LMFDB - Embedded newform 12.18.b.a.11.16

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			11.16
Character	$\chi$	$=$	12.11
Dual form			12.18.b.a.11.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-12.6455 + 361.818i) q^{2} +(2019.11 + 11183.2i) q^{3} +(-130752. - 9150.75i) q^{4} +565044. i q^{5} +(-4.07180e6 + 589135. i) q^{6} +1.52677e7i q^{7} +(4.96433e6 - 4.71927e7i) q^{8} +(-1.20987e8 + 4.51602e7i) q^{9} +O(q^{10})$	\(q+(-12.6455 + 361.818i) q^{2} +(2019.11 + 11183.2i) q^{3} +(-130752. - 9150.75i) q^{4} +565044. i q^{5} +(-4.07180e6 + 589135. i) q^{6} +1.52677e7i q^{7} +(4.96433e6 - 4.71927e7i) q^{8} +(-1.20987e8 + 4.51602e7i) q^{9} +(-2.04443e8 - 7.14527e6i) q^{10} -5.97876e8 q^{11} +(-1.61669e8 - 1.48070e9i) q^{12} +2.03785e8 q^{13} +(-5.52414e9 - 1.93068e8i) q^{14} +(-6.31898e9 + 1.14089e9i) q^{15} +(1.70124e10 + 2.39296e9i) q^{16} +4.19237e10i q^{17} +(-1.48098e10 - 4.43461e10i) q^{18} -8.33979e10i q^{19} +(5.17057e9 - 7.38807e10i) q^{20} +(-1.70742e11 + 3.08273e10i) q^{21} +(7.56045e9 - 2.16322e11i) q^{22} +4.15682e11 q^{23} +(5.37788e11 - 3.97706e10i) q^{24} +4.43665e11 q^{25} +(-2.57697e9 + 7.37330e10i) q^{26} +(-7.49320e11 - 1.26183e12i) q^{27} +(1.39711e11 - 1.99629e12i) q^{28} -4.92569e11i q^{29} +(-3.32887e11 - 2.30075e12i) q^{30} -6.89304e12i q^{31} +(-1.08095e12 + 6.12513e12i) q^{32} +(-1.20718e12 - 6.68615e12i) q^{33} +(-1.51687e13 - 5.30147e11i) q^{34} -8.62694e12 q^{35} +(1.62325e13 - 4.79768e12i) q^{36} +2.23909e12 q^{37} +(3.01748e13 + 1.05461e12i) q^{38} +(4.11465e11 + 2.27896e12i) q^{39} +(2.66660e13 + 2.80507e12i) q^{40} +7.54235e13i q^{41} +(-8.99475e12 - 6.21672e13i) q^{42} +6.86558e13i q^{43} +(7.81736e13 + 5.47101e12i) q^{44} +(-2.55175e13 - 6.83627e13i) q^{45} +(-5.25651e12 + 1.50401e14i) q^{46} -2.72489e14 q^{47} +(7.58910e12 + 1.95084e14i) q^{48} -4.73161e11 q^{49} +(-5.61037e12 + 1.60526e14i) q^{50} +(-4.68840e14 + 8.46488e13i) q^{51} +(-2.66453e13 - 1.86478e12i) q^{52} -8.92333e13i q^{53} +(4.66028e14 - 2.55161e14i) q^{54} -3.37826e14i q^{55} +(7.20526e14 + 7.57941e13i) q^{56} +(9.32653e14 - 1.68390e14i) q^{57} +(1.78220e14 + 6.22879e12i) q^{58} -1.33285e15 q^{59} +(8.36661e14 - 9.13503e13i) q^{60} -1.87588e15 q^{61} +(2.49402e15 + 8.71661e13i) q^{62} +(-6.89494e14 - 1.84719e15i) q^{63} +(-2.20251e15 - 4.68561e14i) q^{64} +1.15147e14i q^{65} +(2.43443e15 - 3.52230e14i) q^{66} -2.83245e15i q^{67} +(3.83633e14 - 5.48162e15i) q^{68} +(8.39310e14 + 4.64864e15i) q^{69} +(1.09092e14 - 3.12138e15i) q^{70} -7.55122e15 q^{71} +(1.53062e15 + 5.93388e15i) q^{72} -1.98068e14 q^{73} +(-2.83144e13 + 8.10142e14i) q^{74} +(8.95810e14 + 4.96158e15i) q^{75} +(-7.63153e14 + 1.09045e16i) q^{76} -9.12821e15i q^{77} +(-8.29772e14 + 1.20057e14i) q^{78} +1.57587e16i q^{79} +(-1.35213e15 + 9.61275e15i) q^{80} +(1.25983e16 - 1.09276e16i) q^{81} +(-2.72896e16 - 9.53769e14i) q^{82} +3.68775e16 q^{83} +(2.26069e16 - 2.46832e15i) q^{84} -2.36887e16 q^{85} +(-2.48409e16 - 8.68188e14i) q^{86} +(5.50848e15 - 9.94553e14i) q^{87} +(-2.96806e15 + 2.82154e16i) q^{88} +3.86091e16i q^{89} +(2.50575e16 - 8.36821e15i) q^{90} +3.11133e15i q^{91} +(-5.43513e16 - 3.80380e15i) q^{92} +(7.70861e16 - 1.39178e16i) q^{93} +(3.44576e15 - 9.85913e16i) q^{94} +4.71235e16 q^{95} +(-7.06809e16 + 2.78929e14i) q^{96} -1.19779e17 q^{97} +(5.98336e12 - 1.71198e14i) q^{98} +(7.23350e16 - 2.70002e16i) 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 $

$2$	−12.6455	+	361.818i	−0.0349286	+	0.999390i
$2$	−12.6455	+	361.818i	−0.0349286	+	0.999390i
$3$	2019.11	+	11183.2i	0.177677	+	0.984089i
$3$	2019.11	+	11183.2i	0.177677	+	0.984089i
$4$	−130752.	−	9150.75i	−0.997560	−	0.0698147i
$5$			565044.i			0.646900i	0.946245	+	0.323450i	$0.104843\pi$
$5$			565044.i			0.646900i	−0.946245	+	0.323450i	$0.895157\pi$
$6$	−4.07180e6	+	589135.i	−0.989694	+	0.143195i
$7$			1.52677e7i			1.00102i	0.865732	+	0.500508i	$0.166853\pi$
$7$			1.52677e7i			1.00102i	−0.865732	+	0.500508i	$0.833147\pi$
$8$	4.96433e6	−	4.71927e7i	0.104615	−	0.994513i
$9$	−1.20987e8	+	4.51602e7i	−0.936862	+	0.349699i
$10$	−2.04443e8	−	7.14527e6i	−0.646505	−	0.0225953i
$11$	−5.97876e8			−0.840956			−0.420478	−	0.907303i	$-0.638138\pi$
$11$	−5.97876e8			−0.840956			−0.420478	+	0.907303i	$0.638138\pi$
$12$	−1.61669e8	−	1.48070e9i	−0.108539	−	0.994092i
$13$	2.03785e8			0.0692873			0.0346436	−	0.999400i	$-0.488970\pi$
$13$	2.03785e8			0.0692873			0.0346436	+	0.999400i	$0.488970\pi$
$14$	−5.52414e9	−	1.93068e8i	−1.00041	−	0.0349641i
$15$	−6.31898e9	+	1.14089e9i	−0.636607	+	0.114939i
$16$	1.70124e10	+	2.39296e9i	0.990252	+	0.139289i
$17$			4.19237e10i			1.45762i	0.684717	+	0.728809i	$0.259926\pi$
$17$			4.19237e10i			1.45762i	−0.684717	+	0.728809i	$0.740074\pi$
$18$	−1.48098e10	−	4.43461e10i	−0.316763	−	0.948505i
$19$		−	8.33979e10i		−	1.12655i	−0.826270	−	0.563274i	$-0.809542\pi$
$19$		−	8.33979e10i		−	1.12655i	0.826270	−	0.563274i	$-0.190458\pi$
$20$	5.17057e9	−	7.38807e10i	0.0451631	−	0.645322i
$21$	−1.70742e11	+	3.08273e10i	−0.985089	+	0.177857i
$22$	7.56045e9	−	2.16322e11i	0.0293735	−	0.840443i
$23$	4.15682e11			1.10681			0.553407	−	0.832911i	$-0.313327\pi$
$23$	4.15682e11			1.10681			0.553407	+	0.832911i	$0.313327\pi$
$24$	5.37788e11	−	3.97706e10i	0.997277	−	0.0737508i
$25$	4.43665e11			0.581520
$26$	−2.57697e9	+	7.37330e10i	−0.00242011	+	0.0692450i
$27$	−7.49320e11	−	1.26183e12i	−0.510594	−	0.859822i
$28$	1.39711e11	−	1.99629e12i	0.0698856	−	0.998574i
$29$		−	4.92569e11i		−	0.182845i	−0.995812	−	0.0914227i	$-0.970859\pi$
$29$		−	4.92569e11i		−	0.182845i	0.995812	−	0.0914227i	$-0.0291414\pi$
$30$	−3.32887e11	−	2.30075e12i	−0.0926331	−	0.640233i
$31$		−	6.89304e12i		−	1.45157i	−0.687924	−	0.725783i	$-0.741478\pi$
$31$		−	6.89304e12i		−	1.45157i	0.687924	−	0.725783i	$-0.258522\pi$
$32$	−1.08095e12	+	6.12513e12i	−0.173792	+	0.984782i
$33$	−1.20718e12	−	6.68615e12i	−0.149418	−	0.827576i
$34$	−1.51687e13	−	5.30147e11i	−1.45673	−	0.0509126i
$35$	−8.62694e12			−0.647558
$36$	1.62325e13	−	4.79768e12i	0.958990	−	0.283439i
$37$	2.23909e12			0.104799			0.0523994	−	0.998626i	$-0.483313\pi$
$37$	2.23909e12			0.104799			0.0523994	+	0.998626i	$0.483313\pi$
$38$	3.01748e13	+	1.05461e12i	1.12586	+	0.0393488i
$39$	4.11465e11	+	2.27896e12i	0.0123107	+	0.0681848i
$40$	2.66660e13	+	2.80507e12i	0.643350	+	0.0676758i
$41$			7.54235e13i			1.47518i	0.675251	+	0.737588i	$0.264035\pi$
$41$			7.54235e13i			1.47518i	−0.675251	+	0.737588i	$0.735965\pi$
$42$	−8.99475e12	−	6.21672e13i	−0.143341	−	0.990700i
$43$			6.86558e13i			0.895768i	0.894092	+	0.447884i	$0.147822\pi$
$43$			6.86558e13i			0.895768i	−0.894092	+	0.447884i	$0.852178\pi$
$44$	7.81736e13	+	5.47101e12i	0.838904	+	0.0587111i
$45$	−2.55175e13	−	6.83627e13i	−0.226220	−	0.606056i
$46$	−5.25651e12	+	1.50401e14i	−0.0386595	+	1.10614i
$47$	−2.72489e14			−1.66923			−0.834617	−	0.550831i	$-0.814311\pi$
$47$	−2.72489e14			−1.66923			−0.834617	+	0.550831i	$0.814311\pi$
$48$	7.58910e12	+	1.95084e14i	0.0388722	+	0.999244i
$49$	−4.73161e11			−0.00203396
$50$	−5.61037e12	+	1.60526e14i	−0.0203117	+	0.581166i
$51$	−4.68840e14	+	8.46488e13i	−1.43443	+	0.258985i
$52$	−2.66453e13	−	1.86478e12i	−0.0691182	−	0.00483727i
$53$		−	8.92333e13i		−	0.196871i	−0.995143	−	0.0984355i	$-0.968616\pi$
$53$		−	8.92333e13i		−	0.196871i	0.995143	−	0.0984355i	$-0.0313838\pi$
$54$	4.66028e14	−	2.55161e14i	0.877132	−	0.480250i
$55$		−	3.37826e14i		−	0.544015i
$56$	7.20526e14	+	7.57941e13i	0.995524	+	0.104722i
$57$	9.32653e14	−	1.68390e14i	1.10862	−	0.200161i
$58$	1.78220e14	+	6.22879e12i	0.182734	+	0.00638654i
$59$	−1.33285e15			−1.18179			−0.590894	−	0.806749i	$-0.701225\pi$
$59$	−1.33285e15			−1.18179			−0.590894	+	0.806749i	$0.701225\pi$
$60$	8.36661e14	−	9.13503e13i	0.643078	−	0.0702141i
$61$	−1.87588e15			−1.25286			−0.626428	−	0.779479i	$-0.715484\pi$
$61$	−1.87588e15			−1.25286			−0.626428	+	0.779479i	$0.715484\pi$
$62$	2.49402e15	+	8.71661e13i	1.45068	+	0.0507012i
$63$	−6.89494e14	−	1.84719e15i	−0.350055	−	0.937814i
$64$	−2.20251e15	−	4.68561e14i	−0.978111	−	0.208083i
$65$			1.15147e14i			0.0448219i
$66$	2.43443e15	−	3.52230e14i	0.832290	−	0.120421i
$67$		−	2.83245e15i		−	0.852172i	−0.904683	−	0.426086i	$-0.859892\pi$
$67$		−	2.83245e15i		−	0.852172i	0.904683	−	0.426086i	$-0.140108\pi$
$68$	3.83633e14	−	5.48162e15i	0.101763	−	1.45406i
$69$	8.39310e14	+	4.64864e15i	0.196655	+	1.08920i
$70$	1.09092e14	−	3.12138e15i	0.0226183	−	0.647162i
$71$	−7.55122e15			−1.38778			−0.693890	−	0.720081i	$-0.744105\pi$
$71$	−7.55122e15			−1.38778			−0.693890	+	0.720081i	$0.744105\pi$
$72$	1.53062e15	+	5.93388e15i	0.249770	+	0.968305i
$73$	−1.98068e14			−0.0287455			−0.0143728	−	0.999897i	$-0.504575\pi$
$73$	−1.98068e14			−0.0287455			−0.0143728	+	0.999897i	$0.504575\pi$
$74$	−2.83144e13	+	8.10142e14i	−0.00366048	+	0.104735i
$75$	8.95810e14	+	4.96158e15i	0.103323	+	0.572268i
$76$	−7.63153e14	+	1.09045e16i	−0.0786495	+	1.12380i
