LMFDB - Embedded newform 8.20.b.a.5.16

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			5.16
Root			$0.500000 - 12610.3i$ of defining polynomial
Character	$\chi$	$=$	8.5
Dual form			8.20.b.a.5.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(564.947 + 452.905i) q^{2} +50441.2i q^{3} +(114042. + 511735. i) q^{4} -7.26212e6i q^{5} +(-2.28451e7 + 2.84966e7i) q^{6} -1.80984e8 q^{7} +(-1.67340e8 + 3.40753e8i) q^{8} -1.38205e9 q^{9} +O(q^{10})$	\(q+(564.947 + 452.905i) q^{2} +50441.2i q^{3} +(114042. + 511735. i) q^{4} -7.26212e6i q^{5} +(-2.28451e7 + 2.84966e7i) q^{6} -1.80984e8 q^{7} +(-1.67340e8 + 3.40753e8i) q^{8} -1.38205e9 q^{9} +(3.28905e9 - 4.10271e9i) q^{10} -1.74633e9i q^{11} +(-2.58125e10 + 5.75241e9i) q^{12} -9.15007e9i q^{13} +(-1.02246e11 - 8.19685e10i) q^{14} +3.66310e11 q^{15} +(-2.48867e11 + 1.16718e11i) q^{16} -2.51544e11 q^{17} +(-7.80786e11 - 6.25938e11i) q^{18} +1.49450e12i q^{19} +(3.71628e12 - 8.28186e11i) q^{20} -9.12904e12i q^{21} +(7.90924e11 - 9.86586e11i) q^{22} -4.50097e12 q^{23} +(-1.71880e13 - 8.44081e12i) q^{24} -3.36649e13 q^{25} +(4.14411e12 - 5.16930e12i) q^{26} -1.10865e13i q^{27} +(-2.06397e13 - 9.26157e13i) q^{28} -3.77104e12i q^{29} +(2.06946e14 + 1.65904e14i) q^{30} +1.61157e14 q^{31} +(-1.93459e14 - 4.67734e13i) q^{32} +8.80872e13 q^{33} +(-1.42109e14 - 1.13926e14i) q^{34} +1.31433e15i q^{35} +(-1.57612e14 - 7.07244e14i) q^{36} -4.58775e13i q^{37} +(-6.76869e14 + 8.44316e14i) q^{38} +4.61540e14 q^{39} +(2.47459e15 + 1.21524e15i) q^{40} -3.30538e15 q^{41} +(4.13459e15 - 5.15742e15i) q^{42} +7.16393e14i q^{43} +(8.93660e14 - 1.99155e14i) q^{44} +1.00366e16i q^{45} +(-2.54281e15 - 2.03851e15i) q^{46} -9.61828e15 q^{47} +(-5.88741e15 - 1.25531e16i) q^{48} +2.13563e16 q^{49} +(-1.90189e16 - 1.52470e16i) q^{50} -1.26882e16i q^{51} +(4.68241e15 - 1.04349e15i) q^{52} +2.87320e16i q^{53} +(5.02112e15 - 6.26327e15i) q^{54} -1.26821e16 q^{55} +(3.02858e16 - 6.16708e16i) q^{56} -7.53846e16 q^{57} +(1.70792e15 - 2.13044e15i) q^{58} +8.42412e16i q^{59} +(4.17747e16 + 1.87453e17i) q^{60} -3.85626e16i q^{61} +(9.10449e16 + 7.29886e16i) q^{62} +2.50129e17 q^{63} +(-8.81101e16 - 1.14043e17i) q^{64} -6.64489e16 q^{65} +(4.97646e16 + 3.98951e16i) q^{66} -3.60891e16i q^{67} +(-2.86866e16 - 1.28724e17i) q^{68} -2.27034e17i q^{69} +(-5.95265e17 + 7.42524e17i) q^{70} -8.39459e16 q^{71} +(2.31272e17 - 4.70938e17i) q^{72} +1.83184e14 q^{73} +(2.07782e16 - 2.59184e16i) q^{74} -1.69810e18i q^{75} +(-7.64790e17 + 1.70436e17i) q^{76} +3.16058e17i q^{77} +(2.60746e17 + 2.09034e17i) q^{78} +1.00888e18 q^{79} +(8.47623e17 + 1.80730e18i) q^{80} -1.04709e18 q^{81} +(-1.86736e18 - 1.49702e18i) q^{82} -1.33411e18i q^{83} +(4.67165e18 - 1.04109e18i) q^{84} +1.82674e18i q^{85} +(-3.24458e17 + 4.04724e17i) q^{86} +1.90216e17 q^{87} +(5.95069e17 + 2.92231e17i) q^{88} -4.03904e18 q^{89} +(-4.54564e18 + 5.67016e18i) q^{90} +1.65601e18i q^{91} +(-5.13299e17 - 2.30330e18i) q^{92} +8.12893e18i q^{93} +(-5.43382e18 - 4.35617e18i) q^{94} +1.08533e19 q^{95} +(2.35930e18 - 9.75829e18i) q^{96} +6.57665e18 q^{97} +(1.20651e19 + 9.67236e18i) q^{98} +2.41352e18i 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 $

$2$	564.947	+	452.905i	0.780230	+	0.625493i
$2$	564.947	+	452.905i	0.780230	+	0.625493i
$3$			50441.2i			1.47956i	0.672847	+	0.739781i	$0.265071\pi$
$3$			50441.2i			1.47956i	−0.672847	+	0.739781i	$0.734929\pi$
$4$	114042.	+	511735.i	0.217518	+	0.976056i
$5$		−	7.26212e6i		−	1.66283i	−0.555651	−	0.831416i	$-0.687531\pi$
$5$		−	7.26212e6i		−	1.66283i	0.555651	−	0.831416i	$-0.312469\pi$
$6$	−2.28451e7	+	2.84966e7i	−0.925456	+	1.15440i
$7$	−1.80984e8			−1.69515			−0.847576	−	0.530675i	$-0.821939\pi$
$7$	−1.80984e8			−1.69515			−0.847576	+	0.530675i	$0.821939\pi$
$8$	−1.67340e8	+	3.40753e8i	−0.440802	+	0.897604i
$9$	−1.38205e9			−1.18911
$10$	3.28905e9	−	4.10271e9i	1.04009	−	1.29739i
$11$		−	1.74633e9i		−	0.223304i	−0.993747	−	0.111652i	$-0.964386\pi$
$11$		−	1.74633e9i		−	0.223304i	0.993747	−	0.111652i	$-0.0356142\pi$
$12$	−2.58125e10	+	5.75241e9i	−1.44414	+	0.321831i
$13$		−	9.15007e9i		−	0.239311i	−0.992815	−	0.119655i	$-0.961821\pi$
$13$		−	9.15007e9i		−	0.239311i	0.992815	−	0.119655i	$-0.0381790\pi$
$14$	−1.02246e11	−	8.19685e10i	−1.32261	−	1.06030i
$15$	3.66310e11			2.46026
$16$	−2.48867e11	+	1.16718e11i	−0.905372	+	0.424619i
$17$	−2.51544e11			−0.514457			−0.257229	−	0.966351i	$-0.582809\pi$
$17$	−2.51544e11			−0.514457			−0.257229	+	0.966351i	$0.582809\pi$
$18$	−7.80786e11	−	6.25938e11i	−0.927776	−	0.743777i
$19$			1.49450e12i			1.06252i	0.847208	+	0.531261i	$0.178282\pi$
$19$			1.49450e12i			1.06252i	−0.847208	+	0.531261i	$0.821718\pi$
$20$	3.71628e12	−	8.28186e11i	1.62302	−	0.361695i
$21$		−	9.12904e12i		−	2.50808i
$22$	7.90924e11	−	9.86586e11i	0.139675	−	0.174229i
$23$	−4.50097e12			−0.521065			−0.260532	−	0.965465i	$-0.583898\pi$
$23$	−4.50097e12			−0.521065			−0.260532	+	0.965465i	$0.583898\pi$
$24$	−1.71880e13	−	8.44081e12i	−1.32806	−	0.652195i
$25$	−3.36649e13			−1.76501
$26$	4.14411e12	−	5.16930e12i	0.149687	−	0.186718i
$27$		−	1.10865e13i		−	0.279794i
$28$	−2.06397e13	−	9.26157e13i	−0.368725	−	1.65456i
$29$		−	3.77104e12i		−	0.0482703i	−0.999709	−	0.0241352i	$-0.992317\pi$
$29$		−	3.77104e12i		−	0.0482703i	0.999709	−	0.0241352i	$-0.00768321\pi$
$30$	2.06946e14	+	1.65904e14i	1.91957	+	1.53888i
$31$	1.61157e14			1.09474			0.547371	−	0.836890i	$-0.315629\pi$
$31$	1.61157e14			1.09474			0.547371	+	0.836890i	$0.315629\pi$
$32$	−1.93459e14	−	4.67734e13i	−0.971995	−	0.235003i
$33$	8.80872e13			0.330393
$34$	−1.42109e14	−	1.13926e14i	−0.401395	−	0.321789i
$35$			1.31433e15i			2.81875i
$36$	−1.57612e14	−	7.07244e14i	−0.258651	−	1.16063i
$37$		−	4.58775e13i		−	0.0580341i	−0.999579	−	0.0290171i	$-0.990762\pi$
$37$		−	4.58775e13i		−	0.0580341i	0.999579	−	0.0290171i	$-0.00923772\pi$
$38$	−6.76869e14	+	8.44316e14i	−0.664600	+	0.829012i
$39$	4.61540e14			0.354076
$40$	2.47459e15	+	1.21524e15i	1.49256	+	0.732980i
$41$	−3.30538e15			−1.57679			−0.788397	−	0.615167i	$-0.789089\pi$
$41$	−3.30538e15			−1.57679			−0.788397	+	0.615167i	$0.789089\pi$
$42$	4.13459e15	−	5.15742e15i	1.56879	−	1.95688i
$43$			7.16393e14i			0.217371i	0.994076	+	0.108685i	$0.0346641\pi$
$43$			7.16393e14i			0.217371i	−0.994076	+	0.108685i	$0.965336\pi$
$44$	8.93660e14	−	1.99155e14i	0.217958	−	0.0485726i
$45$			1.00366e16i			1.97728i
$46$	−2.54281e15	−	2.03851e15i	−0.406550	−	0.325922i
$47$	−9.61828e15			−1.25363			−0.626813	−	0.779170i	$-0.715641\pi$
$47$	−9.61828e15			−1.25363			−0.626813	+	0.779170i	$0.715641\pi$
$48$	−5.88741e15	−	1.25531e16i	−0.628250	−	1.33955i
$49$	2.13563e16			1.87354
$50$	−1.90189e16	−	1.52470e16i	−1.37711	−	1.10400i
$51$		−	1.26882e16i		−	0.761172i
$52$	4.68241e15	−	1.04349e15i	0.233581	−	0.0520543i
$53$			2.87320e16i			1.19604i	0.801482	+	0.598018i	$0.204045\pi$
$53$			2.87320e16i			1.19604i	−0.801482	+	0.598018i	$0.795955\pi$
$54$	5.02112e15	−	6.26327e15i	0.175009	−	0.218303i
$55$	−1.26821e16			−0.371317
$56$	3.02858e16	−	6.16708e16i	0.747227	−	1.52157i
$57$	−7.53846e16			−1.57207
$58$	1.70792e15	−	2.13044e15i	0.0301928	−	0.0376620i
$59$			8.42412e16i			1.26599i	0.774156	+	0.632995i	$0.218175\pi$
$59$			8.42412e16i			1.26599i	−0.774156	+	0.632995i	$0.781825\pi$
$60$	4.17747e16	+	1.87453e17i	0.535151	+	2.40136i
$61$		−	3.85626e16i		−	0.422215i	−0.977463	−	0.211107i	$-0.932293\pi$
$61$		−	3.85626e16i		−	0.422215i	0.977463	−	0.211107i	$-0.0677070\pi$
$62$	9.10449e16	+	7.29886e16i	0.854151	+	0.684753i
$63$	2.50129e17			2.01571
$64$	−8.81101e16	−	1.14043e17i	−0.611386	−	0.791332i
$65$	−6.64489e16			−0.397934
$66$	4.97646e16	+	3.98951e16i	0.257782	+	0.206658i
$67$		−	3.60891e16i		−	0.162056i	−0.996712	−	0.0810281i	$-0.974180\pi$
$67$		−	3.60891e16i		−	0.162056i	0.996712	−	0.0810281i	$-0.0258204\pi$
$68$	−2.86866e16	−	1.28724e17i	−0.111904	−	0.502139i
$69$		−	2.27034e17i		−	0.770948i
$70$	−5.95265e17	+	7.42524e17i	−1.76311	+	2.19927i
$71$	−8.39459e16			−0.217293			−0.108646	−	0.994080i	$-0.534652\pi$
$71$	−8.39459e16			−0.217293			−0.108646	+	0.994080i	$0.534652\pi$
$72$	2.31272e17	−	4.70938e17i	0.524161	−	1.06735i
$73$	1.83184e14			0.000364183			0.000182091	−	1.00000i	$-0.499942\pi$
$73$	1.83184e14			0.000364183			0.000182091		1.00000i	$0.499942\pi$
