LMFDB - Embedded newform 8.20.b.a.5.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8,20,Mod(5,8)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 20, names="a")

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

chi := DirichletCharacter("8.5");

S:= CuspForms(chi, 20);

N := Newforms(S);

Level:	$ N $	$=$	$ 8 = 2^{3} $
Weight:	$ k $	$=$	$ 20 $
Character orbit:	$[\chi]$	$=$	8.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:	$18.3053357245$
Analytic rank:	$0$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 9 x^{17} + 847482358 x^{16} - 6779858660 x^{15} + \cdots + 11\!\cdots\!76 $ x^18 - 9x^17 + 847482358x^16 - 6779858660x^15 + 288755694526787238x^14 - 2021289743039984830x^13 + 51121850635988052944521232x^12 - 306731077539161966630890980x^11 + 5053028465804290954773516593713297x^10 - 25265139517319958838954290038554593x^9 + 277525242785226225995541366728053703523138x^8 - 1110100819550071174104182779845774739997744x^7 + 7843581170028346695466748185748667347430921666496x^6 - 23530739624732277774733733894667178736900394654048x^5 + 88699644118206331836031766951870758907094189945148981184x^4 - 177399249018514584235839520819873862547126510378177038080x^3 + 27738447216461514660719783835924541644179956872586393406592768x^2 - 27738358516840927193180104500114450400133860395870028292288768*x + 1155804113673024778339834102840085457131269774629483366903990104576
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	multiple of $ 2^{153}\cdot 3^{16}\cdot 5^{4}\cdot 7 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			5.6
Root			$0.500000 + 12463.1i$ of defining polynomial
Character	$\chi$	$=$	8.5
Dual form			8.20.b.a.5.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-540.302 + 482.039i) q^{2} -49852.5i q^{3} +(59564.6 - 520893. i) q^{4} +3.24834e6i q^{5} +(2.40309e7 + 2.69354e7i) q^{6} +1.08353e8 q^{7} +(2.18908e8 + 3.10152e8i) q^{8} -1.32301e9 q^{9} +O(q^{10})$	\(q+(-540.302 + 482.039i) q^{2} -49852.5i q^{3} +(59564.6 - 520893. i) q^{4} +3.24834e6i q^{5} +(2.40309e7 + 2.69354e7i) q^{6} +1.08353e8 q^{7} +(2.18908e8 + 3.10152e8i) q^{8} -1.32301e9 q^{9} +(-1.56583e9 - 1.75508e9i) q^{10} +6.67212e9i q^{11} +(-2.59678e10 - 2.96945e9i) q^{12} -4.23789e10i q^{13} +(-5.85433e10 + 5.22303e10i) q^{14} +1.61938e11 q^{15} +(-2.67782e11 - 6.20536e10i) q^{16} +9.60587e11 q^{17} +(7.14826e11 - 6.37743e11i) q^{18} -1.90113e11i q^{19} +(1.69204e12 + 1.93486e11i) q^{20} -5.40167e12i q^{21} +(-3.21622e12 - 3.60496e12i) q^{22} -7.67154e12 q^{23} +(1.54619e13 - 1.09131e13i) q^{24} +8.52179e12 q^{25} +(2.04283e13 + 2.28974e13i) q^{26} +8.01381e12i q^{27} +(6.45400e12 - 5.64403e13i) q^{28} -1.13055e14i q^{29} +(-8.74953e13 + 7.80603e13i) q^{30} -3.94702e13 q^{31} +(1.74595e14 - 9.55537e13i) q^{32} +3.32622e14 q^{33} +(-5.19007e14 + 4.63040e14i) q^{34} +3.51967e14i q^{35} +(-7.88047e13 + 6.89148e14i) q^{36} -6.09095e14i q^{37} +(9.16421e13 + 1.02719e14i) q^{38} -2.11270e15 q^{39} +(-1.00748e15 + 7.11087e14i) q^{40} -1.93765e15 q^{41} +(2.60381e15 + 2.91853e15i) q^{42} -4.35407e15i q^{43} +(3.47547e15 + 3.97422e14i) q^{44} -4.29759e15i q^{45} +(4.14495e15 - 3.69798e15i) q^{46} +1.43084e16 q^{47} +(-3.09353e15 + 1.33496e16i) q^{48} +3.41459e14 q^{49} +(-4.60434e15 + 4.10784e15i) q^{50} -4.78877e16i q^{51} +(-2.20749e16 - 2.52429e15i) q^{52} +3.20081e15i q^{53} +(-3.86297e15 - 4.32988e15i) q^{54} -2.16733e16 q^{55} +(2.37193e16 + 3.36059e16i) q^{56} -9.47763e15 q^{57} +(5.44971e16 + 6.10840e16i) q^{58} +8.85551e16i q^{59} +(9.64576e15 - 8.43523e16i) q^{60} -4.76424e16i q^{61} +(2.13258e16 - 1.90262e16i) q^{62} -1.43352e17 q^{63} +(-4.82737e16 + 1.35790e17i) q^{64} +1.37661e17 q^{65} +(-1.79716e17 + 1.60337e17i) q^{66} +1.35781e17i q^{67} +(5.72170e16 - 5.00363e17i) q^{68} +3.82446e17i q^{69} +(-1.69662e17 - 1.90168e17i) q^{70} -1.68191e17 q^{71} +(-2.89618e17 - 4.10335e17i) q^{72} +7.51049e17 q^{73} +(2.93607e17 + 3.29095e17i) q^{74} -4.24833e17i q^{75} +(-9.90289e16 - 1.13240e16i) q^{76} +7.22944e17i q^{77} +(1.14149e18 - 1.01840e18i) q^{78} +7.44514e17 q^{79} +(2.01571e17 - 8.69846e17i) q^{80} -1.13818e18 q^{81} +(1.04692e18 - 9.34023e17i) q^{82} -1.14882e18i q^{83} +(-2.81369e18 - 3.21748e17i) q^{84} +3.12031e18i q^{85} +(2.09883e18 + 2.35251e18i) q^{86} -5.63609e18 q^{87} +(-2.06937e18 + 1.46058e18i) q^{88} +4.58017e18 q^{89} +(2.07161e18 + 2.32200e18i) q^{90} -4.59188e18i q^{91} +(-4.56952e17 + 3.99606e18i) q^{92} +1.96769e18i q^{93} +(-7.73087e18 + 6.89722e18i) q^{94} +6.17553e17 q^{95} +(-4.76359e18 - 8.70402e18i) q^{96} +5.33795e18 q^{97} +(-1.84491e17 + 1.64597e17i) q^{98} -8.82730e18i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 458 q^{2} - 412108 q^{4} - 47240948 q^{6} - 80707216 q^{7} - 173313752 q^{8} - 6198727826 q^{9}+O(q^{10}) $ 18 * q - 458 * q^2 - 412108 * q^4 - 47240948 * q^6 - 80707216 * q^7 - 173313752 * q^8 - 6198727826 * q^9	$ 18 q - 458 q^{2} - 412108 q^{4} - 47240948 q^{6} - 80707216 q^{7} - 173313752 q^{8} - 6198727826 q^{9} + 758800104 q^{10} - 9351642296 q^{12} - 122453668784 q^{14} + 156097960432 q^{15} - 696212072432 q^{16} + 14121426692 q^{17} + 1813497117770 q^{18} + 6517087595632 q^{20} - 11074654117412 q^{22} + 2177121583952 q^{23} - 36473014189168 q^{24} - 44414474211734 q^{25} + 26782030269304 q^{26} - 97002327802784 q^{28} + 327847200544208 q^{30} + 428505770260416 q^{31} + 122449430282912 q^{32} - 185380269683736 q^{33} - 478448330325748 q^{34} - 10\!\cdots\!36 q^{36}+ \cdots + 88\!\cdots\!22 q^{98}+O(q^{100}) $ 18 * q - 458 * q^2 - 412108 * q^4 - 47240948 * q^6 - 80707216 * q^7 - 173313752 * q^8 - 6198727826 * q^9 + 758800104 * q^10 - 9351642296 * q^12 - 122453668784 * q^14 + 156097960432 * q^15 - 696212072432 * q^16 + 14121426692 * q^17 + 1813497117770 * q^18 + 6517087595632 * q^20 - 11074654117412 * q^22 + 2177121583952 * q^23 - 36473014189168 * q^24 - 44414474211734 * q^25 + 26782030269304 * q^26 - 97002327802784 * q^28 + 327847200544208 * q^30 + 428505770260416 * q^31 + 122449430282912 * q^32 - 185380269683736 * q^33 - 478448330325748 * q^34 - 1053851053424436 * q^36 - 486194587539796 * q^38 + 942830575043152 * q^39 - 1697818250610976 * q^40 + 1200260021141524 * q^41 + 4964410757677984 * q^42 + 7031781193616424 * q^44 - 14917443628457488 * q^46 - 1134160959992928 * q^47 - 3197964747991392 * q^48 + 31570092936329058 * q^49 - 34734151321861826 * q^50 - 26877456911772208 * q^52 + 32102189624395064 * q^54 - 51757047863478736 * q^55 + 52858270161183424 * q^56 - 7740744140670520 * q^57 - 20470056808312424 * q^58 - 25825294995349152 * q^60 + 93766686763697984 * q^62 + 430168668665078416 * q^63 - 253721318369185216 * q^64 - 184007586011668640 * q^65 + 479551889901302712 * q^66 + 201388986348307752 * q^68 - 340698473416023872 * q^70 - 1599477989199799056 * q^71 - 115475454880420648 * q^72 - 93004298989809068 * q^73 - 93558253821761240 * q^74 - 1090379619519933176 * q^76 + 2029949680340770544 * q^78 + 1813975801025264480 * q^79 + 3057120301750869696 * q^80 + 1801762045144484330 * q^81 - 2418785089528546244 * q^82 + 141493317659087296 * q^84 + 1332333723895598620 * q^86 - 13124960835754102512 * q^87 - 3097741184498130608 * q^88 + 4470509771045743540 * q^89 - 288100905697646824 * q^90 - 2965990502259463392 * q^92 - 3533635112749329696 * q^94 + 23809730986995679856 * q^95 - 2990158800543707584 * q^96 + 8246429789464117220 * q^97 + 8841667592735478822 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/8\mathbb{Z}\right)^\times$.