$77$		−	9.12821e15i		−	0.841811i
$78$	−8.29772e14	+	1.20057e14i	−0.0685732	+	0.00992161i
$79$			1.57587e16i			1.16866i	0.811515	+	0.584331i	$0.198643\pi$
$79$			1.57587e16i			1.16866i	−0.811515	+	0.584331i	$0.801357\pi$
$80$	−1.35213e15	+	9.61275e15i	−0.0901058	+	0.640594i
$81$	1.25983e16	−	1.09276e16i	0.755421	−	0.655240i
$82$	−2.72896e16	−	9.53769e14i	−1.47428	−	0.0515259i
$83$	3.68775e16			1.79721			0.898603	−	0.438763i	$-0.144583\pi$
$83$	3.68775e16			1.79721			0.898603	+	0.438763i	$0.144583\pi$
$84$	2.26069e16	−	2.46832e15i	0.995103	−	0.108650i
$85$	−2.36887e16			−0.942933
$86$	−2.48409e16	−	8.68188e14i	−0.895221	−	0.0312879i
$87$	5.50848e15	−	9.94553e14i	0.179936	−	0.0324874i
$88$	−2.96806e15	+	2.82154e16i	−0.0879770	+	0.836342i
$89$			3.86091e16i			1.03962i	0.854282	+	0.519810i	$0.173997\pi$
$89$			3.86091e16i			1.03962i	−0.854282	+	0.519810i	$0.826003\pi$
$90$	2.50575e16	−	8.36821e15i	0.613588	−	0.204914i
$91$			3.11133e15i			0.0693577i
$92$	−5.43513e16	−	3.80380e15i	−1.10411	−	0.0772718i
$93$	7.70861e16	−	1.39178e16i	1.42847	−	0.257909i
$94$	3.44576e15	−	9.85913e16i	0.0583040	−	1.66821i
$95$	4.71235e16			0.728764
$96$	−7.06809e16	+	2.78929e14i	−0.999992	+	0.00394629i
$97$	−1.19779e17			−1.55174			−0.775872	−	0.630891i	$-0.782690\pi$
$97$	−1.19779e17			−1.55174			−0.775872	+	0.630891i	$0.782690\pi$
$98$	5.98336e12	−	1.71198e14i	7.10434e−5	−	0.00203272i
$99$	7.23350e16	−	2.70002e16i	0.787860	−	0.294082i
$100$	−5.80101e16	−	4.05986e15i	−0.580101	−	0.0405986i
$101$			5.47050e16i			0.502684i	0.967898	+	0.251342i	$0.0808719\pi$
$101$			5.47050e16i			0.502684i	−0.967898	+	0.251342i	$0.919128\pi$
$102$	−2.46987e16	−	1.70705e17i	−0.208724	−	1.44260i
$103$		−	9.60355e16i		−	0.746991i	−0.927632	−	0.373496i	$-0.878159\pi$
$103$		−	9.60355e16i		−	0.746991i	0.927632	−	0.373496i	$-0.121841\pi$
$104$	1.01166e15	−	9.61717e15i	0.00724852	−	0.0689071i
$105$	−1.74188e16	−	9.64766e16i	−0.115056	−	0.637254i
$106$	3.22862e16	+	1.12840e15i	0.196751	+	0.00687644i
$107$	7.08552e16			0.398666			0.199333	−	0.979932i	$-0.436122\pi$
$107$	7.08552e16			0.398666			0.199333	+	0.979932i	$0.436122\pi$
$108$	8.64286e16	+	1.71844e17i	0.449320	+	0.893371i
$109$	1.92888e17			0.927213			0.463607	−	0.886041i	$-0.346555\pi$
$109$	1.92888e17			0.927213			0.463607	+	0.886041i	$0.346555\pi$
$110$	1.22232e17	+	4.27199e15i	0.543683	+	0.0190017i
$111$	4.52098e15	+	2.50401e16i	0.0186203	+	0.103131i
$112$	−3.65351e16	+	2.59741e17i	−0.139430	+	0.991258i
$113$		−	1.54228e17i		−	0.545752i	−0.962049	−	0.272876i	$-0.912025\pi$
$113$		−	1.54228e17i		−	0.545752i	0.962049	−	0.272876i	$-0.0879749\pi$
$114$	4.91326e16	+	3.39580e17i	0.161316	+	1.11494i
$115$			2.34879e17i			0.715998i
$116$	−4.50737e15	+	6.44044e16i	−0.0127653	+	0.182399i
$117$	−2.46552e16	+	9.20297e15i	−0.0649126	+	0.0242297i
$118$	1.68546e16	−	4.82249e17i	0.0412782	−	1.18107i
$119$	−6.40080e17			−1.45910
$120$	2.24721e16	+	3.03874e17i	0.0477094	+	0.645138i
$121$	−1.47991e17			−0.292792
$122$	2.37215e16	−	6.78726e17i	0.0437606	−	1.25209i
$123$	−8.43474e17	+	1.52289e17i	−1.45170	+	0.262104i
$124$	−6.30765e16	+	9.01280e17i	−0.101341	+	1.44802i
$125$			6.81784e17i			1.02309i
$126$	6.77065e17	−	2.26113e17i	0.949469	−	0.317085i
$127$			1.39227e17i			0.182554i	0.995826	+	0.0912771i	$0.0290949\pi$
$127$			1.39227e17i			0.182554i	−0.995826	+	0.0912771i	$0.970905\pi$
$128$	1.97386e17	−	7.90982e17i	0.242120	−	0.970246i
$129$	−7.67790e17	+	1.38624e17i	−0.881515	+	0.159157i
$130$	−4.16624e16	−	1.45610e15i	−0.0447946	−	0.00156557i
$131$	−5.02544e17			−0.506254			−0.253127	−	0.967433i	$-0.581459\pi$
$131$	−5.02544e17			−0.506254			−0.253127	+	0.967433i	$0.581459\pi$
$132$	9.66582e16	+	8.85276e17i	0.0912768	+	0.835988i
$133$	1.27330e18			1.12769
$134$	1.02483e18	+	3.58179e16i	0.851652	+	0.0297652i
$135$	7.12989e17	−	4.23399e17i	0.556219	−	0.330303i
$136$	1.97849e18	+	2.08123e17i	1.44962	+	0.152489i
$137$			2.58190e17i			0.177752i	0.996043	+	0.0888759i	$0.0283274\pi$
$137$			2.58190e17i			0.177752i	−0.996043	+	0.0888759i	$0.971673\pi$
$138$	−1.69257e18	+	2.44893e17i	−1.09541	+	0.158491i
$139$		−	2.25732e18i		−	1.37394i	−0.726687	−	0.686969i	$-0.758941\pi$
$139$		−	2.25732e18i		−	1.37394i	0.726687	−	0.686969i	$-0.241059\pi$
$140$	1.12799e18	+	7.89429e16i	0.645978	+	0.0452090i
$141$	−5.50186e17	−	3.04729e18i	−0.296584	−	1.64267i
$142$	9.54890e16	−	2.73216e18i	0.0484733	−	1.38693i
$143$	−1.21838e17			−0.0582676
$144$	−2.16634e18	+	4.78768e17i	−0.976438	+	0.215796i
$145$	2.78323e17			0.118283
$146$	2.50467e15	−	7.16646e16i	0.00100404	−	0.0287280i
$147$	−9.55366e14	−	5.29144e15i	−0.000361387	−	0.00200160i
$148$	−2.92766e17	−	2.04893e16i	−0.104543	−	0.00731650i
$149$			4.63069e18i			1.56157i	0.624797	+	0.780787i	$0.285182\pi$
$149$			4.63069e18i			1.56157i	−0.624797	+	0.780787i	$0.714818\pi$
$150$	−1.80652e18	+	2.61378e17i	−0.575527	+	0.0832710i
$151$			2.20282e18i			0.663248i	0.943412	+	0.331624i	$0.107596\pi$
$151$			2.20282e18i			0.663248i	−0.943412	+	0.331624i	$0.892404\pi$
$152$	−3.93578e18	−	4.14015e17i	−1.12037	−	0.117854i
$153$	−1.89328e18	−	5.07220e18i	−0.509728	−	1.36559i
$154$	3.30275e18	+	1.15431e17i	0.841297	+	0.0294033i
$155$	3.89487e18			0.939017
$156$	−3.29458e16	−	3.01744e17i	−0.00752039	−	0.0688779i
$157$	2.41108e18			0.521273			0.260637	−	0.965437i	$-0.416068\pi$
$157$	2.41108e18			0.521273			0.260637	+	0.965437i	$0.416068\pi$
$158$	−5.70176e18	−	1.99276e17i	−1.16795	−	0.0408198i
$159$	9.97911e17	−	1.80172e17i	0.193739	−	0.0349794i
$160$	−3.46097e18	−	6.10782e17i	−0.637056	−	0.112426i
$161$			6.34652e18i			1.10794i
$162$	3.79447e18	+	4.69647e18i	0.628454	+	0.777847i
$163$			2.75789e18i			0.433493i	0.976228	+	0.216746i	$0.0695445\pi$
$163$			2.75789e18i			0.433493i	−0.976228	+	0.216746i	$0.930456\pi$
$164$	6.90181e17	−	9.86178e18i	0.102989	−	1.47158i
$165$	3.77797e18	−	6.82110e17i	0.535359	−	0.0966587i
$166$	−4.66335e17	+	1.33429e19i	−0.0627740	+	1.79611i
$167$	1.24090e19			1.58725			0.793625	−	0.608407i	$-0.208191\pi$
$167$	1.24090e19			1.58725			0.793625	+	0.608407i	$0.208191\pi$
$168$	6.07207e17	+	8.21081e18i	0.0738257	+	0.998290i
$169$	−8.60889e18			−0.995199
$170$	2.99556e17	−	8.57100e18i	0.0329354	−	0.942358i
$171$	3.76627e18	+	1.00900e19i	0.393953	+	1.05542i
$172$	6.28252e17	−	8.97690e18i	0.0625377	−	0.893582i
$173$			4.84261e18i			0.458867i	0.973324	+	0.229434i	$0.0736874\pi$
$173$			4.84261e18i			0.458867i	−0.973324	+	0.229434i	$0.926313\pi$
$174$	2.90189e17	+	2.00564e18i	0.0261826	+	0.180961i
$175$			6.77376e18i			0.582111i
$176$	−1.01713e19	−	1.43069e18i	−0.832759	−	0.117136i
$177$	−2.69118e18	−	1.49055e19i	−0.209976	−	1.16298i
$178$	−1.39695e19	−	4.88232e17i	−1.03899	−	0.0363125i
$179$	−1.22528e19			−0.868931			−0.434466	−	0.900688i	$-0.643063\pi$
$179$	−1.22528e19			−0.868931			−0.434466	+	0.900688i	$0.643063\pi$
$180$	2.71090e18	+	9.17208e18i	0.183357	+	0.620371i
$181$	1.33229e19			0.859667			0.429833	−	0.902908i	$-0.358572\pi$
$181$	1.33229e19			0.859667			0.429833	+	0.902908i	$0.358572\pi$
$182$	−1.12574e18	−	3.93444e16i	−0.0693154	−	0.00242257i
$183$	−3.78761e18	−	2.09783e19i	−0.222603	−	1.23292i
$184$	2.06358e18	−	1.96172e19i	0.115790	−	1.10074i
$185$			1.26518e18i			0.0677944i
$186$	4.06093e18	+	2.80671e19i	0.207857	+	1.43661i
$187$		−	2.50652e19i		−	1.22579i
$188$	3.56285e19	+	2.49348e18i	1.66516	+	0.116537i
$189$	1.92653e19	−	1.14404e19i	0.860696	−	0.511113i
$190$	−5.95901e17	+	1.70501e19i	−0.0254547	+	0.728319i
$191$	−2.75593e19			−1.12586			−0.562930	−	0.826505i	$-0.690326\pi$
$191$	−2.75593e19			−1.12586			−0.562930	+	0.826505i	$0.690326\pi$
$192$	7.92875e17	−	2.55771e19i	0.0309845	−	0.999520i
$193$	−4.14745e19			−1.55076			−0.775379	−	0.631496i	$-0.782441\pi$
$193$	−4.14745e19			−1.55076			−0.775379	+	0.631496i	$0.782441\pi$
$194$	1.51466e18	−	4.33381e19i	0.0542003	−	1.55080i
$195$	−1.28771e18	+	2.32496e17i	−0.0441088	+	0.00796381i
$196$	6.18668e16	+	4.32977e15i	0.00202899	+	0.000142000i
$197$			3.84665e19i			1.20815i	0.796929	+	0.604073i	$0.206457\pi$
$197$			3.84665e19i			1.20815i	−0.796929	+	0.604073i	$0.793543\pi$
$198$	8.85445e18	+	2.65135e19i	0.266383	+	0.797651i
$199$		−	3.55076e18i		−	0.102346i	−0.998690	−	0.0511730i	$-0.983704\pi$
$199$		−	3.55076e18i		−	0.102346i	0.998690	−	0.0511730i	$-0.0162960\pi$
$200$	2.20250e18	−	2.09378e19i	0.0608360	−	0.578329i
$201$	3.16758e19	−	5.71905e18i	0.838613	−	0.151411i
$202$	−1.97932e19	−	6.91773e17i	−0.502378	−	0.0175581i
$203$	7.52041e18			0.183031
$204$	6.20764e19	−	6.77778e18i	1.44901	−	0.158209i
$205$	−4.26176e19			−0.954291
$206$	3.47474e19	+	1.21442e18i	0.746535	+	0.0260914i
$207$	−5.02919e19	+	1.87723e19i	−1.03693	+	0.387052i
$208$	3.46687e18	+	4.87649e17i	0.0686118	+	0.00965093i
$209$			4.98616e19i			0.947377i
$210$	3.51272e19	−	5.08243e18i	0.640884	−	0.0927272i
$211$			2.63874e19i			0.462377i	0.972909	+	0.231188i	$0.0742613\pi$
