LMFDB - Embedded newform 20.9.d.c.19.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [20,9,Mod(19,20)]

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

lf = mfeigenbasis(mf)

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")

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

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			19.8
Root			$-3.53165 + 7.17826i$ of defining polynomial
Character	$\chi$	$=$	20.19
Dual form			20.9.d.c.19.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-7.06329 + 14.3565i) q^{2} -134.970 q^{3} +(-156.220 - 202.809i) q^{4} +(-416.235 + 466.234i) q^{5} +(953.329 - 1937.69i) q^{6} -1863.96 q^{7} +(4015.06 - 810.276i) q^{8} +11655.8 q^{9} +O(q^{10})$	\(q+(-7.06329 + 14.3565i) q^{2} -134.970 q^{3} +(-156.220 - 202.809i) q^{4} +(-416.235 + 466.234i) q^{5} +(953.329 - 1937.69i) q^{6} -1863.96 q^{7} +(4015.06 - 810.276i) q^{8} +11655.8 q^{9} +(-3753.51 - 9268.83i) q^{10} +5278.32i q^{11} +(21084.9 + 27373.0i) q^{12} +33338.9i q^{13} +(13165.7 - 26760.0i) q^{14} +(56179.0 - 62927.3i) q^{15} +(-16726.8 + 63365.5i) q^{16} -142617. i q^{17} +(-82328.1 + 167336. i) q^{18} -70346.9i q^{19} +(159580. + 11581.1i) q^{20} +251578. q^{21} +(-75778.3 - 37282.3i) q^{22} -255957. q^{23} +(-541910. + 109363. i) q^{24} +(-44122.6 - 388125. i) q^{25} +(-478630. - 235482. i) q^{26} -687639. q^{27} +(291187. + 378027. i) q^{28} +534050. q^{29} +(506609. + 1.25101e6i) q^{30} +1.24954e6i q^{31} +(-791562. - 687707. i) q^{32} -712412. i q^{33} +(2.04748e6 + 1.00735e6i) q^{34} +(775844. - 869041. i) q^{35} +(-1.82086e6 - 2.36389e6i) q^{36} -169861. i q^{37} +(1.00994e6 + 496881. i) q^{38} -4.49973e6i q^{39} +(-1.29343e6 + 2.20922e6i) q^{40} +2.36651e6 q^{41} +(-1.77697e6 + 3.61178e6i) q^{42} +4.03853e6 q^{43} +(1.07049e6 - 824577. i) q^{44} +(-4.85153e6 + 5.43431e6i) q^{45} +(1.80790e6 - 3.67465e6i) q^{46} -1.65928e6 q^{47} +(2.25760e6 - 8.55241e6i) q^{48} -2.29046e6 q^{49} +(5.88378e6 + 2.10799e6i) q^{50} +1.92489e7i q^{51} +(6.76141e6 - 5.20819e6i) q^{52} -981179. i q^{53} +(4.85699e6 - 9.87210e6i) q^{54} +(-2.46093e6 - 2.19702e6i) q^{55} +(-7.48390e6 + 1.51032e6i) q^{56} +9.49469e6i q^{57} +(-3.77215e6 + 7.66710e6i) q^{58} -7.47526e6i q^{59} +(-2.15385e7 - 1.56310e6i) q^{60} -1.41028e7 q^{61} +(-1.79391e7 - 8.82589e6i) q^{62} -2.17259e7 q^{63} +(1.54641e7 - 6.50660e6i) q^{64} +(-1.55437e7 - 1.38768e7i) q^{65} +(1.02278e7 + 5.03197e6i) q^{66} +3.75634e7 q^{67} +(-2.89240e7 + 2.22796e7i) q^{68} +3.45463e7 q^{69} +(6.99639e6 + 1.72767e7i) q^{70} -3.57630e7i q^{71} +(4.67986e7 - 9.44439e6i) q^{72} -7.26944e6i q^{73} +(2.43862e6 + 1.19978e6i) q^{74} +(5.95521e6 + 5.23851e7i) q^{75} +(-1.42670e7 + 1.09896e7i) q^{76} -9.83857e6i q^{77} +(6.46005e7 + 3.17829e7i) q^{78} -3.72731e7i q^{79} +(-2.25809e7 - 3.41735e7i) q^{80} +1.63368e7 q^{81} +(-1.67154e7 + 3.39749e7i) q^{82} -2.09461e7 q^{83} +(-3.93014e7 - 5.10222e7i) q^{84} +(6.64928e7 + 5.93621e7i) q^{85} +(-2.85253e7 + 5.79792e7i) q^{86} -7.20805e7 q^{87} +(4.27689e6 + 2.11927e7i) q^{88} +2.52812e7 q^{89} +(-4.37500e7 - 1.08035e8i) q^{90} -6.21423e7i q^{91} +(3.99855e7 + 5.19102e7i) q^{92} -1.68650e8i q^{93} +(1.17199e7 - 2.38214e7i) q^{94} +(3.27981e7 + 2.92808e7i) q^{95} +(1.06837e8 + 9.28195e7i) q^{96} +1.35709e6i q^{97} +(1.61782e7 - 3.28830e7i) q^{98} +6.15229e7i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 752 q^{4} - 1420 q^{5} + 3408 q^{6} + 2556 q^{9}+O(q^{10}) $ 20 * q - 752 * q^4 - 1420 * q^5 + 3408 * q^6 + 2556 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

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 $

$2$	−7.06329	+	14.3565i	−0.441456	+	0.897283i
$2$	−7.06329	+	14.3565i	−0.441456	+	0.897283i
$3$	−134.970			−1.66629			−0.833145	−	0.553054i	$-0.813462\pi$
$3$	−134.970			−1.66629			−0.833145	+	0.553054i	$0.813462\pi$
$4$	−156.220	−	202.809i	−0.610233	−	0.792222i
$5$	−416.235	+	466.234i	−0.665975	+	0.745974i
$5$	−416.235	+	466.234i	−0.665975	+	0.745974i
$6$	953.329	−	1937.69i	0.735594	−	1.49513i
$7$	−1863.96			−0.776326			−0.388163	−	0.921591i	$-0.626890\pi$
$7$	−1863.96			−0.776326			−0.388163	+	0.921591i	$0.626890\pi$
$8$	4015.06	−	810.276i	0.980238	−	0.197821i
$9$	11655.8			1.77652
$10$	−3753.51	−	9268.83i	−0.375351	−	0.926883i
$11$			5278.32i			0.360516i	0.983619	+	0.180258i	$0.0576933\pi$
$11$			5278.32i			0.360516i	−0.983619	+	0.180258i	$0.942307\pi$
$12$	21084.9	+	27373.0i	1.01683	+	1.32007i
$13$			33338.9i			1.16729i	0.812010	+	0.583643i	$0.198373\pi$
$13$			33338.9i			1.16729i	−0.812010	+	0.583643i	$0.801627\pi$
$14$	13165.7	−	26760.0i	0.342714	−	0.696584i
$15$	56179.0	−	62927.3i	1.10971	−	1.24301i
$16$	−16726.8	+	63365.5i	−0.255230	+	0.966880i
$17$		−	142617.i		−	1.70756i	−0.520636	−	0.853779i	$-0.674305\pi$
$17$		−	142617.i		−	1.70756i	0.520636	−	0.853779i	$-0.325695\pi$
$18$	−82328.1	+	167336.i	−0.784257	+	1.59404i
$19$		−	70346.9i		−	0.539797i	−0.962889	−	0.269899i	$-0.913010\pi$
$19$		−	70346.9i		−	0.539797i	0.962889	−	0.269899i	$-0.0869902\pi$
$20$	159580.	+	11581.1i	0.997377	+	0.0723819i
$21$	251578.			1.29359
$22$	−75778.3	−	37282.3i	−0.323485	−	0.159152i
$23$	−255957.			−0.914650			−0.457325	−	0.889300i	$-0.651192\pi$
$23$	−255957.			−0.914650			−0.457325	+	0.889300i	$0.651192\pi$
$24$	−541910.	+	109363.i	−1.63336	+	0.329628i
$25$	−44122.6	−	388125.i	−0.112954	−	0.993600i
$26$	−478630.	−	235482.i	−1.04739	−	0.515305i
$27$	−687639.			−1.29391
$28$	291187.	+	378027.i	0.473740	+	0.615023i
$29$	534050.			0.755075			0.377537	−	0.925994i	$-0.376771\pi$
$29$	534050.			0.755075			0.377537	+	0.925994i	$0.376771\pi$
$30$	506609.	+	1.25101e6i	0.625444	+	1.54446i
$31$			1.24954e6i			1.35302i	0.736433	+	0.676511i	$0.236509\pi$
$31$			1.24954e6i			1.35302i	−0.736433	+	0.676511i	$0.763491\pi$
$32$	−791562.	−	687707.i	−0.754892	−	0.655849i
$33$		−	712412.i		−	0.600725i
$34$	2.04748e6	+	1.00735e6i	1.53216	+	0.753811i
$35$	775844.	−	869041.i	0.517014	−	0.579119i
$36$	−1.82086e6	−	2.36389e6i	−1.08409	−	1.40740i
$37$		−	169861.i		−	0.0906332i	−0.998973	−	0.0453166i	$-0.985570\pi$
$37$		−	169861.i		−	0.0906332i	0.998973	−	0.0453166i	$-0.0144297\pi$
$38$	1.00994e6	+	496881.i	0.484351	+	0.238297i
$39$		−	4.49973e6i		−	1.94504i
$40$	−1.29343e6	+	2.20922e6i	−0.505245	+	0.862976i
$41$	2.36651e6			0.837479			0.418739	−	0.908106i	$-0.362472\pi$
$41$	2.36651e6			0.837479			0.418739	+	0.908106i	$0.362472\pi$
$42$	−1.77697e6	+	3.61178e6i	−0.571061	+	1.16071i
$43$	4.03853e6			1.18127			0.590635	−	0.806939i	$-0.298877\pi$
$43$	4.03853e6			1.18127			0.590635	+	0.806939i	$0.298877\pi$
$44$	1.07049e6	−	824577.i	0.285609	−	0.219999i
$45$	−4.85153e6	+	5.43431e6i	−1.18312	+	1.32524i
$46$	1.80790e6	−	3.67465e6i	0.403778	−	0.820700i
$47$	−1.65928e6			−0.340038			−0.170019	−	0.985441i	$-0.554383\pi$
$47$	−1.65928e6			−0.340038			−0.170019	+	0.985441i	$0.554383\pi$
$48$	2.25760e6	−	8.55241e6i	0.425288	−	1.61110i
$49$	−2.29046e6			−0.397317
$50$	5.88378e6	+	2.10799e6i	0.941405	+	0.337279i
$51$			1.92489e7i			2.84529i
$52$	6.76141e6	−	5.20819e6i	0.924749	−	0.712317i
$53$		−	981179.i		−	0.124350i	−0.998065	−	0.0621748i	$-0.980196\pi$
$53$		−	981179.i		−	0.124350i	0.998065	−	0.0621748i	$-0.0198036\pi$
$54$	4.85699e6	−	9.87210e6i	0.571206	−	1.16101i
$55$	−2.46093e6	−	2.19702e6i	−0.268936	−	0.240095i
$56$	−7.48390e6	+	1.51032e6i	−0.760985	+	0.153574i
$57$			9.49469e6i			0.899459i
$58$	−3.77215e6	+	7.66710e6i	−0.333332	+	0.677516i
$59$		−	7.47526e6i		−	0.616905i	−0.951240	−	0.308453i	$-0.900189\pi$
$59$		−	7.47526e6i		−	0.616905i	0.951240	−	0.308453i	$-0.0998111\pi$
$60$	−2.15385e7	−	1.56310e6i	−1.66192	−	0.120609i
$61$	−1.41028e7			−1.01856			−0.509280	−	0.860601i	$-0.670088\pi$
$61$	−1.41028e7			−1.01856			−0.509280	+	0.860601i	$0.670088\pi$
$62$	−1.79391e7	−	8.82589e6i	−1.21404	−	0.597299i
$63$	−2.17259e7			−1.37916
$64$	1.54641e7	−	6.50660e6i	0.921734	−	0.387824i
$65$	−1.55437e7	−	1.38768e7i	−0.870765	−	0.777384i
$66$	1.02278e7	+	5.03197e6i	0.539020	+	0.265193i
$67$	3.75634e7			1.86409			0.932043	−	0.362347i	$-0.118024\pi$
$67$	3.75634e7			1.86409			0.932043	+	0.362347i	$0.118024\pi$
$68$	−2.89240e7	+	2.22796e7i	−1.35276	+	1.04201i
$69$	3.45463e7			1.52407
$70$	6.99639e6	+	1.72767e7i	0.291395	+	0.719564i
$71$		−	3.57630e7i		−	1.40734i	−0.710524	−	0.703672i	$-0.751542\pi$
$71$		−	3.57630e7i		−	1.40734i	0.710524	−	0.703672i	$-0.248458\pi$
$72$	4.67986e7	−	9.44439e6i	1.74142	−	0.351434i
$73$		−	7.26944e6i		−	0.255982i	−0.991775	−	0.127991i	$-0.959147\pi$
$73$		−	7.26944e6i		−	0.255982i	0.991775	−	0.127991i	$-0.0408529\pi$
$74$	2.43862e6	+	1.19978e6i	0.0813236	+	0.0400106i
$75$	5.95521e6	+	5.23851e7i	0.188214	+	1.65563i
$76$	−1.42670e7	+	1.09896e7i	−0.427639	+	0.329402i
