LMFDB - Embedded newform 4.31.b.a.3.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4,31,Mod(3,4)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 31, names="a")

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

chi := DirichletCharacter("4.3");

S:= CuspForms(chi, 31);

N := Newforms(S);

Level:	$ N $	$=$	$ 4 = 2^{2} $
Weight:	$ k $	$=$	$ 31 $
Character orbit:	$[\chi]$	$=$	4.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:	$22.8057047611$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 7 x^{13} + 7040347091761 x^{12} - 42242082550475 x^{11} + \cdots + 48\!\cdots\!00 $ x^14 - 7x^13 + 7040347091761x^12 - 42242082550475x^11 + 18008728830670915101223295x^10 - 90043644152967356416070621x^9 + 21189728137694531984698973691059207547x^8 - 84758912550237866073878555288648461401x^7 + 12092215554238283620631700081914283098967933222660x^6 - 36276646662418194667969645897789716351627569494760x^5 + 3068812077928688267104132515948151981977982628865973479570704x^4 - 6137624155796915456437666926180996318216113616424689721741328x^3 + 240224517591297395963498654659405852693819346574594371107838616625453504x^2 - 240224517588228583885606243038964074803354751677171360185114000107450880*x + 4800851985577239247844026939439062575281134066464418947338032535601205573916876800
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	multiple of $ 2^{182}\cdot 3^{19}\cdot 5^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			3.8
Root			$0.500000 - 868866. i$ of defining polynomial
Character	$\chi$	$=$	4.3
Dual form			4.31.b.a.3.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-713.932 + 32760.2i) q^{2} +1.39019e7i q^{3} +(-1.07272e9 - 4.67771e7i) q^{4} -5.42656e10 q^{5} +(-4.55428e11 - 9.92498e9i) q^{6} -5.92817e11i q^{7} +(2.29828e12 - 3.51092e13i) q^{8} +1.26296e13 q^{9} +O(q^{10})$	\(q+(-713.932 + 32760.2i) q^{2} +1.39019e7i q^{3} +(-1.07272e9 - 4.67771e7i) q^{4} -5.42656e10 q^{5} +(-4.55428e11 - 9.92498e9i) q^{6} -5.92817e11i q^{7} +(2.29828e12 - 3.51092e13i) q^{8} +1.26296e13 q^{9} +(3.87420e13 - 1.77775e15i) q^{10} +3.23456e15i q^{11} +(6.50289e14 - 1.49128e16i) q^{12} -2.32090e16 q^{13} +(1.94208e16 + 4.23231e14i) q^{14} -7.54393e17i q^{15} +(1.14855e18 + 1.00358e17i) q^{16} -3.10153e18 q^{17} +(-9.01667e15 + 4.13748e17i) q^{18} +2.48409e19i q^{19} +(5.82120e19 + 2.53839e18i) q^{20} +8.24125e18 q^{21} +(-1.05965e20 - 2.30926e18i) q^{22} -3.89198e20i q^{23} +(4.88083e20 + 3.19503e19i) q^{24} +2.01344e21 q^{25} +(1.65696e19 - 7.60332e20i) q^{26} +3.03784e21i q^{27} +(-2.77303e19 + 6.35928e20i) q^{28} +8.64231e21 q^{29} +(2.47141e22 + 5.38585e20i) q^{30} -1.93494e22i q^{31} +(-4.10772e21 + 3.75550e22i) q^{32} -4.49664e22 q^{33} +(2.21428e21 - 1.01607e23i) q^{34} +3.21696e22i q^{35} +(-1.35480e22 - 5.90776e20i) q^{36} -7.61448e22 q^{37} +(-8.13793e23 - 1.77347e22i) q^{38} -3.22648e23i q^{39} +(-1.24718e23 + 1.90522e24i) q^{40} -6.89135e23 q^{41} +(-5.88369e21 + 2.69985e23i) q^{42} -2.04687e24i q^{43} +(1.51303e23 - 3.46979e24i) q^{44} -6.85353e23 q^{45} +(1.27502e25 + 2.77861e23i) q^{46} -1.46478e25i q^{47} +(-1.39516e24 + 1.59669e25i) q^{48} +2.21879e25 q^{49} +(-1.43746e24 + 6.59606e25i) q^{50} -4.31170e25i q^{51} +(2.48968e25 + 1.08565e24i) q^{52} +3.50489e25 q^{53} +(-9.95204e25 - 2.16881e24i) q^{54} -1.75525e26i q^{55} +(-2.08133e25 - 1.36246e24i) q^{56} -3.45334e26 q^{57} +(-6.17002e24 + 2.83124e26i) q^{58} -4.94749e26i q^{59} +(-3.52883e25 + 8.09254e26i) q^{60} -2.04893e26 q^{61} +(6.33890e26 + 1.38141e25i) q^{62} -7.48704e24i q^{63} +(-1.22738e27 - 1.61382e26i) q^{64} +1.25945e27 q^{65} +(3.21029e25 - 1.47311e27i) q^{66} +3.08821e26i q^{67} +(3.32708e27 + 1.45081e26i) q^{68} +5.41057e27 q^{69} +(-1.05388e27 - 2.29669e25i) q^{70} -9.39686e26i q^{71} +(2.90263e25 - 4.43415e26i) q^{72} -1.34820e28 q^{73} +(5.43622e25 - 2.49452e27i) q^{74} +2.79905e28i q^{75} +(1.16198e27 - 2.66474e28i) q^{76} +1.91750e27 q^{77} +(1.05700e28 + 2.30349e26i) q^{78} +2.95997e28i q^{79} +(-6.23265e28 - 5.44598e27i) q^{80} -3.96313e28 q^{81} +(4.91996e26 - 2.25762e28i) q^{82} -6.94072e28i q^{83} +(-8.84058e27 - 3.85502e26i) q^{84} +1.68306e29 q^{85} +(6.70560e28 + 1.46133e27i) q^{86} +1.20144e29i q^{87} +(1.13563e29 + 7.43393e27i) q^{88} -1.83280e29 q^{89} +(4.89295e26 - 2.24523e28i) q^{90} +1.37587e28i q^{91} +(-1.82055e28 + 4.17501e29i) q^{92} +2.68992e29 q^{93} +(4.79864e29 + 1.04575e28i) q^{94} -1.34801e30i q^{95} +(-5.22083e29 - 5.71050e28i) q^{96} -5.60161e29 q^{97} +(-1.58407e28 + 7.26881e29i) q^{98} +4.08512e28i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 24476 q^{2} - 820787056 q^{4} + 14864798540 q^{5} - 454068012192 q^{6} - 31343321296064 q^{8} - 722181861644898 q^{9}+O(q^{10}) $ 14 * q - 24476 * q^2 - 820787056 * q^4 + 14864798540 * q^5 - 454068012192 * q^6 - 31343321296064 * q^8 - 722181861644898 * q^9	$ 14 q - 24476 q^{2} - 820787056 q^{4} + 14864798540 q^{5} - 454068012192 q^{6} - 31343321296064 q^{8} - 722181861644898 q^{9} - 12\!\cdots\!60 q^{10}+ \cdots + 47\!\cdots\!36 q^{98}+O(q^{100}) $ 14 * q - 24476 * q^2 - 820787056 * q^4 + 14864798540 * q^5 - 454068012192 * q^6 - 31343321296064 * q^8 - 722181861644898 * q^9 - 1287889809124760 * q^10 + 51879382052868480 * q^12 + 73473894124935532 * q^13 + 36761277666527808 * q^14 - 1064191557393108736 * q^16 - 4417201733411195812 * q^17 + 10773613739927673156 * q^18 + 31289641216539815840 * q^20 - 24107806000815293184 * q^21 - 63855041197225323360 * q^22 - 219200204962023547392 * q^24 + 2557307336405009852730 * q^25 + 2662172027973979655720 * q^26 + 2286217156307884458240 * q^28 - 5183126634353006173012 * q^29 - 19995309903793012445760 * q^30 + 42868919292290358744064 * q^32 + 45729663133049254147200 * q^33 + 189270161167001176158280 * q^34 - 265369932957818409094128 * q^36 - 627167100163080968189492 * q^37 - 1048227922470375880434720 * q^38 + 249748411367898391857280 * q^40 + 1494251155359817033760828 * q^41 + 2632732296455102155814400 * q^42 + 724029644533237152067200 * q^44 - 15629634719291168966183700 * q^45 + 6965410628317069602441408 * q^46 + 22826956997174454465976320 * q^48 + 36971394165784621527528302 * q^49 - 6257136580151365293802740 * q^50 - 3584406874106323077960032 * q^52 - 162298735436688848725454068 * q^53 + 103759862824624790541134016 * q^54 - 103480837826586244326484992 * q^56 - 178372120064399401723873920 * q^57 + 292818259345642447695165352 * q^58 + 673940775243590010378428160 * q^60 - 781363600109479145350441172 * q^61 - 700904834820308348700230400 * q^62 - 1886538399231001232282054656 * q^64 - 766208515593499839727344200 * q^65 + 4354147454872998865031212800 * q^66 - 1563708764577905097576648928 * q^68 + 12984546958279555654634831616 * q^69 + 5791600195068600540130627200 * q^70 - 12292930844134853078053553856 * q^72 - 13974688009272270633487568708 * q^73 - 1683916522088046880433965720 * q^74 - 43359191482193415443604585600 * q^76 - 13914563925551368590607269120 * q^77 + 103407672785786602276239960000 * q^78 - 142384583917045013024432289280 * q^80 + 142873441147816769491949878830 * q^81 + 100782649420724457106091722888 * q^82 - 274539668577865429004166211584 * q^84 - 166040172454330922908332123880 * q^85 + 409278053261716222570289186208 * q^86 - 745586494961630729936044285440 * q^88 + 98873747700972853801823899388 * q^89 + 1804754410453947165713321465640 * q^90 - 1825371837423533828188743456000 * q^92 - 123062607213511416597600107520 * q^93 + 2752292471954002780670205710208 * q^94 - 4054034025223909146350873812992 * q^96 - 1029388221334221132711894149732 * q^97 + 4774196460313129800493027312036 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/4\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$-1$

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 $

$2$	−713.932	+	32760.2i	−0.0217875	+	0.999763i
$2$	−713.932	+	32760.2i	−0.0217875	+	0.999763i
$3$			1.39019e7i			0.968844i	0.874834	+	0.484422i	$0.160970\pi$
$3$			1.39019e7i			0.968844i	−0.874834	+	0.484422i	$0.839030\pi$
$4$	−1.07272e9	−	4.67771e7i	−0.999051	−	0.0435646i
$5$	−5.42656e10			−1.77818			−0.889088	−	0.457736i	$-0.848661\pi$
$5$	−5.42656e10			−1.77818			−0.889088	+	0.457736i	$0.848661\pi$
$6$	−4.55428e11	−	9.92498e9i	−0.968614	−	0.0211087i
$7$		−	5.92817e11i		−	0.124868i	−0.998049	−	0.0624338i	$-0.980114\pi$
$7$		−	5.92817e11i		−	0.124868i	0.998049	−	0.0624338i	$-0.0198862\pi$
$8$	2.29828e12	−	3.51092e13i	0.0653210	−	0.997864i
$9$	1.26296e13			0.0613411
$10$	3.87420e13	−	1.77775e15i	0.0387420	−	1.77775i
$11$			3.23456e15i			0.774328i	0.922011	+	0.387164i	$0.126545\pi$
$11$			3.23456e15i			0.774328i	−0.922011	+	0.387164i	$0.873455\pi$
$12$	6.50289e14	−	1.49128e16i	0.0422073	−	0.967924i
$13$	−2.32090e16			−0.453426			−0.226713	−	0.973962i	$-0.572798\pi$
$13$	−2.32090e16			−0.453426			−0.226713	+	0.973962i	$0.572798\pi$
$14$	1.94208e16	+	4.23231e14i	0.124838	+	0.00272055i
$15$		−	7.54393e17i		−	1.72278i
$16$	1.14855e18	+	1.00358e17i	0.996204	+	0.0870465i
$17$	−3.10153e18			−1.08353			−0.541766	−	0.840529i	$-0.682244\pi$
$17$	−3.10153e18			−1.08353			−0.541766	+	0.840529i	$0.682244\pi$
$18$	−9.01667e15	+	4.13748e17i	−0.00133647	+	0.0613266i
$19$			2.48409e19i			1.63630i	0.575005	+	0.818150i	$0.305000\pi$
$19$			2.48409e19i			1.63630i	−0.575005	+	0.818150i	$0.695000\pi$
$20$	5.82120e19	+	2.53839e18i	1.77649	+	0.0774655i
$21$	8.24125e18			0.120977
