LMFDB - Embedded newform 4.31.b.a.3.1

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			3.1
Root			$0.500000 - 287382. i$ of defining polynomial
Character	$\chi$	$=$	4.3
Dual form			4.31.b.a.3.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-31548.7 - 8855.74i) q^{2} +4.59811e6i q^{3} +(9.16894e8 + 5.58773e8i) q^{4} -1.46052e10 q^{5} +(4.07197e10 - 1.45064e11i) q^{6} +9.18461e12i q^{7} +(-2.39784e13 - 2.57483e13i) q^{8} +1.84749e14 q^{9} +O(q^{10})$	\(q+(-31548.7 - 8855.74i) q^{2} +4.59811e6i q^{3} +(9.16894e8 + 5.58773e8i) q^{4} -1.46052e10 q^{5} +(4.07197e10 - 1.45064e11i) q^{6} +9.18461e12i q^{7} +(-2.39784e13 - 2.57483e13i) q^{8} +1.84749e14 q^{9} +(4.60774e14 + 1.29340e14i) q^{10} -4.03801e15i q^{11} +(-2.56930e15 + 4.21598e15i) q^{12} +4.32635e16 q^{13} +(8.13365e16 - 2.89762e17i) q^{14} -6.71562e16i q^{15} +(5.28466e17 + 1.02467e18i) q^{16} -6.32902e17 q^{17} +(-5.82857e18 - 1.63609e18i) q^{18} +1.63717e19i q^{19} +(-1.33914e19 - 8.16098e18i) q^{20} -4.22319e19 q^{21} +(-3.57596e19 + 1.27394e20i) q^{22} -1.15582e19i q^{23} +(1.18394e20 - 1.10255e20i) q^{24} -7.18011e20 q^{25} +(-1.36490e21 - 3.83130e20i) q^{26} +1.79620e21i q^{27} +(-5.13212e21 + 8.42131e21i) q^{28} -1.25904e22 q^{29} +(-5.94718e20 + 2.11869e21i) q^{30} +2.07261e22i q^{31} +(-7.59817e21 - 3.70070e22i) q^{32} +1.85672e22 q^{33} +(1.99672e22 + 5.60482e21i) q^{34} -1.34143e23i q^{35} +(1.69395e23 + 1.03233e23i) q^{36} +1.65423e23 q^{37} +(1.44984e23 - 5.16505e23i) q^{38} +1.98930e23i q^{39} +(3.50209e23 + 3.76059e23i) q^{40} -7.85091e23 q^{41} +(1.33236e24 + 3.73994e23i) q^{42} -1.58710e24i q^{43} +(2.25634e24 - 3.70243e24i) q^{44} -2.69828e24 q^{45} +(-1.02357e23 + 3.64646e23i) q^{46} +1.80678e25i q^{47} +(-4.71155e24 + 2.42994e24i) q^{48} -6.18178e25 q^{49} +(2.26523e25 + 6.35852e24i) q^{50} -2.91015e24i q^{51} +(3.96680e25 + 2.41745e25i) q^{52} -4.74301e25 q^{53} +(1.59067e25 - 5.66678e25i) q^{54} +5.89759e25i q^{55} +(2.36488e26 - 2.20232e26i) q^{56} -7.52789e25 q^{57} +(3.97210e26 + 1.11497e26i) q^{58} -2.91121e26i q^{59} +(3.75251e25 - 6.15751e25i) q^{60} -6.03926e26 q^{61} +(1.83545e26 - 6.53879e26i) q^{62} +1.69684e27i q^{63} +(-8.80122e25 + 1.23481e27i) q^{64} -6.31870e26 q^{65} +(-5.85771e26 - 1.64427e26i) q^{66} -3.55919e27i q^{67} +(-5.80304e26 - 3.53649e26i) q^{68} +5.31459e25 q^{69} +(-1.18793e27 + 4.23203e27i) q^{70} +5.42604e27i q^{71} +(-4.42997e27 - 4.75696e27i) q^{72} +6.40870e27 q^{73} +(-5.21888e27 - 1.46495e27i) q^{74} -3.30150e27i q^{75} +(-9.14808e27 + 1.50111e28i) q^{76} +3.70876e28 q^{77} +(1.76167e27 - 6.27598e27i) q^{78} -4.23310e28i q^{79} +(-7.71834e27 - 1.49655e28i) q^{80} +2.97789e28 q^{81} +(2.47686e28 + 6.95257e27i) q^{82} +4.11957e28i q^{83} +(-3.87221e28 - 2.35980e28i) q^{84} +9.24365e27 q^{85} +(-1.40550e28 + 5.00710e28i) q^{86} -5.78920e28i q^{87} +(-1.03972e29 + 9.68251e28i) q^{88} -3.08901e29 q^{89} +(8.51272e28 + 2.38953e28i) q^{90} +3.97358e29i q^{91} +(6.45842e27 - 1.05977e28i) q^{92} -9.53007e28 q^{93} +(1.60003e29 - 5.70013e29i) q^{94} -2.39112e29i q^{95} +(1.70162e29 - 3.49372e28i) q^{96} -2.56756e29 q^{97} +(1.95027e30 + 5.47442e29i) q^{98} -7.46017e29i 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 $

$2$	−31548.7	−	8855.74i	−0.962789	−	0.270256i
$2$	−31548.7	−	8855.74i	−0.962789	−	0.270256i
$3$			4.59811e6i			0.320450i	0.987081	+	0.160225i	$0.0512220\pi$
$3$			4.59811e6i			0.320450i	−0.987081	+	0.160225i	$0.948778\pi$
$4$	9.16894e8	+	5.58773e8i	0.853924	+	0.520398i
$5$	−1.46052e10			−0.478582			−0.239291	−	0.970948i	$-0.576915\pi$
$5$	−1.46052e10			−0.478582			−0.239291	+	0.970948i	$0.576915\pi$
$6$	4.07197e10	−	1.45064e11i	0.0866035	−	0.308526i
$7$			9.18461e12i			1.93460i	0.253643	+	0.967298i	$0.418371\pi$
$7$			9.18461e12i			1.93460i	−0.253643	+	0.967298i	$0.581629\pi$
$8$	−2.39784e13	−	2.57483e13i	−0.681507	−	0.731811i
$9$	1.84749e14			0.897312
$10$	4.60774e14	+	1.29340e14i	0.460774	+	0.129340i
$11$		−	4.03801e15i		−	0.966669i	−0.875436	−	0.483334i	$-0.839426\pi$
$11$		−	4.03801e15i		−	0.966669i	0.875436	−	0.483334i	$-0.160574\pi$
$12$	−2.56930e15	+	4.21598e15i	−0.166762	+	0.273640i
$13$	4.32635e16			0.845222			0.422611	−	0.906311i	$-0.361114\pi$
$13$	4.32635e16			0.845222			0.422611	+	0.906311i	$0.361114\pi$
$14$	8.13365e16	−	2.89762e17i	0.522836	−	1.86261i
$15$		−	6.71562e16i		−	0.153362i
$16$	5.28466e17	+	1.02467e18i	0.458371	+	0.888761i
$17$	−6.32902e17			−0.221107			−0.110554	−	0.993870i	$-0.535262\pi$
$17$	−6.32902e17			−0.221107			−0.110554	+	0.993870i	$0.535262\pi$
$18$	−5.82857e18	−	1.63609e18i	−0.863921	−	0.242504i
$19$			1.63717e19i			1.07843i	0.842170	+	0.539213i	$0.181278\pi$
$19$			1.63717e19i			1.07843i	−0.842170	+	0.539213i	$0.818722\pi$
$20$	−1.33914e19	−	8.16098e18i	−0.408673	−	0.249053i
$21$	−4.22319e19			−0.619942
$22$	−3.57596e19	+	1.27394e20i	−0.261248	+	0.930697i
$23$		−	1.15582e19i		−	0.0433484i	−0.999765	−	0.0216742i	$-0.993100\pi$
$23$		−	1.15582e19i		−	0.0433484i	0.999765	−	0.0216742i	$-0.00689966\pi$
$24$	1.18394e20	−	1.10255e20i	0.234509	−	0.218389i
$25$	−7.18011e20			−0.770959
$26$	−1.36490e21	−	3.83130e20i	−0.813770	−	0.228426i
$27$			1.79620e21i			0.607994i
$28$	−5.13212e21	+	8.42131e21i	−1.00676	+	1.65200i
$29$	−1.25904e22			−1.45905			−0.729524	−	0.683956i	$-0.760258\pi$
$29$	−1.25904e22			−1.45905			−0.729524	+	0.683956i	$0.760258\pi$
$30$	−5.94718e20	+	2.11869e21i	−0.0414469	+	0.147655i
$31$			2.07261e22i			0.883266i	0.897196	+	0.441633i	$0.145601\pi$
$31$			2.07261e22i			0.883266i	−0.897196	+	0.441633i	$0.854399\pi$
$32$	−7.59817e21	−	3.70070e22i	−0.201122	−	0.979566i
$33$	1.85672e22			0.309769
$34$	1.99672e22	+	5.60482e21i	0.212879	+	0.0597555i
$35$		−	1.34143e23i		−	0.925863i
$36$	1.69395e23	+	1.03233e23i	0.766236	+	0.466960i
$37$	1.65423e23			0.496102			0.248051	−	0.968747i	$-0.420210\pi$
$37$	1.65423e23			0.496102			0.248051	+	0.968747i	$0.420210\pi$
$38$	1.44984e23	−	5.16505e23i	0.291451	−	1.03830i
$39$			1.98930e23i			0.270852i
$40$	3.50209e23	+	3.76059e23i	0.326157	+	0.350232i
$41$	−7.85091e23			−0.504850			−0.252425	−	0.967616i	$-0.581228\pi$
$41$	−7.85091e23			−0.504850			−0.252425	+	0.967616i	$0.581228\pi$
$42$	1.33236e24	+	3.73994e23i	0.596873	+	0.167543i
$43$		−	1.58710e24i		−	0.499550i	−0.968304	−	0.249775i	$-0.919643\pi$
$43$		−	1.58710e24i		−	0.499550i	0.968304	−	0.249775i	$-0.0803566\pi$
$44$	2.25634e24	−	3.70243e24i	0.503053	−	0.825461i
$45$	−2.69828e24			−0.429438
$46$	−1.02357e23	+	3.64646e23i	−0.0117152	+	0.0417354i
$47$			1.80678e25i			1.49774i	0.662717	+	0.748870i	$0.269403\pi$
$47$			1.80678e25i			1.49774i	−0.662717	+	0.748870i	$0.730597\pi$
$48$	−4.71155e24	+	2.42994e24i	−0.284804	+	0.146885i
$49$	−6.18178e25			−2.74266
$50$	2.26523e25	+	6.35852e24i	0.742270	+	0.208356i
$51$		−	2.91015e24i		−	0.0708538i
$52$	3.96680e25	+	2.41745e25i	0.721755	+	0.439852i
$53$	−4.74301e25			−0.648509			−0.324255	−	0.945970i	$-0.605113\pi$
$53$	−4.74301e25			−0.648509			−0.324255	+	0.945970i	$0.605113\pi$
$54$	1.59067e25	−	5.66678e25i	0.164314	−	0.585370i
$55$			5.89759e25i			0.462630i
$56$	2.36488e26	−	2.20232e26i	1.41576	−	1.31844i
$57$	−7.52789e25			−0.345582
$58$	3.97210e26	+	1.11497e26i	1.40475	+	0.394316i
$59$		−	2.91121e26i		−	0.796697i	−0.917234	−	0.398348i	$-0.869584\pi$
$59$		−	2.91121e26i		−	0.796697i	0.917234	−	0.398348i	$-0.130416\pi$
$60$	3.75251e25	−	6.15751e25i	0.0798092	−	0.130959i
$61$	−6.03926e26			−1.00239			−0.501195	−	0.865335i	$-0.667106\pi$
$61$	−6.03926e26			−1.00239			−0.501195	+	0.865335i	$0.667106\pi$
$62$	1.83545e26	−	6.53879e26i	0.238708	−	0.850398i
$63$			1.69684e27i			1.73594i
$64$	−8.80122e25	+	1.23481e27i	−0.0710957	+	0.997469i
$65$	−6.31870e26			−0.404508
$66$	−5.85771e26	−	1.64427e26i	−0.298242	−	0.0837169i
$67$		−	3.55919e27i		−	1.44620i	−0.690742	−	0.723101i	$-0.742716\pi$
$67$		−	3.55919e27i		−	1.44620i	0.690742	−	0.723101i	$-0.257284\pi$
$68$	−5.80304e26	−	3.53649e26i	−0.188809	−	0.115064i
$69$	5.31459e25			0.0138910
$70$	−1.18793e27	+	4.23203e27i	−0.250220	+	0.891411i
$71$			5.42604e27i			0.923864i	0.886915	+	0.461932i	$0.152844\pi$
$71$			5.42604e27i			0.923864i	−0.886915	+	0.461932i	$0.847156\pi$
$72$	−4.42997e27	−	4.75696e27i	−0.611524	−	0.656663i
$73$	6.40870e27			0.719328			0.359664	−	0.933082i	$-0.382891\pi$
$73$	6.40870e27			0.719328			0.359664	+	0.933082i	$0.382891\pi$