$74$	2.07782e16	−	2.59184e16i	0.0362999	−	0.0452800i
$75$		−	1.69810e18i		−	2.61144i
$76$	−7.64790e17	+	1.70436e17i	−1.03708	+	0.231117i
$77$			3.16058e17i			0.378534i
$78$	2.60746e17	+	2.09034e17i	0.276260	+	0.221472i
$79$	1.00888e18			0.947072			0.473536	−	0.880774i	$-0.342977\pi$
$79$	1.00888e18			0.947072			0.473536	+	0.880774i	$0.342977\pi$
$80$	8.47623e17	+	1.80730e18i	0.706070	+	1.50548i
$81$	−1.04709e18			−0.775133
$82$	−1.86736e18	−	1.49702e18i	−1.23026	−	0.986273i
$83$		−	1.33411e18i		−	0.783342i	−0.920105	−	0.391671i	$-0.871897\pi$
$83$		−	1.33411e18i		−	0.783342i	0.920105	−	0.391671i	$-0.128103\pi$
$84$	4.67165e18	−	1.04109e18i	2.44803	−	0.545552i
$85$			1.82674e18i			0.855456i
$86$	−3.24458e17	+	4.04724e17i	−0.135964	+	0.169599i
$87$	1.90216e17			0.0714190
$88$	5.95069e17	+	2.92231e17i	0.200439	+	0.0984330i
$89$	−4.03904e18			−1.22201			−0.611003	−	0.791628i	$-0.709234\pi$
$89$	−4.03904e18			−1.22201			−0.611003	+	0.791628i	$0.709234\pi$
$90$	−4.54564e18	+	5.67016e18i	−1.23678	+	1.54273i
$91$			1.65601e18i			0.405668i
$92$	−5.13299e17	−	2.30330e18i	−0.113341	−	0.508589i
$93$			8.12893e18i			1.61974i
$94$	−5.43382e18	−	4.35617e18i	−0.978116	−	0.784134i
$95$	1.08533e19			1.76680
$96$	2.35930e18	−	9.75829e18i	0.347702	−	1.43813i
$97$	6.57665e18			0.878361			0.439180	−	0.898399i	$-0.355269\pi$
$97$	6.57665e18			0.878361			0.439180	+	0.898399i	$0.355269\pi$
$98$	1.20651e19	+	9.67236e18i	1.46179	+	1.17188i
$99$			2.41352e18i			0.265532i
$100$	−3.83921e18	−	1.72275e19i	−0.383921	−	1.72275i
$101$			1.03910e19i			0.945371i	0.881231	+	0.472686i	$0.156715\pi$
$101$			1.03910e19i			0.945371i	−0.881231	+	0.472686i	$0.843285\pi$
$102$	5.74654e18	−	7.16815e18i	0.476108	−	0.593889i
$103$	3.99368e18			0.301592			0.150796	−	0.988565i	$-0.451816\pi$
$103$	3.99368e18			0.301592			0.150796	+	0.988565i	$0.451816\pi$
$104$	3.11791e18	+	1.53117e18i	0.214806	+	0.105489i
$105$	−6.62962e19			−4.17052
$106$	−1.30129e19	+	1.62320e19i	−0.748112	+	0.933184i
$107$		−	2.02092e19i		−	1.06268i	−0.847158	−	0.531341i	$-0.821688\pi$
$107$		−	2.02092e19i		−	1.06268i	0.847158	−	0.531341i	$-0.178312\pi$
$108$	5.67333e18	−	1.26432e18i	0.273094	−	0.0608601i
$109$		−	2.06686e19i		−	0.911506i	−0.890106	−	0.455753i	$-0.849370\pi$
$109$		−	2.06686e19i		−	0.911506i	0.890106	−	0.455753i	$-0.150630\pi$
$110$	−7.16471e18	−	5.74378e18i	−0.289713	−	0.232256i
$111$	2.31412e18			0.0858651
$112$	4.50409e19	−	2.11241e19i	1.53474	−	0.719793i
$113$	5.61532e19			1.75845			0.879223	−	0.476410i	$-0.158062\pi$
$113$	5.61532e19			1.75845			0.879223	+	0.476410i	$0.158062\pi$
$114$	−4.25883e19	−	3.41421e19i	−1.22657	−	0.983317i
$115$			3.26866e19i			0.866443i
$116$	1.92977e18	−	4.30057e17i	0.0471146	−	0.0104997i
$117$			1.26459e19i			0.284566i
$118$	−3.81533e19	+	4.75918e19i	−0.791867	+	0.987763i
$119$	4.55254e19			0.872083
$120$	−6.12982e19	+	1.24821e20i	−1.08449	+	2.20834i
$121$	5.81094e19			0.950135
$122$	1.74652e19	−	2.17858e19i	0.264092	−	0.329425i
$123$		−	1.66727e20i		−	2.33297i
$124$	1.83786e19	+	8.24694e19i	0.238126	+	1.06853i
$125$			1.05964e20i			1.27208i
$126$	1.41310e20	+	1.13285e20i	1.57272	+	1.26081i
$127$	−1.15835e20			−1.19593			−0.597964	−	0.801523i	$-0.704023\pi$
$127$	−1.15835e20			−1.19593			−0.597964	+	0.801523i	$0.704023\pi$
$128$	1.87314e18	−	1.04334e20i	0.0179505	−	0.999839i
$129$	−3.61357e19			−0.321614
$130$	−3.75401e19	−	3.00950e19i	−0.310480	−	0.248905i
$131$			4.76901e19i			0.366734i	0.983045	+	0.183367i	$0.0586997\pi$
$131$			4.76901e19i			0.366734i	−0.983045	+	0.183367i	$0.941300\pi$
$132$	1.00456e19	+	4.50773e19i	0.0718662	+	0.322482i
$133$		−	2.70481e20i		−	1.80114i
$134$	1.63450e19	−	2.03884e19i	0.101365	−	0.126441i
$135$	−8.05113e19			−0.465250
$136$	4.20933e19	−	8.57144e19i	0.226774	−	0.461779i
$137$	9.73967e19			0.489439			0.244720	−	0.969594i	$-0.421304\pi$
$137$	9.73967e19			0.489439			0.244720	+	0.969594i	$0.421304\pi$
$138$	1.02825e20	−	1.28262e20i	0.482222	−	0.601517i
$139$			2.45863e20i			1.07659i	0.842755	+	0.538297i	$0.180932\pi$
$139$			2.45863e20i			1.07659i	−0.842755	+	0.538297i	$0.819068\pi$
$140$	−6.72586e20	+	1.49888e20i	−2.75126	+	0.613128i
$141$		−	4.85157e20i		−	1.85482i
$142$	−4.74249e19	−	3.80195e19i	−0.169538	−	0.135915i
$143$	−1.59791e19			−0.0534391
$144$	3.43947e20	−	1.61311e20i	1.07658	−	0.504917i
$145$	−2.73858e19			−0.0802655
$146$	1.03489e17	+	8.29648e16i	0.000284146	+	0.000227794i
$147$			1.07723e21i			2.77202i
$148$	2.34771e19	−	5.23196e18i	0.0566446	−	0.0126234i
$149$			2.51129e20i			0.568366i	0.958770	+	0.284183i	$0.0917223\pi$
$149$			2.51129e20i			0.568366i	−0.958770	+	0.284183i	$0.908278\pi$
$150$	7.69076e20	−	9.59334e20i	1.63344	−	2.03752i
$151$	1.43448e20			0.286032			0.143016	−	0.989720i	$-0.454320\pi$
$151$	1.43448e20			0.286032			0.143016	+	0.989720i	$0.454320\pi$
$152$	−5.09257e20	−	2.50090e20i	−0.953725	−	0.468362i
$153$	3.47647e20			0.611744
$154$	−1.43144e20	+	1.78556e20i	−0.236771	+	0.295344i
$155$		−	1.17034e21i		−	1.82037i
$156$	5.26349e19	+	2.36186e20i	0.0770177	+	0.345598i
$157$			1.27765e21i			1.75940i	0.475527	+	0.879701i	$0.342257\pi$
$157$			1.27765e21i			1.75940i	−0.475527	+	0.879701i	$0.657743\pi$
$158$	5.69965e20	+	4.56928e20i	0.738934	+	0.592387i
$159$	−1.44927e21			−1.76961
$160$	−3.39674e20	+	1.40492e21i	−0.390771	+	1.61626i
$161$	8.14603e20			0.883284
$162$	−5.91550e20	−	4.74233e20i	−0.604782	−	0.484840i
$163$			1.69935e21i			1.63870i	0.573292	+	0.819351i	$0.305666\pi$
$163$			1.69935e21i			1.63870i	−0.573292	+	0.819351i	$0.694334\pi$
$164$	−3.76952e20	−	1.69148e21i	−0.342981	−	1.53904i
$165$		−	6.39700e20i		−	0.549387i
$166$	6.04227e20	−	7.53704e20i	0.489974	−	0.611187i
$167$	−2.22279e21			−1.70252			−0.851260	−	0.524744i	$-0.824161\pi$
$167$	−2.22279e21			−1.70252			−0.851260	+	0.524744i	$0.824161\pi$
$168$	3.11075e21	+	1.52765e21i	2.25127	+	1.10557i
$169$	1.37820e21			0.942730
$170$	−8.27341e20	+	1.03201e21i	−0.535082	+	0.667452i
$171$		−	2.06548e21i		−	1.26345i
$172$	−3.66603e20	+	8.16989e19i	−0.212166	+	0.0472820i
$173$		−	6.56078e20i		−	0.359350i	−0.983726	−	0.179675i	$-0.942495\pi$
$173$		−	6.56078e20i		−	0.359350i	0.983726	−	0.179675i	$-0.0575046\pi$
$174$	1.07462e20	+	8.61497e19i	0.0557232	+	0.0446721i
$175$	6.09280e21			2.99196
$176$	2.03829e20	+	4.34605e20i	0.0948192	+	0.202173i
$177$	−4.24922e21			−1.87311
$178$	−2.28185e21	−	1.82930e21i	−0.953446	−	0.764356i
$179$		−	2.05661e21i		−	0.814795i	−0.913251	−	0.407397i	$-0.866436\pi$
$179$		−	2.05661e21i		−	0.814795i	0.913251	−	0.407397i	$-0.133564\pi$
$180$	−5.13609e21	+	1.14460e21i	−1.92994	+	0.430094i
$181$		−	3.76435e21i		−	1.34197i	−0.741470	−	0.670986i	$-0.765871\pi$
$181$		−	3.76435e21i		−	1.34197i	0.741470	−	0.670986i	$-0.234129\pi$
$182$	−7.50018e20	+	9.35560e20i	−0.253743	+	0.316514i
$183$	1.94515e21			0.624693
$184$	7.53191e20	−	1.53372e21i	0.229687	−	0.467710i
$185$	−3.33168e20			−0.0965010
$186$	−3.68163e21	+	4.59241e21i	−1.01314	+	1.26377i
$187$			4.39280e20i			0.114881i
$188$	−1.09689e21	−	4.92201e21i	−0.272686	−	1.22361i
$189$			2.00647e21i			0.474292i
$190$	6.13152e21	+	4.91550e21i	1.37851	+	1.10512i
$191$	−3.90151e21			−0.834479			−0.417240	−	0.908796i	$-0.637002\pi$
$191$	−3.90151e21			−0.834479			−0.417240	+	0.908796i	$0.637002\pi$
$192$	5.75246e21	−	4.44438e21i	1.17083	−	0.904585i
$193$	−4.80647e21			−0.931176			−0.465588	−	0.885001i	$-0.654157\pi$
$193$	−4.80647e21			−0.931176			−0.465588	+	0.885001i	$0.654157\pi$
$194$	3.71545e21	+	2.97860e21i	0.685323	+	0.549408i
$195$		−	3.35176e21i		−	0.588768i
$196$	2.43551e21	+	1.09287e22i	0.407527	+	1.82868i
$197$			1.70873e21i			0.272423i	0.990680	+	0.136211i	$0.0434926\pi$
$197$			1.70873e21i			0.272423i	−0.990680	+	0.136211i	$0.956507\pi$
$198$	−1.09310e21	+	1.36351e21i	−0.166089	+	0.207176i
$199$	6.36199e21			0.921486			0.460743	−	0.887534i	$-0.347583\pi$
$199$	6.36199e21			0.921486			0.460743	+	0.887534i	$0.347583\pi$
$200$	5.63347e21	−	1.14714e22i	0.778020	−	1.58428i
$201$	1.82038e21			0.239772
$202$	−4.70612e21	+	5.87034e21i	−0.591323	+	0.737607i
$203$			6.82498e20i			0.0818255i
$204$	6.49298e21	−	1.44698e21i	0.742947	−	0.165568i
$205$			2.40041e22i			2.62194i
$206$	2.25622e21	+	1.80876e21i	0.235311	+	0.188644i
$207$	6.22057e21			0.619601
$208$	1.06798e21	+	2.27715e21i	0.101616	+	0.216665i
$209$	2.60991e21			0.237266
