LMFDB - Embedded newform 12.16.b.a.11.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [12,16,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, 16, names="a")

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

chi := DirichletCharacter("12.11");

S:= CuspForms(chi, 16);

N := Newforms(S);

Level:	$ N $	$=$	$ 12 = 2^{2} \cdot 3 $
Weight:	$ k $	$=$	$ 16 $
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:	$17.1232206120$
Analytic rank:	$0$
Dimension:	$28$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			11.9
Character	$\chi$	$=$	12.11
Dual form			12.16.b.a.11.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-83.3106 - 160.709i) q^{2} +(3555.47 - 1306.74i) q^{3} +(-18886.7 + 26777.5i) q^{4} +93360.9i q^{5} +(-506212. - 462530. i) q^{6} -1.14542e6i q^{7} +(5.87684e6 + 804409. i) q^{8} +(1.09338e7 - 9.29212e6i) q^{9} +O(q^{10})$	\(q+(-83.3106 - 160.709i) q^{2} +(3555.47 - 1306.74i) q^{3} +(-18886.7 + 26777.5i) q^{4} +93360.9i q^{5} +(-506212. - 462530. i) q^{6} -1.14542e6i q^{7} +(5.87684e6 + 804409. i) q^{8} +(1.09338e7 - 9.29212e6i) q^{9} +(1.50039e7 - 7.77795e6i) q^{10} -1.80841e6 q^{11} +(-3.21598e7 + 1.19886e8i) q^{12} +3.17574e8 q^{13} +(-1.84079e8 + 9.54254e7i) q^{14} +(1.21998e8 + 3.31942e8i) q^{15} +(-3.60328e8 - 1.01148e9i) q^{16} -2.67956e9i q^{17} +(-2.40423e9 - 9.83024e8i) q^{18} -2.07292e9i q^{19} +(-2.49997e9 - 1.76328e9i) q^{20} +(-1.49676e9 - 4.07249e9i) q^{21} +(1.50660e8 + 2.90628e8i) q^{22} -2.43757e10 q^{23} +(2.19461e10 - 4.81944e9i) q^{24} +2.18013e10 q^{25} +(-2.64573e10 - 5.10370e10i) q^{26} +(2.67323e10 - 4.73254e10i) q^{27} +(3.06714e10 + 2.16331e10i) q^{28} +4.77985e9i q^{29} +(4.31822e10 - 4.72604e10i) q^{30} -5.30495e10i q^{31} +(-1.32534e11 + 1.42175e11i) q^{32} +(-6.42975e9 + 2.36312e9i) q^{33} +(-4.30629e11 + 2.23235e11i) q^{34} +1.06937e11 q^{35} +(4.23169e10 + 4.68277e11i) q^{36} +4.06413e11 q^{37} +(-3.33137e11 + 1.72696e11i) q^{38} +(1.12912e12 - 4.14986e11i) q^{39} +(-7.51003e10 + 5.48667e11i) q^{40} +1.36874e12i q^{41} +(-5.29790e11 + 5.79824e11i) q^{42} -2.85013e12i q^{43} +(3.41549e10 - 4.84247e10i) q^{44} +(8.67521e11 + 1.02079e12i) q^{45} +(2.03075e12 + 3.91739e12i) q^{46} +7.27503e11 q^{47} +(-2.60287e12 - 3.12542e12i) q^{48} +3.43558e12 q^{49} +(-1.81628e12 - 3.50367e12i) q^{50} +(-3.50148e12 - 9.52708e12i) q^{51} +(-5.99793e12 + 8.50385e12i) q^{52} -7.05903e12i q^{53} +(-9.83270e12 - 3.53416e11i) q^{54} -1.68835e11i q^{55} +(9.21384e11 - 6.73144e12i) q^{56} +(-2.70876e12 - 7.37020e12i) q^{57} +(7.68164e11 - 3.98212e11i) q^{58} +1.63957e13 q^{59} +(-1.11927e13 - 3.00247e12i) q^{60} +3.06206e13 q^{61} +(-8.52552e12 + 4.41958e12i) q^{62} +(-1.06434e13 - 1.25237e13i) q^{63} +(3.38902e13 + 9.45477e12i) q^{64} +2.96490e13i q^{65} +(9.15440e11 + 8.36445e11i) q^{66} +7.17216e13i q^{67} +(7.17519e13 + 5.06080e13i) q^{68} +(-8.66669e13 + 3.18526e13i) q^{69} +(-8.90900e12 - 1.71857e13i) q^{70} -4.82624e13 q^{71} +(7.17308e13 - 4.58131e13i) q^{72} -9.56538e13 q^{73} +(-3.38585e13 - 6.53141e13i) q^{74} +(7.75139e13 - 2.84886e13i) q^{75} +(5.55077e13 + 3.91506e13i) q^{76} +2.07139e12i q^{77} +(-1.60760e14 - 1.46888e14i) q^{78} +3.27912e14i q^{79} +(9.44324e13 - 3.36405e13i) q^{80} +(3.32041e13 - 2.03196e14i) q^{81} +(2.19969e14 - 1.14031e14i) q^{82} -2.88031e14 q^{83} +(1.37320e14 + 3.68364e13i) q^{84} +2.50166e14 q^{85} +(-4.58041e14 + 2.37446e14i) q^{86} +(6.24600e12 + 1.69946e13i) q^{87} +(-1.06278e13 - 1.45470e12i) q^{88} -2.05245e14i q^{89} +(9.17760e13 - 2.24461e14i) q^{90} -3.63755e14i q^{91} +(4.60376e14 - 6.52720e14i) q^{92} +(-6.93217e13 - 1.88616e14i) q^{93} +(-6.06087e13 - 1.16916e14i) q^{94} +1.93530e14 q^{95} +(-2.85436e14 + 6.78684e14i) q^{96} -5.41919e14 q^{97} +(-2.86220e14 - 5.52128e14i) q^{98} +(-1.97728e13 + 1.68040e13i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 26968 q^{4} + 823656 q^{6} - 3812052 q^{9}+O(q^{10}) $ 28 * q + 26968 * q^4 + 823656 * q^6 - 3812052 * q^9	\( 28 q + 26968 q^{4} + 823656 q^{6} - 3812052 q^{9} - 43831600 q^{10} - 226414248 q^{12} + 124527272 q^{13} - 1459325408 q^{16} - 4234777584 q^{18} - 7261350648 q^{21} - 2533670160 q^{22} - 18487781856 q^{24} - 146804950740 q^{25} + 5481093840 q^{28} + 8237058960 q^{30} + 204574669728 q^{33} + 450165745472 q^{34} + 232631927160 q^{36} + 386069193224 q^{37} + 1945471012160 q^{40} + 1938106219632 q^{42} - 5007113912640 q^{45} + 2270790222432 q^{46} + 5846474725152 q^{48} - 18480860963084 q^{49} - 6113229405424 q^{52} + 1626598700568 q^{54} + 8085872464056 q^{57} - 19395437098192 q^{58} - 10924219377600 q^{60} - 16392792556696 q^{61} + 21633892829056 q^{64} + 4928819126448 q^{66} + 137029869973056 q^{69} + 91772543171040 q^{70} + 66924493142592 q^{72} + 158451626683736 q^{73} - 205265768291280 q^{76} + 58364283489648 q^{78} + 116126816635836 q^{81} - 750029796726880 q^{82} - 92605433207856 q^{84} - 30099357052160 q^{85} - 619691835246912 q^{88} - 471443548913520 q^{90} - 777661615138584 q^{93} + 13\!\cdots\!00 q^{94}+ \cdots - 824166397720648 q^{97}+O(q^{100}) \) 28 * q + 26968 * q^4 + 823656 * q^6 - 3812052 * q^9 - 43831600 * q^10 - 226414248 * q^12 + 124527272 * q^13 - 1459325408 * q^16 - 4234777584 * q^18 - 7261350648 * q^21 - 2533670160 * q^22 - 18487781856 * q^24 - 146804950740 * q^25 + 5481093840 * q^28 + 8237058960 * q^30 + 204574669728 * q^33 + 450165745472 * q^34 + 232631927160 * q^36 + 386069193224 * q^37 + 1945471012160 * q^40 + 1938106219632 * q^42 - 5007113912640 * q^45 + 2270790222432 * q^46 + 5846474725152 * q^48 - 18480860963084 * q^49 - 6113229405424 * q^52 + 1626598700568 * q^54 + 8085872464056 * q^57 - 19395437098192 * q^58 - 10924219377600 * q^60 - 16392792556696 * q^61 + 21633892829056 * q^64 + 4928819126448 * q^66 + 137029869973056 * q^69 + 91772543171040 * q^70 + 66924493142592 * q^72 + 158451626683736 * q^73 - 205265768291280 * q^76 + 58364283489648 * q^78 + 116126816635836 * q^81 - 750029796726880 * q^82 - 92605433207856 * q^84 - 30099357052160 * q^85 - 619691835246912 * q^88 - 471443548913520 * q^90 - 777661615138584 * q^93 + 1301107064491200 * q^94 + 525428335287168 * q^96 - 824166397720648 * 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 $

$2$	−83.3106	−	160.709i	−0.460230	−	0.887800i
$2$	−83.3106	−	160.709i	−0.460230	−	0.887800i
$3$	3555.47	−	1306.74i	0.938614	−	0.344968i
$3$	3555.47	−	1306.74i	0.938614	−	0.344968i
$4$	−18886.7	+	26777.5i	−0.576376	+	0.817185i
$5$			93360.9i			0.534429i	0.963637	+	0.267214i	$0.0861032\pi$
$5$			93360.9i			0.534429i	−0.963637	+	0.267214i	$0.913897\pi$
$6$	−506212.	−	462530.i	−0.738241	−	0.674537i
$7$		−	1.14542e6i		−	0.525688i	−0.964838	−	0.262844i	$-0.915339\pi$
$7$		−	1.14542e6i		−	0.525688i	0.964838	−	0.262844i	$-0.0846605\pi$
$8$	5.87684e6	+	804409.i	0.990762	+	0.135613i
$9$	1.09338e7	−	9.29212e6i	0.761994	−	0.647584i
$10$	1.50039e7	−	7.77795e6i	0.474466	−	0.245960i
$11$	−1.80841e6			−0.0279803			−0.0139901	−	0.999902i	$-0.504453\pi$
$11$	−1.80841e6			−0.0279803			−0.0139901	+	0.999902i	$0.504453\pi$
$12$	−3.21598e7	+	1.19886e8i	−0.259092	+	0.965853i
$13$	3.17574e8			1.40369			0.701843	−	0.712331i	$-0.252361\pi$
$13$	3.17574e8			1.40369			0.701843	+	0.712331i	$0.252361\pi$
$14$	−1.84079e8	+	9.54254e7i	−0.466706	+	0.241938i
$15$	1.21998e8	+	3.31942e8i	0.184361	+	0.501623i
$16$	−3.60328e8	−	1.01148e9i	−0.335581	−	0.942011i
$17$		−	2.67956e9i		−	1.58378i	−0.610661	−	0.791892i	$-0.709096\pi$
$17$		−	2.67956e9i		−	1.58378i	0.610661	−	0.791892i	$-0.290904\pi$
$18$	−2.40423e9	−	9.83024e8i	−0.925618	−	0.378460i
$19$		−	2.07292e9i		−	0.532024i	−0.963970	−	0.266012i	$-0.914294\pi$
$19$		−	2.07292e9i		−	0.532024i	0.963970	−	0.266012i	$-0.0857060\pi$
$20$	−2.49997e9	−	1.76328e9i	−0.436727	−	0.308032i
$21$	−1.49676e9	−	4.07249e9i	−0.181346	−	0.493419i
$22$	1.50660e8	+	2.90628e8i	0.0128774	+	0.0248409i
$23$	−2.43757e10			−1.49279			−0.746393	−	0.665505i	$-0.768216\pi$
$23$	−2.43757e10			−1.49279			−0.746393	+	0.665505i	$0.768216\pi$
$24$	2.19461e10	−	4.81944e9i	0.976726	−	0.214493i
$25$	2.18013e10			0.714386
$26$	−2.64573e10	−	5.10370e10i	−0.646019	−	1.24619i
$27$	2.67323e10	−	4.73254e10i	0.491823	−	0.870695i
$28$	3.06714e10	+	2.16331e10i	0.429584	+	0.302994i
$29$			4.77985e9i			0.0514552i	0.999669	+	0.0257276i	$0.00819025\pi$
$29$			4.77985e9i			0.0514552i	−0.999669	+	0.0257276i	$0.991810\pi$
$30$	4.31822e10	−	4.72604e10i	0.360492	−	0.394537i
$31$		−	5.30495e10i		−	0.346313i	−0.984894	−	0.173156i	$-0.944603\pi$
$31$		−	5.30495e10i		−	0.346313i	0.984894	−	0.173156i	$-0.0553966\pi$
$32$	−1.32534e11	+	1.42175e11i	−0.681872	+	0.731471i
$33$	−6.42975e9	+	2.36312e9i	−0.0262627	+	0.00965230i
$34$	−4.30629e11	+	2.23235e11i	−1.40608	+	0.728906i
$35$	1.06937e11			0.280943
$36$	4.23169e10	+	4.68277e11i	0.0900005	+	0.995942i
$37$	4.06413e11			0.703808			0.351904	−	0.936036i	$-0.385534\pi$
$37$	4.06413e11			0.703808			0.351904	+	0.936036i	$0.385534\pi$
$38$	−3.33137e11	+	1.72696e11i	−0.472330	+	0.244853i
$39$	1.12912e12	−	4.14986e11i	1.31752	−	0.484227i
$40$	−7.51003e10	+	5.48667e11i	−0.0724756	+	0.529492i
$41$			1.36874e12i			1.09760i	0.835954	+	0.548799i	$0.184915\pi$
$41$			1.36874e12i			1.09760i	−0.835954	+	0.548799i	$0.815085\pi$
$42$	−5.29790e11	+	5.79824e11i	−0.354596	+	0.388085i
$43$		−	2.85013e12i		−	1.59901i	−0.600661	−	0.799504i	$-0.705096\pi$
$43$		−	2.85013e12i		−	1.59901i	0.600661	−	0.799504i	$-0.294904\pi$
$44$	3.41549e10	−	4.84247e10i	0.0161272	−	0.0228651i
$45$	8.67521e11	+	1.02079e12i	0.346088	+	0.407232i
