LMFDB - Embedded newform 8.20.b.a.5.18

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			5.18
Root			$0.500000 + 7326.87i$ of defining polynomial
Character	$\chi$	$=$	8.5
Dual form			8.20.b.a.5.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(698.474 + 190.846i) q^{2} -29307.5i q^{3} +(451443. + 266602. i) q^{4} -795283. i q^{5} +(5.59322e6 - 2.04705e7i) q^{6} +3.26570e7 q^{7} +(2.64441e8 + 2.72371e8i) q^{8} +3.03333e8 q^{9} +O(q^{10})$	\(q+(698.474 + 190.846i) q^{2} -29307.5i q^{3} +(451443. + 266602. i) q^{4} -795283. i q^{5} +(5.59322e6 - 2.04705e7i) q^{6} +3.26570e7 q^{7} +(2.64441e8 + 2.72371e8i) q^{8} +3.03333e8 q^{9} +(1.51777e8 - 5.55484e8i) q^{10} -7.73821e9i q^{11} +(7.81344e9 - 1.32307e10i) q^{12} -4.36653e10i q^{13} +(2.28101e10 + 6.23247e9i) q^{14} -2.33077e10 q^{15} +(1.32725e11 + 2.40712e11i) q^{16} +6.06271e10 q^{17} +(2.11870e11 + 5.78899e10i) q^{18} -9.91463e11i q^{19} +(2.12024e11 - 3.59025e11i) q^{20} -9.57095e11i q^{21} +(1.47681e12 - 5.40494e12i) q^{22} +6.78641e12 q^{23} +(7.98251e12 - 7.75012e12i) q^{24} +1.84410e13 q^{25} +(8.33335e12 - 3.04990e13i) q^{26} -4.29529e13i q^{27} +(1.47428e13 + 8.70643e12i) q^{28} +7.31976e13i q^{29} +(-1.62798e13 - 4.44819e12i) q^{30} -1.38011e14 q^{31} +(4.67657e13 + 1.93461e14i) q^{32} -2.26787e14 q^{33} +(4.23464e13 + 1.15704e13i) q^{34} -2.59716e13i q^{35} +(1.36937e14 + 8.08691e13i) q^{36} +9.51542e14i q^{37} +(1.89217e14 - 6.92511e14i) q^{38} -1.27972e15 q^{39} +(2.16612e14 - 2.10306e14i) q^{40} -1.79613e15 q^{41} +(1.82658e14 - 6.68506e14i) q^{42} +4.29602e15i q^{43} +(2.06302e15 - 3.49336e15i) q^{44} -2.41235e14i q^{45} +(4.74013e15 + 1.29516e15i) q^{46} -2.72920e15 q^{47} +(7.05465e15 - 3.88982e15i) q^{48} -1.03324e16 q^{49} +(1.28806e16 + 3.51940e15i) q^{50} -1.77683e15i q^{51} +(1.16413e16 - 1.97124e16i) q^{52} -1.42459e16i q^{53} +(8.19739e15 - 3.00015e16i) q^{54} -6.15406e15 q^{55} +(8.63587e15 + 8.89482e15i) q^{56} -2.90573e16 q^{57} +(-1.39695e16 + 5.11266e16i) q^{58} +5.38728e16i q^{59} +(-1.05221e16 - 6.21389e15i) q^{60} +1.47852e17i q^{61} +(-9.63970e16 - 2.63389e16i) q^{62} +9.90594e15 q^{63} +(-4.25660e15 + 1.44052e17i) q^{64} -3.47262e16 q^{65} +(-1.58405e17 - 4.32815e16i) q^{66} -3.11717e17i q^{67} +(2.73697e16 + 1.61633e16i) q^{68} -1.98893e17i q^{69} +(4.95657e15 - 1.81405e16i) q^{70} +6.27690e17 q^{71} +(8.02137e16 + 8.26189e16i) q^{72} +1.71042e17 q^{73} +(-1.81598e17 + 6.64627e17i) q^{74} -5.40460e17i q^{75} +(2.64326e17 - 4.47589e17i) q^{76} -2.52707e17i q^{77} +(-8.93850e17 - 2.44230e17i) q^{78} +1.66663e18 q^{79} +(1.91434e17 - 1.05554e17i) q^{80} -9.06289e17 q^{81} +(-1.25455e18 - 3.42785e17i) q^{82} +1.40928e18i q^{83} +(2.55164e17 - 4.32075e17i) q^{84} -4.82156e16i q^{85} +(-8.19880e17 + 3.00066e18i) q^{86} +2.14524e18 q^{87} +(2.10766e18 - 2.04630e18i) q^{88} -5.88693e18 q^{89} +(4.60388e16 - 1.68496e17i) q^{90} -1.42598e18i q^{91} +(3.06368e18 + 1.80927e18i) q^{92} +4.04475e18i q^{93} +(-1.90628e18 - 5.20857e17i) q^{94} -7.88493e17 q^{95} +(5.66985e18 - 1.37059e18i) q^{96} -1.38633e19 q^{97} +(-7.21692e18 - 1.97190e18i) q^{98} -2.34725e18i 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 $

$2$	698.474	+	190.846i	0.964640	+	0.263572i
$2$	698.474	+	190.846i	0.964640	+	0.263572i
$3$		−	29307.5i		−	0.859660i	−0.902910	−	0.429830i	$-0.858573\pi$
$3$		−	29307.5i		−	0.859660i	0.902910	−	0.429830i	$-0.141427\pi$
$4$	451443.	+	266602.i	0.861060	+	0.508503i
$5$		−	795283.i		−	0.182099i	−0.995846	−	0.0910493i	$-0.970978\pi$
$5$		−	795283.i		−	0.182099i	0.995846	−	0.0910493i	$-0.0290221\pi$
$6$	5.59322e6	−	2.04705e7i	0.226582	−	0.829262i
$7$	3.26570e7			0.305876			0.152938	−	0.988236i	$-0.451127\pi$
$7$	3.26570e7			0.305876			0.152938	+	0.988236i	$0.451127\pi$
$8$	2.64441e8	+	2.72371e8i	0.696586	+	0.717473i
$9$	3.03333e8			0.260985
$10$	1.51777e8	−	5.55484e8i	0.0479960	−	0.175660i
$11$		−	7.73821e9i		−	0.989487i	−0.869039	−	0.494743i	$-0.835262\pi$
$11$		−	7.73821e9i		−	0.989487i	0.869039	−	0.494743i	$-0.164738\pi$
$12$	7.81344e9	−	1.32307e10i	0.437140	−	0.740219i
$13$		−	4.36653e10i		−	1.14202i	−0.820943	−	0.571011i	$-0.806551\pi$
$13$		−	4.36653e10i		−	1.14202i	0.820943	−	0.571011i	$-0.193449\pi$
$14$	2.28101e10	+	6.23247e9i	0.295060	+	0.0806202i
$15$	−2.33077e10			−0.156543
$16$	1.32725e11	+	2.40712e11i	0.482849	+	0.875704i
$17$	6.06271e10			0.123994			0.0619972	−	0.998076i	$-0.480253\pi$
$17$	6.06271e10			0.123994			0.0619972	+	0.998076i	$0.480253\pi$
$18$	2.11870e11	+	5.78899e10i	0.251756	+	0.0687882i
$19$		−	9.91463e11i		−	0.704883i	−0.935834	−	0.352442i	$-0.885351\pi$
$19$		−	9.91463e11i		−	0.704883i	0.935834	−	0.352442i	$-0.114649\pi$
$20$	2.12024e11	−	3.59025e11i	0.0925977	−	0.156798i
$21$		−	9.57095e11i		−	0.262949i
$22$	1.47681e12	−	5.40494e12i	0.260801	−	0.954498i
$23$	6.78641e12			0.785644			0.392822	−	0.919615i	$-0.371499\pi$
$23$	6.78641e12			0.785644			0.392822	+	0.919615i	$0.371499\pi$
$24$	7.98251e12	−	7.75012e12i	0.616783	−	0.598827i
$25$	1.84410e13			0.966840
$26$	8.33335e12	−	3.04990e13i	0.301004	−	1.10164i
$27$		−	4.29529e13i		−	1.08402i
$28$	1.47428e13	+	8.70643e12i	0.263378	+	0.155539i
$29$			7.31976e13i			0.936949i	0.883477	+	0.468475i	$0.155196\pi$
$29$			7.31976e13i			0.936949i	−0.883477	+	0.468475i	$0.844804\pi$
$30$	−1.62798e13	−	4.44819e12i	−0.151007	−	0.0412602i
$31$	−1.38011e14			−0.937513			−0.468757	−	0.883327i	$-0.655298\pi$
$31$	−1.38011e14			−0.937513			−0.468757	+	0.883327i	$0.655298\pi$
$32$	4.67657e13	+	1.93461e14i	0.234965	+	0.972004i
$33$	−2.26787e14			−0.850622
$34$	4.23464e13	+	1.15704e13i	0.119610	+	0.0326814i
$35$		−	2.59716e13i		−	0.0556996i
$36$	1.36937e14	+	8.08691e13i	0.224724	+	0.132712i
$37$			9.51542e14i			1.20368i	0.798616	+	0.601841i	$0.205566\pi$
$37$			9.51542e14i			1.20368i	−0.798616	+	0.601841i	$0.794434\pi$
$38$	1.89217e14	−	6.92511e14i	0.185787	−	0.679959i
$39$	−1.27972e15			−0.981750
$40$	2.16612e14	−	2.10306e14i	0.130651	−	0.126847i
$41$	−1.79613e15			−0.856823			−0.428412	−	0.903584i	$-0.640927\pi$
$41$	−1.79613e15			−0.856823			−0.428412	+	0.903584i	$0.640927\pi$
$42$	1.82658e14	−	6.68506e14i	0.0693059	−	0.253651i
$43$			4.29602e15i			1.30352i	0.758427	+	0.651758i	$0.225968\pi$
$43$			4.29602e15i			1.30352i	−0.758427	+	0.651758i	$0.774032\pi$
$44$	2.06302e15	−	3.49336e15i	0.503157	−	0.852008i
$45$		−	2.41235e14i		−	0.0475249i
$46$	4.74013e15	+	1.29516e15i	0.757863	+	0.207073i
$47$	−2.72920e15			−0.355718			−0.177859	−	0.984056i	$-0.556917\pi$
$47$	−2.72920e15			−0.355718			−0.177859	+	0.984056i	$0.556917\pi$
$48$	7.05465e15	−	3.88982e15i	0.752807	−	0.415086i
$49$	−1.03324e16			−0.906440
$50$	1.28806e16	+	3.51940e15i	0.932653	+	0.254832i
$51$		−	1.77683e15i		−	0.106593i
$52$	1.16413e16	−	1.97124e16i	0.580722	−	0.983349i
$53$		−	1.42459e16i		−	0.593019i	−0.955030	−	0.296510i	$-0.904177\pi$
$53$		−	1.42459e16i		−	0.593019i	0.955030	−	0.296510i	$-0.0958227\pi$
$54$	8.19739e15	−	3.00015e16i	0.285716	−	1.04569i
$55$	−6.15406e15			−0.180184
$56$	8.63587e15	+	8.89482e15i	0.213069	+	0.219458i
$57$	−2.90573e16			−0.605960
$58$	−1.39695e16	+	5.11266e16i	−0.246953	+	0.903819i
$59$			5.38728e16i			0.809609i	0.914403	+	0.404804i	$0.132660\pi$
$59$			5.38728e16i			0.809609i	−0.914403	+	0.404804i	$0.867340\pi$
$60$	−1.05221e16	−	6.21389e15i	−0.134793	−	0.0796025i
$61$			1.47852e17i			1.61881i	0.587254	+	0.809403i	$0.300209\pi$
$61$			1.47852e17i			1.61881i	−0.587254	+	0.809403i	$0.699791\pi$
$62$	−9.63970e16	−	2.63389e16i	−0.904363	−	0.247102i
$63$	9.90594e15			0.0798290
$64$	−4.25660e15	+	1.44052e17i	−0.0295361	+	0.999564i
$65$	−3.47262e16			−0.207960
$66$	−1.58405e17	−	4.32815e16i	−0.820544	−	0.224200i
$67$		−	3.11717e17i		−	1.39975i	−0.714266	−	0.699874i	$-0.753239\pi$
$67$		−	3.11717e17i		−	1.39975i	0.714266	−	0.699874i	$-0.246761\pi$
$68$	2.73697e16	+	1.61633e16i	0.106767	+	0.0630515i
$69$		−	1.98893e17i		−	0.675386i
$70$	4.95657e15	−	1.81405e16i	0.0146808	−	0.0537300i
$71$	6.27690e17			1.62477			0.812383	−	0.583124i	$-0.198170\pi$
$71$	6.27690e17			1.62477			0.812383	+	0.583124i	$0.198170\pi$
$72$	8.02137e16	+	8.26189e16i	0.181798	+	0.187250i
$73$	1.71042e17			0.340043			0.170022	−	0.985440i	$-0.445616\pi$
$73$	1.71042e17			0.340043			0.170022	+	0.985440i	$0.445616\pi$
$74$	−1.81598e17	+	6.64627e17i	−0.317256	+	1.16112i
$75$		−	5.40460e17i		−	0.831154i