$210$	−3.74538e22	−	3.00259e22i	−3.25396	−	2.60863i
$211$			7.28275e20i			0.0604800i	0.999543	+	0.0302400i	$0.00962716\pi$
$211$			7.28275e20i			0.0604800i	−0.999543	+	0.0302400i	$0.990373\pi$
$212$	−1.47031e22	+	3.27665e21i	−1.16740	+	0.260159i
$213$		−	4.23433e21i		−	0.321498i
$214$	9.15285e21	−	1.14171e22i	0.664700	−	0.829136i
$215$	5.20253e21			0.361451
$216$	3.77775e21	+	1.85521e21i	0.251144	+	0.123334i
$217$	−2.91667e22			−1.85575
$218$	9.36092e21	−	1.16767e22i	0.570141	−	0.711185i
$219$			9.24000e18i			0.000538831i
$220$	−1.44629e21	−	6.48986e21i	−0.0807681	−	0.362427i
$221$			2.30165e21i			0.123115i
$222$	1.30735e21	+	1.04808e21i	0.0669946	+	0.0537080i
$223$	−3.31193e22			−1.62624			−0.813121	−	0.582094i	$-0.802233\pi$
$223$	−3.31193e22			−1.62624			−0.813121	+	0.582094i	$0.802233\pi$
$224$	3.50129e22	+	8.46522e21i	1.64768	+	0.398366i
$225$	4.65266e22			2.09878
$226$	3.17236e22	+	2.54321e22i	1.37199	+	1.09990i
$227$		−	1.74406e22i		−	0.723294i	−0.932315	−	0.361647i	$-0.882215\pi$
$227$		−	1.74406e22i		−	0.723294i	0.932315	−	0.361647i	$-0.117785\pi$
$228$	−8.59700e21	−	3.85769e22i	−0.341953	−	1.53443i
$229$		−	3.93483e22i		−	1.50137i	−0.660659	−	0.750686i	$-0.729723\pi$
$229$		−	3.93483e22i		−	1.50137i	0.660659	−	0.750686i	$-0.270277\pi$
$230$	−1.48039e22	+	1.84662e22i	−0.541954	+	0.676025i
$231$	−1.59424e22			−0.560065
$232$	1.28499e21	+	6.31045e20i	0.0433277	+	0.0212777i
$233$	−3.19709e22			−1.03484			−0.517421	−	0.855731i	$-0.673108\pi$
$233$	−3.19709e22			−1.03484			−0.517421	+	0.855731i	$0.673108\pi$
$234$	−5.72738e21	+	7.14424e21i	−0.177994	+	0.222027i
$235$			6.98491e22i			2.08457i
$236$	−4.31091e22	+	9.60702e21i	−1.23568	+	0.275375i
$237$			5.08892e22i			1.40125i
$238$	2.57194e22	+	2.06187e22i	0.680425	+	0.545482i
$239$	4.84436e22			1.23156			0.615781	−	0.787917i	$-0.288841\pi$
$239$	4.84436e22			1.23156			0.615781	+	0.787917i	$0.288841\pi$
$240$	−9.11624e22	+	4.27551e22i	−2.22745	+	1.04467i
$241$	3.76961e22			0.885389			0.442695	−	0.896672i	$-0.354023\pi$
$241$	3.76961e22			0.885389			0.442695	+	0.896672i	$0.354023\pi$
$242$	3.28287e22	+	2.63180e22i	0.741324	+	0.594303i
$243$		−	6.57019e22i		−	1.42665i
$244$	1.97338e22	−	4.39776e21i	0.412105	−	0.0918392i
$245$		−	1.55092e23i		−	3.11538i
$246$	7.55117e22	−	9.41921e22i	1.45925	−	1.82025i
$247$	1.36748e22			0.254273
$248$	−2.69679e22	+	5.49146e22i	−0.482565	+	0.982645i
$249$	6.72943e22			1.15900
$250$	−4.79918e22	+	5.98642e22i	−0.795677	+	0.992515i
$251$			9.76665e22i			1.55900i	0.626405	+	0.779498i	$0.284526\pi$
$251$			9.76665e22i			1.55900i	−0.626405	+	0.779498i	$0.715474\pi$
$252$	2.85252e22	+	1.28000e23i	0.438453	+	1.96745i
$253$			7.86020e21i			0.116356i
$254$	−6.54407e22	−	5.24623e22i	−0.933098	−	0.748044i
$255$	−9.21431e22			−1.26570
$256$	4.83115e22	−	5.80947e22i	0.639397	−	0.768876i
$257$	−8.14477e22			−1.03876			−0.519379	−	0.854544i	$-0.673837\pi$
$257$	−8.14477e22			−1.03876			−0.519379	+	0.854544i	$0.673837\pi$
$258$	−2.04148e22	−	1.63661e22i	−0.250933	−	0.201167i
$259$			8.30309e21i			0.0983766i
$260$	−7.57796e21	−	3.40042e22i	−0.0865576	−	0.388406i
$261$			5.21178e21i			0.0573985i
$262$	−2.15991e22	+	2.69424e22i	−0.229389	+	0.286137i
$263$	−8.19000e22			−0.838889			−0.419445	−	0.907781i	$-0.637775\pi$
$263$	−8.19000e22			−0.838889			−0.419445	+	0.907781i	$0.637775\pi$
$264$	−1.47405e22	+	3.00160e22i	−0.145638	+	0.296562i
$265$	2.08655e23			1.98881
$266$	1.22502e23	−	1.52808e23i	1.12660	−	1.40530i
$267$		−	2.03734e23i		−	1.80804i
$268$	1.84681e22	−	4.11567e21i	0.158176	−	0.0352501i
$269$			6.49567e22i			0.537004i	0.963279	+	0.268502i	$0.0865285\pi$
$269$			6.49567e22i			0.537004i	−0.963279	+	0.268502i	$0.913471\pi$
$270$	−4.54846e22	−	3.64640e22i	−0.363002	−	0.291010i
$271$	−3.67087e22			−0.282853			−0.141426	−	0.989949i	$-0.545169\pi$
$271$	−3.67087e22			−0.282853			−0.141426	+	0.989949i	$0.545169\pi$
$272$	6.26010e22	−	2.93598e22i	0.465775	−	0.218448i
$273$	−8.35313e22			−0.600212
$274$	5.50239e22	+	4.41115e22i	0.381875	+	0.306141i
$275$			5.87901e22i			0.394134i
$276$	1.16181e23	−	2.58914e22i	0.752489	−	0.167695i
$277$			2.95559e22i			0.184964i	0.995714	+	0.0924818i	$0.0294800\pi$
$277$			2.95559e22i			0.184964i	−0.995714	+	0.0924818i	$0.970520\pi$
$278$	−1.11352e23	+	1.38899e23i	−0.673402	+	0.839991i
$279$	−2.22727e23			−1.30176
$280$	−4.47861e23	−	2.19939e23i	−2.53012	−	1.24251i
$281$	−1.07600e23			−0.587629			−0.293814	−	0.955863i	$-0.594925\pi$
$281$	−1.07600e23			−0.587629			−0.293814	+	0.955863i	$0.594925\pi$
$282$	2.19730e23	−	2.74088e23i	1.16017	−	1.44718i
$283$			1.30141e23i			0.664422i	0.943205	+	0.332211i	$0.107795\pi$
$283$			1.30141e23i			0.664422i	−0.943205	+	0.332211i	$0.892205\pi$
$284$	−9.57334e21	−	4.29580e22i	−0.0472650	−	0.212090i
$285$			5.47452e23i			2.61408i
$286$	−9.02733e21	−	7.23701e21i	−0.0416948	−	0.0334258i
$287$	5.98221e23			2.67290
$288$	2.67370e23	+	6.46432e22i	1.15580	+	0.279444i
$289$	−1.75798e23			−0.735334
$290$	−1.54715e22	−	1.24031e22i	−0.0626255	−	0.0502055i
$291$			3.31734e23i			1.29959i
$292$	2.08906e19	+	9.37414e19i	7.92162e−5	+	0.000355463i
$293$		−	5.20881e23i		−	1.91204i	−0.293308	−	0.956018i	$-0.594756\pi$
$293$		−	5.20881e23i		−	1.91204i	0.293308	−	0.956018i	$-0.405244\pi$
$294$	−4.87885e23	+	6.08580e23i	−1.73388	+	2.16281i
$295$	6.11769e23			2.10513
$296$	1.56329e22	+	7.67713e21i	0.0520917	+	0.0255816i
$297$	−1.93607e22			−0.0624791
$298$	−1.13738e23	+	1.41875e23i	−0.355509	+	0.443456i
$299$			4.11842e22i			0.124697i
$300$	8.68974e23	−	1.93654e23i	2.54891	−	0.568034i
$301$		−	1.29656e23i		−	0.368476i
$302$	8.10406e22	+	6.49684e22i	0.223170	+	0.178911i
$303$	−5.24132e23			−1.39874
$304$	−1.74436e23	−	3.71933e23i	−0.451167	−	0.961978i
$305$	−2.80046e23			−0.702072
$306$	1.96402e23	+	1.57451e23i	0.477301	+	0.382642i
$307$		−	2.72248e23i		−	0.641432i	−0.947175	−	0.320716i	$-0.896076\pi$
$307$		−	2.72248e23i		−	0.641432i	0.947175	−	0.320716i	$-0.103924\pi$
$308$	−1.61738e23	+	3.60439e22i	−0.369471	+	0.0823379i
$309$			2.01446e23i			0.446224i
$310$	5.30052e23	−	6.61179e23i	1.13863	−	1.42031i
$311$	−1.71275e23			−0.356838			−0.178419	−	0.983955i	$-0.557098\pi$
$311$	−1.71275e23			−0.356838			−0.178419	+	0.983955i	$0.557098\pi$
$312$	−7.72340e22	+	1.57271e23i	−0.156077	+	0.317820i
$313$	−9.38024e23			−1.83884			−0.919418	−	0.393283i	$-0.871339\pi$
$313$	−9.38024e23			−1.83884			−0.919418	+	0.393283i	$0.871339\pi$
$314$	−5.78654e23	+	7.21804e23i	−1.10049	+	1.37274i
$315$		−	1.81647e24i		−	3.35179i
$316$	1.15055e23	+	5.16280e23i	0.206005	+	0.924396i
$317$			2.05359e23i			0.356821i	0.983956	+	0.178411i	$0.0570955\pi$
$317$			2.05359e23i			0.356821i	−0.983956	+	0.178411i	$0.942904\pi$
$318$	−8.18763e23	−	6.56384e23i	−1.38070	−	1.10688i
$319$	−6.58550e21			−0.0107790
$320$	−8.28194e23	+	6.39866e23i	−1.31585	+	1.01663i
$321$	1.01938e24			1.57230
$322$	4.60207e23	+	3.68938e23i	0.689164	+	0.552488i
$323$		−	3.75934e23i		−	0.546623i
$324$	−1.19412e23	−	5.35832e23i	−0.168605	−	0.756574i
$325$			3.08036e23i			0.422386i
$326$	−7.69643e23	+	9.60041e23i	−1.02500	+	1.27856i
$327$	1.04255e24			1.34863
$328$	5.53121e23	−	1.12632e24i	0.695055	−	1.41534i
$329$	1.74075e24			2.12508
$330$	2.89723e23	−	3.61396e23i	0.343638	−	0.428648i
$331$		−	6.47395e22i		−	0.0746111i	−0.999304	−	0.0373056i	$-0.988123\pi$
$331$		−	6.47395e22i		−	0.0746111i	0.999304	−	0.0373056i	$-0.0118775\pi$
$332$	6.82712e23	−	1.52145e23i	0.764585	−	0.170391i
$333$			6.34051e22i			0.0690087i
$334$	−1.25576e24	−	1.00671e24i	−1.32836	−	1.06491i
$335$	−2.62084e23			−0.269472
$336$	1.06553e24	+	2.27191e24i	1.06498	+	2.27075i
$337$	−9.98451e23			−0.970158			−0.485079	−	0.874470i	$-0.661209\pi$
$337$	−9.98451e23			−0.970158			−0.485079	+	0.874470i	$0.661209\pi$
$338$	7.78608e23	+	6.24192e23i	0.735546	+	0.589671i
$339$			2.83243e24i			2.60173i
$340$	−9.34808e23	+	2.08325e23i	−0.834973	+	0.186077i
$341$		−	2.81433e23i		−	0.244461i
$342$	9.35468e23	−	1.16689e24i	0.790280	−	0.985783i
$343$	−1.80212e24			−1.48078
$344$	−2.44113e23	−	1.19881e23i	−0.195113	−	0.0958176i
$345$	−1.64875e24			−1.28196
$346$	2.97141e23	−	3.70649e23i	0.224771	−	0.280376i
$347$			8.81398e23i			0.648697i	0.945938	+	0.324348i	$0.105145\pi$
$347$			8.81398e23i			0.648697i	−0.945938	+	0.324348i	$0.894855\pi$
$348$	2.16926e22	+	9.73400e22i	0.0155349	+	0.0697090i
