LMFDB - Embedded newform 12.20.b.a.11.15

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			11.15
Character	$\chi$	$=$	12.11
Dual form			12.20.b.a.11.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-183.227 - 700.511i) q^{2} +(22981.7 + 25181.4i) q^{3} +(-457144. + 256705. i) q^{4} +6.84881e6i q^{5} +(1.34289e7 - 2.07129e7i) q^{6} +8.10387e7i q^{7} +(2.63586e8 + 2.73199e8i) q^{8} +(-1.05940e8 + 1.15742e9i) q^{9} +O(q^{10})$	\(q+(-183.227 - 700.511i) q^{2} +(22981.7 + 25181.4i) q^{3} +(-457144. + 256705. i) q^{4} +6.84881e6i q^{5} +(1.34289e7 - 2.07129e7i) q^{6} +8.10387e7i q^{7} +(2.63586e8 + 2.73199e8i) q^{8} +(-1.05940e8 + 1.15742e9i) q^{9} +(4.79767e9 - 1.25489e9i) q^{10} -1.02621e10 q^{11} +(-1.69701e10 - 5.61196e9i) q^{12} -9.13471e9 q^{13} +(5.67685e10 - 1.48485e10i) q^{14} +(-1.72462e11 + 1.57398e11i) q^{15} +(1.43083e11 - 2.34702e11i) q^{16} -6.29700e11i q^{17} +(8.30199e11 - 1.37859e11i) q^{18} -2.01024e12i q^{19} +(-1.75813e12 - 3.13089e12i) q^{20} +(-2.04066e12 + 1.86241e12i) q^{21} +(1.88029e12 + 7.18871e12i) q^{22} +2.86699e12 q^{23} +(-8.21847e11 + 1.29160e13i) q^{24} -2.78327e13 q^{25} +(1.67373e12 + 6.39897e12i) q^{26} +(-3.15802e13 + 2.39319e13i) q^{27} +(-2.08031e13 - 3.70463e13i) q^{28} +8.26930e12i q^{29} +(1.41859e14 + 9.19723e13i) q^{30} +1.75199e14i q^{31} +(-1.90628e14 - 5.72271e13i) q^{32} +(-2.35841e14 - 2.58413e14i) q^{33} +(-4.41112e14 + 1.15378e14i) q^{34} -5.55019e14 q^{35} +(-2.48687e14 - 5.56304e14i) q^{36} +1.30858e15 q^{37} +(-1.40819e15 + 3.68330e14i) q^{38} +(-2.09932e14 - 2.30024e14i) q^{39} +(-1.87109e15 + 1.80525e15i) q^{40} -5.00469e14i q^{41} +(1.67855e15 + 1.08826e15i) q^{42} +2.29241e15i q^{43} +(4.69125e15 - 2.63433e15i) q^{44} +(-7.92697e15 - 7.25563e14i) q^{45} +(-5.25311e14 - 2.00836e15i) q^{46} -8.03815e15 q^{47} +(9.19841e15 - 1.79086e15i) q^{48} +4.83162e15 q^{49} +(5.09972e15 + 1.94971e16i) q^{50} +(1.58567e16 - 1.44716e16i) q^{51} +(4.17587e15 - 2.34493e15i) q^{52} +2.50512e16i q^{53} +(2.25509e16 + 1.77373e16i) q^{54} -7.02831e16i q^{55} +(-2.21397e16 + 2.13607e16i) q^{56} +(5.06204e16 - 4.61987e16i) q^{57} +(5.79274e15 - 1.51516e15i) q^{58} -6.40298e16 q^{59} +(3.84353e16 - 1.16225e17i) q^{60} +4.18164e16 q^{61} +(1.22729e17 - 3.21012e16i) q^{62} +(-9.37961e16 - 8.58524e15i) q^{63} +(-5.15994e15 + 1.44023e17i) q^{64} -6.25619e16i q^{65} +(-1.37809e17 + 2.12557e17i) q^{66} -8.57571e16i q^{67} +(1.61647e17 + 2.87863e17i) q^{68} +(6.58885e16 + 7.21947e16i) q^{69} +(1.01695e17 + 3.88797e17i) q^{70} -5.20730e17 q^{71} +(-3.44131e17 + 2.76138e17i) q^{72} -3.77163e17 q^{73} +(-2.39767e17 - 9.16672e17i) q^{74} +(-6.39645e17 - 7.00866e17i) q^{75} +(5.16038e17 + 9.18966e17i) q^{76} -8.31627e17i q^{77} +(-1.22669e17 + 1.89206e17i) q^{78} -4.09547e17i q^{79} +(1.60743e18 + 9.79946e17i) q^{80} +(-1.32841e18 - 2.45235e17i) q^{81} +(-3.50584e17 + 9.16996e16i) q^{82} -1.71020e18 q^{83} +(4.54786e17 - 1.37524e18i) q^{84} +4.31270e18 q^{85} +(1.60586e18 - 4.20032e17i) q^{86} +(-2.08232e17 + 1.90043e17i) q^{87} +(-2.70494e18 - 2.80359e18i) q^{88} +6.97699e17i q^{89} +(9.44172e17 + 5.68588e18i) q^{90} -7.40265e17i q^{91} +(-1.31063e18 + 7.35972e17i) q^{92} +(-4.41174e18 + 4.02637e18i) q^{93} +(1.47281e18 + 5.63081e18i) q^{94} +1.37677e19 q^{95} +(-2.93991e18 - 6.11546e18i) q^{96} +8.71166e18 q^{97} +(-8.85285e17 - 3.38460e18i) q^{98} +(1.08717e18 - 1.18776e19i) 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 $

$2$	−183.227	−	700.511i	−0.253049	−	0.967453i
$2$	−183.227	−	700.511i	−0.253049	−	0.967453i
$3$	22981.7	+	25181.4i	0.674111	+	0.738630i
$3$	22981.7	+	25181.4i	0.674111	+	0.738630i
$4$	−457144.	+	256705.i	−0.871932	+	0.489627i
$5$			6.84881e6i			1.56820i	0.620637	+	0.784098i	$0.286874\pi$
$5$			6.84881e6i			1.56820i	−0.620637	+	0.784098i	$0.713126\pi$
$6$	1.34289e7	−	2.07129e7i	0.544007	−	0.839080i
$7$			8.10387e7i			0.759034i	0.925185	+	0.379517i	$0.123910\pi$
$7$			8.10387e7i			0.759034i	−0.925185	+	0.379517i	$0.876090\pi$
$8$	2.63586e8	+	2.73199e8i	0.694333	+	0.719654i
$9$	−1.05940e8	+	1.15742e9i	−0.0911499	+	0.995837i
$10$	4.79767e9	−	1.25489e9i	1.51716	−	0.396831i
$11$	−1.02621e10			−1.31222			−0.656108	−	0.754667i	$-0.727798\pi$
$11$	−1.02621e10			−1.31222			−0.656108	+	0.754667i	$0.727798\pi$
$12$	−1.69701e10	−	5.61196e9i	−0.949432	−	0.313973i
$13$	−9.13471e9			−0.238909			−0.119455	−	0.992840i	$-0.538115\pi$
$13$	−9.13471e9			−0.238909			−0.119455	+	0.992840i	$0.538115\pi$
$14$	5.67685e10	−	1.48485e10i	0.734330	−	0.192073i
$15$	−1.72462e11	+	1.57398e11i	−1.15832	+	1.05714i
$16$	1.43083e11	−	2.34702e11i	0.520532	−	0.853842i
$17$		−	6.29700e11i		−	1.28786i	−0.765084	−	0.643930i	$-0.777303\pi$
$17$		−	6.29700e11i		−	1.28786i	0.765084	−	0.643930i	$-0.222697\pi$
$18$	8.30199e11	−	1.37859e11i	0.986491	−	0.163813i
$19$		−	2.01024e12i		−	1.42918i	−0.699542	−	0.714591i	$-0.746613\pi$
$19$		−	2.01024e12i		−	1.42918i	0.699542	−	0.714591i	$-0.253387\pi$
$20$	−1.75813e12	−	3.13089e12i	−0.767830	−	1.36736i
$21$	−2.04066e12	+	1.86241e12i	−0.560646	+	0.511673i
$22$	1.88029e12	+	7.18871e12i	0.332055	+	1.26951i
$23$	2.86699e12			0.331904			0.165952	−	0.986134i	$-0.446930\pi$
$23$	2.86699e12			0.331904			0.165952	+	0.986134i	$0.446930\pi$
$24$	−8.21847e11	+	1.29160e13i	−0.0635015	+	0.997982i
$25$	−2.78327e13			−1.45924
$26$	1.67373e12	+	6.39897e12i	0.0604558	+	0.231134i
$27$	−3.15802e13	+	2.39319e13i	−0.797001	+	0.603978i
$28$	−2.08031e13	−	3.70463e13i	−0.371643	−	0.661826i
$29$			8.26930e12i			0.105849i	0.998599	+	0.0529246i	$0.0168543\pi$
$29$			8.26930e12i			0.105849i	−0.998599	+	0.0529246i	$0.983146\pi$
$30$	1.41859e14	+	9.19723e13i	1.31584	+	0.853110i
$31$			1.75199e14i			1.19013i	0.803677	+	0.595065i	$0.202874\pi$
$31$			1.75199e14i			1.19013i	−0.803677	+	0.595065i	$0.797126\pi$
$32$	−1.90628e14	−	5.72271e13i	−0.957773	−	0.287526i
$33$	−2.35841e14	−	2.58413e14i	−0.884579	−	0.969243i
$34$	−4.41112e14	+	1.15378e14i	−1.24595	+	0.325892i
$35$	−5.55019e14			−1.19031
$36$	−2.48687e14	−	5.56304e14i	−0.408112	−	0.912932i
$37$	1.30858e15			1.65532			0.827661	−	0.561228i	$-0.189671\pi$
$37$	1.30858e15			1.65532			0.827661	+	0.561228i	$0.189671\pi$
$38$	−1.40819e15	+	3.68330e14i	−1.38267	+	0.361653i
$39$	−2.09932e14	−	2.30024e14i	−0.161051	−	0.176466i
$40$	−1.87109e15	+	1.80525e15i	−1.12856	+	1.08885i
$41$		−	5.00469e14i		−	0.238743i	−0.992850	−	0.119372i	$-0.961912\pi$
$41$		−	5.00469e14i		−	0.238743i	0.992850	−	0.119372i	$-0.0380880\pi$
$42$	1.67855e15	+	1.08826e15i	0.636890	+	0.412920i
$43$			2.29241e15i			0.695573i	0.937574	+	0.347786i	$0.113067\pi$
$43$			2.29241e15i			0.695573i	−0.937574	+	0.347786i	$0.886933\pi$
$44$	4.69125e15	−	2.63433e15i	1.14416	−	0.642496i
$45$	−7.92697e15	−	7.25563e14i	−1.56167	−	0.142941i
$46$	−5.25311e14	−	2.00836e15i	−0.0839879	−	0.321101i
$47$	−8.03815e15			−1.04767			−0.523837	−	0.851818i	$-0.675500\pi$
$47$	−8.03815e15			−1.04767			−0.523837	+	0.851818i	$0.675500\pi$
$48$	9.19841e15	−	1.79086e15i	0.981570	−	0.191104i
$49$	4.83162e15			0.423868
$50$	5.09972e15	+	1.94971e16i	0.369259	+	1.41174i
$51$	1.58567e16	−	1.44716e16i	0.951253	−	0.868161i
$52$	4.17587e15	−	2.34493e15i	0.208313	−	0.116976i
$53$			2.50512e16i			1.04281i	0.853308	+	0.521407i	$0.174593\pi$
$53$			2.50512e16i			1.04281i	−0.853308	+	0.521407i	$0.825407\pi$
$54$	2.25509e16	+	1.77373e16i	0.786001	+	0.618225i
$55$		−	7.02831e16i		−	2.05781i
$56$	−2.21397e16	+	2.13607e16i	−0.546242	+	0.527022i
$57$	5.06204e16	−	4.61987e16i	1.05564	−	0.963427i
$58$	5.79274e15	−	1.51516e15i	0.102404	−	0.0267851i
$59$	−6.40298e16			−0.962250			−0.481125	−	0.876652i	$-0.659772\pi$
$59$	−6.40298e16			−0.962250			−0.481125	+	0.876652i	$0.659772\pi$
$60$	3.84353e16	−	1.16225e17i	0.492371	−	1.48889i
$61$	4.18164e16			0.457840			0.228920	−	0.973445i	$-0.426481\pi$
$61$	4.18164e16			0.457840			0.228920	+	0.973445i	$0.426481\pi$
$62$	1.22729e17	−	3.21012e16i	1.15140	−	0.301162i
$63$	−9.37961e16	−	8.58524e15i	−0.755874	−	0.0691859i
$64$	−5.15994e15	+	1.44023e17i	−0.0358043	+	0.999359i
$65$		−	6.25619e16i		−	0.374656i
$66$	−1.37809e17	+	2.12557e17i	−0.713855	+	1.10105i
$67$		−	8.57571e16i		−	0.385088i	−0.981288	−	0.192544i	$-0.938326\pi$
$67$		−	8.57571e16i		−	0.385088i	0.981288	−	0.192544i	$-0.0616737\pi$
$68$	1.61647e17	+	2.87863e17i	0.630571	+	1.12293i
$69$	6.58885e16	+	7.21947e16i	0.223740	+	0.245154i
$70$	1.01695e17	+	3.88797e17i	0.301208	+	1.15157i
$71$	−5.20730e17			−1.34790			−0.673951	−	0.738776i	$-0.735404\pi$
$71$	−5.20730e17			−1.34790			−0.673951	+	0.738776i	$0.735404\pi$
$72$	−3.44131e17	+	2.76138e17i	−0.779947	+	0.625846i
$73$	−3.77163e17			−0.749828			−0.374914	−	0.927060i	$-0.622328\pi$
$73$	−3.77163e17			−0.749828			−0.374914	+	0.927060i	$0.622328\pi$
$74$	−2.39767e17	−	9.16672e17i	−0.418878	−	1.60145i
$75$	−6.39645e17	−	7.00866e17i	−0.983687	−	1.07784i
