LMFDB - Embedded newform 8.20.b.a.5.3

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			5.3
Root			$0.500000 + 16156.1i$ of defining polynomial
Character	$\chi$	$=$	8.5
Dual form			8.20.b.a.5.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-600.469 - 404.629i) q^{2} -64624.3i q^{3} +(196838. + 485935. i) q^{4} -4.52012e6i q^{5} +(-2.61489e7 + 3.88049e7i) q^{6} -6.45051e7 q^{7} +(7.84279e7 - 3.71435e8i) q^{8} -3.01404e9 q^{9} +O(q^{10})$	\(q+(-600.469 - 404.629i) q^{2} -64624.3i q^{3} +(196838. + 485935. i) q^{4} -4.52012e6i q^{5} +(-2.61489e7 + 3.88049e7i) q^{6} -6.45051e7 q^{7} +(7.84279e7 - 3.71435e8i) q^{8} -3.01404e9 q^{9} +(-1.82897e9 + 2.71419e9i) q^{10} -9.68633e9i q^{11} +(3.14032e10 - 1.27205e10i) q^{12} -7.19211e9i q^{13} +(3.87333e10 + 2.61006e10i) q^{14} -2.92109e11 q^{15} +(-1.97387e11 + 1.91301e11i) q^{16} -9.85697e10 q^{17} +(1.80984e12 + 1.21957e12i) q^{18} +5.79637e11i q^{19} +(2.19648e12 - 8.89734e11i) q^{20} +4.16860e12i q^{21} +(-3.91937e12 + 5.81634e12i) q^{22} +1.28333e13 q^{23} +(-2.40037e13 - 5.06835e12i) q^{24} -1.35800e12 q^{25} +(-2.91014e12 + 4.31864e12i) q^{26} +1.19670e14i q^{27} +(-1.26971e13 - 3.13453e13i) q^{28} -1.42973e14i q^{29} +(1.75403e14 + 1.18196e14i) q^{30} +1.10433e14 q^{31} +(1.95931e14 - 3.50020e13i) q^{32} -6.25972e14 q^{33} +(5.91880e13 + 3.98842e13i) q^{34} +2.91571e14i q^{35} +(-5.93278e14 - 1.46462e15i) q^{36} -4.03841e14i q^{37} +(2.34538e14 - 3.48054e14i) q^{38} -4.64785e14 q^{39} +(-1.67893e15 - 3.54503e14i) q^{40} +2.24379e15 q^{41} +(1.68674e15 - 2.50311e15i) q^{42} +2.18251e15i q^{43} +(4.70692e15 - 1.90664e15i) q^{44} +1.36238e16i q^{45} +(-7.70599e15 - 5.19272e15i) q^{46} -6.50288e15 q^{47} +(1.23627e16 + 1.27560e16i) q^{48} -7.23799e15 q^{49} +(8.15434e14 + 5.49484e14i) q^{50} +6.36999e15i q^{51} +(3.49489e15 - 1.41568e15i) q^{52} +1.93982e16i q^{53} +(4.84218e16 - 7.18579e16i) q^{54} -4.37834e16 q^{55} +(-5.05900e15 + 2.39595e16i) q^{56} +3.74586e16 q^{57} +(-5.78511e16 + 8.58510e16i) q^{58} +1.98749e16i q^{59} +(-5.74984e16 - 1.41946e17i) q^{60} -5.65818e16i q^{61} +(-6.63115e16 - 4.46843e16i) q^{62} +1.94421e17 q^{63} +(-1.31813e17 - 5.82618e16i) q^{64} -3.25092e16 q^{65} +(3.75877e17 + 2.53287e17i) q^{66} +9.83592e16i q^{67} +(-1.94023e16 - 4.78984e16i) q^{68} -8.29342e17i q^{69} +(1.17978e17 - 1.75079e17i) q^{70} -6.44076e17 q^{71} +(-2.36384e17 + 1.11952e18i) q^{72} -1.55928e16 q^{73} +(-1.63406e17 + 2.42494e17i) q^{74} +8.77595e16i q^{75} +(-2.81666e17 + 1.14095e17i) q^{76} +6.24818e17i q^{77} +(2.79089e17 + 1.88065e17i) q^{78} +1.06258e18 q^{79} +(8.64705e17 + 8.92213e17i) q^{80} +4.23046e18 q^{81} +(-1.34733e18 - 9.07904e17i) q^{82} -1.05764e18i q^{83} +(-2.02567e18 + 8.20540e17i) q^{84} +4.45547e17i q^{85} +(8.83106e17 - 1.31053e18i) q^{86} -9.23953e18 q^{87} +(-3.59785e18 - 7.59678e17i) q^{88} -1.47708e16 q^{89} +(5.51259e18 - 8.18067e18i) q^{90} +4.63927e17i q^{91} +(2.52609e18 + 6.23614e18i) q^{92} -7.13664e18i q^{93} +(3.90478e18 + 2.63125e18i) q^{94} +2.62003e18 q^{95} +(-2.26198e18 - 1.26619e19i) q^{96} -3.24606e18 q^{97} +(4.34619e18 + 2.92870e18i) q^{98} +2.91949e19i 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 $

$2$	−600.469	−	404.629i	−0.829289	−	0.558820i
$2$	−600.469	−	404.629i	−0.829289	−	0.558820i
$3$		−	64624.3i		−	1.89559i	−0.318884	−	0.947794i	$-0.603308\pi$
$3$		−	64624.3i		−	1.89559i	0.318884	−	0.947794i	$-0.396692\pi$
$4$	196838.	+	485935.i	0.375440	+	0.926847i
$5$		−	4.52012e6i		−	1.03499i	−0.855687	−	0.517493i	$-0.826865\pi$
$5$		−	4.52012e6i		−	1.03499i	0.855687	−	0.517493i	$-0.173135\pi$
$6$	−2.61489e7	+	3.88049e7i	−1.05929	+	1.57199i
$7$	−6.45051e7			−0.604175			−0.302087	−	0.953280i	$-0.597683\pi$
$7$	−6.45051e7			−0.604175			−0.302087	+	0.953280i	$0.597683\pi$
$8$	7.84279e7	−	3.71435e8i	0.206593	−	0.978427i
$9$	−3.01404e9			−2.59325
$10$	−1.82897e9	+	2.71419e9i	−0.578372	+	0.858303i
$11$		−	9.68633e9i		−	1.23859i	−0.785157	−	0.619297i	$-0.787418\pi$
$11$		−	9.68633e9i		−	1.23859i	0.785157	−	0.619297i	$-0.212582\pi$
$12$	3.14032e10	−	1.27205e10i	1.75692	−	0.711679i
$13$		−	7.19211e9i		−	0.188102i	−0.995567	−	0.0940512i	$-0.970018\pi$
$13$		−	7.19211e9i		−	0.188102i	0.995567	−	0.0940512i	$-0.0299817\pi$
$14$	3.87333e10	+	2.61006e10i	0.501035	+	0.337625i
$15$	−2.92109e11			−1.96191
$16$	−1.97387e11	+	1.91301e11i	−0.718090	+	0.695950i
$17$	−9.85697e10			−0.201594			−0.100797	−	0.994907i	$-0.532139\pi$
$17$	−9.85697e10			−0.201594			−0.100797	+	0.994907i	$0.532139\pi$
$18$	1.80984e12	+	1.21957e12i	2.15055	+	1.44916i
$19$			5.79637e11i			0.412095i	0.978542	+	0.206047i	$0.0660601\pi$
$19$			5.79637e11i			0.412095i	−0.978542	+	0.206047i	$0.933940\pi$
$20$	2.19648e12	−	8.89734e11i	0.959274	−	0.388575i
$21$			4.16860e12i			1.14527i
$22$	−3.91937e12	+	5.81634e12i	−0.692151	+	1.02715i
$23$	1.28333e13			1.48567			0.742837	−	0.669472i	$-0.233480\pi$
$23$	1.28333e13			1.48567			0.742837	+	0.669472i	$0.233480\pi$
$24$	−2.40037e13	−	5.06835e12i	−1.85469	−	0.391615i
$25$	−1.35800e12			−0.0711981
$26$	−2.91014e12	+	4.31864e12i	−0.105115	+	0.155991i
$27$			1.19670e14i			3.02015i
$28$	−1.26971e13	−	3.13453e13i	−0.226831	−	0.559978i
$29$		−	1.42973e14i		−	1.83009i	−0.403347	−	0.915047i	$-0.632153\pi$
$29$		−	1.42973e14i		−	1.83009i	0.403347	−	0.915047i	$-0.367847\pi$
$30$	1.75403e14	+	1.18196e14i	1.62699	+	1.09635i
$31$	1.10433e14			0.750174			0.375087	−	0.926990i	$-0.377613\pi$
$31$	1.10433e14			0.750174			0.375087	+	0.926990i	$0.377613\pi$
$32$	1.95931e14	−	3.50020e13i	0.984415	−	0.175860i
$33$	−6.25972e14			−2.34786
$34$	5.91880e13	+	3.98842e13i	0.167180	+	0.112655i
$35$			2.91571e14i			0.625313i
$36$	−5.93278e14	−	1.46462e15i	−0.973609	−	2.40355i
$37$		−	4.03841e14i		−	0.510850i	−0.966829	−	0.255425i	$-0.917785\pi$
$37$		−	4.03841e14i		−	0.510850i	0.966829	−	0.255425i	$-0.0822154\pi$
$38$	2.34538e14	−	3.48054e14i	0.230287	−	0.341745i
$39$	−4.64785e14			−0.356564
$40$	−1.67893e15	−	3.54503e14i	−1.01266	−	0.213821i
$41$	2.24379e15			1.07038			0.535188	−	0.844733i	$-0.320241\pi$
$41$	2.24379e15			1.07038			0.535188	+	0.844733i	$0.320241\pi$
$42$	1.68674e15	−	2.50311e15i	0.639998	−	0.949756i
$43$			2.18251e15i			0.662225i	0.943591	+	0.331112i	$0.107424\pi$
$43$			2.18251e15i			0.662225i	−0.943591	+	0.331112i	$0.892576\pi$
$44$	4.70692e15	−	1.90664e15i	1.14799	−	0.465017i
$45$			1.36238e16i			2.68398i
$46$	−7.70599e15	−	5.19272e15i	−1.23205	−	0.830225i
$47$	−6.50288e15			−0.847571			−0.423785	−	0.905763i	$-0.639299\pi$
$47$	−6.50288e15			−0.847571			−0.423785	+	0.905763i	$0.639299\pi$
$48$	1.23627e16	+	1.27560e16i	1.31923	+	1.36120i
$49$	−7.23799e15			−0.634973
$50$	8.15434e14	+	5.49484e14i	0.0590438	+	0.0397869i
$51$			6.36999e15i			0.382140i
$52$	3.49489e15	−	1.41568e15i	0.174342	−	0.0706211i
$53$			1.93982e16i			0.807498i	0.914870	+	0.403749i	$0.132293\pi$
$53$			1.93982e16i			0.807498i	−0.914870	+	0.403749i	$0.867707\pi$
$54$	4.84218e16	−	7.18579e16i	1.68772	−	2.50457i
$55$	−4.37834e16			−1.28193
$56$	−5.05900e15	+	2.39595e16i	−0.124818	+	0.591141i
$57$	3.74586e16			0.781161
$58$	−5.78511e16	+	8.58510e16i	−1.02269	+	1.51768i
$59$			1.98749e16i			0.298684i	0.988786	+	0.149342i	$0.0477155\pi$
$59$			1.98749e16i			0.298684i	−0.988786	+	0.149342i	$0.952284\pi$
$60$	−5.74984e16	−	1.41946e17i	−0.736578	−	1.81839i
$61$		−	5.65818e16i		−	0.619502i	−0.950818	−	0.309751i	$-0.899754\pi$
$61$		−	5.65818e16i		−	0.619502i	0.950818	−	0.309751i	$-0.100246\pi$
$62$	−6.63115e16	−	4.46843e16i	−0.622110	−	0.419212i
$63$	1.94421e17			1.56678
$64$	−1.31813e17	−	5.82618e16i	−0.914639	−	0.404272i
$65$	−3.25092e16			−0.194683
$66$	3.75877e17	+	2.53287e17i	1.94706	+	1.31203i
$67$			9.83592e16i			0.441676i	0.975310	+	0.220838i	$0.0708793\pi$
$67$			9.83592e16i			0.441676i	−0.975310	+	0.220838i	$0.929121\pi$
$68$	−1.94023e16	−	4.78984e16i	−0.0756865	−	0.186847i
$69$		−	8.29342e17i		−	2.81622i
$70$	1.17978e17	−	1.75079e17i	0.349438	−	0.518565i
$71$	−6.44076e17			−1.66718			−0.833591	−	0.552383i	$-0.813719\pi$
$71$	−6.44076e17			−1.66718			−0.833591	+	0.552383i	$0.813719\pi$
$72$	−2.36384e17	+	1.11952e18i	−0.535748	+	2.53731i
$73$	−1.55928e16			−0.0309997			−0.0154998	−	0.999880i	$-0.504934\pi$
$73$	−1.55928e16			−0.0309997			−0.0154998	+	0.999880i	$0.504934\pi$
$74$	−1.63406e17	+	2.42494e17i	−0.285474	+	0.423642i
