LMFDB - Embedded newform 12.18.b.a.11.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [12,18,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, 18, names="a")

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

chi := DirichletCharacter("12.11");

S:= CuspForms(chi, 18);

N := Newforms(S);

Level:	$ N $	$=$	$ 12 = 2^{2} \cdot 3 $
Weight:	$ k $	$=$	$ 18 $
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:	$21.9866504813$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			11.11
Character	$\chi$	$=$	12.11
Dual form			12.18.b.a.11.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-207.324 - 296.798i) q^{2} +(11323.4 - 959.175i) q^{3} +(-45105.9 + 123066. i) q^{4} -804702. i q^{5} +(-2.63230e6 - 3.16191e6i) q^{6} +2.45214e7i q^{7} +(4.58773e7 - 1.21272e7i) q^{8} +(1.27300e8 - 2.17223e7i) q^{9} +O(q^{10})$	\(q+(-207.324 - 296.798i) q^{2} +(11323.4 - 959.175i) q^{3} +(-45105.9 + 123066. i) q^{4} -804702. i q^{5} +(-2.63230e6 - 3.16191e6i) q^{6} +2.45214e7i q^{7} +(4.58773e7 - 1.21272e7i) q^{8} +(1.27300e8 - 2.17223e7i) q^{9} +(-2.38834e8 + 1.66834e8i) q^{10} -7.53583e8 q^{11} +(-3.92712e8 + 1.43680e9i) q^{12} -5.41375e9 q^{13} +(7.27791e9 - 5.08387e9i) q^{14} +(-7.71850e8 - 9.11199e9i) q^{15} +(-1.31108e10 - 1.11020e10i) q^{16} +2.92884e10i q^{17} +(-3.28394e10 - 3.32789e10i) q^{18} +4.12729e10i q^{19} +(9.90317e10 + 3.62968e10i) q^{20} +(2.35203e10 + 2.77667e11i) q^{21} +(1.56235e11 + 2.23662e11i) q^{22} -2.06275e11 q^{23} +(5.07857e11 - 1.81326e11i) q^{24} +1.15395e11 q^{25} +(1.12240e12 + 1.60679e12i) q^{26} +(1.42064e12 - 3.68074e11i) q^{27} +(-3.01776e12 - 1.10606e12i) q^{28} +2.39176e12i q^{29} +(-2.54440e12 + 2.11821e12i) q^{30} +2.92599e12i q^{31} +(-5.76889e11 + 6.19297e12i) q^{32} +(-8.53315e12 + 7.22818e11i) q^{33} +(8.69273e12 - 6.07217e12i) q^{34} +1.97324e13 q^{35} +(-3.06870e12 + 1.66462e13i) q^{36} +8.68969e12 q^{37} +(1.22497e13 - 8.55684e12i) q^{38} +(-6.13023e13 + 5.19274e12i) q^{39} +(-9.75879e12 - 3.69176e13i) q^{40} +1.59536e13i q^{41} +(7.75346e13 - 6.45476e13i) q^{42} +7.46925e13i q^{43} +(3.39910e13 - 9.27407e13i) q^{44} +(-1.74800e13 - 1.02439e14i) q^{45} +(4.27657e13 + 6.12221e13i) q^{46} -5.30716e12 q^{47} +(-1.59108e14 - 1.13138e14i) q^{48} -3.68670e14 q^{49} +(-2.39240e13 - 3.42489e13i) q^{50} +(2.80927e13 + 3.31645e14i) q^{51} +(2.44192e14 - 6.66251e14i) q^{52} -5.59069e14i q^{53} +(-4.03775e14 - 3.45332e14i) q^{54} +6.06409e14i q^{55} +(2.97376e14 + 1.12498e15i) q^{56} +(3.95879e13 + 4.67351e14i) q^{57} +(7.09869e14 - 4.95868e14i) q^{58} -8.13593e13 q^{59} +(1.15619e15 + 3.16016e14i) q^{60} -1.52969e15 q^{61} +(8.68427e14 - 6.06626e14i) q^{62} +(5.32662e14 + 3.12158e15i) q^{63} +(1.95766e15 - 1.11273e15i) q^{64} +4.35646e15i q^{65} +(1.98365e15 + 2.38276e15i) q^{66} +3.40080e14i q^{67} +(-3.60442e15 - 1.32108e15i) q^{68} +(-2.33574e15 + 1.97854e14i) q^{69} +(-4.09100e15 - 5.85654e15i) q^{70} -2.49810e15 q^{71} +(5.57676e15 - 2.54036e15i) q^{72} -3.35635e15 q^{73} +(-1.80158e15 - 2.57908e15i) q^{74} +(1.30666e15 - 1.10684e14i) q^{75} +(-5.07930e15 - 1.86165e15i) q^{76} -1.84789e16i q^{77} +(1.42506e16 + 1.71178e16i) q^{78} -7.33851e15i q^{79} +(-8.93383e15 + 1.05503e16i) q^{80} +(1.57335e16 - 5.53050e15i) q^{81} +(4.73499e15 - 3.30756e15i) q^{82} -2.82958e14 q^{83} +(-3.52323e16 - 9.62985e15i) q^{84} +2.35684e16 q^{85} +(2.21686e16 - 1.54855e16i) q^{86} +(2.29412e15 + 2.70829e16i) q^{87} +(-3.45724e16 + 9.13886e15i) q^{88} +9.20486e15i q^{89} +(-2.67796e16 + 2.64260e16i) q^{90} -1.32753e17i q^{91} +(9.30424e15 - 2.53855e16i) q^{92} +(2.80653e15 + 3.31322e16i) q^{93} +(1.10030e15 + 1.57515e15i) q^{94} +3.32124e16 q^{95} +(-5.92223e14 + 7.06790e16i) q^{96} -3.56756e16 q^{97} +(7.64339e16 + 1.09420e17i) q^{98} +(-9.59312e16 + 1.63696e16i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 54808 q^{4} - 4960776 q^{6} + 79874976 q^{9}+O(q^{10}) $ 32 * q - 54808 * q^4 - 4960776 * q^6 + 79874976 * q^9	$ 32 q - 54808 q^{4} - 4960776 q^{6} + 79874976 q^{9} + 46839088 q^{10} + 2598308520 q^{12} + 221287360 q^{13} - 41721285088 q^{16} + 27568791600 q^{18} + 128365169856 q^{21} - 493958165040 q^{22} - 253565784288 q^{24} - 3063689463648 q^{25} - 2695436033040 q^{28} - 2169979068432 q^{30} - 17644793625600 q^{33} + 6944208632512 q^{34} - 12909384040056 q^{36} - 7970760699200 q^{37} + 21066454663744 q^{40} + 55835180334480 q^{42} + 154013263804416 q^{45} + 235918828815264 q^{46} + 299462725247520 q^{48} - 248591781347488 q^{49} + 544732086739120 q^{52} + 487051858173384 q^{54} - 21\!\cdots\!20 q^{57}+ \cdots + 90\!\cdots\!60 q^{97}+O(q^{100}) $ 32 * q - 54808 * q^4 - 4960776 * q^6 + 79874976 * q^9 + 46839088 * q^10 + 2598308520 * q^12 + 221287360 * q^13 - 41721285088 * q^16 + 27568791600 * q^18 + 128365169856 * q^21 - 493958165040 * q^22 - 253565784288 * q^24 - 3063689463648 * q^25 - 2695436033040 * q^28 - 2169979068432 * q^30 - 17644793625600 * q^33 + 6944208632512 * q^34 - 12909384040056 * q^36 - 7970760699200 * q^37 + 21066454663744 * q^40 + 55835180334480 * q^42 + 154013263804416 * q^45 + 235918828815264 * q^46 + 299462725247520 * q^48 - 248591781347488 * q^49 + 544732086739120 * q^52 + 487051858173384 * q^54 - 2151740586697920 * q^57 + 230877304263760 * q^58 - 345098683994304 * q^60 - 4956543779318336 * q^61 + 1003775054518400 * q^64 - 2371521654206832 * q^66 + 891375297976320 * q^69 - 949041839387232 * q^70 + 5817303713532480 * q^72 - 4887976236943040 * q^73 - 2051936325547056 * q^76 + 22261766802491280 * q^78 + 28021308982751520 * q^81 + 7596239161270240 * q^82 - 8356700998055568 * q^84 + 59910783041540096 * q^85 - 18469777603302720 * q^88 - 68814047068261392 * q^90 + 5961488029786560 * q^93 - 61915224567506112 * q^94 - 45410293501908864 * q^96 + 9062030716970560 * 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 $

$2$	−207.324	−	296.798i	−0.572656	−	0.819796i
$2$	−207.324	−	296.798i	−0.572656	−	0.819796i
$3$	11323.4	−	959.175i	0.996432	−	0.0844048i
$3$	11323.4	−	959.175i	0.996432	−	0.0844048i
$4$	−45105.9	+	123066.i	−0.344131	+	0.938922i
$5$		−	804702.i		−	0.921276i	−0.887588	−	0.460638i	$-0.847621\pi$
$5$		−	804702.i		−	0.921276i	0.887588	−	0.460638i	$-0.152379\pi$
$6$	−2.63230e6	−	3.16191e6i	−0.639807	−	0.768536i
$7$			2.45214e7i			1.60773i	0.594814	+	0.803864i	$0.297226\pi$
$7$			2.45214e7i			1.60773i	−0.594814	+	0.803864i	$0.702774\pi$
$8$	4.58773e7	−	1.21272e7i	0.966793	−	0.255562i
$9$	1.27300e8	−	2.17223e7i	0.985752	−	0.168207i
$10$	−2.38834e8	+	1.66834e8i	−0.755259	+	0.527574i
$11$	−7.53583e8			−1.05997			−0.529985	−	0.848007i	$-0.677802\pi$
$11$	−7.53583e8			−1.05997			−0.529985	+	0.848007i	$0.677802\pi$
$12$	−3.92712e8	+	1.43680e9i	−0.263653	+	0.964617i
$13$	−5.41375e9			−1.84069			−0.920344	−	0.391110i	$-0.872091\pi$
$13$	−5.41375e9			−1.84069			−0.920344	+	0.391110i	$0.872091\pi$
$14$	7.27791e9	−	5.08387e9i	1.31801	−	0.920674i
$15$	−7.71850e8	−	9.11199e9i	−0.0777601	−	0.917989i
$16$	−1.31108e10	−	1.11020e10i	−0.763148	−	0.646224i
$17$			2.92884e10i			1.01831i	0.860675	+	0.509155i	$0.170042\pi$
$17$			2.92884e10i			1.01831i	−0.860675	+	0.509155i	$0.829958\pi$
$18$	−3.28394e10	−	3.32789e10i	−0.702392	−	0.711790i
$19$			4.12729e10i			0.557518i	0.960361	+	0.278759i	$0.0899231\pi$
$19$			4.12729e10i			0.557518i	−0.960361	+	0.278759i	$0.910077\pi$
$20$	9.90317e10	+	3.62968e10i	0.865006	+	0.317040i
$21$	2.35203e10	+	2.77667e11i	0.135700	+	1.60199i
$22$	1.56235e11	+	2.23662e11i	0.606997	+	0.868958i
$23$	−2.06275e11			−0.549238			−0.274619	−	0.961553i	$-0.588552\pi$
$23$	−2.06275e11			−0.549238			−0.274619	+	0.961553i	$0.588552\pi$
$24$	5.07857e11	−	1.81326e11i	0.941772	−	0.336252i
$25$	1.15395e11			0.151250
$26$	1.12240e12	+	1.60679e12i	1.05408	+	1.50899i
$27$	1.42064e12	−	3.68074e11i	0.968037	−	0.250809i
$28$	−3.01776e12	−	1.10606e12i	−1.50953	−	0.553269i
$29$			2.39176e12i			0.887840i	0.896066	+	0.443920i	$0.146413\pi$
$29$			2.39176e12i			0.887840i	−0.896066	+	0.443920i	$0.853587\pi$
$30$	−2.54440e12	+	2.11821e12i	−0.708034	+	0.589439i
$31$			2.92599e12i			0.616167i	0.951359	+	0.308083i	$0.0996876\pi$
$31$			2.92599e12i			0.616167i	−0.951359	+	0.308083i	$0.900312\pi$
$32$	−5.76889e11	+	6.19297e12i	−0.0927507	+	0.995689i
$33$	−8.53315e12	+	7.22818e11i	−1.05619	+	0.0894665i
$34$	8.69273e12	−	6.07217e12i	0.834806	−	0.583141i
$35$	1.97324e13			1.48116
$36$	−3.06870e12	+	1.66462e13i	−0.181294	+	0.983429i
$37$	8.68969e12			0.406714			0.203357	−	0.979105i	$-0.434815\pi$
$37$	8.68969e12			0.406714			0.203357	+	0.979105i	$0.434815\pi$
$38$	1.22497e13	−	8.55684e12i	0.457051	−	0.319266i
$39$	−6.13023e13	+	5.19274e12i	−1.83412	+	0.155363i
$40$	−9.75879e12	−	3.69176e13i	−0.235443	−	0.890683i
$41$			1.59536e13i			0.312030i	0.987755	+	0.156015i	$0.0498648\pi$
$41$			1.59536e13i			0.312030i	−0.987755	+	0.156015i	$0.950135\pi$
$42$	7.75346e13	−	6.45476e13i	1.23560	−	1.02864i
$43$			7.46925e13i			0.974530i	0.873254	+	0.487265i	$0.162005\pi$
$43$			7.46925e13i			0.974530i	−0.873254	+	0.487265i	$0.837995\pi$
$44$	3.39910e13	−	9.27407e13i	0.364768	−	0.995228i
$45$	−1.74800e13	−	1.02439e14i	−0.154965	−	0.908150i
$46$	4.27657e13	+	6.12221e13i	0.314524	+	0.450263i
$47$	−5.30716e12			−0.0325110			−0.0162555	−	0.999868i	$-0.505175\pi$
$47$	−5.30716e12			−0.0325110			−0.0162555	+	0.999868i	$0.505175\pi$
$48$	−1.59108e14	−	1.13138e14i	−0.814969	−	0.579504i
$49$	−3.68670e14			−1.58479