$77$		−	9.83857e6i		−	0.279878i
$78$	6.46005e7	+	3.17829e7i	1.74525	+	0.858648i
$79$		−	3.72731e7i		−	0.956945i	−0.878102	−	0.478473i	$-0.841191\pi$
$79$		−	3.72731e7i		−	0.956945i	0.878102	−	0.478473i	$-0.158809\pi$
$80$	−2.25809e7	−	3.41735e7i	−0.551290	−	0.834313i
$81$	1.63368e7			0.379512
$82$	−1.67154e7	+	3.39749e7i	−0.369710	+	0.751455i
$83$	−2.09461e7			−0.441357			−0.220679	−	0.975347i	$-0.570827\pi$
$83$	−2.09461e7			−0.441357			−0.220679	+	0.975347i	$0.570827\pi$
$84$	−3.93014e7	−	5.10222e7i	−0.789389	−	1.02481i
$85$	6.64928e7	+	5.93621e7i	1.27379	+	1.13719i
$86$	−2.85253e7	+	5.79792e7i	−0.521479	+	1.05993i
$87$	−7.20805e7			−1.25817
$88$	4.27689e6	+	2.11927e7i	0.0713177	+	0.353392i
$89$	2.52812e7			0.402938			0.201469	−	0.979495i	$-0.435429\pi$
$89$	2.52812e7			0.402938			0.201469	+	0.979495i	$0.435429\pi$
$90$	−4.37500e7	−	1.08035e8i	−0.666820	−	1.64663i
$91$		−	6.21423e7i		−	0.906195i
$92$	3.99855e7	+	5.19102e7i	0.558150	+	0.724606i
$93$		−	1.68650e8i		−	2.25453i
$94$	1.17199e7	−	2.38214e7i	0.150112	−	0.305110i
$95$	3.27981e7	+	2.92808e7i	0.402674	+	0.359492i
$96$	1.06837e8	+	9.28195e7i	1.25787	+	1.09283i
$97$			1.35709e6i			0.0153293i	0.999971	+	0.00766465i	$0.00243976\pi$
$97$			1.35709e6i			0.0153293i	−0.999971	+	0.00766465i	$0.997560\pi$
$98$	1.61782e7	−	3.28830e7i	0.175398	−	0.356506i
$99$			6.15229e7i			0.640465i
$100$	−7.18223e7	+	6.95813e7i	−0.718223	+	0.695813i
$101$	−1.25091e8			−1.20210			−0.601052	−	0.799210i	$-0.705251\pi$
$101$	−1.25091e8			−1.20210			−0.601052	+	0.799210i	$0.705251\pi$
$102$	−2.76348e8	−	1.35961e8i	−2.55303	−	1.25607i
$103$	4.55443e7			0.404655			0.202327	−	0.979318i	$-0.435149\pi$
$103$	4.55443e7			0.404655			0.202327	+	0.979318i	$0.435149\pi$
$104$	2.70137e7	+	1.33857e8i	0.230914	+	1.14422i
$105$	−1.04715e8	+	1.17294e8i	−0.861496	+	0.964981i
$106$	1.40863e7	+	6.93035e6i	0.111577	+	0.0548949i
$107$	1.11806e7			0.0852959			0.0426480	−	0.999090i	$-0.486421\pi$
$107$	1.11806e7			0.0852959			0.0426480	+	0.999090i	$0.486421\pi$
$108$	1.07423e8	+	1.39459e8i	0.789589	+	1.02507i
$109$	−3.48944e7			−0.247201			−0.123600	−	0.992332i	$-0.539444\pi$
$109$	−3.48944e7			−0.247201			−0.123600	+	0.992332i	$0.539444\pi$
$110$	4.89238e7	−	1.98122e7i	0.334156	−	0.135320i
$111$			2.29261e7i			0.151021i
$112$	3.11780e7	−	1.18111e8i	0.198142	−	0.750615i
$113$		−	1.55089e8i		−	0.951187i	−0.879665	−	0.475594i	$-0.842233\pi$
$113$		−	1.55089e8i		−	0.951187i	0.879665	−	0.475594i	$-0.157767\pi$
$114$	−1.36311e8	−	6.70638e7i	−0.807069	−	0.397071i
$115$	1.06538e8	−	1.19336e8i	0.609135	−	0.682305i
$116$	−8.34292e7	−	1.08310e8i	−0.460772	−	0.598187i
$117$			3.88590e8i			2.07371i
$118$	1.07319e8	+	5.28000e7i	0.553539	+	0.272336i
$119$			2.65832e8i			1.32562i
$120$	1.74573e8	−	2.98177e8i	0.841885	−	1.43797i
$121$	1.86498e8			0.870028
$122$	9.96123e7	−	2.02467e8i	0.449649	−	0.913936i
$123$	−3.19407e8			−1.39548
$124$	2.53418e8	−	1.95203e8i	1.07189	−	0.825659i
$125$	1.99322e8	+	1.40980e8i	0.816424	+	0.577453i
$126$	1.53456e8	−	3.11908e8i	0.608839	−	1.23750i
$127$	2.11442e8			0.812786			0.406393	−	0.913698i	$-0.366786\pi$
$127$	2.11442e8			0.812786			0.406393	+	0.913698i	$0.366786\pi$
$128$	−1.58154e7	+	2.67969e8i	−0.0589170	+	0.998263i
$129$	−5.45078e8			−1.96834
$130$	3.09012e8	−	1.25138e8i	1.08194	−	0.438142i
$131$			1.14013e8i			0.387140i	0.981086	+	0.193570i	$0.0620067\pi$
$131$			1.14013e8i			0.387140i	−0.981086	+	0.193570i	$0.937993\pi$
$132$	−1.44483e8	+	1.11293e8i	−0.475907	+	0.366582i
$133$			1.31124e8i			0.419059i
$134$	−2.65322e8	+	5.39281e8i	−0.822912	+	1.67261i
$135$	2.86219e8	−	3.20600e8i	0.861714	−	0.965226i
$136$	−1.15559e8	−	5.72615e8i	−0.337791	−	1.67381i
$137$		−	3.96731e8i		−	1.12620i	−0.826390	−	0.563098i	$-0.809609\pi$
$137$		−	3.96731e8i		−	1.12620i	0.826390	−	0.563098i	$-0.190391\pi$
$138$	−2.44011e8	+	4.95966e8i	−0.672811	+	1.36752i
$139$		−	2.81838e8i		−	0.754988i	−0.926012	−	0.377494i	$-0.876786\pi$
$139$		−	2.81838e8i		−	0.754988i	0.926012	−	0.377494i	$-0.123214\pi$
$140$	−2.97451e8	−	2.15867e7i	−0.774290	−	0.0561920i
$141$	2.23952e8			0.566601
$142$	5.13433e8	+	2.52605e8i	1.26279	+	0.621281i
$143$	−1.75973e8			−0.420825
$144$	−1.94963e8	+	7.38573e8i	−0.453423	+	1.71769i
$145$	−2.22290e8	+	2.48992e8i	−0.502861	+	0.563266i
$146$	1.04364e8	+	5.13462e7i	0.229688	+	0.113005i
$147$	3.09142e8			0.662046
$148$	−3.44493e7	+	2.65357e7i	−0.0718016	+	0.0553074i
$149$	4.38854e8			0.890379			0.445190	−	0.895436i	$-0.353136\pi$
$149$	4.38854e8			0.890379			0.445190	+	0.895436i	$0.353136\pi$
$150$	−7.94131e8	−	2.84515e8i	−1.56865	−	0.562005i
$151$			7.34766e8i			1.41332i	0.707552	+	0.706662i	$0.249800\pi$
$151$			7.34766e8i			1.41332i	−0.707552	+	0.706662i	$0.750200\pi$
$152$	−5.70004e7	−	2.82447e8i	−0.106783	−	0.529130i
$153$		−	1.66231e9i		−	3.03352i
$154$	1.41248e8	+	6.94927e7i	0.251130	+	0.123554i
$155$	−5.82579e8	−	5.20103e8i	−1.00932	−	0.901079i
$156$	−9.12584e8	+	7.02947e8i	−1.54090	+	1.18693i
$157$			3.92920e8i			0.646704i	0.946279	+	0.323352i	$0.104810\pi$
$157$			3.92920e8i			0.646704i	−0.946279	+	0.323352i	$0.895190\pi$
$158$	5.35112e8	+	2.63271e8i	0.858651	+	0.422449i
$159$			1.32429e8i			0.207203i
$160$	6.50108e8	−	8.28053e7i	0.991986	−	0.126351i
$161$	4.77093e8			0.710067
$162$	−1.15391e8	+	2.34539e8i	−0.167538	+	0.340530i
$163$	−8.78730e8			−1.24482			−0.622408	−	0.782693i	$-0.713845\pi$
$163$	−8.78730e8			−1.24482			−0.622408	+	0.782693i	$0.713845\pi$
$164$	−3.69696e8	−	4.79950e8i	−0.511057	−	0.663469i
$165$	3.32150e8	+	2.96530e8i	0.448125	+	0.400068i
$166$	1.47948e8	−	3.00713e8i	0.194840	−	0.396022i
$167$	−4.28526e8			−0.550948			−0.275474	−	0.961308i	$-0.588835\pi$
$167$	−4.28526e8			−0.550948			−0.275474	+	0.961308i	$0.588835\pi$
$168$	1.01010e9	−	2.03847e8i	1.26802	−	0.255899i
$169$	−2.95749e8			−0.362557
$170$	−1.32189e9	+	5.35314e8i	−1.58271	+	0.640933i
$171$		−	8.19947e8i		−	0.958962i
$172$	−6.30898e8	−	8.19049e8i	−0.720851	−	0.935828i
$173$		−	3.08766e8i		−	0.344703i	−0.985035	−	0.172352i	$-0.944863\pi$
$173$		−	3.08766e8i		−	0.344703i	0.985035	−	0.172352i	$-0.0551366\pi$
$174$	5.09126e8	−	1.03483e9i	0.555428	−	1.12894i
$175$	8.22427e7	+	7.23450e8i	0.0876891	+	0.771358i
$176$	−3.34463e8	−	8.82892e7i	−0.348576	−	0.0920146i
$177$			1.00893e9i			1.02794i
$178$	−1.78569e8	+	3.62950e8i	−0.177879	+	0.361549i
$179$			2.34312e8i			0.228235i	0.993467	+	0.114117i	$0.0364040\pi$
$179$			2.34312e8i			0.228235i	−0.993467	+	0.114117i	$0.963596\pi$
$180$	1.86003e9	+	1.34987e8i	1.77186	+	0.128588i
$181$	−1.98225e8			−0.184691			−0.0923454	−	0.995727i	$-0.529436\pi$
$181$	−1.98225e8			−0.184691			−0.0923454	+	0.995727i	$0.529436\pi$
$182$	8.92147e8	+	4.38929e8i	0.813113	+	0.400045i
$183$	1.90345e9			1.69722
$184$	−1.02768e9	+	2.07395e8i	−0.896575	+	0.180937i
$185$	7.91950e7	+	7.07021e7i	0.0676100	+	0.0603595i
$186$	2.42123e9	+	1.19123e9i	2.02295	+	0.995274i
$187$	7.52778e8			0.615602
$188$	2.59212e8	+	3.36516e8i	0.207502	+	0.269385i
$189$	1.28173e9			1.00450
$190$	−6.52033e8	+	2.64048e8i	−0.500329	+	0.202613i
$191$		−	2.29845e9i		−	1.72704i	−0.504317	−	0.863518i	$-0.668256\pi$
$191$		−	2.29845e9i		−	1.72704i	0.504317	−	0.863518i	$-0.331744\pi$
$192$	−2.08719e9	+	8.78193e8i	−1.53588	+	0.646227i
$193$			6.50744e8i			0.469009i	0.972115	+	0.234505i	$0.0753468\pi$
$193$			6.50744e8i			0.469009i	−0.972115	+	0.234505i	$0.924653\pi$
$194$	−1.94831e7	−	9.58554e6i	−0.0137547	−	0.00676721i
$195$	2.09793e9	+	1.87294e9i	1.45095	+	1.29535i
$196$	3.57814e8	+	4.64524e8i	0.242456	+	0.314763i
$197$		−	1.18078e9i		−	0.783981i	−0.919969	−	0.391990i	$-0.871787\pi$
$197$		−	1.18078e9i		−	0.783981i	0.919969	−	0.391990i	$-0.128213\pi$
$198$	−8.83255e8	−	4.34554e8i	−0.574679	−	0.282737i
$199$		−	8.61830e8i		−	0.549553i	−0.961508	−	0.274776i	$-0.911396\pi$
$199$		−	8.61830e8i		−	0.549553i	0.961508	−	0.274776i	$-0.0886038\pi$
$200$	−4.91643e8	−	1.52259e9i	−0.307277	−	0.951620i
$201$	−5.06992e9			−3.10611
$202$	8.83557e8	−	1.79588e9i	0.530676	−	1.07863i
$203$	−9.95448e8			−0.586185
$204$	3.90385e9	−	3.00707e9i	2.25410	−	1.73629i
$205$	−9.85025e8	+	1.10335e9i	−0.557740	+	0.624737i
$206$	−3.21693e8	+	6.53858e8i	−0.178637	+	0.363090i
$207$	−2.98337e9			−1.62490
$208$	−2.11253e9	−	5.57651e8i	−1.12863	−	0.297927i
$209$	3.71313e8			0.194606
$210$	−9.44299e8	−	2.33183e9i	−0.485548	−	1.19900i
$211$			1.94443e9i			0.980985i	0.871445	+	0.490493i	$0.163183\pi$
$211$			1.94443e9i			0.980985i	−0.871445	+	0.490493i	$0.836817\pi$
$212$	−1.98992e8	+	1.53280e8i	−0.0985125	+	0.0758823i
$213$			4.82691e9i			2.34505i
$214$	−7.89716e7	+	1.60514e8i	−0.0376544	+	0.0765346i
$215$	−1.68097e9	+	1.88290e9i	−0.786697	+	0.881197i
