LMFDB - Embedded newform 12.18.b.a.11.2

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			11.2
Character	$\chi$	$=$	12.11
Dual form			12.18.b.a.11.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-361.348 + 22.3591i) q^{2} +(9139.83 + 6753.05i) q^{3} +(130072. - 16158.8i) q^{4} +841783. i q^{5} +(-3.45365e6 - 2.23584e6i) q^{6} +1.94297e7i q^{7} +(-4.66400e7 + 8.74726e6i) q^{8} +(3.79327e7 + 1.23443e8i) q^{9} +O(q^{10})$	\(q+(-361.348 + 22.3591i) q^{2} +(9139.83 + 6753.05i) q^{3} +(130072. - 16158.8i) q^{4} +841783. i q^{5} +(-3.45365e6 - 2.23584e6i) q^{6} +1.94297e7i q^{7} +(-4.66400e7 + 8.74726e6i) q^{8} +(3.79327e7 + 1.23443e8i) q^{9} +(-1.88215e7 - 3.04176e8i) q^{10} +9.11497e7 q^{11} +(1.29796e9 + 7.30695e8i) q^{12} +3.49139e9 q^{13} +(-4.34431e8 - 7.02086e9i) q^{14} +(-5.68460e9 + 7.69375e9i) q^{15} +(1.66577e10 - 4.20363e9i) q^{16} -3.88930e10i q^{17} +(-1.64670e10 - 4.37579e10i) q^{18} +1.11489e11i q^{19} +(1.36022e10 + 1.09492e11i) q^{20} +(-1.31209e11 + 1.77584e11i) q^{21} +(-3.29367e10 + 2.03803e9i) q^{22} -5.19300e11 q^{23} +(-4.85352e11 - 2.35014e11i) q^{24} +5.43413e10 q^{25} +(-1.26161e12 + 7.80646e10i) q^{26} +(-4.86922e11 + 1.38441e12i) q^{27} +(3.13961e11 + 2.52726e12i) q^{28} -1.20541e12i q^{29} +(1.88209e12 - 2.90722e12i) q^{30} -2.70262e12i q^{31} +(-5.92521e12 + 1.89142e12i) q^{32} +(8.33093e11 + 6.15539e11i) q^{33} +(8.69615e11 + 1.40539e13i) q^{34} -1.63555e13 q^{35} +(6.92869e12 + 1.54436e13i) q^{36} -1.71182e13 q^{37} +(-2.49281e12 - 4.02864e13i) q^{38} +(3.19107e13 + 2.35776e13i) q^{39} +(-7.36329e12 - 3.92607e13i) q^{40} +5.45114e13i q^{41} +(4.34416e13 - 6.71032e13i) q^{42} -3.09151e13i q^{43} +(1.18560e13 - 1.47287e12i) q^{44} +(-1.03913e14 + 3.19311e13i) q^{45} +(1.87648e14 - 1.16111e13i) q^{46} +2.01678e13 q^{47} +(1.80635e14 + 7.40695e13i) q^{48} -1.44881e14 q^{49} +(-1.96361e13 + 1.21502e12i) q^{50} +(2.62647e14 - 3.55476e14i) q^{51} +(4.54133e14 - 5.64169e13i) q^{52} +2.15134e14i q^{53} +(1.44994e14 - 5.11142e14i) q^{54} +7.67283e13i q^{55} +(-1.69956e14 - 9.06198e14i) q^{56} +(-7.52894e14 + 1.01899e15i) q^{57} +(2.69520e13 + 4.35573e14i) q^{58} -5.19006e14 q^{59} +(-6.15086e14 + 1.09260e15i) q^{60} -2.32508e15 q^{61} +(6.04282e13 + 9.76584e14i) q^{62} +(-2.39846e15 + 7.37019e14i) q^{63} +(2.09877e15 - 8.15944e14i) q^{64} +2.93899e15i q^{65} +(-3.14799e14 - 2.03796e14i) q^{66} +3.25141e15i q^{67} +(-6.28467e14 - 5.05890e15i) q^{68} +(-4.74631e15 - 3.50686e15i) q^{69} +(5.91004e15 - 3.65696e14i) q^{70} +2.41851e15 q^{71} +(-2.84897e15 - 5.42559e15i) q^{72} +9.22373e15 q^{73} +(6.18562e15 - 3.82749e14i) q^{74} +(4.96670e14 + 3.66970e14i) q^{75} +(1.80154e15 + 1.45017e16i) q^{76} +1.77101e15i q^{77} +(-1.20580e16 - 7.80620e15i) q^{78} -2.37248e16i q^{79} +(3.53854e15 + 1.40221e16i) q^{80} +(-1.37994e16 + 9.36509e15i) q^{81} +(-1.21883e15 - 1.96976e16i) q^{82} +2.02898e16 q^{83} +(-1.41972e16 + 2.52189e16i) q^{84} +3.27395e16 q^{85} +(6.91236e14 + 1.11711e16i) q^{86} +(8.14022e15 - 1.10173e16i) q^{87} +(-4.25122e15 + 7.97311e14i) q^{88} -6.58333e16i q^{89} +(3.68346e16 - 1.38616e16i) q^{90} +6.78366e16i q^{91} +(-6.75465e16 + 8.39129e15i) q^{92} +(1.82509e16 - 2.47014e16i) q^{93} +(-7.28757e15 + 4.50934e14i) q^{94} -9.38498e16 q^{95} +(-6.69283e16 - 2.27260e16i) q^{96} +1.45982e17 q^{97} +(5.23524e16 - 3.23942e15i) q^{98} +(3.45756e15 + 1.12518e16i) 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 $

$2$	−361.348	+	22.3591i	−0.998091	+	0.0617590i
$2$	−361.348	+	22.3591i	−0.998091	+	0.0617590i
$3$	9139.83	+	6753.05i	0.804280	+	0.594250i
$3$	9139.83	+	6753.05i	0.804280	+	0.594250i
$4$	130072.	−	16158.8i	0.992372	−	0.123282i
$5$			841783.i			0.963729i	0.876246	+	0.481865i	$0.160040\pi$
$5$			841783.i			0.963729i	−0.876246	+	0.481865i	$0.839960\pi$
$6$	−3.45365e6	−	2.23584e6i	−0.839445	−	0.543445i
$7$			1.94297e7i			1.27389i	0.770909	+	0.636945i	$0.219802\pi$
$7$			1.94297e7i			1.27389i	−0.770909	+	0.636945i	$0.780198\pi$
$8$	−4.66400e7	+	8.74726e6i	−0.982864	+	0.184335i
$9$	3.79327e7	+	1.23443e8i	0.293733	+	0.955888i
$10$	−1.88215e7	−	3.04176e8i	−0.0595190	−	0.961889i
$11$	9.11497e7			0.128209			0.0641044	−	0.997943i	$-0.479581\pi$
$11$	9.11497e7			0.128209			0.0641044	+	0.997943i	$0.479581\pi$
$12$	1.29796e9	+	7.30695e8i	0.871405	+	0.490564i
$13$	3.49139e9			1.18708			0.593540	−	0.804804i	$-0.297730\pi$
$13$	3.49139e9			1.18708			0.593540	+	0.804804i	$0.297730\pi$
$14$	−4.34431e8	−	7.02086e9i	−0.0786741	−	1.27146i
$15$	−5.68460e9	+	7.69375e9i	−0.572696	+	0.775108i
$16$	1.66577e10	−	4.20363e9i	0.969603	−	0.244684i
$17$		−	3.88930e10i		−	1.35225i	−0.736788	−	0.676123i	$-0.763659\pi$
$17$		−	3.88930e10i		−	1.35225i	0.736788	−	0.676123i	$-0.236341\pi$
$18$	−1.64670e10	−	4.37579e10i	−0.352207	−	0.935922i
$19$			1.11489e11i			1.50601i	0.658015	+	0.753005i	$0.271396\pi$
$19$			1.11489e11i			1.50601i	−0.658015	+	0.753005i	$0.728604\pi$
$20$	1.36022e10	+	1.09492e11i	0.118811	+	0.956377i
$21$	−1.31209e11	+	1.77584e11i	−0.757009	+	1.02456i
$22$	−3.29367e10	+	2.03803e9i	−0.127964	+	0.00791804i
$23$	−5.19300e11			−1.38271			−0.691356	−	0.722514i	$-0.742986\pi$
$23$	−5.19300e11			−1.38271			−0.691356	+	0.722514i	$0.742986\pi$
$24$	−4.85352e11	−	2.35014e11i	−0.900039	−	0.435810i
$25$	5.43413e10			0.0712262
$26$	−1.26161e12	+	7.80646e10i	−1.18481	+	0.0733129i
$27$	−4.86922e11	+	1.38441e12i	−0.331793	+	0.943352i
$28$	3.13961e11	+	2.52726e12i	0.157048	+	1.26417i
$29$		−	1.20541e12i		−	0.447459i	−0.974651	−	0.223729i	$-0.928177\pi$
$29$		−	1.20541e12i		−	0.447459i	0.974651	−	0.223729i	$-0.0718232\pi$
$30$	1.88209e12	−	2.90722e12i	0.523733	−	0.808998i
$31$		−	2.70262e12i		−	0.569128i	−0.958657	−	0.284564i	$-0.908151\pi$
$31$		−	2.70262e12i		−	0.569128i	0.958657	−	0.284564i	$-0.0918488\pi$
$32$	−5.92521e12	+	1.89142e12i	−0.952641	+	0.304098i
$33$	8.33093e11	+	6.15539e11i	0.103116	+	0.0761881i
$34$	8.69615e11	+	1.40539e13i	0.0835134	+	1.34967i
$35$	−1.63555e13			−1.22768
$36$	6.92869e12	+	1.54436e13i	0.409336	+	0.912384i
$37$	−1.71182e13			−0.801205			−0.400603	−	0.916252i	$-0.631199\pi$
$37$	−1.71182e13			−0.801205			−0.400603	+	0.916252i	$0.631199\pi$
$38$	−2.49281e12	−	4.02864e13i	−0.0930097	−	1.50313i
$39$	3.19107e13	+	2.35776e13i	0.954746	+	0.705423i
$40$	−7.36329e12	−	3.92607e13i	−0.177649	−	0.947214i
$41$			5.45114e13i			1.06617i	0.846063	+	0.533083i	$0.178967\pi$
$41$			5.45114e13i			1.06617i	−0.846063	+	0.533083i	$0.821033\pi$
$42$	4.34416e13	−	6.71032e13i	0.692288	−	1.06936i
$43$		−	3.09151e13i		−	0.403356i	−0.979452	−	0.201678i	$-0.935360\pi$
$43$		−	3.09151e13i		−	0.403356i	0.979452	−	0.201678i	$-0.0646395\pi$
$44$	1.18560e13	−	1.47287e12i	0.127231	−	0.0158059i
$45$	−1.03913e14	+	3.19311e13i	−0.921217	+	0.283079i
$46$	1.87648e14	−	1.16111e13i	1.38007	−	0.0853949i
$47$	2.01678e13			0.123545			0.0617726	−	0.998090i	$-0.480325\pi$
$47$	2.01678e13			0.123545			0.0617726	+	0.998090i	$0.480325\pi$
$48$	1.80635e14	+	7.40695e13i	0.925236	+	0.379393i
$49$	−1.44881e14			−0.622794
$50$	−1.96361e13	+	1.21502e12i	−0.0710902	+	0.00439886i
$51$	2.62647e14	−	3.55476e14i	0.803573	−	1.08759i
$52$	4.54133e14	−	5.64169e13i	1.17803	−	0.146346i
$53$			2.15134e14i			0.474640i	0.971432	+	0.237320i	$0.0762690\pi$
$53$			2.15134e14i			0.474640i	−0.971432	+	0.237320i	$0.923731\pi$
$54$	1.44994e14	−	5.11142e14i	0.272899	−	0.962043i
$55$			7.67283e13i			0.123558i
$56$	−1.69956e14	−	9.06198e14i	−0.234822	−	1.25206i
$57$	−7.52894e14	+	1.01899e15i	−0.894947	+	1.21125i
$58$	2.69520e13	+	4.35573e14i	0.0276346	+	0.446605i
$59$	−5.19006e14			−0.460183			−0.230092	−	0.973169i	$-0.573903\pi$
$59$	−5.19006e14			−0.460183			−0.230092	+	0.973169i	$0.573903\pi$
$60$	−6.15086e14	+	1.09260e15i	−0.472771	+	0.839799i
$61$	−2.32508e15			−1.55287			−0.776433	−	0.630200i	$-0.782973\pi$
$61$	−2.32508e15			−1.55287			−0.776433	+	0.630200i	$0.782973\pi$
$62$	6.04282e13	+	9.76584e14i	0.0351488	+	0.568042i
$63$	−2.39846e15	+	7.37019e14i	−1.21770	+	0.374183i
$64$	2.09877e15	−	8.15944e14i	0.932041	−	0.362352i
$65$			2.93899e15i			1.14402i
$66$	−3.14799e14	−	2.03796e14i	−0.107624	−	0.0696743i
$67$			3.25141e15i			0.978219i	0.872222	+	0.489110i	$0.162678\pi$
$67$			3.25141e15i			0.978219i	−0.872222	+	0.489110i	$0.837322\pi$
$68$	−6.28467e14	−	5.05890e15i	−0.166708	−	1.34193i
$69$	−4.74631e15	−	3.50686e15i	−1.11209	−	0.821678i
$70$	5.91004e15	−	3.65696e14i	1.22534	−	0.0758206i
$71$	2.41851e15			0.444479			0.222240	−	0.974992i	$-0.428663\pi$
$71$	2.41851e15			0.444479			0.222240	+	0.974992i	$0.428663\pi$
$72$	−2.84897e15	−	5.42559e15i	−0.464903	−	0.885362i
$73$	9.22373e15			1.33864			0.669318	−	0.742976i	$-0.266586\pi$
$73$	9.22373e15			1.33864			0.669318	+	0.742976i	$0.266586\pi$
$74$	6.18562e15	−	3.82749e14i	0.799676	−	0.0494816i
$75$	4.96670e14	+	3.66970e14i	0.0572858	+	0.0423262i
$76$	1.80154e15	+	1.45017e16i	0.185664	+	1.49452i