$22$	−1.05965e20	−	2.30926e18i	−0.774144	−	0.0168707i
$23$		−	3.89198e20i		−	1.45966i	−0.683627	−	0.729831i	$-0.739599\pi$
$23$		−	3.89198e20i		−	1.45966i	0.683627	−	0.729831i	$-0.260401\pi$
$24$	4.88083e20	+	3.19503e19i	0.966775	+	0.0632859i
$25$	2.01344e21			2.16191
$26$	1.65696e19	−	7.60332e20i	0.00987899	−	0.453318i
$27$			3.03784e21i			1.02827i
$28$	−2.77303e19	+	6.35928e20i	−0.00543981	+	0.124749i
$29$	8.64231e21			1.00152			0.500760	−	0.865586i	$-0.333054\pi$
$29$	8.64231e21			1.00152			0.500760	+	0.865586i	$0.333054\pi$
$30$	2.47141e22	+	5.38585e20i	1.72237	+	0.0375349i
$31$		−	1.93494e22i		−	0.824597i	−0.911049	−	0.412298i	$-0.864726\pi$
$31$		−	1.93494e22i		−	0.824597i	0.911049	−	0.412298i	$-0.135274\pi$
$32$	−4.10772e21	+	3.75550e22i	−0.108731	+	0.994071i
$33$	−4.49664e22			−0.750203
$34$	2.21428e21	−	1.01607e23i	0.0236074	−	1.08328i
$35$			3.21696e22i			0.222037i
$36$	−1.35480e22	−	5.90776e20i	−0.0612829	−	0.00267230i
$37$	−7.61448e22			−0.228357			−0.114179	−	0.993460i	$-0.536424\pi$
$37$	−7.61448e22			−0.228357			−0.114179	+	0.993460i	$0.536424\pi$
$38$	−8.13793e23	−	1.77347e22i	−1.63591	−	0.0356508i
$39$		−	3.22648e23i		−	0.439299i
$40$	−1.24718e23	+	1.90522e24i	−0.116152	+	1.77438i
$41$	−6.89135e23			−0.443146			−0.221573	−	0.975144i	$-0.571119\pi$
$41$	−6.89135e23			−0.443146			−0.221573	+	0.975144i	$0.571119\pi$
$42$	−5.88369e21	+	2.69985e23i	−0.00263579	+	0.120949i
$43$		−	2.04687e24i		−	0.644264i	−0.946695	−	0.322132i	$-0.895600\pi$
$43$		−	2.04687e24i		−	0.644264i	0.946695	−	0.322132i	$-0.104400\pi$
$44$	1.51303e23	−	3.46979e24i	0.0337333	−	0.773593i
$45$	−6.85353e23			−0.109075
$46$	1.27502e25	+	2.77861e23i	1.45932	+	0.0318024i
$47$		−	1.46478e25i		−	1.21424i	−0.794611	−	0.607119i	$-0.792325\pi$
$47$		−	1.46478e25i		−	1.21424i	0.794611	−	0.607119i	$-0.207675\pi$
$48$	−1.39516e24	+	1.59669e25i	−0.0843345	+	0.965167i
$49$	2.21879e25			0.984408
$50$	−1.43746e24	+	6.59606e25i	−0.0471026	+	2.16140i
$51$		−	4.31170e25i		−	1.04977i
$52$	2.48968e25	+	1.08565e24i	0.452995	+	0.0197533i
$53$	3.50489e25			0.479221			0.239610	−	0.970869i	$-0.422980\pi$
$53$	3.50489e25			0.479221			0.239610	+	0.970869i	$0.422980\pi$
$54$	−9.95204e25	−	2.16881e24i	−1.02803	−	0.0224035i
$55$		−	1.75525e26i		−	1.37689i
$56$	−2.08133e25	−	1.36246e24i	−0.124601	−	0.00815649i
$57$	−3.45334e26			−1.58532
$58$	−6.17002e24	+	2.83124e26i	−0.0218206	+	1.00128i
$59$		−	4.94749e26i		−	1.35396i	−0.736003	−	0.676978i	$-0.763289\pi$
$59$		−	4.94749e26i		−	1.35396i	0.736003	−	0.676978i	$-0.236711\pi$
$60$	−3.52883e25	+	8.09254e26i	−0.0750520	+	1.72114i
$61$	−2.04893e26			−0.340078			−0.170039	−	0.985437i	$-0.554389\pi$
$61$	−2.04893e26			−0.340078			−0.170039	+	0.985437i	$0.554389\pi$
$62$	6.33890e26	+	1.38141e25i	0.824401	+	0.0179659i
$63$		−	7.48704e24i		−	0.00765952i
$64$	−1.22738e27	−	1.61382e26i	−0.991466	−	0.130363i
$65$	1.25945e27			0.806271
$66$	3.21029e25	−	1.47311e27i	0.0163450	−	0.750025i
$67$			3.08821e26i			0.125483i	0.998030	+	0.0627415i	$0.0199844\pi$
$67$			3.08821e26i			0.125483i	−0.998030	+	0.0627415i	$0.980016\pi$
$68$	3.32708e27	+	1.45081e26i	1.08250	+	0.0472037i
$69$	5.41057e27			1.41419
$70$	−1.05388e27	−	2.29669e25i	−0.221984	−	0.00483762i
$71$		−	9.39686e26i		−	0.159995i	−0.996795	−	0.0799977i	$-0.974509\pi$
$71$		−	9.39686e26i		−	0.159995i	0.996795	−	0.0799977i	$-0.0254913\pi$
$72$	2.90263e25	−	4.43415e26i	0.00400687	−	0.0612101i
$73$	−1.34820e28			−1.51325			−0.756626	−	0.653848i	$-0.773154\pi$
$73$	−1.34820e28			−1.51325			−0.756626	+	0.653848i	$0.773154\pi$
$74$	5.43622e25	−	2.49452e27i	0.00497532	−	0.228303i
$75$			2.79905e28i			2.09455i
$76$	1.16198e27	−	2.66474e28i	0.0712847	−	1.63475i
$77$	1.91750e27			0.0966886
$78$	1.05700e28	+	2.30349e26i	0.439194	+	0.00957121i
$79$			2.95997e28i			1.01597i	0.861366	+	0.507986i	$0.169610\pi$
$79$			2.95997e28i			1.01597i	−0.861366	+	0.507986i	$0.830390\pi$
$80$	−6.23265e28	−	5.44598e27i	−1.77143	−	0.154784i
$81$	−3.96313e28			−0.934896
$82$	4.91996e26	−	2.25762e28i	0.00965503	−	0.443041i
$83$		−	6.94072e28i		−	1.13562i	−0.823160	−	0.567810i	$-0.807791\pi$
$83$		−	6.94072e28i		−	1.13562i	0.823160	−	0.567810i	$-0.192209\pi$
$84$	−8.84058e27	−	3.85502e26i	−0.120862	−	0.00527033i
$85$	1.68306e29			1.92671
$86$	6.70560e28	+	1.46133e27i	0.644112	+	0.0140369i
$87$			1.20144e29i			0.970317i
$88$	1.13563e29	+	7.43393e27i	0.772674	+	0.0505799i
$89$	−1.83280e29			−1.05261			−0.526303	−	0.850297i	$-0.676422\pi$
$89$	−1.83280e29			−1.05261			−0.526303	+	0.850297i	$0.676422\pi$
$90$	4.89295e26	−	2.24523e28i	0.00237648	−	0.109049i
$91$			1.37587e28i			0.0566182i
$92$	−1.82055e28	+	4.17501e29i	−0.0635896	+	1.45828i
$93$	2.68992e29			0.798906
$94$	4.79864e29	+	1.04575e28i	1.21395	+	0.0264552i
$95$		−	1.34801e30i		−	2.90963i
$96$	−5.22083e29	−	5.71050e28i	−0.963100	−	0.105343i
$97$	−5.60161e29			−0.884580			−0.442290	−	0.896872i	$-0.645834\pi$
$97$	−5.60161e29			−0.884580			−0.442290	+	0.896872i	$0.645834\pi$
$98$	−1.58407e28	+	7.26881e29i	−0.0214478	+	0.984174i
$99$			4.08512e28i			0.0474982i
$100$	−2.15986e30	−	9.41828e28i	−2.15986	−	0.0941828i
$101$	2.17309e29			0.187179			0.0935894	−	0.995611i	$-0.470166\pi$
$101$	2.17309e29			0.187179			0.0935894	+	0.995611i	$0.470166\pi$
$102$	1.41252e30	+	3.07826e28i	1.04952	+	0.0228719i
$103$			1.74170e30i			1.11793i	0.829192	+	0.558964i	$0.188801\pi$
$103$			1.74170e30i			1.11793i	−0.829192	+	0.558964i	$0.811199\pi$
$104$	−5.33408e28	+	8.14850e29i	−0.0296182	+	0.452457i
$105$	−4.47217e29			−0.215119
$106$	−2.50225e28	+	1.14821e30i	−0.0104410	+	0.479107i
$107$		−	2.39420e30i		−	0.867768i	−0.900969	−	0.433884i	$-0.857143\pi$
$107$		−	2.39420e30i		−	0.867768i	0.900969	−	0.433884i	$-0.142857\pi$
$108$	1.42102e29	−	3.25876e30i	0.0447963	−	1.02730i
$109$	−1.05563e30			−0.289811			−0.144906	−	0.989445i	$-0.546288\pi$
$109$	−1.05563e30			−0.289811			−0.144906	+	0.989445i	$0.546288\pi$
$110$	5.75025e30	+	1.25313e29i	1.37657	+	0.0299990i
$111$		−	1.05855e30i		−	0.221242i
$112$	5.94938e28	−	6.80877e29i	0.0108693	−	0.124394i
$113$	6.94490e30			1.11043			0.555213	−	0.831708i	$-0.312637\pi$
$113$	6.94490e30			1.11043			0.555213	+	0.831708i	$0.312637\pi$
$114$	2.46545e29	−	1.13132e31i	0.0345401	−	1.58494i
$115$			2.11201e31i			2.59554i
$116$	−9.27080e30	−	4.04263e29i	−1.00057	−	0.0436308i
$117$	−2.93120e29			−0.0278136
$118$	1.62081e31	+	3.53217e29i	1.35364	+	0.0294993i
$119$			1.83864e30i			0.135298i
$120$	−2.64862e31	−	1.73381e30i	−1.71910	−	0.112533i
$121$	6.98702e30			0.400416
$122$	1.46279e29	−	6.71233e30i	0.00740944	−	0.339997i
$123$		−	9.58026e30i		−	0.429339i
$124$	−9.05108e29	+	2.07565e31i	−0.0359232	+	0.823814i
$125$	−5.87216e31			−2.06608
$126$	2.45277e29	+	5.34523e27i	0.00765770	+	0.000166882i
$127$		−	1.72450e31i		−	0.478197i	−0.970995	−	0.239099i	$-0.923148\pi$
$127$		−	1.72450e31i		−	0.478197i	0.970995	−	0.239099i	$-0.0768519\pi$
$128$	6.16316e30	−	4.00939e31i	0.151934	−	0.988391i
$129$	2.84553e31			0.624192
$130$	−8.99162e29	+	4.12599e31i	−0.0175666	+	0.806079i
$131$			2.94034e31i			0.512068i	0.966668	+	0.256034i	$0.0824160\pi$
$131$			2.94034e31i			0.512068i	−0.966668	+	0.256034i	$0.917584\pi$
$132$	4.82365e31	+	2.10340e30i	0.749491	+	0.0326823i
$133$	1.47261e31			0.204321
$134$	−1.01170e31	−	2.20477e29i	−0.125453	−	0.00273396i
$135$		−	1.64850e32i		−	1.82845i
$136$	−7.12818e30	+	1.08892e32i	−0.0707775	+	1.08122i
$137$	8.50096e31			0.756240			0.378120	−	0.925757i	$-0.376571\pi$
$137$	8.50096e31			0.756240			0.378120	+	0.925757i	$0.376571\pi$
$138$	−3.86278e30	+	1.77251e32i	−0.0308115	+	1.41385i
$139$		−	3.56834e31i		−	0.255413i	−0.991812	−	0.127707i	$-0.959238\pi$
$139$		−	3.56834e31i		−	0.255413i	0.991812	−	0.127707i	$-0.0407616\pi$
$140$	1.50480e30	−	3.45090e31i	0.00967294	−	0.221826i
$141$	2.03631e32			1.17641
$142$	3.07843e31	+	6.70872e29i	0.159957	+	0.00348589i
$143$		−	7.50709e31i		−	0.351100i
$144$	1.45057e31	+	1.26748e30i	0.0611083	+	0.00533953i
$145$	−4.68981e32			−1.78088
$146$	9.62523e30	−	4.41673e32i	0.0329699	−	1.51289i
$147$			3.08453e32i			0.953738i
$148$	8.16822e31	+	3.56183e30i	0.228140	+	0.00994828i
$149$	−2.63304e32			−0.664757			−0.332379	−	0.943146i	$-0.607851\pi$
$149$	−2.63304e32			−0.664757			−0.332379	+	0.943146i	$0.607851\pi$
$150$	−9.16975e32	−	1.99833e31i	−2.09406	−	0.0456350i
$151$		−	1.55587e32i		−	0.321602i	−0.986987	−	0.160801i	$-0.948592\pi$
$151$		−	1.55587e32i		−	0.321602i	0.986987	−	0.160801i	$-0.0514078\pi$
$152$	8.72144e32	+	5.70913e31i	1.63281	+	0.106885i
$153$	−3.91710e31			−0.0664651
$154$	−1.36897e30	+	6.28178e31i	−0.00210660	+	0.0966656i
$155$			1.05001e33i			1.46628i
$156$	−1.50925e31	+	3.46112e32i	−0.0191379	+	0.438882i
$157$	9.38960e32			1.08181			0.540907	−	0.841083i	$-0.318081\pi$
$157$	9.38960e32			1.08181			0.540907	+	0.841083i	$0.318081\pi$
$158$	−9.69694e32	−	2.11322e31i	−1.01573	−	0.0221354i
$159$			4.87244e32i			0.464290i
$160$	2.22908e32	−	2.03794e33i	0.193342	−	1.76763i
$161$	−2.30723e32			−0.182265
$162$	2.82941e31	−	1.29833e33i	0.0203690	−	0.934674i
$163$			5.48648e32i			0.360147i	0.983653	+	0.180074i	$0.0576336\pi$
$163$			5.48648e32i			0.360147i	−0.983653	+	0.180074i	$0.942366\pi$
$164$	7.39251e32	+	3.22358e31i	0.442725	+	0.0193055i
$165$	2.44013e33			1.33399
$166$	2.27379e33	+	4.95520e31i	1.13535	+	0.0247423i
