e14	+	1.68457e14i	0.378955	+	0.451621i	0.921484	−	0.388416i	$-0.126978\pi$
$821$	1.41353e14	+	1.68457e14i	0.378955	+	0.451621i	−0.542529	+	0.840037i	$0.682533\pi$
$822$		0			0
$823$	8.18590e13	−	4.64245e14i	0.216804	−	1.22956i	−0.660945	−	0.750435i	$-0.729844\pi$
$823$	8.18590e13	−	4.64245e14i	0.216804	−	1.22956i	0.877749	−	0.479122i	$-0.159045\pi$
$824$	−3.99500e13	−	7.04425e12i	−0.105167	−	0.0185438i
$825$		0			0
$826$	−3.71713e13	+	3.11904e13i	−0.0966734	+	0.0811187i
$827$	−5.64853e14	−	3.26118e14i	−1.46019	−	0.843039i	−0.461166	−	0.887314i	$-0.652569\pi$
$827$	−5.64853e14	−	3.26118e14i	−1.46019	−	0.843039i	−0.999019	+	0.0442753i	$0.985902\pi$
$828$		0			0
$829$	1.66209e14	+	2.87883e14i	0.424505	+	0.735265i	0.996374	−	0.0850804i	$-0.0271147\pi$
$829$	1.66209e14	+	2.87883e14i	0.424505	+	0.735265i	−0.571869	+	0.820345i	$0.693781\pi$
$830$	8.50606e13	−	2.33702e14i	0.215942	−	0.593297i
$831$		0			0
$832$	3.16091e13	+	2.65232e13i	0.0792859	+	0.0665288i
$833$	−4.76165e13	−	1.30825e14i	−0.118722	−	0.326187i
$834$		0			0
$835$	−1.07799e14	−	6.11358e14i	−0.265572	−	1.50613i
$836$			7.18119e12i			0.0175859i
$837$		0			0
$838$	8.22304e13			0.198981
$839$	−6.04111e14	+	1.06521e14i	−1.45314	+	0.256227i	−0.843789	−	0.536675i	$-0.819680\pi$
$839$	−6.04111e14	+	1.06521e14i	−1.45314	+	0.256227i	−0.609349	+	0.792902i	$0.708569\pi$
$840$		0			0
$841$	−2.87138e14	+	1.04510e14i	−0.682513	+	0.248414i
$842$	−1.33352e14	+	1.58923e14i	−0.315094	+	0.375514i
$843$		0			0
$844$	−2.87053e14	−	1.04479e14i	−0.670269	−	0.243958i
$845$	1.47178e14	−	8.49733e13i	0.341633	−	0.197242i
$846$		0			0
$847$	−7.44819e13	+	1.29006e14i	−0.170857	+	0.295934i
$848$	8.20634e13	+	9.77994e13i	0.187142	+	0.223027i
$849$		0			0
$850$	8.46478e10	−	4.80061e11i	0.000190775	−	0.00108194i
$851$	2.82447e13	+	4.98030e12i	0.0632833	+	0.0111586i
$852$		0			0
$853$	3.34474e14	−	2.80657e14i	0.740657	−	0.621485i	−0.192357	−	0.981325i	$-0.561613\pi$
$853$	3.34474e14	−	2.80657e14i	0.740657	−	0.621485i	0.933014	+	0.359840i	$0.117169\pi$
$854$	−1.00299e13	−	5.79078e12i	−0.0220805	−	0.0127482i
$855$		0			0
$856$	−2.58448e13	−	4.47644e13i	−0.0562346	−	0.0974012i
$857$	2.63403e14	−	7.23695e14i	0.569793	−	1.56549i	−0.235035	−	0.971987i	$-0.575521\pi$
$857$	2.63403e14	−	7.23695e14i	0.569793	−	1.56549i	0.804829	−	0.593507i	$-0.202257\pi$
$858$		0			0
$859$	−5.90258e14	−	4.95285e14i	−1.26205	−	1.05898i	−0.995461	−	0.0951729i	$-0.969660\pi$
$859$	−5.90258e14	−	4.95285e14i	−1.26205	−	1.05898i	−0.266587	−	0.963811i	$-0.585896\pi$
$860$	−1.14457e14	−	3.14467e14i	−0.243304	−	0.668472i