$50$	−2.39240e13	−	3.42489e13i	−0.0866142	−	0.123994i
$51$	2.80927e13	+	3.31645e14i	0.0859502	+	1.01468i
$52$	2.44192e14	−	6.66251e14i	0.633437	−	1.72826i
$53$		−	5.59069e14i		−	1.23345i	−0.787180	−	0.616723i	$-0.788460\pi$
$53$		−	5.59069e14i		−	1.23345i	0.787180	−	0.616723i	$-0.211540\pi$
$54$	−4.03775e14	−	3.45332e14i	−0.759964	−	0.649965i
$55$			6.06409e14i			0.976524i
$56$	2.97376e14	+	1.12498e15i	0.410874	+	1.55434i
$57$	3.95879e13	+	4.67351e14i	0.0470572	+	0.555529i
$58$	7.09869e14	−	4.95868e14i	0.727848	−	0.508427i
$59$	−8.13593e13			−0.0721382			−0.0360691	−	0.999349i	$-0.511484\pi$
$59$	−8.13593e13			−0.0721382			−0.0360691	+	0.999349i	$0.511484\pi$
$60$	1.15619e15	+	3.16016e14i	0.888679	+	0.242898i
$61$	−1.52969e15			−1.02164			−0.510822	−	0.859687i	$-0.670659\pi$
$61$	−1.52969e15			−1.02164			−0.510822	+	0.859687i	$0.670659\pi$
$62$	8.68427e14	−	6.06626e14i	0.505131	−	0.352851i
$63$	5.32662e14	+	3.12158e15i	0.270431	+	1.58482i
$64$	1.95766e15	−	1.11273e15i	0.869376	−	0.494151i
$65$			4.35646e15i			1.69578i
$66$	1.98365e15	+	2.38276e15i	0.678176	+	0.814624i
$67$			3.40080e14i			0.102316i	0.998691	+	0.0511582i	$0.0162913\pi$
$67$			3.40080e14i			0.102316i	−0.998691	+	0.0511582i	$0.983709\pi$
$68$	−3.60442e15	−	1.32108e15i	−0.956113	−	0.350432i
$69$	−2.33574e15	+	1.97854e14i	−0.547278	+	0.0463583i
$70$	−4.09100e15	−	5.85654e15i	−0.848195	−	1.21425i
$71$	−2.49810e15			−0.459106			−0.229553	−	0.973296i	$-0.573726\pi$
$71$	−2.49810e15			−0.459106			−0.229553	+	0.973296i	$0.573726\pi$
$72$	5.57676e15	−	2.54036e15i	0.910030	−	0.414542i
$73$	−3.35635e15			−0.487105			−0.243553	−	0.969888i	$-0.578313\pi$
$73$	−3.35635e15			−0.487105			−0.243553	+	0.969888i	$0.578313\pi$
$74$	−1.80158e15	−	2.57908e15i	−0.232907	−	0.333423i
$75$	1.30666e15	−	1.10684e14i	0.150710	−	0.0127662i
$76$	−5.07930e15	−	1.86165e15i	−0.523466	−	0.191859i
$77$		−	1.84789e16i		−	1.70414i
$78$	1.42506e16	+	1.71178e16i	1.17768	+	1.41463i
$79$		−	7.33851e15i		−	0.544224i	−0.962266	−	0.272112i	$-0.912278\pi$
$79$		−	7.33851e15i		−	0.544224i	0.962266	−	0.272112i	$-0.0877221\pi$
$80$	−8.93383e15	+	1.05503e16i	−0.595351	+	0.703070i
$81$	1.57335e16	−	5.53050e15i	0.943413	−	0.331621i
$82$	4.73499e15	−	3.30756e15i	0.255801	−	0.178686i
$83$	−2.82958e14			−0.0137898			−0.00689491	−	0.999976i	$-0.502195\pi$
$83$	−2.82958e14			−0.0137898			−0.00689491	+	0.999976i	$0.502195\pi$
$84$	−3.52323e16	−	9.62985e15i	−1.55084	−	0.423883i
$85$	2.35684e16			0.938144
$86$	2.21686e16	−	1.54855e16i	0.798916	−	0.558070i
$87$	2.29412e15	+	2.70829e16i	0.0749379	+	0.884672i
$88$	−3.45724e16	+	9.13886e15i	−1.02477	+	0.270888i
$89$			9.20486e15i			0.247857i	0.992291	+	0.123929i	$0.0395494\pi$
$89$			9.20486e15i			0.247857i	−0.992291	+	0.123929i	$0.960451\pi$
$90$	−2.67796e16	+	2.64260e16i	−0.655756	+	0.647097i
$91$		−	1.32753e17i		−	2.95932i
$92$	9.30424e15	−	2.53855e16i	0.189010	−	0.515691i
$93$	2.80653e15	+	3.31322e16i	0.0520074	+	0.613968i
$94$	1.10030e15	+	1.57515e15i	0.0186176	+	0.0266524i
$95$	3.32124e16			0.513628
$96$	−5.92223e14	+	7.06790e16i	−0.00837876	+	0.999965i
$97$	−3.56756e16			−0.462180			−0.231090	−	0.972932i	$-0.574229\pi$
$97$	−3.56756e16			−0.462180			−0.231090	+	0.972932i	$0.574229\pi$
$98$	7.64339e16	+	1.09420e17i	0.907537	+	1.29920i
$99$	−9.59312e16	+	1.63696e16i	−1.04487	+	0.178294i
$100$	−5.20498e15	+	1.42012e16i	−0.0520498	+	0.142012i
$101$			1.30540e17i			1.19953i	0.800175	+	0.599767i	$0.204740\pi$
$101$			1.30540e17i			1.19953i	−0.800175	+	0.599767i	$0.795260\pi$
$102$	9.26073e16	−	7.70957e16i	0.782607	−	0.651521i
$103$		−	1.46286e16i		−	0.113785i	−0.998380	−	0.0568926i	$-0.981881\pi$
$103$		−	1.46286e16i		−	0.113785i	0.998380	−	0.0568926i	$-0.0181193\pi$
$104$	−2.48369e17	+	6.56537e16i	−1.77956	+	0.470409i
$105$	2.23439e17	−	1.89269e16i	1.47588	−	0.125017i
$106$	−1.65930e17	+	1.15908e17i	−1.01117	+	0.706340i
$107$	2.20691e17			1.24172			0.620859	−	0.783922i	$-0.286784\pi$
$107$	2.20691e17			1.24172			0.620859	+	0.783922i	$0.286784\pi$
$108$	−1.87817e16	+	1.91435e17i	−0.0976411	+	0.995222i
$109$	1.10152e16			0.0529499			0.0264750	−	0.999649i	$-0.491572\pi$
$109$	1.10152e16			0.0529499			0.0264750	+	0.999649i	$0.491572\pi$
$110$	1.79981e17	−	1.25723e17i	0.800551	−	0.559212i
$111$	9.83971e16	−	8.33493e15i	0.405263	−	0.0343286i
$112$	2.72238e17	−	3.21495e17i	1.03895	−	1.22693i
$113$		−	4.32681e17i		−	1.53109i	−0.643382	−	0.765545i	$-0.722469\pi$
$113$		−	4.32681e17i		−	1.53109i	0.643382	−	0.765545i	$-0.277531\pi$
$114$	1.30501e17	−	1.08642e17i	0.428473	−	0.356704i
$115$			1.65990e17i			0.506000i
$116$	−2.94345e17	−	1.07883e17i	−0.833612	−	0.305533i
$117$	−6.89172e17	+	1.17599e17i	−1.81446	+	0.309617i
$118$	1.68677e16	+	2.41473e16i	0.0413103	+	0.0591386i
$119$	−7.18193e17			−1.63716
$120$	−1.45913e17	−	4.08673e17i	−0.309781	−	0.867632i
$121$	6.24401e16			0.123534
$122$	3.17140e17	+	4.54008e17i	0.585050	+	0.837539i
$123$	1.53023e16	+	1.80649e17i	0.0263368	+	0.310916i
$124$	−3.60091e17	−	1.31979e17i	−0.578532	−	0.212042i
$125$		−	7.06797e17i		−	1.06062i
$126$	8.16045e17	−	8.05270e17i	1.14436	−	1.12925i
$127$			1.25317e18i			1.64315i	0.570097	+	0.821577i	$0.306906\pi$
$127$			1.25317e18i			1.64315i	−0.570097	+	0.821577i	$0.693094\pi$
$128$	−7.36125e17	−	3.50335e17i	−0.902956	−	0.429733i
$129$	7.16432e16	+	8.45776e17i	0.0822550	+	0.971053i
$130$	1.29299e18	−	9.03196e17i	1.39020	−	0.971099i
$131$	2.65933e17			0.267896			0.133948	−	0.990988i	$-0.457234\pi$
$131$	2.65933e17			0.267896			0.133948	+	0.990988i	$0.457234\pi$
$132$	2.95941e17	−	1.08275e18i	0.279464	−	1.02246i
$133$	−1.01207e18			−0.896337
$134$	1.00935e17	−	7.05066e16i	0.0838786	−	0.0585921i
$135$	−2.96190e17	−	1.14319e18i	−0.231064	−	0.891829i
$136$	3.55186e17	+	1.34367e18i	0.260241	+	0.984494i
$137$			1.08759e18i			0.748756i	0.927276	+	0.374378i	$0.122144\pi$
$137$			1.08759e18i			0.748756i	−0.927276	+	0.374378i	$0.877856\pi$
$138$	5.42977e17	+	6.52224e17i	0.351406	+	0.422109i
$139$			1.38868e18i			0.845230i	0.906309	+	0.422615i	$0.138888\pi$
$139$			1.38868e18i			0.845230i	−0.906309	+	0.422615i	$0.861112\pi$
$140$	−8.90050e17	+	2.42840e18i	−0.509713	+	1.39069i
$141$	−6.00953e16	+	5.09050e15i	−0.0323950	+	0.00274409i
$142$	5.17914e17	+	7.41430e17i	0.262910	+	0.376374i
$143$	4.07971e18			1.95107
$144$	−1.91017e18	−	1.12849e18i	−0.860974	−	0.508649i
$145$	1.92465e18			0.817946
$146$	6.95850e17	+	9.96157e17i	0.278944	+	0.399327i
$147$	−4.17461e18	+	3.53619e17i	−1.57913	+	0.133764i
$148$	−3.91956e17	+	1.06941e18i	−0.139963	+	0.381873i
$149$		−	2.95240e18i		−	0.995616i	−0.867287	−	0.497808i	$-0.834138\pi$
$149$		−	2.95240e18i		−	0.995616i	0.867287	−	0.497808i	$-0.165862\pi$
$150$	−3.03753e17	−	3.64867e17i	−0.0967708	−	0.116241i
$151$		−	1.96386e18i		−	0.591297i	−0.955297	−	0.295649i	$-0.904464\pi$
$151$		−	1.96386e18i		−	0.591297i	0.955297	−	0.295649i	$-0.0955358\pi$
$152$	5.00525e17	+	1.89349e18i	0.142480	+	0.539005i
$153$	6.36211e17	+	3.72842e18i	0.171287	+	1.00380i
$154$	−5.48451e18	+	3.83112e18i	−1.39705	+	0.975886i
$155$	2.35455e18			0.567660
$156$	2.12605e18	−	7.77847e18i	0.485303	−	1.77556i
$157$	−2.14719e18			−0.464220			−0.232110	−	0.972690i	$-0.574563\pi$
$157$	−2.14719e18			−0.464220			−0.232110	+	0.972690i	$0.574563\pi$
$158$	−2.17805e18	+	1.52145e18i	−0.446152	+	0.311653i
$159$	−5.36245e17	−	6.33058e18i	−0.104109	−	1.22905i
$160$	4.98349e18	+	4.64223e17i	0.917305	+	0.0854490i
$161$		−	5.05816e18i		−	0.883025i
$162$	−4.90336e18	−	3.52305e18i	−0.812112	−	0.583501i
$163$		−	6.59080e18i		−	1.03596i	−0.855392	−	0.517981i	$-0.826684\pi$
$163$		−	6.59080e18i		−	1.03596i	0.855392	−	0.517981i	$-0.173316\pi$
$164$	−1.96335e18	−	7.19602e17i	−0.292971	−	0.107379i
$165$	5.81653e17	+	6.86664e18i	0.0824233	+	0.973040i
$166$	5.86639e16	+	8.39814e16i	0.00789682	+	0.0113048i
$167$	−7.55929e18			−0.966921			−0.483460	−	0.875366i	$-0.660620\pi$
$167$	−7.55929e18			−0.966921			−0.483460	+	0.875366i	$0.660620\pi$
$168$	4.44637e18	+	1.24534e19i	0.540601	+	1.51411i
$169$	2.06583e19			2.38813
$170$	−4.88629e18	−	6.99506e18i	−0.537234	−	0.769087i
$171$	8.96542e17	+	5.25404e18i	0.0937786	+	0.549575i
$172$	−9.19214e18	−	3.36907e18i	−0.915007	−	0.335366i
$173$		−	1.32810e19i		−	1.25846i	−0.777220	−	0.629229i	$-0.783371\pi$
$173$		−	1.32810e19i		−	1.25846i	0.777220	−	0.629229i	$-0.216629\pi$
$174$	7.56253e18	−	6.29582e18i	0.682337	−	0.568046i
$175$			2.82964e18i			0.243169i
$176$	9.88006e18	+	8.36631e18i	0.808913	+	0.684977i
$177$	−9.21267e17	+	7.80378e16i	−0.0718808	+	0.00608881i
$178$	2.73198e18	−	1.90838e18i	0.203193	−	0.141937i
$179$	1.69563e19			1.20249			0.601243	−	0.799066i	$-0.294672\pi$
$179$	1.69563e19			1.20249			0.601243	+	0.799066i	$0.294672\pi$
$180$	1.33952e19	+	2.46939e18i	0.906010	+	0.167022i
$181$	−2.87278e19			−1.85368			−0.926840	−	0.375457i	$-0.877486\pi$
$181$	−2.87278e19			−1.85368			−0.926840	+	0.375457i	$0.877486\pi$
$182$	−3.94008e19	+	2.75228e19i	−2.42604	+	1.69467i
$183$	−1.73213e19	+	1.46724e18i	−1.01800	+	0.0862316i
$184$	−9.46336e18	+	2.50154e18i	−0.530999	+	0.140364i
$185$		−	6.99261e18i		−	0.374696i
$186$	9.25172e18	−	7.70207e18i	0.473546	−	0.394228i
$187$		−	2.20712e19i		−	1.07938i
$188$	2.39384e17	−	6.53133e17i	0.0111880	−	0.0305253i
$189$	9.02570e18	+	3.48361e19i	0.403233	+	1.55634i
$190$	−6.88570e18	−	9.85735e18i	−0.294132	−	0.421070i
$191$	3.11551e19			1.27276			0.636378	−	0.771377i	$-0.280432\pi$