$211$			2.63874e19i			0.462377i	−0.972909	+	0.231188i	$0.925739\pi$
$212$	−8.16551e17	+	1.16674e19i	−0.0137445	+	0.196391i
$213$	−1.52468e19	−	8.44465e19i	−0.246576	−	1.36570i
$214$	−8.96000e17	+	2.56367e19i	−0.0139249	+	0.398423i
$215$	−3.87935e19			−0.579472
$216$	−6.32691e19	+	2.90983e19i	−0.908520	+	0.417841i
$217$	1.05241e20			1.45304
$218$	−2.43917e18	+	6.97902e19i	−0.0323863	+	0.926647i
$219$	−3.99922e17	−	2.21503e18i	−0.00510741	−	0.0282882i
$220$	−3.09136e18	+	4.41715e19i	−0.0379802	+	0.542687i
$221$			8.54341e18i			0.100994i
$222$	−9.11713e18	+	1.31912e18i	−0.103719	+	0.0150067i
$223$			7.98765e19i			0.874637i	0.899307	+	0.437318i	$0.144072\pi$
$223$			7.98765e19i			0.874637i	−0.899307	+	0.437318i	$0.855928\pi$
$224$	−9.35168e19	−	1.65036e19i	−0.985783	−	0.173968i
$225$	−5.36775e19	+	2.00360e19i	−0.544804	+	0.203357i
$226$	5.58023e19	+	1.95029e18i	0.545419	+	0.0190624i
$227$	1.88031e19			0.177015			0.0885074	−	0.996076i	$-0.471790\pi$
$227$	1.88031e19			0.177015			0.0885074	+	0.996076i	$0.471790\pi$
$228$	−1.23487e20	+	1.34829e19i	−1.11989	+	0.122275i
$229$	2.94163e18			0.0257032			0.0128516	−	0.999917i	$-0.495909\pi$
$229$	2.94163e18			0.0257032			0.0128516	+	0.999917i	$0.495909\pi$
$230$	−8.49832e19	−	2.97016e18i	−0.715561	−	0.0250088i
$231$	1.02082e20	−	1.84309e19i	0.828417	−	0.149570i
$232$	−2.32457e19	−	2.44528e18i	−0.181842	−	0.0191285i
$233$		−	1.25858e20i		−	0.949199i	−0.880202	−	0.474599i	$-0.842593\pi$
$233$		−	1.25858e20i		−	0.949199i	0.880202	−	0.474599i	$-0.157407\pi$
$234$	−3.01802e18	−	9.03707e18i	−0.0219476	−	0.0657193i
$235$		−	1.53968e20i		−	1.07983i
$236$	1.74273e20	+	1.21966e19i	1.17890	+	0.0825061i
$237$	−1.76232e20	+	3.18185e19i	−1.15007	+	0.207644i
$238$	8.09414e18	−	2.31592e20i	0.0509644	−	1.45821i
$239$	2.69096e20			1.63503			0.817514	−	0.575908i	$-0.195352\pi$
$239$	2.69096e20			1.63503			0.817514	+	0.575908i	$0.195352\pi$
$240$	−1.10231e20	+	4.28817e18i	−0.646411	+	0.0251465i
$241$	2.17495e20			1.23113			0.615565	−	0.788086i	$-0.288928\pi$
$241$	2.17495e20			1.23113			0.615565	+	0.788086i	$0.288928\pi$
$242$	1.87142e18	−	5.35458e19i	0.0102268	−	0.292614i
$243$	1.47642e20	+	1.18825e20i	0.779035	+	0.626980i
$244$	2.45275e20	+	1.71657e19i	1.24980	+	0.0874677i
$245$		−	2.67357e17i		−	0.00131577i
$246$	−4.44346e19	−	3.07110e20i	−0.211238	−	1.45997i
$247$		−	1.69952e19i		−	0.0780554i
$248$	−3.25302e20	−	3.42193e19i	−1.44360	−	0.151856i
$249$	7.44599e19	+	4.12408e20i	0.319321	+	1.76861i
$250$	−2.46682e20	−	8.62152e18i	−1.02246	−	0.0357350i
$251$	2.72009e19			0.108982			0.0544911	−	0.998514i	$-0.482646\pi$
$251$	2.72009e19			0.108982			0.0544911	+	0.998514i	$0.482646\pi$
$252$	7.32497e19	+	2.47833e20i	0.283727	+	0.959965i
$253$	−2.48526e20			−0.930782
$254$	−5.03748e19	−	1.76060e18i	−0.182443	−	0.00637637i
$255$	−4.78303e19	−	2.64915e20i	−0.167537	−	0.927930i
$256$	2.83695e20	+	8.14200e19i	0.961197	+	0.275862i
$257$		−	3.16345e20i		−	1.03688i	−0.855114	−	0.518441i	$-0.826513\pi$
$257$		−	3.16345e20i		−	1.03688i	0.855114	−	0.518441i	$-0.173487\pi$
$258$	−4.04475e19	−	2.79553e20i	−0.128270	−	0.886536i
$259$			3.41858e19i			0.104905i
$260$	1.05368e18	−	1.50558e19i	0.00312923	−	0.0447126i
$261$	2.22445e19	+	5.95942e19i	0.0639409	+	0.171301i
$262$	6.35493e18	−	1.81829e20i	0.0176828	−	0.505945i
$263$	−1.19500e20			−0.321916			−0.160958	−	0.986961i	$-0.551458\pi$
$263$	−1.19500e20			−0.321916			−0.160958	+	0.986961i	$0.551458\pi$
$264$	−3.21531e20	+	2.37779e19i	−0.838666	+	0.0620212i
$265$	5.04207e19			0.127356
$266$	−1.61015e19	+	4.60702e20i	−0.0393888	+	1.12700i
$267$	−4.31772e20	+	7.79562e19i	−1.02308	+	0.184716i
$268$	−2.59191e19	+	3.70350e20i	−0.0594941	+	0.850092i
$269$		−	5.04415e20i		−	1.12174i	−0.827903	−	0.560872i	$-0.810466\pi$
$269$		−	5.04415e20i		−	1.12174i	0.827903	−	0.560872i	$-0.189534\pi$
$270$	1.44177e20	+	2.63326e20i	0.310674	+	0.567417i
$271$			3.75679e20i			0.784473i	0.919864	+	0.392237i	$0.128299\pi$
$271$			3.75679e20i			0.784473i	−0.919864	+	0.392237i	$0.871701\pi$
$272$	−1.00322e20	+	7.13223e20i	−0.203030	+	1.44341i
$273$	−3.47946e19	+	6.28214e18i	−0.0682541	+	0.0123232i
$274$	−9.34176e19	−	3.26494e18i	−0.177643	−	0.00620863i
$275$	−2.65257e20			−0.489033
$276$	−6.72030e19	−	6.15500e20i	−0.120133	−	1.10027i
$277$	5.33353e20			0.924564			0.462282	−	0.886733i	$-0.347031\pi$
$277$	5.33353e20			0.924564			0.462282	+	0.886733i	$0.347031\pi$
$278$	8.16738e20	+	2.85450e19i	1.37310	+	0.0479898i
$279$	3.11291e20	+	8.33965e20i	0.507611	+	1.35992i
$280$	−4.28270e19	+	4.07129e20i	−0.0677445	+	0.644004i
$281$			1.60538e20i			0.246362i	0.992384	+	0.123181i	$0.0393096\pi$
$281$			1.60538e20i			0.246362i	−0.992384	+	0.123181i	$0.960690\pi$
$282$	1.10952e21	−	1.60533e20i	1.65203	−	0.239026i
$283$		−	1.38333e20i		−	0.199867i	−0.994994	−	0.0999337i	$-0.968137\pi$
$283$		−	1.38333e20i		−	0.199867i	0.994994	−	0.0999337i	$-0.0318631\pi$
$284$	9.87338e20	+	6.90993e19i	1.38439	+	0.0968874i
$285$	9.51477e19	+	5.26990e20i	0.129484	+	0.717168i
$286$	1.54071e18	−	4.40832e19i	0.00203521	−	0.0582320i
$287$	−1.15155e21			−1.47668
$288$	−1.45832e20	−	7.89874e20i	−0.181559	−	0.983380i
$289$	−9.30356e20			−1.12465
$290$	−3.51954e18	+	1.00702e20i	−0.00413145	+	0.118210i
$291$	−2.41847e20	−	1.33951e21i	−0.275709	−	1.52705i
$292$	2.58978e19	+	1.81247e18i	0.0286754	+	0.00200686i
$293$		−	3.64855e19i		−	0.0392415i	−0.999807	−	0.0196208i	$-0.993754\pi$
$293$		−	3.64855e19i		−	0.0392415i	0.999807	−	0.0196208i	$-0.00624588\pi$
$294$	1.92662e18	−	2.78755e17i	0.00201300	−	0.000291253i
$295$		−	7.53119e20i		−	0.764499i
$296$	1.11156e19	−	1.05669e20i	0.0109636	−	0.104224i
$297$	4.48001e20	+	7.54418e20i	0.429387	+	0.723073i
$298$	−1.67547e21	−	5.85575e19i	−1.56062	−	0.0545437i
$299$	8.47097e19			0.0766881
$300$	−7.17270e19	−	6.56935e20i	−0.0631178	−	0.578085i
$301$	−1.04822e21			−0.896678
$302$	−7.97021e20	−	2.78558e19i	−0.662843	−	0.0231663i
$303$	−6.11775e20	+	1.10456e20i	−0.494686	+	0.0893153i
$304$	1.99568e20	−	1.41880e21i	0.156915	−	1.11557i
$305$		−	1.05995e21i		−	0.810473i
$306$	1.85915e21	−	6.20883e20i	1.38256	−	0.461719i
$307$		−	6.15886e19i		−	0.0445476i	−0.999752	−	0.0222738i	$-0.992909\pi$
$307$		−	6.15886e19i		−	0.0445476i	0.999752	−	0.0222738i	$-0.00709055\pi$
$308$	−8.35300e19	+	1.19353e21i	−0.0587708	+	0.839757i
$309$	1.07398e21	−	1.93907e20i	0.735106	−	0.132723i
$310$	−4.92527e19	+	1.40923e21i	−0.0327986	+	0.938444i
$311$	3.90389e20			0.252950			0.126475	−	0.991970i	$-0.459634\pi$
$311$	3.90389e20			0.252950			0.126475	+	0.991970i	$0.459634\pi$
$312$	1.09593e20	−	8.10465e18i	0.0690986	−	0.00510999i
$313$	3.99988e20			0.245426			0.122713	−	0.992442i	$-0.460841\pi$
$313$	3.99988e20			0.245426			0.122713	+	0.992442i	$0.460841\pi$
$314$	−3.04894e19	+	8.72373e20i	−0.0182074	+	0.520955i
$315$	1.04374e21	−	3.89594e20i	0.606672	−	0.226450i
$316$	1.44203e20	−	2.06048e21i	0.0815897	−	1.16581i
$317$			2.67328e20i			0.147245i	0.997286	+	0.0736226i	$0.0234560\pi$
$317$			2.67328e20i			0.147245i	−0.997286	+	0.0736226i	$0.976544\pi$
$318$	5.25704e19	+	3.63340e20i	0.0281910	+	0.194842i
$319$			2.94495e20i			0.153765i
$320$	2.64757e20	−	1.24452e21i	0.134609	−	0.632740i
$321$	1.43065e20	+	7.92385e20i	0.0708337	+	0.392323i
$322$	−2.29628e21	−	8.02550e19i	−1.10726	−	0.0386988i
$323$	3.49635e21			1.64208
$324$	−1.74725e21	+	1.31352e21i	−0.799323	+	0.600902i
$325$	9.04122e19			0.0402920
$326$	−9.97853e20	−	3.48749e19i	−0.433228	−	0.0151413i
$327$	3.89463e20	+	2.15710e21i	0.164744	+	0.912460i
$328$	3.55944e21	+	3.74427e20i	1.46708	+	0.154326i
$329$		−	4.16029e21i		−	1.67093i
$330$	1.99025e20	+	1.37556e21i	0.0779004	+	0.538408i
$331$			1.08009e21i			0.412024i	0.978549	+	0.206012i	$0.0660487\pi$
$331$			1.08009e21i			0.412024i	−0.978549	+	0.206012i	$0.933951\pi$
$332$	−4.82181e21	−	3.37457e20i	−1.79282	−	0.125471i
$333$	−2.70899e20	+	1.01118e20i	−0.0981821	+	0.0366481i
$334$	−1.56918e20	+	4.48978e21i	−0.0554405	+	1.58628i
$335$	1.60046e21			0.551270
$336$	−2.97849e21	+	1.15868e20i	−1.00026	+	0.0389118i
$337$	−1.28409e21			−0.420475			−0.210237	−	0.977650i	$-0.567424\pi$
$337$	−1.28409e21			−0.420475			−0.210237	+	0.977650i	$0.567424\pi$
$338$	1.08864e20	−	3.11485e21i	0.0347610	−	0.994592i
$339$	1.72476e21	−	3.11403e20i	0.537069	−	0.0969675i
$340$	3.09735e21	+	2.16770e20i	0.940632	+	0.0658306i
$341$			4.12119e21i			1.22070i
$342$	−3.69838e21	+	1.23511e21i	−1.06854	+	0.356848i
$343$			3.54452e21i			0.998980i
$344$	3.24006e21	+	3.40830e20i	0.890852	+	0.0937112i
$345$	−2.62669e21	+	4.74247e20i	−0.704605	+	0.127216i
$346$	−1.75214e21	−	6.12373e19i	−0.458587	−	0.0160276i
$347$	−5.08336e21			−1.29823			−0.649113	−	0.760692i	$-0.724860\pi$
$347$	−5.08336e21			−1.29823			−0.649113	+	0.760692i	$0.724860\pi$
$348$	−7.29347e20	+	7.96333e19i	−0.181765	+	0.0198459i
$349$	5.61060e21			1.36456			0.682281	−	0.731090i	$-0.260988\pi$
