LMFDB - Embedded newform 12.20.b.a.11.17

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			11.17
Character	$\chi$	$=$	12.11
Dual form			12.20.b.a.11.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-74.5111 - 720.233i) q^{2} +(32706.8 + 9618.97i) q^{3} +(-513184. + 107331. i) q^{4} -7.07022e6i q^{5} +(4.49088e6 - 2.42733e7i) q^{6} -1.56654e8i q^{7} +(1.15541e8 + 3.61615e8i) q^{8} +(9.77212e8 + 6.29212e8i) q^{9} +O(q^{10})$	\(q+(-74.5111 - 720.233i) q^{2} +(32706.8 + 9618.97i) q^{3} +(-513184. + 107331. i) q^{4} -7.07022e6i q^{5} +(4.49088e6 - 2.42733e7i) q^{6} -1.56654e8i q^{7} +(1.15541e8 + 3.61615e8i) q^{8} +(9.77212e8 + 6.29212e8i) q^{9} +(-5.09221e9 + 5.26810e8i) q^{10} +9.54672e9 q^{11} +(-1.78170e10 - 1.42586e9i) q^{12} -2.20437e10 q^{13} +(-1.12827e11 + 1.16725e10i) q^{14} +(6.80083e10 - 2.31244e11i) q^{15} +(2.51838e11 - 1.10161e11i) q^{16} -1.32854e11i q^{17} +(3.80367e11 - 7.50704e11i) q^{18} -1.26419e11i q^{19} +(7.58852e11 + 3.62833e12i) q^{20} +(1.50685e12 - 5.12365e12i) q^{21} +(-7.11337e11 - 6.87586e12i) q^{22} -1.44365e13 q^{23} +(3.00619e11 + 1.29387e13i) q^{24} -3.09145e13 q^{25} +(1.64250e12 + 1.58766e13i) q^{26} +(2.59091e13 + 2.99793e13i) q^{27} +(1.68138e13 + 8.03923e13i) q^{28} -5.22664e13i q^{29} +(-1.71617e14 - 3.17515e13i) q^{30} +8.91820e12i q^{31} +(-9.81063e13 - 1.73174e14i) q^{32} +(3.12243e14 + 9.18296e13i) q^{33} +(-9.56858e13 + 9.89909e12i) q^{34} -1.10758e15 q^{35} +(-5.69024e14 - 2.18017e14i) q^{36} -5.03102e14 q^{37} +(-9.10509e13 + 9.41960e12i) q^{38} +(-7.20978e14 - 2.12037e14i) q^{39} +(2.55670e15 - 8.16901e14i) q^{40} +1.92871e15i q^{41} +(-3.80250e15 - 7.03514e14i) q^{42} -1.96994e14i q^{43} +(-4.89922e15 + 1.02466e15i) q^{44} +(4.44867e15 - 6.90910e15i) q^{45} +(1.07568e15 + 1.03976e16i) q^{46} +6.24266e15 q^{47} +(9.29646e15 - 1.18059e15i) q^{48} -1.31415e16 q^{49} +(2.30348e15 + 2.22657e16i) q^{50} +(1.27792e15 - 4.34523e15i) q^{51} +(1.13125e16 - 2.36596e15i) q^{52} +9.61536e15i q^{53} +(1.96616e16 - 2.08944e16i) q^{54} -6.74974e16i q^{55} +(5.66484e16 - 1.81000e16i) q^{56} +(1.21602e15 - 4.13475e15i) q^{57} +(-3.76440e16 + 3.89443e15i) q^{58} -2.49085e16 q^{59} +(-1.00811e16 + 1.25970e17i) q^{60} +1.42524e17 q^{61} +(6.42318e15 - 6.64505e14i) q^{62} +(9.85685e16 - 1.53084e17i) q^{63} +(-1.17416e17 + 8.35628e16i) q^{64} +1.55853e17i q^{65} +(4.28732e16 - 2.31730e17i) q^{66} -1.59598e17i q^{67} +(1.42593e16 + 6.81785e16i) q^{68} +(-4.72171e17 - 1.38864e17i) q^{69} +(8.25268e16 + 7.97714e17i) q^{70} -6.13599e17 q^{71} +(-1.14624e17 + 4.26075e17i) q^{72} +4.40811e17 q^{73} +(3.74867e16 + 3.62351e17i) q^{74} +(-1.01112e18 - 2.97366e17i) q^{75} +(1.35686e16 + 6.48761e16i) q^{76} -1.49553e18i q^{77} +(-9.89955e16 + 5.35072e17i) q^{78} -1.92328e18i q^{79} +(-7.78862e17 - 1.78055e18i) q^{80} +(5.59035e17 + 1.22975e18i) q^{81} +(1.38912e18 - 1.43710e17i) q^{82} +1.68268e18 q^{83} +(-2.23366e17 + 2.79111e18i) q^{84} -9.39306e17 q^{85} +(-1.41882e17 + 1.46782e16i) q^{86} +(5.02749e17 - 1.70947e18i) q^{87} +(1.10304e18 + 3.45224e18i) q^{88} +2.75763e18i q^{89} +(-5.30764e18 - 2.68928e18i) q^{90} +3.45322e18i q^{91} +(7.40856e18 - 1.54948e18i) q^{92} +(-8.57839e16 + 2.91686e17i) q^{93} +(-4.65148e17 - 4.49617e18i) q^{94} -8.93808e17 q^{95} +(-1.54299e18 - 6.60765e18i) q^{96} +7.95134e18 q^{97} +(9.79191e17 + 9.46497e18i) q^{98} +(9.32917e18 + 6.00691e18i) 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 $

$2$	−74.5111	−	720.233i	−0.102905	−	0.994691i
$2$	−74.5111	−	720.233i	−0.102905	−	0.994691i
$3$	32706.8	+	9618.97i	0.959371	+	0.282148i
$3$	32706.8	+	9618.97i	0.959371	+	0.282148i
$4$	−513184.	+	107331.i	−0.978821	+	0.204717i
$5$		−	7.07022e6i		−	1.61889i	−0.587194	−	0.809446i	$-0.699768\pi$
$5$		−	7.07022e6i		−	1.61889i	0.587194	−	0.809446i	$-0.300232\pi$
$6$	4.49088e6	−	2.42733e7i	0.181926	−	0.983312i
$7$		−	1.56654e8i		−	1.46727i	−0.679544	−	0.733635i	$-0.737822\pi$
$7$		−	1.56654e8i		−	1.46727i	0.679544	−	0.733635i	$-0.262178\pi$
$8$	1.15541e8	+	3.61615e8i	0.304356	+	0.952558i
$9$	9.77212e8	+	6.29212e8i	0.840785	+	0.541369i
$10$	−5.09221e9	+	5.26810e8i	−1.61030	+	0.166592i
$11$	9.54672e9			1.22074			0.610371	−	0.792116i	$-0.291021\pi$
$11$	9.54672e9			1.22074			0.610371	+	0.792116i	$0.291021\pi$
$12$	−1.78170e10	−	1.42586e9i	−0.996813	−	0.0797726i
$13$	−2.20437e10			−0.576530			−0.288265	−	0.957551i	$-0.593078\pi$
$13$	−2.20437e10			−0.576530			−0.288265	+	0.957551i	$0.593078\pi$
$14$	−1.12827e11	+	1.16725e10i	−1.45948	+	0.150989i
$15$	6.80083e10	−	2.31244e11i	0.456767	−	1.55312i
$16$	2.51838e11	−	1.10161e11i	0.916182	−	0.400763i
$17$		−	1.32854e11i		−	0.271712i	−0.990729	−	0.135856i	$-0.956621\pi$
$17$		−	1.32854e11i		−	0.271712i	0.990729	−	0.135856i	$-0.0433785\pi$
$18$	3.80367e11	−	7.50704e11i	0.451974	−	0.892031i
$19$		−	1.26419e11i		−	0.0898777i	−0.998990	−	0.0449389i	$-0.985691\pi$
$19$		−	1.26419e11i		−	0.0898777i	0.998990	−	0.0449389i	$-0.0143093\pi$
$20$	7.58852e11	+	3.62833e12i	0.331415	+	1.58461i
$21$	1.50685e12	−	5.12365e12i	0.413987	−	1.40766i
$22$	−7.11337e11	−	6.87586e12i	−0.125620	−	1.21426i
$23$	−1.44365e13			−1.67127			−0.835634	−	0.549287i	$-0.814899\pi$
$23$	−1.44365e13			−1.67127			−0.835634	+	0.549287i	$0.814899\pi$
$24$	3.00619e11	+	1.29387e13i	0.0232279	+	0.999730i
$25$	−3.09145e13			−1.62081
$26$	1.64250e12	+	1.58766e13i	0.0593277	+	0.573469i
$27$	2.59091e13	+	2.99793e13i	0.653879	+	0.756599i
$28$	1.68138e13	+	8.03923e13i	0.300375	+	1.43619i
$29$		−	5.22664e13i		−	0.669024i	−0.942391	−	0.334512i	$-0.891428\pi$
$29$		−	5.22664e13i		−	0.669024i	0.942391	−	0.334512i	$-0.108572\pi$
$30$	−1.71617e14	−	3.17515e13i	−1.59188	−	0.294519i
$31$			8.91820e12i			0.0605816i	0.999541	+	0.0302908i	$0.00964334\pi$
$31$			8.91820e12i			0.0605816i	−0.999541	+	0.0302908i	$0.990357\pi$
$32$	−9.81063e13	−	1.73174e14i	−0.492915	−	0.870077i
$33$	3.12243e14	+	9.18296e13i	1.17114	+	0.344430i
$34$	−9.56858e13	+	9.89909e12i	−0.270270	+	0.0279606i
$35$	−1.10758e15			−2.37535
$36$	−5.69024e14	−	2.18017e14i	−0.933806	−	0.357780i
$37$	−5.03102e14			−0.636415			−0.318207	−	0.948021i	$-0.603081\pi$
$37$	−5.03102e14			−0.636415			−0.318207	+	0.948021i	$0.603081\pi$
$38$	−9.10509e13	+	9.41960e12i	−0.0894006	+	0.00924886i
$39$	−7.20978e14	−	2.12037e14i	−0.553106	−	0.162667i
$40$	2.55670e15	−	8.16901e14i	1.54209	−	0.492719i
$41$			1.92871e15i			0.920068i	0.887901	+	0.460034i	$0.152163\pi$
$41$			1.92871e15i			0.920068i	−0.887901	+	0.460034i	$0.847837\pi$
$42$	−3.80250e15	−	7.03514e14i	−1.44278	−	0.266934i
$43$		−	1.96994e14i		−	0.0597727i	−0.999553	−	0.0298863i	$-0.990485\pi$
$43$		−	1.96994e14i		−	0.0597727i	0.999553	−	0.0298863i	$-0.00951453\pi$
$44$	−4.89922e15	+	1.02466e15i	−1.19489	+	0.249907i
$45$	4.44867e15	−	6.90910e15i	0.876418	−	1.36114i
$46$	1.07568e15	+	1.03976e16i	0.171982	+	1.66240i
$47$	6.24266e15			0.813655			0.406827	−	0.913505i	$-0.366635\pi$
$47$	6.24266e15			0.813655			0.406827	+	0.913505i	$0.366635\pi$
$48$	9.29646e15	−	1.18059e15i	0.992033	−	0.125982i
$49$	−1.31415e16			−1.15288
$50$	2.30348e15	+	2.22657e16i	0.166789	+	1.61221i
$51$	1.27792e15	−	4.34523e15i	0.0766631	−	0.260673i
$52$	1.13125e16	−	2.36596e15i	0.564320	−	0.118026i
$53$			9.61536e15i			0.400262i	0.979769	+	0.200131i	$0.0641369\pi$
$53$			9.61536e15i			0.400262i	−0.979769	+	0.200131i	$0.935863\pi$
$54$	1.96616e16	−	2.08944e16i	0.685295	−	0.728265i
$55$		−	6.74974e16i		−	1.97625i
$56$	5.66484e16	−	1.81000e16i	1.39766	−	0.446572i
$57$	1.21602e15	−	4.13475e15i	0.0253588	−	0.0862261i
$58$	−3.76440e16	+	3.89443e15i	−0.665472	+	0.0688459i
$59$	−2.49085e16			−0.374329			−0.187165	−	0.982329i	$-0.559930\pi$
$59$	−2.49085e16			−0.374329			−0.187165	+	0.982329i	$0.559930\pi$
$60$	−1.00811e16	+	1.25970e17i	−0.129143	+	1.61373i
$61$	1.42524e17			1.56047			0.780235	−	0.625487i	$-0.215099\pi$
$61$	1.42524e17			1.56047			0.780235	+	0.625487i	$0.215099\pi$
$62$	6.42318e15	−	6.64505e14i	0.0602600	−	0.00623415i
$63$	9.85685e16	−	1.53084e17i	0.794334	−	1.23366i
$64$	−1.17416e17	+	8.35628e16i	−0.814735	+	0.579834i
$65$			1.55853e17i			0.933339i
$66$	4.28732e16	−	2.31730e17i	0.222085	−	1.20037i
$67$		−	1.59598e17i		−	0.716664i	−0.933594	−	0.358332i	$-0.883346\pi$
$67$		−	1.59598e17i		−	0.716664i	0.933594	−	0.358332i	$-0.116654\pi$
$68$	1.42593e16	+	6.81785e16i	0.0556242	+	0.265958i
$69$	−4.72171e17	−	1.38864e17i	−1.60337	−	0.471545i
$70$	8.25268e16	+	7.97714e17i	0.244435	+	2.36274i
$71$	−6.13599e17			−1.58829			−0.794146	−	0.607727i	$-0.792082\pi$
$71$	−6.13599e17			−1.58829			−0.794146	+	0.607727i	$0.792082\pi$
$72$	−1.14624e17	+	4.26075e17i	−0.259788	+	0.965666i
$73$	4.40811e17			0.876365			0.438182	−	0.898886i	$-0.355622\pi$
$73$	4.40811e17			0.876365			0.438182	+	0.898886i	$0.355622\pi$
$74$	3.74867e16	+	3.62351e17i	0.0654902	+	0.633036i
$75$	−1.01112e18	−	2.97366e17i	−1.55496	−	0.457309i