$167$		−	2.30703e33i		−	1.05270i	−0.850268	−	0.526351i	$-0.823560\pi$
$167$		−	2.30703e33i		−	1.05270i	0.850268	−	0.526351i	$-0.176440\pi$
$168$	1.89407e31	−	2.89344e32i	0.00790236	−	0.120719i
$169$	−2.08134e33			−0.794405
$170$	−1.20159e32	+	5.51376e33i	−0.0419782	+	1.92625i
$171$			3.13730e32i			0.100372i
$172$	−9.57469e31	+	2.19573e33i	−0.0280671	+	0.643653i
$173$	−6.17459e33			−1.65927			−0.829635	−	0.558307i	$-0.811451\pi$
$173$	−6.17459e33			−1.65927			−0.829635	+	0.558307i	$0.811451\pi$
$174$	−3.93595e33	−	8.57747e31i	−0.970087	−	0.0211408i
$175$		−	1.19360e33i		−	0.269953i
$176$	−3.24613e32	+	3.71504e33i	−0.0674025	+	0.771389i
$177$	6.87793e33			1.31177
$178$	1.30850e32	−	6.00431e33i	0.0229336	−	1.05236i
$179$		−	6.10798e33i		−	0.984242i	−0.870527	−	0.492121i	$-0.836222\pi$
$179$		−	6.10798e33i		−	0.984242i	0.870527	−	0.492121i	$-0.163778\pi$
$180$	7.35193e32	+	3.20588e31i	0.108972	+	0.00475182i
$181$	−5.13029e33			−0.699783			−0.349892	−	0.936790i	$-0.613782\pi$
$181$	−5.13029e33			−0.699783			−0.349892	+	0.936790i	$0.613782\pi$
$182$	−4.50738e32	−	9.82276e30i	−0.0566048	−	0.00123357i
$183$		−	2.84839e33i		−	0.329483i
$184$	−1.36644e34	−	8.94485e32i	−1.45655	−	0.0953467i
$185$	4.13205e33			0.406059
$186$	−1.92042e32	+	8.81225e33i	−0.0174061	+	0.798716i
$187$		−	1.00321e34i		−	0.839010i
$188$	−6.85181e32	+	1.57130e34i	−0.0528978	+	1.21309i
$189$	1.80088e33			0.128398
$190$	4.41610e34	+	9.62384e32i	2.90894	+	0.0633935i
$191$			1.96892e34i			1.19875i	0.800469	+	0.599374i	$0.204584\pi$
$191$			1.96892e34i			1.19875i	−0.800469	+	0.599374i	$0.795416\pi$
$192$	2.24350e33	−	1.70628e34i	0.126301	−	0.960576i
$193$	1.17227e34			0.610475			0.305238	−	0.952276i	$-0.401264\pi$
$193$	1.17227e34			0.610475			0.305238	+	0.952276i	$0.401264\pi$
$194$	3.99917e32	−	1.83510e34i	0.0192728	−	0.884370i
$195$			1.75087e34i			0.781150i
$196$	−2.38015e34	−	1.03789e33i	−0.983473	−	0.0428853i
$197$	−1.51623e34			−0.580460			−0.290230	−	0.956957i	$-0.593732\pi$
$197$	−1.51623e34			−0.580460			−0.290230	+	0.956957i	$0.593732\pi$
$198$	−1.33829e33	−	2.91650e31i	−0.0474869	−	0.00103486i
$199$			2.42724e34i			0.798577i	0.916825	+	0.399289i	$0.130743\pi$
$199$			2.42724e34i			0.798577i	−0.916825	+	0.399289i	$0.869257\pi$
$200$	4.62744e33	−	7.06902e34i	0.141218	−	2.15729i
$201$	−4.29318e33			−0.121573
$202$	−1.55144e32	+	7.11908e33i	−0.00407815	+	0.187134i
$203$		−	5.12331e33i		−	0.125058i
$204$	−2.01689e33	+	4.62526e34i	−0.0457330	+	1.04878i
$205$	3.73964e34			0.787992
$206$	−5.70583e34	−	1.24345e33i	−1.11766	−	0.0243568i
$207$		−	4.91541e33i		−	0.0895374i
$208$	−2.66566e34	−	2.32920e33i	−0.451704	−	0.0394691i
$209$	−8.03493e34			−1.26703
$210$	3.19282e32	−	1.46509e34i	0.00468690	−	0.215068i
$211$			1.77900e32i			0.00243187i	0.999999	+	0.00121593i	$0.000387044\pi$
$211$			1.77900e32i			0.00243187i	−0.999999	+	0.00121593i	$0.999613\pi$
$212$	−3.75977e34	−	1.63948e33i	−0.478766	−	0.0208771i
$213$	1.30634e34			0.155011
$214$	7.84345e34	+	1.70930e33i	0.867562	+	0.0189065i
$215$			1.11075e35i			1.14562i
$216$	1.06656e35	+	6.98181e33i	1.02608	+	0.0671679i
$217$	−1.14706e34			−0.102965
$218$	7.53650e32	−	3.45828e34i	0.00631426	−	0.289743i
$219$		−	1.87425e35i		−	1.46611i
$220$	−8.21058e33	+	1.88290e35i	−0.0599837	+	1.37558i
$221$	7.19834e34			0.491301
$222$	3.46785e34	+	7.55735e32i	0.221190	+	0.00482031i
$223$		−	1.62362e35i		−	0.968079i	−0.875046	−	0.484039i	$-0.839169\pi$
$223$		−	1.62362e35i		−	0.968079i	0.875046	−	0.484039i	$-0.160831\pi$
$224$	2.22632e34	+	2.43513e33i	0.124127	+	0.0135769i
$225$	2.54289e34			0.132614
$226$	−4.95819e33	+	2.27517e35i	−0.0241934	+	1.11016i
$227$		−	3.12138e35i		−	1.42547i	−0.701432	−	0.712736i	$-0.747456\pi$
$227$		−	3.12138e35i		−	1.42547i	0.701432	−	0.712736i	$-0.252544\pi$
$228$	3.70448e35	+	1.61537e34i	1.58381	+	0.0690638i
$229$	2.97156e35			1.18974			0.594869	−	0.803822i	$-0.297204\pi$
$229$	2.97156e35			1.18974			0.594869	+	0.803822i	$0.297204\pi$
$230$	−6.91898e35	−	1.50783e34i	−2.59492	−	0.0565502i
$231$			2.66568e34i			0.0936761i
$232$	1.98624e34	−	3.03425e35i	0.0654204	−	0.999382i
$233$	−2.66526e35			−0.823001			−0.411500	−	0.911410i	$-0.634995\pi$
$233$	−2.66526e35			−0.823001			−0.411500	+	0.911410i	$0.634995\pi$
$234$	2.09268e32	−	9.60268e33i	0.000605989	−	0.0278070i
$235$			7.94871e35i			2.15913i
$236$	−2.31429e34	+	5.30728e35i	−0.0589846	+	1.35267i
$237$	−4.11491e35			−0.984318
$238$	−6.02342e34	−	1.31266e33i	−0.135266	−	0.00294781i
$239$		−	1.43981e35i		−	0.303625i	−0.988409	−	0.151812i	$-0.951489\pi$
$239$		−	1.43981e35i		−	0.303625i	0.988409	−	0.151812i	$-0.0485110\pi$
$240$	7.57092e34	−	8.66454e35i	0.149962	−	1.71624i
$241$	2.86014e35			0.532270			0.266135	−	0.963936i	$-0.414253\pi$
$241$	2.86014e35			0.532270			0.266135	+	0.963936i	$0.414253\pi$
$242$	−4.98825e33	+	2.28896e35i	−0.00872405	+	0.400321i
$243$			7.45160e34i			0.122505i
$244$	2.19793e35	+	9.58429e33i	0.339755	+	0.0148154i
$245$	−1.20404e36			−1.75045
$246$	3.13851e35	+	6.83965e33i	0.429237	+	0.00935422i
$247$		−	5.76532e35i		−	0.741940i
$248$	−6.79342e35	−	4.44703e34i	−0.822836	−	0.0538635i
$249$	9.64888e35			1.10024
$250$	4.19232e34	−	1.92373e36i	0.0450147	−	2.06559i
$251$			1.01420e36i			1.02570i	0.858479	+	0.512849i	$0.171410\pi$
$251$			1.01420e36i			1.02570i	−0.858479	+	0.512849i	$0.828590\pi$
$252$	−3.50222e32	+	8.03151e33i	−0.000333684	+	0.00765225i
$253$	1.25888e36			1.13026
$254$	5.64950e35	+	1.23117e34i	0.478084	+	0.0104187i
$255$			2.33977e36i			1.86668i
$256$	1.30908e36	+	2.30531e35i	0.984846	+	0.173432i
$257$	9.08747e35			0.644831			0.322416	−	0.946598i	$-0.395505\pi$
$257$	9.08747e35			0.644831			0.322416	+	0.946598i	$0.395505\pi$
$258$	−2.03152e34	+	9.32203e35i	−0.0135996	+	0.624044i
$259$			4.51399e34i			0.0285144i
$260$	−1.35104e36	−	5.89135e34i	−0.805505	−	0.0351249i
$261$	1.09149e35			0.0614344
$262$	−9.63261e35	−	2.09920e34i	−0.511947	−	0.0111567i
$263$		−	3.06671e36i		−	1.53935i	−0.638438	−	0.769673i	$-0.720419\pi$
$263$		−	3.06671e36i		−	1.53935i	0.638438	−	0.769673i	$-0.279581\pi$
$264$	−1.03345e35	+	1.57874e36i	−0.0490041	+	0.748601i
$265$	−1.90195e36			−0.852139
$266$	−1.05134e34	+	4.82430e35i	−0.00445164	+	0.204272i
$267$		−	2.54794e36i		−	1.01981i
$268$	1.44458e34	−	3.31279e35i	0.00546661	−	0.125364i
$269$	−3.04295e36			−1.08896			−0.544478	−	0.838775i	$-0.683272\pi$
$269$	−3.04295e36			−1.08896			−0.544478	+	0.838775i	$0.683272\pi$
$270$	5.40054e36	+	1.17692e35i	1.82802	+	0.0398374i
$271$		−	4.43516e36i		−	1.42027i	−0.704067	−	0.710134i	$-0.748634\pi$
$271$		−	4.43516e36i		−	1.42027i	0.704067	−	0.710134i	$-0.251366\pi$
$272$	−3.56225e36	−	3.11262e35i	−1.07942	−	0.0943177i
$273$	−1.91271e35			−0.0548542
$274$	−6.06911e34	+	2.78493e36i	−0.0164766	+	0.756060i
$275$			6.51258e36i			1.67403i
$276$	−5.80404e36	−	2.53091e35i	−1.41284	−	0.0616084i
$277$	1.29169e36			0.297826			0.148913	−	0.988850i	$-0.452423\pi$
$277$	1.29169e36			0.297826			0.148913	+	0.988850i	$0.452423\pi$
$278$	1.16899e36	+	2.54755e34i	0.255353	+	0.00556481i
$279$		−	2.44375e35i		−	0.0505817i
$280$	1.12945e36	+	7.39347e34i	0.221563	+	0.0145037i
$281$	−6.58530e36			−1.22456			−0.612281	−	0.790640i	$-0.709748\pi$
$281$	−6.58530e36			−1.22456			−0.612281	+	0.790640i	$0.709748\pi$
$282$	−1.45379e35	+	6.67101e36i	−0.0256309	+	1.17613i
$283$		−	5.91511e36i		−	0.988932i	−0.869197	−	0.494466i	$-0.835364\pi$
$283$		−	5.91511e36i		−	0.988932i	0.869197	−	0.494466i	$-0.164636\pi$
$284$	−4.39558e34	+	1.00802e36i	−0.00697013	+	0.159843i
$285$	1.87398e37			2.81898
$286$	2.45934e36	+	5.35955e34i	0.351017	+	0.00764958i
$287$			4.08531e35i			0.0553346i
$288$	−5.18789e34	+	4.74304e35i	−0.00666965	+	0.0609774i
$289$	1.42601e36			0.174043
$290$	3.34820e35	−	1.53639e37i	0.0388009	−	1.78046i
$291$		−	7.78728e36i		−	0.857020i
$292$	1.44624e37	+	6.30649e35i	1.51182	+	0.0659242i
$293$	−6.73753e36			−0.669093			−0.334546	−	0.942379i	$-0.608583\pi$
$293$	−6.73753e36			−0.669093			−0.334546	+	0.942379i	$0.608583\pi$
$294$	−1.01050e37	−	2.20214e35i	−0.953512	−	0.0207795i
$295$			2.68479e37i			2.40757i
$296$	−1.75002e35	+	2.67339e36i	−0.0149165	+	0.227869i
$297$	−9.82609e36			−0.796222
$298$	1.87981e35	−	8.62589e36i	0.0144834	−	0.664599i
$299$			9.03288e36i			0.661848i
$300$	1.30932e36	−	3.00260e37i	0.0912484	−	2.09257i
$301$	−1.21342e36			−0.0804478
$302$	5.09707e36	+	1.11079e35i	0.321526	+	0.00700690i
$303$			3.02099e36i			0.181347i
$304$	−2.49297e36	+	2.85309e37i	−0.142434	+	1.63009i
$305$	1.11186e37			0.604719
$306$	2.79655e34	−	1.28325e36i	0.00144811	−	0.0664493i
$307$			3.58968e36i			0.177003i	0.996076	+	0.0885013i	$0.0282077\pi$
$307$			3.58968e36i			0.177003i	−0.996076	+	0.0885013i	$0.971792\pi$
$308$	−2.05695e36	−	8.96953e34i	−0.0965968	−	0.00421220i
$309$	−2.42128e37			−1.08310
$310$	−3.43984e37	−	7.49633e35i	−1.46593	−	0.0319465i
$311$		−	2.39875e37i		−	0.974047i	−0.873389	−	0.487024i	$-0.838083\pi$
$311$		−	2.39875e37i		−	0.974047i	0.873389	−	0.487024i	$-0.161917\pi$
$312$	−1.13279e37	−	7.41535e35i	−0.438360	−	0.0286954i
$313$	−1.07376e37			−0.396043			−0.198022	−	0.980198i	$-0.563452\pi$
$313$	−1.07376e37			−0.396043			−0.198022	+	0.980198i	$0.563452\pi$
$314$	−6.70353e35	+	3.07605e37i	−0.0235700	+	1.08156i
$315$			4.06289e35i			0.0136200i
$316$	1.38459e36	−	3.17523e37i	0.0442604	−	1.01501i
$317$	4.27781e37			1.30416			0.652082	−	0.758149i	$-0.273896\pi$