$349$	5.61060e21			1.36456			0.682281	+	0.731090i	$0.260988\pi$
$350$	−2.45087e21	−	8.56577e19i	−0.581756	−	0.0203324i
$351$	−1.52700e20	−	2.57142e20i	−0.0353776	−	0.0595747i
$352$	6.46272e20	−	3.66207e21i	0.146151	−	0.828159i
$353$			8.39696e21i			1.85369i	0.375443	+	0.926845i	$0.377490\pi$
$353$			8.39696e21i			1.85369i	−0.375443	+	0.926845i	$0.622510\pi$
$354$	5.42711e21	−	7.85229e20i	1.16961	−	0.169227i
$355$		−	4.26677e21i		−	0.897756i
$356$	3.53302e20	−	5.04822e21i	0.0725807	−	1.03708i
$357$	−1.29239e21	−	7.15812e21i	−0.259248	−	1.43588i
$358$	1.54943e20	−	4.43329e21i	0.0303506	−	0.868401i
$359$	2.28573e21			0.437242			0.218621	−	0.975810i	$-0.429844\pi$
$359$	2.28573e21			0.437242			0.218621	+	0.975810i	$0.429844\pi$
$360$	−3.35290e21	+	8.64866e20i	−0.626397	+	0.161576i
$361$	−1.47483e21			−0.269110
$362$	−1.68475e20	+	4.82045e21i	−0.0300270	+	0.859142i
$363$	−2.98811e20	−	1.65501e21i	−0.0520224	−	0.288134i
$364$	2.84710e19	−	4.06814e20i	0.00484218	−	0.0691885i
$365$		−	1.11917e20i		−	0.0185955i
$366$	7.63821e21	−	1.10515e21i	1.23994	−	0.179403i
$367$		−	3.51024e20i		−	0.0556770i	−0.999612	−	0.0278385i	$-0.991138\pi$
$367$		−	3.51024e20i		−	0.0556770i	0.999612	−	0.0278385i	$-0.00886241\pi$
$368$	7.07175e21	+	9.94710e20i	1.09602	+	0.154167i
$369$	−3.40614e21	−	9.12522e21i	−0.515868	−	1.38204i
$370$	−4.57766e20	−	1.59989e19i	−0.0677530	−	0.00236797i
$371$	1.36239e21			0.197071
$372$	−1.02065e22	+	1.11439e21i	−1.44299	+	0.157552i
$373$	4.38377e21			0.605791			0.302896	−	0.953024i	$-0.402047\pi$
$373$	4.38377e21			0.605791			0.302896	+	0.953024i	$0.402047\pi$
$374$	9.06903e21	+	3.16962e20i	1.22505	+	0.0428153i
$375$	−7.62451e21	+	1.37660e21i	−1.00681	+	0.181778i
$376$	−1.35273e21	+	1.28595e22i	−0.174628	+	1.66007i
$377$		−	1.00378e20i		−	0.0126689i
$378$	3.89573e21	+	7.11519e21i	0.480738	+	0.878023i
$379$		−	1.45560e22i		−	1.75634i	−0.478353	−	0.878168i	$-0.658766\pi$
$379$		−	1.45560e22i		−	1.75634i	0.478353	−	0.878168i	$-0.341234\pi$
$380$	−6.16150e21	−	4.31215e20i	−0.726986	−	0.0508784i
$381$	−1.55700e21	+	2.81115e20i	−0.179649	+	0.0324356i
$382$	3.48501e20	−	9.97143e21i	0.0393247	−	1.12517i
$383$	−9.97281e21			−1.10060			−0.550298	−	0.834968i	$-0.685486\pi$
$383$	−9.97281e21			−1.10060			−0.550298	+	0.834968i	$0.685486\pi$
$384$	9.24423e21	+	6.10312e20i	0.997828	+	0.0658775i
$385$	5.15784e21			0.544568
$386$	5.24467e20	−	1.50062e22i	0.0541659	−	1.54981i
$387$	−3.10051e21	−	8.30643e21i	−0.313249	−	0.839211i
$388$	1.56613e22	+	1.09606e21i	1.54796	+	0.108334i
$389$			1.26465e22i			1.22292i	0.791274	+	0.611462i	$0.209418\pi$
$389$			1.26465e22i			1.22292i	−0.791274	+	0.611462i	$0.790582\pi$
$390$	−6.78373e19	−	4.68858e20i	−0.00641829	−	0.0443600i
$391$			1.74269e22i			1.61331i
$392$	−2.34893e18	+	2.23297e19i	−0.000212783	+	0.00202280i
$393$	−1.01469e21	−	5.62004e21i	−0.0899495	−	0.498199i
$394$	−1.39179e22	−	4.86429e20i	−1.20741	−	0.0421989i
$395$	−8.90433e21			−0.756007
$396$	−9.70503e21	+	2.86842e21i	−0.806469	+	0.238360i
$397$	−5.30951e21			−0.431852			−0.215926	−	0.976410i	$-0.569277\pi$
$397$	−5.30951e21			−0.431852			−0.215926	+	0.976410i	$0.569277\pi$
$398$	1.28473e21	+	4.49012e19i	0.102283	+	0.00357480i
$399$	2.57093e21	+	1.42395e22i	0.200365	+	1.10975i
$400$	7.54780e21	+	1.06167e21i	0.575852	+	0.0809992i
$401$			8.87682e21i			0.663025i	0.943451	+	0.331513i	$0.107559\pi$
$401$			8.87682e21i			0.663025i	−0.943451	+	0.331513i	$0.892441\pi$
$402$	1.66870e21	+	1.15332e22i	0.122027	+	0.843390i
$403$		−	1.40470e21i		−	0.100575i
$404$	5.00592e20	−	7.15280e21i	0.0350947	−	0.501458i
$405$	6.17455e21	+	7.11859e21i	0.423875	+	0.488682i
$406$	−9.50995e19	+	2.72102e21i	−0.00639303	+	0.182920i
$407$	−1.33870e21			−0.0881313
$408$	1.66733e21	+	2.25461e22i	0.107500	+	1.45365i
$409$	−1.26854e22			−0.801044			−0.400522	−	0.916287i	$-0.631171\pi$
$409$	−1.26854e22			−0.801044			−0.400522	+	0.916287i	$0.631171\pi$
$410$	5.38921e20	−	1.54198e22i	0.0333321	−	0.953709i
$411$	−2.88738e21	+	5.21314e20i	−0.174924	+	0.0315823i
$412$	−8.78797e20	+	1.25569e22i	−0.0521509	+	0.745168i
$413$		−	2.03496e22i		−	1.18299i
$414$	−6.15618e21	−	1.84339e22i	−0.350597	−	1.04982i
$415$			2.08374e22i			1.16261i
$416$	−2.20280e20	+	1.24821e21i	−0.0120416	+	0.0682329i
$417$	2.52440e22	−	4.55779e21i	1.35208	−	0.244117i
$418$	−1.80408e22	−	6.30526e20i	−0.946799	−	0.0330906i
$419$	2.67433e22			1.37530			0.687649	−	0.726044i	$-0.258643\pi$
$419$	2.67433e22			1.37530			0.687649	+	0.726044i	$0.258643\pi$
$420$	1.39471e21	+	1.27739e22i	0.0702854	+	0.643732i
$421$	−3.15277e22			−1.55702			−0.778511	−	0.627631i	$-0.784025\pi$
$421$	−3.15277e22			−1.55702			−0.778511	+	0.627631i	$0.784025\pi$
$422$	−9.54743e21	−	3.33682e20i	−0.462094	−	0.0161502i
$423$	3.29675e22	−	1.23057e22i	1.56384	−	0.583730i
$424$	−4.21116e21	−	4.42984e20i	−0.195791	−	0.0205958i
$425$			1.86001e22i			0.847635i
$426$	3.07471e22	−	4.44868e21i	1.37348	−	0.198724i
$427$		−	2.86404e22i		−	1.25413i
$428$	−9.26447e21	−	6.48378e20i	−0.397693	−	0.0278327i
$429$	−2.46005e20	−	1.36254e21i	−0.0103528	−	0.0573405i
$430$	4.90565e20	−	1.40362e22i	0.0202402	−	0.579119i
$431$	1.04165e22			0.421370			0.210685	−	0.977554i	$-0.432431\pi$
$431$	1.04165e22			0.421370			0.210685	+	0.977554i	$0.432431\pi$
$432$	−9.72822e21	−	2.32598e22i	−0.385853	−	0.922560i
$433$	4.36628e22			1.69811			0.849053	−	0.528308i	$-0.177173\pi$
$433$	4.36628e22			1.69811			0.849053	+	0.528308i	$0.177173\pi$
$434$	−1.33083e21	+	3.80781e22i	−0.0507527	+	1.45215i
$435$	5.61966e20	+	3.11253e21i	0.0210161	+	0.116401i
$436$	−2.52205e22	−	1.76507e21i	−0.924951	−	0.0647331i
$437$		−	3.46670e22i		−	1.24688i
$438$	8.06494e20	−	1.16689e20i	0.0284493	−	0.00411623i
$439$			1.32174e22i			0.457295i	0.973509	+	0.228647i	$0.0734303\pi$
$439$			1.32174e22i			0.457295i	−0.973509	+	0.228647i	$0.926570\pi$
$440$	−1.59430e22	−	1.67708e21i	−0.541030	−	0.0569124i
$441$	5.72461e19	−	2.13680e19i	0.00190554	−	0.000711273i
$442$	−3.09116e21	−	1.08036e20i	−0.100933	−	0.00352760i
$443$	2.56783e22			0.822499			0.411249	−	0.911523i	$-0.365093\pi$
$443$	2.56783e22			0.822499			0.411249	+	0.911523i	$0.365093\pi$
$444$	−3.61992e20	−	3.31542e21i	−0.0113748	−	0.104180i
$445$	−2.18158e22			−0.672530
$446$	−2.89007e22	−	1.01008e21i	−0.874103	−	0.0305499i
$447$	−5.17858e22	+	9.34990e21i	−1.53673	+	0.277455i
$448$	7.15386e21	−	3.36273e22i	0.208294	−	0.979105i
$449$		−	1.27228e19i		−	0.000363487i	−1.00000		0.000181744i	$-0.999942\pi$
$449$		−	1.27228e19i		−	0.000363487i	1.00000		0.000181744i	$-5.78508e-5\pi$
$450$	−6.57060e21	−	1.96748e22i	−0.184204	−	0.551575i
$451$		−	4.50939e22i		−	1.24056i
$452$	−1.41130e21	+	2.01656e22i	−0.0381015	+	0.544421i
$453$	−2.46346e22	+	4.44775e21i	−0.652695	+	0.117844i
$454$	−2.37775e20	+	6.80329e21i	−0.00618288	+	0.176907i
$455$	−1.75804e21			−0.0448675
$456$	−3.31679e21	−	4.48504e22i	−0.0830838	−	1.12348i
$457$	−1.96524e22			−0.483202			−0.241601	−	0.970376i	$-0.577672\pi$
$457$	−1.96524e22			−0.483202			−0.241601	+	0.970376i	$0.577672\pi$
$458$	−3.71984e19	+	1.06433e21i	−0.000897776	+	0.0256875i
$459$	5.29006e22	−	3.14143e22i	1.25329	−	0.744251i
$460$	2.14931e21	−	3.07109e22i	0.0499871	−	0.714251i
$461$			4.39798e22i			1.00414i	0.864826	+	0.502071i	$0.167428\pi$
$461$			4.39798e22i			1.00414i	−0.864826	+	0.502071i	$0.832572\pi$
$462$	5.37775e21	+	3.71683e22i	0.120543	+	0.833136i
$463$			6.34293e22i			1.39589i	0.716151	+	0.697945i	$0.245902\pi$
$463$			6.34293e22i			1.39589i	−0.716151	+	0.697945i	$0.754098\pi$
$464$	1.17870e21	−	8.37978e21i	0.0254683	−	0.181063i
$465$	7.86419e21	+	4.35570e22i	0.166841	+	0.924077i
$466$	4.55378e22	+	1.59155e21i	0.948620	+	0.0331542i
$467$	−1.18753e22			−0.242914			−0.121457	−	0.992597i	$-0.538757\pi$
$467$	−1.18753e22			−0.242914			−0.121457	+	0.992597i	$0.538757\pi$
$468$	3.30794e21	−	9.77695e20i	0.0664458	−	0.0196387i
$469$	4.32452e22			0.853038
$470$	5.57084e22	+	1.94701e21i	1.07917	+	0.0377169i
$471$	4.86826e21	+	2.69636e22i	0.0926181	+	0.512979i
$472$	−6.61671e21	+	6.29009e22i	−0.123633	+	1.17530i
$473$		−	4.10477e22i		−	0.753302i
$474$	−9.28397e21	−	6.41661e22i	−0.167347	−	1.15662i
$475$		−	3.70007e22i		−	0.655110i
$476$	8.36918e22	+	5.85721e21i	1.45554	+	0.101867i
$477$	4.02979e21	+	1.07960e22i	0.0688457	+	0.184441i
$478$	−3.40286e21	+	9.73638e22i	−0.0571093	+	1.63403i
$479$	−8.41399e22			−1.38723			−0.693617	−	0.720344i	$-0.743984\pi$
$479$	−8.41399e22			−1.38723			−0.693617	+	0.720344i	$0.743984\pi$
$480$	−1.57607e20	−	3.99378e22i	−0.00255285	−	0.646895i
$481$	4.56292e20			0.00726123
$482$	−2.75033e21	+	7.86934e22i	−0.0430017	+	1.23038i
$483$	−7.09742e22	+	1.28144e22i	−1.09031	+	0.196855i
$484$	1.93502e22	+	1.35423e21i	0.292078	+	0.0204412i
$485$		−	6.76802e22i		−	1.00382i
$486$	−4.48600e22	+	5.19169e22i	−0.653809	+	0.756660i
$487$			1.00746e23i			1.44288i	0.692476	+	0.721441i	$0.256520\pi$
$487$			1.00746e23i			1.44288i	−0.692476	+	0.721441i	$0.743480\pi$