$76$	5.16038e17	+	9.18966e17i	0.699766	+	1.24615i
$77$		−	8.31627e17i		−	0.996017i
$78$	−1.22669e17	+	1.89206e17i	−0.129968	+	0.200464i
$79$		−	4.09547e17i		−	0.384455i	−0.981350	−	0.192228i	$-0.938429\pi$
$79$		−	4.09547e17i		−	0.384455i	0.981350	−	0.192228i	$-0.0615712\pi$
$80$	1.60743e18	+	9.79946e17i	1.33899	+	0.816295i
$81$	−1.32841e18	−	2.45235e17i	−0.983383	−	0.181541i
$82$	−3.50584e17	+	9.16996e16i	−0.230973	+	0.0604138i
$83$	−1.71020e18			−1.00417			−0.502083	−	0.864820i	$-0.667433\pi$
$83$	−1.71020e18			−1.00417			−0.502083	+	0.864820i	$0.667433\pi$
$84$	4.54786e17	−	1.37524e18i	0.238316	−	0.720651i
$85$	4.31270e18			2.01962
$86$	1.60586e18	−	4.20032e17i	0.672934	−	0.176014i
$87$	−2.08232e17	+	1.90043e17i	−0.0781835	+	0.0713541i
$88$	−2.70494e18	−	2.80359e18i	−0.911115	−	0.944342i
$89$			6.97699e17i			0.211088i	0.994415	+	0.105544i	$0.0336584\pi$
$89$			6.97699e17i			0.211088i	−0.994415	+	0.105544i	$0.966342\pi$
$90$	9.44172e17	+	5.68588e18i	0.256890	+	1.54701i
$91$		−	7.40265e17i		−	0.181340i
$92$	−1.31063e18	+	7.35972e17i	−0.289397	+	0.162509i
$93$	−4.41174e18	+	4.02637e18i	−0.879067	+	0.802280i
$94$	1.47281e18	+	5.63081e18i	0.265113	+	1.01358i
$95$	1.37677e19			2.24124
$96$	−2.93991e18	−	6.11546e18i	−0.433269	−	0.901264i
$97$	8.71166e18			1.16351			0.581754	−	0.813365i	$-0.302367\pi$
$97$	8.71166e18			1.16351			0.581754	+	0.813365i	$0.302367\pi$
$98$	−8.85285e17	−	3.38460e18i	−0.107259	−	0.410072i
$99$	1.08717e18	−	1.18776e19i	0.119608	−	1.30675i
$100$	1.27236e19	−	7.14482e18i	1.27236	−	0.714482i
$101$			1.96631e18i			0.178895i	0.995992	+	0.0894475i	$0.0285101\pi$
$101$			1.96631e18i			0.178895i	−0.995992	+	0.0894475i	$0.971490\pi$
$102$	−1.30429e19	−	8.45620e18i	−1.08062	−	0.700606i
$103$			2.49155e19i			1.88155i	0.339030	+	0.940776i	$0.389901\pi$
$103$			2.49155e19i			1.88155i	−0.339030	+	0.940776i	$0.610099\pi$
$104$	−2.40778e18	−	2.49559e18i	−0.165882	−	0.171932i
$105$	−1.27553e19	−	1.39761e19i	−0.802403	−	0.879202i
$106$	1.75486e19	−	4.59005e18i	1.00887	−	0.263883i
$107$	−2.19584e19			−1.15466			−0.577331	−	0.816510i	$-0.695906\pi$
$107$	−2.19584e19			−1.15466			−0.577331	+	0.816510i	$0.695906\pi$
$108$	8.29323e18	−	1.90471e19i	0.399207	−	0.916861i
$109$	−2.49210e19			−1.09904			−0.549519	−	0.835481i	$-0.685189\pi$
$109$	−2.49210e19			−1.09904			−0.549519	+	0.835481i	$0.685189\pi$
$110$	−4.92341e19	+	1.28778e19i	−1.99084	+	0.520728i
$111$	3.00734e19	+	3.29517e19i	1.11587	+	1.22267i
$112$	1.90200e19	+	1.15952e19i	0.648095	+	0.395101i
$113$			3.46953e19i			1.08649i	0.839575	+	0.543245i	$0.182804\pi$
$113$			3.46953e19i			1.08649i	−0.839575	+	0.543245i	$0.817196\pi$
$114$	−4.16378e19	−	2.69953e19i	−1.19920	−	0.777486i
$115$			1.96355e19i			0.520490i
$116$	−2.12277e18	−	3.78026e18i	−0.0518266	−	0.0922934i
$117$	9.67731e17	−	1.05727e19i	0.0217766	−	0.237915i
$118$	1.17320e19	+	4.48536e19i	0.243497	+	0.930932i
$119$	5.10301e19			0.977530
$120$	−8.84595e19	−	5.62867e18i	−1.56503	−	0.0995828i
$121$	4.41514e19			0.721911
$122$	−7.66190e18	−	2.92929e19i	−0.115856	−	0.442939i
$123$	1.26025e19	−	1.15017e19i	0.176343	−	0.160939i
$124$	−4.49744e19	−	8.00909e19i	−0.582720	−	1.03771i
$125$		−	5.99905e19i		−	0.720174i
$126$	1.11719e19	+	6.72782e19i	0.124339	+	0.748780i
$127$			7.57642e19i			0.782219i	0.920344	+	0.391110i	$0.127909\pi$
$127$			7.57642e19i			0.782219i	−0.920344	+	0.391110i	$0.872091\pi$
$128$	1.01835e20	−	2.27743e19i	0.975893	−	0.218248i
$129$	−5.77261e19	+	5.26837e19i	−0.513771	+	0.468893i
$130$	−4.38253e19	+	1.14630e19i	−0.362463	+	0.0948065i
$131$	−4.27587e19			−0.328812			−0.164406	−	0.986393i	$-0.552571\pi$
$131$	−4.27587e19			−0.328812			−0.164406	+	0.986393i	$0.552571\pi$
$132$	1.74149e20	+	5.75904e19i	1.24586	+	0.412001i
$133$	1.62907e20			1.08480
$134$	−6.00738e19	+	1.57130e19i	−0.372554	+	0.0974461i
$135$	−1.63905e20	−	2.16287e20i	−0.947156	−	1.24985i
$136$	1.72033e20	−	1.65980e20i	0.926815	−	0.894204i
$137$			1.49892e20i			0.753239i	0.926368	+	0.376619i	$0.122914\pi$
$137$			1.49892e20i			0.753239i	−0.926368	+	0.376619i	$0.877086\pi$
$138$	3.85007e19	−	5.93837e19i	0.180558	−	0.278494i
$139$		−	3.48808e20i		−	1.52738i	−0.645585	−	0.763688i	$-0.723386\pi$
$139$		−	3.48808e20i		−	1.52738i	0.645585	−	0.763688i	$-0.276614\pi$
$140$	2.53723e20	−	1.42476e20i	1.03787	−	0.582809i
$141$	−1.84731e20	−	2.02412e20i	−0.706249	−	0.773844i
$142$	9.54120e19	+	3.64777e20i	0.341086	+	1.30403i
$143$	9.37412e19			0.313501
$144$	2.56492e20	+	1.90472e20i	0.802842	+	0.596192i
$145$	−5.66349e19			−0.165992
$146$	6.91064e19	+	2.64207e20i	0.189743	+	0.725423i
$147$	1.11039e20	+	1.21667e20i	0.285734	+	0.313082i
$148$	−5.98207e20	+	3.35918e20i	−1.44333	+	0.810490i
$149$		−	1.03942e20i		−	0.235246i	−0.993058	−	0.117623i	$-0.962473\pi$
$149$		−	1.03942e20i		−	0.235246i	0.993058	−	0.117623i	$-0.0375274\pi$
$150$	−3.73764e20	+	5.76496e20i	−0.793836	+	1.22442i
$151$		−	3.36278e20i		−	0.670528i	−0.942124	−	0.335264i	$-0.891174\pi$
$151$		−	3.36278e20i		−	0.670528i	0.942124	−	0.335264i	$-0.108826\pi$
$152$	5.49194e20	−	5.29870e20i	1.02852	−	0.992328i
$153$	7.28829e20	+	6.67104e19i	1.28250	+	0.117388i
$154$	−5.82564e20	+	1.52377e20i	−0.963600	+	0.252041i
$155$	−1.19990e21			−1.86636
$156$	1.55017e20	+	5.12636e19i	0.226828	+	0.0750111i
$157$	−7.95433e20			−1.09536			−0.547680	−	0.836688i	$-0.684489\pi$
$157$	−7.95433e20			−1.09536			−0.547680	+	0.836688i	$0.684489\pi$
$158$	−2.86892e20	+	7.50401e19i	−0.371943	+	0.0972862i
$159$	−6.30822e20	+	5.75719e20i	−0.770254	+	0.702972i
$160$	3.91938e20	−	1.30558e21i	0.450897	−	1.50198i
$161$			2.32337e20i			0.251926i
$162$	7.16102e19	+	9.75496e20i	0.0732120	+	0.997316i
$163$			4.72147e20i			0.455298i	0.973743	+	0.227649i	$0.0731038\pi$
$163$			4.72147e20i			0.455298i	−0.973743	+	0.227649i	$0.926896\pi$
$164$	1.28473e20	+	2.28786e20i	0.116895	+	0.208168i
$165$	1.76983e21	−	1.61523e21i	1.51996	−	1.38719i
$166$	3.13355e20	+	1.19801e21i	0.254103	+	0.971483i
$167$	−5.99897e20			−0.459484			−0.229742	−	0.973252i	$-0.573788\pi$
$167$	−5.99897e20			−0.459484			−0.229742	+	0.973252i	$0.573788\pi$
$168$	−1.04670e21	−	6.66014e19i	−0.757502	−	0.0481998i
$169$	−1.37848e21			−0.942922
$170$	−7.90203e20	−	3.02109e21i	−0.511063	−	1.95389i
$171$	2.32669e21	+	2.12964e20i	1.42323	+	0.130270i
$172$	−5.88475e20	−	1.04796e21i	−0.340571	−	0.606492i
$173$			2.00004e21i			1.09547i	0.836651	+	0.547736i	$0.184510\pi$
$173$			2.00004e21i			1.09547i	−0.836651	+	0.547736i	$0.815490\pi$
$174$	1.71281e20	+	1.11048e20i	0.0888160	+	0.0575828i
$175$		−	2.25553e21i		−	1.10761i
$176$	−1.46833e21	+	2.40854e21i	−0.683050	+	1.12043i
$177$	−1.47152e21	−	1.61236e21i	−0.648663	−	0.710747i
$178$	4.88746e20	−	1.27837e20i	0.204218	−	0.0534156i
$179$	3.67008e21			1.45402			0.727012	−	0.686625i	$-0.240908\pi$
$179$	3.67008e21			1.45402			0.727012	+	0.686625i	$0.240908\pi$
$180$	3.81002e21	−	1.70321e21i	1.43166	−	0.639999i
$181$	−6.28843e20			−0.224179			−0.112090	−	0.993698i	$-0.535754\pi$
$181$	−6.28843e20			−0.224179			−0.112090	+	0.993698i	$0.535754\pi$
$182$	−5.18564e20	+	1.35637e20i	−0.175438	+	0.0458880i
$183$	9.61014e20	+	1.05299e21i	0.308635	+	0.338174i
$184$	7.55699e20	+	7.83259e20i	0.230452	+	0.238856i
$185$			8.96219e21i			2.59587i
$186$	3.62887e21	+	2.35273e21i	0.998615	+	0.647440i
$187$			6.46204e21i			1.68995i
$188$	3.67459e21	−	2.06344e21i	0.913501	−	0.512969i
$189$	−1.93941e21	−	2.55922e21i	−0.458440	−	0.604951i
$190$	−2.52262e21	−	9.64444e21i	−0.567143	−	2.16829i
$191$	1.15829e21			0.247742			0.123871	−	0.992298i	$-0.460469\pi$
$191$	1.15829e21			0.247742			0.123871	+	0.992298i	$0.460469\pi$
$192$	−3.74527e21	+	3.17996e21i	−0.762293	+	0.647232i
$193$	5.41105e21			1.04830			0.524152	−	0.851625i	$-0.324382\pi$
$193$	5.41105e21			1.04830			0.524152	+	0.851625i	$0.324382\pi$
$194$	−1.59621e21	−	6.10261e21i	−0.294425	−	1.12564i
$195$	1.57539e21	−	1.43778e21i	0.276733	−	0.252560i
$196$	−2.20875e21	+	1.24030e21i	−0.369584	+	0.207537i
$197$		−	1.01071e22i		−	1.61138i	−0.592339	−	0.805689i	$-0.701795\pi$
$197$		−	1.01071e22i		−	1.61138i	0.592339	−	0.805689i	$-0.298205\pi$
$198$	−8.51958e21	+	1.41472e21i	−1.29449	+	0.214957i
$199$		−	1.56297e21i		−	0.226384i	−0.993573	−	0.113192i	$-0.963892\pi$
$199$		−	1.56297e21i		−	0.226384i	0.993573	−	0.113192i	$-0.0361075\pi$
$200$	−7.33633e21	−	7.60387e21i	−1.01320	−	1.05015i
$201$	2.15948e21	−	1.97085e21i	0.284437	−	0.259592i
$202$	1.37742e21	−	3.60281e20i	0.173073	−	0.0452692i
$203$	−6.70133e20			−0.0803432
$204$	−3.53385e21	+	1.06861e22i	−0.404354	+	1.22274i
$205$	3.42762e21			0.374396
$206$	1.74536e22	−	4.56520e21i	1.82031	−	0.476125i
$207$	−3.03729e20	+	3.31832e21i	−0.0302530	+	0.330522i
$208$	−1.30702e21	+	2.14394e21i	−0.124360	+	0.203991i
$209$			2.06292e22i			1.87540i
$210$	−7.45332e21	+	1.14960e22i	−0.647539	+	0.998769i
$211$			2.74487e21i			0.227949i	0.993484	+	0.113975i	$0.0363583\pi$