$317$	4.27781e37			1.30416			0.652082	+	0.758149i	$0.273896\pi$
$318$	−1.59622e37	−	3.47859e35i	−0.464180	−	0.0101157i
$319$			2.79541e37i			0.775506i
$320$	6.66043e37	+	8.75748e36i	1.76300	+	0.231809i
$321$	3.32838e37			0.840732
$322$	1.64720e35	−	7.55853e36i	0.00397109	−	0.182221i
$323$		−	7.70447e37i		−	1.77298i
$324$	4.25134e37	+	1.85384e36i	0.934009	+	0.0407284i
$325$	−4.67298e37			−0.980266
$326$	−1.79738e37	−	3.91697e35i	−0.360062	−	0.00784669i
$327$		−	1.46753e37i		−	0.280782i
$328$	−1.58383e36	+	2.41950e37i	−0.0289468	+	0.442199i
$329$	−8.68345e36			−0.151619
$330$	−1.74209e36	+	7.99392e37i	−0.0290643	+	1.33368i
$331$		−	4.21788e37i		−	0.672472i	−0.941778	−	0.336236i	$-0.890846\pi$
$331$		−	4.21788e37i		−	0.672472i	0.941778	−	0.336236i	$-0.109154\pi$
$332$	−3.24667e36	+	7.44546e37i	−0.0494728	+	1.13454i
$333$	−9.61678e35			−0.0140077
$334$	7.55787e37	+	1.64706e36i	1.05245	+	0.0229357i
$335$		−	1.67584e37i		−	0.223131i
$336$	9.46545e36	+	8.27074e35i	0.120518	+	0.0105306i
$337$	5.16811e37			0.629337			0.314669	−	0.949202i	$-0.398107\pi$
$337$	5.16811e37			0.629337			0.314669	+	0.949202i	$0.398107\pi$
$338$	1.48593e36	−	6.81851e37i	0.0173081	−	0.794217i
$339$			9.65470e37i			1.07583i
$340$	−1.80546e38	−	7.87289e36i	−1.92488	−	0.0839364i
$341$	6.25867e37			0.638508
$342$	−1.02779e37	−	2.23982e35i	−0.100349	−	0.00218686i
$343$		−	2.65151e37i		−	0.247788i
$344$	−7.18642e37	−	4.70429e36i	−0.642889	−	0.0420840i
$345$	−2.93608e38			−2.51467
$346$	4.40824e36	−	2.02281e38i	0.0361513	−	1.65888i
$347$			1.23744e38i			0.971813i	0.874011	+	0.485907i	$0.161511\pi$
$347$			1.23744e38i			0.971813i	−0.874011	+	0.485907i	$0.838489\pi$
$348$	5.62000e36	−	1.28881e38i	0.0422715	−	0.969396i
$349$	1.60255e38			1.15460			0.577300	−	0.816532i	$-0.304106\pi$
$349$	1.60255e38			1.15460			0.577300	+	0.816532i	$0.304106\pi$
$350$	3.91026e37	+	8.52149e35i	0.269889	+	0.00588159i
$351$		−	7.05053e37i		−	0.466246i
$352$	−1.21474e38	−	1.32867e37i	−0.769737	−	0.0841931i
$353$	5.05849e37			0.307185			0.153593	−	0.988134i	$-0.450916\pi$
$353$	5.05849e37			0.307185			0.153593	+	0.988134i	$0.450916\pi$
$354$	−4.91037e36	+	2.25322e38i	−0.0285802	+	1.31146i
$355$			5.09926e37i			0.284500i
$356$	1.96609e38	+	8.57333e36i	1.05161	+	0.0458564i
$357$	−2.55605e37			−0.131083
$358$	2.00099e38	+	4.36068e36i	0.984008	+	0.0214441i
$359$			3.11593e38i			1.46950i	0.678336	+	0.734752i	$0.262701\pi$
$359$			3.11593e38i			1.46950i	−0.678336	+	0.734752i	$0.737299\pi$
$360$	−1.57513e36	+	2.40622e37i	−0.00712491	+	0.108842i
$361$	−3.86602e38			−1.67748
$362$	3.66268e36	−	1.68070e38i	0.0152465	−	0.699617i
$363$			9.71325e37i			0.387941i
$364$	6.43592e35	−	1.47592e37i	0.00246655	−	0.0565644i
$365$	7.31609e38			2.69083
$366$	9.33138e37	+	2.03355e36i	0.329405	+	0.00717859i
$367$		−	1.01205e38i		−	0.342934i	−0.985190	−	0.171467i	$-0.945149\pi$
$367$		−	1.01205e38i		−	0.342934i	0.985190	−	0.171467i	$-0.0548507\pi$
$368$	3.90590e37	−	4.47011e38i	0.127059	−	1.45412i
$369$	−8.70350e36			−0.0271831
$370$	−2.95000e36	+	1.35367e38i	−0.00884700	+	0.405963i
$371$		−	2.07776e37i		−	0.0598392i
$372$	−2.88554e38	−	1.25827e37i	−0.798147	−	0.0348040i
$373$	−1.19989e38			−0.318794			−0.159397	−	0.987215i	$-0.550955\pi$
$373$	−1.19989e38			−0.318794			−0.159397	+	0.987215i	$0.550955\pi$
$374$	3.28653e38	+	7.16222e36i	0.838811	+	0.0182799i
$375$		−	8.16339e38i		−	2.00171i
$376$	−5.14272e38	−	3.36647e37i	−1.21165	−	0.0793153i
$377$	−2.00579e38			−0.454115
$378$	−1.28571e36	+	5.89974e37i	−0.00279747	+	0.128368i
$379$			1.86972e38i			0.391011i	0.980703	+	0.195506i	$0.0626348\pi$
$379$			1.86972e38i			0.391011i	−0.980703	+	0.195506i	$0.937365\pi$
$380$	−6.30558e37	+	1.44604e39i	−0.126757	+	2.90687i
$381$	2.39737e38			0.463299
$382$	−6.45023e38	−	1.40568e37i	−1.19846	−	0.0261177i
$383$		−	5.37466e38i		−	0.960218i	−0.877209	−	0.480109i	$-0.840597\pi$
$383$		−	5.37466e38i		−	0.960218i	0.877209	−	0.480109i	$-0.159403\pi$
$384$	5.57379e38	+	8.56794e37i	0.957596	+	0.147200i
$385$	−1.04054e38			−0.171929
$386$	−8.36921e36	+	3.84038e38i	−0.0133007	+	0.610330i
$387$		−	2.58512e37i		−	0.0395199i
$388$	6.00898e38	+	2.62027e37i	0.883740	+	0.0385364i
$389$	−1.29625e39			−1.83420			−0.917099	−	0.398659i	$-0.869476\pi$
$389$	−1.29625e39			−1.83420			−0.917099	+	0.398659i	$0.869476\pi$
$390$	−5.73589e38	−	1.25000e37i	−0.780965	−	0.0170193i
$391$			1.20711e39i			1.58159i
$392$	5.09940e37	−	7.79000e38i	0.0643026	−	0.982306i
$393$	−4.08762e38			−0.496114
$394$	1.08249e37	−	4.96721e38i	0.0126467	−	0.580322i
$395$		−	1.60625e39i		−	1.80658i
$396$	1.91090e36	−	4.38220e37i	0.00206924	−	0.0474531i
$397$	1.40138e39			1.46116			0.730580	−	0.682827i	$-0.239250\pi$
$397$	1.40138e39			1.46116			0.730580	+	0.682827i	$0.239250\pi$
$398$	−7.95170e38	−	1.73289e37i	−0.798388	−	0.0173990i
$399$			2.04720e38i			0.197955i
$400$	2.31252e39	+	2.02064e38i	2.15371	+	0.188187i
$401$	1.69871e38			0.152389			0.0761946	−	0.997093i	$-0.475723\pi$
$401$	1.69871e38			0.152389			0.0761946	+	0.997093i	$0.475723\pi$
$402$	3.06504e36	−	1.40646e38i	0.00264878	−	0.121545i
$403$			4.49080e38i			0.373893i
$404$	−2.33112e38	−	1.01651e37i	−0.187001	−	0.00815437i
$405$	2.15062e39			1.66241
$406$	1.67841e38	+	3.65769e36i	0.125028	+	0.00272469i
$407$		−	2.46295e38i		−	0.176823i
$408$	−1.51380e39	−	9.90949e37i	−1.04753	−	0.0685723i
$409$	−9.82318e38			−0.655243			−0.327621	−	0.944809i	$-0.606247\pi$
$409$	−9.82318e38			−0.655243			−0.327621	+	0.944809i	$0.606247\pi$
$410$	−2.66985e37	+	1.22511e39i	−0.0171683	+	0.787805i
$411$			1.18179e39i			0.732679i
$412$	8.14715e37	−	1.86836e39i	0.0487021	−	1.11687i
$413$	−2.93296e38			−0.169065
$414$	1.61030e38	+	3.50926e36i	0.0895161	+	0.00195079i
$415$			3.76642e39i			2.01933i
$416$	9.53362e37	−	8.71613e38i	0.0493012	−	0.450737i
$417$	4.96065e38			0.247456
$418$	5.73639e37	−	2.63226e39i	0.0276054	−	1.26673i
$419$		−	1.41920e38i		−	0.0658923i	−0.999457	−	0.0329461i	$-0.989511\pi$
$419$		−	1.41920e38i		−	0.0658923i	0.999457	−	0.0329461i	$-0.0104890\pi$
$420$	4.79740e38	+	2.09195e37i	0.214915	+	0.00937157i
$421$	5.94226e38			0.256874			0.128437	−	0.991718i	$-0.459004\pi$
$421$	5.94226e38			0.256874			0.128437	+	0.991718i	$0.459004\pi$
$422$	−5.82806e36	−	1.27009e35i	−0.00243129	−	5.29843e-5i
$423$		−	1.84995e38i		−	0.0744827i
$424$	8.05521e37	−	1.23054e39i	0.0313032	−	0.478198i
$425$	−6.24473e39			−2.34250
$426$	−9.32636e36	+	4.27959e38i	−0.00337729	+	0.154974i
$427$			1.21464e38i			0.0424648i
$428$	−1.11994e38	+	2.56831e39i	−0.0378040	+	0.866945i
$429$	1.04362e39			0.340161
$430$	−3.63884e39	−	7.92999e37i	−1.14534	−	0.0249601i
$431$		−	2.49998e39i		−	0.759937i	−0.924999	−	0.379969i	$-0.875935\pi$
$431$		−	2.49998e39i		−	0.759937i	0.924999	−	0.379969i	$-0.124065\pi$
$432$	−3.04871e38	+	3.48910e39i	−0.0895076	+	1.02437i
$433$	−5.04651e39			−1.43111			−0.715555	−	0.698556i	$-0.753826\pi$
$433$	−5.04651e39			−1.43111			−0.715555	+	0.698556i	$0.753826\pi$
$434$	8.18925e36	−	3.75781e38i	0.00224336	−	0.102941i
$435$		−	6.51970e39i		−	1.72540i
$436$	1.13240e39	+	4.93795e37i	0.289536	+	0.0126255i
$437$	9.66801e39			2.38845
$438$	6.14008e39	+	1.33808e38i	1.46576	+	0.0319427i
$439$			5.33489e38i			0.123071i	0.998105	+	0.0615357i	$0.0195998\pi$
$439$			5.33489e38i			0.123071i	−0.998105	+	0.0615357i	$0.980400\pi$
$440$	−6.16256e39	−	4.03407e38i	−1.37395	−	0.0899400i
$441$	2.80224e38			0.0603847
$442$	−5.13912e37	+	2.35819e39i	−0.0107042	+	0.491185i
$443$			5.23819e39i			1.05469i	0.849651	+	0.527345i	$0.176813\pi$
$443$			5.23819e39i			1.05469i	−0.849651	+	0.527345i	$0.823187\pi$
$444$	−4.95161e37	+	1.13553e39i	−0.00963833	+	0.221032i
$445$	9.94583e39			1.87172
$446$	5.31901e39	+	1.15915e38i	0.967849	+	0.0210920i
$447$		−	3.66041e39i		−	0.644046i
$448$	−9.56698e37	+	7.27609e38i	−0.0162781	+	0.123802i
$449$	−1.17114e40			−1.92715			−0.963573	−	0.267445i	$-0.913821\pi$
$449$	−1.17114e40			−1.92715			−0.963573	+	0.267445i	$0.913821\pi$
$450$	−1.81545e37	+	8.33056e38i	−0.00288932	+	0.132583i
$451$		−	2.22905e39i		−	0.343140i
$452$	−7.44995e39	−	3.24863e38i	−1.10937	−	0.0483752i
$453$	2.16295e39			0.311583
$454$	1.02257e40	+	2.22845e38i	1.42513	+	0.0310574i
$455$		−	7.46624e38i		−	0.100677i
$456$	−7.93675e38	+	1.21244e40i	−0.103555	+	1.58193i
$457$	6.08596e39			0.768398			0.384199	−	0.923250i	$-0.374478\pi$
$457$	6.08596e39			0.768398			0.384199	+	0.923250i	$0.374478\pi$
$458$	−2.12149e38	+	9.73488e39i	−0.0259214	+	1.18946i
$459$		−	9.42196e39i		−	1.11417i
$460$	9.87935e38	−	2.26560e40i	0.113074	−	2.59307i
$461$	−6.79375e39			−0.752655			−0.376327	−	0.926487i	$-0.622813\pi$
$461$	−6.79375e39			−0.752655			−0.376327	+	0.926487i	$0.622813\pi$
$462$	−8.73284e38	−	1.90312e37i	−0.0936539	−	0.00204097i
$463$		−	1.83193e39i		−	0.190193i	−0.995468	−	0.0950964i	$-0.969684\pi$
$463$		−	1.83193e39i		−	0.190193i	0.995468	−	0.0950964i	$-0.0303159\pi$
$464$	9.92609e39	+	8.67323e38i	0.997719	+	0.0871788i
$465$	−1.45970e40			−1.42060
$466$	1.90281e38	−	8.73144e39i	0.0179311	−	0.822805i
$467$			6.23189e39i			0.568679i	0.958724	+	0.284339i	$0.0917742\pi$
$467$			6.23189e39i			0.568679i	−0.958724	+	0.284339i	$0.908226\pi$
$468$	3.14436e38	+	1.37113e37i	0.0277872	+	0.00121169i
$469$	1.83074e38			0.0156688
$470$	−2.60402e40	−	5.67484e38i	−2.15862	−	0.0470420i
$471$			1.30533e40i			1.04811i
