LMFDB - Embedded newform 20.9.d.c.19.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [20,9,Mod(19,20)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(20, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1])) N = Newforms(chi, 9, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("20.19"); S:= CuspForms(chi, 9); N := Newforms(S);

Level:	$ N $	$=$	$ 20 = 2^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	20.d (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [20,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$8.14757220122$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 94 x^{18} + 5343 x^{16} + 172772 x^{14} + 36131456 x^{12} + 3044563968 x^{10} + \cdots + 11\!\cdots\!76 $ x^20 + 94x^18 + 5343x^16 + 172772x^14 + 36131456x^12 + 3044563968x^10 + 147994443776x^8 + 2898633162752x^6 + 367168164200448x^4 + 26458647810801664*x^2 + 1152921504606846976
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{74}\cdot 3^{4}\cdot 5^{12} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			19.4
Root			$-7.15078 + 3.58697i$ of defining polynomial
Character	$\chi$	$=$	20.19
Dual form			20.9.d.c.19.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-14.3016 + 7.17394i) q^{2} +42.6663 q^{3} +(153.069 - 205.197i) q^{4} +(-560.298 + 276.932i) q^{5} +(-610.194 + 306.085i) q^{6} +869.685 q^{7} +(-717.054 + 4032.75i) q^{8} -4740.59 q^{9} +(6026.43 - 7980.11i) q^{10} -24735.0i q^{11} +(6530.89 - 8754.99i) q^{12} -41128.5i q^{13} +(-12437.9 + 6239.07i) q^{14} +(-23905.8 + 11815.7i) q^{15} +(-18675.7 - 62818.7i) q^{16} +40900.7i q^{17} +(67797.8 - 34008.7i) q^{18} -79502.2i q^{19} +(-28938.6 + 157361. i) q^{20} +37106.2 q^{21} +(177447. + 353749. i) q^{22} -428560. q^{23} +(-30594.0 + 172062. i) q^{24} +(237242. - 310329. i) q^{25} +(295053. + 588201. i) q^{26} -482197. q^{27} +(133122. - 178457. i) q^{28} +184740. q^{29} +(257125. - 340481. i) q^{30} -154752. i q^{31} +(717749. + 764426. i) q^{32} -1.05535e6i q^{33} +(-293419. - 584943. i) q^{34} +(-487283. + 240844. i) q^{35} +(-725638. + 972755. i) q^{36} +1.72203e6i q^{37} +(570344. + 1.13701e6i) q^{38} -1.75480e6i q^{39} +(-715034. - 2.45811e6i) q^{40} -2.00720e6 q^{41} +(-530677. + 266198. i) q^{42} +1.43073e6 q^{43} +(-5.07555e6 - 3.78616e6i) q^{44} +(2.65614e6 - 1.31282e6i) q^{45} +(6.12907e6 - 3.07446e6i) q^{46} +4.98494e6 q^{47} +(-796823. - 2.68024e6i) q^{48} -5.00845e6 q^{49} +(-1.16665e6 + 6.14015e6i) q^{50} +1.74508e6i q^{51} +(-8.43945e6 - 6.29550e6i) q^{52} +6.97640e6i q^{53} +(6.89616e6 - 3.45925e6i) q^{54} +(6.84992e6 + 1.38590e7i) q^{55} +(-623611. + 3.50722e6i) q^{56} -3.39206e6i q^{57} +(-2.64206e6 + 1.32531e6i) q^{58} -5.65200e6i q^{59} +(-1.23470e6 + 6.71402e6i) q^{60} +6.73713e6 q^{61} +(1.11018e6 + 2.21319e6i) q^{62} -4.12282e6 q^{63} +(-1.57489e7 - 5.78340e6i) q^{64} +(1.13898e7 + 2.30442e7i) q^{65} +(7.57102e6 + 1.50931e7i) q^{66} -4.99529e6 q^{67} +(8.39270e6 + 6.26063e6i) q^{68} -1.82850e7 q^{69} +(5.24110e6 - 6.94018e6i) q^{70} +2.07710e7i q^{71} +(3.39926e6 - 1.91176e7i) q^{72} -3.31772e7i q^{73} +(-1.23537e7 - 2.46277e7i) q^{74} +(1.01222e7 - 1.32406e7i) q^{75} +(-1.63136e7 - 1.21693e7i) q^{76} -2.15117e7i q^{77} +(1.25888e7 + 2.50964e7i) q^{78} -7.49445e7i q^{79} +(2.78605e7 + 3.00253e7i) q^{80} +1.05295e7 q^{81} +(2.87061e7 - 1.43996e7i) q^{82} -8.75346e7 q^{83} +(5.67981e6 - 7.61409e6i) q^{84} +(-1.13267e7 - 2.29165e7i) q^{85} +(-2.04616e7 + 1.02639e7i) q^{86} +7.88215e6 q^{87} +(9.97500e7 + 1.77363e7i) q^{88} -1.14653e7 q^{89} +(-2.85689e7 + 3.78304e7i) q^{90} -3.57688e7i q^{91} +(-6.55993e7 + 8.79392e7i) q^{92} -6.60268e6i q^{93} +(-7.12925e7 + 3.57617e7i) q^{94} +(2.20167e7 + 4.45449e7i) q^{95} +(3.06237e7 + 3.26152e7i) q^{96} +8.74640e7i q^{97} +(7.16286e7 - 3.59303e7i) q^{98} +1.17258e8i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 752 q^{4} - 1420 q^{5} + 3408 q^{6} + 2556 q^{9} - 4160 q^{10} + 8848 q^{14} - 59200 q^{16} - 4240 q^{20} + 410256 q^{21} - 156672 q^{24} - 657260 q^{25} - 440448 q^{26} + 660136 q^{29} + 667920 q^{30}+ \cdots + 28850688 q^{96}+O(q^{100}) $ 20 * q - 752 * q^4 - 1420 * q^5 + 3408 * q^6 + 2556 * q^9 - 4160 * q^10 + 8848 * q^14 - 59200 * q^16 - 4240 * q^20 + 410256 * q^21 - 156672 * q^24 - 657260 * q^25 - 440448 * q^26 + 660136 * q^29 + 667920 * q^30 + 4342528 * q^34 - 7191312 * q^36 - 945280 * q^40 + 7068520 * q^41 + 2666880 * q^44 - 18729060 * q^45 + 561168 * q^46 + 11719036 * q^49 + 3914880 * q^50 + 37110816 * q^54 - 35044352 * q^56 - 22734720 * q^60 - 17660440 * q^61 + 20201728 * q^64 - 44202240 * q^65 + 31902720 * q^66 + 111747216 * q^69 - 47166000 * q^70 + 19114368 * q^74 - 54998400 * q^76 + 7968320 * q^80 - 154212444 * q^81 + 101289216 * q^84 + 68800000 * q^85 + 94429648 * q^86 + 105006376 * q^89 - 230808000 * q^90 - 192757872 * q^94 + 28850688 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/20\mathbb{Z}\right)^\times$.

$n$	$11$	$17$
$\chi(n)$	$-1$	$-1$

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 $

$2$	−14.3016	+	7.17394i	−0.893847	+	0.448371i
$2$	−14.3016	+	7.17394i	−0.893847	+	0.448371i
$3$	42.6663			0.526744			0.263372	−	0.964694i	$-0.415165\pi$
$3$	42.6663			0.526744			0.263372	+	0.964694i	$0.415165\pi$
$4$	153.069	−	205.197i	0.597926	−	0.801551i
$5$	−560.298	+	276.932i	−0.896476	+	0.443091i
$5$	−560.298	+	276.932i	−0.896476	+	0.443091i
$6$	−610.194	+	306.085i	−0.470829	+	0.236177i
$7$	869.685			0.362218			0.181109	−	0.983463i	$-0.442031\pi$
$7$	869.685			0.362218			0.181109	+	0.983463i	$0.442031\pi$
$8$	−717.054	+	4032.75i	−0.175062	+	0.984557i
$9$	−4740.59			−0.722541
$10$	6026.43	−	7980.11i	0.602643	−	0.798011i
$11$		−	24735.0i		−	1.68943i	−0.535214	−	0.844717i	$-0.679769\pi$
$11$		−	24735.0i		−	1.68943i	0.535214	−	0.844717i	$-0.320231\pi$
$12$	6530.89	−	8754.99i	0.314954	−	0.422212i
$13$		−	41128.5i		−	1.44002i	−0.693962	−	0.720011i	$-0.744137\pi$
$13$		−	41128.5i		−	1.44002i	0.693962	−	0.720011i	$-0.255863\pi$
$14$	−12437.9	+	6239.07i	−0.323767	+	0.162408i
$15$	−23905.8	+	11815.7i	−0.472214	+	0.233396i
$16$	−18675.7	−	62818.7i	−0.284969	−	0.958537i
$17$			40900.7i			0.489705i	0.969560	+	0.244853i	$0.0787395\pi$
$17$			40900.7i			0.489705i	−0.969560	+	0.244853i	$0.921260\pi$
$18$	67797.8	−	34008.7i	0.645841	−	0.323967i
$19$		−	79502.2i		−	0.610049i	−0.952345	−	0.305024i	$-0.901335\pi$
$19$		−	79502.2i		−	0.610049i	0.952345	−	0.305024i	$-0.0986646\pi$
$20$	−28938.6	+	157361.i	−0.180866	+	0.983508i
$21$	37106.2			0.190796
$22$	177447.	+	353749.i	0.757494	+	1.51010i
$23$	−428560.			−1.53144			−0.765720	−	0.643174i	$-0.777617\pi$
$23$	−428560.			−1.53144			−0.765720	+	0.643174i	$0.777617\pi$
$24$	−30594.0	+	172062.i	−0.0922129	+	0.518610i
$25$	237242.	−	310329.i	0.607340	−	0.794442i
$26$	295053.	+	588201.i	0.645665	+	1.28716i
$27$	−482197.			−0.907338
$28$	133122.	−	178457.i	0.216580	−	0.290336i
$29$	184740.			0.261197			0.130598	−	0.991435i	$-0.458310\pi$
$29$	184740.			0.261197			0.130598	+	0.991435i	$0.458310\pi$
$30$	257125.	−	340481.i	0.317439	−	0.420347i
$31$		−	154752.i		−	0.167567i	−0.996484	−	0.0837835i	$-0.973300\pi$
$31$		−	154752.i		−	0.167567i	0.996484	−	0.0837835i	$-0.0267004\pi$
$32$	717749.	+	764426.i	0.684499	+	0.729014i
$33$		−	1.05535e6i		−	0.889899i
$34$	−293419.	−	584943.i	−0.219570	−	0.437722i
$35$	−487283.	+	240844.i	−0.324720	+	0.160496i
$36$	−725638.	+	972755.i	−0.432026	+	0.579153i
$37$			1.72203e6i			0.918825i	0.888223	+	0.459413i	$0.151940\pi$
$37$			1.72203e6i			0.918825i	−0.888223	+	0.459413i	$0.848060\pi$
$38$	570344.	+	1.13701e6i	0.273529	+	0.545291i
$39$		−	1.75480e6i		−	0.758523i
$40$	−715034.	−	2.45811e6i	−0.279310	−	0.960201i
$41$	−2.00720e6			−0.710323			−0.355162	−	0.934805i	$-0.615574\pi$
$41$	−2.00720e6			−0.710323			−0.355162	+	0.934805i	$0.615574\pi$
$42$	−530677.	+	266198.i	−0.170543	+	0.0855475i
$43$	1.43073e6			0.418488			0.209244	−	0.977863i	$-0.432900\pi$
$43$	1.43073e6			0.418488			0.209244	+	0.977863i	$0.432900\pi$
$44$	−5.07555e6	−	3.78616e6i	−1.35417	−	1.01016i
$45$	2.65614e6	−	1.31282e6i	0.647741	−	0.320152i
$46$	6.12907e6	−	3.07446e6i	1.36887	−	0.686654i
$47$	4.98494e6			1.02157			0.510786	−	0.859708i	$-0.329354\pi$
$47$	4.98494e6			1.02157			0.510786	+	0.859708i	$0.329354\pi$
$48$	−796823.	−	2.68024e6i	−0.150106	−	0.504903i
$49$	−5.00845e6			−0.868798
$50$	−1.16665e6	+	6.14015e6i	−0.186664	+	0.982424i
$51$			1.74508e6i			0.257949i
$52$	−8.43945e6	−	6.29550e6i	−1.15425	−	0.861027i
$53$			6.97640e6i			0.884154i	0.896977	+	0.442077i	$0.145758\pi$
$53$			6.97640e6i			0.884154i	−0.896977	+	0.442077i	$0.854242\pi$
$54$	6.89616e6	−	3.45925e6i	0.811022	−	0.406824i
$55$	6.84992e6	+	1.38590e7i	0.748574	+	1.51454i
$56$	−623611.	+	3.50722e6i	−0.0634106	+	0.356624i
$57$		−	3.39206e6i		−	0.321340i
$58$	−2.64206e6	+	1.32531e6i	−0.233470	+	0.117113i
$59$		−	5.65200e6i		−	0.466438i	−0.972424	−	0.233219i	$-0.925074\pi$