$349$		−	2.58174e24i		−	1.79916i	−0.436754	−	0.899581i	$-0.643872\pi$
$349$		−	2.58174e24i		−	1.79916i	0.436754	−	0.899581i	$-0.356128\pi$
$350$	3.44211e24	+	2.75946e24i	2.33441	+	1.87145i
$351$	−1.01442e23			−0.0669577
$352$	−8.16820e22	+	3.37844e23i	−0.0524772	+	0.217051i
$353$	7.81674e23			0.488839			0.244420	−	0.969670i	$-0.421403\pi$
$353$	7.81674e23			0.488839			0.244420	+	0.969670i	$0.421403\pi$
$354$	−2.40059e24	−	1.92450e24i	−1.46146	−	1.17162i
$355$			6.09625e23i			0.361321i
$356$	−4.60620e23	−	2.06692e24i	−0.265808	−	1.19275i
$357$			2.29636e24i			1.29030i
$358$	9.31449e23	−	1.16188e24i	0.509648	−	0.635727i
$359$	9.42135e23			0.502014			0.251007	−	0.967985i	$-0.419238\pi$
$359$	9.42135e23			0.502014			0.251007	+	0.967985i	$0.419238\pi$
$360$	−3.42001e24	−	1.67952e24i	−1.77482	−	0.871591i
$361$	−2.55125e23			−0.128954
$362$	1.70489e24	−	2.12666e24i	0.839394	−	1.04705i
$363$			2.93111e24i			1.40578i
$364$	−8.47440e23	+	1.88855e23i	−0.395955	+	0.0882400i
$365$		−	1.33030e21i		−	0.000605575i
$366$	1.09890e24	+	8.80966e23i	0.487404	+	0.390741i
$367$	8.36120e23			0.361361			0.180680	−	0.983542i	$-0.442170\pi$
$367$	8.36120e23			0.361361			0.180680	+	0.983542i	$0.442170\pi$
$368$	1.12014e24	−	5.25346e23i	0.471758	−	0.221254i
$369$	4.56821e24			1.87497
$370$	−1.88222e23	−	1.50893e23i	−0.0752930	−	0.0603607i
$371$		−	5.20002e24i		−	2.02746i
$372$	−4.15985e24	+	9.27038e23i	−1.58096	+	0.352322i
$373$			5.26263e23i			0.194971i	0.995237	+	0.0974853i	$0.0310799\pi$
$373$			5.26263e23i			0.194971i	−0.995237	+	0.0974853i	$0.968920\pi$
$374$	−1.98952e23	+	2.48170e23i	−0.0718569	+	0.0896332i
$375$	−5.34497e24			−1.88212
$376$	1.60952e24	−	3.27746e24i	0.552601	−	1.12526i
$377$	−3.45053e22			−0.0115516
$378$	−9.08742e23	+	1.13355e24i	−0.296667	+	0.370057i
$379$			4.20717e24i			1.33942i	0.742622	+	0.669711i	$0.233582\pi$
$379$			4.20717e24i			1.33942i	−0.742622	+	0.669711i	$0.766418\pi$
$380$	1.23773e24	+	5.55399e24i	0.384309	+	1.72449i
$381$		−	5.84286e24i		−	1.76945i
$382$	−2.20415e24	−	1.76701e24i	−0.651086	−	0.521961i
$383$	−4.13138e24			−1.19044			−0.595219	−	0.803563i	$-0.702935\pi$
$383$	−4.13138e24			−1.19044			−0.595219	+	0.803563i	$0.702935\pi$
$384$	5.26272e24	+	9.44835e22i	1.47932	+	0.0265589i
$385$	2.29525e24			0.629439
$386$	−2.71540e24	−	2.17688e24i	−0.726532	−	0.582444i
$387$		−	9.90093e23i		−	0.258477i
$388$	7.50013e23	+	3.36550e24i	0.191059	+	0.857330i
$389$			1.06402e24i			0.264502i	0.991216	+	0.132251i	$0.0422205\pi$
$389$			1.06402e24i			0.264502i	−0.991216	+	0.132251i	$0.957780\pi$
$390$	1.51803e24	−	1.89357e24i	0.368270	−	0.459374i
$391$	1.13219e24			0.268066
$392$	−3.57375e24	+	7.27721e24i	−0.825860	+	1.68169i
$393$	−2.40555e24			−0.542606
$394$	−7.73891e23	+	9.65340e23i	−0.170399	+	0.212552i
$395$		−	7.32662e24i		−	1.57482i
$396$	−1.23508e24	+	2.75243e23i	−0.259175	+	0.0577580i
$397$			2.78360e24i			0.570291i	0.958484	+	0.285145i	$0.0920419\pi$
$397$			2.78360e24i			0.570291i	−0.958484	+	0.285145i	$0.907958\pi$
$398$	3.59419e24	+	2.88138e24i	0.718971	+	0.576383i
$399$	1.36434e25			2.66489
$400$	8.37807e24	−	3.92931e24i	1.59799	−	0.749456i
$401$	−8.83444e24			−1.64554			−0.822768	−	0.568377i	$-0.807571\pi$
$401$	−8.83444e24			−1.64554			−0.822768	+	0.568377i	$0.807571\pi$
$402$	1.02842e24	+	8.24459e23i	0.187078	+	0.149976i
$403$		−	1.47459e24i		−	0.261984i
$404$	−5.31741e24	+	1.18500e24i	−0.922736	+	0.205635i
$405$			7.60409e24i			1.28892i
$406$	−3.09107e23	+	3.85575e23i	−0.0511813	+	0.0638427i
$407$	−8.01175e22			−0.0129593
$408$	4.32354e24	+	2.12324e24i	0.683231	+	0.335526i
$409$	1.20546e25			1.86115			0.930577	−	0.366096i	$-0.119306\pi$
$409$	1.20546e25			1.86115			0.930577	+	0.366096i	$0.119306\pi$
$410$	−1.08716e25	+	1.35610e25i	−1.64001	+	2.04572i
$411$			4.91280e24i			0.724156i
$412$	4.55447e23	+	2.04370e24i	0.0656015	+	0.294371i
$413$		−	1.52463e25i		−	2.14604i
$414$	3.51429e24	+	2.81733e24i	0.483431	+	0.387556i
$415$	−9.68849e24			−1.30256
$416$	−4.27980e23	+	1.77016e24i	−0.0562389	+	0.232609i
$417$	−1.24016e25			−1.59289
$418$	1.47446e24	+	1.18204e24i	0.185122	+	0.148408i
$419$		−	8.92191e24i		−	1.09503i	−0.836797	−	0.547513i	$-0.815575\pi$
$419$		−	8.92191e24i		−	1.09503i	0.836797	−	0.547513i	$-0.184425\pi$
$420$	−7.56054e24	−	3.39260e25i	−0.907161	−	4.07066i
$421$			1.21716e25i			1.42780i	0.700249	+	0.713899i	$0.253072\pi$
$421$			1.21716e25i			1.42780i	−0.700249	+	0.713899i	$0.746928\pi$
$422$	−3.29839e23	+	4.11437e23i	−0.0378298	+	0.0471883i
$423$	1.32930e25			1.49069
$424$	−9.79050e24	−	4.80800e24i	−1.07357	−	0.527216i
$425$	8.46820e24			0.908022
$426$	1.91775e24	−	2.39217e24i	0.201095	−	0.250842i
$427$			6.97922e24i			0.715718i
$428$	1.03418e25	−	2.30470e24i	1.03724	−	0.231152i
$429$		−	8.06004e23i		−	0.0790666i
$430$	2.93915e24	+	2.35625e24i	0.282015	+	0.226085i
$431$	7.90508e24			0.741946			0.370973	−	0.928644i	$-0.379024\pi$
$431$	7.90508e24			0.741946			0.370973	+	0.928644i	$0.379024\pi$
$432$	1.29400e24	+	2.75906e24i	0.118806	+	0.253317i
$433$	−1.73380e25			−1.55727			−0.778635	−	0.627477i	$-0.784088\pi$
$433$	−1.73380e25			−1.55727			−0.778635	+	0.627477i	$0.784088\pi$
$434$	−1.64777e25	−	1.32098e25i	−1.44791	−	1.16076i
$435$		−	1.38137e24i		−	0.118758i
$436$	1.05768e25	−	2.35709e24i	0.889682	−	0.198269i
$437$		−	6.72672e24i		−	0.553643i
$438$	−4.18484e21	+	5.22011e21i	−0.000337035	+	0.000420412i
$439$	−1.72396e24			−0.135867			−0.0679336	−	0.997690i	$-0.521641\pi$
$439$	−1.72396e24			−0.135867			−0.0679336	+	0.997690i	$0.521641\pi$
$440$	2.12222e24	−	4.32146e24i	0.163678	−	0.333296i
$441$	−2.95154e25			−2.22783
$442$	−1.04243e24	+	1.30031e24i	−0.0770077	+	0.0960582i
$443$		−	1.42402e24i		−	0.102963i	−0.998674	−	0.0514815i	$-0.983606\pi$
$443$		−	1.42402e24i		−	0.102963i	0.998674	−	0.0514815i	$-0.0163943\pi$
$444$	2.63906e23	+	1.18421e24i	0.0186772	+	0.0838092i
$445$			2.93320e25i			2.03199i
$446$	−1.87107e25	−	1.49999e25i	−1.26884	−	1.01720i
$447$	−1.26673e25			−0.840933
$448$	1.59465e25	+	2.06399e25i	1.03639	+	1.34143i
$449$	1.13838e25			0.724348			0.362174	−	0.932110i	$-0.382035\pi$
$449$	1.13838e25			0.724348			0.362174	+	0.932110i	$0.382035\pi$
$450$	2.62850e25	+	2.10721e25i	1.63753	+	1.31277i
$451$			5.77230e24i			0.352105i
$452$	6.40381e24	+	2.87355e25i	0.382493	+	1.71634i
$453$			7.23569e24i			0.423202i
$454$	7.89892e24	−	9.85300e24i	0.452415	−	0.564336i
$455$	1.20262e25			0.674558
$456$	1.26148e25	−	2.56875e25i	0.692972	−	1.41110i
$457$	1.60125e25			0.861500			0.430750	−	0.902471i	$-0.358249\pi$
$457$	1.60125e25			0.861500			0.430750	+	0.902471i	$0.358249\pi$
$458$	1.78210e25	−	2.22297e25i	0.939098	−	1.17142i
$459$			2.78874e24i			0.143942i
$460$	−1.67269e25	+	3.72764e24i	−0.845697	+	0.188467i
$461$			5.21427e23i			0.0258247i	0.999917	+	0.0129123i	$0.00411024\pi$
$461$			5.21427e23i			0.0258247i	−0.999917	+	0.0129123i	$0.995890\pi$
$462$	−9.00658e24	−	7.22038e24i	−0.436980	−	0.350317i
$463$	9.52571e24			0.452770			0.226385	−	0.974038i	$-0.427309\pi$
$463$	9.52571e24			0.452770			0.226385	+	0.974038i	$0.427309\pi$
$464$	4.40150e23	+	9.38487e23i	0.0204965	+	0.0437026i
$465$	5.90332e25			2.69335
$466$	−1.80619e25	−	1.44798e25i	−0.807415	−	0.647286i
$467$			1.14674e25i			0.502289i	0.967950	+	0.251145i	$0.0808069\pi$
$467$			1.14674e25i			0.502289i	−0.967950	+	0.251145i	$0.919193\pi$
$468$	−6.47133e24	+	1.44216e24i	−0.277752	+	0.0618981i
$469$			6.53155e24i			0.274710i
$470$	−3.16350e25	+	3.94610e25i	−1.30388	+	1.62644i
$471$	−6.44462e25			−2.60315
$472$	−2.87054e25	−	1.40969e25i	−1.13636	−	0.558051i
$473$	1.25106e24			0.0485398
$474$	−2.30480e25	+	2.87497e25i	−0.876474	+	1.09330i
$475$		−	5.03123e25i		−	1.87536i
$476$	5.19181e24	+	2.32969e25i	0.189693	+	0.851202i
$477$		−	3.97091e25i		−	1.42221i
$478$	2.73681e25	+	2.19404e25i	0.960902	+	0.770333i
$479$	1.59654e25			0.549532			0.274766	−	0.961511i	$-0.411400\pi$
$479$	1.59654e25			0.549532			0.274766	+	0.961511i	$0.411400\pi$
$480$	−7.08659e25	−	1.71335e25i	−2.39136	−	0.578170i
$481$	−4.19782e23			−0.0138882
$482$	2.12963e25	+	1.70727e25i	0.690807	+	0.553804i
$483$			4.10895e25i			1.30687i
$484$	6.62691e24	+	2.97366e25i	0.206671	+	0.927386i
$485$		−	4.77604e25i		−	1.46057i
$486$	2.97567e25	−	3.71181e25i	0.892361	−	1.11312i
$487$	9.29758e24			0.273429			0.136715	−	0.990610i	$-0.456346\pi$