$472$	−1.73703e40	−	1.13707e39i	−1.35107	−	0.0884419i
$473$	6.62074e39			0.498872
$474$	2.93777e38	−	1.34805e40i	0.0214458	−	0.984084i
$475$			5.00155e40i			3.53753i
$476$	8.60062e37	−	1.97235e39i	0.00589421	−	0.135170i
$477$	4.42653e38			0.0293960
$478$	4.71686e39	+	1.02793e38i	0.303553	+	0.00661522i
$479$		−	2.81057e40i		−	1.75292i	−0.481477	−	0.876458i	$-0.659900\pi$
$479$		−	2.81057e40i		−	1.75292i	0.481477	−	0.876458i	$-0.340100\pi$
$480$	2.83312e40	+	3.09884e39i	1.71256	+	0.187318i
$481$	1.76724e39			0.103543
$482$	−2.04195e38	+	9.36989e39i	−0.0115968	+	0.532144i
$483$		−	3.20748e39i		−	0.176586i
$484$	−7.49513e39	−	3.26833e38i	−0.400036	−	0.0174440i
$485$	3.03975e40			1.57294
$486$	−2.44116e39	−	5.31993e37i	−0.122476	−	0.00266908i
$487$			1.14274e40i			0.555920i	0.960593	+	0.277960i	$0.0896583\pi$
$487$			1.14274e40i			0.555920i	−0.960593	+	0.277960i	$0.910342\pi$
$488$	−4.70900e38	+	7.19362e39i	−0.0222143	+	0.339352i
$489$	−7.62723e39			−0.348926
$490$	8.59603e38	−	3.94446e40i	0.0381379	−	1.75004i
$491$		−	4.55678e40i		−	1.96081i	−0.196989	−	0.980406i	$-0.563116\pi$
$491$		−	4.55678e40i		−	1.96081i	0.196989	−	0.980406i	$-0.436884\pi$
$492$	−4.48137e38	+	1.02770e40i	−0.0187040	+	0.428932i
$493$	−2.68044e40			−1.08518
$494$	1.88873e40	+	4.11604e38i	0.741764	+	0.0161650i
$495$		−	2.21682e39i		−	0.0844601i
$496$	1.94186e39	−	2.22236e40i	0.0717782	−	0.821467i
$497$	−5.57062e38			−0.0199782
$498$	−6.88864e38	+	3.16100e40i	−0.0239714	+	1.09998i
$499$			3.39794e40i			1.14738i	0.819072	+	0.573691i	$0.194489\pi$
$499$			3.39794e40i			1.14738i	−0.819072	+	0.573691i	$0.805511\pi$
$500$	6.29920e40	+	2.74683e39i	2.06412	+	0.0900081i
$501$	3.20719e40			1.01990
$502$	−3.32256e40	−	7.24073e38i	−1.02546	−	0.0223474i
$503$			7.23192e39i			0.216638i	0.994116	+	0.108319i	$0.0345467\pi$
$503$			7.23192e39i			0.216638i	−0.994116	+	0.108319i	$0.965453\pi$
$504$	−2.62864e38	−	1.72073e37i	−0.00764316	−	0.000500328i
$505$	−1.17924e40			−0.332837
$506$	−8.98757e38	+	4.12413e40i	−0.0246255	+	1.12999i
$507$		−	2.89345e40i		−	0.769655i
$508$	−8.06671e38	+	1.84991e40i	−0.0208325	+	0.477743i
$509$	4.95785e39			0.124316			0.0621580	−	0.998066i	$-0.480202\pi$
$509$	4.95785e39			0.124316			0.0621580	+	0.998066i	$0.480202\pi$
$510$	−7.66514e40	−	1.67044e39i	−1.86624	−	0.0406703i
$511$			7.99236e39i			0.188956i
$512$	−8.48684e39	+	4.27213e40i	−0.194848	+	0.980833i
$513$	−7.54627e40			−1.68256
$514$	−6.48783e38	+	2.97708e40i	−0.0140492	+	0.644678i
$515$		−	9.45142e40i		−	1.98787i
$516$	−3.05247e40	−	1.33106e39i	−0.623599	−	0.0271927i
$517$	4.73791e40			0.940219
$518$	−1.47879e39	−	3.22268e37i	−0.0285076	−	0.000621257i
$519$		−	8.58383e40i		−	1.60757i
$520$	2.89457e39	−	4.42183e40i	0.0526664	−	0.804549i
$521$	1.00470e40			0.177612			0.0888059	−	0.996049i	$-0.471695\pi$
$521$	1.00470e40			0.177612			0.0888059	+	0.996049i	$0.471695\pi$
$522$	−7.79248e37	+	3.57574e39i	−0.00133850	+	0.0614198i
$523$			8.19607e40i			1.36798i	0.729491	+	0.683990i	$0.239757\pi$
$523$			8.19607e40i			1.36798i	−0.729491	+	0.683990i	$0.760243\pi$
$524$	1.37541e39	−	3.15417e40i	0.0223080	−	0.511582i
$525$	1.65932e40			0.261542
$526$	1.00466e41	+	2.18942e39i	1.53898	+	0.0335385i
$527$			6.00127e40i			0.893477i
$528$	−5.16459e40	−	4.51273e39i	−0.747356	−	0.0653025i
$529$	−8.03804e40			−1.13062
$530$	1.35786e39	−	6.23083e40i	0.0185660	−	0.851937i
$531$		−	6.24848e39i		−	0.0830532i
$532$	−1.57970e40	−	6.88844e38i	−0.204127	−	0.00890116i
$533$	1.59941e40			0.200934
$534$	8.34710e40	+	1.81905e39i	1.01957	+	0.0222191i
$535$			1.29923e41i			1.54305i
$536$	1.08425e40	+	7.09757e38i	0.125215	+	0.00819667i
$537$	8.49122e40			0.953577
$538$	2.17246e39	−	9.96876e40i	0.0237256	−	1.08870i
$539$			7.17681e40i			0.762255i
$540$	−7.71123e39	+	1.76839e41i	−0.0796558	+	1.82672i
$541$	−8.24797e39			−0.0828683			−0.0414341	−	0.999141i	$-0.513193\pi$
$541$	−8.24797e39			−0.0828683			−0.0414341	+	0.999141i	$0.513193\pi$
$542$	1.45297e41	+	3.16640e39i	1.41993	+	0.0309440i
$543$		−	7.13206e40i		−	0.677981i
$544$	1.27402e40	−	1.16478e41i	0.117813	−	1.07711i
$545$	5.72846e40			0.515336
$546$	1.36555e38	−	6.26609e39i	0.00119513	−	0.0548412i
$547$		−	1.47562e41i		−	1.25651i	−0.778008	−	0.628254i	$-0.783770\pi$
$547$		−	1.47562e41i		−	1.25651i	0.778008	−	0.628254i	$-0.216230\pi$
$548$	−9.11917e40	−	3.97651e39i	−0.755522	−	0.0329453i
$549$	−2.58771e39			−0.0208608
$550$	−2.13354e41	−	4.64954e39i	−1.67363	−	0.0364728i
$551$			2.14683e41i			1.63879i
$552$	1.24350e40	−	1.89961e41i	0.0923761	−	1.41117i
$553$	1.75472e40			0.126862
$554$	−9.22181e38	+	4.23162e40i	−0.00648888	+	0.297756i
$555$			5.74431e40i			0.393408i
$556$	−1.66916e39	+	3.82783e40i	−0.0111270	+	0.255171i
$557$	−8.78165e40			−0.569834			−0.284917	−	0.958552i	$-0.591966\pi$
$557$	−8.78165e40			−0.569834			−0.284917	+	0.958552i	$0.591966\pi$
$558$	8.00577e39	+	1.74467e38i	0.0505697	+	0.00110205i
$559$			4.75059e40i			0.292126i
$560$	−3.22847e39	+	3.69482e40i	−0.0193275	+	0.221194i
$561$	1.39465e41			0.812870
$562$	4.70146e39	−	2.15736e41i	0.0266801	−	1.22427i
$563$		−	1.37502e41i		−	0.759773i	−0.925033	−	0.379887i	$-0.875963\pi$
$563$		−	1.37502e41i		−	0.759773i	0.925033	−	0.379887i	$-0.124037\pi$
$564$	−2.18440e41	−	9.52529e39i	−1.17529	−	0.0512497i
$565$	−3.76869e41			−1.97453
$566$	1.93780e41	+	4.22299e39i	0.988698	+	0.0215463i
$567$			2.34941e40i			0.116738i
$568$	−3.29916e40	−	2.15966e39i	−0.159654	−	0.0104511i
$569$	4.21818e40			0.198811			0.0994056	−	0.995047i	$-0.468306\pi$
$569$	4.21818e40			0.198811			0.0994056	+	0.995047i	$0.468306\pi$
$570$	−1.33789e40	+	6.13919e41i	−0.0614184	+	2.81831i
$571$			4.31321e40i			0.192868i	0.995339	+	0.0964338i	$0.0307436\pi$
$571$			4.31321e40i			0.192868i	−0.995339	+	0.0964338i	$0.969256\pi$
$572$	−3.51160e39	+	8.05302e40i	−0.0152955	+	0.350767i
$573$	−2.73717e41			−1.16140
$574$	−1.33836e40	−	2.91663e38i	−0.0553215	−	0.00120560i
$575$		−	7.83625e41i		−	3.15566i
$576$	−1.55013e40	−	2.03818e39i	−0.0608177	−	0.00799662i
$577$	4.39713e41			1.68086			0.840431	−	0.541918i	$-0.182302\pi$
$577$	4.39713e41			1.68086			0.840431	+	0.541918i	$0.182302\pi$
$578$	−1.01808e39	+	4.67166e40i	−0.00379195	+	0.174002i
$579$			1.62967e41i			0.591455i
$580$	5.03086e41	+	2.19376e40i	1.77919	+	0.0775833i
$581$	−4.11457e40			−0.141802
$582$	2.55113e41	+	5.55959e39i	0.856817	+	0.0186723i
$583$			1.13368e41i			0.371074i
$584$	−3.09854e40	+	4.73342e41i	−0.0988472	+	1.51002i
$585$	1.59063e40			0.0494575
$586$	4.81014e39	−	2.20723e41i	0.0145778	−	0.668934i
$587$			1.19770e41i			0.353816i	0.984227	+	0.176908i	$0.0566095\pi$
$587$			1.19770e41i			0.353816i	−0.984227	+	0.176908i	$0.943391\pi$
$588$	1.44285e40	−	3.30885e41i	0.0415492	−	0.952832i
$589$	4.80656e41			1.34929
$590$	−8.79542e41	−	1.91675e40i	−2.40700	−	0.0524549i
$591$		−	2.10784e41i		−	0.562375i
$592$	−8.74558e40	−	7.64172e39i	−0.227490	−	0.0198777i
$593$	1.28775e41			0.326596			0.163298	−	0.986577i	$-0.447787\pi$
$593$	1.28775e41			0.326596			0.163298	+	0.986577i	$0.447787\pi$
$594$	7.01516e39	−	3.21905e41i	0.0173477	−	0.796033i
$595$		−	9.97749e40i		−	0.240584i
$596$	2.82452e41	+	1.23166e40i	0.664126	+	0.0289599i
$597$	−3.37432e41			−0.773697
$598$	−2.95919e41	−	6.44886e39i	−0.661691	−	0.0144200i
$599$			8.38859e40i			0.182931i	0.995808	+	0.0914654i	$0.0291551\pi$
$599$			8.38859e40i			0.182931i	−0.995808	+	0.0914654i	$0.970845\pi$
$600$	9.82725e41	+	6.43300e40i	2.09008	+	0.136818i
$601$	2.80067e41			0.580959			0.290479	−	0.956881i	$-0.406185\pi$
$601$	2.80067e41			0.580959			0.290479	+	0.956881i	$0.406185\pi$
$602$	8.66300e38	−	3.97520e40i	0.00175275	−	0.0804287i
$603$			3.90028e39i			0.00769726i
$604$	−7.27792e39	+	1.66902e41i	−0.0140105	+	0.321297i
$605$	−3.79155e41			−0.712010
$606$	−9.89684e40	−	2.15678e39i	−0.181304	−	0.00395109i
$607$			3.50103e41i			0.625700i	0.949803	+	0.312850i	$0.101284\pi$
$607$			3.50103e41i			0.625700i	−0.949803	+	0.312850i	$0.898716\pi$
$608$	−9.32898e41	−	1.02039e41i	−1.62660	−	0.177916i
$609$	7.12235e40			0.121161
$610$	−7.93794e39	+	3.64249e41i	−0.0131753	+	0.604575i
$611$			3.39960e41i			0.550567i
$612$	4.20197e40	+	1.83231e39i	0.0664020	+	0.00289553i
$613$	−1.05750e42			−1.63069			−0.815347	−	0.578972i	$-0.803454\pi$
$613$	−1.05750e42			−1.63069			−0.815347	+	0.578972i	$0.803454\pi$
$614$	−1.17599e41	−	2.56278e39i	−0.176961	−	0.00385644i
$615$			5.19879e41i			0.763441i
$616$	4.40696e39	−	6.73220e40i	0.00631580	−	0.0964821i
$617$	−1.28136e42			−1.79222			−0.896112	−	0.443829i	$-0.853620\pi$
$617$	−1.28136e42			−1.79222			−0.896112	+	0.443829i	$0.853620\pi$
$618$	1.72863e40	−	7.93216e41i	0.0235980	−	1.08284i
$619$			1.22996e42i			1.63883i	0.573204	+	0.819413i	$0.305700\pi$
$619$			1.22996e42i			1.63883i	−0.573204	+	0.819413i	$0.694300\pi$
$620$	4.91163e40	−	1.12637e42i	0.0638778	−	1.46489i
$621$	1.18232e42			1.50093
$622$	7.85837e41	+	1.71255e40i	0.973816	+	0.0212220i
$623$			1.08652e41i			0.131437i
$624$	3.23802e40	−	3.70576e41i	0.0382394	−	0.437631i
$625$	1.31141e42			1.51195
$626$	7.66592e39	−	3.51766e41i	0.00862878	−	0.395949i
$627$		−	1.11700e42i		−	1.22756i
$628$	−1.00724e42	−	4.39218e40i	−1.08079	−	0.0471288i
$629$	2.36165e41			0.247432
$630$	−1.33101e40	−	2.90062e38i	−0.0136167	−	0.000296745i
$631$		−	1.45119e42i		−	1.44972i	−0.688895	−	0.724861i	$-0.741904\pi$
$631$		−	1.45119e42i		−	1.44972i	0.688895	−	0.724861i	$-0.258096\pi$