$861$		0			0
$862$	2.20109e13	+	1.24830e14i	0.0462489	+	0.262291i
$863$		−	2.54952e14i		−	0.532605i	−0.963890	−	0.266302i	$-0.914198\pi$
$863$		−	2.54952e14i		−	0.532605i	0.963890	−	0.266302i	$-0.0858019\pi$
$864$		0			0
$865$	−1.64131e14			−0.338930
$866$	6.26546e13	−	1.10477e13i	0.128636	−	0.0226821i
$867$		0			0
$868$	1.72185e14	−	6.26701e13i	0.349459	−	0.127193i
$869$	−2.83549e13	+	3.37921e13i	−0.0572176	+	0.0681893i
$870$		0			0
$871$	−6.06493e14	−	2.20745e14i	−1.20986	−	0.440353i
$872$	2.43874e14	−	1.40801e14i	0.483708	−	0.279269i
$873$		0			0
$874$	9.65753e12	−	1.67273e13i	0.0189369	−	0.0327997i
$875$	−1.13406e14	−	1.35152e14i	−0.221103	−	0.263501i
$876$		0			0
$877$	1.40337e14	−	7.95891e14i	0.270505	−	1.53411i	−0.482384	−	0.875960i	$-0.660229\pi$
$877$	1.40337e14	−	7.95891e14i	0.270505	−	1.53411i	0.752889	−	0.658148i	$-0.228660\pi$
$878$	−2.84810e14	−	5.02197e13i	−0.545862	−	0.0962502i
$879$		0			0
$880$	−1.20255e13	+	1.00906e13i	−0.0227872	+	0.0191208i
$881$	−7.59349e14	−	4.38410e14i	−1.43074	−	0.826040i	−0.433566	−	0.901122i	$-0.642745\pi$
$881$	−7.59349e14	−	4.38410e14i	−1.43074	−	0.826040i	−0.997177	+	0.0750815i	$0.976078\pi$
$882$		0			0
$883$	1.36395e14	+	2.36244e14i	0.254095	+	0.440105i	0.964649	−	0.263537i	$-0.0848891\pi$
$883$	1.36395e14	+	2.36244e14i	0.254095	+	0.440105i	−0.710554	+	0.703642i	$0.751556\pi$
$884$	−4.70278e13	+	1.29208e14i	−0.0871150	+	0.239346i
$885$		0			0
$886$	−2.21354e14	−	1.85738e14i	−0.405433	−	0.340199i
$887$	3.17061e14	+	8.71118e14i	0.577464	+	1.58657i	0.792441	+	0.609949i	$0.208810\pi$
$887$	3.17061e14	+	8.71118e14i	0.577464	+	1.58657i	−0.214977	+	0.976619i	$0.568968\pi$
$888$		0			0
$889$	−2.61156e13	−	1.48109e14i	−0.0470318	−	0.266731i
$890$			2.75379e12i			0.00493152i
$891$		0			0
$892$	7.75836e14			1.37387
$893$	3.57565e14	−	6.30484e13i	0.629648	−	0.111024i
$894$		0			0
$895$	−1.28282e14	+	4.66907e13i	−0.223383	+	0.0813046i
$896$	−1.29628e14	+	1.54485e14i	−0.224470	+	0.267513i
$897$		0			0
$898$	2.61801e14	+	9.52877e13i	0.448321	+	0.163176i
$899$	−3.46431e14	+	2.00012e14i	−0.589955	+	0.340611i
$900$		0			0
$901$	−6.45015e13	+	1.11720e14i	−0.108629	+	0.188151i
$902$	−7.96775e11	−	9.49559e11i	−0.00133445	−	0.00159034i
$903$		0			0
$904$	−4.04700e13	+	2.29517e14i	−0.0670333	+	0.380165i
$905$	−8.71765e14	−	1.53716e14i	−1.43601	−	0.253207i
$906$		0			0
$907$	6.23629e14	−	5.23287e14i	1.01599	−	0.852518i	0.0268732	−	0.999639i	$-0.491445\pi$
$907$	6.23629e14	−	5.23287e14i	1.01599	−	0.852518i	0.989119	+	0.147121i	$0.0470005\pi$
$908$	6.18637e14	+	3.57170e14i	1.00232	+	0.578690i
