LMFDB - Embedded newform 12.20.b.a.11.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [12,20,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, 20, names="a")

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

chi := DirichletCharacter("12.11");

S:= CuspForms(chi, 20);

N := Newforms(S);

Level:	$ N $	$=$	$ 12 = 2^{2} \cdot 3 $
Weight:	$ k $	$=$	$ 20 $
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:	$27.4580035868$
Analytic rank:	$0$
Dimension:	$36$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			11.4
Character	$\chi$	$=$	12.11
Dual form			12.20.b.a.11.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-706.401 + 159.015i) q^{2} +(-32549.6 + 10138.3i) q^{3} +(473717. - 224656. i) q^{4} -5.54418e6i q^{5} +(2.13809e7 - 1.23376e7i) q^{6} -1.49965e8i q^{7} +(-2.98910e8 + 2.34025e8i) q^{8} +(9.56692e8 - 6.59995e8i) q^{9} +O(q^{10})$	\(q+(-706.401 + 159.015i) q^{2} +(-32549.6 + 10138.3i) q^{3} +(473717. - 224656. i) q^{4} -5.54418e6i q^{5} +(2.13809e7 - 1.23376e7i) q^{6} -1.49965e8i q^{7} +(-2.98910e8 + 2.34025e8i) q^{8} +(9.56692e8 - 6.59995e8i) q^{9} +(8.81605e8 + 3.91641e9i) q^{10} -2.49508e6 q^{11} +(-1.31417e10 + 1.21151e10i) q^{12} +4.88082e10 q^{13} +(2.38467e10 + 1.05936e11i) q^{14} +(5.62085e10 + 1.80461e11i) q^{15} +(1.73937e11 - 2.12847e11i) q^{16} -4.51471e11i q^{17} +(-5.70859e11 + 6.18349e11i) q^{18} +6.03024e11i q^{19} +(-1.24553e12 - 2.62637e12i) q^{20} +(1.52039e12 + 4.88132e12i) q^{21} +(1.76253e9 - 3.96754e8i) q^{22} +7.40098e12 q^{23} +(7.35680e12 - 1.06479e13i) q^{24} -1.16644e13 q^{25} +(-3.44782e13 + 7.76122e12i) q^{26} +(-2.44487e13 + 3.11818e13i) q^{27} +(-3.36906e13 - 7.10412e13i) q^{28} -1.10755e14i q^{29} +(-6.84016e13 - 1.18540e14i) q^{30} -2.18703e14i q^{31} +(-8.90238e13 + 1.78014e14i) q^{32} +(8.12138e10 - 2.52958e10i) q^{33} +(7.17904e13 + 3.18919e14i) q^{34} -8.31435e14 q^{35} +(3.04929e14 - 5.27577e14i) q^{36} +4.99785e14 q^{37} +(-9.58896e13 - 4.25977e14i) q^{38} +(-1.58869e15 + 4.94832e14i) q^{39} +(1.29748e15 + 1.65721e15i) q^{40} -1.26797e13i q^{41} +(-1.85021e15 - 3.20640e15i) q^{42} -3.26952e15i q^{43} +(-1.18196e12 + 5.60534e11i) q^{44} +(-3.65913e15 - 5.30407e15i) q^{45} +(-5.22806e15 + 1.17686e15i) q^{46} +1.12738e16 q^{47} +(-3.50369e15 + 8.69150e15i) q^{48} -1.10907e16 q^{49} +(8.23976e15 - 1.85481e15i) q^{50} +(4.57714e15 + 1.46952e16i) q^{51} +(2.31213e16 - 1.09651e16i) q^{52} +3.23098e16i q^{53} +(1.23122e16 - 2.59145e16i) q^{54} +1.38332e13i q^{55} +(3.50957e16 + 4.48262e16i) q^{56} +(-6.11364e15 - 1.96282e16i) q^{57} +(1.76117e16 + 7.82375e16i) q^{58} +6.67474e16 q^{59} +(6.71685e16 + 7.28597e16i) q^{60} -1.62842e17 q^{61} +(3.47770e16 + 1.54492e17i) q^{62} +(-9.89764e16 - 1.43471e17i) q^{63} +(3.45797e16 - 1.39905e17i) q^{64} -2.70602e17i q^{65} +(-5.33471e13 + 3.07832e13i) q^{66} -4.88693e15i q^{67} +(-1.01426e17 - 2.13869e17i) q^{68} +(-2.40899e17 + 7.50333e16i) q^{69} +(5.87327e17 - 1.32210e17i) q^{70} -2.98345e17 q^{71} +(-1.31510e17 + 4.21169e17i) q^{72} -9.07454e17 q^{73} +(-3.53049e17 + 7.94731e16i) q^{74} +(3.79672e17 - 1.18257e17i) q^{75} +(1.35473e17 + 2.85663e17i) q^{76} +3.74176e14i q^{77} +(1.04357e18 - 6.02175e17i) q^{78} -3.92004e17i q^{79} +(-1.18006e18 - 9.64339e17i) q^{80} +(4.79666e17 - 1.26282e18i) q^{81} +(2.01625e15 + 8.95693e15i) q^{82} -8.04463e17 q^{83} +(1.81685e18 + 1.97080e18i) q^{84} -2.50303e18 q^{85} +(5.19901e17 + 2.30959e18i) q^{86} +(1.12287e18 + 3.60503e18i) q^{87} +(7.45805e14 - 5.83911e14i) q^{88} -1.37583e18i q^{89} +(3.42824e18 + 3.16494e18i) q^{90} -7.31955e18i q^{91} +(3.50597e18 - 1.66267e18i) q^{92} +(2.21728e18 + 7.11870e18i) q^{93} +(-7.96384e18 + 1.79270e18i) q^{94} +3.34327e18 q^{95} +(1.09293e18 - 6.69682e18i) q^{96} -1.68560e18 q^{97} +(7.83452e18 - 1.76359e18i) q^{98} +(-2.38702e15 + 1.64674e15i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 47880 q^{4} + 21771144 q^{6} - 809473644 q^{9}+O(q^{10}) $ 36 * q - 47880 * q^4 + 21771144 * q^6 - 809473644 * q^9	$ 36 q - 47880 q^{4} + 21771144 q^{6} - 809473644 q^{9} - 4162950000 q^{10} - 2268767880 q^{12} - 25913431656 q^{13} + 791689296672 q^{16} + 2852271258192 q^{18} - 1650825908424 q^{21} + 7247870602416 q^{22} + 23719435803936 q^{24} - 118879690462380 q^{25} - 7629081673968 q^{28} + 37456727138640 q^{30} + 529254701828640 q^{33} - 248241675948480 q^{34} - 11\!\cdots\!16 q^{36}+ \cdots + 12\!\cdots\!88 q^{97}+O(q^{100}) $ 36 * q - 47880 * q^4 + 21771144 * q^6 - 809473644 * q^9 - 4162950000 * q^10 - 2268767880 * q^12 - 25913431656 * q^13 + 791689296672 * q^16 + 2852271258192 * q^18 - 1650825908424 * q^21 + 7247870602416 * q^22 + 23719435803936 * q^24 - 118879690462380 * q^25 - 7629081673968 * q^28 + 37456727138640 * q^30 + 529254701828640 * q^33 - 248241675948480 * q^34 - 1177548745309416 * q^36 + 1847838600168120 * q^37 - 40433256181440 * q^40 - 2709671988768336 * q^42 - 4365410114088000 * q^45 + 17206125364795104 * q^46 + 1561106052682272 * q^48 - 49399737041580084 * q^49 + 16558671470242896 * q^52 + 40087412948587896 * q^54 + 44803667812766472 * q^57 - 34645536255764880 * q^58 + 50260381053157440 * q^60 + 174742350239997144 * q^61 - 139766490424918656 * q^64 - 87772097712685968 * q^66 - 957190369821780672 * q^69 + 244663962371376480 * q^70 + 54134736422921280 * q^72 - 1445122541399481432 * q^73 + 2744130151937256048 * q^76 + 1125465917961999024 * q^78 + 1033298241353042436 * q^81 + 1064985418859680800 * q^82 + 1920709484261873424 * q^84 - 1802899595088057600 * q^85 - 9209792381828477760 * q^88 - 5194944179528261040 * q^90 + 6719944190337314136 * q^93 - 3835186345170303552 * q^94 - 11947184361208227456 * q^96 + 12765226159947004488 * 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 $

$2$	−706.401	+	159.015i	−0.975588	+	0.219610i
$2$	−706.401	+	159.015i	−0.975588	+	0.219610i
$3$	−32549.6	+	10138.3i	−0.954759	+	0.297381i
$3$	−32549.6	+	10138.3i	−0.954759	+	0.297381i
$4$	473717.	−	224656.i	0.903543	−	0.428497i
$5$		−	5.54418e6i		−	1.26947i	−0.772730	−	0.634735i	$-0.781109\pi$
$5$		−	5.54418e6i		−	1.26947i	0.772730	−	0.634735i	$-0.218891\pi$
$6$	2.13809e7	−	1.23376e7i	0.866143	−	0.499795i
$7$		−	1.49965e8i		−	1.40462i	−0.711870	−	0.702312i	$-0.752151\pi$
$7$		−	1.49965e8i		−	1.40462i	0.711870	−	0.702312i	$-0.247849\pi$
$8$	−2.98910e8	+	2.34025e8i	−0.787383	+	0.616464i
$9$	9.56692e8	−	6.59995e8i	0.823129	−	0.567854i
$10$	8.81605e8	+	3.91641e9i	0.278788	+	1.23848i
$11$	−2.49508e6			−0.000319046			−0.000159523	−	1.00000i	$-0.500051\pi$
$11$	−2.49508e6			−0.000319046			−0.000159523		1.00000i	$0.500051\pi$
$12$	−1.31417e10	+	1.21151e10i	−0.735239	+	0.677808i
$13$	4.88082e10			1.27653			0.638265	−	0.769816i	$-0.279652\pi$
$13$	4.88082e10			1.27653			0.638265	+	0.769816i	$0.279652\pi$
$14$	2.38467e10	+	1.05936e11i	0.308469	+	1.37033i
$15$	5.62085e10	+	1.80461e11i	0.377516	+	1.21204i
$16$	1.73937e11	−	2.12847e11i	0.632780	−	0.774332i
$17$		−	4.51471e11i		−	0.923347i	−0.887050	−	0.461673i	$-0.847249\pi$
$17$		−	4.51471e11i		−	0.923347i	0.887050	−	0.461673i	$-0.152751\pi$
$18$	−5.70859e11	+	6.18349e11i	−0.678329	+	0.734759i
$19$			6.03024e11i			0.428722i	0.976755	+	0.214361i	$0.0687669\pi$
$19$			6.03024e11i			0.428722i	−0.976755	+	0.214361i	$0.931233\pi$
$20$	−1.24553e12	−	2.62637e12i	−0.543964	−	1.14702i
$21$	1.52039e12	+	4.88132e12i	0.417708	+	1.34108i
$22$	1.76253e9	−	3.96754e8i	0.000311258	−	7.00657e-5i
$23$	7.40098e12			0.856791			0.428395	−	0.903591i	$-0.359079\pi$
$23$	7.40098e12			0.856791			0.428395	+	0.903591i	$0.359079\pi$
$24$	7.35680e12	−	1.06479e13i	0.568437	−	0.822727i
$25$	−1.16644e13			−0.611552
$26$	−3.44782e13	+	7.76122e12i	−1.24537	+	0.280339i
$27$	−2.44487e13	+	3.11818e13i	−0.617021	+	0.786946i
$28$	−3.36906e13	−	7.10412e13i	−0.601877	−	1.26914i
$29$		−	1.10755e14i		−	1.41770i	−0.705362	−	0.708848i	$-0.749215\pi$
$29$		−	1.10755e14i		−	1.41770i	0.705362	−	0.708848i	$-0.250785\pi$
$30$	−6.84016e13	−	1.18540e14i	−0.634475	−	1.09954i
$31$		−	2.18703e14i		−	1.48566i	−0.669481	−	0.742829i	$-0.733483\pi$
$31$		−	2.18703e14i		−	1.48566i	0.669481	−	0.742829i	$-0.266517\pi$
$32$	−8.90238e13	+	1.78014e14i	−0.447282	+	0.894393i
$33$	8.12138e10	−	2.52958e10i	0.000304612	−	9.48782e-5i
$34$	7.17904e13	+	3.18919e14i	0.202776	+	0.900806i
$35$	−8.31435e14			−1.78313
$36$	3.04929e14	−	5.27577e14i	0.500409	−	0.865789i
$37$	4.99785e14			0.632218			0.316109	−	0.948723i	$-0.397623\pi$
$37$	4.99785e14			0.632218			0.316109	+	0.948723i	$0.397623\pi$
$38$	−9.58896e13	−	4.25977e14i	−0.0941515	−	0.418256i
$39$	−1.58869e15	+	4.94832e14i	−1.21878	+	0.379616i
$40$	1.29748e15	+	1.65721e15i	0.782582	+	0.999559i
$41$		−	1.26797e13i		−	0.00604869i	−0.999995	−	0.00302435i	$-0.999037\pi$
$41$		−	1.26797e13i		−	0.00604869i	0.999995	−	0.00302435i	$-0.000962681\pi$
$42$	−1.85021e15	−	3.20640e15i	−0.702024	−	1.21661i
$43$		−	3.26952e15i		−	0.992050i	−0.868308	−	0.496025i	$-0.834792\pi$
$43$		−	3.26952e15i		−	0.992050i	0.868308	−	0.496025i	$-0.165208\pi$
$44$	−1.18196e12	+	5.60534e11i	−0.000288272	+	0.000136710i
$45$	−3.65913e15	−	5.30407e15i	−0.720873	−	1.04494i
$46$	−5.22806e15	+	1.17686e15i	−0.835874	+	0.188160i
$47$	1.12738e16			1.46940			0.734702	−	0.678390i	$-0.237322\pi$
$47$	1.12738e16			1.46940			0.734702	+	0.678390i	$0.237322\pi$
$48$	−3.50369e15	+	8.69150e15i	−0.373881	+	0.927477i
$49$	−1.10907e16			−0.972967
$50$	8.23976e15	−	1.85481e15i	0.596622	−	0.134303i