$216$	−2.76091e9	+	5.57177e8i	−1.26834	+	0.255964i
$217$		−	2.32910e9i		−	1.05039i
$218$	2.46469e8	−	5.00962e8i	0.109128	−	0.221809i
$219$			9.81153e8i			0.426541i
$220$	−6.11287e7	+	8.42316e8i	−0.0260948	+	0.359571i
$221$	4.75469e9			1.99321
$222$	−3.29139e8	−	1.61934e8i	−0.135509	−	0.0666692i
$223$	−5.65989e8			−0.228870			−0.114435	−	0.993431i	$-0.536506\pi$
$223$	−5.65989e8			−0.228870			−0.114435	+	0.993431i	$0.536506\pi$
$224$	1.47544e9	+	1.28186e9i	0.586043	+	0.509153i
$225$	−5.14283e8	−	4.52390e9i	−0.200665	−	1.76515i
$226$	2.22653e9	+	1.09544e9i	0.853484	+	0.419907i
$227$	2.24952e9			0.847200			0.423600	−	0.905849i	$-0.360766\pi$
$227$	2.24952e9			0.847200			0.423600	+	0.905849i	$0.360766\pi$
$228$	1.92561e9	−	1.48326e9i	0.712571	−	0.548880i
$229$	−1.02108e9			−0.371295			−0.185648	−	0.982616i	$-0.559438\pi$
$229$	−1.02108e9			−0.371295			−0.185648	+	0.982616i	$0.559438\pi$
$230$	9.60736e8	+	2.37242e9i	0.343315	+	0.847774i
$231$			1.32791e9i			0.466358i
$232$	2.14424e9	−	4.32728e8i	0.740153	−	0.149370i
$233$		−	1.60926e9i		−	0.546013i	−0.962012	−	0.273007i	$-0.911982\pi$
$233$		−	1.60926e9i		−	0.546013i	0.962012	−	0.273007i	$-0.0880181\pi$
$234$	−5.57880e9	−	2.74473e9i	−1.86071	−	0.915452i
$235$	6.90648e8	−	7.73610e8i	0.226457	−	0.253659i
$236$	−1.51605e9	+	1.16778e9i	−0.488726	+	0.376456i
$237$			5.03073e9i			1.59455i
$238$	−3.81643e9	−	1.87765e9i	−1.18946	−	0.585204i
$239$		−	6.14150e9i		−	1.88227i	−0.338027	−	0.941136i	$-0.609760\pi$
$239$		−	6.14150e9i		−	1.88227i	0.338027	−	0.941136i	$-0.390240\pi$
$240$	3.04773e9	+	4.61238e9i	0.918610	+	1.39021i
$241$	−1.57617e9			−0.467234			−0.233617	−	0.972329i	$-0.575056\pi$
$241$	−1.57617e9			−0.467234			−0.233617	+	0.972329i	$0.575056\pi$
$242$	−1.31729e9	+	2.67747e9i	−0.384079	+	0.780661i
$243$	2.30663e9			0.661536
$244$	2.20314e9	+	2.86017e9i	0.621559	+	0.806925i
$245$	9.53367e8	−	1.06789e9i	0.264603	−	0.296388i
$246$	2.25607e9	−	4.58558e9i	0.616044	−	1.25214i
$247$	2.34528e9			0.630098
$248$	1.01247e9	+	5.01699e9i	0.267656	+	1.32628i
$249$	2.82708e9			0.735429
$250$	−3.43185e9	+	1.86580e9i	−0.878554	+	0.477644i
$251$			6.05238e8i			0.152486i	0.997089	+	0.0762432i	$0.0242925\pi$
$251$			6.05238e8i			0.152486i	−0.997089	+	0.0762432i	$0.975707\pi$
$252$	3.39401e9	+	4.40620e9i	0.841611	+	1.09260i
$253$		−	1.35102e9i		−	0.329746i
$254$	−1.49348e9	+	3.03557e9i	−0.358809	+	0.729299i
$255$	−8.97450e9	−	8.01207e9i	−2.12251	−	1.89489i
$256$	−3.73540e9	−	2.11980e9i	−0.869715	−	0.493554i
$257$		−	7.33383e9i		−	1.68112i	−0.541720	−	0.840559i	$-0.682227\pi$
$257$		−	7.33383e9i		−	1.68112i	0.541720	−	0.840559i	$-0.317773\pi$
$258$	3.85005e9	−	7.82543e9i	0.868935	−	1.76616i
$259$			3.16614e8i			0.0703609i
$260$	−3.86101e8	+	5.32023e9i	−0.0844903	+	1.16422i
$261$	6.22476e9			1.34141
$262$	−1.63683e9	−	8.05305e8i	−0.347374	−	0.170905i
$263$	8.11216e9			1.69556			0.847780	−	0.530348i	$-0.177939\pi$
$263$	8.11216e9			1.69556			0.847780	+	0.530348i	$0.177939\pi$
$264$	−5.77250e8	−	2.86037e9i	−0.118836	−	0.588853i
$265$	4.57458e8	+	4.08400e8i	0.0927616	+	0.0828138i
$266$	−1.88248e9	−	9.26166e8i	−0.376014	−	0.184996i
$267$	−3.41219e9			−0.671411
$268$	−5.86815e9	−	7.61819e9i	−1.13753	−	1.47677i
$269$	1.31912e9			0.251927			0.125964	−	0.992035i	$-0.459798\pi$
$269$	1.31912e9			0.251927			0.125964	+	0.992035i	$0.459798\pi$
$270$	2.58106e9	+	6.37360e9i	0.485672	+	1.19931i
$271$			3.01624e9i			0.559228i	0.960113	+	0.279614i	$0.0902064\pi$
$271$			3.01624e9i			0.559228i	−0.960113	+	0.279614i	$0.909794\pi$
$272$	9.03699e9	+	2.38552e9i	1.65100	+	0.435821i
$273$			8.38731e9i			1.50998i
$274$	5.69568e9	+	2.80223e9i	1.01052	+	0.497166i
$275$	2.04865e9	−	2.32893e8i	0.358209	−	0.0407217i
$276$	−5.39682e9	−	7.00630e9i	−0.930040	−	1.20740i
$277$		−	1.19710e9i		−	0.203334i	−0.994818	−	0.101667i	$-0.967582\pi$
$277$		−	1.19710e9i		−	0.203334i	0.994818	−	0.101667i	$-0.0324177\pi$
$278$	4.04621e9	+	1.99070e9i	0.677438	+	0.333294i
$279$			1.45644e10i			2.40367i
$280$	2.41090e9	−	4.11789e9i	0.392235	−	0.669951i
$281$	2.05582e9			0.329732			0.164866	−	0.986316i	$-0.447281\pi$
$281$	2.05582e9			0.329732			0.164866	+	0.986316i	$0.447281\pi$
$282$	−1.58184e9	+	3.21517e9i	−0.250130	+	0.508402i
$283$	−1.21382e10			−1.89238			−0.946189	−	0.323616i	$-0.895102\pi$
$283$	−1.21382e10			−1.89238			−0.946189	+	0.323616i	$0.895102\pi$
$284$	−7.25305e9	+	5.58689e9i	−1.11493	+	0.858809i
$285$	−4.42674e9	−	3.95202e9i	−0.670973	−	0.599017i
$286$	1.24295e9	−	2.52636e9i	0.185776	−	0.377600i
$287$	−4.41109e9			−0.650157
$288$	−9.22626e9	−	8.01576e9i	−1.34108	−	1.16513i
$289$	−1.33638e10			−1.91575
$290$	−2.00456e9	−	4.95002e9i	−0.283418	−	0.699866i
$291$		−	1.83166e8i		−	0.0255431i
$292$	−1.47431e9	+	1.13563e9i	−0.202795	+	0.156209i
$293$			8.85830e9i			1.20193i	0.799275	+	0.600966i	$0.205217\pi$
$293$			8.85830e9i			1.20193i	−0.799275	+	0.600966i	$0.794783\pi$
$294$	−2.18356e9	+	4.43820e9i	−0.292264	+	0.594043i
$295$	3.48522e9	+	3.11146e9i	0.460195	+	0.410844i
$296$	−1.37634e8	−	6.82002e8i	−0.0179292	−	0.0888421i
$297$		−	3.62958e9i		−	0.466477i
$298$	−3.09975e9	+	6.30042e9i	−0.393063	+	0.798922i
$299$		−	8.53330e9i		−	1.06766i
$300$	9.69383e9	−	9.39135e9i	1.19677	−	1.15943i
$301$	−7.52765e9			−0.917051
$302$	−1.05487e10	−	5.18987e9i	−1.26815	−	0.623920i
$303$	1.68835e10			2.00305
$304$	4.45756e9	+	1.17668e9i	0.521919	+	0.137773i
$305$	5.87008e9	−	6.57520e9i	0.678335	−	0.759818i
$306$	2.38650e10	+	1.17414e10i	2.72192	+	1.33916i
$307$	2.27115e9			0.255678			0.127839	−	0.991795i	$-0.459196\pi$
$307$	2.27115e9			0.255678			0.127839	+	0.991795i	$0.459196\pi$
$308$	−1.99535e9	+	1.53698e9i	−0.221726	+	0.170791i
$309$	−6.14709e9			−0.674273
$310$	1.15818e10	−	4.69017e9i	1.25409	−	0.507858i
$311$			9.95031e8i			0.106364i	0.998585	+	0.0531820i	$0.0169364\pi$
$311$			9.95031e8i			0.106364i	−0.998585	+	0.0531820i	$0.983064\pi$
$312$	−3.64602e9	−	1.80667e10i	−0.384770	−	1.90660i
$313$			9.67741e9i			1.00828i	0.863621	+	0.504141i	$0.168191\pi$
$313$			9.67741e9i			1.00828i	−0.863621	+	0.504141i	$0.831809\pi$
$314$	−5.64096e9	−	2.77531e9i	−0.580276	−	0.285491i
$315$	9.04306e9	−	1.01293e10i	0.918488	−	1.02882i
$316$	−7.55931e9	+	5.82279e9i	−0.758113	+	0.583960i
$317$			5.41589e9i			0.536330i	0.963373	+	0.268165i	$0.0864173\pi$
$317$			5.41589e9i			0.536330i	−0.963373	+	0.268165i	$0.913583\pi$
$318$	−1.90122e9	−	9.35386e8i	−0.185919	−	0.0914708i
$319$			2.81889e9i			0.272217i
$320$	−3.40311e9	+	9.91817e9i	−0.324545	+	0.945870i
$321$	−1.50903e9			−0.142128
$322$	−3.36985e9	+	6.84940e9i	−0.313463	+	0.637131i
$323$	−1.00327e10			−0.921735
$324$	−2.55212e9	−	3.31324e9i	−0.231591	−	0.300658i
$325$	1.29396e10	−	1.47100e9i	1.15982	−	0.131849i
$326$	6.20673e9	−	1.26155e10i	0.549531	−	1.11695i
$327$	4.70968e9			0.411908
$328$	9.50169e9	−	1.91753e9i	0.820928	−	0.165671i
$329$	3.09282e9			0.263980
$330$	−6.60322e9	+	2.67404e9i	−0.556801	+	0.225483i
$331$		−	1.61383e10i		−	1.34445i	−0.740345	−	0.672227i	$-0.765338\pi$
$331$		−	1.61383e10i		−	1.34445i	0.740345	−	0.672227i	$-0.234662\pi$
$332$	3.27219e9	+	4.24805e9i	0.269331	+	0.349653i
$333$		−	1.97986e9i		−	0.161012i
$334$	3.02680e9	−	6.15214e9i	0.243219	−	0.494357i
$335$	−1.56352e10	+	1.75133e10i	−1.24144	+	1.39056i
$336$	−4.20808e9	+	1.59413e10i	−0.330162	+	1.25074i
$337$			1.60080e10i			1.24113i	0.784154	+	0.620566i	$0.213097\pi$
$337$			1.60080e10i			1.24113i	−0.784154	+	0.620566i	$0.786903\pi$
$338$	2.08896e9	−	4.24592e9i	0.160053	−	0.325316i
$339$			2.09322e10i			1.58495i
$340$	1.65166e9	−	2.27589e10i	0.123596	−	1.70308i
$341$	−6.59549e9			−0.487786
$342$	1.17716e10	+	5.79153e9i	0.860460	+	0.423339i
$343$	1.50147e10			1.08477
$344$	1.62149e10	−	3.27232e9i	1.15793	−	0.233680i
$345$	−1.43794e10	+	1.61067e10i	−1.01499	+	1.13692i
$346$	4.43281e9	+	2.18091e9i	0.309297	+	0.152171i
$347$	−1.34569e10			−0.928168			−0.464084	−	0.885791i	$-0.653616\pi$
$347$	−1.34569e10			−0.928168			−0.464084	+	0.885791i	$0.653616\pi$
$348$	1.12604e10	+	1.46186e10i	0.767780	+	0.996753i
$349$	1.78901e10			1.20590			0.602951	−	0.797779i	$-0.293992\pi$
$349$	1.78901e10			1.20590			0.602951	+	0.797779i	$0.293992\pi$
$350$	−1.09671e10	−	3.92922e9i	−0.730837	−	0.261839i
$351$		−	2.29251e10i		−	1.51037i
$352$	3.62994e9	−	4.17812e9i	0.236444	−	0.272151i
$353$		−	2.70557e10i		−	1.74245i	−0.490886	−	0.871224i	$-0.663327\pi$
$353$		−	2.70557e10i		−	1.74245i	0.490886	−	0.871224i	$-0.336673\pi$
$354$	−1.44848e10	−	7.12639e9i	−0.922356	−	0.453792i
$355$	1.66739e10	+	1.48858e10i	1.04984	+	0.937257i
$356$	−3.94942e9	−	5.12725e9i	−0.245886	−	0.319216i
$357$		−	3.58793e10i		−	2.20887i
$358$	−3.36390e9	−	1.65501e9i	−0.204791	−	0.100756i