$487$	9.29758e24			0.273429			0.136715	+	0.990610i	$0.456346\pi$
$488$	1.31403e25	+	6.45306e24i	0.378982	+	0.186113i
$489$	−8.57171e25			−2.42456
$490$	7.02418e25	−	8.76185e25i	1.94865	−	2.43071i
$491$		−	5.08801e25i		−	1.38444i	−0.721687	−	0.692220i	$-0.756633\pi$
$491$		−	5.08801e25i		−	1.38444i	0.721687	−	0.692220i	$-0.243367\pi$
$492$	8.53202e25	−	1.90139e25i	2.27711	−	0.507461i
$493$			9.48584e23i			0.0248330i
$494$	7.72555e24	+	6.19340e24i	0.198392	+	0.159046i
$495$	1.75273e25			0.441536
$496$	−4.01065e25	+	1.88099e25i	−0.991149	+	0.464848i
$497$	1.51928e25			0.368344
$498$	3.80177e25	+	3.04779e25i	0.904289	+	0.724948i
$499$			7.27577e25i			1.69795i	0.528436	+	0.848973i	$0.322779\pi$
$499$			7.27577e25i			1.69795i	−0.528436	+	0.848973i	$0.677221\pi$
$500$	−5.42256e25	+	1.20844e25i	−1.24162	+	0.276700i
$501$		−	1.12120e26i		−	2.51899i
$502$	−4.42336e25	+	5.51764e25i	−0.975141	+	1.21638i
$503$	−4.06882e25			−0.880182			−0.440091	−	0.897953i	$-0.645054\pi$
$503$	−4.06882e25			−0.880182			−0.440091	+	0.897953i	$0.645054\pi$
$504$	−4.18565e25	+	8.52322e25i	−0.888531	+	1.80931i
$505$	7.54603e25			1.57199
$506$	−3.55993e24	+	4.44060e24i	−0.0727798	+	0.0907844i
$507$			6.95179e25i			1.39483i
$508$	−1.32101e25	−	5.92768e25i	−0.260135	−	1.16729i
$509$			4.81350e24i			0.0930341i	0.998917	+	0.0465170i	$0.0148122\pi$
$509$			4.81350e24i			0.0930341i	−0.998917	+	0.0465170i	$0.985188\pi$
$510$	−5.20559e25	−	4.17321e25i	−0.987538	−	0.791687i
$511$	−3.31533e22			−0.000617345
$512$	5.36048e25	−	1.09399e25i	0.979804	−	0.199962i
$513$	1.65688e25			0.297287
$514$	−4.60136e25	−	3.68881e25i	−0.810470	−	0.649735i
$515$		−	2.90026e25i		−	0.501496i
$516$	−4.12099e24	−	1.84919e25i	−0.0699567	−	0.313913i
$517$			1.67967e25i			0.279940i
$518$	−3.76051e24	+	4.69080e24i	−0.0615339	+	0.0767564i
$519$	3.30934e25			0.531681
$520$	1.11195e25	−	2.26427e25i	0.175410	−	0.357187i
$521$	3.88963e25			0.602490			0.301245	−	0.953547i	$-0.402598\pi$
$521$	3.88963e25			0.602490			0.301245	+	0.953547i	$0.402598\pi$
$522$	−2.36044e24	+	2.94438e24i	−0.0359024	+	0.0447841i
$523$			3.93542e25i			0.587794i	0.955837	+	0.293897i	$0.0949522\pi$
$523$			3.93542e25i			0.587794i	−0.955837	+	0.293897i	$0.905048\pi$
$524$	−2.44047e25	+	5.43867e24i	−0.357953	+	0.0797711i
$525$			3.07328e26i			4.42679i
$526$	−4.62692e25	−	3.70930e25i	−0.654526	−	0.524719i
$527$	−4.05380e25			−0.563198
$528$	−2.19220e25	+	1.02814e25i	−0.299128	+	0.140291i
$529$	−5.43567e25			−0.728491
$530$	1.17879e26	+	9.45009e25i	1.55173	+	1.24398i
$531$		−	1.16426e26i		−	1.50540i
$532$	1.38415e26	−	3.08462e25i	1.75801	−	0.391779i
$533$			3.02445e25i			0.377344i
$534$	9.22723e25	−	1.15099e26i	1.13091	−	1.41068i
$535$	−1.46762e26			−1.76706
$536$	1.22975e25	+	6.03914e24i	0.145462	+	0.0714348i
$537$	1.03738e26			1.20554
$538$	−2.94192e25	+	3.66971e25i	−0.335892	+	0.418986i
$539$		−	3.72952e25i		−	0.418369i
$540$	−9.18166e24	−	4.12004e25i	−0.101200	−	0.454110i
$541$		−	1.37193e26i		−	1.48579i	−0.669407	−	0.742896i	$-0.733452\pi$
$541$		−	1.37193e26i		−	1.48579i	0.669407	−	0.742896i	$-0.266548\pi$
$542$	−2.07384e25	−	1.66255e25i	−0.220690	−	0.176922i
$543$	1.89878e26			1.98553
$544$	4.86634e25	+	1.17656e25i	0.500050	+	0.120899i
$545$	−1.50098e26			−1.51568
$546$	−4.71908e25	−	3.78318e25i	−0.468303	−	0.375428i
$547$			3.94876e25i			0.385106i	0.981287	+	0.192553i	$0.0616768\pi$
$547$			3.94876e25i			0.385106i	−0.981287	+	0.192553i	$0.938323\pi$
$548$	1.11073e25	+	4.98413e25i	0.106462	+	0.477720i
$549$			5.32956e25i			0.502058i
$550$	−2.66263e25	+	3.32133e25i	−0.246528	+	0.307515i
$551$	5.63584e24			0.0512883
$552$	7.73626e25	+	3.79918e25i	0.692006	+	0.339836i
$553$	−1.82591e26			−1.60543
$554$	−1.33860e25	+	1.66975e25i	−0.115693	+	0.144314i
$555$		−	1.68054e25i		−	0.142779i
$556$	−1.25816e26	+	2.80386e25i	−1.05082	+	0.234178i
$557$			1.68878e26i			1.38660i	0.720651	+	0.693298i	$0.243843\pi$
$557$			1.68878e26i			1.38660i	−0.720651	+	0.693298i	$0.756157\pi$
$558$	−1.25829e26	−	1.00874e26i	−1.01568	−	0.814244i
$559$	6.55505e24			0.0520192
$560$	−1.53406e26	−	3.27092e26i	−1.19689	−	2.55202i
$561$	−2.21578e25			−0.169973
$562$	−6.07884e25	−	4.87327e25i	−0.458485	−	0.367557i
$563$		−	5.86777e24i		−	0.0435154i	−0.999763	−	0.0217577i	$-0.993074\pi$
$563$		−	5.86777e24i		−	0.0435154i	0.999763	−	0.0217577i	$-0.00692624\pi$
$564$	2.48272e26	−	5.53283e25i	1.81041	−	0.403455i
$565$		−	4.07791e26i		−	2.92400i
$566$	−5.89417e25	+	7.35229e25i	−0.415591	+	0.518402i
$567$	1.89506e26			1.31397
$568$	1.40475e25	−	2.86048e25i	0.0957831	−	0.195043i
$569$	−6.53987e25			−0.438533			−0.219267	−	0.975665i	$-0.570366\pi$
$569$	−6.53987e25			−0.438533			−0.219267	+	0.975665i	$0.570366\pi$
$570$	−2.47944e26	+	3.09281e26i	−1.63509	+	2.03959i
$571$			4.29504e25i			0.278564i	0.990253	+	0.139282i	$0.0444794\pi$
$571$			4.29504e25i			0.278564i	−0.990253	+	0.139282i	$0.955521\pi$
$572$	−1.82228e24	−	8.17705e24i	−0.0116240	−	0.0521596i
$573$		−	1.96797e26i		−	1.23466i
$574$	3.37963e26	+	2.70937e26i	2.08548	+	1.67188i
$575$	1.51525e26			0.919684
$576$	1.21773e26	+	1.57613e26i	0.727003	+	0.940978i
$577$	4.46022e25			0.261930			0.130965	−	0.991387i	$-0.458192\pi$
$577$	4.46022e25			0.261930			0.130965	+	0.991387i	$0.458192\pi$
$578$	−9.93165e25	−	7.96198e25i	−0.573729	−	0.459946i
$579$		−	2.42444e26i		−	1.37773i
$580$	−3.12312e24	−	1.40142e25i	−0.0174592	−	0.0783436i
$581$			2.41453e26i			1.32788i
$582$	−1.50244e26	+	1.87412e26i	−0.812884	+	1.01398i
$583$	5.01756e25			0.267080
$584$	−3.06539e22	+	6.24204e22i	−0.000160533	+	0.000326892i
$585$	9.18358e25			0.473185
$586$	2.35910e26	−	2.94270e26i	1.19596	−	1.49183i
$587$			1.53270e26i			0.764531i	0.924053	+	0.382265i	$0.124856\pi$
$587$			1.53270e26i			0.764531i	−0.924053	+	0.382265i	$0.875144\pi$
$588$	−5.51258e26	+	1.22850e26i	−2.70564	+	0.602962i
$589$			2.40849e26i			1.16319i
$590$	3.45617e26	+	2.77073e26i	1.64248	+	1.31674i
$591$	−8.61902e25			−0.403067
$592$	5.35475e24	+	1.14174e25i	0.0246424	+	0.0525425i
$593$	−1.50038e25			−0.0679488			−0.0339744	−	0.999423i	$-0.510816\pi$
$593$	−1.50038e25			−0.0679488			−0.0339744	+	0.999423i	$0.510816\pi$
$594$	−1.09378e25	−	8.76856e24i	−0.0487481	−	0.0390802i
$595$		−	3.30611e26i		−	1.45013i
$596$	−1.28512e26	+	2.86393e25i	−0.554757	+	0.123630i
$597$			3.20906e26i			1.36340i
$598$	−1.86525e25	+	2.32669e25i	−0.0779968	+	0.0972920i
$599$	−7.58156e25			−0.312035			−0.156018	−	0.987754i	$-0.549866\pi$
$599$	−7.58156e25			−0.312035			−0.156018	+	0.987754i	$0.549866\pi$
$600$	5.78631e26	+	2.84159e26i	2.34404	+	1.15113i
$601$	1.46902e26			0.585761			0.292881	−	0.956149i	$-0.405386\pi$
$601$	1.46902e26			0.585761			0.292881	+	0.956149i	$0.405386\pi$
$602$	5.87217e25	−	7.32485e25i	0.230479	−	0.287496i
$603$			4.98770e25i			0.192702i
$604$	1.63591e25	+	7.34074e25i	0.0622169	+	0.279183i
$605$		−	4.21997e26i		−	1.57991i
$606$	−2.96107e26	−	2.37382e26i	−1.09134	−	0.874899i
$607$	1.72251e25			0.0624983			0.0312492	−	0.999512i	$-0.490051\pi$
$607$	1.72251e25			0.0624983			0.0312492	+	0.999512i	$0.490051\pi$
$608$	6.99030e25	−	2.89125e26i	0.249696	−	1.03277i
$609$	−3.44260e25			−0.121066
$610$	−1.58211e26	−	1.26834e26i	−0.547778	−	0.439141i
$611$			8.80079e25i			0.300006i
$612$	3.96463e25	+	1.77903e26i	0.133065	+	0.597097i
$613$		−	1.79490e26i		−	0.593151i	−0.955009	−	0.296576i	$-0.904155\pi$
$613$		−	1.79490e26i		−	0.593151i	0.955009	−	0.296576i	$-0.0958447\pi$
$614$	1.23303e26	−	1.53806e26i	0.401211	−	0.500465i
$615$	−1.21079e27			−3.87933
$616$	−1.07698e26	−	5.28891e25i	−0.339774	−	0.166859i
$617$	1.09839e26			0.341231			0.170616	−	0.985338i	$-0.445424\pi$
$617$	1.09839e26			0.341231			0.170616	+	0.985338i	$0.445424\pi$
$618$	−9.12359e25	+	1.13806e26i	−0.279110	+	0.348157i
$619$			8.65454e25i			0.260725i	0.991466	+	0.130363i	$0.0416141\pi$
$619$			8.65454e25i			0.260725i	−0.991466	+	0.130363i	$0.958386\pi$
$620$	5.98903e26	−	1.33468e26i	1.77679	−	0.395963i
$621$			4.98999e25i			0.145791i
$622$	−9.67614e25	−	7.75714e25i	−0.278416	−	0.223199i
$623$	7.31002e26			2.07149
$624$	−1.14862e26	+	5.38702e25i	−0.320570	+	0.150347i
$625$	1.27419e26			0.350247
$626$	−5.29934e26	−	4.24836e26i	−1.43471	−	1.15018i
$627$			1.31647e26i			0.351050i
$628$	−6.53818e26	+	1.45706e26i	−1.71728	+	0.382701i
$629$			1.15402e25i			0.0298561i