$76$	1.35686e16	+	6.48761e16i	0.0183995	+	0.0879742i
$77$		−	1.49553e18i		−	1.79116i
$78$	−9.89955e16	+	5.35072e17i	−0.104886	+	0.566909i
$79$		−	1.92328e18i		−	1.80545i	−0.430223	−	0.902723i	$-0.641565\pi$
$79$		−	1.92328e18i		−	1.80545i	0.430223	−	0.902723i	$-0.358435\pi$
$80$	−7.78862e17	−	1.78055e18i	−0.648792	−	1.48320i
$81$	5.59035e17	+	1.22975e18i	0.413839	+	0.910350i
$82$	1.38912e18	−	1.43710e17i	0.915184	−	0.0946795i
$83$	1.68268e18			0.988006			0.494003	−	0.869460i	$-0.335533\pi$
$83$	1.68268e18			0.988006			0.494003	+	0.869460i	$0.335533\pi$
$84$	−2.23366e17	+	2.79111e18i	−0.117048	+	1.46259i
$85$	−9.39306e17			−0.439873
$86$	−1.41882e17	+	1.46782e16i	−0.0594553	+	0.00615090i
$87$	5.02749e17	−	1.70947e18i	0.188764	−	0.641842i
$88$	1.10304e18	+	3.45224e18i	0.371540	+	1.16283i
$89$			2.75763e18i			0.834317i	0.908834	+	0.417159i	$0.136974\pi$
$89$			2.75763e18i			0.834317i	−0.908834	+	0.417159i	$0.863026\pi$
$90$	−5.30764e18	−	2.68928e18i	−1.44410	−	0.731697i
$91$			3.45322e18i			0.845924i
$92$	7.40856e18	−	1.54948e18i	1.63587	−	0.342137i
$93$	−8.57839e16	+	2.91686e17i	−0.0170930	+	0.0581203i
$94$	−4.65148e17	−	4.49617e18i	−0.0837291	−	0.809335i
$95$	−8.93808e17			−0.145502
$96$	−1.54299e18	−	6.60765e18i	−0.227398	−	0.973802i
$97$	7.95134e18			1.06196			0.530981	−	0.847384i	$-0.321824\pi$
$97$	7.95134e18			1.06196			0.530981	+	0.847384i	$0.321824\pi$
$98$	9.79191e17	+	9.46497e18i	0.118637	+	1.14676i
$99$	9.32917e18	+	6.00691e18i	1.02638	+	0.660871i
$100$	1.58648e19	−	3.31808e18i	1.58648	−	0.331808i
$101$		−	1.14619e18i		−	0.104281i	−0.998640	−	0.0521403i	$-0.983396\pi$
$101$		−	1.14619e18i		−	0.104281i	0.998640	−	0.0521403i	$-0.0166043\pi$
$102$	−3.22480e18	−	5.96631e17i	−0.267178	−	0.0494316i
$103$			4.87634e18i			0.368248i	0.982903	+	0.184124i	$0.0589448\pi$
$103$			4.87634e18i			0.368248i	−0.982903	+	0.184124i	$0.941055\pi$
$104$	−2.54695e18	−	7.97132e18i	−0.175470	−	0.549178i
$105$	−3.62253e19	−	1.06538e19i	−2.27884	−	0.670200i
$106$	6.92530e18	−	7.16451e17i	0.398138	−	0.0411890i
$107$	4.48993e18			0.236099			0.118049	−	0.993008i	$-0.462336\pi$
$107$	4.48993e18			0.236099			0.118049	+	0.993008i	$0.462336\pi$
$108$	−1.65139e19	−	1.26041e19i	−0.794919	−	0.606715i
$109$	2.83035e19			1.24821			0.624106	−	0.781340i	$-0.285463\pi$
$109$	2.83035e19			1.24821			0.624106	+	0.781340i	$0.285463\pi$
$110$	−4.86139e19	+	5.02931e18i	−1.96576	+	0.203366i
$111$	−1.64549e19	−	4.83933e18i	−0.610558	−	0.179563i
$112$	−1.72571e19	−	3.94514e19i	−0.588027	−	1.34429i
$113$			7.79869e18i			0.244217i	0.992517	+	0.122109i	$0.0389656\pi$
$113$			7.79869e18i			0.244217i	−0.992517	+	0.122109i	$0.961034\pi$
$114$	−3.06859e18	−	5.67731e17i	−0.0883778	−	0.0163511i
$115$			1.02069e20i			2.70560i
$116$	5.60980e18	+	2.68223e19i	0.136961	+	0.654855i
$117$	−2.15413e19	−	1.38701e19i	−0.484738	−	0.312115i
$118$	1.85596e18	+	1.79399e19i	0.0385203	+	0.372342i
$119$	−2.08121e19			−0.398675
$120$	9.14792e19	−	2.12544e18i	1.61846	−	0.0376034i
$121$	2.99807e19			0.490209
$122$	−1.06196e19	−	1.02651e20i	−0.160580	−	1.55219i
$123$	−1.85522e19	+	6.30819e19i	−0.259595	+	0.882687i
$124$	−9.57197e17	−	4.57668e18i	−0.0124021	−	0.0592986i
$125$			8.37188e19i			1.00503i
$126$	−1.17601e20	−	5.95859e19i	−1.30885	−	0.663168i
$127$		−	1.25184e20i		−	1.29245i	−0.763148	−	0.646224i	$-0.776347\pi$
$127$		−	1.25184e20i		−	1.29245i	0.763148	−	0.646224i	$-0.223653\pi$
$128$	6.89335e19	+	7.83403e19i	0.660596	+	0.750742i
$129$	1.89488e18	−	6.44305e18i	0.0168647	−	0.0573442i
$130$	1.12251e20	−	1.16128e19i	0.928385	−	0.0960452i
$131$	1.02355e20			0.787106			0.393553	−	0.919302i	$-0.371246\pi$
$131$	1.02355e20			0.787106			0.393553	+	0.919302i	$0.371246\pi$
$132$	−1.70094e20	−	1.36122e19i	−1.21685	−	0.0973817i
$133$	−1.98040e19			−0.131875
$134$	−1.14947e20	+	1.18918e19i	−0.712859	+	0.0737483i
$135$	2.11960e20	−	1.83183e20i	1.22485	−	1.05856i
$136$	4.80420e19	−	1.53501e19i	0.258822	−	0.0826973i
$137$		−	1.67435e20i		−	0.841396i	−0.907201	−	0.420698i	$-0.861785\pi$
$137$		−	1.67435e20i		−	0.841396i	0.907201	−	0.420698i	$-0.138215\pi$
$138$	−6.48324e19	+	3.50420e20i	−0.304047	+	1.64338i
$139$		−	1.80123e20i		−	0.788731i	−0.918954	−	0.394365i	$-0.870964\pi$
$139$		−	1.80123e20i		−	0.788731i	0.918954	−	0.394365i	$-0.129036\pi$
$140$	5.68391e20	−	1.18877e20i	2.32504	−	0.486275i
$141$	2.04178e20	+	6.00480e19i	0.780597	+	0.229571i
$142$	4.57200e19	+	4.41935e20i	0.163443	+	1.57986i
$143$	−2.10445e20			−0.703794
$144$	3.15414e20	+	5.08090e19i	0.987273	+	0.159037i
$145$	−3.69535e20			−1.08308
$146$	−3.28453e19	−	3.17487e20i	−0.0901823	−	0.871713i
$147$	−4.29818e20	−	1.26408e20i	−1.10604	−	0.325282i
$148$	2.58184e20	−	5.39984e19i	0.622936	−	0.130285i
$149$		−	1.23657e20i		−	0.279865i	−0.990161	−	0.139932i	$-0.955311\pi$
$149$		−	1.23657e20i		−	0.279865i	0.990161	−	0.139932i	$-0.0446885\pi$
$150$	−1.38834e20	+	7.50397e20i	−0.294868	+	1.59376i
$151$		−	1.57724e20i		−	0.314497i	−0.987559	−	0.157249i	$-0.949738\pi$
$151$		−	1.57724e20i		−	0.314497i	0.987559	−	0.157249i	$-0.0502624\pi$
$152$	4.57149e19	−	1.46066e19i	0.0856138	−	0.0273548i
$153$	8.35933e19	−	1.29826e20i	0.147097	−	0.228452i
$154$	−1.07713e21	+	1.11434e20i	−1.78165	+	0.184319i
$155$	6.30536e19			0.0980751
$156$	3.92753e20	+	3.14311e19i	0.574692	+	0.0459913i
$157$	4.51136e20			0.621242			0.310621	−	0.950534i	$-0.399463\pi$
$157$	4.51136e20			0.621242			0.310621	+	0.950534i	$0.399463\pi$
$158$	−1.38521e21	+	1.43305e20i	−1.79586	+	0.185789i
$159$	−9.24899e19	+	3.14488e20i	−0.112933	+	0.384000i
$160$	−1.22438e21	+	6.93633e20i	−1.40856	+	0.797976i
$161$			2.26153e21i			2.45220i
$162$	8.44051e20	−	4.94266e20i	0.862931	−	0.505322i
$163$		−	1.58771e21i		−	1.53105i	−0.643408	−	0.765523i	$-0.722480\pi$
$163$		−	1.58771e21i		−	1.53105i	0.643408	−	0.765523i	$-0.277520\pi$
$164$	−2.07010e20	−	9.89783e20i	−0.188354	−	0.900582i
$165$	6.49256e20	−	2.20763e21i	0.557594	−	1.89596i
$166$	−1.25378e20	−	1.21192e21i	−0.101671	−	0.982761i
$167$	−1.26877e21			−0.971802			−0.485901	−	0.874014i	$-0.661508\pi$
$167$	−1.26877e21			−0.971802			−0.485901	+	0.874014i	$0.661508\pi$
$168$	2.02689e21	−	4.70931e19i	1.46687	−	0.0340816i
$169$	−9.75998e20			−0.667613
$170$	6.99888e19	+	6.76520e20i	0.0452651	+	0.437538i
$171$	7.95442e19	−	1.23538e20i	0.0486570	−	0.0755678i
$172$	2.11435e19	+	1.01094e20i	0.0122365	+	0.0585068i
$173$		−	7.11034e20i		−	0.389451i	−0.980858	−	0.194725i	$-0.937618\pi$
$173$		−	7.11034e20i		−	0.389451i	0.980858	−	0.194725i	$-0.0623816\pi$
$174$	−1.26868e21	−	2.34722e20i	−0.657860	−	0.121713i
$175$			4.84288e21i			2.37817i
$176$	2.40423e21	−	1.05168e21i	1.11842	−	0.489228i
$177$	−8.14679e20	−	2.39594e20i	−0.359121	−	0.105616i
$178$	1.98614e21	−	2.05474e20i	0.829888	−	0.0858553i
$179$	1.51538e21			0.600368			0.300184	−	0.953881i	$-0.402952\pi$
$179$	1.51538e21			0.600368			0.300184	+	0.953881i	$0.402952\pi$
$180$	−1.54143e21	+	4.02312e21i	−0.579208	+	1.51173i
$181$	−1.11774e21			−0.398469			−0.199234	−	0.979952i	$-0.563845\pi$
$181$	−1.11774e21			−0.398469			−0.199234	+	0.979952i	$0.563845\pi$
$182$	2.48713e21	−	2.57304e20i	0.841433	−	0.0870498i
$183$	4.66152e21	+	1.37094e21i	1.49707	+	0.440283i
$184$	−1.66800e21	−	5.22044e21i	−0.508660	−	1.59198i
$185$			3.55705e21i			1.03029i
$186$	2.16474e20	+	4.00506e19i	0.0595707	+	0.0110214i
$187$		−	1.26832e21i		−	0.331691i
$188$	−3.20364e21	+	6.70030e20i	−0.796423	+	0.166569i
$189$	4.69638e21	−	4.05877e21i	1.11013	−	0.959416i
$190$	6.65986e19	+	6.43750e20i	0.0149729	+	0.144730i
$191$	4.84369e21			1.03600			0.518000	−	0.855381i	$-0.326677\pi$
$191$	4.84369e21			1.03600			0.518000	+	0.855381i	$0.326677\pi$
$192$	−4.64408e21	+	1.60366e21i	−0.945232	+	0.326400i
$193$	−6.01816e21			−1.16592			−0.582961	−	0.812500i	$-0.698106\pi$
$193$	−6.01816e21			−1.16592			−0.582961	+	0.812500i	$0.698106\pi$
$194$	−5.92463e20	−	5.72682e21i	−0.109281	−	1.05632i
$195$	−1.49915e21	+	5.09747e21i	−0.263340	+	0.895419i
$196$	6.74403e21	−	1.41049e21i	1.12846	−	0.236014i
$197$			9.66538e21i			1.54095i	0.637467	+	0.770477i	$0.279982\pi$
$197$			9.66538e21i			1.54095i	−0.637467	+	0.770477i	$0.720018\pi$
$198$	3.63125e21	−	7.16676e21i	0.551743	−	1.08894i
$199$			3.26555e21i			0.472990i	0.971633	+	0.236495i	$0.0759987\pi$
$199$			3.26555e21i			0.472990i	−0.971633	+	0.236495i	$0.924001\pi$
$200$	−3.57190e21	−	1.11792e22i	−0.493304	−	1.54392i
$201$	1.53516e21	−	5.21993e21i	0.202205	−	0.687547i
$202$	−8.25524e20	+	8.54039e19i	−0.103727	+	0.0107310i
$203$	−8.18774e21			−0.981638
$204$	−1.89430e20	+	2.36706e21i	−0.0216752	+	0.270847i
$205$	1.36364e22			1.48949
$206$	3.51211e21	−	3.63342e20i	0.366293	−	0.0378946i
$207$	−1.41075e22	−	9.08359e21i	−1.40518	−	0.904773i
$208$	−5.55143e21	+	2.42835e21i	−0.528206	+	0.231052i
$209$		−	1.20688e21i		−	0.109717i
$210$	−4.97400e21	+	2.68845e22i	−0.432138	+	2.33571i