$359$		−	5.50402e9i		−	0.331361i	−0.986179	−	0.165681i	$-0.947018\pi$
$359$		−	5.50402e9i		−	0.331361i	0.986179	−	0.165681i	$-0.0529821\pi$
$360$	−1.50759e10	+	2.57501e10i	−0.897579	+	1.53310i
$361$	1.20349e10			0.708619
$362$	1.40012e9	−	2.84583e9i	0.0815328	−	0.165720i
$363$	−2.51716e10			−1.44972
$364$	−1.26030e10	+	9.70785e9i	−0.717907	+	0.552991i
$365$	3.38926e9	+	3.02579e9i	0.190956	+	0.170478i
$366$	−1.34446e10	+	2.73269e10i	−0.749246	+	1.52288i
$367$	−9.67406e9			−0.533267			−0.266633	−	0.963798i	$-0.585911\pi$
$367$	−9.67406e9			−0.533267			−0.266633	+	0.963798i	$0.585911\pi$
$368$	4.28133e9	−	1.62188e10i	0.233446	−	0.884357i
$369$	2.75835e10			1.48780
$370$	−1.57441e9	+	6.37576e8i	−0.0840064	+	0.0340193i
$371$			1.82888e9i			0.0965359i
$372$	−3.42038e10	+	2.63465e10i	−1.78608	+	1.37579i
$373$		−	2.57338e10i		−	1.32944i	−0.747093	−	0.664720i	$-0.768551\pi$
$373$		−	2.57338e10i		−	1.32944i	0.747093	−	0.664720i	$-0.231449\pi$
$374$	−5.31709e9	+	1.08073e10i	−0.271761	+	0.552369i
$375$	−2.69024e10	−	1.90280e10i	−1.36040	−	0.962204i
$376$	−6.66208e9	+	1.34447e9i	−0.333318	+	0.0672667i
$377$			1.78046e10i			0.881388i
$378$	−9.05324e9	+	1.84012e10i	−0.443442	+	0.901320i
$379$		−	3.39099e10i		−	1.64350i	−0.569849	−	0.821749i	$-0.692998\pi$
$379$		−	3.39099e10i		−	1.64350i	0.569849	−	0.821749i	$-0.307002\pi$
$380$	8.14694e8	−	1.12260e10i	0.0390715	−	0.538381i
$381$	−2.85382e10			−1.35434
$382$	3.29978e10	+	1.62346e10i	1.54964	+	0.762411i
$383$	1.07466e10			0.499433			0.249717	−	0.968319i	$-0.419663\pi$
$383$	1.07466e10			0.499433			0.249717	+	0.968319i	$0.419663\pi$
$384$	2.13460e9	−	3.61677e10i	0.0981729	−	1.66340i
$385$	4.58707e9	+	4.09515e9i	0.208782	+	0.186392i
$386$	−9.34243e9	−	4.59640e9i	−0.420834	−	0.207047i
$387$	4.70722e10			2.09855
$388$	2.75230e8	−	2.12005e8i	0.0121442	−	0.00935446i
$389$	−4.17407e10			−1.82289			−0.911446	−	0.411419i	$-0.865033\pi$
$389$	−4.17407e10			−1.82289			−0.911446	+	0.411419i	$0.865033\pi$
$390$	−4.17072e10	+	1.68898e10i	−1.80282	+	0.730072i
$391$			3.65038e10i			1.56182i
$392$	−9.19630e9	+	1.85590e9i	−0.389466	+	0.0785978i
$393$		−	1.53882e10i		−	0.645088i
$394$	1.69520e10	+	8.34022e9i	0.703453	+	0.346093i
$395$	1.73780e10	+	1.55144e10i	0.713856	+	0.637302i
$396$	1.24774e10	−	9.61109e9i	0.507391	−	0.390833i
$397$			1.28145e10i			0.515871i	0.966162	+	0.257936i	$0.0830422\pi$
$397$			1.28145e10i			0.515871i	−0.966162	+	0.257936i	$0.916958\pi$
$398$	1.23729e10	+	6.08736e9i	0.493104	+	0.242603i
$399$		−	1.76977e10i		−	0.698274i
$400$	2.53318e10	+	3.69623e9i	0.989522	+	0.144384i
$401$	4.75527e10			1.83907			0.919533	−	0.393013i	$-0.128567\pi$
$401$	4.75527e10			1.83907			0.919533	+	0.393013i	$0.128567\pi$
$402$	3.58103e10	−	7.27864e10i	1.37121	−	2.78706i
$403$	−4.16584e10			−1.57936
$404$	1.95417e10	+	2.53696e10i	0.733564	+	0.952332i
$405$	−6.79992e9	+	7.61674e9i	−0.252746	+	0.283106i
$406$	7.03114e9	−	1.42912e10i	0.258775	−	0.525973i
$407$	8.96581e8			0.0326747
$408$	1.55969e10	+	7.72856e10i	0.562858	+	2.78906i
$409$	2.44716e10			0.874518			0.437259	−	0.899336i	$-0.355949\pi$
$409$	2.44716e10			0.874518			0.437259	+	0.899336i	$0.355949\pi$
$410$	−8.88273e9	−	2.19348e10i	−0.314348	−	0.776245i
$411$			5.35466e10i			1.87657i
$412$	−7.11492e9	−	9.23678e9i	−0.246934	−	0.320576i
$413$			1.39336e10i			0.478920i
$414$	2.10724e10	−	4.28309e10i	0.717321	−	1.45799i
$415$	8.71848e9	−	9.76576e9i	0.293933	−	0.329241i
$416$	2.29274e10	−	2.63898e10i	0.765563	−	0.881175i
$417$			3.80395e10i			1.25803i
$418$	−2.62269e9	+	5.33077e9i	−0.0859098	+	0.174616i
$419$		−	3.99144e9i		−	0.129501i	−0.997901	−	0.0647505i	$-0.979375\pi$
$419$		−	3.99144e9i		−	0.129501i	0.997901	−	0.0647505i	$-0.0206252\pi$
$420$	4.01469e10	+	2.91355e9i	1.29019	+	0.0936321i
$421$	−8.14500e9			−0.259276			−0.129638	−	0.991561i	$-0.541382\pi$
$421$	−8.14500e9			−0.259276			−0.129638	+	0.991561i	$0.541382\pi$
$422$	−2.79153e10	−	1.37341e10i	−0.880222	−	0.433062i
$423$	−1.93401e10			−0.604085
$424$	−7.95025e8	−	3.93949e9i	−0.0245990	−	0.121892i
$425$	−5.53532e10	+	6.29263e9i	−1.69663	+	0.192875i
$426$	−6.92977e10	−	3.40939e10i	−2.10417	−	1.03523i
$427$	2.62871e10			0.790734
$428$	−1.74662e9	−	2.26752e9i	−0.0520504	−	0.0675733i
$429$	2.37510e10			0.701217
$430$	−1.51587e10	−	3.74324e10i	−0.443391	−	1.09490i
$431$			4.14023e9i			0.119982i	0.998199	+	0.0599909i	$0.0191072\pi$
$431$			4.14023e9i			0.119982i	−0.998199	+	0.0599909i	$0.980893\pi$
$432$	1.15020e10	−	4.35725e10i	0.330246	−	1.25106i
$433$			2.45166e10i			0.697443i	0.937226	+	0.348722i	$0.113384\pi$
$433$			2.45166e10i			0.697443i	−0.937226	+	0.348722i	$0.886616\pi$
$434$	3.34378e10	+	1.64511e10i	0.942494	+	0.463699i
$435$	3.00024e10	−	3.36063e10i	0.837913	−	0.938565i
$436$	5.45119e9	+	7.07689e9i	0.150850	+	0.195838i
$437$			1.80058e10i			0.493726i
$438$	−1.40860e10	−	6.93017e9i	−0.382728	−	0.188299i
$439$		−	5.66902e10i		−	1.52633i	−0.646201	−	0.763167i	$-0.723643\pi$
$439$		−	5.66902e10i		−	1.52633i	0.646201	−	0.763167i	$-0.276357\pi$
$440$	−1.16610e10	−	6.82712e9i	−0.311117	−	0.182149i
$441$	−2.66970e10			−0.705843
$442$	−3.35837e10	+	6.82608e10i	−0.879914	+	1.78847i
$443$	2.12919e10			0.552840			0.276420	−	0.961037i	$-0.410852\pi$
$443$	2.12919e10			0.552840			0.276420	+	0.961037i	$0.410852\pi$
$444$	4.64961e9	−	3.58151e9i	0.119642	−	0.0921582i
$445$	−1.05229e10	+	1.17870e10i	−0.268347	+	0.300581i
$446$	3.99775e9	−	8.12564e9i	0.101036	−	0.205361i
$447$	−5.92319e10			−1.48363
$448$	−2.88245e10	+	1.21280e10i	−0.715566	+	0.301078i
$449$	−5.16478e10			−1.27077			−0.635384	−	0.772196i	$-0.719158\pi$
$449$	−5.16478e10			−1.27077			−0.635384	+	0.772196i	$0.719158\pi$
$450$	6.85800e10	+	2.45703e10i	1.67243	+	0.599184i
$451$			1.24912e10i			0.301925i
$452$	−3.14533e10	+	2.42279e10i	−0.753551	+	0.580446i
$453$		−	9.91711e10i		−	2.35501i
$454$	−1.58890e10	+	3.22953e10i	−0.374001	+	0.760178i
$455$	2.89728e10	+	2.58658e10i	0.675998	+	0.603503i
$456$	7.69331e9	+	3.81217e10i	0.177932	+	0.881684i
$457$		−	6.18862e10i		−	1.41883i	−0.704793	−	0.709413i	$-0.748960\pi$
$457$		−	6.18862e10i		−	1.41883i	0.704793	−	0.709413i	$-0.251040\pi$
$458$	7.21221e9	−	1.46592e10i	0.163910	−	0.333157i
$459$			9.80689e10i			2.20943i
$460$	−4.08456e10	−	2.96426e9i	−0.912251	−	0.0662041i
$461$	1.84997e9			0.0409601			0.0204800	−	0.999790i	$-0.493481\pi$
$461$	1.84997e9			0.0409601			0.0204800	+	0.999790i	$0.493481\pi$
$462$	−1.90641e10	−	9.37940e9i	−0.418455	−	0.205877i
$463$	4.89801e10			1.06585			0.532924	−	0.846163i	$-0.321093\pi$
$463$	4.89801e10			1.06585			0.532924	+	0.846163i	$0.321093\pi$
$464$	−8.93293e9	+	3.38403e10i	−0.192718	+	0.730067i
$465$	7.86304e10	+	7.01981e10i	1.68182	+	1.50146i
$466$	2.31034e10	+	1.13667e10i	0.489928	+	0.241041i
$467$	−2.58985e9			−0.0544511			−0.0272255	−	0.999629i	$-0.508667\pi$
$467$	−2.58985e9			−0.0544511			−0.0272255	+	0.999629i	$0.508667\pi$
$468$	7.88095e10	−	6.07054e10i	1.64284	−	1.26545i
$469$	−7.00167e10			−1.44714
$470$	6.22810e9	+	1.53795e10i	0.127633	+	0.315175i
$471$		−	5.30322e10i		−	1.07760i
$472$	−6.05702e9	−	3.00136e10i	−0.122037	−	0.604714i
$473$			2.13166e10i			0.425867i
$474$	−7.22238e10	−	3.55335e10i	−1.43076	−	0.703923i
$475$	−2.73034e10	+	3.10389e9i	−0.536342	+	0.0609722i
$476$	5.39131e10	−	4.15283e10i	1.05019	−	0.808939i
$477$		−	1.14364e10i		−	0.220910i
$478$	8.81705e10	+	4.33792e10i	1.68893	+	0.830940i
$479$			7.24642e10i			1.37652i	0.725466	+	0.688258i	$0.241624\pi$
$479$			7.24642e10i			1.37652i	−0.725466	+	0.688258i	$0.758376\pi$
$480$	−8.77447e10	+	1.11762e10i	−1.65294	+	0.210537i
$481$	5.66298e9			0.105795
$482$	1.11329e10	−	2.26283e10i	0.206263	−	0.419241i
$483$	−6.43930e10			−1.18318
$484$	−2.91347e10	−	3.78235e10i	−0.530920	−	0.689255i
$485$	−6.32722e8	−	5.64869e8i	−0.0114353	−	0.0102089i
$486$	−1.62924e10	+	3.31153e10i	−0.292039	+	0.593585i
$487$	−6.78628e10			−1.20647			−0.603234	−	0.797564i	$-0.706121\pi$
$487$	−6.78628e10			−1.20647			−0.603234	+	0.797564i	$0.706121\pi$
$488$	−5.66235e10	+	1.14272e10i	−0.998430	+	0.201493i
$489$	1.18602e11			2.07422
$490$	8.59724e9	+	2.12298e10i	0.149133	+	0.368267i
$491$		−	1.04720e11i		−	1.80179i	−0.434032	−	0.900897i	$-0.642910\pi$
$491$		−	1.04720e11i		−	1.80179i	0.434032	−	0.900897i	$-0.357090\pi$
$492$	4.98977e10	+	6.47786e10i	0.851570	+	1.10553i
$493$		−	7.61646e10i		−	1.28933i
$494$	−1.65654e10	+	3.36701e10i	−0.278160	+	0.565376i
$495$	−2.86840e10	−	2.56079e10i	−0.477770	−	0.426534i
$496$	−7.91779e10	−	2.09008e10i	−1.30821	−	0.345332i
$497$			6.66608e10i			1.09256i
$498$	−1.99685e10	+	4.05871e10i	−0.324659	+	0.659888i
$499$		−	5.70756e10i		−	0.920552i	−0.887776	−	0.460276i	$-0.847750\pi$
$499$		−	5.70756e10i		−	0.920552i	0.887776	−	0.460276i	$-0.152250\pi$