$59$		−	5.65200e6i		−	0.466438i	0.972424	−	0.233219i	$-0.0749259\pi$
$60$	−1.23470e6	+	6.71402e6i	−0.0952701	+	0.518057i
$61$	6.73713e6			0.486582			0.243291	−	0.969953i	$-0.421773\pi$
$61$	6.73713e6			0.486582			0.243291	+	0.969953i	$0.421773\pi$
$62$	1.11018e6	+	2.21319e6i	0.0751323	+	0.149779i
$63$	−4.12282e6			−0.261717
$64$	−1.57489e7	−	5.78340e6i	−0.938707	−	0.344717i
$65$	1.13898e7	+	2.30442e7i	0.638062	+	1.29095i
$66$	7.57102e6	+	1.50931e7i	0.399005	+	0.795434i
$67$	−4.99529e6			−0.247891			−0.123946	−	0.992289i	$-0.539555\pi$
$67$	−4.99529e6			−0.247891			−0.123946	+	0.992289i	$0.539555\pi$
$68$	8.39270e6	+	6.26063e6i	0.392524	+	0.292807i
$69$	−1.82850e7			−0.806677
$70$	5.24110e6	−	6.94018e6i	0.218288	−	0.289054i
$71$			2.07710e7i			0.817378i	0.912674	+	0.408689i	$0.134014\pi$
$71$			2.07710e7i			0.817378i	−0.912674	+	0.408689i	$0.865986\pi$
$72$	3.39926e6	−	1.91176e7i	0.126489	−	0.711383i
$73$		−	3.31772e7i		−	1.16828i	−0.811652	−	0.584141i	$-0.801431\pi$
$73$		−	3.31772e7i		−	1.16828i	0.811652	−	0.584141i	$-0.198569\pi$
$74$	−1.23537e7	−	2.46277e7i	−0.411975	−	0.821290i
$75$	1.01222e7	−	1.32406e7i	0.319913	−	0.418468i
$76$	−1.63136e7	−	1.21693e7i	−0.488985	−	0.364764i
$77$		−	2.15117e7i		−	0.611943i
$78$	1.25888e7	+	2.50964e7i	0.340100	+	0.678004i
$79$		−	7.49445e7i		−	1.92412i	−0.272844	−	0.962058i	$-0.587964\pi$
$79$		−	7.49445e7i		−	1.92412i	0.272844	−	0.962058i	$-0.412036\pi$
$80$	2.78605e7	+	3.00253e7i	0.680187	+	0.733038i
$81$	1.05295e7			0.244606
$82$	2.87061e7	−	1.43996e7i	0.634920	−	0.318489i
$83$	−8.75346e7			−1.84445			−0.922226	−	0.386651i	$-0.873632\pi$
$83$	−8.75346e7			−1.84445			−0.922226	+	0.386651i	$0.873632\pi$
$84$	5.67981e6	−	7.61409e6i	0.114082	−	0.152933i
$85$	−1.13267e7	−	2.29165e7i	−0.216984	−	0.439009i
$86$	−2.04616e7	+	1.02639e7i	−0.374064	+	0.187638i
$87$	7.88215e6			0.137584
$88$	9.97500e7	+	1.77363e7i	1.66334	+	0.295756i
$89$	−1.14653e7			−0.182737			−0.0913685	−	0.995817i	$-0.529124\pi$
$89$	−1.14653e7			−0.182737			−0.0913685	+	0.995817i	$0.529124\pi$
$90$	−2.85689e7	+	3.78304e7i	−0.435435	+	0.576595i
$91$		−	3.57688e7i		−	0.521602i
$92$	−6.55993e7	+	8.79392e7i	−0.915688	+	1.22753i
$93$		−	6.60268e6i		−	0.0882649i
$94$	−7.12925e7	+	3.57617e7i	−0.913129	+	0.458044i
$95$	2.20167e7	+	4.45449e7i	0.270307	+	0.546894i
$96$	3.06237e7	+	3.26152e7i	0.360556	+	0.384004i
$97$			8.74640e7i			0.987967i	0.869471	+	0.493983i	$0.164460\pi$
$97$			8.74640e7i			0.987967i	−0.869471	+	0.493983i	$0.835540\pi$
$98$	7.16286e7	−	3.59303e7i	0.776573	−	0.389544i
$99$			1.17258e8i			1.22068i
$100$	−2.73642e7	−	9.61832e7i	−0.273642	−	0.961832i
$101$	1.07960e8			1.03747			0.518736	−	0.854934i	$-0.326403\pi$
$101$	1.07960e8			1.03747			0.518736	+	0.854934i	$0.326403\pi$
$102$	−1.25191e7	−	2.49573e7i	−0.115657	−	0.230567i
$103$	−9.62475e7			−0.855147			−0.427573	−	0.903981i	$-0.640631\pi$
$103$	−9.62475e7			−0.855147			−0.427573	+	0.903981i	$0.640631\pi$
$104$	1.65861e8	+	2.94913e7i	1.41779	+	0.252093i
$105$	−2.07905e7	+	1.02759e7i	−0.171044	+	0.0845401i
$106$	−5.00483e7	−	9.97734e7i	−0.396430	−	0.790299i
$107$	8.83513e7			0.674028			0.337014	−	0.941500i	$-0.390583\pi$
$107$	8.83513e7			0.674028			0.337014	+	0.941500i	$0.390583\pi$
$108$	−7.38094e7	+	9.89453e7i	−0.542521	+	0.727278i
$109$	4.82155e7			0.341571			0.170785	−	0.985308i	$-0.445370\pi$
$109$	4.82155e7			0.341571			0.170785	+	0.985308i	$0.445370\pi$
$110$	−1.97388e8	−	1.49064e8i	−1.34819	−	1.01813i
$111$			7.34724e7i			0.483986i
$112$	−1.62420e7	−	5.46325e7i	−0.103221	−	0.347199i
$113$		−	1.83862e8i		−	1.12766i	−0.825891	−	0.563830i	$-0.809328\pi$
$113$		−	1.83862e8i		−	1.12766i	0.825891	−	0.563830i	$-0.190672\pi$
$114$	2.43345e7	+	4.85118e7i	0.144079	+	0.287229i
$115$	2.40121e8	−	1.18682e8i	1.37290	−	0.678568i
$116$	2.82779e7	−	3.79080e7i	0.156176	−	0.209363i
$117$			1.94973e8i			1.04048i
$118$	4.05471e7	+	8.08324e7i	0.209138	+	0.416924i
$119$			3.55707e7i			0.177380i
$120$	−3.05078e7	−	1.04879e8i	−0.147125	−	0.505780i
$121$	−3.97461e8			−1.85419
$122$	−9.63515e7	+	4.83318e7i	−0.434930	+	0.218169i
$123$	−8.56399e7			−0.374158
$124$	−3.17546e7	−	2.36877e7i	−0.134314	−	0.100193i
$125$	−4.69862e7	+	2.39577e8i	−0.192455	+	0.981306i
$126$	5.89628e7	−	2.95769e7i	0.233935	−	0.117347i
$127$	3.52941e8			1.35671			0.678355	−	0.734734i	$-0.262693\pi$
$127$	3.52941e8			1.35671			0.678355	+	0.734734i	$0.262693\pi$
$128$	2.66723e8	−	3.02700e7i	0.993622	−	0.112765i
$129$	6.10437e7			0.220436
$130$	−3.28210e8	−	2.47858e8i	−1.14915	−	0.867820i
$131$		−	1.20638e8i		−	0.409638i	−0.978800	−	0.204819i	$-0.934339\pi$
$131$		−	1.20638e8i		−	0.409638i	0.978800	−	0.204819i	$-0.0656606\pi$
$132$	−2.16555e8	−	1.61541e8i	−0.713299	−	0.532094i
$133$		−	6.91419e7i		−	0.220971i
$134$	7.14404e7	−	3.58359e7i	0.221577	−	0.111147i
$135$	2.70174e8	−	1.33536e8i	0.813407	−	0.402034i
$136$	−1.64942e8	−	2.93280e7i	−0.482143	−	0.0857288i
$137$		−	2.98009e8i		−	0.845955i	−0.906140	−	0.422978i	$-0.860985\pi$
$137$		−	2.98009e8i		−	0.845955i	0.906140	−	0.422978i	$-0.139015\pi$
$138$	2.61505e8	−	1.31176e8i	0.721046	−	0.361691i
$139$			4.00098e8i			1.07178i	0.844287	+	0.535891i	$0.180024\pi$
$139$			4.00098e8i			1.07178i	−0.844287	+	0.535891i	$0.819976\pi$
$140$	−2.51675e7	+	1.36855e8i	−0.0655129	+	0.356244i
$141$	2.12689e8			0.538107
$142$	−1.49010e8	−	2.97057e8i	−0.366489	−	0.730611i
$143$	−1.01731e9			−2.43282
$144$	8.85339e7	+	2.97798e8i	0.205902	+	0.692582i
$145$	−1.03509e8	+	5.11603e7i	−0.234157	+	0.115734i
$146$	2.38011e8	+	4.74485e8i	0.523825	+	1.04427i
$147$	−2.13692e8			−0.457634
$148$	3.53355e8	+	2.63589e8i	0.736486	+	0.549390i
$149$	7.70799e8			1.56385			0.781927	−	0.623370i	$-0.214237\pi$
$149$	7.70799e8			1.56385			0.781927	+	0.623370i	$0.214237\pi$
$150$	−4.97766e7	+	2.61977e8i	−0.0983241	+	0.517486i
$151$		−	5.11492e8i		−	0.983856i	−0.870636	−	0.491928i	$-0.836292\pi$
$151$		−	5.11492e8i		−	0.983856i	0.870636	−	0.491928i	$-0.163708\pi$
$152$	3.20612e8	+	5.70074e7i	0.600628	+	0.106796i
$153$		−	1.93893e8i		−	0.353832i
$154$	1.54323e8	+	3.07650e8i	0.274378	+	0.546984i
$155$	4.28557e7	+	8.67070e7i	0.0742475	+	0.150220i
$156$	−3.60080e8	−	2.68605e8i	−0.607995	−	0.453541i
$157$		−	8.51365e7i		−	0.140126i	−0.997543	−	0.0700628i	$-0.977680\pi$
$157$		−	8.51365e7i		−	0.140126i	0.997543	−	0.0700628i	$-0.0223200\pi$
$158$	5.37647e8	+	1.07182e9i	0.862719	+	1.71987i
$159$			2.97657e8i			0.465723i
$160$	−6.13848e8	−	2.29538e8i	−0.936657	−	0.350248i
$161$	−3.72712e8			−0.554715
$162$	−1.50588e8	+	7.55380e7i	−0.218640	+	0.109674i
$163$	−2.79284e8			−0.395636			−0.197818	−	0.980239i	$-0.563386\pi$
$163$	−2.79284e8			−0.395636			−0.197818	+	0.980239i	$0.563386\pi$
$164$	−3.07241e8	+	4.11872e8i	−0.424721	+	0.569360i
$165$	2.92260e8	+	5.91310e8i	0.394307	+	0.797773i
$166$	1.25188e9	−	6.27968e8i	1.64866	−	0.827000i
$167$	−4.30699e8			−0.553743			−0.276871	−	0.960907i	$-0.589298\pi$
$167$	−4.30699e8			−0.553743			−0.276871	+	0.960907i	$0.589298\pi$
$168$	−2.66072e7	+	1.49640e8i	−0.0334011	+	0.187850i
$169$	−8.75822e8			−1.07367
$170$	3.26392e8	+	2.46485e8i	0.390790	+	0.295118i
$171$			3.76887e8i			0.440785i
$172$	2.19000e8	−	2.93581e8i	0.250225	−	0.335439i
$173$		−	6.81243e8i		−	0.760533i	−0.924877	−	0.380266i	$-0.875832\pi$
$173$		−	6.81243e8i		−	0.760533i	0.924877	−	0.380266i	$-0.124168\pi$
$174$	−1.12727e8	+	5.65461e7i	−0.122979	+	0.0616887i
$175$	2.06326e8	−	2.69888e8i	0.219989	−	0.287761i
$176$	−1.55382e9	+	4.61944e8i	−1.61938	+	0.481436i
$177$		−	2.41150e8i		−	0.245693i
$178$	1.63972e8	−	8.22517e7i	0.163339	−	0.0819341i
$179$		−	1.86210e9i		−	1.81381i	−0.421336	−	0.906905i	$-0.638439\pi$
$179$		−	1.86210e9i		−	1.81381i	0.421336	−	0.906905i	$-0.361561\pi$
$180$	1.37186e8	−	7.45985e8i	0.130683	−	0.710624i
$181$	9.45023e8			0.880498			0.440249	−	0.897876i	$-0.354890\pi$
$181$	9.45023e8			0.880498			0.440249	+	0.897876i	$0.354890\pi$
$182$	2.56604e8	+	5.11550e8i	0.233871	+	0.466233i
$183$	2.87448e8			0.256304
$184$	3.07301e8	−	1.72827e9i	0.268097	−	1.50779i
$185$	−4.76885e8	−	9.64848e8i	−0.407124	−	0.823705i
$186$	4.73672e7	+	9.44285e7i	0.0395755	+	0.0788954i
$187$	1.01168e9			0.827324
$188$	7.63041e8	−	1.02290e9i	0.610825	−	0.818842i
$189$	−4.19359e8			−0.328654
$190$	−6.34436e8	−	4.79115e8i	−0.486825	−	0.367642i
$191$			6.13867e8i			0.461255i	0.973042	+	0.230627i	$0.0740778\pi$
$191$			6.13867e8i			0.461255i	−0.973042	+	0.230627i	$0.925922\pi$
$192$	−6.71946e8	−	2.46756e8i	−0.494458	−	0.181578i
$193$			7.45004e8i			0.536945i	0.963287	+	0.268472i	$0.0865188\pi$
$193$			7.45004e8i			0.536945i	−0.963287	+	0.268472i	$0.913481\pi$
$194$	−6.27462e8	−	1.25087e9i	−0.442976	−	0.883091i
$195$	4.85960e8	+	9.83210e8i	0.336095	+	0.679998i
$196$	−7.66639e8	+	1.02772e9i	−0.519477	+	0.696386i
$197$			2.47398e9i			1.64260i	0.570498	+	0.821299i	$0.306750\pi$
$197$			2.47398e9i			1.64260i	−0.570498	+	0.821299i	$0.693250\pi$