$46$	2.03075e12	+	3.91739e12i	0.687026	+	1.32530i
$47$	7.27503e11			0.209460			0.104730	−	0.994501i	$-0.466602\pi$
$47$	7.27503e11			0.209460			0.104730	+	0.994501i	$0.466602\pi$
$48$	−2.60287e12	−	3.12542e12i	−0.639945	−	0.768421i
$49$	3.43558e12			0.723652
$50$	−1.81628e12	−	3.50367e12i	−0.328782	−	0.634231i
$51$	−3.50148e12	−	9.52708e12i	−0.546355	−	1.48656i
$52$	−5.99793e12	+	8.50385e12i	−0.809051	+	1.14707i
$53$		−	7.05903e12i		−	0.825422i	−0.910862	−	0.412711i	$-0.864582\pi$
$53$		−	7.05903e12i		−	0.825422i	0.910862	−	0.412711i	$-0.135418\pi$
$54$	−9.83270e12	−	3.53416e11i	−0.999355	−	0.0359197i
$55$		−	1.68835e11i		−	0.0149535i
$56$	9.21384e11	−	6.73144e12i	0.0712903	−	0.520832i
$57$	−2.70876e12	−	7.37020e12i	−0.183531	−	0.499365i
$58$	7.68164e11	−	3.98212e11i	0.0456819	−	0.0236812i
$59$	1.63957e13			0.857707			0.428853	−	0.903374i	$-0.358918\pi$
$59$	1.63957e13			0.857707			0.428853	+	0.903374i	$0.358918\pi$
$60$	−1.11927e13	−	3.00247e12i	−0.516179	−	0.138466i
$61$	3.06206e13			1.24750			0.623749	−	0.781624i	$-0.285609\pi$
$61$	3.06206e13			1.24750			0.623749	+	0.781624i	$0.285609\pi$
$62$	−8.52552e12	+	4.41958e12i	−0.307456	+	0.159384i
$63$	−1.06434e13	−	1.25237e13i	−0.340427	−	0.400571i
$64$	3.38902e13	+	9.45477e12i	0.963218	+	0.268721i
$65$			2.96490e13i			0.750171i
$66$	9.15440e11	+	8.36445e11i	0.0206562	+	0.0188737i
$67$			7.17216e13i			1.44574i	0.690986	+	0.722868i	$0.257177\pi$
$67$			7.17216e13i			1.44574i	−0.690986	+	0.722868i	$0.742823\pi$
$68$	7.17519e13	+	5.06080e13i	1.29424	+	0.912855i
$69$	−8.66669e13	+	3.18526e13i	−1.40115	+	0.514964i
$70$	−8.90900e12	−	1.71857e13i	−0.129299	−	0.249421i
$71$	−4.82624e13			−0.629755			−0.314877	−	0.949132i	$-0.601963\pi$
$71$	−4.82624e13			−0.629755			−0.314877	+	0.949132i	$0.601963\pi$
$72$	7.17308e13	−	4.58131e13i	0.842776	−	0.538265i
$73$	−9.56538e13			−1.01340			−0.506700	−	0.862122i	$-0.669135\pi$
$73$	−9.56538e13			−1.01340			−0.506700	+	0.862122i	$0.669135\pi$
$74$	−3.38585e13	−	6.53141e13i	−0.323914	−	0.624841i
$75$	7.75139e13	−	2.84886e13i	0.670533	−	0.246440i
$76$	5.55077e13	+	3.91506e13i	0.434761	+	0.306646i
$77$			2.07139e12i			0.0147089i
$78$	−1.60760e14	−	1.46888e14i	−1.03626	−	0.946838i
$79$			3.27912e14i			1.92112i	0.278079	+	0.960558i	$0.410302\pi$
$79$			3.27912e14i			1.92112i	−0.278079	+	0.960558i	$0.589698\pi$
$80$	9.44324e13	−	3.36405e13i	0.503438	−	0.179344i
$81$	3.32041e13	−	2.03196e14i	0.161270	−	0.986910i
$82$	2.19969e14	−	1.14031e14i	0.974447	−	0.505148i
$83$	−2.88031e14			−1.16507			−0.582537	−	0.812804i	$-0.697940\pi$
$83$	−2.88031e14			−1.16507			−0.582537	+	0.812804i	$0.697940\pi$
$84$	1.37320e14	+	3.68364e13i	0.507737	+	0.136202i
$85$	2.50166e14			0.846420
$86$	−4.58041e14	+	2.37446e14i	−1.41960	+	0.735912i
$87$	6.24600e12	+	1.69946e13i	0.0177504	+	0.0482966i
$88$	−1.06278e13	−	1.45470e12i	−0.0277218	−	0.00379450i
$89$		−	2.05245e14i		−	0.491866i	−0.969287	−	0.245933i	$-0.920906\pi$
$89$		−	2.05245e14i		−	0.491866i	0.969287	−	0.245933i	$-0.0790944\pi$
$90$	9.17760e13	−	2.24461e14i	0.202260	−	0.494677i
$91$		−	3.63755e14i		−	0.737902i
$92$	4.60376e14	−	6.52720e14i	0.860406	−	1.21988i
$93$	−6.93217e13	−	1.88616e14i	−0.119467	−	0.325054i
$94$	−6.06087e13	−	1.16916e14i	−0.0963998	−	0.185958i
$95$	1.93530e14			0.284329
$96$	−2.85436e14	+	6.78684e14i	−0.387681	+	0.921794i
$97$	−5.41919e14			−0.680999			−0.340500	−	0.940245i	$-0.610596\pi$
$97$	−5.41919e14			−0.680999			−0.340500	+	0.940245i	$0.610596\pi$
$98$	−2.86220e14	−	5.52128e14i	−0.333047	−	0.642458i
$99$	−1.97728e13	+	1.68040e13i	−0.0213208	+	0.0181196i
$100$	−4.11755e14	+	5.83785e14i	−0.411755	+	0.583785i
$101$			2.07469e15i			1.92550i	0.270392	+	0.962750i	$0.412847\pi$
$101$			2.07469e15i			1.92550i	−0.270392	+	0.962750i	$0.587153\pi$
$102$	−1.23938e15	+	1.35642e15i	−1.06832	+	1.16922i
$103$		−	1.33536e15i		−	1.06984i	−0.844902	−	0.534922i	$-0.820341\pi$
$103$		−	1.33536e15i		−	1.06984i	0.844902	−	0.534922i	$-0.179659\pi$
$104$	1.86633e15	+	2.55460e14i	1.39072	+	0.190358i
$105$	3.80211e14	−	1.39739e14i	0.263697	−	0.0969164i
$106$	−1.13445e15	+	5.88092e14i	−0.732809	+	0.379884i
$107$	1.41960e15			0.854647			0.427324	−	0.904099i	$-0.359457\pi$
$107$	1.41960e15			0.854647			0.427324	+	0.904099i	$0.359457\pi$
$108$	7.62371e14	+	1.60965e15i	0.428044	+	0.903758i
$109$	1.76730e15			0.926000			0.463000	−	0.886358i	$-0.346773\pi$
$109$	1.76730e15			0.926000			0.463000	+	0.886358i	$0.346773\pi$
$110$	−2.71333e13	+	1.40657e13i	−0.0132757	+	0.00688204i
$111$	1.44499e15	−	5.31075e14i	0.660605	−	0.242791i
$112$	−1.15856e15	+	4.12725e14i	−0.495204	+	0.176411i
$113$			1.47671e14i			0.0590481i	0.999564	+	0.0295241i	$0.00939917\pi$
$113$			1.47671e14i			0.0590481i	−0.999564	+	0.0295241i	$0.990601\pi$
$114$	−9.58789e14	+	1.04934e15i	−0.358869	+	0.392762i
$115$		−	2.27573e15i		−	0.797788i
$116$	−1.27992e14	−	9.02755e13i	−0.0420484	−	0.0296575i
$117$	3.47229e15	−	2.95094e15i	1.06960	−	0.909005i
$118$	−1.36593e15	−	2.63493e15i	−0.394743	−	0.761472i
$119$	−3.06921e15			−0.832577
$120$	4.49947e14	+	2.04891e15i	0.114631	+	0.521990i
$121$	−4.17398e15			−0.999217
$122$	−2.55102e15	−	4.92100e15i	−0.574137	−	1.10753i
$123$	1.78859e15	+	4.86652e15i	0.378636	+	1.03022i
$124$	1.42053e15	+	1.00193e15i	0.283001	+	0.199606i
$125$			4.88454e15i			0.916217i
$126$	−1.12597e15	+	2.75384e15i	−0.198952	+	0.486586i
$127$		−	2.39188e15i		−	0.398301i	−0.979969	−	0.199151i	$-0.936182\pi$
$127$		−	2.39188e15i		−	0.398301i	0.979969	−	0.199151i	$-0.0638183\pi$
$128$	−1.30395e15	−	6.23414e15i	−0.204732	−	0.978818i
$129$	−3.72437e15	−	1.01335e16i	−0.551607	−	1.50085i
$130$	4.76486e15	−	2.47008e15i	0.666001	−	0.345251i
$131$	−1.23826e16			−1.63410			−0.817049	−	0.576568i	$-0.804392\pi$
$131$	−1.23826e16			−1.63410			−0.817049	+	0.576568i	$0.804392\pi$
$132$	5.81582e13	−	2.16804e14i	0.00724948	−	0.0270248i
$133$	−2.37436e15			−0.279679
$134$	1.15263e16	−	5.97517e15i	1.28352	−	0.665372i
$135$	4.41834e15	+	2.49575e15i	0.465325	+	0.262844i
$136$	2.15546e15	−	1.57473e16i	0.214782	−	1.56915i
$137$			7.11951e15i			0.671500i	0.941951	+	0.335750i	$0.108990\pi$
$137$			7.11951e15i			0.671500i	−0.941951	+	0.335750i	$0.891010\pi$
$138$	1.23393e16	+	1.12745e16i	1.10204	+	1.00694i
$139$			1.47105e16i			1.24456i	0.782794	+	0.622281i	$0.213794\pi$
$139$			1.47105e16i			1.24456i	−0.782794	+	0.622281i	$0.786206\pi$
$140$	−2.01969e15	+	2.86351e15i	−0.161929	+	0.229582i
$141$	2.58661e15	−	9.50656e14i	0.196602	−	0.0722570i
$142$	4.02077e15	+	7.75620e15i	0.289832	+	0.559096i
$143$	−5.74305e14			−0.0392756
$144$	−1.33385e16	−	7.71106e15i	−0.865742	−	0.500490i
$145$	−4.46251e14			−0.0274991
$146$	7.96898e15	+	1.53724e16i	0.466397	+	0.899696i
$147$	1.22151e16	−	4.48940e15i	0.679230	−	0.249637i
$148$	−7.67579e15	+	1.08827e16i	−0.405658	+	0.575141i
$149$			1.71102e16i			0.859720i	0.902896	+	0.429860i	$0.141437\pi$
$149$			1.71102e16i			0.859720i	−0.902896	+	0.429860i	$0.858563\pi$
$150$	−1.10361e16	−	1.00838e16i	−0.527389	−	0.481879i
$151$			3.58511e16i			1.62996i	0.579492	+	0.814978i	$0.303251\pi$
$151$			3.58511e16i			1.62996i	−0.579492	+	0.814978i	$0.696749\pi$
$152$	1.66748e15	−	1.21822e16i	0.0721494	−	0.527109i
$153$	−2.48988e16	−	2.92977e16i	−1.02563	−	1.20683i
$154$	3.32890e14	−	1.72568e14i	0.0130586	−	0.00676949i
$155$	4.95275e15			0.185080
$156$	−1.02131e16	+	3.80729e16i	−0.363684	+	1.35575i
$157$	1.10073e16			0.373623			0.186811	−	0.982396i	$-0.440185\pi$
$157$	1.10073e16			0.373623			0.186811	+	0.982396i	$0.440185\pi$
$158$	5.26983e16	−	2.73185e16i	1.70557	−	0.884156i
$159$	−9.22430e15	−	2.50981e16i	−0.284744	−	0.774753i
$160$	−1.32735e16	−	1.23735e16i	−0.390919	−	0.364412i
$161$			2.79203e16i			0.784741i
$162$	−3.54217e16	+	1.15922e16i	−0.950400	+	0.311031i
$163$		−	5.64997e16i		−	1.44757i	−0.690026	−	0.723785i	$-0.742401\pi$
$163$		−	5.64997e16i		−	1.44757i	0.690026	−	0.723785i	$-0.257599\pi$
$164$	−3.66515e16	−	2.58510e16i	−0.896940	−	0.632629i
$165$	−2.20623e14	−	6.00287e14i	−0.00515847	−	0.0140355i
$166$	2.39960e16	+	4.62891e16i	0.536203	+	1.03435i
$167$	−5.17280e15			−0.110497			−0.0552487	−	0.998473i	$-0.517595\pi$
$167$	−5.17280e15			−0.110497			−0.0552487	+	0.998473i	$0.517595\pi$
$168$	−5.52027e15	−	2.51374e16i	−0.112756	−	0.513453i
$169$	4.96675e16			0.970336
$170$	−2.08415e16	−	4.02039e16i	−0.389548	−	0.751451i
$171$	−1.92618e16	−	2.26649e16i	−0.344530	−	0.405399i
$172$	7.63193e16	+	5.38295e16i	1.30668	+	0.921630i
$173$		−	2.04847e16i		−	0.335802i	−0.985804	−	0.167901i	$-0.946301\pi$
$173$		−	2.04847e16i		−	0.335802i	0.985804	−	0.167901i	$-0.0536990\pi$
$174$	2.21082e15	−	2.41962e15i	0.0347084	−	0.0379863i
$175$		−	2.49716e16i		−	0.375544i
$176$	6.51621e14	+	1.82917e15i	0.00938966	+	0.0263577i
$177$	5.82942e16	−	2.14248e16i	0.805056	−	0.295881i
$178$	−3.29847e16	+	1.70991e16i	−0.436679	+	0.226372i
$179$	−4.73126e15			−0.0600591			−0.0300296	−	0.999549i	$-0.509560\pi$
$179$	−4.73126e15			−0.0600591			−0.0300296	+	0.999549i	$0.509560\pi$
$180$	−4.37187e16	+	3.95074e15i	−0.532260	+	0.0480989i
$181$	3.30439e15			0.0385925			0.0192962	−	0.999814i	$-0.493857\pi$
$181$	3.30439e15			0.0385925			0.0192962	+	0.999814i	$0.493857\pi$
$182$	−5.84587e16	+	3.03046e16i	−0.655109	+	0.339605i
$183$	1.08871e17	−	4.00131e16i	1.17092	−	0.430347i
$184$	−1.43252e17	−	1.96080e16i	−1.47900	−	0.202442i
$185$			3.79431e16i			0.376136i
$186$	−2.45370e16	+	2.68543e16i	−0.233601	+	0.255662i
$187$			4.84574e15i			0.0443147i
$188$	−1.37401e16	+	1.94807e16i	−0.120728	+	0.171167i