$211$			1.05355e21i			0.0874930i	0.999043	+	0.0437465i	$0.0139294\pi$
$211$			1.05355e21i			0.0874930i	−0.999043	+	0.0437465i	$0.986071\pi$
$212$	−1.03202e21	−	4.93445e21i	−0.0819406	−	0.391785i
$213$	−2.00689e22	−	5.90219e21i	−1.52376	−	0.448133i
$214$	−3.34550e20	−	3.23380e21i	−0.0242957	−	0.234845i
$215$	−1.39279e21			−0.0967655
$216$	−7.84740e21	+	1.28330e22i	−0.521693	+	0.853133i
$217$	1.39707e21			0.0888896
$218$	−2.10892e21	−	2.03851e22i	−0.128447	−	1.24159i
$219$	1.44175e22	+	4.24015e21i	0.840759	+	0.247265i
$220$	7.24455e21	+	3.46386e22i	0.404572	+	1.93439i
$221$			2.92859e21i			0.156650i
$222$	−2.25937e21	+	1.22119e22i	−0.115780	+	0.625794i
$223$		−	1.15715e22i		−	0.568192i	−0.958796	−	0.284096i	$-0.908307\pi$
$223$		−	1.15715e22i		−	0.568192i	0.958796	−	0.284096i	$-0.0916934\pi$
$224$	−2.71284e22	+	1.53687e22i	−1.27664	+	0.723239i
$225$	−3.02101e22	−	1.94518e22i	−1.36275	−	0.877457i
$226$	5.61688e21	−	5.81089e20i	0.242921	−	0.0251312i
$227$	−7.86342e21			−0.326111			−0.163056	−	0.986617i	$-0.552135\pi$
$227$	−7.86342e21			−0.326111			−0.163056	+	0.986617i	$0.552135\pi$
$228$	−1.80255e20	+	2.25241e21i	−0.00716978	+	0.0895913i
$229$	4.83174e22			1.84360			0.921800	−	0.387665i	$-0.126718\pi$
$229$	4.83174e22			1.84360			0.921800	+	0.387665i	$0.126718\pi$
$230$	7.35134e22	−	7.60527e21i	2.69124	−	0.278420i
$231$	1.43855e22	−	4.89141e22i	0.505371	−	1.71838i
$232$	1.89003e22	−	6.03892e21i	0.637285	−	0.203621i
$233$			5.28275e22i			1.70993i	0.518683	+	0.854967i	$0.326423\pi$
$233$			5.28275e22i			1.70993i	−0.518683	+	0.854967i	$0.673577\pi$
$234$	−8.38467e21	+	1.65483e22i	−0.260576	+	0.514282i
$235$		−	4.41370e22i		−	1.31722i
$236$	1.27827e22	−	2.67345e21i	0.366401	−	0.0766317i
$237$	1.84999e22	−	6.29043e22i	0.509403	−	1.73209i
$238$	1.55073e21	+	1.49896e22i	0.0410257	+	0.396559i
$239$	−2.89704e22			−0.736502			−0.368251	−	0.929726i	$-0.620043\pi$
$239$	−2.89704e22			−0.736502			−0.368251	+	0.929726i	$0.620043\pi$
$240$	−8.34704e21	−	6.57280e22i	−0.203951	−	1.60599i
$241$	−6.95255e21			−0.163299			−0.0816493	−	0.996661i	$-0.526019\pi$
$241$	−6.95255e21			−0.163299			−0.0816493	+	0.996661i	$0.526019\pi$
$242$	−2.23390e21	−	2.15931e22i	−0.0504449	−	0.487607i
$243$	6.45536e21	+	4.55985e22i	0.140172	+	0.990127i
$244$	−7.31412e22	+	1.52972e22i	−1.52742	+	0.319455i
$245$			9.29136e22i			1.86639i
$246$	4.68161e22	+	8.66161e21i	0.904714	+	0.167384i
$247$			2.78673e21i			0.0518172i
$248$	−3.22495e21	+	1.03042e21i	−0.0577076	+	0.0184384i
$249$	5.50351e22	+	1.61857e22i	0.947864	+	0.278764i
$250$	6.02970e22	−	6.23798e21i	0.999691	−	0.103422i
$251$	7.20931e22			1.15078			0.575391	−	0.817878i	$-0.304850\pi$
$251$	7.20931e22			1.15078			0.575391	+	0.817878i	$0.304850\pi$
$252$	−3.41532e22	+	8.91398e22i	−0.524960	+	1.37014i
$253$	−1.37821e23			−2.04019
$254$	−9.01616e22	+	9.32759e21i	−1.28559	+	0.132999i
$255$	−3.07217e22	−	9.03516e21i	−0.422002	−	0.124109i
$256$	5.12870e22	−	5.54854e22i	0.678778	−	0.734344i
$257$		−	8.57468e22i		−	1.09359i	−0.837268	−	0.546793i	$-0.815848\pi$
$257$		−	8.57468e22i		−	1.09359i	0.837268	−	0.546793i	$-0.184152\pi$
$258$	−4.78169e21	−	8.84677e20i	−0.0587752	−	0.0108742i
$259$			7.88129e22i			0.933791i
$260$	−1.67279e22	−	7.99815e22i	−0.191071	−	0.913572i
$261$	3.28867e22	−	5.10754e22i	0.362189	−	0.562506i
$262$	−7.62661e21	−	7.37197e22i	−0.0809971	−	0.782927i
$263$	4.64463e22			0.475742			0.237871	−	0.971297i	$-0.423550\pi$
$263$	4.64463e22			0.475742			0.237871	+	0.971297i	$0.423550\pi$
$264$	2.86992e21	+	1.23522e23i	0.0283552	+	1.22041i
$265$	6.79827e22			0.647982
$266$	1.47562e21	+	1.42635e22i	0.0135706	+	0.131175i
$267$	−2.65256e22	+	9.01934e22i	−0.235401	+	0.800420i
$268$	1.71297e22	+	8.19029e22i	0.146713	+	0.701486i
$269$		−	7.11907e22i		−	0.588540i	−0.955722	−	0.294270i	$-0.904923\pi$
$269$		−	7.11907e22i		−	0.588540i	0.955722	−	0.294270i	$-0.0950766\pi$
$270$	−1.47728e23	−	1.39012e23i	−1.17898	−	1.10942i
$271$			1.94909e23i			1.50184i	0.660395	+	0.750918i	$0.270389\pi$
$271$			1.94909e23i			1.50184i	−0.660395	+	0.750918i	$0.729611\pi$
$272$	−1.46353e22	−	3.34577e22i	−0.108892	−	0.248938i
$273$	−3.32165e22	+	1.12944e23i	−0.238676	+	0.811555i
$274$	−1.20592e23	+	1.24758e22i	−0.836929	+	0.0865838i
$275$	−2.95132e23			−1.97859
$276$	2.57215e23	+	2.05843e22i	1.66594	+	0.133321i
$277$	−1.58079e23			−0.989272			−0.494636	−	0.869100i	$-0.664699\pi$
$277$	−1.58079e23			−0.989272			−0.494636	+	0.869100i	$0.664699\pi$
$278$	−1.29731e23	+	1.34212e22i	−0.784543	+	0.0811643i
$279$	−5.61144e21	+	8.71497e21i	−0.0327970	+	0.0509361i
$280$	−1.27971e23	−	4.00517e23i	−0.722952	−	2.26266i
$281$		−	6.36293e22i		−	0.347494i	−0.984790	−	0.173747i	$-0.944412\pi$
$281$		−	6.36293e22i		−	0.347494i	0.984790	−	0.173747i	$-0.0555875\pi$
$282$	2.80351e22	−	1.51530e23i	0.148025	−	0.800077i
$283$		−	1.94382e23i		−	0.992396i	−0.868210	−	0.496198i	$-0.834729\pi$
$283$		−	1.94382e23i		−	0.992396i	0.868210	−	0.496198i	$-0.165271\pi$
$284$	3.14889e23	−	6.58581e22i	1.55465	−	0.325151i
$285$	−2.92336e22	−	8.59751e21i	−0.139591	−	0.0410532i
$286$	1.56805e22	+	1.51569e23i	0.0724238	+	0.700057i
$287$	3.02140e23			1.34999
$288$	1.30925e22	−	2.30957e23i	0.0565972	−	0.998397i
$289$	2.21422e23			0.926172
$290$	2.75345e22	+	2.66152e23i	0.111454	+	1.07733i
$291$	2.60063e23	+	7.64837e22i	1.01881	+	0.299630i
$292$	−2.26217e23	+	4.73126e22i	−0.857805	+	0.179407i
$293$			3.73976e23i			1.37278i	0.727234	+	0.686390i	$0.240806\pi$
$293$			3.73976e23i			1.37278i	−0.727234	+	0.686390i	$0.759194\pi$
$294$	−5.90171e22	+	3.18988e23i	−0.209739	+	1.13364i
$295$			1.76109e23i			0.605999i
$296$	−5.81290e22	−	1.81929e23i	−0.193697	−	0.606222i
$297$	2.47347e23	+	2.86204e23i	0.798217	+	0.923612i
$298$	−8.90617e22	+	9.21380e21i	−0.278379	+	0.0287995i
$299$	3.18232e23			0.963536
$300$	5.50805e23	+	4.40796e22i	1.61565	+	0.129296i
$301$	−3.08599e22			−0.0877026
$302$	−1.13598e23	+	1.17522e22i	−0.312827	+	0.0323633i
$303$	1.10252e22	−	3.74882e22i	0.0294226	−	0.100044i
$304$	−1.39264e22	−	3.18370e22i	−0.0360197	−	0.0823443i
$305$		−	1.00768e24i		−	2.52623i
$306$	−9.97340e22	−	5.05332e22i	−0.242376	−	0.122807i
$307$		−	4.50247e23i		−	1.06081i	−0.847746	−	0.530403i	$-0.822041\pi$
$307$		−	4.50247e23i		−	1.06081i	0.847746	−	0.530403i	$-0.177959\pi$
$308$	1.60516e23	+	7.67483e23i	0.366680	+	1.75322i
$309$	−4.69054e22	+	1.59490e23i	−0.103900	+	0.353287i
$310$	−4.69820e21	−	4.54133e22i	−0.0100924	−	0.0975545i
$311$	−4.05652e23			−0.845142			−0.422571	−	0.906330i	$-0.638872\pi$
$311$	−4.05652e23			−0.845142			−0.422571	+	0.906330i	$0.638872\pi$
$312$	−6.62674e21	−	2.85216e23i	−0.0133916	−	0.576374i
$313$	−7.97913e23			−1.56417			−0.782086	−	0.623171i	$-0.785844\pi$
$313$	−7.97913e23			−1.56417			−0.782086	+	0.623171i	$0.785844\pi$
$314$	−3.36147e22	−	3.24923e23i	−0.0639289	−	0.617944i
$315$	−1.08234e24	−	6.96901e23i	−1.99716	−	1.28594i
$316$	2.06427e23	+	9.86995e23i	0.369606	+	1.76721i
$317$			4.17201e23i			0.724907i	0.932002	+	0.362454i	$0.118061\pi$
$317$			4.17201e23i			0.724907i	−0.932002	+	0.362454i	$0.881939\pi$
$318$	2.33396e23	+	4.31815e22i	0.393583	+	0.0728182i
$319$		−	4.98973e23i		−	0.816705i
$320$	5.90808e23	+	8.30155e23i	0.938688	+	1.31897i
$321$	1.46851e23	+	4.31885e22i	0.226506	+	0.0666148i
$322$	1.62883e24	−	1.68509e23i	2.43918	−	0.252343i
$323$	−1.67952e22			−0.0244209
$324$	−4.18878e23	−	5.71085e23i	−0.591439	−	0.806350i
$325$	6.81469e23			0.934446
$326$	−1.14352e24	+	1.18302e23i	−1.52292	+	0.157552i
$327$	9.25718e23	+	2.72251e23i	1.19750	+	0.352180i
$328$	−6.97450e23	+	2.22845e23i	−0.876419	+	0.280028i
$329$		−	9.77937e23i		−	1.19385i
$330$	−1.63838e24	−	3.03123e23i	−1.94327	−	0.359531i
$331$		−	3.07288e23i		−	0.354144i	−0.984198	−	0.177072i	$-0.943337\pi$
$331$		−	3.07288e23i		−	0.354144i	0.984198	−	0.177072i	$-0.0566625\pi$
$332$	−8.63525e23	+	1.80603e23i	−0.967081	+	0.202262i
$333$	−4.91638e23	−	3.16558e23i	−0.535088	−	0.344535i
$334$	9.45378e22	+	9.13813e23i	0.100003	+	0.966643i
$335$	−1.12839e24			−1.16020
$336$	−1.84944e23	−	1.45633e24i	−0.184849	−	1.45558i
$337$	1.65432e24			1.60745			0.803723	−	0.595003i	$-0.202849\pi$
$337$	1.65432e24			1.60745			0.803723	+	0.595003i	$0.202849\pi$
$338$	7.27227e22	+	7.02946e23i	0.0687007	+	0.664069i
$339$	−7.50154e22	+	2.55070e23i	−0.0689054	+	0.234295i
$340$	4.82037e23	−	1.00816e23i	0.430557	−	0.0900496i
$341$			8.51395e22i			0.0739545i
$342$	−9.49030e22	−	4.80854e22i	−0.0801737	−	0.0406224i
$343$			2.72992e23i			0.224314i
$344$	7.12360e22	−	2.27609e22i	0.0569370	−	0.0181922i
$345$	−9.81798e23	+	3.33835e24i	−0.763380	+	2.59568i
$346$	−5.12111e23	+	5.29800e22i	−0.387383	+	0.0400764i
$347$	2.76687e23			0.203638			0.101819	−	0.994803i	$-0.467534\pi$
$347$	2.76687e23			0.203638			0.101819	+	0.994803i	$0.467534\pi$
$348$	−7.45244e22	+	9.31233e23i	−0.0533698	+	0.666892i
