LMFDB - Embedded newform 12.20.b.a.11.31

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [12,20,Mod(11,12)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(12, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 20, names="a")

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

chi := DirichletCharacter("12.11");

S:= CuspForms(chi, 20);

N := Newforms(S);

Level:	$ N $	$=$	$ 12 = 2^{2} \cdot 3 $
Weight:	$ k $	$=$	$ 20 $
Character orbit:	$[\chi]$	$=$	12.b (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:	$27.4580035868$
Analytic rank:	$0$
Dimension:	$36$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			11.31
Character	$\chi$	$=$	12.11
Dual form			12.20.b.a.11.32

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(641.248 - 336.287i) q^{2} +(-33097.3 + 8174.89i) q^{3} +(298110. - 431287. i) q^{4} +2.18420e6i q^{5} +(-1.84745e7 + 1.63723e7i) q^{6} +4.59862e7i q^{7} +(4.61264e7 - 3.76812e8i) q^{8} +(1.02860e9 - 5.41134e8i) q^{9} +O(q^{10})$	\(q+(641.248 - 336.287i) q^{2} +(-33097.3 + 8174.89i) q^{3} +(298110. - 431287. i) q^{4} +2.18420e6i q^{5} +(-1.84745e7 + 1.63723e7i) q^{6} +4.59862e7i q^{7} +(4.61264e7 - 3.76812e8i) q^{8} +(1.02860e9 - 5.41134e8i) q^{9} +(7.34518e8 + 1.40061e9i) q^{10} +1.63317e8 q^{11} +(-6.34092e9 + 1.67115e10i) q^{12} +2.15485e9 q^{13} +(1.54645e10 + 2.94885e10i) q^{14} +(-1.78556e10 - 7.22912e10i) q^{15} +(-9.71387e10 - 2.57142e11i) q^{16} -3.11478e11i q^{17} +(4.77614e11 - 6.92907e11i) q^{18} -2.29703e12i q^{19} +(9.42017e11 + 6.51132e11i) q^{20} +(-3.75932e11 - 1.52202e12i) q^{21} +(1.04727e11 - 5.49213e10i) q^{22} -1.23364e13 q^{23} +(1.55374e12 + 1.28486e13i) q^{24} +1.43028e13 q^{25} +(1.38179e12 - 7.24648e11i) q^{26} +(-2.96203e13 + 2.63188e13i) q^{27} +(1.98332e13 + 1.37089e13i) q^{28} -1.30839e14i q^{29} +(-3.57605e13 - 4.03520e13i) q^{30} -8.17993e13i q^{31} +(-1.48763e14 - 1.32225e14i) q^{32} +(-5.40535e12 + 1.33510e12i) q^{33} +(-1.04746e14 - 1.99734e14i) q^{34} -1.00443e14 q^{35} +(7.32531e13 - 6.04941e14i) q^{36} +2.92779e14 q^{37} +(-7.72461e14 - 1.47297e15i) q^{38} +(-7.13198e13 + 1.76157e13i) q^{39} +(8.23034e14 + 1.00749e14i) q^{40} -2.15250e15i q^{41} +(-7.52901e14 - 8.49570e14i) q^{42} +6.38710e14i q^{43} +(4.86864e13 - 7.04363e13i) q^{44} +(1.18195e15 + 2.24668e15i) q^{45} +(-7.91070e15 + 4.14858e15i) q^{46} -5.11318e15 q^{47} +(5.31714e15 + 7.71661e15i) q^{48} +9.28417e15 q^{49} +(9.17161e15 - 4.80983e15i) q^{50} +(2.54630e15 + 1.03091e16i) q^{51} +(6.42383e14 - 9.29359e14i) q^{52} +5.34552e15i q^{53} +(-1.01433e16 + 2.68378e16i) q^{54} +3.56716e14i q^{55} +(1.73282e16 + 2.12117e15i) q^{56} +(1.87780e16 + 7.60255e16i) q^{57} +(-4.39993e16 - 8.39000e16i) q^{58} +5.99385e16 q^{59} +(-3.65012e16 - 1.38498e16i) q^{60} +8.58272e16 q^{61} +(-2.75080e16 - 5.24536e16i) q^{62} +(2.48847e16 + 4.73015e16i) q^{63} +(-1.39860e17 - 3.47620e16i) q^{64} +4.70663e15i q^{65} +(-3.01719e15 + 2.67388e15i) q^{66} +3.62115e17i q^{67} +(-1.34336e17 - 9.28546e16i) q^{68} +(4.08302e17 - 1.00849e17i) q^{69} +(-6.44089e16 + 3.37777e16i) q^{70} -4.95732e17 q^{71} +(-1.56460e17 - 4.12551e17i) q^{72} +7.06604e17 q^{73} +(1.87744e17 - 9.84577e16i) q^{74} +(-4.73383e17 + 1.16924e17i) q^{75} +(-9.90678e17 - 6.84768e17i) q^{76} +7.51031e15i q^{77} +(-3.98098e16 + 3.52799e16i) q^{78} -1.01984e18i q^{79} +(5.61649e17 - 2.12170e17i) q^{80} +(7.65199e17 - 1.11323e18i) q^{81} +(-7.23857e17 - 1.38029e18i) q^{82} +4.60593e17 q^{83} +(-7.68496e17 - 2.91595e17i) q^{84} +6.80330e17 q^{85} +(2.14790e17 + 4.09572e17i) q^{86} +(1.06959e18 + 4.33041e18i) q^{87} +(7.53321e15 - 6.15398e16i) q^{88} +5.30538e18i q^{89} +(1.51345e18 + 1.04320e18i) q^{90} +9.90933e16i q^{91} +(-3.67761e18 + 5.32053e18i) q^{92} +(6.68701e17 + 2.70734e18i) q^{93} +(-3.27882e18 + 1.71950e18i) q^{94} +5.01717e18 q^{95} +(6.00460e18 + 3.16018e18i) q^{96} -1.13803e19 q^{97} +(5.95345e18 - 3.12215e18i) q^{98} +(1.67988e17 - 8.83763e16i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 47880 q^{4} + 21771144 q^{6} - 809473644 q^{9}+O(q^{10}) $ 36 * q - 47880 * q^4 + 21771144 * q^6 - 809473644 * q^9	$ 36 q - 47880 q^{4} + 21771144 q^{6} - 809473644 q^{9} - 4162950000 q^{10} - 2268767880 q^{12} - 25913431656 q^{13} + 791689296672 q^{16} + 2852271258192 q^{18} - 1650825908424 q^{21} + 7247870602416 q^{22} + 23719435803936 q^{24} - 118879690462380 q^{25} - 7629081673968 q^{28} + 37456727138640 q^{30} + 529254701828640 q^{33} - 248241675948480 q^{34} - 11\!\cdots\!16 q^{36}+ \cdots + 12\!\cdots\!88 q^{97}+O(q^{100}) $ 36 * q - 47880 * q^4 + 21771144 * q^6 - 809473644 * q^9 - 4162950000 * q^10 - 2268767880 * q^12 - 25913431656 * q^13 + 791689296672 * q^16 + 2852271258192 * q^18 - 1650825908424 * q^21 + 7247870602416 * q^22 + 23719435803936 * q^24 - 118879690462380 * q^25 - 7629081673968 * q^28 + 37456727138640 * q^30 + 529254701828640 * q^33 - 248241675948480 * q^34 - 1177548745309416 * q^36 + 1847838600168120 * q^37 - 40433256181440 * q^40 - 2709671988768336 * q^42 - 4365410114088000 * q^45 + 17206125364795104 * q^46 + 1561106052682272 * q^48 - 49399737041580084 * q^49 + 16558671470242896 * q^52 + 40087412948587896 * q^54 + 44803667812766472 * q^57 - 34645536255764880 * q^58 + 50260381053157440 * q^60 + 174742350239997144 * q^61 - 139766490424918656 * q^64 - 87772097712685968 * q^66 - 957190369821780672 * q^69 + 244663962371376480 * q^70 + 54134736422921280 * q^72 - 1445122541399481432 * q^73 + 2744130151937256048 * q^76 + 1125465917961999024 * q^78 + 1033298241353042436 * q^81 + 1064985418859680800 * q^82 + 1920709484261873424 * q^84 - 1802899595088057600 * q^85 - 9209792381828477760 * q^88 - 5194944179528261040 * q^90 + 6719944190337314136 * q^93 - 3835186345170303552 * q^94 - 11947184361208227456 * q^96 + 12765226159947004488 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/12\mathbb{Z}\right)^\times$.

$n$	$5$	$7$
$\chi(n)$	$-1$	$-1$

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 $

$2$	641.248	−	336.287i	0.885607	−	0.464435i
$2$	641.248	−	336.287i	0.885607	−	0.464435i
$3$	−33097.3	+	8174.89i	−0.970825	+	0.239790i
$3$	−33097.3	+	8174.89i	−0.970825	+	0.239790i
$4$	298110.	−	431287.i	0.568600	−	0.822614i
$5$			2.18420e6i			0.500124i	0.968230	+	0.250062i	$0.0804510\pi$
$5$			2.18420e6i			0.500124i	−0.968230	+	0.250062i	$0.919549\pi$
$6$	−1.84745e7	+	1.63723e7i	−0.748403	+	0.663245i
$7$			4.59862e7i			0.430721i	0.976535	+	0.215360i	$0.0690926\pi$
$7$			4.59862e7i			0.430721i	−0.976535	+	0.215360i	$0.930907\pi$
$8$	4.61264e7	−	3.76812e8i	0.121505	−	0.992591i
$9$	1.02860e9	−	5.41134e8i	0.885002	−	0.465587i
$10$	7.34518e8	+	1.40061e9i	0.232275	+	0.442913i
$11$	1.63317e8			0.0208833			0.0104417	−	0.999945i	$-0.496676\pi$
$11$	1.63317e8			0.0208833			0.0104417	+	0.999945i	$0.496676\pi$
$12$	−6.34092e9	+	1.67115e10i	−0.354757	+	0.934959i
$13$	2.15485e9			0.0563580			0.0281790	−	0.999603i	$-0.491029\pi$
$13$	2.15485e9			0.0563580			0.0281790	+	0.999603i	$0.491029\pi$
$14$	1.54645e10	+	2.94885e10i	0.200042	+	0.381449i
$15$	−1.78556e10	−	7.22912e10i	−0.119924	−	0.485533i
$16$	−9.71387e10	−	2.57142e11i	−0.353388	−	0.935477i
$17$		−	3.11478e11i		−	0.637033i	−0.947917	−	0.318517i	$-0.896815\pi$
$17$		−	3.11478e11i		−	0.637033i	0.947917	−	0.318517i	$-0.103185\pi$
$18$	4.77614e11	−	6.92907e11i	0.567529	−	0.823354i
$19$		−	2.29703e12i		−	1.63308i	−0.577289	−	0.816540i	$-0.695889\pi$
$19$		−	2.29703e12i		−	1.63308i	0.577289	−	0.816540i	$-0.304111\pi$
$20$	9.42017e11	+	6.51132e11i	0.411409	+	0.284370i
$21$	−3.75932e11	−	1.52202e12i	−0.103282	−	0.418154i
$22$	1.04727e11	−	5.49213e10i	0.0184944	−	0.00969896i
$23$	−1.23364e13			−1.42815			−0.714076	−	0.700068i	$-0.753153\pi$
$23$	−1.23364e13			−1.42815			−0.714076	+	0.700068i	$0.753153\pi$
$24$	1.55374e12	+	1.28486e13i	0.120053	+	0.992768i
$25$	1.43028e13			0.749876
$26$	1.38179e12	−	7.24648e11i	0.0499110	−	0.0261746i
$27$	−2.96203e13	+	2.63188e13i	−0.747539	+	0.664218i
$28$	1.98332e13	+	1.37089e13i	0.354317	+	0.244908i
$29$		−	1.30839e14i		−	1.67477i	−0.546614	−	0.837384i	$-0.684084\pi$
$29$		−	1.30839e14i		−	1.67477i	0.546614	−	0.837384i	$-0.315916\pi$
$30$	−3.57605e13	−	4.03520e13i	−0.331704	−	0.374294i
$31$		−	8.17993e13i		−	0.555666i	−0.960629	−	0.277833i	$-0.910384\pi$
$31$		−	8.17993e13i		−	0.555666i	0.960629	−	0.277833i	$-0.0896161\pi$
$32$	−1.48763e14	−	1.32225e14i	−0.747432	−	0.664339i
$33$	−5.40535e12	+	1.33510e12i	−0.0202741	+	0.00500761i
$34$	−1.04746e14	−	1.99734e14i	−0.295861	−	0.564161i
$35$	−1.00443e14			−0.215414
$36$	7.32531e13	−	6.04941e14i	0.120213	−	0.992748i
$37$	2.92779e14			0.370359			0.185180	−	0.982705i	$-0.440713\pi$
$37$	2.92779e14			0.370359			0.185180	+	0.982705i	$0.440713\pi$
$38$	−7.72461e14	−	1.47297e15i	−0.758460	−	1.44627i
$39$	−7.13198e13	+	1.76157e13i	−0.0547137	+	0.0135141i
$40$	8.23034e14	+	1.00749e14i	0.496418	+	0.0607676i
$41$		−	2.15250e15i		−	1.02682i	−0.858142	−	0.513412i	$-0.828381\pi$
$41$		−	2.15250e15i		−	1.02682i	0.858142	−	0.513412i	$-0.171619\pi$
$42$	−7.52901e14	−	8.49570e14i	−0.285673	−	0.322353i
$43$			6.38710e14i			0.193800i	0.995294	+	0.0968999i	$0.0308927\pi$
$43$			6.38710e14i			0.193800i	−0.995294	+	0.0968999i	$0.969107\pi$
$44$	4.86864e13	−	7.04363e13i	0.0118743	−	0.0171789i
$45$	1.18195e15	+	2.24668e15i	0.232851	+	0.442611i
$46$	−7.91070e15	+	4.14858e15i	−1.26478	+	0.663284i
$47$	−5.11318e15			−0.666440			−0.333220	−	0.942849i	$-0.608135\pi$