$74$	−5.21888e27	−	1.46495e27i	−0.477641	−	0.134074i
$75$		−	3.30150e27i		−	0.247054i
$76$	−9.14808e27	+	1.50111e28i	−0.561211	+	0.920893i
$77$	3.70876e28			1.87011
$78$	1.76167e27	−	6.27598e27i	0.0731992	−	0.260773i
$79$		−	4.23310e28i		−	1.45295i	−0.687190	−	0.726477i	$-0.741156\pi$
$79$		−	4.23310e28i		−	1.45295i	0.687190	−	0.726477i	$-0.258844\pi$
$80$	−7.71834e27	−	1.49655e28i	−0.219368	−	0.425345i
$81$	2.97789e28			0.702480
$82$	2.47686e28	+	6.95257e27i	0.486064	+	0.136439i
$83$			4.11957e28i			0.674032i	0.941499	+	0.337016i	$0.109418\pi$
$83$			4.11957e28i			0.674032i	−0.941499	+	0.337016i	$0.890582\pi$
$84$	−3.87221e28	−	2.35980e28i	−0.529383	−	0.322617i
$85$	9.24365e27			0.105818
$86$	−1.40550e28	+	5.00710e28i	−0.135006	+	0.480961i
$87$		−	5.78920e28i		−	0.467552i
$88$	−1.03972e29	+	9.68251e28i	−0.707419	+	0.658792i
$89$	−3.08901e29			−1.77407			−0.887033	−	0.461706i	$-0.847237\pi$
$89$	−3.08901e29			−1.77407			−0.887033	+	0.461706i	$0.847237\pi$
$90$	8.51272e28	+	2.38953e28i	0.413458	+	0.116058i
$91$			3.97358e29i			1.63516i
$92$	6.45842e27	−	1.05977e28i	0.0225584	−	0.0370162i
$93$	−9.53007e28			−0.283043
$94$	1.60003e29	−	5.70013e29i	0.404773	−	1.44201i
$95$		−	2.39112e29i		−	0.516115i
$96$	1.70162e29	−	3.49372e28i	0.313902	−	0.0644495i
$97$	−2.56756e29			−0.405457			−0.202728	−	0.979235i	$-0.564981\pi$
$97$	−2.56756e29			−0.405457			−0.202728	+	0.979235i	$0.564981\pi$
$98$	1.95027e30	+	5.47442e29i	2.64060	+	0.741220i
$99$		−	7.46017e29i		−	0.867403i
$100$	−6.58340e29	−	4.01206e29i	−0.658340	−	0.401206i
$101$	−3.34104e29			−0.287780			−0.143890	−	0.989594i	$-0.545961\pi$
$101$	−3.34104e29			−0.287780			−0.143890	+	0.989594i	$0.545961\pi$
$102$	−2.57716e28	+	9.18115e28i	−0.0191487	+	0.0682173i
$103$			1.79330e30i			1.15105i	0.817784	+	0.575526i	$0.195203\pi$
$103$			1.79330e30i			1.15105i	−0.817784	+	0.575526i	$0.804797\pi$
$104$	−1.03739e30	−	1.11396e30i	−0.576025	−	0.618543i
$105$	6.16804e29			0.296693
$106$	1.49636e30	+	4.20029e29i	0.624377	+	0.175263i
$107$		−	1.54591e30i		−	0.560311i	−0.959955	−	0.280155i	$-0.909614\pi$
$107$		−	1.54591e30i		−	0.560311i	0.959955	−	0.280155i	$-0.0903860\pi$
$108$	−1.00367e30	+	1.64693e30i	−0.316399	+	0.519180i
$109$	−1.03092e30			−0.283027			−0.141514	−	0.989936i	$-0.545197\pi$
$109$	−1.03092e30			−0.283027			−0.141514	+	0.989936i	$0.545197\pi$
$110$	5.22275e29	−	1.86061e30i	0.125029	−	0.445415i
$111$			7.60634e29i			0.158976i
$112$	−9.41121e30	+	4.85375e30i	−1.71939	+	0.886763i
$113$	4.96731e30			0.794227			0.397113	−	0.917770i	$-0.370012\pi$
$113$	4.96731e30			0.794227			0.397113	+	0.917770i	$0.370012\pi$
$114$	2.37495e30	+	6.66651e29i	0.332722	+	0.0933954i
$115$			1.68810e29i			0.0207458i
$116$	−1.15440e31	−	7.03518e30i	−1.24591	−	0.759286i
$117$	7.99286e30			0.758428
$118$	−2.57809e30	+	9.18447e30i	−0.215312	+	0.767050i
$119$		−	5.81296e30i		−	0.427753i
$120$	−1.72916e30	+	1.61030e30i	−0.112232	+	0.104517i
$121$	1.14384e30			0.0655519
$122$	1.90531e31	+	5.34821e30i	0.965089	+	0.270901i
$123$		−	3.60994e30i		−	0.161779i
$124$	−1.15812e31	+	1.90036e31i	−0.459650	+	0.754241i
$125$	2.40888e31			0.847550
$126$	1.50268e31	−	5.35331e31i	0.469147	−	1.67134i
$127$		−	1.69228e31i		−	0.469264i	−0.972084	−	0.234632i	$-0.924612\pi$
$127$		−	1.69228e31i		−	0.469264i	0.972084	−	0.234632i	$-0.0753885\pi$
$128$	1.37118e31	−	3.81771e31i	0.338022	−	0.941138i
$129$	7.29768e30			0.160081
$130$	1.99347e31	+	5.59568e30i	0.389456	+	0.109321i
$131$			5.41783e31i			0.943530i	0.881724	+	0.471765i	$0.156383\pi$
$131$			5.41783e31i			0.943530i	−0.881724	+	0.471765i	$0.843617\pi$
$132$	1.70242e31	+	1.03749e31i	0.264519	+	0.161203i
$133$	−1.50368e32			−2.08632
$134$	−3.15192e31	+	1.12288e32i	−0.390844	+	1.39239i
$135$		−	2.62339e31i		−	0.290975i
$136$	1.51760e31	+	1.62962e31i	0.150686	+	0.161809i
$137$	−1.13072e32			−1.00588			−0.502939	−	0.864322i	$-0.667748\pi$
$137$	−1.13072e32			−1.00588			−0.502939	+	0.864322i	$0.667748\pi$
$138$	−1.67668e30	−	4.70647e29i	−0.0133741	−	0.00375412i
$139$			1.97825e32i			1.41599i	0.706219	+	0.707993i	$0.250399\pi$
$139$			1.97825e32i			1.41599i	−0.706219	+	0.707993i	$0.749601\pi$
$140$	7.49555e31	−	1.22995e32i	0.481818	−	0.790617i
$141$	−8.30775e31			−0.479951
$142$	4.80516e31	−	1.71184e32i	0.249679	−	0.889485i
$143$		−	1.74698e32i		−	0.817050i
$144$	9.76333e31	+	1.89307e32i	0.411302	+	0.797496i
$145$	1.83885e32			0.698274
$146$	−2.02186e32	−	5.67538e31i	−0.692561	−	0.194403i
$147$		−	2.84245e32i		−	0.878886i
$148$	1.51675e32	+	9.24341e31i	0.423633	+	0.258170i
$149$	5.74060e32			1.44932			0.724659	−	0.689108i	$-0.241997\pi$
$149$	5.74060e32			1.44932			0.724659	+	0.689108i	$0.241997\pi$
$150$	−2.92372e31	+	1.04158e32i	−0.0667677	+	0.237861i
$151$			3.78117e32i			0.781577i	0.920481	+	0.390788i	$0.127798\pi$
$151$			3.78117e32i			0.781577i	−0.920481	+	0.390788i	$0.872202\pi$
$152$	4.21544e32	−	3.92568e32i	0.789204	−	0.734955i
$153$	−1.16928e32			−0.198402
$154$	−1.17006e33	−	3.28438e32i	−1.80052	−	0.505409i
$155$		−	3.02708e32i		−	0.422715i
$156$	−1.11157e32	+	1.82398e32i	−0.140951	+	0.231287i
$157$	7.42508e32			0.855473			0.427737	−	0.903903i	$-0.359311\pi$
$157$	7.42508e32			0.855473			0.427737	+	0.903903i	$0.359311\pi$
$158$	−3.74872e32	+	1.33549e33i	−0.392669	+	1.39889i
$159$		−	2.18089e32i		−	0.207815i
$160$	1.10973e32	+	5.40493e32i	0.0962533	+	0.468803i
$161$	1.06158e32			0.0838617
$162$	−9.39486e32	−	2.63715e32i	−0.676340	−	0.189849i
$163$		−	7.58715e32i		−	0.498040i	−0.968498	−	0.249020i	$-0.919891\pi$
$163$		−	7.58715e32i		−	0.498040i	0.968498	−	0.249020i	$-0.0801086\pi$
$164$	−7.19845e32	−	4.38688e32i	−0.431103	−	0.262723i
$165$	−2.71178e32			−0.148250
$166$	3.64818e32	−	1.29967e33i	0.182161	−	0.648950i
$167$			1.77138e33i			0.808286i	0.914696	+	0.404143i	$0.132430\pi$
$167$			1.77138e33i			0.808286i	−0.914696	+	0.404143i	$0.867570\pi$
$168$	1.01265e33	+	1.08740e33i	0.422495	+	0.453680i
$169$	−7.48269e32			−0.285599
$170$	−2.91625e32	−	8.18594e31i	−0.101880	−	0.0285979i
$171$			3.02465e33i			0.967684i
$172$	8.86832e32	−	1.45521e33i	0.259965	−	0.426577i
$173$	−3.95709e33			−1.06337			−0.531685	−	0.846942i	$-0.678441\pi$
$173$	−3.95709e33			−1.06337			−0.531685	+	0.846942i	$0.678441\pi$
$174$	−5.12677e32	+	1.82641e33i	−0.126359	+	0.450154i
$175$		−	6.59466e33i		−	1.49149i
$176$	4.13764e33	−	2.13395e33i	0.859137	−	0.443093i
$177$	1.33861e33			0.255302
$178$	9.74542e33	+	2.73555e33i	1.70805	+	0.479451i
$179$			4.06711e33i			0.655376i	0.944786	+	0.327688i	$0.106270\pi$
$179$			4.06711e33i			0.655376i	−0.944786	+	0.327688i	$0.893730\pi$
$180$	−2.47404e33	−	1.50773e33i	−0.366707	−	0.223479i
$181$	6.97338e32			0.0951184			0.0475592	−	0.998868i	$-0.484856\pi$
$181$	6.97338e32			0.0951184			0.0475592	+	0.998868i	$0.484856\pi$
$182$	3.51890e33	−	1.25361e34i	0.441912	−	1.57432i
$183$		−	2.77692e33i		−	0.321216i
$184$	−2.97605e32	+	2.77148e32i	−0.0317229	+	0.0295423i
$185$	−2.41603e33			−0.237425
$186$	3.00661e33	+	8.43958e32i	0.272510	+	0.0764939i
$187$			2.55567e33i			0.213737i
$188$	−1.00958e34	+	1.65662e34i	−0.779421	+	1.27896i
$189$	−1.64974e34			−1.17622
$190$	−2.11751e33	+	7.54365e33i	−0.139483	+	0.496910i
$191$			7.11000e33i			0.432881i	0.976296	+	0.216441i	$0.0694448\pi$
$191$			7.11000e33i			0.432881i	−0.976296	+	0.216441i	$0.930555\pi$
$192$	−5.67778e33	−	4.04690e32i	−0.319639	−	0.0227826i
$193$	−2.36850e32			−0.0123343			−0.00616713	−	0.999981i	$-0.501963\pi$
$193$	−2.36850e32			−0.0123343			−0.00616713	+	0.999981i	$0.501963\pi$
$194$	8.10030e33	+	2.27376e33i	0.390369	+	0.109577i
$195$		−	2.90541e33i		−	0.129625i
$196$	−5.66803e34	−	3.45421e34i	−2.34202	−	1.42728i
$197$	4.54092e34			1.73840			0.869202	−	0.494457i	$-0.164633\pi$
$197$	4.54092e34			1.73840			0.869202	+	0.494457i	$0.164633\pi$
$198$	−6.60654e33	+	2.35358e34i	−0.234421	+	0.835126i
$199$			3.59672e34i			1.18334i	0.806180	+	0.591671i	$0.201532\pi$
$199$			3.59672e34i			1.18334i	−0.806180	+	0.591671i	$0.798468\pi$
$200$	1.72168e34	+	1.84876e34i	0.525414	+	0.564197i
$201$	1.63655e34			0.463436
$202$	1.05405e34	+	2.95874e33i	0.277072	+	0.0777743i
$203$		−	1.15638e35i		−	2.82267i
$204$	1.62612e33	−	2.66830e33i	0.0368722	−	0.0605038i
$205$	1.14664e34			0.241612
$206$	1.58810e34	−	5.65762e34i	0.311078	−	1.10822i
$207$		−	2.13536e33i		−	0.0388970i
$208$	2.28633e34	+	4.43308e34i	0.387425	+	0.751200i