$500$	−2.54618e9	−	6.24481e10i	−0.0407389	−	0.999170i
$501$	5.78379e10			0.918040
$502$	−8.68911e9	−	4.27497e9i	−0.136823	−	0.0673160i
$503$	1.65834e10			0.259061			0.129531	−	0.991575i	$-0.458653\pi$
$503$	1.65834e10			0.259061			0.129531	+	0.991575i	$0.458653\pi$
$504$	−8.72306e10	+	1.76040e10i	−1.35191	+	0.272827i
$505$	5.20673e10	−	5.83218e10i	0.800571	−	0.896738i
$506$	1.93960e10	+	9.54265e9i	0.295876	+	0.145568i
$507$	3.99171e10			0.604125
$508$	−3.30314e10	−	4.28823e10i	−0.495989	−	0.643907i
$509$	3.82746e9			0.0570216			0.0285108	−	0.999593i	$-0.490924\pi$
$509$	3.82746e9			0.0570216			0.0285108	+	0.999593i	$0.490924\pi$
$510$	1.78415e11	−	7.22511e10i	2.63725	−	1.06798i
$511$			1.35499e10i			0.198726i
$512$	5.68172e10	−	3.86546e10i	0.826799	−	0.562498i
$513$			4.83732e10i			0.698451i
$514$	1.05288e11	+	5.18010e10i	1.50844	+	0.742140i
$515$	−1.89571e10	+	2.12343e10i	−0.269490	+	0.301862i
$516$	8.51520e10	+	1.10547e11i	1.20115	+	1.55936i
$517$		−	8.75818e9i		−	0.122589i
$518$	−4.54548e9	−	2.23634e9i	−0.0631337	−	0.0310613i
$519$			4.16740e10i			0.574376i
$520$	−7.36528e10	−	4.31214e10i	−1.00734	−	0.589765i
$521$	−7.15272e10			−0.970779			−0.485389	−	0.874298i	$-0.661322\pi$
$521$	−7.15272e10			−0.970779			−0.485389	+	0.874298i	$0.661322\pi$
$522$	−4.39673e10	+	8.93660e10i	−0.592172	+	1.20362i
$523$	2.30293e10			0.307803			0.153902	−	0.988086i	$-0.450816\pi$
$523$	2.30293e10			0.307803			0.153902	+	0.988086i	$0.450816\pi$
$524$	2.31228e10	−	1.78110e10i	0.306701	−	0.236246i
$525$	−1.11003e10	−	9.76436e10i	−0.146115	−	1.28531i
$526$	−5.72985e10	+	1.16462e11i	−0.748515	+	1.52140i
$527$	1.78206e11			2.31036
$528$	4.51423e10	+	1.19164e10i	0.580829	+	0.153323i
$529$	−1.27972e10			−0.163415
$530$	−9.09438e9	+	3.68286e9i	−0.115258	+	0.0466748i
$531$		−	8.71300e10i		−	1.09595i
$532$	2.65930e10	−	2.04841e10i	0.331987	−	0.255724i
$533$			7.88969e10i			0.977577i
$534$	2.41013e10	−	4.89872e10i	0.296398	−	0.602446i
$535$	−4.65374e9	+	5.21275e9i	−0.0568050	+	0.0636285i
$536$	1.50819e11	−	3.04367e10i	1.82725	−	0.368756i
$537$		−	3.16250e10i		−	0.380306i
$538$	−9.31733e9	+	1.89380e10i	−0.111215	+	0.226050i
$539$		−	1.20897e10i		−	0.143239i
$540$	−1.09734e11	−	7.96361e9i	−1.29052	−	0.0936559i
$541$	5.52906e10			0.645450			0.322725	−	0.946493i	$-0.395401\pi$
$541$	5.52906e10			0.645450			0.322725	+	0.946493i	$0.395401\pi$
$542$	−4.33027e10	−	2.13046e10i	−0.501786	−	0.246874i
$543$	2.67544e10			0.307748
$544$	−9.80787e10	+	1.12890e11i	−1.11990	+	1.28902i
$545$	1.45242e10	−	1.62689e10i	0.164630	−	0.184405i
$546$	−1.20413e11	−	5.92421e10i	−1.35488	−	0.666591i
$547$	−8.25380e10			−0.921945			−0.460972	−	0.887415i	$-0.652499\pi$
$547$	−8.25380e10			−0.921945			−0.460972	+	0.887415i	$0.652499\pi$
$548$	−8.04605e10	+	6.19772e10i	−0.892196	+	0.687242i
$549$	−1.64379e11			−1.80949
$550$	−1.11267e10	+	3.10565e10i	−0.121595	+	0.339392i
$551$		−	3.75688e10i		−	0.407587i
$552$	1.38705e11	−	2.79921e10i	1.49395	−	0.301494i
$553$			6.94755e10i			0.742902i
$554$	1.71862e10	+	8.45545e9i	0.182448	+	0.0897631i
$555$	−1.06889e10	−	9.54263e9i	−0.112658	−	0.100576i
$556$	−5.71592e10	+	4.40286e10i	−0.598118	+	0.460719i
$557$		−	6.76291e10i		−	0.702608i	−0.936261	−	0.351304i	$-0.885738\pi$
$557$		−	6.76291e10i		−	0.702608i	0.936261	−	0.351304i	$-0.114262\pi$
$558$	−2.09094e11	−	1.02873e11i	−2.15678	−	1.06112i
$559$			1.34640e11i			1.37888i
$560$	4.20898e10	+	6.36980e10i	0.427981	+	0.647700i
$561$	−1.01602e11			−1.02577
$562$	−1.45209e10	+	2.95145e10i	−0.145562	+	0.295863i
$563$	−1.16824e11			−1.16278			−0.581391	−	0.813624i	$-0.697491\pi$
$563$	−1.16824e11			−1.16278			−0.581391	+	0.813624i	$0.697491\pi$
$564$	−3.49857e10	−	4.54193e10i	−0.345759	−	0.448874i
$565$	7.23075e10	+	6.45532e10i	0.709561	+	0.633467i
$566$	8.57355e10	−	1.74262e11i	0.835401	−	1.69800i
$567$	−3.04510e10			−0.294625
$568$	−2.89779e10	−	1.43590e11i	−0.278403	−	1.37953i
$569$	−1.83290e9			−0.0174860			−0.00874298	−	0.999962i	$-0.502783\pi$
$569$	−1.83290e9			−0.0174860			−0.00874298	+	0.999962i	$0.502783\pi$
$570$	8.80046e10	−	3.56384e10i	0.833693	−	0.337613i
$571$			1.83754e11i			1.72859i	0.502984	+	0.864296i	$0.332235\pi$
$571$			1.83754e11i			1.72859i	−0.502984	+	0.864296i	$0.667765\pi$
$572$	2.74905e10	+	3.56889e10i	0.256802	+	0.333387i
$573$			3.10221e11i			2.87774i
$574$	3.11568e10	−	6.33279e10i	0.287016	−	0.583375i
$575$	1.12935e10	+	9.93432e10i	0.103313	+	0.908797i
$576$	1.80246e11	−	7.58395e10i	1.63748	−	0.688978i
$577$		−	1.07447e11i		−	0.969374i	−0.874688	−	0.484687i	$-0.838934\pi$
$577$		−	1.07447e11i		−	0.969374i	0.874688	−	0.484687i	$-0.161066\pi$
$578$	9.43927e10	−	1.91858e11i	0.845721	−	1.71897i
$579$		−	8.78307e10i		−	0.781505i
$580$	8.52239e10	+	6.18489e9i	0.753094	+	0.0546537i
$581$	3.90426e10			0.342637
$582$	2.62963e9	+	1.29376e9i	0.0229194	+	0.0112761i
$583$	5.17897e9			0.0448301
$584$	−5.89025e9	−	2.91872e10i	−0.0506387	−	0.250923i
$585$	−1.81174e11	−	1.61745e11i	−1.54693	−	1.38104i
$586$	−1.27174e11	−	6.25688e10i	−1.07847	−	0.530600i
$587$	−8.33835e10			−0.702308			−0.351154	−	0.936318i	$-0.614211\pi$
$587$	−8.33835e10			−0.702308			−0.351154	+	0.936318i	$0.614211\pi$
$588$	−4.82940e10	−	6.26966e10i	−0.404003	−	0.524487i
$589$	8.79015e10			0.730357
$590$	−6.92869e10	+	2.80585e10i	−0.571799	+	0.231556i
$591$			1.59370e11i			1.30634i
$592$	1.07633e10	+	2.84123e9i	0.0876315	+	0.0231323i
$593$		−	8.33128e10i		−	0.673741i	−0.941551	−	0.336871i	$-0.890631\pi$
$593$		−	8.33128e10i		−	0.673741i	0.941551	−	0.336871i	$-0.109369\pi$
$594$	5.21081e10	+	2.56368e10i	0.418562	+	0.205929i
$595$	−1.23940e11	−	1.10649e11i	−0.988880	−	0.882832i
$596$	−6.85577e10	−	8.90034e10i	−0.543339	−	0.705378i
$597$			1.16321e11i			0.915714i
$598$	1.22509e11	+	6.02732e10i	0.957992	+	0.471324i
$599$		−	7.46618e10i		−	0.579951i	−0.957034	−	0.289976i	$-0.906353\pi$
$599$		−	7.46618e10i		−	0.579951i	0.957034	−	0.289976i	$-0.0936472\pi$
$600$	6.63568e10	+	2.05504e11i	0.512012	+	1.58568i
$601$	−1.14915e11			−0.880803			−0.440401	−	0.897801i	$-0.645164\pi$
$601$	−1.14915e11			−0.880803			−0.440401	+	0.897801i	$0.645164\pi$
$602$	5.31700e10	−	1.08071e11i	0.404838	−	0.822855i
$603$	4.37831e11			3.31159
$604$	1.49017e11	−	1.14785e11i	1.11967	−	0.862457i
$605$	−7.76270e10	+	8.69518e10i	−0.579417	+	0.649018i
$606$	−1.19253e11	+	2.42389e11i	−0.884259	+	1.79731i
$607$	3.63432e10			0.267712			0.133856	−	0.991001i	$-0.457264\pi$
$607$	3.63432e10			0.267712			0.133856	+	0.991001i	$0.457264\pi$
$608$	−4.83781e10	+	5.56839e10i	−0.354025	+	0.407489i
$609$	1.34355e11			0.976754
$610$	5.29350e10	+	1.30716e11i	0.382317	+	0.944085i
$611$		−	5.53183e10i		−	0.396921i
$612$	−3.37131e11	+	2.59686e11i	−2.40322	+	1.85115i
$613$			4.54903e10i			0.322164i	0.986941	+	0.161082i	$0.0514983\pi$
$613$			4.54903e10i			0.322164i	−0.986941	+	0.161082i	$0.948502\pi$
$614$	−1.60418e10	+	3.26059e10i	−0.112870	+	0.229415i
$615$	1.32948e11	−	1.48918e11i	0.929357	−	1.04099i
$616$	−7.97195e9	−	3.95024e10i	−0.0553658	−	0.274347i
$617$			9.39914e10i			0.648556i	0.945962	+	0.324278i	$0.105121\pi$
$617$			9.39914e10i			0.648556i	−0.945962	+	0.324278i	$0.894879\pi$
$618$	4.34187e10	−	8.82508e10i	0.297662	−	0.605013i
$619$		−	6.86980e10i		−	0.467931i	−0.972245	−	0.233965i	$-0.924830\pi$
$619$		−	6.86980e10i		−	0.467931i	0.972245	−	0.233965i	$-0.0751702\pi$
$620$	−1.44711e10	+	1.99403e11i	−0.0979342	+	1.34947i
$621$	1.76006e11			1.18348
$622$	−1.42852e10	−	7.02820e9i	−0.0954387	−	0.0469550i
$623$	−4.71232e10			−0.312811
$624$	2.85127e11	+	7.52659e10i	1.88062	+	0.496432i
$625$	−1.48694e11	+	3.42502e10i	−0.974483	+	0.224462i
$626$	−1.38934e11	−	6.83544e10i	−0.904714	−	0.445112i
$627$	−5.01160e10			−0.324269
$628$	7.96876e10	−	6.13818e10i	0.512333	−	0.394640i
$629$	−2.42251e10			−0.154761
$630$	8.15483e10	+	2.01374e11i	0.517670	+	1.27832i
$631$			3.95536e10i			0.249499i	0.992188	+	0.124750i	$0.0398128\pi$
$631$			3.95536e10i			0.249499i	−0.992188	+	0.124750i	$0.960187\pi$
$632$	−3.02015e10	−	1.49654e11i	−0.189304	−	0.938034i
$633$		−	2.62439e11i		−	1.63461i
$634$	−7.77533e10	−	3.82540e10i	−0.481240	−	0.236766i
$635$	−8.80094e10	+	9.85813e10i	−0.541295	+	0.606317i
$636$	2.68578e10	−	2.06881e10i	0.164150	−	0.126442i
$637$		−	7.63612e10i		−	0.463783i
$638$	−4.04694e10	−	1.99106e10i	−0.244255	−	0.120172i
$639$		−	4.16845e11i		−	2.50018i
$640$	−1.18353e11	−	1.18912e11i	−0.705441	−	0.708769i
$641$	3.16726e11			1.87608			0.938040	−	0.346526i	$-0.112639\pi$
$641$	3.16726e11			1.87608			0.938040	+	0.346526i	$0.112639\pi$
$642$	1.06588e10	−	2.16645e10i	0.0627432	−	0.127529i
$643$	2.41563e11			1.41315			0.706574	−	0.707640i	$-0.250240\pi$