$47$	−5.11318e15			−0.666440			−0.333220	+	0.942849i	$0.608135\pi$
$48$	5.31714e15	+	7.71661e15i	0.567396	+	0.823445i
$49$	9.28417e15			0.814480
$50$	9.17161e15	−	4.80983e15i	0.664096	−	0.348269i
$51$	2.54630e15	+	1.03091e16i	0.152754	+	0.618448i
$52$	6.42383e14	−	9.29359e14i	0.0320451	−	0.0463609i
$53$			5.34552e15i			0.222520i	0.993791	+	0.111260i	$0.0354886\pi$
$53$			5.34552e15i			0.222520i	−0.993791	+	0.111260i	$0.964511\pi$
$54$	−1.01433e16	+	2.68378e16i	−0.353540	+	0.935420i
$55$			3.56716e14i			0.0104443i
$56$	1.73282e16	+	2.12117e15i	0.427529	+	0.0523347i
$57$	1.87780e16	+	7.60255e16i	0.391595	+	1.58543i
$58$	−4.39993e16	−	8.39000e16i	−0.777822	−	1.48319i
$59$	5.99385e16			0.900765			0.450383	−	0.892836i	$-0.351288\pi$
$59$	5.99385e16			0.900765			0.450383	+	0.892836i	$0.351288\pi$
$60$	−3.65012e16	−	1.38498e16i	−0.467595	−	0.177422i
$61$	8.58272e16			0.939705			0.469853	−	0.882745i	$-0.344307\pi$
$61$	8.58272e16			0.939705			0.469853	+	0.882745i	$0.344307\pi$
$62$	−2.75080e16	−	5.24536e16i	−0.258071	−	0.492101i
$63$	2.48847e16	+	4.73015e16i	0.200538	+	0.381189i
$64$	−1.39860e17	−	3.47620e16i	−0.970473	−	0.241210i
$65$			4.70663e15i			0.0281860i
$66$	−3.01719e15	+	2.67388e15i	−0.0156292	+	0.0138508i
$67$			3.62115e17i			1.62606i	0.582223	+	0.813029i	$0.302183\pi$
$67$			3.62115e17i			1.62606i	−0.582223	+	0.813029i	$0.697817\pi$
$68$	−1.34336e17	−	9.28546e16i	−0.524033	−	0.362217i
$69$	4.08302e17	−	1.00849e17i	1.38649	−	0.342456i
$70$	−6.44089e16	+	3.37777e16i	−0.190772	+	0.100046i
$71$	−4.95732e17			−1.28319			−0.641597	−	0.767042i	$-0.721728\pi$
$71$	−4.95732e17			−1.28319			−0.641597	+	0.767042i	$0.721728\pi$
$72$	−1.56460e17	−	4.12551e17i	−0.354605	−	0.935016i
$73$	7.06604e17			1.40478			0.702391	−	0.711791i	$-0.252116\pi$
$73$	7.06604e17			1.40478			0.702391	+	0.711791i	$0.252116\pi$
$74$	1.87744e17	−	9.84577e16i	0.327993	−	0.172008i
$75$	−4.73383e17	+	1.16924e17i	−0.727998	+	0.179812i
$76$	−9.90678e17	−	6.84768e17i	−1.34339	−	0.928569i
$77$			7.51031e15i			0.00899489i
$78$	−3.98098e16	+	3.52799e16i	−0.0421785	+	0.0373791i
$79$		−	1.01984e18i		−	0.957356i	−0.877991	−	0.478678i	$-0.841116\pi$
$79$		−	1.01984e18i		−	0.957356i	0.877991	−	0.478678i	$-0.158884\pi$
$80$	5.61649e17	−	2.12170e17i	0.467854	−	0.176738i
$81$	7.65199e17	−	1.11323e18i	0.566457	−	0.824091i
$82$	−7.23857e17	−	1.38029e18i	−0.476893	−	0.909363i
$83$	4.60593e17			0.270443			0.135221	−	0.990815i	$-0.456825\pi$
$83$	4.60593e17			0.270443			0.135221	+	0.990815i	$0.456825\pi$
$84$	−7.68496e17	−	2.91595e17i	−0.402706	−	0.152801i
$85$	6.80330e17			0.318596
$86$	2.14790e17	+	4.09572e17i	0.0900075	+	0.171631i
$87$	1.06959e18	+	4.33041e18i	0.401592	+	1.62591i
$88$	7.53321e15	−	6.15398e16i	0.00253743	−	0.0207286i
$89$			5.30538e18i			1.60513i	0.596562	+	0.802567i	$0.296533\pi$
$89$			5.30538e18i			1.60513i	−0.596562	+	0.802567i	$0.703467\pi$
$90$	1.51345e18	+	1.04320e18i	0.411779	+	0.283835i
$91$			9.90933e16i			0.0242745i
$92$	−3.67761e18	+	5.32053e18i	−0.812047	+	1.17482i
$93$	6.68701e17	+	2.70734e18i	0.133243	+	0.539454i
$94$	−3.27882e18	+	1.71950e18i	−0.590204	+	0.309518i
$95$	5.01717e18			0.816742
$96$	6.00460e18	+	3.16018e18i	0.884927	+	0.465730i
$97$	−1.13803e19			−1.51993			−0.759964	−	0.649966i	$-0.774783\pi$
$97$	−1.13803e19			−1.51993			−0.759964	+	0.649966i	$0.774783\pi$
$98$	5.95345e18	−	3.12215e18i	0.721309	−	0.378273i
$99$	1.67988e17	−	8.83763e16i	0.0184818	−	0.00972302i
$100$	4.26379e18	−	6.16859e18i	0.426379	−	0.616859i
$101$		−	1.00394e19i		−	0.913390i	−0.889623	−	0.456695i	$-0.849033\pi$
$101$		−	1.00394e19i		−	0.913390i	0.889623	−	0.456695i	$-0.150967\pi$
$102$	5.09962e18	+	5.75439e18i	0.422509	+	0.476757i
$103$		−	2.29488e19i		−	1.73303i	−0.499150	−	0.866515i	$-0.666354\pi$
$103$		−	2.29488e19i		−	1.73303i	0.499150	−	0.866515i	$-0.333646\pi$
$104$	9.93954e16	−	8.11974e17i	0.00684778	−	0.0559404i
$105$	3.32439e18	−	8.21111e17i	0.209129	−	0.0516539i
$106$	1.79763e18	+	3.42780e18i	0.103346	+	0.197065i
$107$	−1.35945e19			−0.714854			−0.357427	−	0.933941i	$-0.616346\pi$
$107$	−1.35945e19			−0.714854			−0.357427	+	0.933941i	$0.616346\pi$
$108$	2.52085e18	+	2.06208e19i	0.121345	+	0.992610i
$109$	−2.99913e19			−1.32265			−0.661324	−	0.750100i	$-0.730005\pi$
$109$	−2.99913e19			−1.32265			−0.661324	+	0.750100i	$0.730005\pi$
$110$	1.19959e17	+	2.28744e17i	0.00485068	+	0.00924951i
$111$	−9.69019e18	+	2.39344e18i	−0.359554	+	0.0888083i
$112$	1.18250e19	−	4.46703e18i	0.402929	−	0.152212i
$113$		−	4.50800e19i		−	1.41169i	−0.708368	−	0.705843i	$-0.750568\pi$
$113$		−	4.50800e19i		−	1.41169i	0.708368	−	0.705843i	$-0.249432\pi$
$114$	3.76077e19	+	4.24364e19i	1.08313	+	1.22220i
$115$		−	2.69452e19i		−	0.714253i
$116$	−5.64290e19	−	3.90043e19i	−1.37769	−	0.952273i
$117$	2.21649e18	−	1.16606e18i	0.0498769	−	0.0262396i
$118$	3.84354e19	−	2.01565e19i	0.797724	−	0.418347i
$119$	1.43237e19			0.274383
$120$	−2.80638e19	+	3.39369e18i	−0.496507	+	0.0600413i
$121$	−6.11324e19			−0.999564
$122$	5.50365e19	−	2.88626e19i	0.832209	−	0.436432i
$123$	1.75964e19	+	7.12419e19i	0.246222	+	0.996867i
$124$	−3.52790e19	−	2.43852e19i	−0.457099	−	0.315951i
$125$			7.29004e19i			0.875155i
$126$	3.18641e19	+	2.19636e19i	0.354635	+	0.244446i
$127$		−	4.41892e19i		−	0.456226i	−0.973635	−	0.228113i	$-0.926744\pi$
$127$		−	4.41892e19i		−	0.456226i	0.973635	−	0.228113i	$-0.0732556\pi$
$128$	−1.01375e20	+	2.47420e19i	−0.971484	+	0.237105i
$129$	−5.22139e18	−	2.11396e19i	−0.0464712	−	0.188146i
$130$	1.58278e18	+	3.01812e18i	0.0130906	+	0.0249617i
$131$	9.06188e19			0.696853			0.348426	−	0.937336i	$-0.386716\pi$
$131$	9.06188e19			0.696853			0.348426	+	0.937336i	$0.386716\pi$
$132$	−1.03558e18	+	2.72926e18i	−0.00740851	+	0.0195251i
$133$	1.05632e20			0.703401
$134$	1.21775e20	+	2.32206e20i	0.755198	+	1.44005i
$135$	−5.74856e19	−	6.46967e19i	−0.332191	−	0.373862i
$136$	−1.17369e20	−	1.43673e19i	−0.632313	−	0.0774028i
$137$			1.61018e20i			0.809151i	0.914505	+	0.404575i	$0.132581\pi$
$137$			1.61018e20i			0.809151i	−0.914505	+	0.404575i	$0.867419\pi$
$138$	2.27909e20	−	2.01976e20i	1.06883	−	0.947214i
$139$			1.11823e20i			0.489655i	0.969567	+	0.244827i	$0.0787313\pi$
$139$			1.11823e20i			0.489655i	−0.969567	+	0.244827i	$0.921269\pi$
$140$	−2.99431e19	+	4.33197e19i	−0.122484	+	0.177202i
$141$	1.69233e20	−	4.17997e19i	0.646997	−	0.159805i
$142$	−3.17887e20	+	1.66708e20i	−1.13641	+	0.595961i
$143$	3.51923e17			0.00117694
$144$	−2.39065e20	−	2.11932e20i	−0.748296	−	0.663366i
$145$	2.85778e20			0.837592
$146$	4.53109e20	−	2.37622e20i	1.24409	−	0.652431i
$147$	−3.07281e20	+	7.58971e19i	−0.790717	+	0.195304i
$148$	8.72803e19	−	1.26272e20i	0.210586	−	0.304663i
$149$			3.08924e20i			0.699168i	0.936905	+	0.349584i	$0.113677\pi$
$149$			3.08924e20i			0.699168i	−0.936905	+	0.349584i	$0.886323\pi$
$150$	−2.64236e20	+	2.34169e20i	−0.561209	+	0.497351i
$151$			6.16509e20i			1.22930i	0.788800	+	0.614651i	$0.210703\pi$
$151$			6.16509e20i			1.22930i	−0.788800	+	0.614651i	$0.789297\pi$
$152$	−8.65549e20	−	1.05954e20i	−1.62098	−	0.198427i
$153$	−1.68551e20	−	3.20387e20i	−0.296595	−	0.563776i
$154$	2.52562e18	+	4.81597e18i	0.00417754	+	0.00796594i
$155$	1.78666e20			0.277902
$156$	−1.36637e19	+	3.60107e19i	−0.0199934	+	0.0526924i
$157$	1.17728e21			1.62119			0.810595	−	0.585608i	$-0.199144\pi$
$157$	1.17728e21			1.62119			0.810595	+	0.585608i	$0.199144\pi$
$158$	−3.42958e20	−	6.53969e20i	−0.444630	−	0.847841i
$159$	−4.36990e19	−	1.76922e20i	−0.0533580	−	0.216028i
$160$	2.88807e20	−	3.24929e20i	0.332252	−	0.373808i
$161$		−	5.67304e20i		−	0.615135i
$162$	1.16319e20	−	9.71180e20i	0.118921	−	0.992904i
$163$			1.66607e20i			0.160661i	0.996768	+	0.0803306i	$0.0255976\pi$
$163$			1.66607e20i			0.160661i	−0.996768	+	0.0803306i	$0.974402\pi$
$164$	−9.28344e20	−	6.41681e20i	−0.844680	−	0.583852i
$165$	−2.91612e18	−	1.18064e19i	−0.00250442	−	0.0101395i
$166$	2.95354e20	−	1.54891e20i	0.239506	−	0.125603i
$167$	5.07388e20			0.388627			0.194314	−	0.980939i	$-0.437752\pi$
$167$	5.07388e20			0.388627			0.194314	+	0.980939i	$0.437752\pi$
$168$	−5.90856e20	+	7.14506e19i	−0.427605	+	0.0517092i
$169$	−1.45728e21			−0.996824
$170$	4.36260e20	−	2.28786e20i	0.282150	−	0.147967i
$171$	−1.24300e21	−	2.36273e21i	−0.760341	−	1.44528i
$172$	2.75467e20	+	1.90406e20i	0.159423	+	0.110195i
$173$			8.03156e19i			0.0439908i	0.999758	+	0.0219954i	$0.00700192\pi$
$173$			8.03156e19i			0.0439908i	−0.999758	+	0.0219954i	$0.992998\pi$
$174$	2.14213e21	+	2.41717e21i	1.11078	+	1.25340i
$175$			6.57729e20i			0.322987i
$176$	−1.58644e19	−	4.19956e19i	−0.00737993	−	0.0195359i
$177$	−1.98380e21	+	4.89991e20i	−0.874485	+	0.215994i
$178$	1.78413e21	+	3.40206e21i	0.745481	+	1.42152i
$179$	2.01454e21			0.798128			0.399064	−	0.916923i	$-0.369335\pi$
$179$	2.01454e21			0.798128			0.399064	+	0.916923i	$0.369335\pi$
$180$	1.32131e21	+	1.59999e20i	0.496497	+	0.0601215i
$181$	3.55933e20			0.126888			0.0634441	−	0.997985i	$-0.479792\pi$
$181$	3.55933e20			0.126888			0.0634441	+	0.997985i	$0.479792\pi$
$182$	3.33238e19	+	6.35434e19i	0.0112740	+	0.0214977i
$183$	−2.84065e21	+	7.01628e20i	−0.912289	+	0.225331i
$184$	−5.69034e20	+	4.64851e21i	−0.173528	+	1.41757i
$185$			6.39488e20i			0.185226i
$186$	1.33925e21	+	1.51120e21i	0.368542	+	0.415862i
$187$		−	5.08695e19i		−	0.0133034i
$188$	−1.52429e21	+	2.20525e21i	−0.378938	+	0.548223i
$189$	−1.21030e21	−	1.36212e21i	−0.286092	−	0.321980i
$190$	3.21725e21	−	1.68721e21i	0.723313	−	0.379324i