$632$	1.03922e42	+	6.80285e40i	1.01380	+	0.0663643i
$633$	−2.47315e39			−0.00235610
$634$	−3.05406e40	+	1.40142e42i	−0.0284144	+	1.30385i
$635$			9.35811e41i			0.850319i
$636$	2.27919e40	−	5.22678e41i	0.0202266	−	0.463850i
$637$	−5.14959e41			−0.446356
$638$	−9.15782e41	−	1.99573e40i	−0.775322	−	0.0168963i
$639$		−	1.18678e40i		−	0.00981430i
$640$	−3.34448e41	+	2.17572e42i	−0.270165	+	1.75753i
$641$	2.22904e42			1.75892			0.879461	−	0.475971i	$-0.157903\pi$
$641$	2.22904e42			1.75892			0.879461	+	0.475971i	$0.157903\pi$
$642$	−2.37624e40	+	1.09039e42i	−0.0183174	+	0.840533i
$643$		−	2.20310e42i		−	1.65909i	−0.558442	−	0.829544i	$-0.688600\pi$
$643$		−	2.20310e42i		−	1.65909i	0.558442	−	0.829544i	$-0.311400\pi$
$644$	2.47502e41	+	1.07926e40i	0.182092	+	0.00794029i
$645$	−1.54415e42			−1.10992
$646$	2.52400e42	+	5.50046e40i	1.77256	+	0.0386288i
$647$			2.23245e42i			1.53186i	0.642927	+	0.765928i	$0.277720\pi$
$647$			2.23245e42i			1.53186i	−0.642927	+	0.765928i	$0.722280\pi$
$648$	−9.10839e40	+	1.39143e42i	−0.0610684	+	0.932899i
$649$	1.60030e42			1.04841
$650$	3.33619e40	−	1.53088e42i	0.0213575	−	0.980033i
$651$		−	1.59463e41i		−	0.0997575i
$652$	2.56642e40	−	5.88547e41i	0.0156897	−	0.359805i
$653$	−2.56134e42			−1.53028			−0.765138	−	0.643866i	$-0.777329\pi$
$653$	−2.56134e42			−1.53028			−0.765138	+	0.643866i	$0.777329\pi$
$654$	4.80765e41	+	1.04771e40i	0.280715	+	0.00611753i
$655$		−	1.59559e42i		−	0.910548i
$656$	−7.91503e41	−	6.91601e40i	−0.441464	−	0.0385743i
$657$	−1.70272e41			−0.0928246
$658$	6.19939e39	−	2.84472e41i	0.00330340	−	0.151583i
$659$		−	2.01720e42i		−	1.05067i	−0.850894	−	0.525337i	$-0.823939\pi$
$659$		−	2.01720e42i		−	1.05067i	0.850894	−	0.525337i	$-0.176061\pi$
$660$	−2.61758e42	−	1.14142e41i	−1.33273	−	0.0581149i
$661$	−2.99512e42			−1.49071			−0.745354	−	0.666668i	$-0.767720\pi$
$661$	−2.99512e42			−1.49071			−0.745354	+	0.666668i	$0.767720\pi$
$662$	1.38179e42	+	3.01128e40i	0.672312	+	0.0146515i
$663$			1.00070e42i			0.475994i
$664$	−2.43683e42	−	1.59517e41i	−1.13319	−	0.0741799i
$665$	−7.99121e41			−0.363319
$666$	6.86572e38	−	3.15048e40i	0.000305192	−	0.0140044i
$667$		−	3.36357e42i		−	1.46188i
$668$	−1.07916e41	+	2.47480e42i	−0.0458605	+	1.05170i
$669$	2.25713e42			0.937917
$670$	5.49008e41	+	1.19643e40i	0.223078	+	0.00486145i
$671$		−	6.62738e41i		−	0.263332i
$672$	−3.38528e40	+	3.09500e41i	−0.0131539	+	0.120260i
$673$	1.35684e41			0.0515589			0.0257794	−	0.999668i	$-0.491793\pi$
$673$	1.35684e41			0.0515589			0.0257794	+	0.999668i	$0.491793\pi$
$674$	−3.68968e40	+	1.69309e42i	−0.0137117	+	0.629188i
$675$			6.11650e42i			2.22304i
$676$	2.23270e42	+	9.73590e40i	0.793651	+	0.0346079i
$677$	2.93679e42			1.02104			0.510520	−	0.859866i	$-0.329453\pi$
$677$	2.93679e42			1.02104			0.510520	+	0.859866i	$0.329453\pi$
$678$	−3.16290e42	−	6.89280e40i	−1.07557	−	0.0234396i
$679$			3.32073e41i			0.110455i
$680$	3.86815e41	−	5.90911e42i	0.125855	−	1.92260i
$681$	4.33930e42			1.38106
$682$	−4.46827e40	+	2.05036e42i	−0.0139115	+	0.638357i
$683$			2.79398e42i			0.850968i	0.904966	+	0.425484i	$0.139896\pi$
$683$			2.79398e42i			0.850968i	−0.904966	+	0.425484i	$0.860104\pi$
$684$	1.46754e40	−	3.36545e41i	0.00437269	−	0.100277i
$685$	−4.61310e42			−1.34473
$686$	8.68640e41	+	1.89300e40i	0.247730	+	0.00539868i
$687$			4.13101e42i			1.15267i
$688$	2.05420e41	−	2.35093e42i	0.0560809	−	0.641819i
$689$	−8.13449e41			−0.217291
$690$	2.09616e41	−	9.61866e42i	0.0547883	−	2.51407i
$691$		−	1.50138e42i		−	0.383990i	−0.981396	−	0.191995i	$-0.938504\pi$
$691$		−	1.50138e42i		−	0.383990i	0.981396	−	0.191995i	$-0.0614958\pi$
$692$	6.62363e42	+	2.88830e41i	1.65769	+	0.0722854i
$693$	2.42173e40			0.00593098
$694$	−4.05389e42	−	8.83449e40i	−0.971583	−	0.0211734i
$695$			1.93638e42i			0.454170i
$696$	4.21817e42	+	2.76125e41i	0.968245	+	0.0633821i
$697$	2.13737e42			0.480163
$698$	−1.14411e41	+	5.25001e42i	−0.0251558	+	1.15433i
$699$		−	3.70520e42i		−	0.797360i
$700$	−5.58331e40	+	1.28040e42i	−0.0117604	+	0.269697i
$701$	6.30110e42			1.29911			0.649556	−	0.760314i	$-0.274955\pi$
$701$	6.30110e42			1.29911			0.649556	+	0.760314i	$0.274955\pi$
$702$	2.30977e42	+	5.03360e40i	0.466135	+	0.0101583i
$703$		−	1.89150e42i		−	0.373661i
$704$	5.21999e41	−	3.97002e42i	0.100944	−	0.767720i
$705$	−1.10502e43			−2.09186
$706$	−3.61142e40	+	1.65717e42i	−0.00669279	+	0.307112i
$707$		−	1.28824e41i		−	0.0233726i
$708$	−7.37811e42	−	3.21730e41i	−1.31053	−	0.0571469i
$709$	1.95714e42			0.340351			0.170176	−	0.985414i	$-0.445566\pi$
$709$	1.95714e42			0.340351			0.170176	+	0.985414i	$0.445566\pi$
$710$	−1.67053e42	−	3.64053e40i	−0.284432	−	0.00619853i
$711$			3.73833e41i			0.0623208i
$712$	−4.21230e41	+	6.43483e42i	−0.0687573	+	1.05036i
$713$	−7.53073e42			−1.20363
$714$	1.82484e40	−	8.37367e41i	0.00285596	−	0.131052i
$715$			4.07377e42i			0.624318i
$716$	−2.85714e41	+	6.55216e42i	−0.0428781	+	0.983307i
$717$	2.00161e42			0.294165
$718$	−1.02079e43	−	2.22456e41i	−1.46916	−	0.0320168i
$719$		−	3.94482e42i		−	0.556025i	−0.960578	−	0.278012i	$-0.910324\pi$
$719$		−	3.94482e42i		−	0.556025i	0.960578	−	0.278012i	$-0.0896756\pi$
$720$	−7.87159e41	−	6.87805e40i	−0.108661	−	0.00949462i
$721$	1.03251e42			0.139593
$722$	2.76008e41	−	1.26652e43i	0.0365480	−	1.67708i
$723$			3.97613e42i			0.515687i
$724$	5.50338e42	+	2.39980e41i	0.699119	+	0.0304858i
$725$	1.74007e43			2.16520
$726$	−3.18208e42	−	6.93460e40i	−0.387849	−	0.00845224i
$727$		−	1.38272e43i		−	1.65089i	−0.564482	−	0.825446i	$-0.690924\pi$
$727$		−	1.38272e43i		−	1.65089i	0.564482	−	0.825446i	$-0.309076\pi$
$728$	4.83057e41	+	3.16213e40i	0.0564973	+	0.00369836i
$729$	−9.19565e42			−1.05358
$730$	−5.22319e41	+	2.39677e43i	−0.0586264	+	2.69019i
$731$			6.34844e42i			0.698082i
$732$	−1.33239e41	+	3.05553e42i	−0.0143538	+	0.329170i
$733$	−1.28233e43			−1.35344			−0.676720	−	0.736241i	$-0.736599\pi$
$733$	−1.28233e43			−1.35344			−0.676720	+	0.736241i	$0.736599\pi$
$734$	3.31549e42	+	7.22534e40i	0.342853	+	0.00747166i
$735$		−	1.67384e43i		−	1.69591i
$736$	1.46163e43	+	1.59872e42i	1.45101	+	0.158710i
$737$	−9.98900e41			−0.0971650
$738$	6.21371e39	−	2.85129e41i	0.000592250	−	0.0271766i
$739$		−	1.29054e43i		−	1.20533i	−0.797994	−	0.602665i	$-0.794105\pi$
$739$		−	1.29054e43i		−	1.20533i	0.797994	−	0.602665i	$-0.205895\pi$
$740$	−4.43254e42	−	1.93285e41i	−0.405674	−	0.0176898i
$741$	8.01486e42			0.718824
$742$	6.80677e41	+	1.48338e40i	0.0598250	+	0.00130374i
$743$			5.76235e42i			0.496326i	0.968718	+	0.248163i	$0.0798269\pi$
$743$			5.76235e42i			0.496326i	−0.968718	+	0.248163i	$0.920173\pi$
$744$	6.18219e41	−	9.44411e42i	0.0521853	−	0.797199i
$745$	1.42883e43			1.18206
$746$	8.56642e40	−	3.93088e42i	0.00694571	−	0.318718i
$747$		−	8.76584e41i		−	0.0696602i
$748$	−4.69272e41	+	1.07616e43i	−0.0365511	+	0.838213i
$749$	−1.41932e42			−0.108356
$750$	2.67435e43	+	5.82811e41i	2.00124	+	0.0436122i
$751$			1.83005e43i			1.34235i	0.741301	+	0.671173i	$0.234209\pi$
$751$			1.83005e43i			1.34235i	−0.741301	+	0.671173i	$0.765791\pi$
$752$	1.47002e42	−	1.68236e43i	0.105695	−	1.20963i
$753$	−1.40993e43			−0.993742
$754$	1.43200e41	−	6.57102e42i	0.00989402	−	0.454007i
$755$			8.44303e42i			0.571866i
$756$	−1.93185e42	−	8.42402e40i	−0.128276	−	0.00559361i
$757$	7.50069e42			0.488273			0.244137	−	0.969741i	$-0.421495\pi$
$757$	7.50069e42			0.488273			0.244137	+	0.969741i	$0.421495\pi$
$758$	−6.12526e42	−	1.33486e41i	−0.390918	−	0.00851915i
$759$			1.75008e43i			1.09504i
$760$	−4.73274e43	−	3.09809e42i	−2.90342	−	0.190060i
$761$	9.51455e42			0.572293			0.286146	−	0.958186i	$-0.407626\pi$
$761$	9.51455e42			0.572293			0.286146	+	0.958186i	$0.407626\pi$
$762$	−1.71156e41	+	7.85385e42i	−0.0100941	+	0.463189i
$763$			6.25797e41i			0.0361881i
$764$	9.21005e41	−	2.11211e43i	0.0522230	−	1.19761i
$765$	2.12564e42			0.118187
$766$	1.76075e43	+	3.83714e41i	0.959990	+	0.0209207i
$767$			1.14826e43i			0.613919i
$768$	−3.20481e42	+	1.81987e43i	−0.168029	+	0.954162i
$769$	−7.85154e42			−0.403701			−0.201850	−	0.979416i	$-0.564695\pi$
$769$	−7.85154e42			−0.403701			−0.201850	+	0.979416i	$0.564695\pi$
$770$	7.42878e40	−	3.40885e42i	0.00374590	−	0.171888i
$771$			1.26333e43i			0.624741i
$772$	−1.25752e43	−	5.48354e41i	−0.609896	−	0.0265951i
$773$	−1.79129e43			−0.852065			−0.426033	−	0.904708i	$-0.640089\pi$
$773$	−1.79129e43			−0.852065			−0.426033	+	0.904708i	$0.640089\pi$
$774$	8.46890e41	+	1.84560e40i	0.0395105	+	0.000861039i
$775$		−	3.89587e43i		−	1.78270i
$776$	−1.28741e42	+	1.96668e43i	−0.0577817	+	0.882691i
$777$	−6.27529e41			−0.0276260
$778$	9.25438e41	−	4.24656e43i	0.0399625	−	1.83376i
$779$		−	1.71187e43i		−	0.725120i
$780$	8.19007e41	−	1.87820e43i	0.0340305	−	0.780409i
$781$	3.03947e42			0.123889
$782$	−3.95451e43	−	8.61792e41i	−1.58122	−	0.0344589i
$783$			2.62540e43i			1.02984i
$784$	2.54838e43	+	2.22673e42i	0.980672	+	0.0856892i
$785$	−5.09533e43			−1.92365
$786$	2.91828e41	−	1.33911e43i	0.0108091	−	0.495997i
$787$			3.40916e43i			1.23887i	0.785048	+	0.619435i	$0.212638\pi$
$787$			3.40916e43i			1.23887i	−0.785048	+	0.619435i	$0.787362\pi$
$788$	1.62650e43	+	7.09249e41i	0.579909	+	0.0252875i
$789$	4.26329e43			1.49139
$790$	5.26211e43	+	1.14675e42i	1.80615	+	0.0393607i
$791$		−	4.11706e42i		−	0.138656i
$792$	1.43425e42	+	9.38874e40i	0.0473967	+	0.00310263i