$51$	4.57714e15	+	1.46952e16i	0.274586	+	0.881574i
$52$	2.31213e16	−	1.09651e16i	1.15340	−	0.546990i
$53$			3.23098e16i			1.34497i	0.740109	+	0.672487i	$0.234774\pi$
$53$			3.23098e16i			1.34497i	−0.740109	+	0.672487i	$0.765226\pi$
$54$	1.23122e16	−	2.59145e16i	0.429137	−	0.903239i
$55$			1.38332e13i			0.000405019i
$56$	3.50957e16	+	4.48262e16i	0.865899	+	1.10598i
$57$	−6.11364e15	−	1.96282e16i	−0.127494	−	0.409326i
$58$	1.76117e16	+	7.82375e16i	0.311340	+	1.38309i
$59$	6.67474e16			1.00309			0.501545	−	0.865132i	$-0.332765\pi$
$59$	6.67474e16			1.00309			0.501545	+	0.865132i	$0.332765\pi$
$60$	6.71685e16	+	7.28597e16i	0.860456	+	0.933363i
$61$	−1.62842e17			−1.78293			−0.891464	−	0.453091i	$-0.850321\pi$
$61$	−1.62842e17			−1.78293			−0.891464	+	0.453091i	$0.850321\pi$
$62$	3.47770e16	+	1.54492e17i	0.326265	+	1.44939i
$63$	−9.89764e16	−	1.43471e17i	−0.797621	−	1.15619i
$64$	3.45797e16	−	1.39905e17i	0.239945	−	0.970786i
$65$		−	2.70602e17i		−	1.62052i
$66$	−5.33471e13	+	3.07832e13i	−0.000276340	+	0.000159458i
$67$		−	4.88693e15i		−	0.0219445i	−0.999940	−	0.0109723i	$-0.996507\pi$
$67$		−	4.88693e15i		−	0.0219445i	0.999940	−	0.0109723i	$-0.00349265\pi$
$68$	−1.01426e17	−	2.13869e17i	−0.395652	−	0.834284i
$69$	−2.40899e17	+	7.50333e16i	−0.818028	+	0.254793i
$70$	5.87327e17	−	1.32210e17i	1.73960	−	0.391592i
$71$	−2.98345e17			−0.772261			−0.386131	−	0.922444i	$-0.626189\pi$
$71$	−2.98345e17			−0.772261			−0.386131	+	0.922444i	$0.626189\pi$
$72$	−1.31510e17	+	4.21169e17i	−0.298057	+	0.954548i
$73$	−9.07454e17			−1.80409			−0.902044	−	0.431645i	$-0.857933\pi$
$73$	−9.07454e17			−1.80409			−0.902044	+	0.431645i	$0.857933\pi$
$74$	−3.53049e17	+	7.94731e16i	−0.616784	+	0.138841i
$75$	3.79672e17	−	1.18257e17i	0.583885	−	0.181864i
$76$	1.35473e17	+	2.85663e17i	0.183706	+	0.387369i
$77$			3.74176e14i			0.000448140i
$78$	1.04357e18	−	6.02175e17i	1.10566	−	0.638004i
$79$		−	3.92004e17i		−	0.367987i	−0.982927	−	0.183994i	$-0.941097\pi$
$79$		−	3.92004e17i		−	0.367987i	0.982927	−	0.183994i	$-0.0589026\pi$
$80$	−1.18006e18	−	9.64339e17i	−0.982990	−	0.803295i
$81$	4.79666e17	−	1.26282e18i	0.355084	−	0.934834i
$82$	2.01625e15	+	8.95693e15i	0.00132835	+	0.00590103i
$83$	−8.04463e17			−0.472350			−0.236175	−	0.971711i	$-0.575894\pi$
$83$	−8.04463e17			−0.472350			−0.236175	+	0.971711i	$0.575894\pi$
$84$	1.81685e18	+	1.97080e18i	0.952065	+	1.03273i
$85$	−2.50303e18			−1.17216
$86$	5.19901e17	+	2.30959e18i	0.217864	+	0.967832i
$87$	1.12287e18	+	3.60503e18i	0.421595	+	1.35356i
$88$	7.45805e14	−	5.83911e14i	0.000251212	−	0.000196680i
$89$		−	1.37583e18i		−	0.416255i	−0.978102	−	0.208127i	$-0.933263\pi$
$89$		−	1.37583e18i		−	0.416255i	0.978102	−	0.208127i	$-0.0667368\pi$
$90$	3.42824e18	+	3.16494e18i	0.932753	+	0.861117i
$91$		−	7.31955e18i		−	1.79305i
$92$	3.50597e18	−	1.66267e18i	0.774147	−	0.367132i
$93$	2.21728e18	+	7.11870e18i	0.441806	+	1.41845i
$94$	−7.96384e18	+	1.79270e18i	−1.43353	+	0.322696i
$95$	3.34327e18			0.544249
$96$	1.09293e18	−	6.69682e18i	0.161071	−	0.986943i
$97$	−1.68560e18			−0.225125			−0.112562	−	0.993645i	$-0.535906\pi$
$97$	−1.68560e18			−0.225125			−0.112562	+	0.993645i	$0.535906\pi$
$98$	7.83452e18	−	1.76359e18i	0.949215	−	0.213673i
$99$	−2.38702e15	+	1.64674e15i	−0.000262616	+	0.000181172i
$100$	−5.52563e18	+	2.62048e18i	−0.552563	+	0.262048i
$101$			2.15370e18i			0.195944i	0.995189	+	0.0979722i	$0.0312356\pi$
$101$			2.15370e18i			0.195944i	−0.995189	+	0.0979722i	$0.968764\pi$
$102$	−5.57005e18	−	9.65287e18i	−0.461485	−	0.799751i
$103$			2.29597e19i			1.73385i	0.498438	+	0.866926i	$0.333907\pi$
$103$			2.29597e19i			1.73385i	−0.498438	+	0.866926i	$0.666093\pi$
$104$	−1.45893e19	+	1.14224e19i	−1.00512	+	0.786935i
$105$	2.70629e19	−	8.42933e18i	1.70246	−	0.530267i
$106$	−5.13773e18	−	2.28237e19i	−0.295370	−	1.31214i
$107$	5.85665e18			0.307967			0.153983	−	0.988073i	$-0.450790\pi$
$107$	5.85665e18			0.307967			0.153983	+	0.988073i	$0.450790\pi$
$108$	−4.57659e18	+	2.02639e19i	−0.220301	+	0.975432i
$109$	2.20095e19			0.970641			0.485321	−	0.874336i	$-0.338703\pi$
$109$	2.20095e19			0.970641			0.485321	+	0.874336i	$0.338703\pi$
$110$	−2.19967e15	−	9.77176e15i	−8.89462e−5	−	0.000395132i
$111$	−1.62678e19	+	5.06697e18i	−0.603616	+	0.188009i
$112$	−3.19196e19	−	2.60846e19i	−1.08764	−	0.888818i
$113$			3.71474e19i			1.16328i	0.813447	+	0.581639i	$0.197588\pi$
$113$			3.71474e19i			1.16328i	−0.813447	+	0.581639i	$0.802412\pi$
$114$	7.43985e18	+	1.28932e19i	0.214273	+	0.371335i
$115$		−	4.10323e19i		−	1.08767i
$116$	−2.48818e19	−	5.24666e19i	−0.607479	−	1.28095i
$117$	4.66944e19	−	3.22132e19i	1.05075	−	0.724883i
$118$	−4.71504e19	+	1.06138e19i	−0.978603	+	0.220288i
$119$	−6.77050e19			−1.29695
$120$	−5.90337e19	−	4.07874e19i	−1.04443	−	0.721613i
$121$	−6.11591e19			−1.00000
$122$	1.15032e20	−	2.58943e19i	1.73940	−	0.391549i
$123$	1.28550e17	+	4.12718e17i	0.00179876	+	0.00577504i
$124$	−4.91330e19	−	1.03603e20i	−0.636601	−	1.34236i
$125$		−	4.10772e19i		−	0.493123i
$126$	9.27310e19	+	8.56092e19i	1.03206	+	0.952796i
$127$			7.81349e18i			0.0806695i	0.999186	+	0.0403348i	$0.0128424\pi$
$127$			7.81349e18i			0.0806695i	−0.999186	+	0.0403348i	$0.987158\pi$
$128$	−2.18021e18	+	1.04328e20i	−0.0208932	+	0.999782i
$129$	3.31473e19	+	1.06422e20i	0.295016	+	0.947168i
$130$	4.30296e19	+	1.91153e20i	0.355881	+	1.58096i
$131$	8.54542e19			0.657138			0.328569	−	0.944480i	$-0.393434\pi$
$131$	8.54542e19			0.657138			0.328569	+	0.944480i	$0.393434\pi$
$132$	3.27895e16	−	3.02282e16i	0.000234575	−	0.000216252i
$133$	9.04328e19			0.602193
$134$	7.77093e17	+	3.45213e18i	0.00481923	+	0.0214088i
$135$	1.72877e20	+	1.35548e20i	0.999004	+	0.783289i
$136$	1.05655e20	+	1.34949e20i	0.569210	+	0.727028i
$137$		−	1.34424e20i		−	0.675512i	−0.941234	−	0.337756i	$-0.890332\pi$
$137$		−	1.34424e20i		−	0.675512i	0.941234	−	0.337756i	$-0.109668\pi$
$138$	1.58240e20	−	9.13100e19i	0.742104	−	0.428220i
$139$		−	3.67041e19i		−	0.160722i	−0.996766	−	0.0803608i	$-0.974393\pi$
$139$		−	3.67041e19i		−	0.160722i	0.996766	−	0.0803608i	$-0.0256073\pi$
$140$	−3.93865e20	+	1.86787e20i	−1.61113	+	0.764065i
$141$	−3.66958e20	+	1.14297e20i	−1.40293	+	0.436973i
$142$	2.10751e20	−	4.74412e19i	0.753409	−	0.169596i
$143$	−1.21780e17			−0.000407272
$144$	2.59266e19	−	3.18426e20i	0.0811526	−	0.996702i
$145$	−6.14046e20			−1.79972
$146$	6.41027e20	−	1.44298e20i	1.76005	−	0.396195i
$147$	3.60999e20	−	1.12441e20i	0.928949	−	0.289342i
$148$	2.36757e20	−	1.12280e20i	0.571236	−	0.270904i
$149$			7.43168e19i			0.168197i	0.996457	+	0.0840983i	$0.0268010\pi$
$149$			7.43168e19i			0.168197i	−0.996457	+	0.0840983i	$0.973199\pi$
$150$	−2.49396e20	+	1.43911e20i	−0.529692	+	0.305651i
$151$		−	1.53578e20i		−	0.306231i	−0.988208	−	0.153115i	$-0.951069\pi$
$151$		−	1.53578e20i		−	0.306231i	0.988208	−	0.153115i	$-0.0489306\pi$
$152$	−1.41123e20	−	1.80250e20i	−0.264291	−	0.337568i
$153$	−2.97968e20	−	4.31918e20i	−0.524326	−	0.760034i
$154$	−5.94993e16	−	2.64318e17i	−9.84159e−5	−	0.000437200i
$155$	−1.21253e21			−1.88600
$156$	−6.41421e20	+	5.91319e20i	−0.938555	+	0.865243i
$157$	4.76448e20			0.656098			0.328049	−	0.944661i	$-0.393609\pi$
$157$	4.76448e20			0.656098			0.328049	+	0.944661i	$0.393609\pi$
$158$	6.23343e19	+	2.76912e20i	0.0808137	+	0.359004i
$159$	−3.27566e20	−	1.05167e21i	−0.399969	−	1.28413i
$160$	9.86939e20	+	4.93564e20i	1.13540	+	0.567810i
$161$		−	1.10989e21i		−	1.20347i
$162$	−1.38029e20	+	9.68333e20i	−0.141117	+	0.989993i
$163$			5.72589e20i			0.552155i	0.961135	+	0.276077i	$0.0890346\pi$
$163$			5.72589e20i			0.552155i	−0.961135	+	0.276077i	$0.910965\pi$
$164$	−2.84856e18	−	6.00657e18i	−0.00259185	−	0.00546525i
$165$	−1.40245e17	−	4.50264e17i	−0.000120445	−	0.000386696i
$166$	5.68273e20	−	1.27921e20i	0.460819	−	0.103733i
$167$	−9.88977e19			−0.0757495			−0.0378747	−	0.999282i	$-0.512059\pi$
$167$	−9.88977e19			−0.0757495			−0.0378747	+	0.999282i	$0.512059\pi$
$168$	−1.59681e21	−	1.10327e21i	−1.15562	−	0.798440i
$169$	9.20324e20			0.629531
$170$	1.76815e21	−	3.98019e20i	1.14355	−	0.257418i
$171$	3.97993e20	+	5.76908e20i	0.243451	+	0.352894i
$172$	−7.34517e20	−	1.54883e21i	−0.425091	−	0.896360i
$173$			2.94806e21i			1.61473i	0.590055	+	0.807363i	$0.299106\pi$
$173$			2.94806e21i			1.61473i	−0.590055	+	0.807363i	$0.700894\pi$
$174$	−1.36645e21	−	2.36805e21i	−0.708558	−	1.22793i
$175$			1.74926e21i			0.859000i
$176$	−4.33987e17	+	5.31069e17i	−0.000201886	+	0.000247048i
$177$	−2.17260e21	+	6.76704e20i	−0.957709	+	0.298300i
$178$	2.18777e20	+	9.71886e20i	0.0914136	+	0.406093i
$179$	9.70172e20			0.384366			0.192183	−	0.981359i	$-0.438443\pi$
$179$	9.70172e20			0.384366			0.192183	+	0.981359i	$0.438443\pi$
$180$	−2.92498e21	−	1.69058e21i	−1.09909	−	0.635254i
$181$	3.97411e21			1.41675			0.708375	−	0.705836i	$-0.249429\pi$
$181$	3.97411e21			1.41675			0.708375	+	0.705836i	$0.249429\pi$
$182$	1.16391e21	+	5.17054e21i	0.393770	+	1.74927i
$183$	5.30045e21	−	1.65094e21i	1.70227	−	0.530209i
$184$	−2.21223e21	+	1.73201e21i	−0.674623	+	0.528180i
$185$		−	2.77090e21i		−	0.802581i
$186$	−2.69826e21	−	4.67608e21i	−0.742526	−	1.28679i
$187$			1.12645e18i			0.000294590i
$188$	5.34060e21	−	2.53273e21i	1.32767	−	0.629636i
$189$	4.67619e21	+	3.66646e21i	1.10536	+	0.866683i
$190$	−2.36169e21	+	5.31629e20i	−0.530963	+	0.119522i
$191$	−5.34922e21			−1.14412			−0.572062	−	0.820210i	$-0.693856\pi$