$189$	−5.42073e16	−	3.06197e16i	−0.457714	−	0.258546i
$190$	−1.61231e16	−	3.11020e16i	−0.130857	−	0.252427i
$191$	−2.61282e16			−0.203873			−0.101936	−	0.994791i	$-0.532504\pi$
$191$	−2.61282e16			−0.203873			−0.101936	+	0.994791i	$0.532504\pi$
$192$	1.32850e17	−	1.06695e16i	0.996791	−	0.0800542i
$193$	−7.78195e16			−0.561576			−0.280788	−	0.959770i	$-0.590596\pi$
$193$	−7.78195e16			−0.561576			−0.280788	+	0.959770i	$0.590596\pi$
$194$	4.51476e16	+	8.70912e16i	0.313416	+	0.604591i
$195$	3.87435e16	+	1.05416e17i	0.258785	+	0.704121i
$196$	−6.48868e16	+	9.19963e16i	−0.417096	+	0.591357i
$197$		−	4.41071e16i		−	0.272905i	−0.990647	−	0.136453i	$-0.956430\pi$
$197$		−	4.41071e16i		−	0.272905i	0.990647	−	0.136453i	$-0.0435702\pi$
$198$	4.34783e15	+	1.77771e15i	0.0258990	+	0.0105894i
$199$			2.17749e16i			0.124899i	0.998048	+	0.0624494i	$0.0198912\pi$
$199$			2.17749e16i			0.124899i	−0.998048	+	0.0624494i	$0.980109\pi$
$200$	1.28123e17	+	1.75372e16i	0.707786	+	0.0968802i
$201$	9.37213e16	+	2.55004e17i	0.498733	+	1.35699i
$202$	3.33422e17	−	1.72844e17i	1.70946	−	0.886174i
$203$	5.47492e15			0.0270494
$204$	3.21243e17	+	8.61741e16i	1.52970	+	0.410346i
$205$	−1.27787e17			−0.586588
$206$	−2.14605e17	+	1.11250e17i	−0.949807	+	0.492375i
$207$	−2.66518e17	+	2.26502e17i	−1.13749	+	0.966705i
$208$	−1.14431e17	−	3.21219e17i	−0.471051	−	1.32229i
$209$			3.74870e15i			0.0148862i
$210$	−5.41329e16	−	4.94616e16i	−0.207404	−	0.189506i
$211$			2.03587e16i			0.0752717i	0.999292	+	0.0376358i	$0.0119827\pi$
$211$			2.03587e16i			0.0752717i	−0.999292	+	0.0376358i	$0.988017\pi$
$212$	1.89023e17	+	1.33322e17i	0.674522	+	0.475753i
$213$	−1.71595e17	+	6.30663e16i	−0.591097	+	0.217245i
$214$	−1.18268e17	−	2.28142e17i	−0.393335	−	0.758755i
$215$	2.66090e17			0.854556
$216$	1.95171e17	−	2.56620e17i	0.605357	−	0.795954i
$217$	−6.07638e16			−0.182053
$218$	−1.47235e17	−	2.84021e17i	−0.426174	−	0.822103i
$219$	−3.40094e17	+	1.24994e17i	−0.951192	+	0.349591i
$220$	4.52098e15	+	3.18873e15i	0.0122197	+	0.00861882i
$221$		−	8.50958e17i		−	2.22314i
$222$	−2.05731e17	−	1.87978e17i	−0.519580	−	0.474745i
$223$			5.07606e16i			0.123948i	0.998078	+	0.0619741i	$0.0197396\pi$
$223$			5.07606e16i			0.123948i	−0.998078	+	0.0619741i	$0.980260\pi$
$224$	1.62849e17	+	1.51807e17i	0.384526	+	0.358452i
$225$	2.38371e17	−	2.02581e17i	0.544358	−	0.462625i
$226$	2.37320e16	−	1.23025e16i	0.0524229	−	0.0271757i
$227$	−2.92651e17			−0.625396			−0.312698	−	0.949853i	$-0.601233\pi$
$227$	−2.92651e17			−0.625396			−0.312698	+	0.949853i	$0.601233\pi$
$228$	2.48515e17	+	6.66648e16i	0.513856	+	0.137843i
$229$	−2.19585e17			−0.439375			−0.219688	−	0.975570i	$-0.570504\pi$
$229$	−2.19585e17			−0.439375			−0.219688	+	0.975570i	$0.570504\pi$
$230$	−3.65731e17	+	1.89593e17i	−0.708276	+	0.367166i
$231$	2.70676e15	+	7.36474e15i	0.00507410	+	0.0138060i
$232$	−3.84495e15	+	2.80904e16i	−0.00697800	+	0.0509798i
$233$		−	1.89993e17i		−	0.333863i	−0.985968	−	0.166932i	$-0.946614\pi$
$233$		−	1.89993e17i		−	0.333863i	0.985968	−	0.166932i	$-0.0533859\pi$
$234$	−7.63520e17	−	3.12183e17i	−1.29928	−	0.531240i
$235$			6.79204e16i			0.111941i
$236$	−3.09660e17	+	4.39035e17i	−0.494362	+	0.700905i
$237$	4.28494e17	+	1.16588e18i	0.662724	+	1.80319i
$238$	2.55698e17	+	4.93249e17i	0.383177	+	0.739162i
$239$	9.61316e17			1.39599			0.697994	−	0.716103i	$-0.254076\pi$
$239$	9.61316e17			1.39599			0.697994	+	0.716103i	$0.254076\pi$
$240$	2.91792e17	−	2.43006e17i	0.410666	−	0.342005i
$241$	6.77710e17			0.924519			0.462260	−	0.886745i	$-0.347039\pi$
$241$	6.77710e17			0.924519			0.462260	+	0.886745i	$0.347039\pi$
$242$	3.47737e17	+	6.70795e17i	0.459870	+	0.887104i
$243$	−1.47468e17	−	7.65846e17i	−0.189082	−	0.981961i
$244$	−5.78322e17	+	8.19943e17i	−0.719028	+	1.01944i
$245$			3.20749e17i			0.386740i
$246$	6.33085e17	−	6.92875e17i	0.740370	−	0.810292i
$247$		−	6.58307e17i		−	0.746794i
$248$	4.26735e16	−	3.11764e17i	0.0469646	−	0.343113i
$249$	−1.02408e18	+	3.76381e17i	−1.09356	+	0.401913i
$250$	7.84989e17	−	4.06934e17i	0.813417	−	0.421671i
$251$	1.20926e17			0.121609			0.0608045	−	0.998150i	$-0.480633\pi$
$251$	1.20926e17			0.121609			0.0608045	+	0.998150i	$0.480633\pi$
$252$	5.36372e17	−	4.84705e16i	0.523555	−	0.0473122i
$253$	4.40812e16			0.0417686
$254$	−3.84397e17	+	1.99269e17i	−0.353612	+	0.183310i
$255$	8.89456e17	−	3.26901e17i	0.794462	−	0.291988i
$256$	−8.93249e17	+	7.28926e17i	−0.774770	+	0.632243i
$257$			5.02418e17i			0.423220i	0.977354	+	0.211610i	$0.0678707\pi$
$257$			5.02418e17i			0.423220i	−0.977354	+	0.211610i	$0.932129\pi$
$258$	−1.31827e18	+	1.44277e18i	−1.07859	+	1.18045i
$259$		−	4.65512e17i		−	0.369984i
$260$	−7.93927e17	−	5.59972e17i	−0.613028	−	0.432380i
$261$	4.44149e16	+	5.22618e16i	0.0333215	+	0.0392085i
$262$	1.03160e18	+	1.99000e18i	0.752062	+	1.45075i
$263$	−7.04783e17			−0.499329			−0.249665	−	0.968332i	$-0.580320\pi$
$263$	−7.04783e17			−0.499329			−0.249665	+	0.968332i	$0.580320\pi$
$264$	−3.96875e16	+	8.71553e15i	−0.0273291	+	0.00600157i
$265$	6.59037e17			0.441129
$266$	1.97809e17	+	3.81581e17i	0.128717	+	0.248299i
$267$	−2.68201e17	−	7.29741e17i	−0.169678	−	0.461673i
$268$	−1.92053e18	−	1.35458e18i	−1.18143	−	0.833288i
$269$		−	9.89646e17i		−	0.592022i	−0.955185	−	0.296011i	$-0.904344\pi$
$269$		−	9.89646e17i		−	0.592022i	0.955185	−	0.296011i	$-0.0956565\pi$
$270$	3.29952e16	−	9.17990e17i	0.0191965	−	0.534084i
$271$			1.84926e18i			1.04647i	0.852187	+	0.523237i	$0.175276\pi$
$271$			1.84926e18i			1.04647i	−0.852187	+	0.523237i	$0.824724\pi$
$272$	−2.71031e18	+	9.65519e17i	−1.49194	+	0.531488i
$273$	−4.75332e17	−	1.29332e18i	−0.254553	−	0.692605i
$274$	1.14417e18	−	5.93131e17i	0.596157	−	0.309045i
$275$	−3.94258e16			−0.0199887
$276$	7.83918e17	−	2.92231e18i	0.386770	−	1.44181i
$277$	2.54416e18			1.22165			0.610825	−	0.791766i	$-0.290838\pi$
$277$	2.54416e18			1.22165			0.610825	+	0.791766i	$0.290838\pi$
$278$	2.36411e18	−	1.22554e18i	1.10492	−	0.572785i
$279$	−4.92942e17	−	5.80032e17i	−0.224267	−	0.263888i
$280$	6.28453e17	+	8.60212e16i	0.278348	+	0.0380996i
$281$		−	2.23570e18i		−	0.964089i	−0.876147	−	0.482044i	$-0.839894\pi$
$281$		−	2.23570e18i		−	0.964089i	0.876147	−	0.482044i	$-0.160106\pi$
$282$	−3.68271e17	−	3.36492e17i	−0.154632	−	0.141288i
$283$			9.55778e17i			0.390804i	0.980723	+	0.195402i	$0.0626011\pi$
$283$			9.55778e17i			0.390804i	−0.980723	+	0.195402i	$0.937399\pi$
$284$	9.11517e17	−	1.29235e18i	0.362975	−	0.514626i
$285$	6.88089e17	−	2.52893e17i	0.266875	−	0.0980843i
$286$	4.78457e16	+	9.22959e16i	0.0180758	+	0.0348688i
$287$	1.56778e18			0.576994
$288$	−1.27996e17	+	2.78603e18i	−0.0458938	+	0.998946i
$289$	−4.31760e18			−1.50837
$290$	3.71774e16	+	7.17165e16i	0.0126559	+	0.0244137i
$291$	−1.92678e18	+	7.08146e17i	−0.639196	+	0.234923i
$292$	1.80658e18	−	2.56137e18i	0.584100	−	0.828135i
$293$			3.91767e18i			1.23458i	0.786734	+	0.617292i	$0.211770\pi$
$293$			3.91767e18i			1.23458i	−0.786734	+	0.617292i	$0.788230\pi$
$294$	−1.73913e18	−	1.58906e18i	−0.534230	−	0.488130i
$295$			1.53071e18i			0.458383i
$296$	2.38842e18	+	3.26922e17i	0.697307	+	0.0954457i
$297$	−4.83431e16	+	8.55838e16i	−0.0137613	+	0.0243623i
$298$	2.74975e18	−	1.42546e18i	0.763259	−	0.395669i
$299$	−7.74108e18			−2.09540
$300$	−7.01127e17	+	2.61368e18i	−0.185092	+	0.689991i
$301$	−3.26458e18			−0.840580
$302$	5.76159e18	−	2.98678e18i	1.44707	−	0.750155i
$303$	2.71108e18	+	7.37650e18i	0.664236	+	1.80730i
$304$	−2.09671e18	+	7.46931e17i	−0.501172	+	0.178537i
$305$			2.85877e18i			0.666699i
$306$	−2.63407e18	+	6.44226e18i	−0.599399	+	1.46598i
$307$		−	2.91302e18i		−	0.646853i	−0.946253	−	0.323426i	$-0.895165\pi$
$307$		−	2.91302e18i		−	0.646853i	0.946253	−	0.323426i	$-0.104835\pi$
$308$	−5.54665e16	−	3.91216e16i	−0.0120199	−	0.00847786i
$309$	−1.74497e18	−	4.74784e18i	−0.369062	−	1.00417i
$310$	−4.12616e17	−	7.95950e17i	−0.0851792	−	0.164314i
$311$	8.95070e18			1.80366			0.901829	−	0.432094i	$-0.142225\pi$
$311$	8.95070e18			1.80366			0.901829	+	0.432094i	$0.142225\pi$
$312$	6.96951e18	−	1.53053e18i	1.37102	−	0.301080i
$313$	−2.79248e18			−0.536300			−0.268150	−	0.963377i	$-0.586412\pi$
$313$	−2.79248e18			−0.536300			−0.268150	+	0.963377i	$0.586412\pi$
$314$	−9.17024e17	−	1.76897e18i	−0.171952	−	0.331702i
$315$	1.16923e18	−	9.93673e17i	0.214077	−	0.181934i
$316$	−8.78066e18	−	6.19317e18i	−1.56991	−	1.10729i
$317$			5.57732e18i			0.973826i	0.873450	+	0.486913i	$0.161877\pi$
$317$			5.57732e18i			0.973826i	−0.873450	+	0.486913i	$0.838123\pi$
$318$	−3.26501e18	+	3.57337e18i	−0.556777	+	0.609360i
$319$		−	8.64393e15i		−	0.00143973i
$320$	−8.82706e17	+	3.16402e18i	−0.143612	+	0.514772i
$321$	5.04733e18	−	1.85504e18i	0.802184	−	0.294826i
$322$	4.48704e18	−	2.32606e18i	0.696692	−	0.361161i
$323$	−5.55451e18			−0.842611
$324$	4.81397e18	+	4.72682e18i	0.713536	+	0.700619i
$325$	6.92354e18			1.00277
$326$	−9.08001e18	+	4.70703e18i	−1.28515	+	0.666215i
$327$	6.28357e18	−	2.30940e18i	0.869157	−	0.319441i
$328$	−1.10103e18	+	8.04389e18i	−0.148849	+	1.08746i
$329$		−	8.33295e17i		−	0.110111i
$330$	−7.80912e16	+	8.54663e16i	−0.0100867	+	0.0110393i
$331$		−	5.40300e18i		−	0.682221i	−0.940023	−	0.341110i	$-0.889197\pi$
$331$		−	5.40300e18i		−	0.682221i	0.940023	−	0.341110i	$-0.110803\pi$
$332$	5.43995e18	−	7.71275e18i	0.671521	−	0.952081i
$333$	4.44363e18	−	3.77644e18i	0.536298	−	0.455775i
$334$	4.30949e17	+	8.31315e17i	0.0508543	+	0.0980995i
$335$	−6.69599e18			−0.772643
$336$	−3.57991e18	+	2.98137e18i	−0.403950	+	0.336412i