$n$	$5$	$7$
$\chi(n)$	$-1$	$1$

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 $

$2$	−540.302	+	482.039i	−0.746194	+	0.665729i
$2$	−540.302	+	482.039i	−0.746194	+	0.665729i
$3$		−	49852.5i		−	1.46230i	−0.682219	−	0.731148i	$-0.738985\pi$
$3$		−	49852.5i		−	1.46230i	0.682219	−	0.731148i	$-0.261015\pi$
$4$	59564.6	−	520893.i	0.113610	−	0.993525i
$5$			3.24834e6i			0.743783i	0.928276	+	0.371891i	$0.121291\pi$
$5$			3.24834e6i			0.743783i	−0.928276	+	0.371891i	$0.878709\pi$
$6$	2.40309e7	+	2.69354e7i	0.973492	+	1.09116i
$7$	1.08353e8			1.01487			0.507434	−	0.861691i	$-0.330594\pi$
$7$	1.08353e8			1.01487			0.507434	+	0.861691i	$0.330594\pi$
$8$	2.18908e8	+	3.10152e8i	0.576643	+	0.816996i
$9$	−1.32301e9			−1.13831
$10$	−1.56583e9	−	1.75508e9i	−0.495157	−	0.555006i
$11$			6.67212e9i			0.853166i	0.904448	+	0.426583i	$0.140283\pi$
$11$			6.67212e9i			0.853166i	−0.904448	+	0.426583i	$0.859717\pi$
$12$	−2.59678e10	−	2.96945e9i	−1.45283	−	0.166132i
$13$		−	4.23789e10i		−	1.10838i	−0.832391	−	0.554189i	$-0.813028\pi$
$13$		−	4.23789e10i		−	1.10838i	0.832391	−	0.554189i	$-0.186972\pi$
$14$	−5.85433e10	+	5.22303e10i	−0.757288	+	0.675626i
$15$	1.61938e11			1.08763
$16$	−2.67782e11	−	6.20536e10i	−0.974185	−	0.225750i
$17$	9.60587e11			1.96459			0.982295	−	0.187341i	$-0.0599869\pi$
$17$	9.60587e11			1.96459			0.982295	+	0.187341i	$0.0599869\pi$
$18$	7.14826e11	−	6.37743e11i	0.849399	−	0.757804i
$19$		−	1.90113e11i		−	0.135162i	−0.997714	−	0.0675809i	$-0.978472\pi$
$19$		−	1.90113e11i		−	0.135162i	0.997714	−	0.0675809i	$-0.0215281\pi$
$20$	1.69204e12	+	1.93486e11i	0.738967	+	0.0845015i
$21$		−	5.40167e12i		−	1.48404i
$22$	−3.21622e12	−	3.60496e12i	−0.567977	−	0.636627i
$23$	−7.67154e12			−0.888113			−0.444056	−	0.895999i	$-0.646461\pi$
$23$	−7.67154e12			−0.888113			−0.444056	+	0.895999i	$0.646461\pi$
$24$	1.54619e13	−	1.09131e13i	1.19469	−	0.843222i
$25$	8.52179e12			0.446787
$26$	2.04283e13	+	2.28974e13i	0.737880	+	0.827065i
$27$			8.01381e12i			0.202247i
$28$	6.45400e12	−	5.64403e13i	0.115300	−	1.00830i
$29$		−	1.13055e14i		−	1.44714i	−0.690252	−	0.723569i	$-0.742501\pi$
$29$		−	1.13055e14i		−	1.44714i	0.690252	−	0.723569i	$-0.257499\pi$
$30$	−8.74953e13	+	7.80603e13i	−0.811583	+	0.724067i
$31$	−3.94702e13			−0.268123			−0.134061	−	0.990973i	$-0.542802\pi$
$31$	−3.94702e13			−0.268123			−0.134061	+	0.990973i	$0.542802\pi$
$32$	1.74595e14	−	9.55537e13i	0.877219	−	0.480090i
$33$	3.32622e14			1.24758
$34$	−5.19007e14	+	4.63040e14i	−1.46596	+	1.30788i
$35$			3.51967e14i			0.754841i
$36$	−7.88047e13	+	6.89148e14i	−0.129324	+	1.13094i
$37$		−	6.09095e14i		−	0.770492i	−0.922814	−	0.385246i	$-0.874117\pi$
$37$		−	6.09095e14i		−	0.770492i	0.922814	−	0.385246i	$-0.125883\pi$
$38$	9.16421e13	+	1.02719e14i	0.0899810	+	0.100857i
$39$	−2.11270e15			−1.62078
$40$	−1.00748e15	+	7.11087e14i	−0.607668	+	0.428897i
$41$	−1.93765e15			−0.924333			−0.462167	−	0.886793i	$-0.652928\pi$
$41$	−1.93765e15			−0.924333			−0.462167	+	0.886793i	$0.652928\pi$
$42$	2.60381e15	+	2.91853e15i	0.987965	+	1.10738i
$43$		−	4.35407e15i		−	1.32113i	−0.750770	−	0.660564i	$-0.770317\pi$
$43$		−	4.35407e15i		−	1.32113i	0.750770	−	0.660564i	$-0.229683\pi$
$44$	3.47547e15	+	3.97422e14i	0.847642	+	0.0969286i
$45$		−	4.29759e15i		−	0.846654i
$46$	4.14495e15	−	3.69798e15i	0.662704	−	0.591242i
$47$	1.43084e16			1.86493			0.932464	−	0.361263i	$-0.117654\pi$
$47$	1.43084e16			1.86493			0.932464	+	0.361263i	$0.117654\pi$
$48$	−3.09353e15	+	1.33496e16i	−0.330113	+	1.42455i
$49$	3.41459e14			0.0299554
$50$	−4.60434e15	+	4.10784e15i	−0.333390	+	0.297439i
$51$		−	4.78877e16i		−	2.87281i
$52$	−2.20749e16	−	2.52429e15i	−1.10120	−	0.125923i
$53$			3.20081e15i			0.133241i	0.997778	+	0.0666207i	$0.0212218\pi$
$53$			3.20081e15i			0.133241i	−0.997778	+	0.0666207i	$0.978778\pi$
$54$	−3.86297e15	−	4.32988e15i	−0.134642	−	0.150916i
$55$	−2.16733e16			−0.634570
$56$	2.37193e16	+	3.36059e16i	0.585216	+	0.829143i
$57$	−9.47763e15			−0.197646
$58$	5.44971e16	+	6.10840e16i	0.963401	+	1.07984i
$59$			8.85551e16i			1.33082i	0.746478	+	0.665411i	$0.231744\pi$
$59$			8.85551e16i			1.33082i	−0.746478	+	0.665411i	$0.768256\pi$
$60$	9.64576e15	−	8.43523e16i	0.123566	−	1.08059i
$61$		−	4.76424e16i		−	0.521627i	−0.965389	−	0.260814i	$-0.916009\pi$
$61$		−	4.76424e16i		−	0.521627i	0.965389	−	0.260814i	$-0.0839908\pi$
$62$	2.13258e16	−	1.90262e16i	0.200071	−	0.178497i
$63$	−1.43352e17			−1.15523
$64$	−4.82737e16	+	1.35790e17i	−0.334966	+	0.942230i
$65$	1.37661e17			0.824393
$66$	−1.79716e17	+	1.60337e17i	−0.930937	+	0.830550i
$67$			1.35781e17i			0.609717i	0.952398	+	0.304859i	$0.0986093\pi$
$67$			1.35781e17i			0.609717i	−0.952398	+	0.304859i	$0.901391\pi$
$68$	5.72170e16	−	5.00363e17i	0.223198	−	1.95187i
$69$			3.82446e17i			1.29868i
$70$	−1.69662e17	−	1.90168e17i	−0.502519	−	0.563257i
$71$	−1.68191e17			−0.435359			−0.217679	−	0.976020i	$-0.569849\pi$
$71$	−1.68191e17			−0.435359			−0.217679	+	0.976020i	$0.569849\pi$
$72$	−2.89618e17	−	4.10335e17i	−0.656397	−	0.929994i
$73$	7.51049e17			1.49314			0.746571	−	0.665306i	$-0.231699\pi$
$73$	7.51049e17			1.49314			0.746571	+	0.665306i	$0.231699\pi$
$74$	2.93607e17	+	3.29095e17i	0.512939	+	0.574937i
$75$		−	4.24833e17i		−	0.653335i
$76$	−9.90289e16	−	1.13240e16i	−0.134287	−	0.0153558i
$77$			7.22944e17i			0.865850i
$78$	1.14149e18	−	1.01840e18i	1.20941	−	1.07900i
$79$	7.44514e17			0.698901			0.349450	−	0.936955i	$-0.386368\pi$
$79$	7.44514e17			0.698901			0.349450	+	0.936955i	$0.386368\pi$
$80$	2.01571e17	−	8.69846e17i	0.167909	−	0.724582i
$81$	−1.13818e18			−0.842563
$82$	1.04692e18	−	9.34023e17i	0.689732	−	0.615355i
$83$		−	1.14882e18i		−	0.674542i	−0.941408	−	0.337271i	$-0.890496\pi$
$83$		−	1.14882e18i		−	0.674542i	0.941408	−	0.337271i	$-0.109504\pi$
$84$	−2.81369e18	−	3.21748e17i	−1.47443	−	0.168602i
$85$			3.12031e18i			1.46123i
$86$	2.09883e18	+	2.35251e18i	0.879513	+	0.985817i
$87$	−5.63609e18			−2.11614
$88$	−2.06937e18	+	1.46058e18i	−0.697033	+	0.491972i
$89$	4.58017e18			1.38572			0.692861	−	0.721071i	$-0.256350\pi$
$89$	4.58017e18			1.38572			0.692861	+	0.721071i	$0.256350\pi$
$90$	2.07161e18	+	2.32200e18i	0.563642	+	0.631768i
$91$		−	4.59188e18i		−	1.12486i
$92$	−4.56952e17	+	3.99606e18i	−0.100899	+	0.882363i
$93$			1.96769e18i			0.392075i
$94$	−7.73087e18	+	6.89722e18i	−1.39160	+	1.24154i
$95$	6.17553e17			0.100531
$96$	−4.76359e18	−	8.70402e18i	−0.702034	−	1.28275i
$97$	5.33795e18			0.712923			0.356462	−	0.934310i	$-0.383983\pi$
$97$	5.33795e18			0.712923			0.356462	+	0.934310i	$0.383983\pi$
$98$	−1.84491e17	+	1.64597e17i	−0.0223526	+	0.0199422i
$99$		−	8.82730e18i		−	0.971166i
$100$	5.07597e17	−	4.43895e18i	0.0507597	−	0.443895i
$101$		−	1.38239e19i		−	1.25770i	−0.777525	−	0.628852i	$-0.783525\pi$
$101$		−	1.38239e19i		−	1.25770i	0.777525	−	0.628852i	$-0.216475\pi$
$102$	2.30837e19	+	2.58738e19i	1.91251	+	2.14367i
$103$	−1.91639e19			−1.44721			−0.723604	−	0.690215i	$-0.757516\pi$
$103$	−1.91639e19			−1.44721			−0.723604	+	0.690215i	$0.757516\pi$
$104$	1.31439e19	−	9.27709e18i	0.905541	−	0.639139i
$105$	1.75464e19			1.10380
$106$	−1.54292e18	−	1.72941e18i	−0.0887027	−	0.0994240i
$107$		−	7.06297e18i		−	0.371399i	−0.982607	−	0.185700i	$-0.940545\pi$
$107$		−	7.06297e18i		−	0.371399i	0.982607	−	0.185700i	$-0.0594552\pi$
$108$	4.17434e18	+	4.77339e17i	0.200938	+	0.0229774i
$109$			9.28370e18i			0.409420i	0.978823	+	0.204710i	$0.0656252\pi$
$109$			9.28370e18i			0.409420i	−0.978823	+	0.204710i	$0.934375\pi$
$110$	1.17101e19	−	1.04474e19i	0.473512	−	0.422452i
$111$	−3.03649e19			−1.12669
$112$	−2.90150e19	−	6.72369e18i	−0.988669	−	0.229106i
$113$	−9.46581e17			−0.0296423			−0.0148212	−	0.999890i	$-0.504718\pi$
$113$	−9.46581e17			−0.0296423			−0.0148212	+	0.999890i	$0.504718\pi$
$114$	5.12079e18	−	4.56859e18i	0.147482	−	0.131579i
$115$		−	2.49197e19i		−	0.660563i
$116$	−5.88897e19	−	6.73409e18i	−1.43777	−	0.164410i
$117$			5.60678e19i			1.26168i
$118$	−4.26870e19	−	4.78465e19i	−0.885966	−	0.993051i
$119$	1.04082e20			1.99380
$120$	3.54495e19	+	5.02254e19i	0.627174	+	0.888590i
$121$	1.66419e19			0.272108
$122$	2.29655e19	+	2.57413e19i	0.347262	+	0.389235i
$123$			9.65967e19i			1.35165i
$124$	−2.35103e18	+	2.05598e19i	−0.0304615	+	0.266387i
$125$			8.96388e19i			1.07610i
$126$	7.74535e19	−	6.91014e19i	0.862027	−	0.769071i
$127$	−3.90334e19			−0.402997			−0.201498	−	0.979489i	$-0.564581\pi$
$127$	−3.90334e19			−0.402997			−0.201498	+	0.979489i	$0.564581\pi$
$128$	−3.93736e19	−	9.66372e19i	−0.377320	−	0.926083i
$129$	−2.17061e20			−1.93188
$130$	−7.43786e19	+	6.63580e19i	−0.615157	+	0.548822i
$131$		−	1.83175e19i		−	0.140860i	−0.997517	−	0.0704301i	$-0.977563\pi$
$131$		−	1.83175e19i		−	0.140860i	0.997517	−	0.0704301i	$-0.0224372\pi$
$132$	1.98125e19	−	1.73261e20i	0.141738	−	1.23950i
$133$		−	2.05993e19i		−	0.137171i
$134$	−6.54518e19	−	7.33628e19i	−0.405906	−	0.454967i
$135$	−2.60315e19			−0.150428
$136$	2.10280e20	+	2.97928e20i	1.13287	+	1.60506i
$137$	1.21220e20			0.609159			0.304579	−	0.952487i	$-0.401484\pi$
$137$	1.21220e20			0.609159			0.304579	+	0.952487i	$0.401484\pi$
$138$	−1.84354e20	−	2.06636e20i	−0.864571	−	0.969070i
$139$			2.85008e20i			1.24801i	0.781422	+	0.624003i	$0.214495\pi$
$139$			2.85008e20i			1.24801i	−0.781422	+	0.624003i	$0.785505\pi$
$140$	1.83337e20	+	2.09648e19i	0.749953	+	0.0857578i
$141$		−	7.13311e20i		−	2.72708i
$142$	9.08737e19	−	8.10744e19i	0.324862	−	0.289831i
$143$	2.82757e20			0.945631