$209$	6.61092e34			1.04248
$210$	−1.94593e34	−	5.46225e33i	−0.285653	−	0.0801830i
$211$			8.96230e34i			1.22513i	0.790420	+	0.612566i	$0.209863\pi$
$211$			8.96230e34i			1.22513i	−0.790420	+	0.612566i	$0.790137\pi$
$212$	−4.34884e34	−	2.65027e34i	−0.553777	−	0.337483i
$213$	−2.49495e34			−0.296052
$214$	−1.36902e34	+	4.87715e34i	−0.151427	+	0.539461i
$215$			2.31799e34i			0.239076i
$216$	4.62492e34	−	4.30701e34i	0.444937	−	0.414352i
$217$	−1.90361e35			−1.70876
$218$	3.25242e34	+	9.12958e33i	0.272496	+	0.0764898i
$219$			2.94679e34i			0.230509i
$220$	−3.29542e34	+	5.40746e34i	−0.240752	+	0.395051i
$221$	−2.73815e34			−0.186885
$222$	6.73598e33	−	2.39970e34i	0.0429641	−	0.153060i
$223$		−	1.31862e35i		−	0.786222i	−0.919491	−	0.393111i	$-0.871399\pi$
$223$		−	1.31862e35i		−	0.786222i	0.919491	−	0.393111i	$-0.128601\pi$
$224$	3.39895e35	−	6.97862e34i	1.89506	−	0.389089i
$225$	−1.32652e35			−0.691791
$226$	−1.56712e35	−	4.39892e34i	−0.764672	−	0.214644i
$227$			2.17642e35i			0.993927i	0.867772	+	0.496963i	$0.165552\pi$
$227$			2.17642e35i			0.993927i	−0.867772	+	0.496963i	$0.834448\pi$
$228$	−6.90228e34	−	4.20639e34i	−0.295100	−	0.179840i
$229$	−2.47319e35			−0.990205			−0.495102	−	0.868835i	$-0.664869\pi$
$229$	−2.47319e35			−0.990205			−0.495102	+	0.868835i	$0.664869\pi$
$230$	1.49494e33	−	5.32572e33i	0.00560667	−	0.0199738i
$231$			1.70533e35i			0.599278i
$232$	3.01898e35	+	3.24181e35i	0.994351	+	1.06775i
$233$	2.29128e35			0.707520			0.353760	−	0.935336i	$-0.384903\pi$
$233$	2.29128e35			0.707520			0.353760	+	0.935336i	$0.384903\pi$
$234$	−2.52164e35	−	7.07827e34i	−0.730206	−	0.204969i
$235$		−	2.63883e35i		−	0.716792i
$236$	1.62671e35	−	2.66927e35i	0.414600	−	0.680318i
$237$	1.94643e35			0.465600
$238$	−5.14781e34	+	1.83391e35i	−0.115603	+	0.411836i
$239$		−	6.72205e35i		−	1.41753i	−0.705443	−	0.708767i	$-0.749252\pi$
$239$		−	6.72205e35i		−	1.41753i	0.705443	−	0.708767i	$-0.250748\pi$
$240$	6.88130e34	−	3.54898e34i	0.136302	−	0.0702966i
$241$	3.47392e35			0.646493			0.323246	−	0.946315i	$-0.395226\pi$
$241$	3.47392e35			0.646493			0.323246	+	0.946315i	$0.395226\pi$
$242$	−3.60866e34	−	1.01296e34i	−0.0631126	−	0.0177158i
$243$			5.06749e35i			0.833104i
$244$	−5.53736e35	−	3.37458e35i	−0.855964	−	0.521642i
$245$	9.02859e35			1.31259
$246$	−3.19687e34	+	1.13889e35i	−0.0437218	+	0.155759i
$247$			7.08297e35i			0.911509i
$248$	5.33661e35	−	4.96978e35i	0.646384	−	0.601952i
$249$	−1.89422e35			−0.215994
$250$	−7.59970e35	−	2.13324e35i	−0.816011	−	0.229055i
$251$		−	1.58371e36i		−	1.60166i	−0.598892	−	0.800830i	$-0.704392\pi$
$251$		−	1.58371e36i		−	1.60166i	0.598892	−	0.800830i	$-0.295608\pi$
$252$	−9.48151e35	+	1.55582e36i	−0.903378	+	1.48236i
$253$	−4.66722e34			−0.0419036
$254$	−1.49864e35	+	5.33892e35i	−0.126821	+	0.451802i
$255$			4.25033e34i			0.0339094i
$256$	−7.70675e35	+	1.08301e36i	−0.579792	+	0.814765i
$257$	7.90939e34			0.0561237			0.0280618	−	0.999606i	$-0.491066\pi$
$257$	7.90939e34			0.0561237			0.0280618	+	0.999606i	$0.491066\pi$
$258$	−2.30232e35	−	6.46264e34i	−0.154124	−	0.0432628i
$259$			1.51935e36i			0.959756i
$260$	−5.79358e35	−	3.53072e35i	−0.345419	−	0.210505i
$261$	−2.32606e36			−1.30922
$262$	4.79789e35	−	1.70925e36i	0.254994	−	0.908420i
$263$			1.39255e36i			0.698995i	0.936937	+	0.349498i	$0.113648\pi$
$263$			1.39255e36i			0.698995i	−0.936937	+	0.349498i	$0.886352\pi$
$264$	−4.45213e35	−	4.78075e35i	−0.211110	−	0.226693i
$265$	6.92725e35			0.310365
$266$	4.74390e36	+	1.33162e36i	2.00868	+	0.563839i
$267$		−	1.42036e36i		−	0.568500i
$268$	1.98878e36	−	3.26340e36i	0.752601	−	1.23495i
$269$	1.78834e36			0.639978			0.319989	−	0.947421i	$-0.396321\pi$
$269$	1.78834e36			0.639978			0.319989	+	0.947421i	$0.396321\pi$
$270$	−2.32320e35	+	8.27643e35i	−0.0786377	+	0.280147i
$271$		−	4.22378e36i		−	1.35258i	−0.736637	−	0.676289i	$-0.763587\pi$
$271$		−	4.22378e36i		−	1.35258i	0.736637	−	0.676289i	$-0.236413\pi$
$272$	−3.34467e35	−	6.48517e35i	−0.101349	−	0.196511i
$273$	−1.82710e36			−0.523988
$274$	3.56726e36	+	1.00133e36i	0.968448	+	0.271844i
$275$			2.89934e36i			0.745262i
$276$	4.87292e34	+	2.96965e34i	0.0118619	+	0.00722886i
$277$	−2.87956e36			−0.663941			−0.331970	−	0.943290i	$-0.607713\pi$
$277$	−2.87956e36			−0.663941			−0.331970	+	0.943290i	$0.607713\pi$
$278$	1.75189e36	−	6.24111e36i	0.382678	−	1.36330i
$279$			3.82911e36i			0.792564i
$280$	−3.45395e36	+	3.21653e36i	−0.677557	+	0.630983i
$281$	−2.46449e36			−0.458282			−0.229141	−	0.973393i	$-0.573592\pi$
$281$	−2.46449e36			−0.458282			−0.229141	+	0.973393i	$0.573592\pi$
$282$	2.62098e36	+	7.35713e35i	0.462091	+	0.129709i
$283$			3.08798e36i			0.516271i	0.966109	+	0.258136i	$0.0831082\pi$
$283$			3.08798e36i			0.516271i	−0.966109	+	0.258136i	$0.916892\pi$
$284$	−3.03193e36	+	4.97510e36i	−0.480777	+	0.788909i
$285$	1.09946e36			0.165389
$286$	−1.54708e36	+	5.51150e36i	−0.220812	+	0.786646i
$287$		−	7.21076e36i		−	0.976681i
$288$	−1.40375e36	−	6.83698e36i	−0.180469	−	0.878976i
$289$	−7.79290e36			−0.951112
$290$	−5.80132e36	−	1.62844e36i	−0.672290	−	0.188713i
$291$		−	1.18059e36i		−	0.129929i
$292$	5.87610e36	+	3.58101e36i	0.614252	+	0.374337i
$293$	1.25889e37			1.25018			0.625089	−	0.780554i	$-0.285063\pi$
$293$	1.25889e37			1.25018			0.625089	+	0.780554i	$0.285063\pi$
$294$	−2.51720e36	+	8.96754e36i	−0.237524	+	0.846181i
$295$			4.25187e36i			0.381285i
$296$	−3.96658e36	−	4.25937e36i	−0.338097	−	0.363053i
$297$	7.25310e36			0.587729
$298$	−1.81108e37	−	5.08373e36i	−1.39539	−	0.391687i
$299$		−	5.00048e35i		−	0.0366390i
$300$	1.84479e36	−	3.02712e36i	0.128566	−	0.210965i
$301$	1.45769e37			0.966427
$302$	3.34850e36	−	1.19291e37i	0.211226	−	0.752493i
$303$		−	1.53625e36i		−	0.0922193i
$304$	−1.67756e37	+	8.65189e36i	−0.958462	+	0.494319i
$305$	8.82045e36			0.479726
$306$	3.68891e36	+	1.03548e36i	0.191019	+	0.0536193i
$307$		−	1.47052e37i		−	0.725096i	−0.931965	−	0.362548i	$-0.881907\pi$
$307$		−	1.47052e37i		−	0.725096i	0.931965	−	0.362548i	$-0.118093\pi$
$308$	3.40054e37	+	2.07236e37i	1.59693	+	0.973204i
$309$	−8.24580e36			−0.368855
$310$	−2.68070e36	+	9.55002e36i	−0.114241	+	0.406985i
$311$			4.99396e36i			0.202787i	0.994846	+	0.101393i	$0.0323300\pi$
$311$			4.99396e36i			0.202787i	−0.994846	+	0.101393i	$0.967670\pi$
$312$	5.12212e36	−	4.77003e36i	0.198212	−	0.184587i
$313$	7.88466e36			0.290816			0.145408	−	0.989372i	$-0.453551\pi$
$313$	7.88466e36			0.290816			0.145408	+	0.989372i	$0.453551\pi$
$314$	−2.34251e37	−	6.57546e36i	−0.823640	−	0.231197i
$315$		−	2.47827e37i		−	0.830788i
$316$	2.36534e37	−	3.88130e37i	0.756115	−	1.24071i
$317$	−2.29221e37			−0.698821			−0.349411	−	0.936970i	$-0.613618\pi$
$317$	−2.29221e37			−0.698821			−0.349411	+	0.936970i	$0.613618\pi$
$318$	−1.93134e36	+	6.88041e36i	−0.0561632	+	0.200082i
$319$			5.08402e37i			1.41041i
$320$	1.28543e36	−	1.80346e37i	0.0340251	−	0.477371i
$321$	7.10828e36			0.179552
$322$	−3.34913e36	−	9.40105e35i	−0.0807411	−	0.0226641i
$323$		−	1.03617e37i		−	0.238448i
$324$	2.73041e37	+	1.66397e37i	0.599864	+	0.365569i
$325$	−3.10637e37			−0.651632
$326$	−6.71898e36	+	2.39364e37i	−0.134598	+	0.479508i
$327$		−	4.74029e36i		−	0.0906962i
$328$	1.88252e37	+	2.02148e37i	0.344059	+	0.369455i
$329$	−1.65945e38			−2.89752
$330$	8.55529e36	+	2.40148e36i	0.142733	+	0.0400654i
$331$			5.87487e37i			0.936652i	0.883556	+	0.468326i	$0.155143\pi$
$331$			5.87487e37i			0.936652i	−0.883556	+	0.468326i	$0.844857\pi$
$332$	−2.30191e37	+	3.77721e37i	−0.350765	+	0.575572i
$333$	3.05617e37			0.445158
$334$	1.56869e37	−	5.58847e37i	0.218444	−	0.778209i
$335$			5.19826e37i			0.692127i
$336$	−2.23181e37	−	4.32738e37i	−0.284163	−	0.550980i
$337$	6.78468e37			0.826192			0.413096	−	0.910688i	$-0.364447\pi$
$337$	6.78468e37			0.826192			0.413096	+	0.910688i	$0.364447\pi$
$338$	2.36069e37	+	6.62648e36i	0.274972	+	0.0771849i
$339$			2.28402e37i			0.254510i
$340$	8.47544e36	+	5.16511e36i	0.0903605	+	0.0550675i
$341$	8.36921e37			0.853825
$342$	2.67855e37	−	9.54236e37i	0.261522	−	0.931675i
$343$		−	3.60757e38i		−	3.37134i
$344$	−4.08653e37	+	3.80562e37i	−0.365576	+	0.340447i
$345$	−7.76206e35			−0.00664799
$346$	1.24841e38	+	3.50430e37i	1.02380	+	0.287382i
$347$			1.15694e38i			0.908592i	0.890851	+	0.454296i	$0.150109\pi$
$347$			1.15694e38i			0.908592i	−0.890851	+	0.454296i	$0.849891\pi$