$488$	−9.31248e21	+	8.85279e22i	−0.131068	+	1.24598i
$489$	−3.08419e22	+	5.56849e21i	−0.426595	+	0.0770215i
$490$	9.67343e19	+	3.38086e18i	0.00131496	+	4.59580e-5i
$491$	−4.93130e22			−0.658823			−0.329411	−	0.944186i	$-0.606850\pi$
$491$	−4.93130e22			−0.658823			−0.329411	+	0.944186i	$0.606850\pi$
$492$	1.11680e23	−	1.21937e22i	1.46646	−	0.160115i
$493$	2.06503e22			0.266519
$494$	6.14918e21	+	2.14914e20i	0.0780078	+	0.00272637i
$495$	1.52563e22	+	4.08724e22i	0.190242	+	0.509667i
$496$	1.64948e22	−	1.17267e23i	0.202186	−	1.43741i
$497$		−	1.15290e23i		−	1.38919i
$498$	−1.50158e23	+	2.17258e22i	−1.77868	+	0.257351i
$499$		−	1.28745e23i		−	1.49925i	−0.661863	−	0.749625i	$-0.730234\pi$
$499$		−	1.28745e23i		−	1.49925i	0.661863	−	0.749625i	$-0.269766\pi$
$500$	6.23884e21	−	8.91448e22i	0.0714264	−	1.02059i
$501$	2.50551e22	+	1.38772e23i	0.282017	+	1.56200i
$502$	−3.43969e20	+	9.84175e21i	−0.00380660	+	0.108916i
$503$	−7.67854e22			−0.835509			−0.417754	−	0.908560i	$-0.637183\pi$
$503$	−7.67854e22			−0.835509			−0.417754	+	0.908560i	$0.637183\pi$
$504$	−9.05968e22	+	2.33691e22i	−0.969289	+	0.250024i
$505$	−3.09107e22			−0.325186
$506$	3.14274e21	−	8.99212e22i	0.0325109	−	0.930214i
$507$	−1.73823e22	−	9.62747e22i	−0.176824	−	0.979365i
$508$	1.27403e21	−	1.82042e22i	0.0127450	−	0.182109i
$509$		−	6.69030e22i		−	0.658179i	−0.944299	−	0.329090i	$-0.893258\pi$
$509$		−	6.69030e22i		−	0.658179i	0.944299	−	0.329090i	$-0.106742\pi$
$510$	9.64558e22	−	1.39559e22i	0.933216	−	0.135024i
$511$		−	3.02405e21i		−	0.0287747i
$512$	−3.30467e22	+	1.01616e23i	−0.309267	+	0.950975i
$513$	−1.05234e23	+	6.24917e22i	−0.968631	+	0.575208i
$514$	1.14459e23	+	4.00034e21i	1.03625	+	0.0362169i
$515$	5.42643e22			0.483229
$516$	1.01659e23	−	1.10995e22i	0.890476	−	0.0972260i
$517$	1.62915e23			1.40375
$518$	−1.23690e22	−	4.32297e20i	−0.104841	−	0.00366420i
$519$	−5.41557e22	+	9.77778e21i	−0.451566	+	0.0815300i
$520$	5.43412e21	+	5.71630e20i	0.0445760	+	0.00468907i
$521$			8.63489e22i			0.696845i	0.937338	+	0.348423i	$0.113283\pi$
$521$			8.63489e22i			0.696845i	−0.937338	+	0.348423i	$0.886717\pi$
$522$	−2.18435e22	+	7.29486e21i	−0.173430	+	0.0579186i
$523$		−	6.35536e22i		−	0.496450i	−0.968702	−	0.248225i	$-0.920153\pi$
$523$		−	6.35536e22i		−	0.496450i	0.968702	−	0.248225i	$-0.0798473\pi$
$524$	6.57088e22	+	4.59865e21i	0.505018	+	0.0353439i
$525$	−7.57521e22	+	1.36770e22i	−0.572849	+	0.103428i
$526$	1.51113e21	−	4.32370e22i	0.0112441	−	0.321719i
$527$	2.88982e23			2.11583
$528$	−4.53734e21	−	1.16636e23i	−0.0326899	−	0.840321i
$529$	3.17414e22			0.225036
$530$	−6.37596e20	+	1.82431e22i	−0.00444837	+	0.127278i
$531$	1.61257e23	−	6.01918e22i	1.10717	−	0.413270i
$532$	−1.66486e23	−	1.16516e22i	−1.12494	−	0.0787295i
$533$			1.53702e22i			0.102211i
$534$	−2.27460e22	−	1.57209e23i	−0.148869	−	1.02891i
$535$			4.00363e22i			0.257897i
$536$	−1.33671e23	−	1.40612e22i	−0.847496	−	0.0891503i
$537$	−2.47399e22	−	1.37025e23i	−0.154389	−	0.855106i
$538$	1.82506e23	+	6.37859e21i	1.12106	+	0.0391810i
$539$	2.82891e20			0.00171047
$540$	−9.70993e22	+	4.88359e22i	−0.577922	+	0.290665i
$541$	−1.34125e23			−0.785840			−0.392920	−	0.919573i	$-0.628535\pi$
$541$	−1.34125e23			−0.785840			−0.392920	+	0.919573i	$0.628535\pi$
$542$	−1.35927e23	−	4.75066e21i	−0.783995	−	0.0274006i
$543$	2.69004e22	+	1.48992e23i	0.152743	+	0.845988i
$544$	−2.56788e23	−	4.53173e22i	−1.43544	−	0.253322i
$545$			1.08990e23i			0.599814i
$546$	−1.83299e21	−	1.26687e22i	−0.00993170	−	0.0686429i
$547$			1.35788e23i			0.724386i	0.932103	+	0.362193i	$0.117972\pi$
$547$			1.35788e23i			0.724386i	−0.932103	+	0.362193i	$0.882028\pi$
$548$	2.36263e21	−	3.37589e22i	0.0124097	−	0.177318i
$549$	2.26956e23	−	8.47151e22i	1.17375	−	0.438123i
$550$	3.35431e21	−	9.59746e22i	0.0170813	−	0.488735i
$551$	−4.10792e22			−0.205984
$552$	2.23549e23	−	1.65319e22i	1.10380	−	0.0816284i
$553$	−2.40599e23			−1.16985
$554$	−6.74453e21	+	1.92977e23i	−0.0322938	+	0.924000i
$555$	−1.41488e22	+	2.55455e21i	−0.0667157	+	0.0120455i
$556$	−2.06562e22	+	2.95149e23i	−0.0959210	+	1.37059i
$557$			5.80994e22i			0.265707i	0.991136	+	0.132853i	$0.0424139\pi$
$557$			5.80994e22i			0.265707i	−0.991136	+	0.132853i	$0.957586\pi$
$558$	−3.05680e23	+	1.02085e23i	−1.37682	+	0.459801i
$559$			1.39910e22i			0.0620653i
$560$	−1.46765e23	−	2.06439e22i	−0.641245	−	0.0901974i
$561$	2.80308e23	−	5.06095e22i	1.20629	−	0.217795i
$562$	−5.80855e22	−	2.03009e21i	−0.246212	−	0.00860510i
$563$	−9.37757e22			−0.391534			−0.195767	−	0.980650i	$-0.562720\pi$
$563$	−9.37757e22			−0.391534			−0.195767	+	0.980650i	$0.562720\pi$
$564$	4.40531e22	+	4.03474e23i	0.181177	+	1.65937i
$565$	8.71454e22			0.353047
$566$	5.00514e22	+	1.74930e21i	0.199745	+	0.00698110i
$567$	1.66839e23	+	1.92347e23i	0.655906	+	0.756189i
$568$	−3.74867e22	+	3.56363e23i	−0.145183	+	1.38017i
$569$		−	2.05858e23i		−	0.785439i	−0.919658	−	0.392720i	$-0.871534\pi$
$569$		−	2.05858e23i		−	0.785439i	0.919658	−	0.392720i	$-0.128466\pi$
$570$	−1.91878e23	+	2.77621e22i	−0.721253	+	0.104356i
$571$			1.59377e23i			0.590228i	0.955462	+	0.295114i	$0.0953576\pi$
$571$			1.59377e23i			0.590228i	−0.955462	+	0.295114i	$0.904642\pi$
$572$	1.59306e22	+	1.11491e21i	0.0581254	+	0.00406793i
$573$	−5.56453e22	−	3.08200e23i	−0.200039	−	1.10795i
$574$	1.45619e22	−	4.16650e23i	0.0515783	−	1.47577i
$575$	1.84423e23			0.643635
$576$	2.87634e23	−	4.27763e22i	0.989122	−	0.147100i
$577$	6.71366e22			0.227492			0.113746	−	0.993510i	$-0.463715\pi$
$577$	6.71366e22			0.227492			0.113746	+	0.993510i	$0.463715\pi$
$578$	1.17648e22	−	3.36619e23i	0.0392825	−	1.12396i
$579$	−8.37418e22	−	4.63817e23i	−0.275534	−	1.52608i
$580$	−3.63913e22	−	2.54686e21i	−0.117994	−	0.00825786i
$581$			5.63036e23i			1.79903i
$582$	4.87715e23	−	7.05658e22i	1.53575	−	0.222202i
$583$			5.33504e22i			0.165560i
$584$	−9.83276e20	+	9.34738e21i	−0.00300723	+	0.0285878i
$585$	−5.20008e21	−	1.39313e22i	−0.0156742	−	0.0419920i
$586$	1.32011e22	+	4.61378e20i	0.0392176	+	0.00137065i
$587$	2.50751e23			0.734206			0.367103	−	0.930180i	$-0.380350\pi$
$587$	2.50751e23			0.734206			0.367103	+	0.930180i	$0.380350\pi$
$588$	7.64955e19	+	7.00609e20i	0.000220764	+	0.00202194i
$589$	−5.74865e23			−1.63526
$590$	2.72492e23	+	9.52359e21i	0.764032	+	0.0267029i
$591$	−4.30177e23	+	7.76683e22i	−1.18892	+	0.214659i
$592$	3.80923e22	+	5.35805e21i	0.103777	+	0.0145973i
$593$			3.03923e23i			0.816204i	0.912936	+	0.408102i	$0.133809\pi$
$593$			3.03923e23i			0.816204i	−0.912936	+	0.408102i	$0.866191\pi$
$594$	−2.78627e23	+	1.52555e23i	−0.737630	+	0.403869i
$595$		−	3.61673e23i		−	0.943892i
$596$	4.23743e22	−	6.05473e23i	0.109021	−	1.55776i
$597$	3.97088e22	−	7.16940e21i	0.100717	−	0.0181845i
$598$	−1.07120e21	+	3.06495e22i	−0.00267861	+	0.0766413i
$599$	−7.36624e23			−1.81601			−0.908004	−	0.418961i	$-0.862394\pi$
$599$	−7.36624e23			−1.81601			−0.908004	+	0.418961i	$0.862394\pi$
$600$	2.38598e23	−	1.76448e22i	0.579937	−	0.0428876i
$601$	7.31753e21			0.0175360			0.00876802	−	0.999962i	$-0.497209\pi$
$601$	7.31753e21			0.0175360			0.00876802	+	0.999962i	$0.497209\pi$
$602$	1.32553e22	−	3.79264e23i	0.0313198	−	0.896131i
$603$	1.27914e23	+	3.42689e23i	0.298004	+	0.798367i
$604$	2.01575e22	−	2.88024e23i	0.0463044	−	0.661629i
$605$		−	8.36215e22i		−	0.189407i
$606$	−3.22286e22	−	2.22748e23i	−0.0719821	−	0.497504i
$607$		−	2.71387e23i		−	0.597702i	−0.954300	−	0.298851i	$-0.903397\pi$
$607$		−	2.71387e23i		−	0.597702i	0.954300	−	0.298851i	$-0.0966034\pi$
$608$	5.10823e23	+	9.01487e22i	1.10940	+	0.195785i
$609$	1.51846e22	+	8.41020e22i	0.0325204	+	0.180119i
$610$	3.83510e23	+	1.34037e22i	0.809978	+	0.0283087i
$611$	−5.55291e22			−0.115657
$612$	2.01136e23	+	6.80526e23i	0.413146	+	1.39784i
$613$	7.65431e23			1.55057			0.775286	−	0.631611i	$-0.217606\pi$
$613$	7.65431e23			1.55057			0.775286	+	0.631611i	$0.217606\pi$
$614$	2.22838e22	+	7.78819e20i	0.0445204	+	0.00155599i
$615$	−8.60498e22	−	4.76600e23i	−0.169555	−	0.939107i
$616$	−4.30785e23	−	4.53155e22i	−0.837192	−	0.0880665i
$617$		−	1.40025e23i		−	0.268400i	−0.990954	−	0.134200i	$-0.957153\pi$
$617$		−	1.40025e23i		−	0.268400i	0.990954	−	0.134200i	$-0.0428465\pi$
$618$	5.65778e22	+	3.91038e23i	0.106966	+	0.739293i
$619$		−	5.81070e23i		−	1.08357i	−0.840516	−	0.541786i	$-0.817748\pi$
$619$		−	5.81070e23i		−	1.08357i	0.840516	−	0.541786i	$-0.182252\pi$
$620$	−5.09263e23	−	3.56410e22i	−0.936726	−	0.0655572i
$621$	−3.11479e23	−	5.24520e23i	−0.565132	−	0.951663i
$622$	−4.93667e21	+	1.41250e23i	−0.00883519	+	0.252795i
$623$	−5.89473e23			−1.04068
$624$	1.54654e21	+	3.97552e22i	0.00269335	+	0.0692349i
$625$	−4.67487e22			−0.0803137
$626$	−5.05805e21	+	1.44723e23i	−0.00857238	+	0.245276i
$627$	−5.57611e23	+	1.00676e23i	−0.932304	+	0.168327i
$628$	−3.15254e23	−	2.20632e22i	−0.520001	−	0.0363925i
$629$			9.38709e22i			0.152757i