$198$	−8.41206e8	−	1.67698e9i	−0.547320	−	1.09111i
$199$			8.62436e8i			0.549939i	0.961453	+	0.274969i	$0.0886677\pi$
$199$			8.62436e8i			0.549939i	−0.961453	+	0.274969i	$0.911332\pi$
$200$	1.08136e9	+	1.17926e9i	0.675852	+	0.737038i
$201$	−2.13130e8			−0.130575
$202$	−1.54399e9	+	7.74498e8i	−0.927342	+	0.465173i
$203$	1.60665e8			0.0946102
$204$	3.58085e8	+	2.67118e8i	0.206759	+	0.154235i
$205$	1.12463e9	−	5.55859e8i	0.636788	−	0.314738i
$206$	1.37649e9	−	6.90474e8i	0.764371	−	0.383423i
$207$	2.03163e9			1.10653
$208$	−2.58364e9	+	7.68104e8i	−1.38031	+	0.410361i
$209$	−1.96649e9			−1.03064
$210$	2.23618e8	−	2.96111e8i	0.114982	−	0.152257i
$211$			2.06407e9i			1.04135i	0.853756	+	0.520673i	$0.174319\pi$
$211$			2.06407e9i			1.04135i	−0.853756	+	0.520673i	$0.825681\pi$
$212$	1.43154e9	+	1.06787e9i	0.708695	+	0.528659i
$213$			8.86219e8i			0.430549i
$214$	−1.26356e9	+	6.33827e8i	−0.602478	+	0.302215i
$215$	−8.01633e8	+	3.96214e8i	−0.375164	+	0.185428i
$216$	3.45761e8	−	1.94458e9i	0.158840	−	0.893326i
$217$		−	1.34585e8i		−	0.0606958i
$218$	−6.89557e8	+	3.45895e8i	−0.305312	+	0.153151i
$219$		−	1.41555e9i		−	0.615386i
$220$	3.89233e9	+	7.15796e8i	1.66157	+	0.305561i
$221$	1.68218e9			0.705186
$222$	−5.27087e8	−	1.05077e9i	−0.217005	−	0.432609i
$223$	2.49560e9			1.00915			0.504574	−	0.863368i	$-0.331649\pi$
$223$	2.49560e9			1.00915			0.504574	+	0.863368i	$0.331649\pi$
$224$	6.24216e8	+	6.64810e8i	0.247938	+	0.264062i
$225$	−1.12467e9	+	1.47114e9i	−0.438828	+	0.574017i
$226$	1.31901e9	+	2.62951e9i	0.505610	+	1.00796i
$227$	−4.05348e9			−1.52660			−0.763300	−	0.646045i	$-0.776422\pi$
$227$	−4.05348e9			−1.52660			−0.763300	+	0.646045i	$0.776422\pi$
$228$	−6.96041e8	−	5.19220e8i	−0.257570	−	0.192137i
$229$	2.28775e9			0.831890			0.415945	−	0.909390i	$-0.363451\pi$
$229$	2.28775e9			0.831890			0.415945	+	0.909390i	$0.363451\pi$
$230$	−2.58269e9	+	3.41995e9i	−0.922913	+	1.22211i
$231$		−	9.17822e8i		−	0.322337i
$232$	−1.32468e8	+	7.45008e8i	−0.0457257	+	0.257163i
$233$		−	3.13148e9i		−	1.06249i	−0.847217	−	0.531247i	$-0.821724\pi$
$233$		−	3.13148e9i		−	1.06249i	0.847217	−	0.531247i	$-0.178276\pi$
$234$	−1.39873e9	−	2.78842e9i	−0.466519	−	0.930026i
$235$	−2.79305e9	+	1.38049e9i	−0.915815	+	0.452650i
$236$	−1.15977e9	−	8.65146e8i	−0.373874	−	0.278896i
$237$		−	3.19760e9i		−	1.01352i
$238$	−2.55182e8	−	5.08716e8i	−0.0795321	−	0.158551i
$239$		−	1.66159e9i		−	0.509251i	−0.967040	−	0.254626i	$-0.918048\pi$
$239$		−	1.66159e9i		−	0.509251i	0.967040	−	0.254626i	$-0.0819523\pi$
$240$	1.18870e9	+	1.28107e9i	0.358284	+	0.386124i
$241$	−1.60357e9			−0.475358			−0.237679	−	0.971344i	$-0.576387\pi$
$241$	−1.60357e9			−0.475358			−0.237679	+	0.971344i	$0.576387\pi$
$242$	5.68431e9	−	2.85136e9i	1.65736	−	0.831364i
$243$	3.61295e9			1.03618
$244$	1.03125e9	−	1.38244e9i	0.290940	−	0.390020i
$245$	2.80622e9	−	1.38700e9i	0.778857	−	0.384957i
$246$	1.22478e9	−	6.14375e8i	0.334441	−	0.167762i
$247$	−3.26980e9			−0.878484
$248$	6.24074e8	+	1.10965e8i	0.164979	+	0.0293346i
$249$	−3.73477e9			−0.971554
$250$	−1.04673e9	−	3.76339e9i	−0.267964	−	0.963429i
$251$		−	6.18770e9i		−	1.55896i	−0.626429	−	0.779478i	$-0.715484\pi$
$251$		−	6.18770e9i		−	1.55896i	0.626429	−	0.779478i	$-0.284516\pi$
$252$	−6.31076e8	+	8.45991e8i	−0.156488	+	0.209780i
$253$			1.06004e10i			2.58727i
$254$	−5.04760e9	+	2.53198e9i	−1.21269	+	0.608310i
$255$	−4.83268e8	−	9.77763e8i	−0.114295	−	0.231245i
$256$	−3.59740e9	+	2.34637e9i	−0.837586	+	0.546306i
$257$		−	6.20387e9i		−	1.42210i	−0.703142	−	0.711050i	$-0.748220\pi$
$257$		−	6.20387e9i		−	1.42210i	0.703142	−	0.711050i	$-0.251780\pi$
$258$	−8.73021e8	+	4.37924e8i	−0.197036	+	0.0988372i
$259$			1.49762e9i			0.332815i
$260$	6.47203e9	+	1.19020e9i	1.41627	+	0.260451i
$261$	−8.75775e8			−0.188725
$262$	8.65453e8	+	1.72532e9i	0.183670	+	0.366154i
$263$	−1.96327e9			−0.410353			−0.205177	−	0.978725i	$-0.565777\pi$
$263$	−1.96327e9			−0.410353			−0.205177	+	0.978725i	$0.565777\pi$
$264$	4.25596e9	+	7.56743e8i	0.876156	+	0.155787i
$265$	−1.93199e9	−	3.90886e9i	−0.391761	−	0.792623i
$266$	4.96020e8	+	9.88836e8i	0.0990769	+	0.197514i
$267$	−4.89183e8			−0.0962557
$268$	−7.64625e8	+	1.02502e9i	−0.148221	+	0.198698i
$269$	6.31601e9			1.20624			0.603120	−	0.797651i	$-0.293924\pi$
$269$	6.31601e9			1.20624			0.603120	+	0.797651i	$0.293924\pi$
$270$	−2.90593e9	+	3.84798e9i	−0.546801	+	0.724065i
$271$			4.71258e9i			0.873739i	0.899525	+	0.436869i	$0.143913\pi$
$271$			4.71258e9i			0.873739i	−0.899525	+	0.436869i	$0.856087\pi$
$272$	2.56932e9	−	7.63849e8i	0.469400	−	0.139551i
$273$		−	1.52612e9i		−	0.274751i
$274$	2.13790e9	+	4.26200e9i	0.379302	+	0.756155i
$275$	−7.67599e9	−	5.86818e9i	−1.34216	−	1.02606i
$276$	−2.79888e9	+	3.75204e9i	−0.482333	+	0.646593i
$277$			1.00765e8i			0.0171156i	0.999963	+	0.00855780i	$0.00272406\pi$
$277$			1.00765e8i			0.0171156i	−0.999963	+	0.00855780i	$0.997276\pi$
$278$	−2.87028e9	−	5.72202e9i	−0.480557	−	0.958010i
$279$			7.33614e8i			0.121074i
$280$	−6.21854e8	−	2.13779e9i	−0.101171	−	0.347802i
$281$	−4.26355e9			−0.683827			−0.341914	−	0.939731i	$-0.611075\pi$
$281$	−4.26355e9			−0.683827			−0.341914	+	0.939731i	$0.611075\pi$
$282$	−3.04178e9	+	1.52582e9i	−0.480985	+	0.241272i
$283$	1.16260e10			1.81253			0.906265	−	0.422710i	$-0.138921\pi$
$283$	1.16260e10			1.81253			0.906265	+	0.422710i	$0.138921\pi$
$284$	4.26214e9	+	3.17939e9i	0.655171	+	0.488732i
$285$	9.39371e8	+	1.90056e9i	0.142383	+	0.288073i
$286$	1.45492e10	−	7.29814e9i	2.17457	−	1.09081i
$287$	−1.74563e9			−0.257292
$288$	−3.40256e9	−	3.62383e9i	−0.494578	−	0.526742i
$289$	5.30289e9			0.760189
$290$	1.11332e9	−	1.47424e9i	0.157409	−	0.208438i
$291$			3.73176e9i			0.520405i
$292$	−6.80786e9	−	5.07840e9i	−0.936439	−	0.698547i
$293$		−	3.75705e9i		−	0.509772i	−0.966971	−	0.254886i	$-0.917962\pi$
$293$		−	3.75705e9i		−	0.509772i	0.966971	−	0.254886i	$-0.0820380\pi$
$294$	3.05613e9	−	1.53301e9i	0.409055	−	0.205190i
$295$	1.56522e9	+	3.16680e9i	0.206675	+	0.418151i
$296$	−6.94450e9	−	1.23479e9i	−0.904636	−	0.160851i
$297$			1.19271e10i			1.53289i
$298$	−1.10236e10	+	5.52967e9i	−1.39785	+	0.701188i
$299$			1.76260e10i			2.20531i
$300$	−1.16753e9	−	4.10378e9i	−0.144139	−	0.506639i
$301$	1.24428e9			0.151584
$302$	3.66942e9	+	7.31514e9i	0.441133	+	0.879417i
$303$	4.60624e9			0.546483
$304$	−4.99422e9	+	1.48476e9i	−0.584754	+	0.173845i
$305$	−3.77480e9	+	1.86573e9i	−0.436209	+	0.215600i
$306$	1.39098e9	+	2.77298e9i	0.158648	+	0.316272i
$307$	5.80347e9			0.653333			0.326666	−	0.945140i	$-0.394075\pi$
$307$	5.80347e9			0.653333			0.326666	+	0.945140i	$0.394075\pi$
$308$	−4.41413e9	−	3.29277e9i	−0.490504	−	0.365897i
$309$	−4.10652e9			−0.450443
$310$	−1.23493e9	−	9.32601e8i	−0.133720	−	0.100983i
$311$		−	1.22144e10i		−	1.30566i	−0.757503	−	0.652832i	$-0.773581\pi$
$311$		−	1.22144e10i		−	1.30566i	0.757503	−	0.652832i	$-0.226419\pi$
$312$	7.07666e9	+	1.25829e9i	0.746810	+	0.132789i
$313$			8.99814e9i			0.937509i	0.883328	+	0.468755i	$0.155297\pi$
$313$			8.99814e9i			0.937509i	−0.883328	+	0.468755i	$0.844703\pi$
$314$	6.10765e8	+	1.21758e9i	0.0628283	+	0.125251i
$315$	2.31001e9	−	1.14174e9i	0.234623	−	0.115965i
$316$	−1.53784e10	−	1.14717e10i	−1.54228	−	1.15048i
$317$			2.25206e9i			0.223019i	0.993763	+	0.111510i	$0.0355686\pi$
$317$			2.25206e9i			0.223019i	−0.993763	+	0.111510i	$0.964431\pi$
$318$	−2.13537e9	−	4.25696e9i	−0.208817	−	0.416285i
$319$		−	4.56953e9i		−	0.441275i
$320$	1.04257e10	−	1.12095e9i	0.994270	−	0.106902i
$321$	3.76962e9			0.355040
$322$	5.33036e9	−	2.67382e9i	0.495831	−	0.248718i
$323$	3.25169e9			0.298744
$324$	1.61174e9	−	2.16062e9i	0.146256	−	0.196064i
$325$	−1.27634e10	−	9.75741e9i	−1.14401	−	0.874583i
$326$	3.99420e9	−	2.00357e9i	0.353638	−	0.177392i
$327$	2.05718e9			0.179920
$328$	1.43927e9	−	8.09454e9i	0.124351	−	0.699354i
$329$	4.33533e9			0.370032
$330$	−8.42180e9	−	6.36000e9i	−0.710149	−	0.536292i
$331$		−	1.68572e9i		−	0.140434i	−0.997532	−	0.0702172i	$-0.977631\pi$
$331$		−	1.68572e9i		−	0.140434i	0.997532	−	0.0702172i	$-0.0223692\pi$
$332$	−1.33988e10	+	1.79619e10i	−1.10285	+	1.47842i
$333$		−	8.16342e9i		−	0.663889i
$334$	6.15966e9	−	3.08981e9i	0.494961	−	0.248282i
$335$	2.79885e9	−	1.38336e9i	0.222229	−	0.109839i
$336$	−6.92985e8	−	2.33096e9i	−0.0543709	−	0.182885i
$337$		−	7.73250e9i		−	0.599515i	−0.954015	−	0.299758i	$-0.903094\pi$
$337$		−	7.73250e9i		−	0.599515i	0.954015	−	0.299758i	$-0.0969058\pi$
$338$	1.25256e10	−	6.28310e9i	0.959693	−	0.481401i
$339$		−	7.84470e9i		−	0.593988i
$340$	−6.43618e9	−	1.18361e9i	−0.481629	−	0.0885711i
$341$	−3.82778e9			−0.283093
$342$	−2.70377e9	−	5.39008e9i	−0.197636	−	0.393995i
$343$	−9.36933e9			−0.676912
$344$	−1.02591e9	+	5.76976e9i	−0.0732613	+	0.412025i
$345$	1.02451e10	−	5.06372e9i	0.723167	−	0.357432i
$346$	4.88720e9	+	9.74284e9i	0.341001	+	0.679800i