$211$			2.74487e21i			0.227949i	−0.993484	+	0.113975i	$0.963642\pi$
$212$	−6.43076e21	−	1.14520e22i	−0.510590	−	0.909263i
$213$	−1.19673e22	−	1.31127e22i	−0.908636	−	0.995602i
$214$	4.02337e21	+	1.53821e22i	0.292186	+	1.11708i
$215$	−1.57003e22			−1.09079
$216$	−1.48623e22	−	2.31955e21i	−0.988039	−	0.154203i
$217$	−1.41979e22			−0.903350
$218$	4.56620e21	+	1.74574e22i	0.278111	+	1.06327i
$219$	−8.66785e21	−	9.49747e21i	−0.505467	−	0.553845i
$220$	1.80421e22	+	3.21295e22i	1.00756	+	1.79427i
$221$			5.75213e21i			0.307682i
$222$	1.75728e22	−	2.71044e22i	0.900507	−	1.38895i
$223$			4.85448e21i			0.238367i	0.992872	+	0.119184i	$0.0380277\pi$
$223$			4.85448e21i			0.238367i	−0.992872	+	0.119184i	$0.961972\pi$
$224$	4.63761e21	−	1.54483e22i	0.218242	−	0.726982i
$225$	2.94860e21	−	3.22143e22i	0.133009	−	1.45316i
$226$	2.43044e22	−	6.35712e21i	1.05113	−	0.274935i
$227$	−2.64894e22			−1.09857			−0.549284	−	0.835636i	$-0.685099\pi$
$227$	−2.64894e22			−1.09857			−0.549284	+	0.835636i	$0.685099\pi$
$228$	−1.12814e22	+	3.41140e22i	−0.448725	+	1.35691i
$229$	1.25236e22			0.477852			0.238926	−	0.971038i	$-0.423205\pi$
$229$	1.25236e22			0.477852			0.238926	+	0.971038i	$0.423205\pi$
$230$	1.37549e22	−	3.59776e21i	0.503550	−	0.131710i
$231$	2.09415e22	−	1.91122e22i	0.735688	−	0.671425i
$232$	−2.25916e21	+	2.17967e21i	−0.0761749	+	0.0734946i
$233$			3.04822e22i			0.986653i	0.869844	+	0.493326i	$0.164219\pi$
$233$			3.04822e22i			0.986653i	−0.869844	+	0.493326i	$0.835781\pi$
$234$	−7.58363e21	+	1.25930e21i	−0.235682	+	0.0391363i
$235$		−	5.50518e22i		−	1.64296i
$236$	2.92708e22	−	1.64368e22i	0.839017	−	0.471143i
$237$	1.03129e22	−	9.41210e21i	0.283971	−	0.259166i
$238$	−9.35010e21	−	3.57471e22i	−0.247363	−	0.945715i
$239$	2.00343e22			0.509324			0.254662	−	0.967030i	$-0.418036\pi$
$239$	2.00343e22			0.509324			0.254662	+	0.967030i	$0.418036\pi$
$240$	1.22652e22	+	6.29982e22i	0.299688	+	1.53929i
$241$	8.06864e22			1.89513			0.947564	−	0.319566i	$-0.103537\pi$
$241$	8.06864e22			1.89513			0.947564	+	0.319566i	$0.103537\pi$
$242$	−8.08975e21	−	3.09286e22i	−0.182679	−	0.698416i
$243$	−2.43537e22	−	3.90870e22i	−0.528817	−	0.848736i
$244$	−1.91161e22	+	1.07345e22i	−0.399205	+	0.224170i
$245$			3.30909e22i			0.664707i
$246$	−1.03662e22	−	6.72077e21i	−0.200325	−	0.129878i
$247$			1.83629e22i			0.341445i
$248$	−4.78641e22	+	4.61799e22i	−0.856483	+	0.826347i
$249$	−3.93034e22	−	4.30652e22i	−0.676918	−	0.741707i
$250$	−4.20240e22	+	1.09919e22i	−0.696735	+	0.182240i
$251$	−3.64765e22			−0.582254			−0.291127	−	0.956684i	$-0.594030\pi$
$251$	−3.64765e22			−0.582254			−0.291127	+	0.956684i	$0.594030\pi$
$252$	4.50822e22	−	2.01533e22i	0.692946	−	0.309771i
$253$	−2.94213e22			−0.435529
$254$	5.30737e22	−	1.38821e22i	0.756761	−	0.197940i
$255$	9.91133e22	+	1.08600e23i	1.36145	+	1.49175i
$256$	−3.46126e22	−	6.71637e22i	−0.458094	−	0.888904i
$257$			2.14865e22i			0.274032i	0.990569	+	0.137016i	$0.0437512\pi$
$257$			2.14865e22i			0.274032i	−0.990569	+	0.137016i	$0.956249\pi$
$258$	4.74825e22	+	3.07847e22i	0.583641	+	0.378397i
$259$			1.06045e23i			1.25645i
$260$	1.60600e22	+	2.85998e22i	0.183442	+	0.326675i
$261$	−9.57108e21	−	8.76050e20i	−0.105409	−	0.00964815i
$262$	7.83456e21	+	2.99529e22i	0.0832055	+	0.318110i
$263$	−2.76841e22			−0.283564			−0.141782	−	0.989898i	$-0.545283\pi$
$263$	−2.76841e22			−0.283564			−0.141782	+	0.989898i	$0.545283\pi$
$264$	8.43387e21	−	1.32546e23i	0.0833277	−	1.30957i
$265$	−1.71571e23			−1.63534
$266$	−2.98490e22	−	1.14118e23i	−0.274507	−	1.04949i
$267$	−1.75690e22	+	1.60343e22i	−0.155916	+	0.142297i
$268$	2.20143e22	+	3.92033e22i	0.188549	+	0.335770i
$269$			1.97943e22i			0.163642i	0.996647	+	0.0818209i	$0.0260736\pi$
$269$			1.97943e22i			0.163642i	−0.996647	+	0.0818209i	$0.973926\pi$
$270$	−1.21479e23	+	1.54447e23i	−0.969498	+	1.23260i
$271$		−	6.06849e22i		−	0.467597i	−0.972285	−	0.233799i	$-0.924884\pi$
$271$		−	6.06849e22i		−	0.467597i	0.972285	−	0.233799i	$-0.0751157\pi$
$272$	−1.47792e23	−	9.00991e22i	−1.09963	−	0.670372i
$273$	1.86409e22	−	1.70126e22i	0.133943	−	0.122243i
$274$	1.05001e23	−	2.74643e22i	0.728723	−	0.190606i
$275$	2.85622e23			1.91484
$276$	−4.86533e22	−	1.60894e22i	−0.315120	−	0.104209i
$277$	8.84821e19			0.000553729			0.000276865	−	1.00000i	$-0.499912\pi$
$277$	8.84821e19			0.000553729			0.000276865		1.00000i	$0.499912\pi$
$278$	−2.44344e23	+	6.39112e22i	−1.47767	+	0.386501i
$279$	−2.02779e23	−	1.85606e22i	−1.18518	−	0.108480i
$280$	−1.46295e23	−	1.51630e23i	−0.826474	−	0.856614i
$281$		−	1.80328e23i		−	0.984812i	−0.870366	−	0.492406i	$-0.836118\pi$
$281$		−	1.80328e23i		−	0.984812i	0.870366	−	0.492406i	$-0.163882\pi$
$282$	−1.07944e23	+	1.66493e23i	−0.569943	+	0.879083i
$283$			2.20155e23i			1.12398i	0.827145	+	0.561988i	$0.189963\pi$
$283$			2.20155e23i			1.12398i	−0.827145	+	0.561988i	$0.810037\pi$
$284$	2.38049e23	−	1.33674e23i	1.17528	−	0.659969i
$285$	3.16406e23	+	3.46690e23i	1.51084	+	1.65545i
$286$	−1.71759e22	−	6.56668e22i	−0.0793311	−	0.303297i
$287$	4.05574e22			0.181214
$288$	8.64311e22	−	2.14575e23i	0.373630	−	0.927578i
$289$	−1.57450e23			−0.658586
$290$	1.03771e22	+	3.96734e22i	0.0420042	+	0.160590i
$291$	2.00209e23	+	2.19371e23i	0.784333	+	0.859402i
$292$	1.72417e23	−	9.68197e22i	0.653799	−	0.367136i
$293$		−	9.77957e22i		−	0.358986i	−0.983759	−	0.179493i	$-0.942554\pi$
$293$		−	9.77957e22i		−	0.358986i	0.983759	−	0.179493i	$-0.0574457\pi$
$294$	6.48836e22	−	1.00077e23i	0.230587	−	0.355659i
$295$		−	4.38528e23i		−	1.50900i
$296$	3.44922e23	+	3.57501e23i	1.14934	+	1.19126i
$297$	3.24079e23	−	2.45591e23i	1.04584	−	0.792550i
$298$	−7.28125e22	+	1.90450e22i	−0.227589	+	0.0595287i
$299$	−2.61891e22			−0.0792948
$300$	4.72326e23	+	1.56196e23i	1.38545	+	0.458162i
$301$	−1.85774e23			−0.527963
$302$	−2.35566e23	+	6.16152e22i	−0.648705	+	0.169677i
$303$	−4.95143e22	+	4.51892e22i	−0.132137	+	0.120595i
$304$	−4.71807e23	−	2.87630e23i	−1.22030	−	0.743935i
$305$			2.86393e23i			0.717982i
$306$	−8.68100e22	−	5.22776e23i	−0.210968	−	1.27046i
$307$		−	3.33732e23i		−	0.786291i	−0.919476	−	0.393145i	$-0.871387\pi$
$307$		−	3.33732e23i		−	0.786291i	0.919476	−	0.393145i	$-0.128613\pi$
$308$	2.13483e23	+	3.80173e23i	0.487676	+	0.868459i
$309$	−6.27406e23	+	5.72602e23i	−1.38977	+	1.26837i
$310$	2.19855e23	+	8.40545e23i	0.472280	+	1.80561i
$311$	−2.25691e23			−0.470208			−0.235104	−	0.971970i	$-0.575543\pi$
$311$	−2.25691e23			−0.470208			−0.235104	+	0.971970i	$0.575543\pi$
$312$	7.50733e21	−	1.17984e23i	0.0151711	−	0.238427i
$313$	7.76177e23			1.52156			0.760781	−	0.649009i	$-0.224816\pi$
$313$	7.76177e23			1.52156			0.760781	+	0.649009i	$0.224816\pi$
$314$	1.45745e23	+	5.57210e23i	0.277180	+	1.05971i
$315$	5.87987e22	−	6.42392e23i	0.108497	−	1.18536i
$316$	1.05133e23	+	1.87222e23i	0.188240	+	0.335219i
$317$		−	7.82976e23i		−	1.36046i	−0.733000	−	0.680229i	$-0.761880\pi$
$317$		−	7.82976e23i		−	1.36046i	0.733000	−	0.680229i	$-0.238120\pi$
$318$	5.18881e23	+	3.36410e23i	0.875005	+	0.567299i
$319$		−	8.48603e22i		−	0.138897i
$320$	−9.86385e23	−	3.53394e22i	−1.56719	−	0.0561481i
$321$	−5.04642e23	−	5.52942e23i	−0.778369	−	0.852868i
$322$	1.62755e23	−	4.25705e22i	0.243727	−	0.0637497i
$323$	−1.26585e24			−1.84059
$324$	6.70225e23	−	2.28901e23i	0.946331	−	0.323199i
$325$	2.54244e23			0.348625
$326$	3.30745e23	−	8.65102e22i	0.440479	−	0.115213i
$327$	−5.72727e23	−	6.27544e23i	−0.740874	−	0.811783i
$328$	1.36728e23	−	1.31917e23i	0.171813	−	0.165767i
$329$		−	6.51401e23i		−	0.795221i
$330$	−1.45577e24	−	9.43828e23i	−1.72667	−	1.11946i
$331$			1.04369e24i			1.20283i	0.798935	+	0.601417i	$0.205397\pi$
$331$			1.04369e24i			1.20283i	−0.798935	+	0.601417i	$0.794603\pi$
$332$	7.81807e23	−	4.39018e23i	0.875564	−	0.491666i
$333$	−1.38631e23	+	1.51458e24i	−0.150882	+	1.64843i
$334$	1.09918e23	+	4.20235e23i	0.116272	+	0.444530i
$335$	5.87334e23			0.603893
$336$	1.45129e23	+	7.45428e23i	0.145054	+	0.745045i
$337$	−2.33357e23			−0.226745			−0.113372	−	0.993553i	$-0.536165\pi$
$337$	−2.33357e23			−0.226745			−0.113372	+	0.993553i	$0.536165\pi$
$338$	2.52575e23	+	9.65639e23i	0.238606	+	0.912233i
$339$	−8.73675e23	+	7.97359e23i	−0.802514	+	0.732414i
$340$	−1.97152e24	+	1.10709e24i	−1.76097	+	0.988859i
$341$		−	1.79790e24i		−	1.56171i
$342$	−2.77129e23	−	1.66889e24i	−0.234118	−	1.40988i
$343$			1.31530e24i			1.08076i
$344$	−6.26284e23	+	6.04248e23i	−0.500572	+	0.482959i
$345$	−4.94448e23	+	4.51258e23i	−0.384450	+	0.350868i
$346$	1.40105e24	−	3.66462e23i	1.05982	−	0.277209i
$347$	1.28967e24			0.949177			0.474589	−	0.880208i	$-0.342597\pi$
$347$	1.28967e24			0.949177			0.474589	+	0.880208i	$0.342597\pi$
$348$	4.64070e22	−	1.40331e23i	0.0332338	−	0.100497i
$349$	1.94097e24			1.35262			0.676311	−	0.736616i	$-0.263577\pi$
$349$	1.94097e24			1.35262			0.676311	+	0.736616i	$0.263577\pi$