$191$	6.52917e21			1.39650			0.698250	−	0.715854i	$-0.253963\pi$
$191$	6.52917e21			1.39650			0.698250	+	0.715854i	$0.253963\pi$
$192$	4.91316e21	+	7.18787e18i	0.999999	+	0.00146298i
$193$	−7.77338e21			−1.50597			−0.752983	−	0.658040i	$-0.771386\pi$
$193$	−7.77338e21			−1.50597			−0.752983	+	0.658040i	$0.771386\pi$
$194$	−7.29760e21	+	3.82705e21i	−1.34606	+	0.705908i
$195$	−3.84762e19	−	1.55777e20i	−0.00675870	−	0.0273636i
$196$	2.76770e21	−	4.00414e21i	0.463113	−	0.670003i
$197$			9.04179e21i			1.44154i	0.693176	+	0.720768i	$0.256211\pi$
$197$			9.04179e21i			1.44154i	−0.693176	+	0.720768i	$0.743789\pi$
$198$	7.80023e19	−	1.13163e20i	0.0118519	−	0.0171944i
$199$		−	1.03235e22i		−	1.49528i	−0.664107	−	0.747638i	$-0.731188\pi$
$199$		−	1.03235e22i		−	1.49528i	0.664107	−	0.747638i	$-0.268812\pi$
$200$	6.59734e20	−	5.38945e21i	0.0911137	−	0.744320i
$201$	−2.96025e21	−	1.19850e22i	−0.389912	−	1.57862i
$202$	−3.37613e21	−	6.43777e21i	−0.424210	−	0.808904i
$203$	6.01676e21			0.721358
$204$	5.20524e21	+	1.97506e21i	0.595600	+	0.225992i
$205$	4.70149e21			0.513539
$206$	−7.71738e21	−	1.47159e22i	−0.804881	−	1.53478i
$207$	−1.26893e22	+	6.67566e21i	−1.26392	+	0.664930i
$208$	−2.09319e20	−	5.54102e20i	−0.0199163	−	0.0527216i
$209$		−	3.75143e20i		−	0.0341042i
$210$	1.85563e21	−	1.64449e21i	0.161216	−	0.142872i
$211$			4.72896e21i			0.392720i	0.980532	+	0.196360i	$0.0629121\pi$
$211$			4.72896e21i			0.392720i	−0.980532	+	0.196360i	$0.937088\pi$
$212$	2.30545e21	+	1.59355e21i	0.183048	+	0.126525i
$213$	1.64074e22	−	4.05256e21i	1.24576	−	0.307697i
$214$	−8.71745e21	+	4.57165e21i	−0.633080	+	0.332003i
$215$	−1.39507e21			−0.0969239
$216$	8.55098e21	+	1.23753e22i	0.568467	+	0.822706i
$217$	3.76164e21			0.239337
$218$	−1.92319e22	+	1.00857e22i	−1.17135	+	0.614284i
$219$	−2.33867e22	+	5.77642e21i	−1.36380	+	0.336852i
$220$	1.53847e20	+	1.06341e20i	0.00859160	+	0.00593860i
$221$		−	6.71188e20i		−	0.0359019i
$222$	−5.40894e21	+	4.79347e21i	−0.277178	+	0.245639i
$223$			8.20124e21i			0.402701i	0.979519	+	0.201351i	$0.0645331\pi$
$223$			8.20124e21i			0.402701i	−0.979519	+	0.201351i	$0.935467\pi$
$224$	6.08053e21	−	6.84106e21i	0.286144	−	0.321934i
$225$	1.47119e22	−	7.73971e21i	0.663642	−	0.349133i
$226$	−1.51598e22	−	2.89074e22i	−0.655637	−	1.25020i
$227$	1.82946e22			0.758713			0.379357	−	0.925251i	$-0.376145\pi$
$227$	1.82946e22			0.758713			0.379357	+	0.925251i	$0.376145\pi$
$228$	3.83867e22	+	1.45653e22i	1.52686	+	0.579346i
$229$	9.76485e21			0.372588			0.186294	−	0.982494i	$-0.440352\pi$
$229$	9.76485e21			0.372588			0.186294	+	0.982494i	$0.440352\pi$
$230$	−9.06132e21	−	1.72786e22i	−0.331724	−	0.632548i
$231$	−6.13960e19	−	2.48571e20i	−0.00215688	−	0.00873246i
$232$	−4.93016e22	−	6.03511e21i	−1.66236	−	0.203493i
$233$			3.04179e22i			0.984573i	0.870433	+	0.492287i	$0.163839\pi$
$233$			3.04179e22i			0.984573i	−0.870433	+	0.492287i	$0.836161\pi$
$234$	1.02919e21	−	1.49311e21i	0.0319848	−	0.0464025i
$235$		−	1.11682e22i		−	0.333303i
$236$	1.78683e22	−	2.58507e22i	0.512175	−	0.740982i
$237$	8.33706e21	+	3.37539e22i	0.229564	+	0.929425i
$238$	9.18502e21	−	4.81686e21i	0.242996	−	0.127433i
$239$	5.36873e22			1.36487			0.682435	−	0.730946i	$-0.260921\pi$
$239$	5.36873e22			1.36487			0.682435	+	0.730946i	$0.260921\pi$
$240$	−1.68546e22	+	1.16137e22i	−0.411825	+	0.283768i
$241$	6.69429e20			0.0157233			0.00786163	−	0.999969i	$-0.497498\pi$
$241$	6.69429e20			0.0157233			0.00786163	+	0.999969i	$0.497498\pi$
$242$	−3.92010e22	+	2.05580e22i	−0.885221	+	0.464233i
$243$	−1.62255e22	+	4.31002e22i	−0.352322	+	0.935879i
$244$	2.55860e22	−	3.70161e22i	0.534316	−	0.773015i
$245$			2.02785e22i			0.407341i
$246$	3.52414e22	+	3.97663e22i	0.681036	+	0.768478i
$247$		−	4.94976e21i		−	0.0920371i
$248$	−3.08230e22	−	3.77310e21i	−0.551549	−	0.0675162i
$249$	−1.52444e22	+	3.76530e21i	−0.262553	+	0.0648494i
$250$	2.45155e22	+	4.67472e22i	0.406453	+	0.775043i
$251$	1.58371e22			0.252798			0.126399	−	0.991979i	$-0.459658\pi$
$251$	1.58371e22			0.252798			0.126399	+	0.991979i	$0.459658\pi$
$252$	2.78189e22	+	3.36863e21i	0.427597	+	0.0517783i
$253$	−2.01474e21			−0.0298246
$254$	−1.48602e22	−	2.83362e22i	−0.211888	−	0.404037i
$255$	−2.25171e22	+	5.56162e21i	−0.309300	+	0.0763959i
$256$	−5.66860e22	+	4.99568e22i	−0.750233	+	0.661173i
$257$		−	2.84469e22i		−	0.362802i	−0.983409	−	0.181401i	$-0.941937\pi$
$257$		−	2.84469e22i		−	0.362802i	0.983409	−	0.181401i	$-0.0580633\pi$
$258$	−1.04572e22	−	1.17998e22i	−0.128537	−	0.145040i
$259$			1.34638e22i			0.159521i
$260$	2.02991e21	+	1.40309e21i	0.0231862	+	0.0160265i
$261$	−7.08012e22	−	1.34581e23i	−0.779751	−	1.48217i
$262$	5.81092e22	−	3.04739e22i	0.617138	−	0.323643i
$263$	−6.76401e22			−0.692827			−0.346413	−	0.938082i	$-0.612601\pi$
$263$	−6.76401e22			−0.692827			−0.346413	+	0.938082i	$0.612601\pi$
$264$	2.53752e20	+	2.09838e21i	0.00250710	+	0.0207323i
$265$	−1.16757e22			−0.111288
$266$	6.77360e22	−	3.55225e22i	0.622937	−	0.326684i
$267$	−4.33709e22	−	1.75594e23i	−0.384894	−	1.55830i
$268$	1.56175e23	+	1.07950e23i	1.33762	+	0.924576i
$269$		−	8.86687e22i		−	0.733034i	−0.930411	−	0.366517i	$-0.880550\pi$
$269$		−	8.86687e22i		−	0.733034i	0.930411	−	0.366517i	$-0.119450\pi$
$270$	−5.86192e22	−	2.21550e22i	−0.467826	−	0.176814i
$271$		−	8.36258e22i		−	0.644365i	−0.946678	−	0.322182i	$-0.895584\pi$
$271$		−	8.36258e22i		−	0.644365i	0.946678	−	0.322182i	$-0.104416\pi$
$272$	−8.00939e22	+	3.02565e22i	−0.595930	+	0.225120i
$273$	−8.10077e20	−	3.27972e21i	−0.00582078	−	0.0235663i
$274$	5.41483e22	+	1.03253e23i	0.375798	+	0.716590i
$275$	2.33588e21			0.0156599
$276$	7.82242e22	−	2.06159e23i	0.506647	−	1.33526i
$277$	−1.68159e23			−1.05236			−0.526178	−	0.850374i	$-0.676376\pi$
$277$	−1.68159e23			−1.05236			−0.526178	+	0.850374i	$0.676376\pi$
$278$	3.76046e22	+	7.17062e22i	0.227413	+	0.433642i
$279$	−4.42644e22	−	8.41391e22i	−0.258711	−	0.491765i
$280$	−4.63307e21	+	3.78482e22i	−0.0261738	+	0.213818i
$281$			1.17721e23i			0.642898i	0.946927	+	0.321449i	$0.104170\pi$
$281$			1.17721e23i			0.642898i	−0.946927	+	0.321449i	$0.895830\pi$
$282$	9.44633e22	−	8.37147e22i	0.498766	−	0.442013i
$283$			1.93382e23i			0.987290i	0.869664	+	0.493645i	$0.164336\pi$
$283$			1.93382e23i			0.987290i	−0.869664	+	0.493645i	$0.835664\pi$
$284$	−1.47783e23	+	2.13803e23i	−0.729624	+	1.05557i
$285$	−1.66055e23	+	4.10149e22i	−0.792913	+	0.195846i
$286$	2.25670e20	−	1.18347e20i	0.00104231	−	0.000546614i
$287$	9.89851e22			0.442274
$288$	−2.24570e23	−	5.55064e22i	−0.970786	−	0.239946i
$289$	1.42054e23			0.594189
$290$	1.83254e23	−	9.61033e22i	0.741777	−	0.389007i
$291$	3.76658e23	−	9.30329e22i	1.47558	−	0.364463i
$292$	2.10646e23	−	3.04749e23i	0.798759	−	1.15559i
$293$			1.04801e22i			0.0384699i	0.999815	+	0.0192350i	$0.00612305\pi$
$293$			1.04801e22i			0.0384699i	−0.999815	+	0.0192350i	$0.993877\pi$
$294$	−1.71520e23	+	1.52004e23i	−0.609559	+	0.540199i
$295$			1.30918e23i			0.450494i
$296$	1.35048e22	−	1.10323e23i	0.0450005	−	0.367615i
$297$	−4.83749e21	+	4.29830e21i	−0.0156111	+	0.0138711i
$298$	1.03887e23	+	1.98097e23i	0.324718	+	0.619188i
$299$	−2.65831e22			−0.0804878
$300$	−9.06926e22	+	2.39020e23i	−0.266024	+	0.701103i
$301$	−2.93718e22			−0.0834736
$302$	2.07324e23	+	3.95335e23i	0.570931	+	1.08868i
$303$	8.20713e22	+	3.32278e23i	0.219021	+	0.886742i
$304$	−5.90662e23	+	2.23130e23i	−1.52771	+	0.577111i
$305$			1.87464e23i			0.469969i
$306$	−2.15825e23	−	1.48766e23i	−0.524504	−	0.361535i
$307$		−	1.26257e22i		−	0.0297468i	−0.999889	−	0.0148734i	$-0.995265\pi$
$307$		−	1.26257e22i		−	0.0297468i	0.999889	−	0.0148734i	$-0.00473452\pi$
$308$	3.23910e21	+	2.23890e21i	0.00739932	+	0.00511449i
$309$	1.87604e23	+	7.59544e23i	0.415563	+	1.68247i
$310$	1.14569e23	−	6.00831e22i	0.246112	−	0.129067i
$311$	−6.08260e23			−1.26726			−0.633629	−	0.773637i	$-0.718436\pi$
$311$	−6.08260e23			−1.26726			−0.633629	+	0.773637i	$0.718436\pi$
$312$	3.34808e21	+	2.76867e22i	0.00676593	+	0.0559504i
$313$	7.35615e23			1.44205			0.721024	−	0.692910i	$-0.243672\pi$
$313$	7.35615e23			1.44205			0.721024	+	0.692910i	$0.243672\pi$
$314$	7.54930e23	−	3.95905e23i	1.43574	−	0.752937i
$315$	−1.03316e23	+	5.43531e22i	−0.190642	+	0.100294i
$316$	−4.39842e23	−	3.04024e23i	−0.787535	−	0.544353i
$317$		−	1.00655e24i		−	1.74893i	−0.485088	−	0.874465i	$-0.661212\pi$
$317$		−	1.00655e24i		−	1.74893i	0.485088	−	0.874465i	$-0.338788\pi$
$318$	−8.75186e22	−	9.87556e22i	−0.147585	−	0.166535i
$319$		−	2.13681e22i		−	0.0349748i
$320$	7.59271e22	−	3.05482e23i	0.120635	−	0.485357i
$321$	4.49941e23	−	1.11134e23i	0.693998	−	0.171415i
$322$	−1.90777e23	−	3.63783e23i	−0.285690	−	0.544768i
$323$	−7.15473e23			−1.04033
$324$	−2.52006e23	−	6.61884e23i	−0.355822	−	0.934554i
$325$	3.08203e22			0.0422615
$326$	5.60277e22	+	1.06836e23i	0.0746167	+	0.142283i
$327$	9.92633e23	−	2.45176e23i	1.28406	−	0.317157i
$328$	−8.11088e23	−	9.92869e22i	−1.01922	−	0.124764i
$329$		−	2.35135e23i		−	0.287050i
$330$	−5.84028e21	−	6.59015e21i	−0.00692710	−	0.00781651i
$331$		−	6.87132e23i		−	0.791907i	−0.918271	−	0.395953i	$-0.870414\pi$
$331$		−	6.87132e23i		−	0.791907i	0.918271	−	0.395953i	$-0.129586\pi$
$332$	1.37307e23	−	1.98648e23i	0.153774	−	0.222470i
$333$	3.01153e23	−	1.58433e23i	0.327769	−	0.172435i
$334$	3.25361e23	−	1.70628e23i	0.344171	−	0.180492i
$335$	−7.90932e23			−0.813230
$336$	−3.54857e23	+	2.44515e23i	−0.354675	+	0.244389i