$191$	3.11551e19			1.27276			0.636378	+	0.771377i	$0.280432\pi$
$192$	2.11001e19	−	1.44776e19i	0.824565	−	0.565767i
$193$	−2.14259e19			−0.801129			−0.400565	−	0.916268i	$-0.631186\pi$
$193$	−2.14259e19			−0.801129			−0.400565	+	0.916268i	$0.631186\pi$
$194$	7.39639e18	+	1.05884e19i	0.264670	+	0.378893i
$195$	4.17860e18	+	4.93301e19i	0.143132	+	1.68973i
$196$	1.66292e19	−	4.53708e19i	0.545374	−	1.48799i
$197$			9.67296e18i			0.303806i	0.988395	+	0.151903i	$0.0485401\pi$
$197$			9.67296e18i			0.303806i	−0.988395	+	0.151903i	$0.951460\pi$
$198$	2.47472e19	+	2.50784e19i	0.744514	+	0.754476i
$199$			5.44225e19i			1.56866i	0.620346	+	0.784328i	$0.286992\pi$
$199$			5.44225e19i			1.56866i	−0.620346	+	0.784328i	$0.713008\pi$
$200$	5.29400e18	−	1.39941e18i	0.146227	−	0.0386537i
$201$	3.26196e17	+	3.85087e18i	0.00863600	+	0.101951i
$202$	3.87440e19	−	2.70640e19i	0.983373	−	0.686920i
$203$	−5.86494e19			−1.42740
$204$	−4.20815e19	−	1.15019e19i	−0.982279	−	0.268481i
$205$	1.28379e19			0.287465
$206$	−4.34173e18	+	3.03285e18i	−0.0932806	+	0.0651597i
$207$	−2.62589e19	+	4.48077e18i	−0.541412	+	0.0923858i
$208$	7.09786e19	+	6.01037e19i	1.40472	+	1.18950i
$209$		−	3.11025e19i		−	0.590952i
$210$	−5.19416e19	−	6.23922e19i	−0.947657	−	1.13833i
$211$		−	6.69956e19i		−	1.17394i	−0.809609	−	0.586969i	$-0.800321\pi$
$211$		−	6.69956e19i		−	1.17394i	0.809609	−	0.586969i	$-0.199679\pi$
$212$	6.88025e19	+	2.52173e19i	1.15811	+	0.424467i
$213$	−2.82870e19	+	2.39611e18i	−0.457468	+	0.0387508i
$214$	−4.57545e19	−	6.55007e19i	−0.711077	−	1.01795i
$215$	6.01052e19			0.897811
$216$	6.07114e19	−	3.41146e19i	0.871793	−	0.489874i
$217$	−7.17494e19			−0.990628
$218$	−2.28370e18	−	3.26928e18i	−0.0303221	−	0.0434082i
$219$	−3.80054e19	+	3.21932e18i	−0.485367	+	0.0411140i
$220$	−7.46286e19	−	2.73527e19i	−0.916880	−	0.336052i
$221$		−	1.58560e20i		−	1.87439i
$222$	−2.28738e19	−	2.74760e19i	−0.260219	−	0.312575i
$223$			9.70471e19i			1.06265i	0.847167	+	0.531326i	$0.178306\pi$
$223$			9.70471e19i			1.06265i	−0.847167	+	0.531326i	$0.821694\pi$
$224$	−1.51860e20	−	1.41461e19i	−1.60080	−	0.149118i
$225$	1.46897e19	−	2.50664e18i	0.149095	−	0.0254413i
$226$	−1.28419e20	+	8.97049e19i	−1.25518	+	0.876788i
$227$	1.25717e20			1.18352			0.591759	−	0.806115i	$-0.298434\pi$
$227$	1.25717e20			1.18352			0.591759	+	0.806115i	$0.298434\pi$
$228$	−5.93008e19	−	1.62083e19i	−0.537792	−	0.146992i
$229$	2.03027e20			1.77399			0.886996	−	0.461778i	$-0.152788\pi$
$229$	2.03027e20			1.77399			0.886996	+	0.461778i	$0.152788\pi$
$230$	4.92655e19	−	3.44136e19i	0.414817	−	0.289764i
$231$	−1.77245e19	−	2.09245e20i	−0.143838	−	1.69806i
$232$	2.90054e19	+	1.09728e20i	0.226898	+	0.858357i
$233$			2.26785e20i			1.71037i	0.518324	+	0.855184i	$0.326556\pi$
$233$			2.26785e20i			1.71037i	−0.518324	+	0.855184i	$0.673444\pi$
$234$	1.77785e20	+	1.80164e20i	1.29288	+	1.31018i
$235$			4.27068e18i			0.0299516i
$236$	3.66979e18	−	1.00126e19i	0.0248250	−	0.0677321i
$237$	−7.03891e18	−	8.30971e19i	−0.0459351	−	0.542282i
$238$	1.48898e20	+	2.13158e20i	0.937531	+	1.34214i
$239$	−2.30519e20			−1.40063			−0.700317	−	0.713832i	$-0.746958\pi$
$239$	−2.30519e20			−1.40063			−0.700317	+	0.713832i	$0.746958\pi$
$240$	−9.10421e19	+	1.28034e20i	−0.533884	+	0.750812i
$241$	3.16095e19			0.178926			0.0894629	−	0.995990i	$-0.471485\pi$
$241$	3.16095e19			0.178926			0.0894629	+	0.995990i	$0.471485\pi$
$242$	−1.29453e19	−	1.85321e19i	−0.0707427	−	0.101273i
$243$	1.72852e20	−	7.77154e19i	0.912056	−	0.410066i
$244$	6.89980e19	−	1.88253e20i	0.351579	−	0.959243i
$245$			2.96669e20i			1.46003i
$246$	5.04439e19	−	4.19946e19i	0.239806	−	0.199639i
$247$		−	2.23441e20i		−	1.02622i
$248$	3.54841e19	+	1.34237e20i	0.157469	+	0.595706i
$249$	−3.20406e18	+	2.71406e17i	−0.0137406	+	0.00116393i
$250$	−2.09776e20	+	1.46536e20i	−0.869491	+	0.607370i
$251$	−1.03442e20			−0.414449			−0.207224	−	0.978293i	$-0.566443\pi$
$251$	−1.03442e20			−0.414449			−0.207224	+	0.978293i	$0.566443\pi$
$252$	−4.08188e20	−	7.52490e19i	−1.58109	−	0.291472i
$253$	1.55446e20			0.582175
$254$	3.71938e20	−	2.59812e20i	1.34705	−	0.940962i
$255$	2.66875e20	−	2.26062e19i	0.934796	−	0.0791839i
$256$	4.86373e19	+	2.91113e20i	0.164789	+	0.986329i
$257$		−	1.43915e20i		−	0.471709i	−0.971788	−	0.235855i	$-0.924211\pi$
$257$		−	1.43915e20i		−	0.471709i	0.971788	−	0.235855i	$-0.0757889\pi$
$258$	2.36171e20	−	1.96613e20i	0.748961	−	0.623511i
$259$			2.13084e20i			0.653886i
$260$	−5.36133e20	−	1.96502e20i	−1.59221	−	0.583571i
$261$	5.19545e19	+	3.04471e20i	0.149341	+	0.875190i
$262$	−5.51342e19	−	7.89284e19i	−0.153412	−	0.219620i
$263$	−1.55853e20			−0.419846			−0.209923	−	0.977718i	$-0.567321\pi$
$263$	−1.55853e20			−0.419846			−0.209923	+	0.977718i	$0.567321\pi$
$264$	−3.82712e20	+	1.36644e20i	−0.998249	+	0.356416i
$265$	−4.49884e20			−1.13635
$266$	2.09826e20	+	3.00380e20i	0.513293	+	0.734814i
$267$	8.82907e18	+	1.04231e20i	0.0209204	+	0.246973i
$268$	−4.18524e19	−	1.53396e19i	−0.0960671	−	0.0352102i
$269$		−	3.47600e20i		−	0.773011i	−0.922287	−	0.386505i	$-0.873682\pi$
$269$		−	3.47600e20i		−	0.773011i	0.922287	−	0.386505i	$-0.126318\pi$
$270$	−2.77889e20	+	3.24919e20i	−0.598798	+	0.700137i
$271$		−	3.99150e19i		−	0.0833484i	−0.999131	−	0.0416742i	$-0.986731\pi$
$271$		−	3.99150e19i		−	0.0833484i	0.999131	−	0.0416742i	$-0.0132692\pi$
$272$	3.25161e20	−	3.83994e20i	0.658056	−	0.777121i
$273$	−1.27333e20	−	1.50322e21i	−0.249781	−	2.94876i
$274$	3.22794e20	−	2.25483e20i	0.613827	−	0.428779i
$275$	−8.69594e19			−0.160320
$276$	8.10067e19	−	2.96376e20i	0.144808	−	0.529805i
$277$	3.42228e19			0.0593249			0.0296624	−	0.999560i	$-0.490557\pi$
$277$	3.42228e19			0.0593249			0.0296624	+	0.999560i	$0.490557\pi$
$278$	4.12156e20	−	2.87905e20i	0.692916	−	0.484026i
$279$	6.35592e19	+	3.72479e20i	0.103644	+	0.607387i
$280$	9.05272e20	−	2.39299e20i	1.43198	−	0.378528i
$281$			8.86146e20i			1.35988i	0.733266	+	0.679942i	$0.237995\pi$
$281$			8.86146e20i			1.35988i	−0.733266	+	0.679942i	$0.762005\pi$
$282$	1.39700e19	+	1.67808e19i	0.0208008	+	0.0249859i
$283$			7.66521e20i			1.10749i	0.832687	+	0.553744i	$0.186801\pi$
$283$			7.66521e20i			1.10749i	−0.832687	+	0.553744i	$0.813199\pi$
$284$	1.12679e20	−	3.07432e20i	0.157993	−	0.431065i
$285$	3.76078e20	−	3.18564e19i	0.511795	−	0.0433527i
$286$	−8.45820e20	−	1.21085e21i	−1.11729	−	1.59948i
$287$	−3.91205e20			−0.501659
$288$	6.10875e19	+	8.00897e20i	0.0760530	+	0.997104i
$289$	−3.05696e19			−0.0369537
$290$	−3.99026e20	−	5.71233e20i	−0.468401	−	0.670549i
$291$	−4.03970e20	+	3.42191e19i	−0.460531	+	0.0390102i
$292$	1.51391e20	−	4.13053e20i	0.167628	−	0.457354i
$293$			9.70468e20i			1.04377i	0.853015	+	0.521887i	$0.174772\pi$
$293$			9.70468e20i			1.04377i	−0.853015	+	0.521887i	$0.825228\pi$
$294$	9.70448e20	+	1.16570e21i	1.01396	+	1.21797i
$295$			6.54700e19i			0.0664592i
$296$	3.98660e20	−	1.05382e20i	0.393209	−	0.103941i
$297$	−1.07057e21	+	2.77374e20i	−1.02609	+	0.265850i
$298$	−8.76266e20	+	6.12102e20i	−0.816202	+	0.570145i
$299$	1.11672e21			1.01098
$300$	−4.53168e19	+	1.65799e20i	−0.0398776	+	0.145898i
$301$	−1.83157e21			−1.56678
$302$	−5.82869e20	+	4.07154e20i	−0.484743	+	0.338610i
$303$	1.25211e20	+	1.47816e21i	0.101246	+	1.19525i
$304$	4.58213e20	−	5.41120e20i	0.360282	−	0.425469i
$305$			1.23094e21i			0.941216i
$306$	9.74684e20	−	9.61814e20i	0.724823	−	0.715252i
$307$		−	1.80017e21i		−	1.30208i	−0.759043	−	0.651041i	$-0.774333\pi$
$307$		−	1.80017e21i		−	1.30208i	0.759043	−	0.651041i	$-0.225667\pi$
$308$	2.27413e21	+	8.33509e20i	1.60006	+	0.586448i
$309$	−1.40314e19	−	1.65646e20i	−0.00960401	−	0.113379i
$310$	−4.88153e20	−	6.98825e20i	−0.325074	−	0.465365i
$311$	−1.67295e21			−1.08398			−0.541988	−	0.840386i	$-0.682328\pi$
$311$	−1.67295e21			−1.08398			−0.541988	+	0.840386i	$0.682328\pi$
$312$	−2.74941e21	+	9.81655e20i	−1.73351	+	0.618934i
$313$	3.00064e21			1.84114			0.920570	−	0.390578i	$-0.127725\pi$
$313$	3.00064e21			1.84114			0.920570	+	0.390578i	$0.127725\pi$
$314$	4.45164e20	+	6.37282e20i	0.265838	+	0.380566i
$315$	2.51194e21	−	4.28634e20i	1.46006	−	0.249142i
$316$	9.03123e20	+	3.31010e20i	0.510983	+	0.187284i
$317$		−	2.26005e21i		−	1.24484i	−0.782682	−	0.622422i	$-0.786149\pi$
$317$		−	2.26005e21i		−	1.24484i	0.782682	−	0.622422i	$-0.213851\pi$
$318$	−1.76773e21	+	1.47163e21i	−0.947948	+	0.789168i
$319$		−	1.80239e21i		−	0.941083i
$320$	−8.95414e20	−	1.57533e21i	−0.455249	−	0.800936i
$321$	2.49898e21	−	2.11681e20i	1.23729	−	0.104807i
$322$	−1.50125e21	+	1.04868e21i	−0.723900	+	0.505669i
$323$	−1.20882e21			−0.567726
$324$	−2.90534e19	+	2.18572e21i	−0.0132912	+	0.999912i
$325$	−6.24718e20			−0.278404
$326$	−1.95614e21	+	1.36643e21i	−0.849277	+	0.593249i
$327$	1.24729e20	−	1.05655e19i	0.0527610	−	0.00446923i
$328$	1.93473e20	+	7.31909e20i	0.0797428	+	0.301668i
$329$		−	1.30139e20i		−	0.0522689i
$330$	1.91741e21	−	1.59625e21i	0.750494	−	0.624787i
$331$			1.66358e21i			0.634608i	0.948324	+	0.317304i	$0.102778\pi$
$331$			1.66358e21i			0.634608i	−0.948324	+	0.317304i	$0.897222\pi$
$332$	1.27631e19	−	3.48226e19i	0.00474550	−	0.0129476i
$333$	1.10620e21	−	1.88760e20i	0.400919	−	0.0684123i
$334$	1.56722e21	+	2.24358e21i	0.553713	+	0.792678i
$335$	2.73663e20			0.0942617
$336$	2.77430e21	−	3.90155e21i	0.931685	−	1.31025i
$337$	−1.12958e21			−0.369880			−0.184940	−	0.982750i	$-0.559209\pi$