$348$	3.23485e37	−	5.30808e37i	0.243313	−	0.399254i
$349$	2.39638e38			1.72653			0.863265	−	0.504750i	$-0.168415\pi$
$349$	2.39638e38			1.72653			0.863265	+	0.504750i	$0.168415\pi$
$350$	−5.84006e37	+	2.08053e38i	−0.403085	+	1.43599i
$351$			7.77100e37i			0.513890i
$352$	−1.49435e38	+	3.06815e37i	−0.946916	+	0.194418i
$353$	−3.98792e37			−0.242173			−0.121087	−	0.992642i	$-0.538638\pi$
$353$	−3.98792e37			−0.242173			−0.121087	+	0.992642i	$0.538638\pi$
$354$	−4.22312e37	−	1.18543e37i	−0.245801	−	0.0689967i
$355$		−	7.92483e37i		−	0.442145i
$356$	−2.83230e38	−	1.72606e38i	−1.51492	−	0.923221i
$357$	2.67286e37			0.137074
$358$	3.60173e37	−	1.28312e38i	0.177119	−	0.630989i
$359$			1.83185e38i			0.863922i	0.901892	+	0.431961i	$0.142178\pi$
$359$			1.83185e38i			0.863922i	−0.901892	+	0.431961i	$0.857822\pi$
$360$	6.47005e37	+	6.94763e37i	0.292665	+	0.314267i
$361$	−3.75663e37			−0.163001
$362$	−2.20001e37	−	6.17544e36i	−0.0915789	−	0.0257063i
$363$			5.25951e36i			0.0210061i
$364$	−2.22033e38	+	3.64335e38i	−0.850936	+	1.39630i
$365$	−9.36002e37			−0.344258
$366$	−2.45917e37	+	8.76081e37i	−0.0868104	+	0.309263i
$367$			9.10366e37i			0.308479i	0.988034	+	0.154239i	$0.0492927\pi$
$367$			9.10366e37i			0.308479i	−0.988034	+	0.154239i	$0.950707\pi$
$368$	1.18434e37	−	6.10812e36i	0.0385264	−	0.0198697i
$369$	−1.45044e38			−0.453008
$370$	7.62226e37	+	2.13958e37i	0.228590	+	0.0641656i
$371$		−	4.35627e38i		−	1.25460i
$372$	−8.73806e37	−	5.32515e37i	−0.241697	−	0.147295i
$373$	3.62958e38			0.964327			0.482164	−	0.876081i	$-0.339851\pi$
$373$	3.62958e38			0.964327			0.482164	+	0.876081i	$0.339851\pi$
$374$	2.26323e37	−	8.06279e37i	0.0577638	−	0.205784i
$375$			1.10763e38i			0.271597i
$376$	4.65214e38	−	4.33236e38i	1.09606	−	1.02072i
$377$	−5.44704e38			−1.23322
$378$	5.20472e38	+	1.46097e38i	1.13245	+	0.317881i
$379$			3.18834e38i			0.666770i	0.942791	+	0.333385i	$0.108191\pi$
$379$			3.18834e38i			0.666770i	−0.942791	+	0.333385i	$0.891809\pi$
$380$	1.33609e38	−	2.19240e38i	0.268586	−	0.440723i
$381$	7.78130e37			0.150376
$382$	6.29643e37	−	2.24311e38i	0.116989	−	0.416773i
$383$			6.14024e37i			0.109699i	0.998495	+	0.0548497i	$0.0174680\pi$
$383$			6.14024e37i			0.109699i	−0.998495	+	0.0548497i	$0.982532\pi$
$384$	1.75542e38	+	6.30484e37i	0.301588	+	0.108319i
$385$	−5.41671e38			−0.895003
$386$	7.47228e36	+	2.09748e36i	0.0118753	+	0.00333340i
$387$		−	2.93215e38i		−	0.448252i
$388$	−2.35418e38	−	1.43468e38i	−0.346229	−	0.210999i
$389$	2.65967e37			0.0376343			0.0188171	−	0.999823i	$-0.494010\pi$
$389$	2.65967e37			0.0376343			0.0188171	+	0.999823i	$0.494010\pi$
$390$	−2.57295e37	+	9.16617e37i	−0.0350318	+	0.124801i
$391$			7.31522e36i			0.00958465i
$392$	1.48229e39	+	1.59170e39i	1.86914	+	2.00711i
$393$	−2.49118e38			−0.302354
$394$	−1.43260e39	−	4.02132e38i	−1.67372	−	0.469814i
$395$			6.18251e38i			0.695358i
$396$	4.16855e38	−	6.84018e38i	0.451395	−	0.740696i
$397$	1.17127e39			1.22123			0.610617	−	0.791926i	$-0.290921\pi$
$397$	1.17127e39			1.22123			0.610617	+	0.791926i	$0.290921\pi$
$398$	3.18516e38	−	1.13472e39i	0.319805	−	1.13931i
$399$		−	6.91408e38i		−	0.668561i
$400$	−3.79445e38	−	7.35726e38i	−0.353385	−	0.685198i
$401$	−6.76040e38			−0.606466			−0.303233	−	0.952916i	$-0.598066\pi$
$401$	−6.76040e38			−0.606466			−0.303233	+	0.952916i	$0.598066\pi$
$402$	−5.16311e38	−	1.44929e38i	−0.446190	−	0.125246i
$403$			8.96681e38i			0.746556i
$404$	−3.06338e38	−	1.86688e38i	−0.245742	−	0.149760i
$405$	−4.34927e38			−0.336194
$406$	−1.02406e39	+	3.64822e39i	−0.762842	+	2.71763i
$407$		−	6.67981e38i		−	0.479566i
$408$	−7.49316e37	+	6.97809e37i	−0.0518516	+	0.0482874i
$409$	−3.88174e38			−0.258927			−0.129463	−	0.991584i	$-0.541325\pi$
$409$	−3.88174e38			−0.258927			−0.129463	+	0.991584i	$0.541325\pi$
$410$	−3.61749e38	−	1.01543e38i	−0.232622	−	0.0652971i
$411$		−	5.19916e38i		−	0.322334i
$412$	−1.00205e39	+	1.64427e39i	−0.599006	+	0.982910i
$413$	2.67383e39			1.54129
$414$	−1.89102e37	+	6.73678e37i	−0.0105122	+	0.0374496i
$415$		−	6.01670e38i		−	0.322580i
$416$	−3.28723e38	−	1.60105e39i	−0.169993	−	0.827951i
$417$	−9.09621e38			−0.453753
$418$	−2.08566e39	−	5.85446e38i	−1.00369	−	0.281736i
$419$			6.56808e38i			0.304950i	0.988307	+	0.152475i	$0.0487243\pi$
$419$			6.56808e38i			0.304950i	−0.988307	+	0.152475i	$0.951276\pi$
$420$	5.65543e38	+	3.44653e38i	0.253353	+	0.154399i
$421$	3.64441e39			1.57542			0.787709	−	0.616047i	$-0.211267\pi$
$421$	3.64441e39			1.57542			0.787709	+	0.616047i	$0.211267\pi$
$422$	7.93678e38	−	2.82749e39i	0.331099	−	1.17954i
$423$			3.33799e39i			1.34394i
$424$	1.13730e39	+	1.22125e39i	0.441964	+	0.474586i
$425$	4.54431e38			0.170465
$426$	7.87124e38	+	2.20947e38i	0.285036	+	0.0800098i
$427$		−	5.54683e39i		−	1.93922i
$428$	8.63816e38	−	1.41744e39i	0.291585	−	0.478462i
$429$	8.03283e38			0.261824
$430$	2.05276e38	−	7.31296e38i	0.0646116	−	0.230179i
$431$		−	2.11842e39i		−	0.643950i	−0.946748	−	0.321975i	$-0.895653\pi$
$431$		−	2.11842e39i		−	0.643950i	0.946748	−	0.321975i	$-0.104347\pi$
$432$	−1.84052e39	+	9.49233e38i	−0.540361	+	0.278687i
$433$	−2.40538e39			−0.682127			−0.341064	−	0.940040i	$-0.610787\pi$
$433$	−2.40538e39			−0.682127			−0.341064	+	0.940040i	$0.610787\pi$
$434$	6.00563e39	+	1.68579e39i	1.64518	+	0.461803i
$435$			8.45523e38i			0.223762i
$436$	−9.45246e38	−	5.76052e38i	−0.241684	−	0.147287i
$437$	1.89228e38			0.0467480
$438$	2.60960e38	−	9.29673e38i	0.0622964	−	0.221931i
$439$			5.44956e39i			1.25717i	0.777741	+	0.628585i	$0.216366\pi$
$439$			5.44956e39i			1.25717i	−0.777741	+	0.628585i	$0.783634\pi$
$440$	1.51853e39	−	1.41415e39i	0.338558	−	0.315286i
$441$	−1.14207e40			−2.46102
$442$	8.63851e38	+	2.42484e38i	0.179930	+	0.0505067i
$443$			9.99465e38i			0.201239i	0.994925	+	0.100619i	$0.0320824\pi$
$443$			9.99465e38i			0.201239i	−0.994925	+	0.100619i	$0.967918\pi$
$444$	−4.25022e38	+	6.97420e38i	−0.0827307	+	0.135753i
$445$	4.51156e39			0.849036
$446$	−1.16773e39	+	4.16006e39i	−0.212481	+	0.756966i
$447$			2.63959e39i			0.464434i
$448$	−1.13412e40	−	8.08358e38i	−1.92970	−	0.137541i
$449$	−9.34945e39			−1.53848			−0.769238	−	0.638962i	$-0.779364\pi$
$449$	−9.34945e39			−1.53848			−0.769238	+	0.638962i	$0.779364\pi$
$450$	4.18498e39	+	1.17473e39i	0.666048	+	0.186960i
$451$			3.17021e39i			0.488023i
$452$	4.55449e39	+	2.77560e39i	0.678209	+	0.413314i
$453$	−1.73862e39			−0.250456
$454$	1.92738e39	−	6.86630e39i	0.268614	−	0.956941i
$455$		−	5.80348e39i		−	0.782560i
$456$	1.80507e39	+	1.93831e39i	0.235516	+	0.252901i
$457$	1.42521e39			0.179944			0.0899719	−	0.995944i	$-0.471322\pi$
$457$	1.42521e39			0.179944			0.0899719	+	0.995944i	$0.471322\pi$
$458$	7.80258e39	+	2.19019e39i	0.953358	+	0.267609i
$459$		−	1.13682e39i		−	0.134432i
$460$	−9.43264e37	+	1.54781e38i	−0.0107961	+	0.0177153i
$461$	5.21227e39			0.577448			0.288724	−	0.957412i	$-0.406769\pi$
$461$	5.21227e39			0.577448			0.288724	+	0.957412i	$0.406769\pi$
$462$	1.51019e39	−	5.38008e39i	0.161958	−	0.576978i
$463$		−	8.64425e39i		−	0.897455i	−0.893669	−	0.448727i	$-0.851877\pi$
$463$		−	8.64425e39i		−	0.897455i	0.893669	−	0.448727i	$-0.148123\pi$
$464$	−6.65359e39	−	1.29010e40i	−0.668785	−	1.29674i
$465$	1.39188e39			0.135459
$466$	−7.22867e39	−	2.02910e39i	−0.681192	−	0.191211i
$467$			1.05369e40i			0.961520i	0.876852	+	0.480760i	$0.159639\pi$
$467$			1.05369e40i			0.961520i	−0.876852	+	0.480760i	$0.840361\pi$
$468$	7.32860e39	+	4.46620e39i	0.647639	+	0.394685i
$469$	3.26898e40			2.79782
$470$	−2.33688e39	+	8.32514e39i	−0.193717	+	0.690119i
$471$			3.41413e39i			0.274137i
$472$	−7.49587e39	+	6.98061e39i	−0.583032	+	0.542955i
$473$	−6.40875e39			−0.482899
$474$	−6.14071e39	−	1.72370e39i	−0.448274	−	0.125831i
$475$		−	1.17551e40i		−	0.831422i
$476$	3.24813e39	−	5.32987e39i	0.222602	−	0.365268i
$477$	−8.76264e39			−0.581915
$478$	−5.95287e39	+	2.12072e40i	−0.383096	+	1.36478i
$479$		−	1.55374e40i		−	0.969048i	−0.874778	−	0.484524i	$-0.838993\pi$
$479$		−	1.55374e40i		−	0.969048i	0.874778	−	0.484524i	$-0.161007\pi$
$480$	−2.48525e39	+	5.10264e38i	−0.150228	+	0.0308444i
$481$	7.15678e39			0.419316
$482$	−1.09597e40	−	3.07641e39i	−0.622436	−	0.174718i
$483$			4.88125e38i			0.0268735i
$484$	1.04878e39	+	6.39148e38i	0.0559763	+	0.0341131i
$485$	3.74996e39			0.194044
$486$	4.48764e39	−	1.59873e40i	0.225151	−	0.802103i
