LMFDB - Embedded newform 8.20.b.a.5.9

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			5.9
Root			$0.500000 + 7755.46i$ of defining polynomial
Character	$\chi$	$=$	8.5
Dual form			8.20.b.a.5.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-97.3835 - 717.499i) q^{2} -31021.8i q^{3} +(-505321. + 139745. i) q^{4} +4.13771e6i q^{5} +(-2.22581e7 + 3.02101e6i) q^{6} +1.99482e8 q^{7} +(1.49477e8 + 3.48958e8i) q^{8} +1.99908e8 q^{9} +O(q^{10})$	\(q+(-97.3835 - 717.499i) q^{2} -31021.8i q^{3} +(-505321. + 139745. i) q^{4} +4.13771e6i q^{5} +(-2.22581e7 + 3.02101e6i) q^{6} +1.99482e8 q^{7} +(1.49477e8 + 3.48958e8i) q^{8} +1.99908e8 q^{9} +(2.96880e9 - 4.02945e8i) q^{10} -4.57503e9i q^{11} +(4.33515e9 + 1.56760e10i) q^{12} +6.56627e10i q^{13} +(-1.94262e10 - 1.43128e11i) q^{14} +1.28359e11 q^{15} +(2.35821e11 - 1.41232e11i) q^{16} -4.98732e11 q^{17} +(-1.94677e10 - 1.43434e11i) q^{18} -1.61295e11i q^{19} +(-5.78225e11 - 2.09087e12i) q^{20} -6.18829e12i q^{21} +(-3.28258e12 + 4.45532e11i) q^{22} +1.19892e13 q^{23} +(1.08253e13 - 4.63704e12i) q^{24} +1.95282e12 q^{25} +(4.71129e13 - 6.39447e12i) q^{26} -4.22570e13i q^{27} +(-1.00802e14 + 2.78766e13i) q^{28} +1.67505e13i q^{29} +(-1.25001e13 - 9.20977e13i) q^{30} +9.15425e13 q^{31} +(-1.24299e14 - 1.55447e14i) q^{32} -1.41926e14 q^{33} +(4.85682e13 + 3.57839e14i) q^{34} +8.25399e14i q^{35} +(-1.01018e14 + 2.79361e13i) q^{36} +3.53593e14i q^{37} +(-1.15729e14 + 1.57075e13i) q^{38} +2.03698e15 q^{39} +(-1.44389e15 + 6.18492e14i) q^{40} +1.29695e15 q^{41} +(-4.44009e15 + 6.02637e14i) q^{42} -2.72625e15i q^{43} +(6.39337e14 + 2.31186e15i) q^{44} +8.27161e14i q^{45} +(-1.16755e15 - 8.60222e15i) q^{46} -4.62334e14 q^{47} +(-4.38128e15 - 7.31558e15i) q^{48} +2.83941e16 q^{49} +(-1.90172e14 - 1.40115e15i) q^{50} +1.54716e16i q^{51} +(-9.17604e15 - 3.31807e16i) q^{52} -9.17027e15i q^{53} +(-3.03193e16 + 4.11513e15i) q^{54} +1.89301e16 q^{55} +(2.98179e16 + 6.96108e16i) q^{56} -5.00368e15 q^{57} +(1.20185e16 - 1.63123e15i) q^{58} -1.49941e16i q^{59} +(-6.48627e16 + 1.79376e16i) q^{60} +2.94422e16i q^{61} +(-8.91472e15 - 6.56816e16i) q^{62} +3.98780e16 q^{63} +(-9.94285e16 + 1.04322e17i) q^{64} -2.71693e17 q^{65} +(1.38212e16 + 1.01831e17i) q^{66} +3.06879e17i q^{67} +(2.52020e17 - 6.96953e16i) q^{68} -3.71926e17i q^{69} +(5.92222e17 - 8.03802e16i) q^{70} -3.81373e17 q^{71} +(2.98816e16 + 6.97595e16i) q^{72} +3.05182e17 q^{73} +(2.53702e17 - 3.44341e16i) q^{74} -6.05800e16i q^{75} +(2.25402e16 + 8.15060e16i) q^{76} -9.12635e17i q^{77} +(-1.98368e17 - 1.46153e18i) q^{78} -1.00134e18 q^{79} +(5.84378e17 + 9.75758e17i) q^{80} -1.07854e18 q^{81} +(-1.26302e17 - 9.30563e17i) q^{82} +2.81378e17i q^{83} +(8.64783e17 + 3.12707e18i) q^{84} -2.06361e18i q^{85} +(-1.95608e18 + 2.65492e17i) q^{86} +5.19633e17 q^{87} +(1.59649e18 - 6.83860e17i) q^{88} +5.08438e18 q^{89} +(5.93487e17 - 8.05518e16i) q^{90} +1.30985e19i q^{91} +(-6.05838e18 + 1.67543e18i) q^{92} -2.83981e18i q^{93} +(4.50237e16 + 3.31724e17i) q^{94} +6.67394e17 q^{95} +(-4.82226e18 + 3.85598e18i) q^{96} -4.80840e18 q^{97} +(-2.76512e18 - 2.03727e19i) q^{98} -9.14583e17i 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 $

$2$	−97.3835	−	717.499i	−0.134493	−	0.990915i
$2$	−97.3835	−	717.499i	−0.134493	−	0.990915i
$3$		−	31021.8i		−	0.909946i	−0.890505	−	0.454973i	$-0.849649\pi$
$3$		−	31021.8i		−	0.909946i	0.890505	−	0.454973i	$-0.150351\pi$
$4$	−505321.	+	139745.i	−0.963823	+	0.266543i
$5$			4.13771e6i			0.947426i	0.880679	+	0.473713i	$0.157087\pi$
$5$			4.13771e6i			0.947426i	−0.880679	+	0.473713i	$0.842913\pi$
$6$	−2.22581e7	+	3.02101e6i	−0.901678	+	0.122382i
$7$	1.99482e8			1.86841			0.934205	−	0.356738i	$-0.116111\pi$
$7$	1.99482e8			1.86841			0.934205	+	0.356738i	$0.116111\pi$
$8$	1.49477e8	+	3.48958e8i	0.393749	+	0.919218i
$9$	1.99908e8			0.171999
$10$	2.96880e9	−	4.02945e8i	0.938818	−	0.127422i
$11$		−	4.57503e9i		−	0.585010i	−0.956264	−	0.292505i	$-0.905511\pi$
$11$		−	4.57503e9i		−	0.585010i	0.956264	−	0.292505i	$-0.0944888\pi$
$12$	4.33515e9	+	1.56760e10i	0.242539	+	0.877027i
$13$			6.56627e10i			1.71734i	0.512526	+	0.858671i	$0.328710\pi$
$13$			6.56627e10i			1.71734i	−0.512526	+	0.858671i	$0.671290\pi$
$14$	−1.94262e10	−	1.43128e11i	−0.251288	−	1.85143i
$15$	1.28359e11			0.862106
$16$	2.35821e11	−	1.41232e11i	0.857910	−	0.513800i
$17$	−4.98732e11			−1.02000			−0.510002	−	0.860173i	$-0.670356\pi$
$17$	−4.98732e11			−1.02000			−0.510002	+	0.860173i	$0.670356\pi$
$18$	−1.94677e10	−	1.43434e11i	−0.0231327	−	0.170436i
$19$		−	1.61295e11i		−	0.114673i	−0.998355	−	0.0573367i	$-0.981739\pi$
$19$		−	1.61295e11i		−	0.114673i	0.998355	−	0.0573367i	$-0.0182609\pi$
$20$	−5.78225e11	−	2.09087e12i	−0.252529	−	0.913151i
$21$		−	6.18829e12i		−	1.70015i
$22$	−3.28258e12	+	4.45532e11i	−0.579695	+	0.0786798i
$23$	1.19892e13			1.38795			0.693977	−	0.719997i	$-0.255857\pi$
$23$	1.19892e13			1.38795			0.693977	+	0.719997i	$0.255857\pi$
$24$	1.08253e13	−	4.63704e12i	0.836439	−	0.358290i
$25$	1.95282e12			0.102384
$26$	4.71129e13	−	6.39447e12i	1.70174	−	0.230971i
$27$		−	4.22570e13i		−	1.06646i
$28$	−1.00802e14	+	2.78766e13i	−1.80082	+	0.498011i
$29$			1.67505e13i			0.214411i	0.994237	+	0.107206i	$0.0341904\pi$
$29$			1.67505e13i			0.214411i	−0.994237	+	0.107206i	$0.965810\pi$
$30$	−1.25001e13	−	9.20977e13i	−0.115947	−	0.854273i
$31$	9.15425e13			0.621851			0.310926	−	0.950434i	$-0.399361\pi$
$31$	9.15425e13			0.621851			0.310926	+	0.950434i	$0.399361\pi$
$32$	−1.24299e14	−	1.55447e14i	−0.624515	−	0.781013i
$33$	−1.41926e14			−0.532327
$34$	4.85682e13	+	3.57839e14i	0.137184	+	1.01074i
$35$			8.25399e14i			1.77018i
$36$	−1.01018e14	+	2.79361e13i	−0.165777	+	0.0458450i
$37$			3.53593e14i			0.447288i	0.974671	+	0.223644i	$0.0717952\pi$
$37$			3.53593e14i			0.447288i	−0.974671	+	0.223644i	$0.928205\pi$
$38$	−1.15729e14	+	1.57075e13i	−0.113632	+	0.0154228i
$39$	2.03698e15			1.56269
$40$	−1.44389e15	+	6.18492e14i	−0.870891	+	0.373048i
$41$	1.29695e15			0.618697			0.309348	−	0.950949i	$-0.399889\pi$
$41$	1.29695e15			0.618697			0.309348	+	0.950949i	$0.399889\pi$
$42$	−4.44009e15	+	6.02637e14i	−1.68470	+	0.228659i
$43$		−	2.72625e15i		−	0.827210i	−0.910456	−	0.413605i	$-0.864269\pi$
$43$		−	2.72625e15i		−	0.827210i	0.910456	−	0.413605i	$-0.135731\pi$
$44$	6.39337e14	+	2.31186e15i	0.155930	+	0.563846i
$45$			8.27161e14i			0.162956i
$46$	−1.16755e15	−	8.60222e15i	−0.186670	−	1.37534i
$47$	−4.62334e14			−0.0602595			−0.0301298	−	0.999546i	$-0.509592\pi$
$47$	−4.62334e14			−0.0602595			−0.0301298	+	0.999546i	$0.509592\pi$
$48$	−4.38128e15	−	7.31558e15i	−0.467530	−	0.780652i
$49$	2.83941e16			2.49095
$50$	−1.90172e14	−	1.40115e15i	−0.0137699	−	0.101454i
$51$			1.54716e16i			0.928149i
$52$	−9.17604e15	−	3.31807e16i	−0.457745	−	1.65521i
$53$		−	9.17027e15i		−	0.381734i	−0.981616	−	0.190867i	$-0.938870\pi$
$53$		−	9.17027e15i		−	0.381734i	0.981616	−	0.190867i	$-0.0611300\pi$
$54$	−3.03193e16	+	4.11513e15i	−1.05677	+	0.143431i
$55$	1.89301e16			0.554253
$56$	2.98179e16	+	6.96108e16i	0.735684	+	1.71748i
$57$	−5.00368e15			−0.104347
$58$	1.20185e16	−	1.63123e15i	0.212463	−	0.0288369i
$59$		−	1.49941e16i		−	0.225333i	−0.993633	−	0.112667i	$-0.964061\pi$
$59$		−	1.49941e16i		−	0.225333i	0.993633	−	0.112667i	$-0.0359392\pi$
$60$	−6.48627e16	+	1.79376e16i	−0.830918	+	0.229788i
$61$			2.94422e16i			0.322357i	0.986925	+	0.161178i	$0.0515294\pi$
$61$			2.94422e16i			0.322357i	−0.986925	+	0.161178i	$0.948471\pi$
$62$	−8.91472e15	−	6.56816e16i	−0.0836348	−	0.616201i
$63$	3.98780e16			0.321364
$64$	−9.94285e16	+	1.04322e17i	−0.689924	+	0.723882i
$65$	−2.71693e17			−1.62706
$66$	1.38212e16	+	1.01831e17i	0.0715944	+	0.527491i
$67$			3.06879e17i			1.37802i	0.724750	+	0.689012i	$0.241955\pi$
$67$			3.06879e17i			1.37802i	−0.724750	+	0.689012i	$0.758045\pi$
$68$	2.52020e17	−	6.96953e16i	0.983104	−	0.271875i
$69$		−	3.71926e17i		−	1.26296i
$70$	5.92222e17	−	8.03802e16i	1.75410	−	0.238077i
$71$	−3.81373e17			−0.987177			−0.493589	−	0.869696i	$-0.664315\pi$
$71$	−3.81373e17			−0.987177			−0.493589	+	0.869696i	$0.664315\pi$
$72$	2.98816e16	+	6.97595e16i	0.0677243	+	0.158105i
$73$	3.05182e17			0.606725			0.303363	−	0.952875i	$-0.401891\pi$
$73$	3.05182e17			0.606725			0.303363	+	0.952875i	$0.401891\pi$
$74$	2.53702e17	−	3.44341e16i	0.443224	−	0.0601572i