$337$	−1.12958e21			−0.369880			−0.184940	+	0.982750i	$0.559209\pi$
$338$	−4.28296e21	−	6.13135e21i	−1.36758	−	1.95778i
$339$	−4.15016e20	−	4.89943e21i	−0.129231	−	1.52563i
$340$	−1.06308e21	+	2.90048e21i	−0.322844	+	0.880844i
$341$		−	2.20498e21i		−	0.653118i
$342$	1.37351e21	−	1.35538e21i	0.396836	−	0.391596i
$343$		−	3.33588e21i		−	0.940178i
$344$	9.05812e20	+	3.42669e21i	0.249053	+	0.942169i
$345$	1.59213e20	+	1.87958e21i	0.0427088	+	0.504194i
$346$	−3.94177e21	+	2.75346e21i	−1.03168	+	0.720663i
$347$	3.40394e21			0.869324			0.434662	−	0.900594i	$-0.356868\pi$
$347$	3.40394e21			0.869324			0.434662	+	0.900594i	$0.356868\pi$
$348$	−3.43648e21	−	9.39272e20i	−0.856426	−	0.234082i
$349$	2.41873e21			0.588263			0.294132	−	0.955765i	$-0.404970\pi$
$349$	2.41873e21			0.588263			0.294132	+	0.955765i	$0.404970\pi$
$350$	8.39831e20	−	5.86651e20i	0.199349	−	0.139252i
$351$	−7.69099e21	+	1.99266e21i	−1.78185	+	0.461661i
$352$	4.34733e20	−	4.66691e21i	0.0983129	−	1.05540i
$353$			1.07453e21i			0.237210i	0.992942	+	0.118605i	$0.0378422\pi$
$353$			1.07453e21i			0.237210i	−0.992942	+	0.118605i	$0.962158\pi$
$354$	2.14162e20	+	2.57251e20i	0.0461545	+	0.0554408i
$355$			2.01022e21i			0.422964i
$356$	−1.13281e21	−	4.15194e20i	−0.232719	−	0.0852954i
$357$	−8.13241e21	+	6.88873e20i	−1.63132	+	0.138184i
$358$	−3.51544e21	−	5.03259e21i	−0.688610	−	0.985793i
$359$	−6.02284e20			−0.115212			−0.0576061	−	0.998339i	$-0.518347\pi$
$359$	−6.02284e20			−0.115212			−0.0576061	+	0.998339i	$0.518347\pi$
$360$	−2.04423e21	−	4.48763e21i	−0.381908	−	0.838389i
$361$	3.77694e21			0.689173
$362$	5.95595e21	+	8.52635e21i	1.06152	+	1.51964i
$363$	7.07036e20	−	5.98910e19i	0.123094	−	0.0104269i
$364$	1.63374e22	+	5.98795e21i	2.77857	+	1.01839i
$365$			2.70086e21i			0.448758i
$366$	4.02659e21	+	4.83674e21i	0.653655	+	0.785169i
$367$			9.00210e21i			1.42785i	0.700222	+	0.713925i	$0.253084\pi$
$367$			9.00210e21i			1.42785i	−0.700222	+	0.713925i	$0.746916\pi$
$368$	2.70443e21	+	2.29008e21i	0.419150	+	0.354931i
$369$	3.46549e20	+	2.03089e21i	0.0524856	+	0.307584i
$370$	−2.07539e21	+	1.44973e21i	−0.307175	+	0.214572i
$371$	1.37092e22			1.98305
$372$	−4.20406e21	−	1.14907e21i	−0.594365	−	0.162454i
$373$	6.33233e20			0.0875061			0.0437531	−	0.999042i	$-0.486069\pi$
$373$	6.33233e20			0.0875061			0.0437531	+	0.999042i	$0.486069\pi$
$374$	−6.55069e21	+	4.57588e21i	−0.884868	+	0.618111i
$375$	−6.77942e20	−	8.00337e21i	−0.0895213	−	1.05683i
$376$	−2.43479e20	+	6.43611e19i	−0.0314314	+	0.00830857i
$377$		−	1.29484e22i		−	1.63424i
$378$	8.46804e21	−	9.90115e21i	1.04497	−	1.22181i
$379$			1.48267e22i			1.78901i	0.447060	+	0.894504i	$0.352471\pi$
$379$			1.48267e22i			1.78901i	−0.447060	+	0.894504i	$0.647529\pi$
$380$	−1.49807e21	+	4.08732e21i	−0.176755	+	0.482257i
$381$	1.20201e21	+	1.41902e22i	0.138690	+	1.63729i
$382$	−6.45918e21	−	9.24676e21i	−0.728851	−	1.04340i
$383$	−5.14033e21			−0.567285			−0.283642	−	0.958930i	$-0.591543\pi$
$383$	−5.14033e21			−0.567285			−0.283642	+	0.958930i	$0.591543\pi$
$384$	−8.67149e21	−	3.26092e21i	−0.936005	−	0.351986i
$385$	−1.48700e22			−1.56998
$386$	4.44210e21	+	6.35917e21i	0.458771	+	0.656763i
$387$	1.62249e21	+	9.50837e21i	0.163923	+	0.960645i
$388$	1.60918e21	−	4.39046e21i	0.159050	−	0.433951i
$389$		−	2.51544e21i		−	0.243244i	−0.992577	−	0.121622i	$-0.961190\pi$
$389$		−	2.51544e21i		−	0.243244i	0.992577	−	0.121622i	$-0.0388095\pi$
$390$	1.37747e22	−	1.14675e22i	1.30327	−	1.08497i
$391$		−	6.04147e21i		−	0.559294i
$392$	−1.69136e22	+	4.47094e21i	−1.53216	+	0.405011i
$393$	3.01128e21	−	2.55077e20i	0.266940	−	0.0226117i
$394$	2.87091e21	−	2.00543e21i	0.249059	−	0.173976i
$395$	−5.90531e21			−0.501380
$396$	2.31252e21	−	1.25443e22i	0.192166	−	1.04240i
$397$	−7.45381e21			−0.606260			−0.303130	−	0.952949i	$-0.598032\pi$
$397$	−7.45381e21			−0.606260			−0.303130	+	0.952949i	$0.598032\pi$
$398$	1.61525e22	−	1.12831e22i	1.28598	−	0.898300i
$399$	−1.14601e22	+	9.70752e20i	−0.893139	+	0.0756552i
$400$	−1.51291e21	−	1.28112e21i	−0.115426	−	0.0977413i
$401$		−	6.42923e21i		−	0.480211i	−0.970747	−	0.240105i	$-0.922818\pi$
$401$		−	6.42923e21i		−	0.480211i	0.970747	−	0.240105i	$-0.0771820\pi$
$402$	1.07530e21	−	8.95191e20i	0.0786338	−	0.0654628i
$403$		−	1.58406e22i		−	1.13417i
$404$	−1.60651e22	−	5.88813e21i	−1.12627	−	0.412796i
$405$	−4.45041e21	−	1.26607e22i	−0.305515	−	0.869144i
$406$	1.21594e22	+	1.74070e22i	0.817411	+	1.17018i
$407$	−6.54840e21			−0.431105
$408$	5.31075e21	+	1.48743e22i	0.342408	+	0.959015i
$409$	1.03773e22			0.655291			0.327646	−	0.944801i	$-0.393745\pi$
$409$	1.03773e22			0.655291			0.327646	+	0.944801i	$0.393745\pi$
$410$	−2.66160e21	−	3.81026e21i	−0.164619	−	0.235663i
$411$	1.04319e21	+	1.23152e22i	0.0631986	+	0.746084i
$412$	1.80029e21	+	6.59835e20i	0.106835	+	0.0391570i
$413$		−	1.99505e21i		−	0.115979i
$414$	6.77397e21	+	6.86461e21i	0.385780	+	0.390942i
$415$			2.27697e20i			0.0127042i
$416$	3.12313e21	−	3.35272e22i	0.170725	−	1.83275i
$417$	1.33198e21	+	1.57246e22i	0.0713415	+	0.842214i
$418$	−9.23116e21	+	6.44829e21i	−0.484460	+	0.338412i
$419$	2.80547e22			1.44273			0.721367	−	0.692553i	$-0.243514\pi$
$419$	2.80547e22			1.44273			0.721367	+	0.692553i	$0.243514\pi$
$420$	−7.74916e21	+	2.83515e22i	−0.390513	+	1.42875i
$421$	2.19843e22			1.08571			0.542855	−	0.839826i	$-0.317343\pi$
$421$	2.19843e22			1.08571			0.542855	+	0.839826i	$0.317343\pi$
$422$	−1.98841e22	+	1.38898e22i	−0.962390	+	0.672262i
$423$	−6.75602e20	+	1.15284e20i	−0.0320478	+	0.00546859i
$424$	−6.77994e21	−	2.56486e22i	−0.315222	−	1.19249i
$425$			3.37972e21i			0.154019i
$426$	6.57573e21	+	7.89876e21i	0.293739	+	0.352840i
$427$		−	3.75101e22i		−	1.64252i
$428$	−9.95448e21	+	2.71597e22i	−0.427313	+	1.16588i
$429$	4.61964e22	−	3.91316e21i	1.94411	−	0.164680i
$430$	−1.24612e22	−	1.78391e22i	−0.514137	−	0.736022i
$431$	−2.93679e22			−1.18800			−0.594000	−	0.804465i	$-0.702452\pi$
$431$	−2.93679e22			−1.18800			−0.594000	+	0.804465i	$0.702452\pi$
$432$	−2.27121e22	−	1.09463e22i	−0.900834	−	0.434164i
$433$	−1.70905e22			−0.664671			−0.332336	−	0.943161i	$-0.607837\pi$
$433$	−1.70905e22			−0.664671			−0.332336	+	0.943161i	$0.607837\pi$
$434$	1.48753e22	+	2.12951e22i	0.567289	+	0.812113i
$435$	2.17937e22	−	1.84608e21i	0.815027	−	0.0690385i
$436$	−4.96849e20	+	1.35560e21i	−0.0182217	+	0.0497159i
$437$		−	8.51357e21i		−	0.306210i
$438$	8.83490e21	+	1.06125e22i	0.311653	+	0.374358i
$439$		−	6.45193e21i		−	0.223224i	−0.993752	−	0.111612i	$-0.964399\pi$
$439$		−	6.45193e21i		−	0.223224i	0.993752	−	0.111612i	$-0.0356014\pi$
$440$	7.35405e21	+	2.78205e22i	0.249562	+	0.944097i
$441$	−4.69317e22	+	8.00836e21i	−1.56221	+	0.266573i
$442$	−4.70603e22	+	3.28733e22i	−1.53662	+	1.07338i
$443$	5.67092e22			1.81644			0.908222	−	0.418488i	$-0.137440\pi$
$443$	5.67092e22			1.81644			0.908222	+	0.418488i	$0.137440\pi$
$444$	−3.41254e21	+	1.24853e22i	−0.107232	+	0.392324i
$445$	7.40716e21			0.228345
$446$	2.88034e22	−	2.01202e22i	0.871159	−	0.608534i
$447$	−2.83187e21	−	3.34313e22i	−0.0840347	−	0.992063i
$448$	2.72857e22	+	4.80047e22i	0.794459	+	1.39772i
$449$			3.15966e22i			0.902705i	0.892346	+	0.451353i	$0.149058\pi$
$449$			3.15966e22i			0.902705i	−0.892346	+	0.451353i	$0.850942\pi$
$450$	−3.78949e21	−	3.84020e21i	−0.106237	−	0.107658i
$451$		−	1.20224e22i		−	0.330742i
$452$	5.32484e22	+	1.95165e22i	1.43757	+	0.526895i
$453$	−1.88368e21	−	2.22376e22i	−0.0499083	−	0.589187i
$454$	−2.60641e22	−	3.73126e22i	−0.677749	−	0.970244i
$455$	−1.06827e23			−2.72635
$456$	7.48385e21	+	2.09607e22i	0.187466	+	0.525055i
$457$	2.00722e22			0.493524			0.246762	−	0.969076i	$-0.420633\pi$
$457$	2.00722e22			0.493524			0.246762	+	0.969076i	$0.420633\pi$
$458$	−4.20922e22	−	6.02579e22i	−1.01589	−	1.45431i
$459$	1.07803e22	+	4.16082e22i	0.255401	+	0.985761i
$460$	−2.04278e22	−	7.48714e21i	−0.475094	−	0.174130i
$461$			7.54010e22i			1.72155i	0.508988	+	0.860774i	$0.330020\pi$
$461$			7.54010e22i			1.72155i	−0.508988	+	0.860774i	$0.669980\pi$
$462$	−5.84287e22	+	4.86420e22i	−1.30969	+	1.09032i
$463$			4.33427e22i			0.953845i	0.878945	+	0.476922i	$0.158248\pi$
$463$			4.33427e22i			0.953845i	−0.878945	+	0.476922i	$0.841752\pi$
$464$	2.65534e22	−	3.13578e22i	0.573743	−	0.677553i
$465$	2.66616e22	−	2.25842e21i	0.565634	−	0.0479132i
$466$	6.73094e22	−	4.70179e22i	1.40215	−	0.979452i
$467$	5.97613e22			1.22244			0.611219	−	0.791461i	$-0.290679\pi$
$467$	5.97613e22			1.22244			0.611219	+	0.791461i	$0.290679\pi$
$468$	1.66132e22	−	9.01183e22i	0.333706	−	1.81019i
$469$	−8.33925e21			−0.164497
$470$	1.26753e21	−	8.85413e20i	0.0245542	−	0.0171520i
$471$	−2.43136e22	+	2.05953e21i	−0.462564	+	0.0391824i
$472$	−3.73255e21	+	9.86661e20i	−0.0697427	+	0.0184358i
$473$		−	5.62870e22i		−	1.03297i
$474$	−2.32037e22	+	1.93171e22i	−0.418255	+	0.348198i
$475$			4.76267e21i			0.0843246i
$476$	3.23948e22	−	8.83854e22i	0.563398	−	1.53717i
$477$	−1.21443e22	−	7.11695e22i	−0.207475	−	1.21587i
$478$	4.77920e22	+	6.84176e22i	0.802081	+	1.14823i
$479$	2.28623e22			0.376936			0.188468	−	0.982079i	$-0.439648\pi$
$479$	2.28623e22			0.376936			0.188468	+	0.982079i	$0.439648\pi$
$480$	5.68755e22	+	4.76563e20i	0.921244	+	0.00771915i
$481$	−4.70439e22			−0.748634
$482$	−6.55340e21	−	9.38164e21i	−0.102463	−	0.146683i
$483$	−4.85166e21	−	5.72758e22i	−0.0745315	−	0.879874i
$484$	−2.81642e21	+	7.68427e21i	−0.0425120	+	0.115989i
$485$			2.87082e22i			0.425796i