$77$			1.77101e15i			0.163324i
$78$	−1.20580e16	−	7.80620e15i	−0.996489	−	0.645113i
$79$		−	2.37248e16i		−	1.75943i	−0.475499	−	0.879716i	$-0.657733\pi$
$79$		−	2.37248e16i		−	1.75943i	0.475499	−	0.879716i	$-0.342267\pi$
$80$	3.53854e15	+	1.40221e16i	0.235809	+	0.934435i
$81$	−1.37994e16	+	9.36509e15i	−0.827442	+	0.561551i
$82$	−1.21883e15	−	1.96976e16i	−0.0658453	−	1.06413i
$83$	2.02898e16			0.988815			0.494407	−	0.869230i	$-0.335385\pi$
$83$	2.02898e16			0.988815			0.494407	+	0.869230i	$0.335385\pi$
$84$	−1.41972e16	+	2.52189e16i	−0.624924	+	1.11007i
$85$	3.27395e16			1.30320
$86$	6.91236e14	+	1.11711e16i	0.0249109	+	0.402586i
$87$	8.14022e15	−	1.10173e16i	0.265903	−	0.359882i
$88$	−4.25122e15	+	7.97311e14i	−0.126012	+	0.0236333i
$89$		−	6.58333e16i		−	1.77268i	−0.463034	−	0.886341i	$-0.653239\pi$
$89$		−	6.58333e16i		−	1.77268i	0.463034	−	0.886341i	$-0.346761\pi$
$90$	3.68346e16	−	1.38616e16i	0.901975	−	0.339432i
$91$			6.78366e16i			1.51221i
$92$	−6.75465e16	+	8.39129e15i	−1.37216	+	0.170464i
$93$	1.82509e16	−	2.47014e16i	0.338205	−	0.457738i
$94$	−7.28757e15	+	4.50934e14i	−0.123309	+	0.00763003i
$95$	−9.38498e16			−1.45139
$96$	−6.69283e16	−	2.27260e16i	−0.946900	−	0.321527i
$97$	1.45982e17			1.89121			0.945603	−	0.325324i	$-0.105473\pi$
$97$	1.45982e17			1.89121			0.945603	+	0.325324i	$0.105473\pi$
$98$	5.23524e16	−	3.23942e15i	0.621606	−	0.0384632i
$99$	3.45756e15	+	1.12518e16i	0.0376591	+	0.122553i
$100$	7.06829e15	−	8.78092e14i	0.0706829	−	0.00878092i
$101$			6.79553e16i			0.624441i	0.950010	+	0.312221i	$0.101073\pi$
$101$			6.79553e16i			0.624441i	−0.950010	+	0.312221i	$0.898927\pi$
$102$	−8.69586e16	+	1.34323e17i	−0.734871	+	1.13514i
$103$			6.26792e16i			0.487536i	0.969834	+	0.243768i	$0.0783836\pi$
$103$			6.26792e16i			0.487536i	−0.969834	+	0.243768i	$0.921616\pi$
$104$	−1.62838e17	+	3.05401e16i	−1.16674	+	0.218820i
$105$	−1.49487e17	−	1.10450e17i	−0.987402	−	0.729552i
$106$	−4.81022e15	−	7.77382e16i	−0.0293133	−	0.473734i
$107$	8.60789e16			0.484322			0.242161	−	0.970236i	$-0.422144\pi$
$107$	8.60789e16			0.484322			0.242161	+	0.970236i	$0.422144\pi$
$108$	−4.09645e16	+	1.87942e17i	−0.212964	+	0.977060i
$109$	−4.89510e16			−0.235308			−0.117654	−	0.993055i	$-0.537537\pi$
$109$	−4.89510e16			−0.235308			−0.117654	+	0.993055i	$0.537537\pi$
$110$	−1.71558e15	−	2.77256e16i	−0.00763085	−	0.123323i
$111$	−1.56457e17	−	1.15600e17i	−0.644393	−	0.476116i
$112$	8.16751e16	+	3.23652e17i	0.311700	+	1.23517i
$113$		−	8.82484e16i		−	0.312277i	−0.987735	−	0.156139i	$-0.950095\pi$
$113$		−	8.82484e16i		−	0.312277i	0.987735	−	0.156139i	$-0.0499046\pi$
$114$	2.49272e17	−	3.85045e17i	0.818433	−	1.26421i
$115$		−	4.37138e17i		−	1.33256i
$116$	−1.94781e16	−	1.56791e17i	−0.0551637	−	0.444045i
$117$	1.32438e17	+	4.30990e17i	0.348685	+	1.13472i
$118$	1.87542e17	−	1.16045e16i	0.459305	−	0.0284205i
$119$	7.55678e17			1.72261
$120$	1.97830e17	−	4.08561e17i	0.420003	−	0.867393i
$121$	−4.97139e17			−0.983563
$122$	8.40161e17	−	5.19868e16i	1.54990	−	0.0959034i
$123$	−3.68118e17	+	4.98225e17i	−0.633569	+	0.857495i
$124$	−4.36712e16	−	3.51535e17i	−0.0701634	−	0.564786i
$125$			6.87973e17i			1.03237i
$126$	8.50200e17	−	3.19948e17i	1.19226	−	0.448673i
$127$			2.37752e17i			0.311739i	0.987778	+	0.155870i	$0.0498180\pi$
$127$			2.37752e17i			0.311739i	−0.987778	+	0.155870i	$0.950182\pi$
$128$	−7.40142e17	+	3.41766e17i	−0.907884	+	0.419222i
$129$	2.08771e17	−	2.82559e17i	0.239695	−	0.324411i
$130$	−6.57134e16	−	1.06200e18i	−0.0706538	−	1.14184i
$131$	1.79074e17			0.180396			0.0901980	−	0.995924i	$-0.471250\pi$
$131$	1.79074e17			0.180396			0.0901980	+	0.995924i	$0.471250\pi$
$132$	1.18309e17	+	6.66027e16i	0.111722	+	0.0628946i
$133$	−2.16620e18			−1.91849
$134$	−7.26988e16	−	1.17489e18i	−0.0604139	−	0.976352i
$135$	−1.16538e18	−	4.09883e17i	−0.909136	−	0.319759i
$136$	3.40208e17	+	1.81397e18i	0.249266	+	1.32907i
$137$			4.00745e17i			0.275895i	0.990440	+	0.137947i	$0.0440505\pi$
$137$			4.00745e17i			0.275895i	−0.990440	+	0.137947i	$0.955949\pi$
$138$	1.79348e18	+	1.16107e18i	1.16071	+	0.751428i
$139$			9.99468e16i			0.0608335i	0.999537	+	0.0304168i	$0.00968345\pi$
$139$			9.99468e16i			0.0608335i	−0.999537	+	0.0304168i	$0.990317\pi$
$140$	−2.12740e18	+	2.64287e17i	−1.21832	+	0.151352i
$141$	1.84330e17	+	1.36194e17i	0.0993650	+	0.0734168i
$142$	−8.73921e17	+	5.40757e16i	−0.443631	+	0.0274506i
$143$	3.18240e17			0.152194
$144$	1.15078e18	+	1.89682e18i	0.518694	+	0.854960i
$145$	1.01470e18			0.431229
$146$	−3.33297e18	+	2.06235e17i	−1.33608	+	0.0826728i
$147$	−1.32419e18	−	9.78389e17i	−0.500901	−	0.370096i
$148$	−2.22660e18	+	2.76611e17i	−0.795093	+	0.0987743i
$149$		−	7.54081e16i		−	0.0254293i	−0.999919	−	0.0127147i	$-0.995953\pi$
$149$		−	7.54081e16i		−	0.0254293i	0.999919	−	0.0127147i	$-0.00404731\pi$
$150$	−1.87676e17	−	1.21498e17i	−0.0597905	−	0.0387075i
$151$			2.17992e18i			0.656351i	0.944617	+	0.328176i	$0.106434\pi$
$151$			2.17992e18i			0.656351i	−0.944617	+	0.328176i	$0.893566\pi$
$152$	−9.75227e17	−	5.19986e18i	−0.277610	−	1.48020i
$153$	4.80109e18	−	1.47532e18i	1.29260	−	0.397199i
$154$	−3.95982e16	−	6.39949e17i	−0.0100867	−	0.163012i
$155$	2.27502e18			0.548485
$156$	4.53168e18	+	2.55114e18i	1.03443	+	0.582339i
$157$	1.90589e18			0.412051			0.206026	−	0.978547i	$-0.433947\pi$
$157$	1.90589e18			0.412051			0.206026	+	0.978547i	$0.433947\pi$
$158$	5.30467e17	+	8.57290e18i	0.108661	+	1.75607i
$159$	−1.45281e18	+	1.96629e18i	−0.282055	+	0.381744i
$160$	−1.59217e18	−	4.98774e18i	−0.293068	−	0.918088i
$161$		−	1.00898e19i		−	1.76142i
$162$	4.77698e18	−	3.69260e18i	0.791182	−	0.611581i
$163$		−	5.83239e18i		−	0.916753i	−0.888758	−	0.458376i	$-0.848431\pi$
$163$		−	5.83239e18i		−	0.916753i	0.888758	−	0.458376i	$-0.151569\pi$
$164$	8.80841e17	+	7.09041e18i	0.131439	+	1.05803i
$165$	−5.18150e17	+	7.01283e17i	−0.0734247	+	0.0993756i
$166$	−7.33169e18	+	4.53664e17i	−0.986927	+	0.0610682i
$167$	1.39668e19			1.78652			0.893259	−	0.449542i	$-0.148413\pi$
$167$	1.39668e19			1.78652			0.893259	+	0.449542i	$0.148413\pi$
$168$	4.56623e18	−	9.43022e18i	0.555174	−	1.14655i
$169$	3.53941e18			0.409161
$170$	−1.18303e19	+	7.32027e17i	−1.30071	+	0.0804843i
$171$	−1.37626e19	+	4.22909e18i	−1.43958	+	0.442365i
$172$	−4.99553e17	−	4.02119e18i	−0.0497267	−	0.400279i
$173$			1.41837e19i			1.34399i	0.740554	+	0.671997i	$0.234563\pi$
$173$			1.41837e19i			1.34399i	−0.740554	+	0.671997i	$0.765437\pi$
$174$	−2.69511e18	+	4.16307e18i	−0.243169	+	0.375617i
$175$			1.05583e18i			0.0907343i
$176$	1.51834e18	−	3.83160e17i	0.124312	−	0.0313706i
$177$	−4.74363e18	−	3.50488e18i	−0.370116	−	0.273464i
$178$	1.47198e18	+	2.37887e19i	0.109479	+	1.76930i
$179$	1.96510e19			1.39359			0.696793	−	0.717272i	$-0.254609\pi$
$179$	1.96510e19			1.39359			0.696793	+	0.717272i	$0.254609\pi$
$180$	−1.30002e19	+	5.83245e18i	−0.879291	+	0.394489i
$181$	2.01356e19			1.29926			0.649630	−	0.760251i	$-0.274924\pi$
$181$	2.01356e19			1.29926			0.649630	+	0.760251i	$0.274924\pi$
$182$	−1.51677e18	−	2.45126e19i	−0.0933926	−	1.50932i
$183$	−2.12508e19	−	1.57014e19i	−1.24894	−	0.922791i
$184$	2.42201e19	−	4.54246e18i	1.35902	−	0.254882i
$185$		−	1.44098e19i		−	0.772145i
$186$	−6.04262e18	+	9.33388e18i	−0.309289	+	0.477752i
$187$		−	3.54509e18i		−	0.173370i
$188$	2.62326e18	−	3.25888e17i	0.122603	−	0.0152309i
$189$	−2.68987e19	−	9.46073e18i	−1.20173	−	0.422668i
$190$	3.39124e19	−	2.09840e18i	1.44861	−	0.0896361i
$191$	−6.10702e18			−0.249486			−0.124743	−	0.992189i	$-0.539811\pi$
$191$	−6.10702e18			−0.249486			−0.124743	+	0.992189i	$0.539811\pi$
$192$	2.46925e19	+	6.71552e18i	0.964950	+	0.262434i
$193$	−1.92859e19			−0.721110			−0.360555	−	0.932738i	$-0.617413\pi$
$193$	−1.92859e19			−0.721110			−0.360555	+	0.932738i	$0.617413\pi$
$194$	−5.27501e19	+	3.26403e18i	−1.88760	+	0.116799i
$195$	−1.98472e19	+	2.68619e19i	−0.679837	+	0.920116i
$196$	−1.88450e19	+	2.34111e18i	−0.618044	+	0.0767795i
$197$			4.88600e19i			1.53458i	0.641298	+	0.767292i	$0.278396\pi$
$197$			4.88600e19i			1.53458i	−0.641298	+	0.767292i	$0.721604\pi$
$198$	−1.50096e18	−	3.98852e18i	−0.0451560	−	0.119993i
$199$			5.21182e19i			1.50224i	0.660168	+	0.751118i	$0.270485\pi$
$199$			5.21182e19i			1.50224i	−0.660168	+	0.751118i	$0.729515\pi$
$200$	−2.53447e18	+	4.75337e17i	−0.0700056	+	0.0131295i
$201$	−2.19570e19	+	2.97173e19i	−0.581307	+	0.786762i
$202$	−1.51942e18	−	2.45555e19i	−0.0385649	−	0.623249i
$203$	2.34208e19			0.570013
$204$	2.84189e19	−	5.04815e19i	0.663363	−	1.17835i
$205$	−4.58867e19			−1.02749
$206$	−1.40145e18	−	2.26490e19i	−0.0301098	−	0.486606i
$207$	−1.96985e19	−	6.41042e19i	−0.406148	−	1.32172i
$208$	5.81584e19	−	1.46765e19i	1.15100	−	0.290459i
$209$			1.01622e19i			0.193084i
$210$	5.64863e19	+	3.65684e19i	1.03057	+	0.667178i
$211$		−	3.88995e19i		−	0.681621i	−0.940132	−	0.340811i	$-0.889299\pi$