$349$	−1.31829e24			−0.918689			−0.459345	−	0.888258i	$-0.651916\pi$
$349$	−1.31829e24			−0.918689			−0.459345	+	0.888258i	$0.651916\pi$
$350$	3.48800e24	−	3.60848e23i	2.36554	−	0.244725i
$351$	−5.71132e23	−	6.60854e23i	−0.376980	−	0.436202i
$352$	−9.36593e23	−	1.65324e24i	−0.601722	−	1.06214i
$353$		−	1.45203e24i		−	0.908063i	−0.890986	−	0.454032i	$-0.849985\pi$
$353$		−	1.45203e24i		−	0.908063i	0.890986	−	0.454032i	$-0.150015\pi$
$354$	−1.11861e23	+	6.04611e23i	−0.0681003	+	0.368083i
$355$			4.33828e24i			2.57127i
$356$	−2.95979e23	−	1.41517e24i	−0.170799	−	0.816647i
$357$	−6.80697e23	−	2.00191e23i	−0.382477	−	0.112485i
$358$	−1.12913e23	−	1.09143e24i	−0.0617809	−	0.597181i
$359$	2.45344e24			1.30731			0.653654	−	0.756794i	$-0.273235\pi$
$359$	2.45344e24			1.30731			0.653654	+	0.756794i	$0.273235\pi$
$360$	3.01244e24	+	8.10420e23i	1.56331	+	0.420568i
$361$	1.96244e24			0.991922
$362$	8.32840e22	+	8.05033e23i	0.0410044	+	0.396353i
$363$	9.80575e23	+	2.88384e23i	0.470292	+	0.138311i
$364$	−3.70637e23	−	1.77214e24i	−0.173175	−	0.828009i
$365$		−	3.11663e24i		−	1.41874i
$366$	6.40060e23	−	3.45953e24i	0.283890	−	1.53443i
$367$		−	4.44673e24i		−	1.92182i	−0.276858	−	0.960911i	$-0.589293\pi$
$367$		−	4.44673e24i		−	1.92182i	0.276858	−	0.960911i	$-0.410707\pi$
$368$	−3.63565e24	+	1.59033e24i	−1.53119	+	0.669783i
$369$	−1.21357e24	+	1.88476e24i	−0.498096	+	0.773580i
$370$	2.56190e24	−	2.65039e23i	1.02482	−	0.106022i
$371$	1.50628e24			0.587293
$372$	1.27161e22	−	1.58896e23i	0.00483275	−	0.0603886i
$373$	2.95955e24			1.09646			0.548229	−	0.836328i	$-0.315302\pi$
$373$	2.95955e24			1.09646			0.548229	+	0.836328i	$0.315302\pi$
$374$	−9.13486e23	+	9.45039e22i	−0.329930	+	0.0341326i
$375$	−8.05289e23	+	2.73818e24i	−0.283566	+	0.964194i
$376$	7.21285e23	+	2.25744e24i	0.247641	+	0.775054i
$377$			1.15214e24i			0.385712i
$378$	−3.27319e24	−	3.08006e24i	−1.06856	−	1.00551i
$379$			3.84264e24i			1.22337i	0.791102	+	0.611684i	$0.209507\pi$
$379$			3.84264e24i			1.22337i	−0.791102	+	0.611684i	$0.790493\pi$
$380$	4.58688e23	−	9.59331e22i	0.142421	−	0.0297868i
$381$	1.20414e24	−	4.09437e24i	0.364662	−	1.23994i
$382$	−3.60909e23	−	3.48859e24i	−0.106609	−	1.03050i
$383$	4.60507e24			1.32693			0.663465	−	0.748207i	$-0.269085\pi$
$383$	4.60507e24			1.32693			0.663465	+	0.748207i	$0.269085\pi$
$384$	1.50104e24	+	3.22533e24i	0.421936	+	0.906626i
$385$	−1.05737e25			−2.89969
$386$	4.48420e23	+	4.33448e24i	0.119979	+	1.15973i
$387$	1.23951e23	−	1.92505e23i	0.0323591	−	0.0502560i
$388$	−4.08050e24	+	8.53423e23i	−1.03947	+	0.217402i
$389$			6.56690e24i			1.63245i	0.577736	+	0.816223i	$0.303936\pi$
$389$			6.56690e24i			1.63245i	−0.577736	+	0.816223i	$0.696064\pi$
$390$	3.78307e24	+	6.99920e23i	0.917764	+	0.169799i
$391$			1.91794e24i			0.454104i
$392$	−1.51839e24	−	4.75218e24i	−0.350885	−	1.09818i
$393$	3.34772e24	+	9.84553e23i	0.755126	+	0.222080i
$394$	6.96133e24	−	7.20178e23i	1.53277	−	0.158572i
$395$	−1.35980e25			−2.92282
$396$	−5.43231e24	−	2.08135e24i	−1.13994	−	0.436757i
$397$	3.23839e24			0.663466			0.331733	−	0.943373i	$-0.392367\pi$
$397$	3.23839e24			0.663466			0.331733	+	0.943373i	$0.392367\pi$
$398$	2.35196e24	−	2.43320e23i	0.470479	−	0.0486730i
$399$	−6.47725e23	−	1.90494e23i	−0.126517	−	0.0372082i
$400$	−7.78546e24	+	3.40557e24i	−1.48496	+	0.649561i
$401$		−	1.62463e24i		−	0.302610i	−0.988487	−	0.151305i	$-0.951652\pi$
$401$		−	1.62463e24i		−	0.302610i	0.988487	−	0.151305i	$-0.0483476\pi$
$402$	−3.87396e24	−	7.16734e23i	−0.704705	−	0.130380i
$403$		−	1.96590e23i		−	0.0349271i
$404$	1.23021e23	+	5.88206e23i	0.0213480	+	0.102072i
$405$	8.69459e24	−	3.95250e24i	1.47376	−	0.669961i
$406$	6.10078e23	+	5.89708e24i	0.101015	+	0.976427i
$407$	−4.80298e24			−0.776897
$408$	1.71895e24	−	3.99384e22i	0.271639	−	0.00631131i
$409$	−1.66095e24			−0.256440			−0.128220	−	0.991746i	$-0.540926\pi$
$409$	−1.66095e24			−0.256440			−0.128220	+	0.991746i	$0.540926\pi$
$410$	−1.01606e24	−	9.82139e24i	−0.153276	−	1.48158i
$411$	1.61055e24	−	5.47626e24i	0.237398	−	0.807211i
$412$	−5.23382e23	−	2.50246e24i	−0.0753868	−	0.360449i
$413$			3.90202e24i			0.549242i
$414$	−5.49114e24	+	1.08375e25i	−0.755370	+	1.49082i
$415$		−	1.18969e25i		−	1.59948i
$416$	2.16262e24	+	3.81739e24i	0.284180	+	0.501625i
$417$	1.73260e24	−	5.89125e24i	0.222539	−	0.756685i
$418$	−8.69238e23	+	8.99262e22i	−0.109135	+	0.0112905i
$419$	6.70697e24			0.823177			0.411589	−	0.911370i	$-0.364974\pi$
$419$	6.70697e24			0.823177			0.411589	+	0.911370i	$0.364974\pi$
$420$	1.97338e25	+	1.57925e24i	2.36778	+	0.189488i
$421$	−1.21764e25			−1.42836			−0.714181	−	0.699961i	$-0.753201\pi$
$421$	−1.21764e25			−1.42836			−0.714181	+	0.699961i	$0.753201\pi$
$422$	7.58805e23	−	7.85015e22i	0.0870285	−	0.00900346i
$423$	6.10041e24	+	3.92796e24i	0.684109	+	0.440488i
$424$	−3.47706e24	+	1.11097e24i	−0.381273	+	0.121822i
$425$			4.10712e24i			0.440395i
$426$	−2.75560e24	+	1.48941e25i	−0.288952	+	1.56179i
$427$		−	2.23270e25i		−	2.28963i
$428$	−2.30416e24	+	4.81908e23i	−0.231098	+	0.0483335i
$429$	−6.88297e24	−	2.02426e24i	−0.675199	−	0.198574i
$430$	1.03778e23	+	1.00313e24i	0.00995765	+	0.0962518i
$431$	1.13156e25			1.06204			0.531022	−	0.847358i	$-0.321808\pi$
$431$	1.13156e25			1.06204			0.531022	+	0.847358i	$0.321808\pi$
$432$	9.82746e24	+	4.69576e24i	0.902289	+	0.431132i
$433$	1.07201e25			0.962859			0.481429	−	0.876485i	$-0.340118\pi$
$433$	1.07201e25			0.962859			0.481429	+	0.876485i	$0.340118\pi$
$434$	−1.04097e23	−	1.00622e24i	−0.00914717	−	0.0884177i
$435$	−1.20863e25	−	3.55455e24i	−1.03907	−	0.305588i
$436$	−1.45249e25	+	3.03784e24i	−1.22178	+	0.255530i
$437$			1.82504e24i			0.150210i
$438$	1.97963e24	−	1.06999e25i	0.159434	−	0.861740i
$439$			1.99268e25i			1.57045i	0.619212	+	0.785224i	$0.287452\pi$
$439$			1.99268e25i			1.57045i	−0.619212	+	0.785224i	$0.712548\pi$
$440$	2.44081e25	−	7.79873e24i	1.88249	−	0.601483i
$441$	−1.28421e25	−	8.26882e24i	−0.969323	−	0.624133i
$442$	2.10926e24	−	2.18212e23i	0.155819	−	0.0161201i
$443$	−1.19783e25			−0.866082			−0.433041	−	0.901374i	$-0.642559\pi$
$443$	−1.19783e25			−0.866082			−0.433041	+	0.901374i	$0.642559\pi$
$444$	8.96380e24	+	7.17351e23i	0.634386	+	0.0507684i
$445$	1.94971e25			1.35067
$446$	−8.33421e24	+	8.62208e23i	−0.565175	+	0.0584697i
$447$	1.18945e24	−	4.04442e24i	0.0789633	−	0.268494i
$448$	1.30904e25	+	1.83936e25i	0.850772	+	1.19544i
$449$			8.98737e24i			0.571864i	0.958250	+	0.285932i	$0.0923031\pi$
$449$			8.98737e24i			0.571864i	−0.958250	+	0.285932i	$0.907697\pi$
$450$	−1.17589e25	+	2.32077e25i	−0.732565	+	1.44581i
$451$			1.84128e25i			1.12316i
$452$	−8.37040e23	−	4.00217e24i	−0.0499955	−	0.239045i
$453$	1.51714e24	−	5.15865e24i	0.0887347	−	0.301719i
$454$	5.85912e23	+	5.66350e24i	0.0335585	+	0.324380i
$455$	2.44150e25			1.36946
$456$	1.63569e24	−	3.80038e22i	0.0898535	−	0.00208767i
$457$	4.70541e24			0.253159			0.126579	−	0.991956i	$-0.459600\pi$
$457$	4.70541e24			0.253159			0.126579	+	0.991956i	$0.459600\pi$
$458$	−3.60019e24	−	3.47998e25i	−0.189716	−	1.83381i
$459$	3.98287e24	−	3.44213e24i	0.205578	−	0.177667i
$460$	−1.09551e25	−	5.23801e25i	−0.553883	−	2.64830i
$461$			2.20436e25i			1.09175i	0.837867	+	0.545875i	$0.183802\pi$
$461$			2.20436e25i			1.09175i	−0.837867	+	0.545875i	$0.816198\pi$
$462$	−3.63014e25	−	6.71625e24i	−1.76127	−	0.325858i
$463$		−	1.60558e24i		−	0.0763155i	−0.999272	−	0.0381577i	$-0.987851\pi$
$463$		−	1.60558e24i		−	0.0763155i	0.999272	−	0.0381577i	$-0.0121489\pi$
$464$	−5.75772e24	−	1.31627e25i	−0.268120	−	0.612948i
$465$	2.06228e24	+	6.06511e23i	0.0940904	+	0.0276717i
$466$	3.80482e25	−	3.93624e24i	1.70086	−	0.175961i
$467$	−2.53433e25			−1.11007			−0.555037	−	0.831825i	$-0.687296\pi$
$467$	−2.53433e25			−1.11007			−0.555037	+	0.831825i	$0.687296\pi$
$468$	1.25434e25	+	4.80589e24i	0.538367	+	0.206271i
$469$	−2.50016e25			−1.05154
$470$	−3.17889e25	+	3.28870e24i	−1.31023	+	0.135548i
$471$	1.47552e25	+	4.33947e24i	0.596002	+	0.175282i
$472$	−2.87796e24	−	9.00730e24i	−0.113929	−	0.356571i
$473$		−	1.88065e24i		−	0.0729670i
$474$	−4.66842e25	−	8.63721e24i	−1.77532	−	0.328458i
$475$			3.90817e24i			0.145675i
$476$	1.06804e25	−	2.23378e24i	0.390232	−	0.0816157i
$477$	−6.05010e24	+	9.39625e24i	−0.216690	+	0.336535i
$478$	2.15861e24	+	2.08654e25i	0.0757897	+	0.732592i
$479$	−1.93936e25			−0.667530			−0.333765	−	0.942656i	$-0.608319\pi$
$479$	−1.93936e25			−0.667530			−0.333765	+	0.942656i	$0.608319\pi$
$480$	−4.67176e25	+	1.09093e25i	−1.57648	+	0.368133i
$481$	1.10902e25			0.366912
$482$	5.18042e23	+	5.00746e24i	0.0168042	+	0.162432i
$483$	−2.17536e25	+	7.39674e25i	−0.691883	+	2.35257i
$484$	−1.53856e25	+	3.21786e24i	−0.479827	+	0.100354i
$485$		−	5.62177e25i		−	1.71920i
$486$	3.23606e25	−	8.04696e24i	0.970446	−	0.241317i
$487$			2.01956e25i			0.593925i	0.954889	+	0.296962i	$0.0959736\pi$