$487$			5.50855e38i			0.0267980i	0.999910	+	0.0133990i	$0.00426516\pi$
$487$			5.50855e38i			0.0267980i	−0.999910	+	0.0133990i	$0.995735\pi$
$488$	1.44812e40	+	1.55501e40i	0.683135	+	0.733560i
$489$	3.48865e39			0.159597
$490$	−2.84840e40	−	7.99549e39i	−1.26375	−	0.354735i
$491$			4.04431e40i			1.74029i	0.492794	+	0.870146i	$0.335976\pi$
$491$			4.04431e40i			1.74029i	−0.492794	+	0.870146i	$0.664024\pi$
$492$	2.01714e39	−	3.30993e39i	0.0841897	−	0.138147i
$493$	7.96849e39			0.322606
$494$	6.27249e39	−	2.23458e40i	0.246341	−	0.877590i
$495$			1.08957e40i			0.415124i
$496$	−2.12374e40	+	1.09530e40i	−0.785012	+	0.404863i
$497$	−4.98361e40			−1.78730
$498$	5.97602e39	+	1.67747e39i	0.207956	+	0.0583735i
$499$		−	3.94964e40i		−	1.33367i	−0.745204	−	0.666836i	$-0.767648\pi$
$499$		−	3.94964e40i		−	1.33367i	0.745204	−	0.666836i	$-0.232352\pi$
$500$	2.20869e40	+	1.34602e40i	0.723743	+	0.441063i
$501$	−8.14501e39			−0.259015
$502$	−1.40249e40	+	4.99640e40i	−0.432858	+	1.54206i
$503$			7.79745e38i			0.0233578i	0.999932	+	0.0116789i	$0.00371760\pi$
$503$			7.79745e38i			0.0233578i	−0.999932	+	0.0116789i	$0.996282\pi$
$504$	4.36909e40	−	4.06876e40i	1.27038	−	1.18305i
$505$	4.87965e39			0.137727
$506$	1.47245e39	+	4.13317e38i	0.0403443	+	0.0113247i
$507$		−	3.44062e39i		−	0.0915204i
$508$	9.45603e39	−	1.55164e40i	0.244204	−	0.400716i
$509$	−2.11722e40			−0.530885			−0.265442	−	0.964127i	$-0.585518\pi$
$509$	−2.11722e40			−0.530885			−0.265442	+	0.964127i	$0.585518\pi$
$510$	3.76398e38	−	1.34092e39i	0.00916421	−	0.0326476i
$511$			5.88614e40i			1.39161i
$512$	3.39046e40	−	2.73425e40i	0.778412	−	0.627754i
$513$	−2.94069e40			−0.655676
$514$	−2.49530e39	−	7.00435e38i	−0.0540352	−	0.0151677i
$515$		−	2.61915e40i		−	0.550873i
$516$	6.69120e39	+	4.07775e39i	0.136697	+	0.0833058i
$517$	7.29579e40			1.44782
$518$	1.34550e40	−	4.79334e40i	0.259380	−	0.924042i
$519$		−	1.81951e40i		−	0.340757i
$520$	1.51512e40	+	1.62696e40i	0.275675	+	0.296024i
$521$	−7.14465e40			−1.26303			−0.631517	−	0.775362i	$-0.717567\pi$
$521$	−7.14465e40			−1.26303			−0.631517	+	0.775362i	$0.717567\pi$
$522$	7.33840e40	+	2.05990e40i	1.26050	+	0.353824i
$523$		−	2.03700e40i		−	0.339990i	−0.985445	−	0.169995i	$-0.945625\pi$
$523$		−	2.03700e40i		−	0.339990i	0.985445	−	0.169995i	$-0.0543752\pi$
$524$	−3.02734e40	+	4.96757e40i	−0.491011	+	0.805703i
$525$	3.03230e40			0.477949
$526$	1.23320e40	−	4.39330e40i	0.188907	−	0.672984i
$527$		−	1.31176e40i		−	0.195296i
$528$	9.81215e39	+	1.90253e40i	0.141989	+	0.275311i
$529$	7.09608e40			0.998121
$530$	−2.18545e40	−	6.13459e39i	−0.298816	−	0.0838779i
$531$		−	5.37841e40i		−	0.714885i
$532$	−1.37871e41	−	8.40215e40i	−1.78156	−	1.08572i
$533$	−3.39658e40			−0.426710
$534$	−1.25784e40	+	4.48105e40i	−0.153640	+	0.547345i
$535$			2.25783e40i			0.268155i
$536$	−9.16431e40	+	8.53436e40i	−1.05835	+	0.985597i
$537$	−1.87010e40			−0.210015
$538$	−5.64196e40	−	1.58370e40i	−0.616164	−	0.172958i
$539$			2.49621e41i			2.65124i
$540$	1.46588e40	−	2.40537e40i	0.151423	−	0.248471i
$541$	2.22140e40			0.223186			0.111593	−	0.993754i	$-0.464405\pi$
$541$	2.22140e40			0.223186			0.111593	+	0.993754i	$0.464405\pi$
$542$	−3.74047e40	+	1.33255e41i	−0.365542	+	1.30225i
$543$			3.20644e39i			0.0304807i
$544$	4.80890e39	+	2.34218e40i	0.0444695	+	0.216589i
$545$	1.50568e40			0.135452
$546$	5.76424e40	+	1.61803e40i	0.504490	+	0.141611i
$547$		−	1.50158e41i		−	1.27861i	−0.768953	−	0.639306i	$-0.779222\pi$
$547$		−	1.50158e41i		−	1.27861i	0.768953	−	0.639306i	$-0.220778\pi$
$548$	−1.03675e41	−	6.31814e40i	−0.858943	−	0.523457i
$549$	−1.11574e41			−0.899455
$550$	2.56758e40	−	9.14703e40i	0.201411	−	0.717530i
$551$		−	2.06126e41i		−	1.57347i
$552$	−1.27435e39	−	1.36842e39i	−0.00946682	−	0.0101656i
$553$	3.88794e41			2.81088
$554$	9.08462e40	+	2.55006e40i	0.639234	+	0.179434i
$555$		−	1.11092e40i		−	0.0760830i
$556$	−1.10539e41	+	1.81384e41i	−0.736877	+	1.20914i
$557$	7.07276e39			0.0458945			0.0229473	−	0.999737i	$-0.492695\pi$
$557$	7.07276e39			0.0458945			0.0229473	+	0.999737i	$0.492695\pi$
$558$	3.39096e40	−	1.20803e41i	0.214195	−	0.763072i
$559$		−	6.86636e40i		−	0.422231i
$560$	1.37452e41	−	7.08899e40i	0.822871	−	0.424389i
$561$	−1.17512e40			−0.0684922
$562$	7.77514e40	+	2.18249e40i	0.441229	+	0.123853i
$563$			1.17592e41i			0.649760i	0.945755	+	0.324880i	$0.105324\pi$
$563$			1.17592e41i			0.649760i	−0.945755	+	0.324880i	$0.894676\pi$
$564$	−7.61732e40	−	4.64215e40i	−0.409841	−	0.249766i
$565$	−7.25484e40			−0.380103
$566$	2.73464e40	−	9.74217e40i	0.139525	−	0.497060i
$567$			2.73508e41i			1.35901i
$568$	1.39711e41	−	1.30108e41i	0.676094	−	0.629620i
$569$	−1.41451e41			−0.666689			−0.333344	−	0.942805i	$-0.608177\pi$
$569$	−1.41451e41			−0.666689			−0.333344	+	0.942805i	$0.608177\pi$
$570$	−3.46865e40	−	9.73655e39i	−0.159235	−	0.0446974i
$571$		−	1.40872e41i		−	0.629919i	−0.949105	−	0.314959i	$-0.898009\pi$
$571$		−	1.40872e41i		−	0.629919i	0.949105	−	0.314959i	$-0.101991\pi$
$572$	9.76169e40	−	1.60180e41i	0.425191	−	0.697698i
$573$	−3.26925e40			−0.138717
$574$	−6.38566e40	+	2.27490e41i	−0.263954	+	0.940337i
$575$			8.29893e39i			0.0334199i
$576$	−1.62601e40	+	2.28129e41i	−0.0637950	+	0.895041i
$577$	−1.81912e41			−0.695382			−0.347691	−	0.937609i	$-0.613034\pi$
$577$	−1.81912e41			−0.695382			−0.347691	+	0.937609i	$0.613034\pi$
$578$	2.45856e41	+	6.90119e40i	0.915719	+	0.257043i
$579$		−	1.08906e39i		−	0.00395251i
$580$	1.68603e41	+	1.02750e41i	0.596273	+	0.363381i
$581$	−3.78366e41			−1.30398
$582$	−1.04550e40	+	3.72461e40i	−0.0351140	+	0.125094i
$583$			1.91524e41i			0.626893i
$584$	−1.53670e41	−	1.65013e41i	−0.490228	−	0.526413i
$585$	−1.16737e41			−0.362970
$586$	−3.97161e41	−	1.11484e41i	−1.20366	−	0.337868i
$587$		−	5.86111e40i		−	0.173144i	−0.996246	−	0.0865721i	$-0.972409\pi$
$587$		−	5.86111e40i		−	0.173144i	0.996246	−	0.0865721i	$-0.0275913\pi$
$588$	1.58828e41	−	2.60622e41i	0.457371	−	0.750502i
$589$	−3.39321e41			−0.952536
$590$	3.76534e40	−	1.34141e41i	0.103044	−	0.367097i
$591$			2.08797e41i			0.557072i
$592$	8.74205e40	+	1.69504e41i	0.227399	+	0.440916i
$593$	7.61568e41			1.93147			0.965736	−	0.259528i	$-0.0835670\pi$
$593$	7.61568e41			1.93147			0.965736	+	0.259528i	$0.0835670\pi$
$594$	−2.28825e41	−	6.42316e40i	−0.565858	−	0.158837i
$595$			8.48993e40i			0.204715i
$596$	5.26352e41	+	3.20770e41i	1.23761	+	0.754223i
$597$	−1.65381e41			−0.379202
$598$	−4.42830e39	+	1.57759e40i	−0.00990191	+	0.0352757i
$599$		−	3.31769e41i		−	0.723492i	−0.932277	−	0.361746i	$-0.882181\pi$
$599$		−	3.31769e41i		−	0.723492i	0.932277	−	0.361746i	$-0.117819\pi$
$600$	−8.50080e40	+	7.91646e40i	−0.180797	+	0.168369i
$601$	7.42550e40			0.154031			0.0770156	−	0.997030i	$-0.475461\pi$
$601$	7.42550e40			0.154031			0.0770156	+	0.997030i	$0.475461\pi$
$602$	−4.59883e41	−	1.29090e41i	−0.930465	−	0.261182i
$603$		−	6.57555e41i		−	1.29769i
$604$	−2.11282e41	+	3.46693e41i	−0.406731	+	0.667407i
$605$	−1.67060e40			−0.0313720
$606$	−1.36046e40	+	4.84665e40i	−0.0249228	+	0.0887877i
$607$			2.24000e40i			0.0400329i	0.999800	+	0.0200165i	$0.00637187\pi$
$607$			2.24000e40i			0.0400329i	−0.999800	+	0.0200165i	$0.993628\pi$
$608$	6.05867e41	−	1.24395e41i	1.05639	−	0.216895i
$609$	5.31716e41			0.904524
$610$	−2.78273e41	−	7.81116e40i	−0.461874	−	0.129649i
$611$			7.81673e41i			1.26592i
$612$	−1.07210e41	−	6.53361e40i	−0.169420	−	0.103248i
$613$	2.01179e41			0.310224			0.155112	−	0.987897i	$-0.450426\pi$
$613$	2.01179e41			0.310224			0.155112	+	0.987897i	$0.450426\pi$
$614$	−1.30226e41	+	4.63930e41i	−0.195962	+	0.698115i
$615$			5.27237e40i			0.0774247i
$616$	−8.89301e41	−	9.54943e41i	−1.27450	−	1.36857i
$617$	1.22142e42			1.70839			0.854194	−	0.519955i	$-0.174051\pi$
$617$	1.22142e42			1.70839			0.854194	+	0.519955i	$0.174051\pi$
$618$	2.60144e41	+	7.30226e40i	0.355129	+	0.0996851i
$619$			6.38505e41i			0.850755i	0.905016	+	0.425378i	$0.139859\pi$
$619$			6.38505e41i			0.850755i	−0.905016	+	0.425378i	$0.860141\pi$
$620$	1.69145e41	−	2.77551e41i	0.219980	−	0.360967i
$621$	2.07609e40			0.0263556
$622$	4.42252e40	−	1.57553e41i	0.0548042	−	0.195241i
$623$		−	2.83714e42i		−	3.43210i
$624$	−2.03838e41	+	1.05128e41i	−0.240722	+	0.124151i
$625$	3.16879e41			0.365337
$626$	−2.48750e41	−	6.98245e40i	−0.279994	−	0.0785946i
$627$			3.03977e41i			0.334063i
$628$	6.80801e41	+	4.14894e41i	0.730509	+	0.445187i