$211$		−	3.88995e19i		−	0.681621i	0.940132	−	0.340811i	$-0.110701\pi$
$212$	3.47632e18	+	2.79830e19i	0.0585147	+	0.471019i
$213$	2.21047e19	+	1.63323e19i	0.357486	+	0.264132i
$214$	−3.11044e19	+	1.92465e18i	−0.483398	+	0.0299113i
$215$	2.60238e19			0.388726
$216$	1.06002e19	−	6.88282e19i	0.152215	−	0.988347i
$217$	5.25109e19			0.725006
$218$	1.76883e19	−	1.09450e18i	0.234859	−	0.0145324i
$219$	8.43033e19	+	6.22884e19i	1.07664	+	0.795485i
$220$	1.23984e18	+	9.98021e18i	0.0152326	+	0.122616i
$221$		−	1.35791e20i		−	1.60523i
$222$	5.91202e19	+	3.82736e19i	0.672568	+	0.435411i
$223$		−	1.09511e20i		−	1.19913i	−0.800327	−	0.599564i	$-0.795341\pi$
$223$		−	1.09511e20i		−	1.19913i	0.800327	−	0.599564i	$-0.204659\pi$
$224$	−3.67497e19	−	1.15125e20i	−0.387388	−	1.21356i
$225$	2.06131e18	+	6.70808e18i	0.0209215	+	0.0680842i
$226$	1.97316e18	+	3.18883e19i	0.0192859	+	0.311681i
$227$	−3.11789e18			−0.0293522			−0.0146761	−	0.999892i	$-0.504672\pi$
$227$	−3.11789e18			−0.0293522			−0.0146761	+	0.999892i	$0.504672\pi$
$228$	−8.14647e19	+	1.44709e20i	−0.738794	+	1.31234i
$229$	7.52618e18			0.0657617			0.0328809	−	0.999459i	$-0.489532\pi$
$229$	7.52618e18			0.0657617			0.0328809	+	0.999459i	$0.489532\pi$
$230$	9.77403e18	+	1.57959e20i	0.0822976	+	1.33002i
$231$	−1.19597e19	+	1.61867e19i	−0.0970552	+	0.131358i
$232$	1.05441e19	+	5.62204e19i	0.0824822	+	0.439791i
$233$			1.70121e20i			1.28302i	0.767116	+	0.641509i	$0.221691\pi$
$233$			1.70121e20i			1.28302i	−0.767116	+	0.641509i	$0.778309\pi$
$234$	−5.74927e19	−	1.52776e20i	−0.418098	−	1.11102i
$235$			1.69769e19i			0.119064i
$236$	−6.75083e19	+	8.38655e18i	−0.456673	+	0.0567324i
$237$	1.60215e20	−	2.16841e20i	1.04554	−	1.41508i
$238$	−2.73062e20	+	1.68963e19i	−1.71932	+	0.106387i
$239$	−7.21543e19			−0.438409			−0.219205	−	0.975679i	$-0.570346\pi$
$239$	−7.21543e19			−0.438409			−0.219205	+	0.975679i	$0.570346\pi$
$240$	−6.23505e19	+	1.52056e20i	−0.365632	+	0.891677i
$241$	−9.00463e18			−0.0509707			−0.0254854	−	0.999675i	$-0.508113\pi$
$241$	−9.00463e18			−0.0509707			−0.0254854	+	0.999675i	$0.508113\pi$
$242$	1.79640e20	−	1.11156e19i	0.981685	−	0.0607438i
$243$	−1.89367e20	−	7.59280e18i	−0.999197	−	0.0400635i
$244$	−3.02428e20	+	3.75706e19i	−1.54102	+	0.191441i
$245$		−	1.21958e20i		−	0.600205i
$246$	1.21879e20	−	1.88263e20i	0.579402	−	0.894987i
$247$			3.89253e20i			1.78776i
$248$	2.36405e19	+	1.26050e20i	0.104910	+	0.559375i
$249$	1.85446e20	+	1.37018e20i	0.795284	+	0.587604i
$250$	−1.53825e19	−	2.48597e20i	−0.0637583	−	1.03040i
$251$	−1.53454e20			−0.614824			−0.307412	−	0.951576i	$-0.599463\pi$
$251$	−1.53454e20			−0.614824			−0.307412	+	0.951576i	$0.599463\pi$
$252$	−3.00064e20	+	1.34622e20i	−1.16228	+	0.521449i
$253$	−4.73341e19			−0.177276
$254$	−5.31592e18	−	8.59109e19i	−0.0192527	−	0.311144i
$255$	2.99233e20	+	2.21091e20i	1.04814	+	0.774427i
$256$	2.59807e20	−	1.40045e20i	0.880260	−	0.474492i
$257$		−	4.30595e20i		−	1.41136i	−0.708531	−	0.705680i	$-0.750642\pi$
$257$		−	4.30595e20i		−	1.41136i	0.708531	−	0.705680i	$-0.249358\pi$
$258$	−6.91213e19	+	1.06770e20i	−0.219202	+	0.338596i
$259$		−	3.32601e20i		−	1.02065i
$260$	4.74908e19	+	3.82281e20i	0.141038	+	1.13530i
$261$	1.48800e20	−	4.57246e19i	0.427720	−	0.131433i
$262$	−6.47080e19	+	4.00395e18i	−0.180052	+	0.0111411i
$263$	−1.39516e20			−0.375839			−0.187919	−	0.982184i	$-0.560174\pi$
$263$	−1.39516e20			−0.375839			−0.187919	+	0.982184i	$0.560174\pi$
$264$	−4.42397e19	−	2.14214e19i	−0.115393	−	0.0558747i
$265$	−1.81096e20			−0.457424
$266$	7.82751e20	−	4.84344e19i	1.91483	−	0.118484i
$267$	4.44576e20	−	6.01705e20i	1.05342	−	1.42573i
$268$	5.25391e19	+	4.22918e20i	0.120597	+	0.970757i
$269$			4.73467e20i			1.05292i	0.850200	+	0.526460i	$0.176481\pi$
$269$			4.73467e20i			1.05292i	−0.850200	+	0.526460i	$0.823519\pi$
$270$	4.30270e20	+	1.22053e20i	0.927148	+	0.263001i
$271$		−	2.27306e20i		−	0.474648i	−0.971431	−	0.237324i	$-0.923730\pi$
$271$		−	2.27306e20i		−	0.474648i	0.971431	−	0.237324i	$-0.0762703\pi$
$272$	−1.63492e20	−	6.47867e20i	−0.330873	−	1.31114i
$273$	−4.58104e20	+	6.20015e20i	−0.898631	+	1.21624i
$274$	−8.96032e18	−	1.44808e20i	−0.0170390	−	0.275368i
$275$	4.95319e18			0.00913182
$276$	−6.74030e20	−	3.79450e20i	−1.20490	−	0.678309i
$277$	1.81599e20			0.314800			0.157400	−	0.987535i	$-0.449689\pi$
$277$	1.81599e20			0.314800			0.157400	+	0.987535i	$0.449689\pi$
$278$	−2.23473e18	−	3.61155e19i	−0.00375702	−	0.0607174i
$279$	3.33620e20	−	1.02518e20i	0.544022	−	0.167172i
$280$	7.62822e20	−	1.43066e20i	1.20665	−	0.226305i
$281$			2.94918e20i			0.452582i	0.974060	+	0.226291i	$0.0726600\pi$
$281$			2.94918e20i			0.452582i	−0.974060	+	0.226291i	$0.927340\pi$
$282$	−6.96523e19	−	4.50919e19i	−0.103709	−	0.0671400i
$283$			2.70741e20i			0.391173i	0.980686	+	0.195587i	$0.0626611\pi$
$283$			2.70741e20i			0.391173i	−0.980686	+	0.195587i	$0.937339\pi$
$284$	3.14580e20	−	3.90803e19i	0.441088	−	0.0547964i
$285$	−8.57771e20	−	6.33773e20i	−1.16732	−	0.862486i
$286$	−1.14995e20	+	7.11557e18i	−0.151904	+	0.00939936i
$287$	−1.05914e21			−1.35818
$288$	−4.58243e20	−	6.59682e20i	−0.570506	−	0.821294i
$289$	−6.85428e20			−0.828571
$290$	−3.66658e20	+	2.26877e19i	−0.430406	+	0.0266323i
$291$	1.33425e21	+	9.85822e20i	1.52106	+	1.12385i
$292$	1.19975e21	−	1.49045e20i	1.32842	−	0.165030i
$293$			1.15392e21i			1.24109i	0.784172	+	0.620543i	$0.213088\pi$
$293$			1.15392e21i			1.24109i	−0.784172	+	0.620543i	$0.786912\pi$
$294$	5.00368e20	+	3.23931e20i	0.522802	+	0.338454i
$295$		−	4.36891e20i		−	0.443492i
$296$	7.98393e20	−	1.49737e20i	0.787475	−	0.147690i
$297$	−4.43828e19	+	1.26189e20i	−0.0425388	+	0.120946i
$298$	1.68606e18	+	2.72485e19i	0.00157049	+	0.0253808i
$299$	−1.81308e21			−1.64139
$300$	7.05327e19	+	3.97069e19i	0.0620669	+	0.0349410i
$301$	6.00670e20			0.513831
$302$	−4.87411e19	−	7.87709e20i	−0.0405356	−	0.655098i
$303$	−4.58906e20	+	6.21100e20i	−0.371075	+	0.502226i
$304$	4.68660e20	+	1.85715e21i	0.368496	+	1.46023i
$305$		−	1.95721e21i		−	1.49654i
$306$	−1.70188e21	+	6.40451e20i	−1.26560	+	0.476270i
$307$			1.17742e21i			0.851638i	0.904808	+	0.425819i	$0.140014\pi$
$307$			1.17742e21i			0.851638i	−0.904808	+	0.425819i	$0.859986\pi$
$308$	2.86174e19	+	2.30359e20i	0.0201349	+	0.162078i
$309$	−4.23276e20	+	5.72877e20i	−0.289719	+	0.392116i
$310$	−8.22071e20	+	5.08674e19i	−0.547438	+	0.0338739i
$311$	1.28195e20			0.0830631			0.0415315	−	0.999137i	$-0.486776\pi$
$311$	1.28195e20			0.0830631			0.0415315	+	0.999137i	$0.486776\pi$
$312$	−1.69455e21	−	8.20525e20i	−1.06842	−	0.517342i
$313$	1.59441e21			0.978302			0.489151	−	0.872199i	$-0.337307\pi$
$313$	1.59441e21			0.978302			0.489151	+	0.872199i	$0.337307\pi$
$314$	−6.88689e20	+	4.26141e19i	−0.411265	+	0.0254479i
$315$	−6.20410e20	−	2.01899e21i	−0.360611	−	1.17353i
$316$	−3.83366e20	−	3.08594e21i	−0.216907	−	1.74601i
$317$		−	6.50090e20i		−	0.358072i	−0.983843	−	0.179036i	$-0.942702\pi$
$317$		−	6.50090e20i		−	0.358072i	0.983843	−	0.179036i	$-0.0572978\pi$
$318$	4.81006e20	−	7.42997e20i	0.257941	−	0.398434i
$319$		−	1.09873e20i		−	0.0573681i
$320$	6.86847e20	+	1.76671e21i	0.349209	+	0.898235i
$321$	7.86746e20	+	5.81295e20i	0.389531	+	0.287809i
$322$	2.25600e20	+	3.64593e21i	0.108784	+	1.75806i
$323$	4.33616e21			2.03650
$324$	−1.64359e21	+	1.44112e21i	−0.751901	+	0.659276i
$325$	1.89727e20			0.0845513
$326$	1.30407e20	+	2.10752e21i	0.0566177	+	0.915003i
$327$	−4.47404e20	−	3.30569e20i	−0.189253	−	0.139832i
$328$	−4.76825e20	−	2.54241e21i	−0.196531	−	1.04789i
$329$			3.91853e20i			0.157383i
$330$	1.71552e20	−	2.64992e20i	0.0671472	−	0.103721i
$331$		−	1.67008e21i		−	0.637089i	−0.947908	−	0.318545i	$-0.896806\pi$
$331$		−	1.67008e21i		−	0.637089i	0.947908	−	0.318545i	$-0.103194\pi$
$332$	2.63914e21	−	3.27861e20i	0.981272	−	0.121903i
$333$	−6.49340e20	−	2.11313e21i	−0.235340	−	0.765862i
$334$	−5.04688e21	+	3.12286e20i	−1.78311	+	0.110334i
$335$	−2.73698e21			−0.942739
$336$	−1.43915e21	+	3.50968e21i	−0.483305	+	1.17865i
$337$	3.19232e21			1.04533			0.522664	−	0.852539i	$-0.324938\pi$
$337$	3.19232e21			1.04533			0.522664	+	0.852539i	$0.324938\pi$
$338$	−1.27896e21	+	7.91383e19i	−0.408380	+	0.0252694i
$339$	5.95946e20	−	8.06575e20i	0.185571	−	0.251158i
$340$	4.25849e21	−	5.29032e20i	1.29326	−	0.160661i
$341$		−	2.46343e20i		−	0.0729672i
$342$	4.87854e21	−	1.83589e21i	1.40951	−	0.530427i
$343$			1.70494e21i			0.480518i
$344$	2.70423e20	+	1.44188e21i	0.0743526	+	0.396444i
$345$	2.95202e21	−	3.99537e21i	0.791875	−	1.07175i
$346$	−3.17135e20	−	5.12524e21i	−0.0830037	−	1.34143i
$347$	5.36171e21			1.36931			0.684656	−	0.728866i	$-0.259952\pi$
$347$	5.36171e21			1.36931			0.684656	+	0.728866i	$0.259952\pi$
$348$	8.80790e20	−	1.56458e21i	0.219507	−	0.389918i
$349$	−2.00294e21			−0.487137			−0.243568	−	0.969884i	$-0.578318\pi$