$630$	8.22687e26	−	1.02621e27i	2.09652	−	2.61517i
$631$	4.61119e25			0.115754			0.0578768	−	0.998324i	$-0.481567\pi$
$631$	4.61119e25			0.115754			0.0578768	+	0.998324i	$0.481567\pi$
$632$	−1.68826e26	+	3.43780e26i	−0.417472	+	0.850096i
$633$	−3.67350e25			−0.0894840
$634$	−9.30081e25	+	1.16017e26i	−0.223189	+	0.278403i
$635$			8.41208e26i			1.98863i
$636$	−1.65278e26	−	7.41644e26i	−0.384922	−	1.72724i
$637$		−	1.95411e26i		−	0.448358i
$638$	−3.72046e24	−	2.98261e24i	−0.00841008	−	0.00674217i
$639$	1.16018e26			0.258384
$640$	−7.57684e26	−	1.36030e25i	−1.66256	−	0.0298486i
$641$	4.73241e26			1.02313			0.511566	−	0.859244i	$-0.329066\pi$
$641$	4.73241e26			1.02313			0.511566	+	0.859244i	$0.329066\pi$
$642$	5.75893e26	+	4.61681e26i	1.22676	+	0.983465i
$643$			7.83172e26i			1.64381i	0.569621	+	0.821907i	$0.307090\pi$
$643$			7.83172e26i			1.64381i	−0.569621	+	0.821907i	$0.692910\pi$
$644$	9.28989e25	+	4.16861e26i	0.192130	+	0.862135i
$645$			2.62422e26i			0.534789i
$646$	1.70262e26	−	2.12383e26i	0.341908	−	0.426491i
$647$	−6.86165e26			−1.35781			−0.678903	−	0.734228i	$-0.737544\pi$
$647$	−6.86165e26			−1.35781			−0.678903	+	0.734228i	$0.737544\pi$
$648$	1.75220e26	−	3.56799e26i	0.341681	−	0.695763i
$649$	1.47113e26			0.282701
$650$	−1.39511e26	+	1.74024e26i	−0.264199	+	0.329558i
$651$		−	1.47120e27i		−	2.74570i
$652$	−8.69615e26	+	1.93797e26i	−1.59947	+	0.356447i
$653$		−	1.31157e26i		−	0.237747i	−0.992909	−	0.118873i	$-0.962072\pi$
$653$		−	1.31157e26i		−	0.237747i	0.992909	−	0.118873i	$-0.0379283\pi$
$654$	5.88985e26	+	4.72176e26i	1.05224	+	0.843559i
$655$	3.46331e26			0.609817
$656$	8.22600e26	−	3.85799e26i	1.42759	−	0.669537i
$657$	−2.53169e23			−0.000433052
$658$	9.83433e26	+	7.88396e26i	1.65805	+	1.32922i
$659$			7.21143e26i			1.19842i	0.800591	+	0.599211i	$0.204519\pi$
$659$			7.21143e26i			1.19842i	−0.800591	+	0.599211i	$0.795481\pi$
$660$	3.27356e26	−	7.29525e25i	0.536233	−	0.119501i
$661$			3.54765e26i			0.572832i	0.958105	+	0.286416i	$0.0924639\pi$
$661$			3.54765e26i			0.572832i	−0.958105	+	0.286416i	$0.907536\pi$
$662$	2.93209e25	−	3.65744e25i	0.0466687	−	0.0582138i
$663$	−1.16098e26			−0.182157
$664$	4.54603e26	+	2.23250e26i	0.703131	+	0.345299i
$665$	−1.96427e27			−2.99499
$666$	−2.87165e25	+	3.58205e25i	−0.0431645	+	0.0538427i
$667$			1.69734e25i			0.0251520i
$668$	−2.53491e26	−	1.13748e27i	−0.370328	−	1.66176i
$669$		−	1.67058e27i		−	2.40613i
$670$	−1.48063e26	−	1.18699e26i	−0.210250	−	0.168553i
$671$	−6.73433e25			−0.0942823
$672$	−4.26996e26	+	1.76609e27i	−0.589408	+	2.43784i
$673$	1.29112e27			1.75720			0.878601	−	0.477556i	$-0.158477\pi$
$673$	1.29112e27			1.75720			0.878601	+	0.477556i	$0.158477\pi$
$674$	−5.64072e26	−	4.52203e26i	−0.756947	−	0.606827i
$675$			3.73225e26i			0.493838i
$676$	1.57172e26	+	7.05271e26i	0.205060	+	0.920158i
$677$			1.24632e27i			1.60339i	0.597736	+	0.801693i	$0.296067\pi$
$677$			1.24632e27i			1.60339i	−0.597736	+	0.801693i	$0.703933\pi$
$678$	−1.28282e27	+	1.60017e27i	−1.62736	+	2.02995i
$679$	−1.19027e27			−1.48895
$680$	−6.22468e26	−	3.05687e26i	−0.767861	−	0.377087i
$681$	8.79723e26			1.07016
$682$	1.27463e26	−	1.58995e26i	0.152908	−	0.190735i
$683$		−	3.22408e26i		−	0.381425i	−0.981646	−	0.190713i	$-0.938920\pi$
$683$		−	3.22408e26i		−	0.381425i	0.981646	−	0.190713i	$-0.0610799\pi$
$684$	1.05698e27	−	2.35552e26i	1.23320	−	0.274823i
$685$		−	7.07306e26i		−	0.813855i
$686$	−1.01810e27	−	8.16190e26i	−1.15535	−	0.926216i
$687$	1.98477e27			2.22137
$688$	−8.36163e25	−	1.78287e26i	−0.0922998	−	0.196801i
$689$	2.62899e26			0.286225
$690$	−9.31456e26	−	7.46727e26i	−1.00022	−	0.801855i
$691$		−	1.16772e27i		−	1.23680i	−0.785865	−	0.618398i	$-0.787782\pi$
$691$		−	1.16772e27i		−	1.23680i	0.785865	−	0.618398i	$-0.212218\pi$
$692$	3.35738e26	−	7.48204e25i	0.350746	−	0.0781650i
$693$		−	4.36809e26i		−	0.450117i
$694$	−3.99189e26	+	4.97943e26i	−0.405755	+	0.506133i
$695$	1.78548e27			1.79019
$696$	−3.18307e25	+	6.48166e25i	−0.0314817	+	0.0641060i
$697$	8.31449e26			0.811193
$698$	1.16928e27	−	1.45854e27i	1.12536	−	1.40376i
$699$		−	1.61265e27i		−	1.53111i
$700$	6.94834e26	+	3.11790e27i	0.650803	+	2.92032i
$701$			7.11810e26i			0.657723i	0.944378	+	0.328861i	$0.106665\pi$
$701$			7.11810e26i			0.657723i	−0.944378	+	0.328861i	$0.893335\pi$
$702$	−5.73094e25	−	4.59436e25i	−0.0522424	−	0.0418815i
$703$	6.85642e25			0.0616626
$704$	−1.99157e26	+	1.53870e26i	−0.176708	+	0.136525i
$705$	−3.52327e27			−3.08425
$706$	4.41604e26	+	3.54024e26i	0.381407	+	0.305765i
$707$		−	1.88059e27i		−	1.60255i
$708$	−4.84589e26	−	2.17447e27i	−0.407435	−	1.82826i
$709$			8.30818e26i			0.689234i	0.938743	+	0.344617i	$0.111991\pi$
$709$			8.30818e26i			0.689234i	−0.938743	+	0.344617i	$0.888009\pi$
$710$	−2.76102e26	+	3.44406e26i	−0.226004	+	0.281913i
$711$	−1.39433e27			−1.12617
$712$	6.75892e26	−	1.37632e27i	0.538664	−	1.09688i
$713$	−7.25361e26			−0.570432
$714$	−1.04003e27	+	1.29732e27i	−0.807074	+	1.00673i
$715$			1.16042e26i			0.0888603i
$716$	1.05244e27	−	2.34540e26i	0.795286	−	0.177232i
$717$			2.44355e27i			1.82217i
$718$	5.32256e26	+	4.26698e26i	0.391687	+	0.314006i
$719$	−1.94887e27			−1.41533			−0.707667	−	0.706547i	$-0.750252\pi$
$719$	−1.94887e27			−1.41533			−0.707667	+	0.706547i	$0.750252\pi$
$720$	−1.17146e27	−	2.49778e27i	−0.839592	−	1.79018i
$721$	−7.22792e26			−0.511244
$722$	−1.44132e26	−	1.15547e26i	−0.100614	−	0.0806597i
$723$			1.90143e27i			1.30999i
$724$	1.92635e27	−	4.29293e26i	1.30984	−	0.291903i
$725$			1.26952e26i			0.0851976i
$726$	−1.32751e27	+	1.65592e27i	−0.879308	+	1.09684i
$727$	−2.48654e27			−1.62562			−0.812810	−	0.582529i	$-0.802063\pi$
$727$	−2.48654e27			−1.62562			−0.812810	+	0.582529i	$0.802063\pi$
$728$	−5.64292e26	−	2.77117e26i	−0.364129	−	0.178820i
$729$	2.09709e27			1.33569
$730$	6.02500e23	−	7.51549e23i	0.000378783	−	0.000472487i
$731$		−	1.80205e26i		−	0.111828i
$732$	2.21828e26	+	9.95398e26i	0.135882	+	0.609736i
$733$		−	2.51702e27i		−	1.52195i	−0.648784	−	0.760973i	$-0.724722\pi$
$733$		−	2.51702e27i		−	1.52195i	0.648784	−	0.760973i	$-0.275278\pi$
$734$	4.72363e26	+	3.78683e26i	0.281945	+	0.226029i
$735$	7.82301e27			4.60940
$736$	8.70753e26	+	2.10526e26i	0.506472	+	0.122452i
$737$	−6.30237e25			−0.0361878
$738$	2.58079e27	+	2.06896e27i	1.46291	+	1.17278i
$739$			3.35181e27i			1.87567i	0.347080	+	0.937836i	$0.387173\pi$
$739$			3.35181e27i			1.87567i	−0.347080	+	0.937836i	$0.612827\pi$
$740$	−3.79951e25	−	1.70494e26i	−0.0209907	−	0.0941904i
$741$			6.89774e26i			0.376213i
$742$	2.35512e27	−	2.93774e27i	1.26816	−	1.58189i
$743$	4.93149e26			0.262171			0.131085	−	0.991371i	$-0.458154\pi$
$743$	4.93149e26			0.262171			0.131085	+	0.991371i	$0.458154\pi$
$744$	−2.76996e27	−	1.36029e27i	−1.45389	−	0.713985i
$745$	1.82373e27			0.945097
$746$	−2.38347e26	+	2.97311e26i	−0.121953	+	0.152122i
$747$			1.84381e27i			0.931476i
$748$	−2.24795e26	+	5.00963e25i	−0.112130	+	0.0249885i
$749$			3.65754e27i			1.80141i
$750$	−3.01962e27	−	2.42076e27i	−1.46849	−	1.17725i
$751$	−6.69608e26			−0.321545			−0.160772	−	0.986992i	$-0.551399\pi$
$751$	−6.69608e26			−0.321545			−0.160772	+	0.986992i	$0.551399\pi$
$752$	2.39367e27	−	1.12263e27i	1.13500	−	0.532313i
$753$	−4.92641e27			−2.30663
$754$	−1.94937e25	−	1.56276e25i	−0.00901292	−	0.00722546i
$755$		−	1.04174e27i		−	0.475622i
$756$	−1.02678e27	+	2.28822e26i	−0.462936	+	0.103167i
$757$		−	1.41390e27i		−	0.629517i	−0.949172	−	0.314758i	$-0.898077\pi$
$757$		−	1.41390e27i		−	0.629517i	0.949172	−	0.314758i	$-0.101923\pi$
$758$	−1.90545e27	+	2.37683e27i	−0.837798	+	1.04506i
$759$	−3.96478e26			−0.172156
$760$	−1.81618e27	+	3.69828e27i	−0.778808	+	1.58588i
$761$	−2.32017e27			−0.982573			−0.491286	−	0.870998i	$-0.663473\pi$
$761$	−2.32017e27			−0.982573			−0.491286	+	0.870998i	$0.663473\pi$
$762$	2.64626e27	−	3.30090e27i	1.10678	−	1.38058i
$763$			3.74069e27i			1.54514i
$764$	−4.44935e26	−	1.99654e27i	−0.181514	−	0.814499i
$765$		−	2.52465e27i		−	1.01723i
$766$	−2.33401e27	−	1.87112e27i	−0.928816	−	0.744611i
$767$	7.70812e26			0.302965
$768$	2.93036e27	+	2.43689e27i	1.13760	+	0.946029i
$769$	3.39203e27			1.30065			0.650324	−	0.759657i	$-0.274633\pi$
$769$	3.39203e27			1.30065			0.650324	+	0.759657i	$0.274633\pi$
$770$	1.29670e27	+	1.03953e27i	0.491107	+	0.393710i