$76$	2.64326e17	−	4.47589e17i	0.358435	−	0.606947i
$77$		−	2.52707e17i		−	0.302660i
$78$	−8.93850e17	−	2.44230e17i	−0.947035	−	0.258761i
$79$	1.66663e18			1.56452			0.782261	−	0.622950i	$-0.214066\pi$
$79$	1.66663e18			1.56452			0.782261	+	0.622950i	$0.214066\pi$
$80$	1.91434e17	−	1.05554e17i	0.159464	−	0.0879261i
$81$	−9.06289e17			−0.670902
$82$	−1.25455e18	−	3.42785e17i	−0.826526	−	0.225834i
$83$			1.40928e18i			0.827476i	0.910396	+	0.413738i	$0.135777\pi$
$83$			1.40928e18i			0.827476i	−0.910396	+	0.413738i	$0.864223\pi$
$84$	2.55164e17	−	4.32075e17i	0.133711	−	0.226415i
$85$		−	4.82156e16i		−	0.0225792i
$86$	−8.19880e17	+	3.00066e18i	−0.343570	+	1.25742i
$87$	2.14524e18			0.805458
$88$	2.10766e18	−	2.04630e18i	0.709930	−	0.689263i
$89$	−5.88693e18			−1.78108			−0.890541	−	0.454904i	$-0.849674\pi$
$89$	−5.88693e18			−1.78108			−0.890541	+	0.454904i	$0.849674\pi$
$90$	4.60388e16	−	1.68496e17i	0.0125262	−	0.0458445i
$91$		−	1.42598e18i		−	0.349317i
$92$	3.06368e18	+	1.80927e18i	0.676486	+	0.399502i
$93$			4.04475e18i			0.805943i
$94$	−1.90628e18	−	5.20857e17i	−0.343140	−	0.0937571i
$95$	−7.88493e17			−0.128358
$96$	5.66985e18	−	1.37059e18i	0.835593	−	0.201990i
$97$	−1.38633e19			−1.85155			−0.925777	−	0.378069i	$-0.876588\pi$
$97$	−1.38633e19			−1.85155			−0.925777	+	0.378069i	$0.876588\pi$
$98$	−7.21692e18	−	1.97190e18i	−0.874388	−	0.238912i
$99$		−	2.34725e18i		−	0.258241i
$100$	8.32507e18	+	4.91641e18i	0.832507	+	0.491641i
$101$			1.49264e19i			1.35800i	0.734136	+	0.679002i	$0.237587\pi$
$101$			1.49264e19i			1.35800i	−0.734136	+	0.679002i	$0.762413\pi$
$102$	3.39101e17	−	1.24107e18i	0.0280949	−	0.102824i
$103$	1.02597e19			0.774783			0.387392	−	0.921915i	$-0.373376\pi$
$103$	1.02597e19			0.774783			0.387392	+	0.921915i	$0.373376\pi$
$104$	1.18931e19	−	1.15469e19i	0.819370	−	0.795516i
$105$	−7.61161e17			−0.0478827
$106$	2.71877e18	−	9.95038e18i	0.156303	−	0.572050i
$107$		−	8.70648e18i		−	0.457822i	−0.973447	−	0.228911i	$-0.926484\pi$
$107$		−	8.70648e18i		−	0.457822i	0.973447	−	0.228911i	$-0.0735165\pi$
$108$	1.14513e19	−	1.93908e19i	0.551227	−	0.933405i
$109$		−	1.22608e19i		−	0.540713i	−0.962760	−	0.270357i	$-0.912858\pi$
$109$		−	1.22608e19i		−	0.540713i	0.962760	−	0.270357i	$-0.0871416\pi$
$110$	−4.29845e18	−	1.17448e18i	−0.173813	−	0.0474914i
$111$	2.78873e19			1.03476
$112$	4.33439e18	+	7.86092e18i	0.147692	+	0.267857i
$113$	−1.85291e19			−0.580243			−0.290122	−	0.956990i	$-0.593696\pi$
$113$	−1.85291e19			−0.580243			−0.290122	+	0.956990i	$0.593696\pi$
$114$	−2.02958e19	−	5.54547e18i	−0.584533	−	0.159714i
$115$		−	5.39711e18i		−	0.143065i
$116$	−1.95146e19	+	3.30446e19i	−0.476442	+	0.806770i
$117$		−	1.32451e19i		−	0.298050i
$118$	−1.02814e19	+	3.76287e19i	−0.213390	+	0.780981i
$119$	1.97990e18			0.0379269
$120$	−6.16353e18	−	6.34835e18i	−0.109046	−	0.112315i
$121$	1.27920e18			0.0209160
$122$	−2.82170e19	+	1.03271e20i	−0.426671	+	1.56156i
$123$			5.26401e19i			0.736577i
$124$	−6.23041e19	−	3.67940e19i	−0.807255	−	0.476729i
$125$		−	2.98346e19i		−	0.358159i
$126$	6.91904e18	+	1.89051e18i	0.0770062	+	0.0210406i
$127$	2.87821e18			0.0297158			0.0148579	−	0.999890i	$-0.495270\pi$
$127$	2.87821e18			0.0297158			0.0148579	+	0.999890i	$0.495270\pi$
$128$	−3.04650e19	+	9.98044e19i	−0.291948	+	0.956434i
$129$	1.25906e20			1.12058
$130$	−2.42554e19	−	6.62737e18i	−0.200607	−	0.0548125i
$131$		−	4.07385e19i		−	0.313276i	−0.987656	−	0.156638i	$-0.949934\pi$
$131$		−	4.07385e19i		−	0.313276i	0.987656	−	0.156638i	$-0.0500656\pi$
$132$	−1.02382e20	−	6.04620e19i	−0.732437	−	0.432544i
$133$		−	3.23782e19i		−	0.215607i
$134$	5.94900e19	−	2.17726e20i	0.368934	−	1.35025i
$135$	−3.41597e19			−0.197398
$136$	1.60323e19	+	1.65130e19i	0.0863727	+	0.0889626i
$137$	2.13997e20			1.07538			0.537689	−	0.843143i	$-0.319297\pi$
$137$	2.13997e20			1.07538			0.537689	+	0.843143i	$0.319297\pi$
$138$	3.79579e19	−	1.38921e20i	0.178013	−	0.651505i
$139$		−	1.45435e20i		−	0.636836i	−0.947950	−	0.318418i	$-0.896848\pi$
$139$		−	1.45435e20i		−	0.636836i	0.947950	−	0.318418i	$-0.103152\pi$
$140$	6.92408e18	−	1.17247e19i	0.0283234	−	0.0479607i
$141$			7.99860e19i			0.305797i
$142$	4.38425e20	+	1.19792e20i	1.56731	+	0.428242i
$143$	−3.37891e20			−1.13002
$144$	4.02597e19	+	7.30157e19i	0.126016	+	0.228545i
$145$	5.82128e19			0.170617
$146$	1.19468e20	+	3.26426e19i	0.328020	+	0.0896258i
$147$			3.02817e20i			0.779230i
$148$	−2.53683e20	+	4.29567e20i	−0.612076	+	1.03644i
$149$		−	1.05998e20i		−	0.239899i	−0.992780	−	0.119950i	$-0.961727\pi$
$149$		−	1.05998e20i		−	0.239899i	0.992780	−	0.119950i	$-0.0382733\pi$
$150$	1.03145e20	−	3.77497e20i	0.219068	−	0.801764i
$151$	−8.94254e20			−1.78312			−0.891559	−	0.452905i	$-0.850388\pi$
$151$	−8.94254e20			−1.78312			−0.891559	+	0.452905i	$0.850388\pi$
$152$	2.70046e20	−	2.62184e20i	0.505735	−	0.491012i
$153$	1.83902e19			0.0323606
$154$	4.82281e19	−	1.76509e20i	0.0797726	−	0.291958i
$155$			1.09758e20i			0.170720i
$156$	−5.77721e20	−	3.41176e20i	−0.845346	−	0.499223i
$157$			2.28078e20i			0.314077i	0.987592	+	0.157039i	$0.0501947\pi$
$157$			2.28078e20i			0.314077i	−0.987592	+	0.157039i	$0.949805\pi$
$158$	1.16410e21	+	3.18070e20i	1.50920	+	0.412364i
$159$	−4.17511e20			−0.509795
$160$	1.53856e20	−	3.71920e19i	0.177000	−	0.0427868i
$161$	2.21624e20			0.240309
$162$	−6.33019e20	−	1.72962e20i	−0.647179	−	0.176831i
$163$			1.40108e21i			1.35108i	0.737323	+	0.675540i	$0.236090\pi$
$163$			1.40108e21i			1.35108i	−0.737323	+	0.675540i	$0.763910\pi$
$164$	−8.10851e20	−	4.78852e20i	−0.737776	−	0.435697i
$165$			1.80360e20i			0.154897i
$166$	−2.68956e20	+	9.84345e20i	−0.218099	+	0.798216i
$167$	6.76978e20			0.518523			0.259261	−	0.965807i	$-0.416521\pi$
$167$	6.76978e20			0.518523			0.259261	+	0.965807i	$0.416521\pi$
$168$	2.60685e20	−	2.53096e20i	0.188659	−	0.183167i
$169$	−4.44735e20			−0.304213
$170$	9.20177e18	−	3.36774e19i	0.00595123	−	0.0217808i
$171$		−	3.00743e20i		−	0.183964i
$172$	−1.14533e21	+	1.93941e21i	−0.662842	+	1.12241i
$173$		−	2.61061e21i		−	1.42990i	−0.699177	−	0.714948i	$-0.746450\pi$
$173$		−	2.61061e21i		−	1.42990i	0.699177	−	0.714948i	$-0.253550\pi$
$174$	1.49839e21	+	4.09411e20i	0.776977	+	0.212296i
$175$	6.02229e20			0.295733
$176$	1.86268e21	−	1.02705e21i	0.866497	−	0.477773i
$177$	1.57888e21			0.695988
$178$	−4.11187e21	−	1.12350e21i	−1.71810	−	0.469442i
$179$		−	4.75334e21i		−	1.88319i	−0.336744	−	0.941596i	$-0.609326\pi$
$179$		−	4.75334e21i		−	1.88319i	0.336744	−	0.941596i	$-0.390674\pi$
$180$	6.43138e19	−	1.08904e20i	0.0241666	−	0.0409218i
$181$			2.12829e21i			0.758725i	0.925248	+	0.379362i	$0.123857\pi$
$181$			2.12829e21i			0.758725i	−0.925248	+	0.379362i	$0.876143\pi$
$182$	2.72142e20	−	9.96008e20i	0.0920700	−	0.336965i
$183$	4.33318e21			1.39162
$184$	1.79461e21	+	1.84842e21i	0.547268	+	0.563678i
$185$	7.56745e20			0.219189
$186$	−7.71926e20	+	2.82516e21i	−0.212424	+	0.777444i
$187$		−	4.69145e20i		−	0.122691i
$188$	−1.23208e21	−	7.27611e20i	−0.306295	−	0.180884i
$189$		−	1.40271e21i		−	0.331575i
$190$	−5.50742e20	−	1.50481e20i	−0.123819	−	0.0338316i
$191$	4.33752e21			0.927736			0.463868	−	0.885904i	$-0.346461\pi$
$191$	4.33752e21			0.927736			0.463868	+	0.885904i	$0.346461\pi$
$192$	4.22181e21	+	1.24750e20i	0.859285	+	0.0253910i
$193$	−6.03488e21			−1.16916			−0.584580	−	0.811336i	$-0.698741\pi$
$193$	−6.03488e21			−1.16916			−0.584580	+	0.811336i	$0.698741\pi$
$194$	−9.68318e21	−	2.64577e21i	−1.78608	−	0.488017i
$195$			1.01774e21i			0.178775i
$196$	−4.66450e21	−	2.75464e21i	−0.780499	−	0.460928i
$197$			9.90644e21i			1.57939i	0.613502	+	0.789693i	$0.289760\pi$
$197$			9.90644e21i			1.57939i	−0.613502	+	0.789693i	$0.710240\pi$
$198$	4.47964e20	−	1.63949e21i	0.0680650	−	0.249110i
$199$	−2.78257e21			−0.403034			−0.201517	−	0.979485i	$-0.564587\pi$
$199$	−2.78257e21			−0.403034			−0.201517	+	0.979485i	$0.564587\pi$
$200$	4.87657e21	+	5.02279e21i	0.673487	+	0.693682i
$201$	−9.13564e21			−1.20331
$202$	−2.84864e21	+	1.04257e22i	−0.357931	+	1.30999i
$203$			2.39042e21i			0.286590i
$204$	4.73706e20	−	8.02137e20i	0.0542029	−	0.0917829i
$205$			1.42843e21i			0.156026i
$206$	7.16612e21	+	1.95802e21i	0.747387	+	0.204211i
$207$	2.05854e21			0.205041
$208$	1.05107e22	−	5.79545e21i	1.00007	−	0.551424i
$209$	−7.67215e21			−0.697473
$210$	−5.31651e20	−	1.45265e20i	−0.0461895	−	0.0126205i