$191$	−5.34922e21			−1.14412			−0.572062	+	0.820210i	$0.693856\pi$
$192$	2.92842e20	+	4.90443e21i	0.0596036	+	0.998222i
$193$	2.15483e21			0.417464			0.208732	−	0.977973i	$-0.433066\pi$
$193$	2.15483e21			0.417464			0.208732	+	0.977973i	$0.433066\pi$
$194$	1.19071e21	−	2.68035e20i	0.219629	−	0.0494396i
$195$	2.74344e21	+	8.80797e21i	0.481910	+	1.54720i
$196$	−5.25387e21	+	2.49160e21i	−0.879117	+	0.416914i
$197$		−	2.73703e20i		−	0.0436365i	−0.999762	−	0.0218182i	$-0.993054\pi$
$197$		−	2.73703e20i		−	0.0436365i	0.999762	−	0.0218182i	$-0.00694551\pi$
$198$	1.42434e18	−	1.54283e18i	0.000216418	−	0.000234422i
$199$		−	5.79917e21i		−	0.839965i	−0.907532	−	0.419983i	$-0.862036\pi$
$199$		−	5.79917e21i		−	0.839965i	0.907532	−	0.419983i	$-0.137964\pi$
$200$	3.48662e21	−	2.72977e21i	0.481526	−	0.376999i
$201$	4.95451e19	+	1.59068e20i	0.00652587	+	0.0209517i
$202$	−3.42470e20	−	1.52138e21i	−0.0430313	−	0.191161i
$203$	−1.66094e22			−1.99133
$204$	5.46963e21	+	5.93308e21i	0.625852	+	0.678881i
$205$	−7.02984e19			−0.00767863
$206$	−3.65092e21	−	1.62187e22i	−0.380771	−	1.69152i
$207$	7.08045e21	−	4.88461e21i	0.705249	−	0.486532i
$208$	8.48957e21	−	1.03887e22i	0.807763	−	0.988458i
$209$		−	1.50459e18i		−	0.000136782i
$210$	−1.77769e22	+	1.02579e22i	−1.54444	+	0.891198i
$211$		−	6.69519e21i		−	0.556006i	−0.960580	−	0.278003i	$-0.910328\pi$
$211$		−	6.69519e21i		−	0.556006i	0.960580	−	0.278003i	$-0.0896725\pi$
$212$	7.25860e21	+	1.53057e22i	0.576318	+	1.21524i
$213$	9.71101e21	−	3.02471e21i	0.737323	−	0.229656i
$214$	−4.13715e21	+	9.31293e20i	−0.300448	+	0.0676325i
$215$	−1.81268e22			−1.25938
$216$	1.06554e19	−	1.50422e22i	0.000708367	−	1.00000i
$217$	−3.27979e22			−2.08679
$218$	−1.55475e22	+	3.49983e21i	−0.946946	+	0.213162i
$219$	2.95373e22	−	9.20004e21i	1.72247	−	0.536501i
$220$	3.10770e18	+	6.55300e18i	0.000173550	+	0.000365952i
$221$		−	2.20355e22i		−	1.17868i
$222$	1.06859e22	−	6.16613e21i	0.547591	−	0.315980i
$223$			3.42488e22i			1.68170i	0.541265	+	0.840852i	$0.317945\pi$
$223$			3.42488e22i			1.68170i	−0.541265	+	0.840852i	$0.682055\pi$
$224$	2.66959e22	+	1.33505e22i	1.25629	+	0.628262i
$225$	−1.11593e22	+	7.69846e21i	−0.503386	+	0.347272i
$226$	−5.90698e21	−	2.62410e22i	−0.255467	−	1.13488i
$227$	9.15468e21			0.379662			0.189831	−	0.981817i	$-0.439206\pi$
$227$	9.15468e21			0.379662			0.189831	+	0.981817i	$0.439206\pi$
$228$	−7.30572e21	−	7.92474e21i	−0.290591	−	0.315213i
$229$	−2.34552e22			−0.894957			−0.447479	−	0.894295i	$-0.647678\pi$
$229$	−2.34552e22			−0.894957			−0.447479	+	0.894295i	$0.647678\pi$
$230$	6.52474e21	+	2.89853e22i	0.238863	+	1.06112i
$231$	−3.79350e18	−	1.21793e19i	−0.000133268	−	0.000427866i
$232$	2.59195e22	+	3.31059e22i	0.873958	+	1.11627i
$233$		−	7.75371e21i		−	0.250974i	−0.992095	−	0.125487i	$-0.959951\pi$
$233$		−	7.75371e21i		−	0.250974i	0.992095	−	0.125487i	$-0.0400493\pi$
$234$	−2.78626e22	+	3.01805e22i	−0.865907	+	0.937942i
$235$		−	6.25041e22i		−	1.86536i
$236$	3.16193e22	−	1.49952e22i	0.906335	−	0.429821i
$237$	3.97425e21	+	1.27596e22i	0.109432	+	0.351339i
$238$	4.78269e22	−	1.07661e22i	1.26529	−	0.284824i
$239$	5.58610e21			0.142013			0.0710066	−	0.997476i	$-0.477379\pi$
$239$	5.58610e21			0.142013			0.0710066	+	0.997476i	$0.477379\pi$
$240$	4.81872e22	+	1.94251e22i	1.17740	+	0.474631i
$241$	−7.82487e21			−0.183787			−0.0918935	−	0.995769i	$-0.529292\pi$
$241$	−7.82487e21			−0.183787			−0.0918935	+	0.995769i	$0.529292\pi$
$242$	4.32028e22	−	9.72518e21i	0.975588	−	0.219610i
$243$	−2.81006e21	+	4.59674e22i	−0.0610177	+	0.998137i
$244$	−7.71412e22	+	3.65835e22i	−1.61095	+	0.763980i
$245$			6.14891e22i			1.23515i
$246$	−1.56436e20	−	2.71103e20i	−0.00302311	−	0.00523903i
$247$			2.94326e22i			0.547277i
$248$	5.11820e22	+	6.53727e22i	0.915855	+	1.16978i
$249$	2.61849e22	−	8.15588e21i	0.450981	−	0.140468i
$250$	6.53186e21	+	2.90169e22i	0.108295	+	0.481085i
$251$	−5.35960e22			−0.855523			−0.427762	−	0.903892i	$-0.640698\pi$
$251$	−5.35960e22			−0.855523			−0.427762	+	0.903892i	$0.640698\pi$
$252$	−7.91183e22	−	4.57288e22i	−1.21611	−	0.702886i
$253$	−1.84660e19			−0.000273356
$254$	−1.24246e21	−	5.51945e21i	−0.0177158	−	0.0787002i
$255$	8.14728e22	−	2.53765e22i	1.11913	−	0.348578i
$256$	−1.50495e22	−	7.40439e22i	−0.199179	−	0.979963i
$257$		−	9.24681e22i		−	1.17931i	−0.807656	−	0.589654i	$-0.799264\pi$
$257$		−	9.24681e22i		−	1.17931i	0.807656	−	0.589654i	$-0.200736\pi$
$258$	−4.03379e22	−	6.99054e22i	−0.495822	−	0.859257i
$259$		−	7.49505e22i		−	0.888028i
$260$	−6.07923e22	−	1.28189e23i	−0.694387	−	1.46421i
$261$	−7.30978e22	−	1.05958e23i	−0.805044	−	1.16695i
$262$	−6.03650e22	+	1.35885e22i	−0.641095	+	0.144314i
$263$	−7.84375e22			−0.803423			−0.401712	−	0.915766i	$-0.631585\pi$
$263$	−7.84375e22			−0.803423			−0.401712	+	0.915766i	$0.631585\pi$
$264$	−1.83558e19	+	2.65673e19i	−0.000181358	+	0.000262488i
$265$	1.79131e23			1.70740
$266$	−6.38818e22	+	1.43801e22i	−0.587492	+	0.132247i
$267$	1.39485e22	+	4.47826e22i	0.123786	+	0.397423i
$268$	−1.09788e21	−	2.31502e21i	−0.00940316	−	0.0198278i
$269$			1.45532e23i			1.20313i	0.798824	+	0.601565i	$0.205456\pi$
$269$			1.45532e23i			1.20313i	−0.798824	+	0.601565i	$0.794544\pi$
$270$	−1.43675e23	−	6.82612e22i	−1.14663	−	0.544777i
$271$			1.50170e23i			1.15711i	0.815642	+	0.578557i	$0.196384\pi$
$271$			1.50170e23i			1.15711i	−0.815642	+	0.578557i	$0.803616\pi$
$272$	−9.60940e22	−	7.85276e22i	−0.714977	−	0.584275i
$273$	7.42077e22	+	2.38248e23i	0.533217	+	1.71193i
$274$	2.13754e22	+	9.49575e22i	0.148349	+	0.659021i
$275$	2.91036e19			0.000195113
$276$	−9.72612e22	+	8.96639e22i	−0.629946	+	0.580739i
$277$	2.52142e23			1.57793			0.788964	−	0.614439i	$-0.210618\pi$
$277$	2.52142e23			1.57793			0.788964	+	0.614439i	$0.210618\pi$
$278$	5.83649e21	+	2.59278e22i	0.0352960	+	0.156798i
$279$	−1.44343e23	−	2.09232e23i	−0.843637	−	1.22289i
$280$	2.48525e23	−	1.94577e23i	1.40400	−	1.09923i
$281$		−	1.28348e23i		−	0.700935i	−0.936575	−	0.350467i	$-0.886023\pi$
$281$		−	1.28348e23i		−	0.700935i	0.936575	−	0.350467i	$-0.113977\pi$
$282$	2.41045e23	−	1.39091e23i	1.27272	−	0.734402i
$283$			2.88031e23i			1.47051i	0.677789	+	0.735256i	$0.262938\pi$
$283$			2.88031e23i			1.47051i	−0.677789	+	0.735256i	$0.737062\pi$
$284$	−1.41331e23	+	6.70250e22i	−0.697771	+	0.330912i
$285$	−1.08822e23	+	3.38951e22i	−0.519627	+	0.161849i
$286$	8.60258e19	−	1.93648e19i	0.000397330	−	8.94410e-5i
$287$	−1.90151e21			−0.00849613
$288$	3.23198e22	+	2.29059e23i	0.139714	+	0.990192i
$289$	3.52466e22			0.147431
$290$	4.33763e23	−	9.76422e22i	1.75578	−	0.395236i
$291$	5.48657e22	−	1.70891e22i	0.214940	−	0.0669478i
$292$	−4.29876e23	+	2.03865e23i	−1.63007	+	0.773047i
$293$		−	3.47250e23i		−	1.27468i	−0.770584	−	0.637338i	$-0.780036\pi$
$293$		−	3.47250e23i		−	1.27468i	0.770584	−	0.637338i	$-0.219964\pi$
$294$	−2.37131e23	+	1.36833e23i	−0.842729	+	0.486284i
$295$		−	3.70059e23i		−	1.27339i
$296$	−1.49391e23	+	1.16962e23i	−0.497798	+	0.389739i
$297$	6.10014e19	−	7.78010e19i	0.000196858	−	0.000251072i
$298$	−1.18174e22	−	5.24975e22i	−0.0369376	−	0.164091i
$299$	3.61229e23			1.09372
$300$	1.53290e23	−	1.41316e23i	0.449637	−	0.414515i
$301$	−4.90315e23			−1.39346
$302$	2.44212e22	+	1.08488e23i	0.0672513	+	0.298755i
$303$	−2.18349e22	−	7.01022e22i	−0.0582701	−	0.187080i
$304$	1.28352e23	+	1.04888e23i	0.331973	+	0.271287i
$305$			9.02827e23i			2.26337i
$306$	2.79166e23	+	2.57726e23i	0.678437	+	0.626333i
$307$			1.16531e23i			0.274554i	0.990533	+	0.137277i	$0.0438351\pi$
$307$			1.16531e23i			0.274554i	−0.990533	+	0.137277i	$0.956165\pi$
$308$	8.40608e19	+	1.77253e20i	0.000192027	+	0.000404914i
$309$	−2.32772e23	−	7.47328e23i	−0.515614	−	1.65541i
$310$	8.56532e23	−	1.92810e23i	1.83996	−	0.414184i
$311$	6.98423e23			1.45511			0.727553	−	0.686051i	$-0.240657\pi$
$311$	6.98423e23			1.45511			0.727553	+	0.686051i	$0.240657\pi$
$312$	3.59073e23	−	5.19704e23i	0.725627	−	1.05024i
$313$	−5.99952e22			−0.117610			−0.0588052	−	0.998269i	$-0.518729\pi$
$313$	−5.99952e22			−0.117610			−0.0588052	+	0.998269i	$0.518729\pi$
$314$	−3.36564e23	+	7.57622e22i	−0.640082	+	0.144086i
$315$	−7.95427e23	+	5.48743e23i	−1.46774	+	1.01256i
$316$	−8.80660e22	−	1.85699e23i	−0.157682	−	0.332492i
$317$			4.40158e23i			0.764796i	0.923998	+	0.382398i	$0.124902\pi$
$317$			4.40158e23i			0.764796i	−0.923998	+	0.382398i	$0.875098\pi$
$318$	3.98624e23	+	6.90814e23i	0.672212	+	1.16494i
$319$			2.76343e20i			0.000452310i
$320$	−7.75659e23	−	1.91716e23i	−1.23238	−	0.304603i
$321$	−1.90632e23	+	5.93765e22i	−0.294034	+	0.0915834i
$322$	1.76489e23	+	7.84028e23i	0.264293	+	1.17409i
$323$	2.72248e23			0.395859
$324$	−5.64750e22	−	7.05980e23i	−0.0797405	−	0.996816i
$325$	−5.69320e23			−0.780665
$326$	−9.10500e22	−	4.04478e23i	−0.121259	−	0.538676i
$327$	−7.16401e23	+	2.23139e23i	−0.926728	+	0.288650i
$328$	2.96736e21	+	3.79009e21i	0.00372880	+	0.00476264i
$329$		−	1.69068e24i		−	2.06396i
$330$	1.70667e20	+	2.95766e20i	0.000202427	+	0.000350805i
$331$		−	1.20541e24i		−	1.38921i	−0.719392	−	0.694604i	$-0.755580\pi$
$331$		−	1.20541e24i		−	1.38921i	0.719392	−	0.694604i	$-0.244420\pi$
$332$	−3.81088e23	+	1.80727e23i	−0.426789	+	0.202401i
$333$	4.78140e23	−	3.29855e23i	0.520397	−	0.359007i
$334$	6.98614e22	−	1.57262e22i	0.0739003	−	0.0166353i
$335$	−2.70940e22			−0.0278579
$336$	1.30342e24	+	5.25432e23i	1.30276	+	0.525162i
$337$	−5.16565e23			−0.501928			−0.250964	−	0.967996i	$-0.580748\pi$