$337$	5.89353e18			0.650357			0.325178	−	0.945653i	$-0.394576\pi$
$337$	5.89353e18			0.650357			0.325178	+	0.945653i	$0.394576\pi$
$338$	−4.13783e18	−	7.98201e18i	−0.446578	−	0.861464i
$339$	1.92967e17	+	5.25038e17i	0.0203697	+	0.0554234i
$340$	−4.72480e18	+	6.69882e18i	−0.487856	+	0.691682i
$341$			9.59353e16i			0.00968993i
$342$	−2.03773e18	+	4.98377e18i	−0.201350	+	0.492450i
$343$		−	9.37311e18i		−	0.906104i
$344$	2.29267e18	−	1.67497e19i	0.216847	−	1.58424i
$345$	−2.97379e18	−	8.09130e18i	−0.275211	−	0.748816i
$346$	−3.29207e18	+	1.70659e18i	−0.298125	+	0.154546i
$347$	−9.15634e18			−0.811429			−0.405715	−	0.914000i	$-0.632977\pi$
$347$	−9.15634e18			−0.811429			−0.405715	+	0.914000i	$0.632977\pi$
$348$	−5.73039e17	−	1.53719e17i	−0.0496981	−	0.0133316i
$349$	−9.99695e18			−0.848548			−0.424274	−	0.905534i	$-0.639471\pi$
$349$	−9.99695e18			−0.848548			−0.424274	+	0.905534i	$0.639471\pi$
$350$	−4.01316e18	+	2.08040e18i	−0.333408	+	0.172837i
$351$	8.48950e18	−	1.50293e19i	0.690365	−	1.22218i
$352$	2.39676e17	−	2.57110e17i	0.0190790	−	0.0204668i
$353$			1.19492e19i			0.931171i	0.885003	+	0.465585i	$0.154156\pi$
$353$			1.19492e19i			0.931171i	−0.885003	+	0.465585i	$0.845844\pi$
$354$	−8.29969e18	−	7.58349e18i	−0.633195	−	0.578555i
$355$		−	4.50582e18i		−	0.336559i
$356$	5.49594e18	+	3.87639e18i	0.401946	+	0.283500i
$357$	−1.09125e19	+	4.01065e18i	−0.781469	+	0.287212i
$358$	3.94164e17	+	7.60355e17i	0.0276410	+	0.0533205i
$359$	2.10011e19			1.44223			0.721115	−	0.692816i	$-0.243630\pi$
$359$	2.10011e19			1.44223			0.721115	+	0.692816i	$0.243630\pi$
$360$	4.27715e18	+	6.69685e18i	0.287664	+	0.450404i
$361$	1.08841e19			0.716951
$362$	−2.75291e17	−	5.31045e17i	−0.0177614	−	0.0342624i
$363$	−1.48404e19	+	5.45429e18i	−0.937880	+	0.344698i
$364$	9.74045e18	+	6.87013e18i	0.603002	+	0.425309i
$365$		−	8.93033e18i		−	0.541590i
$366$	−1.55005e19	−	1.41630e19i	−0.920955	−	0.841484i
$367$			1.93513e19i			1.12646i	0.826301	+	0.563229i	$0.190441\pi$
$367$			1.93513e19i			1.12646i	−0.826301	+	0.563229i	$0.809559\pi$
$368$	8.78323e18	+	2.46554e19i	0.500951	+	1.40622i
$369$	1.27185e19	+	1.49655e19i	0.710787	+	0.836363i
$370$	6.09779e18	−	3.16106e18i	0.333933	−	0.173109i
$371$	−8.08553e18			−0.433915
$372$	6.35992e18	+	1.70606e18i	0.334487	+	0.0897270i
$373$	3.61770e18			0.186473			0.0932366	−	0.995644i	$-0.470279\pi$
$373$	3.61770e18			0.186473			0.0932366	+	0.995644i	$0.470279\pi$
$374$	7.78754e17	−	4.03702e17i	0.0393426	−	0.0203950i
$375$	6.38281e18	+	1.73668e19i	0.316066	+	0.859975i
$376$	4.27542e18	+	5.85210e17i	0.207525	+	0.0284055i
$377$			1.51796e18i			0.0722269i
$378$	−4.04809e17	+	1.12625e19i	−0.0188826	+	0.525349i
$379$			2.86795e18i			0.131153i	0.997848	+	0.0655764i	$0.0208886\pi$
$379$			2.86795e18i			0.131153i	−0.997848	+	0.0655764i	$0.979111\pi$
$380$	−3.65514e18	+	5.18224e18i	−0.163880	+	0.232349i
$381$	−3.12556e18	−	8.50426e18i	−0.137401	−	0.373851i
$382$	2.17676e18	+	4.19904e18i	0.0938285	+	0.180998i
$383$	3.73893e19			1.58036			0.790181	−	0.612873i	$-0.209986\pi$
$383$	3.73893e19			1.58036			0.790181	+	0.612873i	$0.209986\pi$
$384$	−1.27825e19	−	2.04614e19i	−0.529825	−	0.848107i
$385$	−1.93386e17			−0.00786087
$386$	6.48319e18	+	1.25063e19i	0.258454	+	0.498567i
$387$	−2.64837e19	−	3.11627e19i	−1.03549	−	1.21843i
$388$	1.02351e19	−	1.45112e19i	0.392512	−	0.556502i
$389$		−	1.22034e19i		−	0.459050i	−0.973303	−	0.229525i	$-0.926283\pi$
$389$		−	1.22034e19i		−	0.459050i	0.973303	−	0.229525i	$-0.0737172\pi$
$390$	1.37136e19	−	1.50087e19i	0.506018	−	0.553807i
$391$			6.53160e19i			2.36425i
$392$	2.01904e19	+	2.76361e18i	0.716967	+	0.0981368i
$393$	−4.40260e19	+	1.61808e19i	−1.53379	+	0.563712i
$394$	−7.08841e18	+	3.67459e18i	−0.242285	+	0.125599i
$395$	−3.06141e19			−1.02670
$396$	−7.65263e16	−	8.46837e17i	−0.00251824	−	0.0278667i
$397$	−3.91968e19			−1.26567			−0.632837	−	0.774285i	$-0.718110\pi$
$397$	−3.91968e19			−1.26567			−0.632837	+	0.774285i	$0.718110\pi$
$398$	3.49942e18	−	1.81408e18i	0.110885	−	0.0574823i
$399$	−8.44196e18	+	3.10266e18i	−0.262510	+	0.0964802i
$400$	−7.85562e18	−	2.20515e19i	−0.239735	−	0.672959i
$401$		−	3.09431e19i		−	0.926789i	−0.886152	−	0.463394i	$-0.846631\pi$
$401$		−	3.09431e19i		−	0.926789i	0.886152	−	0.463394i	$-0.153369\pi$
$402$	3.31734e19	−	3.63064e19i	0.975202	−	1.06730i
$403$		−	1.68472e19i		−	0.486115i
$404$	−5.55551e19	−	3.91841e19i	−1.57349	−	1.10981i
$405$	1.89706e19	+	3.09996e18i	0.527433	+	0.0861873i
$406$	−4.56119e17	−	8.79868e17i	−0.0124489	−	0.0240144i
$407$	−7.34962e17			−0.0196928
$408$	−1.29140e19	−	5.88058e19i	−0.339710	−	1.54692i
$409$	2.59858e19			0.671138			0.335569	−	0.942016i	$-0.391071\pi$
$409$	2.59858e19			0.671138			0.335569	+	0.942016i	$0.391071\pi$
$410$	1.06460e19	+	2.05365e19i	0.269966	+	0.520772i
$411$	9.30333e18	+	2.53132e19i	0.231646	+	0.630279i
$412$	3.57577e19	+	2.52206e19i	0.874260	+	0.616632i
$413$		−	1.87799e19i		−	0.450887i
$414$	5.86046e19	+	2.39619e19i	1.38175	+	0.564960i
$415$		−	2.68908e19i		−	0.622649i
$416$	−4.20895e19	+	4.51510e19i	−0.957135	+	1.02676i
$417$	1.92227e19	+	5.23027e19i	0.429334	+	1.16816i
$418$	6.02449e17	−	3.12306e17i	0.0132159	−	0.00685107i
$419$	−5.98738e19			−1.29012			−0.645062	−	0.764130i	$-0.723168\pi$
$419$	−5.98738e19			−1.29012			−0.645062	+	0.764130i	$0.723168\pi$
$420$	−3.43908e18	+	1.28203e19i	−0.0727902	+	0.271350i
$421$	2.82618e19			0.587604			0.293802	−	0.955866i	$-0.405079\pi$
$421$	2.82618e19			0.587604			0.293802	+	0.955866i	$0.405079\pi$
$422$	3.27182e18	−	1.69610e18i	0.0668262	−	0.0346423i
$423$	7.95436e18	−	6.76005e18i	0.159607	−	0.135643i
$424$	5.67835e18	−	4.14848e19i	0.111938	−	0.817796i
$425$		−	5.84179e19i		−	1.13143i
$426$	2.44310e19	+	2.23228e19i	0.464911	+	0.424793i
$427$		−	3.50734e19i		−	0.655795i
$428$	−2.68115e19	+	3.80133e19i	−0.492598	+	0.698405i
$429$	−2.04192e18	+	7.50466e17i	−0.0368646	+	0.0135488i
$430$	−2.21681e19	−	4.27631e19i	−0.393293	−	0.758675i
$431$	7.47783e19			1.30376			0.651878	−	0.758324i	$-0.273982\pi$
$431$	7.47783e19			1.30376			0.651878	+	0.758324i	$0.273982\pi$
$432$	−5.75010e19	−	9.98649e18i	−0.985251	−	0.171114i
$433$	−1.04109e19			−0.175318			−0.0876592	−	0.996151i	$-0.527939\pi$
$433$	−1.04109e19			−0.175318			−0.0876592	+	0.996151i	$0.527939\pi$
$434$	5.06227e18	+	9.76528e18i	0.0837861	+	0.161626i
$435$	−1.58663e18	+	5.83132e17i	−0.0258111	+	0.00948632i
$436$	−3.33784e19	+	4.73238e19i	−0.533725	+	0.756713i
$437$			5.05288e19i			0.794198i
$438$	4.84211e19	+	4.42428e19i	0.748134	+	0.683576i
$439$		−	8.51076e19i		−	1.29266i	−0.763058	−	0.646330i	$-0.776303\pi$
$439$		−	8.51076e19i		−	1.29266i	0.763058	−	0.646330i	$-0.223697\pi$
$440$	1.35812e17	−	9.92216e17i	0.00202789	−	0.0148153i
$441$	3.75639e19	−	3.19238e19i	0.551418	−	0.468625i
$442$	−1.36757e20	+	7.08938e19i	−1.97370	+	1.02316i
$443$	9.85130e19			1.39787			0.698933	−	0.715187i	$-0.253658\pi$
$443$	9.85130e19			1.39787			0.698933	+	0.715187i	$0.253658\pi$
$444$	−1.30702e19	+	4.87234e19i	−0.182351	+	0.679775i
$445$	1.91618e19			0.262868
$446$	8.15768e18	−	4.22890e18i	0.110041	−	0.0570447i
$447$	2.23585e19	+	6.08346e19i	0.296576	+	0.806946i
$448$	1.08297e19	−	3.88184e19i	0.141263	−	0.506353i
$449$			1.19126e19i			0.152812i	0.997077	+	0.0764061i	$0.0243445\pi$
$449$			1.19126e19i			0.152812i	−0.997077	+	0.0764061i	$0.975655\pi$
$450$	−5.24153e19	−	2.14312e19i	−0.661248	−	0.270367i
$451$		−	2.47525e18i		−	0.0307111i
$452$	−3.95425e18	−	2.78901e18i	−0.0482532	−	0.0340339i
$453$	4.68480e19	+	1.27467e20i	0.562282	+	1.52990i
$454$	2.43809e19	+	4.70315e19i	0.287826	+	0.555227i
$455$	3.39605e19			0.394356
$456$	−9.99032e18	−	4.54925e19i	−0.114115	−	0.519641i
$457$	−1.67073e20			−1.87731			−0.938655	−	0.344858i	$-0.887927\pi$
$457$	−1.67073e20			−1.87731			−0.938655	+	0.344858i	$0.887927\pi$
$458$	1.82937e19	+	3.52892e19i	0.202214	+	0.390077i
$459$	−1.26811e20	−	7.16308e19i	−1.37899	−	0.778941i
$460$	6.09385e19	+	4.29811e19i	0.651940	+	0.459826i
$461$			1.42111e18i			0.0149579i	0.999972	+	0.00747896i	$0.00238065\pi$
$461$			1.42111e18i			0.0149579i	−0.999972	+	0.00747896i	$0.997619\pi$
$462$	9.58078e17	−	1.04856e18i	0.00992170	−	0.0108587i
$463$		−	1.48475e19i		−	0.151285i	−0.997135	−	0.0756427i	$-0.975899\pi$
$463$		−	1.48475e19i		−	0.151285i	0.997135	−	0.0756427i	$-0.0241008\pi$
$464$	4.83470e18	−	1.72231e18i	0.0484713	−	0.0172674i
$465$	1.76093e19	−	6.47194e18i	0.173718	−	0.0638465i
$466$	−3.05336e19	+	1.58285e19i	−0.296404	+	0.153654i
$467$	−5.88375e19			−0.562053			−0.281027	−	0.959700i	$-0.590675\pi$
$467$	−5.88375e19			−0.562053			−0.281027	+	0.959700i	$0.590675\pi$
$468$	1.34388e19	+	1.48713e20i	0.126332	+	1.39799i
$469$	8.21511e19			0.760007
$470$	1.09154e19	−	5.65848e18i	0.0993816	−	0.0515189i
$471$	3.91361e19	−	1.43836e19i	0.350688	−	0.128888i
$472$	9.63548e19	+	1.31888e19i	0.849783	+	0.116316i
$473$			5.15420e18i			0.0447407i
$474$	1.51669e20	−	1.65993e20i	1.29586	−	1.41825i
$475$		−	4.51924e19i		−	0.380070i
$476$	5.79672e19	−	8.21858e19i	0.479877	−	0.680369i
$477$	−6.55934e19	−	7.71819e19i	−0.534530	−	0.628966i
$478$	−8.00878e19	−	1.54492e20i	−0.642476	−	1.23936i
$479$	−6.44754e18			−0.0509188			−0.0254594	−	0.999676i	$-0.508105\pi$
$479$	−6.44754e18			−0.0509188			−0.0254594	+	0.999676i	$0.508105\pi$
$480$	−6.33626e19	−	2.66486e19i	−0.492633	−	0.207188i
$481$	1.29066e20			0.987926
$482$	−5.64604e19	−	1.08914e20i	−0.425492	−	0.820788i
$483$	3.64845e19	+	9.92697e19i	0.270710	+	0.736569i
$484$	7.88326e19	−	1.11769e20i	0.575925	−	0.816545i