$771$		−	4.10832e27i		−	1.53691i
$772$	−5.48139e26	−	2.45964e27i	−0.202547	−	0.908881i
$773$		−	1.90857e27i		−	0.696632i	−0.937377	−	0.348316i	$-0.886754\pi$
$773$		−	1.90857e27i		−	0.696632i	0.937377	−	0.348316i	$-0.113246\pi$
$774$	4.48418e26	−	5.59350e26i	0.161675	−	0.201671i
$775$	−5.42531e27			−1.93223
$776$	−1.10053e27	+	2.24101e27i	−0.387184	+	0.788420i
$777$	−4.18818e26			−0.145554
$778$	−4.81901e26	+	6.01115e26i	−0.165444	+	0.206372i
$779$		−	4.93991e27i		−	1.67538i
$780$	1.71521e27	−	3.82241e26i	0.574671	−	0.128067i
$781$			1.46598e26i			0.0485224i
$782$	6.39629e26	+	5.12776e26i	0.209153	+	0.167673i
$783$	−4.18076e25			−0.0135057
$784$	−5.31486e27	+	2.49267e27i	−1.69625	+	0.795539i
$785$	9.27844e27			2.92559
$786$	−1.35901e27	−	1.08948e27i	−0.423357	−	0.339396i
$787$		−	6.33421e27i		−	1.94954i	−0.223210	−	0.974770i	$-0.571653\pi$
$787$		−	6.33421e27i		−	1.94954i	0.223210	−	0.974770i	$-0.428347\pi$
$788$	−8.74415e26	+	1.94866e26i	−0.265900	+	0.0592568i
$789$		−	4.13114e27i		−	1.24119i
$790$	3.31827e27	−	4.13915e27i	0.985040	−	1.22872i
$791$	−1.01628e28			−2.98083
$792$	−8.22416e26	−	4.03878e26i	−0.238343	−	0.117047i
$793$	−3.52851e26			−0.101041
$794$	−1.26070e27	+	1.57258e27i	−0.356713	+	0.444958i
$795$			1.05248e28i			2.94257i
$796$	7.25534e26	+	3.25565e27i	0.200440	+	0.899423i
$797$			7.06808e27i			1.92951i	0.263149	+	0.964755i	$0.415239\pi$
$797$			7.06808e27i			1.92951i	−0.263149	+	0.964755i	$0.584761\pi$
$798$	7.70779e27	+	6.17916e27i	2.07923	+	1.66687i
$799$	2.41942e27			0.644937
$800$	6.51277e27	+	1.57462e27i	1.71558	+	0.414783i
$801$	5.58217e27			1.45310
$802$	−4.99099e27	−	4.00116e27i	−1.28390	−	1.02927i
$803$		−	3.19900e23i		−	8.13236e-5i
$804$	2.07599e26	+	9.31551e26i	0.0521547	+	0.234031i
$805$		−	5.91574e27i		−	1.46875i
$806$	6.67851e26	−	8.33067e26i	0.163869	−	0.204408i
$807$	−3.27649e27			−0.794531
$808$	−3.54075e27	−	1.73882e27i	−0.848569	−	0.416722i
$809$	−3.17582e27			−0.752220			−0.376110	−	0.926575i	$-0.622739\pi$
$809$	−3.17582e27			−0.752220			−0.376110	+	0.926575i	$0.622739\pi$
$810$	−3.44393e27	+	4.29591e27i	−0.806208	+	1.00565i
$811$		−	3.77221e27i		−	0.872766i	−0.899761	−	0.436383i	$-0.856259\pi$
$811$		−	3.77221e27i		−	0.872766i	0.899761	−	0.436383i	$-0.143741\pi$
$812$	−3.49258e26	+	7.78333e25i	−0.0798663	+	0.0177985i
$813$		−	1.85163e27i		−	0.418498i
$814$	−4.52621e25	−	3.62856e25i	−0.0101112	−	0.00810593i
$815$	1.23409e28			2.72489
$816$	1.48094e27	+	3.15767e27i	0.323208	+	0.689144i
$817$	−1.07065e27			−0.230961
$818$	6.81022e27	+	5.45960e27i	1.45213	+	1.16414i
$819$		−	2.28870e27i		−	0.482382i
$820$	−1.22837e28	+	2.73747e27i	−2.55916	+	0.570319i
$821$		−	4.76749e26i		−	0.0981816i	−0.998794	−	0.0490908i	$-0.984368\pi$
$821$		−	4.76749e26i		−	0.0981816i	0.998794	−	0.0490908i	$-0.0156324\pi$
$822$	−2.22503e27	+	2.77547e27i	−0.452954	+	0.565008i
$823$	3.15583e27			0.635061			0.317530	−	0.948248i	$-0.397146\pi$
$823$	3.15583e27			0.635061			0.317530	+	0.948248i	$0.397146\pi$
$824$	−6.68301e26	+	1.36086e27i	−0.132942	+	0.270710i
$825$	−2.96544e27			−0.583146
$826$	6.90512e27	−	8.61334e27i	1.34233	−	1.67441i
$827$			7.16920e27i			1.37774i	0.724883	+	0.688872i	$0.241894\pi$
$827$			7.16920e27i			1.37774i	−0.724883	+	0.688872i	$0.758106\pi$
$828$	7.09406e26	+	3.18328e27i	0.134774	+	0.604766i
$829$			3.15846e27i			0.593209i	0.955000	+	0.296605i	$0.0958543\pi$
$829$			3.15846e27i			0.593209i	−0.955000	+	0.296605i	$0.904146\pi$
$830$	−5.47348e27	−	4.38797e27i	−1.01630	−	0.814745i
$831$	−1.49083e27			−0.273665
$832$	−1.04350e27	+	8.06213e26i	−0.189374	+	0.146311i
$833$	−5.37204e27			−0.963855
$834$	−7.00625e27	−	5.61675e27i	−1.24282	−	0.996340i
$835$			1.61422e28i			2.83101i
$836$	2.97639e26	+	1.33558e27i	0.0516095	+	0.231585i
$837$		−	1.78666e27i		−	0.306302i
$838$	4.04078e27	−	5.04040e27i	0.684931	−	0.854372i
$839$	8.17013e27			1.36927			0.684637	−	0.728884i	$-0.259961\pi$
$839$	8.17013e27			1.36927			0.684637	+	0.728884i	$0.259961\pi$
$840$	1.10940e28	−	2.25906e28i	1.83837	−	3.74347i
$841$	6.08904e27			0.997670
$842$	−5.51256e27	+	6.87629e27i	−0.893077	+	1.11401i
$843$		−	5.42748e27i		−	0.869433i
$844$	−3.72683e26	+	8.30538e25i	−0.0590319	+	0.0131555i
$845$		−	1.00086e28i		−	1.56760i
$846$	7.50982e27	+	6.02045e27i	1.16308	+	0.932418i
$847$	−1.05169e28			−1.61062
$848$	−3.35355e27	−	7.15043e27i	−0.507860	−	1.08286i
$849$	−6.56448e27			−0.983054
$850$	4.78408e27	+	3.83529e27i	0.708466	+	0.567961i
$851$			2.06493e26i			0.0302395i
$852$	2.16685e27	−	4.82891e26i	0.313800	−	0.0699315i
$853$		−	2.32381e27i		−	0.332801i	−0.986058	−	0.166401i	$-0.946786\pi$
$853$		−	2.32381e27i		−	0.332801i	0.986058	−	0.166401i	$-0.0532145\pi$
$854$	−3.16092e27	+	3.94289e27i	−0.447676	+	0.558424i
$855$	−1.49998e28			−2.10091
$856$	6.88635e27	+	3.38180e27i	0.953868	+	0.468433i
$857$	4.29621e26			0.0588529			0.0294265	−	0.999567i	$-0.490632\pi$
$857$	4.29621e26			0.0588529			0.0294265	+	0.999567i	$0.490632\pi$
$858$	3.65043e26	−	4.55349e26i	0.0494556	−	0.0616901i
$859$		−	5.18888e27i		−	0.695246i	−0.937634	−	0.347623i	$-0.886989\pi$
$859$		−	5.18888e27i		−	0.695246i	0.937634	−	0.347623i	$-0.113011\pi$
$860$	5.93307e26	+	2.66232e27i	0.0786220	+	0.352797i
$861$			3.01750e28i			3.95473i
$862$	4.46595e27	+	3.58025e27i	0.578889	+	0.464082i
$863$	5.91345e27			0.758121			0.379061	−	0.925372i	$-0.376247\pi$
$863$	5.91345e27			0.758121			0.379061	+	0.925372i	$0.376247\pi$
$864$	−5.18552e26	+	2.14478e27i	−0.0657524	+	0.271958i
$865$	−4.76452e27			−0.597539
$866$	−9.79505e27	−	7.85247e27i	−1.21503	−	0.974061i
$867$		−	8.86746e27i		−	1.08797i
$868$	−3.32623e27	−	1.49256e28i	−0.403659	−	1.81132i
$869$		−	1.76185e27i		−	0.211485i
$870$	6.25629e26	−	7.80401e26i	0.0742821	−	0.0926584i
$871$	−3.30218e26			−0.0387818
$872$	7.04289e27	+	3.45868e27i	0.818172	+	0.401794i
$873$	−9.08926e27			−1.04446
$874$	3.04657e27	−	3.80024e27i	0.346300	−	0.431969i
$875$		−	1.91778e28i		−	2.15637i
$876$	−4.72843e24	+	1.05375e24i	−0.000525930	+	0.000117205i
$877$		−	2.34388e27i		−	0.257892i	−0.991652	−	0.128946i	$-0.958841\pi$
$877$		−	2.34388e27i		−	0.257892i	0.991652	−	0.128946i	$-0.0411595\pi$
$878$	−9.73946e26	−	7.80791e26i	−0.106008	−	0.0849839i
$879$	2.62739e28			2.82898
$880$	3.15615e27	−	1.48023e27i	0.336180	−	0.157668i
$881$	4.24718e27			0.447538			0.223769	−	0.974642i	$-0.428164\pi$
$881$	4.24718e27			0.447538			0.223769	+	0.974642i	$0.428164\pi$
$882$	−1.66747e28	−	1.33677e28i	−1.73822	−	1.39349i
$883$			7.50144e27i			0.773602i	0.922163	+	0.386801i	$0.126420\pi$
$883$			7.50144e27i			0.773602i	−0.922163	+	0.386801i	$0.873580\pi$
$884$	−1.17783e27	+	2.62484e26i	−0.120167	+	0.0267797i
$885$			3.08584e28i			3.11467i
$886$	6.44947e26	−	8.04497e26i	0.0644027	−	0.0803349i
$887$	1.83757e27			0.181538			0.0907692	−	0.995872i	$-0.471067\pi$
$887$	1.83757e27			0.181538			0.0907692	+	0.995872i	$0.471067\pi$
$888$	−3.87243e26	+	7.88542e26i	−0.0378496	+	0.0770729i
$889$	2.09643e28			2.02728
$890$	−1.32846e28	+	1.65710e28i	−1.27100	+	1.58542i
$891$			1.82857e27i			0.173091i
$892$	−3.77699e27	−	1.69483e28i	−0.353736	−	1.58730i
$893$		−	1.43746e28i		−	1.33201i
$894$	−7.15633e27	−	5.73707e27i	−0.656121	−	0.525998i
$895$	−1.49353e28			−1.35487
$896$	−3.39009e26	+	1.88827e28i	−0.0304288	+	1.69488i
$897$	−2.07738e27			−0.184496
$898$	6.43125e27	+	5.15579e27i	0.565158	+	0.453075i
$899$		−	6.07728e26i		−	0.0528436i
$900$	5.30598e27	+	2.38093e28i	0.456522	+	2.04853i
$901$		−	7.22736e27i		−	0.615310i
$902$	−2.61431e27	+	3.26104e27i	−0.220239	+	0.274723i
$903$	6.53998e27			0.545184
$904$	−9.39665e27	+	1.91344e28i	−0.775127	+	1.57839i
$905$	−2.73371e28			−2.23147
$906$	−3.27708e27	+	4.08778e27i	−0.264710	+	0.330195i
$907$			9.15113e27i			0.731485i	0.930716	+	0.365743i	$0.119185\pi$
$907$			9.15113e27i			0.731485i	−0.930716	+	0.365743i	$0.880815\pi$
$908$	8.92494e27	−	1.98896e27i	0.705976	−	0.157329i
$909$		−	1.43608e28i		−	1.12415i
$910$	6.79415e27	+	5.44672e27i	0.526310	+	0.421931i
$911$	1.99743e28			1.53125			0.765626	−	0.643286i	$-0.222429\pi$
$911$	1.99743e28			1.53125			0.765626	+	0.643286i	$0.222429\pi$
$912$	1.87607e28	−	8.79877e27i	1.42331	−	0.667530i
$913$	−2.32981e27			−0.174923
$914$	9.04621e27	+	7.25214e27i	0.672168	+	0.538862i
$915$		−	1.41259e28i		−	1.03876i
$916$	2.01359e28	−	4.48735e27i	1.46542	−	0.326575i