$337$	−5.16565e23			−0.501928			−0.250964	+	0.967996i	$0.580748\pi$
$338$	−6.50118e23	+	1.46345e23i	−0.614163	+	0.138251i
$339$	−3.76612e23	−	1.20913e24i	−0.345937	−	1.11065i
$340$	−1.18573e24	+	5.62322e23i	−1.05910	+	0.502268i
$341$			5.45682e20i			0.000473994i
$342$	−3.72879e23	−	3.44242e23i	−0.315007	−	0.290814i
$343$		−	4.62114e22i		−	0.0379713i
$344$	7.65149e23	+	9.77293e23i	0.611563	+	0.781123i
$345$	4.15998e23	+	1.33559e24i	0.323452	+	1.03846i
$346$	−4.68785e23	−	2.08252e24i	−0.354610	−	1.57531i
$347$	1.44732e23			0.106521			0.0532603	−	0.998581i	$-0.483039\pi$
$347$	1.44732e23			0.106521			0.0532603	+	0.998581i	$0.483039\pi$
$348$	1.34181e24	+	1.45551e24i	0.960925	+	1.04234i
$349$	−7.90825e23			−0.551110			−0.275555	−	0.961285i	$-0.588862\pi$
$349$	−7.90825e23			−0.551110			−0.275555	+	0.961285i	$0.588862\pi$
$350$	−2.78158e23	−	1.23568e24i	−0.188645	−	0.838030i
$351$	−1.19330e24	+	1.52193e24i	−0.787647	+	1.00456i
$352$	2.22121e20	−	4.44158e20i	0.000142704	−	0.000285353i
$353$			3.64188e23i			0.227754i	0.993495	+	0.113877i	$0.0363270\pi$
$353$			3.64188e23i			0.227754i	−0.993495	+	0.113877i	$0.963673\pi$
$354$	1.42712e24	−	8.23499e23i	0.868820	−	0.501340i
$355$			1.65408e24i			0.980362i
$356$	−3.09088e23	−	6.51753e23i	−0.178364	−	0.376104i
$357$	2.20377e24	−	6.86413e23i	1.23828	−	0.385689i
$358$	−6.85330e23	+	1.54271e23i	−0.374983	+	0.0844105i
$359$	5.80491e23			0.309313			0.154657	−	0.987968i	$-0.450573\pi$
$359$	5.80491e23			0.309313			0.154657	+	0.987968i	$0.450573\pi$
$360$	2.33504e24	+	7.29114e23i	1.21177	+	0.378374i
$361$	1.61478e24			0.816198
$362$	−2.80731e24	+	6.31941e23i	−1.38216	+	0.311132i
$363$	1.99070e24	−	6.20049e23i	0.954759	−	0.297381i
$364$	−1.64438e24	−	3.46739e24i	−0.768315	−	1.62009i
$365$			5.03109e24i			2.29023i
$366$	−3.48172e24	+	2.00908e24i	−1.54427	+	0.891100i
$367$		−	7.29018e23i		−	0.315073i	−0.987513	−	0.157536i	$-0.949645\pi$
$367$		−	7.29018e23i		−	0.315073i	0.987513	−	0.157536i	$-0.0503551\pi$
$368$	1.28731e24	−	1.57527e24i	0.542160	−	0.663440i
$369$	−8.36852e21	−	1.21305e22i	−0.00343477	−	0.00497886i
$370$	4.40613e23	+	1.95736e24i	0.176255	+	0.782988i
$371$	4.84536e24			1.88918
$372$	2.64962e24	+	2.87412e24i	1.00699	+	1.09231i
$373$	2.85996e24			1.05956			0.529781	−	0.848135i	$-0.322274\pi$
$373$	2.85996e24			1.05956			0.529781	+	0.848135i	$0.322274\pi$
$374$	−1.79123e20	−	7.95729e20i	−6.46949e−5	−	0.000287399i
$375$	4.16452e23	+	1.33705e24i	0.146645	+	0.470814i
$376$	−3.36986e24	+	2.63836e24i	−1.15698	+	0.905835i
$377$		−	5.40576e24i		−	1.80973i
$378$	−3.88629e24	−	1.84641e24i	−1.26871	−	0.602776i
$379$			4.82016e24i			1.53458i	0.641301	+	0.767290i	$0.278395\pi$
$379$			4.82016e24i			1.53458i	−0.641301	+	0.767290i	$0.721605\pi$
$380$	1.58376e24	−	7.51087e23i	0.491752	−	0.233209i
$381$	−7.92154e22	−	2.54326e23i	−0.0239896	−	0.0770200i
$382$	3.77869e24	−	8.50603e23i	1.11619	−	0.251261i
$383$	−5.48430e24			−1.58028			−0.790138	−	0.612929i	$-0.789991\pi$
$383$	−5.48430e24			−1.58028			−0.790138	+	0.612929i	$0.789991\pi$
$384$	−9.86740e23	−	3.41793e24i	−0.277368	−	0.960764i
$385$	2.07450e21			0.000568900
$386$	−1.52217e24	+	3.42649e23i	−0.407273	+	0.0916791i
$387$	−2.15786e24	−	3.12792e24i	−0.563339	−	0.816585i
$388$	−7.98498e23	+	3.78681e23i	−0.203410	+	0.0964654i
$389$			3.68660e24i			0.916442i	0.888838	+	0.458221i	$0.151513\pi$
$389$			3.68660e24i			0.916442i	−0.888838	+	0.458221i	$0.848487\pi$
$390$	−3.33856e24	−	5.78571e24i	−0.809927	−	1.40360i
$391$		−	3.34133e24i		−	0.791115i
$392$	3.31514e24	−	2.59551e24i	0.766098	−	0.599799i
$393$	−2.78150e24	+	8.66360e23i	−0.627408	+	0.195420i
$394$	4.35227e22	+	1.93344e23i	0.00958300	+	0.0425712i
$395$	−2.17334e24			−0.467149
$396$	−7.60822e20	+	1.31635e21i	−0.000159654	+	0.000276227i
$397$	4.75450e24			0.974082			0.487041	−	0.873379i	$-0.338076\pi$
$397$	4.75450e24			0.974082			0.487041	+	0.873379i	$0.338076\pi$
$398$	9.22152e23	+	4.09654e24i	0.184465	+	0.819460i
$399$	−2.94355e24	+	9.16834e23i	−0.574949	+	0.179081i
$400$	−2.02888e24	+	2.48273e24i	−0.386978	+	0.473544i
$401$		−	1.08639e24i		−	0.202356i	−0.994868	−	0.101178i	$-0.967739\pi$
$401$		−	1.08639e24i		−	0.202356i	0.994868	−	0.101178i	$-0.0322611\pi$
$402$	−6.02928e22	−	1.04487e23i	−0.0109678	−	0.0190071i
$403$		−	1.06745e25i		−	1.89649i
$404$	4.83842e23	+	1.02025e24i	0.0839616	+	0.177044i
$405$	−7.00131e24	−	2.65935e24i	−1.18674	−	0.450768i
$406$	1.17329e25	−	2.64114e24i	1.94271	−	0.437315i
$407$	−1.24700e21			−0.000201707
$408$	−4.80720e24	−	3.32138e24i	−0.759662	−	0.524864i
$409$	−7.66016e24			−1.18268			−0.591338	−	0.806423i	$-0.701400\pi$
$409$	−7.66016e24			−1.18268			−0.591338	+	0.806423i	$0.701400\pi$
$410$	4.96588e22	−	1.11785e22i	0.00749117	−	0.00168630i
$411$	1.36283e24	+	4.37546e24i	0.200884	+	0.644951i
$412$	5.15803e24	+	1.08764e25i	0.742951	+	1.56661i
$413$		−	1.00098e25i		−	1.40896i
$414$	−4.22492e24	+	4.57639e24i	−0.581186	+	0.629534i
$415$			4.46009e24i			0.599634i
$416$	−4.34509e24	+	8.68853e24i	−0.570969	+	1.14172i
$417$	3.72117e23	+	1.19470e24i	0.0477955	+	0.153450i
$418$	2.39252e20	+	1.06285e21i	3.00387e−5	+	0.000133443i
$419$	−3.13837e24			−0.385186			−0.192593	−	0.981279i	$-0.561690\pi$
$419$	−3.13837e24			−0.385186			−0.192593	+	0.981279i	$0.561690\pi$
$420$	1.09264e25	−	1.00730e25i	1.31102	−	1.20862i
$421$	3.70615e24			0.434753			0.217377	−	0.976088i	$-0.430250\pi$
$421$	3.70615e24			0.434753			0.217377	+	0.976088i	$0.430250\pi$
$422$	1.06463e24	+	4.72949e24i	0.122104	+	0.542432i
$423$	1.07856e25	−	7.44066e24i	1.20951	−	0.834407i
$424$	−7.56131e24	−	9.65775e24i	−0.829128	−	1.05901i
$425$			5.26615e24i			0.564674i
$426$	−6.37889e24	+	3.68085e24i	−0.668889	+	0.385973i
$427$			2.44207e25i			2.50434i
$428$	2.77440e24	−	1.31573e24i	0.278261	−	0.131963i
$429$	3.96390e21	−	1.23464e21i	0.000388847	−	0.000121115i
$430$	1.28048e25	−	2.88242e24i	1.22863	−	0.276571i
$431$	−3.09919e24			−0.290880			−0.145440	−	0.989367i	$-0.546460\pi$
$431$	−3.09919e24			−0.290880			−0.145440	+	0.989367i	$0.546460\pi$
$432$	2.38440e24	+	1.06275e25i	0.218919	+	0.975743i
$433$	−1.37245e25			−1.23271			−0.616355	−	0.787468i	$-0.711391\pi$
$433$	−1.37245e25			−1.23271			−0.616355	+	0.787468i	$0.711391\pi$
$434$	2.31685e25	−	5.21535e24i	2.03585	−	0.458280i
$435$	1.99870e25	−	6.22538e24i	1.71830	−	0.535202i
$436$	1.04263e25	−	4.94457e24i	0.877016	−	0.415917i
$437$			4.46297e24i			0.367325i
$438$	−1.94022e25	+	1.11958e25i	−1.56260	+	0.901675i
$439$		−	1.81655e25i		−	1.43164i	−0.698283	−	0.715822i	$-0.746052\pi$
$439$		−	1.81655e25i		−	1.43164i	0.698283	−	0.715822i	$-0.253948\pi$
$440$	−3.23731e21	−	4.13488e21i	−0.000249680	−	0.000318905i
$441$	−1.06104e25	+	7.31984e24i	−0.800878	+	0.552503i
$442$	3.50396e24	+	1.55659e25i	0.258850	+	1.14991i
$443$	5.94482e24			0.429836			0.214918	−	0.976632i	$-0.431052\pi$
$443$	5.94482e24			0.429836			0.214918	+	0.976632i	$0.431052\pi$
$444$	−6.56801e24	+	6.05497e24i	−0.464831	+	0.428522i
$445$	−7.62783e24			−0.528422
$446$	−5.44606e24	−	2.41934e25i	−0.369319	−	1.64065i
$447$	−7.53445e23	−	2.41898e24i	−0.0500185	−	0.160587i
$448$	−2.09809e25	−	5.18576e24i	−1.36359	−	0.337032i
$449$		−	5.95675e24i		−	0.379026i	−0.981878	−	0.189513i	$-0.939309\pi$
$449$		−	5.95675e24i		−	0.379026i	0.981878	−	0.189513i	$-0.0606909\pi$
$450$	6.65874e24	−	7.21268e24i	0.414833	−	0.449343i
$451$			3.16368e19i			1.92981e-6i
$452$	8.34539e24	+	1.75974e25i	0.498462	+	1.05107i
$453$	1.55702e24	+	4.99891e24i	0.0910672	+	0.292377i
$454$	−6.46687e24	+	1.45573e24i	−0.370394	+	0.0833776i
$455$	−4.05809e25			−2.27622
$456$	6.42092e24	+	4.43633e24i	0.352721	+	0.243701i
$457$	2.63035e25			1.41517			0.707587	−	0.706626i	$-0.249784\pi$
$457$	2.63035e25			1.41517			0.707587	+	0.706626i	$0.249784\pi$
$458$	1.65688e25	−	3.72972e24i	0.873109	−	0.196541i
$459$	1.40777e25	+	1.10379e25i	0.726625	+	0.569725i
$460$	−9.21816e24	−	1.94377e25i	−0.466063	−	0.982756i
$461$		−	1.31846e25i		−	0.652991i	−0.945199	−	0.326495i	$-0.894132\pi$
$461$		−	1.31846e25i		−	0.652991i	0.945199	−	0.326495i	$-0.105868\pi$
$462$	4.61641e21	+	8.00022e21i	0.000223978	+	0.000388153i
$463$			1.17965e24i			0.0560706i	0.999607	+	0.0280353i	$0.00892508\pi$
$463$			1.17965e24i			0.0560706i	−0.999607	+	0.0280353i	$0.991075\pi$
$464$	−2.35739e25	−	1.92644e25i	−1.09777	−	0.897089i
$465$	3.94674e25	−	1.22930e25i	1.80067	−	0.560859i
$466$	1.23295e24	+	5.47723e24i	0.0551163	+	0.244847i
$467$	−1.27273e25			−0.557475			−0.278737	−	0.960367i	$-0.589916\pi$
$467$	−1.27273e25			−0.557475			−0.278737	+	0.960367i	$0.589916\pi$
$468$	1.48831e25	−	2.57501e25i	0.638787	−	1.10521i
$469$	−7.32871e23			−0.0308238
$470$	9.93905e24	+	4.41529e25i	0.409652	+	1.81983i
$471$	−1.55082e25	+	4.83037e24i	−0.626416	+	0.195111i
$472$	−1.99515e25	+	1.56206e25i	−0.789816	+	0.618369i
$473$			8.15770e21i			0.000316510i
$474$	−4.83637e24	−	8.38141e24i	−0.183918	−	0.318730i
$475$		−	7.03393e24i		−	0.262186i
$476$	−3.20730e25	+	1.52103e25i	−1.17185	+	0.555742i
$477$	2.13243e25	+	3.09105e25i	0.763749	+	1.10709i
$478$	−3.94603e24	+	8.88272e23i	−0.138546	+	0.0311875i
$479$	−1.58667e25			−0.546135			−0.273067	−	0.961995i	$-0.588038\pi$
$479$	−1.58667e25			−0.546135			−0.273067	+	0.961995i	$0.588038\pi$
$480$	−3.71284e25	−	6.05942e24i	−1.25289	−	0.204474i
$481$	2.43936e25			0.807046
$482$	5.52749e24	−	1.24427e24i	0.179300	−	0.0403614i
$483$	1.12524e25	+	3.61265e25i	0.357888	+	1.14902i