$144$	3.54279e20	+	8.20977e19i	1.10892	+	0.256973i
$145$	3.67242e20			1.07636
$146$	−4.05793e20	+	3.62035e20i	−1.11417	+	0.994028i
$147$		−	1.70226e19i		−	0.0438037i
$148$	−3.17273e20	−	3.62805e19i	−0.765504	−	0.0875360i
$149$		−	3.46011e20i		−	0.783106i	−0.920155	−	0.391553i	$-0.871938\pi$
$149$		−	3.46011e20i		−	0.783106i	0.920155	−	0.391553i	$-0.128062\pi$
$150$	2.04786e20	+	2.29538e20i	0.434944	+	0.487515i
$151$	2.26945e20			0.452522			0.226261	−	0.974067i	$-0.427350\pi$
$151$	2.26945e20			0.452522			0.226261	+	0.974067i	$0.427350\pi$
$152$	5.89641e19	−	4.16174e19i	0.110427	−	0.0779400i
$153$	−1.27087e21			−2.23631
$154$	−3.48487e20	−	3.90608e20i	−0.576421	−	0.646092i
$155$		−	1.28213e20i		−	0.199425i
$156$	−1.25842e20	+	1.10049e21i	−0.184137	+	1.61028i
$157$			7.69546e19i			0.105971i	0.998595	+	0.0529856i	$0.0168737\pi$
$157$			7.69546e19i			0.105971i	−0.998595	+	0.0529856i	$0.983126\pi$
$158$	−4.02262e20	+	3.58885e20i	−0.521515	+	0.465278i
$159$	1.59569e20			0.194838
$160$	3.10391e20	+	5.67145e20i	0.357083	+	0.652460i
$161$	−8.31234e20			−0.901317
$162$	6.14959e20	−	5.48646e20i	0.628715	−	0.560918i
$163$		−	2.35119e20i		−	0.226728i	−0.993554	−	0.113364i	$-0.963837\pi$
$163$		−	2.35119e20i		−	0.226728i	0.993554	−	0.113364i	$-0.0361627\pi$
$164$	−1.15415e20	+	1.00931e21i	−0.105014	+	0.918348i
$165$			1.08047e21i			0.927929i
$166$	5.53775e20	+	6.20708e20i	0.449062	+	0.503339i
$167$	3.06448e20			0.234720			0.117360	−	0.993089i	$-0.462557\pi$
$167$	3.06448e20			0.234720			0.117360	+	0.993089i	$0.462557\pi$
$168$	1.67534e21	−	1.18247e21i	1.21245	−	0.855759i
$169$	−3.34054e20			−0.228503
$170$	−1.50411e21	−	1.68591e21i	−0.972781	−	1.09036i
$171$			2.51522e20i			0.153856i
$172$	−2.26801e21	−	2.59348e20i	−1.31257	−	0.150094i
$173$		−	4.05558e20i		−	0.222134i	−0.993813	−	0.111067i	$-0.964573\pi$
$173$		−	4.05558e20i		−	0.222134i	0.993813	−	0.111067i	$-0.0354268\pi$
$174$	3.04519e21	−	2.71682e21i	1.57905	−	1.40878i
$175$	9.23361e20			0.453430
$176$	4.14030e20	−	1.78667e21i	0.192602	−	0.831142i
$177$	4.41470e21			1.94605
$178$	−2.47467e21	+	2.20782e21i	−1.03402	+	0.922515i
$179$		−	5.58910e20i		−	0.221431i	−0.993852	−	0.110715i	$-0.964686\pi$
$179$		−	5.58910e20i		−	0.221431i	0.993852	−	0.110715i	$-0.0353142\pi$
$180$	−2.23859e21	−	2.55984e20i	−0.841172	−	0.0961888i
$181$			5.71923e20i			0.203888i	0.994790	+	0.101944i	$0.0325062\pi$
$181$			5.71923e20i			0.203888i	−0.994790	+	0.101944i	$0.967494\pi$
$182$	2.21347e21	+	2.48100e21i	0.748850	+	0.839362i
$183$	−2.37509e21			−0.762773
$184$	−1.67936e21	−	2.37935e21i	−0.512124	−	0.725585i
$185$	1.97854e21			0.573079
$186$	−9.48503e20	−	1.06315e21i	−0.261015	−	0.292564i
$187$			6.40915e21i			1.67612i
$188$	8.52276e20	−	7.45316e21i	0.211875	−	1.85285i
$189$			8.68319e20i			0.205254i
$190$	−3.33665e20	+	2.97684e20i	−0.0750156	+	0.0669263i
$191$	−5.07893e21			−1.08631			−0.543157	−	0.839631i	$-0.682771\pi$
$191$	−5.07893e21			−1.08631			−0.543157	+	0.839631i	$0.682771\pi$
$192$	6.76946e21	+	2.40656e21i	1.37782	+	0.489819i
$193$	−2.57982e21			−0.499798			−0.249899	−	0.968272i	$-0.580397\pi$
$193$	−2.57982e21			−0.499798			−0.249899	+	0.968272i	$0.580397\pi$
$194$	−2.88410e21	+	2.57310e21i	−0.531979	+	0.474613i
$195$		−	6.86275e21i		−	1.20551i
$196$	2.03389e19	−	1.77864e20i	0.00340325	−	0.0297615i
$197$			1.06709e22i			1.70126i	0.525764	+	0.850630i	$0.323779\pi$
$197$			1.06709e22i			1.70126i	−0.525764	+	0.850630i	$0.676221\pi$
$198$	4.25510e21	+	4.76941e21i	0.646533	+	0.724678i
$199$	−9.52516e21			−1.37965			−0.689823	−	0.723978i	$-0.742312\pi$
$199$	−9.52516e21			−1.37965			−0.689823	+	0.723978i	$0.742312\pi$
$200$	1.86549e21	+	2.64305e21i	0.257637	+	0.365024i
$201$	6.76903e21			0.891587
$202$	6.66367e21	+	7.46910e21i	0.837290	+	0.938491i
$203$		−	1.22499e22i		−	1.46865i
$204$	−2.49444e22	−	2.85241e21i	−2.85421	−	0.326381i
$205$		−	6.29414e21i		−	0.687503i
$206$	1.03543e22	−	9.23777e21i	1.07990	−	0.963448i
$207$	1.01495e22			1.01095
$208$	−2.62977e21	+	1.13483e22i	−0.250216	+	1.07977i
$209$	1.26846e21			0.115315
$210$	−9.48037e21	+	8.45806e21i	−0.823649	+	0.734831i
$211$			4.84082e21i			0.402009i	0.979590	+	0.201004i	$0.0644205\pi$
$211$			4.84082e21i			0.402009i	−0.979590	+	0.201004i	$0.935579\pi$
$212$	1.66728e21	+	1.90655e20i	0.132379	+	0.0151376i
$213$			8.38472e21i			0.636623i
$214$	3.40463e21	+	3.81613e21i	0.247251	+	0.277136i
$215$	1.41435e22			0.982632
$216$	−2.48550e21	+	1.75429e21i	−0.165235	+	0.116625i
$217$	−4.27671e21			−0.272109
$218$	−4.47511e21	−	5.01600e21i	−0.272563	−	0.305507i
$219$		−	3.74417e22i		−	2.18342i
$220$	−1.29096e21	+	1.12895e22i	−0.0720938	+	0.630461i
$221$		−	4.07086e22i		−	2.17751i
$222$	1.64062e22	−	1.46371e22i	0.840727	−	0.750068i
$223$	−3.44558e22			−1.69187			−0.845933	−	0.533289i	$-0.820956\pi$
$223$	−3.44558e22			−1.69187			−0.845933	+	0.533289i	$0.820956\pi$
$224$	1.89179e22	−	1.03535e22i	0.890261	−	0.487228i
$225$	−1.12744e22			−0.508582
$226$	5.11440e20	−	4.56289e20i	0.0221189	−	0.0197338i
$227$			2.02926e22i			0.841575i	0.907159	+	0.420787i	$0.138246\pi$
$227$			2.02926e22i			0.841575i	−0.907159	+	0.420787i	$0.861754\pi$
$228$	−5.64532e20	+	4.93684e21i	−0.0224547	+	0.196367i
$229$			4.45214e22i			1.69876i	0.527783	+	0.849379i	$0.323024\pi$
$229$			4.45214e22i			1.69876i	−0.527783	+	0.849379i	$0.676976\pi$
$230$	1.20123e22	+	1.34642e22i	0.439756	+	0.492908i
$231$	3.60406e22			1.26613
$232$	3.50643e22	−	2.47487e22i	1.18231	−	0.834482i
$233$	2.24432e22			0.726447			0.363224	−	0.931702i	$-0.381676\pi$
$233$	2.24432e22			0.726447			0.363224	+	0.931702i	$0.381676\pi$
$234$	−2.70269e22	−	3.02936e22i	−0.839934	−	0.941455i
$235$			4.64786e22i			1.38710i
$236$	4.61278e22	+	5.27475e21i	1.32220	+	0.151195i
$237$		−	3.71159e22i		−	1.02200i
$238$	−5.62359e22	+	5.01718e22i	−1.48776	+	1.32733i
$239$	−9.79425e21			−0.248995			−0.124498	−	0.992220i	$-0.539732\pi$
$239$	−9.79425e21			−0.248995			−0.124498	+	0.992220i	$0.539732\pi$
$240$	−4.33640e22	−	1.00488e22i	−1.05955	−	0.245532i
$241$	−2.87487e22			−0.675237			−0.337618	−	0.941283i	$-0.609621\pi$
$241$	−2.87487e22			−0.675237			−0.337618	+	0.941283i	$0.609621\pi$
$242$	−8.99163e21	+	8.02203e21i	−0.203045	+	0.181150i
$243$			6.60551e22i			1.43432i
$244$	−2.48166e22	−	2.83780e21i	−0.518250	−	0.0592623i
$245$			1.10917e21i			0.0222803i
$246$	−4.65634e22	−	5.21914e22i	−0.899831	−	1.00859i
$247$	−8.05681e21			−0.149810
$248$	−8.64035e21	−	1.22418e22i	−0.154611	−	0.219055i
$249$	−5.72714e22			−0.986380
$250$	−4.32094e22	−	4.84320e22i	−0.716388	−	0.802976i
$251$			9.38618e22i			1.49826i	0.662421	+	0.749132i	$0.269529\pi$
$251$			9.38618e22i			1.49826i	−0.662421	+	0.749132i	$0.730471\pi$
$252$	−8.53872e21	+	7.46712e22i	−0.131246	+	1.14775i
$253$		−	5.11855e22i		−	0.757708i
$254$	2.10899e22	−	1.88156e22i	0.300714	−	0.268287i
$255$	1.55555e23			2.13675
$256$	6.78566e22	+	3.32337e22i	0.898074	+	0.439844i
$257$	3.38399e22			0.431583			0.215792	−	0.976439i	$-0.430767\pi$
$257$	3.38399e22			0.431583			0.215792	+	0.976439i	$0.430767\pi$
$258$	1.17279e23	−	1.04632e23i	1.44156	−	1.28611i
$259$		−	6.59972e22i		−	0.781948i
$260$	8.19973e21	−	7.17067e22i	0.0936597	−	0.819055i
$261$			1.49573e23i			1.64729i
$262$	8.82974e21	+	9.89697e21i	0.0937747	+	0.105109i
$263$	−8.72821e22			−0.894016			−0.447008	−	0.894530i	$-0.647511\pi$
$263$	−8.72821e22			−0.894016			−0.447008	+	0.894530i	$0.647511\pi$
$264$	7.28137e22	+	1.03164e23i	0.719409	+	1.01927i
$265$	−1.03973e22			−0.0991027
$266$	9.92969e21	+	1.11299e22i	0.0913188	+	0.102356i
$267$		−	2.28333e23i		−	2.02634i
$268$	7.07275e22	+	8.08775e21i	0.605770	+	0.0692703i
$269$		−	1.71472e23i		−	1.41758i	−0.705422	−	0.708788i	$-0.749242\pi$
$269$		−	1.71472e23i		−	1.41758i	0.705422	−	0.708788i	$-0.250758\pi$
$270$	1.40649e22	−	1.25482e22i	0.112249	−	0.100144i
$271$	8.52402e22			0.656804			0.328402	−	0.944538i	$-0.393490\pi$
$271$	8.52402e22			0.656804			0.328402	+	0.944538i	$0.393490\pi$
$272$	−2.57228e23	−	5.96079e22i	−1.91387	−	0.443506i
$273$	−2.28917e23			−1.64487
$274$	−6.54957e22	+	5.84330e22i	−0.454551	+	0.405535i
$275$			5.68585e22i			0.381184i
$276$	1.99213e23	+	2.27802e22i	1.29027	+	0.147544i
$277$		−	4.37653e22i		−	0.273888i	−0.990579	−	0.136944i	$-0.956272\pi$
$277$		−	4.37653e22i		−	0.273888i	0.990579	−	0.136944i	$-0.0437280\pi$
$278$	−1.37385e23	−	1.53990e23i	−0.830833	−	0.931254i
$279$	5.22196e22			0.305206
$280$	−1.09163e23	+	7.70484e22i	−0.616702	+	0.435274i
$281$	−3.82071e21			−0.0208658			−0.0104329	−	0.999946i	$-0.503321\pi$
$281$	−3.82071e21			−0.0208658			−0.0104329	+	0.999946i	$0.503321\pi$
$282$	3.43844e23	+	3.85403e23i	1.81549	+	2.03493i
$283$			5.37010e22i			0.274165i	0.990560	+	0.137082i	$0.0437725\pi$
$283$			5.37010e22i			0.274165i	−0.990560	+	0.137082i	$0.956227\pi$
$284$	−1.00182e22	+	8.76094e22i	−0.0494613	+	0.432540i
$285$		−	3.07865e22i		−	0.147006i
$286$	−1.52774e23	+	1.36300e23i	−0.705624	+	0.629534i
$287$	−2.09950e23			−0.938075
$288$	−2.30992e23	+	1.26419e23i	−0.998546	+	0.546490i
$289$	6.83655e23			2.85961
$290$	−1.98421e23	+	1.77025e23i	−0.803170	+	0.716561i
$291$		−	2.66110e23i		−	1.04250i
$292$	4.47360e22	−	3.91217e23i	0.169637	−	1.48347i
$293$			2.33878e23i			0.858513i	0.903183	+	0.429256i	$0.141224\pi$
$293$			2.33878e23i			0.858513i	−0.903183	+	0.429256i	$0.858776\pi$
$294$	8.20555e21	+	9.19734e21i	0.0291614	+	0.0326860i
$295$	−2.87657e23			−0.989842
$296$	1.88912e23	−	1.33336e23i	0.629489	−	0.444299i
$297$	−5.34691e22			−0.172551