$485$		−	5.05941e19i		−	0.363946i
$486$	−1.10793e20	+	8.75025e19i	−0.784763	+	0.619795i
$487$			9.60597e19i			0.669999i	0.942218	+	0.334999i	$0.108736\pi$
$487$			9.60597e19i			0.669999i	−0.942218	+	0.334999i	$0.891264\pi$
$488$	1.79953e20	+	2.46315e19i	1.23597	+	0.169177i
$489$	−7.38303e19	−	2.00883e20i	−0.499365	−	1.35871i
$490$	5.15472e19	−	2.67218e19i	0.343348	−	0.177990i
$491$	−1.80118e20			−1.18153			−0.590766	−	0.806843i	$-0.701174\pi$
$491$	−1.80118e20			−1.18153			−0.590766	+	0.806843i	$0.701174\pi$
$492$	−1.64094e20	−	4.40186e19i	−1.06012	−	0.284379i
$493$	1.28079e19			0.0814939
$494$	−1.05796e20	+	5.48439e19i	−0.663004	+	0.343697i
$495$	−1.56883e18	−	1.84600e18i	−0.00968363	−	0.0113945i
$496$	−5.36583e19	+	1.91152e19i	−0.326231	+	0.116216i
$497$			5.52806e19i			0.331055i
$498$	1.45805e20	+	1.33223e20i	0.860106	+	0.785885i
$499$			3.33716e20i			1.93920i	0.244698	+	0.969599i	$0.421311\pi$
$499$			3.33716e20i			1.93920i	−0.244698	+	0.969599i	$0.578689\pi$
$500$	−1.30796e20	−	9.22528e19i	−0.748719	−	0.528086i
$501$	−1.83917e19	+	6.75949e18i	−0.103714	+	0.0381181i
$502$	−1.00744e19	−	1.94338e19i	−0.0559682	−	0.107964i
$503$	−1.39726e20			−0.764748			−0.382374	−	0.924008i	$-0.624893\pi$
$503$	−1.39726e20			−0.764748			−0.382374	+	0.924008i	$0.624893\pi$
$504$	−5.24751e19	−	8.21617e19i	−0.282960	−	0.443037i
$505$	−1.93695e20			−1.02904
$506$	−3.67243e18	−	7.08425e18i	−0.0192232	−	0.0370821i
$507$	1.76591e20	−	6.49024e19i	0.910771	−	0.334735i
$508$	6.40486e19	+	4.51747e19i	0.325486	+	0.229571i
$509$		−	4.77462e19i		−	0.239087i	−0.992829	−	0.119543i	$-0.961857\pi$
$509$		−	4.77462e19i		−	0.239087i	0.992829	−	0.119543i	$-0.0381431\pi$
$510$	−1.26637e20	−	1.15709e20i	−0.624862	−	0.570941i
$511$			1.09564e20i			0.532733i
$512$	1.91562e20	+	8.28258e19i	0.917878	+	0.396864i
$513$	−9.81019e19	−	5.54140e19i	−0.463230	−	0.261661i
$514$	8.07430e19	−	4.18567e19i	0.375735	−	0.194779i
$515$	1.24671e20			0.571755
$516$	3.41692e20	+	9.16596e19i	1.54441	+	0.414291i
$517$	−1.31563e18			−0.00586075
$518$	−7.48119e19	+	3.87821e19i	−0.328472	+	0.170278i
$519$	−2.67681e19	−	7.28327e19i	−0.115841	−	0.315189i
$520$	−2.38499e19	+	1.74243e20i	−0.101733	+	0.743240i
$521$			3.52630e20i			1.48264i	0.671151	+	0.741321i	$0.265800\pi$
$521$			3.52630e20i			1.48264i	−0.671151	+	0.741321i	$0.734200\pi$
$522$	4.69870e18	−	1.14918e19i	0.0194737	−	0.0476278i
$523$		−	1.26595e20i		−	0.517194i	−0.965985	−	0.258597i	$-0.916740\pi$
$523$		−	1.26595e20i		−	0.517194i	0.965985	−	0.258597i	$-0.0832602\pi$
$524$	2.33867e20	−	3.31576e20i	0.941855	−	1.33536i
$525$	−3.26313e19	−	8.87857e19i	−0.129551	−	0.352491i
$526$	5.87159e19	+	1.13265e20i	0.229807	+	0.443304i
$527$	−1.42149e20			−0.548485
$528$	4.70706e18	+	5.65204e18i	0.0179059	+	0.0215006i
$529$	3.27538e20			1.22841
$530$	−5.49048e19	−	1.05913e20i	−0.203021	−	0.391634i
$531$	1.79267e20	−	1.52351e20i	0.653568	−	0.555437i
$532$	4.48438e19	−	6.35794e19i	0.161200	−	0.228549i
$533$			4.34678e20i			1.54068i
$534$	−9.49319e19	+	1.03897e20i	−0.331782	+	0.363116i
$535$			1.32535e20i			0.456748i
$536$	−5.76935e19	+	4.21497e20i	−0.196061	+	1.43238i
$537$	−1.68218e19	+	6.18251e18i	−0.0563724	+	0.0207185i
$538$	−1.59045e20	+	8.24480e19i	−0.525597	+	0.272466i
$539$	−6.21294e18			−0.0202480
$540$	−1.50278e20	+	7.11756e19i	−0.482994	+	0.228759i
$541$	−4.04642e20			−1.28260			−0.641300	−	0.767290i	$-0.721605\pi$
$541$	−4.04642e20			−1.28260			−0.641300	+	0.767290i	$0.721605\pi$
$542$	2.97193e20	−	1.54063e20i	0.929060	−	0.481619i
$543$	1.17487e19	−	4.31797e18i	0.0362234	−	0.0133132i
$544$	3.80965e20	+	3.55133e20i	1.15849	+	1.07994i
$545$			1.64997e20i			0.494881i
$546$	−1.68248e20	+	1.84137e20i	−0.497742	+	0.544750i
$547$		−	1.99918e20i		−	0.583374i	−0.956514	−	0.291687i	$-0.905783\pi$
$547$		−	1.99918e20i		−	0.583374i	0.956514	−	0.291687i	$-0.0942166\pi$
$548$	−1.90643e20	−	1.34464e20i	−0.548739	−	0.387036i
$549$	3.34799e20	−	2.84530e20i	0.950587	−	0.807860i
$550$	3.28458e18	+	6.33607e18i	0.00919941	+	0.0177460i
$551$	9.90825e18			0.0273754
$552$	−5.34950e20	+	1.17477e20i	−1.45804	+	0.320192i
$553$	3.75596e20			1.00991
$554$	−2.11956e20	−	4.08870e20i	−0.562240	−	1.08458i
$555$	4.95816e19	+	1.34905e20i	0.129755	+	0.353046i
$556$	−3.93910e20	−	2.77833e20i	−1.01704	−	0.717335i
$557$		−	5.14003e20i		−	1.30934i	−0.755916	−	0.654669i	$-0.772808\pi$
$557$		−	5.14003e20i		−	1.30934i	0.755916	−	0.654669i	$-0.227192\pi$
$558$	−5.21489e19	+	1.27543e20i	−0.131066	+	0.320553i
$559$		−	9.05127e20i		−	2.24451i
$560$	−3.85324e19	−	1.08164e20i	−0.0942792	−	0.264651i
$561$	6.33211e18	+	1.72289e19i	0.0152872	+	0.0415945i
$562$	−3.59298e20	+	1.86258e20i	−0.855917	+	0.443703i
$563$	5.09594e20			1.19787			0.598937	−	0.800796i	$-0.295590\pi$
$563$	5.09594e20			1.19787			0.598937	+	0.800796i	$0.295590\pi$
$564$	−2.33964e19	+	8.72178e19i	−0.0542695	+	0.202307i
$565$	−1.37867e19			−0.0315570
$566$	1.53602e20	−	7.96264e19i	0.346955	−	0.179860i
$567$	−2.32744e20	−	3.80325e19i	−0.518807	−	0.0847778i
$568$	−2.83631e20	−	3.88227e19i	−0.623937	−	0.0854031i
$569$		−	7.13752e20i		−	1.54955i	−0.632237	−	0.774775i	$-0.717863\pi$
$569$		−	7.13752e20i		−	1.54955i	0.632237	−	0.774775i	$-0.282137\pi$
$570$	−9.79672e19	−	8.95133e19i	−0.209903	−	0.191790i
$571$			1.62706e20i			0.344060i	0.985092	+	0.172030i	$0.0550326\pi$
$571$			1.62706e20i			0.344060i	−0.985092	+	0.172030i	$0.944967\pi$
$572$	1.08467e19	−	1.53785e19i	0.0226375	−	0.0320954i
$573$	−9.28980e19	+	3.41427e19i	−0.191358	+	0.0703297i
$574$	−1.30613e20	−	2.51957e20i	−0.265550	−	0.512255i
$575$	−5.31422e20			−1.06643
$576$	4.58403e20	−	2.11536e20i	0.907986	−	0.419001i
$577$	3.74576e20			0.732354			0.366177	−	0.930545i	$-0.380666\pi$
$577$	3.74576e20			0.732354			0.366177	+	0.930545i	$0.380666\pi$
$578$	3.59702e20	+	6.93877e20i	0.694199	+	1.33913i
$579$	−2.76685e20	+	1.01690e20i	−0.527104	+	0.193726i
$580$	8.42820e18	−	1.19495e19i	0.0158498	−	0.0224719i
$581$			3.29916e20i			0.612466i
$582$	2.74326e20	+	2.50654e20i	0.502742	+	0.459359i
$583$			1.27656e19i			0.0230955i
$584$	−5.62143e20	−	7.69448e19i	−1.00404	−	0.137430i
$585$	2.75502e20	+	3.24176e20i	0.485798	+	0.571626i
$586$	6.29605e20	−	3.26384e20i	1.09606	−	0.568193i
$587$	6.77352e20			1.16420			0.582101	−	0.813116i	$-0.302231\pi$
$587$	6.77352e20			1.16420			0.582101	+	0.813116i	$0.302231\pi$
$588$	−1.10488e20	+	4.11880e20i	−0.187493	+	0.698941i
$589$	−1.09967e20			−0.184247
$590$	2.45999e20	−	1.27525e20i	0.406953	−	0.210962i
$591$	−5.76364e19	−	1.56821e20i	−0.0941436	−	0.256153i
$592$	−1.46442e20	−	4.11077e20i	−0.236185	−	0.662995i
$593$			9.95393e20i			1.58520i	0.609741	+	0.792601i	$0.291273\pi$
$593$			9.95393e20i			1.58520i	−0.609741	+	0.792601i	$0.708727\pi$
$594$	1.77816e19	+	6.39122e17i	0.0279622	+	0.00100504i
$595$		−	2.86544e20i		−	0.444953i
$596$	−4.58167e20	−	3.23154e20i	−0.702550	−	0.495522i
$597$	2.84541e19	+	7.74200e19i	0.0430861	+	0.117232i
$598$	6.44914e20	+	1.24406e21i	0.964369	+	1.86030i
$599$	−5.98207e20			−0.883385			−0.441693	−	0.897166i	$-0.645622\pi$
$599$	−5.98207e20			−0.883385			−0.441693	+	0.897166i	$0.645622\pi$
$600$	4.78454e20	−	1.05070e20i	0.697759	−	0.153230i
$601$	−1.11087e21			−1.59995			−0.799974	−	0.600034i	$-0.795154\pi$
$601$	−1.11087e21			−1.59995			−0.799974	+	0.600034i	$0.795154\pi$
$602$	2.71974e20	+	5.24648e20i	0.386860	+	0.746266i
$603$	6.66446e20	+	7.84188e20i	0.936235	+	1.10164i
$604$	−9.60004e20	−	6.77109e20i	−1.33197	−	0.939467i
$605$		−	3.89686e20i		−	0.534010i
$606$	9.59608e20	−	1.05024e21i	1.29882	−	1.42148i
$607$			9.75911e20i			1.30465i	0.757938	+	0.652326i	$0.226207\pi$
$607$			9.75911e20i			1.30465i	−0.757938	+	0.652326i	$0.773793\pi$
$608$	2.94717e20	+	2.74733e20i	0.389160	+	0.362772i
$609$	1.94659e19	−	7.15428e18i	0.0253889	−	0.00933117i
$610$	4.59429e20	−	2.38166e20i	0.591895	−	0.306835i
$611$	2.31036e20			0.294016
$612$	1.25477e21	−	1.13391e20i	1.57736	−	0.142541i
$613$	−7.27082e20			−0.902880			−0.451440	−	0.892301i	$-0.649090\pi$
$613$	−7.27082e20			−0.902880			−0.451440	+	0.892301i	$0.649090\pi$
$614$	−4.68148e20	+	2.42685e20i	−0.574276	+	0.297701i
$615$	−4.54343e20	+	1.66984e20i	−0.550580	+	0.202354i
$616$	−1.66624e18	+	1.21732e19i	−0.00199472	+	0.0145730i
$617$		−	7.45427e20i		−	0.881590i	−0.897608	−	0.440795i	$-0.854697\pi$
$617$		−	7.45427e20i		−	0.881590i	0.897608	−	0.440795i	$-0.145303\pi$
$618$	−6.17646e20	+	6.75978e20i	−0.721649	+	0.789803i
$619$			4.21764e20i			0.486844i	0.969921	+	0.243422i	$0.0782699\pi$
$619$			4.21764e20i			0.486844i	−0.969921	+	0.243422i	$0.921730\pi$
$620$	−9.35410e19	+	1.32622e20i	−0.106675	+	0.151244i
$621$	−6.51619e20	+	1.15359e21i	−0.734187	+	1.29976i
$622$	−7.45688e20	−	1.43846e21i	−0.830098	−	1.60129i
$623$	−2.35091e20			−0.258568
$624$	−8.26604e20	−	9.92553e20i	−0.898283	−	1.07862i
$625$	2.09299e20			0.224733
$626$	2.32643e20	+	4.48776e20i	0.246821	+	0.476126i
$627$	4.89856e18	+	1.33284e19i	0.00513525	+	0.0139724i
$628$	−2.07891e20	+	2.94748e20i	−0.215347	+	0.305319i
$629$		−	1.08901e21i		−	1.11468i
$630$	−2.57101e20	−	1.05122e20i	−0.260046	−	0.106326i
$631$		−	4.96826e20i		−	0.496574i	−0.968687	−	0.248287i	$-0.920132\pi$
$631$		−	4.96826e20i		−	0.496574i	0.968687	−	0.248287i	$-0.0798676\pi$
$632$	−2.63775e20	+	1.92709e21i	−0.260529	+	1.90337i
$633$	2.66035e19	+	7.23847e19i	0.0259663	+	0.0706511i
$634$	8.96325e20	−	4.64650e20i	0.864562	−	0.448184i
$635$	2.23308e20			0.212864
$636$	8.46282e20	+	2.27017e20i	0.797236	+	0.213860i
$637$	1.09105e21			1.01578