$909$		0			0
$910$	−3.38510e13	−	5.86316e13i	−0.0542456	−	0.0939561i
$911$	−2.73888e14	+	7.52502e14i	−0.436497	+	1.19927i	0.505258	+	0.862968i	$0.331397\pi$
$911$	−2.73888e14	+	7.52502e14i	−0.436497	+	1.19927i	−0.941756	+	0.336298i	$0.890825\pi$
$912$		0			0
$913$	4.26735e13	+	3.58073e13i	0.0672674	+	0.0564440i
$914$	2.87934e13	+	7.91093e13i	0.0451401	+	0.124021i
$915$		0			0
$916$	9.18950e13	+	5.21162e14i	0.142500	+	0.808157i
$917$		−	1.00783e14i		−	0.155432i
$918$		0			0
$919$	7.91215e14			1.20703			0.603513	−	0.797353i	$-0.293767\pi$
$919$	7.91215e14			1.20703			0.603513	+	0.797353i	$0.293767\pi$
$920$	1.20468e14	−	2.12417e13i	0.182781	−	0.0322292i
$921$		0			0
$922$	−3.01002e14	+	1.09556e14i	−0.451767	+	0.164430i
$923$	−6.10641e14	+	7.27733e14i	−0.911543	+	1.08633i
$924$		0			0
$925$	1.12414e12	+	4.09153e11i	0.00166001	+	0.000604195i
$926$	1.62783e14	−	9.39830e13i	0.239086	−	0.138037i
$927$		0			0
$928$	1.73593e14	−	3.00672e14i	0.252228	−	0.436871i
$929$	3.54193e14	+	4.22111e14i	0.511873	+	0.610026i	0.958639	−	0.284625i	$-0.0918690\pi$
$929$	3.54193e14	+	4.22111e14i	0.511873	+	0.610026i	−0.446766	+	0.894651i	$0.647425\pi$
$930$		0			0
$931$	3.99554e13	−	2.26598e14i	0.0571251	−	0.323972i
$932$	−1.46444e14	−	2.58220e13i	−0.208253	−	0.0367207i
$933$		0			0
$934$	−3.35739e14	+	2.81718e14i	−0.472353	+	0.396352i
$935$	−1.37372e13	−	7.93119e12i	−0.0192239	−	0.0110989i
$936$		0			0
$937$	5.79781e14	+	1.00421e15i	0.802723	+	1.39036i	0.917818	+	0.397002i	$0.129950\pi$
$937$	5.79781e14	+	1.00421e15i	0.802723	+	1.39036i	−0.115095	+	0.993355i	$0.536717\pi$
$938$	5.76164e13	−	1.58300e14i	0.0793473	−	0.218005i
$939$		0			0
$940$	8.00546e14	+	6.71738e14i	1.09080	+	0.915294i
$941$	1.69971e14	+	4.66991e14i	0.230370	+	0.632937i	0.999984	−	0.00557188i	$-0.00177359\pi$
$941$	1.69971e14	+	4.66991e14i	0.230370	+	0.632937i	−0.769614	+	0.638509i	$0.779551\pi$
$942$		0			0
$943$	−2.88954e12	−	1.63874e13i	−0.00387499	−	0.0219761i
$944$			3.56048e14i			0.474951i
$945$		0			0
$946$	−1.50185e13			−0.0198231
$947$	4.34307e14	−	7.65800e13i	0.570225	−	0.100546i	0.118901	−	0.992906i	$-0.462063\pi$
$947$	4.34307e14	−	7.65800e13i	0.570225	−	0.100546i	0.451324	+	0.892360i	$0.350952\pi$
$948$		0			0
$949$	−1.01988e15	+	3.71206e14i	−1.32501	+	0.482263i
$950$	5.17860e11	−	6.17162e11i	0.000669259	−	0.000797592i
$951$		0			0
$952$	−7.42056e13	−	2.70086e13i	−0.0948969	−	0.0345396i
$953$	1.04006e15	−	6.00480e14i	1.32311	−	0.763896i	0.338883	−	0.940828i	$-0.389951\pi$
$953$	1.04006e15	−	6.00480e14i	1.32311	−	0.763896i	0.984223	+	0.176932i	$0.0566174\pi$
