LMFDB - Embedded newform 12.14.b.a.11.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [12,14,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, 14, names="a")

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

chi := DirichletCharacter("12.11");

S:= CuspForms(chi, 14);

N := Newforms(S);

Level:	$ N $	$=$	$ 12 = 2^{2} \cdot 3 $
Weight:	$ k $	$=$	$ 14 $
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:	$12.8677114742$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			11.17
Character	$\chi$	$=$	12.11
Dual form			12.14.b.a.11.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(61.4564 - 66.4463i) q^{2} +(-544.543 + 1139.21i) q^{3} +(-638.220 - 8167.10i) q^{4} -30890.7i q^{5} +(42230.6 + 106195. i) q^{6} +363071. i q^{7} +(-581896. - 459513. i) q^{8} +(-1.00127e6 - 1.24070e6i) q^{9} +O(q^{10})$	\(q+(61.4564 - 66.4463i) q^{2} +(-544.543 + 1139.21i) q^{3} +(-638.220 - 8167.10i) q^{4} -30890.7i q^{5} +(42230.6 + 106195. i) q^{6} +363071. i q^{7} +(-581896. - 459513. i) q^{8} +(-1.00127e6 - 1.24070e6i) q^{9} +(-2.05257e6 - 1.89843e6i) q^{10} -7.18745e6 q^{11} +(9.65157e6 + 3.72027e6i) q^{12} -2.72736e7 q^{13} +(2.41247e7 + 2.23130e7i) q^{14} +(3.51910e7 + 1.68213e7i) q^{15} +(-6.62942e7 + 1.04248e7i) q^{16} +9.89337e7i q^{17} +(-1.43974e8 - 9.71804e6i) q^{18} -1.64474e8i q^{19} +(-2.52288e8 + 1.97151e7i) q^{20} +(-4.13613e8 - 1.97707e8i) q^{21} +(-4.41715e8 + 4.77579e8i) q^{22} +1.21830e8 q^{23} +(8.40349e8 - 4.12677e8i) q^{24} +2.66466e8 q^{25} +(-1.67614e9 + 1.81223e9i) q^{26} +(1.95864e9 - 4.65043e8i) q^{27} +(2.96523e9 - 2.31719e8i) q^{28} -3.65709e9i q^{29} +(3.28043e9 - 1.30453e9i) q^{30} -7.81568e7i q^{31} +(-3.38151e9 + 5.04568e9i) q^{32} +(3.91387e9 - 8.18801e9i) q^{33} +(6.57378e9 + 6.08011e9i) q^{34} +1.12155e10 q^{35} +(-9.49386e9 + 8.96931e9i) q^{36} -1.32530e10 q^{37} +(-1.09287e10 - 1.01080e10i) q^{38} +(1.48516e10 - 3.10703e10i) q^{39} +(-1.41947e10 + 1.79752e10i) q^{40} -2.10553e10i q^{41} +(-3.85561e10 + 1.53327e10i) q^{42} +2.36583e10i q^{43} +(4.58718e9 + 5.87006e10i) q^{44} +(-3.83260e10 + 3.09299e10i) q^{45} +(7.48726e9 - 8.09518e9i) q^{46} +5.28535e10 q^{47} +(2.42240e10 - 8.11997e10i) q^{48} -3.49312e10 q^{49} +(1.63760e10 - 1.77057e10i) q^{50} +(-1.12706e11 - 5.38736e10i) q^{51} +(1.74066e10 + 2.22746e11i) q^{52} -5.07603e10i q^{53} +(8.94709e10 - 1.58725e11i) q^{54} +2.22026e11i q^{55} +(1.66836e11 - 2.11269e11i) q^{56} +(1.87370e11 + 8.95632e10i) q^{57} +(-2.43000e11 - 2.24752e11i) q^{58} -4.66129e11 q^{59} +(1.14922e11 - 2.98144e11i) q^{60} +6.04553e11 q^{61} +(-5.19323e9 - 4.80324e9i) q^{62} +(4.50460e11 - 3.63531e11i) q^{63} +(1.27451e11 + 5.34778e11i) q^{64} +8.42501e11i q^{65} +(-3.03530e11 - 7.63268e11i) q^{66} +6.66870e11i q^{67} +(8.08001e11 - 6.31415e10i) q^{68} +(-6.63418e10 + 1.38790e11i) q^{69} +(6.89265e11 - 7.45229e11i) q^{70} -1.30645e12 q^{71} +(1.25189e10 + 1.18205e12i) q^{72} -2.10896e12 q^{73} +(-8.14484e11 + 8.80615e11i) q^{74} +(-1.45102e11 + 3.03560e11i) q^{75} +(-1.34328e12 + 1.04971e11i) q^{76} -2.60955e12i q^{77} +(-1.15178e12 - 2.89631e12i) q^{78} -1.10776e12i q^{79} +(3.22030e11 + 2.04788e12i) q^{80} +(-5.36785e11 + 2.48454e12i) q^{81} +(-1.39904e12 - 1.29398e12i) q^{82} +3.62899e12 q^{83} +(-1.35072e12 + 3.50420e12i) q^{84} +3.05613e12 q^{85} +(1.57200e12 + 1.45395e12i) q^{86} +(4.16619e12 + 1.99144e12i) q^{87} +(4.18235e12 + 3.30273e12i) q^{88} -5.87921e12i q^{89} +(-3.00197e11 + 4.44746e12i) q^{90} -9.90224e12i q^{91} +(-7.77546e10 - 9.95001e11i) q^{92} +(8.90369e10 + 4.25597e10i) q^{93} +(3.24819e12 - 3.51192e12i) q^{94} -5.08073e12 q^{95} +(-3.90670e12 - 6.59984e12i) q^{96} +5.06082e11 q^{97} +(-2.14675e12 + 2.32105e12i) q^{98} +(7.19658e12 + 8.91744e12i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 8376 q^{4} - 135720 q^{6} - 327240 q^{9}+O(q^{10}) $ 24 * q - 8376 * q^4 - 135720 * q^6 - 327240 * q^9	$ 24 q - 8376 q^{4} - 135720 q^{6} - 327240 q^{9} + 4403568 q^{10} - 139896 q^{12} - 17520048 q^{13} + 41046816 q^{16} - 102153744 q^{18} + 340864272 q^{21} + 401914896 q^{22} + 14766624 q^{24} - 3043252488 q^{25} + 3306349488 q^{28} + 3523891248 q^{30} - 10577805696 q^{33} + 5461322688 q^{34} + 16126437096 q^{36} - 29352930672 q^{37} - 5243368896 q^{40} + 35399300688 q^{42} + 36221734656 q^{45} + 1675946784 q^{46} + 27878547744 q^{48} - 165718477944 q^{49} - 6459860112 q^{52} - 10955701656 q^{54} + 590611321584 q^{57} - 440462601456 q^{58} - 208761511104 q^{60} + 555426186192 q^{61} - 741528997248 q^{64} + 263546293968 q^{66} - 122266973952 q^{69} - 885399371232 q^{70} + 625428177984 q^{72} + 365028975600 q^{73} + 1427271642000 q^{76} + 1481181276240 q^{78} - 2327652239400 q^{81} + 874644720480 q^{82} - 6757787638224 q^{84} - 3308476422144 q^{85} + 11607512359104 q^{88} + 4426488729648 q^{90} - 3971016902448 q^{93} - 3078833939904 q^{94} - 6470779487616 q^{96} - 4159752429648 q^{97}+O(q^{100}) $ 24 * q - 8376 * q^4 - 135720 * q^6 - 327240 * q^9 + 4403568 * q^10 - 139896 * q^12 - 17520048 * q^13 + 41046816 * q^16 - 102153744 * q^18 + 340864272 * q^21 + 401914896 * q^22 + 14766624 * q^24 - 3043252488 * q^25 + 3306349488 * q^28 + 3523891248 * q^30 - 10577805696 * q^33 + 5461322688 * q^34 + 16126437096 * q^36 - 29352930672 * q^37 - 5243368896 * q^40 + 35399300688 * q^42 + 36221734656 * q^45 + 1675946784 * q^46 + 27878547744 * q^48 - 165718477944 * q^49 - 6459860112 * q^52 - 10955701656 * q^54 + 590611321584 * q^57 - 440462601456 * q^58 - 208761511104 * q^60 + 555426186192 * q^61 - 741528997248 * q^64 + 263546293968 * q^66 - 122266973952 * q^69 - 885399371232 * q^70 + 625428177984 * q^72 + 365028975600 * q^73 + 1427271642000 * q^76 + 1481181276240 * q^78 - 2327652239400 * q^81 + 874644720480 * q^82 - 6757787638224 * q^84 - 3308476422144 * q^85 + 11607512359104 * q^88 + 4426488729648 * q^90 - 3971016902448 * q^93 - 3078833939904 * q^94 - 6470779487616 * q^96 - 4159752429648 * 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 $

$2$	61.4564	−	66.4463i	0.679004	−	0.734135i
$2$	61.4564	−	66.4463i	0.679004	−	0.734135i
$3$	−544.543	+	1139.21i	−0.431265	+	0.902226i
$3$	−544.543	+	1139.21i	−0.431265	+	0.902226i
$4$	−638.220	−	8167.10i	−0.0779077	−	0.996961i
$5$		−	30890.7i		−	0.884144i	−0.896980	−	0.442072i	$-0.854244\pi$
$5$		−	30890.7i		−	0.884144i	0.896980	−	0.442072i	$-0.145756\pi$
$6$	42230.6	+	106195.i	0.369525	+	0.929221i
$7$			363071.i			1.16642i	0.812323	+	0.583208i	$0.198203\pi$
$7$			363071.i			1.16642i	−0.812323	+	0.583208i	$0.801797\pi$
$8$	−581896.	−	459513.i	−0.784803	−	0.619745i
$9$	−1.00127e6	−	1.24070e6i	−0.628022	−	0.778196i
$10$	−2.05257e6	−	1.89843e6i	−0.649081	−	0.600337i
$11$	−7.18745e6			−1.22327			−0.611635	−	0.791140i	$-0.709488\pi$
$11$	−7.18745e6			−1.22327			−0.611635	+	0.791140i	$0.709488\pi$
$12$	9.65157e6	+	3.72027e6i	0.933082	+	0.359663i
$13$	−2.72736e7			−1.56715			−0.783575	−	0.621297i	$-0.786606\pi$
$13$	−2.72736e7			−1.56715			−0.783575	+	0.621297i	$0.786606\pi$
$14$	2.41247e7	+	2.23130e7i	0.856307	+	0.792001i
$15$	3.51910e7	+	1.68213e7i	0.797698	+	0.381300i
$16$	−6.62942e7	+	1.04248e7i	−0.987861	+	0.155342i
$17$			9.89337e7i			0.994091i	0.867725	+	0.497045i	$0.165582\pi$
$17$			9.89337e7i			0.994091i	−0.867725	+	0.497045i	$0.834418\pi$
$18$	−1.43974e8	−	9.71804e6i	−0.997730	−	0.0673453i
$19$		−	1.64474e8i		−	0.802046i	−0.916068	−	0.401023i	$-0.868655\pi$
$19$		−	1.64474e8i		−	0.802046i	0.916068	−	0.401023i	$-0.131345\pi$
$20$	−2.52288e8	+	1.97151e7i	−0.881457	+	0.0688817i
$21$	−4.13613e8	−	1.97707e8i	−1.05237	−	0.503034i
$22$	−4.41715e8	+	4.77579e8i	−0.830605	+	0.898045i
$23$	1.21830e8			0.171603			0.0858014	−	0.996312i	$-0.472655\pi$
$23$	1.21830e8			0.171603			0.0858014	+	0.996312i	$0.472655\pi$
$24$	8.40349e8	−	4.12677e8i	0.897608	−	0.440795i
$25$	2.66466e8			0.218289
$26$	−1.67614e9	+	1.81223e9i	−1.06410	+	1.15050i
$27$	1.95864e9	−	4.65043e8i	0.972952	−	0.231009i
$28$	2.96523e9	−	2.31719e8i	1.16287	−	0.0908729i
$29$		−	3.65709e9i		−	1.14169i	−0.821057	−	0.570846i	$-0.806615\pi$
$29$		−	3.65709e9i		−	1.14169i	0.821057	−	0.570846i	$-0.193385\pi$
$30$	3.28043e9	−	1.30453e9i	0.821565	−	0.326713i
$31$		−	7.81568e7i		−	0.0158167i	−0.999969	−	0.00790835i	$-0.997483\pi$
$31$		−	7.81568e7i		−	0.0158167i	0.999969	−	0.00790835i	$-0.00251733\pi$
$32$	−3.38151e9	+	5.04568e9i	−0.556719	+	0.830701i
$33$	3.91387e9	−	8.18801e9i	0.527553	−	1.10367i
$34$	6.57378e9	+	6.08011e9i	0.729797	+	0.674991i
$35$	1.12155e10			1.03128
$36$	−9.49386e9	+	8.96931e9i	−0.726903	+	0.686740i
$37$	−1.32530e10			−0.849189			−0.424594	−	0.905384i	$-0.639583\pi$
$37$	−1.32530e10			−0.849189			−0.424594	+	0.905384i	$0.639583\pi$
$38$	−1.09287e10	−	1.01080e10i	−0.588810	−	0.544592i
$39$	1.48516e10	−	3.10703e10i	0.675856	−	1.41392i
$40$	−1.41947e10	+	1.79752e10i	−0.547944	+	0.693879i
$41$		−	2.10553e10i		−	0.692254i	−0.938188	−	0.346127i	$-0.887497\pi$
$41$		−	2.10553e10i		−	0.692254i	0.938188	−	0.346127i	$-0.112503\pi$
$42$	−3.85561e10	+	1.53327e10i	−1.08386	+	0.431020i
$43$			2.36583e10i			0.570739i	0.958418	+	0.285370i	$0.0921164\pi$
$43$			2.36583e10i			0.570739i	−0.958418	+	0.285370i	$0.907884\pi$
$44$	4.58718e9	+	5.87006e10i	0.0953022	+	1.21955i
$45$	−3.83260e10	+	3.09299e10i	−0.688037	+	0.555262i
$46$	7.48726e9	−	8.09518e9i	0.116519	−	0.125980i
$47$	5.28535e10			0.715217			0.357608	−	0.933872i	$-0.383592\pi$
$47$	5.28535e10			0.715217			0.357608	+	0.933872i	$0.383592\pi$