$487$			2.01956e25i			0.593925i	−0.954889	+	0.296962i	$0.904026\pi$
$488$	1.64674e25	+	5.15389e25i	0.474938	+	1.48644i
$489$	1.52721e25	−	5.19289e25i	0.431982	−	1.46884i
$490$	6.69195e25	−	6.92309e24i	1.85648	−	0.192060i
$491$	−2.36318e25			−0.643017			−0.321508	−	0.946907i	$-0.604190\pi$
$491$	−2.36318e25			−0.643017			−0.321508	+	0.946907i	$0.604190\pi$
$492$	2.75006e24	−	3.43639e25i	0.0733962	−	0.917136i
$493$	−6.94380e24			−0.181782
$494$	2.00710e24	−	2.07642e23i	0.0515421	−	0.00533224i
$495$	4.24702e25	−	6.59593e25i	1.06988	−	1.66160i
$496$	9.82437e23	+	2.24594e24i	0.0242789	+	0.0555038i
$497$			9.61227e25i			2.33045i
$498$	7.55672e24	−	4.08441e25i	0.179744	−	0.971518i
$499$			6.80557e25i			1.58821i	0.607777	+	0.794107i	$0.292061\pi$
$499$			6.80557e25i			1.58821i	−0.607777	+	0.794107i	$0.707939\pi$
$500$	−8.98560e24	−	4.29631e25i	−0.205746	−	0.983742i
$501$	−4.14976e25	−	1.22043e25i	−0.932318	−	0.274192i
$502$	−5.37174e24	−	5.19238e25i	−0.118421	−	1.14467i
$503$	8.02098e25			1.73513			0.867564	−	0.497325i	$-0.165684\pi$
$503$	8.02098e25			1.73513			0.867564	+	0.497325i	$0.165684\pi$
$504$	6.67462e25	+	1.79564e25i	1.41689	+	0.381178i
$505$	−8.10381e24			−0.168819
$506$	1.02692e25	+	9.92631e25i	0.209945	+	2.02935i
$507$	−3.19218e25	−	9.38810e24i	−0.640489	−	0.188366i
$508$	1.34361e25	+	6.42424e25i	0.264586	+	1.26508i
$509$			1.15430e25i			0.223101i	0.993759	+	0.111550i	$0.0355816\pi$
$509$			1.15430e25i			0.223101i	−0.993759	+	0.111550i	$0.964418\pi$
$510$	−4.21832e24	+	2.28000e25i	−0.0800244	+	0.432533i
$511$		−	6.90547e25i		−	1.28586i
$512$	−4.37839e25	−	3.28043e25i	−0.800295	−	0.599607i
$513$	3.78995e24	−	3.27540e24i	0.0680014	−	0.0587691i
$514$	−6.17577e25	+	6.38909e24i	−1.08778	+	0.112535i
$515$	3.44768e25			0.596154
$516$	−2.80885e23	+	3.50985e24i	−0.00476822	+	0.0595822i
$517$	5.95970e25			0.993262
$518$	5.67637e25	−	5.87244e24i	0.928834	−	0.0960917i
$519$	6.83942e24	−	2.32557e25i	0.109883	−	0.373628i
$520$	−5.63590e25	+	1.80075e25i	−0.889060	+	0.284067i
$521$		−	6.64890e25i		−	1.02989i	−0.857223	−	0.514946i	$-0.827812\pi$
$521$		−	6.64890e25i		−	1.02989i	0.857223	−	0.514946i	$-0.172188\pi$
$522$	−3.92366e25	−	1.98804e25i	−0.596790	−	0.302382i
$523$		−	1.08349e26i		−	1.61830i	−0.587599	−	0.809152i	$-0.699927\pi$
$523$		−	1.08349e26i		−	1.61830i	0.587599	−	0.809152i	$-0.300073\pi$
$524$	−5.25271e25	+	1.09859e25i	−0.770436	+	0.161134i
$525$	−4.65835e25	+	1.58395e26i	−0.670995	+	2.28154i
$526$	−3.46077e24	−	3.34522e25i	−0.0489562	−	0.473216i
$527$	1.18482e24			0.0164608
$528$	8.87507e25	−	1.12708e25i	1.21101	−	0.153791i
$529$	1.33796e26			1.79314
$530$	−5.06547e24	−	4.89634e25i	−0.0666805	−	0.644542i
$531$	−2.43409e25	−	1.56728e25i	−0.314731	−	0.202650i
$532$	1.01631e25	−	2.12558e24i	0.129082	−	0.0269970i
$533$		−	4.25158e25i		−	0.530447i
$534$	6.69367e25	+	1.23842e25i	0.820394	+	0.151784i
$535$		−	3.17448e25i		−	0.382218i
$536$	5.77129e25	−	1.84401e25i	0.682664	−	0.218121i
$537$	4.95633e25	+	1.45764e25i	0.575976	+	0.169393i
$538$	−5.12739e25	+	5.30450e24i	−0.585416	+	0.0605637i
$539$	−1.25459e26			−1.40737
$540$	−8.91135e25	+	1.16757e26i	−0.982207	+	1.28689i
$541$	−1.45055e26			−1.57093			−0.785467	−	0.618904i	$-0.787577\pi$
$541$	−1.45055e26			−1.57093			−0.785467	+	0.618904i	$0.787577\pi$
$542$	1.40380e26	−	1.45229e25i	1.49386	−	0.154546i
$543$	−3.65577e25	−	1.07515e25i	−0.382279	−	0.112427i
$544$	−2.30068e25	+	1.30338e25i	−0.236411	+	0.133931i
$545$		−	2.00112e26i		−	2.02072i
$546$	8.38210e25	+	1.55080e25i	0.831808	+	0.153896i
$547$			4.44080e24i			0.0433093i	0.999766	+	0.0216547i	$0.00689343\pi$
$547$			4.44080e24i			0.0433093i	−0.999766	+	0.0216547i	$0.993107\pi$
$548$	1.79709e25	+	8.59249e25i	0.172248	+	0.823576i
$549$	1.39276e26	+	8.96780e25i	1.31202	+	0.844790i
$550$	2.19906e25	+	2.12564e26i	0.203607	+	1.96809i
$551$	−6.60745e24			−0.0601304
$552$	−4.33987e24	−	1.86788e26i	−0.0388200	−	1.67082i
$553$	−3.01289e26			−2.64907
$554$	1.17786e25	+	1.13854e26i	0.101801	+	0.984020i
$555$	−3.42151e25	+	1.16340e26i	−0.290693	+	0.988427i
$556$	1.93327e25	+	9.24363e25i	0.161467	+	0.772026i
$557$		−	6.95977e25i		−	0.571440i	−0.958313	−	0.285720i	$-0.907767\pi$
$557$		−	6.95977e25i		−	0.571440i	0.958313	−	0.285720i	$-0.0922328\pi$
$558$	6.69493e24	+	3.39218e24i	0.0540407	+	0.0273813i
$559$			4.34247e24i			0.0344607i
$560$	−2.78930e26	+	1.22012e26i	−2.17625	+	0.951953i
$561$	1.21999e25	−	4.14827e25i	0.0935858	−	0.318214i
$562$	−4.58280e25	+	4.74109e24i	−0.345649	+	0.0357589i
$563$	−2.00683e26			−1.48827			−0.744133	−	0.668032i	$-0.767137\pi$
$563$	−2.00683e26			−1.48827			−0.744133	+	0.668032i	$0.767137\pi$
$564$	−1.11226e26	−	8.90114e24i	−0.811062	−	0.0649074i
$565$	5.51385e25			0.395362
$566$	−1.40000e26	+	1.44836e25i	−0.987127	+	0.102122i
$567$	1.92645e26	−	8.75751e25i	1.33573	−	0.607213i
$568$	−7.08959e25	−	2.21887e26i	−0.483406	−	1.51294i
$569$			1.48358e26i			0.994822i	0.867515	+	0.497411i	$0.165716\pi$
$569$			1.48358e26i			0.994822i	−0.867515	+	0.497411i	$0.834284\pi$
$570$	−4.01399e24	+	2.16956e25i	−0.0264707	+	0.143074i
$571$			1.80490e25i			0.117061i	0.998286	+	0.0585303i	$0.0186414\pi$
$571$			1.80490e25i			0.117061i	−0.998286	+	0.0585303i	$0.981359\pi$
$572$	1.07997e26	−	2.25872e25i	0.688888	−	0.144079i
$573$	1.58422e26	+	4.65914e25i	0.993908	+	0.292305i
$574$	−2.25128e25	−	2.17611e26i	−0.138920	−	1.34282i
$575$	4.46296e26			2.70881
$576$	−1.67319e26	+	7.77922e24i	−0.998921	+	0.0464432i
$577$	3.86284e25			0.226849			0.113424	−	0.993547i	$-0.463818\pi$
$577$	3.86284e25			0.226849			0.113424	+	0.993547i	$0.463818\pi$
$578$	−1.64984e25	−	1.59476e26i	−0.0953077	−	0.921255i
$579$	−1.96835e26	−	5.78885e25i	−1.11855	−	0.328962i
$580$	1.89640e26	−	3.96625e25i	1.06014	−	0.221725i
$581$		−	2.63598e26i		−	1.44967i
$582$	3.57085e25	−	1.93005e26i	0.193198	−	1.04424i
$583$			9.17952e25i			0.488617i
$584$	5.09318e25	+	1.59404e26i	0.266727	+	0.834789i
$585$	−9.80649e25	+	1.52302e26i	−0.505281	+	0.784738i
$586$	2.69350e26	−	2.78653e25i	1.36549	−	0.141266i
$587$	−1.28094e26			−0.638948			−0.319474	−	0.947595i	$-0.603506\pi$
$587$	−1.28094e26			−0.638948			−0.319474	+	0.947595i	$0.603506\pi$
$588$	2.34143e26	+	1.87379e25i	1.14920	+	0.0919681i
$589$	1.12743e24			0.00544494
$590$	1.26839e26	−	1.31221e25i	0.602782	−	0.0623603i
$591$	−9.29711e25	+	3.16124e26i	−0.434777	+	1.47835i
$592$	−1.26700e26	+	5.54222e25i	−0.583071	+	0.255051i
$593$			2.75550e26i			1.24790i	0.781463	+	0.623952i	$0.214474\pi$
$593$			2.75550e26i			1.24790i	−0.781463	+	0.623952i	$0.785526\pi$
$594$	1.87704e26	−	1.99473e26i	0.836568	−	0.889023i
$595$			1.47146e26i			0.645412i
$596$	1.32722e25	+	6.34587e25i	0.0572931	+	0.273938i
$597$	−3.14112e25	+	1.06806e26i	−0.133453	+	0.453773i
$598$	−2.37118e25	−	2.29201e26i	−0.0991526	−	0.958420i
$599$	2.45383e26			1.00992			0.504962	−	0.863142i	$-0.331506\pi$
$599$	2.45383e26			1.00992			0.504962	+	0.863142i	$0.331506\pi$
$600$	−9.29349e24	−	3.99993e26i	−0.0376480	−	1.62037i
$601$	1.70604e26			0.680270			0.340135	−	0.940377i	$-0.389527\pi$
$601$	1.70604e26			0.680270			0.340135	+	0.940377i	$0.389527\pi$
$602$	2.29940e24	+	2.22263e25i	0.00902503	+	0.0872370i
$603$	1.00421e26	−	1.55961e26i	0.387980	−	0.602560i
$604$	1.69286e25	+	8.09414e25i	0.0643830	+	0.307836i
$605$		−	2.11970e26i		−	0.793596i
$606$	−2.78218e25	−	5.14741e24i	−0.102540	−	0.0189714i
$607$			9.35857e25i			0.339560i	0.985482	+	0.169780i	$0.0543057\pi$
$607$			9.35857e25i			0.339560i	−0.985482	+	0.169780i	$0.945694\pi$
$608$	−2.18924e25	+	1.24025e25i	−0.0782006	+	0.0443021i
$609$	−2.67795e26	−	7.87576e25i	−0.941755	−	0.276967i
$610$	−7.25763e26	+	7.50832e25i	−2.51282	+	0.259962i
$611$	−1.37611e26			−0.469096
$612$	−2.89644e25	+	7.55970e25i	−0.0972134	+	0.253727i
$613$	1.98207e26			0.655004			0.327502	−	0.944850i	$-0.393793\pi$
$613$	1.98207e26			0.655004			0.327502	+	0.944850i	$0.393793\pi$
$614$	−3.24283e26	+	3.35484e25i	−1.05517	+	0.109162i
$615$	4.46003e26	+	1.31168e26i	1.42897	+	0.420257i
$616$	5.40806e26	−	1.72795e26i	1.70618	−	0.545149i
$617$			3.17344e26i			0.985873i	0.870065	+	0.492937i	$0.164077\pi$
$617$			3.17344e26i			0.985873i	−0.870065	+	0.492937i	$0.835923\pi$
$618$	1.18365e26	+	2.18991e25i	0.362103	+	0.0669940i
$619$			3.39238e26i			1.02198i	0.859586	+	0.510992i	$0.170722\pi$
$619$			3.39238e26i			1.02198i	−0.859586	+	0.510992i	$0.829278\pi$
$620$	−3.23581e25	+	6.76760e24i	−0.0959980	+	0.0200777i
$621$	−3.74036e26	−	4.32795e26i	−1.09281	−	1.26448i
$622$	3.02256e25	+	2.92164e26i	0.0869693	+	0.840656i
$623$	4.31994e26			1.22417
$624$	−2.04928e26	+	2.60245e25i	−0.571936	+	0.0726322i
$625$	2.26228e24			0.00621851
$626$	5.94534e25	+	5.74684e26i	0.160961	+	1.55587i
$627$	1.16090e25	−	3.94733e25i	0.0309565	−	0.105260i
$628$	−2.31516e26	+	4.84208e25i	−0.608085	+	0.127179i
$629$			6.68391e25i			0.172922i
$630$	−4.21285e26	+	8.31463e26i	−1.07360	+	2.11889i