$349$	−2.00294e21			−0.487137			−0.243568	+	0.969884i	$0.578318\pi$
$350$	−2.36075e19	−	3.81522e20i	−0.00560366	−	0.0905611i
$351$	−1.70004e21	+	4.83353e21i	−0.393865	+	1.11984i
$352$	−5.40082e20	+	1.72403e20i	−0.122137	+	0.0389880i
$353$		−	2.37031e21i		−	0.523262i	−0.965168	−	0.261631i	$-0.915740\pi$
$353$		−	2.37031e21i		−	0.523262i	0.965168	−	0.261631i	$-0.0842604\pi$
$354$	1.79247e21	+	1.16042e21i	0.386298	+	0.250084i
$355$			2.03586e21i			0.428357i
$356$	−1.06379e21	−	8.56308e21i	−0.218540	−	1.75916i
$357$	6.90677e21	+	5.10314e21i	1.38546	+	1.02366i
$358$	−7.10084e21	+	4.39380e20i	−1.39093	+	0.0860665i
$359$	−7.29466e20			−0.139541			−0.0697706	−	0.997563i	$-0.522227\pi$
$359$	−7.29466e20			−0.139541			−0.0697706	+	0.997563i	$0.522227\pi$
$360$	4.56717e21	−	2.39822e21i	0.853249	−	0.448040i
$361$	−6.94949e21			−1.26807
$362$	−7.27594e21	+	4.50214e20i	−1.29678	+	0.0802410i
$363$	−4.54376e21	−	3.35720e21i	−0.791060	−	0.584482i
$364$	1.09616e21	+	8.82365e21i	0.186429	+	1.50067i
$365$			7.76438e21i			1.29008i
$366$	8.03000e21	+	5.19850e21i	1.30355	+	0.843896i
$367$		−	5.41138e21i		−	0.858314i	−0.903230	−	0.429157i	$-0.858811\pi$
$367$		−	5.41138e21i		−	0.858314i	0.903230	−	0.429157i	$-0.141189\pi$
$368$	−8.65032e21	+	2.18295e21i	−1.34068	+	0.338327i
$369$	−6.72908e21	+	2.06776e21i	−1.01913	+	0.313168i
$370$	3.22191e20	+	5.20695e21i	0.0476869	+	0.770671i
$371$	−4.17998e21			−0.604639
$372$	1.97479e21	−	3.50788e21i	0.279194	−	0.495941i
$373$	−1.00943e22			−1.39492			−0.697460	−	0.716623i	$-0.745687\pi$
$373$	−1.00943e22			−1.39492			−0.697460	+	0.716623i	$0.745687\pi$
$374$	7.92652e19	+	1.28101e21i	0.0107071	+	0.173039i
$375$	−4.64592e21	+	6.28795e21i	−0.613487	+	0.830316i
$376$	−9.40624e20	+	1.76413e20i	−0.121428	+	0.0227737i
$377$		−	4.20857e21i		−	0.531170i
$378$	9.93131e21	+	2.81718e21i	1.22554	+	0.347644i
$379$		−	8.35331e21i		−	1.00792i	−0.863728	−	0.503959i	$-0.831876\pi$
$379$		−	8.35331e21i		−	1.00792i	0.863728	−	0.503959i	$-0.168124\pi$
$380$	−1.22072e22	+	1.51650e21i	−1.44031	+	0.178930i
$381$	−1.60555e21	+	2.17301e21i	−0.185251	+	0.250726i
$382$	2.20676e21	−	1.36548e20i	0.249010	−	0.0154080i
$383$	5.63427e21			0.621796			0.310898	−	0.950443i	$-0.399370\pi$
$383$	5.63427e21			0.621796			0.310898	+	0.950443i	$0.399370\pi$
$384$	−9.07273e21	−	1.87453e21i	−0.979316	−	0.202338i
$385$	−1.49080e21			−0.157400
$386$	6.96890e21	−	4.31215e20i	0.719734	−	0.0445351i
$387$	3.81627e21	−	1.17269e21i	0.385563	−	0.118479i
$388$	1.89882e22	−	2.35890e21i	1.87678	−	0.233152i
$389$		−	4.38299e20i		−	0.0423837i	−0.999775	−	0.0211919i	$-0.993254\pi$
$389$		−	4.38299e20i		−	0.0423837i	0.999775	−	0.0211919i	$-0.00674608\pi$
$390$	6.57112e21	−	1.01503e22i	0.621714	−	0.960346i
$391$			2.01972e22i			1.86977i
$392$	6.75724e21	−	1.26731e21i	0.612122	−	0.114803i
$393$	1.63671e21	+	1.20930e21i	0.145089	+	0.107200i
$394$	−1.09247e21	−	1.76555e22i	−0.0947744	−	1.53166i
$395$	1.99711e22			1.69562
$396$	6.31548e20	+	1.40768e21i	0.0524805	+	0.116976i
$397$	1.18120e22			0.960734			0.480367	−	0.877067i	$-0.340503\pi$
$397$	1.18120e22			0.960734			0.480367	+	0.877067i	$0.340503\pi$
$398$	−1.16532e21	−	1.88328e22i	−0.0927766	−	1.49937i
$399$	−1.97987e22	−	1.46285e22i	−1.54300	−	1.14006i
$400$	9.05198e20	−	2.28431e20i	0.0690611	−	0.0174279i
$401$			1.91012e22i			1.42670i	0.700807	+	0.713351i	$0.252824\pi$
$401$			1.91012e22i			1.42670i	−0.700807	+	0.713351i	$0.747176\pi$
$402$	7.26964e21	−	1.12292e22i	0.531608	−	0.821161i
$403$		−	9.43590e21i		−	0.675601i
$404$	1.09808e21	+	8.83909e21i	0.0769825	+	0.619678i
$405$	−7.88337e21	−	1.16161e22i	−0.541183	−	0.797430i
$406$	−8.46304e21	+	5.23668e20i	−0.568925	+	0.0352034i
$407$	−1.56032e21			−0.102721
$408$	−9.14039e21	+	1.88768e22i	−0.589323	+	1.21707i
$409$	1.46242e20			0.00923471			0.00461736	−	0.999989i	$-0.498530\pi$
$409$	1.46242e20			0.00923471			0.00461736	+	0.999989i	$0.498530\pi$
$410$	1.65811e22	−	1.02599e21i	1.02553	−	0.0634570i
$411$	−2.70625e21	+	3.66274e21i	−0.163951	+	0.221897i
$412$	1.01282e21	+	8.15282e21i	0.0601046	+	0.483817i
$413$		−	1.00841e22i		−	0.586222i
$414$	8.55131e21	+	2.27235e22i	0.487001	+	1.29411i
$415$			1.70796e22i			0.952950i
$416$	−2.06873e22	+	6.60370e21i	−1.13086	+	0.360989i
$417$	−6.74946e20	+	9.13497e20i	−0.0361504	+	0.0489272i
$418$	−2.27219e20	−	3.67210e21i	−0.0119247	−	0.192715i
$419$	3.16932e22			1.62985			0.814923	−	0.579570i	$-0.196779\pi$
$419$	3.16932e22			1.62985			0.814923	+	0.579570i	$0.196779\pi$
$420$	−2.12288e22	−	1.19509e22i	−1.06981	−	0.602258i
$421$	3.62406e21			0.178977			0.0894885	−	0.995988i	$-0.471477\pi$
$421$	3.62406e21			0.178977			0.0894885	+	0.995988i	$0.471477\pi$
$422$	8.69760e20	+	1.40562e22i	0.0420962	+	0.680320i
$423$	7.65018e20	+	2.48958e21i	0.0362893	+	0.118095i
$424$	−1.88183e21	−	1.00338e22i	−0.0874927	−	0.466506i
$425$		−	2.11350e21i		−	0.0963154i
$426$	−8.35267e21	−	5.40739e21i	−0.373116	−	0.241550i
$427$		−	4.51755e22i		−	1.97818i
$428$	1.11965e22	−	1.39094e21i	0.480628	−	0.0597084i
$429$	2.90865e21	+	2.14909e21i	0.122407	+	0.0904414i
$430$	−9.40364e21	+	5.81870e20i	−0.387984	+	0.0240073i
$431$	−3.44149e22			−1.39216			−0.696082	−	0.717963i	$-0.745075\pi$
$431$	−3.44149e22			−1.39216			−0.696082	+	0.717963i	$0.745075\pi$
$432$	−2.29141e21	+	2.51079e22i	−0.0908849	+	0.995861i
$433$	3.54779e22			1.37978			0.689892	−	0.723913i	$-0.257658\pi$
$433$	3.54779e22			1.37978			0.689892	+	0.723913i	$0.257658\pi$
$434$	−1.89747e22	+	1.17410e21i	−0.723622	+	0.0447757i
$435$	9.27415e21	+	6.85230e21i	0.346829	+	0.256258i
$436$	−6.36716e21	+	7.90992e20i	−0.233513	+	0.0290093i
$437$		−	5.78964e22i		−	2.08238i
$438$	−3.18555e22	−	2.06228e22i	−1.12371	−	0.727474i
$439$			3.76762e22i			1.30352i	0.758424	+	0.651761i	$0.225969\pi$
$439$			3.76762e22i			1.30352i	−0.758424	+	0.651761i	$0.774031\pi$
$440$	−6.71162e20	−	3.57860e21i	−0.0227761	−	0.121441i
$441$	−5.49573e21	−	1.78846e22i	−0.182935	−	0.595321i
$442$	3.03617e21	+	4.90677e22i	0.0991372	+	1.60216i
$443$	−2.19497e22			−0.703069			−0.351534	−	0.936175i	$-0.614340\pi$
$443$	−2.19497e22			−0.703069			−0.351534	+	0.936175i	$0.614340\pi$
$444$	−2.22187e22	−	1.25082e22i	−0.698174	−	0.393042i
$445$	5.54173e22			1.70838
$446$	2.44857e21	+	3.95714e22i	0.0740569	+	1.19684i
$447$	5.09235e20	−	6.89217e20i	0.0151114	−	0.0204523i
$448$	1.58535e22	+	4.07784e22i	0.461596	+	1.18732i
$449$			5.19285e22i			1.48358i	0.670630	+	0.741792i	$0.266024\pi$
$449$			5.19285e22i			1.48358i	−0.670630	+	0.741792i	$0.733976\pi$
$450$	−8.94837e20	−	2.37786e21i	−0.0250863	−	0.0666622i
$451$			4.96870e21i			0.136692i
$452$	−1.42599e21	−	1.14787e22i	−0.0384982	−	0.309895i
$453$	−1.47211e22	+	1.99241e22i	−0.390037	+	0.527890i
$454$	1.12664e21	−	6.97133e19i	0.0292962	−	0.00181276i
$455$	−5.71037e22			−1.45736
$456$	2.62015e22	−	5.41116e22i	0.656335	−	1.35547i
$457$	−3.22782e22			−0.793637			−0.396818	−	0.917897i	$-0.629886\pi$
$457$	−3.22782e22			−0.793637			−0.396818	+	0.917897i	$0.629886\pi$
$458$	−2.71957e21	+	1.68279e20i	−0.0656362	+	0.00406138i
$459$	5.38440e22	+	1.89379e22i	1.27564	+	0.448666i
$460$	−7.06365e21	−	5.68595e22i	−0.164281	−	1.32240i
$461$		−	3.88384e22i		−	0.886755i	−0.896335	−	0.443377i	$-0.853780\pi$
$461$		−	3.88384e22i		−	0.886755i	0.896335	−	0.443377i	$-0.146220\pi$
$462$	3.95969e21	−	6.11644e21i	0.0887574	−	0.137101i
$463$		−	5.35193e21i		−	0.117780i	−0.998264	−	0.0588901i	$-0.981244\pi$
$463$		−	5.35193e21i		−	0.117780i	0.998264	−	0.0588901i	$-0.0187561\pi$
$464$	−5.06711e21	−	2.00794e22i	−0.109486	−	0.433857i
$465$	2.07932e22	+	1.53633e22i	0.441136	+	0.325938i
$466$	−3.80376e21	−	6.14728e22i	−0.0792379	−	1.28057i
$467$	4.07913e22			0.834399			0.417200	−	0.908815i	$-0.363012\pi$
$467$	4.07913e22			0.834399			0.417200	+	0.908815i	$0.363012\pi$
$468$	2.41908e22	+	5.39197e22i	0.485915	+	1.08307i
$469$	−6.31738e22			−1.24614
$470$	−3.79588e20	−	6.13455e21i	−0.00735328	−	0.118837i
$471$	1.74195e22	+	1.28706e22i	0.331405	+	0.244862i
$472$	2.42064e22	−	4.53989e21i	0.452297	−	0.0848278i
$473$		−	2.81790e21i		−	0.0517138i
$474$	−5.30449e22	+	8.19371e22i	−0.956154	+	1.47695i
$475$			6.05847e21i			0.107267i
$476$	9.82927e22	−	1.22109e22i	1.70947	−	0.212368i
$477$	−2.65569e22	+	8.16062e21i	−0.453702	+	0.139417i
$478$	2.60728e22	−	1.61331e21i	0.437573	−	0.0270757i
$479$	−8.45968e22			−1.39477			−0.697384	−	0.716697i	$-0.745653\pi$
$479$	−8.45968e22			−1.39477			−0.697384	+	0.716697i	$0.745653\pi$
$480$	1.91304e22	−	5.63391e22i	0.309865	−	0.912555i
$481$	−5.97664e22			−0.951095
$482$	3.25380e21	−	2.01336e20i	0.0508734	−	0.00314790i
$483$	6.81371e22	−	9.22192e22i	1.04673	−	1.41668i
$484$	−6.46639e22	+	8.03319e21i	−0.976060	+	0.121256i
$485$			1.22885e23i			1.82261i
$486$	6.85971e22	−	1.49045e21i	0.999764	−	0.0217224i
$487$		−	5.01191e22i		−	0.717807i	−0.933375	−	0.358903i	$-0.883151\pi$
$487$		−	5.01191e22i		−	0.717807i	0.933375	−	0.358903i	$-0.116849\pi$