$793$	4.75535e42			0.154200
$794$	−1.00049e42	+	4.59094e43i	−0.0318350	+	1.46081i
$795$		−	2.64406e43i		−	0.825590i
$796$	1.13539e42	−	2.60376e43i	0.0347897	−	0.797819i
$797$	3.35780e43			1.00967			0.504836	−	0.863215i	$-0.331553\pi$
$797$	3.35780e43			1.00967			0.504836	+	0.863215i	$0.331553\pi$
$798$	−6.70667e42	−	1.46156e41i	−0.197908	−	0.00431294i
$799$			4.54305e43i			1.31567i
$800$	−8.27064e42	+	7.56145e43i	−0.235066	+	2.14909i
$801$	−2.31476e42			−0.0645681
$802$	−1.21276e41	+	5.56502e42i	−0.00332017	+	0.152353i
$803$		−	4.36083e43i		−	1.17175i
$804$	4.60539e42	+	2.00823e41i	0.121458	+	0.00529630i
$805$	1.25203e43			0.324099
$806$	−1.47119e43	−	3.20612e41i	−0.373804	−	0.00814619i
$807$		−	4.23026e43i		−	1.05503i
$808$	4.99436e41	−	7.62954e42i	0.0122267	−	0.186779i
$809$	−4.64617e43			−1.11652			−0.558261	−	0.829665i	$-0.688531\pi$
$809$	−4.64617e43			−1.11652			−0.558261	+	0.829665i	$0.688531\pi$
$810$	−1.53540e42	+	7.04548e43i	−0.0362197	+	1.66202i
$811$		−	7.85781e43i		−	1.81965i	−0.414989	−	0.909826i	$-0.636215\pi$
$811$		−	7.85781e43i		−	1.81965i	0.414989	−	0.909826i	$-0.363785\pi$
$812$	−2.39654e41	+	5.49589e42i	−0.00544808	+	0.124939i
$813$	6.16570e43			1.37602
$814$	8.06868e42	+	1.75838e41i	0.176781	+	0.00385253i
$815$		−	2.97727e43i		−	0.640405i
$816$	4.32712e42	−	4.95218e43i	0.0913791	−	1.04579i
$817$	5.08461e43			1.05421
$818$	7.01308e41	−	3.21809e43i	0.0142761	−	0.655087i
$819$			1.73767e41i			0.00347302i
$820$	−4.01159e43	−	1.74929e42i	−0.787243	−	0.0343285i
$821$	−7.47551e42			−0.144043			−0.0720217	−	0.997403i	$-0.522945\pi$
$821$	−7.47551e42			−0.144043			−0.0720217	+	0.997403i	$0.522945\pi$
$822$	−3.87157e43	−	8.43718e41i	−0.732505	−	0.0159632i
$823$			3.99870e43i			0.742884i	0.928456	+	0.371442i	$0.121136\pi$
$823$			3.99870e43i			0.742884i	−0.928456	+	0.371442i	$0.878864\pi$
$824$	6.11496e43	+	4.00290e42i	1.11554	+	0.0730242i
$825$	−9.05370e43			−1.62187
$826$	2.09393e41	−	9.60843e42i	0.00368351	−	0.169025i
$827$			3.27129e43i			0.565115i	0.959250	+	0.282557i	$0.0911828\pi$
$827$			3.27129e43i			0.565115i	−0.959250	+	0.282557i	$0.908817\pi$
$828$	−2.29929e41	+	5.27287e42i	−0.00390066	+	0.0894523i
$829$	−9.41702e43			−1.56890			−0.784451	−	0.620191i	$-0.787055\pi$
$829$	−9.41702e43			−1.56890			−0.784451	+	0.620191i	$0.787055\pi$
$830$	−1.23389e44	−	2.68897e42i	−2.01885	−	0.0439961i
$831$			1.79569e43i			0.288547i
$832$	2.84862e43	+	3.74551e42i	0.449556	+	0.0591099i
$833$	−6.88164e43			−1.06664
$834$	−3.54156e41	+	1.62512e43i	−0.00539143	+	0.247397i
$835$			1.25192e44i			1.87189i
$836$	8.61925e43	+	3.75851e42i	1.26583	+	0.0551978i
$837$	5.87804e43			0.847911
$838$	4.64934e42	+	1.01321e41i	0.0658766	+	0.00143563i
$839$		−	2.76423e42i		−	0.0384720i	−0.999815	−	0.0192360i	$-0.993877\pi$
$839$		−	2.76423e42i		−	0.0384720i	0.999815	−	0.0192360i	$-0.00612339\pi$
$840$	−1.02783e42	+	1.57014e43i	−0.0140518	+	0.214660i
$841$	2.26656e41			0.00304388
$842$	−4.24237e41	+	1.94670e43i	−0.00559664	+	0.256813i
$843$		−	9.15479e43i		−	1.18641i
$844$	8.32167e39	−	1.90838e41i	0.000105943	−	0.00242956i
$845$	1.12945e44			1.41259
$846$	6.06049e42	+	1.32074e41i	0.0744651	+	0.00162279i
$847$		−	4.14202e42i		−	0.0499990i
$848$	4.02552e43	+	3.51742e42i	0.477402	+	0.0417145i
$849$	8.22311e43			0.958121
$850$	4.45831e42	−	2.04579e44i	0.0510372	−	2.34195i
$851$			2.96354e43i			0.333324i
$852$	−1.40134e43	−	6.11067e41i	−0.154863	−	0.00675297i
$853$	−1.29345e44			−1.40448			−0.702238	−	0.711942i	$-0.747816\pi$
$853$	−1.29345e44			−1.40448			−0.702238	+	0.711942i	$0.747816\pi$
$854$	−3.97918e42	−	8.67169e40i	−0.0424547	−	0.000925200i
$855$		−	1.70248e43i		−	0.178480i
$856$	−8.40585e43	−	5.50254e42i	−0.865915	−	0.0566835i
$857$	2.35817e43			0.238705			0.119353	−	0.992852i	$-0.461918\pi$
$857$	2.35817e43			0.238705			0.119353	+	0.992852i	$0.461918\pi$
$858$	−7.45077e41	+	3.41894e43i	−0.00741125	+	0.340081i
$859$			1.97004e44i			1.92565i	0.270118	+	0.962827i	$0.412937\pi$
$859$			1.97004e44i			1.92565i	−0.270118	+	0.962827i	$0.587063\pi$
$860$	5.19576e42	−	1.19153e44i	0.0499083	−	1.14453i
$861$	−5.67934e42			−0.0536106
$862$	8.18999e43	+	1.78482e42i	0.759757	+	0.0165571i
$863$		−	1.27437e43i		−	0.116181i	−0.998311	−	0.0580904i	$-0.981499\pi$
$863$		−	1.27437e43i		−	0.116181i	0.998311	−	0.0580904i	$-0.0185011\pi$
$864$	−1.14086e44	−	1.24786e43i	−1.02218	−	0.111805i
$865$	3.35068e44			2.95047
$866$	3.60287e42	−	1.65325e44i	0.0311803	−	1.43077i
$867$			1.98242e43i			0.168620i
$868$	1.23048e43	+	5.36564e41i	0.102868	+	0.00448565i
$869$	−9.57421e43			−0.786695
$870$	2.13587e44	+	4.65462e42i	1.72499	+	0.0375920i
$871$		−	7.16742e42i		−	0.0568972i
$872$	−2.42614e42	+	3.70625e43i	−0.0189308	+	0.289193i
$873$	−7.07461e42			−0.0542611
$874$	−6.90230e42	+	3.16726e44i	−0.0520382	+	2.38788i
$875$			3.48112e43i			0.257987i
$876$	−8.76719e42	+	2.01055e44i	−0.0638703	+	1.46471i
$877$	−1.58372e44			−1.13419			−0.567093	−	0.823654i	$-0.691932\pi$
$877$	−1.58372e44			−1.13419			−0.567093	+	0.823654i	$0.691932\pi$
$878$	−1.74772e43	−	3.80875e41i	−0.123042	−	0.00268142i
$879$		−	9.36641e43i		−	0.648247i
$880$	1.76153e43	−	2.01599e44i	0.119854	−	1.37167i
$881$	−5.90709e43			−0.395126			−0.197563	−	0.980290i	$-0.563303\pi$
$881$	−5.90709e43			−0.395126			−0.197563	+	0.980290i	$0.563303\pi$
$882$	−2.00061e41	+	9.18021e42i	−0.00131563	+	0.0603704i
$883$		−	1.35461e44i		−	0.875795i	−0.899025	−	0.437898i	$-0.855723\pi$
$883$		−	1.35461e44i		−	0.875795i	0.899025	−	0.437898i	$-0.144277\pi$
$884$	−7.72182e43	−	3.36717e42i	−0.490835	−	0.0214033i
$885$	−3.73235e44			−2.33256
$886$	−1.71604e44	−	3.73971e42i	−1.05444	−	0.0229790i
$887$		−	2.48703e44i		−	1.50254i	−0.659994	−	0.751271i	$-0.729441\pi$
$887$		−	2.48703e44i		−	1.50254i	0.659994	−	0.751271i	$-0.270559\pi$
$888$	−3.71650e43	−	2.43285e42i	−0.220770	−	0.0144518i
$889$	−1.02231e43			−0.0597114
$890$	−7.10064e42	+	3.25828e44i	−0.0407800	+	1.87128i
$891$		−	1.28190e44i		−	0.723916i
$892$	−7.59481e42	+	1.74169e44i	−0.0421740	+	0.967160i
$893$	3.63864e44			1.98686
$894$	1.19916e44	+	2.61328e42i	0.643893	+	0.0140321i
$895$			3.31453e44i			1.75016i
$896$	−2.37683e43	−	3.65363e42i	−0.123418	−	0.0189716i
$897$	−1.25574e44			−0.641228
$898$	8.36116e42	−	3.83669e44i	0.0419876	−	1.92669i
$899$		−	1.67223e44i		−	0.825851i
$900$	−2.72781e43	−	1.18949e42i	−0.132488	−	0.00577728i
$901$	−1.08705e44			−0.519252
$902$	7.30242e43	+	1.59139e42i	0.343059	+	0.00747616i
$903$		−	1.68688e43i		−	0.0779414i
$904$	1.59613e43	−	2.43830e44i	0.0725341	−	1.10805i
$905$	2.78399e44			1.24434
$906$	−1.54420e42	+	7.08587e43i	−0.00678860	+	0.311509i
$907$			1.51209e43i			0.0653837i	0.999465	+	0.0326919i	$0.0104080\pi$
$907$			1.51209e43i			0.0653837i	−0.999465	+	0.0326919i	$0.989592\pi$
$908$	−1.46009e43	+	3.34838e44i	−0.0621001	+	1.42412i
$909$	2.74452e42			0.0114818
$910$	2.44596e43	+	5.33038e41i	0.100653	+	0.00219350i
$911$		−	1.89804e44i		−	0.768299i	−0.923271	−	0.384149i	$-0.874495\pi$
$911$		−	1.89804e44i		−	0.768299i	0.923271	−	0.384149i	$-0.125505\pi$
$912$	−3.96632e44	−	3.46570e43i	−1.57930	−	0.137996i
$913$	2.24502e44			0.879342
$914$	−4.34496e42	+	1.99377e44i	−0.0167414	+	0.768216i
$915$			1.54570e44i			0.585878i
$916$	−3.18765e44	−	1.39001e43i	−1.18861	−	0.0518305i
$917$	1.74308e43			0.0639408
$918$	3.08665e44	+	6.72664e42i	1.11390	+	0.0242749i
$919$		−	1.50291e44i		−	0.533581i	−0.963755	−	0.266791i	$-0.914037\pi$
$919$		−	1.50291e44i		−	0.533581i	0.963755	−	0.266791i	$-0.0859632\pi$
$920$	7.41509e44	+	4.85398e43i	2.58999	+	0.169543i
$921$	−4.99032e43			−0.171488
$922$	4.85027e42	−	2.22565e44i	0.0163984	−	0.752476i
$923$			2.18092e43i			0.0725460i
$924$	1.24693e42	−	2.85954e43i	0.00408096	−	0.0935872i
$925$	−1.53313e44			−0.493688
$926$	6.00145e43	+	1.30787e42i	0.190148	+	0.00414382i
$927$			2.19969e43i			0.0685749i
$928$	−3.55002e43	+	3.24562e44i	−0.108896	+	0.995583i
$929$	2.29947e44			0.694052			0.347026	−	0.937856i	$-0.387192\pi$
$929$	2.29947e44			0.694052			0.347026	+	0.937856i	$0.387192\pi$
$930$	1.04213e43	−	4.78202e44i	0.0309512	−	1.42026i
$931$			5.51167e44i			1.61079i
$932$	2.85908e44	+	1.24673e43i	0.822220	+	0.0358537i
$933$	3.33471e44			0.943700
$934$	−2.04158e44	−	4.44915e42i	−0.568544	−	0.0123901i
$935$			5.44397e44i			1.49191i
$936$	−6.73672e41	+	1.02912e43i	−0.00181682	+	0.0277542i
$937$	−5.38166e44			−1.42831			−0.714155	−	0.699987i	$-0.753189\pi$
$937$	−5.38166e44			−1.42831			−0.714155	+	0.699987i	$0.753189\pi$
$938$	−1.30703e41	+	5.99755e42i	−0.000341383	+	0.0156650i
$939$		−	1.49273e44i		−	0.383704i
$940$	3.71818e43	−	8.52676e44i	0.0940616	−	2.15708i
$941$	−6.83634e44			−1.70208			−0.851039	−	0.525102i	$-0.824027\pi$
$941$	−6.83634e44			−1.70208			−0.851039	+	0.525102i	$0.824027\pi$
$942$	−4.27628e44	−	9.31915e42i	−1.04786	−	0.0228356i
$943$			2.68210e44i			0.646844i
$944$	4.96519e43	−	5.68242e44i	0.117857	−	1.34882i
$945$	−9.77262e43			−0.228315
$946$	−4.72675e42	+	2.16897e44i	−0.0108692	+	0.498754i
$947$		−	2.90385e44i		−	0.657241i	−0.944462	−	0.328620i	$-0.893416\pi$
$947$		−	2.90385e44i		−	0.657241i	0.944462	−	0.328620i	$-0.106584\pi$
$948$	4.41416e44	+	1.92484e43i	0.983383	+	0.0428814i
$949$	3.12904e44			0.686147
$950$	−1.63852e45	−	3.57077e43i	−3.53670	−	0.0770739i
$951$			5.94694e44i			1.26353i
$952$	6.45532e43	+	4.22571e42i	0.135009	+	0.00883782i