$350$	−1.58002e24	+	4.13274e23i	−1.07156	+	0.280280i
$351$	2.88476e23	−	2.18611e23i	0.190411	−	0.144296i
$352$	1.95624e24	+	5.87270e23i	1.25681	+	0.377296i
$353$			2.19130e24i			1.37038i	0.728364	+	0.685191i	$0.240281\pi$
$353$			2.19130e24i			1.37038i	−0.728364	+	0.685191i	$0.759719\pi$
$354$	−8.59852e23	+	1.32624e24i	−0.523471	+	0.807405i
$355$		−	3.56638e24i		−	2.11378i
$356$	−1.79103e23	−	3.18949e23i	−0.103354	−	0.184054i
$357$	1.17276e24	+	1.28501e24i	0.658963	+	0.722033i
$358$	−6.72458e23	−	2.57093e24i	−0.367940	−	1.40670i
$359$	3.32858e24			1.77362			0.886812	−	0.462131i	$-0.152915\pi$
$359$	3.32858e24			1.77362			0.886812	+	0.462131i	$0.152915\pi$
$360$	−1.89122e24	−	2.35689e24i	−0.981449	−	1.22311i
$361$	−2.06263e24			−1.04256
$362$	1.15221e23	+	4.40511e23i	0.0567284	+	0.216883i
$363$	1.01468e24	+	1.11179e24i	0.486648	+	0.533226i
$364$	1.90030e23	+	3.38407e23i	0.0887890	+	0.158116i
$365$		−	2.58312e24i		−	1.17588i
$366$	5.61550e23	−	8.66138e23i	0.249068	−	0.384164i
$367$			2.09535e24i			0.905584i	0.891616	+	0.452792i	$0.149572\pi$
$367$			2.09535e24i			0.905584i	−0.891616	+	0.452792i	$0.850428\pi$
$368$	4.10217e23	−	6.72890e23i	0.172766	−	0.283393i
$369$	5.79255e23	+	5.30197e22i	0.237749	+	0.0217614i
$370$	6.27811e24	−	1.64212e24i	2.51138	−	0.656882i
$371$	−2.03011e24			−0.791531
$372$	9.83208e23	−	2.97315e24i	0.373669	−	1.12995i
$373$	−3.93847e24			−1.45913			−0.729564	−	0.683913i	$-0.760277\pi$
$373$	−3.93847e24			−1.45913			−0.729564	+	0.683913i	$0.760277\pi$
$374$	4.52673e24	−	1.18402e24i	1.63495	−	0.427641i
$375$	1.51064e24	−	1.37869e24i	0.531943	−	0.485477i
$376$	−2.11874e24	−	2.19601e24i	−0.727435	−	0.753964i
$377$		−	7.55377e22i		−	0.0252884i
$378$	−1.43741e24	+	1.82750e24i	−0.469254	+	0.596602i
$379$			4.68882e24i			1.49276i	0.665519	+	0.746381i	$0.268210\pi$
$379$			4.68882e24i			1.49276i	−0.665519	+	0.746381i	$0.731790\pi$
$380$	−6.29383e24	+	3.53425e24i	−1.95421	+	1.09737i
$381$	−1.90784e24	+	1.74119e24i	−0.577771	+	0.527302i
$382$	−2.12230e23	−	8.11394e23i	−0.0626909	−	0.239679i
$383$	1.29389e24			0.372827			0.186414	−	0.982471i	$-0.440314\pi$
$383$	1.29389e24			0.372827			0.186414	+	0.982471i	$0.440314\pi$
$384$	2.91383e24	+	2.04095e24i	0.819065	+	0.573701i
$385$	5.69566e24			1.56195
$386$	−9.91452e23	−	3.79050e24i	−0.265273	−	1.01419i
$387$	−2.65329e24	−	2.42858e23i	−0.692677	−	0.0634014i
$388$	−3.98248e24	+	2.23633e24i	−1.01450	+	0.569684i
$389$			1.33641e24i			0.332215i	0.986108	+	0.166108i	$0.0531199\pi$
$389$			1.33641e24i			0.332215i	−0.986108	+	0.166108i	$0.946880\pi$
$390$	−1.29584e24	−	8.40140e23i	−0.314367	−	0.203816i
$391$		−	1.80534e24i		−	0.427446i
$392$	1.27355e24	+	1.31999e24i	0.294305	+	0.305038i
$393$	−9.82670e23	−	1.07672e24i	−0.221655	−	0.242870i
$394$	−7.08013e24	+	1.85189e24i	−1.55893	+	0.407758i
$395$	2.80491e24			0.602901
$396$	2.55205e24	+	5.70884e24i	0.535531	+	1.19796i
$397$	1.02507e24			0.210012			0.105006	−	0.994472i	$-0.466514\pi$
$397$	1.02507e24			0.210012			0.105006	+	0.994472i	$0.466514\pi$
$398$	−1.09488e24	+	2.86378e23i	−0.219016	+	0.0572863i
$399$	3.74388e24	+	4.10222e24i	0.731274	+	0.801265i
$400$	−3.98238e24	+	6.53241e24i	−0.759579	+	1.24596i
$401$			5.46881e24i			1.01864i	0.860577	+	0.509320i	$0.170103\pi$
$401$			5.46881e24i			1.01864i	−0.860577	+	0.509320i	$0.829897\pi$
$402$	−1.77628e24	−	1.15163e24i	−0.323119	−	0.209490i
$403$		−	1.60039e24i		−	0.284333i
$404$	−5.04761e23	−	8.98884e23i	−0.0875917	−	0.155984i
$405$	1.67957e24	−	9.09800e24i	0.284692	−	1.54214i
$406$	1.22787e23	+	4.69436e23i	0.0203308	+	0.0777283i
$407$	−1.34287e25			−2.17214
$408$	8.13323e24	+	5.17517e23i	1.28526	+	0.0817811i
$409$	−6.57238e24			−1.01473			−0.507366	−	0.861731i	$-0.669381\pi$
$409$	−6.57238e24			−1.01473			−0.507366	+	0.861731i	$0.669381\pi$
$410$	−6.28033e23	−	2.40109e24i	−0.0947406	−	0.362211i
$411$	−3.77448e24	+	3.44478e24i	−0.556365	+	0.507766i
$412$	−6.39594e24	−	1.13900e25i	−0.921257	−	1.64059i
$413$		−	5.18889e24i		−	0.730380i
$414$	2.38017e24	−	3.95241e23i	0.327420	−	0.0543700i
$415$		−	1.17128e25i		−	1.57473i
$416$	1.74133e24	+	5.22753e23i	0.228821	+	0.0686926i
$417$	8.78347e24	−	8.01622e24i	1.12817	−	1.02962i
$418$	1.44510e25	−	3.77983e24i	1.81436	−	0.474568i
$419$	−9.29141e24			−1.14038			−0.570189	−	0.821514i	$-0.693130\pi$
$419$	−9.29141e24			−1.14038			−0.570189	+	0.821514i	$0.693130\pi$
$420$	9.41875e24	+	3.11474e24i	1.13012	+	0.373727i
$421$	−1.67922e23			−0.0196983			−0.00984915	−	0.999951i	$-0.503135\pi$
$421$	−1.67922e23			−0.0196983			−0.00984915	+	0.999951i	$0.503135\pi$
$422$	1.92281e24	−	5.02935e23i	0.220530	−	0.0576824i
$423$	8.51562e23	−	9.30354e24i	0.0954955	−	1.04331i
$424$	−6.84394e24	+	6.60313e24i	−0.750466	+	0.724060i
$425$			1.75263e25i			1.87930i
$426$	−6.99286e24	+	1.07858e25i	−0.733269	+	1.13100i
$427$			3.38875e24i			0.347516i
$428$	1.00381e25	−	5.63684e24i	1.00679	−	0.565353i
$429$	2.15434e24	+	2.36053e24i	0.211334	+	0.231561i
$430$	2.87672e24	+	1.09982e25i	0.276025	+	1.05529i
$431$	9.09431e24			0.853563			0.426782	−	0.904355i	$-0.359647\pi$
$431$	9.09431e24			0.853563			0.426782	+	0.904355i	$0.359647\pi$
$432$	1.09830e24	+	1.08362e25i	0.100838	+	0.994903i
$433$	−9.14015e24			−0.820953			−0.410476	−	0.911871i	$-0.634638\pi$
$433$	−9.14015e24			−0.820953			−0.410476	+	0.911871i	$0.634638\pi$
$434$	2.60144e24	+	9.94577e24i	0.228592	+	0.873949i
$435$	−1.30157e24	−	1.42614e24i	−0.111897	−	0.122607i
$436$	1.13925e25	−	6.39734e24i	0.958287	−	0.538119i
$437$		−	5.76333e24i		−	0.474351i
$438$	−5.06489e24	+	7.81212e24i	−0.407912	+	0.629166i
$439$		−	1.65367e25i		−	1.30327i	−0.758532	−	0.651636i	$-0.774083\pi$
$439$		−	1.65367e25i		−	1.30327i	0.758532	−	0.651636i	$-0.225917\pi$
$440$	1.92013e25	−	1.85257e25i	1.48091	−	1.42881i
$441$	−5.11862e23	+	5.59223e24i	−0.0386355	+	0.422103i
$442$	4.02943e24	−	1.05395e24i	0.297668	−	0.0778586i
$443$	7.33835e24			0.530595			0.265297	−	0.964167i	$-0.414530\pi$
$443$	7.33835e24			0.530595			0.265297	+	0.964167i	$0.414530\pi$
$444$	−2.22067e25	−	7.34367e24i	−1.57162	−	0.519727i
$445$	−4.77841e24			−0.331027
$446$	3.40062e24	−	8.89473e23i	0.230609	−	0.0603186i
$447$	2.61740e24	−	2.38877e24i	0.173760	−	0.158582i
$448$	−1.16714e25	−	4.18155e23i	−0.758547	−	0.0271766i
$449$		−	1.50710e24i		−	0.0958962i	−0.998850	−	0.0479481i	$-0.984732\pi$
$449$		−	1.50710e24i		−	0.0958962i	0.998850	−	0.0479481i	$-0.0152682\pi$
$450$	−2.31067e25	+	3.83700e24i	−1.43953	+	0.239041i
$451$			5.13586e24i			0.313283i
$452$	−8.90647e24	−	1.58607e25i	−0.531974	−	0.947345i
$453$	8.46793e24	−	7.72825e24i	0.495273	−	0.452010i
$454$	4.85358e24	+	1.85561e25i	0.277992	+	1.06281i
$455$	5.06994e24			0.284377
$456$	2.59643e25	+	1.65210e24i	1.42630	+	0.0907552i
$457$	3.33751e25			1.79564			0.897818	−	0.440366i	$-0.145151\pi$
$457$	3.33751e25			1.79564			0.897818	+	0.440366i	$0.145151\pi$
$458$	−2.29467e24	−	8.77295e24i	−0.120920	−	0.462300i
$459$	1.50699e25	+	1.98860e25i	0.777840	+	1.02643i
$460$	−5.04054e24	−	8.97624e24i	−0.254846	−	0.453832i
$461$			3.16764e25i			1.56883i	0.620233	+	0.784417i	$0.287038\pi$
$461$			3.16764e25i			1.56883i	−0.620233	+	0.784417i	$0.712962\pi$
$462$	−1.72254e25	−	1.11679e25i	−0.835738	−	0.541840i
$463$			2.79699e25i			1.32945i	0.747088	+	0.664725i	$0.231451\pi$
$463$			2.79699e25i			1.32945i	−0.747088	+	0.664725i	$0.768549\pi$
$464$	1.94082e24	+	1.18319e24i	0.0903786	+	0.0550979i
$465$	−2.75759e25	−	3.02152e25i	−1.25813	−	1.37855i
$466$	2.13531e25	−	5.58516e24i	0.954541	−	0.249672i
$467$	−2.42851e25			−1.06373			−0.531863	−	0.846830i	$-0.678508\pi$
$467$	−2.42851e25			−1.06373			−0.531863	+	0.846830i	$0.678508\pi$
$468$	2.27168e24	+	5.08167e24i	0.0975017	+	0.218108i
$469$	6.94964e24			0.292294
$470$	−3.85644e25	+	1.00870e25i	−1.58949	+	0.415749i
$471$	−1.82804e25	−	2.00301e25i	−0.738394	−	0.809067i
$472$	−1.68774e25	−	1.74929e25i	−0.668122	−	0.692487i
$473$		−	2.35250e25i		−	0.912742i
$474$	−8.48289e24	−	5.49978e24i	−0.322589	−	0.209147i
$475$			5.59504e25i			2.08552i
$476$	−2.33281e25	+	1.30997e25i	−0.852340	+	0.478625i
$477$	−2.89948e25	−	2.65392e24i	−1.03847	−	0.0950524i
$478$	−3.67083e24	−	1.40342e25i	−0.128884	−	0.492747i
$479$	2.41544e25			0.831399			0.415699	−	0.909502i	$-0.363537\pi$
$479$	2.41544e25			0.831399			0.415699	+	0.909502i	$0.363537\pi$
$480$	4.18836e25	−	2.01349e25i	1.41336	−	0.679451i
$481$	−1.19535e25			−0.395472
$482$	−1.47839e25	−	5.65217e25i	−0.479561	−	1.83345i
$483$	−5.85057e24	+	5.33952e24i	−0.186080	+	0.169826i
$484$	−2.01836e25	+	1.13339e25i	−0.629458	+	0.353467i
$485$			5.96645e25i			1.82461i
$486$	−2.29186e25	+	2.42218e25i	−0.687295	+	0.726378i
$487$		−	3.28871e25i		−	0.967166i	−0.875299	−	0.483583i	$-0.839335\pi$
$487$		−	3.28871e25i		−	0.967166i	0.875299	−	0.483583i	$-0.160665\pi$
$488$	1.10222e25	+	1.14242e25i	0.317893	+	0.329486i