$643$	2.41563e11			1.41315			0.706574	+	0.707640i	$0.250240\pi$
$644$	−7.45313e10	−	9.67586e10i	−0.433307	−	0.562531i
$645$	2.26880e11	−	2.54134e11i	1.31087	−	1.46833i
$646$	7.08636e10	−	1.44034e11i	0.406905	−	0.827057i
$647$	−1.42487e11			−0.813124			−0.406562	−	0.913623i	$-0.633272\pi$
$647$	−1.42487e11			−0.813124			−0.406562	+	0.913623i	$0.633272\pi$
$648$	6.55930e10	−	1.32373e10i	0.372012	−	0.0750755i
$649$	3.94568e10			0.222404
$650$	−7.02781e10	+	1.96158e11i	−0.393701	+	1.09889i
$651$			3.14357e11i			1.75025i
$652$	1.37275e11	+	1.78214e11i	0.759628	+	0.986170i
$653$			1.22267e11i			0.672447i	0.941782	+	0.336224i	$0.109150\pi$
$653$			1.22267e11i			0.672447i	−0.941782	+	0.336224i	$0.890850\pi$
$654$	−3.32658e10	+	6.76146e10i	−0.181839	+	0.369598i
$655$	−5.31566e10	−	4.74560e10i	−0.288796	−	0.257826i
$656$	−3.95841e10	+	1.49955e11i	−0.213750	+	0.809742i
$657$		−	8.47310e10i		−	0.454758i
$658$	−2.18455e10	+	4.44022e10i	−0.116536	+	0.236865i
$659$			1.05381e11i			0.558753i	0.960182	+	0.279377i	$0.0901278\pi$
$659$			1.05381e11i			0.558753i	−0.960182	+	0.279377i	$0.909872\pi$
$660$	8.25051e9	−	1.13687e11i	0.0434816	−	0.599149i
$661$	−2.12360e11			−1.11242			−0.556209	−	0.831043i	$-0.687745\pi$
$661$	−2.12360e11			−1.11242			−0.556209	+	0.831043i	$0.687745\pi$
$662$	2.31690e11	+	1.13990e11i	1.20636	+	0.593517i
$663$	−6.41738e11			−3.32126
$664$	−8.40996e10	+	1.69721e10i	−0.432635	+	0.0873098i
$665$	−6.11343e10	−	5.45782e10i	−0.312607	−	0.279083i
$666$	2.84240e10	+	1.39844e10i	0.144473	+	0.0710797i
$667$	−1.36694e11			−0.690629
$668$	6.69442e10	+	8.69088e10i	0.336207	+	0.436473i
$669$	7.63913e10			0.381364
$670$	−1.40995e11	−	3.48169e11i	−0.699687	−	1.72779i
$671$		−	7.44391e10i		−	0.367207i
$672$	−1.99139e11	−	1.73012e11i	−0.976518	−	0.848396i
$673$			3.80972e11i			1.85709i	0.371219	+	0.928545i	$0.378940\pi$
$673$			3.80972e11i			1.85709i	−0.371219	+	0.928545i	$0.621060\pi$
$674$	−2.29819e11	−	1.13069e11i	−1.11365	−	0.547905i
$675$	3.03404e10	+	2.66890e11i	0.146152	+	1.28563i
$676$	4.62018e10	+	5.99804e10i	0.221244	+	0.287225i
$677$		−	2.80516e11i		−	1.33538i	−0.744441	−	0.667688i	$-0.767284\pi$
$677$		−	2.80516e11i		−	1.33538i	0.744441	−	0.667688i	$-0.232716\pi$
$678$	−3.00514e11	−	1.47850e11i	−1.42215	−	0.699687i
$679$		−	2.52957e9i		−	0.0119005i
$680$	3.15072e11	+	1.84465e11i	1.47358	+	0.862735i
$681$	−3.03616e11			−1.41168
$682$	4.65859e10	−	9.46883e10i	0.215336	−	0.437682i
$683$	5.79360e10			0.266235			0.133118	−	0.991100i	$-0.457501\pi$
$683$	5.79360e10			0.266235			0.133118	+	0.991100i	$0.457501\pi$
$684$	−1.66292e11	+	1.28092e11i	−0.759711	+	0.585191i
$685$	1.84969e11	+	1.65133e11i	0.840112	+	0.750018i
$686$	−1.06053e11	+	2.15559e11i	−0.478880	+	0.973350i
$687$	1.37815e11			0.618686
$688$	−6.75515e10	+	2.55903e11i	−0.301496	+	1.14215i
$689$	3.27114e10			0.145152
$690$	−1.29670e11	−	3.20204e11i	−0.572062	−	1.41264i
$691$		−	2.55640e11i		−	1.12129i	−0.828057	−	0.560644i	$-0.810554\pi$
$691$		−	2.55640e11i		−	1.12129i	0.828057	−	0.560644i	$-0.189446\pi$
$692$	−6.26205e10	+	4.82354e10i	−0.273082	+	0.210350i
$693$		−	1.14676e11i		−	0.497210i
$694$	9.50499e10	−	1.93194e11i	0.409745	−	0.832829i
$695$	1.31402e11	+	1.17311e11i	0.563201	+	0.502803i
$696$	−2.89407e11	+	5.84051e10i	−1.23331	+	0.248893i
$697$		−	3.37505e11i		−	1.43004i
$698$	−1.26363e11	+	2.56840e11i	−0.532352	+	1.08203i
$699$			2.17201e11i			0.909817i
$700$	1.33874e11	−	1.29697e11i	0.557576	−	0.540178i
$701$	1.52264e11			0.630556			0.315278	−	0.948999i	$-0.397902\pi$
$701$	1.52264e11			0.630556			0.315278	+	0.948999i	$0.397902\pi$
$702$	3.29125e11	+	1.61927e11i	1.35523	+	0.666760i
$703$	−1.19492e10			−0.0489235
$704$	3.43439e10	+	8.16245e10i	0.139817	+	0.332300i
$705$	−9.32164e10	+	1.04414e11i	−0.377343	+	0.422670i
$706$	3.88426e11	+	1.91102e11i	1.56347	+	0.769214i
$707$	2.33165e11			0.933225
$708$	2.04620e11	−	1.57615e11i	0.814359	−	0.627285i
$709$	8.99510e10			0.355976			0.177988	−	0.984033i	$-0.443041\pi$
$709$	8.99510e10			0.355976			0.177988	+	0.984033i	$0.443041\pi$
$710$	−3.31481e11	+	1.34237e11i	−1.30444	+	0.528248i
$711$		−	4.34447e11i		−	1.70004i
$712$	1.01505e11	−	2.04847e10i	0.394975	−	0.0797096i
$713$		−	3.19829e11i		−	1.23754i
$714$	5.15101e11	+	2.53426e11i	1.98198	+	0.975119i
$715$	7.32461e10	−	8.20446e10i	0.280259	−	0.313925i
$716$	4.75205e10	−	3.66041e10i	0.180813	−	0.139277i
$717$			8.28915e11i			3.13641i
$718$	7.90186e10	+	3.88765e10i	0.297325	+	0.146281i
$719$			3.34871e11i			1.25303i	0.779409	+	0.626515i	$0.215519\pi$
$719$			3.34871e11i			1.25303i	−0.779409	+	0.626515i	$0.784481\pi$
$720$	−2.63197e11	−	3.98318e11i	−0.979380	−	1.48218i
$721$	−8.48927e10			−0.314144
$722$	−8.50059e10	+	1.72779e11i	−0.312824	+	0.635832i
$723$	2.12735e11			0.778547
$724$	3.09667e10	+	4.02019e10i	0.112704	+	0.146316i
$725$	−2.35637e10	−	2.07278e11i	−0.0852886	−	0.750243i
$726$	1.77794e11	−	3.61376e11i	0.639987	−	1.30081i
$727$	4.68905e11			1.67860			0.839300	−	0.543669i	$-0.182965\pi$
$727$	4.68905e11			1.67860			0.839300	+	0.543669i	$0.182965\pi$
$728$	−5.03524e10	−	2.49505e11i	−0.179265	−	0.888287i
$729$	−4.18511e11			−1.48182
$730$	−6.73792e10	+	2.72859e10i	−0.237265	+	0.0960831i
$731$		−	5.75963e11i		−	2.01709i
$732$	−2.97356e11	−	3.86036e11i	−1.03570	−	1.34457i
$733$			6.30452e10i			0.218392i	0.994020	+	0.109196i	$0.0348276\pi$
$733$			6.30452e10i			0.218392i	−0.994020	+	0.109196i	$0.965172\pi$
$734$	6.83307e10	−	1.38886e11i	0.235414	−	0.478491i
$735$	−1.28675e11	+	1.44132e11i	−0.440906	+	0.493869i
$736$	2.02606e11	+	1.76023e11i	0.690463	+	0.599872i
$737$			1.98272e11i			0.672033i
$738$	−1.94831e11	+	3.96004e11i	−0.656798	+	1.33498i
$739$			2.09954e11i			0.703959i	0.936008	+	0.351979i	$0.114491\pi$
$739$			2.09954e11i			0.703959i	−0.936008	+	0.351979i	$0.885509\pi$
$740$	1.96718e9	−	2.71065e10i	0.00656020	−	0.0903955i
$741$	−3.16542e11			−1.04993
$742$	−2.62563e10	−	1.29179e10i	−0.0866200	−	0.0426164i
$743$	−2.18225e11			−0.716060			−0.358030	−	0.933710i	$-0.616552\pi$
$743$	−2.18225e11			−0.716060			−0.358030	+	0.933710i	$0.616552\pi$
$744$	−1.36653e11	−	6.77140e11i	−0.445993	−	2.20997i
$745$	−1.82666e11	+	2.04608e11i	−0.592970	+	0.664199i
$746$	3.69448e11	+	1.81765e11i	1.19288	+	0.586889i
$747$	−2.44143e11			−0.784081
$748$	−1.17599e11	−	1.52670e11i	−0.375661	−	0.487693i
$749$	−2.08401e10			−0.0662175
$750$	4.63195e11	−	2.51826e11i	1.46393	−	0.795893i
$751$			5.33771e10i			0.167801i	0.996474	+	0.0839006i	$0.0267378\pi$
$751$			5.33771e10i			0.167801i	−0.996474	+	0.0839006i	$0.973262\pi$
$752$	2.77543e10	−	1.05141e11i	0.0867879	−	0.328776i
$753$		−	8.16886e10i		−	0.254087i
$754$	−2.55612e11	−	1.25759e11i	−0.790855	−	0.389094i
$755$	−3.42573e11	−	3.05835e11i	−1.05430	−	0.941238i
$756$	−2.00232e11	−	2.59946e11i	−0.612979	−	0.795786i
$757$			2.91321e11i			0.887132i	0.896242	+	0.443566i	$0.146287\pi$
$757$			2.91321e11i			0.887132i	−0.896242	+	0.443566i	$0.853713\pi$
$758$	4.86828e11	+	2.39515e11i	1.47468	+	0.725532i
$759$			1.82347e11i			0.549453i
$760$	1.55412e11	+	9.09886e10i	0.465832	+	0.272730i
$761$	1.92349e10			0.0573523			0.0286762	−	0.999589i	$-0.490871\pi$
$761$	1.92349e10			0.0573523			0.0286762	+	0.999589i	$0.490871\pi$
$762$	2.01574e11	−	4.09710e11i	0.597880	−	1.21522i
$763$	6.50417e10			0.191908
$764$	−4.66146e11	+	3.59063e11i	−1.36820	+	1.05390i
$765$	7.75025e11	+	6.91911e11i	2.26292	+	2.02025i
$766$	−7.59066e10	+	1.54284e11i	−0.220478	+	0.448133i
$767$	2.49217e11			0.720105
$768$	5.04165e11	+	2.86108e11i	1.44920	+	0.822405i
$769$	3.49604e11			0.999703			0.499852	−	0.866111i	$-0.333388\pi$
$769$	3.49604e11			0.999703			0.499852	+	0.866111i	$0.333388\pi$
$770$	−9.11920e10	+	3.69292e10i	−0.259414	+	0.105053i
$771$			9.89843e11i			2.80123i
$772$	1.31977e11	−	1.01659e11i	0.371559	−	0.286205i
$773$		−	6.52120e11i		−	1.82646i	−0.407447	−	0.913229i	$-0.633581\pi$
$773$		−	6.52120e11i		−	1.82646i	0.407447	−	0.913229i	$-0.366419\pi$
$774$	−3.32484e11	+	6.75793e11i	−0.926419	+	1.88300i
$775$	4.84979e11	−	5.51331e10i	1.34436	−	0.152829i
$776$	1.09962e9	+	5.44880e9i	0.00303246	+	0.0150264i
$777$		−	4.27333e10i		−	0.117242i
$778$	2.94827e11	−	5.99251e11i	0.804727	−	1.63565i
$779$		−	1.66477e11i		−	0.452068i
$780$	5.21118e10	−	7.18068e11i	0.140785	−	1.93994i
$781$	1.88768e11			0.507371
$782$	−5.24067e11	−	2.57837e11i	−1.40139	−	0.689474i
$783$	−3.67233e11			−0.977001
$784$	3.83119e10	−	1.45136e11i	0.101407	−	0.384158i
$785$	−1.83192e11	−	1.63547e11i	−0.482424	−	0.430689i
$786$	2.20922e11	+	1.08692e11i	0.578826	+	0.284778i
$787$	−3.62094e11			−0.943892			−0.471946	−	0.881627i	$-0.656448\pi$
$787$	−3.62094e11			−0.943892			−0.471946	+	0.881627i	$0.656448\pi$
$788$	−2.39473e11	+	1.84462e11i	−0.621087	+	0.478411i