$629$	−1.04697e41			−0.109692
$630$	−2.19469e41	+	7.81861e41i	−0.224525	+	0.799873i
$631$			1.14422e42i			1.14306i	0.820581	+	0.571530i	$0.193650\pi$
$631$			1.14422e42i			1.14306i	−0.820581	+	0.571530i	$0.806350\pi$
$632$	−1.08995e42	+	1.01503e42i	−1.06329	+	0.990199i
$633$	−4.12096e41			−0.392594
$634$	7.23162e41	+	2.02992e41i	0.672817	+	0.188860i
$635$			2.47161e41i			0.224581i
$636$	1.21862e41	−	1.99964e41i	0.108147	−	0.177458i
$637$	−2.67445e42			−2.31816
$638$	4.50228e41	−	1.60394e42i	0.381173	−	1.35793i
$639$			1.00245e42i			0.828994i
$640$	−2.00263e41	+	5.57583e41i	−0.161771	+	0.450412i
$641$	−2.16047e41			−0.170481			−0.0852407	−	0.996360i	$-0.527166\pi$
$641$	−2.16047e41			−0.170481			−0.0852407	+	0.996360i	$0.527166\pi$
$642$	−2.24257e41	−	6.29491e40i	−0.172870	−	0.0485249i
$643$		−	9.34455e41i		−	0.703710i	−0.936055	−	0.351855i	$-0.885551\pi$
$643$		−	9.34455e41i		−	0.703710i	0.936055	−	0.351855i	$-0.114449\pi$
$644$	9.73353e40	+	5.93181e40i	0.0716115	+	0.0436415i
$645$	−1.06584e41			−0.0766118
$646$	−9.17605e40	+	3.26898e41i	−0.0644418	+	0.229575i
$647$			2.63710e42i			1.80951i	0.425927	+	0.904757i	$0.359948\pi$
$647$			2.63710e42i			1.80951i	−0.425927	+	0.904757i	$0.640052\pi$
$648$	−7.14051e41	−	7.66758e41i	−0.478745	−	0.514083i
$649$	−1.17555e42			−0.770142
$650$	9.80017e41	+	2.75092e41i	0.627383	+	0.176107i
$651$		−	8.75300e41i		−	0.547573i
$652$	4.23950e41	−	6.95661e41i	0.259179	−	0.425289i
$653$	1.02912e42			0.614850			0.307425	−	0.951572i	$-0.400533\pi$
$653$	1.02912e42			0.614850			0.307425	+	0.951572i	$0.400533\pi$
$654$	−4.19788e40	+	1.49550e41i	−0.0245112	+	0.0873212i
$655$		−	7.91283e41i		−	0.451557i
$656$	−4.14894e41	−	8.04461e41i	−0.231409	−	0.448691i
$657$	1.18400e42			0.645462
$658$	5.23535e42	+	1.46957e42i	2.78970	+	0.783072i
$659$		−	1.70150e42i		−	0.886240i	−0.896462	−	0.443120i	$-0.853872\pi$
$659$		−	1.70150e42i		−	0.886240i	0.896462	−	0.443120i	$-0.146128\pi$
$660$	−2.48641e41	−	1.51527e41i	−0.126594	−	0.0771491i
$661$	−2.96079e42			−1.47362			−0.736809	−	0.676101i	$-0.763668\pi$
$661$	−2.96079e42			−1.47362			−0.736809	+	0.676101i	$0.763668\pi$
$662$	5.20263e41	−	1.85344e42i	0.253136	−	0.901798i
$663$		−	1.25903e41i		−	0.0598872i
$664$	1.06072e42	−	9.87807e41i	0.493264	−	0.459357i
$665$	2.19615e42			0.998474
$666$	−9.64180e41	−	2.70646e41i	−0.428593	−	0.120306i
$667$			1.45522e41i			0.0632474i
$668$	−9.89801e41	+	1.62417e42i	−0.420631	+	0.690215i
$669$	6.06314e41			0.251945
$670$	4.60344e41	−	1.63998e42i	0.187051	−	0.666372i
$671$			2.43866e42i			0.968978i
$672$	3.20885e41	+	1.56287e42i	0.124684	+	0.607274i
$673$	3.12454e42			1.18730			0.593649	−	0.804724i	$-0.297687\pi$
$673$	3.12454e42			1.18730			0.593649	+	0.804724i	$0.297687\pi$
$674$	−2.14048e42	−	6.00834e41i	−0.795448	−	0.223283i
$675$		−	1.28970e42i		−	0.468738i
$676$	−6.86083e41	−	4.18113e41i	−0.243880	−	0.148625i
$677$	−2.89094e42			−1.00510			−0.502550	−	0.864548i	$-0.667605\pi$
$677$	−2.89094e42			−1.00510			−0.502550	+	0.864548i	$0.667605\pi$
$678$	2.02267e41	−	7.20578e41i	0.0687828	−	0.245039i
$679$		−	2.35820e42i		−	0.784394i
$680$	−2.21648e41	−	2.38008e41i	−0.0721157	−	0.0774388i
$681$	−1.00074e42			−0.318504
$682$	−2.64037e42	−	7.41156e41i	−0.822053	−	0.230751i
$683$			1.85917e42i			0.566250i	0.959083	+	0.283125i	$0.0913711\pi$
$683$			1.85917e42i			0.566250i	−0.959083	+	0.283125i	$0.908629\pi$
$684$	−1.69009e42	+	2.77328e42i	−0.503581	+	0.826328i
$685$	1.65143e42			0.481395
$686$	−3.19477e42	+	1.13814e43i	−0.911125	+	3.24589i
$687$		−	1.13720e42i		−	0.317311i
$688$	1.62626e42	−	8.38731e41i	0.443980	−	0.228979i
$689$	−2.05199e42			−0.548134
$690$	2.44882e40	+	6.87388e39i	0.00640061	+	0.00179666i
$691$			3.50167e42i			0.895581i	0.894139	+	0.447790i	$0.147789\pi$
$691$			3.50167e42i			0.895581i	−0.894139	+	0.447790i	$0.852211\pi$
$692$	−3.62823e42	−	2.21112e42i	−0.908037	−	0.553376i
$693$	6.85188e42			1.67807
$694$	1.02456e42	−	3.64999e42i	0.245552	−	0.874782i
$695$		−	2.88927e42i		−	0.677666i
$696$	−1.49062e42	+	1.38816e42i	−0.342160	+	0.318640i
$697$	4.96886e41			0.111626
$698$	−7.56026e42	−	2.12217e42i	−1.66228	−	0.466605i
$699$			1.05355e42i			0.226725i
$700$	3.68492e42	−	6.04660e42i	0.776171	−	1.27362i
$701$	−2.30147e41			−0.0474500			−0.0237250	−	0.999719i	$-0.507553\pi$
$701$	−2.30147e41			−0.0474500			−0.0237250	+	0.999719i	$0.507553\pi$
$702$	6.88179e41	−	2.45165e42i	0.138882	−	0.494767i
$703$			2.70826e42i			0.535008i
$704$	4.98617e42	+	3.55395e41i	0.964222	+	0.0687260i
$705$	1.21336e42			0.229696
$706$	1.25814e42	+	3.53160e41i	0.233161	+	0.0654487i
$707$		−	3.06862e42i		−	0.556739i
$708$	1.22736e42	+	7.47977e41i	0.218008	+	0.132858i
$709$	−2.05995e42			−0.358231			−0.179115	−	0.983828i	$-0.557324\pi$
$709$	−2.05995e42			−0.358231			−0.179115	+	0.983828i	$0.557324\pi$
$710$	−7.01802e41	+	2.50018e42i	−0.119492	+	0.425692i
$711$		−	7.82059e42i		−	1.30375i
$712$	7.40696e42	+	7.95369e42i	1.20904	+	1.29828i
$713$	2.39556e41			0.0382882
$714$	−8.43253e41	−	2.36702e41i	−0.131973	−	0.0370449i
$715$			2.55150e42i			0.391026i
$716$	−2.27259e42	+	3.72911e42i	−0.341057	+	0.559641i
$717$	3.09087e42			0.454249
$718$	1.62224e42	−	5.77926e42i	0.233480	−	0.831774i
$719$			4.41467e42i			0.622250i	0.950369	+	0.311125i	$0.100706\pi$
$719$			4.41467e42i			0.622250i	−0.950369	+	0.311125i	$0.899294\pi$
$720$	−1.42595e42	−	2.76485e42i	−0.196842	−	0.381667i
$721$	−1.64708e43			−2.22682
$722$	1.18517e42	+	3.32678e41i	0.156936	+	0.0440520i
$723$			1.59735e42i			0.207169i
$724$	6.39384e41	+	3.89654e41i	0.0812238	+	0.0494995i
$725$	9.04005e42			1.12487
$726$	4.65768e40	−	1.65930e41i	0.00567702	−	0.0202244i
$727$			1.94123e41i			0.0231772i	0.999933	+	0.0115886i	$0.00368884\pi$
$727$			1.94123e41i			0.0231772i	−0.999933	+	0.0115886i	$0.996311\pi$
$728$	1.02313e43	−	9.52801e42i	1.19663	−	1.11438i
$729$	3.80113e42			0.435512
$730$	2.95296e42	+	8.28899e41i	0.331448	+	0.0930377i
$731$			1.00448e42i			0.110454i
$732$	1.55167e42	−	2.54614e42i	0.167160	−	0.274294i
$733$	−8.51755e42			−0.898991			−0.449495	−	0.893283i	$-0.648396\pi$
$733$	−8.51755e42			−0.898991			−0.449495	+	0.893283i	$0.648396\pi$
$734$	8.06197e41	−	2.87208e42i	0.0833682	−	0.297000i
$735$			4.15145e42i			0.420619i
$736$	−4.27735e41	+	8.78212e40i	−0.0424626	+	0.00871831i
$737$	−1.43721e43			−1.39800
$738$	4.57596e42	+	1.28448e42i	0.436151	+	0.122428i
$739$		−	8.24054e42i		−	0.769643i	−0.922991	−	0.384821i	$-0.874263\pi$
$739$		−	8.24054e42i		−	0.769643i	0.922991	−	0.384821i	$-0.125737\pi$
$740$	−2.21525e42	−	1.35002e42i	−0.202743	−	0.123556i
$741$	−3.25683e42			−0.292093
$742$	−3.85780e42	+	1.37435e43i	−0.339064	+	1.20792i
$743$			1.08929e42i			0.0938232i	0.998899	+	0.0469116i	$0.0149379\pi$
$743$			1.08929e42i			0.0938232i	−0.998899	+	0.0469116i	$0.985062\pi$
$744$	2.28516e42	+	2.45383e42i	0.192896	+	0.207134i
$745$	−8.38425e42			−0.693618
$746$	−1.14508e43	−	3.21427e42i	−0.928443	−	0.260615i
$747$			7.61084e42i			0.604816i
$748$	−1.42804e42	+	2.34328e42i	−0.111229	+	0.182515i
$749$	1.41986e43			1.08397
$750$	9.80888e41	−	3.49442e42i	0.0734008	−	0.261491i
$751$			1.12607e43i			0.825976i	0.910736	+	0.412988i	$0.135515\pi$
$751$			1.12607e43i			0.825976i	−0.910736	+	0.412988i	$0.864485\pi$
$752$	−1.85135e43	+	9.54819e42i	−1.33113	+	0.686521i
$753$	7.28208e42			0.513252
$754$	1.71847e43	+	4.82376e42i	1.18733	+	0.333285i
$755$		−	5.52246e42i		−	0.374049i
$756$	−1.51264e43	−	9.21833e42i	−1.00440	−	0.612104i
$757$	5.34697e42			0.348072			0.174036	−	0.984739i	$-0.444319\pi$
$757$	5.34697e42			0.348072			0.174036	+	0.984739i	$0.444319\pi$
$758$	2.82351e42	−	1.00588e43i	0.180198	−	0.641959i
$759$		−	2.14604e41i		−	0.0134280i
$760$	−6.15672e42	+	5.73352e42i	−0.377699	+	0.351736i
$761$	−1.35461e41			−0.00814785			−0.00407393	−	0.999992i	$-0.501297\pi$
$761$	−1.35461e41			−0.00814785			−0.00407393	+	0.999992i	$0.501297\pi$
$762$	−2.45490e42	−	6.89092e41i	−0.144780	−	0.0406399i
$763$		−	9.46862e42i		−	0.547544i
$764$	−3.97288e42	+	6.51911e42i	−0.225271	+	0.369648i
$765$	1.70775e42			0.0949517
$766$	5.43764e41	−	1.93716e42i	0.0296469	−	0.105617i
$767$		−	1.25949e43i		−	0.673386i
$768$	−4.97979e42	−	3.54365e42i	−0.261091	−	0.185794i
$769$	1.57194e43			0.808242			0.404121	−	0.914706i	$-0.367577\pi$
$769$	1.57194e43			0.808242			0.404121	+	0.914706i	$0.367577\pi$