$486$	−5.89021e22	−	3.51899e22i	−0.858465	−	0.512873i
$487$			6.83370e22i			0.978723i	0.872081	+	0.489361i	$0.162770\pi$
$487$			6.83370e22i			0.978723i	−0.872081	+	0.489361i	$0.837230\pi$
$488$	−7.01780e22	+	1.85508e22i	−0.987717	+	0.261093i
$489$	−6.32173e21	−	7.46305e22i	−0.0874401	−	1.03226i
$490$	8.80508e22	−	6.15065e22i	1.19692	−	0.836093i
$491$	−8.43641e22			−1.12711			−0.563553	−	0.826080i	$-0.690566\pi$
$491$	−8.43641e22			−1.12711			−0.563553	+	0.826080i	$0.690566\pi$
$492$	−2.29221e22	−	6.26516e21i	−0.300989	−	0.0822677i
$493$	−7.00508e22			−0.904096
$494$	−6.63169e22	+	4.63246e22i	−0.841288	+	0.587669i
$495$	1.31726e22	+	7.71960e22i	0.164258	+	0.962611i
$496$	3.24845e22	−	3.83620e22i	0.398182	−	0.470226i
$497$		−	6.12569e22i		−	0.738118i
$498$	7.44829e20	+	8.94689e20i	0.00882282	+	0.0105980i
$499$			1.23203e23i			1.43471i	0.696707	+	0.717356i	$0.254648\pi$
$499$			1.23203e23i			1.43471i	−0.696707	+	0.717356i	$0.745352\pi$
$500$	8.69829e22	+	3.18807e22i	0.995838	+	0.364992i
$501$	−8.55971e22	+	7.25068e21i	−0.963470	+	0.0816127i
$502$	2.14460e22	+	3.07014e22i	0.237337	+	0.339764i
$503$	−9.22528e22			−1.00381			−0.501905	−	0.864923i	$-0.667367\pi$
$503$	−9.22528e22			−1.00381			−0.501905	+	0.864923i	$0.667367\pi$
$504$	6.22932e22	+	1.36750e23i	0.666470	+	1.46308i
$505$	1.05046e23			1.10510
$506$	−3.22275e22	−	4.61359e22i	−0.333386	−	0.477265i
$507$	2.33923e23	−	1.98149e22i	2.37961	−	0.201570i
$508$	−1.54223e23	−	5.65254e22i	−1.54279	−	0.565460i
$509$			9.80119e22i			0.964224i	0.876110	+	0.482112i	$0.160130\pi$
$509$			9.80119e22i			0.964224i	−0.876110	+	0.482112i	$0.839870\pi$
$510$	−6.20390e22	−	7.45212e22i	−0.600231	−	0.720997i
$511$		−	8.23024e22i		−	0.783132i
$512$	7.63180e22	−	7.47900e22i	0.714221	−	0.699921i
$513$	1.51915e22	+	5.86339e22i	0.139831	+	0.539698i
$514$	−4.27136e22	+	2.98370e22i	−0.386705	+	0.270127i
$515$	−1.17716e22			−0.104828
$516$	−1.07318e23	−	2.93326e22i	−0.940049	−	0.256938i
$517$	3.99939e21			0.0344607
$518$	6.32428e22	−	4.41772e22i	0.536053	−	0.374452i
$519$	−1.27388e22	−	1.50386e23i	−0.106220	−	1.25397i
$520$	5.28317e22	+	1.99863e23i	0.433377	+	1.63947i
$521$			2.08559e23i			1.68309i	0.540187	+	0.841545i	$0.318354\pi$
$521$			2.08559e23i			1.68309i	−0.540187	+	0.841545i	$0.681646\pi$
$522$	7.95951e22	−	7.85441e22i	0.631956	−	0.623612i
$523$			8.16955e22i			0.638166i	0.947727	+	0.319083i	$0.103375\pi$
$523$			8.16955e22i			0.638166i	−0.947727	+	0.319083i	$0.896625\pi$
$524$	−1.19952e22	+	3.27274e22i	−0.0921914	+	0.251534i
$525$	2.71412e21	+	3.20412e22i	0.0205246	+	0.242301i
$526$	3.23119e22	+	4.62567e22i	0.240427	+	0.344188i
$527$	−8.56975e22			−0.627448
$528$	1.19901e23	+	8.52586e22i	0.863842	+	0.614257i
$529$	−9.85005e22			−0.698338
$530$	9.32715e22	+	1.33524e23i	0.650735	+	0.931571i
$531$	−1.03571e22	+	1.76731e21i	−0.0711103	+	0.0121342i
$532$	4.56503e22	−	1.24552e23i	0.308457	−	0.841591i
$533$		−	8.63689e22i		−	0.574349i
$534$	2.91049e22	−	2.42299e22i	0.190487	−	0.158581i
$535$		−	1.77591e23i		−	1.14396i
$536$	4.12422e21	+	1.56020e22i	0.0261482	+	0.0989188i
$537$	1.92003e23	−	1.62640e22i	1.19819	−	0.101496i
$538$	−1.03167e23	+	7.20657e22i	−0.633711	+	0.442669i
$539$	2.77823e23			1.67983
$540$	1.54048e23	+	1.51137e22i	0.916874	+	0.0899545i
$541$	2.61336e23			1.53117			0.765584	−	0.643336i	$-0.222450\pi$
$541$	2.61336e23			1.53117			0.765584	+	0.643336i	$0.222450\pi$
$542$	−1.18467e22	+	8.27532e21i	−0.0683287	+	0.0477299i
$543$	−3.25297e23	+	2.75550e22i	−1.84706	+	0.156459i
$544$	−1.81382e23	−	1.68961e22i	−1.01392	−	0.0944489i
$545$		−	8.86392e21i		−	0.0487815i
$546$	−4.19753e23	+	3.49445e23i	−2.27435	+	1.89340i
$547$			4.39624e22i			0.234525i	0.993101	+	0.117262i	$0.0374119\pi$
$547$			4.39624e22i			0.234525i	−0.993101	+	0.117262i	$0.962588\pi$
$548$	−1.33846e23	−	4.90567e22i	−0.703023	−	0.257670i
$549$	−1.94730e23	+	3.32284e22i	−1.00709	+	0.171848i
$550$	1.80287e22	+	2.58094e22i	0.0918083	+	0.131430i
$551$	−9.87148e22			−0.494987
$552$	−1.04758e23	+	3.74031e22i	−0.517257	+	0.184682i
$553$	1.79951e23			0.874963
$554$	−7.09518e21	−	1.01572e22i	−0.0339727	−	0.0486343i
$555$	−6.70713e21	−	7.91803e22i	−0.0316262	−	0.373359i
$556$	−1.70899e23	−	6.26375e22i	−0.793605	−	0.290870i
$557$		−	4.30064e23i		−	1.96682i	−0.181404	−	0.983409i	$-0.558064\pi$
$557$		−	4.30064e23i		−	1.96682i	0.181404	−	0.983409i	$-0.441936\pi$
$558$	9.73736e22	−	9.60879e22i	0.438582	−	0.432791i
$559$		−	4.04367e23i		−	1.79381i
$560$	−2.58708e23	−	2.19070e23i	−1.13034	−	0.957162i
$561$	−2.11702e22	−	2.49922e23i	−0.0911045	−	1.07552i
$562$	2.63006e23	−	1.83719e23i	1.11483	−	0.778745i
$563$	3.93160e23			1.64153			0.820763	−	0.571268i	$-0.193548\pi$
$563$	3.93160e23			1.64153			0.820763	+	0.571268i	$0.193548\pi$
$564$	2.08418e21	−	7.62532e21i	0.00857164	−	0.0313607i
$565$	−3.48179e23			−1.41056
$566$	2.27502e23	−	1.58918e23i	0.907915	−	0.634210i
$567$	1.35616e23	+	3.85807e23i	0.533156	+	1.51675i
$568$	−1.14606e23	+	3.02949e22i	−0.443861	+	0.117330i
$569$			1.94731e23i			0.742985i	0.928436	+	0.371492i	$0.121154\pi$
$569$			1.94731e23i			0.742985i	−0.928436	+	0.371492i	$0.878846\pi$
$570$	−8.74247e22	−	1.05015e23i	−0.328623	−	0.394742i
$571$		−	4.34006e23i		−	1.60727i	−0.595123	−	0.803635i	$-0.702896\pi$
$571$		−	4.34006e23i		−	1.60727i	0.595123	−	0.803635i	$-0.297104\pi$
$572$	−1.84019e23	+	5.02075e23i	−0.671424	+	1.83190i
$573$	3.52782e23	−	2.98832e22i	1.26821	−	0.107427i
$574$	8.11060e22	+	1.16109e23i	0.287278	+	0.411258i
$575$	−2.38031e22			−0.0830722
$576$	2.25040e23	−	1.84175e23i	0.773869	−	0.633345i
$577$	−8.12887e22			−0.275446			−0.137723	−	0.990471i	$-0.543978\pi$
$577$	−8.12887e22			−0.275446			−0.137723	+	0.990471i	$0.543978\pi$
$578$	6.33779e21	+	9.07298e21i	0.0211617	+	0.0302945i
$579$	−2.42615e23	+	2.05512e22i	−0.798271	+	0.0676192i
$580$	−8.68133e22	+	2.36860e23i	−0.281480	+	0.767987i
$581$		−	6.93854e21i		−	0.0221703i
$582$	9.39087e22	+	1.12803e23i	0.295706	+	0.355202i
$583$			4.21305e23i			1.30742i
$584$	−1.53980e23	+	4.07031e22i	−0.470930	+	0.124485i
$585$	9.46323e22	+	5.54578e23i	0.285243	+	1.67162i
$586$	2.88033e23	−	2.01201e23i	0.855682	−	0.597723i
$587$	−5.39296e23			−1.57908			−0.789538	−	0.613701i	$-0.789680\pi$
$587$	−5.39296e23			−1.57908			−0.789538	+	0.613701i	$0.789680\pi$
$588$	1.44781e23	−	5.29704e23i	0.417834	−	1.52871i
$589$	−1.20764e23			−0.343524
$590$	1.94313e22	−	1.35735e22i	0.0544830	−	0.0380582i
$591$	9.27806e21	+	1.09531e23i	0.0256427	+	0.302722i
$592$	−1.13929e23	−	9.64733e22i	−0.310383	−	0.262829i
$593$		−	3.80911e23i		−	1.02296i	−0.859295	−	0.511480i	$-0.829097\pi$
$593$		−	3.80911e23i		−	1.02296i	0.859295	−	0.511480i	$-0.170903\pi$
$594$	3.04278e23	+	2.60236e23i	0.805538	+	0.688943i
$595$			5.77931e23i			1.50828i
$596$	3.63341e23	+	1.33171e23i	0.934805	+	0.342622i
$597$	5.22007e22	+	6.16250e23i	0.132402	+	1.56306i
$598$	−2.31523e23	−	3.31441e23i	−0.578941	−	0.828794i
$599$	4.56799e23			1.12615			0.563076	−	0.826405i	$-0.309618\pi$
$599$	4.56799e23			1.12615			0.563076	+	0.826405i	$0.309618\pi$
$600$	5.86039e22	−	2.09240e22i	0.142443	−	0.0508581i
$601$	1.18024e23			0.282837			0.141418	−	0.989950i	$-0.454834\pi$
$601$	1.18024e23			0.282837			0.141418	+	0.989950i	$0.454834\pi$
$602$	3.79727e23	+	5.43605e23i	0.897225	+	1.28444i
$603$	7.38732e21	+	4.32922e22i	0.0172104	+	0.100859i
$604$	2.41685e23	+	8.85816e22i	0.555182	+	0.203484i
$605$		−	5.02456e22i		−	0.113809i
$606$	4.12756e23	−	3.43620e23i	0.921884	−	0.767470i
$607$		−	2.19745e23i		−	0.483965i	−0.970281	−	0.241983i	$-0.922202\pi$
$607$		−	2.19745e23i		−	0.483965i	0.970281	−	0.241983i	$-0.0777977\pi$
$608$	−2.55601e23	−	2.38098e22i	−0.555115	−	0.0517102i
$609$	−6.64112e23	+	5.62550e22i	−1.42231	+	0.120480i
$610$	3.65341e23	−	2.55203e23i	0.771605	−	0.538993i
$611$	2.87317e22			0.0598426
$612$	−4.87539e23	−	8.98774e22i	−1.00143	−	0.184614i
$613$	−5.51008e23			−1.11620			−0.558102	−	0.829772i	$-0.688470\pi$
$613$	−5.51008e23			−1.11620			−0.558102	+	0.829772i	$0.688470\pi$
$614$	−5.34288e23	+	3.73218e23i	−1.06744	+	0.745644i
$615$	1.45369e23	−	1.23138e22i	0.286440	−	0.0242635i
$616$	−2.24098e23	−	8.47764e23i	−0.435513	−	1.64755i
$617$		−	6.84346e22i		−	0.131175i	−0.997847	−	0.0655876i	$-0.979108\pi$
$617$		−	6.84346e22i		−	0.131175i	0.997847	−	0.0655876i	$-0.0208922\pi$
$618$	−4.62543e22	+	3.85067e22i	−0.0874480	+	0.0728005i
$619$			6.95396e22i			0.129677i	0.997896	+	0.0648383i	$0.0206532\pi$
$619$			6.95396e22i			0.129677i	−0.997896	+	0.0648383i	$0.979347\pi$
$620$	−1.06204e23	+	2.89766e23i	−0.195349	+	0.532988i
$621$	−2.93043e23	+	7.59246e22i	−0.531682	+	0.137754i
$622$	3.46842e23	+	4.96528e23i	0.620745	+	0.888640i
$623$	−2.25716e23			−0.398487
$624$	8.61371e23	+	6.12500e23i	1.50010	+	1.06669i
$625$	−4.80722e23			−0.825873
$626$	−6.22103e23	−	8.90583e23i	−1.05434	−	1.50936i
$627$	−2.98328e22	−	3.52187e23i	−0.0498792	−	0.588843i
$628$	9.68511e22	−	2.64247e23i	0.159752	−	0.435866i
$629$			2.54507e23i			0.414161i
$630$	−6.48002e23	−	6.56673e23i	−1.04036	−	1.05428i
$631$			1.16465e24i			1.84478i	0.386258	+	0.922391i	$0.373768\pi$
$631$			1.16465e24i			1.84478i	−0.386258	+	0.922391i	$0.626232\pi$
$632$	−8.89956e22	−	3.36671e23i	−0.139083	−	0.526152i
$633$	−6.42605e22	−	7.58620e23i	−0.0990860	−	1.16975i
$634$	−6.70779e23	+	4.68562e23i	−1.02052	+	0.712867i
$635$	1.00843e24			1.51380
$636$	8.03269e23	+	2.19553e23i	1.18980	+	0.325202i