$631$		−	3.28708e26i		−	0.825147i	−0.910924	−	0.412573i	$-0.864630\pi$
$631$		−	3.28708e26i		−	0.825147i	0.910924	−	0.412573i	$-0.135370\pi$
$632$	6.95486e26	−	2.22218e26i	1.71979	−	0.549498i
$633$	−1.01341e25	+	3.44584e25i	−0.0246860	+	0.0839382i
$634$	3.00482e26	−	3.10861e25i	0.721059	−	0.0745965i
$635$	−8.85078e26			−2.09233
$636$	1.37101e25	−	1.71317e26i	0.0319300	−	0.398987i
$637$	2.89688e26			0.664669
$638$	−3.59377e26	+	3.71790e25i	−0.812370	+	0.0840430i
$639$	−5.99616e26	−	3.86084e26i	−1.33541	−	0.859852i
$640$	5.53883e26	−	4.87375e26i	1.21537	−	1.06943i
$641$		−	7.50904e26i		−	1.62343i	−0.584054	−	0.811715i	$-0.698535\pi$
$641$		−	7.50904e26i		−	1.62343i	0.584054	−	0.811715i	$-0.301465\pi$
$642$	2.01637e25	−	1.08985e26i	0.0429525	−	0.232159i
$643$		−	2.12377e26i		−	0.445763i	−0.974846	−	0.222882i	$-0.928454\pi$
$643$		−	2.12377e26i		−	0.445763i	0.974846	−	0.222882i	$-0.0715463\pi$
$644$	−2.42731e26	−	1.16058e27i	−0.502008	−	2.40026i
$645$	−4.55538e25	−	1.33972e25i	−0.0928340	−	0.0273022i
$646$	1.25143e24	+	1.20965e25i	0.00251303	+	0.0242912i
$647$	−7.48256e26			−1.48067			−0.740337	−	0.672236i	$-0.765334\pi$
$647$	−7.48256e26			−1.48067			−0.740337	+	0.672236i	$0.765334\pi$
$648$	−3.80104e26	+	3.44242e26i	−0.741207	+	0.671276i
$649$	−2.37795e26			−0.456959
$650$	−5.07770e25	−	4.90817e26i	−0.0961591	−	0.929485i
$651$	4.56937e25	+	1.34384e25i	0.0852781	+	0.0250800i
$652$	1.70410e26	+	8.14787e26i	0.313432	+	1.49862i
$653$			7.54361e26i			1.36743i	0.729751	+	0.683713i	$0.239636\pi$
$653$			7.54361e26i			1.36743i	−0.729751	+	0.683713i	$0.760364\pi$
$654$	1.27108e26	−	6.87018e26i	0.227082	−	1.22738i
$655$		−	7.23675e26i		−	1.27424i
$656$	2.12468e26	+	4.85722e26i	0.368729	+	0.842950i
$657$	4.30766e26	+	2.77364e26i	0.736835	+	0.474437i
$658$	−7.04343e26	+	7.28672e25i	−1.18751	+	0.122853i
$659$	2.34534e26			0.389758			0.194879	−	0.980827i	$-0.437569\pi$
$659$	2.34534e26			0.389758			0.194879	+	0.980827i	$0.437569\pi$
$660$	−9.62415e25	+	1.20260e27i	−0.157650	+	1.96995i
$661$	4.60565e26			0.743665			0.371832	−	0.928300i	$-0.378730\pi$
$661$	4.60565e26			0.743665			0.371832	+	0.928300i	$0.378730\pi$
$662$	−2.21319e26	+	2.28964e25i	−0.352264	+	0.0364432i
$663$	−2.81700e25	+	9.57847e25i	−0.0441986	+	0.150286i
$664$	1.94419e26	+	6.08482e26i	0.300706	+	0.941134i
$665$			1.40018e26i			0.213491i
$666$	−1.91363e26	+	3.77681e26i	−0.287643	+	0.567702i
$667$			7.54542e26i			1.11812i
$668$	6.51115e26	−	1.36178e26i	0.951220	−	0.198945i
$669$	1.11306e26	−	3.78468e26i	0.160314	−	0.545107i
$670$	8.40776e25	+	8.12704e26i	0.119390	+	1.15404i
$671$	1.36064e27			1.90493
$672$	−1.03511e27	+	2.41715e26i	−1.42883	+	0.333654i
$673$	−1.70271e26			−0.231738			−0.115869	−	0.993264i	$-0.536965\pi$
$673$	−1.70271e26			−0.231738			−0.115869	+	0.993264i	$0.536965\pi$
$674$	−1.23266e26	−	1.19150e27i	−0.165414	−	1.59891i
$675$	−8.00969e26	−	9.26796e26i	−1.05981	−	1.22631i
$676$	5.00867e26	−	1.04755e26i	0.653474	−	0.136672i
$677$			8.34714e26i			1.07385i	0.843629	+	0.536927i	$0.180415\pi$
$677$			8.34714e26i			1.07385i	−0.843629	+	0.536927i	$0.819585\pi$
$678$	1.89300e26	+	3.50230e25i	0.240142	+	0.0444295i
$679$		−	1.24561e27i		−	1.55818i
$680$	−1.08529e26	−	3.39667e26i	−0.133878	−	0.419005i
$681$	−2.57188e26	−	7.56380e25i	−0.312862	−	0.0920116i
$682$	6.13203e25	−	6.34384e24i	0.0735619	−	0.00761028i
$683$	6.93137e26			0.820016			0.410008	−	0.912082i	$-0.365526\pi$
$683$	6.93137e26			0.820016			0.410008	+	0.912082i	$0.365526\pi$
$684$	−2.75614e25	+	7.19352e25i	−0.0321565	+	0.0839283i
$685$	−1.18380e27			−1.36213
$686$	1.96618e26	−	2.03409e25i	0.223123	−	0.0230830i
$687$	1.58031e27	+	4.64764e26i	1.76870	+	0.520168i
$688$	−2.17010e25	−	4.96106e25i	−0.0239547	−	0.0547626i
$689$		−	2.11958e26i		−	0.230763i
$690$	2.47755e27	+	4.58380e26i	2.66045	+	0.492220i
$691$		−	7.13134e24i		−	0.00755317i	−0.999993	−	0.00377659i	$-0.998798\pi$
$691$		−	7.13134e24i		−	0.00755317i	0.999993	−	0.00377659i	$-0.00120213\pi$
$692$	7.63159e25	+	3.64892e26i	0.0797273	+	0.381203i
$693$	9.41006e26	−	1.46145e27i	0.969676	−	1.50598i
$694$	−2.06162e25	−	1.99279e26i	−0.0209553	−	0.202557i
$695$	−1.27351e27			−1.27687
$696$	6.76258e26	−	1.57123e25i	0.668844	−	0.0155400i
$697$	2.56236e26			0.249994
$698$	9.82271e25	+	9.49475e26i	0.0945376	+	0.913812i
$699$	−5.08147e26	+	1.72782e27i	−0.482454	+	1.64046i
$700$	−5.19790e26	−	2.48529e27i	−0.486852	−	2.32780i
$701$			1.41335e27i			1.30596i	0.757376	+	0.652979i	$0.226481\pi$
$701$			1.41335e27i			1.30596i	−0.757376	+	0.652979i	$0.773519\pi$
$702$	−4.33413e26	+	4.60589e26i	−0.395093	+	0.419867i
$703$			6.36015e25i			0.0571995i
$704$	−1.12093e27	+	7.97751e26i	−0.994580	+	0.707827i
$705$	4.24553e26	−	1.44358e27i	0.371651	−	1.26370i
$706$	−1.04580e27	+	1.08192e26i	−0.903242	+	0.0934442i
$707$	−1.79555e26			−0.153008
$708$	4.43796e26	+	3.55160e25i	0.373136	+	0.0298612i
$709$	−7.45463e26			−0.618424			−0.309212	−	0.950993i	$-0.600065\pi$
$709$	−7.45463e26			−0.618424			−0.309212	+	0.950993i	$0.600065\pi$
$710$	3.12457e27	−	3.23250e26i	2.55762	−	0.264597i
$711$	1.21015e27	−	1.87945e27i	0.977412	−	1.51799i
$712$	−9.97201e26	+	3.18620e26i	−0.794736	+	0.253929i
$713$		−	1.28747e26i		−	0.101248i
$714$	−9.34646e25	+	5.05177e26i	−0.0725294	+	0.392022i
$715$			1.48789e27i			1.13937i
$716$	−7.77669e26	+	1.62647e26i	−0.587653	+	0.122906i
$717$	−9.47529e26	−	2.78665e26i	−0.706579	−	0.207803i
$718$	−1.82808e26	−	1.76705e27i	−0.134528	−	1.30037i
$719$	−1.36111e27			−0.988478			−0.494239	−	0.869326i	$-0.664553\pi$
$719$	−1.36111e27			−0.988478			−0.494239	+	0.869326i	$0.664553\pi$
$720$	3.59231e26	−	2.23005e27i	0.257463	−	1.59829i
$721$	7.63898e26			0.540319
$722$	−1.46223e26	−	1.41341e27i	−0.102074	−	0.986656i
$723$	−2.27396e26	−	6.68764e25i	−0.156664	−	0.0460743i
$724$	5.73606e26	−	1.19968e26i	0.390030	−	0.0815734i
$725$			1.61579e27i			1.08436i
$726$	1.34640e26	−	7.27731e26i	0.0891818	−	0.482029i
$727$			1.81528e27i			1.18677i	0.804917	+	0.593387i	$0.202210\pi$
$727$			1.81528e27i			1.18677i	−0.804917	+	0.593387i	$0.797790\pi$
$728$	−1.24874e27	+	3.98989e26i	−0.805792	+	0.257462i
$729$	−2.27476e26	+	1.55348e27i	−0.144885	+	0.989448i
$730$	−2.24470e27	+	2.32224e26i	−1.41121	+	0.145995i
$731$	−2.61714e25			−0.0162410
$732$	−2.53936e27	−	2.03219e26i	−1.55550	−	0.124483i
$733$	3.36526e26			0.203484			0.101742	−	0.994811i	$-0.467558\pi$
$733$	3.36526e26			0.203484			0.101742	+	0.994811i	$0.467558\pi$
$734$	−3.20268e27	+	3.31331e26i	−1.91162	+	0.197765i
$735$	−8.93733e26	+	3.03891e27i	−0.526597	+	1.79056i
$736$	1.41631e27	+	2.50002e27i	0.823793	+	1.45413i
$737$		−	1.52363e27i		−	0.874861i
$738$	1.44789e27	+	7.33616e26i	0.820729	+	0.415847i
$739$		−	1.25717e27i		−	0.703513i	−0.936091	−	0.351757i	$-0.885584\pi$
$739$		−	1.25717e27i		−	0.703513i	0.936091	−	0.351757i	$-0.114416\pi$
$740$	−3.81780e26	−	1.82542e27i	−0.210917	−	1.00847i
$741$	−2.68055e25	+	9.11451e25i	−0.0146201	+	0.0497119i
$742$	−1.12235e26	−	1.08488e27i	−0.0604353	−	0.584175i
$743$	2.74092e27			1.45715			0.728573	−	0.684968i	$-0.240184\pi$
$743$	2.74092e27			1.45715			0.728573	+	0.684968i	$0.240184\pi$
$744$	−1.15390e26	+	2.68098e24i	−0.0605653	+	0.00140718i
$745$	−8.74280e26			−0.453071
$746$	−2.20519e26	−	2.13157e27i	−0.112831	−	1.09064i
$747$	1.64434e27	+	1.05876e27i	0.830701	+	0.534876i
$748$	1.36130e26	+	6.50881e26i	0.0679028	+	0.324666i
$749$		−	7.03365e26i		−	0.346420i
$750$	2.03213e27	+	3.75971e26i	0.988255	+	0.182841i
$751$			4.00986e27i			1.92553i	0.270347	+	0.962763i	$0.412862\pi$
$751$			4.00986e27i			1.92553i	−0.270347	+	0.962763i	$0.587138\pi$
$752$	1.57214e27	−	6.87698e26i	0.745456	−	0.326083i
$753$	2.35794e27	+	6.93462e26i	1.10403	+	0.324691i
$754$	8.29812e26	−	8.58475e25i	0.383665	−	0.0396917i
$755$	−1.11514e27			−0.509137
$756$	−1.97448e27	+	2.58696e27i	−0.890215	+	1.16636i
$757$	−1.39285e27			−0.620145			−0.310072	−	0.950713i	$-0.600353\pi$
$757$	−1.39285e27			−0.620145			−0.310072	+	0.950713i	$0.600353\pi$
$758$	2.76760e27	−	2.86319e26i	1.21687	−	0.125891i
$759$	−4.50768e27	−	1.32569e27i	−1.95729	−	0.575634i
$760$	−1.03272e26	−	3.23214e26i	−0.0442845	−	0.138599i
$761$			1.03070e27i			0.436492i	0.975894	+	0.218246i	$0.0700335\pi$
$761$			1.03070e27i			0.436492i	−0.975894	+	0.218246i	$0.929966\pi$
$762$	−3.03862e27	−	5.62186e26i	−1.27088	−	0.235130i
$763$		−	4.43385e27i		−	1.83146i
$764$	−2.48571e27	+	5.19878e26i	−1.01406	+	0.212087i
$765$	−9.17902e26	−	5.91023e26i	−0.369839	−	0.238134i
$766$	−3.43129e26	−	3.31673e27i	−0.136548	−	1.31989i
$767$	5.49075e26			0.215812
$768$	2.21115e27	−	1.32142e27i	0.858393	−	0.512992i
$769$	3.86660e27			1.48262			0.741308	−	0.671165i	$-0.234206\pi$
$769$	3.86660e27			1.48262			0.741308	+	0.671165i	$0.234206\pi$
$770$	7.87860e26	+	7.61555e27i	0.298392	+	2.88429i
$771$	8.24796e26	−	2.80451e27i	0.308553	−	1.04916i