$638$	−1.38916e18	+	7.20131e17i	−0.00127819	+	0.000662608i
$639$	−5.27691e20	+	4.48460e20i	−0.479869	+	0.407819i
$640$	5.82025e20	−	1.21738e20i	0.523109	−	0.109415i
$641$		−	9.69439e20i		−	0.861163i	−0.902552	−	0.430582i	$-0.858308\pi$
$641$		−	9.69439e20i		−	0.861163i	0.902552	−	0.430582i	$-0.141692\pi$
$642$	−7.18618e20	−	6.56607e20i	−0.630936	−	0.576491i
$643$			1.39592e21i			1.21138i	0.795702	+	0.605688i	$0.207102\pi$
$643$			1.39592e21i			1.21138i	−0.795702	+	0.605688i	$0.792898\pi$
$644$	−7.47636e20	−	5.27322e20i	−0.641278	−	0.452306i
$645$	9.46075e20	−	3.47710e20i	0.802099	−	0.294795i
$646$	4.62750e20	+	8.92659e20i	0.387795	+	0.748069i
$647$	1.63196e20			0.135184			0.0675922	−	0.997713i	$-0.478468\pi$
$647$	1.63196e20			0.135184			0.0675922	+	0.997713i	$0.478468\pi$
$648$	3.58588e20	−	1.16744e21i	0.293618	−	0.955923i
$649$	−2.96501e19			−0.0239989
$650$	−5.76804e20	−	1.11267e21i	−0.461507	−	0.890262i
$651$	−2.16044e20	+	7.94023e19i	−0.170877	+	0.0628023i
$652$	1.51292e21	+	1.06709e21i	1.18293	+	0.834344i
$653$		−	8.17163e19i		−	0.0631626i	−0.999501	−	0.0315813i	$-0.989946\pi$
$653$		−	8.17163e19i		−	0.0631626i	0.999501	−	0.0315813i	$-0.0100543\pi$
$654$	−8.94628e20	−	8.17429e20i	−0.683612	−	0.624621i
$655$		−	1.15605e21i		−	0.873309i
$656$	1.38445e21	−	4.93196e20i	1.03395	−	0.368333i
$657$	−1.04586e21	+	8.88827e20i	−0.772205	+	0.656262i
$658$	−1.33918e20	+	6.94223e19i	−0.0977562	+	0.0506763i
$659$	2.12020e20			0.153016			0.0765079	−	0.997069i	$-0.475623\pi$
$659$	2.12020e20			0.153016			0.0765079	+	0.997069i	$0.475623\pi$
$660$	2.02410e19	+	5.42970e18i	0.0144428	+	0.00387433i
$661$	1.33600e21			0.942528			0.471264	−	0.881992i	$-0.343798\pi$
$661$	1.33600e21			0.942528			0.471264	+	0.881992i	$0.343798\pi$
$662$	−8.68310e20	+	4.50127e20i	−0.605675	+	0.313979i
$663$	−1.11198e21	−	3.02555e21i	−0.766911	−	2.08667i
$664$	−1.69271e21	−	2.31695e20i	−1.15431	−	0.157999i
$665$		−	2.21672e20i		−	0.149468i
$666$	−9.77108e20	−	3.99513e20i	−0.651457	−	0.266363i
$667$		−	1.16512e20i		−	0.0768116i
$668$	9.76970e19	−	1.38515e20i	0.0636881	−	0.0902968i
$669$	6.63308e19	+	1.80478e20i	0.0427582	+	0.116340i
$670$	5.57847e20	+	1.07611e21i	0.355594	+	0.685952i
$671$	−5.53747e19			−0.0349054
$672$	7.77377e20	+	3.26943e20i	0.484576	+	0.203799i
$673$	−6.15680e20			−0.379526			−0.189763	−	0.981830i	$-0.560772\pi$
$673$	−6.15680e20			−0.379526			−0.189763	+	0.981830i	$0.560772\pi$
$674$	−4.90994e20	−	9.47143e20i	−0.299314	−	0.577386i
$675$	5.82800e20	−	1.03176e21i	0.351351	−	0.622012i
$676$	−9.38055e20	+	1.32997e21i	−0.559278	+	0.792944i
$677$			1.84323e21i			1.08684i	0.839462	+	0.543418i	$0.182870\pi$
$677$			1.84323e21i			1.08684i	−0.839462	+	0.543418i	$0.817130\pi$
$678$	6.83022e19	−	7.47528e19i	0.0398301	−	0.0435918i
$679$			6.20724e20i			0.357993i
$680$	1.47019e21	+	2.01236e20i	0.838601	+	0.114786i
$681$	−1.04051e21	+	3.82417e20i	−0.587006	+	0.215742i
$682$	1.54177e19	−	7.99243e18i	0.00860272	−	0.00445960i
$683$	3.10090e21			1.71133			0.855663	−	0.517534i	$-0.173150\pi$
$683$	3.10090e21			1.71133			0.855663	+	0.517534i	$0.173150\pi$
$684$	9.70701e20	−	8.77196e19i	0.529864	−	0.0478824i
$685$	−6.64684e20			−0.358869
$686$	−1.50634e21	+	7.80879e20i	−0.804438	+	0.417016i
$687$	−7.80726e20	+	2.86939e20i	−0.412404	+	0.151570i
$688$	−2.88284e21	+	1.02698e21i	−1.50628	+	0.536597i
$689$		−	2.24177e21i		−	1.15863i
$690$	−1.05260e21	+	1.15200e21i	−0.538137	+	0.588960i
$691$		−	8.03769e20i		−	0.406486i	−0.979128	−	0.203243i	$-0.934852\pi$
$691$		−	8.03769e20i		−	0.406486i	0.979128	−	0.203243i	$-0.0651482\pi$
$692$	5.48529e20	+	3.86888e20i	0.274413	+	0.193548i
$693$	1.92476e19	+	2.26481e19i	0.00952525	+	0.0112081i
$694$	7.62820e20	+	1.47150e21i	0.373444	+	0.720386i
$695$	−1.37338e21			−0.665129
$696$	2.30362e19	+	1.04899e20i	0.0110368	+	0.0502576i
$697$	3.66763e21			1.73836
$698$	8.32851e20	+	1.60660e21i	0.390528	+	0.753341i
$699$	−2.48271e20	−	6.75515e20i	−0.115172	−	0.313369i
$700$	6.68677e20	+	4.71631e20i	0.306889	+	0.216455i
$701$			2.69397e21i			1.22323i	0.791156	+	0.611614i	$0.209479\pi$
$701$			2.69397e21i			1.22323i	−0.791156	+	0.611614i	$0.790521\pi$
$702$	−3.12261e21	−	1.12236e20i	−1.40278	−	0.0504200i
$703$		−	8.42462e20i		−	0.374443i
$704$	−6.12875e19	−	1.70981e19i	−0.0269511	−	0.00751889i
$705$	8.87541e19	+	2.41489e20i	0.0386162	+	0.105070i
$706$	1.92035e21	−	9.95497e20i	0.826693	−	0.428553i
$707$	2.37639e21			1.01221
$708$	−5.27282e20	+	1.96562e21i	−0.222225	+	0.828418i
$709$	−8.29783e20			−0.346033			−0.173017	−	0.984919i	$-0.555351\pi$
$709$	−8.29783e20			−0.346033			−0.173017	+	0.984919i	$0.555351\pi$
$710$	−7.24125e20	+	3.75383e20i	−0.298797	+	0.154895i
$711$	3.04700e21	+	3.58531e21i	1.24408	+	1.46388i
$712$	1.65101e20	−	1.20619e21i	0.0667036	−	0.487322i
$713$			1.29312e21i			0.516971i
$714$	1.55367e21	+	1.41960e21i	0.614643	+	0.561604i
$715$		−	5.36176e19i		−	0.0209900i
$716$	8.93578e19	−	1.26691e20i	0.0346166	−	0.0490794i
$717$	3.41793e21	−	1.25619e21i	1.31030	−	0.481572i
$718$	−1.74962e21	−	3.37507e21i	−0.663758	−	1.28041i
$719$	−1.67240e21			−0.627875			−0.313937	−	0.949444i	$-0.601648\pi$
$719$	−1.67240e21			−0.627875			−0.313937	+	0.949444i	$0.601648\pi$
$720$	7.19911e20	−	1.24530e21i	0.267476	−	0.462678i
$721$	−1.52955e21			−0.562404
$722$	−9.06763e20	−	1.74918e21i	−0.329963	−	0.636509i
$723$	2.40957e21	−	8.85589e20i	0.867767	−	0.318930i
$724$	−6.24091e19	+	8.84834e19i	−0.0222438	+	0.0315372i
$725$			1.04207e20i			0.0367588i
$726$	2.11292e21	+	1.93059e21i	0.737663	+	0.674009i
$727$		−	1.30312e21i		−	0.450273i	−0.974327	−	0.225136i	$-0.927717\pi$
$727$		−	1.30312e21i		−	0.450273i	0.974327	−	0.225136i	$-0.0722828\pi$
$728$	2.92608e20	−	2.13773e21i	0.100069	−	0.731085i
$729$	−1.52508e21	−	2.53024e21i	−0.516221	−	0.856456i
$730$	−1.43518e21	+	7.43991e20i	−0.480824	+	0.249256i
$731$	−7.63708e21			−2.53248
$732$	−9.84754e20	+	3.67100e21i	−0.323217	+	1.20490i
$733$	−2.27379e21			−0.738703			−0.369351	−	0.929290i	$-0.620420\pi$
$733$	−2.27379e21			−0.738703			−0.369351	+	0.929290i	$0.620420\pi$
$734$	3.10993e21	−	1.61217e21i	1.00007	−	0.518430i
$735$	4.19135e20	+	1.14041e21i	0.133413	+	0.363000i
$736$	3.23061e21	−	3.46560e21i	1.01789	−	1.09193i
$737$		−	1.29702e20i		−	0.0404521i
$738$	1.34551e21	−	3.29077e21i	0.415397	−	1.01596i
$739$			9.31882e20i			0.284792i	0.989810	+	0.142396i	$0.0454806\pi$
$739$			9.31882e20i			0.284792i	−0.989810	+	0.142396i	$0.954519\pi$
$740$	−1.01602e21	−	7.16619e20i	−0.307372	−	0.216796i
$741$	−8.60234e20	−	2.34059e21i	−0.257620	−	0.700952i
$742$	6.73610e20	+	1.29942e21i	0.199701	+	0.385229i
$743$	−5.95158e20			−0.174669			−0.0873345	−	0.996179i	$-0.527835\pi$
$743$	−5.95158e20			−0.174669			−0.0873345	+	0.996179i	$0.527835\pi$
$744$	−2.55669e20	−	1.16423e21i	−0.0742815	−	0.338253i
$745$	−1.59742e21			−0.459459
$746$	−3.01393e20	−	5.81397e20i	−0.0858206	−	0.165551i
$747$	−3.14927e21	+	2.67642e21i	−0.887780	+	0.754483i
$748$	−1.29757e20	−	9.15200e19i	−0.0362133	−	0.0255420i
$749$		−	1.62603e21i		−	0.449278i
$750$	2.25925e21	−	2.47261e21i	0.618022	−	0.676389i
$751$			4.22819e21i			1.14513i	0.819859	+	0.572566i	$0.194052\pi$
$751$			4.22819e21i			1.14513i	−0.819859	+	0.572566i	$0.805948\pi$
$752$	−2.62140e20	−	7.35853e20i	−0.0702909	−	0.197314i
$753$	4.29947e20	−	1.58018e20i	0.114144	−	0.0419512i
$754$	2.43949e20	−	1.26462e20i	0.0641230	−	0.0332410i
$755$	−3.34709e21			−0.871095
$756$	1.84372e21	−	8.73233e20i	0.475095	−	0.225018i
$757$	−5.12629e21			−1.30793			−0.653964	−	0.756525i	$-0.726895\pi$
$757$	−5.12629e21			−1.30793			−0.653964	+	0.756525i	$0.726895\pi$
$758$	4.60905e20	−	2.38930e20i	0.116437	−	0.0603605i
$759$	1.56729e20	−	5.76026e19i	0.0392046	−	0.0144088i
$760$	1.13734e21	+	1.55677e20i	0.281702	+	0.0385587i
$761$			5.73318e21i			1.40608i	0.711150	+	0.703041i	$0.248175\pi$
$761$			5.73318e21i			1.40608i	−0.711150	+	0.703041i	$0.751825\pi$
$762$	−1.10632e21	+	1.21080e21i	−0.268669	+	0.294043i
$763$		−	2.02429e21i		−	0.486788i
$764$	4.93476e20	−	6.99649e20i	0.117508	−	0.166602i
$765$	2.73526e21	−	2.32457e21i	0.644967	−	0.548128i
$766$	−3.11493e21	−	6.00880e21i	−0.727331	−	1.40305i
$767$	5.20684e21			1.20395
$768$	−2.22340e21	+	3.75892e21i	−0.509107	+	0.860703i
$769$	3.28042e21			0.743845			0.371922	−	0.928264i	$-0.378699\pi$
$769$	3.28042e21			0.743845			0.371922	+	0.928264i	$0.378699\pi$
$770$	1.61111e19	+	3.10789e19i	0.00361781	+	0.00697887i
$771$	6.56528e20	+	1.78633e21i	0.145997	+	0.397241i
$772$	1.46975e21	−	2.08381e21i	0.323679	−	0.458912i
$773$		−	7.83637e20i		−	0.170911i	−0.996342	−	0.0854553i	$-0.972766\pi$
$773$		−	7.83637e20i		−	0.170911i	0.996342	−	0.0854553i	$-0.0272345\pi$
$774$	−2.80174e21	+	6.85235e21i	−0.605161	+	1.48007i
$775$		−	1.15655e21i		−	0.247401i
$776$	−3.18478e21	−	4.35925e20i	−0.674708	−	0.0923525i
$777$	−6.08302e20	−	1.65511e21i	−0.127633	−	0.347272i
$778$	−1.96120e21	+	1.01667e21i	−0.407544	+	0.211269i
$779$	2.83730e21			0.583948
$780$	−3.55452e21	−	9.53507e20i	−0.724554	−	0.194363i
$781$	8.72783e19			0.0176207
$782$	1.04969e22	−	5.44151e21i	2.09898	−	1.08810i
$783$	2.26208e20	+	1.27776e20i	0.0448018	+	0.0253068i
$784$	−1.23794e21	−	3.47501e21i	−0.242844	−	0.681688i
$785$			1.02765e21i			0.199675i
$786$	6.26824e21	+	5.72734e21i	1.20636	+	1.10226i
$787$			2.61809e21i			0.499085i	0.968364	+	0.249542i	$0.0802802\pi$
$787$			2.61809e21i			0.499085i	−0.968364	+	0.249542i	$0.919720\pi$
$788$	1.18108e21	+	8.33038e20i	0.223014	+	0.157296i
$789$	−2.50583e21	+	9.20966e20i	−0.468678	+	0.172253i
$790$	2.55048e21	+	4.91996e21i	0.472519	+	0.911504i