$789$	−1.09489e12			−2.82530
$790$	−3.45478e11	+	1.39905e11i	−0.886976	+	0.359190i
$791$			2.89079e11i			0.738432i
$792$	4.98505e10	+	2.47018e11i	0.126698	+	0.627809i
$793$		−	4.70171e11i		−	1.18895i
$794$	−1.83972e11	−	9.05129e10i	−0.462882	−	0.227734i
$795$	−6.17430e10	−	5.51216e10i	−0.154568	−	0.137992i
$796$	−1.74787e11	+	1.34635e11i	−0.435368	+	0.335355i
$797$		−	1.33733e11i		−	0.331440i	−0.986173	−	0.165720i	$-0.947005\pi$
$797$		−	1.33733e11i		−	0.331440i	0.986173	−	0.165720i	$-0.0529948\pi$
$798$	2.54078e11	+	1.25004e11i	0.626549	+	0.308257i
$799$			2.36641e11i			0.580634i
$800$	−2.31991e11	+	3.37568e11i	−0.566383	+	0.824142i
$801$	2.94672e11			0.715828
$802$	−3.35878e11	+	6.82691e11i	−0.811866	+	1.65016i
$803$	3.83704e10			0.0922857
$804$	7.92022e11	+	1.02822e12i	1.89545	+	2.46073i
$805$	−1.98583e11	+	2.22437e11i	−0.472887	+	0.529692i
$806$	2.94245e11	−	5.98069e11i	0.697219	−	1.41714i
$807$	−1.78041e11			−0.419784
$808$	−5.02249e11	+	1.01358e11i	−1.17835	+	0.237801i
$809$	4.11621e11			0.960956			0.480478	−	0.877007i	$-0.340463\pi$
$809$	4.11621e11			0.960956			0.480478	+	0.877007i	$0.340463\pi$
$810$	−6.13201e10	−	1.51423e11i	−0.142450	−	0.351763i
$811$		−	7.23209e11i		−	1.67178i	−0.548894	−	0.835892i	$-0.684951\pi$
$811$		−	7.23209e11i		−	1.67178i	0.548894	−	0.835892i	$-0.315049\pi$
$812$	1.55509e11	+	2.01886e11i	0.357709	+	0.464388i
$813$		−	4.07100e11i		−	0.931836i
$814$	−6.33282e9	+	1.28718e10i	−0.0144245	+	0.0293185i
$815$	3.65758e11	−	4.09693e11i	0.829016	−	0.928600i
$816$	−1.21972e12	−	3.21973e11i	−2.75105	−	0.726203i
$817$		−	2.84098e11i		−	0.637646i
$818$	−1.72850e11	+	3.51327e11i	−0.386061	+	0.784691i
$819$		−	7.24316e11i		−	1.60988i
$820$	3.77649e11	+	2.74068e10i	0.835282	+	0.0606183i
$821$	6.38146e11			1.40458			0.702291	−	0.711890i	$-0.252160\pi$
$821$	6.38146e11			1.40458			0.702291	+	0.711890i	$0.252160\pi$
$822$	−7.68743e11	−	3.78215e11i	−1.68381	−	0.828422i
$823$	2.86794e11			0.625130			0.312565	−	0.949896i	$-0.398812\pi$
$823$	2.86794e11			0.625130			0.312565	+	0.949896i	$0.398812\pi$
$824$	1.82863e11	−	3.69034e10i	0.396658	−	0.0800493i
$825$	−2.76505e11	+	3.14335e10i	−0.596880	+	0.0678541i
$826$	−2.00038e11	−	9.84171e10i	−0.429727	−	0.211422i
$827$	−6.21880e11			−1.32949			−0.664745	−	0.747071i	$-0.731460\pi$
$827$	−6.21880e11			−1.32949			−0.664745	+	0.747071i	$0.731460\pi$
$828$	4.66062e11	+	6.05054e11i	0.991567	+	1.28728i
$829$	−5.50205e11			−1.16495			−0.582474	−	0.812849i	$-0.697915\pi$
$829$	−5.50205e11			−1.16495			−0.582474	+	0.812849i	$0.697915\pi$
$830$	7.86212e10	+	1.94145e11i	0.165664	+	0.409086i
$831$			1.61572e11i			0.338814i
$832$	2.16923e11	+	5.15556e11i	0.452701	+	1.07593i
$833$			3.26658e11i			0.678442i
$834$	−5.46115e11	−	2.68684e11i	−1.12881	−	0.555364i
$835$	1.78367e11	−	1.99793e11i	0.366918	−	0.410993i
$836$	−5.80065e10	−	7.53056e10i	−0.118755	−	0.154171i
$837$		−	8.59235e11i		−	1.75069i
$838$	5.73032e10	+	2.81927e10i	0.116199	+	0.0571690i
$839$			9.29570e9i			0.0187601i	0.999956	+	0.00938003i	$0.00298580\pi$
$839$			9.29570e9i			0.0187601i	−0.999956	+	0.00938003i	$0.997014\pi$
$840$	−3.25397e11	+	5.55790e11i	−0.653577	+	1.11633i
$841$	−2.15037e11			−0.429862
$842$	5.75305e10	−	1.16934e11i	0.114459	−	0.232644i
$843$	−2.77474e11			−0.549429
$844$	3.94347e11	−	3.03758e11i	0.777158	−	0.598630i
$845$	1.23101e11	−	1.37888e11i	0.241454	−	0.270458i
$846$	1.36605e11	−	2.77657e11i	0.266677	−	0.542035i
$847$	−3.47625e11			−0.675426
$848$	6.21728e10	+	1.64120e10i	0.120231	+	0.0317378i
$849$	1.63828e12			3.15325
$850$	3.00636e11	−	8.39127e11i	0.575924	−	1.60750i
$851$			4.34771e10i			0.0828977i
$852$	9.78941e11	−	7.54059e11i	1.85780	−	1.43103i
$853$			2.76680e11i			0.522615i	0.965256	+	0.261308i	$0.0841537\pi$
$853$			2.76680e11i			0.522615i	−0.965256	+	0.261308i	$0.915846\pi$
$854$	−1.85673e11	+	3.77391e11i	−0.349074	+	0.709512i
$855$	3.82287e11	+	3.41290e11i	0.715361	+	0.638645i
$856$	4.48906e10	−	9.05933e9i	0.0836103	−	0.0168733i
$857$			8.09328e11i			1.50038i	0.661223	+	0.750190i	$0.270038\pi$
$857$			8.09328e11i			1.50038i	−0.661223	+	0.750190i	$0.729962\pi$
$858$	−1.67760e11	+	3.40982e11i	−0.309557	+	0.629190i
$859$			2.89123e11i			0.531020i	0.964108	+	0.265510i	$0.0855403\pi$
$859$			2.89123e11i			0.531020i	−0.964108	+	0.265510i	$0.914460\pi$
$860$	6.44470e11	+	4.67706e10i	1.17817	+	0.0855025i
$861$	5.95362e11			1.08335
$862$	−5.94393e10	−	2.92436e10i	−0.107658	−	0.0529666i
$863$	−6.16481e11			−1.11142			−0.555708	−	0.831378i	$-0.687553\pi$
$863$	−6.16481e11			−1.11142			−0.555708	+	0.831378i	$0.687553\pi$
$864$	5.44309e11	+	4.72894e11i	0.976765	+	0.848612i
$865$	1.43957e11	+	1.28519e11i	0.257140	+	0.229564i
$866$	−3.51973e11	−	1.73168e11i	−0.625804	−	0.307890i
$867$	1.80371e12			3.19220
$868$	−4.72362e11	+	3.63851e11i	−0.832139	+	0.640981i
$869$	1.96739e11			0.344994
$870$	2.70555e11	+	6.68102e11i	0.472257	+	1.16618i
$871$			1.25232e12i			2.17592i
$872$	−1.40103e11	+	2.82741e10i	−0.242315	+	0.0489015i
$873$			1.58180e10i			0.0272329i
$874$	−2.58500e11	−	1.27180e11i	−0.443012	−	0.217958i
$875$	−3.71529e11	−	2.62780e11i	−0.633812	−	0.448292i
$876$	1.98986e11	−	1.53276e11i	0.337915	−	0.260289i
$877$			6.46830e10i			0.109343i	0.998504	+	0.0546716i	$0.0174112\pi$
$877$			6.46830e10i			0.109343i	−0.998504	+	0.0546716i	$0.982589\pi$
$878$	8.13874e11	+	4.00419e11i	1.36955	+	0.673809i
$879$		−	1.19560e12i		−	2.00277i
$880$	1.80378e11	−	1.19189e11i	0.300783	−	0.198749i
$881$	−9.16075e11			−1.52064			−0.760322	−	0.649547i	$-0.774959\pi$
$881$	−9.16075e11			−1.52064			−0.760322	+	0.649547i	$0.774959\pi$
$882$	1.88569e11	−	3.83276e11i	0.311599	−	0.633341i
$883$	−7.21518e11			−1.18687			−0.593437	−	0.804881i	$-0.702229\pi$
$883$	−7.21518e11			−1.18687			−0.593437	+	0.804881i	$0.702229\pi$
$884$	−7.42776e11	−	9.64292e11i	−1.21632	−	1.57906i
$885$	−4.70398e11	−	4.19953e11i	−0.766819	−	0.684585i
$886$	−1.50391e11	+	3.05678e11i	−0.244055	+	0.496054i
$887$	−1.56512e10			−0.0252844			−0.0126422	−	0.999920i	$-0.504024\pi$
$887$	−1.56512e10			−0.0252844			−0.0126422	+	0.999920i	$0.504024\pi$
$888$	1.85764e10	+	9.20495e10i	0.0298752	+	0.148037i
$889$	−3.94119e11			−0.630987
$890$	−9.48933e10	−	2.34327e11i	−0.151243	−	0.373476i
$891$			8.62306e10i			0.136820i
$892$	8.84187e10	+	1.14788e11i	0.139664	+	0.181316i
$893$			1.16725e11i			0.183551i
$894$	4.18372e11	−	8.50364e11i	0.654957	−	1.33124i
$895$	−1.09244e11	−	9.75287e10i	−0.170257	−	0.151999i
$896$	2.94793e10	−	4.99484e11i	0.0457389	−	0.774978i
$897$			1.15174e12i			1.77903i
$898$	3.64804e11	−	7.41483e11i	0.560988	−	1.14024i
$899$			6.67319e11i			1.02163i
$900$	−8.37145e11	+	8.11023e11i	−1.27594	+	1.23613i
$901$	−1.39933e11			−0.212334
$902$	−1.79330e11	−	8.82291e10i	−0.270912	−	0.133286i
$903$	1.01600e12			1.52807
$904$	−1.25664e11	−	6.22689e11i	−0.188165	−	0.932390i
$905$	8.25083e10	−	9.24194e10i	0.122999	−	0.137774i
$906$	1.42375e12	+	7.00474e11i	2.11311	+	1.03963i
$907$	−7.40442e11			−1.09411			−0.547056	−	0.837096i	$-0.684252\pi$
$907$	−7.40442e11			−1.09411			−0.547056	+	0.837096i	$0.684252\pi$
$908$	−3.51419e11	−	4.56222e11i	−0.516990	−	0.671170i
$909$	−1.45804e12			−2.13556
$910$	−5.75986e11	+	2.33252e11i	−0.839937	+	0.340141i
$911$		−	1.11646e12i		−	1.62095i	−0.585770	−	0.810477i	$-0.699208\pi$
$911$		−	1.11646e12i		−	1.62095i	0.585770	−	0.810477i	$-0.300792\pi$
$912$	−6.01635e11	−	1.58815e11i	−0.869669	−	0.229569i
$913$		−	1.10560e11i		−	0.159116i
$914$	8.88471e11	+	4.37121e11i	1.27309	+	0.626349i
$915$	−7.92281e11	+	8.87452e11i	−1.13030	+	1.26608i
$916$	1.59513e11	+	2.07085e11i	0.226577	+	0.294148i
$917$		−	2.12515e11i		−	0.300547i
$918$	−1.40793e12	−	6.92690e11i	−1.98249	−	0.975367i
$919$			4.29970e11i			0.602804i	0.953497	+	0.301402i	$0.0974546\pi$
$919$			4.29970e11i			0.602804i	−0.953497	+	0.301402i	$0.902545\pi$
$920$	3.31061e11	−	5.65464e11i	0.462122	−	0.789321i
$921$	−3.06536e11			−0.426033
$922$	−1.30669e10	+	2.65591e10i	−0.0180821	+	0.0367528i
$923$	1.19230e12			1.64277
$924$	2.69311e11	−	2.07445e11i	0.369459	−	0.284587i
$925$	−6.59274e10	+	7.49472e9i	−0.0900532	+	0.0102374i
$926$	−3.45961e11	+	7.03184e11i	−0.470525	+	0.956368i
$927$	5.30854e11			0.718879
$928$	−4.22734e11	−	3.67270e11i	−0.570000	−	0.495215i
$929$	1.03621e12			1.39119			0.695594	−	0.718435i	$-0.255141\pi$
$929$	1.03621e12			1.39119			0.695594	+	0.718435i	$0.255141\pi$
$930$	−1.56319e12	+	6.33030e11i	−2.08968	+	0.846238i
$931$			1.61126e11i			0.214471i
$932$	−3.26372e11	+	2.51399e11i	−0.432564	+	0.333196i
$933$		−	1.34299e11i		−	0.177233i
$934$	1.82928e10	−	3.71812e10i	0.0240377	−	0.0488580i
$935$	−3.13332e11	+	3.50970e11i	−0.409976	+	0.459223i