$488$	1.08442e23	−	2.03381e22i	1.52625	−	0.286247i
$489$	3.93865e22	−	5.33071e22i	0.544781	−	0.737326i
$490$	2.72688e21	+	4.40693e22i	0.0370681	+	0.599059i
$491$	6.23757e22			0.833341			0.416671	−	0.909058i	$-0.363197\pi$
$491$	6.23757e22			0.833341			0.416671	+	0.909058i	$0.363197\pi$
$492$	−3.98312e22	+	7.07535e22i	−0.523022	+	0.929062i
$493$	−4.68822e22			−0.605075
$494$	−8.70337e21	−	1.40656e23i	−0.110410	−	1.78434i
$495$	−9.47160e21	+	2.91051e21i	−0.118108	+	0.0362932i
$496$	−1.13608e22	−	4.50192e22i	−0.139256	−	0.551828i
$497$			4.69907e22i			0.566217i
$498$	−7.00740e22	−	4.53649e22i	−0.830056	−	0.537366i
$499$		−	5.10626e22i		−	0.594632i	−0.954779	−	0.297316i	$-0.903909\pi$
$499$		−	5.10626e22i		−	0.594632i	0.954779	−	0.297316i	$-0.0960914\pi$
$500$	1.11168e22	+	8.94861e22i	0.127273	+	1.02450i
$501$	1.27654e23	+	9.43187e22i	1.43686	+	1.06164i
$502$	5.54501e22	−	3.43110e21i	0.613651	−	0.0379709i
$503$	−4.41153e22			−0.480022			−0.240011	−	0.970770i	$-0.577151\pi$
$503$	−4.41153e22			−0.480022			−0.240011	+	0.970770i	$0.577151\pi$
$504$	1.05417e23	−	5.53545e22i	1.12785	−	0.592235i
$505$	−5.72036e22			−0.601792
$506$	1.71041e22	−	1.05835e21i	0.176937	−	0.0109484i
$507$	3.23496e22	+	2.39019e22i	0.329080	+	0.243144i
$508$	3.84179e21	+	3.09249e22i	0.0384319	+	0.309361i
$509$		−	6.31838e22i		−	0.621591i	−0.950477	−	0.310795i	$-0.899405\pi$
$509$		−	6.31838e22i		−	0.621591i	0.950477	−	0.310795i	$-0.100595\pi$
$510$	−1.13071e23	−	7.32003e22i	−1.09396	−	0.708217i
$511$			1.79214e23i			1.70527i
$512$	−9.07493e22	+	5.64141e22i	−0.849275	+	0.527950i
$513$	−1.54347e23	−	5.42866e22i	−1.42070	−	0.499684i
$514$	9.62774e21	+	1.55595e23i	0.0871642	+	1.40867i
$515$	−5.27623e22			−0.469853
$516$	2.25895e22	−	4.01265e22i	0.197872	−	0.351487i
$517$	1.83829e21			0.0158396
$518$	7.43667e21	+	1.20185e23i	0.0630341	+	1.01870i
$519$	−9.57832e22	+	1.29636e23i	−0.798669	+	1.08095i
$520$	−2.57082e22	−	1.37075e23i	−0.210883	−	1.12442i
$521$		−	2.34551e23i		−	1.89285i	−0.322918	−	0.946427i	$-0.604664\pi$
$521$		−	2.34551e23i		−	1.89285i	0.322918	−	0.946427i	$-0.395336\pi$
$522$	−5.27463e22	+	1.98495e22i	−0.418787	+	0.157598i
$523$		−	9.55057e22i		−	0.746045i	−0.927822	−	0.373022i	$-0.878321\pi$
$523$		−	9.55057e22i		−	0.746045i	0.927822	−	0.373022i	$-0.121679\pi$
$524$	2.32926e22	−	2.89363e21i	0.179020	−	0.0222396i
$525$	−7.13009e21	+	9.65012e21i	−0.0539189	+	0.0729758i
$526$	5.04139e22	−	3.11947e21i	0.375121	−	0.0232114i
$527$	−1.05113e23			−0.769601
$528$	1.64649e22	+	6.75142e21i	0.118623	+	0.0486415i
$529$	1.28623e23			0.911894
$530$	6.54387e22	−	4.04916e21i	0.456551	−	0.0282501i
$531$	−1.96873e22	−	6.40680e22i	−0.135171	−	0.439883i
$532$	−2.81762e23	+	3.50033e22i	−1.90386	+	0.236516i
$533$			1.90321e23i			1.26562i
$534$	−1.47193e23	+	2.27365e23i	−0.963354	+	1.48807i
$535$			7.24597e22i			0.466756i
$536$	−2.84410e22	−	1.51646e23i	−0.180320	−	0.961456i
$537$	1.79607e23	+	1.32704e23i	1.12083	+	0.828139i
$538$	−1.05863e22	−	1.71086e23i	−0.0650272	−	1.05091i
$539$	−1.32059e22			−0.0798477
$540$	−1.58206e23	−	3.44832e22i	−0.941621	−	0.205239i
$541$	−4.09820e22			−0.240113			−0.120057	−	0.992767i	$-0.538308\pi$
$541$	−4.09820e22			−0.240113			−0.120057	+	0.992767i	$0.538308\pi$
$542$	5.08237e21	+	8.21365e22i	0.0293138	+	0.473742i
$543$	1.84036e23	+	1.35977e23i	1.04497	+	0.772086i
$544$	7.35632e22	+	2.30449e23i	0.411216	+	1.28821i
$545$		−	4.12061e22i		−	0.226773i
$546$	1.51672e23	−	2.34284e23i	0.821802	−	1.26942i
$547$		−	1.27053e23i		−	0.677787i	−0.940825	−	0.338893i	$-0.889947\pi$
$547$		−	1.27053e23i		−	0.677787i	0.940825	−	0.338893i	$-0.110053\pi$
$548$	6.47558e21	+	5.21258e22i	0.0340129	+	0.273790i
$549$	−8.81965e22	−	2.87016e23i	−0.456128	−	1.48436i
$550$	−1.78982e21	+	1.10749e20i	−0.00911439	+	0.000563972i
$551$	1.34391e23			0.673877
$552$	2.52043e23	+	1.22043e23i	1.24449	+	0.602600i
$553$	4.60965e23			2.24132
$554$	−6.56203e22	+	4.06040e21i	−0.314199	+	0.0194417i
$555$	9.73102e22	−	1.31703e23i	0.458847	−	0.621021i
$556$	1.61503e21	+	1.30003e22i	0.00749969	+	0.0603695i
$557$		−	1.66652e23i		−	0.762150i	−0.924544	−	0.381075i	$-0.875554\pi$
$557$		−	1.66652e23i		−	0.762150i	0.924544	−	0.381075i	$-0.124446\pi$
$558$	−1.18261e23	+	4.45039e22i	−0.532660	+	0.200451i
$559$		−	1.07937e23i		−	0.478817i
$560$	−2.72445e23	+	6.87527e22i	−1.19037	+	0.300394i
$561$	2.39402e22	−	3.24015e22i	0.103025	−	0.139438i
$562$	−6.59411e21	−	1.06568e23i	−0.0279510	−	0.451718i
$563$	1.94740e23			0.813081			0.406541	−	0.913633i	$-0.366735\pi$
$563$	1.94740e23			0.813081			0.406541	+	0.913633i	$0.366735\pi$
$564$	2.61769e22	+	1.47365e22i	0.107658	+	0.0606068i
$565$	7.42860e22			0.300950
$566$	−6.05353e21	−	9.78315e22i	−0.0241585	−	0.390426i
$567$	−1.81960e23	−	2.68118e23i	−0.715354	−	1.05407i
$568$	−1.12799e23	+	2.11553e22i	−0.436862	+	0.0819329i
$569$		−	9.42340e22i		−	0.359545i	−0.983708	−	0.179772i	$-0.942464\pi$
$569$		−	9.42340e22i		−	0.359545i	0.983708	−	0.179772i	$-0.0575362\pi$
$570$	3.24124e23	+	2.09833e23i	1.21836	+	0.788748i
$571$			9.86503e22i			0.365335i	0.983175	+	0.182668i	$0.0584732\pi$
$571$			9.86503e22i			0.365335i	−0.983175	+	0.182668i	$0.941527\pi$
$572$	4.13941e22	−	5.14239e21i	0.151033	−	0.0187628i
$573$	−5.58171e22	−	4.12410e22i	−0.200656	−	0.148257i
$574$	3.82717e23	−	2.36814e22i	1.35558	−	0.0838796i
$575$	−2.82194e22			−0.0984854
$576$	1.80335e23	+	2.28129e23i	0.620139	+	0.784492i
$577$	−3.19521e23			−1.08269			−0.541345	−	0.840800i	$-0.682085\pi$
$577$	−3.19521e23			−1.08269			−0.541345	+	0.840800i	$0.682085\pi$
$578$	2.47678e23	−	1.53256e22i	0.826990	−	0.0511717i
$579$	−1.76269e23	−	1.30238e23i	−0.579975	−	0.428520i
$580$	1.31984e23	−	1.63963e22i	0.427939	−	0.0531629i
$581$			3.94225e23i			1.25964i
$582$	−5.04169e23	−	3.26392e23i	−1.58756	−	1.02777i
$583$			1.96094e22i			0.0608530i
$584$	−4.30194e23	+	8.06824e22i	−1.31570	+	0.246757i
$585$	−3.62800e23	+	1.11484e23i	−1.09356	+	0.336038i
$586$	−2.58007e22	−	4.16967e23i	−0.0766483	−	1.23872i
$587$	5.63111e23			1.64881			0.824404	−	0.566001i	$-0.191510\pi$
$587$	5.63111e23			1.64881			0.824404	+	0.566001i	$0.191510\pi$
$588$	−1.88049e23	−	1.05864e23i	−0.542706	−	0.305520i
$589$	3.01313e23			0.857112
$590$	9.76850e21	+	1.57869e23i	0.0273896	+	0.442645i
$591$	−3.29954e23	+	4.46572e23i	−0.911928	+	1.23424i
$592$	−2.85149e23	+	7.19586e22i	−0.776851	+	0.196042i
$593$			1.37621e23i			0.369589i	0.982777	+	0.184795i	$0.0591620\pi$
$593$			1.37621e23i			0.369589i	−0.982777	+	0.184795i	$0.940838\pi$
$594$	1.32161e22	−	4.65904e22i	0.0349881	−	0.123342i
$595$			6.36117e23i			1.66013i
$596$	−1.21851e21	−	9.80849e21i	−0.00313498	−	0.0252353i
$597$	−3.51957e23	+	4.76351e23i	−0.892704	+	1.20822i
$598$	6.55153e23	−	4.05390e22i	1.63826	−	0.101371i
$599$	−4.71947e23			−1.16350			−0.581749	−	0.813369i	$-0.697631\pi$
$599$	−4.71947e23			−1.16350			−0.581749	+	0.813369i	$0.697631\pi$
$600$	−2.63746e22	−	1.27709e22i	−0.0641063	−	0.0310411i
$601$	−3.31387e23			−0.794149			−0.397074	−	0.917786i	$-0.629974\pi$
$601$	−3.31387e23			−0.794149			−0.397074	+	0.917786i	$0.629974\pi$
$602$	−2.17051e23	+	1.34305e22i	−0.512851	+	0.0317337i
$603$	−4.01366e23	+	1.23335e23i	−0.935068	+	0.287335i
$604$	3.52250e22	+	2.83547e23i	0.0809164	+	0.651344i
$605$		−	4.18483e23i		−	0.947888i
$606$	1.51937e23	−	2.34694e23i	0.339349	−	0.524184i
$607$		−	2.54312e23i		−	0.560097i	−0.959986	−	0.280049i	$-0.909649\pi$
$607$		−	2.54312e23i		−	0.560097i	0.959986	−	0.280049i	$-0.0903506\pi$
$608$	−2.10874e23	−	6.60598e23i	−0.457975	−	1.43469i
$609$	2.14062e23	+	1.58162e23i	0.458450	+	0.338730i
$610$	4.37616e22	+	7.07233e23i	0.0924249	+	1.49368i
$611$	7.04136e22			0.146658
$612$	6.00649e23	−	2.69478e23i	1.23377	−	0.553523i
$613$	−1.59390e23			−0.322885			−0.161443	−	0.986882i	$-0.551615\pi$
$613$	−1.59390e23			−0.322885			−0.161443	+	0.986882i	$0.551615\pi$
$614$	−2.63261e22	−	4.25458e23i	−0.0525963	−	0.850013i
$615$	−4.19397e23	−	3.09876e23i	−0.826393	−	0.610589i
$616$	−1.54915e22	−	8.25997e22i	−0.0301062	−	0.160525i
$617$			1.61253e23i			0.309089i	0.987986	+	0.154545i	$0.0493911\pi$
$617$			1.61253e23i			0.309089i	−0.987986	+	0.154545i	$0.950609\pi$
$618$	1.40141e23	−	2.16472e23i	0.264949	−	0.409260i
$619$		−	2.35015e23i		−	0.438253i	−0.975696	−	0.219126i	$-0.929679\pi$
$619$		−	2.35015e23i		−	0.438253i	0.975696	−	0.219126i	$-0.0703207\pi$
$620$	2.95916e23	−	3.67616e22i	0.544301	−	0.0676185i
$621$	2.52859e23	−	7.18926e23i	0.458775	−	1.30438i
$622$	−4.63230e22	+	2.86633e21i	−0.0829045	+	0.00512989i
$623$	1.27912e24			2.25820
$624$	6.30669e23	+	2.58606e23i	1.09833	+	0.450370i
$625$	−5.37665e23			−0.923701
$626$	−5.76136e23	+	3.56496e22i	−0.976435	+	0.0604190i
$627$	−6.86260e22	+	9.28810e22i	−0.114740	+	0.155293i
$628$	2.47903e23	−	3.07970e22i	0.408908	−	0.0507986i
$629$			6.65779e23i			1.08343i