$484$	−2.89721e25	+	1.37398e25i	−0.903543	+	0.428497i
$485$			9.34527e24i			0.285789i
$486$	−5.32445e24	−	3.29182e25i	−0.159672	−	0.987170i
$487$		−	2.17055e25i		−	0.638329i	−0.947699	−	0.319165i	$-0.896598\pi$
$487$		−	2.17055e25i		−	0.638329i	0.947699	−	0.319165i	$-0.103402\pi$
$488$	4.86753e25	−	3.81092e25i	1.40385	−	1.09911i
$489$	−5.80508e24	−	1.86376e25i	−0.164200	−	0.527175i
$490$	−9.77766e24	−	4.34359e25i	−0.271251	−	1.20500i
$491$	5.61079e25			1.52669			0.763343	−	0.645994i	$-0.223557\pi$
$491$	5.61079e25			1.52669			0.763343	+	0.645994i	$0.223557\pi$
$492$	1.53616e23	+	1.66632e23i	0.00409985	+	0.00444723i
$493$	−5.00027e25			−1.30902
$494$	−4.68020e24	−	2.07912e25i	−0.120187	−	0.533916i
$495$	9.12981e21	+	1.32341e22i	0.000229992	+	0.000333383i
$496$	−4.65502e25	−	3.80406e25i	−1.15039	−	0.940095i
$497$			4.47414e25i			1.08474i
$498$	−1.72002e25	+	9.92511e24i	−0.409123	+	0.236079i
$499$		−	4.70657e25i		−	1.09837i	−0.835700	−	0.549186i	$-0.814938\pi$
$499$		−	4.70657e25i		−	1.09837i	0.835700	−	0.549186i	$-0.185062\pi$
$500$	−9.22823e24	−	1.94589e25i	−0.211302	−	0.445558i
$501$	3.21908e24	−	1.00265e24i	0.0723225	−	0.0225264i
$502$	3.78603e25	−	8.52254e24i	0.834638	−	0.187881i
$503$	−1.83438e25			−0.396821			−0.198410	−	0.980119i	$-0.563578\pi$
$503$	−1.83438e25			−0.396821			−0.198410	+	0.980119i	$0.563578\pi$
$504$	6.31608e25	+	1.97219e25i	1.34078	+	0.418658i
$505$	1.19405e25			0.248745
$506$	1.30444e22	−	2.93636e21i	0.000266683	−	6.00316e-5i
$507$	−2.99562e25	+	9.33051e24i	−0.601050	+	0.187210i
$508$	1.75535e24	+	3.70138e24i	0.0345667	+	0.0728884i
$509$		−	6.09000e25i		−	1.17706i	−0.808475	−	0.588530i	$-0.799707\pi$
$509$		−	6.09000e25i		−	1.17706i	0.808475	−	0.588530i	$-0.200293\pi$
$510$	−5.35172e25	+	3.08813e25i	−1.01526	+	0.585840i
$511$			1.36087e26i			2.53406i
$512$	2.24051e25	+	4.99116e25i	0.409526	+	0.912298i
$513$	−1.88034e25	−	1.47432e25i	−0.337381	−	0.264530i
$514$	1.47038e25	+	6.53196e25i	0.258988	+	1.15052i
$515$	1.27292e26			2.20107
$516$	3.96107e25	+	4.29669e25i	0.672419	+	0.729394i
$517$	−2.81291e22			−0.000468808
$518$	1.19182e25	+	5.29451e25i	0.195020	+	0.866349i
$519$	−2.98883e25	−	9.59583e25i	−0.480188	−	1.54167i
$520$	6.33276e25	+	8.08856e25i	0.998990	+	1.27597i
$521$			8.86506e25i			1.37317i	0.727051	+	0.686584i	$0.240890\pi$
$521$			8.86506e25i			1.37317i	−0.727051	+	0.686584i	$0.759110\pi$
$522$	6.84853e25	+	6.32256e25i	1.04166	+	0.961663i
$523$		−	2.41404e25i		−	0.360561i	−0.983615	−	0.180280i	$-0.942299\pi$
$523$		−	2.41404e25i		−	0.360561i	0.983615	−	0.180280i	$-0.0577005\pi$
$524$	4.04811e25	−	1.91978e25i	0.593752	−	0.281582i
$525$	−1.77345e25	−	5.69377e25i	−0.255450	−	0.820138i
$526$	5.54084e25	−	1.24727e25i	0.783810	−	0.176440i
$527$	−9.87381e25			−1.37178
$528$	8.74197e21	−	2.16860e22i	0.000119285	−	0.000295908i
$529$	−1.98410e25			−0.265910
$530$	−1.26539e26	+	2.84845e25i	−1.66572	+	0.374962i
$531$	6.38566e25	−	4.40529e25i	0.825673	−	0.569609i
$532$	4.28395e25	−	2.03163e25i	0.544107	−	0.258038i
$533$		−	6.18873e23i		−	0.00772134i
$534$	−1.69744e25	−	2.94165e25i	−0.208042	−	0.360536i
$535$		−	3.24703e25i		−	0.390954i
$536$	1.14366e24	+	1.46076e24i	0.0135280	+	0.0172787i
$537$	−3.15787e25	+	9.83589e24i	−0.366977	+	0.114303i
$538$	−2.31417e25	−	1.02804e26i	−0.264219	−	1.17376i
$539$	2.76723e22			0.000310421
$540$	1.12347e26	+	2.53734e25i	1.23828	+	0.279665i
$541$	−6.84884e25			−0.741725			−0.370862	−	0.928688i	$-0.620938\pi$
$541$	−6.84884e25			−0.741725			−0.370862	+	0.928688i	$0.620938\pi$
$542$	−2.38793e25	−	1.06080e26i	−0.254113	−	1.12887i
$543$	−1.29356e26	+	4.02907e25i	−1.35265	+	0.421314i
$544$	8.03680e25	+	4.01916e25i	0.825835	+	0.412996i
$545$		−	1.22025e26i		−	1.23220i
$546$	−9.03054e25	−	1.56499e26i	−0.896156	−	1.55303i
$547$			4.11723e25i			0.401537i	0.979639	+	0.200768i	$0.0643438\pi$
$547$			4.11723e25i			0.401537i	−0.979639	+	0.200768i	$0.935656\pi$
$548$	−3.01993e25	−	6.36791e25i	−0.289455	−	0.610354i
$549$	−1.55790e26	+	1.07475e26i	−1.46758	+	1.01244i
$550$	−2.05588e22	+	4.62790e21i	−0.000190350	+	4.28488e-5i
$551$	6.67880e25			0.607797
$552$	5.44475e25	−	7.88046e25i	0.487031	−	0.704905i
$553$	−5.87870e25			−0.516884
$554$	−1.78113e26	+	4.00942e25i	−1.53941	+	0.346529i
$555$	2.80922e25	+	9.01916e25i	0.238672	+	0.766272i
$556$	−8.24580e24	−	1.73874e25i	−0.0688688	−	0.145219i
$557$		−	1.60444e26i		−	1.31734i	−0.752431	−	0.658671i	$-0.771119\pi$
$557$		−	1.60444e26i		−	1.31734i	0.752431	−	0.658671i	$-0.228881\pi$
$558$	1.35235e26	+	1.24849e26i	1.09160	+	1.00776i
$559$		−	1.59579e26i		−	1.26638i
$560$	−1.44618e26	+	1.76968e26i	−1.12833	+	1.38073i
$561$	−1.14203e22	−	3.66657e22i	−8.76055e−5	−	0.000281263i
$562$	2.04091e25	+	9.06648e25i	0.153932	+	0.683823i
$563$	1.71090e26			1.26881			0.634403	−	0.773002i	$-0.281246\pi$
$563$	1.71090e26			1.26881			0.634403	+	0.773002i	$0.281246\pi$
$564$	−1.48157e26	+	1.36584e26i	−1.08036	+	0.995974i
$565$	2.05952e26			1.47675
$566$	−4.58012e25	−	2.03466e26i	−0.322939	−	1.43461i
$567$	−1.89380e26	−	7.19333e25i	−1.31309	−	0.498759i
$568$	8.91784e25	−	6.98202e25i	0.608066	−	0.476071i
$569$			1.43332e26i			0.961115i	0.876963	+	0.480558i	$0.159566\pi$
$569$			1.43332e26i			0.961115i	−0.876963	+	0.480558i	$0.840434\pi$
$570$	7.14823e25	−	4.12478e25i	0.471398	−	0.272013i
$571$			8.93301e25i			0.579368i	0.957122	+	0.289684i	$0.0935502\pi$
$571$			8.93301e25i			0.579368i	−0.957122	+	0.289684i	$0.906450\pi$
$572$	−5.76894e22	+	2.73587e22i	−0.000367988	+	0.000174515i
$573$	1.74115e26	−	5.42319e25i	1.09236	−	0.340241i
$574$	1.34323e24	−	3.02368e23i	0.00828872	−	0.00186583i
$575$	−8.63282e25			−0.523972
$576$	−5.92545e25	−	1.56668e26i	−0.353759	−	0.935337i
$577$	1.67041e26			0.980961			0.490481	−	0.871452i	$-0.336821\pi$
$577$	1.67041e26			0.980961			0.490481	+	0.871452i	$0.336821\pi$
$578$	−2.48982e25	+	5.60472e24i	−0.143831	+	0.0323772i
$579$	−7.01389e25	+	2.18463e25i	−0.398577	+	0.124146i
$580$	−2.90884e26	+	1.37949e26i	−1.62612	+	0.771175i
$581$			1.20642e26i			0.663474i
$582$	−3.60397e25	+	2.07962e25i	−0.194990	+	0.112516i
$583$		−	8.06155e22i		−	0.000429109i
$584$	2.71248e26	−	2.12367e26i	1.42051	−	1.11215i
$585$	−1.78596e26	−	2.58882e26i	−0.920217	−	1.33389i
$586$	5.52178e25	+	2.45298e26i	0.279931	+	1.24356i
$587$	1.96328e26			0.979311			0.489656	−	0.871916i	$-0.337122\pi$
$587$	1.96328e26			0.979311			0.489656	+	0.871916i	$0.337122\pi$
$588$	1.45751e26	−	1.34366e26i	0.715363	−	0.659485i
$589$	1.31883e26			0.636934
$590$	5.88448e25	+	2.61410e26i	0.279649	+	1.24231i
$591$	2.77488e24	+	8.90891e24i	0.0129766	+	0.0416623i
$592$	8.69312e25	−	1.06378e26i	0.400055	−	0.489546i
$593$			3.26171e26i			1.47715i	0.674170	+	0.738577i	$0.264502\pi$
$593$			3.26171e26i			1.47715i	−0.674170	+	0.738577i	$0.735498\pi$
$594$	−3.07200e22	+	6.46588e22i	−0.000136915	+	0.000288175i
$595$			3.75369e26i			1.64644i
$596$	1.66957e25	+	3.52051e25i	0.0720718	+	0.151973i
$597$	5.87936e25	+	1.88761e26i	0.249790	+	0.801964i
$598$	−2.55172e26	+	5.74406e25i	−1.06702	+	0.240192i
$599$	−1.67035e26			−0.687468			−0.343734	−	0.939067i	$-0.611692\pi$
$599$	−1.67035e26			−0.687468			−0.343734	+	0.939067i	$0.611692\pi$
$600$	−8.58129e25	+	1.24201e26i	−0.347629	+	0.503140i
$601$	−1.82808e26			−0.728932			−0.364466	−	0.931217i	$-0.618749\pi$
$601$	−1.82808e26			−0.728932			−0.364466	+	0.931217i	$0.618749\pi$
$602$	3.46359e26	−	7.79672e25i	1.35944	−	0.306017i
$603$	−3.22535e24	−	4.67529e24i	−0.0124613	−	0.0180632i
$604$	−3.45023e25	−	7.27526e25i	−0.131219	−	0.276693i
$605$			3.39077e26i			1.26947i
$606$	2.65714e25	+	4.60482e25i	0.0979321	+	0.169716i
$607$		−	5.20544e26i		−	1.88871i	−0.328933	−	0.944353i	$-0.606689\pi$
$607$		−	5.20544e26i		−	1.88871i	0.328933	−	0.944353i	$-0.393311\pi$
$608$	−1.07347e26	−	5.36835e25i	−0.383446	−	0.191759i
$609$	5.40631e26	−	1.68391e26i	1.90124	−	0.592183i
$610$	−1.43563e26	−	6.37758e26i	−0.497059	−	2.20812i
$611$	5.50255e26			1.87574
$612$	−2.38186e26	−	1.37667e26i	−0.799424	−	0.462051i
$613$	2.77002e26			0.915396			0.457698	−	0.889108i	$-0.348674\pi$
$613$	2.77002e26			0.915396			0.457698	+	0.889108i	$0.348674\pi$
$614$	−1.85302e25	−	8.23179e25i	−0.0602948	−	0.267852i
$615$	2.28818e24	−	7.12705e23i	0.00733124	−	0.00228348i
$616$	−8.75665e22	−	1.11845e23i	−0.000276262	−	0.000352858i
$617$		−	6.18374e26i		−	1.92106i	−0.278169	−	0.960532i	$-0.589727\pi$
$617$		−	6.18374e26i		−	1.92106i	0.278169	−	0.960532i	$-0.410273\pi$
$618$	2.83266e26	+	4.90899e26i	0.866571	+	1.50176i
$619$			2.78796e26i			0.839897i	0.907548	+	0.419948i	$0.137952\pi$
$619$			2.78796e26i			0.839897i	−0.907548	+	0.419948i	$0.862048\pi$
$620$	−5.74396e26	+	2.72402e26i	−1.70408	+	0.808145i
$621$	−1.80944e26	+	2.30776e26i	−0.528658	+	0.674248i
$622$	−4.93367e26	+	1.11059e26i	−1.41958	+	0.319556i
$623$	−2.06327e26			−0.584681
$624$	−1.71009e26	+	4.24217e26i	−0.477271	+	1.18395i
$625$	−4.50220e26			−1.23756
$626$	4.23807e25	−	9.54011e24i	0.114739	−	0.0258284i
$627$	1.52540e22	+	4.89739e22i	4.06764e−5	+	0.000130594i
$628$	2.25702e26	−	1.07037e26i	0.592813	−	0.281136i
$629$		−	2.25638e26i		−	0.583756i
$630$	4.74632e26	−	5.14117e26i	1.20955	−	1.31017i
$631$			2.48783e26i			0.624514i	0.949998	+	0.312257i	$0.101085\pi$
$631$			2.48783e26i			0.624514i	−0.949998	+	0.312257i	$0.898915\pi$
$632$	9.17387e25	+	1.17174e26i	0.226851	+	0.289747i
$633$	6.78777e25	+	2.17926e26i	0.165345	+	0.530852i