$337$	−3.34020e23			−0.324555			−0.162278	−	0.986745i	$-0.551884\pi$
$337$	−3.34020e23			−0.324555			−0.162278	+	0.986745i	$0.551884\pi$
$338$	−9.34476e23	+	4.90063e23i	−0.882794	+	0.462960i
$339$	3.68524e23	+	1.49203e24i	0.338508	+	1.37050i
$340$	2.02813e23	−	2.93417e23i	0.181153	−	0.262081i
$341$		−	1.33592e22i		−	0.0116042i
$342$	−1.59163e24	−	1.09709e24i	−1.34460	−	0.926820i
$343$			9.51135e23i			0.781534i
$344$	2.40674e23	+	2.94614e22i	0.192364	+	0.0235477i
$345$	2.20274e23	+	8.91814e23i	0.171270	+	0.693415i
$346$	2.70091e22	+	5.15022e22i	0.0204309	+	0.0389586i
$347$	6.12663e23			0.450912			0.225456	−	0.974253i	$-0.427613\pi$
$347$	6.12663e23			0.450912			0.225456	+	0.974253i	$0.427613\pi$
$348$	2.18650e24	+	8.29637e23i	1.56584	+	0.594135i
$349$	−3.04085e23			−0.211911			−0.105956	−	0.994371i	$-0.533790\pi$
$349$	−3.04085e23			−0.211911			−0.105956	+	0.994371i	$0.533790\pi$
$350$	2.21186e23	+	4.21767e23i	0.150007	+	0.286040i
$351$	−6.38274e22	+	5.67131e22i	−0.0421298	+	0.0374340i
$352$	−2.42956e22	−	2.15946e22i	−0.0156089	−	0.0138736i
$353$			8.06696e21i			0.00504488i	0.999997	+	0.00252244i	$0.000802918\pi$
$353$			8.06696e21i			0.00504488i	−0.999997	+	0.00252244i	$0.999197\pi$
$354$	−1.10733e24	+	9.81333e23i	−0.674135	+	0.597428i
$355$		−	1.08278e24i		−	0.641756i
$356$	2.28814e24	+	1.58159e24i	1.32041	+	0.912679i
$357$	−4.74075e23	+	1.17094e23i	−0.266378	+	0.0657943i
$358$	1.29182e24	−	6.77464e23i	0.706828	−	0.370679i
$359$	−4.18286e23			−0.222882			−0.111441	−	0.993771i	$-0.535547\pi$
$359$	−4.18286e23			−0.222882			−0.111441	+	0.993771i	$0.535547\pi$
$360$	9.01094e23	−	3.41741e23i	0.467624	−	0.177347i
$361$	−3.29792e24			−1.66695
$362$	2.28241e23	−	1.19696e23i	0.112373	−	0.0589314i
$363$	2.02332e24	−	4.99751e23i	0.970402	−	0.239685i
$364$	4.27376e22	+	2.95407e22i	0.0199686	+	0.0138025i
$365$			1.54337e24i			0.702565i
$366$	−1.58561e24	+	1.40519e24i	−0.703278	+	0.623254i
$367$		−	4.37679e24i		−	1.89160i	−0.324755	−	0.945798i	$-0.605282\pi$
$367$		−	4.37679e24i		−	1.89160i	0.324755	−	0.945798i	$-0.394718\pi$
$368$	1.19834e24	+	3.17221e24i	0.504692	+	1.33600i
$369$	−1.16479e24	−	2.21407e24i	−0.478076	−	0.908742i
$370$	2.15051e23	+	4.10070e23i	0.0860253	+	0.164037i
$371$	−2.45820e23			−0.0958439
$372$	1.36699e24	+	5.18683e23i	0.519524	+	0.197126i
$373$	−3.67881e23			−0.136293			−0.0681465	−	0.997675i	$-0.521709\pi$
$373$	−3.67881e23			−0.136293			−0.0681465	+	0.997675i	$0.521709\pi$
$374$	−1.71068e22	−	3.26200e22i	−0.00617856	−	0.0117816i
$375$	−5.95953e23	−	2.41281e24i	−0.209853	−	0.849622i
$376$	−2.35852e23	+	1.92671e24i	−0.0809759	+	0.661503i
$377$		−	2.81938e23i		−	0.0943866i
$378$	−1.23417e24	−	4.66451e23i	−0.402905	−	0.152277i
$379$			3.49425e24i			1.11245i	0.831031	+	0.556227i	$0.187751\pi$
$379$			3.49425e24i			1.11245i	−0.831031	+	0.556227i	$0.812249\pi$
$380$	1.49567e24	−	2.16384e24i	0.464399	−	0.671864i
$381$	3.61242e23	+	1.46254e24i	0.109398	+	0.442916i
$382$	4.18681e24	−	2.19567e24i	1.23675	−	0.648583i
$383$	−1.23234e24			−0.355094			−0.177547	−	0.984112i	$-0.556816\pi$
$383$	−1.23234e24			−0.355094			−0.177547	+	0.984112i	$0.556816\pi$
$384$	3.15297e24	−	1.64762e24i	0.886286	−	0.463139i
$385$	−1.64040e22			−0.00449856
$386$	−4.98466e24	+	2.61409e24i	−1.33369	+	0.699424i
$387$	3.45628e23	+	6.56980e23i	0.0902308	+	0.171513i
$388$	−3.39259e24	+	4.90818e24i	−0.864230	+	1.25031i
$389$		−	4.53825e24i		−	1.12815i	−0.825723	−	0.564076i	$-0.809232\pi$
$389$		−	4.53825e24i		−	1.12815i	0.825723	−	0.564076i	$-0.190768\pi$
$390$	−7.70585e22	−	8.69525e22i	−0.0186942	−	0.0210945i
$391$			3.84252e24i			0.909781i
$392$	4.28245e23	−	3.49839e24i	0.0989634	−	0.808445i
$393$	−2.99924e24	+	7.40799e23i	−0.676522	+	0.167098i
$394$	3.04064e24	+	5.79803e24i	0.669500	+	1.27663i
$395$	2.22753e24			0.478797
$396$	1.19635e22	−	9.87969e22i	0.00251045	−	0.0207319i
$397$	4.21065e24			0.862660			0.431330	−	0.902194i	$-0.358045\pi$
$397$	4.21065e24			0.862660			0.431330	+	0.902194i	$0.358045\pi$
$398$	−3.47165e24	−	6.61990e24i	−0.694459	−	1.32423i
$399$	−3.49612e24	+	8.63527e23i	−0.682879	+	0.168668i
$400$	−1.38935e24	−	3.67784e24i	−0.264998	−	0.701492i
$401$			2.73660e23i			0.0509730i	0.999675	+	0.0254865i	$0.00811348\pi$
$401$			2.73660e23i			0.0509730i	−0.999675	+	0.0254865i	$0.991887\pi$
$402$	−5.92867e24	−	6.68989e24i	−1.07847	−	1.21695i
$403$		−	1.76265e23i		−	0.0313162i
$404$	−4.32987e24	−	2.99286e24i	−0.751367	−	0.519353i
$405$	2.43151e24	+	1.67135e24i	0.412148	+	0.283299i
$406$	3.85824e24	−	2.02336e24i	0.638839	−	0.335024i
$407$	4.78157e22			0.00773434
$408$	4.00204e24	−	4.83956e23i	0.632426	−	0.0764776i
$409$	3.26715e24			0.504426			0.252213	−	0.967672i	$-0.418842\pi$
$409$	3.26715e24			0.504426			0.252213	+	0.967672i	$0.418842\pi$
$410$	3.01482e24	−	1.58105e24i	0.454794	−	0.238506i
$411$	−1.31631e24	−	5.32927e24i	−0.194026	−	0.785544i
$412$	−9.89751e24	−	6.84127e24i	−1.42562	−	0.985401i
$413$			2.75634e24i			0.387978i
$414$	−5.89204e24	+	8.54799e24i	−0.810518	+	1.17587i
$415$			1.00603e24i			0.135255i
$416$	−3.20563e23	−	2.84926e23i	−0.0421237	−	0.0374408i
$417$	−9.14140e23	−	3.70104e24i	−0.117414	−	0.475369i
$418$	−1.26156e23	−	2.40560e23i	−0.0158392	−	0.0302029i
$419$	6.97708e24			0.856328			0.428164	−	0.903701i	$-0.359161\pi$
$419$	6.97708e24			0.856328			0.428164	+	0.903701i	$0.359161\pi$
$420$	6.36901e23	−	1.67855e24i	0.0764194	−	0.201403i
$421$	1.17558e25			1.37902			0.689512	−	0.724274i	$-0.257825\pi$
$421$	1.17558e25			1.37902			0.689512	+	0.724274i	$0.257825\pi$
$422$	1.59029e24	+	3.03244e24i	0.182393	+	0.347795i
$423$	−5.25943e24	+	2.76692e24i	−0.589801	+	0.310286i
$424$	2.01426e24	+	2.46569e23i	0.220871	+	0.0270373i
$425$		−	4.45499e24i		−	0.477696i
$426$	9.15839e24	−	8.11629e24i	0.960346	−	0.851072i
$427$			3.94686e24i			0.404750i
$428$	−4.05266e24	+	5.86313e24i	−0.406466	+	0.588049i
$429$	−1.16477e22	+	2.87693e21i	−0.00114261	+	0.000282219i
$430$	−8.94587e23	+	4.69144e23i	−0.0858365	+	0.0450149i
$431$	−2.95422e24			−0.277274			−0.138637	−	0.990343i	$-0.544272\pi$
$431$	−2.95422e24			−0.277274			−0.138637	+	0.990343i	$0.544272\pi$
$432$	9.64495e24	+	5.06005e24i	0.885532	+	0.464578i
$433$	2.96147e24			0.265995			0.132997	−	0.991116i	$-0.457540\pi$
$433$	2.96147e24			0.265995			0.132997	+	0.991116i	$0.457540\pi$
$434$	2.41214e24	−	1.26499e24i	0.211958	−	0.111156i
$435$	−9.45848e24	+	2.33620e24i	−0.813155	+	0.200846i
$436$	−8.94072e24	+	1.29349e25i	−0.752057	+	1.08803i
$437$			2.83371e25i			2.33229i
$438$	−1.30542e25	+	1.15688e25i	−1.05134	+	0.931715i
$439$			1.23072e25i			0.969944i	0.874530	+	0.484972i	$0.161170\pi$
$439$			1.23072e25i			0.969944i	−0.874530	+	0.484972i	$0.838830\pi$
$440$	1.34415e23	+	1.64540e22i	0.0103669	+	0.00126903i
$441$	9.54973e24	−	5.02398e24i	0.720816	−	0.379211i
$442$	−2.25712e23	−	4.30398e23i	−0.0166741	−	0.0317950i
$443$	1.94166e25			1.40391			0.701954	−	0.712222i	$-0.252311\pi$
$443$	1.94166e25			1.40391			0.701954	+	0.712222i	$0.252311\pi$
$444$	−1.85649e24	+	4.89276e24i	−0.131387	+	0.346271i
$445$	−1.15880e25			−0.802766
$446$	2.75797e24	+	5.25903e24i	0.187029	+	0.356635i
$447$	−2.52542e24	−	1.02245e25i	−0.167653	−	0.678770i
$448$	1.59857e24	−	6.43162e24i	0.103894	−	0.418003i
$449$			2.06078e25i			1.31127i	0.755079	+	0.655634i	$0.227599\pi$
$449$			2.06078e25i			1.31127i	−0.755079	+	0.655634i	$0.772401\pi$
$450$	6.83119e24	−	9.91048e24i	0.425576	−	0.617413i
$451$		−	3.51539e23i		−	0.0214435i
$452$	−1.94424e25	−	1.34388e25i	−1.16127	−	0.802685i
$453$	−5.03989e24	−	2.04048e25i	−0.294774	−	1.19344i
$454$	1.17314e25	−	6.15224e24i	0.671922	−	0.352373i
$455$	−2.16440e23			−0.0121403
$456$	2.95135e25	−	3.56899e24i	1.62127	−	0.196056i
$457$	−1.30246e25			−0.700747			−0.350374	−	0.936610i	$-0.613945\pi$
$457$	−1.30246e25			−0.700747			−0.350374	+	0.936610i	$0.613945\pi$
$458$	6.26169e24	−	3.28379e24i	0.329966	−	0.173043i
$459$	8.19772e24	+	9.22606e24i	0.423129	+	0.476207i
$460$	−1.16211e25	−	8.03264e24i	−0.587555	−	0.406124i
$461$		−	3.34568e25i		−	1.65701i	−0.559980	−	0.828506i	$-0.689191\pi$
$461$		−	3.34568e25i		−	1.65701i	0.559980	−	0.828506i	$-0.310809\pi$
$462$	−1.22961e23	−	1.38749e23i	−0.00596581	−	0.00673180i
$463$		−	2.32903e25i		−	1.10702i	−0.832842	−	0.553511i	$-0.813288\pi$
$463$		−	2.32903e25i		−	1.10702i	0.832842	−	0.553511i	$-0.186712\pi$
$464$	−3.36441e25	+	1.27095e25i	−1.56671	+	0.591844i
$465$	−5.91337e24	+	1.46058e24i	−0.269794	+	0.0666379i
$466$	1.02291e25	+	1.95054e25i	0.457271	+	0.871945i
$467$	3.33366e25			1.46020			0.730098	−	0.683343i	$-0.239475\pi$
$467$	3.33366e25			1.46020			0.730098	+	0.683343i	$0.239475\pi$
$468$	1.57850e23	−	1.30356e24i	0.00677497	−	0.0559493i
$469$	−1.66523e25			−0.700377
$470$	−3.75572e24	−	7.16159e24i	−0.154798	−	0.295175i
$471$	−3.89649e25	+	9.62416e24i	−1.57389	+	0.388744i
$472$	2.76474e24	−	2.25856e25i	0.109448	−	0.894091i
$473$			1.04312e23i			0.00404719i
$474$	1.66971e25	+	1.88410e25i	0.634961	+	0.716488i
$475$		−	3.28538e25i		−	1.22461i
$476$	4.27003e24	−	6.17761e24i	0.156014	−	0.225712i
$477$	2.89264e24	+	5.49842e24i	0.103602	+	0.196931i
$478$	3.44269e25	−	1.80543e25i	1.20874	−	0.633894i
$479$	−3.34473e25			−1.15126			−0.575630	−	0.817710i	$-0.695243\pi$
$479$	−3.34473e25			−1.15126			−0.575630	+	0.817710i	$0.695243\pi$
$480$	−6.90246e24	+	1.31152e25i	−0.232923	+	0.442573i
$481$	6.30895e23			0.0208727
$482$	4.29270e23	−	2.25120e23i	0.0139246	−	0.00730243i
$483$	4.63765e24	+	1.87763e25i	0.147503	+	0.597188i