$630$	2.69327e23	+	7.15684e23i	0.432399	+	1.14902i
$631$		−	6.84152e23i		−	1.08368i	−0.840480	−	0.541842i	$-0.817727\pi$
$631$		−	6.84152e23i		−	1.08368i	0.840480	−	0.541842i	$-0.182273\pi$
$632$	2.07527e23	+	1.10652e24i	0.324325	+	1.72928i
$633$	2.62690e23	−	3.55535e23i	0.405054	−	0.548214i
$634$	1.45355e22	+	2.34908e23i	0.0221141	+	0.357388i
$635$	−2.00135e23			−0.300432
$636$	−1.57197e23	+	2.79235e23i	−0.232841	+	0.413604i
$637$	−5.05837e23			−0.739307
$638$	2.45667e21	+	3.97024e22i	0.00354300	+	0.0572586i
$639$	9.17405e22	+	2.98549e23i	0.130558	+	0.424872i
$640$	−2.87693e23	−	6.23039e23i	−0.404017	−	0.874954i
$641$			6.69825e23i			0.928257i	0.885768	+	0.464129i	$0.153632\pi$
$641$			6.69825e23i			0.928257i	−0.885768	+	0.464129i	$0.846368\pi$
$642$	−2.97286e23	−	1.92459e23i	−0.406562	−	0.263202i
$643$		−	3.25627e23i		−	0.439468i	−0.975560	−	0.219734i	$-0.929481\pi$
$643$		−	3.25627e23i		−	0.439468i	0.975560	−	0.219734i	$-0.0705189\pi$
$644$	−1.63040e23	−	1.31240e24i	−0.217152	−	1.74799i
$645$	2.37853e23	+	1.75740e23i	0.312645	+	0.231001i
$646$	−1.56686e24	+	9.69528e22i	−2.03261	+	0.125772i
$647$	2.81491e23			0.360395			0.180197	−	0.983630i	$-0.442326\pi$
$647$	2.81491e23			0.360395			0.180197	+	0.983630i	$0.442326\pi$
$648$	5.61685e23	−	5.57494e23i	0.709749	−	0.704454i
$649$	−4.73073e22			−0.0589995
$650$	−6.85573e22	+	4.24213e21i	−0.0843899	+	0.00522180i
$651$	4.79940e23	+	3.54609e23i	0.583108	+	0.430835i
$652$	−9.42448e22	−	7.58632e23i	−0.113019	−	0.909759i
$653$		−	4.49482e23i		−	0.532048i	−0.963966	−	0.266024i	$-0.914290\pi$
$653$		−	4.49482e23i		−	0.532048i	0.963966	−	0.266024i	$-0.0857100\pi$
$654$	1.69059e23	+	1.09447e23i	0.197528	+	0.127877i
$655$			1.50742e23i			0.173853i
$656$	2.29146e23	+	9.08032e23i	0.260873	+	1.03376i
$657$	3.49881e23	+	1.13861e24i	0.393201	+	1.27959i
$658$	−8.76149e21	−	1.41595e23i	−0.00971981	−	0.157083i
$659$	−1.05622e24			−1.15672			−0.578361	−	0.815781i	$-0.696308\pi$
$659$	−1.05622e24			−1.15672			−0.578361	+	0.815781i	$0.696308\pi$
$660$	−5.60650e22	+	9.95901e22i	−0.0606133	+	0.107670i
$661$	1.31219e24			1.40050			0.700250	−	0.713898i	$-0.253072\pi$
$661$	1.31219e24			1.40050			0.700250	+	0.713898i	$0.253072\pi$
$662$	3.73417e22	+	6.03481e23i	0.0393460	+	0.635873i
$663$	9.17003e23	−	1.24111e24i	0.953906	−	1.29105i
$664$	−9.46318e23	+	1.77481e23i	−0.971870	+	0.182273i
$665$		−	1.82347e24i		−	1.84890i
$666$	2.81885e23	+	7.49056e23i	0.282190	+	0.749866i
$667$			6.25971e23i			0.618707i
$668$	1.81669e24	−	2.25688e23i	1.77289	−	0.220246i
$669$	7.39532e23	−	1.00091e24i	0.712582	−	0.964434i
$670$	9.89002e23	−	6.11966e22i	0.940939	−	0.0582226i
$671$	−2.11930e23			−0.199091
$672$	4.41558e23	−	1.30039e24i	0.409590	−	1.20625i
$673$	1.27329e23			0.116627			0.0583136	−	0.998298i	$-0.481428\pi$
$673$	1.27329e23			0.116627			0.0583136	+	0.998298i	$0.481428\pi$
$674$	−1.15354e24	+	7.13777e22i	−1.04333	+	0.0645585i
$675$	−2.64600e22	+	7.52308e22i	−0.0236324	+	0.0671914i
$676$	4.60379e23	−	5.71929e22i	0.406040	−	0.0504423i
$677$		−	1.51030e24i		−	1.31540i	−0.753280	−	0.657701i	$-0.771529\pi$
$677$		−	1.51030e24i		−	1.31540i	0.753280	−	0.657701i	$-0.228471\pi$
$678$	−1.97309e23	+	3.04779e23i	−0.169705	+	0.262139i
$679$			2.83637e24i			2.40919i
$680$	−1.52697e24	+	2.86381e23i	−1.28087	+	0.240225i
$681$	−2.84969e22	−	2.10553e22i	−0.0236074	−	0.0174426i
$682$	5.50801e21	+	8.90153e22i	0.00450638	+	0.0728279i
$683$	−8.44004e23			−0.681975			−0.340988	−	0.940068i	$-0.610761\pi$
$683$	−8.44004e23			−0.681975			−0.340988	+	0.940068i	$0.610761\pi$
$684$	−1.72180e24	+	7.72475e23i	−1.37406	+	0.616464i
$685$	−3.37341e23			−0.265888
$686$	−3.81211e22	−	6.16077e23i	−0.0296763	−	0.479601i
$687$	6.87880e22	+	5.08247e22i	0.0528909	+	0.0390789i
$688$	−1.29956e23	−	5.14973e23i	−0.0986947	−	0.391096i
$689$			7.51118e23i			0.563436i
$690$	−9.77371e23	+	1.50972e24i	−0.724173	+	1.11861i
$691$		−	1.89304e24i		−	1.38547i	−0.721194	−	0.692733i	$-0.756406\pi$
$691$		−	1.89304e24i		−	1.38547i	0.721194	−	0.692733i	$-0.243594\pi$
$692$	2.29192e23	+	1.84490e24i	0.165691	+	1.33374i
$693$	−2.18619e23	+	6.71791e22i	−0.156119	+	0.0479735i
$694$	−1.93744e24	+	1.19883e23i	−1.36670	+	0.0845674i
$695$	−8.41335e22			−0.0586271
$696$	−2.83289e23	+	5.85050e23i	−0.195007	+	0.402730i
$697$	2.12011e24			1.44172
$698$	7.23756e23	−	4.47839e22i	0.486207	−	0.0300851i
$699$	−1.14884e24	+	1.55488e24i	−0.762434	+	1.03191i
$700$	1.70610e22	+	1.37334e23i	0.0111859	+	0.0900421i
$701$			1.20369e24i			0.779669i	0.920885	+	0.389834i	$0.127468\pi$
$701$			1.20369e24i			0.779669i	−0.920885	+	0.389834i	$0.872532\pi$
$702$	5.06230e23	−	1.78460e24i	0.323954	−	1.14202i
$703$		−	1.90850e24i		−	1.20662i
$704$	1.91302e23	−	7.43731e22i	0.119496	−	0.0464567i
$705$	−1.14646e23	+	1.55166e23i	−0.0707539	+	0.0957609i
$706$	5.29980e22	+	8.56504e23i	0.0323162	+	0.522263i
$707$	−1.32035e24			−0.795469
$708$	−6.73649e23	−	3.79235e23i	−0.401006	−	0.225749i
$709$	−2.15046e24			−1.26485			−0.632424	−	0.774623i	$-0.717940\pi$
$709$	−2.15046e24			−1.26485			−0.632424	+	0.774623i	$0.717940\pi$
$710$	−4.55200e22	−	7.35652e23i	−0.0264549	−	0.427540i
$711$	2.92867e24	−	8.99946e23i	1.68182	−	0.516803i
$712$	5.75861e23	+	3.07046e24i	0.326767	+	1.74230i
$713$			1.40347e24i			0.786940i
$714$	−2.60985e24	−	1.68958e24i	−1.44604	−	0.936145i
$715$			2.67889e23i			0.146674i
$716$	2.55605e24	−	3.17538e23i	1.38296	−	0.171804i
$717$	−6.59478e23	−	4.87262e23i	−0.352604	−	0.260525i
$718$	2.63591e23	−	1.63102e22i	0.139275	−	0.00861793i
$719$	−1.93080e23			−0.100819			−0.0504094	−	0.998729i	$-0.516053\pi$
$719$	−1.93080e23			−0.100819			−0.0504094	+	0.998729i	$0.516053\pi$
$720$	−1.59671e24	+	9.68707e23i	−0.823950	+	0.499881i
$721$	−1.21784e24			−0.621068
$722$	2.51118e24	−	1.55385e23i	1.26564	−	0.0783145i
$723$	−8.23007e22	−	6.08087e22i	−0.0409947	−	0.0302894i
$724$	2.61908e24	−	3.25367e23i	1.28935	−	0.160176i
$725$		−	6.55037e22i		−	0.0318708i
$726$	1.71694e24	+	1.11152e24i	0.825647	+	0.534512i
$727$		−	8.58311e23i		−	0.407946i	−0.978977	−	0.203973i	$-0.934615\pi$
$727$		−	8.58311e23i		−	0.407946i	0.978977	−	0.203973i	$-0.0653854\pi$
$728$	−5.93384e23	−	3.16389e24i	−0.278753	−	1.48630i
$729$	−1.67951e24	−	1.34820e24i	−0.779827	−	0.625996i
$730$	−1.73605e23	−	2.80564e24i	−0.0796742	−	1.28762i
$731$	−1.20238e24			−0.545437
$732$	−3.01785e24	−	1.69892e24i	−1.35318	−	0.761780i
$733$	2.33857e24			1.03649			0.518247	−	0.855231i	$-0.326585\pi$
$733$	2.33857e24			1.03649			0.518247	+	0.855231i	$0.326585\pi$
$734$	1.20994e23	+	1.95539e24i	0.0530086	+	0.856676i
$735$	8.23591e23	−	1.11468e24i	0.356672	−	0.482733i
$736$	3.07696e24	−	9.82216e23i	1.31723	−	0.420480i
$737$			2.96365e23i			0.125416i
$738$	2.38530e24	−	8.97638e23i	0.997848	−	0.375511i
$739$			4.41118e24i			1.82422i	0.409946	+	0.912110i	$0.365547\pi$
$739$			4.41118e24i			1.82422i	−0.409946	+	0.912110i	$0.634453\pi$
$740$	−2.32846e23	−	1.87432e24i	−0.0951917	−	0.766254i
$741$	−2.62865e24	+	3.55771e24i	−1.06237	+	1.43786i
$742$	1.51043e24	−	9.34608e22i	0.603485	−	0.0373419i
$743$	3.31198e24			1.30822			0.654112	−	0.756397i	$-0.273042\pi$
$743$	3.31198e24			1.30822			0.654112	+	0.756397i	$0.273042\pi$
$744$	−6.35152e23	+	1.31172e24i	−0.248032	+	0.512237i
$745$	6.34772e22			0.0245070
$746$	3.64754e24	−	2.25699e23i	1.39226	−	0.0861489i
$747$	7.69649e23	+	2.50465e24i	0.290447	+	0.945196i
$748$	−5.72846e22	−	4.61117e23i	−0.0213734	−	0.172047i
$749$			1.67248e24i			0.616973i
$750$	1.53820e24	−	2.37602e24i	0.561037	−	0.866619i
$751$		−	3.82984e24i		−	1.38115i	−0.723260	−	0.690576i	$-0.757357\pi$
$751$		−	3.82984e24i		−	1.38115i	0.723260	−	0.690576i	$-0.242643\pi$
$752$	3.35948e23	−	8.47779e22i	0.119790	−	0.0302295i
$753$	−1.40254e24	−	1.03628e24i	−0.494491	−	0.365360i
$754$	9.41001e22	+	1.52076e24i	0.0328045	+	0.530156i
$755$	−1.83502e24			−0.632545
$756$	−3.65164e24	−	7.95925e23i	−1.24467	−	0.271292i
$757$	−1.24648e24			−0.420117			−0.210058	−	0.977689i	$-0.567365\pi$
$757$	−1.24648e24			−0.420117			−0.210058	+	0.977689i	$0.567365\pi$
$758$	1.86773e23	+	3.01845e24i	0.0622480	+	1.00599i
$759$	−4.32625e23	−	3.19650e23i	−0.142579	−	0.105346i
$760$	4.37715e24	−	8.20929e23i	1.42651	−	0.267541i
$761$		−	3.60047e24i		−	1.16035i	−0.814491	−	0.580176i	$-0.802984\pi$
$761$		−	3.60047e24i		−	1.16035i	0.814491	−	0.580176i	$-0.197016\pi$
$762$	5.31575e23	−	8.21110e23i	0.169413	−	0.261688i
$763$		−	9.51101e23i		−	0.299756i
$764$	−7.94353e23	+	9.86824e22i	−0.247583	+	0.0307572i
$765$	1.24190e24	+	4.04148e24i	0.382792	+	1.24571i
$766$	−2.03593e24	+	1.25977e23i	−0.620609	+	0.0384015i
$767$	−1.81206e24			−0.546275
$768$	3.32032e24	+	4.74500e23i	0.989942	+	0.141471i
$769$	1.32987e24			0.392136			0.196068	−	0.980590i	$-0.437183\pi$
$769$	1.32987e24			0.392136			0.196068	+	0.980590i	$0.437183\pi$
$770$	5.38698e23	−	3.33331e22i	0.157099	−	0.00972086i