$770$	1.70890e43	+	4.79690e42i	0.861699	+	0.241880i
$771$			3.63682e41i			0.0179848i
$772$	−2.17166e41	−	1.32345e41i	−0.0105325	−	0.00641872i
$773$	3.71967e43			1.76934			0.884671	−	0.466216i	$-0.154383\pi$
$773$	3.71967e43			1.76934			0.884671	+	0.466216i	$0.154383\pi$
$774$	−2.59664e42	+	9.25055e42i	−0.121143	+	0.431572i
$775$		−	1.48815e43i		−	0.680961i
$776$	6.15659e42	+	6.61103e42i	0.276322	+	0.296718i
$777$	−6.98613e42			−0.307554
$778$	−8.39089e41	−	2.35533e41i	−0.0362338	−	0.0101709i
$779$		−	1.28533e43i		−	0.544443i
$780$	1.62347e42	−	2.66395e42i	0.0674565	−	0.110690i
$781$	2.19104e43			0.893070
$782$	6.47817e40	−	2.30785e41i	0.00259031	−	0.00922799i
$783$		−	2.26149e43i		−	0.887092i
$784$	−3.26686e43	−	6.33429e43i	−1.25716	−	2.43757i
$785$	−1.08445e43			−0.409414
$786$	7.85933e42	+	2.20612e42i	0.291103	+	0.0817130i
$787$			4.82487e43i			1.75334i	0.481097	+	0.876668i	$0.340239\pi$
$787$			4.82487e43i			1.75334i	−0.481097	+	0.876668i	$0.659761\pi$
$788$	4.16354e43	+	2.53735e43i	1.48446	+	0.904662i
$789$	−6.40309e42			−0.223993
$790$	5.47507e42	−	1.95050e43i	0.187925	−	0.669483i
$791$			4.56228e43i			1.53651i
$792$	−1.92087e43	+	1.78883e43i	−0.634775	+	0.591141i
$793$	−2.61279e43			−0.847241
$794$	−3.69520e43	−	1.03725e43i	−1.17579	−	0.330046i
$795$			3.18523e42i			0.0994565i
$796$	−2.00975e43	+	3.29781e43i	−0.615809	+	1.01048i
$797$	−1.79137e43			−0.538654			−0.269327	−	0.963049i	$-0.586801\pi$
$797$	−1.79137e43			−0.538654			−0.269327	+	0.963049i	$0.586801\pi$
$798$	−6.12293e42	+	2.18130e43i	−0.180682	+	0.643683i
$799$		−	1.14351e43i		−	0.331161i
$800$	5.45557e42	+	2.65714e43i	0.155057	+	0.755205i
$801$	−5.70691e43			−1.59189
$802$	2.13281e43	+	5.98683e42i	0.583899	+	0.163901i
$803$		−	2.58784e43i		−	0.695352i
$804$	1.50055e43	+	9.14463e42i	0.395739	+	0.241171i
$805$	−1.55045e42			−0.0401347
$806$	7.94077e42	−	2.82891e43i	0.201761	−	0.718775i
$807$			8.22297e42i			0.205081i
$808$	8.01128e42	+	8.60262e42i	0.196124	+	0.210601i
$809$	−5.98487e43			−1.43823			−0.719113	−	0.694894i	$-0.755451\pi$
$809$	−5.98487e43			−1.43823			−0.719113	+	0.694894i	$0.755451\pi$
$810$	1.37213e43	+	3.85160e42i	0.323684	+	0.0908585i
$811$		−	1.17493e43i		−	0.272082i	−0.990703	−	0.136041i	$-0.956562\pi$
$811$		−	1.17493e43i		−	0.272082i	0.990703	−	0.136041i	$-0.0434379\pi$
$812$	6.46154e43	−	1.06028e44i	1.46891	−	2.41034i
$813$	1.94214e43			0.433434
$814$	−5.91547e42	+	2.10739e43i	−0.129605	+	0.461720i
$815$			1.10812e43i			0.238353i
$816$	2.98195e42	−	1.53792e42i	0.0629721	−	0.0324774i
$817$	2.59836e43			0.538727
$818$	1.22464e43	+	3.43757e42i	0.249292	+	0.0699765i
$819$			7.34113e43i			1.46725i
$820$	1.05135e43	+	6.40712e42i	0.206318	+	0.125735i
$821$	4.17096e43			0.803690			0.401845	−	0.915708i	$-0.368369\pi$
$821$	4.17096e43			0.803690			0.401845	+	0.915708i	$0.368369\pi$
$822$	−4.60424e42	+	1.64026e43i	−0.0871126	+	0.310339i
$823$		−	2.13925e43i		−	0.397432i	−0.980057	−	0.198716i	$-0.936323\pi$
$823$		−	2.13925e43i		−	0.397432i	0.980057	−	0.198716i	$-0.0636772\pi$
$824$	4.61745e43	−	4.30005e43i	0.842353	−	0.784450i
$825$	−1.33315e43			−0.238819
$826$	−8.43558e43	−	2.36788e43i	−1.48393	−	0.416541i
$827$		−	9.71015e43i		−	1.67743i	−0.544574	−	0.838713i	$-0.683309\pi$
$827$		−	9.71015e43i		−	1.67743i	0.544574	−	0.838713i	$-0.316691\pi$
$828$	1.19318e42	−	1.95790e42i	0.0202420	−	0.0332151i
$829$	5.23553e42			0.0872254			0.0436127	−	0.999049i	$-0.486113\pi$
$829$	5.23553e42			0.0872254			0.0436127	+	0.999049i	$0.486113\pi$
$830$	−5.32823e42	+	1.89819e43i	−0.0871790	+	0.310576i
$831$		−	1.32405e43i		−	0.212760i
$832$	−3.80771e42	+	5.34220e43i	−0.0600917	+	0.843083i
$833$	3.91246e43			0.606422
$834$	2.86973e43	+	8.05536e42i	0.436868	+	0.122629i
$835$		−	2.58713e43i		−	0.386832i
$836$	6.06151e43	+	3.69401e43i	0.890198	+	0.542505i
$837$	−3.72282e43			−0.537020
$838$	5.81652e42	−	2.07214e43i	0.0824144	−	0.293602i
$839$			1.05137e44i			1.46328i	0.681691	+	0.731640i	$0.261245\pi$
$839$			1.05137e44i			1.46328i	−0.681691	+	0.731640i	$0.738755\pi$
$840$	−1.47900e43	−	1.58817e43i	−0.202198	−	0.217123i
$841$	8.40551e43			1.12882
$842$	−1.14976e44	−	3.22740e43i	−1.51680	−	0.425766i
$843$		−	1.13320e43i		−	0.146857i
$844$	−5.00790e43	+	8.21748e43i	−0.637556	+	1.04617i
$845$	1.09286e43			0.136683
$846$	2.95604e43	−	1.05309e44i	0.363207	−	1.29393i
$847$			1.05057e43i			0.126816i
$848$	−2.50652e43	−	4.86003e43i	−0.297258	−	0.576370i
$849$	−1.41989e43			−0.165439
$850$	−1.43367e43	−	4.02432e42i	−0.164121	−	0.0460690i
$851$		−	1.91200e42i		−	0.0215052i
$852$	−2.28761e43	−	1.39411e43i	−0.252806	−	0.154065i
$853$	2.16486e43			0.235068			0.117534	−	0.993069i	$-0.462501\pi$
$853$	2.16486e43			0.235068			0.117534	+	0.993069i	$0.462501\pi$
$854$	−4.91213e43	+	1.74995e44i	−0.524085	+	1.86706i
$855$		−	4.41755e43i		−	0.463116i
$856$	−3.98047e43	+	3.70686e43i	−0.410042	+	0.381856i
$857$	4.13056e43			0.418116			0.209058	−	0.977903i	$-0.432960\pi$
$857$	4.13056e43			0.418116			0.209058	+	0.977903i	$0.432960\pi$
$858$	−2.53425e43	−	7.11366e42i	−0.252081	−	0.0707594i
$859$		−	7.87426e42i		−	0.0769684i	−0.999259	−	0.0384842i	$-0.987747\pi$
$859$		−	7.87426e42i		−	0.0769684i	0.999259	−	0.0384842i	$-0.0122529\pi$
$860$	−1.29523e43	+	2.12535e43i	−0.124415	+	0.204152i
$861$	3.31559e43			0.312977
$862$	−1.87601e43	+	6.68332e43i	−0.174031	+	0.619988i
$863$		−	1.70821e43i		−	0.155733i	−0.996964	−	0.0778663i	$-0.975189\pi$
$863$		−	1.70821e43i		−	0.155733i	0.996964	−	0.0778663i	$-0.0248107\pi$
$864$	6.64721e43	−	1.36479e43i	0.595570	−	0.122281i
$865$	5.77940e43			0.508910
$866$	7.58865e43	+	2.13014e43i	0.656744	+	0.184349i
$867$		−	3.58326e43i		−	0.304784i
$868$	−1.74541e44	−	1.06369e44i	−1.45915	−	0.889237i
$869$	−1.70933e44			−1.40453
$870$	7.48773e42	−	2.66751e43i	0.0604730	−	0.215436i
$871$		−	1.53983e44i		−	1.22236i
$872$	2.47199e43	+	2.65445e43i	0.192885	+	0.207123i
$873$	−4.74353e43			−0.363821
$874$	−5.96988e42	−	1.67575e42i	−0.0450085	−	0.0126339i
$875$			2.21246e44i			1.63967i
$876$	−1.64659e43	+	2.70189e43i	−0.119956	+	0.196837i
$877$	6.55900e43			0.469725			0.234862	−	0.972029i	$-0.424536\pi$
$877$	6.55900e43			0.469725			0.234862	+	0.972029i	$0.424536\pi$
$878$	4.82599e43	−	1.71926e44i	0.339757	−	1.21039i
$879$			5.78849e43i			0.400620i
$880$	−6.04309e43	+	3.11668e43i	−0.411168	+	0.212056i
$881$	−4.81621e43			−0.322156			−0.161078	−	0.986942i	$-0.551497\pi$
$881$	−4.81621e43			−0.322156			−0.161078	+	0.986942i	$0.551497\pi$
$882$	3.60309e44	+	1.01139e44i	2.36944	+	0.665105i
$883$			2.97410e44i			1.92285i	0.275067	+	0.961425i	$0.411300\pi$
$883$			2.97410e44i			1.92285i	−0.275067	+	0.961425i	$0.588700\pi$
$884$	−2.51060e43	−	1.53001e43i	−0.159585	−	0.0972545i
$885$	−1.95506e43			−0.122183
$886$	8.85101e42	−	3.15318e43i	0.0543860	−	0.193750i
$887$		−	1.89925e44i		−	1.14743i	−0.819054	−	0.573716i	$-0.805501\pi$
$887$		−	1.89925e44i		−	1.14743i	0.819054	−	0.573716i	$-0.194499\pi$
$888$	1.95851e43	−	1.82388e43i	0.116340	−	0.108343i
$889$	1.55430e44			0.907836
$890$	−1.42334e44	−	3.99532e43i	−0.817443	−	0.229457i
$891$		−	1.20248e44i		−	0.679065i
$892$	7.36807e43	−	1.20903e44i	0.409149	−	0.671374i
$893$	−2.95800e44			−1.61520
$894$	2.33756e43	−	8.32756e43i	0.125516	−	0.447152i
$895$		−	5.94009e43i		−	0.313651i
$896$	3.50642e44	+	1.25938e44i	1.82072	+	0.653936i
$897$	2.29928e42			0.0117410
$898$	2.94963e44	+	8.27963e43i	1.48123	+	0.415782i
$899$		−	2.60949e44i		−	1.28873i
$900$	−1.21627e44	−	7.41222e43i	−0.590736	−	0.360007i
$901$	3.00186e43			0.143390
$902$	2.80746e43	−	1.00016e44i	0.131891	−	0.469863i
$903$			6.70264e43i			0.309692i
$904$	−1.19108e44	−	1.27900e44i	−0.541271	−	0.581224i
$905$	−1.01847e43			−0.0455220
$906$	5.48512e43	+	1.53968e43i	0.241137	+	0.0676873i
$907$			7.78783e42i			0.0336750i	0.999858	+	0.0168375i	$0.00535979\pi$
$907$			7.78783e42i			0.0336750i	−0.999858	+	0.0168375i	$0.994640\pi$
$908$	−1.21612e44	+	1.99554e44i	−0.517238	+	0.848737i
$909$	−6.17252e43			−0.258229
$910$	−5.13941e43	+	1.83092e44i	−0.211491	+	0.753440i
$911$			4.00604e44i			1.62158i	0.585334	+	0.810792i	$0.300963\pi$
$911$			4.00604e44i			1.62158i	−0.585334	+	0.810792i	$0.699037\pi$
$912$	−3.97823e43	−	7.71362e43i	−0.158405	−	0.307139i
$913$	1.66349e44			0.651565
$914$	−4.49636e43	−	1.26213e43i	−0.173248	−	0.0486309i
$915$			4.05574e43i			0.153728i