$772$	3.08843e27	−	6.45934e26i	1.14123	−	0.238684i
$773$		−	3.23640e27i		−	1.18129i	−0.806931	−	0.590646i	$-0.798873\pi$
$773$		−	3.23640e27i		−	1.18129i	0.806931	−	0.590646i	$-0.201127\pi$
$774$	−1.47884e26	−	7.49299e25i	−0.0533191	−	0.0270157i
$775$		−	2.75702e26i		−	0.0981914i
$776$	9.18707e26	+	2.87532e27i	0.323214	+	1.01158i
$777$	−7.58100e26	+	2.57772e27i	−0.263467	+	0.895852i
$778$	4.72970e27	−	4.89307e26i	1.62378	−	0.167987i
$779$	2.43825e26			0.0826936
$780$	2.22225e26	−	2.77685e27i	0.0744549	−	0.930365i
$781$	−5.85786e27			−1.93889
$782$	1.38136e27	−	1.42908e26i	0.451694	−	0.0467296i
$783$	1.56691e27	−	1.35418e27i	0.506183	−	0.437461i
$784$	−3.30954e27	+	1.44768e27i	−1.05625	+	0.462031i
$785$		−	3.18963e27i		−	1.00572i
$786$	4.59666e26	−	2.48450e27i	0.143195	−	0.773971i
$787$		−	2.94800e27i		−	0.907336i	−0.891171	−	0.453668i	$-0.850115\pi$
$787$		−	2.94800e27i		−	0.907336i	0.891171	−	0.453668i	$-0.149885\pi$
$788$	−1.03739e27	−	4.96012e27i	−0.315460	−	1.50832i
$789$	1.51911e27	+	4.46766e26i	0.456413	+	0.134230i
$790$	1.01320e27	+	9.79373e27i	0.300773	+	2.90730i
$791$	1.22170e27			0.358333
$792$	−1.09429e27	+	4.06761e27i	−0.317133	+	1.17883i
$793$	−3.14176e27			−0.899657
$794$	−2.41296e26	−	2.33239e27i	−0.0682739	−	0.659944i
$795$	2.22350e27	+	6.53924e26i	0.621655	+	0.182827i
$796$	−3.50494e26	−	1.67583e27i	−0.0968292	−	0.462973i
$797$		−	1.28256e26i		−	0.0350124i	−0.999847	−	0.0175062i	$-0.994427\pi$
$797$		−	1.28256e26i		−	0.0350124i	0.999847	−	0.0175062i	$-0.00557269\pi$
$798$	−8.89373e25	+	4.80707e26i	−0.0239915	+	0.129674i
$799$		−	8.29362e26i		−	0.221080i
$800$	3.03291e27	+	5.35359e27i	0.798923	+	1.41023i
$801$	−1.73514e27	+	2.69479e27i	−0.451673	+	0.701481i
$802$	−1.17011e27	+	1.21053e26i	−0.301004	+	0.0311401i
$803$	4.20830e27			1.06981
$804$	−2.27563e26	+	2.84356e27i	−0.0571701	+	0.714380i
$805$	1.59895e28			3.96985
$806$	−1.41590e26	+	1.46481e25i	−0.0347417	+	0.00359417i
$807$	6.84781e26	−	2.32842e27i	0.166055	−	0.564629i
$808$	4.14479e26	−	1.32432e26i	0.0993334	−	0.0317384i
$809$		−	2.60012e26i		−	0.0615860i	−0.999526	−	0.0307930i	$-0.990197\pi$
$809$		−	2.60012e26i		−	0.0615860i	0.999526	−	0.0307930i	$-0.00980326\pi$
$810$	−3.49457e27	−	5.96763e27i	−0.818061	−	1.39699i
$811$		−	4.06333e27i		−	0.940121i	−0.882634	−	0.470061i	$-0.844232\pi$
$811$		−	4.06333e27i		−	0.940121i	0.882634	−	0.470061i	$-0.155768\pi$
$812$	4.20182e27	−	8.78796e26i	0.960849	−	0.200958i
$813$	−1.87482e27	+	6.37484e27i	−0.423740	+	1.44082i
$814$	3.57875e26	+	3.45926e27i	0.0799466	+	0.772773i
$815$	−1.12254e28			−2.47860
$816$	−1.56846e26	−	1.23507e27i	−0.0342308	−	0.269548i
$817$	−2.49037e25			−0.00537223
$818$	1.23760e26	+	1.19627e27i	0.0263890	+	0.255079i
$819$	−2.17281e27	+	3.37453e27i	−0.457957	+	0.711240i
$820$	−6.99798e27	+	1.46360e27i	−1.45795	+	0.304924i
$821$		−	4.49856e27i		−	0.926433i	−0.886245	−	0.463216i	$-0.846695\pi$
$821$		−	4.49856e27i		−	0.926433i	0.886245	−	0.463216i	$-0.153305\pi$
$822$	−4.06419e27	−	7.51931e26i	−0.827355	−	0.153072i
$823$			2.43580e27i			0.490166i	0.969502	+	0.245083i	$0.0788152\pi$
$823$			2.43580e27i			0.490166i	−0.969502	+	0.245083i	$0.921185\pi$
$824$	−1.76336e27	+	5.63418e26i	−0.350778	+	0.112079i
$825$	−9.65284e27	−	2.83887e27i	−1.89820	−	0.558255i
$826$	2.81036e27	−	2.90744e26i	0.546326	−	0.0565197i
$827$	−2.83732e26			−0.0545264			−0.0272632	−	0.999628i	$-0.508679\pi$
$827$	−2.83732e26			−0.0545264			−0.0272632	+	0.999628i	$0.508679\pi$
$828$	8.21468e27	+	3.14739e27i	1.56064	+	0.597947i
$829$	−1.73789e25			−0.00326403			−0.00163201	−	0.999999i	$-0.500519\pi$
$829$	−1.73789e25			−0.00326403			−0.00163201	+	0.999999i	$0.500519\pi$
$830$	−8.56856e27	+	8.86453e26i	−1.59098	+	0.164594i
$831$	−5.17026e27	−	1.52056e27i	−0.949079	−	0.279121i
$832$	2.58827e27	−	1.84203e27i	0.469719	−	0.334291i
$833$			1.74590e27i			0.313251i
$834$	−4.37218e27	−	8.08912e26i	−0.775568	−	0.143491i
$835$			8.97051e27i			1.57324i
$836$	1.29536e26	+	6.19353e26i	0.0224610	+	0.107394i
$837$	−2.67362e26	+	2.31063e26i	−0.0458360	+	0.0396130i
$838$	−4.99744e26	−	4.83059e27i	−0.0847090	−	0.818807i
$839$	−4.48033e27			−0.750881			−0.375441	−	0.926846i	$-0.622509\pi$
$839$	−4.48033e27			−0.750881			−0.375441	+	0.926846i	$0.622509\pi$
$840$	−3.32959e26	−	1.43306e28i	−0.0551744	−	2.37471i
$841$	3.37148e27			0.552407
$842$	9.07275e26	+	8.76983e27i	0.146985	+	1.42078i
$843$	6.12049e26	−	2.08111e27i	0.0980447	−	0.333376i
$844$	−1.13079e26	−	5.40667e26i	−0.0179113	−	0.0856400i
$845$			6.90052e27i			1.08079i
$846$	2.37450e27	−	4.68639e27i	0.367751	−	0.725806i
$847$		−	4.69660e27i		−	0.719269i
$848$	1.05924e27	+	2.42151e27i	0.160410	+	0.366713i
$849$	1.86976e27	−	6.35762e27i	0.280002	−	0.952075i
$850$	2.95808e27	−	3.06026e26i	0.438057	−	0.0453188i
$851$	7.26302e27			1.06362
$852$	1.09325e28	+	8.74904e26i	1.58323	+	0.126702i
$853$	−7.61698e27			−1.09085			−0.545427	−	0.838158i	$-0.683633\pi$
$853$	−7.61698e27			−1.09085			−0.545427	+	0.838158i	$0.683633\pi$
$854$	−1.60806e28	+	1.66361e27i	−2.27747	+	0.235614i
$855$	−8.73440e26	−	5.62395e26i	−0.122336	−	0.0787704i
$856$	5.18772e26	+	1.62363e27i	0.0718580	+	0.224898i
$857$		−	6.75871e27i		−	0.925862i	−0.886394	−	0.462931i	$-0.846798\pi$
$857$		−	6.75871e27i		−	0.925862i	0.886394	−	0.462931i	$-0.153202\pi$
$858$	−9.45082e26	+	5.10818e27i	−0.128038	+	0.692049i
$859$			3.46563e27i			0.464352i	0.972674	+	0.232176i	$0.0745846\pi$
$859$			3.46563e27i			0.464352i	−0.972674	+	0.232176i	$0.925415\pi$
$860$	7.14758e26	−	1.49489e26i	0.0947161	−	0.0198096i
$861$	9.88203e27	+	2.90627e27i	1.29514	+	0.380896i
$862$	−8.43136e26	−	8.14985e27i	−0.109289	−	1.05641i
$863$	8.58333e27			1.10041			0.550203	−	0.835031i	$-0.314550\pi$
$863$	8.58333e27			1.10041			0.550203	+	0.835031i	$0.314550\pi$
$864$	2.64979e27	−	7.42795e27i	0.335993	−	0.941864i
$865$	−5.02717e27			−0.630479
$866$	−7.98765e26	−	7.72095e27i	−0.0990829	−	0.957747i
$867$	7.24202e27	+	2.12986e27i	0.888543	+	0.261318i
$868$	−7.16954e26	+	1.49949e26i	−0.0870070	+	0.0181972i
$869$		−	1.83610e28i		−	2.20398i
$870$	−1.65954e27	+	8.96983e27i	−0.197040	+	1.06500i
$871$			3.51811e27i			0.413178i
$872$	3.27022e27	+	1.02350e28i	0.379901	+	1.18899i
$873$	7.77014e27	+	5.00308e27i	0.892881	+	0.574913i
$874$	1.31445e27	−	1.35986e26i	0.149412	−	0.0154573i
$875$	1.31149e28			1.47464
$876$	−7.85394e27	−	6.28532e26i	−0.873572	−	0.0699099i
$877$	−5.01769e27			−0.552088			−0.276044	−	0.961145i	$-0.589023\pi$
$877$	−5.01769e27			−0.552088			−0.276044	+	0.961145i	$0.589023\pi$
$878$	1.43519e28	−	1.48476e27i	1.56211	−	0.161607i
$879$	−3.59726e27	+	1.22316e28i	−0.387327	+	1.31701i
$880$	−7.43558e27	−	1.69984e28i	−0.792007	−	1.81060i
$881$			1.82183e28i			1.91972i	0.280482	+	0.959859i	$0.409506\pi$
$881$			1.82183e28i			1.91972i	−0.280482	+	0.959859i	$0.590494\pi$
$882$	−4.99860e27	+	9.86541e27i	−0.521071	+	1.02840i
$883$			1.19707e28i			1.23451i	0.786764	+	0.617254i	$0.211755\pi$
$883$			1.19707e28i			1.23451i	−0.786764	+	0.617254i	$0.788245\pi$
$884$	−3.14327e26	−	1.50290e27i	−0.0320690	−	0.153333i
$885$	−1.69399e27	+	5.75996e27i	−0.170981	+	0.581378i
$886$	8.92515e26	+	8.62715e27i	0.0891241	+	0.861484i
$887$	−1.31720e28			−1.30130			−0.650652	−	0.759376i	$-0.725504\pi$
$887$	−1.31720e28			−1.30130			−0.650652	+	0.759376i	$0.725504\pi$
$888$	−1.51242e26	−	6.50948e27i	−0.0147826	−	0.636243i
$889$	−1.96105e28			−1.89637
$890$	−1.45275e27	−	1.40424e28i	−0.138991	−	1.34350i
$891$	5.33695e27	+	1.17401e28i	0.505191	+	1.11130i
$892$	1.24198e27	+	5.93833e27i	0.116319	+	0.556158i
$893$		−	7.89189e26i		−	0.0731294i
$894$	−3.00155e27	−	5.55328e26i	−0.275194	−	0.0509147i
$895$		−	1.07141e28i		−	0.971932i
$896$	1.22723e28	−	1.07987e28i	1.10154	−	0.969271i
$897$	1.04084e28	+	3.06107e27i	0.924388	+	0.271860i
$898$	6.47301e27	−	6.69659e26i	0.568828	−	0.0588476i
$899$	4.66122e26			0.0405306
$900$	1.75911e28	+	6.73989e27i	1.51352	+	0.579894i
$901$	1.27744e27			0.108756
$902$	1.32615e28	−	1.37196e27i	1.11720	−	0.115579i
$903$	−1.00933e27	−	2.96840e26i	−0.0841393	−	0.0247451i
$904$	−2.82012e27	+	9.01070e26i	−0.232631	+	0.0743290i
$905$			7.90267e27i			0.645078i
$906$	−3.82848e27	−	7.08320e26i	−0.309249	−	0.0572152i
$907$		−	1.98734e28i		−	1.58856i	−0.607552	−	0.794280i	$-0.707849\pi$
$907$		−	1.98734e28i		−	1.58856i	0.607552	−	0.794280i	$-0.292151\pi$
$908$	4.03538e27	−	8.43987e26i	0.319205	−	0.0667606i
$909$	7.21197e26	−	1.12007e27i	0.0564543	−	0.0876776i
$910$	−1.81919e27	−	1.75845e28i	−0.140924	−	1.36219i
$911$	−1.26647e28			−0.970890			−0.485445	−	0.874267i	$-0.661342\pi$
$911$	−1.26647e28			−0.970890			−0.485445	+	0.874267i	$0.661342\pi$
$912$	−1.49249e26	−	1.17525e27i	−0.0113229	−	0.0891616i
$913$	1.60641e28			1.20610
$914$	−3.50605e26	−	3.38899e27i	−0.0260513	−	0.251815i
$915$	9.69283e27	−	3.29580e28i	0.712771	−	2.42359i
$916$	−2.47957e28	+	5.18595e27i	−1.80456	+	0.377417i