$75$			8.77595e16i			0.134962i
$76$	−2.81666e17	+	1.14095e17i	−0.381949	+	0.154717i
$77$			6.24818e17i			0.748327i
$78$	2.79089e17	+	1.88065e17i	0.295695	+	0.199255i
$79$	1.06258e18			0.997481			0.498740	−	0.866751i	$-0.333796\pi$
$79$	1.06258e18			0.997481			0.498740	+	0.866751i	$0.333796\pi$
$80$	8.64705e17	+	8.92213e17i	0.720299	+	0.743214i
$81$	4.23046e18			3.13170
$82$	−1.34733e18	−	9.07904e17i	−0.887650	−	0.598147i
$83$		−	1.05764e18i		−	0.621008i	−0.950572	−	0.310504i	$-0.899502\pi$
$83$		−	1.05764e18i		−	0.621008i	0.950572	−	0.310504i	$-0.100498\pi$
$84$	−2.02567e18	+	8.20540e17i	−1.06149	+	0.429978i
$85$			4.45547e17i			0.208648i
$86$	8.83106e17	−	1.31053e18i	0.370065	−	0.549176i
$87$	−9.23953e18			−3.46910
$88$	−3.59785e18	−	7.59678e17i	−1.21187	−	0.255885i
$89$	−1.47708e16			−0.00446887			−0.00223444	−	0.999998i	$-0.500711\pi$
$89$	−1.47708e16			−0.00446887			−0.00223444	+	0.999998i	$0.500711\pi$
$90$	5.51259e18	−	8.18067e18i	1.49986	−	2.22580i
$91$			4.63927e17i			0.113647i
$92$	2.52609e18	+	6.23614e18i	0.557781	+	1.37699i
$93$		−	7.13664e18i		−	1.42202i
$94$	3.90478e18	+	2.63125e18i	0.702881	+	0.473640i
$95$	2.62003e18			0.426513
$96$	−2.26198e18	−	1.26619e19i	−0.333358	−	1.86604i
$97$	−3.24606e18			−0.433536			−0.216768	−	0.976223i	$-0.569551\pi$
$97$	−3.24606e18			−0.433536			−0.216768	+	0.976223i	$0.569551\pi$
$98$	4.34619e18	+	2.92870e18i	0.526576	+	0.354836i
$99$			2.91949e19i			3.21198i
$100$	−2.67306e17	−	6.59897e17i	−0.0267306	−	0.0659897i
$101$		−	1.69569e18i		−	0.154274i	−0.997020	−	0.0771371i	$-0.975422\pi$
$101$		−	1.69569e18i		−	0.154274i	0.997020	−	0.0771371i	$-0.0245779\pi$
$102$	2.57749e18	−	3.82499e18i	0.213548	−	0.316904i
$103$	−4.99165e18			−0.376956			−0.188478	−	0.982077i	$-0.560355\pi$
$103$	−4.99165e18			−0.376956			−0.188478	+	0.982077i	$0.560355\pi$
$104$	−2.67140e18	−	5.64062e17i	−0.184044	−	0.0388606i
$105$	1.88425e19			1.18534
$106$	7.84909e18	−	1.16480e19i	0.451246	−	0.669649i
$107$			2.04217e19i			1.07385i	0.843629	+	0.536927i	$0.180415\pi$
$107$			2.04217e19i			1.07385i	−0.843629	+	0.536927i	$0.819585\pi$
$108$	−5.81516e19	+	2.35556e19i	−2.79921	+	1.13388i
$109$		−	5.05925e18i		−	0.223118i	−0.993758	−	0.111559i	$-0.964416\pi$
$109$		−	5.05925e18i		−	0.223118i	0.993758	−	0.111559i	$-0.0355844\pi$
$110$	2.62906e19	+	1.77160e19i	1.06309	+	0.716367i
$111$	−2.60979e19			−0.968361
$112$	1.27325e19	−	1.23399e19i	0.433852	−	0.420476i
$113$	2.33273e19			0.730498			0.365249	−	0.930910i	$-0.380984\pi$
$113$	2.33273e19			0.730498			0.365249	+	0.930910i	$0.380984\pi$
$114$	−2.24928e19	−	1.51569e19i	−0.647808	−	0.436529i
$115$		−	5.80080e19i		−	1.53765i
$116$	6.94756e19	−	2.81426e19i	1.69622	−	0.687090i
$117$			2.16773e19i			0.487797i
$118$	8.04198e18	−	1.19343e19i	0.166911	−	0.247695i
$119$	6.35825e18			0.121798
$120$	−2.29095e19	+	1.08500e20i	−0.405317	+	1.91958i
$121$	−3.26659e19			−0.534113
$122$	−2.28946e19	+	3.39756e19i	−0.346191	+	0.513746i
$123$		−	1.45003e20i		−	2.02899i
$124$	2.17374e19	+	5.36631e19i	0.281645	+	0.695296i
$125$		−	8.00761e19i		−	0.961298i
$126$	−1.16744e20	−	7.86683e19i	−1.29931	−	0.875547i
$127$	−9.44202e19			−0.974832			−0.487416	−	0.873170i	$-0.662060\pi$
$127$	−9.44202e19			−0.974832			−0.487416	+	0.873170i	$0.662060\pi$
$128$	5.55754e19	+	8.83199e19i	0.532584	+	0.846377i
$129$	1.41043e20			1.25531
$130$	1.95208e19	+	1.31542e19i	0.161449	+	0.108793i
$131$			1.47993e20i			1.13805i	0.822319	+	0.569027i	$0.192680\pi$
$131$			1.47993e20i			1.13805i	−0.822319	+	0.569027i	$0.807320\pi$
$132$	−1.23215e20	−	3.04181e20i	−0.881480	−	2.17611i
$133$		−	3.73896e19i		−	0.248977i
$134$	3.97990e19	−	5.90617e19i	0.246818	−	0.366277i
$135$	5.40921e20			3.12581
$136$	−7.73061e18	+	3.66123e19i	−0.0416480	+	0.197245i
$137$	−3.22408e20			−1.62017			−0.810086	−	0.586312i	$-0.800579\pi$
$137$	−3.22408e20			−1.62017			−0.810086	+	0.586312i	$0.800579\pi$
$138$	−3.35576e20	+	4.97994e20i	−1.57376	+	2.33546i
$139$		−	1.29879e20i		−	0.568721i	−0.958717	−	0.284360i	$-0.908219\pi$
$139$		−	1.29879e20i		−	0.568721i	0.958717	−	0.284360i	$-0.0917812\pi$
$140$	−1.41684e20	+	5.73923e19i	−0.579569	+	0.234767i
$141$			4.20244e20i			1.60664i
$142$	3.86748e20	+	2.60612e20i	1.38257	+	0.931655i
$143$	−6.96651e19			−0.232982
$144$	5.94932e20	−	5.76589e20i	1.86219	−	1.80477i
$145$	−6.46256e20			−1.89412
$146$	9.36301e18	+	6.30931e18i	0.0257077	+	0.0173233i
$147$			4.67750e20i			1.20365i
$148$	1.96240e20	−	7.94914e19i	0.473480	−	0.191793i
$149$		−	6.85382e18i		−	0.0155118i	−0.999970	−	0.00775591i	$-0.997531\pi$
$149$		−	6.85382e18i		−	0.0155118i	0.999970	−	0.00775591i	$-0.00246881\pi$
$150$	3.55100e19	−	5.26969e19i	0.0754196	−	0.111923i
$151$	−2.91177e20			−0.580598			−0.290299	−	0.956936i	$-0.593755\pi$
$151$	−2.91177e20			−0.580598			−0.290299	+	0.956936i	$0.593755\pi$
$152$	2.15298e20	+	4.54597e19i	0.403205	+	0.0851359i
$153$	2.97093e20			0.522785
$154$	2.52819e20	−	3.75184e20i	0.418180	−	0.620579i
$155$		−	4.99169e20i		−	0.776420i
$156$	−9.14875e19	−	2.25855e20i	−0.133868	−	0.330481i
$157$		−	1.98718e19i		−	0.0273646i	−0.999906	−	0.0136823i	$-0.995645\pi$
$157$		−	1.98718e19i		−	0.0273646i	0.999906	−	0.0136823i	$-0.00435535\pi$
$158$	−6.38047e20	−	4.29951e20i	−0.827199	−	0.557412i
$159$	1.25360e21			1.53068
$160$	−1.58213e20	−	8.85631e20i	−0.182013	−	1.01886i
$161$	−8.27812e20			−0.897607
$162$	−2.54026e21	−	1.71177e21i	−2.59708	−	1.75006i
$163$		−	7.73160e20i		−	0.745568i	−0.927918	−	0.372784i	$-0.878403\pi$
$163$		−	7.73160e20i		−	0.745568i	0.927918	−	0.372784i	$-0.121597\pi$
$164$	4.41665e20	+	1.09034e21i	0.401861	+	0.992074i
$165$			2.82947e21i			2.43001i
$166$	−4.27953e20	+	6.35082e20i	−0.347032	+	0.514995i
$167$	−1.10812e21			−0.848750			−0.424375	−	0.905486i	$-0.639506\pi$
$167$	−1.10812e21			−0.848750			−0.424375	+	0.905486i	$0.639506\pi$
$168$	1.54836e21	+	3.26934e20i	1.12056	+	0.236604i
$169$	1.41019e21			0.964618
$170$	1.80281e20	−	2.67537e20i	0.116597	−	0.173029i
$171$		−	1.74705e21i		−	1.06867i
$172$	−1.06056e21	+	4.29602e20i	−0.613781	+	0.248626i
$173$		−	2.71376e21i		−	1.48639i	−0.669072	−	0.743197i	$-0.733308\pi$
$173$		−	2.71376e21i		−	1.48639i	0.669072	−	0.743197i	$-0.266692\pi$
$174$	5.54806e21	+	3.73859e21i	2.87689	+	1.93861i
$175$	8.75976e19			0.0430161
$176$	1.85301e21	+	1.91196e21i	0.861999	+	0.889422i
$177$	1.28440e21			0.566181
$178$	8.86939e18	+	5.97668e18i	0.00370598	+	0.00249730i
$179$			3.35418e21i			1.32887i	0.747346	+	0.664436i	$0.231328\pi$
$179$			3.35418e21i			1.32887i	−0.747346	+	0.664436i	$0.768672\pi$
$180$	−6.62028e21	+	2.68169e21i	−2.48764	+	1.00767i
$181$		−	1.95478e21i		−	0.696870i	−0.937333	−	0.348435i	$-0.886713\pi$
$181$		−	1.95478e21i		−	0.696870i	0.937333	−	0.348435i	$-0.113287\pi$
$182$	1.87719e20	−	2.78574e20i	0.0635081	−	0.0942459i
$183$	−3.65656e21			−1.17432
$184$	1.00649e21	−	4.76674e21i	0.306930	−	1.45362i
$185$	−1.82541e21			−0.528723
$186$	−2.88769e21	+	4.28533e21i	−0.794653	+	1.17926i
$187$			9.54778e20i			0.249693i
$188$	−1.28002e21	−	3.15997e21i	−0.318212	−	0.785568i
$189$		−	7.71930e21i		−	1.82470i
$190$	−1.57325e21	−	1.06014e21i	−0.353702	−	0.238344i
$191$	8.35363e21			1.78673			0.893364	−	0.449335i	$-0.148339\pi$
$191$	8.35363e21			1.78673			0.893364	+	0.449335i	$0.148339\pi$
$192$	−3.76513e21	+	8.51834e21i	−0.766334	+	1.73378i
$193$	3.59357e21			0.696197			0.348099	−	0.937458i	$-0.386827\pi$
$193$	3.59357e21			0.696197			0.348099	+	0.937458i	$0.386827\pi$
$194$	1.94916e21	+	1.31345e21i	0.359526	+	0.242269i
$195$			2.10088e21i			0.369040i
$196$	−1.42471e21	−	3.51719e21i	−0.238394	−	0.588522i
$197$			2.12043e21i			0.338061i	0.985611	+	0.169031i	$0.0540637\pi$
$197$			2.12043e21i			0.338061i	−0.985611	+	0.169031i	$0.945936\pi$
$198$	1.18131e22	−	1.75307e22i	1.79492	−	2.66366i
$199$	−1.24450e21			−0.180256			−0.0901278	−	0.995930i	$-0.528728\pi$
$199$	−1.24450e21			−0.180256			−0.0901278	+	0.995930i	$0.528728\pi$
$200$	−1.06505e20	+	5.04408e20i	−0.0147090	+	0.0696621i
$201$	6.35639e21			0.837236
$202$	−6.86126e20	+	1.01821e21i	−0.0862116	+	0.127938i
$203$			9.22249e21i			1.10570i
$204$	−3.09540e21	+	1.25386e21i	−0.354185	+	0.143470i
$205$		−	1.01422e22i		−	1.10782i
$206$	2.99733e21	+	2.01977e21i	0.312605	+	0.210651i
$207$	−3.86800e22			−3.85273
$208$	1.37586e21	+	1.41963e21i	0.130910	+	0.135074i