$48$	2.42240e10	−	8.11997e10i	0.285876	−	0.958267i
$49$	−3.49312e10			−0.360528
$50$	1.63760e10	−	1.77057e10i	0.148219	−	0.160253i
$51$	−1.12706e11	−	5.38736e10i	−0.896894	−	0.428716i
$52$	1.74066e10	+	2.22746e11i	0.122093	+	1.56239i
$53$		−	5.07603e10i		−	0.314580i	−0.987552	−	0.157290i	$-0.949724\pi$
$53$		−	5.07603e10i		−	0.314580i	0.987552	−	0.157290i	$-0.0502758\pi$
$54$	8.94709e10	−	1.58725e11i	0.491046	−	0.871134i
$55$			2.22026e11i			1.08155i
$56$	1.66836e11	−	2.11269e11i	0.722881	−	0.915407i
$57$	1.87370e11	+	8.95632e10i	0.723626	+	0.345894i
$58$	−2.43000e11	−	2.24752e11i	−0.838155	−	0.775213i
$59$	−4.66129e11			−1.43869			−0.719346	−	0.694652i	$-0.755558\pi$
$59$	−4.66129e11			−1.43869			−0.719346	+	0.694652i	$0.755558\pi$
$60$	1.14922e11	−	2.98144e11i	0.317994	−	0.824979i
$61$	6.04553e11			1.50242			0.751209	−	0.660065i	$-0.229471\pi$
$61$	6.04553e11			1.50242			0.751209	+	0.660065i	$0.229471\pi$
$62$	−5.19323e9	−	4.80324e9i	−0.0116116	−	0.0107396i
$63$	4.50460e11	−	3.63531e11i	0.907701	−	0.732535i
$64$	1.27451e11	+	5.34778e11i	0.231832	+	0.972756i
$65$			8.42501e11i			1.38559i
$66$	−3.03530e11	−	7.63268e11i	−0.452029	−	1.13669i
$67$			6.66870e11i			0.900648i	0.892865	+	0.450324i	$0.148691\pi$
$67$			6.66870e11i			0.900648i	−0.892865	+	0.450324i	$0.851309\pi$
$68$	8.08001e11	−	6.31415e10i	0.991069	−	0.0774474i
$69$	−6.63418e10	+	1.38790e11i	−0.0740063	+	0.154825i
$70$	6.89265e11	−	7.45229e11i	0.700243	−	0.757099i
$71$	−1.30645e12			−1.21036			−0.605180	−	0.796089i	$-0.706899\pi$
$71$	−1.30645e12			−1.21036			−0.605180	+	0.796089i	$0.706899\pi$
$72$	1.25189e10	+	1.18205e12i	0.0105902	+	0.999944i
$73$	−2.10896e12			−1.63106			−0.815531	−	0.578714i	$-0.803555\pi$
$73$	−2.10896e12			−1.63106			−0.815531	+	0.578714i	$0.803555\pi$
$74$	−8.14484e11	+	8.80615e11i	−0.576602	+	0.623419i
$75$	−1.45102e11	+	3.03560e11i	−0.0941403	+	0.196946i
$76$	−1.34328e12	+	1.04971e11i	−0.799608	+	0.0624856i
$77$		−	2.60955e12i		−	1.42684i
$78$	−1.15178e12	−	2.89631e12i	−0.579101	−	1.45623i
$79$		−	1.10776e12i		−	0.512708i	−0.966583	−	0.256354i	$-0.917479\pi$
$79$		−	1.10776e12i		−	0.512708i	0.966583	−	0.256354i	$-0.0825213\pi$
$80$	3.22030e11	+	2.04788e12i	0.137345	+	0.873411i
$81$	−5.36785e11	+	2.48454e12i	−0.211177	+	0.977448i
$82$	−1.39904e12	−	1.29398e12i	−0.508208	−	0.470043i
$83$	3.62899e12			1.21837			0.609183	−	0.793030i	$-0.291498\pi$
$83$	3.62899e12			1.21837			0.609183	+	0.793030i	$0.291498\pi$
$84$	−1.35072e12	+	3.50420e12i	−0.419517	+	1.08836i
$85$	3.05613e12			0.878920
$86$	1.57200e12	+	1.45395e12i	0.419000	+	0.387534i
$87$	4.16619e12	+	1.99144e12i	1.03006	+	0.492371i
$88$	4.18235e12	+	3.30273e12i	0.960026	+	0.758116i
$89$		−	5.87921e12i		−	1.25396i	−0.779035	−	0.626981i	$-0.784291\pi$
$89$		−	5.87921e12i		−	1.25396i	0.779035	−	0.626981i	$-0.215709\pi$
$90$	−3.00197e11	+	4.44746e12i	−0.0595430	+	0.882137i
$91$		−	9.90224e12i		−	1.82795i
$92$	−7.77546e10	−	9.95001e11i	−0.0133692	−	0.171081i
$93$	8.90369e10	+	4.25597e10i	0.0142702	+	0.00682118i
$94$	3.24819e12	−	3.51192e12i	0.485635	−	0.525066i
$95$	−5.08073e12			−0.709124
$96$	−3.90670e12	−	6.59984e12i	−0.509386	−	0.860538i
$97$	5.06082e11			0.0616886			0.0308443	−	0.999524i	$-0.490180\pi$
$97$	5.06082e11			0.0616886			0.0308443	+	0.999524i	$0.490180\pi$
$98$	−2.14675e12	+	2.32105e12i	−0.244800	+	0.264676i
$99$	7.19658e12	+	8.91744e12i	0.768240	+	0.951944i
$100$	−1.70064e11	−	2.17625e12i	−0.0170064	−	0.217625i
$101$		−	1.36755e13i		−	1.28190i	−0.767583	−	0.640949i	$-0.778541\pi$
$101$		−	1.36755e13i		−	1.28190i	0.767583	−	0.640949i	$-0.221459\pi$
$102$	−1.05062e13	+	4.17802e12i	−0.923730	+	0.367341i
$103$			8.73087e12i			0.720470i	0.932862	+	0.360235i	$0.117303\pi$
$103$			8.73087e12i			0.720470i	−0.932862	+	0.360235i	$0.882697\pi$
$104$	1.58704e13	+	1.25326e13i	1.22990	+	0.971234i
$105$	−6.10733e12	+	1.27768e13i	−0.444755	+	0.930448i
$106$	−3.37284e12	−	3.11955e12i	−0.230944	−	0.213601i
$107$	−1.86040e13			−1.19843			−0.599213	−	0.800589i	$-0.704520\pi$
$107$	−1.86040e13			−1.19843			−0.599213	+	0.800589i	$0.704520\pi$
$108$	−5.04810e12	−	1.56997e13i	−0.306107	−	0.951997i
$109$	−1.31651e13			−0.751888			−0.375944	−	0.926642i	$-0.622682\pi$
$109$	−1.31651e13			−0.751888			−0.375944	+	0.926642i	$0.622682\pi$
$110$	1.47528e13	+	1.36449e13i	0.794002	+	0.734375i
$111$	7.21685e12	−	1.50980e13i	0.366225	−	0.766160i
$112$	−3.78494e12	−	2.40695e13i	−0.181193	−	1.15226i
$113$			2.89611e13i			1.30859i	0.756237	+	0.654297i	$0.227036\pi$
$113$			2.89611e13i			1.30859i	−0.756237	+	0.654297i	$0.772964\pi$
$114$	1.74663e13	−	6.94583e12i	0.745278	−	0.296376i
$115$		−	3.76343e12i		−	0.151722i
$116$	−2.98678e13	+	2.33403e12i	−1.13822	+	0.0889466i
$117$	2.73082e13	+	3.38382e13i	0.984204	+	1.21955i
$118$	−2.86466e13	+	3.09725e13i	−0.976877	+	1.05619i
$119$	−3.59199e13			−1.15952
$120$	−1.27479e13	−	2.59590e13i	−0.389727	−	0.793615i
$121$	1.71367e13			0.496390
$122$	3.71537e13	−	4.01703e13i	1.02015	−	1.10298i
$123$	2.39863e13	+	1.14655e13i	0.624569	+	0.298545i
$124$	−6.38315e11	+	4.98813e10i	−0.0157686	+	0.00123224i
$125$		−	4.59397e13i		−	1.07714i
$126$	3.52833e12	−	5.22727e13i	0.0785527	−	1.16377i
$127$			6.03054e13i			1.27536i	0.770303	+	0.637678i	$0.220105\pi$
$127$			6.03054e13i			1.27536i	−0.770303	+	0.637678i	$0.779895\pi$
$128$	4.33667e13	+	2.43969e13i	0.871549	+	0.490309i
$129$	−2.69517e13	−	1.28829e13i	−0.514936	−	0.246140i
$130$	5.59811e13	+	5.17771e13i	1.01721	+	0.940819i
$131$	−4.70998e13			−0.814247			−0.407123	−	0.913373i	$-0.633468\pi$
$131$	−4.70998e13			−0.814247			−0.407123	+	0.913373i	$0.633468\pi$
$132$	−6.93702e13	−	2.67393e13i	−1.14141	−	0.439966i
$133$	5.97157e13			0.935520
$134$	4.43110e13	+	4.09834e13i	0.661197	+	0.611543i
$135$	−1.43655e13	−	6.05040e13i	−0.204245	−	0.860230i
$136$	4.54613e13	−	5.75691e13i	0.616083	−	0.780166i
$137$		−	5.14878e13i		−	0.665305i	−0.943049	−	0.332652i	$-0.892056\pi$
$137$		−	5.14878e13i		−	0.665305i	0.943049	−	0.332652i	$-0.107944\pi$
$138$	5.14496e12	+	1.29377e13i	0.0634115	+	0.159457i
$139$		−	1.48399e13i		−	0.174515i	−0.996186	−	0.0872576i	$-0.972190\pi$
$139$		−	1.48399e13i		−	0.174515i	0.996186	−	0.0872576i	$-0.0278103\pi$
$140$	−7.15797e12	−	9.15982e13i	−0.0803447	−	1.02815i
$141$	−2.87810e13	+	6.02112e13i	−0.308448	+	0.645287i
$142$	−8.02899e13	+	8.68089e13i	−0.821839	+	0.888567i
$143$	1.96028e14			1.91705
$144$	7.93124e13	+	7.18129e13i	0.741284	+	0.671191i
$145$	−1.12970e14			−1.00942
$146$	−1.29609e14	+	1.40133e14i	−1.10750	+	1.19742i
$147$	1.90215e13	−	3.97939e13i	0.155483	−	0.325277i
$148$	8.45836e12	+	1.08239e14i	0.0661584	+	0.846608i
$149$		−	3.46081e13i		−	0.259100i	−0.991573	−	0.129550i	$-0.958647\pi$
$149$		−	3.46081e13i		−	0.259100i	0.991573	−	0.129550i	$-0.0413533\pi$
$150$	1.12530e13	+	2.82972e13i	0.0806632	+	0.202839i
$151$		−	2.82435e13i		−	0.193896i	−0.995289	−	0.0969479i	$-0.969092\pi$
$151$		−	2.82435e13i		−	0.193896i	0.995289	−	0.0969479i	$-0.0309080\pi$
$152$	−7.55781e13	+	9.57069e13i	−0.497064	+	0.629448i
$153$	1.22747e14	−	9.90593e13i	0.773597	−	0.624311i
$154$	−1.73395e14	−	1.60374e14i	−1.04750	−	0.968832i
$155$	−2.41432e12			−0.0139842
$156$	−2.63233e14	−	1.01465e14i	−1.46228	−	0.563647i
$157$	−2.29032e14			−1.22053			−0.610265	−	0.792197i	$-0.708937\pi$
$157$	−2.29032e14			−1.22053			−0.610265	+	0.792197i	$0.708937\pi$
$158$	−7.36066e13	−	6.80790e13i	−0.376397	−	0.348131i
$159$	5.78266e13	+	2.76412e13i	0.283822	+	0.135667i
$160$	1.55865e14	+	1.04457e14i	0.734459	+	0.492220i
$161$			4.42330e13i			0.200160i
$162$	1.32100e14	+	1.88358e14i	0.574188	+	0.818723i
$163$		−	1.03460e14i		−	0.432069i	−0.976386	−	0.216034i	$-0.930688\pi$
$163$		−	1.03460e14i		−	0.432069i	0.976386	−	0.216034i	$-0.0693124\pi$
$164$	−1.71960e14	+	1.34379e13i	−0.690150	+	0.0539319i
$165$	−2.52933e14	−	1.20902e14i	−0.975800	−	0.466433i
$166$	2.23024e14	−	2.41133e14i	0.827275	−	0.894444i
$167$	−9.70710e13			−0.346284			−0.173142	−	0.984897i	$-0.555392\pi$
$167$	−9.70710e13			−0.346284			−0.173142	+	0.984897i	$0.555392\pi$
$168$	1.49831e14	+	3.05106e14i	0.514151	+	1.04698i
$169$	4.40974e14			1.45596
$170$	1.87819e14	−	2.03069e14i	0.596790	−	0.645246i
$171$	−2.04062e14	+	1.64683e14i	−0.624149	+	0.503702i
$172$	1.93219e14	−	1.50992e13i	0.569005	−	0.0444650i
$173$			5.06532e14i			1.43650i	0.695783	+	0.718252i	$0.255057\pi$
$173$			5.06532e14i			1.43650i	−0.695783	+	0.718252i	$0.744943\pi$
$174$	3.88363e14	−	1.54441e14i	1.06088	−	0.421883i
$175$			9.67459e13i			0.254616i
$176$	4.76486e14	−	7.49279e13i	1.20842	−	0.190025i
$177$	2.53827e14	−	5.31018e14i	0.620457	−	1.29802i
$178$	−3.90652e14	−	3.61315e14i	−0.920577	−	0.851444i
$179$	1.37702e14			0.312893			0.156447	−	0.987686i	$-0.449996\pi$
$179$	1.37702e14			0.312893			0.156447	+	0.987686i	$0.449996\pi$
$180$	2.77068e14	+	2.93272e14i	0.607178	+	0.642687i
$181$	3.48684e14			0.737091			0.368546	−	0.929610i	$-0.379856\pi$
$181$	3.48684e14			0.737091			0.368546	+	0.929610i	$0.379856\pi$
$182$	−6.57967e14	−	6.08556e14i	−1.34196	−	1.24118i
$183$	−3.29205e14	+	6.88712e14i	−0.647939	+	1.35552i
$184$	−7.08926e13	−	5.59827e13i	−0.134674	−	0.106350i
$185$			4.09396e14i			0.750805i
$186$	8.29983e12	−	3.30061e12i	0.0146972	−	0.00584466i
$187$		−	7.11081e14i		−	1.21604i
$188$	−3.37322e13	−	4.31660e14i	−0.0557209	−	0.713043i
$189$	1.68843e14	+	7.11126e14i	0.269453	+	1.13487i
$190$	−3.12243e14	+	3.37595e14i	−0.481498	+	0.520593i