$489$	−1.18893e25	+	1.08508e25i	−0.336297	+	0.306921i
$490$	2.31805e25	−	6.06315e24i	0.643073	−	0.168204i
$491$	1.13908e25			0.309942			0.154971	−	0.987919i	$-0.450472\pi$
$491$	1.13908e25			0.309942			0.154971	+	0.987919i	$0.450472\pi$
$492$	−2.80861e24	+	8.49304e24i	−0.0749590	+	0.226670i
$493$	5.20718e24			0.136319
$494$	1.28634e25	−	3.36458e24i	0.330332	−	0.0864023i
$495$	8.13473e25	+	7.44580e24i	2.04925	+	0.187569i
$496$	4.11195e25	+	2.50679e25i	1.01618	+	0.619501i
$497$		−	4.21993e25i		−	1.02310i
$498$	−2.29662e25	+	3.54232e25i	−0.546273	+	0.842575i
$499$			1.13358e25i			0.264543i	0.991214	+	0.132271i	$0.0422270\pi$
$499$			1.13358e25i			0.264543i	−0.991214	+	0.132271i	$0.957773\pi$
$500$	1.53999e25	+	2.74243e25i	0.352617	+	0.627943i
$501$	−1.37867e25	−	1.51062e25i	−0.309743	−	0.339389i
$502$	6.68348e24	+	2.55522e25i	0.147339	+	0.563303i
$503$	5.32374e25			1.15165			0.575825	−	0.817573i	$-0.304681\pi$
$503$	5.32374e25			1.15165			0.575825	+	0.817573i	$0.304681\pi$
$504$	−2.23779e25	−	2.78879e25i	−0.475038	−	0.592006i
$505$	−1.34669e25			−0.280542
$506$	5.39079e24	+	2.06100e25i	0.110210	+	0.421354i
$507$	−3.16798e25	−	3.47119e25i	−0.635634	−	0.696471i
$508$	−1.94491e25	−	3.46351e25i	−0.382995	−	0.682042i
$509$			2.55740e25i			0.494287i	0.968979	+	0.247143i	$0.0794919\pi$
$509$			2.55740e25i			0.494287i	−0.968979	+	0.247143i	$0.920508\pi$
$510$	5.79150e25	−	8.93284e25i	1.09869	−	1.69462i
$511$		−	3.05648e25i		−	0.569145i
$512$	−4.07069e25	+	3.65527e25i	−0.744053	+	0.668121i
$513$	4.81087e25	+	6.34836e25i	0.863195	+	1.13906i
$514$	1.50515e25	−	3.93691e24i	0.265113	−	0.0693436i
$515$	−1.70642e26			−2.95064
$516$	1.28649e25	−	3.89026e25i	0.218391	−	0.660399i
$517$	8.24882e25			1.37478
$518$	7.42859e25	−	1.94304e25i	1.21555	−	0.317942i
$519$	−5.03638e25	+	4.59645e25i	−0.809150	+	0.738470i
$520$	1.70918e25	−	1.64904e25i	0.269623	−	0.260136i
$521$		−	6.33423e25i		−	0.981150i	−0.871399	−	0.490575i	$-0.836787\pi$
$521$		−	6.33423e25i		−	0.981150i	0.871399	−	0.490575i	$-0.163213\pi$
$522$	1.14000e24	+	6.86516e24i	0.0173394	+	0.104419i
$523$		−	1.28882e25i		−	0.192498i	−0.995357	−	0.0962491i	$-0.969315\pi$
$523$		−	1.28882e25i		−	0.192498i	0.995357	−	0.0962491i	$-0.0306845\pi$
$524$	1.95469e25	−	1.09764e25i	0.286701	−	0.160995i
$525$	5.67973e25	−	5.18360e25i	0.818115	−	0.746652i
$526$	5.07248e24	+	1.93930e25i	0.0717556	+	0.274335i
$527$	1.10323e26			1.53272
$528$	−9.43950e25	+	1.83779e25i	−1.28803	+	0.250769i
$529$	−6.63958e25			−0.889840
$530$	3.14364e25	+	1.20187e26i	0.413821	+	1.58211i
$531$	6.78332e24	−	7.41095e25i	0.0877090	−	0.958244i
$532$	−7.44718e25	+	4.18191e25i	−0.945870	+	0.531146i
$533$			4.57164e24i			0.0570379i
$534$	1.44514e25	+	9.36936e24i	0.177120	+	0.114833i
$535$		−	1.50389e26i		−	1.81074i
$536$	2.34287e25	−	2.26044e25i	0.277130	−	0.267379i
$537$	8.43448e25	+	9.24176e25i	0.980173	+	1.07399i
$538$	1.38662e25	−	3.62686e24i	0.158316	−	0.0414094i
$539$	−4.95826e25			−0.556206
$540$	1.30450e26	+	5.67988e25i	1.43782	+	0.626034i
$541$	−1.10046e26			−1.19179			−0.595896	−	0.803062i	$-0.703203\pi$
$541$	−1.10046e26			−1.19179			−0.595896	+	0.803062i	$0.703203\pi$
$542$	−4.25104e25	+	1.11191e25i	−0.452379	+	0.118325i
$543$	−1.44519e25	−	1.58351e25i	−0.151122	−	0.165586i
$544$	−3.60359e25	+	1.20039e26i	−0.370293	+	1.23348i
$545$		−	1.70679e26i		−	1.72351i
$546$	−1.53330e25	−	9.94097e24i	−0.152159	−	0.0986504i
$547$			5.77446e25i			0.563160i	0.959538	+	0.281580i	$0.0908585\pi$
$547$			5.77446e25i			0.563160i	−0.959538	+	0.281580i	$0.909141\pi$
$548$	−3.84780e25	−	6.85221e25i	−0.368806	−	0.656773i
$549$	−4.43003e24	+	4.83993e25i	−0.0417320	+	0.455934i
$550$	−5.23338e25	−	2.00082e26i	−0.484548	−	1.85251i
$551$	1.66232e25			0.151278
$552$	−2.35623e24	+	3.70302e25i	−0.0210764	+	0.331234i
$553$	3.31891e25			0.291815
$554$	−1.62123e22	−	6.19827e22i	−0.000140121	−	0.000535707i
$555$	−2.25680e26	+	2.05967e26i	−1.91739	+	1.74990i
$556$	8.95410e25	+	1.59455e26i	0.747844	+	1.33177i
$557$		−	9.71955e25i		−	0.798035i	−0.916943	−	0.399017i	$-0.869351\pi$
$557$		−	9.71955e25i		−	0.798035i	0.916943	−	0.399017i	$-0.130649\pi$
$558$	2.41528e25	+	1.45450e26i	0.194958	+	1.17405i
$559$		−	2.09405e25i		−	0.166179i
$560$	−7.94136e25	+	1.30264e26i	−0.619596	+	1.01634i
$561$	−1.62723e26	+	1.48509e26i	−1.24825	+	1.13921i
$562$	−1.26322e26	+	3.30410e25i	−0.952760	+	0.249206i
$563$	5.47152e25			0.405769			0.202884	−	0.979203i	$-0.434968\pi$
$563$	5.47152e25			0.405769			0.202884	+	0.979203i	$0.434968\pi$
$564$	1.36409e26	+	4.51098e25i	0.994696	+	0.328942i
$565$	−2.37622e26			−1.70383
$566$	1.54221e26	−	4.03384e25i	1.08740	−	0.284421i
$567$	1.98735e25	−	1.07652e26i	0.137796	−	0.746421i
$568$	−1.37257e26	−	1.42263e26i	−0.935893	−	0.970024i
$569$			4.65367e25i			0.312053i	0.987753	+	0.156027i	$0.0498686\pi$
$569$			4.65367e25i			0.312053i	−0.987753	+	0.156027i	$0.950131\pi$
$570$	1.84886e26	−	2.85169e26i	1.21925	−	1.88058i
$571$			1.86299e26i			1.20828i	0.796878	+	0.604141i	$0.206484\pi$
$571$			1.86299e26i			1.20828i	−0.796878	+	0.604141i	$0.793516\pi$
$572$	−4.28532e25	+	2.40639e25i	−0.273351	+	0.153498i
$573$	2.66195e25	+	2.91673e25i	0.167005	+	0.182990i
$574$	−7.43122e24	−	2.84109e25i	−0.0458561	−	0.175316i
$575$	−7.97963e25			−0.484326
$576$	−1.66149e26	−	2.12300e25i	−0.991935	−	0.126747i
$577$	2.93815e26			1.72545			0.862727	−	0.505671i	$-0.168755\pi$
$577$	2.93815e26			1.72545			0.862727	+	0.505671i	$0.168755\pi$
$578$	2.88491e25	+	1.10295e26i	0.166655	+	0.637151i
$579$	1.24355e26	+	1.36258e26i	0.706673	+	0.774309i
$580$	2.58903e25	−	1.45385e25i	0.144734	−	0.0812743i
$581$		−	1.38592e26i		−	0.762195i
$582$	1.16988e26	−	1.80443e26i	0.632957	−	0.976277i
$583$		−	2.57077e26i		−	1.36840i
$584$	−9.94148e25	−	1.03040e26i	−0.520630	−	0.539617i
$585$	7.24106e25	+	6.62781e24i	0.373097	+	0.0341499i
$586$	−6.85070e25	+	1.79188e25i	−0.347302	+	0.0908411i
$587$	1.71010e26			0.853022			0.426511	−	0.904482i	$-0.359742\pi$
$587$	1.71010e26			0.853022			0.426511	+	0.904482i	$0.359742\pi$
$588$	−8.19933e25	−	2.71149e25i	−0.402433	−	0.133083i
$589$	3.52190e26			1.70091
$590$	−3.07194e26	+	8.03502e25i	−1.45988	+	0.381850i
$591$	2.54510e26	−	2.32279e26i	1.19021	−	1.08625i
$592$	1.87234e26	−	3.07126e26i	0.861647	−	1.41338i
$593$			2.23812e24i			0.0101359i	0.999987	+	0.00506797i	$0.00161319\pi$
$593$			2.23812e24i			0.0101359i	−0.999987	+	0.00506797i	$0.998387\pi$
$594$	−2.31419e26	−	1.82022e26i	−1.03140	−	0.811245i
$595$			3.49495e26i			1.53296i
$596$	2.66825e25	+	4.75164e25i	0.115182	+	0.205118i
$597$	3.93577e25	−	3.59197e25i	0.167214	−	0.152608i
$598$	4.79856e24	+	1.83458e25i	0.0200655	+	0.0767141i
$599$	1.87477e26			0.771601			0.385801	−	0.922582i	$-0.373925\pi$
$599$	1.87477e26			0.771601			0.385801	+	0.922582i	$0.373925\pi$
$600$	2.28742e25	−	3.59489e26i	0.0926638	−	1.45629i
$601$	−4.30174e26			−1.71529			−0.857644	−	0.514244i	$-0.828072\pi$
$601$	−4.30174e26			−1.71529			−0.857644	+	0.514244i	$0.828072\pi$
$602$	3.40389e25	+	1.30137e26i	0.133601	+	0.510780i
$603$	9.92572e25	+	9.08511e24i	0.383484	+	0.0351007i
$604$	8.63243e25	+	1.53727e26i	0.328308	+	0.584655i
$605$			3.02385e26i			1.13210i
$606$	4.07279e25	+	2.64054e25i	0.150107	+	0.0973202i
$607$			6.47943e25i			0.235096i	0.993067	+	0.117548i	$0.0375033\pi$
$607$			6.47943e25i			0.235096i	−0.993067	+	0.117548i	$0.962497\pi$
$608$	−1.15040e26	+	3.83208e26i	−0.410927	+	1.36883i
$609$	−1.54008e25	−	1.68749e25i	−0.0541602	−	0.0593439i
$610$	2.00621e26	−	5.24749e25i	0.694614	−	0.181685i
$611$	7.34262e25			0.250299
$612$	−3.50305e26	+	1.56598e26i	−1.17573	+	0.525591i
$613$	−6.85698e25			−0.226599			−0.113300	−	0.993561i	$-0.536142\pi$
$613$	−6.85698e25			−0.226599			−0.113300	+	0.993561i	$0.536142\pi$
$614$	−2.33783e26	+	6.11488e25i	−0.760700	+	0.198970i
$615$	7.87727e25	+	8.63122e25i	0.252384	+	0.276540i
$616$	2.27199e26	−	2.19205e26i	0.716787	−	0.691567i
$617$			4.75871e26i			1.47836i	0.673509	+	0.739179i	$0.264786\pi$
$617$			4.75871e26i			1.47836i	−0.673509	+	0.739179i	$0.735214\pi$
$618$	5.16072e26	+	3.34589e26i	1.57877	+	1.02358i
$619$		−	7.07834e25i		−	0.213241i	−0.994300	−	0.106620i	$-0.965997\pi$
$619$		−	7.07834e25i		−	0.213241i	0.994300	−	0.106620i	$-0.0340030\pi$
$620$	5.48528e26	−	3.08021e26i	1.62734	−	0.913818i
$621$	−9.05401e25	+	6.86125e25i	−0.264527	+	0.200463i
$622$	4.13527e25	+	1.58099e26i	0.118986	+	0.454904i
$623$	−5.65407e25			−0.160223
$624$	−8.40248e25	+	1.63590e25i	−0.234506	+	0.0456564i
$625$	−1.20004e26			−0.329863
$626$	−1.42217e26	−	5.43721e26i	−0.385030	−	1.47204i
$627$	−5.19472e26	+	4.74095e26i	−1.38522	+	1.26422i
$628$	3.63627e26	−	2.04192e26i	0.955080	−	0.536318i
$629$		−	8.24010e26i		−	2.13182i
$630$	−4.60776e26	+	7.65145e25i	−1.17423	+	0.194988i
$631$			1.30069e25i			0.0326508i	0.999867	+	0.0163254i	$0.00519677\pi$