$347$	−3.07433e9			−0.212047			−0.106023	−	0.994364i	$-0.533812\pi$
$347$	−3.07433e9			−0.212047			−0.106023	+	0.994364i	$0.533812\pi$
$348$	1.20651e9	−	1.61739e9i	0.0822650	−	0.110281i
$349$	−1.30882e10			−0.882224			−0.441112	−	0.897452i	$-0.645416\pi$
$349$	−1.30882e10			−0.882224			−0.441112	+	0.897452i	$0.645416\pi$
$350$	−1.01462e9	+	5.34000e9i	−0.0676130	+	0.355851i
$351$			1.98320e10i			1.30659i
$352$	1.89081e10	−	1.77535e10i	1.23162	−	1.15642i
$353$			6.61462e9i			0.425996i	0.977053	+	0.212998i	$0.0683229\pi$
$353$			6.61462e9i			0.425996i	−0.977053	+	0.212998i	$0.931677\pi$
$354$	1.72999e9	+	3.44882e9i	0.110162	+	0.219612i
$355$	−5.75215e9	−	1.16379e10i	−0.362173	−	0.732760i
$356$	−1.75499e9	+	2.35265e9i	−0.109263	+	0.146473i
$357$			1.51767e9i			0.0934338i
$358$	1.33586e10	+	2.66310e10i	0.813260	+	1.62127i
$359$		−	3.34086e9i		−	0.201132i	−0.994930	−	0.100566i	$-0.967935\pi$
$359$		−	3.34086e9i		−	0.201132i	0.994930	−	0.100566i	$-0.0320653\pi$
$360$	3.38968e9	+	1.16529e10i	0.201813	+	0.693784i
$361$	1.06630e10			0.627840
$362$	−1.35153e10	+	6.77954e9i	−0.787030	+	0.394790i
$363$	−1.69582e10			−0.976681
$364$	−7.33966e9	−	5.47510e9i	−0.418091	−	0.311879i
$365$	9.18783e9	+	1.85891e10i	0.517656	+	1.04734i
$366$	−4.11096e9	+	2.06214e9i	−0.229097	+	0.114919i
$367$	−9.60705e9			−0.529573			−0.264787	−	0.964307i	$-0.585302\pi$
$367$	−9.60705e9			−0.529573			−0.264787	+	0.964307i	$0.585302\pi$
$368$	8.00366e9	+	2.69216e10i	0.436413	+	1.46794i
$369$	9.51533e9			0.513237
$370$	1.37420e10	+	1.03777e10i	0.733232	+	0.553724i
$371$			6.06727e9i			0.320256i
$372$	−1.35485e9	−	1.01067e9i	−0.0707489	−	0.0527759i
$373$		−	1.82578e10i		−	0.943222i	−0.881807	−	0.471611i	$-0.843673\pi$
$373$		−	1.82578e10i		−	0.943222i	0.881807	−	0.471611i	$-0.156327\pi$
$374$	−1.44686e10	+	7.25772e9i	−0.739501	+	0.370948i
$375$	−2.00472e9	+	1.02218e10i	−0.101375	+	0.516897i
$376$	−3.57447e9	+	2.01030e10i	−0.178838	+	1.00580i
$377$		−	7.59806e9i		−	0.376129i
$378$	5.99749e9	−	3.00846e9i	0.293767	−	0.147359i
$379$		−	2.08206e10i		−	1.00910i	−0.863382	−	0.504551i	$-0.831658\pi$
$379$		−	2.08206e10i		−	1.00910i	0.863382	−	0.504551i	$-0.168342\pi$
$380$	1.25106e10	+	2.30068e9i	0.599988	+	0.110337i
$381$	1.50587e10			0.714639
$382$	−4.40385e9	−	8.77925e9i	−0.206813	−	0.412291i
$383$	−2.29859e10			−1.06824			−0.534118	−	0.845410i	$-0.679356\pi$
$383$	−2.29859e10			−1.06824			−0.534118	+	0.845410i	$0.679356\pi$
$384$	1.13801e10	−	1.29151e9i	0.523384	−	0.0593981i
$385$	5.95727e9	+	1.20529e10i	0.271147	+	0.548592i
$386$	−5.34462e9	−	1.06547e10i	−0.240751	−	0.479947i
$387$	−6.78249e9			−0.302374
$388$	1.79474e10	+	1.33880e10i	0.791906	+	0.590731i
$389$	−1.60076e10			−0.699083			−0.349541	−	0.936921i	$-0.613663\pi$
$389$	−1.60076e10			−0.699083			−0.349541	+	0.936921i	$0.613663\pi$
$390$	−1.40035e10	−	1.05752e10i	−0.605310	−	0.457119i
$391$		−	1.75284e10i		−	0.749954i
$392$	3.59133e9	−	2.01978e10i	0.152094	−	0.855382i
$393$		−	5.14719e9i		−	0.215774i
$394$	−1.77482e10	−	3.53818e10i	−0.736494	−	1.46823i
$395$	2.07545e10	+	4.19912e10i	0.852560	+	1.72492i
$396$	2.40611e10	+	1.79486e10i	0.978441	+	0.729879i
$397$		−	1.72716e10i		−	0.695299i	−0.937625	−	0.347650i	$-0.886980\pi$
$397$		−	1.72716e10i		−	0.695299i	0.937625	−	0.347650i	$-0.113020\pi$
$398$	−6.18706e9	−	1.23342e10i	−0.246577	−	0.491561i
$399$		−	2.95002e9i		−	0.116395i
$400$	−2.39251e10	−	9.10762e9i	−0.934575	−	0.355767i
$401$	−1.56829e10			−0.606524			−0.303262	−	0.952907i	$-0.598076\pi$
$401$	−1.56829e10			−0.606524			−0.303262	+	0.952907i	$0.598076\pi$
$402$	3.04810e9	−	1.52899e9i	0.116714	−	0.0585462i
$403$	−6.36470e9			−0.241300
$404$	1.65253e10	−	2.21530e10i	0.620332	−	0.831588i
$405$	−5.89965e9	+	2.91595e9i	−0.219284	+	0.108383i
$406$	−2.29776e9	+	1.15260e9i	−0.0845671	+	0.0424205i
$407$	4.25943e10			1.55229
$408$	−7.03746e9	−	1.25132e9i	−0.253966	−	0.0451571i
$409$	−1.05519e8			−0.00377082			−0.00188541	−	0.999998i	$-0.500600\pi$
$409$	−1.05519e8			−0.00377082			−0.00188541	+	0.999998i	$0.500600\pi$
$410$	−1.20963e10	+	1.60177e10i	−0.428072	+	0.566845i
$411$		−	1.27149e10i		−	0.445602i
$412$	−1.47325e10	+	1.97497e10i	−0.511315	+	0.685444i
$413$		−	4.91546e9i		−	0.168952i
$414$	−2.90554e10	+	1.45748e10i	−0.989067	+	0.496136i
$415$	4.90454e10	−	2.42412e10i	1.65351	−	0.817261i
$416$	3.14397e10	−	2.95199e10i	1.04980	−	0.985694i
$417$			1.70707e10i			0.564555i
$418$	2.81238e10	−	1.41075e10i	0.921232	−	0.462108i
$419$		−	1.28448e10i		−	0.416746i	−0.978049	−	0.208373i	$-0.933183\pi$
$419$		−	1.28448e10i		−	0.416746i	0.978049	−	0.208373i	$-0.0668168\pi$
$420$	−1.07380e9	+	5.83908e9i	−0.0345085	+	0.187649i
$421$	−3.08274e10			−0.981315			−0.490658	−	0.871353i	$-0.663243\pi$
$421$	−3.08274e10			−0.981315			−0.490658	+	0.871353i	$0.663243\pi$
$422$	−1.48075e10	−	2.95194e10i	−0.466910	−	0.930804i
$423$	−2.36316e10			−0.738127
$424$	−2.81341e10	−	5.00246e9i	−0.870501	−	0.154782i
$425$	1.26927e10	+	9.70336e9i	0.389042	+	0.297417i
$426$	−6.35768e9	−	1.26743e10i	−0.193046	−	0.384845i
$427$	5.85918e9			0.176249
$428$	1.35239e10	−	1.81294e10i	0.403019	−	0.540268i
$429$	−4.34049e10			−1.28147
$430$	8.62218e9	−	1.14173e10i	0.252199	−	0.333958i
$431$			9.59665e9i			0.278106i	0.990285	+	0.139053i	$0.0444058\pi$
$431$			9.59665e9i			0.278106i	−0.990285	+	0.139053i	$0.955594\pi$
$432$	9.00536e9	+	3.02909e10i	0.258563	+	0.869717i
$433$		−	6.69168e8i		−	0.0190363i	−0.999955	−	0.00951817i	$-0.996970\pi$
$433$		−	6.69168e8i		−	0.0190363i	0.999955	−	0.00951817i	$-0.00302977\pi$
$434$	9.65507e8	+	1.92478e9i	0.0272143	+	0.0542528i
$435$	−4.41635e9	+	2.18282e9i	−0.123341	+	0.0609622i
$436$	7.38030e9	−	9.89368e9i	0.204234	−	0.273787i
$437$			3.40714e10i			0.934254i
$438$	1.01550e10	+	2.02445e10i	0.275921	+	0.550061i
$439$			3.75455e10i			1.01088i	0.862862	+	0.505440i	$0.168670\pi$
$439$			3.75455e10i			1.01088i	−0.862862	+	0.505440i	$0.831330\pi$
$440$	−6.08014e10	+	1.76864e10i	−1.62220	+	0.471876i
$441$	2.37430e10			0.627742
$442$	−2.40578e10	+	1.20679e10i	−0.630329	+	0.316185i
$443$	1.19986e10			0.311542			0.155771	−	0.987793i	$-0.450214\pi$
$443$	1.19986e10			0.311542			0.155771	+	0.987793i	$0.450214\pi$
$444$	1.50763e10	+	1.12464e10i	0.387939	+	0.289388i
$445$	6.42400e9	−	3.17512e9i	0.163819	−	0.0809693i
$446$	−3.56909e10	+	1.79033e10i	−0.902025	+	0.452473i
$447$	3.28871e10			0.823751
$448$	−1.36966e10	−	5.02973e9i	−0.340016	−	0.124863i
$449$	6.86153e10			1.68825			0.844123	−	0.536150i	$-0.180122\pi$
$449$	6.86153e10			1.68825			0.844123	+	0.536150i	$0.180122\pi$
$450$	5.53061e9	−	2.91079e10i	0.134872	−	0.709841i
$451$			4.96482e10i			1.20004i
$452$	−3.77279e10	−	2.81436e10i	−0.903876	−	0.674257i
$453$		−	2.18235e10i		−	0.518240i
$454$	5.79711e10	−	2.90795e10i	1.36455	−	0.684483i
$455$	9.90554e9	+	2.00412e10i	0.231117	+	0.467604i
$456$	1.36793e10	+	2.43229e9i	0.316377	+	0.0562544i
$457$			5.08092e10i			1.16487i	0.812877	+	0.582435i	$0.197900\pi$
$457$			5.08092e10i			1.16487i	−0.812877	+	0.582435i	$0.802100\pi$
$458$	−3.27183e10	+	1.64122e10i	−0.743583	+	0.372996i
$459$		−	1.97222e10i		−	0.444328i
$460$	1.24019e10	−	6.74387e10i	0.276986	−	1.50618i
$461$	−3.46473e10			−0.767124			−0.383562	−	0.923515i	$-0.625303\pi$
$461$	−3.46473e10			−0.767124			−0.383562	+	0.923515i	$0.625303\pi$
$462$	6.58440e9	+	1.31263e10i	0.144527	+	0.288120i
$463$	−4.92524e10			−1.07178			−0.535888	−	0.844289i	$-0.680023\pi$
$463$	−4.92524e10			−1.07178			−0.535888	+	0.844289i	$0.680023\pi$
$464$	−3.45014e9	−	1.16051e10i	−0.0744329	−	0.250367i
$465$	1.82849e9	+	3.69946e9i	0.0391094	+	0.0791274i
$466$	2.24651e10	+	4.47851e10i	0.476392	+	0.949707i
$467$	7.83687e9			0.164769			0.0823844	−	0.996601i	$-0.473746\pi$
$467$	7.83687e9			0.164769			0.0823844	+	0.996601i	$0.473746\pi$
$468$	4.00080e10	+	2.98444e10i	0.833994	+	0.622127i
$469$	−4.34433e9			−0.0897907
$470$	3.00414e10	−	3.97804e10i	0.615644	−	0.815225i
$471$		−	3.63246e9i		−	0.0738103i
$472$	2.27931e10	+	4.05279e9i	0.459235	+	0.0816556i
$473$		−	3.53890e10i		−	0.707007i
$474$	2.29394e10	+	4.57307e10i	0.454432	+	0.905929i
$475$	−2.46718e10	−	1.88613e10i	−0.484649	−	0.370507i
$476$	7.29900e9	+	5.44477e9i	0.142179	+	0.106060i
$477$		−	3.30723e10i		−	0.638838i
$478$	1.19202e10	+	2.37633e10i	0.228334	+	0.455193i
$479$			2.94112e10i			0.558689i	0.960191	+	0.279345i	$0.0901172\pi$
$479$			2.94112e10i			0.558689i	−0.960191	+	0.279345i	$0.909883\pi$
$480$	−2.61906e10	−	9.79355e9i	−0.493378	−	0.184491i
$481$	7.08244e10			1.32313
$482$	2.29336e10	−	1.15039e10i	0.424897	−	0.213137i
$483$	−1.59022e10			−0.292193
$484$	−6.08390e10	+	8.15579e10i	−1.10867	+	1.48622i
$485$	−2.42216e10	−	4.90059e10i	−0.437760	−	0.885689i
$486$	−5.16707e10	+	2.59191e10i	−0.926189	+	0.464595i
$487$	−5.85444e10			−1.04080			−0.520402	−	0.853921i	$-0.674218\pi$
$487$	−5.85444e10			−1.04080			−0.520402	+	0.853921i	$0.674218\pi$
$488$	−4.83089e9	+	2.71691e10i	−0.0851820	+	0.479068i