$191$	−5.90056e13			−0.0879380			−0.0439690	−	0.999033i	$-0.514000\pi$
$191$	−5.90056e13			−0.0879380			−0.0439690	+	0.999033i	$0.514000\pi$
$192$	−6.78626e14	−	1.46017e14i	−0.977626	−	0.210351i
$193$	−4.59234e14			−0.639605			−0.319802	−	0.947484i	$-0.603616\pi$
$193$	−4.59234e14			−0.639605			−0.319802	+	0.947484i	$0.603616\pi$
$194$	3.11020e13	−	3.36273e13i	0.0418868	−	0.0452877i
$195$	−9.59785e14	−	4.58778e14i	−1.25011	−	0.597554i
$196$	2.22938e13	+	2.85287e14i	0.0280879	+	0.359432i
$197$		−	1.39793e14i		−	0.170395i	−0.996364	−	0.0851973i	$-0.972848\pi$
$197$		−	1.39793e14i		−	0.170395i	0.996364	−	0.0851973i	$-0.0271521\pi$
$198$	1.03481e15	+	6.98479e13i	1.22049	+	0.0823815i
$199$			5.61318e14i			0.640714i	0.947297	+	0.320357i	$0.103803\pi$
$199$			5.61318e14i			0.640714i	−0.947297	+	0.320357i	$0.896197\pi$
$200$	−1.55056e14	−	1.22445e14i	−0.171314	−	0.135284i
$201$	−7.59704e14	−	3.63139e14i	−0.812587	−	0.388417i
$202$	−9.08685e14	−	8.40446e14i	−0.941086	−	0.870414i
$203$	1.32778e15			1.33169
$204$	−3.68060e14	+	9.54865e14i	−0.357538	+	0.927568i
$205$	−6.50412e14			−0.612052
$206$	5.80134e14	+	5.36568e14i	0.528922	+	0.489202i
$207$	−1.21985e14	−	1.51154e14i	−0.107770	−	0.133541i
$208$	1.80808e15	−	2.84322e14i	1.54813	−	0.243444i
$209$			1.18215e15i			0.981119i
$210$	4.73637e14	+	1.19103e15i	0.381084	+	0.958287i
$211$			1.06970e15i			0.834496i	0.908793	+	0.417248i	$0.137005\pi$
$211$			1.06970e15i			0.834496i	−0.908793	+	0.417248i	$0.862995\pi$
$212$	−4.14565e14	+	3.23963e13i	−0.313624	+	0.0245082i
$213$	7.11419e14	−	1.48832e15i	0.521985	−	1.09202i
$214$	−1.14333e15	+	1.23617e15i	−0.813736	+	0.879807i
$215$	7.30821e14			0.504616
$216$	−1.35342e15	−	6.29417e14i	−0.906742	−	0.421686i
$217$	2.83764e13			0.0184489
$218$	−8.09082e14	+	8.74775e14i	−0.510535	+	0.551987i
$219$	1.14842e15	−	2.40255e15i	0.703419	−	1.47158i
$220$	1.81331e15	−	1.41701e14i	1.07826	−	0.0842609i
$221$		−	2.69828e15i		−	1.55789i
$222$	−5.59683e14	−	1.40740e15i	−0.313796	−	0.789084i
$223$		−	1.01353e14i		−	0.0551894i	−0.999619	−	0.0275947i	$-0.991215\pi$
$223$		−	1.01353e14i		−	0.0551894i	0.999619	−	0.0275947i	$-0.00878478\pi$
$224$	−1.83194e15	−	1.22773e15i	−0.968943	−	0.649367i
$225$	−2.66804e14	−	3.30603e14i	−0.137090	−	0.169872i
$226$	1.92436e15	+	1.77985e15i	0.960685	+	0.888541i
$227$	−2.94873e15			−1.43043			−0.715215	−	0.698904i	$-0.753671\pi$
$227$	−2.94873e15			−1.43043			−0.715215	+	0.698904i	$0.753671\pi$
$228$	6.11888e14	−	1.58743e15i	0.288467	−	0.748375i
$229$	1.06392e15			0.487506			0.243753	−	0.969837i	$-0.421621\pi$
$229$	1.06392e15			0.487506			0.243753	+	0.969837i	$0.421621\pi$
$230$	−2.50066e14	−	2.31287e14i	−0.111384	−	0.103020i
$231$	2.97282e15	+	1.42101e15i	1.28733	+	0.615347i
$232$	−1.68048e15	+	2.12805e15i	−0.707558	+	0.896003i
$233$			1.33954e14i			0.0548458i	0.999624	+	0.0274229i	$0.00873007\pi$
$233$			1.33954e14i			0.0548458i	−0.999624	+	0.0274229i	$0.991270\pi$
$234$	3.92669e15	+	2.65046e14i	1.56359	+	0.105540i
$235$		−	1.63268e15i		−	0.632355i
$236$	2.97493e14	+	3.80692e15i	0.112085	+	1.43432i
$237$	1.26197e15	+	6.03223e14i	0.462578	+	0.221113i
$238$	−2.20751e15	+	2.38674e15i	−0.787321	+	0.851247i
$239$	4.59655e15			1.59531			0.797657	−	0.603112i	$-0.206073\pi$
$239$	4.59655e15			1.59531			0.797657	+	0.603112i	$0.206073\pi$
$240$	−2.50832e15	−	7.48297e14i	−0.847246	−	0.252756i
$241$	−2.61239e14			−0.0858869			−0.0429434	−	0.999078i	$-0.513674\pi$
$241$	−2.61239e14			−0.0858869			−0.0429434	+	0.999078i	$0.513674\pi$
$242$	1.05316e15	−	1.13867e15i	0.337051	−	0.364417i
$243$	−2.53811e15	−	1.96445e15i	−0.790805	−	0.612068i
$244$	−3.85838e14	−	4.93745e15i	−0.117050	−	1.49785i
$245$			1.07905e15i			0.318759i
$246$	2.23595e15	−	8.89175e14i	0.643257	−	0.255805i
$247$			4.48580e15i			1.25693i
$248$	−3.59141e13	+	4.54792e13i	−0.00980233	+	0.0124130i
$249$	−1.97614e15	+	4.13417e15i	−0.525438	+	1.09924i
$250$	−3.05253e15	−	2.82329e15i	−0.790768	−	0.731384i
$251$	−6.38089e15			−1.61065			−0.805326	−	0.592832i	$-0.798010\pi$
$251$	−6.38089e15			−1.61065			−0.805326	+	0.592832i	$0.798010\pi$
$252$	−3.25649e15	−	3.44694e15i	−0.801025	−	0.847872i
$253$	−8.75650e14			−0.209917
$254$	4.00707e15	+	3.70615e15i	0.936284	+	0.865972i
$255$	−1.66419e15	+	3.48157e15i	−0.379047	+	0.792984i
$256$	4.28625e15	−	1.38221e15i	0.951738	−	0.306912i
$257$		−	3.61091e15i		−	0.781720i	−0.920450	−	0.390860i	$-0.872178\pi$
$257$		−	3.61091e15i		−	0.781720i	0.920450	−	0.390860i	$-0.127822\pi$
$258$	−2.51238e15	+	9.99101e14i	−0.530343	+	0.210902i
$259$		−	4.81179e15i		−	0.990508i
$260$	6.88079e15	−	5.37701e14i	1.38138	−	0.107948i
$261$	−4.53734e15	+	3.66173e15i	−0.888459	+	0.717007i
$262$	−2.89459e15	+	3.12961e15i	−0.552877	+	0.597767i
$263$	−6.62030e15			−1.23357			−0.616787	−	0.787130i	$-0.711566\pi$
$263$	−6.62030e15			−1.23357			−0.616787	+	0.787130i	$0.711566\pi$
$264$	−6.03997e15	+	2.96609e15i	−1.09802	+	0.539212i
$265$	−1.56802e15			−0.278134
$266$	3.66991e15	−	3.96789e15i	0.635222	−	0.686798i
$267$	6.69765e15	+	3.20148e15i	1.13136	+	0.540789i
$268$	5.44639e15	−	4.25610e14i	0.897910	−	0.0701674i
$269$			1.71081e15i			0.275303i	0.990481	+	0.137651i	$0.0439554\pi$
$269$			1.71081e15i			0.275303i	−0.990481	+	0.137651i	$0.956045\pi$
$270$	−4.90312e15	−	2.76382e15i	−0.770208	−	0.434156i
$271$			4.02363e15i			0.617046i	0.951217	+	0.308523i	$0.0998347\pi$
$271$			4.02363e15i			0.617046i	−0.951217	+	0.308523i	$0.900165\pi$
$272$	−1.03137e15	−	6.55873e15i	−0.154424	−	0.982023i
$273$	1.12807e16	+	5.39219e15i	1.64922	+	0.788330i
$274$	−3.42117e15	−	3.16426e15i	−0.488423	−	0.451745i
$275$	−1.91521e15			−0.267026
$276$	1.17585e15	+	4.53242e14i	0.160120	+	0.0617193i
$277$	7.58307e15			1.00862			0.504309	−	0.863523i	$-0.331747\pi$
$277$	7.58307e15			1.00862			0.504309	+	0.863523i	$0.331747\pi$
$278$	−9.86053e14	−	9.12004e14i	−0.128118	−	0.118497i
$279$	−9.69688e13	+	7.82560e13i	−0.0123085	+	0.00993323i
$280$	−6.52627e15	−	5.15368e15i	−0.809352	−	0.639131i
$281$		−	2.70668e15i		−	0.327979i	−0.986462	−	0.163989i	$-0.947564\pi$
$281$		−	2.70668e15i		−	0.327979i	0.986462	−	0.163989i	$-0.0524363\pi$
$282$	2.23203e15	+	5.61275e15i	0.264290	+	0.664594i
$283$		−	1.44508e16i		−	1.67217i	−0.548603	−	0.836083i	$-0.684840\pi$
$283$		−	1.44508e16i		−	1.67217i	0.548603	−	0.836083i	$-0.315160\pi$
$284$	8.33804e14	+	1.06699e16i	0.0942964	+	1.20668i
$285$	2.76667e15	−	5.78801e15i	0.305820	−	0.639790i
$286$	1.20472e16	−	1.30253e16i	1.30168	−	1.40737i
$287$	7.64454e15			0.807457
$288$	9.64595e15	−	8.56653e14i	0.996080	−	0.0884614i
$289$	1.16708e14			0.0117833
$290$	−6.94274e15	+	7.50645e15i	−0.685400	+	0.741050i
$291$	−2.75583e14	+	5.76533e14i	−0.0266041	+	0.0556570i
$292$	1.34598e15	+	1.72241e16i	0.127072	+	1.62610i
$293$		−	6.28931e15i		−	0.580716i	−0.956918	−	0.290358i	$-0.906226\pi$
$293$		−	6.28931e15i		−	0.580716i	0.956918	−	0.290358i	$-0.0937744\pi$
$294$	−1.47516e15	−	3.70950e15i	−0.133224	−	0.335010i
$295$			1.43991e16i			1.27201i
$296$	7.71189e15	+	6.08995e15i	0.666446	+	0.526281i
$297$	−1.40777e16	+	3.34247e15i	−1.19018	+	0.282586i
$298$	−2.29958e15	−	2.12689e15i	−0.190214	−	0.175930i
$299$	−3.32275e15			−0.268927
$300$	2.57181e15	+	9.91325e14i	0.203681	+	0.0785105i
$301$	−8.58962e15			−0.665720
$302$	−1.87668e15	−	1.73574e15i	−0.142346	−	0.131656i
$303$	1.55792e16	+	7.44688e15i	1.15656	+	0.552837i
$304$	1.71461e15	+	1.09037e16i	0.124591	+	0.792310i
$305$		−	1.86751e16i		−	1.32835i
$306$	9.61441e14	−	1.42439e16i	0.0669474	−	0.991834i
$307$		−	2.56760e16i		−	1.75036i	−0.483798	−	0.875180i	$-0.660743\pi$
$307$		−	2.56760e16i		−	1.75036i	0.483798	−	0.875180i	$-0.339257\pi$
$308$	−2.13125e16	+	1.66547e15i	−1.42251	+	0.111162i
$309$	−9.94629e15	−	4.75433e15i	−0.650026	−	0.310713i
$310$	−1.48376e14	+	1.60423e14i	−0.00949536	+	0.0102663i
$311$	−5.68930e14			−0.0356547			−0.0178273	−	0.999841i	$-0.505675\pi$
$311$	−5.68930e14			−0.0356547			−0.0178273	+	0.999841i	$0.505675\pi$
$312$	−2.29193e16	+	1.12552e16i	−1.40669	+	0.690792i
$313$	−5.74834e15			−0.345544			−0.172772	−	0.984962i	$-0.555272\pi$
$313$	−5.74834e15			−0.345544			−0.172772	+	0.984962i	$0.555272\pi$
$314$	−1.40755e16	+	1.52183e16i	−0.828745	+	0.896034i
$315$	−1.12298e16	−	1.39150e16i	−0.647667	−	0.802538i
$316$	−9.04720e15	+	7.06995e14i	−0.511150	+	0.0399439i
$317$			2.63733e16i			1.45975i	0.683578	+	0.729877i	$0.260423\pi$
$317$			2.63733e16i			1.45975i	−0.683578	+	0.729877i	$0.739577\pi$
$318$	5.39047e15	−	2.14364e15i	0.292314	−	0.116245i
$319$			2.62852e16i			1.39660i
$320$	1.65197e16	−	3.93705e15i	0.860057	−	0.204973i
$321$	1.01307e16	−	2.11938e16i	0.516839	−	1.08125i
$322$	2.93912e15	+	2.71840e15i	0.146945	+	0.135910i
$323$	1.62720e16			0.797307
$324$	2.06341e16	+	2.79829e15i	0.990929	+	0.134385i
$325$	−7.26748e15			−0.342091
$326$	−6.87453e15	−	6.35828e15i	−0.317197	−	0.293376i
$327$	7.16898e15	−	1.49978e16i	0.324263	−	0.678373i
$328$	−9.67517e15	+	1.22520e16i	−0.429021	+	0.543283i
$329$			1.91895e16i			0.834241i
$330$	−2.35779e16	+	9.37626e15i	−1.00500	+	0.399659i
$331$			3.01078e15i			0.125834i	0.998019	+	0.0629169i	$0.0200403\pi$
$331$			3.01078e15i			0.125834i	−0.998019	+	0.0629169i	$0.979960\pi$
$332$	−2.31609e15	−	2.96383e16i	−0.0949201	−	1.21466i
$333$	1.32699e16	+	1.64430e16i	0.533309	+	0.660835i
$334$	−5.96564e15	+	6.45001e15i	−0.235128	+	0.254219i
$335$	2.06001e16			0.796303
$336$	2.94812e16	+	8.79502e15i	1.11774	+	0.333451i
$337$	3.50625e16			1.30391			0.651957	−	0.758256i	$-0.273948\pi$