$298$	1.66791e23	+	1.86951e23i	0.521336	+	0.584349i
$299$			3.25112e23i			0.984365i
$300$	−2.21293e23	−	2.53050e22i	−0.649105	−	0.0742257i
$301$		−	4.71776e23i		−	1.34077i
$302$	−1.22619e23	+	1.09396e23i	−0.337669	+	0.301257i
$303$	−6.89158e23			−1.83914
$304$	−1.17972e22	+	5.09090e22i	−0.0305127	+	0.131673i
$305$	1.54759e23			0.387977
$306$	6.86652e23	−	6.12608e23i	1.66872	−	1.48878i
$307$		−	6.48358e22i		−	0.152757i	−0.997079	−	0.0763784i	$-0.975664\pi$
$307$		−	6.48358e22i		−	0.152757i	0.997079	−	0.0763784i	$-0.0243357\pi$
$308$	3.76577e23	+	4.30619e22i	0.860244	+	0.0983697i
$309$			9.55370e23i			2.11625i
$310$	6.18035e22	+	6.92735e22i	0.132763	+	0.148810i
$311$	3.48265e23			0.725581			0.362791	−	0.931871i	$-0.381824\pi$
$311$	3.48265e23			0.725581			0.362791	+	0.931871i	$0.381824\pi$
$312$	−4.62486e23	−	6.55258e23i	−0.934610	−	1.32417i
$313$	−2.29940e23			−0.450757			−0.225378	−	0.974271i	$-0.572362\pi$
$313$	−2.29940e23			−0.450757			−0.225378	+	0.974271i	$0.572362\pi$
$314$	−3.70951e22	−	4.15787e22i	−0.0705481	−	0.0790750i
$315$		−	4.65656e23i		−	0.859241i
$316$	4.43467e22	−	3.87812e23i	0.0794025	−	0.694376i
$317$			6.29056e23i			1.09301i	0.837454	+	0.546507i	$0.184043\pi$
$317$			6.29056e23i			1.09301i	−0.837454	+	0.546507i	$0.815957\pi$
$318$	−8.62152e22	+	7.69183e22i	−0.145387	+	0.129710i
$319$	7.54319e23			1.23465
$320$	−4.41091e23	−	1.56809e23i	−0.700815	−	0.249142i
$321$	−3.52107e23			−0.543096
$322$	4.49117e23	−	4.00687e23i	0.672557	−	0.600032i
$323$		−	1.82621e23i		−	0.265537i
$324$	−6.77951e22	+	5.92869e23i	−0.0957240	+	0.837107i
$325$		−	3.61145e23i		−	0.495210i
$326$	1.13337e23	+	1.27035e23i	0.150940	+	0.169183i
$327$	4.62816e23			0.598693
$328$	−4.24167e23	−	6.00966e23i	−0.533010	−	0.755177i
$329$	1.55036e24			1.89265
$330$	−5.20828e23	−	5.83779e23i	−0.617749	−	0.692415i
$331$		−	8.20208e20i		−	0.000945275i	−1.00000		0.000472638i	$-0.999850\pi$
$331$		−	8.20208e20i		−	0.000945275i	1.00000		0.000472638i	$-0.000150445\pi$
$332$	−5.98411e23	−	6.84288e22i	−0.670175	−	0.0766350i
$333$			8.05839e23i			0.877058i
$334$	−1.65575e23	+	1.47720e23i	−0.175147	+	0.156260i
$335$	−4.41063e23			−0.453497
$336$	−3.35193e23	+	1.44647e24i	−0.335021	+	1.44573i
$337$	−9.44584e23			−0.917818			−0.458909	−	0.888483i	$-0.651760\pi$
$337$	−9.44584e23			−0.917818			−0.458909	+	0.888483i	$0.651760\pi$
$338$	1.80490e23	−	1.61027e23i	0.170508	−	0.152121i
$339$			4.71894e22i			0.0433459i
$340$	1.62535e24	+	1.85860e23i	1.45177	+	0.166011i
$341$		−	2.63350e23i		−	0.228753i
$342$	−1.21244e23	−	1.35898e23i	−0.102426	−	0.114806i
$343$	−1.19811e24			−0.984466
$344$	1.35042e24	−	9.53141e23i	1.07936	−	0.761819i
$345$	−1.24231e24			−0.965938
$346$	1.95495e23	+	2.19124e23i	0.147881	+	0.165755i
$347$			2.51038e24i			1.84761i	0.382865	+	0.923804i	$0.374938\pi$
$347$			2.51038e24i			1.84761i	−0.382865	+	0.923804i	$0.625062\pi$
$348$	−3.35711e23	+	2.93580e24i	−0.240416	+	2.10244i
$349$		−	1.66169e24i		−	1.15800i	−0.815329	−	0.578999i	$-0.803444\pi$
$349$		−	1.66169e24i		−	1.15800i	0.815329	−	0.578999i	$-0.196556\pi$
$350$	−4.98894e23	+	4.45096e23i	−0.338347	+	0.301861i
$351$	3.39617e23			0.224167
$352$	6.37546e23	+	1.16492e24i	0.409597	+	0.748414i
$353$	−1.89780e24			−1.18684			−0.593418	−	0.804895i	$-0.702222\pi$
$353$	−1.89780e24			−1.18684			−0.593418	+	0.804895i	$0.702222\pi$
$354$	−2.38527e24	+	2.12806e24i	−1.45213	+	1.29554i
$355$		−	5.46340e23i		−	0.323812i
$356$	2.72816e23	−	2.38578e24i	0.157433	−	1.37675i
$357$		−	5.18877e24i		−	2.91552i
$358$	2.69417e23	+	3.01980e23i	0.147413	+	0.165230i
$359$	1.73809e23			0.0926138			0.0463069	−	0.998927i	$-0.485255\pi$
$359$	1.73809e23			0.0926138			0.0463069	+	0.998927i	$0.485255\pi$
$360$	1.33291e24	−	9.40777e23i	0.691713	−	0.488217i
$361$	1.94228e24			0.981731
$362$	−2.75689e23	−	3.09011e23i	−0.135734	−	0.152140i
$363$		−	8.29639e23i		−	0.397902i
$364$	−2.39188e24	−	2.73514e23i	−1.11757	−	0.127796i
$365$			2.43966e24i			1.11057i
$366$	1.28327e24	−	1.14489e24i	0.569176	−	0.507800i
$367$	2.37308e24			1.02562			0.512808	−	0.858503i	$-0.328605\pi$
$367$	2.37308e24			1.02562			0.512808	+	0.858503i	$0.328605\pi$
$368$	2.05430e24	+	4.76047e23i	0.865187	+	0.200491i
$369$	2.56353e24			1.05218
$370$	−1.06901e24	+	9.53736e23i	−0.427628	+	0.381515i
$371$			3.46817e23i			0.135222i
$372$	1.02496e24	+	1.17205e23i	0.389536	+	0.0445438i
$373$		−	2.60620e24i		−	0.965547i	−0.875745	−	0.482773i	$-0.839629\pi$
$373$		−	2.60620e24i		−	0.965547i	0.875745	−	0.482773i	$-0.160371\pi$
$374$	−3.08946e24	−	3.46288e24i	−1.11584	−	1.25071i
$375$	4.46872e24			1.57357
$376$	3.13223e24	+	4.43779e24i	1.07540	+	1.52364i
$377$	−4.79116e24			−1.60398
$378$	−4.18564e23	−	4.69155e23i	−0.136644	−	0.153160i
$379$		−	3.73330e24i		−	1.18856i	−0.804258	−	0.594280i	$-0.797437\pi$
$379$		−	3.73330e24i		−	1.18856i	0.804258	−	0.594280i	$-0.202563\pi$
$380$	3.67843e22	−	3.21679e23i	0.0114214	−	0.0998800i
$381$			1.94592e24i			0.589300i
$382$	2.74416e24	−	2.44824e24i	0.810601	−	0.723190i
$383$	5.20583e23			0.150003			0.0750017	−	0.997183i	$-0.476104\pi$
$383$	5.20583e23			0.150003			0.0750017	+	0.997183i	$0.476104\pi$
$384$	−4.81761e24	+	1.96287e24i	−1.35421	+	0.551754i
$385$	−2.34837e24			−0.644004
$386$	1.39388e24	−	1.24357e24i	0.372946	−	0.332730i
$387$			5.76048e24i			1.50385i
$388$	3.17953e23	−	2.78050e24i	0.0809956	−	0.708307i
$389$			3.58050e24i			0.890066i	0.895514	+	0.445033i	$0.146808\pi$
$389$			3.58050e24i			0.890066i	−0.895514	+	0.445033i	$0.853192\pi$
$390$	3.30811e24	+	3.70796e24i	0.802540	+	0.899541i
$391$	−7.36918e24			−1.74478
$392$	7.47481e22	+	1.05904e23i	0.0172736	+	0.0244735i
$393$	−9.13172e23			−0.205979
$394$	−5.14378e24	−	5.76550e24i	−1.13258	−	1.26947i
$395$			2.41843e24i			0.519830i
$396$	−4.59808e24	−	5.25795e23i	−0.964878	−	0.110335i
$397$			6.94274e24i			1.42240i	0.702991	+	0.711199i	$0.251847\pi$
$397$			6.94274e24i			1.42240i	−0.702991	+	0.711199i	$0.748153\pi$
$398$	5.14646e24	−	4.59150e24i	1.02948	−	0.918471i
$399$	−1.02693e24			−0.200585
$400$	−2.28198e24	−	5.28808e23i	−0.435254	−	0.100862i
$401$	9.52158e23			0.177353			0.0886763	−	0.996060i	$-0.471736\pi$
$401$	9.52158e23			0.177353			0.0886763	+	0.996060i	$0.471736\pi$
$402$	−3.65732e24	+	3.26294e24i	−0.665297	+	0.593555i
$403$			1.67271e24i			0.297181i
$404$	−7.20079e24	−	8.23417e23i	−1.24956	−	0.142888i
$405$		−	3.69718e24i		−	0.626683i
$406$	5.90491e24	+	6.61863e24i	0.977724	+	1.09590i
$407$	4.06395e24			0.657358
$408$	1.48525e25	−	1.04830e25i	2.34708	−	1.65659i
$409$	2.62892e24			0.405887			0.202944	−	0.979190i	$-0.434949\pi$
$409$	2.62892e24			0.405887			0.202944	+	0.979190i	$0.434949\pi$
$410$	3.03402e24	+	3.40074e24i	0.457690	+	0.513010i
$411$		−	6.04315e24i		−	0.890770i
$412$	−1.14149e24	+	9.98237e24i	−0.164418	+	1.43784i
$413$			9.59521e24i			1.35061i
$414$	−5.48382e24	+	4.89247e24i	−0.754362	+	0.673016i
$415$	3.73174e24			0.501713
$416$	−4.04946e24	−	7.39917e24i	−0.532122	−	0.972291i
$417$	1.42084e25			1.82495
$418$	−6.85352e23	+	6.11448e23i	−0.0860476	+	0.0767688i
$419$			1.31213e24i			0.161044i	0.996753	+	0.0805219i	$0.0256587\pi$
$419$			1.31213e24i			0.161044i	−0.996753	+	0.0805219i	$0.974341\pi$
$420$	1.04515e24	−	9.13982e24i	0.125403	−	1.09665i
$421$		−	5.96864e24i		−	0.700157i	−0.936720	−	0.350079i	$-0.886155\pi$
$421$		−	5.96864e24i		−	0.700157i	0.936720	−	0.350079i	$-0.113845\pi$
$422$	−2.33346e24	−	2.61550e24i	−0.267629	−	0.299976i
$423$	−1.89302e25			−2.12286
$424$	−9.92739e23	+	7.00684e23i	−0.108858	+	0.0768328i
$425$	8.18592e24			0.877754
$426$	−4.04176e24	−	4.53028e24i	−0.423818	−	0.475044i
$427$		−	5.16219e24i		−	0.529382i
$428$	−3.67905e24	−	4.20703e23i	−0.368995	−	0.0421949i
$429$		−	1.40962e25i		−	1.38279i
$430$	−7.64175e24	+	6.81771e24i	−0.733234	+	0.654166i
$431$	−8.91123e24			−0.836380			−0.418190	−	0.908360i	$-0.637335\pi$
$431$	−8.91123e24			−0.836380			−0.418190	+	0.908360i	$0.637335\pi$
$432$	4.97286e23	−	2.14595e24i	0.0456573	−	0.197027i
$433$	−6.03283e24			−0.541859			−0.270929	−	0.962599i	$-0.587331\pi$
$433$	−6.03283e24			−0.541859			−0.270929	+	0.962599i	$0.587331\pi$
$434$	2.31072e24	−	2.06154e24i	0.203046	−	0.181151i
$435$		−	1.83079e25i		−	1.57395i
$436$	4.83582e24	+	5.52980e23i	0.406769	+	0.0465144i
$437$			1.45846e24i			0.120039i
$438$	1.80484e25	+	2.02298e25i	1.45356	+	1.62925i
$439$	1.30807e25			1.03090			0.515451	−	0.856919i	$-0.327624\pi$
$439$	1.30807e25			1.03090			0.515451	+	0.856919i	$0.327624\pi$
$440$	−4.74446e24	−	6.72202e24i	−0.365920	−	0.518441i
$441$	−4.51754e23			−0.0340985
$442$	1.96232e25	+	2.19950e25i	1.44963	+	1.62484i
$443$			5.83057e24i			0.421576i	0.977532	+	0.210788i	$0.0676029\pi$
$443$			5.83057e24i			0.421576i	−0.977532	+	0.210788i	$0.932397\pi$
$444$	−1.80867e24	+	1.58169e25i	−0.128004	+	1.11939i
$445$			1.48779e25i			1.03068i
$446$	1.86165e25	−	1.66090e25i	1.26246	−	1.12632i
$447$	−1.72495e25			−1.14513
$448$	−5.23059e24	+	1.47132e25i	−0.339946	+	0.956239i
$449$	3.10018e24			0.197263			0.0986317	−	0.995124i	$-0.468553\pi$
$449$	3.10018e24			0.197263			0.0986317	+	0.995124i	$0.468553\pi$
$450$	6.09160e24	−	5.43472e24i	0.379501	−	0.338577i
$451$		−	1.29282e25i		−	0.788610i
$452$	−5.63827e22	+	4.93068e23i	−0.00336768	+	0.0294504i
$453$		−	1.13138e25i		−	0.661721i
$454$	−9.78184e24	−	1.09641e25i	−0.560260	−	0.627978i
$455$	1.49160e25			0.836649
$456$	−2.07473e24	−	2.93951e24i	−0.113971	−	0.161476i
$457$	−2.62842e25			−1.41414			−0.707068	−	0.707146i	$-0.749982\pi$