$630$	1.27764e23	+	3.82572e23i	0.205122	+	0.614212i
$631$			5.39686e23i			0.854854i	0.904050	+	0.427427i	$0.140580\pi$
$631$			5.39686e23i			0.854854i	−0.904050	+	0.427427i	$0.859420\pi$
$632$	7.43694e23	+	7.82312e22i	1.16225	+	0.122260i
$633$	−2.95095e23	+	5.32792e22i	−0.455020	+	0.0821535i
$634$	−9.67241e22	−	3.38050e21i	−0.147155	−	0.00514307i
$635$	−7.86693e22			−0.118094
$636$	−1.32128e23	+	1.44263e22i	−0.195708	+	0.0213682i
$637$	−9.64230e19			−0.000140927
$638$	−1.06554e23	−	3.72404e21i	−0.153671	−	0.00537080i
$639$	9.13595e23	−	3.41015e23i	1.30016	−	0.485306i
$640$	4.46940e23	+	1.11532e23i	0.627652	+	0.156627i
$641$		−	3.45898e22i		−	0.0479352i	−0.999713	−	0.0239676i	$-0.992370\pi$
$641$		−	3.45898e22i		−	0.0479352i	0.999713	−	0.0239676i	$-0.00762985\pi$
$642$	−2.88508e23	+	4.17432e22i	−0.394558	+	0.0570871i
$643$			1.43120e24i			1.93155i	0.259378	+	0.965776i	$0.416482\pi$
$643$			1.43120e24i			1.93155i	−0.259378	+	0.965776i	$0.583518\pi$
$644$	5.80754e22	−	8.29821e23i	0.0773504	−	1.10524i
$645$	−7.83286e22	−	4.33835e23i	−0.102959	−	0.570252i
$646$	−4.42132e22	+	1.26504e24i	−0.0573555	+	1.64107i
$647$	8.07312e23			1.03361			0.516803	−	0.856104i	$-0.327122\pi$
$647$	8.07312e23			1.03361			0.516803	+	0.856104i	$0.327122\pi$
$648$	−4.53159e23	−	6.48796e23i	−0.572616	−	0.819824i
$649$	7.96880e23			0.993832
$650$	−1.14331e21	+	3.27127e22i	−0.00140734	+	0.0402674i
$651$	2.12494e23	+	1.17693e24i	0.258171	+	1.42992i
$652$	2.52367e22	−	3.60600e23i	0.0302641	−	0.432435i
$653$			6.04400e23i			0.715422i	0.933832	+	0.357711i	$0.116443\pi$
$653$			6.04400e23i			0.715422i	−0.933832	+	0.357711i	$0.883557\pi$
$654$	−7.85401e23	+	1.13637e23i	−0.917658	+	0.132773i
$655$		−	2.83960e23i		−	0.327496i
$656$	−1.80485e23	+	1.28313e24i	−0.205475	+	1.46080i
$657$	2.39636e22	−	8.94480e21i	0.0269306	−	0.0100523i
$658$	1.50527e24	+	5.26090e22i	1.66991	+	0.0583633i
$659$	4.71222e23			0.516060			0.258030	−	0.966137i	$-0.416927\pi$
$659$	4.71222e23			0.516060			0.258030	+	0.966137i	$0.416927\pi$
$660$	−5.00220e23	+	5.46161e22i	−0.540801	+	0.0590470i
$661$	−9.23979e23			−0.986165			−0.493082	−	0.869983i	$-0.664130\pi$
$661$	−9.23979e23			−0.986165			−0.493082	+	0.869983i	$0.664130\pi$
$662$	−3.90797e23	−	1.36583e22i	−0.411773	−	0.0143915i
$663$	−9.55425e22	+	1.72501e22i	−0.0993874	+	0.0179443i
$664$	1.83072e23	−	1.74035e24i	0.188016	−	1.78734i
$665$			7.19469e23i			0.729505i
$666$	−3.31605e22	−	9.92949e22i	−0.0331964	−	0.0994022i
$667$		−	2.04752e23i		−	0.202376i
$668$	−1.62250e24	−	1.13551e23i	−1.58338	−	0.110813i
$669$	−8.93273e23	+	1.61280e23i	−0.860720	+	0.155402i
$670$	−2.02387e22	+	5.79075e23i	−0.0192551	+	0.550934i
$671$	1.12154e24			1.05360
$672$	−4.25862e21	−	1.07914e24i	−0.00395030	−	1.00101i
$673$	1.70485e24			1.56156			0.780780	−	0.624805i	$-0.214822\pi$
$673$	1.70485e24			1.56156			0.780780	+	0.624805i	$0.214822\pi$
$674$	1.62379e22	−	4.64605e23i	0.0146866	−	0.420218i
$675$	−3.32447e23	−	5.59829e23i	−0.296921	−	0.500004i
$676$	1.12563e24	+	7.87777e22i	0.992771	+	0.0694795i
$677$		−	6.51055e23i		−	0.567041i	−0.958966	−	0.283520i	$-0.908498\pi$
$677$		−	6.51055e23i		−	0.567041i	0.958966	−	0.283520i	$-0.0915024\pi$
$678$	9.08609e22	+	6.27985e23i	0.0781492	+	0.540128i
$679$		−	1.82875e24i		−	1.55332i
$680$	−1.17599e23	+	1.11794e24i	−0.0986454	+	0.937759i
$681$	3.79656e22	+	2.10278e23i	0.0314514	+	0.174198i
$682$	−1.49112e24	−	5.21145e22i	−1.21996	−	0.0426375i
$683$	−1.84411e23			−0.149009			−0.0745043	−	0.997221i	$-0.523737\pi$
$683$	−1.84411e23			−0.149009			−0.0745043	+	0.997221i	$0.523737\pi$
$684$	−4.00117e23	−	1.35376e24i	−0.319308	−	1.08035i
$685$	−1.45888e23			−0.114988
$686$	−1.28247e24	−	4.48222e22i	−0.998371	−	0.0348930i
$687$	5.93949e21	+	3.28968e22i	0.00456685	+	0.0252942i
$688$	−1.64291e23	+	1.16800e24i	−0.124770	+	0.887036i
$689$		−	1.81844e22i		−	0.0136407i
$690$	−1.38375e23	−	9.56379e23i	−0.102528	−	0.708619i
$691$			1.25562e24i			0.918959i	0.888188	+	0.459480i	$0.151964\pi$
$691$			1.25562e24i			0.918959i	−0.888188	+	0.459480i	$0.848036\pi$
$692$	4.43135e22	−	6.33181e23i	0.0320357	−	0.457748i
$693$	4.12232e23	+	1.10439e24i	0.294381	+	0.788661i
$694$	6.42817e22	−	1.83925e24i	0.0453453	−	1.29743i
$695$	1.27548e24			0.888801
$696$	−1.95898e22	−	2.64898e23i	−0.0134850	−	0.182347i
$697$	−3.16203e24			−2.15024
$698$	−7.09490e22	+	2.03001e24i	−0.0476623	+	1.36373i
$699$	1.40750e24	−	2.54123e23i	0.934096	−	0.168650i
$700$	6.19849e22	−	8.85683e23i	0.0406399	−	0.580691i
$701$		−	2.62624e24i		−	1.70111i	−0.525889	−	0.850553i	$-0.676267\pi$
$701$		−	2.62624e24i		−	1.70111i	0.525889	−	0.850553i	$-0.323733\pi$
$702$	9.49694e22	−	5.19979e22i	0.0607741	−	0.0332752i
$703$		−	1.86735e23i		−	0.118061i
$704$	1.31683e24	+	2.80141e23i	0.822549	+	0.174989i
$705$	1.72185e24	−	3.10879e23i	1.06265	−	0.191860i
$706$	−3.03817e24	−	1.06184e23i	−1.85256	−	0.0647469i
$707$	−8.35221e23			−0.503195
$708$	2.15481e23	+	1.97355e24i	0.128270	+	1.17481i
$709$	1.24832e24			0.734231			0.367115	−	0.930175i	$-0.380345\pi$
$709$	1.24832e24			0.734231			0.367115	+	0.930175i	$0.380345\pi$
$710$	1.54379e24	+	5.39555e22i	0.897208	+	0.0313574i
$711$	−7.11664e23	−	1.90658e24i	−0.408680	−	1.09487i
$712$	1.82207e24	+	1.91668e23i	1.03392	+	0.108760i
$713$		−	2.86531e24i		−	1.60661i
$714$	2.60628e24	−	3.77093e23i	1.44406	−	0.208936i
$715$		−	6.88439e22i		−	0.0376933i
$716$	1.60208e24	+	1.12122e23i	0.866811	+	0.0606641i
$717$	5.43336e23	+	3.00935e24i	0.290506	+	1.60901i
$718$	−2.89042e22	+	8.27017e23i	−0.0152723	+	0.436975i
$719$	−1.62290e24			−0.847414			−0.423707	−	0.905799i	$-0.639271\pi$
$719$	−1.62290e24			−0.847414			−0.423707	+	0.905799i	$0.639271\pi$
$720$	−2.70525e23	−	1.22408e24i	−0.139599	−	0.631658i
$721$	1.46624e24			0.747750
$722$	1.86499e22	−	5.33618e23i	0.00939964	−	0.268946i
$723$	4.39147e23	+	2.43228e24i	0.218743	+	1.21154i
$724$	−1.74199e24	−	1.21914e23i	−0.857569	−	0.0600173i
$725$		−	2.18535e23i		−	0.106328i
$726$	6.02590e23	−	8.71867e22i	0.289775	−	0.0419265i
$727$			1.98161e23i			0.0941838i	0.998891	+	0.0470919i	$0.0149954\pi$
$727$			1.98161e23i			0.0941838i	−0.998891	+	0.0470919i	$0.985005\pi$
$728$	1.46832e23	+	1.54457e22i	0.0689771	+	0.00725589i
$729$	−1.03073e24	+	1.89103e24i	−0.478588	+	0.878039i
$730$	4.04936e22	+	1.41525e21i	0.0185841	+	0.000649515i
$731$	−2.87831e24			−1.30569
$732$	3.03272e23	+	2.77761e24i	0.135984	+	1.24545i
$733$	−2.15183e24			−0.953728			−0.476864	−	0.878977i	$-0.658227\pi$
$733$	−2.15183e24			−0.953728			−0.476864	+	0.878977i	$0.658227\pi$
$734$	1.27007e23	+	4.43888e21i	0.0556430	+	0.00194472i
$735$	2.98989e21	−	5.39824e20i	0.00129483	−	0.000233781i
$736$	−4.49330e23	+	2.54610e24i	−0.192355	+	1.08997i
$737$			1.69346e24i			0.716639i
$738$	3.34474e24	−	1.11701e24i	1.39921	−	0.467280i
$739$			7.57431e23i			0.313231i	0.987660	+	0.156616i	$0.0500584\pi$
$739$			7.57431e23i			0.313231i	−0.987660	+	0.156616i	$0.949942\pi$
$740$	1.15774e22	−	1.65425e23i	0.00473304	−	0.0676290i
$741$	1.90061e23	−	3.43153e22i	0.0768135	−	0.0138686i
$742$	−1.72281e22	+	4.92937e23i	−0.00688343	+	0.196951i
$743$	−6.98860e23			−0.276049			−0.138024	−	0.990429i	$-0.544075\pi$
$743$	−6.98860e23			−0.276049			−0.138024	+	0.990429i	$0.544075\pi$
$744$	−2.74140e23	−	3.70700e24i	−0.107054	−	1.44761i
$745$	−2.61655e24			−1.01018
$746$	−5.54351e22	+	1.58613e24i	−0.0211595	+	0.605421i
$747$	−4.46168e24	+	1.66540e24i	−1.68373	+	0.628481i
$748$	−2.29365e23	+	3.27733e24i	−0.0855783	+	1.22280i
$749$			1.08180e24i			0.399071i
$750$	−4.01663e23	−	2.77609e24i	−0.146501	−	1.01254i
$751$		−	1.13235e24i		−	0.408357i	−0.978934	−	0.204178i	$-0.934548\pi$
$751$		−	1.13235e24i		−	0.408357i	0.978934	−	0.204178i	$-0.0654523\pi$
$752$	−4.63569e24	−	6.52055e23i	−1.65296	−	0.232505i
$753$	5.49216e22	+	3.04192e23i	0.0193636	+	0.107248i
$754$	3.63186e22	+	1.26933e21i	0.0126611	+	0.000442506i
$755$	−1.24469e24			−0.429055
$756$	−2.62366e24	+	1.31957e24i	−0.894279	+	0.449776i
$757$	3.55465e24			1.19807			0.599035	−	0.800723i	$-0.295551\pi$
$757$	3.55465e24			1.19807			0.599035	+	0.800723i	$0.295551\pi$
$758$	5.26660e24	+	1.84068e23i	1.75526	+	0.0613464i
$759$	−5.01803e23	−	2.77931e24i	−0.165378	−	0.915972i
$760$	2.33937e23	−	2.22389e24i	0.0762400	−	0.724765i
$761$		−	3.37026e24i		−	1.08616i	−0.839681	−	0.543080i	$-0.817258\pi$
$761$		−	3.37026e24i		−	1.08616i	0.839681	−	0.543080i	$-0.182742\pi$
$762$	−8.20234e22	−	5.66905e23i	−0.0261409	−	0.180673i
$763$			2.94496e24i			0.928156i
$764$	3.60343e24	+	2.52188e23i	1.12311	+	0.0786015i
$765$	2.86602e24	−	1.06979e24i	0.883398	−	0.329743i
$766$	1.26111e23	−	3.60834e24i	0.0384423	−	1.09992i
$767$	−2.71615e23			−0.0818828
$768$	−3.37720e23	+	3.33701e24i	−0.100690	+	0.994918i
$769$	−4.58946e24			−1.35328			−0.676641	−	0.736313i	$-0.736565\pi$
$769$	−4.58946e24			−1.35328			−0.676641	+	0.736313i	$0.736565\pi$
$770$	−6.52236e22	+	1.86620e24i	−0.0190210	+	0.544235i