$337$	3.50625e16			1.30391			0.651957	+	0.758256i	$0.273948\pi$
$338$	2.71007e16	−	2.93011e16i	0.988602	−	1.06887i
$339$	−3.29927e16	−	1.57706e16i	−1.18065	−	0.564351i
$340$	−1.95049e15	−	2.49597e16i	−0.0684746	−	0.876248i
$341$			5.61748e14i			0.0193481i
$342$	−1.59837e15	+	2.36800e16i	−0.0540140	+	0.800225i
$343$			2.24951e16i			0.745891i
$344$	1.08713e16	−	1.37667e16i	0.353713	−	0.447918i
$345$	4.28733e15	+	2.04935e15i	0.136887	+	0.0654322i
$346$	3.36571e16	+	3.11296e16i	1.05459	+	0.975392i
$347$	−2.88211e16			−0.886275			−0.443138	−	0.896454i	$-0.646135\pi$
$347$	−2.88211e16			−0.886275			−0.443138	+	0.896454i	$0.646135\pi$
$348$	1.36054e16	−	3.52967e16i	0.410625	−	1.06529i
$349$	−2.70842e16			−0.802326			−0.401163	−	0.916007i	$-0.631394\pi$
$349$	−2.70842e16			−0.802326			−0.401163	+	0.916007i	$0.631394\pi$
$350$	6.42841e15	+	5.94566e15i	0.186922	+	0.172885i
$351$	−5.34193e16	+	1.26834e16i	−1.52476	+	0.362026i
$352$	2.43045e16	−	3.62656e16i	0.681018	−	1.01617i
$353$		−	2.12568e16i		−	0.584740i	−0.956305	−	0.292370i	$-0.905556\pi$
$353$		−	2.12568e16i		−	0.584740i	0.956305	−	0.292370i	$-0.0944438\pi$
$354$	−1.96849e16	−	4.95003e16i	−0.531632	−	1.33686i
$355$			4.03573e16i			1.07013i
$356$	−4.80161e16	+	3.75223e15i	−1.25015	+	0.0976933i
$357$	1.95599e16	−	4.09203e16i	0.500062	−	1.04615i
$358$	8.46268e15	−	9.14980e15i	0.212456	−	0.229706i
$359$	1.20413e16			0.296866			0.148433	−	0.988922i	$-0.452577\pi$
$359$	1.20413e16			0.296866			0.148433	+	0.988922i	$0.452577\pi$
$360$	3.65145e16	−	3.86718e14i	0.884095	−	0.00936329i
$361$	1.50012e16			0.356722
$362$	2.14289e16	−	2.31688e16i	0.500488	−	0.541124i
$363$	−9.33169e15	+	1.95223e16i	−0.214076	+	0.447856i
$364$	−8.08726e16	+	6.31981e15i	−1.82239	+	0.142411i
$365$			6.51474e16i			1.44209i
$366$	2.55306e16	+	6.42002e16i	0.555181	+	1.39608i
$367$		−	3.89048e16i		−	0.831140i	−0.909561	−	0.415570i	$-0.863582\pi$
$367$		−	3.89048e16i		−	0.831140i	0.909561	−	0.415570i	$-0.136418\pi$
$368$	−8.07665e15	+	1.27006e15i	−0.169520	+	0.0266571i
$369$	−2.61232e16	+	2.10820e16i	−0.538709	+	0.434751i
$370$	2.72029e16	+	2.51600e16i	0.551192	+	0.509800i
$371$	1.84296e16			0.366932
$372$	2.90764e14	−	7.54336e14i	0.00568869	−	0.0147583i
$373$	4.58954e16			0.882393			0.441196	−	0.897411i	$-0.354554\pi$
$373$	4.58954e16			0.882393			0.441196	+	0.897411i	$0.354554\pi$
$374$	−4.72487e16	−	4.37005e16i	−0.892739	−	0.825697i
$375$	5.23349e16	+	2.50161e16i	0.971826	+	0.464534i
$376$	−3.07553e16	−	2.42869e16i	−0.561304	−	0.443252i
$377$			9.97420e16i			1.78920i
$378$	5.76282e16	+	3.24842e16i	1.01610	+	0.572764i
$379$		−	9.69561e16i		−	1.68043i	−0.542254	−	0.840214i	$-0.682429\pi$
$379$		−	9.69561e16i		−	1.68043i	0.542254	−	0.840214i	$-0.317571\pi$
$380$	3.24262e15	+	4.14948e16i	0.0552463	+	0.706969i
$381$	−6.87004e16	−	3.28388e16i	−1.15066	−	0.550016i
$382$	−3.62627e15	+	3.92071e15i	−0.0597102	+	0.0645583i
$383$	7.96675e15			0.128970			0.0644851	−	0.997919i	$-0.479460\pi$
$383$	7.96675e15			0.128970			0.0644851	+	0.997919i	$0.479460\pi$
$384$	−5.14082e16	+	3.61186e16i	−0.818238	+	0.574880i
$385$	−8.06110e16			−1.26154
$386$	−2.82229e16	+	3.05144e16i	−0.434294	+	0.469556i
$387$	2.93527e16	−	2.36883e16i	0.444147	−	0.358437i
$388$	−3.22992e14	−	4.13322e15i	−0.00480601	−	0.0615011i
$389$		−	9.84348e16i		−	1.44038i	−0.693778	−	0.720188i	$-0.744055\pi$
$389$		−	9.84348e16i		−	1.44038i	0.693778	−	0.720188i	$-0.255945\pi$
$390$	−8.94690e16	+	3.55793e16i	−1.28752	+	0.512009i
$391$			1.20531e16i			0.170589i
$392$	2.03263e16	+	1.60513e16i	0.282943	+	0.223435i
$393$	2.56479e16	−	5.36565e16i	0.351156	−	0.734634i
$394$	−9.28875e15	−	8.59119e15i	−0.125093	−	0.115699i
$395$	−3.42196e16			−0.453308
$396$	6.82366e16	−	6.44664e16i	0.889199	−	0.840069i
$397$	3.68868e16			0.472861			0.236430	−	0.971648i	$-0.424023\pi$
$397$	3.68868e16			0.472861			0.236430	+	0.971648i	$0.424023\pi$
$398$	3.72975e16	+	3.44966e16i	0.470370	+	0.435047i
$399$	−3.25178e16	+	6.80287e16i	−0.403457	+	0.844050i
$400$	−1.76652e16	+	2.77786e15i	−0.215639	+	0.0339094i
$401$		−	3.59297e16i		−	0.431534i	−0.976445	−	0.215767i	$-0.930775\pi$
$401$		−	3.59297e16i		−	0.431534i	0.976445	−	0.215767i	$-0.0692252\pi$
$402$	−7.08179e16	+	2.81623e16i	−0.836901	+	0.332812i
$403$			2.13162e15i			0.0247871i
$404$	−1.11689e17	+	8.72796e15i	−1.27800	+	0.0998698i
$405$	7.67493e16	+	1.65817e16i	0.864205	+	0.186711i
$406$	8.16007e16	−	8.82262e16i	0.904221	−	0.977638i
$407$	9.52556e16			1.03879
$408$	4.08276e16	+	8.31388e16i	0.438190	+	0.892304i
$409$	−1.48533e17			−1.56899			−0.784495	−	0.620135i	$-0.787078\pi$
$409$	−1.48533e17			−1.56899			−0.784495	+	0.620135i	$0.787078\pi$
$410$	−3.99720e16	+	4.32175e16i	−0.415586	+	0.449329i
$411$	5.86554e16	+	2.80373e16i	0.600255	+	0.286922i
$412$	7.13059e16	−	5.57222e15i	0.718280	−	0.0561302i
$413$		−	1.69238e17i		−	1.67811i
$414$	−1.75404e16	−	1.18395e15i	−0.171213	−	0.0115567i
$415$		−	1.12102e17i		−	1.07721i
$416$	9.22260e16	−	1.37614e17i	0.872463	−	1.30183i
$417$	1.69057e16	+	8.08094e15i	0.157452	+	0.0752623i
$418$	7.85495e16	+	7.26507e16i	0.720274	+	0.666184i
$419$	6.59954e16			0.595830			0.297915	−	0.954592i	$-0.403709\pi$
$419$	6.59954e16			0.595830			0.297915	+	0.954592i	$0.403709\pi$
$420$	1.08247e17	+	4.17247e16i	0.962270	+	0.370914i
$421$	1.68507e17			1.47498			0.737489	−	0.675359i	$-0.236011\pi$
$421$	1.68507e17			1.47498			0.737489	+	0.675359i	$0.236011\pi$
$422$	7.10773e16	+	6.57397e16i	0.612633	+	0.566626i
$423$	−5.29206e16	−	6.55751e16i	−0.449172	−	0.556579i
$424$	−2.33251e16	+	2.95373e16i	−0.194960	+	0.246884i
$425$			2.63625e16i			0.216999i
$426$	−5.51722e16	−	1.38738e17i	−0.447258	−	1.12469i
$427$			2.19495e17i			1.75244i
$428$	1.18734e16	+	1.51941e17i	0.0933667	+	1.19478i
$429$	−1.06745e17	+	2.23316e17i	−0.826755	+	1.72961i
$430$	4.49136e16	−	4.85603e16i	0.342636	−	0.370456i
$431$	−1.95455e17			−1.46874			−0.734371	−	0.678748i	$-0.762523\pi$
$431$	−1.95455e17			−1.46874			−0.734371	+	0.678748i	$0.762523\pi$
$432$	−1.24999e17	+	5.12482e16i	−0.925255	+	0.379345i
$433$	1.26586e17			0.923023			0.461512	−	0.887134i	$-0.347307\pi$
$433$	1.26586e17			0.923023			0.461512	+	0.887134i	$0.347307\pi$
$434$	1.74391e15	−	1.88551e15i	0.0125268	−	0.0135440i
$435$	6.15171e16	−	1.28697e17i	0.435327	−	0.910724i
$436$	8.40226e15	+	1.07521e17i	0.0585779	+	0.749603i
$437$		−	2.00379e16i		−	0.137633i
$438$	−8.90626e16	−	2.23960e17i	−0.602718	−	1.51562i
$439$		−	1.12010e17i		−	0.746857i	−0.927659	−	0.373429i	$-0.878182\pi$
$439$		−	1.12010e17i		−	0.746857i	0.927659	−	0.373429i	$-0.121818\pi$
$440$	1.02024e17	−	1.29196e17i	0.670284	−	0.848802i
$441$	3.49755e16	+	4.33390e16i	0.226419	+	0.280561i
$442$	−1.79290e17	−	1.65826e17i	−1.14370	−	1.05781i
$443$	2.53524e15			0.0159366			0.00796829	−	0.999968i	$-0.497464\pi$
$443$	2.53524e15			0.0159366			0.00796829	+	0.999968i	$0.497464\pi$
$444$	−1.27913e17	−	4.93049e16i	−0.792363	−	0.305422i
$445$	−1.81613e17			−1.10868
$446$	−6.73454e15	−	6.22880e15i	−0.0405164	−	0.0374738i
$447$	3.94259e16	+	1.88456e16i	0.233767	+	0.111741i
$448$	−1.94162e17	+	4.62736e16i	−1.13464	+	0.270412i
$449$			8.43043e16i			0.485566i	0.970081	+	0.242783i	$0.0780603\pi$
$449$			8.43043e16i			0.485566i	−0.970081	+	0.242783i	$0.921940\pi$
$450$	−3.83642e16	−	2.58953e15i	−0.217793	−	0.0147007i
$451$			1.51334e17i			0.846814i
$452$	2.36528e17	−	1.84836e16i	1.30462	−	0.101950i
$453$	3.21752e16	+	1.53798e16i	0.174938	+	0.0836204i
$454$	−1.81218e17	+	1.95932e17i	−0.971268	+	1.05013i
$455$	−3.05887e17			−1.61617
$456$	−6.78746e16	−	1.38216e17i	−0.353538	−	0.719923i
$457$	2.03895e16			0.104701			0.0523504	−	0.998629i	$-0.483329\pi$
$457$	2.03895e16			0.104701			0.0523504	+	0.998629i	$0.483329\pi$
$458$	6.53850e16	−	7.06938e16i	0.331019	−	0.357895i
$459$	4.60084e16	+	1.93776e17i	0.229644	+	0.967202i
$460$	−3.07363e16	+	2.40190e15i	−0.151261	+	0.0118203i
$461$			1.54196e17i			0.748198i	0.927389	+	0.374099i	$0.122048\pi$
$461$			1.54196e17i			0.748198i	−0.927389	+	0.374099i	$0.877952\pi$
$462$	2.77120e17	−	1.10203e17i	1.32585	−	0.527254i
$463$			1.75720e17i			0.828981i	0.910054	+	0.414491i	$0.136040\pi$
$463$			1.75720e17i			0.828981i	−0.910054	+	0.414491i	$0.863960\pi$
$464$	3.81245e16	+	2.42444e17i	0.177352	+	1.12783i
$465$	1.31470e15	−	2.75042e15i	0.00603091	−	0.0126169i
$466$	8.90076e15	+	8.23235e15i	0.0402642	+	0.0372405i
$467$	−1.95110e17			−0.870404			−0.435202	−	0.900333i	$-0.643323\pi$
$467$	−1.95110e17			−0.870404			−0.435202	+	0.900333i	$0.643323\pi$
$468$	2.58932e17	−	2.44625e17i	1.13917	−	1.07623i
$469$	−2.42121e17			−1.05053
$470$	−1.08486e17	−	1.00339e17i	−0.464234	−	0.429371i
$471$	1.24718e17	−	2.60915e17i	0.526372	−	1.10119i
$472$	2.71239e17	+	2.14192e17i	1.12909	+	0.891622i
$473$		−	1.70043e17i		−	0.698169i
$474$	1.17638e17	−	4.67814e16i	0.476419	−	0.189458i
$475$		−	4.38268e16i		−	0.175078i
$476$	2.29248e16	+	2.93361e17i	0.0903359	+	1.15600i
$477$	−6.29781e16	+	5.08248e16i	−0.244805	+	0.197563i
$478$	2.82488e17	−	3.05424e17i	1.08322	−	1.17118i
$479$	−3.79131e16			−0.143420			−0.0717098	−	0.997426i	$-0.522846\pi$
$479$	−3.79131e16			−0.143420			−0.0717098	+	0.997426i	$0.522846\pi$
$480$	−2.03874e17	+	1.20681e17i	−0.760840	+	0.450371i
$481$	3.61458e17			1.33081
$482$	−1.60548e16	+	1.73583e16i	−0.0583175	+	0.0630526i
$483$	−5.03906e16	−	2.40868e16i	−0.180590	−	0.0863221i
$484$	−1.09370e16	−	1.39957e17i	−0.0386726	−	0.494882i