$953$	5.97482e44			1.23007			0.615037	−	0.788498i	$-0.289141\pi$
$953$	5.97482e44			1.23007			0.615037	+	0.788498i	$0.289141\pi$
$954$	−3.16024e41	+	1.45014e43i	−0.000640463	+	0.0293890i
$955$		−	1.06845e45i		−	2.13159i
$956$	−6.73503e42	+	1.54452e44i	−0.0132273	+	0.303337i
$957$	−3.88614e44			−0.751344
$958$	9.20748e44	+	2.00655e43i	1.75250	+	0.0381916i
$959$		−	5.03951e43i		−	0.0944299i
$960$	−1.21745e44	+	9.25924e44i	−0.224586	+	1.70807i
$961$	1.76220e44			0.320040
$962$	−1.26169e42	+	5.78953e43i	−0.00225594	+	0.103518i
$963$		−	3.02378e43i		−	0.0532299i
$964$	−3.06814e44	−	1.33789e43i	−0.531765	−	0.0231881i
$965$	−6.36140e44			−1.08553
$966$	1.05078e44	+	2.28992e42i	0.176544	+	0.00384736i
$967$		−	4.21285e43i		−	0.0696913i	−0.999393	−	0.0348457i	$-0.988906\pi$
$967$		−	4.21285e43i		−	0.0696913i	0.999393	−	0.0348457i	$-0.0110940\pi$
$968$	1.60581e43	−	2.45309e44i	0.0261556	−	0.399561i
$969$	1.07106e45			1.71775
$970$	−2.17018e43	+	9.95829e44i	−0.0342704	+	1.57257i
$971$			1.13716e45i			1.76821i	0.467285	+	0.884107i	$0.345232\pi$
$971$			1.13716e45i			1.76821i	−0.467285	+	0.884107i	$0.654768\pi$
$972$	3.48564e42	−	7.99350e43i	0.00533690	−	0.122389i
$973$	−2.11537e43			−0.0318929
$974$	−3.74364e44	−	8.15837e42i	−0.555788	−	0.0121121i
$975$		−	6.49631e44i		−	0.949725i
$976$	−2.35328e44	−	2.05626e43i	−0.338787	−	0.0296026i
$977$	−5.49221e44			−0.778626			−0.389313	−	0.921106i	$-0.627287\pi$
$977$	−5.49221e44			−0.778626			−0.389313	+	0.921106i	$0.627287\pi$
$978$	5.44532e42	−	2.49870e44i	0.00760222	−	0.348844i
$979$		−	5.92832e44i		−	0.815063i
$980$	1.29160e45	+	5.63216e43i	1.74879	+	0.0762577i
$981$	−1.33322e43			−0.0177774
$982$	1.49281e45	+	3.25323e43i	1.96035	+	0.0427211i
$983$		−	1.66215e44i		−	0.214964i	−0.994207	−	0.107482i	$-0.965721\pi$
$983$		−	1.66215e44i		−	0.214964i	0.994207	−	0.107482i	$-0.0342788\pi$
$984$	−3.36356e44	−	2.20181e43i	−0.428422	−	0.0280449i
$985$	8.22792e44			1.03216
$986$	1.91365e43	−	8.78117e44i	0.0236433	−	1.08492i
$987$		−	1.20716e44i		−	0.146895i
$988$	−2.69685e43	+	6.18458e44i	−0.0323223	+	0.741236i
$989$	−7.96638e44			−0.940409
$990$	7.26234e43	+	1.58265e42i	0.0844400	+	0.00184017i
$991$		−	1.32085e45i		−	1.51269i	−0.654175	−	0.756343i	$-0.726984\pi$
$991$		−	1.32085e45i		−	1.51269i	0.654175	−	0.756343i	$-0.273016\pi$
$992$	7.26665e44	+	7.94819e43i	0.819708	+	0.0896589i
$993$	5.86363e44			0.651520
$994$	3.97704e41	−	1.82495e43i	0.000435275	−	0.0199735i
$995$		−	1.31716e45i		−	1.42001i
$996$	−1.03506e45	−	4.51347e43i	−1.09919	−	0.0479314i
$997$	−1.84920e44			−0.193445			−0.0967224	−	0.995311i	$-0.530836\pi$
$997$	−1.84920e44			−0.193445			−0.0967224	+	0.995311i	$0.530836\pi$
$998$	−1.11317e45	−	2.42590e43i	−1.14711	−	0.0249985i
$999$		−	2.31316e44i		−	0.234814i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4.31.b.a.3.8	yes	14
3.2	odd	2		36.31.d.c.19.7		14
4.3	odd	2	inner	4.31.b.a.3.7	✓	14
12.11	even	2		36.31.d.c.19.8		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4.31.b.a.3.7	✓	14	4.3	odd	2	inner
4.31.b.a.3.8	yes	14	1.1	even	1	trivial
36.31.d.c.19.7		14	3.2	odd	2
36.31.d.c.19.8		14	12.11	even	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:	\( N \)	\(=\)	\( 4 = 2^{2} \)
Weight:	\( k \)	\(=\)	\( 31 \)
Character orbit:	\([\chi]\)	\(=\)	4.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-713.932 + 32760.2i) q^{2} +1.39019e7i q^{3} +(-1.07272e9 - 4.67771e7i) q^{4} -5.42656e10 q^{5} +(-4.55428e11 - 9.92498e9i) q^{6} -5.92817e11i q^{7} +(2.29828e12 - 3.51092e13i) q^{8} +1.26296e13 q^{9} +O(q^{10})\)	\(q+(-713.932 + 32760.2i) q^{2} +1.39019e7i q^{3} +(-1.07272e9 - 4.67771e7i) q^{4} -5.42656e10 q^{5} +(-4.55428e11 - 9.92498e9i) q^{6} -5.92817e11i q^{7} +(2.29828e12 - 3.51092e13i) q^{8} +1.26296e13 q^{9} +(3.87420e13 - 1.77775e15i) q^{10} +3.23456e15i q^{11} +(6.50289e14 - 1.49128e16i) q^{12} -2.32090e16 q^{13} +(1.94208e16 + 4.23231e14i) q^{14} -7.54393e17i q^{15} +(1.14855e18 + 1.00358e17i) q^{16} -3.10153e18 q^{17} +(-9.01667e15 + 4.13748e17i) q^{18} +2.48409e19i q^{19} +(5.82120e19 + 2.53839e18i) q^{20} +8.24125e18 q^{21} +(-1.05965e20 - 2.30926e18i) q^{22} -3.89198e20i q^{23} +(4.88083e20 + 3.19503e19i) q^{24} +2.01344e21 q^{25} +(1.65696e19 - 7.60332e20i) q^{26} +3.03784e21i q^{27} +(-2.77303e19 + 6.35928e20i) q^{28} +8.64231e21 q^{29} +(2.47141e22 + 5.38585e20i) q^{30} -1.93494e22i q^{31} +(-4.10772e21 + 3.75550e22i) q^{32} -4.49664e22 q^{33} +(2.21428e21 - 1.01607e23i) q^{34} +3.21696e22i q^{35} +(-1.35480e22 - 5.90776e20i) q^{36} -7.61448e22 q^{37} +(-8.13793e23 - 1.77347e22i) q^{38} -3.22648e23i q^{39} +(-1.24718e23 + 1.90522e24i) q^{40} -6.89135e23 q^{41} +(-5.88369e21 + 2.69985e23i) q^{42} -2.04687e24i q^{43} +(1.51303e23 - 3.46979e24i) q^{44} -6.85353e23 q^{45} +(1.27502e25 + 2.77861e23i) q^{46} -1.46478e25i q^{47} +(-1.39516e24 + 1.59669e25i) q^{48} +2.21879e25 q^{49} +(-1.43746e24 + 6.59606e25i) q^{50} -4.31170e25i q^{51} +(2.48968e25 + 1.08565e24i) q^{52} +3.50489e25 q^{53} +(-9.95204e25 - 2.16881e24i) q^{54} -1.75525e26i q^{55} +(-2.08133e25 - 1.36246e24i) q^{56} -3.45334e26 q^{57} +(-6.17002e24 + 2.83124e26i) q^{58} -4.94749e26i q^{59} +(-3.52883e25 + 8.09254e26i) q^{60} -2.04893e26 q^{61} +(6.33890e26 + 1.38141e25i) q^{62} -7.48704e24i q^{63} +(-1.22738e27 - 1.61382e26i) q^{64} +1.25945e27 q^{65} +(3.21029e25 - 1.47311e27i) q^{66} +3.08821e26i q^{67} +(3.32708e27 + 1.45081e26i) q^{68} +5.41057e27 q^{69} +(-1.05388e27 - 2.29669e25i) q^{70} -9.39686e26i q^{71} +(2.90263e25 - 4.43415e26i) q^{72} -1.34820e28 q^{73} +(5.43622e25 - 2.49452e27i) q^{74} +2.79905e28i q^{75} +(1.16198e27 - 2.66474e28i) q^{76} +1.91750e27 q^{77} +(1.05700e28 + 2.30349e26i) q^{78} +2.95997e28i q^{79} +(-6.23265e28 - 5.44598e27i) q^{80} -3.96313e28 q^{81} +(4.91996e26 - 2.25762e28i) q^{82} -6.94072e28i q^{83} +(-8.84058e27 - 3.85502e26i) q^{84} +1.68306e29 q^{85} +(6.70560e28 + 1.46133e27i) q^{86} +1.20144e29i q^{87} +(1.13563e29 + 7.43393e27i) q^{88} -1.83280e29 q^{89} +(4.89295e26 - 2.24523e28i) q^{90} +1.37587e28i q^{91} +(-1.82055e28 + 4.17501e29i) q^{92} +2.68992e29 q^{93} +(4.79864e29 + 1.04575e28i) q^{94} -1.34801e30i q^{95} +(-5.22083e29 - 5.71050e28i) q^{96} -5.60161e29 q^{97} +(-1.58407e28 + 7.26881e29i) q^{98} +4.08512e28i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 24476 q^{2} - 820787056 q^{4} + 14864798540 q^{5} - 454068012192 q^{6} - 31343321296064 q^{8} - 722181861644898 q^{9}+O(q^{10}) \) 14 * q - 24476 * q^2 - 820787056 * q^4 + 14864798540 * q^5 - 454068012192 * q^6 - 31343321296064 * q^8 - 722181861644898 * q^9	\( 14 q - 24476 q^{2} - 820787056 q^{4} + 14864798540 q^{5} - 454068012192 q^{6} - 31343321296064 q^{8} - 722181861644898 q^{9} - 12\!\cdots\!60 q^{10}+ \cdots + 47\!\cdots\!36 q^{98}+O(q^{100}) \) 14 * q - 24476 * q^2 - 820787056 * q^4 + 14864798540 * q^5 - 454068012192 * q^6 - 31343321296064 * q^8 - 722181861644898 * q^9 - 1287889809124760 * q^10 + 51879382052868480 * q^12 + 73473894124935532 * q^13 + 36761277666527808 * q^14 - 1064191557393108736 * q^16 - 4417201733411195812 * q^17 + 10773613739927673156 * q^18 + 31289641216539815840 * q^20 - 24107806000815293184 * q^21 - 63855041197225323360 * q^22 - 219200204962023547392 * q^24 + 2557307336405009852730 * q^25 + 2662172027973979655720 * q^26 + 2286217156307884458240 * q^28 - 5183126634353006173012 * q^29 - 19995309903793012445760 * q^30 + 42868919292290358744064 * q^32 + 45729663133049254147200 * q^33 + 189270161167001176158280 * q^34 - 265369932957818409094128 * q^36 - 627167100163080968189492 * q^37 - 1048227922470375880434720 * q^38 + 249748411367898391857280 * q^40 + 1494251155359817033760828 * q^41 + 2632732296455102155814400 * q^42 + 724029644533237152067200 * q^44 - 15629634719291168966183700 * q^45 + 6965410628317069602441408 * q^46 + 22826956997174454465976320 * q^48 + 36971394165784621527528302 * q^49 - 6257136580151365293802740 * q^50 - 3584406874106323077960032 * q^52 - 162298735436688848725454068 * q^53 + 103759862824624790541134016 * q^54 - 103480837826586244326484992 * q^56 - 178372120064399401723873920 * q^57 + 292818259345642447695165352 * q^58 + 673940775243590010378428160 * q^60 - 781363600109479145350441172 * q^61 - 700904834820308348700230400 * q^62 - 1886538399231001232282054656 * q^64 - 766208515593499839727344200 * q^65 + 4354147454872998865031212800 * q^66 - 1563708764577905097576648928 * q^68 + 12984546958279555654634831616 * q^69 + 5791600195068600540130627200 * q^70 - 12292930844134853078053553856 * q^72 - 13974688009272270633487568708 * q^73 - 1683916522088046880433965720 * q^74 - 43359191482193415443604585600 * q^76 - 13914563925551368590607269120 * q^77 + 103407672785786602276239960000 * q^78 - 142384583917045013024432289280 * q^80 + 142873441147816769491949878830 * q^81 + 100782649420724457106091722888 * q^82 - 274539668577865429004166211584 * q^84 - 166040172454330922908332123880 * q^85 + 409278053261716222570289186208 * q^86 - 745586494961630729936044285440 * q^88 + 98873747700972853801823899388 * q^89 + 1804754410453947165713321465640 * q^90 - 1825371837423533828188743456000 * q^92 - 123062607213511416597600107520 * q^93 + 2752292471954002780670205710208 * q^94 - 4054034025223909146350873812992 * q^96 - 1029388221334221132711894149732 * q^97 + 4774196460313129800493027312036 * q^98

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