$457$	−2.62842e25			−1.41414			−0.707068	+	0.707146i	$0.749982\pi$
$458$	−2.14611e25	−	2.40550e25i	−1.13091	−	1.26760i
$459$			7.69796e24i			0.397333i
$460$	−1.29805e25	−	1.48434e24i	−0.656286	−	0.0750469i
$461$			1.14359e25i			0.566384i	0.959063	+	0.283192i	$0.0913934\pi$
$461$			1.14359e25i			0.566384i	−0.959063	+	0.283192i	$0.908607\pi$
$462$	−1.94728e25	+	1.73730e25i	−0.944778	+	0.842898i
$463$	1.33811e25			0.636024			0.318012	−	0.948087i	$-0.396985\pi$
$463$	1.33811e25			0.636024			0.318012	+	0.948087i	$0.396985\pi$
$464$	−7.01549e24	+	3.02742e25i	−0.326691	+	1.40978i
$465$	−6.39172e24			−0.291618
$466$	−1.21261e25	+	1.08185e25i	−0.542071	+	0.483617i
$467$			4.46496e24i			0.195572i	0.995207	+	0.0977861i	$0.0311761\pi$
$467$			4.46496e24i			0.195572i	−0.995207	+	0.0977861i	$0.968824\pi$
$468$	2.92054e25	+	3.33966e24i	1.25351	+	0.143340i
$469$			1.47123e25i			0.618782i
$470$	−2.24045e25	−	2.51125e25i	−0.923433	−	1.03505i
$471$	3.83638e24			0.154961
$472$	−2.74656e25	+	1.93854e25i	−1.08728	+	0.767409i
$473$	2.90509e25			1.12714
$474$	1.78913e25	+	2.00538e25i	0.680374	+	0.762610i
$475$		−	1.62011e24i		−	0.0603885i
$476$	6.19963e24	−	5.42158e25i	0.226516	−	1.98089i
$477$		−	4.23471e24i		−	0.151670i
$478$	5.29185e24	−	4.72121e24i	0.185799	−	0.165763i
$479$	3.95808e25			1.36238			0.681188	−	0.732108i	$-0.261463\pi$
$479$	3.95808e25			1.36238			0.681188	+	0.732108i	$0.261463\pi$
$480$	2.82736e25	−	1.54738e25i	0.954090	−	0.522160i
$481$	−2.58128e25			−0.853998
$482$	1.55330e25	−	1.38580e25i	0.503858	−	0.449525i
$483$			4.14391e25i			1.31799i
$484$	9.91266e23	−	8.66864e24i	0.0309143	−	0.270346i
$485$			1.73394e25i			0.530260i
$486$	−3.18412e25	−	3.56897e25i	−0.954870	−	1.07028i
$487$	−4.66024e25			−1.37051			−0.685256	−	0.728302i	$-0.740310\pi$
$487$	−4.66024e25			−1.37051			−0.685256	+	0.728302i	$0.740310\pi$
$488$	1.47764e25	−	1.04293e25i	0.426167	−	0.300793i
$489$	−1.17213e25			−0.331544
$490$	−5.34665e23	−	5.99289e23i	−0.0148327	−	0.0166254i
$491$			4.13355e25i			1.12473i	0.826889	+	0.562365i	$0.190109\pi$
$491$			4.13355e25i			1.12473i	−0.826889	+	0.562365i	$0.809891\pi$
$492$	5.03166e25	+	5.75374e24i	1.34290	+	0.153561i
$493$		−	1.08599e26i		−	2.84303i
$494$	4.35311e24	−	3.88370e24i	0.111788	−	0.0997331i
$495$	2.86740e25			0.722336
$496$	1.05694e25	+	2.44927e24i	0.261201	+	0.0605286i
$497$	−1.82239e25			−0.441831
$498$	3.09439e25	−	2.76071e25i	0.736030	−	0.656661i
$499$			4.26378e25i			0.995038i	0.867453	+	0.497519i	$0.165755\pi$
$499$			4.26378e25i			0.995038i	−0.867453	+	0.497519i	$0.834245\pi$
$500$	4.66922e25	+	5.33930e24i	1.06913	+	0.122256i
$501$		−	1.52772e25i		−	0.343231i
$502$	−4.52450e25	−	5.07137e25i	−0.997438	−	1.11800i
$503$	−3.12731e25			−0.676512			−0.338256	−	0.941054i	$-0.609837\pi$
$503$	−3.12731e25			−0.676512			−0.338256	+	0.941054i	$0.609837\pi$
$504$	−3.13810e25	−	4.44610e25i	−0.666156	−	0.943820i
$505$	4.49048e25			0.935458
$506$	2.46734e25	+	2.76556e25i	0.504428	+	0.565397i
$507$			1.66534e25i			0.334140i
$508$	−2.32501e24	+	2.03323e25i	−0.0457847	+	0.400387i
$509$			9.07982e24i			0.175492i	0.996143	+	0.0877462i	$0.0279665\pi$
$509$			9.07982e24i			0.175492i	−0.996143	+	0.0877462i	$0.972034\pi$
$510$	−8.40468e25	+	7.49837e25i	−1.59443	+	1.42249i
$511$	8.13784e25			1.51534
$512$	−5.26830e25	+	1.47533e25i	−0.962954	+	0.269665i
$513$	1.52353e24			0.0273361
$514$	−1.82838e25	+	1.63122e25i	−0.322045	+	0.287317i
$515$		−	6.22509e25i		−	1.07641i
$516$	−1.29292e25	+	1.13066e26i	−0.219482	+	1.91937i
$517$			9.54676e25i			1.59109i
$518$	3.18132e25	+	3.56584e25i	0.520565	+	0.583484i
$519$	−2.02181e25			−0.324825
$520$	3.01351e25	+	4.26959e25i	0.475380	+	0.673526i
$521$	−6.28755e25			−0.973920			−0.486960	−	0.873424i	$-0.661894\pi$
$521$	−6.28755e25			−0.973920			−0.486960	+	0.873424i	$0.661894\pi$
$522$	−7.21002e25	−	8.08148e25i	−1.09665	−	1.22920i
$523$		−	2.85949e25i		−	0.427093i	−0.976933	−	0.213546i	$-0.931499\pi$
$523$		−	2.85949e25i		−	0.427093i	0.976933	−	0.213546i	$-0.0685014\pi$
$524$	−9.54145e24	−	1.09107e24i	−0.139948	−	0.0160032i
$525$		−	4.60319e25i		−	0.663048i
$526$	4.71587e25	−	4.20734e25i	0.667109	−	0.595172i
$527$	−3.79146e25			−0.526751
$528$	−8.90702e25	−	2.06404e25i	−1.21537	−	0.281641i
$529$	−1.57629e25			−0.211256
$530$	5.61769e24	−	5.01191e24i	0.0739498	−	0.0659755i
$531$		−	1.17160e26i		−	1.51488i
$532$	−1.07301e25	−	1.22699e24i	−0.136283	−	0.0155841i
$533$			8.21155e25i			1.02451i
$534$	1.10065e26	+	1.23369e26i	1.34899	+	1.51204i
$535$	2.29429e25			0.276240
$536$	−4.21128e25	+	2.97236e25i	−0.498137	+	0.351589i
$537$	−2.78631e25			−0.323798
$538$	8.26562e25	+	9.26466e25i	0.943721	+	1.05779i
$539$			2.27826e24i			0.0255570i
$540$	−1.55056e24	+	1.35597e25i	−0.0170902	+	0.149454i
$541$		−	1.29199e26i		−	1.39921i	−0.714528	−	0.699607i	$-0.753358\pi$
$541$		−	1.29199e26i		−	1.39921i	0.714528	−	0.699607i	$-0.246642\pi$
$542$	−4.60554e25	+	4.10891e25i	−0.490103	+	0.437253i
$543$	2.85118e25			0.298144
$544$	1.67714e26	−	9.17876e25i	1.72338	−	0.943180i
$545$	−3.01566e25			−0.304520
$546$	1.23684e26	−	1.10347e26i	1.22739	−	1.09504i
$547$		−	4.90707e25i		−	0.478567i	−0.970950	−	0.239284i	$-0.923087\pi$
$547$		−	4.90707e25i		−	0.478567i	0.970950	−	0.239284i	$-0.0769126\pi$
$548$	7.22045e24	−	6.31430e25i	0.0692069	−	0.605215i
$549$			6.30314e25i			0.593772i
$550$	−2.74080e25	−	3.07207e25i	−0.253765	−	0.284437i
$551$	−2.14933e25			−0.195598
$552$	−1.18616e26	+	8.37204e25i	−1.06102	+	0.748877i
$553$	8.06703e25			0.709291
$554$	2.10966e25	+	2.36465e25i	0.182335	+	0.204373i
$555$		−	9.86354e25i		−	0.838011i
$556$	1.48459e26	+	1.69764e25i	1.23992	+	0.141787i
$557$		−	1.47557e25i		−	0.121153i	−0.998164	−	0.0605766i	$-0.980706\pi$
$557$		−	1.47557e25i		−	0.121153i	0.998164	−	0.0605766i	$-0.0192939\pi$
$558$	−2.82143e25	+	2.51719e25i	−0.227743	+	0.203185i
$559$	−1.84521e26			−1.46431
$560$	2.18408e25	−	9.42504e25i	0.170405	−	0.735355i
$561$	3.19512e26			2.45098
$562$	2.06434e24	−	1.84173e24i	0.0155699	−	0.0138909i
$563$			1.71235e26i			1.26988i	0.772561	+	0.634940i	$0.218975\pi$
$563$			1.71235e26i			1.26988i	−0.772561	+	0.634940i	$0.781025\pi$
$564$	−3.71559e26	−	4.24881e25i	−2.70942	−	0.309824i
$565$		−	3.07481e24i		−	0.0220475i
$566$	−2.58860e25	−	2.90148e25i	−0.182519	−	0.204580i
$567$	−1.23325e26			−0.855089
$568$	−3.68183e25	−	5.21647e25i	−0.251047	−	0.355687i
$569$	5.00277e25			0.335463			0.167731	−	0.985833i	$-0.446356\pi$
$569$	5.00277e25			0.335463			0.167731	+	0.985833i	$0.446356\pi$
$570$	1.48403e25	+	1.66340e25i	0.0978661	+	0.109695i
$571$		−	7.56372e25i		−	0.490561i	−0.969452	−	0.245280i	$-0.921120\pi$
$571$		−	7.56372e25i		−	0.490561i	0.969452	−	0.245280i	$-0.0788800\pi$
$572$	1.68423e25	−	1.47287e26i	0.107434	−	0.939508i
$573$			2.53197e26i			1.58851i
$574$	1.13436e26	−	1.01204e26i	0.699986	−	0.624504i
$575$	−6.53753e25			−0.396798
$576$	6.38666e25	−	1.79651e26i	0.381294	−	1.07255i
$577$	9.40149e25			0.552111			0.276055	−	0.961142i	$-0.410973\pi$
$577$	9.40149e25			0.552111			0.276055	+	0.961142i	$0.410973\pi$
$578$	−3.69380e26	+	3.29548e26i	−2.13383	+	1.90373i
$579$			1.28610e26i			0.730852i
$580$	2.18746e25	−	1.91294e26i	0.122285	−	1.06939i
$581$		−	1.24478e26i		−	0.684571i
$582$	1.28275e26	+	1.43780e26i	0.694025	+	0.777910i
$583$	−2.13562e25			−0.113677
$584$	1.64411e26	+	2.32940e26i	0.861010	+	1.21989i
$585$	−1.82127e26			−0.938413
$586$	−1.12738e26	−	1.26365e26i	−0.571537	−	0.640617i
$587$			4.89889e25i			0.244363i	0.992508	+	0.122181i	$0.0389890\pi$
$587$			4.89889e25i			0.244363i	−0.992508	+	0.122181i	$0.961011\pi$
$588$	−8.86695e24	−	1.01394e24i	−0.0435201	−	0.00497656i
$589$			7.50382e24i			0.0362399i
$590$	1.55422e26	−	1.38662e26i	0.738614	−	0.658966i
$591$	5.31970e26			2.48775
$592$	−3.77965e25	+	1.63105e26i	−0.173939	+	0.750602i
$593$	2.09589e25			0.0949182			0.0474591	−	0.998873i	$-0.484888\pi$
$593$	2.09589e25			0.0949182			0.0474591	+	0.998873i	$0.484888\pi$
$594$	2.88895e25	−	2.57742e25i	0.128756	−	0.114872i
$595$			3.38095e26i			1.48295i
$596$	−1.80235e26	−	2.06100e25i	−0.778036	−	0.0889691i
$597$			4.74853e26i			2.01745i
$598$	−1.56717e26	−	1.75659e26i	−0.655320	−	0.734527i
$599$	−4.37283e26			−1.79973			−0.899866	−	0.436167i	$-0.856336\pi$
$599$	−4.37283e26			−1.79973			−0.899866	+	0.436167i	$0.856336\pi$
$600$	1.31763e26	−	9.29994e25i	0.533772	−	0.376741i
$601$	−1.76961e26			−0.705621			−0.352810	−	0.935695i	$-0.614774\pi$
$601$	−1.76961e26			−0.705621			−0.352810	+	0.935695i	$0.614774\pi$
$602$	2.27414e26	+	2.54901e26i	0.892589	+	1.00047i
$603$		−	1.79640e26i		−	0.694046i
$604$	1.35179e25	−	1.18214e26i	0.0514113	−	0.449592i
$605$			5.40584e25i			0.202389i
$606$	3.72353e26	−	3.32201e26i	1.37235	−	1.22437i
$607$	2.20019e26			0.798302			0.399151	−	0.916885i	$-0.369305\pi$
$607$	2.20019e26			0.798302			0.399151	+	0.916885i	$0.369305\pi$
$608$	−1.81660e25	−	3.31929e25i	−0.0648898	−	0.118566i
$609$	−6.10687e26			−2.14760
$610$	−8.36164e25	+	7.45997e25i	−0.289506	+	0.258288i
$611$		−	6.06376e26i		−	2.06705i
$612$	−7.56988e25	+	6.61987e26i	−0.254068	+	2.22183i
$613$		−	5.09110e26i		−	1.68243i	−0.540701	−	0.841215i	$-0.681841\pi$
$613$		−	5.09110e26i		−	1.68243i	0.540701	−	0.841215i	$-0.318159\pi$
$614$	3.12534e25	+	3.50309e25i	0.101695	+	0.113986i
$615$	−3.13779e26			−1.00533
$616$	−2.24223e26	+	1.58258e26i	−0.707396	+	0.499286i
$617$	4.19716e26			1.30391			0.651953	−	0.758260i	$-0.273950\pi$
$617$	4.19716e26			1.30391			0.651953	+	0.758260i	$0.273950\pi$