$485$		−	1.56332e16i		−	0.0545416i
$486$	−2.86513e17	+	4.79199e16i	−0.986300	+	0.164961i
$487$		−	2.15491e17i		−	0.731966i	−0.930622	−	0.365983i	$-0.880733\pi$
$487$		−	2.15491e17i		−	0.731966i	0.930622	−	0.365983i	$-0.119267\pi$
$488$	−3.51787e17	−	2.77800e17i	−1.17910	−	0.931116i
$489$	1.17863e17	+	5.63384e16i	0.389824	+	0.186336i
$490$	7.16989e16	+	6.63145e16i	0.234012	+	0.216438i
$491$	3.43728e17			1.10710			0.553548	−	0.832817i	$-0.313274\pi$
$491$	3.43728e17			1.10710			0.553548	+	0.832817i	$0.313274\pi$
$492$	7.83312e16	−	2.03216e17i	0.248978	−	0.645930i
$493$	3.61809e17			1.13495
$494$	2.98065e17	+	2.75681e17i	0.922753	+	0.853458i
$495$	2.75466e17	−	2.22307e17i	0.841656	−	0.679235i
$496$	8.14771e14	+	5.18135e15i	0.00245700	+	0.0156247i
$497$		−	4.74334e17i		−	1.41178i
$498$	1.53254e17	+	3.85378e17i	0.450216	+	1.13213i
$499$			5.60930e17i			1.62650i	0.581912	+	0.813252i	$0.302305\pi$
$499$			5.60930e17i			1.62650i	−0.581912	+	0.813252i	$0.697695\pi$
$500$	−3.75194e17	+	2.93197e16i	−1.07387	+	0.0839178i
$501$	5.28593e16	−	1.10584e17i	0.149340	−	0.312426i
$502$	−3.92146e17	+	4.23986e17i	−1.09364	+	1.18244i
$503$	3.78380e17			1.04169			0.520843	−	0.853653i	$-0.325618\pi$
$503$	3.78380e17			1.04169			0.520843	+	0.853653i	$0.325618\pi$
$504$	−4.29169e17	+	4.54525e15i	−1.16635	+	0.0123526i
$505$	−4.22445e17			−1.13338
$506$	−5.38143e16	+	5.81837e16i	−0.142534	+	0.154107i
$507$	−2.40129e17	+	5.02361e17i	−0.627904	+	1.31360i
$508$	4.92520e17	−	3.84881e16i	1.27148	−	0.0993601i
$509$			4.11215e16i			0.104810i	0.998626	+	0.0524051i	$0.0166887\pi$
$509$			4.11215e16i			0.104810i	−0.998626	+	0.0524051i	$0.983311\pi$
$510$	1.29062e17	+	3.24545e17i	0.324783	+	0.816711i
$511$		−	7.65702e17i		−	1.90250i
$512$	1.71575e17	−	3.69751e17i	0.420919	−	0.907098i
$513$	−7.64876e16	−	3.22146e17i	−0.185280	−	0.780352i
$514$	−2.39932e17	−	2.21914e17i	−0.573888	−	0.530791i
$515$	2.69703e17			0.636999
$516$	−8.80151e16	+	2.28339e17i	−0.205274	+	0.532547i
$517$	−3.79882e17			−0.874904
$518$	−3.19725e17	−	2.95715e17i	−0.727166	−	0.672559i
$519$	−5.77045e17	−	2.75828e17i	−1.29605	−	0.619513i
$520$	3.87141e17	−	4.90248e17i	0.858711	−	1.08741i
$521$			1.35246e17i			0.296263i	0.988968	+	0.148132i	$0.0473259\pi$
$521$			1.35246e17i			0.296263i	−0.988968	+	0.148132i	$0.952674\pi$
$522$	−3.55398e16	+	5.26526e17i	−0.0768876	+	1.13910i
$523$		−	7.96183e17i		−	1.70119i	−0.525824	−	0.850594i	$-0.676243\pi$
$523$		−	7.96183e17i		−	1.70119i	0.525824	−	0.850594i	$-0.323757\pi$
$524$	3.00601e16	+	3.84669e17i	0.0634361	+	0.811772i
$525$	−1.10214e17	−	5.26823e16i	−0.229721	−	0.109807i
$526$	−4.06860e17	+	4.39894e17i	−0.837601	+	0.905610i
$527$	7.73234e15			0.0157232
$528$	−1.74109e17	+	5.83619e17i	−0.349704	+	1.17222i
$529$	−4.89194e17			−0.970552
$530$	−9.63651e16	+	1.04189e17i	−0.188854	+	0.204188i
$531$	4.66720e17	+	5.78324e17i	0.903530	+	1.11958i
$532$	−3.81118e16	−	4.87704e17i	−0.0728842	−	0.932676i
$533$			5.74252e17i			1.08487i
$534$	6.24340e17	−	2.48282e17i	1.16521	−	0.463370i
$535$			5.74691e17i			1.05958i
$536$	3.06436e17	−	3.88049e17i	0.558172	−	0.706831i
$537$	−7.49847e16	+	1.56872e17i	−0.134940	+	0.282300i
$538$	1.13677e17	+	1.05140e17i	0.202109	+	0.186932i
$539$	2.51066e17			0.441023
$540$	−4.84974e17	+	1.55940e17i	−0.841703	+	0.270643i
$541$	6.00845e17			1.03034			0.515169	−	0.857088i	$-0.327729\pi$
$541$	6.00845e17			1.03034			0.515169	+	0.857088i	$0.327729\pi$
$542$	2.67355e17	+	2.47278e17i	0.452995	+	0.418977i
$543$	−1.89873e17	+	3.97224e17i	−0.317881	+	0.665022i
$544$	−4.99187e17	−	3.34546e17i	−0.825792	−	0.553430i
$545$			4.06681e17i			0.664778i
$546$	1.05156e18	−	4.18177e17i	1.69857	−	0.675473i
$547$			2.81795e17i			0.449796i	0.974382	+	0.224898i	$0.0722050\pi$
$547$			2.81795e17i			0.449796i	−0.974382	+	0.224898i	$0.927795\pi$
$548$	−4.20506e17	+	3.28606e16i	−0.663283	+	0.0518324i
$549$	−6.05321e17	−	7.50066e17i	−0.943551	−	1.16917i
$550$	−1.17702e17	+	1.27259e17i	−0.181312	+	0.196033i
$551$	−6.01497e17			−0.915689
$552$	1.02380e17	−	5.02765e16i	0.154032	−	0.0756417i
$553$	4.02195e17			0.598031
$554$	4.66028e17	−	5.03867e17i	0.684855	−	0.740461i
$555$	−4.66388e17	−	2.22934e17i	−0.677396	−	0.323796i
$556$	−1.21199e17	+	9.47109e15i	−0.173985	+	0.0135961i
$557$		−	5.05028e17i		−	0.716567i	−0.933613	−	0.358284i	$-0.883362\pi$
$557$		−	5.05028e17i		−	0.716567i	0.933613	−	0.358284i	$-0.116638\pi$
$558$	−7.59531e14	+	1.12526e16i	−0.00106518	+	0.0157808i
$559$		−	6.45246e17i		−	0.894434i
$560$	−7.43524e17	+	1.16920e17i	−1.01876	+	0.160201i
$561$	8.10069e17	+	3.87214e17i	1.09714	+	0.524436i
$562$	−1.79849e17	−	1.66343e17i	−0.240781	−	0.222699i
$563$	2.50841e17			0.331966			0.165983	−	0.986129i	$-0.446920\pi$
$563$	2.50841e17			0.331966			0.165983	+	0.986129i	$0.446920\pi$
$564$	5.10119e17	+	1.96629e17i	0.667356	+	0.257237i
$565$	8.94630e17			1.15699
$566$	−9.60200e17	−	8.88093e17i	−1.22759	−	1.13541i
$567$	−9.02064e17	−	1.94891e17i	−1.14011	−	0.246321i
$568$	7.60220e17	+	6.00332e17i	0.949894	+	0.750114i
$569$			1.17397e18i			1.45020i	0.688643	+	0.725101i	$0.258207\pi$
$569$			1.17397e18i			1.45020i	−0.688643	+	0.725101i	$0.741793\pi$
$570$	−2.14562e17	−	5.39545e17i	−0.262039	−	0.658933i
$571$			6.75710e17i			0.815879i	0.913009	+	0.407940i	$0.133753\pi$
$571$			6.75710e17i			0.815879i	−0.913009	+	0.407940i	$0.866247\pi$
$572$	−1.25109e17	−	1.60098e18i	−0.149353	−	1.91122i
$573$	3.21311e16	−	6.72197e16i	0.0379245	−	0.0793399i
$574$	4.69806e17	−	5.07952e17i	0.548266	−	0.592782i
$575$	3.24636e16			0.0374590
$576$	5.35884e17	−	6.93585e17i	0.611399	−	0.791322i
$577$	−2.90480e17			−0.327698			−0.163849	−	0.986485i	$-0.552391\pi$
$577$	−2.90480e17			−0.327698			−0.163849	+	0.986485i	$0.552391\pi$
$578$	7.17246e15	−	7.75482e15i	0.00800087	−	0.00865050i
$579$	2.50073e17	−	5.23163e17i	0.275839	−	0.577068i
$580$	7.20999e16	+	9.22639e17i	0.0786416	+	1.00635i
$581$			1.31758e18i			1.42112i
$582$	2.13721e16	+	5.37431e16i	0.0227955	+	0.0573223i
$583$			3.64837e17i			0.384817i
$584$	1.22720e18	+	9.69096e17i	1.28006	+	1.01084i
$585$	1.04529e18	−	8.43571e17i	1.07826	−	0.870179i
$586$	−4.17902e17	−	3.86519e17i	−0.426324	−	0.394308i
$587$	−1.36766e17			−0.137985			−0.0689923	−	0.997617i	$-0.521978\pi$
$587$	−1.36766e17			−0.137985			−0.0689923	+	0.997617i	$0.521978\pi$
$588$	−3.37141e17	−	1.29953e17i	−0.336402	−	0.129669i
$589$	−1.28548e16			−0.0126857
$590$	9.56764e17	+	8.84914e17i	0.933828	+	0.863700i
$591$	1.59254e17	+	7.61234e16i	0.153734	+	0.0734852i
$592$	8.78600e17	−	1.38161e17i	0.838880	−	0.131915i
$593$		−	9.69286e17i		−	0.915370i	−0.889114	−	0.457685i	$-0.848679\pi$
$593$		−	9.69286e17i		−	0.915370i	0.889114	−	0.457685i	$-0.151321\pi$
$594$	−6.43068e17	+	1.14083e18i	−0.600682	+	1.06563i
$595$			1.10959e18i			1.02519i
$596$	−2.82648e17	+	2.20876e16i	−0.258312	+	0.0201859i
$597$	−6.39459e17	−	3.05662e17i	−0.578068	−	0.276317i
$598$	−2.04204e17	+	2.20785e17i	−0.182603	+	0.197429i
$599$	1.63317e17			0.144463			0.0722315	−	0.997388i	$-0.476988\pi$
$599$	1.63317e17			0.144463			0.0722315	+	0.997388i	$0.476988\pi$
$600$	2.23924e17	−	1.09964e17i	0.195938	−	0.0962207i
$601$	−1.85947e18			−1.60955			−0.804775	−	0.593580i	$-0.797714\pi$
$601$	−1.85947e18			−1.60955			−0.804775	+	0.593580i	$0.797714\pi$
$602$	−5.27887e17	+	5.70748e17i	−0.452026	+	0.488728i
$603$	8.27383e17	−	6.67717e17i	0.700880	−	0.565626i
$604$	−2.30668e17	+	1.80256e16i	−0.193306	+	0.0151060i
$605$		−	5.29366e17i		−	0.438881i
$606$	1.45226e18	−	5.77523e17i	1.19117	−	0.473693i
$607$			3.37893e17i			0.274190i	0.990558	+	0.137095i	$0.0437766\pi$
$607$			3.37893e17i			0.274190i	−0.990558	+	0.137095i	$0.956223\pi$
$608$	8.29883e17	+	5.56172e17i	0.666260	+	0.446515i
$609$	−7.23034e17	+	1.51262e18i	−0.574310	+	1.20148i
$610$	−1.24089e18	−	1.14770e18i	−0.975191	−	0.901957i
$611$	−1.44150e18			−1.12085
$612$	−8.87366e17	−	9.39262e17i	−0.682682	−	0.722607i
$613$	2.32532e17			0.177007			0.0885034	−	0.996076i	$-0.471792\pi$
$613$	2.32532e17			0.177007			0.0885034	+	0.996076i	$0.471792\pi$
$614$	−1.70607e18	−	1.57795e18i	−1.28500	−	1.18850i
$615$	3.54177e17	−	7.40955e17i	0.263957	−	0.552209i
$616$	−1.19912e18	+	1.51849e18i	−0.884279	+	1.11979i
$617$		−	1.03485e18i		−	0.755131i	−0.925983	−	0.377566i	$-0.876761\pi$
$617$		−	1.03485e18i		−	0.755131i	0.925983	−	0.377566i	$-0.123239\pi$
$618$	−9.27171e17	+	3.68710e17i	−0.669476	+	0.266231i
$619$		−	4.53178e17i		−	0.323802i	−0.986807	−	0.161901i	$-0.948237\pi$
$619$		−	4.53178e17i		−	0.323802i	0.986807	−	0.161901i	$-0.0517625\pi$
$620$	1.54087e15	+	1.97180e16i	0.00108948	+	0.0139417i
$621$	2.38622e17	−	5.66564e16i	0.166961	−	0.0396418i
$622$	−3.49644e16	+	3.78033e16i	−0.0242096	+	0.0261753i
$623$	2.13457e18			1.46264
$624$	−6.60675e17	+	2.21461e18i	−0.448011	+	1.50175i
$625$	−1.09384e18			−0.734061
$626$	−3.53272e17	+	3.81956e17i	−0.234626	+	0.253676i
$627$	−1.34672e18	−	6.43731e17i	−0.885191	−	0.423122i
$628$	1.46173e17	+	1.87053e18i	0.0950888	+	1.21682i
$629$		−	1.31117e18i		−	0.844171i
$630$	−1.61474e18	−	1.08993e17i	−1.02894	−	0.0694519i
$631$		−	1.03414e18i		−	0.652211i	−0.945333	−	0.326105i	$-0.894264\pi$
$631$		−	1.03414e18i		−	0.652211i	0.945333	−	0.326105i	$-0.105736\pi$
$632$	−5.09031e17	+	6.44602e17i	−0.317748	+	0.402375i
$633$	−1.21861e18	−	5.82495e17i	−0.752904	−	0.359889i
$634$	1.75241e18	+	1.62081e18i	1.07166	+	0.991179i
$635$	1.86288e18			1.12760
$636$	1.88842e17	−	4.89917e17i	0.113143	−	0.293529i