$211$			6.29228e21i			0.522546i	0.965265	+	0.261273i	$0.0841423\pi$
$211$			6.29228e21i			0.522546i	−0.965265	+	0.261273i	$0.915858\pi$
$212$	3.79799e21	−	6.43121e21i	0.301552	−	0.510625i
$213$		−	1.83960e22i		−	1.39675i
$214$	1.66160e21	−	6.08125e21i	0.120669	−	0.441633i
$215$	3.41655e21			0.237368
$216$	1.16991e22	−	1.13585e22i	0.777754	−	0.755112i
$217$	−4.50703e21			−0.286763
$218$	2.33993e21	−	8.56384e21i	0.142517	−	0.521593i
$219$		−	5.01280e21i		−	0.292322i
$220$	−2.77821e21	−	1.64069e21i	−0.155149	−	0.0916242i
$221$		−	2.64730e21i		−	0.141604i
$222$	1.94785e22	+	5.32218e21i	0.998167	+	0.272732i
$223$	−5.36245e21			−0.263310			−0.131655	−	0.991296i	$-0.542029\pi$
$223$	−5.36245e21			−0.263310			−0.131655	+	0.991296i	$0.542029\pi$
$224$	1.52723e21	+	6.31785e21i	0.0718701	+	0.297313i
$225$	5.59376e21			0.252331
$226$	−1.29421e22	−	3.53622e21i	−0.559726	−	0.152936i
$227$			1.49703e21i			0.0620849i	0.999518	+	0.0310425i	$0.00988271\pi$
$227$			1.49703e21i			0.0620849i	−0.999518	+	0.0310425i	$0.990117\pi$
$228$	−1.31177e22	−	7.74673e21i	−0.521768	−	0.308133i
$229$			4.99153e22i			1.90457i	0.305212	+	0.952285i	$0.401273\pi$
$229$			4.99153e22i			1.90457i	−0.305212	+	0.952285i	$0.598727\pi$
$230$	1.03002e21	−	3.76974e21i	0.0377077	−	0.138006i
$231$	−7.40621e21			−0.260185
$232$	−1.99369e22	+	1.93565e22i	−0.672236	+	0.652666i
$233$	3.89844e22			1.26186			0.630928	−	0.775842i	$-0.282674\pi$
$233$	3.89844e22			1.26186			0.630928	+	0.775842i	$0.282674\pi$
$234$	2.52778e21	−	9.25135e21i	0.0785575	−	0.287511i
$235$			2.17049e21i			0.0647757i
$236$	−1.43626e22	+	2.43205e22i	−0.411689	+	0.697122i
$237$		−	4.88448e22i		−	1.34496i
$238$	1.38291e21	+	3.77856e20i	0.0365858	+	0.00999644i
$239$	−1.73696e22			−0.441580			−0.220790	−	0.975321i	$-0.570864\pi$
$239$	−1.73696e22			−0.441580			−0.220790	+	0.975321i	$0.570864\pi$
$240$	−3.09351e21	−	5.61044e21i	−0.0755865	−	0.137085i
$241$	2.16192e22			0.507782			0.253891	−	0.967233i	$-0.418289\pi$
$241$	2.16192e22			0.507782			0.253891	+	0.967233i	$0.418289\pi$
$242$	8.93489e20	+	2.44131e20i	0.0201764	+	0.00551286i
$243$		−	2.33614e22i		−	0.507270i
$244$	−3.94177e22	+	6.67470e22i	−0.823168	+	1.39389i
$245$			8.21719e21i			0.165061i
$246$	−1.00462e22	+	3.67677e22i	−0.194141	+	0.710531i
$247$	−4.32925e22			−0.804992
$248$	−3.64958e22	−	3.75902e22i	−0.653059	−	0.672641i
$249$	4.13025e22			0.711348
$250$	5.69382e21	−	2.08387e22i	0.0944004	−	0.345494i
$251$		−	9.73253e21i		−	0.155355i	−0.996979	−	0.0776775i	$-0.975250\pi$
$251$		−	9.73253e21i		−	0.155355i	0.996979	−	0.0776775i	$-0.0247505\pi$
$252$	4.47197e21	+	2.64094e21i	0.0687375	+	0.0405933i
$253$		−	5.25146e22i		−	0.777384i
$254$	2.01035e21	+	5.49295e20i	0.0286650	+	0.00783223i
$255$	−1.41308e21			−0.0194104
$256$	−4.03263e22	+	6.38967e22i	−0.533714	+	0.845665i
$257$	7.91267e22			1.00916			0.504578	−	0.863366i	$-0.331648\pi$
$257$	7.91267e22			1.00916			0.504578	+	0.863366i	$0.331648\pi$
$258$	8.79418e22	+	2.40286e22i	1.08096	+	0.295353i
$259$			3.10745e22i			0.368177i
$260$	−1.56769e22	−	9.25809e21i	−0.179066	−	0.105749i
$261$			2.22032e22i			0.244530i
$262$	7.77478e21	−	2.84548e22i	0.0825707	−	0.302199i
$263$	3.11136e22			0.318692			0.159346	−	0.987223i	$-0.449061\pi$
$263$	3.11136e22			0.318692			0.159346	+	0.987223i	$0.449061\pi$
$264$	−5.99720e22	−	6.17703e22i	−0.592531	−	0.610299i
$265$	−1.13295e22			−0.107988
$266$	6.17926e21	−	2.26153e22i	0.0568278	−	0.207983i
$267$			1.72531e23i			1.53112i
$268$	8.31044e22	−	1.40723e23i	0.711776	−	1.20527i
$269$		−	1.37189e23i		−	1.13416i	−0.823663	−	0.567079i	$-0.808073\pi$
$269$		−	1.37189e23i		−	1.13416i	0.823663	−	0.567079i	$-0.191927\pi$
$270$	−2.38596e22	−	6.51924e21i	−0.190418	−	0.0520285i
$271$	−5.84094e22			−0.450064			−0.225032	−	0.974351i	$-0.572249\pi$
$271$	−5.84094e22			−0.450064			−0.225032	+	0.974351i	$0.572249\pi$
$272$	8.04670e21	+	1.45936e22i	0.0598705	+	0.108582i
$273$	−4.17918e22			−0.300294
$274$	1.49471e23	+	4.08404e22i	1.03735	+	0.283439i
$275$		−	1.42700e23i		−	0.956675i
$276$	5.30252e22	−	8.97888e22i	0.343436	−	0.581548i
$277$			1.67395e23i			1.04757i	0.851849	+	0.523787i	$0.175481\pi$
$277$			1.67395e23i			1.04757i	−0.851849	+	0.523787i	$0.824519\pi$
$278$	2.77557e22	−	1.01582e23i	0.167852	−	0.614318i
$279$	−4.18632e22			−0.244677
$280$	7.07390e21	−	6.86796e21i	0.0399630	−	0.0387995i
$281$	−1.26739e23			−0.692152			−0.346076	−	0.938207i	$-0.612486\pi$
$281$	−1.26739e23			−0.692152			−0.346076	+	0.938207i	$0.612486\pi$
$282$	−1.52650e22	+	5.58681e22i	−0.0805993	+	0.294983i
$283$		−	1.60387e23i		−	0.818838i	−0.912346	−	0.409419i	$-0.865731\pi$
$283$		−	1.60387e23i		−	0.818838i	0.912346	−	0.409419i	$-0.134269\pi$
$284$	2.83366e23	+	1.67343e23i	1.39902	+	0.826199i
$285$			2.31088e22i			0.110344i
$286$	−2.36008e23	−	6.44852e22i	−1.09006	−	0.297840i
$287$	−5.86563e22			−0.262082
$288$	1.41856e22	+	5.86829e22i	0.0613222	+	0.253678i
$289$	−2.35397e23			−0.984625
$290$	4.06601e22	+	1.11097e22i	0.164584	+	0.0449698i
$291$			4.06300e23i			1.59171i
$292$	7.72156e22	+	4.56000e22i	0.292798	+	0.172913i
$293$			3.06965e23i			1.12680i	0.826185	+	0.563399i	$0.190507\pi$
$293$			3.06965e23i			1.12680i	−0.826185	+	0.563399i	$0.809493\pi$
$294$	−5.77915e22	+	2.11510e23i	−0.205383	+	0.751676i
$295$	4.28441e22			0.147429
$296$	−2.59172e23	+	2.51627e23i	−0.863609	+	0.838467i
$297$	−3.32378e23			−1.07262
$298$	2.02294e22	−	7.40370e22i	0.0632306	−	0.231416i
$299$		−	2.96330e23i		−	0.897222i
$300$	1.44088e23	−	2.43987e23i	0.422644	−	0.715673i
$301$			1.40295e23i			0.398714i
$302$	−6.24613e23	−	1.70665e23i	−1.72007	−	0.469979i
$303$	4.37454e23			1.16742
$304$	2.38657e23	−	1.31591e23i	0.617269	−	0.340352i
$305$	1.17584e23			0.294782
$306$	1.28450e22	+	3.50969e21i	0.0312163	+	0.00852934i
$307$		−	3.82764e23i		−	0.901814i	−0.892571	−	0.450907i	$-0.851101\pi$
$307$		−	3.82764e23i		−	0.901814i	0.892571	−	0.450907i	$-0.148899\pi$
$308$	6.73722e22	−	1.14083e23i	0.153904	−	0.260609i
$309$		−	3.00685e23i		−	0.666050i
$310$	−2.09468e22	+	7.66629e22i	−0.0449969	+	0.164683i
$311$	6.73059e23			1.40226			0.701132	−	0.713032i	$-0.252679\pi$
$311$	6.73059e23			1.40226			0.701132	+	0.713032i	$0.252679\pi$
$312$	−3.38411e23	−	3.48558e23i	−0.683873	−	0.704380i
$313$	4.06604e23			0.797077			0.398539	−	0.917152i	$-0.369518\pi$
$313$	4.06604e23			0.797077			0.398539	+	0.917152i	$0.369518\pi$
$314$	−4.35278e22	+	1.59306e23i	−0.0827818	+	0.302971i
$315$		−	7.87802e21i		−	0.0145367i
$316$	7.52389e23	+	4.44327e23i	1.34715	+	0.795565i
$317$		−	2.80601e23i		−	0.487559i	−0.969831	−	0.243779i	$-0.921613\pi$
$317$		−	2.80601e23i		−	0.487559i	0.969831	−	0.243779i	$-0.0783873\pi$
$318$	−2.91621e23	−	7.96804e22i	−0.491769	−	0.134367i
$319$	5.66419e23			0.927099
$320$	1.14562e23	+	3.38520e21i	0.182019	+	0.00537848i
$321$	−2.55165e23			−0.393571
$322$	1.54799e23	+	4.22961e22i	0.231812	+	0.0633387i
$323$		−	6.01095e22i		−	0.0874015i
$324$	−4.09138e23	−	2.41619e23i	−0.577687	−	0.341156i
$325$		−	8.05232e23i		−	1.10415i
$326$	−2.67391e23	+	9.78619e23i	−0.356106	+	1.30331i
$327$	−3.59333e23			−0.464829
$328$	−4.74971e23	−	4.89214e23i	−0.596851	−	0.614748i
$329$	−8.91276e22			−0.108806
$330$	−3.44210e22	+	1.25977e23i	−0.0408265	+	0.149420i
$331$			1.29565e23i			0.149321i	0.997209	+	0.0746604i	$0.0237873\pi$
$331$			1.29565e23i			0.149321i	−0.997209	+	0.0746604i	$0.976213\pi$
$332$	−3.75717e23	+	6.36210e23i	−0.420774	+	0.712507i
$333$			2.88634e23i			0.314142i
$334$	4.72851e23	+	1.29199e23i	0.500188	+	0.136668i
$335$	−2.47903e23			−0.254892
$336$	2.30384e23	−	1.27030e23i	0.230266	−	0.126965i
$337$	2.93005e22			0.0284702			0.0142351	−	0.999899i	$-0.495469\pi$
$337$	2.93005e22			0.0284702			0.0142351	+	0.999899i	$0.495469\pi$
$338$	−3.10636e23	−	8.48760e22i	−0.293456	−	0.0801819i
$339$			5.43043e23i			0.498812i
$340$	1.28544e22	−	2.17666e22i	0.0114816	−	0.0194420i
$341$			1.06796e24i			0.927657i
$342$	5.73956e22	−	2.10061e23i	0.0484876	−	0.177459i
$343$	−7.09680e23			−0.583134
$344$	−1.17011e24	+	1.13605e24i	−0.935238	+	0.908011i
$345$	−1.58176e23			−0.122987
$346$	4.98226e23	−	1.82345e24i	0.376880	−	1.37934i
$347$			7.32835e23i			0.539357i	0.962950	+	0.269678i	$0.0869174\pi$
$347$			7.32835e23i			0.539357i	−0.962950	+	0.269678i	$0.913083\pi$
$348$	9.68454e23	+	5.71925e23i	0.693548	+	0.409578i