$916$	−2.26765e44	−	1.38195e44i	−0.845559	−	0.515301i
$917$	−4.97606e44			−1.82535
$918$	−1.00674e43	+	3.58652e43i	−0.0363310	+	0.129429i
$919$		−	5.02901e43i		−	0.178546i	−0.996007	−	0.0892730i	$-0.971546\pi$
$919$		−	5.02901e43i		−	0.178546i	0.996007	−	0.0892730i	$-0.0284543\pi$
$920$	4.34657e42	−	4.04779e42i	0.0151820	−	0.0141384i
$921$	6.76162e43			0.232357
$922$	−1.64440e44	−	4.61585e43i	−0.555960	−	0.156059i
$923$			2.34749e44i			0.780870i
$924$	−9.52892e43	+	1.56360e44i	−0.311863	+	0.511738i
$925$	−1.18776e44			−0.382474
$926$	−7.65513e43	+	2.72715e44i	−0.242542	+	0.864059i
$927$			3.31310e44i			1.03285i
$928$	9.56639e43	+	4.65932e44i	0.293446	+	1.42923i
$929$	2.10776e44			0.636187			0.318093	−	0.948059i	$-0.396957\pi$
$929$	2.10776e44			0.636187			0.318093	+	0.948059i	$0.396957\pi$
$930$	−4.39120e43	−	1.23262e43i	−0.130419	−	0.0366086i
$931$		−	1.01206e45i		−	2.95775i
$932$	2.10086e44	+	1.28031e44i	0.604168	+	0.368192i
$933$	−2.29628e43			−0.0649830
$934$	9.33118e43	−	3.32424e44i	0.259856	−	0.925741i
$935$		−	3.73260e43i		−	0.102291i
$936$	−1.91656e44	−	2.05803e44i	−0.516874	−	0.555026i
$937$	6.33865e44			1.68230			0.841149	−	0.540803i	$-0.181880\pi$
$937$	6.33865e44			1.68230			0.841149	+	0.540803i	$0.181880\pi$
$938$	−1.03132e45	−	2.89492e44i	−2.69370	−	0.756126i
$939$			3.62545e43i			0.0931920i
$940$	1.47451e44	−	2.41952e44i	0.373017	−	0.612085i
$941$	6.44850e44			1.60551			0.802757	−	0.596306i	$-0.203366\pi$
$941$	6.44850e44			1.60551			0.802757	+	0.596306i	$0.203366\pi$
$942$	3.02347e43	−	1.07711e44i	0.0740870	−	0.263935i
$943$			9.07426e42i			0.0218845i
$944$	2.98303e44	−	1.53847e44i	0.708073	−	0.365183i
$945$	2.40948e44			0.562919
$946$	2.02188e44	+	5.67542e43i	0.464930	+	0.130506i
$947$			4.22327e44i			0.955870i	0.878395	+	0.477935i	$0.158615\pi$
$947$			4.22327e44i			0.955870i	−0.878395	+	0.477935i	$0.841385\pi$
$948$	1.78466e44	+	1.08761e44i	0.397586	+	0.242297i
$949$	2.77263e44			0.607992
$950$	−1.04100e44	+	3.70857e44i	−0.224697	+	0.800483i
$951$		−	1.05398e44i		−	0.223937i
$952$	−1.49674e44	+	1.39386e44i	−0.313035	+	0.291517i
$953$	−5.34853e44			−1.10114			−0.550568	−	0.834790i	$-0.685589\pi$
$953$	−5.34853e44			−1.10114			−0.550568	+	0.834790i	$0.685589\pi$
$954$	2.76450e44	+	7.75997e43i	0.560261	+	0.157266i
$955$		−	1.03843e44i		−	0.207169i
$956$	3.75610e44	−	6.16340e44i	0.737682	−	1.21046i
$957$	−2.33769e44			−0.451968
$958$	−1.37595e44	+	4.90184e44i	−0.261891	+	0.932988i
$959$		−	1.03852e45i		−	1.94597i
$960$	8.29250e43	+	5.91056e42i	0.152974	+	0.0109034i
$961$	1.21049e44			0.219842
$962$	−2.25787e44	−	6.33786e43i	−0.403713	−	0.113323i
$963$		−	2.85605e44i		−	0.502773i
$964$	3.18521e44	+	1.94113e44i	0.552056	+	0.336434i
$965$	3.45923e42			0.00590296
$966$	4.32271e42	−	1.53997e43i	0.00726271	−	0.0258735i
$967$			7.95596e44i			1.31612i	0.752965	+	0.658060i	$0.228623\pi$
$967$			7.95596e44i			1.31612i	−0.752965	+	0.658060i	$0.771377\pi$
$968$	−2.74275e43	−	2.94520e43i	−0.0446741	−	0.0479716i
$969$	4.76442e43			0.0764106
$970$	−1.18306e44	−	3.32087e43i	−0.186824	−	0.0524416i
$971$			9.46268e44i			1.47138i	0.677317	+	0.735692i	$0.263143\pi$
$971$			9.46268e44i			1.47138i	−0.677317	+	0.735692i	$0.736857\pi$
$972$	−2.83158e44	+	4.64635e44i	−0.433546	+	0.711407i
$973$	−1.81695e45			−2.73936
$974$	4.87823e42	−	1.73787e43i	0.00724232	−	0.0258008i
$975$		−	1.42834e44i		−	0.208815i
$976$	−3.19154e44	−	6.18826e44i	−0.459466	−	0.890884i
$977$	4.88100e44			0.691974			0.345987	−	0.938239i	$-0.387544\pi$
$977$	4.88100e44			0.691974			0.345987	+	0.938239i	$0.387544\pi$
$978$	−1.10062e44	−	3.08946e43i	−0.153658	−	0.0431320i
$979$			1.24735e45i			1.71493i
$980$	8.27826e44	+	5.04494e44i	1.12085	+	0.683069i
$981$	−1.90461e44			−0.253964
$982$	3.58154e44	−	1.27593e45i	0.470324	−	1.67553i
$983$		−	4.47461e44i		−	0.578699i	−0.957224	−	0.289349i	$-0.906561\pi$
$983$		−	4.47461e44i		−	0.578699i	0.957224	−	0.289349i	$-0.0934389\pi$
$984$	−9.29498e43	+	8.65605e43i	−0.118392	+	0.110254i
$985$	−6.63210e44			−0.831969
$986$	−2.51395e44	−	7.05669e43i	−0.310601	−	0.0871861i
$987$		−	7.63035e44i		−	0.928511i
$988$	−3.95777e44	+	6.49433e44i	−0.474348	+	0.778359i
$989$	−1.83441e43			−0.0216547
$990$	9.64896e43	−	3.43745e44i	0.112190	−	0.399676i
$991$			2.54382e44i			0.291327i	0.989334	+	0.145664i	$0.0465317\pi$
$991$			2.54382e44i			0.291327i	−0.989334	+	0.145664i	$0.953468\pi$
$992$	7.67008e44	−	1.57480e44i	0.865217	−	0.177644i
$993$	−2.70133e44			−0.300150
$994$	1.57226e45	+	4.41335e44i	1.72079	+	0.483029i
$995$		−	5.25307e44i		−	0.566327i
$996$	−1.73680e44	−	1.05844e44i	−0.184442	−	0.112403i
$997$	−6.26232e44			−0.655101			−0.327550	−	0.944834i	$-0.606223\pi$
$997$	−6.26232e44			−0.655101			−0.327550	+	0.944834i	$0.606223\pi$
$998$	−3.49770e44	+	1.24606e45i	−0.360433	+	1.28404i
$999$			2.97134e44i			0.301627i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4.31.b.a.3.1	✓	14
3.2	odd	2		36.31.d.c.19.14		14
4.3	odd	2	inner	4.31.b.a.3.2	yes	14
12.11	even	2		36.31.d.c.19.13		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4.31.b.a.3.1	✓	14	1.1	even	1	trivial
4.31.b.a.3.2	yes	14	4.3	odd	2	inner
36.31.d.c.19.13		14	12.11	even	2
36.31.d.c.19.14		14	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:	\( N \)	\(=\)	\( 4 = 2^{2} \)
Weight:	\( k \)	\(=\)	\( 31 \)
Character orbit:	\([\chi]\)	\(=\)	4.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-31548.7 - 8855.74i) q^{2} +4.59811e6i q^{3} +(9.16894e8 + 5.58773e8i) q^{4} -1.46052e10 q^{5} +(4.07197e10 - 1.45064e11i) q^{6} +9.18461e12i q^{7} +(-2.39784e13 - 2.57483e13i) q^{8} +1.84749e14 q^{9} +O(q^{10})\)	\(q+(-31548.7 - 8855.74i) q^{2} +4.59811e6i q^{3} +(9.16894e8 + 5.58773e8i) q^{4} -1.46052e10 q^{5} +(4.07197e10 - 1.45064e11i) q^{6} +9.18461e12i q^{7} +(-2.39784e13 - 2.57483e13i) q^{8} +1.84749e14 q^{9} +(4.60774e14 + 1.29340e14i) q^{10} -4.03801e15i q^{11} +(-2.56930e15 + 4.21598e15i) q^{12} +4.32635e16 q^{13} +(8.13365e16 - 2.89762e17i) q^{14} -6.71562e16i q^{15} +(5.28466e17 + 1.02467e18i) q^{16} -6.32902e17 q^{17} +(-5.82857e18 - 1.63609e18i) q^{18} +1.63717e19i q^{19} +(-1.33914e19 - 8.16098e18i) q^{20} -4.22319e19 q^{21} +(-3.57596e19 + 1.27394e20i) q^{22} -1.15582e19i q^{23} +(1.18394e20 - 1.10255e20i) q^{24} -7.18011e20 q^{25} +(-1.36490e21 - 3.83130e20i) q^{26} +1.79620e21i q^{27} +(-5.13212e21 + 8.42131e21i) q^{28} -1.25904e22 q^{29} +(-5.94718e20 + 2.11869e21i) q^{30} +2.07261e22i q^{31} +(-7.59817e21 - 3.70070e22i) q^{32} +1.85672e22 q^{33} +(1.99672e22 + 5.60482e21i) q^{34} -1.34143e23i q^{35} +(1.69395e23 + 1.03233e23i) q^{36} +1.65423e23 q^{37} +(1.44984e23 - 5.16505e23i) q^{38} +1.98930e23i q^{39} +(3.50209e23 + 3.76059e23i) q^{40} -7.85091e23 q^{41} +(1.33236e24 + 3.73994e23i) q^{42} -1.58710e24i q^{43} +(2.25634e24 - 3.70243e24i) q^{44} -2.69828e24 q^{45} +(-1.02357e23 + 3.64646e23i) q^{46} +1.80678e25i q^{47} +(-4.71155e24 + 2.42994e24i) q^{48} -6.18178e25 q^{49} +(2.26523e25 + 6.35852e24i) q^{50} -2.91015e24i q^{51} +(3.96680e25 + 2.41745e25i) q^{52} -4.74301e25 q^{53} +(1.59067e25 - 5.66678e25i) q^{54} +5.89759e25i q^{55} +(2.36488e26 - 2.20232e26i) q^{56} -7.52789e25 q^{57} +(3.97210e26 + 1.11497e26i) q^{58} -2.91121e26i q^{59} +(3.75251e25 - 6.15751e25i) q^{60} -6.03926e26 q^{61} +(1.83545e26 - 6.53879e26i) q^{62} +1.69684e27i q^{63} +(-8.80122e25 + 1.23481e27i) q^{64} -6.31870e26 q^{65} +(-5.85771e26 - 1.64427e26i) q^{66} -3.55919e27i q^{67} +(-5.80304e26 - 3.53649e26i) q^{68} +5.31459e25 q^{69} +(-1.18793e27 + 4.23203e27i) q^{70} +5.42604e27i q^{71} +(-4.42997e27 - 4.75696e27i) q^{72} +6.40870e27 q^{73} +(-5.21888e27 - 1.46495e27i) q^{74} -3.30150e27i q^{75} +(-9.14808e27 + 1.50111e28i) q^{76} +3.70876e28 q^{77} +(1.76167e27 - 6.27598e27i) q^{78} -4.23310e28i q^{79} +(-7.71834e27 - 1.49655e28i) q^{80} +2.97789e28 q^{81} +(2.47686e28 + 6.95257e27i) q^{82} +4.11957e28i q^{83} +(-3.87221e28 - 2.35980e28i) q^{84} +9.24365e27 q^{85} +(-1.40550e28 + 5.00710e28i) q^{86} -5.78920e28i q^{87} +(-1.03972e29 + 9.68251e28i) q^{88} -3.08901e29 q^{89} +(8.51272e28 + 2.38953e28i) q^{90} +3.97358e29i q^{91} +(6.45842e27 - 1.05977e28i) q^{92} -9.53007e28 q^{93} +(1.60003e29 - 5.70013e29i) q^{94} -2.39112e29i q^{95} +(1.70162e29 - 3.49372e28i) q^{96} -2.56756e29 q^{97} +(1.95027e30 + 5.47442e29i) q^{98} -7.46017e29i 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more