$618$	−4.60526e26	−	5.16189e26i	−1.40885	−	1.57913i
$619$			2.09098e26i			0.629926i	0.949104	+	0.314963i	$0.101992\pi$
$619$			2.09098e26i			0.629926i	−0.949104	+	0.314963i	$0.898008\pi$
$620$	−6.67851e25	−	7.63693e24i	−0.198134	−	0.0226568i
$621$		−	6.14783e25i		−	0.179619i
$622$	−1.88168e26	+	1.67877e26i	−0.541424	+	0.483040i
$623$	4.96274e26			1.40632
$624$	5.65742e26	+	1.31100e26i	1.57894	+	0.365890i
$625$	−1.28637e26			−0.353594
$626$	1.24237e26	−	1.10840e26i	0.336352	−	0.300082i
$627$		−	6.32359e25i		−	0.168625i
$628$	4.00851e25	+	4.58377e24i	0.105285	+	0.0120394i
$629$		−	5.85088e26i		−	1.51370i
$630$	2.24464e26	+	2.51595e26i	0.572022	+	0.641161i
$631$	5.75808e26			1.44544			0.722718	−	0.691143i	$-0.242893\pi$
$631$	5.75808e26			1.44544			0.722718	+	0.691143i	$0.242893\pi$
$632$	1.62980e26	+	2.30913e26i	0.403016	+	0.570999i
$633$	2.41327e26			0.587855
$634$	−3.03229e26	−	3.39880e26i	−0.727651	−	0.815601i
$635$		−	1.26794e26i		−	0.299742i
$636$	9.50464e24	−	8.31182e25i	0.0221357	−	0.193577i
$637$		−	1.44707e25i		−	0.0332020i
$638$	−4.07560e26	+	3.63611e26i	−0.921287	+	0.821941i
$639$	2.22518e26			0.495573
$640$	3.13910e26	−	1.27899e26i	0.688804	−	0.280644i
$641$	2.10914e26			0.455990			0.227995	−	0.973662i	$-0.426783\pi$
$641$	2.10914e26			0.455990			0.227995	+	0.973662i	$0.426783\pi$
$642$	1.90244e26	−	1.69729e26i	0.405255	−	0.361554i
$643$			7.02503e26i			1.47450i	0.675622	+	0.737249i	$0.263875\pi$
$643$			7.02503e26i			1.47450i	−0.675622	+	0.737249i	$0.736125\pi$
$644$	−4.95121e25	+	4.32984e26i	−0.102399	+	0.895481i
$645$		−	7.05088e26i		−	1.43690i
$646$	8.80302e25	+	9.86702e25i	0.176776	+	0.198142i
$647$	−1.43888e26			−0.284730			−0.142365	−	0.989814i	$-0.545471\pi$
$647$	−1.43888e26			−0.284730			−0.142365	+	0.989814i	$0.545471\pi$
$648$	−2.49156e26	−	3.53008e26i	−0.485858	−	0.688371i
$649$	−5.90851e26			−1.13541
$650$	1.74086e26	+	1.95127e26i	0.329675	+	0.369522i
$651$			2.13205e26i			0.397904i
$652$	−1.22472e26	−	1.40048e25i	−0.225260	−	0.0257587i
$653$		−	5.08869e26i		−	0.922425i	−0.887290	−	0.461213i	$-0.847415\pi$
$653$		−	5.08869e26i		−	0.922425i	0.887290	−	0.461213i	$-0.152585\pi$
$654$	−2.50060e26	+	2.23095e26i	−0.446741	+	0.398567i
$655$	5.95013e25			0.104769
$656$	5.18868e26	+	1.20238e26i	0.900472	+	0.208668i
$657$	−9.93647e26			−1.69966
$658$	−8.37662e26	+	7.47334e26i	−1.41229	+	1.25999i
$659$		−	3.48001e26i		−	0.578321i	−0.957281	−	0.289160i	$-0.906624\pi$
$659$		−	3.48001e26i		−	0.578321i	0.957281	−	0.289160i	$-0.0933761\pi$
$660$	5.62809e26	+	6.43577e25i	0.921921	+	0.105422i
$661$			5.73431e26i			0.925907i	0.886383	+	0.462953i	$0.153210\pi$
$661$			5.73431e26i			0.925907i	−0.886383	+	0.462953i	$0.846790\pi$
$662$	3.95372e23	+	4.43160e23i	0.000629297	+	0.000705358i
$663$	−2.02943e27			−3.18416
$664$	3.56308e26	−	2.51485e26i	0.551098	−	0.388970i
$665$	6.69136e25			0.102026
$666$	−3.88446e26	−	4.35397e26i	−0.583883	−	0.654455i
$667$			8.67308e26i			1.28522i
$668$	1.82535e25	−	1.59627e26i	0.0266667	−	0.233201i
$669$			1.71771e27i			2.47401i
$670$	2.38307e26	−	2.12609e26i	0.338397	−	0.301906i
$671$	3.17876e26			0.445034
$672$	−5.16149e26	−	9.43106e26i	−0.712471	−	1.30182i
$673$	9.22067e26			1.25493			0.627465	−	0.778645i	$-0.284093\pi$
$673$	9.22067e26			1.25493			0.627465	+	0.778645i	$0.284093\pi$
$674$	5.10361e26	−	4.55326e26i	0.684870	−	0.611018i
$675$			6.82920e25i			0.0903616i
$676$	−1.98978e25	+	1.74006e26i	−0.0259604	+	0.227024i
$677$		−	4.92154e26i		−	0.633153i	−0.948567	−	0.316576i	$-0.897467\pi$
$677$		−	4.92154e26i		−	0.633153i	0.948567	−	0.316576i	$-0.102533\pi$
$678$	−2.27472e25	−	2.54966e25i	−0.0288566	−	0.0323444i
$679$	5.78382e26			0.723522
$680$	−9.67771e26	+	6.83061e26i	−1.19382	+	0.842607i
$681$	1.01164e27			1.23063
$682$	1.26945e26	+	1.42289e26i	0.152288	+	0.170694i
$683$			4.82762e26i			0.571132i	0.958359	+	0.285566i	$0.0921815\pi$
$683$			4.82762e26i			0.571132i	−0.958359	+	0.285566i	$0.907818\pi$
$684$	1.31016e26	+	1.49818e25i	0.152860	+	0.0174796i
$685$			3.93765e26i			0.453082i
$686$	6.47339e26	−	5.77534e26i	0.734603	−	0.655388i
$687$	2.21950e27			2.48409
$688$	−2.70186e26	+	1.16594e27i	−0.298244	+	1.28702i
$689$	1.35647e26			0.147682
$690$	6.71224e26	−	5.98843e26i	0.720777	−	0.643053i
$691$		−	9.84631e26i		−	1.04287i	−0.853290	−	0.521437i	$-0.825396\pi$
$691$		−	9.84631e26i		−	1.04287i	0.853290	−	0.521437i	$-0.174604\pi$
$692$	−2.11252e26	−	2.41569e25i	−0.220696	−	0.0252367i
$693$		−	9.56463e26i		−	0.985604i
$694$	−1.21010e27	−	1.35637e27i	−1.23001	−	1.37867i
$695$	−9.25802e26			−0.928245
$696$	−1.23379e27	−	1.74805e27i	−1.22026	−	1.72888i
$697$	−1.86128e27			−1.81594
$698$	8.00998e26	+	8.97813e26i	0.770912	+	0.864090i
$699$		−	1.11885e27i		−	1.06228i
$700$	5.49997e25	−	4.80973e26i	0.0515144	−	0.450494i
$701$			1.70700e27i			1.57729i	0.614846	+	0.788647i	$0.289218\pi$
$701$			1.70700e27i			1.57729i	−0.614846	+	0.788647i	$0.710782\pi$
$702$	−1.83496e26	+	1.63708e26i	−0.167272	+	0.149234i
$703$	−1.15797e26			−0.104141
$704$	−9.06006e26	−	3.22088e26i	−0.803879	−	0.285781i
$705$	2.31707e27			2.02835
$706$	1.02538e27	−	9.14813e26i	0.885609	−	0.790110i
$707$		−	1.49786e27i		−	1.27640i
$708$	2.62960e26	−	2.29959e27i	0.221092	−	1.93345i
$709$			1.25967e27i			1.04500i	0.852638	+	0.522502i	$0.175001\pi$
$709$			1.25967e27i			1.04500i	−0.852638	+	0.522502i	$0.824999\pi$
$710$	2.63357e26	+	2.95188e26i	0.215571	+	0.241627i
$711$	−9.85001e26			−0.795565
$712$	1.00264e27	+	1.42055e27i	0.799067	+	1.13213i
$713$	3.02797e26			0.238123
$714$	2.50119e27	+	2.80350e27i	1.94095	+	2.17554i
$715$			9.18492e26i			0.703344i
$716$	−2.91133e26	−	3.32913e25i	−0.219997	−	0.0251569i
$717$			4.88268e26i			0.364105i
$718$	−9.39096e25	+	8.37829e25i	−0.0691079	+	0.0616557i
$719$	−1.11025e27			−0.806303			−0.403151	−	0.915133i	$-0.632085\pi$
$719$	−1.11025e27			−0.806303			−0.403151	+	0.915133i	$0.632085\pi$
$720$	−2.66681e26	+	1.15082e27i	−0.191132	+	0.824798i
$721$	−2.07647e27			−1.46872
$722$	−1.04942e27	+	9.36253e26i	−0.732562	+	0.653567i
$723$			1.43319e27i			0.987396i
$724$	2.97911e26	+	3.40664e25i	0.202568	+	0.0231638i
$725$		−	9.63433e26i		−	0.646563i
$726$	3.99918e26	+	4.48255e26i	0.264895	+	0.296912i
$727$	−1.66901e27			−1.09114			−0.545571	−	0.838065i	$-0.683687\pi$
$727$	−1.66901e27			−1.09114			−0.545571	+	0.838065i	$0.683687\pi$
$728$	1.42418e27	−	1.00520e27i	0.919004	−	0.648641i
$729$	1.97016e27			1.25484
$730$	−1.17601e27	−	1.31815e27i	−0.739341	−	0.828703i
$731$		−	4.18246e27i		−	2.59547i
$732$	−1.41472e26	+	1.23717e27i	−0.0866590	+	0.757834i
$733$		−	1.71730e27i		−	1.03839i	−0.854657	−	0.519193i	$-0.826233\pi$
$733$		−	1.71730e27i		−	1.03839i	0.854657	−	0.519193i	$-0.173767\pi$
$734$	−1.28218e27	+	1.14392e27i	−0.765309	+	0.682782i
$735$	5.52951e25			0.0325804
$736$	−1.33942e27	+	7.33044e26i	−0.779070	+	0.426374i
$737$	−9.05948e26			−0.520190
$738$	−1.38508e27	+	1.23572e27i	−0.785127	+	0.700464i
$739$			1.15277e27i			0.645088i	0.946554	+	0.322544i	$0.104538\pi$
$739$			1.15277e27i			0.645088i	−0.946554	+	0.322544i	$0.895462\pi$
$740$	1.17851e26	−	1.03061e27i	0.0651078	−	0.569368i
$741$			4.01652e26i			0.219067i
$742$	−1.67180e26	−	1.87386e26i	−0.0900214	−	0.100902i
$743$	−1.30371e27			−0.693084			−0.346542	−	0.938034i	$-0.612644\pi$
$743$	−1.30371e27			−0.693084			−0.346542	+	0.938034i	$0.612644\pi$
$744$	−6.10283e26	+	4.30743e26i	−0.320323	+	0.226087i
$745$	1.12396e27			0.582461
$746$	1.25629e27	+	1.40813e27i	0.642792	+	0.720485i
$747$			1.51990e27i			0.767837i
$748$	3.33849e27	+	3.81759e26i	1.66527	+	0.190425i
$749$		−	7.65293e26i		−	0.376921i
$750$	−2.41446e27	+	2.15410e27i	−1.17419	+	1.04757i
$751$	3.01810e27			1.44929			0.724643	−	0.689125i	$-0.242005\pi$
$751$	3.01810e27			1.44929			0.724643	+	0.689125i	$0.242005\pi$
$752$	−3.83154e27	−	8.87890e26i	−1.81679	−	0.421007i
$753$	4.67925e27			2.19091
$754$	2.58867e27	−	2.30953e27i	1.19688	−	1.06781i
$755$			7.37195e26i			0.336578i
$756$	4.52302e26	+	5.17211e25i	0.203925	+	0.0233190i
$757$		−	1.21517e27i		−	0.541034i	−0.962715	−	0.270517i	$-0.912805\pi$
$757$		−	1.21517e27i		−	0.541034i	0.962715	−	0.270517i	$-0.0871947\pi$
$758$	1.79960e27	+	2.01711e27i	0.791258	+	0.886896i
$759$	−2.55172e27			−1.10799
$760$	1.35187e26	+	1.91535e26i	0.0579705	+	0.0821334i
$761$	−2.83984e27			−1.20265			−0.601326	−	0.799004i	$-0.705361\pi$
$761$	−2.83984e27			−1.20265			−0.601326	+	0.799004i	$0.705361\pi$
$762$	−9.38007e26	−	1.05138e27i	−0.392314	−	0.439732i
$763$			1.00592e27i			0.415507i
$764$	−3.02525e26	+	2.64558e27i	−0.123417	+	1.07928i
$765$		−	4.12821e27i		−	1.66333i
$766$	−2.81272e26	+	2.50941e26i	−0.111932	+	0.0998616i
$767$	3.75287e27			1.47505
$768$	1.65678e27	−	3.38282e27i	0.643182	−	1.31325i
$769$	−2.44029e27			−0.935711			−0.467856	−	0.883805i	$-0.654973\pi$
$769$	−2.44029e27			−0.935711			−0.467856	+	0.883805i	$0.654973\pi$
$770$	1.26883e27	−	1.13200e27i	0.480552	−	0.428732i
$771$		−	1.68700e27i		−	0.631102i
$772$	−1.53666e26	+	1.34381e27i	−0.0567823	+	0.496562i
$773$			4.44946e27i			1.62406i	0.583616	+	0.812030i	$0.301637\pi$
$773$			4.44946e27i			1.62406i	−0.583616	+	0.812030i	$0.698363\pi$
$774$	−2.77678e27	−	3.11240e27i	−1.00116	−	1.12216i
$775$	−3.36357e26			−0.119794
$776$	1.16852e27	+	1.65558e27i	0.411102	+	0.582456i
$777$	−3.29013e27			−1.14344
$778$	−1.72594e27	−	1.93455e27i	−0.592543	−	0.664162i
$779$			3.68373e26i			0.124934i
$780$	−3.57476e27	−	4.08777e26i	−1.19770	−	0.136958i