$771$	2.90783e24	−	3.93557e24i	0.838701	−	1.13513i
$772$	−2.50855e24	+	3.11637e23i	−0.715610	+	0.0889001i
$773$			1.37841e24i			0.388913i	0.980911	+	0.194456i	$0.0622943\pi$
$773$			1.37841e24i			0.388913i	−0.980911	+	0.194456i	$0.937706\pi$
$774$	−1.35278e24	+	5.09079e23i	−0.377510	+	0.142065i
$775$		−	1.46864e23i		−	0.0405368i
$776$	−6.80858e24	+	1.27694e24i	−1.85880	+	0.348615i
$777$	2.24607e24	−	3.03991e24i	0.606520	−	0.820886i
$778$	9.79999e21	+	1.58378e23i	0.00261758	+	0.0423028i
$779$	−6.07744e24			−1.60566
$780$	−2.14751e24	+	3.81469e24i	−0.561217	+	0.996909i
$781$	2.20446e23			0.0569861
$782$	−4.51591e23	−	7.29819e24i	−0.115475	−	1.86620i
$783$	1.66879e24	+	5.86942e23i	0.422111	+	0.148464i
$784$	−2.41338e24	+	6.09026e23i	−0.603863	+	0.152388i
$785$			1.60435e24i			0.397106i
$786$	−6.18459e23	−	4.00381e23i	−0.151433	−	0.0980352i
$787$			7.88343e24i			1.90954i	0.297338	+	0.954772i	$0.403901\pi$
$787$			7.88343e24i			1.90954i	−0.297338	+	0.954772i	$0.596099\pi$
$788$	7.89522e23	+	6.35533e24i	0.189187	+	1.52288i
$789$	−1.27516e24	−	9.42162e23i	−0.302280	−	0.223342i
$790$	−7.21652e24	+	4.46538e23i	−1.69238	+	0.104720i
$791$	1.71464e24			0.397806
$792$	−2.59683e23	−	4.94541e23i	−0.0596046	−	0.113511i
$793$	−8.11776e24			−1.84338
$794$	−4.26823e24	+	2.64106e23i	−0.958900	+	0.0593340i
$795$	−1.65519e24	−	1.22295e24i	−0.367897	−	0.271825i
$796$	8.42170e23	+	6.77912e24i	0.185199	+	1.49078i
$797$		−	3.58451e24i		−	0.779892i	−0.920838	−	0.389946i	$-0.872494\pi$
$797$		−	3.58451e24i		−	0.779892i	0.920838	−	0.389946i	$-0.127506\pi$
$798$	7.48129e24	+	4.84328e24i	1.61047	+	1.04259i
$799$		−	7.84385e23i		−	0.167064i
$800$	−3.21984e23	+	1.02782e23i	−0.0678530	+	0.0216598i
$801$	8.12669e24	−	2.49724e24i	1.69448	−	0.520695i
$802$	−4.27087e23	−	6.90217e24i	−0.0881117	−	1.42398i
$803$	8.40741e23			0.171625
$804$	−2.37579e24	+	4.22020e24i	−0.479879	+	0.852426i
$805$	8.49344e24			1.69753
$806$	2.10979e23	+	3.40964e24i	0.0417244	+	0.674311i
$807$	−3.19735e24	+	4.32740e24i	−0.625698	+	0.846842i
$808$	−5.94423e23	−	3.16943e24i	−0.115106	−	0.613741i
$809$		−	1.04819e24i		−	0.200852i	−0.994945	−	0.100426i	$-0.967979\pi$
$809$		−	1.04819e24i		−	0.200852i	0.994945	−	0.100426i	$-0.0320206\pi$
$810$	3.10836e24	+	4.02118e24i	0.589399	+	0.762485i
$811$		−	5.36384e24i		−	1.00646i	−0.864151	−	0.503232i	$-0.832144\pi$
$811$		−	5.36384e24i		−	1.00646i	0.864151	−	0.503232i	$-0.167856\pi$
$812$	3.04639e24	−	3.78453e23i	0.565665	−	0.0702725i
$813$	1.53501e24	−	2.07754e24i	0.282060	−	0.381750i
$814$	5.63818e23	−	3.48874e22i	0.102525	−	0.00634398i
$815$	4.90961e24			0.883501
$816$	2.88079e24	−	7.02546e24i	0.513033	−	1.25115i
$817$	3.44671e24			0.607459
$818$	−5.28441e22	+	3.26984e21i	−0.00921708	+	0.000570327i
$819$	−8.37398e24	+	2.57322e24i	−1.44550	+	0.444186i
$820$	−5.96859e24	+	7.41477e23i	−1.01966	+	0.126672i
$821$		−	6.07978e24i		−	1.02795i	−0.857806	−	0.513974i	$-0.828173\pi$
$821$		−	6.07978e24i		−	1.02795i	0.857806	−	0.513974i	$-0.171827\pi$
$822$	8.96003e23	−	1.38403e24i	0.149934	−	0.231599i
$823$		−	4.92079e24i		−	0.814959i	−0.913214	−	0.407480i	$-0.866408\pi$
$823$		−	4.92079e24i		−	0.814959i	0.913214	−	0.407480i	$-0.133592\pi$
$824$	−5.48271e23	−	2.92336e24i	−0.0898699	−	0.479182i
$825$	4.52713e22	+	3.34492e22i	0.00734454	+	0.00542659i
$826$	2.25472e23	+	3.64387e24i	0.0362045	+	0.585103i
$827$	8.85083e24			1.40665			0.703327	−	0.710866i	$-0.251697\pi$
$827$	8.85083e24			1.40665			0.703327	+	0.710866i	$0.251697\pi$
$828$	−3.59807e24	−	8.01987e24i	−0.565994	−	1.26156i
$829$	−3.77531e24			−0.587813			−0.293907	−	0.955834i	$-0.594955\pi$
$829$	−3.77531e24			−0.587813			−0.293907	+	0.955834i	$0.594955\pi$
$830$	−3.81886e23	−	6.17169e24i	−0.0588532	−	0.951131i
$831$	1.65978e24	+	1.22635e24i	0.253188	+	0.187070i
$832$	7.32763e24	−	2.84878e24i	1.10641	−	0.430141i
$833$			5.63486e24i			0.842172i
$834$	2.23465e23	−	3.45181e23i	0.0330597	−	0.0510664i
$835$			1.17570e25i			1.72172i
$836$	1.64210e23	+	1.32182e24i	0.0238038	+	0.191611i
$837$	3.74154e24	+	1.31596e24i	0.536888	+	0.188833i
$838$	−1.14522e25	+	7.08632e23i	−1.62673	+	0.100658i
$839$	1.62142e24			0.227991			0.113996	−	0.993481i	$-0.463635\pi$
$839$	1.62142e24			0.227991			0.113996	+	0.993481i	$0.463635\pi$
$840$	7.93820e24	+	3.84378e24i	1.10496	+	0.535038i
$841$	5.80413e24			0.799781
$842$	−1.30954e24	+	8.10308e22i	−0.178635	+	0.0110534i
$843$	−1.99160e24	+	2.69550e24i	−0.268947	+	0.364003i
$844$	−6.28571e23	−	5.05974e24i	−0.0840318	−	0.676422i
$845$			2.97942e24i			0.394320i
$846$	−3.32102e23	−	8.82498e23i	−0.0435135	−	0.115629i
$847$		−	9.65923e24i		−	1.25295i
$848$	9.04345e23	+	3.58363e24i	0.116137	+	0.460212i
$849$	−1.82833e24	+	2.47452e24i	−0.232455	+	0.314613i
$850$	4.72560e22	+	7.63707e23i	0.00594834	+	0.0961315i
$851$	8.88949e24			1.10784
$852$	3.13912e24	+	1.76719e24i	0.387321	+	0.218045i
$853$	−1.15683e25			−1.41319			−0.706596	−	0.707617i	$-0.749770\pi$
$853$	−1.15683e25			−1.41319			−0.706596	+	0.707617i	$0.749770\pi$
$854$	1.01008e24	+	1.63240e25i	0.122170	+	1.97440i
$855$	−3.55998e24	−	1.15851e25i	−0.426320	−	1.38736i
$856$	−4.01472e24	+	7.52955e23i	−0.476023	+	0.0892775i
$857$			2.78912e24i			0.327439i	0.986507	+	0.163719i	$0.0523491\pi$
$857$			2.78912e24i			0.327439i	−0.986507	+	0.163719i	$0.947651\pi$
$858$	−1.09909e24	−	7.11533e23i	−0.127759	−	0.0827091i
$859$		−	1.28545e25i		−	1.47949i	−0.672887	−	0.739745i	$-0.734946\pi$
$859$		−	1.28545e25i		−	1.47949i	0.672887	−	0.739745i	$-0.265054\pi$
$860$	3.38497e24	−	4.20515e23i	0.385761	−	0.0479230i
$861$	−9.68033e24	−	7.15241e24i	−1.09235	−	0.807097i
$862$	1.24358e25	−	7.69489e23i	1.38951	−	0.0859786i
$863$	9.46578e24			1.04728			0.523642	−	0.851938i	$-0.324573\pi$
$863$	9.46578e24			1.04728			0.523642	+	0.851938i	$0.324573\pi$
$864$	2.66605e23	−	9.12392e24i	0.0292080	−	0.999573i
$865$	−1.19396e25			−1.29525
$866$	−1.28199e25	+	7.93256e23i	−1.37715	+	0.0852140i
$867$	−6.26469e24	−	4.62873e24i	−0.666403	−	0.492379i
$868$	6.83020e24	−	8.48516e23i	0.719476	−	0.0893804i
$869$		−	2.16251e24i		−	0.225575i
$870$	−3.50440e24	−	2.26870e24i	−0.361993	−	0.234349i
$871$			1.13520e25i			1.16123i
$872$	2.28307e24	−	4.28187e23i	0.231275	−	0.0433754i
$873$	5.53748e24	+	1.80205e25i	0.555509	+	1.80778i
$874$	1.29452e24	+	2.09207e25i	0.128606	+	2.07840i
$875$	−1.33671e25			−1.31513
$876$	1.19720e25	+	6.73973e24i	1.16649	+	0.656686i
$877$	8.83194e24			0.852235			0.426118	−	0.904668i	$-0.359881\pi$
$877$	8.83194e24			0.852235			0.426118	+	0.904668i	$0.359881\pi$
$878$	−8.42407e23	−	1.36142e25i	−0.0805042	−	1.30103i
$879$	−7.79250e24	+	1.05467e25i	−0.737516	+	0.998181i
$880$	3.22537e23	+	1.27811e24i	0.0302327	+	0.119803i
$881$		−	8.32196e23i		−	0.0772557i	−0.999254	−	0.0386278i	$-0.987701\pi$
$881$		−	8.32196e23i		−	0.0772557i	0.999254	−	0.0386278i	$-0.0122987\pi$
$882$	2.38575e24	+	6.33968e24i	0.219352	+	0.582887i
$883$			2.34851e24i			0.213859i	0.994267	+	0.106929i	$0.0341018\pi$
$883$			2.34851e24i			0.213859i	−0.994267	+	0.106929i	$0.965898\pi$
$884$	−2.19422e24	−	1.76626e25i	−0.197896	−	1.59298i
$885$	2.95035e24	−	3.99311e24i	0.263545	−	0.356692i
$886$	7.93149e24	−	4.90778e23i	0.701727	−	0.0434208i
$887$	5.97488e24			0.523574			0.261787	−	0.965126i	$-0.415688\pi$
$887$	5.97488e24			0.523574			0.261787	+	0.965126i	$0.415688\pi$
$888$	8.30835e24	+	4.02301e24i	0.721115	+	0.349173i
$889$	−4.61943e24			−0.397122
$890$	−2.00249e25	+	1.23908e24i	−1.70512	+	0.105508i
$891$	−1.25781e24	+	8.53625e23i	−0.106085	+	0.0719958i
$892$	−1.76957e24	−	1.42443e25i	−0.147831	−	1.18998i
$893$			2.24849e24i			0.186060i
$894$	−1.68600e23	+	2.60433e23i	−0.0138194	+	0.0213465i
$895$			1.65419e25i			1.34304i
$896$	−6.64040e24	−	1.43807e25i	−0.534043	−	1.15654i
$897$	−1.65713e25	−	1.22438e25i	−1.32014	−	0.975398i
$898$	−1.16108e24	−	1.87642e25i	−0.0916247	−	1.48075i
$899$	−3.25777e24			−0.254661
$900$	3.76514e23	+	8.39225e23i	0.0291555	+	0.0649856i
$901$	8.36722e24			0.641830
$902$	−1.11096e23	−	1.79543e24i	−0.00844194	−	0.136431i
$903$	5.49002e24	+	4.05636e24i	0.413264	+	0.305345i
$904$	7.71932e23	+	4.11590e24i	0.0575635	+	0.306926i
$905$			1.69498e25i			1.25213i
$906$	4.87395e24	−	7.52867e24i	0.356691	−	0.550971i
$907$			1.10613e24i			0.0801941i	0.999196	+	0.0400970i	$0.0127667\pi$
$907$			1.10613e24i			0.0801941i	−0.999196	+	0.0400970i	$0.987233\pi$
$908$	−4.05550e23	+	5.03815e22i	−0.0291283	+	0.00361860i
$909$	−8.38864e24	+	2.57773e24i	−0.596896	+	0.183419i
$910$	2.06343e25	−	1.27679e24i	1.45458	−	0.0900051i
$911$	−2.46409e25			−1.72088			−0.860440	−	0.509552i	$-0.829811\pi$
$911$	−2.46409e25			−1.72088			−0.860440	+	0.509552i	$0.829811\pi$
$912$	−8.25797e24	+	2.01389e25i	−0.571369	+	1.39341i
$913$	1.84941e24			0.126775
$914$	1.16637e25	−	7.21713e23i	0.792122	−	0.0490142i
$915$	1.32171e25	−	1.78886e25i	0.889321	−	1.20364i
$916$	9.78947e23	−	1.21614e23i	0.0652601	−	0.00810725i