$489$	−1.19160e10			−0.208399
$490$	−3.01831e10	+	3.99680e10i	−0.523576	+	0.693310i
$491$		−	8.05466e10i		−	1.38587i	−0.721002	−	0.692933i	$-0.756318\pi$
$491$		−	8.05466e10i		−	1.38587i	0.721002	−	0.692933i	$-0.243682\pi$
$492$	−1.31088e10	+	1.75731e10i	−0.223719	+	0.299907i
$493$			7.55597e9i			0.127909i
$494$	4.67633e10	−	2.34574e10i	0.785231	−	0.393887i
$495$	−3.24726e10	−	6.56997e10i	−0.540875	−	1.09431i
$496$	−9.72129e9	+	2.89010e9i	−0.160619	+	0.0477514i
$497$			1.80642e10i			0.296069i
$498$	5.34131e10	−	2.67931e10i	0.868421	−	0.435617i
$499$			2.25270e10i			0.363330i	0.983360	+	0.181665i	$0.0581487\pi$
$499$			2.25270e10i			0.363330i	−0.983360	+	0.181665i	$0.941851\pi$
$500$	4.19683e10	+	4.63132e10i	0.671493	+	0.741011i
$501$	−1.83763e10			−0.291681
$502$	4.43902e10	+	8.84937e10i	0.698992	+	1.39347i
$503$	4.17996e10			0.652981			0.326491	−	0.945200i	$-0.394134\pi$
$503$	4.17996e10			0.652981			0.326491	+	0.945200i	$0.394134\pi$
$504$	2.95629e9	−	1.66263e10i	0.0458167	−	0.257676i
$505$	−6.04897e10	+	2.98976e10i	−0.930070	+	0.459695i
$506$	−7.60468e10	−	1.51603e11i	−1.16006	−	2.31262i
$507$	−3.73680e10			−0.565547
$508$	5.40243e10	−	7.24224e10i	0.811212	−	1.08747i
$509$	1.06239e10			0.158276			0.0791378	−	0.996864i	$-0.474783\pi$
$509$	1.06239e10			0.158276			0.0791378	+	0.996864i	$0.474783\pi$
$510$	1.39259e10	+	1.05166e10i	0.205846	+	0.155451i
$511$		−	2.88537e10i		−	0.423173i
$512$	3.46158e10	−	5.93643e10i	0.503726	−	0.863864i
$513$			3.83357e10i			0.553521i
$514$	4.45062e10	+	8.87250e10i	0.637629	+	1.27114i
$515$	5.39273e10	−	2.66540e10i	0.766619	−	0.378908i
$516$	9.34391e9	−	1.25260e10i	0.131804	−	0.176691i
$517$		−	1.23303e11i		−	1.72588i
$518$	−1.07438e10	−	2.14183e10i	−0.149225	−	0.297486i
$519$		−	2.90661e10i		−	0.400606i
$520$	−1.01099e11	+	2.94083e10i	−1.38271	+	0.402213i
$521$	−6.29819e10			−0.854800			−0.427400	−	0.904063i	$-0.640570\pi$
$521$	−6.29819e10			−0.854800			−0.427400	+	0.904063i	$0.640570\pi$
$522$	1.25249e10	−	6.28276e9i	0.168692	−	0.0846191i
$523$	−2.56642e10			−0.343021			−0.171511	−	0.985182i	$-0.554865\pi$
$523$	−2.56642e10			−0.343021			−0.171511	+	0.985182i	$0.554865\pi$
$524$	−2.47547e10	−	1.84660e10i	−0.328346	−	0.244933i
$525$	8.80316e9	−	1.15151e10i	0.115878	−	0.151576i
$526$	2.80779e10	−	1.40844e10i	0.366793	−	0.183991i
$527$	6.32945e9			0.0820584
$528$	−6.62957e10	+	1.97094e10i	−0.853001	+	0.253593i
$529$	1.05353e11			1.34531
$530$	5.56724e10	+	4.20428e10i	0.705564	+	0.532830i
$531$			2.67938e10i			0.337021i
$532$	−1.41877e10	−	1.05835e10i	−0.177119	−	0.132124i
$533$			8.25532e10i			1.02288i
$534$	6.99608e9	−	3.50937e9i	0.0860379	−	0.0431583i
$535$	−4.95031e10	+	2.44673e10i	−0.604250	+	0.298656i
$536$	3.58189e9	−	2.01447e10i	0.0433964	−	0.244063i
$537$		−	7.94490e10i		−	0.955413i
$538$	−9.03288e10	+	4.53107e10i	−1.07819	+	0.540843i
$539$			1.23884e11i			1.46778i
$540$	1.39541e10	−	7.58790e10i	0.164107	−	0.892374i
$541$	7.25189e10			0.846569			0.423285	−	0.905997i	$-0.360877\pi$
$541$	7.25189e10			0.846569			0.423285	+	0.905997i	$0.360877\pi$
$542$	−3.38078e10	−	6.73972e10i	−0.391760	−	0.780989i
$543$	4.03206e10			0.463797
$544$	−3.12655e10	+	2.93564e10i	−0.357002	+	0.335203i
$545$	−2.70150e10	+	1.33524e10i	−0.306210	+	0.151347i
$546$	1.09483e10	+	2.18259e10i	0.123190	+	0.245585i
$547$	−2.29110e10			−0.255914			−0.127957	−	0.991780i	$-0.540842\pi$
$547$	−2.29110e10			−0.255914			−0.127957	+	0.991780i	$0.540842\pi$
$548$	−6.11506e10	−	4.56160e10i	−0.678077	−	0.505819i
$549$	−3.19380e10			−0.351575
$550$	1.51877e11	+	2.88571e10i	1.65974	+	0.315356i
$551$		−	1.46872e10i		−	0.159343i
$552$	1.31114e10	−	7.37390e10i	0.141219	−	0.794220i
$553$		−	6.51781e10i		−	0.696949i
$554$	−7.22884e8	−	1.44110e9i	−0.00767414	−	0.0152987i
$555$	−2.03469e10	−	4.11664e10i	−0.214450	−	0.433882i
$556$	8.20989e10	+	6.12426e10i	0.859089	+	0.640847i
$557$			1.28630e11i			1.33636i	0.744001	+	0.668178i	$0.232926\pi$
$557$			1.28630e11i			1.33636i	−0.744001	+	0.668178i	$0.767074\pi$
$558$	−5.26291e9	−	1.04918e10i	−0.0542861	−	0.108222i
$559$		−	5.88436e10i		−	0.602632i
$560$	2.42298e10	+	2.61125e10i	0.246376	+	0.265520i
$561$	4.31645e10			0.435788
$562$	6.09754e10	−	3.05865e10i	0.611237	−	0.306609i
$563$	1.71738e11			1.70936			0.854678	−	0.519159i	$-0.173755\pi$
$563$	1.71738e11			1.70936			0.854678	+	0.519159i	$0.173755\pi$
$564$	3.25561e10	−	4.36432e10i	0.321748	−	0.431320i
$565$	5.09173e10	+	1.03017e11i	0.499656	+	1.01092i
$566$	−1.66270e11	+	8.34044e10i	−1.62012	+	0.812686i
$567$	9.15734e9			0.0886007
$568$	−8.37640e10	−	1.48939e10i	−0.804756	−	0.143092i
$569$	−8.20809e10			−0.783056			−0.391528	−	0.920166i	$-0.628053\pi$
$569$	−8.20809e10			−0.783056			−0.391528	+	0.920166i	$0.628053\pi$
$570$	−2.70690e10	−	2.04420e10i	−0.256432	−	0.193653i
$571$			1.07462e11i			1.01090i	0.862855	+	0.505452i	$0.168674\pi$
$571$			1.07462e11i			1.01090i	−0.862855	+	0.505452i	$0.831326\pi$
$572$	−1.55719e11	+	2.08750e11i	−1.45465	+	1.95003i
$573$			2.61914e10i			0.242963i
$574$	2.49653e10	−	1.25231e10i	0.229980	−	0.115362i
$575$	−1.01672e11	+	1.32995e11i	−0.930105	+	1.21664i
$576$	7.46590e10	+	2.74167e10i	0.678254	+	0.249072i
$577$			3.37727e10i			0.304693i	0.988327	+	0.152346i	$0.0486830\pi$
$577$			3.37727e10i			0.304693i	−0.988327	+	0.152346i	$0.951317\pi$
$578$	−7.58396e10	+	3.80427e10i	−0.679493	+	0.340847i
$579$			3.17866e10i			0.282832i
$580$	−5.34610e9	+	2.90709e10i	−0.0472417	+	0.256889i
$581$	−7.61276e10			−0.668094
$582$	−2.67714e10	−	5.33700e10i	−0.233335	−	0.465163i
$583$	1.72561e11			1.49372
$584$	1.33795e11	+	2.37898e10i	1.15024	+	0.204522i
$585$	−5.39944e10	−	1.09243e11i	−0.461026	−	0.932761i
$586$	2.69528e10	+	5.37316e10i	0.228567	+	0.455659i
$587$	1.01250e11			0.852793			0.426396	−	0.904536i	$-0.359783\pi$
$587$	1.01250e11			0.852793			0.426396	+	0.904536i	$0.359783\pi$
$588$	−3.27096e10	+	4.38489e10i	−0.273631	+	0.366817i
$589$	−1.23031e10			−0.102224
$590$	−4.51036e10	−	3.40614e10i	−0.372223	−	0.281096i
$591$			1.05555e11i			0.865229i
$592$	1.08175e11	−	3.21601e10i	0.880728	−	0.261836i
$593$			1.86134e11i			1.50525i	0.658451	+	0.752624i	$0.271212\pi$
$593$			1.86134e11i			1.50525i	−0.658451	+	0.752624i	$0.728788\pi$
$594$	−8.55645e10	−	1.70577e11i	−0.687303	−	1.37017i
$595$	−9.85067e9	−	1.99302e10i	−0.0785955	−	0.159017i
$596$	1.17986e11	−	1.58166e11i	0.935069	−	1.25351i
$597$			3.67969e10i			0.289677i
$598$	−1.26448e11	−	2.52080e11i	−0.988798	−	1.97121i
$599$		−	7.77748e10i		−	0.604131i	−0.953287	−	0.302066i	$-0.902324\pi$
$599$		−	7.77748e10i		−	0.604131i	0.953287	−	0.302066i	$-0.0976762\pi$
$600$	4.61377e10	+	5.03146e10i	0.356001	+	0.388230i
$601$	−1.76175e11			−1.35035			−0.675176	−	0.737657i	$-0.735932\pi$
$601$	−1.76175e11			−1.35035			−0.675176	+	0.737657i	$0.735932\pi$
$602$	−1.77952e10	+	8.92640e9i	−0.135493	+	0.0679658i
$603$	2.36806e10			0.179112
$604$	−1.04957e11	−	7.82937e10i	−0.788611	−	0.588273i
$605$	2.22697e11	−	1.10070e11i	1.66223	−	0.821574i
$606$	−6.58764e10	+	3.30449e10i	−0.488472	+	0.245027i
$607$	−1.04822e11			−0.772143			−0.386071	−	0.922469i	$-0.626168\pi$
$607$	−1.04822e11			−0.772143			−0.386071	+	0.922469i	$0.626168\pi$
$608$	6.07736e10	−	5.70626e10i	0.444734	−	0.417578i
$609$	6.85499e9			0.0498353
$610$	4.06009e10	−	5.37630e10i	0.293235	−	0.388297i
$611$		−	2.05023e11i		−	1.47109i
$612$	−3.97863e10	−	2.96791e10i	−0.283614	−	0.211565i
$613$		−	1.64383e10i		−	0.116417i	−0.998304	−	0.0582085i	$-0.981461\pi$
$613$		−	1.64383e10i		−	0.116417i	0.998304	−	0.0582085i	$-0.0185388\pi$
$614$	−8.29987e10	+	4.16338e10i	−0.583980	+	0.292936i
$615$	4.79838e10	−	2.37164e10i	0.335424	−	0.165786i
$616$	8.67511e10	+	1.54250e10i	0.602493	+	0.107128i
$617$		−	2.58887e11i		−	1.78636i	−0.449698	−	0.893181i	$-0.648468\pi$
$617$		−	2.58887e11i		−	1.78636i	0.449698	−	0.893181i	$-0.351532\pi$
$618$	5.87296e10	−	2.94599e10i	0.402628	−	0.201966i
$619$		−	1.40280e11i		−	0.955508i	−0.878494	−	0.477754i	$-0.841451\pi$
$619$		−	1.40280e11i		−	0.955508i	0.878494	−	0.477754i	$-0.158549\pi$
$620$	2.43519e10	+	4.47829e9i	0.164803	+	0.0303072i
$621$	2.06650e11			1.38953
$622$	8.76256e10	+	1.74685e11i	0.585422	+	1.16706i
$623$	−9.97123e9			−0.0661906
$624$	−1.10234e11	+	3.27721e10i	−0.727072	+	0.216155i
$625$	−4.00202e10	−	1.47246e11i	−0.262277	−	0.964993i
$626$	−6.45522e10	−	1.28687e11i	−0.420352	−	0.837990i
$627$	−8.39026e10			−0.542882
$628$	−1.74698e10	−	1.30318e10i	−0.112318	−	0.0837847i
$629$	−7.04320e10			−0.449953
$630$	−2.48459e10	+	3.29005e10i	−0.157722	+	0.208853i
$631$			3.75788e10i			0.237042i	0.992952	+	0.118521i	$0.0378153\pi$
$631$			3.75788e10i			0.237042i	−0.992952	+	0.118521i	$0.962185\pi$
$632$	3.02232e11	+	5.37392e10i	1.89440	+	0.336840i
$633$			8.80662e10i			0.548523i
$634$	−1.61561e10	−	3.22079e10i	−0.0999955	−	0.199345i
$635$	−1.97752e11	+	9.77406e10i	−1.21626	+	0.601146i