$349$			5.02074e23i			0.349885i	0.984579	+	0.174943i	$0.0559740\pi$
$349$			5.02074e23i			0.349885i	−0.984579	+	0.174943i	$0.944026\pi$
$350$	4.20641e23	+	1.14933e23i	0.285276	+	0.0779468i
$351$	−1.87555e24			−1.23797
$352$	1.49704e24	−	3.61883e23i	0.961785	−	0.232495i
$353$	1.15074e24			0.719644			0.359822	−	0.933021i	$-0.382837\pi$
$353$	1.15074e24			0.719644			0.359822	+	0.933021i	$0.382837\pi$
$354$	1.10280e24	+	3.01322e23i	0.671378	+	0.183443i
$355$		−	4.99191e23i		−	0.295867i
$356$	−2.65762e24	−	1.56947e24i	−1.53362	−	0.905686i
$357$		−	5.80259e22i		−	0.0326042i
$358$	9.07156e23	−	3.32008e24i	0.496356	−	1.81660i
$359$	−1.36386e24			−0.726728			−0.363364	−	0.931647i	$-0.618372\pi$
$359$	−1.36386e24			−0.726728			−0.363364	+	0.931647i	$0.618372\pi$
$360$	6.57054e22	−	6.37926e22i	0.0340979	−	0.0331052i
$361$	9.95421e23			0.503139
$362$	−4.06176e23	+	1.48655e24i	−0.199978	+	0.731896i
$363$		−	3.74902e22i		−	0.0179806i
$364$	3.80169e23	−	6.43748e23i	0.177629	−	0.300783i
$365$		−	1.36026e23i		−	0.0619214i
$366$	3.02661e24	+	8.26971e23i	1.34241	+	0.366792i
$367$	−1.90863e24			−0.824887			−0.412443	−	0.910983i	$-0.635325\pi$
$367$	−1.90863e24			−0.824887			−0.412443	+	0.910983i	$0.635325\pi$
$368$	9.00723e23	+	1.63357e24i	0.379347	+	0.687991i
$369$	−5.44825e23			−0.223618
$370$	5.28566e23	+	1.44422e23i	0.211438	+	0.0577719i
$371$		−	4.65228e23i		−	0.181390i
$372$	−1.07834e24	+	1.82598e24i	−0.409824	+	0.693965i
$373$		−	1.13984e24i		−	0.422289i	−0.977455	−	0.211145i	$-0.932281\pi$
$373$		−	1.13984e24i		−	0.422289i	0.977455	−	0.211145i	$-0.0677191\pi$
$374$	8.95345e22	−	3.27685e23i	0.0323378	−	0.118352i
$375$	−8.74378e23			−0.307895
$376$	−7.21714e23	−	7.43355e23i	−0.247788	−	0.255218i
$377$	3.19619e24			1.07002
$378$	2.67702e23	−	9.79759e23i	0.0873937	−	0.319850i
$379$			9.13985e23i			0.290982i	0.989360	+	0.145491i	$0.0464762\pi$
$379$			9.13985e23i			0.290982i	−0.989360	+	0.145491i	$0.953524\pi$
$380$	−3.55960e23	−	2.10214e23i	−0.110524	−	0.0652706i
$381$		−	8.43531e22i		−	0.0255455i
$382$	3.02965e24	+	8.27799e23i	0.894932	+	0.244525i
$383$	4.22487e24			1.21738			0.608689	−	0.793409i	$-0.291696\pi$
$383$	4.22487e24			1.21738			0.608689	+	0.793409i	$0.291696\pi$
$384$	2.92502e24	+	8.92851e23i	0.822208	+	0.250976i
$385$	−2.00973e23			−0.0551140
$386$	−4.21521e24	−	1.15173e24i	−1.12782	−	0.308157i
$387$			1.30312e24i			0.340198i
$388$	−6.25852e24	−	3.69600e24i	−1.59430	−	0.941521i
$389$		−	7.15501e24i		−	1.77864i	−0.457281	−	0.889322i	$-0.651176\pi$
$389$		−	7.15501e24i		−	1.77864i	0.457281	−	0.889322i	$-0.348824\pi$
$390$	−1.94232e23	+	7.10864e23i	−0.0471201	+	0.172454i
$391$	4.11440e23			0.0974153
$392$	−2.73232e24	−	2.81425e24i	−0.631413	−	0.650347i
$393$	−1.19394e24			−0.269311
$394$	−1.89061e24	+	6.91939e24i	−0.416281	+	1.52354i
$395$		−	1.32544e24i		−	0.284897i
$396$	6.25782e23	−	1.05965e24i	0.131316	−	0.222361i
$397$			6.50441e24i			1.33259i	0.745686	+	0.666297i	$0.232122\pi$
$397$			6.50441e24i			1.33259i	−0.745686	+	0.666297i	$0.767878\pi$
$398$	−1.94355e24	−	5.31043e23i	−0.388783	−	0.106228i
$399$	−9.48925e23			−0.185349
$400$	2.44757e24	+	4.43897e24i	0.466838	+	0.846665i
$401$	4.87600e24			0.908222			0.454111	−	0.890945i	$-0.349957\pi$
$401$	4.87600e24			0.908222			0.454111	+	0.890945i	$0.349957\pi$
$402$	−6.38101e24	−	1.74350e24i	−1.16076	−	0.317158i
$403$			6.02629e24i			1.07066i
$404$	−3.97940e24	+	6.73841e24i	−0.690550	+	1.16932i
$405$			7.20756e23i			0.122170i
$406$	−4.56202e23	+	1.66964e24i	−0.0755370	+	0.276456i
$407$	7.36323e24			1.19103
$408$	4.83956e23	−	4.69867e23i	0.0764776	−	0.0742511i
$409$	−8.61854e24			−1.33065			−0.665323	−	0.746556i	$-0.731706\pi$
$409$	−8.61854e24			−1.33065			−0.665323	+	0.746556i	$0.731706\pi$
$410$	−2.72611e23	+	9.97722e23i	−0.0411241	+	0.150509i
$411$		−	6.27170e24i		−	0.924460i
$412$	4.63167e24	+	2.73525e24i	0.667135	+	0.393980i
$413$			1.75932e24i			0.247640i
$414$	1.43784e24	+	3.92864e23i	0.197791	+	0.0540430i
$415$	1.12078e24			0.150682
$416$	8.44751e24	−	2.04204e24i	1.11005	−	0.268335i
$417$	−4.26233e24			−0.547463
$418$	−5.35879e24	−	1.46420e24i	−0.672810	−	0.183834i
$419$		−	1.60381e25i		−	1.96843i	−0.176970	−	0.984216i	$-0.556629\pi$
$419$		−	1.60381e25i		−	1.96843i	0.176970	−	0.984216i	$-0.443371\pi$
$420$	−3.43621e23	−	2.02927e23i	−0.0412299	−	0.0243485i
$421$		−	2.27683e24i		−	0.267086i	−0.991043	−	0.133543i	$-0.957365\pi$
$421$		−	2.27683e24i		−	0.267086i	0.991043	−	0.133543i	$-0.0426354\pi$
$422$	−1.20086e24	+	4.39499e24i	−0.137728	+	0.504069i
$423$	−8.27855e23			−0.0928370
$424$	3.88017e24	−	3.76720e24i	0.425476	−	0.413089i
$425$	1.11802e24			0.119883
$426$	3.51081e24	−	1.28491e25i	0.368143	−	1.34736i
$427$			4.82842e24i			0.495154i
$428$	2.32117e24	−	3.93048e24i	0.232804	−	0.394212i
$429$			9.90274e24i			0.971429i
$430$	2.38637e24	+	6.52036e23i	0.228975	+	0.0625635i
$431$	1.72009e25			1.61442			0.807210	−	0.590264i	$-0.200977\pi$
$431$	1.72009e25			1.61442			0.807210	+	0.590264i	$0.200977\pi$
$432$	1.03393e25	−	5.70090e24i	0.949279	−	0.523417i
$433$	−1.11679e25			−1.00308			−0.501540	−	0.865134i	$-0.667233\pi$
$433$	−1.11679e25			−1.00308			−0.501540	+	0.865134i	$0.667233\pi$
$434$	−3.14804e24	−	8.60149e23i	−0.276623	−	0.0755825i
$435$		−	1.70607e24i		−	0.146673i
$436$	3.26875e24	−	5.53505e24i	0.274954	−	0.465586i
$437$		−	6.72847e24i		−	0.553787i
$438$	9.56673e23	−	3.50131e24i	0.0770477	−	0.281985i
$439$	−1.17130e25			−0.923115			−0.461558	−	0.887110i	$-0.652709\pi$
$439$	−1.17130e25			−0.923115			−0.461558	+	0.887110i	$0.652709\pi$
$440$	−1.62739e24	−	1.67619e24i	−0.125514	−	0.129277i
$441$	−3.13416e24			−0.236567
$442$	5.05226e23	−	1.84907e24i	0.0373228	−	0.136597i
$443$			1.41698e25i			1.02454i	0.858824	+	0.512271i	$0.171196\pi$
$443$			1.41698e25i			1.02454i	−0.858824	+	0.512271i	$0.828804\pi$
$444$	1.25895e25	+	7.43481e24i	0.890987	+	0.526177i
$445$			4.68177e24i			0.324332i
$446$	−3.74553e24	−	1.02340e24i	−0.253999	−	0.0694010i
$447$	−3.10654e24			−0.206232
$448$	−1.39008e23	+	4.70432e24i	−0.00903438	+	0.305742i
$449$	−4.84456e24			−0.308258			−0.154129	−	0.988051i	$-0.549257\pi$
$449$	−4.84456e24			−0.308258			−0.154129	+	0.988051i	$0.549257\pi$
$450$	3.90709e24	+	1.06755e24i	0.243408	+	0.0665071i
$451$			1.38988e25i			0.847815i
$452$	−8.36486e24	−	4.93991e24i	−0.499624	−	0.295056i
$453$			2.62083e25i			1.53287i
$454$	−2.85703e23	+	1.04564e24i	−0.0163638	+	0.0598896i
$455$	−1.13406e24			−0.0636101
$456$	−7.68395e24	−	7.91436e24i	−0.422103	−	0.434760i
$457$	−1.68529e25			−0.906713			−0.453357	−	0.891329i	$-0.649774\pi$
$457$	−1.68529e25			−0.906713			−0.453357	+	0.891329i	$0.649774\pi$
$458$	−9.52615e24	+	3.48645e25i	−0.501990	+	1.83722i
$459$		−	2.60411e24i		−	0.134412i
$460$	1.43888e24	−	2.43649e24i	0.0727488	−	0.123187i
$461$		−	3.75553e25i		−	1.86000i	−0.367561	−	0.929999i	$-0.619807\pi$
$461$		−	3.75553e25i		−	1.86000i	0.367561	−	0.929999i	$-0.380193\pi$
$462$	−5.17304e24	−	1.41345e24i	−0.250985	−	0.0685773i
$463$	−1.74872e25			−0.831191			−0.415595	−	0.909550i	$-0.636427\pi$
$463$	−1.74872e25			−0.831191			−0.415595	+	0.909550i	$0.636427\pi$
$464$	−1.76195e25	+	9.71512e24i	−0.820490	+	0.452405i
$465$	3.21672e24			0.146761
$466$	2.72296e25	+	7.44002e24i	1.21724	+	0.332589i
$467$			4.10320e24i			0.179726i	0.995954	+	0.0898632i	$0.0286430\pi$
$467$			4.10320e24i			0.179726i	−0.995954	+	0.0898632i	$0.971357\pi$
$468$	3.53117e24	−	5.97941e24i	0.151559	−	0.256639i
$469$		−	1.01798e25i		−	0.428149i
$470$	−4.14229e23	+	1.51603e24i	−0.0170730	+	0.0624852i
$471$	6.68439e24			0.270000
$472$	−1.46734e25	+	1.42462e25i	−0.580873	+	0.563962i
$473$	3.32435e25			1.28981
$474$	9.32183e24	−	3.41168e25i	0.354493	−	1.29740i
$475$		−	1.82836e25i		−	0.681509i
$476$	8.93813e23	+	5.27845e23i	0.0326573	+	0.0192859i
$477$		−	4.32124e24i		−	0.154769i
$478$	−1.21322e25	−	3.31492e24i	−0.425966	−	0.116388i
$479$	1.78115e25			0.613076			0.306538	−	0.951858i	$-0.400829\pi$
$479$	1.78115e25			0.613076			0.306538	+	0.951858i	$0.400829\pi$
$480$	−1.09000e24	−	4.50913e24i	−0.0367821	−	0.152160i
$481$	4.15493e25			1.37463
$482$	1.51004e25	+	4.12594e24i	0.489827	+	0.133837i
$483$		−	6.49524e24i		−	0.206584i
$484$	5.77487e23	+	3.41038e23i	0.0180099	+	0.0106358i
$485$			1.10253e25i			0.337165i
$486$	4.45844e24	−	1.63173e25i	0.133702	−	0.489333i
$487$	−3.10187e25			−0.912217			−0.456109	−	0.889924i	$-0.650757\pi$