$484$	−1.82242e25	+	2.63656e25i	−0.568352	+	0.822255i
$485$		−	2.48569e25i		−	0.760152i
$486$	4.08944e24	+	3.30944e25i	0.122636	+	0.992452i
$487$		−	5.17030e25i		−	1.52052i	−0.649622	−	0.760258i	$-0.725073\pi$
$487$		−	5.17030e25i		−	1.52052i	0.649622	−	0.760258i	$-0.274927\pi$
$488$	3.95890e24	−	3.23408e25i	0.114179	−	0.932743i
$489$	−1.36199e24	−	5.51424e24i	−0.0385249	−	0.155974i
$490$	6.81939e24	+	1.30035e25i	0.189183	+	0.360744i
$491$	1.40058e24			0.0381096			0.0190548	−	0.999818i	$-0.493934\pi$
$491$	1.40058e24			0.0381096			0.0190548	+	0.999818i	$0.493934\pi$
$492$	3.59714e25	+	1.36488e25i	0.960038	+	0.364273i
$493$	−4.07533e25			−1.06688
$494$	−1.66454e24	−	3.17402e24i	−0.0427453	−	0.0815087i
$495$	1.93031e23	+	3.66920e23i	0.00486271	+	0.00924319i
$496$	−2.10340e25	+	7.94588e24i	−0.519812	+	0.196366i
$497$		−	2.27968e25i		−	0.552698i
$498$	−8.50922e24	+	7.54098e24i	−0.202400	+	0.179370i
$499$			4.98463e25i			1.16326i	0.813452	+	0.581632i	$0.197586\pi$
$499$			4.98463e25i			1.16326i	−0.813452	+	0.581632i	$0.802414\pi$
$500$	3.14410e25	+	2.17323e25i	0.719915	+	0.497613i
$501$	−1.67932e25	+	4.14784e24i	−0.377289	+	0.0931888i
$502$	1.01555e25	−	5.32580e24i	0.223880	−	0.117408i
$503$	−2.32816e25			−0.503637			−0.251818	−	0.967775i	$-0.581029\pi$
$503$	−2.32816e25			−0.503637			−0.251818	+	0.967775i	$0.581029\pi$
$504$	1.89716e25	−	7.19501e24i	0.402731	−	0.152736i
$505$	2.19281e25			0.456808
$506$	−1.29195e24	+	6.77532e23i	−0.0264129	+	0.0138516i
$507$	4.82320e25	−	1.19131e25i	0.967741	−	0.239028i
$508$	−1.90582e25	−	1.31732e25i	−0.375298	−	0.259410i
$509$			5.50733e25i			1.06444i	0.846605	+	0.532221i	$0.178643\pi$
$509$			5.50733e25i			1.06444i	−0.846605	+	0.532221i	$0.821357\pi$
$510$	−1.25687e25	+	1.11386e25i	−0.238438	+	0.211307i
$511$			3.24940e25i			0.605069i
$512$	−1.95500e25	+	5.10975e25i	−0.357340	+	0.933974i
$513$	6.04551e25	+	6.80387e25i	1.08472	+	1.22079i
$514$	−9.56632e24	−	1.82415e25i	−0.168498	−	0.321300i
$515$	5.01248e25			0.866730
$516$	−1.06738e25	−	4.05001e24i	−0.181195	−	0.0687518i
$517$	−8.35068e23			−0.0139175
$518$	4.52769e24	+	8.63362e24i	0.0740874	+	0.141273i
$519$	−6.56572e23	−	2.65823e24i	−0.0105485	−	0.0427074i
$520$	1.77352e24	+	2.17100e23i	0.0279771	+	0.00342474i
$521$			2.98947e25i			0.463059i	0.972828	+	0.231529i	$0.0743729\pi$
$521$			2.98947e25i			0.463059i	−0.972828	+	0.231529i	$0.925627\pi$
$522$	−9.06590e25	−	6.24903e25i	−1.37893	−	0.950480i
$523$			5.08283e25i			0.759171i	0.925157	+	0.379585i	$0.123933\pi$
$523$			5.08283e25i			0.759171i	−0.925157	+	0.379585i	$0.876067\pi$
$524$	2.70144e25	−	3.90827e25i	0.396231	−	0.573241i
$525$	−5.37686e24	−	2.17691e25i	−0.0774489	−	0.313564i
$526$	−4.33741e25	+	2.27465e25i	−0.613572	+	0.321773i
$527$	−2.54787e25			−0.353978
$528$	8.68377e23	+	1.26025e24i	0.0118491	+	0.0171963i
$529$	7.75717e25			1.03962
$530$	−7.48701e24	+	3.92638e24i	−0.0985570	+	0.0516858i
$531$	6.16529e25	−	3.24348e25i	0.797179	−	0.419385i
$532$	3.14898e25	−	4.55575e25i	0.399954	−	0.578628i
$533$		−	4.63831e24i		−	0.0578697i
$534$	−8.68614e25	−	9.80141e25i	−1.06460	−	1.20129i
$535$		−	2.96931e25i		−	0.357515i
$536$	1.36449e26	+	1.67030e25i	1.61401	+	0.197574i
$537$	−6.66759e25	+	1.64687e25i	−0.774843	+	0.191383i
$538$	−2.98181e25	−	5.68586e25i	−0.340447	−	0.649180i
$539$	1.51626e24			0.0170091
$540$	−4.50399e25	+	5.50603e24i	−0.496428	+	0.0606873i
$541$	7.99502e25			0.865856			0.432928	−	0.901429i	$-0.357480\pi$
$541$	7.99502e25			0.865856			0.432928	+	0.901429i	$0.357480\pi$
$542$	−2.81223e25	−	5.36249e25i	−0.299266	−	0.570654i
$543$	−1.17804e25	+	2.90971e24i	−0.123186	+	0.0304265i
$544$	−4.11852e25	+	4.63365e25i	−0.423206	+	0.476139i
$545$		−	6.55071e25i		−	0.661488i
$546$	−1.62239e24	−	1.83070e24i	−0.0161000	−	0.0181671i
$547$			1.32405e26i			1.29129i	0.763637	+	0.645646i	$0.223412\pi$
$547$			1.32405e26i			1.29129i	−0.763637	+	0.645646i	$0.776588\pi$
$548$	6.94450e25	+	4.80011e25i	0.665619	+	0.460083i
$549$	8.82822e25	−	4.64440e25i	0.831641	−	0.437515i
$550$	1.49788e24	−	7.85526e23i	0.0138685	−	0.00727302i
$551$	−3.00540e26			−2.73503
$552$	−1.91676e25	−	1.58505e26i	−0.171454	−	1.41782i
$553$	4.68984e25			0.412353
$554$	−1.07832e26	+	5.65498e25i	−0.931974	+	0.488751i
$555$	−5.22774e24	−	2.11653e25i	−0.0444151	−	0.179822i
$556$	4.82277e25	+	3.33355e25i	0.402797	+	0.278418i
$557$		−	2.47116e24i		−	0.0202897i	−0.999949	−	0.0101449i	$-0.996771\pi$
$557$		−	2.47116e24i		−	0.0202897i	0.999949	−	0.0101449i	$-0.00322927\pi$
$558$	−5.66793e25	−	3.90685e25i	−0.457509	−	0.315356i
$559$			1.37633e24i			0.0109222i
$560$	9.75690e24	+	2.58281e25i	0.0761247	+	0.201514i
$561$	4.15853e23	+	1.68364e24i	0.00319001	+	0.0129153i
$562$	3.95879e25	+	7.54881e25i	0.298585	+	0.569355i
$563$	5.43011e25			0.402698			0.201349	−	0.979520i	$-0.435468\pi$
$563$	5.43011e25			0.402698			0.201349	+	0.979520i	$0.435468\pi$
$564$	3.24223e25	−	8.54487e25i	0.236424	−	0.623094i
$565$	9.84637e25			0.706018
$566$	6.50318e25	+	1.24006e26i	0.458532	+	0.874351i
$567$	5.11929e25	+	3.51886e25i	0.354953	+	0.243985i
$568$	−2.28663e25	+	1.86798e26i	−0.155915	+	1.27369i
$569$		−	1.70737e26i		−	1.14488i	−0.819946	−	0.572440i	$-0.805997\pi$
$569$		−	1.70737e26i		−	1.14488i	0.819946	−	0.572440i	$-0.194003\pi$
$570$	−9.26897e25	+	8.21428e25i	−0.611252	+	0.541700i
$571$		−	1.27254e26i		−	0.825330i	−0.910883	−	0.412665i	$-0.864598\pi$
$571$		−	1.27254e26i		−	0.825330i	0.910883	−	0.412665i	$-0.135402\pi$
$572$	1.04912e23	−	1.51780e23i	0.000669210	−	0.000968170i
$573$	−2.16098e26	+	5.33752e25i	−1.35576	+	0.334866i
$574$	6.34740e25	−	3.32874e25i	0.391681	−	0.205408i
$575$	−1.76445e26			−1.07094
$576$	−1.62671e26	+	3.99267e25i	−0.971175	+	0.238369i
$577$	−1.36184e26			−0.799751			−0.399875	−	0.916570i	$-0.630947\pi$
$577$	−1.36184e26			−0.799751			−0.399875	+	0.916570i	$0.630947\pi$
$578$	9.10919e25	−	4.77710e25i	0.526218	−	0.275962i
$579$	2.57278e26	−	6.35465e25i	1.46203	−	0.361115i
$580$	8.51932e25	−	1.23252e26i	0.476255	−	0.689015i
$581$			2.11809e25i			0.116485i
$582$	2.10245e26	−	1.86322e26i	1.13752	−	1.00808i
$583$			8.73012e23i			0.00464696i
$584$	3.25931e25	−	2.66257e26i	0.170688	−	1.39437i
$585$	2.54692e24	+	4.84125e24i	0.0131230	+	0.0249446i
$586$	3.52431e24	+	6.72031e24i	0.0178668	+	0.0340692i
$587$	3.62218e26			1.80679			0.903396	−	0.428806i	$-0.141066\pi$
$587$	3.62218e26			1.80679			0.903396	+	0.428806i	$0.141066\pi$
$588$	−5.88702e25	+	1.55152e26i	−0.288942	+	0.761505i
$589$	−1.87895e26			−0.907446
$590$	4.40259e25	+	8.39507e25i	0.209225	+	0.398961i
$591$	−7.39157e25	−	2.99259e26i	−0.345665	−	1.39948i
$592$	−2.84401e25	−	7.52857e25i	−0.130881	−	0.346463i
$593$			1.53554e26i			0.695410i	0.937604	+	0.347705i	$0.113039\pi$
$593$			1.53554e26i			0.695410i	−0.937604	+	0.347705i	$0.886961\pi$
$594$	−1.65657e24	+	4.38306e24i	−0.00738309	+	0.0195347i
$595$			3.12857e25i			0.137226i
$596$	1.33235e26	+	9.20932e25i	0.575145	+	0.397547i
$597$	8.43932e25	+	3.41679e26i	0.358551	+	1.45165i
$598$	−1.70464e25	+	8.93956e24i	−0.0712805	+	0.0373814i
$599$	−1.14623e26			−0.471754			−0.235877	−	0.971783i	$-0.575796\pi$
$599$	−1.14623e26			−0.471754			−0.235877	+	0.971783i	$0.575796\pi$
$600$	2.22228e25	+	1.83770e26i	0.0900247	+	0.744453i
$601$	−4.40187e26			−1.75521			−0.877607	−	0.479380i	$-0.840861\pi$
$601$	−4.40187e26			−1.75521			−0.877607	+	0.479380i	$0.840861\pi$
$602$	−1.88346e25	+	9.87736e24i	−0.0739248	+	0.0387681i
$603$	1.95953e26	+	3.72473e26i	0.757072	+	1.43906i
$604$	2.65892e26	+	1.83787e26i	1.01124	+	0.698980i
$605$		−	1.33525e26i		−	0.499906i
$606$	1.64369e26	+	1.85473e26i	0.605801	+	0.683583i
$607$		−	3.90853e25i		−	0.141815i	−0.997483	−	0.0709073i	$-0.977411\pi$
$607$		−	3.90853e25i		−	0.141815i	0.997483	−	0.0709073i	$-0.0225894\pi$
$608$	−3.03725e26	+	3.41714e26i	−1.08492	+	1.22062i
$609$	−1.99139e26	+	4.91864e25i	−0.700312	+	0.172974i
$610$	6.30417e25	+	1.20211e26i	0.218270	+	0.416208i
$611$	−1.10181e25			−0.0375592
$612$	−1.88426e26	−	2.28167e25i	−0.632414	−	0.0765798i
$613$	1.55280e26			0.513145			0.256573	−	0.966525i	$-0.417407\pi$
$613$	1.55280e26			0.513145			0.256573	+	0.966525i	$0.417407\pi$
$614$	−4.24585e24	−	8.09619e24i	−0.0138154	−	0.0263440i
$615$	−1.55607e26	+	3.84342e25i	−0.498557	+	0.123141i
$616$	2.82998e24	+	3.46423e23i	0.00892824	+	0.00109292i
$617$		−	1.90605e26i		−	0.592142i	−0.955166	−	0.296071i	$-0.904324\pi$
$617$		−	1.90605e26i		−	0.592142i	0.955166	−	0.296071i	$-0.0956764\pi$
$618$	3.75725e26	+	4.23967e26i	1.14942	+	1.29700i
$619$		−	1.95485e26i		−	0.588914i	−0.955665	−	0.294457i	$-0.904861\pi$
$619$		−	1.95485e26i		−	0.588914i	0.955665	−	0.294457i	$-0.0951387\pi$
$620$	5.32622e25	−	7.70563e25i	0.158015	−	0.228606i
$621$	3.65408e26	−	3.24680e26i	1.06760	−	0.948605i
$622$	−3.90045e26	+	2.04550e26i	−1.12229	+	0.588560i
$623$	−2.43974e26			−0.691365
$624$	1.14576e25	+	1.66281e25i	0.0319773	+	0.0464077i
$625$	1.13574e26			0.312190
$626$	4.71712e26	−	2.47378e26i	1.27709	−	0.669738i
$627$	3.06676e24	+	1.24162e25i	0.00817782	+	0.0331092i
$628$	3.50960e26	−	5.07746e26i	0.921808	−	1.33361i
$629$		−	9.11941e25i		−	0.235931i
$630$	−4.79729e25	+	6.95977e25i	−0.122253	+	0.177362i
$631$		−	1.41529e26i		−	0.355278i	−0.984096	−	0.177639i	$-0.943154\pi$
$631$		−	1.41529e26i		−	0.355278i	0.984096	−	0.177639i	$-0.0568459\pi$
$632$	−3.84287e26	−	4.70414e25i	−0.950263	−	0.116324i
$633$	−3.86588e25	−	1.56516e26i	−0.0941701	−	0.381262i