$791$	1.69145e20			0.0310409
$792$	−1.29719e20	+	8.28490e19i	−0.0235811	+	0.0150608i
$793$	9.72432e21			1.75110
$794$	3.26551e21	+	6.29927e21i	0.582501	+	1.12366i
$795$	2.34318e21	−	8.61188e20i	0.414050	−	0.152175i
$796$	−5.83078e20	−	4.11256e20i	−0.102065	−	0.0719887i
$797$		−	1.04205e19i		−	0.00180697i	−1.00000		0.000903486i	$-0.999712\pi$
$797$		−	1.04205e19i		−	0.00180697i	1.00000		0.000903486i	$-0.000287589\pi$
$798$	1.20193e21	+	1.09821e21i	0.206470	+	0.188653i
$799$		−	1.94939e21i		−	0.331739i
$800$	−2.88942e21	+	3.09959e21i	−0.487120	+	0.522553i
$801$	−1.90716e21	−	2.24410e21i	−0.318525	−	0.374799i
$802$	−4.97283e21	+	2.57789e21i	−0.822803	+	0.426536i
$803$	1.72981e20			0.0283552
$804$	−8.59845e21	−	2.30656e21i	−1.39637	−	0.374579i
$805$	−2.60666e21			−0.419388
$806$	−2.70749e21	+	1.40355e21i	−0.431572	+	0.223725i
$807$	−1.29321e21	−	3.51865e21i	−0.204229	−	0.555680i
$808$	−1.66890e21	+	1.21927e22i	−0.261123	+	1.90771i
$809$			1.25064e22i			1.93874i	0.245606	+	0.969370i	$0.421013\pi$
$809$			1.25064e22i			1.93874i	−0.245606	+	0.969370i	$0.578987\pi$
$810$	−1.08226e21	−	3.30700e21i	−0.166224	−	0.507921i
$811$		−	3.82062e21i		−	0.581404i	−0.956814	−	0.290702i	$-0.906111\pi$
$811$		−	3.82062e21i		−	0.581404i	0.956814	−	0.290702i	$-0.0938887\pi$
$812$	−1.03403e20	+	1.46605e20i	−0.0155906	+	0.0221043i
$813$	2.41650e21	+	6.57499e21i	0.361000	+	0.982236i
$814$	6.12301e19	+	1.18115e20i	0.00906321	+	0.0174832i
$815$	5.27486e21			0.773623
$816$	−8.37474e21	+	6.97453e21i	−1.21701	+	1.01354i
$817$	−5.90809e21			−0.850710
$818$	−2.16489e21	−	4.17615e21i	−0.308878	−	0.595836i
$819$	−3.38006e21	−	3.97722e21i	−0.477853	−	0.562277i
$820$	2.41348e21	−	3.42182e21i	0.338095	−	0.479351i
$821$		−	8.70492e21i		−	1.20834i	−0.796854	−	0.604172i	$-0.793504\pi$
$821$		−	8.70492e21i		−	1.20834i	0.796854	−	0.604172i	$-0.206496\pi$
$822$	3.29299e21	−	3.60398e21i	0.452951	−	0.495729i
$823$		−	2.82336e21i		−	0.384828i	−0.981314	−	0.192414i	$-0.938368\pi$
$823$		−	2.82336e21i		−	0.384828i	0.981314	−	0.192414i	$-0.0616317\pi$
$824$	1.07418e21	−	7.84772e21i	0.145085	−	1.05996i
$825$	−1.40177e20	+	5.15191e19i	−0.0187617	+	0.00689547i
$826$	−3.01809e21	+	1.56456e21i	−0.400297	+	0.207512i
$827$	−9.37205e21			−1.23181			−0.615904	−	0.787821i	$-0.711209\pi$
$827$	−9.37205e21			−1.23181			−0.615904	+	0.787821i	$0.711209\pi$
$828$	−1.03150e21	−	1.14146e22i	−0.134352	−	1.48673i
$829$	1.32221e21			0.170664			0.0853322	−	0.996353i	$-0.472805\pi$
$829$	1.32221e21			0.170664			0.0853322	+	0.996353i	$0.472805\pi$
$830$	−4.32160e21	+	2.24029e21i	−0.552788	+	0.286562i
$831$	9.04569e21	−	3.32455e21i	1.14666	−	0.421430i
$832$	1.07627e22	+	3.00259e21i	1.35206	+	0.377200i
$833$		−	9.20584e21i		−	1.14611i
$834$	6.80404e21	−	7.44663e21i	0.839502	−	0.918786i
$835$		−	4.82937e20i		−	0.0590530i
$836$	−1.00381e20	−	7.08004e19i	−0.0121647	−	0.00858003i
$837$	−2.51059e21	−	1.41814e21i	−0.301533	−	0.170325i
$838$	4.98812e21	+	9.62224e21i	0.593754	+	1.14537i
$839$	5.76818e21			0.680494			0.340247	−	0.940336i	$-0.389489\pi$
$839$	5.76818e21			0.680494			0.340247	+	0.940336i	$0.389489\pi$
$840$	2.34685e21	−	5.15377e20i	0.274404	−	0.0602602i
$841$	8.60634e21			0.997352
$842$	−2.35451e21	−	4.54193e21i	−0.270433	−	0.521675i
$843$	−2.92148e21	−	7.94897e21i	−0.332580	−	0.904907i
$844$	−5.45155e20	−	3.84508e20i	−0.0615109	−	0.0433848i
$845$			4.63700e21i			0.518576i
$846$	−1.74908e21	−	7.15153e20i	−0.193880	−	0.0792723i
$847$			4.78095e21i			0.525277i
$848$	−7.14004e21	+	2.54356e21i	−0.777557	+	0.276996i
$849$	1.24895e21	+	3.39824e21i	0.134815	+	0.366814i
$850$	−9.38827e21	+	4.86683e21i	−1.00449	+	0.520720i
$851$	−9.90658e21			−1.05064
$852$	1.55211e21	−	5.78601e21i	0.163165	−	0.608250i
$853$	8.12588e21			0.846745			0.423372	−	0.905956i	$-0.360846\pi$
$853$	8.12588e21			0.846745			0.423372	+	0.905956i	$0.360846\pi$
$854$	−5.63660e21	+	2.92198e21i	−0.582215	+	0.301817i
$855$	2.11601e21	−	1.79830e21i	0.216657	−	0.184127i
$856$	8.34275e21	+	1.14194e21i	0.846752	+	0.115901i
$857$		−	9.30072e21i		−	0.935751i	−0.883794	−	0.467875i	$-0.845020\pi$
$857$		−	9.30072e21i		−	0.935751i	0.883794	−	0.467875i	$-0.154980\pi$
$858$	2.90720e20	+	2.65633e20i	0.0289948	+	0.0264928i
$859$		−	2.78845e21i		−	0.275685i	−0.990454	−	0.137843i	$-0.955983\pi$
$859$		−	2.78845e21i		−	0.275685i	0.990454	−	0.137843i	$-0.0440168\pi$
$860$	−5.02556e21	+	7.12523e21i	−0.492546	+	0.698330i
$861$	5.57420e21	−	2.04868e21i	0.541575	−	0.199045i
$862$	−6.22983e21	−	1.20175e22i	−0.600028	−	1.15747i
$863$	4.43618e21			0.423573			0.211786	−	0.977316i	$-0.432072\pi$
$863$	4.43618e21			0.423573			0.211786	+	0.977316i	$0.432072\pi$
$864$	3.18552e21	+	1.00729e22i	0.301528	+	0.953457i
$865$	1.91247e21			0.179463
$866$	8.67335e20	+	1.67312e21i	0.0806868	+	0.155648i
$867$	−1.53511e22	+	5.64197e21i	−1.41578	+	0.520341i
$868$	1.14763e21	−	1.62710e21i	0.104931	−	0.148771i
$869$		−	5.92999e20i		−	0.0537534i
$870$	2.25898e20	+	2.06404e20i	0.0203010	+	0.0185492i
$871$			2.27769e22i			2.02936i
$872$	1.03861e22	+	1.42163e21i	0.917446	+	0.125578i
$873$	−5.92523e21	+	5.03558e21i	−0.518917	+	0.441004i
$874$	8.12043e21	−	4.20959e21i	0.705088	−	0.365514i
$875$	5.59483e21			0.481645
$876$	3.07621e21	−	1.14676e22i	0.262564	−	0.978795i
$877$	−1.35482e22			−1.14653			−0.573263	−	0.819372i	$-0.694322\pi$
$877$	−1.35482e22			−1.14653			−0.573263	+	0.819372i	$0.694322\pi$
$878$	−1.36775e22	+	7.09036e21i	−1.14762	+	0.594921i
$879$	5.11937e21	+	1.39292e22i	0.425892	+	1.15880i
$880$	−1.70773e20	+	6.08359e19i	−0.0140863	+	0.00501811i
$881$		−	1.29638e22i		−	1.06026i	−0.847916	−	0.530130i	$-0.822143\pi$
$881$		−	1.29638e22i		−	1.06026i	0.847916	−	0.530130i	$-0.177857\pi$
$882$	−8.25992e21	−	3.37726e21i	−0.669825	−	0.273873i
$883$		−	1.12482e22i		−	0.904434i	−0.891908	−	0.452217i	$-0.850633\pi$
$883$		−	1.12482e22i		−	0.904434i	0.891908	−	0.452217i	$-0.149367\pi$
$884$	2.27865e22	+	1.60718e22i	1.81671	+	1.28136i
$885$	2.00024e21	+	5.44240e21i	0.158128	+	0.430245i
$886$	−8.20718e21	−	1.58319e22i	−0.643341	−	1.24103i
$887$	8.20002e21			0.637365			0.318682	−	0.947862i	$-0.396760\pi$
$887$	8.20002e21			0.637365			0.318682	+	0.947862i	$0.396760\pi$
$888$	8.91917e21	−	1.95868e21i	0.687428	−	0.150962i
$889$	−2.73970e21			−0.209382
$890$	−1.59638e21	−	3.07948e21i	−0.120980	−	0.233374i
$891$	−6.00466e19	+	3.67462e20i	−0.00451238	+	0.0276140i
$892$	−1.35924e21	−	9.58700e20i	−0.101289	−	0.0714408i
$893$		−	1.50806e21i		−	0.111438i
$894$	7.91396e21	−	8.66137e21i	0.579913	−	0.634681i
$895$		−	4.41715e20i		−	0.0320973i
$896$	−7.14069e21	+	1.49356e21i	−0.514553	+	0.107625i
$897$	−2.75232e22	+	1.01156e22i	−1.96678	+	0.722848i
$898$	1.91446e21	−	9.92444e20i	0.135667	−	0.0703288i
$899$	2.53568e20			0.0178196
$900$	9.22564e20	+	1.02091e22i	0.0642951	+	0.711487i
$901$	−1.89151e22			−1.30729
$902$	−3.97795e20	+	2.06215e20i	−0.0272653	+	0.0141342i
$903$	−1.16071e22	+	4.26595e21i	−0.788980	+	0.289973i
$904$	−1.18788e20	+	8.67838e20i	−0.00800771	+	0.0585026i
$905$			3.08501e20i			0.0206249i
$906$	1.65822e22	−	1.81483e22i	1.09946	−	1.20330i
$907$			8.83521e21i			0.580982i	0.956878	+	0.290491i	$0.0938186\pi$
$907$			8.83521e21i			0.580982i	−0.956878	+	0.290491i	$0.906181\pi$
$908$	5.52720e21	−	7.83645e21i	0.360463	−	0.511064i
$909$	1.92783e22	+	2.26842e22i	1.24692	+	1.46722i
$910$	−2.82927e21	−	5.45775e21i	−0.181495	−	0.350109i
$911$	8.84940e21			0.563023			0.281511	−	0.959558i	$-0.409164\pi$
$911$	8.84940e21			0.563023			0.281511	+	0.959558i	$0.409164\pi$
$912$	−6.47875e21	+	5.39554e21i	−0.408818	+	0.340466i
$913$	5.20879e20			0.0325991
$914$	1.39190e22	+	2.68502e22i	0.863995	+	1.66667i
$915$	3.73566e21	+	1.01643e22i	0.229990	+	0.625774i
$916$	4.14723e21	−	5.87993e21i	0.253245	−	0.359051i
$917$			1.41833e22i			0.859026i
$918$	−9.46998e20	+	2.63473e22i	−0.0568891	+	1.58276i
$919$			7.44235e21i			0.443449i	0.975109	+	0.221725i	$0.0711686\pi$
$919$			7.44235e21i			0.443449i	−0.975109	+	0.221725i	$0.928831\pi$
$920$	1.83062e21	−	1.33741e22i	0.108191	−	0.790418i
$921$	−3.80655e21	−	1.03571e22i	−0.223144	−	0.607145i
$922$	2.28385e20	−	1.18394e20i	0.0132796	−	0.00688409i
$923$	−1.53269e22			−0.883978
$924$	−2.48331e20	−	6.66154e19i	−0.0142066	−	0.00381097i
$925$	8.86034e21			0.502791
$926$	−2.38613e21	+	1.23696e21i	−0.134311	+	0.0696261i
$927$	−1.24084e22	−	1.46006e22i	−0.692814	−	0.815215i
$928$	−6.79573e20	−	6.33493e20i	−0.0376380	−	0.0350859i
$929$		−	3.00958e21i		−	0.165344i	−0.996577	−	0.0826719i	$-0.973655\pi$
$929$		−	3.00958e21i		−	0.165344i	0.996577	−	0.0826719i	$-0.0263453\pi$
$930$	−2.50714e21	−	2.29079e21i	−0.136633	−	0.124843i
$931$		−	7.12169e21i		−	0.385000i
$932$	5.08755e21	+	3.58834e21i	0.272828	+	0.192431i
$933$	3.18239e22	−	1.16962e22i	1.69294	−	0.622204i
$934$	4.90178e21	+	9.45570e21i	0.258674	+	0.498990i
$935$	−4.52403e20			−0.0236831
$936$	2.27799e22	−	1.45491e22i	1.18299	−	0.755555i
$937$	1.12536e22			0.579756			0.289878	−	0.957064i	$-0.406385\pi$
$937$	1.12536e22			0.579756			0.289878	+	0.957064i	$0.406385\pi$
$938$	−6.84406e21	−	1.32024e22i	−0.349778	−	0.674733i
$939$	−9.92857e21	+	3.64904e21i	−0.503378	+	0.185006i
$940$	−1.81874e21	−	1.28279e21i	−0.0914768	−	0.0645204i
$941$		−	3.45502e22i		−	1.72396i	−0.506939	−	0.861982i	$-0.669223\pi$
$941$		−	3.45502e22i		−	1.72396i	0.506939	−	0.861982i	$-0.330777\pi$
$942$	−5.57203e21	−	5.09120e21i	−0.275824	−	0.252022i
$943$		−	3.33640e22i		−	1.63848i
$944$	−5.90781e21	−	1.65838e22i	−0.287830	−	0.807970i