$917$			3.47935e24i			0.229805i
$918$	−1.98798e25	−	5.63925e24i	−1.30092	−	0.369027i
$919$			6.80463e24i			0.441187i	0.975366	+	0.220593i	$0.0707994\pi$
$919$			6.80463e24i			0.441187i	−0.975366	+	0.220593i	$0.929201\pi$
$920$	3.82376e24	+	2.03881e25i	0.245637	+	1.30972i
$921$	−7.95118e24	+	1.07614e25i	−0.506087	+	0.684956i
$922$	8.68394e23	+	1.40342e25i	0.0547651	+	0.885062i
$923$	8.44396e24			0.527633
$924$	−1.29407e24	+	2.29869e24i	−0.0801207	+	0.142321i
$925$	−9.30225e23			−0.0570668
$926$	1.19665e23	+	1.93391e24i	0.00727398	+	0.117555i
$927$	−7.73734e24	+	2.37759e24i	−0.466030	+	0.143205i
$928$	2.27995e24	+	7.14233e24i	0.136071	+	0.426267i
$929$		−	2.06033e25i		−	1.21844i	−0.793002	−	0.609219i	$-0.791483\pi$
$929$		−	2.06033e25i		−	1.21844i	0.793002	−	0.609219i	$-0.208517\pi$
$930$	−7.85710e24	−	5.08657e24i	−0.460423	−	0.298071i
$931$		−	1.61527e25i		−	0.937935i
$932$	2.74896e24	+	2.21280e25i	0.158173	+	1.27323i
$933$	1.17168e24	+	8.65708e23i	0.0668060	+	0.0493603i
$934$	−1.47398e25	+	9.12058e23i	−0.832806	+	0.0515317i
$935$	2.98420e24			0.167082
$936$	−9.94688e24	−	1.89429e25i	−0.551877	−	1.05100i
$937$	7.41976e24			0.407947			0.203973	−	0.978976i	$-0.434614\pi$
$937$	7.41976e24			0.407947			0.203973	+	0.978976i	$0.434614\pi$
$938$	2.28277e25	−	1.41251e24i	1.24376	−	0.0769606i
$939$	1.45726e25	+	1.07671e25i	0.786829	+	0.581356i
$940$	2.74327e23	+	2.20822e24i	0.0146785	+	0.118156i
$941$			5.88974e24i			0.312309i	0.987733	+	0.156154i	$0.0499098\pi$
$941$			5.88974e24i			0.312309i	−0.987733	+	0.156154i	$0.950090\pi$
$942$	−6.58228e24	−	4.26127e24i	−0.345894	−	0.223927i
$943$		−	2.83078e25i		−	1.47420i
$944$	−8.64543e24	+	2.18171e24i	−0.446195	+	0.112599i
$945$	7.96388e24	−	2.26428e25i	0.407337	−	1.15814i
$946$	6.30059e22	+	1.01824e24i	0.00319379	+	0.0516151i
$947$	2.31462e25			1.16280			0.581399	−	0.813619i	$-0.302506\pi$
$947$	2.31462e25			1.16280			0.581399	+	0.813619i	$0.302506\pi$
$948$	1.73356e25	−	3.07938e25i	0.863114	−	1.53318i
$949$	3.22037e25			1.58907
$950$	−1.35462e23	−	2.18921e24i	−0.00662472	−	0.107063i
$951$	4.39009e24	−	5.94171e24i	0.212784	−	0.287990i
$952$	−3.52448e25	+	6.61012e24i	−1.69309	+	0.317537i
$953$		−	2.32417e25i		−	1.10657i	−0.832993	−	0.553283i	$-0.813375\pi$
$953$		−	2.32417e25i		−	1.10657i	0.832993	−	0.553283i	$-0.186625\pi$
$954$	9.41381e24	−	3.54261e24i	0.444226	−	0.167171i
$955$		−	5.14078e24i		−	0.240437i
$956$	−9.38526e24	+	1.16593e24i	−0.435065	+	0.0540481i
$957$	7.41979e23	−	1.00422e24i	0.0340910	−	0.0461400i
$958$	3.05689e25	−	1.89151e24i	1.39211	−	0.0861395i
$959$	−7.78634e24			−0.351460
$960$	−5.65301e24	+	2.07857e25i	−0.252915	+	0.929950i
$961$	1.52460e25			0.676093
$962$	2.15964e25	−	1.33633e24i	0.949280	−	0.0587387i
$963$	3.26521e24	+	1.06259e25i	0.142261	+	0.462958i
$964$	−1.17125e24	+	1.45504e23i	−0.0505819	+	0.00628378i
$965$		−	1.62345e25i		−	0.694955i
$966$	−2.25592e25	+	3.48467e25i	−0.957236	+	1.47862i
$967$			7.07700e24i			0.297662i	0.988863	+	0.148831i	$0.0475511\pi$
$967$			7.07700e24i			0.297662i	−0.988863	+	0.148831i	$0.952449\pi$
$968$	2.31865e25	−	4.34860e24i	0.966708	−	0.181305i
$969$	3.96317e25	+	2.92823e25i	1.63791	+	1.21019i
$970$	−2.74760e24	−	4.44041e25i	−0.112563	−	1.81913i
$971$	1.33349e25			0.541536			0.270768	−	0.962645i	$-0.412722\pi$
$971$	1.33349e25			0.541536			0.270768	+	0.962645i	$0.412722\pi$
$972$	−2.47541e25	+	2.07234e24i	−0.996514	+	0.0834254i
$973$	−1.94193e24			−0.0774952
$974$	1.12062e24	+	1.81104e25i	0.0443310	+	0.716436i
$975$	1.73407e24	+	1.28124e24i	0.0680029	+	0.0502446i
$976$	−3.87303e25	+	9.77377e24i	−1.50566	+	0.379961i
$977$		−	1.42699e24i		−	0.0549943i	−0.999622	−	0.0274972i	$-0.991246\pi$
$977$		−	1.42699e24i		−	0.0549943i	0.999622	−	0.0274972i	$-0.00875372\pi$
$978$	−1.30403e25	+	2.01430e25i	−0.498204	+	0.769564i
$979$		−	6.00069e24i		−	0.227273i
$980$	−1.97071e24	−	1.58634e25i	−0.0739946	−	0.595627i
$981$	−1.85684e24	−	6.04268e24i	−0.0691176	−	0.224928i
$982$	−2.25393e25	+	1.39467e24i	−0.831750	+	0.0514663i
$983$	−4.95078e25			−1.81121			−0.905604	−	0.424123i	$-0.860582\pi$
$983$	−4.95078e25			−1.81121			−0.905604	+	0.424123i	$0.860582\pi$
$984$	1.28109e25	−	2.64572e25i	0.464646	−	0.959590i
$985$	−4.11295e25			−1.47892
$986$	1.69408e25	−	1.04825e24i	0.603920	−	0.0373688i
$987$	−2.64620e24	+	3.58147e24i	−0.0935249	+	0.126580i
$988$	6.28988e24	+	5.06310e25i	0.220398	+	1.77412i
$989$			1.60542e25i			0.557726i
$990$	3.35746e24	−	1.26348e24i	0.115641	−	0.0435181i
$991$			5.44989e25i			1.86107i	0.366208	+	0.930533i	$0.380656\pi$
$991$			5.44989e25i			1.86107i	−0.366208	+	0.930533i	$0.619344\pi$
$992$	5.11179e24	+	1.60136e25i	0.173071	+	0.542174i
$993$	1.12782e25	−	1.52643e25i	0.378591	−	0.512398i
$994$	−1.05067e24	−	1.69800e25i	−0.0349690	−	0.565136i
$995$	−4.38722e25			−1.44775
$996$	2.63354e25	+	1.48257e25i	0.861659	+	0.485077i
$997$	−2.83830e25			−0.920768			−0.460384	−	0.887720i	$-0.652288\pi$
$997$	−2.83830e25			−0.920768			−0.460384	+	0.887720i	$0.652288\pi$
$998$	1.14172e24	+	1.84513e25i	0.0367239	+	0.593496i
$999$	8.33523e24	−	2.36987e25i	0.265834	−	0.755819i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	12.18.b.a.11.2	yes	32
3.2	odd	2	inner	12.18.b.a.11.31	yes	32
4.3	odd	2	inner	12.18.b.a.11.32	yes	32
12.11	even	2	inner	12.18.b.a.11.1	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
12.18.b.a.11.1	✓	32	12.11	even	2	inner
12.18.b.a.11.2	yes	32	1.1	even	1	trivial
12.18.b.a.11.31	yes	32	3.2	odd	2	inner
12.18.b.a.11.32	yes	32	4.3	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)

\(f(q)\)	\(=\)	\(q+(-361.348 + 22.3591i) q^{2} +(9139.83 + 6753.05i) q^{3} +(130072. - 16158.8i) q^{4} +841783. i q^{5} +(-3.45365e6 - 2.23584e6i) q^{6} +1.94297e7i q^{7} +(-4.66400e7 + 8.74726e6i) q^{8} +(3.79327e7 + 1.23443e8i) q^{9} +O(q^{10})\)	\(q+(-361.348 + 22.3591i) q^{2} +(9139.83 + 6753.05i) q^{3} +(130072. - 16158.8i) q^{4} +841783. i q^{5} +(-3.45365e6 - 2.23584e6i) q^{6} +1.94297e7i q^{7} +(-4.66400e7 + 8.74726e6i) q^{8} +(3.79327e7 + 1.23443e8i) q^{9} +(-1.88215e7 - 3.04176e8i) q^{10} +9.11497e7 q^{11} +(1.29796e9 + 7.30695e8i) q^{12} +3.49139e9 q^{13} +(-4.34431e8 - 7.02086e9i) q^{14} +(-5.68460e9 + 7.69375e9i) q^{15} +(1.66577e10 - 4.20363e9i) q^{16} -3.88930e10i q^{17} +(-1.64670e10 - 4.37579e10i) q^{18} +1.11489e11i q^{19} +(1.36022e10 + 1.09492e11i) q^{20} +(-1.31209e11 + 1.77584e11i) q^{21} +(-3.29367e10 + 2.03803e9i) q^{22} -5.19300e11 q^{23} +(-4.85352e11 - 2.35014e11i) q^{24} +5.43413e10 q^{25} +(-1.26161e12 + 7.80646e10i) q^{26} +(-4.86922e11 + 1.38441e12i) q^{27} +(3.13961e11 + 2.52726e12i) q^{28} -1.20541e12i q^{29} +(1.88209e12 - 2.90722e12i) q^{30} -2.70262e12i q^{31} +(-5.92521e12 + 1.89142e12i) q^{32} +(8.33093e11 + 6.15539e11i) q^{33} +(8.69615e11 + 1.40539e13i) q^{34} -1.63555e13 q^{35} +(6.92869e12 + 1.54436e13i) q^{36} -1.71182e13 q^{37} +(-2.49281e12 - 4.02864e13i) q^{38} +(3.19107e13 + 2.35776e13i) q^{39} +(-7.36329e12 - 3.92607e13i) q^{40} +5.45114e13i q^{41} +(4.34416e13 - 6.71032e13i) q^{42} -3.09151e13i q^{43} +(1.18560e13 - 1.47287e12i) q^{44} +(-1.03913e14 + 3.19311e13i) q^{45} +(1.87648e14 - 1.16111e13i) q^{46} +2.01678e13 q^{47} +(1.80635e14 + 7.40695e13i) q^{48} -1.44881e14 q^{49} +(-1.96361e13 + 1.21502e12i) q^{50} +(2.62647e14 - 3.55476e14i) q^{51} +(4.54133e14 - 5.64169e13i) q^{52} +2.15134e14i q^{53} +(1.44994e14 - 5.11142e14i) q^{54} +7.67283e13i q^{55} +(-1.69956e14 - 9.06198e14i) q^{56} +(-7.52894e14 + 1.01899e15i) q^{57} +(2.69520e13 + 4.35573e14i) q^{58} -5.19006e14 q^{59} +(-6.15086e14 + 1.09260e15i) q^{60} -2.32508e15 q^{61} +(6.04282e13 + 9.76584e14i) q^{62} +(-2.39846e15 + 7.37019e14i) q^{63} +(2.09877e15 - 8.15944e14i) q^{64} +2.93899e15i q^{65} +(-3.14799e14 - 2.03796e14i) q^{66} +3.25141e15i q^{67} +(-6.28467e14 - 5.05890e15i) q^{68} +(-4.74631e15 - 3.50686e15i) q^{69} +(5.91004e15 - 3.65696e14i) q^{70} +2.41851e15 q^{71} +(-2.84897e15 - 5.42559e15i) q^{72} +9.22373e15 q^{73} +(6.18562e15 - 3.82749e14i) q^{74} +(4.96670e14 + 3.66970e14i) q^{75} +(1.80154e15 + 1.45017e16i) q^{76} +1.77101e15i q^{77} +(-1.20580e16 - 7.80620e15i) q^{78} -2.37248e16i q^{79} +(3.53854e15 + 1.40221e16i) q^{80} +(-1.37994e16 + 9.36509e15i) q^{81} +(-1.21883e15 - 1.96976e16i) q^{82} +2.02898e16 q^{83} +(-1.41972e16 + 2.52189e16i) q^{84} +3.27395e16 q^{85} +(6.91236e14 + 1.11711e16i) q^{86} +(8.14022e15 - 1.10173e16i) q^{87} +(-4.25122e15 + 7.97311e14i) q^{88} -6.58333e16i q^{89} +(3.68346e16 - 1.38616e16i) q^{90} +6.78366e16i q^{91} +(-6.75465e16 + 8.39129e15i) q^{92} +(1.82509e16 - 2.47014e16i) q^{93} +(-7.28757e15 + 4.50934e14i) q^{94} -9.38498e16 q^{95} +(-6.69283e16 - 2.27260e16i) q^{96} +1.45982e17 q^{97} +(5.23524e16 - 3.23942e15i) q^{98} +(3.45756e15 + 1.12518e16i) 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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