$209$	5.61456e21			0.510418
$210$	−1.13144e22	−	7.62424e21i	−0.982985	−	0.662390i
$211$		−	1.62712e22i		−	1.35126i	−0.737243	−	0.675628i	$-0.763873\pi$
$211$		−	1.62712e22i		−	1.35126i	0.737243	−	0.675628i	$-0.236127\pi$
$212$	−9.42627e21	+	3.81832e21i	−0.748427	+	0.303167i
$213$			4.16230e22i			3.16029i
$214$	8.26321e21	−	1.22626e22i	0.600092	−	0.890536i
$215$	9.86520e21			0.685394
$216$	4.44495e22	+	9.38543e21i	2.95499	+	0.623941i
$217$	−7.12347e21			−0.453236
$218$	−2.04712e21	+	3.03792e21i	−0.124683	+	0.185029i
$219$			1.00767e21i			0.0587626i
$220$	−8.61825e21	−	2.12759e22i	−0.481287	−	1.18815i
$221$			7.08923e20i			0.0379204i
$222$	1.56710e22	+	1.05600e22i	0.803051	+	0.541140i
$223$	8.63102e21			0.423805			0.211902	−	0.977291i	$-0.432034\pi$
$223$	8.63102e21			0.423805			0.211902	+	0.977291i	$0.432034\pi$
$224$	−1.26385e22	+	2.25780e21i	−0.594759	+	0.106250i
$225$	4.09305e21			0.184634
$226$	−1.40073e22	−	9.43890e21i	−0.605794	−	0.408217i
$227$			3.29137e22i			1.36499i	0.730888	+	0.682497i	$0.239106\pi$
$227$			3.29137e22i			1.36499i	−0.730888	+	0.682497i	$0.760894\pi$
$228$	7.37330e21	+	1.82024e22i	0.293279	+	0.724017i
$229$		−	1.00427e22i		−	0.383189i	−0.981474	−	0.191594i	$-0.938634\pi$
$229$		−	1.00427e22i		−	0.383189i	0.981474	−	0.191594i	$-0.0613658\pi$
$230$	−2.34717e22	+	3.48320e22i	−0.859272	+	1.27516i
$231$	4.03784e22			1.41852
$232$	−5.31053e22	−	1.12131e22i	−1.79061	−	0.378085i
$233$	1.66997e21			0.0540541			0.0270270	−	0.999635i	$-0.491396\pi$
$233$	1.66997e21			0.0540541			0.0270270	+	0.999635i	$0.491396\pi$
$234$	8.77125e21	−	1.30165e22i	0.272591	−	0.404524i
$235$			2.93938e22i			0.877225i
$236$	−9.65792e21	+	3.91215e21i	−0.276834	+	0.112138i
$237$		−	6.86685e22i		−	1.89081i
$238$	−3.81793e21	−	2.57273e21i	−0.101006	−	0.0680634i
$239$	2.79522e22			0.710618			0.355309	−	0.934749i	$-0.384376\pi$
$239$	2.79522e22			0.710618			0.355309	+	0.934749i	$0.384376\pi$
$240$	5.76586e22	−	5.58809e22i	1.40883	−	1.36539i
$241$	−7.63764e22			−1.79389			−0.896947	−	0.442137i	$-0.854220\pi$
$241$	−7.63764e22			−1.79389			−0.896947	+	0.442137i	$0.854220\pi$
$242$	1.96148e22	+	1.32176e22i	0.442934	+	0.298473i
$243$		−	1.34303e23i		−	2.91627i
$244$	2.74950e22	−	1.11375e22i	0.574184	−	0.232586i
$245$			3.27166e22i			0.657189i
$246$	−5.86726e22	+	8.70701e22i	−1.13384	+	1.68262i
$247$	4.16881e21			0.0775160
$248$	8.66101e21	−	4.10186e22i	0.154981	−	0.733990i
$249$	−6.83494e22			−1.17718
$250$	−3.24011e22	+	4.80833e22i	−0.537193	+	0.797194i
$251$		−	5.12863e22i		−	0.818655i	−0.912388	−	0.409327i	$-0.865763\pi$
$251$		−	5.12863e22i		−	0.818655i	0.912388	−	0.409327i	$-0.134237\pi$
$252$	3.82695e22	+	9.44758e22i	0.588230	+	1.45216i
$253$		−	1.24307e23i		−	1.84015i
$254$	5.66964e22	+	3.82052e22i	0.808417	+	0.544756i
$255$	2.87931e22			0.395510
$256$	2.36549e21	−	7.55208e22i	0.0313070	−	0.999510i
$257$	9.06211e22			1.15575			0.577876	−	0.816124i	$-0.303882\pi$
$257$	9.06211e22			1.15575			0.577876	+	0.816124i	$0.303882\pi$
$258$	−8.46920e22	−	5.70701e22i	−1.04101	−	0.701490i
$259$			2.60498e22i			0.308643i
$260$	−6.39906e21	−	1.57973e22i	−0.0730919	−	0.180442i
$261$			4.30926e23i			4.74589i
$262$	5.98822e22	−	8.88651e22i	0.635968	−	0.943776i
$263$	−4.91748e22			−0.503689			−0.251845	−	0.967768i	$-0.581037\pi$
$263$	−4.91748e22			−0.503689			−0.251845	+	0.967768i	$0.581037\pi$
$264$	−4.90937e22	+	2.32508e23i	−0.485052	+	2.29721i
$265$	8.76823e22			0.835750
$266$	−1.51289e22	+	2.24513e22i	−0.139134	+	0.206474i
$267$			9.54550e20i			0.00847113i
$268$	−4.77961e22	+	1.93609e22i	−0.409366	+	0.165823i
$269$		−	1.36727e23i		−	1.13034i	−0.824976	−	0.565168i	$-0.808811\pi$
$269$		−	1.36727e23i		−	1.13034i	0.824976	−	0.565168i	$-0.191189\pi$
$270$	−3.24806e23	−	2.18872e23i	−2.59220	−	1.74677i
$271$	2.12389e23			1.63653			0.818267	−	0.574839i	$-0.194935\pi$
$271$	2.12389e23			1.63653			0.818267	+	0.574839i	$0.194935\pi$
$272$	1.94564e22	−	1.88565e22i	0.144763	−	0.140300i
$273$	2.99810e22			0.215427
$274$	1.93596e23	+	1.30456e23i	1.34359	+	0.905385i
$275$			1.31540e22i			0.0881854i
$276$	4.03006e23	−	1.63246e23i	2.61021	−	1.05732i
$277$			7.86880e22i			0.492437i	0.969214	+	0.246219i	$0.0791881\pi$
$277$			7.86880e22i			0.492437i	−0.969214	+	0.246219i	$0.920812\pi$
$278$	−5.25529e22	+	7.79885e22i	−0.317813	+	0.471634i
$279$	−3.32848e23			−1.94539
$280$	1.08300e23	+	2.28673e22i	0.611823	+	0.129185i
$281$	−3.52668e23			−1.92600			−0.963000	−	0.269503i	$-0.913141\pi$
$281$	−3.52668e23			−1.92600			−0.963000	+	0.269503i	$0.913141\pi$
$282$	1.70043e23	−	2.52343e23i	0.897826	−	1.33237i
$283$			1.94559e23i			0.993299i	0.867951	+	0.496649i	$0.165436\pi$
$283$			1.94559e23i			0.993299i	−0.867951	+	0.496649i	$0.834564\pi$
$284$	−1.26779e23	−	3.12979e23i	−0.625926	−	1.54522i
$285$		−	1.69318e23i		−	0.808492i
$286$	4.18317e22	+	2.81885e22i	0.193210	+	0.130195i
$287$	−1.44736e23			−0.646694
$288$	−5.90543e23	+	1.05497e23i	−2.55284	+	0.456050i
$289$	−2.29356e23			−0.959360
$290$	3.88057e23	+	2.61494e23i	1.57078	+	1.05847i
$291$			2.09774e23i			0.821805i
$292$	−3.06927e21	−	7.57709e21i	−0.0116385	−	0.0287320i
$293$		−	3.42750e23i		−	1.25816i	−0.777341	−	0.629080i	$-0.783432\pi$
$293$		−	3.42750e23i		−	1.25816i	0.777341	−	0.629080i	$-0.216568\pi$
$294$	1.89265e23	−	2.80869e23i	0.672622	−	0.998170i
$295$	8.98371e22			0.309134
$296$	−1.50001e23	−	3.16724e22i	−0.499830	−	0.105538i
$297$	1.15916e24			3.74073
$298$	−2.77325e21	+	4.11550e21i	−0.00866832	+	0.0128638i
$299$		−	9.22984e22i		−	0.279459i
$300$	−4.26454e22	+	1.72744e22i	−0.125089	+	0.0506701i
$301$		−	1.40783e23i		−	0.400100i
$302$	1.74843e23	+	1.17819e23i	0.481483	+	0.324450i
$303$	−1.09583e23			−0.292440
$304$	−1.10885e23	−	1.14413e23i	−0.286797	−	0.295921i
$305$	−2.55756e23			−0.641177
$306$	−1.78395e23	−	1.20212e23i	−0.433540	−	0.292143i
$307$			5.99264e23i			1.41190i	0.708263	+	0.705949i	$0.249479\pi$
$307$			5.99264e23i			1.41190i	−0.708263	+	0.705949i	$0.750521\pi$
$308$	−3.03621e23	+	1.22988e23i	−0.693584	+	0.280952i
$309$			3.22582e23i			0.714553i
$310$	−2.01978e23	+	2.99736e23i	−0.433879	+	0.643876i
$311$	6.01963e23			1.25414			0.627070	−	0.778963i	$-0.284254\pi$
$311$	6.01963e23			1.25414			0.627070	+	0.778963i	$0.284254\pi$
$312$	−3.64521e22	+	1.72637e23i	−0.0736637	+	0.348872i
$313$	−4.52824e23			−0.887684			−0.443842	−	0.896105i	$-0.646385\pi$
$313$	−4.52824e23			−0.887684			−0.443842	+	0.896105i	$0.646385\pi$
$314$	−8.04070e21	+	1.19324e22i	−0.0152919	+	0.0226932i
$315$		−	8.78805e23i		−	1.62159i
$316$	2.09157e23	+	5.16345e23i	0.374494	+	0.924512i
$317$		−	6.86620e23i		−	1.19304i	−0.802600	−	0.596518i	$-0.796551\pi$
$317$		−	6.86620e23i		−	1.19304i	0.802600	−	0.596518i	$-0.203449\pi$
$318$	−7.52746e23	−	5.07242e23i	−1.26938	−	0.855377i
$319$	−1.38488e24			−2.26674
$320$	−2.63350e23	+	5.95812e23i	−0.418417	+	0.946639i
$321$	1.31974e24			2.03559
$322$	4.97076e23	+	3.34957e23i	0.744375	+	0.501601i
$323$		−	5.71346e22i		−	0.0830760i
$324$	8.32718e23	+	2.05573e24i	1.17576	+	2.90261i
$325$			9.76685e21i			0.0133925i
$326$	−3.12843e23	+	4.64259e23i	−0.416638	+	0.618291i
$327$	−3.26950e23			−0.422939
$328$	1.75976e23	−	8.33424e23i	0.221132	−	1.04728i
$329$	4.19469e23			0.512081
$330$	1.14489e24	−	1.69901e24i	1.35794	−	2.01518i
$331$			3.31719e22i			0.0382300i	0.999817	+	0.0191150i	$0.00608487\pi$
$331$			3.31719e22i			0.0382300i	−0.999817	+	0.0191150i	$0.993915\pi$
$332$	5.13945e23	−	2.08185e23i	0.575579	−	0.233151i
$333$			1.21719e24i			1.32476i
$334$	6.65391e23	+	4.48377e23i	0.703859	+	0.474299i
$335$	4.44595e23			0.457129
$336$	−7.97458e23	−	8.22827e23i	−0.797048	−	0.822404i
$337$	−1.40563e23			−0.136580			−0.0682898	−	0.997666i	$-0.521754\pi$
$337$	−1.40563e23			−0.136580			−0.0682898	+	0.997666i	$0.521754\pi$
$338$	−8.46778e23	−	5.70606e23i	−0.799946	−	0.539048i
$339$		−	1.50751e24i		−	1.38472i
$340$	−2.16507e23	+	8.77007e22i	−0.193384	+	0.0783346i
$341$		−	1.06969e24i		−	0.929160i
$342$	−7.06906e23	+	1.04905e24i	−0.597192	+	0.886232i
$343$	1.20217e24			0.987809
$344$	8.10661e23	+	1.71170e23i	0.647939	+	0.136811i
$345$	−3.74873e24			−2.91476
$346$	−1.09807e24	+	1.62953e24i	−0.830627	+	1.23265i
$347$			1.97204e23i			0.145140i	0.997363	+	0.0725699i	$0.0231201\pi$
$347$			1.97204e23i			0.145140i	−0.997363	+	0.0725699i	$0.976880\pi$