$945$	2.85868e21	−	5.06084e21i	0.138174	−	0.244616i
$946$	8.28326e20	−	4.29400e20i	0.0397208	−	0.0205910i
$947$	2.47689e22			1.17837			0.589185	−	0.807998i	$-0.299449\pi$
$947$	2.47689e22			1.17837			0.589185	+	0.807998i	$0.299449\pi$
$948$	−3.93122e22	−	1.05456e22i	−1.85552	−	0.497746i
$949$	−3.03772e22			−1.42250
$950$	−7.26283e21	+	3.76501e21i	−0.337426	+	0.174920i
$951$	7.28810e21	+	1.98300e22i	0.335939	+	0.914047i
$952$	−1.80373e22	−	2.46890e21i	−0.824886	−	0.112908i
$953$			2.78172e20i			0.0126217i	0.999980	+	0.00631083i	$0.00200881\pi$
$953$			2.78172e20i			0.0126217i	−0.999980	+	0.00631083i	$0.997991\pi$
$954$	−6.93919e21	+	1.69715e22i	−0.312389	+	0.764025i
$955$		−	2.43935e21i		−	0.108956i
$956$	−1.81561e22	+	2.57416e22i	−0.804615	+	1.14078i
$957$	−1.12953e19	−	3.07332e19i	−0.000496661	−	0.00135135i
$958$	5.37149e20	+	1.03618e21i	0.0234344	+	0.0452057i
$959$	8.15481e21			0.353000
$960$	9.96112e20	+	1.24030e22i	0.0427833	+	0.532714i
$961$	2.06510e22			0.880067
$962$	−1.07526e22	−	2.07421e22i	−0.454674	−	0.877081i
$963$	1.55216e22	−	1.31911e22i	0.651236	−	0.553456i
$964$	−1.27997e22	+	1.81474e22i	−0.532871	+	0.755503i
$965$		−	7.26530e21i		−	0.300123i
$966$	1.29140e22	−	1.41336e22i	0.529336	−	0.579328i
$967$		−	3.40228e22i		−	1.38379i	−0.721996	−	0.691897i	$-0.756775\pi$
$967$		−	3.40228e22i		−	1.38379i	0.721996	−	0.691897i	$-0.243225\pi$
$968$	−2.45298e22	−	3.35759e21i	−0.989986	−	0.135507i
$969$	−1.97489e22	+	7.25829e21i	−0.790887	+	0.290674i
$970$	−8.13091e21	+	4.21502e21i	−0.323111	+	0.167499i
$971$	−4.21128e22			−1.66062			−0.830309	−	0.557304i	$-0.811836\pi$
$971$	−4.21128e22			−1.66062			−0.830309	+	0.557304i	$0.811836\pi$
$972$	2.32926e22	+	1.05155e22i	0.911426	+	0.411464i
$973$	1.68496e22			0.654251
$974$	1.54377e22	−	8.00279e21i	0.594825	−	0.308354i
$975$	2.46164e22	−	9.04725e21i	0.941218	−	0.345925i
$976$	−1.10335e22	−	3.09720e22i	−0.418637	−	1.17516i
$977$			2.28470e22i			0.860239i	0.902772	+	0.430120i	$0.141529\pi$
$977$			2.28470e22i			0.860239i	−0.902772	+	0.430120i	$0.858471\pi$
$978$	−2.61328e22	+	2.86009e22i	−0.976439	+	1.06866i
$979$			3.71167e20i			0.0137626i
$980$	−8.58886e21	−	6.05789e21i	−0.316038	−	0.222908i
$981$	1.93233e22	−	1.64220e22i	0.705607	−	0.599663i
$982$	1.50057e22	+	2.89465e22i	0.543777	+	1.04896i
$983$	−2.33254e21			−0.0838837			−0.0419419	−	0.999120i	$-0.513354\pi$
$983$	−2.33254e21			−0.0838837			−0.0419419	+	0.999120i	$0.513354\pi$
$984$	6.59658e21	+	3.00386e22i	0.235427	+	1.07205i
$985$	4.11788e21			0.145849
$986$	−1.06703e21	−	2.05834e21i	−0.0375060	−	0.0723502i
$987$	−1.08890e21	−	2.96275e21i	−0.0379847	−	0.103351i
$988$	1.76278e22	+	1.24332e22i	0.610269	+	0.430434i
$989$			6.94737e22i			2.38698i
$990$	−1.65969e20	+	4.05917e20i	−0.00565929	+	0.0138412i
$991$			4.96892e22i			1.68155i	0.541386	+	0.840774i	$0.317900\pi$
$991$			4.96892e22i			1.68155i	−0.541386	+	0.840774i	$0.682100\pi$
$992$	7.54229e21	+	7.03087e21i	0.253318	+	0.236141i
$993$	−7.06030e21	−	1.92102e22i	−0.235344	−	0.640342i
$994$	8.88408e21	−	4.60546e21i	0.293910	−	0.152361i
$995$	−2.03293e21			−0.0667496
$996$	9.26303e21	−	3.45310e22i	0.301862	−	1.12529i
$997$	−4.42015e21			−0.142963			−0.0714815	−	0.997442i	$-0.522773\pi$
$997$	−4.42015e21			−0.142963			−0.0714815	+	0.997442i	$0.522773\pi$
$998$	5.36310e22	−	2.78020e22i	1.72162	−	0.892478i
$999$	1.08644e22	−	1.92337e22i	0.346149	−	0.612803i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	12.16.b.a.11.9	✓	28
3.2	odd	2	inner	12.16.b.a.11.20	yes	28
4.3	odd	2	inner	12.16.b.a.11.19	yes	28
12.11	even	2	inner	12.16.b.a.11.10	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
12.16.b.a.11.9	✓	28	1.1	even	1	trivial
12.16.b.a.11.10	yes	28	12.11	even	2	inner
12.16.b.a.11.19	yes	28	4.3	odd	2	inner
12.16.b.a.11.20	yes	28	3.2	odd	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:	\( k \)	\(=\)	\( 16 \)
Character orbit:	\([\chi]\)	\(=\)	12.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-83.3106 - 160.709i) q^{2} +(3555.47 - 1306.74i) q^{3} +(-18886.7 + 26777.5i) q^{4} +93360.9i q^{5} +(-506212. - 462530. i) q^{6} -1.14542e6i q^{7} +(5.87684e6 + 804409. i) q^{8} +(1.09338e7 - 9.29212e6i) q^{9} +O(q^{10})\)	\(q+(-83.3106 - 160.709i) q^{2} +(3555.47 - 1306.74i) q^{3} +(-18886.7 + 26777.5i) q^{4} +93360.9i q^{5} +(-506212. - 462530. i) q^{6} -1.14542e6i q^{7} +(5.87684e6 + 804409. i) q^{8} +(1.09338e7 - 9.29212e6i) q^{9} +(1.50039e7 - 7.77795e6i) q^{10} -1.80841e6 q^{11} +(-3.21598e7 + 1.19886e8i) q^{12} +3.17574e8 q^{13} +(-1.84079e8 + 9.54254e7i) q^{14} +(1.21998e8 + 3.31942e8i) q^{15} +(-3.60328e8 - 1.01148e9i) q^{16} -2.67956e9i q^{17} +(-2.40423e9 - 9.83024e8i) q^{18} -2.07292e9i q^{19} +(-2.49997e9 - 1.76328e9i) q^{20} +(-1.49676e9 - 4.07249e9i) q^{21} +(1.50660e8 + 2.90628e8i) q^{22} -2.43757e10 q^{23} +(2.19461e10 - 4.81944e9i) q^{24} +2.18013e10 q^{25} +(-2.64573e10 - 5.10370e10i) q^{26} +(2.67323e10 - 4.73254e10i) q^{27} +(3.06714e10 + 2.16331e10i) q^{28} +4.77985e9i q^{29} +(4.31822e10 - 4.72604e10i) q^{30} -5.30495e10i q^{31} +(-1.32534e11 + 1.42175e11i) q^{32} +(-6.42975e9 + 2.36312e9i) q^{33} +(-4.30629e11 + 2.23235e11i) q^{34} +1.06937e11 q^{35} +(4.23169e10 + 4.68277e11i) q^{36} +4.06413e11 q^{37} +(-3.33137e11 + 1.72696e11i) q^{38} +(1.12912e12 - 4.14986e11i) q^{39} +(-7.51003e10 + 5.48667e11i) q^{40} +1.36874e12i q^{41} +(-5.29790e11 + 5.79824e11i) q^{42} -2.85013e12i q^{43} +(3.41549e10 - 4.84247e10i) q^{44} +(8.67521e11 + 1.02079e12i) q^{45} +(2.03075e12 + 3.91739e12i) q^{46} +7.27503e11 q^{47} +(-2.60287e12 - 3.12542e12i) q^{48} +3.43558e12 q^{49} +(-1.81628e12 - 3.50367e12i) q^{50} +(-3.50148e12 - 9.52708e12i) q^{51} +(-5.99793e12 + 8.50385e12i) q^{52} -7.05903e12i q^{53} +(-9.83270e12 - 3.53416e11i) q^{54} -1.68835e11i q^{55} +(9.21384e11 - 6.73144e12i) q^{56} +(-2.70876e12 - 7.37020e12i) q^{57} +(7.68164e11 - 3.98212e11i) q^{58} +1.63957e13 q^{59} +(-1.11927e13 - 3.00247e12i) q^{60} +3.06206e13 q^{61} +(-8.52552e12 + 4.41958e12i) q^{62} +(-1.06434e13 - 1.25237e13i) q^{63} +(3.38902e13 + 9.45477e12i) q^{64} +2.96490e13i q^{65} +(9.15440e11 + 8.36445e11i) q^{66} +7.17216e13i q^{67} +(7.17519e13 + 5.06080e13i) q^{68} +(-8.66669e13 + 3.18526e13i) q^{69} +(-8.90900e12 - 1.71857e13i) q^{70} -4.82624e13 q^{71} +(7.17308e13 - 4.58131e13i) q^{72} -9.56538e13 q^{73} +(-3.38585e13 - 6.53141e13i) q^{74} +(7.75139e13 - 2.84886e13i) q^{75} +(5.55077e13 + 3.91506e13i) q^{76} +2.07139e12i q^{77} +(-1.60760e14 - 1.46888e14i) q^{78} +3.27912e14i q^{79} +(9.44324e13 - 3.36405e13i) q^{80} +(3.32041e13 - 2.03196e14i) q^{81} +(2.19969e14 - 1.14031e14i) q^{82} -2.88031e14 q^{83} +(1.37320e14 + 3.68364e13i) q^{84} +2.50166e14 q^{85} +(-4.58041e14 + 2.37446e14i) q^{86} +(6.24600e12 + 1.69946e13i) q^{87} +(-1.06278e13 - 1.45470e12i) q^{88} -2.05245e14i q^{89} +(9.17760e13 - 2.24461e14i) q^{90} -3.63755e14i q^{91} +(4.60376e14 - 6.52720e14i) q^{92} +(-6.93217e13 - 1.88616e14i) q^{93} +(-6.06087e13 - 1.16916e14i) q^{94} +1.93530e14 q^{95} +(-2.85436e14 + 6.78684e14i) q^{96} -5.41919e14 q^{97} +(-2.86220e14 - 5.52128e14i) q^{98} +(-1.97728e13 + 1.68040e13i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 26968 q^{4} + 823656 q^{6} - 3812052 q^{9}+O(q^{10}) \) 28 * q + 26968 * q^4 + 823656 * q^6 - 3812052 * q^9	\( 28 q + 26968 q^{4} + 823656 q^{6} - 3812052 q^{9} - 43831600 q^{10} - 226414248 q^{12} + 124527272 q^{13} - 1459325408 q^{16} - 4234777584 q^{18} - 7261350648 q^{21} - 2533670160 q^{22} - 18487781856 q^{24} - 146804950740 q^{25} + 5481093840 q^{28} + 8237058960 q^{30} + 204574669728 q^{33} + 450165745472 q^{34} + 232631927160 q^{36} + 386069193224 q^{37} + 1945471012160 q^{40} + 1938106219632 q^{42} - 5007113912640 q^{45} + 2270790222432 q^{46} + 5846474725152 q^{48} - 18480860963084 q^{49} - 6113229405424 q^{52} + 1626598700568 q^{54} + 8085872464056 q^{57} - 19395437098192 q^{58} - 10924219377600 q^{60} - 16392792556696 q^{61} + 21633892829056 q^{64} + 4928819126448 q^{66} + 137029869973056 q^{69} + 91772543171040 q^{70} + 66924493142592 q^{72} + 158451626683736 q^{73} - 205265768291280 q^{76} + 58364283489648 q^{78} + 116126816635836 q^{81} - 750029796726880 q^{82} - 92605433207856 q^{84} - 30099357052160 q^{85} - 619691835246912 q^{88} - 471443548913520 q^{90} - 777661615138584 q^{93} + 13\!\cdots\!00 q^{94}+ \cdots - 824166397720648 q^{97}+O(q^{100}) \) 28 * q + 26968 * q^4 + 823656 * q^6 - 3812052 * q^9 - 43831600 * q^10 - 226414248 * q^12 + 124527272 * q^13 - 1459325408 * q^16 - 4234777584 * q^18 - 7261350648 * q^21 - 2533670160 * q^22 - 18487781856 * q^24 - 146804950740 * q^25 + 5481093840 * q^28 + 8237058960 * q^30 + 204574669728 * q^33 + 450165745472 * q^34 + 232631927160 * q^36 + 386069193224 * q^37 + 1945471012160 * q^40 + 1938106219632 * q^42 - 5007113912640 * q^45 + 2270790222432 * q^46 + 5846474725152 * q^48 - 18480860963084 * q^49 - 6113229405424 * q^52 + 1626598700568 * q^54 + 8085872464056 * q^57 - 19395437098192 * q^58 - 10924219377600 * q^60 - 16392792556696 * q^61 + 21633892829056 * q^64 + 4928819126448 * q^66 + 137029869973056 * q^69 + 91772543171040 * q^70 + 66924493142592 * q^72 + 158451626683736 * q^73 - 205265768291280 * q^76 + 58364283489648 * q^78 + 116126816635836 * q^81 - 750029796726880 * q^82 - 92605433207856 * q^84 - 30099357052160 * q^85 - 619691835246912 * q^88 - 471443548913520 * q^90 - 777661615138584 * q^93 + 1301107064491200 * q^94 + 525428335287168 * q^96 - 824166397720648 * q^97

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