$487$	−3.10187e25			−0.912217			−0.456109	+	0.889924i	$0.650757\pi$
$488$	−4.02707e25	+	3.90983e25i	−1.16145	+	1.12764i
$489$	4.10622e25			1.16147
$490$	−1.56822e24	+	5.73949e24i	−0.0435055	+	0.159225i
$491$		−	2.66913e25i		−	0.726265i	−0.931738	−	0.363132i	$-0.881707\pi$
$491$		−	2.66913e25i		−	0.726265i	0.931738	−	0.363132i	$-0.118293\pi$
$492$	−1.40340e25	+	2.37640e25i	−0.374552	+	0.634237i
$493$			4.43776e24i			0.116176i
$494$	−3.02387e25	−	8.26221e24i	−0.776527	−	0.212173i
$495$	−1.86673e24			−0.0470253
$496$	−1.83174e25	−	3.32208e25i	−0.452677	−	0.820984i
$497$	2.04985e25			0.496977
$498$	2.88487e25	+	7.88242e24i	0.686195	+	0.187491i
$499$			2.16376e25i			0.504956i	0.967603	+	0.252478i	$0.0812456\pi$
$499$			2.16376e25i			0.504956i	−0.967603	+	0.252478i	$0.918754\pi$
$500$	7.95398e24	−	1.34686e25i	0.182125	−	0.308396i
$501$		−	1.98405e25i		−	0.445753i
$502$	1.85742e24	−	6.79792e24i	0.0409472	−	0.149862i
$503$	−1.14391e25			−0.247454			−0.123727	−	0.992316i	$-0.539485\pi$
$503$	−1.14391e25			−0.247454			−0.123727	+	0.992316i	$0.539485\pi$
$504$	2.61954e24	+	2.69809e24i	0.0556077	+	0.0572751i
$505$	1.18707e25			0.247291
$506$	1.00222e25	−	3.66801e25i	0.204896	−	0.749895i
$507$			1.30341e25i			0.261520i
$508$	1.29935e24	+	7.67337e23i	0.0255871	+	0.0151106i
$509$		−	9.86077e24i		−	0.190586i	−0.995449	−	0.0952932i	$-0.969621\pi$
$509$		−	9.86077e24i		−	0.190586i	0.995449	−	0.0952932i	$-0.0303789\pi$
$510$	−9.86999e23	−	2.69681e23i	−0.0187241	−	0.00511603i
$511$	5.58571e24			0.104011
$512$	−4.03613e25	+	3.69340e25i	−0.737735	+	0.675091i
$513$	−4.25862e25			−0.764106
$514$	5.52679e25	+	1.51010e25i	0.973472	+	0.265985i
$515$		−	8.15935e24i		−	0.141087i
$516$	5.68393e25	+	3.35667e25i	0.964887	+	0.569819i
$517$			2.11191e25i			0.351978i
$518$	−5.93045e24	+	2.17047e25i	−0.0970410	+	0.355158i
$519$	−7.65105e25			−1.22922
$520$	−9.18306e24	−	9.45841e24i	−0.144862	−	0.149206i
$521$	−1.79677e25			−0.278313			−0.139156	−	0.990270i	$-0.544439\pi$
$521$	−1.79677e25			−0.278313			−0.139156	+	0.990270i	$0.544439\pi$
$522$	−4.23740e24	+	1.55084e25i	−0.0644510	+	0.235883i
$523$			3.25014e25i			0.485440i	0.970096	+	0.242720i	$0.0780396\pi$
$523$			3.25014e25i			0.485440i	−0.970096	+	0.242720i	$0.921960\pi$
$524$	1.08610e25	−	1.83911e25i	0.159302	−	0.269750i
$525$		−	1.76498e25i		−	0.254230i
$526$	2.17321e25	+	5.93792e24i	0.307423	+	0.0839981i
$527$	−8.36720e24			−0.116246
$528$	−3.01003e25	−	5.45904e25i	−0.410722	−	0.744893i
$529$	−2.85601e25			−0.382764
$530$	−7.91337e24	−	2.16219e24i	−0.104169	−	0.0284626i
$531$			1.63414e25i			0.211296i
$532$	8.63210e24	−	1.46169e25i	0.109637	−	0.185650i
$533$			7.84285e25i			0.978510i
$534$	−3.29269e25	+	1.20508e26i	−0.403561	+	1.47698i
$535$	−6.92411e24			−0.0833687
$536$	8.49026e25	−	8.24309e25i	1.00428	−	0.975045i
$537$	−1.39308e26			−1.61891
$538$	2.61821e25	−	9.58232e25i	0.298932	−	1.09405i
$539$			7.99544e25i			0.896910i
$540$	−1.54212e25	−	9.10704e24i	−0.169972	−	0.100378i
$541$		−	6.64278e25i		−	0.719409i	−0.933066	−	0.359705i	$-0.882877\pi$
$541$		−	6.64278e25i		−	0.719409i	0.933066	−	0.359705i	$-0.117123\pi$
$542$	−4.07974e25	−	1.11472e25i	−0.434150	−	0.118624i
$543$	6.23748e25			0.652245
$544$	2.83527e24	+	1.17290e25i	0.0291343	+	0.120523i
$545$	−9.75080e24			−0.0984631
$546$	−2.91905e25	−	7.97581e24i	−0.289675	−	0.0791489i
$547$			1.34963e25i			0.131624i	0.997832	+	0.0658121i	$0.0209638\pi$
$547$			1.34963e25i			0.131624i	−0.997832	+	0.0658121i	$0.979036\pi$
$548$	9.66073e25	+	5.70519e25i	0.925966	+	0.546833i
$549$			4.48484e25i			0.422484i
$550$	2.72338e25	−	9.96725e25i	0.252152	−	0.922847i
$551$	7.25727e25			0.660440
$552$	5.41725e25	−	5.25954e25i	0.484572	−	0.470465i
$553$	5.44272e25			0.478550
$554$	−3.19467e25	+	1.16921e26i	−0.276111	+	1.01053i
$555$		−	2.21783e25i		−	0.188428i
$556$	3.87732e25	−	6.56556e25i	0.323833	−	0.548354i
$557$			3.63965e25i			0.298838i	0.988774	+	0.149419i	$0.0477402\pi$
$557$			3.63965e25i			0.298838i	−0.988774	+	0.149419i	$0.952260\pi$
$558$	−2.92404e25	−	7.98943e24i	−0.236025	−	0.0644898i
$559$	1.87587e26			1.48864
$560$	6.25166e24	−	3.44706e24i	0.0487763	−	0.0268945i
$561$	−1.37495e25			−0.105472
$562$	−8.85241e25	−	2.41877e25i	−0.667677	−	0.182431i
$563$		−	2.57792e26i		−	1.91179i	−0.293715	−	0.955893i	$-0.594892\pi$
$563$		−	2.57792e26i		−	1.91179i	0.293715	−	0.955893i	$-0.405108\pi$
$564$	−2.13244e25	+	3.61092e25i	−0.155499	+	0.263309i
$565$			1.47359e25i			0.105661i
$566$	3.06093e25	−	1.12026e26i	0.215822	−	0.789884i
$567$	−2.95967e25			−0.205213
$568$	1.65987e26	+	1.70964e26i	1.13179	+	1.16573i
$569$	−8.91378e25			−0.597717			−0.298858	−	0.954298i	$-0.596606\pi$
$569$	−8.91378e25			−0.597717			−0.298858	+	0.954298i	$0.596606\pi$
$570$	−4.41022e24	+	1.61409e25i	−0.0290836	+	0.106443i
$571$		−	2.57024e26i		−	1.66698i	−0.552535	−	0.833490i	$-0.686339\pi$
$571$		−	2.57024e26i		−	1.66698i	0.552535	−	0.833490i	$-0.313661\pi$
$572$	−1.52539e26	−	9.00825e25i	−0.973011	−	0.574616i
$573$		−	1.27122e26i		−	0.797538i
$574$	−4.09699e25	−	1.11943e25i	−0.252814	−	0.0690772i
$575$	1.25148e26			0.759592
$576$	−1.29117e24	+	4.36958e25i	−0.00770847	+	0.260871i
$577$	2.75366e25			0.161711			0.0808555	−	0.996726i	$-0.474235\pi$
$577$	2.75366e25			0.161711			0.0808555	+	0.996726i	$0.474235\pi$
$578$	−1.64419e26	−	4.49246e25i	−0.949809	−	0.259519i
$579$			1.76867e26i			1.00508i
$580$	2.62798e25	+	1.55197e25i	0.146912	+	0.0867594i
$581$			4.60229e25i			0.253105i
$582$	−7.75408e25	+	2.83790e26i	−0.419529	+	1.53542i
$583$	−1.10238e26			−0.586785
$584$	4.52305e25	+	4.65867e25i	0.236870	+	0.243972i
$585$	−1.05336e25			−0.0542745
$586$	−5.85831e25	+	2.14407e26i	−0.296992	+	1.08695i
$587$			2.09730e26i			1.04616i	0.852283	+	0.523081i	$0.175218\pi$
$587$			2.09730e26i			1.04616i	−0.852283	+	0.523081i	$0.824782\pi$
$588$	−8.07317e25	+	1.36705e26i	−0.396241	+	0.670964i
$589$			1.36833e26i			0.660838i
$590$	2.99255e25	+	8.17663e24i	0.142215	+	0.0388580i
$591$	2.90333e26			1.35774
$592$	−2.29047e26	+	1.26293e26i	−1.05407	+	0.581196i
$593$	−9.93128e25			−0.449765			−0.224882	−	0.974386i	$-0.572200\pi$
$593$	−9.93128e25			−0.449765			−0.224882	+	0.974386i	$0.572200\pi$
$594$	−2.32158e26	−	6.34331e25i	−1.03469	−	0.282713i
$595$		−	1.57458e24i		−	0.00690643i
$596$	2.82593e25	−	4.78522e25i	0.121990	−	0.206568i
$597$			8.15502e25i			0.346473i
$598$	5.65535e25	−	2.06979e26i	0.236482	−	0.865496i
$599$	−2.67985e26			−1.10295			−0.551475	−	0.834191i	$-0.685935\pi$
$599$	−2.67985e26			−1.10295			−0.551475	+	0.834191i	$0.685935\pi$
$600$	1.47205e26	−	1.42920e26i	0.596331	−	0.578970i
$601$	3.04760e26			1.21521			0.607603	−	0.794241i	$-0.292131\pi$
$601$	3.04760e26			1.21521			0.607603	+	0.794241i	$0.292131\pi$
$602$	−2.67748e25	+	9.79927e25i	−0.105090	+	0.384616i
$603$		−	9.45539e25i		−	0.365313i
$604$	−4.03705e26	−	2.38410e26i	−1.53537	−	0.906721i
$605$		−	1.01733e24i		−	0.00380877i
$606$	3.05551e26	+	8.34865e25i	1.12614	+	0.307699i
$607$	−5.80740e25			−0.210712			−0.105356	−	0.994435i	$-0.533598\pi$
$607$	−5.80740e25			−0.210712			−0.105356	+	0.994435i	$0.533598\pi$
$608$	1.91809e26	−	4.63665e25i	0.685149	−	0.165623i
$609$	7.00571e25			0.246370
$610$	8.21296e25	+	2.24405e25i	0.284359	+	0.0776962i
$611$			1.19171e26i			0.406238i
$612$	8.30212e24	+	4.90286e24i	0.0278644	+	0.0164555i
$613$		−	4.37513e26i		−	1.44583i	−0.690938	−	0.722914i	$-0.742802\pi$
$613$		−	4.37513e26i		−	1.44583i	0.690938	−	0.722914i	$-0.257198\pi$
$614$	7.30491e25	−	2.67351e26i	0.237692	−	0.869925i
$615$	4.18637e25			0.134130
$616$	6.88300e25	−	6.68262e25i	0.217151	−	0.210829i
$617$	−2.93608e26			−0.912135			−0.456068	−	0.889945i	$-0.650742\pi$
$617$	−2.93608e26			−0.912135			−0.456068	+	0.889945i	$0.650742\pi$
$618$	5.73847e25	−	2.10021e26i	0.175552	−	0.642498i
$619$			1.19728e26i			0.360690i	0.983603	+	0.180345i	$0.0577215\pi$
$619$			1.19728e26i			0.360690i	−0.983603	+	0.180345i	$0.942279\pi$
$620$	−2.92616e25	+	4.95494e25i	−0.0868116	+	0.147000i
$621$		−	2.91496e26i		−	0.851652i
$622$	4.70114e26	+	1.28451e26i	1.35268	+	0.369597i
$623$	−1.92250e26			−0.544790
$624$	−1.69850e26	−	3.08043e26i	−0.474037	−	0.859722i
$625$	3.28007e26			0.901620
$626$	2.84002e26	+	7.75988e25i	0.768892	+	0.210087i
$627$			2.24851e26i			0.599589i
$628$	−6.08060e25	+	1.02964e26i	−0.159709	+	0.270439i