$637$	9.52699e17			0.565001
$638$	1.74655e18	+	1.61539e18i	1.02529	+	0.948295i
$639$	1.30811e18	+	1.62091e18i	0.760132	+	0.941897i
$640$	7.53638e17	−	1.33963e18i	0.433504	−	0.770575i
$641$			7.87488e17i			0.448401i	0.974543	+	0.224200i	$0.0719770\pi$
$641$			7.87488e17i			0.448401i	−0.974543	+	0.224200i	$0.928023\pi$
$642$	−7.85657e17	−	1.97564e18i	−0.442848	−	1.11360i
$643$		−	1.99674e18i		−	1.11417i	−0.830457	−	0.557083i	$-0.811921\pi$
$643$		−	1.99674e18i		−	1.11417i	0.830457	−	0.557083i	$-0.188079\pi$
$644$	3.61255e17	−	2.82304e16i	0.199552	−	0.0155940i
$645$	−3.97963e17	+	8.32557e17i	−0.217623	+	0.455277i
$646$	1.00002e18	−	1.08122e18i	0.541374	−	0.585331i
$647$	5.36795e16			0.0287694			0.0143847	−	0.999897i	$-0.495421\pi$
$647$	5.36795e16			0.0287694			0.0143847	+	0.999897i	$0.495421\pi$
$648$	1.45403e18	−	1.19909e18i	0.771501	−	0.636228i
$649$	3.35028e18			1.75991
$650$	−4.46633e17	+	4.82897e17i	−0.232281	+	0.251141i
$651$	−1.54522e16	+	3.23267e16i	−0.00795634	+	0.0166450i
$652$	−8.44968e17	+	6.60303e16i	−0.430756	+	0.0336615i
$653$		−	2.98189e18i		−	1.50507i	−0.658554	−	0.752534i	$-0.728832\pi$
$653$		−	2.98189e18i		−	1.50507i	0.658554	−	0.752534i	$-0.271168\pi$
$654$	−5.55971e17	−	1.39807e18i	−0.277841	−	0.698670i
$655$			1.45495e18i			0.719912i
$656$	2.19497e17	+	1.39584e18i	0.107536	+	0.683851i
$657$	2.11164e18	+	2.61658e18i	1.02434	+	1.26928i
$658$	1.27507e18	+	1.17932e18i	0.612445	+	0.566453i
$659$	−2.01436e18			−0.958038			−0.479019	−	0.877805i	$-0.659007\pi$
$659$	−2.01436e18			−0.958038			−0.479019	+	0.877805i	$0.659007\pi$
$660$	−8.25995e17	+	2.14290e18i	−0.388993	+	1.00917i
$661$	5.62389e17			0.262257			0.131128	−	0.991365i	$-0.458140\pi$
$661$	5.62389e17			0.262257			0.131128	+	0.991365i	$0.458140\pi$
$662$	2.00055e17	+	1.85032e17i	0.0923789	+	0.0854416i
$663$	3.07390e18	+	1.46933e18i	1.40557	+	0.671863i
$664$	−2.11169e18	−	1.66757e18i	−0.956177	−	0.755076i
$665$		−	1.84466e18i		−	0.827135i
$666$	1.90809e18	+	1.28794e17i	0.847261	+	0.0571889i
$667$		−	4.45545e17i		−	0.195918i
$668$	6.19527e16	+	7.92789e17i	0.0269782	+	0.345232i
$669$	1.15462e17	+	5.51911e16i	0.0497933	+	0.0238012i
$670$	1.26601e18	−	1.36880e18i	0.540692	−	0.584593i
$671$	−4.34520e18			−1.83786
$672$	2.39621e18	−	1.41841e18i	1.00375	−	0.594156i
$673$	−4.08186e18			−1.69340			−0.846702	−	0.532068i	$-0.821415\pi$
$673$	−4.08186e18			−1.69340			−0.846702	+	0.532068i	$0.821415\pi$
$674$	2.15482e18	−	2.32978e18i	0.885363	−	0.957249i
$675$	5.21912e17	−	1.23918e17i	0.212385	−	0.0504267i
$676$	−2.81438e17	−	3.60148e18i	−0.113430	−	1.45153i
$677$			3.49666e18i			1.39581i	0.716188	+	0.697907i	$0.245885\pi$
$677$			3.49666e18i			1.39581i	−0.716188	+	0.697907i	$0.754115\pi$
$678$	−3.07551e18	+	1.22304e18i	−1.21597	+	0.483558i
$679$			1.83743e17i			0.0719546i
$680$	−1.77835e18	−	1.40433e18i	−0.689779	−	0.544706i
$681$	1.60571e18	−	3.35922e18i	0.616894	−	1.29057i
$682$	3.73261e16	+	3.45230e16i	0.0142041	+	0.0131374i
$683$	−4.50069e18			−1.69646			−0.848231	−	0.529627i	$-0.822332\pi$
$683$	−4.50069e18			−1.69646			−0.848231	+	0.529627i	$0.822332\pi$
$684$	1.47522e18	+	1.56149e18i	0.550797	+	0.583009i
$685$	−1.59050e18			−0.588226
$686$	1.49471e18	+	1.38247e18i	0.547584	+	0.506463i
$687$	−5.79352e17	+	1.21203e18i	−0.210244	+	0.439841i
$688$	−2.46633e17	−	1.56841e18i	−0.0886597	−	0.563811i
$689$			1.38442e18i			0.492994i
$690$	3.99655e17	−	1.58932e17i	0.140983	−	0.0560649i
$691$		−	1.29278e17i		−	0.0451769i	−0.999745	−	0.0225884i	$-0.992809\pi$
$691$		−	1.29278e17i		−	0.0451769i	0.999745	−	0.0225884i	$-0.00719074\pi$
$692$	4.13689e18	−	3.23279e17i	1.43214	−	0.111915i
$693$	−3.23766e18	+	2.61286e18i	−1.11036	+	0.896088i
$694$	−1.77124e18	+	1.91505e18i	−0.601784	+	0.650645i
$695$	−4.58414e17			−0.154297
$696$	−1.50920e18	−	3.07323e18i	−0.503252	−	1.02479i
$697$	2.08307e18			0.688163
$698$	−1.66450e18	+	1.79964e18i	−0.544782	+	0.589015i
$699$	−1.52602e17	−	7.29438e16i	−0.0494832	−	0.0236530i
$700$	7.90134e17	−	6.17452e16i	0.253842	−	0.0198365i
$701$			2.12881e18i			0.677595i	0.940859	+	0.338798i	$0.110020\pi$
$701$			2.12881e18i			0.677595i	−0.940859	+	0.338798i	$0.889980\pi$
$702$	−2.44019e18	+	4.32899e18i	−0.769543	+	1.36520i
$703$			2.17978e18i			0.681089i
$704$	−9.16047e17	−	3.84369e18i	−0.283593	−	1.18994i
$705$	1.85997e18	+	8.89066e17i	0.570527	+	0.272712i
$706$	−1.41244e18	−	1.30637e18i	−0.429278	−	0.397041i
$707$	4.96516e18			1.49523
$708$	−4.49887e18	−	1.73412e18i	−1.34242	−	0.517445i
$709$	3.63816e18			1.07568			0.537838	−	0.843048i	$-0.319241\pi$
$709$	3.63816e18			1.07568			0.537838	+	0.843048i	$0.319241\pi$
$710$	2.68159e18	+	2.48021e18i	0.785621	+	0.726624i
$711$	−1.37439e18	+	1.10917e18i	−0.398987	+	0.321992i
$712$	−2.70158e18	+	3.42109e18i	−0.777136	+	0.984113i
$713$		−	9.52187e15i		−	0.00271419i
$714$	−1.51692e18	−	3.81450e18i	−0.428473	−	1.07745i
$715$		−	6.05544e18i		−	1.69495i
$716$	−8.78843e16	−	1.12463e18i	−0.0243768	−	0.311942i
$717$	−2.50302e18	+	5.23643e18i	−0.688002	+	1.43933i
$718$	7.40018e17	−	8.00103e17i	0.201573	−	0.217940i
$719$	1.36445e18			0.368316			0.184158	−	0.982897i	$-0.441044\pi$
$719$	1.36445e18			0.368316			0.184158	+	0.982897i	$0.441044\pi$
$720$	2.21835e18	−	2.45002e18i	0.593430	−	0.655402i
$721$	−3.16992e18			−0.840368
$722$	9.21922e17	−	9.96776e17i	0.242216	−	0.261882i
$723$	1.42256e17	−	2.97605e17i	0.0370400	−	0.0774893i
$724$	−2.22537e17	−	2.84774e18i	−0.0574251	−	0.734851i
$725$		−	9.74490e17i		−	0.249219i
$726$	7.23694e17	+	1.81983e18i	0.183429	+	0.461256i
$727$			1.97492e18i			0.496108i	0.968746	+	0.248054i	$0.0797910\pi$
$727$			1.97492e18i			0.496108i	−0.968746	+	0.248054i	$0.920209\pi$
$728$	−4.55021e18	+	5.76208e18i	−1.13286	+	1.43458i
$729$	3.62002e18	−	1.82171e18i	0.893270	−	0.449521i
$730$	4.32880e18	+	4.00372e18i	1.05869	+	0.979187i
$731$	−2.34060e18			−0.567367
$732$	5.83489e18	+	2.24910e18i	1.40188	+	0.540365i
$733$	1.84301e18			0.438886			0.219443	−	0.975625i	$-0.429576\pi$
$733$	1.84301e18			0.438886			0.219443	+	0.975625i	$0.429576\pi$
$734$	−2.58508e18	−	2.39095e18i	−0.610169	−	0.564347i
$735$	−1.22926e18	−	5.87589e17i	−0.287592	−	0.137469i
$736$	−4.11971e17	+	6.14717e17i	−0.0955346	+	0.142551i
$737$		−	4.79310e18i		−	1.10174i
$738$	−2.04616e17	+	3.03141e18i	−0.0466201	+	0.690682i
$739$		−	5.03483e15i		−	0.00113709i	−1.00000		0.000568546i	$-0.999819\pi$
$739$		−	5.03483e15i		−	0.00113709i	1.00000		0.000568546i	$-0.000180974\pi$
$740$	3.34358e18	−	2.61285e17i	0.748523	−	0.0584935i
$741$	−5.11026e18	−	2.44271e18i	−1.13403	−	0.542068i
$742$	1.13262e18	−	1.22458e18i	0.249148	−	0.269377i
$743$	5.57973e18			1.21671			0.608353	−	0.793667i	$-0.291831\pi$
$743$	5.57973e18			1.21671			0.608353	+	0.793667i	$0.291831\pi$
$744$	−3.22535e16	−	6.56790e16i	−0.00697193	−	0.0141972i
$745$	−1.06907e18			−0.229082
$746$	2.82057e18	−	3.04958e18i	0.599148	−	0.647795i
$747$	−3.63359e18	−	4.50247e18i	−0.765160	−	0.948127i
$748$	−5.80747e18	+	4.53826e17i	−1.21235	+	0.0947391i
$749$		−	6.75456e18i		−	1.39786i
$750$	4.87855e18	−	1.94006e18i	1.00090	−	0.398031i
$751$			9.49299e18i			1.93083i	0.260722	+	0.965414i	$0.416039\pi$
$751$			9.49299e18i			1.93083i	−0.260722	+	0.965414i	$0.583961\pi$
$752$	−3.50388e18	+	5.50988e17i	−0.706535	+	0.111103i
$753$	3.47467e18	−	7.26916e18i	0.694617	−	1.45317i
$754$	6.62749e18	+	6.12978e18i	1.31352	+	1.21487i
$755$	−8.72462e17			−0.171432
$756$	5.70008e18	−	1.83282e18i	1.11043	−	0.357049i
$757$	6.33084e17			0.122275			0.0611376	−	0.998129i	$-0.480527\pi$
$757$	6.33084e17			0.122275			0.0611376	+	0.998129i	$0.480527\pi$
$758$	−6.44237e18	−	5.95857e18i	−1.23366	−	1.14102i
$759$	4.76829e17	−	9.97548e17i	0.0905297	−	0.189392i
$760$	2.95646e18	+	2.33466e18i	0.556523	+	0.439476i
$761$			8.93208e18i			1.66706i	0.552471	+	0.833532i	$0.313685\pi$
$761$			8.93208e18i			1.66706i	−0.552471	+	0.833532i	$0.686315\pi$
$762$	−6.40410e18	+	2.54673e18i	−1.18509	+	0.471276i
$763$		−	4.77987e18i		−	0.877015i
$764$	3.76586e16	+	4.81905e17i	0.00685105	+	0.0876707i
$765$	−3.06001e18	−	3.79173e18i	−0.551981	−	0.683972i
$766$	4.89608e17	−	5.29361e17i	0.0875712	−	0.0946815i
$767$	1.27130e19			2.25465
$768$	−7.59419e17	+	5.63560e18i	−0.133547	+	0.991043i
$769$	−4.41706e18			−0.770215			−0.385108	−	0.922872i	$-0.625836\pi$
$769$	−4.41706e18			−0.770215			−0.385108	+	0.922872i	$0.625836\pi$
$770$	−4.95406e18	+	5.35630e18i	−0.856587	+	0.926137i
$771$	4.11358e18	+	1.96629e18i	0.705288	+	0.337128i
$772$	2.93092e17	+	3.75061e18i	0.0498301	+	0.637660i
$773$		−	9.90533e17i		−	0.166995i	−0.996508	−	0.0834973i	$-0.973391\pi$
$773$		−	9.90533e17i		−	0.166995i	0.996508	−	0.0834973i	$-0.0266090\pi$
$774$	2.29912e17	−	3.40618e18i	0.0384366	−	0.569444i
$775$		−	2.08261e16i		−	0.00345261i
$776$	−2.94487e17	−	2.32551e17i	−0.0484134	−	0.0382312i
$777$	5.48163e18	+	2.62022e18i	0.893662	+	0.427171i
$778$	−6.54063e18	−	6.04945e18i	−1.05743	−	0.978021i
$779$	−3.46305e18			−0.555220
$780$	−3.13433e18	+	8.13146e18i	−0.498345	+	1.29287i
$781$	9.39006e18			1.48060
$782$	8.00885e17	+	7.40742e17i	0.125235	+	0.115830i
$783$	−1.70070e18	−	7.16294e18i	−0.263741	−	1.11081i
$784$	2.31574e18	−	3.64151e17i	0.356151	−	0.0560051i
$785$			7.07497e18i			1.07913i
$786$	−1.98905e18	−	5.00174e18i	−0.300884	−	0.756615i
$787$		−	4.15769e18i		−	0.623759i	−0.950122	−	0.311879i	$-0.899042\pi$
$787$		−	4.15769e18i		−	0.623759i	0.950122	−	0.311879i	$-0.100958\pi$
$788$	−1.14171e18	+	8.92189e16i	−0.169877	+	0.0132751i