$636$	6.10784e10	+	4.55621e10i	0.373301	+	0.278468i
$637$			2.05990e11i			1.25109i
$638$	3.27816e10	+	6.53514e10i	0.197855	+	0.394432i
$639$		−	9.84666e10i		−	0.590589i
$640$	−1.41062e11	+	9.08245e10i	−0.840793	+	0.541356i
$641$	−9.09734e10			−0.538868			−0.269434	−	0.963019i	$-0.586837\pi$
$641$	−9.09734e10			−0.538868			−0.269434	+	0.963019i	$0.586837\pi$
$642$	−5.39115e10	+	2.70430e10i	−0.317352	+	0.159190i
$643$	3.82679e10			0.223868			0.111934	−	0.993716i	$-0.464296\pi$
$643$	3.82679e10			0.223868			0.111934	+	0.993716i	$0.464296\pi$
$644$	−5.70507e10	+	7.64794e10i	−0.331679	+	0.444633i
$645$	−3.42027e10	+	1.69050e10i	−0.197616	+	0.0976733i
$646$	−4.65043e10	+	2.33274e10i	−0.267032	+	0.133948i
$647$	−1.00170e11			−0.571635			−0.285818	−	0.958284i	$-0.592265\pi$
$647$	−1.00170e11			−0.571635			−0.285818	+	0.958284i	$0.592265\pi$
$648$	−7.55021e9	+	4.24628e10i	−0.0428212	+	0.240829i
$649$	−1.39802e11			−0.788016
$650$	2.52535e11	+	4.79825e10i	1.41471	+	0.268800i
$651$		−	5.74225e9i		−	0.0319711i
$652$	−4.27498e10	+	5.73083e10i	−0.236561	+	0.317123i
$653$		−	1.26162e11i		−	0.693869i	−0.937889	−	0.346934i	$-0.887223\pi$
$653$		−	1.26162e11i		−	0.693869i	0.937889	−	0.346934i	$-0.112777\pi$
$654$	−2.94208e10	+	1.47581e10i	−0.160821	+	0.0806712i
$655$	3.34087e10	+	6.75934e10i	0.181507	+	0.367231i
$656$	3.74859e10	+	1.26090e11i	0.202420	+	0.680871i
$657$			1.57279e11i			0.844132i
$658$	−6.20020e10	+	3.11014e10i	−0.330752	+	0.165912i
$659$			1.89374e9i			0.0100410i	0.999987	+	0.00502051i	$0.00159809\pi$
$659$			1.89374e9i			0.0100410i	−0.999987	+	0.00502051i	$0.998402\pi$
$660$	1.66071e11	+	3.05403e10i	0.875222	+	0.160953i
$661$	2.06198e11			1.08014			0.540068	−	0.841622i	$-0.318399\pi$
$661$	2.06198e11			1.08014			0.540068	+	0.841622i	$0.318399\pi$
$662$	1.20933e10	+	2.41084e10i	0.0629668	+	0.125527i
$663$	7.17724e10			0.371453
$664$	6.27671e10	−	3.53005e11i	0.322894	−	1.81597i
$665$	1.91476e10	+	3.87400e10i	0.0979102	+	0.198095i
$666$	5.85639e10	+	1.16750e11i	0.297669	+	0.593415i
$667$	−7.91720e10			−0.400008
$668$	−6.59267e10	+	8.83782e10i	−0.331097	+	0.443853i
$669$	1.06478e11			0.531563
$670$	−3.01038e10	+	3.98629e10i	−0.149390	+	0.197820i
$671$		−	1.66643e11i		−	0.822047i
$672$	2.66330e10	+	2.83650e10i	0.130600	+	0.139093i
$673$		−	2.75305e11i		−	1.34200i	−0.741455	−	0.671002i	$-0.765864\pi$
$673$		−	2.75305e11i		−	1.34200i	0.741455	−	0.671002i	$-0.234136\pi$
$674$	5.54725e10	+	1.10587e11i	0.268806	+	0.535875i
$675$	−1.14397e11	+	1.49640e11i	−0.551063	+	0.720827i
$676$	−1.34061e11	+	1.79716e11i	−0.641973	+	0.860598i
$677$		−	2.05068e11i		−	0.976208i	−0.872785	−	0.488104i	$-0.837689\pi$
$677$		−	2.05068e11i		−	0.976208i	0.872785	−	0.488104i	$-0.162311\pi$
$678$	5.62774e10	+	1.12191e11i	0.266327	+	0.530934i
$679$			7.60661e10i			0.357859i
$680$	1.00538e11	−	2.92453e10i	0.470215	−	0.136780i
$681$	−1.72947e11			−0.804127
$682$	5.47432e10	−	2.74603e10i	0.253042	−	0.126931i
$683$	−3.92855e11			−1.80530			−0.902649	−	0.430377i	$-0.858380\pi$
$683$	−3.92855e11			−1.80530			−0.902649	+	0.430377i	$0.858380\pi$
$684$	7.73362e10	+	5.76898e10i	0.353312	+	0.263557i
$685$	8.25284e10	+	1.66974e11i	0.374836	+	0.758379i
$686$	1.33996e11	−	6.72151e10i	0.605056	−	0.303508i
$687$	9.76096e10			0.438193
$688$	−2.67198e10	−	8.98763e10i	−0.119256	−	0.401136i
$689$	2.86929e11			1.27320
$690$	−1.10194e11	+	1.45917e11i	−0.486139	+	0.643737i
$691$			1.92324e11i			0.843570i	0.906696	+	0.421785i	$0.138596\pi$
$691$			1.92324e11i			0.843570i	−0.906696	+	0.421785i	$0.861404\pi$
$692$	−1.39789e11	−	1.04277e11i	−0.609606	−	0.454742i
$693$			1.01978e11i			0.442154i
$694$	4.39677e10	−	2.20550e10i	0.189538	−	0.0950758i
$695$	−1.10800e11	−	2.24174e11i	−0.474898	−	0.960828i
$696$	−5.65193e9	+	3.17867e10i	−0.0240857	+	0.135459i
$697$		−	8.20959e10i		−	0.347849i
$698$	1.87182e11	−	9.38942e10i	0.788574	−	0.395564i
$699$		−	1.33609e11i		−	0.559662i
$700$	−2.37982e10	−	8.36491e10i	−0.0991179	−	0.348393i
$701$	2.51795e11			1.04274			0.521369	−	0.853331i	$-0.325421\pi$
$701$	2.51795e11			1.04274			0.521369	+	0.853331i	$0.325421\pi$
$702$	−1.42274e11	−	2.83629e11i	−0.585836	−	1.16789i
$703$	1.36905e11			0.560528
$704$	−1.43052e11	+	3.89549e11i	−0.582377	+	1.58588i
$705$	−1.19169e11	+	5.89004e10i	−0.482400	+	0.238431i
$706$	−4.74529e10	−	9.45993e10i	−0.191005	−	0.380776i
$707$	9.38911e10			0.375791
$708$	−4.94832e10	−	3.69126e10i	−0.196936	−	0.146907i
$709$	−4.10364e11			−1.62400			−0.811998	−	0.583661i	$-0.801620\pi$
$709$	−4.10364e11			−1.62400			−0.811998	+	0.583661i	$0.801620\pi$
$710$	1.65754e11	+	1.25175e11i	0.652277	+	0.492588i
$711$			3.55281e11i			1.39025i
$712$	8.22126e9	−	4.62368e10i	0.0319903	−	0.179915i
$713$			6.63204e10i			0.256619i
$714$	−1.08877e10	−	2.17050e10i	−0.0418930	−	0.0835156i
$715$	5.69998e11	−	2.81727e11i	2.18097	−	1.07796i
$716$	−3.82098e11	−	2.85030e11i	−1.45386	−	1.08452i
$717$		−	7.08938e10i		−	0.268245i
$718$	2.39672e10	+	4.77795e10i	0.0901817	+	0.179781i
$719$			2.36375e11i			0.884474i	0.896898	+	0.442237i	$0.145815\pi$
$719$			2.36375e11i			0.884474i	−0.896898	+	0.442237i	$0.854185\pi$
$720$	−1.32075e11	−	1.42337e11i	−0.491463	−	0.529650i
$721$	−8.37050e10			−0.309749
$722$	−1.52497e11	+	7.64955e10i	−0.561193	+	0.281506i
$723$	−6.84185e10			−0.250392
$724$	1.44654e11	−	1.93916e11i	0.526472	−	0.705764i
$725$	4.38280e10	−	5.73300e10i	0.158635	−	0.207506i
$726$	2.42528e11	−	1.21657e11i	0.873004	−	0.437916i
$727$	1.16942e11			0.418631			0.209316	−	0.977848i	$-0.432876\pi$
$727$	1.16942e11			0.418631			0.209316	+	0.977848i	$0.432876\pi$
$728$	1.44247e11	+	2.56482e10i	0.513547	+	0.0913127i
$729$	8.50669e10			0.301197
$730$	−2.64757e11	−	1.99940e11i	−0.932302	−	0.704058i
$731$			5.85176e10i			0.204936i
$732$	4.39994e10	−	5.89835e10i	0.153251	−	0.205441i
$733$			4.81267e11i			1.66713i	0.552420	+	0.833566i	$0.313704\pi$
$733$			4.81267e11i			1.66713i	−0.552420	+	0.833566i	$0.686296\pi$
$734$	1.37396e11	−	6.89205e10i	0.473358	−	0.237445i
$735$	1.19731e11	−	5.91781e10i	0.410258	−	0.202774i
$736$	−3.07599e11	−	3.27602e11i	−1.04827	−	1.11644i
$737$			1.23558e11i			0.418796i
$738$	−1.36084e11	+	6.82624e10i	−0.458756	+	0.230121i
$739$		−	9.92996e10i		−	0.332943i	−0.986046	−	0.166471i	$-0.946763\pi$
$739$		−	9.92996e10i		−	0.332943i	0.986046	−	0.166471i	$-0.0532374\pi$
$740$	−2.70980e11	−	4.98330e10i	−0.903672	−	0.166184i
$741$	−1.39510e11			−0.462736
$742$	−4.35263e10	−	8.67715e10i	−0.143594	−	0.286260i
$743$	−6.32997e10			−0.207705			−0.103852	−	0.994593i	$-0.533117\pi$
$743$	−6.32997e10			−0.207705			−0.103852	+	0.994593i	$0.533117\pi$
$744$	2.66269e10	+	4.73447e9i	0.0869019	+	0.0154518i
$745$	−4.31877e11	+	2.13459e11i	−1.40196	+	0.692931i
$746$	1.30981e11	+	2.61116e11i	0.422914	+	0.843097i
$747$	4.14966e11			1.33269
$748$	1.54857e11	−	2.07593e11i	0.494679	−	0.663143i
$749$	7.68378e10			0.244145
$750$	−4.46602e10	−	1.60570e11i	−0.141148	−	0.507480i
$751$		−	4.98905e11i		−	1.56840i	−0.620505	−	0.784202i	$-0.713072\pi$
$751$		−	4.98905e11i		−	1.56840i	0.620505	−	0.784202i	$-0.286928\pi$
$752$	−9.30974e10	−	3.13148e11i	−0.291116	−	0.979214i
$753$		−	2.64006e11i		−	0.821171i
$754$	5.45081e10	+	1.08664e11i	0.168646	+	0.336202i
$755$	1.41649e11	+	2.86588e11i	0.435938	+	0.882003i
$756$	−6.41909e10	+	8.60513e10i	−0.196511	+	0.263433i
$757$		−	1.79684e11i		−	0.547174i	−0.961847	−	0.273587i	$-0.911790\pi$
$757$		−	1.79684e11i		−	0.547174i	0.961847	−	0.273587i	$-0.0882101\pi$
$758$	1.49365e11	+	2.97766e11i	0.452453	+	0.901984i
$759$			4.52281e11i			1.36283i
$760$	−1.95425e11	+	5.68467e10i	−0.585770	+	0.170393i
$761$	−3.04576e11			−0.908148			−0.454074	−	0.890964i	$-0.650030\pi$
$761$	−3.04576e11			−0.908148			−0.454074	+	0.890964i	$0.650030\pi$
$762$	−2.15362e11	+	1.08030e11i	−0.638778	+	0.320424i
$763$	4.19323e10			0.123723
$764$	1.25964e11	+	9.39640e10i	0.369719	+	0.275796i
$765$	5.36953e10	+	1.08638e11i	0.156780	+	0.317202i
$766$	3.28734e11	−	1.64900e11i	0.954839	−	0.478966i
$767$	−2.32458e11			−0.671682
$768$	−1.53488e11	+	1.00111e11i	−0.441193	+	0.287763i
$769$	2.22920e11			0.637446			0.318723	−	0.947848i	$-0.396746\pi$
$769$	2.22920e11			0.637446			0.318723	+	0.947848i	$0.396746\pi$
$770$	−1.71665e11	−	1.29639e11i	−0.488337	−	0.368783i
$771$		−	2.64696e11i		−	0.749082i
$772$	1.52873e11	+	1.14037e11i	0.430389	+	0.321053i
$773$		−	5.59182e11i		−	1.56616i	−0.621924	−	0.783078i	$-0.713649\pi$
$773$		−	5.59182e11i		−	1.56616i	0.621924	−	0.783078i	$-0.286351\pi$
$774$	9.70001e10	−	4.86572e10i	0.270277	−	0.135576i
$775$	−4.80239e10	−	3.67136e10i	−0.133122	−	0.101770i
$776$	−3.52720e11	−	6.27164e10i	−0.972710	−	0.172955i
$777$			6.38979e10i			0.175308i
$778$	2.28934e11	−	1.14838e11i	0.624873	−	0.313449i
$779$			1.59577e11i			0.433332i
$780$	2.76137e11	+	5.07814e10i	0.746013	+	0.137191i
$781$	5.13770e11			1.38091
$782$	1.25748e11	+	2.50683e11i	0.336258	+	0.670345i