$631$			1.30069e25i			0.0326508i	−0.999867	+	0.0163254i	$0.994803\pi$
$632$	1.11888e26	−	1.07951e26i	0.276675	−	0.266940i
$633$	−6.91196e25	+	6.30819e25i	−0.168370	+	0.153663i
$634$	−5.48483e26	+	1.43462e26i	−1.31618	+	0.344263i
$635$	−5.18895e26			−1.22667
$636$	1.40586e26	−	4.25122e26i	0.327416	−	0.990081i
$637$	−4.41355e25			−0.101266
$638$	−5.94456e25	+	1.55487e25i	−0.134376	+	0.0351478i
$639$	5.51662e25	−	6.02705e26i	0.122861	−	1.34229i
$640$	1.55977e26	+	6.97449e26i	0.342256	+	1.53039i
$641$		−	3.20078e26i		−	0.691998i	−0.938235	−	0.345999i	$-0.887540\pi$
$641$		−	3.20078e26i		−	0.691998i	0.938235	−	0.345999i	$-0.112460\pi$
$642$	−2.94878e26	+	4.54822e26i	−0.628144	+	0.968854i
$643$			3.32867e25i			0.0698661i	0.999390	+	0.0349330i	$0.0111218\pi$
$643$			3.32867e25i			0.0698661i	−0.999390	+	0.0349330i	$0.988878\pi$
$644$	−5.96422e25	−	1.06212e26i	−0.123350	−	0.219662i
$645$	−3.60821e26	−	3.95355e26i	−0.735316	−	0.805694i
$646$	2.31937e26	+	8.86739e26i	0.465759	+	1.78068i
$647$	6.57665e26			1.30141			0.650705	−	0.759331i	$-0.274473\pi$
$647$	6.57665e26			1.30141			0.650705	+	0.759331i	$0.274473\pi$
$648$	−2.83151e26	−	4.27559e26i	−0.552149	−	0.833746i
$649$	6.57079e26			1.26268
$650$	−4.65844e25	−	1.78101e26i	−0.0882193	−	0.337279i
$651$	−3.26292e26	−	3.57522e26i	−0.608957	−	0.667241i
$652$	−1.21203e26	−	2.15839e26i	−0.222926	−	0.396989i
$653$			5.01928e26i			0.909842i	0.890532	+	0.454921i	$0.150332\pi$
$653$			5.01928e26i			0.909842i	−0.890532	+	0.454921i	$0.849668\pi$
$654$	−3.34662e26	+	5.16185e26i	−0.597885	+	0.922182i
$655$		−	2.92846e26i		−	0.515641i
$656$	−1.17461e26	−	7.16085e25i	−0.203849	−	0.124273i
$657$	3.99566e25	−	4.36537e26i	0.0683467	−	0.746706i
$658$	−4.56314e26	+	1.19354e26i	−0.769339	+	0.201230i
$659$	−1.13283e27			−1.88258			−0.941291	−	0.337597i	$-0.890386\pi$
$659$	−1.13283e27			−1.88258			−0.941291	+	0.337597i	$0.890386\pi$
$660$	−3.94426e26	+	1.19272e27i	−0.646098	+	1.95375i
$661$	8.61177e26			1.39052			0.695262	−	0.718757i	$-0.255288\pi$
$661$	8.61177e26			1.39052			0.695262	+	0.718757i	$0.255288\pi$
$662$	7.31116e26	−	1.91232e26i	1.16369	−	0.304376i
$663$	−1.44846e26	+	1.32194e26i	−0.227263	+	0.207412i
$664$	−4.50785e26	−	4.67225e26i	−0.697225	−	0.722652i
$665$			1.11572e27i			1.70118i
$666$	1.08638e27	−	1.80399e26i	1.63296	−	0.271162i
$667$			2.37080e25i			0.0351317i
$668$	2.74239e26	−	1.53997e26i	0.400639	−	0.224976i
$669$	−1.22242e26	+	1.11564e26i	−0.176065	+	0.160686i
$670$	−1.07616e26	−	4.11434e26i	−0.152815	−	0.584238i
$671$	−4.29124e26			−0.600785
$672$	4.95589e26	−	2.38247e26i	0.684090	−	0.328866i
$673$	3.14093e26			0.427479			0.213740	−	0.976891i	$-0.431436\pi$
$673$	3.14093e26			0.427479			0.213740	+	0.976891i	$0.431436\pi$
$674$	4.27574e25	+	1.63469e26i	0.0573775	+	0.219365i
$675$	8.78963e26	−	6.66090e26i	1.16301	−	0.881348i
$676$	6.30162e26	−	3.53863e26i	0.822164	−	0.461680i
$677$		−	3.75912e26i		−	0.483608i	−0.970325	−	0.241804i	$-0.922261\pi$
$677$		−	3.75912e26i		−	0.483608i	0.970325	−	0.241804i	$-0.0777392\pi$
$678$	7.18639e26	+	4.65921e26i	0.911652	+	0.591058i
$679$			7.05981e26i			0.883142i
$680$	1.13677e27	+	1.17822e27i	1.40229	+	1.45343i
$681$	−6.08773e26	−	6.67040e26i	−0.740556	−	0.811436i
$682$	−1.25945e27	+	3.29425e26i	−1.51088	+	0.395189i
$683$	−5.89424e26			−0.697319			−0.348659	−	0.937249i	$-0.613363\pi$
$683$	−5.89424e26			−0.697319			−0.348659	+	0.937249i	$0.613363\pi$
$684$	−1.11830e27	+	4.99919e26i	−1.30475	+	0.583266i
$685$	−1.02658e27			−1.18123
$686$	9.21382e26	−	2.40999e26i	1.04559	−	0.273486i
$687$	2.87815e26	+	3.15362e26i	0.322125	+	0.352956i
$688$	5.38035e26	+	3.28004e26i	0.593910	+	0.362068i
$689$		−	2.28835e26i		−	0.249138i
$690$	4.06707e26	+	2.63684e26i	0.436733	+	0.283150i
$691$		−	8.23647e26i		−	0.872368i	−0.899857	−	0.436184i	$-0.856330\pi$
$691$		−	8.23647e26i		−	0.872368i	0.899857	−	0.436184i	$-0.143670\pi$
$692$	−5.13422e26	−	9.14307e26i	−0.536373	−	0.955178i
$693$	9.62544e26	+	8.81026e25i	0.991870	+	0.0907868i
$694$	−2.36302e26	−	9.03425e26i	−0.240189	−	0.918285i
$695$	2.38892e27			2.39523
$696$	−1.06807e26	−	6.79610e24i	−0.105636	−	0.00672159i
$697$	−3.15146e26			−0.307468
$698$	−3.55638e26	−	1.35967e27i	−0.342280	−	1.30860i
$699$	−7.67582e26	+	7.00533e26i	−0.728772	+	0.665113i
$700$	5.79007e26	+	1.03110e27i	0.542316	+	0.965761i
$701$			1.95748e27i			1.80874i	0.426750	+	0.904369i	$0.359658\pi$
$701$			1.95748e27i			1.80874i	−0.426750	+	0.904369i	$0.640342\pi$
$702$	−2.05996e26	−	1.62025e26i	−0.187783	−	0.147700i
$703$		−	2.63054e27i		−	2.36576i
$704$	5.29517e25	−	1.47798e27i	0.0469829	−	1.31137i
$705$	1.38628e27	−	1.26519e27i	1.21354	−	1.10754i
$706$	1.53503e27	−	4.01505e26i	1.32578	−	0.346774i
$707$	−1.59347e26			−0.135787
$708$	1.08659e27	+	3.59332e26i	0.913591	+	0.302121i
$709$	−1.32128e27			−1.09611			−0.548057	−	0.836441i	$-0.684632\pi$
$709$	−1.32128e27			−1.09611			−0.548057	+	0.836441i	$0.684632\pi$
$710$	−2.49829e27	+	6.53459e26i	−2.04498	+	0.534889i
$711$	4.74019e26	+	4.33874e25i	0.382855	+	0.0350431i
$712$	−1.90611e26	+	1.83904e26i	−0.151910	+	0.146565i
$713$			5.02293e26i			0.395009i
$714$	6.85280e26	−	1.05698e27i	0.531784	−	0.820226i
$715$			6.42016e26i			0.491630i
$716$	−1.67775e27	+	9.42129e26i	−1.26781	+	0.711929i
$717$	4.60423e26	+	5.04491e26i	0.343341	+	0.376202i
$718$	−6.09886e26	−	2.33171e27i	−0.448814	−	1.71590i
$719$	−1.98161e27			−1.43911			−0.719553	−	0.694438i	$-0.755653\pi$
$719$	−1.98161e27			−1.43911			−0.719553	+	0.694438i	$0.755653\pi$
$720$	−1.30450e27	+	1.75666e27i	−0.934946	+	1.25901i
$721$	−2.01912e27			−1.42816
$722$	3.77929e26	+	1.44489e27i	0.263820	+	1.00863i
$723$	1.85431e27	+	2.03179e27i	1.27753	+	1.39980i
$724$	2.87472e26	−	1.61427e26i	0.195469	−	0.109764i
$725$		−	2.30157e26i		−	0.154459i
$726$	5.92907e26	−	9.14504e26i	0.392725	−	0.605742i
$727$			2.83819e27i			1.85551i	0.373185	+	0.927757i	$0.378266\pi$
$727$			2.83819e27i			1.85551i	−0.373185	+	0.927757i	$0.621734\pi$
$728$	2.02239e26	−	1.95124e26i	0.130502	−	0.125910i
$729$	4.24572e26	−	1.51155e27i	0.270421	−	0.962742i
$730$	−1.80950e27	+	4.73297e26i	−1.13761	+	0.297555i
$731$	1.44353e27			0.895801
$732$	−7.09631e26	−	2.34672e26i	−0.434688	−	0.143749i
$733$	1.03374e27			0.625064			0.312532	−	0.949907i	$-0.398823\pi$
$733$	1.03374e27			0.625064			0.312532	+	0.949907i	$0.398823\pi$
$734$	1.46782e27	−	3.83925e26i	0.876111	−	0.229157i
$735$	−8.33273e26	+	7.60486e26i	−0.490973	+	0.448086i
$736$	−5.46530e26	−	1.64070e26i	−0.317888	−	0.0954309i
$737$			8.80047e26i			0.505318i
$738$	−6.89943e25	−	4.15489e26i	−0.0391091	−	0.235518i
$739$			2.99468e27i			1.67583i	0.545805	+	0.837913i	$0.316224\pi$
$739$			2.99468e27i			1.67583i	−0.545805	+	0.837913i	$0.683776\pi$
$740$	−2.30064e27	−	4.09701e27i	−1.27101	−	2.26342i
$741$	−4.62403e26	+	4.22012e26i	−0.252202	+	0.230172i
$742$	3.71972e26	+	1.42212e27i	0.200296	+	0.765770i
$743$	−7.43215e26			−0.395113			−0.197556	−	0.980292i	$-0.563301\pi$
$743$	−7.43215e26			−0.395113			−0.197556	+	0.980292i	$0.563301\pi$
$744$	−2.26287e27	−	1.43986e26i	−1.18773	−	0.0755751i
$745$	7.11879e26			0.368911
$746$	7.21634e26	+	2.75894e27i	0.369231	+	1.41164i
$747$	1.81179e26	−	1.97943e27i	0.0915296	−	0.999985i
$748$	−1.65884e27	−	2.95408e27i	−0.827446	−	1.47352i
$749$		−	1.77948e27i		−	0.876427i
$750$	−1.24258e27	−	8.05609e26i	−0.604284	−	0.391780i
$751$			1.16386e26i			0.0558883i	0.999609	+	0.0279441i	$0.00889605\pi$
$751$			1.16386e26i			0.0558883i	−0.999609	+	0.0279441i	$0.991104\pi$
$752$	−1.15012e27	+	1.88657e27i	−0.545348	+	0.894549i
$753$	−8.38293e26	−	9.18527e26i	−0.392503	−	0.430070i
$754$	−5.29150e25	+	1.38406e25i	−0.0244653	+	0.00639920i
$755$	2.30310e27			1.05152
$756$	1.54355e27	+	6.72073e26i	0.695928	+	0.303012i
$757$	−4.60430e26			−0.204999			−0.102500	−	0.994733i	$-0.532684\pi$
$757$	−4.60430e26			−0.204999			−0.102500	+	0.994733i	$0.532684\pi$
$758$	3.28457e27	−	8.59119e26i	1.44418	−	0.377742i
$759$	−6.76154e26	−	7.40869e26i	−0.293595	−	0.321695i
$760$	3.62898e27	+	3.76132e27i	1.55616	+	1.61292i
$761$			7.62087e26i			0.322738i	0.986894	+	0.161369i	$0.0515909\pi$
$761$			7.62087e26i			0.322738i	−0.986894	+	0.161369i	$0.948409\pi$
$762$	1.56929e27	+	1.01743e27i	0.656345	+	0.425533i
$763$		−	2.01956e27i		−	0.834208i
$764$	−5.29504e26	+	2.97339e26i	−0.216014	+	0.121301i
$765$	−4.56887e26	+	4.99162e27i	−0.184088	+	2.01121i
$766$	−2.37075e26	−	9.06381e26i	−0.0943436	−	0.360693i
$767$	5.84893e26			0.229890
$768$	8.95815e26	−	2.41513e27i	0.347766	−	0.937582i
$769$	8.04603e26			0.308519			0.154259	−	0.988030i	$-0.450701\pi$
$769$	8.04603e26			0.308519			0.154259	+	0.988030i	$0.450701\pi$
$770$	−1.04360e27	−	3.98987e27i	−0.395250	−	1.51111i
$771$	−5.41060e26	+	4.93798e26i	−0.202408	+	0.184728i
$772$	−2.47363e27	+	1.38905e27i	−0.914050	+	0.513278i
$773$		−	2.45018e27i		−	0.894319i	−0.894454	−	0.447160i	$-0.852436\pi$