$634$	−6.99915e25	−	3.10928e26i	−0.167957	−	0.746125i
$635$	4.33194e25			0.102407
$636$	−3.91438e26	−	4.24605e26i	−0.911634	−	0.988877i
$637$	−5.41320e26			−1.24202
$638$	−4.39425e22	−	1.95209e23i	−9.93318e−5	−	0.000441268i
$639$	−2.85424e26	+	1.96906e26i	−0.635671	+	0.438532i
$640$	5.78412e26	+	1.20875e25i	1.26919	+	0.0265232i
$641$		−	3.31518e26i		−	0.716730i	−0.933581	−	0.358365i	$-0.883334\pi$
$641$		−	3.31518e26i		−	0.716730i	0.933581	−	0.358365i	$-0.116666\pi$
$642$	1.25221e26	−	7.22568e25i	0.266743	−	0.153920i
$643$		−	3.39062e26i		−	0.711665i	−0.934550	−	0.355832i	$-0.884197\pi$
$643$		−	3.39062e26i		−	0.711665i	0.934550	−	0.355832i	$-0.115803\pi$
$644$	−2.49344e26	−	5.25774e26i	−0.515683	−	1.08739i
$645$	5.90020e26	−	1.83775e26i	1.20240	−	0.374514i
$646$	−1.92316e26	+	4.32914e25i	−0.386195	+	0.0869345i
$647$	−9.61083e26			−1.90182			−0.950912	−	0.309463i	$-0.899851\pi$
$647$	−9.61083e26			−1.90182			−0.950912	+	0.309463i	$0.899851\pi$
$648$	1.52155e26	+	4.89725e26i	0.296704	+	0.954969i
$649$	−1.66540e23			−0.000320032
$650$	4.02168e26	−	9.05301e25i	0.761607	−	0.171442i
$651$	1.06756e27	−	3.32515e26i	1.99238	−	0.620572i
$652$	1.28636e26	+	2.71245e26i	0.236597	+	0.498896i
$653$			4.95688e26i			0.898531i	0.893398	+	0.449265i	$0.148314\pi$
$653$			4.95688e26i			0.898531i	−0.893398	+	0.449265i	$0.851686\pi$
$654$	4.70584e26	−	2.71544e26i	0.840714	−	0.485122i
$655$		−	4.73774e26i		−	0.834216i
$656$	−2.69883e24	−	2.20547e24i	−0.00468369	−	0.00382749i
$657$	−8.68154e26	+	5.98915e26i	−1.48500	+	1.02446i
$658$	2.68843e26	+	1.19430e27i	0.453266	+	2.01357i
$659$	−1.20198e27			−1.99750			−0.998749	−	0.0500136i	$-0.984074\pi$
$659$	−1.20198e27			−1.99750			−0.998749	+	0.0500136i	$0.984074\pi$
$660$	−1.67591e23	−	1.81791e23i	−0.000274525	−	0.000297786i
$661$	−2.59952e26			−0.419739			−0.209870	−	0.977729i	$-0.567304\pi$
$661$	−2.59952e26			−0.419739			−0.209870	+	0.977729i	$0.567304\pi$
$662$	1.91677e26	+	8.51500e26i	0.305084	+	1.35529i
$663$	2.23402e26	+	7.17247e26i	0.350517	+	1.12536i
$664$	2.40462e26	−	1.88265e26i	0.371921	−	0.291187i
$665$		−	5.01376e26i		−	0.764465i
$666$	−2.85307e26	+	3.09041e26i	−0.428852	+	0.464528i
$667$		−	8.19696e26i		−	1.21467i
$668$	−4.68495e25	+	2.22180e25i	−0.0684429	+	0.0324584i
$669$	−3.47225e26	−	1.11479e27i	−0.500106	−	1.60562i
$670$	1.91392e25	−	4.30834e24i	0.0271778	−	0.00611786i
$671$	4.06304e23			0.000568837
$672$	−1.00429e27	−	1.63902e26i	−1.38628	−	0.226244i
$673$	1.96867e26			0.267935			0.133968	−	0.990986i	$-0.457228\pi$
$673$	1.96867e26			0.267935			0.133968	+	0.990986i	$0.457228\pi$
$674$	3.64902e26	−	8.21414e25i	0.489675	−	0.110228i
$675$	2.85180e26	−	3.63718e26i	0.377340	−	0.481259i
$676$	4.35973e26	−	2.06756e26i	0.568808	−	0.269752i
$677$		−	6.59183e26i		−	0.848035i	−0.905654	−	0.424018i	$-0.860619\pi$
$677$		−	6.59183e26i		−	0.848035i	0.905654	−	0.424018i	$-0.139381\pi$
$678$	4.58309e26	+	7.94247e26i	0.581401	+	1.00757i
$679$			2.52782e26i			0.316216i
$680$	7.48183e26	−	5.85773e26i	0.922940	−	0.722594i
$681$	−2.97981e26	+	9.28128e25i	−0.362486	+	0.112904i
$682$	−8.67713e22	−	3.85470e23i	−0.000104094	−	0.000462423i
$683$	1.37366e27			1.62511			0.812554	−	0.582886i	$-0.198077\pi$
$683$	1.37366e27			1.62511			0.812554	+	0.582886i	$0.198077\pi$
$684$	3.18142e26	+	1.83880e26i	0.371183	+	0.214536i
$685$	−7.45273e26			−0.857541
$686$	7.34829e24	+	3.26438e25i	0.00833887	+	0.0370443i
$687$	7.63458e26	−	2.37796e26i	0.854468	−	0.266143i
$688$	−6.95906e26	−	5.68691e26i	−0.768175	−	0.627749i
$689$			1.57699e27i			1.71690i
$690$	−5.06239e26	−	8.77310e26i	−0.543612	−	0.942077i
$691$			1.46759e27i			1.55440i	0.629253	+	0.777201i	$0.283361\pi$
$691$			1.46759e27i			1.55440i	−0.629253	+	0.777201i	$0.716639\pi$
$692$	6.62300e26	+	1.39655e27i	0.691906	+	1.45897i
$693$	2.46954e23	+	3.57971e23i	0.000254478	+	0.000368877i
$694$	−1.02239e26	+	2.30144e25i	−0.103920	+	0.0233930i
$695$	−2.03494e26			−0.204031
$696$	−1.17931e27	−	8.14803e26i	−1.16638	−	0.805870i
$697$	−5.72450e24			−0.00558504
$698$	5.58639e26	−	1.25753e26i	0.537657	−	0.121029i
$699$	7.86094e25	+	2.52380e26i	0.0746348	+	0.239619i
$700$	3.92982e26	+	8.28654e26i	0.368079	+	0.776143i
$701$		−	2.82602e25i		−	0.0261128i	−0.999915	−	0.0130564i	$-0.995844\pi$
$701$		−	2.82602e25i		−	0.0261128i	0.999915	−	0.0130564i	$-0.00415610\pi$
$702$	6.00939e26	−	1.26484e27i	0.547807	−	1.15301i
$703$			3.01382e26i			0.271046i
$704$	−8.62791e22	+	3.49074e23i	−7.65536e−5	+	0.000309726i
$705$	6.33684e26	+	2.03448e27i	0.554723	+	1.78097i
$706$	−5.79111e25	−	2.57263e26i	−0.0500170	−	0.222194i
$707$	3.22981e26			0.275228
$708$	−8.77171e26	+	8.08654e26i	−0.737511	+	0.679903i
$709$	1.61811e27			1.34236			0.671181	−	0.741293i	$-0.265787\pi$
$709$	1.61811e27			1.34236			0.671181	+	0.741293i	$0.265787\pi$
$710$	−2.63022e26	−	1.16844e27i	−0.215297	−	0.956429i
$711$	−2.58720e26	−	3.75027e26i	−0.208963	−	0.302901i
$712$	3.21978e26	+	4.11249e26i	0.256606	+	0.327752i
$713$		−	1.61862e27i		−	1.27290i
$714$	−1.44760e27	+	8.35315e26i	−1.12335	+	0.648212i
$715$			6.75172e23i			0.000517020i
$716$	4.59587e26	−	2.17955e26i	0.347291	−	0.164700i
$717$	−1.81825e26	+	5.66336e25i	−0.135588	+	0.0422320i
$718$	−4.10060e26	+	9.23065e25i	−0.301762	+	0.0679282i
$719$	−1.73484e27			−1.25990			−0.629948	−	0.776638i	$-0.716924\pi$
$719$	−1.73484e27			−1.25990			−0.629948	+	0.776638i	$0.716924\pi$
$720$	−1.76541e27	−	1.43742e26i	−1.26528	−	0.103021i
$721$	3.44316e27			2.43541
$722$	−1.14068e27	+	2.56774e26i	−0.796272	+	0.179245i
$723$	2.54696e26	−	7.93308e25i	0.175472	−	0.0546547i
$724$	1.88260e27	−	8.92807e26i	1.28009	−	0.607073i
$725$			1.29189e27i			0.866994i
$726$	−1.30764e27	+	7.54554e26i	−0.866143	+	0.499795i
$727$			4.19437e26i			0.274214i	0.990556	+	0.137107i	$0.0437804\pi$
$727$			4.19437e26i			0.274214i	−0.990556	+	0.137107i	$0.956220\pi$
$728$	1.71296e27	+	2.18789e27i	1.10535	+	1.41181i
$729$	−3.74564e26	−	1.52471e27i	−0.238569	−	0.971125i
$730$	−8.00016e26	−	3.55397e27i	−0.502958	−	2.23432i
$731$	−1.47609e27			−0.916006
$732$	2.14002e27	−	1.97286e27i	1.31088	−	1.20848i
$733$	−9.43357e26			−0.570411			−0.285206	−	0.958466i	$-0.592062\pi$
$733$	−9.43357e26			−0.570411			−0.285206	+	0.958466i	$0.592062\pi$
$734$	1.15924e26	+	5.14979e26i	0.0691931	+	0.307381i
$735$	−6.23394e26	−	2.00145e27i	−0.367310	−	1.17927i
$736$	−6.58863e26	+	1.31747e27i	−0.383227	+	0.766308i
$737$			1.21933e22i			7.00131e-6i
$738$	7.84046e24	+	7.23831e24i	0.00444433	+	0.00410300i
$739$			8.35344e26i			0.467459i	0.972302	+	0.233729i	$0.0750929\pi$
$739$			8.35344e26i			0.467459i	−0.972302	+	0.233729i	$0.924907\pi$
$740$	−6.22499e26	−	1.31262e27i	−0.343904	−	0.725167i
$741$	−2.98396e26	−	9.58018e26i	−0.162750	−	0.522517i
$742$	−3.42277e27	+	7.70482e26i	−1.84306	+	0.414883i
$743$	2.64337e26			0.140528			0.0702642	−	0.997528i	$-0.477616\pi$
$743$	2.64337e26			0.140528			0.0702642	+	0.997528i	$0.477616\pi$
$744$	−2.32872e27	−	1.60896e27i	−1.22229	−	0.844503i
$745$	4.12026e26			0.213520
$746$	−2.02028e27	+	4.54775e26i	−1.03370	+	0.232690i
$747$	−7.69623e26	+	5.30941e26i	−0.388805	+	0.268226i
$748$	2.53065e23	+	5.33621e23i	0.000126231	+	0.000266175i
$749$		−	8.78296e26i		−	0.432577i
$750$	−5.06792e26	−	8.78268e26i	−0.246461	−	0.427115i
$751$		−	7.40863e26i		−	0.355761i	−0.984052	−	0.177881i	$-0.943076\pi$
$751$		−	7.40863e26i		−	0.355761i	0.984052	−	0.177881i	$-0.0569241\pi$
$752$	1.96094e27	−	2.39959e27i	0.929810	−	1.13781i
$753$	1.74453e27	−	5.43372e26i	0.816819	−	0.254416i
$754$	8.59595e26	+	3.81864e27i	0.397435	+	1.76555i
$755$	−8.51466e26			−0.388751
$756$	3.03888e27	+	6.86330e26i	1.37011	+	0.309440i
$757$	4.40332e26			0.196051			0.0980256	−	0.995184i	$-0.468747\pi$
$757$	4.40332e26			0.196051			0.0980256	+	0.995184i	$0.468747\pi$
$758$	−7.66476e26	−	3.40497e27i	−0.337009	−	1.49712i
$759$	6.01062e23	−	1.87214e23i	0.000260989	−	8.12908e-5i
$760$	−9.99339e26	+	7.82410e26i	−0.428533	+	0.335510i
$761$			9.18035e26i			0.388781i	0.980924	+	0.194391i	$0.0622729\pi$
$761$			9.18035e26i			0.388781i	−0.980924	+	0.194391i	$0.937727\pi$
$762$	9.63993e25	+	1.67060e26i	0.0403183	+	0.0698714i
$763$		−	3.30067e27i		−	1.36339i
$764$	−2.53401e27	+	1.20173e27i	−1.03377	+	0.490254i
$765$	−2.39463e27	+	1.65199e27i	−0.964840	+	0.665616i
$766$	3.87412e27	−	8.72084e26i	1.54170	−	0.347044i
$767$	3.25782e27			1.28048
$768$	1.24053e27	+	2.25752e27i	0.481590	+	0.876397i
$769$	−1.39213e27			−0.533803			−0.266902	−	0.963724i	$-0.586000\pi$
$769$	−1.39213e27			−0.533803			−0.266902	+	0.963724i	$0.586000\pi$
$770$	−1.46543e24	+	3.29875e23i	−0.000555012	+	0.000124936i
$771$	9.37469e26	+	3.00980e27i	0.350704	+	1.12596i
$772$	1.02078e27	−	4.84096e26i	0.377196	−	0.178882i
$773$			3.07759e27i			1.12333i	0.827366	+	0.561663i	$0.189838\pi$
$773$			3.07759e27i			1.12333i	−0.827366	+	0.561663i	$0.810162\pi$
$774$	2.02170e27	+	1.86643e27i	0.728917	+	0.672936i
$775$			2.55105e27i			0.908557i
$776$	5.03844e26	−	3.94473e26i	0.177260	−	0.138781i
$777$	7.59870e26	+	2.43961e27i	0.264082	+	0.847853i
$778$	−5.86223e26	−	2.60422e27i	−0.201260	−	0.894070i
$779$	7.64615e24			0.00259321
$780$	3.27838e27	+	3.55615e27i	1.09840	+	1.19147i
$781$	7.44394e23			0.000246387
$782$	5.31319e26	+	2.36032e27i	0.173737	+	0.771802i
$783$	3.45354e27	+	2.70782e27i	1.11565	+	0.874748i
$784$	−1.92909e27	+	2.36063e27i	−0.615674	+	0.753399i
$785$		−	2.64151e27i		−	0.832897i
$786$	1.82709e27	−	1.05430e27i	0.569175	−	0.328434i