$783$	−8.90808e10			−0.236994
$784$	9.35363e10	+	3.14624e11i	0.247580	+	0.832775i
$785$	2.35770e10	+	4.77018e10i	0.0620884	+	0.125619i
$786$	3.69256e10	+	7.36128e10i	0.0967471	+	0.192869i
$787$	−1.13289e11			−0.295318			−0.147659	−	0.989038i	$-0.547174\pi$
$787$	−1.13289e11			−0.295318			−0.147659	+	0.989038i	$0.547174\pi$
$788$	5.07654e11	+	3.78690e11i	1.31663	+	0.982152i
$789$	−8.37655e10			−0.216151
$790$	−5.98065e11	−	4.51648e11i	−1.53547	−	1.15956i
$791$		−	1.59902e11i		−	0.408458i
$792$	−4.72874e11	−	8.40807e10i	−1.20183	−	0.213696i
$793$		−	2.77088e11i		−	0.700689i
$794$	1.23906e11	+	2.47011e11i	0.311752	+	0.621491i
$795$	−8.24308e10	−	1.66777e11i	−0.206358	−	0.417510i
$796$	1.76969e11	+	1.32012e11i	0.440804	+	0.328823i
$797$			7.63543e11i			1.89234i	0.323663	+	0.946172i	$0.395086\pi$
$797$			7.63543e11i			1.89234i	−0.323663	+	0.946172i	$0.604914\pi$
$798$	2.11633e10	+	4.21899e10i	0.0521882	+	0.104039i
$799$			2.03888e11i			0.500269i
$800$	4.07504e11	−	4.13842e10i	0.994883	−	0.101036i
$801$	5.43525e10			0.132035
$802$	2.24289e11	−	1.12508e11i	0.542140	−	0.271948i
$803$	−8.20637e11			−1.97374
$804$	−3.26237e10	+	4.37337e10i	−0.0780744	+	0.104663i
$805$	2.08830e11	−	1.03216e11i	0.497289	−	0.245790i
$806$	9.10252e10	−	4.56600e10i	0.215686	−	0.108192i
$807$	2.69480e11			0.635379
$808$	−7.74130e10	+	4.35375e11i	−0.181622	+	1.02145i
$809$	4.67881e11			1.09230			0.546149	−	0.837688i	$-0.316093\pi$
$809$	4.67881e11			1.09230			0.546149	+	0.837688i	$0.316093\pi$
$810$	6.34553e10	−	8.40264e10i	0.147410	−	0.195198i
$811$			6.66951e11i			1.54174i	0.636994	+	0.770869i	$0.280178\pi$
$811$			6.66951e11i			1.54174i	−0.636994	+	0.770869i	$0.719822\pi$
$812$	2.45929e10	−	3.29681e10i	0.0565699	−	0.0758349i
$813$			2.01068e11i			0.460237i
$814$	−6.09165e11	+	3.05569e11i	−1.38751	+	0.696004i
$815$	1.56482e11	−	7.73428e10i	0.354678	−	0.175303i
$816$	1.09623e11	−	3.25906e10i	0.247254	−	0.0735074i
$817$		−	1.13746e11i		−	0.255298i
$818$	1.50908e9	−	7.56985e8i	0.00337054	−	0.00169073i
$819$			1.69565e11i			0.376879i
$820$	5.80856e10	−	3.15856e11i	0.128473	−	0.698608i
$821$	−4.34647e11			−0.956674			−0.478337	−	0.878176i	$-0.658760\pi$
$821$	−4.34647e11			−0.956674			−0.478337	+	0.878176i	$0.658760\pi$
$822$	9.12163e10	+	1.81843e11i	0.199795	+	0.398300i
$823$	−6.53323e11			−1.42406			−0.712030	−	0.702149i	$-0.752224\pi$
$823$	−6.53323e11			−1.42406			−0.712030	+	0.702149i	$0.752224\pi$
$824$	6.90147e10	−	3.88142e11i	0.149704	−	0.841941i
$825$	−3.27506e11	−	2.50373e11i	−0.706973	−	0.540471i
$826$	3.52632e10	+	7.02987e10i	0.0757534	+	0.151017i
$827$	8.42913e10			0.180203			0.0901013	−	0.995933i	$-0.471281\pi$
$827$	8.42913e10			0.180203			0.0901013	+	0.995933i	$0.471281\pi$
$828$	3.10979e11	−	4.16884e11i	0.661622	−	0.886939i
$829$	1.67984e11			0.355672			0.177836	−	0.984060i	$-0.443090\pi$
$829$	1.67984e11			0.355672			0.177836	+	0.984060i	$0.443090\pi$
$830$	−5.27522e11	+	6.98535e11i	−1.11155	+	1.47189i
$831$			4.29928e9i			0.00901553i
$832$	−2.37862e11	+	6.47728e11i	−0.496401	+	1.35176i
$833$		−	2.04849e11i		−	0.425455i
$834$	−1.22464e11	−	2.44137e11i	−0.253130	−	0.504626i
$835$	2.41320e11	−	1.19274e11i	0.496417	−	0.245359i
$836$	−3.01008e11	+	4.03517e11i	−0.616245	+	0.826108i
$837$			7.46207e10i			0.152040i
$838$	9.21479e10	+	1.83701e11i	0.186857	+	0.372507i
$839$		−	8.94664e11i		−	1.80556i	−0.430102	−	0.902780i	$-0.641523\pi$
$839$		−	8.94664e11i		−	1.80556i	0.430102	−	0.902780i	$-0.358477\pi$
$840$	−2.65322e10	−	9.12113e10i	−0.0532913	−	0.183203i
$841$	−4.66118e11			−0.931776
$842$	4.40880e11	−	2.21154e11i	0.877146	−	0.439994i
$843$	−1.81910e11			−0.360202
$844$	4.23542e11	+	3.15946e11i	0.834692	+	0.622648i
$845$	4.90721e11	−	2.42543e11i	0.962516	−	0.475732i
$846$	3.37968e11	−	1.69532e11i	0.659773	−	0.330955i
$847$	−3.45666e11			−0.671619
$848$	4.38248e11	−	1.30289e11i	0.847494	−	0.251956i
$849$	4.96039e11			0.954739
$850$	−2.51136e11	−	4.77167e10i	−0.481098	−	0.0914103i
$851$		−	7.37991e11i		−	1.40713i
$852$	1.81850e11	+	1.35653e11i	0.345107	+	0.257437i
$853$		−	1.57864e11i		−	0.298186i	−0.988823	−	0.149093i	$-0.952365\pi$
$853$		−	1.57864e11i		−	0.298186i	0.988823	−	0.149093i	$-0.0476353\pi$
$854$	−8.37954e10	+	4.20334e10i	−0.157539	+	0.0790248i
$855$	−1.04372e11	−	2.11169e11i	−0.195308	−	0.395154i
$856$	−6.33527e10	+	3.56299e11i	−0.117997	+	0.663619i
$857$			1.15753e10i			0.0214590i	0.999942	+	0.0107295i	$0.00341538\pi$
$857$			1.15753e10i			0.0214590i	−0.999942	+	0.0107295i	$0.996585\pi$
$858$	6.20758e11	−	3.11385e11i	1.14544	−	0.574577i
$859$		−	5.96689e10i		−	0.109591i	−0.998498	−	0.0547956i	$-0.982549\pi$
$859$		−	5.96689e10i		−	0.109591i	0.998498	−	0.0547956i	$-0.0174507\pi$
$860$	−4.14032e10	+	2.25141e11i	−0.0756903	+	0.411586i
$861$	−7.44797e10			−0.135527
$862$	−6.88458e10	−	1.37247e11i	−0.124695	−	0.248584i
$863$	−1.49504e11			−0.269532			−0.134766	−	0.990877i	$-0.543028\pi$
$863$	−1.49504e11			−0.269532			−0.134766	+	0.990877i	$0.543028\pi$
$864$	−3.46096e11	−	3.68604e11i	−0.621072	−	0.661462i
$865$	1.88658e11	+	3.81699e11i	0.336986	+	0.681800i
$866$	4.80057e9	+	9.57014e9i	0.00853535	+	0.0170156i
$867$	2.26255e11			0.400425
$868$	−2.76165e10	−	2.06008e10i	−0.0486508	−	0.0362916i
$869$	−1.85375e12			−3.25067
$870$	4.75013e10	−	6.29004e10i	0.0829140	−	0.109793i
$871$			2.05449e11i			0.356969i
$872$	−3.45731e10	+	1.94441e11i	−0.0597961	+	0.336296i
$873$		−	4.14631e11i		−	0.713846i
$874$	−2.44427e11	−	4.87275e11i	−0.418893	−	0.835080i
$875$	−4.08632e10	+	2.08356e11i	−0.0697108	+	0.355446i
$876$	−2.90466e11	−	2.16676e11i	−0.493263	−	0.367955i
$877$		−	8.95446e11i		−	1.51370i	−0.653587	−	0.756852i	$-0.726736\pi$
$877$		−	8.95446e11i		−	1.51370i	0.653587	−	0.756852i	$-0.273264\pi$
$878$	−2.69349e11	−	5.36959e11i	−0.453250	−	0.903573i
$879$		−	1.60299e11i		−	0.268519i
$880$	7.42675e11	−	6.89129e11i	1.23842	−	1.14913i
$881$	9.41351e11			1.56260			0.781300	−	0.624155i	$-0.214557\pi$
$881$	9.41351e11			1.56260			0.781300	+	0.624155i	$0.214557\pi$
$882$	−3.39562e11	+	1.70331e11i	−0.561106	+	0.281462i
$883$	8.12182e11			1.33601			0.668006	−	0.744156i	$-0.267148\pi$
$883$	8.12182e11			1.33601			0.668006	+	0.744156i	$0.267148\pi$
$884$	2.57490e11	−	3.45179e11i	0.421649	−	0.565243i
$885$	6.67821e10	+	1.35116e11i	0.108865	+	0.220258i
$886$	−1.71599e11	+	8.60775e10i	−0.278471	+	0.139687i
$887$	4.35414e11			0.703409			0.351704	−	0.936111i	$-0.385602\pi$
$887$	4.35414e11			0.703409			0.351704	+	0.936111i	$0.385602\pi$
$888$	−2.96296e11	−	5.26837e10i	−0.476512	−	0.0847275i
$889$	3.06947e11			0.491424
$890$	−6.90951e10	+	9.14946e10i	−0.110125	+	0.145826i
$891$		−	2.60447e11i		−	0.413246i
$892$	3.81999e11	−	5.12089e11i	0.603396	−	0.808884i
$893$		−	3.96314e11i		−	0.623209i
$894$	−4.70337e11	+	2.35930e11i	−0.736308	+	0.369346i
$895$	5.15676e11	+	1.04333e12i	0.803683	+	1.62604i
$896$	2.31965e11	−	2.63254e10i	0.359908	−	0.0408454i
$897$			7.52036e11i			1.16163i
$898$	−9.81306e11	+	4.92242e11i	−1.50903	+	0.756961i
$899$		−	2.85888e10i		−	0.0437680i
$900$	1.29722e11	+	4.55965e11i	0.197717	+	0.694963i
$901$	−2.85339e11			−0.432975
$902$	−3.56173e11	−	7.10046e11i	−0.538065	−	1.07266i
$903$	5.30888e10			0.0798458
$904$	7.41468e11	+	1.31839e11i	1.11025	+	0.197410i
$905$	−5.29494e11	+	2.61707e11i	−0.789345	+	0.390141i
$906$	1.56560e11	+	3.12110e11i	0.232364	+	0.463227i
$907$	−8.59055e11			−1.26938			−0.634690	−	0.772766i	$-0.718872\pi$
$907$	−8.59055e11			−1.26938			−0.634690	+	0.772766i	$0.718872\pi$
$908$	−6.20463e11	+	8.31763e11i	−0.912793	+	1.22365i
$909$	−5.11793e11			−0.749617
$910$	−2.85439e11	−	2.15559e11i	−0.416244	−	0.314340i
$911$			9.78674e11i			1.42090i	0.703746	+	0.710452i	$0.251509\pi$
$911$			9.78674e11i			1.42090i	−0.703746	+	0.710452i	$0.748491\pi$
$912$	−2.13085e11	+	6.33491e10i	−0.308016	+	0.0915717i
$913$			2.16517e12i			3.11608i
$914$	−3.64502e11	−	7.26650e11i	−0.522294	−	1.04122i
$915$	−1.61057e11	+	7.96037e10i	−0.229770	+	0.113566i
$916$	3.50183e11	−	4.69439e11i	0.497409	−	0.666803i
$917$		−	1.04917e11i		−	0.148378i
$918$	1.41486e11	+	2.82058e11i	0.199224	+	0.397161i
$919$		−	3.76307e11i		−	0.527571i	−0.964581	−	0.263785i	$-0.915029\pi$
$919$		−	3.76307e11i		−	0.527571i	0.964581	−	0.263785i	$-0.0849711\pi$
$920$	3.06435e11	+	1.05345e12i	0.427747	+	1.47049i
$921$	2.47613e11			0.344139
$922$	4.95510e11	−	2.48558e11i	0.685692	−	0.343957i
$923$	8.54278e11			1.17704
$924$	−1.88334e11	−	1.40490e11i	−0.258370	−	0.192734i
$925$	5.34395e11	+	4.08537e11i	0.729954	+	0.558039i
$926$	7.04387e11	−	3.53334e11i	0.958004	−	0.480553i
$927$	4.56270e11			0.617878
$928$	1.32597e11	+	1.41220e11i	0.178789	+	0.190416i
$929$	1.22156e12			1.64003			0.820013	−	0.572345i	$-0.193966\pi$
$929$	1.22156e12			1.64003			0.820013	+	0.572345i	$0.193966\pi$
$930$	−5.26900e10	−	3.97906e10i	−0.0704363	−	0.0531923i
$931$			3.98183e11i			0.530009i
$932$	−6.42571e11	−	4.79333e11i	−0.851643	−	0.635293i