$637$	1.99589e24			2.91710
$638$	−5.34945e23	+	3.73678e23i	−0.771496	+	0.538916i
$639$	−3.18008e23	+	5.42644e22i	−0.452565	+	0.0772250i
$640$	−2.81915e23	+	5.92361e23i	−0.395903	+	0.831872i
$641$		−	9.71291e23i		−	1.34603i	−0.739627	−	0.673017i	$-0.764998\pi$
$641$		−	9.71291e23i		−	1.34603i	0.739627	−	0.673017i	$-0.235002\pi$
$642$	−5.80924e23	−	6.97806e23i	−0.794459	−	0.954304i
$643$		−	4.51372e23i		−	0.609174i	−0.952485	−	0.304587i	$-0.901482\pi$
$643$		−	4.51372e23i		−	0.609174i	0.952485	−	0.304587i	$-0.0985184\pi$
$644$	6.22490e23	+	2.28153e23i	0.829091	+	0.303876i
$645$	6.80597e23	−	5.76514e22i	0.894608	−	0.0757796i
$646$	2.50616e23	+	3.58774e23i	0.325112	+	0.465419i
$647$	−3.67251e23			−0.470194			−0.235097	−	0.971972i	$-0.575541\pi$
$647$	−3.67251e23			−0.470194			−0.235097	+	0.971972i	$0.575541\pi$
$648$	6.54740e23	−	4.44528e23i	0.827335	−	0.561709i
$649$	6.13110e22			0.0764642
$650$	1.29519e23	+	1.85415e23i	0.159430	+	0.228234i
$651$	−8.12450e23	+	6.88202e22i	−0.987093	+	0.0836138i
$652$	8.11106e23	+	2.97284e23i	0.972687	+	0.356506i
$653$		−	2.83636e23i		−	0.335738i	−0.985809	−	0.167869i	$-0.946311\pi$
$653$		−	2.83636e23i		−	0.335738i	0.985809	−	0.167869i	$-0.0536885\pi$
$654$	−2.89951e22	−	3.48290e22i	−0.0338777	−	0.0406939i
$655$		−	2.13997e23i		−	0.246807i
$656$	1.77117e23	−	2.09164e23i	0.201641	−	0.238125i
$657$	−4.27264e23	+	7.29076e22i	−0.480165	+	0.0819346i
$658$	−3.86250e22	+	2.69809e22i	−0.0428498	+	0.0299321i
$659$	−5.63732e23			−0.617371			−0.308686	−	0.951164i	$-0.599889\pi$
$659$	−5.63732e23			−0.617371			−0.308686	+	0.951164i	$0.599889\pi$
$660$	−8.71288e23	−	2.38144e23i	−0.941972	−	0.257464i
$661$	−8.23719e23			−0.879158			−0.439579	−	0.898204i	$-0.644872\pi$
$661$	−8.23719e23			−0.879158			−0.439579	+	0.898204i	$0.644872\pi$
$662$	4.93747e23	−	3.44899e23i	0.520249	−	0.363412i
$663$	−1.52087e23	−	1.79545e24i	−0.158207	−	1.86770i
$664$	−1.29814e22	+	3.43149e21i	−0.0133319	+	0.00352415i
$665$			8.14414e23i			0.825774i
$666$	−2.85365e23	−	2.89183e23i	−0.285673	−	0.289495i
$667$		−	4.93361e23i		−	0.487635i
$668$	3.40969e23	−	9.30294e23i	0.332747	−	0.907863i
$669$	9.30852e22	+	1.09891e24i	0.0896930	+	1.05886i
$670$	−5.67368e22	−	8.12226e22i	−0.0539795	−	0.0772753i
$671$	1.15275e24			1.08291
$672$	−1.73315e24	−	1.45221e22i	−1.60767	−	0.0134708i
$673$	−2.59042e23			−0.237270			−0.118635	−	0.992938i	$-0.537852\pi$
$673$	−2.59042e23			−0.237270			−0.118635	+	0.992938i	$0.537852\pi$
$674$	2.34188e23	+	3.35256e23i	0.211814	+	0.303226i
$675$	1.63934e23	−	4.24738e22i	0.146416	−	0.0379349i
$676$	−9.31813e23	+	2.54234e24i	−0.821830	+	2.24227i
$677$		−	2.67061e23i		−	0.232599i	−0.993214	−	0.116299i	$-0.962897\pi$
$677$		−	2.67061e23i		−	0.232599i	0.993214	−	0.116299i	$-0.0371032\pi$
$678$	−1.36810e24	+	1.13894e24i	−1.17670	+	0.979602i
$679$		−	8.74816e23i		−	0.743060i
$680$	1.08126e24	−	2.85819e23i	0.906991	−	0.239754i
$681$	1.42355e24	−	1.20585e23i	1.17930	−	0.0998946i
$682$	−6.54432e23	+	4.57143e23i	−0.535423	+	0.374012i
$683$	−1.41179e24			−1.14076			−0.570378	−	0.821382i	$-0.693203\pi$
$683$	−1.41179e24			−1.14076			−0.570378	+	0.821382i	$0.693203\pi$
$684$	−6.87035e23	−	1.26654e23i	−0.548280	−	0.101075i
$685$	8.75185e23			0.689811
$686$	−9.90081e23	+	6.91606e23i	−0.770754	+	0.538398i
$687$	2.29896e24	−	1.94738e23i	1.76766	−	0.149733i
$688$	8.29239e23	−	9.79277e23i	0.629765	−	0.743711i
$689$			3.02666e24i			2.27039i
$690$	5.24846e23	−	4.36935e23i	0.388879	−	0.323742i
$691$			4.63062e23i			0.338903i	0.985539	+	0.169452i	$0.0541996\pi$
$691$			4.63062e23i			0.338903i	−0.985539	+	0.169452i	$0.945800\pi$
$692$	1.63444e24	+	5.99052e23i	1.18159	+	0.433074i
$693$	−4.01405e23	−	2.35237e24i	−0.286649	−	1.67986i
$694$	−7.05717e23	−	1.01028e24i	−0.497823	−	0.712668i
$695$	1.11747e24			0.778691
$696$	4.33688e23	+	1.21467e24i	0.298538	+	0.836143i
$697$	−4.67255e23			−0.317743
$698$	−5.01460e23	−	7.17875e23i	−0.336872	−	0.482256i
$699$	2.17527e23	+	2.56799e24i	0.144363	+	1.70427i
$700$	−3.48233e23	−	1.27634e23i	−0.228316	−	0.0836819i
$701$		−	3.06029e23i		−	0.198226i	−0.995076	−	0.0991129i	$-0.968400\pi$
$701$		−	3.06029e23i		−	0.198226i	0.995076	−	0.0991129i	$-0.0316005\pi$
$702$	2.18594e24	+	1.86954e24i	1.39886	+	1.19638i
$703$			3.58648e23i			0.226751i
$704$	−1.47526e24	+	8.38533e23i	−0.921512	+	0.523784i
$705$	4.09633e21	+	4.83588e22i	0.00252806	+	0.0298448i
$706$	3.18917e23	−	2.22775e23i	0.194464	−	0.135839i
$707$	−3.20103e24			−1.92852
$708$	3.19508e22	−	1.16897e23i	0.0190195	−	0.0695857i
$709$	1.14384e24			0.672781			0.336390	−	0.941723i	$-0.390794\pi$
$709$	1.14384e24			0.672781			0.336390	+	0.941723i	$0.390794\pi$
$710$	5.96630e23	−	4.16767e23i	0.346744	−	0.242213i
$711$	−1.59409e23	−	9.34193e23i	−0.0915423	−	0.536469i
$712$	1.11629e23	+	4.22294e23i	0.0633429	+	0.239627i
$713$		−	6.03559e23i		−	0.338422i
$714$	1.89050e24	+	2.27086e24i	1.04747	+	1.25822i
$715$		−	3.28295e24i		−	1.79748i
$716$	−7.64829e23	+	2.08675e24i	−0.413812	+	1.12904i
$717$	−2.61027e24	+	2.21108e23i	−1.39564	+	0.118220i
$718$	1.24868e23	+	1.78757e23i	0.0659769	+	0.0944505i
$719$	2.63276e24			1.37473			0.687363	−	0.726314i	$-0.258768\pi$
$719$	2.63276e24			1.37473			0.687363	+	0.726314i	$0.258768\pi$
$720$	−9.08102e23	+	1.53711e24i	−0.468607	+	0.793195i
$721$	3.58714e23			0.182936
$722$	−7.83048e23	−	1.12099e24i	−0.394659	−	0.564982i
$723$	3.57928e23	−	3.03191e22i	0.178287	−	0.0151022i
$724$	1.29579e24	−	3.53543e24i	0.637908	−	1.74046i
$725$			2.75996e23i			0.134286i
$726$	−1.64361e23	−	1.97430e23i	−0.0790382	−	0.0949406i
$727$			3.00564e24i			1.42855i	0.699868	+	0.714273i	$0.253242\pi$
$727$			3.00564e24i			1.42855i	−0.699868	+	0.714273i	$0.746758\pi$
$728$	−1.60992e24	−	6.09035e24i	−0.756290	−	2.86105i
$729$	1.88274e24	−	1.04580e24i	0.874190	−	0.485585i
$730$	8.01609e23	−	5.59952e23i	0.367890	−	0.256984i
$731$	−2.18762e24			−0.992373
$732$	6.00727e23	−	2.19785e24i	0.269360	−	0.985495i
$733$	−2.15529e24			−0.955262			−0.477631	−	0.878561i	$-0.658504\pi$
$733$	−2.15529e24			−0.955262			−0.477631	+	0.878561i	$0.658504\pi$
$734$	2.67180e24	−	1.86635e24i	1.17055	−	0.817666i
$735$	2.84558e23	+	3.35931e24i	0.123233	+	1.45482i
$736$	1.18998e23	−	1.27746e24i	0.0509422	−	0.546870i
$737$		−	2.56278e23i		−	0.108452i
$738$	5.30917e23	−	5.23907e23i	0.222100	−	0.219167i
$739$			3.24620e24i			1.34245i	0.741254	+	0.671224i	$0.234231\pi$
$739$			3.24620e24i			1.34245i	−0.741254	+	0.671224i	$0.765769\pi$
$740$	8.60555e23	+	3.15408e23i	0.351811	+	0.128945i
$741$	−2.14319e23	−	2.53012e24i	−0.0866176	−	1.02255i
$742$	−2.84223e24	−	4.06885e24i	−1.13560	−	1.62569i
$743$	−1.97981e24			−0.782023			−0.391011	−	0.920386i	$-0.627875\pi$
$743$	−1.97981e24			−0.782023			−0.391011	+	0.920386i	$0.627875\pi$
$744$	5.30558e23	+	1.48598e24i	0.207187	+	0.580289i
$745$	−2.37580e24			−0.917237
$746$	−1.31284e23	−	1.87942e23i	−0.0501109	−	0.0717372i
$747$	−3.60206e22	+	6.14650e21i	−0.0135933	+	0.00231955i
$748$	2.71623e24	+	9.95543e23i	1.01345	+	0.371447i
$749$			5.41166e24i			1.99634i
$750$	−2.23483e24	+	1.86050e24i	−0.815124	+	0.678592i
$751$		−	2.57163e24i		−	0.927404i	−0.885991	−	0.463702i	$-0.846521\pi$
$751$		−	2.57163e24i		−	0.927404i	0.885991	−	0.463702i	$-0.153479\pi$
$752$	6.95810e22	+	5.89203e22i	0.0248107	+	0.0210094i
$753$	−1.17132e24	+	9.92191e22i	−0.412970	+	0.0349815i
$754$	−3.84306e24	+	2.68451e24i	−1.33974	+	0.935855i
$755$	−1.58032e24			−0.544748
$756$	−4.69426e24	−	4.60554e23i	−1.60005	−	0.156980i
$757$	−3.48655e24			−1.17511			−0.587557	−	0.809182i	$-0.699910\pi$
$757$	−3.48655e24			−1.17511			−0.587557	+	0.809182i	$0.699910\pi$
$758$	4.40054e24	−	3.07393e24i	1.46662	−	1.02449i
$759$	1.76018e24	−	1.49099e23i	0.580098	−	0.0491384i
$760$	1.52369e24	−	4.02773e23i	0.496572	−	0.131264i
$761$		−	5.85950e24i		−	1.88839i	−0.329392	−	0.944193i	$-0.606844\pi$
$761$		−	5.85950e24i		−	1.88839i	0.329392	−	0.944193i	$-0.393156\pi$
$762$	3.96241e24	−	3.29871e24i	1.26282	−	1.05130i
$763$			2.70107e23i			0.0851291i
$764$	−1.40528e24	+	3.83414e24i	−0.437995	+	1.19502i
$765$	3.00026e24	−	5.11960e23i	0.924777	−	0.157803i
$766$	1.06571e24	+	1.52564e24i	0.324859	+	0.465058i
$767$	4.40459e23			0.132784
$768$	8.29969e23	+	3.24975e24i	0.247452	+	0.968900i
$769$	2.24881e24			0.663099			0.331549	−	0.943438i	$-0.392429\pi$
$769$	2.24881e24			0.663099			0.331549	+	0.943438i	$0.392429\pi$
$770$	3.08291e24	+	4.41339e24i	0.899061	+	1.28707i
$771$	−1.38040e23	−	1.62961e24i	−0.0398145	−	0.470026i
$772$	9.66437e23	−	2.63681e24i	0.275693	−	0.752198i
$773$			4.99284e23i			0.140871i	0.997516	+	0.0704355i	$0.0224389\pi$
$773$			4.99284e23i			0.140871i	−0.997516	+	0.0704355i	$0.977561\pi$
$774$	2.48568e24	−	2.45286e24i	0.693661	−	0.684502i
$775$			3.37643e23i			0.0931952i
$776$	−1.63670e24	+	4.32645e23i	−0.446832	+	0.118116i
$777$	2.04384e23	+	2.41284e24i	0.0551911	+	0.651553i
$778$	−7.46576e23	+	5.21509e23i	−0.199410	+	0.139295i
$779$	−6.58451e23			−0.173962
$780$	−6.25935e24	−	1.71083e24i	−1.63578	−	0.447099i
$781$	1.88252e24			0.486639
$782$	−1.79310e24	+	1.25254e24i	−0.458507	+	0.320283i
$783$	8.80345e23	+	3.39783e24i	0.222678	+	0.859462i
$784$	4.83355e24	+	4.09299e24i	1.20943	+	1.02413i
$785$			1.72785e24i			0.427675i
$786$	−7.00015e23	−	8.40858e23i	−0.171402	−	0.205888i
$787$		−	4.59281e24i		−	1.11248i	−0.831021	−	0.556241i	$-0.812243\pi$
$787$		−	4.59281e24i		−	1.11248i	0.831021	−	0.556241i	$-0.187757\pi$