$75$		−	6.05800e16i		−	0.0931638i
$76$	2.25402e16	+	8.15060e16i	0.0305654	+	0.110525i
$77$		−	9.12635e17i		−	1.09304i
$78$	−1.98368e17	−	1.46153e18i	−0.210171	−	1.54849i
$79$	−1.00134e18			−0.939989			−0.469995	−	0.882669i	$-0.655744\pi$
$79$	−1.00134e18			−0.939989			−0.469995	+	0.882669i	$0.655744\pi$
$80$	5.84378e17	+	9.75758e17i	0.486787	+	0.812806i
$81$	−1.07854e18			−0.798417
$82$	−1.26302e17	−	9.30563e17i	−0.0832105	−	0.613076i
$83$			2.81378e17i			0.165214i	0.996582	+	0.0826072i	$0.0263247\pi$
$83$			2.81378e17i			0.165214i	−0.996582	+	0.0826072i	$0.973675\pi$
$84$	8.64783e17	+	3.12707e18i	0.453163	+	1.63864i
$85$		−	2.06361e18i		−	0.966379i
$86$	−1.95608e18	+	2.65492e17i	−0.819694	+	0.111254i
$87$	5.19633e17			0.195103
$88$	1.59649e18	−	6.83860e17i	0.537751	−	0.230347i
$89$	5.08438e18			1.53827			0.769136	−	0.639085i	$-0.220687\pi$
$89$	5.08438e18			1.53827			0.769136	+	0.639085i	$0.220687\pi$
$90$	5.93487e17	−	8.05518e16i	0.161476	−	0.0219165i
$91$			1.30985e19i			3.20870i
$92$	−6.05838e18	+	1.67543e18i	−1.33774	+	0.369949i
$93$		−	2.83981e18i		−	0.565851i
$94$	4.50237e16	+	3.31724e17i	0.00810450	+	0.0597121i
$95$	6.67394e17			0.108645
$96$	−4.82226e18	+	3.85598e18i	−0.710679	+	0.568274i
$97$	−4.80840e18			−0.642199			−0.321099	−	0.947046i	$-0.604052\pi$
$97$	−4.80840e18			−0.642199			−0.321099	+	0.947046i	$0.604052\pi$
$98$	−2.76512e18	−	2.03727e19i	−0.335016	−	2.46832i
$99$		−	9.14583e17i		−	0.100621i
$100$	−9.86800e17	+	2.72897e17i	−0.0986800	+	0.0272897i
$101$		−	7.71399e18i		−	0.701821i	−0.936409	−	0.350910i	$-0.885872\pi$
$101$		−	7.71399e18i		−	0.701821i	0.936409	−	0.350910i	$-0.114128\pi$
$102$	1.11008e19	−	1.50668e18i	0.919716	−	0.124830i
$103$	1.40439e19			1.06056			0.530280	−	0.847823i	$-0.322087\pi$
$103$	1.40439e19			1.06056			0.530280	+	0.847823i	$0.322087\pi$
$104$	−2.29135e19	+	9.81506e18i	−1.57861	+	0.676201i
$105$	2.56054e19			1.61077
$106$	−6.57966e18	+	8.93033e17i	−0.378266	+	0.0513407i
$107$			5.34860e18i			0.281251i	0.990063	+	0.140626i	$0.0449114\pi$
$107$			5.34860e18i			0.281251i	−0.990063	+	0.140626i	$0.955089\pi$
$108$	5.90520e18	+	2.13533e19i	0.284256	+	1.02787i
$109$		−	3.76071e19i		−	1.65851i	−0.558870	−	0.829255i	$-0.688765\pi$
$109$		−	3.76071e19i		−	1.65851i	0.558870	−	0.829255i	$-0.311235\pi$
$110$	−1.84348e18	−	1.35824e19i	−0.0745433	−	0.549218i
$111$	1.09691e19			0.407007
$112$	4.70419e19	−	2.81733e19i	1.60293	−	0.959988i
$113$	−4.67551e19			−1.46415			−0.732073	−	0.681227i	$-0.761447\pi$
$113$	−4.67551e19			−1.46415			−0.732073	+	0.681227i	$0.761447\pi$
$114$	4.87276e17	+	3.59013e18i	0.0140339	+	0.103399i
$115$			4.96078e19i			1.31498i
$116$	−2.34081e18	−	8.46440e18i	−0.0571498	−	0.206655i
$117$			1.31265e19i			0.295381i
$118$	−1.07582e19	+	1.46017e18i	−0.223286	+	0.0303058i
$119$	−9.94879e19			−1.90579
$120$	1.91868e19	+	4.47921e19i	0.339453	+	0.792464i
$121$	4.02282e19			0.657764
$122$	2.11247e19	−	2.86718e18i	0.319428	−	0.0433548i
$123$		−	4.02339e19i		−	0.562981i
$124$	−4.62583e19	+	1.27926e19i	−0.599355	+	0.165750i
$125$			8.70008e19i			1.04443i
$126$	−3.88346e18	−	2.86124e19i	−0.0432213	−	0.318445i
$127$	−8.35505e19			−0.862608			−0.431304	−	0.902207i	$-0.641946\pi$
$127$	−8.35505e19			−0.862608			−0.431304	+	0.902207i	$0.641946\pi$
$128$	8.45339e19	+	6.11806e19i	0.810095	+	0.586299i
$129$	−8.45733e19			−0.752716
$130$	2.64585e19	+	1.94940e20i	0.218828	+	1.61227i
$131$		−	2.06831e20i		−	1.59052i	−0.606271	−	0.795258i	$-0.707335\pi$
$131$		−	2.06831e20i		−	1.59052i	0.606271	−	0.795258i	$-0.292665\pi$
$132$	7.17180e19	−	1.98334e19i	0.513069	−	0.141888i
$133$		−	3.21755e19i		−	0.214257i
$134$	2.20186e20	−	2.98850e19i	1.36550	−	0.185335i
$135$	1.74847e20			1.01039
$136$	−7.45488e19	−	1.74037e20i	−0.401625	−	0.937607i
$137$	−1.41521e19			−0.0711174			−0.0355587	−	0.999368i	$-0.511321\pi$
$137$	−1.41521e19			−0.0711174			−0.0355587	+	0.999368i	$0.511321\pi$
$138$	−2.66857e20	+	3.62195e19i	−1.25149	+	0.169860i
$139$			1.86769e20i			0.817832i	0.912572	+	0.408916i	$0.134093\pi$
$139$			1.86769e20i			0.817832i	−0.912572	+	0.408916i	$0.865907\pi$
$140$	−1.15345e20	−	4.17091e20i	−0.471828	−	1.70614i
$141$			1.43424e19i			0.0548329i
$142$	3.71394e19	+	2.73634e20i	0.132769	+	0.978208i
$143$	3.00409e20			1.00466
$144$	4.71424e19	−	2.82334e19i	0.147560	−	0.0883730i
$145$	−6.93090e19			−0.203139
$146$	−2.97197e19	−	2.18968e20i	−0.0816004	−	0.601213i
$147$		−	8.80837e20i		−	2.26663i
$148$	−4.94128e19	−	1.78678e20i	−0.119221	−	0.431106i
$149$			7.59665e20i			1.71930i	0.510880	+	0.859652i	$0.329320\pi$
$149$			7.59665e20i			1.71930i	−0.510880	+	0.859652i	$0.670680\pi$
$150$	−4.34661e19	+	5.89949e18i	−0.0923174	+	0.0125299i
$151$	2.87041e20			0.572351			0.286176	−	0.958177i	$-0.407616\pi$
$151$	2.87041e20			0.572351			0.286176	+	0.958177i	$0.407616\pi$
$152$	5.62854e19	−	2.41099e19i	0.105410	−	0.0451525i
$153$	−9.97003e19			−0.175440
$154$	−6.54814e20	+	8.88755e19i	−1.08311	+	0.147006i
$155$			3.78776e20i			0.589158i
$156$	−1.02933e21	+	2.84658e20i	−1.50616	+	0.416523i
$157$			9.59877e20i			1.32181i	0.750470	+	0.660905i	$0.229827\pi$
$157$			9.59877e20i			1.32181i	−0.750470	+	0.660905i	$0.770173\pi$
$158$	9.75137e19	+	7.18458e20i	0.126422	+	0.931449i
$159$	−2.84478e20			−0.347358
$160$	6.43196e20	−	5.14313e20i	0.739952	−	0.591682i
$161$	2.39162e21			2.59327
$162$	1.05032e20	+	7.73854e20i	0.107382	+	0.791163i
$163$		−	3.08315e20i		−	0.297312i	−0.988889	−	0.148656i	$-0.952505\pi$
$163$		−	3.08315e20i		−	0.297312i	0.988889	−	0.148656i	$-0.0474948\pi$
$164$	−6.55378e20	+	1.81243e20i	−0.596314	+	0.164909i
$165$		−	5.87248e20i		−	0.504340i
$166$	2.01888e20	−	2.74015e19i	0.163713	−	0.0222202i
$167$	−1.11914e21			−0.857192			−0.428596	−	0.903496i	$-0.640992\pi$
$167$	−1.11914e21			−0.857192			−0.428596	+	0.903496i	$0.640992\pi$
$168$	2.15946e21	−	9.25006e20i	1.56281	−	0.669432i
$169$	−2.84967e21			−1.94927
$170$	−1.48064e21	+	2.00961e20i	−0.957599	+	0.129971i
$171$		−	3.22442e19i		−	0.0197237i
$172$	3.80980e20	+	1.37763e21i	0.220487	+	0.797284i
$173$		−	2.10335e21i		−	1.15206i	−0.817429	−	0.576029i	$-0.804602\pi$
$173$		−	2.10335e21i		−	1.15206i	0.817429	−	0.576029i	$-0.195398\pi$
$174$	−5.06036e19	−	3.72836e20i	−0.0262400	−	0.193330i
$175$	3.89552e20			0.191295
$176$	−6.46141e20	−	1.07888e21i	−0.300578	−	0.501886i
$177$	−4.65143e20			−0.205041
$178$	−4.95135e20	−	3.64804e21i	−0.206887	−	1.52430i
$179$		−	6.31027e20i		−	0.250002i	−0.992157	−	0.125001i	$-0.960107\pi$
$179$		−	6.31027e20i		−	0.250002i	0.992157	−	0.125001i	$-0.0398935\pi$
$180$	−1.15592e20	−	4.17982e20i	−0.0434348	−	0.157061i
$181$			2.79988e21i			0.998144i	0.866561	+	0.499072i	$0.166326\pi$
$181$			2.79988e21i			0.998144i	−0.866561	+	0.499072i	$0.833674\pi$
$182$	9.39817e21	−	1.27558e21i	3.17955	−	0.431548i
$183$	9.13351e20			0.293327
$184$	1.79210e21	+	4.18372e21i	0.546505	+	1.27583i
$185$	−1.46306e21			−0.423772
$186$	−2.03756e21	+	2.76551e20i	−0.560710	+	0.0761031i
$187$			2.28171e21i			0.596713i
$188$	2.33627e20	−	6.46089e19i	0.0580795	−	0.0160617i
$189$		−	8.42950e21i		−	1.99258i
$190$	−6.49932e19	−	4.78855e20i	−0.0146120	−	0.107658i
$191$	−3.15698e21			−0.675235			−0.337617	−	0.941283i	$-0.609621\pi$
$191$	−3.15698e21			−0.675235			−0.337617	+	0.941283i	$0.609621\pi$
$192$	3.23627e21	+	3.08445e21i	0.658693	+	0.627793i
$193$	−2.43398e21			−0.471544			−0.235772	−	0.971808i	$-0.575762\pi$
$193$	−2.43398e21			−0.471544			−0.235772	+	0.971808i	$0.575762\pi$
$194$	4.68259e20	+	3.45002e21i	0.0863714	+	0.636364i
$195$			8.42843e21i			1.48053i
$196$	−1.43481e22	+	3.96794e21i	−2.40084	+	0.663945i
$197$		−	6.13502e21i		−	0.978109i	−0.872253	−	0.489054i	$-0.837342\pi$
$197$		−	6.13502e21i		−	0.978109i	0.872253	−	0.489054i	$-0.162658\pi$
$198$	−6.56212e20	+	8.90653e19i	−0.0997069	+	0.0135328i
$199$	−1.73967e21			−0.251979			−0.125989	−	0.992032i	$-0.540211\pi$
$199$	−1.73967e21			−0.251979			−0.125989	+	0.992032i	$0.540211\pi$
$200$	2.91901e20	+	6.81452e20i	0.0403135	+	0.0941132i
$201$	9.51996e21			1.25393
$202$	−5.53478e21	+	7.51216e20i	−0.695444	+	0.0943902i
$203$			3.34143e21i			0.400608i
$204$	−2.16208e21	−	7.81811e21i	−0.247391	−	0.894571i
$205$			5.36642e21i			0.586170i
$206$	−1.36765e21	−	1.00765e22i	−0.142638	−	1.05092i
$207$	2.39673e21			0.238727
$208$	9.27369e21	+	1.54846e22i	0.882370	+	1.47333i
$209$	−7.37931e20			−0.0670851