$634$	−3.38490e26	−	6.45449e26i	−0.812265	−	1.54887i
$635$	9.65180e25			0.228170
$636$	−8.93314e25	−	3.38955e25i	−0.208047	−	0.0789404i
$637$	2.00060e25			0.0459024
$638$	−7.18582e24	−	1.37023e25i	−0.0162435	−	0.0309739i
$639$	−5.09912e26	+	2.68257e26i	−1.13563	+	0.597439i
$640$	−5.40416e25	−	2.21423e26i	−0.118582	−	0.485862i
$641$			1.89800e26i			0.410341i	0.978726	+	0.205171i	$0.0657749\pi$
$641$			1.89800e26i			0.410341i	−0.978726	+	0.205171i	$0.934225\pi$
$642$	2.51151e26	−	2.22574e26i	0.534999	−	0.474123i
$643$		−	5.08915e26i		−	1.06817i	−0.845430	−	0.534085i	$-0.820656\pi$
$643$		−	5.08915e26i		−	1.06817i	0.845430	−	0.534085i	$-0.179344\pi$
$644$	−2.44671e26	−	1.69119e26i	−0.506019	−	0.349766i
$645$	4.61731e25	−	1.14046e25i	0.0940962	−	0.0232413i
$646$	−4.58796e26	+	2.40604e26i	−0.921320	+	0.483164i
$647$	9.80984e25			0.194120			0.0970602	−	0.995279i	$-0.469056\pi$
$647$	9.80984e25			0.194120			0.0970602	+	0.995279i	$0.469056\pi$
$648$	−3.84181e26	−	3.39686e26i	−0.749158	−	0.662391i
$649$	9.78896e24			0.0188110
$650$	1.97635e25	−	1.03645e25i	0.0374271	−	0.0196277i
$651$	−1.24500e26	+	3.07510e25i	−0.232354	+	0.0573904i
$652$	7.18554e25	+	4.96672e25i	0.132162	+	0.0913519i
$653$			4.05951e26i			0.735865i	0.929852	+	0.367933i	$0.119934\pi$
$653$			4.05951e26i			0.735865i	−0.929852	+	0.367933i	$0.880066\pi$
$654$	5.54075e26	−	4.91028e26i	0.989873	−	0.877239i
$655$			1.97930e26i			0.348513i
$656$	−5.53497e26	+	2.09091e26i	−0.960570	+	0.362868i
$657$	7.26816e26	−	3.82368e26i	1.24324	−	0.654049i
$658$	−7.90730e25	−	1.50780e26i	−0.133316	−	0.254213i
$659$	6.46283e26			1.07402			0.537009	−	0.843577i	$-0.319554\pi$
$659$	6.46283e26			1.07402			0.537009	+	0.843577i	$0.319554\pi$
$660$	−5.96125e24	−	2.26191e24i	−0.00976495	−	0.00370517i
$661$	3.56894e26			0.576269			0.288135	−	0.957590i	$-0.406965\pi$
$661$	3.56894e26			0.576269			0.288135	+	0.957590i	$0.406965\pi$
$662$	−2.31074e26	−	4.40622e26i	−0.367789	−	0.701318i
$663$	5.48689e24	+	2.22145e25i	0.00860890	+	0.0348545i
$664$	2.12455e25	−	1.73557e26i	0.0328602	−	0.268439i
$665$			2.30721e26i			0.351788i
$666$	1.39835e26	−	2.02869e26i	0.210190	−	0.304937i
$667$			1.61408e27i			2.39183i
$668$	1.51257e26	−	2.18830e26i	0.220974	−	0.319690i
$669$	−6.70442e25	−	2.71439e26i	−0.0965636	−	0.390953i
$670$	−5.07184e26	+	2.65980e26i	−0.720202	+	0.377693i
$671$	1.40170e25			0.0196242
$672$	−1.45324e26	+	2.76128e26i	−0.200600	+	0.381156i
$673$	9.43031e26			1.28346			0.641731	−	0.766930i	$-0.278217\pi$
$673$	9.43031e26			1.28346			0.641731	+	0.766930i	$0.278217\pi$
$674$	−2.14190e26	+	1.12327e26i	−0.287429	+	0.150735i
$675$	−4.23652e26	+	3.76432e26i	−0.560562	+	0.498081i
$676$	−4.34429e26	+	6.28504e26i	−0.566794	+	0.820001i
$677$			1.28852e27i			1.65767i	0.559491	+	0.828836i	$0.310997\pi$
$677$			1.28852e27i			1.65767i	−0.559491	+	0.828836i	$0.689003\pi$
$678$	7.38064e26	+	8.32829e26i	0.936294	+	1.05651i
$679$		−	5.23337e26i		−	0.654664i
$680$	3.13811e25	−	2.56357e26i	0.0387110	−	0.316235i
$681$	−6.05503e26	+	1.49557e26i	−0.736578	+	0.181931i
$682$	−4.49252e24	−	8.56656e24i	−0.00538938	−	0.0102767i
$683$	1.01186e27			1.19709			0.598543	−	0.801091i	$-0.295747\pi$
$683$	1.01186e27			1.19709			0.598543	+	0.801091i	$0.295747\pi$
$684$	−1.38957e27	−	1.68265e26i	−1.62124	−	0.196318i
$685$	−3.51696e26			−0.404676
$686$	3.19854e26	+	6.09913e26i	0.362972	+	0.692132i
$687$	−3.23191e26	+	7.98267e25i	−0.361718	+	0.0893427i
$688$	1.64239e26	−	6.20435e25i	0.181295	−	0.0684866i
$689$			1.15188e25i			0.0125408i
$690$	4.41156e26	+	4.97799e26i	0.473724	+	0.534549i
$691$		−	7.56562e25i		−	0.0801315i	−0.999197	−	0.0400658i	$-0.987243\pi$
$691$		−	7.56562e25i		−	0.0801315i	0.999197	−	0.0400658i	$-0.0127567\pi$
$692$	3.46391e25	+	2.39429e25i	0.0361875	+	0.0250132i
$693$	4.06408e24	+	7.72513e24i	0.00418791	+	0.00796049i
$694$	3.92869e26	−	2.06031e26i	0.399331	−	0.209419i
$695$	−2.44244e26			−0.244888
$696$	1.68109e27	−	2.03289e26i	1.66266	−	0.201061i
$697$	−6.70455e26			−0.654121
$698$	−1.94994e26	+	1.02260e26i	−0.187670	+	0.0984190i
$699$	−2.48663e26	−	1.00675e27i	−0.236090	−	0.955848i
$700$	2.83670e26	+	1.96076e26i	0.265694	+	0.183650i
$701$		−	1.54289e27i		−	1.42565i	−0.701340	−	0.712827i	$-0.747415\pi$
$701$		−	1.54289e27i		−	1.42565i	0.701340	−	0.712827i	$-0.252585\pi$
$702$	−2.18573e25	+	5.78315e25i	−0.0199248	+	0.0527184i
$703$		−	6.72522e26i		−	0.604826i
$704$	−2.28415e25	−	5.67721e24i	−0.0202667	−	0.00503726i
$705$	9.12989e25	+	3.69638e26i	0.0799225	+	0.323579i
$706$	2.71282e24	+	5.17292e24i	0.00234302	+	0.00446778i
$707$	4.61675e26			0.393416
$708$	−3.80065e26	+	1.00166e27i	−0.319552	+	0.842178i
$709$	1.74705e26			0.144933			0.0724665	−	0.997371i	$-0.476913\pi$
$709$	1.74705e26			0.144933			0.0724665	+	0.997371i	$0.476913\pi$
$710$	−3.64124e26	−	6.94329e26i	−0.298054	−	0.568344i
$711$	−5.51869e26	−	1.04901e27i	−0.445733	−	0.847262i
$712$	1.99913e27	+	2.44718e26i	1.59324	+	0.195032i
$713$			1.00911e27i			0.793575i
$714$	−2.64622e26	+	2.34512e26i	−0.205349	+	0.181983i
$715$			7.68671e23i			0.000588617i
$716$	6.00555e26	−	8.68845e26i	0.453815	−	0.656551i
$717$	−1.77691e27	+	4.38888e26i	−1.32505	+	0.327282i
$718$	−2.68225e26	+	1.40664e26i	−0.197386	+	0.103514i
$719$	−1.38061e26			−0.100264			−0.0501322	−	0.998743i	$-0.515964\pi$
$719$	−1.38061e26			−0.100264			−0.0501322	+	0.998743i	$0.515964\pi$
$720$	4.62902e26	−	5.22167e26i	0.331765	−	0.374240i
$721$	1.05533e27			0.746452
$722$	−2.11479e27	+	1.10905e27i	−1.47626	+	0.774190i
$723$	−2.21563e25	+	5.47251e24i	−0.0152645	+	0.00377027i
$724$	1.06107e26	−	1.53509e26i	0.0721487	−	0.104380i
$725$		−	1.87135e27i		−	1.25587i
$726$	1.12939e27	−	1.00088e27i	0.748076	−	0.662955i
$727$			1.53336e27i			1.00246i	0.865314	+	0.501230i	$0.167119\pi$
$727$			1.53336e27i			1.00246i	−0.865314	+	0.501230i	$0.832881\pi$
$728$	3.73396e25	+	4.57081e24i	0.0240947	+	0.00294948i
$729$	1.84683e26	−	1.55914e27i	0.117629	−	0.993058i
$730$	5.19014e26	+	9.89680e26i	0.326296	+	0.622197i
$731$	1.98944e26			0.123457
$732$	−5.44224e26	+	1.43430e27i	−0.333367	+	0.878585i
$733$	−3.15907e27			−1.91017			−0.955084	−	0.296335i	$-0.904236\pi$
$733$	−3.15907e27			−1.91017			−0.955084	+	0.296335i	$0.904236\pi$
$734$	−1.47186e27	−	2.80661e27i	−0.878524	−	1.67521i
$735$	−1.65775e26	−	6.71164e26i	−0.0976760	−	0.395456i
$736$	1.83521e27	+	1.63119e27i	1.06745	+	0.948777i
$737$			5.91394e25i			0.0339575i
$738$	−1.49148e27	−	1.02806e27i	−0.845439	−	0.582752i
$739$		−	4.80014e26i		−	0.268616i	−0.990940	−	0.134308i	$-0.957119\pi$
$739$		−	4.80014e26i		−	0.268616i	0.990940	−	0.134308i	$-0.0428812\pi$
$740$	2.75803e26	+	1.90638e26i	0.152369	+	0.105319i
$741$	4.04637e25	+	1.63824e26i	0.0220695	+	0.0893519i
$742$	−1.57631e26	+	8.26660e25i	−0.0848801	+	0.0445133i
$743$	1.11721e27			0.593940			0.296970	−	0.954887i	$-0.404024\pi$
$743$	1.11721e27			0.593940			0.296970	+	0.954887i	$0.404024\pi$
$744$	1.05100e27	−	1.27095e26i	0.551647	−	0.0667092i
$745$	−6.74751e26			−0.349670
$746$	−2.35903e26	+	1.23714e26i	−0.120702	+	0.0632993i
$747$	4.73768e26	−	2.49243e26i	0.239342	−	0.125915i
$748$	−2.19393e25	−	1.51647e25i	−0.0109436	−	0.00756430i
$749$		−	6.25159e26i		−	0.307902i
$750$	−1.19355e27	−	1.34680e27i	−0.580442	−	0.654968i
$751$			9.35237e26i			0.449099i	0.974463	+	0.224550i	$0.0720910\pi$
$751$			9.35237e26i			0.449099i	−0.974463	+	0.224550i	$0.927909\pi$
$752$	4.96687e26	+	1.31481e27i	0.235512	+	0.623440i
$753$	−5.24164e26	+	1.29466e26i	−0.245423	+	0.0606184i
$754$	−9.48120e25	−	1.80792e26i	−0.0438365	−	0.0835894i
$755$	−1.34658e27			−0.614803
$756$	−9.48269e26	+	1.15924e26i	−0.427538	+	0.0522656i
$757$	1.70298e27			0.758225			0.379112	−	0.925351i	$-0.376229\pi$
$757$	1.70298e27			0.758225			0.379112	+	0.925351i	$0.376229\pi$
$758$	1.17507e27	+	2.24068e27i	0.516662	+	0.985197i
$759$	6.66826e25	−	1.64703e25i	0.0289545	−	0.00715163i
$760$	2.31424e26	−	1.89053e27i	0.0992383	−	0.810691i
$761$			8.30549e26i			0.351731i	0.984414	+	0.175866i	$0.0562725\pi$
$761$			8.30549e26i			0.351731i	−0.984414	+	0.175866i	$0.943728\pi$
$762$	7.23480e26	+	8.16372e26i	0.302590	+	0.341441i
$763$		−	1.37919e27i		−	0.569692i
$764$	1.94641e27	−	2.81594e27i	0.794049	−	1.14878i
$765$	6.99790e26	−	3.68150e26i	0.281958	−	0.148334i
$766$	−7.90239e26	+	4.14422e26i	−0.314474	+	0.164918i
$767$	1.29158e26			0.0507653
$768$	1.46776e27	−	2.11684e27i	0.569803	−	0.821782i
$769$	1.41968e27			0.544367			0.272183	−	0.962245i	$-0.412254\pi$
$769$	1.41968e27			0.544367			0.272183	+	0.962245i	$0.412254\pi$
$770$	−1.05190e25	+	5.51646e24i	−0.00398396	+	0.00208929i
$771$	2.32550e26	+	9.41516e26i	0.0869962	+	0.352218i
$772$	−2.31732e27	+	3.35255e27i	−0.856292	+	1.23883i
$773$			2.96986e27i			1.08401i	0.840377	+	0.542003i	$0.182334\pi$
$773$			2.96986e27i			1.08401i	−0.840377	+	0.542003i	$0.817666\pi$
$774$	4.42567e26	+	3.05057e26i	0.159566	+	0.109987i
$775$		−	1.16996e27i		−	0.416680i
$776$	−5.24932e26	+	4.28824e27i	−0.184679	+	1.50867i
$777$	−1.10065e26	−	4.45615e26i	−0.0382516	−	0.154867i
$778$	−1.52616e27	−	2.91015e27i	−0.523954	−	0.999099i
$779$	−4.94435e27			−1.67689
$780$	−7.86546e25	−	2.98443e25i	−0.0263527	−	0.00999916i
$781$	−8.09613e25			−0.0267974
$782$	1.29219e27	+	2.46401e27i	0.422534	+	0.805708i
$783$	3.44352e27	+	3.87548e27i	1.11241	+	1.25195i
$784$	−9.01852e26	−	2.38735e27i	−0.287828	−	0.761927i
$785$			2.57142e27i			0.810795i
$786$	−1.67414e27	+	1.48364e27i	−0.521527	+	0.462184i