$781$		−	1.12219e27i		−	0.371433i
$782$	3.98158e27	−	3.55223e27i	1.30194	−	1.16155i
$783$	9.06003e26			0.292680
$784$	−9.14365e25	−	2.11888e25i	−0.0291821	−	0.00676243i
$785$	−2.49974e26			−0.0788195
$786$	4.93389e26	−	4.40185e26i	0.153700	−	0.137126i
$787$		−	1.79506e27i		−	0.552482i	−0.961088	−	0.276241i	$-0.910911\pi$
$787$		−	1.79506e27i		−	0.552482i	0.961088	−	0.276241i	$-0.0890887\pi$
$788$	5.55839e27	+	6.35607e26i	1.69025	+	0.193281i
$789$			4.35123e27i			1.30732i
$790$	−1.16578e27	−	1.30668e27i	−0.346066	−	0.387894i
$791$	−1.02565e26			−0.0300830
$792$	2.73781e27	−	1.93237e27i	0.793439	−	0.560016i
$793$	−2.01903e27			−0.578160
$794$	−3.34667e27	−	3.75118e27i	−0.946931	−	1.06138i
$795$			5.18332e26i			0.144917i
$796$	−5.67362e26	+	4.96159e27i	−0.156742	+	1.37071i
$797$			2.30489e27i			0.629211i	0.949223	+	0.314605i	$0.101872\pi$
$797$			2.30489e27i			0.629211i	−0.949223	+	0.314605i	$0.898128\pi$
$798$	5.54852e26	−	4.95020e26i	0.149675	−	0.133535i
$799$	1.37445e28			3.66382
$800$	1.48787e27	−	8.14289e26i	0.391930	−	0.214498i
$801$	−6.05961e27			−1.57738
$802$	−5.14453e26	+	4.58978e26i	−0.132339	+	0.118069i
$803$			5.01109e27i			1.27390i
$804$	4.03195e26	−	3.52594e27i	0.101294	−	0.885814i
$805$		−	2.70013e27i		−	0.670384i
$806$	−8.06310e26	−	9.03766e26i	−0.197842	−	0.221755i
$807$	−8.54830e27			−2.07291
$808$	4.28752e27	−	3.02617e27i	1.02754	−	0.725246i
$809$	7.21315e27			1.70850			0.854248	−	0.519866i	$-0.174018\pi$
$809$	7.21315e27			1.70850			0.854248	+	0.519866i	$0.174018\pi$
$810$	1.78219e27	+	1.99760e27i	0.417201	+	0.467627i
$811$			6.07611e27i			1.40581i	0.711282	+	0.702907i	$0.248115\pi$
$811$			6.07611e27i			1.40581i	−0.711282	+	0.702907i	$0.751885\pi$
$812$	−6.38087e27	−	7.29659e26i	−1.45914	−	0.166854i
$813$		−	4.24944e27i		−	0.960442i
$814$	−2.19576e27	+	1.95899e27i	−0.490517	+	0.437622i
$815$	7.63746e26			0.168637
$816$	−2.97160e27	+	1.28235e28i	−0.648537	+	2.79865i
$817$	−8.27767e26			−0.178566
$818$	−1.42041e27	+	1.26724e27i	−0.302871	+	0.270211i
$819$			6.07511e27i			1.28043i
$820$	−3.27857e27	−	3.74908e26i	−0.683052	−	0.0781075i
$821$			7.09411e27i			1.46096i	0.682935	+	0.730479i	$0.260703\pi$
$821$			7.09411e27i			1.46096i	−0.682935	+	0.730479i	$0.739297\pi$
$822$	2.91303e27	+	3.26512e27i	0.593012	+	0.664687i
$823$	−1.84261e27			−0.370796			−0.185398	−	0.982663i	$-0.559358\pi$
$823$	−1.84261e27			−0.370796			−0.185398	+	0.982663i	$0.559358\pi$
$824$	−4.19514e27	−	5.94374e27i	−0.834522	−	1.18236i
$825$	2.83454e27			0.557403
$826$	−4.62527e27	−	5.18431e27i	−0.899138	−	1.00781i
$827$		−	7.94719e27i		−	1.52725i	−0.645657	−	0.763627i	$-0.723416\pi$
$827$		−	7.94719e27i		−	1.52725i	0.645657	−	0.763627i	$-0.276584\pi$
$828$	6.04553e26	−	5.28683e27i	0.114854	−	1.00440i
$829$		−	1.02585e28i		−	1.92670i	−0.268247	−	0.963350i	$-0.586444\pi$
$829$		−	1.02585e28i		−	1.92670i	0.268247	−	0.963350i	$-0.413556\pi$
$830$	−2.01627e27	+	1.79885e27i	−0.374375	+	0.334005i
$831$	−2.18181e27			−0.400505
$832$	5.75462e27	+	2.04579e27i	1.04435	+	0.371269i
$833$	3.28001e26			0.0588501
$834$	−7.67681e27	+	6.84899e27i	−1.36177	+	1.21492i
$835$			9.95448e26i			0.174581i
$836$	7.55554e25	−	6.60733e26i	0.0131010	−	0.114569i
$837$		−	3.16307e26i		−	0.0542271i
$838$	−6.32498e26	−	7.08947e26i	−0.107211	−	0.120170i
$839$	−4.15109e27			−0.695702			−0.347851	−	0.937550i	$-0.613088\pi$
$839$	−4.15109e27			−0.695702			−0.347851	+	0.937550i	$0.613088\pi$
$840$	3.84106e27	+	5.44206e27i	0.636499	+	0.901801i
$841$	−6.67823e27			−1.09421
$842$	2.87712e27	+	3.22487e27i	0.466115	+	0.522453i
$843$			1.90472e26i			0.0305119i
$844$	2.52155e27	+	2.88341e26i	0.399406	+	0.0456724i
$845$		−	1.08512e27i		−	0.169957i
$846$	1.02280e28	−	9.12510e27i	1.58407	−	1.41325i
$847$	1.80319e27			0.276153
$848$	1.98622e26	−	8.57120e26i	0.0300792	−	0.129802i
$849$	2.67713e27			0.400910
$850$	−4.42287e27	+	3.94593e27i	−0.654975	+	0.584346i
$851$			4.67269e27i			0.684284i
$852$	4.36755e27	+	4.99433e26i	0.632501	+	0.0723271i
$853$		−	1.07973e28i		−	1.54633i	−0.634207	−	0.773163i	$-0.718673\pi$
$853$		−	1.07973e28i		−	1.54633i	0.634207	−	0.773163i	$-0.281327\pi$
$854$	2.48838e27	+	2.78914e27i	0.352425	+	0.395022i
$855$	−8.17029e26			−0.114435
$856$	2.19059e27	−	1.54614e27i	0.303432	−	0.214165i
$857$	1.39277e28			1.90792			0.953960	−	0.299934i	$-0.0969648\pi$
$857$	1.39277e28			1.90792			0.953960	+	0.299934i	$0.0969648\pi$
$858$	6.79491e27	+	7.61619e27i	0.920564	+	1.03183i
$859$		−	1.18324e28i		−	1.58540i	−0.609613	−	0.792699i	$-0.708675\pi$
$859$		−	1.18324e28i		−	1.58540i	0.609613	−	0.792699i	$-0.291325\pi$
$860$	8.42451e26	−	7.36724e27i	0.111637	−	0.976270i
$861$			1.04665e28i			1.37174i
$862$	4.81475e27	−	4.29556e27i	0.624101	−	0.556802i
$863$	−1.25518e28			−1.60917			−0.804586	−	0.593836i	$-0.797613\pi$
$863$	−1.25518e28			−1.60917			−0.804586	+	0.593836i	$0.797613\pi$
$864$	7.65749e26	+	1.39917e27i	0.0970970	+	0.177415i
$865$	1.31739e27			0.165219
$866$	3.25955e27	−	2.90806e27i	0.404332	−	0.360731i
$867$		−	3.40819e28i		−	4.18160i
$868$	−2.54741e26	+	2.22771e27i	−0.0309144	+	0.270347i
$869$			4.96749e27i			0.596278i
$870$	8.82513e27	+	9.89180e27i	1.04782	+	1.17447i
$871$	5.75426e27			0.675798
$872$	−2.87936e27	+	2.03228e27i	−0.334495	+	0.236089i
$873$	−7.06217e27			−0.811526
$874$	−7.03036e26	−	7.88011e26i	−0.0799133	−	0.0895723i
$875$			9.71262e27i			1.09209i
$876$	−1.95031e28	−	2.23020e27i	−2.16928	−	0.248059i
$877$			7.63666e26i			0.0840248i	0.999117	+	0.0420124i	$0.0133769\pi$
$877$			7.63666e26i			0.0840248i	−0.999117	+	0.0420124i	$0.986623\pi$
$878$	−7.06752e27	+	6.30540e27i	−0.769253	+	0.686302i
$879$	1.16594e28			1.25540
$880$	5.80372e27	+	1.34491e27i	0.618189	+	0.143254i
$881$	−3.52443e27			−0.371379			−0.185690	−	0.982608i	$-0.559452\pi$
$881$	−3.52443e27			−0.371379			−0.185690	+	0.982608i	$0.559452\pi$
$882$	2.44084e26	−	2.17763e26i	0.0254441	−	0.0227004i
$883$			8.12815e27i			0.838233i	0.907932	+	0.419117i	$0.137660\pi$
$883$			8.12815e27i			0.838233i	−0.907932	+	0.419117i	$0.862340\pi$
$884$	−2.12049e28	−	2.42480e27i	−2.16341	−	0.247388i
$885$			1.43404e28i			1.44744i
$886$	−2.81056e27	−	3.15027e27i	−0.280655	−	0.314577i
$887$	1.97455e27			0.195072			0.0975359	−	0.995232i	$-0.468904\pi$
$887$	1.97455e27			0.195072			0.0975359	+	0.995232i	$0.468904\pi$
$888$	−6.64712e27	−	9.41774e27i	−0.649697	−	0.920500i
$889$	−4.22939e27			−0.408988
$890$	−7.17174e27	−	8.03857e27i	−0.686151	−	0.769084i
$891$		−	7.59406e27i		−	0.718846i
$892$	−2.05235e27	+	1.79478e28i	−0.192214	+	1.68091i
$893$		−	2.72022e27i		−	0.252067i
$894$	9.31996e27	−	8.31495e27i	0.854491	−	0.762348i
$895$	1.81553e27			0.164697
$896$	−4.26624e27	−	1.04709e28i	−0.382930	−	0.939851i
$897$	1.62076e28			1.43943
$898$	−1.67503e27	+	1.49441e27i	−0.147197	+	0.131324i
$899$			4.46232e27i			0.388010i
$900$	−6.71557e26	+	5.87278e27i	−0.0577802	+	0.505289i
$901$			3.07466e27i			0.261765i
$902$	6.23191e27	+	6.98515e27i	0.525000	+	0.588456i
$903$	−2.35192e28			−1.96060
$904$	−2.07214e26	−	2.93584e26i	−0.0170930	−	0.0242177i
$905$	−1.85780e27			−0.151648
$906$	5.45369e27	+	6.11286e27i	0.440527	+	0.493772i
$907$			2.34497e28i			1.87443i	0.348758	+	0.937213i	$0.386604\pi$
$907$			2.34497e28i			1.87443i	−0.348758	+	0.937213i	$0.613396\pi$
$908$	1.05703e28	+	1.20872e27i	0.836126	+	0.0956117i
$909$			1.82892e28i			1.43165i
$910$	−8.05913e27	+	7.19008e27i	−0.624303	+	0.556981i
$911$	−4.33758e27			−0.332524			−0.166262	−	0.986082i	$-0.553170\pi$
$911$	−4.33758e27			−0.332524			−0.166262	+	0.986082i	$0.553170\pi$
$912$	2.53794e27	+	5.88122e26i	0.192544	+	0.0446186i
$913$	7.66505e27			0.575496
$914$	1.42014e28	−	1.26700e28i	1.05522	−	0.941431i
$915$		−	7.71510e27i		−	0.567337i
$916$	2.31909e28	+	2.65190e27i	1.68776	+	0.192997i
$917$		−	1.98475e27i		−	0.142954i
$918$	−3.71072e27	−	4.15922e27i	−0.264516	−	0.296488i
$919$	−1.56252e28			−1.10237			−0.551187	−	0.834382i	$-0.685825\pi$
$919$	−1.56252e28			−1.10237			−0.551187	+	0.834382i	$0.685825\pi$
$920$	7.72892e27	−	5.45514e27i	0.539677	−	0.380909i
$921$	−3.23223e27			−0.223376
$922$	−5.51254e27	−	6.17883e27i	−0.377058	−	0.422632i
$923$			7.12774e27i			0.482543i
$924$	2.14674e27	−	1.87733e28i	0.143846	−	1.25793i
$925$		−	5.19058e27i		−	0.344246i
$926$	−7.22985e27	+	6.45023e27i	−0.474597	+	0.423419i
$927$	2.53541e28			1.64737
$928$	−1.08028e28	−	1.97389e28i	−0.694756	−	1.26946i
$929$	4.07635e27			0.259491			0.129746	−	0.991547i	$-0.458584\pi$
$929$	4.07635e27			0.259491			0.129746	+	0.991547i	$0.458584\pi$
$930$	3.45346e27	−	3.08106e27i	0.217604	−	0.194139i
$931$		−	6.49159e25i		−	0.00404883i
$932$	1.33682e27	−	1.16905e28i	0.0825320	−	0.721744i
$933$		−	1.73619e28i		−	1.06101i
$934$	−2.15228e27	−	2.41243e27i	−0.130198	−	0.145935i
$935$	−2.08191e28			−1.24667
$936$	−1.73896e28	+	1.22737e28i	−1.03079	+	0.727537i
$937$	−1.43374e28			−0.841285			−0.420642	−	0.907227i	$-0.638195\pi$
$937$	−1.43374e28			−0.841285			−0.420642	+	0.907227i	$0.638195\pi$
$938$	−7.09189e27	−	7.94907e27i	−0.411941	−	0.461732i
$939$			1.14631e28i			0.659140i
$940$	2.42104e28	+	2.76848e27i	1.37812	+	0.157589i
$941$			2.14704e28i			1.20987i	0.796275	+	0.604935i	$0.206801\pi$
$941$			2.14704e28i			1.20987i	−0.796275	+	0.604935i	$0.793199\pi$
$942$	−2.07280e27	+	1.84928e27i	−0.115631	+	0.103162i
$943$	1.48648e28			0.820912
$944$	5.49517e27	−	2.37135e28i	0.300433	−	1.29647i
$945$	−2.82059e27			−0.152665
$946$	−1.56962e28	+	1.40037e28i	−0.841066	+	0.750370i
$947$			6.72605e27i			0.356809i	0.983957	+	0.178404i	$0.0570935\pi$