$210$	−2.49354e21	−	1.83718e22i	−0.216637	−	1.59613i
$211$			7.52340e21i			0.624785i	0.949953	+	0.312393i	$0.101130\pi$
$211$			7.52340e21i			0.624785i	−0.949953	+	0.312393i	$0.898870\pi$
$212$	1.28150e21	+	4.63393e21i	0.101748	+	0.367924i
$213$			1.18309e22i			0.898278i
$214$	3.83762e21	−	5.20866e20i	0.278696	−	0.0378264i
$215$	1.12805e22			0.783720
$216$	1.47459e22	−	6.31644e21i	0.980305	−	0.419915i
$217$	1.82611e22			1.16187
$218$	−2.69831e22	+	3.66231e21i	−1.64344	+	0.223058i
$219$		−	9.46731e21i		−	0.552087i
$220$	−9.56580e21	+	2.64539e21i	−0.534202	+	0.147732i
$221$		−	3.27481e22i		−	1.75170i
$222$	−1.06821e21	−	7.87031e21i	−0.0547397	−	0.403310i
$223$	7.44415e21			0.365526			0.182763	−	0.983157i	$-0.441496\pi$
$223$	7.44415e21			0.365526			0.182763	+	0.983157i	$0.441496\pi$
$224$	−2.47954e22	−	3.10089e22i	−1.16685	−	1.45925i
$225$	3.90384e20			0.0176099
$226$	4.55318e21	+	3.35467e22i	0.196918	+	1.45084i
$227$		−	1.39850e22i		−	0.579985i	−0.957029	−	0.289993i	$-0.906347\pi$
$227$		−	1.39850e22i		−	0.579985i	0.957029	−	0.289993i	$-0.0936528\pi$
$228$	2.52846e21	−	6.99240e20i	0.100572	−	0.0278128i
$229$			5.66250e21i			0.216059i	0.994148	+	0.108029i	$0.0344540\pi$
$229$			5.66250e21i			0.216059i	−0.994148	+	0.108029i	$0.965546\pi$
$230$	3.55935e22	−	4.83098e21i	1.30304	−	0.176856i
$231$	−2.83116e22			−0.994605
$232$	−5.84524e21	+	2.50382e21i	−0.197091	+	0.0844242i
$233$	−1.45417e22			−0.470690			−0.235345	−	0.971912i	$-0.575622\pi$
$233$	−1.45417e22			−0.470690			−0.235345	+	0.971912i	$0.575622\pi$
$234$	9.41824e21	−	1.27830e21i	0.292698	−	0.0397268i
$235$		−	1.91300e21i		−	0.0570915i
$236$	2.09535e21	+	7.57682e21i	0.0600609	+	0.217181i
$237$			3.10633e22i			0.855339i
$238$	9.68848e21	+	7.13825e22i	0.256315	+	1.88847i
$239$	1.30002e22			0.330498			0.165249	−	0.986252i	$-0.447157\pi$
$239$	1.30002e22			0.330498			0.165249	+	0.986252i	$0.447157\pi$
$240$	3.02698e22	−	1.81285e22i	0.739610	−	0.442950i
$241$	−7.23517e22			−1.69937			−0.849683	−	0.527293i	$-0.823207\pi$
$241$	−7.23517e22			−1.69937			−0.849683	+	0.527293i	$0.823207\pi$
$242$	−3.91757e21	−	2.88637e22i	−0.0884648	−	0.651788i
$243$		−	1.56553e22i		−	0.339939i
$244$	−4.11440e21	−	1.48778e22i	−0.0859218	−	0.310695i
$245$			1.17487e23i			2.35999i
$246$	−2.88678e22	+	3.91812e21i	−0.557866	+	0.0757171i
$247$	1.05911e22			0.196934
$248$	1.36835e22	+	3.19445e22i	0.244853	+	0.571617i
$249$	8.72885e21			0.150336
$250$	6.24230e22	−	8.47244e21i	1.03494	−	0.140468i
$251$		−	9.98560e22i		−	1.59395i	−0.604015	−	0.796973i	$-0.706433\pi$
$251$		−	9.98560e22i		−	1.59395i	0.604015	−	0.796973i	$-0.293567\pi$
$252$	−2.01512e22	+	5.57275e21i	−0.309739	+	0.0856573i
$253$		−	5.48508e22i		−	0.811966i
$254$	8.13644e21	+	5.99474e22i	0.116015	+	0.854771i
$255$	−6.40169e22			−0.879352
$256$	3.56648e22	−	6.66109e22i	0.472020	−	0.881588i
$257$	−4.78055e22			−0.609696			−0.304848	−	0.952401i	$-0.598606\pi$
$257$	−4.78055e22			−0.609696			−0.304848	+	0.952401i	$0.598606\pi$
$258$	8.23605e21	+	6.06813e22i	0.101235	+	0.745877i
$259$			7.05353e22i			0.835716i
$260$	1.37292e23	−	3.79678e22i	1.56819	−	0.433680i
$261$			3.34856e21i			0.0368786i
$262$	−1.48401e23	+	2.01419e22i	−1.57607	+	0.213914i
$263$	3.49017e22			0.357493			0.178746	−	0.983895i	$-0.442796\pi$
$263$	3.49017e22			0.357493			0.178746	+	0.983895i	$0.442796\pi$
$264$	−2.12146e22	−	4.95261e22i	−0.209603	−	0.489325i
$265$	3.79439e22			0.361665
$266$	−2.30859e22	+	3.13336e21i	−0.212310	+	0.0288161i
$267$		−	1.57727e23i		−	1.39974i
$268$	−4.28849e22	−	1.55073e23i	−0.367302	−	1.32817i
$269$		−	9.92799e22i		−	0.820757i	−0.911915	−	0.410378i	$-0.865397\pi$
$269$		−	9.92799e22i		−	0.820757i	0.911915	−	0.410378i	$-0.134603\pi$
$270$	−1.70272e22	−	1.25453e23i	−0.135890	−	1.00121i
$271$	−1.06206e22			−0.0818350			−0.0409175	−	0.999163i	$-0.513028\pi$
$271$	−1.06206e22			−0.0818350			−0.0409175	+	0.999163i	$0.513028\pi$
$272$	−1.17611e23	+	7.04370e22i	−0.875072	+	0.524078i
$273$	4.06340e23			2.91974
$274$	1.37818e21	+	1.01541e22i	0.00956481	+	0.0704713i
$275$		−	8.93420e21i		−	0.0598956i
$276$	5.19749e22	+	1.87942e23i	0.336633	+	1.21727i
$277$			2.31666e23i			1.44979i	0.688861	+	0.724894i	$0.258111\pi$
$277$			2.31666e23i			1.44979i	−0.688861	+	0.724894i	$0.741889\pi$
$278$	1.34007e23	−	1.81882e22i	0.810402	−	0.109993i
$279$	1.83000e22			0.106958
$280$	−2.88030e23	+	1.23378e23i	−1.62718	+	0.697006i
$281$	−2.77000e23			−1.51276			−0.756379	−	0.654133i	$-0.773033\pi$
$281$	−2.77000e23			−1.51276			−0.756379	+	0.654133i	$0.773033\pi$
$282$	1.02907e22	−	1.39672e21i	0.0543347	−	0.00737465i
$283$			2.41819e23i			1.23458i	0.786735	+	0.617290i	$0.211770\pi$
$283$			2.41819e23i			1.23458i	−0.786735	+	0.617290i	$0.788230\pi$
$284$	1.92716e23	−	5.32949e22i	0.951464	−	0.263125i
$285$		−	2.07038e22i		−	0.0988607i
$286$	−2.92548e22	−	2.15543e23i	−0.135120	−	0.995534i
$287$	2.58719e23			1.15598
$288$	−2.48483e22	−	3.10751e22i	−0.107416	−	0.134333i
$289$	9.66089e21			0.0404099
$290$	6.74955e21	+	4.97291e22i	0.0273208	+	0.201293i
$291$			1.49165e23i			0.584366i
$292$	−1.54215e23	+	4.26477e22i	−0.584776	+	0.161718i
$293$		−	1.53173e23i		−	0.562262i	−0.959669	−	0.281131i	$-0.909290\pi$
$293$		−	1.53173e23i		−	0.562262i	0.959669	−	0.281131i	$-0.0907096\pi$
$294$	−6.32000e23	+	8.57790e22i	−2.24604	+	0.304847i
$295$	6.20411e22			0.213487
$296$	−1.23389e23	+	5.28539e22i	−0.411155	+	0.176119i
$297$	−1.93327e23			−0.623887
$298$	5.45059e23	−	7.39788e22i	1.70368	−	0.231235i
$299$			7.87242e23i			2.38359i
$300$	8.46576e21	+	3.06123e22i	0.0248321	+	0.0897935i
$301$		−	5.43838e23i		−	1.54557i
$302$	−2.79530e22	−	2.05951e23i	−0.0769774	−	0.567151i
$303$	−2.39302e23			−0.638619
$304$	−2.27801e22	−	3.80368e22i	−0.0589192	−	0.0983795i
$305$	−1.21823e23			−0.305409
$306$	9.70917e21	+	7.15349e22i	0.0235955	+	0.173846i
$307$		−	7.97844e23i		−	1.87976i	−0.341499	−	0.939882i	$-0.610934\pi$
$307$		−	7.97844e23i		−	1.87976i	0.341499	−	0.939882i	$-0.389066\pi$
$308$	1.27536e23	+	4.61173e23i	0.291341	+	1.05349i
$309$		−	4.35668e23i		−	0.965051i
$310$	2.71772e23	−	3.68866e22i	0.583805	−	0.0792378i
$311$	−2.79286e23			−0.581870			−0.290935	−	0.956743i	$-0.593966\pi$
$311$	−2.79286e23			−0.581870			−0.290935	+	0.956743i	$0.593966\pi$
$312$	3.04481e23	+	7.10820e23i	0.615306	+	1.43645i
$313$	3.46353e23			0.678966			0.339483	−	0.940612i	$-0.389748\pi$
$313$	3.46353e23			0.678966			0.339483	+	0.940612i	$0.389748\pi$
$314$	6.88711e23	−	9.34762e22i	1.30980	−	0.177774i
$315$			1.65004e23i			0.304469i
$316$	5.05997e23	−	1.39932e23i	0.905983	−	0.250547i
$317$			1.56822e23i			0.272485i	0.990675	+	0.136243i	$0.0435027\pi$
$317$			1.56822e23i			0.272485i	−0.990675	+	0.136243i	$0.956497\pi$
$318$	2.77035e22	+	2.04113e23i	0.0467172	+	0.344202i
$319$	7.66342e22			0.125433
$320$	−4.31656e23	−	4.11407e23i	−0.685824	−	0.653652i
$321$	1.65923e23			0.255923
$322$	−2.32905e23	−	1.71599e24i	−0.348777	−	2.56970i
$323$			8.04432e22i			0.116968i
$324$	5.45011e23	−	1.50721e23i	0.769533	−	0.212812i
$325$			1.28227e23i			0.175828i
$326$	−2.21216e23	+	3.00248e22i	−0.294611	+	0.0399865i
$327$	−1.16664e24			−1.50915
$328$	1.93865e23	+	4.52583e23i	0.243611	+	0.568717i
$329$	−9.22272e22			−0.112589
$330$	−4.21349e23	+	5.71882e22i	−0.499758	+	0.0678304i
$331$		−	2.31290e23i		−	0.266558i	−0.991079	−	0.133279i	$-0.957449\pi$
$331$		−	2.31290e23i		−	0.266558i	0.991079	−	0.133279i	$-0.0425506\pi$
$332$	−3.93212e22	−	1.42186e23i	−0.0440367	−	0.159237i
$333$			7.06859e22i			0.0769330i
$334$	1.08986e23	+	8.02982e23i	0.115287	+	0.849404i
$335$	−1.26978e24			−1.30558
$336$	−8.73986e23	−	1.45933e24i	−0.873537	−	1.45858i
$337$	−1.20234e24			−1.16827			−0.584133	−	0.811658i	$-0.698565\pi$
$337$	−1.20234e24			−1.16827			−0.584133	+	0.811658i	$0.698565\pi$
$338$	2.77511e23	+	2.04464e24i	0.262163	+	1.93156i
$339$			1.45043e24i			1.33229i
$340$	2.88379e23	+	1.04278e24i	0.257581	+	0.931419i
$341$		−	4.18809e23i		−	0.363789i
$342$	−2.31352e22	+	3.14005e21i	−0.0195445	+	0.00265271i
$343$	3.39024e24			2.78571
$344$	9.51348e23	−	4.07512e23i	0.760387	−	0.325713i
$345$	1.53892e24			1.19656
$346$	−1.50915e24	+	2.04832e23i	−1.14159	+	0.154944i
$347$		−	1.44600e24i		−	1.06424i	−0.846669	−	0.532120i	$-0.821396\pi$
$347$		−	1.44600e24i		−	1.06424i	0.846669	−	0.532120i	$-0.178604\pi$
$348$	−2.62581e23	+	7.26161e22i	−0.188045	+	0.0520032i