$788$	−1.19042e24	−	4.36308e23i	−0.285250	−	0.104549i
$789$	−1.76479e24	+	1.49490e23i	−0.418348	+	0.0354370i
$790$	1.22431e24	+	1.75268e24i	0.287118	+	0.411030i
$791$	1.06099e25			2.46158
$792$	−4.20255e24	+	1.91437e24i	−0.964604	+	0.439402i
$793$	8.28136e24			1.88053
$794$	1.54535e24	+	2.21227e24i	0.347178	+	0.497010i
$795$	−5.09423e24	+	4.31517e23i	−1.13229	+	0.0959130i
$796$	−6.69758e24	−	2.45478e24i	−1.47285	−	0.539823i
$797$			8.27683e23i			0.180081i	0.995938	+	0.0900406i	$0.0286997\pi$
$797$			8.27683e23i			0.180081i	−0.995938	+	0.0900406i	$0.971300\pi$
$798$	2.66407e24	+	3.20007e24i	0.573483	+	0.688867i
$799$		−	1.55438e23i		−	0.0331063i
$800$	−6.65698e22	+	7.14635e23i	−0.0140285	+	0.150598i
$801$	1.99951e23	+	1.17178e24i	0.0416914	+	0.244326i
$802$	−1.90818e24	+	1.33293e24i	−0.393675	+	0.274995i
$803$	2.52929e24			0.516316
$804$	−4.88626e23	−	1.33553e23i	−0.0986962	−	0.0269761i
$805$	−4.07031e24			−0.813510
$806$	−4.70145e24	+	3.28413e24i	−0.929789	+	0.649489i
$807$	−3.33409e23	−	3.93603e24i	−0.0652458	−	0.770252i
$808$	1.58309e24	+	5.98883e24i	0.306555	+	1.15970i
$809$			5.47863e24i			1.04981i	0.851162	+	0.524904i	$0.175899\pi$
$809$			5.47863e24i			1.04981i	−0.851162	+	0.524904i	$0.824101\pi$
$810$	−2.83501e24	+	3.94574e24i	−0.537566	+	0.748180i
$811$			3.19132e24i			0.598816i	0.954125	+	0.299408i	$0.0967892\pi$
$811$			3.19132e24i			0.598816i	−0.954125	+	0.299408i	$0.903211\pi$
$812$	2.64543e24	−	7.21776e24i	0.491214	−	1.34022i
$813$	−3.82855e22	−	4.51975e23i	−0.00703501	−	0.0830510i
$814$	1.35764e24	+	1.94355e24i	0.246875	+	0.353418i
$815$	−5.30363e24			−0.954407
$816$	3.31362e24	−	4.66001e24i	0.590115	−	0.829890i
$817$	−3.08277e24			−0.543318
$818$	−2.15145e24	−	3.07995e24i	−0.375256	−	0.537205i
$819$	−2.88370e24	−	1.68995e25i	−0.497780	−	2.91716i
$820$	−5.79065e23	+	1.57991e24i	−0.0989257	+	0.269908i
$821$		−	1.32926e24i		−	0.224747i	−0.993666	−	0.112374i	$-0.964155\pi$
$821$		−	1.32926e24i		−	0.224747i	0.993666	−	0.112374i	$-0.0358453\pi$
$822$	3.43886e24	−	2.86286e24i	0.575445	−	0.479059i
$823$		−	2.81209e24i		−	0.465727i	−0.972509	−	0.232863i	$-0.925191\pi$
$823$		−	2.81209e24i		−	0.465727i	0.972509	−	0.232863i	$-0.0748095\pi$
$824$	−1.77404e23	−	6.71120e23i	−0.0290791	−	0.110007i
$825$	−9.84679e23	+	8.34092e22i	−0.159748	+	0.0135318i
$826$	−5.92125e23	+	4.13620e23i	−0.0950787	+	0.0664158i
$827$	−4.78787e24			−0.760931			−0.380466	−	0.924795i	$-0.624236\pi$
$827$	−4.78787e24			−0.760931			−0.380466	+	0.924795i	$0.624236\pi$
$828$	6.32998e23	−	3.43369e24i	0.0995737	−	0.540137i
$829$	5.44694e24			0.848084			0.424042	−	0.905643i	$-0.360611\pi$
$829$	5.44694e24			0.848084			0.424042	+	0.905643i	$0.360611\pi$
$830$	6.75800e22	−	4.72069e22i	0.0104149	−	0.00727515i
$831$	3.87519e23	−	3.28256e22i	0.0591132	−	0.00500730i
$832$	−1.05983e25	+	6.02404e24i	−1.60025	+	0.909577i
$833$		−	1.07977e25i		−	1.61380i
$834$	4.39087e24	−	3.65540e24i	0.649590	−	0.540784i
$835$			6.08297e24i			0.890801i
$836$	3.82767e24	+	1.40291e24i	0.554858	+	0.203365i
$837$	1.07698e24	+	4.15677e24i	0.154540	+	0.596472i
$838$	−5.81640e24	−	8.32658e24i	−0.826190	−	1.18275i
$839$	3.95388e24			0.555964			0.277982	−	0.960586i	$-0.410335\pi$
$839$	3.95388e24			0.555964			0.277982	+	0.960586i	$0.410335\pi$
$840$	1.00213e25	−	3.57800e24i	1.39492	−	0.498043i
$841$	1.53663e24			0.211740
$842$	−4.55786e24	−	6.52488e24i	−0.621738	−	0.890061i
$843$	8.49969e23	+	1.00342e25i	0.114781	+	1.35503i
$844$	8.24490e24	+	3.02190e24i	1.10224	+	0.403988i
$845$		−	1.66238e25i		−	2.20013i
$846$	1.74284e23	+	1.76616e23i	0.0228355	+	0.0231410i
$847$			1.53112e24i			0.198610i
$848$	−6.20680e24	+	7.32983e24i	−0.797083	+	0.941302i
$849$	7.35227e23	+	8.67965e24i	0.0934773	+	1.10354i
$850$	1.00309e24	−	7.00696e23i	0.126264	−	0.0882000i
$851$	−1.79247e24			−0.223383
$852$	9.81032e23	−	3.58926e24i	0.121045	−	0.442862i
$853$	1.20508e25			1.47214			0.736069	−	0.676906i	$-0.236680\pi$
$853$	1.20508e25			1.47214			0.736069	+	0.676906i	$0.236680\pi$
$854$	−1.11329e25	+	7.77673e24i	−1.34653	+	0.940601i
$855$	4.22794e24	−	7.21449e23i	0.506310	−	0.0863960i
$856$	1.01247e25	−	2.67637e24i	1.20048	−	0.317336i
$857$		−	6.36721e23i		−	0.0747501i	−0.999301	−	0.0373751i	$-0.988100\pi$
$857$		−	6.36721e23i		−	0.0747501i	0.999301	−	0.0373751i	$-0.0118996\pi$
$858$	−1.07390e25	−	1.28997e25i	−1.24831	−	1.49947i
$859$			2.36373e23i			0.0272055i	0.999907	+	0.0136027i	$0.00433002\pi$
$859$			2.36373e23i			0.0272055i	−0.999907	+	0.0136027i	$0.995670\pi$
$860$	−2.71110e24	+	7.39693e24i	−0.308965	+	0.842975i
$861$	−4.42978e24	+	3.75234e23i	−0.499868	+	0.0423424i
$862$	6.08866e24	+	8.71633e24i	0.680315	+	0.973917i
$863$	−7.22307e24			−0.799153			−0.399576	−	0.916700i	$-0.630843\pi$
$863$	−7.22307e24			−0.799153			−0.399576	+	0.916700i	$0.630843\pi$
$864$	1.45992e24	+	9.01031e24i	0.159942	+	0.987126i
$865$	−1.06872e25			−1.15939
$866$	3.54326e24	+	5.07241e24i	0.380628	+	0.544895i
$867$	−3.46152e23	+	2.93216e22i	−0.0368218	+	0.00311907i
$868$	3.23632e24	−	8.82994e24i	0.340906	−	0.930122i
$869$			5.53017e24i			0.576860i
$870$	−5.06626e24	−	6.08558e24i	−0.523327	−	0.628621i
$871$		−	1.84111e24i		−	0.188333i
$872$	5.05346e23	−	1.33583e23i	0.0511916	−	0.0135320i
$873$	−4.54151e24	+	7.74956e23i	−0.455595	+	0.0777420i
$874$	−2.52681e24	+	1.76506e24i	−0.251030	+	0.175353i
$875$	1.73317e25			1.70519
$876$	1.31808e24	−	4.82239e24i	0.128427	−	0.469870i
$877$	−7.50212e24			−0.723914			−0.361957	−	0.932195i	$-0.617891\pi$
$877$	−7.50212e24			−0.723914			−0.361957	+	0.932195i	$0.617891\pi$
$878$	−1.91492e24	+	1.33764e24i	−0.182998	+	0.127831i
$879$	9.30848e23	+	1.09890e25i	0.0880995	+	1.04005i
$880$	6.73238e24	−	7.95050e24i	0.631053	−	0.745233i
$881$		−	1.70601e24i		−	0.158375i	−0.996860	−	0.0791875i	$-0.974767\pi$
$881$		−	1.70601e24i		−	0.158375i	0.996860	−	0.0791875i	$-0.0252326\pi$
$882$	1.21069e25	+	1.22689e25i	1.11314	+	1.12804i
$883$			1.55931e25i			1.41993i	0.704238	+	0.709964i	$0.251289\pi$
$883$			1.55931e25i			1.41993i	−0.704238	+	0.709964i	$0.748711\pi$
$884$	1.95134e25	+	7.15200e24i	1.75990	+	0.645035i
$885$	6.27972e22	+	7.41345e23i	0.00560947	+	0.0662220i
$886$	−1.17572e25	−	1.68312e25i	−1.04020	−	1.48911i
$887$	7.39485e24			0.648006			0.324003	−	0.946056i	$-0.394971\pi$
$887$	7.39485e24			0.648006			0.324003	+	0.946056i	$0.394971\pi$
$888$	4.41312e24	−	1.57567e24i	0.383032	−	0.136758i
$889$	−3.07295e25			−2.64175
$890$	−1.53568e24	−	2.19843e24i	−0.130763	−	0.187196i
$891$	−1.18565e25	+	4.16769e24i	−0.999988	+	0.351508i
$892$	−1.19432e25	−	4.37740e24i	−0.997748	−	0.365692i
$893$		−	2.19042e23i		−	0.0181255i
$894$	−9.33522e24	+	7.77158e24i	−0.765166	+	0.637002i
$895$		−	1.36447e25i		−	1.10782i
$896$	8.59071e24	−	1.80508e25i	0.690894	−	1.45171i
$897$	1.26451e25	−	1.07113e24i	1.00737	−	0.0853312i
$898$	9.37779e24	−	6.55071e24i	0.740034	−	0.516939i
$899$	−6.99826e24			−0.547058
$900$	−3.54112e23	+	1.92088e24i	−0.0274207	+	0.148744i
$901$	1.63742e25			1.25603
$902$	−3.56821e24	+	2.49252e24i	−0.271141	+	0.189401i
$903$	−2.07396e25	+	1.75679e24i	−1.56119	+	0.132244i
$904$	−5.24721e24	−	1.98502e25i	−0.391288	−	1.48025i
$905$			2.31173e25i			1.70775i
$906$	−6.20954e24	+	5.16945e24i	−0.454433	+	0.378316i
$907$		−	9.22023e24i		−	0.668467i	−0.942490	−	0.334233i	$-0.891523\pi$
$907$		−	9.22023e24i		−	0.668467i	0.942490	−	0.334233i	$-0.108477\pi$
$908$	−5.67059e24	+	1.54716e25i	−0.407285	+	1.11123i
$909$	2.83563e24	+	1.66178e25i	0.201770	+	1.18244i
$910$	2.21477e25	+	3.17059e25i	1.56126	+	2.23505i
$911$	9.68173e24			0.676156			0.338078	−	0.941118i	$-0.390223\pi$
$911$	9.68173e24			0.676156			0.338078	+	0.941118i	$0.390223\pi$
$912$	4.66952e24	−	6.56684e24i	0.323084	−	0.454360i
$913$	2.13232e23			0.0146168
$914$	−4.16145e24	−	5.95740e24i	−0.282619	−	0.404589i
$915$	1.18069e24	+	1.39385e25i	0.0794431	+	0.937857i
$916$	−9.15771e24	+	2.49858e25i	−0.610485	+	1.66564i
$917$			6.52107e24i			0.430704i
$918$	1.01142e25	−	1.18259e25i	0.661866	−	0.773878i
$919$			1.16402e25i			0.754705i	0.926070	+	0.377352i	$0.123165\pi$
$919$			1.16402e25i			0.754705i	−0.926070	+	0.377352i	$0.876835\pi$
$920$	2.01300e24	+	7.61518e24i	0.129314	+	0.489197i
$921$	−1.72668e24	−	2.03841e25i	−0.109902	−	1.29744i
$922$	2.23788e25	−	1.56324e25i	1.41132	−	0.985854i
$923$	1.35241e25			0.845072
$924$	2.65505e25	+	7.25689e24i	1.64384	+	0.449303i
$925$	1.00274e24			0.0615156
$926$	1.28640e25	−	8.98597e24i	0.781958	−	0.546225i
$927$	−3.17766e23	−	1.86222e24i	−0.0191395	−	0.112164i
$928$	−1.48121e25	−	1.37978e24i	−0.884013	−	0.0823478i
$929$		−	2.83164e25i		−	1.67458i	−0.546762	−	0.837288i	$-0.684140\pi$
$929$		−	2.83164e25i		−	1.67458i	0.546762	−	0.837288i	$-0.315860\pi$
$930$	−6.19787e24	−	7.44487e24i	−0.363193	−	0.436267i
$931$		−	1.52161e25i		−	0.883548i
$932$	−2.79096e25	−	1.02294e25i	−1.60590	−	0.588591i
$933$	−1.89435e25	+	1.60465e24i	−1.08011	+	0.0914928i
$934$	−1.23899e25	−	1.77370e25i	−0.700036	−	1.00215i
$935$	−1.77608e25			−0.994404
$936$	−3.01912e25	+	1.37529e25i	−1.67508	+	0.763042i
$937$	9.49963e24			0.522300			0.261150	−	0.965298i	$-0.415898\pi$
$937$	9.49963e24			0.522300			0.261150	+	0.965298i	$0.415898\pi$
$938$	1.72892e24	+	2.47507e24i	0.0942001	+	0.134854i
$939$	3.39775e25	−	2.87814e24i	1.83457	−	0.155401i
$940$	−5.25577e23	−	1.92633e23i	−0.0281222	−	0.0103073i
$941$		−	3.89632e24i		−	0.206606i	−0.994650	−	0.103303i	$-0.967059\pi$