$348$	−1.81870e24	−	4.48981e24i	−1.30244	−	3.21533i
$349$			1.37315e24i			0.956925i	0.878108	+	0.478462i	$0.158806\pi$
$349$			1.37315e24i			0.956925i	−0.878108	+	0.478462i	$0.841194\pi$
$350$	−5.25997e22	−	3.54445e22i	−0.0356727	−	0.0240383i
$351$	8.60676e23			0.568097
$352$	−3.39040e23	−	1.89785e24i	−0.217819	−	1.21929i
$353$	8.90549e23			0.556927			0.278463	−	0.960447i	$-0.410175\pi$
$353$	8.90549e23			0.556927			0.278463	+	0.960447i	$0.410175\pi$
$354$	−7.71245e23	−	5.19707e23i	−0.469528	−	0.316394i
$355$			2.91130e24i			1.72551i
$356$	−2.90745e21	−	7.17762e21i	−0.00167779	−	0.00414196i
$357$		−	4.10897e23i		−	0.230879i
$358$	1.35720e24	−	2.01408e24i	0.742600	−	1.10202i
$359$	5.79647e23			0.308863			0.154432	−	0.988003i	$-0.450645\pi$
$359$	5.79647e23			0.308863			0.154432	+	0.988003i	$0.450645\pi$
$360$	5.06036e24	+	1.06849e24i	2.62608	+	0.554492i
$361$	1.64244e24			0.830178
$362$	−7.90962e23	+	1.17379e24i	−0.389425	+	0.577907i
$363$			2.11101e24i			1.01246i
$364$	−2.25438e23	+	9.13188e22i	−0.105333	+	0.0426675i
$365$			7.04814e22i			0.0320843i
$366$	2.19565e24	+	1.47955e24i	0.973851	+	0.656234i
$367$	2.84618e24			1.23008			0.615041	−	0.788495i	$-0.289139\pi$
$367$	2.84618e24			1.23008			0.615041	+	0.788495i	$0.289139\pi$
$368$	−2.53313e24	+	2.45502e24i	−1.06685	+	1.03395i
$369$	−6.76287e24			−2.77575
$370$	1.09610e24	+	7.38613e23i	0.438464	+	0.295461i
$371$		−	1.25128e24i		−	0.487870i
$372$	3.46794e24	−	1.40476e24i	1.31799	−	0.533882i
$373$			1.59988e24i			0.592725i	0.955076	+	0.296362i	$0.0957736\pi$
$373$			1.59988e24i			0.592725i	−0.955076	+	0.296362i	$0.904226\pi$
$374$	3.86331e23	−	5.73315e23i	0.139534	−	0.207068i
$375$	−5.17486e24			−1.82222
$376$	−5.10007e23	+	2.41540e24i	−0.175102	+	0.829286i
$377$	−1.02828e24			−0.344245
$378$	−3.12345e24	+	4.63520e24i	−1.01968	+	1.51320i
$379$		−	2.91277e24i		−	0.927329i	−0.886011	−	0.463664i	$-0.846534\pi$
$379$		−	2.91277e24i		−	0.927329i	0.886011	−	0.463664i	$-0.153466\pi$
$380$	5.15723e23	+	1.27316e24i	0.160130	+	0.395312i
$381$			6.10184e24i			1.84788i
$382$	−5.01610e24	−	3.38012e24i	−1.48171	−	0.998459i
$383$	5.08645e24			1.46564			0.732818	−	0.680425i	$-0.238205\pi$
$383$	5.08645e24			1.46564			0.732818	+	0.680425i	$0.238205\pi$
$384$	5.70761e24	−	3.59152e24i	1.60438	−	1.00956i
$385$	2.82425e24			0.774509
$386$	−2.15783e24	−	1.45407e24i	−0.577348	−	0.389049i
$387$		−	6.57816e24i		−	1.71732i
$388$	−6.38949e23	−	1.57737e24i	−0.162767	−	0.401821i
$389$		−	6.51472e24i		−	1.61947i	−0.586792	−	0.809737i	$-0.699610\pi$
$389$		−	6.51472e24i		−	1.61947i	0.586792	−	0.809737i	$-0.300390\pi$
$390$	8.50078e23	−	1.26152e24i	0.206227	−	0.306040i
$391$	−1.26497e24			−0.299504
$392$	−5.67660e23	+	2.68844e24i	−0.131181	+	0.621274i
$393$	9.56392e24			2.15728
$394$	8.57989e23	−	1.27326e24i	0.188916	−	0.280351i
$395$		−	4.80299e24i		−	1.03238i
$396$	−1.41868e25	+	5.74669e24i	−2.97702	+	1.20591i
$397$			8.25203e24i			1.69064i	0.534261	+	0.845319i	$0.320590\pi$
$397$			8.25203e24i			1.69064i	−0.534261	+	0.845319i	$0.679410\pi$
$398$	7.47281e23	+	5.03559e23i	0.149484	+	0.100731i
$399$	−2.41627e24			−0.471958
$400$	2.68051e23	−	2.59786e23i	0.0511266	−	0.0495503i
$401$	6.97232e24			1.29869			0.649346	−	0.760493i	$-0.275043\pi$
$401$	6.97232e24			1.29869			0.649346	+	0.760493i	$0.275043\pi$
$402$	−3.81682e24	−	2.57198e24i	−0.694311	−	0.467865i
$403$		−	7.94244e23i		−	0.141109i
$404$	8.23995e23	−	3.33777e23i	0.142989	−	0.0579207i
$405$		−	1.91222e25i		−	3.24127i
$406$	3.73169e24	−	5.53782e24i	0.617886	−	0.916942i
$407$	−3.91173e24			−0.632736
$408$	2.36604e24	+	4.99585e23i	0.373896	+	0.0789474i
$409$	−9.72462e24			−1.50142			−0.750708	−	0.660634i	$-0.770287\pi$
$409$	−9.72462e24			−1.50142			−0.750708	+	0.660634i	$0.770287\pi$
$410$	−4.10383e24	+	6.09008e24i	−0.619075	+	0.918706i
$411$			2.08354e25i			3.07118i
$412$	−9.82549e23	−	2.42562e24i	−0.141524	−	0.349380i
$413$		−	1.28203e24i		−	0.180457i
$414$	2.32261e25	+	1.56511e25i	3.19502	+	2.15298i
$415$	−4.78067e24			−0.642735
$416$	−2.51738e23	−	1.40916e24i	−0.0330797	−	0.185171i
$417$	−8.39335e24			−1.07806
$418$	−3.37137e24	−	2.27181e24i	−0.423284	−	0.285232i
$419$		−	8.46057e24i		−	1.03840i	−0.854652	−	0.519202i	$-0.826229\pi$
$419$		−	8.46057e24i		−	1.03840i	0.854652	−	0.519202i	$-0.173771\pi$
$420$	3.70894e24	+	9.15625e24i	0.445022	+	1.09862i
$421$		−	5.21037e24i		−	0.611208i	−0.952159	−	0.305604i	$-0.901142\pi$
$421$		−	5.21037e24i		−	0.611208i	0.952159	−	0.305604i	$-0.0988583\pi$
$422$	−6.58382e24	+	9.77038e24i	−0.755109	+	1.12058i
$423$	1.95999e25			2.19796
$424$	7.20519e24	+	1.52136e24i	0.790078	+	0.166823i
$425$	1.33857e23			0.0143531
$426$	1.68419e25	−	2.49933e25i	1.76603	−	2.62079i
$427$			3.64981e24i			0.374288i
$428$	−9.92360e24	+	4.01977e24i	−0.995299	+	0.403168i
$429$			4.50206e24i			0.441638i
$430$	−5.92375e24	−	3.99175e24i	−0.568390	−	0.383012i
$431$	−1.66772e25			−1.56527			−0.782633	−	0.622483i	$-0.786124\pi$
$431$	−1.66772e25			−1.56527			−0.782633	+	0.622483i	$0.786124\pi$
$432$	−2.28929e25	−	2.36212e25i	−2.10187	−	2.16874i
$433$	1.04186e25			0.935778			0.467889	−	0.883787i	$-0.345015\pi$
$433$	1.04186e25			0.935778			0.467889	+	0.883787i	$0.345015\pi$
$434$	4.27743e24	+	2.88237e24i	0.375863	+	0.253277i
$435$			4.17638e25i			3.59048i
$436$	2.45846e24	−	9.95855e23i	0.206796	−	0.0837673i
$437$			7.43865e24i			0.612238i
$438$	4.07734e23	−	6.05077e23i	0.0328377	−	0.0487312i
$439$	−1.70791e25			−1.34602			−0.673011	−	0.739633i	$-0.734999\pi$
$439$	−1.70791e25			−1.34602			−0.673011	+	0.739633i	$0.734999\pi$
$440$	−3.43384e24	+	1.62627e25i	−0.264837	+	1.25427i
$441$	2.18156e25			1.64664
$442$	2.86851e23	−	4.25687e23i	0.0211907	−	0.0314470i
$443$		−	1.49238e25i		−	1.07905i	−0.841969	−	0.539527i	$-0.818603\pi$
$443$		−	1.49238e25i		−	1.07905i	0.841969	−	0.539527i	$-0.181397\pi$
$444$	−5.13707e24	−	1.26819e25i	−0.363561	−	0.897523i
$445$			6.67656e22i			0.00462522i
$446$	−5.18266e24	−	3.49236e24i	−0.351457	−	0.236831i
$447$	−4.42923e23			−0.0294040
$448$	8.50263e24	+	3.75818e24i	0.552602	+	0.244251i
$449$	9.26546e24			0.589558			0.294779	−	0.955565i	$-0.404754\pi$
$449$	9.26546e24			0.589558			0.294779	+	0.955565i	$0.404754\pi$
$450$	−2.45775e24	−	1.65617e24i	−0.153115	−	0.103177i
$451$		−	2.17341e25i		−	1.32576i
$452$	4.59171e24	+	1.13355e25i	0.274258	+	0.677060i
$453$			1.88171e25i			1.10057i
$454$	1.33178e25	−	1.97637e25i	0.762787	−	1.13197i
$455$	2.09701e24			0.117623
$456$	2.93780e24	−	1.39135e25i	0.161383	−	0.764309i
$457$	−2.13314e25			−1.14767			−0.573834	−	0.818972i	$-0.694544\pi$
$457$	−2.13314e25			−1.14767			−0.573834	+	0.818972i	$0.694544\pi$
$458$	−4.06356e24	+	6.03032e24i	−0.214134	+	0.317774i
$459$		−	1.17958e25i		−	0.608845i
$460$	2.81881e25	−	1.14182e25i	1.42517	−	0.577296i
$461$			1.17430e25i			0.581593i	0.956785	+	0.290796i	$0.0939202\pi$
$461$			1.17430e25i			0.581593i	−0.956785	+	0.290796i	$0.906080\pi$
$462$	−2.42460e25	−	1.63383e25i	−1.17636	−	0.792697i
$463$	−2.88846e24			−0.137293			−0.0686463	−	0.997641i	$-0.521868\pi$
$463$	−2.88846e24			−0.137293			−0.0686463	+	0.997641i	$0.521868\pi$
$464$	2.73509e25	+	2.82211e25i	1.27365	+	1.31417i
$465$	−3.22584e25			−1.47177
$466$	−1.00277e24	−	6.75720e23i	−0.0448264	−	0.0302065i
$467$		−	3.47643e25i		−	1.52273i	−0.648322	−	0.761366i	$-0.724529\pi$
$467$		−	3.47643e25i		−	1.52273i	0.648322	−	0.761366i	$-0.275471\pi$
$468$	−1.05337e25	+	4.26692e24i	−0.452113	+	0.183138i
$469$		−	6.34467e24i		−	0.266850i
$470$	1.18936e25	−	1.76501e25i	0.490211	−	0.727473i
$471$	−1.28420e24			−0.0518721
$472$	7.38226e24	+	1.55875e24i	0.292240	+	0.0617060i
$473$	2.11405e25			0.820227
$474$	−2.77853e25	+	4.12333e25i	−1.05662	+	1.56803i
$475$		−	7.87145e23i		−	0.0293403i
$476$	1.25155e24	+	3.08969e24i	0.0457279	+	0.112888i
$477$		−	5.84670e25i		−	2.09405i
$478$	−1.67844e25	−	1.13103e25i	−0.589307	−	0.397108i
$479$	3.05777e25			1.05249			0.526244	−	0.850334i	$-0.323600\pi$
$479$	3.05777e25			1.05249			0.526244	+	0.850334i	$0.323600\pi$
$480$	−5.72333e25	+	1.02244e25i	−1.93133	+	0.345022i
$481$	−2.90447e24			−0.0960922
$482$	4.58616e25	+	3.09041e25i	1.48766	+	1.00246i
$483$			5.34968e25i			1.70149i
$484$	−6.42990e24	−	1.58735e25i	−0.200527	−	0.495041i
$485$			1.46726e25i			0.448704i
$486$	−5.43430e25	+	8.06450e25i	−1.62967	+	2.41843i