$349$			1.34094e24i			0.934474i	0.884132	+	0.467237i	$0.154751\pi$
$349$			1.34094e24i			0.934474i	−0.884132	+	0.467237i	$0.845249\pi$
$350$	−3.79359e22	−	2.79503e23i	−0.0257279	−	0.189557i
$351$	2.77471e24			1.83147
$352$	−7.11175e23	+	5.68671e23i	−0.456900	+	0.365347i
$353$	−1.54294e24			−0.964916			−0.482458	−	0.875919i	$-0.660256\pi$
$353$	−1.54294e24			−0.964916			−0.482458	+	0.875919i	$0.660256\pi$
$354$	4.52973e22	+	3.33740e23i	0.0275766	+	0.203178i
$355$		−	1.57801e24i		−	0.935277i
$356$	−2.56924e24	+	7.10517e23i	−1.48262	+	0.410015i
$357$			3.08630e24i			1.73416i
$358$	−4.52761e23	+	6.14516e22i	−0.247731	+	0.0336236i
$359$	−2.95210e24			−1.57302			−0.786509	−	0.617579i	$-0.788114\pi$
$359$	−2.95210e24			−1.57302			−0.786509	+	0.617579i	$0.788114\pi$
$360$	−2.88645e23	+	1.23641e23i	−0.149792	+	0.0641638i
$361$	1.95240e24			0.986850
$362$	2.00891e24	−	2.72662e23i	0.989075	−	0.134244i
$363$		−	1.24795e24i		−	0.598529i
$364$	−1.83045e24	−	6.61896e24i	−0.855255	−	3.09262i
$365$			1.26276e24i			0.574827i
$366$	−8.89453e22	−	6.55328e23i	−0.0394505	−	0.290662i
$367$	3.31290e23			0.143179			0.0715897	−	0.997434i	$-0.477193\pi$
$367$	3.31290e23			0.143179			0.0715897	+	0.997434i	$0.477193\pi$
$368$	2.82729e24	−	1.69326e24i	1.19074	−	0.713130i
$369$	2.59271e23			0.106415
$370$	1.42478e23	+	1.04975e24i	0.0569945	+	0.419922i
$371$		−	1.82930e24i		−	0.713236i
$372$	3.96850e23	+	1.43502e24i	0.150823	+	0.545380i
$373$		−	3.88171e24i		−	1.43810i	−0.694959	−	0.719049i	$-0.744578\pi$
$373$		−	3.88171e24i		−	1.43810i	0.694959	−	0.719049i	$-0.255422\pi$
$374$	1.63712e24	−	2.22201e23i	0.591291	−	0.0802538i
$375$	2.69892e24			0.950372
$376$	−6.91082e22	−	1.61335e23i	−0.0237271	−	0.0553917i
$377$	−1.09989e24			−0.368218
$378$	−6.04816e24	+	8.20894e23i	−1.97447	+	0.267988i
$379$			2.11088e24i			0.672035i	0.941856	+	0.336018i	$0.109080\pi$
$379$			2.11088e24i			0.672035i	−0.941856	+	0.336018i	$0.890920\pi$
$380$	−3.37248e23	+	9.32651e22i	−0.104714	+	0.0289584i
$381$			2.59189e24i			0.784926i
$382$	3.07438e23	+	2.26513e24i	0.0908145	+	0.669100i
$383$	−1.98043e24			−0.570652			−0.285326	−	0.958431i	$-0.592102\pi$
$383$	−1.98043e24			−0.570652			−0.285326	+	0.958431i	$0.592102\pi$
$384$	1.89793e24	−	2.62239e24i	0.533500	−	0.737142i
$385$	3.77622e24			1.03557
$386$	2.37029e23	+	1.74638e24i	0.0634195	+	0.467260i
$387$		−	5.44999e23i		−	0.142279i
$388$	2.42979e24	−	6.71951e23i	0.618966	−	0.171173i
$389$		−	1.22247e24i		−	0.303891i	−0.988389	−	0.151946i	$-0.951446\pi$
$389$		−	1.22247e24i		−	0.303891i	0.988389	−	0.151946i	$-0.0485538\pi$
$390$	6.04739e24	−	8.20790e23i	1.46708	−	0.199122i
$391$	−5.97938e24			−1.41572
$392$	4.24426e24	+	9.90836e24i	0.980809	+	2.28973i
$393$	−6.41627e24			−1.44728
$394$	−4.40187e24	+	5.97450e23i	−0.969222	+	0.131549i
$395$		−	4.14325e24i		−	0.890570i
$396$	1.27808e23	+	4.62158e23i	0.0268198	+	0.0969809i
$397$			4.16074e24i			0.852435i	0.904621	+	0.426217i	$0.140154\pi$
$397$			4.16074e24i			0.852435i	−0.904621	+	0.426217i	$0.859846\pi$
$398$	1.69416e23	+	1.24821e24i	0.0338894	+	0.249689i
$399$	−9.98143e23			−0.194962
$400$	4.60515e23	−	2.75801e23i	0.0878362	−	0.0526049i
$401$	−1.58548e24			−0.295317			−0.147659	−	0.989038i	$-0.547174\pi$
$401$	−1.58548e24			−0.295317			−0.147659	+	0.989038i	$0.547174\pi$
$402$	−9.27087e23	−	6.83056e24i	−0.168645	−	1.24254i
$403$			6.01093e24i			1.06793i
$404$	1.07799e24	+	3.89804e24i	0.187065	+	0.676431i
$405$		−	4.46270e24i		−	0.756441i
$406$	2.39747e24	−	3.25400e23i	0.396969	−	0.0538791i
$407$	1.61770e24			0.261668
$408$	−5.39893e24	+	2.31264e24i	−0.853171	+	0.365457i
$409$	−3.75980e24			−0.580488			−0.290244	−	0.956953i	$-0.593737\pi$
$409$	−3.75980e24			−0.580488			−0.290244	+	0.956953i	$0.593737\pi$
$410$	3.85040e24	−	5.22601e23i	0.580844	−	0.0788358i
$411$			4.39025e23i			0.0647130i
$412$	−7.09669e24	+	1.96257e24i	−1.02219	+	0.282684i
$413$		−	2.99104e24i		−	0.421015i
$414$	−2.33402e23	−	1.71965e24i	−0.0321071	−	0.236558i
$415$	−1.16426e24			−0.156528
$416$	1.02071e25	−	8.16181e24i	1.34127	−	1.07251i
$417$	5.79392e24			0.744183
$418$	7.18623e22	+	5.29465e23i	0.00902249	+	0.0664756i
$419$			1.07424e25i			1.31846i	0.751942	+	0.659229i	$0.229117\pi$
$419$			1.07424e25i			1.31846i	−0.751942	+	0.659229i	$0.770883\pi$
$420$	−1.29389e25	+	3.57822e24i	−1.55249	+	0.429338i
$421$		−	1.11373e25i		−	1.30648i	−0.757153	−	0.653238i	$-0.773410\pi$
$421$		−	1.11373e25i		−	1.30648i	0.757153	−	0.653238i	$-0.226590\pi$
$422$	5.39803e24	−	7.32655e23i	0.619109	−	0.0840294i
$423$	−9.24241e22			−0.0103646
$424$	3.20004e24	−	1.37074e24i	0.350897	−	0.150307i
$425$	−9.73933e23			−0.104432
$426$	8.48864e24	−	1.15213e24i	0.890116	−	0.120812i
$427$			5.87318e24i			0.602294i
$428$	−7.47441e23	−	2.70276e24i	−0.0749654	−	0.271076i
$429$		−	9.31922e24i		−	0.914188i
$430$	−1.09853e24	−	8.09371e24i	−0.105405	−	0.776600i
$431$	3.26188e24			0.306150			0.153075	−	0.988215i	$-0.451082\pi$
$431$	3.26188e24			0.306150			0.153075	+	0.988215i	$0.451082\pi$
$432$	−5.96805e24	−	9.96506e24i	−0.547945	−	0.914923i
$433$	1.10816e25			0.995327			0.497663	−	0.867370i	$-0.334191\pi$
$433$	1.10816e25			0.995327			0.497663	+	0.867370i	$0.334191\pi$
$434$	−1.77833e24	−	1.31023e25i	−0.156264	−	1.15132i
$435$			2.15009e24i			0.184845i
$436$	5.25541e24	+	1.90037e25i	0.442064	+	1.59851i
$437$		−	1.93380e24i		−	0.159161i
$438$	−6.79278e24	+	9.21959e23i	−0.547071	+	0.0742519i
$439$	1.83855e25			1.44898			0.724489	−	0.689286i	$-0.242076\pi$
$439$	1.83855e25			1.44898			0.724489	+	0.689286i	$0.242076\pi$
$440$	2.82962e24	+	6.60583e24i	0.218236	+	0.509480i
$441$	5.67620e24			0.428441
$442$	−2.34967e25	+	3.18912e24i	−1.73578	+	0.235592i
$443$		−	8.55980e24i		−	0.618911i	−0.950914	−	0.309456i	$-0.899853\pi$
$443$		−	8.55980e24i		−	0.618911i	0.950914	−	0.309456i	$-0.100147\pi$
$444$	−5.54291e24	+	1.53288e24i	−0.392283	+	0.108485i
$445$			2.10377e25i			1.45740i
$446$	−7.24937e23	−	5.34117e24i	−0.0491608	−	0.362205i
$447$	2.35662e25			1.56447
$448$	−1.98342e25	+	2.08104e25i	−1.28906	+	1.35251i
$449$	−1.57616e25			−1.00290			−0.501452	−	0.865186i	$-0.667201\pi$
$449$	−1.57616e25			−1.00290			−0.501452	+	0.865186i	$0.667201\pi$
$450$	−3.80169e22	−	2.80100e23i	−0.00236842	−	0.0174499i
$451$		−	5.93360e24i		−	0.361944i
$452$	2.36263e25	−	6.53380e24i	1.41118	−	0.390257i
$453$		−	8.90453e24i		−	0.520809i
$454$	−1.00342e25	+	1.36191e24i	−0.574716	+	0.0780041i
$455$	−5.41979e25			−3.04001
$456$	−7.47934e23	−	1.74608e24i	−0.0410863	−	0.0959173i
$457$	1.77137e25			0.953030			0.476515	−	0.879166i	$-0.341900\pi$
$457$	1.77137e25			0.953030			0.476515	+	0.879166i	$0.341900\pi$
$458$	4.06284e24	−	5.51434e23i	0.214096	−	0.0290584i
$459$			2.10749e25i			1.08779i
$460$	−6.93244e24	−	2.50678e25i	−0.350499	−	1.26741i
$461$		−	2.03466e25i		−	1.00771i	−0.863789	−	0.503853i	$-0.831915\pi$
$461$		−	2.03466e25i		−	1.00771i	0.863789	−	0.503853i	$-0.168085\pi$
$462$	2.75708e24	+	2.03135e25i	0.133768	+	0.985568i
$463$	−1.80863e25			−0.859665			−0.429833	−	0.902909i	$-0.641427\pi$
$463$	−1.80863e25			−0.859665			−0.429833	+	0.902909i	$0.641427\pi$
$464$	2.36572e24	+	3.95012e24i	0.110165	+	0.183946i
$465$	1.17503e25			0.536102
$466$	1.41613e24	+	1.04337e25i	0.0633046	+	0.466414i
$467$			9.60386e24i			0.420664i	0.977630	+	0.210332i	$0.0674545\pi$
$467$			9.60386e24i			0.420664i	−0.977630	+	0.210332i	$0.932545\pi$
$468$	−1.83436e24	−	6.63309e24i	−0.0787317	−	0.284695i
$469$			6.12169e25i			2.57471i
$470$	−1.37258e24	+	1.86295e23i	−0.0565728	+	0.00767841i
$471$	2.97771e25			1.20278
$472$	5.23230e24	−	2.24127e24i	0.207130	−	0.0887247i
$473$	−1.24727e25			−0.483926
$474$	2.22879e25	−	3.02505e24i	0.847568	−	0.115037i
$475$		−	3.14981e23i		−	0.0117407i
$476$	5.02733e25	−	1.39029e25i	1.83684	−	0.507973i
$477$		−	1.83321e24i		−	0.0656579i
$478$	−1.26600e24	−	9.32759e24i	−0.0444497	−	0.327495i
$479$	1.16951e24			0.0402546			0.0201273	−	0.999797i	$-0.493593\pi$
$479$	1.16951e24			0.0402546			0.0201273	+	0.999797i	$0.493593\pi$
$480$	−1.59549e25	−	1.99531e25i	−0.538398	−	0.673316i
$481$	−2.32179e25			−0.768146
$482$	7.04587e24	+	5.19123e25i	0.228553	+	1.68393i
$483$		−	7.41925e25i		−	2.35973i
$484$	−2.03282e25	+	5.62170e24i	−0.633968	+	0.175322i
$485$		−	1.98958e25i		−	0.608436i
$486$	−1.12326e25	+	1.52456e24i	−0.336850	+	0.0457195i