$629$			5.76892e25i			0.149250i
$630$	1.50349e24	−	5.50259e24i	0.00383147	−	0.0140227i
$631$	−6.54034e26			−1.64181			−0.820903	−	0.571068i	$-0.806529\pi$
$631$	−6.54034e26			−1.64181			−0.820903	+	0.571068i	$0.806529\pi$
$632$	4.40726e26	+	4.53942e26i	1.08982	+	1.12250i
$633$	1.84411e26			0.449212
$634$	5.35517e25	−	1.95993e26i	0.128507	−	0.470319i
$635$		−	2.28899e24i		−	0.00541120i
$636$	−1.88483e26	−	1.11309e26i	−0.438964	−	0.259232i
$637$			4.51168e26i			1.03517i
$638$	3.95629e26	+	1.08099e26i	0.894317	+	0.244357i
$639$	1.90399e26			0.424039
$640$	7.93727e25	+	2.42283e25i	0.174165	+	0.0531633i
$641$	−2.14805e26			−0.464401			−0.232200	−	0.972668i	$-0.574593\pi$
$641$	−2.14805e26			−0.464401			−0.232200	+	0.972668i	$0.574593\pi$
$642$	−1.78226e26	−	4.86973e25i	−0.379654	−	0.103734i
$643$		−	3.88932e26i		−	0.816337i	−0.912907	−	0.408168i	$-0.866168\pi$
$643$		−	3.88932e26i		−	0.816337i	0.912907	−	0.408168i	$-0.133832\pi$
$644$	1.00051e26	+	5.90854e25i	0.206921	+	0.122198i
$645$		−	1.00131e26i		−	0.204056i
$646$	1.14717e25	−	4.19849e25i	0.0230366	−	0.0843110i
$647$	−8.92411e26			−1.76593			−0.882967	−	0.469436i	$-0.844457\pi$
$647$	−8.92411e26			−1.76593			−0.882967	+	0.469436i	$0.844457\pi$
$648$	−2.39661e26	−	2.46847e26i	−0.467341	−	0.481354i
$649$	4.16879e26			0.801097
$650$	1.53675e26	−	5.62433e26i	0.291023	−	1.06511i
$651$			1.32090e26i			0.246518i
$652$	−3.73531e26	+	6.32509e26i	−0.687029	+	1.16336i
$653$			9.75745e26i			1.76873i	0.466798	+	0.884364i	$0.345407\pi$
$653$			9.75745e26i			1.76873i	−0.466798	+	0.884364i	$0.654593\pi$
$654$	−2.50985e26	−	6.85773e25i	−0.448393	−	0.122516i
$655$	−3.23986e25			−0.0570471
$656$	−2.38391e26	−	4.32349e26i	−0.413716	−	0.750323i
$657$	5.18825e25			0.0887462
$658$	−6.22533e25	−	1.70097e25i	−0.104958	−	0.0286780i
$659$			1.75108e26i			0.291000i	0.989358	+	0.145500i	$0.0464792\pi$
$659$			1.75108e26i			0.291000i	−0.989358	+	0.145500i	$0.953521\pi$
$660$	−4.80844e25	+	8.14224e25i	−0.0787656	+	0.133376i
$661$		−	7.52641e26i		−	1.21527i	−0.794215	−	0.607637i	$-0.792118\pi$
$661$		−	7.52641e26i		−	1.21527i	0.794215	−	0.607637i	$-0.207882\pi$
$662$	−2.47269e25	+	9.04975e25i	−0.0393567	+	0.144041i
$663$	−7.75856e25			−0.121731
$664$	−3.83847e26	+	3.72672e26i	−0.593692	+	0.576408i
$665$	−2.57498e25			−0.0392617
$666$	−5.50846e25	+	2.01603e26i	−0.0827990	+	0.303034i
$667$			4.96749e26i			0.736108i
$668$	3.05617e26	+	1.80484e26i	0.446479	+	0.263671i
$669$			1.57160e26i			0.226357i
$670$	−1.73154e26	−	4.73114e25i	−0.245879	−	0.0671823i
$671$	1.14411e27			1.60179
$672$	1.85160e26	−	4.47593e25i	0.255588	−	0.0617838i
$673$	3.04772e26			0.414793			0.207396	−	0.978257i	$-0.433501\pi$
$673$	3.04772e26			0.414793			0.207396	+	0.978257i	$0.433501\pi$
$674$	2.04656e25	+	5.59188e24i	0.0274635	+	0.00750393i
$675$		−	7.92095e26i		−	1.04807i
$676$	−2.00773e26	−	1.18567e26i	−0.261946	−	0.154693i
$677$		−	2.86445e26i		−	0.368509i	−0.982879	−	0.184255i	$-0.941013\pi$
$677$		−	2.86445e26i		−	0.368509i	0.982879	−	0.184255i	$-0.0589871\pi$
$678$	−1.03638e26	+	3.79301e26i	−0.131473	+	0.481174i
$679$	−4.52736e26			−0.566346
$680$	1.31325e25	−	1.27502e25i	0.0162000	−	0.0157283i
$681$	4.38743e25			0.0533719
$682$	−2.03816e26	+	7.45941e26i	−0.244504	+	0.894855i
$683$		−	5.96662e26i		−	0.705881i	−0.935646	−	0.352940i	$-0.885182\pi$
$683$		−	5.96662e26i		−	0.705881i	0.935646	−	0.352940i	$-0.114818\pi$
$684$	8.01787e25	−	1.35768e26i	0.0935462	−	0.158404i
$685$		−	1.70188e26i		−	0.195825i
$686$	−4.95693e26	−	1.35440e26i	−0.562514	−	0.153698i
$687$	1.46289e27			1.63728
$688$	−1.03410e27	+	5.70188e26i	−1.14149	+	0.629401i
$689$	−6.22051e26			−0.677241
$690$	−1.10482e26	−	3.01873e25i	−0.118638	−	0.0324158i
$691$			9.15537e26i			0.969694i	0.874599	+	0.484847i	$0.161125\pi$
$691$			9.15537e26i			0.969694i	−0.874599	+	0.484847i	$0.838875\pi$
$692$	6.95995e26	−	1.17854e27i	0.727107	−	1.23123i
$693$		−	7.66542e25i		−	0.0789897i
$694$	−1.39859e26	+	5.11866e26i	−0.142159	+	0.520285i
$695$	−1.15662e26			−0.115967
$696$	5.67290e26	+	5.84301e26i	0.561071	+	0.577895i
$697$	−1.08894e26			−0.106241
$698$	−9.58188e25	+	3.50685e26i	−0.0922198	+	0.337513i
$699$		−	1.14254e27i		−	1.08477i
$700$	2.71872e26	+	1.60555e26i	0.254644	+	0.150381i
$701$		−	1.64726e27i		−	1.52209i	−0.648696	−	0.761047i	$-0.724685\pi$
$701$		−	1.64726e27i		−	1.52209i	0.648696	−	0.761047i	$-0.275315\pi$
$702$	−1.31002e27	−	3.57941e26i	−1.19420	−	0.326294i
$703$	9.43418e26			0.848455
$704$	1.11471e27	+	3.29385e25i	0.989055	+	0.0292256i
$705$	6.36115e25			0.0556851
$706$	8.03762e26	+	2.19614e26i	0.694197	+	0.189678i
$707$			4.87451e26i			0.415381i
$708$	7.12773e26	+	4.20932e26i	0.599288	+	0.353912i
$709$			3.73183e26i			0.309587i	0.987947	+	0.154793i	$0.0494712\pi$
$709$			3.73183e26i			0.309587i	−0.987947	+	0.154793i	$0.950529\pi$
$710$	9.52687e25	−	3.48672e26i	0.0779822	−	0.285406i
$711$	5.05543e26			0.408317
$712$	−1.55675e27	−	1.60343e27i	−1.24068	−	1.27788i
$713$	−9.36599e26			−0.736551
$714$	1.10740e25	−	4.05296e25i	0.00859354	−	0.0314513i
$715$			2.68719e26i			0.205774i
$716$	1.26725e27	−	2.14586e27i	0.957609	−	1.62154i
$717$			5.09059e26i			0.379609i
$718$	−9.52620e26	−	2.60287e26i	−0.701031	−	0.191545i
$719$	2.23350e27			1.62204			0.811019	−	0.585019i	$-0.198913\pi$
$719$	2.23350e27			1.62204			0.811019	+	0.585019i	$0.198913\pi$
$720$	5.80681e25	−	3.20178e25i	0.0416178	−	0.0229474i
$721$	3.35051e26			0.236988
$722$	6.95276e26	+	1.89972e26i	0.485348	+	0.132613i
$723$		−	6.33604e26i		−	0.436520i
$724$	−5.67407e26	+	9.60803e26i	−0.385814	+	0.653308i
$725$			1.34984e27i			0.905880i
$726$	7.15486e24	−	2.61859e25i	0.00473918	−	0.0173448i
$727$	−2.66240e27			−1.74059			−0.870294	−	0.492533i	$-0.836071\pi$
$727$	−2.66240e27			−1.74059			−0.870294	+	0.492533i	$0.836071\pi$
$728$	3.88395e26	−	3.77088e26i	0.250626	−	0.243329i
$729$	−1.73801e27			−1.10698
$730$	2.59601e25	−	9.50109e25i	0.0163207	−	0.0597319i
$731$			2.60455e26i			0.161629i
$732$	1.95619e27	+	1.15523e27i	1.19827	+	0.707644i
$733$			2.41798e27i			1.46206i	0.682346	+	0.731029i	$0.260960\pi$
$733$			2.41798e27i			1.46206i	−0.682346	+	0.731029i	$0.739040\pi$
$734$	−1.33313e27	−	3.64255e26i	−0.795719	−	0.217417i
$735$	2.40825e26			0.141897
$736$	3.17371e26	+	1.31290e27i	0.184599	+	0.763649i
$737$	−2.41213e27			−1.38503
$738$	−3.80546e26	−	1.03978e26i	−0.215711	−	0.0589393i
$739$			1.80945e25i			0.0101257i	0.999987	+	0.00506284i	$0.00161156\pi$
$739$			1.80945e25i			0.0101257i	−0.999987	+	0.00506284i	$0.998388\pi$
$740$	3.41627e26	+	2.01750e26i	0.188735	+	0.111458i
$741$			1.26879e27i			0.692019i
$742$	8.87871e25	−	3.24950e26i	0.0478093	−	0.174976i
$743$	−2.23556e27			−1.18848			−0.594240	−	0.804288i	$-0.702547\pi$
$743$	−2.23556e27			−1.18848			−0.594240	+	0.804288i	$0.702547\pi$
$744$	−1.10167e27	+	1.06960e27i	−0.578242	+	0.561408i
$745$	−8.42985e25			−0.0436853
$746$	2.17534e26	−	7.96148e26i	0.111303	−	0.407357i
$747$			4.27480e26i			0.215959i
$748$	1.25075e26	−	2.11792e26i	0.0623886	−	0.105644i
$749$		−	2.84328e26i		−	0.140037i
$750$	−6.10730e26	−	1.66872e26i	−0.297008	−	0.0811523i
$751$	1.82803e26			0.0877817			0.0438908	−	0.999036i	$-0.486025\pi$
$751$	1.82803e26			0.0877817			0.0438908	+	0.999036i	$0.486025\pi$
$752$	−3.62232e26	−	6.56950e26i	−0.171758	−	0.311504i
$753$	−2.85236e26			−0.133553
$754$	2.23246e27	+	6.09982e26i	1.03218	+	0.282026i
$755$			7.11185e26i			0.324703i
$756$	3.73966e26	−	6.33246e26i	0.168607	−	0.285506i
$757$		−	3.30915e27i		−	1.47335i	−0.676248	−	0.736674i	$-0.736395\pi$
$757$		−	3.30915e27i		−	1.47335i	0.676248	−	0.736674i	$-0.263605\pi$
$758$	−1.74431e26	+	6.38395e26i	−0.0766947	+	0.280693i
$759$	−1.53907e27			−0.668286
$760$	−2.08510e26	−	2.14763e26i	−0.0894125	−	0.0920936i
$761$	7.89323e26			0.334273			0.167136	−	0.985934i	$-0.446548\pi$
$761$	7.89323e26			0.334273			0.167136	+	0.985934i	$0.446548\pi$
$762$	1.60985e25	−	5.89185e25i	0.00673306	−	0.0246422i
$763$		−	4.00401e26i		−	0.165391i
$764$	1.95815e27	+	1.15639e27i	0.798837	+	0.471757i
$765$		−	1.46254e25i		−	0.00589282i
$766$	2.95096e27	+	8.06301e26i	1.17433	+	0.320866i
$767$	2.35237e27			0.924591
$768$	1.87265e27	+	1.18186e27i	0.726985	+	0.458812i
$769$	4.53233e27			1.73789			0.868943	−	0.494912i	$-0.164800\pi$
$769$	4.53233e27			1.73789			0.868943	+	0.494912i	$0.164800\pi$