$917$		−	8.63114e27i		−	0.621669i
$918$	−1.26303e27	+	1.57549e27i	−0.0900346	+	0.112308i
$919$	−1.78542e28			−1.25963			−0.629817	−	0.776744i	$-0.716870\pi$
$919$	−1.78542e28			−1.25963			−0.629817	+	0.776744i	$0.716870\pi$
$920$	−1.11381e28	−	5.46976e27i	−0.777723	−	0.381930i
$921$	1.37325e28			0.949039
$922$	−2.36157e26	+	2.94579e26i	−0.0161532	+	0.0201492i
$923$			7.68110e26i			0.0520005i
$924$	−1.81810e27	−	8.15826e27i	−0.121824	−	0.546655i
$925$			1.54446e27i			0.102431i
$926$	5.38152e27	+	4.31424e27i	0.353265	+	0.283205i
$927$	−5.51947e27			−0.358625
$928$	−1.76384e26	+	7.29542e26i	−0.0113437	+	0.0469185i
$929$	−1.93770e28			−1.23349			−0.616747	−	0.787161i	$-0.711550\pi$
$929$	−1.93770e28			−1.23349			−0.616747	+	0.787161i	$0.711550\pi$
$930$	3.33506e28	+	2.67365e28i	2.10144	+	1.68467i
$931$			3.19170e28i			1.99068i
$932$	−3.64603e27	−	1.63606e28i	−0.225096	−	1.01006i
$933$		−	8.63932e27i		−	0.527964i
$934$	−5.19363e27	+	6.47846e27i	−0.314178	+	0.391901i
$935$	3.19010e27			0.191027
$936$	−4.30912e27	−	2.11616e27i	−0.255428	−	0.125437i
$937$	1.76914e28			1.03809			0.519047	−	0.854746i	$-0.326287\pi$
$937$	1.76914e28			1.03809			0.519047	+	0.854746i	$0.326287\pi$
$938$	−2.95817e27	+	3.68998e27i	−0.171829	+	0.214337i
$939$		−	4.73151e28i		−	2.72067i
$940$	−3.57442e28	+	7.96572e27i	−2.03466	+	0.453430i
$941$		−	1.10227e28i		−	0.621135i	−0.950551	−	0.310568i	$-0.899481\pi$
$941$		−	1.10227e28i		−	0.621135i	0.950551	−	0.310568i	$-0.100519\pi$
$942$	−3.64087e28	−	2.91880e28i	−2.03105	−	1.62825i
$943$	1.48774e28			0.821612
$944$	−9.83249e27	−	2.09648e28i	−0.537563	−	1.14619i
$945$	1.45712e28			0.788669
$946$	7.06784e26	+	5.66613e26i	0.0378722	+	0.0303613i
$947$		−	8.90099e27i		−	0.472186i	−0.971730	−	0.236093i	$-0.924133\pi$
$947$		−	8.90099e27i		−	0.472186i	0.971730	−	0.236093i	$-0.0758670\pi$
$948$	−2.60418e28	+	5.80350e27i	−1.36770	+	0.304797i
$949$		−	1.67614e24i		−	8.71529e-5i
$950$	2.27867e28	−	2.84238e28i	1.17302	−	1.46321i
$951$	−1.03585e28			−0.527939
$952$	−7.61821e27	+	1.55129e28i	−0.384416	+	0.782785i
$953$	−1.26463e28			−0.631803			−0.315901	−	0.948792i	$-0.602307\pi$
$953$	−1.26463e28			−0.631803			−0.315901	+	0.948792i	$0.602307\pi$
$954$	1.79844e28	−	2.24335e28i	0.889585	−	1.10965i
$955$			2.83332e28i			1.38760i
$956$	5.52460e27	+	2.47903e28i	0.267887	+	1.20207i
$957$		−	3.32181e26i		−	0.0159482i
$958$	9.01961e27	+	7.23082e27i	0.428761	+	0.343728i
$959$	−1.76272e28			−0.829673
$960$	−3.22756e28	−	4.17751e28i	−1.50417	−	1.94689i
$961$	4.30078e27			0.198461
$962$	−2.37155e26	−	1.90122e26i	−0.0108360	−	0.00868697i
$963$			2.79302e28i			1.26364i
$964$	4.29893e27	+	1.92904e28i	0.192588	+	0.864190i
$965$			3.49052e28i			1.54839i
$966$	−1.86097e28	+	2.32134e28i	−0.817440	+	1.01966i
$967$	−1.72995e28			−0.752457			−0.376229	−	0.926527i	$-0.622779\pi$
$967$	−1.72995e28			−0.752457			−0.376229	+	0.926527i	$0.622779\pi$
$968$	−9.72401e27	+	1.98010e28i	−0.418822	+	0.852845i
$969$	1.89626e28			0.808762
$970$	2.16309e28	−	2.69821e28i	0.913573	−	1.13958i
$971$		−	2.99309e26i		−	0.0125181i	−0.999980	−	0.00625903i	$-0.998008\pi$
$971$		−	2.99309e26i		−	0.0125181i	0.999980	−	0.00625903i	$-0.00199232\pi$
$972$	3.36219e28	−	7.49276e27i	1.39249	−	0.310322i
$973$		−	4.44972e28i		−	1.82499i
$974$	5.25264e27	+	4.21092e27i	0.213338	+	0.171028i
$975$	−1.55377e28			−0.624946
$976$	4.50097e27	+	9.59696e27i	0.179280	+	0.382261i
$977$	2.26299e28			0.892654			0.446327	−	0.894870i	$-0.352732\pi$
$977$	2.26299e28			0.892654			0.446327	+	0.894870i	$0.352732\pi$
$978$	−4.84256e28	−	3.88217e28i	−1.89172	−	1.51655i
$979$			7.05352e27i			0.272879i
$980$	7.93658e28	−	1.76869e28i	3.04078	−	0.677649i
$981$			2.85651e28i			1.08388i
$982$	2.30439e28	−	2.87446e28i	0.865957	−	1.08018i
$983$	−1.67929e28			−0.624980			−0.312490	−	0.949921i	$-0.601163\pi$
$983$	−1.67929e28			−0.624980			−0.312490	+	0.949921i	$0.601163\pi$
$984$	5.68129e28	+	2.79001e28i	2.09408	+	1.02838i
$985$	1.24090e28			0.452993
$986$	−4.29618e26	+	5.35899e26i	−0.0155329	+	0.0193755i
$987$			8.78057e28i			3.14420i
$988$	1.55950e27	+	6.99788e27i	0.0553089	+	0.248185i
$989$		−	3.22447e27i		−	0.113264i
$990$	9.90199e27	+	7.93820e27i	0.344499	+	0.276177i
$991$	2.17389e28			0.749096			0.374548	−	0.927207i	$-0.377798\pi$
$991$	2.17389e28			0.749096			0.374548	+	0.927207i	$0.377798\pi$
$992$	−3.11772e28	−	7.53784e27i	−1.06408	−	0.257268i
$993$	3.26554e27			0.110392
$994$	8.58315e27	+	6.88092e27i	0.287393	+	0.230396i
$995$		−	4.62015e28i		−	1.53228i
$996$	7.67437e27	+	3.44368e28i	0.252104	+	1.13125i
$997$			4.16044e28i			1.35374i	0.736102	+	0.676870i	$0.236664\pi$
$997$			4.16044e28i			1.35374i	−0.736102	+	0.676870i	$0.763336\pi$
$998$	−3.29524e28	+	4.11043e28i	−1.06205	+	1.32479i
$999$	−5.08620e26			−0.0162376

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8.20.b.a.5.16	yes	18
3.2	odd	2		72.20.d.b.37.3		18
4.3	odd	2		32.20.b.a.17.2		18
8.3	odd	2		32.20.b.a.17.17		18
8.5	even	2	inner	8.20.b.a.5.15	✓	18
24.5	odd	2		72.20.d.b.37.4		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8.20.b.a.5.15	✓	18	8.5	even	2	inner
8.20.b.a.5.16	yes	18	1.1	even	1	trivial
32.20.b.a.17.2		18	4.3	odd	2
32.20.b.a.17.17		18	8.3	odd	2
72.20.d.b.37.3		18	3.2	odd	2
72.20.d.b.37.4		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)

\(f(q)\)	\(=\)	\(q+(564.947 + 452.905i) q^{2} +50441.2i q^{3} +(114042. + 511735. i) q^{4} -7.26212e6i q^{5} +(-2.28451e7 + 2.84966e7i) q^{6} -1.80984e8 q^{7} +(-1.67340e8 + 3.40753e8i) q^{8} -1.38205e9 q^{9} +O(q^{10})\)	\(q+(564.947 + 452.905i) q^{2} +50441.2i q^{3} +(114042. + 511735. i) q^{4} -7.26212e6i q^{5} +(-2.28451e7 + 2.84966e7i) q^{6} -1.80984e8 q^{7} +(-1.67340e8 + 3.40753e8i) q^{8} -1.38205e9 q^{9} +(3.28905e9 - 4.10271e9i) q^{10} -1.74633e9i q^{11} +(-2.58125e10 + 5.75241e9i) q^{12} -9.15007e9i q^{13} +(-1.02246e11 - 8.19685e10i) q^{14} +3.66310e11 q^{15} +(-2.48867e11 + 1.16718e11i) q^{16} -2.51544e11 q^{17} +(-7.80786e11 - 6.25938e11i) q^{18} +1.49450e12i q^{19} +(3.71628e12 - 8.28186e11i) q^{20} -9.12904e12i q^{21} +(7.90924e11 - 9.86586e11i) q^{22} -4.50097e12 q^{23} +(-1.71880e13 - 8.44081e12i) q^{24} -3.36649e13 q^{25} +(4.14411e12 - 5.16930e12i) q^{26} -1.10865e13i q^{27} +(-2.06397e13 - 9.26157e13i) q^{28} -3.77104e12i q^{29} +(2.06946e14 + 1.65904e14i) q^{30} +1.61157e14 q^{31} +(-1.93459e14 - 4.67734e13i) q^{32} +8.80872e13 q^{33} +(-1.42109e14 - 1.13926e14i) q^{34} +1.31433e15i q^{35} +(-1.57612e14 - 7.07244e14i) q^{36} -4.58775e13i q^{37} +(-6.76869e14 + 8.44316e14i) q^{38} +4.61540e14 q^{39} +(2.47459e15 + 1.21524e15i) q^{40} -3.30538e15 q^{41} +(4.13459e15 - 5.15742e15i) q^{42} +7.16393e14i q^{43} +(8.93660e14 - 1.99155e14i) q^{44} +1.00366e16i q^{45} +(-2.54281e15 - 2.03851e15i) q^{46} -9.61828e15 q^{47} +(-5.88741e15 - 1.25531e16i) q^{48} +2.13563e16 q^{49} +(-1.90189e16 - 1.52470e16i) q^{50} -1.26882e16i q^{51} +(4.68241e15 - 1.04349e15i) q^{52} +2.87320e16i q^{53} +(5.02112e15 - 6.26327e15i) q^{54} -1.26821e16 q^{55} +(3.02858e16 - 6.16708e16i) q^{56} -7.53846e16 q^{57} +(1.70792e15 - 2.13044e15i) q^{58} +8.42412e16i q^{59} +(4.17747e16 + 1.87453e17i) q^{60} -3.85626e16i q^{61} +(9.10449e16 + 7.29886e16i) q^{62} +2.50129e17 q^{63} +(-8.81101e16 - 1.14043e17i) q^{64} -6.64489e16 q^{65} +(4.97646e16 + 3.98951e16i) q^{66} -3.60891e16i q^{67} +(-2.86866e16 - 1.28724e17i) q^{68} -2.27034e17i q^{69} +(-5.95265e17 + 7.42524e17i) q^{70} -8.39459e16 q^{71} +(2.31272e17 - 4.70938e17i) q^{72} +1.83184e14 q^{73} +(2.07782e16 - 2.59184e16i) q^{74} -1.69810e18i q^{75} +(-7.64790e17 + 1.70436e17i) q^{76} +3.16058e17i q^{77} +(2.60746e17 + 2.09034e17i) q^{78} +1.00888e18 q^{79} +(8.47623e17 + 1.80730e18i) q^{80} -1.04709e18 q^{81} +(-1.86736e18 - 1.49702e18i) q^{82} -1.33411e18i q^{83} +(4.67165e18 - 1.04109e18i) q^{84} +1.82674e18i q^{85} +(-3.24458e17 + 4.04724e17i) q^{86} +1.90216e17 q^{87} +(5.95069e17 + 2.92231e17i) q^{88} -4.03904e18 q^{89} +(-4.54564e18 + 5.67016e18i) q^{90} +1.65601e18i q^{91} +(-5.13299e17 - 2.30330e18i) q^{92} +8.12893e18i q^{93} +(-5.43382e18 - 4.35617e18i) q^{94} +1.08533e19 q^{95} +(2.35930e18 - 9.75829e18i) q^{96} +6.57665e18 q^{97} +(1.20651e19 + 9.67236e18i) q^{98} +2.41352e18i 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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