$487$	−1.84466e25			−0.542489			−0.271245	−	0.962510i	$-0.587435\pi$
$487$	−1.84466e25			−0.542489			−0.271245	+	0.962510i	$0.587435\pi$
$488$	−1.02741e25	+	4.40093e24i	−0.296316	+	0.126928i
$489$	−9.56451e24			−0.270538
$490$	8.42966e25	−	1.14413e25i	2.33855	−	0.317403i
$491$		−	5.10156e25i		−	1.38813i	−0.719914	−	0.694063i	$-0.755819\pi$
$491$		−	5.10156e25i		−	1.38813i	0.719914	−	0.694063i	$-0.244181\pi$
$492$	5.62249e24	+	2.03310e25i	0.150058	+	0.542614i
$493$		−	8.35403e24i		−	0.218701i
$494$	−1.03140e24	−	7.59910e24i	−0.0264862	−	0.195144i
$495$	3.78428e24			0.0953310
$496$	2.15876e25	−	1.29287e25i	0.533492	−	0.319507i
$497$	−7.60769e25			−1.84445
$498$	−8.50046e23	−	6.26294e24i	−0.0202192	−	0.148970i
$499$		−	5.98162e25i		−	1.39593i	−0.716132	−	0.697965i	$-0.754089\pi$
$499$		−	5.98162e25i		−	1.39593i	0.716132	−	0.697965i	$-0.245911\pi$
$500$	−1.21579e25	−	4.39633e25i	−0.278384	−	1.00664i
$501$			3.47178e25i			0.779998i
$502$	−7.16465e25	+	9.72433e24i	−1.57946	+	0.214375i
$503$	2.84016e25			0.614395			0.307197	−	0.951646i	$-0.400609\pi$
$503$	2.84016e25			0.614395			0.307197	+	0.951646i	$0.400609\pi$
$504$	5.96083e24	+	1.39157e25i	0.126537	+	0.295404i
$505$	3.19183e25			0.664923
$506$	−3.93554e25	+	5.34156e24i	−0.804589	+	0.109204i
$507$			8.84021e25i			1.77373i
$508$	4.22198e25	−	1.16758e25i	0.831402	−	0.229922i
$509$			4.01807e25i			0.776602i	0.921533	+	0.388301i	$0.126938\pi$
$509$			4.01807e25i			0.776602i	−0.921533	+	0.388301i	$0.873062\pi$
$510$	6.23419e24	+	4.59321e25i	0.118267	+	0.871363i
$511$	6.08783e25			1.13361
$512$	−5.12664e25	−	1.91026e25i	−0.937062	−	0.349163i
$513$	−6.81586e24			−0.122294
$514$	4.65547e24	+	3.43004e25i	0.0820000	+	0.604156i
$515$			5.81097e25i			1.00480i
$516$	4.27367e25	−	1.18187e25i	0.725485	−	0.200631i
$517$			2.11519e24i			0.0352524i
$518$	5.06090e25	−	6.86898e24i	0.828123	−	0.112398i
$519$	−6.52498e25			−1.04831
$520$	−4.06119e25	−	9.48097e25i	−0.640651	−	1.49562i
$521$	8.57420e25			1.32811			0.664057	−	0.747682i	$-0.268833\pi$
$521$	8.57420e25			1.32811			0.664057	+	0.747682i	$0.268833\pi$
$522$	2.40259e24	−	3.26095e23i	0.0365435	−	0.00495992i
$523$			2.38471e25i			0.356180i	0.984014	+	0.178090i	$0.0569918\pi$
$523$			2.38471e25i			0.356180i	−0.984014	+	0.178090i	$0.943008\pi$
$524$	2.89036e25	+	1.04516e26i	0.423940	+	1.53298i
$525$		−	1.20846e25i		−	0.174068i
$526$	−3.39885e24	−	2.50419e25i	−0.0480803	−	0.354245i
$527$	−4.56551e25			−0.634291
$528$	−3.34690e25	+	2.00445e25i	−0.456689	+	0.273509i
$529$	6.91250e25			0.926416
$530$	−3.69511e24	−	2.72247e25i	−0.0486415	−	0.358379i
$531$		−	2.99743e24i		−	0.0387571i
$532$	4.49637e24	+	1.62590e25i	0.0571086	+	0.206506i
$533$			8.51615e25i			1.06251i
$534$	−1.13169e26	+	1.53600e25i	−1.38703	+	0.188256i
$535$	−2.21310e25			−0.266465
$536$	−1.07088e26	+	4.58714e25i	−1.26671	+	0.542595i
$537$	−1.95756e25			−0.227488
$538$	−7.12332e25	+	9.66822e24i	−0.813300	+	0.110386i
$539$		−	1.29904e26i		−	1.45723i
$540$	−8.83540e25	+	2.44340e25i	−0.973835	+	0.269311i
$541$		−	1.26619e26i		−	1.37128i	−0.727943	−	0.685638i	$-0.759523\pi$
$541$		−	1.26619e26i		−	1.37128i	0.727943	−	0.685638i	$-0.240477\pi$
$542$	1.03427e24	+	7.62024e24i	0.0110063	+	0.0810915i
$543$	8.68574e25			0.908256
$544$	6.19918e25	+	7.75265e25i	0.637008	+	0.796637i
$545$	1.55607e26			1.57132
$546$	−3.95708e25	−	2.91548e26i	−0.392686	−	2.89321i
$547$			1.00193e26i			0.977142i	0.872524	+	0.488571i	$0.162482\pi$
$547$			1.00193e26i			0.977142i	−0.872524	+	0.488571i	$0.837518\pi$
$548$	7.15136e24	−	1.97769e24i	0.0685446	−	0.0189558i
$549$			5.88572e24i			0.0554450i
$550$	−6.41028e24	+	8.70043e23i	−0.0593514	+	0.00805555i
$551$	2.70179e24			0.0245873
$552$	1.29787e26	−	5.55944e25i	1.16094	−	0.497290i
$553$	−1.99749e26			−1.75628
$554$	1.66220e26	−	2.25604e25i	1.43662	−	0.194987i
$555$			4.53869e25i			0.385609i
$556$	−2.61000e25	−	9.43783e25i	−0.217987	−	0.788246i
$557$		−	2.03627e26i		−	1.67191i	−0.548801	−	0.835953i	$-0.684916\pi$
$557$		−	2.03627e26i		−	1.67191i	0.548801	−	0.835953i	$-0.315084\pi$
$558$	−1.78212e24	−	1.31303e25i	−0.0143851	−	0.105986i
$559$	1.79013e26			1.42060
$560$	1.16573e26	+	1.94646e26i	0.909518	+	1.51865i
$561$	7.07828e25			0.542976
$562$	2.69752e25	+	1.98747e26i	0.203456	+	1.49901i
$563$			2.57011e26i			1.90600i	0.302973	+	0.952999i	$0.402021\pi$
$563$			2.57011e26i			1.90600i	−0.302973	+	0.952999i	$0.597979\pi$
$564$	−2.00428e24	−	7.24753e24i	−0.0146153	−	0.0528492i
$565$		−	1.93459e26i		−	1.38717i
$566$	1.73505e26	−	2.35492e25i	1.22336	−	0.166043i
$567$	−2.15150e26			−1.49177
$568$	−5.70064e25	−	1.33083e26i	−0.388700	−	0.907431i
$569$	−1.67857e26			−1.12557			−0.562784	−	0.826604i	$-0.690270\pi$
$569$	−1.67857e26			−1.12557			−0.562784	+	0.826604i	$0.690270\pi$
$570$	−1.48549e25	+	2.01621e24i	−0.0979625	+	0.0132961i
$571$		−	1.06055e26i		−	0.687839i	−0.938999	−	0.343920i	$-0.888245\pi$
$571$		−	1.06055e26i		−	0.687839i	0.938999	−	0.343920i	$-0.111755\pi$
$572$	−1.51803e26	+	4.19806e25i	−0.968317	+	0.267785i
$573$			9.79353e25i			0.614427i
$574$	−2.51949e25	−	1.85630e26i	−0.155471	−	1.14548i
$575$	2.34127e25			0.142104
$576$	−1.98765e25	+	2.08548e25i	−0.118666	+	0.124507i
$577$	−5.23761e25			−0.307584			−0.153792	−	0.988103i	$-0.549149\pi$
$577$	−5.23761e25			−0.307584			−0.153792	+	0.988103i	$0.549149\pi$
$578$	−9.40811e23	−	6.93168e24i	−0.00543486	−	0.0400427i
$579$			7.55065e25i			0.429080i
$580$	3.50233e25	−	9.68559e24i	0.195790	−	0.0541452i
$581$			5.61298e25i			0.308688i
$582$	1.07026e26	−	1.45263e25i	0.579057	−	0.0785932i
$583$	−4.19542e25			−0.223318
$584$	4.56177e25	+	1.06496e26i	0.238897	+	0.557713i
$585$	−5.43136e25			−0.279852
$586$	−1.09901e26	+	1.49165e25i	−0.557154	+	0.0756205i
$587$			1.70287e26i			0.849416i	0.905330	+	0.424708i	$0.139623\pi$
$587$			1.70287e26i			0.849416i	−0.905330	+	0.424708i	$0.860377\pi$
$588$	1.23093e26	+	4.45106e26i	0.604154	+	2.18463i
$589$		−	1.47654e25i		−	0.0713098i
$590$	−6.04178e24	−	4.45144e25i	−0.0287125	−	0.211547i
$591$	−1.90320e26			−0.890026
$592$	4.99387e25	+	8.33844e25i	0.229816	+	0.383733i
$593$	−1.16620e26			−0.528144			−0.264072	−	0.964503i	$-0.585066\pi$
$593$	−1.16620e26			−0.528144			−0.264072	+	0.964503i	$0.585066\pi$
$594$	1.88268e25	+	1.38712e26i	0.0839085	+	0.618218i
$595$		−	4.11652e26i		−	1.80559i
$596$	−1.06159e26	−	3.83875e26i	−0.458268	−	1.65710i
$597$			5.39679e25i			0.229287i
$598$	5.64845e26	−	7.66644e25i	2.36194	−	0.320577i
$599$	−2.28516e26			−0.940508			−0.470254	−	0.882531i	$-0.655838\pi$
$599$	−2.28516e26			−0.940508			−0.470254	+	0.882531i	$0.655838\pi$
$600$	2.11399e25	−	9.05531e24i	0.0856379	−	0.0366831i
$601$	1.94054e26			0.773774			0.386887	−	0.922127i	$-0.373550\pi$
$601$	1.94054e26			0.773774			0.386887	+	0.922127i	$0.373550\pi$
$602$	−3.90203e26	+	5.29608e25i	−1.53152	+	0.207868i
$603$			6.13476e25i			0.237019i
$604$	−1.45048e26	+	4.01126e25i	−0.551646	+	0.152556i
$605$			1.66453e26i			0.623182i
$606$	2.33041e25	+	1.71699e26i	0.0858899	+	0.632817i
$607$	2.58105e25			0.0936491			0.0468246	−	0.998903i	$-0.485090\pi$
$607$	2.58105e25			0.0936491			0.0468246	+	0.998903i	$0.485090\pi$
$608$	−2.50729e25	+	2.00489e25i	−0.0895615	+	0.0716153i
$609$	1.03657e26			0.364532
$610$	1.18636e25	+	8.74081e25i	0.0410755	+	0.302634i
$611$		−	3.03581e25i		−	0.103486i
$612$	5.03807e25	−	1.39326e25i	0.169093	−	0.0467622i
$613$			1.87034e26i			0.618082i	0.951049	+	0.309041i	$0.100008\pi$
$613$			1.87034e26i			0.618082i	−0.951049	+	0.309041i	$0.899992\pi$
$614$	−5.72452e26	+	7.76968e25i	−1.86269	+	0.252816i
$615$	1.66476e26			0.533382
$616$	3.18471e26	−	1.36418e26i	1.00474	−	0.430382i
$617$	4.15442e26			1.29063			0.645314	−	0.763917i	$-0.276726\pi$
$617$	4.15442e26			1.29063			0.645314	+	0.763917i	$0.276726\pi$
$618$	−3.12591e26	+	4.24269e25i	−0.956283	+	0.129793i
$619$		−	1.21773e26i		−	0.366851i	−0.983034	−	0.183425i	$-0.941281\pi$
$619$		−	1.21773e26i		−	0.366851i	0.983034	−	0.183425i	$-0.0587186\pi$
$620$	−5.29321e25	−	1.91404e26i	−0.157036	−	0.567844i
$621$		−	5.06626e26i		−	1.48019i
$622$	2.71979e25	+	2.00388e26i	0.0782576	+	0.576584i
$623$	1.01424e27			2.87412
$624$	4.80361e26	−	2.87687e26i	1.34065	−	0.802909i
$625$	−3.22737e26			−0.887134
$626$	−3.37291e25	−	2.48508e26i	−0.0913164	−	0.672798i
$627$			2.28920e25i			0.0610438i
$628$	−1.34138e26	−	4.85046e26i	−0.352319	−	1.27399i