$771$	3.53774e24	−	6.38737e23i	1.02038	−	0.184230i
$772$	5.42288e24	+	3.79523e23i	1.54697	+	0.108266i
$773$		−	2.47448e23i		−	0.0698166i	−0.999391	−	0.0349083i	$-0.988886\pi$
$773$		−	2.47448e23i		−	0.0698166i	0.999391	−	0.0349083i	$-0.0111139\pi$
$774$	3.04462e24	−	1.01678e24i	0.849640	−	0.283746i
$775$		−	3.05820e24i		−	0.844115i
$776$	−5.94621e23	+	5.65269e24i	−0.162336	+	1.54323i
$777$	−3.82306e23	+	6.90251e22i	−0.103236	+	0.0186392i
$778$	−4.57574e24	−	1.59922e23i	−1.22218	−	0.0427151i
$779$	6.29016e24			1.66186
$780$	1.70499e23	−	1.86158e22i	0.0445571	−	0.00486494i
$781$	4.51469e24			1.16706
$782$	−6.30537e24	−	2.20372e23i	−1.61233	−	0.0563508i
$783$	−6.21538e23	+	3.69092e23i	−0.157214	+	0.0933597i
$784$	−8.04960e21	−	1.13225e21i	−0.00201413	−	0.000283307i
$785$			1.36237e24i			0.337212i
$786$	2.04626e24	−	2.96066e23i	0.501037	−	0.0724932i
$787$			3.39857e24i			0.823211i	0.911362	+	0.411606i	$0.135032\pi$
$787$			3.39857e24i			0.823211i	−0.911362	+	0.411606i	$0.864968\pi$
$788$	3.51997e23	−	5.02958e24i	0.0843464	−	1.20520i
$789$	−2.41283e23	−	1.33638e24i	−0.0571969	−	0.316794i
$790$	1.12600e23	−	3.22175e24i	0.0264063	−	0.755546i
$791$	2.35471e24			0.546307
$792$	−9.15120e23	−	3.54772e24i	−0.210046	−	0.814302i
$793$	−3.82276e23			−0.0868070
$794$	6.71415e22	−	1.92108e24i	0.0150840	−	0.431589i
$795$	1.01805e23	+	5.63864e23i	0.0226282	+	0.125330i
$796$	−3.24921e22	+	4.64270e23i	−0.00714524	+	0.102096i
$797$			3.27565e22i			0.00712693i	0.999994	+	0.00356346i	$0.00113429\pi$
$797$			3.27565e22i			0.00712693i	−0.999994	+	0.00356346i	$0.998866\pi$
$798$	−5.18462e24	+	7.50143e23i	−1.11607	+	0.161480i
$799$		−	1.14237e25i		−	2.43310i
$800$	−4.79578e23	+	2.71750e24i	−0.101063	+	0.572671i
$801$	−1.74360e24	−	4.67118e24i	−0.363554	−	0.973980i
$802$	−3.21179e24	−	1.12252e23i	−0.662621	−	0.0231586i
$803$	1.18420e23			0.0241737
$804$	−4.19402e24	+	4.57921e23i	−0.847137	+	0.0924941i
$805$	−3.58606e24			−0.716726
$806$	5.08244e23	+	1.77631e22i	0.100514	+	0.00351295i
$807$	5.64096e24	−	1.01847e24i	1.10390	−	0.199308i
$808$	2.58168e24	+	2.71574e23i	0.499926	+	0.0525886i
$809$			4.60075e24i			0.881589i	0.897608	+	0.440794i	$0.145303\pi$
$809$			4.60075e24i			0.881589i	−0.897608	+	0.440794i	$0.854697\pi$
$810$	−2.65371e24	+	2.14404e24i	−0.503189	+	0.406547i
$811$			3.39295e24i			0.636650i	0.947982	+	0.318325i	$0.103120\pi$
$811$			3.39295e24i			0.636650i	−0.947982	+	0.318325i	$0.896880\pi$
$812$	−9.83310e23	−	6.88174e22i	−0.182585	−	0.0127783i
$813$	−4.20128e24	+	7.58539e23i	−0.771991	+	0.139383i
$814$	1.69285e22	−	4.84365e23i	0.00307831	−	0.0880775i
$815$	−1.55833e24			−0.280426
$816$	−8.17865e24	+	3.18163e23i	−1.45652	+	0.0566609i
$817$	5.72575e24			1.00913
$818$	1.60414e23	−	4.58981e24i	0.0279794	−	0.800556i
$819$	−1.40508e23	−	3.76429e23i	−0.0242543	−	0.0649786i
$820$	5.57234e24	+	3.89983e23i	0.951963	+	0.0666235i
$821$			5.88601e24i			0.995186i	0.867411	+	0.497593i	$0.165783\pi$
$821$			5.88601e24i			0.995186i	−0.867411	+	0.497593i	$0.834217\pi$
$822$	−1.52108e23	−	1.05130e24i	−0.0254532	−	0.175920i
$823$			7.54954e24i			1.25032i	0.780496	+	0.625161i	$0.214967\pi$
$823$			7.54954e24i			1.25032i	−0.780496	+	0.625161i	$0.785033\pi$
$824$	−4.53218e24	−	4.76752e23i	−0.742892	−	0.0781468i
$825$	−5.35584e23	−	2.96641e24i	−0.0868898	−	0.481252i
$826$	7.36285e24	+	2.57331e23i	1.18227	+	0.0413202i
$827$	3.22513e23			0.0512567			0.0256283	−	0.999672i	$-0.491841\pi$
$827$	3.22513e23			0.0512567			0.0256283	+	0.999672i	$0.491841\pi$
$828$	6.74756e24	−	1.99431e24i	1.06142	−	0.313714i
$829$	5.95870e24			0.927765			0.463882	−	0.885897i	$-0.346456\pi$
$829$	5.95870e24			0.927765			0.463882	+	0.885897i	$0.346456\pi$
$830$	−7.53935e24	−	2.63500e23i	−1.16190	−	0.0406085i
$831$	1.07690e24	+	5.96458e24i	0.164273	+	0.909853i
$832$	−4.48838e23	−	9.54856e22i	−0.0677706	−	0.0144175i
$833$		−	1.98366e22i		−	0.00296473i
$834$	1.32986e24	+	9.19136e24i	0.196742	+	1.35978i
$835$			7.01161e24i			1.02679i
$836$	4.56271e23	−	6.51952e24i	0.0661408	−	0.945066i
$837$	−8.69784e24	+	5.16509e24i	−1.24809	+	0.741160i
$838$	−3.38183e23	+	9.67622e24i	−0.0480373	+	1.37446i
$839$	6.63935e24			0.933574			0.466787	−	0.884370i	$-0.345411\pi$
$839$	6.63935e24			0.933574			0.466787	+	0.884370i	$0.345411\pi$
$840$	−4.63947e24	+	3.43099e23i	−0.645794	+	0.0477579i
$841$	7.01452e24			0.966568
$842$	3.98684e23	−	1.14073e25i	0.0543846	−	1.55607i
$843$	−1.79532e24	+	3.24145e23i	−0.242442	+	0.0437728i
$844$	2.41464e23	−	3.45021e24i	0.0322807	−	0.461248i
$845$		−	4.86440e24i		−	0.643794i
$846$	4.03551e24	+	1.20838e25i	0.528751	+	1.58328i
$847$		−	2.25949e24i		−	0.293090i
$848$	2.13532e23	−	1.51807e24i	0.0274219	−	0.194952i
$849$	1.54701e24	−	2.79311e23i	0.196687	−	0.0355118i
$850$	−6.72984e24	−	2.35208e23i	−0.847117	−	0.0296067i
$851$	9.30749e23			0.115993
$852$	1.22080e24	+	1.11811e25i	0.150629	+	1.37958i
$853$	−3.47488e24			−0.424496			−0.212248	−	0.977216i	$-0.568078\pi$
$853$	−3.47488e24			−0.424496			−0.212248	+	0.977216i	$0.568078\pi$
$854$	1.03626e25	+	3.62173e23i	1.25336	+	0.0438050i
$855$	−5.70131e24	+	2.12811e24i	−0.682751	+	0.254848i
$856$	3.51749e23	−	3.34385e24i	0.0417066	−	0.396479i
$857$			5.85321e24i			0.687159i	0.939124	+	0.343579i	$0.111639\pi$
$857$			5.85321e24i			0.687159i	−0.939124	+	0.343579i	$0.888361\pi$
$858$	4.96101e23	−	7.17791e22i	0.0576671	−	0.00834364i
$859$		−	6.29819e24i		−	0.724893i	−0.932005	−	0.362447i	$-0.881942\pi$
$859$		−	6.29819e24i		−	0.724893i	0.932005	−	0.362447i	$-0.118058\pi$
$860$	5.07234e24	+	3.54990e23i	0.578058	+	0.0404556i
$861$	−2.32510e24	−	1.28779e25i	−0.262371	−	1.45318i
$862$	−1.31722e23	+	3.76886e24i	−0.0147179	+	0.421113i
$863$	−4.42972e24			−0.490100			−0.245050	−	0.969510i	$-0.578804\pi$
$863$	−4.42972e24			−0.490100			−0.245050	+	0.969510i	$0.578804\pi$
$864$	8.53884e24	−	3.22571e24i	0.935475	−	0.353394i
$865$	−2.73629e24			−0.296841
$866$	−5.52139e23	+	1.57980e25i	−0.0593125	+	1.69707i
$867$	−1.87850e24	−	1.04043e25i	−0.199824	−	1.10676i
$868$	−1.37605e25	−	9.63035e23i	−1.44950	−	0.101444i
$869$		−	9.42173e24i		−	0.982794i
$870$	−1.13328e24	+	1.63970e23i	−0.117064	+	0.0169375i
$871$		−	5.77211e23i		−	0.0590447i
$872$	9.57559e23	−	9.10291e24i	0.0970008	−	0.922125i
$873$	1.44916e25	−	5.40923e24i	1.45377	−	0.542643i
$874$	1.25431e25	+	4.38382e23i	1.24612	+	0.0435518i
$875$	−1.04093e25			−1.02413
$876$	3.20215e22	+	2.93280e23i	0.00312002	+	0.0285757i
$877$	−1.24671e25			−1.20301			−0.601506	−	0.798869i	$-0.705432\pi$
$877$	−1.24671e25			−1.20301			−0.601506	+	0.798869i	$0.705432\pi$
$878$	−4.78227e24	−	1.67140e23i	−0.457016	−	0.0159727i
$879$	4.08024e23	−	7.36684e22i	0.0386171	−	0.00697230i
$880$	8.08405e23	−	5.74724e24i	0.0757750	−	0.538712i
$881$			1.13021e25i			1.04922i	0.851344	+	0.524608i	$0.175788\pi$
$881$			1.13021e25i			1.04922i	−0.851344	+	0.524608i	$0.824212\pi$
$882$	7.00743e21	+	2.09828e22i	0.000644282	+	0.00192922i
$883$		−	3.67359e24i		−	0.334522i	−0.985913	−	0.167261i	$-0.946508\pi$
$883$		−	3.67359e24i		−	0.334522i	0.985913	−	0.167261i	$-0.0534923\pi$
$884$	7.81786e22	−	1.11707e24i	0.00705089	−	0.100748i
$885$	8.42226e24	−	1.52063e24i	0.752335	−	0.135834i
$886$	−3.24716e23	+	9.29088e24i	−0.0287288	+	0.821997i
$887$	−1.40887e25			−1.23458			−0.617290	−	0.786736i	$-0.711769\pi$
$887$	−1.40887e25			−1.23458			−0.617290	+	0.786736i	$0.711769\pi$
$888$	1.20416e24	−	8.90499e22i	0.104513	−	0.00772900i
$889$	−2.12568e24			−0.182740
$890$	2.75873e23	−	7.89336e24i	0.0234906	−	0.672120i
$891$	−7.53222e24	+	6.53332e24i	−0.635276	+	0.551028i
$892$	7.30930e23	−	1.04440e25i	0.0610625	−	0.872502i
$893$			2.27250e25i			1.88047i
$894$	−2.72810e24	−	1.88553e25i	−0.223610	−	1.54548i
$895$		−	6.92338e24i		−	0.562112i
$896$	1.20765e25	+	3.01363e24i	0.971233	+	0.242366i
$897$	1.71039e23	+	9.47323e23i	0.0136257	+	0.0754679i
$898$	4.60334e21	+	1.60887e20i	0.000363266	+	1.26961e-5i
$899$	−3.39530e24			−0.265412
$900$	7.20179e24	−	2.12856e24i	0.557672	−	0.164826i
$901$	3.74099e24			0.286963
$902$	1.63158e25	+	5.70236e23i	1.23980	+	0.0433310i
$903$	−2.11647e24	−	1.17224e25i	−0.159319	−	0.882411i
$904$	−7.27843e24	−	7.65638e23i	−0.542758	−	0.0570941i
$905$			7.52801e24i			0.556118i
$906$	−1.29776e24	−	8.96946e24i	−0.0949740	−	0.656412i
$907$		−	6.53758e24i		−	0.473974i	−0.971513	−	0.236987i	$-0.923840\pi$
$907$		−	6.53758e24i		−	0.473974i	0.971513	−	0.236987i	$-0.0761599\pi$
$908$	−2.45854e24	−	1.72062e23i	−0.176583	−	0.0123582i
$909$	−2.47049e24	−	6.61857e24i	−0.175788	−	0.470946i
$910$	2.22313e22	−	6.36090e23i	0.00156716	−	0.0448401i
$911$	1.02693e25			0.717191			0.358596	−	0.933493i	$-0.383256\pi$
$911$	1.02693e25			0.717191			0.358596	+	0.933493i	$0.383256\pi$
$912$	1.62696e25	−	6.32915e23i	1.12570	−	0.0437914i
$913$	−2.20482e25			−1.51137
$914$	2.48515e23	−	7.11059e24i	0.0168776	−	0.482907i
$915$	1.18536e25	−	2.14017e24i	0.797577	−	0.144002i