$773$		−	2.45018e27i		−	0.894319i	0.894454	−	0.447160i	$-0.147564\pi$
$774$	3.16030e26	+	1.90316e27i	0.113944	+	0.686177i
$775$		−	4.87626e27i		−	1.73668i
$776$	2.29627e27	+	2.38001e27i	0.807861	+	0.837323i
$777$	−2.67036e27	+	2.43711e27i	−0.928049	+	0.846983i
$778$	9.36172e26	−	2.44867e26i	0.321403	−	0.0840668i
$779$	−1.00606e27			−0.341208
$780$	−3.51095e26	+	1.06168e27i	−0.117632	+	0.355711i
$781$	5.34378e27			1.76874
$782$	−1.26466e27	+	3.30788e26i	−0.413534	+	0.108165i
$783$	−1.97900e26	−	2.61146e26i	−0.0639306	−	0.0843619i
$784$	6.91321e26	−	1.13399e27i	0.220636	−	0.361916i
$785$		−	5.44777e27i		−	1.71774i
$786$	−5.74204e26	+	8.85656e26i	−0.178876	+	0.275899i
$787$		−	2.68602e27i		−	0.826703i	−0.910571	−	0.413352i	$-0.864358\pi$
$787$		−	2.68602e27i		−	0.826703i	0.910571	−	0.413352i	$-0.135642\pi$
$788$	2.59455e27	+	4.62039e27i	0.788973	+	1.40501i
$789$	−6.36229e26	−	6.97124e26i	−0.191153	−	0.209449i
$790$	−5.13936e26	−	1.96487e27i	−0.152564	−	0.583279i
$791$	−2.81166e27			−0.824682
$792$	3.53150e27	−	2.83375e27i	1.02346	−	0.821245i
$793$	−3.81981e26			−0.109382
$794$	−1.87821e26	−	7.18073e26i	−0.0531434	−	0.203177i
$795$	−3.94299e27	−	4.32038e27i	−1.10240	−	1.20791i
$796$	4.01222e26	+	7.14501e26i	0.110844	+	0.197392i
$797$			1.02884e27i			0.280861i	0.990091	+	0.140431i	$0.0448487\pi$
$797$			1.02884e27i			0.280861i	−0.990091	+	0.140431i	$0.955151\pi$
$798$	2.18767e27	−	3.37427e27i	0.590138	−	0.910233i
$799$			5.06162e27i			1.34926i
$800$	5.30571e27	+	1.59279e27i	1.39762	+	0.419569i
$801$	−8.07533e26	−	7.39143e25i	−0.210209	−	0.0192406i
$802$	3.83096e27	−	1.00203e27i	0.985487	−	0.257766i
$803$	3.87048e27			0.983936
$804$	−4.81265e26	+	1.45531e27i	−0.120907	+	0.365614i
$805$	−1.59123e27			−0.395069
$806$	−1.12109e27	+	2.93235e26i	−0.275079	+	0.0719503i
$807$	−4.98448e26	+	4.54909e26i	−0.120871	+	0.110313i
$808$	−5.37192e26	+	5.18291e26i	−0.128743	+	0.124213i
$809$			1.61127e27i			0.381643i	0.981625	+	0.190821i	$0.0611152\pi$
$809$			1.61127e27i			0.381643i	−0.981625	+	0.190821i	$0.938885\pi$
$810$	−6.68099e27	+	4.90445e26i	−1.56399	+	0.114811i
$811$			7.29737e26i			0.168837i	0.996430	+	0.0844186i	$0.0269033\pi$
$811$			7.29737e26i			0.168837i	−0.996430	+	0.0844186i	$0.973097\pi$
$812$	3.06347e26	−	1.72027e26i	0.0700538	−	0.0393382i
$813$	1.52813e27	−	1.39464e27i	0.345382	−	0.315212i
$814$	2.46051e27	+	9.40697e27i	0.549658	+	2.10144i
$815$	−3.23365e27			−0.713996
$816$	−1.12770e27	−	5.79224e27i	−0.246115	−	1.26413i
$817$	4.60829e27			0.994100
$818$	1.20424e27	+	4.60402e27i	0.256777	+	0.981705i
$819$	8.56800e26	+	7.84237e25i	0.180585	+	0.0165291i
$820$	−1.56692e27	+	8.79889e26i	−0.326448	+	0.183314i
$821$		−	4.82805e26i		−	0.0994288i	−0.998763	−	0.0497144i	$-0.984169\pi$
$821$		−	4.82805e26i		−	0.0994288i	0.998763	−	0.0497144i	$-0.0158311\pi$
$822$	3.10469e27	+	2.01289e27i	0.632028	+	0.409767i
$823$			1.78983e27i			0.360174i	0.983651	+	0.180087i	$0.0576379\pi$
$823$			1.78983e27i			0.360174i	−0.983651	+	0.180087i	$0.942362\pi$
$824$	−6.80688e27	+	6.56738e27i	−1.35407	+	1.30642i
$825$	6.56410e27	+	7.19236e27i	1.29081	+	1.41436i
$826$	−3.63488e27	+	9.50746e26i	−0.706609	+	0.184822i
$827$	3.88511e26			0.0746622			0.0373311	−	0.999303i	$-0.488114\pi$
$827$	3.88511e26			0.0746622			0.0373311	+	0.999303i	$0.488114\pi$
$828$	−7.12983e26	−	1.59492e27i	−0.135454	−	0.303005i
$829$	−8.91483e27			−1.67435			−0.837173	−	0.546939i	$-0.815793\pi$
$829$	−8.91483e27			−1.67435			−0.837173	+	0.546939i	$0.815793\pi$
$830$	−8.20498e27	+	2.14611e27i	−1.52348	+	0.398483i
$831$	2.03347e24	+	2.22810e24i	0.000373275	+	0.000409001i
$832$	4.71345e25	−	1.31561e27i	0.00855397	−	0.238756i
$833$		−	3.04247e27i		−	0.545883i
$834$	−7.22482e27	−	4.68413e27i	−1.28159	−	0.830904i
$835$		−	4.10859e27i		−	0.720561i
$836$	−5.29563e27	−	9.43051e27i	−0.918244	−	1.63522i
$837$	−4.19284e27	−	5.53280e27i	−0.718813	−	0.948535i
$838$	1.70244e27	+	6.50874e27i	0.288572	+	1.10326i
$839$	−9.48739e27			−1.59004			−0.795020	−	0.606583i	$-0.792540\pi$
$839$	−9.48739e27			−1.59004			−0.795020	+	0.606583i	$0.792540\pi$
$840$	4.56140e26	−	7.16865e27i	0.0755867	−	1.18791i
$841$	6.03488e27			0.988796
$842$	3.07679e25	+	1.17632e26i	0.00498464	+	0.0190572i
$843$	4.54091e27	−	4.14425e27i	0.727412	−	0.663872i
$844$	−7.04623e26	−	1.25480e27i	−0.111610	−	0.198756i
$845$		−	9.44093e27i		−	1.47869i
$846$	−6.67326e27	+	1.10813e27i	−1.03352	+	0.171622i
$847$			3.57798e27i			0.547955i
$848$	5.87957e27	+	3.58438e27i	0.890399	+	0.542818i
$849$	−5.54380e27	+	5.05955e27i	−0.830204	+	0.757685i
$850$	1.22774e28	−	3.21129e27i	1.81813	−	0.475554i
$851$	3.75168e27			0.549407
$852$	8.83687e27	+	2.92232e27i	1.27974	+	0.423205i
$853$	7.33843e26			0.105096			0.0525481	−	0.998618i	$-0.483266\pi$
$853$	7.33843e26			0.105096			0.0525481	+	0.998618i	$0.483266\pi$
$854$	2.37386e27	−	6.20911e26i	0.336205	−	0.0879386i
$855$	−1.45855e27	+	1.59351e28i	−0.204289	+	2.23191i
$856$	−5.78793e27	−	5.99901e27i	−0.801719	−	0.830957i
$857$			2.19336e27i			0.300463i	0.988651	+	0.150232i	$0.0480019\pi$
$857$			2.19336e27i			0.300463i	−0.988651	+	0.150232i	$0.951998\pi$
$858$	1.25885e27	−	1.94165e27i	0.170547	−	0.263052i
$859$			5.56537e27i			0.745692i	0.927893	+	0.372846i	$0.121618\pi$
$859$			5.56537e27i			0.745692i	−0.927893	+	0.372846i	$0.878382\pi$
$860$	7.17730e27	−	4.03035e27i	0.951099	−	0.534082i
$861$	9.32080e26	+	1.02129e27i	0.122158	+	0.133850i
$862$	−1.66632e27	−	6.37067e27i	−0.215993	−	0.825783i
$863$	1.15030e28			1.47471			0.737355	−	0.675505i	$-0.236074\pi$
$863$	1.15030e28			1.47471			0.737355	+	0.675505i	$0.236074\pi$
$864$	7.38963e27	−	2.75485e27i	0.937005	−	0.349316i
$865$	−1.36979e28			−1.71792
$866$	1.67472e27	+	6.40277e27i	0.207741	+	0.794234i
$867$	−3.61847e27	−	3.96480e27i	−0.443960	−	0.486452i
$868$	6.49047e27	−	3.64467e27i	0.787660	−	0.442304i
$869$			4.20281e27i			0.504489i
$870$	−7.60546e26	+	1.17307e27i	−0.0903011	+	0.139281i
$871$			7.83366e26i			0.0920009i
$872$	−6.56882e27	−	6.80837e27i	−0.763098	−	0.790928i
$873$	−9.22913e26	+	1.00831e28i	−0.106054	+	1.15866i
$874$	−4.03727e27	+	1.05600e27i	−0.458912	+	0.120034i
$875$	4.86156e27			0.546637
$876$	6.40050e27	+	2.11662e27i	0.711910	+	0.235426i
$877$	4.56288e27			0.502045			0.251023	−	0.967981i	$-0.419233\pi$
$877$	4.56288e27			0.502045			0.251023	+	0.967981i	$0.419233\pi$
$878$	−1.15841e28	+	3.02997e27i	−1.26085	+	0.329792i
$879$	2.46263e27	−	2.24752e27i	0.265158	−	0.241996i
$880$	−1.64956e28	−	1.00563e28i	−1.75705	−	1.07116i
$881$			1.71287e26i			0.0180490i	0.999959	+	0.00902451i	$0.00287263\pi$
$881$			1.71287e26i			0.0180490i	−0.999959	+	0.00902451i	$0.997127\pi$
$882$	4.01121e27	−	6.66084e26i	0.418142	−	0.0694348i
$883$		−	1.68442e28i		−	1.73709i	−0.495607	−	0.868547i	$-0.665054\pi$
$883$		−	1.68442e28i		−	1.73709i	0.495607	−	0.868547i	$-0.334946\pi$
$884$	−1.47660e27	−	2.62955e27i	−0.150649	−	0.268278i
$885$	1.10427e28	−	1.00781e28i	1.11459	−	1.01723i
$886$	−1.34458e27	−	5.14059e27i	−0.134267	−	0.513326i
$887$	1.23707e28			1.22214			0.611068	−	0.791578i	$-0.290740\pi$
$887$	1.23707e28			1.22214			0.611068	+	0.791578i	$0.290740\pi$
$888$	−1.07545e27	+	1.69016e28i	−0.105115	+	1.65198i
$889$	−6.13983e27			−0.593731
$890$	8.75535e26	+	3.34733e27i	0.0837661	+	0.320253i
$891$	1.36322e28	+	2.51662e27i	1.29041	+	0.238221i
$892$	−1.24617e27	−	2.21919e27i	−0.116711	−	0.207840i
$893$			1.61586e28i			1.49732i
$894$	−2.15294e27	−	1.39583e27i	−0.197390	−	0.127975i
$895$			2.51357e28i			2.28019i
$896$	1.84560e27	+	8.25258e27i	0.165658	+	0.740736i
$897$	−6.01872e26	−	6.59478e26i	−0.0534535	−	0.0585696i
$898$	−1.05574e27	+	2.76141e26i	−0.0927751	+	0.0242665i
$899$	−1.44877e27			−0.125974
$900$	6.92164e27	+	1.54835e28i	0.595532	+	1.33218i
$901$	1.57747e28			1.34300
$902$	3.59773e27	−	9.41030e26i	0.303086	−	0.0792759i
$903$	−4.26942e27	−	4.67805e27i	−0.355906	−	0.389970i
$904$	−9.47871e27	+	9.14520e27i	−0.781896	+	0.754385i
$905$		−	4.30683e27i		−	0.351557i
$906$	−6.96528e27	−	4.51585e27i	−0.562627	−	0.364772i
$907$		−	1.71691e28i		−	1.37239i	−0.727417	−	0.686195i	$-0.759280\pi$
$907$		−	1.71691e28i		−	1.37239i	0.727417	−	0.686195i	$-0.240720\pi$
$908$	1.21095e28	−	6.79998e27i	0.957877	−	0.537888i
$909$	−2.27585e27	−	2.08311e26i	−0.178150	−	0.0163063i
$910$	−9.28950e26	−	3.55155e27i	−0.0719613	−	0.275121i
$911$	−5.54547e27			−0.425122			−0.212561	−	0.977148i	$-0.568180\pi$
$911$	−5.54547e27			−0.425122			−0.212561	+	0.977148i	$0.568180\pi$
$912$	−3.60004e27	−	1.84910e28i	−0.273122	−	1.40284i
$913$	1.75502e28			1.31768
$914$	−6.11522e27	−	2.33796e28i	−0.454384	−	1.73719i
$915$	−7.21176e27	+	6.58181e27i	−0.530323	+	0.483999i
$916$	−5.72510e27	+	3.21489e27i	−0.416655	+	0.233969i
$917$		−	3.46511e27i		−	0.249579i
$918$	1.11692e28	−	1.42003e28i	0.796188	−	1.01226i
$919$		−	4.55467e26i		−	0.0321336i	−0.999871	−	0.0160668i	$-0.994886\pi$