$629$		−	1.76348e26i		−	0.456236i
$630$	1.18390e26	−	1.60686e25i	0.301703	−	0.0409490i
$631$	−6.55585e26			−1.64570			−0.822850	−	0.568259i	$-0.807617\pi$
$631$	−6.55585e26			−1.64570			−0.822850	+	0.568259i	$0.807617\pi$
$632$	−1.49677e26	−	3.49425e26i	−0.370119	−	0.864055i
$633$	2.33390e26			0.568521
$634$	1.12519e26	−	1.52718e25i	0.270010	−	0.0366474i
$635$		−	3.45708e26i		−	0.817257i
$636$	1.43753e26	−	3.97545e25i	0.334791	−	0.0925856i
$637$			1.86443e27i			4.27782i
$638$	−7.46291e24	−	5.49849e25i	−0.0168699	−	0.124293i
$639$	−7.62393e25			−0.169793
$640$	−2.53148e26	+	3.49777e26i	−0.555475	+	0.767505i
$641$	−2.05990e26			−0.445344			−0.222672	−	0.974893i	$-0.571478\pi$
$641$	−2.05990e26			−0.445344			−0.222672	+	0.974893i	$0.571478\pi$
$642$	−1.61582e25	−	1.19050e26i	−0.0344200	−	0.253598i
$643$		−	3.00977e26i		−	0.631726i	−0.948805	−	0.315863i	$-0.897706\pi$
$643$		−	3.00977e26i		−	0.631726i	0.948805	−	0.315863i	$-0.102294\pi$
$644$	−1.20854e27	+	3.34218e26i	−2.49945	+	0.691216i
$645$		−	3.49940e26i		−	0.713143i
$646$	5.77179e25	−	7.83384e24i	0.115905	−	0.0157313i
$647$	3.88104e26			0.767994			0.383997	−	0.923334i	$-0.374547\pi$
$647$	3.88104e26			0.767994			0.383997	+	0.923334i	$0.374547\pi$
$648$	−1.61217e26	−	3.76367e26i	−0.314376	−	0.733920i
$649$	−6.85982e25			−0.131822
$650$	9.20030e25	−	1.24872e25i	0.174231	−	0.0236477i
$651$		−	5.66491e26i		−	1.05724i
$652$	4.30856e25	+	1.55798e26i	0.0792464	+	0.286557i
$653$		−	1.04255e26i		−	0.188983i	−0.995526	−	0.0944915i	$-0.969877\pi$
$653$		−	1.04255e26i		−	0.188983i	0.995526	−	0.0944915i	$-0.0301225\pi$
$654$	1.13612e26	+	8.37064e26i	0.202971	+	1.49544i
$655$	8.55807e26			1.50690
$656$	3.05848e26	−	1.83172e26i	0.530786	−	0.317886i
$657$	6.10083e25			0.104356
$658$	8.98140e24	+	6.61729e25i	0.0151425	+	0.111567i
$659$			5.78463e26i			0.961312i	0.876909	+	0.480656i	$0.159601\pi$
$659$			5.78463e26i			0.961312i	−0.876909	+	0.480656i	$0.840399\pi$
$660$	8.20650e25	+	2.96748e26i	0.134428	+	0.486095i
$661$			1.24616e26i			0.201215i	0.994926	+	0.100608i	$0.0320786\pi$
$661$			1.24616e26i			0.201215i	−0.994926	+	0.100608i	$0.967921\pi$
$662$	−1.65951e26	+	2.25239e25i	−0.264136	+	0.0358502i
$663$	−1.01591e27			−1.59395
$664$	−9.81891e25	+	4.20595e25i	−0.151868	+	0.0650529i
$665$	1.33133e26			0.202993
$666$	5.07171e25	−	6.88364e24i	0.0762340	−	0.0103470i
$667$			2.00825e26i			0.297593i
$668$	5.65525e26	−	1.56394e26i	0.826182	−	0.228478i
$669$		−	2.30931e26i		−	0.332609i
$670$	1.23655e26	+	9.11065e26i	0.175591	+	1.29371i
$671$	1.34699e26			0.188582
$672$	−9.61953e26	+	7.69198e26i	−1.32784	+	1.06177i
$673$	−7.71919e26			−1.05058			−0.525289	−	0.850924i	$-0.676043\pi$
$673$	−7.71919e26			−1.05058			−0.525289	+	0.850924i	$0.676043\pi$
$674$	1.17088e26	+	8.62675e26i	0.157124	+	1.15765i
$675$		−	8.25202e25i		−	0.109188i
$676$	1.44000e27	−	3.98228e26i	1.87875	−	0.519563i
$677$		−	5.37060e26i		−	0.690924i	−0.938433	−	0.345462i	$-0.887722\pi$
$677$		−	5.37060e26i		−	0.690924i	0.938433	−	0.345462i	$-0.112278\pi$
$678$	1.04068e27	−	1.41248e26i	1.32019	−	0.179184i
$679$	−9.59189e26			−1.19989
$680$	7.20113e26	−	3.08462e26i	0.888313	−	0.380510i
$681$	−4.33840e26			−0.527755
$682$	−3.00495e26	+	4.07851e25i	−0.360484	+	0.0489271i
$683$			1.29728e27i			1.53475i	0.641199	+	0.767374i	$0.278437\pi$
$683$			1.29728e27i			1.53475i	−0.641199	+	0.767374i	$0.721563\pi$
$684$	4.50597e24	+	1.62937e25i	0.00525721	+	0.0190102i
$685$		−	5.85574e25i		−	0.0673785i
$686$	−3.30153e26	−	2.43249e27i	−0.374659	−	2.76040i
$687$	1.75661e26			0.196602
$688$	−3.85035e26	−	6.42906e26i	−0.425020	−	0.709672i
$689$	6.02145e26			0.655569
$690$	−1.49866e26	−	1.10418e27i	−0.160930	−	1.18569i
$691$		−	1.00043e27i		−	1.05960i	−0.848121	−	0.529802i	$-0.822266\pi$
$691$		−	1.00043e27i		−	1.05960i	0.848121	−	0.529802i	$-0.177734\pi$
$692$	2.93933e26	+	1.06287e27i	0.307072	+	1.11038i
$693$		−	1.82443e26i		−	0.188001i
$694$	−1.03751e27	+	1.40817e26i	−1.05457	+	0.143133i
$695$	−7.72796e26			−0.774835
$696$	7.76730e25	+	1.81330e26i	0.0768215	+	0.179342i
$697$	−6.46832e26			−0.631074
$698$	9.62122e26	−	1.30585e26i	0.925984	−	0.125680i
$699$			4.51111e26i			0.428302i
$700$	−1.96849e26	+	5.44380e25i	−0.184375	+	0.0509883i
$701$		−	4.42213e26i		−	0.408612i	−0.978907	−	0.204306i	$-0.934506\pi$
$701$		−	4.42213e26i		−	0.408612i	0.978907	−	0.204306i	$-0.0654937\pi$
$702$	−2.70211e26	−	1.99085e27i	−0.246320	−	1.81483i
$703$	5.70329e25			0.0512920
$704$	4.77277e26	+	4.54888e26i	0.423478	+	0.403612i
$705$	−5.93449e25			−0.0519501
$706$	1.50257e26	+	1.10706e27i	0.129775	+	0.956149i
$707$		−	1.53880e27i		−	1.31129i
$708$	2.35047e26	−	6.50015e25i	0.197623	−	0.0546522i
$709$		−	1.27993e27i		−	1.06181i	−0.847432	−	0.530904i	$-0.821853\pi$
$709$		−	1.27993e27i		−	1.06181i	0.847432	−	0.530904i	$-0.178147\pi$
$710$	−1.13222e27	+	1.53672e26i	−0.926780	+	0.125788i
$711$	−2.00175e26			−0.161677
$712$	7.59997e26	+	1.77424e27i	0.605692	+	1.41401i
$713$	1.09752e27			0.863101
$714$	2.21441e27	−	3.00554e26i	1.71841	−	0.233233i
$715$			1.24300e27i			0.951843i
$716$	8.81829e25	+	3.18871e26i	0.0666363	+	0.240958i
$717$		−	4.03288e26i		−	0.300735i
$718$	2.87486e26	+	2.11813e27i	0.211560	+	1.55873i
$719$	1.32916e27			0.965282			0.482641	−	0.875818i	$-0.339678\pi$
$719$	1.32916e27			0.965282			0.482641	+	0.875818i	$0.339678\pi$
$720$	1.16822e26	+	1.95062e26i	0.0837269	+	0.139802i
$721$	2.80151e27			1.98156
$722$	−1.90132e26	−	1.40085e27i	−0.132725	−	0.977884i
$723$			2.24448e27i			1.54633i
$724$	−3.91269e26	−	1.41484e27i	−0.266048	−	0.962034i
$725$			3.27108e25i			0.0219523i
$726$	−8.95405e26	+	1.21530e26i	−0.593091	+	0.0804981i
$727$	−2.53403e27			−1.65666			−0.828332	−	0.560238i	$-0.810710\pi$
$727$	−2.53403e27			−1.65666			−0.828332	+	0.560238i	$0.810710\pi$
$728$	−4.57084e27	+	1.95793e27i	−2.94949	+	1.26342i
$729$	−1.73920e27			−1.10774
$730$	9.06026e26	−	1.22972e26i	0.569605	−	0.0773103i
$731$			1.35967e27i			0.843758i
$732$	−4.61535e26	+	1.27636e26i	−0.282715	+	0.0781842i
$733$		−	8.42031e26i		−	0.509144i	−0.967054	−	0.254572i	$-0.918065\pi$
$733$		−	8.42031e26i		−	0.509144i	0.967054	−	0.254572i	$-0.0819345\pi$
$734$	−3.22622e25	−	2.37700e26i	−0.0192567	−	0.141878i
$735$	3.64465e27			2.14747
$736$	−1.49024e27	−	1.86369e27i	−0.866798	−	1.08401i
$737$	1.40398e27			0.806158
$738$	−2.52487e25	−	1.86027e26i	−0.0143121	−	0.105448i
$739$			8.50294e26i			0.475825i	0.971287	+	0.237912i	$0.0764631\pi$
$739$			8.50294e26i			0.475825i	−0.971287	+	0.237912i	$0.923537\pi$
$740$	7.39317e26	−	2.04456e26i	0.408441	−	0.112953i
$741$		−	3.28555e26i		−	0.179199i
$742$	−1.31252e27	+	1.78144e26i	−0.706756	+	0.0959254i
$743$	−6.04663e24			−0.00321455			−0.00160727	−	0.999999i	$-0.500512\pi$
$743$	−6.04663e24			−0.00321455			−0.00160727	+	0.999999i	$0.500512\pi$
$744$	9.90977e26	−	4.24486e26i	0.520140	−	0.222803i
$745$	−3.14328e27			−1.62891
$746$	−2.78512e27	+	3.78014e26i	−1.42503	+	0.193415i
$747$			5.62496e25i			0.0284167i
$748$	−3.18858e26	−	1.15300e27i	−0.159049	−	0.575125i
$749$			1.06695e27i			0.525492i
$750$	−2.62831e26	−	1.93647e27i	−0.127819	−	0.941737i
$751$	2.16633e27			1.04027			0.520133	−	0.854085i	$-0.325882\pi$
$751$	2.16633e27			1.04027			0.520133	+	0.854085i	$0.325882\pi$
$752$	−1.09028e26	+	6.52964e25i	−0.0516973	+	0.0309613i
$753$	−3.09772e27			−1.45040
$754$	1.07111e26	+	7.89167e26i	0.0495228	+	0.364873i
$755$			1.18769e27i			0.542261i
$756$	1.17798e27	+	4.25960e27i	0.531106	+	1.92049i
$757$			4.11343e27i			1.83144i	0.401813	+	0.915722i	$0.368380\pi$
$757$			4.11343e27i			1.83144i	−0.401813	+	0.915722i	$0.631620\pi$
$758$	1.51456e27	−	2.05565e26i	0.665929	−	0.0903842i
$759$	−1.70157e27			−0.738845
$760$	9.97600e25	+	2.32893e26i	0.0427787	+	0.0998681i
$761$	4.00109e27			1.69443			0.847216	−	0.531249i	$-0.178277\pi$
$761$	4.00109e27			1.69443			0.847216	+	0.531249i	$0.178277\pi$
$762$	1.85968e27	−	2.52407e26i	0.777795	−	0.105567i
$763$		−	7.50194e27i		−	3.09878i
$764$	1.59529e27	−	4.41172e26i	0.650807	−	0.179979i
$765$		−	4.12531e26i		−	0.166216i
$766$	1.92861e26	+	1.42096e27i	0.0767488	+	0.565467i
$767$	9.84551e26			0.386975
$768$	−2.06639e27	−	1.10639e27i	−0.802197	−	0.429512i
$769$	1.95943e27			0.751328			0.375664	−	0.926756i	$-0.377415\pi$
$769$	1.95943e27			0.751328			0.375664	+	0.926756i	$0.377415\pi$
$770$	−3.67741e26	−	2.70943e27i	−0.139277	−	1.02616i