$916$	−3.84625e23	−	2.69181e22i	−0.0256404	−	0.00179446i
$917$		−	7.67271e24i		−	0.506768i
$918$	1.06973e25	+	1.95376e25i	0.700021	+	1.27852i
$919$			1.21357e25i			0.786835i	0.919360	+	0.393418i	$0.128707\pi$
$919$			1.21357e25i			0.786835i	−0.919360	+	0.393418i	$0.871293\pi$
$920$	1.10846e25	+	1.16601e24i	0.712069	+	0.0749044i
$921$	6.88756e23	−	1.24354e23i	0.0438388	−	0.00791506i
$922$	−1.59127e25	−	5.56147e23i	−1.00353	−	0.0350733i
$923$	−1.53882e24			−0.0961555
$924$	−1.35162e25	+	1.47575e24i	−0.836838	+	0.0913696i
$925$	9.93405e23			0.0609427
$926$	−2.29498e25	−	8.02096e23i	−1.39504	−	0.0487565i
$927$	4.33698e24	+	1.16190e25i	0.261222	+	0.699828i
$928$	3.01705e24	+	5.32440e23i	0.180063	+	0.0317770i
$929$		−	2.33277e25i		−	1.37955i	−0.724022	−	0.689777i	$-0.757708\pi$
$929$		−	2.33277e25i		−	1.37955i	0.724022	−	0.689777i	$-0.242292\pi$
$930$	−1.58591e25	+	2.29460e24i	−0.929340	+	0.134463i
$931$			3.94606e22i			0.00229135i
$932$	−1.15170e24	+	1.64563e25i	−0.0662680	+	0.946883i
$933$	7.88240e23	+	4.36579e24i	0.0449433	+	0.248925i
$934$	1.50170e23	−	4.29670e24i	0.00848464	−	0.242765i
$935$	1.41629e25			0.792966
$936$	3.11917e23	+	1.20923e24i	0.0173059	+	0.0670912i
$937$	2.58377e25			1.42058			0.710292	−	0.703907i	$-0.248563\pi$
$937$	2.58377e25			1.42058			0.710292	+	0.703907i	$0.248563\pi$
$938$	−5.46857e23	+	1.56469e25i	−0.0297955	+	0.852517i
$939$	8.07621e23	+	4.47313e24i	0.0436064	+	0.241521i
$940$	−1.40892e24	+	2.01317e25i	−0.0753877	+	1.07719i
$941$			1.13612e25i			0.602438i	0.953555	+	0.301219i	$0.0973935\pi$
$941$			1.13612e25i			0.602438i	−0.953555	+	0.301219i	$0.902606\pi$
$942$	−9.81746e24	+	1.42045e24i	−0.515901	+	0.0746439i
$943$			3.13522e25i			1.63274i
$944$	−2.26750e25	−	3.18946e24i	−1.17027	−	0.164610i
$945$	6.46434e24	+	1.08857e25i	0.330639	+	0.556784i
$946$	1.48518e25	+	5.19069e23i	0.752842	+	0.0263118i
$947$	1.36643e25			0.686454			0.343227	−	0.939252i	$-0.388480\pi$
$947$	1.36643e25			0.686454			0.343227	+	0.939252i	$0.388480\pi$
$948$	2.33339e25	−	2.54769e24i	1.16176	−	0.126846i
$949$	−4.03633e22			−0.00199170
$950$	1.33875e25	+	4.67893e23i	0.654711	+	0.0228821i
$951$	−2.98958e24	+	5.39766e23i	−0.144902	+	0.0261620i
$952$	−3.17757e24	+	3.02071e25i	−0.152644	+	1.45109i
$953$		−	2.16685e25i		−	1.03167i	−0.856689	−	0.515833i	$-0.827482\pi$
$953$		−	2.16685e25i		−	1.03167i	0.856689	−	0.515833i	$-0.172518\pi$
$954$	−3.95715e24	+	1.32153e24i	−0.186733	+	0.0623614i
$955$		−	1.55722e25i		−	0.728318i
$956$	−3.51849e25	−	2.46243e24i	−1.63104	−	0.114149i
$957$	−3.29339e24	+	5.94620e23i	−0.151318	+	0.0273204i
$958$	1.06399e24	−	3.04433e25i	0.0484542	−	1.38639i
$959$	−3.94197e24			−0.177932
$960$	1.44522e25	+	4.48009e23i	0.646589	+	0.0200439i
$961$	−2.49639e25			−1.10704
$962$	−5.77005e21	+	1.65095e23i	−0.000253625	+	0.00725680i
$963$	−8.57252e24	+	3.19983e24i	−0.373495	+	0.139413i
$964$	−2.84379e25	−	1.99024e24i	−1.22813	−	0.0859509i
$965$		−	2.34349e25i		−	1.00319i
$966$	−3.73895e24	−	2.58418e25i	−0.158652	−	1.09652i
$967$			1.49043e25i			0.626883i	0.949607	+	0.313442i	$0.101482\pi$
$967$			1.49043e25i			0.626883i	−0.949607	+	0.313442i	$0.898518\pi$
$968$	−7.34677e23	+	6.98410e24i	−0.0306306	+	0.291186i
$969$	7.05953e24	+	3.91003e25i	0.291759	+	1.61595i
$970$	2.44879e25	+	8.55852e23i	1.00321	+	0.0350622i
$971$	3.02273e25			1.22754			0.613771	−	0.789484i	$-0.289652\pi$
$971$	3.02273e25			1.22754			0.613771	+	0.789484i	$0.289652\pi$
$972$	−1.82172e25	−	1.68876e25i	−0.733362	−	0.679839i
$973$	3.44641e25			1.37533
$974$	−3.64516e25	−	1.27398e24i	−1.44200	−	0.0503979i
$975$	1.82553e23	+	1.01109e24i	0.00715894	+	0.0396509i
$976$	−3.19132e25	−	4.48890e24i	−1.24064	−	0.174509i
$977$		−	3.21566e25i		−	1.23927i	−0.784890	−	0.619635i	$-0.787281\pi$
$977$		−	3.21566e25i		−	1.23927i	0.784890	−	0.619635i	$-0.212719\pi$
$978$	−1.62477e24	−	1.12296e25i	−0.0620741	−	0.429025i
$979$		−	2.30835e25i		−	0.874275i
$980$	−2.44651e21	+	3.49574e22i	−9.18598e−5	+	0.00131256i
$981$	−2.33368e25	+	8.71086e24i	−0.868671	+	0.324246i
$982$	6.23588e23	−	1.78423e25i	0.0230118	−	0.658421i
$983$	−1.10484e25			−0.404197			−0.202098	−	0.979365i	$-0.564776\pi$
$983$	−1.10484e25			−0.404197			−0.202098	+	0.979365i	$0.564776\pi$
$984$	2.99964e24	+	4.05619e25i	0.108795	+	1.47116i
$985$	−2.17353e25			−0.781550
$986$	−2.61134e23	+	7.47165e24i	−0.00930914	+	0.266356i
$987$	4.65252e25	−	8.40010e24i	1.64434	−	0.296885i
$988$	−1.55519e23	+	2.22216e24i	−0.00544941	+	0.0778650i
$989$			2.85390e25i			0.991448i
$990$	−1.49813e25	+	5.00315e24i	−0.516001	+	0.172323i
$991$			1.23144e25i			0.420520i	0.977645	+	0.210260i	$0.0674311\pi$
$991$			1.23144e25i			0.420520i	−0.977645	+	0.210260i	$0.932569\pi$
$992$	4.22208e25	+	7.45101e24i	1.42948	+	0.252270i
$993$	−1.20789e25	+	2.18083e24i	−0.405469	+	0.0732071i
$994$	4.17139e25	+	1.45790e24i	1.38834	+	0.0485226i
$995$	2.00634e24			0.0662076
$996$	−5.96196e24	−	5.46045e25i	−0.195067	−	1.78659i
$997$	8.02428e24			0.260314			0.130157	−	0.991493i	$-0.458452\pi$
$997$	8.02428e24			0.260314			0.130157	+	0.991493i	$0.458452\pi$
$998$	4.65820e25	+	1.62804e24i	1.49834	+	0.0523668i
$999$	−1.67779e24	−	2.82535e24i	−0.0535096	−	0.0901084i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	12.18.b.a.11.16	yes	32
3.2	odd	2	inner	12.18.b.a.11.17	yes	32
4.3	odd	2	inner	12.18.b.a.11.18	yes	32
12.11	even	2	inner	12.18.b.a.11.15	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
12.18.b.a.11.15	✓	32	12.11	even	2	inner
12.18.b.a.11.16	yes	32	1.1	even	1	trivial
12.18.b.a.11.17	yes	32	3.2	odd	2	inner
12.18.b.a.11.18	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)

\(f(q)\)	\(=\)	\(q+(-12.6455 + 361.818i) q^{2} +(2019.11 + 11183.2i) q^{3} +(-130752. - 9150.75i) q^{4} +565044. i q^{5} +(-4.07180e6 + 589135. i) q^{6} +1.52677e7i q^{7} +(4.96433e6 - 4.71927e7i) q^{8} +(-1.20987e8 + 4.51602e7i) q^{9} +O(q^{10})\)	\(q+(-12.6455 + 361.818i) q^{2} +(2019.11 + 11183.2i) q^{3} +(-130752. - 9150.75i) q^{4} +565044. i q^{5} +(-4.07180e6 + 589135. i) q^{6} +1.52677e7i q^{7} +(4.96433e6 - 4.71927e7i) q^{8} +(-1.20987e8 + 4.51602e7i) q^{9} +(-2.04443e8 - 7.14527e6i) q^{10} -5.97876e8 q^{11} +(-1.61669e8 - 1.48070e9i) q^{12} +2.03785e8 q^{13} +(-5.52414e9 - 1.93068e8i) q^{14} +(-6.31898e9 + 1.14089e9i) q^{15} +(1.70124e10 + 2.39296e9i) q^{16} +4.19237e10i q^{17} +(-1.48098e10 - 4.43461e10i) q^{18} -8.33979e10i q^{19} +(5.17057e9 - 7.38807e10i) q^{20} +(-1.70742e11 + 3.08273e10i) q^{21} +(7.56045e9 - 2.16322e11i) q^{22} +4.15682e11 q^{23} +(5.37788e11 - 3.97706e10i) q^{24} +4.43665e11 q^{25} +(-2.57697e9 + 7.37330e10i) q^{26} +(-7.49320e11 - 1.26183e12i) q^{27} +(1.39711e11 - 1.99629e12i) q^{28} -4.92569e11i q^{29} +(-3.32887e11 - 2.30075e12i) q^{30} -6.89304e12i q^{31} +(-1.08095e12 + 6.12513e12i) q^{32} +(-1.20718e12 - 6.68615e12i) q^{33} +(-1.51687e13 - 5.30147e11i) q^{34} -8.62694e12 q^{35} +(1.62325e13 - 4.79768e12i) q^{36} +2.23909e12 q^{37} +(3.01748e13 + 1.05461e12i) q^{38} +(4.11465e11 + 2.27896e12i) q^{39} +(2.66660e13 + 2.80507e12i) q^{40} +7.54235e13i q^{41} +(-8.99475e12 - 6.21672e13i) q^{42} +6.86558e13i q^{43} +(7.81736e13 + 5.47101e12i) q^{44} +(-2.55175e13 - 6.83627e13i) q^{45} +(-5.25651e12 + 1.50401e14i) q^{46} -2.72489e14 q^{47} +(7.58910e12 + 1.95084e14i) q^{48} -4.73161e11 q^{49} +(-5.61037e12 + 1.60526e14i) q^{50} +(-4.68840e14 + 8.46488e13i) q^{51} +(-2.66453e13 - 1.86478e12i) q^{52} -8.92333e13i q^{53} +(4.66028e14 - 2.55161e14i) q^{54} -3.37826e14i q^{55} +(7.20526e14 + 7.57941e13i) q^{56} +(9.32653e14 - 1.68390e14i) q^{57} +(1.78220e14 + 6.22879e12i) q^{58} -1.33285e15 q^{59} +(8.36661e14 - 9.13503e13i) q^{60} -1.87588e15 q^{61} +(2.49402e15 + 8.71661e13i) q^{62} +(-6.89494e14 - 1.84719e15i) q^{63} +(-2.20251e15 - 4.68561e14i) q^{64} +1.15147e14i q^{65} +(2.43443e15 - 3.52230e14i) q^{66} -2.83245e15i q^{67} +(3.83633e14 - 5.48162e15i) q^{68} +(8.39310e14 + 4.64864e15i) q^{69} +(1.09092e14 - 3.12138e15i) q^{70} -7.55122e15 q^{71} +(1.53062e15 + 5.93388e15i) q^{72} -1.98068e14 q^{73} +(-2.83144e13 + 8.10142e14i) q^{74} +(8.95810e14 + 4.96158e15i) q^{75} +(-7.63153e14 + 1.09045e16i) q^{76} -9.12821e15i q^{77} +(-8.29772e14 + 1.20057e14i) q^{78} +1.57587e16i q^{79} +(-1.35213e15 + 9.61275e15i) q^{80} +(1.25983e16 - 1.09276e16i) q^{81} +(-2.72896e16 - 9.53769e14i) q^{82} +3.68775e16 q^{83} +(2.26069e16 - 2.46832e15i) q^{84} -2.36887e16 q^{85} +(-2.48409e16 - 8.68188e14i) q^{86} +(5.50848e15 - 9.94553e14i) q^{87} +(-2.96806e15 + 2.82154e16i) q^{88} +3.86091e16i q^{89} +(2.50575e16 - 8.36821e15i) q^{90} +3.11133e15i q^{91} +(-5.43513e16 - 3.80380e15i) q^{92} +(7.70861e16 - 1.39178e16i) q^{93} +(3.44576e15 - 9.85913e16i) q^{94} +4.71235e16 q^{95} +(-7.06809e16 + 2.78929e14i) q^{96} -1.19779e17 q^{97} +(5.98336e12 - 1.71198e14i) q^{98} +(7.23350e16 - 2.70002e16i) 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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