$954$		0			0
$955$	−6.70765e14	+	1.16180e15i	−0.844410	+	1.46256i
$956$	4.21994e14	+	5.02913e14i	0.528466	+	0.629801i
$957$		0			0
$958$	−4.16132e13	+	2.36000e14i	−0.0515708	+	0.292472i
$959$	3.64373e14	+	6.42488e13i	0.449214	+	0.0792086i
$960$		0			0
$961$	4.36754e14	−	3.66480e14i	0.532868	−	0.447129i
$962$	5.85507e13	+	3.38042e13i	0.0710651	+	0.0410295i
$963$		0			0
$964$	−3.13759e14	−	5.43447e14i	−0.376887	−	0.652787i
$965$	1.56901e14	−	4.31082e14i	0.187495	−	0.515138i
$966$		0			0
$967$	−2.53618e14	−	2.12811e14i	−0.299949	−	0.251687i	0.480374	−	0.877064i	$-0.340501\pi$
$967$	−2.53618e14	−	2.12811e14i	−0.299949	−	0.251687i	−0.780323	+	0.625376i	$0.784945\pi$
$968$	−2.17003e14	−	5.96210e14i	−0.255322	−	0.701492i
$969$		0			0
$970$	−4.33902e13	−	2.46078e14i	−0.0505281	−	0.286559i
$971$		−	9.10849e14i		−	1.05524i	−0.849481	−	0.527619i	$-0.823085\pi$
$971$		−	9.10849e14i		−	1.05524i	0.849481	−	0.527619i	$-0.176915\pi$
$972$		0			0
$973$	−2.09897e14			−0.240681
$974$	−4.06609e14	+	7.16961e13i	−0.463855	+	0.0817901i
$975$		0			0
$976$	−7.98562e13	+	2.90653e13i	−0.0901694	+	0.0328190i
$977$	1.01387e15	−	1.20829e15i	1.13897	−	1.35737i	0.214219	−	0.976786i	$-0.431279\pi$
$977$	1.01387e15	−	1.20829e15i	1.13897	−	1.35737i	0.924747	−	0.380582i	$-0.124276\pi$
$978$		0			0
$979$	−5.79621e11	−	2.10965e11i	−0.000644511	−	0.000234583i
$980$	5.73541e14	−	3.31134e14i	0.634503	−	0.366331i
$981$		0			0
$982$	1.94229e14	−	3.36414e14i	0.212694	−	0.368398i
$983$	5.04430e14	+	6.01156e14i	0.549583	+	0.654967i	0.967308	−	0.253606i	$-0.0816167\pi$
$983$	5.04430e14	+	6.01156e14i	0.549583	+	0.654967i	−0.417725	+	0.908574i	$0.637172\pi$
$984$		0			0
$985$	−2.18717e14	+	1.24041e15i	−0.235886	+	1.33777i
$986$	7.71590e13	+	1.36052e13i	0.0827946	+	0.0145989i
$987$		0			0
$988$	−1.74083e14	+	1.46073e14i	−0.184915	+	0.155162i
$989$	−1.74601e14	−	1.00806e14i	−0.184530	−	0.106538i
$990$		0			0
$991$	2.81731e14	+	4.87972e14i	0.294758	+	0.510536i	0.974929	−	0.222518i	$-0.0714275\pi$
$991$	2.81731e14	+	4.87972e14i	0.294758	+	0.510536i	−0.680170	+	0.733054i	$0.738094\pi$
$992$	−4.12544e14	+	1.13346e15i	−0.429449	+	1.17990i
$993$		0			0
$994$	−1.89945e14	−	1.59382e14i	−0.195747	−	0.164251i
$995$	−2.27826e14	−	6.25947e14i	−0.233608	−	0.641834i
$996$		0			0
$997$	−1.13387e14	−	6.43047e14i	−0.115103	−	0.652780i	−0.986699	−	0.162556i	$-0.948026\pi$
$997$	−1.13387e14	−	6.43047e14i	−0.115103	−	0.652780i	0.871597	−	0.490224i	$-0.163085\pi$
$998$		−	3.88752e13i		−	0.0392663i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.11.f.a.71.11		174