$771$			1.48301e27i			0.554790i
$772$	1.22994e27	−	3.40137e26i	0.454485	−	0.125687i
$773$		−	2.28430e27i		−	0.833774i	−0.908958	−	0.416887i	$-0.863121\pi$
$773$		−	2.28430e27i		−	0.833774i	0.908958	−	0.416887i	$-0.136879\pi$
$774$	−3.91036e26	+	5.30739e25i	−0.140987	+	0.0191356i
$775$	1.78766e26			0.0636676
$776$	−7.18745e26	−	1.67793e27i	−0.252865	−	0.590321i
$777$	2.18813e27			0.760456
$778$	−8.77123e26	+	1.19049e26i	−0.301130	+	0.0408713i
$779$		−	2.09193e26i		−	0.0709481i
$780$	−1.17783e27	−	4.25906e27i	−0.394625	−	1.42697i
$781$			1.74479e27i			0.577508i
$782$	5.82293e26	+	4.29020e27i	0.190405	+	1.40286i
$783$	7.07828e26			0.228660
$784$	6.69592e27	−	4.01016e27i	2.13701	−	1.27985i
$785$	−3.97170e27			−1.25232
$786$	6.24839e26	+	4.60367e27i	0.194650	+	1.43413i
$787$		−	2.95095e27i		−	0.908242i	−0.890940	−	0.454121i	$-0.849953\pi$
$787$		−	2.95095e27i		−	0.908242i	0.890940	−	0.454121i	$-0.150047\pi$
$788$	8.57339e26	+	3.10016e27i	0.260708	+	0.942724i
$789$		−	1.08271e27i		−	0.325299i
$790$	−2.97277e27	+	4.03484e26i	−0.882479	+	0.119776i
$791$	−9.32680e27			−2.73562
$792$	3.19151e26	−	1.36709e26i	0.0924927	−	0.0396194i
$793$	−1.93325e27			−0.553597
$794$	2.98533e27	−	4.05188e26i	0.844690	−	0.114647i
$795$		−	1.17709e27i		−	0.329096i
$796$	8.79094e26	−	2.43111e26i	0.242863	−	0.0671630i
$797$		−	3.79871e27i		−	1.03701i	−0.855075	−	0.518504i	$-0.826489\pi$
$797$		−	3.79871e27i		−	1.03701i	0.855075	−	0.518504i	$-0.173511\pi$
$798$	9.72027e25	+	7.16167e26i	0.0262211	+	0.193191i
$799$	2.30580e26			0.0614650
$800$	−2.42733e26	−	3.03560e26i	−0.0639403	−	0.0799632i
$801$	1.01641e27			0.264581
$802$	1.54399e26	+	1.13758e27i	0.0397181	+	0.292634i
$803$		−	1.39622e27i		−	0.354940i
$804$	−4.81063e27	+	1.33037e27i	−1.20856	+	0.334225i
$805$			9.89585e27i			2.45693i
$806$	4.31283e27	−	5.85365e26i	1.05823	−	0.143630i
$807$	−3.07984e27			−0.746844
$808$	2.69186e27	−	1.15306e27i	0.645126	−	0.276341i
$809$	−9.58569e26			−0.227045			−0.113523	−	0.993535i	$-0.536213\pi$
$809$	−9.58569e26			−0.227045			−0.113523	+	0.993535i	$0.536213\pi$
$810$	−3.20198e27	+	4.34594e26i	−0.749569	+	0.101736i
$811$		−	4.26244e27i		−	0.986188i	−0.869976	−	0.493094i	$-0.835866\pi$
$811$		−	4.26244e27i		−	0.986188i	0.869976	−	0.493094i	$-0.164134\pi$
$812$	−4.66948e26	−	1.68849e27i	−0.106779	−	0.386116i
$813$			3.29469e26i			0.0744654i
$814$	−1.57537e26	−	1.16069e27i	−0.0351925	−	0.259290i
$815$	1.27572e27			0.281682
$816$	2.18508e27	+	3.64851e27i	0.476883	+	0.796268i
$817$	−4.39732e26			−0.0948591
$818$	3.66143e26	+	2.69765e27i	0.0780718	+	0.575214i
$819$			2.61850e27i			0.551893i
$820$	−7.49931e26	−	2.71177e27i	−0.156239	−	0.564964i
$821$			4.96530e27i			1.02255i	0.859416	+	0.511276i	$0.170827\pi$
$821$			4.96530e27i			1.02255i	−0.859416	+	0.511276i	$0.829173\pi$
$822$	3.15000e26	−	4.27538e25i	0.0641251	−	0.00870346i
$823$	9.12982e27			1.83723			0.918615	−	0.395153i	$-0.129308\pi$
$823$	9.12982e27			1.83723			0.918615	+	0.395153i	$0.129308\pi$
$824$	2.09924e27	+	4.90074e27i	0.417594	+	0.974885i
$825$	−2.77155e26			−0.0545017
$826$	−2.14607e27	+	2.91278e26i	−0.417190	+	0.0566236i
$827$			4.71662e27i			0.906417i	0.891404	+	0.453209i	$0.149721\pi$
$827$			4.71662e27i			0.906417i	−0.891404	+	0.453209i	$0.850279\pi$
$828$	−1.21112e27	+	3.34931e26i	−0.230090	+	0.0636308i
$829$			5.13444e27i			0.964328i	0.876081	+	0.482164i	$0.160149\pi$
$829$			5.13444e27i			0.964328i	−0.876081	+	0.482164i	$0.839851\pi$
$830$	1.13380e26	+	8.35355e26i	0.0210520	+	0.155106i
$831$	7.18670e27			1.31923
$832$	−6.85009e27	−	6.52875e27i	−1.24315	−	1.18484i
$833$	−1.41610e28			−2.54078
$834$	−5.64232e26	−	4.15713e27i	−0.100088	−	0.737422i
$835$		−	4.63068e27i		−	0.812126i
$836$	3.72892e26	−	1.03122e26i	0.0646582	−	0.0178810i
$837$		−	3.86831e27i		−	0.663177i
$838$	7.70763e27	−	1.04613e27i	1.30648	−	0.177324i
$839$	−9.88322e27			−1.65638			−0.828190	−	0.560447i	$-0.810629\pi$
$839$	−9.88322e27			−1.65638			−0.828190	+	0.560447i	$0.810629\pi$
$840$	3.82741e27	+	8.93521e27i	0.634237	+	1.48065i
$841$	5.82268e27			0.954028
$842$	−7.99102e27	+	1.08459e27i	−1.29461	+	0.175712i
$843$			8.59304e27i			1.37653i
$844$	−1.05136e27	−	3.80173e27i	−0.166532	−	0.602182i
$845$		−	1.17911e28i		−	1.84679i
$846$	9.00058e24	+	6.63142e25i	0.00139397	+	0.0102704i
$847$	8.02480e27			1.22897
$848$	−1.29514e27	−	2.16254e27i	−0.196135	−	0.327494i
$849$	7.50167e27			1.12340
$850$	9.48450e25	+	6.98796e26i	0.0140454	+	0.103483i
$851$			4.23929e27i			0.620815i
$852$	−1.65331e27	−	5.97839e27i	−0.239429	−	0.865781i
$853$		−	6.33913e27i		−	0.907850i	−0.891040	−	0.453925i	$-0.850023\pi$
$853$		−	6.33913e27i		−	0.907850i	0.891040	−	0.453925i	$-0.149977\pi$
$854$	4.21400e27	−	5.71951e26i	0.596822	−	0.0810045i
$855$	1.33417e26			0.0186868
$856$	−1.86644e27	+	7.99492e26i	−0.258531	+	0.110742i
$857$	1.20667e28			1.65300			0.826498	−	0.562940i	$-0.190330\pi$
$857$	1.20667e28			1.65300			0.826498	+	0.562940i	$0.190330\pi$
$858$	−6.68653e27	+	9.07539e26i	−0.905882	+	0.122952i
$859$		−	1.12273e28i		−	1.50432i	−0.658983	−	0.752158i	$-0.729013\pi$
$859$		−	1.12273e28i		−	1.50432i	0.658983	−	0.752158i	$-0.270987\pi$
$860$	−5.70025e27	+	1.57639e27i	−0.755368	+	0.208895i
$861$		−	8.02593e27i		−	1.05188i
$862$	−3.17654e26	−	2.34040e27i	−0.0411751	−	0.303368i
$863$	9.86947e27			1.26529			0.632647	−	0.774441i	$-0.281969\pi$
$863$	9.86947e27			1.26529			0.632647	+	0.774441i	$0.281969\pi$
$864$	−6.56873e27	+	5.25250e27i	−0.832915	+	0.666017i
$865$	8.70307e27			1.09149
$866$	−1.07916e27	−	7.95100e27i	−0.133865	−	0.986284i
$867$		−	2.99698e26i		−	0.0367708i
$868$	−9.22770e27	+	2.55189e27i	−1.11984	+	0.309689i
$869$			4.58114e27i			0.549903i
$870$	1.54269e27	−	2.09383e26i	0.183166	−	0.0248605i
$871$	−2.01505e28			−2.36654
$872$	1.31233e28	−	5.62139e27i	1.52453	−	0.653036i
$873$	−9.61237e26			−0.110457
$874$	−1.38750e27	+	1.88320e26i	−0.157715	+	0.0214061i
$875$			1.73551e28i			1.95142i
$876$	1.32301e27	+	4.78403e27i	0.147155	+	0.532114i
$877$			5.55723e27i			0.611452i	0.952119	+	0.305726i	$0.0988992\pi$
$877$			5.55723e27i			0.611452i	−0.952119	+	0.305726i	$0.901101\pi$
$878$	−1.79044e27	−	1.31916e28i	−0.194878	−	1.43581i
$879$	−4.75170e27			−0.511628
$880$	4.46412e27	−	2.67355e27i	0.475500	−	0.284775i
$881$	−6.61653e27			−0.697203			−0.348601	−	0.937271i	$-0.613343\pi$
$881$	−6.61653e27			−0.697203			−0.348601	+	0.937271i	$0.613343\pi$
$882$	−5.52769e26	−	4.07267e27i	−0.0576225	−	0.424549i
$883$		−	1.69841e27i		−	0.175152i	−0.996158	−	0.0875759i	$-0.972088\pi$
$883$		−	1.69841e27i		−	0.175152i	0.996158	−	0.0875759i	$-0.0279120\pi$
$884$	4.57638e27	+	1.65483e28i	0.466902	+	1.68833i
$885$		−	1.92463e27i		−	0.194261i
$886$	−6.14165e27	+	8.33583e26i	−0.613288	+	0.0832394i
$887$	1.13898e28			1.12523			0.562613	−	0.826720i	$-0.309796\pi$
$887$	1.13898e28			1.12523			0.562613	+	0.826720i	$0.309796\pi$
$888$	1.63962e27	+	3.82775e27i	0.160259	+	0.374129i
$889$	−1.66668e28			−1.61170
$890$	1.50945e28	−	2.04873e27i	1.44416	−	0.196010i
$891$			4.93436e27i			0.467082i
$892$	−3.76168e27	+	1.04028e27i	−0.352303	+	0.0974283i
$893$			7.45723e25i			0.00691017i
$894$	−2.29496e27	−	1.69087e28i	−0.210411	−	1.55026i
$895$	2.61101e27			0.236859
$896$	1.68630e28	+	1.22044e28i	1.51359	+	1.09545i
$897$	2.44217e28			2.16894
$898$	1.53492e27	+	1.13089e28i	0.134884	+	0.993792i
$899$			1.53339e27i			0.133332i
$900$	−1.97269e26	+	5.45542e25i	−0.0169729	+	0.00469380i
$901$			4.57350e27i			0.389371i
$902$	−4.25735e27	+	5.77834e26i	−0.358655	+	0.0486790i
$903$	−1.68708e28			−1.40638
$904$	−6.98881e27	−	1.63156e28i	−0.576505	−	1.34587i
$905$	−1.15851e28			−0.945667
$906$	−6.38899e27	+	8.67155e26i	−0.516077	+	0.0700452i
$907$			1.71923e28i			1.37425i	0.726540	+	0.687124i	$0.241127\pi$
$907$			1.71923e28i			1.37425i	−0.726540	+	0.687124i	$0.758873\pi$
$908$	1.95433e27	+	7.06691e27i	0.154591	+	0.559003i
$909$		−	1.54209e27i		−	0.120712i
$910$	5.27798e27	+	3.88869e28i	0.408860	+	3.01239i
$911$	−9.54729e27			−0.731906			−0.365953	−	0.930633i	$-0.619257\pi$
$911$	−9.54729e27			−0.731906			−0.365953	+	0.930633i	$0.619257\pi$
$912$	−1.17997e27	+	7.06681e26i	−0.0895200	+	0.0536133i
$913$	1.28731e27			0.0966520
$914$	−1.72503e27	−	1.27096e28i	−0.128176	−	0.944371i
$915$			3.77918e27i			0.277906i
$916$	−7.91307e26	−	2.86138e27i	−0.0575888	−	0.208242i