$770$	−1.40375e26	−	3.83550e25i	−0.0531651	−	0.0145265i
$771$		−	2.31901e27i		−	0.867531i
$772$	−2.72441e27	−	1.60891e27i	−1.00672	−	0.594522i
$773$			1.78188e27i			0.650388i	0.945647	+	0.325194i	$0.105430\pi$
$773$			1.78188e27i			0.650388i	−0.945647	+	0.325194i	$0.894570\pi$
$774$	−2.48696e26	+	9.10198e26i	−0.0896665	+	0.328168i
$775$	−2.54506e27			−0.906426
$776$	−3.66604e27	−	3.77597e27i	−1.28977	−	1.32844i
$777$	9.10716e26			0.316507
$778$	1.36551e27	−	4.99759e27i	0.468800	−	1.71575i
$779$			1.78080e27i			0.603960i
$780$	−2.71331e26	+	4.59451e26i	−0.0909078	+	0.153936i
$781$		−	4.85720e27i		−	1.60768i
$782$	2.87380e26	+	7.85217e25i	0.0939707	+	0.0256759i
$783$	3.14405e27			1.01567
$784$	−1.37136e27	−	2.48713e27i	−0.437674	−	0.793773i
$785$	1.81386e26			0.0571930
$786$	−8.33937e26	−	2.27859e26i	−0.259788	−	0.0709827i
$787$			1.48340e27i			0.456559i	0.973596	+	0.228280i	$0.0733101\pi$
$787$			1.48340e27i			0.456559i	−0.973596	+	0.228280i	$0.926690\pi$
$788$	−2.64108e27	+	4.47220e27i	−0.803123	+	1.35995i
$789$		−	9.11863e26i		−	0.273967i
$790$	2.52956e26	−	9.25787e26i	0.0750908	−	0.274823i
$791$	−6.05107e26			−0.177482
$792$	6.39323e26	−	6.20710e26i	0.185281	−	0.179887i
$793$	6.45601e27			1.84871
$794$	−1.24134e27	+	4.54316e27i	−0.351234	+	1.28547i
$795$			3.32040e26i			0.0928329i
$796$	−1.25617e27	−	7.41840e26i	−0.347037	−	0.204944i
$797$		−	9.65498e26i		−	0.263571i	−0.991278	−	0.131785i	$-0.957929\pi$
$797$		−	9.65498e26i		−	0.263571i	0.991278	−	0.131785i	$-0.0420710\pi$
$798$	−6.62799e26	−	1.81099e26i	−0.178795	−	0.0488526i
$799$	−1.65463e26			−0.0441070
$800$	8.62407e26	+	3.56761e27i	0.227173	+	0.939772i
$801$	−1.78570e27			−0.464835
$802$	3.40576e27	+	9.30566e26i	0.876108	+	0.239382i
$803$		−	1.32356e27i		−	0.336469i
$804$	−4.12423e27	−	2.43558e27i	−1.03612	−	0.611886i
$805$		−	1.76254e26i		−	0.0437600i
$806$	−1.15009e27	+	4.20920e27i	−0.282196	+	1.03280i
$807$	−4.02068e27			−0.974991
$808$	−4.06551e27	+	3.94715e27i	−0.974332	+	0.945967i
$809$	6.74372e26			0.159731			0.0798654	−	0.996806i	$-0.474551\pi$
$809$	6.74372e26			0.159731			0.0798654	+	0.996806i	$0.474551\pi$
$810$	−1.37554e26	+	5.03429e26i	−0.0322006	+	0.117850i
$811$			4.45790e27i			1.03141i	0.856766	+	0.515706i	$0.172470\pi$
$811$			4.45790e27i			1.03141i	−0.856766	+	0.515706i	$0.827530\pi$
$812$	−6.37290e26	+	1.07914e27i	−0.145732	+	0.246771i
$813$			1.71183e27i			0.386902i
$814$	5.14302e27	+	1.40524e27i	1.14891	+	0.313921i
$815$	1.11426e27			0.246030
$816$	4.27703e26	−	2.35828e26i	0.0933438	−	0.0514683i
$817$	4.25935e27			0.918827
$818$	−6.01983e27	−	1.64482e27i	−1.28359	−	0.350720i
$819$		−	4.32545e26i		−	0.0911664i
$820$	−3.80823e26	+	6.44856e26i	−0.0793398	+	0.134348i
$821$			3.34188e27i			0.688225i	0.938928	+	0.344112i	$0.111820\pi$
$821$			3.34188e27i			0.688225i	−0.938928	+	0.344112i	$0.888180\pi$
$822$	1.19693e27	−	4.38062e27i	0.243661	−	0.891771i
$823$	−9.09406e27			−1.83004			−0.915018	−	0.403414i	$-0.867824\pi$
$823$	−9.09406e27			−1.83004			−0.915018	+	0.403414i	$0.867824\pi$
$824$	2.71309e27	+	2.79444e27i	0.539703	+	0.555886i
$825$	−4.18219e27			−0.822416
$826$	−3.35760e26	+	1.22884e27i	−0.0652708	+	0.238883i
$827$		−	8.34703e27i		−	1.60409i	−0.597261	−	0.802047i	$-0.703744\pi$
$827$		−	8.34703e27i		−	1.60409i	0.597261	−	0.802047i	$-0.296256\pi$
$828$	9.29314e26	+	5.48811e26i	0.176553	+	0.104264i
$829$		−	6.90715e27i		−	1.29727i	−0.761099	−	0.648636i	$-0.775340\pi$
$829$		−	6.90715e27i		−	1.29727i	0.761099	−	0.648636i	$-0.224660\pi$
$830$	7.82833e26	+	2.13896e26i	0.145354	+	0.0397155i
$831$	4.90593e27			0.900557
$832$	6.29008e27	+	1.85866e26i	1.14152	+	0.0337309i
$833$	−6.26424e26			−0.112393
$834$	−2.97713e27	−	8.13449e26i	−0.528104	−	0.144296i
$835$		−	5.38389e26i		−	0.0944223i
$836$	−3.46354e27	−	2.04541e27i	−0.600566	−	0.354667i
$837$			5.92797e27i			1.01628i
$838$	3.06082e27	−	1.12022e28i	0.518823	−	1.89883i
$839$	8.70341e26			0.145865			0.0729325	−	0.997337i	$-0.476764\pi$
$839$	8.70341e26			0.145865			0.0729325	+	0.997337i	$0.476764\pi$
$840$	−2.01283e26	−	2.07318e26i	−0.0333544	−	0.0343545i
$841$	7.45366e26			0.122126
$842$	4.34524e26	−	1.59031e27i	0.0703962	−	0.257642i
$843$			3.71441e27i			0.595015i
$844$	−1.67753e27	+	2.84061e27i	−0.265716	+	0.449944i
$845$			3.53690e26i			0.0553967i
$846$	−5.78235e26	−	1.57993e26i	−0.0895542	−	0.0244692i
$847$	4.17749e25			0.00639769
$848$	3.42915e27	−	1.89078e27i	0.519309	−	0.286339i
$849$	−4.70054e27			−0.703923
$850$	7.80911e26	+	2.13371e26i	0.115644	+	0.0315977i
$851$			6.45755e27i			0.945664i
$852$	4.90442e27	−	8.30476e27i	0.710250	−	1.20268i
$853$			1.15497e28i			1.65408i	0.562142	+	0.827041i	$0.309977\pi$
$853$			1.15497e28i			1.65408i	−0.562142	+	0.827041i	$0.690023\pi$
$854$	−9.21485e26	+	3.37252e27i	−0.130508	+	0.477645i
$855$	−2.39176e26			−0.0334995
$856$	2.37139e27	−	2.30235e27i	0.328475	−	0.318912i
$857$	−5.52459e27			−0.756802			−0.378401	−	0.925642i	$-0.623526\pi$
$857$	−5.52459e27			−0.756802			−0.378401	+	0.925642i	$0.623526\pi$
$858$	−1.88990e27	+	6.91680e27i	−0.256041	+	0.937079i
$859$		−	8.11694e27i		−	1.08757i	−0.839225	−	0.543785i	$-0.816991\pi$
$859$		−	8.11694e27i		−	1.08757i	0.839225	−	0.543785i	$-0.183009\pi$
$860$	1.54238e27	+	9.10860e26i	0.204388	+	0.120703i
$861$			1.71907e27i			0.225301i
$862$	1.20144e28	+	3.28272e27i	1.55733	+	0.425515i
$863$	1.34135e28			1.71965			0.859823	−	0.510593i	$-0.170574\pi$
$863$	1.34135e28			1.71965			0.859823	+	0.510593i	$0.170574\pi$
$864$	8.30969e27	−	2.00872e27i	1.05367	−	0.254706i
$865$	−2.07618e27			−0.260382
$866$	−7.80047e27	−	2.13135e27i	−0.967611	−	0.264383i
$867$			6.89889e27i			0.846443i
$868$	−2.03467e27	−	1.20158e27i	−0.246920	−	0.145820i
$869$		−	1.28967e28i		−	1.54807i
$870$	3.25597e26	−	1.19165e27i	0.0386588	−	0.141486i
$871$	−1.36112e28			−1.59854
$872$	3.33948e27	−	3.24226e27i	0.387947	−	0.376653i
$873$	−4.20520e27			−0.483228
$874$	1.28410e27	−	4.69966e27i	0.145962	−	0.534205i
$875$		−	9.74310e26i		−	0.109552i
$876$	1.33642e27	−	2.26300e27i	0.148647	−	0.251707i
$877$		−	2.16557e27i		−	0.238274i	−0.992878	−	0.119137i	$-0.961987\pi$
$877$		−	2.16557e27i		−	0.238274i	0.992878	−	0.119137i	$-0.0380127\pi$
$878$	−8.18124e27	−	2.23539e27i	−0.890474	−	0.243307i
$879$	8.99637e27			0.968664
$880$	−8.16795e26	−	1.48135e27i	−0.0870017	−	0.157788i
$881$	−7.11442e27			−0.749667			−0.374834	−	0.927092i	$-0.622300\pi$
$881$	−7.11442e27			−0.749667			−0.374834	+	0.927092i	$0.622300\pi$
$882$	−2.18913e27	−	5.98142e26i	−0.228202	−	0.0623523i
$883$		−	9.14050e27i		−	0.942634i	−0.881964	−	0.471317i	$-0.843779\pi$
$883$		−	9.14050e27i		−	0.942634i	0.881964	−	0.471317i	$-0.156221\pi$
$884$	7.05775e26	−	1.19510e27i	0.0720062	−	0.121930i
$885$		−	1.25565e27i		−	0.126738i
$886$	−2.70426e27	+	9.89727e27i	−0.270040	+	0.988314i
$887$	1.12008e28			1.10656			0.553282	−	0.832994i	$-0.313375\pi$
$887$	1.12008e28			1.10656			0.553282	+	0.832994i	$0.313375\pi$
$888$	7.37456e27	+	7.59569e27i	0.720797	+	0.742410i
$889$	9.39938e25			0.00908934
$890$	−8.93498e26	+	3.27010e27i	−0.0854848	+	0.312864i
$891$			7.01306e27i			0.663849i
$892$	−2.42084e27	−	1.42964e27i	−0.226726	−	0.133894i
$893$			2.70590e27i			0.250740i
$894$	−2.16984e27	−	5.92872e26i	−0.198939	−	0.0543568i
$895$	−3.78025e27			−0.342927
$896$	−9.94895e26	+	3.25932e27i	−0.0892999	+	0.292550i
$897$	−8.68470e27			−0.771306
$898$	−3.38380e27	−	9.24566e26i	−0.297358	−	0.0812480i
$899$		−	1.01021e28i		−	0.878403i
$900$	2.52527e27	+	1.49131e27i	0.217272	+	0.128311i
$901$		−	8.63687e26i		−	0.0735310i
$902$	−2.65254e27	+	9.70797e27i	−0.223460	+	0.817836i
$903$	4.11171e27			0.342759
$904$	−4.89987e27	−	5.04680e27i	−0.404189	−	0.416309i
$905$	1.69259e27			0.138163
$906$	−5.00176e27	+	1.83058e28i	−0.404022	+	1.47867i
$907$			2.24862e28i			1.79741i	0.438557	+	0.898703i	$0.355490\pi$
$907$			2.24862e28i			1.79741i	−0.438557	+	0.898703i	$0.644510\pi$
$908$	−3.99113e26	+	6.75826e26i	−0.0315704	+	0.0534589i
$909$			4.52765e27i			0.354418i
$910$	−7.92108e26	−	2.16430e26i	−0.0613608	−	0.0167658i
$911$	1.36989e28			1.05018			0.525088	−	0.851048i	$-0.324032\pi$
$911$	1.36989e28			1.05018			0.525088	+	0.851048i	$0.324032\pi$
$912$	−3.85661e27	−	6.99443e27i	−0.292587	−	0.530641i
$913$	1.09053e28			0.818776
$914$	−1.17713e28	−	3.21631e27i	−0.874652	−	0.238984i
$915$		−	3.44610e27i		−	0.253412i