$933$		−	5.21144e11i		−	0.687751i
$934$	−1.12079e11	+	5.62212e10i	−0.147278	+	0.0738776i
$935$	−5.66841e11	+	2.80166e11i	−0.741677	+	0.366580i
$936$	−7.86278e11	−	1.39806e11i	−1.02441	−	0.182148i
$937$		−	5.06116e11i		−	0.656586i	−0.944576	−	0.328293i	$-0.893527\pi$
$937$		−	5.06116e11i		−	0.656586i	0.944576	−	0.328293i	$-0.106473\pi$
$938$	6.21307e10	−	3.11660e10i	0.0802592	−	0.0402596i
$939$			3.83917e11i			0.493827i
$940$	−1.44257e11	+	7.84437e11i	−0.184768	+	1.00472i
$941$	−6.00360e9			−0.00765690			−0.00382845	−	0.999993i	$-0.501219\pi$
$941$	−6.00360e9			−0.00765690			−0.00382845	+	0.999993i	$0.501219\pi$
$942$	2.60590e10	+	5.19498e10i	0.0330944	+	0.0659751i
$943$	8.60207e11			1.08782
$944$	−3.55051e11	+	1.05555e11i	−0.447098	+	0.132920i
$945$	2.34966e11	−	1.16134e11i	0.294631	−	0.145624i
$946$	2.53879e11	+	5.06118e11i	0.317002	+	0.631957i
$947$	3.08522e11			0.383606			0.191803	−	0.981433i	$-0.438567\pi$
$947$	3.08522e11			0.383606			0.191803	+	0.981433i	$0.438567\pi$
$948$	−6.56138e11	−	4.89454e11i	−0.812385	−	0.606008i
$949$	−1.36453e12			−1.68235
$950$	4.88155e11	+	9.27512e10i	0.599327	+	0.113874i
$951$			9.60868e10i			0.117474i
$952$	−1.43448e11	−	2.55061e10i	−0.174641	−	0.0310525i
$953$			6.14491e11i			0.744979i	0.928036	+	0.372489i	$0.121496\pi$
$953$			6.14491e11i			0.744979i	−0.928036	+	0.372489i	$0.878504\pi$
$954$	2.37259e11	+	4.72985e11i	0.286436	+	0.571023i
$955$	−1.69999e11	−	3.43948e11i	−0.204378	−	0.413504i
$956$	−3.40953e11	−	2.54338e11i	−0.408191	−	0.304495i
$957$		−	1.94965e11i		−	0.232439i
$958$	−2.10994e11	−	4.20625e11i	−0.250500	−	0.499383i
$959$		−	2.59174e11i		−	0.306420i
$960$	4.44824e11	−	4.78267e10i	0.523725	−	0.0563100i
$961$	8.28943e11			0.971921
$962$	−1.01290e12	+	5.08090e11i	−1.18268	+	0.593253i
$963$	−4.18838e11			−0.487013
$964$	−2.45458e11	+	3.29049e11i	−0.284229	+	0.381024i
$965$	−2.06316e11	−	4.17424e11i	−0.237916	−	0.481358i
$966$	2.27427e11	−	1.14082e11i	0.261176	−	0.131011i
$967$	−7.29374e11			−0.834150			−0.417075	−	0.908872i	$-0.636945\pi$
$967$	−7.29374e11			−0.834150			−0.417075	+	0.908872i	$0.636945\pi$
$968$	2.85001e11	−	1.60286e12i	0.324597	−	1.82555i
$969$	1.38738e11			0.157362
$970$	6.97972e11	+	5.27096e11i	0.788408	+	0.595392i
$971$			4.05501e11i			0.456158i	0.973643	+	0.228079i	$0.0732444\pi$
$971$			4.05501e11i			0.456158i	−0.973643	+	0.228079i	$0.926756\pi$
$972$	5.53030e11	−	7.41366e11i	0.619561	−	0.830553i
$973$			3.47959e11i			0.388219i
$974$	8.37276e11	−	4.19994e11i	0.930320	−	0.466667i
$975$	−5.44565e11	−	4.16312e11i	−0.602603	−	0.460681i
$976$	−1.25821e11	−	4.23218e11i	−0.138661	−	0.466406i
$977$		−	5.72274e11i		−	0.628096i	−0.949407	−	0.314048i	$-0.898315\pi$
$977$		−	5.72274e11i		−	0.628096i	0.949407	−	0.314048i	$-0.101685\pi$
$978$	1.70418e11	−	8.54848e10i	0.186277	−	0.0934401i
$979$			2.83595e11i			0.308722i
$980$	1.44937e11	−	7.88136e11i	0.157136	−	0.854470i
$981$	−2.28570e11			−0.246799
$982$	5.77837e11	+	1.15194e12i	0.621383	+	1.23875i
$983$	8.31746e11			0.890792			0.445396	−	0.895334i	$-0.353063\pi$
$983$	8.31746e11			0.890792			0.445396	+	0.895334i	$0.353063\pi$
$984$	6.14084e10	−	3.45364e11i	0.0655009	−	0.368380i
$985$	−6.85125e11	−	1.38617e12i	−0.727821	−	1.47255i
$986$	−5.42061e10	−	1.08062e11i	−0.0573509	−	0.114332i
$987$	1.84972e11			0.194912
$988$	−5.00506e11	+	6.70954e11i	−0.525269	+	0.704150i
$989$	−6.13152e11			−0.640889
$990$	9.35735e11	+	7.06651e11i	0.974119	+	0.735638i
$991$		−	1.13988e12i		−	1.18186i	−0.806724	−	0.590928i	$-0.798762\pi$
$991$		−	1.13988e12i		−	1.18186i	0.806724	−	0.590928i	$-0.201238\pi$
$992$	1.18296e11	−	1.11073e11i	0.122159	−	0.114699i
$993$		−	7.19234e10i		−	0.0739729i
$994$	−1.29591e11	−	2.58346e11i	−0.132749	−	0.264641i
$995$	−2.38836e11	−	4.83221e11i	−0.243673	−	0.493007i
$996$	−5.71679e11	+	7.66365e11i	−0.580918	+	0.778750i
$997$			1.49273e11i			0.151078i	0.997143	+	0.0755390i	$0.0240677\pi$
$997$			1.49273e11i			0.151078i	−0.997143	+	0.0755390i	$0.975932\pi$
$998$	−1.61608e11	−	3.22172e11i	−0.162907	−	0.324762i
$999$		−	8.30355e11i		−	0.833685i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	20.9.d.c.19.4	yes	20
4.3	odd	2	inner	20.9.d.c.19.18	yes	20
5.2	odd	4		100.9.b.g.51.7		20
5.3	odd	4		100.9.b.g.51.14		20
5.4	even	2	inner	20.9.d.c.19.17	yes	20
8.3	odd	2		320.9.h.g.319.11		20
8.5	even	2		320.9.h.g.319.9		20
20.3	even	4		100.9.b.g.51.13		20
20.7	even	4		100.9.b.g.51.8		20
20.19	odd	2	inner	20.9.d.c.19.3	✓	20
40.19	odd	2		320.9.h.g.319.10		20
40.29	even	2		320.9.h.g.319.12		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.9.d.c.19.3	✓	20	20.19	odd	2	inner
20.9.d.c.19.4	yes	20	1.1	even	1	trivial
20.9.d.c.19.17	yes	20	5.4	even	2	inner
20.9.d.c.19.18	yes	20	4.3	odd	2	inner
100.9.b.g.51.7		20	5.2	odd	4
100.9.b.g.51.8		20	20.7	even	4
100.9.b.g.51.13		20	20.3	even	4
100.9.b.g.51.14		20	5.3	odd	4
320.9.h.g.319.9		20	8.5	even	2
320.9.h.g.319.10		20	40.19	odd	2
320.9.h.g.319.11		20	8.3	odd	2
320.9.h.g.319.12		20	40.29	even	2

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:	\( N \)	\(=\)	\( 20 = 2^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	20.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-14.3016 + 7.17394i) q^{2} +42.6663 q^{3} +(153.069 - 205.197i) q^{4} +(-560.298 + 276.932i) q^{5} +(-610.194 + 306.085i) q^{6} +869.685 q^{7} +(-717.054 + 4032.75i) q^{8} -4740.59 q^{9} +(6026.43 - 7980.11i) q^{10} -24735.0i q^{11} +(6530.89 - 8754.99i) q^{12} -41128.5i q^{13} +(-12437.9 + 6239.07i) q^{14} +(-23905.8 + 11815.7i) q^{15} +(-18675.7 - 62818.7i) q^{16} +40900.7i q^{17} +(67797.8 - 34008.7i) q^{18} -79502.2i q^{19} +(-28938.6 + 157361. i) q^{20} +37106.2 q^{21} +(177447. + 353749. i) q^{22} -428560. q^{23} +(-30594.0 + 172062. i) q^{24} +(237242. - 310329. i) q^{25} +(295053. + 588201. i) q^{26} -482197. q^{27} +(133122. - 178457. i) q^{28} +184740. q^{29} +(257125. - 340481. i) q^{30} -154752. i q^{31} +(717749. + 764426. i) q^{32} -1.05535e6i q^{33} +(-293419. - 584943. i) q^{34} +(-487283. + 240844. i) q^{35} +(-725638. + 972755. i) q^{36} +1.72203e6i q^{37} +(570344. + 1.13701e6i) q^{38} -1.75480e6i q^{39} +(-715034. - 2.45811e6i) q^{40} -2.00720e6 q^{41} +(-530677. + 266198. i) q^{42} +1.43073e6 q^{43} +(-5.07555e6 - 3.78616e6i) q^{44} +(2.65614e6 - 1.31282e6i) q^{45} +(6.12907e6 - 3.07446e6i) q^{46} +4.98494e6 q^{47} +(-796823. - 2.68024e6i) q^{48} -5.00845e6 q^{49} +(-1.16665e6 + 6.14015e6i) q^{50} +1.74508e6i q^{51} +(-8.43945e6 - 6.29550e6i) q^{52} +6.97640e6i q^{53} +(6.89616e6 - 3.45925e6i) q^{54} +(6.84992e6 + 1.38590e7i) q^{55} +(-623611. + 3.50722e6i) q^{56} -3.39206e6i q^{57} +(-2.64206e6 + 1.32531e6i) q^{58} -5.65200e6i q^{59} +(-1.23470e6 + 6.71402e6i) q^{60} +6.73713e6 q^{61} +(1.11018e6 + 2.21319e6i) q^{62} -4.12282e6 q^{63} +(-1.57489e7 - 5.78340e6i) q^{64} +(1.13898e7 + 2.30442e7i) q^{65} +(7.57102e6 + 1.50931e7i) q^{66} -4.99529e6 q^{67} +(8.39270e6 + 6.26063e6i) q^{68} -1.82850e7 q^{69} +(5.24110e6 - 6.94018e6i) q^{70} +2.07710e7i q^{71} +(3.39926e6 - 1.91176e7i) q^{72} -3.31772e7i q^{73} +(-1.23537e7 - 2.46277e7i) q^{74} +(1.01222e7 - 1.32406e7i) q^{75} +(-1.63136e7 - 1.21693e7i) q^{76} -2.15117e7i q^{77} +(1.25888e7 + 2.50964e7i) q^{78} -7.49445e7i q^{79} +(2.78605e7 + 3.00253e7i) q^{80} +1.05295e7 q^{81} +(2.87061e7 - 1.43996e7i) q^{82} -8.75346e7 q^{83} +(5.67981e6 - 7.61409e6i) q^{84} +(-1.13267e7 - 2.29165e7i) q^{85} +(-2.04616e7 + 1.02639e7i) q^{86} +7.88215e6 q^{87} +(9.97500e7 + 1.77363e7i) q^{88} -1.14653e7 q^{89} +(-2.85689e7 + 3.78304e7i) q^{90} -3.57688e7i q^{91} +(-6.55993e7 + 8.79392e7i) q^{92} -6.60268e6i q^{93} +(-7.12925e7 + 3.57617e7i) q^{94} +(2.20167e7 + 4.45449e7i) q^{95} +(3.06237e7 + 3.26152e7i) q^{96} +8.74640e7i q^{97} +(7.16286e7 - 3.59303e7i) q^{98} +1.17258e8i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 752 q^{4} - 1420 q^{5} + 3408 q^{6} + 2556 q^{9} - 4160 q^{10} + 8848 q^{14} - 59200 q^{16} - 4240 q^{20} + 410256 q^{21} - 156672 q^{24} - 657260 q^{25} - 440448 q^{26} + 660136 q^{29} + 667920 q^{30}+ \cdots + 28850688 q^{96}+O(q^{100}) \) 20 * q - 752 * q^4 - 1420 * q^5 + 3408 * q^6 + 2556 * q^9 - 4160 * q^10 + 8848 * q^14 - 59200 * q^16 - 4240 * q^20 + 410256 * q^21 - 156672 * q^24 - 657260 * q^25 - 440448 * q^26 + 660136 * q^29 + 667920 * q^30 + 4342528 * q^34 - 7191312 * q^36 - 945280 * q^40 + 7068520 * q^41 + 2666880 * q^44 - 18729060 * q^45 + 561168 * q^46 + 11719036 * q^49 + 3914880 * q^50 + 37110816 * q^54 - 35044352 * q^56 - 22734720 * q^60 - 17660440 * q^61 + 20201728 * q^64 - 44202240 * q^65 + 31902720 * q^66 + 111747216 * q^69 - 47166000 * q^70 + 19114368 * q^74 - 54998400 * q^76 + 7968320 * q^80 - 154212444 * q^81 + 101289216 * q^84 + 68800000 * q^85 + 94429648 * q^86 + 105006376 * q^89 - 230808000 * q^90 - 192757872 * q^94 + 28850688 * q^96

Introduction

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