$917$		−	4.12590e28i		−	2.97174i
$918$	1.51212e28	−	2.05235e27i	1.07791	−	0.146300i
$919$	1.03376e28			0.729330			0.364665	−	0.931139i	$-0.381184\pi$
$919$	1.03376e28			0.729330			0.364665	+	0.931139i	$0.381184\pi$
$920$	−1.73110e28	+	7.41521e27i	−1.20876	+	0.517773i
$921$	−2.47506e28			−1.71048
$922$	−1.45987e28	+	1.98143e27i	−0.998551	+	0.135530i
$923$		−	2.50420e28i		−	1.69532i
$924$	1.43064e28	−	3.95641e27i	0.958623	−	0.265104i
$925$			6.90502e26i			0.0457951i
$926$	1.76130e27	+	1.29769e28i	0.115619	+	0.851855i
$927$	2.80749e27			0.182415
$928$	2.60383e27	−	2.08208e27i	0.167458	−	0.133903i
$929$	−2.42856e28			−1.54596			−0.772981	−	0.634429i	$-0.781235\pi$
$929$	−2.42856e28			−1.54596			−0.772981	+	0.634429i	$0.781235\pi$
$930$	−1.14429e27	−	8.43085e27i	−0.0721021	−	0.531231i
$931$		−	4.57984e27i		−	0.285646i
$932$	7.34824e27	−	2.03214e27i	0.453662	−	0.125459i
$933$			8.66397e27i			0.529470i
$934$	6.89076e27	−	9.35257e26i	0.416842	−	0.0565765i
$935$	−9.44106e27			−0.565341
$936$	−4.58060e27	+	1.96211e27i	−0.271520	+	0.116306i
$937$	2.98973e27			0.175431			0.0877153	−	0.996146i	$-0.472043\pi$
$937$	2.98973e27			0.175431			0.0877153	+	0.996146i	$0.472043\pi$
$938$	4.39230e28	−	5.96151e27i	2.55132	−	0.346282i
$939$		−	1.07445e28i		−	0.617823i
$940$	2.67333e26	+	9.66681e26i	0.0152173	+	0.0550261i
$941$			3.34561e28i			1.88527i	0.333824	+	0.942635i	$0.391661\pi$
$941$			3.34561e28i			1.88527i	−0.333824	+	0.942635i	$0.608339\pi$
$942$	−2.89980e27	−	2.13651e28i	−0.161765	−	1.19185i
$943$	1.55494e28			0.858723
$944$	−2.11765e27	−	3.53591e27i	−0.115776	−	0.193316i
$945$	3.48789e28			1.88782
$946$	1.21463e27	+	8.94913e27i	0.0650847	+	0.479529i
$947$		−	8.34425e27i		−	0.442652i	−0.975200	−	0.221326i	$-0.928962\pi$
$947$		−	8.34425e27i		−	0.442652i	0.975200	−	0.221326i	$-0.0710385\pi$
$948$	−4.34094e27	−	1.56969e28i	−0.227984	−	0.824396i
$949$			2.00391e28i			1.04195i
$950$	−2.25998e26	+	3.06739e25i	−0.0116341	+	0.00157905i
$951$	4.86490e27			0.247947
$952$	−1.48711e28	−	3.47171e28i	−0.750401	−	1.75183i
$953$	2.34539e28			1.17174			0.585871	−	0.810404i	$-0.300752\pi$
$953$	2.34539e28			1.17174			0.585871	+	0.810404i	$0.300752\pi$
$954$	−1.31532e27	+	1.78524e26i	−0.0650614	+	0.00883055i
$955$		−	1.30627e28i		−	0.639735i
$956$	−6.56925e27	+	1.81671e27i	−0.318541	+	0.0880917i
$957$		−	2.37733e27i		−	0.114137i
$958$	−1.13891e26	−	8.39121e26i	−0.00541397	−	0.0398889i
$959$	−2.82309e27			−0.132877
$960$	−1.27626e28	+	1.33908e28i	−0.594788	+	0.624063i
$961$	−1.32906e28			−0.613301
$962$	2.26104e27	+	1.66588e28i	0.103310	+	0.761167i
$963$			1.06923e27i			0.0483749i
$964$	3.65608e28	−	1.01108e28i	1.63789	−	0.452954i
$965$		−	1.00711e28i		−	0.446753i
$966$	−5.32331e28	+	7.22513e27i	−2.33829	+	0.317368i
$967$	1.35360e28			0.588762			0.294381	−	0.955688i	$-0.404886\pi$
$967$	1.35360e28			0.588762			0.294381	+	0.955688i	$0.404886\pi$
$968$	6.01319e27	+	1.40380e28i	0.258994	+	0.604628i
$969$	2.49549e27			0.106434
$970$	−1.42752e28	+	1.93752e27i	−0.602908	+	0.0818305i
$971$			1.46624e28i			0.613230i	0.951834	+	0.306615i	$0.0991964\pi$
$971$			1.46624e28i			0.613230i	−0.951834	+	0.306615i	$0.900804\pi$
$972$	2.18775e27	+	7.91093e27i	0.0906082	+	0.327641i
$973$			3.72570e28i			1.52805i
$974$	1.79639e27	+	1.32354e28i	0.0729612	+	0.537561i
$975$	3.97785e27			0.159994
$976$	4.15819e27	+	6.94308e27i	0.165627	+	0.276553i
$977$	−2.81625e28			−1.11089			−0.555447	−	0.831552i	$-0.687453\pi$
$977$	−2.81625e28			−1.11089			−0.555447	+	0.831552i	$0.687453\pi$
$978$	9.31425e26	+	6.86252e27i	0.0363855	+	0.268080i
$979$		−	2.32612e28i		−	0.899904i
$980$	−1.64182e28	−	5.93685e28i	−0.629039	−	2.27462i
$981$		−	7.51795e27i		−	0.285262i
$982$	−3.66036e28	+	4.96808e27i	−1.37551	+	0.186694i
$983$	−1.27493e28			−0.474492			−0.237246	−	0.971450i	$-0.576245\pi$
$983$	−1.27493e28			−0.474492			−0.237246	+	0.971450i	$0.576245\pi$
$984$	1.40399e28	−	6.01403e27i	0.517502	−	0.221673i
$985$	2.53850e28			0.926686
$986$	−5.99401e27	+	8.13545e26i	−0.216714	+	0.0294138i
$987$			2.86106e27i			0.102450i
$988$	−5.35190e27	+	1.48005e27i	−0.189809	+	0.0524912i
$989$		−	3.26855e28i		−	1.14813i
$990$	−3.68527e26	−	2.71522e27i	−0.0128214	−	0.0944649i
$991$	5.64468e27			0.194509			0.0972545	−	0.995260i	$-0.468994\pi$
$991$	5.64468e27			0.194509			0.0972545	+	0.995260i	$0.468994\pi$
$992$	−1.13786e28	−	1.42300e28i	−0.388355	−	0.485674i
$993$	−7.17505e27			−0.242553
$994$	7.40863e27	+	5.45851e28i	0.248066	+	1.82769i
$995$		−	7.19827e27i		−	0.238731i
$996$	−4.41087e27	+	1.21981e27i	−0.144897	+	0.0400710i
$997$			4.64862e28i			1.51259i	0.654233	+	0.756293i	$0.272992\pi$
$997$			4.64862e28i			1.51259i	−0.654233	+	0.756293i	$0.727008\pi$
$998$	−4.29181e28	+	5.82511e27i	−1.38325	+	0.187743i
$999$	1.49418e28			0.477012

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8.20.b.a.5.9	✓	18
3.2	odd	2		72.20.d.b.37.10		18
4.3	odd	2		32.20.b.a.17.14		18
8.3	odd	2		32.20.b.a.17.5		18
8.5	even	2	inner	8.20.b.a.5.10	yes	18
24.5	odd	2		72.20.d.b.37.9		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8.20.b.a.5.9	✓	18	1.1	even	1	trivial
8.20.b.a.5.10	yes	18	8.5	even	2	inner
32.20.b.a.17.5		18	8.3	odd	2
32.20.b.a.17.14		18	4.3	odd	2
72.20.d.b.37.9		18	24.5	odd	2
72.20.d.b.37.10		18	3.2	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)

\(f(q)\)	\(=\)	\(q+(-97.3835 - 717.499i) q^{2} -31021.8i q^{3} +(-505321. + 139745. i) q^{4} +4.13771e6i q^{5} +(-2.22581e7 + 3.02101e6i) q^{6} +1.99482e8 q^{7} +(1.49477e8 + 3.48958e8i) q^{8} +1.99908e8 q^{9} +O(q^{10})\)	\(q+(-97.3835 - 717.499i) q^{2} -31021.8i q^{3} +(-505321. + 139745. i) q^{4} +4.13771e6i q^{5} +(-2.22581e7 + 3.02101e6i) q^{6} +1.99482e8 q^{7} +(1.49477e8 + 3.48958e8i) q^{8} +1.99908e8 q^{9} +(2.96880e9 - 4.02945e8i) q^{10} -4.57503e9i q^{11} +(4.33515e9 + 1.56760e10i) q^{12} +6.56627e10i q^{13} +(-1.94262e10 - 1.43128e11i) q^{14} +1.28359e11 q^{15} +(2.35821e11 - 1.41232e11i) q^{16} -4.98732e11 q^{17} +(-1.94677e10 - 1.43434e11i) q^{18} -1.61295e11i q^{19} +(-5.78225e11 - 2.09087e12i) q^{20} -6.18829e12i q^{21} +(-3.28258e12 + 4.45532e11i) q^{22} +1.19892e13 q^{23} +(1.08253e13 - 4.63704e12i) q^{24} +1.95282e12 q^{25} +(4.71129e13 - 6.39447e12i) q^{26} -4.22570e13i q^{27} +(-1.00802e14 + 2.78766e13i) q^{28} +1.67505e13i q^{29} +(-1.25001e13 - 9.20977e13i) q^{30} +9.15425e13 q^{31} +(-1.24299e14 - 1.55447e14i) q^{32} -1.41926e14 q^{33} +(4.85682e13 + 3.57839e14i) q^{34} +8.25399e14i q^{35} +(-1.01018e14 + 2.79361e13i) q^{36} +3.53593e14i q^{37} +(-1.15729e14 + 1.57075e13i) q^{38} +2.03698e15 q^{39} +(-1.44389e15 + 6.18492e14i) q^{40} +1.29695e15 q^{41} +(-4.44009e15 + 6.02637e14i) q^{42} -2.72625e15i q^{43} +(6.39337e14 + 2.31186e15i) q^{44} +8.27161e14i q^{45} +(-1.16755e15 - 8.60222e15i) q^{46} -4.62334e14 q^{47} +(-4.38128e15 - 7.31558e15i) q^{48} +2.83941e16 q^{49} +(-1.90172e14 - 1.40115e15i) q^{50} +1.54716e16i q^{51} +(-9.17604e15 - 3.31807e16i) q^{52} -9.17027e15i q^{53} +(-3.03193e16 + 4.11513e15i) q^{54} +1.89301e16 q^{55} +(2.98179e16 + 6.96108e16i) q^{56} -5.00368e15 q^{57} +(1.20185e16 - 1.63123e15i) q^{58} -1.49941e16i q^{59} +(-6.48627e16 + 1.79376e16i) q^{60} +2.94422e16i q^{61} +(-8.91472e15 - 6.56816e16i) q^{62} +3.98780e16 q^{63} +(-9.94285e16 + 1.04322e17i) q^{64} -2.71693e17 q^{65} +(1.38212e16 + 1.01831e17i) q^{66} +3.06879e17i q^{67} +(2.52020e17 - 6.96953e16i) q^{68} -3.71926e17i q^{69} +(5.92222e17 - 8.03802e16i) q^{70} -3.81373e17 q^{71} +(2.98816e16 + 6.97595e16i) q^{72} +3.05182e17 q^{73} +(2.53702e17 - 3.44341e16i) q^{74} -6.05800e16i q^{75} +(2.25402e16 + 8.15060e16i) q^{76} -9.12635e17i q^{77} +(-1.98368e17 - 1.46153e18i) q^{78} -1.00134e18 q^{79} +(5.84378e17 + 9.75758e17i) q^{80} -1.07854e18 q^{81} +(-1.26302e17 - 9.30563e17i) q^{82} +2.81378e17i q^{83} +(8.64783e17 + 3.12707e18i) q^{84} -2.06361e18i q^{85} +(-1.95608e18 + 2.65492e17i) q^{86} +5.19633e17 q^{87} +(1.59649e18 - 6.83860e17i) q^{88} +5.08438e18 q^{89} +(5.93487e17 - 8.05518e16i) q^{90} +1.30985e19i q^{91} +(-6.05838e18 + 1.67543e18i) q^{92} -2.83981e18i q^{93} +(4.50237e16 + 3.31724e17i) q^{94} +6.67394e17 q^{95} +(-4.82226e18 + 3.85598e18i) q^{96} -4.80840e18 q^{97} +(-2.76512e18 - 2.03727e19i) q^{98} -9.14583e17i 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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