$789$	3.60504e18	−	7.54190e18i	0.531997	−	1.11296i
$790$	−2.10301e18	+	2.27376e18i	−0.307798	+	0.332789i
$791$	−1.05149e19			−1.52637
$792$	−8.99791e16	−	8.49595e18i	−0.0129547	−	1.22320i
$793$	−1.64883e19			−2.35451
$794$	2.26693e18	−	2.45099e18i	0.321074	−	0.347143i
$795$	8.53856e17	−	1.78631e18i	0.119949	−	0.250940i
$796$	4.58434e18	−	3.58245e17i	0.638767	−	0.0499166i
$797$			8.66685e18i			1.19779i	0.800826	+	0.598897i	$0.204394\pi$
$797$			8.66685e18i			1.19779i	−0.800826	+	0.598897i	$0.795606\pi$
$798$	2.52183e18	+	6.34148e18i	0.345698	+	0.869305i
$799$			5.22899e18i			0.710991i
$800$	−9.01058e17	+	1.34450e18i	−0.121526	+	0.181333i
$801$	−7.29431e18	+	5.88668e18i	−0.975827	+	0.787515i
$802$	−2.38740e18	−	2.20811e18i	−0.316804	−	0.293014i
$803$	1.51581e19			1.99523
$804$	−2.48094e18	+	6.43634e18i	−0.323930	+	0.840378i
$805$	1.36639e18			0.176971
$806$	1.41638e17	+	1.31002e17i	0.0181971	+	0.0168306i
$807$	−1.94896e18	−	9.31607e17i	−0.248385	−	0.118728i
$808$	−6.28406e18	+	7.95771e18i	−0.794450	+	1.00604i
$809$		−	3.13528e18i		−	0.393197i	−0.980484	−	0.196599i	$-0.937010\pi$
$809$		−	3.13528e18i		−	0.393197i	0.980484	−	0.196599i	$-0.0629896\pi$
$810$	5.81853e18	−	4.08066e18i	0.723870	−	0.507665i
$811$			1.19771e19i			1.47815i	0.673625	+	0.739074i	$0.264737\pi$
$811$			1.19771e19i			1.47815i	−0.673625	+	0.739074i	$0.735263\pi$
$812$	−8.47417e17	−	1.08441e19i	−0.103749	−	1.32764i
$813$	−4.58375e18	−	2.19104e18i	−0.556715	−	0.266110i
$814$	5.85407e18	−	6.32938e18i	0.705341	−	0.762610i
$815$	−3.19595e18			−0.382011
$816$	8.03338e18	+	2.39657e18i	0.952604	+	0.284187i
$817$	3.89117e18			0.457759
$818$	−9.12828e18	+	9.86944e18i	−1.06535	+	1.15185i
$819$	−1.22857e19	+	9.91481e18i	−1.42250	+	1.14799i
$820$	4.15106e17	+	5.31198e18i	0.0476836	+	0.610192i
$821$			8.78678e18i			1.00138i	0.865627	+	0.500690i	$0.166920\pi$
$821$			8.78678e18i			1.00138i	−0.865627	+	0.500690i	$0.833080\pi$
$822$	5.46772e18	−	2.17436e18i	0.618215	−	0.245847i
$823$		−	1.72810e19i		−	1.93852i	−0.246046	−	0.969258i	$-0.579131\pi$
$823$		−	1.72810e19i		−	1.93852i	0.246046	−	0.969258i	$-0.420869\pi$
$824$	4.01195e18	−	5.08046e18i	0.446508	−	0.565427i
$825$	1.04291e18	−	2.18182e18i	0.115159	−	0.240918i
$826$	−1.12452e19	−	1.04007e19i	−1.23196	−	1.13945i
$827$	−1.76711e19			−1.92078			−0.960390	−	0.278659i	$-0.910110\pi$
$827$	−1.76711e19			−1.92078			−0.960390	+	0.278659i	$0.910110\pi$
$828$	−1.15664e18	+	1.09273e18i	−0.124739	+	0.117847i
$829$	1.38369e19			1.48059			0.740296	−	0.672281i	$-0.234685\pi$
$829$	1.38369e19			1.48059			0.740296	+	0.672281i	$0.234685\pi$
$830$	−7.44876e18	−	6.88939e18i	−0.790818	−	0.731430i
$831$	−4.12930e18	+	8.63870e18i	−0.434981	+	0.910000i
$832$	−3.47604e18	−	1.45853e19i	−0.363315	−	1.52445i
$833$		−	3.45587e18i		−	0.358398i
$834$	1.57591e18	−	6.26695e17i	0.162163	−	0.0644877i
$835$			2.99860e18i			0.306165i
$836$	9.65474e18	−	7.54472e17i	0.978137	−	0.0764368i
$837$	−3.63463e16	−	1.53081e17i	−0.00365380	−	0.0153889i
$838$	4.05584e18	−	4.38515e18i	0.404571	−	0.437419i
$839$	6.53527e18			0.646860			0.323430	−	0.946252i	$-0.395164\pi$
$839$	6.53527e18			0.646860			0.323430	+	0.946252i	$0.395164\pi$
$840$	9.42494e18	−	4.62838e18i	0.925685	−	0.454584i
$841$	−3.11368e18			−0.303459
$842$	1.03559e19	−	1.11967e19i	1.00152	−	1.08283i
$843$	3.08347e18	+	1.47390e18i	0.295911	+	0.141446i
$844$	8.73631e18	−	6.82701e17i	0.831960	−	0.0650137i
$845$		−	1.36220e19i		−	1.28728i
$846$	−7.60953e18	−	5.13632e17i	−0.713593	−	0.0481665i
$847$			6.22185e18i			0.578998i
$848$	5.29167e17	+	3.36512e18i	0.0488675	+	0.310761i
$849$	1.64624e19	+	7.86906e18i	1.50867	+	0.721146i
$850$	1.75169e18	+	1.62014e18i	0.159307	+	0.147343i
$851$	−1.61462e18			−0.145723
$852$	−1.26093e19	−	4.86036e18i	−1.12936	−	0.435322i
$853$	−4.23393e18			−0.376335			−0.188168	−	0.982137i	$-0.560255\pi$
$853$	−4.23393e18			−0.376335			−0.188168	+	0.982137i	$0.560255\pi$
$854$	1.45847e19	+	1.34894e19i	1.28653	+	1.18992i
$855$	5.08718e18	+	6.30364e18i	0.445346	+	0.551838i
$856$	1.08256e19	+	8.54878e18i	0.940529	+	0.742719i
$857$			9.99684e18i			0.861960i	0.902361	+	0.430980i	$0.141832\pi$
$857$			9.99684e18i			0.861960i	−0.902361	+	0.430980i	$0.858168\pi$
$858$	8.27835e18	+	2.08171e19i	0.708397	+	1.78136i
$859$		−	1.78994e19i		−	1.52014i	−0.649844	−	0.760068i	$-0.725166\pi$
$859$		−	1.78994e19i		−	1.52014i	0.649844	−	0.760068i	$-0.274834\pi$
$860$	−4.66425e17	−	5.96869e18i	−0.0393135	−	0.503082i
$861$	−4.16278e18	+	8.70873e18i	−0.348227	+	0.728508i
$862$	−1.20120e19	+	1.29873e19i	−0.997281	+	1.07825i
$863$	3.86200e18			0.318231			0.159115	−	0.987260i	$-0.449136\pi$
$863$	3.86200e18			0.318231			0.159115	+	0.987260i	$0.449136\pi$
$864$	−4.27673e18	+	1.14552e19i	−0.349762	+	0.936839i
$865$	1.56471e19			1.27008
$866$	7.77949e18	−	8.41114e18i	0.626736	−	0.677624i
$867$	−6.35526e16	+	1.32955e17i	−0.00508170	+	0.0106312i
$868$	−1.81104e16	−	2.31753e17i	−0.00143731	−	0.0183928i
$869$			7.96198e18i			0.627180i
$870$	−4.77079e18	−	1.19968e19i	−0.373006	−	0.937974i
$871$		−	1.81879e19i		−	1.41145i
$872$	7.66075e18	+	6.04956e18i	0.590084	+	0.465979i
$873$	−5.06724e17	−	6.27894e17i	−0.0387418	−	0.0480058i
$874$	−1.33145e18	−	1.23146e18i	−0.101041	−	0.0934536i
$875$	1.66794e19			1.25640
$876$	−2.03548e19	−	7.84591e18i	−1.52191	−	0.586633i
$877$	−3.38597e17			−0.0251296			−0.0125648	−	0.999921i	$-0.504000\pi$
$877$	−3.38597e17			−0.0251296			−0.0125648	+	0.999921i	$0.504000\pi$
$878$	−7.44265e18	−	6.88374e18i	−0.548294	−	0.507119i
$879$	7.16484e18	+	3.42480e18i	0.523937	+	0.250442i
$880$	−2.31458e18	−	1.47190e19i	−0.168010	−	1.06842i
$881$		−	2.00078e19i		−	1.44164i	−0.693123	−	0.720820i	$-0.743766\pi$
$881$		−	2.00078e19i		−	1.44164i	0.693123	−	0.720820i	$-0.256234\pi$
$882$	5.02919e18	+	3.39463e17i	0.359709	+	0.0242799i
$883$			1.92196e19i			1.36458i	0.731079	+	0.682292i	$0.239017\pi$
$883$			1.92196e19i			1.36458i	−0.731079	+	0.682292i	$0.760983\pi$
$884$	−2.20371e19	+	1.72209e18i	−1.55315	+	0.121372i
$885$	−1.64035e19	−	7.84090e18i	−1.14764	−	0.548573i
$886$	1.55807e17	−	1.68457e17i	0.0108210	−	0.0116996i
$887$	−2.19666e19			−1.51446			−0.757231	−	0.653147i	$-0.773448\pi$
$887$	−2.19666e19			−1.51446			−0.757231	+	0.653147i	$0.773448\pi$
$888$	−1.11372e19	+	5.46922e18i	−0.762238	+	0.374318i
$889$	−2.18951e19			−1.48760
$890$	−1.11613e19	+	1.20675e19i	−0.752800	+	0.813922i
$891$	3.85811e18	−	1.78575e19i	0.258327	−	1.19568i
$892$	−8.27761e17	+	6.46856e16i	−0.0550216	+	0.00429968i
$893$		−	8.69304e18i		−	0.573637i
$894$	3.67519e18	−	1.46152e18i	0.240761	−	0.0957438i
$895$		−	4.25372e18i		−	0.276643i
$896$	−8.85780e18	+	1.57452e19i	−0.571905	+	1.01659i
$897$	1.80938e18	−	3.78531e18i	0.115979	−	0.242633i
$898$	5.60171e18	+	5.18104e18i	0.356471	+	0.329701i
$899$	−2.85827e17			−0.0180578
$900$	−2.52979e18	+	2.39001e18i	−0.158675	+	0.149908i
$901$	5.02191e18			0.312721
$902$	1.00556e19	+	9.30042e18i	0.621675	+	0.574990i
$903$	4.67741e18	−	9.78537e18i	0.287101	−	0.600630i
$904$	1.33080e19	−	1.68524e19i	0.810995	−	1.02699i
$905$		−	1.07711e19i		−	0.651695i
$906$	2.99931e18	−	1.19274e18i	0.180172	−	0.0716493i
$907$			2.99530e19i			1.78646i	0.449598	+	0.893231i	$0.351567\pi$
$907$			2.99530e19i			1.78646i	−0.449598	+	0.893231i	$0.648433\pi$
$908$	1.88194e18	+	2.40826e19i	0.111442	+	1.42608i
$909$	−1.69671e19	+	1.36928e19i	−0.997568	+	0.805060i
$910$	−1.87987e19	+	2.03251e19i	−1.09739	+	1.18649i
$911$	−1.66189e19			−0.963235			−0.481617	−	0.876382i	$-0.659950\pi$
$911$	−1.66189e19			−0.963235			−0.481617	+	0.876382i	$0.659950\pi$
$912$	−1.33553e19	−	3.98422e18i	−0.768574	−	0.229286i
$913$	−2.60832e19			−1.49039
$914$	1.25306e18	−	1.35480e18i	0.0710923	−	0.0768646i
$915$	2.12748e19	+	1.01694e19i	1.19847	+	0.572872i
$916$	−6.79018e17	−	8.68918e18i	−0.0379805	−	0.486024i
$917$		−	1.71006e19i		−	0.949751i
$918$	1.57032e19	+	8.85168e18i	0.865986	+	0.488145i
$919$		−	2.00918e19i		−	1.10019i	−0.835102	−	0.550095i	$-0.814591\pi$
$919$		−	2.00918e19i		−	1.10019i	0.835102	−	0.550095i	$-0.185409\pi$
$920$	−1.72935e18	+	2.18993e18i	−0.0940288	+	0.119072i
$921$	2.92503e19	+	1.39817e19i	1.57922	+	0.754868i
$922$	1.02457e19	+	9.47633e18i	0.549278	+	0.508030i
$923$	3.56317e19			1.89681
$924$	9.70824e18	−	2.51863e19i	0.513183	−	1.33136i
$925$	−3.53148e18			−0.185369
$926$	1.16759e19	+	1.07991e19i	0.608584	+	0.562882i
$927$	1.08324e19	−	8.74196e18i	0.560667	−	0.452471i
$928$	1.84525e19	+	1.23665e19i	0.948404	+	0.635602i
$929$		−	3.47974e18i		−	0.177601i	−0.996049	−	0.0888003i	$-0.971697\pi$
$929$		−	3.47974e18i		−	0.177601i	0.996049	−	0.0888003i	$-0.0283033\pi$
$930$	−1.01958e17	−	2.56388e17i	−0.00516753	−	0.0129945i
$931$			5.74528e18i			0.289160i
$932$	1.09402e18	−	8.54923e16i	0.0546791	−	0.00427291i
$933$	3.09807e17	−	6.48130e17i	0.0153766	−	0.0321685i
$934$	−1.19908e19	+	1.29644e19i	−0.591008	+	0.638994i
$935$	−2.19658e19			−1.07516
$936$	−3.41436e17	−	3.22388e19i	−0.0165965	−	1.56706i
$937$	−1.35902e19			−0.656023			−0.328012	−	0.944674i	$-0.606379\pi$
$937$	−1.35902e19			−0.656023			−0.328012	+	0.944674i	$0.606379\pi$
$938$	−1.48799e19	+	1.60880e19i	−0.713314	+	0.771231i
$939$	3.13021e18	−	6.54855e18i	0.149021	−	0.311759i
$940$	−1.33343e19	+	1.04201e18i	−0.630433	+	0.0492653i
$941$			3.56327e19i			1.67308i	0.547907	+	0.836539i	$0.315425\pi$
$941$			3.56327e19i			1.67308i	−0.547907	+	0.836539i	$0.684575\pi$