$487$	1.99581e24			0.0586941			0.0293470	−	0.999569i	$-0.490657\pi$
$487$	1.99581e24			0.0586941			0.0293470	+	0.999569i	$0.490657\pi$
$488$	−2.10165e25	−	4.43759e24i	−0.606138	−	0.127985i
$489$	−4.99649e25			−1.41329
$490$	1.32381e25	−	1.96453e25i	0.367250	−	0.544999i
$491$		−	8.79091e24i		−	0.239199i	−0.992822	−	0.119600i	$-0.961839\pi$
$491$		−	8.79091e24i		−	0.239199i	0.992822	−	0.119600i	$-0.0381611\pi$
$492$	7.04622e25	−	2.85423e25i	1.88056	−	0.761763i
$493$			1.40928e25i			0.368937i
$494$	−2.50324e24	−	1.68682e24i	−0.0642831	−	0.0433175i
$495$	1.31965e26			3.32436
$496$	−2.17980e25	+	2.11259e25i	−0.538692	+	0.522083i
$497$	4.15462e25			1.00727
$498$	4.10417e25	+	2.76562e25i	0.976218	+	0.657829i
$499$			1.07605e24i			0.0251118i	0.999921	+	0.0125559i	$0.00399678\pi$
$499$			1.07605e24i			0.0251118i	−0.999921	+	0.0125559i	$0.996003\pi$
$500$	3.89118e25	−	1.57621e25i	0.890976	−	0.360909i
$501$			7.16114e25i			1.60888i
$502$	−2.07519e25	+	3.07958e25i	−0.457481	+	0.678901i
$503$	−1.65399e25			−0.357797			−0.178898	−	0.983868i	$-0.557253\pi$
$503$	−1.65399e25			−0.357797			−0.178898	+	0.983868i	$0.557253\pi$
$504$	1.52480e25	−	7.22147e25i	0.323685	−	1.53298i
$505$	−7.66472e24			−0.159672
$506$	−5.02984e25	+	7.46428e25i	−1.02831	+	1.52601i
$507$		−	9.11328e25i		−	1.82852i
$508$	−1.85855e25	−	4.58821e25i	−0.365990	−	0.903520i
$509$		−	9.88228e25i		−	1.91002i	−0.296570	−	0.955011i	$-0.595843\pi$
$509$		−	9.88228e25i		−	1.91002i	0.296570	−	0.955011i	$-0.404157\pi$
$510$	−1.72894e25	−	1.16505e25i	−0.327992	−	0.221019i
$511$	1.00582e24			0.0187292
$512$	−3.19783e25	+	4.43908e25i	−0.584509	+	0.811387i
$513$	−6.93649e25			−1.24459
$514$	−5.44152e25	−	3.66680e25i	−0.958453	−	0.645858i
$515$			2.25629e25i			0.390144i
$516$	2.77627e25	+	6.85377e25i	0.471291	+	1.16348i
$517$			6.29890e25i			1.04980i
$518$	1.05405e25	−	1.56421e25i	0.172476	−	0.255954i
$519$	−1.75375e26			−2.81759
$520$	−2.54963e24	+	1.20751e25i	−0.0402202	+	0.190484i
$521$	−9.73743e25			−1.50829			−0.754147	−	0.656706i	$-0.771949\pi$
$521$	−9.73743e25			−1.50829			−0.754147	+	0.656706i	$0.771949\pi$
$522$	1.74365e26	−	2.58758e26i	2.65210	−	3.93572i
$523$			3.90204e25i			0.582808i	0.956600	+	0.291404i	$0.0941224\pi$
$523$			3.90204e25i			0.582808i	−0.956600	+	0.291404i	$0.905878\pi$
$524$	−7.19148e25	+	2.91307e25i	−1.05480	+	0.427271i
$525$		−	5.66093e24i		−	0.0815407i
$526$	2.95279e25	+	1.98975e25i	0.417704	+	0.281472i
$527$	−1.08853e25			−0.151231
$528$	1.23559e26	−	1.19749e26i	1.68598	−	1.63399i
$529$	9.00778e25			1.20723
$530$	−5.26505e25	−	3.54788e25i	−0.693078	−	0.467034i
$531$		−	5.99038e25i		−	0.774562i
$532$	1.81689e25	−	7.35970e24i	0.230764	−	0.0934759i
$533$		−	1.61376e25i		−	0.201340i
$534$	3.86239e23	−	5.73178e23i	0.00473384	−	0.00702502i
$535$	9.23084e25			1.11143
$536$	3.65341e25	+	7.71410e24i	0.432148	+	0.0912473i
$537$	2.16762e26			2.51899
$538$	−5.53237e25	+	8.21003e25i	−0.631654	+	0.937374i
$539$			7.01095e25i			0.786473i
$540$	1.06474e26	+	2.62852e26i	1.17355	+	2.89715i
$541$			1.19711e26i			1.29646i	0.761445	+	0.648229i	$0.224490\pi$
$541$			1.19711e26i			1.29646i	−0.761445	+	0.648229i	$0.775510\pi$
$542$	−1.27533e26	−	8.59390e25i	−1.35716	−	0.914528i
$543$	−1.26326e26			−1.32098
$544$	−1.93129e25	+	3.45013e24i	−0.198453	+	0.0354524i
$545$	−2.28684e25			−0.230924
$546$	−1.80027e25	−	1.21312e25i	−0.178651	−	0.120385i
$547$			4.21648e25i			0.411216i	0.978634	+	0.205608i	$0.0659172\pi$
$547$			4.21648e25i			0.411216i	−0.978634	+	0.205608i	$0.934083\pi$
$548$	−6.34624e25	−	1.56669e26i	−0.608276	−	1.50165i
$549$			1.70539e26i			1.60653i
$550$	5.32249e24	−	7.89856e24i	0.0492798	−	0.0731312i
$551$	8.28725e25			0.754172
$552$	−3.08047e26	−	6.50435e25i	−2.75547	−	0.581812i
$553$	−6.85419e25			−0.602653
$554$	3.18395e25	−	4.72497e25i	0.275184	−	0.408373i
$555$			1.17966e26i			1.00224i
$556$	6.31128e25	−	2.55652e25i	0.527117	−	0.213520i
$557$		−	1.90162e26i		−	1.56134i	−0.624941	−	0.780672i	$-0.714877\pi$
$557$		−	1.90162e26i		−	1.56134i	0.624941	−	0.780672i	$-0.285123\pi$
$558$	1.99865e26	+	1.34680e26i	1.61329	+	1.08712i
$559$	1.56968e25			0.124566
$560$	−5.57779e25	−	5.75523e25i	−0.435187	−	0.449031i
$561$	6.17019e25			0.473316
$562$	2.11766e26	+	1.42700e26i	1.59721	+	1.07629i
$563$			5.34079e25i			0.396073i	0.980195	+	0.198037i	$0.0634565\pi$
$563$			5.34079e25i			0.396073i	−0.980195	+	0.198037i	$0.936544\pi$
$564$	−2.04211e26	+	8.27202e25i	−1.48911	+	0.603198i
$565$		−	1.05442e26i		−	0.756056i
$566$	7.87242e25	−	1.16827e26i	0.555075	−	0.823731i
$567$	−2.72886e26			−1.89209
$568$	−5.05135e25	+	2.39233e26i	−0.344428	+	1.63122i
$569$	1.41834e26			0.951071			0.475535	−	0.879697i	$-0.342254\pi$
$569$	1.41834e26			0.951071			0.475535	+	0.879697i	$0.342254\pi$
$570$	−6.85108e25	+	1.01670e26i	−0.451802	+	0.670473i
$571$			6.11609e25i			0.396671i	0.980134	+	0.198336i	$0.0635536\pi$
$571$			6.11609e25i			0.396671i	−0.980134	+	0.198336i	$0.936446\pi$
$572$	−1.37128e25	−	3.38527e25i	−0.0874708	−	0.215939i
$573$		−	5.39847e26i		−	3.38690i
$574$	8.69095e25	+	5.85644e25i	0.536296	+	0.361386i
$575$	−1.74275e25			−0.105777
$576$	3.97290e26	+	1.75603e26i	2.37189	+	1.04838i
$577$	−2.16525e26			−1.27156			−0.635780	−	0.771870i	$-0.719321\pi$
$577$	−2.16525e26			−1.27156			−0.635780	+	0.771870i	$0.719321\pi$
$578$	1.37721e26	+	9.28043e25i	0.795586	+	0.536110i
$579$		−	2.32232e26i		−	1.31970i
$580$	−1.27208e26	−	3.14038e26i	−0.711129	−	1.75556i
$581$			6.82234e25i			0.375197i
$582$	8.48808e25	−	1.25963e26i	0.459241	−	0.681514i
$583$	1.87898e26			1.00016
$584$	−1.22291e24	+	5.79172e24i	−0.00640432	+	0.0303309i
$585$	9.79838e25			0.504863
$586$	−1.38687e26	+	2.05811e26i	−0.703085	+	1.04338i
$587$			1.04214e26i			0.519835i	0.965631	+	0.259917i	$0.0836954\pi$
$587$			1.04214e26i			0.519835i	−0.965631	+	0.259917i	$0.916305\pi$
$588$	−2.27296e26	+	9.20712e25i	−1.11560	+	0.451897i
$589$			6.40109e25i			0.309143i
$590$	−5.39444e25	−	3.63507e25i	−0.256361	−	0.172750i
$591$	1.37032e26			0.640825
$592$	7.72553e25	+	7.97130e25i	0.355526	+	0.366837i
$593$	−8.03008e25			−0.363664			−0.181832	−	0.983330i	$-0.558203\pi$
$593$	−8.03008e25			−0.363664			−0.181832	+	0.983330i	$0.558203\pi$
$594$	−6.96039e26	−	4.69030e26i	−3.10215	−	2.09040i
$595$		−	2.87400e25i		−	0.126060i
$596$	3.33051e24	−	1.34909e24i	0.0143771	−	0.00582375i
$597$			8.04246e25i			0.341690i
$598$	−3.73466e25	+	5.54223e25i	−0.156167	+	0.231752i
$599$	−1.93079e25			−0.0794659			−0.0397329	−	0.999210i	$-0.512651\pi$
$599$	−1.93079e25			−0.0794659			−0.0397329	+	0.999210i	$0.512651\pi$
$600$	3.25970e25	+	6.88279e24i	0.132051	+	0.0278822i
$601$	7.48742e25			0.298555			0.149278	−	0.988795i	$-0.452305\pi$
$601$	7.48742e25			0.298555			0.149278	+	0.988795i	$0.452305\pi$
$602$	−5.69649e25	+	8.45358e25i	−0.223584	+	0.331798i
$603$		−	2.96458e26i		−	1.14538i
$604$	−5.73148e25	−	1.41493e26i	−0.217979	−	0.538125i
$605$			1.47654e26i			0.552800i
$606$	6.58011e25	+	4.43404e25i	0.242517	+	0.163422i
$607$	2.83453e26			1.02846			0.514232	−	0.857651i	$-0.328077\pi$
$607$	2.83453e26			1.02846			0.514232	+	0.857651i	$0.328077\pi$
$608$	2.02884e25	+	1.13569e26i	0.0724710	+	0.405672i
$609$	5.95997e26			2.09594
$610$	1.53574e26	+	1.03486e26i	0.531721	+	0.358303i
$611$			4.67694e25i			0.159430i
$612$	5.84792e25	+	1.44368e26i	0.196274	+	0.484542i
$613$		−	3.37082e26i		−	1.11394i	−0.830533	−	0.556969i	$-0.811964\pi$
$613$		−	3.37082e26i		−	1.11394i	0.830533	−	0.556969i	$-0.188036\pi$
$614$	2.42480e26	−	3.59839e26i	0.788998	−	1.17087i
$615$	−6.55433e26			−2.09998
$616$	2.32079e26	+	4.90031e25i	0.732183	+	0.154599i
$617$	−2.70240e26			−0.839539			−0.419770	−	0.907631i	$-0.637889\pi$
$617$	−2.70240e26			−0.839539			−0.419770	+	0.907631i	$0.637889\pi$
$618$	1.30526e26	−	1.93700e26i	0.399307	−	0.592571i
$619$		−	1.36859e26i		−	0.412299i	−0.978521	−	0.206149i	$-0.933907\pi$
$619$		−	1.36859e26i		−	0.412299i	0.978521	−	0.206149i	$-0.0660933\pi$
$620$	2.42564e26	−	9.82557e25i	0.719622	−	0.291499i
$621$			1.53575e27i			4.48695i
$622$	−3.61460e26	−	2.43572e26i	−1.04004	−	0.700839i
$623$	9.52789e23			0.00269998
$624$	9.17425e25	−	8.89139e25i	0.256045	−	0.248151i
$625$	−3.87855e26			−1.06613
$626$	2.71907e26	+	1.83226e26i	0.736147	+	0.496056i
$627$		−	3.62837e26i		−	0.967541i
$628$	9.65638e24	−	3.91153e24i	0.0253628	−	0.0102738i