$787$			1.17722e27i			0.362323i	0.983453	+	0.181162i	$0.0579857\pi$
$787$			1.17722e27i			0.362323i	−0.983453	+	0.181162i	$0.942014\pi$
$788$	−6.14889e25	−	1.29657e26i	−0.0186981	−	0.0394274i
$789$	2.55311e27	−	7.95223e26i	0.767075	−	0.238923i
$790$	1.53525e27	−	3.45592e26i	0.455745	−	0.102590i
$791$	5.57083e27			1.63397
$792$	3.28127e23	−	1.05085e24i	9.50940e−5	−	0.000304545i
$793$	−7.94805e27			−2.27596
$794$	−3.35859e27	+	7.56035e26i	−0.950302	+	0.213918i
$795$	−5.83066e27	+	1.81609e27i	−1.63016	+	0.507749i
$796$	−1.30282e27	−	2.74716e27i	−0.359923	−	0.758945i
$797$		−	4.60115e27i		−	1.25606i	−0.778187	−	0.628032i	$-0.783861\pi$
$797$		−	4.60115e27i		−	1.25606i	0.778187	−	0.628032i	$-0.216139\pi$
$798$	1.93354e27	−	1.11572e27i	0.521585	−	0.300973i
$799$		−	5.08980e27i		−	1.35677i
$800$	1.03841e27	−	2.07643e27i	0.273536	−	0.546968i
$801$	−9.08039e26	−	1.31624e27i	−0.236372	−	0.342631i
$802$	1.72752e26	+	7.67429e26i	0.0444393	+	0.197416i
$803$	2.26417e24			0.000575587
$804$	5.92059e25	+	6.42224e25i	0.0148742	+	0.0161345i
$805$	−6.15343e27			−1.52777
$806$	1.69740e27	+	7.54049e27i	0.416488	+	1.85019i
$807$	−1.47545e27	−	4.73702e27i	−0.357788	−	1.14870i
$808$	−5.04020e26	−	6.43764e26i	−0.120793	−	0.154283i
$809$		−	3.58857e26i		−	0.0849984i	−0.999097	−	0.0424992i	$-0.986468\pi$
$809$		−	3.58857e26i		−	0.0849984i	0.999097	−	0.0424992i	$-0.0135320\pi$
$810$	5.36861e27	+	7.65258e26i	1.25677	+	0.179143i
$811$		−	4.33582e27i		−	1.00317i	−0.865109	−	0.501583i	$-0.832751\pi$
$811$		−	4.33582e27i		−	1.00317i	0.865109	−	0.501583i	$-0.167249\pi$
$812$	−7.86817e27	+	3.73141e27i	−1.79925	+	0.853279i
$813$	−1.52247e27	−	4.88799e27i	−0.344103	−	1.10476i
$814$	8.80884e23	−	1.98291e23i	0.000196783	−	4.42968e-5i
$815$	3.17454e27			0.700944
$816$	3.92396e27	+	1.58181e27i	0.856383	+	0.345222i
$817$	1.97160e27			0.425313
$818$	5.41114e27	−	1.21808e27i	1.15381	−	0.259727i
$819$	−4.83086e27	−	7.00255e27i	−1.01819	−	1.47591i
$820$	−3.33015e25	+	1.57930e25i	−0.00693797	+	0.00329027i
$821$			5.12796e27i			1.05605i	0.849229	+	0.528025i	$0.177067\pi$
$821$			5.12796e27i			1.05605i	−0.849229	+	0.528025i	$0.822933\pi$
$822$	−1.65847e27	−	2.87412e27i	−0.337618	−	0.585090i
$823$			6.26001e27i			1.25973i	0.776706	+	0.629864i	$0.216889\pi$
$823$			6.26001e27i			1.25973i	−0.776706	+	0.629864i	$0.783111\pi$
$824$	−5.37314e27	−	6.86288e27i	−1.06886	−	1.36521i
$825$	−9.47312e23	+	2.95061e23i	−0.000186286	+	5.80229e-5i
$826$	1.59170e27	+	7.07093e27i	0.309422	+	1.37457i
$827$	−1.47904e27			−0.284235			−0.142117	−	0.989850i	$-0.545391\pi$
$827$	−1.47904e27			−0.284235			−0.142117	+	0.989850i	$0.545391\pi$
$828$	2.25677e27	−	3.90459e27i	0.428746	−	0.741800i
$829$	4.98144e27			0.935593			0.467797	−	0.883836i	$-0.345048\pi$
$829$	4.98144e27			0.935593			0.467797	+	0.883836i	$0.345048\pi$
$830$	−7.09218e26	−	3.15061e27i	−0.131686	−	0.584996i
$831$	−8.20712e27	+	2.55629e27i	−1.50654	+	0.469246i
$832$	1.68778e27	−	6.82852e27i	0.306297	−	1.23924i
$833$			5.00715e27i			0.898386i
$834$	−4.52839e26	−	7.84769e26i	−0.0803279	−	0.139208i
$835$			5.48306e26i			0.0961616i
$836$	−3.38016e23	−	7.12751e23i	−5.86108e−5	−	0.000123588i
$837$	6.81956e27	+	5.34701e27i	1.16913	+	0.916683i
$838$	2.21695e27	−	4.99046e26i	0.375783	−	0.0845906i
$839$	−3.55811e27			−0.596323			−0.298161	−	0.954516i	$-0.596373\pi$
$839$	−3.55811e27			−0.596323			−0.298161	+	0.954516i	$0.596373\pi$
$840$	−6.11670e27	+	8.85301e27i	−1.01359	+	1.46703i
$841$	−6.16344e27			−1.00986
$842$	−2.61803e27	+	5.89331e26i	−0.424140	+	0.0954761i
$843$	1.30122e27	+	4.17766e27i	0.208444	+	0.669224i
$844$	−1.50411e27	−	3.17162e27i	−0.238247	−	0.502375i
$845$		−	5.10244e27i		−	0.799170i
$846$	−6.43576e27	+	6.97115e27i	−0.996739	+	1.07966i
$847$			9.17175e27i			1.40462i
$848$	6.87704e27	+	5.61988e27i	1.04146	+	0.851073i
$849$	−2.92015e27	−	9.37531e27i	−0.437302	−	1.40398i
$850$	−8.37394e26	−	3.72001e27i	−0.124008	−	0.550889i
$851$	3.69890e27			0.541678
$852$	3.92075e27	−	3.61449e27i	0.567797	−	0.523445i
$853$	9.03837e27			1.29442			0.647209	−	0.762313i	$-0.275936\pi$
$853$	9.03837e27			1.29442			0.647209	+	0.762313i	$0.275936\pi$
$854$	−3.88325e27	−	1.72508e28i	−0.549978	−	2.44321i
$855$	3.19848e27	−	2.20654e27i	0.447987	−	0.309054i
$856$	−1.75061e27	+	1.37060e27i	−0.242488	+	0.189850i
$857$			2.45385e27i			0.336148i	0.985774	+	0.168074i	$0.0537547\pi$
$857$			2.45385e27i			0.336148i	−0.985774	+	0.168074i	$0.946245\pi$
$858$	−2.60378e24	+	1.50247e24i	−0.000352756	+	0.000203553i
$859$		−	9.67531e27i		−	1.29637i	−0.761482	−	0.648186i	$-0.775528\pi$
$859$		−	9.67531e27i		−	1.29637i	0.761482	−	0.648186i	$-0.224472\pi$
$860$	−8.58696e27	+	4.07229e27i	−1.13790	+	0.539639i
$861$	6.18935e25	−	1.92781e25i	0.00811176	−	0.00252659i
$862$	2.18927e27	−	4.92816e26i	0.283779	−	0.0638801i
$863$	1.31764e28			1.68925			0.844624	−	0.535361i	$-0.179824\pi$
$863$	1.31764e28			1.68925			0.844624	+	0.535361i	$0.179824\pi$
$864$	−3.37427e27	−	7.12812e27i	−0.427857	−	0.903846i
$865$	1.63446e28			2.04984
$866$	9.69499e27	−	2.18239e27i	1.20262	−	0.270715i
$867$	−1.14726e27	+	3.57340e26i	−0.140761	+	0.0438430i
$868$	−1.55369e28	+	7.36825e27i	−1.88551	+	0.894184i
$869$			9.78080e23i			0.000117405i
$870$	−1.31289e28	+	7.57583e27i	−1.55882	+	0.899492i
$871$		−	2.38523e26i		−	0.0280128i
$872$	−6.57887e27	+	5.15078e27i	−0.764267	+	0.598365i
$873$	−1.61260e27	+	1.11249e27i	−0.185307	+	0.127838i
$874$	−7.09677e26	−	3.15265e27i	−0.0806681	−	0.358358i
$875$	−6.16016e27			−0.692652
$876$	1.19255e28	−	1.09939e28i	1.32644	−	1.22282i
$877$	−6.64144e27			−0.730745			−0.365373	−	0.930861i	$-0.619058\pi$
$877$	−6.64144e27			−0.730745			−0.365373	+	0.930861i	$0.619058\pi$
$878$	2.88858e27	+	1.28321e28i	0.314403	+	1.39669i
$879$	3.52052e27	+	1.13028e28i	0.379064	+	1.21701i
$880$	2.94434e24	+	2.40610e24i	0.000313619	+	0.000256288i
$881$			8.95581e27i			0.943699i	0.881679	+	0.471850i	$0.156413\pi$
$881$			8.95581e27i			0.943699i	−0.881679	+	0.471850i	$0.843587\pi$
$882$	6.33125e27	−	6.85795e27i	0.659991	−	0.714896i
$883$			2.47145e27i			0.254873i	0.991847	+	0.127437i	$0.0406750\pi$
$883$			2.47145e27i			0.254873i	−0.991847	+	0.127437i	$0.959325\pi$
$884$	−4.95041e27	−	1.04386e28i	−0.505062	−	1.06499i
$885$	3.75177e27	+	1.20453e28i	0.378682	+	1.21578i
$886$	−4.19942e27	+	9.45312e26i	−0.419343	+	0.0943963i
$887$	8.06467e27			0.796732			0.398366	−	0.917227i	$-0.369577\pi$
$887$	8.06467e27			0.796732			0.398366	+	0.917227i	$0.369577\pi$
$888$	3.67682e27	−	5.32164e27i	0.359376	−	0.520143i
$889$	1.17175e27			0.113310
$890$	5.38831e27	−	1.21294e27i	0.515522	−	0.116047i
$891$	−1.19680e24	+	3.15084e24i	−0.000113288	+	0.000298255i
$892$	7.69420e27	+	1.62242e28i	0.720605	+	1.51949i
$893$			6.79839e27i			0.629966i
$894$	9.16888e26	+	1.58896e27i	0.0840639	+	0.145682i
$895$		−	5.37881e27i		−	0.487941i
$896$	1.56456e28	+	3.26957e26i	1.40432	+	0.0293470i
$897$	−1.17579e28	+	3.66224e27i	−1.04424	+	0.325251i
$898$	9.47210e26	+	4.20785e27i	0.0832379	+	0.369773i
$899$	−2.42225e28			−2.10621
$900$	−3.55682e27	+	6.15388e27i	−0.306026	+	0.529475i
$901$	1.45869e28			1.24188
$902$	−5.03071e21	−	2.23482e22i	−4.23806e−7	−	1.88270e-6i
$903$	1.59596e28	−	4.97095e27i	1.33041	−	0.414387i
$904$	−8.69343e27	−	1.11038e28i	−0.717119	−	0.915946i
$905$		−	2.20332e28i		−	1.79852i
$906$	−1.89478e27	−	3.28365e27i	−0.153053	−	0.265240i
$907$			1.25220e28i			1.00093i	0.865755	+	0.500467i	$0.166838\pi$
$907$			1.25220e28i			1.00093i	−0.865755	+	0.500467i	$0.833162\pi$
$908$	4.33672e27	−	2.05665e27i	0.343041	−	0.162684i
$909$	1.42143e27	+	2.06043e27i	0.111268	+	0.161288i
$910$	2.86664e28	−	6.45295e27i	2.22065	−	0.499879i
$911$	−1.09901e27			−0.0842511			−0.0421255	−	0.999112i	$-0.513413\pi$
$911$	−1.09901e27			−0.0842511			−0.0421255	+	0.999112i	$0.513413\pi$
$912$	−5.24119e27	−	2.11281e27i	−0.397629	−	0.160291i
$913$	2.00720e24			0.000150702
$914$	−1.85808e28	+	4.18264e27i	−1.38063	+	0.310786i
$915$	−9.15312e27	−	2.93867e28i	−0.673084	−	2.16098i
$916$	−1.11111e28	+	5.26935e27i	−0.808632	+	0.383487i
$917$		−	1.28152e28i		−	0.923031i
$918$	−1.16997e28	−	5.55861e27i	−0.834003	−	0.396243i
$919$			1.83014e27i			0.129118i	0.997914	+	0.0645591i	$0.0205641\pi$
$919$			1.83014e27i			0.129118i	−0.997914	+	0.0645591i	$0.979436\pi$
$920$	9.60260e27	+	1.22650e28i	0.670509	+	0.856413i
$921$	−1.18143e27	−	3.79305e27i	−0.0816472	−	0.262133i
$922$	2.09654e27	+	9.31359e27i	0.143403	+	0.637050i
$923$	−1.45617e28			−0.985815
$924$	−4.53319e24	−	4.91729e24i	−0.000303753	−	0.000329490i
$925$	−5.82970e27			−0.386634
$926$	−1.87582e26	−	8.33308e26i	−0.0123136	−	0.0547018i
$927$	1.51533e28	+	2.19653e28i	0.984574	+	1.42718i
$928$	1.97159e28	+	9.85984e27i	1.26798	+	0.634109i
$929$			2.18069e27i			0.138818i	0.997588	+	0.0694088i	$0.0221113\pi$
$929$			2.18069e27i			0.138818i	−0.997588	+	0.0694088i	$0.977889\pi$
$930$	−2.59250e28	+	1.49597e28i	−1.63354	+	0.942613i
$931$		−	6.68799e27i		−	0.417132i
$932$	−1.74192e27	−	3.67306e27i	−0.107542	−	0.226766i
$933$	−2.27334e28	+	7.08082e27i	−1.38928	+	0.432721i
$934$	8.99057e27	−	2.02382e27i	0.543866	−	0.122427i
$935$	6.24527e24			0.000373973
$936$	−6.41876e27	+	2.05565e28i	−0.380479	+	1.21851i
$937$	7.08161e27			0.415534			0.207767	−	0.978178i	$-0.433380\pi$
$937$	7.08161e27			0.415534			0.207767	+	0.978178i	$0.433380\pi$
$938$	5.17701e26	−	1.16537e26i	0.0300713	−	0.00676920i