3.2	odd	2		27.11.f.a.14.19	yes	174
27.2	odd	18	inner	81.11.f.a.8.11		174
27.25	even	9		27.11.f.a.2.19	✓	174

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.11.f.a.2.19	✓	174	27.25	even	9
27.11.f.a.14.19	yes	174	3.2	odd	2
81.11.f.a.8.11		174	27.2	odd	18	inner
81.11.f.a.71.11		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+(-12.8751 + 2.27023i) q^{2} +(-801.631 + 291.770i) q^{4} +(2001.83 - 2385.69i) q^{5} +(-5414.20 - 1970.61i) q^{7} +(21252.6 - 12270.2i) q^{8} +(-20357.7 + 35260.6i) q^{10} +(-5862.12 - 6986.20i) q^{11} +(50114.5 - 284213. i) q^{13} +(74182.1 + 13080.3i) q^{14} +(423406. - 355280. i) q^{16} +(483672. + 279248. i) q^{17} +(461520. + 799376. i) q^{19} +(-908659. + 2.49652e6i) q^{20} +(91335.7 + 76639.7i) q^{22} +(547430. + 1.50405e6i) q^{23} +(11593.0 + 65747.1i) q^{25} +3.77305e6i q^{26} +4.91516e6 q^{28} +(-1.05674e7 + 1.86331e6i) q^{29} +(3.50314e7 - 1.27504e7i) q^{31} +(-2.07977e7 + 2.47857e7i) q^{32} +(-6.86129e6 - 2.49731e6i) q^{34} +(-1.55396e7 + 8.97179e6i) q^{35} +(8.95940e6 - 1.55181e7i) q^{37} +(-7.75688e6 - 9.24429e6i) q^{38} +(1.32713e7 - 7.52651e7i) q^{40} +(-1.02384e7 - 1.80531e6i) q^{41} +(-9.64927e7 + 8.09670e7i) q^{43} +(6.73762e6 + 3.88997e6i) q^{44} +(-1.04628e7 - 1.81220e7i) q^{46} +(1.34535e8 - 3.69632e8i) q^{47} +(-1.90958e8 - 1.60233e8i) q^{49} +(-298522. - 820182. i) q^{50} +(4.27516e7 + 2.42456e8i) q^{52} +2.30982e8i q^{53} -2.84019e7 q^{55} +(-1.39246e8 + 2.45528e7i) q^{56} +(1.31826e8 - 4.79807e7i) q^{58} +(-4.14069e8 + 4.93469e8i) q^{59} +(-1.44479e8 - 5.25861e7i) q^{61} +(-4.22086e8 + 2.43692e8i) q^{62} +(-7.14884e7 + 1.23821e8i) q^{64} +(-5.77725e8 - 6.88506e8i) q^{65} +(3.88344e8 - 2.20241e9i) q^{67} +(-4.69203e8 - 8.27332e7i) q^{68} +(1.79706e8 - 1.50791e8i) q^{70} +(-2.85073e9 - 1.64587e9i) q^{71} +(-1.88036e9 - 3.25688e9i) q^{73} +(-8.01235e7 + 2.20137e8i) q^{74} +(-6.03202e8 - 5.06147e8i) q^{76} +(1.79716e7 + 4.93766e7i) q^{77} +(-8.39932e8 - 4.76349e9i) q^{79} -1.72133e9i q^{80} +1.35919e8 q^{82} +(-6.01546e9 + 1.06069e9i) q^{83} +(1.63443e9 - 5.94885e8i) q^{85} +(1.05854e9 - 1.26152e9i) q^{86} +(-2.10307e8 - 7.65456e7i) q^{88} +(5.85736e7 - 3.38175e7i) q^{89} +(-8.31403e8 + 1.44003e9i) q^{91} +(-8.77673e8 - 1.04597e9i) q^{92} +(-8.93003e8 + 5.06447e9i) q^{94} +(2.83095e9 + 4.99173e8i) q^{95} +(-4.70128e9 + 3.94484e9i) q^{97} +(2.82237e9 + 1.62950e9i) 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

Modular forms

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Database

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