$629$			3.98064e25i			0.102985i
$630$	−3.55590e26	+	5.27695e26i	−0.906180	+	1.34477i
$631$	−4.79896e26			−1.20467			−0.602336	−	0.798243i	$-0.705763\pi$
$631$	−4.79896e26			−1.20467			−0.602336	+	0.798243i	$0.705763\pi$
$632$	8.33359e25	−	3.94680e26i	0.206073	−	0.975962i
$633$	−1.05152e27			−2.56142
$634$	−2.77826e26	+	4.12294e26i	−0.666692	+	0.989371i
$635$			4.26791e26i			1.00894i
$636$	2.46756e26	+	6.09166e26i	0.574679	+	1.41871i
$637$			5.20564e25i			0.119440i
$638$	8.31581e26	+	5.60365e26i	1.87978	+	1.26670i
$639$	1.94127e27			4.32342
$640$	3.99217e26	−	2.51208e26i	0.875989	−	0.551217i
$641$	8.55974e25			0.185059			0.0925293	−	0.995710i	$-0.470505\pi$
$641$	8.55974e25			0.185059			0.0925293	+	0.995710i	$0.470505\pi$
$642$	−7.92461e26	−	5.34004e26i	−1.68809	−	1.13753i
$643$			3.96786e26i			0.832821i	0.909177	+	0.416411i	$0.136712\pi$
$643$			3.96786e26i			0.832821i	−0.909177	+	0.416411i	$0.863288\pi$
$644$	−1.62945e26	−	4.02263e26i	−0.336997	−	0.831944i
$645$		−	6.37531e26i		−	1.29922i
$646$	−2.31183e25	+	3.43076e25i	−0.0464246	+	0.0688940i
$647$	−5.95094e26			−1.17759			−0.588796	−	0.808282i	$-0.700398\pi$
$647$	−5.95094e26			−1.17759			−0.588796	+	0.808282i	$0.700398\pi$
$648$	3.31786e26	−	1.57134e27i	0.646988	−	3.06414i
$649$	1.92515e26			0.369948
$650$	3.95195e24	−	5.86469e24i	0.00748401	−	0.0111063i
$651$			4.60349e26i			0.859148i
$652$	3.75705e26	−	1.52188e26i	0.691027	−	0.279916i
$653$			1.29817e26i			0.235318i	0.993054	+	0.117659i	$0.0375390\pi$
$653$			1.29817e26i			0.235318i	−0.993054	+	0.117659i	$0.962461\pi$
$654$	1.96324e26	+	1.32294e26i	0.350739	+	0.236347i
$655$	6.68945e26			1.17787
$656$	−4.42896e26	+	4.29240e26i	−0.768626	+	0.744928i
$657$	4.69973e25			0.0803900
$658$	−2.51878e26	−	1.69729e26i	−0.424663	−	0.286161i
$659$			6.39727e26i			1.06312i	0.847020	+	0.531561i	$0.178395\pi$
$659$			6.39727e26i			1.06312i	−0.847020	+	0.531561i	$0.821605\pi$
$660$	−1.37494e27	+	5.56948e26i	−2.25224	+	0.912321i
$661$		−	1.19632e27i		−	1.93166i	−0.259168	−	0.965832i	$-0.583448\pi$
$661$		−	1.19632e27i		−	1.93166i	0.259168	−	0.965832i	$-0.416552\pi$
$662$	1.34223e25	−	1.99187e25i	0.0213637	−	0.0317037i
$663$	4.58137e25			0.0718814
$664$	−3.92846e26	−	8.29487e25i	−0.607611	−	0.128296i
$665$	−1.69005e26			−0.257688
$666$	4.92511e26	−	7.30885e26i	0.740305	−	1.09861i
$667$		−	1.83482e27i		−	2.71892i
$668$	−2.18120e26	−	5.38473e26i	−0.318655	−	0.786662i
$669$		−	5.57774e26i		−	0.803359i
$670$	−2.66966e26	−	1.79896e26i	−0.379092	−	0.255453i
$671$	−5.48070e26			−0.767311
$672$	1.45909e26	+	8.16757e26i	0.201407	+	1.12742i
$673$	−1.12227e27			−1.52741			−0.763704	−	0.645567i	$-0.776621\pi$
$673$	−1.12227e27			−1.52741			−0.763704	+	0.645567i	$0.776621\pi$
$674$	8.44036e25	+	5.68758e25i	0.113264	+	0.0763235i
$675$		−	1.62511e26i		−	0.215029i
$676$	2.77580e26	+	6.85262e26i	0.362156	+	0.894053i
$677$			8.45276e26i			1.08744i	0.839266	+	0.543721i	$0.182985\pi$
$677$			8.45276e26i			1.08744i	−0.839266	+	0.543721i	$0.817015\pi$
$678$	−6.09982e26	+	9.05213e26i	−0.773811	+	1.14834i
$679$	2.09387e26			0.261931
$680$	1.65492e26	+	3.49433e25i	0.204146	+	0.0431051i
$681$	2.12702e27			2.58747
$682$	−4.32827e26	+	6.42315e26i	−0.519233	+	0.770542i
$683$			1.04931e26i			0.124138i	0.998072	+	0.0620691i	$0.0197699\pi$
$683$			1.04931e26i			0.124138i	−0.998072	+	0.0620691i	$0.980230\pi$
$684$	8.48951e26	−	3.43886e26i	0.990489	−	0.401219i
$685$			1.45732e27i			1.67686i
$686$	−7.21868e26	−	4.86435e26i	−0.819179	−	0.552008i
$687$	−6.49001e26			−0.726367
$688$	−4.17517e26	−	4.30799e26i	−0.460876	−	0.475537i
$689$	1.39514e26			0.151892
$690$	2.25099e27	+	1.51684e27i	2.41717	+	1.62882i
$691$		−	8.44716e26i		−	0.894683i	−0.894363	−	0.447341i	$-0.852371\pi$
$691$		−	8.44716e26i		−	0.894683i	0.894363	−	0.447341i	$-0.147629\pi$
$692$	1.31871e27	−	5.34173e26i	1.37766	−	0.558051i
$693$		−	1.88322e27i		−	1.94060i
$694$	7.97947e25	−	1.18415e26i	0.0811071	−	0.120363i
$695$	−5.87070e26			−0.588619
$696$	−7.24637e26	+	3.43189e27i	−0.716692	+	3.39426i
$697$	−2.21170e26			−0.215782
$698$	5.55618e26	−	8.24537e26i	0.534749	−	0.793567i
$699$		−	1.07921e26i		−	0.102464i
$700$	1.72426e25	+	4.25667e25i	0.0161499	+	0.0398693i
$701$			1.24902e27i			1.15411i	0.816704	+	0.577056i	$0.195799\pi$
$701$			1.24902e27i			1.15411i	−0.816704	+	0.577056i	$0.804201\pi$
$702$	−5.16810e26	−	3.48255e26i	−0.471116	−	0.317464i
$703$	2.34081e26			0.210519
$704$	−5.64343e26	+	1.27679e27i	−0.500729	+	1.13287i
$705$	1.89955e27			1.66286
$706$	−5.34747e26	−	3.60342e26i	−0.461853	−	0.311222i
$707$			1.09381e26i			0.0932086i
$708$	2.52820e26	+	6.24136e26i	0.212567	+	0.524763i
$709$			1.88921e26i			0.156726i	0.996925	+	0.0783629i	$0.0249693\pi$
$709$			1.88921e26i			0.156726i	−0.996925	+	0.0783629i	$0.975031\pi$
$710$	1.17800e27	−	1.74815e27i	0.964251	−	1.43095i
$711$	−3.20266e27			−2.58672
$712$	−1.15844e24	+	5.48638e24i	−0.000923237	+	0.00437246i
$713$	1.41722e27			1.11451
$714$	−1.66261e26	+	2.46731e26i	−0.129020	+	0.191466i
$715$			3.14895e26i			0.241134i
$716$	−1.62991e27	+	6.60232e26i	−1.23166	+	0.498911i
$717$		−	1.80639e27i		−	1.34704i
$718$	−3.48060e26	−	2.34542e26i	−0.256137	−	0.172599i
$719$	2.45238e25			0.0178100			0.00890498	−	0.999960i	$-0.497165\pi$
$719$	2.45238e25			0.0178100			0.00890498	+	0.999960i	$0.497165\pi$
$720$	−2.60625e27	−	2.68916e27i	−1.86792	−	1.92734i
$721$	3.21987e26			0.227747
$722$	−9.86235e26	−	6.64579e26i	−0.688457	−	0.463920i
$723$			4.93577e27i			3.40048i
$724$	9.49897e26	−	3.84777e26i	0.645892	−	0.261633i
$725$			1.94157e26i			0.130299i
$726$	8.54175e26	−	1.26760e27i	0.565782	−	0.839620i
$727$	2.20831e27			1.44372			0.721861	−	0.692038i	$-0.243287\pi$
$727$	2.20831e27			1.44372			0.721861	+	0.692038i	$0.243287\pi$
$728$	1.72319e26	+	3.63849e25i	0.111195	+	0.0234786i
$729$	−3.76235e27			−2.39633
$730$	2.85188e25	−	4.23219e25i	0.0179293	−	0.0266071i
$731$		−	2.15129e26i		−	0.133501i
$732$	−7.19751e26	−	1.77685e27i	−0.440887	−	1.08842i
$733$		−	9.24345e26i		−	0.558916i	−0.960158	−	0.279458i	$-0.909845\pi$
$733$		−	9.24345e26i		−	0.558916i	0.960158	−	0.279458i	$-0.0901547\pi$
$734$	−1.70904e27	−	1.15165e27i	−1.02009	−	0.687395i
$735$	2.11428e27			1.24576
$736$	2.51444e27	−	4.49190e26i	1.46252	−	0.261271i
$737$	9.52739e26			0.547057
$738$	4.06090e27	+	2.73645e27i	2.30190	+	1.55115i
$739$		−	3.38925e27i		−	1.89662i	−0.317340	−	0.948312i	$-0.602790\pi$
$739$		−	3.38925e27i		−	1.89662i	0.317340	−	0.948312i	$-0.397210\pi$
$740$	−3.59311e26	−	8.87029e26i	−0.198504	−	0.490046i
$741$		−	2.69406e26i		−	0.146938i
$742$	−5.06306e26	+	7.51358e26i	−0.272632	+	0.404585i
$743$	−6.83961e26			−0.363611			−0.181806	−	0.983334i	$-0.558194\pi$
$743$	−6.83961e26			−0.363611			−0.181806	+	0.983334i	$0.558194\pi$
$744$	−2.65080e27	−	5.59711e26i	−1.39134	−	0.293779i
$745$	−3.09801e25			−0.0160545
$746$	6.47358e26	−	9.60678e26i	0.331227	−	0.491540i
$747$			3.18777e27i			1.61043i
$748$	−4.63960e26	+	1.87937e26i	−0.231428	+	0.0937448i
$749$		−	1.31730e27i		−	0.648796i
$750$	3.10735e27	+	2.09390e27i	1.51115	+	1.01830i
$751$	9.08813e26			0.436410			0.218205	−	0.975903i	$-0.429980\pi$
$751$	9.08813e26			0.436410			0.218205	+	0.975903i	$0.429980\pi$
$752$	1.28358e27	−	1.24401e27i	0.608632	−	0.589867i
$753$	−3.31434e27			−1.55183
$754$	6.17449e26	+	4.16071e26i	0.285479	+	0.192371i
$755$			1.31615e27i			0.600911i
$756$	3.75107e27	−	1.51946e27i	1.69121	−	0.685064i
$757$			3.88800e27i			1.73107i	0.500845	+	0.865537i	$0.333023\pi$
$757$			3.88800e27i			1.73107i	−0.500845	+	0.865537i	$0.666977\pi$
$758$	−1.17859e27	+	1.74903e27i	−0.518210	+	0.769023i
$759$	−8.03328e27			−3.48816
$760$	2.05483e26	−	9.73172e26i	0.0881145	−	0.417311i
$761$	2.48281e27			1.05145			0.525726	−	0.850654i	$-0.323794\pi$
$761$	2.48281e27			1.05145			0.525726	+	0.850654i	$0.323794\pi$
$762$	2.46898e27	−	3.66397e27i	1.03263	−	1.53243i
$763$			3.26347e26i			0.134802i
$764$	1.64432e27	+	4.05932e27i	0.670808	+	1.65602i
$765$		−	1.34289e27i		−	0.541076i
$766$	−3.05425e27	−	2.05812e27i	−1.21544	−	0.819027i
$767$	1.42943e26			0.0561831
$768$	−4.88048e27	−	1.52868e26i	−1.89466	−	0.0593451i
$769$	−7.20400e26			−0.276232			−0.138116	−	0.990416i	$-0.544105\pi$
$769$	−7.20400e26			−0.276232			−0.138116	+	0.990416i	$0.544105\pi$
$770$	−1.69588e27	−	1.14277e27i	−0.642291	−	0.432811i