$939$	1.95282e27	−	6.08249e26i	0.112290	−	0.0349750i
$940$	−1.40419e28	−	2.96092e28i	−0.799303	−	1.68544i
$941$		−	4.27735e27i		−	0.241031i	−0.992711	−	0.120516i	$-0.961545\pi$
$941$		−	4.27735e27i		−	0.241031i	0.992711	−	0.120516i	$-0.0384548\pi$
$942$	1.01869e28	−	5.87821e27i	0.568275	−	0.327915i
$943$		−	9.38420e25i		−	0.00518246i
$944$	1.16099e28	−	1.42070e28i	0.634735	−	0.776724i
$945$	2.03275e28	−	2.59256e28i	1.10023	−	1.40322i
$946$	−1.29719e24	−	5.76261e24i	−6.95086e−5	−	0.000308783i
$947$	9.95537e27			0.528120			0.264060	−	0.964506i	$-0.414938\pi$
$947$	9.95537e27			0.528120			0.264060	+	0.964506i	$0.414938\pi$
$948$	4.74918e27	+	5.15158e27i	0.249425	+	0.270559i
$949$	−4.42912e28			−2.30297
$950$	1.11850e27	+	4.96878e27i	0.0575785	+	0.255785i
$951$	−4.46245e27	−	1.43270e28i	−0.227436	−	0.730196i
$952$	2.02377e28	−	1.58447e28i	1.02120	−	0.799525i
$953$			2.48300e28i			1.24049i	0.784406	+	0.620247i	$0.212968\pi$
$953$			2.48300e28i			1.24049i	−0.784406	+	0.620247i	$0.787032\pi$
$954$	−1.99787e28	−	1.84444e28i	−0.988231	−	0.912334i
$955$			2.96570e28i			1.45243i
$956$	2.64623e27	−	1.25495e27i	0.128315	−	0.0608523i
$957$	−2.80164e24	−	8.99484e24i	−0.000134508	−	0.000431847i
$958$	1.12083e28	−	2.52304e27i	0.532802	−	0.119937i
$959$	−2.01590e28			−0.948839
$960$	2.71911e28	−	1.62357e27i	1.26721	−	0.0756649i
$961$	−2.61604e28			−1.20718
$962$	−1.72317e28	+	3.87894e27i	−0.787344	+	0.177235i
$963$	5.60301e27	−	3.86536e27i	0.253496	−	0.174880i
$964$	−3.70677e27	+	1.75790e27i	−0.166060	+	0.0787523i
$965$		−	1.19468e28i		−	0.529957i
$966$	−1.36933e28	−	2.37305e28i	−0.601488	−	1.04238i
$967$		−	4.29422e28i		−	1.86781i	−0.357523	−	0.933904i	$-0.616379\pi$
$967$		−	4.29422e28i		−	1.86781i	0.357523	−	0.933904i	$-0.383621\pi$
$968$	1.82811e28	−	1.43128e28i	0.787383	−	0.616464i
$969$	−8.86156e27	+	2.76013e27i	−0.377950	+	0.117721i
$970$	−1.48603e27	−	6.60151e27i	−0.0627621	−	0.278812i
$971$	−2.21794e28			−0.927614			−0.463807	−	0.885936i	$-0.653517\pi$
$971$	−2.21794e28			−0.927614			−0.463807	+	0.885936i	$0.653517\pi$
$972$	8.99567e27	+	2.24068e28i	0.372567	+	0.928005i
$973$	−5.50435e27			−0.225753
$974$	3.45149e27	+	1.53328e28i	0.140183	+	0.622746i
$975$	1.85311e28	−	5.77193e27i	0.745347	−	0.232155i
$976$	−2.83244e28	+	3.46605e28i	−1.12820	+	1.38058i
$977$			1.59999e28i			0.631129i	0.948904	+	0.315565i	$0.102194\pi$
$977$			1.59999e28i			0.631129i	−0.948904	+	0.315565i	$0.897806\pi$
$978$	7.06435e27	+	1.22425e28i	0.275965	+	0.478245i
$979$			3.43280e24i			0.000132804i
$980$	1.38139e28	+	2.91284e28i	0.529259	+	1.11601i
$981$	2.10563e28	−	1.45262e28i	0.798963	−	0.551182i
$982$	−3.96346e28	+	8.92196e27i	−1.48942	+	0.335275i
$983$	4.61641e28			1.71809			0.859045	−	0.511900i	$-0.171058\pi$
$983$	4.61641e28			1.71809			0.859045	+	0.511900i	$0.171058\pi$
$984$	−1.35011e26	−	9.32818e25i	−0.00497642	−	0.00343830i
$985$	−1.51746e27			−0.0553952
$986$	3.53220e28	−	7.95115e27i	1.27707	−	0.287475i
$987$	1.71406e28	+	5.50311e28i	0.613782	+	1.97058i
$988$	6.61220e27	+	1.39427e28i	0.234507	+	0.494488i
$989$		−	2.41976e28i		−	0.849979i
$990$	−8.55372e24	−	7.89678e24i	−0.000297591	−	0.000274736i
$991$		−	2.59012e28i		−	0.892525i	−0.894902	−	0.446262i	$-0.852755\pi$
$991$		−	2.59012e28i		−	0.892525i	0.894902	−	0.446262i	$-0.147245\pi$
$992$	3.89322e28	+	1.94698e28i	1.32876	+	0.664508i
$993$	1.22208e28	+	3.92355e28i	0.413124	+	1.32636i
$994$	−7.11454e27	−	3.16054e28i	−0.238219	−	1.05826i
$995$	−3.21516e28			−1.06631
$996$	1.05720e28	−	9.74618e27i	0.347290	−	0.320163i
$997$	3.83937e28			1.24927			0.624635	−	0.780917i	$-0.285248\pi$
$997$	3.83937e28			1.24927			0.624635	+	0.780917i	$0.285248\pi$
$998$	7.48414e27	+	3.32473e28i	0.241213	+	1.07156i
$999$	−1.22191e28	+	1.55842e28i	−0.390092	+	0.497522i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	12.20.b.a.11.4	yes	36
3.2	odd	2	inner	12.20.b.a.11.33	yes	36
4.3	odd	2	inner	12.20.b.a.11.34	yes	36
12.11	even	2	inner	12.20.b.a.11.3	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
12.20.b.a.11.3	✓	36	12.11	even	2	inner
12.20.b.a.11.4	yes	36	1.1	even	1	trivial
12.20.b.a.11.33	yes	36	3.2	odd	2	inner
12.20.b.a.11.34	yes	36	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:	\( k \)	\(=\)	\( 20 \)
Character orbit:	\([\chi]\)	\(=\)	12.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-706.401 + 159.015i) q^{2} +(-32549.6 + 10138.3i) q^{3} +(473717. - 224656. i) q^{4} -5.54418e6i q^{5} +(2.13809e7 - 1.23376e7i) q^{6} -1.49965e8i q^{7} +(-2.98910e8 + 2.34025e8i) q^{8} +(9.56692e8 - 6.59995e8i) q^{9} +O(q^{10})\)	\(q+(-706.401 + 159.015i) q^{2} +(-32549.6 + 10138.3i) q^{3} +(473717. - 224656. i) q^{4} -5.54418e6i q^{5} +(2.13809e7 - 1.23376e7i) q^{6} -1.49965e8i q^{7} +(-2.98910e8 + 2.34025e8i) q^{8} +(9.56692e8 - 6.59995e8i) q^{9} +(8.81605e8 + 3.91641e9i) q^{10} -2.49508e6 q^{11} +(-1.31417e10 + 1.21151e10i) q^{12} +4.88082e10 q^{13} +(2.38467e10 + 1.05936e11i) q^{14} +(5.62085e10 + 1.80461e11i) q^{15} +(1.73937e11 - 2.12847e11i) q^{16} -4.51471e11i q^{17} +(-5.70859e11 + 6.18349e11i) q^{18} +6.03024e11i q^{19} +(-1.24553e12 - 2.62637e12i) q^{20} +(1.52039e12 + 4.88132e12i) q^{21} +(1.76253e9 - 3.96754e8i) q^{22} +7.40098e12 q^{23} +(7.35680e12 - 1.06479e13i) q^{24} -1.16644e13 q^{25} +(-3.44782e13 + 7.76122e12i) q^{26} +(-2.44487e13 + 3.11818e13i) q^{27} +(-3.36906e13 - 7.10412e13i) q^{28} -1.10755e14i q^{29} +(-6.84016e13 - 1.18540e14i) q^{30} -2.18703e14i q^{31} +(-8.90238e13 + 1.78014e14i) q^{32} +(8.12138e10 - 2.52958e10i) q^{33} +(7.17904e13 + 3.18919e14i) q^{34} -8.31435e14 q^{35} +(3.04929e14 - 5.27577e14i) q^{36} +4.99785e14 q^{37} +(-9.58896e13 - 4.25977e14i) q^{38} +(-1.58869e15 + 4.94832e14i) q^{39} +(1.29748e15 + 1.65721e15i) q^{40} -1.26797e13i q^{41} +(-1.85021e15 - 3.20640e15i) q^{42} -3.26952e15i q^{43} +(-1.18196e12 + 5.60534e11i) q^{44} +(-3.65913e15 - 5.30407e15i) q^{45} +(-5.22806e15 + 1.17686e15i) q^{46} +1.12738e16 q^{47} +(-3.50369e15 + 8.69150e15i) q^{48} -1.10907e16 q^{49} +(8.23976e15 - 1.85481e15i) q^{50} +(4.57714e15 + 1.46952e16i) q^{51} +(2.31213e16 - 1.09651e16i) q^{52} +3.23098e16i q^{53} +(1.23122e16 - 2.59145e16i) q^{54} +1.38332e13i q^{55} +(3.50957e16 + 4.48262e16i) q^{56} +(-6.11364e15 - 1.96282e16i) q^{57} +(1.76117e16 + 7.82375e16i) q^{58} +6.67474e16 q^{59} +(6.71685e16 + 7.28597e16i) q^{60} -1.62842e17 q^{61} +(3.47770e16 + 1.54492e17i) q^{62} +(-9.89764e16 - 1.43471e17i) q^{63} +(3.45797e16 - 1.39905e17i) q^{64} -2.70602e17i q^{65} +(-5.33471e13 + 3.07832e13i) q^{66} -4.88693e15i q^{67} +(-1.01426e17 - 2.13869e17i) q^{68} +(-2.40899e17 + 7.50333e16i) q^{69} +(5.87327e17 - 1.32210e17i) q^{70} -2.98345e17 q^{71} +(-1.31510e17 + 4.21169e17i) q^{72} -9.07454e17 q^{73} +(-3.53049e17 + 7.94731e16i) q^{74} +(3.79672e17 - 1.18257e17i) q^{75} +(1.35473e17 + 2.85663e17i) q^{76} +3.74176e14i q^{77} +(1.04357e18 - 6.02175e17i) q^{78} -3.92004e17i q^{79} +(-1.18006e18 - 9.64339e17i) q^{80} +(4.79666e17 - 1.26282e18i) q^{81} +(2.01625e15 + 8.95693e15i) q^{82} -8.04463e17 q^{83} +(1.81685e18 + 1.97080e18i) q^{84} -2.50303e18 q^{85} +(5.19901e17 + 2.30959e18i) q^{86} +(1.12287e18 + 3.60503e18i) q^{87} +(7.45805e14 - 5.83911e14i) q^{88} -1.37583e18i q^{89} +(3.42824e18 + 3.16494e18i) q^{90} -7.31955e18i q^{91} +(3.50597e18 - 1.66267e18i) q^{92} +(2.21728e18 + 7.11870e18i) q^{93} +(-7.96384e18 + 1.79270e18i) q^{94} +3.34327e18 q^{95} +(1.09293e18 - 6.69682e18i) q^{96} -1.68560e18 q^{97} +(7.83452e18 - 1.76359e18i) q^{98} +(-2.38702e15 + 1.64674e15i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 47880 q^{4} + 21771144 q^{6} - 809473644 q^{9}+O(q^{10}) \) 36 * q - 47880 * q^4 + 21771144 * q^6 - 809473644 * q^9	\( 36 q - 47880 q^{4} + 21771144 q^{6} - 809473644 q^{9} - 4162950000 q^{10} - 2268767880 q^{12} - 25913431656 q^{13} + 791689296672 q^{16} + 2852271258192 q^{18} - 1650825908424 q^{21} + 7247870602416 q^{22} + 23719435803936 q^{24} - 118879690462380 q^{25} - 7629081673968 q^{28} + 37456727138640 q^{30} + 529254701828640 q^{33} - 248241675948480 q^{34} - 11\!\cdots\!16 q^{36}+ \cdots + 12\!\cdots\!88 q^{97}+O(q^{100}) \) 36 * q - 47880 * q^4 + 21771144 * q^6 - 809473644 * q^9 - 4162950000 * q^10 - 2268767880 * q^12 - 25913431656 * q^13 + 791689296672 * q^16 + 2852271258192 * q^18 - 1650825908424 * q^21 + 7247870602416 * q^22 + 23719435803936 * q^24 - 118879690462380 * q^25 - 7629081673968 * q^28 + 37456727138640 * q^30 + 529254701828640 * q^33 - 248241675948480 * q^34 - 1177548745309416 * q^36 + 1847838600168120 * q^37 - 40433256181440 * q^40 - 2709671988768336 * q^42 - 4365410114088000 * q^45 + 17206125364795104 * q^46 + 1561106052682272 * q^48 - 49399737041580084 * q^49 + 16558671470242896 * q^52 + 40087412948587896 * q^54 + 44803667812766472 * q^57 - 34645536255764880 * q^58 + 50260381053157440 * q^60 + 174742350239997144 * q^61 - 139766490424918656 * q^64 - 87772097712685968 * q^66 - 957190369821780672 * q^69 + 244663962371376480 * q^70 + 54134736422921280 * q^72 - 1445122541399481432 * q^73 + 2744130151937256048 * q^76 + 1125465917961999024 * q^78 + 1033298241353042436 * q^81 + 1064985418859680800 * q^82 + 1920709484261873424 * q^84 - 1802899595088057600 * q^85 - 9209792381828477760 * q^88 - 5194944179528261040 * q^90 + 6719944190337314136 * q^93 - 3835186345170303552 * q^94 - 11947184361208227456 * q^96 + 12765226159947004488 * q^97

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