$947$			6.72605e27i			0.356809i	−0.983957	+	0.178404i	$0.942907\pi$
$948$	−1.93334e28	−	2.21079e27i	−1.01538	−	0.116110i
$949$		−	3.18287e28i		−	1.65497i
$950$	7.80955e26	+	8.75347e26i	0.0402024	+	0.0450616i
$951$	3.13600e28			1.59831
$952$	2.27845e28	+	3.22814e28i	1.14971	+	1.62893i
$953$	2.63734e28			1.31760			0.658801	−	0.752317i	$-0.271064\pi$
$953$	2.63734e28			1.31760			0.658801	+	0.752317i	$0.271064\pi$
$954$	2.04130e27	+	2.28802e27i	0.100971	+	0.113175i
$955$		−	1.64981e28i		−	0.807981i
$956$	−5.83391e26	+	5.10176e27i	−0.0282885	+	0.247383i
$957$		−	3.76047e28i		−	1.80542i
$958$	−2.13856e28	+	1.90795e28i	−1.01660	+	0.906973i
$959$	1.31346e28			0.618215
$960$	−7.81733e27	+	2.19895e28i	−0.364319	+	1.02480i
$961$	−2.01128e28			−0.928110
$962$	1.39467e28	−	1.24428e28i	0.637248	−	0.568531i
$963$			9.34439e27i			0.422767i
$964$	−1.71240e27	+	1.49750e28i	−0.0767140	+	0.670865i
$965$		−	8.38011e27i		−	0.371741i
$966$	−1.99753e28	−	2.23896e28i	−0.877425	−	0.983477i
$967$	1.20363e28			0.523530			0.261765	−	0.965132i	$-0.415695\pi$
$967$	1.20363e28			0.523530			0.261765	+	0.965132i	$0.415695\pi$
$968$	3.64304e27	+	5.16151e27i	0.156909	+	0.222311i
$969$	−9.10409e27			−0.388294
$970$	−8.35829e27	−	9.36854e27i	−0.353009	−	0.395677i
$971$		−	6.80649e27i		−	0.284669i	−0.989819	−	0.142335i	$-0.954539\pi$
$971$		−	6.80649e27i		−	0.284669i	0.989819	−	0.142335i	$-0.0454609\pi$
$972$	3.44077e28	+	3.93455e27i	1.42504	+	0.162954i
$973$			3.08814e28i			1.26656i
$974$	2.51794e28	−	2.24642e28i	1.02267	−	0.912389i
$975$	−1.80040e28			−0.724143
$976$	−2.95638e27	+	1.27578e28i	−0.117757	+	0.508161i
$977$	−2.87955e28			−1.13586			−0.567932	−	0.823076i	$-0.692256\pi$
$977$	−2.87955e28			−1.13586			−0.567932	+	0.823076i	$0.692256\pi$
$978$	6.33303e27	−	5.65012e27i	0.247396	−	0.220718i
$979$			3.05594e28i			1.18225i
$980$	5.77761e26	+	6.60675e25i	0.0221361	+	0.00253128i
$981$		−	1.22824e28i		−	0.466046i
$982$	−1.99253e28	−	2.23336e28i	−0.748766	−	0.839267i
$983$	1.22714e28			0.456705			0.228352	−	0.973579i	$-0.426666\pi$
$983$	1.22714e28			0.456705			0.228352	+	0.973579i	$0.426666\pi$
$984$	−2.99597e28	+	2.11458e28i	−1.10429	+	0.779418i
$985$	−3.46626e28			−1.26537
$986$	5.23492e28	+	5.86765e28i	1.89269	+	2.12145i
$987$		−	7.72893e28i		−	2.76762i
$988$	−4.79901e26	+	4.19674e27i	−0.0170200	+	0.148840i
$989$			3.34024e28i			1.17331i
$990$	−1.54926e28	+	1.38220e28i	−0.539003	+	0.480880i
$991$	−2.34043e28			−0.806484			−0.403242	−	0.915093i	$-0.632117\pi$
$991$	−2.34043e28			−0.806484			−0.403242	+	0.915093i	$0.632117\pi$
$992$	−6.89132e27	+	3.77153e27i	−0.235202	+	0.128723i
$993$	−4.08894e25			−0.00138227
$994$	9.84643e27	−	8.78465e27i	0.329692	−	0.294140i
$995$		−	3.09409e28i		−	1.02616i
$996$	−3.41135e27	+	2.98323e28i	−0.112063	+	0.979993i
$997$		−	4.36013e28i		−	1.41872i	−0.704848	−	0.709359i	$-0.748985\pi$
$997$		−	4.36013e28i		−	1.41872i	0.704848	−	0.709359i	$-0.251015\pi$
$998$	−2.05531e28	−	2.30373e28i	−0.662425	−	0.742491i
$999$	4.88117e27			0.155830

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8.20.b.a.5.6	yes	18
3.2	odd	2		72.20.d.b.37.13		18
4.3	odd	2		32.20.b.a.17.16		18
8.3	odd	2		32.20.b.a.17.3		18
8.5	even	2	inner	8.20.b.a.5.5	✓	18
24.5	odd	2		72.20.d.b.37.14		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8.20.b.a.5.5	✓	18	8.5	even	2	inner
8.20.b.a.5.6	yes	18	1.1	even	1	trivial
32.20.b.a.17.3		18	8.3	odd	2
32.20.b.a.17.16		18	4.3	odd	2
72.20.d.b.37.13		18	3.2	odd	2
72.20.d.b.37.14		18	24.5	odd	2

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:	\( N \)	\(=\)	\( 8 = 2^{3} \)
Weight:	\( k \)	\(=\)	\( 20 \)
Character orbit:	\([\chi]\)	\(=\)	8.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-540.302 + 482.039i) q^{2} -49852.5i q^{3} +(59564.6 - 520893. i) q^{4} +3.24834e6i q^{5} +(2.40309e7 + 2.69354e7i) q^{6} +1.08353e8 q^{7} +(2.18908e8 + 3.10152e8i) q^{8} -1.32301e9 q^{9} +O(q^{10})\)	\(q+(-540.302 + 482.039i) q^{2} -49852.5i q^{3} +(59564.6 - 520893. i) q^{4} +3.24834e6i q^{5} +(2.40309e7 + 2.69354e7i) q^{6} +1.08353e8 q^{7} +(2.18908e8 + 3.10152e8i) q^{8} -1.32301e9 q^{9} +(-1.56583e9 - 1.75508e9i) q^{10} +6.67212e9i q^{11} +(-2.59678e10 - 2.96945e9i) q^{12} -4.23789e10i q^{13} +(-5.85433e10 + 5.22303e10i) q^{14} +1.61938e11 q^{15} +(-2.67782e11 - 6.20536e10i) q^{16} +9.60587e11 q^{17} +(7.14826e11 - 6.37743e11i) q^{18} -1.90113e11i q^{19} +(1.69204e12 + 1.93486e11i) q^{20} -5.40167e12i q^{21} +(-3.21622e12 - 3.60496e12i) q^{22} -7.67154e12 q^{23} +(1.54619e13 - 1.09131e13i) q^{24} +8.52179e12 q^{25} +(2.04283e13 + 2.28974e13i) q^{26} +8.01381e12i q^{27} +(6.45400e12 - 5.64403e13i) q^{28} -1.13055e14i q^{29} +(-8.74953e13 + 7.80603e13i) q^{30} -3.94702e13 q^{31} +(1.74595e14 - 9.55537e13i) q^{32} +3.32622e14 q^{33} +(-5.19007e14 + 4.63040e14i) q^{34} +3.51967e14i q^{35} +(-7.88047e13 + 6.89148e14i) q^{36} -6.09095e14i q^{37} +(9.16421e13 + 1.02719e14i) q^{38} -2.11270e15 q^{39} +(-1.00748e15 + 7.11087e14i) q^{40} -1.93765e15 q^{41} +(2.60381e15 + 2.91853e15i) q^{42} -4.35407e15i q^{43} +(3.47547e15 + 3.97422e14i) q^{44} -4.29759e15i q^{45} +(4.14495e15 - 3.69798e15i) q^{46} +1.43084e16 q^{47} +(-3.09353e15 + 1.33496e16i) q^{48} +3.41459e14 q^{49} +(-4.60434e15 + 4.10784e15i) q^{50} -4.78877e16i q^{51} +(-2.20749e16 - 2.52429e15i) q^{52} +3.20081e15i q^{53} +(-3.86297e15 - 4.32988e15i) q^{54} -2.16733e16 q^{55} +(2.37193e16 + 3.36059e16i) q^{56} -9.47763e15 q^{57} +(5.44971e16 + 6.10840e16i) q^{58} +8.85551e16i q^{59} +(9.64576e15 - 8.43523e16i) q^{60} -4.76424e16i q^{61} +(2.13258e16 - 1.90262e16i) q^{62} -1.43352e17 q^{63} +(-4.82737e16 + 1.35790e17i) q^{64} +1.37661e17 q^{65} +(-1.79716e17 + 1.60337e17i) q^{66} +1.35781e17i q^{67} +(5.72170e16 - 5.00363e17i) q^{68} +3.82446e17i q^{69} +(-1.69662e17 - 1.90168e17i) q^{70} -1.68191e17 q^{71} +(-2.89618e17 - 4.10335e17i) q^{72} +7.51049e17 q^{73} +(2.93607e17 + 3.29095e17i) q^{74} -4.24833e17i q^{75} +(-9.90289e16 - 1.13240e16i) q^{76} +7.22944e17i q^{77} +(1.14149e18 - 1.01840e18i) q^{78} +7.44514e17 q^{79} +(2.01571e17 - 8.69846e17i) q^{80} -1.13818e18 q^{81} +(1.04692e18 - 9.34023e17i) q^{82} -1.14882e18i q^{83} +(-2.81369e18 - 3.21748e17i) q^{84} +3.12031e18i q^{85} +(2.09883e18 + 2.35251e18i) q^{86} -5.63609e18 q^{87} +(-2.06937e18 + 1.46058e18i) q^{88} +4.58017e18 q^{89} +(2.07161e18 + 2.32200e18i) q^{90} -4.59188e18i q^{91} +(-4.56952e17 + 3.99606e18i) q^{92} +1.96769e18i q^{93} +(-7.73087e18 + 6.89722e18i) q^{94} +6.17553e17 q^{95} +(-4.76359e18 - 8.70402e18i) q^{96} +5.33795e18 q^{97} +(-1.84491e17 + 1.64597e17i) q^{98} -8.82730e18i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 458 q^{2} - 412108 q^{4} - 47240948 q^{6} - 80707216 q^{7} - 173313752 q^{8} - 6198727826 q^{9}+O(q^{10}) \) 18 * q - 458 * q^2 - 412108 * q^4 - 47240948 * q^6 - 80707216 * q^7 - 173313752 * q^8 - 6198727826 * q^9	\( 18 q - 458 q^{2} - 412108 q^{4} - 47240948 q^{6} - 80707216 q^{7} - 173313752 q^{8} - 6198727826 q^{9} + 758800104 q^{10} - 9351642296 q^{12} - 122453668784 q^{14} + 156097960432 q^{15} - 696212072432 q^{16} + 14121426692 q^{17} + 1813497117770 q^{18} + 6517087595632 q^{20} - 11074654117412 q^{22} + 2177121583952 q^{23} - 36473014189168 q^{24} - 44414474211734 q^{25} + 26782030269304 q^{26} - 97002327802784 q^{28} + 327847200544208 q^{30} + 428505770260416 q^{31} + 122449430282912 q^{32} - 185380269683736 q^{33} - 478448330325748 q^{34} - 10\!\cdots\!36 q^{36}+ \cdots + 88\!\cdots\!22 q^{98}+O(q^{100}) \) 18 * q - 458 * q^2 - 412108 * q^4 - 47240948 * q^6 - 80707216 * q^7 - 173313752 * q^8 - 6198727826 * q^9 + 758800104 * q^10 - 9351642296 * q^12 - 122453668784 * q^14 + 156097960432 * q^15 - 696212072432 * q^16 + 14121426692 * q^17 + 1813497117770 * q^18 + 6517087595632 * q^20 - 11074654117412 * q^22 + 2177121583952 * q^23 - 36473014189168 * q^24 - 44414474211734 * q^25 + 26782030269304 * q^26 - 97002327802784 * q^28 + 327847200544208 * q^30 + 428505770260416 * q^31 + 122449430282912 * q^32 - 185380269683736 * q^33 - 478448330325748 * q^34 - 1053851053424436 * q^36 - 486194587539796 * q^38 + 942830575043152 * q^39 - 1697818250610976 * q^40 + 1200260021141524 * q^41 + 4964410757677984 * q^42 + 7031781193616424 * q^44 - 14917443628457488 * q^46 - 1134160959992928 * q^47 - 3197964747991392 * q^48 + 31570092936329058 * q^49 - 34734151321861826 * q^50 - 26877456911772208 * q^52 + 32102189624395064 * q^54 - 51757047863478736 * q^55 + 52858270161183424 * q^56 - 7740744140670520 * q^57 - 20470056808312424 * q^58 - 25825294995349152 * q^60 + 93766686763697984 * q^62 + 430168668665078416 * q^63 - 253721318369185216 * q^64 - 184007586011668640 * q^65 + 479551889901302712 * q^66 + 201388986348307752 * q^68 - 340698473416023872 * q^70 - 1599477989199799056 * q^71 - 115475454880420648 * q^72 - 93004298989809068 * q^73 - 93558253821761240 * q^74 - 1090379619519933176 * q^76 + 2029949680340770544 * q^78 + 1813975801025264480 * q^79 + 3057120301750869696 * q^80 + 1801762045144484330 * q^81 - 2418785089528546244 * q^82 + 141493317659087296 * q^84 + 1332333723895598620 * q^86 - 13124960835754102512 * q^87 - 3097741184498130608 * q^88 + 4470509771045743540 * q^89 - 288100905697646824 * q^90 - 2965990502259463392 * q^92 - 3533635112749329696 * q^94 + 23809730986995679856 * q^95 - 2990158800543707584 * q^96 + 8246429789464117220 * q^97 + 8841667592735478822 * q^98

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