$771$		−	5.85633e27i		−	2.19083i
$772$	7.07354e26	+	1.74624e27i	0.261380	+	0.645268i
$773$		−	1.30265e27i		−	0.475468i	−0.971330	−	0.237734i	$-0.923595\pi$
$773$		−	1.30265e27i		−	0.475468i	0.971330	−	0.237734i	$-0.0764047\pi$
$774$	−2.66171e27	+	3.94998e27i	−0.959671	+	1.42415i
$775$	−1.49967e26			−0.0534109
$776$	−2.54582e26	+	1.20570e27i	−0.0895655	+	0.424183i
$777$	1.68345e27			0.585060
$778$	−2.63604e27	+	3.91189e27i	−0.904996	+	1.34301i
$779$			1.30059e27i			0.441096i
$780$	−1.02089e27	+	4.13535e26i	−0.342043	+	0.138552i
$781$			6.23873e27i			2.06496i
$782$	7.59577e26	+	5.11845e26i	0.248375	+	0.167369i
$783$	1.71095e28			5.52715
$784$	1.42869e27	−	1.38464e27i	0.455968	−	0.441909i
$785$	−8.98228e25			−0.0283220
$786$	−5.74284e27	−	3.86984e27i	−1.78901	−	1.20553i
$787$		−	1.96729e27i		−	0.605493i	−0.953071	−	0.302747i	$-0.902096\pi$
$787$		−	1.96729e27i		−	0.605493i	0.953071	−	0.302747i	$-0.0979036\pi$
$788$	−1.03039e27	+	4.17383e26i	−0.313331	+	0.126922i
$789$			3.17788e27i			0.954787i
$790$	−1.94343e27	+	2.88405e27i	−0.576915	+	0.856141i
$791$	−1.50473e27			−0.441349
$792$	1.08440e28	+	2.28970e27i	3.14269	+	0.663573i
$793$	−4.06942e26			−0.116530
$794$	3.33901e27	−	4.95509e27i	0.944763	−	1.40203i
$795$		−	5.66641e27i		−	1.58424i
$796$	−2.44965e26	−	6.04743e26i	−0.0676751	−	0.167069i
$797$		−	1.83306e27i		−	0.500407i	−0.968193	−	0.250203i	$-0.919502\pi$
$797$		−	1.83306e27i		−	0.500407i	0.968193	−	0.250203i	$-0.0804975\pi$
$798$	1.45090e27	+	9.77694e26i	0.391390	+	0.263740i
$799$	6.40987e26			0.170866
$800$	−2.66073e26	+	4.75325e25i	−0.0700885	+	0.0125209i
$801$	4.45196e25			0.0115889
$802$	−4.18667e27	−	2.82121e27i	−1.07699	−	0.725735i
$803$			1.51037e26i			0.0383960i
$804$	1.25118e27	+	3.08879e27i	0.314332	+	0.775990i
$805$			3.74181e27i			0.929011i
$806$	−3.21374e26	+	4.76919e26i	−0.0788548	+	0.117020i
$807$	−8.83588e27			−2.14265
$808$	−6.29839e26	−	1.32989e26i	−0.150946	−	0.0318720i
$809$	−5.01713e27			−1.18835			−0.594175	−	0.804336i	$-0.702521\pi$
$809$	−5.01713e27			−1.18835			−0.594175	+	0.804336i	$0.702521\pi$
$810$	−7.73740e27	+	1.14823e28i	−1.81129	+	2.68795i
$811$		−	8.52097e26i		−	0.197147i	−0.995130	−	0.0985737i	$-0.968572\pi$
$811$		−	8.52097e26i		−	0.197147i	0.995130	−	0.0985737i	$-0.0314280\pi$
$812$	−4.48153e27	+	1.81534e27i	−1.02481	+	0.415122i
$813$		−	1.37255e28i		−	3.10219i
$814$	2.34888e27	+	1.58280e27i	0.524721	+	0.353586i
$815$	−3.49478e27			−0.771653
$816$	−1.21859e27	−	1.25735e27i	−0.265950	−	0.274411i
$817$	−1.26506e27			−0.272899
$818$	5.83933e27	+	3.93486e27i	1.24511	+	0.839022i
$819$		−	1.39829e27i		−	0.294714i
$820$	4.92845e27	−	1.99638e27i	1.02678	−	0.415921i
$821$		−	6.09515e25i		−	0.0125523i	−0.999980	−	0.00627616i	$-0.998002\pi$
$821$		−	6.09515e25i		−	0.0125523i	0.999980	−	0.00627616i	$-0.00199778\pi$
$822$	8.43061e27	−	1.25110e28i	1.71624	−	2.54689i
$823$	3.83071e27			0.770870			0.385435	−	0.922735i	$-0.374051\pi$
$823$	3.83071e27			0.770870			0.385435	+	0.922735i	$0.374051\pi$
$824$	−3.91485e26	+	1.85408e27i	−0.0778765	+	0.368824i
$825$	8.50067e26			0.167163
$826$	−5.18749e26	+	7.69823e26i	−0.100843	+	0.149651i
$827$		−	5.23010e27i		−	1.00510i	−0.864549	−	0.502548i	$-0.832396\pi$
$827$		−	5.23010e27i		−	1.00510i	0.864549	−	0.502548i	$-0.167604\pi$
$828$	−7.61371e27	−	1.87959e28i	−1.44647	−	3.57089i
$829$		−	5.22266e27i		−	0.980898i	−0.871470	−	0.490449i	$-0.836833\pi$
$829$		−	5.22266e27i		−	0.980898i	0.871470	−	0.490449i	$-0.163167\pi$
$830$	2.87065e27	+	1.93440e27i	0.533013	+	0.359174i
$831$	5.08516e27			0.933458
$832$	−4.19025e26	+	9.48015e26i	−0.0760446	+	0.172046i
$833$	7.13446e26			0.128007
$834$	5.03995e27	+	3.39619e27i	0.894023	+	0.602442i
$835$			5.00883e27i			0.878446i
$836$	1.10516e27	+	2.72831e27i	0.191631	+	0.473079i
$837$			1.32154e28i			2.26563i
$838$	−3.42339e27	+	5.08031e27i	−0.580281	+	0.861137i
$839$	5.21861e27			0.874614			0.437307	−	0.899312i	$-0.355932\pi$
$839$	5.21861e27			0.874614			0.437307	+	0.899312i	$0.355932\pi$
$840$	1.47778e27	−	6.99879e27i	0.244882	−	1.15976i
$841$	−1.43381e28			−2.34924
$842$	−2.10827e27	+	3.12867e27i	−0.341555	+	0.506868i
$843$			2.27909e28i			3.65090i
$844$	7.90676e27	−	3.20281e27i	1.25241	−	0.507315i
$845$		−	6.37425e27i		−	0.998367i
$846$	−1.17691e28	−	7.93069e27i	−1.82275	−	1.22827i
$847$	2.10711e27			0.322698
$848$	−3.71091e27	−	3.82896e27i	−0.561978	−	0.579856i
$849$	1.25732e28			1.88288
$850$	−8.03771e25	−	5.41625e25i	−0.0119029	−	0.00802082i
$851$		−	5.18260e27i		−	0.758957i
$852$	−2.02260e28	+	8.19300e27i	−2.92910	+	1.18650i
$853$			6.83904e27i			0.979444i	0.871879	+	0.489722i	$0.162902\pi$
$853$			6.83904e27i			0.979444i	−0.871879	+	0.489722i	$0.837098\pi$
$854$	1.47682e27	−	2.19160e27i	0.209160	−	0.310393i
$855$	−7.89686e27			−1.10605
$856$	7.58533e27	+	1.60163e27i	1.05069	+	0.221851i
$857$	1.11397e28			1.52600			0.762999	−	0.646400i	$-0.223726\pi$
$857$	1.11397e28			1.52600			0.762999	+	0.646400i	$0.223726\pi$
$858$	1.82166e27	−	2.70335e27i	0.246796	−	0.366246i
$859$		−	5.20147e27i		−	0.696934i	−0.937321	−	0.348467i	$-0.886702\pi$
$859$		−	5.20147e27i		−	0.696934i	0.937321	−	0.348467i	$-0.113298\pi$
$860$	1.94185e27	+	4.79384e27i	0.257324	+	0.635255i
$861$			9.35346e27i			1.22586i
$862$	1.00141e28	+	6.74807e27i	1.29806	+	0.874703i
$863$	−3.28370e27			−0.420980			−0.210490	−	0.977596i	$-0.567506\pi$
$863$	−3.28370e27			−0.420980			−0.210490	+	0.977596i	$0.567506\pi$
$864$	4.18867e27	+	2.34470e28i	0.531124	+	2.97308i
$865$	−1.22665e28			−1.53840
$866$	−6.25603e27	−	4.21566e27i	−0.776031	−	0.522932i
$867$			1.48220e28i			1.81855i
$868$	−1.40217e27	−	3.46154e27i	−0.170163	−	0.420080i
$869$		−	1.02925e28i		−	1.23547i
$870$	1.68989e28	−	2.50779e28i	2.00643	−	2.97754i
$871$	7.07410e26			0.0830804
$872$	−1.87918e27	−	3.96786e26i	−0.218304	−	0.0460946i
$873$	9.78374e27			1.12427
$874$	3.00989e27	−	4.46668e27i	0.342131	−	0.507722i
$875$			5.16532e27i			0.580792i
$876$	−4.89664e26	+	1.98349e26i	−0.0544640	+	0.0220618i
$877$			3.30000e27i			0.363093i	0.983382	+	0.181546i	$0.0581102\pi$
$877$			3.30000e27i			0.363093i	−0.983382	+	0.181546i	$0.941890\pi$
$878$	1.02555e28	+	6.91070e27i	1.11624	+	0.752184i
$879$	−2.21500e28			−2.38495
$880$	8.64227e27	−	8.37581e27i	0.920540	−	0.892158i
$881$	1.30695e28			1.37717			0.688586	−	0.725155i	$-0.258232\pi$
$881$	1.30695e28			1.37717			0.688586	+	0.725155i	$0.258232\pi$
$882$	−1.30996e28	−	8.82721e27i	−1.36554	−	0.920178i
$883$			7.16198e27i			0.738595i	0.929311	+	0.369297i	$0.120402\pi$
$883$			7.16198e27i			0.738595i	−0.929311	+	0.369297i	$0.879598\pi$
$884$	−3.44491e26	+	1.39543e26i	−0.0351464	+	0.0142368i
$885$		−	5.80566e27i		−	0.585990i
$886$	−6.03859e27	+	8.96126e27i	−0.602997	+	0.894847i
$887$	−1.66024e28			−1.64020			−0.820101	−	0.572219i	$-0.806083\pi$
$887$	−1.66024e28			−1.64020			−0.820101	+	0.572219i	$0.806083\pi$
$888$	−2.04680e27	+	9.69369e27i	−0.200057	+	0.947471i
$889$	6.09059e27			0.588969
$890$	2.70153e25	−	4.00907e25i	0.00258467	−	0.00383565i
$891$		−	4.09777e28i		−	3.87890i
$892$	1.69892e27	+	4.19411e27i	0.159113	+	0.392802i
$893$		−	3.76931e27i		−	0.349279i
$894$	2.65962e26	+	1.79220e26i	0.0243844	+	0.0164316i
$895$	1.51613e28			1.37536
$896$	−3.58490e27	−	5.69708e27i	−0.321774	−	0.511360i
$897$	−5.96472e27			−0.529738
$898$	−5.56362e27	−	3.74908e27i	−0.488914	−	0.329457i
$899$		−	1.57889e28i		−	1.37289i
$900$	8.05669e26	+	1.98895e27i	0.0693191	+	0.171128i
$901$		−	1.91208e27i		−	0.162787i
$902$	−8.79425e27	+	1.30507e28i	−0.740861	+	1.09944i
$903$	−9.09799e27			−0.758424
$904$	1.82951e27	−	8.66458e27i	0.150916	−	0.714739i
$905$	−8.83585e27			−0.721252
$906$	7.61394e27	−	1.12991e28i	0.615023	−	0.912694i
$907$			7.94729e27i			0.635257i	0.948215	+	0.317629i	$0.102887\pi$
$907$			7.94729e27i			0.635257i	−0.948215	+	0.317629i	$0.897113\pi$
$908$	−1.59939e28	+	6.47868e27i	−1.26514	+	0.512473i
$909$			5.11087e27i			0.400072i
$910$	−1.25919e27	−	8.48510e26i	−0.0975433	−	0.0657301i
$911$	7.55273e27			0.579001			0.289500	−	0.957178i	$-0.406511\pi$
$911$	7.55273e27			0.579001			0.289500	+	0.957178i	$0.406511\pi$
$912$	−7.39385e27	+	7.16589e27i	−0.560944	+	0.543649i
$913$	−1.02447e28			−0.769176
$914$	1.28089e28	+	8.63132e27i	0.951748	+	0.641340i
$915$			1.65281e28i			1.21541i