$941$		−	3.89632e24i		−	0.206606i	0.994650	−	0.103303i	$-0.0329411\pi$
$942$	5.65205e24	+	6.78923e24i	0.297011	+	0.356770i
$943$		−	3.29083e24i		−	0.171379i
$944$	1.06668e24	+	9.03254e23i	0.0550521	+	0.0466174i
$945$	2.80327e25	−	7.26300e24i	1.43382	−	0.371489i
$946$	−1.67059e25	+	1.16696e25i	−0.846826	+	0.591537i
$947$	−1.71722e25			−0.862685			−0.431343	−	0.902188i	$-0.641960\pi$
$947$	−1.71722e25			−0.862685			−0.431343	+	0.902188i	$0.641960\pi$
$948$	1.05440e25	+	2.88192e24i	0.524968	+	0.143486i
$949$	1.81704e25			0.896608
$950$	1.41355e24	−	9.87413e23i	0.0691290	−	0.0482890i
$951$	−2.16779e24	−	2.55916e25i	−0.105071	−	1.24040i
$952$	−3.29488e25	+	8.70968e24i	−1.58280	+	0.418396i
$953$		−	1.38882e25i		−	0.661237i	−0.943764	−	0.330619i	$-0.892743\pi$
$953$		−	1.38882e25i		−	0.661237i	0.943764	−	0.330619i	$-0.107257\pi$
$954$	−1.86052e25	+	1.83595e25i	−0.877955	+	0.866363i
$955$		−	2.50705e25i		−	1.17256i
$956$	1.03978e25	−	2.83691e25i	0.482002	−	1.31509i
$957$	−1.72881e24	−	2.04092e25i	−0.0794319	−	0.937725i
$958$	−4.73989e24	−	6.78548e24i	−0.215855	−	0.309011i
$959$	−2.66692e25			−1.20379
$960$	−1.16502e25	−	1.69793e25i	−0.521227	−	0.759652i
$961$	1.39887e25			0.620338
$962$	9.75330e24	+	1.39625e25i	0.428710	+	0.613727i
$963$	2.80940e25	−	4.79392e24i	1.22403	−	0.208866i
$964$	−1.42578e24	+	3.89007e24i	−0.0615739	+	0.167997i
$965$			1.72415e25i			0.738062i
$966$	−1.59935e25	+	1.33146e25i	−0.678636	+	0.564965i
$967$			1.34533e25i			0.565854i	0.959141	+	0.282927i	$0.0913054\pi$
$967$			1.34533e25i			0.565854i	−0.959141	+	0.282927i	$0.908695\pi$
$968$	2.86459e24	−	7.57224e23i	0.119432	−	0.0315707i
$969$	−1.36879e25	+	1.15947e24i	−0.565700	+	0.0479188i
$970$	8.52053e24	−	5.95189e24i	0.349066	−	0.243834i
$971$	1.24151e25			0.504179			0.252090	−	0.967704i	$-0.418882\pi$
$971$	1.24151e25			0.504179			0.252090	+	0.967704i	$0.418882\pi$
$972$	1.76750e24	+	2.47777e25i	0.0711535	+	0.997465i
$973$	−3.40523e25			−1.35890
$974$	2.02823e25	−	1.41679e25i	0.802353	−	0.560471i
$975$	−7.07395e24	+	5.99214e23i	−0.277411	+	0.0234986i
$976$	2.00554e25	+	1.69827e25i	0.779665	+	0.660210i
$977$			2.82421e25i			1.08841i	0.838952	+	0.544206i	$0.183169\pi$
$977$			2.82421e25i			1.08841i	−0.838952	+	0.544206i	$0.816831\pi$
$978$	−2.08395e25	+	1.73489e25i	−0.796173	+	0.662815i
$979$		−	6.93662e24i		−	0.262721i
$980$	−3.65100e25	−	1.33815e25i	−1.37085	−	0.502440i
$981$	1.40223e24	−	2.39275e23i	0.0521955	−	0.00890656i
$982$	1.74907e25	+	2.50391e25i	0.645444	+	0.923997i
$983$	−3.86771e25			−1.41498			−0.707488	−	0.706726i	$-0.750172\pi$
$983$	−3.86771e25			−1.41498			−0.707488	+	0.706726i	$0.750172\pi$
$984$	2.89280e24	+	8.10214e24i	0.104921	+	0.293861i
$985$	7.78385e24			0.279889
$986$	1.45232e25	+	2.07909e25i	0.517736	+	0.741174i
$987$	−1.24826e23	−	1.47362e24i	−0.00441174	−	0.0520823i
$988$	2.74981e25	+	1.00785e25i	0.963537	+	0.353153i
$989$		−	1.54072e25i		−	0.535249i
$990$	2.01806e25	−	1.99141e25i	0.695081	−	0.685903i
$991$			6.80813e24i			0.232489i	0.993221	+	0.116244i	$0.0370856\pi$
$991$			6.80813e24i			0.232489i	−0.993221	+	0.116244i	$0.962914\pi$
$992$	−1.81206e25	−	1.68797e24i	−0.613511	−	0.0571499i
$993$	1.59566e24	+	1.88374e25i	0.0535640	+	0.632344i
$994$	−1.81809e25	+	1.27000e25i	−0.605106	+	0.422687i
$995$	4.37939e25			1.44517
$996$	1.11121e23	−	4.06554e23i	0.00363573	−	0.0133019i
$997$	4.86905e25			1.57956			0.789778	−	0.613393i	$-0.210196\pi$
$997$	4.86905e25			1.57956			0.789778	+	0.613393i	$0.210196\pi$
$998$	3.65662e25	−	2.55428e25i	1.17617	−	0.821596i
$999$	1.23449e25	−	3.19845e24i	0.393714	−	0.102008i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	12.18.b.a.11.11	✓	32
3.2	odd	2	inner	12.18.b.a.11.22	yes	32
4.3	odd	2	inner	12.18.b.a.11.21	yes	32
12.11	even	2	inner	12.18.b.a.11.12	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
12.18.b.a.11.11	✓	32	1.1	even	1	trivial
12.18.b.a.11.12	yes	32	12.11	even	2	inner
12.18.b.a.11.21	yes	32	4.3	odd	2	inner
12.18.b.a.11.22	yes	32	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:	\( k \)	\(=\)	\( 18 \)
Character orbit:	\([\chi]\)	\(=\)	12.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-207.324 - 296.798i) q^{2} +(11323.4 - 959.175i) q^{3} +(-45105.9 + 123066. i) q^{4} -804702. i q^{5} +(-2.63230e6 - 3.16191e6i) q^{6} +2.45214e7i q^{7} +(4.58773e7 - 1.21272e7i) q^{8} +(1.27300e8 - 2.17223e7i) q^{9} +O(q^{10})\)	\(q+(-207.324 - 296.798i) q^{2} +(11323.4 - 959.175i) q^{3} +(-45105.9 + 123066. i) q^{4} -804702. i q^{5} +(-2.63230e6 - 3.16191e6i) q^{6} +2.45214e7i q^{7} +(4.58773e7 - 1.21272e7i) q^{8} +(1.27300e8 - 2.17223e7i) q^{9} +(-2.38834e8 + 1.66834e8i) q^{10} -7.53583e8 q^{11} +(-3.92712e8 + 1.43680e9i) q^{12} -5.41375e9 q^{13} +(7.27791e9 - 5.08387e9i) q^{14} +(-7.71850e8 - 9.11199e9i) q^{15} +(-1.31108e10 - 1.11020e10i) q^{16} +2.92884e10i q^{17} +(-3.28394e10 - 3.32789e10i) q^{18} +4.12729e10i q^{19} +(9.90317e10 + 3.62968e10i) q^{20} +(2.35203e10 + 2.77667e11i) q^{21} +(1.56235e11 + 2.23662e11i) q^{22} -2.06275e11 q^{23} +(5.07857e11 - 1.81326e11i) q^{24} +1.15395e11 q^{25} +(1.12240e12 + 1.60679e12i) q^{26} +(1.42064e12 - 3.68074e11i) q^{27} +(-3.01776e12 - 1.10606e12i) q^{28} +2.39176e12i q^{29} +(-2.54440e12 + 2.11821e12i) q^{30} +2.92599e12i q^{31} +(-5.76889e11 + 6.19297e12i) q^{32} +(-8.53315e12 + 7.22818e11i) q^{33} +(8.69273e12 - 6.07217e12i) q^{34} +1.97324e13 q^{35} +(-3.06870e12 + 1.66462e13i) q^{36} +8.68969e12 q^{37} +(1.22497e13 - 8.55684e12i) q^{38} +(-6.13023e13 + 5.19274e12i) q^{39} +(-9.75879e12 - 3.69176e13i) q^{40} +1.59536e13i q^{41} +(7.75346e13 - 6.45476e13i) q^{42} +7.46925e13i q^{43} +(3.39910e13 - 9.27407e13i) q^{44} +(-1.74800e13 - 1.02439e14i) q^{45} +(4.27657e13 + 6.12221e13i) q^{46} -5.30716e12 q^{47} +(-1.59108e14 - 1.13138e14i) q^{48} -3.68670e14 q^{49} +(-2.39240e13 - 3.42489e13i) q^{50} +(2.80927e13 + 3.31645e14i) q^{51} +(2.44192e14 - 6.66251e14i) q^{52} -5.59069e14i q^{53} +(-4.03775e14 - 3.45332e14i) q^{54} +6.06409e14i q^{55} +(2.97376e14 + 1.12498e15i) q^{56} +(3.95879e13 + 4.67351e14i) q^{57} +(7.09869e14 - 4.95868e14i) q^{58} -8.13593e13 q^{59} +(1.15619e15 + 3.16016e14i) q^{60} -1.52969e15 q^{61} +(8.68427e14 - 6.06626e14i) q^{62} +(5.32662e14 + 3.12158e15i) q^{63} +(1.95766e15 - 1.11273e15i) q^{64} +4.35646e15i q^{65} +(1.98365e15 + 2.38276e15i) q^{66} +3.40080e14i q^{67} +(-3.60442e15 - 1.32108e15i) q^{68} +(-2.33574e15 + 1.97854e14i) q^{69} +(-4.09100e15 - 5.85654e15i) q^{70} -2.49810e15 q^{71} +(5.57676e15 - 2.54036e15i) q^{72} -3.35635e15 q^{73} +(-1.80158e15 - 2.57908e15i) q^{74} +(1.30666e15 - 1.10684e14i) q^{75} +(-5.07930e15 - 1.86165e15i) q^{76} -1.84789e16i q^{77} +(1.42506e16 + 1.71178e16i) q^{78} -7.33851e15i q^{79} +(-8.93383e15 + 1.05503e16i) q^{80} +(1.57335e16 - 5.53050e15i) q^{81} +(4.73499e15 - 3.30756e15i) q^{82} -2.82958e14 q^{83} +(-3.52323e16 - 9.62985e15i) q^{84} +2.35684e16 q^{85} +(2.21686e16 - 1.54855e16i) q^{86} +(2.29412e15 + 2.70829e16i) q^{87} +(-3.45724e16 + 9.13886e15i) q^{88} +9.20486e15i q^{89} +(-2.67796e16 + 2.64260e16i) q^{90} -1.32753e17i q^{91} +(9.30424e15 - 2.53855e16i) q^{92} +(2.80653e15 + 3.31322e16i) q^{93} +(1.10030e15 + 1.57515e15i) q^{94} +3.32124e16 q^{95} +(-5.92223e14 + 7.06790e16i) q^{96} -3.56756e16 q^{97} +(7.64339e16 + 1.09420e17i) q^{98} +(-9.59312e16 + 1.63696e16i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 54808 q^{4} - 4960776 q^{6} + 79874976 q^{9}+O(q^{10}) \) 32 * q - 54808 * q^4 - 4960776 * q^6 + 79874976 * q^9	\( 32 q - 54808 q^{4} - 4960776 q^{6} + 79874976 q^{9} + 46839088 q^{10} + 2598308520 q^{12} + 221287360 q^{13} - 41721285088 q^{16} + 27568791600 q^{18} + 128365169856 q^{21} - 493958165040 q^{22} - 253565784288 q^{24} - 3063689463648 q^{25} - 2695436033040 q^{28} - 2169979068432 q^{30} - 17644793625600 q^{33} + 6944208632512 q^{34} - 12909384040056 q^{36} - 7970760699200 q^{37} + 21066454663744 q^{40} + 55835180334480 q^{42} + 154013263804416 q^{45} + 235918828815264 q^{46} + 299462725247520 q^{48} - 248591781347488 q^{49} + 544732086739120 q^{52} + 487051858173384 q^{54} - 21\!\cdots\!20 q^{57}+ \cdots + 90\!\cdots\!60 q^{97}+O(q^{100}) \) 32 * q - 54808 * q^4 - 4960776 * q^6 + 79874976 * q^9 + 46839088 * q^10 + 2598308520 * q^12 + 221287360 * q^13 - 41721285088 * q^16 + 27568791600 * q^18 + 128365169856 * q^21 - 493958165040 * q^22 - 253565784288 * q^24 - 3063689463648 * q^25 - 2695436033040 * q^28 - 2169979068432 * q^30 - 17644793625600 * q^33 + 6944208632512 * q^34 - 12909384040056 * q^36 - 7970760699200 * q^37 + 21066454663744 * q^40 + 55835180334480 * q^42 + 154013263804416 * q^45 + 235918828815264 * q^46 + 299462725247520 * q^48 - 248591781347488 * q^49 + 544732086739120 * q^52 + 487051858173384 * q^54 - 2151740586697920 * q^57 + 230877304263760 * q^58 - 345098683994304 * q^60 - 4956543779318336 * q^61 + 1003775054518400 * q^64 - 2371521654206832 * q^66 + 891375297976320 * q^69 - 949041839387232 * q^70 + 5817303713532480 * q^72 - 4887976236943040 * q^73 - 2051936325547056 * q^76 + 22261766802491280 * q^78 + 28021308982751520 * q^81 + 7596239161270240 * q^82 - 8356700998055568 * q^84 + 59910783041540096 * q^85 - 18469777603302720 * q^88 - 68814047068261392 * q^90 + 5961488029786560 * q^93 - 61915224567506112 * q^94 - 45410293501908864 * q^96 + 9062030716970560 * q^97

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