$942$	−9.67215e18	−	2.43220e19i	−0.451016	−	1.13414i
$943$		−	2.56517e18i		−	0.118793i
$944$	3.09016e19	−	4.85931e18i	1.42123	−	0.223489i
$945$	2.19672e19	−	5.21570e18i	1.00339	−	0.238235i
$946$	−1.12987e19	−	1.04502e19i	−0.512550	−	0.474059i
$947$	−2.50279e19			−1.12759			−0.563793	−	0.825916i	$-0.690659\pi$
$947$	−2.50279e19			−1.12759			−0.563793	+	0.825916i	$0.690659\pi$
$948$	4.12117e18	−	1.06916e19i	0.184402	−	0.478399i
$949$	5.75190e19			2.55612
$950$	−2.91213e18	−	2.69344e18i	−0.128531	−	0.118878i
$951$	−3.00447e19	−	1.43614e19i	−1.31703	−	0.629540i
$952$	2.09017e19	+	1.65057e19i	0.909998	+	0.718610i
$953$		−	2.88209e19i		−	1.24625i	−0.782124	−	0.623123i	$-0.785864\pi$
$953$		−	2.88209e19i		−	1.24625i	0.782124	−	0.623123i	$-0.214136\pi$
$954$	−4.93291e17	+	7.30817e18i	−0.0211855	+	0.313866i
$955$			1.82273e18i			0.0777499i
$956$	−2.93361e18	−	3.75405e19i	−0.124287	−	1.59046i
$957$	−2.99443e19	−	1.43134e19i	−1.26005	−	0.602303i
$958$	−2.33000e18	+	2.51919e18i	−0.0973825	+	0.105289i
$959$	1.86937e19			0.776023
$960$	−4.51056e18	+	2.09633e19i	−0.185980	+	0.864362i
$961$	2.44114e19			0.999750
$962$	2.22139e19	−	2.40175e19i	0.903622	−	0.976991i
$963$	1.86276e19	+	2.30819e19i	0.752638	+	0.932611i
$964$	1.66728e17	+	2.13356e18i	0.00669125	+	0.0856258i
$965$			1.41861e19i			0.565503i
$966$	−4.69730e18	+	1.86798e18i	−0.185993	+	0.0739643i
$967$			1.11299e19i			0.437742i	0.975754	+	0.218871i	$0.0702373\pi$
$967$			1.11299e19i			0.437742i	−0.975754	+	0.218871i	$0.929763\pi$
$968$	−9.97181e18	−	7.87456e18i	−0.389569	−	0.307636i
$969$	−8.86082e18	+	1.85372e19i	−0.343850	+	0.719350i
$970$	−1.03877e18	−	9.60763e17i	−0.0400409	−	0.0370339i
$971$	−4.03453e19			−1.54479			−0.772393	−	0.635145i	$-0.780940\pi$
$971$	−4.03453e19			−1.54479			−0.772393	+	0.635145i	$0.780940\pi$
$972$	−1.44240e19	+	2.19827e19i	−0.548598	+	0.836086i
$973$	5.38791e18			0.203558
$974$	−1.43186e19	−	1.32433e19i	−0.537362	−	0.497008i
$975$	3.95746e18	−	8.27918e18i	0.147532	−	0.308644i
$976$	−4.00784e19	+	6.30236e18i	−1.48418	+	0.233388i
$977$		−	5.16641e18i		−	0.190053i	−0.995475	−	0.0950264i	$-0.969706\pi$
$977$		−	5.16641e18i		−	0.190053i	0.995475	−	0.0950264i	$-0.0302935\pi$
$978$	1.09869e19	−	4.36917e18i	0.401487	−	0.159660i
$979$			4.22566e19i			1.53393i
$980$	8.81271e18	−	6.88671e17i	0.317790	−	0.0248338i
$981$	1.31819e19	+	1.63339e19i	0.472202	+	0.585116i
$982$	2.11243e19	−	2.28395e19i	0.751722	−	0.812757i
$983$	9.71175e18			0.343320			0.171660	−	0.985156i	$-0.445087\pi$
$983$	9.71175e18			0.343320			0.171660	+	0.985156i	$0.445087\pi$
$984$	−8.68901e18	−	1.76938e19i	−0.305142	−	0.621373i
$985$	−4.31832e18			−0.150653
$986$	2.22355e19	−	2.40409e19i	0.770632	−	0.833203i
$987$	−2.18609e19	−	1.04495e19i	−0.752673	−	0.359779i
$988$	3.66360e19	−	2.86293e18i	1.25311	−	0.0979243i
$989$			2.88229e18i			0.0979405i
$990$	2.15765e18	−	3.19659e19i	0.0728372	−	1.07909i
$991$			2.49910e18i			0.0838117i	0.999122	+	0.0419059i	$0.0133430\pi$
$991$			2.49910e18i			0.0838117i	−0.999122	+	0.0419059i	$0.986657\pi$
$992$	3.94354e17	+	2.64288e17i	0.0131389	+	0.00880546i
$993$	−3.42991e18	−	1.63950e18i	−0.113530	−	0.0542676i
$994$	−3.15178e19	−	2.91509e19i	−1.03644	−	0.958606i
$995$	1.73395e19			0.566484
$996$	3.50254e19	+	1.35008e19i	1.13684	+	0.438202i
$997$	−2.51955e19			−0.812464			−0.406232	−	0.913770i	$-0.633157\pi$
$997$	−2.51955e19			−0.812464			−0.406232	+	0.913770i	$0.633157\pi$
$998$	3.72717e19	+	3.44727e19i	1.19407	+	1.10440i
$999$	−2.59580e19	+	6.16323e18i	−0.826220	+	0.196170i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	12.14.b.a.11.17	yes	24
3.2	odd	2	inner	12.14.b.a.11.8	yes	24
4.3	odd	2	inner	12.14.b.a.11.7	✓	24
12.11	even	2	inner	12.14.b.a.11.18	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
12.14.b.a.11.7	✓	24	4.3	odd	2	inner
12.14.b.a.11.8	yes	24	3.2	odd	2	inner
12.14.b.a.11.17	yes	24	1.1	even	1	trivial
12.14.b.a.11.18	yes	24	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:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	12.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(61.4564 - 66.4463i) q^{2} +(-544.543 + 1139.21i) q^{3} +(-638.220 - 8167.10i) q^{4} -30890.7i q^{5} +(42230.6 + 106195. i) q^{6} +363071. i q^{7} +(-581896. - 459513. i) q^{8} +(-1.00127e6 - 1.24070e6i) q^{9} +O(q^{10})\)	\(q+(61.4564 - 66.4463i) q^{2} +(-544.543 + 1139.21i) q^{3} +(-638.220 - 8167.10i) q^{4} -30890.7i q^{5} +(42230.6 + 106195. i) q^{6} +363071. i q^{7} +(-581896. - 459513. i) q^{8} +(-1.00127e6 - 1.24070e6i) q^{9} +(-2.05257e6 - 1.89843e6i) q^{10} -7.18745e6 q^{11} +(9.65157e6 + 3.72027e6i) q^{12} -2.72736e7 q^{13} +(2.41247e7 + 2.23130e7i) q^{14} +(3.51910e7 + 1.68213e7i) q^{15} +(-6.62942e7 + 1.04248e7i) q^{16} +9.89337e7i q^{17} +(-1.43974e8 - 9.71804e6i) q^{18} -1.64474e8i q^{19} +(-2.52288e8 + 1.97151e7i) q^{20} +(-4.13613e8 - 1.97707e8i) q^{21} +(-4.41715e8 + 4.77579e8i) q^{22} +1.21830e8 q^{23} +(8.40349e8 - 4.12677e8i) q^{24} +2.66466e8 q^{25} +(-1.67614e9 + 1.81223e9i) q^{26} +(1.95864e9 - 4.65043e8i) q^{27} +(2.96523e9 - 2.31719e8i) q^{28} -3.65709e9i q^{29} +(3.28043e9 - 1.30453e9i) q^{30} -7.81568e7i q^{31} +(-3.38151e9 + 5.04568e9i) q^{32} +(3.91387e9 - 8.18801e9i) q^{33} +(6.57378e9 + 6.08011e9i) q^{34} +1.12155e10 q^{35} +(-9.49386e9 + 8.96931e9i) q^{36} -1.32530e10 q^{37} +(-1.09287e10 - 1.01080e10i) q^{38} +(1.48516e10 - 3.10703e10i) q^{39} +(-1.41947e10 + 1.79752e10i) q^{40} -2.10553e10i q^{41} +(-3.85561e10 + 1.53327e10i) q^{42} +2.36583e10i q^{43} +(4.58718e9 + 5.87006e10i) q^{44} +(-3.83260e10 + 3.09299e10i) q^{45} +(7.48726e9 - 8.09518e9i) q^{46} +5.28535e10 q^{47} +(2.42240e10 - 8.11997e10i) q^{48} -3.49312e10 q^{49} +(1.63760e10 - 1.77057e10i) q^{50} +(-1.12706e11 - 5.38736e10i) q^{51} +(1.74066e10 + 2.22746e11i) q^{52} -5.07603e10i q^{53} +(8.94709e10 - 1.58725e11i) q^{54} +2.22026e11i q^{55} +(1.66836e11 - 2.11269e11i) q^{56} +(1.87370e11 + 8.95632e10i) q^{57} +(-2.43000e11 - 2.24752e11i) q^{58} -4.66129e11 q^{59} +(1.14922e11 - 2.98144e11i) q^{60} +6.04553e11 q^{61} +(-5.19323e9 - 4.80324e9i) q^{62} +(4.50460e11 - 3.63531e11i) q^{63} +(1.27451e11 + 5.34778e11i) q^{64} +8.42501e11i q^{65} +(-3.03530e11 - 7.63268e11i) q^{66} +6.66870e11i q^{67} +(8.08001e11 - 6.31415e10i) q^{68} +(-6.63418e10 + 1.38790e11i) q^{69} +(6.89265e11 - 7.45229e11i) q^{70} -1.30645e12 q^{71} +(1.25189e10 + 1.18205e12i) q^{72} -2.10896e12 q^{73} +(-8.14484e11 + 8.80615e11i) q^{74} +(-1.45102e11 + 3.03560e11i) q^{75} +(-1.34328e12 + 1.04971e11i) q^{76} -2.60955e12i q^{77} +(-1.15178e12 - 2.89631e12i) q^{78} -1.10776e12i q^{79} +(3.22030e11 + 2.04788e12i) q^{80} +(-5.36785e11 + 2.48454e12i) q^{81} +(-1.39904e12 - 1.29398e12i) q^{82} +3.62899e12 q^{83} +(-1.35072e12 + 3.50420e12i) q^{84} +3.05613e12 q^{85} +(1.57200e12 + 1.45395e12i) q^{86} +(4.16619e12 + 1.99144e12i) q^{87} +(4.18235e12 + 3.30273e12i) q^{88} -5.87921e12i q^{89} +(-3.00197e11 + 4.44746e12i) q^{90} -9.90224e12i q^{91} +(-7.77546e10 - 9.95001e11i) q^{92} +(8.90369e10 + 4.25597e10i) q^{93} +(3.24819e12 - 3.51192e12i) q^{94} -5.08073e12 q^{95} +(-3.90670e12 - 6.59984e12i) q^{96} +5.06082e11 q^{97} +(-2.14675e12 + 2.32105e12i) q^{98} +(7.19658e12 + 8.91744e12i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 8376 q^{4} - 135720 q^{6} - 327240 q^{9}+O(q^{10}) \) 24 * q - 8376 * q^4 - 135720 * q^6 - 327240 * q^9	\( 24 q - 8376 q^{4} - 135720 q^{6} - 327240 q^{9} + 4403568 q^{10} - 139896 q^{12} - 17520048 q^{13} + 41046816 q^{16} - 102153744 q^{18} + 340864272 q^{21} + 401914896 q^{22} + 14766624 q^{24} - 3043252488 q^{25} + 3306349488 q^{28} + 3523891248 q^{30} - 10577805696 q^{33} + 5461322688 q^{34} + 16126437096 q^{36} - 29352930672 q^{37} - 5243368896 q^{40} + 35399300688 q^{42} + 36221734656 q^{45} + 1675946784 q^{46} + 27878547744 q^{48} - 165718477944 q^{49} - 6459860112 q^{52} - 10955701656 q^{54} + 590611321584 q^{57} - 440462601456 q^{58} - 208761511104 q^{60} + 555426186192 q^{61} - 741528997248 q^{64} + 263546293968 q^{66} - 122266973952 q^{69} - 885399371232 q^{70} + 625428177984 q^{72} + 365028975600 q^{73} + 1427271642000 q^{76} + 1481181276240 q^{78} - 2327652239400 q^{81} + 874644720480 q^{82} - 6757787638224 q^{84} - 3308476422144 q^{85} + 11607512359104 q^{88} + 4426488729648 q^{90} - 3971016902448 q^{93} - 3078833939904 q^{94} - 6470779487616 q^{96} - 4159752429648 q^{97}+O(q^{100}) \) 24 * q - 8376 * q^4 - 135720 * q^6 - 327240 * q^9 + 4403568 * q^10 - 139896 * q^12 - 17520048 * q^13 + 41046816 * q^16 - 102153744 * q^18 + 340864272 * q^21 + 401914896 * q^22 + 14766624 * q^24 - 3043252488 * q^25 + 3306349488 * q^28 + 3523891248 * q^30 - 10577805696 * q^33 + 5461322688 * q^34 + 16126437096 * q^36 - 29352930672 * q^37 - 5243368896 * q^40 + 35399300688 * q^42 + 36221734656 * q^45 + 1675946784 * q^46 + 27878547744 * q^48 - 165718477944 * q^49 - 6459860112 * q^52 - 10955701656 * q^54 + 590611321584 * q^57 - 440462601456 * q^58 - 208761511104 * q^60 + 555426186192 * q^61 - 741528997248 * q^64 + 263546293968 * q^66 - 122266973952 * q^69 - 885399371232 * q^70 + 625428177984 * q^72 + 365028975600 * q^73 + 1427271642000 * q^76 + 1481181276240 * q^78 - 2327652239400 * q^81 + 874644720480 * q^82 - 6757787638224 * q^84 - 3308476422144 * q^85 + 11607512359104 * q^88 + 4426488729648 * q^90 - 3971016902448 * q^93 - 3078833939904 * q^94 - 6470779487616 * q^96 - 4159752429648 * q^97

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