$917$		−	1.60344e28i		−	1.15490i
$918$	−2.77590e27	−	2.61212e27i	−0.197879	−	0.186203i
$919$			2.58517e28i			1.82386i	0.410348	+	0.911929i	$0.365407\pi$
$919$			2.58517e28i			1.82386i	−0.410348	+	0.911929i	$0.634593\pi$
$920$	−3.69096e28	+	1.17932e28i	−2.57724	+	0.823466i
$921$	4.33091e27	−	1.47261e28i	0.299304	−	1.01771i
$922$	1.58765e28	−	1.64249e27i	1.08595	−	0.112346i
$923$	1.35260e28			0.915698
$924$	−2.13241e27	+	2.66459e28i	−0.142885	+	1.78545i
$925$	1.55532e28			1.03151
$926$	−1.15639e27	+	1.19634e26i	−0.0759103	+	0.00785324i
$927$	−3.06826e27	+	4.76522e27i	−0.199358	+	0.309618i
$928$	−9.05119e27	+	5.12767e27i	−0.582103	+	0.329772i
$929$			2.14849e28i			1.36768i	0.729632	+	0.683840i	$0.239692\pi$
$929$			2.14849e28i			1.36768i	−0.729632	+	0.683840i	$0.760308\pi$
$930$	2.83167e26	−	1.53052e27i	0.0178424	−	0.0964385i
$931$			1.66134e27i			0.103618i
$932$	−5.67002e27	−	2.71103e28i	−0.350053	−	1.67372i
$933$	−1.32676e28	−	3.90195e27i	−0.810805	−	0.238455i
$934$	1.88836e27	+	1.82531e28i	0.114232	+	1.10418i
$935$	−8.96729e27			−0.536971
$936$	2.52674e27	−	9.39224e27i	0.149775	−	0.556735i
$937$	−8.68497e27			−0.509615			−0.254808	−	0.966992i	$-0.582012\pi$
$937$	−8.68497e27			−0.509615			−0.254808	+	0.966992i	$0.582012\pi$
$938$	1.86290e27	+	1.80070e28i	0.108209	+	1.04596i
$939$	−2.60972e28	−	7.67510e27i	−1.50062	−	0.441328i
$940$	4.73726e27	+	2.26504e28i	0.269658	+	1.28932i
$941$			1.26775e28i			0.714385i	0.934031	+	0.357192i	$0.116266\pi$
$941$			1.26775e28i			0.714385i	−0.934031	+	0.357192i	$0.883734\pi$
$942$	2.02600e27	−	1.09506e28i	0.113020	−	0.610875i
$943$		−	2.78437e28i		−	1.53768i
$944$	−6.27292e27	+	2.74395e27i	−0.342954	+	0.150017i
$945$	−2.86964e28	−	3.32044e28i	−1.55319	−	1.79719i
$946$	−1.35450e27	+	1.40129e26i	−0.0725796	+	0.00750866i
$947$	−7.42814e27			−0.394054			−0.197027	−	0.980398i	$-0.563129\pi$
$947$	−7.42814e27			−0.394054			−0.197027	+	0.980398i	$0.563129\pi$
$948$	−2.74231e27	+	3.42671e28i	−0.144025	+	1.79969i
$949$	−9.71708e27			−0.505250
$950$	2.81480e27	−	2.91202e26i	0.144901	−	0.0149907i
$951$	−4.01305e27	+	1.36453e28i	−0.204531	+	0.695455i
$952$	−2.40465e27	−	7.52596e27i	−0.121339	−	0.379761i
$953$		−	5.94189e27i		−	0.296853i	−0.988923	−	0.148427i	$-0.952579\pi$
$953$		−	5.94189e27i		−	0.296853i	0.988923	−	0.148427i	$-0.0474209\pi$
$954$	7.21829e27	+	3.65736e27i	0.357047	+	0.180908i
$955$		−	3.42460e28i		−	1.67717i
$956$	1.48671e28	−	3.10941e27i	0.720904	−	0.150775i
$957$	4.79961e27	−	1.63198e28i	0.230432	−	0.783523i
$958$	1.44504e27	+	1.39679e28i	0.0686921	+	0.663986i
$959$	−2.62293e28			−1.23455
$960$	1.13382e28	+	3.28347e28i	0.528406	+	1.53023i
$961$	2.15911e28			0.996330
$962$	−8.26344e26	−	7.98754e27i	−0.0377570	−	0.364964i
$963$	4.38761e27	+	2.82512e27i	0.198508	+	0.127817i
$964$	3.56794e27	−	7.46223e26i	0.159840	−	0.0334300i
$965$			4.25497e28i			1.88750i
$966$	5.48946e28	+	1.01563e28i	2.41128	+	0.446119i
$967$			2.07669e28i			0.903275i	0.892202	+	0.451637i	$0.149160\pi$
$967$			2.07669e28i			0.903275i	−0.892202	+	0.451637i	$0.850840\pi$
$968$	3.46401e27	+	1.08415e28i	0.149198	+	0.466953i
$969$	−5.49318e26	−	1.61553e26i	−0.0234287	−	0.00689030i
$970$	−4.04899e28	+	4.18884e27i	−1.71007	+	0.176914i
$971$	1.26288e28			0.528177			0.264088	−	0.964499i	$-0.414929\pi$
$971$	1.26288e28			0.528177			0.264088	+	0.964499i	$0.414929\pi$
$972$	−8.20691e27	−	2.27076e28i	−0.339899	−	0.940462i
$973$	−2.82170e28			−1.15728
$974$	1.45455e28	−	1.50480e27i	0.590772	−	0.0611178i
$975$	2.22887e28	+	6.55503e27i	0.896480	+	0.263652i
$976$	3.58930e28	−	1.57006e28i	1.42967	−	0.625379i
$977$		−	1.57941e28i		−	0.623012i	−0.950244	−	0.311506i	$-0.899167\pi$
$977$		−	1.57941e28i		−	0.623012i	0.950244	−	0.311506i	$-0.100833\pi$
$978$	−3.85389e28	−	7.13021e27i	−1.50550	−	0.278537i
$979$			2.63263e28i			1.01849i
$980$	−9.97249e27	−	4.76818e28i	−0.382081	−	1.82686i
$981$	2.76585e28	+	1.78089e28i	1.04948	+	0.675743i
$982$	1.76083e27	+	1.70204e28i	0.0661696	+	0.639603i
$983$	1.82221e28			0.678172			0.339086	−	0.940755i	$-0.389882\pi$
$983$	1.82221e28			0.678172			0.339086	+	0.940755i	$0.389882\pi$
$984$	−2.49549e28	+	5.79806e26i	−0.919820	+	0.0213712i
$985$	6.83364e28			2.49464
$986$	5.17390e26	+	5.00116e27i	0.0187063	+	0.180817i
$987$	9.40675e27	−	3.19852e28i	0.336843	−	1.14535i
$988$	−2.99102e26	−	1.43011e27i	−0.0106079	−	0.0507197i
$989$			2.84389e27i			0.0998961i
$990$	−5.06706e28	−	2.56738e28i	−1.76287	−	0.893213i
$991$		−	3.62781e28i		−	1.25010i	−0.780585	−	0.625049i	$-0.785079\pi$
$991$		−	3.62781e28i		−	1.25010i	0.780585	−	0.625049i	$-0.214921\pi$
$992$	1.54440e27	−	8.74932e26i	0.0527107	−	0.0298616i
$993$	2.95580e27	−	1.00504e28i	0.0999210	−	0.339755i
$994$	6.92308e28	−	7.16221e27i	2.31808	−	0.239815i
$995$	2.30882e28			0.765720
$996$	−2.99804e28	−	2.39926e27i	−0.984857	−	0.0788158i
$997$	−1.05444e28			−0.343097			−0.171549	−	0.985176i	$-0.554877\pi$
$997$	−1.05444e28			−0.343097			−0.171549	+	0.985176i	$0.554877\pi$
$998$	4.90160e28	−	5.07091e27i	1.57978	−	0.163435i
$999$	−1.30349e28	−	1.50827e28i	−0.416138	−	0.481511i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	12.20.b.a.11.17	✓	36
3.2	odd	2	inner	12.20.b.a.11.20	yes	36
4.3	odd	2	inner	12.20.b.a.11.19	yes	36
12.11	even	2	inner	12.20.b.a.11.18	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
12.20.b.a.11.17	✓	36	1.1	even	1	trivial
12.20.b.a.11.18	yes	36	12.11	even	2	inner
12.20.b.a.11.19	yes	36	4.3	odd	2	inner
12.20.b.a.11.20	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)

\(f(q)\)	\(=\)	\(q+(-74.5111 - 720.233i) q^{2} +(32706.8 + 9618.97i) q^{3} +(-513184. + 107331. i) q^{4} -7.07022e6i q^{5} +(4.49088e6 - 2.42733e7i) q^{6} -1.56654e8i q^{7} +(1.15541e8 + 3.61615e8i) q^{8} +(9.77212e8 + 6.29212e8i) q^{9} +O(q^{10})\)	\(q+(-74.5111 - 720.233i) q^{2} +(32706.8 + 9618.97i) q^{3} +(-513184. + 107331. i) q^{4} -7.07022e6i q^{5} +(4.49088e6 - 2.42733e7i) q^{6} -1.56654e8i q^{7} +(1.15541e8 + 3.61615e8i) q^{8} +(9.77212e8 + 6.29212e8i) q^{9} +(-5.09221e9 + 5.26810e8i) q^{10} +9.54672e9 q^{11} +(-1.78170e10 - 1.42586e9i) q^{12} -2.20437e10 q^{13} +(-1.12827e11 + 1.16725e10i) q^{14} +(6.80083e10 - 2.31244e11i) q^{15} +(2.51838e11 - 1.10161e11i) q^{16} -1.32854e11i q^{17} +(3.80367e11 - 7.50704e11i) q^{18} -1.26419e11i q^{19} +(7.58852e11 + 3.62833e12i) q^{20} +(1.50685e12 - 5.12365e12i) q^{21} +(-7.11337e11 - 6.87586e12i) q^{22} -1.44365e13 q^{23} +(3.00619e11 + 1.29387e13i) q^{24} -3.09145e13 q^{25} +(1.64250e12 + 1.58766e13i) q^{26} +(2.59091e13 + 2.99793e13i) q^{27} +(1.68138e13 + 8.03923e13i) q^{28} -5.22664e13i q^{29} +(-1.71617e14 - 3.17515e13i) q^{30} +8.91820e12i q^{31} +(-9.81063e13 - 1.73174e14i) q^{32} +(3.12243e14 + 9.18296e13i) q^{33} +(-9.56858e13 + 9.89909e12i) q^{34} -1.10758e15 q^{35} +(-5.69024e14 - 2.18017e14i) q^{36} -5.03102e14 q^{37} +(-9.10509e13 + 9.41960e12i) q^{38} +(-7.20978e14 - 2.12037e14i) q^{39} +(2.55670e15 - 8.16901e14i) q^{40} +1.92871e15i q^{41} +(-3.80250e15 - 7.03514e14i) q^{42} -1.96994e14i q^{43} +(-4.89922e15 + 1.02466e15i) q^{44} +(4.44867e15 - 6.90910e15i) q^{45} +(1.07568e15 + 1.03976e16i) q^{46} +6.24266e15 q^{47} +(9.29646e15 - 1.18059e15i) q^{48} -1.31415e16 q^{49} +(2.30348e15 + 2.22657e16i) q^{50} +(1.27792e15 - 4.34523e15i) q^{51} +(1.13125e16 - 2.36596e15i) q^{52} +9.61536e15i q^{53} +(1.96616e16 - 2.08944e16i) q^{54} -6.74974e16i q^{55} +(5.66484e16 - 1.81000e16i) q^{56} +(1.21602e15 - 4.13475e15i) q^{57} +(-3.76440e16 + 3.89443e15i) q^{58} -2.49085e16 q^{59} +(-1.00811e16 + 1.25970e17i) q^{60} +1.42524e17 q^{61} +(6.42318e15 - 6.64505e14i) q^{62} +(9.85685e16 - 1.53084e17i) q^{63} +(-1.17416e17 + 8.35628e16i) q^{64} +1.55853e17i q^{65} +(4.28732e16 - 2.31730e17i) q^{66} -1.59598e17i q^{67} +(1.42593e16 + 6.81785e16i) q^{68} +(-4.72171e17 - 1.38864e17i) q^{69} +(8.25268e16 + 7.97714e17i) q^{70} -6.13599e17 q^{71} +(-1.14624e17 + 4.26075e17i) q^{72} +4.40811e17 q^{73} +(3.74867e16 + 3.62351e17i) q^{74} +(-1.01112e18 - 2.97366e17i) q^{75} +(1.35686e16 + 6.48761e16i) q^{76} -1.49553e18i q^{77} +(-9.89955e16 + 5.35072e17i) q^{78} -1.92328e18i q^{79} +(-7.78862e17 - 1.78055e18i) q^{80} +(5.59035e17 + 1.22975e18i) q^{81} +(1.38912e18 - 1.43710e17i) q^{82} +1.68268e18 q^{83} +(-2.23366e17 + 2.79111e18i) q^{84} -9.39306e17 q^{85} +(-1.41882e17 + 1.46782e16i) q^{86} +(5.02749e17 - 1.70947e18i) q^{87} +(1.10304e18 + 3.45224e18i) q^{88} +2.75763e18i q^{89} +(-5.30764e18 - 2.68928e18i) q^{90} +3.45322e18i q^{91} +(7.40856e18 - 1.54948e18i) q^{92} +(-8.57839e16 + 2.91686e17i) q^{93} +(-4.65148e17 - 4.49617e18i) q^{94} -8.93808e17 q^{95} +(-1.54299e18 - 6.60765e18i) q^{96} +7.95134e18 q^{97} +(9.79191e17 + 9.46497e18i) q^{98} +(9.32917e18 + 6.00691e18i) 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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