$787$		−	3.51595e27i		−	1.08214i	−0.840978	−	0.541069i	$-0.818020\pi$
$787$		−	3.51595e27i		−	1.08214i	0.840978	−	0.541069i	$-0.181980\pi$
$788$	3.89961e27	+	2.69545e27i	1.18583	+	0.819657i
$789$	2.23871e27	−	5.52951e26i	0.672613	−	0.166133i
$790$	1.42840e27	−	7.49089e26i	0.424026	−	0.222370i
$791$	2.07305e27			0.608043
$792$	−2.55526e25	−	6.73765e25i	−0.00740535	−	0.0195263i
$793$	1.84945e26			0.0529599
$794$	2.70007e27	−	1.41599e27i	0.763978	−	0.400650i
$795$	3.86434e26	−	9.54475e25i	0.108041	−	0.0266856i
$796$	−4.45237e27	−	3.07753e27i	−1.23004	−	0.850214i
$797$		−	2.12508e27i		−	0.580124i	−0.957008	−	0.290062i	$-0.906324\pi$
$797$		−	2.12508e27i		−	0.580124i	0.957008	−	0.290062i	$-0.0936759\pi$
$798$	−1.95149e27	+	1.72944e27i	−0.526427	+	0.466527i
$799$			1.59264e27i			0.424545i
$800$	−2.12773e27	−	1.89119e27i	−0.560481	−	0.498172i
$801$	2.87092e27	+	5.45713e27i	0.747330	+	1.42055i
$802$	9.20283e25	+	1.75484e26i	0.0236736	+	0.0451420i
$803$	1.15400e26			0.0293366
$804$	−6.05147e27	−	2.29614e27i	−1.52030	−	0.576855i
$805$	1.23911e27			0.307644
$806$	−5.92757e25	−	1.13030e26i	−0.0145443	−	0.0277338i
$807$	7.24858e26	+	2.93470e27i	0.175774	+	0.711647i
$808$	−3.78298e27	−	4.63083e26i	−0.906622	−	0.110981i
$809$		−	7.46409e27i		−	1.76793i	−0.467550	−	0.883967i	$-0.654863\pi$
$809$		−	7.46409e27i		−	1.76793i	0.467550	−	0.883967i	$-0.345137\pi$
$810$	2.12125e27	+	2.54065e26i	0.496575	+	0.0594753i
$811$			7.01509e27i			1.62306i	0.584309	+	0.811531i	$0.301366\pi$
$811$			7.01509e27i			1.62306i	−0.584309	+	0.811531i	$0.698634\pi$
$812$	1.79366e27	−	2.59495e27i	0.410164	−	0.593399i
$813$	6.83632e26	+	2.76779e27i	0.154512	+	0.625565i
$814$	3.06617e25	−	1.60798e25i	0.00684959	−	0.00359210i
$815$	−3.63903e26			−0.0803505
$816$	2.40355e27	−	1.65617e27i	0.524562	−	0.361450i
$817$	1.46714e27			0.316491
$818$	2.09505e27	−	1.09870e27i	0.446723	−	0.234273i
$819$	5.36228e25	+	1.01928e26i	0.0113019	+	0.0214830i
$820$	1.40156e27	−	2.02769e27i	0.291998	−	0.422445i
$821$			2.54670e27i			0.524467i	0.965004	+	0.262233i	$0.0844590\pi$
$821$			2.54670e27i			0.524467i	−0.965004	+	0.262233i	$0.915541\pi$
$822$	−2.63624e27	−	2.97473e27i	−0.536665	−	0.605571i
$823$		−	3.07972e27i		−	0.619745i	−0.950778	−	0.309873i	$-0.899714\pi$
$823$		−	3.07972e27i		−	0.619745i	0.950778	−	0.309873i	$-0.100286\pi$
$824$	−8.64739e27	−	1.05854e27i	−1.72019	−	0.210572i
$825$	−7.73113e25	+	1.90956e25i	−0.0152030	+	0.00375509i
$826$	9.26921e26	+	1.76750e27i	0.180191	+	0.343596i
$827$	−6.38966e27			−1.22794			−0.613968	−	0.789331i	$-0.710427\pi$
$827$	−6.38966e27			−1.22794			−0.613968	+	0.789331i	$0.710427\pi$
$828$	−9.03681e26	+	7.46280e27i	−0.171683	+	1.41780i
$829$	1.61704e27			0.303705			0.151853	−	0.988403i	$-0.451476\pi$
$829$	1.61704e27			0.303705			0.151853	+	0.988403i	$0.451476\pi$
$830$	3.38314e26	+	6.45113e26i	0.0628171	+	0.119783i
$831$	5.56562e27	−	1.37468e27i	1.02165	−	0.252344i
$832$	−3.01377e26	−	7.49069e25i	−0.0546939	−	0.0135941i
$833$		−	2.89181e27i		−	0.518851i
$834$	−1.83080e27	−	2.06587e27i	−0.324761	−	0.366459i
$835$			1.10824e27i			0.194362i
$836$	−1.61794e26	−	1.11834e26i	−0.0280546	−	0.0193916i
$837$	2.15286e27	+	2.42292e27i	0.369083	+	0.415382i
$838$	4.47404e27	−	2.34630e27i	0.758370	−	0.397709i
$839$	−5.11693e27			−0.857572			−0.428786	−	0.903406i	$-0.641059\pi$
$839$	−5.11693e27			−0.857572			−0.428786	+	0.903406i	$0.641059\pi$
$840$	−1.56063e26	−	1.29055e27i	−0.0258610	−	0.213856i
$841$	−1.10155e28			−1.80485
$842$	7.53838e27	−	3.95332e27i	1.22127	−	0.640467i
$843$	−9.62353e26	−	3.89624e27i	−0.154160	−	0.624142i
$844$	2.03954e27	+	1.40975e27i	0.323057	+	0.223300i
$845$		−	3.18299e27i		−	0.498535i
$846$	−2.44212e27	+	3.54296e27i	−0.378224	+	0.548716i
$847$		−	2.81124e27i		−	0.430533i
$848$	1.37456e27	−	5.19256e26i	0.208162	−	0.0786360i
$849$	−1.58088e27	−	6.40042e27i	−0.236742	−	0.958486i
$850$	−1.49815e27	−	2.85675e27i	−0.221859	−	0.423051i
$851$	−3.61184e27			−0.528930
$852$	3.14340e27	−	8.28440e27i	0.455222	−	1.19973i
$853$	4.51339e27			0.646379			0.323189	−	0.946334i	$-0.395245\pi$
$853$	4.51339e27			0.646379			0.323189	+	0.946334i	$0.395245\pi$
$854$	1.32728e27	+	2.53092e27i	0.187980	+	0.358450i
$855$	5.16068e27	−	2.71496e27i	0.722818	−	0.380265i
$856$	−6.27065e26	+	5.12258e27i	−0.0868584	+	0.709557i
$857$		−	7.55223e27i		−	1.03456i	−0.855815	−	0.517282i	$-0.826944\pi$
$857$		−	7.55223e27i		−	1.03456i	0.855815	−	0.517282i	$-0.173056\pi$
$858$	−6.50160e24	+	5.76180e24i	−0.000880827	+	0.000780601i
$859$		−	1.11592e28i		−	1.49520i	−0.664152	−	0.747598i	$-0.731207\pi$
$859$		−	1.11592e28i		−	1.49520i	0.664152	−	0.747598i	$-0.268793\pi$
$860$	−4.15885e26	+	6.01676e26i	−0.0551109	+	0.0797310i
$861$	−3.27614e27	+	8.09193e26i	−0.429371	+	0.106053i
$862$	−1.89439e27	+	9.93466e26i	−0.245556	+	0.128776i
$863$	6.29777e27			0.807391			0.403696	−	0.914893i	$-0.367725\pi$
$863$	6.29777e27			0.807391			0.403696	+	0.914893i	$0.367725\pi$
$864$	7.88643e27	+	1.27457e24i	1.00000	+	0.000161615i
$865$	−1.75425e26			−0.0220009
$866$	1.89904e27	−	9.95905e26i	0.235567	−	0.123537i
$867$	−4.70161e27	+	1.16128e27i	−0.576853	+	0.142480i
$868$	1.12138e27	−	1.62234e27i	0.136087	−	0.196882i
$869$		−	1.66556e26i		−	0.0199928i
$870$	−5.27960e27	+	4.67885e27i	−0.626856	+	0.555528i
$871$			7.80304e26i			0.0916413i
$872$	−1.38339e27	+	1.13011e28i	−0.160708	+	1.31285i
$873$	−1.17058e28	+	6.15828e27i	−1.34514	+	0.707659i
$874$	9.52940e27	+	1.81711e28i	1.08320	+	2.06549i
$875$	−3.35241e27			−0.376947
$876$	−4.48052e27	+	1.18084e28i	−0.498356	+	1.31341i
$877$	−7.50340e27			−0.825585			−0.412792	−	0.910825i	$-0.635447\pi$
$877$	−7.50340e27			−0.825585			−0.412792	+	0.910825i	$0.635447\pi$
$878$	4.13876e27	+	7.89198e27i	0.450476	+	0.858990i
$879$	−8.56733e25	−	3.46862e26i	−0.00922468	−	0.0373475i
$880$	9.17267e25	−	3.46510e25i	0.00977036	−	0.00369088i
$881$			1.32340e28i			1.39450i	0.716827	+	0.697251i	$0.245594\pi$
$881$			1.32340e28i			1.39450i	−0.716827	+	0.697251i	$0.754406\pi$
$882$	4.43425e27	−	6.43307e27i	0.462241	−	0.670605i
$883$			1.32731e28i			1.36882i	0.729098	+	0.684409i	$0.239940\pi$
$883$			1.32731e28i			1.36882i	−0.729098	+	0.684409i	$0.760060\pi$
$884$	−2.89474e26	−	2.00088e26i	−0.0295334	−	0.0204138i
$885$	−1.07024e27	−	4.33302e27i	−0.108024	−	0.437351i
$886$	1.24509e28	−	6.52956e27i	1.24331	−	0.652024i
$887$	1.69464e28			1.67418			0.837091	−	0.547063i	$-0.184254\pi$
$887$	1.69464e28			1.67418			0.837091	+	0.547063i	$0.184254\pi$
$888$	4.54903e26	+	3.76179e27i	0.0444627	+	0.367681i
$889$	2.03209e27			0.196506
$890$	−7.43079e27	+	3.89690e27i	−0.710935	+	0.372833i
$891$	1.24970e26	−	1.81808e26i	0.0118295	−	0.0172098i
$892$	3.53708e27	+	2.44487e27i	0.331268	+	0.228976i
$893$			1.17451e28i			1.08835i
$894$	−5.05780e27	−	5.70720e27i	−0.463719	−	0.523259i
$895$			4.40016e27i			0.399163i
$896$	−1.13779e27	−	4.66184e27i	−0.102126	−	0.418438i
$897$	8.79831e26	−	2.17314e26i	0.0781395	−	0.0193001i
$898$	6.93014e27	+	1.32147e28i	0.608999	+	1.16127i
$899$	−1.07025e28			−0.930612
$900$	1.04772e27	−	8.65232e27i	0.0901450	−	0.744438i
$901$	1.66501e27			0.141753
$902$	−1.18218e26	−	2.25424e26i	−0.00995913	−	0.0189905i
$903$	9.72129e26	−	2.40112e26i	0.0810383	−	0.0200161i
$904$	−1.69867e28	−	2.07937e27i	−1.40123	−	0.171527i
$905$			7.77429e26i			0.0634598i
$906$	−1.00937e28	−	1.13897e28i	−0.815327	−	0.920012i
$907$		−	9.89997e27i		−	0.791343i	−0.918392	−	0.395671i	$-0.870512\pi$
$907$		−	9.89997e27i		−	0.791343i	0.918392	−	0.395671i	$-0.129488\pi$
$908$	5.45381e27	−	7.89022e27i	0.431404	−	0.624128i
$909$	−5.43268e27	−	1.03266e28i	−0.425263	−	0.808352i
$910$	−1.38792e26	+	7.27859e25i	−0.0107515	+	0.00563837i
$911$	2.18861e28			1.67781			0.838907	−	0.544274i	$-0.183195\pi$
$911$	2.18861e28			1.67781			0.838907	+	0.544274i	$0.183195\pi$
$912$	1.77253e28	−	1.22136e28i	1.34475	−	0.926602i
$913$	7.52225e25			0.00564775
$914$	−8.35202e27	+	4.38001e27i	−0.620587	+	0.325452i
$915$	−1.53250e27	−	6.20455e27i	−0.112694	−	0.456257i
$916$	2.91100e27	−	4.21145e27i	0.211853	−	0.306496i
$917$			4.16721e27i			0.300149i
$918$	8.35938e27	+	3.15941e27i	0.595893	+	0.225216i
$919$			2.12744e28i			1.50093i	0.660910	+	0.750465i	$0.270170\pi$
$919$			2.12744e28i			1.50093i	−0.660910	+	0.750465i	$0.729830\pi$
$920$	−1.01533e28	−	1.24288e27i	−0.708961	−	0.0867853i
$921$	1.03214e26	+	4.17876e26i	0.00713297	+	0.0288789i
$922$	−1.12511e28	−	2.14541e28i	−0.769575	−	1.46746i
$923$	−1.06823e27			−0.0723182
$924$	−1.25508e26	−	4.76223e25i	−0.00840985	−	0.00319100i
$925$	4.18754e27			0.277724
$926$	−7.83224e27	−	1.49349e28i	−0.514140	−	0.980387i
$927$	−1.24184e28	−	2.36052e28i	−0.806877	−	1.53374i
$928$	−1.73002e28	+	1.94640e28i	−1.11261	+	1.25178i
$929$		−	2.00768e28i		−	1.27804i	−0.769190	−	0.639020i	$-0.779340\pi$
$929$		−	2.00768e28i		−	1.27804i	0.769190	−	0.639020i	$-0.220660\pi$
$930$	−3.30076e27	+	2.92518e27i	−0.207982	+	0.184317i
$931$		−	2.13260e28i		−	1.33011i
$932$	1.31188e28	+	9.06789e27i	0.809924	+	0.559828i
$933$	2.01318e28	−	4.97246e27i	1.23029	−	0.303875i
$934$	2.13770e28	−	1.12107e28i	1.29316	−	0.678166i
$935$	1.11109e26			0.00665334
$936$	−3.37149e26	−	8.88986e26i	−0.0199848	−	0.0526956i
$937$	2.19414e28			1.28747			0.643736	−	0.765248i	$-0.277383\pi$
$937$	2.19414e28			1.28747			0.643736	+	0.765248i	$0.277383\pi$
$938$	−1.06782e28	+	5.59994e27i	−0.620259	+	0.325280i
$939$	−2.43469e28	+	6.01358e27i	−1.39998	+	0.345788i
$940$	−4.81670e27	−	3.32936e27i	−0.274180	−	0.189516i