$936$	3.14865e11	+	1.56021e12i	0.410224	+	2.03273i
$937$		−	9.79343e11i		−	1.27051i	−0.772304	−	0.635253i	$-0.780896\pi$
$937$		−	9.79343e11i		−	1.27051i	0.772304	−	0.635253i	$-0.219104\pi$
$938$	4.94549e11	−	1.00520e12i	0.638848	−	1.29849i
$939$		−	1.30616e12i		−	1.68009i
$940$	−2.64788e11	−	1.92162e10i	−0.339146	−	0.0246126i
$941$	−3.95736e11			−0.504715			−0.252358	−	0.967634i	$-0.581206\pi$
$941$	−3.95736e11			−0.504715			−0.252358	+	0.967634i	$0.581206\pi$
$942$	7.61358e11	+	3.74582e11i	0.966909	+	0.475711i
$943$	−6.05725e11			−0.766000
$944$	4.73674e11	+	1.25037e11i	0.596474	+	0.157453i
$945$	−5.33501e11	+	5.97586e11i	−0.668972	+	0.749330i
$946$	−3.06033e11	−	1.50566e11i	−0.382123	−	0.188001i
$947$	7.08577e11			0.881022			0.440511	−	0.897747i	$-0.354797\pi$
$947$	7.08577e11			0.881022			0.440511	+	0.897747i	$0.354797\pi$
$948$	1.02028e12	−	7.85900e11i	1.26324	−	0.973047i
$949$	2.42355e11			0.298804
$950$	1.48291e11	−	4.13906e11i	0.182062	−	0.508167i
$951$		−	7.30979e11i		−	0.893682i
$952$	2.15397e11	+	1.06733e12i	0.262236	+	1.29943i
$953$			4.04943e11i			0.490932i	0.969405	+	0.245466i	$0.0789411\pi$
$953$			4.04943e11i			0.490932i	−0.969405	+	0.245466i	$0.921059\pi$
$954$	1.64187e11	+	8.07786e10i	0.198219	+	0.0975221i
$955$	1.07161e12	+	9.56694e11i	1.28832	+	1.15016i
$956$	−1.24555e12	+	9.59423e11i	−1.49118	+	1.14863i
$957$		−	3.80464e11i		−	0.453592i
$958$	−1.04033e12	−	5.11836e11i	−1.23512	−	0.607671i
$959$			7.39490e11i			0.874295i
$960$	4.59315e11	−	1.33865e12i	0.540787	−	1.57609i
$961$	−7.08468e11			−0.830667
$962$	−3.99993e10	+	8.13007e10i	−0.0467038	+	0.0949279i
$963$	1.30318e11			0.151530
$964$	2.46228e11	+	3.19660e11i	0.285122	+	0.370153i
$965$	−3.03399e11	−	2.70862e11i	−0.349868	−	0.312348i
$966$	4.54827e11	−	9.24460e11i	0.522321	−	1.06165i
$967$	−1.36193e12			−1.55758			−0.778789	−	0.627286i	$-0.784166\pi$
$967$	−1.36193e12			−1.55758			−0.778789	+	0.627286i	$0.784166\pi$
$968$	7.48801e11	−	1.51115e11i	0.852835	−	0.172110i
$969$	1.35410e12			1.53588
$970$	1.25787e10	−	5.09386e9i	0.0142085	−	0.00575387i
$971$			1.12453e12i			1.26501i	0.774556	+	0.632505i	$0.217973\pi$
$971$			1.12453e12i			1.26501i	−0.774556	+	0.632505i	$0.782027\pi$
$972$	−3.60342e11	−	4.67806e11i	−0.403691	−	0.524083i
$973$			5.25334e11i			0.586117i
$974$	4.79335e11	−	9.74274e11i	0.532602	−	1.08254i
$975$	−1.74646e12	+	1.98540e11i	−1.93259	+	0.219699i
$976$	2.35894e11	−	8.93631e11i	0.259967	−	0.984825i
$977$			1.36587e12i			1.49910i	0.661949	+	0.749549i	$0.269730\pi$
$977$			1.36587e12i			1.49910i	−0.661949	+	0.749549i	$0.730270\pi$
$978$	−8.37719e11	+	1.70271e12i	−0.915678	+	1.86117i
$979$			1.33442e11i			0.145266i
$980$	−3.65512e11	−	2.65260e10i	−0.396275	−	0.0287586i
$981$	−4.06721e11			−0.439158
$982$	1.50342e12	+	7.39671e11i	1.61672	+	0.795413i
$983$	1.23632e12			1.32409			0.662046	−	0.749463i	$-0.269688\pi$
$983$	1.23632e12			1.32409			0.662046	+	0.749463i	$0.269688\pi$
$984$	−1.28244e12	+	2.58808e11i	−1.36791	+	0.276056i
$985$	5.50521e11	+	4.91483e11i	0.584829	+	0.522112i
$986$	1.09346e12	+	5.37973e11i	1.15690	+	0.569184i
$987$	−4.17437e11			−0.439868
$988$	−3.66380e11	−	4.75644e11i	−0.384507	−	0.499177i
$989$	−1.03369e12			−1.08045
$990$	5.70245e11	−	2.30927e11i	0.593636	−	0.240399i
$991$		−	1.30551e12i		−	1.35359i	−0.736172	−	0.676794i	$-0.763369\pi$
$991$		−	1.30551e12i		−	1.35359i	0.736172	−	0.676794i	$-0.236631\pi$
$992$	8.59320e11	−	9.89091e11i	0.887377	−	1.02139i
$993$			2.17818e12i			2.24025i
$994$	−9.57018e11	−	4.70845e11i	−0.980335	−	0.482317i
$995$	4.01814e11	+	3.58723e11i	0.409952	+	0.365989i
$996$	−4.41646e11	−	5.73357e11i	−0.448783	−	0.582623i
$997$		−	1.69693e12i		−	1.71744i	−0.512441	−	0.858722i	$-0.671259\pi$
$997$		−	1.69693e12i		−	1.71744i	0.512441	−	0.858722i	$-0.328741\pi$
$998$	8.19408e11	+	4.03142e11i	0.825996	+	0.406383i
$999$			1.16803e11i			0.117272i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	20.9.d.c.19.8	yes	20
4.3	odd	2	inner	20.9.d.c.19.14	yes	20
5.2	odd	4		100.9.b.g.51.3		20
5.3	odd	4		100.9.b.g.51.18		20
5.4	even	2	inner	20.9.d.c.19.13	yes	20
8.3	odd	2		320.9.h.g.319.1		20
8.5	even	2		320.9.h.g.319.19		20
20.3	even	4		100.9.b.g.51.17		20
20.7	even	4		100.9.b.g.51.4		20
20.19	odd	2	inner	20.9.d.c.19.7	✓	20
40.19	odd	2		320.9.h.g.319.20		20
40.29	even	2		320.9.h.g.319.2		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.9.d.c.19.7	✓	20	20.19	odd	2	inner
20.9.d.c.19.8	yes	20	1.1	even	1	trivial
20.9.d.c.19.13	yes	20	5.4	even	2	inner
20.9.d.c.19.14	yes	20	4.3	odd	2	inner
100.9.b.g.51.3		20	5.2	odd	4
100.9.b.g.51.4		20	20.7	even	4
100.9.b.g.51.17		20	20.3	even	4
100.9.b.g.51.18		20	5.3	odd	4
320.9.h.g.319.1		20	8.3	odd	2
320.9.h.g.319.2		20	40.29	even	2
320.9.h.g.319.19		20	8.5	even	2
320.9.h.g.319.20		20	40.19	odd	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-7.06329 + 14.3565i) q^{2} -134.970 q^{3} +(-156.220 - 202.809i) q^{4} +(-416.235 + 466.234i) q^{5} +(953.329 - 1937.69i) q^{6} -1863.96 q^{7} +(4015.06 - 810.276i) q^{8} +11655.8 q^{9} +O(q^{10})\)	\(q+(-7.06329 + 14.3565i) q^{2} -134.970 q^{3} +(-156.220 - 202.809i) q^{4} +(-416.235 + 466.234i) q^{5} +(953.329 - 1937.69i) q^{6} -1863.96 q^{7} +(4015.06 - 810.276i) q^{8} +11655.8 q^{9} +(-3753.51 - 9268.83i) q^{10} +5278.32i q^{11} +(21084.9 + 27373.0i) q^{12} +33338.9i q^{13} +(13165.7 - 26760.0i) q^{14} +(56179.0 - 62927.3i) q^{15} +(-16726.8 + 63365.5i) q^{16} -142617. i q^{17} +(-82328.1 + 167336. i) q^{18} -70346.9i q^{19} +(159580. + 11581.1i) q^{20} +251578. q^{21} +(-75778.3 - 37282.3i) q^{22} -255957. q^{23} +(-541910. + 109363. i) q^{24} +(-44122.6 - 388125. i) q^{25} +(-478630. - 235482. i) q^{26} -687639. q^{27} +(291187. + 378027. i) q^{28} +534050. q^{29} +(506609. + 1.25101e6i) q^{30} +1.24954e6i q^{31} +(-791562. - 687707. i) q^{32} -712412. i q^{33} +(2.04748e6 + 1.00735e6i) q^{34} +(775844. - 869041. i) q^{35} +(-1.82086e6 - 2.36389e6i) q^{36} -169861. i q^{37} +(1.00994e6 + 496881. i) q^{38} -4.49973e6i q^{39} +(-1.29343e6 + 2.20922e6i) q^{40} +2.36651e6 q^{41} +(-1.77697e6 + 3.61178e6i) q^{42} +4.03853e6 q^{43} +(1.07049e6 - 824577. i) q^{44} +(-4.85153e6 + 5.43431e6i) q^{45} +(1.80790e6 - 3.67465e6i) q^{46} -1.65928e6 q^{47} +(2.25760e6 - 8.55241e6i) q^{48} -2.29046e6 q^{49} +(5.88378e6 + 2.10799e6i) q^{50} +1.92489e7i q^{51} +(6.76141e6 - 5.20819e6i) q^{52} -981179. i q^{53} +(4.85699e6 - 9.87210e6i) q^{54} +(-2.46093e6 - 2.19702e6i) q^{55} +(-7.48390e6 + 1.51032e6i) q^{56} +9.49469e6i q^{57} +(-3.77215e6 + 7.66710e6i) q^{58} -7.47526e6i q^{59} +(-2.15385e7 - 1.56310e6i) q^{60} -1.41028e7 q^{61} +(-1.79391e7 - 8.82589e6i) q^{62} -2.17259e7 q^{63} +(1.54641e7 - 6.50660e6i) q^{64} +(-1.55437e7 - 1.38768e7i) q^{65} +(1.02278e7 + 5.03197e6i) q^{66} +3.75634e7 q^{67} +(-2.89240e7 + 2.22796e7i) q^{68} +3.45463e7 q^{69} +(6.99639e6 + 1.72767e7i) q^{70} -3.57630e7i q^{71} +(4.67986e7 - 9.44439e6i) q^{72} -7.26944e6i q^{73} +(2.43862e6 + 1.19978e6i) q^{74} +(5.95521e6 + 5.23851e7i) q^{75} +(-1.42670e7 + 1.09896e7i) q^{76} -9.83857e6i q^{77} +(6.46005e7 + 3.17829e7i) q^{78} -3.72731e7i q^{79} +(-2.25809e7 - 3.41735e7i) q^{80} +1.63368e7 q^{81} +(-1.67154e7 + 3.39749e7i) q^{82} -2.09461e7 q^{83} +(-3.93014e7 - 5.10222e7i) q^{84} +(6.64928e7 + 5.93621e7i) q^{85} +(-2.85253e7 + 5.79792e7i) q^{86} -7.20805e7 q^{87} +(4.27689e6 + 2.11927e7i) q^{88} +2.52812e7 q^{89} +(-4.37500e7 - 1.08035e8i) q^{90} -6.21423e7i q^{91} +(3.99855e7 + 5.19102e7i) q^{92} -1.68650e8i q^{93} +(1.17199e7 - 2.38214e7i) q^{94} +(3.27981e7 + 2.92808e7i) q^{95} +(1.06837e8 + 9.28195e7i) q^{96} +1.35709e6i q^{97} +(1.61782e7 - 3.28830e7i) q^{98} +6.15229e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 752 q^{4} - 1420 q^{5} + 3408 q^{6} + 2556 q^{9}+O(q^{10}) \) 20 * q - 752 * q^4 - 1420 * q^5 + 3408 * q^6 + 2556 * q^9	\( 20 q - 752 q^{4} - 1420 q^{5} + 3408 q^{6} + 2556 q^{9} - 4160 q^{10} + 8848 q^{14} - 59200 q^{16} - 4240 q^{20} + 410256 q^{21} - 156672 q^{24} - 657260 q^{25} - 440448 q^{26} + 660136 q^{29} + 667920 q^{30} + 4342528 q^{34} - 7191312 q^{36} - 945280 q^{40} + 7068520 q^{41} + 2666880 q^{44} - 18729060 q^{45} + 561168 q^{46} + 11719036 q^{49} + 3914880 q^{50} + 37110816 q^{54} - 35044352 q^{56} - 22734720 q^{60} - 17660440 q^{61} + 20201728 q^{64} - 44202240 q^{65} + 31902720 q^{66} + 111747216 q^{69} - 47166000 q^{70} + 19114368 q^{74} - 54998400 q^{76} + 7968320 q^{80} - 154212444 q^{81} + 101289216 q^{84} + 68800000 q^{85} + 94429648 q^{86} + 105006376 q^{89} - 230808000 q^{90} - 192757872 q^{94} + 28850688 q^{96}+O(q^{100}) \) 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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more