$916$	−1.33075e28	+	2.25339e28i	−0.968479	+	1.63995i
$917$		−	1.33040e27i		−	0.0958236i
$918$	4.96984e26	−	1.81890e27i	0.0354272	−	0.129659i
$919$	−5.92561e27			−0.418057			−0.209029	−	0.977910i	$-0.567030\pi$
$919$	−5.92561e27			−0.418057			−0.209029	+	0.977910i	$0.567030\pi$
$920$	1.47002e27	−	1.42722e27i	0.102645	−	0.0996567i
$921$	−1.12179e28			−0.775253
$922$	7.16729e27	−	2.62314e28i	0.490243	−	1.79423i
$923$		−	2.74082e28i		−	1.85552i
$924$	−3.34348e27	−	1.97451e27i	−0.224035	−	0.132305i
$925$			1.75474e28i			1.16377i
$926$	−1.22143e28	−	3.33736e27i	−0.801800	−	0.219078i
$927$	3.11209e27			0.202207
$928$	−1.41609e28	+	3.42314e27i	−0.910718	+	0.220150i
$929$	2.61342e28			1.66364			0.831821	−	0.555044i	$-0.187299\pi$
$929$	2.61342e28			1.66364			0.831821	+	0.555044i	$0.187299\pi$
$930$	2.24680e27	+	6.13899e26i	0.141572	+	0.0386820i
$931$			1.02442e28i			0.638934i
$932$	1.75993e28	+	1.03933e28i	1.08653	+	0.641658i
$933$		−	1.97257e28i		−	1.20547i
$934$	−7.83079e26	+	2.86597e27i	−0.0473708	+	0.173371i
$935$	−3.73103e26			−0.0223418
$936$	3.60758e27	−	3.50255e27i	0.213843	−	0.207618i
$937$	1.12675e28			0.661153			0.330577	−	0.943779i	$-0.392757\pi$
$937$	1.12675e28			0.661153			0.330577	+	0.943779i	$0.392757\pi$
$938$	1.94277e27	−	7.11029e27i	0.112848	−	0.413010i
$939$		−	1.19165e28i		−	0.685215i
$940$	−5.78656e26	+	9.79852e26i	−0.0329387	+	0.0557758i
$941$			7.61783e27i			0.429270i	0.976694	+	0.214635i	$0.0688561\pi$
$941$			7.61783e27i			0.429270i	−0.976694	+	0.214635i	$0.931144\pi$
$942$	4.66887e27	+	1.27569e27i	0.260452	+	0.0711642i
$943$	−1.21893e28			−0.673158
$944$	−1.29678e28	+	7.15024e27i	−0.708977	+	0.390919i
$945$	−1.11555e27			−0.0603793
$946$	2.32197e28	+	6.34440e27i	1.24420	+	0.339958i
$947$		−	6.16915e27i		−	0.327266i	−0.986521	−	0.163633i	$-0.947679\pi$
$947$		−	6.16915e27i		−	0.327266i	0.986521	−	0.163633i	$-0.0523213\pi$
$948$	1.30221e28	−	2.20506e28i	0.683915	−	1.15809i
$949$		−	7.46858e27i		−	0.388337i
$950$	3.48935e27	−	1.27706e28i	0.179626	−	0.657411i
$951$	−8.22373e27			−0.419135
$952$	5.23568e26	+	5.39267e26i	0.0264193	+	0.0272115i
$953$	1.87596e28			0.937221			0.468611	−	0.883405i	$-0.344755\pi$
$953$	1.87596e28			0.937221			0.468611	+	0.883405i	$0.344755\pi$
$954$	8.24693e26	−	3.01827e27i	0.0407927	−	0.149296i
$955$		−	3.44956e27i		−	0.168939i
$956$	−7.84138e27	−	4.63077e27i	−0.380227	−	0.224545i
$957$		−	1.66003e28i		−	0.796990i
$958$	1.24409e28	+	3.39926e27i	0.591397	+	0.161589i
$959$	6.98849e27			0.328932
$960$	9.92117e25	−	3.35753e27i	0.00462366	−	0.156475i
$961$	−2.62364e27			−0.121069
$962$	2.90211e28	+	7.92953e27i	1.32602	+	0.362313i
$963$		−	2.64096e27i		−	0.119485i
$964$	9.75985e27	+	5.76372e27i	0.437231	+	0.258209i
$965$			4.79944e27i			0.212902i
$966$	1.23959e27	−	4.53676e27i	0.0544498	−	0.199280i
$967$	−3.54689e28			−1.54275			−0.771376	−	0.636379i	$-0.780431\pi$
$967$	−3.54689e28			−1.54275			−0.771376	+	0.636379i	$0.780431\pi$
$968$	3.38274e26	+	3.48417e26i	0.0145698	+	0.0150067i
$969$	−1.76166e27			−0.0751356
$970$	−2.10413e27	+	7.70087e27i	−0.0888672	+	0.325243i
$971$			3.65508e28i			1.52867i	0.644817	+	0.764337i	$0.276933\pi$
$971$			3.65508e28i			1.52867i	−0.644817	+	0.764337i	$0.723067\pi$
$972$	6.22820e27	−	1.05464e28i	0.257949	−	0.436790i
$973$		−	4.74947e27i		−	0.194793i
$974$	−2.16657e28	−	5.91980e27i	−0.879961	−	0.240435i
$975$	−2.35993e28			−0.949195
$976$	−3.55898e28	+	1.96236e28i	−1.41759	+	0.781639i
$977$	−2.93618e28			−1.15820			−0.579101	−	0.815256i	$-0.696596\pi$
$977$	−2.93618e28			−1.15820			−0.579101	+	0.815256i	$0.696596\pi$
$978$	2.86809e28	+	7.83656e27i	1.12040	+	0.306130i
$979$			4.55543e28i			1.76236i
$980$	−2.19072e27	+	3.70960e27i	−0.0839342	+	0.142128i
$981$		−	3.71910e27i		−	0.141118i
$982$	5.09393e27	−	1.86432e28i	0.191423	−	0.700584i
$983$	−5.50097e27			−0.204730			−0.102365	−	0.994747i	$-0.532641\pi$
$983$	−5.50097e27			−0.204730			−0.102365	+	0.994747i	$0.532641\pi$
$984$	−1.43376e28	+	1.39202e28i	−0.528474	+	0.513089i
$985$	7.87842e27			0.287604
$986$	−8.46929e26	+	3.09966e27i	−0.0306208	+	0.112068i
$987$			2.61211e27i			0.0935358i
$988$	−1.95441e28	−	1.15419e28i	−0.693146	−	0.409341i
$989$			2.91546e28i			1.02410i
$990$	−1.30386e27	−	3.56258e26i	−0.0453625	−	0.0123945i
$991$	−4.20101e28			−1.44762			−0.723809	−	0.690000i	$-0.757611\pi$
$991$	−4.20101e28			−1.44762			−0.723809	+	0.690000i	$0.757611\pi$
$992$	−6.45418e27	−	2.66997e28i	−0.220283	−	0.911267i
$993$	3.79721e27			0.128365
$994$	1.43177e28	+	3.91206e27i	0.479404	+	0.130989i
$995$			2.21293e27i			0.0733920i
$996$	1.86457e28	+	1.10113e28i	0.612513	+	0.361723i
$997$			1.33768e28i			0.435259i	0.976032	+	0.217629i	$0.0698324\pi$
$997$			1.33768e28i			0.435259i	−0.976032	+	0.217629i	$0.930168\pi$
$998$	−4.12945e27	+	1.51133e28i	−0.133092	+	0.487101i
$999$	4.08715e28			1.30481

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8.20.b.a.5.18	yes	18
3.2	odd	2		72.20.d.b.37.1		18
4.3	odd	2		32.20.b.a.17.13		18
8.3	odd	2		32.20.b.a.17.6		18
8.5	even	2	inner	8.20.b.a.5.17	✓	18
24.5	odd	2		72.20.d.b.37.2		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8.20.b.a.5.17	✓	18	8.5	even	2	inner
8.20.b.a.5.18	yes	18	1.1	even	1	trivial
32.20.b.a.17.6		18	8.3	odd	2
32.20.b.a.17.13		18	4.3	odd	2
72.20.d.b.37.1		18	3.2	odd	2
72.20.d.b.37.2		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)

\(f(q)\)	\(=\)	\(q+(698.474 + 190.846i) q^{2} -29307.5i q^{3} +(451443. + 266602. i) q^{4} -795283. i q^{5} +(5.59322e6 - 2.04705e7i) q^{6} +3.26570e7 q^{7} +(2.64441e8 + 2.72371e8i) q^{8} +3.03333e8 q^{9} +O(q^{10})\)	\(q+(698.474 + 190.846i) q^{2} -29307.5i q^{3} +(451443. + 266602. i) q^{4} -795283. i q^{5} +(5.59322e6 - 2.04705e7i) q^{6} +3.26570e7 q^{7} +(2.64441e8 + 2.72371e8i) q^{8} +3.03333e8 q^{9} +(1.51777e8 - 5.55484e8i) q^{10} -7.73821e9i q^{11} +(7.81344e9 - 1.32307e10i) q^{12} -4.36653e10i q^{13} +(2.28101e10 + 6.23247e9i) q^{14} -2.33077e10 q^{15} +(1.32725e11 + 2.40712e11i) q^{16} +6.06271e10 q^{17} +(2.11870e11 + 5.78899e10i) q^{18} -9.91463e11i q^{19} +(2.12024e11 - 3.59025e11i) q^{20} -9.57095e11i q^{21} +(1.47681e12 - 5.40494e12i) q^{22} +6.78641e12 q^{23} +(7.98251e12 - 7.75012e12i) q^{24} +1.84410e13 q^{25} +(8.33335e12 - 3.04990e13i) q^{26} -4.29529e13i q^{27} +(1.47428e13 + 8.70643e12i) q^{28} +7.31976e13i q^{29} +(-1.62798e13 - 4.44819e12i) q^{30} -1.38011e14 q^{31} +(4.67657e13 + 1.93461e14i) q^{32} -2.26787e14 q^{33} +(4.23464e13 + 1.15704e13i) q^{34} -2.59716e13i q^{35} +(1.36937e14 + 8.08691e13i) q^{36} +9.51542e14i q^{37} +(1.89217e14 - 6.92511e14i) q^{38} -1.27972e15 q^{39} +(2.16612e14 - 2.10306e14i) q^{40} -1.79613e15 q^{41} +(1.82658e14 - 6.68506e14i) q^{42} +4.29602e15i q^{43} +(2.06302e15 - 3.49336e15i) q^{44} -2.41235e14i q^{45} +(4.74013e15 + 1.29516e15i) q^{46} -2.72920e15 q^{47} +(7.05465e15 - 3.88982e15i) q^{48} -1.03324e16 q^{49} +(1.28806e16 + 3.51940e15i) q^{50} -1.77683e15i q^{51} +(1.16413e16 - 1.97124e16i) q^{52} -1.42459e16i q^{53} +(8.19739e15 - 3.00015e16i) q^{54} -6.15406e15 q^{55} +(8.63587e15 + 8.89482e15i) q^{56} -2.90573e16 q^{57} +(-1.39695e16 + 5.11266e16i) q^{58} +5.38728e16i q^{59} +(-1.05221e16 - 6.21389e15i) q^{60} +1.47852e17i q^{61} +(-9.63970e16 - 2.63389e16i) q^{62} +9.90594e15 q^{63} +(-4.25660e15 + 1.44052e17i) q^{64} -3.47262e16 q^{65} +(-1.58405e17 - 4.32815e16i) q^{66} -3.11717e17i q^{67} +(2.73697e16 + 1.61633e16i) q^{68} -1.98893e17i q^{69} +(4.95657e15 - 1.81405e16i) q^{70} +6.27690e17 q^{71} +(8.02137e16 + 8.26189e16i) q^{72} +1.71042e17 q^{73} +(-1.81598e17 + 6.64627e17i) q^{74} -5.40460e17i q^{75} +(2.64326e17 - 4.47589e17i) q^{76} -2.52707e17i q^{77} +(-8.93850e17 - 2.44230e17i) q^{78} +1.66663e18 q^{79} +(1.91434e17 - 1.05554e17i) q^{80} -9.06289e17 q^{81} +(-1.25455e18 - 3.42785e17i) q^{82} +1.40928e18i q^{83} +(2.55164e17 - 4.32075e17i) q^{84} -4.82156e16i q^{85} +(-8.19880e17 + 3.00066e18i) q^{86} +2.14524e18 q^{87} +(2.10766e18 - 2.04630e18i) q^{88} -5.88693e18 q^{89} +(4.60388e16 - 1.68496e17i) q^{90} -1.42598e18i q^{91} +(3.06368e18 + 1.80927e18i) q^{92} +4.04475e18i q^{93} +(-1.90628e18 - 5.20857e17i) q^{94} -7.88493e17 q^{95} +(5.66985e18 - 1.37059e18i) q^{96} -1.38633e19 q^{97} +(-7.21692e18 - 1.97190e18i) q^{98} -2.34725e18i 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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