$919$		−	4.55467e26i		−	0.0321336i	0.999871	−	0.0160668i	$-0.00511444\pi$
$920$	−5.36439e27	+	5.17564e27i	−0.374573	+	0.361393i
$921$	8.40382e27	−	7.66974e27i	0.580778	−	0.530047i
$922$	2.21897e28	−	5.80398e27i	1.51777	−	0.396992i
$923$	4.75672e27			0.322026
$924$	−4.66705e27	+	1.41128e28i	−0.312723	+	0.945650i
$925$	−3.64213e28			−2.41551
$926$	1.95932e28	−	5.12485e27i	1.28618	−	0.336416i
$927$	−2.88378e28	−	2.63955e27i	−1.87372	−	0.171503i
$928$	4.73228e26	−	1.57636e27i	0.0304344	−	0.101380i
$929$		−	1.81649e28i		−	1.15634i	−0.815917	−	0.578169i	$-0.803767\pi$
$929$		−	1.81649e28i		−	1.15634i	0.815917	−	0.578169i	$-0.196233\pi$
$930$	−1.61134e28	+	2.48534e28i	−1.01531	+	1.56602i
$931$		−	9.71270e27i		−	0.605784i
$932$	−7.82493e27	−	1.39347e28i	−0.483092	−	0.860295i
$933$	−5.18677e27	−	5.68320e27i	−0.316972	−	0.347310i
$934$	4.44969e27	+	1.70120e28i	0.269175	+	1.02911i
$935$	−4.42573e28			−2.65018
$936$	3.14354e27	−	2.52244e27i	0.186336	−	0.149520i
$937$	−1.87439e28			−1.09985			−0.549927	−	0.835213i	$-0.685344\pi$
$937$	−1.87439e28			−1.09985			−0.549927	+	0.835213i	$0.685344\pi$
$938$	−1.27336e27	−	4.86830e27i	−0.0739649	−	0.282781i
$939$	1.78379e28	+	1.95452e28i	1.02570	+	1.12387i
$940$	1.41321e28	+	2.51666e28i	0.804436	+	1.43255i
$941$			1.30004e28i			0.732580i	0.930501	+	0.366290i	$0.119372\pi$
$941$			1.30004e28i			0.732580i	−0.930501	+	0.366290i	$0.880628\pi$
$942$	−1.06818e28	+	1.64757e28i	−0.595884	+	0.919095i
$943$		−	1.43484e27i		−	0.0792397i
$944$	−9.16155e27	+	1.50279e28i	−0.500881	+	0.821610i
$945$	1.75276e28	−	1.32827e28i	0.948681	−	0.718924i
$946$	−1.64795e28	+	4.31041e27i	−0.883035	+	0.230969i
$947$	−9.18774e27			−0.487398			−0.243699	−	0.969851i	$-0.578361\pi$
$947$	−9.18774e27			−0.487398			−0.243699	+	0.969851i	$0.578361\pi$
$948$	−2.29836e27	+	6.95007e27i	−0.120709	+	0.365014i
$949$	3.44527e27			0.179141
$950$	3.91939e28	−	1.02516e28i	2.01764	−	0.527738i
$951$	1.97164e28	−	1.79941e28i	1.00488	−	0.917099i
$952$	1.34508e28	+	1.39414e28i	0.678731	+	0.703484i
$953$			2.91741e28i			1.45752i	0.684768	+	0.728761i	$0.259904\pi$
$953$			2.91741e28i			1.45752i	−0.684768	+	0.728761i	$0.740096\pi$
$954$	3.45353e27	+	2.07974e28i	0.170826	+	1.02873i
$955$			7.93290e27i			0.388508i
$956$	−9.15855e27	+	5.14291e27i	−0.444096	+	0.249379i
$957$	2.13690e27	−	1.95024e27i	0.102594	−	0.0936320i
$958$	−4.42575e27	−	1.69204e28i	−0.210385	−	0.804340i
$959$	−1.21470e28			−0.571734
$960$	−2.17790e28	−	2.56507e28i	−1.01499	−	1.19542i
$961$	−9.02391e27			−0.416411
$962$	2.19020e27	+	8.37353e27i	0.100074	+	0.382600i
$963$	2.32627e27	−	2.54152e28i	0.105247	−	1.14985i
$964$	−3.68853e28	+	2.07126e28i	−1.65242	+	0.927905i
$965$			3.70593e28i			1.64395i
$966$	4.81237e27	+	3.12004e27i	0.211386	+	0.137050i
$967$		−	1.31393e28i		−	0.571504i	−0.958304	−	0.285752i	$-0.907757\pi$
$967$		−	1.31393e28i		−	0.571504i	0.958304	−	0.285752i	$-0.0922434\pi$
$968$	1.16377e28	+	1.20621e28i	0.501247	+	0.519527i
$969$	−2.90913e28	−	3.18757e28i	−1.24076	−	1.35951i
$970$	4.17956e28	−	1.09322e28i	1.76522	−	0.461716i
$971$	1.66913e28			0.698083			0.349041	−	0.937107i	$-0.386507\pi$
$971$	1.66913e28			0.698083			0.349041	+	0.937107i	$0.386507\pi$
$972$	2.11670e28	+	1.16166e28i	0.876657	+	0.481117i
$973$	2.82670e28			1.15933
$974$	−2.30378e28	+	6.02582e27i	−0.935688	+	0.244741i
$975$	5.84297e27	+	6.40221e27i	0.235012	+	0.257505i
$976$	5.98320e27	−	9.81441e27i	0.238320	−	0.390923i
$977$		−	1.76585e28i		−	0.696554i	−0.937392	−	0.348277i	$-0.886767\pi$
$977$		−	1.76585e28i		−	0.696554i	0.937392	−	0.348277i	$-0.113233\pi$
$978$	9.77953e27	+	6.34044e27i	0.382031	+	0.247685i
$979$		−	7.15985e27i		−	0.276993i
$980$	−8.49460e27	−	1.51273e28i	−0.325458	−	0.579580i
$981$	2.64013e27	−	2.88441e28i	0.100177	−	1.09446i
$982$	−2.08711e27	−	7.97939e27i	−0.0784306	−	0.299855i
$983$	−2.04442e28			−0.760873			−0.380436	−	0.924807i	$-0.624226\pi$
$983$	−2.04442e28			−0.760873			−0.380436	+	0.924807i	$0.624226\pi$
$984$	6.46408e27	+	4.11309e26i	0.238261	+	0.0151605i
$985$	6.92216e28			2.52696
$986$	−9.54097e26	−	3.64769e27i	−0.0344954	−	0.131882i
$987$	1.64032e28	−	1.49703e28i	0.587374	−	0.536067i
$988$	−4.71386e27	−	8.39449e27i	−0.167180	−	0.297717i
$989$			6.57233e27i			0.230863i
$990$	−9.68918e27	−	5.83490e28i	−0.337095	−	2.03001i
$991$			4.08251e27i			0.140678i	0.997523	+	0.0703391i	$0.0224082\pi$
$991$			4.08251e27i			0.140678i	−0.997523	+	0.0703391i	$0.977592\pi$
$992$	1.00261e28	−	3.33978e28i	0.342193	−	1.13987i
$993$	−2.62815e28	+	2.39858e28i	−0.888449	+	0.810843i
$994$	−2.95611e28	+	7.73206e27i	−0.989805	+	0.258896i
$995$	1.07045e28			0.355015
$996$	2.90224e28	+	9.59757e27i	0.953386	+	0.315281i
$997$	−1.11355e28			−0.362331			−0.181166	−	0.983453i	$-0.557987\pi$
$997$	−1.11355e28			−0.362331			−0.181166	+	0.983453i	$0.557987\pi$
$998$	7.94083e27	−	2.07702e27i	0.255933	−	0.0669423i
$999$	−4.13250e28	+	3.13167e28i	−1.31929	+	0.999778i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	12.20.b.a.11.15	✓	36
3.2	odd	2	inner	12.20.b.a.11.22	yes	36
4.3	odd	2	inner	12.20.b.a.11.21	yes	36
12.11	even	2	inner	12.20.b.a.11.16	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
12.20.b.a.11.15	✓	36	1.1	even	1	trivial
12.20.b.a.11.16	yes	36	12.11	even	2	inner
12.20.b.a.11.21	yes	36	4.3	odd	2	inner
12.20.b.a.11.22	yes	36	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 12 = 2^{2} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 20 \)
Character orbit:	\([\chi]\)	\(=\)	12.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-183.227 - 700.511i) q^{2} +(22981.7 + 25181.4i) q^{3} +(-457144. + 256705. i) q^{4} +6.84881e6i q^{5} +(1.34289e7 - 2.07129e7i) q^{6} +8.10387e7i q^{7} +(2.63586e8 + 2.73199e8i) q^{8} +(-1.05940e8 + 1.15742e9i) q^{9} +O(q^{10})\)	\(q+(-183.227 - 700.511i) q^{2} +(22981.7 + 25181.4i) q^{3} +(-457144. + 256705. i) q^{4} +6.84881e6i q^{5} +(1.34289e7 - 2.07129e7i) q^{6} +8.10387e7i q^{7} +(2.63586e8 + 2.73199e8i) q^{8} +(-1.05940e8 + 1.15742e9i) q^{9} +(4.79767e9 - 1.25489e9i) q^{10} -1.02621e10 q^{11} +(-1.69701e10 - 5.61196e9i) q^{12} -9.13471e9 q^{13} +(5.67685e10 - 1.48485e10i) q^{14} +(-1.72462e11 + 1.57398e11i) q^{15} +(1.43083e11 - 2.34702e11i) q^{16} -6.29700e11i q^{17} +(8.30199e11 - 1.37859e11i) q^{18} -2.01024e12i q^{19} +(-1.75813e12 - 3.13089e12i) q^{20} +(-2.04066e12 + 1.86241e12i) q^{21} +(1.88029e12 + 7.18871e12i) q^{22} +2.86699e12 q^{23} +(-8.21847e11 + 1.29160e13i) q^{24} -2.78327e13 q^{25} +(1.67373e12 + 6.39897e12i) q^{26} +(-3.15802e13 + 2.39319e13i) q^{27} +(-2.08031e13 - 3.70463e13i) q^{28} +8.26930e12i q^{29} +(1.41859e14 + 9.19723e13i) q^{30} +1.75199e14i q^{31} +(-1.90628e14 - 5.72271e13i) q^{32} +(-2.35841e14 - 2.58413e14i) q^{33} +(-4.41112e14 + 1.15378e14i) q^{34} -5.55019e14 q^{35} +(-2.48687e14 - 5.56304e14i) q^{36} +1.30858e15 q^{37} +(-1.40819e15 + 3.68330e14i) q^{38} +(-2.09932e14 - 2.30024e14i) q^{39} +(-1.87109e15 + 1.80525e15i) q^{40} -5.00469e14i q^{41} +(1.67855e15 + 1.08826e15i) q^{42} +2.29241e15i q^{43} +(4.69125e15 - 2.63433e15i) q^{44} +(-7.92697e15 - 7.25563e14i) q^{45} +(-5.25311e14 - 2.00836e15i) q^{46} -8.03815e15 q^{47} +(9.19841e15 - 1.79086e15i) q^{48} +4.83162e15 q^{49} +(5.09972e15 + 1.94971e16i) q^{50} +(1.58567e16 - 1.44716e16i) q^{51} +(4.17587e15 - 2.34493e15i) q^{52} +2.50512e16i q^{53} +(2.25509e16 + 1.77373e16i) q^{54} -7.02831e16i q^{55} +(-2.21397e16 + 2.13607e16i) q^{56} +(5.06204e16 - 4.61987e16i) q^{57} +(5.79274e15 - 1.51516e15i) q^{58} -6.40298e16 q^{59} +(3.84353e16 - 1.16225e17i) q^{60} +4.18164e16 q^{61} +(1.22729e17 - 3.21012e16i) q^{62} +(-9.37961e16 - 8.58524e15i) q^{63} +(-5.15994e15 + 1.44023e17i) q^{64} -6.25619e16i q^{65} +(-1.37809e17 + 2.12557e17i) q^{66} -8.57571e16i q^{67} +(1.61647e17 + 2.87863e17i) q^{68} +(6.58885e16 + 7.21947e16i) q^{69} +(1.01695e17 + 3.88797e17i) q^{70} -5.20730e17 q^{71} +(-3.44131e17 + 2.76138e17i) q^{72} -3.77163e17 q^{73} +(-2.39767e17 - 9.16672e17i) q^{74} +(-6.39645e17 - 7.00866e17i) q^{75} +(5.16038e17 + 9.18966e17i) q^{76} -8.31627e17i q^{77} +(-1.22669e17 + 1.89206e17i) q^{78} -4.09547e17i q^{79} +(1.60743e18 + 9.79946e17i) q^{80} +(-1.32841e18 - 2.45235e17i) q^{81} +(-3.50584e17 + 9.16996e16i) q^{82} -1.71020e18 q^{83} +(4.54786e17 - 1.37524e18i) q^{84} +4.31270e18 q^{85} +(1.60586e18 - 4.20032e17i) q^{86} +(-2.08232e17 + 1.90043e17i) q^{87} +(-2.70494e18 - 2.80359e18i) q^{88} +6.97699e17i q^{89} +(9.44172e17 + 5.68588e18i) q^{90} -7.40265e17i q^{91} +(-1.31063e18 + 7.35972e17i) q^{92} +(-4.41174e18 + 4.02637e18i) q^{93} +(1.47281e18 + 5.63081e18i) q^{94} +1.37677e19 q^{95} +(-2.93991e18 - 6.11546e18i) q^{96} +8.71166e18 q^{97} +(-8.85285e17 - 3.38460e18i) q^{98} +(1.08717e18 - 1.18776e19i) 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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