$916$	4.88009e27	−	1.97679e27i	0.355157	−	0.143864i
$917$		−	9.54629e27i		−	0.687584i
$918$	−4.77292e27	+	7.08301e27i	−0.340235	+	0.504908i
$919$	1.42129e28			1.00273			0.501367	−	0.865235i	$-0.332831\pi$
$919$	1.42129e28			1.00273			0.501367	+	0.865235i	$0.332831\pi$
$920$	−2.15462e28	−	4.54944e27i	−1.50448	−	0.317668i
$921$	3.87270e28			2.67638
$922$	4.75155e27	−	7.05129e27i	0.325006	−	0.482308i
$923$			4.63226e27i			0.313601i
$924$	7.94802e27	+	1.96213e28i	0.532568	+	1.31475i
$925$			5.48414e26i			0.0363716i
$926$	1.73443e27	+	1.16876e27i	0.113855	+	0.0767219i
$927$	1.50450e28			0.977541
$928$	−5.00434e27	−	2.80129e28i	−0.321841	−	1.80157i
$929$	1.48036e28			0.942362			0.471181	−	0.882037i	$-0.343828\pi$
$929$	1.48036e28			0.942362			0.471181	+	0.882037i	$0.343828\pi$
$930$	1.93702e28	+	1.30527e28i	1.22052	+	0.822456i
$931$		−	4.19541e27i		−	0.261669i
$932$	3.28715e26	+	8.11498e26i	0.0202940	+	0.0500998i
$933$		−	3.89014e28i		−	2.37733i
$934$	−1.40667e28	+	2.08749e28i	−0.850934	+	1.26279i
$935$	4.31571e27			0.258430
$936$	8.05170e27	+	1.70010e27i	0.477273	+	0.100775i
$937$	−2.39822e28			−1.40722			−0.703611	−	0.710586i	$-0.748430\pi$
$937$	−2.39822e28			−1.40722			−0.703611	+	0.710586i	$0.748430\pi$
$938$	−2.56724e27	+	3.80978e27i	−0.149121	+	0.221296i
$939$			2.92634e28i			1.68268i
$940$	−1.42835e28	+	5.78583e27i	−0.813053	+	0.329345i
$941$		−	7.77486e27i		−	0.438118i	−0.975712	−	0.219059i	$-0.929701\pi$
$941$		−	7.77486e27i		−	0.438118i	0.975712	−	0.219059i	$-0.0702987\pi$
$942$	7.71122e26	+	5.19624e26i	0.0430169	+	0.0289872i
$943$	2.87952e28			1.59023
$944$	−3.80210e27	−	3.92306e27i	−0.207869	−	0.214482i
$945$	−3.48922e28			−1.88854
$946$	−1.26942e28	−	8.55406e27i	−0.680205	−	0.458360i
$947$			2.74522e28i			1.45630i	0.685416	+	0.728152i	$0.259620\pi$
$947$			2.74522e28i			1.45630i	−0.685416	+	0.728152i	$0.740380\pi$
$948$	3.33684e28	−	1.35166e28i	1.75249	−	0.709886i
$949$			1.12145e26i			0.00583111i
$950$	−3.18502e26	+	4.72656e26i	−0.0163960	+	0.0243316i
$951$	−4.43723e28			−2.26150
$952$	4.98664e26	−	2.36168e27i	0.0251627	−	0.119171i
$953$	−3.58967e28			−1.79338			−0.896690	−	0.442659i	$-0.854035\pi$
$953$	−3.58967e28			−1.79338			−0.896690	+	0.442659i	$0.854035\pi$
$954$	−2.36574e28	+	3.51076e28i	−1.17020	+	1.73657i
$955$		−	3.77594e28i		−	1.84924i
$956$	5.50207e27	+	1.35829e28i	0.266794	+	0.658634i
$957$			8.94972e28i			4.29681i
$958$	−1.83610e28	−	1.23726e28i	−0.872817	−	0.588152i
$959$	2.07970e28			0.978867
$960$	3.85039e28	+	1.70188e28i	1.79444	+	0.793145i
$961$	−9.47527e27			−0.437240
$962$	1.74404e27	+	1.17523e27i	0.0796881	+	0.0536983i
$963$		−	6.15517e28i		−	2.78477i
$964$	−1.50338e28	−	3.71139e28i	−0.673499	−	1.66267i
$965$		−	1.62434e28i		−	0.720555i
$966$	2.16464e28	−	3.21232e28i	0.950828	−	1.41103i
$967$	−3.95436e27			−0.171998			−0.0859992	−	0.996295i	$-0.527408\pi$
$967$	−3.95436e27			−0.171998			−0.0859992	+	0.996295i	$0.527408\pi$
$968$	−2.56191e27	+	1.21333e28i	−0.110344	+	0.522591i
$969$	−3.69229e27			−0.157478
$970$	5.93695e27	−	8.81043e27i	0.250745	−	0.372105i
$971$			3.30188e28i			1.38095i	0.723354	+	0.690477i	$0.242599\pi$
$971$			3.30188e28i			1.38095i	−0.723354	+	0.690477i	$0.757401\pi$
$972$	6.52626e28	−	2.64361e28i	2.70293	−	1.09488i
$973$			8.37787e27i			0.343607i
$974$	−1.19842e27	−	8.07563e26i	−0.0486743	−	0.0327994i
$975$	6.31175e26			0.0253867
$976$	1.08242e28	+	1.11685e28i	0.431143	+	0.444859i
$977$	4.86322e28			1.91834			0.959170	−	0.282831i	$-0.0912734\pi$
$977$	4.86322e28			1.91834			0.959170	+	0.282831i	$0.0912734\pi$
$978$	3.00024e28	+	2.02173e28i	1.17202	+	0.789774i
$979$			1.43074e26i			0.00553511i
$980$	−1.58981e28	+	6.43988e27i	−0.609113	+	0.246735i
$981$			1.52488e28i			0.578600i
$982$	−3.55706e27	+	5.27867e27i	−0.133669	+	0.198365i
$983$	3.73367e27			0.138956			0.0694780	−	0.997583i	$-0.477867\pi$
$983$	3.73367e27			0.138956			0.0694780	+	0.997583i	$0.477867\pi$
$984$	−5.38594e28	−	1.13723e28i	−1.98522	−	0.419175i
$985$	9.58461e27			0.349889
$986$	5.70236e27	−	8.46230e27i	0.206169	−	0.305955i
$987$		−	2.71079e28i		−	0.970694i
$988$	8.20583e26	+	2.02577e27i	0.0291026	+	0.0718454i
$989$			2.80088e28i			0.983850i
$990$	−7.92407e28	−	5.33967e28i	−2.75686	−	1.85772i
$991$	−3.36373e28			−1.15910			−0.579550	−	0.814936i	$-0.696772\pi$
$991$	−3.36373e28			−1.15910			−0.579550	+	0.814936i	$0.696772\pi$
$992$	2.16372e28	−	3.86536e27i	0.738482	−	0.131926i
$993$	2.14371e27			0.0724684
$994$	−2.49472e28	−	1.68108e28i	−0.835317	−	0.562882i
$995$			5.62527e27i			0.186562i
$996$	−1.34538e28	−	3.32134e28i	−0.441958	−	1.09106i
$997$			3.77219e28i			1.22741i	0.789536	+	0.613704i	$0.210321\pi$
$997$			3.77219e28i			1.22741i	−0.789536	+	0.613704i	$0.789679\pi$
$998$	4.35402e26	−	6.46136e26i	0.0140330	−	0.0208250i
$999$	4.83275e28			1.54284

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8.20.b.a.5.3	✓	18
3.2	odd	2		72.20.d.b.37.16		18
4.3	odd	2		32.20.b.a.17.18		18
8.3	odd	2		32.20.b.a.17.1		18
8.5	even	2	inner	8.20.b.a.5.4	yes	18
24.5	odd	2		72.20.d.b.37.15		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8.20.b.a.5.3	✓	18	1.1	even	1	trivial
8.20.b.a.5.4	yes	18	8.5	even	2	inner
32.20.b.a.17.1		18	8.3	odd	2
32.20.b.a.17.18		18	4.3	odd	2
72.20.d.b.37.15		18	24.5	odd	2
72.20.d.b.37.16		18	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-600.469 - 404.629i) q^{2} -64624.3i q^{3} +(196838. + 485935. i) q^{4} -4.52012e6i q^{5} +(-2.61489e7 + 3.88049e7i) q^{6} -6.45051e7 q^{7} +(7.84279e7 - 3.71435e8i) q^{8} -3.01404e9 q^{9} +O(q^{10})\)	\(q+(-600.469 - 404.629i) q^{2} -64624.3i q^{3} +(196838. + 485935. i) q^{4} -4.52012e6i q^{5} +(-2.61489e7 + 3.88049e7i) q^{6} -6.45051e7 q^{7} +(7.84279e7 - 3.71435e8i) q^{8} -3.01404e9 q^{9} +(-1.82897e9 + 2.71419e9i) q^{10} -9.68633e9i q^{11} +(3.14032e10 - 1.27205e10i) q^{12} -7.19211e9i q^{13} +(3.87333e10 + 2.61006e10i) q^{14} -2.92109e11 q^{15} +(-1.97387e11 + 1.91301e11i) q^{16} -9.85697e10 q^{17} +(1.80984e12 + 1.21957e12i) q^{18} +5.79637e11i q^{19} +(2.19648e12 - 8.89734e11i) q^{20} +4.16860e12i q^{21} +(-3.91937e12 + 5.81634e12i) q^{22} +1.28333e13 q^{23} +(-2.40037e13 - 5.06835e12i) q^{24} -1.35800e12 q^{25} +(-2.91014e12 + 4.31864e12i) q^{26} +1.19670e14i q^{27} +(-1.26971e13 - 3.13453e13i) q^{28} -1.42973e14i q^{29} +(1.75403e14 + 1.18196e14i) q^{30} +1.10433e14 q^{31} +(1.95931e14 - 3.50020e13i) q^{32} -6.25972e14 q^{33} +(5.91880e13 + 3.98842e13i) q^{34} +2.91571e14i q^{35} +(-5.93278e14 - 1.46462e15i) q^{36} -4.03841e14i q^{37} +(2.34538e14 - 3.48054e14i) q^{38} -4.64785e14 q^{39} +(-1.67893e15 - 3.54503e14i) q^{40} +2.24379e15 q^{41} +(1.68674e15 - 2.50311e15i) q^{42} +2.18251e15i q^{43} +(4.70692e15 - 1.90664e15i) q^{44} +1.36238e16i q^{45} +(-7.70599e15 - 5.19272e15i) q^{46} -6.50288e15 q^{47} +(1.23627e16 + 1.27560e16i) q^{48} -7.23799e15 q^{49} +(8.15434e14 + 5.49484e14i) q^{50} +6.36999e15i q^{51} +(3.49489e15 - 1.41568e15i) q^{52} +1.93982e16i q^{53} +(4.84218e16 - 7.18579e16i) q^{54} -4.37834e16 q^{55} +(-5.05900e15 + 2.39595e16i) q^{56} +3.74586e16 q^{57} +(-5.78511e16 + 8.58510e16i) q^{58} +1.98749e16i q^{59} +(-5.74984e16 - 1.41946e17i) q^{60} -5.65818e16i q^{61} +(-6.63115e16 - 4.46843e16i) q^{62} +1.94421e17 q^{63} +(-1.31813e17 - 5.82618e16i) q^{64} -3.25092e16 q^{65} +(3.75877e17 + 2.53287e17i) q^{66} +9.83592e16i q^{67} +(-1.94023e16 - 4.78984e16i) q^{68} -8.29342e17i q^{69} +(1.17978e17 - 1.75079e17i) q^{70} -6.44076e17 q^{71} +(-2.36384e17 + 1.11952e18i) q^{72} -1.55928e16 q^{73} +(-1.63406e17 + 2.42494e17i) q^{74} +8.77595e16i q^{75} +(-2.81666e17 + 1.14095e17i) q^{76} +6.24818e17i q^{77} +(2.79089e17 + 1.88065e17i) q^{78} +1.06258e18 q^{79} +(8.64705e17 + 8.92213e17i) q^{80} +4.23046e18 q^{81} +(-1.34733e18 - 9.07904e17i) q^{82} -1.05764e18i q^{83} +(-2.02567e18 + 8.20540e17i) q^{84} +4.45547e17i q^{85} +(8.83106e17 - 1.31053e18i) q^{86} -9.23953e18 q^{87} +(-3.59785e18 - 7.59678e17i) q^{88} -1.47708e16 q^{89} +(5.51259e18 - 8.18067e18i) q^{90} +4.63927e17i q^{91} +(2.52609e18 + 6.23614e18i) q^{92} -7.13664e18i q^{93} +(3.90478e18 + 2.63125e18i) q^{94} +2.62003e18 q^{95} +(-2.26198e18 - 1.26619e19i) q^{96} -3.24606e18 q^{97} +(4.34619e18 + 2.92870e18i) q^{98} +2.91949e19i 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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