$941$		−	1.97479e27i		−	0.111281i	−0.998451	−	0.0556403i	$-0.982280\pi$
$941$		−	1.97479e27i		−	0.111281i	0.998451	−	0.0556403i	$-0.0177200\pi$
$942$	−2.17497e28	+	1.92749e28i	−1.21330	+	1.07525i
$943$			2.65541e28i			1.46646i
$944$	−5.82234e27	−	1.54127e28i	−0.318320	−	0.842645i
$945$	2.97515e27	−	2.64354e27i	0.161030	−	0.143082i
$946$	3.50788e25	+	6.68899e25i	0.00187966	+	0.00358422i
$947$	−2.38881e28			−1.26724			−0.633618	−	0.773646i	$-0.718431\pi$
$947$	−2.38881e28			−1.26724			−0.633618	+	0.773646i	$0.718431\pi$
$948$	1.70430e28	+	6.46671e27i	0.895088	+	0.339628i
$949$	1.52263e27			0.0791707
$950$	−1.10483e28	−	2.10675e28i	−0.568751	−	1.08452i
$951$	8.22845e27	+	3.33141e28i	0.419375	+	1.69791i
$952$	6.60698e26	−	5.39733e27i	0.0333390	−	0.272350i
$953$			2.21552e28i			1.10686i	0.832896	+	0.553430i	$0.186681\pi$
$953$			2.21552e28i			1.10686i	−0.832896	+	0.553430i	$0.813319\pi$
$954$	3.70395e27	+	2.55309e27i	0.183213	+	0.126286i
$955$			1.42610e28i			0.698422i
$956$	1.60047e28	−	2.31546e28i	0.776065	−	1.12276i
$957$	1.74682e26	+	7.07228e26i	0.00838659	+	0.0339544i
$958$	−2.14480e28	+	1.12479e28i	−1.01956	+	0.534686i
$959$	−7.40461e27			−0.348518
$960$	−1.56998e25	+	1.07313e28i	−0.000731672	+	0.500123i
$961$	1.49795e28			0.691236
$962$	4.04560e26	−	2.12162e26i	0.0184850	−	0.00969402i
$963$	−1.39834e28	+	7.35645e27i	−0.632647	+	0.332827i
$964$	1.99563e26	−	2.88716e26i	0.00894024	−	0.0129342i
$965$		−	1.69786e28i		−	0.753170i
$966$	9.28810e27	+	1.04807e28i	0.407985	+	0.460369i
$967$		−	3.77617e28i		−	1.64248i	−0.570583	−	0.821240i	$-0.693283\pi$
$967$		−	3.77617e28i		−	1.64248i	0.570583	−	0.821240i	$-0.306717\pi$
$968$	−2.81982e27	+	2.30355e28i	−0.121452	+	0.992158i
$969$	2.36803e28	−	5.84892e27i	1.00997	−	0.249459i
$970$	−8.35905e27	−	1.59394e28i	−0.353041	−	0.673196i
$971$	4.28177e28			1.79077			0.895387	−	0.445289i	$-0.146899\pi$
$971$	4.28177e28			1.79077			0.895387	+	0.445289i	$0.146899\pi$
$972$	1.37515e28	+	1.98465e28i	0.569537	+	0.821966i
$973$	−5.14230e27			−0.210904
$974$	−1.73871e28	−	3.31545e28i	−0.706181	−	1.34658i
$975$	−1.02007e27	+	2.51953e26i	−0.0410285	+	0.0101339i
$976$	−8.33714e27	−	2.20698e28i	−0.332081	−	0.879072i
$977$			2.80430e28i			1.10618i	0.833121	+	0.553090i	$0.186551\pi$
$977$			2.80430e28i			1.10618i	−0.833121	+	0.553090i	$0.813449\pi$
$978$	−2.72774e27	−	3.07798e27i	−0.106558	−	0.120239i
$979$			8.66457e26i			0.0335206i
$980$	8.74584e27	+	6.04522e27i	0.335084	+	0.231614i
$981$	−3.08492e28	+	1.62293e28i	−1.17055	+	0.615808i
$982$	8.98119e26	−	4.70997e26i	0.0337501	−	0.0176994i
$983$	2.97250e28			1.10628			0.553138	−	0.833089i	$-0.313430\pi$
$983$	2.97250e28			1.10628			0.553138	+	0.833089i	$0.313430\pi$
$984$	2.76565e28	−	3.34443e27i	1.01940	−	0.123273i
$985$	−1.97491e28			−0.720946
$986$	−2.61330e28	+	1.37048e28i	−0.944840	+	0.495498i
$987$	1.92221e27	+	7.78235e27i	0.0688315	+	0.278675i
$988$	−2.13476e27	−	1.47557e27i	−0.0757110	−	0.0523323i
$989$		−	7.87939e27i		−	0.276776i
$990$	2.47171e26	+	1.70373e26i	0.00859932	+	0.00592742i
$991$		−	1.52440e28i		−	0.525290i	−0.964892	−	0.262645i	$-0.915405\pi$
$991$		−	1.52440e28i		−	0.525290i	0.964892	−	0.262645i	$-0.0845949\pi$
$992$	−1.08159e28	+	1.21687e28i	−0.369150	+	0.415322i
$993$	5.61723e27	+	2.27422e28i	0.189891	+	0.768803i
$994$	−7.66627e27	−	1.46184e28i	−0.256693	−	0.489474i
$995$	2.25485e28			0.747823
$996$	−2.92058e27	+	7.69718e27i	−0.0959414	+	0.252853i
$997$	−3.72997e28			−1.21367			−0.606836	−	0.794827i	$-0.707562\pi$
$997$	−3.72997e28			−1.21367			−0.606836	+	0.794827i	$0.707562\pi$
$998$	1.67627e28	+	3.19639e28i	0.540261	+	1.03019i
$999$	−8.67220e27	+	7.70559e27i	−0.276858	+	0.245999i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	12.20.b.a.11.31	yes	36
3.2	odd	2	inner	12.20.b.a.11.6	yes	36
4.3	odd	2	inner	12.20.b.a.11.5	✓	36
12.11	even	2	inner	12.20.b.a.11.32	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
12.20.b.a.11.5	✓	36	4.3	odd	2	inner
12.20.b.a.11.6	yes	36	3.2	odd	2	inner
12.20.b.a.11.31	yes	36	1.1	even	1	trivial
12.20.b.a.11.32	yes	36	12.11	even	2	inner

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:	\( N \)	\(=\)	\( 12 = 2^{2} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 20 \)
Character orbit:	\([\chi]\)	\(=\)	12.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(641.248 - 336.287i) q^{2} +(-33097.3 + 8174.89i) q^{3} +(298110. - 431287. i) q^{4} +2.18420e6i q^{5} +(-1.84745e7 + 1.63723e7i) q^{6} +4.59862e7i q^{7} +(4.61264e7 - 3.76812e8i) q^{8} +(1.02860e9 - 5.41134e8i) q^{9} +O(q^{10})\)	\(q+(641.248 - 336.287i) q^{2} +(-33097.3 + 8174.89i) q^{3} +(298110. - 431287. i) q^{4} +2.18420e6i q^{5} +(-1.84745e7 + 1.63723e7i) q^{6} +4.59862e7i q^{7} +(4.61264e7 - 3.76812e8i) q^{8} +(1.02860e9 - 5.41134e8i) q^{9} +(7.34518e8 + 1.40061e9i) q^{10} +1.63317e8 q^{11} +(-6.34092e9 + 1.67115e10i) q^{12} +2.15485e9 q^{13} +(1.54645e10 + 2.94885e10i) q^{14} +(-1.78556e10 - 7.22912e10i) q^{15} +(-9.71387e10 - 2.57142e11i) q^{16} -3.11478e11i q^{17} +(4.77614e11 - 6.92907e11i) q^{18} -2.29703e12i q^{19} +(9.42017e11 + 6.51132e11i) q^{20} +(-3.75932e11 - 1.52202e12i) q^{21} +(1.04727e11 - 5.49213e10i) q^{22} -1.23364e13 q^{23} +(1.55374e12 + 1.28486e13i) q^{24} +1.43028e13 q^{25} +(1.38179e12 - 7.24648e11i) q^{26} +(-2.96203e13 + 2.63188e13i) q^{27} +(1.98332e13 + 1.37089e13i) q^{28} -1.30839e14i q^{29} +(-3.57605e13 - 4.03520e13i) q^{30} -8.17993e13i q^{31} +(-1.48763e14 - 1.32225e14i) q^{32} +(-5.40535e12 + 1.33510e12i) q^{33} +(-1.04746e14 - 1.99734e14i) q^{34} -1.00443e14 q^{35} +(7.32531e13 - 6.04941e14i) q^{36} +2.92779e14 q^{37} +(-7.72461e14 - 1.47297e15i) q^{38} +(-7.13198e13 + 1.76157e13i) q^{39} +(8.23034e14 + 1.00749e14i) q^{40} -2.15250e15i q^{41} +(-7.52901e14 - 8.49570e14i) q^{42} +6.38710e14i q^{43} +(4.86864e13 - 7.04363e13i) q^{44} +(1.18195e15 + 2.24668e15i) q^{45} +(-7.91070e15 + 4.14858e15i) q^{46} -5.11318e15 q^{47} +(5.31714e15 + 7.71661e15i) q^{48} +9.28417e15 q^{49} +(9.17161e15 - 4.80983e15i) q^{50} +(2.54630e15 + 1.03091e16i) q^{51} +(6.42383e14 - 9.29359e14i) q^{52} +5.34552e15i q^{53} +(-1.01433e16 + 2.68378e16i) q^{54} +3.56716e14i q^{55} +(1.73282e16 + 2.12117e15i) q^{56} +(1.87780e16 + 7.60255e16i) q^{57} +(-4.39993e16 - 8.39000e16i) q^{58} +5.99385e16 q^{59} +(-3.65012e16 - 1.38498e16i) q^{60} +8.58272e16 q^{61} +(-2.75080e16 - 5.24536e16i) q^{62} +(2.48847e16 + 4.73015e16i) q^{63} +(-1.39860e17 - 3.47620e16i) q^{64} +4.70663e15i q^{65} +(-3.01719e15 + 2.67388e15i) q^{66} +3.62115e17i q^{67} +(-1.34336e17 - 9.28546e16i) q^{68} +(4.08302e17 - 1.00849e17i) q^{69} +(-6.44089e16 + 3.37777e16i) q^{70} -4.95732e17 q^{71} +(-1.56460e17 - 4.12551e17i) q^{72} +7.06604e17 q^{73} +(1.87744e17 - 9.84577e16i) q^{74} +(-4.73383e17 + 1.16924e17i) q^{75} +(-9.90678e17 - 6.84768e17i) q^{76} +7.51031e15i q^{77} +(-3.98098e16 + 3.52799e16i) q^{78} -1.01984e18i q^{79} +(5.61649e17 - 2.12170e17i) q^{80} +(7.65199e17 - 1.11323e18i) q^{81} +(-7.23857e17 - 1.38029e18i) q^{82} +4.60593e17 q^{83} +(-7.68496e17 - 2.91595e17i) q^{84} +6.80330e17 q^{85} +(2.14790e17 + 4.09572e17i) q^{86} +(1.06959e18 + 4.33041e18i) q^{87} +(7.53321e15 - 6.15398e16i) q^{88} +5.30538e18i q^{89} +(1.51345e18 + 1.04320e18i) q^{90} +9.90933e16i q^{91} +(-3.67761e18 + 5.32053e18i) q^{92} +(6.68701e17 + 2.70734e18i) q^{93} +(-3.27882e18 + 1.71950e18i) q^{94} +5.01717e18 q^{95} +(6.00460e18 + 3.16018e18i) q^{96} -1.13803e19 q^{97} +(5.95345e18 - 3.12215e18i) q^{98} +(1.67988e17 - 8.83763e16i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 47880 q^{4} + 21771144 q^{6} - 809473644 q^{9}+O(q^{10}) \) 36 * q - 47880 * q^4 + 21771144 * q^6 - 809473644 * q^9	\( 36 q - 47880 q^{4} + 21771144 q^{6} - 809473644 q^{9} - 4162950000 q^{10} - 2268767880 q^{12} - 25913431656 q^{13} + 791689296672 q^{16} + 2852271258192 q^{18} - 1650825908424 q^{21} + 7247870602416 q^{22} + 23719435803936 q^{24} - 118879690462380 q^{25} - 7629081673968 q^{28} + 37456727138640 q^{30} + 529254701828640 q^{33} - 248241675948480 q^{34} - 11\!\cdots\!16 q^{36}+ \cdots + 12\!\cdots\!88 q^{97}+O(q^{100}) \) 36 * q - 47880 * q^4 + 21771144 * q^6 - 809473644 * q^9 - 4162950000 * q^10 - 2268767880 * q^12 - 25913431656 * q^13 + 791689296672 * q^16 + 2852271258192 * q^18 - 1650825908424 * q^21 + 7247870602416 * q^22 + 23719435803936 * q^24 - 118879690462380 * q^25 - 7629081673968 * q^28 + 37456727138640 * q^30 + 529254701828640 * q^33 - 248241675948480 * q^34 - 1177548745309416 * q^36 + 1847838600168120 * q^37 - 40433256181440 * q^40 - 2709671988768336 * q^42 - 4365410114088000 * q^45 + 17206125364795104 * q^46 + 1561106052682272 * q^48 - 49399737041580084 * q^49 + 16558671470242896 * q^52 + 40087412948587896 * q^54 + 44803667812766472 * q^57 - 34645536255764880 * q^58 + 50260381053157440 * q^60 + 174742350239997144 * q^61 - 139766490424918656 * q^64 - 87772097712685968 * q^66 - 957190369821780672 * q^69 + 244663962371376480 * q^70 + 54134736422921280 * q^72 - 1445122541399481432 * q^73 + 2744130151937256048 * q^76 + 1125465917961999024 * q^78 + 1033298241353042436 * q^81 + 1064985418859680800 * q^82 + 1920709484261873424 * q^84 - 1802899595088057600 * q^85 - 9209792381828477760 * q^88 - 5194944179528261040 * q^90 + 6719944190337314136 * q^93 - 3835186345170303552 * q^94 - 11947184361208227456 * q^96 + 12765226159947004488 * q^97

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